Subgroups — C₂×#62919 #10586261

Order 512.

34456 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#62919	C₂	1	64	yes	maximal, direct product factor
2	C₂×#3500	C₂	1	2	yes	maximal, complemented
3	C₂×#3489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#3488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#3524	C₂	1	2	yes	maximal, complemented
6	C₂×#3516	C₂	1	2	yes	maximal, complemented
7	C₂×#3497	C₂	1	2	yes	maximal, complemented
8	C₂×#3486	C₂	1	2	yes	maximal, complemented
9	C₂×#3514	C₂	1	6	yes	maximal, complemented
10	C₂×#3505	C₂	1	3	yes	maximal, complemented
11	C₂×#3547	C₂	1	6	yes	maximal, complemented
12	C₂×#3562	C₂	1	6	yes	maximal, complemented
13	C₂×#3551	C₂	1	6	yes	maximal, complemented
14	C₂×#3561	C₂	1	6	yes	maximal, complemented
15	C₂×#3538	C₂	1	3	yes	maximal, complemented
16	C₂×#3536	C₂	1	3	yes	maximal, complemented
17	C₂×#3542	C₂	1	6	yes	maximal, complemented
18	C₂×#3482	C₂	1	2	yes	maximal, complemented
19	C₂²×#548	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#3460	C₂	1	3	yes	maximal, complemented
21	C₂²×2₋¹⁺⁴	C₂²	1	2	yes	complemented
22	C₂²×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
23	C₂²×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
24	C₂³×#41	C₂²	1	1	yes	characteristic
25	C₂⁴×Q₈	C₂²	1	1	yes	characteristic, complemented
26	#3562	C₂²	1	192	yes	complemented
27	#3561	C₂²	1	192	yes	complemented
28	#3551	C₂²	1	192	yes	complemented
29	#3547	C₂²	1	192	yes	complemented
30	#3542	C₂²	1	192	yes	complemented
31	#3538	C₂²	1	96	yes	complemented
32	#3536	C₂²	1	96	yes	complemented
33	C₂×#563	C₂²	1	12	yes	complemented
34	C₂×#562	C₂²	1	12	yes	complemented
35	C₂×#562	C₂²	1	12	yes	complemented
36	C₂×#560	C₂²	1	12	yes	complemented
37	#3524	C₂²	1	64	yes	complemented
38	#3516	C₂²	1	64	yes	complemented
39	#3514	C₂²	1	192	yes	complemented
40	#3505	C₂²	1	96	yes	complemented
41	#3500	C₂²	1	64	yes	complemented
42	#3497	C₂²	1	64	yes	complemented
43	#3489	C₂²	1	32	yes	complemented
44	#3488	C₂²	1	32	yes	complemented
45	#3486	C₂²	1	64	yes	complemented
46	#3482	C₂²	1	64	yes	complemented
47	C₂×#559	C₂²	1	6	yes	complemented
48	C₂×#557	C₂²	1	2	yes	complemented
49	C₂×#556	C₂²	1	6	yes	complemented
50	C₂×#556	C₂²	1	6	yes	complemented
51	C₂×#555	C₂²	1	12	yes	complemented
52	C₂×#555	C₂²	1	6	yes	complemented
53	C₂×#554	C₂²	1	6	yes	complemented
54	C₂×#553	C₂²	1	6	yes	complemented
55	C₂×#553	C₂²	1	6	yes	complemented
56	C₂×#553	C₂²	1	12	yes	complemented
57	C₂×#552	C₂²	1	6	yes	complemented
58	C₂×#552	C₂²	1	6	yes	complemented
59	C₂×#552	C₂²	1	6	yes	complemented
60	C₂×#552	C₂²	1	6	yes	complemented
61	C₂×#551	C₂²	1	12	yes	complemented
62	C₂×#551	C₂²	1	12	yes	complemented
63	C₂×#551	C₂²	1	12	yes	complemented
64	C₂×#550	C₂²	1	6	yes	complemented
65	C₂×#550	C₂²	1	2	yes	complemented
66	C₂×D₄×Q₈	C₂²	1	6	yes	complemented
67	C₂×D₄×Q₈	C₂²	1	6	yes	complemented
68	C₂×D₄×Q₈	C₂²	1	6	yes	complemented
69	C₂×D₄×Q₈	C₂²	1	2	yes	complemented
70	C₂×D₄×Q₈	C₂²	1	2	yes	complemented
71	C₂×#548	C₂²	1	2	yes	—
72	C₂×#548	C₂²	1	2	yes	—
73	C₂×#548	C₂²	1	6	yes	complemented
74	C₂×#548	C₂²	1	6	yes	complemented
75	C₂×#548	C₂²	1	6	yes	complemented
76	C₂×#548	C₂²	1	6	yes	complemented
77	C₂×#548	C₂²	1	6	yes	complemented
78	C₂×#548	C₂²	1	6	yes	complemented
79	C₂×#548	C₂²	1	2	yes	complemented
80	C₂×#548	C₂²	1	2	yes	complemented
81	C₂×#548	C₂²	1	2	yes	complemented
82	C₂×#548	C₂²	1	2	yes	complemented
83	C₂×#548	C₂²	1	32	yes	complemented
84	C₂×#547	C₂²	1	6	yes	complemented
85	C₂×#547	C₂²	1	6	yes	complemented
86	C₂×#546	C₂²	1	6	yes	complemented
87	C₂×#546	C₂²	1	12	yes	complemented
88	C₂×#546	C₂²	1	6	yes	complemented
89	C₂×#546	C₂²	1	6	yes	complemented
90	C₂×#546	C₂²	1	6	yes	complemented
91	C₂×#546	C₂²	1	6	yes	complemented
92	C₂×#546	C₂²	1	6	yes	complemented
93	C₂×D₄²	C₂²	1	6	yes	—
94	#3460	C₂²	1	96	yes	complemented
95	C₂×#544	C₂²	1	3	yes	complemented
96	C₂×#544	C₂²	1	6	yes	complemented
97	C₂×#543	C₂²	1	6	yes	complemented
98	C₂×#542	C₂²	1	6	yes	complemented
99	C₂×#542	C₂²	1	6	yes	complemented
100	C₂×#542	C₂²	1	12	yes	complemented
101	C₂×#542	C₂²	1	6	yes	complemented
102	C₂×#542	C₂²	1	6	yes	complemented
103	C₂×#541	C₂²	1	6	yes	complemented
104	C₂×#540	C₂²	1	6	yes	complemented
105	C₂×#540	C₂²	1	12	yes	complemented
106	C₂×#540	C₂²	1	6	yes	complemented
107	C₂×#540	C₂²	1	6	yes	complemented
108	C₂×#539	C₂²	1	6	yes	complemented
109	C₂×#539	C₂²	1	6	yes	complemented
110	C₂×#538	C₂²	1	6	yes	complemented
111	C₂×#538	C₂²	1	12	yes	complemented
112	C₂×#538	C₂²	1	12	yes	complemented
113	C₂×#538	C₂²	1	3	yes	complemented
114	C₂×#538	C₂²	1	6	yes	complemented
115	C₂×#538	C₂²	1	1	yes	characteristic, complemented
116	C₂×#537	C₂²	1	3	yes	complemented
117	C₂×#537	C₂²	1	6	yes	complemented
118	C₂×#537	C₂²	1	3	yes	complemented
119	C₂×#537	C₂²	1	3	yes	complemented
120	C₂×#537	C₂²	1	6	yes	complemented
121	C₂×#536	C₂²	1	6	yes	complemented
122	C₂×#536	C₂²	1	3	yes	complemented
123	C₂×#536	C₂²	1	6	yes	complemented
124	C₂×#536	C₂²	1	6	yes	complemented
125	C₂×#535	C₂²	1	6	yes	complemented
126	C₂×#535	C₂²	1	3	yes	complemented
127	C₂×#535	C₂²	1	6	yes	complemented
128	C₂×#534	C₂²	1	6	yes	complemented
129	C₂×#533	C₂²	1	6	yes	complemented
130	C₂×#532	C₂²	1	6	yes	complemented
131	C₂×#532	C₂²	1	6	yes	complemented
132	C₂×#532	C₂²	1	6	yes	complemented
133	C₂×#529	C₂²	1	6	yes	complemented
134	C₂×#529	C₂²	1	6	yes	complemented
135	C₂×#529	C₂²	1	6	yes	complemented
136	C₂×#529	C₂²	1	6	yes	complemented
137	C₂×#529	C₂²	1	6	yes	complemented
138	C₂×#529	C₂²	1	6	yes	complemented
139	C₂²×#124	C₂²	1	6	yes	complemented
140	C₂²×#124	C₂²	1	3	yes	complemented
141	C₂×#525	C₂²	1	3	yes	—
142	C₂×#525	C₂²	1	3	yes	complemented
