Subgroups — #6345439

Order 512.

1641 conjugacy classes of subgroups.

The subgroup lattice has 1564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#60570	C₂	1	1	yes	maximal, characteristic
2	#60325	C₂	1	1	yes	maximal, characteristic, complemented
3	#60319	C₂	1	1	yes	maximal, characteristic, complemented
4	#18059	C₂	1	1	yes	maximal, characteristic, complemented
5	#18054	C₂	1	1	yes	maximal, characteristic, complemented
6	#18052	C₂	1	1	yes	maximal, characteristic, complemented
7	#18052	C₂	1	1	yes	maximal, characteristic, complemented
8	#18048	C₂	1	1	yes	maximal, characteristic, complemented
9	#18046	C₂	1	1	yes	maximal, characteristic, complemented
10	#18037	C₂	1	1	yes	maximal, characteristic, complemented
11	M₁₆×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#18033	C₂	1	1	yes	maximal, characteristic, complemented
13	#18026	C₂	1	1	yes	maximal, characteristic, complemented
14	#18018	C₂	1	1	yes	maximal, characteristic, complemented
15	#18014	C₂	1	1	yes	maximal, characteristic, complemented
16	#18011	C₂	1	1	yes	maximal, characteristic, complemented
17	#18006	C₂	1	1	yes	maximal, characteristic, complemented
18	#17999	C₂	1	1	yes	maximal, characteristic, complemented
19	#17994	C₂	1	1	yes	maximal, characteristic, complemented
20	#17950	C₂	1	1	yes	maximal, characteristic, complemented
21	#17946	C₂	1	1	yes	maximal, characteristic, complemented
22	#17942	C₂	1	1	yes	maximal, characteristic, complemented
23	#17928	C₂	1	1	yes	maximal, characteristic, complemented
24	#17926	C₂	1	1	yes	maximal, characteristic, complemented
25	#17920	C₂	1	1	yes	maximal, characteristic, complemented
26	#17912	C₂	1	1	yes	maximal, characteristic, complemented
27	#17904	C₂	1	1	yes	maximal, characteristic, complemented
28	#17825	C₂	1	1	yes	maximal, characteristic, complemented
29	#17505	C₂	1	1	yes	maximal, characteristic, complemented
30	#17453	C₂	1	1	yes	maximal, characteristic, complemented
31	#17341	C₂	1	1	yes	maximal, characteristic, complemented
32	#3460	C₂²	1	1	yes	characteristic
33	C₄×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
34	#3124	C₄	1	1	yes	characteristic
35	#3124	C₄	1	1	yes	characteristic
36	#3122	C₄	1	1	yes	characteristic
37	#3122	C₄	1	1	yes	characteristic
38	#3119	C₄	1	1	yes	characteristic
39	#3119	C₄	1	1	yes	characteristic
40	#3118	C₄	1	1	yes	characteristic
41	#3118	C₄	1	1	yes	characteristic
42	#3106	C₂²	1	1	yes	characteristic
43	#3106	C₂²	1	1	yes	characteristic
44	#3105	C₂²	1	1	yes	characteristic
45	#3105	C₂²	1	1	yes	characteristic
46	#3102	C₂²	1	1	yes	characteristic
47	#3102	C₂²	1	1	yes	characteristic
48	#3100	C₂²	1	1	yes	characteristic
49	#3100	C₂²	1	1	yes	characteristic
50	#3098	C₄	1	1	yes	characteristic
51	#3096	C₄	1	1	yes	characteristic
52	#3083	C₄	1	1	yes	characteristic
53	#3081	C₄	1	1	yes	characteristic
54	#3045	C₄	1	1	yes	characteristic
55	#3041	C₄	1	1	yes	characteristic
56	#3012	C₄	1	1	yes	characteristic
57	#3008	C₄	1	1	yes	characteristic
58	#2995	—	2	1	no	—
59	#2994	C₂²	1	1	yes	characteristic, complemented
60	#2993	C₂²	1	1	yes	characteristic, complemented
61	#2991	C₂²	1	1	yes	characteristic
62	#2991	C₂²	1	1	yes	characteristic, complemented
63	#2991	C₂²	1	1	yes	characteristic, complemented
64	#2989	—	2	1	no	—
65	#2989	C₂²	1	1	yes	characteristic
66	#2989	C₂²	1	1	yes	characteristic
67	#2988	C₂²	1	1	yes	characteristic, complemented
68	#2981	—	2	1	no	—
69	#2981	C₂²	1	1	yes	characteristic, complemented
70	#2979	C₂²	1	1	yes	characteristic, complemented
71	#2978	—	2	1	no	—
72	#2976	—	2	1	no	—
73	#2975	—	2	1	no	—
74	#2975	C₂²	1	1	yes	characteristic, complemented
75	#2974	—	2	1	no	—
76	#2974	—	2	1	no	—
77	#2974	C₂²	1	1	yes	characteristic
78	#2974	C₂²	1	1	yes	characteristic, complemented
79	#2974	C₂²	1	1	yes	characteristic, complemented
80	#2971	C₂²	1	1	yes	characteristic
81	#2971	C₂²	1	1	yes	characteristic, complemented
82	#2970	C₂²	1	1	yes	characteristic, complemented
83	#2969	C₂²	1	1	yes	characteristic, complemented
84	#2968	—	2	1	no	—
85	#2966	C₂²	1	1	yes	characteristic, complemented
86	#2965	—	2	1	no	—
87	#2965	C₂²	1	1	yes	characteristic
88	#2965	C₂²	1	1	yes	characteristic
89	C₈×#41	C₂²	1	1	yes	characteristic, complemented
90	C₄×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
91	C₄×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
92	C₄×#135	C₂²	1	1	yes	characteristic
93	C₂×C₄×D₈	C₂²	1	1	yes	characteristic
94	#2935	C₂²	1	1	yes	characteristic, complemented
95	D₄×M₁₆	—	2	1	no	—
96	D₄×M₁₆	—	2	1	no	—
97	D₄×M₁₆	C₂²	1	1	yes	characteristic
98	D₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
99	D₄×M₁₆	C₂²	1	1	yes	characteristic, complemented
100	#2933	—	2	1	no	—
101	#2932	—	2	1	no	—
102	#2931	C₂²	1	1	yes	characteristic, complemented
103	#2930	—	2	1	no	—
104	C₂×#436	—	2	1	no	—
105	C₂×#436	C₂²	1	1	yes	characteristic, complemented
106	#2922	C₂²	1	1	yes	characteristic
107	#1594	C₂²	1	1	yes	characteristic, complemented
108	#1594	C₂²	1	1	yes	characteristic, complemented
109	#1594	C₂²	1	1	yes	characteristic, complemented
110	#1592	C₂²	1	1	yes	characteristic, complemented
111	#1590	C₂²	1	1	yes	characteristic, complemented
112	#1590	C₂²	1	1	yes	characteristic, complemented
113	#1590	C₂²	1	1	yes	characteristic, complemented
114	#1589	C₂²	1	1	yes	characteristic, complemented
115	#1589	C₂²	1	1	yes	characteristic, complemented
116	#1589	C₂²	1	1	yes	characteristic, complemented
117	#1589	C₂²	1	1	yes	characteristic, complemented
118	#1589	C₂²	1	1	yes	characteristic, complemented
119	#1589	C₂²	1	1	yes	characteristic, complemented
120	#1589	C₂²	1	1	yes	characteristic, complemented
121	#1589	C₂²	1	1	yes	characteristic, complemented
122	#1589	C₂²	1	1	yes	characteristic, complemented
123	#1588	C₂²	1	1	yes	characteristic, complemented
124	#1588	C₂²	1	1	yes	characteristic, complemented
125	#1588	C₂²	1	1	yes	characteristic, complemented
126	#1588	C₂²	1	1	yes	characteristic, complemented
127	#1588	C₂²	1	1	yes	characteristic, complemented
128	#1588	C₂²	1	1	yes	characteristic, complemented
129	#1588	C₂²	1	1	yes	characteristic, complemented
130	#1586	C₂²	1	1	yes	characteristic, complemented
131	#1586	C₂²	1	1	yes	characteristic, complemented
132	#1586	C₂²	1	1	yes	characteristic, complemented
133	#1586	C₂²	1	1	yes	characteristic, complemented
134	#1586	C₂²	1	1	yes	characteristic, complemented
135	#1586	C₂²	1	1	yes	characteristic, complemented
136	#1586	C₂²	1	1	yes	characteristic, complemented
137	#1586	C₂²	1	1	yes	characteristic, complemented
138	#1585	C₂²	1	1	yes	characteristic, complemented
139	#1584	C₂²	1	1	yes	characteristic, complemented
140	#1584	C₂²	1	1	yes	characteristic, complemented
141	#1583	C₂²	1	1	yes	characteristic, complemented
142	#1583	C₂²	1	1	yes	characteristic, complemented
143	#1583	C₂²	1	1	yes	characteristic, complemented
144	#1582	C₂²	1	1	yes	characteristic, complemented
145	#1581	C₂²	1	1	yes	characteristic, complemented
146	#1581	C₂²	1	1	yes	characteristic, complemented
147	#1581	C₂²	1	1	yes	characteristic, complemented
148	#1581	C₂²	1	1	yes	characteristic, complemented
149	#1581	C₂²	1	1	yes	characteristic, complemented
