Subgroups — C₃₁×#7541 #21464300

Order 7936.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×D₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃₁×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#1425	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×D₁₆	—	2	1	no	—
5	C₃₁×D₃₂	—	2	1	no	—
6	C₃₁×D₃₂	C₄	1	2	yes	—
7	C₂×C₃₁×C₃₂	C₂²	1	1	yes	characteristic
8	C₃₁×#368	—	2	1	no	—
9	C₃₁×C₆₄	—	2	1	no	—
10	C₂×D₈×C₃₁	—	4	1	no	—
11	C₃₁×D₁₆	—	2	2	no	—
12	C₃₁×D₁₆	—	4	1	no	—
13	C₂×C₁₆×C₃₁	D₄	1	1	yes	characteristic
14	C₃₁×#108	—	4	1	no	—
15	C₃₁×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₃₁×C₃₂	D₄	1	1	yes	characteristic
17	C₂×D₄×C₃₁	—	8	1	no	—
18	D₈×C₃₁	—	4	2	no	—
19	D₈×C₃₁	—	8	1	no	—
20	M₁₆×C₃₁	—	8	1	no	—
21	C₂×C₈×C₃₁	D₈	1	1	yes	characteristic
22	C₁₆×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₃₁	SD₁₆	1	1	yes	characteristic
24	#7541	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₃₁	—	16	1	no	—
26	D₄×C₃₁	—	8	2	no	—
27	D₄×C₃₁	—	16	1	no	—
28	C₂×C₄×C₃₁	D₁₆	1	1	yes	characteristic
29	C₈×C₃₁	—	16	1	no	—
30	C₈×C₃₁	#102	1	1	yes	characteristic
31	C₈×C₃₁	SD₃₂	1	1	yes	characteristic
32	C₂×D₃₂	C₂×C₃₁	1	1	yes	characteristic
33	M₁₂₈	C₂×C₃₁	1	1	yes	characteristic, complemented
34	#1425	C₂×C₃₁	1	1	yes	characteristic, complemented
35	C₂²×C₃₁	—	16	2	no	—
36	C₂²×C₃₁	—	32	2	no	—
37	C₂²×C₃₁	SD₆₄	1	1	yes	characteristic
38	C₄×C₃₁	#357	1	1	yes	characteristic
39	C₄×C₃₁	D₃₂	1	1	yes	characteristic
40	C₂×D₁₆	—	2	1	no	—
41	D₃₂	—	2	1	no	—
42	D₃₂	C₄×C₃₁	1	2	yes	—
43	C₂×C₃₂	C₂²×C₃₁	1	1	yes	characteristic
44	#368	—	2	1	no	—
45	C₆₄	—	2	1	no	—
46	C₂×C₃₁	—	2	1	no	—
47	C₂×C₃₁	—	32	2	no	—
48	C₂×C₃₁	#1415	1	1	yes	characteristic
49	C₂×D₈	—	4	1	no	—
50	D₁₆	—	2	2	no	—
51	D₁₆	—	4	1	no	—
52	C₂×C₁₆	D₄×C₃₁	1	1	yes	characteristic
53	#108	—	4	1	no	—
54	C₃₂	C₂×C₄×C₃₁	1	1	yes	characteristic
55	C₃₂	D₄×C₃₁	1	1	yes	characteristic
56	C₃₁	#7541	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×D₄	—	8	1	no	—
58	D₈	—	4	2	no	—
59	D₈	—	8	1	no	—
60	M₁₆	—	8	1	no	—
61	C₂×C₈	D₈×C₃₁	1	1	yes	characteristic
62	C₁₆	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
63	C₁₆	SD₁₆×C₃₁	1	1	yes	characteristic
64	C₂³	—	16	1	no	—
65	D₄	—	8	2	no	—
66	D₄	—	16	1	no	—
67	C₂×C₄	C₃₁×D₁₆	1	1	yes	characteristic
68	C₈	—	16	1	no	—
69	C₈	C₃₁×#102	1	1	yes	characteristic
70	C₈	C₃₁×SD₃₂	1	1	yes	characteristic
71	C₂²	—	16	2	no	—
72	C₂²	—	32	2	no	—
73	C₂²	C₃₁×SD₆₄	1	1	yes	characteristic
74	C₄	C₃₁×#357	1	1	yes	characteristic
75	C₄	C₃₁×D₃₂	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	32	2	no	—
78	C₂	C₃₁×#1415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃₁	#1415
commutator	C₃₂	C₂×C₄×C₃₁
Frattini, cosocle	C₂×C₃₂	C₂²×C₃₁
prime radical	C₂×C₃₁×D₃₂	C₂
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₈×C₃₁ ◁ C₂×C₁₆×C₃₁ ◁ C₂×C₃₁×C₃₂ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×M₁₂₈	C₂	semidirect
3. C₃₁×#1425	C₂	semidirect
24. #7541	C₃₁	direct (N × H)
33. M₁₂₈	C₂×C₃₁	semidirect
34. #1425	C₂×C₃₁	semidirect
56. C₃₁	#7541	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×D₃₂	2
C₃₁×M₁₂₈	2
C₃₁×#1425	2
#7541	31

Subgroups — C31×#7541 #21464300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#7541 #21464300