Subgroups — C₃₁×#20468 #21477227

Order 7936.

950 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	C₂×C₃₁×#433	C₂	1	2	yes	maximal
2	C₄×C₃₁×#117	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1768	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₃₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1750	C₂	1	2	yes	maximal
7	C₃₁×#1749	C₂	1	1	yes	maximal, characteristic
8	C₄×C₃₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#1745	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1744	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#1726	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
15	C₃₁×#433	C₄	1	16	yes	complemented
16	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₃₁×#97	C₂²	1	2	yes	—
21	C₂×C₃₁×#97	C₂²	1	2	yes	—
22	C₂×C₃₁×#97	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
27	C₄×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
28	C₄×C₂²⋊C₄×C₃₁	C₄	1	2	yes	—
29	C₄×C₂²⋊C₄×C₃₁	C₄	1	2	yes	—
30	C₃₁×#376	C₂²	1	1	yes	characteristic
31	C₃₁×#376	C₂²	1	1	yes	characteristic
32	C₄³×C₃₁	C₂²	1	1	yes	characteristic
33	C₄³×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#336	C₂²	1	1	yes	characteristic
35	C₃₁×#336	C₂²	1	1	yes	characteristic
36	C₃₁×#336	C₂²	1	2	yes	—
37	C₃₁×#336	C₂²	1	1	yes	characteristic
38	C₃₁×#336	C₂²	1	1	yes	characteristic
39	C₃₁×#336	C₂²	1	2	yes	—
40	C₂³×C₄×C₃₁	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
46	C₃₁×#117	—	2	2	no	—
47	C₃₁×#117	—	2	2	no	—
48	C₃₁×#117	C₂×C₄	1	8	yes	—
49	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₃₁	—	2	4	no	—
56	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
67	C₃₁×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
68	C₃₁×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
69	C₃₁×C₂²⋊C₈	C₂×C₄	1	8	yes	—
70	C₃₁×C₂²⋊C₈	C₂×C₄	1	8	yes	—
71	C₃₁×#97	—	2	4	no	—
72	C₃₁×#97	—	2	4	no	—
73	C₃₁×#97	C₂×C₄	1	8	yes	complemented
74	C₄×C₈×C₃₁	—	2	4	no	—
75	C₄×C₈×C₃₁	—	2	4	no	—
76	C₄×C₈×C₃₁	C₂×C₄	1	8	yes	complemented
77	C₃₁×#95	C₂×C₄	1	2	yes	—
78	C₃₁×#95	C₂×C₄	1	2	yes	—
79	C₃₁×#95	C₂×C₄	1	2	yes	—
80	C₃₁×#95	C₂×C₄	1	2	yes	—
81	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	—	2	2	no	—
83	C₂²×C₄×C₃₁	—	2	1	no	—
84	C₂²×C₄×C₃₁	—	2	1	no	—
85	C₂²×C₄×C₃₁	—	2	4	no	—
86	C₂²×C₄×C₃₁	—	2	4	no	—
87	C₂²×C₄×C₃₁	—	4	2	no	—
88	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₃₁	—	2	2	no	—
100	C₂×C₈×C₃₁	—	2	2	no	—
101	C₂×C₈×C₃₁	—	2	2	no	—
102	C₂×C₈×C₃₁	—	2	2	no	—
103	C₂×C₈×C₃₁	—	2	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	C₂²×C₄	1	4	yes	—
108	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
109	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
110	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
111	C₄⋊C₄×C₃₁	—	2	4	no	—
112	C₄⋊C₄×C₃₁	C₄²	1	4	yes	—
113	C₄⋊C₄×C₃₁	C₄²	1	4	yes	—
114	C₂²⋊C₄×C₃₁	—	2	4	no	—
115	C₂²⋊C₄×C₃₁	C₄²	1	4	yes	—
116	C₂²⋊C₄×C₃₁	C₄²	1	4	yes	—
117	C₄²×C₃₁	—	2	4	no	—
118	C₄²×C₃₁	—	2	4	no	—
119	C₄²×C₃₁	—	2	4	no	—
120	C₄²×C₃₁	—	2	2	no	—
121	C₄²×C₃₁	—	2	1	no	—
122	C₄²×C₃₁	—	2	1	no	—
123	C₄²×C₃₁	—	4	2	no	—
124	C₄²×C₃₁	—	4	2	no	—
125	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
126	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
127	C₄²×C₃₁	#41	1	2	yes	—
128	C₄²×C₃₁	#41	1	4	yes	—
129	C₄²×C₃₁	#41	1	2	yes	—
130	#20468	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₃₁	—	2	1	no	—
132	C₂³×C₃₁	—	2	1	no	—
133	C₂³×C₃₁	—	2	2	no	—
134	C₂³×C₃₁	—	2	2	no	—
135	C₂³×C₃₁	C₂×C₄²	1	2	yes	—
136	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₃₁	—	2	2	no	—
138	C₂×C₄×C₃₁	—	2	1	no	—
139	C₂×C₄×C₃₁	—	2	1	no	—
140	C₂×C₄×C₃₁	—	2	2	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	2	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	—	2	4	no	—
150	C₂×C₄×C₃₁	—	2	4	no	—
151	C₂×C₄×C₃₁	—	2	2	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	2	2	no	—
154	C₂×C₄×C₃₁	—	4	8	no	—
155	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
156	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
