Subgroups — C₂³×#3540 #72324997

Order 1024.

484877 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#3540	C₂	1	224	yes	maximal, direct product factor
2	C₂³×H(3,𝔽₄)	C₂	1	2	yes	maximal, complemented
3	C₂³×#560	C₂	1	2	yes	maximal, complemented
4	C₂³×#559	C₂	1	2	yes	maximal, complemented
5	C₂³×#555	C₂	1	2	yes	maximal, complemented
6	C₂³×#556	C₂	1	2	yes	maximal, complemented
7	C₂³×#551	C₂	1	2	yes	maximal, complemented
8	C₂³×#548	C₂	1	2	yes	maximal, complemented
9	C₂³×#546	C₂	1	2	yes	maximal, complemented
10	C₂³×#536	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×#542	C₂	1	2	yes	maximal, complemented
12	C₂³×#542	C₂	1	4	yes	maximal, complemented
13	C₂³×#535	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×#538	C₂	1	4	yes	maximal, complemented
15	C₂³×#525	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×#525	C₂	1	2	yes	maximal, complemented
17	C₂⁴×#41	C₂²	1	1	yes	characteristic
18	C₂⁴×#41	C₂²	1	2	yes	—
19	C₂⁵×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂⁵×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₂⁶×C₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×#3540	C₂²	1	7168	yes	direct product factor
23	C₂²×#559	C₂²	1	224	yes	complemented
24	C₂²×#555	C₂²	1	224	yes	complemented
25	C₂²×#556	C₂²	1	224	yes	complemented
26	C₂²×#551	C₂²	1	224	yes	complemented
27	C₂²×#548	C₂²	1	224	yes	complemented
28	C₂²×#546	C₂²	1	224	yes	complemented
29	C₂²×H(3,𝔽₄)	C₂²	1	224	yes	complemented
30	C₂²×#560	C₂²	1	224	yes	complemented
31	C₂²×#536	C₂²	1	112	yes	complemented
32	C₂²×#542	C₂²	1	224	yes	complemented
33	C₂²×#542	C₂²	1	448	yes	complemented
34	C₂²×#535	C₂²	1	112	yes	complemented
35	C₂²×#538	C₂²	1	448	yes	complemented
36	C₂³×C₄⋊Q₈	C₂²	1	2	yes	complemented
37	C₂³×C₄⋊Q₈	C₂²	1	2	yes	complemented
38	C₂³×#127	C₂²	1	2	yes	—
39	C₂³×#126	C₂²	1	4	yes	complemented
40	C₂³×#126	C₂²	1	4	yes	complemented
41	C₂³×#126	C₂²	1	4	yes	complemented
42	C₂³×#124	C₂²	1	4	yes	—
43	C₂³×#124	C₂²	1	2	yes	—
44	C₂³×#124	C₂²	1	4	yes	complemented
45	C₂³×#124	C₂²	1	2	yes	complemented
46	C₂³×#124	C₂²	1	2	yes	complemented
47	C₂³×#124	C₂²	1	4	yes	complemented
48	C₂³×#124	C₂²	1	4	yes	complemented
49	C₂³×#124	C₂²	1	4	yes	complemented
50	C₂²×#525	C₂²	1	112	yes	complemented
51	C₂²×#525	C₂²	1	224	yes	complemented
52	C₂³×#123	C₂²	1	1	yes	characteristic
53	C₂³×#123	C₂²	1	4	yes	complemented
54	C₂³×#123	C₂²	1	1	yes	characteristic, complemented
55	C₂³×#123	C₂²	1	2	yes	complemented
56	C₂³×#123	C₂²	1	4	yes	complemented
57	C₂³×#123	C₂²	1	4	yes	complemented
58	C₂³×#123	C₂²	1	2	yes	complemented
59	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	complemented
60	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	complemented
61	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	complemented
63	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	complemented
64	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	complemented
65	C₂³×#121	C₂²	1	2	yes	—
66	C₂³×#121	C₂²	1	2	yes	—
67	C₂³×#121	C₂²	1	2	yes	—
68	C₂³×#121	C₂²	1	4	yes	—
69	C₂³×#121	C₂²	1	4	yes	complemented
70	C₂³×#121	C₂²	1	4	yes	complemented
71	C₂³×#121	C₂²	1	2	yes	complemented
72	C₂³×#120	C₂²	1	1	yes	characteristic
73	C₂³×#120	C₂²	1	4	yes	—
74	C₂³×#120	C₂²	1	2	yes	—
75	C₂³×#120	C₂²	1	1	yes	characteristic, complemented
76	C₂³×#120	C₂²	1	4	yes	complemented
77	C₂³×#120	C₂²	1	2	yes	complemented
78	C₂³×C₄×Q₈	C₂²	1	2	yes	complemented
79	C₂³×C₄×Q₈	C₂²	1	4	yes	complemented
80	C₂³×C₄×D₄	C₂²	1	2	yes	—
81	C₂³×C₄×D₄	C₂²	1	4	yes	complemented
82	C₂³×C₄×D₄	C₂²	1	2	yes	complemented
83	C₂³×C₄×D₄	C₂²	1	4	yes	complemented
84	C₂³×C₄×D₄	C₂²	1	4	yes	complemented
85	C₂³×C₄×D₄	C₂²	1	2	yes	complemented
86	C₂³×#117	C₂²	1	1	yes	characteristic, complemented
87	C₂³×#117	C₂²	1	2	yes	complemented
88	C₂³×#117	C₂²	1	1	yes	characteristic, complemented
89	C₂³×#117	C₂²	1	4	yes	complemented
90	C₂³×#117	C₂²	1	1	yes	characteristic, complemented
91	C₂⁴×C₂²⋊C₄	C₂²	1	4	yes	complemented
92	C₂⁷	C₂³	1	1	yes	characteristic
93	C₂⁷	C₂³	1	2	yes	—
94	C₂³×#41	—	4	16	no	—
95	C₂³×#41	—	4	32	no	—
96	C₂³×#41	C₂³	1	56	yes	—
97	C₂³×#41	C₂³	1	112	yes	—
98	C₂⁴×Q₈	—	4	16	no	—
99	C₂⁴×Q₈	C₂³	1	2	yes	—
100	C₂⁴×Q₈	C₂³	1	2	yes	—
101	C₂⁴×Q₈	C₂³	1	1	yes	characteristic
102	C₂⁴×Q₈	C₂³	1	4	yes	—
103	C₂⁴×Q₈	C₂³	1	56	yes	complemented
104	C₂⁴×D₄	—	4	16	no	—
105	C₂⁴×D₄	C₂³	1	2	yes	—
106	C₂⁴×D₄	C₂³	1	2	yes	—
107	C₂⁴×D₄	C₂³	1	1	yes	characteristic
