Subgroups — C₂×#62888 #10586223

Order 512.

33806 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#62888	C₂	1	64	yes	maximal, direct product factor
2	C₂×#3512	C₂	1	2	yes	maximal, complemented
3	C₂×#3499	C₂	1	2	yes	maximal, complemented
4	C₂×#3489	C₂	1	4	yes	maximal, complemented
5	C₂×#3497	C₂	1	2	yes	maximal, complemented
6	C₂×#3507	C₂	1	2	yes	maximal, complemented
7	C₂×#3552	C₂	1	8	yes	maximal, complemented
8	C₂×#3562	C₂	1	8	yes	maximal, complemented
9	C₂×#3560	C₂	1	8	yes	maximal, complemented
10	C₂×#3559	C₂	1	8	yes	maximal, complemented
11	C₂×#3539	C₂	1	4	yes	maximal, complemented
12	C₂×#3538	C₂	1	4	yes	maximal, complemented
13	C₂×#3541	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×#541	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×2₋¹⁺⁴	C₂²	1	4	yes	complemented
18	C₂³×#41	C₂²	1	2	yes	—
19	#3562	C₂²	1	256	yes	complemented
20	#3560	C₂²	1	256	yes	complemented
21	#3559	C₂²	1	256	yes	complemented
22	#3552	C₂²	1	256	yes	complemented
23	#3541	C₂²	1	256	yes	complemented
24	#3539	C₂²	1	128	yes	complemented
25	#3538	C₂²	1	128	yes	complemented
26	C₂×#563	C₂²	1	16	yes	complemented
27	C₂×#563	C₂²	1	16	yes	complemented
28	C₂×#562	C₂²	1	16	yes	complemented
29	C₂×#560	C₂²	1	16	yes	complemented
30	#3512	C₂²	1	64	yes	complemented
31	#3507	C₂²	1	64	yes	complemented
32	#3499	C₂²	1	64	yes	complemented
33	#3497	C₂²	1	64	yes	complemented
34	#3489	C₂²	1	128	yes	complemented
35	C₂×#559	C₂²	1	4	yes	complemented
36	C₂×#557	C₂²	1	4	yes	complemented
37	C₂×#556	C₂²	1	4	yes	complemented
38	C₂×#556	C₂²	1	8	yes	complemented
39	C₂×#554	C₂²	1	4	yes	complemented
40	C₂×#554	C₂²	1	16	yes	complemented
41	C₂×#553	C₂²	1	8	yes	complemented
42	C₂×#553	C₂²	1	16	yes	complemented
43	C₂×#553	C₂²	1	16	yes	complemented
44	C₂×#553	C₂²	1	16	yes	complemented
45	C₂×#552	C₂²	1	8	yes	complemented
46	C₂×#552	C₂²	1	8	yes	complemented
47	C₂×#551	C₂²	1	16	yes	complemented
48	C₂×#550	C₂²	1	4	yes	complemented
49	C₂×#550	C₂²	1	4	yes	complemented
50	C₂×D₄×Q₈	C₂²	1	8	yes	complemented
51	C₂×D₄×Q₈	C₂²	1	4	yes	complemented
52	C₂×D₄×Q₈	C₂²	1	4	yes	complemented
53	C₂×D₄×Q₈	C₂²	1	8	yes	complemented
54	C₂×#548	C₂²	1	8	yes	—
55	C₂×#548	C₂²	1	8	yes	complemented
56	C₂×#548	C₂²	1	8	yes	complemented
57	C₂×#547	C₂²	1	8	yes	—
58	C₂×#547	C₂²	1	8	yes	complemented
59	C₂×#547	C₂²	1	16	yes	complemented
60	C₂×#547	C₂²	1	16	yes	complemented
61	C₂×#546	C₂²	1	16	yes	—
62	C₂×#546	C₂²	1	8	yes	complemented
63	C₂×#544	C₂²	1	16	yes	complemented
64	#3455	C₂²	1	32	yes	complemented
65	C₂×#542	C₂²	1	4	yes	complemented
66	C₂×#542	C₂²	1	16	yes	complemented
67	C₂×#541	C₂²	1	4	yes	complemented
68	C₂×#541	C₂²	1	2	yes	complemented
69	C₂×#541	C₂²	1	4	yes	complemented
70	C₂×#541	C₂²	1	8	yes	complemented
71	C₂×#541	C₂²	1	4	yes	complemented
72	C₂×#541	C₂²	1	32	yes	complemented
73	C₂×#540	C₂²	1	2	yes	complemented
74	C₂×#540	C₂²	1	16	yes	complemented
75	C₂×#540	C₂²	1	4	yes	complemented
76	C₂×#539	C₂²	1	16	yes	complemented
77	C₂×#539	C₂²	1	16	yes	complemented
78	C₂×#539	C₂²	1	16	yes	complemented
79	C₂×#539	C₂²	1	4	yes	complemented
80	C₂×#539	C₂²	1	8	yes	complemented
81	C₂×#538	C₂²	1	4	yes	—
82	C₂×#538	C₂²	1	16	yes	complemented
83	C₂×#538	C₂²	1	16	yes	complemented
84	#3449	C₂²	1	32	yes	complemented
85	C₂×#537	C₂²	1	8	yes	—
86	C₂×#537	C₂²	1	4	yes	—
87	C₂×#537	C₂²	1	8	yes	complemented
88	C₂×#537	C₂²	1	4	yes	complemented
89	C₂×#536	C₂²	1	8	yes	—
90	C₂×#536	C₂²	1	4	yes	—
91	C₂×#536	C₂²	1	8	yes	complemented
92	C₂×#536	C₂²	1	4	yes	complemented
93	C₂×#535	C₂²	1	4	yes	—
94	C₂×#534	C₂²	1	4	yes	—
95	C₂×#533	C₂²	1	1	yes	characteristic, complemented
96	C₂×#532	C₂²	1	2	yes	—
97	C₂×#532	C₂²	1	2	yes	—
98	C₂×#532	C₂²	1	8	yes	complemented
99	C₂×#532	C₂²	1	4	yes	complemented
100	C₂×#532	C₂²	1	1	yes	characteristic, complemented
101	C₂²×C₄⋊Q₈	C₂²	1	4	yes	complemented
102	C₂²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
103	C₂×#529	C₂²	1	8	yes	complemented
104	C₂×#529	C₂²	1	8	yes	complemented
105	C₂×#529	C₂²	1	8	yes	complemented