150	#1581	C₂²	1	1	yes	characteristic, complemented
151	#1581	C₂²	1	1	yes	characteristic, complemented
152	#1581	C₂²	1	1	yes	characteristic, complemented
153	#1581	C₂²	1	1	yes	characteristic, complemented
154	#1581	C₂²	1	1	yes	characteristic, complemented
155	#1580	C₂²	1	1	yes	characteristic, complemented
156	SD₁₆⋊C₈	C₂²	1	1	yes	characteristic, complemented
157	SD₁₆⋊C₈	C₂²	1	1	yes	characteristic, complemented
158	SD₁₆⋊C₈	C₂²	1	1	yes	characteristic, complemented
159	C₈×Q₁₆	C₂²	1	1	yes	characteristic, complemented
160	C₈×Q₁₆	C₂²	1	1	yes	characteristic, complemented
161	C₈×SD₁₆	C₂²	1	1	yes	characteristic, complemented
162	C₈×SD₁₆	C₂²	1	1	yes	characteristic, complemented
163	C₈×SD₁₆	C₂²	1	1	yes	characteristic, complemented
164	C₈×SD₁₆	C₂²	1	1	yes	characteristic, complemented
165	C₈×SD₁₆	C₂²	1	1	yes	characteristic, complemented
166	C₈×D₈	C₂²	1	1	yes	characteristic, complemented
167	C₈×D₈	C₂²	1	1	yes	characteristic, complemented
168	C₈×D₈	C₂²	1	1	yes	characteristic, complemented
169	C₈×D₈	C₂²	1	1	yes	characteristic, complemented
170	C₈×D₈	C₂²	1	1	yes	characteristic, complemented
171	#1574	C₂²	1	1	yes	characteristic, complemented
172	#1574	C₂²	1	1	yes	characteristic, complemented
173	#1573	C₂²	1	1	yes	characteristic, complemented
174	#1573	C₂²	1	1	yes	characteristic, complemented
175	#1572	C₂²	1	1	yes	characteristic, complemented
176	#1572	C₂²	1	1	yes	characteristic, complemented
177	#1571	C₂²	1	1	yes	characteristic, complemented
178	#1571	C₂²	1	1	yes	characteristic, complemented
179	#1569	C₂²	1	1	yes	characteristic, complemented
180	#1569	C₂²	1	1	yes	characteristic, complemented
181	#1568	C₂²	1	1	yes	characteristic, complemented
182	#1567	C₂²	1	1	yes	characteristic, complemented
183	#1496	C₂²	1	1	yes	characteristic, complemented
184	#1495	C₂²	1	1	yes	characteristic, complemented
185	#1494	C₂²	1	1	yes	characteristic, complemented
186	#1492	C₂²	1	1	yes	characteristic, complemented
187	#1490	C₂²	1	1	yes	characteristic
188	#1490	C₂²	1	1	yes	characteristic, complemented
189	#1490	C₂²	1	1	yes	characteristic, complemented
190	#1489	C₂²	1	1	yes	characteristic
191	#1489	C₂²	1	1	yes	characteristic, complemented
192	#1489	C₂²	1	1	yes	characteristic, complemented
193	#1488	C₂²	1	1	yes	characteristic
194	#1488	C₂²	1	1	yes	characteristic, complemented
195	#1488	C₂²	1	1	yes	characteristic, complemented
196	#1486	C₂²	1	1	yes	characteristic
197	#1486	C₂²	1	1	yes	characteristic, complemented
198	#1486	C₂²	1	1	yes	characteristic, complemented
199	#1484	C₂²	1	1	yes	characteristic, complemented
200	#1483	C₂²	1	1	yes	characteristic, complemented
201	#1482	C₂²	1	1	yes	characteristic, complemented
202	#1480	C₂²	1	1	yes	characteristic, complemented
203	#1478	C₂²	1	1	yes	characteristic, complemented
204	#1477	C₂²	1	1	yes	characteristic, complemented
205	#1476	C₂²	1	1	yes	characteristic, complemented
206	C₂×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
207	#1455	C₂²	1	1	yes	characteristic, complemented
208	#1454	C₂²	1	1	yes	characteristic, complemented
209	#1454	C₂²	1	1	yes	characteristic, complemented
210	#1453	C₂²	1	1	yes	characteristic, complemented
211	#1453	C₂²	1	1	yes	characteristic, complemented
212	#1453	C₂²	1	1	yes	characteristic, complemented
213	#1450	C₂²	1	1	yes	characteristic, complemented
214	#1450	C₂²	1	1	yes	characteristic, complemented
215	C₈×M₁₆	C₂²	1	1	yes	characteristic, complemented
216	C₈×M₁₆	C₂²	1	1	yes	characteristic, complemented
217	C₈×M₁₆	C₂²	1	1	yes	characteristic, complemented
218	C₈×M₁₆	C₂²	1	1	yes	characteristic, complemented
219	C₂×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic
220	C₂×AGL(1,ℤ/8)	C₂×C₄	1	1	yes	characteristic
221	C₂×AGL(1,ℤ/8)	C₂×C₄	1	1	yes	characteristic
222	C₂×#135	C₂×C₄	1	1	yes	characteristic
223	C₂²×D₈	C₂×C₄	1	1	yes	characteristic
224	C₂×#131	—	2	1	no	—
225	C₂×#131	—	2	1	no	—
226	C₂²×M₁₆	—	2	1	no	—
227	C₂²×M₁₆	—	2	1	no	—
228	C₂²×M₁₆	—	2	1	no	—
229	C₂²×M₁₆	—	2	1	no	—
230	#544	C₂×C₄	1	1	yes	characteristic
231	#542	—	2	1	no	—
232	#542	C₂×C₄	1	1	yes	characteristic
233	#542	C₂×C₄	1	1	yes	characteristic
234	#540	—	2	1	no	—
235	#540	C₂×C₄	1	1	yes	characteristic
236	#540	C₂×C₄	1	1	yes	characteristic
237	#538	—	2	1	no	—
238	#538	—	2	1	no	—
239	#537	C₂×C₄	1	1	yes	characteristic
240	#535	C₂×C₄	1	1	yes	characteristic
241	#535	C₂×C₄	1	1	yes	characteristic
242	#532	—	2	1	no	—
243	#532	C₂³	1	1	yes	characteristic
244	#532	C₂³	1	1	yes	characteristic
245	#529	—	2	1	no	—
246	#529	C₂³	1	1	yes	characteristic
247	#529	C₂³	1	1	yes	characteristic
248	#525	—	2	1	no	—
249	#525	—	2	1	no	—
250	#520	—	2	1	no	—
251	#520	C₂×C₄	1	1	yes	characteristic
252	#520	C₂×C₄	1	1	yes	characteristic
253	#520	C₂×C₄	1	1	yes	characteristic
254	#520	C₂×C₄	1	1	yes	characteristic
255	#518	—	2	1	no	—
256	#518	—	2	1	no	—
257	#518	—	2	1	no	—
258	#518	C₂×C₄	1	1	yes	characteristic
259	#518	C₂×C₄	1	1	yes	characteristic
260	#518	C₂×C₄	1	1	yes	characteristic
261	C₄×#41	—	2	1	no	—
262	C₄×#41	C₂³	1	1	yes	characteristic
263	C₄×#41	C₂³	1	1	yes	characteristic
264	C₄×#41	C₂³	1	1	yes	characteristic
265	C₄×#41	C₂³	1	1	yes	characteristic
266	C₄×#41	C₂³	1	1	yes	characteristic
267	C₂×C₄×D₄	—	2	1	no	—
268	C₂×C₄×D₄	—	2	1	no	—
269	C₂×C₄×D₄	—	2	1	no	—
270	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
271	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
272	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
273	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
274	#485	C₂×C₄	1	1	yes	characteristic
275	#485	C₂×C₄	1	1	yes	characteristic
276	#484	C₂×C₄	1	1	yes	characteristic
277	#484	C₂×C₄	1	1	yes	characteristic
278	#482	C₂×C₄	1	1	yes	characteristic
279	#482	C₂×C₄	1	1	yes	characteristic
280	#482	C₂×C₄	1	1	yes	characteristic
281	#482	C₂×C₄	1	1	yes	characteristic
282	#482	C₂×C₄	1	1	yes	characteristic
283	#482	C₂×C₄	1	1	yes	characteristic
284	#481	C₂×C₄	1	1	yes	characteristic
285	#481	C₂×C₄	1	1	yes	characteristic
286	#480	C₂×C₄	1	1	yes	characteristic
287	#480	C₂×C₄	1	1	yes	characteristic
288	#480	C₂×C₄	1	1	yes	characteristic
289	#480	C₂×C₄	1	1	yes	characteristic
290	#479	C₂×C₄	1	1	yes	characteristic
291	#479	C₂×C₄	1	1	yes	characteristic
292	#478	C₂×C₄	1	1	yes	characteristic
293	#478	C₂×C₄	1	1	yes	characteristic
294	#478	C₂×C₄	1	1	yes	characteristic
295	#478	C₂×C₄	1	1	yes	characteristic
296	#478	C₂×C₄	1	1	yes	characteristic
297	#478	C₂×C₄	1	1	yes	characteristic
298	#477	C₂×C₄	1	1	yes	characteristic
299	#477	C₂×C₄	1	1	yes	characteristic
300	#476	C₂×C₄	1	1	yes	characteristic
301	#476	C₂×C₄	1	1	yes	characteristic
302	#474	C₂×C₄	1	1	yes	characteristic
303	#474	C₂×C₄	1	1	yes	characteristic
304	#474	C₂×C₄	1	1	yes	characteristic
305	#474	C₂×C₄	1	1	yes	characteristic
306	#464	C₂×C₄	1	1	yes	characteristic
307	#464	C₂×C₄	1	1	yes	characteristic
308	#463	C₂×C₄	1	1	yes	characteristic
309	#463	C₂×C₄	1	1	yes	characteristic
310	#463	C₂×C₄	1	1	yes	characteristic
311	#463	C₂×C₄	1	1	yes	characteristic
312	#463	C₂×C₄	1	1	yes	characteristic
313	#463	C₂×C₄	1	1	yes	characteristic
314	#460	C₂×C₄	1	1	yes	characteristic
