Subgroups — #6345777

Order 512.

1594 conjugacy classes of subgroups.

The subgroup lattice has 985 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#60695	C₂	1	1	yes	maximal, characteristic
2	#60319	C₂	1	2	yes	maximal, complemented
3	#18087	C₂	1	1	yes	maximal, characteristic, complemented
4	#18084	C₂	1	1	yes	maximal, characteristic, complemented
5	#18082	C₂	1	2	yes	maximal, complemented
6	#18076	C₂	1	2	yes	maximal, complemented
7	#18069	C₂	1	1	yes	maximal, characteristic, complemented
8	#18066	C₂	1	1	yes	maximal, characteristic, complemented
9	#18059	C₂	1	1	yes	maximal, characteristic, complemented
10	#18054	C₂	1	1	yes	maximal, characteristic, complemented
11	#18052	C₂	1	2	yes	maximal, complemented
12	#18046	C₂	1	2	yes	maximal, complemented
13	#18035	C₂	1	1	yes	maximal, characteristic, complemented
14	M₁₆×D₈	C₂	1	1	yes	maximal, characteristic, complemented
15	#17987	C₂	1	2	yes	maximal, complemented
16	#17983	C₂	1	2	yes	maximal, complemented
17	#17973	C₂	1	1	yes	maximal, characteristic, complemented
18	#17970	C₂	1	1	yes	maximal, characteristic, complemented
19	#17959	C₂	1	1	yes	maximal, characteristic, complemented
20	#17956	C₂	1	1	yes	maximal, characteristic, complemented
21	#17799	C₂	1	1	yes	maximal, characteristic, complemented
22	#17505	C₂	1	2	yes	maximal, complemented
23	#17335	C₂	1	1	yes	maximal, characteristic, complemented
24	#3460	C₂²	1	2	yes	—
25	#3179	C₄	1	2	yes	—
26	#3179	C₄	1	2	yes	—
27	#3176	C₄	1	1	yes	characteristic
28	#3176	C₄	1	1	yes	characteristic
29	#3175	C₄	1	1	yes	characteristic
30	#3175	C₄	1	1	yes	characteristic
31	#3171	C₂²	1	2	yes	—
32	#3171	C₂²	1	2	yes	—
33	#3169	C₂²	1	1	yes	characteristic
34	#3169	C₂²	1	1	yes	characteristic
35	#3168	C₂²	1	1	yes	characteristic
36	#3168	C₂²	1	1	yes	characteristic
37	#3164	C₄	1	1	yes	characteristic
38	#3155	C₄	1	1	yes	characteristic
39	#3136	C₄	1	2	yes	—
40	#3062	C₄	1	2	yes	—
41	#3061	C₄	1	1	yes	characteristic
42	#3058	C₄	1	1	yes	characteristic
43	#2995	—	2	2	no	—
44	#2994	C₂²	1	2	yes	complemented
45	#2993	C₂²	1	2	yes	complemented
46	#2991	C₂²	1	2	yes	—
47	#2989	C₂²	1	2	yes	—
48	#2981	—	2	2	no	—
49	#2981	C₂²	1	2	yes	complemented
50	#2979	C₂²	1	2	yes	complemented
51	#2978	—	2	2	no	—
52	#2976	—	2	2	no	—
53	#2974	C₂²	1	2	yes	—
54	#2970	C₂²	1	2	yes	—
55	#2969	C₂²	1	2	yes	complemented
56	#2968	—	2	2	no	—
57	#2966	C₂²	1	2	yes	complemented
58	#2965	C₂²	1	1	yes	characteristic
59	#2965	C₂²	1	1	yes	characteristic
60	C₄×AGL(1,ℤ/8)	C₂²	1	2	yes	—
61	C₄×#135	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₈	C₂²	1	1	yes	characteristic
63	#2935	C₂²	1	2	yes	complemented
64	D₄×M₁₆	C₂²	1	2	yes	—
65	#2933	—	2	2	no	—
66	#2932	—	2	2	no	—
67	#2931	C₂²	1	2	yes	complemented
68	#2930	—	2	2	no	—
69	C₄×#131	C₂²	1	1	yes	characteristic
70	#1594	C₂²	1	2	yes	complemented
71	#1592	C₂²	1	2	yes	complemented
72	#1591	C₂²	1	1	yes	characteristic, complemented
73	#1591	C₂²	1	1	yes	characteristic, complemented
74	#1590	C₂²	1	2	yes	complemented
75	#1589	C₂²	1	1	yes	characteristic
76	#1589	C₂²	1	1	yes	characteristic
77	#1589	C₂²	1	1	yes	characteristic
78	#1589	C₂²	1	1	yes	characteristic
79	#1589	C₂²	1	2	yes	complemented
80	#1589	C₂²	1	1	yes	characteristic, complemented
81	#1589	C₂²	1	1	yes	characteristic, complemented
82	#1588	C₂²	1	2	yes	complemented
83	#1588	C₂²	1	2	yes	complemented
84	#1588	C₂²	1	2	yes	complemented
85	#1586	C₂²	1	2	yes	—
86	#1586	C₂²	1	2	yes	—
87	#1586	C₂²	1	2	yes	complemented
88	#1586	C₂²	1	2	yes	complemented
89	#1585	C₂²	1	2	yes	complemented
90	#1583	C₂²	1	2	yes	complemented
91	#1582	C₂²	1	2	yes	complemented
92	#1582	C₂²	1	2	yes	complemented
93	#1582	C₂²	1	2	yes	complemented
94	#1581	C₂²	1	2	yes	—
95	#1581	C₂²	1	2	yes	—
96	#1581	C₂²	1	2	yes	complemented
97	#1581	C₂²	1	2	yes	complemented
