Subgroups — #6455097

Order 512.

1621 conjugacy classes of subgroups.

The subgroup lattice has 1227 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#35577	C₂	1	1	yes	maximal, characteristic, complemented
2	#34261	C₂	1	1	yes	maximal, characteristic
3	#26115	C₂	1	1	yes	maximal, characteristic, complemented
4	#26111	C₂	1	1	yes	maximal, characteristic, complemented
5	#26103	C₂	1	1	yes	maximal, characteristic, complemented
6	#26098	C₂	1	1	yes	maximal, characteristic, complemented
7	#26058	C₂	1	1	yes	maximal, characteristic, complemented
8	#26052	C₂	1	1	yes	maximal, characteristic, complemented
9	#26030	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020	C₂	1	1	yes	maximal, characteristic, complemented
11	#26015	C₂	1	1	yes	maximal, characteristic, complemented
12	#26011	C₂	1	1	yes	maximal, characteristic, complemented
13	#25993	C₂	1	1	yes	maximal, characteristic, complemented
14	#25989	C₂	1	1	yes	maximal, characteristic, complemented
15	#25974	C₂	1	1	yes	maximal, characteristic
16	#25966	C₂	1	1	yes	maximal, characteristic
17	#25960	C₂	1	1	yes	maximal, characteristic
18	#25950	C₂	1	1	yes	maximal, characteristic
19	#23787	C₂	1	1	yes	maximal, characteristic, complemented
20	#23787	C₂	1	1	yes	maximal, characteristic, complemented
21	#23781	C₂	1	1	yes	maximal, characteristic, complemented
22	#23778	C₂	1	1	yes	maximal, characteristic, complemented
23	#21624	C₂	1	1	yes	maximal, characteristic, complemented
24	#21623	C₂	1	1	yes	maximal, characteristic, complemented
25	#21617	C₂	1	1	yes	maximal, characteristic, complemented
26	C₄×#474	C₂	1	1	yes	maximal, characteristic, complemented
27	#21368	C₂	1	1	yes	maximal, characteristic, complemented
28	#21357	C₂	1	1	yes	maximal, characteristic, complemented
29	#20822	C₂	1	1	yes	maximal, characteristic, complemented
30	#20744	C₂	1	1	yes	maximal, characteristic
31	#20416	C₂	1	1	yes	maximal, characteristic
32	C₂×#518	C₂²	1	1	yes	characteristic
33	C₂×#478	C₂²	1	1	yes	characteristic
34	C₂×#476	C₂²	1	1	yes	characteristic
35	C₂×#474	C₂²	1	1	yes	characteristic
36	C₂×#474	C₂²	1	1	yes	characteristic
37	C₂×#433	C₂²	1	1	yes	characteristic
38	C₂×#418	C₂²	1	1	yes	characteristic
39	C₂²×#102	C₂²	1	1	yes	characteristic
40	C₂×#405	C₂²	1	1	yes	characteristic
41	#2588	—	2	1	no	—
42	#2587	—	2	1	no	—
43	#2586	—	2	1	no	—
44	#2574	—	2	1	no	—
45	#2571	C₂²	1	1	yes	characteristic, complemented
46	#2570	C₂²	1	1	yes	characteristic, complemented
47	#2551	C₂²	1	1	yes	characteristic, complemented
48	#2550	C₂²	1	1	yes	characteristic, complemented
49	#2520	—	2	1	no	—
50	#2492	—	2	1	no	—
51	#2465	—	2	1	no	—
52	#2446	—	2	1	no	—
53	#2442	C₂²	1	1	yes	characteristic
54	#2440	C₂²	1	1	yes	characteristic
55	#2439	C₂²	1	1	yes	characteristic
56	#2439	C₂²	1	1	yes	characteristic
57	#2357	C₂²	1	1	yes	characteristic
58	#2354	C₂²	1	1	yes	characteristic
59	#2353	—	2	1	no	—
60	#2352	—	2	1	no	—
61	#2349	C₂²	1	1	yes	characteristic
62	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
63	#2347	C₂²	1	1	yes	characteristic
64	#2346	C₂²	1	1	yes	characteristic
65	#2342	—	2	1	no	—
66	#2342	—	2	1	no	—
67	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
68	D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
69	#2331	C₂²	1	1	yes	characteristic, complemented
70	#2331	C₂²	1	1	yes	characteristic, complemented
71	#2319	C₂²	1	1	yes	characteristic
72	#2318	—	2	1	no	—
73	#2314	C₂²	1	1	yes	characteristic
74	#2314	C₂²	1	1	yes	characteristic
75	#2312	—	2	1	no	—
76	C₄×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
77	C₄×#125	C₂²	1	1	yes	characteristic, complemented
78	#2298	C₂²	1	1	yes	characteristic
79	#2293	C₂²	1	1	yes	characteristic
80	#2290	—	2	1	no	—
81	C₂×#388	—	2	1	no	—
82	#2275	C₂²	1	1	yes	characteristic
83	#2274	C₂²	1	1	yes	characteristic
84	C₄²×D₄	C₂²	1	1	yes	characteristic
85	#2101	C₂²	1	1	yes	characteristic, complemented
86	#2101	C₂²	1	1	yes	characteristic, complemented
87	#2101	C₂²	1	1	yes	characteristic, complemented
88	#2099	C₂²	1	1	yes	characteristic, complemented
89	#2093	C₂²	1	1	yes	characteristic
90	#2092	C₂²	1	1	yes	characteristic
91	#2092	C₂²	1	1	yes	characteristic
92	#2092	C₂²	1	1	yes	characteristic
93	#2088	C₂²	1	1	yes	characteristic, complemented
94	#2088	C₂²	1	1	yes	characteristic, complemented
95	#2088	C₂²	1	1	yes	characteristic, complemented
96	#2087	C₂²	1	1	yes	characteristic, complemented
97	#2087	C₂²	1	1	yes	characteristic, complemented
