Subgroups — C₂×C₅×D₇₅₃ #28418924

Order 15060.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₇₅₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₂₅₁	—	3	1	no	maximal, Hall
4	C₃×C₅×C₂₅₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₇₅₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₂₅₁	D₃	1	1	yes	characteristic, complemented
7	C₅×D₂₅₁	—	3	2	no	—
8	C₂×C₃×C₂₅₁	C₂×C₅	1	1	yes	characteristic, complemented
9	D₇₅₃	C₂×C₅	1	2	yes	direct product factor
10	C₅×C₂₅₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₂₅₁	—	3	1	no	Hall
12	C₃×C₂₅₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₂₅₁	C₅×D₃	1	1	yes	characteristic, complemented
14	D₂₅₁	—	3	2	no	—
15	C₂₅₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₅×D₃	—	251	1	no	maximal, Hall
17	C₂×C₃×C₅	D₂₅₁	1	1	yes	characteristic, complemented
18	C₅×D₃	—	251	2	no	—
19	C₂²×C₅	—	753	1	no	Hall
20	C₃×C₅	C₂×D₂₅₁	1	1	yes	characteristic, complemented, Hall
21	C₂×D₃	—	251	1	no	Hall
22	C₂×C₅	—	753	2	no	—
23	C₂×C₅	D₇₅₃	1	1	yes	characteristic, direct product factor
24	C₂×C₃	C₅×D₂₅₁	1	1	yes	characteristic, complemented
25	D₃	—	251	2	no	—
26	C₅	C₂×D₇₅₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²	—	753	1	no	Sylow
28	C₃	C₂×C₅×D₂₅₁	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	753	2	no	—
30	C₂	C₅×D₇₅₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	D₇₅₃
commutator, cosocle, hypocenter	C₃×C₂₅₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₂₅₁	C₂
LCS	G ▷ C₃×C₂₅₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×D₇₅₃	C₂	direct (N × H)
2. C₂×C₃×C₅×C₂₅₁	C₂	semidirect
4. C₃×C₅×C₂₅₁	C₂²	semidirect
5. C₂×D₇₅₃	C₅	direct (N × H)
6. C₂×C₅×C₂₅₁	D₃	semidirect
8. C₂×C₃×C₂₅₁	C₂×C₅	semidirect
9. D₇₅₃	C₂×C₅	direct (N × H)
10. C₅×C₂₅₁	C₂×D₃	semidirect
12. C₃×C₂₅₁	C₂²×C₅	semidirect
13. C₂×C₂₅₁	C₅×D₃	semidirect
15. C₂₅₁	C₂×C₅×D₃	semidirect
17. C₂×C₃×C₅	D₂₅₁	semidirect
20. C₃×C₅	C₂×D₂₅₁	semidirect
23. C₂×C₅	D₇₅₃	direct (N × H)
24. C₂×C₃	C₅×D₂₅₁	semidirect
26. C₅	C₂×D₇₅₃	direct (N × H)
28. C₃	C₂×C₅×D₂₅₁	semidirect
30. C₂	C₅×D₇₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×D₇₅₃	2
C₂×C₃×C₅×C₂₅₁	2
C₂×C₅×D₂₅₁	3
C₂×D₇₅₃	5
C₂×C₅×D₃	251

Subgroups — C2×C5×D753 #28418924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₇₅₃ #28418924