Subgroups — C₃₁×#34205 #21490964

Order 7936.

3642 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#121	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#518	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2364	C₂	1	4	yes	maximal, complemented
4	C₃₁×#2361	C₂	1	4	yes	maximal, complemented
5	C₃₁×#2344	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2342	C₂	1	4	yes	maximal, complemented
7	D₄×C₂²⋊C₄×C₃₁	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2325	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2308	C₂	1	2	yes	maximal, complemented
10	C₄×C₃₁×#121	C₂	1	4	yes	maximal, complemented
11	C₂×C₃₁×#380	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
14	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×#121	C₄	1	16	yes	complemented
17	C₂×C₃₁×#121	C₂²	1	2	yes	—
18	C₂×C₃₁×#121	C₂²	1	2	yes	—
19	C₂×C₃₁×#121	C₂²	1	2	yes	—
20	C₂×C₃₁×#121	C₂²	1	2	yes	—
21	C₃₁×#518	—	2	16	no	—
22	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
23	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
24	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
25	C₂×C₃₁×#117	C₂²	1	4	yes	—
26	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
28	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
31	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
34	C₃₁×#390	C₂²	1	4	yes	complemented
35	C₃₁×#389	C₂²	1	4	yes	complemented
36	C₃₁×#388	C₂²	1	8	yes	complemented
37	C₃₁×#388	C₂²	1	8	yes	complemented
38	C₃₁×#387	C₂²	1	8	yes	complemented
39	C₃₁×#386	C₂²	1	8	yes	complemented
40	C₃₁×#386	C₂²	1	8	yes	complemented
41	C₃₁×#386	C₂²	1	8	yes	complemented
42	C₃₁×#385	C₂²	1	8	yes	complemented
43	C₃₁×#381	C₂²	1	4	yes	—
44	C₃₁×#380	C₂²	1	2	yes	—
45	C₃₁×#380	C₂²	1	2	yes	—
46	C₃₁×#380	C₂²	1	2	yes	complemented
47	C₃₁×#380	C₂²	1	2	yes	complemented
48	C₃₁×#379	C₂²	1	4	yes	—
49	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
50	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
51	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
52	C₄×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	complemented
53	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
55	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
56	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
57	C₂⁵×C₃₁	C₂³	1	2	yes	—
58	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₃₁	—	2	8	no	—
60	C₂²×D₄×C₃₁	—	2	8	no	—
61	C₂²×D₄×C₃₁	—	4	4	no	—
62	C₂²×D₄×C₃₁	C₂×C₄	1	16	yes	complemented
63	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
64	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
65	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
66	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
67	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
68	C₂³×C₄×C₃₁	—	4	4	no	—
69	C₂³×C₄×C₃₁	C₂×C₄	1	8	yes	complemented
70	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
72	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
75	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
76	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
77	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
81	C₃₁×#121	C₂×C₄	1	16	yes	complemented
82	C₃₁×#121	C₂×C₄	1	16	yes	complemented
83	C₃₁×#121	C₂×C₄	1	16	yes	complemented
84	C₃₁×#121	C₂×C₄	1	16	yes	complemented
85	C₄×D₄×C₃₁	—	2	32	no	—
86	C₄×D₄×C₃₁	—	2	32	no	—
87	C₄×D₄×C₃₁	—	4	8	no	—
88	C₃₁×#117	—	2	16	no	—
89	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
90	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	complemented