98	#2087	C₂²	1	1	yes	characteristic, complemented
99	#2087	C₂²	1	1	yes	characteristic, complemented
100	#2087	C₂²	1	1	yes	characteristic, complemented
101	#2067	C₂²	1	1	yes	characteristic
102	#2067	C₂²	1	1	yes	characteristic
103	#2067	C₂²	1	1	yes	characteristic
104	#2067	C₂²	1	1	yes	characteristic
105	#2067	C₂²	1	1	yes	characteristic
106	#2065	C₂²	1	1	yes	characteristic
107	#2065	C₂²	1	1	yes	characteristic
108	#2065	C₂²	1	1	yes	characteristic
109	#2059	C₂²	1	1	yes	characteristic, complemented
110	#2058	C₂²	1	1	yes	characteristic, complemented
111	#2057	C₂²	1	1	yes	characteristic, complemented
112	#2057	C₂²	1	1	yes	characteristic, complemented
113	#2025	C₂²	1	1	yes	characteristic
114	#2023	C₂²	1	1	yes	characteristic
115	#2023	C₂²	1	1	yes	characteristic
116	#2023	C₂²	1	1	yes	characteristic
117	#1989	C₂²	1	1	yes	characteristic, complemented
118	#1988	C₂²	1	1	yes	characteristic, complemented
119	#1988	C₂²	1	1	yes	characteristic, complemented
120	#1987	C₂²	1	1	yes	characteristic, complemented
121	#1949	C₂²	1	1	yes	characteristic, complemented
122	#1949	C₂²	1	1	yes	characteristic, complemented
123	#1949	C₂²	1	1	yes	characteristic, complemented
124	#1949	C₂²	1	1	yes	characteristic, complemented
125	#1949	C₂²	1	1	yes	characteristic, complemented
126	#1947	C₂²	1	1	yes	characteristic, complemented
127	#1947	C₂²	1	1	yes	characteristic, complemented
128	#1947	C₂²	1	1	yes	characteristic, complemented
129	#1940	C₂²	1	1	yes	characteristic, complemented
130	#1940	C₂²	1	1	yes	characteristic, complemented
131	#1939	C₂²	1	1	yes	characteristic, complemented
132	#1939	C₂²	1	1	yes	characteristic, complemented
133	#1921	C₂²	1	1	yes	characteristic, complemented
134	#1920	C₂²	1	1	yes	characteristic, complemented
135	#1920	C₂²	1	1	yes	characteristic, complemented
136	#1919	C₂²	1	1	yes	characteristic, complemented
137	#1918	C₂²	1	1	yes	characteristic, complemented
138	#1918	C₂²	1	1	yes	characteristic, complemented
139	#1918	C₂²	1	1	yes	characteristic, complemented
140	#1918	C₂²	1	1	yes	characteristic, complemented
141	#1864	C₂²	1	1	yes	characteristic
142	#1864	C₂²	1	1	yes	characteristic
143	#1864	C₂²	1	1	yes	characteristic
144	#1862	C₂²	1	1	yes	characteristic
145	#1862	C₂²	1	1	yes	characteristic
146	#1862	C₂²	1	1	yes	characteristic
147	#1862	C₂²	1	1	yes	characteristic
148	#1862	C₂²	1	1	yes	characteristic
149	#1854	C₂²	1	1	yes	characteristic
150	#1854	C₂²	1	1	yes	characteristic
151	#1852	C₂²	1	1	yes	characteristic
152	#1852	C₂²	1	1	yes	characteristic
153	#1851	C₂²	1	1	yes	characteristic
154	#1851	C₂²	1	1	yes	characteristic
155	#1850	C₂²	1	1	yes	characteristic
156	#1850	C₂²	1	1	yes	characteristic
157	#1847	C₂²	1	1	yes	characteristic, complemented
158	#1847	C₂²	1	1	yes	characteristic, complemented
159	#1835	C₂²	1	1	yes	characteristic, complemented
160	#1834	C₂²	1	1	yes	characteristic, complemented
161	#1825	C₂²	1	1	yes	characteristic
162	#1825	C₂²	1	1	yes	characteristic
163	#1809	C₂²	1	1	yes	characteristic
164	#1809	C₂²	1	1	yes	characteristic
165	#1808	C₂²	1	1	yes	characteristic
166	#1807	C₂²	1	1	yes	characteristic
167	#1804	C₂²	1	1	yes	characteristic
168	#1804	C₂²	1	1	yes	characteristic
169	#1804	C₂²	1	1	yes	characteristic
170	#1804	C₂²	1	1	yes	characteristic
171	#1804	C₂²	1	1	yes	characteristic
172	#1802	C₂²	1	1	yes	characteristic
173	#1802	C₂²	1	1	yes	characteristic
174	#1802	C₂²	1	1	yes	characteristic
175	#1786	C₂²	1	1	yes	characteristic
176	#1786	C₂²	1	1	yes	characteristic
177	#1776	C₂²	1	1	yes	characteristic, complemented
178	#1776	C₂²	1	1	yes	characteristic, complemented
179	#1776	C₂²	1	1	yes	characteristic, complemented
180	#1776	C₂²	1	1	yes	characteristic, complemented
181	C₄×#107	C₂²	1	1	yes	characteristic, complemented
182	C₄×#107	C₂²	1	1	yes	characteristic, complemented
183	C₄×#107	C₂²	1	1	yes	characteristic, complemented
184	C₄×#106	C₂²	1	1	yes	characteristic, complemented
185	#1768	C₂²	1	1	yes	characteristic, complemented
186	#1768	C₂²	1	1	yes	characteristic, complemented
187	#1767	C₂²	1	1	yes	characteristic, complemented
188	C₄×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
189	#1762	C₂²	1	1	yes	characteristic
190	#1762	C₂²	1	1	yes	characteristic
191	#1762	C₂²	1	1	yes	characteristic
192	#1762	C₂²	1	1	yes	characteristic
193	#1762	C₂²	1	1	yes	characteristic
194	#1762	C₂²	1	1	yes	characteristic
195	C₄×#102	C₂²	1	1	yes	characteristic
196	C₄×#102	C₂²	1	1	yes	characteristic
