Subgroups — C₂×C₁₁×C₂²⋊Dic₅ #13183165

Order 1760.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×Dic₅	C₂	1	2	yes	maximal, complemented
3	C₁₁×C₂²⋊Dic₅	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₅×C₁₁	—	2	4	no	—
5	C₂³×C₅×C₁₁	C₄	1	4	yes	complemented
6	C₂³×C₅×C₁₁	C₂²	1	2	yes	—
7	C₂³×C₅×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₁×Dic₅	—	2	4	no	—
9	C₂×C₁₁×Dic₅	C₂²	1	4	yes	complemented
10	C₂×C₁₁×C₂²⋊C₄	—	5	1	no	maximal, Hall
11	C₂²×C₅×C₁₁	—	2	8	no	—
12	C₂²×C₅×C₁₁	—	2	4	no	—
13	C₂²×C₅×C₁₁	C₂×C₄	1	2	yes	—
14	C₂²×C₅×C₁₁	C₂×C₄	1	4	yes	complemented
15	C₂²×C₅×C₁₁	D₄	1	4	yes	—
16	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
17	C₁₁×Dic₅	—	2	4	no	—
18	C₂⁴×C₁₁	D₅	1	1	yes	characteristic
19	C₂²×C₄×C₁₁	—	5	2	no	—
20	C₁₁×C₂²⋊C₄	—	5	4	no	—
21	C₂×C₂²⋊Dic₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×C₁₁	—	2	4	no	—
23	C₂×C₅×C₁₁	C₂²⋊C₄	1	4	yes	complemented
24	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₅×C₁₁	C₂×D₄	1	2	yes	—
26	C₂³×C₁₁	—	2	4	no	—
27	C₂³×C₁₁	Dic₅	1	4	yes	complemented
28	C₂³×C₁₁	C₂×D₅	1	2	yes	—
29	C₂³×C₁₁	C₂×D₅	1	1	yes	characteristic
30	C₂×C₄×C₁₁	—	5	4	no	—
31	C₂×C₄×C₁₁	—	10	4	no	—
32	C₂⁴×C₅	C₂×C₁₁	1	1	yes	characteristic
33	C₂²×Dic₅	C₂×C₁₁	1	2	yes	complemented
34	C₂²⋊Dic₅	C₂×C₁₁	1	4	yes	direct product factor
35	C₅×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₁₁	—	2	8	no	—
37	C₂²×C₁₁	—	2	4	no	—
38	C₂²×C₁₁	C₂×Dic₅	1	2	yes	—
39	C₂²×C₁₁	C₂×Dic₅	1	4	yes	complemented
40	C₂²×C₁₁	C₂²⋊D₅	1	4	yes	—
41	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
42	C₄×C₁₁	—	10	4	no	—
43	C₂³×C₅	—	2	4	no	—
44	C₂³×C₅	C₄×C₁₁	1	4	yes	complemented
45	C₂³×C₅	C₂²×C₁₁	1	2	yes	—
46	C₂³×C₅	C₂²×C₁₁	1	1	yes	characteristic
47	C₂×Dic₅	—	2	4	no	—
48	C₂×Dic₅	C₂²×C₁₁	1	4	yes	complemented
49	C₂×C₂²⋊C₄	—	5	1	no	Sylow
50	C₂×C₁₁	—	2	4	no	—
51	C₂×C₁₁	C₂²⋊Dic₅	1	4	yes	direct product factor
52	C₂×C₁₁	C₂²×Dic₅	1	1	yes	characteristic
53	C₂×C₁₁	C₂×C₂²⋊D₅	1	2	yes	—
54	C₂²×C₅	—	2	8	no	—
55	C₂²×C₅	—	2	4	no	—
56	C₂²×C₅	C₂×C₄×C₁₁	1	2	yes	—
57	C₂²×C₅	C₂×C₄×C₁₁	1	4	yes	complemented
58	C₂²×C₅	D₄×C₁₁	1	4	yes	—
59	C₂²×C₅	C₂³×C₁₁	1	1	yes	characteristic
60	Dic₅	—	2	4	no	—
61	C₂⁴	D₅×C₁₁	1	1	yes	characteristic
62	C₂²×C₄	—	5	2	no	—
63	C₂²⋊C₄	—	5	4	no	—
64	C₁₁	C₂×C₂²⋊Dic₅	1	1	yes	characteristic, direct product factor, Sylow
65	C₂×C₅	—	2	4	no	—
66	C₂×C₅	C₁₁×C₂²⋊C₄	1	4	yes	complemented
67	C₂×C₅	C₂²×C₄×C₁₁	1	1	yes	characteristic
68	C₂×C₅	C₂×D₄×C₁₁	1	2	yes	—
69	C₂³	—	2	4	no	—
70	C₂³	C₁₁×Dic₅	1	4	yes	complemented
71	C₂³	C₂×D₅×C₁₁	1	2	yes	—
72	C₂³	C₂×D₅×C₁₁	1	1	yes	characteristic
73	C₂×C₄	—	5	4	no	—
74	C₂×C₄	—	10	4	no	—
75	C₅	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
76	C₂²	—	2	8	no	—
77	C₂²	—	2	4	no	—
78	C₂²	C₂×C₁₁×Dic₅	1	2	yes	—
79	C₂²	C₂×C₁₁×Dic₅	1	4	yes	complemented
80	C₂²	C₁₁×C₂²⋊D₅	1	4	yes	—
81	C₂²	C₂²×D₅×C₁₁	1	1	yes	characteristic
82	C₄	—	10	4	no	—
83	C₂	—	2	4	no	—
84	C₂	C₁₁×C₂²⋊Dic₅	1	4	yes	direct product factor
85	C₂	C₂²×C₁₁×Dic₅	1	1	yes	characteristic
86	C₂	C₂×C₁₁×C₂²⋊D₅	1	2	yes	—