157	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
158	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
159	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
160	C₂×C₄×C₃₁	#117	1	4	yes	—
161	C₂×C₄×C₃₁	#117	1	4	yes	—
162	C₂×C₄×C₃₁	#131	1	4	yes	—
163	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
164	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
165	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
167	C₈×C₃₁	—	2	4	no	—
168	C₈×C₃₁	—	2	4	no	—
169	C₈×C₃₁	—	2	4	no	—
170	C₈×C₃₁	—	2	4	no	—
171	C₂×#433	C₂×C₃₁	1	2	yes	—
172	C₄×#117	C₂×C₃₁	1	1	yes	characteristic
173	#1768	C₂×C₃₁	1	2	yes	complemented
174	#1767	C₂×C₃₁	1	1	yes	characteristic, complemented
175	C₄×C₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#1750	C₂×C₃₁	1	2	yes	—
177	#1749	C₂×C₃₁	1	1	yes	characteristic
178	C₄×C₂²⋊C₈	C₂×C₃₁	1	1	yes	characteristic
179	#1745	C₂×C₃₁	1	1	yes	characteristic, complemented
180	#1744	C₂×C₃₁	1	1	yes	characteristic, complemented
181	#1726	C₂×C₃₁	1	2	yes	complemented
182	C₂²×C₃₁	—	2	2	no	—
183	C₂²×C₃₁	—	2	2	no	—
184	C₂²×C₃₁	—	2	2	no	—
185	C₂²×C₃₁	—	4	2	no	—
186	C₂²×C₃₁	—	4	2	no	—
187	C₂²×C₃₁	C₂²×C₄²	1	1	yes	characteristic
188	C₂²×C₃₁	C₂×#117	1	1	yes	characteristic
189	C₂²×C₃₁	C₂×#117	1	1	yes	characteristic
190	C₂²×C₃₁	C₂×#131	1	2	yes	—
191	C₂²×C₃₁	#568	1	2	yes	—
192	C₄×C₃₁	—	2	2	no	—
193	C₄×C₃₁	—	2	2	no	—
194	C₄×C₃₁	—	2	2	no	—
195	C₄×C₃₁	—	2	2	no	—
196	C₄×C₃₁	—	2	4	no	—
197	C₄×C₃₁	—	2	4	no	—
198	C₄×C₃₁	—	2	4	no	—
199	C₄×C₃₁	—	2	2	no	—
200	C₄×C₃₁	—	4	2	no	—
201	C₄×C₃₁	C₄×#41	1	2	yes	—
202	C₄×C₃₁	C₄×#41	1	2	yes	—
203	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
204	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
205	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
206	#433	C₄×C₃₁	1	16	yes	complemented
207	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
208	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
209	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
210	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
211	C₂×#97	C₂²×C₃₁	1	2	yes	—
212	C₂×#97	C₂²×C₃₁	1	2	yes	—
213	C₂×#97	C₂²×C₃₁	1	2	yes	—
214	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
215	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
216	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
217	C₄×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
218	C₄×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
219	C₄×C₂²⋊C₄	C₄×C₃₁	1	2	yes	—
220	C₄×C₂²⋊C₄	C₄×C₃₁	1	2	yes	—
221	#376	C₂²×C₃₁	1	1	yes	characteristic
222	#376	C₂²×C₃₁	1	1	yes	characteristic
223	C₄³	C₂²×C₃₁	1	1	yes	characteristic
224	C₄³	C₂²×C₃₁	1	1	yes	characteristic
225	#336	C₂²×C₃₁	1	1	yes	characteristic
226	#336	C₂²×C₃₁	1	1	yes	characteristic
227	#336	C₂²×C₃₁	1	2	yes	—
228	#336	C₂²×C₃₁	1	1	yes	characteristic
229	#336	C₂²×C₃₁	1	1	yes	characteristic
230	#336	C₂²×C₃₁	1	2	yes	—
231	C₂×C₃₁	—	4	2	no	—
232	C₂×C₃₁	C₄×#117	1	1	yes	characteristic
233	C₂×C₃₁	C₄×#131	1	1	yes	characteristic
234	C₂×C₃₁	#2875	1	1	yes	characteristic
235	C₂×C₃₁	#2924	1	2	yes	—
236	C₂×C₃₁	#2925	1	2	yes	—
237	C₂³×C₄	C₂×C₄×C₃₁	1	2	yes	—
238	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
240	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
241	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
242	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
243	#117	—	2	2	no	—
244	#117	—	2	2	no	—
245	#117	C₂×C₄×C₃₁	1	8	yes	—
246	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
247	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
250	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
252	C₂×C₄²	—	2	4	no	—
253	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
254	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
255	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
256	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
257	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
258	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
