Subgroups — C₃₁×#18093 #21474852

Order 7936.

598 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2994	C₂	1	2	yes	maximal, complemented
3	C₃₁×#1594	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1583	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1582	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1580	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1579	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1483	C₂	1	2	yes	maximal, complemented
11	C₃₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#529	C₂²	1	2	yes	—
13	C₃₁×#499	C₄	1	1	yes	characteristic
14	C₃₁×#495	C₄	1	1	yes	characteristic
15	C₃₁×#488	C₄	1	2	yes	—
16	C₃₁×#467	C₄	1	1	yes	characteristic
17	C₃₁×#466	C₄	1	1	yes	characteristic
18	C₃₁×#465	C₄	1	2	yes	—
19	C₃₁×#446	C₂²	1	2	yes	—
20	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
21	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
22	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
23	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#436	C₂²	1	2	yes	—
25	C₃₁×#435	—	2	2	no	—
26	C₈×D₄×C₃₁	—	2	2	no	—
27	C₈×D₄×C₃₁	C₂²	1	2	yes	—
28	C₃₁×#433	—	2	2	no	—
29	C₃₁×#431	C₂²	1	1	yes	characteristic
30	C₃₁×#424	—	2	2	no	—
31	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
32	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#334	C₂²	1	1	yes	characteristic
35	C₃₁×#334	C₂²	1	2	yes	—
36	C₃₁×#334	C₂²	1	1	yes	characteristic
37	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₃₁×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₃₁×D₄⋊C₈	C₂²	1	2	yes	—
40	C₃₁×D₄⋊C₈	C₂²	1	2	yes	—
41	C₃₁×#322	C₂²	1	1	yes	characteristic
42	C₃₁×#322	C₂²	1	1	yes	characteristic
43	C₃₁×#322	C₂²	1	1	yes	characteristic
44	C₃₁×#322	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
46	C₂×SD₁₆×C₃₁	C₂×C₄	1	2	yes	—
47	C₂×D₈×C₃₁	C₂×C₄	1	1	yes	characteristic
48	C₂×M₁₆×C₃₁	—	2	1	no	—
49	C₂×M₁₆×C₃₁	—	2	2	no	—
50	C₂²×C₈×C₃₁	—	2	2	no	—
51	C₂²×C₈×C₃₁	—	2	2	no	—
52	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
54	C₃₁×#126	—	2	2	no	—
55	C₃₁×#125	C₂×C₄	1	2	yes	—
56	C₃₁×#124	C₂×C₄	1	2	yes	—
57	C₃₁×#123	—	2	2	no	—
58	C₃₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
59	C₃₁×#121	C₂×C₄	1	2	yes	—
60	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
61	C₄×D₄×C₃₁	—	2	2	no	—
62	C₄×D₄×C₃₁	C₂³	1	2	yes	—
63	C₃₁×#117	—	2	2	no	—
64	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
65	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
66	C₃₁×#107	C₂×C₄	1	1	yes	characteristic
67	C₃₁×#106	C₂×C₄	1	2	yes	—
68	C₃₁×C₄⋊C₈	—	2	2	no	—
69	C₃₁×C₄⋊C₈	—	2	2	no	—
70	C₃₁×C₄⋊C₈	—	2	2	no	—
71	C₃₁×C₄⋊C₈	D₄	1	2	yes	—
72	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
73	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
74	C₃₁×#103	C₂×C₄	1	2	yes	—
75	C₃₁×#103	C₂×C₄	1	2	yes	—
76	C₃₁×#102	C₂×C₄	1	2	yes	—
77	C₃₁×#102	C₂×C₄	1	2	yes	—
78	C₃₁×C₂²⋊C₈	—	2	2	no	—
79	C₃₁×C₂²⋊C₈	—	2	2	no	—
80	C₃₁×C₂²⋊C₈	D₄	1	2	yes	—
81	C₃₁×#97	—	2	2	no	—
82	C₃₁×#97	—	2	1	no	—
