Subgroups — D₁₅⋊D₃₀₅ #32913145

Order 18300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₉₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₅×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅⋊D₃₀₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₃₀₅	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₅⋊D₆₁	—	5	1	no	maximal
7	D₃×D₃₀₅	—	5	1	no	maximal
8	C₅⋊D₃₀₅	D₃	1	1	yes	characteristic, complemented
9	C₅×D₃₀₅	—	3	1	no	—
10	C₅×D₅×C₆₁	—	3	1	no	—
11	D₉₁₅	D₅	1	1	yes	characteristic, complemented
12	D₁₅×C₆₁	D₅	1	1	yes	characteristic, complemented
13	C₅×D₁₈₃	—	5	1	no	—
14	C₅×D₃×C₆₁	—	5	1	no	—
15	C₃×D₃₀₅	—	5	1	no	—
16	C₃×D₃₀₅	—	5	1	no	—
17	C₃×D₃₀₅	—	10	2	no	—
18	C₅²×C₆₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
19	C₂×D₃₀₅	—	15	1	no	—
20	D₅×D₆₁	—	15	1	no	—
21	C₃×C₅×C₆₁	—	2	2	no	—
22	C₃×C₅×C₆₁	C₂×D₅	1	1	yes	characteristic, complemented
23	C₃×C₅×C₆₁	C₂×D₅	1	1	yes	characteristic, complemented
24	D₃×D₆₁	—	25	1	no	Hall
25	C₂×C₅×C₆₁	—	15	1	no	—
26	D₃₀₅	—	3	1	no	—
27	D₃₀₅	—	5	1	no	—
28	D₃₀₅	—	5	1	no	—
29	D₃₀₅	—	10	2	no	—
30	C₅×D₆₁	—	15	1	no	—
31	D₅×C₆₁	—	3	1	no	—
32	D₁₈₃	—	5	1	no	—
33	C₃×D₆₁	—	25	1	no	—
34	D₃×C₆₁	—	5	1	no	—
35	C₅×C₆₁	—	2	2	no	—
36	C₅×C₆₁	D₃×D₅	1	1	yes	characteristic, complemented
37	C₅×C₆₁	D₃×D₅	1	1	yes	characteristic, complemented
38	D₁₅⋊D₅	—	61	1	no	maximal, Hall
39	C₂×D₆₁	—	75	1	no	Hall
40	C₃×C₆₁	D₅²	1	1	yes	characteristic, complemented, Hall
41	C₅×D₁₅	—	61	1	no	—
42	C₅×D₁₅	D₆₁	1	1	yes	characteristic, complemented
43	C₃×C₅⋊D₅	—	61	1	no	—
44	C₂×C₆₁	—	15	1	no	—
45	D₆₁	—	15	1	no	—
46	D₆₁	—	25	1	no	—
47	D₅²	—	183	1	no	Hall
48	C₃×C₅²	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
49	C₆₁	D₁₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
50	D₃×D₅	—	305	1	no	—
51	D₃×D₅	—	305	1	no	—
52	C₅⋊D₅	—	61	1	no	—
53	C₅×D₅	—	3	1	no	—
54	C₅×D₅	—	183	1	no	—
55	D₁₅	—	61	1	no	—
56	D₁₅	D₃₀₅	1	1	yes	characteristic, complemented
57	C₃×D₅	—	305	1	no	—
58	C₃×D₅	—	305	1	no	—
59	C₃×D₅	—	610	2	no	—
60	C₅×D₃	—	5	1	no	—
61	C₅×D₃	—	305	1	no	—
62	C₅²	D₃×D₆₁	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₅	—	915	1	no	—
64	C₂×D₅	—	915	1	no	—
65	C₃×C₅	—	2	2	no	—
66	C₃×C₅	D₅×D₆₁	1	1	yes	characteristic, complemented
67	C₃×C₅	C₂×D₃₀₅	1	1	yes	characteristic, complemented
68	C₂×D₃	—	1525	1	no	Hall
69	C₂×C₅	—	15	1	no	—
70	C₂×C₅	—	915	1	no	—
71	D₅	—	3	1	no	—
72	D₅	—	305	1	no	—
73	D₅	—	305	1	no	—
74	D₅	—	610	2	no	—
75	D₅	—	183	1	no	—
76	C₂×C₃	—	1525	1	no	—
77	D₃	—	5	1	no	—
78	D₃	—	305	1	no	—
79	C₅	—	2	2	no	—
80	C₅	D₃×D₃₀₅	1	1	yes	characteristic, complemented
81	C₅	D₁₅⋊D₆₁	1	1	yes	characteristic, complemented
82	C₂²	—	4575	1	no	Sylow
83	C₃	D₅×D₃₀₅	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	15	1	no	—
85	C₂	—	915	1	no	—
86	C₂	—	1525	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅²×C₆₁	C₂²
LCS	G ▷ C₃×C₅²×C₆₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅×D₉₁₅	C₂	semidirect
2. C₅×D₁₅×C₆₁	C₂	semidirect
3. C₃×C₅⋊D₃₀₅	C₂	semidirect
5. C₃×C₅²×C₆₁	C₂²	semidirect
8. C₅⋊D₃₀₅	D₃	semidirect
11. D₉₁₅	D₅	semidirect
12. D₁₅×C₆₁	D₅	semidirect
18. C₅²×C₆₁	C₂×D₃	semidirect
22. C₃×C₅×C₆₁	C₂×D₅	semidirect
23. C₃×C₅×C₆₁	C₂×D₅	semidirect
36. C₅×C₆₁	D₃×D₅	semidirect
37. C₅×C₆₁	D₃×D₅	semidirect
40. C₃×C₆₁	D₅²	semidirect
42. C₅×D₁₅	D₆₁	semidirect
48. C₃×C₅²	C₂×D₆₁	semidirect
49. C₆₁	D₁₅⋊D₅	semidirect
56. D₁₅	D₃₀₅	semidirect
62. C₅²	D₃×D₆₁	semidirect
66. C₃×C₅	D₅×D₆₁	semidirect
67. C₃×C₅	C₂×D₃₀₅	semidirect
80. C₅	D₃×D₃₀₅	semidirect
81. C₅	D₁₅⋊D₆₁	semidirect
83. C₃	D₅×D₃₀₅	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₉₁₅	2
C₅×D₁₅×C₆₁	2
C₃×C₅⋊D₃₀₅	2
D₅×D₃₀₅	3
D₁₅⋊D₆₁	5
D₃×D₃₀₅	5
D₁₅⋊D₅	61

Subgroups — D15⋊D305 #32913145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅⋊D₃₀₅ #32913145