Subgroups — C₃×D₅×D₂₅₃ #29503293

Order 15180.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₂₆₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₅×C₁₁×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₂₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₂₅₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₁×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₂₅₃	—	5	1	no	maximal, Hall
7	D₁₂₆₅	C₂×C₃	1	1	yes	characteristic, complemented
8	D₅×C₁₁×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₂₅₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₁₁×C₂₃	—	5	1	no	—
11	C₃×D₂₅₃	—	5	1	no	—
12	C₃×D₂₅₃	D₅	1	1	yes	characteristic, direct product factor
13	C₃×D₅×D₂₃	—	11	1	no	maximal, Hall
14	C₅×C₁₁×C₂₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₂₅₃	—	5	1	no	Hall
16	C₃×C₁₁×C₂₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₃×D₁₁₅	—	11	1	no	—
18	C₃×D₅×C₂₃	D₁₁	1	1	yes	characteristic, complemented
19	C₃×C₅×D₂₃	—	11	1	no	—
20	C₃×D₅×D₁₁	—	23	1	no	maximal, Hall
21	C₂×C₁₁×C₂₃	—	5	1	no	—
22	D₂₅₃	—	5	1	no	—
23	D₂₅₃	C₃×D₅	1	1	yes	characteristic, direct product factor
24	D₅×D₂₃	—	11	1	no	Hall
25	C₃×C₅×C₂₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
26	C₃×D₅₅	—	23	1	no	—
27	C₃×D₅×C₁₁	D₂₃	1	1	yes	characteristic, complemented
28	C₃×C₅×D₁₁	—	23	1	no	—
29	C₂×C₃×D₂₃	—	55	1	no	Hall
30	C₁₁×C₂₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
31	D₁₁₅	—	11	1	no	—
32	C₅×D₂₃	—	11	1	no	—
33	D₅×C₂₃	C₃×D₁₁	1	1	yes	characteristic, complemented
34	D₅×D₁₁	—	23	1	no	Hall
35	C₃×C₅×C₁₁	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₂₃	—	5	1	no	—
37	C₃×D₂₃	—	11	1	no	—
38	C₃×D₂₃	—	55	1	no	—
39	C₂×C₃×D₁₁	—	115	1	no	Hall
40	C₅×C₂₃	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
41	D₅₅	—	23	1	no	—
42	C₅×D₁₁	—	23	1	no	—
43	D₅×C₁₁	C₃×D₂₃	1	1	yes	characteristic, complemented
44	C₂×D₂₃	—	55	1	no	Hall
45	C₃×C₂₃	D₅×D₁₁	1	1	yes	characteristic, complemented, Hall
46	C₂×C₃×C₁₁	—	5	1	no	—
47	C₃×D₁₁	—	23	1	no	—
48	C₃×D₁₁	—	115	1	no	—
49	C₂×C₃×D₅	—	253	1	no	Hall
50	C₅×C₁₁	C₂×C₃×D₂₃	1	1	yes	characteristic, complemented, Hall
51	C₂×C₂₃	—	5	1	no	—
52	D₂₃	—	11	1	no	—
53	D₂₃	—	55	1	no	—
54	C₂×D₁₁	—	115	1	no	Hall
55	C₃×C₁₁	D₅×D₂₃	1	1	yes	characteristic, complemented, Hall
56	C₂×C₃×C₅	—	253	1	no	—
57	C₃×D₅	—	253	1	no	—
58	C₃×D₅	D₂₅₃	1	1	yes	characteristic, direct product factor
59	C₂₃	C₃×D₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₁₁	—	5	1	no	—
61	D₁₁	—	23	1	no	—
62	D₁₁	—	115	1	no	—
63	C₂×D₅	—	253	1	no	Hall
64	C₃×C₅	C₂×D₂₅₃	1	1	yes	characteristic, complemented, Hall
65	C₂²×C₃	—	1265	1	no	Hall
66	C₁₁	C₃×D₅×D₂₃	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₅	—	253	1	no	—
68	D₅	—	253	1	no	—
69	D₅	C₃×D₂₅₃	1	1	yes	characteristic, direct product factor
70	C₂×C₃	—	5	1	no	—
71	C₂×C₃	—	1265	1	no	—
72	C₂×C₃	—	253	1	no	—
73	C₅	C₂×C₃×D₂₅₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	1265	1	no	Sylow
75	C₃	D₅×D₂₅₃	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	5	1	no	—
77	C₂	—	1265	1	no	—
78	C₂	—	253	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅×D₂₅₃
commutator, cosocle, hypocenter	C₅×C₁₁×C₂₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₂₃	C₂²
LCS	G ▷ C₅×C₁₁×C₂₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₂₆₅	C₂	semidirect
2. C₃×D₅×C₁₁×C₂₃	C₂	semidirect
3. C₃×C₅×D₂₅₃	C₂	semidirect
4. D₅×D₂₅₃	C₃	direct (N × H)
5. C₃×C₅×C₁₁×C₂₃	C₂²	semidirect
7. D₁₂₆₅	C₂×C₃	semidirect
8. D₅×C₁₁×C₂₃	C₂×C₃	semidirect
9. C₅×D₂₅₃	C₂×C₃	semidirect
12. C₃×D₂₅₃	D₅	direct (N × H)
14. C₅×C₁₁×C₂₃	C₂²×C₃	semidirect
16. C₃×C₁₁×C₂₃	C₂×D₅	semidirect
18. C₃×D₅×C₂₃	D₁₁	semidirect
23. D₂₅₃	C₃×D₅	direct (N × H)
25. C₃×C₅×C₂₃	C₂×D₁₁	semidirect
27. C₃×D₅×C₁₁	D₂₃	semidirect
30. C₁₁×C₂₃	C₂×C₃×D₅	semidirect
33. D₅×C₂₃	C₃×D₁₁	semidirect
35. C₃×C₅×C₁₁	C₂×D₂₃	semidirect
40. C₅×C₂₃	C₂×C₃×D₁₁	semidirect
43. D₅×C₁₁	C₃×D₂₃	semidirect
45. C₃×C₂₃	D₅×D₁₁	semidirect
50. C₅×C₁₁	C₂×C₃×D₂₃	semidirect
55. C₃×C₁₁	D₅×D₂₃	semidirect
58. C₃×D₅	D₂₅₃	direct (N × H)
59. C₂₃	C₃×D₅×D₁₁	semidirect
64. C₃×C₅	C₂×D₂₅₃	semidirect
66. C₁₁	C₃×D₅×D₂₃	semidirect
69. D₅	C₃×D₂₅₃	direct (N × H)
73. C₅	C₂×C₃×D₂₅₃	semidirect
75. C₃	D₅×D₂₅₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×D₁₂₆₅	2
C₃×D₅×C₁₁×C₂₃	2
C₃×C₅×D₂₅₃	2
D₅×D₂₅₃	3
C₂×C₃×D₂₅₃	5
C₃×D₅×D₂₃	11
C₃×D₅×D₁₁	23

Subgroups — C3×D5×D253 #29503293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×D₂₅₃ #29503293