Subgroups — #6345085

Order 512.

1787 conjugacy classes of subgroups.

The subgroup lattice has 1309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#60283	C₂	1	1	yes	maximal, characteristic, complemented
2	#60263	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#575	C₂	1	1	yes	maximal, characteristic
4	#18053	C₂	1	2	yes	maximal, complemented
5	#18052	C₂	1	2	yes	maximal, complemented
6	#18051	C₂	1	2	yes	maximal, complemented
7	#18050	C₂	1	2	yes	maximal, complemented
8	#18049	C₂	1	2	yes	maximal, complemented
9	#18048	C₂	1	2	yes	maximal, complemented
10	#18047	C₂	1	2	yes	maximal, complemented
11	#18046	C₂	1	2	yes	maximal, complemented
12	#17899	C₂	1	1	yes	maximal, characteristic, complemented
13	#17898	C₂	1	1	yes	maximal, characteristic, complemented
14	#17882	C₂	1	1	yes	maximal, characteristic, complemented
15	#17882	C₂	1	1	yes	maximal, characteristic, complemented
16	#17881	C₂	1	1	yes	maximal, characteristic, complemented
17	#17881	C₂	1	1	yes	maximal, characteristic, complemented
18	#17858	C₂	1	1	yes	maximal, characteristic, complemented
19	#17857	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#1569	C₂	1	1	yes	maximal, characteristic, complemented
21	#17452	C₂	1	1	yes	maximal, characteristic, complemented
22	#17451	C₂	1	1	yes	maximal, characteristic, complemented
23	#17334	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#575	C₄	1	1	yes	characteristic
25	C₂×C₄×#41	C₂²	1	1	yes	characteristic
26	C₂×C₄×#41	C₂²	1	1	yes	characteristic
27	#2991	C₂²	1	2	yes	—
28	#2990	—	2	2	no	—
29	#2990	C₂²	1	2	yes	—
30	#2989	—	2	1	no	—
31	#2989	—	2	1	no	—
32	#2989	—	2	1	no	—
33	#2989	—	2	1	no	—
34	#2989	C₂²	1	1	yes	characteristic, complemented
35	#2989	C₂²	1	1	yes	characteristic, complemented
36	#2989	C₂²	1	1	yes	characteristic, complemented
37	#2989	C₂²	1	1	yes	characteristic, complemented
38	#2988	C₂²	1	1	yes	characteristic, complemented
39	#2988	C₂²	1	1	yes	characteristic, complemented
40	#2988	C₂²	1	1	yes	characteristic, complemented
41	#2988	C₂²	1	1	yes	characteristic, complemented
42	#2984	C₂²	1	2	yes	complemented
43	#2974	—	2	2	no	—
44	#2974	C₂²	1	2	yes	complemented
45	#2971	C₂²	1	2	yes	—
46	#2970	—	2	2	no	—
47	#2970	C₂²	1	2	yes	—
48	Q₈×M₁₆	C₂²	1	2	yes	complemented
49	C₄×#137	C₄	1	1	yes	characteristic
50	C₄×#137	C₄	1	1	yes	characteristic
51	C₄×#137	C₄	1	1	yes	characteristic
52	C₄×#137	C₄	1	1	yes	characteristic
53	C₄×#137	C₂²	1	1	yes	characteristic
54	C₄×#137	C₂²	1	1	yes	characteristic
55	C₄×#137	C₂²	1	1	yes	characteristic
56	C₄×#137	C₂²	1	1	yes	characteristic
57	C₄×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic
58	C₄×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic
59	C₄×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic
60	C₄×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic
61	C₄×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
62	C₄×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
63	C₄×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
64	C₄×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
65	#2943	C₄	1	1	yes	characteristic
66	#2943	C₄	1	1	yes	characteristic
67	#2943	C₄	1	1	yes	characteristic
68	#2943	C₄	1	1	yes	characteristic
69	C₄×#135	C₂²	1	1	yes	characteristic
70	C₄×#135	C₂²	1	1	yes	characteristic
71	C₄×#135	C₂²	1	1	yes	characteristic
72	C₄×#135	C₂²	1	1	yes	characteristic
73	D₄×M₁₆	—	2	2	no	—
74	D₄×M₁₆	C₂²	1	2	yes	complemented
75	#2920	—	2	1	no	—
76	#2920	—	2	1	no	—
77	#2920	C₂²	1	1	yes	characteristic
78	#2920	C₂²	1	1	yes	characteristic
79	C₂×#432	—	2	1	no	—
80	C₂×#432	C₂²	1	1	yes	characteristic
81	#2911	C₄	1	1	yes	characteristic
82	C₂×#423	—	2	1	no	—
83	C₂×#423	C₂²	1	1	yes	characteristic
84	#2896	C₄	1	1	yes	characteristic
85	#2896	C₄	1	1	yes	characteristic
86	C₂×C₄×M₁₆	C₂²	1	1	yes	characteristic
87	#1594	C₂²	1	2	yes	complemented
88	#1593	C₂²	1	2	yes	complemented
89	#1592	C₂²	1	2	yes	complemented
90	#1592	C₂²	1	2	yes	complemented
91	#1591	C₂²	1	2	yes	complemented
92	#1590	C₂²	1	2	yes	complemented
93	#1590	C₂²	1	2	yes	complemented
94	#1589	C₂²	1	2	yes	complemented
95	#1588	C₂²	1	2	yes	complemented
96	#1588	C₂²	1	2	yes	complemented
97	#1587	C₂²	1	2	yes	complemented
98	#1587	C₂²	1	2	yes	complemented
99	#1586	C₂²	1	2	yes	complemented
100	#1586	C₂²	1	2	yes	complemented
101	#1585	C₂²	1	2	yes	complemented
102	#1585	C₂²	1	2	yes	complemented
103	#1584	C₂²	1	2	yes	complemented
104	#1584	C₂²	1	2	yes	complemented
105	#1583	C₂²	1	2	yes	complemented
106	#1583	C₂²	1	2	yes	complemented
107	#1582	C₂²	1	2	yes	complemented
108	#1582	C₂²	1	2	yes	complemented
109	#1581	C₂²	1	2	yes	complemented
110	#1581	C₂²	1	2	yes	complemented
111	#1580	C₂²	1	2	yes	complemented
112	#1579	C₂²	1	2	yes	complemented
113	SD₁₆⋊C₈	C₂²	1	2	yes	complemented
114	SD₁₆⋊C₈	C₂²	1	2	yes	complemented
115	C₈×Q₁₆	C₂²	1	2	yes	complemented
116	C₈×SD₁₆	C₂²	1	2	yes	complemented
117	C₈×SD₁₆	C₂²	1	2	yes	complemented
118	C₈×D₈	C₂²	1	2	yes	complemented
119	#1569	C₂²	1	2	yes	complemented
120	#1569	C₂²	1	2	yes	complemented
121	#1569	C₂²	1	2	yes	complemented
122	#1569	C₂²	1	2	yes	complemented
123	C₂×#335	C₂²	1	1	yes	characteristic, complemented
124	C₂×#335	C₂²	1	1	yes	characteristic, complemented
125	C₂×#334	C₂²	1	1	yes	characteristic, complemented
126	C₂×#334	C₂²	1	1	yes	characteristic, complemented
