Subgroups — #7536151

Order 512.

1608 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#45149	C₂	1	1	yes	maximal, characteristic
2	#35749	C₂	1	1	yes	maximal, characteristic
3	#32653	C₂	1	1	yes	maximal, characteristic, complemented
4	#32619	C₂	1	1	yes	maximal, characteristic, complemented
5	#32168	C₂	1	1	yes	maximal, characteristic, complemented
6	#30744	C₂	1	1	yes	maximal, characteristic, complemented
7	#28887	C₂	1	1	yes	maximal, characteristic, complemented
8	#28588	C₂	1	1	yes	maximal, characteristic
9	#28355	C₂	1	1	yes	maximal, characteristic
10	#28322	C₂	1	1	yes	maximal, characteristic
11	#27501	C₂	1	1	yes	maximal, characteristic, complemented
12	#27209	C₂	1	1	yes	maximal, characteristic, complemented
13	#27205	C₂	1	1	yes	maximal, characteristic, complemented
14	#27067	C₂	1	1	yes	maximal, characteristic, complemented
15	#26607	C₂	1	1	yes	maximal, characteristic, complemented
16	#26590	C₂	1	1	yes	maximal, characteristic, complemented
17	#26255	C₂	1	1	yes	maximal, characteristic, complemented
18	#25780	C₂	1	1	yes	maximal, characteristic
19	#25634	C₂	1	1	yes	maximal, characteristic, complemented
20	#25215	C₂	1	1	yes	maximal, characteristic
21	#25095	C₂	1	1	yes	maximal, characteristic
22	#24496	C₂	1	1	yes	maximal, characteristic
23	#24360	C₂	1	1	yes	maximal, characteristic
24	#24203	C₂	1	1	yes	maximal, characteristic, complemented
25	#23244	C₂	1	1	yes	maximal, characteristic
26	#23187	C₂	1	1	yes	maximal, characteristic, complemented
27	#23096	C₂	1	1	yes	maximal, characteristic, complemented
28	#22919	C₂	1	1	yes	maximal, characteristic
29	#22869	C₂	1	1	yes	maximal, characteristic
30	#21463	C₂	1	1	yes	maximal, characteristic
31	#20935	C₂	1	1	yes	maximal, characteristic
32	C₂³×Q₁₆	C₂²	1	1	yes	characteristic
33	C₂×#557	C₂²	1	1	yes	characteristic
34	C₂×#519	C₂²	1	1	yes	characteristic
35	C₂×#494	C₂²	1	1	yes	characteristic
36	C₂×#494	C₂²	1	1	yes	characteristic
37	C₂×#485	C₂²	1	1	yes	characteristic
38	C₂×#485	C₂²	1	1	yes	characteristic
39	C₂×#470	C₂²	1	1	yes	characteristic
40	C₂×#467	C₂²	1	1	yes	characteristic
41	C₂×#462	C₂²	1	1	yes	characteristic
42	C₂×#462	C₂²	1	1	yes	characteristic
43	C₂×#462	C₂²	1	1	yes	characteristic
44	C₂×#451	C₂²	1	1	yes	characteristic
45	C₂×#451	C₂²	1	1	yes	characteristic
46	C₂×#451	C₂²	1	1	yes	characteristic
47	C₂×#441	C₂²	1	1	yes	characteristic
48	C₂×#441	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₁₆	C₂²	1	1	yes	characteristic
50	C₂×#419	C₂²	1	1	yes	characteristic
51	C₂×#419	C₂²	1	1	yes	characteristic
52	#2762	—	2	1	no	—
53	#2758	—	2	1	no	—
54	#2745	—	2	1	no	—
55	#2739	—	2	1	no	—
56	#2634	—	2	1	no	—
57	#2621	C₂²	1	1	yes	characteristic
58	#2611	—	2	1	no	—
59	#2599	—	2	1	no	—
60	#2586	—	2	1	no	—
61	#2581	C₂²	1	1	yes	characteristic
62	#2581	C₂²	1	1	yes	characteristic
63	#2575	—	2	1	no	—
64	#2568	C₂²	1	1	yes	characteristic
65	#2546	C₂²	1	1	yes	characteristic
66	#2520	—	2	1	no	—
67	#2515	—	2	1	no	—
68	#2514	C₂²	1	1	yes	characteristic
69	#2511	C₂²	1	1	yes	characteristic
70	#2499	C₂²	1	1	yes	characteristic
71	#2475	—	2	1	no	—
72	#2475	—	2	1	no	—
73	#2462	—	2	1	no	—
74	#2462	—	2	1	no	—
75	#2446	C₂²	1	1	yes	characteristic
76	#2446	C₂²	1	1	yes	characteristic
77	#2446	C₂²	1	1	yes	characteristic
78	#2446	C₂²	1	1	yes	characteristic
79	#2434	C₂²	1	1	yes	characteristic
80	#2434	C₂²	1	1	yes	characteristic
81	#2434	C₂²	1	1	yes	characteristic
82	#2399	—	2	1	no	—
83	#2396	C₂²	1	1	yes	characteristic
84	#2365	C₂²	1	1	yes	characteristic
85	#2365	C₂²	1	1	yes	characteristic
86	#2365	C₂²	1	1	yes	characteristic
87	#2362	C₂²	1	1	yes	characteristic
88	#2362	C₂²	1	1	yes	characteristic
89	#2356	C₂²	1	1	yes	characteristic
90	#2355	C₂²	1	1	yes	characteristic
91	#2347	C₂²	1	1	yes	characteristic
92	Q₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
93	#2323	C₂²	1	1	yes	characteristic
94	#2310	C₂²	1	1	yes	characteristic
95	#2097	C₂²	1	1	yes	characteristic
96	#2097	C₂²	1	1	yes	characteristic
97	#2097	C₂²	1	1	yes	characteristic
98	#2096	C₂²	1	1	yes	characteristic
99	#2085	C₂²	1	1	yes	characteristic
100	#2085	C₂²	1	1	yes	characteristic
101	#2074	C₂²	1	1	yes	characteristic
102	#2072	C₂²	1	1	yes	characteristic
103	#2068	C₂²	1	1	yes	characteristic
104	#2066	C₂²	1	1	yes	characteristic
105	#2066	C₂²	1	1	yes	characteristic
