Subgroups — C₂×C₅⋊(C₁₇⋊(D₃₁⋊C₃)) #44539332

Order 31620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(C₁₇⋊(D₃₁⋊C₃))	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₇×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₆₃₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₁₇×C₃₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₇⋊(D₃₁⋊C₃)	—	5	1	no	maximal, Hall
6	D₂₆₃₅	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₁₇×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₇⋊(D₃₁⋊C₃)	—	5	2	no	—
9	C₂×C₁₇×C₃₁⋊C₃	D₅	1	1	yes	characteristic, complemented
10	C₅×C₁₇×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅₂₇	—	5	1	no	Hall
12	C₂×C₅⋊(D₃₁⋊C₃)	—	17	1	no	maximal, Hall
13	C₁₇×C₃₁⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₇×C₃₁	C₃×D₅	1	1	yes	characteristic, complemented
15	D₅₂₇	—	5	2	no	—
16	C₂×C₃×D₈₅	—	31	1	no	maximal, Hall
17	C₂×C₅×C₃₁⋊C₃	D₁₇	1	1	yes	characteristic, complemented
18	C₅⋊(D₃₁⋊C₃)	—	17	2	no	—
19	C₂×D₁₅₅	—	17	1	no	Hall
20	C₁₇×C₃₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₅×C₁₇	—	31	1	no	—
22	C₃×D₈₅	—	31	2	no	—
23	C₅×C₃₁⋊C₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
24	C₂×D₃₁⋊C₃	—	85	1	no	Hall
25	C₂×D₈₅	—	31	1	no	Hall
26	C₂×C₅×C₃₁	C₃×D₁₇	1	1	yes	characteristic, complemented
27	D₁₅₅	—	17	2	no	—
28	C₃×C₅×C₁₇	—	31	1	no	Hall
29	C₂×C₃×D₁₇	—	155	1	no	Hall
30	C₂×C₃₁⋊C₃	D₈₅	1	1	yes	characteristic, complemented
31	D₃₁⋊C₃	—	85	2	no	—
32	C₂×C₅×C₁₇	D₃₁⋊C₃	1	1	yes	characteristic, complemented
33	D₈₅	—	31	2	no	—
34	C₅×C₃₁	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
35	C₂×D₃₁	—	85	1	no	Hall
36	C₂×C₃×C₁₇	—	31	1	no	—
37	C₃×D₁₇	—	155	2	no	—
38	C₃₁⋊C₃	C₂×D₈₅	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₇	C₂×D₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
40	C₂×D₁₇	—	155	1	no	Hall
41	C₂×C₃₁	C₃×D₈₅	1	1	yes	characteristic, complemented
42	D₃₁	—	85	2	no	—
43	C₂×C₃×D₅	—	527	1	no	Hall
44	C₃×C₁₇	—	31	1	no	Hall
45	C₂×C₁₇	C₅⋊(D₃₁⋊C₃)	1	1	yes	characteristic, complemented
46	D₁₇	—	155	2	no	—
47	C₃₁	C₂×C₃×D₈₅	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃×C₅	—	31	1	no	—
49	C₃×D₅	—	527	2	no	—
50	C₂×D₅	—	527	1	no	Hall
51	C₁₇	C₂×C₅⋊(D₃₁⋊C₃)	1	1	yes	characteristic, complemented, Sylow
52	C₃×C₅	—	31	1	no	Hall
53	C₂²×C₃	—	2635	1	no	Hall
54	C₂×C₅	C₁₇⋊(D₃₁⋊C₃)	1	1	yes	characteristic, complemented
55	D₅	—	527	2	no	—
56	C₂×C₃	—	31	1	no	—
57	C₂×C₃	—	2635	2	no	—
58	C₅	C₂×C₁₇⋊(D₃₁⋊C₃)	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	2635	1	no	Sylow
60	C₃	—	31	1	no	Sylow
61	C₂	—	2635	2	no	—
62	C₂	C₅⋊(C₁₇⋊(D₃₁⋊C₃))	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊(C₁₇⋊(D₃₁⋊C₃))
commutator, cosocle, hypocenter	C₅×C₁₇×C₃₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₇×C₃₁	C₂×C₃
LCS	G ▷ C₅×C₁₇×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₅⋊(C₁₇⋊(D₃₁⋊C₃))	C₂	direct (N × H)
2. C₂×C₅×C₁₇×C₃₁⋊C₃	C₂	semidirect
3. C₂×D₂₆₃₅	C₃	semidirect
4. C₅×C₁₇×C₃₁⋊C₃	C₂²	semidirect
6. D₂₆₃₅	C₂×C₃	semidirect
7. C₂×C₅×C₁₇×C₃₁	C₂×C₃	semidirect
9. C₂×C₁₇×C₃₁⋊C₃	D₅	semidirect
10. C₅×C₁₇×C₃₁	C₂²×C₃	semidirect
13. C₁₇×C₃₁⋊C₃	C₂×D₅	semidirect
14. C₂×C₁₇×C₃₁	C₃×D₅	semidirect
17. C₂×C₅×C₃₁⋊C₃	D₁₇	semidirect
20. C₁₇×C₃₁	C₂×C₃×D₅	semidirect
23. C₅×C₃₁⋊C₃	C₂×D₁₇	semidirect
26. C₂×C₅×C₃₁	C₃×D₁₇	semidirect
30. C₂×C₃₁⋊C₃	D₈₅	semidirect
32. C₂×C₅×C₁₇	D₃₁⋊C₃	semidirect
34. C₅×C₃₁	C₂×C₃×D₁₇	semidirect
38. C₃₁⋊C₃	C₂×D₈₅	semidirect
39. C₅×C₁₇	C₂×D₃₁⋊C₃	semidirect
41. C₂×C₃₁	C₃×D₈₅	semidirect
45. C₂×C₁₇	C₅⋊(D₃₁⋊C₃)	semidirect
47. C₃₁	C₂×C₃×D₈₅	semidirect
51. C₁₇	C₂×C₅⋊(D₃₁⋊C₃)	semidirect
54. C₂×C₅	C₁₇⋊(D₃₁⋊C₃)	semidirect
58. C₅	C₂×C₁₇⋊(D₃₁⋊C₃)	semidirect
62. C₂	C₅⋊(C₁₇⋊(D₃₁⋊C₃))	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅⋊(C₁₇⋊(D₃₁⋊C₃))	2
C₂×C₅×C₁₇×C₃₁⋊C₃	2
C₂×D₂₆₃₅	3
C₂×C₁₇⋊(D₃₁⋊C₃)	5
C₂×C₅⋊(D₃₁⋊C₃)	17
C₂×C₃×D₈₅	31

Subgroups — C2×C5⋊(C17⋊(D31⋊C3)) #44539332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊(C₁₇⋊(D₃₁⋊C₃)) #44539332