127	#1491	C₂²	1	2	yes	complemented
128	#1490	C₂²	1	2	yes	complemented
129	#1489	C₂²	1	2	yes	—
130	#1489	C₂²	1	2	yes	—
131	#1488	C₂²	1	2	yes	—
132	#1488	C₂²	1	2	yes	—
133	#1487	C₂²	1	2	yes	complemented
134	#1486	C₂²	1	2	yes	complemented
135	#1477	C₂²	1	1	yes	characteristic, complemented
136	#1477	C₂²	1	1	yes	characteristic, complemented
137	#1477	C₂²	1	1	yes	characteristic, complemented
138	#1477	C₂²	1	1	yes	characteristic, complemented
139	#1477	C₂²	1	1	yes	characteristic, complemented
140	#1477	C₂²	1	1	yes	characteristic, complemented
141	#1477	C₂²	1	1	yes	characteristic, complemented
142	#1477	C₂²	1	1	yes	characteristic, complemented
143	#1455	C₂²	1	2	yes	complemented
144	#1455	C₂²	1	2	yes	complemented
145	#1453	C₂²	1	2	yes	complemented
146	#1453	C₂²	1	2	yes	complemented
147	#1452	C₂²	1	1	yes	characteristic, complemented
148	#1452	C₂²	1	1	yes	characteristic, complemented
149	#1450	C₂²	1	1	yes	characteristic, complemented
150	#1450	C₂²	1	1	yes	characteristic, complemented
151	C₂²×#41	C₂×C₄	1	1	yes	characteristic
152	C₂²×#41	C₂×C₄	1	1	yes	characteristic
153	#575	—	2	8	no	—
154	C₂×#137	C₂×C₄	1	1	yes	characteristic
155	C₂×#137	C₂×C₄	1	1	yes	characteristic
156	C₂×#137	C₂×C₄	1	1	yes	characteristic
157	C₂×#137	C₂×C₄	1	1	yes	characteristic
158	C₂×AGL(1,ℤ/8)	C₂×C₄	1	1	yes	characteristic
159	C₂×AGL(1,ℤ/8)	C₂×C₄	1	1	yes	characteristic
160	C₂×AGL(1,ℤ/8)	C₂×C₄	1	1	yes	characteristic
161	C₂×AGL(1,ℤ/8)	C₂×C₄	1	1	yes	characteristic
162	C₂×#135	C₂×C₄	1	1	yes	characteristic
163	C₂×#135	C₂×C₄	1	1	yes	characteristic
164	C₂×#135	C₂×C₄	1	1	yes	characteristic
165	C₂×#135	C₂×C₄	1	1	yes	characteristic
166	C₂²×M₁₆	—	2	1	no	—
167	C₂²×M₁₆	—	2	2	no	—
168	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
169	C₂²×M₁₆	C₂×C₄	1	1	yes	characteristic
170	C₄×#41	—	2	1	no	—
171	C₄×#41	—	2	1	no	—
172	C₄×#41	—	2	1	no	—
173	C₄×#41	—	2	1	no	—
174	C₄×#41	—	2	1	no	—
175	C₄×#41	—	2	1	no	—
176	C₄×#41	—	2	1	no	—
177	C₄×#41	—	2	1	no	—
178	C₄×#41	C₂×C₄	1	1	yes	characteristic
179	C₄×#41	C₂×C₄	1	1	yes	characteristic
180	C₄×#41	C₂×C₄	1	1	yes	characteristic
181	C₄×#41	C₂×C₄	1	1	yes	characteristic
182	C₄×#41	C₂×C₄	1	1	yes	characteristic
183	C₄×#41	C₂×C₄	1	1	yes	characteristic
184	C₄×#41	C₂×C₄	1	1	yes	characteristic
185	C₄×#41	C₂×C₄	1	1	yes	characteristic
186	C₄×#41	C₂³	1	1	yes	characteristic
187	C₄×#41	C₂³	1	1	yes	characteristic
188	C₄×#41	C₂³	1	1	yes	characteristic
189	C₄×#41	C₂³	1	1	yes	characteristic
190	C₄×#41	C₂³	1	1	yes	characteristic
191	C₄×#41	C₂³	1	1	yes	characteristic
192	C₄×#41	C₂³	1	1	yes	characteristic
193	C₄×#41	C₂³	1	1	yes	characteristic
194	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
195	C₂×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
196	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
197	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
198	C₂×C₄×D₄	—	2	1	no	—
199	C₂×C₄×D₄	—	2	1	no	—
200	C₂×C₄×D₄	—	2	1	no	—
201	C₂×C₄×D₄	—	2	1	no	—
202	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
203	C₂×C₄×D₄	C₂×C₄	1	1	yes	characteristic
204	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
205	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
206	C₂×#117	—	2	1	no	—
207	C₂×#117	—	2	1	no	—
208	C₂×#117	C₂×C₄	1	1	yes	characteristic
209	C₂×#117	C₂×C₄	1	1	yes	characteristic
210	C₂²×C₄²	—	2	1	no	—
211	C₂²×C₄²	—	2	1	no	—
212	C₂²×C₄²	C₂³	1	1	yes	characteristic
213	#446	—	2	2	no	—
214	#446	—	2	2	no	—
215	#446	—	2	2	no	—
216	#446	—	2	2	no	—
217	#446	C₂³	1	2	yes	—
218	#446	C₂³	1	2	yes	—
219	#446	C₂³	1	2	yes	—
220	#446	C₂³	1	2	yes	—
221	C₈×Q₈	C₂³	1	2	yes	—
222	C₈×Q₈	C₂³	1	2	yes	—
223	C₈×Q₈	C₂³	1	2	yes	—
224	C₈×Q₈	C₂³	1	2	yes	—
225	#442	C₂×C₄	1	1	yes	characteristic
226	#442	C₂×C₄	1	1	yes	characteristic
227	#442	C₂×C₄	1	1	yes	characteristic
228	#442	C₂×C₄	1	1	yes	characteristic
229	#442	C₂×C₄	1	1	yes	characteristic
230	#442	C₂×C₄	1	1	yes	characteristic
231	#442	C₂×C₄	1	1	yes	characteristic
232	#442	C₂×C₄	1	1	yes	characteristic
233	#441	C₂×C₄	1	1	yes	characteristic
234	#441	C₂×C₄	1	1	yes	characteristic
235	#441	C₂×C₄	1	1	yes	characteristic
236	#441	C₂×C₄	1	1	yes	characteristic
237	#441	C₂×C₄	1	1	yes	characteristic
238	#441	C₂×C₄	1	1	yes	characteristic
239	#441	C₂×C₄	1	1	yes	characteristic
240	#441	C₂×C₄	1	1	yes	characteristic
241	#440	C₂×C₄	1	1	yes	characteristic
242	#440	C₂×C₄	1	1	yes	characteristic
243	#440	C₂×C₄	1	1	yes	characteristic
244	#440	C₂×C₄	1	1	yes	characteristic
245	#440	C₂×C₄	1	1	yes	characteristic
246	#440	C₂×C₄	1	1	yes	characteristic
247	#440	C₂×C₄	1	1	yes	characteristic
248	#440	C₂×C₄	1	1	yes	characteristic
249	#440	C₂×C₄	1	1	yes	characteristic
250	#440	C₂×C₄	1	1	yes	characteristic
251	#440	C₂×C₄	1	1	yes	characteristic
252	#440	C₂×C₄	1	1	yes	characteristic
253	#440	C₂×C₄	1	1	yes	characteristic
254	#440	C₂×C₄	1	1	yes	characteristic
255	#440	C₂×C₄	1	1	yes	characteristic
256	#440	C₂×C₄	1	1	yes	characteristic
257	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
258	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
259	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
260	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
261	C₄×Q₁₆	C₂³	1	1	yes	characteristic
262	C₄×Q₁₆	C₂³	1	1	yes	characteristic
263	C₄×Q₁₆	C₂³	1	1	yes	characteristic
264	C₄×Q₁₆	C₂³	1	1	yes	characteristic
