Subgroups — C₃₁×#34265 #21491024

Order 7936.

3586 conjugacy classes of subgroups.

The subgroup lattice has 632 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	C₂×C₃₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2367	C₂	1	4	yes	maximal, complemented
5	C₃₁×#2366	C₂	1	4	yes	maximal, complemented
6	C₃₁×#2363	C₂	1	4	yes	maximal, complemented
7	C₃₁×#2361	C₂	1	4	yes	maximal, complemented
8	C₃₁×#2321	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2309	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₃₁×#120	C₂	1	4	yes	maximal, complemented
11	C₃₁×#2297	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2296	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#2274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
17	C₃₁×#535	C₄	1	16	yes	complemented
18	C₂×C₃₁×#127	C₂²	1	2	yes	—
19	C₂×C₃₁×#124	C₂²	1	2	yes	—
20	C₂×C₃₁×#121	C₂²	1	4	yes	—
21	C₂×C₃₁×#120	C₂²	1	4	yes	—
22	C₃₁×#520	—	2	8	no	—
23	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
24	C₂×C₄×D₄×C₃₁	—	2	8	no	—
25	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
29	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
30	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
34	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
36	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
37	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#391	C₂²	1	2	yes	complemented
39	C₃₁×#390	C₂²	1	2	yes	—
40	C₃₁×#390	C₂²	1	2	yes	—
41	C₃₁×#390	C₂²	1	4	yes	—
42	C₃₁×#390	C₂²	1	8	yes	complemented
43	C₃₁×#390	C₂²	1	2	yes	complemented
44	C₃₁×#389	C₂²	1	2	yes	complemented
45	C₃₁×#389	C₂²	1	2	yes	complemented
46	C₃₁×#388	C₂²	1	8	yes	complemented
47	C₃₁×#388	C₂²	1	8	yes	complemented
48	C₃₁×#386	C₂²	1	2	yes	—
49	C₃₁×#386	C₂²	1	2	yes	—
50	C₃₁×#386	C₂²	1	8	yes	complemented
51	C₃₁×#386	C₂²	1	8	yes	complemented
52	C₃₁×#385	C₂²	1	2	yes	—
53	C₃₁×#385	C₂²	1	2	yes	—
54	C₃₁×#385	C₂²	1	8	yes	complemented
55	C₃₁×#379	C₂²	1	4	yes	—
56	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
57	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
58	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
59	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
60	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
61	C₄×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	complemented
62	C₂⁵×C₃₁	C₂³	1	2	yes	—
63	C₂×#41×C₃₁	—	2	4	no	—
64	C₂×#41×C₃₁	—	2	4	no	—
65	C₂×#41×C₃₁	C₂×C₄	1	8	yes	complemented
66	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₃₁	—	2	4	no	—
68	C₂²×D₄×C₃₁	—	2	4	no	—
69	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
70	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
71	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
72	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
73	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
75	C₂³×C₄×C₃₁	—	2	8	no	—
76	C₂³×C₄×C₃₁	—	4	8	no	—
77	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
79	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
80	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
82	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
83	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
84	C₃₁×#127	C₂×C₄	1	16	yes	complemented
85	C₃₁×#124	C₂×C₄	1	16	yes	complemented
86	C₃₁×#121	C₂×C₄	1	32	yes	complemented
87	C₃₁×#120	C₂×C₄	1	32	yes	complemented
88	C₄×Q₈×C₃₁	—	2	8	no	—
89	C₄×D₄×C₃₁	—	2	16	no	—
90	C₄×D₄×C₃₁	—	2	16	no	—
91	C₄×D₄×C₃₁	—	2	16	no	—