108	C₂⁴×D₄	C₂³	1	4	yes	—
109	C₂⁴×D₄	C₂³	1	1	yes	characteristic
110	C₂⁴×D₄	C₂³	1	1	yes	characteristic
111	C₂⁴×D₄	C₂³	1	2	yes	—
112	C₂⁴×D₄	C₂³	1	4	yes	—
113	C₂⁴×D₄	C₂³	1	4	yes	—
114	C₂⁴×D₄	C₂³	1	2	yes	—
115	C₂⁴×D₄	C₂³	1	4	yes	—
116	C₂⁴×D₄	C₂³	1	56	yes	complemented
117	C₂⁵×C₄	—	4	16	no	—
118	C₂⁵×C₄	C₂³	1	2	yes	—
119	C₂⁵×C₄	C₂³	1	1	yes	characteristic
120	C₂⁵×C₄	C₂³	1	1	yes	characteristic
121	C₂⁵×C₄	C₂³	1	1	yes	characteristic
122	C₂⁵×C₄	C₂³	1	1	yes	characteristic
123	C₂⁵×C₄	C₂³	1	2	yes	—
124	C₂⁵×C₄	C₂³	1	2	yes	—
125	C₂⁵×C₄	C₂³	1	4	yes	—
126	C₂⁵×C₄	C₂³	1	4	yes	—
127	C₂⁵×C₄	C₂³	1	56	yes	complemented
128	#3540	C₂³	1	32768	yes	direct product factor
129	C₂×H(3,𝔽₄)	C₂³	1	3584	yes	complemented
130	C₂×#560	C₂³	1	3584	yes	complemented
131	C₂×#559	C₂³	1	3584	yes	complemented
132	C₂×#556	C₂³	1	3584	yes	complemented
133	C₂×#555	C₂³	1	3584	yes	complemented
134	C₂×#551	C₂³	1	3584	yes	complemented
135	C₂×#548	C₂³	1	3584	yes	complemented
136	C₂×#546	C₂³	1	3584	yes	complemented
137	C₂×#542	C₂³	1	3584	yes	complemented
138	C₂×#542	C₂³	1	7168	yes	complemented
139	C₂×#538	C₂³	1	7168	yes	complemented
140	C₂×#536	C₂³	1	1792	yes	complemented
141	C₂×#535	C₂³	1	1792	yes	complemented
142	C₂²×C₄⋊Q₈	C₂³	1	112	yes	complemented
143	C₂²×C₄⋊Q₈	C₂³	1	112	yes	complemented
144	C₂²×#127	C₂³	1	112	yes	—
145	C₂²×#126	C₂³	1	224	yes	complemented
146	C₂²×#126	C₂³	1	224	yes	complemented
147	C₂²×#126	C₂³	1	224	yes	complemented
148	C₂²×#124	C₂³	1	224	yes	—
149	C₂²×#124	C₂³	1	112	yes	—
150	C₂²×#124	C₂³	1	224	yes	complemented
151	C₂²×#124	C₂³	1	112	yes	complemented
152	C₂²×#124	C₂³	1	224	yes	complemented
153	C₂²×#124	C₂³	1	224	yes	complemented
154	C₂²×#124	C₂³	1	224	yes	complemented
155	C₂²×#124	C₂³	1	112	yes	complemented
156	C₂×#525	C₂³	1	1792	yes	complemented
157	C₂×#525	C₂³	1	3584	yes	complemented
158	C₂²×#123	C₂³	1	56	yes	—
159	C₂²×#123	C₂³	1	224	yes	complemented
160	C₂²×#123	C₂³	1	56	yes	complemented
161	C₂²×#123	C₂³	1	112	yes	complemented
162	C₂²×#123	C₂³	1	224	yes	complemented
163	C₂²×#123	C₂³	1	224	yes	complemented
164	C₂²×#123	C₂³	1	112	yes	complemented
165	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	complemented
166	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	complemented
167	C₂²×C₂²⋊Q₈	C₂³	1	112	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	112	yes	complemented
171	C₂²×#121	C₂³	1	112	yes	—
172	C₂²×#121	C₂³	1	112	yes	—
173	C₂²×#121	C₂³	1	112	yes	—
174	C₂²×#121	C₂³	1	224	yes	—
175	C₂²×#121	C₂³	1	224	yes	complemented
176	C₂²×#121	C₂³	1	224	yes	complemented
177	C₂²×#121	C₂³	1	112	yes	complemented
178	C₂²×#120	C₂³	1	56	yes	—
179	C₂²×#120	C₂³	1	224	yes	—
180	C₂²×#120	C₂³	1	112	yes	—
181	C₂²×#120	C₂³	1	56	yes	complemented
182	C₂²×#120	C₂³	1	224	yes	complemented
183	C₂²×#120	C₂³	1	112	yes	complemented
184	C₂²×C₄×Q₈	C₂³	1	112	yes	complemented
185	C₂²×C₄×Q₈	C₂³	1	224	yes	complemented
186	C₂²×C₄×D₄	C₂³	1	112	yes	—
187	C₂²×C₄×D₄	C₂³	1	224	yes	complemented
188	C₂²×C₄×D₄	C₂³	1	112	yes	complemented
189	C₂²×C₄×D₄	C₂³	1	224	yes	complemented
190	C₂²×C₄×D₄	C₂³	1	224	yes	complemented
191	C₂²×C₄×D₄	C₂³	1	112	yes	complemented
192	C₂²×#117	C₂³	1	56	yes	complemented
193	C₂²×#117	C₂³	1	112	yes	complemented
194	C₂²×#117	C₂³	1	56	yes	complemented
195	C₂²×#117	C₂³	1	224	yes	complemented
196	C₂²×#117	C₂³	1	56	yes	complemented
197	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
202	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
204	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
205	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
206	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
207	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
209	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
210	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
211	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
213	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
215	C₂³×C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
220	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
222	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
223	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
224	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
225	C₂³×C₂²⋊C₄	C₂³	1	224	yes	complemented
226	C₂³×C₄²	C₂³	1	2	yes	—
227	C₂³×C₄²	C₂³	1	4	yes	—
228	C₂³×C₄²	C₂³	1	2	yes	—
