Subgroups — C₂³×#3536 #72301666

Order 1024.

514605 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	C₂²×#3536	C₂	1	224	yes	maximal, direct product factor
2	C₂³×#562	C₂	1	4	yes	maximal, complemented
3	C₂³×#554	C₂	1	2	yes	maximal, complemented
4	C₂³×#547	C₂	1	2	yes	maximal, complemented
5	C₂³×#548	C₂	1	2	yes	maximal, complemented
6	C₂³×#546	C₂	1	2	yes	maximal, complemented
7	C₂³×#546	C₂	1	4	yes	maximal, complemented
8	C₂³×#542	C₂	1	2	yes	maximal, complemented
9	C₂³×#537	C₂	1	2	yes	maximal, complemented
10	C₂³×#537	C₂	1	2	yes	maximal, complemented
11	C₂³×#539	C₂	1	2	yes	maximal, complemented
12	C₂³×#538	C₂	1	2	yes	maximal, complemented
13	C₂³×#543	C₂	1	2	yes	maximal, complemented
14	C₂³×#525	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁴×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×#121	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁴×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂⁴×#41	C₂²	1	2	yes	complemented
19	C₂⁴×#41	C₂²	1	4	yes	complemented
20	C₂⁵×Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂⁵×D₄	C₂²	1	1	yes	characteristic
22	C₂⁵×D₄	C₂²	1	2	yes	—
23	C₂⁶×C₄	C₂²	1	1	yes	characteristic
24	C₂×#3536	C₂²	1	7168	yes	direct product factor
25	C₂²×#554	C₂²	1	224	yes	complemented
26	C₂²×#547	C₂²	1	224	yes	complemented
27	C₂²×#548	C₂²	1	224	yes	complemented
28	C₂²×#546	C₂²	1	224	yes	complemented
29	C₂²×#546	C₂²	1	448	yes	complemented
30	C₂²×#562	C₂²	1	448	yes	complemented
31	C₂²×#542	C₂²	1	224	yes	complemented
32	C₂²×#537	C₂²	1	224	yes	complemented
33	C₂²×#537	C₂²	1	224	yes	complemented
34	C₂²×#539	C₂²	1	224	yes	complemented
35	C₂²×#538	C₂²	1	224	yes	complemented
36	C₂²×#543	C₂²	1	224	yes	complemented
37	C₂³×C₄⋊Q₈	C₂²	1	2	yes	complemented
38	C₂³×#126	C₂²	1	4	yes	complemented
39	C₂³×#125	C₂²	1	4	yes	complemented
40	C₂³×#124	C₂²	1	4	yes	complemented
41	C₂³×#124	C₂²	1	4	yes	complemented
42	C₂³×#124	C₂²	1	2	yes	complemented
43	C₂²×#525	C₂²	1	112	yes	complemented
44	C₂³×#123	C₂²	1	2	yes	complemented
45	C₂³×#123	C₂²	1	4	yes	complemented
46	C₂³×#123	C₂²	1	4	yes	complemented
47	C₂³×#123	C₂²	1	4	yes	complemented
48	C₂³×#123	C₂²	1	4	yes	complemented
49	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	—
50	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₂³×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
52	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	—
53	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	complemented
54	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	complemented
55	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	complemented
56	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	complemented
57	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	complemented
58	C₂³×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
59	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	complemented
61	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₂³×C₂²⋊Q₈	C₂²	1	112	yes	complemented
63	C₂³×#121	C₂²	1	2	yes	—
64	C₂³×#121	C₂²	1	2	yes	—
65	C₂³×#121	C₂²	1	2	yes	—
66	C₂³×#121	C₂²	1	2	yes	—
67	C₂³×#121	C₂²	1	1	yes	characteristic
68	C₂³×#121	C₂²	1	112	yes	complemented
69	C₂³×#121	C₂²	1	4	yes	complemented
70	C₂³×#121	C₂²	1	4	yes	complemented
71	C₂³×#121	C₂²	1	4	yes	complemented
72	C₂³×#121	C₂²	1	1	yes	characteristic, complemented
73	C₂³×#121	C₂²	1	4	yes	complemented
74	C₂³×#121	C₂²	1	4	yes	complemented
75	C₂³×#121	C₂²	1	2	yes	complemented
76	C₂³×#120	C₂²	1	2	yes	—
77	C₂³×#120	C₂²	1	4	yes	—
78	C₂³×C₄×Q₈	C₂²	1	2	yes	complemented
79	C₂³×C₄×D₄	C₂²	1	2	yes	—
80	C₂³×C₄×D₄	C₂²	1	4	yes	—
81	C₂³×C₄×D₄	C₂²	1	2	yes	complemented
82	C₂³×C₄×D₄	C₂²	1	4	yes	complemented
83	C₂³×C₄×D₄	C₂²	1	2	yes	complemented
84	C₂³×#117	C₂²	1	1	yes	characteristic, complemented
85	C₂⁴×C₄⋊C₄	C₂²	1	1	yes	characteristic
86	C₂⁴×C₄⋊C₄	C₂²	1	2	yes	complemented
87	C₂⁴×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
88	C₂⁴×C₄⋊C₄	C₂²	1	2	yes	complemented
89	C₂⁴×C₂²⋊C₄	C₂²	1	2	yes	—
90	C₂⁴×C₂²⋊C₄	C₂²	1	2	yes	—
91	C₂⁴×C₂²⋊C₄	C₂²	1	4	yes	—
92	C₂⁷	C₂³	1	1	yes	characteristic
93	C₂⁷	C₂³	1	2	yes	—
94	C₂³×#41	—	4	16	no	—
95	C₂³×#41	—	4	64	no	—
96	C₂³×#41	—	4	32	no	—
97	C₂³×#41	C₂³	1	56	yes	complemented
98	C₂³×#41	C₂³	1	112	yes	complemented
99	C₂³×#41	C₂³	1	224	yes	complemented
100	C₂⁴×Q₈	—	4	16	no	—
101	C₂⁴×Q₈	C₂³	1	2	yes	—
102	C₂⁴×Q₈	C₂³	1	2	yes	—
103	C₂⁴×Q₈	C₂³	1	1	yes	characteristic
104	C₂⁴×Q₈	C₂³	1	4	yes	—
105	C₂⁴×Q₈	C₂³	1	56	yes	complemented
106	C₂⁴×D₄	—	4	16	no	—
107	C₂⁴×D₄	—	4	32	no	—
108	C₂⁴×D₄	C₂³	1	4	yes	—
109	C₂⁴×D₄	C₂³	1	2	yes	—
