Subgroups — C₂×C₉×C₂₃×C₅₃ #36346751

Order 21942.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₃×C₅₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₂₃×C₅₃	C₃	1	1	yes	maximal, characteristic
3	C₃×C₂₃×C₅₃	C₂×C₃	1	1	yes	characteristic
4	C₂×C₂₃×C₅₃	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₂₃×C₅₃	C₂×C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₉×C₅₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₉×C₅₃	C₂×C₂₃	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₉×C₂₃	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅₃	C₃×C₂₃	1	1	yes	characteristic
10	C₉×C₂₃	C₂×C₅₃	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₅₃	C₂×C₃×C₂₃	1	1	yes	characteristic
12	C₂×C₃×C₂₃	C₃×C₅₃	1	1	yes	characteristic
13	C₂×C₅₃	C₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₂₃	C₂×C₃×C₅₃	1	1	yes	characteristic
15	C₅₃	C₂×C₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₂₃	C₉×C₅₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂₃	C₂×C₉×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₉	C₂₃×C₅₃	1	1	yes	characteristic, direct product factor, Hall
19	C₉	C₂×C₂₃×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	C₃×C₂₃×C₅₃	1	1	yes	characteristic
21	C₃	C₂×C₃×C₂₃×C₅₃	1	1	yes	characteristic
22	C₂	C₉×C₂₃×C₅₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₂₃×C₅₃
socle, prime radical	C₂×C₃×C₂₃×C₅₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×C₂₃×C₅₃	C₂	direct (N × H)
4. C₂×C₂₃×C₅₃	C₉	direct (N × H)
5. C₂₃×C₅₃	C₂×C₉	direct (N × H)
6. C₂×C₉×C₅₃	C₂₃	direct (N × H)
7. C₉×C₅₃	C₂×C₂₃	direct (N × H)
8. C₂×C₉×C₂₃	C₅₃	direct (N × H)
10. C₉×C₂₃	C₂×C₅₃	direct (N × H)
13. C₂×C₅₃	C₉×C₂₃	direct (N × H)
15. C₅₃	C₂×C₉×C₂₃	direct (N × H)
16. C₂×C₂₃	C₉×C₅₃	direct (N × H)
17. C₂₃	C₂×C₉×C₅₃	direct (N × H)
18. C₂×C₉	C₂₃×C₅₃	direct (N × H)
19. C₉	C₂×C₂₃×C₅₃	direct (N × H)
22. C₂	C₉×C₂₃×C₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₂₃×C₅₃	2
C₂×C₃×C₂₃×C₅₃	3
C₂×C₉×C₅₃	23
C₂×C₉×C₂₃	53

Subgroups — C2×C9×C23×C53 #36346751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₂₃×C₅₃ #36346751