91	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
93	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
96	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
97	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₃₁	—	2	16	no	—
99	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	16	yes	complemented
100	C₂×C₂²⋊C₄×C₃₁	D₄	1	8	yes	complemented
101	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
104	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
107	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
108	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
112	C₂×C₄²×C₃₁	—	4	4	no	—
113	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
114	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
115	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
116	C₃₁×#95	C₂³	1	4	yes	—
117	C₃₁×#95	C₂³	1	4	yes	—
118	C₃₁×#95	C₂³	1	4	yes	—
119	C₃₁×#95	C₂³	1	4	yes	—
120	C₃₁×#95	C₂³	1	8	yes	—
121	C₃₁×#95	C₂³	1	8	yes	—
122	C₂⁴×C₃₁	—	2	4	no	—
123	C₂⁴×C₃₁	—	2	4	no	—
124	C₂⁴×C₃₁	—	4	2	no	—
125	C₂⁴×C₃₁	—	4	2	no	—
126	C₂⁴×C₃₁	—	4	4	no	—
127	C₂⁴×C₃₁	—	4	4	no	—
128	C₂⁴×C₃₁	C₂²×C₄	1	8	yes	—
129	C₂⁴×C₃₁	C₂²×C₄	1	4	yes	—
130	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
131	C₂⁴×C₃₁	#41	1	4	yes	—
132	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
133	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
134	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
135	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
136	C₂×D₄×C₃₁	—	2	64	no	—
137	C₂×D₄×C₃₁	—	2	8	no	—
138	C₂×D₄×C₃₁	—	2	8	no	—
139	C₂×D₄×C₃₁	—	2	8	no	—
140	C₂×D₄×C₃₁	—	2	8	no	—
141	C₂×D₄×C₃₁	—	2	8	no	—
142	C₂×D₄×C₃₁	—	4	16	no	—
143	C₂×D₄×C₃₁	—	4	4	no	—
144	C₂×D₄×C₃₁	C₂²×C₄	1	16	yes	—
145	C₂×D₄×C₃₁	C₂²×C₄	1	16	yes	—
146	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
147	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
148	C₂²×C₄×C₃₁	—	2	4	no	—
149	C₂²×C₄×C₃₁	—	2	4	no	—
150	C₂²×C₄×C₃₁	—	2	4	no	—
151	C₂²×C₄×C₃₁	—	2	4	no	—
152	C₂²×C₄×C₃₁	—	2	4	no	—
153	C₂²×C₄×C₃₁	—	2	4	no	—
154	C₂²×C₄×C₃₁	—	2	8	no	—
155	C₂²×C₄×C₃₁	—	2	16	no	—
156	C₂²×C₄×C₃₁	—	4	16	no	—
157	C₂²×C₄×C₃₁	—	4	2	no	—
158	C₂²×C₄×C₃₁	—	4	2	no	—
159	C₂²×C₄×C₃₁	—	4	2	no	—
160	C₂²×C₄×C₃₁	—	4	2	no	—
161	C₂²×C₄×C₃₁	—	4	2	no	—
162	C₂²×C₄×C₃₁	—	4	2	no	—
163	C₂²×C₄×C₃₁	—	4	2	no	—
164	C₂²×C₄×C₃₁	—	4	4	no	—
165	C₂²×C₄×C₃₁	—	4	8	no	—
166	C₂²×C₄×C₃₁	—	4	8	no	—
167	C₂²×C₄×C₃₁	—	4	4	no	—
168	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
169	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
170	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
171	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
172	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	complemented
176	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
178	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
184	C₄⋊C₄×C₃₁	—	2	16	no	—
185	C₄⋊C₄×C₃₁	—	2	8	no	—
186	C₄⋊C₄×C₃₁	—	4	4	no	—
187	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
188	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
189	C₂²⋊C₄×C₃₁	—	2	8	no	—
190	C₂²⋊C₄×C₃₁	—	2	8	no	—
191	C₂²⋊C₄×C₃₁	—	2	4	no	—
192	C₂²⋊C₄×C₃₁	—	2	4	no	—
193	C₂²⋊C₄×C₃₁	—	2	16	no	—
194	C₂²⋊C₄×C₃₁	—	4	8	no	—
195	C₂²⋊C₄×C₃₁	—	4	8	no	—
196	C₂²⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
197	C₂²⋊C₄×C₃₁	C₂²×C₄	1	16	yes	—
198	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
199	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	complemented
