Subgroups — C₅×Dic₃×C₂₅ #13093721

Order 1500.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₂₅	—	3	1	no	maximal, Hall
3	C₃×C₅×C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅²×Dic₃	C₅	1	1	yes	maximal, characteristic
5	Dic₃×C₂₅	C₅	1	5	yes	maximal, direct product factor
6	C₂×C₅×C₂₅	D₃	1	1	yes	characteristic
7	C₂×C₃×C₅²	C₂×C₅	1	1	yes	characteristic
8	C₂×C₃×C₂₅	C₂×C₅	1	5	yes	—
9	C₅×C₂₅	Dic₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₄×C₅²	—	3	1	no	—
11	C₄×C₂₅	—	3	5	no	—
12	C₃×C₅²	C₄×C₅	1	1	yes	characteristic
13	C₃×C₂₅	C₄×C₅	1	5	yes	complemented
14	C₅×Dic₃	C₂₅	1	5	yes	direct product factor
15	C₅×Dic₃	C₅²	1	1	yes	characteristic
16	C₂×C₅²	C₅×D₃	1	1	yes	characteristic
17	C₂×C₂₅	C₅×D₃	1	5	yes	—
18	C₂×C₃×C₅	C₂×C₂₅	1	5	yes	—
19	C₂×C₃×C₅	C₂×C₅²	1	1	yes	characteristic
20	C₅²	C₅×Dic₃	1	1	yes	characteristic
21	C₂₅	C₅×Dic₃	1	5	yes	direct product factor
22	C₄×C₅	—	3	5	no	—
23	C₄×C₅	—	3	1	no	—
24	C₃×C₅	C₄×C₂₅	1	5	yes	complemented
25	C₃×C₅	C₄×C₅²	1	1	yes	characteristic
26	Dic₃	C₅×C₂₅	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₅	D₃×C₂₅	1	5	yes	—
28	C₂×C₅	C₅²×D₃	1	1	yes	characteristic
29	C₂×C₃	C₂×C₅×C₂₅	1	1	yes	characteristic
30	C₅	Dic₃×C₂₅	1	5	yes	direct product factor
31	C₅	C₅²×Dic₃	1	1	yes	characteristic
32	C₄	—	3	1	no	Sylow
33	C₃	C₄×C₅×C₂₅	1	1	yes	characteristic, complemented, Sylow
34	C₂	C₅×D₃×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₂₅	D₃
commutator, hypocenter	C₃	C₄×C₅×C₂₅
Frattini	C₂×C₅	C₅²×D₃
Fitting	C₂×C₃×C₅×C₂₅	C₂
socle, prime radical	C₂×C₃×C₅²	C₂×C₅
cosocle	C₂×C₃×C₅	C₂×C₅²
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₂₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₂₅	C₄	semidirect
5. Dic₃×C₂₅	C₅	direct (N × H)
9. C₅×C₂₅	Dic₃	direct (N × H)
13. C₃×C₂₅	C₄×C₅	semidirect
14. C₅×Dic₃	C₂₅	direct (N × H)
21. C₂₅	C₅×Dic₃	direct (N × H)
24. C₃×C₅	C₄×C₂₅	semidirect
26. Dic₃	C₅×C₂₅	direct (N × H)
30. C₅	Dic₃×C₂₅	direct (N × H)
33. C₃	C₄×C₅×C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₂₅	2
C₄×C₅×C₂₅	3
C₅²×Dic₃	5
Dic₃×C₂₅	5

Subgroups — C5×Dic3×C25 #13093721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×Dic₃×C₂₅ #13093721