143	C₂×#525	C₂²	1	6	yes	complemented
144	C₂×#525	C₂²	1	6	yes	complemented
145	C₂²×C₂²⋊Q₈	C₂²	1	3	yes	complemented
146	C₂²×C₂²⋊Q₈	C₂²	1	3	yes	complemented
147	C₂²×#121	C₂²	1	3	yes	—
148	C₂²×#121	C₂²	1	3	yes	complemented
149	C₂×#520	C₂²	1	1	yes	characteristic, complemented
150	C₂×#520	C₂²	1	1	yes	characteristic, complemented
151	C₂×#519	C₂²	1	2	yes	complemented
152	C₂×#518	C₂²	1	6	yes	complemented
153	C₂×C₄×#41	C₂²	1	6	yes	complemented
154	C₂×C₄×#41	C₂²	1	2	yes	complemented
155	C₂²×C₄×Q₈	C₂²	1	2	yes	complemented
156	C₂²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
157	C₂²×C₄×D₄	C₂²	1	3	yes	complemented
158	C₂×2₋¹⁺⁴	—	4	16	no	—
159	C₂×2₋¹⁺⁴	—	4	8	no	—
160	C₂×2₋¹⁺⁴	C₂³	1	32	yes	complemented
161	C₂×2₋¹⁺⁴	C₂³	1	16	yes	complemented
162	C₂×H(5,𝔽₂)	—	4	8	no	—
163	C₂×H(5,𝔽₂)	C₂³	1	16	yes	complemented
164	C₂²×#41	—	4	8	no	—
165	C₂²×#41	C₂³	1	1	yes	characteristic
166	C₂²×#41	C₂³	1	1	yes	characteristic
167	C₂²×#41	C₂³	1	2	yes	—
168	C₂²×#41	C₂³	1	3	yes	—
169	C₂²×#41	C₂³	1	3	yes	—
170	C₂²×#41	C₂³	1	16	yes	—
171	C₂²×#41	C₂³	1	3	yes	—
172	C₂²×#41	C₂³	1	6	yes	—
173	C₂²×#41	C₂³	1	3	yes	—
174	C₂²×#41	C₂³	1	6	yes	—
175	C₂²×#41	C₂³	1	6	yes	—
176	C₂²×#41	C₂³	1	6	yes	—
177	C₂²×#41	C₂³	1	6	yes	—
178	C₂³×Q₈	—	4	8	no	—
179	C₂³×Q₈	C₂³	1	1	yes	characteristic
180	C₂³×Q₈	C₂³	1	2	yes	—
181	C₂³×Q₈	C₂³	1	2	yes	—
182	C₂³×Q₈	C₂³	1	3	yes	—
183	C₂³×Q₈	C₂³	1	6	yes	—
184	C₂³×Q₈	C₂³	1	3	yes	—
185	C₂³×Q₈	C₂³	1	6	yes	—
186	C₂³×Q₈	C₂³	1	16	yes	complemented
187	C₂³×D₄	C₂³	1	3	yes	—
188	C₂³×D₄	C₂³	1	3	yes	—
189	C₂³×D₄	C₂³	1	6	yes	—
190	C₂³×D₄	C₂³	1	3	yes	—
191	C₂³×D₄	C₂³	1	6	yes	—
192	C₂⁴×C₄	C₂³	1	3	yes	—
193	C₂⁴×C₄	C₂³	1	3	yes	—
194	#563	C₂³	1	192	yes	complemented
195	#562	C₂³	1	192	yes	complemented
196	#562	C₂³	1	192	yes	complemented
197	#560	C₂³	1	192	yes	complemented
198	#559	C₂³	1	96	yes	complemented
199	#557	C₂³	1	32	yes	complemented
200	#556	C₂³	1	96	yes	complemented
201	#556	C₂³	1	96	yes	complemented
202	#555	C₂³	1	192	yes	complemented
203	#555	C₂³	1	96	yes	complemented
204	#554	C₂³	1	96	yes	complemented
205	#553	C₂³	1	96	yes	complemented
206	#553	C₂³	1	192	yes	complemented
207	#553	C₂³	1	96	yes	complemented
208	#552	C₂³	1	96	yes	complemented
209	#552	C₂³	1	96	yes	complemented
210	#552	C₂³	1	96	yes	complemented
211	#552	C₂³	1	96	yes	complemented
212	#551	C₂³	1	192	yes	complemented
213	#551	C₂³	1	192	yes	complemented
214	#551	C₂³	1	192	yes	complemented
215	#550	C₂³	1	32	yes	complemented
216	#550	C₂³	1	96	yes	complemented
217	D₄×Q₈	C₂³	1	32	yes	complemented
218	D₄×Q₈	C₂³	1	32	yes	complemented
219	D₄×Q₈	C₂³	1	96	yes	complemented
220	D₄×Q₈	C₂³	1	96	yes	complemented
221	D₄×Q₈	C₂³	1	96	yes	complemented
222	#548	C₂³	1	32	yes	—
223	#548	C₂³	1	32	yes	—
224	#548	C₂³	1	32	yes	complemented
225	#548	C₂³	1	96	yes	complemented
226	#548	C₂³	1	96	yes	complemented
227	#548	C₂³	1	32	yes	complemented
228	#548	C₂³	1	32	yes	complemented
229	#548	C₂³	1	96	yes	complemented
230	#548	C₂³	1	96	yes	complemented
231	#548	C₂³	1	32	yes	complemented
232	#548	C₂³	1	96	yes	complemented
233	#548	C₂³	1	96	yes	complemented
234	#547	C₂³	1	96	yes	complemented
235	#547	C₂³	1	96	yes	complemented
236	#546	C₂³	1	96	yes	complemented
237	#546	C₂³	1	96	yes	complemented
238	#546	C₂³	1	96	yes	complemented
239	#546	C₂³	1	96	yes	complemented
240	#546	C₂³	1	96	yes	complemented
241	#546	C₂³	1	96	yes	complemented
242	#546	C₂³	1	192	yes	complemented
243	D₄²	C₂³	1	96	yes	—
244	#544	C₂³	1	48	yes	complemented
245	#544	C₂³	1	96	yes	complemented
246	#543	C₂³	1	96	yes	complemented
247	#542	C₂³	1	96	yes	complemented
248	#542	C₂³	1	96	yes	complemented
249	#542	C₂³	1	192	yes	complemented
250	#542	C₂³	1	96	yes	complemented
251	#542	C₂³	1	96	yes	complemented
252	#541	C₂³	1	96	yes	complemented
253	#540	C₂³	1	96	yes	complemented
254	#540	C₂³	1	96	yes	complemented
255	#540	C₂³	1	96	yes	complemented
256	#540	C₂³	1	192	yes	complemented
257	#539	C₂³	1	96	yes	complemented
258	#539	C₂³	1	96	yes	complemented
259	#538	C₂³	1	16	yes	complemented
260	#538	C₂³	1	48	yes	complemented
261	#538	C₂³	1	96	yes	complemented
262	#538	C₂³	1	192	yes	complemented
263	#538	C₂³	1	96	yes	complemented
264	#538	C₂³	1	192	yes	complemented
265	#537	C₂³	1	48	yes	complemented
266	#537	C₂³	1	48	yes	complemented
267	#537	C₂³	1	48	yes	complemented
268	#537	C₂³	1	96	yes	complemented
269	#537	C₂³	1	96	yes	complemented
270	#536	C₂³	1	96	yes	complemented
271	#536	C₂³	1	96	yes	complemented
272	#536	C₂³	1	48	yes	complemented
273	#536	C₂³	1	96	yes	complemented
274	#535	C₂³	1	96	yes	complemented
275	#535	C₂³	1	48	yes	complemented
276	#535	C₂³	1	96	yes	complemented
277	#534	C₂³	1	96	yes	complemented
278	#533	C₂³	1	96	yes	complemented
279	#532	C₂³	1	96	yes	complemented
280	#532	C₂³	1	96	yes	complemented
281	#532	C₂³	1	96	yes	complemented
282	C₂×C₄⋊Q₈	C₂³	1	6	yes	—
283	C₂×C₄⋊Q₈	C₂³	1	6	yes	—
284	C₂×C₄⋊Q₈	C₂³	1	6	yes	—
285	C₂×C₄⋊Q₈	C₂³	1	6	yes	—
286	C₂×C₄⋊Q₈	C₂³	1	6	yes	—
287	C₂×C₄⋊Q₈	C₂³	1	12	yes	—
288	C₂×#127	C₂³	1	6	yes	—
289	C₂×#127	C₂³	1	6	yes	—
290	C₂×#127	C₂³	1	6	yes	—
291	#529	C₂³	1	96	yes	complemented
292	#529	C₂³	1	96	yes	complemented
293	#529	C₂³	1	96	yes	complemented
294	#529	C₂³	1	96	yes	complemented
295	#529	C₂³	1	96	yes	complemented
296	#529	C₂³	1	96	yes	complemented
297	C₂×#126	C₂³	1	2	yes	—
298	C₂×#126	C₂³	1	6	yes	—
299	C₂×#126	C₂³	1	12	yes	—
300	C₂×#126	C₂³	1	6	yes	—
301	C₂×#126	C₂³	1	12	yes	—
302	C₂×#126	C₂³	1	6	yes	—
303	C₂×#126	C₂³	1	12	yes	—
304	C₂×#126	C₂³	1	12	yes	—
305	C₂×#126	C₂³	1	12	yes	—
306	C₂×#125	C₂³	1	6	yes	—
307	C₂×#125	C₂³	1	6	yes	—
308	C₂×#125	C₂³	1	6	yes	—
309	C₂×#125	C₂³	1	6	yes	—
