Subgroups — C₃₁×#60518 #21517277

Order 7936.

2298 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#535	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3096	C₂	1	16	yes	maximal, complemented
4	C₃₁×#3094	C₂	1	8	yes	maximal, complemented
5	C₃₁×#2911	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#418	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2879	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
11	C₃₁×#535	—	2	4	no	—
12	C₃₁×#535	C₂²	1	8	yes	—
13	C₂×C₃₁×#127	—	2	1	no	—
14	C₂×C₃₁×#124	—	2	1	no	—
15	C₂×C₃₁×#121	C₂²	1	4	yes	—
16	C₂×C₃₁×#120	—	2	2	no	—
17	C₃₁×#520	C₂²	1	8	yes	complemented
18	C₃₁×#519	—	2	1	no	—
19	C₃₁×#518	—	2	2	no	—
20	C₃₁×#518	—	2	1	no	—
21	C₄×#41×C₃₁	—	2	4	no	—
22	C₂×C₃₁×#117	C₂²	1	2	yes	—
23	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#117	C₂²	1	4	yes	complemented
25	C₃₁×#482	C₂²	1	32	yes	complemented
26	C₃₁×#481	C₂²	1	16	yes	complemented
27	C₃₁×#480	C₂²	1	16	yes	complemented
28	C₃₁×#428	C₂²	1	8	yes	complemented
29	C₃₁×#428	C₂²	1	8	yes	complemented
30	C₃₁×#427	C₂²	1	8	yes	complemented
31	C₃₁×#418	C₂²	1	8	yes	—
32	C₃₁×#418	C₂²	1	8	yes	complemented
33	C₂×C₃₁×#102	C₂²	1	8	yes	complemented
34	C₃₁×#408	C₂²	1	8	yes	complemented
35	C₃₁×#407	C₂²	1	4	yes	complemented
36	C₂⁵×C₃₁	—	2	1	no	—
37	C₂×#41×C₃₁	—	2	8	no	—
38	C₂×#41×C₃₁	D₄	1	4	yes	—
39	C₂×#41×C₃₁	C₂³	1	4	yes	—
40	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₃₁	—	2	4	no	—
42	C₂²×D₄×C₃₁	—	2	1	no	—
43	C₂²×D₄×C₃₁	—	2	2	no	—
44	C₂²×D₄×C₃₁	—	2	8	no	—
45	C₂²×D₄×C₃₁	D₄	1	2	yes	—
46	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
48	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
50	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₃₁	—	2	8	no	—
52	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
53	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
54	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
55	C₃₁×#127	—	2	8	no	—
56	C₃₁×#124	—	2	8	no	—
57	C₃₁×#121	—	2	8	no	—
58	C₃₁×#121	C₂³	1	16	yes	—
59	C₃₁×#120	—	2	16	no	—
60	C₄×Q₈×C₃₁	—	2	8	no	—
61	C₄×D₄×C₃₁	—	2	8	no	—
62	C₄×D₄×C₃₁	—	2	16	no	—
63	C₃₁×#117	—	2	2	no	—
64	C₃₁×#117	—	2	2	no	—
65	C₃₁×#117	—	2	2	no	—
66	C₃₁×#117	—	2	4	no	—
67	C₃₁×#117	—	2	4	no	—
68	C₃₁×#117	C₂³	1	4	yes	—
69	C₃₁×#117	C₂³	1	4	yes	—
70	C₃₁×#117	C₂³	1	4	yes	—
71	C₃₁×#117	C₂³	1	8	yes	complemented
72	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	complemented
75	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
79	C₂×C₄²×C₃₁	—	2	2	no	—
80	C₂×C₄²×C₃₁	—	2	1	no	—
81	C₂×C₄²×C₃₁	—	2	4	no	—
82	C₃₁×#107	C₂³	1	16	yes	complemented
83	C₃₁×#106	C₂³	1	16	yes	complemented
84	C₃₁×#102	C₂³	1	32	yes	—
85	C₃₁×C₂²⋊C₈	C₂³	1	16	yes	complemented
86	C₂⁴×C₃₁	—	2	2	no	—