110	C₂⁴×D₄	C₂³	1	2	yes	—
111	C₂⁴×D₄	C₂³	1	2	yes	—
112	C₂⁴×D₄	C₂³	1	2	yes	—
113	C₂⁴×D₄	C₂³	1	4	yes	—
114	C₂⁴×D₄	C₂³	1	56	yes	—
115	C₂⁴×D₄	C₂³	1	112	yes	—
116	C₂⁴×D₄	C₂³	1	2	yes	—
117	C₂⁴×D₄	C₂³	1	4	yes	—
118	C₂⁴×D₄	C₂³	1	4	yes	—
119	C₂⁴×D₄	C₂³	1	1	yes	characteristic
120	C₂⁵×C₄	—	4	16	no	—
121	C₂⁵×C₄	C₂³	1	1	yes	characteristic
122	C₂⁵×C₄	C₂³	1	1	yes	characteristic
123	C₂⁵×C₄	C₂³	1	1	yes	characteristic
124	C₂⁵×C₄	C₂³	1	2	yes	—
125	C₂⁵×C₄	C₂³	1	2	yes	—
126	C₂⁵×C₄	C₂³	1	1	yes	characteristic
127	C₂⁵×C₄	C₂³	1	1	yes	characteristic
128	C₂⁵×C₄	C₂³	1	1	yes	characteristic
129	C₂⁵×C₄	C₂³	1	56	yes	—
130	C₂⁵×C₄	C₂³	1	2	yes	—
131	C₂⁵×C₄	C₂³	1	2	yes	—
132	C₂⁵×C₄	C₂³	1	4	yes	—
133	C₂⁵×C₄	C₂³	1	4	yes	—
134	C₂⁵×C₄	C₂³	1	4	yes	—
135	#3536	C₂³	1	32768	yes	direct product factor
136	C₂×#562	C₂³	1	7168	yes	complemented
137	C₂×#554	C₂³	1	3584	yes	complemented
138	C₂×#548	C₂³	1	3584	yes	complemented
139	C₂×#547	C₂³	1	3584	yes	complemented
140	C₂×#546	C₂³	1	7168	yes	complemented
141	C₂×#546	C₂³	1	3584	yes	complemented
142	C₂×#543	C₂³	1	3584	yes	complemented
143	C₂×#542	C₂³	1	3584	yes	complemented
144	C₂×#539	C₂³	1	3584	yes	complemented
145	C₂×#538	C₂³	1	3584	yes	complemented
146	C₂×#537	C₂³	1	3584	yes	complemented
147	C₂×#537	C₂³	1	3584	yes	complemented
148	C₂²×C₄⋊Q₈	C₂³	1	112	yes	complemented
149	C₂²×#126	C₂³	1	224	yes	complemented
150	C₂²×#125	C₂³	1	224	yes	complemented
151	C₂²×#124	C₂³	1	224	yes	complemented
152	C₂²×#124	C₂³	1	224	yes	complemented
153	C₂²×#124	C₂³	1	112	yes	complemented
154	C₂×#525	C₂³	1	1792	yes	complemented
155	C₂²×#123	C₂³	1	112	yes	complemented
156	C₂²×#123	C₂³	1	224	yes	complemented
157	C₂²×#123	C₂³	1	224	yes	complemented
158	C₂²×#123	C₂³	1	224	yes	complemented
159	C₂²×#123	C₂³	1	224	yes	complemented
160	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	—
161	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	—
162	C₂²×C₂²⋊Q₈	C₂³	1	56	yes	—
163	C₂²×C₂²⋊Q₈	C₂³	1	224	yes	—
164	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	complemented
165	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	complemented
166	C₂²×C₂²⋊Q₈	C₂³	1	56	yes	complemented
167	C₂²×C₂²⋊Q₈	C₂³	1	224	yes	complemented
168	C₂²×C₂²⋊Q₈	C₂³	1	224	yes	complemented
169	C₂²×C₂²⋊Q₈	C₂³	1	224	yes	complemented
170	C₂²×C₂²⋊Q₈	C₂³	1	224	yes	complemented
171	C₂²×C₂²⋊Q₈	C₂³	1	224	yes	complemented
172	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	complemented
173	C₂²×C₂²⋊Q₈	C₂³	1	1792	yes	complemented
174	C₂²×#121	C₂³	1	112	yes	—
175	C₂²×#121	C₂³	1	112	yes	—
176	C₂²×#121	C₂³	1	112	yes	—
177	C₂²×#121	C₂³	1	112	yes	—
178	C₂²×#121	C₂³	1	56	yes	—
179	C₂²×#121	C₂³	1	1792	yes	complemented
180	C₂²×#121	C₂³	1	56	yes	complemented
181	C₂²×#121	C₂³	1	224	yes	complemented
182	C₂²×#121	C₂³	1	224	yes	complemented
183	C₂²×#121	C₂³	1	224	yes	complemented
184	C₂²×#121	C₂³	1	224	yes	complemented
185	C₂²×#121	C₂³	1	224	yes	complemented
186	C₂²×#121	C₂³	1	112	yes	complemented
187	C₂²×#120	C₂³	1	112	yes	—
188	C₂²×#120	C₂³	1	224	yes	—
189	C₂²×C₄×Q₈	C₂³	1	112	yes	complemented
190	C₂²×C₄×D₄	C₂³	1	112	yes	—
191	C₂²×C₄×D₄	C₂³	1	224	yes	—
192	C₂²×C₄×D₄	C₂³	1	112	yes	complemented
193	C₂²×C₄×D₄	C₂³	1	224	yes	complemented
194	C₂²×C₄×D₄	C₂³	1	112	yes	complemented
195	C₂²×#117	C₂³	1	56	yes	complemented
196	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂³×C₄⋊C₄	C₂³	1	56	yes	—
199	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
201	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
202	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
203	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
207	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
208	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
209	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
210	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
211	C₂³×C₄⋊C₄	C₂³	1	112	yes	complemented
212	C₂³×C₄⋊C₄	C₂³	1	56	yes	complemented
213	C₂³×C₄⋊C₄	C₂³	1	112	yes	complemented
214	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
215	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
217	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
218	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
219	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
220	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
221	C₂³×C₂²⋊C₄	C₂³	1	112	yes	—
222	C₂³×C₂²⋊C₄	C₂³	1	112	yes	—
223	C₂³×C₂²⋊C₄	C₂³	1	224	yes	—
224	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
227	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
