Subgroups — C₂×#62880 #10586214

Order 512.

35430 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#62880	C₂	1	64	yes	maximal, direct product factor
2	C₂×#3512	C₂	1	2	yes	maximal, complemented
3	C₂×#3498	C₂	1	2	yes	maximal, complemented
4	C₂×#3488	C₂	1	4	yes	maximal, complemented
5	C₂×#3506	C₂	1	2	yes	maximal, complemented
6	C₂×#3496	C₂	1	2	yes	maximal, complemented
7	C₂×#3543	C₂	1	8	yes	maximal, complemented
8	C₂×#3562	C₂	1	8	yes	maximal, complemented
9	C₂×#3539	C₂	1	4	yes	maximal, complemented
10	C₂×#3537	C₂	1	8	yes	maximal, complemented
11	C₂×#3537	C₂	1	4	yes	maximal, complemented
12	C₂×#3534	C₂	1	8	yes	maximal, complemented
13	C₂×#3542	C₂	1	8	yes	maximal, complemented
14	C₂×#3455	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#3449	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#540	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×H(5,𝔽₂)	C₂²	1	4	yes	complemented
18	C₂³×#41	C₂²	1	2	yes	complemented
19	#3562	C₂²	1	256	yes	complemented
20	#3543	C₂²	1	256	yes	complemented
21	#3542	C₂²	1	256	yes	complemented
22	#3539	C₂²	1	128	yes	complemented
23	#3537	C₂²	1	256	yes	complemented
24	#3537	C₂²	1	128	yes	complemented
25	#3534	C₂²	1	256	yes	complemented
26	C₂×#562	C₂²	1	16	yes	complemented
27	C₂×#560	C₂²	1	16	yes	complemented
28	C₂×#560	C₂²	1	16	yes	complemented
29	C₂×#560	C₂²	1	16	yes	complemented
30	#3512	C₂²	1	64	yes	complemented
31	#3506	C₂²	1	64	yes	complemented
32	#3498	C₂²	1	64	yes	complemented
33	#3496	C₂²	1	64	yes	complemented
34	#3488	C₂²	1	128	yes	complemented
35	C₂×#559	C₂²	1	8	yes	complemented
36	C₂×#556	C₂²	1	4	yes	complemented
37	C₂×#555	C₂²	1	4	yes	complemented
38	C₂×#553	C₂²	1	16	yes	complemented
39	C₂×#553	C₂²	1	16	yes	complemented
40	C₂×#553	C₂²	1	8	yes	complemented
41	C₂×#553	C₂²	1	8	yes	complemented
42	C₂×#552	C₂²	1	8	yes	complemented
43	C₂×#551	C₂²	1	16	yes	complemented
44	C₂×#550	C₂²	1	8	yes	complemented
45	C₂×#550	C₂²	1	8	yes	complemented
46	C₂×#550	C₂²	1	4	yes	complemented
47	C₂×#548	C₂²	1	8	yes	complemented
48	C₂×#547	C₂²	1	4	yes	complemented
49	C₂×#547	C₂²	1	4	yes	complemented
50	C₂×#547	C₂²	1	4	yes	complemented
51	C₂×#546	C₂²	1	16	yes	complemented
52	C₂×#546	C₂²	1	16	yes	complemented
53	C₂×#546	C₂²	1	8	yes	complemented
54	C₂×#546	C₂²	1	8	yes	complemented
55	C₂×#546	C₂²	1	8	yes	complemented
56	C₂×D₄²	C₂²	1	16	yes	complemented
57	C₂×D₄²	C₂²	1	16	yes	complemented
58	C₂×D₄²	C₂²	1	4	yes	complemented
59	C₂×D₄²	C₂²	1	16	yes	complemented
60	C₂×D₄²	C₂²	1	8	yes	complemented
61	C₂×D₄²	C₂²	1	4	yes	complemented
62	C₂×D₄²	C₂²	1	8	yes	complemented
63	#3455	C₂²	1	32	yes	complemented
64	C₂×#542	C₂²	1	4	yes	complemented
65	C₂×#541	C₂²	1	2	yes	complemented
66	C₂×#541	C₂²	1	4	yes	complemented
67	C₂×#540	C₂²	1	16	yes	complemented
68	C₂×#540	C₂²	1	2	yes	complemented
69	C₂×#540	C₂²	1	4	yes	complemented
70	C₂×#540	C₂²	1	16	yes	complemented
71	C₂×#540	C₂²	1	8	yes	complemented
72	C₂×#540	C₂²	1	4	yes	complemented
73	C₂×#540	C₂²	1	4	yes	complemented
74	C₂×#540	C₂²	1	32	yes	complemented
75	C₂×#539	C₂²	1	4	yes	complemented
76	C₂×#539	C₂²	1	16	yes	complemented
77	C₂×#538	C₂²	1	16	yes	complemented
78	C₂×#538	C₂²	1	8	yes	complemented
79	C₂×#538	C₂²	1	4	yes	complemented
80	C₂×#538	C₂²	1	16	yes	complemented
81	#3449	C₂²	1	32	yes	complemented
82	C₂×#537	C₂²	1	4	yes	complemented
83	C₂×#537	C₂²	1	8	yes	complemented
84	C₂×#537	C₂²	1	4	yes	complemented
85	C₂×#536	C₂²	1	4	yes	complemented
86	C₂×#535	C₂²	1	16	yes	complemented
87	C₂×#535	C₂²	1	8	yes	complemented
88	C₂×#535	C₂²	1	8	yes	complemented
89	C₂×#535	C₂²	1	4	yes	complemented
90	C₂×#535	C₂²	1	4	yes	complemented
91	C₂×#534	C₂²	1	16	yes	complemented
92	C₂×#534	C₂²	1	8	yes	complemented
93	C₂×#534	C₂²	1	4	yes	complemented
94	C₂×#534	C₂²	1	16	yes	complemented
95	C₂×#533	C₂²	1	1	yes	characteristic, complemented
96	C₂×#532	C₂²	1	4	yes	complemented
97	C₂×#532	C₂²	1	1	yes	characteristic, complemented
98	C₂×#532	C₂²	1	2	yes	complemented
99	C₂×#532	C₂²	1	2	yes	complemented
100	C₂²×#127	C₂²	1	4	yes	complemented
101	C₂²×#127	C₂²	1	1	yes	characteristic, complemented
102	C₂×#529	C₂²	1	8	yes	complemented
103	C₂×#529	C₂²	1	8	yes	complemented
104	C₂²×#125	C₂²	1	1	yes	characteristic, complemented
105	C₂×#525	C₂²	1	8	yes	complemented
106	C₂×#525	C₂²	1	4	yes	complemented
