Subgroups — C₂²×#3535 #10586122

Order 512.

35430 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3535	C₂	1	96	yes	maximal, direct product factor
2	C₂²×#552	C₂	1	2	yes	maximal, complemented
3	C₂²×#551	C₂	1	2	yes	maximal, complemented
4	C₂²×#551	C₂	1	2	yes	maximal, complemented
5	C₂²×#554	C₂	1	2	yes	maximal, complemented
6	C₂²×#547	C₂	1	2	yes	maximal, complemented
7	C₂²×#546	C₂	1	2	yes	maximal, complemented
8	C₂²×#563	C₂	1	2	yes	maximal, complemented
9	C₂²×#562	C₂	1	2	yes	maximal, complemented
10	C₂²×#536	C₂	1	2	yes	maximal, complemented
11	C₂²×#542	C₂	1	2	yes	maximal, complemented
12	C₂²×#544	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#539	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#539	C₂	1	2	yes	maximal, complemented
15	C₂²×#539	C₂	1	2	yes	maximal, complemented
16	C₂²×#538	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#543	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#525	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂³×#123	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂³×#41	C₂²	1	2	yes	—
22	C₂³×#41	C₂²	1	1	yes	characteristic, complemented
23	C₂⁴×Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂⁴×D₄	C₂²	1	1	yes	characteristic
25	C₂⁵×C₄	C₂²	1	1	yes	characteristic
26	#3535	C₂²	1	1024	yes	direct product factor
27	C₂×#563	C₂²	1	96	yes	complemented
28	C₂×#562	C₂²	1	96	yes	complemented
29	C₂×#554	C₂²	1	96	yes	complemented
30	C₂×#552	C₂²	1	96	yes	complemented
31	C₂×#551	C₂²	1	96	yes	complemented
32	C₂×#551	C₂²	1	96	yes	complemented
33	C₂×#547	C₂²	1	96	yes	complemented
34	C₂×#546	C₂²	1	96	yes	complemented
35	C₂×#544	C₂²	1	48	yes	complemented
36	C₂×#543	C₂²	1	48	yes	complemented
37	C₂×#542	C₂²	1	96	yes	complemented
38	C₂×#539	C₂²	1	48	yes	complemented
39	C₂×#539	C₂²	1	96	yes	complemented
40	C₂×#539	C₂²	1	96	yes	complemented
41	C₂×#538	C₂²	1	48	yes	complemented
42	C₂×#536	C₂²	1	96	yes	complemented
43	C₂²×C₄⋊Q₈	C₂²	1	2	yes	complemented
44	C₂²×C₄⋊Q₈	C₂²	1	2	yes	complemented
45	C₂²×C₄⋊Q₈	C₂²	1	2	yes	complemented
46	C₂²×#126	C₂²	1	2	yes	complemented
47	C₂²×#126	C₂²	1	2	yes	complemented
48	C₂²×#126	C₂²	1	2	yes	complemented
49	C₂²×#126	C₂²	1	2	yes	complemented
50	C₂²×#126	C₂²	1	2	yes	complemented
51	C₂²×#126	C₂²	1	2	yes	complemented
52	C₂²×#125	C₂²	1	2	yes	complemented
53	C₂²×#125	C₂²	1	2	yes	complemented
54	C₂²×#125	C₂²	1	2	yes	complemented
55	C₂²×#125	C₂²	1	2	yes	complemented
56	C₂²×#125	C₂²	1	2	yes	complemented
57	C₂²×#124	C₂²	1	2	yes	—
58	C₂²×#124	C₂²	1	2	yes	complemented
59	C₂²×#124	C₂²	1	2	yes	complemented
60	C₂²×#124	C₂²	1	2	yes	complemented
61	C₂×#525	C₂²	1	48	yes	complemented
62	C₂²×#123	C₂²	1	2	yes	—
63	C₂²×#123	C₂²	1	2	yes	—
64	C₂²×#123	C₂²	1	2	yes	—
65	C₂²×#123	C₂²	1	2	yes	—
66	C₂²×#123	C₂²	1	2	yes	—
67	C₂²×#123	C₂²	1	2	yes	—
68	C₂²×#123	C₂²	1	2	yes	—
69	C₂²×#123	C₂²	1	48	yes	complemented
70	C₂²×#123	C₂²	1	2	yes	complemented
71	C₂²×#123	C₂²	1	2	yes	complemented
72	C₂²×#123	C₂²	1	2	yes	complemented
73	C₂²×#123	C₂²	1	2	yes	complemented
74	C₂²×#123	C₂²	1	2	yes	complemented
75	C₂²×#123	C₂²	1	2	yes	complemented
76	C₂²×#123	C₂²	1	2	yes	complemented
77	C₂²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
78	C₂²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
79	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	—
80	C₂²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
81	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	—
82	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	—
83	C₂²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
84	C₂²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
85	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
86	C₂²×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
87	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
88	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
89	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
90	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
91	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
92	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
93	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
94	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
95	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
96	C₂²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
97	C₂²×C₂²⋊Q₈	C₂²	1	48	yes	complemented
98	C₂²×#121	C₂²	1	1	yes	characteristic
99	C₂²×#121	C₂²	1	2	yes	—
100	C₂²×#121	C₂²	1	2	yes	—
101	C₂²×#121	C₂²	1	2	yes	—
