Subgroups — C₃×D₅×D₅₁₅ #44525508

Order 30900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₅₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅⋊D₅₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₅₁₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅²×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₅₁₅	—	5	1	no	maximal
7	C₃×D₅×D₁₀₃	—	5	1	no	maximal
8	C₅⋊D₅₁₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₅₁₅	C₂×C₃	1	1	yes	characteristic, complemented
10	C₅×D₅×C₁₀₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×D₅₁₅	—	5	1	no	—
12	C₃×D₅₁₅	—	5	1	no	—
13	C₃×D₅₁₅	—	10	2	no	—
14	C₃×D₅₁₅	D₅	1	1	yes	characteristic, direct product factor
15	C₃×D₅×C₁₀₃	D₅	1	1	yes	characteristic, complemented
16	C₃×C₅×D₁₀₃	—	5	1	no	—
17	C₂×C₃×C₅×C₁₀₃	—	5	1	no	—
18	C₅²×C₁₀₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
19	C₂×D₅₁₅	—	5	1	no	—
20	D₅×D₁₀₃	—	5	1	no	—
21	C₃×C₅×C₁₀₃	—	2	2	no	—
22	C₃×C₅×C₁₀₃	C₂×D₅	1	1	yes	characteristic, complemented
23	C₃×C₅×C₁₀₃	C₂×D₅	1	1	yes	characteristic, complemented
24	C₂×C₃×D₁₀₃	—	25	1	no	Hall
25	C₂×C₅×C₁₀₃	—	5	1	no	—
26	D₅₁₅	—	5	1	no	—
27	D₅₁₅	—	5	1	no	—
28	D₅₁₅	—	10	2	no	—
29	D₅₁₅	C₃×D₅	1	1	yes	characteristic, direct product factor
30	C₅×D₁₀₃	—	5	1	no	—
31	D₅×C₁₀₃	C₃×D₅	1	1	yes	characteristic, complemented
32	C₂×C₃×C₁₀₃	—	5	1	no	—
33	C₃×D₁₀₃	—	5	1	no	—
34	C₃×D₁₀₃	—	25	1	no	—
35	C₅×C₁₀₃	—	2	2	no	—
36	C₅×C₁₀₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented
37	C₅×C₁₀₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented
38	C₂×D₁₀₃	—	25	1	no	Hall
39	C₃×C₁₀₃	D₅²	1	1	yes	characteristic, complemented, Hall
40	C₃×D₅²	—	103	1	no	maximal, Hall
41	C₂×C₁₀₃	—	5	1	no	—
42	D₁₀₃	—	5	1	no	—
43	D₁₀₃	—	25	1	no	—
44	C₃×C₅⋊D₅	—	103	1	no	—
45	C₃×C₅×D₅	—	103	1	no	—
46	C₃×C₅×D₅	D₁₀₃	1	1	yes	characteristic, complemented
47	C₁₀₃	C₃×D₅²	1	1	yes	characteristic, complemented, Sylow
48	D₅²	—	103	1	no	Hall
49	C₃×C₅²	C₂×D₁₀₃	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃×D₅	—	515	1	no	—
51	C₂×C₃×D₅	—	515	1	no	—
52	C₅⋊D₅	—	103	1	no	—
53	C₅×D₅	—	103	1	no	—
54	C₅×D₅	C₃×D₁₀₃	1	1	yes	characteristic, complemented
55	C₂×C₃×C₅	—	515	1	no	—
56	C₂×C₃×C₅	—	5	1	no	—
57	C₃×D₅	—	515	1	no	—
58	C₃×D₅	—	515	1	no	—
59	C₃×D₅	—	1030	2	no	—
