Subgroups — #6392834

Order 512.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#2989	C₂	1	1	yes	maximal, characteristic
2	#34191	C₂	1	1	yes	maximal, characteristic
3	#34127	C₂	1	1	yes	maximal, characteristic
4	#22745	C₂	1	1	yes	maximal, characteristic, complemented
5	#22744	C₂	1	1	yes	maximal, characteristic, complemented
6	#22731	C₂	1	1	yes	maximal, characteristic, complemented
7	#22730	C₂	1	1	yes	maximal, characteristic, complemented
8	#22716	C₂	1	1	yes	maximal, characteristic, complemented
9	#22714	C₂	1	1	yes	maximal, characteristic, complemented
10	#22711	C₂	1	1	yes	maximal, characteristic, complemented
11	#22711	C₂	1	1	yes	maximal, characteristic, complemented
12	#22709	C₂	1	1	yes	maximal, characteristic, complemented
13	#22709	C₂	1	1	yes	maximal, characteristic, complemented
14	#22666	C₂	1	1	yes	maximal, characteristic, complemented
15	#22664	C₂	1	1	yes	maximal, characteristic, complemented
16	#22661	C₂	1	1	yes	maximal, characteristic, complemented
17	#22661	C₂	1	1	yes	maximal, characteristic, complemented
18	#22659	C₂	1	1	yes	maximal, characteristic, complemented
19	#22659	C₂	1	1	yes	maximal, characteristic, complemented
20	#21989	C₂	1	1	yes	maximal, characteristic, complemented
21	#21986	C₂	1	1	yes	maximal, characteristic, complemented
22	#21983	C₂	1	1	yes	maximal, characteristic, complemented
23	#21965	C₂	1	1	yes	maximal, characteristic, complemented
24	#21963	C₂	1	1	yes	maximal, characteristic, complemented
25	#21960	C₂	1	1	yes	maximal, characteristic, complemented
26	#21366	C₂	1	1	yes	maximal, characteristic, complemented
27	#21363	C₂	1	1	yes	maximal, characteristic, complemented
28	#21361	C₂	1	1	yes	maximal, characteristic, complemented
29	#21172	C₂	1	1	yes	maximal, characteristic, complemented
30	#21170	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×#1949	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×C₄×#41	C₂²	1	1	yes	characteristic
33	#2989	C₄	1	16	yes	complemented
34	C₂×#446	C₂²	1	1	yes	characteristic
35	C₂×#446	C₂²	1	1	yes	characteristic
36	C₂×#436	C₂²	1	1	yes	characteristic
37	C₂×#436	C₂²	1	1	yes	characteristic
38	C₂×#435	C₂²	1	1	yes	characteristic
39	C₂×#435	C₂²	1	1	yes	characteristic
40	C₂×#435	C₂²	1	1	yes	characteristic
41	C₂×#435	C₂²	1	1	yes	characteristic
42	C₂×#432	C₂²	1	1	yes	characteristic
43	C₂×#432	C₂²	1	1	yes	characteristic
44	C₂×#431	C₂²	1	1	yes	characteristic
45	C₂×#428	C₂²	1	1	yes	characteristic
46	C₂×#428	C₂²	1	1	yes	characteristic
47	C₂×#428	C₂²	1	1	yes	characteristic
48	C₂×#428	C₂²	1	1	yes	characteristic
49	C₂²×#107	C₂²	1	1	yes	characteristic
50	C₂²×#106	C₂²	1	1	yes	characteristic
51	C₂×#423	C₂²	1	1	yes	characteristic
52	C₂×#423	C₂²	1	1	yes	characteristic
53	C₂²×C₄⋊C₈	C₂²	1	1	yes	characteristic
54	#2355	C₂²	1	1	yes	characteristic
55	#2355	C₂²	1	1	yes	characteristic
56	#2355	C₂²	1	1	yes	characteristic
57	#2355	C₂²	1	1	yes	characteristic
58	#2352	C₂²	1	1	yes	characteristic
59	#2352	C₂²	1	1	yes	characteristic
60	#2352	C₂²	1	1	yes	characteristic
61	#2352	C₂²	1	1	yes	characteristic
62	#2352	C₂²	1	1	yes	characteristic
63	#2352	C₂²	1	1	yes	characteristic
64	#2352	C₂²	1	1	yes	characteristic
65	#2352	C₂²	1	1	yes	characteristic
66	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
67	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	D₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	#2347	—	2	1	no	—
71	#2346	—	2	1	no	—
72	#2343	—	2	1	no	—
73	#2343	—	2	1	no	—
74	#2343	—	2	1	no	—
75	#2343	—	2	1	no	—
76	#2339	—	2	1	no	—
77	#2339	—	2	1	no	—
78	#2320	—	2	1	no	—
79	#2318	—	2	1	no	—
80	#2318	—	2	1	no	—
81	#2295	—	2	1	no	—
82	#2290	—	2	1	no	—
83	#2290	—	2	1	no	—
84	#2285	C₂²	1	1	yes	characteristic
85	#2285	C₂²	1	1	yes	characteristic
86	#2283	C₂²	1	1	yes	characteristic
87	#2283	C₂²	1	1	yes	characteristic
88	#2283	C₂²	1	1	yes	characteristic
89	#2283	C₂²	1	1	yes	characteristic
90	#2283	C₂²	1	1	yes	characteristic
91	C₂×#382	C₂²	1	1	yes	characteristic
92	C₂×#382	C₂²	1	1	yes	characteristic
93	#2275	—	2	1	no	—
94	C₄²×D₄	—	2	1	no	—
95	C₄×#117	C₂²	1	1	yes	characteristic
96	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
97	C₂×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
98	#1949	C₂²	1	1	yes	characteristic
