Subgroups — C₂×C₇×C₂₃×D₅₃ #46802432

Order 34132.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₃×D₅₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₂₃×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂₃×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₂₃×D₅₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₂₃×C₅₃	C₂×C₇	1	1	yes	characteristic, complemented
6	C₂₃×D₅₃	C₂×C₇	1	2	yes	direct product factor
7	C₂×C₇×D₅₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂₃×C₅₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
9	C₂×C₇×C₅₃	C₂×C₂₃	1	1	yes	characteristic, complemented
10	C₇×D₅₃	C₂×C₂₃	1	2	yes	direct product factor
11	C₂²×C₇×C₂₃	—	53	1	no	maximal, Hall
12	C₇×C₅₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇×C₂₃	—	53	2	no	—
14	C₂×C₇×C₂₃	D₅₃	1	1	yes	characteristic, direct product factor
15	C₂×D₅₃	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
16	C₇×C₂₃	C₂×D₅₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅₃	C₂×C₇×C₂₃	1	1	yes	characteristic, complemented
18	D₅₃	C₂×C₇×C₂₃	1	2	yes	direct product factor
19	C₂²×C₂₃	—	53	1	no	Hall
20	C₅₃	C₂²×C₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₂₃	—	53	2	no	—
22	C₂×C₂₃	C₇×D₅₃	1	1	yes	characteristic, direct product factor
23	C₂²×C₇	—	53	1	no	Hall
24	C₂₃	C₂×C₇×D₅₃	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₇	—	53	2	no	—
26	C₂×C₇	C₂₃×D₅₃	1	1	yes	characteristic, direct product factor
27	C₇	C₂×C₂₃×D₅₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	—	53	1	no	Sylow
29	C₂	—	53	2	no	—
30	C₂	C₇×C₂₃×D₅₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₂₃	D₅₃
commutator, cosocle, hypocenter	C₅₃	C₂²×C₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₂₃×C₅₃	C₂
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂×C₇×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₃×D₅₃	C₂	direct (N × H)
2. C₂×C₇×C₂₃×C₅₃	C₂	semidirect
3. C₇×C₂₃×C₅₃	C₂²	semidirect
4. C₂×C₂₃×D₅₃	C₇	direct (N × H)
5. C₂×C₂₃×C₅₃	C₂×C₇	semidirect
6. C₂₃×D₅₃	C₂×C₇	direct (N × H)
7. C₂×C₇×D₅₃	C₂₃	direct (N × H)
8. C₂₃×C₅₃	C₂²×C₇	semidirect
9. C₂×C₇×C₅₃	C₂×C₂₃	semidirect
10. C₇×D₅₃	C₂×C₂₃	direct (N × H)
12. C₇×C₅₃	C₂²×C₂₃	semidirect
14. C₂×C₇×C₂₃	D₅₃	direct (N × H)
15. C₂×D₅₃	C₇×C₂₃	direct (N × H)
16. C₇×C₂₃	C₂×D₅₃	direct (N × H)
17. C₂×C₅₃	C₂×C₇×C₂₃	semidirect
18. D₅₃	C₂×C₇×C₂₃	direct (N × H)
20. C₅₃	C₂²×C₇×C₂₃	semidirect
22. C₂×C₂₃	C₇×D₅₃	direct (N × H)
24. C₂₃	C₂×C₇×D₅₃	direct (N × H)
26. C₂×C₇	C₂₃×D₅₃	direct (N × H)
27. C₇	C₂×C₂₃×D₅₃	direct (N × H)
30. C₂	C₇×C₂₃×D₅₃	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×C₂₃×D₅₃	2
C₂×C₇×C₂₃×C₅₃	2
C₂×C₂₃×D₅₃	7
C₂×C₇×D₅₃	23
C₂²×C₇×C₂₃	53

Subgroups — C2×C7×C23×D53 #46802432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₂₃×D₅₃ #46802432