106	C₂²×#126	C₂²	1	4	yes	—
107	C₂²×#125	C₂²	1	4	yes	complemented
108	C₂²×#125	C₂²	1	1	yes	characteristic, complemented
109	C₂×#525	C₂²	1	4	yes	—
110	C₂×#525	C₂²	1	4	yes	—
111	C₂×#525	C₂²	1	2	yes	—
112	C₂×#525	C₂²	1	8	yes	complemented
113	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	—
114	C₂²×C₂²⋊Q₈	C₂²	1	8	yes	complemented
115	C₂×#520	C₂²	1	4	yes	complemented
116	C₂×C₄×#41	C₂²	1	2	yes	complemented
117	C₂²×C₄×Q₈	C₂²	1	2	yes	complemented
118	C₂²×#117	C₂²	1	1	yes	characteristic
119	C₂×2₋¹⁺⁴	—	4	32	no	—
120	C₂×2₋¹⁺⁴	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	32	yes	—
128	C₂²×#41	C₂³	1	8	yes	—
129	C₂²×#41	C₂³	1	8	yes	—
130	C₂²×#41	C₂³	1	16	yes	—
131	C₂³×Q₈	C₂³	1	2	yes	—
132	C₂³×Q₈	C₂³	1	2	yes	—
133	C₂³×Q₈	C₂³	1	8	yes	—
134	C₂³×Q₈	C₂³	1	8	yes	—
135	C₂³×D₄	C₂³	1	4	yes	—
136	C₂³×D₄	C₂³	1	2	yes	—
137	C₂⁴×C₄	C₂³	1	1	yes	characteristic
138	C₂⁴×C₄	C₂³	1	4	yes	—
139	#563	C₂³	1	256	yes	complemented
140	#563	C₂³	1	256	yes	complemented
141	#562	C₂³	1	256	yes	complemented
142	#560	C₂³	1	256	yes	complemented
143	#559	C₂³	1	64	yes	complemented
144	#557	C₂³	1	64	yes	complemented
145	#556	C₂³	1	64	yes	complemented
146	#556	C₂³	1	128	yes	complemented
147	#554	C₂³	1	64	yes	complemented
148	#554	C₂³	1	256	yes	complemented
149	#553	C₂³	1	128	yes	complemented
150	#553	C₂³	1	256	yes	complemented
151	#553	C₂³	1	256	yes	complemented
152	#553	C₂³	1	256	yes	complemented
153	#552	C₂³	1	128	yes	complemented
154	#552	C₂³	1	128	yes	complemented
155	#551	C₂³	1	256	yes	complemented
156	#550	C₂³	1	64	yes	complemented
157	#550	C₂³	1	64	yes	complemented
158	D₄×Q₈	C₂³	1	128	yes	complemented
159	D₄×Q₈	C₂³	1	64	yes	complemented
160	D₄×Q₈	C₂³	1	64	yes	complemented
161	D₄×Q₈	C₂³	1	128	yes	complemented
162	#548	C₂³	1	128	yes	—
163	#548	C₂³	1	128	yes	complemented
164	#548	C₂³	1	128	yes	complemented
165	#547	C₂³	1	128	yes	—
166	#547	C₂³	1	256	yes	complemented
167	#547	C₂³	1	128	yes	complemented
168	#547	C₂³	1	256	yes	complemented
169	#546	C₂³	1	256	yes	—
170	#546	C₂³	1	128	yes	complemented
171	#544	C₂³	1	256	yes	complemented
172	#542	C₂³	1	64	yes	complemented
173	#542	C₂³	1	256	yes	complemented
174	#541	C₂³	1	64	yes	complemented
175	#541	C₂³	1	64	yes	complemented
176	#541	C₂³	1	128	yes	complemented
177	#541	C₂³	1	32	yes	complemented
178	#541	C₂³	1	64	yes	complemented
179	#540	C₂³	1	32	yes	complemented
180	#540	C₂³	1	64	yes	complemented
181	#540	C₂³	1	256	yes	complemented
182	#539	C₂³	1	64	yes	complemented
183	#539	C₂³	1	128	yes	complemented
184	#539	C₂³	1	256	yes	complemented
185	#539	C₂³	1	256	yes	complemented
186	#539	C₂³	1	256	yes	complemented
187	#538	C₂³	1	64	yes	—
188	#538	C₂³	1	256	yes	complemented
189	#538	C₂³	1	256	yes	complemented
190	#537	C₂³	1	64	yes	—
191	#537	C₂³	1	128	yes	—
192	#537	C₂³	1	64	yes	complemented
193	#537	C₂³	1	128	yes	complemented
194	#536	C₂³	1	64	yes	—
195	#536	C₂³	1	128	yes	—
196	#536	C₂³	1	64	yes	complemented
197	#536	C₂³	1	128	yes	complemented
198	#535	C₂³	1	64	yes	—
199	#534	C₂³	1	64	yes	—
200	#533	C₂³	1	16	yes	complemented
201	#532	C₂³	1	32	yes	—
202	#532	C₂³	1	32	yes	—
203	#532	C₂³	1	16	yes	complemented
204	#532	C₂³	1	128	yes	complemented
205	#532	C₂³	1	64	yes	complemented
206	C₂×C₄⋊Q₈	C₂³	1	2	yes	—
207	C₂×C₄⋊Q₈	C₂³	1	4	yes	—
208	C₂×C₄⋊Q₈	C₂³	1	8	yes	—
209	C₂×C₄⋊Q₈	C₂³	1	4	yes	—
210	C₂×C₄⋊Q₈	C₂³	1	16	yes	—
211	C₂×C₄⋊Q₈	C₂³	1	2	yes	—
212	C₂×C₄⋊Q₈	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊Q₈	C₂³	1	8	yes	—
214	C₂×C₄⋊Q₈	C₂³	1	2	yes	—
215	C₂×C₄⋊Q₈	C₂³	1	16	yes	—
216	C₂×C₄⋊Q₈	C₂³	1	16	yes	complemented
217	C₂×C₄⋊Q₈	C₂³	1	64	yes	complemented
218	C₂×#127	C₂³	1	2	yes	—
219	C₂×#127	C₂³	1	2	yes	—
220	C₂×#127	C₂³	1	1	yes	characteristic
221	C₂×#127	C₂³	1	8	yes	—
222	#529	C₂³	1	128	yes	complemented
223	#529	C₂³	1	128	yes	complemented
224	#529	C₂³	1	128	yes	complemented
225	C₂×#126	C₂³	1	16	yes	—
226	C₂×#126	C₂³	1	16	yes	—
227	C₂×#126	C₂³	1	64	yes	—
228	C₂×#126	C₂³	1	8	yes	—
229	C₂×#126	C₂³	1	16	yes	—
