Subgroups — C₂²×C₃₁×#386 #21490773

Order 7936.

11630 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂⁵×C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#386	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₃₁×#95	C₂	1	2	yes	maximal, complemented
7	C₂⁶×C₃₁	C₂²	1	1	yes	characteristic
8	C₂⁶×C₃₁	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₃₁	—	2	8	no	—
10	C₂³×D₄×C₃₁	—	2	8	no	—
11	C₂³×D₄×C₃₁	C₄	1	16	yes	complemented
12	C₂³×D₄×C₃₁	C₂²	1	12	yes	—
13	C₂⁴×C₄×C₃₁	—	2	8	no	—
14	C₂⁴×C₄×C₃₁	—	2	16	no	—
15	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₃₁	C₂²	1	12	yes	complemented
19	C₂²×C₂²⋊C₄×C₃₁	—	2	8	no	—
20	C₂²×C₂²⋊C₄×C₃₁	—	2	16	no	—
21	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	12	yes	complemented
22	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	24	yes	complemented
23	C₃₁×#386	C₂²	1	64	yes	direct product factor
24	C₂×C₃₁×#95	C₂²	1	24	yes	complemented
25	C₂⁵×C₃₁	—	2	8	no	—
26	C₂⁵×C₃₁	—	2	8	no	—
27	C₂⁵×C₃₁	—	2	8	no	—
28	C₂⁵×C₃₁	—	2	4	no	—
29	C₂⁵×C₃₁	—	2	4	no	—
30	C₂⁵×C₃₁	—	2	8	no	—
31	C₂⁵×C₃₁	C₂×C₄	1	8	yes	—
32	C₂⁵×C₃₁	C₂×C₄	1	8	yes	complemented
33	C₂⁵×C₃₁	D₄	1	8	yes	—
34	C₂⁵×C₃₁	D₄	1	8	yes	—
35	C₂⁵×C₃₁	C₂³	1	6	yes	—
36	C₂⁵×C₃₁	C₂³	1	6	yes	—
37	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₃₁	—	2	128	no	—
39	C₂²×D₄×C₃₁	—	2	48	no	—
40	C₂²×D₄×C₃₁	—	2	48	no	—
41	C₂²×D₄×C₃₁	C₂×C₄	1	96	yes	complemented
42	C₂²×D₄×C₃₁	C₂³	1	16	yes	—
43	C₂³×C₄×C₃₁	—	2	128	no	—
44	C₂³×C₄×C₃₁	—	2	8	no	—
45	C₂³×C₄×C₃₁	—	2	8	no	—
46	C₂³×C₄×C₃₁	—	2	48	no	—
47	C₂³×C₄×C₃₁	—	2	4	no	—
48	C₂³×C₄×C₃₁	—	2	4	no	—
49	C₂³×C₄×C₃₁	—	2	96	no	—
50	C₂³×C₄×C₃₁	—	2	8	no	—
51	C₂³×C₄×C₃₁	—	2	8	no	—
52	C₂³×C₄×C₃₁	—	2	8	no	—
53	C₂³×C₄×C₃₁	C₂×C₄	1	8	yes	complemented
54	C₂³×C₄×C₃₁	D₄	1	16	yes	complemented
55	C₂³×C₄×C₃₁	C₂³	1	12	yes	—
56	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
57	C₂³×C₄×C₃₁	C₂³	1	12	yes	—
58	C₂³×C₄×C₃₁	C₂³	1	16	yes	complemented
59	C₂×C₂²⋊C₄×C₃₁	—	2	48	no	—
60	C₂×C₂²⋊C₄×C₃₁	—	2	96	no	—
61	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	complemented
62	C₂×C₂²⋊C₄×C₃₁	C₂³	1	32	yes	complemented
63	C₃₁×#95	C₂³	1	32	yes	complemented
64	C₂⁴×C₃₁	—	2	64	no	—
65	C₂⁴×C₃₁	—	2	32	no	—
66	C₂⁴×C₃₁	—	2	64	no	—
67	C₂⁴×C₃₁	—	2	32	no	—
68	C₂⁴×C₃₁	—	2	24	no	—
69	C₂⁴×C₃₁	—	2	24	no	—
70	C₂⁴×C₃₁	—	2	32	no	—
71	C₂⁴×C₃₁	—	2	64	no	—
72	C₂⁴×C₃₁	—	2	24	no	—
73	C₂⁴×C₃₁	—	2	12	no	—
74	C₂⁴×C₃₁	—	2	12	no	—
75	C₂⁴×C₃₁	—	2	24	no	—
76	C₂⁴×C₃₁	—	4	16	no	—
77	C₂⁴×C₃₁	—	4	32	no	—
78	C₂⁴×C₃₁	—	4	16	no	—
79	C₂⁴×C₃₁	C₂²⋊C₄	1	64	yes	complemented
80	C₂⁴×C₃₁	C₂²×C₄	1	24	yes	—