229	C₂³×C₄²	C₂³	1	2	yes	—
230	C₂³×C₄²	C₂³	1	4	yes	—
231	C₂⁶	—	4	8	no	—
232	C₂⁶	—	4	16	no	—
233	C₂⁶	—	4	16	no	—
234	C₂⁶	—	4	32	no	—
235	C₂⁶	C₂⁴	1	1	yes	characteristic
236	C₂⁶	C₂⁴	1	2	yes	—
237	C₂⁶	C₂⁴	1	1	yes	characteristic
238	C₂⁶	C₂⁴	1	4	yes	—
239	C₂⁶	C₂⁴	1	1	yes	characteristic
240	C₂⁶	C₂⁴	1	28	yes	—
241	C₂⁶	C₂⁴	1	56	yes	—
242	C₂²×#41	—	4	448	no	—
243	C₂²×#41	—	4	896	no	—
244	C₂²×#41	C₂⁴	1	448	yes	—
245	C₂²×#41	C₂⁴	1	896	yes	—
246	C₂³×Q₈	—	2	32	no	—
247	C₂³×Q₈	—	4	16	no	—
248	C₂³×Q₈	—	4	32	no	—
249	C₂³×Q₈	—	4	8	no	—
250	C₂³×Q₈	—	4	448	no	—
251	C₂³×Q₈	C₂⁴	1	56	yes	—
252	C₂³×Q₈	C₂⁴	1	56	yes	—
253	C₂³×Q₈	C₂⁴	1	28	yes	—
254	C₂³×Q₈	C₂⁴	1	112	yes	—
255	C₂³×Q₈	C₂⁴	1	448	yes	complemented
256	C₂³×D₄	—	2	32	no	—
257	C₂³×D₄	—	4	448	no	—
258	C₂³×D₄	—	4	16	no	—
259	C₂³×D₄	—	4	16	no	—
260	C₂³×D₄	—	4	32	no	—
261	C₂³×D₄	—	4	32	no	—
262	C₂³×D₄	—	4	32	no	—
263	C₂³×D₄	—	4	16	no	—
264	C₂³×D₄	—	4	8	no	—
265	C₂³×D₄	—	4	8	no	—
266	C₂³×D₄	—	4	8	no	—
267	C₂³×D₄	—	4	32	no	—
268	C₂³×D₄	C₂⁴	1	56	yes	—
269	C₂³×D₄	C₂⁴	1	56	yes	—
270	C₂³×D₄	C₂⁴	1	28	yes	—
271	C₂³×D₄	C₂⁴	1	112	yes	—
272	C₂³×D₄	C₂⁴	1	28	yes	—
273	C₂³×D₄	C₂⁴	1	28	yes	—
274	C₂³×D₄	C₂⁴	1	56	yes	—
275	C₂³×D₄	C₂⁴	1	112	yes	—
276	C₂³×D₄	C₂⁴	1	112	yes	—
277	C₂³×D₄	C₂⁴	1	56	yes	—
278	C₂³×D₄	C₂⁴	1	112	yes	—
279	C₂³×D₄	C₂⁴	1	448	yes	complemented
280	C₂⁴×C₄	—	2	32	no	—
281	C₂⁴×C₄	—	2	16	no	—
282	C₂⁴×C₄	—	2	16	no	—
283	C₂⁴×C₄	—	2	16	no	—
284	C₂⁴×C₄	—	4	448	no	—
285	C₂⁴×C₄	—	4	8	no	—
286	C₂⁴×C₄	—	4	16	no	—
287	C₂⁴×C₄	—	4	32	no	—
288	C₂⁴×C₄	—	4	16	no	—
289	C₂⁴×C₄	—	4	32	no	—
290	C₂⁴×C₄	C₂⁴	1	56	yes	—
291	C₂⁴×C₄	C₂⁴	1	28	yes	—
292	C₂⁴×C₄	C₂⁴	1	28	yes	—
293	C₂⁴×C₄	C₂⁴	1	28	yes	—
294	C₂⁴×C₄	C₂⁴	1	2	yes	—
295	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
296	C₂⁴×C₄	C₂⁴	1	4	yes	—
297	C₂⁴×C₄	C₂⁴	1	2	yes	—
298	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
299	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
300	C₂⁴×C₄	C₂⁴	1	4	yes	—
301	C₂⁴×C₄	C₂⁴	1	4	yes	—
302	C₂⁴×C₄	C₂⁴	1	2	yes	—
303	C₂⁴×C₄	C₂⁴	1	28	yes	—
304	C₂⁴×C₄	C₂⁴	1	56	yes	—
305	C₂⁴×C₄	C₂⁴	1	56	yes	—
306	C₂⁴×C₄	C₂⁴	1	112	yes	—
307	C₂⁴×C₄	C₂⁴	1	112	yes	—
308	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
309	C₂⁴×C₄	C₂⁴	1	448	yes	complemented
310	H(3,𝔽₄)	C₂⁴	1	8192	yes	complemented
311	#560	C₂⁴	1	8192	yes	complemented
312	#559	C₂⁴	1	8192	yes	complemented
313	#556	C₂⁴	1	8192	yes	complemented
314	#555	C₂⁴	1	8192	yes	complemented
315	#551	C₂⁴	1	8192	yes	complemented
316	#548	C₂⁴	1	8192	yes	complemented
317	#546	C₂⁴	1	8192	yes	complemented
318	#542	C₂⁴	1	8192	yes	complemented
319	#542	C₂⁴	1	16384	yes	complemented
320	#538	C₂⁴	1	16384	yes	complemented
321	#536	C₂⁴	1	4096	yes	complemented
322	#535	C₂⁴	1	4096	yes	complemented
323	C₂×C₄⋊Q₈	C₂⁴	1	896	yes	complemented
324	C₂×C₄⋊Q₈	C₂⁴	1	896	yes	complemented
325	C₂×#127	C₂⁴	1	896	yes	—
326	C₂×#126	C₂⁴	1	1792	yes	complemented
327	C₂×#126	C₂⁴	1	1792	yes	complemented
328	C₂×#126	C₂⁴	1	1792	yes	complemented
329	C₂×#124	C₂⁴	1	896	yes	—
330	C₂×#124	C₂⁴	1	1792	yes	—
331	C₂×#124	C₂⁴	1	896	yes	complemented
332	C₂×#124	C₂⁴	1	1792	yes	complemented
333	C₂×#124	C₂⁴	1	896	yes	complemented
334	C₂×#124	C₂⁴	1	1792	yes	complemented
335	C₂×#124	C₂⁴	1	1792	yes	complemented
336	C₂×#124	C₂⁴	1	1792	yes	complemented
337	#525	C₂⁴	1	4096	yes	complemented
338	#525	C₂⁴	1	8192	yes	complemented
339	C₂×#123	C₂⁴	1	448	yes	—
340	C₂×#123	C₂⁴	1	1792	yes	complemented
341	C₂×#123	C₂⁴	1	448	yes	complemented
342	C₂×#123	C₂⁴	1	896	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×C₂²⋊Q₈	C₂⁴	1	896	yes	complemented
347	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	complemented
348	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	complemented
349	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	complemented
350	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	complemented
351	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	complemented
352	C₂×#121	C₂⁴	1	896	yes	—
353	C₂×#121	C₂⁴	1	896	yes	—
354	C₂×#121	C₂⁴	1	896	yes	—
355	C₂×#121	C₂⁴	1	1792	yes	—
356	C₂×#121	C₂⁴	1	896	yes	complemented
357	C₂×#121	C₂⁴	1	1792	yes	complemented
358	C₂×#121	C₂⁴	1	1792	yes	complemented
359	C₂×#120	C₂⁴	1	448	yes	—
360	C₂×#120	C₂⁴	1	896	yes	—
361	C₂×#120	C₂⁴	1	1792	yes	—
362	C₂×#120	C₂⁴	1	448	yes	complemented
363	C₂×#120	C₂⁴	1	1792	yes	complemented
364	C₂×#120	C₂⁴	1	896	yes	complemented
