Subgroups — C₂²×C₃₁×#388 #21490775

Order 7936.

5966 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×#388	C₂	1	24	yes	maximal, direct product factor
7	C₂²×C₃₁×#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₃₁×#95	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁶×C₃₁	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₃₁	—	2	8	no	—
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	12	yes	complemented
18	C₂²×C₂²⋊C₄×C₃₁	—	2	8	no	—
19	C₂²×C₂²⋊C₄×C₃₁	—	2	8	no	—
20	C₂²×C₂²⋊C₄×C₃₁	C₄	1	16	yes	complemented
21	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	12	yes	—
22	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	12	yes	—
23	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	12	yes	—
24	C₂²×C₄²×C₃₁	—	2	8	no	—
25	C₂²×C₄²×C₃₁	C₂²	1	12	yes	complemented
26	C₃₁×#388	C₂²	1	64	yes	direct product factor
27	C₂×C₃₁×#95	C₂²	1	12	yes	complemented
28	C₂×C₃₁×#95	C₂²	1	12	yes	complemented
29	C₂⁵×C₃₁	—	2	4	no	—
30	C₂⁵×C₃₁	—	2	4	no	—
31	C₂⁵×C₃₁	—	2	4	no	—
32	C₂⁵×C₃₁	—	2	4	no	—
33	C₂⁵×C₃₁	—	2	4	no	—
34	C₂⁵×C₃₁	—	2	4	no	—
35	C₂⁵×C₃₁	C₂×C₄	1	8	yes	—
36	C₂⁵×C₃₁	C₂³	1	6	yes	—
37	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₃₁	—	2	4	no	—
39	C₂³×C₄×C₃₁	—	2	4	no	—
40	C₂³×C₄×C₃₁	—	2	4	no	—
41	C₂³×C₄×C₃₁	—	2	4	no	—
42	C₂³×C₄×C₃₁	—	2	4	no	—
43	C₂³×C₄×C₃₁	—	2	4	no	—
44	C₂³×C₄×C₃₁	—	2	4	no	—
45	C₂³×C₄×C₃₁	—	2	4	no	—
46	C₂³×C₄×C₃₁	—	2	4	no	—
47	C₂³×C₄×C₃₁	—	2	4	no	—
48	C₂³×C₄×C₃₁	—	2	4	no	—
49	C₂³×C₄×C₃₁	—	2	4	no	—
50	C₂³×C₄×C₃₁	—	2	4	no	—
51	C₂³×C₄×C₃₁	—	2	4	no	—
52	C₂³×C₄×C₃₁	C₂×C₄	1	8	yes	—
53	C₂³×C₄×C₃₁	C₂×C₄	1	8	yes	—
54	C₂³×C₄×C₃₁	D₄	1	8	yes	—
55	C₂³×C₄×C₃₁	D₄	1	8	yes	—
56	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
57	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
58	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
59	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
60	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
61	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
62	C₂×C₄⋊C₄×C₃₁	—	2	48	no	—
63	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	complemented
64	C₂×C₂²⋊C₄×C₃₁	—	2	48	no	—
65	C₂×C₂²⋊C₄×C₃₁	—	2	48	no	—
66	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	96	yes	complemented
67	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
68	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
69	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
70	C₂×C₄²×C₃₁	—	2	48	no	—
71	C₂×C₄²×C₃₁	C₂³	1	16	yes	complemented
72	C₃₁×#95	C₂³	1	16	yes	complemented
73	C₃₁×#95	C₂³	1	16	yes	complemented
74	C₂⁴×C₃₁	—	2	32	no	—
75	C₂⁴×C₃₁	—	2	32	no	—
76	C₂⁴×C₃₁	—	2	32	no	—
77	C₂⁴×C₃₁	—	2	12	no	—
78	C₂⁴×C₃₁	—	2	12	no	—
79	C₂⁴×C₃₁	—	2	12	no	—