106	#2066	C₂²	1	1	yes	characteristic
107	#2056	C₂²	1	1	yes	characteristic
108	#2056	C₂²	1	1	yes	characteristic
109	#2056	C₂²	1	1	yes	characteristic
110	#2056	C₂²	1	1	yes	characteristic
111	#2043	C₂²	1	1	yes	characteristic
112	#2043	C₂²	1	1	yes	characteristic
113	#2043	C₂²	1	1	yes	characteristic
114	#2043	C₂²	1	1	yes	characteristic
115	#2016	C₂²	1	1	yes	characteristic
116	#2016	C₂²	1	1	yes	characteristic
117	#2016	C₂²	1	1	yes	characteristic
118	#2016	C₂²	1	1	yes	characteristic
119	#2016	C₂²	1	1	yes	characteristic
120	#2016	C₂²	1	1	yes	characteristic
121	#2016	C₂²	1	1	yes	characteristic
122	#2016	C₂²	1	1	yes	characteristic
123	#2016	C₂²	1	1	yes	characteristic
124	#2016	C₂²	1	1	yes	characteristic
125	#2016	C₂²	1	1	yes	characteristic
126	#2016	C₂²	1	1	yes	characteristic
127	#1985	C₂²	1	1	yes	characteristic
128	#1984	C₂²	1	1	yes	characteristic
129	#1981	C₂²	1	1	yes	characteristic
130	#1981	C₂²	1	1	yes	characteristic
131	#1981	C₂²	1	1	yes	characteristic
132	#1971	C₂²	1	1	yes	characteristic
133	#1971	C₂²	1	1	yes	characteristic
134	#1971	C₂²	1	1	yes	characteristic
135	#1969	C₂²	1	1	yes	characteristic
136	#1969	C₂²	1	1	yes	characteristic
137	#1969	C₂²	1	1	yes	characteristic
138	#1969	C₂²	1	1	yes	characteristic
139	#1969	C₂²	1	1	yes	characteristic
140	#1969	C₂²	1	1	yes	characteristic
141	#1960	C₂²	1	1	yes	characteristic
142	#1956	C₂²	1	1	yes	characteristic
143	#1947	C₂²	1	1	yes	characteristic
144	#1942	C₂²	1	1	yes	characteristic
145	#1935	C₂²	1	1	yes	characteristic
146	#1933	C₂²	1	1	yes	characteristic
147	#1928	C₂²	1	1	yes	characteristic
148	#1928	C₂²	1	1	yes	characteristic
149	#1928	C₂²	1	1	yes	characteristic
150	#1928	C₂²	1	1	yes	characteristic
151	#1927	C₂²	1	1	yes	characteristic
152	#1927	C₂²	1	1	yes	characteristic
153	#1927	C₂²	1	1	yes	characteristic
154	#1927	C₂²	1	1	yes	characteristic
155	#1919	C₂²	1	1	yes	characteristic
156	#1918	C₂²	1	1	yes	characteristic
157	#1917	C₂²	1	1	yes	characteristic
158	#1916	C₂²	1	1	yes	characteristic
159	#1916	C₂²	1	1	yes	characteristic
160	#1916	C₂²	1	1	yes	characteristic
161	#1894	C₂²	1	1	yes	characteristic
162	#1892	C₂²	1	1	yes	characteristic
163	#1878	C₂²	1	1	yes	characteristic
164	#1878	C₂²	1	1	yes	characteristic
165	#1878	C₂²	1	1	yes	characteristic
166	#1878	C₂²	1	1	yes	characteristic
167	#1878	C₂²	1	1	yes	characteristic
168	#1878	C₂²	1	1	yes	characteristic
169	#1878	C₂²	1	1	yes	characteristic
170	#1878	C₂²	1	1	yes	characteristic
171	#1878	C₂²	1	1	yes	characteristic
172	#1878	C₂²	1	1	yes	characteristic
173	#1878	C₂²	1	1	yes	characteristic
174	#1878	C₂²	1	1	yes	characteristic
175	#1878	C₂²	1	1	yes	characteristic
176	#1878	C₂²	1	1	yes	characteristic
177	#1878	C₂²	1	1	yes	characteristic
178	#1878	C₂²	1	1	yes	characteristic
179	#1878	C₂²	1	1	yes	characteristic
180	#1878	C₂²	1	1	yes	characteristic
181	#1873	C₂²	1	1	yes	characteristic
182	#1865	C₂²	1	1	yes	characteristic
183	#1865	C₂²	1	1	yes	characteristic
184	#1863	C₂²	1	1	yes	characteristic
185	#1863	C₂²	1	1	yes	characteristic
186	#1854	C₂²	1	1	yes	characteristic
187	#1851	C₂²	1	1	yes	characteristic
188	#1850	C₂²	1	1	yes	characteristic
189	#1805	C₂²	1	1	yes	characteristic
190	#1787	C₂²	1	1	yes	characteristic
191	C₄×#106	C₂²	1	1	yes	characteristic
192	#1770	C₂²	1	1	yes	characteristic
193	C₈×C₄⋊C₄	C₂²	1	1	yes	characteristic
194	#1763	C₂²	1	1	yes	characteristic
195	C₄×#103	C₂²	1	1	yes	characteristic
196	C₄×#103	C₂²	1	1	yes	characteristic
197	C₄×#103	C₂²	1	1	yes	characteristic
198	#1753	C₂²	1	1	yes	characteristic
199	C₈×C₂²⋊C₄	C₂²	1	1	yes	characteristic
200	#1750	C₂²	1	1	yes	characteristic
201	#1735	C₂²	1	1	yes	characteristic
202	#1729	C₂²	1	1	yes	characteristic
203	C₂³×Q₈	C₂³	1	1	yes	characteristic
204	C₂³×Q₈	C₂³	1	1	yes	characteristic
205	C₂²×Q₁₆	—	2	4	no	—
206	C₂²×Q₁₆	—	4	2	no	—
207	C₂²×Q₁₆	—	4	2	no	—
208	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
209	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
210	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
211	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
212	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
213	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
214	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
215	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