265	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
266	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
267	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
268	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
269	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
270	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
271	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
272	C₄×SD₁₆	C₂×C₄	1	1	yes	characteristic
273	C₄×SD₁₆	C₂³	1	1	yes	characteristic
274	C₄×SD₁₆	C₂³	1	1	yes	characteristic
275	C₄×SD₁₆	C₂³	1	1	yes	characteristic
276	C₄×SD₁₆	C₂³	1	1	yes	characteristic
277	C₄×SD₁₆	C₂³	1	1	yes	characteristic
278	C₄×SD₁₆	C₂³	1	1	yes	characteristic
279	C₄×SD₁₆	C₂³	1	1	yes	characteristic
280	C₄×SD₁₆	C₂³	1	1	yes	characteristic
281	C₄×D₈	C₂×C₄	1	1	yes	characteristic
282	C₄×D₈	C₂×C₄	1	1	yes	characteristic
283	C₄×D₈	C₂×C₄	1	1	yes	characteristic
284	C₄×D₈	C₂×C₄	1	1	yes	characteristic
285	C₄×D₈	C₂³	1	1	yes	characteristic
286	C₄×D₈	C₂³	1	1	yes	characteristic
287	C₄×D₈	C₂³	1	1	yes	characteristic
288	C₄×D₈	C₂³	1	1	yes	characteristic
289	#436	—	2	2	no	—
290	#436	—	2	2	no	—
291	#436	—	2	2	no	—
292	#436	—	2	2	no	—
293	#436	C₂³	1	2	yes	—
294	#436	C₂³	1	2	yes	—
295	#436	C₂³	1	2	yes	—
296	#436	C₂³	1	2	yes	—
297	#435	—	2	2	no	—
298	#435	—	2	2	no	—
299	#435	—	2	2	no	—
300	#435	—	2	2	no	—
301	#435	—	2	2	no	—
302	#435	—	2	2	no	—
303	#435	—	2	2	no	—
304	#435	—	2	2	no	—
305	#435	—	2	2	no	—
306	#435	—	2	2	no	—
307	#435	—	2	2	no	—
308	#435	—	2	2	no	—
309	C₈×D₄	—	2	2	no	—
310	C₈×D₄	—	2	2	no	—
311	C₈×D₄	—	2	2	no	—
312	C₈×D₄	—	2	2	no	—
313	C₈×D₄	C₂³	1	2	yes	—
314	C₈×D₄	C₂³	1	2	yes	—
315	C₈×D₄	C₂³	1	2	yes	—
316	C₈×D₄	C₂³	1	2	yes	—
317	#432	—	2	1	no	—
318	#432	—	2	1	no	—
319	#432	—	2	1	no	—
320	#432	—	2	1	no	—
321	#432	—	2	1	no	—
322	#432	—	2	1	no	—
323	#432	—	2	1	no	—
324	#432	—	2	1	no	—
325	#432	—	2	2	no	—
326	#432	—	2	2	no	—
327	#432	—	2	2	no	—
328	#432	—	2	2	no	—
329	#432	D₄	1	1	yes	characteristic
330	#432	D₄	1	1	yes	characteristic
331	#432	D₄	1	2	yes	—
332	#432	C₂³	1	2	yes	—
333	#432	C₂³	1	2	yes	—
334	#431	—	2	1	no	—
335	#431	—	2	1	no	—
336	#431	—	2	1	no	—
337	#431	—	2	1	no	—
338	#431	—	2	2	no	—
339	#431	—	2	2	no	—
340	#431	C₂³	1	1	yes	characteristic
341	#431	C₂³	1	1	yes	characteristic
342	#431	C₂³	1	2	yes	—
343	#431	C₂³	1	2	yes	—
344	#431	C₂³	1	1	yes	characteristic
345	#431	C₂³	1	1	yes	characteristic
346	#428	C₂×C₄	1	1	yes	characteristic
347	#428	C₂×C₄	1	1	yes	characteristic
348	#428	C₂×C₄	1	1	yes	characteristic
349	#428	C₂×C₄	1	1	yes	characteristic
350	#428	C₂×C₄	1	1	yes	characteristic
351	#428	C₂×C₄	1	1	yes	characteristic
352	#428	C₂×C₄	1	1	yes	characteristic
353	#428	C₂×C₄	1	1	yes	characteristic
354	#427	C₂×C₄	1	1	yes	characteristic
355	#427	C₂×C₄	1	1	yes	characteristic
356	#427	C₂×C₄	1	1	yes	characteristic
357	#427	C₂×C₄	1	1	yes	characteristic
358	#423	—	2	2	no	—
359	#423	—	2	1	no	—
360	#423	—	2	1	no	—
361	#423	—	2	1	no	—
362	#423	—	2	1	no	—
363	#423	—	2	1	no	—
364	#423	—	2	2	no	—
365	#423	—	2	1	no	—
366	#423	—	2	1	no	—
367	#423	D₄	1	1	yes	characteristic
368	#423	D₄	1	1	yes	characteristic
369	#423	C₂³	1	2	yes	—
370	#423	C₂³	1	2	yes	—
371	C₂×C₄⋊C₈	—	2	1	no	—
372	C₂×C₄⋊C₈	—	2	1	no	—
373	C₂×C₄⋊C₈	—	2	1	no	—
374	C₂×C₄⋊C₈	—	2	2	no	—
375	C₂×C₄⋊C₈	—	2	1	no	—
376	C₂×C₄⋊C₈	—	2	1	no	—
377	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
378	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
379	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
380	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
381	#419	C₂×C₄	1	1	yes	characteristic
382	#419	C₂×C₄	1	1	yes	characteristic
383	#419	C₂×C₄	1	1	yes	characteristic
384	#419	C₂×C₄	1	1	yes	characteristic
385	#418	C₂×C₄	1	1	yes	characteristic
386	#418	C₂×C₄	1	1	yes	characteristic
387	#418	C₂×C₄	1	1	yes	characteristic
388	#418	C₂×C₄	1	1	yes	characteristic
389	#417	C₂×C₄	1	1	yes	characteristic
390	#417	C₂×C₄	1	1	yes	characteristic
391	#417	C₂×C₄	1	1	yes	characteristic
392	#417	C₂×C₄	1	1	yes	characteristic
393	#417	C₂×C₄	1	1	yes	characteristic
394	#417	C₂×C₄	1	1	yes	characteristic
395	#417	C₂×C₄	1	1	yes	characteristic
396	#417	C₂×C₄	1	1	yes	characteristic
397	#416	C₂×C₄	1	1	yes	characteristic
398	#416	C₂×C₄	1	1	yes	characteristic
399	#416	C₂×C₄	1	1	yes	characteristic
400	#416	C₂×C₄	1	1	yes	characteristic
401	#416	C₂×C₄	1	1	yes	characteristic
402	#416	C₂×C₄	1	1	yes	characteristic
403	#416	C₂×C₄	1	1	yes	characteristic
404	#416	C₂×C₄	1	1	yes	characteristic
405	#407	—	2	1	no	—
406	#407	—	2	2	no	—
407	#407	—	2	2	no	—
408	#407	D₄	1	2	yes	—
409	C₂×C₂²⋊C₈	—	2	1	no	—
410	C₂×C₂²⋊C₈	—	2	2	no	—
411	C₄×M₁₆	—	2	2	no	—
412	C₄×M₁₆	—	2	2	no	—
413	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
414	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
415	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
416	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
417	C₄×M₁₆	C₂³	1	2	yes	—
418	C₄×M₁₆	C₂³	1	1	yes	characteristic
419	C₄×M₁₆	C₂³	1	1	yes	characteristic
420	C₄×M₁₆	C₂³	1	1	yes	characteristic
421	C₄×M₁₆	C₂³	1	1	yes	characteristic
422	C₄×M₁₆	C₂³	1	2	yes	—
423	C₂×#97	—	2	1	no	—
424	C₂×#97	—	2	2	no	—
425	C₂×#97	C₂×C₄	1	1	yes	characteristic
426	C₂×#97	C₂×C₄	1	1	yes	characteristic
427	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