87	C₂⁴×C₃₁	—	2	4	no	—
88	C₂⁴×C₃₁	—	4	4	no	—
89	C₂⁴×C₃₁	—	8	4	no	—
90	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
91	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
92	#41×C₃₁	—	2	16	no	—
93	#41×C₃₁	—	2	8	no	—
94	#41×C₃₁	—	2	8	no	—
95	C₂×Q₈×C₃₁	—	2	4	no	—
96	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
97	C₂×D₄×C₃₁	—	2	8	no	—
98	C₂×D₄×C₃₁	—	2	16	no	—
99	C₂×D₄×C₃₁	—	2	4	no	—
100	C₂×D₄×C₃₁	—	2	2	no	—
101	C₂×D₄×C₃₁	—	2	4	no	—
102	C₂×D₄×C₃₁	—	2	8	no	—
103	C₂×D₄×C₃₁	—	2	8	no	—
104	C₂×D₄×C₃₁	—	2	8	no	—
105	C₂×D₄×C₃₁	—	4	4	no	—
106	C₂×D₄×C₃₁	—	4	8	no	—
107	C₂×D₄×C₃₁	—	8	8	no	—
108	C₂×D₄×C₃₁	C₂×D₄	1	8	yes	—
109	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
110	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₃₁	—	2	8	no	—
112	C₂²×C₄×C₃₁	—	2	2	no	—
113	C₂²×C₄×C₃₁	—	2	4	no	—
114	C₂²×C₄×C₃₁	—	2	8	no	—
115	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₃₁	#41	1	8	yes	—
120	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
123	M₁₆×C₃₁	—	2	8	no	—
124	M₁₆×C₃₁	—	2	8	no	—
125	C₂×C₈×C₃₁	—	2	8	no	—
126	C₂×C₈×C₃₁	C₂⁴	1	8	yes	—
127	C₄⋊C₄×C₃₁	—	2	4	no	—
128	C₄⋊C₄×C₃₁	—	2	2	no	—
129	C₄⋊C₄×C₃₁	—	2	8	no	—
130	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
131	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
132	C₂²⋊C₄×C₃₁	—	2	4	no	—
133	C₂²⋊C₄×C₃₁	—	2	4	no	—
134	C₂²⋊C₄×C₃₁	—	2	4	no	—
135	C₂²⋊C₄×C₃₁	—	2	8	no	—
136	C₂²⋊C₄×C₃₁	—	2	16	no	—
137	C₄²×C₃₁	—	2	4	no	—
138	C₄²×C₃₁	—	2	4	no	—
139	C₄²×C₃₁	—	2	4	no	—
140	C₄²×C₃₁	—	2	8	no	—
141	#60518	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₃₁	—	2	4	no	—
143	C₂³×C₃₁	—	2	4	no	—
144	C₂³×C₃₁	—	4	2	no	—
145	C₂³×C₃₁	—	4	4	no	—
146	C₂³×C₃₁	—	4	8	no	—
147	C₂³×C₃₁	—	4	4	no	—
148	C₂³×C₃₁	—	4	8	no	—
149	C₂³×C₃₁	—	8	8	no	—
150	C₂³×C₃₁	—	8	16	no	—
151	C₂³×C₃₁	#123	1	4	yes	—
152	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
153	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
154	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
155	Q₈×C₃₁	—	2	8	no	—
156	D₄×C₃₁	—	2	16	no	—
157	D₄×C₃₁	—	2	8	no	—
158	D₄×C₃₁	—	2	8	no	—
159	D₄×C₃₁	—	4	4	no	—
160	D₄×C₃₁	—	4	8	no	—
161	D₄×C₃₁	—	8	16	no	—
162	C₂×C₄×C₃₁	—	2	4	no	—
163	C₂×C₄×C₃₁	—	2	8	no	—
164	C₂×C₄×C₃₁	—	2	8	no	—
165	C₂×C₄×C₃₁	—	2	8	no	—
166	C₂×C₄×C₃₁	—	2	4	no	—
167	C₂×C₄×C₃₁	—	4	4	no	—
168	C₂×C₄×C₃₁	—	8	4	no	—
169	C₂×C₄×C₃₁	—	8	8	no	—
170	C₂×C₄×C₃₁	#123	1	4	yes	—
171	C₂×C₄×C₃₁	#123	1	8	yes	—
172	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
173	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
176	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
177	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
178	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
