Subgroups — C₂³×#3520 #72301664

Order 1024.

513125 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#3520	C₂	1	224	yes	maximal, direct product factor
2	C₂³×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×#552	C₂	1	2	yes	maximal, complemented
4	C₂³×#551	C₂	1	4	yes	maximal, complemented
5	C₂³×#554	C₂	1	2	yes	maximal, complemented
6	C₂³×#547	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×#547	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×#548	C₂	1	2	yes	maximal, complemented
9	C₂³×#546	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×#542	C₂	1	2	yes	maximal, complemented
12	C₂³×#539	C₂	1	4	yes	maximal, complemented
13	C₂³×#533	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×#529	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×#525	C₂	1	2	yes	maximal, complemented
16	C₂⁴×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
17	C₂³×#520	C₂	1	2	yes	maximal, complemented
18	C₂⁴×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂⁴×#41	C₂²	1	2	yes	—
20	C₂⁴×#41	C₂²	1	2	yes	complemented
21	C₂⁵×Q₈	C₂²	1	2	yes	complemented
22	C₂⁵×D₄	C₂²	1	1	yes	characteristic
23	C₂⁶×C₄	C₂²	1	2	yes	—
24	C₂×#3520	C₂²	1	7168	yes	direct product factor
25	C₂²×#556	C₂²	1	112	yes	complemented
26	C₂²×#552	C₂²	1	224	yes	complemented
27	C₂²×#551	C₂²	1	448	yes	complemented
28	C₂²×#554	C₂²	1	224	yes	complemented
29	C₂²×#547	C₂²	1	112	yes	complemented
30	C₂²×#547	C₂²	1	112	yes	complemented
31	C₂²×#548	C₂²	1	224	yes	complemented
32	C₂²×#546	C₂²	1	224	yes	complemented
33	C₂²×D₄×Q₈	C₂²	1	112	yes	complemented
34	C₂²×#542	C₂²	1	224	yes	complemented
35	C₂²×#539	C₂²	1	448	yes	complemented
36	C₂²×#533	C₂²	1	112	yes	complemented
37	C₂³×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂³×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂³×C₄⋊Q₈	C₂²	1	2	yes	complemented
40	C₂²×#529	C₂²	1	112	yes	complemented
41	C₂³×#126	C₂²	1	2	yes	complemented
42	C₂³×#126	C₂²	1	4	yes	complemented
43	C₂³×#126	C₂²	1	4	yes	complemented
44	C₂³×#125	C₂²	1	1	yes	characteristic, complemented
45	C₂³×#125	C₂²	1	2	yes	complemented
46	C₂³×#125	C₂²	1	4	yes	complemented
47	C₂³×#124	C₂²	1	2	yes	—
48	C₂³×#124	C₂²	1	1	yes	characteristic, complemented
49	C₂³×#124	C₂²	1	4	yes	complemented
50	C₂²×#525	C₂²	1	224	yes	complemented
51	C₂³×#123	C₂²	1	2	yes	—
52	C₂³×#123	C₂²	1	4	yes	—
53	C₂³×#123	C₂²	1	4	yes	complemented
54	C₂³×#123	C₂²	1	4	yes	complemented
55	C₂³×#123	C₂²	1	4	yes	complemented
56	C₂³×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
57	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	—
58	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	—
59	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	—
60	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	complemented
61	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	complemented
65	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	complemented
66	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	complemented
67	C₂³×C₂²⋊Q₈	C₂²	1	224	yes	complemented
68	C₂³×#121	C₂²	1	1	yes	characteristic
69	C₂³×#121	C₂²	1	4	yes	—
70	C₂³×#121	C₂²	1	2	yes	—
71	C₂³×#121	C₂²	1	2	yes	complemented
72	C₂³×#120	C₂²	1	4	yes	—
73	C₂²×#520	C₂²	1	224	yes	complemented
74	C₂³×C₄×Q₈	C₂²	1	2	yes	complemented
75	C₂³×C₄×Q₈	C₂²	1	2	yes	complemented
76	C₂³×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
77	C₂³×C₄×Q₈	C₂²	1	2	yes	complemented
78	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic
79	C₂³×C₄×D₄	C₂²	1	2	yes	—
80	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic
81	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic
82	C₂³×C₄×D₄	C₂²	1	2	yes	—
83	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic
84	C₂³×C₄×D₄	C₂²	1	2	yes	—
85	C₂³×C₄×D₄	C₂²	1	4	yes	—
86	C₂³×C₄×D₄	C₂²	1	2	yes	—
87	C₂³×C₄×D₄	C₂²	1	112	yes	complemented
88	C₂³×C₄×D₄	C₂²	1	4	yes	complemented
89	C₂³×C₄×D₄	C₂²	1	4	yes	complemented
90	C₂³×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
91	C₂³×#117	C₂²	1	2	yes	—
92	C₂³×#117	C₂²	1	2	yes	complemented
93	C₂³×#117	C₂²	1	4	yes	complemented
94	C₂³×#117	C₂²	1	2	yes	complemented
95	C₂⁴×C₄⋊C₄	C₂²	1	1	yes	characteristic
96	C₂⁴×C₄⋊C₄	C₂²	1	4	yes	complemented
97	C₂⁴×C₄⋊C₄	C₂²	1	2	yes	complemented
98	C₂⁴×C₄⋊C₄	C₂²	1	2	yes	complemented
99	C₂⁴×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₂⁴×C₂²⋊C₄	C₂²	1	4	yes	—
101	C₂⁴×C₄²	C₂²	1	1	yes	characteristic
102	C₂⁷	C₂³	1	2	yes	—
103	C₂³×#41	—	2	64	no	—
104	C₂³×#41	—	4	32	no	—
105	C₂³×#41	C₂³	1	112	yes	—
106	C₂³×#41	C₂³	1	112	yes	complemented
107	C₂⁴×Q₈	—	4	32	no	—
108	C₂⁴×Q₈	C₂³	1	1	yes	characteristic
109	C₂⁴×Q₈	C₂³	1	2	yes	—
110	C₂⁴×Q₈	C₂³	1	2	yes	—
111	C₂⁴×Q₈	C₂³	1	4	yes	—
112	C₂⁴×Q₈	C₂³	1	112	yes	complemented
113	C₂⁴×D₄	—	2	32	no	—
114	C₂⁴×D₄	C₂³	1	2	yes	—
115	C₂⁴×D₄	C₂³	1	1	yes	characteristic