197	C₄×#102	C₂²	1	1	yes	characteristic
198	C₄×#102	C₂²	1	1	yes	characteristic
199	C₄×#102	C₂²	1	1	yes	characteristic
200	C₄×#102	C₂²	1	1	yes	characteristic
201	#1736	C₂²	1	1	yes	characteristic
202	#1735	C₂²	1	1	yes	characteristic
203	C₂³×D₄	C₂³	1	1	yes	characteristic
204	C₂²×M₁₆	C₂³	1	1	yes	characteristic
205	C₂³×C₈	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊Q₈	—	2	1	no	—
207	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂×#125	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊Q₈	—	2	1	no	—
212	#518	—	2	4	no	—
213	#518	Q₈	1	8	yes	complemented
214	C₂×C₄×Q₈	—	2	1	no	—
215	C₂×C₄×D₄	—	2	1	no	—
216	C₂×C₄×D₄	—	2	1	no	—
217	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂³	1	1	yes	characteristic
225	C₂×#117	—	2	1	no	—
226	C₂×#117	—	2	1	no	—
227	C₂×#117	C₂³	1	1	yes	characteristic
228	C₂×#117	C₂³	1	1	yes	characteristic
229	C₂×#117	C₂³	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	—	2	1	no	—
231	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
232	C₂²×C₂²⋊C₄	—	2	1	no	—
233	C₂²×C₂²⋊C₄	—	2	1	no	—
234	C₂²×C₂²⋊C₄	—	2	1	no	—
235	C₂²×C₂²⋊C₄	—	2	1	no	—
236	C₂²×C₄²	—	2	1	no	—
237	#478	—	2	4	no	—
238	#476	—	2	4	no	—
239	#474	—	2	4	no	—
240	#474	—	2	4	no	—
241	#433	—	2	4	no	—
242	C₂×#107	C₂³	1	1	yes	characteristic
243	C₂×#107	C₂³	1	1	yes	characteristic
244	C₂×#107	C₂³	1	1	yes	characteristic
245	C₂×#107	C₂³	1	1	yes	characteristic
246	C₂×#107	C₂³	1	1	yes	characteristic
247	C₂×#107	C₂³	1	1	yes	characteristic
248	C₂×#107	C₂³	1	1	yes	characteristic
249	C₂×#107	C₂³	1	1	yes	characteristic
250	C₂×#107	C₂³	1	1	yes	characteristic
251	C₂×#107	C₂³	1	1	yes	characteristic
252	C₂×#106	C₂³	1	1	yes	characteristic
253	C₂×#106	C₂³	1	1	yes	characteristic
254	C₂×#106	C₂³	1	1	yes	characteristic
255	C₂×#106	C₂³	1	1	yes	characteristic
256	C₂×#106	C₂³	1	1	yes	characteristic
257	C₂×#106	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	#418	—	2	4	no	—
269	C₂×#102	—	2	4	no	—
270	C₂×#102	C₂³	1	1	yes	characteristic
271	C₂×#102	C₂³	1	1	yes	characteristic
272	C₂×#102	C₂³	1	1	yes	characteristic
273	C₂×#102	C₂³	1	1	yes	characteristic
274	C₂×#102	C₂³	1	1	yes	characteristic
275	C₂×#102	C₂³	1	1	yes	characteristic
276	C₂×#102	C₂³	1	1	yes	characteristic
277	C₂×#102	C₂³	1	1	yes	characteristic
278	C₂×#102	C₂³	1	1	yes	characteristic
279	C₂×#102	C₂³	1	1	yes	characteristic
280	C₂×#102	C₂³	1	1	yes	characteristic
281	C₂×#102	C₂³	1	1	yes	characteristic
282	C₂×#102	C₂³	1	1	yes	characteristic
283	C₂×#102	C₂³	1	1	yes	characteristic
284	C₂×#102	C₂³	1	1	yes	characteristic
285	C₂×#102	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	#405	—	2	4	no	—
289	C₂×#97	C₂³	1	1	yes	characteristic
290	C₂×#97	C₂³	1	1	yes	characteristic
291	C₂×#97	C₂³	1	1	yes	characteristic
292	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
294	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
295	#400	—	2	1	no	—
296	#400	—	2	1	no	—
297	#400	—	2	1	no	—
298	#400	—	2	1	no	—
299	#398	—	2	1	no	—
300	#398	—	2	1	no	—
301	#398	—	2	1	no	—
302	#398	—	2	1	no	—
303	#396	—	2	1	no	—
304	#396	—	2	1	no	—
305	#395	—	2	1	no	—
306	#395	—	2	1	no	—
307	#395	—	2	1	no	—
308	#395	—	2	1	no	—
309	#393	—	2	1	no	—
310	#393	—	2	1	no	—
311	#391	—	2	1	no	—
312	#391	—	2	1	no	—
313	#391	—	2	1	no	—
314	#391	—	2	1	no	—
315	#391	—	2	1	no	—
316	#391	—	2	1	no	—
317	#391	—	2	1	no	—
318	#391	—	2	1	no	—
319	#390	C₂³	1	1	yes	characteristic
320	#390	C₂³	1	1	yes	characteristic
321	#390	C₂³	1	1	yes	characteristic
322	#390	C₂³	1	1	yes	characteristic
323	#389	—	2	1	no	—
324	#389	—	2	1	no	—
325	#389	—	2	1	no	—
326	#389	—	2	1	no	—
327	#389	C₂³	1	1	yes	characteristic
328	#389	C₂³	1	1	yes	characteristic
329	#389	C₂³	1	1	yes	characteristic
330	#389	C₂³	1	1	yes	characteristic
331	#389	C₂³	1	1	yes	characteristic
332	#389	C₂³	1	1	yes	characteristic
333	#389	C₂³	1	1	yes	characteristic
334	#389	C₂³	1	1	yes	characteristic
335	#389	C₂³	1	1	yes	characteristic
336	#389	C₂³	1	1	yes	characteristic
337	#389	C₂³	1	1	yes	characteristic
338	#389	C₂³	1	1	yes	characteristic
339	#388	—	2	1	no	—
340	#388	—	2	1	no	—
341	#388	—	2	1	no	—
342	#388	—	2	1	no	—
343	#388	—	2	1	no	—
344	#388	—	2	1	no	—
345	#388	—	2	1	no	—
346	#388	—	2	1	no	—
347	#388	—	2	1	no	—
348	#388	—	2	1	no	—
349	#388	—	2	1	no	—
350	#388	—	2	1	no	—
351	#388	—	2	1	no	—
352	#388	—	2	1	no	—
353	#388	—	2	1	no	—
354	#388	—	2	1	no	—
355	#388	D₄	1	1	yes	characteristic
356	#388	D₄	1	1	yes	characteristic