230	C₂×#126	C₂³	1	16	yes	—
231	C₂×#126	C₂³	1	8	yes	—
232	C₂×#126	C₂³	1	16	yes	—
233	C₂×#126	C₂³	1	16	yes	—
234	C₂×#125	C₂³	1	4	yes	—
235	C₂×#125	C₂³	1	16	yes	—
236	C₂×#125	C₂³	1	4	yes	—
237	C₂×#125	C₂³	1	16	yes	—
238	C₂×#125	C₂³	1	8	yes	—
239	C₂×#125	C₂³	1	8	yes	—
240	C₂×#125	C₂³	1	2	yes	—
241	C₂×#125	C₂³	1	16	yes	—
242	C₂×#125	C₂³	1	16	yes	—
243	C₂×#125	C₂³	1	16	yes	complemented
244	C₂×#125	C₂³	1	64	yes	complemented
245	C₂×#124	C₂³	1	4	yes	—
246	C₂×#124	C₂³	1	8	yes	—
247	C₂×#124	C₂³	1	8	yes	—
248	C₂×#124	C₂³	1	4	yes	—
249	C₂×#124	C₂³	1	8	yes	—
250	C₂×#124	C₂³	1	16	yes	—
251	C₂×#124	C₂³	1	2	yes	—
252	C₂×#124	C₂³	1	16	yes	—
253	#525	C₂³	1	64	yes	—
254	#525	C₂³	1	64	yes	—
255	#525	C₂³	1	32	yes	—
256	#525	C₂³	1	128	yes	complemented
257	C₂×#123	C₂³	1	8	yes	—
258	C₂×#123	C₂³	1	8	yes	—
259	C₂×#123	C₂³	1	4	yes	—
260	C₂×#123	C₂³	1	16	yes	—
261	C₂×#123	C₂³	1	16	yes	—
262	C₂×#123	C₂³	1	8	yes	—
263	C₂×#123	C₂³	1	8	yes	—
264	C₂×#123	C₂³	1	16	yes	—
265	C₂×#123	C₂³	1	16	yes	—
266	C₂×#123	C₂³	1	16	yes	—
267	C₂×#123	C₂³	1	16	yes	—
268	C₂×#123	C₂³	1	16	yes	—
269	C₂×#123	C₂³	1	16	yes	—
270	C₂×#123	C₂³	1	16	yes	—
271	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
272	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
273	C₂×C₂²⋊Q₈	C₂³	1	32	yes	—
274	C₂×C₂²⋊Q₈	C₂³	1	4	yes	—
275	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
276	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
277	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
278	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
279	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
280	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
281	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
282	C₂×C₂²⋊Q₈	C₂³	1	4	yes	—
283	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
284	C₂×C₂²⋊Q₈	C₂³	1	8	yes	—
285	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
286	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
287	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
288	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
289	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
290	C₂×C₂²⋊Q₈	C₂³	1	16	yes	—
291	C₂×C₂²⋊Q₈	C₂³	1	128	yes	complemented
292	C₂×#121	C₂³	1	4	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	4	yes	—
297	C₂×#121	C₂³	1	8	yes	—
298	C₂×#121	C₂³	1	8	yes	—
299	C₂×#121	C₂³	1	4	yes	—
300	C₂×#121	C₂³	1	8	yes	—
301	C₂×#121	C₂³	1	4	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	16	yes	—
307	C₂×#121	C₂³	1	16	yes	—
308	C₂×#121	C₂³	1	16	yes	—
309	C₂×#121	C₂³	1	16	yes	—
310	C₂×#120	C₂³	1	8	yes	—
311	C₂×#120	C₂³	1	8	yes	—
312	C₂×#120	C₂³	1	4	yes	—
313	C₂×#120	C₂³	1	16	yes	—
314	#520	C₂³	1	64	yes	complemented
315	C₄×#41	C₂³	1	32	yes	complemented
316	C₂×C₄×Q₈	C₂³	1	4	yes	—
317	C₂×C₄×Q₈	C₂³	1	4	yes	—
318	C₂×C₄×Q₈	C₂³	1	4	yes	—
319	C₂×C₄×Q₈	C₂³	1	4	yes	—
320	C₂×C₄×Q₈	C₂³	1	4	yes	—
321	C₂×C₄×Q₈	C₂³	1	8	yes	—
322	C₂×C₄×Q₈	C₂³	1	4	yes	—
323	C₂×C₄×Q₈	C₂³	1	8	yes	—
324	C₂×C₄×Q₈	C₂³	1	32	yes	complemented
325	C₂×C₄×D₄	C₂³	1	8	yes	—
326	C₂×C₄×D₄	C₂³	1	4	yes	—
327	C₂×C₄×D₄	C₂³	1	16	yes	—
328	C₂×C₄×D₄	C₂³	1	8	yes	—
329	C₂×C₄×D₄	C₂³	1	8	yes	—
330	C₂×C₄×D₄	C₂³	1	4	yes	—
331	C₂×C₄×D₄	C₂³	1	4	yes	—
332	C₂×C₄×D₄	C₂³	1	8	yes	—
333	C₂×C₄×D₄	C₂³	1	16	yes	—
334	C₂×C₄×D₄	C₂³	1	16	yes	—
335	C₂×C₄×D₄	C₂³	1	4	yes	—
336	C₂×C₄×D₄	C₂³	1	8	yes	—
337	C₂×C₄×D₄	C₂³	1	16	yes	—
338	C₂×C₄×D₄	C₂³	1	16	yes	—
339	C₂×C₄×D₄	C₂³	1	16	yes	—
340	C₂×C₄×D₄	C₂³	1	8	yes	—
341	C₂×C₄×D₄	C₂³	1	8	yes	—
342	C₂×#117	C₂³	1	2	yes	—
343	C₂×#117	C₂³	1	2	yes	—
344	C₂×#117	C₂³	1	4	yes	—
345	C₂×#117	C₂³	1	16	yes	—
346	C₂×#117	C₂³	1	2	yes	—
347	C₂×#117	C₂³	1	4	yes	—
348	C₂×#117	C₂³	1	8	yes	—
349	C₂×#117	C₂³	1	16	yes	—
350	C₂×#117	C₂³	1	16	yes	—
351	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
352	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
353	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
354	C₂²×C₄⋊C₄	C₂³	1	8	yes	—
355	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