107	C₂×#525	C₂²	1	8	yes	complemented
108	C₂×#525	C₂²	1	2	yes	complemented
109	C₂×#525	C₂²	1	4	yes	complemented
110	C₂²×#123	C₂²	1	4	yes	complemented
111	C₂²×#121	C₂²	1	8	yes	complemented
112	C₂²×#121	C₂²	1	4	yes	complemented
113	C₂²×#121	C₂²	1	8	yes	complemented
114	C₂²×#121	C₂²	1	2	yes	complemented
115	C₂×#520	C₂²	1	4	yes	complemented
116	C₂×C₄×#41	C₂²	1	2	yes	complemented
117	C₂²×C₄×D₄	C₂²	1	2	yes	complemented
118	C₂²×#117	C₂²	1	1	yes	characteristic, complemented
119	C₂×H(5,𝔽₂)	—	4	32	no	—
120	C₂×H(5,𝔽₂)	C₂³	1	64	yes	complemented
121	C₂²×#41	—	4	16	no	—
122	C₂²×#41	C₂³	1	4	yes	—
123	C₂²×#41	C₂³	1	2	yes	—
124	C₂²×#41	C₂³	1	4	yes	—
125	C₂²×#41	C₂³	1	4	yes	—
126	C₂²×#41	C₂³	1	4	yes	—
127	C₂²×#41	C₂³	1	8	yes	—
128	C₂²×#41	C₂³	1	8	yes	—
129	C₂²×#41	C₂³	1	8	yes	—
130	C₂²×#41	C₂³	1	32	yes	complemented
131	C₂³×Q₈	C₂³	1	2	yes	—
132	C₂³×D₄	C₂³	1	2	yes	—
133	C₂³×D₄	C₂³	1	4	yes	—
134	C₂³×D₄	C₂³	1	2	yes	—
135	C₂³×D₄	C₂³	1	16	yes	—
136	C₂³×D₄	C₂³	1	8	yes	—
137	C₂³×D₄	C₂³	1	8	yes	—
138	C₂³×D₄	C₂³	1	4	yes	—
139	C₂³×D₄	C₂³	1	4	yes	—
140	C₂³×D₄	C₂³	1	8	yes	—
141	C₂³×D₄	C₂³	1	16	yes	—
142	C₂³×D₄	C₂³	1	16	yes	—
143	C₂⁴×C₄	C₂³	1	1	yes	characteristic
144	C₂⁴×C₄	C₂³	1	4	yes	—
145	C₂⁴×C₄	C₂³	1	4	yes	—
146	#562	C₂³	1	256	yes	complemented
147	#560	C₂³	1	256	yes	complemented
148	#560	C₂³	1	256	yes	complemented
149	#560	C₂³	1	256	yes	complemented
150	#559	C₂³	1	128	yes	complemented
151	#556	C₂³	1	64	yes	complemented
152	#555	C₂³	1	64	yes	complemented
153	#553	C₂³	1	128	yes	complemented
154	#553	C₂³	1	256	yes	complemented
155	#553	C₂³	1	128	yes	complemented
156	#553	C₂³	1	256	yes	complemented
157	#552	C₂³	1	128	yes	complemented
158	#551	C₂³	1	256	yes	complemented
159	#550	C₂³	1	128	yes	complemented
160	#550	C₂³	1	128	yes	complemented
161	#550	C₂³	1	64	yes	complemented
162	#548	C₂³	1	128	yes	complemented
163	#547	C₂³	1	64	yes	complemented
164	#547	C₂³	1	64	yes	complemented
165	#547	C₂³	1	64	yes	complemented
166	#546	C₂³	1	256	yes	complemented
167	#546	C₂³	1	128	yes	complemented
168	#546	C₂³	1	128	yes	complemented
169	#546	C₂³	1	128	yes	complemented
170	#546	C₂³	1	256	yes	complemented
171	D₄²	C₂³	1	256	yes	complemented
172	D₄²	C₂³	1	128	yes	complemented
173	D₄²	C₂³	1	64	yes	complemented
174	D₄²	C₂³	1	64	yes	complemented
175	D₄²	C₂³	1	256	yes	complemented
176	D₄²	C₂³	1	128	yes	complemented
177	D₄²	C₂³	1	256	yes	complemented
178	#542	C₂³	1	64	yes	complemented
179	#541	C₂³	1	32	yes	complemented
180	#541	C₂³	1	64	yes	complemented
181	#540	C₂³	1	64	yes	complemented
182	#540	C₂³	1	64	yes	complemented
183	#540	C₂³	1	128	yes	complemented
184	#540	C₂³	1	32	yes	complemented
185	#540	C₂³	1	64	yes	complemented
186	#540	C₂³	1	256	yes	complemented
187	#540	C₂³	1	256	yes	complemented
188	#539	C₂³	1	64	yes	complemented
189	#539	C₂³	1	256	yes	complemented
190	#538	C₂³	1	64	yes	complemented
191	#538	C₂³	1	128	yes	complemented
192	#538	C₂³	1	256	yes	complemented
193	#538	C₂³	1	256	yes	complemented
194	#537	C₂³	1	64	yes	complemented
195	#537	C₂³	1	64	yes	complemented
196	#537	C₂³	1	128	yes	complemented
197	#536	C₂³	1	64	yes	complemented
198	#535	C₂³	1	64	yes	complemented
199	#535	C₂³	1	64	yes	complemented
200	#535	C₂³	1	128	yes	complemented
201	#535	C₂³	1	128	yes	complemented
202	#535	C₂³	1	256	yes	complemented
203	#534	C₂³	1	64	yes	complemented
204	#534	C₂³	1	128	yes	complemented
205	#534	C₂³	1	256	yes	complemented
206	#534	C₂³	1	256	yes	complemented
207	#533	C₂³	1	16	yes	complemented
208	#532	C₂³	1	32	yes	complemented
209	#532	C₂³	1	32	yes	complemented
210	#532	C₂³	1	16	yes	complemented
211	#532	C₂³	1	64	yes	complemented
212	C₂×C₄⋊Q₈	C₂³	1	2	yes	—
213	C₂×C₄⋊Q₈	C₂³	1	2	yes	—
214	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂³	1	2	yes	—
216	C₂×#127	C₂³	1	2	yes	—
217	C₂×#127	C₂³	1	4	yes	—
218	C₂×#127	C₂³	1	8	yes	—
219	C₂×#127	C₂³	1	16	yes	—
220	C₂×#127	C₂³	1	4	yes	—
221	C₂×#127	C₂³	1	2	yes	—
222	C₂×#127	C₂³	1	1	yes	characteristic
223	C₂×#127	C₂³	1	16	yes	—
224	C₂×#127	C₂³	1	16	yes	complemented
225	C₂×#127	C₂³	1	64	yes	complemented
226	#529	C₂³	1	128	yes	complemented
227	#529	C₂³	1	128	yes	complemented
228	C₂×#126	C₂³	1	16	yes	—
229	C₂×#126	C₂³	1	8	yes	—
230	C₂×#126	C₂³	1	8	yes	—
231	C₂×#126	C₂³	1	16	yes	—
232	C₂×#126	C₂³	1	16	yes	—
233	C₂×#125	C₂³	1	4	yes	—
