Subgroups — C₃×C₅×D₆₇₉ #35205010

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	C₅×D₆₇₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₆₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₉₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×D₉₇	—	7	1	no	maximal, Hall
6	C₃×C₇×C₉₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₉₇	D₇	1	1	yes	characteristic, complemented, Hall
8	D₆₇₉	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₅×D₉₇	—	7	1	no	Hall
10	C₇×C₉₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃×D₉₇	—	7	1	no	Hall
12	C₅×C₉₇	C₃×D₇	1	1	yes	characteristic, complemented, Hall
13	C₃×C₉₇	C₅×D₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×D₇	—	97	1	no	maximal, Hall
15	D₉₇	—	7	1	no	Hall
16	C₃×C₅×C₇	D₉₇	1	1	yes	characteristic, complemented, Hall
17	C₉₇	C₃×C₅×D₇	1	1	yes	characteristic, complemented, Sylow
18	C₅×D₇	—	97	1	no	Hall
19	C₃×D₇	—	97	1	no	Hall
20	C₅×C₇	C₃×D₉₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₅	—	679	1	no	Hall
22	C₃×C₇	C₅×D₉₇	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	D₆₇₉	1	1	yes	characteristic, direct product factor, Hall
24	D₇	—	97	1	no	Hall
25	C₂×C₅	—	679	1	no	Hall
26	C₇	C₃×C₅×D₉₇	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	679	1	no	Hall
28	C₅	C₃×D₆₇₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×D₆₇₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	679	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	D₆₇₉
commutator, cosocle, hypocenter	C₇×C₉₇	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₉₇	C₂
LCS	G ▷ C₇×C₉₇
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₉₇	C₂	semidirect
2. C₅×D₆₇₉	C₃	direct (N × H)
3. C₃×D₆₇₉	C₅	direct (N × H)
4. C₅×C₇×C₉₇	C₂×C₃	semidirect
6. C₃×C₇×C₉₇	C₂×C₅	semidirect
7. C₃×C₅×C₉₇	D₇	semidirect
8. D₆₇₉	C₃×C₅	direct (N × H)
10. C₇×C₉₇	C₂×C₃×C₅	semidirect
12. C₅×C₉₇	C₃×D₇	semidirect
13. C₃×C₉₇	C₅×D₇	semidirect
16. C₃×C₅×C₇	D₉₇	semidirect
17. C₉₇	C₃×C₅×D₇	semidirect
20. C₅×C₇	C₃×D₉₇	semidirect
22. C₃×C₇	C₅×D₉₇	semidirect
23. C₃×C₅	D₆₇₉	direct (N × H)
26. C₇	C₃×C₅×D₉₇	semidirect
28. C₅	C₃×D₆₇₉	direct (N × H)
29. C₃	C₅×D₆₇₉	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
C₅×D₆₇₉	3
C₃×D₆₇₉	5
C₃×C₅×D₉₇	7
C₃×C₅×D₇	97

Subgroups — C3×C5×D679 #35205010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₆₇₉ #35205010