Subgroups — C₃₁×#540 #14520721

Order 1984.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#123	C₂	1	4	yes	maximal, complemented
4	C₃₁×#121	C₂	1	4	yes	maximal, complemented
5	C₃₁×#121	C₂	1	2	yes	maximal, complemented
6	C₄×D₄×C₃₁	C₂	1	2	yes	maximal, complemented
7	C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄×C₃₁	C₂²	1	2	yes	—
9	C₂×D₄×C₃₁	C₂²	1	4	yes	—
10	C₂×D₄×C₃₁	C₂²	1	4	yes	—
11	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₃₁	C₂²	1	4	yes	—
13	C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
14	C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
15	C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
16	C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
17	C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
18	C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
19	C₄²×C₃₁	C₂²	1	1	yes	characteristic
20	C₄²×C₃₁	C₂²	1	1	yes	characteristic
21	C₂³×C₃₁	C₂³	1	1	yes	characteristic
22	C₂³×C₃₁	C₂³	1	4	yes	—
23	D₄×C₃₁	—	2	4	no	—
24	D₄×C₃₁	—	4	4	no	—
25	D₄×C₃₁	—	4	4	no	—
26	C₂×C₄×C₃₁	—	2	2	no	—
27	C₂×C₄×C₃₁	—	4	4	no	—
28	C₂×C₄×C₃₁	C₂³	1	2	yes	—
29	C₂×C₄×C₃₁	C₂³	1	2	yes	—
30	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
31	C₂×C₄×C₃₁	C₂³	1	4	yes	—
32	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
33	C₂²×C₃₁	—	2	1	no	—
34	C₂²×C₃₁	—	2	4	no	—
35	C₂²×C₃₁	—	2	4	no	—
36	C₂²×C₃₁	—	2	2	no	—
37	C₂²×C₃₁	—	2	4	no	—
38	C₂²×C₃₁	C₂⁴	1	1	yes	characteristic
39	C₄×C₃₁	—	2	1	no	—
40	C₄×C₃₁	—	2	2	no	—
41	C₄×C₃₁	—	2	4	no	—
42	C₄×C₃₁	—	2	2	no	—
43	C₄×C₃₁	#41	1	2	yes	—
44	#540	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×C₃₁	—	4	1	no	—
46	C₂×C₃₁	—	4	4	no	—
47	C₂×C₃₁	C₂×#41	1	1	yes	characteristic
48	C₂×C₃₁	H(5,𝔽₂)	1	2	yes	—
49	#127	C₂×C₃₁	1	1	yes	characteristic, complemented
50	#125	C₂×C₃₁	1	1	yes	characteristic, complemented
51	#123	C₂×C₃₁	1	4	yes	complemented
52	#121	C₂×C₃₁	1	4	yes	complemented
53	#121	C₂×C₃₁	1	2	yes	complemented
54	C₄×D₄	C₂×C₃₁	1	2	yes	complemented
55	#117	C₂×C₃₁	1	1	yes	characteristic, complemented
56	C₃₁	#540	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×D₄	C₂²×C₃₁	1	2	yes	—
58	C₂×D₄	C₂²×C₃₁	1	4	yes	—
59	C₂×D₄	C₂²×C₃₁	1	4	yes	—
60	C₂²×C₄	C₂²×C₃₁	1	1	yes	characteristic
61	C₂²×C₄	C₂²×C₃₁	1	4	yes	—
62	C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
63	C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
64	C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
65	C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
66	C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
67	C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
68	C₄²	C₂²×C₃₁	1	1	yes	characteristic
69	C₄²	C₂²×C₃₁	1	1	yes	characteristic
70	C₂³	C₂³×C₃₁	1	1	yes	characteristic
71	C₂³	C₂³×C₃₁	1	4	yes	—
72	D₄	—	2	4	no	—
73	D₄	—	4	4	no	—
74	D₄	—	4	4	no	—
75	C₂×C₄	—	2	2	no	—
76	C₂×C₄	—	4	4	no	—
77	C₂×C₄	C₂³×C₃₁	1	2	yes	—
78	C₂×C₄	C₂³×C₃₁	1	2	yes	—
79	C₂×C₄	C₂³×C₃₁	1	1	yes	characteristic
80	C₂×C₄	C₂³×C₃₁	1	4	yes	—
81	C₂×C₄	C₂³×C₃₁	1	1	yes	characteristic
82	C₂²	—	2	1	no	—
83	C₂²	—	2	4	no	—
84	C₂²	—	2	4	no	—
85	C₂²	—	2	2	no	—
86	C₂²	—	2	4	no	—
87	C₂²	C₂⁴×C₃₁	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	2	no	—
90	C₄	—	2	4	no	—
91	C₄	—	2	2	no	—
92	C₄	#41×C₃₁	1	2	yes	—
93	C₂	—	4	1	no	—
94	C₂	—	4	4	no	—
95	C₂	C₂×#41×C₃₁	1	1	yes	characteristic
96	C₂	C₃₁×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#127	C₂	semidirect
2. C₃₁×#125	C₂	semidirect
3. C₃₁×#123	C₂	semidirect
4. C₃₁×#121	C₂	semidirect
5. C₃₁×#121	C₂	semidirect
6. C₄×D₄×C₃₁	C₂	semidirect
7. C₃₁×#117	C₂	semidirect
44. #540	C₃₁	direct (N × H)
49. #127	C₂×C₃₁	semidirect
50. #125	C₂×C₃₁	semidirect
51. #123	C₂×C₃₁	semidirect
52. #121	C₂×C₃₁	semidirect
53. #121	C₂×C₃₁	semidirect
54. C₄×D₄	C₂×C₃₁	semidirect
55. #117	C₂×C₃₁	semidirect
56. C₃₁	#540	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×#127	2
C₃₁×#125	2
C₃₁×#123	2
C₃₁×#121	2
C₄×D₄×C₃₁	2
C₃₁×#117	2
#540	31

Subgroups — C31×#540 #14520721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#540 #14520721