216	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
217	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
218	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
219	C₂²×Q₁₆	C₂³	1	1	yes	characteristic
220	C₂²×M₁₆	C₂³	1	1	yes	characteristic
221	C₂³×C₈	C₂³	1	1	yes	characteristic
222	#557	—	4	2	no	—
223	#557	—	4	2	no	—
224	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
231	C₂×#125	—	2	1	no	—
232	C₂×#125	—	2	1	no	—
233	C₂×#125	—	2	1	no	—
234	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
237	#519	—	4	2	no	—
238	#519	—	4	2	no	—
239	C₂×C₄×Q₈	—	2	1	no	—
240	C₂×C₄×Q₈	—	2	1	no	—
241	C₂×C₄×Q₈	—	2	1	no	—
242	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
243	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
244	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
245	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
247	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
251	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
252	C₂×#117	—	2	1	no	—
253	C₂×#117	—	2	1	no	—
254	C₂×#117	C₂³	1	1	yes	characteristic
255	C₂×#117	C₂³	1	1	yes	characteristic
256	C₂×#117	C₂³	1	1	yes	characteristic
257	#494	—	2	4	no	—
258	#494	—	4	2	no	—
259	#485	—	2	4	no	—
260	#485	—	4	2	no	—
261	#470	—	4	2	no	—
262	#467	—	4	2	no	—
263	#462	—	2	4	no	—
264	#462	—	4	2	no	—
265	#462	—	4	2	no	—
266	#451	—	2	4	no	—
267	#451	—	2	4	no	—
268	#451	—	4	2	no	—
269	#441	—	4	2	no	—
270	#441	—	4	2	no	—
271	C₄×Q₁₆	—	4	2	no	—
272	C₂×#107	C₂³	1	1	yes	characteristic
273	C₂×#107	C₂³	1	1	yes	characteristic
274	C₂×#107	C₂³	1	1	yes	characteristic
275	C₂×#107	C₂³	1	1	yes	characteristic
276	C₂×#106	C₂³	1	1	yes	characteristic
277	C₂×#106	C₂³	1	1	yes	characteristic
278	C₂×#106	C₂³	1	1	yes	characteristic
279	C₂×#106	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	#419	—	4	2	no	—
285	#419	—	4	2	no	—
286	C₂×#103	C₂³	1	1	yes	characteristic
287	C₂×#103	C₂³	1	1	yes	characteristic
288	C₂×#103	C₂³	1	1	yes	characteristic
289	C₂×#103	C₂³	1	1	yes	characteristic
290	C₂×#103	C₂³	1	1	yes	characteristic
291	C₂×#103	C₂³	1	1	yes	characteristic
292	C₂×#103	C₂³	1	1	yes	characteristic
293	C₂×#103	C₂³	1	1	yes	characteristic
294	C₂×#103	C₂³	1	1	yes	characteristic
295	C₂×#103	C₂³	1	1	yes	characteristic
296	C₂×#103	C₂³	1	1	yes	characteristic
297	C₂×#103	C₂³	1	1	yes	characteristic
298	C₂×#103	C₂³	1	1	yes	characteristic
299	C₂×#103	C₂³	1	1	yes	characteristic
300	C₂×#103	C₂³	1	1	yes	characteristic
301	C₂×#103	C₂³	1	1	yes	characteristic
302	C₂×#103	C₂³	1	1	yes	characteristic
303	C₂×#103	C₂³	1	1	yes	characteristic
304	C₂×#103	C₂³	1	1	yes	characteristic
305	C₂×#103	C₂³	1	1	yes	characteristic
306	C₂×#103	C₂³	1	1	yes	characteristic
307	C₂×#103	C₂³	1	1	yes	characteristic
308	C₂×#103	C₂³	1	1	yes	characteristic
309	C₂×#103	C₂³	1	1	yes	characteristic
310	C₂×#103	C₂³	1	1	yes	characteristic
311	C₂×#103	C₂³	1	1	yes	characteristic
312	C₂×#103	C₂³	1	1	yes	characteristic
313	C₂×#103	C₂³	1	1	yes	characteristic
314	C₂×#103	C₂³	1	1	yes	characteristic
315	C₂×#103	C₂³	1	1	yes	characteristic
316	C₂×#103	C₂³	1	1	yes	characteristic
317	C₂×#103	C₂³	1	1	yes	characteristic
318	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
319	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
320	C₂×#97	C₂³	1	1	yes	characteristic
321	C₂×#97	C₂³	1	1	yes	characteristic
322	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
323	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
324	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
325	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
326	#401	—	2	1	no	—
327	#400	—	2	1	no	—
328	#400	—	2	1	no	—
329	#400	—	2	1	no	—
330	#400	—	2	1	no	—
331	#400	—	2	1	no	—
332	#400	—	2	1	no	—
333	#400	—	2	1	no	—
334	#400	—	2	1	no	—
335	#400	—	2	1	no	—
336	#400	—	2	1	no	—
337	#400	—	2	1	no	—
338	#400	D₄	1	1	yes	characteristic
339	#399	D₄	1	1	yes	characteristic
340	#398	—	2	1	no	—
341	#398	—	2	1	no	—
342	#398	—	2	1	no	—
343	#398	—	2	1	no	—
344	#398	—	2	1	no	—
345	#398	—	2	1	no	—
346	#398	—	2	1	no	—
347	#398	—	2	1	no	—
348	#398	D₄	1	1	yes	characteristic
349	#398	D₄	1	1	yes	characteristic
350	#397	—	2	1	no	—
351	#397	—	2	1	no	—
352	#397	—	2	1	no	—
353	#397	—	2	1	no	—
354	#396	D₄	1	1	yes	characteristic
355	#396	D₄	1	1	yes	characteristic
