Subgroups — C₂²×D₅×D₁₁ #11725049

Order 880.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅×D₁₁	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₅×C₁₁	C₂²	1	1	yes	characteristic, complemented
6	C₂×D₅₅	C₂²	1	6	yes	complemented
7	C₂×D₅×C₁₁	C₂²	1	6	yes	complemented
8	C₂×C₅×D₁₁	C₂²	1	6	yes	complemented
9	D₅×D₁₁	C₂²	1	16	yes	direct product factor
10	C₂³×D₁₁	—	5	1	no	maximal, Hall
11	C₂×C₅×C₁₁	C₂³	1	3	yes	complemented
12	D₅₅	C₂³	1	4	yes	complemented
13	C₅×D₁₁	C₂³	1	4	yes	complemented
14	D₅×C₁₁	C₂³	1	4	yes	complemented
15	C₂³×C₁₁	—	5	1	no	—
16	C₂²×D₁₁	—	5	1	no	—
17	C₂²×D₁₁	—	5	12	no	—
18	C₂²×D₁₁	D₅	1	1	yes	characteristic, direct product factor
19	C₂³×D₅	—	11	1	no	maximal, Hall
20	C₅×C₁₁	C₂⁴	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₁₁	—	5	6	no	—
22	C₂²×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented
23	C₂×D₁₁	—	5	6	no	—
24	C₂×D₁₁	—	5	16	no	—
25	C₂×D₁₁	C₂×D₅	1	6	yes	direct product factor
26	C₂³×C₅	—	11	1	no	—
27	C₂²×D₅	—	11	1	no	—
28	C₂²×D₅	—	11	12	no	—
29	C₂²×D₅	D₁₁	1	1	yes	characteristic, direct product factor
30	C₂×C₁₁	—	5	4	no	—
31	C₂×C₁₁	C₂²×D₅	1	3	yes	complemented
32	D₁₁	—	5	4	no	—
33	D₁₁	C₂²×D₅	1	4	yes	direct product factor
34	C₂²×C₅	—	11	6	no	—
35	C₂²×C₅	C₂×D₁₁	1	1	yes	characteristic, complemented
36	C₂×D₅	—	11	6	no	—
37	C₂×D₅	—	11	16	no	—
38	C₂×D₅	C₂×D₁₁	1	6	yes	direct product factor
39	C₂⁴	—	55	1	no	Sylow
40	C₁₁	C₂³×D₅	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	11	4	no	—
42	C₂×C₅	C₂²×D₁₁	1	3	yes	complemented
43	D₅	—	11	4	no	—
44	D₅	C₂²×D₁₁	1	4	yes	direct product factor
45	C₂³	—	5	1	no	—
46	C₂³	—	11	1	no	—
47	C₂³	—	55	12	no	—
48	C₂³	—	55	1	no	—
49	C₅	C₂³×D₁₁	1	1	yes	characteristic, complemented, Sylow
50	C₂²	—	5	6	no	—
51	C₂²	—	11	6	no	—
52	C₂²	—	55	16	no	—
53	C₂²	—	55	6	no	—
54	C₂²	D₅×D₁₁	1	1	yes	characteristic, direct product factor
55	C₂	—	5	4	no	—
56	C₂	—	11	4	no	—
57	C₂	—	55	4	no	—
58	C₂	C₂×D₅×D₁₁	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	D₅×D₁₁
commutator, cosocle, hypocenter	C₅×C₁₁	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₁	C₂²
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×D₅₅	C₂	semidirect
2. C₂²×D₅×C₁₁	C₂	semidirect
3. C₂²×C₅×D₁₁	C₂	semidirect
4. C₂×D₅×D₁₁	C₂	direct (N × H)
5. C₂²×C₅×C₁₁	C₂²	semidirect
6. C₂×D₅₅	C₂²	semidirect
7. C₂×D₅×C₁₁	C₂²	semidirect
8. C₂×C₅×D₁₁	C₂²	semidirect
9. D₅×D₁₁	C₂²	direct (N × H)
11. C₂×C₅×C₁₁	C₂³	semidirect
12. D₅₅	C₂³	semidirect
13. C₅×D₁₁	C₂³	semidirect
14. D₅×C₁₁	C₂³	semidirect
18. C₂²×D₁₁	D₅	direct (N × H)
20. C₅×C₁₁	C₂⁴	semidirect
22. C₂²×C₁₁	C₂×D₅	semidirect
25. C₂×D₁₁	C₂×D₅	direct (N × H)
29. C₂²×D₅	D₁₁	direct (N × H)
31. C₂×C₁₁	C₂²×D₅	semidirect
33. D₁₁	C₂²×D₅	direct (N × H)
35. C₂²×C₅	C₂×D₁₁	semidirect
38. C₂×D₅	C₂×D₁₁	direct (N × H)
40. C₁₁	C₂³×D₅	semidirect
42. C₂×C₅	C₂²×D₁₁	semidirect
44. D₅	C₂²×D₁₁	direct (N × H)
49. C₅	C₂³×D₁₁	semidirect
54. C₂²	D₅×D₁₁	direct (N × H)
58. C₂	C₂×D₅×D₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₅₅	2
C₂²×D₅×C₁₁	2
C₂²×C₅×D₁₁	2
C₂×D₅×D₁₁	2
C₂³×D₁₁	5
C₂³×D₅	11

Subgroups — C22×D5×D11 #11725049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₅×D₁₁ #11725049