Subgroups — D₁₅₃⋊(C₅⋊D₅) #29505817

Order 15300.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₅⋊D₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₁₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₅⋊D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅₁⋊(C₅⋊D₅)	—	3	1	no	maximal
5	C₅²×C₉×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₄₅⋊D₁₇	—	5	6	no	maximal
7	C₁₇×C₃⋊(C₅⋊D₅)	—	3	1	no	—
8	C₅²×D₅₁	—	3	1	no	—
9	C₃×C₅⋊D₈₅	D₃	1	1	yes	characteristic
10	D₁₇×C₅⋊D₅	—	9	1	no	Hall
11	C₁₇×D₄₅	—	5	6	no	—
12	C₅×D₁₅₃	D₅	1	6	yes	complemented
13	C₉×D₈₅	—	5	6	no	—
14	C₃×C₅²×C₁₇	C₂×D₃	1	1	yes	characteristic
15	D₁₅⋊D₁₇	—	15	6	no	—
16	D₉×C₅⋊D₅	—	17	1	no	maximal, Hall
17	C₅⋊D₈₅	D₉	1	1	yes	characteristic, complemented
18	C₁₇×C₅⋊D₅	—	9	1	no	—
19	C₅²×D₁₇	—	9	1	no	—
20	C₅×C₉×C₁₇	C₂×D₅	1	6	yes	complemented
21	D₉×D₁₇	—	25	1	no	Hall
22	C₁₇×D₁₅	—	15	6	no	—
23	C₅×D₅₁	—	3	6	no	—
24	C₃×D₈₅	—	5	6	no	—
25	C₅⋊D₄₅	D₁₇	1	1	yes	characteristic, complemented
26	C₅²×D₉	—	17	1	no	—
27	C₉×C₅⋊D₅	—	17	1	no	—
28	C₅²×C₁₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
29	D₅×D₁₇	—	45	6	no	—
30	D₁₅₃	C₅⋊D₅	1	1	yes	characteristic, complemented
31	C₉×D₁₇	—	25	1	no	—
32	C₁₇×D₉	—	25	1	no	—
33	D₃×C₅⋊D₅	—	51	1	no	—
34	C₃×C₅×C₁₇	D₃×D₅	1	6	yes	—
35	C₅²×C₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
36	D₃×D₁₇	—	75	1	no	—
37	D₅×D₉	—	85	6	no	—
38	D₈₅	—	5	6	no	—
39	C₅×D₁₇	—	9	6	no	—
40	D₅×C₁₇	—	45	6	no	—
41	C₉×C₁₇	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
42	C₃⋊(C₅⋊D₅)	—	3	1	no	—
43	C₅²×D₃	—	51	1	no	—
44	C₃×C₅⋊D₅	—	17	1	no	—
45	D₅₁	—	3	1	no	—
46	C₃×D₁₇	—	25	1	no	—
47	D₃×C₁₇	—	75	1	no	—
48	C₂×C₅⋊D₅	—	153	1	no	Hall
49	D₄₅	—	5	6	no	—
50	C₉×D₅	—	85	6	no	—
51	C₅×D₉	—	17	6	no	—
52	C₅×C₁₇	D₅×D₉	1	6	yes	complemented
53	C₃×C₅²	D₃×D₁₇	1	1	yes	characteristic
54	C₂×D₁₇	—	225	1	no	Hall
55	D₃×D₅	—	255	6	no	—
56	C₃×C₁₇	D₃×C₅⋊D₅	1	1	yes	characteristic
57	C₂×C₅²	—	153	1	no	—
58	C₅⋊D₅	—	9	1	no	—
59	C₅⋊D₅	—	17	1	no	—
60	C₅×C₉	D₅×D₁₇	1	6	yes	complemented
61	C₂×D₉	—	425	1	no	Hall
62	C₂×C₁₇	—	225	1	no	—
63	D₁₇	—	9	1	no	—
64	D₁₇	—	25	1	no	—
65	D₁₅	—	15	6	no	—
66	C₃×D₅	—	85	6	no	—
67	C₅×D₃	—	51	6	no	—
68	C₅²	D₉×D₁₇	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₅	—	765	6	no	—
70	C₂×C₉	—	425	1	no	—
71	D₉	—	17	1	no	—
72	D₉	—	25	1	no	—
73	C₁₇	D₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
74	C₃×C₅	D₁₅⋊D₁₇	1	6	yes	—
75	C₂×D₃	—	1275	1	no	—
76	C₂×C₅	—	153	6	no	—
77	D₅	—	45	6	no	—
78	D₅	—	85	6	no	—
79	C₉	D₁₇×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₃	—	425	1	no	—
81	D₃	—	51	1	no	—
82	D₃	—	75	1	no	—
83	C₅	D₄₅⋊D₁₇	1	6	yes	complemented
84	C₂²	—	3825	1	no	Sylow
85	C₃	D₅₁⋊(C₅⋊D₅)	1	1	yes	characteristic
86	C₂	—	153	1	no	—
87	C₂	—	425	1	no	—
88	C₂	—	225	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅²×C₉×C₁₇	C₂²
Frattini	C₃	D₅₁⋊(C₅⋊D₅)
socle	C₃×C₅²×C₁₇	C₂×D₃
LCS	G ▷ C₅²×C₉×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₅⋊D₄₅	C₂	semidirect
2. C₅²×D₁₅₃	C₂	semidirect
3. C₉×C₅⋊D₈₅	C₂	semidirect
5. C₅²×C₉×C₁₇	C₂²	semidirect
12. C₅×D₁₅₃	D₅	semidirect
17. C₅⋊D₈₅	D₉	semidirect
20. C₅×C₉×C₁₇	C₂×D₅	semidirect
25. C₅⋊D₄₅	D₁₇	semidirect
28. C₅²×C₁₇	C₂×D₉	semidirect
30. D₁₅₃	C₅⋊D₅	semidirect
35. C₅²×C₉	C₂×D₁₇	semidirect
41. C₉×C₁₇	C₂×C₅⋊D₅	semidirect
52. C₅×C₁₇	D₅×D₉	semidirect
60. C₅×C₉	D₅×D₁₇	semidirect
68. C₅²	D₉×D₁₇	semidirect
73. C₁₇	D₉×C₅⋊D₅	semidirect
79. C₉	D₁₇×C₅⋊D₅	semidirect
83. C₅	D₄₅⋊D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×C₅⋊D₄₅	2
C₅²×D₁₅₃	2
C₉×C₅⋊D₈₅	2
D₅₁⋊(C₅⋊D₅)	3
D₄₅⋊D₁₇	5
D₉×C₅⋊D₅	17

Subgroups — D153⋊(C5⋊D5) #29505817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅₃⋊(C₅⋊D₅) #29505817