Subgroups — C₃₁×#20574 #21477333

Order 7936.

806 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#446	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2295	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1771	C₂	1	2	yes	maximal
5	C₃₁×#1770	C₂	1	2	yes	maximal
6	C₃₁×#1770	C₂	1	1	yes	maximal, characteristic
7	C₈×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1768	C₂	1	2	yes	maximal
9	C₃₁×#1767	C₂	1	1	yes	maximal, characteristic
10	C₃₁×#1746	C₂	1	2	yes	maximal
11	C₃₁×#1744	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₃₁×#446	C₄	1	8	yes	complemented
14	C₈×Q₈×C₃₁	C₄	1	8	yes	complemented
15	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₃₁×#97	C₂²	1	2	yes	—
20	C₂×C₃₁×#97	C₂²	1	2	yes	—
21	C₂×C₃₁×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#391	C₄	1	2	yes	—
27	C₃₁×#389	C₄	1	2	yes	—
28	C₃₁×#387	C₄	1	4	yes	—
29	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
31	C₃₁×#376	C₂²	1	2	yes	—
32	C₄³×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#336	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	1	yes	characteristic
37	C₃₁×#336	C₂²	1	2	yes	—
38	C₃₁×#336	C₂²	1	2	yes	—
39	C₃₁×#336	C₂²	1	2	yes	—
40	C₂²×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
47	C₄×Q₈×C₃₁	C₂×C₄	1	4	yes	—
48	C₄×Q₈×C₃₁	C₂×C₄	1	4	yes	—
49	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
56	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
60	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
61	C₃₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
62	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
63	C₃₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
64	C₃₁×#97	—	4	2	no	—
65	C₃₁×#97	—	4	2	no	—
66	C₃₁×#97	C₂×C₄	1	8	yes	—
67	C₄×C₈×C₃₁	—	4	2	no	—
68	C₄×C₈×C₃₁	C₂×C₄	1	4	yes	—
69	C₄×C₈×C₃₁	C₂×C₄	1	8	yes	—
70	C₄×C₈×C₃₁	C₂×C₄	1	4	yes	—
71	C₃₁×#95	C₂×C₄	1	4	yes	—
72	C₃₁×#95	C₂×C₄	1	4	yes	—
73	C₃₁×#95	C₂×C₄	1	2	yes	—
74	C₃₁×#95	C₂×C₄	1	4	yes	—
75	C₂×Q₈×C₃₁	—	2	4	no	—
76	C₂×Q₈×C₃₁	C₄²	1	4	yes	—
77	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
85	C₂×C₈×C₃₁	—	2	1	no	—
86	C₂×C₈×C₃₁	—	2	2	no	—
87	C₂×C₈×C₃₁	—	2	1	no	—
88	C₂×C₈×C₃₁	—	2	2	no	—
89	C₂×C₈×C₃₁	—	2	1	no	—
90	C₂×C₈×C₃₁	—	2	1	no	—
91	C₂×C₈×C₃₁	—	2	1	no	—
92	C₂×C₈×C₃₁	—	2	1	no	—
93	C₂×C₈×C₃₁	—	2	1	no	—
94	C₂×C₈×C₃₁	—	2	2	no	—
95	C₂×C₈×C₃₁	—	2	2	no	—
96	C₂×C₈×C₃₁	—	2	1	no	—
97	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
99	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
103	C₄⋊C₄×C₃₁	—	2	4	no	—
104	C₄⋊C₄×C₃₁	—	4	4	no	—
105	C₄⋊C₄×C₃₁	C₄²	1	8	yes	—
106	C₄⋊C₄×C₃₁	C₄²	1	4	yes	—
107	C₄²×C₃₁	—	2	4	no	—
108	C₄²×C₃₁	—	2	2	no	—
109	C₄²×C₃₁	—	2	1	no	—
110	C₄²×C₃₁	—	2	1	no	—
111	C₄²×C₃₁	—	2	1	no	—
112	C₄²×C₃₁	—	2	2	no	—
113	C₄²×C₃₁	—	2	1	no	—
114	C₄²×C₃₁	—	4	2	no	—
115	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
116	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
117	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
118	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
119	#20574	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
121	Q₈×C₃₁	—	2	8	no	—
122	C₂×C₄×C₃₁	—	2	4	no	—
123	C₂×C₄×C₃₁	—	2	2	no	—
124	C₂×C₄×C₃₁	—	2	4	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	2	4	no	—
127	C₂×C₄×C₃₁	—	2	2	no	—
128	C₂×C₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	2	no	—
130	C₂×C₄×C₃₁	—	2	4	no	—
131	C₂×C₄×C₃₁	—	2	2	no	—
132	C₂×C₄×C₃₁	—	2	2	no	—
133	C₂×C₄×C₃₁	—	2	4	no	—
134	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
135	C₂×C₄×C₃₁	C₂×C₄²	1	4	yes	—
136	C₂×C₄×C₃₁	C₂×C₄²	1	4	yes	—
137	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
138	C₂×C₄×C₃₁	#131	1	4	yes	—
139	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
140	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
