Subgroups — C₂×#62887 #10586222

Order 512.

33822 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#62887	C₂	1	64	yes	maximal, direct product factor
2	C₂×#3510	C₂	1	2	yes	maximal, complemented
3	C₂×#3500	C₂	1	2	yes	maximal, complemented
4	C₂×#3509	C₂	1	2	yes	maximal, complemented
5	C₂×#3499	C₂	1	2	yes	maximal, complemented
6	C₂×#3487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#3486	C₂	1	2	yes	maximal, complemented
8	C₂×#3485	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#3554	C₂	1	8	yes	maximal, complemented
10	C₂×#3552	C₂	1	8	yes	maximal, complemented
11	C₂×#3562	C₂	1	8	yes	maximal, complemented
12	C₂×#3561	C₂	1	8	yes	maximal, complemented
13	C₂×#3533	C₂	1	8	yes	maximal, complemented
14	C₂×#3535	C₂	1	8	yes	maximal, complemented
15	C₂×#3455	C₂	1	2	yes	maximal, complemented
16	C₂²×#536	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×2₋¹⁺⁴	C₂²	1	2	yes	—
18	C₂²×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
19	C₂²×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
20	C₂³×#41	C₂²	1	1	yes	characteristic
21	C₂⁴×Q₈	C₂²	1	1	yes	characteristic, complemented
22	#3562	C₂²	1	256	yes	complemented
23	#3561	C₂²	1	256	yes	complemented
24	#3554	C₂²	1	256	yes	complemented
25	#3552	C₂²	1	256	yes	complemented
26	#3535	C₂²	1	256	yes	complemented
27	#3533	C₂²	1	256	yes	complemented
28	C₂×#563	C₂²	1	16	yes	complemented
29	C₂×#563	C₂²	1	8	yes	complemented
30	C₂×#562	C₂²	1	16	yes	complemented
31	C₂×#562	C₂²	1	16	yes	complemented
32	C₂×#560	C₂²	1	8	yes	complemented
33	#3510	C₂²	1	64	yes	complemented
34	#3509	C₂²	1	64	yes	complemented
35	#3500	C₂²	1	64	yes	complemented
36	#3499	C₂²	1	64	yes	complemented
37	#3487	C₂²	1	32	yes	complemented
38	#3486	C₂²	1	64	yes	complemented
39	#3485	C₂²	1	32	yes	complemented
40	C₂×#559	C₂²	1	8	yes	complemented
41	C₂×#559	C₂²	1	8	yes	complemented
42	C₂×#557	C₂²	1	8	yes	complemented
43	C₂×#556	C₂²	1	8	yes	complemented
44	C₂×#556	C₂²	1	8	yes	complemented
45	C₂×#554	C₂²	1	16	yes	complemented
46	C₂×#553	C₂²	1	16	yes	complemented
47	C₂×#552	C₂²	1	16	yes	complemented
48	C₂×#551	C₂²	1	16	yes	complemented
49	C₂×#551	C₂²	1	16	yes	complemented
50	C₂×#551	C₂²	1	8	yes	complemented
51	C₂×#550	C₂²	1	8	yes	complemented
52	C₂×D₄×Q₈	C₂²	1	8	yes	complemented
53	C₂×D₄×Q₈	C₂²	1	8	yes	complemented
54	C₂×D₄×Q₈	C₂²	1	8	yes	complemented
55	C₂×#548	C₂²	1	8	yes	complemented
56	C₂×#548	C₂²	1	8	yes	complemented
57	C₂×#548	C₂²	1	8	yes	complemented
58	C₂×#548	C₂²	1	8	yes	complemented
59	C₂×#547	C₂²	1	8	yes	—
60	C₂×#547	C₂²	1	16	yes	complemented
61	C₂×#547	C₂²	1	8	yes	complemented
62	C₂×#546	C₂²	1	16	yes	—
63	C₂×#546	C₂²	1	8	yes	—
64	C₂×#546	C₂²	1	8	yes	complemented
65	C₂×#544	C₂²	1	8	yes	complemented
66	C₂×#543	C₂²	1	8	yes	complemented
67	#3455	C₂²	1	64	yes	complemented
68	C₂×#542	C₂²	1	16	yes	complemented
69	C₂×#542	C₂²	1	16	yes	complemented
70	C₂×#542	C₂²	1	4	yes	complemented
71	C₂×#542	C₂²	1	8	yes	complemented
72	C₂×#542	C₂²	1	4	yes	complemented
73	C₂×#541	C₂²	1	8	yes	complemented
74	C₂×#541	C₂²	1	4	yes	complemented
75	C₂×#540	C₂²	1	16	yes	complemented
76	C₂×#540	C₂²	1	4	yes	complemented
77	C₂×#539	C₂²	1	8	yes	complemented
78	C₂×#539	C₂²	1	16	yes	complemented
79	C₂×#539	C₂²	1	8	yes	complemented
80	C₂×#539	C₂²	1	16	yes	complemented
81	C₂×#538	C₂²	1	8	yes	complemented
82	C₂×#538	C₂²	1	8	yes	complemented
83	C₂×#538	C₂²	1	16	yes	complemented
84	C₂×#536	C₂²	1	2	yes	—
85	C₂×#536	C₂²	1	2	yes	—
86	C₂×#536	C₂²	1	8	yes	complemented
87	C₂×#536	C₂²	1	4	yes	complemented
88	C₂×#536	C₂²	1	8	yes	complemented
89	C₂×#536	C₂²	1	8	yes	complemented
90	C₂×#536	C₂²	1	4	yes	complemented
91	C₂×#536	C₂²	1	4	yes	complemented
92	C₂×#536	C₂²	1	2	yes	complemented
93	C₂×#536	C₂²	1	32	yes	complemented
94	C₂×#535	C₂²	1	2	yes	—
95	C₂×#535	C₂²	1	4	yes	complemented
96	C₂×#535	C₂²	1	4	yes	complemented
97	C₂×#534	C₂²	1	4	yes	—
98	C₂×#533	C₂²	1	8	yes	complemented
99	C₂×#533	C₂²	1	2	yes	complemented
100	C₂×#532	C₂²	1	2	yes	—
101	C₂×#532	C₂²	1	4	yes	complemented
102	C₂×#532	C₂²	1	4	yes	complemented
103	C₂²×C₄⋊Q₈	C₂²	1	4	yes	complemented
104	C₂²×C₄⋊Q₈	C₂²	1	2	yes	complemented
105	C₂×#529	C₂²	1	8	yes	complemented
106	C₂×#529	C₂²	1	8	yes	complemented
107	C₂×#529	C₂²	1	8	yes	complemented
108	C₂²×#124	C₂²	1	2	yes	—
109	C₂²×#124	C₂²	1	4	yes	complemented
