Subgroups — (C₃³⋊C₁₃)⋊C₂₇ #23748635

Order 9477.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃³⋊C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₃×C₃³⋊C₁₃	C₉	1	1	yes	characteristic
3	#10624444	—	13	1	no	maximal, Sylow
4	C₃³⋊C₁₃	C₂₇	1	1	yes	characteristic, complemented
5	C₁₃⋊C₂₇	—	27	1	no	maximal
6	C₃³×C₉	C₁₃⋊C₃	1	1	yes	characteristic
7	C₃²⋊C₂₇	—	13	2	no	—
8	C₃²⋊C₂₇	—	13	1	no	—
9	C₉×C₁₃	—	27	1	no	—
10	C₃⁴	C₁₃⋊C₉	1	1	yes	characteristic
11	C₃²×C₉	—	13	1	no	—
12	C₃²×C₉	—	13	2	no	—
13	C₃×C₂₇	—	39	2	no	—
14	C₃×C₂₇	—	39	1	no	—
15	C₃×C₁₃	—	27	1	no	—
16	C₃³	—	13	1	no	—
17	C₃³	—	13	2	no	—
18	C₃³	C₁₃⋊C₂₇	1	1	yes	characteristic, complemented
19	C₃×C₉	—	13	1	no	—
20	C₃×C₉	—	13	2	no	—
21	C₃×C₉	—	39	2	no	—
22	C₂₇	—	117	2	no	—
23	C₂₇	—	117	1	no	—
24	C₁₃	—	27	1	no	Sylow
25	C₃²	—	13	1	no	—
26	C₃²	—	13	2	no	—
27	C₃²	—	13	1	no	—
28	C₃²	—	39	2	no	—
29	C₉	—	13	2	no	—
30	C₉	(C₃³⋊C₁₃)⋊C₃	1	1	yes	characteristic
31	C₃	—	13	1	no	—
32	C₃	—	13	2	no	—
33	C₃	(C₃³⋊C₁₃)⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₉	(C₃³⋊C₁₃)⋊C₃
commutator, hypocenter	C₃³⋊C₁₃	C₂₇
Fitting	C₃³×C₉	C₁₃⋊C₃
socle	C₃⁴	C₁₃⋊C₉
prime radical	C₃×C₃³⋊C₁₃	C₉
cosocle	C₉×C₃³⋊C₁₃	C₃
LCS	G ▷ C₃³⋊C₁₃
UCS	C₁ ◁ C₉

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

N	H ≅ G/N	type
4. C₃³⋊C₁₃	C₂₇	semidirect
18. C₃³	C₁₃⋊C₂₇	semidirect