Subgroups — C₉⋊#10621730 #20258803

Order 6084.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#10621730	—	3	1	no	maximal
3	C₉×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₃×D₁₃	D₃	1	1	yes	characteristic
5	#10621730	—	9	1	no	Hall
6	C₃×C₁₃²	Dic₃	1	1	yes	characteristic
7	C₉⋊#261	—	13	1	no	maximal
8	Dic₁₁₇	—	13	1	no	maximal
9	C₁₃×D₁₃	D₉	1	1	yes	characteristic
10	C₂×C₉×C₁₃	—	13	1	no	—
11	C₉×D₁₃	D₁₃	1	1	yes	characteristic
12	C₁₃²	Dic₉	1	1	yes	characteristic, complemented, Sylow
13	C₃⋊#261	—	39	1	no	—
14	Dic₃₉	—	39	1	no	—
15	C₉×C₁₃	—	4	3	no	—
16	C₉×C₁₃	Dic₁₃	1	1	yes	characteristic, complemented
17	C₉×C₁₃	#261	1	1	yes	characteristic, complemented
18	C₂×C₃×C₁₃	—	13	1	no	—
19	C₃×D₁₃	D₃₉	1	1	yes	characteristic
20	#261	—	117	1	no	—
21	Dic₁₃	—	117	1	no	—
22	C₃×C₁₃	—	4	3	no	—
23	C₃×C₁₃	Dic₃₉	1	1	yes	characteristic
24	C₃×C₁₃	C₃⋊#261	1	1	yes	characteristic
25	Dic₉	—	169	1	no	Hall
26	C₂×C₁₃	—	13	1	no	—
27	D₁₃	D₁₁₇	1	1	yes	characteristic
28	C₂×C₉	—	13	1	no	—
29	C₁₃	—	4	3	no	—
30	C₁₃	Dic₁₁₇	1	1	yes	characteristic, complemented
31	C₁₃	C₉⋊#261	1	1	yes	characteristic, complemented
32	Dic₃	—	507	1	no	—
33	C₉	#10621730	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃	—	13	1	no	—
35	C₄	—	1521	1	no	Sylow
36	C₃	C₃⋊#10621730	1	1	yes	characteristic
37	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₉×C₁₃²	C₄
Frattini	C₃	C₃⋊#10621730
socle	C₃×C₁₃²	Dic₃
LCS	G ▷ C₉×C₁₃²
UCS	C₁

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