229	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
230	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂³×C₄²	C₂³	1	2	yes	—
232	C₂³×C₄²	C₂³	1	4	yes	—
233	C₂⁶	—	2	16	no	—
234	C₂⁶	—	2	16	no	—
235	C₂⁶	—	2	32	no	—
236	C₂⁶	—	4	8	no	—
237	C₂⁶	—	4	16	no	—
238	C₂⁶	—	4	16	no	—
239	C₂⁶	C₂⁴	1	2	yes	—
240	C₂⁶	C₂⁴	1	1	yes	characteristic
241	C₂⁶	C₂⁴	1	4	yes	—
242	C₂⁶	C₂⁴	1	28	yes	—
243	C₂⁶	C₂⁴	1	1	yes	characteristic
244	C₂⁶	C₂⁴	1	1	yes	characteristic
245	C₂⁶	C₂⁴	1	56	yes	—
246	C₂²×#41	—	4	448	no	—
247	C₂²×#41	—	4	1792	no	—
248	C₂²×#41	—	4	896	no	—
249	C₂²×#41	C₂⁴	1	448	yes	complemented
250	C₂²×#41	C₂⁴	1	1792	yes	complemented
251	C₂²×#41	C₂⁴	1	896	yes	complemented
252	C₂³×Q₈	—	2	32	no	—
253	C₂³×Q₈	—	4	16	no	—
254	C₂³×Q₈	—	4	8	no	—
255	C₂³×Q₈	—	4	32	no	—
256	C₂³×Q₈	—	4	448	no	—
257	C₂³×Q₈	C₂⁴	1	56	yes	—
258	C₂³×Q₈	C₂⁴	1	56	yes	—
259	C₂³×Q₈	C₂⁴	1	28	yes	—
260	C₂³×Q₈	C₂⁴	1	112	yes	—
261	C₂³×Q₈	C₂⁴	1	448	yes	complemented
262	C₂³×D₄	—	2	64	no	—
263	C₂³×D₄	—	2	32	no	—
264	C₂³×D₄	—	2	32	no	—
265	C₂³×D₄	—	2	32	no	—
266	C₂³×D₄	—	4	448	no	—
267	C₂³×D₄	—	4	16	no	—
268	C₂³×D₄	—	4	32	no	—
269	C₂³×D₄	—	4	16	no	—
270	C₂³×D₄	—	4	8	no	—
271	C₂³×D₄	—	4	32	no	—
272	C₂³×D₄	—	4	32	no	—
273	C₂³×D₄	—	4	896	no	—
274	C₂³×D₄	C₂⁴	1	112	yes	—
275	C₂³×D₄	C₂⁴	1	56	yes	—
276	C₂³×D₄	C₂⁴	1	56	yes	—
277	C₂³×D₄	C₂⁴	1	56	yes	—
278	C₂³×D₄	C₂⁴	1	56	yes	—
279	C₂³×D₄	C₂⁴	1	112	yes	—
280	C₂³×D₄	C₂⁴	1	448	yes	—
281	C₂³×D₄	C₂⁴	1	896	yes	—
282	C₂³×D₄	C₂⁴	1	56	yes	—
283	C₂³×D₄	C₂⁴	1	112	yes	—
284	C₂³×D₄	C₂⁴	1	112	yes	—
285	C₂³×D₄	C₂⁴	1	28	yes	—
286	C₂⁴×C₄	—	2	32	no	—
287	C₂⁴×C₄	—	2	16	no	—
288	C₂⁴×C₄	—	2	16	no	—
289	C₂⁴×C₄	—	2	16	no	—
290	C₂⁴×C₄	—	2	32	no	—
291	C₂⁴×C₄	—	4	448	no	—
292	C₂⁴×C₄	—	4	8	no	—
293	C₂⁴×C₄	—	4	8	no	—
294	C₂⁴×C₄	—	4	8	no	—
295	C₂⁴×C₄	—	4	16	no	—
296	C₂⁴×C₄	—	4	16	no	—
297	C₂⁴×C₄	—	4	32	no	—
298	C₂⁴×C₄	—	4	32	no	—
299	C₂⁴×C₄	—	4	32	no	—
300	C₂⁴×C₄	C₂⁴	1	28	yes	—
301	C₂⁴×C₄	C₂⁴	1	28	yes	—
302	C₂⁴×C₄	C₂⁴	1	28	yes	—
303	C₂⁴×C₄	C₂⁴	1	56	yes	—
304	C₂⁴×C₄	C₂⁴	1	56	yes	—
305	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
306	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
307	C₂⁴×C₄	C₂⁴	1	4	yes	—
308	C₂⁴×C₄	C₂⁴	1	2	yes	—
309	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
310	C₂⁴×C₄	C₂⁴	1	4	yes	—
311	C₂⁴×C₄	C₂⁴	1	2	yes	—
312	C₂⁴×C₄	C₂⁴	1	4	yes	—
313	C₂⁴×C₄	C₂⁴	1	2	yes	—
314	C₂⁴×C₄	C₂⁴	1	28	yes	—
315	C₂⁴×C₄	C₂⁴	1	28	yes	—
316	C₂⁴×C₄	C₂⁴	1	28	yes	—
317	C₂⁴×C₄	C₂⁴	1	448	yes	—
318	C₂⁴×C₄	C₂⁴	1	56	yes	—
319	C₂⁴×C₄	C₂⁴	1	56	yes	—
320	C₂⁴×C₄	C₂⁴	1	112	yes	—
321	C₂⁴×C₄	C₂⁴	1	112	yes	—
322	C₂⁴×C₄	C₂⁴	1	112	yes	—
323	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
324	#562	C₂⁴	1	16384	yes	complemented
325	#554	C₂⁴	1	8192	yes	complemented
326	#548	C₂⁴	1	8192	yes	complemented
327	#547	C₂⁴	1	8192	yes	complemented
328	#546	C₂⁴	1	16384	yes	complemented
329	#546	C₂⁴	1	8192	yes	complemented
330	#543	C₂⁴	1	8192	yes	complemented
331	#542	C₂⁴	1	8192	yes	complemented
332	#539	C₂⁴	1	8192	yes	complemented
333	#538	C₂⁴	1	8192	yes	complemented
334	#537	C₂⁴	1	8192	yes	complemented
335	#537	C₂⁴	1	8192	yes	complemented
336	C₂×C₄⋊Q₈	C₂⁴	1	896	yes	complemented
337	C₂×#126	C₂⁴	1	1792	yes	complemented
338	C₂×#125	C₂⁴	1	1792	yes	complemented
339	C₂×#124	C₂⁴	1	1792	yes	complemented
340	C₂×#124	C₂⁴	1	896	yes	complemented
341	C₂×#124	C₂⁴	1	1792	yes	complemented
342	#525	C₂⁴	1	4096	yes	complemented
343	C₂×#123	C₂⁴	1	896	yes	complemented
344	C₂×#123	C₂⁴	1	1792	yes	complemented
345	C₂×#123	C₂⁴	1	1792	yes	complemented
346	C₂×#123	C₂⁴	1	1792	yes	complemented
347	C₂×#123	C₂⁴	1	1792	yes	complemented
348	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	—
349	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	—
350	C₂×C₂²⋊Q₈	C₂⁴	1	448	yes	—
351	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	—
352	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	complemented
353	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	complemented
354	C₂×C₂²⋊Q₈	C₂⁴	1	448	yes	complemented
355	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	complemented
356	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	complemented
357	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	complemented
358	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	complemented
359	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	complemented
360	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	complemented
361	C₂×C₂²⋊Q₈	C₂⁴	1	4096	yes	complemented
362	C₂×#121	C₂⁴	1	896	yes	—
363	C₂×#121	C₂⁴	1	896	yes	—
364	C₂×#121	C₂⁴	1	896	yes	—
