Subgroups — C₉×D₅×C₃₅₃ #44540922

Order 31770.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₃₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₅×C₃₅₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉×C₃₅₃	—	5	1	no	maximal, Hall
4	C₃×C₅×C₃₅₃	C₂×C₃	1	1	yes	characteristic
5	D₅×C₃₅₃	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₃₅₃	D₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₃₅₃	—	5	1	no	—
8	C₅×C₃₅₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₃₅₃	C₃×D₅	1	1	yes	characteristic
10	C₂×C₃₅₃	—	5	1	no	Hall
11	C₃₅₃	C₉×D₅	1	1	yes	characteristic, direct product factor, Sylow
12	C₉×D₅	C₃₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×C₉	C₂×C₃₅₃	1	1	yes	characteristic, complemented, Hall
14	C₃×D₅	C₃×C₃₅₃	1	1	yes	characteristic
15	C₂×C₉	—	5	1	no	Hall
16	C₃×C₅	C₂×C₃×C₃₅₃	1	1	yes	characteristic
17	D₅	C₉×C₃₅₃	1	1	yes	characteristic, direct product factor, Hall
18	C₉	D₅×C₃₅₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	—	5	1	no	—
20	C₅	C₂×C₉×C₃₅₃	1	1	yes	characteristic, complemented, Sylow
21	C₃	C₃×D₅×C₃₅₃	1	1	yes	characteristic
22	C₂	—	5	1	no	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.