234	C₂×#125	C₂³	1	4	yes	—
235	C₂×#125	C₂³	1	8	yes	—
236	C₂×#125	C₂³	1	2	yes	—
237	C₂×#125	C₂³	1	16	yes	—
238	C₂×#125	C₂³	1	16	yes	complemented
239	C₂×#124	C₂³	1	4	yes	—
240	C₂×#124	C₂³	1	8	yes	—
241	C₂×#124	C₂³	1	8	yes	—
242	C₂×#124	C₂³	1	4	yes	—
243	C₂×#124	C₂³	1	2	yes	—
244	C₂×#124	C₂³	1	16	yes	—
245	C₂×#124	C₂³	1	16	yes	—
246	#525	C₂³	1	64	yes	complemented
247	#525	C₂³	1	64	yes	complemented
248	#525	C₂³	1	32	yes	complemented
249	#525	C₂³	1	128	yes	complemented
250	#525	C₂³	1	128	yes	complemented
251	C₂×#123	C₂³	1	16	yes	—
252	C₂×#123	C₂³	1	16	yes	—
253	C₂×#123	C₂³	1	8	yes	—
254	C₂×#123	C₂³	1	8	yes	—
255	C₂×#123	C₂³	1	16	yes	—
256	C₂×#123	C₂³	1	4	yes	—
257	C₂×#123	C₂³	1	16	yes	—
258	C₂×#123	C₂³	1	8	yes	—
259	C₂×#123	C₂³	1	8	yes	—
260	C₂×#123	C₂³	1	16	yes	—
261	C₂×#123	C₂³	1	16	yes	—
262	C₂×#123	C₂³	1	16	yes	—
263	C₂×#123	C₂³	1	16	yes	—
264	C₂×#123	C₂³	1	16	yes	—
265	C₂×#123	C₂³	1	64	yes	complemented
266	C₂×C₂²⋊Q₈	C₂³	1	4	yes	—
267	C₂×C₂²⋊Q₈	C₂³	1	4	yes	—
268	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
269	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
270	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
271	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
272	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
273	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
274	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
275	C₂×#121	C₂³	1	4	yes	—
276	C₂×#121	C₂³	1	8	yes	—
277	C₂×#121	C₂³	1	4	yes	—
278	C₂×#121	C₂³	1	4	yes	—
279	C₂×#121	C₂³	1	16	yes	—
280	C₂×#121	C₂³	1	16	yes	—
281	C₂×#121	C₂³	1	16	yes	—
282	C₂×#121	C₂³	1	8	yes	—
283	C₂×#121	C₂³	1	8	yes	—
284	C₂×#121	C₂³	1	16	yes	—
285	C₂×#121	C₂³	1	8	yes	—
286	C₂×#121	C₂³	1	16	yes	—
287	C₂×#121	C₂³	1	8	yes	—
288	C₂×#121	C₂³	1	8	yes	—
289	C₂×#121	C₂³	1	16	yes	—
290	C₂×#121	C₂³	1	4	yes	—
291	C₂×#121	C₂³	1	8	yes	—
292	C₂×#121	C₂³	1	8	yes	—
293	C₂×#121	C₂³	1	8	yes	—
294	C₂×#121	C₂³	1	8	yes	—
295	C₂×#121	C₂³	1	8	yes	—
296	C₂×#121	C₂³	1	8	yes	—
297	C₂×#121	C₂³	1	8	yes	—
298	C₂×#121	C₂³	1	16	yes	—
299	C₂×#121	C₂³	1	16	yes	—
300	C₂×#121	C₂³	1	16	yes	—
301	C₂×#121	C₂³	1	16	yes	—
302	C₂×#121	C₂³	1	16	yes	—
303	C₂×#121	C₂³	1	16	yes	—
304	C₂×#121	C₂³	1	16	yes	—
305	C₂×#121	C₂³	1	16	yes	—
306	C₂×#121	C₂³	1	32	yes	complemented
307	C₂×#121	C₂³	1	64	yes	complemented
308	C₂×#121	C₂³	1	128	yes	complemented
309	C₂×#121	C₂³	1	128	yes	complemented
310	C₂×#120	C₂³	1	8	yes	—
311	C₂×#120	C₂³	1	8	yes	—
312	C₂×#120	C₂³	1	16	yes	—
313	C₂×#120	C₂³	1	16	yes	—
314	C₂×#120	C₂³	1	4	yes	—
315	C₂×#120	C₂³	1	16	yes	—
316	C₂×#120	C₂³	1	16	yes	—
317	C₂×#120	C₂³	1	16	yes	—
318	C₂×#120	C₂³	1	16	yes	—
319	C₂×#120	C₂³	1	16	yes	—
320	C₂×#120	C₂³	1	16	yes	—
321	#520	C₂³	1	64	yes	complemented
322	C₄×#41	C₂³	1	32	yes	complemented
323	C₂×C₄×Q₈	C₂³	1	4	yes	—
324	C₂×C₄×Q₈	C₂³	1	8	yes	—
325	C₂×C₄×Q₈	C₂³	1	4	yes	—
326	C₂×C₄×D₄	C₂³	1	4	yes	—
327	C₂×C₄×D₄	C₂³	1	4	yes	—
328	C₂×C₄×D₄	C₂³	1	4	yes	—
329	C₂×C₄×D₄	C₂³	1	4	yes	—
330	C₂×C₄×D₄	C₂³	1	8	yes	—
331	C₂×C₄×D₄	C₂³	1	4	yes	—
332	C₂×C₄×D₄	C₂³	1	16	yes	—
333	C₂×C₄×D₄	C₂³	1	8	yes	—
334	C₂×C₄×D₄	C₂³	1	4	yes	—
335	C₂×C₄×D₄	C₂³	1	8	yes	—
336	C₂×C₄×D₄	C₂³	1	4	yes	—
337	C₂×C₄×D₄	C₂³	1	8	yes	—
338	C₂×C₄×D₄	C₂³	1	16	yes	—
339	C₂×C₄×D₄	C₂³	1	16	yes	—
340	C₂×C₄×D₄	C₂³	1	16	yes	—
341	C₂×C₄×D₄	C₂³	1	4	yes	—
342	C₂×C₄×D₄	C₂³	1	16	yes	—
343	C₂×C₄×D₄	C₂³	1	16	yes	—
344	C₂×C₄×D₄	C₂³	1	32	yes	complemented
345	C₂×#117	C₂³	1	2	yes	—
346	C₂×#117	C₂³	1	2	yes	—
347	C₂×#117	C₂³	1	4	yes	—
348	C₂×#117	C₂³	1	2	yes	—
349	C₂×#117	C₂³	1	4	yes	—
350	C₂×#117	C₂³	1	8	yes	—
351	C₂×#117	C₂³	1	8	yes	—
352	C₂×#117	C₂³	1	16	yes	—
353	C₂×#117	C₂³	1	16	yes	complemented
354	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
355	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
356	C₂²×C₄⋊C₄	C₂³	1	8	yes	—
357	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
358	C₂²×C₄⋊C₄	C₂³	1	8	yes	—
359	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
360	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
361	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
362	C₂²×C₂²⋊C₄	C₂³	1	16	yes	—
363	C₂²×C₂²⋊C₄	C₂³	1	16	yes	—
364	C₂²×C₄²	C₂³	1	1	yes	characteristic
365	C₂²×C₄²	C₂³	1	1	yes	characteristic
366	C₂²×C₄²	C₂³	1	4	yes	—
367	C₂⁵	C₂⁴	1	1	yes	characteristic
368	C₂⁵	C₂⁴	1	4	yes	—