365	C₂×#121	C₂⁴	1	896	yes	—
366	C₂×#121	C₂⁴	1	448	yes	—
367	C₂×#121	C₂⁴	1	4096	yes	complemented
368	C₂×#121	C₂⁴	1	448	yes	complemented
369	C₂×#121	C₂⁴	1	1792	yes	complemented
370	C₂×#121	C₂⁴	1	896	yes	complemented
371	C₂×#121	C₂⁴	1	1792	yes	complemented
372	C₂×#121	C₂⁴	1	1792	yes	complemented
373	C₂×#121	C₂⁴	1	1792	yes	complemented
374	C₂×#121	C₂⁴	1	1792	yes	complemented
375	C₂×#120	C₂⁴	1	896	yes	—
376	C₂×#120	C₂⁴	1	1792	yes	—
377	C₂×C₄×Q₈	C₂⁴	1	896	yes	complemented
378	C₂×C₄×D₄	C₂⁴	1	896	yes	—
379	C₂×C₄×D₄	C₂⁴	1	1792	yes	—
380	C₂×C₄×D₄	C₂⁴	1	896	yes	complemented
381	C₂×C₄×D₄	C₂⁴	1	1792	yes	complemented
382	C₂×C₄×D₄	C₂⁴	1	896	yes	complemented
383	C₂×#117	C₂⁴	1	448	yes	complemented
384	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
385	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
386	C₂²×C₄⋊C₄	C₂⁴	1	448	yes	—
387	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
388	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
389	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
390	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
391	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
392	C₂²×C₄⋊C₄	C₂⁴	1	28	yes	—
393	C₂²×C₄⋊C₄	C₂⁴	1	28	yes	—
394	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
395	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
396	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
397	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
398	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
399	C₂²×C₄⋊C₄	C₂⁴	1	896	yes	complemented
400	C₂²×C₄⋊C₄	C₂⁴	1	448	yes	complemented
401	C₂²×C₄⋊C₄	C₂⁴	1	896	yes	complemented
402	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
403	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
404	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
405	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
406	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
407	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
408	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
409	C₂²×C₂²⋊C₄	C₂⁴	1	896	yes	—
410	C₂²×C₂²⋊C₄	C₂⁴	1	896	yes	—
411	C₂²×C₂²⋊C₄	C₂⁴	1	1792	yes	—
412	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
413	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
414	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
415	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
416	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
417	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
418	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
419	C₂²×C₄²	C₂⁴	1	56	yes	—
420	C₂²×C₄²	C₂⁴	1	112	yes	—
421	C₂⁵	—	2	8	no	—
422	C₂⁵	—	2	8	no	—
423	C₂⁵	—	2	8	no	—
424	C₂⁵	—	2	8	no	—
425	C₂⁵	—	2	8	no	—
426	C₂⁵	—	2	16	no	—
427	C₂⁵	—	2	16	no	—
428	C₂⁵	—	2	32	no	—
429	C₂⁵	—	2	32	no	—
430	C₂⁵	—	2	224	no	—
431	C₂⁵	—	2	8	no	—
432	C₂⁵	—	2	16	no	—
433	C₂⁵	—	2	224	no	—
434	C₂⁵	—	2	8	no	—
435	C₂⁵	—	2	32	no	—
436	C₂⁵	—	2	448	no	—
437	C₂⁵	—	4	112	no	—
438	C₂⁵	—	4	224	no	—
439	C₂⁵	—	4	224	no	—
440	C₂⁵	—	4	256	no	—
441	C₂⁵	—	8	256	no	—
442	C₂⁵	H(5,𝔽₂)	1	16	yes	—
443	C₂⁵	2₋¹⁺⁴	1	16	yes	—
444	C₂⁵	C₂⁵	1	14	yes	—
445	C₂⁵	C₂⁵	1	56	yes	—
446	C₂⁵	C₂⁵	1	28	yes	—
447	C₂⁵	C₂⁵	1	112	yes	—
448	C₂⁵	C₂⁵	1	14	yes	—
449	C₂⁵	C₂⁵	1	14	yes	—
450	C₂⁵	C₂⁵	1	224	yes	—
451	C₂⁵	C₂⁵	1	1	yes	characteristic
452	C₂×#41	—	4	1792	no	—
453	C₂×#41	—	4	7168	no	—
454	C₂×#41	—	4	3584	no	—
455	C₂×#41	C₂⁵	1	512	yes	complemented
456	C₂×#41	C₂⁵	1	2048	yes	complemented
457	C₂×#41	C₂⁵	1	1024	yes	complemented
458	C₂²×Q₈	—	2	448	no	—
459	C₂²×Q₈	—	4	224	no	—
460	C₂²×Q₈	—	4	112	no	—
461	C₂²×Q₈	—	4	448	no	—
462	C₂²×Q₈	—	4	1792	no	—
463	C₂²×Q₈	C₂⁵	1	224	yes	—
464	C₂²×Q₈	C₂⁵	1	112	yes	—
465	C₂²×Q₈	C₂⁵	1	224	yes	—
466	C₂²×Q₈	C₂⁵	1	448	yes	—
467	C₂²×Q₈	C₂⁵	1	512	yes	complemented
468	C₂²×D₄	—	2	896	no	—
469	C₂²×D₄	—	2	448	no	—
470	C₂²×D₄	—	2	448	no	—
471	C₂²×D₄	—	2	448	no	—
472	C₂²×D₄	—	4	1792	no	—
473	C₂²×D₄	—	4	224	no	—
474	C₂²×D₄	—	4	448	no	—
475	C₂²×D₄	—	4	224	no	—
476	C₂²×D₄	—	4	112	no	—
477	C₂²×D₄	—	4	448	no	—
478	C₂²×D₄	—	4	448	no	—
479	C₂²×D₄	—	4	3584	no	—
480	C₂²×D₄	C₂⁵	1	224	yes	—
481	C₂²×D₄	C₂⁵	1	224	yes	—
482	C₂²×D₄	C₂⁵	1	448	yes	—
483	C₂²×D₄	C₂⁵	1	224	yes	—
484	C₂²×D₄	C₂⁵	1	224	yes	—
485	C₂²×D₄	C₂⁵	1	448	yes	—
486	C₂²×D₄	C₂⁵	1	448	yes	—
487	C₂²×D₄	C₂⁵	1	224	yes	—
488	C₂²×D₄	C₂⁵	1	448	yes	—
489	C₂²×D₄	C₂⁵	1	112	yes	—
490	C₂²×D₄	C₂⁵	1	512	yes	—
491	C₂²×D₄	C₂⁵	1	1024	yes	—
492	C₂³×C₄	—	2	8	no	—
493	C₂³×C₄	—	2	32	no	—
494	C₂³×C₄	—	2	8	no	—
495	C₂³×C₄	—	2	16	no	—
496	C₂³×C₄	—	2	8	no	—
497	C₂³×C₄	—	2	448	no	—
498	C₂³×C₄	—	2	32	no	—