99	#1949	C₂²	1	1	yes	characteristic
100	#1949	C₂²	1	1	yes	characteristic
101	#1949	C₂²	1	1	yes	characteristic
102	#1949	C₂²	1	1	yes	characteristic
103	#1949	C₂²	1	1	yes	characteristic
104	#1949	C₂²	1	1	yes	characteristic
105	#1949	C₂²	1	1	yes	characteristic
106	#1949	C₂²	1	1	yes	characteristic
107	#1949	C₂²	1	1	yes	characteristic
108	#1949	C₂²	1	1	yes	characteristic
109	#1949	C₂²	1	1	yes	characteristic
110	#1949	C₂²	1	1	yes	characteristic
111	#1949	C₂²	1	1	yes	characteristic
112	#1949	C₂²	1	1	yes	characteristic
113	#1949	C₂²	1	1	yes	characteristic
114	#1949	C₂²	1	1	yes	characteristic
115	#1949	C₂²	1	1	yes	characteristic
116	#1949	C₂²	1	1	yes	characteristic
117	#1949	C₂²	1	1	yes	characteristic
118	#1949	C₂²	1	1	yes	characteristic
119	#1949	C₂²	1	1	yes	characteristic
120	#1949	C₂²	1	1	yes	characteristic
121	#1949	C₂²	1	1	yes	characteristic
122	#1949	C₂²	1	1	yes	characteristic
123	#1949	C₂²	1	1	yes	characteristic
124	#1949	C₂²	1	1	yes	characteristic
125	#1949	C₂²	1	1	yes	characteristic
126	#1949	C₂²	1	1	yes	characteristic
127	#1949	C₂²	1	1	yes	characteristic
128	#1949	C₂²	1	1	yes	characteristic
129	#1949	C₂²	1	1	yes	characteristic
130	#1948	C₂²	1	1	yes	characteristic
131	#1948	C₂²	1	1	yes	characteristic
132	#1948	C₂²	1	1	yes	characteristic
133	#1948	C₂²	1	1	yes	characteristic
134	#1947	C₂²	1	1	yes	characteristic
135	#1947	C₂²	1	1	yes	characteristic
136	#1947	C₂²	1	1	yes	characteristic
137	#1947	C₂²	1	1	yes	characteristic
138	#1854	C₂²	1	1	yes	characteristic
139	#1854	C₂²	1	1	yes	characteristic
140	#1854	C₂²	1	1	yes	characteristic
141	#1854	C₂²	1	1	yes	characteristic
142	#1854	C₂²	1	1	yes	characteristic
143	#1854	C₂²	1	1	yes	characteristic
144	#1854	C₂²	1	1	yes	characteristic
145	#1854	C₂²	1	1	yes	characteristic
146	#1853	C₂²	1	1	yes	characteristic
147	#1853	C₂²	1	1	yes	characteristic
148	#1853	C₂²	1	1	yes	characteristic
149	#1853	C₂²	1	1	yes	characteristic
150	#1853	C₂²	1	1	yes	characteristic
151	#1853	C₂²	1	1	yes	characteristic
152	#1853	C₂²	1	1	yes	characteristic
153	#1853	C₂²	1	1	yes	characteristic
154	#1852	C₂²	1	1	yes	characteristic
155	#1852	C₂²	1	1	yes	characteristic
156	#1852	C₂²	1	1	yes	characteristic
157	#1852	C₂²	1	1	yes	characteristic
158	#1852	C₂²	1	1	yes	characteristic
159	#1852	C₂²	1	1	yes	characteristic
160	#1852	C₂²	1	1	yes	characteristic
161	#1852	C₂²	1	1	yes	characteristic
162	#1847	C₂²	1	1	yes	characteristic
163	#1847	C₂²	1	1	yes	characteristic
164	#1847	C₂²	1	1	yes	characteristic
165	#1847	C₂²	1	1	yes	characteristic
166	#1846	C₂²	1	1	yes	characteristic
167	#1846	C₂²	1	1	yes	characteristic
168	#1836	C₂²	1	1	yes	characteristic
169	#1836	C₂²	1	1	yes	characteristic
170	#1836	C₂²	1	1	yes	characteristic
171	#1836	C₂²	1	1	yes	characteristic
172	#1835	C₂²	1	1	yes	characteristic
173	#1835	C₂²	1	1	yes	characteristic
174	#1809	C₂²	1	1	yes	characteristic
175	#1809	C₂²	1	1	yes	characteristic
176	#1809	C₂²	1	1	yes	characteristic
177	#1809	C₂²	1	1	yes	characteristic
178	#1809	C₂²	1	1	yes	characteristic
179	#1809	C₂²	1	1	yes	characteristic
180	#1809	C₂²	1	1	yes	characteristic
181	#1809	C₂²	1	1	yes	characteristic
182	#1808	C₂²	1	1	yes	characteristic
183	#1808	C₂²	1	1	yes	characteristic
184	#1807	C₂²	1	1	yes	characteristic
185	#1807	C₂²	1	1	yes	characteristic
186	#1776	C₂²	1	1	yes	characteristic
187	#1776	C₂²	1	1	yes	characteristic
188	#1776	C₂²	1	1	yes	characteristic
189	#1776	C₂²	1	1	yes	characteristic
190	#1776	C₂²	1	1	yes	characteristic
191	#1776	C₂²	1	1	yes	characteristic
192	#1776	C₂²	1	1	yes	characteristic
193	#1776	C₂²	1	1	yes	characteristic
194	C₄×#107	C₂²	1	1	yes	characteristic
195	C₄×#107	C₂²	1	1	yes	characteristic
196	C₄×#106	C₂²	1	1	yes	characteristic
197	C₄×#106	C₂²	1	1	yes	characteristic
198	#1736	C₂²	1	1	yes	characteristic
199	#1736	C₂²	1	1	yes	characteristic
200	#1736	C₂²	1	1	yes	characteristic
201	#1736	C₂²	1	1	yes	characteristic
202	C₂×#340	C₂²	1	1	yes	characteristic
203	C₂×#340	C₂²	1	1	yes	characteristic
204	C₂²×#41	D₄	1	1	yes	characteristic
205	C₂²×M₁₆	C₂³	1	1	yes	characteristic
206	C₂²×M₁₆	C₂³	1	1	yes	characteristic
207	C₂²×M₁₆	C₂³	1	1	yes	characteristic
208	C₂²×M₁₆	C₂³	1	1	yes	characteristic