357	#388	D₄	1	1	yes	characteristic
358	#388	D₄	1	1	yes	characteristic
359	#387	—	2	1	no	—
360	#387	—	2	1	no	—
361	#387	—	2	1	no	—
362	#387	—	2	1	no	—
363	#387	—	2	1	no	—
364	#387	—	2	1	no	—
365	#387	—	2	1	no	—
366	#387	—	2	1	no	—
367	#387	—	2	1	no	—
368	#387	—	2	1	no	—
369	#387	—	2	1	no	—
370	#387	—	2	1	no	—
371	#387	—	2	1	no	—
372	#387	—	2	1	no	—
373	#387	D₄	1	1	yes	characteristic
374	#387	D₄	1	1	yes	characteristic
375	#387	D₄	1	1	yes	characteristic
376	#387	D₄	1	1	yes	characteristic
377	#386	—	2	1	no	—
378	#386	—	2	1	no	—
379	#386	—	2	1	no	—
380	#386	—	2	1	no	—
381	#385	—	2	1	no	—
382	#385	—	2	1	no	—
383	#385	—	2	1	no	—
384	#385	—	2	1	no	—
385	#385	—	2	1	no	—
386	#385	—	2	1	no	—
387	#384	C₂³	1	1	yes	characteristic
388	#384	C₂³	1	1	yes	characteristic
389	#384	C₂³	1	1	yes	characteristic
390	#383	—	2	1	no	—
391	#382	—	2	1	no	—
392	#382	—	2	1	no	—
393	#382	C₂³	1	1	yes	characteristic
394	#382	C₂³	1	1	yes	characteristic
395	#382	C₂³	1	1	yes	characteristic
396	#382	C₂³	1	1	yes	characteristic
397	#382	C₂³	1	1	yes	characteristic
398	#381	—	2	1	no	—
399	#381	—	2	1	no	—
400	#380	—	2	1	no	—
401	#380	—	2	1	no	—
402	#380	—	2	1	no	—
403	#380	—	2	1	no	—
404	#380	—	2	1	no	—
405	#380	C₂³	1	1	yes	characteristic
406	#380	C₂³	1	1	yes	characteristic
407	#380	C₂³	1	1	yes	characteristic
408	#380	C₂³	1	1	yes	characteristic
409	#379	—	2	1	no	—
410	#379	—	2	1	no	—
411	C₄×C₄⋊C₄	—	2	1	no	—
412	C₄×C₄⋊C₄	—	2	1	no	—
413	C₄×C₄⋊C₄	—	2	1	no	—
414	C₄×C₄⋊C₄	—	2	1	no	—
415	C₄×C₄⋊C₄	—	2	1	no	—
416	C₄×C₄⋊C₄	—	2	1	no	—
417	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
418	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
419	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
420	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
421	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
422	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
423	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
424	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
425	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
426	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
427	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
428	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
429	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
430	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
431	C₄×C₂²⋊C₄	—	2	1	no	—
432	C₄×C₂²⋊C₄	—	2	1	no	—
433	C₄×C₂²⋊C₄	—	2	1	no	—
434	C₄×C₂²⋊C₄	—	2	1	no	—
435	C₄×C₂²⋊C₄	—	2	1	no	—
436	C₄×C₂²⋊C₄	—	2	1	no	—
437	C₄×C₂²⋊C₄	—	2	1	no	—
438	C₄×C₂²⋊C₄	—	2	1	no	—
439	C₄×C₂²⋊C₄	—	2	1	no	—
440	C₄×C₂²⋊C₄	—	2	1	no	—
441	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
442	C₄×C₂²⋊C₄	C₂³	1	1	yes	characteristic
443	#376	—	2	1	no	—
444	#376	C₂³	1	1	yes	characteristic
445	C₂×#95	—	2	1	no	—
446	C₂×#95	—	2	1	no	—
447	C₄³	C₂³	1	1	yes	characteristic
448	#340	C₂³	1	1	yes	characteristic
449	#340	C₂³	1	1	yes	characteristic
450	#340	C₂³	1	1	yes	characteristic
451	#340	C₂³	1	1	yes	characteristic
452	#340	C₂³	1	1	yes	characteristic
453	#340	C₂³	1	1	yes	characteristic
454	#340	C₂³	1	1	yes	characteristic
455	#340	C₂³	1	1	yes	characteristic
456	#340	C₂³	1	1	yes	characteristic
457	#340	C₂³	1	1	yes	characteristic
458	#340	C₂³	1	1	yes	characteristic
459	#340	C₂³	1	1	yes	characteristic
460	#340	C₂³	1	1	yes	characteristic
461	#340	C₂³	1	1	yes	characteristic
462	#340	C₂³	1	1	yes	characteristic
463	#340	C₂³	1	1	yes	characteristic
464	#340	C₂³	1	1	yes	characteristic
465	#340	C₂³	1	1	yes	characteristic
466	#340	C₂³	1	1	yes	characteristic
467	#340	C₂³	1	1	yes	characteristic
468	#340	C₂³	1	1	yes	characteristic
469	#340	C₂³	1	1	yes	characteristic
470	#340	C₂³	1	1	yes	characteristic
471	#340	C₂³	1	1	yes	characteristic
472	#340	C₂³	1	1	yes	characteristic
473	#340	C₂³	1	1	yes	characteristic
474	#340	C₂³	1	1	yes	characteristic
475	#340	C₂³	1	1	yes	characteristic
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	#336	C₂³	1	1	yes	characteristic
481	#336	C₂³	1	1	yes	characteristic
482	#336	C₂³	1	1	yes	characteristic
483	#336	C₂³	1	1	yes	characteristic
484	#336	C₂³	1	1	yes	characteristic
485	#336	C₂³	1	1	yes	characteristic
486	#336	C₂³	1	1	yes	characteristic
487	#336	C₂³	1	1	yes	characteristic
488	C₂⁵	—	2	1	no	—
489	C₂²×Q₈	—	2	1	no	—
490	C₂²×Q₈	—	2	1	no	—
491	C₂²×Q₈	—	2	1	no	—
492	C₂²×D₄	—	2	2	no	—
493	C₂²×D₄	—	2	2	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	2	no	—