102	C₂²×#121	C₂²	1	1	yes	characteristic, complemented
103	C₂²×#121	C₂²	1	2	yes	complemented
104	C₂²×#120	C₂²	1	2	yes	—
105	C₂²×#120	C₂²	1	2	yes	—
106	C₂²×C₄×Q₈	C₂²	1	2	yes	complemented
107	C₂²×C₄×D₄	C₂²	1	2	yes	—
108	C₂²×C₄×D₄	C₂²	1	2	yes	—
109	C₂²×C₄×D₄	C₂²	1	2	yes	—
110	C₂²×C₄×D₄	C₂²	1	2	yes	—
111	C₂²×C₄×D₄	C₂²	1	2	yes	complemented
112	C₂²×C₄×D₄	C₂²	1	2	yes	complemented
113	C₂²×C₄×D₄	C₂²	1	2	yes	complemented
114	C₂²×#117	C₂²	1	2	yes	—
115	C₂²×#117	C₂²	1	1	yes	characteristic, complemented
116	C₂²×#117	C₂²	1	2	yes	complemented
117	C₂²×#117	C₂²	1	2	yes	complemented
118	C₂³×C₄⋊C₄	C₂²	1	1	yes	characteristic
119	C₂³×C₄⋊C₄	C₂²	1	1	yes	characteristic
120	C₂³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
121	C₂³×C₄⋊C₄	C₂²	1	2	yes	complemented
122	C₂³×C₄⋊C₄	C₂²	1	2	yes	complemented
123	C₂³×C₂²⋊C₄	C₂²	1	2	yes	—
124	C₂³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
125	C₂³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
126	C₂³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
127	C₂³×C₂²⋊C₄	C₂²	1	2	yes	—
128	C₂⁶	C₂³	1	1	yes	characteristic
129	C₂⁶	C₂³	1	1	yes	characteristic
130	C₂²×#41	—	4	16	no	—
131	C₂²×#41	—	4	8	no	—
132	C₂²×#41	C₂³	1	48	yes	—
133	C₂²×#41	C₂³	1	24	yes	complemented
134	C₂³×Q₈	—	4	8	no	—
135	C₂³×Q₈	C₂³	1	1	yes	characteristic
136	C₂³×Q₈	C₂³	1	2	yes	—
137	C₂³×Q₈	C₂³	1	1	yes	characteristic
138	C₂³×Q₈	C₂³	1	2	yes	—
139	C₂³×Q₈	C₂³	1	1	yes	characteristic
140	C₂³×Q₈	C₂³	1	2	yes	—
141	C₂³×Q₈	C₂³	1	24	yes	complemented
142	C₂³×D₄	—	4	8	no	—
143	C₂³×D₄	C₂³	1	2	yes	—
144	C₂³×D₄	C₂³	1	2	yes	—
145	C₂³×D₄	C₂³	1	2	yes	—
146	C₂³×D₄	C₂³	1	2	yes	—
147	C₂³×D₄	C₂³	1	24	yes	—
148	C₂³×D₄	C₂³	1	2	yes	—
149	C₂³×D₄	C₂³	1	1	yes	characteristic
150	C₂³×D₄	C₂³	1	2	yes	—
151	C₂³×D₄	C₂³	1	2	yes	—
152	C₂⁴×C₄	—	4	8	no	—
153	C₂⁴×C₄	C₂³	1	1	yes	characteristic
154	C₂⁴×C₄	C₂³	1	1	yes	characteristic
155	C₂⁴×C₄	C₂³	1	2	yes	—
156	C₂⁴×C₄	C₂³	1	1	yes	characteristic
157	C₂⁴×C₄	C₂³	1	1	yes	characteristic
158	C₂⁴×C₄	C₂³	1	1	yes	characteristic
159	C₂⁴×C₄	C₂³	1	1	yes	characteristic
160	C₂⁴×C₄	C₂³	1	1	yes	characteristic
161	C₂⁴×C₄	C₂³	1	24	yes	—
162	C₂⁴×C₄	C₂³	1	1	yes	characteristic
163	C₂⁴×C₄	C₂³	1	2	yes	—
164	C₂⁴×C₄	C₂³	1	2	yes	—
165	C₂⁴×C₄	C₂³	1	2	yes	—
166	C₂⁴×C₄	C₂³	1	1	yes	characteristic
167	C₂⁴×C₄	C₂³	1	2	yes	—
168	C₂⁴×C₄	C₂³	1	2	yes	—
169	C₂⁴×C₄	C₂³	1	2	yes	—
170	#563	C₂³	1	512	yes	complemented
171	#562	C₂³	1	512	yes	complemented
172	#554	C₂³	1	512	yes	complemented
173	#552	C₂³	1	512	yes	complemented
174	#551	C₂³	1	512	yes	complemented
175	#551	C₂³	1	512	yes	complemented
176	#547	C₂³	1	512	yes	complemented
177	#546	C₂³	1	512	yes	complemented
178	#544	C₂³	1	256	yes	complemented
179	#543	C₂³	1	256	yes	complemented
180	#542	C₂³	1	512	yes	complemented
181	#539	C₂³	1	256	yes	complemented
182	#539	C₂³	1	512	yes	complemented
183	#539	C₂³	1	512	yes	complemented
184	#538	C₂³	1	256	yes	complemented
185	#536	C₂³	1	512	yes	complemented
186	C₂×C₄⋊Q₈	C₂³	1	48	yes	complemented
187	C₂×C₄⋊Q₈	C₂³	1	48	yes	complemented
188	C₂×C₄⋊Q₈	C₂³	1	48	yes	complemented
189	C₂×#126	C₂³	1	48	yes	complemented
190	C₂×#126	C₂³	1	48	yes	complemented
191	C₂×#126	C₂³	1	48	yes	complemented
192	C₂×#126	C₂³	1	48	yes	complemented
193	C₂×#126	C₂³	1	48	yes	complemented
194	C₂×#126	C₂³	1	48	yes	complemented
195	C₂×#125	C₂³	1	48	yes	complemented
196	C₂×#125	C₂³	1	48	yes	complemented
197	C₂×#125	C₂³	1	48	yes	complemented
198	C₂×#125	C₂³	1	48	yes	complemented
199	C₂×#125	C₂³	1	48	yes	complemented
200	C₂×#124	C₂³	1	48	yes	—
201	C₂×#124	C₂³	1	48	yes	complemented
202	C₂×#124	C₂³	1	48	yes	complemented
203	C₂×#124	C₂³	1	48	yes	complemented
204	#525	C₂³	1	256	yes	complemented
205	C₂×#123	C₂³	1	48	yes	—
206	C₂×#123	C₂³	1	48	yes	—
207	C₂×#123	C₂³	1	48	yes	—
208	C₂×#123	C₂³	1	48	yes	—
209	C₂×#123	C₂³	1	48	yes	—
210	C₂×#123	C₂³	1	48	yes	—
211	C₂×#123	C₂³	1	48	yes	—
212	C₂×#123	C₂³	1	256	yes	complemented
213	C₂×#123	C₂³	1	48	yes	complemented
214	C₂×#123	C₂³	1	48	yes	complemented
215	C₂×#123	C₂³	1	48	yes	complemented
216	C₂×#123	C₂³	1	48	yes	complemented
217	C₂×#123	C₂³	1	48	yes	complemented
218	C₂×#123	C₂³	1	48	yes	complemented
219	C₂×#123	C₂³	1	48	yes	complemented
220	C₂×C₂²⋊Q₈	C₂³	1	24	yes	—
221	C₂×C₂²⋊Q₈	C₂³	1	24	yes	—
222	C₂×C₂²⋊Q₈	C₂³	1	48	yes	—
223	C₂×C₂²⋊Q₈	C₂³	1	24	yes	—
224	C₂×C₂²⋊Q₈	C₂³	1	48	yes	—
225	C₂×C₂²⋊Q₈	C₂³	1	48	yes	—
226	C₂×C₂²⋊Q₈	C₂³	1	24	yes	complemented
227	C₂×C₂²⋊Q₈	C₂³	1	24	yes	complemented
228	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