83	C₄×C₈×C₃₁	—	2	2	no	—
84	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
85	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
86	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
92	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
93	C₂×D₄×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₃₁	—	2	2	no	—
96	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
99	Q₁₆×C₃₁	—	2	2	no	—
100	SD₁₆×C₃₁	—	4	2	no	—
101	D₈×C₃₁	—	2	2	no	—
102	M₁₆×C₃₁	—	4	2	no	—
103	M₁₆×C₃₁	—	8	2	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	2	2	no	—
106	C₂×C₈×C₃₁	—	2	2	no	—
107	C₂×C₈×C₃₁	—	2	1	no	—
108	C₂×C₈×C₃₁	—	2	1	no	—
109	C₂×C₈×C₃₁	—	4	1	no	—
110	C₂×C₈×C₃₁	—	8	2	no	—
111	C₂×C₈×C₃₁	—	8	2	no	—
112	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
118	C₄⋊C₄×C₃₁	—	2	2	no	—
119	C₄⋊C₄×C₃₁	—	2	2	no	—
120	C₄⋊C₄×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	2	2	no	—
122	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
123	C₄⋊C₄×C₃₁	C₂²×C₄	1	2	yes	—
124	C₂²⋊C₄×C₃₁	—	2	2	no	—
125	C₂²⋊C₄×C₃₁	—	2	2	no	—
126	C₂²⋊C₄×C₃₁	—	2	2	no	—
127	C₂²⋊C₄×C₃₁	—	2	2	no	—
128	C₂²⋊C₄×C₃₁	—	2	2	no	—
129	C₄²×C₃₁	—	2	2	no	—
130	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₃₁	#41	1	1	yes	characteristic
133	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
134	#18093	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₃₁	—	2	2	no	—
136	C₂³×C₃₁	C₄×D₄	1	1	yes	characteristic
137	Q₈×C₃₁	—	2	2	no	—
138	Q₈×C₃₁	—	2	2	no	—
139	D₄×C₃₁	—	2	2	no	—
140	D₄×C₃₁	—	2	2	no	—
141	D₄×C₃₁	—	4	4	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	2	1	no	—
144	C₂×C₄×C₃₁	—	2	1	no	—
145	C₂×C₄×C₃₁	—	2	2	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	2	no	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
157	C₈×C₃₁	—	2	1	no	—
158	C₈×C₃₁	—	2	1	no	—
159	C₈×C₃₁	—	2	1	no	—
160	C₈×C₃₁	—	2	2	no	—
161	C₈×C₃₁	—	2	2	no	—
162	C₈×C₃₁	—	4	1	no	—
163	C₈×C₃₁	—	4	1	no	—
164	C₈×C₃₁	—	4	2	no	—
165	C₈×C₃₁	—	4	2	no	—
166	C₈×C₃₁	#131	1	2	yes	—
167	#3168	C₂×C₃₁	1	1	yes	characteristic
168	#2994	C₂×C₃₁	1	2	yes	complemented
169	#1594	C₂×C₃₁	1	1	yes	characteristic, complemented
170	#1593	C₂×C₃₁	1	1	yes	characteristic, complemented
171	#1583	C₂×C₃₁	1	2	yes	complemented
172	#1582	C₂×C₃₁	1	2	yes	complemented
173	#1580	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#1579	C₂×C₃₁	1	1	yes	characteristic, complemented
175	C₂×#334	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#1483	C₂×C₃₁	1	2	yes	complemented
177	#1451	C₂×C₃₁	1	1	yes	characteristic, complemented
178	C₂²×C₃₁	—	2	1	no	—
179	C₂²×C₃₁	—	2	1	no	—
180	C₂²×C₃₁	—	4	2	no	—
181	C₂²×C₃₁	—	4	2	no	—
182	C₂²×C₃₁	—	4	2	no	—
183	C₂²×C₃₁	#444	1	2	yes	—
184	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
185	C₄×C₃₁	—	2	1	no	—
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	2	1	no	—
188	C₄×C₃₁	—	2	1	no	—
189	C₄×C₃₁	—	4	2	no	—
190	C₄×C₃₁	—	4	2	no	—
191	C₄×C₃₁	—	4	2	no	—
192	C₄×C₃₁	C₂×#131	1	1	yes	characteristic
193	C₄×C₃₁	#568	1	1	yes	characteristic