92	C₄×D₄×C₃₁	—	2	8	no	—
93	C₄×D₄×C₃₁	—	4	16	no	—
94	C₃₁×#117	—	2	4	no	—
95	C₃₁×#117	—	2	4	no	—
96	C₃₁×#117	—	2	8	no	—
97	C₃₁×#117	C₂×C₄	1	8	yes	complemented
98	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
99	C₂×C₄⋊C₄×C₃₁	D₄	1	8	yes	complemented
100	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
110	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
111	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
116	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
117	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
120	C₂×C₄²×C₃₁	—	2	4	no	—
121	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
122	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
123	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
124	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
125	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
126	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
127	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
128	C₃₁×#95	C₂³	1	8	yes	—
129	C₃₁×#95	C₂³	1	4	yes	—
130	C₃₁×#95	C₂³	1	4	yes	—
131	C₃₁×#95	C₂³	1	4	yes	—
132	C₃₁×#95	C₂³	1	4	yes	—
133	C₂⁴×C₃₁	—	2	4	no	—
134	C₂⁴×C₃₁	—	2	4	no	—
135	C₂⁴×C₃₁	—	4	4	no	—
136	C₂⁴×C₃₁	—	4	4	no	—
137	C₂⁴×C₃₁	C₂²×C₄	1	8	yes	—
138	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
139	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
140	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
141	#41×C₃₁	—	2	32	no	—
142	C₂×Q₈×C₃₁	—	2	2	no	—
143	C₂×Q₈×C₃₁	—	2	2	no	—
144	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	complemented
145	C₂×D₄×C₃₁	—	2	4	no	—
146	C₂×D₄×C₃₁	—	2	4	no	—
147	C₂×D₄×C₃₁	—	2	32	no	—
148	C₂×D₄×C₃₁	—	2	4	no	—
149	C₂×D₄×C₃₁	—	2	4	no	—
150	C₂×D₄×C₃₁	—	2	2	no	—
151	C₂×D₄×C₃₁	—	2	4	no	—
152	C₂×D₄×C₃₁	—	2	4	no	—
153	C₂×D₄×C₃₁	—	2	2	no	—
154	C₂×D₄×C₃₁	—	4	8	no	—
155	C₂×D₄×C₃₁	—	4	8	no	—
156	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
157	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
158	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
159	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	complemented
160	C₂×D₄×C₃₁	C₂²×C₄	1	32	yes	complemented
161	C₂²×C₄×C₃₁	—	2	2	no	—
162	C₂²×C₄×C₃₁	—	2	4	no	—
163	C₂²×C₄×C₃₁	—	2	4	no	—
164	C₂²×C₄×C₃₁	—	2	4	no	—
165	C₂²×C₄×C₃₁	—	2	2	no	—
166	C₂²×C₄×C₃₁	—	2	16	no	—
167	C₂²×C₄×C₃₁	—	2	16	no	—
168	C₂²×C₄×C₃₁	—	2	8	no	—
169	C₂²×C₄×C₃₁	—	4	4	no	—
170	C₂²×C₄×C₃₁	—	4	8	no	—
171	C₂²×C₄×C₃₁	—	4	2	no	—
172	C₂²×C₄×C₃₁	—	4	8	no	—
173	C₂²×C₄×C₃₁	—	4	32	no	—
174	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
176	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
177	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
178	C₂²×C₄×C₃₁	#41	1	4	yes	—
179	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
189	C₄⋊C₄×C₃₁	—	2	2	no	—
190	C₄⋊C₄×C₃₁	—	2	8	no	—
191	C₄⋊C₄×C₃₁	—	2	2	no	—
192	C₄⋊C₄×C₃₁	—	2	4	no	—
193	C₄⋊C₄×C₃₁	—	2	8	no	—
194	C₄⋊C₄×C₃₁	—	4	4	no	—
195	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	complemented
196	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
197	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
198	C₂²⋊C₄×C₃₁	—	2	4	no	—
199	C₂²⋊C₄×C₃₁	—	2	4	no	—
200	C₂²⋊C₄×C₃₁	—	2	16	no	—
201	C₂²⋊C₄×C₃₁	—	2	8	no	—
202	C₂²⋊C₄×C₃₁	—	2	8	no	—
203	C₂²⋊C₄×C₃₁	—	4	8	no	—
204	C₂²⋊C₄×C₃₁	—	4	4	no	—
205	C₂²⋊C₄×C₃₁	—	4	8	no	—
206	C₂²⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
207	C₂²⋊C₄×C₃₁	C₂²×C₄	1	32	yes	complemented
208	C₄²×C₃₁	—	2	4	no	—