179	C₈×C₃₁	—	2	8	no	—
180	C₂×#535	C₂×C₃₁	1	1	yes	characteristic
181	#3428	C₂×C₃₁	1	1	yes	characteristic, complemented
182	#3096	C₂×C₃₁	1	16	yes	complemented
183	#3094	C₂×C₃₁	1	8	yes	complemented
184	#2911	C₂×C₃₁	1	2	yes	complemented
185	C₂×#418	C₂×C₃₁	1	2	yes	complemented
186	#2879	C₂×C₃₁	1	1	yes	characteristic, complemented
187	C₂²×C₃₁	—	2	2	no	—
188	C₂²×C₃₁	—	2	4	no	—
189	C₂²×C₃₁	—	2	8	no	—
190	C₂²×C₃₁	—	2	4	no	—
191	C₂²×C₃₁	—	4	4	no	—
192	C₂²×C₃₁	—	4	8	no	—
193	C₂²×C₃₁	—	4	4	no	—
194	C₂²×C₃₁	—	8	4	no	—
195	C₂²×C₃₁	—	8	8	no	—
196	C₂²×C₃₁	—	8	16	no	—
197	C₂²×C₃₁	C₂×#123	1	2	yes	—
198	C₂²×C₃₁	C₂×#123	1	4	yes	—
199	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
200	C₄×C₃₁	—	2	4	no	—
201	C₄×C₃₁	—	4	4	no	—
202	C₄×C₃₁	—	4	8	no	—
203	C₄×C₃₁	C₂×#123	1	2	yes	—
204	C₄×C₃₁	C₂×#123	1	4	yes	—
205	C₄×C₃₁	C₂²×#41	1	2	yes	—
206	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
207	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
209	#535	—	2	4	no	—
210	#535	C₂²×C₃₁	1	8	yes	—
211	C₂×#127	—	2	1	no	—
212	C₂×#124	—	2	1	no	—
213	C₂×#121	C₂²×C₃₁	1	4	yes	—
214	C₂×#120	—	2	2	no	—
215	#520	C₂²×C₃₁	1	8	yes	complemented
216	#519	—	2	1	no	—
217	#518	—	2	2	no	—
218	#518	—	2	1	no	—
219	C₄×#41	—	2	4	no	—
220	C₂×#117	C₂²×C₃₁	1	2	yes	—
221	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
222	C₂×#117	C₂²×C₃₁	1	4	yes	complemented
223	#482	C₂²×C₃₁	1	32	yes	complemented
224	#481	C₂²×C₃₁	1	16	yes	complemented
225	#480	C₂²×C₃₁	1	16	yes	complemented
226	#428	C₂²×C₃₁	1	8	yes	complemented
227	#428	C₂²×C₃₁	1	8	yes	complemented
228	#427	C₂²×C₃₁	1	8	yes	complemented
229	#418	C₂²×C₃₁	1	8	yes	—
230	#418	C₂²×C₃₁	1	8	yes	complemented
231	C₂×#102	C₂²×C₃₁	1	8	yes	complemented
232	#408	C₂²×C₃₁	1	8	yes	complemented
233	#407	C₂²×C₃₁	1	4	yes	complemented
234	C₂×C₃₁	—	2	2	no	—
235	C₂×C₃₁	—	2	4	no	—
236	C₂×C₃₁	—	4	4	no	—
237	C₂×C₃₁	—	8	4	no	—
238	C₂×C₃₁	C₂²×#123	1	1	yes	characteristic
239	C₂×C₃₁	#3585	1	2	yes	—
240	C₂⁵	—	2	1	no	—
241	C₂×#41	—	2	8	no	—
242	C₂×#41	D₄×C₃₁	1	4	yes	—
243	C₂×#41	C₂³×C₃₁	1	4	yes	—
244	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
245	C₂²×D₄	—	2	4	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	—	2	2	no	—
248	C₂²×D₄	—	2	8	no	—
249	C₂²×D₄	D₄×C₃₁	1	2	yes	—
250	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
251	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
252	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
253	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
254	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
255	C₂×M₁₆	—	2	8	no	—
256	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
257	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
258	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
