Subgroups — C₃×D₁₇₂₅ #23780342

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	D₁₇₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₅₇₅	—	3	1	no	maximal
4	C₃×D₃₄₅	—	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	D₅₇₅	—	3	1	no	Hall
9	C₃²×C₅×C₂₃	D₅	1	1	yes	characteristic
10	D₃₄₅	—	5	1	no	—
11	C₃×D₁₁₅	—	15	1	no	—
12	C₂₃×C₂₅	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₇₅	—	23	1	no	maximal, Hall
14	C₃×D₆₉	—	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	D₁₁₅	—	15	1	no	—
19	C₃²×C₂₅	D₂₃	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₂₃	D₂₅	1	1	yes	characteristic, complemented, Hall
21	D₇₅	—	23	1	no	—
22	C₃×D₂₅	—	69	1	no	—
23	D₆₉	—	25	1	no	—
24	C₃×D₂₃	—	75	1	no	—
25	C₅×C₂₃	C₃×D₁₅	1	1	yes	characteristic
26	C₃×D₁₅	—	115	1	no	—
27	C₃×C₂₅	—	2	1	no	—
28	C₃×C₂₅	C₃×D₂₃	1	1	yes	characteristic, complemented
29	C₃×C₂₅	D₆₉	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, complemented
33	D₂₅	—	69	1	no	Hall
34	D₂₃	—	75	1	no	Hall
35	C₃²×C₅	D₁₁₅	1	1	yes	characteristic
36	D₁₅	—	115	1	no	—
37	C₃×D₅	—	345	1	no	—
38	C₂₅	C₃×D₆₉	1	1	yes	characteristic, complemented, Sylow
39	C₂₃	C₃×D₇₅	1	1	yes	characteristic, complemented, Sylow
40	C₃×D₃	—	575	1	no	Hall
41	C₃×C₅	—	2	1	no	—
42	C₃×C₅	C₃×D₁₁₅	1	1	yes	characteristic
43	C₃×C₅	D₃₄₅	1	1	yes	characteristic
44	D₅	—	345	1	no	—
45	C₃²	D₅₇₅	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	1725	1	no	—
47	D₃	—	575	1	no	—
48	C₅	C₃×D₃₄₅	1	1	yes	characteristic
49	C₃	—	2	1	no	—
50	C₃	C₃×D₅₇₅	1	1	yes	characteristic, complemented
51	C₃	D₁₇₂₅	1	1	yes	characteristic, direct product factor
52	C₂	—	1725	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₁₇₂₅
commutator, cosocle, hypocenter	C₃×C₂₃×C₂₅	C₂×C₃
Frattini	C₅	C₃×D₃₄₅
Fitting	C₃²×C₂₃×C₂₅	C₂
socle	C₃²×C₅×C₂₃	D₅
LCS	G ▷ C₃×C₂₃×C₂₅
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₃×C₂₅	C₂	semidirect
2. D₁₇₂₅	C₃	direct (N × H)
6. C₃×C₂₃×C₂₅	D₃	semidirect
7. C₃×C₂₃×C₂₅	C₂×C₃	semidirect
12. C₂₃×C₂₅	C₃×D₃	semidirect
19. C₃²×C₂₅	D₂₃	semidirect
20. C₃²×C₂₃	D₂₅	semidirect
28. C₃×C₂₅	C₃×D₂₃	semidirect
29. C₃×C₂₅	D₆₉	semidirect
31. C₃×C₂₃	C₃×D₂₅	semidirect
32. C₃×C₂₃	D₇₅	semidirect
38. C₂₅	C₃×D₆₉	semidirect
39. C₂₃	C₃×D₇₅	semidirect
45. C₃²	D₅₇₅	semidirect
50. C₃	C₃×D₅₇₅	semidirect
51. C₃	D₁₇₂₅	direct (N × H)

Subgroups — C3×D1725 #23780342

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₁₇₂₅ #23780342