Subgroups — C₃²×C₂₃×D₂₅ #23780337

Order 10350.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₃×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₂₃×D₂₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₅×C₂₃	—	5	1	no	maximal
4	C₃×C₂₃×C₂₅	C₂×C₃	1	4	yes	complemented
5	C₂₃×D₂₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₅×C₂₃	D₅	1	1	yes	characteristic
7	C₃×D₅×C₂₃	—	5	4	no	—
8	C₂₃×C₂₅	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×D₂₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃²×C₂₃	—	25	1	no	Hall
11	C₃×C₅×C₂₃	C₃×D₅	1	4	yes	—
12	D₅×C₂₃	—	5	1	no	—
13	C₃²×C₂₅	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
14	C₃²×C₂₃	D₂₅	1	1	yes	characteristic, direct product factor, Hall
15	C₃×D₂₅	C₃×C₂₃	1	4	yes	direct product factor
16	C₂×C₃×C₂₃	—	25	4	no	—
17	C₅×C₂₃	C₃²×D₅	1	1	yes	characteristic
18	C₃²×D₅	—	5	1	no	—
19	C₃×C₂₅	C₂×C₃×C₂₃	1	4	yes	complemented
20	C₃×C₂₃	C₃×D₂₅	1	4	yes	direct product factor
21	D₂₅	C₃²×C₂₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₂₃	—	25	1	no	Hall
23	C₃²×C₅	D₅×C₂₃	1	1	yes	characteristic
24	C₃×D₅	—	5	4	no	—
25	C₂₅	C₂×C₃²×C₂₃	1	1	yes	characteristic, complemented, Sylow
26	C₂₃	C₃²×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃²	—	25	1	no	Hall
28	C₃×C₅	C₃×D₅×C₂₃	1	4	yes	—
29	D₅	—	5	1	no	—
30	C₃²	C₂₃×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	25	4	no	—
32	C₅	C₃²×D₅×C₂₃	1	1	yes	characteristic
33	C₃	C₃×C₂₃×D₂₅	1	4	yes	direct product factor
34	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₂₃	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂×C₃²×C₂₃
Frattini	C₅	C₃²×D₅×C₂₃
Fitting	C₃²×C₂₃×C₂₅	C₂
socle	C₃²×C₅×C₂₃	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₃²×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₃×C₂₅	C₂	semidirect
2. C₃×C₂₃×D₂₅	C₃	direct (N × H)
4. C₃×C₂₃×C₂₅	C₂×C₃	semidirect
5. C₂₃×D₂₅	C₃²	direct (N × H)
8. C₂₃×C₂₅	C₂×C₃²	semidirect
9. C₃²×D₂₅	C₂₃	direct (N × H)
13. C₃²×C₂₅	C₂×C₂₃	semidirect
14. C₃²×C₂₃	D₂₅	direct (N × H)
15. C₃×D₂₅	C₃×C₂₃	direct (N × H)
19. C₃×C₂₅	C₂×C₃×C₂₃	semidirect
20. C₃×C₂₃	C₃×D₂₅	direct (N × H)
21. D₂₅	C₃²×C₂₃	direct (N × H)
25. C₂₅	C₂×C₃²×C₂₃	semidirect
26. C₂₃	C₃²×D₂₅	direct (N × H)
30. C₃²	C₂₃×D₂₅	direct (N × H)
33. C₃	C₃×C₂₃×D₂₅	direct (N × H)

Subgroups — C32×C23×D25 #23780337

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₂₃×D₂₅ #23780337