110	C₂×#525	C₂²	1	2	yes	—
111	C₂×#525	C₂²	1	4	yes	complemented
112	C₂×#525	C₂²	1	8	yes	complemented
113	C₂×#525	C₂²	1	2	yes	complemented
114	C₂²×#123	C₂²	1	4	yes	—
115	C₂²×#123	C₂²	1	4	yes	complemented
116	C₂²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
117	C₂×#519	C₂²	1	2	yes	complemented
118	C₂×#519	C₂²	1	1	yes	characteristic, complemented
119	C₂×#518	C₂²	1	1	yes	characteristic
120	C₂×C₄×#41	C₂²	1	2	yes	—
121	C₂×C₄×#41	C₂²	1	2	yes	complemented
122	C₂²×#117	C₂²	1	1	yes	characteristic, complemented
123	C₂×2₋¹⁺⁴	—	4	16	no	—
124	C₂×2₋¹⁺⁴	—	4	8	no	—
125	C₂×2₋¹⁺⁴	C₂³	1	32	yes	—
126	C₂×2₋¹⁺⁴	C₂³	1	16	yes	complemented
127	C₂×H(5,𝔽₂)	—	4	8	no	—
128	C₂×H(5,𝔽₂)	C₂³	1	16	yes	—
129	C₂²×#41	—	4	8	no	—
130	C₂²×#41	C₂³	1	2	yes	—
131	C₂²×#41	C₂³	1	2	yes	—
132	C₂²×#41	C₂³	1	8	yes	—
133	C₂²×#41	C₂³	1	16	yes	—
134	C₂²×#41	C₂³	1	4	yes	—
135	C₂²×#41	C₂³	1	8	yes	—
136	C₂²×#41	C₂³	1	4	yes	—
137	C₂²×#41	C₂³	1	4	yes	—
138	C₂²×#41	C₂³	1	4	yes	—
139	C₂²×#41	C₂³	1	4	yes	—
140	C₂³×Q₈	—	4	8	no	—
141	C₂³×Q₈	C₂³	1	2	yes	—
142	C₂³×Q₈	C₂³	1	1	yes	characteristic
143	C₂³×Q₈	C₂³	1	2	yes	—
144	C₂³×Q₈	C₂³	1	8	yes	—
145	C₂³×Q₈	C₂³	1	4	yes	—
146	C₂³×Q₈	C₂³	1	4	yes	—
147	C₂³×Q₈	C₂³	1	4	yes	—
148	C₂³×Q₈	C₂³	1	16	yes	complemented
149	C₂³×D₄	C₂³	1	1	yes	characteristic
150	C₂³×D₄	C₂³	1	2	yes	—
151	C₂³×D₄	C₂³	1	4	yes	—
152	C₂³×D₄	C₂³	1	4	yes	—
153	C₂⁴×C₄	C₂³	1	1	yes	characteristic
154	C₂⁴×C₄	C₂³	1	2	yes	—
155	C₂⁴×C₄	C₂³	1	2	yes	—
156	#563	C₂³	1	128	yes	complemented
157	#563	C₂³	1	256	yes	complemented
158	#562	C₂³	1	256	yes	complemented
159	#562	C₂³	1	256	yes	complemented
160	#560	C₂³	1	128	yes	complemented
161	#559	C₂³	1	128	yes	complemented
162	#559	C₂³	1	128	yes	complemented
163	#557	C₂³	1	128	yes	complemented
164	#556	C₂³	1	128	yes	complemented
165	#556	C₂³	1	128	yes	complemented
166	#554	C₂³	1	256	yes	complemented
167	#553	C₂³	1	256	yes	complemented
168	#552	C₂³	1	256	yes	complemented
169	#551	C₂³	1	256	yes	complemented
170	#551	C₂³	1	128	yes	complemented
171	#551	C₂³	1	256	yes	complemented
172	#550	C₂³	1	128	yes	complemented
173	D₄×Q₈	C₂³	1	128	yes	complemented
174	D₄×Q₈	C₂³	1	128	yes	complemented
175	D₄×Q₈	C₂³	1	128	yes	complemented
176	#548	C₂³	1	128	yes	complemented
177	#548	C₂³	1	128	yes	complemented
178	#548	C₂³	1	128	yes	complemented
179	#548	C₂³	1	128	yes	complemented
180	#547	C₂³	1	128	yes	—
181	#547	C₂³	1	256	yes	complemented
182	#547	C₂³	1	128	yes	complemented
183	#546	C₂³	1	128	yes	—
184	#546	C₂³	1	256	yes	—
185	#546	C₂³	1	128	yes	complemented
186	#544	C₂³	1	128	yes	complemented
187	#543	C₂³	1	128	yes	complemented
188	#542	C₂³	1	64	yes	complemented
189	#542	C₂³	1	64	yes	complemented
190	#542	C₂³	1	128	yes	complemented
191	#542	C₂³	1	256	yes	complemented
192	#542	C₂³	1	256	yes	complemented
193	#541	C₂³	1	64	yes	complemented
194	#541	C₂³	1	128	yes	complemented
195	#540	C₂³	1	64	yes	complemented
196	#540	C₂³	1	256	yes	complemented
197	#539	C₂³	1	128	yes	complemented
198	#539	C₂³	1	256	yes	complemented
199	#539	C₂³	1	256	yes	complemented
200	#539	C₂³	1	128	yes	complemented
201	#538	C₂³	1	128	yes	complemented
202	#538	C₂³	1	256	yes	complemented
203	#538	C₂³	1	128	yes	complemented
204	#536	C₂³	1	32	yes	—
205	#536	C₂³	1	32	yes	—
206	#536	C₂³	1	128	yes	complemented
207	#536	C₂³	1	128	yes	complemented
208	#536	C₂³	1	32	yes	complemented
209	#536	C₂³	1	128	yes	complemented
210	#536	C₂³	1	64	yes	complemented
211	#536	C₂³	1	64	yes	complemented
212	#536	C₂³	1	64	yes	complemented
213	#535	C₂³	1	32	yes	—
214	#535	C₂³	1	64	yes	complemented
215	#535	C₂³	1	64	yes	complemented
216	#534	C₂³	1	64	yes	—
217	#533	C₂³	1	32	yes	complemented
218	#533	C₂³	1	128	yes	complemented
219	#532	C₂³	1	32	yes	—
220	#532	C₂³	1	64	yes	complemented
221	#532	C₂³	1	64	yes	complemented
222	C₂×C₄⋊Q₈	C₂³	1	2	yes	—
223	C₂×C₄⋊Q₈	C₂³	1	4	yes	—
224	C₂×C₄⋊Q₈	C₂³	1	4	yes	—
225	C₂×C₄⋊Q₈	C₂³	1	4	yes	—
226	C₂×C₄⋊Q₈	C₂³	1	8	yes	—
227	C₂×C₄⋊Q₈	C₂³	1	4	yes	—
228	C₂×C₄⋊Q₈	C₂³	1	16	yes	—
229	C₂×C₄⋊Q₈	C₂³	1	4	yes	—
230	C₂×C₄⋊Q₈	C₂³	1	4	yes	—
231	C₂×C₄⋊Q₈	C₂³	1	16	yes	—
232	C₂×C₄⋊Q₈	C₂³	1	32	yes	complemented
233	C₂×C₄⋊Q₈	C₂³	1	64	yes	complemented
234	C₂×#127	C₂³	1	2	yes	—
235	C₂×#127	C₂³	1	4	yes	—
236	C₂×#127	C₂³	1	8	yes	—
237	#529	C₂³	1	128	yes	complemented
238	#529	C₂³	1	128	yes	complemented