81	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
82	C₂⁴×C₃₁	C₂²×C₄	1	24	yes	complemented
83	C₂⁴×C₃₁	C₂×D₄	1	24	yes	—
84	C₂⁴×C₃₁	C₂×D₄	1	24	yes	—
85	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
86	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
87	C₂⁴×C₃₁	C₂×D₄	1	8	yes	—
88	C₂⁴×C₃₁	#41	1	8	yes	—
89	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
90	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
91	C₂⁴×C₃₁	C₂⁴	1	3	yes	—
92	C₂×D₄×C₃₁	—	2	384	no	—
93	C₂×D₄×C₃₁	—	2	32	no	—
94	C₂×D₄×C₃₁	—	2	32	no	—
95	C₂×D₄×C₃₁	C₂²×C₄	1	64	yes	complemented
96	C₂²×C₄×C₃₁	—	2	384	no	—
97	C₂²×C₄×C₃₁	—	2	32	no	—
98	C₂²×C₄×C₃₁	—	2	64	no	—
99	C₂²×C₄×C₃₁	—	2	24	no	—
100	C₂²×C₄×C₃₁	—	2	24	no	—
101	C₂²×C₄×C₃₁	—	2	32	no	—
102	C₂²×C₄×C₃₁	—	2	12	no	—
103	C₂²×C₄×C₃₁	—	2	12	no	—
104	C₂²×C₄×C₃₁	—	2	64	no	—
105	C₂²×C₄×C₃₁	—	2	24	no	—
106	C₂²×C₄×C₃₁	—	2	24	no	—
107	C₂²×C₄×C₃₁	—	2	24	no	—
108	C₂²×C₄×C₃₁	—	4	32	no	—
109	C₂²×C₄×C₃₁	C₂²×C₄	1	24	yes	complemented
110	C₂²×C₄×C₃₁	C₂×D₄	1	48	yes	complemented
111	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
112	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
113	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
114	C₂²⋊C₄×C₃₁	—	2	32	no	—
115	C₂²⋊C₄×C₃₁	—	2	64	no	—
116	C₂²×#386	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₃₁	—	2	96	no	—
118	C₂³×C₃₁	—	2	48	no	—
119	C₂³×C₃₁	—	2	96	no	—
120	C₂³×C₃₁	—	2	48	no	—
121	C₂³×C₃₁	—	2	8	no	—
122	C₂³×C₃₁	—	2	8	no	—
123	C₂³×C₃₁	—	2	256	no	—
124	C₂³×C₃₁	—	2	48	no	—
125	C₂³×C₃₁	—	2	96	no	—
126	C₂³×C₃₁	—	2	8	no	—
127	C₂³×C₃₁	—	2	4	no	—
128	C₂³×C₃₁	—	2	4	no	—
129	C₂³×C₃₁	—	2	8	no	—
130	C₂³×C₃₁	—	4	24	no	—
131	C₂³×C₃₁	—	4	48	no	—
132	C₂³×C₃₁	—	4	24	no	—
133	C₂³×C₃₁	—	4	128	no	—
134	C₂³×C₃₁	C₂×C₂²⋊C₄	1	16	yes	—
135	C₂³×C₃₁	C₂×C₂²⋊C₄	1	96	yes	complemented
136	C₂³×C₃₁	C₄×D₄	1	32	yes	—
137	C₂³×C₃₁	#120	1	16	yes	—
138	C₂³×C₃₁	#121	1	32	yes	—
139	C₂³×C₃₁	#123	1	16	yes	—
140	C₂³×C₃₁	C₂³×C₄	1	8	yes	—
141	C₂³×C₃₁	C₂³×C₄	1	6	yes	—
142	C₂³×C₃₁	C₂³×C₄	1	8	yes	complemented
143	C₂³×C₃₁	C₂²×D₄	1	8	yes	—
144	C₂³×C₃₁	C₂²×D₄	1	8	yes	—
145	C₂³×C₃₁	C₂²×D₄	1	6	yes	—
146	C₂³×C₃₁	C₂²×D₄	1	6	yes	—
147	C₂³×C₃₁	C₂²×D₄	1	12	yes	—
148	C₂³×C₃₁	C₂×#41	1	12	yes	—
149	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
150	D₄×C₃₁	—	2	128	no	—
151	C₂×C₄×C₃₁	—	2	128	no	—
152	C₂×C₄×C₃₁	—	2	48	no	—
153	C₂×C₄×C₃₁	—	2	96	no	—
154	C₂×C₄×C₃₁	—	2	8	no	—
155	C₂×C₄×C₃₁	—	2	8	no	—
156	C₂×C₄×C₃₁	—	2	4	no	—
157	C₂×C₄×C₃₁	—	2	4	no	—
158	C₂×C₄×C₃₁	—	2	8	no	—
159	C₂×C₄×C₃₁	—	2	8	no	—
160	C₂×C₄×C₃₁	—	2	8	no	—