	subgroup	G/H
center	C₂³×C₁₁	C₂×D₅
commutator	C₂×C₅	C₂²×C₄×C₁₁
Frattini	C₂²	C₂²×D₅×C₁₁
Fitting, prime radical	C₂⁴×C₅×C₁₁	C₂
socle	C₂³×C₅×C₁₁	C₂²
cosocle	C₂²×C₅	C₂³×C₁₁
hypercenter	C₂⁴×C₁₁	D₅
hypocenter	C₅	C₂×C₁₁×C₂²⋊C₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂⁴×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₁×Dic₅	C₂	semidirect
3. C₁₁×C₂²⋊Dic₅	C₂	direct (N × H)
5. C₂³×C₅×C₁₁	C₄	semidirect
9. C₂×C₁₁×Dic₅	C₂²	semidirect
14. C₂²×C₅×C₁₁	C₂×C₄	semidirect
21. C₂×C₂²⋊Dic₅	C₁₁	direct (N × H)
23. C₂×C₅×C₁₁	C₂²⋊C₄	semidirect
27. C₂³×C₁₁	Dic₅	semidirect
33. C₂²×Dic₅	C₂×C₁₁	semidirect
34. C₂²⋊Dic₅	C₂×C₁₁	direct (N × H)
35. C₅×C₁₁	C₂×C₂²⋊C₄	semidirect
39. C₂²×C₁₁	C₂×Dic₅	semidirect
44. C₂³×C₅	C₄×C₁₁	semidirect
48. C₂×Dic₅	C₂²×C₁₁	semidirect
51. C₂×C₁₁	C₂²⋊Dic₅	direct (N × H)
57. C₂²×C₅	C₂×C₄×C₁₁	semidirect
64. C₁₁	C₂×C₂²⋊Dic₅	direct (N × H)
66. C₂×C₅	C₁₁×C₂²⋊C₄	semidirect
70. C₂³	C₁₁×Dic₅	semidirect
75. C₅	C₂×C₁₁×C₂²⋊C₄	semidirect
79. C₂²	C₂×C₁₁×Dic₅	semidirect
84. C₂	C₁₁×C₂²⋊Dic₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₅×C₁₁	2
C₂²×C₁₁×Dic₅	2
C₁₁×C₂²⋊Dic₅	2
C₂×C₁₁×C₂²⋊C₄	5
C₂×C₂²⋊Dic₅	11

Subgroups — C2×C11×C22⋊Dic5 #13183165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×C₂²⋊Dic₅ #13183165