Subgroups — C₃₁×#33205 #21489964

Order 7936.

864 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#478	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#476	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2660	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2275	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1989	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1949	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1948	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1843	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1804	C₂	1	2	yes	maximal
11	C₃₁×#1802	C₂	1	2	yes	maximal
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
16	C₃₁×#478	—	2	4	no	—
17	C₃₁×#476	—	2	4	no	—
18	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#106	C₂²	1	2	yes	—
21	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#102	C₂²	1	2	yes	—
27	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
28	C₃₁×#398	—	2	1	no	—
29	C₃₁×#398	—	2	1	no	—
30	C₃₁×#395	—	2	2	no	—
31	C₃₁×#384	C₂²	1	2	yes	—
32	C₃₁×#382	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₄×C₂²⋊C₄×C₃₁	—	2	2	no	—
36	C₄×C₂²⋊C₄×C₃₁	—	2	1	no	—
37	C₃₁×#376	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#95	—	2	1	no	—
39	C₃₁×#340	C₂²	1	2	yes	—
40	C₃₁×#340	C₂²	1	2	yes	—
41	C₃₁×#340	C₂²	1	2	yes	—
42	C₃₁×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₃₁	—	2	1	no	—
44	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₃₁	—	2	1	no	—
46	C₂³×C₄×C₃₁	—	2	2	no	—
47	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
50	C₃₁×C₄⋊Q₈	—	2	2	no	—
51	C₃₁×C₄⋊Q₈	—	2	2	no	—
52	C₃₁×#125	—	2	2	no	—
53	C₃₁×#125	—	2	2	no	—
54	C₄×D₄×C₃₁	—	2	2	no	—
55	C₄×D₄×C₃₁	—	2	4	no	—
56	C₄×D₄×C₃₁	D₄	1	4	yes	—
57	C₄×D₄×C₃₁	Q₈	1	8	yes	complemented
58	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
70	C₂×C₄²×C₃₁	—	2	1	no	—
71	C₂×C₄²×C₃₁	—	2	2	no	—
72	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
74	C₃₁×#107	—	2	2	no	—
75	C₃₁×#106	—	2	4	no	—
76	C₃₁×#106	—	2	2	no	—
77	C₃₁×C₄⋊C₈	—	2	2	no	—
78	C₃₁×C₄⋊C₈	—	2	2	no	—
79	C₃₁×C₄⋊C₈	—	2	4	no	—
80	C₃₁×C₄⋊C₈	—	2	4	no	—
81	C₃₁×#102	—	2	4	no	—
82	C₃₁×#102	—	2	2	no	—
83	C₃₁×#102	—	2	2	no	—
84	C₃₁×#95	—	2	2	no	—
85	C₃₁×#95	—	2	2	no	—
86	C₃₁×#95	—	2	1	no	—
87	C₃₁×#95	—	2	2	no	—
88	C₃₁×#95	D₄	1	2	yes	—
89	C₃₁×#95	D₄	1	1	yes	characteristic
90	C₃₁×#95	D₄	1	1	yes	characteristic
91	C₂⁴×C₃₁	—	2	1	no	—
92	C₂×Q₈×C₃₁	—	4	2	no	—
93	C₂×Q₈×C₃₁	—	8	1	no	—
94	C₂×Q₈×C₃₁	—	8	1	no	—
95	C₂×D₄×C₃₁	—	2	2	no	—
96	C₂×D₄×C₃₁	—	2	1	no	—
97	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
98	C₂×D₄×C₃₁	C₂×Q₈	1	4	yes	—
99	C₂²×C₄×C₃₁	—	2	1	no	—
100	C₂²×C₄×C₃₁	—	2	2	no	—
101	C₂²×C₄×C₃₁	—	2	4	no	—
102	C₂²×C₄×C₃₁	—	2	8	no	—
103	C₂²×C₄×C₃₁	—	2	1	no	—
104	C₂²×C₄×C₃₁	—	2	2	no	—
105	C₂²×C₄×C₃₁	—	2	1	no	—
106	C₂²×C₄×C₃₁	—	8	2	no	—
107	C₂²×C₄×C₃₁	—	8	2	no	—
108	C₂²×C₄×C₃₁	—	8	2	no	—
