Subgroups — D₄×D₅×C₁₁ #11725022

Order 880.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅×C₁₁	C₂	1	2	yes	maximal, complemented
2	C₅×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
4	C₁₁×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×C₁₁	C₂²	1	2	yes	complemented
7	C₂×D₅×C₁₁	—	2	4	no	—
8	C₂×D₅×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×D₅×C₁₁	C₂²	1	2	yes	complemented
10	C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic, complemented
11	C₁₁×Dic₅	C₂²	1	1	yes	characteristic, complemented
12	C₂×D₄×C₁₁	—	5	1	no	maximal, Hall
13	C₂×C₅×C₁₁	—	2	2	no	—
14	C₂×C₅×C₁₁	C₂³	1	1	yes	characteristic
15	D₅×C₁₁	—	2	2	no	—
16	D₅×C₁₁	D₄	1	2	yes	direct product factor
17	C₂³×C₁₁	—	5	2	no	—
18	D₄×C₁₁	—	5	2	no	—
19	D₄×C₁₁	—	5	1	no	—
20	D₄×C₁₁	D₅	1	1	yes	characteristic, direct product factor
21	C₂×C₄×C₁₁	—	5	1	no	—
22	D₄×D₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₅×C₁₁	C₂×D₄	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₁₁	—	5	1	no	—
25	C₂²×C₁₁	—	5	2	no	—
26	C₂²×C₁₁	—	10	4	no	—
27	C₂²×C₁₁	C₂×D₅	1	2	yes	complemented
28	C₄×C₁₁	—	5	1	no	—
29	C₄×C₁₁	C₂×D₅	1	1	yes	characteristic, complemented
30	C₂²×D₅	C₂×C₁₁	1	2	yes	complemented
31	C₅×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
32	C₂²⋊D₅	C₂×C₁₁	1	2	yes	complemented
33	D₂₀	C₂×C₁₁	1	1	yes	characteristic, complemented
34	C₄×D₅	C₂×C₁₁	1	1	yes	characteristic, complemented
35	C₂×C₁₁	—	2	2	no	—
36	C₂×C₁₁	—	5	2	no	—
37	C₂×C₁₁	—	10	2	no	—
38	C₂×C₁₁	C₂²×D₅	1	1	yes	characteristic
39	C₂²×C₅	C₂²×C₁₁	1	2	yes	complemented
40	C₂×D₅	—	2	4	no	—
41	C₂×D₅	C₂²×C₁₁	1	1	yes	characteristic
42	C₂×D₅	C₂²×C₁₁	1	2	yes	complemented
43	C₄×C₅	C₂²×C₁₁	1	1	yes	characteristic, complemented
44	Dic₅	C₂²×C₁₁	1	1	yes	characteristic, complemented
45	C₂×D₄	—	5	1	no	Sylow
46	C₁₁	D₄×D₅	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₅	—	2	2	no	—
48	C₂×C₅	C₂³×C₁₁	1	1	yes	characteristic
49	D₅	—	2	2	no	—
50	D₅	D₄×C₁₁	1	2	yes	direct product factor
51	C₂³	—	5	2	no	—
52	D₄	—	5	2	no	—
53	D₄	—	5	1	no	—
54	D₄	D₅×C₁₁	1	1	yes	characteristic, direct product factor
55	C₂×C₄	—	5	1	no	—
56	C₅	C₂×D₄×C₁₁	1	1	yes	characteristic, complemented, Sylow
57	C₂²	—	5	1	no	—
58	C₂²	—	5	2	no	—
59	C₂²	—	10	4	no	—
60	C₂²	C₂×D₅×C₁₁	1	2	yes	complemented
61	C₄	—	5	1	no	—
62	C₄	C₂×D₅×C₁₁	1	1	yes	characteristic, complemented
63	C₂	—	2	2	no	—
64	C₂	—	5	2	no	—
65	C₂	—	10	2	no	—
66	C₂	C₂²×D₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₁	C₂²×D₅
commutator, cosocle	C₂×C₅	C₂³×C₁₁
Frattini	C₂	C₂²×D₅×C₁₁
Fitting	C₅×D₄×C₁₁	C₂
socle	C₂×C₅×C₁₁	C₂³
hypercenter	D₄×C₁₁	D₅
hypocenter	C₅	C₂×D₄×C₁₁
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₁ ◁ D₄×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂²×D₅×C₁₁	C₂	semidirect
2. C₅×D₄×C₁₁	C₂	semidirect
3. C₁₁×C₂²⋊D₅	C₂	semidirect
4. C₁₁×D₂₀	C₂	semidirect
5. C₄×D₅×C₁₁	C₂	semidirect
6. C₂²×C₅×C₁₁	C₂²	semidirect
9. C₂×D₅×C₁₁	C₂²	semidirect
10. C₄×C₅×C₁₁	C₂²	semidirect
11. C₁₁×Dic₅	C₂²	semidirect
16. D₅×C₁₁	D₄	direct (N × H)
20. D₄×C₁₁	D₅	direct (N × H)
22. D₄×D₅	C₁₁	direct (N × H)
23. C₅×C₁₁	C₂×D₄	semidirect
27. C₂²×C₁₁	C₂×D₅	semidirect
29. C₄×C₁₁	C₂×D₅	semidirect
30. C₂²×D₅	C₂×C₁₁	semidirect
31. C₅×D₄	C₂×C₁₁	semidirect
32. C₂²⋊D₅	C₂×C₁₁	semidirect
33. D₂₀	C₂×C₁₁	semidirect
34. C₄×D₅	C₂×C₁₁	semidirect
39. C₂²×C₅	C₂²×C₁₁	semidirect
42. C₂×D₅	C₂²×C₁₁	semidirect
43. C₄×C₅	C₂²×C₁₁	semidirect
44. Dic₅	C₂²×C₁₁	semidirect
46. C₁₁	D₄×D₅	direct (N × H)
50. D₅	D₄×C₁₁	direct (N × H)
54. D₄	D₅×C₁₁	direct (N × H)
56. C₅	C₂×D₄×C₁₁	semidirect
60. C₂²	C₂×D₅×C₁₁	semidirect
62. C₄	C₂×D₅×C₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₅×C₁₁	2
C₅×D₄×C₁₁	2
C₁₁×C₂²⋊D₅	2
C₁₁×D₂₀	2
C₄×D₅×C₁₁	2
C₂×D₄×C₁₁	5
D₄×D₅	11

Subgroups — D4×D5×C11 #11725022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×D₅×C₁₁ #11725022