Subgroups — C₇×D₂₃×D₅₃ #46802423

Order 34132.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₂₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₂₃×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂₃×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₂₃×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₃×D₅₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	D₁₂₁₉	C₂×C₇	1	1	yes	characteristic, complemented
7	C₂₃×D₅₃	C₂×C₇	1	1	yes	characteristic, complemented
8	D₂₃×C₅₃	C₂×C₇	1	1	yes	characteristic, complemented
9	C₂×C₇×D₅₃	—	23	1	no	maximal, Hall
10	C₂₃×C₅₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
11	C₂×C₇×C₅₃	—	23	1	no	—
12	C₇×D₅₃	—	23	1	no	—
13	C₇×D₅₃	D₂₃	1	1	yes	characteristic, direct product factor
14	C₂×C₇×D₂₃	—	53	1	no	maximal, Hall
15	C₇×C₅₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇×C₂₃	—	53	1	no	—
17	C₇×D₂₃	—	53	1	no	—
18	C₇×D₂₃	D₅₃	1	1	yes	characteristic, direct product factor
19	C₂×D₅₃	—	23	1	no	Hall
20	C₇×C₂₃	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅₃	—	23	1	no	—
22	D₅₃	—	23	1	no	—
23	D₅₃	C₇×D₂₃	1	1	yes	characteristic, direct product factor
24	C₂×D₂₃	—	53	1	no	Hall
25	C₅₃	C₂×C₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₂₃	—	53	1	no	—
27	D₂₃	—	53	1	no	—
28	D₂₃	C₇×D₅₃	1	1	yes	characteristic, direct product factor
29	C₂²×C₇	—	1219	1	no	Hall
30	C₂₃	C₂×C₇×D₅₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₇	—	23	1	no	—
32	C₂×C₇	—	53	1	no	—
33	C₂×C₇	—	1219	1	no	—
34	C₇	D₂₃×D₅₃	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	—	1219	1	no	Sylow
36	C₂	—	23	1	no	—
37	C₂	—	53	1	no	—
38	C₂	—	1219	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₂₃×D₅₃
commutator, cosocle, hypocenter	C₂₃×C₅₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₂₃×C₅₃	C₂²
LCS	G ▷ C₂₃×C₅₃
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₂₁₉	C₂	semidirect
2. C₇×D₂₃×C₅₃	C₂	semidirect
3. C₇×C₂₃×D₅₃	C₂	semidirect
4. C₇×C₂₃×C₅₃	C₂²	semidirect
5. D₂₃×D₅₃	C₇	direct (N × H)
6. D₁₂₁₉	C₂×C₇	semidirect
7. C₂₃×D₅₃	C₂×C₇	semidirect
8. D₂₃×C₅₃	C₂×C₇	semidirect
10. C₂₃×C₅₃	C₂²×C₇	semidirect
13. C₇×D₅₃	D₂₃	direct (N × H)
15. C₇×C₅₃	C₂×D₂₃	semidirect
18. C₇×D₂₃	D₅₃	direct (N × H)
20. C₇×C₂₃	C₂×D₅₃	semidirect
23. D₅₃	C₇×D₂₃	direct (N × H)
25. C₅₃	C₂×C₇×D₂₃	semidirect
28. D₂₃	C₇×D₅₃	direct (N × H)
30. C₂₃	C₂×C₇×D₅₃	semidirect
34. C₇	D₂₃×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×D₁₂₁₉	2
C₇×D₂₃×C₅₃	2
C₇×C₂₃×D₅₃	2
D₂₃×D₅₃	7
C₂×C₇×D₅₃	23
C₂×C₇×D₂₃	53

Subgroups — C7×D23×D53 #46802423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₂₃×D₅₃ #46802423