356	C₂²×C₄⋊C₄	C₂³	1	16	yes	—
357	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
358	C₂²×C₄⋊C₄	C₂³	1	4	yes	—
359	C₂²×C₄⋊C₄	C₂³	1	16	yes	—
360	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
361	C₂²×C₂²⋊C₄	C₂³	1	4	yes	—
362	C₂²×C₂²⋊C₄	C₂³	1	16	yes	—
363	C₂²×C₄²	C₂³	1	1	yes	characteristic
364	C₂²×C₄²	C₂³	1	1	yes	characteristic
365	C₂²×C₄²	C₂³	1	4	yes	—
366	C₂²×C₄²	C₂³	1	4	yes	—
367	C₂⁵	C₂⁴	1	1	yes	characteristic
368	C₂⁵	C₂⁴	1	4	yes	—
369	2₋¹⁺⁴	—	4	256	no	—
370	C₂×#41	—	2	32	no	—
371	C₂×#41	—	2	16	no	—
372	C₂×#41	—	4	16	no	—
373	C₂×#41	—	4	16	no	—
374	C₂×#41	—	4	64	no	—
375	C₂×#41	—	4	16	no	—
376	C₂×#41	—	4	32	no	—
377	C₂×#41	—	4	32	no	—
378	C₂×#41	—	4	128	no	—
379	C₂×#41	C₂⁴	1	16	yes	—
380	C₂×#41	C₂⁴	1	32	yes	—
381	C₂×#41	C₂⁴	1	32	yes	—
382	C₂×#41	C₂⁴	1	64	yes	—
383	C₂×#41	C₂⁴	1	64	yes	—
384	C₂×#41	C₂⁴	1	128	yes	—
385	C₂×#41	C₂⁴	1	32	yes	—
386	C₂×#41	C₂⁴	1	32	yes	—
387	C₂²×Q₈	—	2	16	no	—
388	C₂²×Q₈	—	4	8	no	—
389	C₂²×Q₈	—	4	32	no	—
390	C₂²×Q₈	—	4	32	no	—
391	C₂²×Q₈	C₂⁴	1	2	yes	—
392	C₂²×Q₈	C₂⁴	1	4	yes	—
393	C₂²×Q₈	C₂⁴	1	4	yes	—
394	C₂²×Q₈	C₂⁴	1	4	yes	—
395	C₂²×Q₈	C₂⁴	1	16	yes	—
396	C₂²×Q₈	C₂⁴	1	4	yes	—
397	C₂²×Q₈	C₂⁴	1	4	yes	—
398	C₂²×Q₈	C₂⁴	1	16	yes	—
399	C₂²×Q₈	C₂⁴	1	64	yes	—
400	C₂²×Q₈	C₂⁴	1	64	yes	—
401	C₂²×Q₈	C₂⁴	1	16	yes	—
402	C₂²×D₄	—	4	8	no	—
403	C₂²×D₄	—	4	16	no	—
404	C₂²×D₄	C₂⁴	1	4	yes	—
405	C₂²×D₄	C₂⁴	1	8	yes	—
406	C₂²×D₄	C₂⁴	1	2	yes	—
407	C₂²×D₄	C₂⁴	1	4	yes	—
408	C₂²×D₄	C₂⁴	1	8	yes	—
409	C₂²×D₄	C₂⁴	1	8	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	8	yes	—
415	C₂²×D₄	C₂⁴	1	16	yes	—
416	C₂²×D₄	C₂⁴	1	4	yes	—
417	C₂²×D₄	C₂⁴	1	32	yes	—
418	C₂²×D₄	C₂⁴	1	16	yes	—
419	C₂³×C₄	—	2	8	no	—
420	C₂³×C₄	—	4	16	no	—
421	C₂³×C₄	C₂⁴	1	4	yes	—
422	C₂³×C₄	C₂⁴	1	1	yes	characteristic
423	C₂³×C₄	C₂⁴	1	8	yes	—
424	C₂³×C₄	C₂⁴	1	2	yes	—
425	C₂³×C₄	C₂⁴	1	2	yes	—
426	C₂³×C₄	C₂⁴	1	8	yes	—
427	C₂³×C₄	C₂⁴	1	4	yes	—
428	C₂³×C₄	C₂⁴	1	2	yes	—
429	C₂³×C₄	C₂⁴	1	4	yes	—
430	C₂³×C₄	C₂⁴	1	2	yes	—
431	C₂³×C₄	C₂⁴	1	16	yes	—
432	C₂³×C₄	C₂⁴	1	16	yes	—
433	C₂³×C₄	C₂⁴	1	8	yes	—
434	C₂³×C₄	C₂⁴	1	16	yes	—
435	C₂³×C₄	C₂⁴	1	8	yes	—
436	C₂³×C₄	C₂⁴	1	4	yes	—
437	C₂³×C₄	C₂⁴	1	32	yes	—
438	C₂³×C₄	C₂⁴	1	1	yes	characteristic
439	C₄⋊Q₈	C₂⁴	1	16	yes	—
440	C₄⋊Q₈	C₂⁴	1	32	yes	—
441	C₄⋊Q₈	C₂⁴	1	64	yes	—
442	C₄⋊Q₈	C₂⁴	1	32	yes	—
443	C₄⋊Q₈	C₂⁴	1	128	yes	—
444	C₄⋊Q₈	C₂⁴	1	16	yes	—
445	C₄⋊Q₈	C₂⁴	1	8	yes	—
446	C₄⋊Q₈	C₂⁴	1	64	yes	—
447	C₄⋊Q₈	C₂⁴	1	16	yes	—
448	C₄⋊Q₈	C₂⁴	1	128	yes	—
449	#127	C₂⁴	1	16	yes	—
450	#127	C₂⁴	1	16	yes	—
451	#127	C₂⁴	1	8	yes	—
452	#127	C₂⁴	1	64	yes	—
453	#126	C₂⁴	1	128	yes	—
454	#126	C₂⁴	1	128	yes	—
455	#126	C₂⁴	1	64	yes	—
456	#126	C₂⁴	1	128	yes	—
457	#126	C₂⁴	1	128	yes	—
458	#126	C₂⁴	1	64	yes	—
459	#126	C₂⁴	1	128	yes	—
460	#126	C₂⁴	1	128	yes	—
461	#125	C₂⁴	1	32	yes	—
462	#125	C₂⁴	1	128	yes	—
463	#125	C₂⁴	1	32	yes	—
464	#125	C₂⁴	1	128	yes	—
465	#125	C₂⁴	1	64	yes	—
466	#125	C₂⁴	1	64	yes	—
467	#125	C₂⁴	1	16	yes	—
468	#125	C₂⁴	1	128	yes	—
469	#125	C₂⁴	1	128	yes	—
470	#124	C₂⁴	1	32	yes	—
471	#124	C₂⁴	1	64	yes	—
472	#124	C₂⁴	1	64	yes	—
473	#124	C₂⁴	1	32	yes	—
474	#124	C₂⁴	1	64	yes	—
475	#124	C₂⁴	1	128	yes	—
476	#124	C₂⁴	1	16	yes	—
477	#124	C₂⁴	1	128	yes	—
478	#123	C₂⁴	1	64	yes	—
479	#123	C₂⁴	1	64	yes	—
480	#123	C₂⁴	1	32	yes	—
481	#123	C₂⁴	1	128	yes	—
482	#123	C₂⁴	1	128	yes	—
483	#123	C₂⁴	1	64	yes	—
484	#123	C₂⁴	1	64	yes	—
485	#123	C₂⁴	1	128	yes	—
486	#123	C₂⁴	1	128	yes	—
487	#123	C₂⁴	1	128	yes	—
488	#123	C₂⁴	1	128	yes	—
489	#123	C₂⁴	1	128	yes	—
490	#123	C₂⁴	1	128	yes	—
491	#123	C₂⁴	1	128	yes	—
492	C₂²⋊Q₈	C₂⁴	1	64	yes	—
493	C₂²⋊Q₈	C₂⁴	1	64	yes	—
494	C₂²⋊Q₈	C₂⁴	1	32	yes	—
495	C₂²⋊Q₈	C₂⁴	1	64	yes	—
496	C₂²⋊Q₈	C₂⁴	1	64	yes	—
497	C₂²⋊Q₈	C₂⁴	1	128	yes	—
498	C₂²⋊Q₈	C₂⁴	1	128	yes	—
499	C₂²⋊Q₈	C₂⁴	1	64	yes	—
500	C₂²⋊Q₈	C₂⁴	1	64	yes	—
501	C₂²⋊Q₈	C₂⁴	1	64	yes	—
502	C₂²⋊Q₈	C₂⁴	1	32	yes	—
503	C₂²⋊Q₈	C₂⁴	1	64	yes	—
504	C₂²⋊Q₈	C₂⁴	1	64	yes	—
505	C₂²⋊Q₈	C₂⁴	1	128	yes	—
506	C₂²⋊Q₈	C₂⁴	1	128	yes	—
507	C₂²⋊Q₈	C₂⁴	1	128	yes	—
508	C₂²⋊Q₈	C₂⁴	1	128	yes	—