161	C₂×C₄×C₃₁	—	4	48	no	—
162	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	complemented
163	C₂×C₄×C₃₁	C₂²×D₄	1	16	yes	complemented
164	C₂⁴×D₄	C₂×C₃₁	1	1	yes	characteristic
165	C₂⁵×C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
166	C₂³×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
167	C₂³×C₂²⋊C₄	C₂×C₃₁	1	2	yes	complemented
168	C₂×#386	C₂×C₃₁	1	24	yes	direct product factor
169	C₂²×#95	C₂×C₃₁	1	2	yes	complemented
170	C₂²×C₃₁	—	2	16	no	—
171	C₂²×C₃₁	—	2	8	no	—
172	C₂²×C₃₁	—	2	16	no	—
173	C₂²×C₃₁	—	2	8	no	—
174	C₂²×C₃₁	—	2	192	no	—
175	C₂²×C₃₁	—	2	8	no	—
176	C₂²×C₃₁	—	2	16	no	—
177	C₂²×C₃₁	—	4	4	no	—
178	C₂²×C₃₁	—	4	8	no	—
179	C₂²×C₃₁	—	4	4	no	—
180	C₂²×C₃₁	—	4	96	no	—
181	C₂²×C₃₁	#386	1	64	yes	direct product factor
182	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	12	yes	—
183	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	16	yes	complemented
184	C₂²×C₃₁	C₂×C₄×D₄	1	24	yes	—
185	C₂²×C₃₁	C₂×#120	1	12	yes	—
186	C₂²×C₃₁	C₂×#121	1	24	yes	—
187	C₂²×C₃₁	C₂×#123	1	12	yes	—
188	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
189	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
190	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
191	C₂²×C₃₁	C₂³×D₄	1	2	yes	—
192	C₂²×C₃₁	C₂²×#41	1	2	yes	—
193	C₄×C₃₁	—	2	8	no	—
194	C₄×C₃₁	—	2	16	no	—
195	C₄×C₃₁	—	4	8	no	—
196	C₂⁶	C₂²×C₃₁	1	1	yes	characteristic
197	C₂⁶	C₂²×C₃₁	1	1	yes	characteristic
198	C₂³×D₄	—	2	8	no	—
199	C₂³×D₄	—	2	8	no	—
200	C₂³×D₄	C₄×C₃₁	1	16	yes	complemented
201	C₂³×D₄	C₂²×C₃₁	1	12	yes	—
202	C₂⁴×C₄	—	2	8	no	—
203	C₂⁴×C₄	—	2	16	no	—
204	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
205	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
206	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
207	C₂⁴×C₄	C₂²×C₃₁	1	12	yes	complemented
208	C₂²×C₂²⋊C₄	—	2	8	no	—
209	C₂²×C₂²⋊C₄	—	2	16	no	—
210	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	12	yes	complemented
211	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	24	yes	complemented
212	#386	C₂²×C₃₁	1	64	yes	direct product factor
213	C₂×#95	C₂²×C₃₁	1	24	yes	complemented
214	C₂×C₃₁	—	2	16	no	—
215	C₂×C₃₁	—	4	8	no	—
216	C₂×C₃₁	C₂×#386	1	24	yes	direct product factor
217	C₂×C₃₁	C₂³×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₃₁	C₂²×C₄×D₄	1	2	yes	—
219	C₂×C₃₁	C₂²×#120	1	1	yes	characteristic
220	C₂×C₃₁	C₂²×#121	1	2	yes	—
221	C₂×C₃₁	C₂²×#123	1	1	yes	characteristic
222	C₂⁵	—	2	8	no	—
223	C₂⁵	—	2	8	no	—
224	C₂⁵	—	2	8	no	—
225	C₂⁵	—	2	4	no	—
226	C₂⁵	—	2	4	no	—
227	C₂⁵	—	2	8	no	—
228	C₂⁵	C₂×C₄×C₃₁	1	8	yes	—