499	C₂³×C₄	—	2	16	no	—
500	C₂³×C₄	—	2	32	no	—
501	C₂³×C₄	—	2	16	no	—
502	C₂³×C₄	—	2	224	no	—
503	C₂³×C₄	—	2	224	no	—
504	C₂³×C₄	—	2	224	no	—
505	C₂³×C₄	—	2	448	no	—
506	C₂³×C₄	—	4	1792	no	—
507	C₂³×C₄	—	4	112	no	—
508	C₂³×C₄	—	4	112	no	—
509	C₂³×C₄	—	4	112	no	—
510	C₂³×C₄	—	4	224	no	—
511	C₂³×C₄	—	4	224	no	—
512	C₂³×C₄	—	4	448	no	—
513	C₂³×C₄	—	4	448	no	—
514	C₂³×C₄	—	4	448	no	—
515	C₂³×C₄	H(5,𝔽₂)	1	16	yes	—
516	C₂³×C₄	C₂⁵	1	28	yes	—
517	C₂³×C₄	C₂⁵	1	14	yes	—
518	C₂³×C₄	C₂⁵	1	28	yes	—
519	C₂³×C₄	C₂⁵	1	56	yes	—
520	C₂³×C₄	C₂⁵	1	28	yes	—
521	C₂³×C₄	C₂⁵	1	56	yes	—
522	C₂³×C₄	C₂⁵	1	14	yes	—
523	C₂³×C₄	C₂⁵	1	56	yes	—
524	C₂³×C₄	C₂⁵	1	14	yes	—
525	C₂³×C₄	C₂⁵	1	224	yes	—
526	C₂³×C₄	C₂⁵	1	112	yes	—
527	C₂³×C₄	C₂⁵	1	224	yes	—
528	C₂³×C₄	C₂⁵	1	112	yes	—
529	C₂³×C₄	C₂⁵	1	112	yes	—
530	C₂³×C₄	C₂⁵	1	112	yes	—
531	C₂³×C₄	C₂⁵	1	224	yes	—
532	C₂³×C₄	C₂⁵	1	224	yes	—
533	C₂³×C₄	C₂⁵	1	448	yes	—
534	C₂³×C₄	C₂⁵	1	448	yes	—
535	C₂³×C₄	C₂⁵	1	112	yes	—
536	C₂³×C₄	C₂⁵	1	448	yes	—
537	C₂³×C₄	C₂⁵	1	112	yes	—
538	C₂³×C₄	C₂⁵	1	512	yes	—
539	C₂³×C₄	C₂⁵	1	14	yes	—
540	C₄⋊Q₈	C₂⁵	1	1024	yes	complemented
541	#126	C₂⁵	1	2048	yes	complemented
542	#125	C₂⁵	1	2048	yes	complemented
543	#124	C₂⁵	1	2048	yes	complemented
544	#124	C₂⁵	1	1024	yes	complemented
545	#124	C₂⁵	1	2048	yes	complemented
546	#123	C₂⁵	1	1024	yes	complemented
547	#123	C₂⁵	1	2048	yes	complemented
548	#123	C₂⁵	1	2048	yes	complemented
549	#123	C₂⁵	1	2048	yes	complemented
550	#123	C₂⁵	1	2048	yes	complemented
551	C₂²⋊Q₈	C₂⁵	1	1024	yes	—
552	C₂²⋊Q₈	C₂⁵	1	1024	yes	—
553	C₂²⋊Q₈	C₂⁵	1	512	yes	—
554	C₂²⋊Q₈	C₂⁵	1	2048	yes	—
555	C₂²⋊Q₈	C₂⁵	1	1024	yes	complemented
556	C₂²⋊Q₈	C₂⁵	1	1024	yes	complemented
557	C₂²⋊Q₈	C₂⁵	1	512	yes	complemented
558	C₂²⋊Q₈	C₂⁵	1	2048	yes	complemented
559	C₂²⋊Q₈	C₂⁵	1	2048	yes	complemented
560	C₂²⋊Q₈	C₂⁵	1	1024	yes	complemented
561	C₂²⋊Q₈	C₂⁵	1	2048	yes	complemented
562	C₂²⋊Q₈	C₂⁵	1	2048	yes	complemented
563	C₂²⋊Q₈	C₂⁵	1	2048	yes	complemented
564	#121	C₂⁵	1	1024	yes	—
565	#121	C₂⁵	1	1024	yes	—
566	#121	C₂⁵	1	1024	yes	—
567	#121	C₂⁵	1	1024	yes	—
568	#121	C₂⁵	1	512	yes	—
569	#121	C₂⁵	1	512	yes	complemented
570	#121	C₂⁵	1	2048	yes	complemented
571	#121	C₂⁵	1	1024	yes	complemented
572	#121	C₂⁵	1	2048	yes	complemented
573	#121	C₂⁵	1	2048	yes	complemented
574	#121	C₂⁵	1	2048	yes	complemented
575	#121	C₂⁵	1	2048	yes	complemented
576	#120	C₂⁵	1	1024	yes	—
577	#120	C₂⁵	1	2048	yes	—
578	C₄×Q₈	C₂⁵	1	1024	yes	complemented
579	C₄×D₄	C₂⁵	1	1024	yes	—
580	C₄×D₄	C₂⁵	1	2048	yes	—
581	C₄×D₄	C₂⁵	1	1024	yes	complemented
582	C₄×D₄	C₂⁵	1	2048	yes	complemented
583	C₄×D₄	C₂⁵	1	1024	yes	complemented
584	#117	C₂⁵	1	512	yes	complemented
585	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
586	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
587	C₂×C₄⋊C₄	C₂⁵	1	512	yes	—
588	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
589	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
590	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
591	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
592	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
593	C₂×C₄⋊C₄	C₂⁵	1	112	yes	—
594	C₂×C₄⋊C₄	C₂⁵	1	112	yes	—
595	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
596	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
597	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
598	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
599	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
600	C₂×C₄⋊C₄	C₂⁵	1	1024	yes	complemented
601	C₂×C₄⋊C₄	C₂⁵	1	512	yes	complemented
602	C₂×C₄⋊C₄	C₂⁵	1	1024	yes	complemented
603	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
604	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
605	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
606	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
607	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
608	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
609	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
610	C₂×C₂²⋊C₄	C₂⁵	1	1024	yes	—
611	C₂×C₂²⋊C₄	C₂⁵	1	1024	yes	—
612	C₂×C₂²⋊C₄	C₂⁵	1	2048	yes	—
613	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
614	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
615	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
616	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
617	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
618	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
619	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
620	C₂×C₄²	C₂⁵	1	224	yes	—
621	C₂×C₄²	C₂⁵	1	448	yes	—