428	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
429	#335	C₂³	1	2	yes	—
430	#335	C₂³	1	2	yes	—
431	#335	C₂³	1	2	yes	—
432	#335	C₂³	1	2	yes	—
433	#334	C₂³	1	2	yes	—
434	#334	C₂³	1	2	yes	—
435	#334	C₂³	1	2	yes	—
436	#334	C₂³	1	2	yes	—
437	Q₈⋊C₈	C₂³	1	2	yes	—
438	Q₈⋊C₈	C₂³	1	2	yes	—
439	Q₈⋊C₈	C₂³	1	2	yes	—
440	Q₈⋊C₈	C₂³	1	2	yes	—
441	Q₈⋊C₈	C₂³	1	2	yes	—
442	Q₈⋊C₈	C₂³	1	2	yes	—
443	Q₈⋊C₈	C₂³	1	2	yes	—
444	Q₈⋊C₈	C₂³	1	2	yes	—
445	D₄⋊C₈	C₂³	1	2	yes	—
446	D₄⋊C₈	C₂³	1	2	yes	—
447	D₄⋊C₈	C₂³	1	2	yes	—
448	D₄⋊C₈	C₂³	1	2	yes	—
449	D₄⋊C₈	C₂³	1	2	yes	—
450	D₄⋊C₈	C₂³	1	2	yes	—
451	D₄⋊C₈	C₂³	1	2	yes	—
452	D₄⋊C₈	C₂³	1	2	yes	—
453	#322	C₂³	1	2	yes	—
454	#322	C₂³	1	2	yes	—
455	#322	C₂³	1	2	yes	—
456	#322	C₂³	1	2	yes	—
457	#322	C₂³	1	2	yes	—
458	#322	C₂³	1	2	yes	—
459	C₈²	C₂³	1	2	yes	—
460	C₈²	C₂³	1	2	yes	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	1	no	—
463	C₂×#41	—	2	1	no	—
464	C₂×#41	—	2	1	no	—
465	C₂×#41	—	2	4	no	—
466	C₂×#41	—	2	4	no	—
467	C₂×#41	—	4	2	no	—
468	C₂×#41	—	4	2	no	—
469	C₂×#41	C₂²×C₄	1	1	yes	characteristic
470	C₂×#41	C₂²×C₄	1	1	yes	characteristic
471	C₂×#41	C₂²×C₄	1	1	yes	characteristic
472	C₂×#41	C₂²×C₄	1	1	yes	characteristic
473	C₂×#41	C₂²×C₄	1	1	yes	characteristic
474	C₂×#41	C₂²×C₄	1	1	yes	characteristic
475	C₂×#41	C₂²×C₄	1	1	yes	characteristic
476	C₂×#41	C₂²×C₄	1	1	yes	characteristic
477	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
478	C₂²×Q₈	C₂²×C₄	1	1	yes	characteristic
479	C₂²×D₄	—	2	1	no	—
480	C₂²×D₄	—	2	1	no	—
481	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
482	C₂²×D₄	C₂²×C₄	1	1	yes	characteristic
483	C₂³×C₄	—	2	1	no	—
484	C₂³×C₄	—	2	1	no	—
485	C₂³×C₄	—	2	1	no	—
486	C₂³×C₄	—	2	1	no	—
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	C₂²×C₄	1	1	yes	characteristic
490	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
491	C₂³×C₄	#41	1	1	yes	characteristic
492	#137	—	2	4	no	—
493	#137	—	2	4	no	—
494	#137	—	2	4	no	—
495	#137	—	2	4	no	—
496	AGL(1,ℤ/8)	—	2	4	no	—
497	AGL(1,ℤ/8)	—	2	4	no	—
498	AGL(1,ℤ/8)	—	2	4	no	—
499	AGL(1,ℤ/8)	—	2	4	no	—
500	#135	—	2	4	no	—
501	#135	—	2	4	no	—
502	#135	—	2	4	no	—
503	#135	M₁₆	1	8	yes	complemented
504	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
505	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
506	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
507	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
508	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
509	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
510	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
511	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
512	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
513	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
514	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
515	C₂×SD₁₆	C₂²×C₄	1	1	yes	characteristic
516	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
517	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
518	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
519	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
520	C₂×M₁₆	—	2	2	no	—
521	C₂×M₁₆	—	2	2	no	—
522	C₂×M₁₆	—	2	2	no	—
523	C₂×M₁₆	—	2	4	no	—
524	C₂×M₁₆	—	2	2	no	—
525	C₂×M₁₆	—	2	2	no	—
526	C₂×M₁₆	—	2	2	no	—
527	C₂×M₁₆	—	2	2	no	—
528	C₂×M₁₆	—	4	2	no	—
529	C₂×M₁₆	—	8	4	no	—
530	C₂×M₁₆	—	8	2	no	—
531	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
532	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
533	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
534	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
535	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
536	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
537	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
538	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
539	C₂×M₁₆	C₂×D₄	1	2	yes	—
540	C₂×M₁₆	C₂×D₄	1	2	yes	—
541	C₂²×C₈	—	2	1	no	—
542	C₂²×C₈	—	2	1	no	—
543	C₂²×C₈	—	2	1	no	—
544	C₂²×C₈	—	2	1	no	—
545	C₂²×C₈	—	2	2	no	—
546	C₂²×C₈	—	2	2	no	—
547	C₂²×C₈	—	2	2	no	—
548	C₂²×C₈	—	2	2	no	—
549	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
550	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
551	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
552	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
553	C₄×Q₈	—	2	1	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
562	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
563	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
564	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
565	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
566	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
567	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
568	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
569	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
570	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
571	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
572	C₄×Q₈	C₂²×C₄	1	1	yes	characteristic
573	C₄×Q₈	C₂⁴	1	1	yes	characteristic
574	C₄×Q₈	C₂⁴	1	1	yes	characteristic
575	C₄×Q₈	C₂⁴	1	1	yes	characteristic
576	C₄×Q₈	C₂⁴	1	1	yes	characteristic
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	—	2	1	no	—
584	C₄×D₄	—	2	1	no	—
585	C₄×D₄	—	2	1	no	—