141	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
142	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
143	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
144	C₂×C₄×C₃₁	2₋¹⁺⁴	1	1	yes	characteristic
145	C₈×C₃₁	—	2	2	no	—
146	C₈×C₃₁	—	2	2	no	—
147	C₈×C₃₁	—	2	2	no	—
148	C₈×C₃₁	—	2	4	no	—
149	C₈×C₃₁	—	2	4	no	—
150	C₈×C₃₁	—	2	2	no	—
151	C₂×#446	C₂×C₃₁	1	1	yes	characteristic
152	C₂×C₈×Q₈	C₂×C₃₁	1	1	yes	characteristic
153	#2295	C₂×C₃₁	1	1	yes	characteristic
154	#1771	C₂×C₃₁	1	2	yes	—
155	#1770	C₂×C₃₁	1	2	yes	—
156	#1770	C₂×C₃₁	1	1	yes	characteristic
157	C₈×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic
158	#1768	C₂×C₃₁	1	2	yes	—
159	#1767	C₂×C₃₁	1	1	yes	characteristic
160	#1746	C₂×C₃₁	1	2	yes	—
161	#1744	C₂×C₃₁	1	1	yes	characteristic
162	C₂²×C₃₁	C₂²×C₄²	1	1	yes	characteristic
163	C₂²×C₃₁	#519	1	1	yes	characteristic
164	C₂²×C₃₁	#520	1	1	yes	characteristic
165	C₂²×C₃₁	C₂×#131	1	2	yes	—
166	C₂²×C₃₁	#568	1	2	yes	—
167	C₄×C₃₁	—	2	4	no	—
168	C₄×C₃₁	—	2	2	no	—
169	C₄×C₃₁	—	2	4	no	—
170	C₄×C₃₁	—	4	2	no	—
171	C₄×C₃₁	—	4	2	no	—
172	C₄×C₃₁	—	4	4	no	—
173	C₄×C₃₁	#405	1	4	yes	—
174	C₄×C₃₁	#519	1	1	yes	characteristic
175	C₄×C₃₁	#519	1	1	yes	characteristic
176	C₄×C₃₁	#520	1	1	yes	characteristic
177	C₄×C₃₁	#520	1	1	yes	characteristic
178	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
179	#446	C₄×C₃₁	1	8	yes	complemented
180	C₈×Q₈	C₄×C₃₁	1	8	yes	complemented
181	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
182	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
183	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
184	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
185	C₂×#97	C₂²×C₃₁	1	2	yes	—
186	C₂×#97	C₂²×C₃₁	1	2	yes	—
187	C₂×#97	C₂²×C₃₁	1	2	yes	—
188	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
189	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
190	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
191	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
192	#391	C₄×C₃₁	1	2	yes	—
193	#389	C₄×C₃₁	1	2	yes	—
194	#387	C₄×C₃₁	1	4	yes	—
195	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
196	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
197	#376	C₂²×C₃₁	1	2	yes	—
198	C₄³	C₂²×C₃₁	1	1	yes	characteristic
199	#336	C₂²×C₃₁	1	1	yes	characteristic
200	#336	C₂²×C₃₁	1	1	yes	characteristic
201	#336	C₂²×C₃₁	1	1	yes	characteristic
202	#336	C₂²×C₃₁	1	1	yes	characteristic
203	#336	C₂²×C₃₁	1	2	yes	—
204	#336	C₂²×C₃₁	1	2	yes	—
205	#336	C₂²×C₃₁	1	2	yes	—
206	C₂×C₃₁	#2276	1	1	yes	characteristic
207	C₂×C₃₁	C₂×#405	1	1	yes	characteristic
208	C₂×C₃₁	#2875	1	1	yes	characteristic
209	C₂×C₃₁	#2985	1	2	yes	—
210	C₂×C₃₁	#2993	1	2	yes	—
211	C₂²×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
212	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
213	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
214	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
216	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
218	C₄×Q₈	C₂×C₄×C₃₁	1	4	yes	—
219	C₄×Q₈	C₂×C₄×C₃₁	1	4	yes	—
220	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
221	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
222	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
223	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
225	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
226	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
229	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
231	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
232	C₄⋊C₈	C₂×C₄×C₃₁	1	8	yes	—
233	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
234	C₄⋊C₈	C₂×C₄×C₃₁	1	8	yes	—
235	#97	—	4	2	no	—
236	#97	—	4	2	no	—
237	#97	C₂×C₄×C₃₁	1	8	yes	—
238	C₄×C₈	—	4	2	no	—
239	C₄×C₈	C₂×C₄×C₃₁	1	4	yes	—