365	C₂×C₄×Q₈	C₂⁴	1	896	yes	complemented
366	C₂×C₄×Q₈	C₂⁴	1	1792	yes	complemented
367	C₂×C₄×D₄	C₂⁴	1	896	yes	—
368	C₂×C₄×D₄	C₂⁴	1	1792	yes	complemented
369	C₂×C₄×D₄	C₂⁴	1	896	yes	complemented
370	C₂×C₄×D₄	C₂⁴	1	1792	yes	complemented
371	C₂×C₄×D₄	C₂⁴	1	1792	yes	complemented
372	C₂×C₄×D₄	C₂⁴	1	896	yes	complemented
373	C₂×#117	C₂⁴	1	448	yes	complemented
374	C₂×#117	C₂⁴	1	896	yes	complemented
375	C₂×#117	C₂⁴	1	448	yes	complemented
376	C₂×#117	C₂⁴	1	448	yes	complemented
377	C₂×#117	C₂⁴	1	1792	yes	complemented
378	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
379	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
380	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
381	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
382	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
383	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
384	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
385	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
386	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
387	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
388	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
389	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
390	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
391	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
392	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
393	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
394	C₂²×C₂²⋊C₄	C₂⁴	1	28	yes	—
395	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
396	C₂²×C₂²⋊C₄	C₂⁴	1	28	yes	—
397	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
398	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
399	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
400	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
401	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
402	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
403	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
404	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
405	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
406	C₂²×C₂²⋊C₄	C₂⁴	1	1792	yes	complemented
407	C₂²×C₄²	C₂⁴	1	56	yes	—
408	C₂²×C₄²	C₂⁴	1	112	yes	—
409	C₂²×C₄²	C₂⁴	1	56	yes	—
410	C₂²×C₄²	C₂⁴	1	56	yes	—
411	C₂²×C₄²	C₂⁴	1	112	yes	—
412	C₂⁵	—	2	8	no	—
413	C₂⁵	—	2	16	no	—
414	C₂⁵	—	2	8	no	—
415	C₂⁵	—	2	8	no	—
416	C₂⁵	—	2	32	no	—
417	C₂⁵	—	2	32	no	—
418	C₂⁵	—	2	16	no	—
419	C₂⁵	—	2	16	no	—
420	C₂⁵	—	2	16	no	—
421	C₂⁵	—	2	16	no	—
422	C₂⁵	—	2	32	no	—
423	C₂⁵	—	2	16	no	—
424	C₂⁵	—	4	112	no	—
425	C₂⁵	—	4	224	no	—
426	C₂⁵	—	4	224	no	—
427	C₂⁵	—	4	448	no	—
428	C₂⁵	—	4	256	no	—
429	C₂⁵	—	8	256	no	—
430	C₂⁵	C₂⁵	1	14	yes	—
431	C₂⁵	C₂⁵	1	14	yes	—
432	C₂⁵	C₂⁵	1	28	yes	—
433	C₂⁵	C₂⁵	1	56	yes	—
434	C₂⁵	C₂⁵	1	14	yes	—
435	C₂⁵	C₂⁵	1	224	yes	—
436	C₂⁵	C₂⁵	1	112	yes	—
437	C₂⁵	C₂⁵	1	1	yes	characteristic
438	C₂×#41	—	4	1792	no	—
439	C₂×#41	—	4	3584	no	—
440	C₂×#41	C₂⁵	1	512	yes	—
441	C₂×#41	C₂⁵	1	1024	yes	—
442	C₂²×Q₈	—	2	448	no	—
443	C₂²×Q₈	—	4	224	no	—
444	C₂²×Q₈	—	4	448	no	—
445	C₂²×Q₈	—	4	112	no	—
446	C₂²×Q₈	—	4	1792	no	—
447	C₂²×Q₈	C₂⁵	1	224	yes	—
448	C₂²×Q₈	C₂⁵	1	448	yes	—
449	C₂²×Q₈	C₂⁵	1	224	yes	—
450	C₂²×Q₈	C₂⁵	1	112	yes	—
451	C₂²×Q₈	C₂⁵	1	512	yes	complemented
452	C₂²×D₄	—	2	448	no	—
453	C₂²×D₄	—	4	1792	no	—
454	C₂²×D₄	—	4	224	no	—
455	C₂²×D₄	—	4	224	no	—
456	C₂²×D₄	—	4	448	no	—
457	C₂²×D₄	—	4	448	no	—
458	C₂²×D₄	—	4	448	no	—
459	C₂²×D₄	—	4	224	no	—
460	C₂²×D₄	—	4	112	no	—
461	C₂²×D₄	—	4	112	no	—
462	C₂²×D₄	—	4	112	no	—
463	C₂²×D₄	—	4	448	no	—
464	C₂²×D₄	C₂⁵	1	224	yes	—
465	C₂²×D₄	C₂⁵	1	224	yes	—
466	C₂²×D₄	C₂⁵	1	448	yes	—
467	C₂²×D₄	C₂⁵	1	448	yes	—
468	C₂²×D₄	C₂⁵	1	224	yes	—
469	C₂²×D₄	C₂⁵	1	448	yes	—
470	C₂²×D₄	C₂⁵	1	112	yes	—
471	C₂²×D₄	C₂⁵	1	448	yes	—
472	C₂²×D₄	C₂⁵	1	112	yes	—
473	C₂²×D₄	C₂⁵	1	112	yes	—
474	C₂²×D₄	C₂⁵	1	224	yes	—
475	C₂²×D₄	C₂⁵	1	512	yes	complemented
476	C₂³×C₄	—	2	16	no	—
477	C₂³×C₄	—	2	8	no	—
478	C₂³×C₄	—	2	8	no	—
479	C₂³×C₄	—	2	8	no	—
480	C₂³×C₄	—	2	32	no	—
481	C₂³×C₄	—	2	16	no	—
482	C₂³×C₄	—	2	32	no	—
483	C₂³×C₄	—	2	32	no	—
484	C₂³×C₄	—	2	16	no	—
485	C₂³×C₄	—	2	448	no	—
486	C₂³×C₄	—	2	224	no	—
487	C₂³×C₄	—	2	224	no	—
488	C₂³×C₄	—	2	224	no	—
489	C₂³×C₄	—	4	1792	no	—
490	C₂³×C₄	—	4	112	no	—
491	C₂³×C₄	—	4	224	no	—
492	C₂³×C₄	—	4	448	no	—
493	C₂³×C₄	—	4	224	no	—
494	C₂³×C₄	—	4	448	no	—
495	C₂³×C₄	H(5,𝔽₂)	1	16	yes	—
