Subgroups — C₂³×#3539 #72324991

Order 1024.

480781 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#3539	C₂	1	224	yes	maximal, direct product factor
2	C₂³×#560	C₂	1	4	yes	maximal, complemented
3	C₂³×#553	C₂	1	2	yes	maximal, complemented
4	C₂³×#553	C₂	1	4	yes	maximal, complemented
5	C₂³×#552	C₂	1	2	yes	maximal, complemented
6	C₂³×#550	C₂	1	2	yes	maximal, complemented
7	C₂³×#547	C₂	1	2	yes	maximal, complemented
8	C₂³×#541	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×#540	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×#540	C₂	1	4	yes	maximal, complemented
11	C₂³×#537	C₂	1	2	yes	maximal, complemented
12	C₂³×#539	C₂	1	4	yes	maximal, complemented
13	C₂³×#525	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×#525	C₂	1	2	yes	maximal, complemented
15	C₂⁴×#41	C₂²	1	1	yes	characteristic
16	C₂⁴×#41	C₂²	1	2	yes	—
17	C₂⁴×#41	C₂²	1	2	yes	complemented
18	C₂⁶×C₄	C₂²	1	1	yes	characteristic
19	C₂×#3539	C₂²	1	7168	yes	direct product factor
20	C₂²×#553	C₂²	1	224	yes	complemented
21	C₂²×#553	C₂²	1	448	yes	complemented
22	C₂²×#552	C₂²	1	224	yes	complemented
23	C₂²×#550	C₂²	1	224	yes	complemented
24	C₂²×#547	C₂²	1	224	yes	complemented
25	C₂²×#560	C₂²	1	448	yes	complemented
26	C₂²×#541	C₂²	1	112	yes	complemented
27	C₂²×#540	C₂²	1	112	yes	complemented
28	C₂²×#540	C₂²	1	448	yes	complemented
29	C₂²×#537	C₂²	1	224	yes	complemented
30	C₂²×#539	C₂²	1	448	yes	complemented
31	C₂³×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂³×#127	C₂²	1	4	yes	—
33	C₂³×#127	C₂²	1	1	yes	characteristic, complemented
34	C₂³×#126	C₂²	1	4	yes	—
35	C₂³×#126	C₂²	1	4	yes	—
36	C₂³×#126	C₂²	1	4	yes	complemented
37	C₂³×#125	C₂²	1	4	yes	complemented
38	C₂³×#125	C₂²	1	4	yes	complemented
39	C₂³×#125	C₂²	1	1	yes	characteristic, complemented
40	C₂³×#125	C₂²	1	1	yes	characteristic, complemented
41	C₂²×#525	C₂²	1	112	yes	complemented
42	C₂²×#525	C₂²	1	224	yes	complemented
43	C₂³×#123	C₂²	1	4	yes	—
44	C₂³×#123	C₂²	1	2	yes	—
45	C₂³×#123	C₂²	1	4	yes	—
46	C₂³×#123	C₂²	1	4	yes	—
47	C₂³×#123	C₂²	1	4	yes	—
48	C₂³×#123	C₂²	1	4	yes	complemented
49	C₂³×#123	C₂²	1	4	yes	complemented
50	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	—
52	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	—
53	C₂³×C₂²⋊Q₈	C₂²	1	4	yes	complemented
54	C₂³×C₂²⋊Q₈	C₂²	1	2	yes	complemented
55	C₂³×#121	C₂²	1	2	yes	—
56	C₂³×#121	C₂²	1	2	yes	—
57	C₂³×#121	C₂²	1	2	yes	—
58	C₂³×#121	C₂²	1	4	yes	—
59	C₂³×#121	C₂²	1	4	yes	—
60	C₂³×#121	C₂²	1	4	yes	—
61	C₂³×#121	C₂²	1	4	yes	—
62	C₂³×#121	C₂²	1	4	yes	—
63	C₂³×#121	C₂²	1	4	yes	—
64	C₂³×#121	C₂²	1	4	yes	complemented
65	C₂³×#121	C₂²	1	2	yes	complemented
66	C₂³×#121	C₂²	1	4	yes	complemented
67	C₂³×#120	C₂²	1	2	yes	—
68	C₂³×#120	C₂²	1	4	yes	—
69	C₂³×C₄×Q₈	C₂²	1	2	yes	complemented
70	C₂³×C₄×D₄	C₂²	1	4	yes	—
71	C₂³×C₄×D₄	C₂²	1	2	yes	—
72	C₂³×C₄×D₄	C₂²	1	2	yes	—
73	C₂³×C₄×D₄	C₂²	1	4	yes	—
74	C₂³×C₄×D₄	C₂²	1	4	yes	complemented
75	C₂³×C₄×D₄	C₂²	1	2	yes	complemented
76	C₂³×C₄×D₄	C₂²	1	4	yes	complemented
77	C₂³×#117	C₂²	1	1	yes	characteristic
78	C₂³×#117	C₂²	1	2	yes	—
79	C₂³×#117	C₂²	1	4	yes	complemented
80	C₂⁴×C₄⋊C₄	C₂²	1	4	yes	complemented
81	C₂⁴×C₄⋊C₄	C₂²	1	2	yes	complemented
82	C₂⁷	C₂³	1	1	yes	characteristic
83	C₂³×#41	—	4	16	no	—
84	C₂³×#41	—	4	32	no	—
85	C₂³×#41	—	4	32	no	—
86	C₂³×#41	C₂³	1	56	yes	—
87	C₂³×#41	C₂³	1	112	yes	—
88	C₂³×#41	C₂³	1	112	yes	complemented
89	C₂⁴×Q₈	C₂³	1	2	yes	—
90	C₂⁴×Q₈	C₂³	1	1	yes	characteristic
91	C₂⁴×D₄	C₂³	1	2	yes	—
92	C₂⁴×D₄	C₂³	1	2	yes	—
93	C₂⁴×D₄	C₂³	1	4	yes	—
94	C₂⁴×D₄	C₂³	1	1	yes	characteristic
