Subgroups — C₅×C₇×D₃₉₁ #41032840

Order 27370.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₃₉₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×D₃₉₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₇×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₇×C₂₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	C₅×C₇×D₂₃	—	17	1	no	maximal, Hall
7	C₅×C₇×D₁₇	—	23	1	no	maximal, Hall
8	C₅×C₇×C₂₃	D₁₇	1	1	yes	characteristic, complemented, Hall
9	D₃₉₁	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₅×C₇×C₁₇	D₂₃	1	1	yes	characteristic, complemented, Hall
11	C₁₇×C₂₃	C₂×C₅×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×D₂₃	—	17	1	no	Hall
13	C₇×D₁₇	—	23	1	no	Hall
14	C₅×D₂₃	—	17	1	no	Hall
15	C₅×D₁₇	—	23	1	no	Hall
16	C₇×C₂₃	C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
17	C₇×C₁₇	C₅×D₂₃	1	1	yes	characteristic, complemented, Hall
18	C₅×C₂₃	C₇×D₁₇	1	1	yes	characteristic, complemented, Hall
19	C₅×C₁₇	C₇×D₂₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₇	—	391	1	no	Hall
21	D₂₃	—	17	1	no	Hall
22	C₅×C₇	D₃₉₁	1	1	yes	characteristic, direct product factor, Hall
23	D₁₇	—	23	1	no	Hall
24	C₂₃	C₅×C₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
25	C₁₇	C₅×C₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₇	—	391	1	no	Hall
27	C₂×C₅	—	391	1	no	Hall
28	C₇	C₅×D₃₉₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₅	C₇×D₃₉₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	391	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₇	D₃₉₁
commutator, cosocle, hypocenter	C₁₇×C₂₃	C₂×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₇×C₂₃	C₂
LCS	G ▷ C₁₇×C₂₃
UCS	C₁ ◁ C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₇×C₂₃	C₂	semidirect
2. C₇×D₃₉₁	C₅	direct (N × H)
3. C₅×D₃₉₁	C₇	direct (N × H)
4. C₇×C₁₇×C₂₃	C₂×C₅	semidirect
5. C₅×C₁₇×C₂₃	C₂×C₇	semidirect
8. C₅×C₇×C₂₃	D₁₇	semidirect
9. D₃₉₁	C₅×C₇	direct (N × H)
10. C₅×C₇×C₁₇	D₂₃	semidirect
11. C₁₇×C₂₃	C₂×C₅×C₇	semidirect
16. C₇×C₂₃	C₅×D₁₇	semidirect
17. C₇×C₁₇	C₅×D₂₃	semidirect
18. C₅×C₂₃	C₇×D₁₇	semidirect
19. C₅×C₁₇	C₇×D₂₃	semidirect
22. C₅×C₇	D₃₉₁	direct (N × H)
24. C₂₃	C₅×C₇×D₁₇	semidirect
25. C₁₇	C₅×C₇×D₂₃	semidirect
28. C₇	C₅×D₃₉₁	direct (N × H)
29. C₅	C₇×D₃₉₁	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×C₁₇×C₂₃	2
C₇×D₃₉₁	5
C₅×D₃₉₁	7
C₅×C₇×D₂₃	17
C₅×C₇×D₁₇	23

Subgroups — C5×C7×D391 #41032840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×D₃₉₁ #41032840