369	C₂⁵	C₂⁴	1	16	yes	—
370	C₂⁵	C₂⁴	1	4	yes	—
371	H(5,𝔽₂)	—	4	256	no	—
372	C₂×#41	—	2	32	no	—
373	C₂×#41	—	2	16	no	—
374	C₂×#41	—	4	16	no	—
375	C₂×#41	—	4	16	no	—
376	C₂×#41	—	4	16	no	—
377	C₂×#41	—	4	32	no	—
378	C₂×#41	—	4	32	no	—
379	C₂×#41	—	4	128	no	—
380	C₂×#41	—	8	16	no	—
381	C₂×#41	C₂⁴	1	16	yes	—
382	C₂×#41	C₂⁴	1	32	yes	—
383	C₂×#41	C₂⁴	1	32	yes	—
384	C₂×#41	C₂⁴	1	64	yes	—
385	C₂×#41	C₂⁴	1	64	yes	—
386	C₂×#41	C₂⁴	1	32	yes	—
387	C₂×#41	C₂⁴	1	32	yes	—
388	C₂×#41	C₂⁴	1	64	yes	—
389	C₂²×Q₈	—	4	8	no	—
390	C₂²×Q₈	C₂⁴	1	2	yes	—
391	C₂²×Q₈	C₂⁴	1	4	yes	—
392	C₂²×Q₈	C₂⁴	1	4	yes	—
393	C₂²×Q₈	C₂⁴	1	4	yes	—
394	C₂²×Q₈	C₂⁴	1	16	yes	—
395	C₂²×D₄	—	2	16	no	—
396	C₂²×D₄	—	4	8	no	—
397	C₂²×D₄	—	4	32	no	—
398	C₂²×D₄	—	4	32	no	—
399	C₂²×D₄	—	4	16	no	—
400	C₂²×D₄	—	4	64	no	—
401	C₂²×D₄	—	8	8	no	—
402	C₂²×D₄	—	8	16	no	—
403	C₂²×D₄	—	8	8	no	—
404	C₂²×D₄	—	8	32	no	—
405	C₂²×D₄	—	8	32	no	—
406	C₂²×D₄	C₂⁴	1	8	yes	—
407	C₂²×D₄	C₂⁴	1	4	yes	—
408	C₂²×D₄	C₂⁴	1	2	yes	—
409	C₂²×D₄	C₂⁴	1	4	yes	—
410	C₂²×D₄	C₂⁴	1	4	yes	—
411	C₂²×D₄	C₂⁴	1	4	yes	—
412	C₂²×D₄	C₂⁴	1	16	yes	—
413	C₂²×D₄	C₂⁴	1	4	yes	—
414	C₂²×D₄	C₂⁴	1	4	yes	—
415	C₂²×D₄	C₂⁴	1	16	yes	—
416	C₂²×D₄	C₂⁴	1	16	yes	—
417	C₂²×D₄	C₂⁴	1	8	yes	—
418	C₂²×D₄	C₂⁴	1	4	yes	—
419	C₂²×D₄	C₂⁴	1	16	yes	—
420	C₂²×D₄	C₂⁴	1	16	yes	—
421	C₂²×D₄	C₂⁴	1	8	yes	—
422	C₂²×D₄	C₂⁴	1	16	yes	—
423	C₂²×D₄	C₂⁴	1	4	yes	—
424	C₂²×D₄	C₂⁴	1	8	yes	—
425	C₂²×D₄	C₂⁴	1	16	yes	—
426	C₂²×D₄	C₂⁴	1	16	yes	—
427	C₂²×D₄	C₂⁴	1	128	yes	—
428	C₂²×D₄	C₂⁴	1	64	yes	—
429	C₂²×D₄	C₂⁴	1	64	yes	—
430	C₂²×D₄	C₂⁴	1	32	yes	—
431	C₂²×D₄	C₂⁴	1	16	yes	—
432	C₂²×D₄	C₂⁴	1	32	yes	—
433	C₂²×D₄	C₂⁴	1	32	yes	—
434	C₂²×D₄	C₂⁴	1	64	yes	—
435	C₂²×D₄	C₂⁴	1	128	yes	—
436	C₂²×D₄	C₂⁴	1	128	yes	—
437	C₂³×C₄	—	2	8	no	—
438	C₂³×C₄	—	4	16	no	—
439	C₂³×C₄	—	8	8	no	—
440	C₂³×C₄	C₂⁴	1	1	yes	characteristic
441	C₂³×C₄	C₂⁴	1	8	yes	—
442	C₂³×C₄	C₂⁴	1	2	yes	—
443	C₂³×C₄	C₂⁴	1	2	yes	—
444	C₂³×C₄	C₂⁴	1	4	yes	—
445	C₂³×C₄	C₂⁴	1	8	yes	—
446	C₂³×C₄	C₂⁴	1	2	yes	—
447	C₂³×C₄	C₂⁴	1	4	yes	—
448	C₂³×C₄	C₂⁴	1	8	yes	—
449	C₂³×C₄	C₂⁴	1	8	yes	—
450	C₂³×C₄	C₂⁴	1	2	yes	—
451	C₂³×C₄	C₂⁴	1	16	yes	—
452	C₂³×C₄	C₂⁴	1	16	yes	—
453	C₂³×C₄	C₂⁴	1	8	yes	—
454	C₂³×C₄	C₂⁴	1	4	yes	—
455	C₂³×C₄	C₂⁴	1	8	yes	—
456	C₂³×C₄	C₂⁴	1	32	yes	—
457	C₂³×C₄	C₂⁴	1	32	yes	—
458	C₂³×C₄	C₂⁴	1	1	yes	characteristic
459	C₄⋊Q₈	C₂⁴	1	16	yes	—
460	C₄⋊Q₈	C₂⁴	1	16	yes	—
461	C₄⋊Q₈	C₂⁴	1	8	yes	—
462	C₄⋊Q₈	C₂⁴	1	16	yes	—
463	#127	C₂⁴	1	32	yes	—
464	#127	C₂⁴	1	16	yes	—
465	#127	C₂⁴	1	64	yes	—
466	#127	C₂⁴	1	128	yes	—
467	#127	C₂⁴	1	32	yes	—
468	#127	C₂⁴	1	16	yes	—
469	#127	C₂⁴	1	8	yes	—
470	#127	C₂⁴	1	128	yes	—
471	#126	C₂⁴	1	128	yes	—
472	#126	C₂⁴	1	64	yes	—
473	#126	C₂⁴	1	64	yes	—
474	#126	C₂⁴	1	128	yes	—
475	#126	C₂⁴	1	128	yes	—
476	#125	C₂⁴	1	32	yes	—
477	#125	C₂⁴	1	32	yes	—
478	#125	C₂⁴	1	64	yes	—
479	#125	C₂⁴	1	16	yes	—
480	#125	C₂⁴	1	128	yes	—
481	#124	C₂⁴	1	32	yes	—
482	#124	C₂⁴	1	64	yes	—
483	#124	C₂⁴	1	64	yes	—
484	#124	C₂⁴	1	32	yes	—
485	#124	C₂⁴	1	16	yes	—
486	#124	C₂⁴	1	128	yes	—
487	#124	C₂⁴	1	128	yes	—
488	#123	C₂⁴	1	128	yes	—
489	#123	C₂⁴	1	128	yes	—
490	#123	C₂⁴	1	64	yes	—
491	#123	C₂⁴	1	64	yes	—
492	#123	C₂⁴	1	128	yes	—
493	#123	C₂⁴	1	32	yes	—
494	#123	C₂⁴	1	128	yes	—
495	#123	C₂⁴	1	64	yes	—
496	#123	C₂⁴	1	64	yes	—
497	#123	C₂⁴	1	128	yes	—
498	#123	C₂⁴	1	128	yes	—
499	#123	C₂⁴	1	128	yes	—
500	#123	C₂⁴	1	128	yes	—
501	#123	C₂⁴	1	128	yes	—
502	C₂²⋊Q₈	C₂⁴	1	32	yes	—
503	C₂²⋊Q₈	C₂⁴	1	32	yes	—
504	C₂²⋊Q₈	C₂⁴	1	64	yes	—
505	C₂²⋊Q₈	C₂⁴	1	64	yes	—
506	C₂²⋊Q₈	C₂⁴	1	64	yes	—
507	C₂²⋊Q₈	C₂⁴	1	64	yes	—
508	C₂²⋊Q₈	C₂⁴	1	64	yes	—
509	C₂²⋊Q₈	C₂⁴	1	64	yes	—
510	C₂²⋊Q₈	C₂⁴	1	128	yes	—
511	#121	C₂⁴	1	32	yes	—
512	#121	C₂⁴	1	64	yes	—
513	#121	C₂⁴	1	32	yes	—
514	#121	C₂⁴	1	32	yes	—
515	#121	C₂⁴	1	128	yes	—
516	#121	C₂⁴	1	128	yes	—
517	#121	C₂⁴	1	128	yes	—
518	#121	C₂⁴	1	64	yes	—
519	#121	C₂⁴	1	64	yes	—
520	#121	C₂⁴	1	128	yes	—
521	#121	C₂⁴	1	64	yes	—
522	#121	C₂⁴	1	128	yes	—
523	#121	C₂⁴	1	64	yes	—
524	#121	C₂⁴	1	64	yes	—
525	#121	C₂⁴	1	128	yes	—
526	#121	C₂⁴	1	32	yes	—
527	#121	C₂⁴	1	64	yes	—
528	#121	C₂⁴	1	64	yes	—
529	#121	C₂⁴	1	64	yes	—
530	#121	C₂⁴	1	64	yes	—
531	#121	C₂⁴	1	64	yes	—
532	#121	C₂⁴	1	64	yes	—
533	#121	C₂⁴	1	64	yes	—
534	#121	C₂⁴	1	128	yes	—
535	#121	C₂⁴	1	128	yes	—
536	#121	C₂⁴	1	128	yes	—
537	#121	C₂⁴	1	128	yes	—
