Subgroups — C₇×D₅×C₁₂₇⋊C₃ #40998708

Order 26670.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₂₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₇×C₁₂₇⋊C₃	—	5	1	no	maximal, Hall
4	C₅×C₇×C₁₂₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	D₅×C₁₂₇⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₂₇⋊C₃	D₅	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₁₂₇⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₂×C₇×C₁₂₇	—	5	1	no	Hall
9	D₅×C₁₂₇	C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₁₂₇	C₃×D₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₂₇⋊C₃	—	5	1	no	Hall
12	C₅×C₁₂₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
13	C₁₂₇⋊C₃	C₇×D₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₂₇	—	5	1	no	Hall
15	C₃×C₇×D₅	—	127	1	no	maximal, Hall
16	C₁₂₇	C₃×C₇×D₅	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅×C₇	—	127	1	no	Hall
18	C₇×D₅	C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₇	—	635	1	no	Hall
20	C₅×C₇	C₂×C₁₂₇⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₃×D₅	—	127	1	no	Hall
22	C₃×C₇	—	127	1	no	Hall
23	C₃×C₅	—	127	1	no	Hall
24	C₂×C₇	—	5	1	no	Hall
25	D₅	C₇×C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
26	C₇	D₅×C₁₂₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	—	635	1	no	Hall
28	C₅	C₂×C₇×C₁₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	127	1	no	Sylow
30	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₅×C₁₂₇⋊C₃
commutator, cosocle, hypocenter	C₅×C₁₂₇	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₂₇	C₂×C₃
LCS	G ▷ C₅×C₁₂₇
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₂₇⋊C₃	C₂	semidirect
2. C₇×D₅×C₁₂₇	C₃	semidirect
4. C₅×C₇×C₁₂₇	C₂×C₃	semidirect
5. D₅×C₁₂₇⋊C₃	C₇	direct (N × H)
6. C₇×C₁₂₇⋊C₃	D₅	direct (N × H)
7. C₅×C₁₂₇⋊C₃	C₂×C₇	semidirect
9. D₅×C₁₂₇	C₃×C₇	semidirect
10. C₇×C₁₂₇	C₃×D₅	semidirect
12. C₅×C₁₂₇	C₂×C₃×C₇	semidirect
13. C₁₂₇⋊C₃	C₇×D₅	direct (N × H)
16. C₁₂₇	C₃×C₇×D₅	semidirect
18. C₇×D₅	C₁₂₇⋊C₃	direct (N × H)
20. C₅×C₇	C₂×C₁₂₇⋊C₃	semidirect
25. D₅	C₇×C₁₂₇⋊C₃	direct (N × H)
26. C₇	D₅×C₁₂₇⋊C₃	direct (N × H)
28. C₅	C₂×C₇×C₁₂₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×C₁₂₇⋊C₃	2
C₇×D₅×C₁₂₇	3
C₂×C₇×C₁₂₇⋊C₃	5
D₅×C₁₂₇⋊C₃	7
C₃×C₇×D₅	127

Subgroups — C7×D5×C127⋊C3 #40998708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₅×C₁₂₇⋊C₃ #40998708