Subgroups — #1035×C₁₀₉⋊C₃ #45658182

Order 32700.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₅×C₁₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#1035×C₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₅×C₁₀₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	AGL(1,𝔽₅)×C₁₀₉⋊C₃	—	5	1	no	maximal
5	D₂₅×C₁₀₉	C₂×C₃	1	1	yes	characteristic
6	D₅×C₁₀₉⋊C₃	—	5	1	no	—
7	C₂₅×C₁₀₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	AGL(1,𝔽₅)×C₁₀₉	—	5	1	no	—
9	C₅×C₁₀₉⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic
10	C₄×C₁₀₉⋊C₃	—	25	1	no	Hall
11	D₅×C₁₀₉	—	5	1	no	—
12	C₂×C₁₀₉⋊C₃	—	25	1	no	—
13	C₅×C₁₀₉	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
14	C₄×C₁₀₉	—	25	1	no	Hall
15	C₁₀₉⋊C₃	#1035	1	1	yes	characteristic, direct product factor, Hall
16	C₃×#1035	—	109	1	no	maximal, Hall
17	C₂×C₁₀₉	—	25	1	no	—
18	C₃×D₂₅	—	109	1	no	—
19	C₁₀₉	C₃×#1035	1	1	yes	characteristic, complemented, Sylow
20	#1035	C₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₂₅	—	109	1	no	Hall
22	C₃×AGL(1,𝔽₅)	—	545	1	no	—
23	D₂₅	C₂×C₁₀₉⋊C₃	1	1	yes	characteristic
24	C₃×D₅	—	545	1	no	—
25	C₂₅	C₄×C₁₀₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	5	1	no	—
27	C₃×C₅	—	109	1	no	—
28	C₃×C₄	—	2725	1	no	Hall
29	D₅	—	5	1	no	—
30	C₂×C₃	—	2725	1	no	—
31	C₅	AGL(1,𝔽₅)×C₁₀₉⋊C₃	1	1	yes	characteristic
32	C₄	—	25	1	no	Sylow
33	C₃	—	109	1	no	Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₂₅×C₁₀₉	C₃×C₄
Frattini	C₅	AGL(1,𝔽₅)×C₁₀₉⋊C₃
socle	C₅×C₁₀₉	C₃×AGL(1,𝔽₅)
prime radical	D₂₅×C₁₀₉⋊C₃	C₂
cosocle	D₂₅×C₁₀₉	C₂×C₃
LCS	G ▷ C₂₅×C₁₀₉
UCS	C₁

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

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