200	C₄²×C₃₁	—	2	16	no	—
201	C₄²×C₃₁	—	2	8	no	—
202	C₄²×C₃₁	—	4	4	no	—
203	#34205	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂³×C₃₁	—	2	2	no	—
205	C₂³×C₃₁	—	2	2	no	—
206	C₂³×C₃₁	—	2	2	no	—
207	C₂³×C₃₁	—	2	2	no	—
208	C₂³×C₃₁	—	2	2	no	—
209	C₂³×C₃₁	—	2	2	no	—
210	C₂³×C₃₁	—	2	4	no	—
211	C₂³×C₃₁	—	2	4	no	—
212	C₂³×C₃₁	—	2	8	no	—
213	C₂³×C₃₁	—	2	8	no	—
214	C₂³×C₃₁	—	2	16	no	—
215	C₂³×C₃₁	—	4	4	no	—
216	C₂³×C₃₁	—	4	4	no	—
217	C₂³×C₃₁	—	4	8	no	—
218	C₂³×C₃₁	—	4	8	no	—
219	C₂³×C₃₁	—	4	8	no	—
220	C₂³×C₃₁	—	4	8	no	—
221	C₂³×C₃₁	—	8	8	no	—
222	C₂³×C₃₁	—	8	8	no	—
223	C₂³×C₃₁	C₄×D₄	1	16	yes	complemented
224	C₂³×C₃₁	C₂³×C₄	1	8	yes	—
225	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
226	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
227	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
228	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
229	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
230	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
231	C₂³×C₃₁	C₂×#41	1	2	yes	—
232	C₂³×C₃₁	C₂×#41	1	2	yes	—
233	C₂³×C₃₁	C₂×#41	1	2	yes	—
234	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
235	D₄×C₃₁	—	2	32	no	—
236	D₄×C₃₁	—	2	32	no	—
237	D₄×C₃₁	—	2	16	no	—
238	D₄×C₃₁	—	4	8	no	—
239	C₂×C₄×C₃₁	—	2	16	no	—
240	C₂×C₄×C₃₁	—	2	4	no	—
241	C₂×C₄×C₃₁	—	2	4	no	—
242	C₂×C₄×C₃₁	—	2	4	no	—
243	C₂×C₄×C₃₁	—	2	2	no	—
244	C₂×C₄×C₃₁	—	2	2	no	—
245	C₂×C₄×C₃₁	—	2	2	no	—
246	C₂×C₄×C₃₁	—	2	4	no	—
247	C₂×C₄×C₃₁	—	2	8	no	—
248	C₂×C₄×C₃₁	—	2	8	no	—
249	C₂×C₄×C₃₁	—	2	8	no	—
250	C₂×C₄×C₃₁	—	2	8	no	—
251	C₂×C₄×C₃₁	—	2	4	no	—
252	C₂×C₄×C₃₁	—	2	4	no	—
253	C₂×C₄×C₃₁	—	2	8	no	—
254	C₂×C₄×C₃₁	—	2	4	no	—
255	C₂×C₄×C₃₁	—	2	8	no	—
256	C₂×C₄×C₃₁	—	4	4	no	—
257	C₂×C₄×C₃₁	—	4	4	no	—
258	C₂×C₄×C₃₁	—	4	4	no	—
259	C₂×C₄×C₃₁	—	4	8	no	—
260	C₂×C₄×C₃₁	—	4	8	no	—
261	C₂×C₄×C₃₁	—	8	16	no	—
262	C₂×C₄×C₃₁	—	8	8	no	—
263	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
264	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
265	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
266	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
267	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
268	C₂×C₄×C₃₁	C₂²×D₄	1	8	yes	—
269	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
270	C₂²×#121	C₂×C₃₁	1	1	yes	characteristic
271	C₂×#518	C₂×C₃₁	1	2	yes	complemented
272	#2364	C₂×C₃₁	1	4	yes	complemented
273	#2361	C₂×C₃₁	1	4	yes	complemented
274	#2344	C₂×C₃₁	1	2	yes	complemented
275	#2342	C₂×C₃₁	1	4	yes	complemented
276	D₄×C₂²⋊C₄	C₂×C₃₁	1	2	yes	complemented
277	#2325	C₂×C₃₁	1	4	yes	complemented
278	#2308	C₂×C₃₁	1	2	yes	complemented
279	C₄×#121	C₂×C₃₁	1	4	yes	complemented
280	C₂×#380	C₂×C₃₁	1	1	yes	characteristic, complemented
281	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
282	C₂²×C₃₁	—	2	2	no	—
283	C₂²×C₃₁	—	2	2	no	—
284	C₂²×C₃₁	—	2	2	no	—
285	C₂²×C₃₁	—	2	2	no	—
286	C₂²×C₃₁	—	2	2	no	—
287	C₂²×C₃₁	—	2	2	no	—
288	C₂²×C₃₁	—	2	4	no	—
289	C₂²×C₃₁	—	2	4	no	—
290	C₂²×C₃₁	—	2	4	no	—
291	C₂²×C₃₁	—	2	4	no	—
292	C₂²×C₃₁	—	2	4	no	—
293	C₂²×C₃₁	—	2	4	no	—
294	C₂²×C₃₁	—	2	8	no	—
295	C₂²×C₃₁	—	2	8	no	—
296	C₂²×C₃₁	—	2	8	no	—
297	C₂²×C₃₁	—	4	16	no	—
298	C₂²×C₃₁	—	4	8	no	—
299	C₂²×C₃₁	—	4	8	no	—
300	C₂²×C₃₁	—	8	16	no	—
301	C₂²×C₃₁	C₂×C₄×D₄	1	4	yes	—
302	C₂²×C₃₁	C₂×C₄×D₄	1	4	yes	—
303	C₂²×C₃₁	C₂×C₄×D₄	1	4	yes	—
304	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
305	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
306	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