116	C₂⁴×D₄	C₂³	1	56	yes	—
117	C₂⁴×D₄	C₂³	1	4	yes	—
118	C₂⁴×D₄	C₂³	1	1	yes	characteristic
119	C₂⁴×D₄	C₂³	1	2	yes	—
120	C₂⁴×D₄	C₂³	1	4	yes	—
121	C₂⁴×D₄	C₂³	1	1	yes	characteristic
122	C₂⁵×C₄	—	4	32	no	—
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	4	yes	—
128	C₂⁵×C₄	C₂³	1	2	yes	—
129	C₂⁵×C₄	C₂³	1	1	yes	characteristic
130	C₂⁵×C₄	C₂³	1	2	yes	—
131	C₂⁵×C₄	C₂³	1	2	yes	—
132	C₂⁵×C₄	C₂³	1	2	yes	—
133	C₂⁵×C₄	C₂³	1	112	yes	—
134	C₂⁵×C₄	C₂³	1	4	yes	—
135	C₂⁵×C₄	C₂³	1	4	yes	—
136	#3520	C₂³	1	32768	yes	direct product factor
137	C₂×#556	C₂³	1	1792	yes	complemented
138	C₂×#554	C₂³	1	3584	yes	complemented
139	C₂×#552	C₂³	1	3584	yes	complemented
140	C₂×#551	C₂³	1	7168	yes	complemented
141	C₂×D₄×Q₈	C₂³	1	1792	yes	complemented
142	C₂×#548	C₂³	1	3584	yes	complemented
143	C₂×#547	C₂³	1	1792	yes	complemented
144	C₂×#547	C₂³	1	1792	yes	complemented
145	C₂×#546	C₂³	1	3584	yes	complemented
146	C₂×#542	C₂³	1	3584	yes	complemented
147	C₂×#539	C₂³	1	7168	yes	complemented
148	C₂×#533	C₂³	1	1792	yes	complemented
149	C₂²×C₄⋊Q₈	C₂³	1	56	yes	complemented
150	C₂²×C₄⋊Q₈	C₂³	1	56	yes	complemented
151	C₂²×C₄⋊Q₈	C₂³	1	112	yes	complemented
152	C₂×#529	C₂³	1	1792	yes	complemented
153	C₂²×#126	C₂³	1	112	yes	complemented
154	C₂²×#126	C₂³	1	224	yes	complemented
155	C₂²×#126	C₂³	1	224	yes	complemented
156	C₂²×#125	C₂³	1	56	yes	complemented
157	C₂²×#125	C₂³	1	112	yes	complemented
158	C₂²×#125	C₂³	1	224	yes	complemented
159	C₂²×#124	C₂³	1	112	yes	—
160	C₂²×#124	C₂³	1	56	yes	complemented
161	C₂²×#124	C₂³	1	224	yes	complemented
162	C₂×#525	C₂³	1	3584	yes	complemented
163	C₂²×#123	C₂³	1	112	yes	—
164	C₂²×#123	C₂³	1	224	yes	—
165	C₂²×#123	C₂³	1	224	yes	complemented
166	C₂²×#123	C₂³	1	224	yes	complemented
167	C₂²×#123	C₂³	1	224	yes	complemented
168	C₂²×C₂²⋊Q₈	C₂³	1	56	yes	—
169	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	—
170	C₂²×C₂²⋊Q₈	C₂³	1	224	yes	—
171	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	—
172	C₂²×C₂²⋊Q₈	C₂³	1	224	yes	complemented
173	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	complemented
174	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	complemented
175	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	complemented
176	C₂²×C₂²⋊Q₈	C₂³	1	224	yes	complemented
177	C₂²×C₂²⋊Q₈	C₂³	1	224	yes	complemented
178	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	complemented
179	C₂²×C₂²⋊Q₈	C₂³	1	3584	yes	complemented
180	C₂²×#121	C₂³	1	56	yes	—
181	C₂²×#121	C₂³	1	224	yes	—
182	C₂²×#121	C₂³	1	112	yes	—
183	C₂²×#121	C₂³	1	112	yes	complemented
184	C₂²×#120	C₂³	1	224	yes	—
185	C₂×#520	C₂³	1	3584	yes	complemented
186	C₂²×C₄×Q₈	C₂³	1	112	yes	complemented
187	C₂²×C₄×Q₈	C₂³	1	112	yes	complemented
188	C₂²×C₄×Q₈	C₂³	1	56	yes	complemented
189	C₂²×C₄×Q₈	C₂³	1	112	yes	complemented
190	C₂²×C₄×D₄	C₂³	1	56	yes	—
191	C₂²×C₄×D₄	C₂³	1	112	yes	—
192	C₂²×C₄×D₄	C₂³	1	56	yes	—
193	C₂²×C₄×D₄	C₂³	1	56	yes	—
194	C₂²×C₄×D₄	C₂³	1	112	yes	—
195	C₂²×C₄×D₄	C₂³	1	56	yes	—
196	C₂²×C₄×D₄	C₂³	1	112	yes	—
197	C₂²×C₄×D₄	C₂³	1	224	yes	—
198	C₂²×C₄×D₄	C₂³	1	112	yes	—
199	C₂²×C₄×D₄	C₂³	1	1792	yes	complemented
200	C₂²×C₄×D₄	C₂³	1	224	yes	complemented
201	C₂²×C₄×D₄	C₂³	1	224	yes	complemented
202	C₂²×C₄×D₄	C₂³	1	56	yes	complemented
203	C₂²×#117	C₂³	1	112	yes	—
204	C₂²×#117	C₂³	1	112	yes	complemented
205	C₂²×#117	C₂³	1	224	yes	complemented
206	C₂²×#117	C₂³	1	112	yes	complemented
207	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
208	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
209	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
210	C₂³×C₄⋊C₄	C₂³	1	56	yes	—
211	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
212	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
213	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
214	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
215	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
216	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
217	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
218	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
219	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
220	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
221	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
222	C₂³×C₄⋊C₄	C₂³	1	1	yes	characteristic
223	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
224	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
225	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
226	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
227	C₂³×C₄⋊C₄	C₂³	1	224	yes	complemented
228	C₂³×C₄⋊C₄	C₂³	1	112	yes	complemented
229	C₂³×C₄⋊C₄	C₂³	1	112	yes	complemented
230	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
231	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