622	C₂⁴	—	2	56	no	—
623	C₂⁴	—	2	56	no	—
624	C₂⁴	—	2	56	no	—
625	C₂⁴	—	2	56	no	—
626	C₂⁴	—	2	128	no	—
627	C₂⁴	—	2	128	no	—
628	C₂⁴	—	2	56	no	—
629	C₂⁴	—	2	112	no	—
630	C₂⁴	—	2	112	no	—
631	C₂⁴	—	2	224	no	—
632	C₂⁴	—	2	224	no	—
633	C₂⁴	—	2	448	no	—
634	C₂⁴	—	2	56	no	—
635	C₂⁴	—	2	112	no	—
636	C₂⁴	—	2	448	no	—
637	C₂⁴	—	2	56	no	—
638	C₂⁴	—	2	224	no	—
639	C₂⁴	—	2	896	no	—
640	C₂⁴	—	4	224	no	—
641	C₂⁴	—	4	448	no	—
642	C₂⁴	—	4	448	no	—
643	C₂⁴	—	4	1792	no	—
644	C₂⁴	—	4	128	no	—
645	C₂⁴	—	4	64	no	—
646	C₂⁴	—	4	256	no	—
647	C₂⁴	—	8	1792	no	—
648	C₂⁴	C₂×H(5,𝔽₂)	1	112	yes	—
649	C₂⁴	C₂×H(5,𝔽₂)	1	8	yes	—
650	C₂⁴	C₂×H(5,𝔽₂)	1	8	yes	—
651	C₂⁴	C₂×2₋¹⁺⁴	1	112	yes	—
652	C₂⁴	C₂×2₋¹⁺⁴	1	8	yes	—
653	C₂⁴	C₂⁶	1	28	yes	—
654	C₂⁴	C₂⁶	1	112	yes	—
655	C₂⁴	C₂⁶	1	56	yes	—
656	C₂⁴	C₂⁶	1	64	yes	—
657	C₂⁴	C₂⁶	1	28	yes	—
658	C₂⁴	C₂⁶	1	28	yes	—
659	C₂⁴	C₂⁶	1	128	yes	—
660	C₂⁴	C₂⁶	1	7	yes	—
661	#41	—	4	1024	no	—
662	#41	—	4	4096	no	—
663	#41	—	4	2048	no	—
664	C₂×Q₈	—	2	896	no	—
665	C₂×Q₈	—	4	448	no	—
666	C₂×Q₈	—	4	224	no	—
667	C₂×Q₈	—	4	896	no	—
668	C₂×Q₈	—	4	1024	no	—
669	C₂×Q₈	C₂⁶	1	128	yes	—
670	C₂×Q₈	C₂⁶	1	64	yes	—
671	C₂×Q₈	C₂⁶	1	128	yes	—
672	C₂×Q₈	C₂⁶	1	256	yes	—
673	C₂×D₄	—	2	1792	no	—
674	C₂×D₄	—	2	896	no	—
675	C₂×D₄	—	2	896	no	—
676	C₂×D₄	—	2	896	no	—
677	C₂×D₄	—	4	1024	no	—
678	C₂×D₄	—	4	448	no	—
679	C₂×D₄	—	4	896	no	—
680	C₂×D₄	—	4	448	no	—
681	C₂×D₄	—	4	224	no	—
682	C₂×D₄	—	4	896	no	—
683	C₂×D₄	—	4	896	no	—
684	C₂×D₄	—	4	2048	no	—
685	C₂×D₄	C₂⁶	1	128	yes	—
686	C₂×D₄	C₂⁶	1	128	yes	—
687	C₂×D₄	C₂⁶	1	256	yes	—
688	C₂×D₄	C₂⁶	1	128	yes	—
689	C₂×D₄	C₂⁶	1	128	yes	—
690	C₂×D₄	C₂⁶	1	256	yes	—
691	C₂×D₄	C₂⁶	1	256	yes	—
692	C₂×D₄	C₂⁶	1	128	yes	—
693	C₂×D₄	C₂⁶	1	256	yes	—
694	C₂×D₄	C₂⁶	1	64	yes	—
695	C₂²×C₄	—	2	56	no	—
696	C₂²×C₄	—	2	224	no	—
697	C₂²×C₄	—	2	56	no	—
698	C₂²×C₄	—	2	112	no	—
699	C₂²×C₄	—	2	56	no	—
700	C₂²×C₄	—	2	896	no	—
701	C₂²×C₄	—	2	224	no	—
702	C₂²×C₄	—	2	112	no	—
703	C₂²×C₄	—	2	224	no	—
704	C₂²×C₄	—	2	112	no	—
705	C₂²×C₄	—	2	448	no	—
706	C₂²×C₄	—	2	448	no	—
707	C₂²×C₄	—	2	448	no	—
708	C₂²×C₄	—	2	896	no	—
709	C₂²×C₄	—	4	1024	no	—
710	C₂²×C₄	—	4	224	no	—
711	C₂²×C₄	—	4	224	no	—
712	C₂²×C₄	—	4	224	no	—
713	C₂²×C₄	—	4	448	no	—
714	C₂²×C₄	—	4	448	no	—
715	C₂²×C₄	—	4	896	no	—
716	C₂²×C₄	—	4	896	no	—
717	C₂²×C₄	—	4	896	no	—
718	C₂²×C₄	C₂×H(5,𝔽₂)	1	112	yes	—
719	C₂²×C₄	C₂⁶	1	56	yes	—
720	C₂²×C₄	C₂⁶	1	56	yes	—
721	C₂²×C₄	C₂⁶	1	112	yes	—
722	C₂²×C₄	C₂⁶	1	112	yes	—
723	C₂²×C₄	C₂⁶	1	28	yes	—
724	C₂²×C₄	C₂⁶	1	56	yes	—
725	C₂²×C₄	C₂⁶	1	112	yes	—
726	C₂²×C₄	C₂⁶	1	28	yes	—
727	C₂²×C₄	C₂⁶	1	28	yes	—
728	C₂²×C₄	C₂⁶	1	128	yes	—
729	C₂²×C₄	C₂⁶	1	64	yes	—
730	C₂²×C₄	C₂⁶	1	128	yes	—
731	C₂²×C₄	C₂⁶	1	64	yes	—
732	C₂²×C₄	C₂⁶	1	64	yes	—
733	C₂²×C₄	C₂⁶	1	64	yes	—
734	C₂²×C₄	C₂⁶	1	128	yes	—
735	C₂²×C₄	C₂⁶	1	128	yes	—
736	C₂²×C₄	C₂⁶	1	256	yes	—
737	C₂²×C₄	C₂⁶	1	256	yes	—
738	C₂²×C₄	C₂⁶	1	64	yes	—
739	C₂²×C₄	C₂⁶	1	256	yes	—
740	C₂²×C₄	C₂⁶	1	64	yes	—
741	C₂²×C₄	C₂⁶	1	28	yes	—
742	C₄⋊C₄	C₂⁶	1	128	yes	—
743	C₄⋊C₄	C₂⁶	1	128	yes	—
744	C₄⋊C₄	C₂⁶	1	128	yes	—
745	C₄⋊C₄	C₂⁶	1	256	yes	—
746	C₄⋊C₄	C₂⁶	1	256	yes	—
747	C₄⋊C₄	C₂⁶	1	256	yes	—
748	C₄⋊C₄	C₂⁶	1	128	yes	—
749	C₄⋊C₄	C₂⁶	1	64	yes	—
750	C₄⋊C₄	C₂⁶	1	64	yes	—
751	C₄⋊C₄	C₂⁶	1	128	yes	—
752	C₄⋊C₄	C₂⁶	1	256	yes	—
753	C₄⋊C₄	C₂⁶	1	256	yes	—
754	C₄⋊C₄	C₂⁶	1	128	yes	—
755	C₄⋊C₄	C₂⁶	1	256	yes	—
756	C₂²⋊C₄	C₂⁶	1	256	yes	—
757	C₂²⋊C₄	C₂⁶	1	128	yes	—
758	C₂²⋊C₄	C₂⁶	1	256	yes	—
759	C₂²⋊C₄	C₂⁶	1	256	yes	—
760	C₂²⋊C₄	C₂⁶	1	256	yes	—
761	C₂²⋊C₄	C₂⁶	1	256	yes	—
762	C₂²⋊C₄	C₂⁶	1	256	yes	—
763	C₂²⋊C₄	C₂⁶	1	128	yes	—
764	C₂²⋊C₄	C₂⁶	1	128	yes	—
765	C₂²⋊C₄	C₂⁶	1	256	yes	—
766	C₂²⋊C₄	C₂⁶	1	128	yes	—
767	C₂²⋊C₄	C₂⁶	1	256	yes	—
768	C₂²⋊C₄	C₂⁶	1	256	yes	—
769	C₂²⋊C₄	C₂⁶	1	128	yes	—
770	C₄²	C₂⁶	1	128	yes	—
771	C₄²	C₂⁶	1	256	yes	—
772	C₂³	—	2	448	no	—
773	C₂³	—	2	448	no	—
774	C₂³	—	2	56	no	—
775	C₂³	—	2	56	no	—
776	C₂³	—	2	56	no	—
777	C₂³	—	2	56	no	—
778	C₂³	—	2	56	no	—
779	C₂³	—	2	112	no	—
780	C₂³	—	2	112	no	—
781	C₂³	—	2	224	no	—
782	C₂³	—	2	224	no	—
783	C₂³	—	2	128	no	—
784	C₂³	—	2	56	no	—
785	C₂³	—	2	112	no	—
786	C₂³	—	2	128	no	—
787	C₂³	—	2	56	no	—
788	C₂³	—	2	224	no	—
789	C₂³	—	2	256	no	—
790	C₂³	—	4	64	no	—
791	C₂³	—	4	128	no	—
792	C₂³	—	4	128	no	—
793	C₂³	—	4	1792	no	—
794	C₂³	—	4	448	no	—
795	C₂³	—	4	224	no	—
796	C₂³	—	4	896	no	—
797	C₂³	—	8	1792	no	—
798	C₂³	#3536	1	64	yes	direct product factor
799	C₂³	C₂²×H(5,𝔽₂)	1	112	yes	—
800	C₂³	C₂²×H(5,𝔽₂)	1	28	yes	—
801	C₂³	C₂²×H(5,𝔽₂)	1	28	yes	—
802	C₂³	C₂²×2₋¹⁺⁴	1	112	yes	—
803	C₂³	C₂²×2₋¹⁺⁴	1	28	yes	—
804	C₂³	C₂⁷	1	8	yes	—
