Subgroups — C₅×C₉×D₃₅₃ #44540921

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×C₅×D₃₅₃	C₃	1	1	yes	maximal, characteristic
3	C₉×D₃₅₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₃₅₃	C₂×C₃	1	1	yes	characteristic
5	C₅×D₃₅₃	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₃₅₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×D₃₅₃	C₃×C₅	1	1	yes	characteristic
8	C₅×C₃₅₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₃₅₃	C₂×C₃×C₅	1	1	yes	characteristic
10	D₃₅₃	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₃₅₃	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₅×C₉	—	353	1	no	maximal, Hall
13	C₅×C₉	D₃₅₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₅	—	353	1	no	—
15	C₂×C₉	—	353	1	no	Hall
16	C₃×C₅	C₃×D₃₅₃	1	1	yes	characteristic
17	C₂×C₅	—	353	1	no	Hall
18	C₉	C₅×D₃₅₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	—	353	1	no	—
20	C₅	C₉×D₃₅₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₃×C₅×D₃₅₃	1	1	yes	characteristic
22	C₂	—	353	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.