232	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
234	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₂³×C₂²⋊C₄	C₂³	1	112	yes	—
237	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
238	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
239	C₂³×C₂²⋊C₄	C₂³	1	224	yes	—
240	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
241	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
242	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
243	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
244	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
245	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
246	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
247	C₂³×C₄²	C₂³	1	1	yes	characteristic
248	C₂³×C₄²	C₂³	1	1	yes	characteristic
249	C₂³×C₄²	C₂³	1	1	yes	characteristic
250	C₂³×C₄²	C₂³	1	1	yes	characteristic
251	C₂³×C₄²	C₂³	1	56	yes	—
252	C₂³×C₄²	C₂³	1	4	yes	—
253	C₂³×C₄²	C₂³	1	4	yes	—
254	C₂³×C₄²	C₂³	1	2	yes	—
255	C₂⁶	—	2	32	no	—
256	C₂⁶	—	2	32	no	—
257	C₂⁶	—	4	16	no	—
258	C₂⁶	C₂⁴	1	2	yes	—
259	C₂⁶	C₂⁴	1	2	yes	—
260	C₂⁶	C₂⁴	1	56	yes	—
261	C₂⁶	C₂⁴	1	2	yes	—
262	C₂⁶	C₂⁴	1	1	yes	characteristic
263	C₂²×#41	—	2	1792	no	—
264	C₂²×#41	—	4	896	no	—
265	C₂²×#41	C₂⁴	1	896	yes	—
266	C₂²×#41	C₂⁴	1	896	yes	complemented
267	C₂³×Q₈	—	2	32	no	—
268	C₂³×Q₈	—	2	16	no	—
269	C₂³×Q₈	—	2	32	no	—
270	C₂³×Q₈	—	4	32	no	—
271	C₂³×Q₈	—	4	896	no	—
272	C₂³×Q₈	C₂⁴	1	28	yes	—
273	C₂³×Q₈	C₂⁴	1	56	yes	—
274	C₂³×Q₈	C₂⁴	1	56	yes	—
275	C₂³×Q₈	C₂⁴	1	112	yes	—
276	C₂³×Q₈	C₂⁴	1	896	yes	complemented
277	C₂³×D₄	—	2	32	no	—
278	C₂³×D₄	—	2	64	no	—
279	C₂³×D₄	—	2	32	no	—
280	C₂³×D₄	—	2	896	no	—
281	C₂³×D₄	—	2	16	no	—
282	C₂³×D₄	—	2	16	no	—
283	C₂³×D₄	—	4	32	no	—
284	C₂³×D₄	#41	1	32	yes	complemented
285	C₂³×D₄	C₂⁴	1	56	yes	—
286	C₂³×D₄	C₂⁴	1	28	yes	—
287	C₂³×D₄	C₂⁴	1	448	yes	—
288	C₂³×D₄	C₂⁴	1	112	yes	—
289	C₂³×D₄	C₂⁴	1	28	yes	—
290	C₂³×D₄	C₂⁴	1	56	yes	—
291	C₂³×D₄	C₂⁴	1	112	yes	—
292	C₂³×D₄	C₂⁴	1	28	yes	—
293	C₂⁴×C₄	—	2	64	no	—
294	C₂⁴×C₄	—	2	16	no	—
295	C₂⁴×C₄	—	2	16	no	—
296	C₂⁴×C₄	—	2	32	no	—
297	C₂⁴×C₄	—	2	16	no	—
298	C₂⁴×C₄	—	2	32	no	—
299	C₂⁴×C₄	—	2	32	no	—
300	C₂⁴×C₄	—	4	896	no	—
301	C₂⁴×C₄	—	4	16	no	—
302	C₂⁴×C₄	—	4	16	no	—
303	C₂⁴×C₄	—	4	16	no	—
304	C₂⁴×C₄	—	4	32	no	—
305	C₂⁴×C₄	—	4	32	no	—
306	C₂⁴×C₄	C₂⁴	1	28	yes	—
307	C₂⁴×C₄	C₂⁴	1	56	yes	—
308	C₂⁴×C₄	C₂⁴	1	56	yes	—
309	C₂⁴×C₄	C₂⁴	1	28	yes	—
310	C₂⁴×C₄	C₂⁴	1	112	yes	—
311	C₂⁴×C₄	C₂⁴	1	56	yes	—
312	C₂⁴×C₄	C₂⁴	1	28	yes	—
313	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
314	C₂⁴×C₄	C₂⁴	1	2	yes	—
315	C₂⁴×C₄	C₂⁴	1	2	yes	—
316	C₂⁴×C₄	C₂⁴	1	2	yes	—
317	C₂⁴×C₄	C₂⁴	1	4	yes	—
318	C₂⁴×C₄	C₂⁴	1	2	yes	—
319	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
320	C₂⁴×C₄	C₂⁴	1	4	yes	—
321	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
322	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
323	C₂⁴×C₄	C₂⁴	1	2	yes	—
324	C₂⁴×C₄	C₂⁴	1	56	yes	—
325	C₂⁴×C₄	C₂⁴	1	56	yes	—
326	C₂⁴×C₄	C₂⁴	1	56	yes	—
327	C₂⁴×C₄	C₂⁴	1	896	yes	—
328	C₂⁴×C₄	C₂⁴	1	112	yes	—
329	C₂⁴×C₄	C₂⁴	1	112	yes	—
330	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
331	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
332	#556	C₂⁴	1	4096	yes	complemented
333	#554	C₂⁴	1	8192	yes	complemented
334	#552	C₂⁴	1	8192	yes	complemented
335	#551	C₂⁴	1	16384	yes	complemented
336	D₄×Q₈	C₂⁴	1	4096	yes	complemented
337	#548	C₂⁴	1	8192	yes	complemented
338	#547	C₂⁴	1	4096	yes	complemented
339	#547	C₂⁴	1	4096	yes	complemented
340	#546	C₂⁴	1	8192	yes	complemented
341	#542	C₂⁴	1	8192	yes	complemented
342	#539	C₂⁴	1	16384	yes	complemented
343	#533	C₂⁴	1	4096	yes	complemented
344	C₂×C₄⋊Q₈	C₂⁴	1	448	yes	complemented
345	C₂×C₄⋊Q₈	C₂⁴	1	448	yes	complemented
346	C₂×C₄⋊Q₈	C₂⁴	1	896	yes	complemented
347	#529	C₂⁴	1	4096	yes	complemented
348	C₂×#126	C₂⁴	1	896	yes	complemented
349	C₂×#126	C₂⁴	1	1792	yes	complemented
350	C₂×#126	C₂⁴	1	1792	yes	complemented
351	C₂×#125	C₂⁴	1	448	yes	complemented
352	C₂×#125	C₂⁴	1	896	yes	complemented
353	C₂×#125	C₂⁴	1	1792	yes	complemented
354	C₂×#124	C₂⁴	1	896	yes	—
355	C₂×#124	C₂⁴	1	448	yes	complemented
356	C₂×#124	C₂⁴	1	1792	yes	complemented
357	#525	C₂⁴	1	8192	yes	complemented
358	C₂×#123	C₂⁴	1	896	yes	—
359	C₂×#123	C₂⁴	1	1792	yes	—
360	C₂×#123	C₂⁴	1	1792	yes	complemented
361	C₂×#123	C₂⁴	1	1792	yes	complemented
362	C₂×#123	C₂⁴	1	1792	yes	complemented
363	C₂×C₂²⋊Q₈	C₂⁴	1	448	yes	—
364	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	—
365	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	—
366	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	—
367	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	complemented
368	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	complemented
369	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	complemented
