Subgroups — D₁₇×C₅⋊(D₃₁⋊C₃) #44539316

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	1	yes	maximal, characteristic, complemented
2	C₁₇×C₅⋊(D₃₁⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₇×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇×D₁₅₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅×C₁₇×C₃₁⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₇×D₃₁⋊C₃	—	5	1	no	maximal, Hall
7	D₂₆₃₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₇×D₁₅₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₃₁×D₁₇	C₂×C₃	1	1	yes	characteristic, complemented
10	C₁₇⋊(D₃₁⋊C₃)	—	5	1	no	—
11	D₁₇×C₃₁⋊C₃	D₅	1	1	yes	characteristic, complemented
12	C₁₇×D₃₁⋊C₃	—	5	1	no	—
13	C₅×C₁₇×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	D₁₇×D₃₁	—	5	1	no	Hall
15	C₂×C₅⋊(D₃₁⋊C₃)	—	17	1	no	maximal, Hall
16	C₁₇×C₃₁⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	D₅₂₇	—	5	1	no	—
18	C₁₇×D₃₁	—	5	1	no	—
19	C₃₁×D₁₇	C₃×D₅	1	1	yes	characteristic, complemented
20	C₃×D₅×D₁₇	—	31	1	no	maximal, Hall
21	C₂×C₅×C₃₁⋊C₃	—	17	1	no	—
22	C₅⋊(D₃₁⋊C₃)	—	17	1	no	—
23	C₅⋊(D₃₁⋊C₃)	D₁₇	1	1	yes	characteristic, direct product factor
24	C₂×D₁₅₅	—	17	1	no	Hall
25	C₁₇×C₃₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
26	C₃×D₈₅	—	31	1	no	—
27	C₃×D₅×C₁₇	—	31	1	no	—
28	C₃×C₅×D₁₇	—	31	1	no	—
29	C₅×C₃₁⋊C₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
30	C₂×D₃₁⋊C₃	—	85	1	no	Hall
31	D₅×D₁₇	—	31	1	no	Hall
32	C₂×C₅×C₃₁	—	17	1	no	—
33	D₁₅₅	—	17	1	no	—
34	D₁₅₅	C₃×D₁₇	1	1	yes	characteristic, complemented
35	C₃×C₅×C₁₇	—	31	1	no	Hall
36	C₂×C₃×D₁₇	—	155	1	no	Hall
37	C₂×C₃₁⋊C₃	—	17	1	no	—
38	D₃₁⋊C₃	—	5	1	no	—
39	D₃₁⋊C₃	—	85	1	no	—
40	D₈₅	—	31	1	no	—
41	C₅×D₁₇	D₃₁⋊C₃	1	1	yes	characteristic, complemented
42	D₅×C₁₇	—	31	1	no	—
43	C₅×C₃₁	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
44	C₂×D₃₁	—	85	1	no	Hall
45	C₂×C₃×C₁₇	—	155	1	no	—
46	C₃×D₁₇	—	31	1	no	—
47	C₃×D₁₇	—	155	1	no	—
48	C₃₁⋊C₃	D₅×D₁₇	1	1	yes	characteristic, complemented, Hall
49	C₅×C₁₇	C₂×D₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
50	C₂×D₁₇	—	155	1	no	Hall
51	C₂×C₃₁	—	17	1	no	—
52	D₃₁	—	5	1	no	—
53	D₃₁	—	85	1	no	—
54	C₂×C₃×D₅	—	527	1	no	Hall
55	C₃×C₁₇	—	31	1	no	Hall
56	C₂×C₁₇	—	155	1	no	—
57	D₁₇	—	155	1	no	—
58	D₁₇	C₅⋊(D₃₁⋊C₃)	1	1	yes	characteristic, direct product factor
59	C₃₁	C₃×D₅×D₁₇	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃×C₅	—	527	1	no	—
61	C₃×D₅	—	527	1	no	—
62	C₃×D₅	—	31	1	no	—
63	C₂×D₅	—	527	1	no	Hall
64	C₁₇	C₂×C₅⋊(D₃₁⋊C₃)	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	—	31	1	no	Hall
66	C₂²×C₃	—	2635	1	no	Hall
67	C₂×C₅	—	17	1	no	—
68	D₅	—	527	1	no	—
69	D₅	—	31	1	no	—
70	C₂×C₃	—	527	1	no	—
71	C₂×C₃	—	2635	1	no	—
72	C₂×C₃	—	155	1	no	—
73	C₅	D₁₇×D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	2635	1	no	Sylow
75	C₃	—	31	1	no	Sylow
76	C₂	—	17	1	no	—
77	C₂	—	2635	1	no	—
78	C₂	—	155	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₇×C₃₁	C₂²×C₃
LCS	G ▷ C₅×C₁₇×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅⋊(C₁₇⋊(D₃₁⋊C₃))	C₂	semidirect
2. C₁₇×C₅⋊(D₃₁⋊C₃)	C₂	semidirect
3. C₅×D₁₇×C₃₁⋊C₃	C₂	semidirect
4. D₁₇×D₁₅₅	C₃	semidirect
5. C₅×C₁₇×C₃₁⋊C₃	C₂²	semidirect
7. D₂₆₃₅	C₂×C₃	semidirect
8. C₁₇×D₁₅₅	C₂×C₃	semidirect
9. C₅×C₃₁×D₁₇	C₂×C₃	semidirect
11. D₁₇×C₃₁⋊C₃	D₅	semidirect
13. C₅×C₁₇×C₃₁	C₂²×C₃	semidirect
16. C₁₇×C₃₁⋊C₃	C₂×D₅	semidirect
19. C₃₁×D₁₇	C₃×D₅	semidirect
23. C₅⋊(D₃₁⋊C₃)	D₁₇	direct (N × H)
25. C₁₇×C₃₁	C₂×C₃×D₅	semidirect
29. C₅×C₃₁⋊C₃	C₂×D₁₇	semidirect
34. D₁₅₅	C₃×D₁₇	semidirect
41. C₅×D₁₇	D₃₁⋊C₃	semidirect
43. C₅×C₃₁	C₂×C₃×D₁₇	semidirect
48. C₃₁⋊C₃	D₅×D₁₇	semidirect
49. C₅×C₁₇	C₂×D₃₁⋊C₃	semidirect
58. D₁₇	C₅⋊(D₃₁⋊C₃)	direct (N × H)
59. C₃₁	C₃×D₅×D₁₇	semidirect
64. C₁₇	C₂×C₅⋊(D₃₁⋊C₃)	semidirect
73. C₅	D₁₇×D₃₁⋊C₃	semidirect

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
C₁₇×C₅⋊(D₃₁⋊C₃)	2
C₅×D₁₇×C₃₁⋊C₃	2
D₁₇×D₁₅₅	3
D₁₇×D₃₁⋊C₃	5
C₂×C₅⋊(D₃₁⋊C₃)	17
C₃×D₅×D₁₇	31

Subgroups — D17×C5⋊(D31⋊C3) #44539316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₇×C₅⋊(D₃₁⋊C₃) #44539316