239	#529	C₂³	1	128	yes	complemented
240	C₂×#126	C₂³	1	8	yes	—
241	C₂×#126	C₂³	1	16	yes	—
242	C₂×#126	C₂³	1	8	yes	—
243	C₂×#126	C₂³	1	8	yes	—
244	C₂×#126	C₂³	1	8	yes	—
245	C₂×#126	C₂³	1	16	yes	—
246	C₂×#126	C₂³	1	16	yes	—
247	C₂×#126	C₂³	1	16	yes	—
248	C₂×#125	C₂³	1	4	yes	—
249	C₂×#125	C₂³	1	8	yes	—
250	C₂×#125	C₂³	1	8	yes	—
251	C₂×#125	C₂³	1	16	yes	—
252	C₂×#125	C₂³	1	16	yes	—
253	C₂×#125	C₂³	1	16	yes	—
254	C₂×#124	C₂³	1	4	yes	—
255	C₂×#124	C₂³	1	4	yes	—
256	C₂×#124	C₂³	1	8	yes	—
257	C₂×#124	C₂³	1	32	yes	—
258	C₂×#124	C₂³	1	2	yes	—
259	C₂×#124	C₂³	1	4	yes	—
260	C₂×#124	C₂³	1	4	yes	—
261	C₂×#124	C₂³	1	16	yes	—
262	C₂×#124	C₂³	1	8	yes	—
263	C₂×#124	C₂³	1	8	yes	—
264	C₂×#124	C₂³	1	2	yes	—
265	C₂×#124	C₂³	1	4	yes	—
266	C₂×#124	C₂³	1	4	yes	—
267	C₂×#124	C₂³	1	8	yes	—
268	C₂×#124	C₂³	1	16	yes	—
269	C₂×#124	C₂³	1	16	yes	—
270	C₂×#124	C₂³	1	64	yes	complemented
271	#525	C₂³	1	32	yes	—
272	#525	C₂³	1	32	yes	complemented
273	#525	C₂³	1	128	yes	complemented
274	#525	C₂³	1	64	yes	complemented
275	C₂×#123	C₂³	1	4	yes	—
276	C₂×#123	C₂³	1	8	yes	—
277	C₂×#123	C₂³	1	16	yes	—
278	C₂×#123	C₂³	1	64	yes	—
279	C₂×#123	C₂³	1	16	yes	—
280	C₂×#123	C₂³	1	8	yes	—
281	C₂×#123	C₂³	1	8	yes	—
282	C₂×#123	C₂³	1	4	yes	—
283	C₂×#123	C₂³	1	8	yes	—
284	C₂×#123	C₂³	1	8	yes	—
285	C₂×#123	C₂³	1	8	yes	—
286	C₂×#123	C₂³	1	8	yes	—
287	C₂×#123	C₂³	1	8	yes	—
288	C₂×#123	C₂³	1	16	yes	—
289	C₂×#123	C₂³	1	8	yes	—
290	C₂×#123	C₂³	1	8	yes	—
291	C₂×#123	C₂³	1	16	yes	—
292	C₂×#123	C₂³	1	16	yes	—
293	C₂×#123	C₂³	1	16	yes	—
294	C₂×#123	C₂³	1	16	yes	—
295	C₂×#123	C₂³	1	64	yes	complemented
296	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
297	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
298	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
299	C₂×C₂²⋊Q₈	C₂³	1	4	yes	—
300	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
301	C₂×C₂²⋊Q₈	C₂³	1	4	yes	—
302	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
303	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
304	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
305	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
306	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
307	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
308	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
309	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
310	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
311	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
312	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
313	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
314	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
315	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
316	C₂×C₂²⋊Q₈	C₂³	1	64	yes	complemented
317	C₂×#121	C₂³	1	4	yes	—
318	C₂×#121	C₂³	1	8	yes	—
319	C₂×#121	C₂³	1	16	yes	—
320	C₂×#121	C₂³	1	4	yes	—
321	C₂×#121	C₂³	1	8	yes	—
322	C₂×#121	C₂³	1	8	yes	—
323	C₂×#121	C₂³	1	8	yes	—
324	C₂×#121	C₂³	1	8	yes	—
325	C₂×#121	C₂³	1	16	yes	—
326	C₂×#121	C₂³	1	16	yes	—
327	C₂×#121	C₂³	1	16	yes	—
328	C₂×#121	C₂³	1	16	yes	—
329	C₂×#121	C₂³	1	16	yes	—
330	C₂×#120	C₂³	1	4	yes	—
331	C₂×#120	C₂³	1	4	yes	—
332	C₂×#120	C₂³	1	8	yes	—
333	C₂×#120	C₂³	1	8	yes	—
334	C₂×#120	C₂³	1	16	yes	—
335	#519	C₂³	1	32	yes	complemented
336	#519	C₂³	1	16	yes	complemented
337	#518	C₂³	1	16	yes	—
338	C₄×#41	C₂³	1	32	yes	—
339	C₄×#41	C₂³	1	32	yes	complemented
340	C₂×C₄×Q₈	C₂³	1	4	yes	—
341	C₂×C₄×Q₈	C₂³	1	4	yes	—
342	C₂×C₄×Q₈	C₂³	1	8	yes	—
343	C₂×C₄×Q₈	C₂³	1	8	yes	—
344	C₂×C₄×Q₈	C₂³	1	8	yes	—
345	C₂×C₄×Q₈	C₂³	1	8	yes	—
346	C₂×C₄×Q₈	C₂³	1	16	yes	—
347	C₂×C₄×D₄	C₂³	1	8	yes	—
348	C₂×C₄×D₄	C₂³	1	4	yes	—
349	C₂×C₄×D₄	C₂³	1	8	yes	—
350	C₂×C₄×D₄	C₂³	1	4	yes	—
351	C₂×C₄×D₄	C₂³	1	8	yes	—
352	C₂×C₄×D₄	C₂³	1	8	yes	—
353	C₂×C₄×D₄	C₂³	1	8	yes	—
354	C₂×C₄×D₄	C₂³	1	16	yes	—
355	C₂×C₄×D₄	C₂³	1	16	yes	—
356	C₂×C₄×D₄	C₂³	1	16	yes	—
357	C₂×C₄×D₄	C₂³	1	8	yes	—
358	C₂×C₄×D₄	C₂³	1	16	yes	—
359	C₂×C₄×D₄	C₂³	1	16	yes	—
360	C₂×C₄×D₄	C₂³	1	16	yes	—
361	C₂×#117	C₂³	1	4	yes	—
362	C₂×#117	C₂³	1	4	yes	—
363	C₂×#117	C₂³	1	2	yes	—
364	C₂×#117	C₂³	1	4	yes	—
365	C₂×#117	C₂³	1	2	yes	—
366	C₂×#117	C₂³	1	4	yes	—
367	C₂×#117	C₂³	1	4	yes	—
368	C₂×#117	C₂³	1	8	yes	—
369	C₂×#117	C₂³	1	16	yes	—
370	C₂×#117	C₂³	1	16	yes	—