370	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	complemented
371	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	complemented
372	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	complemented
373	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	complemented
374	C₂×C₂²⋊Q₈	C₂⁴	1	8192	yes	complemented
375	C₂×#121	C₂⁴	1	448	yes	—
376	C₂×#121	C₂⁴	1	1792	yes	—
377	C₂×#121	C₂⁴	1	896	yes	—
378	C₂×#121	C₂⁴	1	896	yes	complemented
379	C₂×#120	C₂⁴	1	1792	yes	—
380	#520	C₂⁴	1	8192	yes	complemented
381	C₂×C₄×Q₈	C₂⁴	1	896	yes	complemented
382	C₂×C₄×Q₈	C₂⁴	1	896	yes	complemented
383	C₂×C₄×Q₈	C₂⁴	1	448	yes	complemented
384	C₂×C₄×Q₈	C₂⁴	1	896	yes	complemented
385	C₂×C₄×D₄	C₂⁴	1	448	yes	—
386	C₂×C₄×D₄	C₂⁴	1	896	yes	—
387	C₂×C₄×D₄	C₂⁴	1	448	yes	—
388	C₂×C₄×D₄	C₂⁴	1	448	yes	—
389	C₂×C₄×D₄	C₂⁴	1	448	yes	—
390	C₂×C₄×D₄	C₂⁴	1	896	yes	—
391	C₂×C₄×D₄	C₂⁴	1	896	yes	—
392	C₂×C₄×D₄	C₂⁴	1	1792	yes	—
393	C₂×C₄×D₄	C₂⁴	1	896	yes	—
394	C₂×C₄×D₄	C₂⁴	1	4096	yes	complemented
395	C₂×C₄×D₄	C₂⁴	1	1792	yes	complemented
396	C₂×C₄×D₄	C₂⁴	1	1792	yes	complemented
397	C₂×C₄×D₄	C₂⁴	1	448	yes	complemented
398	C₂×#117	C₂⁴	1	896	yes	—
399	C₂×#117	C₂⁴	1	896	yes	complemented
400	C₂×#117	C₂⁴	1	1792	yes	complemented
401	C₂×#117	C₂⁴	1	896	yes	complemented
402	C₂²×C₄⋊C₄	C₂⁴	1	28	yes	—
403	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
404	C₂²×C₄⋊C₄	C₂⁴	1	28	yes	—
405	C₂²×C₄⋊C₄	C₂⁴	1	448	yes	—
406	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
407	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
408	C₂²×C₄⋊C₄	C₂⁴	1	28	yes	—
409	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
410	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
411	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
412	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
413	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
414	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
415	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
416	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
417	C₂²×C₄⋊C₄	C₂⁴	1	28	yes	—
418	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
419	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
420	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
421	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
422	C₂²×C₄⋊C₄	C₂⁴	1	1792	yes	complemented
423	C₂²×C₄⋊C₄	C₂⁴	1	896	yes	complemented
424	C₂²×C₄⋊C₄	C₂⁴	1	896	yes	complemented
425	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
426	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
427	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
428	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
429	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
430	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
431	C₂²×C₂²⋊C₄	C₂⁴	1	896	yes	—
432	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
433	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
434	C₂²×C₂²⋊C₄	C₂⁴	1	1792	yes	—
435	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
436	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
437	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
438	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
439	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
440	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
441	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
442	C₂²×C₄²	C₂⁴	1	28	yes	—
443	C₂²×C₄²	C₂⁴	1	28	yes	—
444	C₂²×C₄²	C₂⁴	1	28	yes	—
445	C₂²×C₄²	C₂⁴	1	28	yes	—
446	C₂²×C₄²	C₂⁴	1	448	yes	—
447	C₂²×C₄²	C₂⁴	1	112	yes	—
448	C₂²×C₄²	C₂⁴	1	112	yes	—
449	C₂²×C₄²	C₂⁴	1	56	yes	—
450	C₂⁵	—	2	8	no	—
451	C₂⁵	—	2	16	no	—
452	C₂⁵	—	2	8	no	—
453	C₂⁵	—	2	16	no	—
454	C₂⁵	—	2	16	no	—
455	C₂⁵	—	2	448	no	—
456	C₂⁵	—	2	16	no	—
457	C₂⁵	—	2	16	no	—
458	C₂⁵	—	2	16	no	—
459	C₂⁵	—	2	16	no	—
460	C₂⁵	—	2	448	no	—
461	C₂⁵	—	2	16	no	—
462	C₂⁵	—	4	224	no	—
463	C₂⁵	—	4	512	no	—
464	C₂⁵	C₂×#41	1	32	yes	—
465	C₂⁵	2₋¹⁺⁴	1	16	yes	—
466	C₂⁵	C₂⁵	1	28	yes	—
467	C₂⁵	C₂⁵	1	28	yes	—
468	C₂⁵	C₂⁵	1	224	yes	—
469	C₂⁵	C₂⁵	1	28	yes	—
470	C₂⁵	C₂⁵	1	14	yes	—
471	C₂⁵	C₂⁵	1	1	yes	characteristic
472	C₂×#41	—	2	7168	no	—
473	C₂×#41	—	4	3584	no	—
474	C₂×#41	C₂⁵	1	1024	yes	—
475	C₂×#41	C₂⁵	1	1024	yes	complemented
476	C₂²×Q₈	—	2	448	no	—
477	C₂²×Q₈	—	2	224	no	—
478	C₂²×Q₈	—	2	448	no	—
479	C₂²×Q₈	—	4	448	no	—
480	C₂²×Q₈	—	4	3584	no	—
481	C₂²×Q₈	C₂⁵	1	224	yes	—
482	C₂²×Q₈	C₂⁵	1	112	yes	—
483	C₂²×Q₈	C₂⁵	1	224	yes	—
484	C₂²×Q₈	C₂⁵	1	448	yes	—
485	C₂²×Q₈	C₂⁵	1	1024	yes	complemented
486	C₂²×D₄	—	2	448	no	—
487	C₂²×D₄	—	2	896	no	—
488	C₂²×D₄	—	2	448	no	—
489	C₂²×D₄	—	2	3584	no	—
490	C₂²×D₄	—	2	224	no	—
491	C₂²×D₄	—	2	224	no	—
492	C₂²×D₄	—	4	448	no	—
493	C₂²×D₄	C₂×#41	1	448	yes	complemented
494	C₂²×D₄	C₂⁵	1	224	yes	—
495	C₂²×D₄	C₂⁵	1	224	yes	—
496	C₂²×D₄	C₂⁵	1	112	yes	—