496	C₂³×C₄	C₂⁵	1	28	yes	—
497	C₂³×C₄	C₂⁵	1	56	yes	—
498	C₂³×C₄	C₂⁵	1	14	yes	—
499	C₂³×C₄	C₂⁵	1	28	yes	—
500	C₂³×C₄	C₂⁵	1	56	yes	—
501	C₂³×C₄	C₂⁵	1	56	yes	—
502	C₂³×C₄	C₂⁵	1	14	yes	—
503	C₂³×C₄	C₂⁵	1	28	yes	—
504	C₂³×C₄	C₂⁵	1	14	yes	—
505	C₂³×C₄	C₂⁵	1	112	yes	—
506	C₂³×C₄	C₂⁵	1	224	yes	—
507	C₂³×C₄	C₂⁵	1	112	yes	—
508	C₂³×C₄	C₂⁵	1	112	yes	—
509	C₂³×C₄	C₂⁵	1	448	yes	—
510	C₂³×C₄	C₂⁵	1	448	yes	—
511	C₂³×C₄	C₂⁵	1	112	yes	—
512	C₂³×C₄	C₂⁵	1	224	yes	—
513	C₂³×C₄	C₂⁵	1	224	yes	—
514	C₂³×C₄	C₂⁵	1	14	yes	—
515	C₂³×C₄	C₂⁵	1	512	yes	complemented
516	C₄⋊Q₈	C₂⁵	1	1024	yes	complemented
517	C₄⋊Q₈	C₂⁵	1	1024	yes	complemented
518	#127	C₂⁵	1	1024	yes	—
519	#126	C₂⁵	1	2048	yes	complemented
520	#126	C₂⁵	1	2048	yes	complemented
521	#126	C₂⁵	1	2048	yes	complemented
522	#124	C₂⁵	1	1024	yes	—
523	#124	C₂⁵	1	2048	yes	—
524	#124	C₂⁵	1	1024	yes	complemented
525	#124	C₂⁵	1	2048	yes	complemented
526	#124	C₂⁵	1	1024	yes	complemented
527	#124	C₂⁵	1	2048	yes	complemented
528	#124	C₂⁵	1	2048	yes	complemented
529	#124	C₂⁵	1	2048	yes	complemented
530	#123	C₂⁵	1	512	yes	—
531	#123	C₂⁵	1	2048	yes	complemented
532	#123	C₂⁵	1	512	yes	complemented
533	#123	C₂⁵	1	1024	yes	complemented
534	#123	C₂⁵	1	1024	yes	complemented
535	#123	C₂⁵	1	2048	yes	complemented
536	#123	C₂⁵	1	2048	yes	complemented
537	C₂²⋊Q₈	C₂⁵	1	1024	yes	complemented
538	C₂²⋊Q₈	C₂⁵	1	1024	yes	complemented
539	C₂²⋊Q₈	C₂⁵	1	1024	yes	complemented
540	C₂²⋊Q₈	C₂⁵	1	1024	yes	complemented
541	C₂²⋊Q₈	C₂⁵	1	2048	yes	complemented
542	C₂²⋊Q₈	C₂⁵	1	2048	yes	complemented
543	#121	C₂⁵	1	1024	yes	—
544	#121	C₂⁵	1	1024	yes	—
545	#121	C₂⁵	1	1024	yes	—
546	#121	C₂⁵	1	2048	yes	—
547	#121	C₂⁵	1	1024	yes	complemented
548	#121	C₂⁵	1	2048	yes	complemented
549	#121	C₂⁵	1	2048	yes	complemented
550	#120	C₂⁵	1	512	yes	—
551	#120	C₂⁵	1	1024	yes	—
552	#120	C₂⁵	1	2048	yes	—
553	#120	C₂⁵	1	512	yes	complemented
554	#120	C₂⁵	1	2048	yes	complemented
555	#120	C₂⁵	1	1024	yes	complemented
556	C₄×Q₈	C₂⁵	1	1024	yes	complemented
557	C₄×Q₈	C₂⁵	1	2048	yes	complemented
558	C₄×D₄	C₂⁵	1	1024	yes	—
559	C₄×D₄	C₂⁵	1	2048	yes	complemented
560	C₄×D₄	C₂⁵	1	1024	yes	complemented
561	C₄×D₄	C₂⁵	1	2048	yes	complemented
562	C₄×D₄	C₂⁵	1	2048	yes	complemented
563	C₄×D₄	C₂⁵	1	1024	yes	complemented
564	#117	C₂⁵	1	512	yes	complemented
565	#117	C₂⁵	1	1024	yes	complemented
566	#117	C₂⁵	1	512	yes	complemented
567	#117	C₂⁵	1	512	yes	complemented
568	#117	C₂⁵	1	2048	yes	complemented
569	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
570	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
571	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
572	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
573	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
574	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
575	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
576	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
577	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
578	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
579	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
580	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
581	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
582	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
583	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
584	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
585	C₂×C₂²⋊C₄	C₂⁵	1	112	yes	—
586	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
587	C₂×C₂²⋊C₄	C₂⁵	1	112	yes	—
588	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
589	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
590	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
591	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
592	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
593	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
594	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
595	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
596	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
597	C₂×C₂²⋊C₄	C₂⁵	1	2048	yes	complemented
598	C₂×C₄²	C₂⁵	1	224	yes	—
599	C₂×C₄²	C₂⁵	1	448	yes	—
600	C₂×C₄²	C₂⁵	1	224	yes	—
601	C₂×C₄²	C₂⁵	1	224	yes	—
602	C₂×C₄²	C₂⁵	1	448	yes	—
603	C₂⁴	—	2	56	no	—
604	C₂⁴	—	2	112	no	—
605	C₂⁴	—	2	56	no	—
606	C₂⁴	—	2	56	no	—
607	C₂⁴	—	2	224	no	—
608	C₂⁴	—	2	224	no	—