586	C₄×D₄	—	2	1	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	1	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	1	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
618	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
619	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
620	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
621	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
622	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
623	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
624	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
625	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
626	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
627	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
628	C₄×D₄	C₂²×C₄	1	1	yes	characteristic
629	C₄×D₄	C₂⁴	1	1	yes	characteristic
630	C₄×D₄	C₂⁴	1	1	yes	characteristic
631	C₄×D₄	C₂⁴	1	1	yes	characteristic
632	C₄×D₄	C₂⁴	1	1	yes	characteristic
633	#117	—	2	1	no	—
634	#117	—	2	1	no	—
635	#117	—	2	1	no	—
636	#117	—	2	1	no	—
637	#117	—	2	1	no	—
638	#117	—	2	1	no	—
639	#117	—	2	1	no	—
640	#117	—	2	1	no	—
641	#117	—	2	1	no	—
642	#117	—	2	1	no	—
643	#117	—	2	1	no	—
644	#117	—	2	1	no	—
645	#117	—	2	1	no	—
646	#117	—	2	1	no	—
647	#117	—	2	1	no	—
648	#117	—	2	1	no	—
649	#117	—	2	1	no	—
650	#117	—	2	1	no	—
651	#117	—	2	1	no	—
652	#117	—	2	1	no	—
653	#117	C₂²×C₄	1	1	yes	characteristic
654	#117	C₂²×C₄	1	1	yes	characteristic
655	#117	C₂²×C₄	1	1	yes	characteristic
656	#117	C₂²×C₄	1	1	yes	characteristic
657	#117	C₂²×C₄	1	1	yes	characteristic
658	#117	C₂²×C₄	1	1	yes	characteristic
659	#117	C₂²×C₄	1	1	yes	characteristic
660	#117	C₂²×C₄	1	1	yes	characteristic
661	C₂×C₄⋊C₄	—	2	1	no	—
662	C₂×C₄⋊C₄	—	2	1	no	—
663	C₂×C₄⋊C₄	—	2	1	no	—
664	C₂×C₄⋊C₄	—	2	1	no	—
665	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	1	no	—
671	C₂×C₂²⋊C₄	—	2	1	no	—
672	C₂×C₂²⋊C₄	—	2	1	no	—
673	C₂×C₂²⋊C₄	—	2	1	no	—
674	C₂×C₂²⋊C₄	—	2	1	no	—
675	C₂×C₄²	—	2	1	no	—
676	C₂×C₄²	—	2	1	no	—
677	C₂×C₄²	—	2	1	no	—
678	C₂×C₄²	—	2	1	no	—
679	C₂×C₄²	—	2	1	no	—
680	C₂×C₄²	—	2	1	no	—
681	C₂×C₄²	—	2	1	no	—
682	C₂×C₄²	—	2	1	no	—
683	C₂×C₄²	—	2	1	no	—
684	C₂×C₄²	—	2	1	no	—
685	C₂×C₄²	—	2	1	no	—
686	C₂×C₄²	—	2	1	no	—
687	C₂×C₄²	—	2	1	no	—
688	C₂×C₄²	—	2	1	no	—
689	C₂×C₄²	—	2	1	no	—
690	C₂×C₄²	—	2	1	no	—
691	C₂×C₄²	—	2	1	no	—
692	C₂×C₄²	—	2	1	no	—
693	C₂×C₄²	—	2	1	no	—
694	C₂×C₄²	—	2	1	no	—
695	C₂×C₄²	—	2	1	no	—
696	C₂×C₄²	—	2	1	no	—
697	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
698	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
699	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
700	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
701	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
702	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
703	C₂×C₄²	#41	1	1	yes	characteristic
704	C₂×C₄²	#41	1	1	yes	characteristic
705	C₂×C₄²	#41	1	1	yes	characteristic
706	C₂×C₄²	C₂⁴	1	1	yes	characteristic
707	C₂×C₄²	C₂⁴	1	1	yes	characteristic
708	C₂×C₄²	C₂⁴	1	1	yes	characteristic
709	#107	C₂²×C₄	1	1	yes	characteristic
710	#107	C₂²×C₄	1	1	yes	characteristic
711	#107	C₂²×C₄	1	1	yes	characteristic
712	#107	C₂²×C₄	1	1	yes	characteristic
713	#107	C₂²×C₄	1	1	yes	characteristic
714	#107	C₂²×C₄	1	1	yes	characteristic
715	#107	C₂²×C₄	1	1	yes	characteristic
716	#107	C₂²×C₄	1	1	yes	characteristic
717	#106	C₂²×C₄	1	1	yes	characteristic
718	#106	C₂²×C₄	1	1	yes	characteristic
719	#106	C₂²×C₄	1	1	yes	characteristic
720	#106	C₂²×C₄	1	1	yes	characteristic
721	#106	C₂²×C₄	1	1	yes	characteristic
722	#106	C₂²×C₄	1	1	yes	characteristic
723	#106	C₂²×C₄	1	1	yes	characteristic
724	#106	C₂²×C₄	1	1	yes	characteristic
725	C₄⋊C₈	—	2	2	no	—
726	C₄⋊C₈	—	2	2	no	—
727	C₄⋊C₈	—	2	2	no	—
728	C₄⋊C₈	—	2	2	no	—
729	C₄⋊C₈	—	2	2	no	—
730	C₄⋊C₈	—	2	2	no	—
731	C₄⋊C₈	—	2	2	no	—
732	C₄⋊C₈	—	2	2	no	—
733	C₄⋊C₈	—	2	2	no	—
734	C₄⋊C₈	—	2	1	no	—
735	C₄⋊C₈	—	2	1	no	—
736	C₄⋊C₈	—	2	1	no	—
737	C₄⋊C₈	—	2	1	no	—
738	C₄⋊C₈	—	2	2	no	—
739	C₄⋊C₈	—	2	1	no	—
740	C₄⋊C₈	—	2	1	no	—
741	C₄⋊C₈	—	2	2	no	—
742	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
743	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
744	C₄⋊C₈	C₂×D₄	1	2	yes	—
745	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
746	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
747	C₄⋊C₈	C₂×D₄	1	2	yes	—
748	C₄⋊C₈	C₂⁴	1	2	yes	—
749	C₄⋊C₈	C₂⁴	1	2	yes	—
750	C₄⋊C₈	C₂⁴	1	2	yes	—
751	C₄⋊C₈	C₂⁴	1	2	yes	—
752	#103	C₂²×C₄	1	1	yes	characteristic
753	#103	C₂²×C₄	1	1	yes	characteristic
754	#103	C₂²×C₄	1	1	yes	characteristic
755	#103	C₂²×C₄	1	1	yes	characteristic
756	#103	C₂²×C₄	1	1	yes	characteristic
757	#103	C₂²×C₄	1	1	yes	characteristic
758	#103	C₂²×C₄	1	1	yes	characteristic
759	#103	C₂²×C₄	1	1	yes	characteristic
760	#103	C₂²×C₄	1	1	yes	characteristic
761	#103	C₂²×C₄	1	1	yes	characteristic
762	#103	C₂²×C₄	1	1	yes	characteristic
763	#103	C₂²×C₄	1	1	yes	characteristic
764	#103	C₂²×C₄	1	1	yes	characteristic
765	#103	C₂²×C₄	1	1	yes	characteristic
766	#103	C₂²×C₄	1	1	yes	characteristic
767	#103	C₂²×C₄	1	1	yes	characteristic
768	#102	C₂²×C₄	1	1	yes	characteristic
769	#102	C₂²×C₄	1	1	yes	characteristic
770	#102	C₂²×C₄	1	1	yes	characteristic
771	#102	C₂²×C₄	1	1	yes	characteristic
772	#102	C₂²×C₄	1	1	yes	characteristic
773	#102	C₂²×C₄	1	1	yes	characteristic
