Subgroups — C₅₃×#90866 #37613708

Order 24804.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₃×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅₃×D₃₉	—	6	2	no	—
4	#261×C₅₃	—	9	1	no	maximal, Hall
5	C₃×C₁₃×C₅₃	—	2	2	no	—
6	#157×C₅₃	—	13	1	no	maximal, Hall
7	D₁₃×C₅₃	—	9	1	no	—
8	C₃⋊D₃×C₅₃	—	13	1	no	—
9	C₁₃×C₅₃	#157	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₅₃	#261	1	1	yes	characteristic, complemented, Hall
11	#90866	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	D₃×C₅₃	—	78	2	no	—
13	C₃⋊D₃₉	C₂×C₅₃	1	1	yes	characteristic
14	C₄×C₅₃	—	117	1	no	Hall
15	C₃×C₅₃	—	2	2	no	—
16	C₃²×C₁₃	C₄×C₅₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅₃	—	117	1	no	—
18	D₃₉	—	6	2	no	—
19	C₅₃	#90866	1	1	yes	characteristic, direct product factor, Sylow
20	#261	—	9	1	no	Hall
21	C₃×C₁₃	—	2	2	no	—
22	#157	—	13	1	no	Hall
23	D₁₃	—	9	1	no	—
24	C₃⋊D₃	—	13	1	no	—
25	C₁₃	#157×C₅₃	1	1	yes	characteristic, complemented, Sylow
26	C₃²	#261×C₅₃	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	78	2	no	—
28	C₄	—	117	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	117	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.