497	C₂²×D₄	C₂⁵	1	448	yes	—
498	C₂²×D₄	C₂⁵	1	512	yes	—
499	C₂²×D₄	C₂⁵	1	112	yes	—
500	C₂²×D₄	C₂⁵	1	448	yes	—
501	C₂²×D₄	C₂⁵	1	112	yes	—
502	C₂³×C₄	—	2	16	no	—
503	C₂³×C₄	—	2	8	no	—
504	C₂³×C₄	—	2	32	no	—
505	C₂³×C₄	—	2	896	no	—
506	C₂³×C₄	—	2	8	no	—
507	C₂³×C₄	—	2	16	no	—
508	C₂³×C₄	—	2	16	no	—
509	C₂³×C₄	—	2	32	no	—
510	C₂³×C₄	—	2	16	no	—
511	C₂³×C₄	—	2	224	no	—
512	C₂³×C₄	—	2	8	no	—
513	C₂³×C₄	—	2	8	no	—
514	C₂³×C₄	—	2	16	no	—
515	C₂³×C₄	—	2	224	no	—
516	C₂³×C₄	—	2	448	no	—
517	C₂³×C₄	—	2	224	no	—
518	C₂³×C₄	—	2	448	no	—
519	C₂³×C₄	—	2	448	no	—
520	C₂³×C₄	—	4	3584	no	—
521	C₂³×C₄	—	4	224	no	—
522	C₂³×C₄	—	4	224	no	—
523	C₂³×C₄	—	4	224	no	—
524	C₂³×C₄	—	4	448	no	—
525	C₂³×C₄	—	4	448	no	—
526	C₂³×C₄	C₂×#41	1	16	yes	—
527	C₂³×C₄	H(5,𝔽₂)	1	16	yes	—
528	C₂³×C₄	C₂⁵	1	14	yes	—
529	C₂³×C₄	C₂⁵	1	14	yes	—
530	C₂³×C₄	C₂⁵	1	28	yes	—
531	C₂³×C₄	C₂⁵	1	28	yes	—
532	C₂³×C₄	C₂⁵	1	28	yes	—
533	C₂³×C₄	C₂⁵	1	28	yes	—
534	C₂³×C₄	C₂⁵	1	56	yes	—
535	C₂³×C₄	C₂⁵	1	112	yes	—
536	C₂³×C₄	C₂⁵	1	56	yes	—
537	C₂³×C₄	C₂⁵	1	14	yes	—
538	C₂³×C₄	C₂⁵	1	28	yes	—
539	C₂³×C₄	C₂⁵	1	14	yes	—
540	C₂³×C₄	C₂⁵	1	448	yes	—
541	C₂³×C₄	C₂⁵	1	112	yes	—
542	C₂³×C₄	C₂⁵	1	224	yes	—
543	C₂³×C₄	C₂⁵	1	224	yes	—
544	C₂³×C₄	C₂⁵	1	224	yes	—
545	C₂³×C₄	C₂⁵	1	112	yes	—
546	C₂³×C₄	C₂⁵	1	224	yes	—
547	C₂³×C₄	C₂⁵	1	448	yes	—
548	C₂³×C₄	C₂⁵	1	224	yes	—
549	C₂³×C₄	C₂⁵	1	448	yes	—
550	C₂³×C₄	C₂⁵	1	224	yes	—
551	C₂³×C₄	C₂⁵	1	1024	yes	—
552	C₂³×C₄	C₂⁵	1	14	yes	—
553	C₂³×C₄	C₂⁵	1	14	yes	—
554	C₄⋊Q₈	C₂⁵	1	512	yes	complemented
555	C₄⋊Q₈	C₂⁵	1	512	yes	complemented
556	C₄⋊Q₈	C₂⁵	1	1024	yes	complemented
557	#126	C₂⁵	1	1024	yes	complemented
558	#126	C₂⁵	1	2048	yes	complemented
559	#126	C₂⁵	1	2048	yes	complemented
560	#125	C₂⁵	1	512	yes	complemented
561	#125	C₂⁵	1	1024	yes	complemented
562	#125	C₂⁵	1	2048	yes	complemented
563	#124	C₂⁵	1	1024	yes	—
564	#124	C₂⁵	1	512	yes	complemented
565	#124	C₂⁵	1	2048	yes	complemented
566	#123	C₂⁵	1	1024	yes	—
567	#123	C₂⁵	1	2048	yes	—
568	#123	C₂⁵	1	2048	yes	complemented
569	#123	C₂⁵	1	2048	yes	complemented
570	#123	C₂⁵	1	2048	yes	complemented
571	C₂²⋊Q₈	C₂⁵	1	512	yes	—
572	C₂²⋊Q₈	C₂⁵	1	1024	yes	—
573	C₂²⋊Q₈	C₂⁵	1	2048	yes	—
574	C₂²⋊Q₈	C₂⁵	1	1024	yes	—
575	C₂²⋊Q₈	C₂⁵	1	2048	yes	complemented
576	C₂²⋊Q₈	C₂⁵	1	1024	yes	complemented
577	C₂²⋊Q₈	C₂⁵	1	1024	yes	complemented
578	C₂²⋊Q₈	C₂⁵	1	1024	yes	complemented
579	C₂²⋊Q₈	C₂⁵	1	2048	yes	complemented
580	C₂²⋊Q₈	C₂⁵	1	2048	yes	complemented
581	C₂²⋊Q₈	C₂⁵	1	1024	yes	complemented
582	#121	C₂⁵	1	512	yes	—
583	#121	C₂⁵	1	2048	yes	—
584	#121	C₂⁵	1	1024	yes	—
585	#121	C₂⁵	1	1024	yes	complemented
586	#120	C₂⁵	1	2048	yes	—
587	C₄×Q₈	C₂⁵	1	1024	yes	complemented
588	C₄×Q₈	C₂⁵	1	1024	yes	complemented
589	C₄×Q₈	C₂⁵	1	512	yes	complemented
590	C₄×Q₈	C₂⁵	1	1024	yes	complemented
591	C₄×D₄	C₂⁵	1	512	yes	—
592	C₄×D₄	C₂⁵	1	1024	yes	—
593	C₄×D₄	C₂⁵	1	512	yes	—
594	C₄×D₄	C₂⁵	1	512	yes	—
595	C₄×D₄	C₂⁵	1	512	yes	—
596	C₄×D₄	C₂⁵	1	1024	yes	—
597	C₄×D₄	C₂⁵	1	1024	yes	—
598	C₄×D₄	C₂⁵	1	2048	yes	—
599	C₄×D₄	C₂⁵	1	1024	yes	—
600	C₄×D₄	C₂⁵	1	2048	yes	complemented
601	C₄×D₄	C₂⁵	1	2048	yes	complemented
602	C₄×D₄	C₂⁵	1	512	yes	complemented
603	#117	C₂⁵	1	1024	yes	—
604	#117	C₂⁵	1	1024	yes	complemented
605	#117	C₂⁵	1	2048	yes	complemented
606	#117	C₂⁵	1	1024	yes	complemented
607	C₂×C₄⋊C₄	C₂⁵	1	112	yes	—
608	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
609	C₂×C₄⋊C₄	C₂⁵	1	112	yes	—
610	C₂×C₄⋊C₄	C₂⁵	1	512	yes	—
611	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
612	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
613	C₂×C₄⋊C₄	C₂⁵	1	112	yes	—
614	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
615	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
616	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
617	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
618	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
619	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
620	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
621	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
622	C₂×C₄⋊C₄	C₂⁵	1	112	yes	—
623	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
624	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
625	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
626	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
627	C₂×C₄⋊C₄	C₂⁵	1	2048	yes	complemented
628	C₂×C₄⋊C₄	C₂⁵	1	1024	yes	complemented
629	C₂×C₄⋊C₄	C₂⁵	1	1024	yes	complemented
630	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
631	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
632	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
633	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
634	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
635	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