609	C₂⁴	—	2	112	no	—
610	C₂⁴	—	2	112	no	—
611	C₂⁴	—	2	112	no	—
612	C₂⁴	—	2	112	no	—
613	C₂⁴	—	2	224	no	—
614	C₂⁴	—	2	112	no	—
615	C₂⁴	—	4	224	no	—
616	C₂⁴	—	4	448	no	—
617	C₂⁴	—	4	448	no	—
618	C₂⁴	—	4	896	no	—
619	C₂⁴	—	4	1792	no	—
620	C₂⁴	—	4	64	no	—
621	C₂⁴	—	4	128	no	—
622	C₂⁴	—	4	64	no	—
623	C₂⁴	—	4	256	no	—
624	C₂⁴	—	4	64	no	—
625	C₂⁴	—	8	1792	no	—
626	C₂⁴	C₂×H(5,𝔽₂)	1	8	yes	—
627	C₂⁴	#585	1	16	yes	—
628	C₂⁴	C₂⁶	1	28	yes	—
629	C₂⁴	C₂⁶	1	28	yes	—
630	C₂⁴	C₂⁶	1	56	yes	—
631	C₂⁴	C₂⁶	1	112	yes	—
632	C₂⁴	C₂⁶	1	28	yes	—
633	C₂⁴	C₂⁶	1	128	yes	—
634	C₂⁴	C₂⁶	1	64	yes	—
635	C₂⁴	C₂⁶	1	7	yes	—
636	#41	—	4	1024	no	—
637	#41	—	4	2048	no	—
638	C₂×Q₈	—	2	896	no	—
639	C₂×Q₈	—	4	448	no	—
640	C₂×Q₈	—	4	896	no	—
641	C₂×Q₈	—	4	224	no	—
642	C₂×Q₈	—	4	1024	no	—
643	C₂×Q₈	C₂⁶	1	128	yes	—
644	C₂×Q₈	C₂⁶	1	256	yes	—
645	C₂×Q₈	C₂⁶	1	128	yes	—
646	C₂×Q₈	C₂⁶	1	64	yes	—
647	C₂×D₄	—	2	896	no	—
648	C₂×D₄	—	4	1024	no	—
649	C₂×D₄	—	4	448	no	—
650	C₂×D₄	—	4	448	no	—
651	C₂×D₄	—	4	896	no	—
652	C₂×D₄	—	4	896	no	—
653	C₂×D₄	—	4	896	no	—
654	C₂×D₄	—	4	448	no	—
655	C₂×D₄	—	4	224	no	—
656	C₂×D₄	—	4	224	no	—
657	C₂×D₄	—	4	224	no	—
658	C₂×D₄	—	4	896	no	—
659	C₂×D₄	C₂⁶	1	128	yes	—
660	C₂×D₄	C₂⁶	1	128	yes	—
661	C₂×D₄	C₂⁶	1	256	yes	—
662	C₂×D₄	C₂⁶	1	256	yes	—
663	C₂×D₄	C₂⁶	1	128	yes	—
664	C₂×D₄	C₂⁶	1	256	yes	—
665	C₂×D₄	C₂⁶	1	64	yes	—
666	C₂×D₄	C₂⁶	1	256	yes	—
667	C₂×D₄	C₂⁶	1	64	yes	—
668	C₂×D₄	C₂⁶	1	64	yes	—
669	C₂×D₄	C₂⁶	1	128	yes	—
670	C₂²×C₄	—	2	112	no	—
671	C₂²×C₄	—	2	56	no	—
672	C₂²×C₄	—	2	56	no	—
673	C₂²×C₄	—	2	56	no	—
674	C₂²×C₄	—	2	224	no	—
675	C₂²×C₄	—	2	112	no	—
676	C₂²×C₄	—	2	224	no	—
677	C₂²×C₄	—	2	224	no	—
678	C₂²×C₄	—	2	112	no	—
679	C₂²×C₄	—	2	896	no	—
680	C₂²×C₄	—	2	448	no	—
681	C₂²×C₄	—	2	448	no	—
682	C₂²×C₄	—	2	448	no	—
683	C₂²×C₄	—	4	1024	no	—
684	C₂²×C₄	—	4	224	no	—
685	C₂²×C₄	—	4	448	no	—
686	C₂²×C₄	—	4	896	no	—
687	C₂²×C₄	—	4	448	no	—
688	C₂²×C₄	—	4	896	no	—
689	C₂²×C₄	C₂×H(5,𝔽₂)	1	112	yes	—
690	C₂²×C₄	C₂⁶	1	56	yes	—
691	C₂²×C₄	C₂⁶	1	112	yes	—
692	C₂²×C₄	C₂⁶	1	112	yes	—
693	C₂²×C₄	C₂⁶	1	28	yes	—
694	C₂²×C₄	C₂⁶	1	56	yes	—
695	C₂²×C₄	C₂⁶	1	28	yes	—
696	C₂²×C₄	C₂⁶	1	56	yes	—
697	C₂²×C₄	C₂⁶	1	112	yes	—
698	C₂²×C₄	C₂⁶	1	28	yes	—
699	C₂²×C₄	C₂⁶	1	64	yes	—
700	C₂²×C₄	C₂⁶	1	128	yes	—
701	C₂²×C₄	C₂⁶	1	64	yes	—
702	C₂²×C₄	C₂⁶	1	64	yes	—
703	C₂²×C₄	C₂⁶	1	256	yes	—
704	C₂²×C₄	C₂⁶	1	256	yes	—
705	C₂²×C₄	C₂⁶	1	64	yes	—
706	C₂²×C₄	C₂⁶	1	128	yes	—
707	C₂²×C₄	C₂⁶	1	128	yes	—
708	C₂²×C₄	C₂⁶	1	28	yes	—
709	C₄⋊C₄	C₂⁶	1	128	yes	—
710	C₄⋊C₄	C₂⁶	1	128	yes	—
711	C₄⋊C₄	C₂⁶	1	128	yes	—
712	C₄⋊C₄	C₂⁶	1	128	yes	—
713	C₄⋊C₄	C₂⁶	1	256	yes	—
714	C₄⋊C₄	C₂⁶	1	128	yes	—
715	C₄⋊C₄	C₂⁶	1	256	yes	—
716	C₄⋊C₄	C₂⁶	1	256	yes	—
717	C₄⋊C₄	C₂⁶	1	256	yes	—
718	C₄⋊C₄	C₂⁶	1	256	yes	—
719	C₂²⋊C₄	C₂⁶	1	128	yes	—
720	C₂²⋊C₄	C₂⁶	1	256	yes	—
721	C₂²⋊C₄	C₂⁶	1	256	yes	—
722	C₂²⋊C₄	C₂⁶	1	256	yes	—
723	C₂²⋊C₄	C₂⁶	1	128	yes	—
724	C₂²⋊C₄	C₂⁶	1	256	yes	—
725	C₂²⋊C₄	C₂⁶	1	64	yes	—
726	C₂²⋊C₄	C₂⁶	1	256	yes	—
727	C₂²⋊C₄	C₂⁶	1	64	yes	—
728	C₂²⋊C₄	C₂⁶	1	128	yes	—
729	C₂²⋊C₄	C₂⁶	1	128	yes	—
730	C₂²⋊C₄	C₂⁶	1	128	yes	—
731	C₂²⋊C₄	C₂⁶	1	256	yes	—
732	C₂²⋊C₄	C₂⁶	1	128	yes	—
733	C₂²⋊C₄	C₂⁶	1	256	yes	—
734	C₂²⋊C₄	C₂⁶	1	256	yes	—
735	C₂²⋊C₄	C₂⁶	1	256	yes	—
736	C₂²⋊C₄	C₂⁶	1	256	yes	—
737	C₄²	C₂⁶	1	128	yes	—
738	C₄²	C₂⁶	1	256	yes	—
739	C₄²	C₂⁶	1	128	yes	—
740	C₄²	C₂⁶	1	128	yes	—
741	C₄²	C₂⁶	1	256	yes	—
742	C₂³	—	2	56	no	—
743	C₂³	—	2	112	no	—
744	C₂³	—	2	56	no	—
745	C₂³	—	2	56	no	—
746	C₂³	—	2	224	no	—
747	C₂³	—	2	224	no	—
748	C₂³	—	2	112	no	—
749	C₂³	—	2	112	no	—
750	C₂³	—	2	112	no	—
751	C₂³	—	2	112	no	—
752	C₂³	—	2	224	no	—
753	C₂³	—	2	112	no	—
754	C₂³	—	4	64	no	—
755	C₂³	—	4	128	no	—
756	C₂³	—	4	128	no	—
757	C₂³	—	4	256	no	—
758	C₂³	—	4	1792	no	—
759	C₂³	—	4	224	no	—
760	C₂³	—	4	448	no	—
761	C₂³	—	4	224	no	—
762	C₂³	—	4	896	no	—
763	C₂³	—	4	224	no	—
764	C₂³	—	8	1792	no	—
765	C₂³	#3540	1	64	yes	direct product factor
766	C₂³	C₂²×H(5,𝔽₂)	1	28	yes	—
767	C₂³	C₂×#585	1	56	yes	—
768	C₂³	C₂⁷	1	8	yes	—
769	C₂³	C₂⁷	1	8	yes	—
770	C₂³	C₂⁷	1	16	yes	—
771	C₂³	C₂⁷	1	32	yes	—
772	C₂³	C₂⁷	1	8	yes	—
773	C₂³	C₂⁷	1	7	yes	—
774	Q₈	—	2	256	no	—
775	Q₈	—	4	128	no	—
776	Q₈	—	4	256	no	—
777	Q₈	—	4	64	no	—
778	D₄	—	2	256	no	—
779	D₄	—	4	128	no	—
780	D₄	—	4	128	no	—
781	D₄	—	4	256	no	—
782	D₄	—	4	256	no	—
783	D₄	—	4	256	no	—
784	D₄	—	4	128	no	—
785	D₄	—	4	64	no	—
786	D₄	—	4	64	no	—
787	D₄	—	4	64	no	—
