Subgroups — C₃×C₂₃×D₇₅ #23780341

Order 10350.

54 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	C₂₃×D₇₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₂₃×D₂₅	—	3	1	no	maximal
4	C₃×C₂₃×D₁₅	—	5	1	no	maximal
5	C₃×C₂₃×C₂₅	—	2	1	no	—
6	C₃×C₂₃×C₂₅	D₃	1	1	yes	characteristic, complemented
7	C₃×C₂₃×C₂₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂₃×D₂₅	—	3	1	no	Hall
9	C₃²×C₅×C₂₃	D₅	1	1	yes	characteristic
10	C₂₃×D₁₅	—	5	1	no	—
11	C₃×D₅×C₂₃	—	15	1	no	—
12	C₂₃×C₂₅	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₇₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₃×D₃×C₂₃	—	25	1	no	Hall
15	C₃×C₅×C₂₃	—	2	1	no	—
16	C₃×C₅×C₂₃	C₃×D₅	1	1	yes	characteristic
17	C₃×C₅×C₂₃	D₁₅	1	1	yes	characteristic
18	D₅×C₂₃	—	15	1	no	—
19	C₃²×C₂₅	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₂₃	D₂₅	1	1	yes	characteristic, complemented, Hall
21	D₇₅	C₃×C₂₃	1	1	yes	characteristic, direct product factor
22	C₃×D₂₅	—	3	1	no	—
23	C₂×C₃×C₂₃	—	75	1	no	—
24	D₃×C₂₃	—	25	1	no	—
25	C₅×C₂₃	C₃×D₁₅	1	1	yes	characteristic
26	C₃×D₁₅	—	5	1	no	—
27	C₃×C₂₅	—	2	1	no	—
28	C₃×C₂₅	D₃×C₂₃	1	1	yes	characteristic, complemented
29	C₃×C₂₅	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
30	C₃×C₂₃	—	2	1	no	—
31	C₃×C₂₃	C₃×D₂₅	1	1	yes	characteristic, complemented
32	C₃×C₂₃	D₇₅	1	1	yes	characteristic, direct product factor
33	D₂₅	—	3	1	no	Hall
34	C₂×C₂₃	—	75	1	no	Hall
35	C₃²×C₅	D₅×C₂₃	1	1	yes	characteristic
36	D₁₅	—	5	1	no	—
37	C₃×D₅	—	15	1	no	—
38	C₂₅	C₃×D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
39	C₂₃	C₃×D₇₅	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×D₃	—	25	1	no	Hall
41	C₃×C₅	—	2	1	no	—
42	C₃×C₅	C₃×D₅×C₂₃	1	1	yes	characteristic
43	C₃×C₅	C₂₃×D₁₅	1	1	yes	characteristic
44	D₅	—	15	1	no	—
45	C₃²	C₂₃×D₂₅	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	75	1	no	—
47	D₃	—	25	1	no	—
48	C₅	C₃×C₂₃×D₁₅	1	1	yes	characteristic
49	C₃	—	2	1	no	—
50	C₃	C₃×C₂₃×D₂₅	1	1	yes	characteristic, complemented
51	C₃	C₂₃×D₇₅	1	1	yes	characteristic, direct product factor
52	C₂	—	75	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₃	D₇₅
commutator, cosocle, hypocenter	C₃×C₂₅	C₂×C₃×C₂₃
Frattini	C₅	C₃×C₂₃×D₁₅
Fitting	C₃²×C₂₃×C₂₅	C₂
socle	C₃²×C₅×C₂₃	D₅
LCS	G ▷ C₃×C₂₅
UCS	C₁ ◁ C₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₃×C₂₅	C₂	semidirect
2. C₂₃×D₇₅	C₃	direct (N × H)
6. C₃×C₂₃×C₂₅	D₃	semidirect
7. C₃×C₂₃×C₂₅	C₂×C₃	semidirect
12. C₂₃×C₂₅	C₃×D₃	semidirect
13. C₃×D₇₅	C₂₃	direct (N × H)
19. C₃²×C₂₅	C₂×C₂₃	semidirect
20. C₃²×C₂₃	D₂₅	semidirect
21. D₇₅	C₃×C₂₃	direct (N × H)
28. C₃×C₂₅	D₃×C₂₃	semidirect
29. C₃×C₂₅	C₂×C₃×C₂₃	semidirect
31. C₃×C₂₃	C₃×D₂₅	semidirect
32. C₃×C₂₃	D₇₅	direct (N × H)
38. C₂₅	C₃×D₃×C₂₃	semidirect
39. C₂₃	C₃×D₇₅	direct (N × H)
45. C₃²	C₂₃×D₂₅	semidirect
50. C₃	C₃×C₂₃×D₂₅	semidirect
51. C₃	C₂₃×D₇₅	direct (N × H)

Subgroups — C3×C23×D75 #23780341

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₂₃×D₇₅ #23780341