Subgroups — C₂×C₃₁×#2632 #21491358

Order 7936.

2806 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#124	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2632	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#399	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#395	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#394	C₂	1	2	yes	maximal
7	C₂×C₃₁×#393	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#388	C₂	1	4	yes	maximal, complemented
9	C₂×C₃₁×#383	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#124	—	2	8	no	—
14	C₂×C₃₁×#124	C₂²	1	8	yes	—
15	C₂×C₄×Q₈×C₃₁	—	2	8	no	—
16	C₂×C₄×Q₈×C₃₁	C₂²	1	8	yes	complemented
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
20	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
21	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
24	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
25	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#399	C₂²	1	16	yes	complemented
27	C₃₁×#395	C₂²	1	16	yes	complemented
28	C₃₁×#394	C₂²	1	16	yes	—
29	C₃₁×#393	C₂²	1	16	yes	complemented
30	C₃₁×#388	C₂²	1	32	yes	complemented
31	C₃₁×#383	C₂²	1	8	yes	complemented
32	C₂×C₃₁×#95	C₂²	1	4	yes	—
33	C₂×C₃₁×#95	C₂²	1	2	yes	—
34	C₂×C₃₁×#95	C₂²	1	2	yes	—
35	C₂×C₃₁×#95	C₂²	1	2	yes	—
36	C₂⁵×C₃₁	C₂³	1	2	yes	—
37	C₂²×Q₈×C₃₁	—	2	4	no	—
38	C₂²×Q₈×C₃₁	—	2	4	no	—
39	C₂²×Q₈×C₃₁	—	2	8	no	—
40	C₂²×Q₈×C₃₁	—	4	4	no	—
41	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
42	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
43	C₂²×D₄×C₃₁	—	2	4	no	—
44	C₂²×D₄×C₃₁	—	4	4	no	—
45	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
46	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
47	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
48	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
49	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
53	C₃₁×#124	—	2	32	no	—
54	C₄×Q₈×C₃₁	—	2	32	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
57	C₂×C₄⋊C₄×C₃₁	—	4	8	no	—
58	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
61	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
62	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
63	C₂×C₂²⋊C₄×C₃₁	—	2	16	no	—
64	C₂×C₂²⋊C₄×C₃₁	—	4	8	no	—
65	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
66	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
67	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
68	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
69	C₂×C₄²×C₃₁	—	2	8	no	—
70	C₂×C₄²×C₃₁	D₄	1	8	yes	—
71	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
72	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
73	C₃₁×#95	C₂³	1	8	yes	—
74	C₃₁×#95	C₂³	1	16	yes	—
75	C₃₁×#95	C₂³	1	8	yes	—
76	C₃₁×#95	C₂³	1	8	yes	—
77	C₂⁴×C₃₁	—	2	4	no	—
78	C₂⁴×C₃₁	—	2	8	no	—
79	C₂⁴×C₃₁	—	2	8	no	—
80	C₂⁴×C₃₁	—	2	8	no	—
81	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
82	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
83	C₂×Q₈×C₃₁	—	2	32	no	—
84	C₂×Q₈×C₃₁	—	2	8	no	—
85	C₂×Q₈×C₃₁	—	2	8	no	—
86	C₂×Q₈×C₃₁	—	2	16	no	—
87	C₂×Q₈×C₃₁	—	4	8	no	—
88	C₂×Q₈×C₃₁	—	4	16	no	—
89	C₂×D₄×C₃₁	—	2	8	no	—
90	C₂×D₄×C₃₁	—	4	8	no	—
91	C₂×D₄×C₃₁	—	4	16	no	—
92	C₂²×C₄×C₃₁	—	2	4	no	—
93	C₂²×C₄×C₃₁	—	2	4	no	—
94	C₂²×C₄×C₃₁	—	2	4	no	—
95	C₂²×C₄×C₃₁	—	2	4	no	—
96	C₂²×C₄×C₃₁	—	2	4	no	—
97	C₂²×C₄×C₃₁	—	2	4	no	—
98	C₂²×C₄×C₃₁	—	2	4	no	—
99	C₂²×C₄×C₃₁	—	2	8	no	—
100	C₂²×C₄×C₃₁	—	2	8	no	—
101	C₂²×C₄×C₃₁	—	2	8	no	—
