Finite Group Databasebeta

← C₂×C₅×C₉₇⋊C₃ #15668564

Subgroups — C₂×C₅×C₉₇⋊C₃ #15668564

Order 2910.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉₇⋊C₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₉₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₉₇⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₉₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₉₇⋊C₃	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₉₇	C₃×C₅	1	1	yes	characteristic, complemented, Hall
7	C₉₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₅	—	97	1	no	maximal, Hall
9	C₃×C₅	—	97	1	no	Hall
10	C₂×C₅	C₉₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃	—	97	1	no	Hall
12	C₅	C₂×C₉₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₃	—	97	1	no	Sylow
14	C₂	C₅×C₉₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₅×C₉₇⋊C₃	C₂	direct (N × H)
2. C₂×C₅×C₉₇	C₃	semidirect
3. C₂×C₉₇⋊C₃	C₅	direct (N × H)
4. C₅×C₉₇	C₂×C₃	semidirect
5. C₉₇⋊C₃	C₂×C₅	direct (N × H)
6. C₂×C₉₇	C₃×C₅	semidirect
7. C₉₇	C₂×C₃×C₅	semidirect
10. C₂×C₅	C₉₇⋊C₃	direct (N × H)
12. C₅	C₂×C₉₇⋊C₃	direct (N × H)
14. C₂	C₅×C₉₇⋊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×C₉₇⋊C₃	2
C₂×C₅×C₉₇	3
C₂×C₉₇⋊C₃	5
C₂×C₃×C₅	97