95	C₂⁴×D₄	C₂³	1	4	yes	—
96	C₂⁴×D₄	C₂³	1	2	yes	—
97	C₂⁴×D₄	C₂³	1	4	yes	—
98	C₂⁴×D₄	C₂³	1	4	yes	—
99	C₂⁴×D₄	C₂³	1	2	yes	—
100	C₂⁴×D₄	C₂³	1	4	yes	—
101	C₂⁴×D₄	C₂³	1	4	yes	—
102	C₂⁵×C₄	—	4	16	no	—
103	C₂⁵×C₄	C₂³	1	2	yes	—
104	C₂⁵×C₄	C₂³	1	1	yes	characteristic
105	C₂⁵×C₄	C₂³	1	2	yes	—
106	C₂⁵×C₄	C₂³	1	1	yes	characteristic
107	C₂⁵×C₄	C₂³	1	2	yes	—
108	C₂⁵×C₄	C₂³	1	56	yes	—
109	C₂⁵×C₄	C₂³	1	4	yes	—
110	C₂⁵×C₄	C₂³	1	4	yes	—
111	C₂⁵×C₄	C₂³	1	4	yes	—
112	C₂⁵×C₄	C₂³	1	4	yes	—
113	#3539	C₂³	1	32768	yes	direct product factor
114	C₂×#560	C₂³	1	7168	yes	complemented
115	C₂×#553	C₂³	1	3584	yes	complemented
116	C₂×#553	C₂³	1	7168	yes	complemented
117	C₂×#552	C₂³	1	3584	yes	complemented
118	C₂×#550	C₂³	1	3584	yes	complemented
119	C₂×#547	C₂³	1	3584	yes	complemented
120	C₂×#541	C₂³	1	1792	yes	complemented
121	C₂×#540	C₂³	1	1792	yes	complemented
122	C₂×#540	C₂³	1	7168	yes	complemented
123	C₂×#539	C₂³	1	7168	yes	complemented
124	C₂×#537	C₂³	1	3584	yes	complemented
125	C₂²×C₄⋊Q₈	C₂³	1	56	yes	complemented
126	C₂²×#127	C₂³	1	224	yes	—
127	C₂²×#127	C₂³	1	56	yes	complemented
128	C₂²×#126	C₂³	1	224	yes	—
129	C₂²×#126	C₂³	1	224	yes	—
130	C₂²×#126	C₂³	1	224	yes	complemented
131	C₂²×#125	C₂³	1	224	yes	complemented
132	C₂²×#125	C₂³	1	224	yes	complemented
133	C₂²×#125	C₂³	1	56	yes	complemented
134	C₂²×#125	C₂³	1	56	yes	complemented
135	C₂×#525	C₂³	1	1792	yes	complemented
136	C₂×#525	C₂³	1	3584	yes	complemented
137	C₂²×#123	C₂³	1	224	yes	—
138	C₂²×#123	C₂³	1	112	yes	—
139	C₂²×#123	C₂³	1	224	yes	—
140	C₂²×#123	C₂³	1	224	yes	—
141	C₂²×#123	C₂³	1	224	yes	—
142	C₂²×#123	C₂³	1	224	yes	complemented
143	C₂²×#123	C₂³	1	224	yes	complemented
144	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	—
145	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	—
146	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	—
147	C₂²×C₂²⋊Q₈	C₂³	1	224	yes	complemented
148	C₂²×C₂²⋊Q₈	C₂³	1	112	yes	complemented
149	C₂²×#121	C₂³	1	112	yes	—
150	C₂²×#121	C₂³	1	112	yes	—
151	C₂²×#121	C₂³	1	112	yes	—
152	C₂²×#121	C₂³	1	224	yes	—
153	C₂²×#121	C₂³	1	224	yes	—
154	C₂²×#121	C₂³	1	224	yes	—
155	C₂²×#121	C₂³	1	224	yes	—
156	C₂²×#121	C₂³	1	224	yes	—
157	C₂²×#121	C₂³	1	224	yes	—
158	C₂²×#121	C₂³	1	224	yes	complemented
159	C₂²×#121	C₂³	1	112	yes	complemented
160	C₂²×#121	C₂³	1	224	yes	complemented
161	C₂²×#120	C₂³	1	112	yes	—
162	C₂²×#120	C₂³	1	224	yes	—
163	C₂²×C₄×Q₈	C₂³	1	112	yes	complemented
164	C₂²×C₄×D₄	C₂³	1	224	yes	—
165	C₂²×C₄×D₄	C₂³	1	112	yes	—
166	C₂²×C₄×D₄	C₂³	1	112	yes	—
167	C₂²×C₄×D₄	C₂³	1	224	yes	—
168	C₂²×C₄×D₄	C₂³	1	224	yes	complemented
169	C₂²×C₄×D₄	C₂³	1	112	yes	complemented
170	C₂²×C₄×D₄	C₂³	1	224	yes	complemented
171	C₂²×#117	C₂³	1	56	yes	—
172	C₂²×#117	C₂³	1	112	yes	—
173	C₂²×#117	C₂³	1	224	yes	complemented
174	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
175	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
176	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
177	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
178	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
179	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
180	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
181	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
183	C₂³×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
185	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
186	C₂³×C₄⋊C₄	C₂³	1	4	yes	—
187	C₂³×C₄⋊C₄	C₂³	1	224	yes	complemented
188	C₂³×C₄⋊C₄	C₂³	1	112	yes	complemented
189	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