307	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
308	C₂²×C₃₁	#585	1	2	yes	—
309	C₄×C₃₁	—	2	8	no	—
310	C₄×C₃₁	—	2	2	no	—
311	C₄×C₃₁	—	2	2	no	—
312	C₄×C₃₁	—	2	2	no	—
313	C₄×C₃₁	—	2	8	no	—
314	C₄×C₃₁	—	4	8	no	—
315	C₄×C₃₁	—	4	4	no	—
316	C₄×C₃₁	#518	1	4	yes	complemented
317	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
318	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
319	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
320	C₂×#121	C₄×C₃₁	1	16	yes	complemented
321	C₂×#121	C₂²×C₃₁	1	2	yes	—
322	C₂×#121	C₂²×C₃₁	1	2	yes	—
323	C₂×#121	C₂²×C₃₁	1	2	yes	—
324	C₂×#121	C₂²×C₃₁	1	2	yes	—
325	#518	—	2	16	no	—
326	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
327	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
328	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
329	C₂×#117	C₂²×C₃₁	1	4	yes	—
330	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
331	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
332	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
333	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
334	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
335	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
336	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
337	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
338	#390	C₂²×C₃₁	1	4	yes	complemented
339	#389	C₂²×C₃₁	1	4	yes	complemented
340	#388	C₂²×C₃₁	1	8	yes	complemented
341	#388	C₂²×C₃₁	1	8	yes	complemented
342	#387	C₂²×C₃₁	1	8	yes	complemented
343	#386	C₂²×C₃₁	1	8	yes	complemented
344	#386	C₂²×C₃₁	1	8	yes	complemented
345	#386	C₂²×C₃₁	1	8	yes	complemented
346	#385	C₂²×C₃₁	1	8	yes	complemented
347	#381	C₂²×C₃₁	1	4	yes	—
348	#380	C₂²×C₃₁	1	2	yes	—
349	#380	C₂²×C₃₁	1	2	yes	—
350	#380	C₂²×C₃₁	1	2	yes	complemented
351	#380	C₂²×C₃₁	1	2	yes	complemented
352	#379	C₂²×C₃₁	1	4	yes	—
353	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
354	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
355	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
356	C₄×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	complemented
357	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
358	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
359	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
360	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
361	C₂×C₃₁	—	2	4	no	—
362	C₂×C₃₁	—	2	4	no	—
363	C₂×C₃₁	—	2	4	no	—
364	C₂×C₃₁	—	4	8	no	—
365	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
366	C₂×C₃₁	C₂×#518	1	1	yes	characteristic
367	C₂×C₃₁	#3428	1	1	yes	characteristic
368	C₂×C₃₁	#3496	1	2	yes	—
369	C₂×C₃₁	#3505	1	2	yes	—
370	C₂⁵	C₂³×C₃₁	1	2	yes	—
371	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
372	C₂²×D₄	—	2	8	no	—
373	C₂²×D₄	—	2	8	no	—
374	C₂²×D₄	—	4	4	no	—
375	C₂²×D₄	C₂×C₄×C₃₁	1	16	yes	complemented
376	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
377	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
378	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
379	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
380	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
381	C₂³×C₄	—	4	4	no	—
382	C₂³×C₄	C₂×C₄×C₃₁	1	8	yes	complemented
383	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
384	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
388	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
389	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
390	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