209	C₂³×C₈	C₂³	1	1	yes	characteristic
210	C₂³×C₈	C₂³	1	1	yes	characteristic
211	C₄×#41	C₂×C₄	1	8	yes	—
212	C₄×#41	Q₈	1	8	yes	—
213	C₂×C₄×Q₈	D₄	1	1	yes	characteristic
214	C₂×C₄×Q₈	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₄	—	2	1	no	—
216	C₂×C₄×D₄	—	2	1	no	—
217	C₂×C₄×D₄	—	2	1	no	—
218	C₂×C₄×D₄	—	2	1	no	—
219	C₂×C₄×D₄	D₄	1	1	yes	characteristic
220	C₂×C₄×D₄	D₄	1	1	yes	characteristic
221	C₂×C₄×D₄	D₄	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	D₄	1	1	yes	characteristic
227	C₂×#117	D₄	1	1	yes	characteristic
228	C₂×#117	D₄	1	1	yes	characteristic
229	C₂×#117	C₂³	1	1	yes	characteristic
230	C₂×#117	C₂³	1	1	yes	characteristic
231	C₂×#117	C₂³	1	1	yes	characteristic
232	C₂×#117	C₂³	1	1	yes	characteristic
233	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
238	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
241	C₂²×C₄²	—	2	1	no	—
242	C₂²×C₄²	—	2	1	no	—
243	C₂²×C₄²	C₂³	1	1	yes	characteristic
244	C₂²×C₄²	C₂³	1	1	yes	characteristic
245	C₂²×C₄²	C₂³	1	1	yes	characteristic
246	#446	C₂×C₄	1	8	yes	complemented
247	#446	C₂×C₄	1	8	yes	complemented
248	#436	C₂×C₄	1	8	yes	complemented
249	#436	C₂×C₄	1	8	yes	complemented
250	#435	C₂×C₄	1	8	yes	complemented
251	#435	C₂×C₄	1	8	yes	complemented
252	#435	C₂×C₄	1	8	yes	complemented
253	#435	C₂×C₄	1	8	yes	complemented
254	#432	C₂×C₄	1	8	yes	complemented
255	#432	C₂×C₄	1	8	yes	complemented
256	#431	C₂×C₄	1	8	yes	complemented
257	#428	—	4	2	no	—
258	#428	—	4	2	no	—
259	#428	—	4	2	no	—
260	#428	—	4	2	no	—
261	C₂×#107	—	4	2	no	—
262	C₂×#107	C₂³	1	1	yes	characteristic
263	C₂×#107	C₂³	1	1	yes	characteristic
264	C₂×#107	C₂³	1	1	yes	characteristic
265	C₂×#107	C₂³	1	1	yes	characteristic
266	C₂×#107	C₂³	1	1	yes	characteristic
267	C₂×#107	C₂³	1	1	yes	characteristic
268	C₂×#107	C₂³	1	1	yes	characteristic
269	C₂×#107	C₂³	1	1	yes	characteristic
270	C₂×#107	C₂³	1	1	yes	characteristic
271	C₂×#107	C₂³	1	1	yes	characteristic
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×#107	C₂³	1	1	yes	characteristic
277	C₂×#107	C₂³	1	1	yes	characteristic
278	C₂×#106	—	4	2	no	—
279	C₂×#106	C₂³	1	1	yes	characteristic
280	C₂×#106	C₂³	1	1	yes	characteristic
281	C₂×#106	C₂³	1	1	yes	characteristic
282	C₂×#106	C₂³	1	1	yes	characteristic
283	C₂×#106	C₂³	1	1	yes	characteristic
284	C₂×#106	C₂³	1	1	yes	characteristic
285	C₂×#106	C₂³	1	1	yes	characteristic
286	C₂×#106	C₂³	1	1	yes	characteristic
287	C₂×#106	C₂³	1	1	yes	characteristic
288	C₂×#106	C₂³	1	1	yes	characteristic
289	C₂×#106	C₂³	1	1	yes	characteristic
290	C₂×#106	C₂³	1	1	yes	characteristic
291	C₂×#106	C₂³	1	1	yes	characteristic
292	C₂×#106	C₂³	1	1	yes	characteristic
293	C₂×#106	C₂³	1	1	yes	characteristic
294	C₂×#106	C₂³	1	1	yes	characteristic
295	#423	C₂×C₄	1	8	yes	complemented
296	#423	C₂×C₄	1	8	yes	complemented
297	C₂×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
298	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
300	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
301	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
302	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
303	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
304	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
305	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
306	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
307	C₂×C₄⋊C₈	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
312	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
313	C₂×C₂²⋊C₈	C₂³	1	1	yes	characteristic
314	C₂×#97	C₂³	1	1	yes	characteristic
315	C₂×#97	C₂³	1	1	yes	characteristic
316	C₂×#97	C₂³	1	1	yes	characteristic
317	C₂×#97	C₂³	1	1	yes	characteristic
318	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
319	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
320	#391	—	2	1	no	—
321	#391	—	2	1	no	—
322	#391	—	2	1	no	—
323	#391	—	2	1	no	—
324	#389	—	2	1	no	—
325	#389	—	2	1	no	—
326	#389	—	2	1	no	—
327	#389	—	2	1	no	—
328	#388	—	2	1	no	—
329	#388	—	2	1	no	—
330	#388	—	2	1	no	—
331	#388	—	2	1	no	—
332	#388	—	2	1	no	—
333	#388	—	2	1	no	—
334	#388	—	2	1	no	—
335	#388	—	2	1	no	—
336	#387	—	2	1	no	—
337	#387	—	2	1	no	—
338	#387	—	2	1	no	—
339	#387	—	2	1	no	—
340	#387	—	2	1	no	—
341	#387	—	2	1	no	—