509	C₂²⋊Q₈	C₂⁴	1	128	yes	—
510	C₂²⋊Q₈	C₂⁴	1	128	yes	—
511	#121	C₂⁴	1	32	yes	—
512	#121	C₂⁴	1	64	yes	—
513	#121	C₂⁴	1	64	yes	—
514	#121	C₂⁴	1	64	yes	—
515	#121	C₂⁴	1	32	yes	—
516	#121	C₂⁴	1	64	yes	—
517	#121	C₂⁴	1	64	yes	—
518	#121	C₂⁴	1	32	yes	—
519	#121	C₂⁴	1	64	yes	—
520	#121	C₂⁴	1	32	yes	—
521	#121	C₂⁴	1	128	yes	—
522	#121	C₂⁴	1	128	yes	—
523	#121	C₂⁴	1	128	yes	—
524	#121	C₂⁴	1	128	yes	—
525	#121	C₂⁴	1	128	yes	—
526	#121	C₂⁴	1	128	yes	—
527	#121	C₂⁴	1	128	yes	—
528	#121	C₂⁴	1	128	yes	—
529	#120	C₂⁴	1	64	yes	—
530	#120	C₂⁴	1	64	yes	—
531	#120	C₂⁴	1	32	yes	—
532	#120	C₂⁴	1	128	yes	—
533	C₄×Q₈	C₂⁴	1	32	yes	—
534	C₄×Q₈	C₂⁴	1	32	yes	—
535	C₄×Q₈	C₂⁴	1	32	yes	—
536	C₄×Q₈	C₂⁴	1	32	yes	—
537	C₄×Q₈	C₂⁴	1	32	yes	—
538	C₄×Q₈	C₂⁴	1	64	yes	—
539	C₄×Q₈	C₂⁴	1	32	yes	—
540	C₄×Q₈	C₂⁴	1	64	yes	—
541	C₄×D₄	C₂⁴	1	64	yes	—
542	C₄×D₄	C₂⁴	1	32	yes	—
543	C₄×D₄	C₂⁴	1	128	yes	—
544	C₄×D₄	C₂⁴	1	64	yes	—
545	C₄×D₄	C₂⁴	1	64	yes	—
546	C₄×D₄	C₂⁴	1	32	yes	—
547	C₄×D₄	C₂⁴	1	32	yes	—
548	C₄×D₄	C₂⁴	1	64	yes	—
549	C₄×D₄	C₂⁴	1	128	yes	—
550	C₄×D₄	C₂⁴	1	128	yes	—
551	C₄×D₄	C₂⁴	1	32	yes	—
552	C₄×D₄	C₂⁴	1	64	yes	—
553	C₄×D₄	C₂⁴	1	128	yes	—
554	C₄×D₄	C₂⁴	1	128	yes	—
555	C₄×D₄	C₂⁴	1	128	yes	—
556	C₄×D₄	C₂⁴	1	64	yes	—
557	C₄×D₄	C₂⁴	1	64	yes	—
558	#117	C₂⁴	1	16	yes	—
559	#117	C₂⁴	1	16	yes	—
560	#117	C₂⁴	1	32	yes	—
561	#117	C₂⁴	1	16	yes	—
562	#117	C₂⁴	1	32	yes	—
563	#117	C₂⁴	1	64	yes	—
564	#117	C₂⁴	1	128	yes	—
565	#117	C₂⁴	1	128	yes	—
566	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
567	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
568	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
569	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
570	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
571	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
572	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
573	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
574	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
575	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
576	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
577	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
578	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
579	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
580	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
581	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
582	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
583	C₂×C₄⋊C₄	C₂⁴	1	16	yes	—
584	C₂×C₄⋊C₄	C₂⁴	1	32	yes	—
585	C₂×C₄⋊C₄	C₂⁴	1	64	yes	—
586	C₂×C₄⋊C₄	C₂⁴	1	32	yes	—
587	C₂×C₄⋊C₄	C₂⁴	1	128	yes	—
588	C₂×C₄⋊C₄	C₂⁴	1	32	yes	—
589	C₂×C₄⋊C₄	C₂⁴	1	32	yes	—
590	C₂×C₄⋊C₄	C₂⁴	1	128	yes	—
591	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
592	C₂×C₄⋊C₄	C₂⁴	1	8	yes	—
593	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
594	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
595	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
596	C₂×C₄⋊C₄	C₂⁴	1	4	yes	—
597	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
598	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
599	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
600	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
601	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
602	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
603	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
604	C₂×C₂²⋊C₄	C₂⁴	1	32	yes	—
605	C₂×C₂²⋊C₄	C₂⁴	1	128	yes	—
606	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
607	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
608	C₂×C₂²⋊C₄	C₂⁴	1	4	yes	—
609	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
610	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
611	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
612	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
613	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
614	C₂×C₂²⋊C₄	C₂⁴	1	16	yes	—
615	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