98	#1580	C₂²	1	2	yes	complemented
99	SD₁₆⋊C₈	C₂²	1	2	yes	complemented
100	C₈×Q₁₆	C₂²	1	1	yes	characteristic, complemented
101	C₈×Q₁₆	C₂²	1	1	yes	characteristic, complemented
102	C₈×SD₁₆	C₂²	1	2	yes	complemented
103	C₈×D₈	C₂²	1	1	yes	characteristic
104	C₈×D₈	C₂²	1	1	yes	characteristic
105	C₈×D₈	C₂²	1	1	yes	characteristic
106	C₈×D₈	C₂²	1	1	yes	characteristic
107	C₈×D₈	C₂²	1	1	yes	characteristic, complemented
108	C₈×D₈	C₂²	1	2	yes	complemented
109	C₈×D₈	C₂²	1	1	yes	characteristic, complemented
110	#1569	C₂²	1	2	yes	—
111	#1569	C₂²	1	2	yes	complemented
112	#1568	C₂²	1	1	yes	characteristic
113	#1568	C₂²	1	1	yes	characteristic, complemented
114	#1567	C₂²	1	1	yes	characteristic
115	#1567	C₂²	1	1	yes	characteristic, complemented
116	#1565	C₂²	1	2	yes	complemented
117	#1564	C₂²	1	1	yes	characteristic, complemented
118	C₂×#335	C₂²	1	1	yes	characteristic, complemented
119	#1496	C₂²	1	2	yes	complemented
120	#1495	C₂²	1	2	yes	complemented
121	#1494	C₂²	1	2	yes	complemented
122	#1492	C₂²	1	2	yes	complemented
123	#1490	C₂²	1	2	yes	—
124	#1489	C₂²	1	2	yes	—
125	#1488	C₂²	1	2	yes	—
126	#1486	C₂²	1	2	yes	—
127	#1484	C₂²	1	2	yes	complemented
128	#1483	C₂²	1	2	yes	complemented
129	#1482	C₂²	1	2	yes	complemented
130	#1480	C₂²	1	2	yes	complemented
131	#1455	C₂²	1	1	yes	characteristic
132	#1455	C₂²	1	1	yes	characteristic, complemented
133	#1453	C₂²	1	1	yes	characteristic
134	#1453	C₂²	1	1	yes	characteristic, complemented
135	#1451	C₂²	1	1	yes	characteristic, complemented
136	#1451	C₂²	1	1	yes	characteristic, complemented
137	#1450	C₂²	1	1	yes	characteristic, complemented
138	C₈×M₁₆	C₂²	1	1	yes	characteristic
139	C₈×M₁₆	C₂²	1	1	yes	characteristic
140	C₈×M₁₆	C₂²	1	1	yes	characteristic, complemented
141	C₈×M₁₆	C₂²	1	1	yes	characteristic, complemented
142	C₂×C₈²	C₂²	1	1	yes	characteristic, complemented
143	C₂×AGL(1,ℤ/8)	C₂×C₄	1	2	yes	—
144	C₂×#135	C₂×C₄	1	1	yes	characteristic
145	C₂²×D₈	C₂×C₄	1	1	yes	characteristic
146	C₂×#131	—	2	2	no	—
147	C₂×#131	—	2	2	no	—
148	C₂×#131	C₂×C₄	1	1	yes	characteristic
149	C₂×#131	C₂×C₄	1	1	yes	characteristic
150	C₂²×M₁₆	—	2	2	no	—
151	#544	C₂×C₄	1	2	yes	—
152	#542	—	2	2	no	—
153	#542	C₂×C₄	1	2	yes	—
154	#542	C₂×C₄	1	2	yes	—
155	#540	—	2	2	no	—
156	#540	C₂×C₄	1	2	yes	—
157	#540	C₂×C₄	1	2	yes	—
158	#538	—	2	2	no	—
159	#538	—	2	2	no	—
160	#537	C₂×C₄	1	2	yes	—
161	#535	C₂×C₄	1	2	yes	—
162	#535	C₂×C₄	1	2	yes	—
163	#532	—	2	2	no	—
164	#532	C₂³	1	2	yes	—
165	#532	C₂³	1	2	yes	—
166	#529	—	2	2	no	—
167	#529	C₂³	1	2	yes	—
168	#529	C₂³	1	2	yes	—
169	#525	—	2	2	no	—
170	#525	—	2	2	no	—
171	C₄×#41	C₂³	1	2	yes	—
172	C₄×#41	C₂³	1	1	yes	characteristic
173	C₂×C₄×D₄	C₂³	1	2	yes	—
174	#501	C₂×C₄	1	2	yes	—
175	#501	C₂×C₄	1	2	yes	—
176	#500	C₂×C₄	1	1	yes	characteristic
177	#500	C₂×C₄	1	1	yes	characteristic
178	#499	C₂×C₄	1	1	yes	characteristic
179	#499	C₂×C₄	1	1	yes	characteristic
180	#496	C₂×C₄	1	2	yes	—
181	#496	C₂×C₄	1	2	yes	—
182	#495	C₂×C₄	1	1	yes	characteristic
183	#495	C₂×C₄	1	1	yes	characteristic
184	#493	C₂×C₄	1	1	yes	characteristic
185	#493	C₂×C₄	1	1	yes	characteristic
186	#490	C₂×C₄	1	2	yes	—
187	#490	C₂×C₄	1	2	yes	—
188	#489	C₂×C₄	1	2	yes	—
189	#489	C₂×C₄	1	2	yes	—
190	#488	C₂×C₄	1	2	yes	—
191	#488	C₂×C₄	1	2	yes	—
192	#486	C₂×C₄	1	2	yes	—
193	#486	C₂×C₄	1	2	yes	—
194	#469	C₂×C₄	1	2	yes	—
195	#469	C₂×C₄	1	2	yes	—
196	#469	C₂×C₄	1	2	yes	—
197	#469	C₂×C₄	1	2	yes	—
198	#468	C₂×C₄	1	2	yes	—
199	#468	C₂×C₄	1	2	yes	—
200	#468	C₂×C₄	1	2	yes	—
201	#468	C₂×C₄	1	2	yes	—
202	#467	C₂×C₄	1	1	yes	characteristic
203	#467	C₂×C₄	1	1	yes	characteristic
204	#466	C₂×C₄	1	1	yes	characteristic
205	#466	C₂×C₄	1	1	yes	characteristic
206	#466	C₂×C₄	1	1	yes	characteristic
207	#466	C₂×C₄	1	1	yes	characteristic
208	#466	C₂×C₄	1	1	yes	characteristic
209	#466	C₂×C₄	1	1	yes	characteristic