538	#121	C₂⁴	1	128	yes	—
539	#121	C₂⁴	1	128	yes	—
540	#121	C₂⁴	1	128	yes	—
541	#121	C₂⁴	1	128	yes	—
542	#120	C₂⁴	1	64	yes	—
543	#120	C₂⁴	1	64	yes	—
544	#120	C₂⁴	1	128	yes	—
545	#120	C₂⁴	1	128	yes	—
546	#120	C₂⁴	1	32	yes	—
547	#120	C₂⁴	1	128	yes	—
548	#120	C₂⁴	1	128	yes	—
549	#120	C₂⁴	1	128	yes	—
550	#120	C₂⁴	1	128	yes	—
551	#120	C₂⁴	1	128	yes	—
552	#120	C₂⁴	1	128	yes	—
553	C₄×Q₈	C₂⁴	1	32	yes	—
554	C₄×Q₈	C₂⁴	1	64	yes	—
555	C₄×Q₈	C₂⁴	1	32	yes	—
556	C₄×D₄	C₂⁴	1	32	yes	—
557	C₄×D₄	C₂⁴	1	32	yes	—
558	C₄×D₄	C₂⁴	1	32	yes	—
559	C₄×D₄	C₂⁴	1	32	yes	—
560	C₄×D₄	C₂⁴	1	64	yes	—
561	C₄×D₄	C₂⁴	1	32	yes	—
562	C₄×D₄	C₂⁴	1	128	yes	—
563	C₄×D₄	C₂⁴	1	64	yes	—
564	C₄×D₄	C₂⁴	1	32	yes	—
565	C₄×D₄	C₂⁴	1	64	yes	—
566	C₄×D₄	C₂⁴	1	32	yes	—
567	C₄×D₄	C₂⁴	1	64	yes	—
568	C₄×D₄	C₂⁴	1	128	yes	—
569	C₄×D₄	C₂⁴	1	128	yes	—
570	C₄×D₄	C₂⁴	1	128	yes	—
571	C₄×D₄	C₂⁴	1	32	yes	—
572	C₄×D₄	C₂⁴	1	128	yes	—
573	C₄×D₄	C₂⁴	1	128	yes	—
574	#117	C₂⁴	1	16	yes	—
575	#117	C₂⁴	1	16	yes	—
576	#117	C₂⁴	1	32	yes	—
577	#117	C₂⁴	1	16	yes	—
578	#117	C₂⁴	1	32	yes	—
579	#117	C₂⁴	1	64	yes	—
580	#117	C₂⁴	1	64	yes	—
581	#117	C₂⁴	1	128	yes	—
582	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
583	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
584	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
585	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
586	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
587	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
588	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
589	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
590	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
591	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
592	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
593	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
594	C₂×C₄⋊C₄	C₂⁴	1	64	yes	—
595	C₂×C₄⋊C₄	C₂⁴	1	32	yes	—
596	C₂×C₄⋊C₄	C₂⁴	1	64	yes	—
597	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
598	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
599	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
600	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
601	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
602	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
603	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
604	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
605	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
606	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
607	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
608	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
609	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
610	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
611	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
612	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
613	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
614	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
615	C₂×C₂²⋊C₄	C₂⁴	1	32	yes	—
616	C₂×C₂²⋊C₄	C₂⁴	1	32	yes	—
617	C₂×C₂²⋊C₄	C₂⁴	1	128	yes	—
618	C₂×C₂²⋊C₄	C₂⁴	1	128	yes	—
619	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
620	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
621	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
622	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
623	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
624	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
625	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
626	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
627	C₂×C₄²	C₂⁴	1	2	yes	—
628	C₂×C₄²	C₂⁴	1	16	yes	—
629	C₂×C₄²	C₂⁴	1	1	yes	characteristic
630	C₂×C₄²	C₂⁴	1	1	yes	characteristic
631	C₂×C₄²	C₂⁴	1	2	yes	—
632	C₂×C₄²	C₂⁴	1	2	yes	—
633	C₂×C₄²	C₂⁴	1	4	yes	—
634	C₂×C₄²	C₂⁴	1	8	yes	—
635	C₂×C₄²	C₂⁴	1	8	yes	—
636	C₂×C₄²	C₂⁴	1	8	yes	—
637	C₂×C₄²	C₂⁴	1	32	yes	—
638	C₂⁴	—	2	4	no	—
639	C₂⁴	—	2	16	no	—
640	C₂⁴	—	4	8	no	—
641	C₂⁴	—	4	8	no	—
642	C₂⁴	—	4	4	no	—
643	C₂⁴	—	4	8	no	—
644	C₂⁴	—	4	16	no	—
645	C₂⁴	—	4	32	no	—
646	C₂⁴	—	4	32	no	—
647	C₂⁴	—	4	32	no	—
648	C₂⁴	C₂⁵	1	4	yes	—
649	C₂⁴	C₂⁵	1	2	yes	—
650	C₂⁴	C₂⁵	1	8	yes	—
651	C₂⁴	C₂⁵	1	8	yes	—
652	C₂⁴	C₂⁵	1	1	yes	characteristic
653	C₂⁴	C₂⁵	1	4	yes	—
654	C₂⁴	C₂⁵	1	16	yes	—
655	C₂⁴	C₂⁵	1	64	yes	—
