Subgroups — C₅₃×#6897 #27166232

Order 12879.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×C₉⋊C₉	C₃	1	8	yes	maximal, complemented
2	C₅₃×C₃²⋊C₉	C₃	1	4	yes	maximal
3	C₉²×C₅₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₅₃	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₅₃	C₃²	1	4	yes	—
6	C₃×C₉×C₅₃	C₃²	1	8	yes	—
7	C₃²×C₅₃	—	3	4	no	—
8	C₃²×C₅₃	C₃³	1	1	yes	characteristic
9	C₉×C₅₃	—	3	4	no	—
10	C₉×C₅₃	—	3	8	no	—
11	#6897	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃×C₅₃	—	9	1	no	—
13	C₃×C₅₃	#737	1	4	yes	—
14	C₉⋊C₉	C₃×C₅₃	1	8	yes	complemented
15	C₃²⋊C₉	C₃×C₅₃	1	4	yes	—
16	C₉²	C₃×C₅₃	1	1	yes	characteristic, complemented
17	C₅₃	#6897	1	1	yes	characteristic, direct product factor, Sylow
18	C₃³	C₃²×C₅₃	1	1	yes	characteristic
19	C₃×C₉	C₃²×C₅₃	1	4	yes	—
20	C₃×C₉	C₃²×C₅₃	1	8	yes	—
21	C₃²	—	3	4	no	—
22	C₃²	C₃³×C₅₃	1	1	yes	characteristic
23	C₉	—	3	4	no	—
24	C₉	—	3	8	no	—
25	C₃	—	9	1	no	—
26	C₃	C₅₃×#737	1	4	yes	—

	subgroup	G/H
center, socle	C₃²×C₅₃	C₃³
commutator, Frattini, cosocle	C₃²	C₃³×C₅₃
prime radical	C₃³×C₅₃	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₅₃ ◁ G

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.