229	C₂⁵	C₂×C₄×C₃₁	1	8	yes	complemented
230	C₂⁵	D₄×C₃₁	1	8	yes	—
231	C₂⁵	D₄×C₃₁	1	8	yes	—
232	C₂⁵	C₂³×C₃₁	1	6	yes	—
233	C₂⁵	C₂³×C₃₁	1	6	yes	—
234	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
235	C₂²×D₄	—	2	128	no	—
236	C₂²×D₄	—	2	48	no	—
237	C₂²×D₄	—	2	48	no	—
238	C₂²×D₄	C₂×C₄×C₃₁	1	96	yes	complemented
239	C₂²×D₄	C₂³×C₃₁	1	16	yes	—
240	C₂³×C₄	—	2	128	no	—
241	C₂³×C₄	—	2	8	no	—
242	C₂³×C₄	—	2	8	no	—
243	C₂³×C₄	—	2	48	no	—
244	C₂³×C₄	—	2	4	no	—
245	C₂³×C₄	—	2	4	no	—
246	C₂³×C₄	—	2	96	no	—
247	C₂³×C₄	—	2	8	no	—
248	C₂³×C₄	—	2	8	no	—
249	C₂³×C₄	—	2	8	no	—
250	C₂³×C₄	C₂×C₄×C₃₁	1	8	yes	complemented
251	C₂³×C₄	D₄×C₃₁	1	16	yes	complemented
252	C₂³×C₄	C₂³×C₃₁	1	12	yes	—
253	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
254	C₂³×C₄	C₂³×C₃₁	1	12	yes	—
255	C₂³×C₄	C₂³×C₃₁	1	16	yes	complemented
256	C₂×C₂²⋊C₄	—	2	48	no	—
257	C₂×C₂²⋊C₄	—	2	96	no	—
258	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	complemented
259	C₂×C₂²⋊C₄	C₂³×C₃₁	1	32	yes	complemented
260	#95	C₂³×C₃₁	1	32	yes	complemented
261	C₃₁	C₂²×#386	1	1	yes	characteristic, direct product factor, Sylow
262	C₂⁴	—	2	64	no	—
263	C₂⁴	—	2	32	no	—
264	C₂⁴	—	2	64	no	—
265	C₂⁴	—	2	32	no	—
266	C₂⁴	—	2	24	no	—
267	C₂⁴	—	2	24	no	—
268	C₂⁴	—	2	32	no	—
269	C₂⁴	—	2	64	no	—
270	C₂⁴	—	2	24	no	—
271	C₂⁴	—	2	12	no	—
272	C₂⁴	—	2	12	no	—
273	C₂⁴	—	2	24	no	—
274	C₂⁴	—	4	16	no	—
275	C₂⁴	—	4	32	no	—
276	C₂⁴	—	4	16	no	—
277	C₂⁴	C₂²⋊C₄×C₃₁	1	64	yes	complemented
278	C₂⁴	C₂²×C₄×C₃₁	1	24	yes	—
279	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
280	C₂⁴	C₂²×C₄×C₃₁	1	24	yes	complemented
281	C₂⁴	C₂×D₄×C₃₁	1	24	yes	—
282	C₂⁴	C₂×D₄×C₃₁	1	24	yes	—
283	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
284	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
285	C₂⁴	C₂×D₄×C₃₁	1	8	yes	—
286	C₂⁴	#41×C₃₁	1	8	yes	—
287	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
288	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
289	C₂⁴	C₂⁴×C₃₁	1	3	yes	—
290	C₂×D₄	—	2	384	no	—
291	C₂×D₄	—	2	32	no	—
292	C₂×D₄	—	2	32	no	—
293	C₂×D₄	C₂²×C₄×C₃₁	1	64	yes	complemented
294	C₂²×C₄	—	2	384	no	—
295	C₂²×C₄	—	2	32	no	—
296	C₂²×C₄	—	2	64	no	—
297	C₂²×C₄	—	2	24	no	—
298	C₂²×C₄	—	2	24	no	—
299	C₂²×C₄	—	2	32	no	—
300	C₂²×C₄	—	2	12	no	—
301	C₂²×C₄	—	2	12	no	—
302	C₂²×C₄	—	2	64	no	—
303	C₂²×C₄	—	2	24	no	—
304	C₂²×C₄	—	2	24	no	—
305	C₂²×C₄	—	2	24	no	—
306	C₂²×C₄	—	4	32	no	—
307	C₂²×C₄	C₂²×C₄×C₃₁	1	24	yes	complemented
308	C₂²×C₄	C₂×D₄×C₃₁	1	48	yes	complemented
309	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
310	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
