Subgroups — C₅₃×C₉⋊#261 #37613613

Order 24804.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₁₃×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₅₃×C₃⋊#261	—	3	1	no	maximal
3	C₉×C₁₃×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₃×C₅₃	D₃	1	1	yes	characteristic
5	#261×C₅₃	—	9	1	no	Hall
6	C₃×C₁₃×C₅₃	Dic₃	1	1	yes	characteristic
7	Dic₉×C₅₃	—	13	1	no	maximal, Hall
8	D₁₃×C₅₃	D₉	1	1	yes	characteristic
9	C₂×C₉×C₅₃	—	13	1	no	—
10	C₁₃×C₅₃	Dic₉	1	1	yes	characteristic, complemented, Hall
11	Dic₃×C₅₃	—	39	1	no	—
12	C₉×C₅₃	#261	1	1	yes	characteristic, complemented, Hall
13	C₉⋊#261	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₅₃	—	13	1	no	—
15	C₉×D₁₃	C₂×C₅₃	1	1	yes	characteristic
16	C₄×C₅₃	—	117	1	no	Hall
17	C₃×C₅₃	C₃⋊#261	1	1	yes	characteristic
18	C₃⋊#261	—	3	1	no	—
19	C₉×C₁₃	C₄×C₅₃	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅₃	—	13	1	no	—
21	C₃×D₁₃	D₃×C₅₃	1	1	yes	characteristic
22	C₅₃	C₉⋊#261	1	1	yes	characteristic, direct product factor, Sylow
23	#261	—	9	1	no	Hall
24	C₃×C₁₃	Dic₃×C₅₃	1	1	yes	characteristic
25	Dic₉	—	13	1	no	Hall
26	D₁₃	D₉×C₅₃	1	1	yes	characteristic
27	C₂×C₉	—	13	1	no	—
28	C₁₃	Dic₉×C₅₃	1	1	yes	characteristic, complemented, Sylow
29	Dic₃	—	39	1	no	—
30	C₉	#261×C₅₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	13	1	no	—
32	C₄	—	117	1	no	Sylow
33	C₃	C₅₃×C₃⋊#261	1	1	yes	characteristic
34	C₂	—	13	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.