80	C₂⁴×C₃₁	—	2	12	no	—
81	C₂⁴×C₃₁	—	2	12	no	—
82	C₂⁴×C₃₁	—	2	12	no	—
83	C₂⁴×C₃₁	—	4	16	no	—
84	C₂⁴×C₃₁	—	4	16	no	—
85	C₂⁴×C₃₁	—	4	16	no	—
86	C₂⁴×C₃₁	—	4	16	no	—
87	C₂⁴×C₃₁	C₂²×C₄	1	24	yes	—
88	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
89	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
90	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
91	C₂⁴×C₃₁	#41	1	4	yes	—
92	C₂⁴×C₃₁	#41	1	4	yes	—
93	C₂⁴×C₃₁	#41	1	4	yes	—
94	C₂⁴×C₃₁	#41	1	4	yes	—
95	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
96	C₂⁴×C₃₁	C₂⁴	1	3	yes	—
97	C₂²×C₄×C₃₁	—	2	32	no	—
98	C₂²×C₄×C₃₁	—	2	32	no	—
99	C₂²×C₄×C₃₁	—	2	32	no	—
100	C₂²×C₄×C₃₁	—	2	32	no	—
101	C₂²×C₄×C₃₁	—	2	12	no	—
102	C₂²×C₄×C₃₁	—	2	12	no	—
103	C₂²×C₄×C₃₁	—	2	12	no	—
104	C₂²×C₄×C₃₁	—	2	12	no	—
105	C₂²×C₄×C₃₁	—	2	12	no	—
106	C₂²×C₄×C₃₁	—	2	12	no	—
107	C₂²×C₄×C₃₁	—	2	12	no	—
108	C₂²×C₄×C₃₁	—	2	12	no	—
109	C₂²×C₄×C₃₁	—	2	12	no	—
110	C₂²×C₄×C₃₁	—	2	12	no	—
111	C₂²×C₄×C₃₁	—	2	12	no	—
112	C₂²×C₄×C₃₁	—	2	12	no	—
113	C₂²×C₄×C₃₁	—	2	12	no	—
114	C₂²×C₄×C₃₁	—	2	12	no	—
115	C₂²×C₄×C₃₁	—	4	16	no	—
116	C₂²×C₄×C₃₁	—	4	16	no	—
117	C₂²×C₄×C₃₁	C₂²×C₄	1	24	yes	—
118	C₂²×C₄×C₃₁	C₂²×C₄	1	24	yes	—
119	C₂²×C₄×C₃₁	C₂×D₄	1	24	yes	—
120	C₂²×C₄×C₃₁	C₂×D₄	1	24	yes	—
121	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
127	C₄⋊C₄×C₃₁	—	2	32	no	—
128	C₂²⋊C₄×C₃₁	—	2	32	no	—
129	C₂²⋊C₄×C₃₁	—	2	32	no	—
130	C₂²⋊C₄×C₃₁	C₂²×C₄	1	64	yes	complemented
131	C₄²×C₃₁	—	2	32	no	—
132	C₂²×#388	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₃₁	—	2	48	no	—
134	C₂³×C₃₁	—	2	48	no	—
135	C₂³×C₃₁	—	2	48	no	—
136	C₂³×C₃₁	—	2	4	no	—
137	C₂³×C₃₁	—	2	4	no	—
138	C₂³×C₃₁	—	2	4	no	—
139	C₂³×C₃₁	—	2	4	no	—
140	C₂³×C₃₁	—	2	4	no	—
141	C₂³×C₃₁	—	2	4	no	—
142	C₂³×C₃₁	—	4	24	no	—
143	C₂³×C₃₁	—	4	24	no	—
144	C₂³×C₃₁	—	4	24	no	—
145	C₂³×C₃₁	—	4	24	no	—
146	C₂³×C₃₁	—	4	128	no	—
147	C₂³×C₃₁	#117	1	16	yes	—
148	C₂³×C₃₁	C₄×D₄	1	16	yes	—
149	C₂³×C₃₁	C₄×D₄	1	16	yes	—
150	C₂³×C₃₁	#121	1	16	yes	—
151	C₂³×C₃₁	#123	1	16	yes	—
152	C₂³×C₃₁	#124	1	16	yes	—
153	C₂³×C₃₁	#126	1	16	yes	—
154	C₂³×C₃₁	C₂³×C₄	1	8	yes	—
155	C₂³×C₃₁	C₂³×C₄	1	6	yes	—
156	C₂³×C₃₁	C₂²×D₄	1	6	yes	—
157	C₂³×C₃₁	C₂²×D₄	1	6	yes	—
158	C₂³×C₃₁	C₂×#41	1	6	yes	—
159	C₂³×C₃₁	C₂×#41	1	6	yes	—
160	C₂³×C₃₁	C₂×#41	1	6	yes	—
161	C₂³×C₃₁	C₂×#41	1	6	yes	—
162	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
163	C₂×C₄×C₃₁	—	2	48	no	—
164	C₂×C₄×C₃₁	—	2	48	no	—
165	C₂×C₄×C₃₁	—	2	48	no	—
166	C₂×C₄×C₃₁	—	2	48	no	—
167	C₂×C₄×C₃₁	—	2	4	no	—
168	C₂×C₄×C₃₁	—	2	4	no	—
169	C₂×C₄×C₃₁	—	2	4	no	—
170	C₂×C₄×C₃₁	—	2	4	no	—
171	C₂×C₄×C₃₁	—	2	4	no	—
172	C₂×C₄×C₃₁	—	2	4	no	—
173	C₂×C₄×C₃₁	—	2	4	no	—
174	C₂×C₄×C₃₁	—	2	4	no	—
175	C₂×C₄×C₃₁	—	2	4	no	—