656	C₂⁴	C₂⁵	1	16	yes	—
657	#41	—	2	128	no	—
658	#41	—	2	64	no	—
659	#41	—	4	64	no	—
660	#41	—	4	64	no	—
661	#41	—	4	64	no	—
662	#41	—	4	128	no	—
663	#41	—	4	128	no	—
664	#41	—	8	64	no	—
665	C₂×Q₈	—	2	16	no	—
666	C₂×Q₈	—	2	8	no	—
667	C₂×Q₈	—	4	8	no	—
668	C₂×Q₈	—	4	8	no	—
669	C₂×Q₈	—	4	32	no	—
670	C₂×Q₈	C₂⁵	1	8	yes	—
671	C₂×Q₈	C₂⁵	1	16	yes	—
672	C₂×Q₈	C₂⁵	1	16	yes	—
673	C₂×Q₈	C₂⁵	1	16	yes	—
674	C₂×D₄	—	2	16	no	—
675	C₂×D₄	—	2	32	no	—
676	C₂×D₄	—	2	16	no	—
677	C₂×D₄	—	2	16	no	—
678	C₂×D₄	—	2	64	no	—
679	C₂×D₄	—	2	8	no	—
680	C₂×D₄	—	2	16	no	—
681	C₂×D₄	—	4	32	no	—
682	C₂×D₄	—	4	128	no	—
683	C₂×D₄	—	4	128	no	—
684	C₂×D₄	—	4	32	no	—
685	C₂×D₄	—	4	32	no	—
686	C₂×D₄	—	4	8	no	—
687	C₂×D₄	—	4	16	no	—
688	C₂×D₄	—	4	8	no	—
689	C₂×D₄	—	4	32	no	—
690	C₂×D₄	—	4	8	no	—
691	C₂×D₄	—	4	32	no	—
692	C₂×D₄	—	4	32	no	—
693	C₂×D₄	—	4	16	no	—
694	C₂×D₄	—	4	16	no	—
695	C₂×D₄	—	4	32	no	—
696	C₂×D₄	—	4	32	no	—
697	C₂×D₄	—	4	8	no	—
698	C₂×D₄	—	4	64	no	—
699	C₂×D₄	—	4	256	no	—
700	C₂×D₄	—	8	32	no	—
701	C₂×D₄	—	8	64	no	—
702	C₂×D₄	—	8	32	no	—
703	C₂×D₄	—	8	128	no	—
704	C₂×D₄	—	8	128	no	—
705	C₂×D₄	C₂⁵	1	32	yes	—
706	C₂×D₄	C₂⁵	1	16	yes	—
707	C₂×D₄	C₂⁵	1	8	yes	—
708	C₂×D₄	C₂⁵	1	16	yes	—
709	C₂×D₄	C₂⁵	1	16	yes	—
710	C₂×D₄	C₂⁵	1	16	yes	—
711	C₂×D₄	C₂⁵	1	16	yes	—
712	C₂×D₄	C₂⁵	1	16	yes	—
713	C₂×D₄	C₂⁵	1	64	yes	—
714	C₂×D₄	C₂⁵	1	64	yes	—
715	C₂×D₄	C₂⁵	1	32	yes	—
716	C₂×D₄	C₂⁵	1	16	yes	—
717	C₂×D₄	C₂⁵	1	64	yes	—
718	C₂×D₄	C₂⁵	1	64	yes	—
719	C₂×D₄	C₂⁵	1	32	yes	—
720	C₂×D₄	C₂⁵	1	64	yes	—
721	C₂×D₄	C₂⁵	1	16	yes	—
722	C₂×D₄	C₂⁵	1	32	yes	—
723	C₂×D₄	C₂⁵	1	64	yes	—
724	C₂×D₄	C₂⁵	1	64	yes	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	8	no	—
727	C₂²×C₄	—	2	8	no	—
728	C₂²×C₄	—	2	32	no	—
729	C₂²×C₄	—	2	32	no	—
730	C₂²×C₄	—	2	16	no	—
731	C₂²×C₄	—	4	64	no	—
732	C₂²×C₄	—	4	8	no	—
733	C₂²×C₄	—	4	16	no	—
734	C₂²×C₄	—	4	4	no	—
735	C₂²×C₄	—	4	8	no	—
736	C₂²×C₄	—	4	16	no	—
737	C₂²×C₄	—	4	16	no	—
738	C₂²×C₄	—	4	32	no	—
739	C₂²×C₄	—	4	4	no	—
740	C₂²×C₄	—	4	16	no	—
741	C₂²×C₄	—	4	32	no	—
742	C₂²×C₄	—	8	32	no	—
743	C₂²×C₄	H(5,𝔽₂)	1	8	yes	—
744	C₂²×C₄	C₂⁵	1	16	yes	—
745	C₂²×C₄	C₂⁵	1	4	yes	—
746	C₂²×C₄	C₂⁵	1	32	yes	—
747	C₂²×C₄	C₂⁵	1	8	yes	—
748	C₂²×C₄	C₂⁵	1	8	yes	—
749	C₂²×C₄	C₂⁵	1	8	yes	—
750	C₂²×C₄	C₂⁵	1	4	yes	—
751	C₂²×C₄	C₂⁵	1	2	yes	—
752	C₂²×C₄	C₂⁵	1	8	yes	—
753	C₂²×C₄	C₂⁵	1	2	yes	—
754	C₂²×C₄	C₂⁵	1	8	yes	—
755	C₂²×C₄	C₂⁵	1	4	yes	—
756	C₂²×C₄	C₂⁵	1	2	yes	—
757	C₂²×C₄	C₂⁵	1	8	yes	—
758	C₂²×C₄	C₂⁵	1	8	yes	—
759	C₂²×C₄	C₂⁵	1	32	yes	—
760	C₂²×C₄	C₂⁵	1	16	yes	—
761	C₂²×C₄	C₂⁵	1	32	yes	—
762	C₂²×C₄	C₂⁵	1	32	yes	—
763	C₂²×C₄	C₂⁵	1	64	yes	—
764	C₂²×C₄	C₂⁵	1	64	yes	—
765	C₂²×C₄	C₂⁵	1	32	yes	—
766	C₂²×C₄	C₂⁵	1	16	yes	—
767	C₂²×C₄	C₂⁵	1	4	yes	—
768	C₂²×C₄	C₂⁵	1	1	yes	characteristic
769	C₂²×C₄	C₂⁵	1	1	yes	characteristic
770	C₄⋊C₄	C₂⁵	1	16	yes	—
771	C₄⋊C₄	C₂⁵	1	16	yes	—
772	C₄⋊C₄	C₂⁵	1	16	yes	—
773	C₄⋊C₄	C₂⁵	1	16	yes	—
774	C₄⋊C₄	C₂⁵	1	16	yes	—
775	C₄⋊C₄	C₂⁵	1	16	yes	—
776	C₄⋊C₄	C₂⁵	1	64	yes	—
777	C₄⋊C₄	C₂⁵	1	64	yes	—
778	C₄⋊C₄	C₂⁵	1	16	yes	—
779	C₄⋊C₄	C₂⁵	1	64	yes	—
780	C₄⋊C₄	C₂⁵	1	16	yes	—
781	C₄⋊C₄	C₂⁵	1	16	yes	—
782	C₄⋊C₄	C₂⁵	1	32	yes	—
783	C₄⋊C₄	C₂⁵	1	32	yes	—
784	C₄⋊C₄	C₂⁵	1	32	yes	—
785	C₄⋊C₄	C₂⁵	1	32	yes	—
786	C₂²⋊C₄	C₂⁵	1	64	yes	—
787	C₂²⋊C₄	C₂⁵	1	32	yes	—
788	C₂²⋊C₄	C₂⁵	1	32	yes	—
789	C₂²⋊C₄	C₂⁵	1	64	yes	—
790	C₂²⋊C₄	C₂⁵	1	32	yes	—
791	C₂²⋊C₄	C₂⁵	1	16	yes	—
792	C₂²⋊C₄	C₂⁵	1	16	yes	—
793	C₂²⋊C₄	C₂⁵	1	64	yes	—
794	C₂²⋊C₄	C₂⁵	1	64	yes	—
795	C₂²⋊C₄	C₂⁵	1	32	yes	—
796	C₂²⋊C₄	C₂⁵	1	32	yes	—
797	C₂²⋊C₄	C₂⁵	1	32	yes	—
798	C₂²⋊C₄	C₂⁵	1	16	yes	—
799	C₂²⋊C₄	C₂⁵	1	32	yes	—
800	C₂²⋊C₄	C₂⁵	1	64	yes	—
801	C₂²⋊C₄	C₂⁵	1	32	yes	—
802	C₂²⋊C₄	C₂⁵	1	32	yes	—
803	C₂²⋊C₄	C₂⁵	1	64	yes	—
804	C₂²⋊C₄	C₂⁵	1	32	yes	—
805	C₄²	C₂⁵	1	8	yes	—
806	C₄²	C₂⁵	1	4	yes	—
807	C₄²	C₂⁵	1	4	yes	—
808	C₄²	C₂⁵	1	8	yes	—
809	C₄²	C₂⁵	1	8	yes	—
810	C₄²	C₂⁵	1	16	yes	—
811	C₄²	C₂⁵	1	32	yes	—
812	C₄²	C₂⁵	1	64	yes	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	16	no	—
816	C₂³	—	2	8	no	—
817	C₂³	—	2	16	no	—
818	C₂³	—	2	16	no	—
819	C₂³	—	2	16	no	—
820	C₂³	—	2	16	no	—
821	C₂³	—	2	8	no	—
822	C₂³	—	2	16	no	—
823	C₂³	—	2	16	no	—
824	C₂³	—	2	8	no	—
825	C₂³	—	2	32	no	—
826	C₂³	—	4	16	no	—
827	C₂³	—	4	16	no	—
828	C₂³	—	4	8	no	—
829	C₂³	—	4	16	no	—
830	C₂³	—	4	32	no	—
831	C₂³	—	4	64	no	—
832	C₂³	—	4	64	no	—
833	C₂³	—	4	64	no	—