191	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
193	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
194	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
197	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
198	C₂³×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
200	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
201	C₂³×C₂²⋊C₄	C₂³	1	4	yes	—
202	C₂³×C₄²	C₂³	1	4	yes	—
203	C₂³×C₄²	C₂³	1	1	yes	characteristic
204	C₂³×C₄²	C₂³	1	1	yes	characteristic
205	C₂³×C₄²	C₂³	1	4	yes	—
206	C₂⁶	—	4	8	no	—
207	C₂⁶	—	4	16	no	—
208	C₂⁶	C₂⁴	1	2	yes	—
209	C₂⁶	C₂⁴	1	4	yes	—
210	C₂⁶	C₂⁴	1	2	yes	—
211	C₂⁶	C₂⁴	1	1	yes	characteristic
212	C₂⁶	C₂⁴	1	28	yes	—
213	C₂²×#41	—	4	448	no	—
214	C₂²×#41	—	4	896	no	—
215	C₂²×#41	—	4	896	no	—
216	C₂²×#41	C₂⁴	1	448	yes	—
217	C₂²×#41	C₂⁴	1	896	yes	—
218	C₂²×#41	C₂⁴	1	896	yes	complemented
219	C₂³×Q₈	—	2	32	no	—
220	C₂³×Q₈	—	4	8	no	—
221	C₂³×Q₈	C₂⁴	1	56	yes	—
222	C₂³×Q₈	C₂⁴	1	28	yes	—
223	C₂³×D₄	—	2	32	no	—
224	C₂³×D₄	—	4	16	no	—
225	C₂³×D₄	—	4	32	no	—
226	C₂³×D₄	—	4	32	no	—
227	C₂³×D₄	—	4	32	no	—
228	C₂³×D₄	—	4	16	no	—
229	C₂³×D₄	—	4	32	no	—
230	C₂³×D₄	—	4	16	no	—
231	C₂³×D₄	—	4	8	no	—
232	C₂³×D₄	—	4	32	no	—
233	C₂³×D₄	—	4	32	no	—
234	C₂³×D₄	C₂⁴	1	56	yes	—
235	C₂³×D₄	C₂⁴	1	56	yes	—
236	C₂³×D₄	C₂⁴	1	112	yes	—
237	C₂³×D₄	C₂⁴	1	28	yes	—
238	C₂³×D₄	C₂⁴	1	112	yes	—
239	C₂³×D₄	C₂⁴	1	56	yes	—
240	C₂³×D₄	C₂⁴	1	112	yes	—
241	C₂³×D₄	C₂⁴	1	112	yes	—
242	C₂³×D₄	C₂⁴	1	56	yes	—
243	C₂³×D₄	C₂⁴	1	112	yes	—
244	C₂³×D₄	C₂⁴	1	112	yes	—
245	C₂⁴×C₄	—	2	32	no	—
246	C₂⁴×C₄	—	2	16	no	—
247	C₂⁴×C₄	—	2	32	no	—
248	C₂⁴×C₄	—	4	448	no	—
249	C₂⁴×C₄	—	4	8	no	—
250	C₂⁴×C₄	—	4	16	no	—
251	C₂⁴×C₄	—	4	32	no	—
252	C₂⁴×C₄	—	4	32	no	—
253	C₂⁴×C₄	—	4	32	no	—
254	C₂⁴×C₄	—	4	32	no	—
255	C₂⁴×C₄	C₂⁴	1	56	yes	—
256	C₂⁴×C₄	C₂⁴	1	28	yes	—
257	C₂⁴×C₄	C₂⁴	1	56	yes	—
258	C₂⁴×C₄	C₂⁴	1	2	yes	—
259	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
260	C₂⁴×C₄	C₂⁴	1	2	yes	—
261	C₂⁴×C₄	C₂⁴	1	4	yes	—
262	C₂⁴×C₄	C₂⁴	1	4	yes	—
263	C₂⁴×C₄	C₂⁴	1	2	yes	—
264	C₂⁴×C₄	C₂⁴	1	4	yes	—
265	C₂⁴×C₄	C₂⁴	1	2	yes	—
266	C₂⁴×C₄	C₂⁴	1	28	yes	—
267	C₂⁴×C₄	C₂⁴	1	56	yes	—
268	C₂⁴×C₄	C₂⁴	1	448	yes	—
269	C₂⁴×C₄	C₂⁴	1	112	yes	—
270	C₂⁴×C₄	C₂⁴	1	112	yes	—
271	C₂⁴×C₄	C₂⁴	1	112	yes	—
272	C₂⁴×C₄	C₂⁴	1	112	yes	—
273	C₂⁴×C₄	C₂⁴	1	1	yes	characteristic
274	#560	C₂⁴	1	16384	yes	complemented
275	#553	C₂⁴	1	8192	yes	complemented
276	#553	C₂⁴	1	16384	yes	complemented
277	#552	C₂⁴	1	8192	yes	complemented
278	#550	C₂⁴	1	8192	yes	complemented
279	#547	C₂⁴	1	8192	yes	complemented
280	#541	C₂⁴	1	4096	yes	complemented
281	#540	C₂⁴	1	4096	yes	complemented
282	#540	C₂⁴	1	16384	yes	complemented
283	#539	C₂⁴	1	16384	yes	complemented
284	#537	C₂⁴	1	8192	yes	complemented
285	C₂×C₄⋊Q₈	C₂⁴	1	448	yes	complemented
286	C₂×#127	C₂⁴	1	1792	yes	—
287	C₂×#127	C₂⁴	1	448	yes	complemented
288	C₂×#126	C₂⁴	1	1792	yes	—
289	C₂×#126	C₂⁴	1	1792	yes	—
290	C₂×#126	C₂⁴	1	1792	yes	complemented
291	C₂×#125	C₂⁴	1	1792	yes	complemented
292	C₂×#125	C₂⁴	1	1792	yes	complemented
293	C₂×#125	C₂⁴	1	448	yes	complemented
294	C₂×#125	C₂⁴	1	448	yes	complemented
295	#525	C₂⁴	1	4096	yes	complemented
296	#525	C₂⁴	1	8192	yes	complemented
297	C₂×#123	C₂⁴	1	1792	yes	—
298	C₂×#123	C₂⁴	1	896	yes	—
299	C₂×#123	C₂⁴	1	1792	yes	—
300	C₂×#123	C₂⁴	1	1792	yes	—
301	C₂×#123	C₂⁴	1	1792	yes	—
302	C₂×#123	C₂⁴	1	1792	yes	complemented
303	C₂×#123	C₂⁴	1	1792	yes	complemented
304	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	—
305	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	—
306	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	—