310	C₂×#125	C₂³	1	12	yes	—
311	C₂×#125	C₂³	1	12	yes	—
312	C₂×#124	C₂³	1	6	yes	—
313	C₂×#124	C₂³	1	6	yes	—
314	C₂×#124	C₂³	1	6	yes	—
315	C₂×#124	C₂³	1	6	yes	—
316	C₂×#124	C₂³	1	12	yes	—
317	C₂×#124	C₂³	1	6	yes	—
318	C₂×#124	C₂³	1	6	yes	—
319	C₂×#124	C₂³	1	12	yes	—
320	C₂×#124	C₂³	1	6	yes	—
321	C₂×#124	C₂³	1	6	yes	—
322	C₂×#124	C₂³	1	6	yes	—
323	C₂×#124	C₂³	1	2	yes	—
324	C₂×#124	C₂³	1	6	yes	—
325	C₂×#124	C₂³	1	6	yes	—
326	C₂×#124	C₂³	1	12	yes	—
327	C₂×#124	C₂³	1	12	yes	—
328	C₂×#124	C₂³	1	48	yes	complemented
329	C₂×#124	C₂³	1	96	yes	complemented
330	#525	C₂³	1	48	yes	—
331	#525	C₂³	1	96	yes	complemented
332	#525	C₂³	1	48	yes	complemented
333	#525	C₂³	1	96	yes	complemented
334	C₂×#123	C₂³	1	6	yes	—
335	C₂×#123	C₂³	1	6	yes	—
336	C₂×#123	C₂³	1	6	yes	—
337	C₂×#123	C₂³	1	12	yes	—
338	C₂×#123	C₂³	1	6	yes	—
339	C₂×#123	C₂³	1	6	yes	—
340	C₂×#123	C₂³	1	2	yes	—
341	C₂×#123	C₂³	1	12	yes	—
342	C₂×#123	C₂³	1	12	yes	—
343	C₂×#123	C₂³	1	6	yes	—
344	C₂×#123	C₂³	1	6	yes	—
345	C₂×#123	C₂³	1	12	yes	—
346	C₂×#123	C₂³	1	12	yes	—
347	C₂×#123	C₂³	1	12	yes	—
348	C₂×#123	C₂³	1	12	yes	—
349	C₂×#123	C₂³	1	12	yes	—
350	C₂×#123	C₂³	1	12	yes	—
351	C₂×C₂²⋊Q₈	C₂³	1	3	yes	—
352	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
353	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
354	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
355	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
356	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
357	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
358	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
359	C₂×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
360	C₂×C₂²⋊Q₈	C₂³	1	3	yes	—
361	C₂×C₂²⋊Q₈	C₂³	1	3	yes	—
362	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
363	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
364	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
365	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
366	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
367	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
368	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
369	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
370	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
371	C₂×C₂²⋊Q₈	C₂³	1	6	yes	—
372	C₂×C₂²⋊Q₈	C₂³	1	12	yes	—
373	C₂×C₂²⋊Q₈	C₂³	1	12	yes	—
374	C₂×C₂²⋊Q₈	C₂³	1	12	yes	—
375	C₂×C₂²⋊Q₈	C₂³	1	12	yes	—
376	C₂×C₂²⋊Q₈	C₂³	1	12	yes	—
377	C₂×C₂²⋊Q₈	C₂³	1	12	yes	—
378	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
379	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
380	C₂×#121	C₂³	1	3	yes	—
381	C₂×#121	C₂³	1	6	yes	—
382	C₂×#121	C₂³	1	6	yes	—
383	C₂×#121	C₂³	1	6	yes	—
384	C₂×#121	C₂³	1	48	yes	—
385	C₂×#121	C₂³	1	6	yes	—
386	C₂×#121	C₂³	1	6	yes	—
387	C₂×#121	C₂³	1	12	yes	—
388	C₂×#121	C₂³	1	3	yes	—
389	C₂×#121	C₂³	1	1	yes	characteristic
390	C₂×#121	C₂³	1	6	yes	—
391	C₂×#121	C₂³	1	3	yes	—
392	C₂×#121	C₂³	1	6	yes	—
393	C₂×#121	C₂³	1	6	yes	—
394	C₂×#121	C₂³	1	6	yes	—
395	C₂×#121	C₂³	1	6	yes	—
396	C₂×#121	C₂³	1	6	yes	—
397	C₂×#121	C₂³	1	6	yes	—
398	C₂×#121	C₂³	1	6	yes	—
399	C₂×#121	C₂³	1	6	yes	—
400	C₂×#121	C₂³	1	2	yes	—
401	C₂×#121	C₂³	1	6	yes	—
402	C₂×#121	C₂³	1	6	yes	—
403	C₂×#121	C₂³	1	6	yes	—
404	C₂×#121	C₂³	1	12	yes	—
405	C₂×#121	C₂³	1	6	yes	—
406	C₂×#121	C₂³	1	6	yes	—
407	C₂×#121	C₂³	1	6	yes	—
408	C₂×#121	C₂³	1	12	yes	—
409	C₂×#121	C₂³	1	12	yes	—
410	C₂×#121	C₂³	1	12	yes	—
411	C₂×#121	C₂³	1	12	yes	—
412	C₂×#121	C₂³	1	12	yes	—
413	C₂×#121	C₂³	1	48	yes	complemented
414	C₂×#120	C₂³	1	6	yes	—
415	C₂×#120	C₂³	1	6	yes	—
416	C₂×#120	C₂³	1	2	yes	—
417	C₂×#120	C₂³	1	6	yes	—
418	C₂×#120	C₂³	1	12	yes	—
419	C₂×#120	C₂³	1	12	yes	—
420	C₂×#120	C₂³	1	12	yes	—
421	#520	C₂³	1	16	yes	complemented
422	#520	C₂³	1	16	yes	complemented
423	#519	C₂³	1	32	yes	complemented
424	#518	C₂³	1	96	yes	complemented
425	C₄×#41	C₂³	1	96	yes	complemented
426	C₄×#41	C₂³	1	32	yes	complemented
427	C₂×C₄×Q₈	C₂³	1	2	yes	—
428	C₂×C₄×Q₈	C₂³	1	2	yes	—
429	C₂×C₄×Q₈	C₂³	1	6	yes	—
430	C₂×C₄×Q₈	C₂³	1	6	yes	—
431	C₂×C₄×Q₈	C₂³	1	6	yes	—
432	C₂×C₄×Q₈	C₂³	1	2	yes	—
433	C₂×C₄×Q₈	C₂³	1	6	yes	—
434	C₂×C₄×Q₈	C₂³	1	6	yes	—
435	C₂×C₄×Q₈	C₂³	1	6	yes	—
436	C₂×C₄×Q₈	C₂³	1	6	yes	—
437	C₂×C₄×Q₈	C₂³	1	16	yes	complemented
438	C₂×C₄×Q₈	C₂³	1	32	yes	complemented
439	C₂×C₄×D₄	C₂³	1	6	yes	—
440	C₂×C₄×D₄	C₂³	1	6	yes	—
441	C₂×C₄×D₄	C₂³	1	6	yes	—
442	C₂×C₄×D₄	C₂³	1	6	yes	—
443	C₂×C₄×D₄	C₂³	1	2	yes	—
444	C₂×C₄×D₄	C₂³	1	6	yes	—
445	C₂×C₄×D₄	C₂³	1	6	yes	—
446	C₂×C₄×D₄	C₂³	1	6	yes	—
447	C₂×C₄×D₄	C₂³	1	6	yes	—
448	C₂×C₄×D₄	C₂³	1	6	yes	—
449	C₂×C₄×D₄	C₂³	1	6	yes	—
450	C₂×C₄×D₄	C₂³	1	6	yes	—
451	C₂×C₄×D₄	C₂³	1	12	yes	—
452	C₂×C₄×D₄	C₂³	1	12	yes	—
453	C₂×C₄×D₄	C₂³	1	12	yes	—
454	C₂×C₄×D₄	C₂³	1	6	yes	—
455	C₂×C₄×D₄	C₂³	1	6	yes	—
456	C₂×C₄×D₄	C₂³	1	6	yes	—
457	C₂×C₄×D₄	C₂³	1	6	yes	—
458	C₂×C₄×D₄	C₂³	1	6	yes	—
459	C₂×C₄×D₄	C₂³	1	6	yes	—
460	C₂×C₄×D₄	C₂³	1	12	yes	—
461	C₂×C₄×D₄	C₂³	1	12	yes	—
462	C₂×C₄×D₄	C₂³	1	12	yes	—
463	C₂×C₄×D₄	C₂³	1	48	yes	complemented
464	C₂×#117	C₂³	1	6	yes	—
465	C₂×#117	C₂³	1	6	yes	—
466	C₂×#117	C₂³	1	6	yes	—
467	C₂×#117	C₂³	1	6	yes	—
468	C₂×#117	C₂³	1	12	yes	—
469	C₂×#117	C₂³	1	6	yes	—
470	C₂×#117	C₂³	1	6	yes	—
471	C₂×#117	C₂³	1	3	yes	—
472	C₂×#117	C₂³	1	3	yes	—
473	C₂×#117	C₂³	1	12	yes	—
474	C₂×#117	C₂³	1	12	yes	—
475	C₂²×C₄⋊C₄	C₂³	1	3	yes	—
476	C₂²×C₄⋊C₄	C₂³	1	3	yes	—
477	C₂²×C₄⋊C₄	C₂³	1	6	yes	—
478	C₂²×C₄⋊C₄	C₂³	1	3	yes	—
479	C₂²×C₄⋊C₄	C₂³	1	3	yes	—
480	C₂²×C₄⋊C₄	C₂³	1	6	yes	—
481	C₂²×C₂²⋊C₄	C₂³	1	1	yes	characteristic
482	C₂²×C₂²⋊C₄	C₂³	1	3	yes	—
483	C₂²×C₂²⋊C₄	C₂³	1	6	yes	—
484	C₂²×C₂²⋊C₄	C₂³	1	12	yes	—
485	C₂²×C₂²⋊C₄	C₂³	1	6	yes	—
486	C₂²×C₂²⋊C₄	C₂³	1	6	yes	—