311	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
312	C₂²⋊C₄	—	2	32	no	—
313	C₂²⋊C₄	—	2	64	no	—
314	C₂³	—	2	96	no	—
315	C₂³	—	2	48	no	—
316	C₂³	—	2	96	no	—
317	C₂³	—	2	48	no	—
318	C₂³	—	2	8	no	—
319	C₂³	—	2	8	no	—
320	C₂³	—	2	256	no	—
321	C₂³	—	2	48	no	—
322	C₂³	—	2	96	no	—
323	C₂³	—	2	8	no	—
324	C₂³	—	2	4	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	2	8	no	—
327	C₂³	—	4	24	no	—
328	C₂³	—	4	48	no	—
329	C₂³	—	4	24	no	—
330	C₂³	—	4	128	no	—
331	C₂³	C₂×C₂²⋊C₄×C₃₁	1	16	yes	—
332	C₂³	C₂×C₂²⋊C₄×C₃₁	1	96	yes	complemented
333	C₂³	C₄×D₄×C₃₁	1	32	yes	—
334	C₂³	C₃₁×#120	1	16	yes	—
335	C₂³	C₃₁×#121	1	32	yes	—
336	C₂³	C₃₁×#123	1	16	yes	—
337	C₂³	C₂³×C₄×C₃₁	1	8	yes	—
338	C₂³	C₂³×C₄×C₃₁	1	6	yes	—
339	C₂³	C₂³×C₄×C₃₁	1	8	yes	complemented
340	C₂³	C₂²×D₄×C₃₁	1	8	yes	—
341	C₂³	C₂²×D₄×C₃₁	1	8	yes	—
342	C₂³	C₂²×D₄×C₃₁	1	6	yes	—
343	C₂³	C₂²×D₄×C₃₁	1	6	yes	—
344	C₂³	C₂²×D₄×C₃₁	1	12	yes	—
345	C₂³	C₂×#41×C₃₁	1	12	yes	—
346	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
347	D₄	—	2	128	no	—
348	C₂×C₄	—	2	128	no	—
349	C₂×C₄	—	2	48	no	—
350	C₂×C₄	—	2	96	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	4	48	no	—
359	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	complemented
360	C₂×C₄	C₂²×D₄×C₃₁	1	16	yes	complemented
361	C₂²	—	2	16	no	—
362	C₂²	—	2	8	no	—
363	C₂²	—	2	16	no	—
364	C₂²	—	2	8	no	—
365	C₂²	—	2	192	no	—
366	C₂²	—	2	8	no	—
367	C₂²	—	2	16	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	4	8	no	—
370	C₂²	—	4	4	no	—
371	C₂²	—	4	96	no	—
372	C₂²	C₃₁×#386	1	64	yes	direct product factor
373	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	12	yes	—
374	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	16	yes	complemented
375	C₂²	C₂×C₄×D₄×C₃₁	1	24	yes	—
376	C₂²	C₂×C₃₁×#120	1	12	yes	—
377	C₂²	C₂×C₃₁×#121	1	24	yes	—
378	C₂²	C₂×C₃₁×#123	1	12	yes	—
379	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
380	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
381	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
382	C₂²	C₂³×D₄×C₃₁	1	2	yes	—
383	C₂²	C₂²×#41×C₃₁	1	2	yes	—
384	C₄	—	2	8	no	—
385	C₄	—	2	16	no	—
386	C₄	—	4	8	no	—
387	C₂	—	2	16	no	—
388	C₂	—	4	8	no	—
389	C₂	C₂×C₃₁×#386	1	24	yes	direct product factor
390	C₂	C₂³×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
391	C₂	C₂²×C₄×D₄×C₃₁	1	2	yes	—
392	C₂	C₂²×C₃₁×#120	1	1	yes	characteristic
393	C₂	C₂²×C₃₁×#121	1	2	yes	—
394	C₂	C₂²×C₃₁×#123	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁵×C₃₁	C₂³