259	#127	—	2	8	no	—
260	#124	—	2	8	no	—
261	#121	—	2	8	no	—
262	#121	C₂³×C₃₁	1	16	yes	—
263	#120	—	2	16	no	—
264	C₄×Q₈	—	2	8	no	—
265	C₄×D₄	—	2	8	no	—
266	C₄×D₄	—	2	16	no	—
267	#117	—	2	2	no	—
268	#117	—	2	2	no	—
269	#117	—	2	2	no	—
270	#117	—	2	4	no	—
271	#117	—	2	4	no	—
272	#117	C₂³×C₃₁	1	4	yes	—
273	#117	C₂³×C₃₁	1	4	yes	—
274	#117	C₂³×C₃₁	1	4	yes	—
275	#117	C₂³×C₃₁	1	8	yes	complemented
276	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
277	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	complemented
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	4	no	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	—	2	4	no	—
286	#107	C₂³×C₃₁	1	16	yes	complemented
287	#106	C₂³×C₃₁	1	16	yes	complemented
288	#102	C₂³×C₃₁	1	32	yes	—
289	C₂²⋊C₈	C₂³×C₃₁	1	16	yes	complemented
290	C₃₁	#60518	1	1	yes	characteristic, direct product factor, Sylow
291	C₂⁴	—	2	2	no	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	4	4	no	—
294	C₂⁴	—	8	4	no	—
295	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
296	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
297	#41	—	2	16	no	—
298	#41	—	2	8	no	—
299	#41	—	2	8	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
302	C₂×D₄	—	2	8	no	—
303	C₂×D₄	—	2	16	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	8	no	—
308	C₂×D₄	—	2	8	no	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	—	4	4	no	—
311	C₂×D₄	—	4	8	no	—
312	C₂×D₄	—	8	8	no	—
313	C₂×D₄	C₂×D₄×C₃₁	1	8	yes	—
314	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
315	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
321	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
324	C₂²×C₄	#41×C₃₁	1	8	yes	—
325	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
326	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
328	M₁₆	—	2	8	no	—
329	M₁₆	—	2	8	no	—
330	C₂×C₈	—	2	8	no	—
331	C₂×C₈	C₂⁴×C₃₁	1	8	yes	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
336	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	—	2	16	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	2	4	no	—
345	C₄²	—	2	8	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	8	no	—
351	C₂³	—	4	4	no	—
352	C₂³	—	4	8	no	—
353	C₂³	—	8	8	no	—
354	C₂³	—	8	16	no	—
355	C₂³	C₃₁×#123	1	4	yes	—
356	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
357	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
358	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
359	Q₈	—	2	8	no	—
360	D₄	—	2	16	no	—
361	D₄	—	2	8	no	—
362	D₄	—	2	8	no	—
363	D₄	—	4	4	no	—
364	D₄	—	4	8	no	—
365	D₄	—	8	16	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	8	4	no	—
373	C₂×C₄	—	8	8	no	—
374	C₂×C₄	C₃₁×#123	1	4	yes	—
375	C₂×C₄	C₃₁×#123	1	8	yes	—