371	C₂×#117	C₂³	1	16	yes	complemented
372	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
373	C₂²×C₄⋊C₄	C₂³	1	8	yes	—
374	C₂²×C₄⋊C₄	C₂³	1	8	yes	—
375	C₂²×C₄⋊C₄	C₂³	1	16	yes	—
376	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
377	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
378	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
379	C₂²×C₂²⋊C₄	C₂³	1	8	yes	—
380	C₂²×C₂²⋊C₄	C₂³	1	16	yes	—
381	C₂²×C₄²	C₂³	1	2	yes	—
382	C₂²×C₄²	C₂³	1	4	yes	—
383	C₂²×C₄²	C₂³	1	4	yes	—
384	C₂⁵	C₂⁴	1	2	yes	—
385	C₂⁵	C₂⁴	1	1	yes	characteristic
386	C₂⁵	C₂⁴	1	4	yes	—
387	2₋¹⁺⁴	—	4	128	no	—
388	2₋¹⁺⁴	—	4	64	no	—
389	H(5,𝔽₂)	—	4	64	no	—
390	C₂×#41	—	2	16	no	—
391	C₂×#41	—	2	16	no	—
392	C₂×#41	—	4	16	no	—
393	C₂×#41	—	4	32	no	—
394	C₂×#41	—	4	32	no	—
395	C₂×#41	—	4	64	no	—
396	C₂×#41	—	4	16	no	—
397	C₂×#41	—	4	16	no	—
398	C₂×#41	—	4	16	no	—
399	C₂×#41	—	4	16	no	—
400	C₂×#41	C₂⁴	1	16	yes	—
401	C₂×#41	C₂⁴	1	16	yes	—
402	C₂×#41	C₂⁴	1	32	yes	—
403	C₂×#41	C₂⁴	1	64	yes	—
404	C₂×#41	C₂⁴	1	32	yes	—
405	C₂×#41	C₂⁴	1	32	yes	—
406	C₂×#41	C₂⁴	1	32	yes	—
407	C₂×#41	C₂⁴	1	32	yes	—
408	C₂×#41	C₂⁴	1	64	yes	—
409	C₂²×Q₈	—	2	16	no	—
410	C₂²×Q₈	—	2	8	no	—
411	C₂²×Q₈	—	4	8	no	—
412	C₂²×Q₈	—	4	32	no	—
413	C₂²×Q₈	—	4	64	no	—
414	C₂²×Q₈	—	4	16	no	—
415	C₂²×Q₈	—	4	16	no	—
416	C₂²×Q₈	—	4	16	no	—
417	C₂²×Q₈	C₂⁴	1	4	yes	—
418	C₂²×Q₈	C₂⁴	1	4	yes	—
419	C₂²×Q₈	C₂⁴	1	2	yes	—
420	C₂²×Q₈	C₂⁴	1	4	yes	—
421	C₂²×Q₈	C₂⁴	1	2	yes	—
422	C₂²×Q₈	C₂⁴	1	16	yes	—
423	C₂²×Q₈	C₂⁴	1	8	yes	—
424	C₂²×Q₈	C₂⁴	1	8	yes	—
425	C₂²×Q₈	C₂⁴	1	8	yes	—
426	C₂²×Q₈	C₂⁴	1	8	yes	—
427	C₂²×Q₈	C₂⁴	1	4	yes	—
428	C₂²×Q₈	C₂⁴	1	16	yes	—
429	C₂²×Q₈	C₂⁴	1	32	yes	—
430	C₂²×Q₈	C₂⁴	1	32	yes	—
431	C₂²×Q₈	C₂⁴	1	32	yes	—
432	C₂²×Q₈	C₂⁴	1	64	yes	—
433	C₂²×D₄	—	2	8	no	—
434	C₂²×D₄	—	4	16	no	—
435	C₂²×D₄	—	4	8	no	—
436	C₂²×D₄	—	4	16	no	—
437	C₂²×D₄	C₂⁴	1	4	yes	—
438	C₂²×D₄	C₂⁴	1	4	yes	—
439	C₂²×D₄	C₂⁴	1	4	yes	—
440	C₂²×D₄	C₂⁴	1	2	yes	—
441	C₂²×D₄	C₂⁴	1	2	yes	—
442	C₂²×D₄	C₂⁴	1	8	yes	—
443	C₂²×D₄	C₂⁴	1	8	yes	—
444	C₂²×D₄	C₂⁴	1	8	yes	—
445	C₂²×D₄	C₂⁴	1	16	yes	—
446	C₂²×D₄	C₂⁴	1	8	yes	—
447	C₂²×D₄	C₂⁴	1	8	yes	—
448	C₂²×D₄	C₂⁴	1	8	yes	—
449	C₂²×D₄	C₂⁴	1	8	yes	—
450	C₂²×D₄	C₂⁴	1	4	yes	—
451	C₂²×D₄	C₂⁴	1	32	yes	—
452	C₂²×D₄	C₂⁴	1	16	yes	—
453	C₂²×D₄	C₂⁴	1	32	yes	—
454	C₂³×C₄	—	2	8	no	—
455	C₂³×C₄	—	4	8	no	—
456	C₂³×C₄	—	4	8	no	—
457	C₂³×C₄	C₂⁴	1	4	yes	—
458	C₂³×C₄	C₂⁴	1	2	yes	—
459	C₂³×C₄	C₂⁴	1	1	yes	characteristic
460	C₂³×C₄	C₂⁴	1	4	yes	—
461	C₂³×C₄	C₂⁴	1	4	yes	—
462	C₂³×C₄	C₂⁴	1	4	yes	—
463	C₂³×C₄	C₂⁴	1	8	yes	—
464	C₂³×C₄	C₂⁴	1	4	yes	—
465	C₂³×C₄	C₂⁴	1	8	yes	—
466	C₂³×C₄	C₂⁴	1	8	yes	—
467	C₂³×C₄	C₂⁴	1	8	yes	—
468	C₂³×C₄	C₂⁴	1	8	yes	—
469	C₂³×C₄	C₂⁴	1	8	yes	—
470	C₂³×C₄	C₂⁴	1	8	yes	—
471	C₂³×C₄	C₂⁴	1	8	yes	—
472	C₂³×C₄	C₂⁴	1	4	yes	—
473	C₂³×C₄	C₂⁴	1	8	yes	—
474	C₂³×C₄	C₂⁴	1	16	yes	—
475	C₂³×C₄	C₂⁴	1	16	yes	—
476	C₂³×C₄	C₂⁴	1	1	yes	characteristic
477	C₄⋊Q₈	C₂⁴	1	16	yes	—
478	C₄⋊Q₈	C₂⁴	1	32	yes	—
479	C₄⋊Q₈	C₂⁴	1	32	yes	—
480	C₄⋊Q₈	C₂⁴	1	32	yes	—
481	C₄⋊Q₈	C₂⁴	1	64	yes	—
482	C₄⋊Q₈	C₂⁴	1	32	yes	—
483	C₄⋊Q₈	C₂⁴	1	128	yes	—
484	C₄⋊Q₈	C₂⁴	1	32	yes	—
485	C₄⋊Q₈	C₂⁴	1	32	yes	—
486	C₄⋊Q₈	C₂⁴	1	128	yes	—
487	#127	C₂⁴	1	16	yes	—
488	#127	C₂⁴	1	32	yes	—
489	#127	C₂⁴	1	64	yes	—
490	#126	C₂⁴	1	64	yes	—
491	#126	C₂⁴	1	128	yes	—
492	#126	C₂⁴	1	64	yes	—
493	#126	C₂⁴	1	64	yes	—
494	#126	C₂⁴	1	64	yes	—
495	#126	C₂⁴	1	128	yes	—
496	#126	C₂⁴	1	128	yes	—
497	#126	C₂⁴	1	128	yes	—
498	#125	C₂⁴	1	32	yes	—
499	#125	C₂⁴	1	64	yes	—
500	#125	C₂⁴	1	64	yes	—
501	#125	C₂⁴	1	128	yes	—
502	#125	C₂⁴	1	128	yes	—
503	#125	C₂⁴	1	128	yes	—
504	#124	C₂⁴	1	32	yes	—
505	#124	C₂⁴	1	32	yes	—
506	#124	C₂⁴	1	64	yes	—
507	#124	C₂⁴	1	16	yes	—
508	#124	C₂⁴	1	32	yes	—
509	#124	C₂⁴	1	32	yes	—
510	#124	C₂⁴	1	128	yes	—
511	#124	C₂⁴	1	64	yes	—
512	#124	C₂⁴	1	64	yes	—
513	#124	C₂⁴	1	16	yes	—
514	#124	C₂⁴	1	32	yes	—
515	#124	C₂⁴	1	32	yes	—
516	#124	C₂⁴	1	64	yes	—
517	#124	C₂⁴	1	128	yes	—
518	#124	C₂⁴	1	128	yes	—
519	#123	C₂⁴	1	32	yes	—
520	#123	C₂⁴	1	64	yes	—
521	#123	C₂⁴	1	128	yes	—
522	#123	C₂⁴	1	128	yes	—
523	#123	C₂⁴	1	64	yes	—
524	#123	C₂⁴	1	64	yes	—
525	#123	C₂⁴	1	32	yes	—
526	#123	C₂⁴	1	64	yes	—
527	#123	C₂⁴	1	64	yes	—
528	#123	C₂⁴	1	64	yes	—
529	#123	C₂⁴	1	64	yes	—
530	#123	C₂⁴	1	64	yes	—
531	#123	C₂⁴	1	128	yes	—
532	#123	C₂⁴	1	64	yes	—
533	#123	C₂⁴	1	64	yes	—
