Subgroups — Dic₆₃₂₅ #38760673

Order 25300.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₂₃×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₂₃×C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₂₆₅	—	5	1	no	maximal
4	C₂×C₅×C₁₁×C₂₃	D₅	1	1	yes	characteristic
5	Dic₅₇₅	—	11	1	no	maximal, Hall
6	C₅×C₁₁×C₂₃	Dic₅	1	1	yes	characteristic
7	C₂×C₂₃×C₂₅	D₁₁	1	1	yes	characteristic
8	Dic₂₇₅	—	23	1	no	maximal, Hall
9	Dic₂₅₃	—	25	1	no	Hall
10	C₂₃×C₂₅	Dic₁₁	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₁×C₂₅	D₂₃	1	1	yes	characteristic
12	C₂×C₁₁×C₂₃	D₂₅	1	1	yes	characteristic
13	Dic₁₁₅	—	55	1	no	—
14	C₁₁×C₂₅	Dic₂₃	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₂₃	Dic₂₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₂₃	D₅₅	1	1	yes	characteristic
17	Dic₅₅	—	115	1	no	—
18	C₅×C₂₃	Dic₅₅	1	1	yes	characteristic
19	C₂×C₅×C₁₁	D₁₁₅	1	1	yes	characteristic
20	Dic₂₅	—	253	1	no	Hall
21	Dic₂₃	—	275	1	no	Hall
22	C₅×C₁₁	Dic₁₁₅	1	1	yes	characteristic
23	C₂×C₂₅	D₂₅₃	1	1	yes	characteristic
24	C₂×C₂₃	D₂₇₅	1	1	yes	characteristic
25	Dic₁₁	—	575	1	no	Hall
26	C₂₅	Dic₂₅₃	1	1	yes	characteristic, complemented, Sylow
27	C₂₃	Dic₂₇₅	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₁₁	D₅₇₅	1	1	yes	characteristic
29	Dic₅	—	1265	1	no	—
30	C₁₁	Dic₅₇₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	D₁₂₆₅	1	1	yes	characteristic
32	C₅	Dic₁₂₆₅	1	1	yes	characteristic
33	C₄	—	6325	1	no	Sylow
34	C₂	D₆₃₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₆₃₂₅
commutator, hypocenter	C₁₁×C₂₃×C₂₅	C₄
Frattini	C₂×C₅	D₁₂₆₅
Fitting, cosocle	C₂×C₁₁×C₂₃×C₂₅	C₂
socle, prime radical	C₂×C₅×C₁₁×C₂₃	D₅
LCS	G ▷ C₁₁×C₂₃×C₂₅
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₂₃×C₂₅	C₄	semidirect
10. C₂₃×C₂₅	Dic₁₁	semidirect
14. C₁₁×C₂₅	Dic₂₃	semidirect
15. C₁₁×C₂₃	Dic₂₅	semidirect
26. C₂₅	Dic₂₅₃	semidirect
27. C₂₃	Dic₂₇₅	semidirect
30. C₁₁	Dic₅₇₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×C₂₃×C₂₅	2
Dic₁₂₆₅	5
Dic₅₇₅	11
Dic₂₇₅	23

Subgroups — Dic6325 #38760673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₆₃₂₅ #38760673