264	C₄⋊C₈	C₂×C₄×C₃₁	1	8	yes	complemented
265	C₄⋊C₈	C₂×C₄×C₃₁	1	8	yes	complemented
266	C₂²⋊C₈	C₂×C₄×C₃₁	1	8	yes	—
267	C₂²⋊C₈	C₂×C₄×C₃₁	1	8	yes	—
268	#97	—	2	4	no	—
269	#97	—	2	4	no	—
270	#97	C₂×C₄×C₃₁	1	8	yes	complemented
271	C₄×C₈	—	2	4	no	—
272	C₄×C₈	—	2	4	no	—
273	C₄×C₈	C₂×C₄×C₃₁	1	8	yes	complemented
274	#95	C₂×C₄×C₃₁	1	2	yes	—
275	#95	C₂×C₄×C₃₁	1	2	yes	—
276	#95	C₂×C₄×C₃₁	1	2	yes	—
277	#95	C₂×C₄×C₃₁	1	2	yes	—
278	C₃₁	#20468	1	1	yes	characteristic, direct product factor, Sylow
279	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
293	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
294	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
295	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
296	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
306	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
307	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
308	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	C₄²×C₃₁	1	4	yes	—
311	C₄⋊C₄	C₄²×C₃₁	1	4	yes	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₂²⋊C₄	C₄²×C₃₁	1	4	yes	—
314	C₂²⋊C₄	C₄²×C₃₁	1	4	yes	—
315	C₄²	—	2	4	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	4	2	no	—
322	C₄²	—	4	2	no	—
323	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
324	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
325	C₄²	#41×C₃₁	1	2	yes	—
326	C₄²	#41×C₃₁	1	4	yes	—
327	C₄²	#41×C₃₁	1	2	yes	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	C₂×C₄²×C₃₁	1	2	yes	—
333	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	8	no	—
352	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
353	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
354	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
355	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
356	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
357	C₂×C₄	C₃₁×#117	1	4	yes	—
358	C₂×C₄	C₃₁×#117	1	4	yes	—
359	C₂×C₄	C₃₁×#131	1	4	yes	—
360	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
361	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
362	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
363	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
364	C₈	—	2	4	no	—
365	C₈	—	2	4	no	—
366	C₈	—	2	4	no	—
367	C₈	—	2	4	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	C₂²×C₄²×C₃₁	1	1	yes	characteristic
374	C₂²	C₂×C₃₁×#117	1	1	yes	characteristic
375	C₂²	C₂×C₃₁×#117	1	1	yes	characteristic
376	C₂²	C₂×C₃₁×#131	1	2	yes	—
377	C₂²	C₃₁×#568	1	2	yes	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	4	no	—
383	C₄	—	2	4	no	—
384	C₄	—	2	4	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	2	no	—
387	C₄	C₄×#41×C₃₁	1	2	yes	—
388	C₄	C₄×#41×C₃₁	1	2	yes	—
389	C₂	—	4	2	no	—
390	C₂	C₄×C₃₁×#117	1	1	yes	characteristic
391	C₂	C₄×C₃₁×#131	1	1	yes	characteristic
392	C₂	C₃₁×#2875	1	1	yes	characteristic
393	C₂	C₃₁×#2924	1	2	yes	—
394	C₂	C₃₁×#2925	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₃₁×#1768	C₂	semidirect
4. C₃₁×#1767	C₂	semidirect
5. C₄×C₃₁×C₄⋊C₈	C₂	semidirect
9. C₃₁×#1745	C₂	semidirect
10. C₃₁×#1744	C₂	semidirect
11. C₃₁×#1726	C₂	semidirect
15. C₃₁×#433	C₄	semidirect
67. C₃₁×C₄⋊C₈	C₂×C₄	semidirect
68. C₃₁×C₄⋊C₈	C₂×C₄	semidirect
73. C₃₁×#97	C₂×C₄	semidirect
76. C₄×C₈×C₃₁	C₂×C₄	semidirect
130. #20468	C₃₁	direct (N × H)
173. #1768	C₂×C₃₁	semidirect
174. #1767	C₂×C₃₁	semidirect
175. C₄×C₄⋊C₈	C₂×C₃₁	semidirect
179. #1745	C₂×C₃₁	semidirect
180. #1744	C₂×C₃₁	semidirect
181. #1726	C₂×C₃₁	semidirect
206. #433	C₄×C₃₁	semidirect
264. C₄⋊C₈	C₂×C₄×C₃₁	semidirect
265. C₄⋊C₈	C₂×C₄×C₃₁	semidirect
270. #97	C₂×C₄×C₃₁	semidirect
273. C₄×C₈	C₂×C₄×C₃₁	semidirect
278. C₃₁	#20468	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#433	2
C₄×C₃₁×#117	2
C₃₁×#1768	2
C₃₁×#1767	2
C₄×C₃₁×C₄⋊C₈	2
C₃₁×#1750	2
C₃₁×#1749	2
C₄×C₃₁×C₂²⋊C₈	2
C₃₁×#1745	2
C₃₁×#1744	2
C₃₁×#1726	2
#20468	31

Subgroups — C31×#20468 #21477227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#20468 #21477227