315	#460	C₂×C₄	1	1	yes	characteristic
316	#459	C₂×C₄	1	1	yes	characteristic
317	#459	C₂×C₄	1	1	yes	characteristic
318	#459	C₂×C₄	1	1	yes	characteristic
319	#459	C₂×C₄	1	1	yes	characteristic
320	#459	C₂×C₄	1	1	yes	characteristic
321	#459	C₂×C₄	1	1	yes	characteristic
322	#452	C₂×C₄	1	1	yes	characteristic
323	#452	C₂×C₄	1	1	yes	characteristic
324	#450	C₂×C₄	1	1	yes	characteristic
325	#450	C₂×C₄	1	1	yes	characteristic
326	#449	C₂×C₄	1	1	yes	characteristic
327	#449	C₂×C₄	1	1	yes	characteristic
328	#449	C₂×C₄	1	1	yes	characteristic
329	#449	C₂×C₄	1	1	yes	characteristic
330	#449	C₂×C₄	1	1	yes	characteristic
331	#449	C₂×C₄	1	1	yes	characteristic
332	#447	C₂×C₄	1	1	yes	characteristic
333	#447	C₂×C₄	1	1	yes	characteristic
334	#447	C₂×C₄	1	1	yes	characteristic
335	#447	C₂×C₄	1	1	yes	characteristic
336	#447	C₂×C₄	1	1	yes	characteristic
337	#447	C₂×C₄	1	1	yes	characteristic
338	#446	—	2	1	no	—
339	#446	—	2	1	no	—
340	#446	—	2	1	no	—
341	#446	D₄	1	1	yes	characteristic
342	#446	D₄	1	1	yes	characteristic
343	#446	C₂³	1	1	yes	characteristic
344	#446	C₂³	1	1	yes	characteristic
345	C₈×Q₈	C₂³	1	1	yes	characteristic
346	C₈×Q₈	C₂³	1	1	yes	characteristic
347	C₈×Q₈	C₂³	1	1	yes	characteristic
348	C₈×Q₈	C₂³	1	1	yes	characteristic
349	C₈×Q₈	C₂³	1	1	yes	characteristic
350	C₈×Q₈	C₂³	1	1	yes	characteristic
351	#442	C₂×C₄	1	1	yes	characteristic
352	#442	C₂×C₄	1	1	yes	characteristic
353	#442	C₂×C₄	1	1	yes	characteristic
354	#442	C₂×C₄	1	1	yes	characteristic
355	#440	C₂×C₄	1	1	yes	characteristic
356	#440	C₂×C₄	1	1	yes	characteristic
357	#440	C₂×C₄	1	1	yes	characteristic
358	#440	C₂×C₄	1	1	yes	characteristic
359	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
360	C₄×Q₁₆	C₂³	1	1	yes	characteristic
361	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
362	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
363	C₄×SD₁₆	C₂³	1	1	yes	characteristic
364	C₄×SD₁₆	C₂³	1	1	yes	characteristic
365	C₄×SD₁₆	C₂³	1	1	yes	characteristic
366	C₄×SD₁₆	C₂³	1	1	yes	characteristic
367	C₄×SD₁₆	C₂³	1	1	yes	characteristic
368	C₄×SD₁₆	C₂³	1	1	yes	characteristic
369	C₄×D₈	C₂×C₄	1	1	yes	characteristic
370	C₄×D₈	C₂×C₄	1	1	yes	characteristic
371	C₄×D₈	C₂×C₄	1	1	yes	characteristic
372	C₄×D₈	C₂×C₄	1	1	yes	characteristic
373	C₄×D₈	C₂×C₄	1	1	yes	characteristic
374	C₄×D₈	C₂³	1	1	yes	characteristic
375	C₄×D₈	C₂³	1	1	yes	characteristic
376	C₄×D₈	C₂³	1	1	yes	characteristic
377	C₄×D₈	C₂³	1	1	yes	characteristic
378	C₄×D₈	C₂³	1	1	yes	characteristic
379	C₄×D₈	C₂³	1	1	yes	characteristic
380	C₄×D₈	C₂³	1	1	yes	characteristic
381	C₄×D₈	C₂³	1	1	yes	characteristic
382	C₄×D₈	C₂³	1	1	yes	characteristic
383	#436	—	2	1	no	—
384	#436	—	2	1	no	—
385	#436	—	2	1	no	—
386	#436	—	2	1	no	—
387	#436	—	2	1	no	—
388	#436	—	2	1	no	—
389	#436	—	2	1	no	—
390	#436	—	2	1	no	—
391	#436	—	2	1	no	—
392	#436	—	2	1	no	—
393	#436	—	2	1	no	—
394	#436	—	2	1	no	—
395	#436	—	2	1	no	—
396	#436	—	2	1	no	—
397	#436	—	2	1	no	—
398	#436	—	2	1	no	—
399	#436	—	2	1	no	—
400	#436	—	2	1	no	—
401	#436	—	2	1	no	—
402	#436	—	2	1	no	—
403	#436	—	2	1	no	—
404	#436	D₄	1	1	yes	characteristic
405	#436	D₄	1	1	yes	characteristic
406	#436	C₂³	1	1	yes	characteristic
407	#436	C₂³	1	1	yes	characteristic
408	#436	C₂³	1	1	yes	characteristic
409	#436	C₂³	1	1	yes	characteristic
410	#436	C₂³	1	1	yes	characteristic
411	#436	C₂³	1	1	yes	characteristic
412	#436	C₂³	1	1	yes	characteristic
413	#436	C₂³	1	1	yes	characteristic
414	#436	C₂³	1	1	yes	characteristic
415	#436	C₂³	1	1	yes	characteristic
416	#436	C₂³	1	1	yes	characteristic
417	#436	C₂³	1	1	yes	characteristic
418	#436	C₂³	1	1	yes	characteristic
419	#436	C₂³	1	1	yes	characteristic
420	#435	—	2	1	no	—
421	#435	—	2	1	no	—
422	#435	—	2	1	no	—
423	#435	—	2	1	no	—
424	#435	—	2	1	no	—
425	#435	—	2	1	no	—
426	#435	—	2	1	no	—
427	#435	—	2	1	no	—
428	#435	—	2	1	no	—
429	#435	—	2	1	no	—
430	#435	—	2	1	no	—
431	#435	—	2	1	no	—
432	#435	—	2	1	no	—
433	#435	—	2	1	no	—
434	#435	—	2	1	no	—
435	#435	—	2	1	no	—
436	#435	—	2	1	no	—
437	#435	—	2	1	no	—
438	#435	—	2	1	no	—
439	#435	—	2	1	no	—
440	#435	—	2	1	no	—
441	#435	—	2	1	no	—
442	#435	—	2	1	no	—
443	#435	—	2	1	no	—
444	#435	—	2	1	no	—
445	#435	—	2	1	no	—
446	#435	—	2	1	no	—
447	#435	—	2	1	no	—
448	#435	D₄	1	1	yes	characteristic
449	#435	D₄	1	1	yes	characteristic
450	#435	D₄	1	1	yes	characteristic
451	#435	D₄	1	1	yes	characteristic
452	C₈×D₄	—	2	1	no	—
453	C₈×D₄	—	2	1	no	—
454	C₈×D₄	—	2	1	no	—
455	C₈×D₄	—	2	1	no	—
456	C₈×D₄	—	2	1	no	—
457	C₈×D₄	—	2	1	no	—
458	C₈×D₄	—	2	1	no	—
459	C₈×D₄	—	2	1	no	—
460	C₈×D₄	C₂³	1	1	yes	characteristic
461	C₈×D₄	C₂³	1	1	yes	characteristic
462	C₈×D₄	C₂³	1	1	yes	characteristic
463	C₈×D₄	C₂³	1	1	yes	characteristic
464	C₈×D₄	C₂³	1	1	yes	characteristic
465	C₈×D₄	C₂³	1	1	yes	characteristic
466	C₈×D₄	C₂³	1	1	yes	characteristic
467	C₈×D₄	C₂³	1	1	yes	characteristic
468	C₈×D₄	C₂³	1	1	yes	characteristic
469	C₈×D₄	C₂³	1	1	yes	characteristic
470	#433	—	2	1	no	—
471	#433	—	2	1	no	—
472	#433	—	2	1	no	—
473	#433	—	2	1	no	—
474	#433	C₂×C₄	1	1	yes	characteristic
475	#433	C₂×C₄	1	1	yes	characteristic
476	#433	C₂×C₄	1	1	yes	characteristic
477	#433	C₂×C₄	1	1	yes	characteristic
478	#432	—	2	1	no	—
479	#432	—	2	1	no	—
480	#432	—	2	1	no	—
481	#432	C₂³	1	1	yes	characteristic
482	#432	C₂³	1	1	yes	characteristic
483	#432	C₂³	1	1	yes	characteristic
484	#432	C₂³	1	1	yes	characteristic
485	#431	—	2	1	no	—
486	#431	—	2	1	no	—
487	#431	—	2	1	no	—
488	#431	—	2	1	no	—
489	#431	—	2	1	no	—
490	#431	C₂³	1	1	yes	characteristic
491	#431	C₂³	1	1	yes	characteristic
492	#431	C₂³	1	1	yes	characteristic
493	#431	C₂³	1	1	yes	characteristic
494	#431	C₂³	1	1	yes	characteristic
495	#431	C₂³	1	1	yes	characteristic
496	#431	C₂³	1	1	yes	characteristic
497	#431	C₂³	1	1	yes	characteristic
498	#431	C₂³	1	1	yes	characteristic
499	#431	C₂³	1	1	yes	characteristic
500	#431	C₂³	1	1	yes	characteristic
501	#431	C₂³	1	1	yes	characteristic
502	#428	C₂×C₄	1	1	yes	characteristic
503	#428	C₂×C₄	1	1	yes	characteristic
504	#427	C₂×C₄	1	1	yes	characteristic
505	C₂×#107	C₂×C₄	1	1	yes	characteristic
506	#424	—	2	1	no	—
507	#424	—	2	1	no	—
508	#424	C₂×C₄	1	1	yes	characteristic
509	#424	C₂×C₄	1	1	yes	characteristic
510	#423	—	2	1	no	—
511	#423	—	2	1	no	—
512	#423	—	2	1	no	—
513	#423	C₂³	1	1	yes	characteristic
514	#423	C₂³	1	1	yes	characteristic
515	#423	C₂³	1	1	yes	characteristic
516	#423	C₂³	1	1	yes	characteristic
517	C₂×C₄⋊C₈	—	2	1	no	—
518	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
519	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
520	#418	C₂×C₄	1	1	yes	characteristic
521	#418	C₂×C₄	1	1	yes	characteristic
522	#417	C₂×C₄	1	1	yes	characteristic
523	#417	C₂×C₄	1	1	yes	characteristic
524	#416	C₂×C₄	1	1	yes	characteristic
525	#416	C₂×C₄	1	1	yes	characteristic
526	C₂×#102	C₂×C₄	1	1	yes	characteristic
527	C₂×#102	C₂×C₄	1	1	yes	characteristic
528	#408	—	2	1	no	—
529	#408	—	2	1	no	—
530	#408	—	2	1	no	—
531	#408	—	2	1	no	—
532	#408	—	2	1	no	—
533	#408	—	2	1	no	—
534	#408	C₂×C₄	1	1	yes	characteristic
535	#408	C₂×C₄	1	1	yes	characteristic
536	#407	—	2	1	no	—
537	#407	—	2	1	no	—