210	#466	C₂×C₄	1	2	yes	—
211	#466	C₂×C₄	1	2	yes	—
212	#465	C₂×C₄	1	2	yes	—
213	#465	C₂×C₄	1	2	yes	—
214	#446	—	2	2	no	—
215	#446	—	2	1	no	—
216	#446	D₄	1	1	yes	characteristic
217	#446	D₄	1	1	yes	characteristic
218	#446	C₂³	1	2	yes	—
219	#446	C₂³	1	2	yes	—
220	C₈×Q₈	C₂³	1	2	yes	—
221	C₈×Q₈	C₂³	1	2	yes	—
222	#442	C₂×C₄	1	2	yes	—
223	#442	C₂×C₄	1	2	yes	—
224	#440	C₂×C₄	1	2	yes	—
225	#440	C₂×C₄	1	2	yes	—
226	C₄×Q₁₆	C₂×C₄	1	1	yes	characteristic
227	C₄×Q₁₆	C₂³	1	1	yes	characteristic
228	C₄×SD₁₆	C₂×C₄	1	2	yes	—
229	C₄×SD₁₆	C₂³	1	2	yes	—
230	C₄×SD₁₆	C₂³	1	2	yes	—
231	C₄×SD₁₆	C₂³	1	2	yes	—
232	C₄×D₈	C₂×C₄	1	1	yes	characteristic
233	C₄×D₈	C₂×C₄	1	1	yes	characteristic
234	C₄×D₈	C₂×C₄	1	1	yes	characteristic
235	C₄×D₈	C₂×C₄	1	2	yes	—
236	C₄×D₈	C₂³	1	1	yes	characteristic
237	C₄×D₈	C₂³	1	1	yes	characteristic
238	C₄×D₈	C₂³	1	1	yes	characteristic
239	C₄×D₈	C₂³	1	2	yes	—
240	C₄×D₈	C₂³	1	2	yes	—
241	C₄×D₈	C₂³	1	2	yes	—
242	#436	—	2	2	no	—
243	#436	—	2	2	no	—
244	#436	—	2	1	no	—
245	#436	—	2	2	no	—
246	#436	—	2	2	no	—
247	#436	—	2	2	no	—
248	#436	—	2	2	no	—
249	#436	—	2	2	no	—
250	#436	D₄	1	1	yes	characteristic
251	#436	D₄	1	1	yes	characteristic
252	#436	C₂³	1	2	yes	—
253	#436	C₂³	1	2	yes	—
254	#436	C₂³	1	2	yes	—
255	#436	C₂³	1	2	yes	—
256	#436	C₂³	1	2	yes	—
257	#436	C₂³	1	2	yes	—
258	#435	—	2	2	no	—
259	#435	—	2	2	no	—
260	#435	—	2	2	no	—
261	#435	—	2	2	no	—
262	#435	—	2	2	no	—
263	#435	—	2	2	no	—
264	#435	—	2	1	no	—
265	#435	—	2	1	no	—
266	#435	—	2	2	no	—
267	#435	—	2	2	no	—
268	#435	—	2	2	no	—
269	#435	—	2	2	no	—
270	#435	—	2	2	no	—
271	#435	—	2	2	no	—
272	#435	—	2	2	no	—
273	#435	—	2	2	no	—
274	#435	—	2	2	no	—
275	#435	—	2	2	no	—
276	#435	D₄	1	1	yes	characteristic
277	#435	D₄	1	1	yes	characteristic
278	#435	D₄	1	1	yes	characteristic
279	#435	D₄	1	1	yes	characteristic
280	C₈×D₄	—	2	2	no	—
281	C₈×D₄	—	2	2	no	—
282	C₈×D₄	—	2	2	no	—
283	C₈×D₄	—	2	2	no	—
284	C₈×D₄	C₂³	1	2	yes	—
285	C₈×D₄	C₂³	1	2	yes	—
286	C₈×D₄	C₂³	1	2	yes	—
287	C₈×D₄	C₂³	1	2	yes	—
288	C₈×D₄	C₂³	1	2	yes	—
289	C₈×D₄	C₂³	1	2	yes	—
290	#433	—	2	2	no	—
291	#433	—	2	2	no	—
292	#433	—	2	2	no	—
293	#433	—	2	2	no	—
294	#432	—	2	2	no	—
295	#432	C₂³	1	2	yes	—
296	#432	C₂³	1	2	yes	—
297	#431	—	2	2	no	—
298	#431	C₂³	1	2	yes	—
299	#431	C₂³	1	1	yes	characteristic
300	#431	C₂³	1	1	yes	characteristic
301	#431	C₂³	1	1	yes	characteristic
302	#431	C₂³	1	1	yes	characteristic
303	#431	C₂³	1	1	yes	characteristic
304	#431	C₂³	1	1	yes	characteristic
305	#428	C₂×C₄	1	2	yes	—
306	#427	C₂×C₄	1	1	yes	characteristic
307	C₂×#107	C₂×C₄	1	1	yes	characteristic
308	#424	—	2	2	no	—
309	#424	—	2	2	no	—
310	#423	—	2	2	no	—
311	#423	C₂³	1	2	yes	—
312	#423	C₂³	1	2	yes	—
313	C₂×C₄⋊C₈	C₂³	1	2	yes	—
314	#418	C₂×C₄	1	2	yes	—
315	#417	C₂×C₄	1	2	yes	—
316	#416	C₂×C₄	1	2	yes	—
317	C₂×#102	C₂×C₄	1	2	yes	—
318	#408	—	2	2	no	—
319	#408	—	2	2	no	—
320	#408	—	2	2	no	—
321	#408	—	2	2	no	—
322	#408	—	2	2	no	—
323	#408	—	2	2	no	—
324	#407	—	2	2	no	—
325	#407	—	2	2	no	—
326	C₂×C₂²⋊C₈	—	2	2	no	—
327	#405	—	2	2	no	—
328	#405	—	2	2	no	—
329	#405	C₂×C₄	1	1	yes	characteristic
330	#405	C₂×C₄	1	1	yes	characteristic
331	#405	C₂×C₄	1	1	yes	characteristic
332	#405	C₂×C₄	1	1	yes	characteristic
333	#405	C₂×C₄	1	1	yes	characteristic
334	#405	C₂×C₄	1	1	yes	characteristic
335	C₄×M₁₆	C₂³	1	1	yes	characteristic
336	C₄×M₁₆	C₂³	1	1	yes	characteristic
337	C₄×M₁₆	C₂³	1	1	yes	characteristic
338	C₄×M₁₆	C₂³	1	1	yes	characteristic
339	C₄×M₁₆	C₂³	1	1	yes	characteristic
340	C₄×M₁₆	C₂³	1	1	yes	characteristic
341	C₄×M₁₆	C₂³	1	1	yes	characteristic
342	C₂×#97	—	2	2	no	—
343	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
344	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
345	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
