Subgroups — D₁₅⋊D₅₁₅ #44525531

Order 30900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₅₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₅×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₅₄₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₅₁₅	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₅⋊D₁₀₃	—	5	1	no	maximal
7	D₃×D₅₁₅	—	5	1	no	maximal
8	C₅⋊D₅₁₅	D₃	1	1	yes	characteristic, complemented
9	C₅×D₅₁₅	—	3	1	no	—
10	C₅×D₅×C₁₀₃	—	3	1	no	—
11	D₁₅₄₅	D₅	1	1	yes	characteristic, complemented
12	D₁₅×C₁₀₃	D₅	1	1	yes	characteristic, complemented
13	C₅×D₃₀₉	—	5	1	no	—
14	C₅×D₃×C₁₀₃	—	5	1	no	—
15	C₃×D₅₁₅	—	5	1	no	—
16	C₃×D₅₁₅	—	5	1	no	—
17	C₃×D₅₁₅	—	10	2	no	—
18	C₅²×C₁₀₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×D₅₁₅	—	15	1	no	—
20	D₅×D₁₀₃	—	15	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	D₃×D₁₀₃	—	25	1	no	Hall
25	C₂×C₅×C₁₀₃	—	15	1	no	—
26	D₅₁₅	—	3	1	no	—
27	D₅₁₅	—	5	1	no	—
28	D₅₁₅	—	5	1	no	—
29	D₅₁₅	—	10	2	no	—
30	C₅×D₁₀₃	—	15	1	no	—
31	D₅×C₁₀₃	—	3	1	no	—
32	D₃₀₉	—	5	1	no	—
33	C₃×D₁₀₃	—	25	1	no	—
34	D₃×C₁₀₃	—	5	1	no	—
35	C₅×C₁₀₃	—	2	2	no	—
36	C₅×C₁₀₃	D₃×D₅	1	1	yes	characteristic, complemented
37	C₅×C₁₀₃	D₃×D₅	1	1	yes	characteristic, complemented
38	C₂×D₁₀₃	—	75	1	no	Hall
39	C₃×C₁₀₃	D₅²	1	1	yes	characteristic, complemented, Hall
40	D₁₅⋊D₅	—	103	1	no	maximal, Hall
41	C₂×C₁₀₃	—	15	1	no	—
42	D₁₀₃	—	15	1	no	—
43	D₁₀₃	—	25	1	no	—
44	C₅×D₁₅	—	103	1	no	—
45	C₅×D₁₅	D₁₀₃	1	1	yes	characteristic, complemented
46	C₃×C₅⋊D₅	—	103	1	no	—
47	C₁₀₃	D₁₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
48	D₅²	—	309	1	no	Hall
49	C₃×C₅²	C₂×D₁₀₃	1	1	yes	characteristic, complemented, Hall
50	D₃×D₅	—	515	1	no	—
51	D₃×D₅	—	515	1	no	—
52	C₅⋊D₅	—	103	1	no	—
53	C₅×D₅	—	3	1	no	—
54	C₅×D₅	—	309	1	no	—
55	D₁₅	—	103	1	no	—
56	D₁₅	D₅₁₅	1	1	yes	characteristic, complemented
57	C₃×D₅	—	515	1	no	—
58	C₃×D₅	—	515	1	no	—
59	C₃×D₅	—	1030	2	no	—
60	C₅×D₃	—	515	1	no	—
61	C₅×D₃	—	5	1	no	—
62	C₅²	D₃×D₁₀₃	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₅	—	1545	1	no	—
64	C₂×D₅	—	1545	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	C₂×D₃	—	2575	1	no	Hall
69	C₂×C₅	—	1545	1	no	—
70	C₂×C₅	—	15	1	no	—
71	D₅	—	3	1	no	—
72	D₅	—	515	1	no	—
73	D₅	—	515	1	no	—
74	D₅	—	1030	2	no	—
75	D₅	—	309	1	no	—
76	C₂×C₃	—	2575	1	no	—
77	D₃	—	515	1	no	—
78	D₃	—	5	1	no	—
79	C₅	—	2	2	no	—
80	C₅	D₃×D₅₁₅	1	1	yes	characteristic, complemented
81	C₅	D₁₅⋊D₁₀₃	1	1	yes	characteristic, complemented
82	C₂²	—	7725	1	no	Sylow
83	C₃	D₅×D₅₁₅	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	1545	1	no	—
85	C₂	—	15	1	no	—
86	C₂	—	2575	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₅⋊D₅₁₅	C₂	semidirect
2. C₅×D₁₅×C₁₀₃	C₂	semidirect
3. C₅×D₁₅₄₅	C₂	semidirect
5. C₃×C₅²×C₁₀₃	C₂²	semidirect
8. C₅⋊D₅₁₅	D₃	semidirect
11. D₁₅₄₅	D₅	semidirect
12. D₁₅×C₁₀₃	D₅	semidirect
18. C₅²×C₁₀₃	C₂×D₃	semidirect
22. C₃×C₅×C₁₀₃	C₂×D₅	semidirect
23. C₃×C₅×C₁₀₃	C₂×D₅	semidirect
36. C₅×C₁₀₃	D₃×D₅	semidirect
37. C₅×C₁₀₃	D₃×D₅	semidirect
39. C₃×C₁₀₃	D₅²	semidirect
45. C₅×D₁₅	D₁₀₃	semidirect
47. C₁₀₃	D₁₅⋊D₅	semidirect
49. C₃×C₅²	C₂×D₁₀₃	semidirect
56. D₁₅	D₅₁₅	semidirect
62. C₅²	D₃×D₁₀₃	semidirect
66. C₃×C₅	D₅×D₁₀₃	semidirect
67. C₃×C₅	C₂×D₅₁₅	semidirect
80. C₅	D₃×D₅₁₅	semidirect
81. C₅	D₁₅⋊D₁₀₃	semidirect
83. C₃	D₅×D₅₁₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅⋊D₅₁₅	2
C₅×D₁₅×C₁₀₃	2
C₅×D₁₅₄₅	2
D₅×D₅₁₅	3
D₁₅⋊D₁₀₃	5
D₃×D₅₁₅	5
D₁₅⋊D₅	103

Subgroups — D15⋊D515 #44525531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅⋊D₅₁₅ #44525531