788	D₄	—	4	256	no	—
789	C₂×C₄	—	2	112	no	—
790	C₂×C₄	—	2	56	no	—
791	C₂×C₄	—	2	56	no	—
792	C₂×C₄	—	2	56	no	—
793	C₂×C₄	—	2	224	no	—
794	C₂×C₄	—	2	112	no	—
795	C₂×C₄	—	2	224	no	—
796	C₂×C₄	—	2	224	no	—
797	C₂×C₄	—	2	112	no	—
798	C₂×C₄	—	2	256	no	—
799	C₂×C₄	—	2	128	no	—
800	C₂×C₄	—	2	128	no	—
801	C₂×C₄	—	2	128	no	—
802	C₂×C₄	—	4	64	no	—
803	C₂×C₄	—	4	128	no	—
804	C₂×C₄	—	4	256	no	—
805	C₂×C₄	—	4	128	no	—
806	C₂×C₄	—	4	256	no	—
807	C₂×C₄	C₂²×H(5,𝔽₂)	1	112	yes	—
808	C₂×C₄	C₂⁷	1	16	yes	—
809	C₂×C₄	C₂⁷	1	32	yes	—
810	C₂×C₄	C₂⁷	1	32	yes	—
811	C₂×C₄	C₂⁷	1	8	yes	—
812	C₂×C₄	C₂⁷	1	16	yes	—
813	C₂×C₄	C₂⁷	1	8	yes	—
814	C₂×C₄	C₂⁷	1	16	yes	—
815	C₂×C₄	C₂⁷	1	32	yes	—
816	C₂×C₄	C₂⁷	1	8	yes	—
817	C₂×C₄	C₂⁷	1	8	yes	—
818	C₂²	—	2	8	no	—
819	C₂²	—	2	16	no	—
820	C₂²	—	2	8	no	—
821	C₂²	—	2	8	no	—
822	C₂²	—	2	32	no	—
823	C₂²	—	2	32	no	—
824	C₂²	—	2	16	no	—
825	C₂²	—	2	16	no	—
826	C₂²	—	2	16	no	—
827	C₂²	—	2	16	no	—
828	C₂²	—	2	32	no	—
829	C₂²	—	2	16	no	—
830	C₂²	—	4	256	no	—
831	C₂²	—	4	112	no	—
832	C₂²	—	4	224	no	—
833	C₂²	—	4	112	no	—
834	C₂²	—	4	448	no	—
835	C₂²	—	4	112	no	—
836	C₂²	—	8	256	no	—
837	C₂²	C₂×#3540	1	112	yes	direct product factor
838	C₂²	C₂³×H(5,𝔽₂)	1	14	yes	—
839	C₂²	C₂²×#585	1	28	yes	—
840	C₂²	C₂⁸	1	1	yes	characteristic
841	C₄	—	2	16	no	—
842	C₄	—	2	8	no	—
843	C₄	—	2	8	no	—
844	C₄	—	2	8	no	—
845	C₄	—	2	32	no	—
846	C₄	—	2	16	no	—
847	C₄	—	2	32	no	—
848	C₄	—	2	32	no	—
849	C₄	—	2	16	no	—
850	C₄	C₂³×H(5,𝔽₂)	1	16	yes	—
851	C₂	—	4	8	no	—
852	C₂	—	4	16	no	—
853	C₂	—	4	8	no	—
854	C₂	—	4	32	no	—
855	C₂	—	4	8	no	—
856	C₂	C₂²×#3540	1	28	yes	direct product factor
857	C₂	C₂⁴×H(5,𝔽₂)	1	1	yes	characteristic
858	C₂	C₂³×#585	1	2	yes	—

	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×#3540	C₂	direct (N × H)
2. C₂³×H(3,𝔽₄)	C₂	semidirect
3. C₂³×#560	C₂	semidirect
4. C₂³×#559	C₂	semidirect
5. C₂³×#555	C₂	semidirect
6. C₂³×#556	C₂	semidirect
7. C₂³×#551	C₂	semidirect
8. C₂³×#548	C₂	semidirect
9. C₂³×#546	C₂	semidirect
10. C₂³×#536	C₂	semidirect
11. C₂³×#542	C₂	semidirect
12. C₂³×#542	C₂	semidirect
13. C₂³×#535	C₂	semidirect
14. C₂³×#538	C₂	semidirect
15. C₂³×#525	C₂	semidirect
16. C₂³×#525	C₂	semidirect
19. C₂⁵×Q₈	C₂²	semidirect
20. C₂⁵×D₄	C₂²	semidirect
21. C₂⁶×C₄	C₂²	semidirect
22. C₂×#3540	C₂²	direct (N × H)
23. C₂²×#559	C₂²	semidirect
24. C₂²×#555	C₂²	semidirect
25. C₂²×#556	C₂²	semidirect
26. C₂²×#551	C₂²	semidirect
27. C₂²×#548	C₂²	semidirect
28. C₂²×#546	C₂²	semidirect
29. C₂²×H(3,𝔽₄)	C₂²	semidirect
30. C₂²×#560	C₂²	semidirect
31. C₂²×#536	C₂²	semidirect
32. C₂²×#542	C₂²	semidirect
33. C₂²×#542	C₂²	semidirect
34. C₂²×#535	C₂²	semidirect
35. C₂²×#538	C₂²	semidirect
36. C₂³×C₄⋊Q₈	C₂²	semidirect
37. C₂³×C₄⋊Q₈	C₂²	semidirect
39. C₂³×#126	C₂²	semidirect
40. C₂³×#126	C₂²	semidirect
41. C₂³×#126	C₂²	semidirect
44. C₂³×#124	C₂²	semidirect
45. C₂³×#124	C₂²	semidirect
46. C₂³×#124	C₂²	semidirect
47. C₂³×#124	C₂²	semidirect
48. C₂³×#124	C₂²	semidirect
49. C₂³×#124	C₂²	semidirect
50. C₂²×#525	C₂²	semidirect
51. C₂²×#525	C₂²	semidirect
53. C₂³×#123	C₂²	semidirect
54. C₂³×#123	C₂²	semidirect
55. C₂³×#123	C₂²	semidirect
56. C₂³×#123	C₂²	semidirect
57. C₂³×#123	C₂²	semidirect
58. C₂³×#123	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
63. C₂³×C₂²⋊Q₈	C₂²	semidirect
64. C₂³×C₂²⋊Q₈	C₂²	semidirect
69. C₂³×#121	C₂²	semidirect
70. C₂³×#121	C₂²	semidirect
71. C₂³×#121	C₂²	semidirect
75. C₂³×#120	C₂²	semidirect
76. C₂³×#120	C₂²	semidirect
77. C₂³×#120	C₂²	semidirect
78. C₂³×C₄×Q₈	C₂²	semidirect
79. 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×C₄×D₄	C₂²	semidirect
85. C₂³×C₄×D₄	C₂²	semidirect
86. C₂³×#117	C₂²	semidirect
87. C₂³×#117	C₂²	semidirect
88. C₂³×#117	C₂²	semidirect
89. C₂³×#117	C₂²	semidirect
90. C₂³×#117	C₂²	semidirect
91. C₂⁴×C₂²⋊C₄	C₂²	semidirect
103. C₂⁴×Q₈	C₂³	semidirect
116. C₂⁴×D₄	C₂³	semidirect
127. C₂⁵×C₄	C₂³	semidirect
128. #3540	C₂³	direct (N × H)
129. C₂×H(3,𝔽₄)	C₂³	semidirect
130. C₂×#560	C₂³	semidirect
131. C₂×#559	C₂³	semidirect
132. C₂×#556	C₂³	semidirect
133. C₂×#555	C₂³	semidirect
134. C₂×#551	C₂³	semidirect
135. C₂×#548	C₂³	semidirect
136. C₂×#546	C₂³	semidirect
137. C₂×#542	C₂³	semidirect
138. C₂×#542	C₂³	semidirect
139. C₂×#538	C₂³	semidirect
140. C₂×#536	C₂³	semidirect
141. C₂×#535	C₂³	semidirect
142. C₂²×C₄⋊Q₈	C₂³	semidirect
143. C₂²×C₄⋊Q₈	C₂³	semidirect
145. C₂²×#126	C₂³	semidirect
