Subgroups — C₂×C₅₃×D₁₆₁ #46802437

Order 34132.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×D₁₆₁	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×D₂₃×C₅₃	—	7	1	no	maximal, Hall
5	C₂×C₂₃×C₅₃	D₇	1	1	yes	characteristic, complemented
6	D₂₃×C₅₃	—	7	2	no	—
7	C₂×D₇×C₅₃	—	23	1	no	maximal, Hall
8	C₂₃×C₅₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
9	C₂×C₇×C₅₃	D₂₃	1	1	yes	characteristic, complemented
10	D₇×C₅₃	—	23	2	no	—
11	C₂×D₁₆₁	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₅₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₇×C₂₃	C₂×C₅₃	1	1	yes	characteristic, complemented
14	D₁₆₁	C₂×C₅₃	1	2	yes	direct product factor
15	C₂²×C₅₃	—	161	1	no	Hall
16	C₇×C₂₃	C₂²×C₅₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅₃	—	161	2	no	—
18	C₂×C₅₃	D₁₆₁	1	1	yes	characteristic, direct product factor
19	C₂×D₂₃	—	7	1	no	Hall
20	C₅₃	C₂×D₁₆₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₂₃	D₇×C₅₃	1	1	yes	characteristic, complemented
22	D₂₃	—	7	2	no	—
23	C₂×D₇	—	23	1	no	Hall
24	C₂₃	C₂×D₇×C₅₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇	D₂₃×C₅₃	1	1	yes	characteristic, complemented
26	D₇	—	23	2	no	—
27	C₇	C₂×D₂₃×C₅₃	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	161	1	no	Sylow
29	C₂	—	161	2	no	—
30	C₂	C₅₃×D₁₆₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅₃	D₁₆₁
commutator, cosocle, hypocenter	C₇×C₂₃	C₂²×C₅₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₂₃×C₅₃	C₂
LCS	G ▷ C₇×C₂₃
UCS	C₁ ◁ C₂×C₅₃

Complements

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

N	H ≅ G/N	type
1. C₅₃×D₁₆₁	C₂	direct (N × H)
2. C₂×C₇×C₂₃×C₅₃	C₂	semidirect
3. C₇×C₂₃×C₅₃	C₂²	semidirect
5. C₂×C₂₃×C₅₃	D₇	semidirect
8. C₂₃×C₅₃	C₂×D₇	semidirect
9. C₂×C₇×C₅₃	D₂₃	semidirect
11. C₂×D₁₆₁	C₅₃	direct (N × H)
12. C₇×C₅₃	C₂×D₂₃	semidirect
13. C₂×C₇×C₂₃	C₂×C₅₃	semidirect
14. D₁₆₁	C₂×C₅₃	direct (N × H)
16. C₇×C₂₃	C₂²×C₅₃	semidirect
18. C₂×C₅₃	D₁₆₁	direct (N × H)
20. C₅₃	C₂×D₁₆₁	direct (N × H)
21. C₂×C₂₃	D₇×C₅₃	semidirect
24. C₂₃	C₂×D₇×C₅₃	semidirect
25. C₂×C₇	D₂₃×C₅₃	semidirect
27. C₇	C₂×D₂₃×C₅₃	semidirect
30. C₂	C₅₃×D₁₆₁	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×D₁₆₁	2
C₂×C₇×C₂₃×C₅₃	2
C₂×D₂₃×C₅₃	7
C₂×D₇×C₅₃	23
C₂×D₁₆₁	53

Subgroups — C2×C53×D161 #46802437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₃×D₁₆₁ #46802437