Subgroups — C₃₁×#26061 #21482820

Order 7936.

794 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#427	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2439	C₂	1	2	yes	maximal
4	C₃₁×#2085	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2057	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1941	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1941	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1854	C₂	1	2	yes	maximal
9	C₃₁×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#1807	C₂	1	1	yes	maximal, characteristic
11	C₈×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₃₁×#117	C₂²	1	2	yes	—
15	C₃₁×#498	—	2	4	no	—
16	C₃₁×#427	—	2	4	no	—
17	C₂×C₃₁×#107	C₂²	1	2	yes	—
18	C₂×C₃₁×#107	C₂²	1	2	yes	—
19	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#106	C₂²	1	2	yes	—
22	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#396	—	2	2	no	—
28	C₃₁×#393	—	2	2	no	—
29	C₃₁×#391	—	2	2	no	—
30	C₃₁×#389	C₂²	1	2	yes	—
31	C₃₁×#389	C₂²	1	2	yes	—
32	C₃₁×#387	—	2	2	no	—
33	C₃₁×#382	C₂²	1	2	yes	—
34	C₃₁×#380	C₂²	1	2	yes	—
35	C₄×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₃₁×#340	C₂²	1	2	yes	—
37	C₃₁×#340	C₂²	1	2	yes	—
38	C₃₁×#340	C₂²	1	2	yes	—
39	C₃₁×#336	C₂²	1	1	yes	characteristic
40	C₃₁×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₃₁	—	2	2	no	—
42	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₃₁	—	2	2	no	—
44	C₂²×C₈×C₃₁	—	2	2	no	—
45	C₂²×C₈×C₃₁	Q₈	1	4	yes	complemented
46	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
50	C₃₁×C₄⋊Q₈	—	2	4	no	—
51	C₃₁×C₄⋊Q₈	—	4	2	no	—
52	C₃₁×#117	—	2	4	no	—
53	C₃₁×#117	—	4	2	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
64	C₂×C₄²×C₃₁	—	2	2	no	—
65	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
67	C₃₁×#107	—	2	4	no	—
68	C₃₁×#107	—	4	2	no	—
69	C₃₁×#106	—	2	2	no	—
70	C₃₁×#106	—	2	2	no	—
71	C₃₁×#106	—	2	2	no	—
72	C₃₁×#106	—	2	4	no	—
73	C₃₁×#106	D₄	1	4	yes	—
74	C₃₁×C₂²⋊C₈	Q₈	1	4	yes	complemented
75	C₄×C₈×C₃₁	—	2	2	no	—
76	C₄×C₈×C₃₁	—	2	2	no	—
77	C₃₁×#95	—	2	2	no	—
78	C₃₁×#95	—	2	2	no	—
79	C₃₁×#95	—	2	2	no	—
80	C₃₁×#95	—	2	2	no	—
81	C₃₁×#95	—	2	2	no	—
82	C₃₁×#95	D₄	1	2	yes	—
83	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
84	C₂×Q₈×C₃₁	—	4	4	no	—
85	C₂×Q₈×C₃₁	—	4	4	no	—
86	C₂×Q₈×C₃₁	—	8	2	no	—
87	C₂²×C₄×C₃₁	—	2	1	no	—
88	C₂²×C₄×C₃₁	—	2	1	no	—
89	C₂²×C₄×C₃₁	—	2	1	no	—
90	C₂²×C₄×C₃₁	—	2	1	no	—
91	C₂²×C₄×C₃₁	—	2	2	no	—
92	C₂²×C₄×C₃₁	—	2	2	no	—
93	C₂²×C₄×C₃₁	—	2	2	no	—
94	C₂²×C₄×C₃₁	—	2	2	no	—
95	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₃₁	—	2	1	no	—
102	C₂×C₈×C₃₁	—	2	1	no	—
103	C₂×C₈×C₃₁	—	2	1	no	—
104	C₂×C₈×C₃₁	—	2	1	no	—
105	C₂×C₈×C₃₁	—	2	1	no	—
106	C₂×C₈×C₃₁	—	2	1	no	—
107	C₂×C₈×C₃₁	—	2	8	no	—
108	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
110	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
111	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
112	C₂×C₈×C₃₁	C₂×Q₈	1	2	yes	—
113	C₂×C₈×C₃₁	#41	1	2	yes	—
114	C₄⋊C₄×C₃₁	—	2	2	no	—
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	2	2	no	—
117	C₄⋊C₄×C₃₁	—	2	2	no	—
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	—	4	4	no	—
122	C₄⋊C₄×C₃₁	—	4	4	no	—
123	C₄⋊C₄×C₃₁	—	8	2	no	—
124	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
125	C₂²⋊C₄×C₃₁	—	2	4	no	—
126	C₂²⋊C₄×C₃₁	—	4	4	no	—
127	C₂²⋊C₄×C₃₁	—	8	2	no	—
128	C₄²×C₃₁	—	2	1	no	—
129	C₄²×C₃₁	—	2	1	no	—
130	C₄²×C₃₁	—	2	1	no	—
131	C₄²×C₃₁	—	2	1	no	—
132	C₄²×C₃₁	—	4	4	no	—
133	#26061	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₃₁	—	2	1	no	—