616	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
617	C₂×C₄²	C₂⁴	1	2	yes	—
618	C₂×C₄²	C₂⁴	1	16	yes	—
619	C₂×C₄²	C₂⁴	1	2	yes	—
620	C₂×C₄²	C₂⁴	1	1	yes	characteristic
621	C₂×C₄²	C₂⁴	1	4	yes	—
622	C₂×C₄²	C₂⁴	1	1	yes	characteristic
623	C₂×C₄²	C₂⁴	1	8	yes	—
624	C₂×C₄²	C₂⁴	1	2	yes	—
625	C₂×C₄²	C₂⁴	1	8	yes	—
626	C₂×C₄²	C₂⁴	1	8	yes	—
627	C₂×C₄²	C₂⁴	1	8	yes	—
628	C₂×C₄²	C₂⁴	1	8	yes	—
629	C₂×C₄²	C₂⁴	1	32	yes	—
630	C₂×C₄²	C₂⁴	1	32	yes	—
631	C₂⁴	—	2	4	no	—
632	C₂⁴	—	4	8	no	—
633	C₂⁴	—	4	4	no	—
634	C₂⁴	—	4	16	no	—
635	C₂⁴	C₂⁵	1	2	yes	—
636	C₂⁴	C₂⁵	1	8	yes	—
637	C₂⁴	C₂⁵	1	4	yes	—
638	C₂⁴	C₂⁵	1	1	yes	characteristic
639	C₂⁴	C₂⁵	1	4	yes	—
640	C₂⁴	C₂⁵	1	16	yes	—
641	#41	—	2	128	no	—
642	#41	—	2	64	no	—
643	#41	—	4	64	no	—
644	#41	—	4	64	no	—
645	#41	—	4	256	no	—
646	#41	—	4	64	no	—
647	#41	—	4	128	no	—
648	#41	—	4	128	no	—
649	C₂×Q₈	—	2	16	no	—
650	C₂×Q₈	—	2	16	no	—
651	C₂×Q₈	—	2	64	no	—
652	C₂×Q₈	—	2	8	no	—
653	C₂×Q₈	—	2	16	no	—
654	C₂×Q₈	—	4	32	no	—
655	C₂×Q₈	—	4	8	no	—
656	C₂×Q₈	—	4	8	no	—
657	C₂×Q₈	—	4	32	no	—
658	C₂×Q₈	—	4	128	no	—
659	C₂×Q₈	—	4	128	no	—
660	C₂×Q₈	C₂⁵	1	8	yes	—
661	C₂×Q₈	C₂⁵	1	16	yes	—
662	C₂×Q₈	C₂⁵	1	16	yes	—
663	C₂×Q₈	C₂⁵	1	16	yes	—
664	C₂×Q₈	C₂⁵	1	16	yes	—
665	C₂×Q₈	C₂⁵	1	16	yes	—
666	C₂×Q₈	C₂⁵	1	64	yes	—
667	C₂×D₄	—	2	32	no	—
668	C₂×D₄	—	2	16	no	—
669	C₂×D₄	—	2	16	no	—
670	C₂×D₄	—	2	8	no	—
671	C₂×D₄	—	4	32	no	—
672	C₂×D₄	—	4	8	no	—
673	C₂×D₄	—	4	16	no	—
674	C₂×D₄	—	4	16	no	—
675	C₂×D₄	—	4	32	no	—
676	C₂×D₄	—	4	16	no	—
677	C₂×D₄	—	4	8	no	—
678	C₂×D₄	—	4	8	no	—
679	C₂×D₄	—	4	8	no	—
680	C₂×D₄	—	4	32	no	—
681	C₂×D₄	—	4	64	no	—
682	C₂×D₄	C₂⁵	1	16	yes	—
683	C₂×D₄	C₂⁵	1	32	yes	—
684	C₂×D₄	C₂⁵	1	8	yes	—
685	C₂×D₄	C₂⁵	1	16	yes	—
686	C₂×D₄	C₂⁵	1	32	yes	—
687	C₂×D₄	C₂⁵	1	32	yes	—
688	C₂×D₄	C₂⁵	1	16	yes	—
689	C₂×D₄	C₂⁵	1	16	yes	—
690	C₂×D₄	C₂⁵	1	64	yes	—
691	C₂×D₄	C₂⁵	1	16	yes	—
692	C₂×D₄	C₂⁵	1	32	yes	—
693	C₂×D₄	C₂⁵	1	64	yes	—
694	C₂×D₄	C₂⁵	1	16	yes	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	16	no	—
697	C₂²×C₄	—	2	8	no	—
698	C₂²×C₄	—	2	8	no	—
699	C₂²×C₄	—	2	32	no	—
700	C₂²×C₄	—	2	32	no	—
701	C₂²×C₄	—	2	16	no	—
702	C₂²×C₄	—	4	64	no	—
703	C₂²×C₄	—	4	8	no	—
704	C₂²×C₄	—	4	16	no	—
705	C₂²×C₄	—	4	4	no	—
706	C₂²×C₄	—	4	8	no	—
707	C₂²×C₄	—	4	32	no	—
708	C₂²×C₄	—	4	16	no	—
709	C₂²×C₄	—	4	4	no	—
710	C₂²×C₄	—	4	32	no	—
711	C₂²×C₄	—	4	32	no	—
712	C₂²×C₄	H(5,𝔽₂)	1	8	yes	—
713	C₂²×C₄	C₂⁵	1	16	yes	—
714	C₂²×C₄	C₂⁵	1	16	yes	—
715	C₂²×C₄	C₂⁵	1	4	yes	—
716	C₂²×C₄	C₂⁵	1	32	yes	—
717	C₂²×C₄	C₂⁵	1	8	yes	—
718	C₂²×C₄	C₂⁵	1	8	yes	—
719	C₂²×C₄	C₂⁵	1	2	yes	—
720	C₂²×C₄	C₂⁵	1	2	yes	—
721	C₂²×C₄	C₂⁵	1	8	yes	—
722	C₂²×C₄	C₂⁵	1	4	yes	—
723	C₂²×C₄	C₂⁵	1	8	yes	—
724	C₂²×C₄	C₂⁵	1	4	yes	—
725	C₂²×C₄	C₂⁵	1	8	yes	—
726	C₂²×C₄	C₂⁵	1	8	yes	—
727	C₂²×C₄	C₂⁵	1	2	yes	—
728	C₂²×C₄	C₂⁵	1	8	yes	—
729	C₂²×C₄	C₂⁵	1	8	yes	—
730	C₂²×C₄	C₂⁵	1	16	yes	—
731	C₂²×C₄	C₂⁵	1	32	yes	—
732	C₂²×C₄	C₂⁵	1	64	yes	—
733	C₂²×C₄	C₂⁵	1	64	yes	—
734	C₂²×C₄	C₂⁵	1	64	yes	—
735	C₂²×C₄	C₂⁵	1	32	yes	—
736	C₂²×C₄	C₂⁵	1	16	yes	—
737	C₂²×C₄	C₂⁵	1	4	yes	—
738	C₂²×C₄	C₂⁵	1	1	yes	characteristic
739	C₂²×C₄	C₂⁵	1	1	yes	characteristic
740	C₄⋊C₄	C₂⁵	1	16	yes	—
741	C₄⋊C₄	C₂⁵	1	16	yes	—
742	C₄⋊C₄	C₂⁵	1	64	yes	—
743	C₄⋊C₄	C₂⁵	1	64	yes	—
744	C₄⋊C₄	C₂⁵	1	32	yes	—
745	C₄⋊C₄	C₂⁵	1	32	yes	—
746	C₄⋊C₄	C₂⁵	1	64	yes	—
747	C₄⋊C₄	C₂⁵	1	16	yes	—
748	C₄⋊C₄	C₂⁵	1	16	yes	—
749	C₄⋊C₄	C₂⁵	1	64	yes	—
750	C₄⋊C₄	C₂⁵	1	64	yes	—
751	C₄⋊C₄	C₂⁵	1	64	yes	—
752	C₄⋊C₄	C₂⁵	1	16	yes	—
753	C₄⋊C₄	C₂⁵	1	64	yes	—
754	C₄⋊C₄	C₂⁵	1	32	yes	—
755	C₄⋊C₄	C₂⁵	1	32	yes	—
756	C₄⋊C₄	C₂⁵	1	32	yes	—
757	C₄⋊C₄	C₂⁵	1	32	yes	—
758	C₄⋊C₄	C₂⁵	1	16	yes	—
759	C₄⋊C₄	C₂⁵	1	16	yes	—
760	C₄⋊C₄	C₂⁵	1	16	yes	—
761	C₄⋊C₄	C₂⁵	1	16	yes	—
762	C₂²⋊C₄	C₂⁵	1	64	yes	—
763	C₂²⋊C₄	C₂⁵	1	32	yes	—
764	C₂²⋊C₄	C₂⁵	1	16	yes	—
765	C₂²⋊C₄	C₂⁵	1	16	yes	—
766	C₂²⋊C₄	C₂⁵	1	64	yes	—
767	C₂²⋊C₄	C₂⁵	1	64	yes	—
768	C₂²⋊C₄	C₂⁵	1	32	yes	—
769	C₂²⋊C₄	C₂⁵	1	32	yes	—
770	C₂²⋊C₄	C₂⁵	1	16	yes	—
771	C₂²⋊C₄	C₂⁵	1	64	yes	—
772	C₂²⋊C₄	C₂⁵	1	32	yes	—
773	C₂²⋊C₄	C₂⁵	1	32	yes	—