356	#395	—	2	1	no	—
357	#395	—	2	1	no	—
358	#395	—	2	1	no	—
359	#395	—	2	1	no	—
360	#395	—	2	1	no	—
361	#395	—	2	1	no	—
362	#395	—	2	1	no	—
363	#395	—	2	1	no	—
364	#395	D₄	1	1	yes	characteristic
365	#393	D₄	1	1	yes	characteristic
366	#391	—	2	1	no	—
367	#391	—	2	1	no	—
368	#391	—	2	1	no	—
369	#391	—	2	1	no	—
370	#391	—	2	1	no	—
371	#391	C₂³	1	1	yes	characteristic
372	#391	C₂³	1	1	yes	characteristic
373	#391	C₂³	1	1	yes	characteristic
374	#391	C₂³	1	1	yes	characteristic
375	#391	C₂³	1	1	yes	characteristic
376	#391	C₂³	1	1	yes	characteristic
377	#391	C₂³	1	1	yes	characteristic
378	#391	C₂³	1	1	yes	characteristic
379	#391	C₂³	1	1	yes	characteristic
380	#391	C₂³	1	1	yes	characteristic
381	#391	C₂³	1	1	yes	characteristic
382	#391	C₂³	1	1	yes	characteristic
383	#391	C₂³	1	1	yes	characteristic
384	#391	C₂³	1	1	yes	characteristic
385	#391	C₂³	1	1	yes	characteristic
386	#391	C₂³	1	1	yes	characteristic
387	#391	C₂³	1	1	yes	characteristic
388	#391	C₂³	1	1	yes	characteristic
389	#391	C₂³	1	1	yes	characteristic
390	#389	—	2	1	no	—
391	#389	—	2	1	no	—
392	#389	—	2	1	no	—
393	#389	—	2	1	no	—
394	#389	—	2	1	no	—
395	#389	—	2	1	no	—
396	#389	C₂³	1	1	yes	characteristic
397	#389	C₂³	1	1	yes	characteristic
398	#389	C₂³	1	1	yes	characteristic
399	#389	C₂³	1	1	yes	characteristic
400	#389	C₂³	1	1	yes	characteristic
401	#388	—	2	1	no	—
402	#388	—	2	1	no	—
403	#388	—	2	1	no	—
404	#388	—	2	1	no	—
405	#388	—	2	1	no	—
406	#388	—	2	1	no	—
407	#388	—	2	1	no	—
408	#388	—	2	1	no	—
409	#387	—	2	1	no	—
410	#387	—	2	1	no	—
411	#387	—	2	1	no	—
412	#387	—	2	1	no	—
413	#387	—	2	1	no	—
414	#387	—	2	1	no	—
415	#387	—	2	1	no	—
416	#387	—	2	1	no	—
417	#387	—	2	1	no	—
418	#387	—	2	1	no	—
419	#387	—	2	1	no	—
420	#387	—	2	1	no	—
421	#387	—	2	1	no	—
422	#387	—	2	1	no	—
423	#387	—	2	1	no	—
424	#387	—	2	1	no	—
425	#387	—	2	1	no	—
426	#387	—	2	1	no	—
427	#387	—	2	1	no	—
428	#387	—	2	1	no	—
429	#387	—	2	1	no	—
430	#387	—	2	1	no	—
431	#387	—	2	1	no	—
432	#387	—	2	1	no	—
433	#387	—	2	1	no	—
434	#387	—	2	1	no	—
435	#387	—	2	1	no	—
436	#387	—	2	1	no	—
437	#387	—	2	1	no	—
438	#387	—	2	1	no	—
439	#385	—	2	1	no	—
440	#385	—	2	1	no	—
441	#385	—	2	1	no	—
442	#385	—	2	1	no	—
443	#385	—	2	1	no	—
444	#385	—	2	1	no	—
445	#384	C₂³	1	1	yes	characteristic
446	#383	—	2	1	no	—
447	#383	—	2	1	no	—
448	#383	—	2	1	no	—
449	#382	—	2	1	no	—
450	#382	—	2	1	no	—
451	#382	C₂³	1	1	yes	characteristic
452	#382	C₂³	1	1	yes	characteristic
453	#381	—	2	1	no	—
454	#381	—	2	1	no	—
455	#380	—	2	1	no	—
456	#380	C₂³	1	1	yes	characteristic
457	C₄×C₄⋊C₄	—	2	1	no	—
458	C₄×C₄⋊C₄	—	2	1	no	—
459	C₄×C₄⋊C₄	—	2	1	no	—
460	C₄×C₄⋊C₄	—	2	1	no	—
461	C₄×C₄⋊C₄	—	2	1	no	—
462	C₄×C₄⋊C₄	—	2	1	no	—
463	C₄×C₄⋊C₄	—	2	1	no	—
464	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
465	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
466	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
467	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
468	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
469	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
470	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
471	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
472	C₄×C₂²⋊C₄	—	2	1	no	—
473	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
474	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
475	#376	—	2	1	no	—
476	#340	C₂³	1	1	yes	characteristic
477	#340	C₂³	1	1	yes	characteristic
478	#340	C₂³	1	1	yes	characteristic
479	#340	C₂³	1	1	yes	characteristic
480	#340	C₂³	1	1	yes	characteristic
481	#340	C₂³	1	1	yes	characteristic
482	#340	C₂³	1	1	yes	characteristic
483	#340	C₂³	1	1	yes	characteristic
484	#340	C₂³	1	1	yes	characteristic
485	#340	C₂³	1	1	yes	characteristic
486	#340	C₂³	1	1	yes	characteristic
487	#340	C₂³	1	1	yes	characteristic
488	#336	C₂³	1	1	yes	characteristic
489	#336	C₂³	1	1	yes	characteristic
490	#336	C₂³	1	1	yes	characteristic
491	#336	C₂³	1	1	yes	characteristic
492	#336	C₂³	1	1	yes	characteristic
493	#336	C₂³	1	1	yes	characteristic
494	#336	C₂³	1	1	yes	characteristic
495	#336	C₂³	1	1	yes	characteristic
496	#336	C₂³	1	1	yes	characteristic
497	#336	C₂³	1	1	yes	characteristic
498	#336	C₂³	1	1	yes	characteristic
499	#336	C₂³	1	1	yes	characteristic
500	#336	C₂³	1	1	yes	characteristic