534	#123	C₂⁴	1	128	yes	—
535	#123	C₂⁴	1	128	yes	—
536	#123	C₂⁴	1	128	yes	—
537	#123	C₂⁴	1	128	yes	—
538	C₂²⋊Q₈	C₂⁴	1	64	yes	—
539	C₂²⋊Q₈	C₂⁴	1	64	yes	—
540	C₂²⋊Q₈	C₂⁴	1	128	yes	—
541	C₂²⋊Q₈	C₂⁴	1	32	yes	—
542	C₂²⋊Q₈	C₂⁴	1	128	yes	—
543	C₂²⋊Q₈	C₂⁴	1	32	yes	—
544	C₂²⋊Q₈	C₂⁴	1	64	yes	—
545	C₂²⋊Q₈	C₂⁴	1	64	yes	—
546	C₂²⋊Q₈	C₂⁴	1	64	yes	—
547	C₂²⋊Q₈	C₂⁴	1	64	yes	—
548	C₂²⋊Q₈	C₂⁴	1	64	yes	—
549	C₂²⋊Q₈	C₂⁴	1	64	yes	—
550	C₂²⋊Q₈	C₂⁴	1	64	yes	—
551	C₂²⋊Q₈	C₂⁴	1	128	yes	—
552	C₂²⋊Q₈	C₂⁴	1	128	yes	—
553	C₂²⋊Q₈	C₂⁴	1	128	yes	—
554	C₂²⋊Q₈	C₂⁴	1	128	yes	—
555	C₂²⋊Q₈	C₂⁴	1	128	yes	—
556	C₂²⋊Q₈	C₂⁴	1	128	yes	—
557	C₂²⋊Q₈	C₂⁴	1	128	yes	—
558	#121	C₂⁴	1	32	yes	—
559	#121	C₂⁴	1	64	yes	—
560	#121	C₂⁴	1	128	yes	—
561	#121	C₂⁴	1	32	yes	—
562	#121	C₂⁴	1	64	yes	—
563	#121	C₂⁴	1	64	yes	—
564	#121	C₂⁴	1	64	yes	—
565	#121	C₂⁴	1	64	yes	—
566	#121	C₂⁴	1	128	yes	—
567	#121	C₂⁴	1	128	yes	—
568	#121	C₂⁴	1	128	yes	—
569	#121	C₂⁴	1	128	yes	—
570	#121	C₂⁴	1	128	yes	—
571	#120	C₂⁴	1	32	yes	—
572	#120	C₂⁴	1	32	yes	—
573	#120	C₂⁴	1	64	yes	—
574	#120	C₂⁴	1	64	yes	—
575	#120	C₂⁴	1	128	yes	—
576	C₄×Q₈	C₂⁴	1	32	yes	—
577	C₄×Q₈	C₂⁴	1	32	yes	—
578	C₄×Q₈	C₂⁴	1	64	yes	—
579	C₄×Q₈	C₂⁴	1	64	yes	—
580	C₄×Q₈	C₂⁴	1	64	yes	—
581	C₄×Q₈	C₂⁴	1	64	yes	—
582	C₄×Q₈	C₂⁴	1	128	yes	—
583	C₄×D₄	C₂⁴	1	64	yes	—
584	C₄×D₄	C₂⁴	1	32	yes	—
585	C₄×D₄	C₂⁴	1	64	yes	—
586	C₄×D₄	C₂⁴	1	32	yes	—
587	C₄×D₄	C₂⁴	1	64	yes	—
588	C₄×D₄	C₂⁴	1	64	yes	—
589	C₄×D₄	C₂⁴	1	64	yes	—
590	C₄×D₄	C₂⁴	1	128	yes	—
591	C₄×D₄	C₂⁴	1	128	yes	—
592	C₄×D₄	C₂⁴	1	128	yes	—
593	C₄×D₄	C₂⁴	1	64	yes	—
594	C₄×D₄	C₂⁴	1	128	yes	—
595	C₄×D₄	C₂⁴	1	128	yes	—
596	C₄×D₄	C₂⁴	1	128	yes	—
597	#117	C₂⁴	1	32	yes	—
598	#117	C₂⁴	1	32	yes	—
599	#117	C₂⁴	1	16	yes	—
600	#117	C₂⁴	1	32	yes	—
601	#117	C₂⁴	1	16	yes	—
602	#117	C₂⁴	1	32	yes	—
603	#117	C₂⁴	1	32	yes	—
604	#117	C₂⁴	1	64	yes	—
605	#117	C₂⁴	1	128	yes	—
606	#117	C₂⁴	1	128	yes	—
607	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
608	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
609	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
610	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
611	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
612	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
613	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
614	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
615	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
616	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
617	C₂×C₄⋊C₄	C₂⁴	1	64	yes	—
618	C₂×C₄⋊C₄	C₂⁴	1	64	yes	—
619	C₂×C₄⋊C₄	C₂⁴	1	128	yes	—
620	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
621	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
622	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
623	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
624	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
625	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
626	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
627	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
628	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
629	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
630	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
631	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
632	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
633	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
634	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
635	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
637	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
639	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
640	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
641	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
642	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
643	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
644	C₂×C₂²⋊C₄	C₂⁴	1	32	yes	—
645	C₂×C₂²⋊C₄	C₂⁴	1	64	yes	—
646	C₂×C₂²⋊C₄	C₂⁴	1	64	yes	—
647	C₂×C₂²⋊C₄	C₂⁴	1	128	yes	—
648	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
649	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
650	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
651	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
652	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