394	#121	C₂×C₄×C₃₁	1	16	yes	complemented
395	#121	C₂×C₄×C₃₁	1	16	yes	complemented
396	#121	C₂×C₄×C₃₁	1	16	yes	complemented
397	#121	C₂×C₄×C₃₁	1	16	yes	complemented
398	C₄×D₄	—	2	32	no	—
399	C₄×D₄	—	2	32	no	—
400	C₄×D₄	—	4	8	no	—
401	#117	—	2	16	no	—
402	C₂×C₄⋊C₄	—	4	4	no	—
403	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	complemented
404	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
405	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
406	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
407	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
409	C₂×C₂²⋊C₄	—	2	8	no	—
410	C₂×C₂²⋊C₄	—	2	4	no	—
411	C₂×C₂²⋊C₄	—	2	16	no	—
412	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	16	yes	complemented
413	C₂×C₂²⋊C₄	D₄×C₃₁	1	8	yes	complemented
414	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
425	C₂×C₄²	—	4	4	no	—
426	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
427	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
428	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
429	#95	C₂³×C₃₁	1	4	yes	—
430	#95	C₂³×C₃₁	1	4	yes	—
431	#95	C₂³×C₃₁	1	4	yes	—
432	#95	C₂³×C₃₁	1	4	yes	—
433	#95	C₂³×C₃₁	1	8	yes	—
434	#95	C₂³×C₃₁	1	8	yes	—
435	C₃₁	#34205	1	1	yes	characteristic, direct product factor, Sylow
436	C₂⁴	—	2	4	no	—
437	C₂⁴	—	2	4	no	—
438	C₂⁴	—	4	2	no	—
439	C₂⁴	—	4	2	no	—
440	C₂⁴	—	4	4	no	—
441	C₂⁴	—	4	4	no	—
442	C₂⁴	C₂²×C₄×C₃₁	1	8	yes	—
443	C₂⁴	C₂²×C₄×C₃₁	1	4	yes	—
444	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
445	C₂⁴	#41×C₃₁	1	4	yes	—
446	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
447	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
448	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
449	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
450	C₂×D₄	—	2	64	no	—
451	C₂×D₄	—	2	8	no	—
452	C₂×D₄	—	2	8	no	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	2	8	no	—
456	C₂×D₄	—	4	16	no	—
457	C₂×D₄	—	4	4	no	—
458	C₂×D₄	C₂²×C₄×C₃₁	1	16	yes	—
459	C₂×D₄	C₂²×C₄×C₃₁	1	16	yes	—
460	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
461	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	8	no	—
469	C₂²×C₄	—	2	16	no	—
470	C₂²×C₄	—	4	16	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	4	no	—
479	C₂²×C₄	—	4	8	no	—
480	C₂²×C₄	—	4	8	no	—
481	C₂²×C₄	—	4	4	no	—
482	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
483	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
484	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
485	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
486	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
487	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
488	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
489	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	complemented
490	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
491	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
492	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
493	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
496	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
498	C₄⋊C₄	—	2	16	no	—
499	C₄⋊C₄	—	2	8	no	—
500	C₄⋊C₄	—	4	4	no	—
501	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
502	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
503	C₂²⋊C₄	—	2	8	no	—
504	C₂²⋊C₄	—	2	8	no	—
505	C₂²⋊C₄	—	2	4	no	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	2	16	no	—
508	C₂²⋊C₄	—	4	8	no	—
509	C₂²⋊C₄	—	4	8	no	—