135	C₂³×C₃₁	—	2	1	no	—
136	C₂³×C₃₁	—	2	2	no	—
137	C₂³×C₃₁	—	2	2	no	—
138	C₂³×C₃₁	C₄⋊Q₈	1	2	yes	—
139	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₃₁	—	8	8	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	1	no	—
143	C₂×C₄×C₃₁	—	2	1	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	2	no	—
151	C₂×C₄×C₃₁	—	2	2	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	—	4	2	no	—
156	C₂×C₄×C₃₁	—	4	2	no	—
157	C₂×C₄×C₃₁	—	4	2	no	—
158	C₂×C₄×C₃₁	—	4	2	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	4	2	no	—
161	C₂×C₄×C₃₁	—	4	2	no	—
162	C₂×C₄×C₃₁	—	4	2	no	—
163	C₂×C₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
165	C₂×C₄×C₃₁	#135	1	4	yes	—
166	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
168	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
172	C₈×C₃₁	—	2	2	no	—
173	C₈×C₃₁	—	2	2	no	—
174	C₈×C₃₁	—	2	2	no	—
175	C₈×C₃₁	C₂²⋊Q₈	1	4	yes	—
176	C₂×#498	C₂×C₃₁	1	1	yes	characteristic, complemented
177	C₂×#427	C₂×C₃₁	1	1	yes	characteristic
178	#2439	C₂×C₃₁	1	2	yes	—
179	#2085	C₂×C₃₁	1	2	yes	complemented
180	#2057	C₂×C₃₁	1	2	yes	complemented
181	#1941	C₂×C₃₁	1	1	yes	characteristic, complemented
182	#1941	C₂×C₃₁	1	1	yes	characteristic, complemented
183	#1854	C₂×C₃₁	1	2	yes	—
184	#1846	C₂×C₃₁	1	1	yes	characteristic, complemented
185	#1807	C₂×C₃₁	1	1	yes	characteristic
186	C₈×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
187	C₂²×C₃₁	—	2	2	no	—
188	C₂²×C₃₁	—	2	2	no	—
189	C₂²×C₃₁	—	2	2	no	—
190	C₂²×C₃₁	—	4	2	no	—
191	C₂²×C₃₁	—	4	2	no	—
192	C₂²×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
193	C₂²×C₃₁	D₄²	1	1	yes	characteristic
194	C₂²×C₃₁	#547	1	1	yes	characteristic
195	C₂²×C₃₁	C₂×#135	1	2	yes	—
196	C₂²×C₃₁	#577	1	2	yes	—
197	C₄×C₃₁	—	2	2	no	—
198	C₄×C₃₁	—	2	4	no	—
199	C₄×C₃₁	—	4	2	no	—
200	C₄×C₃₁	—	4	4	no	—
201	C₄×C₃₁	—	8	2	no	—
202	C₄×C₃₁	—	8	2	no	—
203	C₄×C₃₁	—	8	2	no	—
204	C₄×C₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
205	C₄×C₃₁	#544	1	1	yes	characteristic
206	C₄×C₃₁	D₄×Q₈	1	1	yes	characteristic
207	C₄×C₃₁	#554	1	1	yes	characteristic
208	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
210	C₂×#117	C₂²×C₃₁	1	2	yes	—
211	#498	—	2	4	no	—
212	#427	—	2	4	no	—
213	C₂×#107	C₂²×C₃₁	1	2	yes	—
214	C₂×#107	C₂²×C₃₁	1	2	yes	—
215	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
216	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
217	C₂×#106	C₂²×C₃₁	1	2	yes	—
218	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
219	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
220	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
223	#396	—	2	2	no	—
224	#393	—	2	2	no	—
225	#391	—	2	2	no	—
226	#389	C₂²×C₃₁	1	2	yes	—
227	#389	C₂²×C₃₁	1	2	yes	—
228	#387	—	2	2	no	—
229	#382	C₂²×C₃₁	1	2	yes	—
230	#380	C₂²×C₃₁	1	2	yes	—
231	C₄×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
232	#340	C₂²×C₃₁	1	2	yes	—
233	#340	C₂²×C₃₁	1	2	yes	—
234	#340	C₂²×C₃₁	1	2	yes	—
235	#336	C₂²×C₃₁	1	1	yes	characteristic
236	#336	C₂²×C₃₁	1	1	yes	characteristic
237	C₂×C₃₁	—	4	2	no	—
238	C₂×C₃₁	#2440	1	1	yes	characteristic
239	C₂×C₃₁	#3160	1	1	yes	characteristic
240	C₂×C₃₁	#3163	1	1	yes	characteristic
241	C₂×C₃₁	#3282	1	2	yes	—
242	C₂×C₃₁	#3340	1	2	yes	—
243	C₂²×Q₈	—	2	2	no	—
244	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	Q₈×C₃₁	1	4	yes	complemented
248	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
252	C₄⋊Q₈	—	2	4	no	—
253	C₄⋊Q₈	—	4	2	no	—
254	#117	—	2	4	no	—
255	#117	—	4	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
