Subgroups — #20300024

Order 7260.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊#11925890	C₂	1	2	yes	maximal, complemented
2	C₃×#11925893	C₂	1	1	yes	maximal, characteristic, complemented
3	#11925890⋊C₂	—	3	1	no	maximal, Hall
4	C₃×#10597245	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃₃⋊D₁₁	—	5	1	no	maximal, Hall
6	#11925893	D₃	1	1	yes	characteristic, complemented
7	#11925890	—	3	2	no	—
8	C₁₁×D₃₃	—	5	2	no	—
9	C₃×C₁₁⋊D₁₁	D₅	1	1	yes	characteristic, complemented
10	#10597245	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₁₁²	—	15	1	no	Hall
12	C₃×C₁₁²	C₂×D₅	1	1	yes	characteristic, complemented, Hall
13	C₃×AGL(1,𝔽₁₁)	—	22	1	no	—
14	C₁₁⋊D₁₁	D₁₅	1	1	yes	characteristic, complemented
15	C₁₁×D₁₁	—	15	2	no	—
16	C₃×C₁₁⋊C₅	—	22	1	no	—
17	D₃×D₁₁	—	55	2	no	—
18	C₁₁²	C₂×D₁₅	1	1	yes	characteristic, complemented, Sylow
19	AGL(1,𝔽₁₁)	—	22	1	no	—
20	D₃₃	—	5	2	no	—
21	C₃×D₁₁	—	22	1	no	—
22	C₃×D₁₁	—	55	2	no	—
23	D₃×C₁₁	—	55	2	no	—
24	C₂×D₁₅	—	121	1	no	maximal, Hall
25	C₁₁⋊C₅	—	22	1	no	—
26	C₂×D₁₁	—	165	2	no	—
27	C₃×C₁₁	—	2	1	no	—
28	C₃×C₁₁	—	5	2	no	—
29	C₂×C₃×C₅	—	121	1	no	—
30	D₁₅	—	121	2	no	—
31	C₂×C₁₁	—	165	2	no	—
32	D₁₁	—	15	2	no	—
33	D₁₁	—	22	1	no	—
34	D₁₁	—	55	2	no	—
35	C₂×D₅	—	363	1	no	Hall
36	C₃×C₅	—	121	1	no	Hall
37	C₂×D₃	—	605	1	no	Hall
38	C₁₁	—	2	1	no	—
39	C₁₁	—	5	2	no	—
40	C₂×C₅	—	121	1	no	—
41	D₅	—	363	2	no	—
42	C₂×C₃	—	121	1	no	—
43	D₃	—	55	2	no	—
44	C₅	—	121	1	no	Sylow
45	C₂²	—	1815	1	no	Sylow
46	C₃	#11925890⋊C₂	1	1	yes	characteristic, complemented, Sylow
47	C₂	—	121	1	no	—
48	C₂	—	165	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₃×#10597245	C₂²
Fitting, socle	C₃×C₁₁²	C₂×D₅
LCS	G ▷ C₃×#10597245
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊#11925890	C₂	semidirect
2. C₃×#11925893	C₂	semidirect
4. C₃×#10597245	C₂²	semidirect
6. #11925893	D₃	semidirect
9. C₃×C₁₁⋊D₁₁	D₅	semidirect
10. #10597245	C₂×D₃	semidirect
12. C₃×C₁₁²	C₂×D₅	semidirect
14. C₁₁⋊D₁₁	D₁₅	semidirect
18. C₁₁²	C₂×D₁₅	semidirect
46. C₃	#11925890⋊C₂	semidirect