Subgroups — C₅²×A₄×C₁₀₉ #45658365

Order 32700.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅²×C₁₀₉	—	4	1	no	maximal, Hall
3	C₅×A₄×C₁₀₉	C₅	1	6	yes	maximal, direct product factor
4	C₂×C₅²×C₁₀₉	—	3	1	no	—
5	C₅²×C₁₀₉	A₄	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₅×C₁₀₉	C₃×C₅	1	6	yes	complemented
7	C₃×C₅×C₁₀₉	—	4	6	no	—
8	A₄×C₁₀₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₁₀₉	—	3	6	no	—
10	C₅×C₁₀₉	C₅×A₄	1	6	yes	direct product factor
11	C₂²×C₁₀₉	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₀₉	—	4	1	no	Hall
13	C₅²×A₄	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₁₀₉	—	3	1	no	—
15	C₁₀₉	C₅²×A₄	1	1	yes	characteristic, direct product factor, Sylow
16	C₂²×C₅²	C₃×C₁₀₉	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅²	—	4	1	no	Hall
18	C₅×A₄	C₅×C₁₀₉	1	6	yes	direct product factor
19	C₂×C₅²	—	3	1	no	—
20	C₅²	A₄×C₁₀₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₅	C₃×C₅×C₁₀₉	1	6	yes	complemented
22	C₃×C₅	—	4	6	no	—
23	A₄	C₅²×C₁₀₉	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₅	—	3	6	no	—
25	C₅	C₅×A₄×C₁₀₉	1	6	yes	direct product factor
26	C₂²	C₃×C₅²×C₁₀₉	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	4	1	no	Sylow
28	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅²×C₁₀₉	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₅²×C₁₀₉
Frattini	C₁	G
Fitting, socle	C₂²×C₅²×C₁₀₉	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₅²×C₁₀₉

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.