653	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
654	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
655	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
656	C₂×C₄²	C₂⁴	1	2	yes	—
657	C₂×C₄²	C₂⁴	1	2	yes	—
658	C₂×C₄²	C₂⁴	1	16	yes	—
659	C₂×C₄²	C₂⁴	1	8	yes	—
660	C₂×C₄²	C₂⁴	1	4	yes	—
661	C₂×C₄²	C₂⁴	1	4	yes	—
662	C₂×C₄²	C₂⁴	1	8	yes	—
663	C₂×C₄²	C₂⁴	1	4	yes	—
664	C₂×C₄²	C₂⁴	1	16	yes	—
665	C₂×C₄²	C₂⁴	1	8	yes	—
666	C₂×C₄²	C₂⁴	1	32	yes	—
667	C₂×C₄²	C₂⁴	1	32	yes	—
668	C₂⁴	—	2	4	no	—
669	C₂⁴	—	2	8	no	—
670	C₂⁴	—	4	4	no	—
671	C₂⁴	—	4	8	no	—
672	C₂⁴	—	4	8	no	—
673	C₂⁴	—	4	16	no	—
674	C₂⁴	C₂⁵	1	4	yes	—
675	C₂⁴	C₂⁵	1	4	yes	—
676	C₂⁴	C₂⁵	1	2	yes	—
677	C₂⁴	C₂⁵	1	4	yes	—
678	C₂⁴	C₂⁵	1	1	yes	characteristic
679	C₂⁴	C₂⁵	1	8	yes	—
680	C₂⁴	C₂⁵	1	4	yes	—
681	C₂⁴	C₂⁵	1	16	yes	—
682	#41	—	2	64	no	—
683	#41	—	2	64	no	—
684	#41	—	4	64	no	—
685	#41	—	4	128	no	—
686	#41	—	4	128	no	—
687	#41	—	4	64	no	—
688	#41	—	4	64	no	—
689	#41	—	4	64	no	—
690	#41	—	4	64	no	—
691	C₂×Q₈	—	2	16	no	—
692	C₂×Q₈	—	2	16	no	—
693	C₂×Q₈	—	2	64	no	—
694	C₂×Q₈	—	2	16	no	—
695	C₂×Q₈	—	2	32	no	—
696	C₂×Q₈	—	2	8	no	—
697	C₂×Q₈	—	2	8	no	—
698	C₂×Q₈	—	4	16	no	—
699	C₂×Q₈	—	4	32	no	—
700	C₂×Q₈	—	4	16	no	—
701	C₂×Q₈	—	4	8	no	—
702	C₂×Q₈	—	4	16	no	—
703	C₂×Q₈	—	4	128	no	—
704	C₂×Q₈	—	4	64	no	—
705	C₂×Q₈	—	4	64	no	—
706	C₂×Q₈	—	4	64	no	—
707	C₂×Q₈	C₂⁵	1	16	yes	—
708	C₂×Q₈	C₂⁵	1	16	yes	—
709	C₂×Q₈	C₂⁵	1	8	yes	—
710	C₂×Q₈	C₂⁵	1	16	yes	—
711	C₂×Q₈	C₂⁵	1	8	yes	—
712	C₂×Q₈	C₂⁵	1	32	yes	—
713	C₂×Q₈	C₂⁵	1	32	yes	—
714	C₂×Q₈	C₂⁵	1	32	yes	—
715	C₂×Q₈	C₂⁵	1	16	yes	—
716	C₂×D₄	—	2	16	no	—
717	C₂×D₄	—	2	16	no	—
718	C₂×D₄	—	2	16	no	—
719	C₂×D₄	—	2	32	no	—
720	C₂×D₄	—	2	8	no	—
721	C₂×D₄	—	2	8	no	—
722	C₂×D₄	—	4	64	no	—
723	C₂×D₄	—	4	16	no	—
724	C₂×D₄	—	4	16	no	—
725	C₂×D₄	—	4	32	no	—
726	C₂×D₄	—	4	16	no	—
727	C₂×D₄	—	4	16	no	—
728	C₂×D₄	—	4	32	no	—
729	C₂×D₄	—	4	16	no	—
730	C₂×D₄	—	4	8	no	—
731	C₂×D₄	—	4	16	no	—
732	C₂×D₄	—	4	64	no	—
733	C₂×D₄	C₂⁵	1	16	yes	—
734	C₂×D₄	C₂⁵	1	16	yes	—
735	C₂×D₄	C₂⁵	1	16	yes	—
736	C₂×D₄	C₂⁵	1	8	yes	—
737	C₂×D₄	C₂⁵	1	8	yes	—
738	C₂×D₄	C₂⁵	1	32	yes	—
739	C₂×D₄	C₂⁵	1	32	yes	—
740	C₂×D₄	C₂⁵	1	64	yes	—
741	C₂×D₄	C₂⁵	1	32	yes	—
742	C₂×D₄	C₂⁵	1	32	yes	—
743	C₂×D₄	C₂⁵	1	32	yes	—
744	C₂×D₄	C₂⁵	1	32	yes	—
745	C₂×D₄	C₂⁵	1	16	yes	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	—	2	8	no	—
748	C₂²×C₄	—	2	16	no	—
749	C₂²×C₄	—	2	16	no	—
750	C₂²×C₄	—	2	32	no	—
751	C₂²×C₄	—	2	16	no	—
752	C₂²×C₄	—	2	16	no	—
753	C₂²×C₄	—	4	16	no	—
754	C₂²×C₄	—	4	32	no	—
755	C₂²×C₄	—	4	16	no	—
756	C₂²×C₄	—	4	32	no	—
757	C₂²×C₄	—	4	16	no	—
758	C₂²×C₄	—	4	8	no	—
759	C₂²×C₄	—	4	16	no	—
760	C₂²×C₄	—	4	16	no	—
761	C₂²×C₄	—	4	8	no	—
762	C₂²×C₄	—	4	16	no	—
763	C₂²×C₄	—	4	16	no	—
764	C₂²×C₄	—	4	16	no	—
765	C₂²×C₄	H(5,𝔽₂)	1	8	yes	—
766	C₂²×C₄	C₂⁵	1	16	yes	—
767	C₂²×C₄	C₂⁵	1	16	yes	—
768	C₂²×C₄	C₂⁵	1	16	yes	—
769	C₂²×C₄	C₂⁵	1	8	yes	—
770	C₂²×C₄	C₂⁵	1	4	yes	—
771	C₂²×C₄	C₂⁵	1	16	yes	—
772	C₂²×C₄	C₂⁵	1	8	yes	—
773	C₂²×C₄	C₂⁵	1	4	yes	—
774	C₂²×C₄	C₂⁵	1	8	yes	—
775	C₂²×C₄	C₂⁵	1	4	yes	—
776	C₂²×C₄	C₂⁵	1	4	yes	—
777	C₂²×C₄	C₂⁵	1	8	yes	—
778	C₂²×C₄	C₂⁵	1	4	yes	—
779	C₂²×C₄	C₂⁵	1	4	yes	—
780	C₂²×C₄	C₂⁵	1	2	yes	—
781	C₂²×C₄	C₂⁵	1	16	yes	—
782	C₂²×C₄	C₂⁵	1	32	yes	—
783	C₂²×C₄	C₂⁵	1	32	yes	—
784	C₂²×C₄	C₂⁵	1	32	yes	—
785	C₂²×C₄	C₂⁵	1	32	yes	—
786	C₂²×C₄	C₂⁵	1	32	yes	—
787	C₂²×C₄	C₂⁵	1	32	yes	—
788	C₂²×C₄	C₂⁵	1	32	yes	—
789	C₂²×C₄	C₂⁵	1	16	yes	—
790	C₂²×C₄	C₂⁵	1	32	yes	—
791	C₂²×C₄	C₂⁵	1	4	yes	—
792	C₂²×C₄	C₂⁵	1	2	yes	—
793	C₄⋊C₄	C₂⁵	1	64	yes	—
794	C₄⋊C₄	C₂⁵	1	32	yes	—
795	C₄⋊C₄	C₂⁵	1	32	yes	—
796	C₄⋊C₄	C₂⁵	1	64	yes	—
797	C₄⋊C₄	C₂⁵	1	8	yes	—
798	C₄⋊C₄	C₂⁵	1	16	yes	—
799	C₄⋊C₄	C₂⁵	1	8	yes	—
800	C₄⋊C₄	C₂⁵	1	64	yes	—
801	C₄⋊C₄	C₂⁵	1	64	yes	—
802	C₄⋊C₄	C₂⁵	1	32	yes	—
803	C₄⋊C₄	C₂⁵	1	32	yes	—
804	C₄⋊C₄	C₂⁵	1	16	yes	—
805	C₄⋊C₄	C₂⁵	1	16	yes	—
806	C₄⋊C₄	C₂⁵	1	32	yes	—
807	C₄⋊C₄	C₂⁵	1	32	yes	—
808	C₄⋊C₄	C₂⁵	1	32	yes	—
809	C₄⋊C₄	C₂⁵	1	64	yes	—
810	C₄⋊C₄	C₂⁵	1	32	yes	—
811	C₄⋊C₄	C₂⁵	1	64	yes	—
812	C₄⋊C₄	C₂⁵	1	32	yes	—
813	C₂²⋊C₄	C₂⁵	1	16	yes	—
814	C₂²⋊C₄	C₂⁵	1	32	yes	—
815	C₂²⋊C₄	C₂⁵	1	64	yes	—
816	C₂²⋊C₄	C₂⁵	1	32	yes	—
817	C₂²⋊C₄	C₂⁵	1	8	yes	—
818	C₂²⋊C₄	C₂⁵	1	16	yes	—
819	C₂²⋊C₄	C₂⁵	1	8	yes	—
820	C₂²⋊C₄	C₂⁵	1	64	yes	—
821	C₂²⋊C₄	C₂⁵	1	64	yes	—
822	C₂²⋊C₄	C₂⁵	1	64	yes	—
823	C₂²⋊C₄	C₂⁵	1	64	yes	—