176	C₂×C₄×C₃₁	—	2	4	no	—
177	C₂×C₄×C₃₁	—	2	4	no	—
178	C₂×C₄×C₃₁	—	2	4	no	—
179	C₂×C₄×C₃₁	—	2	4	no	—
180	C₂×C₄×C₃₁	—	2	4	no	—
181	C₂×C₄×C₃₁	—	4	24	no	—
182	C₂×C₄×C₃₁	—	4	24	no	—
183	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
184	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
185	C₂×C₄×C₃₁	C₂²×D₄	1	8	yes	—
186	C₂×C₄×C₃₁	C₂²×D₄	1	8	yes	—
187	C₂³×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
188	C₂³×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
189	C₂³×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
190	C₂³×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
191	C₂³×C₄²	C₂×C₃₁	1	1	yes	characteristic, complemented
192	C₂×#388	C₂×C₃₁	1	24	yes	direct product factor
193	C₂²×#95	C₂×C₃₁	1	1	yes	characteristic, complemented
194	C₂²×#95	C₂×C₃₁	1	1	yes	characteristic, complemented
195	C₂²×C₃₁	—	2	8	no	—
196	C₂²×C₃₁	—	2	8	no	—
197	C₂²×C₃₁	—	2	8	no	—
198	C₂²×C₃₁	—	4	4	no	—
199	C₂²×C₃₁	—	4	4	no	—
200	C₂²×C₃₁	—	4	4	no	—
201	C₂²×C₃₁	—	4	4	no	—
202	C₂²×C₃₁	—	4	96	no	—
203	C₂²×C₃₁	#388	1	64	yes	direct product factor
204	C₂²×C₃₁	C₂×#117	1	12	yes	—
205	C₂²×C₃₁	C₂×C₄×D₄	1	12	yes	—
206	C₂²×C₃₁	C₂×C₄×D₄	1	12	yes	—
207	C₂²×C₃₁	C₂×#121	1	12	yes	—
208	C₂²×C₃₁	C₂×#123	1	12	yes	—
209	C₂²×C₃₁	C₂×#124	1	12	yes	—
210	C₂²×C₃₁	C₂×#126	1	12	yes	—
211	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
212	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
213	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
214	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
215	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
216	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
217	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
218	C₄×C₃₁	—	2	8	no	—
219	C₄×C₃₁	—	2	8	no	—
220	C₄×C₃₁	—	2	8	no	—
221	C₄×C₃₁	—	2	8	no	—
222	C₄×C₃₁	—	4	4	no	—
223	C₄×C₃₁	—	4	4	no	—
224	C₂⁶	C₂²×C₃₁	1	1	yes	characteristic
225	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
226	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
227	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
228	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
229	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
230	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	—	2	8	no	—
232	C₂²×C₄⋊C₄	C₂²×C₃₁	1	12	yes	complemented
233	C₂²×C₂²⋊C₄	—	2	8	no	—
234	C₂²×C₂²⋊C₄	—	2	8	no	—
235	C₂²×C₂²⋊C₄	C₄×C₃₁	1	16	yes	complemented
236	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	12	yes	—
237	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	12	yes	—
238	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	12	yes	—
239	C₂²×C₄²	—	2	8	no	—
240	C₂²×C₄²	C₂²×C₃₁	1	12	yes	complemented