501	#336	C₂³	1	1	yes	characteristic
502	C₂²×Q₈	—	2	1	no	—
503	C₂²×Q₈	—	2	1	no	—
504	C₂²×Q₈	—	2	2	no	—
505	C₂²×Q₈	—	2	2	no	—
506	C₂²×Q₈	—	2	2	no	—
507	C₂²×Q₈	—	2	2	no	—
508	C₂²×Q₈	—	2	2	no	—
509	C₂²×Q₈	—	2	2	no	—
510	C₂²×Q₈	—	2	2	no	—
511	C₂²×Q₈	—	4	1	no	—
512	C₂²×Q₈	—	4	1	no	—
513	C₂²×Q₈	—	4	1	no	—
514	C₂²×Q₈	—	4	1	no	—
515	C₂²×Q₈	—	4	1	no	—
516	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
517	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
518	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
519	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
520	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
521	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
522	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
523	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
524	C₂³×C₄	—	2	1	no	—
525	C₂³×C₄	—	2	1	no	—
526	C₂³×C₄	C₂⁴	1	1	yes	characteristic
527	C₂×Q₁₆	—	2	2	no	—
528	C₂×Q₁₆	—	2	2	no	—
529	C₂×Q₁₆	—	2	2	no	—
530	C₂×Q₁₆	—	2	2	no	—
531	C₂×Q₁₆	—	2	2	no	—
532	C₂×Q₁₆	—	2	2	no	—
533	C₂×Q₁₆	—	2	2	no	—
534	C₂×Q₁₆	—	2	2	no	—
535	C₂×Q₁₆	—	2	2	no	—
536	C₂×Q₁₆	—	2	2	no	—
537	C₂×Q₁₆	—	2	2	no	—
538	C₂×Q₁₆	—	2	2	no	—
539	C₂×Q₁₆	—	2	2	no	—
540	C₂×Q₁₆	—	2	2	no	—
541	C₂×Q₁₆	—	4	1	no	—
542	C₂×Q₁₆	—	4	1	no	—
543	C₂×Q₁₆	—	4	1	no	—
544	C₂×Q₁₆	—	4	1	no	—
545	C₂×Q₁₆	—	4	1	no	—
546	C₂×Q₁₆	—	4	1	no	—
547	C₂×Q₁₆	—	4	1	no	—
548	C₂×Q₁₆	—	4	1	no	—
549	C₂×Q₁₆	—	4	1	no	—
550	C₂×Q₁₆	—	4	1	no	—
551	C₂×Q₁₆	—	4	1	no	—
552	C₂×Q₁₆	—	4	1	no	—
553	C₂×Q₁₆	—	4	1	no	—
554	C₂×Q₁₆	—	4	1	no	—
555	C₂×Q₁₆	—	4	1	no	—
556	C₂×Q₁₆	—	4	1	no	—
557	C₂×Q₁₆	—	4	1	no	—
558	C₂×Q₁₆	—	4	1	no	—
559	C₂×Q₁₆	—	4	1	no	—
560	C₂×Q₁₆	—	4	1	no	—
561	C₂×Q₁₆	—	4	1	no	—
562	C₂×Q₁₆	—	4	16	no	—
563	C₂×Q₁₆	#41	1	4	yes	—
564	C₂×M₁₆	—	2	2	no	—
565	C₂×M₁₆	—	4	1	no	—
566	C₂×M₁₆	—	4	1	no	—
567	C₂²×C₈	—	2	2	no	—
568	C₂²×C₈	—	2	2	no	—
569	C₂²×C₈	—	4	1	no	—
570	C₂²×C₈	C₂⁴	1	1	yes	characteristic
571	C₂²×C₈	C₂⁴	1	1	yes	characteristic
572	C₂²×C₈	C₂⁴	1	1	yes	characteristic
573	C₂²×C₈	C₂⁴	1	1	yes	characteristic
574	C₂²×C₈	C₂⁴	1	1	yes	characteristic
575	C₂²×C₈	C₂⁴	1	1	yes	characteristic
576	C₂²×C₈	C₂⁴	1	1	yes	characteristic
577	C₂²×C₈	C₂⁴	1	1	yes	characteristic
578	C₄⋊Q₈	—	2	2	no	—
579	C₄⋊Q₈	—	2	2	no	—
580	C₄⋊Q₈	—	2	2	no	—
581	C₄⋊Q₈	—	2	2	no	—
582	C₄⋊Q₈	—	2	2	no	—
583	C₄⋊Q₈	—	4	1	no	—
584	C₄⋊Q₈	—	4	1	no	—
585	C₄⋊Q₈	—	4	1	no	—
586	C₄⋊Q₈	—	4	1	no	—
587	C₄⋊Q₈	—	4	1	no	—
588	C₄⋊Q₈	—	4	1	no	—
589	C₄⋊Q₈	—	4	1	no	—
590	C₄⋊Q₈	—	4	1	no	—
591	C₄⋊Q₈	—	4	1	no	—
592	#125	—	4	4	no	—
593	#125	—	4	4	no	—
594	#125	—	4	4	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	—	2	2	no	—
601	C₄×Q₈	—	2	2	no	—
602	C₄×Q₈	—	2	2	no	—
603	C₄×Q₈	—	2	2	no	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	—	2	2	no	—
606	C₄×Q₈	—	2	2	no	—
607	C₄×Q₈	—	2	2	no	—
608	C₄×Q₈	—	4	1	no	—
609	C₄×Q₈	—	4	1	no	—
610	C₄×Q₈	—	4	1	no	—
611	C₄×Q₈	—	4	1	no	—
612	C₄×Q₈	—	4	1	no	—
613	C₄×Q₈	—	4	1	no	—
614	C₄×Q₈	—	4	1	no	—
615	C₄×Q₈	—	4	1	no	—
616	C₄×Q₈	—	4	1	no	—
617	C₄×Q₈	—	4	4	no	—
618	C₄×Q₈	—	4	4	no	—
619	C₄×Q₈	—	4	1	no	—
620	C₄×Q₈	—	4	1	no	—
621	C₄×Q₈	—	4	1	no	—
622	C₄×Q₈	—	4	1	no	—
623	C₄×Q₈	—	4	4	no	—
624	#117	—	2	2	no	—
625	#117	—	2	2	no	—
626	#117	—	2	2	no	—
627	#117	—	4	1	no	—
628	#117	—	4	1	no	—
629	#117	—	4	4	no	—
630	#117	—	4	1	no	—
631	#117	—	4	4	no	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	1	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	—	2	1	no	—
639	C₂×C₄⋊C₄	—	2	1	no	—
640	C₂×C₄⋊C₄	—	2	1	no	—
641	C₂×C₄⋊C₄	—	2	1	no	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	—	2	1	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	—	2	1	no	—
652	C₂×C₄⋊C₄	—	2	1	no	—
653	C₂×C₄⋊C₄	—	2	1	no	—
654	C₂×C₄⋊C₄	—	2	1	no	—
655	C₂×C₄⋊C₄	—	2	1	no	—
656	C₂×C₄⋊C₄	—	2	1	no	—
657	C₂×C₄⋊C₄	—	2	1	no	—
658	C₂×C₄⋊C₄	—	2	1	no	—
659	C₂×C₄⋊C₄	—	2	1	no	—
660	C₂×C₄⋊C₄	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
668	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
670	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
673	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
680	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
685	C₂×C₂²⋊C₄	—	2	1	no	—
686	C₂×C₂²⋊C₄	—	2	1	no	—
687	C₂×C₂²⋊C₄	—	2	1	no	—
688	C₂×C₂²⋊C₄	—	2	1	no	—
689	C₂×C₂²⋊C₄	—	2	1	no	—
690	C₂×C₂²⋊C₄	—	2	1	no	—
