Subgroups — C₂×(C₂₄₁⋊C₃)⋊C₂₅ #49116156

Order 36150.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₂₄₁⋊C₃)⋊C₂₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₂₄₁⋊C₂₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₅×C₂₄₁⋊C₃	C₅	1	1	yes	maximal, characteristic
4	C₂₄₁⋊C₂₅	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×C₂₄₁⋊C₃	C₂×C₅	1	1	yes	characteristic
6	C₂×C₅×C₂₄₁	C₃×C₅	1	1	yes	characteristic
7	C₂×C₂₄₁⋊C₃	C₂₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₂₄₁	C₂×C₃×C₅	1	1	yes	characteristic
9	C₂₄₁⋊C₃	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₂₄₁	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
11	C₂₄₁	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃×C₂₅	—	241	1	no	maximal, Hall
13	C₃×C₂₅	—	241	1	no	Hall
14	C₂×C₂₅	—	241	1	no	Hall
15	C₂×C₃×C₅	—	241	1	no	—
16	C₂₅	—	241	1	no	Sylow
17	C₃×C₅	—	241	1	no	—
18	C₂×C₅	(C₂₄₁⋊C₃)⋊C₅	1	1	yes	characteristic
19	C₂×C₃	—	241	1	no	Hall
20	C₅	C₂×(C₂₄₁⋊C₃)⋊C₅	1	1	yes	characteristic
21	C₃	—	241	1	no	Sylow
22	C₂	(C₂₄₁⋊C₃)⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow

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.