487	C₂²×C₂²⋊C₄	C₂³	1	12	yes	—
488	C₂²×C₄²	C₂³	1	3	yes	—
489	C₂²×C₄²	C₂³	1	6	yes	—
490	C₂²×C₄²	C₂³	1	6	yes	—
491	C₂⁵	C₂⁴	1	3	yes	—
492	C₂⁵	C₂⁴	1	1	yes	characteristic
493	C₂⁵	C₂⁴	1	6	yes	—
494	2₋¹⁺⁴	—	4	128	no	—
495	2₋¹⁺⁴	—	4	64	no	—
496	H(5,𝔽₂)	—	4	64	no	—
497	C₂×#41	—	2	8	no	—
498	C₂×#41	—	2	8	no	—
499	C₂×#41	—	2	16	no	—
500	C₂×#41	—	4	12	no	—
501	C₂×#41	—	4	24	no	—
502	C₂×#41	—	4	12	no	—
503	C₂×#41	—	4	24	no	—
504	C₂×#41	—	4	12	no	—
505	C₂×#41	—	4	12	no	—
506	C₂×#41	—	4	24	no	—
507	C₂×#41	—	4	24	no	—
508	C₂×#41	—	4	24	no	—
509	C₂×#41	—	4	64	no	—
510	C₂×#41	C₂⁴	1	16	yes	—
511	C₂×#41	C₂⁴	1	8	yes	—
512	C₂×#41	C₂⁴	1	8	yes	—
513	C₂×#41	C₂⁴	1	48	yes	—
514	C₂×#41	C₂⁴	1	24	yes	—
515	C₂×#41	C₂⁴	1	48	yes	—
516	C₂×#41	C₂⁴	1	24	yes	—
517	C₂×#41	C₂⁴	1	48	yes	—
518	C₂×#41	C₂⁴	1	48	yes	—
519	C₂×#41	C₂⁴	1	48	yes	—
520	C₂×#41	C₂⁴	1	24	yes	—
521	C₂×#41	C₂⁴	1	24	yes	—
522	C₂²×Q₈	—	2	8	no	—
523	C₂²×Q₈	—	2	16	no	—
524	C₂²×Q₈	—	2	16	no	—
525	C₂²×Q₈	—	4	12	no	—
526	C₂²×Q₈	—	4	24	no	—
527	C₂²×Q₈	—	4	12	no	—
528	C₂²×Q₈	—	4	24	no	—
529	C₂²×Q₈	—	4	64	no	—
530	C₂²×Q₈	C₂⁴	1	6	yes	—
531	C₂²×Q₈	C₂⁴	1	3	yes	—
532	C₂²×Q₈	C₂⁴	1	6	yes	—
533	C₂²×Q₈	C₂⁴	1	8	yes	—
534	C₂²×Q₈	C₂⁴	1	16	yes	—
535	C₂²×Q₈	C₂⁴	1	16	yes	—
536	C₂²×Q₈	C₂⁴	1	6	yes	—
537	C₂²×Q₈	C₂⁴	1	3	yes	—
538	C₂²×Q₈	C₂⁴	1	6	yes	—
539	C₂²×Q₈	C₂⁴	1	6	yes	—
540	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
541	C₂²×Q₈	C₂⁴	1	24	yes	—
542	C₂²×Q₈	C₂⁴	1	24	yes	—
543	C₂²×Q₈	C₂⁴	1	48	yes	—
544	C₂²×Q₈	C₂⁴	1	48	yes	—
545	C₂²×Q₈	C₂⁴	1	1	yes	characteristic
546	C₂²×D₄	—	4	12	no	—
547	C₂²×D₄	—	4	12	no	—
548	C₂²×D₄	—	4	24	no	—
549	C₂²×D₄	—	4	12	no	—
550	C₂²×D₄	—	4	24	no	—
551	C₂²×D₄	C₂⁴	1	2	yes	—
552	C₂²×D₄	C₂⁴	1	6	yes	—
553	C₂²×D₄	C₂⁴	1	3	yes	—
554	C₂²×D₄	C₂⁴	1	6	yes	—
555	C₂²×D₄	C₂⁴	1	3	yes	—
556	C₂²×D₄	C₂⁴	1	6	yes	—
557	C₂²×D₄	C₂⁴	1	6	yes	—
558	C₂²×D₄	C₂⁴	1	6	yes	—
559	C₂²×D₄	C₂⁴	1	2	yes	—
560	C₂²×D₄	C₂⁴	1	6	yes	—
561	C₂²×D₄	C₂⁴	1	6	yes	—
562	C₂²×D₄	C₂⁴	1	12	yes	—
563	C₂²×D₄	C₂⁴	1	6	yes	—
564	C₂²×D₄	C₂⁴	1	24	yes	—
565	C₂²×D₄	C₂⁴	1	48	yes	—
566	C₂²×D₄	C₂⁴	1	6	yes	—
567	C₂²×D₄	C₂⁴	1	6	yes	—
568	C₂²×D₄	C₂⁴	1	6	yes	—
569	C₂²×D₄	C₂⁴	1	6	yes	—
570	C₂²×D₄	C₂⁴	1	6	yes	—
571	C₂²×D₄	C₂⁴	1	2	yes	—
572	C₂²×D₄	C₂⁴	1	1	yes	characteristic
573	C₂²×D₄	C₂⁴	1	3	yes	—
574	C₂²×D₄	C₂⁴	1	24	yes	—
575	C₂²×D₄	C₂⁴	1	24	yes	—
576	C₂²×D₄	C₂⁴	1	48	yes	—
577	C₂³×C₄	—	4	12	no	—
578	C₂³×C₄	—	4	12	no	—
579	C₂³×C₄	C₂⁴	1	3	yes	—
580	C₂³×C₄	C₂⁴	1	3	yes	—
581	C₂³×C₄	C₂⁴	1	3	yes	—
582	C₂³×C₄	C₂⁴	1	3	yes	—
583	C₂³×C₄	C₂⁴	1	6	yes	—
584	C₂³×C₄	C₂⁴	1	6	yes	—
585	C₂³×C₄	C₂⁴	1	6	yes	—
586	C₂³×C₄	C₂⁴	1	1	yes	characteristic
587	C₂³×C₄	C₂⁴	1	3	yes	—
588	C₂³×C₄	C₂⁴	1	6	yes	—
589	C₂³×C₄	C₂⁴	1	6	yes	—
590	C₂³×C₄	C₂⁴	1	12	yes	—
591	C₂³×C₄	C₂⁴	1	3	yes	—
592	C₂³×C₄	C₂⁴	1	1	yes	characteristic
593	C₂³×C₄	C₂⁴	1	6	yes	—
594	C₂³×C₄	C₂⁴	1	6	yes	—
595	C₂³×C₄	C₂⁴	1	6	yes	—
596	C₂³×C₄	C₂⁴	1	6	yes	—
597	C₂³×C₄	C₂⁴	1	3	yes	—
598	C₂³×C₄	C₂⁴	1	2	yes	—
599	C₂³×C₄	C₂⁴	1	6	yes	—
600	C₂³×C₄	C₂⁴	1	24	yes	—
601	C₂³×C₄	C₂⁴	1	24	yes	—
602	C₄⋊Q₈	C₂⁴	1	48	yes	—
603	C₄⋊Q₈	C₂⁴	1	48	yes	—
604	C₄⋊Q₈	C₂⁴	1	48	yes	—
605	C₄⋊Q₈	C₂⁴	1	48	yes	—
606	C₄⋊Q₈	C₂⁴	1	48	yes	—
607	C₄⋊Q₈	C₂⁴	1	96	yes	—
608	#127	C₂⁴	1	48	yes	—
609	#127	C₂⁴	1	48	yes	—
610	#127	C₂⁴	1	48	yes	—
611	#126	C₂⁴	1	16	yes	—
612	#126	C₂⁴	1	48	yes	—
613	#126	C₂⁴	1	96	yes	—
614	#126	C₂⁴	1	48	yes	—
615	#126	C₂⁴	1	96	yes	—
616	#126	C₂⁴	1	48	yes	—
617	#126	C₂⁴	1	96	yes	—
618	#126	C₂⁴	1	96	yes	—
619	#126	C₂⁴	1	96	yes	—
620	#125	C₂⁴	1	48	yes	—
621	#125	C₂⁴	1	48	yes	—
622	#125	C₂⁴	1	48	yes	—
623	#125	C₂⁴	1	48	yes	—
624	#125	C₂⁴	1	96	yes	—
625	#125	C₂⁴	1	96	yes	—
626	#124	C₂⁴	1	48	yes	—
627	#124	C₂⁴	1	48	yes	—
628	#124	C₂⁴	1	48	yes	—
629	#124	C₂⁴	1	48	yes	—
630	#124	C₂⁴	1	96	yes	—
631	#124	C₂⁴	1	48	yes	—
632	#124	C₂⁴	1	48	yes	—
633	#124	C₂⁴	1	96	yes	—
634	#124	C₂⁴	1	48	yes	—
635	#124	C₂⁴	1	48	yes	—
636	#124	C₂⁴	1	48	yes	—
637	#124	C₂⁴	1	16	yes	—
638	#124	C₂⁴	1	48	yes	—
639	#124	C₂⁴	1	48	yes	—
640	#124	C₂⁴	1	96	yes	—
641	#124	C₂⁴	1	96	yes	—
642	#123	C₂⁴	1	48	yes	—
643	#123	C₂⁴	1	48	yes	—
644	#123	C₂⁴	1	48	yes	—
645	#123	C₂⁴	1	96	yes	—
646	#123	C₂⁴	1	48	yes	—
647	#123	C₂⁴	1	48	yes	—
648	#123	C₂⁴	1	16	yes	—
649	#123	C₂⁴	1	96	yes	—
650	#123	C₂⁴	1	96	yes	—
651	#123	C₂⁴	1	48	yes	—
652	#123	C₂⁴	1	48	yes	—
653	#123	C₂⁴	1	96	yes	—
654	#123	C₂⁴	1	96	yes	—
655	#123	C₂⁴	1	96	yes	—
656	#123	C₂⁴	1	96	yes	—
657	#123	C₂⁴	1	96	yes	—
658	#123	C₂⁴	1	96	yes	—
659	C₂²⋊Q₈	C₂⁴	1	24	yes	—
660	C₂²⋊Q₈	C₂⁴	1	48	yes	—
661	C₂²⋊Q₈	C₂⁴	1	48	yes	—
662	C₂²⋊Q₈	C₂⁴	1	48	yes	—
663	C₂²⋊Q₈	C₂⁴	1	48	yes	—
664	C₂²⋊Q₈	C₂⁴	1	48	yes	—
665	C₂²⋊Q₈	C₂⁴	1	48	yes	—
666	C₂²⋊Q₈	C₂⁴	1	48	yes	—
667	C₂²⋊Q₈	C₂⁴	1	8	yes	—
668	C₂²⋊Q₈	C₂⁴	1	24	yes	—
669	C₂²⋊Q₈	C₂⁴	1	24	yes	—
670	C₂²⋊Q₈	C₂⁴	1	48	yes	—
671	C₂²⋊Q₈	C₂⁴	1	48	yes	—
672	C₂²⋊Q₈	C₂⁴	1	48	yes	—
673	C₂²⋊Q₈	C₂⁴	1	48	yes	—
674	C₂²⋊Q₈	C₂⁴	1	48	yes	—
675	C₂²⋊Q₈	C₂⁴	1	48	yes	—
676	C₂²⋊Q₈	C₂⁴	1	48	yes	—
677	C₂²⋊Q₈	C₂⁴	1	48	yes	—
678	C₂²⋊Q₈	C₂⁴	1	48	yes	—
679	C₂²⋊Q₈	C₂⁴	1	48	yes	—
680	C₂²⋊Q₈	C₂⁴	1	96	yes	—
681	C₂²⋊Q₈	C₂⁴	1	96	yes	—
682	C₂²⋊Q₈	C₂⁴	1	96	yes	—
683	C₂²⋊Q₈	C₂⁴	1	96	yes	—
684	C₂²⋊Q₈	C₂⁴	1	96	yes	—
685	C₂²⋊Q₈	C₂⁴	1	96	yes	—
686	#121	C₂⁴	1	24	yes	—
687	#121	C₂⁴	1	48	yes	—
688	#121	C₂⁴	1	48	yes	—
689	#121	C₂⁴	1	48	yes	—
690	#121	C₂⁴	1	48	yes	—
691	#121	C₂⁴	1	48	yes	—
692	#121	C₂⁴	1	96	yes	—
693	#121	C₂⁴	1	24	yes	—
694	#121	C₂⁴	1	8	yes	—
695	#121	C₂⁴	1	48	yes	—
696	#121	C₂⁴	1	24	yes	—
697	#121	C₂⁴	1	48	yes	—
698	#121	C₂⁴	1	48	yes	—
699	#121	C₂⁴	1	48	yes	—
700	#121	C₂⁴	1	48	yes	—
701	#121	C₂⁴	1	48	yes	—
702	#121	C₂⁴	1	48	yes	—
703	#121	C₂⁴	1	48	yes	—
704	#121	C₂⁴	1	48	yes	—
705	#121	C₂⁴	1	16	yes	—
706	#121	C₂⁴	1	48	yes	—