307	C₂×C₂²⋊Q₈	C₂⁴	1	1792	yes	complemented
308	C₂×C₂²⋊Q₈	C₂⁴	1	896	yes	complemented
309	C₂×#121	C₂⁴	1	896	yes	—
310	C₂×#121	C₂⁴	1	896	yes	—
311	C₂×#121	C₂⁴	1	896	yes	—
312	C₂×#121	C₂⁴	1	1792	yes	—
313	C₂×#121	C₂⁴	1	1792	yes	—
314	C₂×#121	C₂⁴	1	1792	yes	—
315	C₂×#121	C₂⁴	1	1792	yes	—
316	C₂×#121	C₂⁴	1	1792	yes	—
317	C₂×#121	C₂⁴	1	1792	yes	—
318	C₂×#121	C₂⁴	1	1792	yes	complemented
319	C₂×#121	C₂⁴	1	896	yes	complemented
320	C₂×#121	C₂⁴	1	1792	yes	complemented
321	C₂×#120	C₂⁴	1	896	yes	—
322	C₂×#120	C₂⁴	1	1792	yes	—
323	C₂×C₄×Q₈	C₂⁴	1	896	yes	complemented
324	C₂×C₄×D₄	C₂⁴	1	1792	yes	—
325	C₂×C₄×D₄	C₂⁴	1	896	yes	—
326	C₂×C₄×D₄	C₂⁴	1	896	yes	—
327	C₂×C₄×D₄	C₂⁴	1	1792	yes	—
328	C₂×C₄×D₄	C₂⁴	1	1792	yes	complemented
329	C₂×C₄×D₄	C₂⁴	1	896	yes	complemented
330	C₂×C₄×D₄	C₂⁴	1	1792	yes	complemented
331	C₂×#117	C₂⁴	1	448	yes	—
332	C₂×#117	C₂⁴	1	896	yes	—
333	C₂×#117	C₂⁴	1	1792	yes	complemented
334	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
335	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
336	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
337	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
338	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
339	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
340	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
341	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
342	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
343	C₂²×C₄⋊C₄	C₂⁴	1	56	yes	—
344	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
345	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
346	C₂²×C₄⋊C₄	C₂⁴	1	112	yes	—
347	C₂²×C₄⋊C₄	C₂⁴	1	896	yes	complemented
348	C₂²×C₄⋊C₄	C₂⁴	1	1792	yes	complemented
349	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
350	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
351	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
352	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
353	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
354	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
355	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
356	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
357	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
358	C₂²×C₂²⋊C₄	C₂⁴	1	56	yes	—
359	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
360	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
361	C₂²×C₂²⋊C₄	C₂⁴	1	112	yes	—
362	C₂²×C₄²	C₂⁴	1	112	yes	—
363	C₂²×C₄²	C₂⁴	1	28	yes	—
364	C₂²×C₄²	C₂⁴	1	28	yes	—
365	C₂²×C₄²	C₂⁴	1	112	yes	—
366	C₂⁵	—	2	16	no	—
367	C₂⁵	—	2	8	no	—
368	C₂⁵	—	2	16	no	—
369	C₂⁵	—	2	32	no	—
370	C₂⁵	—	2	16	no	—
371	C₂⁵	—	2	32	no	—
372	C₂⁵	—	2	16	no	—
373	C₂⁵	—	2	32	no	—
374	C₂⁵	—	2	16	no	—
375	C₂⁵	—	2	16	no	—
376	C₂⁵	—	2	16	no	—
377	C₂⁵	—	4	112	no	—
378	C₂⁵	—	4	224	no	—
379	C₂⁵	—	4	256	no	—
380	C₂⁵	C₂⁵	1	14	yes	—
381	C₂⁵	C₂⁵	1	28	yes	—
382	C₂⁵	C₂⁵	1	28	yes	—
383	C₂⁵	C₂⁵	1	56	yes	—
384	C₂⁵	C₂⁵	1	112	yes	—
385	C₂⁵	C₂⁵	1	1	yes	characteristic
386	C₂×#41	—	4	1792	no	—
387	C₂×#41	—	4	3584	no	—
388	C₂×#41	—	4	3584	no	—
389	C₂×#41	C₂⁵	1	512	yes	—
390	C₂×#41	C₂⁵	1	1024	yes	—
391	C₂×#41	C₂⁵	1	1024	yes	complemented
392	C₂²×Q₈	—	2	448	no	—
393	C₂²×Q₈	—	4	112	no	—
394	C₂²×Q₈	C₂⁵	1	224	yes	—
395	C₂²×Q₈	C₂⁵	1	112	yes	—
396	C₂²×D₄	—	2	448	no	—
397	C₂²×D₄	—	4	224	no	—
398	C₂²×D₄	—	4	448	no	—
399	C₂²×D₄	—	4	448	no	—
400	C₂²×D₄	—	4	448	no	—
401	C₂²×D₄	—	4	224	no	—
402	C₂²×D₄	—	4	448	no	—
403	C₂²×D₄	—	4	224	no	—
404	C₂²×D₄	—	4	112	no	—
405	C₂²×D₄	—	4	448	no	—
406	C₂²×D₄	—	4	448	no	—
407	C₂²×D₄	C₂⁵	1	224	yes	—
