Subgroups — C₅×C₁₇×C₃⋊(C₇⋊D₇) #38735995

Order 24990.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₇×C₇⋊D₇	—	3	1	no	maximal, Hall
3	C₁₇×C₃⋊(C₇⋊D₇)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇²×C₁₇	D₃	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₇×D₂₁	—	7	8	no	maximal
6	C₃×C₇²×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₇×C₁₇	D₇	1	8	yes	complemented
8	C₁₇×C₇⋊D₇	—	3	1	no	Hall
9	C₅×C₃⋊(C₇⋊D₇)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅×D₇×C₁₇	—	21	8	no	—
11	C₇²×C₁₇	C₅×D₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×C₇²	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
13	C₁₇×D₂₁	—	7	8	no	—
14	C₅×C₇×C₁₇	D₂₁	1	8	yes	complemented
15	C₅×D₃×C₁₇	—	49	1	no	Hall
16	C₅×C₇⋊D₇	—	3	1	no	Hall
17	C₃×C₇×C₁₇	C₅×D₇	1	8	yes	complemented
18	C₃⋊(C₇⋊D₇)	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₅×C₁₇	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
20	C₅×C₇²	D₃×C₁₇	1	1	yes	characteristic, complemented, Hall
21	D₇×C₁₇	—	21	8	no	—
22	C₅×D₂₁	—	7	8	no	—
23	C₂×C₅×C₁₇	—	147	1	no	Hall
24	C₃×C₇²	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
25	C₇×C₁₇	C₅×D₂₁	1	8	yes	complemented
26	C₃×C₅×C₇	D₇×C₁₇	1	8	yes	complemented
27	D₃×C₁₇	—	49	1	no	Hall
28	C₇⋊D₇	—	3	1	no	Hall
29	C₅×C₁₇	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor, Hall
30	C₅×D₇	—	21	8	no	—
31	C₃×C₁₇	C₅×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
32	C₇²	C₅×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
33	D₂₁	—	7	8	no	—
34	C₅×C₇	C₁₇×D₂₁	1	8	yes	complemented
35	C₂×C₁₇	—	147	1	no	Hall
36	C₅×D₃	—	49	1	no	Hall
37	C₃×C₇	C₅×D₇×C₁₇	1	8	yes	complemented
38	C₁₇	C₅×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor, Sylow
39	C₃×C₅	C₁₇×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
40	D₇	—	21	8	no	—
41	C₂×C₅	—	147	1	no	Hall
42	C₇	C₅×C₁₇×D₂₁	1	8	yes	complemented
43	D₃	—	49	1	no	Hall
44	C₅	C₁₇×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₅×C₁₇×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	147	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₇	C₃⋊(C₇⋊D₇)
commutator, cosocle, hypocenter	C₃×C₇²	C₂×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₇	C₂
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇²×C₁₇	C₂	semidirect
3. C₁₇×C₃⋊(C₇⋊D₇)	C₅	direct (N × H)
4. C₅×C₇²×C₁₇	D₃	semidirect
6. C₃×C₇²×C₁₇	C₂×C₅	semidirect
7. C₃×C₅×C₇×C₁₇	D₇	semidirect
9. C₅×C₃⋊(C₇⋊D₇)	C₁₇	direct (N × H)
11. C₇²×C₁₇	C₅×D₃	semidirect
12. C₃×C₅×C₇²	C₂×C₁₇	semidirect
14. C₅×C₇×C₁₇	D₂₁	semidirect
17. C₃×C₇×C₁₇	C₅×D₇	semidirect
18. C₃⋊(C₇⋊D₇)	C₅×C₁₇	direct (N × H)
19. C₃×C₅×C₁₇	C₇⋊D₇	semidirect
20. C₅×C₇²	D₃×C₁₇	semidirect
24. C₃×C₇²	C₂×C₅×C₁₇	semidirect
25. C₇×C₁₇	C₅×D₂₁	semidirect
26. C₃×C₅×C₇	D₇×C₁₇	semidirect
29. C₅×C₁₇	C₃⋊(C₇⋊D₇)	direct (N × H)
31. C₃×C₁₇	C₅×C₇⋊D₇	semidirect
32. C₇²	C₅×D₃×C₁₇	semidirect
34. C₅×C₇	C₁₇×D₂₁	semidirect
37. C₃×C₇	C₅×D₇×C₁₇	semidirect
38. C₁₇	C₅×C₃⋊(C₇⋊D₇)	direct (N × H)
39. C₃×C₅	C₁₇×C₇⋊D₇	semidirect
42. C₇	C₅×C₁₇×D₂₁	semidirect
44. C₅	C₁₇×C₃⋊(C₇⋊D₇)	direct (N × H)
45. C₃	C₅×C₁₇×C₇⋊D₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇²×C₁₇	2
C₅×C₁₇×C₇⋊D₇	3
C₁₇×C₃⋊(C₇⋊D₇)	5
C₅×C₁₇×D₂₁	7
C₅×C₃⋊(C₇⋊D₇)	17

Subgroups — C5×C17×C3⋊(C7⋊D7) #38735995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₇×C₃⋊(C₇⋊D₇) #38735995