707	#121	C₂⁴	1	48	yes	—
708	#121	C₂⁴	1	48	yes	—
709	#121	C₂⁴	1	96	yes	—
710	#121	C₂⁴	1	48	yes	—
711	#121	C₂⁴	1	48	yes	—
712	#121	C₂⁴	1	48	yes	—
713	#121	C₂⁴	1	96	yes	—
714	#121	C₂⁴	1	96	yes	—
715	#121	C₂⁴	1	96	yes	—
716	#121	C₂⁴	1	96	yes	—
717	#121	C₂⁴	1	96	yes	—
718	#120	C₂⁴	1	48	yes	—
719	#120	C₂⁴	1	48	yes	—
720	#120	C₂⁴	1	16	yes	—
721	#120	C₂⁴	1	48	yes	—
722	#120	C₂⁴	1	96	yes	—
723	#120	C₂⁴	1	96	yes	—
724	#120	C₂⁴	1	96	yes	—
725	C₄×Q₈	C₂⁴	1	16	yes	—
726	C₄×Q₈	C₂⁴	1	16	yes	—
727	C₄×Q₈	C₂⁴	1	48	yes	—
728	C₄×Q₈	C₂⁴	1	48	yes	—
729	C₄×Q₈	C₂⁴	1	48	yes	—
730	C₄×Q₈	C₂⁴	1	16	yes	—
731	C₄×Q₈	C₂⁴	1	48	yes	—
732	C₄×Q₈	C₂⁴	1	48	yes	—
733	C₄×Q₈	C₂⁴	1	48	yes	—
734	C₄×Q₈	C₂⁴	1	48	yes	—
735	C₄×D₄	C₂⁴	1	48	yes	—
736	C₄×D₄	C₂⁴	1	48	yes	—
737	C₄×D₄	C₂⁴	1	48	yes	—
738	C₄×D₄	C₂⁴	1	48	yes	—
739	C₄×D₄	C₂⁴	1	16	yes	—
740	C₄×D₄	C₂⁴	1	48	yes	—
741	C₄×D₄	C₂⁴	1	48	yes	—
742	C₄×D₄	C₂⁴	1	48	yes	—
743	C₄×D₄	C₂⁴	1	48	yes	—
744	C₄×D₄	C₂⁴	1	48	yes	—
745	C₄×D₄	C₂⁴	1	48	yes	—
746	C₄×D₄	C₂⁴	1	48	yes	—
747	C₄×D₄	C₂⁴	1	96	yes	—
748	C₄×D₄	C₂⁴	1	96	yes	—
749	C₄×D₄	C₂⁴	1	96	yes	—
750	C₄×D₄	C₂⁴	1	48	yes	—
751	C₄×D₄	C₂⁴	1	48	yes	—
752	C₄×D₄	C₂⁴	1	48	yes	—
753	C₄×D₄	C₂⁴	1	48	yes	—
754	C₄×D₄	C₂⁴	1	48	yes	—
755	C₄×D₄	C₂⁴	1	48	yes	—
756	C₄×D₄	C₂⁴	1	96	yes	—
757	C₄×D₄	C₂⁴	1	96	yes	—
758	C₄×D₄	C₂⁴	1	96	yes	—
759	#117	C₂⁴	1	48	yes	—
760	#117	C₂⁴	1	48	yes	—
761	#117	C₂⁴	1	48	yes	—
762	#117	C₂⁴	1	48	yes	—
763	#117	C₂⁴	1	96	yes	—
764	#117	C₂⁴	1	48	yes	—
765	#117	C₂⁴	1	48	yes	—
766	#117	C₂⁴	1	24	yes	—
767	#117	C₂⁴	1	24	yes	—
768	#117	C₂⁴	1	96	yes	—
769	#117	C₂⁴	1	96	yes	—
770	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
771	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
772	C₂×C₄⋊C₄	C₂⁴	1	3	yes	—
773	C₂×C₄⋊C₄	C₂⁴	1	3	yes	—
774	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
775	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
776	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
777	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
778	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
779	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
780	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
781	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
782	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
783	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
784	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
785	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
786	C₂×C₄⋊C₄	C₂⁴	1	48	yes	—
787	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
788	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
789	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
790	C₂×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
791	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
792	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
793	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
794	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
795	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
796	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
797	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
798	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
799	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
800	C₂×C₄⋊C₄	C₂⁴	1	6	yes	—
801	C₂×C₄⋊C₄	C₂⁴	1	2	yes	—
802	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
803	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
804	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
805	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
806	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
807	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
808	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
809	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
810	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
811	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
812	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
813	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
814	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
815	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
816	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
817	C₂×C₂²⋊C₄	C₂⁴	1	8	yes	—
818	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
819	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
820	C₂×C₂²⋊C₄	C₂⁴	1	96	yes	—
821	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
822	C₂×C₂²⋊C₄	C₂⁴	1	48	yes	—
823	C₂×C₂²⋊C₄	C₂⁴	1	96	yes	—
824	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
825	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
826	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
827	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
828	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
829	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
830	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
831	C₂×C₂²⋊C₄	C₂⁴	1	12	yes	—
832	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
833	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
834	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
835	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
836	C₂×C₂²⋊C₄	C₂⁴	1	2	yes	—
837	C₂×C₂²⋊C₄	C₂⁴	1	6	yes	—
838	C₂×C₄²	C₂⁴	1	6	yes	—
839	C₂×C₄²	C₂⁴	1	6	yes	—
840	C₂×C₄²	C₂⁴	1	6	yes	—
841	C₂×C₄²	C₂⁴	1	12	yes	—
842	C₂×C₄²	C₂⁴	1	6	yes	—
843	C₂×C₄²	C₂⁴	1	6	yes	—
844	C₂×C₄²	C₂⁴	1	6	yes	—
845	C₂×C₄²	C₂⁴	1	6	yes	—
846	C₂×C₄²	C₂⁴	1	2	yes	—
847	C₂×C₄²	C₂⁴	1	24	yes	—
848	C₂×C₄²	C₂⁴	1	48	yes	—
849	C₂×C₄²	C₂⁴	1	48	yes	—
850	C₂⁴	—	2	4	no	—
851	C₂⁴	—	2	12	no	—
852	C₂⁴	—	4	2	no	—
853	C₂⁴	—	4	2	no	—