538	#407	—	2	1	no	—
539	#407	—	2	1	no	—
540	#407	—	2	1	no	—
541	#407	—	2	1	no	—
542	#407	—	2	1	no	—
543	#407	—	2	1	no	—
544	C₂×C₂²⋊C₈	—	2	1	no	—
545	C₂×C₂²⋊C₈	—	2	1	no	—
546	C₂×C₂²⋊C₈	—	2	1	no	—
547	C₂×C₂²⋊C₈	—	2	1	no	—
548	#405	—	2	1	no	—
549	#405	—	2	1	no	—
550	C₄×M₁₆	—	2	1	no	—
551	C₄×M₁₆	—	2	1	no	—
552	C₄×M₁₆	C₂³	1	1	yes	characteristic
553	C₄×M₁₆	C₂³	1	1	yes	characteristic
554	C₄×M₁₆	C₂³	1	1	yes	characteristic
555	C₄×M₁₆	C₂³	1	1	yes	characteristic
556	C₄×M₁₆	C₂³	1	1	yes	characteristic
557	C₂×#97	—	2	1	no	—
558	C₂×C₄×C₈	—	2	1	no	—
559	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
560	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
561	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
562	#335	C₂³	1	1	yes	characteristic
563	#335	C₂³	1	1	yes	characteristic
564	#335	C₂³	1	1	yes	characteristic
565	#335	C₂³	1	1	yes	characteristic
566	#335	C₂³	1	1	yes	characteristic
567	#335	C₂³	1	1	yes	characteristic
568	#335	C₂³	1	1	yes	characteristic
569	#335	C₂³	1	1	yes	characteristic
570	#335	C₂³	1	1	yes	characteristic
571	#335	C₂³	1	1	yes	characteristic
572	#334	C₂³	1	1	yes	characteristic
573	#334	C₂³	1	1	yes	characteristic
574	#334	C₂³	1	1	yes	characteristic
575	#334	C₂³	1	1	yes	characteristic
576	#334	C₂³	1	1	yes	characteristic
577	#334	C₂³	1	1	yes	characteristic
578	Q₈⋊C₈	C₂³	1	1	yes	characteristic
579	Q₈⋊C₈	C₂³	1	1	yes	characteristic
580	Q₈⋊C₈	C₂³	1	1	yes	characteristic
581	Q₈⋊C₈	C₂³	1	1	yes	characteristic
582	Q₈⋊C₈	C₂³	1	1	yes	characteristic
583	Q₈⋊C₈	C₂³	1	1	yes	characteristic
584	Q₈⋊C₈	C₂³	1	1	yes	characteristic
585	Q₈⋊C₈	C₂³	1	1	yes	characteristic
586	D₄⋊C₈	C₂³	1	1	yes	characteristic
587	D₄⋊C₈	C₂³	1	1	yes	characteristic
588	D₄⋊C₈	C₂³	1	1	yes	characteristic
589	D₄⋊C₈	C₂³	1	1	yes	characteristic
590	D₄⋊C₈	C₂³	1	1	yes	characteristic
591	D₄⋊C₈	C₂³	1	1	yes	characteristic
592	D₄⋊C₈	C₂³	1	1	yes	characteristic
593	D₄⋊C₈	C₂³	1	1	yes	characteristic
594	D₄⋊C₈	C₂³	1	1	yes	characteristic
595	D₄⋊C₈	C₂³	1	1	yes	characteristic
596	D₄⋊C₈	C₂³	1	1	yes	characteristic
597	D₄⋊C₈	C₂³	1	1	yes	characteristic
598	D₄⋊C₈	C₂³	1	1	yes	characteristic
599	D₄⋊C₈	C₂³	1	1	yes	characteristic
600	D₄⋊C₈	C₂³	1	1	yes	characteristic
601	D₄⋊C₈	C₂³	1	1	yes	characteristic
602	D₄⋊C₈	C₂³	1	1	yes	characteristic
603	D₄⋊C₈	C₂³	1	1	yes	characteristic
604	D₄⋊C₈	C₂³	1	1	yes	characteristic
605	D₄⋊C₈	C₂³	1	1	yes	characteristic
606	D₄⋊C₈	C₂³	1	1	yes	characteristic
607	D₄⋊C₈	C₂³	1	1	yes	characteristic
608	D₄⋊C₈	C₂³	1	1	yes	characteristic
609	D₄⋊C₈	C₂³	1	1	yes	characteristic
610	#322	C₂³	1	1	yes	characteristic
611	#322	C₂³	1	1	yes	characteristic
612	#322	C₂³	1	1	yes	characteristic
613	#322	C₂³	1	1	yes	characteristic
614	#322	C₂³	1	1	yes	characteristic
615	#322	C₂³	1	1	yes	characteristic
616	#322	C₂³	1	1	yes	characteristic
617	#322	C₂³	1	1	yes	characteristic
618	#322	C₂³	1	1	yes	characteristic
619	#322	C₂³	1	1	yes	characteristic
620	C₈²	C₂³	1	1	yes	characteristic
621	C₈²	C₂³	1	1	yes	characteristic
622	C₈²	C₂³	1	1	yes	characteristic
623	C₈²	C₂³	1	1	yes	characteristic
624	C₈²	C₂³	1	1	yes	characteristic
625	C₈²	C₂³	1	1	yes	characteristic
626	H(5,𝔽₂)	—	4	2	no	—
627	H(5,𝔽₂)	—	4	2	no	—
628	C₂×#41	—	2	1	no	—
629	C₂×#41	—	2	1	no	—
630	C₂×#41	—	2	1	no	—
631	C₂×#41	C₂²×C₄	1	1	yes	characteristic
632	C₂×#41	C₂²×C₄	1	1	yes	characteristic
633	C₂×#41	C₂²×C₄	1	1	yes	characteristic
634	C₂×#41	C₂²×C₄	1	1	yes	characteristic
635	C₂×#41	C₂²×C₄	1	1	yes	characteristic
636	C₂²×D₄	—	2	1	no	—
637	C₂²×D₄	—	2	1	no	—
638	C₂²×D₄	—	2	1	no	—
639	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
640	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
641	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
642	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
643	C₂³×C₄	—	2	1	no	—
644	C₂³×C₄	—	2	1	no	—
645	C₂³×C₄	—	2	1	no	—
646	C₂³×C₄	—	2	1	no	—
647	AGL(1,ℤ/8)	—	4	2	no	—
648	AGL(1,ℤ/8)	—	4	2	no	—
649	#135	—	4	2	no	—
650	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
651	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
652	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
653	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
654	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
655	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
656	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
657	C₂×D₈	—	4	2	no	—
658	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
659	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
660	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
661	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
662	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
663	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
664	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
665	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
666	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
667	#131	—	8	2	no	—
668	#131	—	8	2	no	—
669	C₂×M₁₆	—	2	1	no	—
670	C₂×M₁₆	—	2	1	no	—
671	C₂×M₁₆	—	2	1	no	—
672	C₂×M₁₆	—	2	1	no	—
673	C₂×M₁₆	—	2	1	no	—
674	C₂×M₁₆	—	2	1	no	—
675	C₂×M₁₆	—	2	1	no	—
676	C₂×M₁₆	—	2	1	no	—
677	C₂×M₁₆	—	2	1	no	—
678	C₂×M₁₆	—	2	1	no	—
679	C₂×M₁₆	—	2	1	no	—
680	C₂×M₁₆	—	2	1	no	—
681	C₂×M₁₆	—	2	1	no	—
682	C₂×M₁₆	—	2	1	no	—
683	C₂×M₁₆	—	2	1	no	—
684	C₂×M₁₆	—	2	1	no	—
685	C₂×M₁₆	—	2	1	no	—
686	C₂×M₁₆	—	2	1	no	—
687	C₂×M₁₆	—	2	1	no	—
688	C₂×M₁₆	—	2	1	no	—
689	C₂×M₁₆	—	8	2	no	—
690	C₂×M₁₆	—	8	2	no	—
691	C₂×M₁₆	—	8	2	no	—
692	C₂×M₁₆	—	8	2	no	—
693	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
694	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
695	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
696	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
697	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
698	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
699	C₂²×C₈	—	2	1	no	—
700	C₂²×C₈	—	2	1	no	—
701	C₂²×C₈	—	2	1	no	—
702	C₂²×C₈	—	2	1	no	—
703	C₂²×C₈	—	2	1	no	—
704	C₂²×C₈	—	2	1	no	—
705	C₂²×C₈	—	2	1	no	—
706	C₂²×C₈	—	2	1	no	—
707	C₂²×C₈	—	2	1	no	—
708	C₂²×C₈	—	2	1	no	—
709	C₂²×C₈	—	2	1	no	—
710	C₂²×C₈	—	2	1	no	—
711	C₂²×C₈	—	2	1	no	—
712	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
713	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
714	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
715	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
718	C₄⋊Q₈	C₂²×C₄	1	1	yes	characteristic
719	#127	—	2	1	no	—
720	#127	C₂²×C₄	1	1	yes	characteristic
721	#127	C₂²×C₄	1	1	yes	characteristic
722	#126	—	2	1	no	—
723	#126	—	2	1	no	—
724	#126	—	2	1	no	—
725	#126	—	2	1	no	—
726	#125	—	2	1	no	—
727	#125	C₂²×C₄	1	1	yes	characteristic
728	#125	C₂²×C₄	1	1	yes	characteristic
729	#124	—	2	1	no	—
730	#124	—	2	1	no	—
731	#124	—	2	1	no	—
732	#124	—	2	1	no	—
733	#124	—	2	1	no	—
734	#124	C₂²×C₄	1	1	yes	characteristic
735	#124	C₂²×C₄	1	1	yes	characteristic
736	#123	—	2	1	no	—
737	#123	—	2	1	no	—
738	#123	—	2	1	no	—
739	#123	—	2	1	no	—
740	#123	—	2	1	no	—
741	#123	—	2	1	no	—
742	#123	—	2	1	no	—
743	#123	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
750	C₂²⋊Q₈	C₂²×C₄	1	1	yes	characteristic