194	C₄×C₃₁	#577	1	2	yes	—
195	#529	C₂²×C₃₁	1	2	yes	—
196	#499	C₄×C₃₁	1	1	yes	characteristic
197	#495	C₄×C₃₁	1	1	yes	characteristic
198	#488	C₄×C₃₁	1	2	yes	—
199	#467	C₄×C₃₁	1	1	yes	characteristic
200	#466	C₄×C₃₁	1	1	yes	characteristic
201	#465	C₄×C₃₁	1	2	yes	—
202	#446	C₂²×C₃₁	1	2	yes	—
203	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
204	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
205	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
206	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
207	#436	C₂²×C₃₁	1	2	yes	—
208	#435	—	2	2	no	—
209	C₈×D₄	—	2	2	no	—
210	C₈×D₄	C₂²×C₃₁	1	2	yes	—
211	#433	—	2	2	no	—
212	#431	C₂²×C₃₁	1	1	yes	characteristic
213	#424	—	2	2	no	—
214	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
215	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
217	#334	C₂²×C₃₁	1	1	yes	characteristic
218	#334	C₂²×C₃₁	1	2	yes	—
219	#334	C₂²×C₃₁	1	1	yes	characteristic
220	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
221	Q₈⋊C₈	C₂²×C₃₁	1	2	yes	—
222	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
223	D₄⋊C₈	C₂²×C₃₁	1	2	yes	—
224	#322	C₂²×C₃₁	1	1	yes	characteristic
225	#322	C₂²×C₃₁	1	1	yes	characteristic
226	#322	C₂²×C₃₁	1	1	yes	characteristic
227	#322	C₂²×C₃₁	1	1	yes	characteristic
228	C₂×C₃₁	—	2	2	no	—
229	C₂×C₃₁	—	8	2	no	—
230	C₂×C₃₁	#2935	1	1	yes	characteristic
231	C₂×C₃₁	#2952	1	1	yes	characteristic
232	C₂×C₃₁	C₂×#444	1	1	yes	characteristic
233	C₂×Q₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
234	C₂×SD₁₆	C₂×C₄×C₃₁	1	2	yes	—
235	C₂×D₈	C₂×C₄×C₃₁	1	1	yes	characteristic
236	C₂×M₁₆	—	2	1	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
241	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
242	#126	—	2	2	no	—
243	#125	C₂×C₄×C₃₁	1	2	yes	—
244	#124	C₂×C₄×C₃₁	1	2	yes	—
245	#123	—	2	2	no	—
246	C₂²⋊Q₈	C₂×C₄×C₃₁	1	2	yes	—
247	#121	C₂×C₄×C₃₁	1	2	yes	—
248	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	C₂³×C₃₁	1	2	yes	—
251	#117	—	2	2	no	—
252	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
253	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
254	#107	C₂×C₄×C₃₁	1	1	yes	characteristic
255	#106	C₂×C₄×C₃₁	1	2	yes	—
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	2	2	no	—
259	C₄⋊C₈	D₄×C₃₁	1	2	yes	—
260	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
261	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
262	#103	C₂×C₄×C₃₁	1	2	yes	—
263	#103	C₂×C₄×C₃₁	1	2	yes	—
264	#102	C₂×C₄×C₃₁	1	2	yes	—
265	#102	C₂×C₄×C₃₁	1	2	yes	—
266	C₂²⋊C₈	—	2	2	no	—
267	C₂²⋊C₈	—	2	2	no	—
268	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
269	#97	—	2	2	no	—
270	#97	—	2	1	no	—
271	C₄×C₈	—	2	2	no	—
272	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
273	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
275	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
276	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
280	C₃₁	#18093	1	1	yes	characteristic, direct product factor, Sylow
