Subgroups — C₃×D₃₅×C₉₇ #35205013

Order 20370.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₅×C₉₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₇×C₉₇	—	5	1	no	maximal, Hall
4	C₅×C₇×C₉₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×D₅×C₉₇	—	7	1	no	maximal, Hall
6	C₃×C₇×C₉₇	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₉₇	D₇	1	1	yes	characteristic, complemented, Hall
8	D₇×C₉₇	—	5	1	no	Hall
9	D₅×C₉₇	—	7	1	no	Hall
10	C₇×C₉₇	C₃×D₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₉₇	—	35	1	no	Hall
12	C₅×C₉₇	C₃×D₇	1	1	yes	characteristic, complemented, Hall
13	C₃×C₉₇	D₃₅	1	1	yes	characteristic, direct product factor, Hall
14	C₃×D₃₅	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₉₇	—	35	1	no	Hall
16	C₃×C₅×C₇	C₂×C₉₇	1	1	yes	characteristic, complemented, Hall
17	C₉₇	C₃×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
18	D₃₅	C₃×C₉₇	1	1	yes	characteristic, direct product factor, Hall
19	C₃×D₇	—	5	1	no	Hall
20	C₅×C₇	C₂×C₃×C₉₇	1	1	yes	characteristic, complemented, Hall
21	C₃×D₅	—	7	1	no	Hall
22	C₃×C₇	D₅×C₉₇	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	D₇×C₉₇	1	1	yes	characteristic, complemented, Hall
24	D₇	—	5	1	no	Hall
25	D₅	—	7	1	no	Hall
26	C₇	C₃×D₅×C₉₇	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	35	1	no	Hall
28	C₅	C₃×D₇×C₉₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₃₅×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	35	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₉₇	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂×C₃×C₉₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₉₇	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₃×C₉₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₉₇	C₂	semidirect
2. D₃₅×C₉₇	C₃	direct (N × H)
4. C₅×C₇×C₉₇	C₂×C₃	semidirect
6. C₃×C₇×C₉₇	D₅	semidirect
7. C₃×C₅×C₉₇	D₇	semidirect
10. C₇×C₉₇	C₃×D₅	semidirect
12. C₅×C₉₇	C₃×D₇	semidirect
13. C₃×C₉₇	D₃₅	direct (N × H)
14. C₃×D₃₅	C₉₇	direct (N × H)
16. C₃×C₅×C₇	C₂×C₉₇	semidirect
17. C₉₇	C₃×D₃₅	direct (N × H)
18. D₃₅	C₃×C₉₇	direct (N × H)
20. C₅×C₇	C₂×C₃×C₉₇	semidirect
22. C₃×C₇	D₅×C₉₇	semidirect
23. C₃×C₅	D₇×C₉₇	semidirect
26. C₇	C₃×D₅×C₉₇	semidirect
28. C₅	C₃×D₇×C₉₇	semidirect
29. C₃	D₃₅×C₉₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇×C₉₇	2
D₃₅×C₉₇	3
C₃×D₇×C₉₇	5
C₃×D₅×C₉₇	7
C₃×D₃₅	97

Subgroups — C3×D35×C97 #35205013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₅×C₉₇ #35205013