496	C₂²×D₄	—	4	1	no	—
497	C₂²×D₄	—	4	1	no	—
498	C₂²×D₄	C₂×Q₈	1	4	yes	—
499	C₂²×D₄	C₂⁴	1	1	yes	characteristic
500	C₂²×D₄	C₂⁴	1	1	yes	characteristic
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	—	2	1	no	—
507	C₂³×C₄	—	2	1	no	—
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	C₂⁴	1	1	yes	characteristic
511	C₂×M₁₆	—	2	2	no	—
512	C₂×M₁₆	—	2	2	no	—
513	C₂×M₁₆	—	4	1	no	—
514	C₂²×C₈	—	2	2	no	—
515	C₂²×C₈	—	2	2	no	—
516	C₂²×C₈	—	4	1	no	—
517	C₂²×C₈	C₂⁴	1	1	yes	characteristic
518	C₂²×C₈	C₂⁴	1	1	yes	characteristic
519	C₂²×C₈	C₂⁴	1	1	yes	characteristic
520	C₂²×C₈	C₂⁴	1	1	yes	characteristic
521	C₂²×C₈	C₂⁴	1	1	yes	characteristic
522	C₂²×C₈	C₂⁴	1	1	yes	characteristic
523	C₂²×C₈	C₂⁴	1	1	yes	characteristic
524	C₂²×C₈	C₂⁴	1	1	yes	characteristic
525	C₄⋊Q₈	—	2	2	no	—
526	C₄⋊Q₈	—	2	2	no	—
527	C₄⋊Q₈	—	2	2	no	—
528	C₄⋊Q₈	—	4	1	no	—
529	C₄⋊Q₈	—	4	1	no	—
530	C₄⋊Q₈	—	4	1	no	—
531	C₄⋊Q₈	—	8	2	no	—
532	#125	—	2	2	no	—
533	#125	—	4	1	no	—
534	C₂²⋊Q₈	—	8	2	no	—
535	C₄×Q₈	—	8	2	no	—
536	C₄×D₄	—	2	8	no	—
537	C₄×D₄	—	2	8	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	2	2	no	—
544	C₄×D₄	—	2	2	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	4	1	no	—
547	C₄×D₄	—	4	1	no	—
548	C₄×D₄	—	4	1	no	—
549	C₄×D₄	—	4	1	no	—
550	C₄×D₄	C₂×Q₈	1	4	yes	—
551	C₄×D₄	C₂×Q₈	1	4	yes	—
552	C₄×D₄	C₂×Q₈	1	4	yes	—
553	C₄×D₄	C₂×Q₈	1	4	yes	—
554	#117	—	2	2	no	—
555	#117	—	2	2	no	—
556	#117	—	4	1	no	—
557	#117	—	8	2	no	—
558	#117	—	8	2	no	—
559	#117	C₂×Q₈	1	4	yes	—
560	#117	C₂×Q₈	1	4	yes	—
561	#117	#41	1	4	yes	—
562	C₂×C₄⋊C₄	—	2	2	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	—	2	1	no	—
569	C₂×C₄⋊C₄	—	2	1	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	—	2	1	no	—
583	C₂×C₄⋊C₄	—	2	1	no	—
584	C₂×C₄⋊C₄	—	2	1	no	—
585	C₂×C₄⋊C₄	—	2	1	no	—
586	C₂×C₄⋊C₄	—	2	1	no	—
587	C₂×C₄⋊C₄	—	4	1	no	—
588	C₂×C₄⋊C₄	—	8	2	no	—
589	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
606	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	—	2	1	no	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	8	no	—
615	C₂×C₂²⋊C₄	—	2	8	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	8	2	no	—
634	C₂×C₂²⋊C₄	—	8	2	no	—
635	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
637	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
638	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
640	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
641	C₂×C₄²	—	2	1	no	—
642	C₂×C₄²	—	2	1	no	—
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	—	2	1	no	—
645	C₂×C₄²	—	2	1	no	—
646	C₂×C₄²	—	2	1	no	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	—	2	1	no	—
650	C₂×C₄²	—	2	1	no	—
651	C₂×C₄²	—	2	1	no	—
652	C₂×C₄²	—	2	1	no	—
653	C₂×C₄²	—	2	1	no	—
654	C₂×C₄²	—	2	1	no	—
655	C₂×C₄²	—	8	2	no	—
656	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
657	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
658	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
659	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
660	C₂×C₄²	C₂⁴	1	1	yes	characteristic
661	C₂×C₄²	C₂⁴	1	1	yes	characteristic
662	C₂×C₄²	C₂⁴	1	1	yes	characteristic
663	C₂×C₄²	C₂⁴	1	1	yes	characteristic
664	C₂×C₄²	C₂⁴	1	1	yes	characteristic
665	C₂×C₄²	C₂⁴	1	1	yes	characteristic
666	#107	—	2	2	no	—
667	#107	—	2	2	no	—
668	#107	—	2	2	no	—
669	#107	—	2	2	no	—
670	#107	—	2	2	no	—
671	#107	—	4	1	no	—
672	#107	—	4	1	no	—
673	#107	—	4	1	no	—
674	#107	—	4	1	no	—
675	#107	—	4	1	no	—
676	#106	—	2	2	no	—
677	#106	—	2	2	no	—
678	#106	—	2	2	no	—
679	#106	—	4	1	no	—
680	#106	—	4	1	no	—
681	#106	—	4	1	no	—
682	C₄⋊C₈	—	2	2	no	—
683	C₄⋊C₈	—	2	2	no	—
684	C₄⋊C₈	—	2	2	no	—
685	C₄⋊C₈	—	2	2	no	—
686	C₄⋊C₈	—	2	2	no	—
687	C₄⋊C₈	—	2	2	no	—
688	C₄⋊C₈	—	4	1	no	—
689	C₄⋊C₈	—	4	1	no	—
690	C₄⋊C₈	—	4	1	no	—
691	C₄⋊C₈	—	4	1	no	—
692	#102	—	2	2	no	—
693	#102	—	2	2	no	—
694	#102	—	2	2	no	—
695	#102	—	2	2	no	—
696	#102	—	2	2	no	—
697	#102	—	2	2	no	—
698	#102	—	2	2	no	—
699	#102	—	2	2	no	—
700	#102	—	2	2	no	—
701	#102	—	2	2	no	—
702	#102	—	4	1	no	—
703	#102	—	4	1	no	—
704	#102	—	4	1	no	—
705	#102	—	4	1	no	—
706	#102	#41	1	4	yes	—
707	#102	#41	1	4	yes	—
708	C₂²⋊C₈	—	2	2	no	—
709	C₂²⋊C₈	—	2	2	no	—
710	#97	—	2	2	no	—
711	#97	—	2	2	no	—
712	#97	—	2	2	no	—
713	C₄×C₈	—	2	2	no	—
714	C₄×C₈	—	2	2	no	—
715	C₄×C₈	—	2	2	no	—
716	#95	—	2	1	no	—
717	#95	—	2	1	no	—
718	#95	—	2	1	no	—
719	#95	—	2	1	no	—
720	#95	—	2	1	no	—
721	#95	—	2	1	no	—
722	#95	—	2	1	no	—
723	#95	—	2	1	no	—