146. C₂²×#126	C₂³	semidirect
147. C₂²×#126	C₂³	semidirect
150. C₂²×#124	C₂³	semidirect
151. C₂²×#124	C₂³	semidirect
152. C₂²×#124	C₂³	semidirect
153. C₂²×#124	C₂³	semidirect
154. C₂²×#124	C₂³	semidirect
155. C₂²×#124	C₂³	semidirect
156. C₂×#525	C₂³	semidirect
157. C₂×#525	C₂³	semidirect
159. C₂²×#123	C₂³	semidirect
160. C₂²×#123	C₂³	semidirect
161. C₂²×#123	C₂³	semidirect
162. C₂²×#123	C₂³	semidirect
163. C₂²×#123	C₂³	semidirect
164. C₂²×#123	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
175. C₂²×#121	C₂³	semidirect
176. C₂²×#121	C₂³	semidirect
177. C₂²×#121	C₂³	semidirect
181. C₂²×#120	C₂³	semidirect
182. C₂²×#120	C₂³	semidirect
183. C₂²×#120	C₂³	semidirect
184. C₂²×C₄×Q₈	C₂³	semidirect
185. C₂²×C₄×Q₈	C₂³	semidirect
187. C₂²×C₄×D₄	C₂³	semidirect
188. C₂²×C₄×D₄	C₂³	semidirect
189. C₂²×C₄×D₄	C₂³	semidirect
190. C₂²×C₄×D₄	C₂³	semidirect
191. C₂²×C₄×D₄	C₂³	semidirect
192. C₂²×#117	C₂³	semidirect
193. C₂²×#117	C₂³	semidirect
194. C₂²×#117	C₂³	semidirect
195. C₂²×#117	C₂³	semidirect
196. C₂²×#117	C₂³	semidirect
225. C₂³×C₂²⋊C₄	C₂³	semidirect
255. C₂³×Q₈	C₂⁴	semidirect
279. C₂³×D₄	C₂⁴	semidirect
309. C₂⁴×C₄	C₂⁴	semidirect
310. H(3,𝔽₄)	C₂⁴	semidirect
311. #560	C₂⁴	semidirect
312. #559	C₂⁴	semidirect
313. #556	C₂⁴	semidirect
314. #555	C₂⁴	semidirect
315. #551	C₂⁴	semidirect
316. #548	C₂⁴	semidirect
317. #546	C₂⁴	semidirect
318. #542	C₂⁴	semidirect
319. #542	C₂⁴	semidirect
320. #538	C₂⁴	semidirect
321. #536	C₂⁴	semidirect
322. #535	C₂⁴	semidirect
323. C₂×C₄⋊Q₈	C₂⁴	semidirect
324. C₂×C₄⋊Q₈	C₂⁴	semidirect
326. C₂×#126	C₂⁴	semidirect
327. C₂×#126	C₂⁴	semidirect
328. C₂×#126	C₂⁴	semidirect
331. C₂×#124	C₂⁴	semidirect
332. C₂×#124	C₂⁴	semidirect
333. C₂×#124	C₂⁴	semidirect
334. C₂×#124	C₂⁴	semidirect
335. C₂×#124	C₂⁴	semidirect
336. C₂×#124	C₂⁴	semidirect
337. #525	C₂⁴	semidirect
338. #525	C₂⁴	semidirect
340. C₂×#123	C₂⁴	semidirect
341. C₂×#123	C₂⁴	semidirect
342. C₂×#123	C₂⁴	semidirect
343. C₂×#123	C₂⁴	semidirect
344. C₂×#123	C₂⁴	semidirect
345. C₂×#123	C₂⁴	semidirect
346. C₂×C₂²⋊Q₈	C₂⁴	semidirect
347. C₂×C₂²⋊Q₈	C₂⁴	semidirect
348. C₂×C₂²⋊Q₈	C₂⁴	semidirect
349. C₂×C₂²⋊Q₈	C₂⁴	semidirect
350. C₂×C₂²⋊Q₈	C₂⁴	semidirect
351. C₂×C₂²⋊Q₈	C₂⁴	semidirect
356. C₂×#121	C₂⁴	semidirect
357. C₂×#121	C₂⁴	semidirect
358. C₂×#121	C₂⁴	semidirect
362. C₂×#120	C₂⁴	semidirect
363. C₂×#120	C₂⁴	semidirect
364. C₂×#120	C₂⁴	semidirect
365. C₂×C₄×Q₈	C₂⁴	semidirect
366. C₂×C₄×Q₈	C₂⁴	semidirect
368. C₂×C₄×D₄	C₂⁴	semidirect
369. C₂×C₄×D₄	C₂⁴	semidirect
370. C₂×C₄×D₄	C₂⁴	semidirect
371. C₂×C₄×D₄	C₂⁴	semidirect
372. C₂×C₄×D₄	C₂⁴	semidirect
373. C₂×#117	C₂⁴	semidirect
374. C₂×#117	C₂⁴	semidirect
375. C₂×#117	C₂⁴	semidirect
376. C₂×#117	C₂⁴	semidirect
377. C₂×#117	C₂⁴	semidirect
406. C₂²×C₂²⋊C₄	C₂⁴	semidirect
451. C₂²×Q₈	C₂⁵	semidirect
475. C₂²×D₄	C₂⁵	semidirect
515. C₂³×C₄	C₂⁵	semidirect
516. C₄⋊Q₈	C₂⁵	semidirect
517. C₄⋊Q₈	C₂⁵	semidirect
519. #126	C₂⁵	semidirect
520. #126	C₂⁵	semidirect
521. #126	C₂⁵	semidirect
524. #124	C₂⁵	semidirect
525. #124	C₂⁵	semidirect
526. #124	C₂⁵	semidirect
527. #124	C₂⁵	semidirect
528. #124	C₂⁵	semidirect
529. #124	C₂⁵	semidirect
531. #123	C₂⁵	semidirect
532. #123	C₂⁵	semidirect
533. #123	C₂⁵	semidirect
534. #123	C₂⁵	semidirect
535. #123	C₂⁵	semidirect
536. #123	C₂⁵	semidirect
537. C₂²⋊Q₈	C₂⁵	semidirect
538. C₂²⋊Q₈	C₂⁵	semidirect
539. C₂²⋊Q₈	C₂⁵	semidirect
540. C₂²⋊Q₈	C₂⁵	semidirect
541. C₂²⋊Q₈	C₂⁵	semidirect
542. C₂²⋊Q₈	C₂⁵	semidirect
547. #121	C₂⁵	semidirect
548. #121	C₂⁵	semidirect
549. #121	C₂⁵	semidirect
553. #120	C₂⁵	semidirect
554. #120	C₂⁵	semidirect
555. #120	C₂⁵	semidirect
556. C₄×Q₈	C₂⁵	semidirect
557. C₄×Q₈	C₂⁵	semidirect
559. C₄×D₄	C₂⁵	semidirect
560. C₄×D₄	C₂⁵	semidirect
561. C₄×D₄	C₂⁵	semidirect
562. C₄×D₄	C₂⁵	semidirect
563. C₄×D₄	C₂⁵	semidirect
564. #117	C₂⁵	semidirect
565. #117	C₂⁵	semidirect
566. #117	C₂⁵	semidirect
567. #117	C₂⁵	semidirect
568. #117	C₂⁵	semidirect
597. C₂×C₂²⋊C₄	C₂⁵	semidirect
765. C₂³	#3540	direct (N × H)
837. C₂²	C₂×#3540	direct (N × H)
856. C₂	C₂²×#3540	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×#3540	2
C₂³×H(3,𝔽₄)	2
C₂³×#560	2
C₂³×#559	2
C₂³×#555	2
C₂³×#556	2
C₂³×#551	2
C₂³×#548	2
C₂³×#546	2
C₂³×#536	2
C₂³×#542	2
C₂³×#535	2
C₂³×#538	2
C₂³×#525	2

Subgroups — C23×#3540 #72324997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#3540 #72324997