834	C₂³	—	8	8	no	—
835	C₂³	—	8	32	no	—
836	C₂³	—	8	32	no	—
837	C₂³	—	16	64	no	—
838	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
839	C₂³	C₂⁶	1	8	yes	—
840	C₂³	C₂⁶	1	4	yes	—
841	C₂³	C₂⁶	1	16	yes	—
842	C₂³	C₂⁶	1	16	yes	—
843	C₂³	C₂⁶	1	2	yes	—
844	C₂³	C₂⁶	1	1	yes	characteristic
845	Q₈	—	2	32	no	—
846	Q₈	—	2	16	no	—
847	Q₈	—	4	16	no	—
848	Q₈	—	4	16	no	—
849	D₄	—	2	32	no	—
850	D₄	—	2	64	no	—
851	D₄	—	2	32	no	—
852	D₄	—	2	32	no	—
853	D₄	—	2	16	no	—
854	D₄	—	2	32	no	—
855	D₄	—	4	64	no	—
856	D₄	—	4	64	no	—
857	D₄	—	4	16	no	—
858	D₄	—	4	32	no	—
859	D₄	—	4	16	no	—
860	D₄	—	4	64	no	—
861	D₄	—	4	16	no	—
862	D₄	—	4	64	no	—
863	D₄	—	4	64	no	—
864	D₄	—	4	32	no	—
865	D₄	—	4	32	no	—
866	D₄	—	4	64	no	—
867	D₄	—	4	64	no	—
868	D₄	—	4	16	no	—
869	C₂×C₄	—	2	4	no	—
870	C₂×C₄	—	2	8	no	—
871	C₂×C₄	—	2	8	no	—
872	C₂×C₄	—	2	16	no	—
873	C₂×C₄	—	2	4	no	—
874	C₂×C₄	—	2	16	no	—
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	8	no	—
877	C₂×C₄	—	2	16	no	—
878	C₂×C₄	—	2	16	no	—
879	C₂×C₄	—	2	16	no	—
880	C₂×C₄	—	2	64	no	—
881	C₂×C₄	—	2	32	no	—
882	C₂×C₄	—	4	16	no	—
883	C₂×C₄	—	4	32	no	—
884	C₂×C₄	—	4	8	no	—
885	C₂×C₄	—	4	16	no	—
886	C₂×C₄	—	4	32	no	—
887	C₂×C₄	—	4	32	no	—
888	C₂×C₄	—	4	64	no	—
889	C₂×C₄	—	4	8	no	—
890	C₂×C₄	—	4	32	no	—
891	C₂×C₄	—	4	64	no	—
892	C₂×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
893	C₂×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
894	C₂×C₄	C₂×H(5,𝔽₂)	1	16	yes	—
895	C₂×C₄	C₂⁶	1	16	yes	—
896	C₂×C₄	C₂⁶	1	8	yes	—
897	C₂×C₄	C₂⁶	1	4	yes	—
898	C₂×C₄	C₂⁶	1	4	yes	—
899	C₂×C₄	C₂⁶	1	16	yes	—
900	C₂×C₄	C₂⁶	1	16	yes	—
901	C₂×C₄	C₂⁶	1	8	yes	—
902	C₂×C₄	C₂⁶	1	4	yes	—
903	C₂×C₄	C₂⁶	1	2	yes	—
904	C₂×C₄	C₂⁶	1	2	yes	—
905	C₂²	—	2	4	no	—
906	C₂²	—	2	8	no	—
907	C₂²	—	2	4	no	—
908	C₂²	—	2	16	no	—
909	C₂²	—	2	8	no	—
910	C₂²	—	2	16	no	—
911	C₂²	—	2	16	no	—
912	C₂²	—	2	16	no	—
913	C₂²	—	2	16	no	—
914	C₂²	—	2	8	no	—
915	C₂²	—	2	16	no	—
916	C₂²	—	2	16	no	—
917	C₂²	—	4	8	no	—
918	C₂²	—	4	32	no	—
919	C₂²	—	4	32	no	—
920	C₂²	—	4	16	no	—
921	C₂²	—	8	8	no	—
922	C₂²	—	8	32	no	—
923	C₂²	—	8	32	no	—
924	C₂²	—	16	64	no	—
925	C₂²	C₂²×H(5,𝔽₂)	1	4	yes	—
926	C₂²	C₂²×H(5,𝔽₂)	1	2	yes	—
927	C₂²	H(7,𝔽₂)	1	4	yes	—
928	C₂²	C₂⁷	1	1	yes	characteristic
929	C₄	—	2	4	no	—
930	C₄	—	2	8	no	—
931	C₄	—	2	16	no	—
932	C₄	—	2	4	no	—
933	C₄	—	2	16	no	—
934	C₄	—	2	4	no	—
935	C₄	—	2	8	no	—
936	C₄	—	2	16	no	—
937	C₄	C₂²×H(5,𝔽₂)	1	4	yes	—
938	C₄	C₂²×H(5,𝔽₂)	1	4	yes	—
939	C₂	—	2	4	no	—
940	C₂	—	4	4	no	—
941	C₂	—	4	16	no	—
942	C₂	—	4	16	no	—
943	C₂	—	4	8	no	—
944	C₂	#62880	1	4	yes	direct product factor
945	C₂	C₂³×H(5,𝔽₂)	1	1	yes	characteristic
946	C₂	C₂×H(7,𝔽₂)	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. #62880	C₂	direct (N × H)
2. C₂×#3512	C₂	semidirect
3. C₂×#3498	C₂	semidirect
4. C₂×#3488	C₂	semidirect
5. C₂×#3506	C₂	semidirect
6. C₂×#3496	C₂	semidirect
7. C₂×#3543	C₂	semidirect
8. C₂×#3562	C₂	semidirect
9. C₂×#3539	C₂	semidirect
10. C₂×#3537	C₂	semidirect
11. C₂×#3537	C₂	semidirect
12. C₂×#3534	C₂	semidirect
13. C₂×#3542	C₂	semidirect
14. C₂×#3455	C₂	semidirect
15. C₂×#3449	C₂	semidirect
16. C₂²×#540	C₂	semidirect
17. C₂²×H(5,𝔽₂)	C₂²	semidirect
18. C₂³×#41	C₂²	semidirect
19. #3562	C₂²	semidirect
20. #3543	C₂²	semidirect
21. #3542	C₂²	semidirect
22. #3539	C₂²	semidirect
23. #3537	C₂²	semidirect
24. #3537	C₂²	semidirect
25. #3534	C₂²	semidirect
26. C₂×#562	C₂²	semidirect
27. C₂×#560	C₂²	semidirect
28. C₂×#560	C₂²	semidirect
29. C₂×#560	C₂²	semidirect
30. #3512	C₂²	semidirect
31. #3506	C₂²	semidirect
32. #3498	C₂²	semidirect
33. #3496	C₂²	semidirect
34. #3488	C₂²	semidirect
35. C₂×#559	C₂²	semidirect
36. C₂×#556	C₂²	semidirect
37. C₂×#555	C₂²	semidirect
38. C₂×#553	C₂²	semidirect
39. C₂×#553	C₂²	semidirect
40. C₂×#553	C₂²	semidirect
41. C₂×#553	C₂²	semidirect
42. C₂×#552	C₂²	semidirect
43. C₂×#551	C₂²	semidirect
44. C₂×#550	C₂²	semidirect
45. C₂×#550	C₂²	semidirect
46. C₂×#550	C₂²	semidirect
47. C₂×#548	C₂²	semidirect
48. C₂×#547	C₂²	semidirect
49. C₂×#547	C₂²	semidirect
50. C₂×#547	C₂²	semidirect
51. C₂×#546	C₂²	semidirect
52. C₂×#546	C₂²	semidirect
53. C₂×#546	C₂²	semidirect
54. C₂×#546	C₂²	semidirect
55. C₂×#546	C₂²	semidirect
56. C₂×D₄²	C₂²	semidirect
57. C₂×D₄²	C₂²	semidirect
58. C₂×D₄²	C₂²	semidirect
59. C₂×D₄²	C₂²	semidirect
60. C₂×D₄²	C₂²	semidirect