724	#95	—	2	1	no	—
725	#95	—	2	1	no	—
726	#95	—	2	1	no	—
727	#95	—	2	1	no	—
728	#95	—	2	1	no	—
729	#95	—	2	1	no	—
730	#95	—	2	1	no	—
731	#95	—	2	1	no	—
732	#95	—	2	1	no	—
733	#95	—	2	1	no	—
734	#95	—	2	1	no	—
735	#95	—	2	1	no	—
736	#95	—	2	1	no	—
737	#95	—	2	1	no	—
738	#95	—	2	1	no	—
739	#95	—	2	1	no	—
740	#95	—	2	1	no	—
741	#95	—	2	1	no	—
742	#95	—	2	1	no	—
743	#95	—	2	1	no	—
744	#95	—	2	1	no	—
745	#95	—	2	1	no	—
746	#95	—	2	1	no	—
747	#95	—	2	1	no	—
748	#95	—	2	1	no	—
749	#95	—	2	1	no	—
750	#95	—	2	1	no	—
751	#95	—	2	1	no	—
752	#95	—	2	1	no	—
753	#95	—	2	1	no	—
754	#95	C₂×D₄	1	1	yes	characteristic
755	#95	C₂×D₄	1	1	yes	characteristic
756	#95	C₂×D₄	1	1	yes	characteristic
757	#95	C₂×D₄	1	1	yes	characteristic
758	#95	C₂×D₄	1	1	yes	characteristic
759	#95	C₂×D₄	1	1	yes	characteristic
760	#95	C₂×D₄	1	1	yes	characteristic
761	#95	C₂×D₄	1	1	yes	characteristic
762	#95	C₂×D₄	1	1	yes	characteristic
763	#95	C₂×D₄	1	1	yes	characteristic
764	#95	C₂×D₄	1	1	yes	characteristic
765	#95	C₂×D₄	1	1	yes	characteristic
766	C₂⁴	—	2	1	no	—
767	C₂⁴	—	2	1	no	—
768	C₂⁴	—	2	4	no	—
769	C₂⁴	—	4	2	no	—
770	C₂⁴	—	4	2	no	—
771	C₂⁴	—	8	1	no	—
772	C₂⁴	—	8	1	no	—
773	C₂⁴	—	8	1	no	—
774	C₂⁴	—	8	1	no	—
775	C₂⁴	C₂²×D₄	1	1	yes	characteristic
776	C₂×Q₈	—	4	2	no	—
777	C₂×Q₈	—	4	2	no	—
778	C₂×Q₈	—	4	2	no	—
779	C₂×Q₈	—	4	2	no	—
780	C₂×Q₈	—	8	1	no	—
781	C₂×Q₈	—	8	1	no	—
782	C₂×Q₈	—	8	1	no	—
783	C₂×Q₈	—	8	1	no	—
784	C₂×Q₈	—	8	1	no	—
785	C₂×D₄	—	2	8	no	—
786	C₂×D₄	—	2	4	no	—
787	C₂×D₄	—	2	1	no	—
788	C₂×D₄	—	2	1	no	—
789	C₂×D₄	—	2	1	no	—
790	C₂×D₄	—	2	1	no	—
791	C₂×D₄	—	2	1	no	—
792	C₂×D₄	—	2	1	no	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	4	4	no	—
796	C₂×D₄	—	4	4	no	—
797	C₂×D₄	—	4	4	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	—	4	2	no	—
800	C₂×D₄	C₂²×Q₈	1	2	yes	—
801	C₂×D₄	C₂²×Q₈	1	2	yes	—
802	C₂×D₄	C₂×#41	1	2	yes	—
803	C₂×D₄	C₂×#41	1	2	yes	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	1	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	1	no	—
812	C₂²×C₄	—	2	4	no	—
813	C₂²×C₄	—	2	4	no	—
814	C₂²×C₄	—	2	4	no	—
815	C₂²×C₄	—	2	4	no	—
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	—	4	2	no	—
828	C₂²×C₄	—	4	2	no	—
829	C₂²×C₄	—	4	2	no	—
830	C₂²×C₄	—	4	2	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	4	2	no	—
833	C₂²×C₄	—	8	1	no	—
834	C₂²×C₄	—	8	1	no	—
835	C₂²×C₄	—	8	1	no	—
836	C₂²×C₄	—	8	1	no	—
837	C₂²×C₄	—	8	1	no	—
838	C₂²×C₄	—	8	1	no	—
839	C₂²×C₄	—	8	1	no	—
840	C₂²×C₄	—	8	1	no	—
841	C₂²×C₄	—	8	1	no	—
842	C₂²×C₄	—	8	1	no	—
843	C₂²×C₄	—	8	1	no	—
844	C₂²×C₄	—	8	1	no	—
845	C₂²×C₄	—	8	1	no	—
846	C₂²×C₄	—	8	1	no	—
847	C₂²×C₄	—	8	1	no	—
848	C₂²×C₄	—	8	1	no	—
849	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
850	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
851	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
852	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
853	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
854	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
855	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
856	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
857	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
858	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
859	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
860	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
861	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
862	C₂²×C₄	C₂²×Q₈	1	2	yes	—
863	C₂²×C₄	C₂×#41	1	2	yes	—
864	C₂²×C₄	C₂⁵	1	1	yes	characteristic
865	M₁₆	—	4	4	no	—
866	C₂×C₈	—	2	1	no	—
867	C₂×C₈	—	2	1	no	—
868	C₂×C₈	—	2	1	no	—
869	C₂×C₈	—	2	1	no	—
870	C₂×C₈	—	2	1	no	—
871	C₂×C₈	—	2	1	no	—
872	C₂×C₈	—	2	1	no	—
873	C₂×C₈	—	2	1	no	—
874	C₂×C₈	—	2	1	no	—
875	C₂×C₈	—	2	1	no	—
876	C₂×C₈	—	2	1	no	—
877	C₂×C₈	—	2	1	no	—
878	C₂×C₈	—	2	1	no	—
879	C₂×C₈	—	2	1	no	—
880	C₂×C₈	—	2	1	no	—
881	C₂×C₈	—	2	1	no	—
882	C₂×C₈	—	2	1	no	—
883	C₂×C₈	—	2	1	no	—
884	C₂×C₈	—	2	1	no	—
885	C₂×C₈	—	2	1	no	—
886	C₂×C₈	—	2	1	no	—
887	C₂×C₈	—	2	1	no	—
888	C₂×C₈	—	4	4	no	—
889	C₂×C₈	C₂×#41	1	2	yes	—
890	C₂×C₈	C₂×#41	1	2	yes	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	1	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	4	1	no	—
917	C₄⋊C₄	—	4	1	no	—
918	C₄⋊C₄	—	4	1	no	—
919	C₄⋊C₄	—	4	2	no	—
920	C₄⋊C₄	—	4	2	no	—
921	C₄⋊C₄	—	4	2	no	—
922	C₄⋊C₄	—	4	2	no	—
923	C₄⋊C₄	—	4	2	no	—
924	C₄⋊C₄	—	4	2	no	—
925	C₄⋊C₄	—	4	2	no	—
926	C₄⋊C₄	—	4	2	no	—