376	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
377	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
378	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
379	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
380	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
381	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
382	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
383	C₈	—	2	8	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	8	no	—
391	C₂²	—	8	4	no	—
392	C₂²	—	8	8	no	—
393	C₂²	—	8	16	no	—
394	C₂²	C₂×C₃₁×#123	1	2	yes	—
395	C₂²	C₂×C₃₁×#123	1	4	yes	—
396	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
397	C₄	—	2	4	no	—
398	C₄	—	4	4	no	—
399	C₄	—	4	8	no	—
400	C₄	C₂×C₃₁×#123	1	2	yes	—
401	C₄	C₂×C₃₁×#123	1	4	yes	—
402	C₄	C₂²×#41×C₃₁	1	2	yes	—
403	C₂	—	2	2	no	—
404	C₂	—	2	4	no	—
405	C₂	—	4	4	no	—
406	C₂	—	8	4	no	—
407	C₂	C₂²×C₃₁×#123	1	1	yes	characteristic
408	C₂	C₃₁×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3428	C₂	semidirect
3. C₃₁×#3096	C₂	semidirect
4. C₃₁×#3094	C₂	semidirect
5. C₃₁×#2911	C₂	semidirect
6. C₂×C₃₁×#418	C₂	semidirect
7. C₃₁×#2879	C₂	semidirect
17. C₃₁×#520	C₂²	semidirect
24. C₂×C₃₁×#117	C₂²	semidirect
25. C₃₁×#482	C₂²	semidirect
26. C₃₁×#481	C₂²	semidirect
27. C₃₁×#480	C₂²	semidirect
28. C₃₁×#428	C₂²	semidirect
29. C₃₁×#428	C₂²	semidirect
30. C₃₁×#427	C₂²	semidirect
32. C₃₁×#418	C₂²	semidirect
33. C₂×C₃₁×#102	C₂²	semidirect
34. C₃₁×#408	C₂²	semidirect
35. C₃₁×#407	C₂²	semidirect
71. C₃₁×#117	C₂³	semidirect
74. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
82. C₃₁×#107	C₂³	semidirect
83. C₃₁×#106	C₂³	semidirect
85. C₃₁×C₂²⋊C₈	C₂³	semidirect
141. #60518	C₃₁	direct (N × H)
181. #3428	C₂×C₃₁	semidirect
182. #3096	C₂×C₃₁	semidirect
183. #3094	C₂×C₃₁	semidirect
184. #2911	C₂×C₃₁	semidirect
185. C₂×#418	C₂×C₃₁	semidirect
186. #2879	C₂×C₃₁	semidirect
215. #520	C₂²×C₃₁	semidirect
222. C₂×#117	C₂²×C₃₁	semidirect
223. #482	C₂²×C₃₁	semidirect
224. #481	C₂²×C₃₁	semidirect
225. #480	C₂²×C₃₁	semidirect
226. #428	C₂²×C₃₁	semidirect
227. #428	C₂²×C₃₁	semidirect
228. #427	C₂²×C₃₁	semidirect
230. #418	C₂²×C₃₁	semidirect
231. C₂×#102	C₂²×C₃₁	semidirect
232. #408	C₂²×C₃₁	semidirect
233. #407	C₂²×C₃₁	semidirect
275. #117	C₂³×C₃₁	semidirect
278. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
286. #107	C₂³×C₃₁	semidirect
287. #106	C₂³×C₃₁	semidirect
289. C₂²⋊C₈	C₂³×C₃₁	semidirect
290. C₃₁	#60518	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×#535	2
C₃₁×#3428	2
C₃₁×#3096	2
C₃₁×#3094	2
C₃₁×#2911	2
C₂×C₃₁×#418	2
C₃₁×#2879	2
#60518	31

Subgroups — C31×#60518 #21517277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60518 #21517277