Subgroups — C₃×C₂₃×(C₅⋊D₅)⋊C₃ #23780368

Order 10350.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₃×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₂₃×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂₃×(C₅⋊D₅)⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₅²×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₂₃×C₅²⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₂₃×C₅⋊D₅	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×D₅×C₂₃	—	15	2	no	—
8	C₅²×C₂₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×(C₅⋊D₅)⋊C₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃²×C₂₃	—	25	1	no	maximal, Hall
11	C₃×C₅×C₂₃	—	3	2	no	—
12	D₅×C₂₃	—	15	2	no	—
13	C₃×C₅²⋊C₃	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
14	C₃²×C₂₃	—	25	1	no	Hall
15	C₃×C₅⋊D₅	C₃×C₂₃	1	1	yes	characteristic, complemented
16	(C₅⋊D₅)⋊C₃	C₃×C₂₃	1	3	yes	direct product factor
17	C₂×C₃×C₂₃	—	25	3	no	—
18	C₂×C₃×C₂₃	—	25	1	no	—
19	C₅×C₂₃	—	3	2	no	—
20	C₃×C₅²	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
21	C₅²⋊C₃	C₂×C₃×C₂₃	1	3	yes	complemented
22	C₃×C₂₃	—	25	3	no	—
23	C₃×C₂₃	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, direct product factor
24	C₅⋊D₅	C₃²×C₂₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₂₃	—	25	1	no	Hall
26	C₃×D₅	—	15	2	no	—
27	C₅²	C₂×C₃²×C₂₃	1	1	yes	characteristic, complemented, Sylow
28	C₂₃	C₃×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃²	—	25	1	no	Hall
30	C₃×C₅	—	3	2	no	—
31	D₅	—	15	2	no	—
32	C₃²	—	25	1	no	Sylow
33	C₂×C₃	—	25	3	no	—
34	C₂×C₃	—	25	1	no	—
35	C₅	—	3	2	no	—
36	C₃	—	25	3	no	—
37	C₃	C₂₃×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, direct product factor
38	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₃	(C₅⋊D₅)⋊C₃
commutator, cosocle, hypocenter	C₅²	C₂×C₃²×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₃	C₂×C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₃×C₅²⋊C₃	C₂	semidirect
2. C₃×C₂₃×C₅⋊D₅	C₃	semidirect
3. C₂₃×(C₅⋊D₅)⋊C₃	C₃	direct (N × H)
4. C₃×C₅²×C₂₃	C₂×C₃	semidirect
5. C₂₃×C₅²⋊C₃	C₂×C₃	semidirect
6. C₂₃×C₅⋊D₅	C₃²	semidirect
8. C₅²×C₂₃	C₂×C₃²	semidirect
9. C₃×(C₅⋊D₅)⋊C₃	C₂₃	direct (N × H)
13. C₃×C₅²⋊C₃	C₂×C₂₃	semidirect
15. C₃×C₅⋊D₅	C₃×C₂₃	semidirect
16. (C₅⋊D₅)⋊C₃	C₃×C₂₃	direct (N × H)
20. C₃×C₅²	C₂×C₃×C₂₃	semidirect
21. C₅²⋊C₃	C₂×C₃×C₂₃	semidirect
23. C₃×C₂₃	(C₅⋊D₅)⋊C₃	direct (N × H)
24. C₅⋊D₅	C₃²×C₂₃	semidirect
27. C₅²	C₂×C₃²×C₂₃	semidirect
28. C₂₃	C₃×(C₅⋊D₅)⋊C₃	direct (N × H)
37. C₃	C₂₃×(C₅⋊D₅)⋊C₃	direct (N × H)

Subgroups — C3×C23×(C5⋊D5)⋊C3 #23780368

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₂₃×(C₅⋊D₅)⋊C₃ #23780368