229	C₂×C₂²⋊Q₈	C₂³	1	24	yes	complemented
230	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
231	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
232	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
233	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
234	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
235	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
236	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
237	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
238	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
239	C₂×C₂²⋊Q₈	C₂³	1	48	yes	complemented
240	C₂×C₂²⋊Q₈	C₂³	1	256	yes	complemented
241	C₂×#121	C₂³	1	24	yes	—
242	C₂×#121	C₂³	1	48	yes	—
243	C₂×#121	C₂³	1	48	yes	—
244	C₂×#121	C₂³	1	48	yes	—
245	C₂×#121	C₂³	1	24	yes	complemented
246	C₂×#121	C₂³	1	48	yes	complemented
247	C₂×#120	C₂³	1	48	yes	—
248	C₂×#120	C₂³	1	48	yes	—
249	C₂×C₄×Q₈	C₂³	1	48	yes	complemented
250	C₂×C₄×D₄	C₂³	1	48	yes	—
251	C₂×C₄×D₄	C₂³	1	48	yes	—
252	C₂×C₄×D₄	C₂³	1	48	yes	—
253	C₂×C₄×D₄	C₂³	1	48	yes	—
254	C₂×C₄×D₄	C₂³	1	48	yes	complemented
255	C₂×C₄×D₄	C₂³	1	48	yes	complemented
256	C₂×C₄×D₄	C₂³	1	48	yes	complemented
257	C₂×#117	C₂³	1	48	yes	—
258	C₂×#117	C₂³	1	24	yes	complemented
259	C₂×#117	C₂³	1	48	yes	complemented
260	C₂×#117	C₂³	1	48	yes	complemented
261	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
263	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
265	C₂²×C₄⋊C₄	C₂³	1	24	yes	—
266	C₂²×C₄⋊C₄	C₂³	1	24	yes	—
267	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
268	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
269	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
270	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
271	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
272	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
274	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
275	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
276	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
277	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
278	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	C₂³	1	1	yes	characteristic
280	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
281	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
282	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
283	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
284	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
285	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
286	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
287	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
288	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
289	C₂²×C₄⋊C₄	C₂³	1	2	yes	—
290	C₂²×C₄⋊C₄	C₂³	1	24	yes	complemented
291	C₂²×C₄⋊C₄	C₂³	1	48	yes	complemented
292	C₂²×C₄⋊C₄	C₂³	1	48	yes	complemented
293	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
294	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
295	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
296	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
297	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
298	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
299	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
300	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
301	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
302	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
303	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
304	C₂²×C₂²⋊C₄	C₂³	1	48	yes	—
305	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
306	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
307	C₂²×C₂²⋊C₄	C₂³	1	24	yes	—
308	C₂²×C₂²⋊C₄	C₂³	1	24	yes	—
309	C₂²×C₂²⋊C₄	C₂³	1	24	yes	—
310	C₂²×C₂²⋊C₄	C₂³	1	48	yes	—
311	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
312	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
313	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
314	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
315	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
316	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
317	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
318	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
319	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
320	C₂²×C₂²⋊C₄	C₂³	1	2	yes	—
321	C₂²×C₄²	C₂³	1	2	yes	—
322	C₂²×C₄²	C₂³	1	2	yes	—
323	C₂²×C₄²	C₂³	1	2	yes	—
324	C₂²×C₄²	C₂³	1	2	yes	—
