Subgroups — C₂×C₁₃×D₄₅₃ #37555599

Order 23556.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×D₄₅₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₃×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×D₁₅₁	—	3	1	no	maximal, Hall
4	C₃×C₁₃×C₁₅₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₁₅₁	D₃	1	1	yes	characteristic, complemented
6	C₁₃×D₁₅₁	—	3	2	no	—
7	C₁₃×C₁₅₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₄₅₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₁₅₁	C₂×C₁₃	1	1	yes	characteristic, complemented
10	D₄₅₃	C₂×C₁₃	1	2	yes	direct product factor
11	C₂×D₁₅₁	—	3	1	no	Hall
12	C₃×C₁₅₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₅₁	D₃×C₁₃	1	1	yes	characteristic, complemented
14	D₁₅₁	—	3	2	no	—
15	C₂×D₃×C₁₃	—	151	1	no	maximal, Hall
16	C₁₅₁	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×C₁₃	D₁₅₁	1	1	yes	characteristic, complemented
18	D₃×C₁₃	—	151	2	no	—
19	C₂²×C₁₃	—	453	1	no	Hall
20	C₃×C₁₃	C₂×D₁₅₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₃	—	453	2	no	—
22	C₂×C₁₃	D₄₅₃	1	1	yes	characteristic, direct product factor
23	C₁₃	C₂×D₄₅₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×D₃	—	151	1	no	Hall
25	C₂×C₃	C₁₃×D₁₅₁	1	1	yes	characteristic, complemented
26	D₃	—	151	2	no	—
27	C₂²	—	453	1	no	Sylow
28	C₃	C₂×C₁₃×D₁₅₁	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	453	2	no	—
30	C₂	C₁₃×D₄₅₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₄₅₃
commutator, cosocle, hypocenter	C₃×C₁₅₁	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₅₁	C₂
LCS	G ▷ C₃×C₁₅₁
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×D₄₅₃	C₂	direct (N × H)
2. C₂×C₃×C₁₃×C₁₅₁	C₂	semidirect
4. C₃×C₁₃×C₁₅₁	C₂²	semidirect
5. C₂×C₁₃×C₁₅₁	D₃	semidirect
7. C₁₃×C₁₅₁	C₂×D₃	semidirect
8. C₂×D₄₅₃	C₁₃	direct (N × H)
9. C₂×C₃×C₁₅₁	C₂×C₁₃	semidirect
10. D₄₅₃	C₂×C₁₃	direct (N × H)
12. C₃×C₁₅₁	C₂²×C₁₃	semidirect
13. C₂×C₁₅₁	D₃×C₁₃	semidirect
16. C₁₅₁	C₂×D₃×C₁₃	semidirect
17. C₂×C₃×C₁₃	D₁₅₁	semidirect
20. C₃×C₁₃	C₂×D₁₅₁	semidirect
22. C₂×C₁₃	D₄₅₃	direct (N × H)
23. C₁₃	C₂×D₄₅₃	direct (N × H)
25. C₂×C₃	C₁₃×D₁₅₁	semidirect
28. C₃	C₂×C₁₃×D₁₅₁	semidirect
30. C₂	C₁₃×D₄₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×D₄₅₃	2
C₂×C₃×C₁₃×C₁₅₁	2
C₂×C₁₃×D₁₅₁	3
C₂×D₄₅₃	13
C₂×D₃×C₁₃	151

Subgroups — C2×C13×D453 #37555599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×D₄₅₃ #37555599