854	C₂⁴	—	4	6	no	—
855	C₂⁴	—	4	6	no	—
856	C₂⁴	—	4	12	no	—
857	C₂⁴	—	4	12	no	—
858	C₂⁴	—	4	12	no	—
859	C₂⁴	C₂⁵	1	3	yes	—
860	C₂⁴	C₂⁵	1	6	yes	—
861	C₂⁴	C₂⁵	1	2	yes	—
862	C₂⁴	C₂⁵	1	3	yes	—
863	C₂⁴	C₂⁵	1	2	yes	—
864	C₂⁴	C₂⁵	1	1	yes	characteristic
865	C₂⁴	C₂⁵	1	12	yes	—
866	C₂⁴	C₂⁵	1	4	yes	—
867	C₂⁴	C₂⁵	1	24	yes	—
868	#41	—	2	32	no	—
869	#41	—	2	32	no	—
870	#41	—	2	64	no	—
871	#41	—	4	48	no	—
872	#41	—	4	96	no	—
873	#41	—	4	48	no	—
874	#41	—	4	96	no	—
875	#41	—	4	48	no	—
876	#41	—	4	48	no	—
877	#41	—	4	96	no	—
878	#41	—	4	96	no	—
879	#41	—	4	96	no	—
880	C₂×Q₈	—	2	32	no	—
881	C₂×Q₈	—	2	64	no	—
882	C₂×Q₈	—	2	64	no	—
883	C₂×Q₈	—	2	24	no	—
884	C₂×Q₈	—	2	12	no	—
885	C₂×Q₈	—	2	24	no	—
886	C₂×Q₈	—	4	12	no	—
887	C₂×Q₈	—	4	6	no	—
888	C₂×Q₈	—	4	12	no	—
889	C₂×Q₈	—	4	12	no	—
890	C₂×Q₈	—	4	2	no	—
891	C₂×Q₈	—	4	48	no	—
892	C₂×Q₈	—	4	96	no	—
893	C₂×Q₈	—	4	48	no	—
894	C₂×Q₈	—	4	96	no	—
895	C₂×Q₈	H(5,𝔽₂)	1	8	yes	—
896	C₂×Q₈	C₂⁵	1	24	yes	—
897	C₂×Q₈	C₂⁵	1	12	yes	—
898	C₂×Q₈	C₂⁵	1	24	yes	—
899	C₂×Q₈	C₂⁵	1	24	yes	—
900	C₂×Q₈	C₂⁵	1	12	yes	—
901	C₂×Q₈	C₂⁵	1	24	yes	—
902	C₂×Q₈	C₂⁵	1	24	yes	—
903	C₂×Q₈	C₂⁵	1	4	yes	—
904	C₂×Q₈	C₂⁵	1	4	yes	—
905	C₂×D₄	—	2	24	no	—
906	C₂×D₄	—	2	8	no	—
907	C₂×D₄	—	2	12	no	—
908	C₂×D₄	—	2	24	no	—
909	C₂×D₄	—	2	12	no	—
910	C₂×D₄	—	4	48	no	—
911	C₂×D₄	—	4	48	no	—
912	C₂×D₄	—	4	96	no	—
913	C₂×D₄	—	4	6	no	—
914	C₂×D₄	—	4	12	no	—
915	C₂×D₄	—	4	12	no	—
916	C₂×D₄	—	4	12	no	—
917	C₂×D₄	—	4	48	no	—
918	C₂×D₄	—	4	24	no	—
919	C₂×D₄	—	4	12	no	—
920	C₂×D₄	—	4	12	no	—
921	C₂×D₄	—	4	12	no	—
922	C₂×D₄	—	4	12	no	—
923	C₂×D₄	—	4	4	no	—
924	C₂×D₄	—	4	12	no	—
925	C₂×D₄	—	4	2	no	—
926	C₂×D₄	—	4	4	no	—
927	C₂×D₄	—	4	12	no	—
928	C₂×D₄	—	4	12	no	—
929	C₂×D₄	—	4	12	no	—
930	C₂×D₄	—	4	96	no	—
931	C₂×D₄	C₂⁵	1	8	yes	—
932	C₂×D₄	C₂⁵	1	24	yes	—
933	C₂×D₄	C₂⁵	1	12	yes	—
934	C₂×D₄	C₂⁵	1	24	yes	—
935	C₂×D₄	C₂⁵	1	12	yes	—
936	C₂×D₄	C₂⁵	1	24	yes	—
937	C₂×D₄	C₂⁵	1	24	yes	—
938	C₂×D₄	C₂⁵	1	24	yes	—
939	C₂×D₄	C₂⁵	1	8	yes	—
940	C₂×D₄	C₂⁵	1	24	yes	—
941	C₂×D₄	C₂⁵	1	24	yes	—
942	C₂×D₄	C₂⁵	1	48	yes	—
943	C₂×D₄	C₂⁵	1	24	yes	—
944	C₂×D₄	C₂⁵	1	24	yes	—
945	C₂×D₄	C₂⁵	1	24	yes	—
946	C₂×D₄	C₂⁵	1	24	yes	—
947	C₂×D₄	C₂⁵	1	24	yes	—
948	C₂×D₄	C₂⁵	1	24	yes	—
949	C₂×D₄	C₂⁵	1	8	yes	—
950	C₂×D₄	C₂⁵	1	4	yes	—
951	C₂×D₄	C₂⁵	1	12	yes	—
952	C₂²×C₄	—	2	12	no	—
953	C₂²×C₄	—	2	12	no	—
954	C₂²×C₄	—	2	12	no	—
955	C₂²×C₄	—	2	24	no	—
956	C₂²×C₄	—	2	12	no	—
957	C₂²×C₄	—	2	24	no	—
958	C₂²×C₄	—	2	24	no	—
959	C₂²×C₄	—	4	48	no	—
960	C₂²×C₄	—	4	48	no	—
961	C₂²×C₄	—	4	2	no	—
962	C₂²×C₄	—	4	12	no	—
963	C₂²×C₄	—	4	6	no	—
964	C₂²×C₄	—	4	6	no	—
965	C₂²×C₄	—	4	6	no	—
966	C₂²×C₄	—	4	2	no	—
967	C₂²×C₄	—	4	12	no	—
968	C₂²×C₄	—	4	4	no	—
969	C₂²×C₄	—	4	12	no	—
970	C₂²×C₄	—	4	12	no	—
971	C₂²×C₄	—	4	12	no	—
972	C₂²×C₄	—	4	24	no	—
973	C₂²×C₄	—	4	12	no	—
974	C₂²×C₄	—	4	12	no	—
975	C₂²×C₄	C₂⁵	1	12	yes	—
976	C₂²×C₄	C₂⁵	1	12	yes	—
977	C₂²×C₄	C₂⁵	1	24	yes	—
978	C₂²×C₄	C₂⁵	1	24	yes	—
979	C₂²×C₄	C₂⁵	1	12	yes	—
980	C₂²×C₄	C₂⁵	1	12	yes	—
981	C₂²×C₄	C₂⁵	1	24	yes	—
982	C₂²×C₄	C₂⁵	1	2	yes	—
983	C₂²×C₄	C₂⁵	1	2	yes	—
984	C₂²×C₄	C₂⁵	1	2	yes	—
985	C₂²×C₄	C₂⁵	1	6	yes	—
986	C₂²×C₄	C₂⁵	1	6	yes	—
987	C₂²×C₄	C₂⁵	1	6	yes	—
988	C₂²×C₄	C₂⁵	1	2	yes	—
989	C₂²×C₄	C₂⁵	1	6	yes	—
990	C₂²×C₄	C₂⁵	1	3	yes	—
991	C₂²×C₄	C₂⁵	1	6	yes	—
992	C₂²×C₄	C₂⁵	1	1	yes	characteristic
993	C₂²×C₄	C₂⁵	1	1	yes	characteristic
994	C₂²×C₄	C₂⁵	1	4	yes	—
995	C₂²×C₄	C₂⁵	1	8	yes	—
996	C₂²×C₄	C₂⁵	1	24	yes	—
997	C₂²×C₄	C₂⁵	1	24	yes	—
998	C₂²×C₄	C₂⁵	1	24	yes	—
999	C₂²×C₄	C₂⁵	1	12	yes	—
1000	C₂²×C₄	C₂⁵	1	48	yes	—
1001	C₂²×C₄	C₂⁵	1	12	yes	—
1002	C₂²×C₄	C₂⁵	1	4	yes	—
1003	C₂²×C₄	C₂⁵	1	24	yes	—
1004	C₂²×C₄	C₂⁵	1	24	yes	—
1005	C₂²×C₄	C₂⁵	1	24	yes	—
1006	C₂²×C₄	C₂⁵	1	12	yes	—
1007	C₂²×C₄	C₂⁵	1	24	yes	—
1008	C₂²×C₄	C₂⁵	1	3	yes	—
1009	C₄⋊C₄	C₂⁵	1	24	yes	—
1010	C₄⋊C₄	C₂⁵	1	24	yes	—
1011	C₄⋊C₄	C₂⁵	1	12	yes	—
1012	C₄⋊C₄	C₂⁵	1	12	yes	—
1013	C₄⋊C₄	C₂⁵	1	24	yes	—
1014	C₄⋊C₄	C₂⁵	1	24	yes	—
1015	C₄⋊C₄	C₂⁵	1	48	yes	—
1016	C₄⋊C₄	C₂⁵	1	24	yes	—
1017	C₄⋊C₄	C₂⁵	1	24	yes	—
1018	C₄⋊C₄	C₂⁵	1	24	yes	—
1019	C₄⋊C₄	C₂⁵	1	48	yes	—
1020	C₄⋊C₄	C₂⁵	1	24	yes	—
1021	C₄⋊C₄	C₂⁵	1	8	yes	—
1022	C₄⋊C₄	C₂⁵	1	4	yes	—
1023	C₄⋊C₄	C₂⁵	1	4	yes	—
1024	C₄⋊C₄	C₂⁵	1	24	yes	—
1025	C₄⋊C₄	C₂⁵	1	48	yes	—
1026	C₄⋊C₄	C₂⁵	1	48	yes	—
1027	C₄⋊C₄	C₂⁵	1	24	yes	—
1028	C₄⋊C₄	C₂⁵	1	24	yes	—
1029	C₄⋊C₄	C₂⁵	1	24	yes	—
1030	C₄⋊C₄	C₂⁵	1	24	yes	—
1031	C₄⋊C₄	C₂⁵	1	24	yes	—
1032	C₄⋊C₄	C₂⁵	1	24	yes	—
1033	C₄⋊C₄	C₂⁵	1	24	yes	—
1034	C₄⋊C₄	C₂⁵	1	8	yes	—
1035	C₂²⋊C₄	C₂⁵	1	24	yes	—
1036	C₂²⋊C₄	C₂⁵	1	24	yes	—
1037	C₂²⋊C₄	C₂⁵	1	24	yes	—
1038	C₂²⋊C₄	C₂⁵	1	48	yes	—
1039	C₂²⋊C₄	C₂⁵	1	48	yes	—
1040	C₂²⋊C₄	C₂⁵	1	24	yes	—
1041	C₂²⋊C₄	C₂⁵	1	24	yes	—
1042	C₂²⋊C₄	C₂⁵	1	24	yes	—
1043	C₂²⋊C₄	C₂⁵	1	48	yes	—
1044	C₂²⋊C₄	C₂⁵	1	48	yes	—
1045	C₂²⋊C₄	C₂⁵	1	48	yes	—
1046	C₂²⋊C₄	C₂⁵	1	8	yes	—
1047	C₂²⋊C₄	C₂⁵	1	8	yes	—
1048	C₂²⋊C₄	C₂⁵	1	24	yes	—
1049	C₂²⋊C₄	C₂⁵	1	48	yes	—
1050	C₂²⋊C₄	C₂⁵	1	8	yes	—
1051	C₂²⋊C₄	C₂⁵	1	8	yes	—
1052	C₂²⋊C₄	C₂⁵	1	24	yes	—
1053	C₂²⋊C₄	C₂⁵	1	8	yes	—
1054	C₂²⋊C₄	C₂⁵	1	24	yes	—
1055	C₂²⋊C₄	C₂⁵	1	24	yes	—
1056	C₂²⋊C₄	C₂⁵	1	24	yes	—
1057	C₂²⋊C₄	C₂⁵	1	48	yes	—
1058	C₂²⋊C₄	C₂⁵	1	24	yes	—
1059	C₂²⋊C₄	C₂⁵	1	24	yes	—
1060	C₂²⋊C₄	C₂⁵	1	24	yes	—
1061	C₂²⋊C₄	C₂⁵	1	8	yes	—
1062	C₂²⋊C₄	C₂⁵	1	8	yes	—
1063	C₂²⋊C₄	C₂⁵	1	24	yes	—
1064	C₄²	C₂⁵	1	24	yes	—
1065	C₄²	C₂⁵	1	8	yes	—
1066	C₄²	C₂⁵	1	24	yes	—
1067	C₄²	C₂⁵	1	24	yes	—
1068	C₄²	C₂⁵	1	24	yes	—
1069	C₄²	C₂⁵	1	24	yes	—
1070	C₄²	C₂⁵	1	24	yes	—
1071	C₄²	C₂⁵	1	24	yes	—
1072	C₄²	C₂⁵	1	48	yes	—
1073	C₂³	—	2	2	no	—
1074	C₂³	—	2	2	no	—
1075	C₂³	—	2	4	no	—
1076	C₂³	—	2	4	no	—
1077	C₂³	—	2	6	no	—
1078	C₂³	—	2	12	no	—
1079	C₂³	—	2	6	no	—
1080	C₂³	—	2	4	no	—
1081	C₂³	—	2	6	no	—
1082	C₂³	—	2	12	no	—