408	C₂²×D₄	C₂⁵	1	224	yes	—
409	C₂²×D₄	C₂⁵	1	448	yes	—
410	C₂²×D₄	C₂⁵	1	448	yes	—
411	C₂²×D₄	C₂⁵	1	224	yes	—
412	C₂²×D₄	C₂⁵	1	448	yes	—
413	C₂²×D₄	C₂⁵	1	448	yes	—
414	C₂²×D₄	C₂⁵	1	224	yes	—
415	C₂²×D₄	C₂⁵	1	448	yes	—
416	C₂²×D₄	C₂⁵	1	112	yes	—
417	C₂²×D₄	C₂⁵	1	448	yes	—
418	C₂³×C₄	—	2	16	no	—
419	C₂³×C₄	—	2	8	no	—
420	C₂³×C₄	—	2	16	no	—
421	C₂³×C₄	—	2	32	no	—
422	C₂³×C₄	—	2	16	no	—
423	C₂³×C₄	—	2	32	no	—
424	C₂³×C₄	—	2	32	no	—
425	C₂³×C₄	—	2	16	no	—
426	C₂³×C₄	—	2	448	no	—
427	C₂³×C₄	—	2	224	no	—
428	C₂³×C₄	—	2	448	no	—
429	C₂³×C₄	—	4	1792	no	—
430	C₂³×C₄	—	4	112	no	—
431	C₂³×C₄	—	4	224	no	—
432	C₂³×C₄	—	4	448	no	—
433	C₂³×C₄	—	4	448	no	—
434	C₂³×C₄	—	4	448	no	—
435	C₂³×C₄	—	4	448	no	—
436	C₂³×C₄	H(5,𝔽₂)	1	16	yes	—
437	C₂³×C₄	C₂⁵	1	28	yes	—
438	C₂³×C₄	C₂⁵	1	56	yes	—
439	C₂³×C₄	C₂⁵	1	28	yes	—
440	C₂³×C₄	C₂⁵	1	14	yes	—
441	C₂³×C₄	C₂⁵	1	56	yes	—
442	C₂³×C₄	C₂⁵	1	28	yes	—
443	C₂³×C₄	C₂⁵	1	56	yes	—
444	C₂³×C₄	C₂⁵	1	28	yes	—
445	C₂³×C₄	C₂⁵	1	224	yes	—
446	C₂³×C₄	C₂⁵	1	224	yes	—
447	C₂³×C₄	C₂⁵	1	112	yes	—
448	C₂³×C₄	C₂⁵	1	448	yes	—
449	C₂³×C₄	C₂⁵	1	448	yes	—
450	C₂³×C₄	C₂⁵	1	448	yes	—
451	C₂³×C₄	C₂⁵	1	448	yes	—
452	C₂³×C₄	C₂⁵	1	112	yes	—
453	C₂³×C₄	C₂⁵	1	224	yes	—
454	C₂³×C₄	C₂⁵	1	512	yes	—
455	C₂³×C₄	C₂⁵	1	14	yes	—
456	C₄⋊Q₈	C₂⁵	1	512	yes	complemented
457	#127	C₂⁵	1	2048	yes	—
458	#127	C₂⁵	1	512	yes	complemented
459	#126	C₂⁵	1	2048	yes	—
460	#126	C₂⁵	1	2048	yes	—
461	#126	C₂⁵	1	2048	yes	complemented
462	#125	C₂⁵	1	2048	yes	complemented
463	#125	C₂⁵	1	2048	yes	complemented
464	#125	C₂⁵	1	512	yes	complemented
465	#125	C₂⁵	1	512	yes	complemented
466	#123	C₂⁵	1	2048	yes	—
467	#123	C₂⁵	1	1024	yes	—
468	#123	C₂⁵	1	2048	yes	—
469	#123	C₂⁵	1	2048	yes	—
470	#123	C₂⁵	1	2048	yes	—
471	#123	C₂⁵	1	2048	yes	complemented
472	#123	C₂⁵	1	2048	yes	complemented
473	C₂²⋊Q₈	C₂⁵	1	1024	yes	—
474	C₂²⋊Q₈	C₂⁵	1	1024	yes	—
475	C₂²⋊Q₈	C₂⁵	1	1024	yes	—
476	C₂²⋊Q₈	C₂⁵	1	2048	yes	complemented
477	C₂²⋊Q₈	C₂⁵	1	1024	yes	complemented
478	#121	C₂⁵	1	1024	yes	—
479	#121	C₂⁵	1	1024	yes	—
480	#121	C₂⁵	1	1024	yes	—
481	#121	C₂⁵	1	2048	yes	—
482	#121	C₂⁵	1	2048	yes	—
483	#121	C₂⁵	1	2048	yes	—
484	#121	C₂⁵	1	2048	yes	—
485	#121	C₂⁵	1	2048	yes	—
486	#121	C₂⁵	1	2048	yes	—
487	#121	C₂⁵	1	2048	yes	complemented
488	#121	C₂⁵	1	1024	yes	complemented
489	#121	C₂⁵	1	2048	yes	complemented
490	#120	C₂⁵	1	1024	yes	—
491	#120	C₂⁵	1	2048	yes	—
492	C₄×Q₈	C₂⁵	1	1024	yes	complemented
493	C₄×D₄	C₂⁵	1	2048	yes	—
494	C₄×D₄	C₂⁵	1	1024	yes	—
495	C₄×D₄	C₂⁵	1	1024	yes	—
496	C₄×D₄	C₂⁵	1	2048	yes	—
497	C₄×D₄	C₂⁵	1	2048	yes	complemented
498	C₄×D₄	C₂⁵	1	1024	yes	complemented
499	C₄×D₄	C₂⁵	1	2048	yes	complemented
500	#117	C₂⁵	1	512	yes	—
501	#117	C₂⁵	1	1024	yes	—
502	#117	C₂⁵	1	2048	yes	complemented
503	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
504	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
505	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
506	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
507	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
508	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
509	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
510	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
511	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
512	C₂×C₄⋊C₄	C₂⁵	1	224	yes	—
513	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
514	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
515	C₂×C₄⋊C₄	C₂⁵	1	448	yes	—
516	C₂×C₄⋊C₄	C₂⁵	1	1024	yes	complemented
517	C₂×C₄⋊C₄	C₂⁵	1	2048	yes	complemented
518	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