774	C₂²⋊C₄	C₂⁵	1	32	yes	—
775	C₂²⋊C₄	C₂⁵	1	64	yes	—
776	C₂²⋊C₄	C₂⁵	1	64	yes	—
777	C₂²⋊C₄	C₂⁵	1	32	yes	—
778	C₂²⋊C₄	C₂⁵	1	32	yes	—
779	C₄²	C₂⁵	1	8	yes	—
780	C₄²	C₂⁵	1	8	yes	—
781	C₄²	C₂⁵	1	4	yes	—
782	C₄²	C₂⁵	1	16	yes	—
783	C₄²	C₂⁵	1	4	yes	—
784	C₄²	C₂⁵	1	32	yes	—
785	C₄²	C₂⁵	1	8	yes	—
786	C₄²	C₂⁵	1	32	yes	—
787	C₄²	C₂⁵	1	32	yes	—
788	C₄²	C₂⁵	1	64	yes	—
789	C₂³	—	2	4	no	—
790	C₂³	—	2	4	no	—
791	C₂³	—	2	8	no	—
792	C₂³	—	2	16	no	—
793	C₂³	—	2	16	no	—
794	C₂³	—	2	16	no	—
795	C₂³	—	2	16	no	—
796	C₂³	—	2	8	no	—
797	C₂³	—	2	8	no	—
798	C₂³	—	4	16	no	—
799	C₂³	—	4	8	no	—
800	C₂³	—	4	32	no	—
801	C₂³	—	8	8	no	—
802	C₂³	—	8	32	no	—
803	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
804	C₂³	C₂⁶	1	4	yes	—
805	C₂³	C₂⁶	1	16	yes	—
806	C₂³	C₂⁶	1	8	yes	—
807	C₂³	C₂⁶	1	2	yes	—
808	C₂³	C₂⁶	1	1	yes	characteristic
809	Q₈	—	2	32	no	—
810	Q₈	—	2	32	no	—
811	Q₈	—	2	16	no	—
812	Q₈	—	2	32	no	—
813	Q₈	—	4	64	no	—
814	Q₈	—	4	16	no	—
815	Q₈	—	4	16	no	—
816	D₄	—	2	64	no	—
817	D₄	—	2	32	no	—
818	D₄	—	2	32	no	—
819	D₄	—	2	16	no	—
820	D₄	—	4	16	no	—
821	D₄	—	4	32	no	—
822	D₄	—	4	32	no	—
823	D₄	—	4	64	no	—
824	D₄	—	4	32	no	—
825	D₄	—	4	16	no	—
826	D₄	—	4	16	no	—
827	D₄	—	4	16	no	—
828	D₄	—	4	64	no	—
829	C₂×C₄	—	2	4	no	—
830	C₂×C₄	—	2	8	no	—
831	C₂×C₄	—	2	16	no	—
832	C₂×C₄	—	2	8	no	—
833	C₂×C₄	—	2	16	no	—
834	C₂×C₄	—	2	32	no	—
835	C₂×C₄	—	2	16	no	—
836	C₂×C₄	—	2	8	no	—
837	C₂×C₄	—	2	16	no	—
838	C₂×C₄	—	2	4	no	—
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	16	no	—
841	C₂×C₄	—	2	16	no	—
842	C₂×C₄	—	2	64	no	—
843	C₂×C₄	—	2	32	no	—
844	C₂×C₄	—	4	16	no	—
845	C₂×C₄	—	4	32	no	—
846	C₂×C₄	—	4	8	no	—
847	C₂×C₄	—	4	16	no	—
848	C₂×C₄	—	4	64	no	—
849	C₂×C₄	—	4	32	no	—
850	C₂×C₄	—	4	8	no	—
851	C₂×C₄	—	4	64	no	—
852	C₂×C₄	—	4	64	no	—
853	C₂×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
854	C₂×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
855	C₂×C₄	C₂×H(5,𝔽₂)	1	16	yes	—
856	C₂×C₄	C₂⁶	1	4	yes	—
857	C₂×C₄	C₂⁶	1	4	yes	—
858	C₂×C₄	C₂⁶	1	16	yes	—
859	C₂×C₄	C₂⁶	1	8	yes	—
860	C₂×C₄	C₂⁶	1	16	yes	—
861	C₂×C₄	C₂⁶	1	8	yes	—
862	C₂×C₄	C₂⁶	1	16	yes	—
863	C₂×C₄	C₂⁶	1	16	yes	—
864	C₂×C₄	C₂⁶	1	4	yes	—
865	C₂×C₄	C₂⁶	1	2	yes	—
866	C₂×C₄	C₂⁶	1	2	yes	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	8	no	—
869	C₂²	—	2	4	no	—
870	C₂²	—	2	8	no	—
871	C₂²	—	2	16	no	—
872	C₂²	—	2	16	no	—
873	C₂²	—	2	16	no	—
874	C₂²	—	2	16	no	—
875	C₂²	—	2	8	no	—
876	C₂²	—	4	16	no	—
877	C₂²	—	4	32	no	—
878	C₂²	—	4	8	no	—
879	C₂²	—	8	8	no	—
880	C₂²	—	8	32	no	—
881	C₂²	C₂²×H(5,𝔽₂)	1	4	yes	—
882	C₂²	C₂²×H(5,𝔽₂)	1	2	yes	—
883	C₂²	2₋¹⁺⁶	1	4	yes	—
884	C₂²	C₂⁷	1	1	yes	characteristic
885	C₄	—	2	4	no	—
886	C₄	—	2	16	no	—
887	C₄	—	2	8	no	—
888	C₄	—	2	16	no	—
889	C₄	—	2	16	no	—
890	C₄	—	2	8	no	—
891	C₄	—	2	16	no	—
892	C₄	—	2	4	no	—
893	C₄	—	2	4	no	—
894	C₄	C₂²×H(5,𝔽₂)	1	4	yes	—
895	C₄	C₂²×H(5,𝔽₂)	1	4	yes	—
896	C₂	—	2	4	no	—
897	C₂	—	4	8	no	—
898	C₂	—	4	16	no	—
899	C₂	—	4	4	no	—
900	C₂	#62888	1	4	yes	direct product factor
901	C₂	C₂³×H(5,𝔽₂)	1	1	yes	characteristic
902	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. #62888	C₂	direct (N × H)
2. C₂×#3512	C₂	semidirect
3. C₂×#3499	C₂	semidirect
4. C₂×#3489	C₂	semidirect
5. C₂×#3497	C₂	semidirect
6. C₂×#3507	C₂	semidirect
7. C₂×#3552	C₂	semidirect
8. C₂×#3562	C₂	semidirect
9. C₂×#3560	C₂	semidirect
10. C₂×#3559	C₂	semidirect
11. C₂×#3539	C₂	semidirect
12. C₂×#3538	C₂	semidirect
13. C₂×#3541	C₂	semidirect
14. C₂×#3455	C₂	semidirect
15. C₂×#3449	C₂	semidirect
16. C₂²×#541	C₂	semidirect
17. C₂²×2₋¹⁺⁴	C₂²	semidirect
19. #3562	C₂²	semidirect
20. #3560	C₂²	semidirect
21. #3559	C₂²	semidirect
22. #3552	C₂²	semidirect
23. #3541	C₂²	semidirect
24. #3539	C₂²	semidirect
25. #3538	C₂²	semidirect
26. C₂×#563	C₂²	semidirect
27. C₂×#563	C₂²	semidirect
28. C₂×#562	C₂²	semidirect
29. C₂×#560	C₂²	semidirect
30. #3512	C₂²	semidirect
31. #3507	C₂²	semidirect
32. #3499	C₂²	semidirect
33. #3497	C₂²	semidirect
34. #3489	C₂²	semidirect
35. C₂×#559	C₂²	semidirect