325	C₂²×C₄²	C₂³	1	2	yes	—
326	C₂⁵	—	2	8	no	—
327	C₂⁵	—	2	8	no	—
328	C₂⁵	—	2	8	no	—
329	C₂⁵	—	4	4	no	—
330	C₂⁵	—	4	4	no	—
331	C₂⁵	—	4	4	no	—
332	C₂⁵	C₂⁴	1	1	yes	characteristic
333	C₂⁵	C₂⁴	1	2	yes	—
334	C₂⁵	C₂⁴	1	2	yes	—
335	C₂⁵	C₂⁴	1	12	yes	—
336	C₂⁵	C₂⁴	1	1	yes	characteristic
337	C₂⁵	C₂⁴	1	1	yes	characteristic
338	C₂⁵	C₂⁴	1	12	yes	—
339	C₂×#41	—	4	192	no	—
340	C₂×#41	—	4	96	no	—
341	C₂×#41	C₂⁴	1	128	yes	—
342	C₂×#41	C₂⁴	1	64	yes	complemented
343	C₂²×Q₈	—	4	4	no	—
344	C₂²×Q₈	—	4	8	no	—
345	C₂²×Q₈	—	4	4	no	—
346	C₂²×Q₈	—	4	96	no	—
347	C₂²×Q₈	—	4	8	no	—
348	C₂²×Q₈	—	4	4	no	—
349	C₂²×Q₈	—	4	8	no	—
350	C₂²×Q₈	C₂⁴	1	24	yes	—
351	C₂²×Q₈	C₂⁴	1	12	yes	—
352	C₂²×Q₈	C₂⁴	1	24	yes	—
353	C₂²×Q₈	C₂⁴	1	12	yes	—
354	C₂²×Q₈	C₂⁴	1	24	yes	—
355	C₂²×Q₈	C₂⁴	1	12	yes	—
356	C₂²×Q₈	C₂⁴	1	64	yes	complemented
357	C₂²×D₄	—	2	16	no	—
358	C₂²×D₄	—	2	16	no	—
359	C₂²×D₄	—	2	16	no	—
360	C₂²×D₄	—	4	8	no	—
361	C₂²×D₄	—	4	8	no	—
362	C₂²×D₄	—	4	8	no	—
363	C₂²×D₄	—	4	4	no	—
364	C₂²×D₄	—	4	8	no	—
365	C₂²×D₄	—	4	96	no	—
366	C₂²×D₄	C₂⁴	1	24	yes	—
367	C₂²×D₄	C₂⁴	1	24	yes	—
368	C₂²×D₄	C₂⁴	1	24	yes	—
369	C₂²×D₄	C₂⁴	1	24	yes	—
370	C₂²×D₄	C₂⁴	1	24	yes	—
371	C₂²×D₄	C₂⁴	1	24	yes	—
372	C₂²×D₄	C₂⁴	1	24	yes	—
373	C₂²×D₄	C₂⁴	1	12	yes	—
374	C₂²×D₄	C₂⁴	1	64	yes	—
375	C₂³×C₄	—	2	8	no	—
376	C₂³×C₄	—	2	8	no	—
377	C₂³×C₄	—	2	16	no	—
378	C₂³×C₄	—	2	8	no	—
379	C₂³×C₄	—	4	4	no	—
380	C₂³×C₄	—	4	4	no	—
381	C₂³×C₄	—	4	4	no	—
382	C₂³×C₄	—	4	4	no	—
383	C₂³×C₄	—	4	96	no	—
384	C₂³×C₄	—	4	8	no	—
385	C₂³×C₄	—	4	8	no	—
386	C₂³×C₄	—	4	4	no	—
387	C₂³×C₄	—	4	8	no	—
388	C₂³×C₄	—	4	4	no	—
389	C₂³×C₄	—	4	8	no	—
390	C₂³×C₄	—	4	8	no	—
391	C₂³×C₄	—	4	8	no	—
392	C₂³×C₄	C₂⁴	1	12	yes	—
393	C₂³×C₄	C₂⁴	1	24	yes	—
394	C₂³×C₄	C₂⁴	1	12	yes	—
395	C₂³×C₄	C₂⁴	1	12	yes	—
396	C₂³×C₄	C₂⁴	1	2	yes	—
397	C₂³×C₄	C₂⁴	1	2	yes	—
398	C₂³×C₄	C₂⁴	1	2	yes	—
399	C₂³×C₄	C₂⁴	1	2	yes	—
400	C₂³×C₄	C₂⁴	1	2	yes	—
401	C₂³×C₄	C₂⁴	1	1	yes	characteristic
402	C₂³×C₄	C₂⁴	1	1	yes	characteristic
403	C₂³×C₄	C₂⁴	1	2	yes	—
404	C₂³×C₄	C₂⁴	1	2	yes	—
405	C₂³×C₄	C₂⁴	1	2	yes	—
406	C₂³×C₄	C₂⁴	1	2	yes	—
407	C₂³×C₄	C₂⁴	1	1	yes	characteristic
408	C₂³×C₄	C₂⁴	1	1	yes	characteristic
409	C₂³×C₄	C₂⁴	1	2	yes	—
410	C₂³×C₄	C₂⁴	1	12	yes	—
411	C₂³×C₄	C₂⁴	1	12	yes	—
412	C₂³×C₄	C₂⁴	1	12	yes	—
413	C₂³×C₄	C₂⁴	1	24	yes	—
414	C₂³×C₄	C₂⁴	1	24	yes	—
415	C₂³×C₄	C₂⁴	1	24	yes	—
416	C₂³×C₄	C₂⁴	1	12	yes	—
417	C₂³×C₄	C₂⁴	1	24	yes	—
418	C₂³×C₄	C₂⁴	1	24	yes	—
419	C₂³×C₄	C₂⁴	1	24	yes	—
420	C₂³×C₄	C₂⁴	1	12	yes	—
421	C₂³×C₄	C₂⁴	1	12	yes	—
422	C₂³×C₄	C₂⁴	1	64	yes	—
423	C₄⋊Q₈	C₂⁴	1	128	yes	complemented
424	C₄⋊Q₈	C₂⁴	1	128	yes	complemented
425	C₄⋊Q₈	C₂⁴	1	128	yes	complemented
426	#126	C₂⁴	1	128	yes	complemented
427	#126	C₂⁴	1	128	yes	complemented
428	#126	C₂⁴	1	128	yes	complemented
429	#126	C₂⁴	1	128	yes	complemented
430	#126	C₂⁴	1	128	yes	complemented
431	#126	C₂⁴	1	128	yes	complemented
432	#125	C₂⁴	1	128	yes	complemented
433	#125	C₂⁴	1	128	yes	complemented
434	#125	C₂⁴	1	128	yes	complemented
435	#125	C₂⁴	1	128	yes	complemented
436	#125	C₂⁴	1	128	yes	complemented
437	#124	C₂⁴	1	128	yes	—
438	#124	C₂⁴	1	128	yes	complemented
439	#124	C₂⁴	1	128	yes	complemented
440	#124	C₂⁴	1	128	yes	complemented
441	#123	C₂⁴	1	128	yes	—
442	#123	C₂⁴	1	128	yes	—
443	#123	C₂⁴	1	128	yes	—
444	#123	C₂⁴	1	128	yes	—
445	#123	C₂⁴	1	128	yes	—
446	#123	C₂⁴	1	128	yes	—
447	#123	C₂⁴	1	128	yes	—
448	#123	C₂⁴	1	128	yes	complemented
449	#123	C₂⁴	1	128	yes	complemented
450	#123	C₂⁴	1	128	yes	complemented
451	#123	C₂⁴	1	128	yes	complemented
452	#123	C₂⁴	1	128	yes	complemented
453	#123	C₂⁴	1	128	yes	complemented
454	#123	C₂⁴	1	128	yes	complemented
455	C₂²⋊Q₈	C₂⁴	1	64	yes	—
456	C₂²⋊Q₈	C₂⁴	1	64	yes	—
457	C₂²⋊Q₈	C₂⁴	1	128	yes	—
458	C₂²⋊Q₈	C₂⁴	1	64	yes	—
459	C₂²⋊Q₈	C₂⁴	1	128	yes	—
460	C₂²⋊Q₈	C₂⁴	1	128	yes	—
461	C₂²⋊Q₈	C₂⁴	1	64	yes	complemented
462	C₂²⋊Q₈	C₂⁴	1	64	yes	complemented
463	C₂²⋊Q₈	C₂⁴	1	128	yes	complemented
464	C₂²⋊Q₈	C₂⁴	1	64	yes	complemented
465	C₂²⋊Q₈	C₂⁴	1	128	yes	complemented
466	C₂²⋊Q₈	C₂⁴	1	128	yes	complemented
467	C₂²⋊Q₈	C₂⁴	1	128	yes	complemented
468	C₂²⋊Q₈	C₂⁴	1	128	yes	complemented
469	C₂²⋊Q₈	C₂⁴	1	128	yes	complemented
470	C₂²⋊Q₈	C₂⁴	1	128	yes	complemented
471	C₂²⋊Q₈	C₂⁴	1	128	yes	complemented
472	C₂²⋊Q₈	C₂⁴	1	128	yes	complemented
473	C₂²⋊Q₈	C₂⁴	1	128	yes	complemented
474	C₂²⋊Q₈	C₂⁴	1	128	yes	complemented
475	#121	C₂⁴	1	64	yes	—
476	#121	C₂⁴	1	128	yes	—
477	#121	C₂⁴	1	128	yes	—
478	#121	C₂⁴	1	128	yes	—
479	#121	C₂⁴	1	64	yes	complemented
480	#121	C₂⁴	1	128	yes	complemented
