Subgroups — #1043×C₁₀₉⋊C₃ #45658287

Order 32700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅×C₁₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#1043×C₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₁₀₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	AGL(1,𝔽₅)×C₁₀₉⋊C₃	—	5	6	no	maximal
5	C₅⋊D₅×C₁₀₉	C₂×C₃	1	1	yes	characteristic
6	D₅×C₁₀₉⋊C₃	—	5	6	no	—
7	C₅²×C₁₀₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	AGL(1,𝔽₅)×C₁₀₉	—	5	6	no	—
9	C₅×C₁₀₉⋊C₃	AGL(1,𝔽₅)	1	6	yes	complemented
10	C₄×C₁₀₉⋊C₃	—	25	1	no	Hall
11	D₅×C₁₀₉	—	5	6	no	—
12	C₂×C₁₀₉⋊C₃	—	25	1	no	—
13	C₅×C₁₀₉	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
14	C₄×C₁₀₉	—	25	1	no	Hall
15	C₁₀₉⋊C₃	#1043	1	1	yes	characteristic, direct product factor, Hall
16	C₃×#1043	—	109	1	no	maximal, Hall
17	C₂×C₁₀₉	—	25	1	no	—
18	C₃×C₅⋊D₅	—	109	1	no	—
19	C₁₀₉	C₃×#1043	1	1	yes	characteristic, complemented, Sylow
20	#1043	C₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₅²	—	109	1	no	Hall
22	C₃×AGL(1,𝔽₅)	—	545	6	no	—
23	C₅⋊D₅	C₂×C₁₀₉⋊C₃	1	1	yes	characteristic
24	C₃×D₅	—	545	6	no	—
25	C₅²	C₄×C₁₀₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	5	6	no	—
27	C₃×C₅	—	109	6	no	—
28	C₃×C₄	—	2725	1	no	Hall
29	D₅	—	5	6	no	—
30	C₂×C₃	—	2725	1	no	—
31	C₅	AGL(1,𝔽₅)×C₁₀₉⋊C₃	1	6	yes	complemented
32	C₄	—	25	1	no	Sylow
33	C₃	—	109	1	no	Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₁₀₉	C₃×C₄
prime radical	C₅⋊D₅×C₁₀₉⋊C₃	C₂
cosocle	C₅⋊D₅×C₁₀₉	C₂×C₃
LCS	G ▷ C₅²×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.