Subgroups — C₃₁×D₂₁⋊D₁₃ #46799600

Order 33852.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃₁×D₂₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₃₁×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃₁×D₉₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₁₃×C₃₁	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃₁×D₉₁	D₃	1	1	yes	characteristic, complemented
7	C₁₃×D₇×C₃₁	—	3	1	no	—
8	C₇×D₁₃×C₃₁	—	3	1	no	—
9	D₃×D₁₃×C₃₁	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×D₇×C₃₁	—	13	1	no	maximal, Hall
12	C₃₁×D₃₉	D₇	1	1	yes	characteristic, complemented
13	D₃×C₁₃×C₃₁	—	7	1	no	—
14	C₃×D₁₃×C₃₁	—	7	1	no	—
15	C₂×D₁₃×C₃₁	—	21	1	no	Hall
16	C₃₁×D₂₁	D₁₃	1	1	yes	characteristic, complemented
17	D₃×C₇×C₃₁	—	13	1	no	—
18	C₃×D₇×C₃₁	—	13	1	no	—
19	C₃×C₁₃×C₃₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	D₂₁⋊D₁₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×D₇×C₃₁	—	39	1	no	Hall
22	C₂×C₁₃×C₃₁	—	21	1	no	—
23	D₁₃×C₃₁	—	3	1	no	—
24	D₁₃×C₃₁	—	7	1	no	—
25	C₃×C₇×C₃₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
26	C₁₃×D₂₁	C₂×C₃₁	1	1	yes	characteristic, complemented
27	C₇×D₃₉	C₂×C₃₁	1	1	yes	characteristic, complemented
28	C₃×D₉₁	C₂×C₃₁	1	1	yes	characteristic, complemented
29	C₂×C₇×C₃₁	—	39	1	no	—
30	D₇×C₃₁	—	3	1	no	—
31	D₇×C₃₁	—	13	1	no	—
32	C₁₃×C₃₁	D₃×D₇	1	1	yes	characteristic, complemented, Hall
33	C₂×D₃×C₃₁	—	91	1	no	Hall
34	D₇×D₁₃	—	3	1	no	Hall
35	C₃×C₇×C₁₃	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
36	C₇×C₃₁	D₃×D₁₃	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₃₁	—	91	1	no	—
38	D₃×C₃₁	—	7	1	no	—
39	D₃×C₃₁	—	13	1	no	—
40	D₉₁	D₃×C₃₁	1	1	yes	characteristic, complemented
41	C₇×D₁₃	—	3	1	no	—
42	C₁₃×D₇	—	3	1	no	—
43	D₃×D₁₃	—	7	1	no	Hall
44	C₂²×C₃₁	—	273	1	no	Hall
45	C₃×C₃₁	D₇×D₁₃	1	1	yes	characteristic, complemented, Hall
46	C₇×C₁₃	C₂×D₃×C₃₁	1	1	yes	characteristic, complemented, Hall
47	D₃×D₇	—	13	1	no	Hall
48	D₃₉	D₇×C₃₁	1	1	yes	characteristic, complemented
49	C₃×D₁₃	—	7	1	no	—
50	D₃×C₁₃	—	7	1	no	—
51	C₂×C₃₁	—	21	1	no	—
52	C₂×C₃₁	—	39	1	no	—
53	C₂×C₃₁	—	91	1	no	—
54	C₂×D₁₃	—	21	1	no	Hall
55	D₂₁	D₁₃×C₃₁	1	1	yes	characteristic, complemented
56	C₃×D₇	—	13	1	no	—
57	D₃×C₇	—	13	1	no	—
58	C₃×C₁₃	C₂×D₇×C₃₁	1	1	yes	characteristic, complemented, Hall
59	C₃₁	D₂₁⋊D₁₃	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×D₇	—	39	1	no	Hall
61	C₂×C₁₃	—	21	1	no	—
62	D₁₃	—	3	1	no	—
63	D₁₃	—	7	1	no	—
64	C₃×C₇	C₂×D₁₃×C₃₁	1	1	yes	characteristic, complemented, Hall
65	C₂×C₇	—	39	1	no	—
66	D₇	—	3	1	no	—
67	D₇	—	13	1	no	—
68	C₁₃	D₃×D₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	91	1	no	Hall
70	C₇	D₃×D₁₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	91	1	no	—
72	D₃	—	7	1	no	—
73	D₃	—	13	1	no	—
74	C₂²	—	273	1	no	Sylow
75	C₃	D₇×D₁₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	21	1	no	—
77	C₂	—	39	1	no	—
78	C₂	—	91	1	no	—

	subgroup	G/H
center, hypercenter	C₃₁	D₂₁⋊D₁₃
commutator, cosocle, hypocenter	C₃×C₇×C₁₃	C₂²×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₃₁	C₂²
LCS	G ▷ C₃×C₇×C₁₃
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃₁×D₂₁	C₂	semidirect
2. C₇×C₃₁×D₃₉	C₂	semidirect
3. C₃×C₃₁×D₉₁	C₂	semidirect
5. C₃×C₇×C₁₃×C₃₁	C₂²	semidirect
6. C₃₁×D₉₁	D₃	semidirect
10. C₇×C₁₃×C₃₁	C₂×D₃	semidirect
12. C₃₁×D₃₉	D₇	semidirect
16. C₃₁×D₂₁	D₁₃	semidirect
19. C₃×C₁₃×C₃₁	C₂×D₇	semidirect
20. D₂₁⋊D₁₃	C₃₁	direct (N × H)
25. C₃×C₇×C₃₁	C₂×D₁₃	semidirect
26. C₁₃×D₂₁	C₂×C₃₁	semidirect
27. C₇×D₃₉	C₂×C₃₁	semidirect
28. C₃×D₉₁	C₂×C₃₁	semidirect
32. C₁₃×C₃₁	D₃×D₇	semidirect
35. C₃×C₇×C₁₃	C₂²×C₃₁	semidirect
36. C₇×C₃₁	D₃×D₁₃	semidirect
40. D₉₁	D₃×C₃₁	semidirect
45. C₃×C₃₁	D₇×D₁₃	semidirect
46. C₇×C₁₃	C₂×D₃×C₃₁	semidirect
48. D₃₉	D₇×C₃₁	semidirect
55. D₂₁	D₁₃×C₃₁	semidirect
58. C₃×C₁₃	C₂×D₇×C₃₁	semidirect
59. C₃₁	D₂₁⋊D₁₃	direct (N × H)
64. C₃×C₇	C₂×D₁₃×C₃₁	semidirect
68. C₁₃	D₃×D₇×C₃₁	semidirect
70. C₇	D₃×D₁₃×C₃₁	semidirect
75. C₃	D₇×D₁₃×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₃₁×D₂₁	2
C₇×C₃₁×D₃₉	2
C₃×C₃₁×D₉₁	2
D₇×D₁₃×C₃₁	3
D₃×D₁₃×C₃₁	7
D₃×D₇×C₃₁	13
D₂₁⋊D₁₃	31

Subgroups — C31×D21⋊D13 #46799600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×D₂₁⋊D₁₃ #46799600