927	C₄⋊C₄	—	4	2	no	—
928	C₄⋊C₄	—	4	2	no	—
929	C₄⋊C₄	—	8	1	no	—
930	C₄⋊C₄	—	8	1	no	—
931	C₄⋊C₄	—	8	1	no	—
932	C₄⋊C₄	—	8	1	no	—
933	C₄⋊C₄	—	8	1	no	—
934	C₄⋊C₄	—	8	1	no	—
935	C₄⋊C₄	—	8	1	no	—
936	C₄⋊C₄	—	8	1	no	—
937	C₄⋊C₄	—	8	1	no	—
938	C₄⋊C₄	—	8	1	no	—
939	C₄⋊C₄	—	8	1	no	—
940	C₄⋊C₄	—	8	1	no	—
941	C₄⋊C₄	—	8	1	no	—
942	C₄⋊C₄	—	8	1	no	—
943	C₄⋊C₄	C₂²⋊Q₈	1	4	yes	—
944	C₄⋊C₄	C₂²⋊Q₈	1	4	yes	—
945	C₄⋊C₄	C₂²×Q₈	1	2	yes	—
946	C₄⋊C₄	C₂²×Q₈	1	2	yes	—
947	C₄⋊C₄	C₂×#41	1	2	yes	—
948	C₄⋊C₄	C₂×#41	1	2	yes	—
949	C₂²⋊C₄	—	2	4	no	—
950	C₂²⋊C₄	—	2	4	no	—
951	C₂²⋊C₄	—	2	4	no	—
952	C₂²⋊C₄	—	2	4	no	—
953	C₂²⋊C₄	—	2	4	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	4	1	no	—
956	C₂²⋊C₄	—	4	1	no	—
957	C₂²⋊C₄	—	4	1	no	—
958	C₂²⋊C₄	—	4	2	no	—
959	C₂²⋊C₄	—	4	2	no	—
960	C₂²⋊C₄	—	4	2	no	—
961	C₂²⋊C₄	—	4	2	no	—
962	C₂²⋊C₄	—	4	2	no	—
963	C₂²⋊C₄	—	4	2	no	—
964	C₂²⋊C₄	—	4	2	no	—
965	C₂²⋊C₄	—	8	1	no	—
966	C₂²⋊C₄	—	8	1	no	—
967	C₂²⋊C₄	—	8	1	no	—
968	C₂²⋊C₄	—	8	1	no	—
969	C₂²⋊C₄	—	8	1	no	—
970	C₂²⋊C₄	—	8	1	no	—
971	C₂²⋊C₄	—	8	1	no	—
972	C₂²⋊C₄	—	8	1	no	—
973	C₂²⋊C₄	—	8	1	no	—
974	C₂²⋊C₄	—	8	1	no	—
975	C₂²⋊C₄	C₂²⋊Q₈	1	4	yes	—
976	C₂²⋊C₄	C₂²⋊Q₈	1	4	yes	—
977	C₄²	—	2	4	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	1	no	—
981	C₄²	—	2	1	no	—
982	C₄²	—	2	1	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	1	no	—
986	C₄²	—	2	1	no	—
987	C₄²	—	4	1	no	—
988	C₄²	—	4	1	no	—
989	C₄²	—	4	1	no	—
990	C₄²	—	4	2	no	—
991	C₄²	—	4	2	no	—
992	C₄²	—	8	1	no	—
993	C₄²	—	8	1	no	—
994	C₄²	—	8	1	no	—
995	C₄²	—	8	1	no	—
996	C₄²	—	8	1	no	—
997	C₄²	—	8	1	no	—
998	C₄²	—	8	1	no	—
999	C₄²	—	8	1	no	—
1000	C₄²	—	8	1	no	—
1001	C₄²	—	8	1	no	—
1002	C₄²	—	8	1	no	—
1003	C₄²	C₂²×Q₈	1	2	yes	—
1004	C₄²	C₂²×Q₈	1	2	yes	—
1005	C₄²	C₂×#41	1	2	yes	—
1006	C₄²	C₂×#41	1	2	yes	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	1	no	—
1009	C₂³	—	2	1	no	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	2	no	—
1013	C₂³	—	2	2	no	—
1014	C₂³	—	2	1	no	—
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	2	no	—
1017	C₂³	—	4	8	no	—
1018	C₂³	—	4	1	no	—
1019	C₂³	—	4	1	no	—
1020	C₂³	—	4	1	no	—
1021	C₂³	—	4	1	no	—
1022	C₂³	—	4	1	no	—
1023	C₂³	—	4	1	no	—
1024	C₂³	—	4	1	no	—
1025	C₂³	—	4	1	no	—
1026	C₂³	—	4	1	no	—
1027	C₂³	—	4	1	no	—
1028	C₂³	—	8	4	no	—
1029	C₂³	—	8	4	no	—
1030	C₂³	—	16	2	no	—
1031	C₂³	—	16	2	no	—
1032	C₂³	—	16	2	no	—
1033	C₂³	—	16	2	no	—
1034	C₂³	C₂×C₂²⋊Q₈	1	2	yes	—
1035	C₂³	C₂³×D₄	1	1	yes	characteristic
1036	Q₈	—	8	4	no	—
1037	Q₈	—	16	2	no	—
1038	Q₈	—	16	2	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	2	no	—
1042	D₄	—	2	2	no	—
1043	D₄	—	2	2	no	—
1044	D₄	—	4	8	no	—
1045	D₄	—	4	1	no	—
1046	D₄	—	4	1	no	—
1047	D₄	#533	1	4	yes	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	1	no	—
1093	C₂×C₄	—	4	1	no	—
1094	C₂×C₄	—	4	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	1	no	—
1097	C₂×C₄	—	4	1	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	1	no	—
1102	C₂×C₄	—	4	1	no	—
1103	C₂×C₄	—	4	1	no	—
1104	C₂×C₄	—	4	1	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	1	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	4	1	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	1	no	—
1112	C₂×C₄	—	4	1	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	—	4	1	no	—
1116	C₂×C₄	—	4	1	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	1	no	—
1121	C₂×C₄	—	4	1	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	4	1	no	—
1126	C₂×C₄	—	4	1	no	—
1127	C₂×C₄	—	8	4	no	—
1128	C₂×C₄	—	8	4	no	—
1129	C₂×C₄	—	8	4	no	—
1130	C₂×C₄	—	8	4	no	—
1131	C₂×C₄	—	8	4	no	—
1132	C₂×C₄	—	8	4	no	—
1133	C₂×C₄	—	16	2	no	—
1134	C₂×C₄	—	16	2	no	—
1135	C₂×C₄	—	16	2	no	—
1136	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1137	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1138	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1139	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1140	C₂×C₄	C₂×C₂²⋊Q₈	1	2	yes	—
1141	C₂×C₄	#576	1	2	yes	—
1142	C₂×C₄	C₂³×Q₈	1	1	yes	characteristic
1143	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1144	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1145	C₂×C₄	C₂²×#41	1	1	yes	characteristic
1146	C₂×C₄	#585	1	1	yes	characteristic
1147	C₂×C₄	#585	1	1	yes	characteristic
1148	C₈	—	2	2	no	—
1149	C₈	—	2	2	no	—
1150	C₈	—	4	1	no	—
1151	C₈	—	4	1	no	—
1152	C₈	—	4	1	no	—
1153	C₈	—	4	1	no	—
1154	C₈	—	4	1	no	—
1155	C₈	—	4	1	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	2	4	no	—