346	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
347	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
348	#335	C₂³	1	1	yes	characteristic
349	#335	C₂³	1	1	yes	characteristic
350	#335	C₂³	1	2	yes	—
351	#335	C₂³	1	1	yes	characteristic
352	#335	C₂³	1	1	yes	characteristic
353	#335	C₂³	1	2	yes	—
354	#335	C₂³	1	2	yes	—
355	#334	C₂³	1	2	yes	—
356	#334	C₂³	1	2	yes	—
357	#334	C₂³	1	2	yes	—
358	Q₈⋊C₈	C₂³	1	2	yes	—
359	Q₈⋊C₈	C₂³	1	2	yes	—
360	Q₈⋊C₈	C₂³	1	2	yes	—
361	Q₈⋊C₈	C₂³	1	2	yes	—
362	D₄⋊C₈	C₂³	1	2	yes	—
363	D₄⋊C₈	C₂³	1	2	yes	—
364	D₄⋊C₈	C₂³	1	2	yes	—
365	D₄⋊C₈	C₂³	1	2	yes	—
366	D₄⋊C₈	C₂³	1	2	yes	—
367	D₄⋊C₈	C₂³	1	2	yes	—
368	D₄⋊C₈	C₂³	1	2	yes	—
369	D₄⋊C₈	C₂³	1	2	yes	—
370	D₄⋊C₈	C₂³	1	2	yes	—
371	D₄⋊C₈	C₂³	1	2	yes	—
372	D₄⋊C₈	C₂³	1	2	yes	—
373	D₄⋊C₈	C₂³	1	2	yes	—
374	#322	C₂³	1	1	yes	characteristic
375	#322	C₂³	1	1	yes	characteristic
376	#322	C₂³	1	1	yes	characteristic
377	#322	C₂³	1	1	yes	characteristic
378	#322	C₂³	1	1	yes	characteristic
379	#322	C₂³	1	1	yes	characteristic
380	#322	C₂³	1	1	yes	characteristic
381	#322	C₂³	1	1	yes	characteristic
382	#322	C₂³	1	1	yes	characteristic
383	#322	C₂³	1	1	yes	characteristic
384	C₈²	C₂³	1	1	yes	characteristic
385	C₈²	C₂³	1	1	yes	characteristic
386	C₈²	C₂³	1	1	yes	characteristic
387	C₈²	C₂³	1	1	yes	characteristic
388	C₈²	C₂³	1	1	yes	characteristic
389	C₈²	C₂³	1	1	yes	characteristic
390	C₂×#41	—	2	2	no	—
391	C₂×#41	—	2	2	no	—
392	C₂×#41	C₂²×C₄	1	2	yes	—
393	C₂×#41	C₂²×C₄	1	1	yes	characteristic
394	C₂²×D₄	C₂²×C₄	1	2	yes	—
395	C₂³×C₄	—	2	2	no	—
396	AGL(1,ℤ/8)	—	4	4	no	—
397	#135	—	4	2	no	—
398	C₂×Q₁₆	C₂²×C₄	1	1	yes	characteristic
399	C₂×SD₁₆	C₂²×C₄	1	2	yes	—
400	C₂×SD₁₆	C₂²×C₄	1	2	yes	—
401	C₂×SD₁₆	C₂²×C₄	1	2	yes	—
402	C₂×D₈	—	4	2	no	—
403	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
404	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
405	C₂×D₈	C₂²×C₄	1	1	yes	characteristic
406	C₂×D₈	C₂²×C₄	1	2	yes	—
407	C₂×D₈	C₂²×C₄	1	2	yes	—
408	C₂×D₈	C₂²×C₄	1	2	yes	—
409	#131	—	4	2	no	—
410	#131	—	4	2	no	—
411	#131	—	8	4	no	—
412	#131	—	8	4	no	—
413	C₂×M₁₆	—	2	1	no	—
414	C₂×M₁₆	—	2	1	no	—
415	C₂×M₁₆	—	2	2	no	—
416	C₂×M₁₆	—	2	2	no	—
417	C₂×M₁₆	—	2	2	no	—
418	C₂×M₁₆	—	2	2	no	—
419	C₂×M₁₆	—	2	2	no	—
420	C₂×M₁₆	—	2	2	no	—
421	C₂×M₁₆	—	2	2	no	—
422	C₂×M₁₆	—	2	2	no	—
423	C₂×M₁₆	—	8	4	no	—
424	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
425	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
426	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
427	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
428	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
429	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
430	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
431	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
432	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
433	C₂×M₁₆	C₂×D₄	1	1	yes	characteristic
434	C₂²×C₈	—	2	1	no	—
435	C₂²×C₈	—	2	2	no	—
436	C₂²×C₈	—	2	2	no	—
437	C₂²×C₈	—	2	2	no	—
438	C₂²×C₈	—	2	2	no	—
439	C₂²×C₈	—	2	2	no	—
440	C₂²×C₈	—	2	2	no	—
441	C₂²×C₈	—	2	2	no	—
442	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
443	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
444	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
445	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
446	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
447	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
448	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
449	C₂²×C₈	C₂×D₄	1	1	yes	characteristic
450	C₄⋊Q₈	—	2	2	no	—
451	C₄⋊Q₈	C₂²×C₄	1	2	yes	—
452	C₄⋊Q₈	C₂²×C₄	1	2	yes	—
453	#127	—	2	2	no	—
454	#127	C₂²×C₄	1	2	yes	—
455	#127	C₂²×C₄	1	2	yes	—
456	#126	—	2	2	no	—
457	#126	—	2	2	no	—
458	#126	—	2	2	no	—
459	#126	—	2	2	no	—
460	#125	—	2	2	no	—
461	#125	C₂²×C₄	1	2	yes	—