824	C₂²⋊C₄	C₂⁵	1	32	yes	—
825	C₂²⋊C₄	C₂⁵	1	16	yes	—
826	C₂²⋊C₄	C₂⁵	1	32	yes	—
827	C₂²⋊C₄	C₂⁵	1	32	yes	—
828	C₂²⋊C₄	C₂⁵	1	32	yes	—
829	C₂²⋊C₄	C₂⁵	1	32	yes	—
830	C₂²⋊C₄	C₂⁵	1	32	yes	—
831	C₂²⋊C₄	C₂⁵	1	32	yes	—
832	C₂²⋊C₄	C₂⁵	1	64	yes	—
833	C₄²	C₂⁵	1	8	yes	—
834	C₄²	C₂⁵	1	8	yes	—
835	C₄²	C₂⁵	1	16	yes	—
836	C₄²	C₂⁵	1	16	yes	—
837	C₄²	C₂⁵	1	32	yes	—
838	C₄²	C₂⁵	1	16	yes	—
839	C₄²	C₂⁵	1	32	yes	—
840	C₄²	C₂⁵	1	64	yes	—
841	C₄²	C₂⁵	1	32	yes	—
842	C₂³	—	2	4	no	—
843	C₂³	—	2	8	no	—
844	C₂³	—	2	4	no	—
845	C₂³	—	2	8	no	—
846	C₂³	—	2	8	no	—
847	C₂³	—	2	8	no	—
848	C₂³	—	2	16	no	—
849	C₂³	—	2	16	no	—
850	C₂³	—	2	16	no	—
851	C₂³	—	2	8	no	—
852	C₂³	—	2	16	no	—
853	C₂³	—	4	8	no	—
854	C₂³	—	4	16	no	—
855	C₂³	—	4	16	no	—
856	C₂³	—	4	32	no	—
857	C₂³	—	4	16	no	—
858	C₂³	—	8	16	no	—
859	C₂³	—	16	16	no	—
860	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
861	C₂³	C₂⁶	1	8	yes	—
862	C₂³	C₂⁶	1	8	yes	—
863	C₂³	C₂⁶	1	4	yes	—
864	C₂³	C₂⁶	1	8	yes	—
865	C₂³	C₂⁶	1	2	yes	—
866	C₂³	C₂⁶	1	1	yes	characteristic
867	Q₈	—	2	32	no	—
868	Q₈	—	2	32	no	—
869	Q₈	—	2	32	no	—
870	Q₈	—	2	16	no	—
871	Q₈	—	2	16	no	—
872	Q₈	—	4	32	no	—
873	Q₈	—	4	32	no	—
874	Q₈	—	4	16	no	—
875	Q₈	—	4	32	no	—
876	D₄	—	2	32	no	—
877	D₄	—	2	32	no	—
878	D₄	—	2	32	no	—
879	D₄	—	2	16	no	—
880	D₄	—	2	16	no	—
881	D₄	—	4	32	no	—
882	D₄	—	4	32	no	—
883	D₄	—	4	32	no	—
884	D₄	—	4	32	no	—
885	D₄	—	4	64	no	—
886	D₄	—	4	32	no	—
887	D₄	—	4	16	no	—
888	D₄	—	4	32	no	—
889	C₂×C₄	—	2	8	no	—
890	C₂×C₄	—	2	4	no	—
891	C₂×C₄	—	2	8	no	—
892	C₂×C₄	—	2	8	no	—
893	C₂×C₄	—	2	8	no	—
894	C₂×C₄	—	2	16	no	—
895	C₂×C₄	—	2	16	no	—
896	C₂×C₄	—	2	32	no	—
897	C₂×C₄	—	2	8	no	—
898	C₂×C₄	—	2	16	no	—
899	C₂×C₄	—	2	8	no	—
900	C₂×C₄	—	2	16	no	—
901	C₂×C₄	—	2	32	no	—
902	C₂×C₄	—	2	32	no	—
903	C₂×C₄	—	2	32	no	—
904	C₂×C₄	—	4	32	no	—
905	C₂×C₄	—	4	32	no	—
906	C₂×C₄	—	4	32	no	—
907	C₂×C₄	—	4	16	no	—
908	C₂×C₄	—	4	32	no	—
909	C₂×C₄	—	4	32	no	—
910	C₂×C₄	—	4	16	no	—
911	C₂×C₄	—	4	32	no	—
912	C₂×C₄	—	4	32	no	—
913	C₂×C₄	—	4	32	no	—
914	C₂×C₄	C₂×H(5,𝔽₂)	1	8	yes	—
915	C₂×C₄	C₂×H(5,𝔽₂)	1	16	yes	—
916	C₂×C₄	C₂⁶	1	16	yes	—
917	C₂×C₄	C₂⁶	1	8	yes	—
918	C₂×C₄	C₂⁶	1	16	yes	—
919	C₂×C₄	C₂⁶	1	8	yes	—
920	C₂×C₄	C₂⁶	1	8	yes	—
921	C₂×C₄	C₂⁶	1	16	yes	—
922	C₂×C₄	C₂⁶	1	8	yes	—
923	C₂×C₄	C₂⁶	1	8	yes	—
924	C₂×C₄	C₂⁶	1	4	yes	—
925	C₂×C₄	C₂⁶	1	4	yes	—
926	C₂²	—	2	4	no	—
927	C₂²	—	2	8	no	—
928	C₂²	—	2	4	no	—
929	C₂²	—	2	8	no	—
930	C₂²	—	2	8	no	—
931	C₂²	—	2	8	no	—
932	C₂²	—	2	16	no	—
933	C₂²	—	2	16	no	—
934	C₂²	—	2	16	no	—
935	C₂²	—	2	8	no	—
936	C₂²	—	4	16	no	—
937	C₂²	—	4	16	no	—
938	C₂²	—	4	8	no	—
939	C₂²	—	4	16	no	—
940	C₂²	—	4	16	no	—
941	C₂²	—	8	16	no	—
942	C₂²	—	16	16	no	—
943	C₂²	C₂²×H(5,𝔽₂)	1	4	yes	—
944	C₂²	C₂²×H(5,𝔽₂)	1	2	yes	—
945	C₂²	2₋¹⁺⁶	1	4	yes	—
946	C₂²	C₂⁷	1	1	yes	characteristic
947	C₄	—	2	4	no	—
948	C₄	—	2	8	no	—
949	C₄	—	2	8	no	—
950	C₄	—	2	8	no	—
951	C₄	—	2	16	no	—
952	C₄	—	2	8	no	—
953	C₄	—	2	16	no	—
954	C₄	—	2	8	no	—
955	C₄	—	2	16	no	—
956	C₄	C₂²×H(5,𝔽₂)	1	8	yes	—
957	C₂	—	2	4	no	—
958	C₂	—	4	8	no	—
959	C₂	—	4	4	no	—
960	C₂	—	4	8	no	—
961	C₂	—	4	8	no	—
962	C₂	#62887	1	4	yes	direct product factor
963	C₂	C₂³×H(5,𝔽₂)	1	1	yes	characteristic
964	C₂	C₂×2₋¹⁺⁶	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁷
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #62887	C₂	direct (N × H)
2. C₂×#3510	C₂	semidirect
3. C₂×#3500	C₂	semidirect
4. C₂×#3509	C₂	semidirect
5. C₂×#3499	C₂	semidirect
6. C₂×#3487	C₂	semidirect
7. C₂×#3486	C₂	semidirect
8. C₂×#3485	C₂	semidirect
9. C₂×#3554	C₂	semidirect
10. C₂×#3552	C₂	semidirect
11. C₂×#3562	C₂	semidirect
12. C₂×#3561	C₂	semidirect
13. C₂×#3533	C₂	semidirect
14. C₂×#3535	C₂	semidirect
15. C₂×#3455	C₂	semidirect
16. C₂²×#536	C₂	semidirect
18. C₂²×2₋¹⁺⁴	C₂²	semidirect
21. C₂⁴×Q₈	C₂²	semidirect
22. #3562	C₂²	semidirect
23. #3561	C₂²	semidirect
24. #3554	C₂²	semidirect
25. #3552	C₂²	semidirect
26. #3535	C₂²	semidirect
27. #3533	C₂²	semidirect
28. C₂×#563	C₂²	semidirect
29. C₂×#563	C₂²	semidirect
30. C₂×#562	C₂²	semidirect
31. C₂×#562	C₂²	semidirect
32. C₂×#560	C₂²	semidirect
33. #3510	C₂²	semidirect
34. #3509	C₂²	semidirect
35. #3500	C₂²	semidirect
36. #3499	C₂²	semidirect
37. #3487	C₂²	semidirect
38. #3486	C₂²	semidirect
39. #3485	C₂²	semidirect
40. C₂×#559	C₂²	semidirect