342	#387	—	2	1	no	—
343	#387	—	2	1	no	—
344	#387	—	2	1	no	—
345	#387	—	2	1	no	—
346	#387	—	2	1	no	—
347	#387	—	2	1	no	—
348	#387	—	2	1	no	—
349	#387	—	2	1	no	—
350	#387	—	2	1	no	—
351	#387	—	2	1	no	—
352	#386	—	2	1	no	—
353	#386	—	2	1	no	—
354	#386	—	2	1	no	—
355	#386	—	2	1	no	—
356	#386	—	2	1	no	—
357	#386	—	2	1	no	—
358	#386	—	2	1	no	—
359	#386	—	2	1	no	—
360	#385	—	2	1	no	—
361	#385	—	2	1	no	—
362	#385	—	2	1	no	—
363	#385	—	2	1	no	—
364	#385	—	2	1	no	—
365	#385	—	2	1	no	—
366	#385	—	2	1	no	—
367	#385	—	2	1	no	—
368	#384	C₂³	1	1	yes	characteristic
369	#384	C₂³	1	1	yes	characteristic
370	#384	C₂³	1	1	yes	characteristic
371	#384	C₂³	1	1	yes	characteristic
372	#383	—	2	1	no	—
373	#383	—	2	1	no	—
374	#383	—	2	1	no	—
375	#383	—	2	1	no	—
376	#383	—	2	1	no	—
377	#382	—	2	1	no	—
378	#382	—	2	1	no	—
379	#382	—	2	1	no	—
380	#382	—	2	1	no	—
381	#382	—	2	1	no	—
382	#382	C₂³	1	1	yes	characteristic
383	#382	C₂³	1	1	yes	characteristic
384	#382	C₂³	1	1	yes	characteristic
385	#382	C₂³	1	1	yes	characteristic
386	#382	C₂³	1	1	yes	characteristic
387	#382	C₂³	1	1	yes	characteristic
388	#382	C₂³	1	1	yes	characteristic
389	#382	C₂³	1	1	yes	characteristic
390	#382	C₂³	1	1	yes	characteristic
391	#382	C₂³	1	1	yes	characteristic
392	#382	C₂³	1	1	yes	characteristic
393	#382	C₂³	1	1	yes	characteristic
394	#381	—	2	1	no	—
395	#381	—	2	1	no	—
396	#381	—	2	1	no	—
397	#381	—	2	1	no	—
398	#381	—	2	1	no	—
399	#380	—	2	1	no	—
400	#380	—	2	1	no	—
401	#380	—	2	1	no	—
402	#380	C₂³	1	1	yes	characteristic
403	#380	C₂³	1	1	yes	characteristic
404	#380	C₂³	1	1	yes	characteristic
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	#380	C₂³	1	1	yes	characteristic
410	#380	C₂³	1	1	yes	characteristic
411	#380	C₂³	1	1	yes	characteristic
412	#380	C₂³	1	1	yes	characteristic
413	#380	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
418	C₄×C₄⋊C₄	—	2	1	no	—
419	C₄×C₄⋊C₄	—	2	1	no	—
420	C₄×C₄⋊C₄	—	2	1	no	—
421	C₄×C₄⋊C₄	—	2	1	no	—
422	C₄×C₄⋊C₄	—	2	1	no	—
423	C₄×C₄⋊C₄	—	2	1	no	—
424	C₄×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³	1	1	yes	characteristic
432	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
433	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
435	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
436	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂³	1	1	yes	characteristic
441	C₄×C₂²⋊C₄	—	2	1	no	—
442	C₄×C₂²⋊C₄	—	2	1	no	—
443	C₄×C₂²⋊C₄	—	2	1	no	—
444	C₄×C₂²⋊C₄	—	2	1	no	—
445	C₄×C₂²⋊C₄	—	2	1	no	—
446	C₄×C₂²⋊C₄	—	2	1	no	—
447	C₄×C₂²⋊C₄	—	2	1	no	—
448	C₄×C₂²⋊C₄	—	2	1	no	—
449	C₄×C₂²⋊C₄	—	2	1	no	—
450	C₄×C₂²⋊C₄	—	2	1	no	—
451	C₄×C₂²⋊C₄	—	2	1	no	—
452	C₄×C₂²⋊C₄	—	2	1	no	—
453	C₄×C₂²⋊C₄	—	2	1	no	—
454	C₄×C₂²⋊C₄	—	2	1	no	—
455	C₄×C₂²⋊C₄	—	2	1	no	—
456	#376	—	2	1	no	—
457	#376	—	2	1	no	—
458	#376	—	2	1	no	—
459	#376	—	2	1	no	—
460	#376	—	2	1	no	—
461	#376	—	2	1	no	—
462	C₂×#95	—	2	1	no	—
463	C₂×#95	—	2	1	no	—
464	C₂×#95	—	2	1	no	—
465	C₂×#95	—	2	1	no	—
466	C₂×#95	—	2	1	no	—
467	C₂×#95	—	2	1	no	—
468	C₄³	—	2	1	no	—
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	#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	#340	C₂³	1	1	yes	characteristic
489	#340	C₂³	1	1	yes	characteristic
490	#340	C₂³	1	1	yes	characteristic
491	#340	C₂³	1	1	yes	characteristic
492	#340	C₂³	1	1	yes	characteristic
493	#340	C₂³	1	1	yes	characteristic
494	#340	C₂³	1	1	yes	characteristic
495	#340	C₂³	1	1	yes	characteristic
496	#340	C₂³	1	1	yes	characteristic
497	#340	C₂³	1	1	yes	characteristic
498	#340	C₂³	1	1	yes	characteristic
499	#340	C₂³	1	1	yes	characteristic
500	#340	C₂³	1	1	yes	characteristic
501	C₂×#41	—	4	2	no	—
502	C₂×#41	—	4	2	no	—
503	C₂×#41	C₄⋊C₄	1	8	yes	—
504	C₂²×Q₈	C₂×D₄	1	1	yes	characteristic
505	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
506	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
507	C₂²×D₄	C₂×D₄	1	1	yes	characteristic
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	—	2	1	no	—
512	C₂³×C₄	—	2	1	no	—
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	—	2	1	no	—
515	C₂³×C₄	—	2	1	no	—
516	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
517	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
518	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