241	#388	C₂²×C₃₁	1	64	yes	direct product factor
242	C₂×#95	C₂²×C₃₁	1	12	yes	complemented
243	C₂×#95	C₂²×C₃₁	1	12	yes	complemented
244	C₂×C₃₁	—	4	8	no	—
245	C₂×C₃₁	C₂×#388	1	24	yes	direct product factor
246	C₂×C₃₁	C₂²×#117	1	1	yes	characteristic
247	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
248	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
249	C₂×C₃₁	C₂²×#121	1	1	yes	characteristic
250	C₂×C₃₁	C₂²×#123	1	1	yes	characteristic
251	C₂×C₃₁	C₂²×#124	1	1	yes	characteristic
252	C₂×C₃₁	C₂²×#126	1	1	yes	characteristic
253	C₂⁵	—	2	4	no	—
254	C₂⁵	—	2	4	no	—
255	C₂⁵	—	2	4	no	—
256	C₂⁵	—	2	4	no	—
257	C₂⁵	—	2	4	no	—
258	C₂⁵	—	2	4	no	—
259	C₂⁵	C₂×C₄×C₃₁	1	8	yes	—
260	C₂⁵	C₂³×C₃₁	1	6	yes	—
261	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
262	C₂³×C₄	—	2	4	no	—
263	C₂³×C₄	—	2	4	no	—
264	C₂³×C₄	—	2	4	no	—
265	C₂³×C₄	—	2	4	no	—
266	C₂³×C₄	—	2	4	no	—
267	C₂³×C₄	—	2	4	no	—
268	C₂³×C₄	—	2	4	no	—
269	C₂³×C₄	—	2	4	no	—
270	C₂³×C₄	—	2	4	no	—
271	C₂³×C₄	—	2	4	no	—
272	C₂³×C₄	—	2	4	no	—
273	C₂³×C₄	—	2	4	no	—
274	C₂³×C₄	—	2	4	no	—
275	C₂³×C₄	—	2	4	no	—
276	C₂³×C₄	C₂×C₄×C₃₁	1	8	yes	—
277	C₂³×C₄	C₂×C₄×C₃₁	1	8	yes	—
278	C₂³×C₄	D₄×C₃₁	1	8	yes	—
279	C₂³×C₄	D₄×C₃₁	1	8	yes	—
280	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
281	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
282	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
283	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
284	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
285	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
286	C₂×C₄⋊C₄	—	2	48	no	—
287	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	complemented
288	C₂×C₂²⋊C₄	—	2	48	no	—
289	C₂×C₂²⋊C₄	—	2	48	no	—
290	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	96	yes	complemented
291	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
294	C₂×C₄²	—	2	48	no	—
295	C₂×C₄²	C₂³×C₃₁	1	16	yes	complemented
296	#95	C₂³×C₃₁	1	16	yes	complemented
297	#95	C₂³×C₃₁	1	16	yes	complemented
298	C₃₁	C₂²×#388	1	1	yes	characteristic, direct product factor, Sylow
299	C₂⁴	—	2	32	no	—
300	C₂⁴	—	2	32	no	—
301	C₂⁴	—	2	32	no	—
302	C₂⁴	—	2	12	no	—
303	C₂⁴	—	2	12	no	—
304	C₂⁴	—	2	12	no	—
305	C₂⁴	—	2	12	no	—
306	C₂⁴	—	2	12	no	—
307	C₂⁴	—	2	12	no	—
308	C₂⁴	—	4	16	no	—
309	C₂⁴	—	4	16	no	—
310	C₂⁴	—	4	16	no	—
311	C₂⁴	—	4	16	no	—
312	C₂⁴	C₂²×C₄×C₃₁	1	24	yes	—
313	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
314	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
315	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
316	C₂⁴	#41×C₃₁	1	4	yes	—
317	C₂⁴	#41×C₃₁	1	4	yes	—
318	C₂⁴	#41×C₃₁	1	4	yes	—
319	C₂⁴	#41×C₃₁	1	4	yes	—
320	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
