Subgroups — C₅×C₇×C₁₇×C₁₃⋊C₃ #37550939

Order 23205.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₃×C₁₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₁₇×C₁₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₁₇×C₁₃⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₇×C₁₇	—	13	1	no	maximal, Hall
5	C₇×C₁₃×C₁₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×C₇×C₁₃⋊C₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₃×C₁₇	C₃×C₇	1	1	yes	characteristic, complemented, Hall
8	C₁₇×C₁₃⋊C₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₅×C₇×C₁₇	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
10	C₅×C₇×C₁₃	C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₁₇	—	13	1	no	Hall
12	C₇×C₁₃⋊C₃	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₁₇	—	13	1	no	Hall
14	C₁₃×C₁₇	C₃×C₅×C₇	1	1	yes	characteristic, complemented, Hall
15	C₅×C₁₃⋊C₃	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
16	C₇×C₁₇	C₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₅×C₇	—	13	1	no	Hall
18	C₇×C₁₃	C₃×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
19	C₅×C₁₇	C₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₁₃	C₃×C₇×C₁₇	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₇	—	13	1	no	Hall
22	C₁₃⋊C₃	C₅×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
23	C₅×C₇	C₁₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₇	—	13	1	no	Hall
25	C₁₇	C₅×C₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₃×C₅	—	13	1	no	Hall
27	C₁₃	C₃×C₅×C₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
28	C₇	C₅×C₁₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₅	C₇×C₁₇×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₃	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇×C₁₇	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₅×C₇×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₁₇	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅×C₇×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₃×C₁₇	C₃	semidirect
2. C₇×C₁₇×C₁₃⋊C₃	C₅	direct (N × H)
3. C₅×C₁₇×C₁₃⋊C₃	C₇	direct (N × H)
5. C₇×C₁₃×C₁₇	C₃×C₅	semidirect
6. C₅×C₇×C₁₃⋊C₃	C₁₇	direct (N × H)
7. C₅×C₁₃×C₁₇	C₃×C₇	semidirect
8. C₁₇×C₁₃⋊C₃	C₅×C₇	direct (N × H)
9. C₅×C₇×C₁₇	C₁₃⋊C₃	direct (N × H)
10. C₅×C₇×C₁₃	C₃×C₁₇	semidirect
12. C₇×C₁₃⋊C₃	C₅×C₁₇	direct (N × H)
14. C₁₃×C₁₇	C₃×C₅×C₇	semidirect
15. C₅×C₁₃⋊C₃	C₇×C₁₇	direct (N × H)
16. C₇×C₁₇	C₅×C₁₃⋊C₃	direct (N × H)
18. C₇×C₁₃	C₃×C₅×C₁₇	semidirect
19. C₅×C₁₇	C₇×C₁₃⋊C₃	direct (N × H)
20. C₅×C₁₃	C₃×C₇×C₁₇	semidirect
22. C₁₃⋊C₃	C₅×C₇×C₁₇	direct (N × H)
23. C₅×C₇	C₁₇×C₁₃⋊C₃	direct (N × H)
25. C₁₇	C₅×C₇×C₁₃⋊C₃	direct (N × H)
27. C₁₃	C₃×C₅×C₇×C₁₇	semidirect
28. C₇	C₅×C₁₇×C₁₃⋊C₃	direct (N × H)
29. C₅	C₇×C₁₇×C₁₃⋊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×C₇×C₁₃×C₁₇	3
C₇×C₁₇×C₁₃⋊C₃	5
C₅×C₁₇×C₁₃⋊C₃	7
C₃×C₅×C₇×C₁₇	13
C₅×C₇×C₁₃⋊C₃	17

Subgroups — C5×C7×C17×C13⋊C3 #37550939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×C₁₇×C₁₃⋊C₃ #37550939