1083	C₂³	—	2	8	no	—
1084	C₂³	—	2	4	no	—
1085	C₂³	—	2	6	no	—
1086	C₂³	—	2	6	no	—
1087	C₂³	—	2	4	no	—
1088	C₂³	—	2	12	no	—
1089	C₂³	—	2	4	no	—
1090	C₂³	—	2	6	no	—
1091	C₂³	—	2	24	no	—
1092	C₂³	—	4	4	no	—
1093	C₂³	—	4	4	no	—
1094	C₂³	—	4	12	no	—
1095	C₂³	—	4	12	no	—
1096	C₂³	—	4	24	no	—
1097	C₂³	—	4	24	no	—
1098	C₂³	—	4	24	no	—
1099	C₂³	—	4	16	no	—
1100	C₂³	—	8	24	no	—
1101	C₂³	—	16	24	no	—
1102	C₂³	#585	1	4	yes	—
1103	C₂³	C₂⁶	1	6	yes	—
1104	C₂³	C₂⁶	1	12	yes	—
1105	C₂³	C₂⁶	1	4	yes	—
1106	C₂³	C₂⁶	1	6	yes	—
1107	C₂³	C₂⁶	1	4	yes	—
1108	C₂³	C₂⁶	1	2	yes	—
1109	C₂³	C₂⁶	1	1	yes	characteristic
1110	Q₈	—	2	48	no	—
1111	Q₈	—	2	24	no	—
1112	Q₈	—	2	48	no	—
1113	Q₈	—	4	24	no	—
1114	Q₈	—	4	12	no	—
1115	Q₈	—	4	24	no	—
1116	Q₈	—	4	24	no	—
1117	Q₈	—	4	4	no	—
1118	Q₈	C₂×H(5,𝔽₂)	1	16	yes	—
1119	D₄	—	2	48	no	—
1120	D₄	—	2	16	no	—
1121	D₄	—	2	24	no	—
1122	D₄	—	2	48	no	—
1123	D₄	—	2	24	no	—
1124	D₄	—	4	12	no	—
1125	D₄	—	4	24	no	—
1126	D₄	—	4	24	no	—
1127	D₄	—	4	24	no	—
1128	D₄	—	4	48	no	—
1129	D₄	—	4	24	no	—
1130	D₄	—	4	24	no	—
1131	D₄	—	4	24	no	—
1132	D₄	—	4	24	no	—
1133	D₄	—	4	8	no	—
1134	D₄	—	4	24	no	—
1135	D₄	—	4	4	no	—
1136	D₄	—	4	8	no	—
1137	D₄	—	4	24	no	—
1138	D₄	—	4	24	no	—
1139	D₄	—	4	24	no	—
1140	C₂×C₄	—	2	2	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	4	no	—
1143	C₂×C₄	—	2	6	no	—
1144	C₂×C₄	—	2	12	no	—
1145	C₂×C₄	—	2	12	no	—
1146	C₂×C₄	—	2	12	no	—
1147	C₂×C₄	—	2	24	no	—
1148	C₂×C₄	—	2	12	no	—
1149	C₂×C₄	—	2	4	no	—
1150	C₂×C₄	—	2	4	no	—
1151	C₂×C₄	—	2	12	no	—
1152	C₂×C₄	—	2	4	no	—
1153	C₂×C₄	—	2	24	no	—
1154	C₂×C₄	—	2	24	no	—
1155	C₂×C₄	—	2	48	no	—
1156	C₂×C₄	—	2	24	no	—
1157	C₂×C₄	—	2	48	no	—
1158	C₂×C₄	—	2	48	no	—
1159	C₂×C₄	—	4	4	no	—
1160	C₂×C₄	—	4	24	no	—
1161	C₂×C₄	—	4	12	no	—
1162	C₂×C₄	—	4	12	no	—
1163	C₂×C₄	—	4	12	no	—
1164	C₂×C₄	—	4	4	no	—
1165	C₂×C₄	—	4	24	no	—
1166	C₂×C₄	—	4	8	no	—
1167	C₂×C₄	—	4	24	no	—
1168	C₂×C₄	—	4	24	no	—
1169	C₂×C₄	—	4	24	no	—
1170	C₂×C₄	—	4	48	no	—
1171	C₂×C₄	—	4	24	no	—
1172	C₂×C₄	—	4	24	no	—
1173	C₂×C₄	C₂×H(5,𝔽₂)	1	12	yes	—
1174	C₂×C₄	C₂⁶	1	4	yes	—
1175	C₂×C₄	C₂⁶	1	4	yes	—
1176	C₂×C₄	C₂⁶	1	4	yes	—
1177	C₂×C₄	C₂⁶	1	12	yes	—
1178	C₂×C₄	C₂⁶	1	12	yes	—
1179	C₂×C₄	C₂⁶	1	12	yes	—
1180	C₂×C₄	C₂⁶	1	4	yes	—
1181	C₂×C₄	C₂⁶	1	12	yes	—
1182	C₂×C₄	C₂⁶	1	6	yes	—
1183	C₂×C₄	C₂⁶	1	12	yes	—
1184	C₂×C₄	C₂⁶	1	2	yes	—
1185	C₂×C₄	C₂⁶	1	2	yes	—
1186	C₂×C₄	C₂⁶	1	6	yes	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	2	8	no	—
1190	C₂²	—	2	4	no	—
1191	C₂²	—	2	4	no	—
1192	C₂²	—	2	6	no	—
1193	C₂²	—	2	12	no	—
1194	C₂²	—	2	6	no	—
1195	C₂²	—	2	4	no	—
1196	C₂²	—	2	6	no	—
1197	C₂²	—	2	12	no	—
1198	C₂²	—	2	4	no	—
1199	C₂²	—	2	6	no	—
1200	C₂²	—	2	6	no	—
1201	C₂²	—	2	4	no	—
1202	C₂²	—	2	12	no	—
1203	C₂²	—	2	4	no	—
1204	C₂²	—	2	6	no	—
1205	C₂²	—	4	16	no	—
1206	C₂²	—	4	8	no	—
1207	C₂²	—	4	8	no	—
1208	C₂²	—	4	12	no	—
1209	C₂²	—	4	12	no	—
1210	C₂²	—	4	24	no	—
1211	C₂²	—	8	24	no	—
1212	C₂²	—	16	24	no	—
1213	C₂²	C₂²×H(5,𝔽₂)	1	2	yes	—
1214	C₂²	C₂×#585	1	4	yes	—
1215	C₂²	C₂×#585	1	2	yes	—
1216	C₂²	2₋¹⁺⁶	1	2	yes	—
1217	C₂²	C₂⁷	1	1	yes	characteristic
1218	C₄	—	2	2	no	—
1219	C₄	—	2	2	no	—
1220	C₄	—	2	4	no	—
1221	C₄	—	2	6	no	—
1222	C₄	—	2	12	no	—
1223	C₄	—	2	12	no	—
1224	C₄	—	2	12	no	—
1225	C₄	—	2	12	no	—
1226	C₄	—	2	4	no	—
1227	C₄	—	2	4	no	—
1228	C₄	—	2	12	no	—
1229	C₄	—	2	4	no	—
1230	C₄	C₂²×H(5,𝔽₂)	1	12	yes	—
1231	C₂	—	2	4	no	—
1232	C₂	—	4	4	no	—
1233	C₂	—	4	4	no	—
1234	C₂	—	4	6	no	—
1235	C₂	—	4	6	no	—
1236	C₂	—	4	12	no	—
1237	C₂	#62919	1	4	yes	direct product factor
1238	C₂	C₂³×H(5,𝔽₂)	1	1	yes	characteristic
1239	C₂	C₂²×#585	1	1	yes	characteristic
1240	C₂	C₂×2₋¹⁺⁶	1	1	yes	characteristic

	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. #62919	C₂	direct (N × H)
2. C₂×#3500	C₂	semidirect
3. C₂×#3489	C₂	semidirect
4. C₂×#3488	C₂	semidirect
5. C₂×#3524	C₂	semidirect
6. C₂×#3516	C₂	semidirect
7. C₂×#3497	C₂	semidirect
8. C₂×#3486	C₂	semidirect
9. C₂×#3514	C₂	semidirect
10. C₂×#3505	C₂	semidirect
11. C₂×#3547	C₂	semidirect
12. C₂×#3562	C₂	semidirect
13. C₂×#3551	C₂	semidirect
14. C₂×#3561	C₂	semidirect
15. C₂×#3538	C₂	semidirect
16. C₂×#3536	C₂	semidirect
17. C₂×#3542	C₂	semidirect
18. C₂×#3482	C₂	semidirect
19. C₂²×#548	C₂	semidirect
20. C₂×#3460	C₂	semidirect
21. C₂²×2₋¹⁺⁴	C₂²	semidirect
22. C₂²×2₋¹⁺⁴	C₂²	semidirect
23. C₂²×H(5,𝔽₂)	C₂²	semidirect
25. C₂⁴×Q₈	C₂²	semidirect
26. #3562	C₂²	semidirect
27. #3561	C₂²	semidirect
28. #3551	C₂²	semidirect
29. #3547	C₂²	semidirect
30. #3542	C₂²	semidirect
31. #3538	C₂²	semidirect
32. #3536	C₂²	semidirect
33. C₂×#563	C₂²	semidirect
34. C₂×#562	C₂²	semidirect
35. C₂×#562	C₂²	semidirect
36. C₂×#560	C₂²	semidirect
37. #3524	C₂²	semidirect
38. #3516	C₂²	semidirect
39. #3514	C₂²	semidirect
40. #3505	C₂²	semidirect
41. #3500	C₂²	semidirect
42. #3497	C₂²	semidirect
43. #3489	C₂²	semidirect
44. #3488	C₂²	semidirect
45. #3486	C₂²	semidirect
46. #3482	C₂²	semidirect
47. C₂×#559	C₂²	semidirect
48. C₂×#557	C₂²	semidirect
49. C₂×#556	C₂²	semidirect
50. C₂×#556	C₂²	semidirect
51. C₂×#555	C₂²	semidirect
52. C₂×#555	C₂²	semidirect
53. C₂×#554	C₂²	semidirect
54. C₂×#553	C₂²	semidirect
55. C₂×#553	C₂²	semidirect
56. C₂×#553	C₂²	semidirect
57. C₂×#552	C₂²	semidirect
58. C₂×#552	C₂²	semidirect
59. C₂×#552	C₂²	semidirect
60. C₂×#552	C₂²	semidirect
61. C₂×#551	C₂²	semidirect
62. C₂×#551	C₂²	semidirect
63. C₂×#551	C₂²	semidirect
64. C₂×#550	C₂²	semidirect
65. C₂×#550	C₂²	semidirect
66. C₂×D₄×Q₈	C₂²	semidirect
67. C₂×D₄×Q₈	C₂²	semidirect
68. C₂×D₄×Q₈	C₂²	semidirect
69. C₂×D₄×Q₈	C₂²	semidirect
70. C₂×D₄×Q₈	C₂²	semidirect
73. C₂×#548	C₂²	semidirect
74. C₂×#548	C₂²	semidirect
75. C₂×#548	C₂²	semidirect