60	C₃×D₅	—	103	1	no	—
61	C₃×D₅	D₅₁₅	1	1	yes	characteristic, direct product factor
62	C₅²	C₂×C₃×D₁₀₃	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₅	—	515	1	no	—
64	C₂×D₅	—	515	1	no	—
65	C₃×C₅	—	2	2	no	—
66	C₃×C₅	D₅×D₁₀₃	1	1	yes	characteristic, complemented
67	C₃×C₅	C₂×D₅₁₅	1	1	yes	characteristic, complemented
68	C₂²×C₃	—	2575	1	no	Hall
69	C₂×C₅	—	515	1	no	—
70	C₂×C₅	—	5	1	no	—
71	D₅	—	515	1	no	—
72	D₅	—	515	1	no	—
73	D₅	—	1030	2	no	—
74	D₅	—	103	1	no	—
75	D₅	C₃×D₅₁₅	1	1	yes	characteristic, direct product factor
76	C₂×C₃	—	515	1	no	—
77	C₂×C₃	—	5	1	no	—
78	C₂×C₃	—	2575	1	no	—
79	C₅	—	2	2	no	—
80	C₅	C₃×D₅×D₁₀₃	1	1	yes	characteristic, complemented
81	C₅	C₂×C₃×D₅₁₅	1	1	yes	characteristic, complemented
82	C₂²	—	2575	1	no	Sylow
83	C₃	D₅×D₅₁₅	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	—	515	1	no	—
85	C₂	—	5	1	no	—
86	C₂	—	2575	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅×D₅₁₅
commutator, cosocle, hypocenter	C₅²×C₁₀₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₀₃	C₂²
LCS	G ▷ C₅²×C₁₀₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₅×C₁₀₃	C₂	semidirect
2. C₃×C₅×D₅₁₅	C₂	semidirect
3. C₃×C₅⋊D₅₁₅	C₂	semidirect
4. D₅×D₅₁₅	C₃	direct (N × H)
5. C₃×C₅²×C₁₀₃	C₂²	semidirect
8. C₅⋊D₅₁₅	C₂×C₃	semidirect
9. C₅×D₅₁₅	C₂×C₃	semidirect
10. C₅×D₅×C₁₀₃	C₂×C₃	semidirect
14. C₃×D₅₁₅	D₅	direct (N × H)
15. C₃×D₅×C₁₀₃	D₅	semidirect
18. C₅²×C₁₀₃	C₂²×C₃	semidirect
22. C₃×C₅×C₁₀₃	C₂×D₅	semidirect
23. C₃×C₅×C₁₀₃	C₂×D₅	semidirect
29. D₅₁₅	C₃×D₅	direct (N × H)
31. D₅×C₁₀₃	C₃×D₅	semidirect
36. C₅×C₁₀₃	C₂×C₃×D₅	semidirect
37. C₅×C₁₀₃	C₂×C₃×D₅	semidirect
39. C₃×C₁₀₃	D₅²	semidirect
46. C₃×C₅×D₅	D₁₀₃	semidirect
47. C₁₀₃	C₃×D₅²	semidirect
49. C₃×C₅²	C₂×D₁₀₃	semidirect
54. C₅×D₅	C₃×D₁₀₃	semidirect
61. C₃×D₅	D₅₁₅	direct (N × H)
62. C₅²	C₂×C₃×D₁₀₃	semidirect
66. C₃×C₅	D₅×D₁₀₃	semidirect
67. C₃×C₅	C₂×D₅₁₅	semidirect
75. D₅	C₃×D₅₁₅	direct (N × H)
80. C₅	C₃×D₅×D₁₀₃	semidirect
81. C₅	C₂×C₃×D₅₁₅	semidirect
83. C₃	D₅×D₅₁₅	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×C₅×D₅×C₁₀₃	2
C₃×C₅×D₅₁₅	2
C₃×C₅⋊D₅₁₅	2
D₅×D₅₁₅	3
C₂×C₃×D₅₁₅	5
C₃×D₅×D₁₀₃	5
C₃×D₅²	103

Subgroups — C3×D5×D515 #44525508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×D₅₁₅ #44525508