321	C₂⁴	C₂⁴×C₃₁	1	3	yes	—
322	C₂²×C₄	—	2	32	no	—
323	C₂²×C₄	—	2	32	no	—
324	C₂²×C₄	—	2	32	no	—
325	C₂²×C₄	—	2	32	no	—
326	C₂²×C₄	—	2	12	no	—
327	C₂²×C₄	—	2	12	no	—
328	C₂²×C₄	—	2	12	no	—
329	C₂²×C₄	—	2	12	no	—
330	C₂²×C₄	—	2	12	no	—
331	C₂²×C₄	—	2	12	no	—
332	C₂²×C₄	—	2	12	no	—
333	C₂²×C₄	—	2	12	no	—
334	C₂²×C₄	—	2	12	no	—
335	C₂²×C₄	—	2	12	no	—
336	C₂²×C₄	—	2	12	no	—
337	C₂²×C₄	—	2	12	no	—
338	C₂²×C₄	—	2	12	no	—
339	C₂²×C₄	—	2	12	no	—
340	C₂²×C₄	—	4	16	no	—
341	C₂²×C₄	—	4	16	no	—
342	C₂²×C₄	C₂²×C₄×C₃₁	1	24	yes	—
343	C₂²×C₄	C₂²×C₄×C₃₁	1	24	yes	—
344	C₂²×C₄	C₂×D₄×C₃₁	1	24	yes	—
345	C₂²×C₄	C₂×D₄×C₃₁	1	24	yes	—
346	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
347	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
348	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
349	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
350	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
351	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
352	C₄⋊C₄	—	2	32	no	—
353	C₂²⋊C₄	—	2	32	no	—
354	C₂²⋊C₄	—	2	32	no	—
355	C₂²⋊C₄	C₂²×C₄×C₃₁	1	64	yes	complemented
356	C₄²	—	2	32	no	—
357	C₂³	—	2	48	no	—
358	C₂³	—	2	48	no	—
359	C₂³	—	2	48	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	4	24	no	—
367	C₂³	—	4	24	no	—
368	C₂³	—	4	24	no	—
369	C₂³	—	4	24	no	—
370	C₂³	—	4	128	no	—
371	C₂³	C₃₁×#117	1	16	yes	—
372	C₂³	C₄×D₄×C₃₁	1	16	yes	—
373	C₂³	C₄×D₄×C₃₁	1	16	yes	—
374	C₂³	C₃₁×#121	1	16	yes	—
375	C₂³	C₃₁×#123	1	16	yes	—
376	C₂³	C₃₁×#124	1	16	yes	—
377	C₂³	C₃₁×#126	1	16	yes	—
378	C₂³	C₂³×C₄×C₃₁	1	8	yes	—
379	C₂³	C₂³×C₄×C₃₁	1	6	yes	—
380	C₂³	C₂²×D₄×C₃₁	1	6	yes	—
381	C₂³	C₂²×D₄×C₃₁	1	6	yes	—
382	C₂³	C₂×#41×C₃₁	1	6	yes	—
383	C₂³	C₂×#41×C₃₁	1	6	yes	—
384	C₂³	C₂×#41×C₃₁	1	6	yes	—
385	C₂³	C₂×#41×C₃₁	1	6	yes	—
386	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
387	C₂×C₄	—	2	48	no	—
388	C₂×C₄	—	2	48	no	—
389	C₂×C₄	—	2	48	no	—
390	C₂×C₄	—	2	48	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	24	no	—
406	C₂×C₄	—	4	24	no	—
407	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
408	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
409	C₂×C₄	C₂²×D₄×C₃₁	1	8	yes	—
410	C₂×C₄	C₂²×D₄×C₃₁	1	8	yes	—
411	C₂²	—	2	8	no	—
412	C₂²	—	2	8	no	—
413	C₂²	—	2	8	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	96	no	—
419	C₂²	C₃₁×#388	1	64	yes	direct product factor
420	C₂²	C₂×C₃₁×#117	1	12	yes	—
421	C₂²	C₂×C₄×D₄×C₃₁	1	12	yes	—
422	C₂²	C₂×C₄×D₄×C₃₁	1	12	yes	—
423	C₂²	C₂×C₃₁×#121	1	12	yes	—
424	C₂²	C₂×C₃₁×#123	1	12	yes	—
425	C₂²	C₂×C₃₁×#124	1	12	yes	—
426	C₂²	C₂×C₃₁×#126	1	12	yes	—
427	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
428	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