481	#120	C₂⁴	1	128	yes	—
482	#120	C₂⁴	1	128	yes	—
483	C₄×Q₈	C₂⁴	1	128	yes	complemented
484	C₄×D₄	C₂⁴	1	128	yes	—
485	C₄×D₄	C₂⁴	1	128	yes	—
486	C₄×D₄	C₂⁴	1	128	yes	—
487	C₄×D₄	C₂⁴	1	128	yes	—
488	C₄×D₄	C₂⁴	1	128	yes	complemented
489	C₄×D₄	C₂⁴	1	128	yes	complemented
490	C₄×D₄	C₂⁴	1	128	yes	complemented
491	#117	C₂⁴	1	128	yes	—
492	#117	C₂⁴	1	64	yes	complemented
493	#117	C₂⁴	1	128	yes	complemented
494	#117	C₂⁴	1	128	yes	complemented
495	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
496	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
497	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
498	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
499	C₂×C₄⋊C₄	C₂⁴	1	64	yes	—
500	C₂×C₄⋊C₄	C₂⁴	1	64	yes	—
501	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
502	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
503	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
504	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
505	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
506	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
507	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
508	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
509	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
510	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
511	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
512	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
513	C₂×C₄⋊C₄	C₂⁴	1	12	yes	—
514	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
515	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
516	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
517	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
518	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
519	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
520	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
521	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
522	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
523	C₂×C₄⋊C₄	C₂⁴	1	24	yes	—
524	C₂×C₄⋊C₄	C₂⁴	1	64	yes	complemented
525	C₂×C₄⋊C₄	C₂⁴	1	128	yes	complemented
526	C₂×C₄⋊C₄	C₂⁴	1	128	yes	complemented
527	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
528	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
529	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
530	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
531	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
532	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
533	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
534	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
535	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
536	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
537	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
538	C₂×C₂²⋊C₄	C₂⁴	1	128	yes	—
539	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
540	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
541	C₂×C₂²⋊C₄	C₂⁴	1	64	yes	—
542	C₂×C₂²⋊C₄	C₂⁴	1	64	yes	—
543	C₂×C₂²⋊C₄	C₂⁴	1	64	yes	—
544	C₂×C₂²⋊C₄	C₂⁴	1	128	yes	—
545	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
546	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
547	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
548	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
549	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
550	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
551	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
552	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
553	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
554	C₂×C₂²⋊C₄	C₂⁴	1	24	yes	—
555	C₂×C₄²	C₂⁴	1	24	yes	—
556	C₂×C₄²	C₂⁴	1	24	yes	—
557	C₂×C₄²	C₂⁴	1	24	yes	—
558	C₂×C₄²	C₂⁴	1	24	yes	—
559	C₂×C₄²	C₂⁴	1	24	yes	—
560	C₂⁴	—	2	4	no	—
561	C₂⁴	—	2	4	no	—
562	C₂⁴	—	2	4	no	—
563	C₂⁴	—	2	4	no	—
564	C₂⁴	—	2	8	no	—
565	C₂⁴	—	2	48	no	—
566	C₂⁴	—	2	4	no	—
567	C₂⁴	—	2	8	no	—
568	C₂⁴	—	2	8	no	—
569	C₂⁴	—	2	48	no	—
570	C₂⁴	—	2	4	no	—
571	C₂⁴	—	2	8	no	—
572	C₂⁴	—	2	8	no	—
573	C₂⁴	—	2	8	no	—
574	C₂⁴	—	2	4	no	—
575	C₂⁴	—	2	48	no	—
576	C₂⁴	—	4	24	no	—
577	C₂⁴	—	4	24	no	—
578	C₂⁴	—	4	24	no	—
579	C₂⁴	—	4	64	no	—
580	C₂⁴	—	8	32	no	—
581	C₂⁴	H(5,𝔽₂)	1	8	yes	—
582	C₂⁴	2₋¹⁺⁴	1	8	yes	—
583	C₂⁴	C₂⁵	1	6	yes	—
584	C₂⁴	C₂⁵	1	12	yes	—
585	C₂⁴	C₂⁵	1	12	yes	—
586	C₂⁴	C₂⁵	1	16	yes	—
587	C₂⁴	C₂⁵	1	6	yes	—
588	C₂⁴	C₂⁵	1	6	yes	—
589	C₂⁴	C₂⁵	1	16	yes	—
590	C₂⁴	C₂⁵	1	1	yes	characteristic
591	#41	—	4	256	no	—
592	#41	—	4	128	no	—