691	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
693	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
694	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
696	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
697	C₂×C₄²	—	2	1	no	—
698	C₂×C₄²	—	2	1	no	—
699	C₂×C₄²	—	2	1	no	—
700	C₂×C₄²	—	2	1	no	—
701	C₂×C₄²	—	2	1	no	—
702	C₂×C₄²	—	2	1	no	—
703	C₂×C₄²	—	2	1	no	—
704	C₂×C₄²	—	2	1	no	—
705	C₂×C₄²	—	2	1	no	—
706	C₂×C₄²	—	2	1	no	—
707	C₂×C₄²	—	2	1	no	—
708	C₂×C₄²	—	2	1	no	—
709	C₂×C₄²	—	2	1	no	—
710	C₂×C₄²	—	2	1	no	—
711	C₂×C₄²	—	2	1	no	—
712	C₂×C₄²	—	2	1	no	—
713	C₂×C₄²	C₂⁴	1	1	yes	characteristic
714	C₂×C₄²	C₂⁴	1	1	yes	characteristic
715	C₂×C₄²	C₂⁴	1	1	yes	characteristic
716	C₂×C₄²	C₂⁴	1	1	yes	characteristic
717	C₂×C₄²	C₂⁴	1	1	yes	characteristic
718	C₂×C₄²	C₂⁴	1	1	yes	characteristic
719	#107	—	2	2	no	—
720	#107	—	4	1	no	—
721	#107	—	4	1	no	—
722	#107	—	4	1	no	—
723	#106	—	2	2	no	—
724	#106	—	2	2	no	—
725	#106	—	4	1	no	—
726	#106	—	4	1	no	—
727	C₄⋊C₈	—	2	2	no	—
728	C₄⋊C₈	—	4	1	no	—
729	C₄⋊C₈	—	4	1	no	—
730	C₄⋊C₈	—	4	1	no	—
731	#103	—	2	2	no	—
732	#103	—	2	2	no	—
733	#103	—	2	2	no	—
734	#103	—	2	2	no	—
735	#103	—	2	2	no	—
736	#103	—	2	2	no	—
737	#103	—	2	2	no	—
738	#103	—	2	2	no	—
739	#103	—	2	2	no	—
740	#103	—	2	2	no	—
741	#103	—	2	2	no	—
742	#103	—	2	2	no	—
743	#103	—	4	1	no	—
744	#103	—	4	1	no	—
745	#103	—	4	1	no	—
746	#103	—	4	1	no	—
747	#103	—	4	1	no	—
748	#103	—	4	1	no	—
749	#103	—	4	1	no	—
750	#103	—	4	1	no	—
751	#103	—	4	1	no	—
752	#103	—	4	1	no	—
753	#103	—	4	1	no	—
754	#103	—	4	1	no	—
755	#103	—	4	1	no	—
756	#103	—	4	1	no	—
757	#103	—	4	1	no	—
758	#103	—	4	1	no	—
759	#103	—	4	1	no	—
760	#103	—	4	1	no	—
761	#103	—	4	1	no	—
762	#103	—	4	1	no	—
763	C₂²⋊C₈	—	2	2	no	—
764	C₂²⋊C₈	#41	1	4	yes	—
765	#97	—	4	1	no	—
766	#97	—	4	1	no	—
767	C₄×C₈	—	2	2	no	—
768	C₄×C₈	—	4	1	no	—
769	C₄×C₈	—	4	1	no	—
770	C₄×C₈	—	4	1	no	—
771	#95	—	2	1	no	—
772	#95	—	2	1	no	—
773	#95	—	2	1	no	—
774	#95	—	2	1	no	—
775	#95	—	2	1	no	—
776	#95	—	2	1	no	—
777	#95	—	2	1	no	—
778	#95	—	2	1	no	—
779	#95	—	2	1	no	—
780	#95	—	2	1	no	—
781	#95	—	2	1	no	—
782	#95	—	2	1	no	—
783	#95	—	2	1	no	—
784	#95	—	2	1	no	—
785	#95	—	2	1	no	—
786	#95	—	2	1	no	—
787	#95	—	2	1	no	—
788	#95	—	2	1	no	—
789	#95	—	2	1	no	—
790	#95	—	2	1	no	—
791	#95	—	2	1	no	—
792	#95	—	2	1	no	—
793	#95	—	2	1	no	—
794	#95	—	2	1	no	—
795	#95	—	2	1	no	—
796	#95	—	2	1	no	—
797	#95	—	2	1	no	—
798	#95	—	2	1	no	—
799	#95	—	2	1	no	—
800	#95	—	2	1	no	—
801	#95	—	2	1	no	—
802	#95	—	2	1	no	—
803	#95	—	2	1	no	—
804	#95	—	2	1	no	—
805	#95	—	2	1	no	—
806	#95	—	2	1	no	—
807	#95	—	2	1	no	—
808	#95	—	2	1	no	—
809	#95	—	2	1	no	—
810	#95	—	2	1	no	—
811	#95	—	2	1	no	—
812	#95	—	2	1	no	—
813	#95	—	2	1	no	—
814	#95	—	2	1	no	—
815	#95	—	2	1	no	—
816	#95	—	2	1	no	—
817	#95	—	2	1	no	—
818	#95	—	2	1	no	—
819	#95	—	2	1	no	—
820	#95	—	2	1	no	—
821	#95	—	2	1	no	—
822	#95	—	2	1	no	—
823	#95	—	2	1	no	—
824	#95	C₂×D₄	1	1	yes	characteristic
825	#95	C₂×D₄	1	1	yes	characteristic
826	#95	C₂×D₄	1	1	yes	characteristic
827	#95	C₂×D₄	1	1	yes	characteristic
828	#95	C₂×D₄	1	1	yes	characteristic
829	#95	C₂×D₄	1	1	yes	characteristic
830	#95	C₂×D₄	1	1	yes	characteristic
831	#95	C₂×D₄	1	1	yes	characteristic
832	#95	C₂×D₄	1	1	yes	characteristic
833	#95	C₂×D₄	1	1	yes	characteristic
834	C₂⁴	C₂²×D₄	1	1	yes	characteristic
835	C₂×Q₈	—	2	2	no	—
836	C₂×Q₈	—	2	1	no	—
837	C₂×Q₈	—	2	1	no	—
838	C₂×Q₈	—	2	1	no	—
839	C₂×Q₈	—	2	8	no	—
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	—	2	1	no	—
842	C₂×Q₈	—	2	1	no	—
843	C₂×Q₈	—	2	1	no	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	1	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	2	1	no	—
848	C₂×Q₈	—	2	1	no	—
849	C₂×Q₈	—	2	1	no	—
850	C₂×Q₈	—	2	1	no	—
851	C₂×Q₈	—	2	1	no	—
852	C₂×Q₈	—	2	1	no	—
853	C₂×Q₈	—	2	1	no	—
854	C₂×Q₈	—	2	1	no	—
855	C₂×Q₈	—	2	1	no	—
856	C₂×Q₈	—	2	1	no	—
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	1	no	—
862	C₂×Q₈	—	2	1	no	—
863	C₂×Q₈	—	2	1	no	—
864	C₂×Q₈	—	2	1	no	—
865	C₂×Q₈	—	2	1	no	—
866	C₂×Q₈	—	2	1	no	—
867	C₂×Q₈	—	2	1	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	2	1	no	—
874	C₂×Q₈	—	2	1	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	4	1	no	—
877	C₂×Q₈	—	4	1	no	—
878	C₂×Q₈	—	4	2	no	—
879	C₂×Q₈	—	4	2	no	—