462	#125	C₂²×C₄	1	2	yes	—
463	#124	—	2	2	no	—
464	#124	—	2	2	no	—
465	#124	—	2	2	no	—
466	#124	—	2	2	no	—
467	#124	—	2	2	no	—
468	#124	C₂²×C₄	1	2	yes	—
469	#124	C₂²×C₄	1	2	yes	—
470	#123	—	2	2	no	—
471	#123	—	2	2	no	—
472	#123	—	2	2	no	—
473	#123	—	2	2	no	—
474	#123	—	2	2	no	—
475	#123	—	2	2	no	—
476	#123	—	2	2	no	—
477	#123	—	2	2	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	—	2	2	no	—
481	C₂²⋊Q₈	—	2	2	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
484	C₂²⋊Q₈	C₂²×C₄	1	2	yes	—
485	#121	—	2	2	no	—
486	#121	—	2	2	no	—
487	#121	—	2	2	no	—
488	#121	—	2	2	no	—
489	#121	—	2	2	no	—
490	#121	—	2	2	no	—
491	#121	—	2	2	no	—
492	#121	—	2	2	no	—
493	#121	—	2	2	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	C₂²×C₄	1	2	yes	—
497	#121	C₂²×C₄	1	2	yes	—
498	#121	C₂²×C₄	1	2	yes	—
499	#121	C₂²×C₄	1	2	yes	—
500	#121	C₂²×C₄	1	2	yes	—
501	#121	C₂²×C₄	1	2	yes	—
502	#120	—	2	2	no	—
503	#120	—	2	2	no	—
504	#120	—	2	2	no	—
505	#120	—	2	2	no	—
506	C₄×Q₈	C₂²×C₄	1	2	yes	—
507	C₄×Q₈	C₂×D₄	1	1	yes	characteristic
508	C₄×Q₈	#41	1	1	yes	characteristic
509	C₄×Q₈	C₂⁴	1	2	yes	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	C₂²×C₄	1	2	yes	—
519	C₄×D₄	C₂²×C₄	1	2	yes	—
520	C₄×D₄	C₂²×C₄	1	2	yes	—
521	C₄×D₄	C₂×D₄	1	1	yes	characteristic
522	C₄×D₄	C₂×D₄	1	1	yes	characteristic
523	C₄×D₄	C₂×D₄	1	1	yes	characteristic
524	C₄×D₄	#41	1	1	yes	characteristic
525	C₄×D₄	#41	1	1	yes	characteristic
526	C₄×D₄	#41	1	1	yes	characteristic
527	C₄×D₄	C₂⁴	1	2	yes	—
528	C₄×D₄	C₂⁴	1	2	yes	—
529	C₄×D₄	C₂⁴	1	2	yes	—
530	#117	—	2	2	no	—
531	#117	—	2	2	no	—
532	#117	—	2	2	no	—
533	#117	C₂²×C₄	1	2	yes	—
534	#117	C₂²×C₄	1	1	yes	characteristic
535	#117	C₂²×C₄	1	1	yes	characteristic
536	#117	C₂²×C₄	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂²×C₄	1	2	yes	—
538	C₂×C₂²⋊C₄	—	2	2	no	—
539	C₂×C₄²	—	2	2	no	—
540	C₂×C₄²	C₂⁴	1	1	yes	characteristic
541	C₂×C₄²	C₂⁴	1	1	yes	characteristic
542	C₂×C₄²	C₂⁴	1	1	yes	characteristic
543	#107	C₂²×C₄	1	1	yes	characteristic
544	#107	C₂²×C₄	1	1	yes	characteristic
545	#107	C₂²×C₄	1	2	yes	—
546	#107	C₂²×C₄	1	1	yes	characteristic
547	#107	C₂²×C₄	1	1	yes	characteristic
548	#107	C₂²×C₄	1	2	yes	—
549	#107	C₂²×C₄	1	2	yes	—
550	#106	C₂²×C₄	1	2	yes	—
551	#106	C₂²×C₄	1	2	yes	—
552	#106	C₂²×C₄	1	2	yes	—
553	C₄⋊C₈	—	2	2	no	—
554	C₄⋊C₈	—	2	2	no	—
555	C₄⋊C₈	—	2	2	no	—
556	C₄⋊C₈	—	2	2	no	—
557	C₄⋊C₈	—	2	2	no	—
558	C₄⋊C₈	—	2	2	no	—
559	C₄⋊C₈	—	2	2	no	—
560	C₄⋊C₈	—	2	1	no	—
561	C₄⋊C₈	—	2	1	no	—
562	C₄⋊C₈	—	2	1	no	—
563	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
564	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
565	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
566	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
567	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
568	C₄⋊C₈	C₂×D₄	1	1	yes	characteristic
569	C₄⋊C₈	C₂⁴	1	2	yes	—
570	C₄⋊C₈	C₂⁴	1	2	yes	—
571	C₄⋊C₈	C₂⁴	1	2	yes	—
572	C₄⋊C₈	C₂⁴	1	2	yes	—
573	#103	C₂²×C₄	1	2	yes	—
574	#103	C₂²×C₄	1	2	yes	—
575	#103	C₂²×C₄	1	2	yes	—
576	#103	C₂²×C₄	1	2	yes	—
577	#102	C₂²×C₄	1	2	yes	—
578	#102	C₂²×C₄	1	2	yes	—
579	#102	C₂²×C₄	1	2	yes	—
580	#102	C₂²×C₄	1	2	yes	—
581	#102	C₂²×C₄	1	2	yes	—
582	#102	C₂²×C₄	1	2	yes	—
583	#102	C₂²×C₄	1	2	yes	—
584	#102	C₂²×C₄	1	2	yes	—
585	#102	C₂²×C₄	1	2	yes	—
586	#102	C₂²×C₄	1	2	yes	—
587	#102	C₂²×C₄	1	2	yes	—
588	#102	C₂²×C₄	1	2	yes	—
589	C₂²⋊C₈	—	2	2	no	—
590	C₂²⋊C₈	—	2	2	no	—
591	C₂²⋊C₈	—	2	2	no	—
592	C₂²⋊C₈	—	2	1	no	—
593	C₂²⋊C₈	—	2	1	no	—
594	C₂²⋊C₈	—	2	1	no	—
595	C₂²⋊C₈	—	2	2	no	—
596	C₂²⋊C₈	—	2	2	no	—
597	C₂²⋊C₈	—	2	2	no	—
598	C₂²⋊C₈	—	2	2	no	—
599	C₂²⋊C₈	—	2	2	no	—
600	C₂²⋊C₈	—	2	2	no	—
601	C₂²⋊C₈	—	2	2	no	—
602	C₂²⋊C₈	—	2	2	no	—
603	C₂²⋊C₈	—	2	2	no	—
604	C₂²⋊C₈	—	2	2	no	—
605	C₂²⋊C₈	—	2	2	no	—
606	C₂²⋊C₈	—	2	2	no	—
