Subgroups — C₃₁×#12902 #21469661

Order 7936.

278 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2153	C₂	1	3	yes	maximal
2	C₃₁×#2151	C₂	1	3	yes	maximal
3	C₃₁×#1747	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₁×M₃₂	C₂²	1	3	yes	—
5	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
6	C₃₁×#405	C₂²	1	3	yes	—
7	C₃₁×#364	—	2	6	no	—
8	C₃₁×C₄⋊C₁₆	—	2	6	no	—
9	C₃₁×#338	C₄	1	1	yes	characteristic
10	C₃₁×H(3,ℤ/4)	C₄	1	3	yes	—
11	C₂×M₁₆×C₃₁	C₂×C₄	1	3	yes	—
12	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
13	C₃₁×#117	C₂×C₄	1	3	yes	—
14	C₃₁×M₃₂	—	2	6	no	—
15	C₂×C₁₆×C₃₁	—	2	3	no	—
16	C₂×C₁₆×C₃₁	—	2	3	no	—
17	C₃₁×#97	Q₈	1	6	yes	—
18	C₄×C₈×C₃₁	D₄	1	6	yes	—
19	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
20	M₁₆×C₃₁	—	2	6	no	—
21	C₂×C₈×C₃₁	C₄⋊C₄	1	6	yes	—
22	C₂×C₈×C₃₁	C₂×D₄	1	3	yes	—
23	C₂×C₈×C₃₁	C₂×Q₈	1	3	yes	—
24	C₄⋊C₄×C₃₁	—	2	3	no	—
25	C₂²⋊C₄×C₃₁	—	2	3	no	—
26	C₄²×C₃₁	C₄⋊C₄	1	6	yes	—
27	C₁₆×C₃₁	—	4	1	no	—
28	C₁₆×C₃₁	—	4	3	no	—
29	#12902	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂³×C₃₁	#131	1	1	yes	characteristic
31	C₂×C₄×C₃₁	—	2	6	no	—
32	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	3	yes	—
33	C₂×C₄×C₃₁	#131	1	3	yes	—
34	C₈×C₃₁	—	2	6	no	—
35	C₈×C₃₁	#127	1	1	yes	characteristic
36	C₈×C₃₁	C₄⋊Q₈	1	3	yes	—
37	#2153	C₂×C₃₁	1	3	yes	—
38	#2151	C₂×C₃₁	1	3	yes	—
39	#1747	C₂×C₃₁	1	1	yes	characteristic
40	C₂²×C₃₁	—	4	1	no	—
41	C₂²×C₃₁	#424	1	3	yes	—
42	C₄×C₃₁	—	4	6	no	—
43	C₄×C₃₁	#384	1	1	yes	characteristic
44	C₄×C₃₁	#424	1	3	yes	—
45	C₂×M₃₂	C₂²×C₃₁	1	3	yes	—
46	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
47	#405	C₂²×C₃₁	1	3	yes	—
48	#364	—	2	6	no	—
49	C₄⋊C₁₆	—	2	6	no	—
50	#338	C₄×C₃₁	1	1	yes	characteristic
51	H(3,ℤ/4)	C₄×C₃₁	1	3	yes	—
52	C₂×C₃₁	—	2	3	no	—
53	C₂×C₃₁	#1843	1	1	yes	characteristic
54	C₂×M₁₆	C₂×C₄×C₃₁	1	3	yes	—
55	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
56	#117	C₂×C₄×C₃₁	1	3	yes	—
57	M₃₂	—	2	6	no	—
58	C₂×C₁₆	—	2	3	no	—
59	C₂×C₁₆	—	2	3	no	—
60	#97	Q₈×C₃₁	1	6	yes	—
61	C₄×C₈	D₄×C₃₁	1	6	yes	—
62	C₃₁	#12902	1	1	yes	characteristic, direct product factor, Sylow
63	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
64	M₁₆	—	2	6	no	—
65	C₂×C₈	C₄⋊C₄×C₃₁	1	6	yes	—
66	C₂×C₈	C₂×D₄×C₃₁	1	3	yes	—
67	C₂×C₈	C₂×Q₈×C₃₁	1	3	yes	—
68	C₄⋊C₄	—	2	3	no	—
69	C₂²⋊C₄	—	2	3	no	—
70	C₄²	C₄⋊C₄×C₃₁	1	6	yes	—
71	C₁₆	—	4	1	no	—
72	C₁₆	—	4	3	no	—
73	C₂³	C₃₁×#131	1	1	yes	characteristic
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	3	yes	—
76	C₂×C₄	C₃₁×#131	1	3	yes	—
77	C₈	—	2	6	no	—
78	C₈	C₃₁×#127	1	1	yes	characteristic
79	C₈	C₃₁×C₄⋊Q₈	1	3	yes	—
80	C₂²	—	4	1	no	—
81	C₂²	C₃₁×#424	1	3	yes	—
82	C₄	—	4	6	no	—
83	C₄	C₃₁×#384	1	1	yes	characteristic
84	C₄	C₃₁×#424	1	3	yes	—
85	C₂	—	2	3	no	—
86	C₂	C₃₁×#1843	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₃₁	#127
commutator	C₂²×C₄	C₂²×C₄×C₃₁
Frattini, cosocle	C₂²×C₈	C₂³×C₃₁
socle	C₂×C₃₁	#1843
prime radical	C₂³×C₃₁	#131
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₃₁ ◁ C₂²×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
29. #12902	C₃₁	direct (N × H)
62. C₃₁	#12902	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×#2153	2
C₃₁×#2151	2
C₃₁×#1747	2
#12902	31

Subgroups — C31×#12902 #21469661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#12902 #21469661