Finite Group Databasebeta

← C₂×C₅³×C₉₇ #72201539

Subgroups — C₂×C₅³×C₉₇ #72201539

Order 24250.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅³×C₉₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅²×C₉₇	C₅	1	31	yes	maximal, direct product factor
3	C₅²×C₉₇	C₂×C₅	1	31	yes	direct product factor
4	C₂×C₅×C₉₇	C₅²	1	31	yes	direct product factor
5	C₅×C₉₇	C₂×C₅²	1	31	yes	direct product factor
6	C₂×C₅³	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₉₇	C₅³	1	1	yes	characteristic, direct product factor, Hall
8	C₅³	C₂×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
9	C₉₇	C₂×C₅³	1	1	yes	characteristic, direct product factor, Sylow
10	C₂×C₅²	C₅×C₉₇	1	31	yes	direct product factor
11	C₅²	C₂×C₅×C₉₇	1	31	yes	direct product factor
12	C₂×C₅	C₅²×C₉₇	1	31	yes	direct product factor
13	C₅	C₂×C₅²×C₉₇	1	31	yes	direct product factor
14	C₂	C₅³×C₉₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅³×C₉₇	C₂	direct (N × H)
2. C₂×C₅²×C₉₇	C₅	direct (N × H)
3. C₅²×C₉₇	C₂×C₅	direct (N × H)
4. C₂×C₅×C₉₇	C₅²	direct (N × H)
5. C₅×C₉₇	C₂×C₅²	direct (N × H)
6. C₂×C₅³	C₉₇	direct (N × H)
7. C₂×C₉₇	C₅³	direct (N × H)
8. C₅³	C₂×C₉₇	direct (N × H)
9. C₉₇	C₂×C₅³	direct (N × H)
10. C₂×C₅²	C₅×C₉₇	direct (N × H)
11. C₅²	C₂×C₅×C₉₇	direct (N × H)
12. C₂×C₅	C₅²×C₉₇	direct (N × H)
13. C₅	C₂×C₅²×C₉₇	direct (N × H)
14. C₂	C₅³×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
C₅³×C₉₇	2
C₂×C₅²×C₉₇	5
C₂×C₅³	97