774	#102	C₂²×C₄	1	1	yes	characteristic
775	#102	C₂²×C₄	1	1	yes	characteristic
776	#102	C₂²×C₄	1	1	yes	characteristic
777	#102	C₂²×C₄	1	1	yes	characteristic
778	#102	C₂²×C₄	1	1	yes	characteristic
779	#102	C₂²×C₄	1	1	yes	characteristic
780	#102	C₂²×C₄	1	1	yes	characteristic
781	#102	C₂²×C₄	1	1	yes	characteristic
782	#102	C₂²×C₄	1	1	yes	characteristic
783	#102	C₂²×C₄	1	1	yes	characteristic
784	C₂²⋊C₈	—	2	2	no	—
785	C₂²⋊C₈	—	2	2	no	—
786	C₂²⋊C₈	—	2	2	no	—
787	C₂²⋊C₈	—	2	1	no	—
788	C₂²⋊C₈	—	2	1	no	—
789	C₂²⋊C₈	—	2	2	no	—
790	C₂²⋊C₈	—	2	2	no	—
791	C₂²⋊C₈	—	2	2	no	—
792	C₂²⋊C₈	—	2	2	no	—
793	C₂²⋊C₈	—	2	2	no	—
794	C₂²⋊C₈	—	2	2	no	—
795	C₂²⋊C₈	—	2	2	no	—
796	C₂²⋊C₈	—	2	2	no	—
797	C₂²⋊C₈	C₂×D₄	1	2	yes	—
798	C₂²⋊C₈	C₂×D₄	1	2	yes	—
799	C₂²⋊C₈	C₂×D₄	1	2	yes	—
800	C₂²⋊C₈	C₂×D₄	1	2	yes	—
801	#97	—	2	2	no	—
802	#97	—	2	2	no	—
803	#97	—	2	2	no	—
804	#97	—	2	2	no	—
805	#97	—	2	2	no	—
806	#97	—	2	2	no	—
807	#97	—	2	2	no	—
808	#97	C₂²×C₄	1	1	yes	characteristic
809	#97	C₂²×C₄	1	1	yes	characteristic
810	#97	C₂²×C₄	1	1	yes	characteristic
811	#97	C₂²×C₄	1	1	yes	characteristic
812	#97	C₂²×C₄	1	1	yes	characteristic
813	#97	C₂²×C₄	1	1	yes	characteristic
814	#97	C₂²×C₄	1	1	yes	characteristic
815	#97	C₂²×C₄	1	1	yes	characteristic
816	#97	C₂×D₄	1	2	yes	—
817	#97	C₂×D₄	1	2	yes	—
818	C₄×C₈	—	2	2	no	—
819	C₄×C₈	—	2	2	no	—
820	C₄×C₈	—	2	2	no	—
821	C₄×C₈	—	2	2	no	—
822	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
823	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
824	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
825	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
826	C₄×C₈	C₂⁴	1	2	yes	—
827	C₄×C₈	C₂⁴	1	2	yes	—
828	C₄×C₈	C₂⁴	1	1	yes	characteristic
829	C₄×C₈	C₂⁴	1	1	yes	characteristic
830	C₄×C₈	C₂⁴	1	1	yes	characteristic
831	C₄×C₈	C₂⁴	1	1	yes	characteristic
832	C₄×C₈	C₂⁴	1	2	yes	—
833	C₄×C₈	C₂⁴	1	2	yes	—
834	C₂⁴	—	2	1	no	—
835	C₂⁴	—	2	1	no	—
836	C₂⁴	C₄×D₄	1	1	yes	characteristic
837	#41	—	2	2	no	—
838	#41	—	2	2	no	—
839	#41	—	2	2	no	—
840	#41	—	2	2	no	—
841	#41	—	2	2	no	—
842	#41	—	2	2	no	—
843	#41	—	2	2	no	—
844	#41	—	2	2	no	—
845	#41	—	2	2	no	—
846	#41	—	2	2	no	—
847	#41	—	4	4	no	—
848	#41	—	4	4	no	—
849	#41	—	4	1	no	—
850	#41	—	4	1	no	—
851	#41	—	4	1	no	—
852	#41	—	4	1	no	—
853	#41	—	4	4	no	—
854	#41	—	4	4	no	—
855	#41	C₂×M₁₆	1	4	yes	—
856	#41	C₂×M₁₆	1	4	yes	complemented
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	2	no	—
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	4	1	no	—
862	C₂×Q₈	—	4	1	no	—
863	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
864	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
865	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
866	C₂×Q₈	C₂³×C₄	1	1	yes	characteristic
867	C₂×D₄	—	2	1	no	—
868	C₂×D₄	—	2	1	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	2	1	no	—
872	C₂×D₄	—	2	1	no	—
873	C₂×D₄	—	2	1	no	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	—	2	1	no	—
877	C₂×D₄	—	2	1	no	—
878	C₂×D₄	—	2	1	no	—
879	C₂×D₄	—	4	1	no	—
880	C₂×D₄	—	4	1	no	—
881	C₂×D₄	—	4	4	no	—
882	C₂×D₄	—	4	4	no	—
883	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
884	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
885	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
886	C₂×D₄	C₂³×C₄	1	1	yes	characteristic
887	C₂²×C₄	—	2	1	no	—
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	1	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	4	1	no	—
920	C₂²×C₄	—	4	1	no	—
921	C₂²×C₄	—	4	4	no	—
922	C₂²×C₄	—	4	4	no	—
923	C₂²×C₄	—	4	2	no	—
924	C₂²×C₄	—	4	2	no	—
925	C₂²×C₄	—	8	1	no	—
926	C₂²×C₄	—	8	1	no	—
927	C₂²×C₄	—	8	1	no	—
928	C₂²×C₄	—	8	2	no	—
929	C₂²×C₄	—	8	2	no	—
930	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
931	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
932	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
933	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
934	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
935	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
936	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
937	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
938	C₂²×C₄	C₄×D₄	1	1	yes	characteristic
939	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
940	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
941	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
942	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
943	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
944	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
945	C₂²×C₄	C₂×#41	1	1	yes	characteristic
946	C₂²×C₄	C₂×#41	1	1	yes	characteristic
947	C₂²×C₄	C₂×#41	1	1	yes	characteristic
948	Q₁₆	—	2	2	no	—
949	Q₁₆	—	2	2	no	—
950	Q₁₆	—	2	2	no	—
951	Q₁₆	C₂×M₁₆	1	4	yes	complemented
952	SD₁₆	—	2	2	no	—
953	SD₁₆	—	2	2	no	—
954	SD₁₆	—	2	2	no	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	2	2	no	—
957	SD₁₆	—	2	2	no	—
958	SD₁₆	C₂×M₁₆	1	4	yes	complemented
959	SD₁₆	C₂×M₁₆	1	4	yes	complemented
960	D₈	—	2	2	no	—
961	D₈	—	2	2	no	—
962	D₈	—	2	2	no	—
963	D₈	C₂×M₁₆	1	4	yes	complemented
964	M₁₆	—	2	2	no	—
965	M₁₆	—	2	2	no	—
966	M₁₆	—	2	2	no	—
967	M₁₆	—	2	2	no	—
968	M₁₆	—	4	1	no	—
969	M₁₆	—	4	1	no	—
970	M₁₆	—	4	1	no	—
971	M₁₆	—	4	1	no	—
972	M₁₆	—	4	2	no	—
973	M₁₆	—	4	2	no	—
974	M₁₆	—	4	4	no	—
975	M₁₆	—	8	2	no	—
976	M₁₆	—	8	2	no	—