109	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₃₁	—	2	2	no	—
115	C₂×C₈×C₃₁	—	2	1	no	—
116	C₂×C₈×C₃₁	—	2	1	no	—
117	C₂×C₈×C₃₁	—	2	2	no	—
118	C₂×C₈×C₃₁	—	2	2	no	—
119	C₂×C₈×C₃₁	—	2	2	no	—
120	C₂×C₈×C₃₁	—	2	2	no	—
121	C₄⋊C₄×C₃₁	—	2	1	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	1	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	2	1	no	—
126	C₄⋊C₄×C₃₁	—	2	1	no	—
127	C₄⋊C₄×C₃₁	—	2	1	no	—
128	C₄⋊C₄×C₃₁	—	2	2	no	—
129	C₄⋊C₄×C₃₁	—	4	2	no	—
130	C₄⋊C₄×C₃₁	—	4	2	no	—
131	C₄⋊C₄×C₃₁	—	4	2	no	—
132	C₄⋊C₄×C₃₁	—	8	2	no	—
133	C₄⋊C₄×C₃₁	—	8	2	no	—
134	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₃₁	C₂×Q₈	1	4	yes	—
136	C₂²⋊C₄×C₃₁	—	2	4	no	—
137	C₂²⋊C₄×C₃₁	—	2	8	no	—
138	C₄²×C₃₁	—	8	1	no	—
139	C₄²×C₃₁	—	8	2	no	—
140	C₄²×C₃₁	C₂×D₄	1	2	yes	—
141	C₄²×C₃₁	C₂×Q₈	1	4	yes	—
142	C₄²×C₃₁	#41	1	2	yes	—
143	C₄²×C₃₁	#41	1	4	yes	—
144	#33205	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂³×C₃₁	—	2	2	no	—
146	C₂³×C₃₁	—	2	4	no	—
147	C₂³×C₃₁	—	4	1	no	—
148	C₂³×C₃₁	—	4	2	no	—
149	C₂³×C₃₁	—	4	1	no	—
150	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₃₁	—	8	4	no	—
152	D₄×C₃₁	—	2	2	no	—
153	D₄×C₃₁	—	2	4	no	—
154	D₄×C₃₁	C₄⋊Q₈	1	4	yes	—
155	C₂×C₄×C₃₁	—	2	1	no	—
156	C₂×C₄×C₃₁	—	2	2	no	—
157	C₂×C₄×C₃₁	—	2	2	no	—
158	C₂×C₄×C₃₁	—	2	2	no	—
159	C₂×C₄×C₃₁	—	2	2	no	—
160	C₂×C₄×C₃₁	—	2	2	no	—
161	C₂×C₄×C₃₁	—	2	1	no	—
162	C₂×C₄×C₃₁	—	2	2	no	—
163	C₂×C₄×C₃₁	—	2	4	no	—
164	C₂×C₄×C₃₁	—	4	2	no	—
165	C₂×C₄×C₃₁	—	4	2	no	—
166	C₂×C₄×C₃₁	—	4	2	no	—
167	C₂×C₄×C₃₁	—	4	1	no	—
168	C₂×C₄×C₃₁	—	4	1	no	—
169	C₂×C₄×C₃₁	—	4	2	no	—
170	C₂×C₄×C₃₁	—	4	1	no	—
171	C₂×C₄×C₃₁	—	4	2	no	—
172	C₂×C₄×C₃₁	—	4	1	no	—
173	C₂×C₄×C₃₁	—	4	2	no	—
174	C₂×C₄×C₃₁	—	4	2	no	—
175	C₂×C₄×C₃₁	—	8	8	no	—
176	C₂×C₄×C₃₁	—	8	4	no	—
177	C₂×C₄×C₃₁	#121	1	2	yes	—
178	C₂×C₄×C₃₁	#121	1	2	yes	—
179	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
180	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
181	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
183	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
184	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
185	C₈×C₃₁	—	4	2	no	—
186	C₈×C₃₁	—	4	1	no	—
187	C₈×C₃₁	—	4	1	no	—
188	C₂×#478	C₂×C₃₁	1	1	yes	characteristic
189	C₂×#476	C₂×C₃₁	1	1	yes	characteristic
190	#2660	C₂×C₃₁	1	1	yes	characteristic, complemented
191	#2275	C₂×C₃₁	1	1	yes	characteristic
192	#1989	C₂×C₃₁	1	1	yes	characteristic, complemented
193	#1988	C₂×C₃₁	1	1	yes	characteristic, complemented
194	#1949	C₂×C₃₁	1	2	yes	complemented
195	#1948	C₂×C₃₁	1	2	yes	complemented
196	#1843	C₂×C₃₁	1	1	yes	characteristic, complemented
197	#1804	C₂×C₃₁	1	2	yes	—
198	#1802	C₂×C₃₁	1	2	yes	—
199	C₂²×C₃₁	—	2	4	no	—
200	C₂²×C₃₁	—	4	4	no	—
201	C₂²×C₃₁	—	4	4	no	—
202	C₂²×C₃₁	—	4	2	no	—
203	C₂²×C₃₁	—	4	2	no	—
204	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
205	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