209	C₄²×C₃₁	—	2	4	no	—
210	C₄²×C₃₁	—	2	8	no	—
211	C₄²×C₃₁	—	2	4	no	—
212	C₄²×C₃₁	—	2	4	no	—
213	C₄²×C₃₁	—	4	8	no	—
214	C₄²×C₃₁	C₂²×C₄	1	8	yes	complemented
215	#34265	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₃₁	—	2	2	no	—
217	C₂³×C₃₁	—	2	2	no	—
218	C₂³×C₃₁	—	2	16	no	—
219	C₂³×C₃₁	—	2	2	no	—
220	C₂³×C₃₁	—	2	4	no	—
221	C₂³×C₃₁	—	2	2	no	—
222	C₂³×C₃₁	—	2	4	no	—
223	C₂³×C₃₁	—	2	4	no	—
224	C₂³×C₃₁	—	2	8	no	—
225	C₂³×C₃₁	—	2	4	no	—
226	C₂³×C₃₁	—	2	8	no	—
227	C₂³×C₃₁	—	4	16	no	—
228	C₂³×C₃₁	—	4	8	no	—
229	C₂³×C₃₁	—	4	8	no	—
230	C₂³×C₃₁	—	4	16	no	—
231	C₂³×C₃₁	C₂³×C₄	1	8	yes	—
232	C₂³×C₃₁	C₂³×C₄	1	4	yes	—
233	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
234	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
235	C₂³×C₃₁	C₂×#41	1	2	yes	—
236	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
237	Q₈×C₃₁	—	2	8	no	—
238	D₄×C₃₁	—	2	16	no	—
239	D₄×C₃₁	—	2	16	no	—
240	D₄×C₃₁	—	2	16	no	—
241	D₄×C₃₁	—	2	8	no	—
242	D₄×C₃₁	—	4	32	no	—
243	C₂×C₄×C₃₁	—	2	8	no	—
244	C₂×C₄×C₃₁	—	2	2	no	—
245	C₂×C₄×C₃₁	—	2	2	no	—
246	C₂×C₄×C₃₁	—	2	2	no	—
247	C₂×C₄×C₃₁	—	2	4	no	—
248	C₂×C₄×C₃₁	—	2	8	no	—
249	C₂×C₄×C₃₁	—	2	2	no	—
250	C₂×C₄×C₃₁	—	2	4	no	—
251	C₂×C₄×C₃₁	—	2	16	no	—
252	C₂×C₄×C₃₁	—	2	2	no	—
253	C₂×C₄×C₃₁	—	2	2	no	—
254	C₂×C₄×C₃₁	—	2	2	no	—
255	C₂×C₄×C₃₁	—	2	4	no	—
256	C₂×C₄×C₃₁	—	2	4	no	—
257	C₂×C₄×C₃₁	—	2	4	no	—
258	C₂×C₄×C₃₁	—	2	4	no	—
259	C₂×C₄×C₃₁	—	2	4	no	—
260	C₂×C₄×C₃₁	—	2	2	no	—
261	C₂×C₄×C₃₁	—	2	2	no	—
262	C₂×C₄×C₃₁	—	4	8	no	—
263	C₂×C₄×C₃₁	—	4	32	no	—
264	C₂×C₄×C₃₁	—	4	4	no	—
265	C₂×C₄×C₃₁	—	8	8	no	—
266	C₂×C₄×C₃₁	C₄×D₄	1	16	yes	complemented
267	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
268	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
269	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
270	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
271	C₂×C₄×C₃₁	C₂²×D₄	1	8	yes	—
272	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
274	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
275	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
276	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
277	C₂×#535	C₂×C₃₁	1	1	yes	characteristic
278	C₂×#520	C₂×C₃₁	1	1	yes	characteristic, complemented
279	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
280	#2367	C₂×C₃₁	1	4	yes	complemented
281	#2366	C₂×C₃₁	1	4	yes	complemented
282	#2363	C₂×C₃₁	1	4	yes	complemented
283	#2361	C₂×C₃₁	1	4	yes	complemented
284	#2321	C₂×C₃₁	1	4	yes	complemented
285	#2309	C₂×C₃₁	1	1	yes	characteristic, complemented
286	C₄×#120	C₂×C₃₁	1	4	yes	complemented
287	#2297	C₂×C₃₁	1	1	yes	characteristic, complemented
288	#2296	C₂×C₃₁	1	1	yes	characteristic, complemented
289	#2274	C₂×C₃₁	1	1	yes	characteristic, complemented
290	C₂²×C₃₁	—	2	4	no	—
291	C₂²×C₃₁	—	2	2	no	—
292	C₂²×C₃₁	—	2	2	no	—
293	C₂²×C₃₁	—	2	4	no	—
294	C₂²×C₃₁	—	2	4	no	—
295	C₂²×C₃₁	—	2	8	no	—
296	C₂²×C₃₁	—	2	8	no	—
297	C₂²×C₃₁	—	2	16	no	—
298	C₂²×C₃₁	—	4	32	no	—
299	C₂²×C₃₁	—	4	4	no	—
300	C₂²×C₃₁	—	4	2	no	—
301	C₂²×C₃₁	—	4	2	no	—
302	C₂²×C₃₁	—	4	4	no	—
303	C₂²×C₃₁	—	4	4	no	—
304	C₂²×C₃₁	—	4	8	no	—
305	C₂²×C₃₁	C₂×C₄×D₄	1	4	yes	—
306	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
307	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
308	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
309	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
310	C₂²×C₃₁	#585	1	2	yes	—
311	C₄×C₃₁	—	2	4	no	—
312	C₄×C₃₁	—	2	8	no	—
313	C₄×C₃₁	—	2	4	no	—