41. C₂×#559	C₂²	semidirect
42. C₂×#557	C₂²	semidirect
43. C₂×#556	C₂²	semidirect
44. C₂×#556	C₂²	semidirect
45. C₂×#554	C₂²	semidirect
46. C₂×#553	C₂²	semidirect
47. C₂×#552	C₂²	semidirect
48. C₂×#551	C₂²	semidirect
49. C₂×#551	C₂²	semidirect
50. C₂×#551	C₂²	semidirect
51. C₂×#550	C₂²	semidirect
52. C₂×D₄×Q₈	C₂²	semidirect
53. C₂×D₄×Q₈	C₂²	semidirect
54. C₂×D₄×Q₈	C₂²	semidirect
55. C₂×#548	C₂²	semidirect
56. C₂×#548	C₂²	semidirect
57. C₂×#548	C₂²	semidirect
58. C₂×#548	C₂²	semidirect
60. C₂×#547	C₂²	semidirect
61. C₂×#547	C₂²	semidirect
64. C₂×#546	C₂²	semidirect
65. C₂×#544	C₂²	semidirect
66. C₂×#543	C₂²	semidirect
67. #3455	C₂²	semidirect
68. C₂×#542	C₂²	semidirect
69. C₂×#542	C₂²	semidirect
70. C₂×#542	C₂²	semidirect
71. C₂×#542	C₂²	semidirect
72. C₂×#542	C₂²	semidirect
73. C₂×#541	C₂²	semidirect
74. C₂×#541	C₂²	semidirect
75. C₂×#540	C₂²	semidirect
76. C₂×#540	C₂²	semidirect
77. C₂×#539	C₂²	semidirect
78. C₂×#539	C₂²	semidirect
79. C₂×#539	C₂²	semidirect
80. C₂×#539	C₂²	semidirect
81. C₂×#538	C₂²	semidirect
82. C₂×#538	C₂²	semidirect
83. C₂×#538	C₂²	semidirect
86. C₂×#536	C₂²	semidirect
87. C₂×#536	C₂²	semidirect
88. C₂×#536	C₂²	semidirect
89. C₂×#536	C₂²	semidirect
90. C₂×#536	C₂²	semidirect
91. C₂×#536	C₂²	semidirect
92. C₂×#536	C₂²	semidirect
93. C₂×#536	C₂²	semidirect
95. C₂×#535	C₂²	semidirect
96. C₂×#535	C₂²	semidirect
98. C₂×#533	C₂²	semidirect
99. C₂×#533	C₂²	semidirect
101. C₂×#532	C₂²	semidirect
102. C₂×#532	C₂²	semidirect
103. C₂²×C₄⋊Q₈	C₂²	semidirect
104. C₂²×C₄⋊Q₈	C₂²	semidirect
105. C₂×#529	C₂²	semidirect
106. C₂×#529	C₂²	semidirect
107. C₂×#529	C₂²	semidirect
109. C₂²×#124	C₂²	semidirect
111. C₂×#525	C₂²	semidirect
112. C₂×#525	C₂²	semidirect
113. C₂×#525	C₂²	semidirect
115. C₂²×#123	C₂²	semidirect
116. C₂²×C₂²⋊Q₈	C₂²	semidirect
117. C₂×#519	C₂²	semidirect
118. C₂×#519	C₂²	semidirect
121. C₂×C₄×#41	C₂²	semidirect
122. C₂²×#117	C₂²	semidirect
126. C₂×2₋¹⁺⁴	C₂³	semidirect
148. C₂³×Q₈	C₂³	semidirect
156. #563	C₂³	semidirect
157. #563	C₂³	semidirect
158. #562	C₂³	semidirect
159. #562	C₂³	semidirect
160. #560	C₂³	semidirect
161. #559	C₂³	semidirect
162. #559	C₂³	semidirect
163. #557	C₂³	semidirect
164. #556	C₂³	semidirect
165. #556	C₂³	semidirect
166. #554	C₂³	semidirect
167. #553	C₂³	semidirect
168. #552	C₂³	semidirect
169. #551	C₂³	semidirect
170. #551	C₂³	semidirect
171. #551	C₂³	semidirect
172. #550	C₂³	semidirect
173. D₄×Q₈	C₂³	semidirect
174. D₄×Q₈	C₂³	semidirect
175. D₄×Q₈	C₂³	semidirect
176. #548	C₂³	semidirect
177. #548	C₂³	semidirect
178. #548	C₂³	semidirect
179. #548	C₂³	semidirect
181. #547	C₂³	semidirect
182. #547	C₂³	semidirect
185. #546	C₂³	semidirect
186. #544	C₂³	semidirect
187. #543	C₂³	semidirect
188. #542	C₂³	semidirect
189. #542	C₂³	semidirect
190. #542	C₂³	semidirect
191. #542	C₂³	semidirect
192. #542	C₂³	semidirect
193. #541	C₂³	semidirect
194. #541	C₂³	semidirect
195. #540	C₂³	semidirect
196. #540	C₂³	semidirect
197. #539	C₂³	semidirect
198. #539	C₂³	semidirect
199. #539	C₂³	semidirect
200. #539	C₂³	semidirect
201. #538	C₂³	semidirect
202. #538	C₂³	semidirect
203. #538	C₂³	semidirect
206. #536	C₂³	semidirect
207. #536	C₂³	semidirect
208. #536	C₂³	semidirect
209. #536	C₂³	semidirect
210. #536	C₂³	semidirect
211. #536	C₂³	semidirect
212. #536	C₂³	semidirect
214. #535	C₂³	semidirect
215. #535	C₂³	semidirect
217. #533	C₂³	semidirect
218. #533	C₂³	semidirect
220. #532	C₂³	semidirect
221. #532	C₂³	semidirect
232. C₂×C₄⋊Q₈	C₂³	semidirect
233. C₂×C₄⋊Q₈	C₂³	semidirect
237. #529	C₂³	semidirect
238. #529	C₂³	semidirect
239. #529	C₂³	semidirect
270. C₂×#124	C₂³	semidirect
272. #525	C₂³	semidirect
273. #525	C₂³	semidirect
274. #525	C₂³	semidirect
295. C₂×#123	C₂³	semidirect
316. C₂×C₂²⋊Q₈	C₂³	semidirect
335. #519	C₂³	semidirect
336. #519	C₂³	semidirect
339. C₄×#41	C₂³	semidirect
371. C₂×#117	C₂³	semidirect
962. C₂	#62887	direct (N × H)

Maximal subgroups

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

subgroup	index
#62887	2
C₂×#3510	2
C₂×#3500	2
C₂×#3509	2
C₂×#3499	2
C₂×#3487	2
C₂×#3486	2
C₂×#3485	2
C₂×#3554	2
C₂×#3552	2
C₂×#3562	2
C₂×#3561	2
C₂×#3533	2
C₂×#3535	2
C₂×#3455	2
C₂²×#536	2

Subgroups — C2×#62887 #10586222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#62887 #10586222