206	C₂²×C₃₁	#576	1	1	yes	characteristic
207	C₂²×C₃₁	#577	1	2	yes	—
208	C₂²×C₃₁	#577	1	1	yes	characteristic
209	C₄×C₃₁	—	2	4	no	—
210	C₄×C₃₁	—	2	4	no	—
211	C₄×C₃₁	—	2	2	no	—
212	C₄×C₃₁	—	2	2	no	—
213	C₄×C₃₁	—	4	4	no	—
214	C₄×C₃₁	—	4	2	no	—
215	C₄×C₃₁	—	8	1	no	—
216	C₄×C₃₁	—	8	1	no	—
217	C₄×C₃₁	—	8	2	no	—
218	C₄×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
219	C₄×C₃₁	#532	1	1	yes	characteristic
220	C₄×C₃₁	#533	1	2	yes	—
221	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
222	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
223	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
225	#478	—	2	4	no	—
226	#476	—	2	4	no	—
227	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
228	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
229	C₂×#106	C₂²×C₃₁	1	2	yes	—
230	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
232	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
233	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
234	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
235	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
236	C₂×#102	C₂²×C₃₁	1	2	yes	—
237	#398	—	2	1	no	—
238	#398	—	2	1	no	—
239	#395	—	2	2	no	—
240	#384	C₂²×C₃₁	1	2	yes	—
241	#382	C₂²×C₃₁	1	2	yes	—
242	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
243	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
244	C₄×C₂²⋊C₄	—	2	2	no	—
245	C₄×C₂²⋊C₄	—	2	1	no	—
246	#376	C₂²×C₃₁	1	1	yes	characteristic
247	C₂×#95	—	2	1	no	—
248	#340	C₂²×C₃₁	1	2	yes	—
249	#340	C₂²×C₃₁	1	2	yes	—
250	#340	C₂²×C₃₁	1	2	yes	—
251	#340	C₂²×C₃₁	1	2	yes	—
252	C₂×C₃₁	—	4	4	no	—
253	C₂×C₃₁	#2857	1	1	yes	characteristic
254	C₂×C₃₁	#3042	1	1	yes	characteristic
255	C₂×C₃₁	#3045	1	1	yes	characteristic
256	C₂×C₃₁	#3081	1	2	yes	—
257	C₂×C₃₁	#3084	1	2	yes	—
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	—	2	2	no	—
262	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
263	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	—	2	2	no	—
267	#125	—	2	2	no	—
268	#125	—	2	2	no	—
269	C₄×D₄	—	2	2	no	—
270	C₄×D₄	—	2	4	no	—
271	C₄×D₄	D₄×C₃₁	1	4	yes	—
272	C₄×D₄	Q₈×C₃₁	1	8	yes	complemented
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
289	#107	—	2	2	no	—
290	#106	—	2	4	no	—
291	#106	—	2	2	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	—	2	4	no	—
295	C₄⋊C₈	—	2	4	no	—
296	#102	—	2	4	no	—
297	#102	—	2	2	no	—
298	#102	—	2	2	no	—
299	#95	—	2	1	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	D₄×C₃₁	1	1	yes	characteristic
304	#95	D₄×C₃₁	1	2	yes	—
305	#95	D₄×C₃₁	1	1	yes	characteristic
306	C₃₁	#33205	1	1	yes	characteristic, direct product factor, Sylow
307	C₂⁴	—	2	1	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×Q₈	—	8	1	no	—
310	C₂×Q₈	—	8	1	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
314	C₂×D₄	C₂×Q₈×C₃₁	1	4	yes	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	8	2	no	—
