Subgroups — C₅²⋊#11758281 #37589255

Order 24525.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₀₉⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₅²×C₁₀₉	C₉	1	1	yes	characteristic, complemented, Hall
3	C₅×C₁₀₉⋊C₃	—	3	2	no	—
4	#11758281	—	25	1	no	maximal, Hall
5	C₅×C₁₀₉	—	3	2	no	—
6	C₁₀₉⋊C₃	C₅²⋊C₃	1	1	yes	characteristic
7	C₅²⋊C₉	—	109	1	no	maximal, Hall
8	C₁₀₉	C₅²⋊C₉	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₅²	—	109	1	no	—
10	C₅²	#11758281	1	1	yes	characteristic, complemented, Sylow
11	C₃×C₅	—	327	2	no	—
12	C₉	—	2725	1	no	Sylow
13	C₅	—	3	2	no	—
14	C₃	—	109	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₁₀₉	C₉
prime radical, cosocle	C₅²×C₁₀₉⋊C₃	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.