76. C₂×#548	C₂²	semidirect
77. C₂×#548	C₂²	semidirect
78. C₂×#548	C₂²	semidirect
79. C₂×#548	C₂²	semidirect
80. C₂×#548	C₂²	semidirect
81. C₂×#548	C₂²	semidirect
82. C₂×#548	C₂²	semidirect
83. C₂×#548	C₂²	semidirect
84. C₂×#547	C₂²	semidirect
85. C₂×#547	C₂²	semidirect
86. C₂×#546	C₂²	semidirect
87. C₂×#546	C₂²	semidirect
88. C₂×#546	C₂²	semidirect
89. C₂×#546	C₂²	semidirect
90. C₂×#546	C₂²	semidirect
91. C₂×#546	C₂²	semidirect
92. C₂×#546	C₂²	semidirect
94. #3460	C₂²	semidirect
95. C₂×#544	C₂²	semidirect
96. C₂×#544	C₂²	semidirect
97. C₂×#543	C₂²	semidirect
98. C₂×#542	C₂²	semidirect
99. C₂×#542	C₂²	semidirect
100. C₂×#542	C₂²	semidirect
101. C₂×#542	C₂²	semidirect
102. C₂×#542	C₂²	semidirect
103. C₂×#541	C₂²	semidirect
104. C₂×#540	C₂²	semidirect
105. C₂×#540	C₂²	semidirect
106. C₂×#540	C₂²	semidirect
107. C₂×#540	C₂²	semidirect
108. C₂×#539	C₂²	semidirect
109. C₂×#539	C₂²	semidirect
110. C₂×#538	C₂²	semidirect
111. C₂×#538	C₂²	semidirect
112. C₂×#538	C₂²	semidirect
113. C₂×#538	C₂²	semidirect
114. C₂×#538	C₂²	semidirect
115. C₂×#538	C₂²	semidirect
116. C₂×#537	C₂²	semidirect
117. C₂×#537	C₂²	semidirect
118. C₂×#537	C₂²	semidirect
119. C₂×#537	C₂²	semidirect
120. C₂×#537	C₂²	semidirect
121. C₂×#536	C₂²	semidirect
122. C₂×#536	C₂²	semidirect
123. C₂×#536	C₂²	semidirect
124. C₂×#536	C₂²	semidirect
125. C₂×#535	C₂²	semidirect
126. C₂×#535	C₂²	semidirect
127. C₂×#535	C₂²	semidirect
128. C₂×#534	C₂²	semidirect
129. C₂×#533	C₂²	semidirect
130. C₂×#532	C₂²	semidirect
131. C₂×#532	C₂²	semidirect
132. C₂×#532	C₂²	semidirect
133. C₂×#529	C₂²	semidirect
134. C₂×#529	C₂²	semidirect
135. C₂×#529	C₂²	semidirect
136. C₂×#529	C₂²	semidirect
137. C₂×#529	C₂²	semidirect
138. C₂×#529	C₂²	semidirect
139. C₂²×#124	C₂²	semidirect
140. C₂²×#124	C₂²	semidirect
142. C₂×#525	C₂²	semidirect
143. C₂×#525	C₂²	semidirect
144. C₂×#525	C₂²	semidirect
145. C₂²×C₂²⋊Q₈	C₂²	semidirect
146. C₂²×C₂²⋊Q₈	C₂²	semidirect
148. C₂²×#121	C₂²	semidirect
149. C₂×#520	C₂²	semidirect
150. C₂×#520	C₂²	semidirect
151. C₂×#519	C₂²	semidirect
152. C₂×#518	C₂²	semidirect
153. C₂×C₄×#41	C₂²	semidirect
154. C₂×C₄×#41	C₂²	semidirect
155. C₂²×C₄×Q₈	C₂²	semidirect
156. C₂²×C₄×Q₈	C₂²	semidirect
157. C₂²×C₄×D₄	C₂²	semidirect
160. C₂×2₋¹⁺⁴	C₂³	semidirect
161. C₂×2₋¹⁺⁴	C₂³	semidirect
163. C₂×H(5,𝔽₂)	C₂³	semidirect
186. C₂³×Q₈	C₂³	semidirect
194. #563	C₂³	semidirect
195. #562	C₂³	semidirect
196. #562	C₂³	semidirect
197. #560	C₂³	semidirect
198. #559	C₂³	semidirect
199. #557	C₂³	semidirect
200. #556	C₂³	semidirect
201. #556	C₂³	semidirect
202. #555	C₂³	semidirect
203. #555	C₂³	semidirect
204. #554	C₂³	semidirect
205. #553	C₂³	semidirect
206. #553	C₂³	semidirect
207. #553	C₂³	semidirect
208. #552	C₂³	semidirect
209. #552	C₂³	semidirect
210. #552	C₂³	semidirect
211. #552	C₂³	semidirect
212. #551	C₂³	semidirect
213. #551	C₂³	semidirect
214. #551	C₂³	semidirect
215. #550	C₂³	semidirect
216. #550	C₂³	semidirect
217. D₄×Q₈	C₂³	semidirect
218. D₄×Q₈	C₂³	semidirect
219. D₄×Q₈	C₂³	semidirect
220. D₄×Q₈	C₂³	semidirect
221. D₄×Q₈	C₂³	semidirect
224. #548	C₂³	semidirect
225. #548	C₂³	semidirect
226. #548	C₂³	semidirect
227. #548	C₂³	semidirect
228. #548	C₂³	semidirect
229. #548	C₂³	semidirect
230. #548	C₂³	semidirect
231. #548	C₂³	semidirect
232. #548	C₂³	semidirect
233. #548	C₂³	semidirect
234. #547	C₂³	semidirect
235. #547	C₂³	semidirect
236. #546	C₂³	semidirect
237. #546	C₂³	semidirect
238. #546	C₂³	semidirect
239. #546	C₂³	semidirect
240. #546	C₂³	semidirect
241. #546	C₂³	semidirect
242. #546	C₂³	semidirect
244. #544	C₂³	semidirect
245. #544	C₂³	semidirect
246. #543	C₂³	semidirect
247. #542	C₂³	semidirect
248. #542	C₂³	semidirect
249. #542	C₂³	semidirect
250. #542	C₂³	semidirect
251. #542	C₂³	semidirect
252. #541	C₂³	semidirect
253. #540	C₂³	semidirect
254. #540	C₂³	semidirect
255. #540	C₂³	semidirect
256. #540	C₂³	semidirect
257. #539	C₂³	semidirect
258. #539	C₂³	semidirect
259. #538	C₂³	semidirect
260. #538	C₂³	semidirect
261. #538	C₂³	semidirect
262. #538	C₂³	semidirect
263. #538	C₂³	semidirect
264. #538	C₂³	semidirect
265. #537	C₂³	semidirect
266. #537	C₂³	semidirect
267. #537	C₂³	semidirect
268. #537	C₂³	semidirect
269. #537	C₂³	semidirect
270. #536	C₂³	semidirect
271. #536	C₂³	semidirect
272. #536	C₂³	semidirect
273. #536	C₂³	semidirect
274. #535	C₂³	semidirect
275. #535	C₂³	semidirect
276. #535	C₂³	semidirect
277. #534	C₂³	semidirect
278. #533	C₂³	semidirect
279. #532	C₂³	semidirect
280. #532	C₂³	semidirect
281. #532	C₂³	semidirect
291. #529	C₂³	semidirect
292. #529	C₂³	semidirect
293. #529	C₂³	semidirect
294. #529	C₂³	semidirect
295. #529	C₂³	semidirect
296. #529	C₂³	semidirect
328. C₂×#124	C₂³	semidirect
329. C₂×#124	C₂³	semidirect
331. #525	C₂³	semidirect
332. #525	C₂³	semidirect
333. #525	C₂³	semidirect
378. C₂×C₂²⋊Q₈	C₂³	semidirect
379. C₂×C₂²⋊Q₈	C₂³	semidirect
413. C₂×#121	C₂³	semidirect
421. #520	C₂³	semidirect
422. #520	C₂³	semidirect
423. #519	C₂³	semidirect
424. #518	C₂³	semidirect
425. C₄×#41	C₂³	semidirect
426. C₄×#41	C₂³	semidirect
437. C₂×C₄×Q₈	C₂³	semidirect
438. C₂×C₄×Q₈	C₂³	semidirect
463. C₂×C₄×D₄	C₂³	semidirect
1237. C₂	#62919	direct (N × H)

Maximal subgroups

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

subgroup	index
#62919	2
C₂×#3500	2
C₂×#3489	2
C₂×#3488	2
C₂×#3524	2
C₂×#3516	2
C₂×#3497	2
C₂×#3486	2
C₂×#3514	2
C₂×#3505	2
C₂×#3547	2
C₂×#3562	2
C₂×#3551	2
C₂×#3561	2
C₂×#3538	2
C₂×#3536	2
C₂×#3542	2
C₂×#3482	2
C₂²×#548	2
C₂×#3460	2

Subgroups — C2×#62919 #10586261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#62919 #10586261