Subgroups — C₅²×#89137 #24926262

Order 10900.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₀₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×#89137	C₅	1	6	yes	maximal, direct product factor
4	C₅×D₁₀₉	C₂×C₅	1	6	yes	—
5	C₅×C₁₀₉	C₄×C₅	1	6	yes	complemented
6	#89137	C₅²	1	1	yes	characteristic, direct product factor, Hall
7	D₁₀₉	C₂×C₅²	1	1	yes	characteristic
8	C₁₀₉	C₄×C₅²	1	1	yes	characteristic, complemented, Sylow
9	C₄×C₅²	—	109	1	no	maximal, Hall
10	C₂×C₅²	—	109	1	no	—
11	C₅²	#89137	1	1	yes	characteristic, direct product factor, Sylow
12	C₄×C₅	—	109	6	no	—
13	C₂×C₅	—	109	6	no	—
14	C₅	C₅×#89137	1	6	yes	direct product factor
15	C₄	—	109	1	no	Sylow
16	C₂	—	109	1	no	—

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.