751	#121	—	2	1	no	—
752	#121	—	2	1	no	—
753	#121	—	2	1	no	—
754	#121	—	2	1	no	—
755	#121	—	2	1	no	—
756	#121	—	2	1	no	—
757	#121	—	2	1	no	—
758	#121	—	2	1	no	—
759	#121	—	2	1	no	—
760	#121	—	2	1	no	—
761	#121	—	2	1	no	—
762	#121	C₂²×C₄	1	1	yes	characteristic
763	#121	C₂²×C₄	1	1	yes	characteristic
764	#121	C₂²×C₄	1	1	yes	characteristic
765	#121	C₂²×C₄	1	1	yes	characteristic
766	#121	C₂²×C₄	1	1	yes	characteristic
767	#121	C₂²×C₄	1	1	yes	characteristic
768	#120	—	2	1	no	—
769	#120	—	2	1	no	—
770	#120	—	2	1	no	—
771	#120	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
774	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
775	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
776	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
777	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
778	C₄×Q₈	#41	1	1	yes	characteristic
779	C₄×Q₈	C₂⁴	1	1	yes	characteristic
780	C₄×Q₈	C₂⁴	1	1	yes	characteristic
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
817	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
818	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
819	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
820	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
821	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
822	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
823	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
824	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
825	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
826	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
827	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
828	C₄×D₄	C₂×D₄	1	1	yes	characteristic
829	C₄×D₄	C₂×D₄	1	1	yes	characteristic
830	C₄×D₄	C₂×D₄	1	1	yes	characteristic
831	C₄×D₄	#41	1	1	yes	characteristic
832	C₄×D₄	#41	1	1	yes	characteristic
833	C₄×D₄	#41	1	1	yes	characteristic
834	C₄×D₄	C₂⁴	1	1	yes	characteristic
835	C₄×D₄	C₂⁴	1	1	yes	characteristic
836	C₄×D₄	C₂⁴	1	1	yes	characteristic
837	C₄×D₄	C₂⁴	1	1	yes	characteristic
838	C₄×D₄	C₂⁴	1	1	yes	characteristic
839	C₄×D₄	C₂⁴	1	1	yes	characteristic
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	—	2	1	no	—
843	#117	—	2	1	no	—
844	#117	—	2	1	no	—
845	#117	—	2	1	no	—
846	#117	—	2	1	no	—
847	#117	—	2	1	no	—
848	#117	—	2	1	no	—
849	#117	C₂²×C₄	1	1	yes	characteristic
850	#117	C₂²×C₄	1	1	yes	characteristic
851	#117	C₂²×C₄	1	1	yes	characteristic
852	#117	C₂²×C₄	1	1	yes	characteristic
853	#117	C₂²×C₄	1	1	yes	characteristic
854	#117	C₂²×C₄	1	1	yes	characteristic
855	#117	C₂²×C₄	1	1	yes	characteristic
856	C₂×C₄⋊C₄	—	2	1	no	—
857	C₂×C₄⋊C₄	—	2	1	no	—
858	C₂×C₄⋊C₄	—	2	1	no	—
859	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
860	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
861	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
862	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
863	C₂×C₂²⋊C₄	—	2	1	no	—
864	C₂×C₂²⋊C₄	—	2	1	no	—
865	C₂×C₂²⋊C₄	—	2	1	no	—
866	C₂×C₂²⋊C₄	—	2	1	no	—
867	C₂×C₂²⋊C₄	—	2	1	no	—
868	C₂×C₂²⋊C₄	—	2	1	no	—
869	C₂×C₂²⋊C₄	—	2	1	no	—
870	C₂×C₂²⋊C₄	—	2	1	no	—
871	C₂×C₂²⋊C₄	—	2	1	no	—
872	C₂×C₂²⋊C₄	—	2	1	no	—
873	C₂×C₄²	—	2	1	no	—
874	C₂×C₄²	—	2	1	no	—
875	C₂×C₄²	—	2	1	no	—
876	C₂×C₄²	—	2	1	no	—
877	C₂×C₄²	C₂⁴	1	1	yes	characteristic
878	C₂×C₄²	C₂⁴	1	1	yes	characteristic
879	C₂×C₄²	C₂⁴	1	1	yes	characteristic
880	#107	C₂²×C₄	1	1	yes	characteristic
881	#107	C₂²×C₄	1	1	yes	characteristic
882	#107	C₂²×C₄	1	1	yes	characteristic
883	#107	C₂²×C₄	1	1	yes	characteristic
884	#107	C₂²×C₄	1	1	yes	characteristic
885	#107	C₂²×C₄	1	1	yes	characteristic
886	#107	C₂²×C₄	1	1	yes	characteristic
887	#107	C₂²×C₄	1	1	yes	characteristic
888	#107	C₂²×C₄	1	1	yes	characteristic
889	#107	C₂²×C₄	1	1	yes	characteristic
890	#106	C₂²×C₄	1	1	yes	characteristic
891	#106	C₂²×C₄	1	1	yes	characteristic
892	#106	C₂²×C₄	1	1	yes	characteristic
893	#106	C₂²×C₄	1	1	yes	characteristic
894	#106	C₂²×C₄	1	1	yes	characteristic
895	#106	C₂²×C₄	1	1	yes	characteristic
896	C₄⋊C₈	—	2	1	no	—
897	C₄⋊C₈	—	2	1	no	—
898	C₄⋊C₈	—	2	1	no	—
899	C₄⋊C₈	—	2	1	no	—
900	C₄⋊C₈	—	2	1	no	—
901	C₄⋊C₈	—	2	1	no	—
902	C₄⋊C₈	—	2	1	no	—
903	C₄⋊C₈	—	2	1	no	—
904	C₄⋊C₈	—	2	1	no	—
905	C₄⋊C₈	—	2	1	no	—
906	C₄⋊C₈	—	2	1	no	—
907	C₄⋊C₈	—	2	1	no	—
908	C₄⋊C₈	—	2	1	no	—
909	C₄⋊C₈	—	2	1	no	—
910	C₄⋊C₈	—	2	1	no	—
911	C₄⋊C₈	—	2	1	no	—
912	C₄⋊C₈	—	2	1	no	—
913	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
914	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
915	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
916	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
917	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
918	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
919	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
920	C₄⋊C₈	C₂²×C₄	1	1	yes	characteristic
921	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
922	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
923	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
924	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
925	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
926	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
927	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
928	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
929	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
930	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
931	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
932	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
933	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
934	C₄⋊C₈	C₂⁴	1	1	yes	characteristic
935	#103	C₂²×C₄	1	1	yes	characteristic
936	#103	C₂²×C₄	1	1	yes	characteristic
937	#103	C₂²×C₄	1	1	yes	characteristic
938	#103	C₂²×C₄	1	1	yes	characteristic
939	#103	C₂²×C₄	1	1	yes	characteristic
940	#103	C₂²×C₄	1	1	yes	characteristic
941	#103	C₂²×C₄	1	1	yes	characteristic
942	#103	C₂²×C₄	1	1	yes	characteristic
943	#102	C₂²×C₄	1	1	yes	characteristic
944	#102	C₂²×C₄	1	1	yes	characteristic
945	#102	C₂²×C₄	1	1	yes	characteristic
946	#102	C₂²×C₄	1	1	yes	characteristic
947	#102	C₂²×C₄	1	1	yes	characteristic
948	#102	C₂²×C₄	1	1	yes	characteristic
949	#102	C₂²×C₄	1	1	yes	characteristic
950	#102	C₂²×C₄	1	1	yes	characteristic
951	#102	C₂²×C₄	1	1	yes	characteristic
952	#102	C₂²×C₄	1	1	yes	characteristic
953	#102	C₂²×C₄	1	1	yes	characteristic
954	#102	C₂²×C₄	1	1	yes	characteristic
955	#102	C₂²×C₄	1	1	yes	characteristic
956	#102	C₂²×C₄	1	1	yes	characteristic
957	#102	C₂²×C₄	1	1	yes	characteristic
958	#102	C₂²×C₄	1	1	yes	characteristic
959	#102	C₂²×C₄	1	1	yes	characteristic
960	#102	C₂²×C₄	1	1	yes	characteristic
961	#102	C₂²×C₄	1	1	yes	characteristic
962	#102	C₂²×C₄	1	1	yes	characteristic
963	#102	C₂²×C₄	1	1	yes	characteristic
964	#102	C₂²×C₄	1	1	yes	characteristic
965	#102	C₂²×C₄	1	1	yes	characteristic
966	#102	C₂²×C₄	1	1	yes	characteristic
967	C₂²⋊C₈	—	2	1	no	—
968	C₂²⋊C₈	—	2	1	no	—
969	C₂²⋊C₈	—	2	1	no	—
970	C₂²⋊C₈	—	2	1	no	—
971	C₂²⋊C₈	—	2	1	no	—
972	C₂²⋊C₈	—	2	1	no	—
973	C₂²⋊C₈	—	2	1	no	—
974	C₂²⋊C₈	—	2	1	no	—
975	C₂²⋊C₈	—	2	1	no	—