240	C₄×C₈	C₂×C₄×C₃₁	1	8	yes	—
241	C₄×C₈	C₂×C₄×C₃₁	1	4	yes	—
242	#95	C₂×C₄×C₃₁	1	4	yes	—
243	#95	C₂×C₄×C₃₁	1	4	yes	—
244	#95	C₂×C₄×C₃₁	1	2	yes	—
245	#95	C₂×C₄×C₃₁	1	4	yes	—
246	C₃₁	#20574	1	1	yes	characteristic, direct product factor, Sylow
247	C₂×Q₈	—	2	4	no	—
248	C₂×Q₈	C₄²×C₃₁	1	4	yes	—
249	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
250	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
251	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
252	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
256	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
257	C₂×C₈	—	2	1	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	1	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	1	no	—
262	C₂×C₈	—	2	1	no	—
263	C₂×C₈	—	2	1	no	—
264	C₂×C₈	—	2	1	no	—
265	C₂×C₈	—	2	1	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	1	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
270	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
271	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
272	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
273	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
274	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₄⋊C₄	C₄²×C₃₁	1	8	yes	—
278	C₄⋊C₄	C₄²×C₃₁	1	4	yes	—
279	C₄²	—	2	4	no	—
280	C₄²	—	2	2	no	—
281	C₄²	—	2	1	no	—
282	C₄²	—	2	1	no	—
283	C₄²	—	2	1	no	—
284	C₄²	—	2	1	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	4	2	no	—
287	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
288	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
289	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
290	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
291	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
292	Q₈	—	2	8	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	4	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
306	C₂×C₄	C₂×C₄²×C₃₁	1	4	yes	—
307	C₂×C₄	C₂×C₄²×C₃₁	1	4	yes	—
308	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
309	C₂×C₄	C₃₁×#131	1	4	yes	—
310	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
311	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
312	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
314	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
315	C₂×C₄	C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
316	C₈	—	2	2	no	—
317	C₈	—	2	2	no	—
318	C₈	—	2	2	no	—
319	C₈	—	2	4	no	—
320	C₈	—	2	4	no	—
321	C₈	—	2	2	no	—
322	C₂²	C₂²×C₄²×C₃₁	1	1	yes	characteristic
323	C₂²	C₃₁×#519	1	1	yes	characteristic
324	C₂²	C₃₁×#520	1	1	yes	characteristic
325	C₂²	C₂×C₃₁×#131	1	2	yes	—
326	C₂²	C₃₁×#568	1	2	yes	—
327	C₄	—	2	4	no	—
328	C₄	—	2	2	no	—
329	C₄	—	2	4	no	—
330	C₄	—	4	2	no	—
331	C₄	—	4	2	no	—
332	C₄	—	4	4	no	—
333	C₄	C₃₁×#405	1	4	yes	—
334	C₄	C₃₁×#519	1	1	yes	characteristic
335	C₄	C₃₁×#519	1	1	yes	characteristic
336	C₄	C₃₁×#520	1	1	yes	characteristic
337	C₄	C₃₁×#520	1	1	yes	characteristic
338	C₂	C₃₁×#2276	1	1	yes	characteristic
339	C₂	C₂×C₃₁×#405	1	1	yes	characteristic
340	C₂	C₃₁×#2875	1	1	yes	characteristic
341	C₂	C₃₁×#2985	1	2	yes	—
342	C₂	C₃₁×#2993	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator	C₂²	C₂²×C₄²×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle, prime radical	C₂³×C₃₁	C₂³×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
13. C₃₁×#446	C₄	semidirect
14. C₈×Q₈×C₃₁	C₄	semidirect
119. #20574	C₃₁	direct (N × H)
179. #446	C₄×C₃₁	semidirect
180. C₈×Q₈	C₄×C₃₁	semidirect
246. C₃₁	#20574	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×#446	2
C₂×C₈×Q₈×C₃₁	2
C₃₁×#2295	2
C₃₁×#1771	2
C₃₁×#1770	2
C₈×C₄⋊C₄×C₃₁	2
C₃₁×#1768	2
C₃₁×#1767	2
C₃₁×#1746	2
C₃₁×#1744	2
#20574	31

Subgroups — C31×#20574 #21477333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#20574 #21477333