880	C₂×Q₈	—	4	2	no	—
881	C₂×Q₈	—	4	4	no	—
882	C₂×Q₈	—	4	4	no	—
883	C₂×Q₈	—	4	4	no	—
884	C₂×Q₈	—	4	4	no	—
885	C₂×Q₈	—	4	4	no	—
886	C₂×Q₈	—	4	2	no	—
887	C₂×Q₈	—	4	2	no	—
888	C₂×Q₈	—	8	1	no	—
889	C₂×Q₈	—	8	2	no	—
890	C₂×Q₈	—	8	2	no	—
891	C₂×Q₈	C₂×#41	1	2	yes	—
892	C₂×Q₈	C₂×#41	1	2	yes	—
893	C₂×Q₈	H(5,𝔽₂)	1	2	yes	—
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	—	4	2	no	—
915	C₂²×C₄	—	4	2	no	—
916	C₂²×C₄	—	4	2	no	—
917	C₂²×C₄	—	4	2	no	—
918	C₂²×C₄	—	4	2	no	—
919	C₂²×C₄	—	8	1	no	—
920	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
921	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
922	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
923	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
924	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
925	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
926	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
927	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
928	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
929	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
930	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
931	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
932	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
933	C₂²×C₄	C₂×#41	1	2	yes	—
934	C₂²×C₄	H(5,𝔽₂)	1	2	yes	—
935	C₂²×C₄	C₂⁵	1	1	yes	characteristic
936	Q₁₆	—	4	4	no	—
937	Q₁₆	—	4	4	no	—
938	Q₁₆	—	4	4	no	—
939	Q₁₆	—	4	4	no	—
940	Q₁₆	—	4	4	no	—
941	Q₁₆	—	4	4	no	—
942	Q₁₆	—	4	4	no	—
943	Q₁₆	—	8	2	no	—
944	Q₁₆	—	8	2	no	—
945	Q₁₆	—	8	2	no	—
946	Q₁₆	—	8	2	no	—
947	Q₁₆	—	8	2	no	—
948	M₁₆	—	8	2	no	—
949	C₂×C₈	—	2	1	no	—
950	C₂×C₈	—	2	1	no	—
951	C₂×C₈	—	2	1	no	—
952	C₂×C₈	—	2	1	no	—
953	C₂×C₈	—	2	1	no	—
954	C₂×C₈	—	2	1	no	—
955	C₂×C₈	—	2	1	no	—
956	C₂×C₈	—	2	1	no	—
957	C₂×C₈	—	2	1	no	—
958	C₂×C₈	—	2	1	no	—
959	C₂×C₈	—	2	1	no	—
960	C₂×C₈	—	2	1	no	—
961	C₂×C₈	—	2	1	no	—
962	C₂×C₈	—	2	1	no	—
963	C₂×C₈	—	2	1	no	—
964	C₂×C₈	—	2	1	no	—
965	C₂×C₈	—	2	1	no	—
966	C₂×C₈	—	2	1	no	—
967	C₂×C₈	—	2	1	no	—
968	C₂×C₈	—	2	1	no	—
969	C₂×C₈	—	2	1	no	—
970	C₂×C₈	—	4	4	no	—
971	C₂×C₈	C₂×#41	1	2	yes	—
972	C₂×C₈	C₂×#41	1	2	yes	—
973	C₂×C₈	C₂×#41	1	2	yes	—
974	C₄⋊C₄	—	2	4	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	4	1	no	—
998	C₄⋊C₄	—	4	1	no	—
999	C₄⋊C₄	—	4	1	no	—
1000	C₄⋊C₄	—	4	1	no	—
1001	C₄⋊C₄	—	4	1	no	—
1002	C₄⋊C₄	—	4	1	no	—
1003	C₄⋊C₄	—	4	2	no	—
1004	C₄⋊C₄	—	4	2	no	—
1005	C₄⋊C₄	—	4	2	no	—
1006	C₄⋊C₄	—	4	2	no	—
1007	C₄⋊C₄	—	4	2	no	—
1008	C₄⋊C₄	—	4	2	no	—
1009	C₄⋊C₄	—	4	2	no	—
1010	C₄⋊C₄	—	4	2	no	—
1011	C₄⋊C₄	—	4	2	no	—
1012	C₄⋊C₄	—	4	2	no	—
1013	C₄⋊C₄	—	4	2	no	—
1014	C₄⋊C₄	—	4	2	no	—
1015	C₄⋊C₄	—	4	2	no	—
1016	C₄⋊C₄	—	4	2	no	—
1017	C₄⋊C₄	—	4	2	no	—
1018	C₄⋊C₄	—	4	2	no	—
1019	C₄⋊C₄	—	4	2	no	—
1020	C₄⋊C₄	—	4	2	no	—
1021	C₄⋊C₄	—	4	2	no	—
1022	C₄⋊C₄	—	4	2	no	—
1023	C₄⋊C₄	—	4	2	no	—
1024	C₄⋊C₄	—	4	2	no	—
1025	C₄⋊C₄	—	4	2	no	—
1026	C₄⋊C₄	—	4	2	no	—
1027	C₄⋊C₄	—	4	2	no	—
1028	C₄⋊C₄	—	4	2	no	—
1029	C₄⋊C₄	—	8	1	no	—
1030	C₄⋊C₄	—	8	1	no	—
1031	C₄⋊C₄	—	8	1	no	—
1032	C₄⋊C₄	—	8	1	no	—
1033	C₄⋊C₄	—	8	1	no	—
1034	C₄⋊C₄	—	8	1	no	—
1035	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	4	1	no	—
1040	C₂²⋊C₄	—	4	1	no	—
1041	C₂²⋊C₄	—	4	1	no	—
1042	C₂²⋊C₄	—	4	2	no	—
1043	C₂²⋊C₄	—	4	2	no	—
1044	C₂²⋊C₄	—	4	2	no	—
1045	C₂²⋊C₄	—	4	2	no	—
1046	C₂²⋊C₄	—	4	2	no	—
1047	C₂²⋊C₄	—	8	1	no	—
1048	C₄²	—	2	4	no	—
1049	C₄²	—	2	1	no	—
1050	C₄²	—	2	1	no	—
1051	C₄²	—	2	1	no	—
1052	C₄²	—	2	1	no	—
1053	C₄²	—	2	1	no	—
1054	C₄²	—	2	1	no	—
1055	C₄²	—	2	1	no	—
1056	C₄²	—	2	1	no	—
1057	C₄²	—	2	1	no	—
1058	C₄²	—	2	1	no	—
1059	C₄²	—	2	1	no	—
1060	C₄²	—	2	1	no	—
1061	C₄²	—	4	2	no	—
1062	C₄²	—	4	2	no	—
1063	C₄²	—	4	2	no	—
1064	C₄²	—	4	2	no	—
1065	C₄²	—	4	2	no	—
1066	C₄²	—	4	2	no	—
1067	C₄²	—	4	2	no	—
1068	C₄²	—	4	2	no	—
1069	C₄²	—	4	2	no	—
1070	C₄²	—	4	2	no	—
1071	C₄²	—	8	1	no	—
1072	C₄²	—	8	1	no	—
1073	C₄²	—	8	1	no	—
1074	C₄²	—	8	1	no	—
1075	C₄²	—	8	1	no	—
1076	C₂³	—	2	1	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	2	1	no	—
1079	C₂³	—	2	1	no	—
1080	C₂³	—	2	1	no	—
1081	C₂³	—	2	1	no	—
1082	C₂³	#550	1	2	yes	—
1083	C₂³	C₂³×D₄	1	1	yes	characteristic
1084	Q₈	—	2	2	no	—
1085	Q₈	—	2	2	no	—
1086	Q₈	—	2	2	no	—
1087	Q₈	—	2	2	no	—
1088	Q₈	—	2	2	no	—
1089	Q₈	—	2	2	no	—
1090	Q₈	—	4	4	no	—
1091	Q₈	—	4	8	no	—
1092	Q₈	—	4	1	no	—
