Subgroups — C₄×(C₁₈₁⋊C₃)⋊C₅ #24925788

Order 10860.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×(C₁₈₁⋊C₃)⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₈₁⋊C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	(C₁₈₁⋊C₃)⋊C₅	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₄×C₁₈₁⋊C₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₈₁⋊C₅	C₂×C₃	1	1	yes	characteristic
6	C₂×C₁₈₁⋊C₃	C₂×C₅	1	1	yes	characteristic
7	C₁₈₁⋊C₅	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₄×C₁₈₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₁₈₁⋊C₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₈₁	C₂×C₃×C₅	1	1	yes	characteristic
11	C₁₈₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₄×C₅	—	181	1	no	maximal, Hall
13	C₂×C₃×C₅	—	181	1	no	—
14	C₄×C₅	—	181	1	no	Hall
15	C₃×C₅	—	181	1	no	Hall
16	C₃×C₄	—	181	1	no	Hall
17	C₂×C₅	—	181	1	no	—
18	C₂×C₃	—	181	1	no	—
19	C₅	—	181	1	no	Sylow
20	C₄	(C₁₈₁⋊C₃)⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	181	1	no	Sylow
22	C₂	C₂×(C₁₈₁⋊C₃)⋊C₅	1	1	yes	characteristic

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.