976	C₂²⋊C₈	—	2	1	no	—
977	C₂²⋊C₈	—	2	1	no	—
978	C₂²⋊C₈	—	2	1	no	—
979	C₂²⋊C₈	—	2	1	no	—
980	C₂²⋊C₈	—	2	1	no	—
981	C₂²⋊C₈	—	2	1	no	—
982	C₂²⋊C₈	—	2	1	no	—
983	C₂²⋊C₈	—	2	1	no	—
984	C₂²⋊C₈	—	2	1	no	—
985	C₂²⋊C₈	—	2	1	no	—
986	C₂²⋊C₈	—	2	1	no	—
987	C₂²⋊C₈	—	2	1	no	—
988	C₂²⋊C₈	—	2	1	no	—
989	C₂²⋊C₈	—	2	1	no	—
990	C₂²⋊C₈	—	2	1	no	—
991	C₂²⋊C₈	—	2	1	no	—
992	C₂²⋊C₈	—	2	1	no	—
993	C₂²⋊C₈	—	2	1	no	—
994	C₂²⋊C₈	—	2	1	no	—
995	C₂²⋊C₈	—	2	1	no	—
996	C₂²⋊C₈	—	2	1	no	—
997	C₂²⋊C₈	—	2	1	no	—
998	C₂²⋊C₈	—	2	1	no	—
999	C₂²⋊C₈	—	2	1	no	—
1000	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
1001	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
1002	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
1003	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
1004	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
1005	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
1006	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
1007	C₂²⋊C₈	C₂²×C₄	1	1	yes	characteristic
1008	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
1009	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
1010	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
1011	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
1012	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
1013	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
1014	#97	—	2	1	no	—
1015	#97	—	2	1	no	—
1016	#97	—	2	1	no	—
1017	#97	—	2	1	no	—
1018	#97	—	2	1	no	—
1019	#97	—	2	1	no	—
1020	#97	—	2	1	no	—
1021	#97	—	2	1	no	—
1022	#97	C₂²×C₄	1	1	yes	characteristic
1023	#97	C₂²×C₄	1	1	yes	characteristic
1024	#97	C₂×D₄	1	1	yes	characteristic
1025	#97	C₂×D₄	1	1	yes	characteristic
1026	#97	C₂×D₄	1	1	yes	characteristic
1027	#97	C₂×D₄	1	1	yes	characteristic
1028	C₄×C₈	—	2	1	no	—
1029	C₄×C₈	—	2	1	no	—
1030	C₄×C₈	—	2	1	no	—
1031	C₄×C₈	—	2	1	no	—
1032	C₄×C₈	—	2	1	no	—
1033	C₄×C₈	—	2	1	no	—
1034	C₄×C₈	—	2	1	no	—
1035	C₄×C₈	—	2	1	no	—
1036	C₄×C₈	—	2	1	no	—
1037	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
1038	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
1039	C₄×C₈	C₂×D₄	1	1	yes	characteristic
1040	C₄×C₈	C₂×D₄	1	1	yes	characteristic
1041	C₄×C₈	C₂⁴	1	1	yes	characteristic
1042	C₄×C₈	C₂⁴	1	1	yes	characteristic
1043	C₄×C₈	C₂⁴	1	1	yes	characteristic
1044	C₄×C₈	C₂⁴	1	1	yes	characteristic
1045	C₄×C₈	C₂⁴	1	1	yes	characteristic
1046	C₄×C₈	C₂⁴	1	1	yes	characteristic
1047	C₄×C₈	C₂⁴	1	1	yes	characteristic
1048	C₄×C₈	C₂⁴	1	1	yes	characteristic
1049	C₄×C₈	C₂⁴	1	1	yes	characteristic
1050	C₄×C₈	C₂⁴	1	1	yes	characteristic
1051	C₄×C₈	C₂⁴	1	1	yes	characteristic
1052	C₄×C₈	C₂⁴	1	1	yes	characteristic
1053	C₂⁴	—	2	1	no	—
1054	C₂⁴	—	2	1	no	—
1055	C₂⁴	—	2	1	no	—
1056	C₂⁴	—	2	1	no	—
1057	#41	—	2	2	no	—
1058	#41	—	2	2	no	—
1059	#41	—	2	2	no	—
1060	#41	—	2	2	no	—
1061	#41	—	4	1	no	—
1062	#41	—	4	1	no	—
1063	#41	—	4	1	no	—
1064	#41	—	4	1	no	—
1065	#41	—	4	4	no	—
1066	#41	—	4	1	no	—
1067	#41	—	4	1	no	—
1068	#41	—	8	1	no	—
1069	#41	—	8	1	no	—
1070	#41	—	8	1	no	—
1071	#41	—	8	1	no	—
1072	C₂×Q₈	—	2	1	no	—
1073	C₂×Q₈	—	2	1	no	—
1074	C₂×Q₈	C₄×D₄	1	1	yes	characteristic
1075	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
1076	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
1077	C₂×D₄	—	2	1	no	—
1078	C₂×D₄	—	2	2	no	—
1079	C₂×D₄	—	2	2	no	—
1080	C₂×D₄	—	2	1	no	—
1081	C₂×D₄	—	2	1	no	—
1082	C₂×D₄	—	2	1	no	—
1083	C₂×D₄	—	2	1	no	—
1084	C₂×D₄	—	2	1	no	—
1085	C₂×D₄	—	2	1	no	—
1086	C₂×D₄	—	2	1	no	—
1087	C₂×D₄	—	2	1	no	—
1088	C₂×D₄	—	2	1	no	—
1089	C₂×D₄	—	2	1	no	—
1090	C₂×D₄	—	2	1	no	—
1091	C₂×D₄	—	2	1	no	—
1092	C₂×D₄	—	2	1	no	—
1093	C₂×D₄	—	2	1	no	—
1094	C₂×D₄	—	2	1	no	—
1095	C₂×D₄	—	2	1	no	—
1096	C₂×D₄	—	2	1	no	—
1097	C₂×D₄	—	4	1	no	—
1098	C₂×D₄	—	4	1	no	—
1099	C₂×D₄	—	4	1	no	—
1100	C₂×D₄	—	4	1	no	—
1101	C₂×D₄	—	4	1	no	—
1102	C₂×D₄	—	4	1	no	—
1103	C₂×D₄	—	4	4	no	—
1104	C₂×D₄	—	4	4	no	—
1105	C₂×D₄	—	4	4	no	—
1106	C₂×D₄	C₄×D₄	1	1	yes	characteristic
1107	C₂×D₄	C₄×D₄	1	1	yes	characteristic
1108	C₂×D₄	C₄×D₄	1	1	yes	characteristic
1109	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
1110	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
1111	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
1112	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
1113	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
1114	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
1115	C₂²×C₄	—	2	1	no	—
1116	C₂²×C₄	—	2	1	no	—
1117	C₂²×C₄	—	2	1	no	—
1118	C₂²×C₄	—	2	1	no	—
1119	C₂²×C₄	—	2	1	no	—
1120	C₂²×C₄	—	2	1	no	—
1121	C₂²×C₄	—	2	1	no	—
1122	C₂²×C₄	—	2	1	no	—
1123	C₂²×C₄	—	2	1	no	—
1124	C₂²×C₄	—	2	1	no	—
1125	C₂²×C₄	—	2	1	no	—
1126	C₂²×C₄	—	2	1	no	—
1127	C₂²×C₄	—	2	1	no	—
1128	C₂²×C₄	—	2	1	no	—
1129	C₂²×C₄	—	2	1	no	—
1130	C₂²×C₄	—	2	1	no	—
1131	C₂²×C₄	—	2	1	no	—
1132	C₂²×C₄	—	2	1	no	—
1133	C₂²×C₄	—	2	1	no	—
1134	C₂²×C₄	—	2	1	no	—
1135	C₂²×C₄	—	2	1	no	—
1136	C₂²×C₄	—	2	1	no	—
1137	C₂²×C₄	—	2	1	no	—
1138	C₂²×C₄	—	2	1	no	—
1139	C₂²×C₄	—	2	1	no	—
1140	C₂²×C₄	—	2	1	no	—
1141	C₂²×C₄	—	8	1	no	—
1142	C₂²×C₄	—	8	1	no	—
1143	C₂²×C₄	—	8	1	no	—
1144	C₂²×C₄	—	8	1	no	—
1145	C₂²×C₄	—	8	1	no	—
1146	C₂²×C₄	—	8	1	no	—
1147	C₂²×C₄	—	8	1	no	—
1148	C₂²×C₄	—	8	1	no	—
1149	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
1150	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
1151	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
1152	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
1153	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
1154	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
1155	C₂²×C₄	C₂×#41	1	1	yes	characteristic
1156	C₂²×C₄	C₂×#41	1	1	yes	characteristic
1157	C₂²×C₄	C₂×#41	1	1	yes	characteristic
1158	Q₁₆	—	2	2	no	—
1159	SD₁₆	—	2	2	no	—
1160	SD₁₆	—	2	2	no	—
1161	SD₁₆	—	2	2	no	—
1162	SD₁₆	—	2	2	no	—
1163	SD₁₆	—	4	1	no	—
1164	SD₁₆	—	4	1	no	—
1165	D₈	—	2	2	no	—
1166	D₈	—	2	2	no	—
1167	D₈	—	2	2	no	—
1168	D₈	—	4	1	no	—
1169	D₈	—	4	1	no	—
1170	D₈	—	4	1	no	—
1171	D₈	—	4	1	no	—
1172	D₈	—	4	1	no	—
1173	D₈	—	4	1	no	—
1174	M₁₆	—	2	2	no	—
1175	M₁₆	—	2	2	no	—
1176	M₁₆	—	4	1	no	—
1177	M₁₆	—	4	1	no	—
1178	M₁₆	—	4	1	no	—
1179	M₁₆	—	4	1	no	—
1180	M₁₆	—	4	2	no	—
1181	M₁₆	—	4	2	no	—
1182	M₁₆	—	4	2	no	—
1183	M₁₆	—	4	2	no	—
1184	M₁₆	—	4	2	no	—
1185	M₁₆	—	8	1	no	—
1186	M₁₆	—	8	1	no	—
1187	M₁₆	—	8	1	no	—
1188	M₁₆	—	8	1	no	—
1189	M₁₆	—	8	1	no	—
1190	M₁₆	—	8	1	no	—
1191	M₁₆	—	8	1	no	—
1192	M₁₆	—	8	1	no	—
1193	M₁₆	—	8	1	no	—
1194	M₁₆	—	8	1	no	—
1195	M₁₆	—	8	1	no	—
1196	M₁₆	—	8	1	no	—
1197	M₁₆	—	8	1	no	—
1198	M₁₆	—	8	1	no	—
1199	M₁₆	—	8	1	no	—
1200	C₂×C₈	—	2	1	no	—
1201	C₂×C₈	—	2	2	no	—
1202	C₂×C₈	—	2	1	no	—
1203	C₂×C₈	—	2	1	no	—
1204	C₂×C₈	—	2	1	no	—
1205	C₂×C₈	—	2	1	no	—
1206	C₂×C₈	—	2	1	no	—
1207	C₂×C₈	—	2	1	no	—
1208	C₂×C₈	—	2	1	no	—
1209	C₂×C₈	—	2	1	no	—
1210	C₂×C₈	—	2	1	no	—
1211	C₂×C₈	—	2	1	no	—
1212	C₂×C₈	—	2	1	no	—
1213	C₂×C₈	—	4	1	no	—
1214	C₂×C₈	—	4	1	no	—
1215	C₂×C₈	—	4	1	no	—
1216	C₂×C₈	—	4	2	no	—
1217	C₂×C₈	—	4	2	no	—
1218	C₂×C₈	—	4	2	no	—
1219	C₂×C₈	—	4	2	no	—
1220	C₂×C₈	—	8	1	no	—
1221	C₂×C₈	—	8	1	no	—
1222	C₂×C₈	—	8	1	no	—
1223	C₂×C₈	—	8	1	no	—
1224	C₂×C₈	—	8	1	no	—