510	C₂²⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
511	C₂²⋊C₄	C₂²×C₄×C₃₁	1	16	yes	—
512	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
513	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	complemented
514	C₄²	—	2	16	no	—
515	C₄²	—	2	8	no	—
516	C₄²	—	4	4	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	8	no	—
526	C₂³	—	2	8	no	—
527	C₂³	—	2	16	no	—
528	C₂³	—	4	4	no	—
529	C₂³	—	4	4	no	—
530	C₂³	—	4	8	no	—
531	C₂³	—	4	8	no	—
532	C₂³	—	4	8	no	—
533	C₂³	—	4	8	no	—
534	C₂³	—	8	8	no	—
535	C₂³	—	8	8	no	—
536	C₂³	C₄×D₄×C₃₁	1	16	yes	complemented
537	C₂³	C₂³×C₄×C₃₁	1	8	yes	—
538	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
539	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
540	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
541	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
542	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
543	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
544	C₂³	C₂×#41×C₃₁	1	2	yes	—
545	C₂³	C₂×#41×C₃₁	1	2	yes	—
546	C₂³	C₂×#41×C₃₁	1	2	yes	—
547	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
548	D₄	—	2	32	no	—
549	D₄	—	2	32	no	—
550	D₄	—	2	16	no	—
551	D₄	—	4	8	no	—
552	C₂×C₄	—	2	16	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	8	no	—
561	C₂×C₄	—	2	8	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	8	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	8	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	8	no	—
569	C₂×C₄	—	4	4	no	—
570	C₂×C₄	—	4	4	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	8	no	—
573	C₂×C₄	—	4	8	no	—
574	C₂×C₄	—	8	16	no	—
575	C₂×C₄	—	8	8	no	—
576	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
577	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
578	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
579	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
580	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
581	C₂×C₄	C₂²×D₄×C₃₁	1	8	yes	—
582	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	4	no	—
590	C₂²	—	2	4	no	—
591	C₂²	—	2	4	no	—
592	C₂²	—	2	4	no	—
593	C₂²	—	2	4	no	—
594	C₂²	—	2	4	no	—
595	C₂²	—	2	8	no	—
596	C₂²	—	2	8	no	—
597	C₂²	—	2	8	no	—
598	C₂²	—	4	16	no	—
599	C₂²	—	4	8	no	—
600	C₂²	—	4	8	no	—
601	C₂²	—	8	16	no	—
602	C₂²	C₂×C₄×D₄×C₃₁	1	4	yes	—
603	C₂²	C₂×C₄×D₄×C₃₁	1	4	yes	—
604	C₂²	C₂×C₄×D₄×C₃₁	1	4	yes	—
605	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
606	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
607	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
608	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
609	C₂²	C₃₁×#585	1	2	yes	—
610	C₄	—	2	8	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	8	no	—
615	C₄	—	4	8	no	—
616	C₄	—	4	4	no	—
617	C₄	C₃₁×#518	1	4	yes	complemented
618	C₂	—	2	4	no	—
619	C₂	—	2	4	no	—
620	C₂	—	2	4	no	—
621	C₂	—	4	8	no	—
622	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
623	C₂	C₂×C₃₁×#518	1	1	yes	characteristic
624	C₂	C₃₁×#3428	1	1	yes	characteristic
625	C₂	C₃₁×#3496	1	2	yes	—
626	C₂	C₃₁×#3505	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂²×C₃₁×#121	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×#518	C₂	semidirect
3. C₃₁×#2364	C₂	semidirect
4. C₃₁×#2361	C₂	semidirect
5. C₃₁×#2344	C₂	semidirect
6. C₃₁×#2342	C₂	semidirect
7. D₄×C₂²⋊C₄×C₃₁	C₂	semidirect
8. C₃₁×#2325	C₂	semidirect
9. C₃₁×#2308	C₂	semidirect
10. C₄×C₃₁×#121	C₂	semidirect
11. C₂×C₃₁×#380	C₂	semidirect
12. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
