Subgroups — D₃₀₉⋊(C₅⋊D₅) #44525536

Order 30900.

160 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	C₅²×D₃₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₃×C₃⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅×D₁₀₃	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₁₀₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₅⋊D₁₀₃	—	5	6	no	maximal
7	C₅⋊D₅₁₅	D₃	1	1	yes	characteristic, complemented
8	C₅⋊D₅×C₁₀₃	—	3	1	no	—
9	C₅²×D₁₀₃	—	3	1	no	—
10	D₁₅×C₁₀₃	—	5	6	no	—
11	C₅×D₃₀₉	D₅	1	6	yes	complemented
12	C₃×D₅₁₅	—	5	6	no	—
13	C₅²×C₁₀₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₅×D₁₀₃	—	15	6	no	—
15	C₃×C₅×C₁₀₃	C₂×D₅	1	6	yes	complemented
16	D₃×D₁₀₃	—	25	1	no	Hall
17	D₅₁₅	—	5	6	no	—
18	C₅×D₁₀₃	—	3	6	no	—
19	D₅×C₁₀₃	—	15	6	no	—
20	D₃₀₉	C₅⋊D₅	1	1	yes	characteristic, complemented
21	C₃×D₁₀₃	—	25	1	no	—
22	D₃×C₁₀₃	—	25	1	no	—
23	C₅×C₁₀₃	D₃×D₅	1	6	yes	complemented
24	C₂×D₁₀₃	—	75	1	no	Hall
25	C₃×C₁₀₃	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
26	D₃×C₅⋊D₅	—	103	1	no	maximal, Hall
27	C₂×C₁₀₃	—	75	1	no	—
28	D₁₀₃	—	3	1	no	—
29	D₁₀₃	—	25	1	no	—
30	C₃⋊(C₅⋊D₅)	D₁₀₃	1	1	yes	characteristic, complemented
31	C₅²×D₃	—	103	1	no	—
32	C₃×C₅⋊D₅	—	103	1	no	—
33	C₁₀₃	D₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₅⋊D₅	—	309	1	no	Hall
35	C₃×C₅²	C₂×D₁₀₃	1	1	yes	characteristic, complemented, Hall
36	D₃×D₅	—	515	6	no	—
37	C₂×C₅²	—	309	1	no	—
38	C₅⋊D₅	—	3	1	no	—
39	C₅⋊D₅	—	103	1	no	—
40	D₁₅	—	5	6	no	—
41	C₃×D₅	—	515	6	no	—
42	C₅×D₃	—	103	6	no	—
43	C₅²	D₃×D₁₀₃	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₅	—	1545	6	no	—
45	C₃×C₅	D₅×D₁₀₃	1	6	yes	complemented
46	C₂×D₃	—	2575	1	no	Hall
47	C₂×C₅	—	309	6	no	—
48	D₅	—	515	6	no	—
49	D₅	—	15	6	no	—
50	C₂×C₃	—	2575	1	no	—
51	D₃	—	25	1	no	—
52	D₃	—	103	1	no	—
53	C₅	D₁₅⋊D₁₀₃	1	6	yes	complemented
54	C₂²	—	7725	1	no	Sylow
55	C₃	C₅⋊D₅×D₁₀₃	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	2575	1	no	—
57	C₂	—	309	1	no	—
58	C₂	—	75	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. C₅²×D₃₀₉	C₂	semidirect
3. C₁₀₃×C₃⋊(C₅⋊D₅)	C₂	semidirect
5. C₃×C₅²×C₁₀₃	C₂²	semidirect
7. C₅⋊D₅₁₅	D₃	semidirect
11. C₅×D₃₀₉	D₅	semidirect
13. C₅²×C₁₀₃	C₂×D₃	semidirect
15. C₃×C₅×C₁₀₃	C₂×D₅	semidirect
20. D₃₀₉	C₅⋊D₅	semidirect
23. C₅×C₁₀₃	D₃×D₅	semidirect
25. C₃×C₁₀₃	C₂×C₅⋊D₅	semidirect
30. C₃⋊(C₅⋊D₅)	D₁₀₃	semidirect
33. C₁₀₃	D₃×C₅⋊D₅	semidirect
35. C₃×C₅²	C₂×D₁₀₃	semidirect
43. C₅²	D₃×D₁₀₃	semidirect
45. C₃×C₅	D₅×D₁₀₃	semidirect
53. C₅	D₁₅⋊D₁₀₃	semidirect
55. C₃	C₅⋊D₅×D₁₀₃	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
C₅²×D₃₀₉	2
C₁₀₃×C₃⋊(C₅⋊D₅)	2
C₅⋊D₅×D₁₀₃	3
D₁₅⋊D₁₀₃	5
D₃×C₅⋊D₅	103

Subgroups — D309⋊(C5⋊D5) #44525536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₀₉⋊(C₅⋊D₅) #44525536