314	C₄×C₃₁	—	2	8	no	—
315	C₄×C₃₁	—	4	2	no	—
316	C₄×C₃₁	—	4	2	no	—
317	C₄×C₃₁	—	4	2	no	—
318	C₄×C₃₁	—	4	4	no	—
319	C₄×C₃₁	C₂×C₄×D₄	1	4	yes	—
320	C₄×C₃₁	C₂×C₄×D₄	1	4	yes	—
321	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
322	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
323	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
324	#535	C₄×C₃₁	1	16	yes	complemented
325	C₂×#127	C₂²×C₃₁	1	2	yes	—
326	C₂×#124	C₂²×C₃₁	1	2	yes	—
327	C₂×#121	C₂²×C₃₁	1	4	yes	—
328	C₂×#120	C₂²×C₃₁	1	4	yes	—
329	#520	—	2	8	no	—
330	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
331	C₂×C₄×D₄	—	2	8	no	—
332	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
333	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
334	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
335	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
336	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
337	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
338	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
339	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
340	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
341	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
343	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
344	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
345	#391	C₂²×C₃₁	1	2	yes	complemented
346	#390	C₂²×C₃₁	1	2	yes	—
347	#390	C₂²×C₃₁	1	2	yes	—
348	#390	C₂²×C₃₁	1	4	yes	—
349	#390	C₂²×C₃₁	1	8	yes	complemented
350	#390	C₂²×C₃₁	1	2	yes	complemented
351	#389	C₂²×C₃₁	1	2	yes	complemented
352	#389	C₂²×C₃₁	1	2	yes	complemented
353	#388	C₂²×C₃₁	1	8	yes	complemented
354	#388	C₂²×C₃₁	1	8	yes	complemented
355	#386	C₂²×C₃₁	1	2	yes	—
356	#386	C₂²×C₃₁	1	2	yes	—
357	#386	C₂²×C₃₁	1	8	yes	complemented
358	#386	C₂²×C₃₁	1	8	yes	complemented
359	#385	C₂²×C₃₁	1	2	yes	—
360	#385	C₂²×C₃₁	1	2	yes	—
361	#385	C₂²×C₃₁	1	8	yes	complemented
362	#379	C₂²×C₃₁	1	4	yes	—
363	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
364	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
365	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
366	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
367	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
368	C₄×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	complemented
369	C₂×C₃₁	—	2	4	no	—
370	C₂×C₃₁	—	4	4	no	—
371	C₂×C₃₁	—	4	8	no	—
372	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
373	C₂×C₃₁	C₄×H(5,𝔽₂)	1	2	yes	—
374	C₂×C₃₁	#3484	1	1	yes	characteristic
375	C₂×C₃₁	#3487	1	1	yes	characteristic
376	C₂×C₃₁	#3506	1	2	yes	—
377	C₂⁵	C₂³×C₃₁	1	2	yes	—
378	C₂×#41	—	2	4	no	—
379	C₂×#41	—	2	4	no	—
380	C₂×#41	C₂×C₄×C₃₁	1	8	yes	complemented
381	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
382	C₂²×D₄	—	2	4	no	—
383	C₂²×D₄	—	2	4	no	—
384	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
385	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
386	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
387	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
388	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
389	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
390	C₂³×C₄	—	2	8	no	—
391	C₂³×C₄	—	4	8	no	—
392	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
394	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
395	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
396	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
