Subgroups — C₂×C₃×#11925893 #20300050

Order 7260.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃	#11925893
commutator, hypocenter	C₁₁²	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁²	C₂×C₅
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#10597245	C₂	semidirect
2. C₃×#11925893	C₂	direct (N × H)
3. C₂×#11925893	C₃	direct (N × H)
4. C₃×#10597245	C₂²	semidirect
5. C₂×C₃×C₁₁⋊D₁₁	C₅	semidirect
6. C₂×#10597245	C₂×C₃	semidirect
7. #11925893	C₂×C₃	direct (N × H)
8. C₂×C₃×C₁₁²	C₂×C₅	semidirect
9. C₃×C₁₁⋊D₁₁	C₂×C₅	semidirect
11. #10597245	C₂²×C₃	semidirect
12. C₂×C₁₁⋊D₁₁	C₃×C₅	semidirect
13. C₃×C₁₁²	C₂²×C₅	semidirect
16. C₂×C₁₁²	C₂×C₃×C₅	semidirect
17. C₁₁⋊D₁₁	C₂×C₃×C₅	semidirect
22. C₁₁²	C₂²×C₃×C₅	semidirect
26. C₂×C₃×C₁₁	AGL(1,𝔽₁₁)	semidirect
34. C₃×C₁₁	C₂×AGL(1,𝔽₁₁)	semidirect
38. C₂×C₁₁	C₃×AGL(1,𝔽₁₁)	semidirect
45. C₁₁	C₂×C₃×AGL(1,𝔽₁₁)	semidirect
49. C₂×C₃	#11925893	direct (N × H)
52. C₃	C₂×#11925893	direct (N × H)
54. C₂	C₃×#11925893	direct (N × H)

Subgroups — C2×C3×#11925893 #20300050

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×#11925893 #20300050