Subgroups — D₇₅⋊D₄₇ #28381237

Order 14100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×D₇₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₅×D₁₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₁₇₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₅×D₄₇	—	3	1	no	maximal, Hall
5	C₃×C₂₅×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₅⋊D₄₇	—	5	1	no	maximal
7	D₁₁₇₅	D₃	1	1	yes	characteristic, complemented
8	C₂₅×D₄₇	—	3	1	no	—
9	C₄₇×D₂₅	—	3	1	no	—
10	D₁₅×C₄₇	—	5	1	no	—
11	C₅×D₁₄₁	D₅	1	1	yes	characteristic
12	C₃×D₂₃₅	—	5	1	no	—
13	C₂₅×C₄₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₅×D₄₇	—	15	1	no	—
15	C₃×C₅×C₄₇	C₂×D₅	1	1	yes	characteristic
16	D₃×D₄₇	—	25	1	no	Hall
17	D₂₃₅	—	5	1	no	—
18	C₅×D₄₇	—	3	1	no	—
19	D₅×C₄₇	—	15	1	no	—
20	D₃×D₂₅	—	47	1	no	maximal, Hall
21	D₁₄₁	D₂₅	1	1	yes	characteristic, complemented
22	C₃×D₄₇	—	25	1	no	—
23	D₃×C₄₇	—	25	1	no	—
24	C₅×C₄₇	D₃×D₅	1	1	yes	characteristic
25	C₂×D₄₇	—	75	1	no	Hall
26	D₇₅	D₄₇	1	1	yes	characteristic, complemented
27	C₃×D₂₅	—	47	1	no	—
28	D₃×C₂₅	—	47	1	no	—
29	C₃×C₄₇	C₂×D₂₅	1	1	yes	characteristic, complemented, Hall
30	C₂×D₂₅	—	141	1	no	Hall
31	C₂×C₄₇	—	75	1	no	—
32	D₄₇	—	3	1	no	—
33	D₄₇	—	25	1	no	—
34	C₃×C₂₅	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
35	D₃×D₅	—	235	1	no	—
36	C₂×C₂₅	—	141	1	no	—
37	D₂₅	—	3	1	no	—
38	D₂₅	—	47	1	no	—
39	C₄₇	D₃×D₂₅	1	1	yes	characteristic, complemented, Sylow
40	D₁₅	—	5	1	no	—
41	C₃×D₅	—	235	1	no	—
42	C₅×D₃	—	47	1	no	—
43	C₂₅	D₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₅	—	705	1	no	—
45	C₃×C₅	D₅×D₄₇	1	1	yes	characteristic
46	C₂×D₃	—	1175	1	no	Hall
47	C₂×C₅	—	141	1	no	—
48	D₅	—	15	1	no	—
49	D₅	—	235	1	no	—
50	C₂×C₃	—	1175	1	no	—
51	D₃	—	25	1	no	—
52	D₃	—	47	1	no	—
53	C₅	D₁₅⋊D₄₇	1	1	yes	characteristic
54	C₂²	—	3525	1	no	Sylow
55	C₃	D₂₅×D₄₇	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	75	1	no	—
57	C₂	—	141	1	no	—
58	C₂	—	1175	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₂₅×C₄₇	C₂²
Frattini	C₅	D₁₅⋊D₄₇
socle	C₃×C₅×C₄₇	C₂×D₅
LCS	G ▷ C₃×C₂₅×C₄₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₄₇×D₇₅	C₂	semidirect
2. C₂₅×D₁₄₁	C₂	semidirect
3. C₃×D₁₁₇₅	C₂	semidirect
5. C₃×C₂₅×C₄₇	C₂²	semidirect
7. D₁₁₇₅	D₃	semidirect
13. C₂₅×C₄₇	C₂×D₃	semidirect
21. D₁₄₁	D₂₅	semidirect
26. D₇₅	D₄₇	semidirect
29. C₃×C₄₇	C₂×D₂₅	semidirect
34. C₃×C₂₅	C₂×D₄₇	semidirect
39. C₄₇	D₃×D₂₅	semidirect
43. C₂₅	D₃×D₄₇	semidirect
55. C₃	D₂₅×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×D₇₅	2
C₂₅×D₁₄₁	2
C₃×D₁₁₇₅	2
D₂₅×D₄₇	3
D₁₅⋊D₄₇	5
D₃×D₂₅	47

Subgroups — D75⋊D47 #28381237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇₅⋊D₄₇ #28381237