805	C₂³	C₂⁷	1	32	yes	—
806	C₂³	C₂⁷	1	16	yes	—
807	C₂³	C₂⁷	1	8	yes	—
808	C₂³	C₂⁷	1	8	yes	—
809	C₂³	C₂⁷	1	7	yes	—
810	Q₈	—	2	256	no	—
811	Q₈	—	4	128	no	—
812	Q₈	—	4	64	no	—
813	Q₈	—	4	256	no	—
814	D₄	—	2	512	no	—
815	D₄	—	2	256	no	—
816	D₄	—	2	256	no	—
817	D₄	—	2	256	no	—
818	D₄	—	4	128	no	—
819	D₄	—	4	256	no	—
820	D₄	—	4	128	no	—
821	D₄	—	4	64	no	—
822	D₄	—	4	256	no	—
823	D₄	—	4	256	no	—
824	C₂×C₄	—	2	56	no	—
825	C₂×C₄	—	2	224	no	—
826	C₂×C₄	—	2	56	no	—
827	C₂×C₄	—	2	112	no	—
828	C₂×C₄	—	2	56	no	—
829	C₂×C₄	—	2	256	no	—
830	C₂×C₄	—	2	224	no	—
831	C₂×C₄	—	2	112	no	—
832	C₂×C₄	—	2	224	no	—
833	C₂×C₄	—	2	112	no	—
834	C₂×C₄	—	2	128	no	—
835	C₂×C₄	—	2	128	no	—
836	C₂×C₄	—	2	128	no	—
837	C₂×C₄	—	2	256	no	—
838	C₂×C₄	—	4	64	no	—
839	C₂×C₄	—	4	64	no	—
840	C₂×C₄	—	4	64	no	—
841	C₂×C₄	—	4	128	no	—
842	C₂×C₄	—	4	128	no	—
843	C₂×C₄	—	4	256	no	—
844	C₂×C₄	—	4	256	no	—
845	C₂×C₄	—	4	256	no	—
846	C₂×C₄	C₂²×H(5,𝔽₂)	1	112	yes	—
847	C₂×C₄	C₂⁷	1	16	yes	—
848	C₂×C₄	C₂⁷	1	16	yes	—
849	C₂×C₄	C₂⁷	1	32	yes	—
850	C₂×C₄	C₂⁷	1	32	yes	—
851	C₂×C₄	C₂⁷	1	8	yes	—
852	C₂×C₄	C₂⁷	1	16	yes	—
853	C₂×C₄	C₂⁷	1	32	yes	—
854	C₂×C₄	C₂⁷	1	8	yes	—
855	C₂×C₄	C₂⁷	1	8	yes	—
856	C₂×C₄	C₂⁷	1	8	yes	—
857	C₂²	—	2	224	no	—
858	C₂²	—	2	224	no	—
859	C₂²	—	2	8	no	—
860	C₂²	—	2	8	no	—
861	C₂²	—	2	8	no	—
862	C₂²	—	2	8	no	—
863	C₂²	—	2	8	no	—
864	C₂²	—	2	16	no	—
865	C₂²	—	2	16	no	—
866	C₂²	—	2	32	no	—
867	C₂²	—	2	32	no	—
868	C₂²	—	2	8	no	—
869	C₂²	—	2	16	no	—
870	C₂²	—	2	8	no	—
871	C₂²	—	2	32	no	—
872	C₂²	—	4	256	no	—
873	C₂²	—	4	224	no	—
874	C₂²	—	4	112	no	—
875	C₂²	—	4	448	no	—
876	C₂²	—	8	256	no	—
877	C₂²	C₂×#3536	1	112	yes	direct product factor
878	C₂²	C₂³×H(5,𝔽₂)	1	16	yes	—
879	C₂²	C₂³×H(5,𝔽₂)	1	14	yes	—
880	C₂²	C₂³×H(5,𝔽₂)	1	14	yes	—
881	C₂²	C₂³×2₋¹⁺⁴	1	16	yes	—
882	C₂²	C₂³×2₋¹⁺⁴	1	14	yes	—
883	C₂²	C₂⁸	1	1	yes	characteristic
884	C₄	—	2	8	no	—
885	C₄	—	2	32	no	—
886	C₄	—	2	8	no	—
887	C₄	—	2	16	no	—
888	C₄	—	2	8	no	—
889	C₄	—	2	32	no	—
890	C₄	—	2	16	no	—
891	C₄	—	2	32	no	—
892	C₄	—	2	16	no	—
893	C₄	C₂³×H(5,𝔽₂)	1	16	yes	—
894	C₂	—	2	16	no	—
895	C₂	—	2	16	no	—
896	C₂	—	4	16	no	—
897	C₂	—	4	8	no	—
898	C₂	—	4	32	no	—
899	C₂	C₂²×#3536	1	28	yes	direct product factor
900	C₂	C₂⁴×H(5,𝔽₂)	1	1	yes	characteristic
901	C₂	C₂⁴×H(5,𝔽₂)	1	1	yes	characteristic
902	C₂	C₂⁴×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁵	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁸
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂²×#3536	C₂	direct (N × H)
2. C₂³×#562	C₂	semidirect
3. C₂³×#554	C₂	semidirect
4. C₂³×#547	C₂	semidirect
5. C₂³×#548	C₂	semidirect
6. C₂³×#546	C₂	semidirect
7. C₂³×#546	C₂	semidirect
8. C₂³×#542	C₂	semidirect
9. C₂³×#537	C₂	semidirect
10. C₂³×#537	C₂	semidirect
11. C₂³×#539	C₂	semidirect
12. C₂³×#538	C₂	semidirect
13. C₂³×#543	C₂	semidirect
14. C₂³×#525	C₂	semidirect
15. C₂⁴×C₂²⋊Q₈	C₂	semidirect
16. C₂⁴×#121	C₂	semidirect
17. C₂⁴×#41	C₂²	semidirect
18. C₂⁴×#41	C₂²	semidirect
19. C₂⁴×#41	C₂²	semidirect
20. C₂⁵×Q₈	C₂²	semidirect
24. C₂×#3536	C₂²	direct (N × H)
25. C₂²×#554	C₂²	semidirect
26. C₂²×#547	C₂²	semidirect
27. C₂²×#548	C₂²	semidirect
28. C₂²×#546	C₂²	semidirect
29. C₂²×#546	C₂²	semidirect
30. C₂²×#562	C₂²	semidirect
31. C₂²×#542	C₂²	semidirect
32. C₂²×#537	C₂²	semidirect
33. C₂²×#537	C₂²	semidirect
34. C₂²×#539	C₂²	semidirect
35. C₂²×#538	C₂²	semidirect
36. C₂²×#543	C₂²	semidirect
37. C₂³×C₄⋊Q₈	C₂²	semidirect
38. C₂³×#126	C₂²	semidirect
39. C₂³×#125	C₂²	semidirect
40. C₂³×#124	C₂²	semidirect
41. C₂³×#124	C₂²	semidirect
42. C₂³×#124	C₂²	semidirect
43. C₂²×#525	C₂²	semidirect
44. C₂³×#123	C₂²	semidirect
45. C₂³×#123	C₂²	semidirect
46. C₂³×#123	C₂²	semidirect
47. C₂³×#123	C₂²	semidirect
48. C₂³×#123	C₂²	semidirect
53. C₂³×C₂²⋊Q₈	C₂²	semidirect
54. C₂³×C₂²⋊Q₈	C₂²	semidirect
55. C₂³×C₂²⋊Q₈	C₂²	semidirect
56. C₂³×C₂²⋊Q₈	C₂²	semidirect
57. C₂³×C₂²⋊Q₈	C₂²	semidirect
58. C₂³×C₂²⋊Q₈	C₂²	semidirect
59. C₂³×C₂²⋊Q₈	C₂²	semidirect
60. C₂³×C₂²⋊Q₈	C₂²	semidirect
61. C₂³×C₂²⋊Q₈	C₂²	semidirect
62. C₂³×C₂²⋊Q₈	C₂²	semidirect
68. C₂³×#121	C₂²	semidirect
69. C₂³×#121	C₂²	semidirect
70. C₂³×#121	C₂²	semidirect
71. C₂³×#121	C₂²	semidirect
72. C₂³×#121	C₂²	semidirect
73. C₂³×#121	C₂²	semidirect
74. C₂³×#121	C₂²	semidirect
75. C₂³×#121	C₂²	semidirect
78. C₂³×C₄×Q₈	C₂²	semidirect
81. C₂³×C₄×D₄	C₂²	semidirect
82. C₂³×C₄×D₄	C₂²	semidirect
83. C₂³×C₄×D₄	C₂²	semidirect
84. C₂³×#117	C₂²	semidirect
86. C₂⁴×C₄⋊C₄	C₂²	semidirect
87. C₂⁴×C₄⋊C₄	C₂²	semidirect
88. C₂⁴×C₄⋊C₄	C₂²	semidirect
97. C₂³×#41	C₂³	semidirect
98. C₂³×#41	C₂³	semidirect