61. C₂×D₄²	C₂²	semidirect
62. C₂×D₄²	C₂²	semidirect
63. #3455	C₂²	semidirect
64. C₂×#542	C₂²	semidirect
65. C₂×#541	C₂²	semidirect
66. C₂×#541	C₂²	semidirect
67. C₂×#540	C₂²	semidirect
68. C₂×#540	C₂²	semidirect
69. C₂×#540	C₂²	semidirect
70. C₂×#540	C₂²	semidirect
71. C₂×#540	C₂²	semidirect
72. C₂×#540	C₂²	semidirect
73. C₂×#540	C₂²	semidirect
74. C₂×#540	C₂²	semidirect
75. C₂×#539	C₂²	semidirect
76. C₂×#539	C₂²	semidirect
77. C₂×#538	C₂²	semidirect
78. C₂×#538	C₂²	semidirect
79. C₂×#538	C₂²	semidirect
80. C₂×#538	C₂²	semidirect
81. #3449	C₂²	semidirect
82. C₂×#537	C₂²	semidirect
83. C₂×#537	C₂²	semidirect
84. C₂×#537	C₂²	semidirect
85. C₂×#536	C₂²	semidirect
86. C₂×#535	C₂²	semidirect
87. C₂×#535	C₂²	semidirect
88. C₂×#535	C₂²	semidirect
89. C₂×#535	C₂²	semidirect
90. C₂×#535	C₂²	semidirect
91. C₂×#534	C₂²	semidirect
92. C₂×#534	C₂²	semidirect
93. C₂×#534	C₂²	semidirect
94. C₂×#534	C₂²	semidirect
95. C₂×#533	C₂²	semidirect
96. C₂×#532	C₂²	semidirect
97. C₂×#532	C₂²	semidirect
98. C₂×#532	C₂²	semidirect
99. C₂×#532	C₂²	semidirect
100. C₂²×#127	C₂²	semidirect
101. C₂²×#127	C₂²	semidirect
102. C₂×#529	C₂²	semidirect
103. C₂×#529	C₂²	semidirect
104. C₂²×#125	C₂²	semidirect
105. C₂×#525	C₂²	semidirect
106. C₂×#525	C₂²	semidirect
107. C₂×#525	C₂²	semidirect
108. C₂×#525	C₂²	semidirect
109. C₂×#525	C₂²	semidirect
110. C₂²×#123	C₂²	semidirect
111. C₂²×#121	C₂²	semidirect
112. C₂²×#121	C₂²	semidirect
113. C₂²×#121	C₂²	semidirect
114. C₂²×#121	C₂²	semidirect
115. C₂×#520	C₂²	semidirect
116. C₂×C₄×#41	C₂²	semidirect
117. C₂²×C₄×D₄	C₂²	semidirect
118. C₂²×#117	C₂²	semidirect
120. C₂×H(5,𝔽₂)	C₂³	semidirect
130. C₂²×#41	C₂³	semidirect
146. #562	C₂³	semidirect
147. #560	C₂³	semidirect
148. #560	C₂³	semidirect
149. #560	C₂³	semidirect
150. #559	C₂³	semidirect
151. #556	C₂³	semidirect
152. #555	C₂³	semidirect
153. #553	C₂³	semidirect
154. #553	C₂³	semidirect
155. #553	C₂³	semidirect
156. #553	C₂³	semidirect
157. #552	C₂³	semidirect
158. #551	C₂³	semidirect
159. #550	C₂³	semidirect
160. #550	C₂³	semidirect
161. #550	C₂³	semidirect
162. #548	C₂³	semidirect
163. #547	C₂³	semidirect
164. #547	C₂³	semidirect
165. #547	C₂³	semidirect
166. #546	C₂³	semidirect
167. #546	C₂³	semidirect
168. #546	C₂³	semidirect
169. #546	C₂³	semidirect
170. #546	C₂³	semidirect
171. D₄²	C₂³	semidirect
172. D₄²	C₂³	semidirect
173. D₄²	C₂³	semidirect
174. D₄²	C₂³	semidirect
175. D₄²	C₂³	semidirect
176. D₄²	C₂³	semidirect
177. D₄²	C₂³	semidirect
178. #542	C₂³	semidirect
179. #541	C₂³	semidirect
180. #541	C₂³	semidirect
181. #540	C₂³	semidirect
182. #540	C₂³	semidirect
183. #540	C₂³	semidirect
184. #540	C₂³	semidirect
185. #540	C₂³	semidirect
186. #540	C₂³	semidirect
187. #540	C₂³	semidirect
188. #539	C₂³	semidirect
189. #539	C₂³	semidirect
190. #538	C₂³	semidirect
191. #538	C₂³	semidirect
192. #538	C₂³	semidirect
193. #538	C₂³	semidirect
194. #537	C₂³	semidirect
195. #537	C₂³	semidirect
196. #537	C₂³	semidirect
197. #536	C₂³	semidirect
198. #535	C₂³	semidirect
199. #535	C₂³	semidirect
200. #535	C₂³	semidirect
201. #535	C₂³	semidirect
202. #535	C₂³	semidirect
203. #534	C₂³	semidirect
204. #534	C₂³	semidirect
205. #534	C₂³	semidirect
206. #534	C₂³	semidirect
207. #533	C₂³	semidirect
208. #532	C₂³	semidirect
209. #532	C₂³	semidirect
210. #532	C₂³	semidirect
211. #532	C₂³	semidirect
224. C₂×#127	C₂³	semidirect
225. C₂×#127	C₂³	semidirect
226. #529	C₂³	semidirect
227. #529	C₂³	semidirect
238. C₂×#125	C₂³	semidirect
246. #525	C₂³	semidirect
247. #525	C₂³	semidirect
248. #525	C₂³	semidirect
249. #525	C₂³	semidirect
250. #525	C₂³	semidirect
265. C₂×#123	C₂³	semidirect
306. C₂×#121	C₂³	semidirect
307. C₂×#121	C₂³	semidirect
308. C₂×#121	C₂³	semidirect
309. C₂×#121	C₂³	semidirect
321. #520	C₂³	semidirect
322. C₄×#41	C₂³	semidirect
344. C₂×C₄×D₄	C₂³	semidirect
353. C₂×#117	C₂³	semidirect
944. C₂	#62880	direct (N × H)

Maximal subgroups

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

subgroup	index
#62880	2
C₂×#3512	2
C₂×#3498	2
C₂×#3488	2
C₂×#3506	2
C₂×#3496	2
C₂×#3543	2
C₂×#3562	2
C₂×#3539	2
C₂×#3537	2
C₂×#3534	2
C₂×#3542	2
C₂×#3455	2
C₂×#3449	2
C₂²×#540	2

Subgroups — C2×#62880 #10586214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#62880 #10586214