323	C₂²×C₄	—	8	2	no	—
324	C₂²×C₄	—	8	2	no	—
325	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
329	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	8	2	no	—
349	C₄⋊C₄	—	8	2	no	—
350	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
351	C₄⋊C₄	C₂×Q₈×C₃₁	1	4	yes	—
352	C₂²⋊C₄	—	2	4	no	—
353	C₂²⋊C₄	—	2	8	no	—
354	C₄²	—	8	1	no	—
355	C₄²	—	8	2	no	—
356	C₄²	C₂×D₄×C₃₁	1	2	yes	—
357	C₄²	C₂×Q₈×C₃₁	1	4	yes	—
358	C₄²	#41×C₃₁	1	2	yes	—
359	C₄²	#41×C₃₁	1	4	yes	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	1	no	—
365	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
366	Q₈	—	8	4	no	—
367	D₄	—	2	2	no	—
368	D₄	—	2	4	no	—
369	D₄	C₃₁×C₄⋊Q₈	1	4	yes	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	8	no	—
391	C₂×C₄	—	8	4	no	—
392	C₂×C₄	C₃₁×#121	1	2	yes	—
393	C₂×C₄	C₃₁×#121	1	2	yes	—
394	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
395	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
396	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
397	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
398	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
399	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
400	C₈	—	4	2	no	—
401	C₈	—	4	1	no	—
402	C₈	—	4	1	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
409	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
410	C₂²	C₃₁×#576	1	1	yes	characteristic
411	C₂²	C₃₁×#577	1	2	yes	—
412	C₂²	C₃₁×#577	1	1	yes	characteristic
413	C₄	—	2	4	no	—
414	C₄	—	2	4	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	4	no	—
418	C₄	—	4	2	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	2	no	—
421	C₄	—	8	1	no	—
422	C₄	C₂×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
423	C₄	C₃₁×#532	1	1	yes	characteristic
424	C₄	C₃₁×#533	1	2	yes	—
425	C₂	—	4	4	no	—
426	C₂	C₃₁×#2857	1	1	yes	characteristic
427	C₂	C₃₁×#3042	1	1	yes	characteristic
428	C₂	C₃₁×#3045	1	1	yes	characteristic
429	C₂	C₃₁×#3081	1	2	yes	—
430	C₂	C₃₁×#3084	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂²×D₄×C₃₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₃₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₁×#2660	C₂	semidirect
5. C₃₁×#1989	C₂	semidirect
6. C₃₁×#1988	C₂	semidirect
7. C₃₁×#1949	C₂	semidirect
8. C₃₁×#1948	C₂	semidirect
9. C₃₁×#1843	C₂	semidirect
57. C₄×D₄×C₃₁	Q₈	semidirect
144. #33205	C₃₁	direct (N × H)
190. #2660	C₂×C₃₁	semidirect
192. #1989	C₂×C₃₁	semidirect
193. #1988	C₂×C₃₁	semidirect
194. #1949	C₂×C₃₁	semidirect
195. #1948	C₂×C₃₁	semidirect
196. #1843	C₂×C₃₁	semidirect
272. C₄×D₄	Q₈×C₃₁	semidirect
306. C₃₁	#33205	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×#478	2
C₂×C₃₁×#476	2
C₃₁×#2660	2
C₃₁×#2275	2
C₃₁×#1989	2
C₃₁×#1988	2
C₃₁×#1949	2
C₃₁×#1948	2
C₃₁×#1843	2
C₃₁×#1804	2
C₃₁×#1802	2
#33205	31

Subgroups — C31×#33205 #21489964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33205 #21489964