Subgroups — C₅×C₉×D₅₃ #18012003

Order 4770.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×D₅₃	C₃	1	1	yes	maximal, characteristic
3	C₉×D₅₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₅₃	C₂×C₃	1	1	yes	characteristic
5	C₅×D₅₃	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₅₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×D₅₃	C₃×C₅	1	1	yes	characteristic
8	C₅×C₅₃	C₂×C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅₃	C₂×C₃×C₅	1	1	yes	characteristic
10	D₅₃	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₉	—	53	1	no	maximal, Hall
12	C₅₃	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
13	C₅×C₉	D₅₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₅	—	53	1	no	—
15	C₂×C₉	—	53	1	no	Hall
16	C₃×C₅	C₃×D₅₃	1	1	yes	characteristic
17	C₂×C₅	—	53	1	no	Hall
18	C₉	C₅×D₅₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃	—	53	1	no	—
20	C₅	C₉×D₅₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₃×C₅×D₅₃	1	1	yes	characteristic
22	C₂	—	53	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.