102	C₂²×C₄×C₃₁	—	2	8	no	—
103	C₂²×C₄×C₃₁	—	2	8	no	—
104	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₃₁	#41	1	8	yes	—
108	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
109	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
112	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
113	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
115	C₄⋊C₄×C₃₁	—	2	16	no	—
116	C₄⋊C₄×C₃₁	—	2	8	no	—
117	C₄⋊C₄×C₃₁	—	4	16	no	—
118	C₂²⋊C₄×C₃₁	—	2	16	no	—
119	C₂²⋊C₄×C₃₁	—	2	16	no	—
120	C₂²⋊C₄×C₃₁	—	2	32	no	—
121	C₂²⋊C₄×C₃₁	—	4	16	no	—
122	C₄²×C₃₁	—	2	16	no	—
123	C₄²×C₃₁	C₂×D₄	1	16	yes	—
124	C₂×#2632	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
125	C₂³×C₃₁	—	2	4	no	—
126	C₂³×C₃₁	—	2	8	no	—
127	C₂³×C₃₁	—	2	8	no	—
128	C₂³×C₃₁	—	2	8	no	—
129	C₂³×C₃₁	—	4	8	no	—
130	C₂³×C₃₁	—	4	8	no	—
131	C₂³×C₃₁	—	4	8	no	—
132	C₂³×C₃₁	—	4	32	no	—
133	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
134	C₂³×C₃₁	C₂×#41	1	4	yes	—
135	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
136	C₂³×C₃₁	2₋¹⁺⁴	1	4	yes	—
137	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
138	Q₈×C₃₁	—	2	32	no	—
139	Q₈×C₃₁	—	4	16	no	—
140	D₄×C₃₁	—	4	16	no	—
141	C₂×C₄×C₃₁	—	2	8	no	—
142	C₂×C₄×C₃₁	—	2	16	no	—
143	C₂×C₄×C₃₁	—	2	8	no	—
144	C₂×C₄×C₃₁	—	2	8	no	—
145	C₂×C₄×C₃₁	—	2	4	no	—
146	C₂×C₄×C₃₁	—	2	4	no	—
147	C₂×C₄×C₃₁	—	2	4	no	—
148	C₂×C₄×C₃₁	—	2	4	no	—
149	C₂×C₄×C₃₁	—	2	4	no	—
150	C₂×C₄×C₃₁	—	2	4	no	—
151	C₂×C₄×C₃₁	—	2	4	no	—
152	C₂×C₄×C₃₁	—	2	8	no	—
153	C₂×C₄×C₃₁	—	2	8	no	—
154	C₂×C₄×C₃₁	—	2	8	no	—
155	C₂×C₄×C₃₁	—	2	8	no	—
156	C₂×C₄×C₃₁	—	2	8	no	—
157	C₂×C₄×C₃₁	—	4	8	no	—
158	C₂×C₄×C₃₁	—	4	8	no	—
159	C₂×C₄×C₃₁	—	4	16	no	—
160	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
161	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
162	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
163	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
164	C₂²×#124	C₂×C₃₁	1	1	yes	characteristic
165	C₂²×C₄×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
166	#2632	C₂×C₃₁	1	16	yes	direct product factor
167	C₂×#399	C₂×C₃₁	1	2	yes	complemented
168	C₂×#395	C₂×C₃₁	1	2	yes	complemented
169	C₂×#394	C₂×C₃₁	1	2	yes	—
170	C₂×#393	C₂×C₃₁	1	2	yes	complemented
171	C₂×#388	C₂×C₃₁	1	4	yes	complemented
172	C₂×#383	C₂×C₃₁	1	1	yes	characteristic, complemented
173	C₂²×C₃₁	—	4	4	no	—
174	C₂²×C₃₁	—	4	4	no	—
175	C₂²×C₃₁	—	4	4	no	—
176	C₂²×C₃₁	—	4	16	no	—
177	C₂²×C₃₁	—	8	16	no	—
178	C₂²×C₃₁	#525	1	4	yes	—
179	C₂²×C₃₁	#535	1	4	yes	—
180	C₂²×C₃₁	#536	1	4	yes	—
181	C₂²×C₃₁	#542	1	16	yes	—
182	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
183	C₂²×C₃₁	C₂²×#41	1	2	yes	—
184	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
185	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
186	C₄×C₃₁	—	2	4	no	—
187	C₄×C₃₁	—	2	8	no	—
188	C₄×C₃₁	—	2	4	no	—
189	C₄×C₃₁	—	2	4	no	—
190	C₄×C₃₁	—	4	4	no	—
191	C₄×C₃₁	—	4	4	no	—
192	C₄×C₃₁	—	4	8	no	—
193	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
194	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
195	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
196	C₂×#124	—	2	8	no	—
197	C₂×#124	C₂²×C₃₁	1	8	yes	—
198	C₂×C₄×Q₈	—	2	8	no	—
199	C₂×C₄×Q₈	C₂²×C₃₁	1	8	yes	complemented
200	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
201	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
202	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
203	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
