Subgroups — C₅₃×#6887 #27166222

Order 12879.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉×C₅₃	C₃	1	1	yes	maximal, characteristic
2	C₅₃×C₉⋊C₉	C₃	1	6	yes	maximal, complemented
3	C₅₃×C₃²⋊C₉	C₃	1	3	yes	maximal
4	C₉²×C₅₃	C₃	1	3	yes	maximal, complemented
5	C₃³×C₅₃	C₃²	1	1	yes	characteristic
6	C₃×C₉×C₅₃	C₉	1	9	yes	complemented
7	C₃×C₉×C₅₃	C₃²	1	9	yes	—
8	C₃×C₉×C₅₃	C₃²	1	2	yes	—
9	C₃×C₉×C₅₃	C₃²	1	1	yes	characteristic
10	C₃²×C₅₃	—	3	3	no	—
11	C₃²×C₅₃	C₃×C₉	1	3	yes	—
12	C₃²×C₅₃	C₃³	1	1	yes	characteristic
13	C₉×C₅₃	—	3	9	no	—
14	C₉×C₅₃	C₃×C₉	1	6	yes	—
15	C₉×C₅₃	C₃×C₉	1	3	yes	—
16	#6887	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×C₅₃	—	3	3	no	—
18	C₃×C₅₃	C₃²×C₉	1	1	yes	characteristic
19	C₃×C₅₃	#737	1	3	yes	—
20	C₃²×C₉	C₃×C₅₃	1	1	yes	characteristic
21	C₉⋊C₉	C₃×C₅₃	1	6	yes	complemented
22	C₃²⋊C₉	C₃×C₅₃	1	3	yes	—
23	C₉²	C₃×C₅₃	1	3	yes	complemented
24	C₅₃	#6887	1	1	yes	characteristic, direct product factor, Sylow
25	C₃³	C₃²×C₅₃	1	1	yes	characteristic
26	C₃×C₉	C₉×C₅₃	1	9	yes	complemented
27	C₃×C₉	C₃²×C₅₃	1	9	yes	—
28	C₃×C₉	C₃²×C₅₃	1	2	yes	—
29	C₃×C₉	C₃²×C₅₃	1	1	yes	characteristic
30	C₃²	—	3	3	no	—
31	C₃²	C₃×C₉×C₅₃	1	3	yes	—
32	C₃²	C₃³×C₅₃	1	1	yes	characteristic
33	C₉	—	3	9	no	—
34	C₉	C₃×C₉×C₅₃	1	6	yes	—
35	C₉	C₃×C₉×C₅₃	1	3	yes	—
36	C₃	—	3	3	no	—
37	C₃	C₃²×C₉×C₅₃	1	1	yes	characteristic
38	C₃	C₅₃×#737	1	3	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.