593	C₂×Q₈	—	4	24	no	—
594	C₂×Q₈	—	4	48	no	—
595	C₂×Q₈	—	4	24	no	—
596	C₂×Q₈	—	4	128	no	—
597	C₂×Q₈	—	4	48	no	—
598	C₂×Q₈	—	4	24	no	—
599	C₂×Q₈	—	4	48	no	—
600	C₂×Q₈	C₂⁵	1	32	yes	—
601	C₂×Q₈	C₂⁵	1	16	yes	—
602	C₂×Q₈	C₂⁵	1	32	yes	—
603	C₂×Q₈	C₂⁵	1	16	yes	—
604	C₂×Q₈	C₂⁵	1	32	yes	—
605	C₂×Q₈	C₂⁵	1	16	yes	—
606	C₂×D₄	—	2	96	no	—
607	C₂×D₄	—	2	96	no	—
608	C₂×D₄	—	2	96	no	—
609	C₂×D₄	—	4	48	no	—
610	C₂×D₄	—	4	48	no	—
611	C₂×D₄	—	4	48	no	—
612	C₂×D₄	—	4	24	no	—
613	C₂×D₄	—	4	48	no	—
614	C₂×D₄	—	4	128	no	—
615	C₂×D₄	C₂⁵	1	32	yes	—
616	C₂×D₄	C₂⁵	1	32	yes	—
617	C₂×D₄	C₂⁵	1	32	yes	—
618	C₂×D₄	C₂⁵	1	32	yes	—
619	C₂×D₄	C₂⁵	1	32	yes	—
620	C₂×D₄	C₂⁵	1	32	yes	—
621	C₂×D₄	C₂⁵	1	32	yes	—
622	C₂×D₄	C₂⁵	1	16	yes	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	48	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	8	no	—
629	C₂²×C₄	—	2	48	no	—
630	C₂²×C₄	—	2	8	no	—
631	C₂²×C₄	—	2	96	no	—
632	C₂²×C₄	—	2	8	no	—
633	C₂²×C₄	—	2	8	no	—
634	C₂²×C₄	—	2	48	no	—
635	C₂²×C₄	—	2	8	no	—
636	C₂²×C₄	—	2	8	no	—
637	C₂²×C₄	—	2	8	no	—
638	C₂²×C₄	—	2	8	no	—
639	C₂²×C₄	—	2	8	no	—
640	C₂²×C₄	—	2	8	no	—
641	C₂²×C₄	—	4	24	no	—
642	C₂²×C₄	—	4	24	no	—
643	C₂²×C₄	—	4	24	no	—
644	C₂²×C₄	—	4	24	no	—
645	C₂²×C₄	—	4	128	no	—
646	C₂²×C₄	—	4	48	no	—
647	C₂²×C₄	—	4	48	no	—
648	C₂²×C₄	—	4	24	no	—
649	C₂²×C₄	—	4	48	no	—
650	C₂²×C₄	—	4	24	no	—
651	C₂²×C₄	—	4	48	no	—
652	C₂²×C₄	—	4	48	no	—
653	C₂²×C₄	—	4	48	no	—
654	C₂²×C₄	C₂⁵	1	12	yes	—
655	C₂²×C₄	C₂⁵	1	12	yes	—
656	C₂²×C₄	C₂⁵	1	12	yes	—
657	C₂²×C₄	C₂⁵	1	12	yes	—
658	C₂²×C₄	C₂⁵	1	6	yes	—
659	C₂²×C₄	C₂⁵	1	12	yes	—
660	C₂²×C₄	C₂⁵	1	12	yes	—
661	C₂²×C₄	C₂⁵	1	12	yes	—
662	C₂²×C₄	C₂⁵	1	12	yes	—
663	C₂²×C₄	C₂⁵	1	12	yes	—
664	C₂²×C₄	C₂⁵	1	12	yes	—
665	C₂²×C₄	C₂⁵	1	6	yes	—
666	C₂²×C₄	C₂⁵	1	6	yes	—
667	C₂²×C₄	C₂⁵	1	16	yes	—
668	C₂²×C₄	C₂⁵	1	6	yes	—
669	C₂²×C₄	C₂⁵	1	32	yes	—
670	C₂²×C₄	C₂⁵	1	16	yes	—
671	C₂²×C₄	C₂⁵	1	16	yes	—
672	C₂²×C₄	C₂⁵	1	16	yes	—
673	C₂²×C₄	C₂⁵	1	16	yes	—
674	C₂²×C₄	C₂⁵	1	16	yes	—
675	C₂²×C₄	C₂⁵	1	32	yes	—
676	C₂²×C₄	C₂⁵	1	32	yes	—
677	C₂²×C₄	C₂⁵	1	32	yes	—
678	C₂²×C₄	C₂⁵	1	16	yes	—
679	C₂²×C₄	C₂⁵	1	32	yes	—
680	C₂²×C₄	C₂⁵	1	32	yes	—
681	C₂²×C₄	C₂⁵	1	32	yes	—
682	C₂²×C₄	C₂⁵	1	16	yes	—
683	C₂²×C₄	C₂⁵	1	16	yes	—
684	C₄⋊C₄	C₂⁵	1	32	yes	—
685	C₄⋊C₄	C₂⁵	1	32	yes	—
686	C₄⋊C₄	C₂⁵	1	32	yes	—
687	C₄⋊C₄	C₂⁵	1	32	yes	—
688	C₄⋊C₄	C₂⁵	1	32	yes	—
689	C₄⋊C₄	C₂⁵	1	32	yes	—
690	C₄⋊C₄	C₂⁵	1	32	yes	—
691	C₄⋊C₄	C₂⁵	1	32	yes	—
692	C₄⋊C₄	C₂⁵	1	32	yes	—
693	C₄⋊C₄	C₂⁵	1	16	yes	—
694	C₄⋊C₄	C₂⁵	1	32	yes	—
695	C₄⋊C₄	C₂⁵	1	32	yes	—
696	C₄⋊C₄	C₂⁵	1	16	yes	—
697	C₄⋊C₄	C₂⁵	1	32	yes	—
698	C₄⋊C₄	C₂⁵	1	32	yes	—
699	C₄⋊C₄	C₂⁵	1	16	yes	—
700	C₄⋊C₄	C₂⁵	1	16	yes	—
701	C₄⋊C₄	C₂⁵	1	32	yes	—
702	C₄⋊C₄	C₂⁵	1	32	yes	—
703	C₄⋊C₄	C₂⁵	1	32	yes	—
704	C₄⋊C₄	C₂⁵	1	32	yes	—
705	C₄⋊C₄	C₂⁵	1	32	yes	—
706	C₄⋊C₄	C₂⁵	1	32	yes	—
707	C₄⋊C₄	C₂⁵	1	32	yes	—
708	C₄⋊C₄	C₂⁵	1	32	yes	—
709	C₄⋊C₄	C₂⁵	1	32	yes	—
710	C₄⋊C₄	C₂⁵	1	32	yes	—
711	C₂²⋊C₄	C₂⁵	1	32	yes	—
712	C₂²⋊C₄	C₂⁵	1	32	yes	—
713	C₂²⋊C₄	C₂⁵	1	32	yes	—
714	C₂²⋊C₄	C₂⁵	1	32	yes	—
715	C₂²⋊C₄	C₂⁵	1	32	yes	—
716	C₂²⋊C₄	C₂⁵	1	32	yes	—
717	C₂²⋊C₄	C₂⁵	1	32	yes	—
718	C₂²⋊C₄	C₂⁵	1	32	yes	—
719	C₂²⋊C₄	C₂⁵	1	32	yes	—
720	C₂²⋊C₄	C₂⁵	1	32	yes	—
721	C₂²⋊C₄	C₂⁵	1	32	yes	—
722	C₂²⋊C₄	C₂⁵	1	32	yes	—
723	C₂²⋊C₄	C₂⁵	1	32	yes	—
724	C₂²⋊C₄	C₂⁵	1	32	yes	—
725	C₂²⋊C₄	C₂⁵	1	32	yes	—
726	C₂²⋊C₄	C₂⁵	1	32	yes	—
727	C₂²⋊C₄	C₂⁵	1	32	yes	—
728	C₂²⋊C₄	C₂⁵	1	32	yes	—
729	C₂²⋊C₄	C₂⁵	1	32	yes	—
730	C₂²⋊C₄	C₂⁵	1	32	yes	—
731	C₂²⋊C₄	C₂⁵	1	32	yes	—
732	C₂²⋊C₄	C₂⁵	1	32	yes	—
733	C₂²⋊C₄	C₂⁵	1	32	yes	—
734	C₄²	C₂⁵	1	32	yes	—
735	C₄²	C₂⁵	1	32	yes	—
736	C₄²	C₂⁵	1	32	yes	—
737	C₄²	C₂⁵	1	32	yes	—
738	C₄²	C₂⁵	1	32	yes	—
739	C₂³	—	2	12	no	—
740	C₂³	—	2	12	no	—
741	C₂³	—	2	12	no	—
742	C₂³	—	2	12	no	—
743	C₂³	—	2	32	no	—
744	C₂³	—	2	32	no	—
745	C₂³	—	2	24	no	—
746	C₂³	—	2	32	no	—
747	C₂³	—	2	12	no	—
748	C₂³	—	2	24	no	—
749	C₂³	—	2	24	no	—
750	C₂³	—	2	32	no	—
751	C₂³	—	2	12	no	—
752	C₂³	—	2	24	no	—
753	C₂³	—	2	24	no	—
754	C₂³	—	2	24	no	—
755	C₂³	—	2	12	no	—
756	C₂³	—	2	32	no	—
757	C₂³	—	4	16	no	—
758	C₂³	—	4	16	no	—
759	C₂³	—	4	16	no	—
760	C₂³	—	4	192	no	—
761	C₂³	—	4	32	no	—
762	C₂³	—	4	16	no	—
763	C₂³	—	4	32	no	—
764	C₂³	—	8	96	no	—
765	C₂³	C₂×H(5,𝔽₂)	1	24	yes	—
766	C₂³	C₂×H(5,𝔽₂)	1	4	yes	—
767	C₂³	C₂×2₋¹⁺⁴	1	24	yes	—
768	C₂³	C₂×2₋¹⁺⁴	1	4	yes	—
769	C₂³	#585	1	4	yes	—
770	C₂³	C₂⁶	1	4	yes	—
771	C₂³	C₂⁶	1	8	yes	—
772	C₂³	C₂⁶	1	8	yes	—
773	C₂³	C₂⁶	1	4	yes	—
774	C₂³	C₂⁶	1	4	yes	—
775	C₂³	C₂⁶	1	3	yes	—
776	Q₈	—	4	16	no	—
777	Q₈	—	4	32	no	—