204	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
205	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
206	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
207	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
208	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
209	#399	C₂²×C₃₁	1	16	yes	complemented
210	#395	C₂²×C₃₁	1	16	yes	complemented
211	#394	C₂²×C₃₁	1	16	yes	—
212	#393	C₂²×C₃₁	1	16	yes	complemented
213	#388	C₂²×C₃₁	1	32	yes	complemented
214	#383	C₂²×C₃₁	1	8	yes	complemented
215	C₂×#95	C₂²×C₃₁	1	4	yes	—
216	C₂×#95	C₂²×C₃₁	1	2	yes	—
217	C₂×#95	C₂²×C₃₁	1	2	yes	—
218	C₂×#95	C₂²×C₃₁	1	2	yes	—
219	C₂×C₃₁	—	8	4	no	—
220	C₂×C₃₁	#2632	1	8	yes	direct product factor
221	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
222	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
223	C₂×C₃₁	C₂×#536	1	1	yes	characteristic
224	C₂×C₃₁	C₂×#542	1	4	yes	—
225	C₂⁵	C₂³×C₃₁	1	2	yes	—
226	C₂²×Q₈	—	2	4	no	—
227	C₂²×Q₈	—	2	4	no	—
228	C₂²×Q₈	—	2	8	no	—
229	C₂²×Q₈	—	4	4	no	—
230	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
231	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
232	C₂²×D₄	—	2	4	no	—
233	C₂²×D₄	—	4	4	no	—
234	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
235	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
236	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
237	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
238	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
241	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
242	#124	—	2	32	no	—
243	C₄×Q₈	—	2	32	no	—
244	C₂×C₄⋊C₄	—	2	8	no	—
245	C₂×C₄⋊C₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	4	8	no	—
247	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
248	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
249	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
250	C₂×C₂²⋊C₄	—	2	8	no	—
251	C₂×C₂²⋊C₄	—	2	8	no	—
252	C₂×C₂²⋊C₄	—	2	16	no	—
253	C₂×C₂²⋊C₄	—	4	8	no	—
254	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
255	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
256	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
257	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
258	C₂×C₄²	—	2	8	no	—
259	C₂×C₄²	D₄×C₃₁	1	8	yes	—
260	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
261	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
262	#95	C₂³×C₃₁	1	8	yes	—
263	#95	C₂³×C₃₁	1	8	yes	—
264	#95	C₂³×C₃₁	1	8	yes	—
265	#95	C₂³×C₃₁	1	16	yes	—
266	C₃₁	C₂×#2632	1	1	yes	characteristic, direct product factor, Sylow
267	C₂⁴	—	2	4	no	—
268	C₂⁴	—	2	8	no	—
269	C₂⁴	—	2	8	no	—
270	C₂⁴	—	2	8	no	—
271	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
272	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
273	C₂×Q₈	—	2	32	no	—
274	C₂×Q₈	—	2	8	no	—
275	C₂×Q₈	—	2	8	no	—
276	C₂×Q₈	—	2	16	no	—
277	C₂×Q₈	—	4	8	no	—
278	C₂×Q₈	—	4	16	no	—
279	C₂×D₄	—	2	8	no	—
280	C₂×D₄	—	4	8	no	—
281	C₂×D₄	—	4	16	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	8	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
295	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
296	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
297	C₂²×C₄	#41×C₃₁	1	8	yes	—
298	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
299	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
300	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
301	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