429	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
430	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
431	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
432	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
433	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
434	C₄	—	2	8	no	—
435	C₄	—	2	8	no	—
436	C₄	—	2	8	no	—
437	C₄	—	2	8	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	4	no	—
440	C₂	—	4	8	no	—
441	C₂	C₂×C₃₁×#388	1	24	yes	direct product factor
442	C₂	C₂²×C₃₁×#117	1	1	yes	characteristic
443	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
444	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
445	C₂	C₂²×C₃₁×#121	1	1	yes	characteristic
446	C₂	C₂²×C₃₁×#123	1	1	yes	characteristic
447	C₂	C₂²×C₃₁×#124	1	1	yes	characteristic
448	C₂	C₂²×C₃₁×#126	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁵×C₃₁	C₂³
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁶×C₃₁	C₂²
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
1. C₂³×C₄⋊C₄×C₃₁	C₂	semidirect
5. C₂³×C₄²×C₃₁	C₂	semidirect
6. C₂×C₃₁×#388	C₂	direct (N × H)
7. C₂²×C₃₁×#95	C₂	semidirect
8. C₂²×C₃₁×#95	C₂	semidirect
17. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
20. C₂²×C₂²⋊C₄×C₃₁	C₄	semidirect
25. C₂²×C₄²×C₃₁	C₂²	semidirect
26. C₃₁×#388	C₂²	direct (N × H)
27. C₂×C₃₁×#95	C₂²	semidirect
28. C₂×C₃₁×#95	C₂²	semidirect
63. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
66. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
71. C₂×C₄²×C₃₁	C₂³	semidirect
72. C₃₁×#95	C₂³	semidirect
73. C₃₁×#95	C₂³	semidirect
130. C₂²⋊C₄×C₃₁	C₂²×C₄	semidirect
132. C₂²×#388	C₃₁	direct (N × H)
187. C₂³×C₄⋊C₄	C₂×C₃₁	semidirect
191. C₂³×C₄²	C₂×C₃₁	semidirect
192. C₂×#388	C₂×C₃₁	direct (N × H)
193. C₂²×#95	C₂×C₃₁	semidirect
194. C₂²×#95	C₂×C₃₁	semidirect
203. C₂²×C₃₁	#388	direct (N × H)
232. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
235. C₂²×C₂²⋊C₄	C₄×C₃₁	semidirect
240. C₂²×C₄²	C₂²×C₃₁	semidirect
241. #388	C₂²×C₃₁	direct (N × H)
242. C₂×#95	C₂²×C₃₁	semidirect
243. C₂×#95	C₂²×C₃₁	semidirect
245. C₂×C₃₁	C₂×#388	direct (N × H)
287. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
290. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
295. C₂×C₄²	C₂³×C₃₁	semidirect
296. #95	C₂³×C₃₁	semidirect
297. #95	C₂³×C₃₁	semidirect
298. C₃₁	C₂²×#388	direct (N × H)
355. C₂²⋊C₄	C₂²×C₄×C₃₁	semidirect
419. C₂²	C₃₁×#388	direct (N × H)
441. C₂	C₂×C₃₁×#388	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₃₁	2
C₂³×C₂²⋊C₄×C₃₁	2
C₂³×C₄²×C₃₁	2
C₂×C₃₁×#388	2
C₂²×C₃₁×#95	2
C₂²×#388	31

Subgroups — C22×C31×#388 #21490775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃₁×#388 #21490775