778	Q₈	—	4	16	no	—
779	Q₈	—	4	32	no	—
780	Q₈	—	4	16	no	—
781	Q₈	—	4	32	no	—
782	D₄	—	2	64	no	—
783	D₄	—	2	64	no	—
784	D₄	—	2	64	no	—
785	D₄	—	4	32	no	—
786	D₄	—	4	32	no	—
787	D₄	—	4	32	no	—
788	D₄	—	4	16	no	—
789	D₄	—	4	32	no	—
790	C₂×C₄	—	2	12	no	—
791	C₂×C₄	—	2	12	no	—
792	C₂×C₄	—	2	32	no	—
793	C₂×C₄	—	2	12	no	—
794	C₂×C₄	—	2	12	no	—
795	C₂×C₄	—	2	24	no	—
796	C₂×C₄	—	2	32	no	—
797	C₂×C₄	—	2	24	no	—
798	C₂×C₄	—	2	64	no	—
799	C₂×C₄	—	2	24	no	—
800	C₂×C₄	—	2	24	no	—
801	C₂×C₄	—	2	32	no	—
802	C₂×C₄	—	2	24	no	—
803	C₂×C₄	—	2	24	no	—
804	C₂×C₄	—	2	24	no	—
805	C₂×C₄	—	2	24	no	—
806	C₂×C₄	—	2	24	no	—
807	C₂×C₄	—	2	24	no	—
808	C₂×C₄	—	4	16	no	—
809	C₂×C₄	—	4	16	no	—
810	C₂×C₄	—	4	16	no	—
811	C₂×C₄	—	4	16	no	—
812	C₂×C₄	—	4	32	no	—
813	C₂×C₄	—	4	32	no	—
814	C₂×C₄	—	4	16	no	—
815	C₂×C₄	—	4	32	no	—
816	C₂×C₄	—	4	16	no	—
817	C₂×C₄	—	4	32	no	—
818	C₂×C₄	—	4	32	no	—
819	C₂×C₄	—	4	32	no	—
820	C₂×C₄	C₂⁶	1	8	yes	—
821	C₂×C₄	C₂⁶	1	8	yes	—
822	C₂×C₄	C₂⁶	1	8	yes	—
823	C₂×C₄	C₂⁶	1	8	yes	—
824	C₂×C₄	C₂⁶	1	4	yes	—
825	C₂×C₄	C₂⁶	1	8	yes	—
826	C₂×C₄	C₂⁶	1	8	yes	—
827	C₂×C₄	C₂⁶	1	8	yes	—
828	C₂×C₄	C₂⁶	1	8	yes	—
829	C₂×C₄	C₂⁶	1	8	yes	—
830	C₂×C₄	C₂⁶	1	8	yes	—
831	C₂×C₄	C₂⁶	1	4	yes	—
832	C₂×C₄	C₂⁶	1	4	yes	—
833	C₂×C₄	C₂⁶	1	4	yes	—
834	C₂²	—	2	48	no	—
835	C₂²	—	2	48	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	4	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	2	8	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	8	no	—
843	C₂²	—	2	8	no	—
844	C₂²	—	2	4	no	—
845	C₂²	—	2	8	no	—
846	C₂²	—	2	8	no	—
847	C₂²	—	2	8	no	—
848	C₂²	—	2	4	no	—
849	C₂²	—	4	64	no	—
850	C₂²	—	4	48	no	—
851	C₂²	—	4	24	no	—
852	C₂²	—	4	48	no	—
853	C₂²	—	8	32	no	—
854	C₂²	#3535	1	16	yes	direct product factor
855	C₂²	C₂²×H(5,𝔽₂)	1	8	yes	—
856	C₂²	C₂²×H(5,𝔽₂)	1	6	yes	—
857	C₂²	C₂²×2₋¹⁺⁴	1	8	yes	—
858	C₂²	C₂²×2₋¹⁺⁴	1	6	yes	—
859	C₂²	C₂×#585	1	6	yes	—
860	C₂²	C₂⁷	1	1	yes	characteristic
861	C₄	—	2	4	no	—
862	C₄	—	2	4	no	—
863	C₄	—	2	4	no	—
864	C₄	—	2	4	no	—
865	C₄	—	2	8	no	—
866	C₄	—	2	8	no	—
867	C₄	—	2	8	no	—
868	C₄	—	2	8	no	—
869	C₄	—	2	8	no	—
870	C₄	—	2	8	no	—
871	C₄	—	2	8	no	—
872	C₄	—	2	8	no	—
873	C₄	—	2	8	no	—
874	C₄	—	2	8	no	—
875	C₂	—	2	8	no	—
876	C₂	—	2	8	no	—
877	C₂	—	4	8	no	—
878	C₂	—	4	4	no	—
879	C₂	—	4	8	no	—
880	C₂	C₂×#3535	1	12	yes	direct product factor
881	C₂	C₂³×H(5,𝔽₂)	1	1	yes	characteristic
882	C₂	C₂³×2₋¹⁺⁴	1	1	yes	characteristic
883	C₂	C₂²×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁷
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#3535	C₂	direct (N × H)
2. C₂²×#552	C₂	semidirect
3. C₂²×#551	C₂	semidirect
4. C₂²×#551	C₂	semidirect
5. C₂²×#554	C₂	semidirect
6. C₂²×#547	C₂	semidirect
7. C₂²×#546	C₂	semidirect
8. C₂²×#563	C₂	semidirect
9. C₂²×#562	C₂	semidirect
10. C₂²×#536	C₂	semidirect
11. C₂²×#542	C₂	semidirect
12. C₂²×#544	C₂	semidirect
13. C₂²×#539	C₂	semidirect
14. C₂²×#539	C₂	semidirect
15. C₂²×#539	C₂	semidirect
16. C₂²×#538	C₂	semidirect
17. C₂²×#543	C₂	semidirect
18. C₂²×#525	C₂	semidirect
19. C₂³×#123	C₂	semidirect
20. C₂³×C₂²⋊Q₈	C₂	semidirect
22. C₂³×#41	C₂²	semidirect
23. C₂⁴×Q₈	C₂²	semidirect
26. #3535	C₂²	direct (N × H)
27. C₂×#563	C₂²	semidirect
28. C₂×#562	C₂²	semidirect
29. C₂×#554	C₂²	semidirect
30. C₂×#552	C₂²	semidirect
31. C₂×#551	C₂²	semidirect
32. C₂×#551	C₂²	semidirect
33. C₂×#547	C₂²	semidirect
34. C₂×#546	C₂²	semidirect
35. C₂×#544	C₂²	semidirect
36. C₂×#543	C₂²	semidirect
37. C₂×#542	C₂²	semidirect
38. C₂×#539	C₂²	semidirect
39. C₂×#539	C₂²	semidirect
40. C₂×#539	C₂²	semidirect
41. C₂×#538	C₂²	semidirect
42. C₂×#536	C₂²	semidirect
43. C₂²×C₄⋊Q₈	C₂²	semidirect
44. C₂²×C₄⋊Q₈	C₂²	semidirect
45. C₂²×C₄⋊Q₈	C₂²	semidirect
46. C₂²×#126	C₂²	semidirect
47. C₂²×#126	C₂²	semidirect
48. C₂²×#126	C₂²	semidirect
49. C₂²×#126	C₂²	semidirect
50. C₂²×#126	C₂²	semidirect
51. C₂²×#126	C₂²	semidirect
52. C₂²×#125	C₂²	semidirect
53. C₂²×#125	C₂²	semidirect
54. C₂²×#125	C₂²	semidirect
55. C₂²×#125	C₂²	semidirect
56. C₂²×#125	C₂²	semidirect
58. C₂²×#124	C₂²	semidirect
59. C₂²×#124	C₂²	semidirect
60. C₂²×#124	C₂²	semidirect
61. C₂×#525	C₂²	semidirect
69. C₂²×#123	C₂²	semidirect
70. C₂²×#123	C₂²	semidirect
71. C₂²×#123	C₂²	semidirect
72. C₂²×#123	C₂²	semidirect
73. C₂²×#123	C₂²	semidirect
74. C₂²×#123	C₂²	semidirect
75. C₂²×#123	C₂²	semidirect
76. C₂²×#123	C₂²	semidirect
83. C₂²×C₂²⋊Q₈	C₂²	semidirect
84. C₂²×C₂²⋊Q₈	C₂²	semidirect
85. C₂²×C₂²⋊Q₈	C₂²	semidirect
86. C₂²×C₂²⋊Q₈	C₂²	semidirect
87. C₂²×C₂²⋊Q₈	C₂²	semidirect
