Subgroups — C₂₅×C₃⋊#87938 #44475868

Order 30300.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₅×D₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₂₅×#87938	—	3	1	no	maximal, Hall
3	C₃×C₂₅×C₁₀₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×C₃⋊#87938	C₅	1	1	yes	maximal, characteristic
5	C₂₅×D₁₀₁	D₃	1	1	yes	characteristic
6	C₃×C₅×D₁₀₁	C₂×C₅	1	1	yes	characteristic
7	C₂₅×C₁₀₁	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₅×#87938	—	3	1	no	—
9	C₃×C₅×C₁₀₁	C₄×C₅	1	1	yes	characteristic
10	C₃⋊#87938	C₂₅	1	1	yes	characteristic, direct product factor, Hall
11	C₅×D₁₀₁	C₅×D₃	1	1	yes	characteristic
12	C₃×D₁₀₁	C₂×C₂₅	1	1	yes	characteristic
13	C₅×C₁₀₁	C₅×Dic₃	1	1	yes	characteristic
14	#87938	—	3	1	no	Hall
15	C₃×C₁₀₁	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
16	Dic₃×C₂₅	—	101	1	no	maximal, Hall
17	D₁₀₁	D₃×C₂₅	1	1	yes	characteristic
18	C₂×C₃×C₂₅	—	101	1	no	—
19	C₁₀₁	Dic₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
20	C₄×C₂₅	—	303	1	no	Hall
21	C₃×C₂₅	#87938	1	1	yes	characteristic, complemented, Hall
22	C₅×Dic₃	—	101	1	no	—
23	C₂×C₂₅	—	101	1	no	—
24	C₂×C₃×C₅	—	101	1	no	—
25	C₂₅	C₃⋊#87938	1	1	yes	characteristic, direct product factor, Sylow
26	C₄×C₅	—	303	1	no	—
27	C₃×C₅	C₅×#87938	1	1	yes	characteristic
28	Dic₃	—	101	1	no	Hall
29	C₂×C₅	—	101	1	no	—
30	C₂×C₃	—	101	1	no	—
31	C₅	C₅×C₃⋊#87938	1	1	yes	characteristic
32	C₄	—	303	1	no	Sylow
33	C₃	C₂₅×#87938	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	101	1	no	—

	subgroup	G/H
center, hypercenter	C₂₅	C₃⋊#87938
commutator, hypocenter	C₃×C₁₀₁	C₄×C₂₅
Frattini	C₅	C₅×C₃⋊#87938
Fitting	C₃×C₂₅×C₁₀₁	C₄
socle	C₃×C₅×C₁₀₁	C₄×C₅
prime radical, cosocle	C₃×C₅×D₁₀₁	C₂×C₅
LCS	G ▷ C₃×C₁₀₁
UCS	C₁ ◁ C₂₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₂₅×C₁₀₁	C₄	semidirect
7. C₂₅×C₁₀₁	Dic₃	semidirect
10. C₃⋊#87938	C₂₅	direct (N × H)
15. C₃×C₁₀₁	C₄×C₂₅	semidirect
19. C₁₀₁	Dic₃×C₂₅	semidirect
21. C₃×C₂₅	#87938	semidirect
25. C₂₅	C₃⋊#87938	direct (N × H)
33. C₃	C₂₅×#87938	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₂₅×D₁₀₁	2
C₂₅×#87938	3
C₅×C₃⋊#87938	5
Dic₃×C₂₅	101

Subgroups — C25×C3⋊#87938 #44475868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₅×C₃⋊#87938 #44475868