519	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
520	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
521	C₂³×C₄	C₂×D₄	1	1	yes	characteristic
522	C₂³×C₄	C₂⁴	1	1	yes	characteristic
523	C₂³×C₄	C₂⁴	1	1	yes	characteristic
524	C₂³×C₄	C₂⁴	1	1	yes	characteristic
525	C₂×M₁₆	—	4	1	no	—
526	C₂×M₁₆	—	4	1	no	—
527	C₂×M₁₆	—	4	1	no	—
528	C₂×M₁₆	—	4	1	no	—
529	C₂×M₁₆	—	4	1	no	—
530	C₂×M₁₆	—	4	1	no	—
531	C₂×M₁₆	—	4	1	no	—
532	C₂×M₁₆	—	4	1	no	—
533	C₂×M₁₆	C₂²×C₄	1	4	yes	—
534	C₂×M₁₆	C₂²×C₄	1	4	yes	—
535	C₂×M₁₆	C₂²×C₄	1	4	yes	—
536	C₂×M₁₆	C₂²×C₄	1	4	yes	—
537	C₂²×C₈	—	4	1	no	—
538	C₂²×C₈	—	4	1	no	—
539	C₂²×C₈	—	4	1	no	—
540	C₂²×C₈	—	4	1	no	—
541	C₂²×C₈	C₂²×C₄	1	4	yes	—
542	C₂²×C₈	C₂²×C₄	1	4	yes	—
543	C₂²×C₈	C₂⁴	1	1	yes	characteristic
544	C₂²×C₈	C₂⁴	1	1	yes	characteristic
545	C₂²×C₈	C₂⁴	1	1	yes	characteristic
546	C₂²×C₈	C₂⁴	1	1	yes	characteristic
547	C₂²×C₈	C₂⁴	1	1	yes	characteristic
548	C₂²×C₈	C₂⁴	1	1	yes	characteristic
549	C₂²×C₈	C₂⁴	1	1	yes	characteristic
550	C₂²×C₈	C₂⁴	1	1	yes	characteristic
551	C₄×Q₈	C₄⋊C₄	1	8	yes	—
552	C₄×Q₈	C₂²×C₄	1	4	yes	—
553	C₄×Q₈	C₂×Q₈	1	4	yes	—
554	C₄×D₄	—	4	4	no	—
555	C₄×D₄	—	4	4	no	—
556	C₄×D₄	—	4	4	no	—
557	C₄×D₄	—	4	4	no	—
558	C₄×D₄	C₄⋊C₄	1	8	yes	—
559	C₄×D₄	C₄⋊C₄	1	8	yes	—
560	C₄×D₄	C₄⋊C₄	1	8	yes	—
561	C₄×D₄	C₂²×C₄	1	4	yes	—
562	C₄×D₄	C₂²×C₄	1	4	yes	—
563	C₄×D₄	C₂²×C₄	1	4	yes	—
564	C₄×D₄	C₂×Q₈	1	4	yes	—
565	C₄×D₄	C₂×Q₈	1	4	yes	—
566	C₄×D₄	C₂×Q₈	1	4	yes	—
567	#117	—	2	2	no	—
568	#117	—	2	2	no	—
569	#117	—	4	1	no	—
570	#117	—	4	1	no	—
571	#117	—	4	1	no	—
572	#117	—	4	1	no	—
573	#117	—	4	1	no	—
574	#117	—	4	1	no	—
575	#117	—	8	2	no	—
576	#117	C₄⋊C₄	1	8	yes	—
577	#117	C₄⋊C₄	1	8	yes	—
578	#117	C₄⋊C₄	1	8	yes	—
579	C₂×C₄⋊C₄	—	2	2	no	—
580	C₂×C₄⋊C₄	—	2	2	no	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	—	2	2	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	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	1	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	1	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	1	no	—
597	C₂×C₄⋊C₄	—	2	1	no	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	4	1	no	—
600	C₂×C₄⋊C₄	—	4	1	no	—
601	C₂×C₄⋊C₄	—	4	1	no	—
602	C₂×C₄⋊C₄	—	4	1	no	—
603	C₂×C₄⋊C₄	—	4	1	no	—
604	C₂×C₄⋊C₄	—	4	1	no	—
605	C₂×C₄⋊C₄	—	4	1	no	—
606	C₂×C₄⋊C₄	—	4	1	no	—
607	C₂×C₄⋊C₄	—	4	1	no	—
608	C₂×C₄⋊C₄	—	4	1	no	—
609	C₂×C₄⋊C₄	—	4	1	no	—
610	C₂×C₄⋊C₄	—	4	1	no	—
611	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
627	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	—	2	1	no	—
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	1	no	—
638	C₂×C₂²⋊C₄	—	2	1	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	1	no	—
642	C₂×C₂²⋊C₄	—	2	1	no	—
643	C₂×C₂²⋊C₄	—	2	1	no	—
644	C₂×C₂²⋊C₄	—	2	1	no	—
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
655	C₂×C₄²	—	2	1	no	—
656	C₂×C₄²	—	2	1	no	—
657	C₂×C₄²	—	2	1	no	—
658	C₂×C₄²	—	2	1	no	—
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	—	2	1	no	—
661	C₂×C₄²	—	2	1	no	—
662	C₂×C₄²	—	2	1	no	—
663	C₂×C₄²	—	2	1	no	—
664	C₂×C₄²	—	2	1	no	—
665	C₂×C₄²	—	2	1	no	—
666	C₂×C₄²	—	2	1	no	—
667	C₂×C₄²	—	2	1	no	—
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	—	2	1	no	—
670	C₂×C₄²	—	2	1	no	—
671	C₂×C₄²	—	2	1	no	—
672	C₂×C₄²	—	2	1	no	—
673	C₂×C₄²	—	2	1	no	—
674	C₂×C₄²	—	2	1	no	—
675	C₂×C₄²	—	8	2	no	—
676	C₂×C₄²	—	8	2	no	—
677	C₂×C₄²	C₂²×C₄	1	4	yes	—
678	C₂×C₄²	C₂²×C₄	1	4	yes	—
679	C₂×C₄²	C₂²×C₄	1	4	yes	—
680	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
681	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
682	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
683	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
684	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
685	C₂×C₄²	C₂×D₄	1	1	yes	characteristic
686	C₂×C₄²	C₂×Q₈	1	4	yes	—
687	C₂×C₄²	C₂×Q₈	1	4	yes	—
688	C₂×C₄²	C₂×Q₈	1	4	yes	—
689	C₂×C₄²	C₂⁴	1	1	yes	characteristic
690	C₂×C₄²	C₂⁴	1	1	yes	characteristic
691	C₂×C₄²	C₂⁴	1	1	yes	characteristic
692	C₂×C₄²	C₂⁴	1	1	yes	characteristic
693	#107	—	2	2	no	—
694	#107	—	2	2	no	—
695	#107	—	2	2	no	—
696	#107	—	2	2	no	—
697	#107	—	4	1	no	—
698	#107	—	4	1	no	—
699	#107	—	4	1	no	—
700	#107	—	4	1	no	—
701	#107	—	4	1	no	—
702	#107	—	4	1	no	—
