Subgroups — C₅₃×#10624554 #50311439

Order 38637.

458 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₃×C₉⋊C₉	C₃	1	12	yes	maximal
2	C₃×C₉²×C₅₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₉×C₅₃	C₃²	1	9	yes	—
4	C₃²×C₉×C₅₃	C₃²	1	4	yes	—
5	C₅₃×C₉⋊C₉	—	3	36	no	—
6	C₉²×C₅₃	C₉	1	9	yes	complemented
7	C₃³×C₅₃	C₃³	1	1	yes	characteristic
8	C₃×C₉×C₅₃	—	3	36	no	—
9	C₃×C₉×C₅₃	C₃×C₉	1	12	yes	—
10	C₃×C₉×C₅₃	3₋¹⁺²	1	36	yes	—
11	#10624554	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃²×C₅₃	C₃²×C₉	1	1	yes	characteristic
13	C₃²×C₅₃	C₃×3₋¹⁺²	1	12	yes	—
14	C₉×C₅₃	—	9	9	no	—
15	C₉×C₅₃	C₉⋊C₉	1	36	yes	complemented
16	C₃×C₉⋊C₉	C₃×C₅₃	1	12	yes	—
17	C₃×C₉²	C₃×C₅₃	1	1	yes	characteristic
18	C₃×C₅₃	C₃×C₉⋊C₉	1	4	yes	—
19	C₃×C₅₃	#6900	1	9	yes	—
20	C₃²×C₉	C₃²×C₅₃	1	9	yes	—
21	C₃²×C₉	C₃²×C₅₃	1	4	yes	—
22	C₉⋊C₉	—	3	36	no	—
23	C₉²	C₉×C₅₃	1	9	yes	complemented
24	C₅₃	#10624554	1	1	yes	characteristic, direct product factor, Sylow
25	C₃³	C₃³×C₅₃	1	1	yes	characteristic
26	C₃×C₉	—	3	36	no	—
27	C₃×C₉	C₃×C₉×C₅₃	1	12	yes	—
28	C₃×C₉	3₋¹⁺²×C₅₃	1	36	yes	—
29	C₃²	C₃²×C₉×C₅₃	1	1	yes	characteristic
30	C₃²	C₃×3₋¹⁺²×C₅₃	1	12	yes	—
31	C₉	—	9	9	no	—
32	C₉	C₅₃×C₉⋊C₉	1	36	yes	complemented
33	C₃	C₃×C₅₃×C₉⋊C₉	1	4	yes	—
34	C₃	C₅₃×#6900	1	9	yes	—

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.