519	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
520	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
521	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
522	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
523	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
524	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
525	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
526	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
527	C₂×C₂²⋊C₄	C₂⁵	1	224	yes	—
528	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
529	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
530	C₂×C₂²⋊C₄	C₂⁵	1	448	yes	—
531	C₂×C₄²	C₂⁵	1	448	yes	—
532	C₂×C₄²	C₂⁵	1	112	yes	—
533	C₂×C₄²	C₂⁵	1	112	yes	—
534	C₂×C₄²	C₂⁵	1	448	yes	—
535	C₂⁴	—	2	112	no	—
536	C₂⁴	—	2	56	no	—
537	C₂⁴	—	2	112	no	—
538	C₂⁴	—	2	224	no	—
539	C₂⁴	—	2	112	no	—
540	C₂⁴	—	2	224	no	—
541	C₂⁴	—	2	112	no	—
542	C₂⁴	—	2	224	no	—
543	C₂⁴	—	2	112	no	—
544	C₂⁴	—	2	112	no	—
545	C₂⁴	—	2	112	no	—
546	C₂⁴	—	4	224	no	—
547	C₂⁴	—	4	448	no	—
548	C₂⁴	—	4	1792	no	—
549	C₂⁴	—	4	128	no	—
550	C₂⁴	—	4	256	no	—
551	C₂⁴	—	4	128	no	—
552	C₂⁴	—	4	64	no	—
553	C₂⁴	C₂×H(5,𝔽₂)	1	8	yes	—
554	C₂⁴	#585	1	16	yes	—
555	C₂⁴	C₂⁶	1	28	yes	—
556	C₂⁴	C₂⁶	1	56	yes	—
557	C₂⁴	C₂⁶	1	56	yes	—
558	C₂⁴	C₂⁶	1	112	yes	—
559	C₂⁴	C₂⁶	1	64	yes	—
560	C₂⁴	C₂⁶	1	7	yes	—
561	#41	—	4	1024	no	—
562	#41	—	4	2048	no	—
563	#41	—	4	2048	no	—
564	C₂×Q₈	—	2	896	no	—
565	C₂×Q₈	—	4	224	no	—
566	C₂×Q₈	C₂⁶	1	128	yes	—
567	C₂×Q₈	C₂⁶	1	64	yes	—
568	C₂×D₄	—	2	896	no	—
569	C₂×D₄	—	4	448	no	—
570	C₂×D₄	—	4	896	no	—
571	C₂×D₄	—	4	896	no	—
572	C₂×D₄	—	4	896	no	—
573	C₂×D₄	—	4	448	no	—
574	C₂×D₄	—	4	896	no	—
575	C₂×D₄	—	4	448	no	—
576	C₂×D₄	—	4	224	no	—
577	C₂×D₄	—	4	896	no	—
578	C₂×D₄	—	4	896	no	—
579	C₂×D₄	C₂⁶	1	128	yes	—
580	C₂×D₄	C₂⁶	1	128	yes	—
581	C₂×D₄	C₂⁶	1	256	yes	—
582	C₂×D₄	C₂⁶	1	256	yes	—
583	C₂×D₄	C₂⁶	1	128	yes	—
584	C₂×D₄	C₂⁶	1	256	yes	—
585	C₂×D₄	C₂⁶	1	256	yes	—
586	C₂×D₄	C₂⁶	1	128	yes	—
587	C₂×D₄	C₂⁶	1	256	yes	—
588	C₂×D₄	C₂⁶	1	64	yes	—
589	C₂×D₄	C₂⁶	1	256	yes	—
590	C₂²×C₄	—	2	112	no	—
591	C₂²×C₄	—	2	56	no	—
592	C₂²×C₄	—	2	112	no	—
593	C₂²×C₄	—	2	224	no	—
594	C₂²×C₄	—	2	112	no	—
595	C₂²×C₄	—	2	224	no	—
596	C₂²×C₄	—	2	224	no	—
597	C₂²×C₄	—	2	112	no	—
598	C₂²×C₄	—	2	896	no	—
599	C₂²×C₄	—	2	448	no	—
600	C₂²×C₄	—	2	896	no	—
601	C₂²×C₄	—	4	1024	no	—
602	C₂²×C₄	—	4	224	no	—
603	C₂²×C₄	—	4	448	no	—
604	C₂²×C₄	—	4	896	no	—
605	C₂²×C₄	—	4	896	no	—
606	C₂²×C₄	—	4	896	no	—
607	C₂²×C₄	—	4	896	no	—
608	C₂²×C₄	C₂×H(5,𝔽₂)	1	112	yes	—
609	C₂²×C₄	C₂⁶	1	56	yes	—
610	C₂²×C₄	C₂⁶	1	112	yes	—
611	C₂²×C₄	C₂⁶	1	56	yes	—
612	C₂²×C₄	C₂⁶	1	112	yes	—
613	C₂²×C₄	C₂⁶	1	56	yes	—
614	C₂²×C₄	C₂⁶	1	112	yes	—
615	C₂²×C₄	C₂⁶	1	56	yes	—
616	C₂²×C₄	C₂⁶	1	28	yes	—
617	C₂²×C₄	C₂⁶	1	128	yes	—
618	C₂²×C₄	C₂⁶	1	128	yes	—
619	C₂²×C₄	C₂⁶	1	64	yes	—
620	C₂²×C₄	C₂⁶	1	256	yes	—
621	C₂²×C₄	C₂⁶	1	256	yes	—
622	C₂²×C₄	C₂⁶	1	256	yes	—
623	C₂²×C₄	C₂⁶	1	256	yes	—
624	C₂²×C₄	C₂⁶	1	64	yes	—
625	C₂²×C₄	C₂⁶	1	128	yes	—
626	C₂²×C₄	C₂⁶	1	28	yes	—
627	C₄⋊C₄	C₂⁶	1	128	yes	—
628	C₄⋊C₄	C₂⁶	1	128	yes	—
629	C₄⋊C₄	C₂⁶	1	128	yes	—
630	C₄⋊C₄	C₂⁶	1	256	yes	—
631	C₄⋊C₄	C₂⁶	1	256	yes	—
632	C₄⋊C₄	C₂⁶	1	256	yes	—
633	C₄⋊C₄	C₂⁶	1	256	yes	—
634	C₄⋊C₄	C₂⁶	1	128	yes	—
635	C₄⋊C₄	C₂⁶	1	256	yes	—
636	C₄⋊C₄	C₂⁶	1	128	yes	—
637	C₄⋊C₄	C₂⁶	1	256	yes	—
638	C₄⋊C₄	C₂⁶	1	256	yes	—
639	C₄⋊C₄	C₂⁶	1	256	yes	—
640	C₂²⋊C₄	C₂⁶	1	128	yes	—
641	C₂²⋊C₄	C₂⁶	1	256	yes	—
642	C₂²⋊C₄	C₂⁶	1	128	yes	—
643	C₂²⋊C₄	C₂⁶	1	256	yes	—
644	C₂²⋊C₄	C₂⁶	1	256	yes	—
645	C₂²⋊C₄	C₂⁶	1	128	yes	—