636	C₂×C₂²⋊C₄	C₂⁵	1	1024	yes	—
637	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
638	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
639	C₂×C₂²⋊C₄	C₂⁵	1	2048	yes	—
640	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
641	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
642	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
643	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
644	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
645	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
646	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
647	C₂×C₄²	C₂⁵	1	448	yes	—
648	C₂×C₄²	C₂⁵	1	112	yes	—
649	C₂×C₄²	C₂⁵	1	448	yes	—
650	C₂×C₄²	C₂⁵	1	224	yes	—
651	C₂×C₄²	C₂⁵	1	112	yes	—
652	C₂×C₄²	C₂⁵	1	112	yes	—
653	C₂×C₄²	C₂⁵	1	112	yes	—
654	C₂×C₄²	C₂⁵	1	512	yes	—
655	C₂⁴	—	2	56	no	—
656	C₂⁴	—	2	112	no	—
657	C₂⁴	—	2	56	no	—
658	C₂⁴	—	2	112	no	—
659	C₂⁴	—	2	128	no	—
660	C₂⁴	—	2	256	no	—
661	C₂⁴	—	2	112	no	—
662	C₂⁴	—	2	896	no	—
663	C₂⁴	—	2	112	no	—
664	C₂⁴	—	2	112	no	—
665	C₂⁴	—	2	112	no	—
666	C₂⁴	—	2	112	no	—
667	C₂⁴	—	2	896	no	—
668	C₂⁴	—	2	112	no	—
669	C₂⁴	—	4	448	no	—
670	C₂⁴	—	4	3584	no	—
671	C₂⁴	—	4	128	no	—
672	C₂⁴	—	4	128	no	—
673	C₂⁴	C₂²×#41	1	224	yes	—
674	C₂⁴	C₂²×#41	1	8	yes	—
675	C₂⁴	C₂×H(5,𝔽₂)	1	8	yes	—
676	C₂⁴	C₂×2₋¹⁺⁴	1	112	yes	—
677	C₂⁴	C₂×2₋¹⁺⁴	1	8	yes	—
678	C₂⁴	C₂⁶	1	56	yes	—
679	C₂⁴	C₂⁶	1	56	yes	—
680	C₂⁴	C₂⁶	1	128	yes	—
681	C₂⁴	C₂⁶	1	56	yes	—
682	C₂⁴	C₂⁶	1	28	yes	—
683	C₂⁴	C₂⁶	1	7	yes	—
684	#41	—	2	4096	no	—
685	#41	—	4	2048	no	—
686	C₂×Q₈	—	2	896	no	—
687	C₂×Q₈	—	2	448	no	—
688	C₂×Q₈	—	2	896	no	—
689	C₂×Q₈	—	4	896	no	—
690	C₂×Q₈	—	4	2048	no	—
691	C₂×Q₈	C₂⁶	1	128	yes	—
692	C₂×Q₈	C₂⁶	1	64	yes	—
693	C₂×Q₈	C₂⁶	1	128	yes	—
694	C₂×Q₈	C₂⁶	1	256	yes	—
695	C₂×D₄	—	2	896	no	—
696	C₂×D₄	—	2	1792	no	—
697	C₂×D₄	—	2	896	no	—
698	C₂×D₄	—	2	2048	no	—
699	C₂×D₄	—	2	448	no	—
700	C₂×D₄	—	2	448	no	—
701	C₂×D₄	—	4	896	no	—
702	C₂×D₄	C₂²×#41	1	896	yes	complemented
703	C₂×D₄	C₂⁶	1	128	yes	—
704	C₂×D₄	C₂⁶	1	128	yes	—
705	C₂×D₄	C₂⁶	1	64	yes	—
706	C₂×D₄	C₂⁶	1	256	yes	—
707	C₂×D₄	C₂⁶	1	64	yes	—
708	C₂×D₄	C₂⁶	1	256	yes	—
709	C₂×D₄	C₂⁶	1	64	yes	—
710	C₂²×C₄	—	2	112	no	—
711	C₂²×C₄	—	2	56	no	—
712	C₂²×C₄	—	2	224	no	—
713	C₂²×C₄	—	2	1792	no	—
714	C₂²×C₄	—	2	56	no	—
715	C₂²×C₄	—	2	112	no	—
716	C₂²×C₄	—	2	112	no	—
717	C₂²×C₄	—	2	224	no	—
718	C₂²×C₄	—	2	112	no	—
719	C₂²×C₄	—	2	448	no	—
720	C₂²×C₄	—	2	56	no	—
721	C₂²×C₄	—	2	56	no	—
722	C₂²×C₄	—	2	112	no	—
723	C₂²×C₄	—	2	448	no	—
724	C₂²×C₄	—	2	896	no	—
725	C₂²×C₄	—	2	448	no	—
726	C₂²×C₄	—	2	896	no	—
727	C₂²×C₄	—	2	896	no	—
728	C₂²×C₄	—	4	2048	no	—
729	C₂²×C₄	—	4	448	no	—
730	C₂²×C₄	—	4	448	no	—
731	C₂²×C₄	—	4	448	no	—
732	C₂²×C₄	—	4	896	no	—
733	C₂²×C₄	—	4	896	no	—
734	C₂²×C₄	C₂²×#41	1	112	yes	—
735	C₂²×C₄	C₂×H(5,𝔽₂)	1	112	yes	—
736	C₂²×C₄	C₂⁶	1	28	yes	—
737	C₂²×C₄	C₂⁶	1	56	yes	—
738	C₂²×C₄	C₂⁶	1	28	yes	—
739	C₂²×C₄	C₂⁶	1	112	yes	—
740	C₂²×C₄	C₂⁶	1	64	yes	—
741	C₂²×C₄	C₂⁶	1	28	yes	—
742	C₂²×C₄	C₂⁶	1	28	yes	—
743	C₂²×C₄	C₂⁶	1	56	yes	—
744	C₂²×C₄	C₂⁶	1	64	yes	—
745	C₂²×C₄	C₂⁶	1	64	yes	—
746	C₂²×C₄	C₂⁶	1	56	yes	—
747	C₂²×C₄	C₂⁶	1	112	yes	—
748	C₂²×C₄	C₂⁶	1	56	yes	—
749	C₂²×C₄	C₂⁶	1	56	yes	—
750	C₂²×C₄	C₂⁶	1	256	yes	—
751	C₂²×C₄	C₂⁶	1	128	yes	—
752	C₂²×C₄	C₂⁶	1	128	yes	—
753	C₂²×C₄	C₂⁶	1	128	yes	—
754	C₂²×C₄	C₂⁶	1	128	yes	—
755	C₂²×C₄	C₂⁶	1	256	yes	—
756	C₂²×C₄	C₂⁶	1	128	yes	—
757	C₂²×C₄	C₂⁶	1	256	yes	—
758	C₂²×C₄	C₂⁶	1	128	yes	—
759	C₂²×C₄	C₂⁶	1	28	yes	—
760	C₂²×C₄	C₂⁶	1	28	yes	—
761	C₄⋊C₄	C₂⁶	1	64	yes	—
762	C₄⋊C₄	C₂⁶	1	128	yes	—
763	C₄⋊C₄	C₂⁶	1	64	yes	—
764	C₄⋊C₄	C₂⁶	1	128	yes	—
765	C₄⋊C₄	C₂⁶	1	256	yes	—
766	C₄⋊C₄	C₂⁶	1	64	yes	—
767	C₄⋊C₄	C₂⁶	1	128	yes	—
768	C₄⋊C₄	C₂⁶	1	128	yes	—
769	C₄⋊C₄	C₂⁶	1	256	yes	—
770	C₄⋊C₄	C₂⁶	1	256	yes	—
771	C₄⋊C₄	C₂⁶	1	256	yes	—
772	C₄⋊C₄	C₂⁶	1	128	yes	—
773	C₄⋊C₄	C₂⁶	1	128	yes	—
774	C₄⋊C₄	C₂⁶	1	128	yes	—
775	C₄⋊C₄	C₂⁶	1	64	yes	—
776	C₄⋊C₄	C₂⁶	1	256	yes	—
777	C₄⋊C₄	C₂⁶	1	128	yes	—
778	C₄⋊C₄	C₂⁶	1	256	yes	—
779	C₄⋊C₄	C₂⁶	1	128	yes	—
780	C₂²⋊C₄	C₂⁶	1	128	yes	—
781	C₂²⋊C₄	C₂⁶	1	256	yes	—
782	C₂²⋊C₄	C₂⁶	1	128	yes	—
783	C₂²⋊C₄	C₂⁶	1	128	yes	—
784	C₂²⋊C₄	C₂⁶	1	128	yes	—
785	C₂²⋊C₄	C₂⁶	1	128	yes	—
786	C₂²⋊C₄	C₂⁶	1	256	yes	—
787	C₂²⋊C₄	C₂⁶	1	256	yes	—
788	C₂²⋊C₄	C₂⁶	1	256	yes	—
789	C₂²⋊C₄	C₂⁶	1	128	yes	—
790	C₂²⋊C₄	C₂⁶	1	128	yes	—
791	C₂²⋊C₄	C₂⁶	1	256	yes	—
792	C₂²⋊C₄	C₂⁶	1	128	yes	—
793	C₂²⋊C₄	C₂⁶	1	256	yes	—
794	C₂²⋊C₄	C₂⁶	1	128	yes	—
795	C₄²	C₂⁶	1	64	yes	—
796	C₄²	C₂⁶	1	64	yes	—
797	C₄²	C₂⁶	1	64	yes	—
798	C₄²	C₂⁶	1	64	yes	—
799	C₄²	C₂⁶	1	256	yes	—
800	C₄²	C₂⁶	1	256	yes	—
801	C₄²	C₂⁶	1	128	yes	—
802	C₂³	—	2	448	no	—
803	C₂³	—	2	896	no	—
804	C₂³	—	2	56	no	—
805	C₂³	—	2	112	no	—
806	C₂³	—	2	56	no	—
807	C₂³	—	2	112	no	—
808	C₂³	—	2	112	no	—
809	C₂³	—	2	256	no	—
810	C₂³	—	2	112	no	—