397	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
398	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
399	#127	C₂×C₄×C₃₁	1	16	yes	complemented
400	#124	C₂×C₄×C₃₁	1	16	yes	complemented
401	#121	C₂×C₄×C₃₁	1	32	yes	complemented
402	#120	C₂×C₄×C₃₁	1	32	yes	complemented
403	C₄×Q₈	—	2	8	no	—
404	C₄×D₄	—	2	16	no	—
405	C₄×D₄	—	2	16	no	—
406	C₄×D₄	—	2	16	no	—
407	C₄×D₄	—	2	8	no	—
408	C₄×D₄	—	4	16	no	—
409	#117	—	2	4	no	—
410	#117	—	2	4	no	—
411	#117	—	2	8	no	—
412	#117	C₂×C₄×C₃₁	1	8	yes	complemented
413	C₂×C₄⋊C₄	—	2	8	no	—
414	C₂×C₄⋊C₄	D₄×C₃₁	1	8	yes	complemented
415	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
417	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
420	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
421	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
424	C₂×C₂²⋊C₄	—	2	8	no	—
425	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
435	C₂×C₄²	—	2	4	no	—
436	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
437	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
438	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
439	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
440	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
441	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
442	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
443	#95	C₂³×C₃₁	1	8	yes	—
444	#95	C₂³×C₃₁	1	4	yes	—
445	#95	C₂³×C₃₁	1	4	yes	—
446	#95	C₂³×C₃₁	1	4	yes	—
447	#95	C₂³×C₃₁	1	4	yes	—
448	C₃₁	#34265	1	1	yes	characteristic, direct product factor, Sylow
449	C₂⁴	—	2	4	no	—
450	C₂⁴	—	2	4	no	—
451	C₂⁴	—	4	4	no	—
452	C₂⁴	—	4	4	no	—
453	C₂⁴	C₂²×C₄×C₃₁	1	8	yes	—
454	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
455	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
456	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
457	#41	—	2	32	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	complemented
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	32	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	4	8	no	—
471	C₂×D₄	—	4	8	no	—
472	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
473	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
474	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
475	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	complemented
476	C₂×D₄	C₂²×C₄×C₃₁	1	32	yes	complemented
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	16	no	—
483	C₂²×C₄	—	2	16	no	—
484	C₂²×C₄	—	2	8	no	—
485	C₂²×C₄	—	4	4	no	—
486	C₂²×C₄	—	4	8	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	—	4	8	no	—
489	C₂²×C₄	—	4	32	no	—
490	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
491	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
492	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
493	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
494	C₂²×C₄	#41×C₃₁	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
499	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
500	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
502	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
504	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	2	8	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	2	8	no	—
510	C₄⋊C₄	—	4	4	no	—
511	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	complemented
512	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
513	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