281	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
287	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
288	Q₁₆	—	2	2	no	—
289	SD₁₆	—	4	2	no	—
290	D₈	—	2	2	no	—
291	M₁₆	—	4	2	no	—
292	M₁₆	—	8	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	4	1	no	—
299	C₂×C₈	—	8	2	no	—
300	C₂×C₈	—	8	2	no	—
301	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
302	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
303	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
304	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
306	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
312	C₄⋊C₄	C₂²×C₄×C₃₁	1	2	yes	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
320	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
321	C₄²	#41×C₃₁	1	1	yes	characteristic
322	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
323	C₂³	—	2	2	no	—
324	C₂³	C₄×D₄×C₃₁	1	1	yes	characteristic
325	Q₈	—	2	2	no	—
326	Q₈	—	2	2	no	—
327	D₄	—	2	2	no	—
328	D₄	—	2	2	no	—
329	D₄	—	4	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
340	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
341	C₂×C₄	C₄×D₄×C₃₁	1	1	yes	characteristic
342	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
344	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
345	C₈	—	2	1	no	—
346	C₈	—	2	1	no	—
347	C₈	—	2	1	no	—
348	C₈	—	2	2	no	—
349	C₈	—	2	2	no	—
350	C₈	—	4	1	no	—
351	C₈	—	4	1	no	—
352	C₈	—	4	2	no	—
353	C₈	—	4	2	no	—
354	C₈	C₃₁×#131	1	2	yes	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	C₃₁×#444	1	2	yes	—
361	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	2	no	—
369	C₄	C₂×C₃₁×#131	1	1	yes	characteristic
370	C₄	C₃₁×#568	1	1	yes	characteristic
371	C₄	C₃₁×#577	1	2	yes	—
372	C₂	—	2	2	no	—
373	C₂	—	8	2	no	—
374	C₂	C₃₁×#2935	1	1	yes	characteristic
375	C₂	C₃₁×#2952	1	1	yes	characteristic
376	C₂	C₂×C₃₁×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₄²	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×C₄×D₄
prime radical	C₃₁×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₃₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2994	C₂	semidirect
3. C₃₁×#1594	C₂	semidirect
4. C₃₁×#1593	C₂	semidirect
5. C₃₁×#1583	C₂	semidirect
6. C₃₁×#1582	C₂	semidirect
7. C₃₁×#1580	C₂	semidirect
8. C₃₁×#1579	C₂	semidirect
9. C₂×C₃₁×#334	C₂	semidirect
10. C₃₁×#1483	C₂	semidirect
11. C₃₁×#1451	C₂	semidirect
134. #18093	C₃₁	direct (N × H)
168. #2994	C₂×C₃₁	semidirect
169. #1594	C₂×C₃₁	semidirect
170. #1593	C₂×C₃₁	semidirect
171. #1583	C₂×C₃₁	semidirect
172. #1582	C₂×C₃₁	semidirect
173. #1580	C₂×C₃₁	semidirect
174. #1579	C₂×C₃₁	semidirect
175. C₂×#334	C₂×C₃₁	semidirect
176. #1483	C₂×C₃₁	semidirect
177. #1451	C₂×C₃₁	semidirect
280. C₃₁	#18093	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3168	2
C₃₁×#2994	2
C₃₁×#1594	2
C₃₁×#1593	2
C₃₁×#1583	2
C₃₁×#1582	2
C₃₁×#1580	2
C₃₁×#1579	2
C₂×C₃₁×#334	2
C₃₁×#1483	2
C₃₁×#1451	2
#18093	31

Subgroups — C31×#18093 #21474852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#18093 #21474852