977	M₁₆	—	8	2	no	—
978	M₁₆	—	8	2	no	—
979	M₁₆	—	8	2	no	—
980	M₁₆	—	8	2	no	—
981	C₂×C₈	—	2	2	no	—
982	C₂×C₈	—	2	2	no	—
983	C₂×C₈	—	2	2	no	—
984	C₂×C₈	—	2	2	no	—
985	C₂×C₈	—	2	2	no	—
986	C₂×C₈	—	2	2	no	—
987	C₂×C₈	—	2	2	no	—
988	C₂×C₈	—	2	2	no	—
989	C₂×C₈	—	2	2	no	—
990	C₂×C₈	—	8	2	no	—
991	C₂×C₈	—	8	2	no	—
992	C₂×C₈	—	8	2	no	—
993	C₂×C₈	—	8	2	no	—
994	C₂×C₈	—	8	1	no	—
995	C₂×C₈	—	8	1	no	—
996	C₂×C₈	—	8	1	no	—
997	C₂×C₈	—	8	1	no	—
998	C₂×C₈	C₂×M₁₆	1	4	yes	complemented
999	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1000	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1001	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1002	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1003	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1004	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1005	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1006	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
1007	C₂×C₈	C₂²×D₄	1	2	yes	—
1008	C₂×C₈	C₂²×D₄	1	2	yes	—
1009	C₂×C₈	C₂²×D₄	1	2	yes	—
1010	C₂×C₈	C₂²×D₄	1	2	yes	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	1	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	1	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1032	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1033	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1034	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1035	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1036	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1037	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1038	C₄⋊C₄	C₂³×C₄	1	1	yes	characteristic
1039	C₂²⋊C₄	—	2	1	no	—
1040	C₂²⋊C₄	—	2	1	no	—
1041	C₂²⋊C₄	—	2	1	no	—
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	1	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	1	no	—
1056	C₂²⋊C₄	—	2	1	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₄²	—	2	1	no	—
1064	C₄²	—	2	1	no	—
1065	C₄²	—	2	1	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	—	2	1	no	—
1070	C₄²	—	2	1	no	—
1071	C₄²	—	2	1	no	—
1072	C₄²	—	2	1	no	—
1073	C₄²	—	2	1	no	—
1074	C₄²	—	2	1	no	—
1075	C₄²	—	2	1	no	—
1076	C₄²	—	2	1	no	—
1077	C₄²	—	2	1	no	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	1	no	—
1080	C₄²	—	2	1	no	—
1081	C₄²	—	2	1	no	—
1082	C₄²	—	2	1	no	—
1083	C₄²	—	2	1	no	—
1084	C₄²	—	2	1	no	—
1085	C₄²	—	2	1	no	—
1086	C₄²	—	2	1	no	—
1087	C₄²	C₄×D₄	1	1	yes	characteristic
1088	C₄²	C₄×D₄	1	1	yes	characteristic
1089	C₄²	C₄×D₄	1	1	yes	characteristic
1090	C₄²	C₄×D₄	1	1	yes	characteristic
1091	C₄²	C₄×D₄	1	1	yes	characteristic
1092	C₄²	C₄×D₄	1	1	yes	characteristic
1093	C₄²	C₂³×C₄	1	1	yes	characteristic
1094	C₄²	C₂³×C₄	1	1	yes	characteristic
1095	C₄²	C₂³×C₄	1	1	yes	characteristic
1096	C₄²	C₂²×D₄	1	1	yes	characteristic
1097	C₄²	C₂²×D₄	1	1	yes	characteristic
1098	C₄²	C₂²×D₄	1	1	yes	characteristic
1099	C₄²	C₂×#41	1	1	yes	characteristic
1100	C₄²	C₂×#41	1	1	yes	characteristic
1101	C₄²	C₂×#41	1	1	yes	characteristic
1102	C₄²	C₂⁵	1	1	yes	characteristic
1103	C₂³	—	2	1	no	—
1104	C₂³	—	2	1	no	—
1105	C₂³	—	2	2	no	—
1106	C₂³	—	2	1	no	—
1107	C₂³	—	2	1	no	—
1108	C₂³	—	4	1	no	—
1109	C₂³	—	4	1	no	—
1110	C₂³	—	4	2	no	—
1111	C₂³	—	4	2	no	—
1112	C₂³	—	4	2	no	—
1113	C₂³	—	4	2	no	—
1114	C₂³	—	8	1	no	—
1115	C₂³	—	8	1	no	—
1116	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
1117	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
1118	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
1119	Q₈	—	2	1	no	—
1120	Q₈	—	2	1	no	—
1121	Q₈	—	2	1	no	—
1122	Q₈	—	2	1	no	—
1123	Q₈	—	2	1	no	—
1124	Q₈	—	2	1	no	—
1125	Q₈	—	4	2	no	—
1126	Q₈	—	4	2	no	—
1127	Q₈	C₂²×M₁₆	1	2	yes	—
1128	Q₈	C₂²×M₁₆	1	2	yes	—
1129	D₄	—	2	4	no	—
1130	D₄	—	2	4	no	—
1131	D₄	—	2	1	no	—
1132	D₄	—	2	1	no	—
1133	D₄	—	2	1	no	—
1134	D₄	—	2	1	no	—
1135	D₄	—	2	1	no	—
1136	D₄	—	2	1	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	2	no	—
1139	D₄	—	4	2	no	—
1140	D₄	—	4	2	no	—
1141	D₄	—	4	2	no	—
1142	D₄	—	4	2	no	—
1143	D₄	—	4	2	no	—
1144	D₄	—	4	2	no	—
1145	D₄	C₂²×M₁₆	1	2	yes	—
1146	D₄	C₂²×M₁₆	1	2	yes	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	4	no	—
1159	C₂×C₄	—	2	4	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	1	no	—
1179	C₂×C₄	—	4	1	no	—
1180	C₂×C₄	—	4	1	no	—
1181	C₂×C₄	—	4	1	no	—
1182	C₂×C₄	—	4	1	no	—
1183	C₂×C₄	—	4	2	no	—
1184	C₂×C₄	—	4	2	no	—
1185	C₂×C₄	—	4	2	no	—
1186	C₂×C₄	—	4	2	no	—
1187	C₂×C₄	—	4	2	no	—
1188	C₂×C₄	—	4	2	no	—
1189	C₂×C₄	—	4	2	no	—
1190	C₂×C₄	—	4	2	no	—
1191	C₂×C₄	—	4	2	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	4	2	no	—
1194	C₂×C₄	—	4	2	no	—
1195	C₂×C₄	—	4	1	no	—
1196	C₂×C₄	—	4	1	no	—
1197	C₂×C₄	—	4	1	no	—
1198	C₂×C₄	—	4	1	no	—
1199	C₂×C₄	—	4	1	no	—
1200	C₂×C₄	—	4	1	no	—
1201	C₂×C₄	—	4	1	no	—
1202	C₂×C₄	—	4	1	no	—
1203	C₂×C₄	—	4	2	no	—
1204	C₂×C₄	—	4	2	no	—
1205	C₂×C₄	—	8	1	no	—
1206	C₂×C₄	—	8	1	no	—
1207	C₂×C₄	—	8	1	no	—
1208	C₂×C₄	—	8	1	no	—
1209	C₂×C₄	—	8	1	no	—
1210	C₂×C₄	—	8	1	no	—
1211	C₂×C₄	—	8	1	no	—
1212	C₂×C₄	—	8	1	no	—
1213	C₂×C₄	—	8	1	no	—
1214	C₂×C₄	—	8	1	no	—
1215	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1216	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1217	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1218	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1219	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1220	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1221	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1222	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1223	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