811	C₂³	—	2	112	no	—
812	C₂³	—	2	112	no	—
813	C₂³	—	2	112	no	—
814	C₂³	—	2	256	no	—
815	C₂³	—	2	112	no	—
816	C₂³	—	4	128	no	—
817	C₂³	—	4	3584	no	—
818	C₂³	—	4	448	no	—
819	C₂³	—	4	448	no	—
820	C₂³	#3520	1	64	yes	direct product factor
821	C₂³	C₂³×#41	1	224	yes	—
822	C₂³	C₂³×#41	1	28	yes	—
823	C₂³	C₂²×H(5,𝔽₂)	1	28	yes	—
824	C₂³	C₂²×2₋¹⁺⁴	1	112	yes	—
825	C₂³	C₂²×2₋¹⁺⁴	1	28	yes	—
826	C₂³	C₂⁷	1	16	yes	—
827	C₂³	C₂⁷	1	16	yes	—
828	C₂³	C₂⁷	1	16	yes	—
829	C₂³	C₂⁷	1	8	yes	—
830	C₂³	C₂⁷	1	7	yes	—
831	Q₈	—	2	256	no	—
832	Q₈	—	2	128	no	—
833	Q₈	—	2	256	no	—
834	Q₈	—	4	256	no	—
835	D₄	—	2	256	no	—
836	D₄	—	2	512	no	—
837	D₄	—	2	256	no	—
838	D₄	—	2	128	no	—
839	D₄	—	2	128	no	—
840	D₄	—	4	256	no	—
841	D₄	C₂³×#41	1	256	yes	complemented
842	C₂×C₄	—	2	112	no	—
843	C₂×C₄	—	2	56	no	—
844	C₂×C₄	—	2	224	no	—
845	C₂×C₄	—	2	512	no	—
846	C₂×C₄	—	2	56	no	—
847	C₂×C₄	—	2	112	no	—
848	C₂×C₄	—	2	112	no	—
849	C₂×C₄	—	2	224	no	—
850	C₂×C₄	—	2	112	no	—
851	C₂×C₄	—	2	128	no	—
852	C₂×C₄	—	2	56	no	—
853	C₂×C₄	—	2	56	no	—
854	C₂×C₄	—	2	112	no	—
855	C₂×C₄	—	2	128	no	—
856	C₂×C₄	—	2	256	no	—
857	C₂×C₄	—	2	128	no	—
858	C₂×C₄	—	2	256	no	—
859	C₂×C₄	—	2	256	no	—
860	C₂×C₄	—	4	128	no	—
861	C₂×C₄	—	4	128	no	—
862	C₂×C₄	—	4	128	no	—
863	C₂×C₄	—	4	256	no	—
864	C₂×C₄	—	4	256	no	—
865	C₂×C₄	C₂³×#41	1	112	yes	—
866	C₂×C₄	C₂²×H(5,𝔽₂)	1	112	yes	—
867	C₂×C₄	C₂⁷	1	8	yes	—
868	C₂×C₄	C₂⁷	1	16	yes	—
869	C₂×C₄	C₂⁷	1	8	yes	—
870	C₂×C₄	C₂⁷	1	32	yes	—
871	C₂×C₄	C₂⁷	1	8	yes	—
872	C₂×C₄	C₂⁷	1	8	yes	—
873	C₂×C₄	C₂⁷	1	16	yes	—
874	C₂×C₄	C₂⁷	1	16	yes	—
875	C₂×C₄	C₂⁷	1	32	yes	—
876	C₂×C₄	C₂⁷	1	16	yes	—
877	C₂×C₄	C₂⁷	1	16	yes	—
878	C₂×C₄	C₂⁷	1	8	yes	—
879	C₂×C₄	C₂⁷	1	8	yes	—
880	C₂²	—	2	224	no	—
881	C₂²	—	2	448	no	—
882	C₂²	—	2	8	no	—
883	C₂²	—	2	16	no	—
884	C₂²	—	2	8	no	—
885	C₂²	—	2	16	no	—
886	C₂²	—	2	16	no	—
887	C₂²	—	2	16	no	—
888	C₂²	—	2	16	no	—
889	C₂²	—	2	16	no	—
890	C₂²	—	2	16	no	—
891	C₂²	—	2	16	no	—
892	C₂²	—	4	512	no	—
893	C₂²	—	4	224	no	—
894	C₂²	—	4	224	no	—
895	C₂²	C₂×#3520	1	112	yes	direct product factor
896	C₂²	C₂⁴×#41	1	32	yes	—
897	C₂²	C₂⁴×#41	1	14	yes	—
898	C₂²	C₂³×H(5,𝔽₂)	1	14	yes	—
899	C₂²	C₂³×2₋¹⁺⁴	1	16	yes	—
900	C₂²	C₂³×2₋¹⁺⁴	1	14	yes	—
901	C₂²	C₂⁸	1	1	yes	characteristic
902	C₄	—	2	16	no	—
903	C₄	—	2	8	no	—
904	C₄	—	2	32	no	—
905	C₄	—	2	8	no	—
906	C₄	—	2	16	no	—
907	C₄	—	2	16	no	—
908	C₄	—	2	32	no	—
909	C₄	—	2	16	no	—
910	C₄	—	2	8	no	—
911	C₄	—	2	8	no	—
912	C₄	—	2	16	no	—
913	C₄	C₂⁴×#41	1	16	yes	—
914	C₄	C₂³×H(5,𝔽₂)	1	16	yes	—
915	C₂	—	2	16	no	—
916	C₂	—	2	32	no	—
917	C₂	—	4	16	no	—
918	C₂	—	4	16	no	—
919	C₂	C₂²×#3520	1	28	yes	direct product factor
920	C₂	C₂⁵×#41	1	1	yes	characteristic
921	C₂	C₂⁴×H(5,𝔽₂)	1	1	yes	characteristic
922	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×#3520	C₂	direct (N × H)
2. C₂³×#556	C₂	semidirect
3. C₂³×#552	C₂	semidirect
4. C₂³×#551	C₂	semidirect
5. C₂³×#554	C₂	semidirect
6. C₂³×#547	C₂	semidirect
7. C₂³×#547	C₂	semidirect
8. C₂³×#548	C₂	semidirect
9. C₂³×#546	C₂	semidirect
10. C₂³×D₄×Q₈	C₂	semidirect
11. C₂³×#542	C₂	semidirect
12. C₂³×#539	C₂	semidirect
13. C₂³×#533	C₂	semidirect
14. C₂³×#529	C₂	semidirect
15. C₂³×#525	C₂	semidirect
16. C₂⁴×C₂²⋊Q₈	C₂	semidirect
17. C₂³×#520	C₂	semidirect
18. C₂⁴×C₄×D₄	C₂	semidirect
20. C₂⁴×#41	C₂²	semidirect
21. C₂⁵×Q₈	C₂²	semidirect
24. C₂×#3520	C₂²	direct (N × H)
25. C₂²×#556	C₂²	semidirect
26. C₂²×#552	C₂²	semidirect
27. C₂²×#551	C₂²	semidirect
28. C₂²×#554	C₂²	semidirect
29. C₂²×#547	C₂²	semidirect
30. C₂²×#547	C₂²	semidirect
31. C₂²×#548	C₂²	semidirect
32. C₂²×#546	C₂²	semidirect
33. C₂²×D₄×Q₈	C₂²	semidirect
34. C₂²×#542	C₂²	semidirect
35. C₂²×#539	C₂²	semidirect
36. C₂²×#533	C₂²	semidirect
37. C₂³×C₄⋊Q₈	C₂²	semidirect
38. C₂³×C₄⋊Q₈	C₂²	semidirect
39. C₂³×C₄⋊Q₈	C₂²	semidirect
40. C₂²×#529	C₂²	semidirect
41. C₂³×#126	C₂²	semidirect
42. C₂³×#126	C₂²	semidirect
43. C₂³×#126	C₂²	semidirect
44. C₂³×#125	C₂²	semidirect
45. C₂³×#125	C₂²	semidirect
46. C₂³×#125	C₂²	semidirect
48. C₂³×#124	C₂²	semidirect
49. C₂³×#124	C₂²	semidirect
50. C₂²×#525	C₂²	semidirect
53. C₂³×#123	C₂²	semidirect
54. C₂³×#123	C₂²	semidirect
55. C₂³×#123	C₂²	semidirect
60. C₂³×C₂²⋊Q₈	C₂²	semidirect
61. C₂³×C₂²⋊Q₈	C₂²	semidirect
62. C₂³×C₂²⋊Q₈	C₂²	semidirect
63. C₂³×C₂²⋊Q₈	C₂²	semidirect
64. C₂³×C₂²⋊Q₈	C₂²	semidirect
65. C₂³×C₂²⋊Q₈	C₂²	semidirect
66. C₂³×C₂²⋊Q₈	C₂²	semidirect
67. C₂³×C₂²⋊Q₈	C₂²	semidirect
71. C₂³×#121	C₂²	semidirect
73. C₂²×#520	C₂²	semidirect
74. C₂³×C₄×Q₈	C₂²	semidirect
75. C₂³×C₄×Q₈	C₂²	semidirect
76. C₂³×C₄×Q₈	C₂²	semidirect
77. C₂³×C₄×Q₈	C₂²	semidirect
87. C₂³×C₄×D₄	C₂²	semidirect
88. C₂³×C₄×D₄	C₂²	semidirect
89. C₂³×C₄×D₄	C₂²	semidirect
90. C₂³×C₄×D₄	C₂²	semidirect
92. C₂³×#117	C₂²	semidirect
93. C₂³×#117	C₂²	semidirect
94. C₂³×#117	C₂²	semidirect
96. C₂⁴×C₄⋊C₄	C₂²	semidirect