1225	C₂×C₈	—	8	1	no	—
1226	C₂×C₈	—	8	1	no	—
1227	C₂×C₈	—	8	1	no	—
1228	C₂×C₈	—	8	1	no	—
1229	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1230	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1231	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1232	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1233	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1234	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1235	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1236	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1237	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1238	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1239	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1240	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1241	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1242	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1243	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1244	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
1245	C₄⋊C₄	—	2	1	no	—
1246	C₄⋊C₄	—	2	1	no	—
1247	C₄⋊C₄	—	2	1	no	—
1248	C₄⋊C₄	—	2	1	no	—
1249	C₄⋊C₄	—	2	1	no	—
1250	C₄⋊C₄	—	2	1	no	—
1251	C₄⋊C₄	—	2	1	no	—
1252	C₄⋊C₄	—	2	1	no	—
1253	C₄⋊C₄	—	2	1	no	—
1254	C₄⋊C₄	—	2	1	no	—
1255	C₄⋊C₄	—	2	1	no	—
1256	C₄⋊C₄	—	2	1	no	—
1257	C₄⋊C₄	—	2	1	no	—
1258	C₄⋊C₄	—	2	1	no	—
1259	C₄⋊C₄	—	2	1	no	—
1260	C₄⋊C₄	—	2	1	no	—
1261	C₄⋊C₄	—	2	1	no	—
1262	C₄⋊C₄	—	2	1	no	—
1263	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
1264	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
1265	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
1266	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
1267	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
1268	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
1269	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1270	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1271	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1272	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1273	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1274	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1275	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1276	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1277	C₂²⋊C₄	—	2	1	no	—
1278	C₂²⋊C₄	—	2	1	no	—
1279	C₂²⋊C₄	—	2	1	no	—
1280	C₂²⋊C₄	—	2	1	no	—
1281	C₂²⋊C₄	—	2	1	no	—
1282	C₂²⋊C₄	—	2	1	no	—
1283	C₂²⋊C₄	—	2	1	no	—
1284	C₂²⋊C₄	—	2	1	no	—
1285	C₂²⋊C₄	—	2	1	no	—
1286	C₂²⋊C₄	—	2	1	no	—
1287	C₂²⋊C₄	—	2	1	no	—
1288	C₂²⋊C₄	—	2	1	no	—
1289	C₂²⋊C₄	—	2	1	no	—
1290	C₂²⋊C₄	—	2	1	no	—
1291	C₂²⋊C₄	—	2	1	no	—
1292	C₂²⋊C₄	—	2	1	no	—
1293	C₂²⋊C₄	—	2	1	no	—
1294	C₂²⋊C₄	—	2	1	no	—
1295	C₂²⋊C₄	—	2	1	no	—
1296	C₂²⋊C₄	—	2	1	no	—
1297	C₂²⋊C₄	—	2	1	no	—
1298	C₂²⋊C₄	—	2	1	no	—
1299	C₂²⋊C₄	—	2	1	no	—
1300	C₂²⋊C₄	—	2	1	no	—
1301	C₂²⋊C₄	—	2	1	no	—
1302	C₂²⋊C₄	—	2	1	no	—
1303	C₂²⋊C₄	—	2	1	no	—
1304	C₂²⋊C₄	—	2	1	no	—
1305	C₂²⋊C₄	—	2	1	no	—
1306	C₂²⋊C₄	—	2	1	no	—
1307	C₂²⋊C₄	—	2	1	no	—
1308	C₂²⋊C₄	—	2	1	no	—
1309	C₂²⋊C₄	—	2	1	no	—
1310	C₂²⋊C₄	—	2	1	no	—
1311	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
1312	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
1313	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
1314	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
1315	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
1316	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
1317	C₄²	—	2	1	no	—
1318	C₄²	—	2	1	no	—
1319	C₄²	—	2	1	no	—
1320	C₄²	—	2	1	no	—
1321	C₄²	—	2	1	no	—
1322	C₄²	—	2	1	no	—
1323	C₄²	—	2	1	no	—
1324	C₄²	—	2	1	no	—
1325	C₄²	—	2	1	no	—
1326	C₄²	—	2	1	no	—
1327	C₄²	C₂³×C₄	1	1	yes	characteristic
1328	C₄²	C₂³×C₄	1	1	yes	characteristic
1329	C₄²	C₂³×C₄	1	1	yes	characteristic
1330	C₄²	C₂²×D₄	1	1	yes	characteristic
1331	C₄²	C₂²×D₄	1	1	yes	characteristic
1332	C₄²	C₂²×D₄	1	1	yes	characteristic
1333	C₄²	C₂×#41	1	1	yes	characteristic
1334	C₄²	C₂×#41	1	1	yes	characteristic
1335	C₄²	C₂×#41	1	1	yes	characteristic
1336	C₄²	C₂⁵	1	1	yes	characteristic
1337	C₂³	—	2	1	no	—
1338	C₂³	—	2	1	no	—
1339	C₂³	—	2	1	no	—
1340	C₂³	—	2	1	no	—
1341	C₂³	—	2	1	no	—
1342	C₂³	—	2	1	no	—
1343	C₂³	—	4	2	no	—
1344	C₂³	—	4	2	no	—
1345	C₂³	—	4	2	no	—
1346	C₂³	—	8	1	no	—
1347	C₂³	—	8	1	no	—
1348	C₂³	—	8	1	no	—
1349	C₂³	—	8	1	no	—
1350	C₂³	—	8	1	no	—
1351	C₂³	—	8	1	no	—
1352	C₂³	—	8	1	no	—
1353	C₂³	—	8	1	no	—
1354	C₂³	—	8	1	no	—
1355	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
1356	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
1357	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
1358	Q₈	—	2	1	no	—
1359	Q₈	—	2	1	no	—
1360	Q₈	—	2	1	no	—
1361	Q₈	—	4	1	no	—
1362	Q₈	—	8	1	no	—
1363	Q₈	—	8	1	no	—
1364	Q₈	#568	1	2	yes	—
1365	D₄	—	2	4	no	—
1366	D₄	—	2	1	no	—
1367	D₄	—	2	1	no	—
1368	D₄	—	2	1	no	—
1369	D₄	—	2	1	no	—
1370	D₄	—	2	1	no	—
1371	D₄	—	2	1	no	—
1372	D₄	—	2	1	no	—
1373	D₄	—	2	1	no	—
1374	D₄	—	2	1	no	—
1375	D₄	—	2	1	no	—
1376	D₄	—	2	1	no	—
1377	D₄	—	4	1	no	—
1378	D₄	—	4	1	no	—
1379	D₄	—	4	1	no	—
1380	D₄	—	4	2	no	—
1381	D₄	—	4	2	no	—
1382	D₄	—	4	2	no	—
1383	D₄	—	4	2	no	—
1384	D₄	—	4	2	no	—
1385	D₄	—	8	1	no	—
1386	D₄	—	8	1	no	—
1387	D₄	—	8	1	no	—
1388	D₄	—	8	1	no	—
1389	D₄	—	8	1	no	—
1390	D₄	—	8	1	no	—
1391	D₄	—	8	1	no	—
1392	D₄	—	8	1	no	—
1393	D₄	—	8	1	no	—
1394	D₄	—	8	1	no	—
1395	D₄	—	8	1	no	—
1396	D₄	—	8	1	no	—
1397	D₄	#568	1	2	yes	—
1398	C₂×C₄	—	2	4	no	—
1399	C₂×C₄	—	2	1	no	—
1400	C₂×C₄	—	2	1	no	—
1401	C₂×C₄	—	2	1	no	—
1402	C₂×C₄	—	2	1	no	—
1403	C₂×C₄	—	2	1	no	—
1404	C₂×C₄	—	2	1	no	—
1405	C₂×C₄	—	2	1	no	—
1406	C₂×C₄	—	2	1	no	—
1407	C₂×C₄	—	2	1	no	—
1408	C₂×C₄	—	2	1	no	—
1409	C₂×C₄	—	2	1	no	—
1410	C₂×C₄	—	2	1	no	—
1411	C₂×C₄	—	2	1	no	—
1412	C₂×C₄	—	2	1	no	—
1413	C₂×C₄	—	2	1	no	—
1414	C₂×C₄	—	2	1	no	—
1415	C₂×C₄	—	2	1	no	—
1416	C₂×C₄	—	2	1	no	—
1417	C₂×C₄	—	2	1	no	—
1418	C₂×C₄	—	2	1	no	—
1419	C₂×C₄	—	2	1	no	—
1420	C₂×C₄	—	2	1	no	—
1421	C₂×C₄	—	4	1	no	—
1422	C₂×C₄	—	4	1	no	—
1423	C₂×C₄	—	4	1	no	—
1424	C₂×C₄	—	4	2	no	—
1425	C₂×C₄	—	4	2	no	—
1426	C₂×C₄	—	4	1	no	—
1427	C₂×C₄	—	4	1	no	—
1428	C₂×C₄	—	4	1	no	—
1429	C₂×C₄	—	4	1	no	—
1430	C₂×C₄	—	4	1	no	—
1431	C₂×C₄	—	4	1	no	—
1432	C₂×C₄	—	4	1	no	—
1433	C₂×C₄	—	4	1	no	—
1434	C₂×C₄	—	4	1	no	—
1435	C₂×C₄	—	4	1	no	—
1436	C₂×C₄	—	4	1	no	—
1437	C₂×C₄	—	4	1	no	—
1438	C₂×C₄	—	8	1	no	—
1439	C₂×C₄	—	8	1	no	—
1440	C₂×C₄	—	8	1	no	—
1441	C₂×C₄	—	8	1	no	—
1442	C₂×C₄	—	8	1	no	—
1443	C₂×C₄	—	8	1	no	—
1444	C₂×C₄	—	8	1	no	—
1445	C₂×C₄	—	8	1	no	—
1446	C₂×C₄	—	8	1	no	—
1447	C₂×C₄	—	8	1	no	—
1448	C₂×C₄	—	8	1	no	—
1449	C₂×C₄	—	8	1	no	—
1450	C₂×C₄	—	8	1	no	—
1451	C₂×C₄	—	8	1	no	—
1452	C₂×C₄	—	8	1	no	—
1453	C₂×C₄	—	8	1	no	—
1454	C₂×C₄	—	8	1	no	—
1455	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1456	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1457	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1458	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1459	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1460	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1461	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1462	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1463	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1464	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1465	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1466	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1467	C₈	—	2	2	no	—
