Subgroups — C₃×C₅₃×C₂₇⋊C₃ #27166237

Order 12879.

120 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×C₂₇⋊C₃	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₂₇×C₅₃	C₃	1	3	yes	maximal, complemented
4	C₃³×C₅₃	C₉	1	1	yes	characteristic
5	C₃×C₉×C₅₃	C₉	1	2	yes	—
6	C₃×C₉×C₅₃	C₉	1	6	yes	—
7	C₃×C₉×C₅₃	C₃²	1	3	yes	—
8	C₃×C₉×C₅₃	C₃²	1	1	yes	characteristic
9	C₂₇×C₅₃	C₃²	1	9	yes	complemented
10	C₃²×C₅₃	—	3	3	no	—
11	C₃²×C₅₃	C₃×C₉	1	3	yes	—
12	C₃²×C₅₃	C₃×C₉	1	1	yes	characteristic
13	C₉×C₅₃	C₃×C₉	1	6	yes	—
14	C₉×C₅₃	C₃×C₉	1	2	yes	—
15	C₉×C₅₃	C₃³	1	1	yes	characteristic
16	C₃×C₂₇⋊C₃	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×C₅₃	—	3	3	no	—
18	C₃×C₅₃	C₂₇⋊C₃	1	3	yes	direct product factor
19	C₃×C₅₃	C₃²×C₉	1	1	yes	characteristic
20	C₃²×C₉	C₃×C₅₃	1	1	yes	characteristic
21	C₂₇⋊C₃	C₃×C₅₃	1	9	yes	direct product factor
22	C₃×C₂₇	C₃×C₅₃	1	3	yes	complemented
23	C₅₃	C₃×C₂₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₃³	C₉×C₅₃	1	1	yes	characteristic
25	C₃×C₉	C₉×C₅₃	1	6	yes	—
26	C₃×C₉	C₉×C₅₃	1	2	yes	—
27	C₃×C₉	C₃²×C₅₃	1	3	yes	—
28	C₃×C₉	C₃²×C₅₃	1	1	yes	characteristic
29	C₂₇	C₃²×C₅₃	1	9	yes	complemented
30	C₃²	—	3	3	no	—
31	C₃²	C₃×C₉×C₅₃	1	3	yes	—
32	C₃²	C₃×C₉×C₅₃	1	1	yes	characteristic
33	C₉	C₃×C₉×C₅₃	1	6	yes	—
34	C₉	C₃×C₉×C₅₃	1	2	yes	—
35	C₉	C₃³×C₅₃	1	1	yes	characteristic
36	C₃	—	3	3	no	—
37	C₃	C₅₃×C₂₇⋊C₃	1	3	yes	direct product factor
38	C₃	C₃²×C₉×C₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉×C₅₃	C₃²
commutator	C₃	C₃²×C₉×C₅₃
Frattini, cosocle	C₉	C₃³×C₅₃
socle	C₃²×C₅₃	C₃×C₉
prime radical	C₃³×C₅₃	C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₅₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅₃×C₂₇⋊C₃	C₃	direct (N × H)
3. C₃×C₂₇×C₅₃	C₃	semidirect
9. C₂₇×C₅₃	C₃²	semidirect
16. C₃×C₂₇⋊C₃	C₅₃	direct (N × H)
18. C₃×C₅₃	C₂₇⋊C₃	direct (N × H)
21. C₂₇⋊C₃	C₃×C₅₃	direct (N × H)
22. C₃×C₂₇	C₃×C₅₃	semidirect
23. C₅₃	C₃×C₂₇⋊C₃	direct (N × H)
29. C₂₇	C₃²×C₅₃	semidirect
37. C₃	C₅₃×C₂₇⋊C₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₉×C₅₃	3
C₅₃×C₂₇⋊C₃	3
C₃×C₂₇×C₅₃	3
C₃×C₂₇⋊C₃	53

Subgroups — C3×C53×C27⋊C3 #27166237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅₃×C₂₇⋊C₃ #27166237