607	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
608	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
609	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
610	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
611	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
612	C₂²⋊C₈	C₂×D₄	1	1	yes	characteristic
613	#97	—	2	2	no	—
614	#97	—	2	2	no	—
615	#97	—	2	2	no	—
616	#97	—	2	2	no	—
617	#97	—	2	1	no	—
618	#97	—	2	1	no	—
619	#97	C₂²×C₄	1	1	yes	characteristic
620	#97	C₂²×C₄	1	1	yes	characteristic
621	#97	C₂²×C₄	1	1	yes	characteristic
622	#97	C₂²×C₄	1	1	yes	characteristic
623	#97	C₂²×C₄	1	1	yes	characteristic
624	#97	C₂²×C₄	1	1	yes	characteristic
625	#97	C₂×D₄	1	1	yes	characteristic
626	#97	C₂×D₄	1	1	yes	characteristic
627	#97	C₂×D₄	1	1	yes	characteristic
628	#97	C₂×D₄	1	1	yes	characteristic
629	C₄×C₈	—	2	2	no	—
630	C₄×C₈	—	2	2	no	—
631	C₄×C₈	—	2	2	no	—
632	C₄×C₈	—	2	1	no	—
633	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
634	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
635	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
636	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
637	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
638	C₄×C₈	C₂²×C₄	1	1	yes	characteristic
639	C₄×C₈	C₂×D₄	1	1	yes	characteristic
640	C₄×C₈	C₂×D₄	1	1	yes	characteristic
641	C₄×C₈	C₂⁴	1	1	yes	characteristic
642	C₄×C₈	C₂⁴	1	1	yes	characteristic
643	C₄×C₈	C₂⁴	1	1	yes	characteristic
644	C₄×C₈	C₂⁴	1	1	yes	characteristic
645	C₄×C₈	C₂⁴	1	1	yes	characteristic
646	C₄×C₈	C₂⁴	1	1	yes	characteristic
647	C₄×C₈	C₂⁴	1	1	yes	characteristic
648	C₄×C₈	C₂⁴	1	1	yes	characteristic
649	C₄×C₈	C₂⁴	1	1	yes	characteristic
650	C₄×C₈	C₂⁴	1	1	yes	characteristic
651	C₄×C₈	C₂⁴	1	1	yes	characteristic
652	C₄×C₈	C₂⁴	1	1	yes	characteristic
653	C₂⁴	—	2	2	no	—
654	#41	—	4	1	no	—
655	#41	—	4	1	no	—
656	#41	—	4	2	no	—
657	#41	—	4	2	no	—
658	#41	—	8	2	no	—
659	#41	—	8	2	no	—
660	#41	—	8	2	no	—
661	#41	—	8	2	no	—
662	C₂×Q₈	—	2	2	no	—
663	C₂×Q₈	—	2	2	no	—
664	C₂×Q₈	C₄×D₄	1	1	yes	characteristic
665	C₂×Q₈	C₂³×C₄	1	2	yes	—
666	C₂×D₄	—	2	2	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	4	2	no	—
679	C₂×D₄	—	4	2	no	—
680	C₂×D₄	C₄×D₄	1	1	yes	characteristic
681	C₂×D₄	C₄×D₄	1	1	yes	characteristic
682	C₂×D₄	C₄×D₄	1	1	yes	characteristic
683	C₂×D₄	C₂³×C₄	1	2	yes	—
684	C₂×D₄	C₂³×C₄	1	2	yes	—
685	C₂×D₄	C₂³×C₄	1	2	yes	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	8	2	no	—
695	C₂²×C₄	—	8	2	no	—
696	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
697	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
698	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
699	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
700	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
701	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
702	C₂²×C₄	C₂×#41	1	1	yes	characteristic
703	C₂²×C₄	C₂×#41	1	1	yes	characteristic
704	C₂²×C₄	C₂×#41	1	1	yes	characteristic
705	Q₁₆	—	2	2	no	—
706	SD₁₆	—	2	4	no	—
707	SD₁₆	—	4	2	no	—
708	SD₁₆	—	4	2	no	—
709	D₈	—	2	2	no	—
710	D₈	—	2	2	no	—
711	D₈	—	2	2	no	—
712	D₈	—	2	4	no	—
713	D₈	—	4	2	no	—
714	D₈	—	4	2	no	—
715	M₁₆	—	2	2	no	—
716	M₁₆	—	2	2	no	—
717	M₁₆	—	2	2	no	—
718	M₁₆	—	2	2	no	—
719	M₁₆	—	4	1	no	—
720	M₁₆	—	4	1	no	—
721	M₁₆	—	4	1	no	—
722	M₁₆	—	4	1	no	—
723	M₁₆	—	4	1	no	—
724	M₁₆	—	4	1	no	—
725	M₁₆	—	4	2	no	—
726	M₁₆	—	4	2	no	—
727	M₁₆	—	4	4	no	—
728	M₁₆	—	8	2	no	—
729	M₁₆	—	8	2	no	—
730	M₁₆	—	8	2	no	—
731	M₁₆	—	8	2	no	—
732	M₁₆	—	8	2	no	—
733	M₁₆	—	8	2	no	—
734	M₁₆	—	8	2	no	—
735	C₂×C₈	—	2	1	no	—
736	C₂×C₈	—	2	2	no	—
737	C₂×C₈	—	2	2	no	—
738	C₂×C₈	—	2	2	no	—
739	C₂×C₈	—	2	2	no	—
740	C₂×C₈	—	2	2	no	—
741	C₂×C₈	—	2	2	no	—
742	C₂×C₈	—	2	2	no	—
743	C₂×C₈	—	2	2	no	—
744	C₂×C₈	—	2	2	no	—
745	C₂×C₈	—	2	1	no	—
746	C₂×C₈	—	2	1	no	—
747	C₂×C₈	—	2	1	no	—