1160	C₂²	—	4	2	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	2	no	—
1171	C₂²	—	4	2	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	8	1	no	—
1174	C₂²	—	8	1	no	—
1175	C₂²	—	8	1	no	—
1176	C₂²	—	8	1	no	—
1177	C₂²	—	16	8	no	—
1178	C₂²	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
1179	C₂²	D₄×#41	1	1	yes	characteristic
1180	C₂²	D₄×#41	1	1	yes	characteristic
1181	C₂²	C₂×#576	1	1	yes	characteristic
1182	C₂²	#3584	1	1	yes	characteristic
1183	C₂²	#3585	1	1	yes	characteristic
1184	C₂²	#3586	1	1	yes	characteristic
1185	C₄	—	2	2	no	—
1186	C₄	—	2	2	no	—
1187	C₄	—	2	2	no	—
1188	C₄	—	2	2	no	—
1189	C₄	—	2	2	no	—
1190	C₄	—	2	2	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	2	no	—
1193	C₄	—	4	1	no	—
1194	C₄	—	4	1	no	—
1195	C₄	—	4	2	no	—
1196	C₄	—	4	2	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	1	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	2	no	—
1202	C₄	—	8	1	no	—
1203	C₄	—	8	1	no	—
1204	C₄	—	8	1	no	—
1205	C₄	—	8	1	no	—
1206	C₄	—	8	1	no	—
1207	C₄	—	8	1	no	—
1208	C₄	—	8	1	no	—
1209	C₄	—	8	1	no	—
1210	C₄	—	8	1	no	—
1211	C₄	—	8	1	no	—
1212	C₄	C₂×#533	1	1	yes	characteristic
1213	C₄	#3458	1	1	yes	characteristic
1214	C₄	#3475	1	1	yes	characteristic
1215	C₄	#3475	1	1	yes	characteristic
1216	C₂	—	4	2	no	—
1217	C₂	—	4	4	no	—
1218	C₂	—	8	2	no	—
1219	C₂	#34739	1	1	yes	characteristic
1220	C₂	#60494	1	1	yes	characteristic
1221	C₂	#60496	1	1	yes	characteristic
1222	C₂	#61489	1	1	yes	characteristic
1223	C₂	#61513	1	1	yes	characteristic
1224	C₂	#61528	1	1	yes	characteristic
1225	C₂	#61539	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂³×D₄	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ #2298 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #35577	C₂	semidirect
3. #26115	C₂	semidirect
4. #26111	C₂	semidirect
5. #26103	C₂	semidirect
6. #26098	C₂	semidirect
7. #26058	C₂	semidirect
8. #26052	C₂	semidirect
9. #26030	C₂	semidirect
10. #26020	C₂	semidirect
11. #26015	C₂	semidirect
12. #26011	C₂	semidirect
13. #25993	C₂	semidirect
14. #25989	C₂	semidirect
19. #23787	C₂	semidirect
20. #23787	C₂	semidirect
21. #23781	C₂	semidirect
22. #23778	C₂	semidirect
23. #21624	C₂	semidirect
24. #21623	C₂	semidirect
25. #21617	C₂	semidirect
26. C₄×#474	C₂	semidirect
27. #21368	C₂	semidirect
28. #21357	C₂	semidirect
29. #20822	C₂	semidirect
45. #2571	C₂²	semidirect
46. #2570	C₂²	semidirect
47. #2551	C₂²	semidirect
48. #2550	C₂²	semidirect
69. #2331	C₂²	semidirect
70. #2331	C₂²	semidirect
76. C₄×C₄⋊Q₈	C₂²	semidirect
77. C₄×#125	C₂²	semidirect
85. #2101	C₂²	semidirect
86. #2101	C₂²	semidirect
87. #2101	C₂²	semidirect
88. #2099	C₂²	semidirect
93. #2088	C₂²	semidirect
94. #2088	C₂²	semidirect
95. #2088	C₂²	semidirect
96. #2087	C₂²	semidirect
97. #2087	C₂²	semidirect
98. #2087	C₂²	semidirect
99. #2087	C₂²	semidirect
100. #2087	C₂²	semidirect
109. #2059	C₂²	semidirect
110. #2058	C₂²	semidirect
111. #2057	C₂²	semidirect
112. #2057	C₂²	semidirect
117. #1989	C₂²	semidirect
118. #1988	C₂²	semidirect
119. #1988	C₂²	semidirect
120. #1987	C₂²	semidirect
121. #1949	C₂²	semidirect
122. #1949	C₂²	semidirect
123. #1949	C₂²	semidirect
124. #1949	C₂²	semidirect
125. #1949	C₂²	semidirect
126. #1947	C₂²	semidirect
127. #1947	C₂²	semidirect
128. #1947	C₂²	semidirect
129. #1940	C₂²	semidirect
130. #1940	C₂²	semidirect
131. #1939	C₂²	semidirect
132. #1939	C₂²	semidirect
133. #1921	C₂²	semidirect
134. #1920	C₂²	semidirect
135. #1920	C₂²	semidirect
136. #1919	C₂²	semidirect
137. #1918	C₂²	semidirect
138. #1918	C₂²	semidirect
139. #1918	C₂²	semidirect
140. #1918	C₂²	semidirect
157. #1847	C₂²	semidirect
158. #1847	C₂²	semidirect
159. #1835	C₂²	semidirect
160. #1834	C₂²	semidirect
177. #1776	C₂²	semidirect
178. #1776	C₂²	semidirect
179. #1776	C₂²	semidirect
180. #1776	C₂²	semidirect
181. C₄×#107	C₂²	semidirect
182. C₄×#107	C₂²	semidirect
183. C₄×#107	C₂²	semidirect
184. C₄×#106	C₂²	semidirect
185. #1768	C₂²	semidirect
186. #1768	C₂²	semidirect
187. #1767	C₂²	semidirect
188. C₄×C₄⋊C₈	C₂²	semidirect
213. #518	Q₈	semidirect

Maximal subgroups

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

subgroup	index
#35577	2
#34261	2
#26115	2
#26111	2
#26103	2
#26098	2
#26058	2
#26052	2
#26030	2
#26020	2
#26015	2
#26011	2
#25993	2
#25989	2
#25974	2
#25966	2
#25960	2
#25950	2
#23787	2
#23781	2
#23778	2
#21624	2
#21623	2
#21617	2
C₄×#474	2
#21368	2
#21357	2
#20822	2
#20744	2
#20416	2