Subgroups — C₂×C₇×C₉×C₂₅₇ #44569199

Order 32382.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₂₅₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₇×C₂₅₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₂₅₇	C₂×C₃	1	1	yes	characteristic
4	C₂×C₉×C₂₅₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₂₅₇	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₂₅₇	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
7	C₇×C₂₅₇	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃×C₂₅₇	C₃×C₇	1	1	yes	characteristic
9	C₃×C₂₅₇	C₂×C₃×C₇	1	1	yes	characteristic
10	C₂×C₂₅₇	C₇×C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂₅₇	C₂×C₇×C₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₇×C₉	C₂₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₇×C₉	C₂×C₂₅₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₇	C₃×C₂₅₇	1	1	yes	characteristic
15	C₃×C₇	C₂×C₃×C₂₅₇	1	1	yes	characteristic
16	C₂×C₉	C₇×C₂₅₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₇	C₉×C₂₅₇	1	1	yes	characteristic, direct product factor, Hall
18	C₉	C₂×C₇×C₂₅₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₇	C₂×C₉×C₂₅₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	C₃×C₇×C₂₅₇	1	1	yes	characteristic
21	C₃	C₂×C₃×C₇×C₂₅₇	1	1	yes	characteristic
22	C₂	C₇×C₉×C₂₅₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₇×C₂₅₇
socle, prime radical	C₂×C₃×C₇×C₂₅₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×C₉×C₂₅₇	C₂	direct (N × H)
4. C₂×C₉×C₂₅₇	C₇	direct (N × H)
5. C₂×C₇×C₂₅₇	C₉	direct (N × H)
6. C₉×C₂₅₇	C₂×C₇	direct (N × H)
7. C₇×C₂₅₇	C₂×C₉	direct (N × H)
10. C₂×C₂₅₇	C₇×C₉	direct (N × H)
11. C₂₅₇	C₂×C₇×C₉	direct (N × H)
12. C₂×C₇×C₉	C₂₅₇	direct (N × H)
13. C₇×C₉	C₂×C₂₅₇	direct (N × H)
16. C₂×C₉	C₇×C₂₅₇	direct (N × H)
17. C₂×C₇	C₉×C₂₅₇	direct (N × H)
18. C₉	C₂×C₇×C₂₅₇	direct (N × H)
19. C₇	C₂×C₉×C₂₅₇	direct (N × H)
22. C₂	C₇×C₉×C₂₅₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₉×C₂₅₇	2
C₂×C₃×C₇×C₂₅₇	3
C₂×C₉×C₂₅₇	7
C₂×C₇×C₉	257

Subgroups — C2×C7×C9×C257 #44569199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₉×C₂₅₇ #44569199