703	#107	—	4	1	no	—
704	#107	—	4	1	no	—
705	#107	—	4	1	no	—
706	#107	—	4	1	no	—
707	#107	—	4	1	no	—
708	#107	—	4	1	no	—
709	#106	—	2	2	no	—
710	#106	—	2	2	no	—
711	#106	—	2	2	no	—
712	#106	—	2	2	no	—
713	#106	—	4	1	no	—
714	#106	—	4	1	no	—
715	#106	—	4	1	no	—
716	#106	—	4	1	no	—
717	#106	—	4	1	no	—
718	#106	—	4	1	no	—
719	#106	—	4	1	no	—
720	#106	—	4	1	no	—
721	#106	—	4	1	no	—
722	#106	—	4	1	no	—
723	#106	—	4	1	no	—
724	#106	—	4	1	no	—
725	C₄⋊C₈	C₂²×C₄	1	4	yes	—
726	C₄⋊C₈	C₂²×C₄	1	4	yes	—
727	C₄⋊C₈	C₂²×C₄	1	4	yes	—
728	C₄⋊C₈	C₂²×C₄	1	4	yes	—
729	C₄⋊C₈	C₂²×C₄	1	4	yes	—
730	C₄⋊C₈	C₂²×C₄	1	4	yes	—
731	C₄⋊C₈	C₂²×C₄	1	4	yes	—
732	C₄⋊C₈	C₂²×C₄	1	4	yes	—
733	C₄⋊C₈	C₂²×C₄	1	4	yes	—
734	C₄⋊C₈	C₂²×C₄	1	4	yes	—
735	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
736	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
737	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
738	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
739	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
740	C₂²⋊C₈	C₂²×C₄	1	4	yes	—
741	#97	C₂²×C₄	1	4	yes	—
742	#97	C₂²×C₄	1	4	yes	—
743	#97	C₂²×C₄	1	4	yes	—
744	#97	C₂²×C₄	1	4	yes	—
745	C₄×C₈	C₂²×C₄	1	4	yes	—
746	C₄×C₈	C₂²×C₄	1	4	yes	—
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	—	2	1	no	—
755	#95	—	2	1	no	—
756	#95	—	2	1	no	—
757	#95	—	2	1	no	—
758	#95	—	2	1	no	—
759	#95	—	2	1	no	—
760	#95	—	2	1	no	—
761	#95	—	2	1	no	—
762	#95	—	2	1	no	—
763	#95	—	2	1	no	—
764	#95	—	2	1	no	—
765	#95	—	2	1	no	—
766	#95	—	2	1	no	—
767	#95	—	2	1	no	—
768	#95	—	2	1	no	—
769	#95	—	2	1	no	—
770	#95	—	2	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	C₂⁴	C₂²×D₄	1	1	yes	characteristic
800	C₂⁴	C₂²×D₄	1	1	yes	characteristic
801	C₂⁴	C₂²×D₄	1	1	yes	characteristic
802	#41	—	4	16	no	—
803	C₂×Q₈	—	4	1	no	—
804	C₂×Q₈	—	4	1	no	—
805	C₂×Q₈	C₂×C₄⋊C₄	1	4	yes	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	4	1	no	—
811	C₂×D₄	—	4	1	no	—
812	C₂×D₄	C₂×C₄⋊C₄	1	4	yes	—
813	C₂×D₄	C₂×C₄⋊C₄	1	4	yes	—
814	C₂×D₄	C₂×C₄⋊C₄	1	4	yes	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	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	—	2	1	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	2	1	no	—
839	C₂²×C₄	—	2	1	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	2	1	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	1	no	—
844	C₂²×C₄	—	2	1	no	—
845	C₂²×C₄	—	4	1	no	—
846	C₂²×C₄	—	4	1	no	—
847	C₂²×C₄	—	4	1	no	—
848	C₂²×C₄	—	4	1	no	—
849	C₂²×C₄	—	4	1	no	—
850	C₂²×C₄	—	4	1	no	—
851	C₂²×C₄	—	4	1	no	—
852	C₂²×C₄	—	4	1	no	—
853	C₂²×C₄	—	4	1	no	—
854	C₂²×C₄	—	4	1	no	—
855	C₂²×C₄	—	4	2	no	—
856	C₂²×C₄	—	4	2	no	—
857	C₂²×C₄	—	4	2	no	—
858	C₂²×C₄	—	4	2	no	—
859	C₂²×C₄	—	4	2	no	—
860	C₂²×C₄	—	4	2	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	8	1	no	—
868	C₂²×C₄	—	8	1	no	—
869	C₂²×C₄	—	8	1	no	—
870	C₂²×C₄	—	8	1	no	—
871	C₂²×C₄	—	8	1	no	—
872	C₂²×C₄	—	8	1	no	—
873	C₂²×C₄	—	8	1	no	—
874	C₂²×C₄	—	8	1	no	—
875	C₂²×C₄	—	8	1	no	—
876	C₂²×C₄	—	8	1	no	—
877	C₂²×C₄	—	8	1	no	—
878	C₂²×C₄	—	8	1	no	—
879	C₂²×C₄	C₂×C₄⋊C₄	1	4	yes	—
880	C₂²×C₄	C₂×C₄⋊C₄	1	4	yes	—
881	C₂²×C₄	C₂×C₄⋊C₄	1	4	yes	—
882	C₂²×C₄	C₂×C₄⋊C₄	1	4	yes	—
883	C₂²×C₄	C₂×C₄⋊C₄	1	4	yes	—
884	C₂²×C₄	C₂×C₄⋊C₄	1	4	yes	—
885	C₂²×C₄	C₂³×C₄	1	2	yes	—
886	C₂²×C₄	C₂³×C₄	1	2	yes	—
887	C₂²×C₄	C₂³×C₄	1	2	yes	—
888	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
889	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
890	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
891	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
892	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
893	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
894	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
895	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
896	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
897	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
898	C₂²×C₄	C₂²×D₄	1	1	yes	characteristic
899	C₂²×C₄	C₂²×Q₈	1	2	yes	—
900	C₂²×C₄	C₂²×Q₈	1	2	yes	—
901	C₂²×C₄	C₂²×Q₈	1	2	yes	—
902	C₂²×C₄	C₂⁵	1	1	yes	characteristic
903	M₁₆	—	4	4	no	—
904	M₁₆	—	4	4	no	—
905	M₁₆	—	4	4	no	—
906	M₁₆	—	4	4	no	—
907	C₂×C₈	—	2	1	no	—
908	C₂×C₈	—	2	1	no	—
909	C₂×C₈	—	2	1	no	—
910	C₂×C₈	—	2	1	no	—
