Subgroups — C₃×C₂₃×#3874 #23780366

Order 10350.

52 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×C₅×D₅×C₂₃	—	3	1	no	maximal
3	C₂₃×#3874	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×C₅²×C₂₃	D₃	1	1	yes	characteristic, complemented
5	C₂₃×C₅²⋊C₃	—	2	1	no	—
6	C₂₃×C₅²⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×D₅×C₂₃	—	3	1	no	Hall
8	C₂×C₃×C₅×C₂₃	—	15	1	no	—
9	C₃×D₅×C₂₃	—	3	1	no	—
10	C₅²×C₂₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	C₃×#3874	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃×D₃×C₂₃	—	25	1	no	maximal, Hall
13	C₃×C₅×C₂₃	—	3	1	no	—
14	C₃×C₅×C₂₃	—	3	1	no	—
15	C₂×C₅×C₂₃	—	15	1	no	—
16	D₅×C₂₃	—	3	1	no	—
17	C₃×C₅²⋊C₃	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
18	C₃²×C₂₃	—	25	1	no	Hall
19	C₃×C₅×D₅	—	3	1	no	—
20	#3874	C₃×C₂₃	1	1	yes	characteristic, direct product factor
21	C₂×C₃×C₂₃	—	15	1	no	—
22	D₃×C₂₃	—	25	1	no	—
23	C₅×C₂₃	—	3	1	no	—
24	C₅×C₂₃	—	3	1	no	—
25	C₃×C₅²	D₃×C₂₃	1	1	yes	characteristic, complemented
26	C₅²⋊C₃	—	2	1	no	—
27	C₅²⋊C₃	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
28	C₃×C₂₃	—	25	1	no	—
29	C₃×C₂₃	—	50	1	no	—
30	C₃×C₂₃	#3874	1	1	yes	characteristic, direct product factor
31	C₅×D₅	—	3	1	no	Hall
32	C₂×C₂₃	—	15	1	no	Hall
33	C₂×C₃×C₅	—	15	1	no	—
34	C₃×D₅	—	3	1	no	—
35	C₅²	C₃×D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
36	C₂₃	C₃×#3874	1	1	yes	characteristic, direct product factor, Sylow
37	C₃×D₃	—	25	1	no	Hall
38	C₃×C₅	—	3	1	no	—
39	C₃×C₅	—	3	1	no	—
40	C₂×C₅	—	15	1	no	—
41	D₅	—	3	1	no	—
42	C₃²	—	25	1	no	Sylow
43	C₂×C₃	—	15	1	no	—
44	D₃	—	25	1	no	—
45	C₅	—	3	1	no	—
46	C₅	—	3	1	no	—
47	C₃	—	25	1	no	—
48	C₃	—	50	1	no	—
49	C₃	C₂₃×#3874	1	1	yes	characteristic, direct product factor
50	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₃	#3874
commutator, cosocle, hypocenter	C₅²⋊C₃	C₂×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₃	D₃
LCS	G ▷ C₅²⋊C₃
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
3. C₂₃×#3874	C₃	direct (N × H)
4. C₃×C₅²×C₂₃	D₃	semidirect
6. C₂₃×C₅²⋊C₃	C₂×C₃	semidirect
10. C₅²×C₂₃	C₃×D₃	semidirect
11. C₃×#3874	C₂₃	direct (N × H)
17. C₃×C₅²⋊C₃	C₂×C₂₃	semidirect
20. #3874	C₃×C₂₃	direct (N × H)
25. C₃×C₅²	D₃×C₂₃	semidirect
27. C₅²⋊C₃	C₂×C₃×C₂₃	semidirect
30. C₃×C₂₃	#3874	direct (N × H)
35. C₅²	C₃×D₃×C₂₃	semidirect
36. C₂₃	C₃×#3874	direct (N × H)
49. C₃	C₂₃×#3874	direct (N × H)

Subgroups — C3×C23×#3874 #23780366

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₂₃×#3874 #23780366