748	C₂×C₈	—	4	1	no	—
749	C₂×C₈	—	4	1	no	—
750	C₂×C₈	—	4	1	no	—
751	C₂×C₈	—	4	2	no	—
752	C₂×C₈	—	4	4	no	—
753	C₂×C₈	—	4	4	no	—
754	C₂×C₈	—	8	2	no	—
755	C₂×C₈	—	8	2	no	—
756	C₂×C₈	—	8	2	no	—
757	C₂×C₈	—	8	2	no	—
758	C₂×C₈	—	8	2	no	—
759	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
760	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
761	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
762	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
763	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
764	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
765	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
766	C₂×C₈	C₂³×C₄	1	1	yes	characteristic
767	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
768	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
769	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
770	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
771	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
772	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
773	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
774	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
787	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
788	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
789	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
790	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
791	C₄⋊C₄	C₄×D₄	1	1	yes	characteristic
792	C₄⋊C₄	C₂³×C₄	1	2	yes	—
793	C₄⋊C₄	C₂³×C₄	1	2	yes	—
794	C₄⋊C₄	C₂³×C₄	1	2	yes	—
795	C₄⋊C₄	C₂³×C₄	1	2	yes	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
816	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
817	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
818	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
819	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
820	C₂²⋊C₄	C₄×D₄	1	1	yes	characteristic
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	C₂³×C₄	1	1	yes	characteristic
825	C₄²	C₂³×C₄	1	1	yes	characteristic
826	C₄²	C₂³×C₄	1	1	yes	characteristic
827	C₄²	C₂²×D₄	1	1	yes	characteristic
828	C₄²	C₂²×D₄	1	1	yes	characteristic
829	C₄²	C₂²×D₄	1	1	yes	characteristic
830	C₄²	C₂×#41	1	1	yes	characteristic
831	C₄²	C₂×#41	1	1	yes	characteristic
832	C₄²	C₂×#41	1	1	yes	characteristic
833	C₄²	C₂⁵	1	1	yes	characteristic
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	8	2	no	—
838	C₂³	—	8	2	no	—
839	C₂³	—	8	2	no	—
840	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
841	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
842	C₂³	C₂×C₄×D₄	1	1	yes	characteristic
843	Q₈	—	2	2	no	—
844	Q₈	—	2	2	no	—
845	Q₈	—	4	1	no	—
846	Q₈	—	8	2	no	—
847	Q₈	—	8	2	no	—
848	D₄	—	2	2	no	—
849	D₄	—	2	2	no	—
850	D₄	—	2	2	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	2	no	—
853	D₄	—	2	2	no	—
854	D₄	—	4	1	no	—
855	D₄	—	4	1	no	—
856	D₄	—	4	1	no	—
857	D₄	—	8	2	no	—
858	D₄	—	8	2	no	—
859	D₄	—	8	2	no	—
860	D₄	—	8	2	no	—
861	D₄	—	8	2	no	—
862	D₄	—	8	2	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	2	no	—
865	D₄	—	8	2	no	—
866	D₄	—	8	2	no	—
867	D₄	—	8	2	no	—
868	D₄	—	8	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	4	1	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	4	2	no	—
891	C₂×C₄	—	4	2	no	—
892	C₂×C₄	—	4	2	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	4	2	no	—
895	C₂×C₄	—	8	2	no	—
896	C₂×C₄	—	8	2	no	—
897	C₂×C₄	—	8	2	no	—
898	C₂×C₄	—	8	2	no	—
899	C₂×C₄	—	8	2	no	—
900	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
901	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
902	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
903	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
904	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
905	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
