Subgroups — C₃₁×#469 #14520650

Order 1984.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#121	C₂	1	2	yes	maximal, complemented
4	C₃₁×#106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#102	C₂	1	2	yes	maximal, complemented
6	C₂×D₄×C₃₁	—	2	2	no	—
7	C₂×D₄×C₃₁	C₂²	1	2	yes	—
8	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
9	D₈×C₃₁	—	2	2	no	—
10	M₁₆×C₃₁	—	2	2	no	—
11	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
14	C₂²⋊C₄×C₃₁	—	2	2	no	—
15	C₂³×C₃₁	—	2	2	no	—
16	C₂³×C₃₁	D₄	1	1	yes	characteristic
17	D₄×C₃₁	—	2	2	no	—
18	D₄×C₃₁	—	2	2	no	—
19	D₄×C₃₁	—	4	4	no	—
20	C₂×C₄×C₃₁	—	2	1	no	—
21	C₂×C₄×C₃₁	—	2	1	no	—
22	C₂×C₄×C₃₁	—	2	2	no	—
23	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
24	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
25	C₈×C₃₁	—	2	1	no	—
26	C₈×C₃₁	D₄	1	2	yes	complemented
27	C₂²×C₃₁	—	2	1	no	—
28	C₂²×C₃₁	—	2	2	no	—
29	C₂²×C₃₁	—	4	2	no	—
30	C₂²×C₃₁	—	4	2	no	—
31	C₂²×C₃₁	—	4	2	no	—
32	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
33	C₄×C₃₁	—	2	1	no	—
34	C₄×C₃₁	—	4	2	no	—
35	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
36	C₄×C₃₁	#41	1	1	yes	characteristic
37	#469	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂×C₃₁	—	4	1	no	—
39	C₂×C₃₁	—	8	2	no	—
40	C₂×C₃₁	#121	1	1	yes	characteristic
41	C₂×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
42	C₂×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
43	C₂×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
44	#121	C₂×C₃₁	1	2	yes	complemented
45	#106	C₂×C₃₁	1	1	yes	characteristic, complemented
46	#102	C₂×C₃₁	1	2	yes	complemented
47	C₃₁	#469	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×D₄	—	2	2	no	—
49	C₂×D₄	C₂²×C₃₁	1	2	yes	—
50	C₂²×C₄	C₂²×C₃₁	1	1	yes	characteristic
51	D₈	—	2	2	no	—
52	M₁₆	—	2	2	no	—
53	C₂×C₈	C₂²×C₃₁	1	1	yes	characteristic
54	C₂×C₈	C₂²×C₃₁	1	1	yes	characteristic
55	C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
56	C₂²⋊C₄	—	2	2	no	—
57	C₂³	—	2	2	no	—
58	C₂³	D₄×C₃₁	1	1	yes	characteristic
59	D₄	—	2	2	no	—
60	D₄	—	2	2	no	—
61	D₄	—	4	4	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	D₄×C₃₁	1	1	yes	characteristic
66	C₂×C₄	C₂³×C₃₁	1	1	yes	characteristic
67	C₈	—	2	1	no	—
68	C₈	D₄×C₃₁	1	2	yes	complemented
69	C₂²	—	2	1	no	—
70	C₂²	—	2	2	no	—
71	C₂²	—	4	2	no	—
72	C₂²	—	4	2	no	—
73	C₂²	—	4	2	no	—
74	C₂²	C₂×D₄×C₃₁	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	2	no	—
77	C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
78	C₄	#41×C₃₁	1	1	yes	characteristic
79	C₂	—	4	1	no	—
80	C₂	—	8	2	no	—
81	C₂	C₃₁×#121	1	1	yes	characteristic
82	C₂	C₃₁×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₈×C₃₁	C₂	semidirect
2. C₂×M₁₆×C₃₁	C₂	semidirect
3. C₃₁×#121	C₂	semidirect
4. C₃₁×#106	C₂	semidirect
5. C₃₁×#102	C₂	semidirect
26. C₈×C₃₁	D₄	semidirect
37. #469	C₃₁	direct (N × H)
42. C₂×D₈	C₂×C₃₁	semidirect
43. C₂×M₁₆	C₂×C₃₁	semidirect
44. #121	C₂×C₃₁	semidirect
45. #106	C₂×C₃₁	semidirect
46. #102	C₂×C₃₁	semidirect
47. C₃₁	#469	direct (N × H)
68. C₈	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×D₈×C₃₁	2
C₂×M₁₆×C₃₁	2
C₃₁×#121	2
C₃₁×#106	2
C₃₁×#102	2
#469	31

Subgroups — C31×#469 #14520650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#469 #14520650