88. C₂²×C₂²⋊Q₈	C₂²	semidirect
89. C₂²×C₂²⋊Q₈	C₂²	semidirect
90. C₂²×C₂²⋊Q₈	C₂²	semidirect
91. C₂²×C₂²⋊Q₈	C₂²	semidirect
92. C₂²×C₂²⋊Q₈	C₂²	semidirect
93. C₂²×C₂²⋊Q₈	C₂²	semidirect
94. C₂²×C₂²⋊Q₈	C₂²	semidirect
95. C₂²×C₂²⋊Q₈	C₂²	semidirect
96. C₂²×C₂²⋊Q₈	C₂²	semidirect
97. C₂²×C₂²⋊Q₈	C₂²	semidirect
102. C₂²×#121	C₂²	semidirect
103. C₂²×#121	C₂²	semidirect
106. C₂²×C₄×Q₈	C₂²	semidirect
111. C₂²×C₄×D₄	C₂²	semidirect
112. C₂²×C₄×D₄	C₂²	semidirect
113. C₂²×C₄×D₄	C₂²	semidirect
115. C₂²×#117	C₂²	semidirect
116. C₂²×#117	C₂²	semidirect
117. C₂²×#117	C₂²	semidirect
120. C₂³×C₄⋊C₄	C₂²	semidirect
121. C₂³×C₄⋊C₄	C₂²	semidirect
122. C₂³×C₄⋊C₄	C₂²	semidirect
133. C₂²×#41	C₂³	semidirect
141. C₂³×Q₈	C₂³	semidirect
170. #563	C₂³	semidirect
171. #562	C₂³	semidirect
172. #554	C₂³	semidirect
173. #552	C₂³	semidirect
174. #551	C₂³	semidirect
175. #551	C₂³	semidirect
176. #547	C₂³	semidirect
177. #546	C₂³	semidirect
178. #544	C₂³	semidirect
179. #543	C₂³	semidirect
180. #542	C₂³	semidirect
181. #539	C₂³	semidirect
182. #539	C₂³	semidirect
183. #539	C₂³	semidirect
184. #538	C₂³	semidirect
185. #536	C₂³	semidirect
186. C₂×C₄⋊Q₈	C₂³	semidirect
187. C₂×C₄⋊Q₈	C₂³	semidirect
188. C₂×C₄⋊Q₈	C₂³	semidirect
189. C₂×#126	C₂³	semidirect
190. C₂×#126	C₂³	semidirect
191. C₂×#126	C₂³	semidirect
192. C₂×#126	C₂³	semidirect
193. C₂×#126	C₂³	semidirect
194. C₂×#126	C₂³	semidirect
195. C₂×#125	C₂³	semidirect
196. C₂×#125	C₂³	semidirect
197. C₂×#125	C₂³	semidirect
198. C₂×#125	C₂³	semidirect
199. C₂×#125	C₂³	semidirect
201. C₂×#124	C₂³	semidirect
202. C₂×#124	C₂³	semidirect
203. C₂×#124	C₂³	semidirect
204. #525	C₂³	semidirect
212. C₂×#123	C₂³	semidirect
213. C₂×#123	C₂³	semidirect
214. C₂×#123	C₂³	semidirect
215. C₂×#123	C₂³	semidirect
216. C₂×#123	C₂³	semidirect
217. C₂×#123	C₂³	semidirect
218. C₂×#123	C₂³	semidirect
219. C₂×#123	C₂³	semidirect
226. C₂×C₂²⋊Q₈	C₂³	semidirect
227. C₂×C₂²⋊Q₈	C₂³	semidirect
228. C₂×C₂²⋊Q₈	C₂³	semidirect
229. C₂×C₂²⋊Q₈	C₂³	semidirect
230. C₂×C₂²⋊Q₈	C₂³	semidirect
231. C₂×C₂²⋊Q₈	C₂³	semidirect
232. C₂×C₂²⋊Q₈	C₂³	semidirect
233. C₂×C₂²⋊Q₈	C₂³	semidirect
234. C₂×C₂²⋊Q₈	C₂³	semidirect
235. C₂×C₂²⋊Q₈	C₂³	semidirect
236. C₂×C₂²⋊Q₈	C₂³	semidirect
237. C₂×C₂²⋊Q₈	C₂³	semidirect
238. C₂×C₂²⋊Q₈	C₂³	semidirect
239. C₂×C₂²⋊Q₈	C₂³	semidirect
240. C₂×C₂²⋊Q₈	C₂³	semidirect
245. C₂×#121	C₂³	semidirect
246. C₂×#121	C₂³	semidirect
249. C₂×C₄×Q₈	C₂³	semidirect
254. C₂×C₄×D₄	C₂³	semidirect
255. C₂×C₄×D₄	C₂³	semidirect
256. C₂×C₄×D₄	C₂³	semidirect
258. C₂×#117	C₂³	semidirect
259. C₂×#117	C₂³	semidirect
260. C₂×#117	C₂³	semidirect
290. C₂²×C₄⋊C₄	C₂³	semidirect
291. C₂²×C₄⋊C₄	C₂³	semidirect
292. C₂²×C₄⋊C₄	C₂³	semidirect
342. C₂×#41	C₂⁴	semidirect
356. C₂²×Q₈	C₂⁴	semidirect
423. C₄⋊Q₈	C₂⁴	semidirect
424. C₄⋊Q₈	C₂⁴	semidirect
425. C₄⋊Q₈	C₂⁴	semidirect
426. #126	C₂⁴	semidirect
427. #126	C₂⁴	semidirect
428. #126	C₂⁴	semidirect
429. #126	C₂⁴	semidirect
430. #126	C₂⁴	semidirect
431. #126	C₂⁴	semidirect
432. #125	C₂⁴	semidirect
433. #125	C₂⁴	semidirect
434. #125	C₂⁴	semidirect
435. #125	C₂⁴	semidirect
436. #125	C₂⁴	semidirect
438. #124	C₂⁴	semidirect
439. #124	C₂⁴	semidirect
440. #124	C₂⁴	semidirect
448. #123	C₂⁴	semidirect
449. #123	C₂⁴	semidirect
450. #123	C₂⁴	semidirect
451. #123	C₂⁴	semidirect
452. #123	C₂⁴	semidirect
453. #123	C₂⁴	semidirect
454. #123	C₂⁴	semidirect
461. C₂²⋊Q₈	C₂⁴	semidirect
462. C₂²⋊Q₈	C₂⁴	semidirect
463. C₂²⋊Q₈	C₂⁴	semidirect
464. C₂²⋊Q₈	C₂⁴	semidirect
465. C₂²⋊Q₈	C₂⁴	semidirect
466. C₂²⋊Q₈	C₂⁴	semidirect
467. C₂²⋊Q₈	C₂⁴	semidirect
468. C₂²⋊Q₈	C₂⁴	semidirect
469. C₂²⋊Q₈	C₂⁴	semidirect
470. C₂²⋊Q₈	C₂⁴	semidirect
471. C₂²⋊Q₈	C₂⁴	semidirect
472. C₂²⋊Q₈	C₂⁴	semidirect
473. C₂²⋊Q₈	C₂⁴	semidirect
474. C₂²⋊Q₈	C₂⁴	semidirect
479. #121	C₂⁴	semidirect
480. #121	C₂⁴	semidirect
483. C₄×Q₈	C₂⁴	semidirect
488. C₄×D₄	C₂⁴	semidirect
489. C₄×D₄	C₂⁴	semidirect
490. C₄×D₄	C₂⁴	semidirect
492. #117	C₂⁴	semidirect
493. #117	C₂⁴	semidirect
494. #117	C₂⁴	semidirect
524. C₂×C₄⋊C₄	C₂⁴	semidirect
525. C₂×C₄⋊C₄	C₂⁴	semidirect
526. C₂×C₄⋊C₄	C₂⁴	semidirect
854. C₂²	#3535	direct (N × H)
880. C₂	C₂×#3535	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#3535	2
C₂²×#552	2
C₂²×#551	2
C₂²×#554	2
C₂²×#547	2
C₂²×#546	2
C₂²×#563	2
C₂²×#562	2
C₂²×#536	2
C₂²×#542	2
C₂²×#544	2
C₂²×#539	2
C₂²×#538	2
C₂²×#543	2
C₂²×#525	2
C₂³×#123	2
C₂³×C₂²⋊Q₈	2

Subgroups — C22×#3535 #10586122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#3535 #10586122