1468	C₈	—	2	1	no	—
1469	C₈	—	2	1	no	—
1470	C₈	—	2	1	no	—
1471	C₈	—	2	1	no	—
1472	C₈	—	2	1	no	—
1473	C₈	—	2	1	no	—
1474	C₈	—	2	1	no	—
1475	C₈	—	2	1	no	—
1476	C₈	—	2	1	no	—
1477	C₈	—	2	1	no	—
1478	C₈	—	2	1	no	—
1479	C₈	—	2	1	no	—
1480	C₈	—	2	1	no	—
1481	C₈	—	2	1	no	—
1482	C₈	—	2	1	no	—
1483	C₈	—	4	1	no	—
1484	C₈	—	4	1	no	—
1485	C₈	—	4	1	no	—
1486	C₈	—	4	1	no	—
1487	C₈	—	4	1	no	—
1488	C₈	—	4	1	no	—
1489	C₈	—	4	1	no	—
1490	C₈	—	4	1	no	—
1491	C₈	—	4	1	no	—
1492	C₈	—	4	1	no	—
1493	C₈	—	4	1	no	—
1494	C₈	#576	1	2	yes	—
1495	C₂²	—	2	1	no	—
1496	C₂²	—	2	1	no	—
1497	C₂²	—	2	1	no	—
1498	C₂²	—	2	1	no	—
1499	C₂²	—	2	1	no	—
1500	C₂²	—	2	1	no	—
1501	C₂²	—	2	1	no	—
1502	C₂²	—	2	2	no	—
1503	C₂²	—	2	1	no	—
1504	C₂²	—	2	1	no	—
1505	C₂²	—	4	1	no	—
1506	C₂²	—	4	1	no	—
1507	C₂²	—	4	1	no	—
1508	C₂²	—	4	1	no	—
1509	C₂²	—	4	1	no	—
1510	C₂²	—	4	1	no	—
1511	C₂²	—	4	1	no	—
1512	C₂²	—	4	1	no	—
1513	C₂²	—	4	1	no	—
1514	C₂²	—	4	1	no	—
1515	C₂²	—	4	1	no	—
1516	C₂²	—	4	1	no	—
1517	C₂²	—	4	1	no	—
1518	C₂²	—	4	1	no	—
1519	C₂²	—	4	1	no	—
1520	C₂²	—	4	1	no	—
1521	C₂²	—	4	1	no	—
1522	C₂²	—	16	2	no	—
1523	C₂²	—	16	2	no	—
1524	C₂²	—	16	2	no	—
1525	C₂²	—	16	2	no	—
1526	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
1527	C₄	—	2	1	no	—
1528	C₄	—	2	1	no	—
1529	C₄	—	2	1	no	—
1530	C₄	—	2	1	no	—
1531	C₄	—	2	1	no	—
1532	C₄	—	2	1	no	—
1533	C₄	—	2	1	no	—
1534	C₄	—	2	1	no	—
1535	C₄	—	2	2	no	—
1536	C₄	—	2	1	no	—
1537	C₄	—	2	1	no	—
1538	C₄	—	4	1	no	—
1539	C₄	—	4	1	no	—
1540	C₄	—	4	1	no	—
1541	C₄	—	4	1	no	—
1542	C₄	—	4	1	no	—
1543	C₄	—	4	1	no	—
1544	C₄	—	4	1	no	—
1545	C₄	—	4	1	no	—
1546	C₄	—	4	1	no	—
1547	C₄	C₂×#568	1	1	yes	characteristic
1548	C₄	C₂×#568	1	1	yes	characteristic
1549	C₄	C₂×#576	1	1	yes	characteristic
1550	C₄	#3584	1	1	yes	characteristic
1551	C₂	—	4	1	no	—
1552	C₂	—	4	1	no	—
1553	C₂	—	4	1	no	—
1554	C₂	—	4	2	no	—
1555	C₂	—	8	1	no	—
1556	C₂	—	8	1	no	—
1557	C₂	—	8	1	no	—
1558	C₂	—	8	1	no	—
1559	C₂	—	8	1	no	—
1560	C₂	#60141	1	1	yes	characteristic
1561	C₂	C₄×#576	1	1	yes	characteristic
1562	C₂	#60183	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₄
commutator	C₂×C₄	C₂⁴×C₄
Frattini, cosocle	C₄²	C₂⁵
socle	C₂²	C₂²×C₄×D₄
prime radical	#60570	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ #2965 ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #60325	C₂	semidirect
3. #60319	C₂	semidirect
4. #18059	C₂	semidirect
5. #18054	C₂	semidirect
6. #18052	C₂	semidirect
7. #18052	C₂	semidirect
8. #18048	C₂	semidirect
9. #18046	C₂	semidirect
10. #18037	C₂	semidirect
11. M₁₆×D₈	C₂	semidirect
12. #18033	C₂	semidirect
13. #18026	C₂	semidirect
14. #18018	C₂	semidirect
15. #18014	C₂	semidirect
16. #18011	C₂	semidirect
17. #18006	C₂	semidirect
18. #17999	C₂	semidirect
19. #17994	C₂	semidirect
20. #17950	C₂	semidirect
21. #17946	C₂	semidirect
22. #17942	C₂	semidirect
23. #17928	C₂	semidirect
24. #17926	C₂	semidirect
25. #17920	C₂	semidirect
26. #17912	C₂	semidirect
27. #17904	C₂	semidirect
28. #17825	C₂	semidirect
29. #17505	C₂	semidirect
30. #17453	C₂	semidirect
31. #17341	C₂	semidirect
59. #2994	C₂²	semidirect
60. #2993	C₂²	semidirect
62. #2991	C₂²	semidirect
63. #2991	C₂²	semidirect
67. #2988	C₂²	semidirect
69. #2981	C₂²	semidirect
70. #2979	C₂²	semidirect
74. #2975	C₂²	semidirect
78. #2974	C₂²	semidirect
79. #2974	C₂²	semidirect
81. #2971	C₂²	semidirect
82. #2970	C₂²	semidirect
83. #2969	C₂²	semidirect
85. #2966	C₂²	semidirect
89. C₈×#41	C₂²	semidirect
94. #2935	C₂²	semidirect
98. D₄×M₁₆	C₂²	semidirect
99. D₄×M₁₆	C₂²	semidirect
102. #2931	C₂²	semidirect
105. C₂×#436	C₂²	semidirect
107. #1594	C₂²	semidirect
108. #1594	C₂²	semidirect
109. #1594	C₂²	semidirect
110. #1592	C₂²	semidirect
111. #1590	C₂²	semidirect
112. #1590	C₂²	semidirect
113. #1590	C₂²	semidirect
114. #1589	C₂²	semidirect
115. #1589	C₂²	semidirect
116. #1589	C₂²	semidirect
117. #1589	C₂²	semidirect
118. #1589	C₂²	semidirect
119. #1589	C₂²	semidirect
120. #1589	C₂²	semidirect
121. #1589	C₂²	semidirect
122. #1589	C₂²	semidirect
123. #1588	C₂²	semidirect
124. #1588	C₂²	semidirect
125. #1588	C₂²	semidirect
126. #1588	C₂²	semidirect
127. #1588	C₂²	semidirect
128. #1588	C₂²	semidirect
129. #1588	C₂²	semidirect
130. #1586	C₂²	semidirect
131. #1586	C₂²	semidirect
132. #1586	C₂²	semidirect
133. #1586	C₂²	semidirect
134. #1586	C₂²	semidirect
135. #1586	C₂²	semidirect
136. #1586	C₂²	semidirect
137. #1586	C₂²	semidirect
138. #1585	C₂²	semidirect
139. #1584	C₂²	semidirect
140. #1584	C₂²	semidirect
141. #1583	C₂²	semidirect
142. #1583	C₂²	semidirect
143. #1583	C₂²	semidirect
144. #1582	C₂²	semidirect
145. #1581	C₂²	semidirect
146. #1581	C₂²	semidirect
147. #1581	C₂²	semidirect
148. #1581	C₂²	semidirect
149. #1581	C₂²	semidirect
150. #1581	C₂²	semidirect
151. #1581	C₂²	semidirect
152. #1581	C₂²	semidirect
153. #1581	C₂²	semidirect
154. #1581	C₂²	semidirect
155. #1580	C₂²	semidirect
156. SD₁₆⋊C₈	C₂²	semidirect
157. SD₁₆⋊C₈	C₂²	semidirect
158. SD₁₆⋊C₈	C₂²	semidirect
159. C₈×Q₁₆	C₂²	semidirect
160. C₈×Q₁₆	C₂²	semidirect
161. C₈×SD₁₆	C₂²	semidirect
162. C₈×SD₁₆	C₂²	semidirect
163. C₈×SD₁₆	C₂²	semidirect
164. C₈×SD₁₆	C₂²	semidirect
165. C₈×SD₁₆	C₂²	semidirect
166. C₈×D₈	C₂²	semidirect
167. C₈×D₈	C₂²	semidirect
168. C₈×D₈	C₂²	semidirect
169. C₈×D₈	C₂²	semidirect
170. C₈×D₈	C₂²	semidirect
171. #1574	C₂²	semidirect
172. #1574	C₂²	semidirect
173. #1573	C₂²	semidirect
174. #1573	C₂²	semidirect
175. #1572	C₂²	semidirect
176. #1572	C₂²	semidirect
177. #1571	C₂²	semidirect
178. #1571	C₂²	semidirect
179. #1569	C₂²	semidirect
180. #1569	C₂²	semidirect
181. #1568	C₂²	semidirect
182. #1567	C₂²	semidirect
183. #1496	C₂²	semidirect
184. #1495	C₂²	semidirect
185. #1494	C₂²	semidirect
186. #1492	C₂²	semidirect
188. #1490	C₂²	semidirect
189. #1490	C₂²	semidirect
191. #1489	C₂²	semidirect
192. #1489	C₂²	semidirect
194. #1488	C₂²	semidirect
195. #1488	C₂²	semidirect
197. #1486	C₂²	semidirect
198. #1486	C₂²	semidirect
199. #1484	C₂²	semidirect
200. #1483	C₂²	semidirect
201. #1482	C₂²	semidirect
202. #1480	C₂²	semidirect
203. #1478	C₂²	semidirect
204. #1477	C₂²	semidirect
205. #1476	C₂²	semidirect
206. C₂×D₄⋊C₈	C₂²	semidirect
207. #1455	C₂²	semidirect
208. #1454	C₂²	semidirect
209. #1454	C₂²	semidirect
210. #1453	C₂²	semidirect
211. #1453	C₂²	semidirect
212. #1453	C₂²	semidirect
213. #1450	C₂²	semidirect
214. #1450	C₂²	semidirect
215. C₈×M₁₆	C₂²	semidirect
216. C₈×M₁₆	C₂²	semidirect
217. C₈×M₁₆	C₂²	semidirect
218. C₈×M₁₆	C₂²	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#60570	2
#60325	2
#60319	2
#18059	2
#18054	2
#18052	2
#18048	2
#18046	2
#18037	2
M₁₆×D₈	2
#18033	2
#18026	2
#18018	2
#18014	2
#18011	2
#18006	2
#17999	2
#17994	2
#17950	2
#17946	2
#17942	2
#17928	2
#17926	2
#17920	2
#17912	2
#17904	2
#17825	2
#17505	2
#17453	2
#17341	2