269	#107	—	2	4	no	—
270	#107	—	4	2	no	—
271	#106	—	2	2	no	—
272	#106	—	2	2	no	—
273	#106	—	2	2	no	—
274	#106	—	2	4	no	—
275	#106	D₄×C₃₁	1	4	yes	—
276	C₂²⋊C₈	Q₈×C₃₁	1	4	yes	complemented
277	C₄×C₈	—	2	2	no	—
278	C₄×C₈	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	D₄×C₃₁	1	2	yes	—
285	C₃₁	#26061	1	1	yes	characteristic, direct product factor, Sylow
286	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
287	C₂×Q₈	—	4	4	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×Q₈	—	8	2	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
301	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
302	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
303	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	8	no	—
311	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
312	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
313	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
314	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
315	C₂×C₈	C₂×Q₈×C₃₁	1	2	yes	—
316	C₂×C₈	#41×C₃₁	1	2	yes	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	4	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	8	2	no	—
327	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	8	2	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	4	4	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	C₃₁×C₄⋊Q₈	1	2	yes	—
341	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
342	Q₈	—	8	8	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
367	C₂×C₄	C₃₁×#135	1	4	yes	—
368	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
369	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
370	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
372	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
374	C₈	—	2	2	no	—
375	C₈	—	2	2	no	—
376	C₈	—	2	2	no	—
377	C₈	C₃₁×C₂²⋊Q₈	1	4	yes	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	C₂×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
384	C₂²	D₄²×C₃₁	1	1	yes	characteristic
385	C₂²	C₃₁×#547	1	1	yes	characteristic
386	C₂²	C₂×C₃₁×#135	1	2	yes	—
387	C₂²	C₃₁×#577	1	2	yes	—
388	C₄	—	2	2	no	—
389	C₄	—	2	4	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	4	no	—
392	C₄	—	8	2	no	—
393	C₄	—	8	2	no	—
394	C₄	—	8	2	no	—
395	C₄	C₂×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
396	C₄	C₃₁×#544	1	1	yes	characteristic
397	C₄	D₄×Q₈×C₃₁	1	1	yes	characteristic
398	C₄	C₃₁×#554	1	1	yes	characteristic
399	C₂	—	4	2	no	—
400	C₂	C₃₁×#2440	1	1	yes	characteristic
401	C₂	C₃₁×#3160	1	1	yes	characteristic
402	C₂	C₃₁×#3163	1	1	yes	characteristic
403	C₂	C₃₁×#3282	1	2	yes	—
404	C₂	C₃₁×#3340	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#498	C₂	semidirect
4. C₃₁×#2085	C₂	semidirect
5. C₃₁×#2057	C₂	semidirect
6. C₃₁×#1941	C₂	semidirect
7. C₃₁×#1941	C₂	semidirect
9. C₃₁×#1846	C₂	semidirect
45. C₂²×C₈×C₃₁	Q₈	semidirect
74. C₃₁×C₂²⋊C₈	Q₈	semidirect
133. #26061	C₃₁	direct (N × H)
176. C₂×#498	C₂×C₃₁	semidirect
179. #2085	C₂×C₃₁	semidirect
180. #2057	C₂×C₃₁	semidirect
181. #1941	C₂×C₃₁	semidirect
182. #1941	C₂×C₃₁	semidirect
184. #1846	C₂×C₃₁	semidirect
247. C₂²×C₈	Q₈×C₃₁	semidirect
276. C₂²⋊C₈	Q₈×C₃₁	semidirect
285. C₃₁	#26061	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×#498	2
C₂×C₃₁×#427	2
C₃₁×#2439	2
C₃₁×#2085	2
C₃₁×#2057	2
C₃₁×#1941	2
C₃₁×#1854	2
C₃₁×#1846	2
C₃₁×#1807	2
C₈×C₂²⋊C₄×C₃₁	2
#26061	31

Subgroups — C31×#26061 #21482820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#26061 #21482820