Subgroups — C₃×C₇×C₂₃×C₅⋊D₅ #37563406

Order 24150.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₂₃×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×D₅×C₂₃	—	5	6	no	maximal
4	C₅²×C₇×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₂₃×C₅⋊D₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₇×C₂₃	D₅	1	6	yes	complemented
7	C₃×C₅²×C₂₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×D₅×C₂₃	—	5	6	no	—
9	C₂₃×C₅⋊D₅	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₇×C₅⋊D₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₇×C₂₃	—	25	1	no	Hall
12	C₅×C₇×C₂₃	C₃×D₅	1	6	yes	complemented
13	C₃×D₅×C₂₃	—	5	6	no	—
14	C₅²×C₂₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅²×C₇	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇×C₂₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
17	C₇×C₅⋊D₅	C₃×C₂₃	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₅×C₂₃	C₇×D₅	1	6	yes	complemented
19	C₂×C₇×C₂₃	—	25	1	no	Hall
20	D₅×C₂₃	—	5	6	no	—
21	C₃×C₇×D₅	—	5	6	no	—
22	C₅²×C₇	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented, Hall
23	C₇×C₂₃	C₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₅⋊D₅	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×C₂₃	—	25	1	no	Hall
26	C₅×C₂₃	C₃×C₇×D₅	1	6	yes	complemented
27	C₃×C₅×C₇	D₅×C₂₃	1	6	yes	complemented
28	C₃×C₅²	C₂×C₇×C₂₃	1	1	yes	characteristic, complemented, Hall
29	C₇×D₅	—	5	6	no	—
30	C₃×C₂₃	C₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
31	C₅⋊D₅	C₃×C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
32	C₂×C₂₃	—	25	1	no	Hall
33	C₂×C₃×C₇	—	25	1	no	Hall
34	C₅×C₇	C₃×D₅×C₂₃	1	6	yes	complemented
35	C₃×D₅	—	5	6	no	—
36	C₅²	C₂×C₃×C₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
37	C₂₃	C₃×C₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₇	C₂₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
39	C₃×C₅	C₇×D₅×C₂₃	1	6	yes	complemented
40	C₂×C₇	—	25	1	no	Hall
41	D₅	—	5	6	no	—
42	C₇	C₃×C₂₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	25	1	no	Hall
44	C₅	C₃×C₇×D₅×C₂₃	1	6	yes	complemented
45	C₃	C₇×C₂₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇×C₂₃	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₃×C₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₂₃	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₇×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₇×C₂₃	C₂	semidirect
2. C₇×C₂₃×C₅⋊D₅	C₃	direct (N × H)
4. C₅²×C₇×C₂₃	C₂×C₃	semidirect
5. C₃×C₂₃×C₅⋊D₅	C₇	direct (N × H)
6. C₃×C₅×C₇×C₂₃	D₅	semidirect
7. C₃×C₅²×C₂₃	C₂×C₇	semidirect
9. C₂₃×C₅⋊D₅	C₃×C₇	direct (N × H)
10. C₃×C₇×C₅⋊D₅	C₂₃	direct (N × H)
12. C₅×C₇×C₂₃	C₃×D₅	semidirect
14. C₅²×C₂₃	C₂×C₃×C₇	semidirect
15. C₃×C₅²×C₇	C₂×C₂₃	semidirect
16. C₃×C₇×C₂₃	C₅⋊D₅	direct (N × H)
17. C₇×C₅⋊D₅	C₃×C₂₃	direct (N × H)
18. C₃×C₅×C₂₃	C₇×D₅	semidirect
22. C₅²×C₇	C₂×C₃×C₂₃	semidirect
23. C₇×C₂₃	C₃×C₅⋊D₅	direct (N × H)
24. C₃×C₅⋊D₅	C₇×C₂₃	direct (N × H)
26. C₅×C₂₃	C₃×C₇×D₅	semidirect
27. C₃×C₅×C₇	D₅×C₂₃	semidirect
28. C₃×C₅²	C₂×C₇×C₂₃	semidirect
30. C₃×C₂₃	C₇×C₅⋊D₅	direct (N × H)
31. C₅⋊D₅	C₃×C₇×C₂₃	direct (N × H)
34. C₅×C₇	C₃×D₅×C₂₃	semidirect
36. C₅²	C₂×C₃×C₇×C₂₃	semidirect
37. C₂₃	C₃×C₇×C₅⋊D₅	direct (N × H)
38. C₃×C₇	C₂₃×C₅⋊D₅	direct (N × H)
39. C₃×C₅	C₇×D₅×C₂₃	semidirect
42. C₇	C₃×C₂₃×C₅⋊D₅	direct (N × H)
44. C₅	C₃×C₇×D₅×C₂₃	semidirect
45. C₃	C₇×C₂₃×C₅⋊D₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₇×C₂₃	2
C₇×C₂₃×C₅⋊D₅	3
C₃×C₇×D₅×C₂₃	5
C₃×C₂₃×C₅⋊D₅	7
C₃×C₇×C₅⋊D₅	23

Subgroups — C3×C7×C23×C5⋊D5 #37563406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×C₂₃×C₅⋊D₅ #37563406