99. C₂³×#41	C₂³	semidirect
105. C₂⁴×Q₈	C₂³	semidirect
135. #3536	C₂³	direct (N × H)
136. C₂×#562	C₂³	semidirect
137. C₂×#554	C₂³	semidirect
138. C₂×#548	C₂³	semidirect
139. C₂×#547	C₂³	semidirect
140. C₂×#546	C₂³	semidirect
141. C₂×#546	C₂³	semidirect
142. C₂×#543	C₂³	semidirect
143. C₂×#542	C₂³	semidirect
144. C₂×#539	C₂³	semidirect
145. C₂×#538	C₂³	semidirect
146. C₂×#537	C₂³	semidirect
147. C₂×#537	C₂³	semidirect
148. C₂²×C₄⋊Q₈	C₂³	semidirect
149. C₂²×#126	C₂³	semidirect
150. C₂²×#125	C₂³	semidirect
151. C₂²×#124	C₂³	semidirect
152. C₂²×#124	C₂³	semidirect
153. C₂²×#124	C₂³	semidirect
154. C₂×#525	C₂³	semidirect
155. C₂²×#123	C₂³	semidirect
156. C₂²×#123	C₂³	semidirect
157. C₂²×#123	C₂³	semidirect
158. C₂²×#123	C₂³	semidirect
159. C₂²×#123	C₂³	semidirect
164. C₂²×C₂²⋊Q₈	C₂³	semidirect
165. C₂²×C₂²⋊Q₈	C₂³	semidirect
166. C₂²×C₂²⋊Q₈	C₂³	semidirect
167. C₂²×C₂²⋊Q₈	C₂³	semidirect
168. C₂²×C₂²⋊Q₈	C₂³	semidirect
169. C₂²×C₂²⋊Q₈	C₂³	semidirect
170. C₂²×C₂²⋊Q₈	C₂³	semidirect
171. C₂²×C₂²⋊Q₈	C₂³	semidirect
172. C₂²×C₂²⋊Q₈	C₂³	semidirect
173. C₂²×C₂²⋊Q₈	C₂³	semidirect
179. C₂²×#121	C₂³	semidirect
180. C₂²×#121	C₂³	semidirect
181. C₂²×#121	C₂³	semidirect
182. C₂²×#121	C₂³	semidirect
183. C₂²×#121	C₂³	semidirect
184. C₂²×#121	C₂³	semidirect
185. C₂²×#121	C₂³	semidirect
186. C₂²×#121	C₂³	semidirect
189. C₂²×C₄×Q₈	C₂³	semidirect
192. C₂²×C₄×D₄	C₂³	semidirect
193. C₂²×C₄×D₄	C₂³	semidirect
194. C₂²×C₄×D₄	C₂³	semidirect
195. C₂²×#117	C₂³	semidirect
211. C₂³×C₄⋊C₄	C₂³	semidirect
212. C₂³×C₄⋊C₄	C₂³	semidirect
213. C₂³×C₄⋊C₄	C₂³	semidirect
249. C₂²×#41	C₂⁴	semidirect
250. C₂²×#41	C₂⁴	semidirect
251. C₂²×#41	C₂⁴	semidirect
261. C₂³×Q₈	C₂⁴	semidirect
324. #562	C₂⁴	semidirect
325. #554	C₂⁴	semidirect
326. #548	C₂⁴	semidirect
327. #547	C₂⁴	semidirect
328. #546	C₂⁴	semidirect
329. #546	C₂⁴	semidirect
330. #543	C₂⁴	semidirect
331. #542	C₂⁴	semidirect
332. #539	C₂⁴	semidirect
333. #538	C₂⁴	semidirect
334. #537	C₂⁴	semidirect
335. #537	C₂⁴	semidirect
336. C₂×C₄⋊Q₈	C₂⁴	semidirect
337. C₂×#126	C₂⁴	semidirect
338. C₂×#125	C₂⁴	semidirect
339. C₂×#124	C₂⁴	semidirect
340. C₂×#124	C₂⁴	semidirect
341. C₂×#124	C₂⁴	semidirect
342. #525	C₂⁴	semidirect
343. C₂×#123	C₂⁴	semidirect
344. C₂×#123	C₂⁴	semidirect
345. C₂×#123	C₂⁴	semidirect
346. C₂×#123	C₂⁴	semidirect
347. C₂×#123	C₂⁴	semidirect
352. C₂×C₂²⋊Q₈	C₂⁴	semidirect
353. C₂×C₂²⋊Q₈	C₂⁴	semidirect
354. C₂×C₂²⋊Q₈	C₂⁴	semidirect
355. C₂×C₂²⋊Q₈	C₂⁴	semidirect
356. C₂×C₂²⋊Q₈	C₂⁴	semidirect
357. C₂×C₂²⋊Q₈	C₂⁴	semidirect
358. C₂×C₂²⋊Q₈	C₂⁴	semidirect
359. C₂×C₂²⋊Q₈	C₂⁴	semidirect
360. C₂×C₂²⋊Q₈	C₂⁴	semidirect
361. C₂×C₂²⋊Q₈	C₂⁴	semidirect
367. C₂×#121	C₂⁴	semidirect
368. C₂×#121	C₂⁴	semidirect
369. C₂×#121	C₂⁴	semidirect
370. C₂×#121	C₂⁴	semidirect
371. C₂×#121	C₂⁴	semidirect
372. C₂×#121	C₂⁴	semidirect
373. C₂×#121	C₂⁴	semidirect
374. C₂×#121	C₂⁴	semidirect
377. C₂×C₄×Q₈	C₂⁴	semidirect
380. C₂×C₄×D₄	C₂⁴	semidirect
381. C₂×C₄×D₄	C₂⁴	semidirect
382. C₂×C₄×D₄	C₂⁴	semidirect
383. C₂×#117	C₂⁴	semidirect
399. C₂²×C₄⋊C₄	C₂⁴	semidirect
400. C₂²×C₄⋊C₄	C₂⁴	semidirect
401. C₂²×C₄⋊C₄	C₂⁴	semidirect
455. C₂×#41	C₂⁵	semidirect
456. C₂×#41	C₂⁵	semidirect
457. C₂×#41	C₂⁵	semidirect
467. C₂²×Q₈	C₂⁵	semidirect
540. C₄⋊Q₈	C₂⁵	semidirect
541. #126	C₂⁵	semidirect
542. #125	C₂⁵	semidirect
543. #124	C₂⁵	semidirect
544. #124	C₂⁵	semidirect
545. #124	C₂⁵	semidirect
546. #123	C₂⁵	semidirect
547. #123	C₂⁵	semidirect
548. #123	C₂⁵	semidirect
549. #123	C₂⁵	semidirect
550. #123	C₂⁵	semidirect
555. C₂²⋊Q₈	C₂⁵	semidirect
556. C₂²⋊Q₈	C₂⁵	semidirect
557. C₂²⋊Q₈	C₂⁵	semidirect
558. C₂²⋊Q₈	C₂⁵	semidirect
559. C₂²⋊Q₈	C₂⁵	semidirect
560. C₂²⋊Q₈	C₂⁵	semidirect
561. C₂²⋊Q₈	C₂⁵	semidirect
562. C₂²⋊Q₈	C₂⁵	semidirect
563. C₂²⋊Q₈	C₂⁵	semidirect
569. #121	C₂⁵	semidirect
570. #121	C₂⁵	semidirect
571. #121	C₂⁵	semidirect
572. #121	C₂⁵	semidirect
573. #121	C₂⁵	semidirect
574. #121	C₂⁵	semidirect
575. #121	C₂⁵	semidirect
578. C₄×Q₈	C₂⁵	semidirect
581. C₄×D₄	C₂⁵	semidirect
582. C₄×D₄	C₂⁵	semidirect
583. C₄×D₄	C₂⁵	semidirect
584. #117	C₂⁵	semidirect
600. C₂×C₄⋊C₄	C₂⁵	semidirect
601. C₂×C₄⋊C₄	C₂⁵	semidirect
602. C₂×C₄⋊C₄	C₂⁵	semidirect
798. C₂³	#3536	direct (N × H)
877. C₂²	C₂×#3536	direct (N × H)
899. C₂	C₂²×#3536	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#3536	2
C₂³×#562	2
C₂³×#554	2
C₂³×#547	2
C₂³×#548	2
C₂³×#546	2
C₂³×#542	2
C₂³×#537	2
C₂³×#539	2
C₂³×#538	2
C₂³×#543	2
C₂³×#525	2
C₂⁴×C₂²⋊Q₈	2
C₂⁴×#121	2

Subgroups — C23×#3536 #72301666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#3536 #72301666