911	C₂×C₈	—	2	1	no	—
912	C₂×C₈	—	2	1	no	—
913	C₂×C₈	—	2	1	no	—
914	C₂×C₈	—	2	1	no	—
915	C₂×C₈	—	2	1	no	—
916	C₂×C₈	—	2	1	no	—
917	C₂×C₈	—	2	1	no	—
918	C₂×C₈	—	2	1	no	—
919	C₂×C₈	—	2	1	no	—
920	C₂×C₈	—	2	1	no	—
921	C₂×C₈	—	2	1	no	—
922	C₂×C₈	—	2	1	no	—
923	C₂×C₈	—	4	4	no	—
924	C₂×C₈	—	4	4	no	—
925	C₂×C₈	C₂³×C₄	1	2	yes	—
926	C₂×C₈	C₂³×C₄	1	2	yes	—
927	C₂×C₈	C₂³×C₄	1	2	yes	—
928	C₂×C₈	C₂³×C₄	1	2	yes	—
929	C₂×C₈	C₂³×C₄	1	2	yes	—
930	C₂×C₈	C₂³×C₄	1	2	yes	—
931	C₂×C₈	C₂³×C₄	1	2	yes	—
932	C₂×C₈	C₂³×C₄	1	2	yes	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	4	2	no	—
964	C₄⋊C₄	—	4	2	no	—
965	C₄⋊C₄	—	4	2	no	—
966	C₄⋊C₄	—	4	2	no	—
967	C₄⋊C₄	—	4	2	no	—
968	C₄⋊C₄	—	4	2	no	—
969	C₄⋊C₄	—	4	2	no	—
970	C₄⋊C₄	—	4	2	no	—
971	C₄⋊C₄	—	8	1	no	—
972	C₄⋊C₄	—	8	1	no	—
973	C₄⋊C₄	—	8	1	no	—
974	C₄⋊C₄	—	8	1	no	—
975	C₄⋊C₄	—	8	1	no	—
976	C₄⋊C₄	—	8	1	no	—
977	C₄⋊C₄	—	8	1	no	—
978	C₄⋊C₄	—	8	1	no	—
979	C₄⋊C₄	C₂×C₄⋊C₄	1	4	yes	—
980	C₄⋊C₄	C₂×C₄⋊C₄	1	4	yes	—
981	C₄⋊C₄	C₂×C₄⋊C₄	1	4	yes	—
982	C₄⋊C₄	C₂×C₄⋊C₄	1	4	yes	—
983	C₄⋊C₄	C₂×C₄⋊C₄	1	4	yes	—
984	C₄⋊C₄	C₂×C₄⋊C₄	1	4	yes	—
985	C₄⋊C₄	H(5,𝔽₂)	1	2	yes	—
986	C₄⋊C₄	2₋¹⁺⁴	1	2	yes	—
987	C₂²⋊C₄	—	4	2	no	—
988	C₂²⋊C₄	—	4	2	no	—
989	C₂²⋊C₄	—	4	2	no	—
990	C₂²⋊C₄	—	4	2	no	—
991	C₂²⋊C₄	—	4	2	no	—
992	C₂²⋊C₄	—	4	2	no	—
993	C₂²⋊C₄	—	4	2	no	—
994	C₂²⋊C₄	—	4	2	no	—
995	C₂²⋊C₄	—	4	2	no	—
996	C₂²⋊C₄	—	4	2	no	—
997	C₂²⋊C₄	—	8	1	no	—
998	C₂²⋊C₄	—	8	1	no	—
999	C₂²⋊C₄	—	8	1	no	—
1000	C₂²⋊C₄	—	8	1	no	—
1001	C₂²⋊C₄	—	8	1	no	—
1002	C₂²⋊C₄	—	8	1	no	—
1003	C₂²⋊C₄	C₂×C₄⋊C₄	1	4	yes	—
1004	C₂²⋊C₄	C₂×C₄⋊C₄	1	4	yes	—
1005	C₂²⋊C₄	C₂×C₄⋊C₄	1	4	yes	—
1006	C₂²⋊C₄	C₂×C₄⋊C₄	1	4	yes	—
1007	C₂²⋊C₄	C₂×C₄⋊C₄	1	4	yes	—
1008	C₂²⋊C₄	C₂×C₄⋊C₄	1	4	yes	—
1009	C₄²	—	4	2	no	—
1010	C₄²	—	4	2	no	—
1011	C₄²	—	4	2	no	—
1012	C₄²	—	4	2	no	—
1013	C₄²	—	4	2	no	—
1014	C₄²	—	4	2	no	—
1015	C₄²	—	4	2	no	—
1016	C₄²	—	4	2	no	—
1017	C₄²	—	4	2	no	—
1018	C₄²	—	4	2	no	—
1019	C₄²	—	8	1	no	—
1020	C₄²	—	8	1	no	—
1021	C₄²	—	8	1	no	—
1022	C₄²	—	8	1	no	—
1023	C₄²	—	8	1	no	—
1024	C₄²	—	8	1	no	—
1025	C₄²	—	8	1	no	—
1026	C₄²	—	8	1	no	—
1027	C₄²	—	8	1	no	—
1028	C₄²	—	8	1	no	—
1029	C₄²	C₂×C₄⋊C₄	1	4	yes	—
1030	C₄²	C₂×C₄⋊C₄	1	4	yes	—
1031	C₄²	C₂×C₄⋊C₄	1	4	yes	—
1032	C₄²	C₂×C₄⋊C₄	1	4	yes	—
1033	C₄²	C₂×C₄⋊C₄	1	4	yes	—
1034	C₄²	C₂×C₄⋊C₄	1	4	yes	—
1035	C₄²	C₂³×C₄	1	2	yes	—
1036	C₄²	C₂³×C₄	1	2	yes	—
1037	C₄²	C₂³×C₄	1	2	yes	—
1038	C₄²	C₂³×C₄	1	2	yes	—
1039	C₄²	C₂²×Q₈	1	2	yes	—
1040	C₄²	C₂²×Q₈	1	2	yes	—
1041	C₄²	C₂²×Q₈	1	2	yes	—
1042	C₄²	C₂²×Q₈	1	2	yes	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	—	2	1	no	—
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	1	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	1	no	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	C₂²×C₄⋊C₄	1	2	yes	—
1060	C₂³	C₂²×C₄⋊C₄	1	2	yes	—
1061	C₂³	C₂²×C₄⋊C₄	1	2	yes	—
1062	C₂³	#575	1	2	yes	—
1063	C₂³	#575	1	2	yes	—
1064	C₂³	C₂³×D₄	1	1	yes	characteristic
1065	Q₈	—	4	4	no	—
1066	D₄	—	2	8	no	—
1067	D₄	—	2	8	no	—
1068	D₄	—	4	4	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	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	8	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	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	4	4	no	—
1107	C₂×C₄	—	4	4	no	—
1108	C₂×C₄	—	4	4	no	—
1109	C₂×C₄	—	4	4	no	—
1110	C₂×C₄	—	4	4	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	—	4	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	1	no	—
1131	C₂×C₄	—	4	1	no	—
1132	C₂×C₄	—	4	1	no	—
1133	C₂×C₄	—	4	1	no	—
1134	C₂×C₄	—	4	1	no	—
1135	C₂×C₄	—	4	1	no	—
1136	C₂×C₄	—	4	1	no	—
1137	C₂×C₄	—	4	1	no	—
1138	C₂×C₄	—	4	1	no	—
1139	C₂×C₄	—	4	1	no	—
1140	C₂×C₄	—	4	1	no	—
1141	C₂×C₄	—	4	1	no	—
1142	C₂×C₄	—	4	1	no	—
1143	C₂×C₄	—	4	1	no	—
1144	C₂×C₄	—	4	1	no	—
1145	C₂×C₄	—	4	1	no	—
1146	C₂×C₄	—	4	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	1	no	—
1152	C₂×C₄	—	4	1	no	—
1153	C₂×C₄	—	4	1	no	—
1154	C₂×C₄	—	4	1	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	4	1	no	—
1157	C₂×C₄	—	8	4	no	—
1158	C₂×C₄	—	8	4	no	—
1159	C₂×C₄	—	8	4	no	—
1160	C₂×C₄	—	8	4	no	—
1161	C₂×C₄	—	16	2	no	—
1162	C₂×C₄	—	16	2	no	—
1163	C₂×C₄	—	16	2	no	—
1164	C₂×C₄	—	16	2	no	—
1165	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