646	C₂²⋊C₄	C₂⁶	1	128	yes	—
647	C₂²⋊C₄	C₂⁶	1	256	yes	—
648	C₂²⋊C₄	C₂⁶	1	256	yes	—
649	C₂²⋊C₄	C₂⁶	1	128	yes	—
650	C₂²⋊C₄	C₂⁶	1	256	yes	—
651	C₂²⋊C₄	C₂⁶	1	256	yes	—
652	C₂²⋊C₄	C₂⁶	1	256	yes	—
653	C₄²	C₂⁶	1	256	yes	—
654	C₄²	C₂⁶	1	64	yes	—
655	C₄²	C₂⁶	1	64	yes	—
656	C₄²	C₂⁶	1	256	yes	—
657	C₂³	—	2	112	no	—
658	C₂³	—	2	56	no	—
659	C₂³	—	2	112	no	—
660	C₂³	—	2	224	no	—
661	C₂³	—	2	112	no	—
662	C₂³	—	2	224	no	—
663	C₂³	—	2	112	no	—
664	C₂³	—	2	224	no	—
665	C₂³	—	2	112	no	—
666	C₂³	—	2	112	no	—
667	C₂³	—	2	112	no	—
668	C₂³	—	4	64	no	—
669	C₂³	—	4	128	no	—
670	C₂³	—	4	1792	no	—
671	C₂³	—	4	448	no	—
672	C₂³	—	4	896	no	—
673	C₂³	—	4	448	no	—
674	C₂³	—	4	224	no	—
675	C₂³	#3539	1	64	yes	direct product factor
676	C₂³	C₂²×H(5,𝔽₂)	1	28	yes	—
677	C₂³	C₂×#585	1	56	yes	—
678	C₂³	C₂⁷	1	8	yes	—
679	C₂³	C₂⁷	1	16	yes	—
680	C₂³	C₂⁷	1	16	yes	—
681	C₂³	C₂⁷	1	32	yes	—
682	C₂³	C₂⁷	1	7	yes	—
683	Q₈	—	2	256	no	—
684	Q₈	—	4	64	no	—
685	D₄	—	2	256	no	—
686	D₄	—	4	128	no	—
687	D₄	—	4	256	no	—
688	D₄	—	4	256	no	—
689	D₄	—	4	256	no	—
690	D₄	—	4	128	no	—
691	D₄	—	4	256	no	—
692	D₄	—	4	128	no	—
693	D₄	—	4	64	no	—
694	D₄	—	4	256	no	—
695	D₄	—	4	256	no	—
696	C₂×C₄	—	2	112	no	—
697	C₂×C₄	—	2	56	no	—
698	C₂×C₄	—	2	112	no	—
699	C₂×C₄	—	2	224	no	—
700	C₂×C₄	—	2	112	no	—
701	C₂×C₄	—	2	224	no	—
702	C₂×C₄	—	2	224	no	—
703	C₂×C₄	—	2	112	no	—
704	C₂×C₄	—	2	256	no	—
705	C₂×C₄	—	2	128	no	—
706	C₂×C₄	—	2	256	no	—
707	C₂×C₄	—	4	64	no	—
708	C₂×C₄	—	4	128	no	—
709	C₂×C₄	—	4	256	no	—
710	C₂×C₄	—	4	256	no	—
711	C₂×C₄	—	4	256	no	—
712	C₂×C₄	—	4	256	no	—
713	C₂×C₄	C₂²×H(5,𝔽₂)	1	112	yes	—
714	C₂×C₄	C₂⁷	1	16	yes	—
715	C₂×C₄	C₂⁷	1	32	yes	—
716	C₂×C₄	C₂⁷	1	16	yes	—
717	C₂×C₄	C₂⁷	1	32	yes	—
718	C₂×C₄	C₂⁷	1	16	yes	—
719	C₂×C₄	C₂⁷	1	32	yes	—
720	C₂×C₄	C₂⁷	1	16	yes	—
721	C₂×C₄	C₂⁷	1	8	yes	—
722	C₂×C₄	C₂⁷	1	8	yes	—
723	C₂²	—	2	16	no	—
724	C₂²	—	2	8	no	—
725	C₂²	—	2	16	no	—
726	C₂²	—	2	32	no	—
727	C₂²	—	2	16	no	—
728	C₂²	—	2	32	no	—
729	C₂²	—	2	16	no	—
730	C₂²	—	2	32	no	—
731	C₂²	—	2	16	no	—
732	C₂²	—	2	16	no	—
733	C₂²	—	2	16	no	—
734	C₂²	—	4	256	no	—
735	C₂²	—	4	224	no	—
736	C₂²	—	4	448	no	—
737	C₂²	—	4	224	no	—
738	C₂²	—	4	112	no	—
739	C₂²	C₂×#3539	1	112	yes	direct product factor
740	C₂²	C₂³×H(5,𝔽₂)	1	14	yes	—
741	C₂²	C₂²×#585	1	28	yes	—
742	C₂²	C₂⁸	1	1	yes	characteristic
743	C₄	—	2	16	no	—
744	C₄	—	2	8	no	—
745	C₄	—	2	16	no	—
746	C₄	—	2	32	no	—
747	C₄	—	2	16	no	—
748	C₄	—	2	32	no	—
749	C₄	—	2	32	no	—
750	C₄	—	2	16	no	—
751	C₄	C₂³×H(5,𝔽₂)	1	16	yes	—
752	C₂	—	4	16	no	—
753	C₂	—	4	32	no	—
754	C₂	—	4	16	no	—
755	C₂	—	4	8	no	—
756	C₂	C₂²×#3539	1	28	yes	direct product factor
757	C₂	C₂⁴×H(5,𝔽₂)	1	1	yes	characteristic
758	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×#3539	C₂	direct (N × H)
2. C₂³×#560	C₂	semidirect
3. C₂³×#553	C₂	semidirect
4. C₂³×#553	C₂	semidirect
5. C₂³×#552	C₂	semidirect
6. C₂³×#550	C₂	semidirect
7. C₂³×#547	C₂	semidirect
8. C₂³×#541	C₂	semidirect
9. C₂³×#540	C₂	semidirect
10. C₂³×#540	C₂	semidirect
11. C₂³×#537	C₂	semidirect
12. C₂³×#539	C₂	semidirect
13. C₂³×#525	C₂	semidirect
14. C₂³×#525	C₂	semidirect
17. C₂⁴×#41	C₂²	semidirect
19. C₂×#3539	C₂²	direct (N × H)
20. C₂²×#553	C₂²	semidirect
21. C₂²×#553	C₂²	semidirect
22. C₂²×#552	C₂²	semidirect
23. C₂²×#550	C₂²	semidirect
24. C₂²×#547	C₂²	semidirect
25. C₂²×#560	C₂²	semidirect
26. C₂²×#541	C₂²	semidirect
27. C₂²×#540	C₂²	semidirect
28. C₂²×#540	C₂²	semidirect
29. C₂²×#537	C₂²	semidirect
30. C₂²×#539	C₂²	semidirect
31. C₂³×C₄⋊Q₈	C₂²	semidirect
33. C₂³×#127	C₂²	semidirect
36. C₂³×#126	C₂²	semidirect
