Subgroups — C₃₁×#13732 #21470491

Order 7936.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2253	C₂	1	2	yes	maximal
2	C₃₁×#1424	C₂	1	2	yes	maximal
3	C₃₁×#1423	C₂	1	2	yes	maximal
4	C₄×C₃₁×C₃₂	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#499	—	2	2	no	—
6	C₂×C₃₁×C₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₃₁×C₃₂	C₂²	1	1	yes	characteristic
8	C₃₁×#367	—	2	2	no	—
9	C₃₁×#366	C₂²	1	4	yes	—
10	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
11	C₃₁×#125	—	4	2	no	—
12	C₂×C₁₆×C₃₁	D₄	1	1	yes	characteristic
13	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
14	C₃₁×#107	—	2	4	no	—
15	C₃₁×#106	—	4	2	no	—
16	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
17	C₃₁×C₃₂	Q₈	1	2	yes	—
18	C₃₁×C₃₂	Q₈	1	2	yes	—
19	C₂×C₈×C₃₁	D₈	1	1	yes	characteristic
20	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
21	C₄⋊C₄×C₃₁	—	4	4	no	—
22	C₄⋊C₄×C₃₁	—	8	4	no	—
23	C₄²×C₃₁	D₈	1	1	yes	characteristic
24	C₁₆×C₃₁	Q₁₆	1	2	yes	—
25	C₁₆×C₃₁	C₂×Q₈	1	1	yes	characteristic
26	C₁₆×C₃₁	C₂×Q₈	1	1	yes	characteristic
27	#13732	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂×C₄×C₃₁	—	8	4	no	—
29	C₂×C₄×C₃₁	D₁₆	1	2	yes	—
30	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
31	C₈×C₃₁	Q₃₂	1	2	yes	—
32	C₈×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
33	C₈×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
34	#2253	C₂×C₃₁	1	2	yes	—
35	#1424	C₂×C₃₁	1	2	yes	—
36	#1423	C₂×C₃₁	1	2	yes	—
37	C₄×C₃₂	C₂×C₃₁	1	1	yes	characteristic
38	C₂²×C₃₁	C₂×D₁₆	1	1	yes	characteristic
39	C₄×C₃₁	—	2	2	no	—
40	C₄×C₃₁	—	16	4	no	—
41	C₄×C₃₁	#500	1	1	yes	characteristic
42	C₄×C₃₁	C₂×Q₃₂	1	1	yes	characteristic
43	#499	—	2	2	no	—
44	C₂×C₃₂	C₂²×C₃₁	1	1	yes	characteristic
45	C₂×C₃₂	C₂²×C₃₁	1	1	yes	characteristic
46	#367	—	2	2	no	—
47	#366	C₂²×C₃₁	1	4	yes	—
48	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
49	C₂×C₃₁	#2252	1	1	yes	characteristic
50	C₂×C₃₁	#2262	1	2	yes	—
51	#125	—	4	2	no	—
52	C₂×C₁₆	D₄×C₃₁	1	1	yes	characteristic
53	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
54	#107	—	2	4	no	—
55	#106	—	4	2	no	—
56	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
57	C₃₂	Q₈×C₃₁	1	2	yes	—
58	C₃₂	Q₈×C₃₁	1	2	yes	—
59	C₃₁	#13732	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×C₈	D₈×C₃₁	1	1	yes	characteristic
61	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
62	C₄⋊C₄	—	4	4	no	—
63	C₄⋊C₄	—	8	4	no	—
64	C₄²	D₈×C₃₁	1	1	yes	characteristic
65	C₁₆	Q₁₆×C₃₁	1	2	yes	—
66	C₁₆	C₂×Q₈×C₃₁	1	1	yes	characteristic
67	C₁₆	C₂×Q₈×C₃₁	1	1	yes	characteristic
68	C₂×C₄	—	8	4	no	—
69	C₂×C₄	C₃₁×D₁₆	1	2	yes	—
70	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
71	C₈	C₃₁×Q₃₂	1	2	yes	—
72	C₈	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
73	C₈	C₂×Q₁₆×C₃₁	1	1	yes	characteristic
74	C₂²	C₂×C₃₁×D₁₆	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	16	4	no	—
77	C₄	C₃₁×#500	1	1	yes	characteristic
78	C₄	C₂×C₃₁×Q₃₂	1	1	yes	characteristic
79	C₂	C₃₁×#2252	1	1	yes	characteristic
80	C₂	C₃₁×#2262	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₁	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₃₁
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ C₄×C₈×C₃₁ ◁ C₄×C₁₆×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
27. #13732	C₃₁	direct (N × H)
59. C₃₁	#13732	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#2253	2
C₃₁×#1424	2
C₃₁×#1423	2
C₄×C₃₁×C₃₂	2
#13732	31

Subgroups — C31×#13732 #21470491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#13732 #21470491