97. C₂⁴×C₄⋊C₄	C₂²	semidirect
98. C₂⁴×C₄⋊C₄	C₂²	semidirect
106. C₂³×#41	C₂³	semidirect
112. C₂⁴×Q₈	C₂³	semidirect
136. #3520	C₂³	direct (N × H)
137. C₂×#556	C₂³	semidirect
138. C₂×#554	C₂³	semidirect
139. C₂×#552	C₂³	semidirect
140. C₂×#551	C₂³	semidirect
141. C₂×D₄×Q₈	C₂³	semidirect
142. C₂×#548	C₂³	semidirect
143. C₂×#547	C₂³	semidirect
144. C₂×#547	C₂³	semidirect
145. C₂×#546	C₂³	semidirect
146. C₂×#542	C₂³	semidirect
147. C₂×#539	C₂³	semidirect
148. C₂×#533	C₂³	semidirect
149. C₂²×C₄⋊Q₈	C₂³	semidirect
150. C₂²×C₄⋊Q₈	C₂³	semidirect
151. C₂²×C₄⋊Q₈	C₂³	semidirect
152. C₂×#529	C₂³	semidirect
153. C₂²×#126	C₂³	semidirect
154. C₂²×#126	C₂³	semidirect
155. C₂²×#126	C₂³	semidirect
156. C₂²×#125	C₂³	semidirect
157. C₂²×#125	C₂³	semidirect
158. C₂²×#125	C₂³	semidirect
160. C₂²×#124	C₂³	semidirect
161. C₂²×#124	C₂³	semidirect
162. C₂×#525	C₂³	semidirect
165. C₂²×#123	C₂³	semidirect
166. C₂²×#123	C₂³	semidirect
167. C₂²×#123	C₂³	semidirect
172. C₂²×C₂²⋊Q₈	C₂³	semidirect
173. C₂²×C₂²⋊Q₈	C₂³	semidirect
174. C₂²×C₂²⋊Q₈	C₂³	semidirect
175. C₂²×C₂²⋊Q₈	C₂³	semidirect
176. C₂²×C₂²⋊Q₈	C₂³	semidirect
177. C₂²×C₂²⋊Q₈	C₂³	semidirect
178. C₂²×C₂²⋊Q₈	C₂³	semidirect
179. C₂²×C₂²⋊Q₈	C₂³	semidirect
183. C₂²×#121	C₂³	semidirect
185. C₂×#520	C₂³	semidirect
186. C₂²×C₄×Q₈	C₂³	semidirect
187. C₂²×C₄×Q₈	C₂³	semidirect
188. C₂²×C₄×Q₈	C₂³	semidirect
189. C₂²×C₄×Q₈	C₂³	semidirect
199. C₂²×C₄×D₄	C₂³	semidirect
200. C₂²×C₄×D₄	C₂³	semidirect
201. C₂²×C₄×D₄	C₂³	semidirect
202. C₂²×C₄×D₄	C₂³	semidirect
204. C₂²×#117	C₂³	semidirect
205. C₂²×#117	C₂³	semidirect
206. C₂²×#117	C₂³	semidirect
227. C₂³×C₄⋊C₄	C₂³	semidirect
228. C₂³×C₄⋊C₄	C₂³	semidirect
229. C₂³×C₄⋊C₄	C₂³	semidirect
266. C₂²×#41	C₂⁴	semidirect
276. C₂³×Q₈	C₂⁴	semidirect
284. C₂³×D₄	#41	semidirect
332. #556	C₂⁴	semidirect
333. #554	C₂⁴	semidirect
334. #552	C₂⁴	semidirect
335. #551	C₂⁴	semidirect
336. D₄×Q₈	C₂⁴	semidirect
337. #548	C₂⁴	semidirect
338. #547	C₂⁴	semidirect
339. #547	C₂⁴	semidirect
340. #546	C₂⁴	semidirect
341. #542	C₂⁴	semidirect
342. #539	C₂⁴	semidirect
343. #533	C₂⁴	semidirect
344. C₂×C₄⋊Q₈	C₂⁴	semidirect
345. C₂×C₄⋊Q₈	C₂⁴	semidirect
346. C₂×C₄⋊Q₈	C₂⁴	semidirect
347. #529	C₂⁴	semidirect
348. C₂×#126	C₂⁴	semidirect
349. C₂×#126	C₂⁴	semidirect
350. C₂×#126	C₂⁴	semidirect
351. C₂×#125	C₂⁴	semidirect
352. C₂×#125	C₂⁴	semidirect
353. C₂×#125	C₂⁴	semidirect
355. C₂×#124	C₂⁴	semidirect
356. C₂×#124	C₂⁴	semidirect
357. #525	C₂⁴	semidirect
360. C₂×#123	C₂⁴	semidirect
361. C₂×#123	C₂⁴	semidirect
362. C₂×#123	C₂⁴	semidirect
367. C₂×C₂²⋊Q₈	C₂⁴	semidirect
368. C₂×C₂²⋊Q₈	C₂⁴	semidirect
369. C₂×C₂²⋊Q₈	C₂⁴	semidirect
370. C₂×C₂²⋊Q₈	C₂⁴	semidirect
371. C₂×C₂²⋊Q₈	C₂⁴	semidirect
372. C₂×C₂²⋊Q₈	C₂⁴	semidirect
373. C₂×C₂²⋊Q₈	C₂⁴	semidirect
374. C₂×C₂²⋊Q₈	C₂⁴	semidirect
378. C₂×#121	C₂⁴	semidirect
380. #520	C₂⁴	semidirect
381. C₂×C₄×Q₈	C₂⁴	semidirect
382. C₂×C₄×Q₈	C₂⁴	semidirect
383. C₂×C₄×Q₈	C₂⁴	semidirect
384. C₂×C₄×Q₈	C₂⁴	semidirect
394. C₂×C₄×D₄	C₂⁴	semidirect
395. C₂×C₄×D₄	C₂⁴	semidirect
396. C₂×C₄×D₄	C₂⁴	semidirect
397. C₂×C₄×D₄	C₂⁴	semidirect
399. C₂×#117	C₂⁴	semidirect
400. C₂×#117	C₂⁴	semidirect
401. C₂×#117	C₂⁴	semidirect
422. C₂²×C₄⋊C₄	C₂⁴	semidirect
423. C₂²×C₄⋊C₄	C₂⁴	semidirect
424. C₂²×C₄⋊C₄	C₂⁴	semidirect
475. C₂×#41	C₂⁵	semidirect
485. C₂²×Q₈	C₂⁵	semidirect
493. C₂²×D₄	C₂×#41	semidirect
554. C₄⋊Q₈	C₂⁵	semidirect
555. C₄⋊Q₈	C₂⁵	semidirect
556. C₄⋊Q₈	C₂⁵	semidirect
557. #126	C₂⁵	semidirect
558. #126	C₂⁵	semidirect
559. #126	C₂⁵	semidirect
560. #125	C₂⁵	semidirect
561. #125	C₂⁵	semidirect
562. #125	C₂⁵	semidirect
564. #124	C₂⁵	semidirect
565. #124	C₂⁵	semidirect
568. #123	C₂⁵	semidirect
569. #123	C₂⁵	semidirect
570. #123	C₂⁵	semidirect
575. C₂²⋊Q₈	C₂⁵	semidirect
576. C₂²⋊Q₈	C₂⁵	semidirect
577. C₂²⋊Q₈	C₂⁵	semidirect
578. C₂²⋊Q₈	C₂⁵	semidirect
579. C₂²⋊Q₈	C₂⁵	semidirect
580. C₂²⋊Q₈	C₂⁵	semidirect
581. C₂²⋊Q₈	C₂⁵	semidirect
585. #121	C₂⁵	semidirect
587. C₄×Q₈	C₂⁵	semidirect
588. C₄×Q₈	C₂⁵	semidirect
589. C₄×Q₈	C₂⁵	semidirect
590. C₄×Q₈	C₂⁵	semidirect
600. C₄×D₄	C₂⁵	semidirect
601. C₄×D₄	C₂⁵	semidirect
602. C₄×D₄	C₂⁵	semidirect
604. #117	C₂⁵	semidirect
605. #117	C₂⁵	semidirect
606. #117	C₂⁵	semidirect
627. C₂×C₄⋊C₄	C₂⁵	semidirect
628. C₂×C₄⋊C₄	C₂⁵	semidirect
629. C₂×C₄⋊C₄	C₂⁵	semidirect
702. C₂×D₄	C₂²×#41	semidirect
820. C₂³	#3520	direct (N × H)
841. D₄	C₂³×#41	semidirect
895. C₂²	C₂×#3520	direct (N × H)
919. C₂	C₂²×#3520	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×#3520	2
C₂³×#556	2
C₂³×#552	2
C₂³×#551	2
C₂³×#554	2
C₂³×#547	2
C₂³×#548	2
C₂³×#546	2
C₂³×D₄×Q₈	2
C₂³×#542	2
C₂³×#539	2
C₂³×#533	2
C₂³×#529	2
C₂³×#525	2
C₂⁴×C₂²⋊Q₈	2
C₂³×#520	2
C₂⁴×C₄×D₄	2

Subgroups — C23×#3520 #72301664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#3520 #72301664