Subgroups — C₅×#13109888⋊C₃ #37589342

Order 24540.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₄₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅×#13109888	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₄₀₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	#13109888⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×D₄₀₉	C₂×C₃	1	1	yes	characteristic
6	D₄₀₉⋊C₃	C₂×C₅	1	1	yes	characteristic
7	C₅×C₄₀₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#13109888	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₄₀₉⋊C₃	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	D₄₀₉	C₂×C₃×C₅	1	1	yes	characteristic
11	C₄₀₉	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₄×C₅	—	409	1	no	maximal, Hall
13	C₂×C₃×C₅	—	409	1	no	—
14	C₄×C₅	—	409	1	no	Hall
15	C₃×C₅	—	409	1	no	Hall
16	C₃×C₄	—	409	1	no	Hall
17	C₂×C₅	—	409	1	no	—
18	C₂×C₃	—	409	1	no	—
19	C₅	#13109888⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₄	—	409	1	no	Sylow
21	C₃	—	409	1	no	Sylow
22	C₂	—	409	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.