1093	Q₈	—	4	1	no	—
1094	Q₈	—	4	1	no	—
1095	Q₈	—	4	1	no	—
1096	Q₈	—	4	1	no	—
1097	Q₈	—	4	1	no	—
1098	Q₈	—	4	1	no	—
1099	Q₈	—	4	1	no	—
1100	Q₈	—	4	1	no	—
1101	Q₈	—	4	1	no	—
1102	Q₈	—	4	1	no	—
1103	Q₈	—	4	1	no	—
1104	Q₈	—	4	1	no	—
1105	Q₈	—	4	1	no	—
1106	Q₈	—	4	1	no	—
1107	Q₈	—	4	1	no	—
1108	Q₈	—	4	1	no	—
1109	Q₈	—	4	1	no	—
1110	Q₈	—	4	1	no	—
1111	Q₈	—	4	1	no	—
1112	Q₈	—	4	1	no	—
1113	Q₈	—	4	1	no	—
1114	Q₈	—	8	4	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	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	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	4	8	no	—
1159	C₂×C₄	—	4	1	no	—
1160	C₂×C₄	—	4	1	no	—
1161	C₂×C₄	—	4	1	no	—
1162	C₂×C₄	—	4	1	no	—
1163	C₂×C₄	—	4	1	no	—
1164	C₂×C₄	—	4	1	no	—
1165	C₂×C₄	—	4	1	no	—
1166	C₂×C₄	—	4	1	no	—
1167	C₂×C₄	—	4	1	no	—
1168	C₂×C₄	—	4	1	no	—
1169	C₂×C₄	—	4	1	no	—
1170	C₂×C₄	—	4	1	no	—
1171	C₂×C₄	—	4	1	no	—
1172	C₂×C₄	—	4	1	no	—
1173	C₂×C₄	—	4	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	1	no	—
1184	C₂×C₄	—	4	1	no	—
1185	C₂×C₄	—	4	1	no	—
1186	C₂×C₄	—	4	1	no	—
1187	C₂×C₄	—	4	1	no	—
1188	C₂×C₄	—	4	1	no	—
1189	C₂×C₄	—	4	1	no	—
1190	C₂×C₄	—	4	1	no	—
1191	C₂×C₄	—	4	1	no	—
1192	C₂×C₄	—	4	1	no	—
1193	C₂×C₄	—	4	1	no	—
1194	C₂×C₄	—	4	1	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	—	8	4	no	—
1204	C₂×C₄	#550	1	2	yes	—
1205	C₂×C₄	#578	1	2	yes	—
1206	C₂×C₄	#578	1	2	yes	—
1207	C₂×C₄	#578	1	2	yes	—
1208	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1209	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1210	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1211	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1212	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1213	C₂×C₄	#585	1	1	yes	characteristic
1214	C₈	—	2	2	no	—
1215	C₈	—	2	2	no	—
1216	C₈	—	2	2	no	—
1217	C₈	—	4	1	no	—
1218	C₈	—	4	1	no	—
1219	C₈	—	4	1	no	—
1220	C₈	—	4	1	no	—
1221	C₈	—	4	1	no	—
1222	C₂²	—	2	2	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	2	2	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	—	4	1	no	—
1227	C₂²	—	4	1	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	C₂×#550	1	1	yes	characteristic
1230	C₂²	D₄×#41	1	1	yes	characteristic
1231	C₂²	#3484	1	1	yes	characteristic
1232	C₂²	C₂×#578	1	1	yes	characteristic
1233	C₂²	C₂×#578	1	1	yes	characteristic
1234	C₂²	C₂×#578	1	1	yes	characteristic
1235	C₂²	#3586	1	1	yes	characteristic
1236	C₄	—	2	2	no	—
1237	C₄	—	2	2	no	—
1238	C₄	—	2	2	no	—
1239	C₄	—	2	2	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	2	no	—
1243	C₄	—	4	2	no	—
1244	C₄	—	4	2	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	1	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	4	2	no	—
1253	C₄	—	8	1	no	—
1254	C₄	—	8	1	no	—
1255	C₄	—	8	1	no	—
1256	C₄	—	8	1	no	—
1257	C₄	—	8	1	no	—
1258	C₄	—	8	1	no	—
1259	C₄	—	8	1	no	—
1260	C₄	—	8	1	no	—
1261	C₄	—	8	1	no	—
1262	C₄	—	8	1	no	—
1263	C₄	—	8	1	no	—
1264	C₄	—	8	1	no	—
1265	C₄	#3481	1	1	yes	characteristic
1266	C₄	#3490	1	1	yes	characteristic
1267	C₄	#3513	1	1	yes	characteristic
1268	C₄	#3542	1	1	yes	characteristic
1269	C₂	—	4	2	no	—
1270	C₂	#59045	1	1	yes	characteristic
1271	C₂	#61411	1	1	yes	characteristic
1272	C₂	#61422	1	1	yes	characteristic
1273	C₂	#61484	1	1	yes	characteristic
1274	C₂	#61525	1	1	yes	characteristic
1275	C₂	#61612	1	1	yes	characteristic
1276	C₂	#61665	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂⁴	C₂²×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2396 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #32653	C₂	semidirect
4. #32619	C₂	semidirect
5. #32168	C₂	semidirect
6. #30744	C₂	semidirect
7. #28887	C₂	semidirect
11. #27501	C₂	semidirect
12. #27209	C₂	semidirect
13. #27205	C₂	semidirect
14. #27067	C₂	semidirect
15. #26607	C₂	semidirect
16. #26590	C₂	semidirect
17. #26255	C₂	semidirect
19. #25634	C₂	semidirect
24. #24203	C₂	semidirect
26. #23187	C₂	semidirect
27. #23096	C₂	semidirect

Maximal subgroups

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

subgroup	index
#45149	2
#35749	2
#32653	2
#32619	2
#32168	2
#30744	2
#28887	2
#28588	2
#28355	2
#28322	2
#27501	2
#27209	2
#27205	2
#27067	2
#26607	2
#26590	2
#26255	2
#25780	2
#25634	2
#25215	2
#25095	2
#24496	2
#24360	2
#24203	2
#23244	2
#23187	2
#23096	2
#22919	2
#22869	2
#21463	2
#20935	2