906	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
907	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
908	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
909	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
910	C₂×C₄	C₂³×D₄	1	1	yes	characteristic
911	C₂×C₄	C₂²×#41	1	1	yes	characteristic
912	C₈	—	2	2	no	—
913	C₈	—	2	1	no	—
914	C₈	—	2	1	no	—
915	C₈	—	2	1	no	—
916	C₈	—	2	1	no	—
917	C₈	—	2	1	no	—
918	C₈	—	2	1	no	—
919	C₈	—	2	1	no	—
920	C₈	—	2	1	no	—
921	C₈	—	2	1	no	—
922	C₈	—	2	1	no	—
923	C₈	—	2	1	no	—
924	C₈	—	2	1	no	—
925	C₈	—	2	1	no	—
926	C₈	—	4	1	no	—
927	C₈	—	4	1	no	—
928	C₈	—	4	1	no	—
929	C₈	—	4	2	no	—
930	C₈	—	4	2	no	—
931	C₈	—	4	2	no	—
932	C₈	—	4	2	no	—
933	C₈	#568	1	2	yes	—
934	C₈	#568	1	2	yes	—
935	C₈	#576	1	2	yes	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	16	4	no	—
955	C₂²	C₂²×C₄×D₄	1	1	yes	characteristic
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	1	no	—
960	C₄	—	2	1	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	C₂×#568	1	1	yes	characteristic
972	C₄	C₂×#568	1	1	yes	characteristic
973	C₄	C₂×#576	1	1	yes	characteristic
974	C₄	#3584	1	1	yes	characteristic
975	C₂	—	4	1	no	—
976	C₂	—	4	1	no	—
977	C₂	—	4	1	no	—
978	C₂	—	8	2	no	—
979	C₂	—	8	2	no	—
980	C₂	—	8	2	no	—
981	C₂	#60144	1	1	yes	characteristic
982	C₂	C₄×#576	1	1	yes	characteristic
983	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	#60695	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. #60319	C₂	semidirect
3. #18087	C₂	semidirect
4. #18084	C₂	semidirect
5. #18082	C₂	semidirect
6. #18076	C₂	semidirect
7. #18069	C₂	semidirect
8. #18066	C₂	semidirect
9. #18059	C₂	semidirect
10. #18054	C₂	semidirect
11. #18052	C₂	semidirect
12. #18046	C₂	semidirect
13. #18035	C₂	semidirect
14. M₁₆×D₈	C₂	semidirect
15. #17987	C₂	semidirect
16. #17983	C₂	semidirect
17. #17973	C₂	semidirect
18. #17970	C₂	semidirect
19. #17959	C₂	semidirect
20. #17956	C₂	semidirect
21. #17799	C₂	semidirect
22. #17505	C₂	semidirect
23. #17335	C₂	semidirect
44. #2994	C₂²	semidirect
45. #2993	C₂²	semidirect
49. #2981	C₂²	semidirect
50. #2979	C₂²	semidirect
55. #2969	C₂²	semidirect
57. #2966	C₂²	semidirect
63. #2935	C₂²	semidirect
67. #2931	C₂²	semidirect
70. #1594	C₂²	semidirect
71. #1592	C₂²	semidirect
72. #1591	C₂²	semidirect
73. #1591	C₂²	semidirect
74. #1590	C₂²	semidirect
79. #1589	C₂²	semidirect
80. #1589	C₂²	semidirect
81. #1589	C₂²	semidirect
82. #1588	C₂²	semidirect
83. #1588	C₂²	semidirect
84. #1588	C₂²	semidirect
87. #1586	C₂²	semidirect
88. #1586	C₂²	semidirect
89. #1585	C₂²	semidirect
90. #1583	C₂²	semidirect
91. #1582	C₂²	semidirect
92. #1582	C₂²	semidirect
93. #1582	C₂²	semidirect
96. #1581	C₂²	semidirect
97. #1581	C₂²	semidirect
98. #1580	C₂²	semidirect
99. SD₁₆⋊C₈	C₂²	semidirect
100. C₈×Q₁₆	C₂²	semidirect
101. C₈×Q₁₆	C₂²	semidirect
102. C₈×SD₁₆	C₂²	semidirect
107. C₈×D₈	C₂²	semidirect
108. C₈×D₈	C₂²	semidirect
109. C₈×D₈	C₂²	semidirect
111. #1569	C₂²	semidirect
113. #1568	C₂²	semidirect
115. #1567	C₂²	semidirect
116. #1565	C₂²	semidirect
117. #1564	C₂²	semidirect
118. C₂×#335	C₂²	semidirect
119. #1496	C₂²	semidirect
120. #1495	C₂²	semidirect
121. #1494	C₂²	semidirect
122. #1492	C₂²	semidirect
127. #1484	C₂²	semidirect
128. #1483	C₂²	semidirect
129. #1482	C₂²	semidirect
130. #1480	C₂²	semidirect
132. #1455	C₂²	semidirect
134. #1453	C₂²	semidirect
135. #1451	C₂²	semidirect
136. #1451	C₂²	semidirect
137. #1450	C₂²	semidirect
140. C₈×M₁₆	C₂²	semidirect
141. C₈×M₁₆	C₂²	semidirect
142. C₂×C₈²	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#60695	2
#60319	2
#18087	2
#18084	2
#18082	2
#18076	2
#18069	2
#18066	2
#18059	2
#18054	2
#18052	2
#18046	2
#18035	2
M₁₆×D₈	2
#17987	2
#17983	2
#17973	2
#17970	2
#17959	2
#17956	2
#17799	2
#17505	2
#17335	2