Subgroups — D₂₅₈₇₅ #72289005

Order 51750.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₆₂₅	—	3	1	no	maximal
2	D₂₈₇₅	—	9	1	no	Hall
3	D₁₁₂₅	—	23	1	no	maximal, Hall
4	C₉×C₂₃×C₁₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×C₂₃×C₁₂₅	D₃	1	1	yes	characteristic
6	D₅₁₇₅	—	5	1	no	maximal
7	C₉×C₂₃×C₂₅	D₅	1	1	yes	characteristic
8	D₁₇₂₅	—	15	1	no	—
9	C₂₃×C₁₂₅	D₉	1	1	yes	characteristic, complemented, Hall
10	D₁₀₃₅	—	25	1	no	—
11	C₃×C₂₃×C₂₅	D₁₅	1	1	yes	characteristic
12	D₅₇₅	—	45	1	no	—
13	C₉×C₁₂₅	D₂₃	1	1	yes	characteristic, complemented, Hall
14	C₅×C₉×C₂₃	D₂₅	1	1	yes	characteristic
15	D₃₇₅	—	69	1	no	—
16	D₃₄₅	—	75	1	no	—
17	C₂₃×C₂₅	D₄₅	1	1	yes	characteristic
18	D₂₂₅	—	115	1	no	—
19	D₂₀₇	—	125	1	no	Hall
20	C₃×C₁₂₅	D₆₉	1	1	yes	characteristic
21	C₃×C₅×C₂₃	D₇₅	1	1	yes	characteristic
22	D₁₂₅	—	207	1	no	Hall
23	D₁₁₅	—	225	1	no	—
24	C₉×C₂₅	D₁₁₅	1	1	yes	characteristic
25	C₉×C₂₃	D₁₂₅	1	1	yes	characteristic, complemented, Hall
26	D₇₅	—	345	1	no	—
27	D₆₉	—	375	1	no	—
28	C₁₂₅	D₂₀₇	1	1	yes	characteristic, complemented, Sylow
29	C₅×C₂₃	D₂₂₅	1	1	yes	characteristic
30	D₄₅	—	575	1	no	—
31	C₃×C₂₅	D₃₄₅	1	1	yes	characteristic
32	C₃×C₂₃	D₃₇₅	1	1	yes	characteristic
33	D₂₅	—	1035	1	no	—
34	D₂₃	—	1125	1	no	Hall
35	C₅×C₉	D₅₇₅	1	1	yes	characteristic
36	D₁₅	—	1725	1	no	—
37	C₂₅	D₁₀₃₅	1	1	yes	characteristic
38	C₂₃	D₁₁₂₅	1	1	yes	characteristic, complemented, Sylow
39	D₉	—	2875	1	no	Hall
40	C₃×C₅	D₁₇₂₅	1	1	yes	characteristic
41	D₅	—	5175	1	no	—
42	C₉	D₂₈₇₅	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	8625	1	no	—
44	C₅	D₅₁₇₅	1	1	yes	characteristic
45	C₃	D₈₆₂₅	1	1	yes	characteristic
46	C₂	—	25875	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₂₃×C₁₂₅	C₂
Frattini	C₃×C₂₅	D₃₄₅
socle	C₃×C₅×C₂₃	D₇₅
LCS	G ▷ C₉×C₂₃×C₁₂₅
UCS	C₁

Complements

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

N	H ≅ G/N	type
4. C₉×C₂₃×C₁₂₅	C₂	semidirect
9. C₂₃×C₁₂₅	D₉	semidirect
13. C₉×C₁₂₅	D₂₃	semidirect
25. C₉×C₂₃	D₁₂₅	semidirect
28. C₁₂₅	D₂₀₇	semidirect
38. C₂₃	D₁₁₂₅	semidirect
42. C₉	D₂₈₇₅	semidirect

Maximal subgroups

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

subgroup	index
D₈₆₂₅	3
D₁₁₂₅	23
C₉×C₂₃×C₁₂₅	2
D₅₁₇₅	5

Subgroups — D25875 #72289005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₅₈₇₅ #72289005