1166	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
1167	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
1168	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
1169	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
1170	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
1171	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
1172	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
1173	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
1174	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
1175	C₂×C₄	C₂²×C₄⋊C₄	1	2	yes	—
1176	C₂×C₄	C₂⁴×C₄	1	1	yes	characteristic
1177	C₂×C₄	C₂³×Q₈	1	1	yes	characteristic
1178	C₂×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1179	C₂×C₄	C₂×2₋¹⁺⁴	1	1	yes	characteristic
1180	C₂×C₄	#585	1	1	yes	characteristic
1181	C₂×C₄	#585	1	1	yes	characteristic
1182	C₈	—	2	2	no	—
1183	C₈	—	2	2	no	—
1184	C₈	—	2	2	no	—
1185	C₈	—	2	2	no	—
1186	C₈	—	2	2	no	—
1187	C₈	—	2	2	no	—
1188	C₈	—	2	2	no	—
1189	C₈	—	2	2	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	2	2	no	—
1194	C₂²	—	2	2	no	—
1195	C₂²	—	2	2	no	—
1196	C₂²	—	2	2	no	—
1197	C₂²	—	2	2	no	—
1198	C₂²	—	2	2	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	4	1	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	#2911	1	4	yes	—
1211	C₂²	C₂³×C₄⋊C₄	1	1	yes	characteristic
1212	C₂²	#3488	1	1	yes	characteristic
1213	C₂²	#3489	1	1	yes	characteristic
1214	C₂²	C₂×#575	1	1	yes	characteristic
1215	C₂²	C₂×#575	1	1	yes	characteristic
1216	C₂²	#3585	1	1	yes	characteristic
1217	C₂²	#3586	1	1	yes	characteristic
1218	C₄	—	2	2	no	—
1219	C₄	—	2	2	no	—
1220	C₄	—	2	2	no	—
1221	C₄	—	2	2	no	—
1222	C₄	—	2	2	no	—
1223	C₄	—	2	2	no	—
1224	C₄	—	2	2	no	—
1225	C₄	—	2	2	no	—
1226	C₄	—	2	2	no	—
1227	C₄	—	2	2	no	—
1228	C₄	—	2	2	no	—
1229	C₄	—	4	2	no	—
1230	C₄	—	4	2	no	—
1231	C₄	—	8	1	no	—
1232	C₄	—	8	1	no	—
1233	C₄	—	8	1	no	—
1234	C₄	—	8	1	no	—
1235	C₄	—	8	1	no	—
1236	C₄	—	8	1	no	—
1237	C₄	—	8	1	no	—
1238	C₄	—	8	1	no	—
1239	C₄	—	8	1	no	—
1240	C₄	—	8	1	no	—
1241	C₄	—	8	1	no	—
1242	C₄	—	8	1	no	—
1243	C₄	—	8	1	no	—
1244	C₄	—	8	1	no	—
1245	C₄	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1246	C₄	C₄×2₋¹⁺⁴	1	1	yes	characteristic
1247	C₄	#3503	1	1	yes	characteristic
1248	C₄	#3504	1	1	yes	characteristic
1249	C₂	—	2	4	no	—
1250	C₂	—	4	2	no	—
1251	C₂	—	4	2	no	—
1252	C₂	#34250	1	1	yes	characteristic
1253	C₂	C₂×#2911	1	1	yes	characteristic
1254	C₂	#60109	1	1	yes	characteristic
1255	C₂	#61971	1	1	yes	characteristic
1256	C₂	#61972	1	1	yes	characteristic
1257	C₂	#62119	1	1	yes	characteristic
1258	C₂	#62120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×D₄
commutator	C₂×C₄	C₂⁴×C₄
Frattini, cosocle	C₂²×C₄	C₂⁵
prime radical	C₂²×#41	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×#41 ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #22745	C₂	semidirect
5. #22744	C₂	semidirect
6. #22731	C₂	semidirect
7. #22730	C₂	semidirect
8. #22716	C₂	semidirect
9. #22714	C₂	semidirect
10. #22711	C₂	semidirect
11. #22711	C₂	semidirect
12. #22709	C₂	semidirect
13. #22709	C₂	semidirect
14. #22666	C₂	semidirect
15. #22664	C₂	semidirect
16. #22661	C₂	semidirect
17. #22661	C₂	semidirect
18. #22659	C₂	semidirect
19. #22659	C₂	semidirect
20. #21989	C₂	semidirect
21. #21986	C₂	semidirect
22. #21983	C₂	semidirect
23. #21965	C₂	semidirect
24. #21963	C₂	semidirect
25. #21960	C₂	semidirect
26. #21366	C₂	semidirect
27. #21363	C₂	semidirect
28. #21361	C₂	semidirect
29. #21172	C₂	semidirect
30. #21170	C₂	semidirect
31. C₂×#1949	C₂	semidirect
33. #2989	C₄	semidirect
246. #446	C₂×C₄	semidirect
247. #446	C₂×C₄	semidirect
248. #436	C₂×C₄	semidirect
249. #436	C₂×C₄	semidirect
250. #435	C₂×C₄	semidirect
251. #435	C₂×C₄	semidirect
252. #435	C₂×C₄	semidirect
253. #435	C₂×C₄	semidirect
254. #432	C₂×C₄	semidirect
255. #432	C₂×C₄	semidirect
256. #431	C₂×C₄	semidirect
295. #423	C₂×C₄	semidirect
296. #423	C₂×C₄	semidirect
297. C₂×C₄⋊C₈	C₂×C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#2989	2
#34191	2
#34127	2
#22745	2
#22744	2
#22731	2
#22730	2
#22716	2
#22714	2
#22711	2
#22709	2
#22666	2
#22664	2
#22661	2
#22659	2
#21989	2
#21986	2
#21983	2
#21965	2
#21963	2
#21960	2
#21366	2
#21363	2
#21361	2
#21172	2
#21170	2
C₂×#1949	2