1224	C₂×C₄	C₂²×M₁₆	1	2	yes	—
1225	C₂×C₄	#568	1	2	yes	—
1226	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1227	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
1228	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1229	C₈	—	2	2	no	—
1230	C₈	—	2	2	no	—
1231	C₈	—	2	2	no	—
1232	C₈	—	2	2	no	—
1233	C₈	—	2	1	no	—
1234	C₈	—	2	1	no	—
1235	C₈	—	2	1	no	—
1236	C₈	—	2	1	no	—
1237	C₈	—	2	1	no	—
1238	C₈	—	2	1	no	—
1239	C₈	—	4	2	no	—
1240	C₈	—	4	2	no	—
1241	C₈	—	4	2	no	—
1242	C₈	—	4	2	no	—
1243	C₈	—	4	2	no	—
1244	C₈	—	4	2	no	—
1245	C₈	C₂²×M₁₆	1	2	yes	—
1246	C₈	C₂²×M₁₆	1	2	yes	—
1247	C₂²	—	2	1	no	—
1248	C₂²	—	2	1	no	—
1249	C₂²	—	2	1	no	—
1250	C₂²	—	2	1	no	—
1251	C₂²	—	2	1	no	—
1252	C₂²	—	2	1	no	—
1253	C₂²	—	2	1	no	—
1254	C₂²	—	2	1	no	—
1255	C₂²	—	2	2	no	—
1256	C₂²	—	2	2	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	4	1	no	—
1260	C₂²	—	4	1	no	—
1261	C₂²	—	4	1	no	—
1262	C₂²	—	4	1	no	—
1263	C₂²	—	4	1	no	—
1264	C₂²	—	4	1	no	—
1265	C₂²	—	4	1	no	—
1266	C₂²	—	4	1	no	—
1267	C₂²	—	8	2	no	—
1268	C₂²	—	8	4	no	—
1269	C₂²	—	8	4	no	—
1270	C₂²	D₄×M₁₆	1	2	yes	—
1271	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
1272	C₄	—	2	1	no	—
1273	C₄	—	2	1	no	—
1274	C₄	—	2	1	no	—
1275	C₄	—	2	1	no	—
1276	C₄	—	2	1	no	—
1277	C₄	—	2	1	no	—
1278	C₄	—	2	1	no	—
1279	C₄	—	2	1	no	—
1280	C₄	—	2	1	no	—
1281	C₄	—	2	2	no	—
1282	C₄	—	2	2	no	—
1283	C₄	—	4	1	no	—
1284	C₄	—	4	1	no	—
1285	C₄	—	4	1	no	—
1286	C₄	—	4	1	no	—
1287	C₄	—	4	1	no	—
1288	C₄	—	4	1	no	—
1289	C₄	—	4	1	no	—
1290	C₄	—	4	1	no	—
1291	C₄	—	4	1	no	—
1292	C₄	—	4	1	no	—
1293	C₄	D₄×M₁₆	1	2	yes	—
1294	C₄	C₂³×M₁₆	1	1	yes	characteristic
1295	C₄	C₂×#568	1	1	yes	characteristic
1296	C₄	#3585	1	1	yes	characteristic
1297	C₄	#3586	1	1	yes	characteristic
1298	C₂	—	2	2	no	—
1299	C₂	—	4	1	no	—
1300	C₂	—	4	1	no	—
1301	C₂	—	4	2	no	—
1302	C₂	—	4	2	no	—
1303	C₂	—	8	1	no	—
1304	C₂	—	8	1	no	—
1305	C₂	C₂×D₄×M₁₆	1	1	yes	characteristic
1306	C₂	#60170	1	1	yes	characteristic
1307	C₂	#60182	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	C₂×#575	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ #2920 ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #60283	C₂	semidirect
2. #60263	C₂	semidirect
4. #18053	C₂	semidirect
5. #18052	C₂	semidirect
6. #18051	C₂	semidirect
7. #18050	C₂	semidirect
8. #18049	C₂	semidirect
9. #18048	C₂	semidirect
10. #18047	C₂	semidirect
11. #18046	C₂	semidirect
12. #17899	C₂	semidirect
13. #17898	C₂	semidirect
14. #17882	C₂	semidirect
15. #17882	C₂	semidirect
16. #17881	C₂	semidirect
17. #17881	C₂	semidirect
18. #17858	C₂	semidirect
19. #17857	C₂	semidirect
20. C₂×#1569	C₂	semidirect
21. #17452	C₂	semidirect
22. #17451	C₂	semidirect
23. #17334	C₂	semidirect
34. #2989	C₂²	semidirect
35. #2989	C₂²	semidirect
36. #2989	C₂²	semidirect
37. #2989	C₂²	semidirect
38. #2988	C₂²	semidirect
39. #2988	C₂²	semidirect
40. #2988	C₂²	semidirect
41. #2988	C₂²	semidirect
42. #2984	C₂²	semidirect
44. #2974	C₂²	semidirect
48. Q₈×M₁₆	C₂²	semidirect
74. D₄×M₁₆	C₂²	semidirect
87. #1594	C₂²	semidirect
88. #1593	C₂²	semidirect
89. #1592	C₂²	semidirect
90. #1592	C₂²	semidirect
91. #1591	C₂²	semidirect
92. #1590	C₂²	semidirect
93. #1590	C₂²	semidirect
94. #1589	C₂²	semidirect
95. #1588	C₂²	semidirect
96. #1588	C₂²	semidirect
97. #1587	C₂²	semidirect
98. #1587	C₂²	semidirect
99. #1586	C₂²	semidirect
100. #1586	C₂²	semidirect
101. #1585	C₂²	semidirect
102. #1585	C₂²	semidirect
103. #1584	C₂²	semidirect
104. #1584	C₂²	semidirect
105. #1583	C₂²	semidirect
106. #1583	C₂²	semidirect
107. #1582	C₂²	semidirect
108. #1582	C₂²	semidirect
109. #1581	C₂²	semidirect
110. #1581	C₂²	semidirect
111. #1580	C₂²	semidirect
112. #1579	C₂²	semidirect
113. SD₁₆⋊C₈	C₂²	semidirect
114. SD₁₆⋊C₈	C₂²	semidirect
115. C₈×Q₁₆	C₂²	semidirect
116. C₈×SD₁₆	C₂²	semidirect
117. C₈×SD₁₆	C₂²	semidirect
118. C₈×D₈	C₂²	semidirect
119. #1569	C₂²	semidirect
120. #1569	C₂²	semidirect
121. #1569	C₂²	semidirect
122. #1569	C₂²	semidirect
123. C₂×#335	C₂²	semidirect
124. C₂×#335	C₂²	semidirect
125. C₂×#334	C₂²	semidirect
126. C₂×#334	C₂²	semidirect
127. #1491	C₂²	semidirect
128. #1490	C₂²	semidirect
133. #1487	C₂²	semidirect
134. #1486	C₂²	semidirect
135. #1477	C₂²	semidirect
136. #1477	C₂²	semidirect
137. #1477	C₂²	semidirect
138. #1477	C₂²	semidirect
139. #1477	C₂²	semidirect
140. #1477	C₂²	semidirect
141. #1477	C₂²	semidirect
142. #1477	C₂²	semidirect
143. #1455	C₂²	semidirect
144. #1455	C₂²	semidirect
145. #1453	C₂²	semidirect
146. #1453	C₂²	semidirect
147. #1452	C₂²	semidirect
148. #1452	C₂²	semidirect
149. #1450	C₂²	semidirect
150. #1450	C₂²	semidirect
503. #135	M₁₆	semidirect
856. #41	C₂×M₁₆	semidirect
951. Q₁₆	C₂×M₁₆	semidirect
958. SD₁₆	C₂×M₁₆	semidirect
959. SD₁₆	C₂×M₁₆	semidirect
963. D₈	C₂×M₁₆	semidirect
998. C₂×C₈	C₂×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
#60283	2
#60263	2
C₄×#575	2
#18053	2
#18052	2
#18051	2
#18050	2
#18049	2
#18048	2
#18047	2
#18046	2
#17899	2
#17898	2
#17882	2
#17881	2
#17858	2
#17857	2
C₂×#1569	2
#17452	2
#17451	2
#17334	2