302	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
303	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
304	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
305	C₄⋊C₄	—	2	16	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	4	16	no	—
308	C₂²⋊C₄	—	2	16	no	—
309	C₂²⋊C₄	—	2	16	no	—
310	C₂²⋊C₄	—	2	32	no	—
311	C₂²⋊C₄	—	4	16	no	—
312	C₄²	—	2	16	no	—
313	C₄²	C₂×D₄×C₃₁	1	16	yes	—
314	C₂³	—	2	4	no	—
315	C₂³	—	2	8	no	—
316	C₂³	—	2	8	no	—
317	C₂³	—	2	8	no	—
318	C₂³	—	4	8	no	—
319	C₂³	—	4	8	no	—
320	C₂³	—	4	8	no	—
321	C₂³	—	4	32	no	—
322	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
323	C₂³	C₂×#41×C₃₁	1	4	yes	—
324	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
325	C₂³	C₃₁×2₋¹⁺⁴	1	4	yes	—
326	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
327	Q₈	—	2	32	no	—
328	Q₈	—	4	16	no	—
329	D₄	—	4	16	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	16	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	8	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	—	4	8	no	—
348	C₂×C₄	—	4	16	no	—
349	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
350	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
351	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
352	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
353	C₂²	—	4	4	no	—
354	C₂²	—	4	4	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	4	16	no	—
357	C₂²	—	8	16	no	—
358	C₂²	C₃₁×#525	1	4	yes	—
359	C₂²	C₃₁×#535	1	4	yes	—
360	C₂²	C₃₁×#536	1	4	yes	—
361	C₂²	C₃₁×#542	1	16	yes	—
362	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
363	C₂²	C₂²×#41×C₃₁	1	2	yes	—
364	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
365	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
366	C₄	—	2	4	no	—
367	C₄	—	2	8	no	—
368	C₄	—	2	4	no	—
369	C₄	—	2	4	no	—
370	C₄	—	4	4	no	—
371	C₄	—	4	4	no	—
372	C₄	—	4	8	no	—
373	C₂	—	8	4	no	—
374	C₂	C₃₁×#2632	1	8	yes	direct product factor
375	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
376	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
377	C₂	C₂×C₃₁×#536	1	1	yes	characteristic
378	C₂	C₂×C₃₁×#542	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₃₁	C₂	semidirect
3. C₃₁×#2632	C₂	direct (N × H)
4. C₂×C₃₁×#399	C₂	semidirect
5. C₂×C₃₁×#395	C₂	semidirect
7. C₂×C₃₁×#393	C₂	semidirect
8. C₂×C₃₁×#388	C₂	semidirect
9. C₂×C₃₁×#383	C₂	semidirect
16. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
26. C₃₁×#399	C₂²	semidirect
27. C₃₁×#395	C₂²	semidirect
29. C₃₁×#393	C₂²	semidirect
30. C₃₁×#388	C₂²	semidirect
31. C₃₁×#383	C₂²	semidirect
124. C₂×#2632	C₃₁	direct (N × H)
165. C₂²×C₄×Q₈	C₂×C₃₁	semidirect
166. #2632	C₂×C₃₁	direct (N × H)
167. C₂×#399	C₂×C₃₁	semidirect
168. C₂×#395	C₂×C₃₁	semidirect
170. C₂×#393	C₂×C₃₁	semidirect
171. C₂×#388	C₂×C₃₁	semidirect
172. C₂×#383	C₂×C₃₁	semidirect
199. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
209. #399	C₂²×C₃₁	semidirect
210. #395	C₂²×C₃₁	semidirect
212. #393	C₂²×C₃₁	semidirect
213. #388	C₂²×C₃₁	semidirect
214. #383	C₂²×C₃₁	semidirect
220. C₂×C₃₁	#2632	direct (N × H)
266. C₃₁	C₂×#2632	direct (N × H)
374. C₂	C₃₁×#2632	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×C₃₁×#124	2
C₂²×C₄×Q₈×C₃₁	2
C₃₁×#2632	2
C₂×C₃₁×#399	2
C₂×C₃₁×#395	2
C₂×C₃₁×#394	2
C₂×C₃₁×#393	2
C₂×C₃₁×#388	2
C₂×C₃₁×#383	2
C₂×#2632	31

Subgroups — C2×C31×#2632 #21491358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2632 #21491358