16. C₂×C₃₁×#121	C₄	semidirect
22. C₂×C₄×D₄×C₃₁	C₂²	semidirect
23. C₂×C₄×D₄×C₃₁	C₂²	semidirect
24. C₂×C₄×D₄×C₃₁	C₂²	semidirect
27. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
33. C₂²×C₄²×C₃₁	C₂²	semidirect
34. C₃₁×#390	C₂²	semidirect
35. C₃₁×#389	C₂²	semidirect
36. C₃₁×#388	C₂²	semidirect
37. C₃₁×#388	C₂²	semidirect
38. C₃₁×#387	C₂²	semidirect
39. C₃₁×#386	C₂²	semidirect
40. C₃₁×#386	C₂²	semidirect
41. C₃₁×#386	C₂²	semidirect
42. C₃₁×#385	C₂²	semidirect
46. C₃₁×#380	C₂²	semidirect
47. C₃₁×#380	C₂²	semidirect
49. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
52. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
53. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
54. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
55. C₂×C₃₁×#95	C₂²	semidirect
56. C₂×C₃₁×#95	C₂²	semidirect
62. C₂²×D₄×C₃₁	C₂×C₄	semidirect
63. C₂²×D₄×C₃₁	C₂×C₄	semidirect
69. C₂³×C₄×C₃₁	C₂×C₄	semidirect
81. C₃₁×#121	C₂×C₄	semidirect
82. C₃₁×#121	C₂×C₄	semidirect
83. C₃₁×#121	C₂×C₄	semidirect
84. C₃₁×#121	C₂×C₄	semidirect
90. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
99. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
100. C₂×C₂²⋊C₄×C₃₁	D₄	semidirect
175. C₂²×C₄×C₃₁	C₂×D₄	semidirect
199. C₂²⋊C₄×C₃₁	C₂×D₄	semidirect
203. #34205	C₃₁	direct (N × H)
223. C₂³×C₃₁	C₄×D₄	semidirect
271. C₂×#518	C₂×C₃₁	semidirect
272. #2364	C₂×C₃₁	semidirect
273. #2361	C₂×C₃₁	semidirect
274. #2344	C₂×C₃₁	semidirect
275. #2342	C₂×C₃₁	semidirect
276. D₄×C₂²⋊C₄	C₂×C₃₁	semidirect
277. #2325	C₂×C₃₁	semidirect
278. #2308	C₂×C₃₁	semidirect
279. C₄×#121	C₂×C₃₁	semidirect
280. C₂×#380	C₂×C₃₁	semidirect
281. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
316. C₄×C₃₁	#518	semidirect
320. C₂×#121	C₄×C₃₁	semidirect
326. C₂×C₄×D₄	C₂²×C₃₁	semidirect
327. C₂×C₄×D₄	C₂²×C₃₁	semidirect
328. C₂×C₄×D₄	C₂²×C₃₁	semidirect
331. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
337. C₂²×C₄²	C₂²×C₃₁	semidirect
338. #390	C₂²×C₃₁	semidirect
339. #389	C₂²×C₃₁	semidirect
340. #388	C₂²×C₃₁	semidirect
341. #388	C₂²×C₃₁	semidirect
342. #387	C₂²×C₃₁	semidirect
343. #386	C₂²×C₃₁	semidirect
344. #386	C₂²×C₃₁	semidirect
345. #386	C₂²×C₃₁	semidirect
346. #385	C₂²×C₃₁	semidirect
350. #380	C₂²×C₃₁	semidirect
351. #380	C₂²×C₃₁	semidirect
353. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
356. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
357. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
358. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
359. C₂×#95	C₂²×C₃₁	semidirect
360. C₂×#95	C₂²×C₃₁	semidirect
375. C₂²×D₄	C₂×C₄×C₃₁	semidirect
376. C₂²×D₄	C₂×C₄×C₃₁	semidirect
382. C₂³×C₄	C₂×C₄×C₃₁	semidirect
394. #121	C₂×C₄×C₃₁	semidirect
395. #121	C₂×C₄×C₃₁	semidirect
396. #121	C₂×C₄×C₃₁	semidirect
397. #121	C₂×C₄×C₃₁	semidirect
403. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
412. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
413. C₂×C₂²⋊C₄	D₄×C₃₁	semidirect
435. C₃₁	#34205	direct (N × H)
489. C₂²×C₄	C₂×D₄×C₃₁	semidirect
513. C₂²⋊C₄	C₂×D₄×C₃₁	semidirect
536. C₂³	C₄×D₄×C₃₁	semidirect
617. C₄	C₃₁×#518	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃₁×#121	2
C₂×C₃₁×#518	2
C₃₁×#2364	2
C₃₁×#2361	2
C₃₁×#2344	2
C₃₁×#2342	2
D₄×C₂²⋊C₄×C₃₁	2
C₃₁×#2325	2
C₃₁×#2308	2
C₄×C₃₁×#121	2
C₂×C₃₁×#380	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
#34205	31

Subgroups — C31×#34205 #21490964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34205 #21490964