37. C₂³×#125	C₂²	semidirect
38. C₂³×#125	C₂²	semidirect
39. C₂³×#125	C₂²	semidirect
40. C₂³×#125	C₂²	semidirect
41. C₂²×#525	C₂²	semidirect
42. C₂²×#525	C₂²	semidirect
48. C₂³×#123	C₂²	semidirect
49. C₂³×#123	C₂²	semidirect
53. C₂³×C₂²⋊Q₈	C₂²	semidirect
54. C₂³×C₂²⋊Q₈	C₂²	semidirect
64. C₂³×#121	C₂²	semidirect
65. C₂³×#121	C₂²	semidirect
66. C₂³×#121	C₂²	semidirect
69. C₂³×C₄×Q₈	C₂²	semidirect
74. C₂³×C₄×D₄	C₂²	semidirect
75. C₂³×C₄×D₄	C₂²	semidirect
76. C₂³×C₄×D₄	C₂²	semidirect
79. C₂³×#117	C₂²	semidirect
80. C₂⁴×C₄⋊C₄	C₂²	semidirect
81. C₂⁴×C₄⋊C₄	C₂²	semidirect
88. C₂³×#41	C₂³	semidirect
113. #3539	C₂³	direct (N × H)
114. C₂×#560	C₂³	semidirect
115. C₂×#553	C₂³	semidirect
116. C₂×#553	C₂³	semidirect
117. C₂×#552	C₂³	semidirect
118. C₂×#550	C₂³	semidirect
119. C₂×#547	C₂³	semidirect
120. C₂×#541	C₂³	semidirect
121. C₂×#540	C₂³	semidirect
122. C₂×#540	C₂³	semidirect
123. C₂×#539	C₂³	semidirect
124. C₂×#537	C₂³	semidirect
125. C₂²×C₄⋊Q₈	C₂³	semidirect
127. C₂²×#127	C₂³	semidirect
130. C₂²×#126	C₂³	semidirect
131. C₂²×#125	C₂³	semidirect
132. C₂²×#125	C₂³	semidirect
133. C₂²×#125	C₂³	semidirect
134. C₂²×#125	C₂³	semidirect
135. C₂×#525	C₂³	semidirect
136. C₂×#525	C₂³	semidirect
142. C₂²×#123	C₂³	semidirect
143. C₂²×#123	C₂³	semidirect
147. C₂²×C₂²⋊Q₈	C₂³	semidirect
148. C₂²×C₂²⋊Q₈	C₂³	semidirect
158. C₂²×#121	C₂³	semidirect
159. C₂²×#121	C₂³	semidirect
160. C₂²×#121	C₂³	semidirect
163. C₂²×C₄×Q₈	C₂³	semidirect
168. C₂²×C₄×D₄	C₂³	semidirect
169. C₂²×C₄×D₄	C₂³	semidirect
170. C₂²×C₄×D₄	C₂³	semidirect
173. C₂²×#117	C₂³	semidirect
187. C₂³×C₄⋊C₄	C₂³	semidirect
188. C₂³×C₄⋊C₄	C₂³	semidirect
218. C₂²×#41	C₂⁴	semidirect
274. #560	C₂⁴	semidirect
275. #553	C₂⁴	semidirect
276. #553	C₂⁴	semidirect
277. #552	C₂⁴	semidirect
278. #550	C₂⁴	semidirect
279. #547	C₂⁴	semidirect
280. #541	C₂⁴	semidirect
281. #540	C₂⁴	semidirect
282. #540	C₂⁴	semidirect
283. #539	C₂⁴	semidirect
284. #537	C₂⁴	semidirect
285. C₂×C₄⋊Q₈	C₂⁴	semidirect
287. C₂×#127	C₂⁴	semidirect
290. C₂×#126	C₂⁴	semidirect
291. C₂×#125	C₂⁴	semidirect
292. C₂×#125	C₂⁴	semidirect
293. C₂×#125	C₂⁴	semidirect
294. C₂×#125	C₂⁴	semidirect
295. #525	C₂⁴	semidirect
296. #525	C₂⁴	semidirect
302. C₂×#123	C₂⁴	semidirect
303. C₂×#123	C₂⁴	semidirect
307. C₂×C₂²⋊Q₈	C₂⁴	semidirect
308. C₂×C₂²⋊Q₈	C₂⁴	semidirect
318. C₂×#121	C₂⁴	semidirect
319. C₂×#121	C₂⁴	semidirect
320. C₂×#121	C₂⁴	semidirect
323. C₂×C₄×Q₈	C₂⁴	semidirect
328. C₂×C₄×D₄	C₂⁴	semidirect
329. C₂×C₄×D₄	C₂⁴	semidirect
330. C₂×C₄×D₄	C₂⁴	semidirect
333. C₂×#117	C₂⁴	semidirect
347. C₂²×C₄⋊C₄	C₂⁴	semidirect
348. C₂²×C₄⋊C₄	C₂⁴	semidirect
391. C₂×#41	C₂⁵	semidirect
456. C₄⋊Q₈	C₂⁵	semidirect
458. #127	C₂⁵	semidirect
461. #126	C₂⁵	semidirect
462. #125	C₂⁵	semidirect
463. #125	C₂⁵	semidirect
464. #125	C₂⁵	semidirect
465. #125	C₂⁵	semidirect
471. #123	C₂⁵	semidirect
472. #123	C₂⁵	semidirect
476. C₂²⋊Q₈	C₂⁵	semidirect
477. C₂²⋊Q₈	C₂⁵	semidirect
487. #121	C₂⁵	semidirect
488. #121	C₂⁵	semidirect
489. #121	C₂⁵	semidirect
492. C₄×Q₈	C₂⁵	semidirect
497. C₄×D₄	C₂⁵	semidirect
498. C₄×D₄	C₂⁵	semidirect
499. C₄×D₄	C₂⁵	semidirect
502. #117	C₂⁵	semidirect
516. C₂×C₄⋊C₄	C₂⁵	semidirect
517. C₂×C₄⋊C₄	C₂⁵	semidirect
675. C₂³	#3539	direct (N × H)
739. C₂²	C₂×#3539	direct (N × H)
756. C₂	C₂²×#3539	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×#3539	2
C₂³×#560	2
C₂³×#553	2
C₂³×#552	2
C₂³×#550	2
C₂³×#547	2
C₂³×#541	2
C₂³×#540	2
C₂³×#537	2
C₂³×#539	2
C₂³×#525	2

Subgroups — C23×#3539 #72324991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#3539 #72324991