36. C₂×#557	C₂²	semidirect
37. C₂×#556	C₂²	semidirect
38. C₂×#556	C₂²	semidirect
39. C₂×#554	C₂²	semidirect
40. C₂×#554	C₂²	semidirect
41. C₂×#553	C₂²	semidirect
42. C₂×#553	C₂²	semidirect
43. C₂×#553	C₂²	semidirect
44. C₂×#553	C₂²	semidirect
45. C₂×#552	C₂²	semidirect
46. C₂×#552	C₂²	semidirect
47. C₂×#551	C₂²	semidirect
48. C₂×#550	C₂²	semidirect
49. C₂×#550	C₂²	semidirect
50. C₂×D₄×Q₈	C₂²	semidirect
51. C₂×D₄×Q₈	C₂²	semidirect
52. C₂×D₄×Q₈	C₂²	semidirect
53. C₂×D₄×Q₈	C₂²	semidirect
55. C₂×#548	C₂²	semidirect
56. C₂×#548	C₂²	semidirect
58. C₂×#547	C₂²	semidirect
59. C₂×#547	C₂²	semidirect
60. C₂×#547	C₂²	semidirect
62. C₂×#546	C₂²	semidirect
63. C₂×#544	C₂²	semidirect
64. #3455	C₂²	semidirect
65. C₂×#542	C₂²	semidirect
66. C₂×#542	C₂²	semidirect
67. C₂×#541	C₂²	semidirect
68. C₂×#541	C₂²	semidirect
69. C₂×#541	C₂²	semidirect
70. C₂×#541	C₂²	semidirect
71. C₂×#541	C₂²	semidirect
72. C₂×#541	C₂²	semidirect
73. C₂×#540	C₂²	semidirect
74. C₂×#540	C₂²	semidirect
75. C₂×#540	C₂²	semidirect
76. C₂×#539	C₂²	semidirect
77. C₂×#539	C₂²	semidirect
78. C₂×#539	C₂²	semidirect
79. C₂×#539	C₂²	semidirect
80. C₂×#539	C₂²	semidirect
82. C₂×#538	C₂²	semidirect
83. C₂×#538	C₂²	semidirect
84. #3449	C₂²	semidirect
87. C₂×#537	C₂²	semidirect
88. C₂×#537	C₂²	semidirect
91. C₂×#536	C₂²	semidirect
92. C₂×#536	C₂²	semidirect
95. C₂×#533	C₂²	semidirect
98. C₂×#532	C₂²	semidirect
99. C₂×#532	C₂²	semidirect
100. C₂×#532	C₂²	semidirect
101. C₂²×C₄⋊Q₈	C₂²	semidirect
102. C₂²×C₄⋊Q₈	C₂²	semidirect
103. C₂×#529	C₂²	semidirect
104. C₂×#529	C₂²	semidirect
105. C₂×#529	C₂²	semidirect
107. C₂²×#125	C₂²	semidirect
108. C₂²×#125	C₂²	semidirect
112. C₂×#525	C₂²	semidirect
114. C₂²×C₂²⋊Q₈	C₂²	semidirect
115. C₂×#520	C₂²	semidirect
116. C₂×C₄×#41	C₂²	semidirect
117. C₂²×C₄×Q₈	C₂²	semidirect
120. C₂×2₋¹⁺⁴	C₂³	semidirect
139. #563	C₂³	semidirect
140. #563	C₂³	semidirect
141. #562	C₂³	semidirect
142. #560	C₂³	semidirect
143. #559	C₂³	semidirect
144. #557	C₂³	semidirect
145. #556	C₂³	semidirect
146. #556	C₂³	semidirect
147. #554	C₂³	semidirect
148. #554	C₂³	semidirect
149. #553	C₂³	semidirect
150. #553	C₂³	semidirect
151. #553	C₂³	semidirect
152. #553	C₂³	semidirect
153. #552	C₂³	semidirect
154. #552	C₂³	semidirect
155. #551	C₂³	semidirect
156. #550	C₂³	semidirect
157. #550	C₂³	semidirect
158. D₄×Q₈	C₂³	semidirect
159. D₄×Q₈	C₂³	semidirect
160. D₄×Q₈	C₂³	semidirect
161. D₄×Q₈	C₂³	semidirect
163. #548	C₂³	semidirect
164. #548	C₂³	semidirect
166. #547	C₂³	semidirect
167. #547	C₂³	semidirect
168. #547	C₂³	semidirect
170. #546	C₂³	semidirect
171. #544	C₂³	semidirect
172. #542	C₂³	semidirect
173. #542	C₂³	semidirect
174. #541	C₂³	semidirect
175. #541	C₂³	semidirect
176. #541	C₂³	semidirect
177. #541	C₂³	semidirect
178. #541	C₂³	semidirect
179. #540	C₂³	semidirect
180. #540	C₂³	semidirect
181. #540	C₂³	semidirect
182. #539	C₂³	semidirect
183. #539	C₂³	semidirect
184. #539	C₂³	semidirect
185. #539	C₂³	semidirect
186. #539	C₂³	semidirect
188. #538	C₂³	semidirect
189. #538	C₂³	semidirect
192. #537	C₂³	semidirect
193. #537	C₂³	semidirect
196. #536	C₂³	semidirect
197. #536	C₂³	semidirect
200. #533	C₂³	semidirect
203. #532	C₂³	semidirect
204. #532	C₂³	semidirect
205. #532	C₂³	semidirect
216. C₂×C₄⋊Q₈	C₂³	semidirect
217. C₂×C₄⋊Q₈	C₂³	semidirect
222. #529	C₂³	semidirect
223. #529	C₂³	semidirect
224. #529	C₂³	semidirect
243. C₂×#125	C₂³	semidirect
244. C₂×#125	C₂³	semidirect
256. #525	C₂³	semidirect
291. C₂×C₂²⋊Q₈	C₂³	semidirect
314. #520	C₂³	semidirect
315. C₄×#41	C₂³	semidirect
324. C₂×C₄×Q₈	C₂³	semidirect
900. C₂	#62888	direct (N × H)

Maximal subgroups

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

subgroup	index
#62888	2
C₂×#3512	2
C₂×#3499	2
C₂×#3489	2
C₂×#3497	2
C₂×#3507	2
C₂×#3552	2
C₂×#3562	2
C₂×#3560	2
C₂×#3559	2
C₂×#3539	2
C₂×#3538	2
C₂×#3541	2
C₂×#3455	2
C₂×#3449	2
C₂²×#541	2

Subgroups — C2×#62888 #10586223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#62888 #10586223