Subgroups — C₅⋊D₅×D₂₄₉ #38735285

Order 24900.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₅×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₂₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₅⋊D₄₁₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅×D₈₃	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₈₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₅×D₂₄₉	—	5	6	no	maximal
7	C₅⋊D₄₁₅	—	3	1	no	—
8	C₅⋊D₅×C₈₃	D₃	1	1	yes	characteristic, complemented
9	C₅²×D₈₃	—	3	1	no	—
10	D₁₂₄₅	—	5	6	no	—
11	C₅×D₂₄₉	D₅	1	6	yes	complemented
12	C₃×D₅×C₈₃	—	5	6	no	—
13	C₅²×C₈₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₅×D₈₃	—	15	6	no	—
15	C₃×C₅×C₈₃	C₂×D₅	1	6	yes	complemented
16	C₂×D₂₄₉	—	25	1	no	Hall
17	D₄₁₅	—	15	6	no	—
18	C₅×D₈₃	—	3	6	no	—
19	D₅×C₈₃	—	5	6	no	—
20	C₂×C₃×C₈₃	—	25	1	no	—
21	D₂₄₉	—	25	1	no	—
22	D₂₄₉	C₅⋊D₅	1	1	yes	characteristic, direct product factor
23	C₅×C₈₃	D₃×D₅	1	6	yes	complemented
24	C₂×D₈₃	—	75	1	no	Hall
25	D₃×C₅⋊D₅	—	83	1	no	maximal, Hall
26	C₃×C₈₃	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₈₃	—	25	1	no	—
28	D₈₃	—	3	1	no	—
29	D₈₃	—	75	1	no	—
30	C₃⋊(C₅⋊D₅)	—	83	1	no	—
31	C₅²×D₃	—	83	1	no	—
32	C₃×C₅⋊D₅	D₈₃	1	1	yes	characteristic, complemented
33	C₂×C₅⋊D₅	—	249	1	no	Hall
34	C₈₃	D₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
35	C₃×C₅²	C₂×D₈₃	1	1	yes	characteristic, complemented, Hall
36	D₃×D₅	—	415	6	no	—
37	C₂×C₅²	—	249	1	no	—
38	C₅⋊D₅	—	249	1	no	—
39	C₅⋊D₅	D₂₄₉	1	1	yes	characteristic, direct product factor
40	D₁₅	—	415	6	no	—
41	C₃×D₅	—	5	6	no	—
42	C₅×D₃	—	83	6	no	—
43	C₅²	C₂×D₂₄₉	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₅	—	1245	6	no	—
45	C₃×C₅	D₅×D₈₃	1	6	yes	complemented
46	C₂×D₃	—	2075	1	no	Hall
47	C₂×C₅	—	249	6	no	—
48	D₅	—	5	6	no	—
49	D₅	—	1245	6	no	—
50	C₂×C₃	—	25	1	no	—
51	D₃	—	2075	1	no	—
52	D₃	—	83	1	no	—
53	C₅	D₅×D₂₄₉	1	6	yes	complemented
54	C₂²	—	6225	1	no	Sylow
55	C₃	C₅⋊D₅×D₈₃	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	25	1	no	—
57	C₂	—	6225	1	no	—
58	C₂	—	249	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅²×C₈₃	C₂²
LCS	G ▷ C₃×C₅²×C₈₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅⋊D₅×C₈₃	C₂	semidirect
2. C₅²×D₂₄₉	C₂	semidirect
3. C₃⋊(C₅⋊D₄₁₅)	C₂	semidirect
5. C₃×C₅²×C₈₃	C₂²	semidirect
8. C₅⋊D₅×C₈₃	D₃	semidirect
11. C₅×D₂₄₉	D₅	semidirect
13. C₅²×C₈₃	C₂×D₃	semidirect
15. C₃×C₅×C₈₃	C₂×D₅	semidirect
22. D₂₄₉	C₅⋊D₅	direct (N × H)
23. C₅×C₈₃	D₃×D₅	semidirect
26. C₃×C₈₃	C₂×C₅⋊D₅	semidirect
32. C₃×C₅⋊D₅	D₈₃	semidirect
34. C₈₃	D₃×C₅⋊D₅	semidirect
35. C₃×C₅²	C₂×D₈₃	semidirect
39. C₅⋊D₅	D₂₄₉	direct (N × H)
43. C₅²	C₂×D₂₄₉	semidirect
45. C₃×C₅	D₅×D₈₃	semidirect
53. C₅	D₅×D₂₄₉	semidirect
55. C₃	C₅⋊D₅×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅⋊D₅×C₈₃	2
C₅²×D₂₄₉	2
C₃⋊(C₅⋊D₄₁₅)	2
C₅⋊D₅×D₈₃	3
D₅×D₂₄₉	5
D₃×C₅⋊D₅	83

Subgroups — C5⋊D5×D249 #38735285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊D₅×D₂₄₉ #38735285