514	C₂²⋊C₄	—	2	4	no	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	16	no	—
517	C₂²⋊C₄	—	2	8	no	—
518	C₂²⋊C₄	—	2	8	no	—
519	C₂²⋊C₄	—	4	8	no	—
520	C₂²⋊C₄	—	4	4	no	—
521	C₂²⋊C₄	—	4	8	no	—
522	C₂²⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
523	C₂²⋊C₄	C₂²×C₄×C₃₁	1	32	yes	complemented
524	C₄²	—	2	4	no	—
525	C₄²	—	2	4	no	—
526	C₄²	—	2	8	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	2	4	no	—
529	C₄²	—	4	8	no	—
530	C₄²	C₂²×C₄×C₃₁	1	8	yes	complemented
531	C₂³	—	2	2	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	16	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	8	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	8	no	—
542	C₂³	—	4	16	no	—
543	C₂³	—	4	8	no	—
544	C₂³	—	4	8	no	—
545	C₂³	—	4	16	no	—
546	C₂³	C₂³×C₄×C₃₁	1	8	yes	—
547	C₂³	C₂³×C₄×C₃₁	1	4	yes	—
548	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
549	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
550	C₂³	C₂×#41×C₃₁	1	2	yes	—
551	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
552	Q₈	—	2	8	no	—
553	D₄	—	2	16	no	—
554	D₄	—	2	16	no	—
555	D₄	—	2	16	no	—
556	D₄	—	2	8	no	—
557	D₄	—	4	32	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	8	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	16	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	4	8	no	—
578	C₂×C₄	—	4	32	no	—
579	C₂×C₄	—	4	4	no	—
580	C₂×C₄	—	8	8	no	—
581	C₂×C₄	C₄×D₄×C₃₁	1	16	yes	complemented
582	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
583	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
584	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
585	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
586	C₂×C₄	C₂²×D₄×C₃₁	1	8	yes	—
587	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
588	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
589	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
590	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
591	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
592	C₂²	—	2	4	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	2	4	no	—
597	C₂²	—	2	8	no	—
598	C₂²	—	2	8	no	—
599	C₂²	—	2	16	no	—
600	C₂²	—	4	32	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	4	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	8	no	—
606	C₂²	—	4	4	no	—
607	C₂²	C₂×C₄×D₄×C₃₁	1	4	yes	—
608	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
609	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
610	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
611	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
612	C₂²	C₃₁×#585	1	2	yes	—
613	C₄	—	2	4	no	—
614	C₄	—	2	8	no	—
615	C₄	—	2	4	no	—
616	C₄	—	2	8	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	4	no	—
621	C₄	C₂×C₄×D₄×C₃₁	1	4	yes	—
622	C₄	C₂×C₄×D₄×C₃₁	1	4	yes	—
623	C₂	—	2	4	no	—
624	C₂	—	4	8	no	—
625	C₂	—	4	4	no	—
626	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
627	C₂	C₄×C₃₁×H(5,𝔽₂)	1	2	yes	—
628	C₂	C₃₁×#3484	1	1	yes	characteristic
629	C₂	C₃₁×#3487	1	1	yes	characteristic
630	C₂	C₃₁×#3506	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#535	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#520	C₂	semidirect
3. C₂²×C₄×D₄×C₃₁	C₂	semidirect
4. C₃₁×#2367	C₂	semidirect
5. C₃₁×#2366	C₂	semidirect
6. C₃₁×#2363	C₂	semidirect
7. C₃₁×#2361	C₂	semidirect
8. C₃₁×#2321	C₂	semidirect
9. C₃₁×#2309	C₂	semidirect
10. C₄×C₃₁×#120	C₂	semidirect
11. C₃₁×#2297	C₂	semidirect
12. C₃₁×#2296	C₂	semidirect
13. C₃₁×#2274	C₂	semidirect