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁴×D₄×C₃₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁵×C₄×C₃₁	C₂	semidirect
3. C₂³×C₂²⋊C₄×C₃₁	C₂	semidirect
4. C₂³×C₂²⋊C₄×C₃₁	C₂	semidirect
5. C₂×C₃₁×#386	C₂	direct (N × H)
6. C₂²×C₃₁×#95	C₂	semidirect
11. C₂³×D₄×C₃₁	C₄	semidirect
18. C₂⁴×C₄×C₃₁	C₂²	semidirect
21. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
22. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
23. C₃₁×#386	C₂²	direct (N × H)
24. C₂×C₃₁×#95	C₂²	semidirect
32. C₂⁵×C₃₁	C₂×C₄	semidirect
41. C₂²×D₄×C₃₁	C₂×C₄	semidirect
53. C₂³×C₄×C₃₁	C₂×C₄	semidirect
54. C₂³×C₄×C₃₁	D₄	semidirect
58. C₂³×C₄×C₃₁	C₂³	semidirect
61. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
62. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
63. C₃₁×#95	C₂³	semidirect
79. C₂⁴×C₃₁	C₂²⋊C₄	semidirect
82. C₂⁴×C₃₁	C₂²×C₄	semidirect
95. C₂×D₄×C₃₁	C₂²×C₄	semidirect
109. C₂²×C₄×C₃₁	C₂²×C₄	semidirect
110. C₂²×C₄×C₃₁	C₂×D₄	semidirect
116. C₂²×#386	C₃₁	direct (N × H)
135. C₂³×C₃₁	C₂×C₂²⋊C₄	semidirect
142. C₂³×C₃₁	C₂³×C₄	semidirect
162. C₂×C₄×C₃₁	C₂³×C₄	semidirect
163. C₂×C₄×C₃₁	C₂²×D₄	semidirect
165. C₂⁵×C₄	C₂×C₃₁	semidirect
166. C₂³×C₂²⋊C₄	C₂×C₃₁	semidirect
167. C₂³×C₂²⋊C₄	C₂×C₃₁	semidirect
168. C₂×#386	C₂×C₃₁	direct (N × H)
169. C₂²×#95	C₂×C₃₁	semidirect
181. C₂²×C₃₁	#386	direct (N × H)
183. C₂²×C₃₁	C₂²×C₂²⋊C₄	semidirect
200. C₂³×D₄	C₄×C₃₁	semidirect
207. C₂⁴×C₄	C₂²×C₃₁	semidirect
210. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
211. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
212. #386	C₂²×C₃₁	direct (N × H)
213. C₂×#95	C₂²×C₃₁	semidirect
216. C₂×C₃₁	C₂×#386	direct (N × H)
229. C₂⁵	C₂×C₄×C₃₁	semidirect
238. C₂²×D₄	C₂×C₄×C₃₁	semidirect
250. C₂³×C₄	C₂×C₄×C₃₁	semidirect
251. C₂³×C₄	D₄×C₃₁	semidirect
255. C₂³×C₄	C₂³×C₃₁	semidirect
258. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
259. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
260. #95	C₂³×C₃₁	semidirect
261. C₃₁	C₂²×#386	direct (N × H)
277. C₂⁴	C₂²⋊C₄×C₃₁	semidirect
280. C₂⁴	C₂²×C₄×C₃₁	semidirect
293. C₂×D₄	C₂²×C₄×C₃₁	semidirect
307. C₂²×C₄	C₂²×C₄×C₃₁	semidirect
308. C₂²×C₄	C₂×D₄×C₃₁	semidirect
332. C₂³	C₂×C₂²⋊C₄×C₃₁	semidirect
339. C₂³	C₂³×C₄×C₃₁	semidirect
359. C₂×C₄	C₂³×C₄×C₃₁	semidirect
360. C₂×C₄	C₂²×D₄×C₃₁	semidirect
372. C₂²	C₃₁×#386	direct (N × H)
374. C₂²	C₂²×C₂²⋊C₄×C₃₁	semidirect
389. C₂	C₂×C₃₁×#386	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₃₁	2
C₂⁵×C₄×C₃₁	2
C₂³×C₂²⋊C₄×C₃₁	2
C₂×C₃₁×#386	2
C₂²×C₃₁×#95	2
C₂²×#386	31

Subgroups — C22×C31×#386 #21490773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃₁×#386 #21490773