17. C₃₁×#535	C₄	semidirect
23. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
28. C₂×C₄×D₄×C₃₁	C₂²	semidirect
29. C₂×C₄×D₄×C₃₁	C₂²	semidirect
33. C₂×C₃₁×#117	C₂²	semidirect
35. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
38. C₃₁×#391	C₂²	semidirect
42. C₃₁×#390	C₂²	semidirect
43. C₃₁×#390	C₂²	semidirect
44. C₃₁×#389	C₂²	semidirect
45. C₃₁×#389	C₂²	semidirect
46. C₃₁×#388	C₂²	semidirect
47. C₃₁×#388	C₂²	semidirect
50. C₃₁×#386	C₂²	semidirect
51. C₃₁×#386	C₂²	semidirect
54. C₃₁×#385	C₂²	semidirect
56. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
57. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
58. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
60. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
61. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
65. C₂×#41×C₃₁	C₂×C₄	semidirect
69. C₂²×D₄×C₃₁	C₂×C₄	semidirect
84. C₃₁×#127	C₂×C₄	semidirect
85. C₃₁×#124	C₂×C₄	semidirect
86. C₃₁×#121	C₂×C₄	semidirect
87. C₃₁×#120	C₂×C₄	semidirect
97. C₃₁×#117	C₂×C₄	semidirect
99. C₂×C₄⋊C₄×C₃₁	D₄	semidirect
144. C₂×Q₈×C₃₁	C₂²×C₄	semidirect
159. C₂×D₄×C₃₁	C₂²×C₄	semidirect
160. C₂×D₄×C₃₁	C₂²×C₄	semidirect
175. C₂²×C₄×C₃₁	C₂²×C₄	semidirect
195. C₄⋊C₄×C₃₁	C₂²×C₄	semidirect
207. C₂²⋊C₄×C₃₁	C₂²×C₄	semidirect
214. C₄²×C₃₁	C₂²×C₄	semidirect
215. #34265	C₃₁	direct (N × H)
266. C₂×C₄×C₃₁	C₄×D₄	semidirect
278. C₂×#520	C₂×C₃₁	semidirect
279. C₂²×C₄×D₄	C₂×C₃₁	semidirect
280. #2367	C₂×C₃₁	semidirect
281. #2366	C₂×C₃₁	semidirect
282. #2363	C₂×C₃₁	semidirect
283. #2361	C₂×C₃₁	semidirect
284. #2321	C₂×C₃₁	semidirect
285. #2309	C₂×C₃₁	semidirect
286. C₄×#120	C₂×C₃₁	semidirect
287. #2297	C₂×C₃₁	semidirect
288. #2296	C₂×C₃₁	semidirect
289. #2274	C₂×C₃₁	semidirect
324. #535	C₄×C₃₁	semidirect
330. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
335. C₂×C₄×D₄	C₂²×C₃₁	semidirect
336. C₂×C₄×D₄	C₂²×C₃₁	semidirect
340. C₂×#117	C₂²×C₃₁	semidirect
342. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
345. #391	C₂²×C₃₁	semidirect
349. #390	C₂²×C₃₁	semidirect
350. #390	C₂²×C₃₁	semidirect
351. #389	C₂²×C₃₁	semidirect
352. #389	C₂²×C₃₁	semidirect
353. #388	C₂²×C₃₁	semidirect
354. #388	C₂²×C₃₁	semidirect
357. #386	C₂²×C₃₁	semidirect
358. #386	C₂²×C₃₁	semidirect
361. #385	C₂²×C₃₁	semidirect
363. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
364. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
365. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
367. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
368. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
380. C₂×#41	C₂×C₄×C₃₁	semidirect
384. C₂²×D₄	C₂×C₄×C₃₁	semidirect
399. #127	C₂×C₄×C₃₁	semidirect
400. #124	C₂×C₄×C₃₁	semidirect
401. #121	C₂×C₄×C₃₁	semidirect
402. #120	C₂×C₄×C₃₁	semidirect
412. #117	C₂×C₄×C₃₁	semidirect
414. C₂×C₄⋊C₄	D₄×C₃₁	semidirect
448. C₃₁	#34265	direct (N × H)
460. C₂×Q₈	C₂²×C₄×C₃₁	semidirect
475. C₂×D₄	C₂²×C₄×C₃₁	semidirect
476. C₂×D₄	C₂²×C₄×C₃₁	semidirect
491. C₂²×C₄	C₂²×C₄×C₃₁	semidirect
511. C₄⋊C₄	C₂²×C₄×C₃₁	semidirect
523. C₂²⋊C₄	C₂²×C₄×C₃₁	semidirect
530. C₄²	C₂²×C₄×C₃₁	semidirect
581. C₂×C₄	C₄×D₄×C₃₁	semidirect

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
C₂×C₃₁×#520	2
C₂²×C₄×D₄×C₃₁	2
C₃₁×#2367	2
C₃₁×#2366	2
C₃₁×#2363	2
C₃₁×#2361	2
C₃₁×#2321	2
C₃₁×#2309	2
C₄×C₃₁×#120	2
C₃₁×#2297	2
C₃₁×#2296	2
C₃₁×#2274	2
#34265	31

Subgroups — C31×#34265 #21491024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34265 #21491024