Subgroups — C₂×C₂²⋊(Dic₁₁⋊C₅) #13182553

Order 1760.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₁₁⋊C₅	C₂	1	2	yes	maximal, complemented
3	C₂²⋊(Dic₁₁⋊C₅)	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₁₁⋊C₅	—	2	4	no	—
5	C₂³×C₁₁⋊C₅	C₄	1	4	yes	complemented
6	C₂³×C₁₁⋊C₅	C₂²	1	2	yes	—
7	C₂³×C₁₁⋊C₅	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₁⋊C₅	—	2	4	no	—
9	C₂×Dic₁₁⋊C₅	C₂²	1	4	yes	complemented
10	C₂×C₂²⋊Dic₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
11	C₂²×C₁₁⋊C₅	—	2	8	no	—
12	C₂²×C₁₁⋊C₅	—	2	4	no	—
13	C₂²×C₁₁⋊C₅	C₂×C₄	1	2	yes	—
14	C₂²×C₁₁⋊C₅	C₂×C₄	1	4	yes	complemented
15	C₂²×C₁₁⋊C₅	D₄	1	4	yes	—
16	C₂²×C₁₁⋊C₅	C₂³	1	1	yes	characteristic
17	Dic₁₁⋊C₅	—	2	4	no	—
18	C₂⁴×C₁₁	C₂×C₅	1	1	yes	characteristic
19	C₂²×Dic₁₁	C₂×C₅	1	2	yes	complemented
20	C₂²⋊Dic₁₁	C₂×C₅	1	4	yes	complemented
21	C₂×C₅×C₂²⋊C₄	—	11	1	no	maximal, Hall
22	C₂×C₁₁⋊C₅	—	2	4	no	—
23	C₂×C₁₁⋊C₅	C₂²⋊C₄	1	4	yes	complemented
24	C₂×C₁₁⋊C₅	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₁₁⋊C₅	C₂×D₄	1	2	yes	—
26	C₂³×C₁₁	—	2	4	no	—
27	C₂³×C₁₁	C₄×C₅	1	4	yes	complemented
28	C₂³×C₁₁	C₂²×C₅	1	2	yes	—
29	C₂³×C₁₁	C₂²×C₅	1	1	yes	characteristic
30	C₂×Dic₁₁	—	2	4	no	—
31	C₂×Dic₁₁	C₂²×C₅	1	4	yes	complemented
32	C₂⁴×C₅	—	11	1	no	—
33	C₂²×C₄×C₅	—	11	2	no	—
34	C₅×C₂²⋊C₄	—	11	4	no	—
35	C₁₁⋊C₅	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×C₄×C₅	1	2	yes	—
39	C₂²×C₁₁	C₂×C₄×C₅	1	4	yes	complemented
40	C₂²×C₁₁	C₅×D₄	1	4	yes	—
41	C₂²×C₁₁	C₂³×C₅	1	1	yes	characteristic
42	Dic₁₁	—	2	4	no	—
43	C₂³×C₅	—	11	4	no	—
44	C₂³×C₅	—	11	2	no	—
45	C₂³×C₅	—	11	1	no	—
46	C₂³×C₅	—	22	4	no	—
47	C₂×C₄×C₅	—	11	4	no	—
48	C₂×C₄×C₅	—	22	4	no	—
49	C₂×C₂²⋊C₄	—	11	1	no	Sylow
50	C₂×C₁₁	—	2	4	no	—
51	C₂×C₁₁	C₅×C₂²⋊C₄	1	4	yes	complemented
52	C₂×C₁₁	C₂²×C₄×C₅	1	1	yes	characteristic
53	C₂×C₁₁	C₂×C₅×D₄	1	2	yes	—
54	C₂²×C₅	—	11	2	no	—
55	C₂²×C₅	—	11	4	no	—
56	C₂²×C₅	—	11	4	no	—
57	C₂²×C₅	—	11	1	no	—
58	C₂²×C₅	—	22	8	no	—
59	C₂²×C₅	—	22	4	no	—
60	C₄×C₅	—	22	4	no	—
61	C₂⁴	AGL(1,𝔽₁₁)	1	1	yes	characteristic
62	C₂²×C₄	—	11	2	no	—
63	C₂²⋊C₄	—	11	4	no	—
64	C₁₁	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₅	—	11	4	no	—
66	C₂×C₅	—	11	1	no	—
67	C₂×C₅	—	11	2	no	—
68	C₂×C₅	—	22	4	no	—
69	C₂³	—	2	4	no	—
70	C₂³	Dic₁₁⋊C₅	1	4	yes	complemented
71	C₂³	C₂×AGL(1,𝔽₁₁)	1	2	yes	—
72	C₂³	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic
73	C₂×C₄	—	11	4	no	—
74	C₂×C₄	—	22	4	no	—
75	C₅	—	11	1	no	Sylow
76	C₂²	—	2	8	no	—
77	C₂²	—	2	4	no	—
78	C₂²	C₂×Dic₁₁⋊C₅	1	2	yes	—
79	C₂²	C₂×Dic₁₁⋊C₅	1	4	yes	complemented
80	C₂²	C₂²⋊AGL(1,𝔽₁₁)	1	4	yes	—
81	C₂²	C₂²×AGL(1,𝔽₁₁)	1	1	yes	characteristic
82	C₄	—	22	4	no	—
83	C₂	—	2	4	no	—
84	C₂	C₂²⋊(Dic₁₁⋊C₅)	1	4	yes	direct product factor
85	C₂	C₂²×Dic₁₁⋊C₅	1	1	yes	characteristic
86	C₂	C₂×C₂²⋊AGL(1,𝔽₁₁)	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×AGL(1,𝔽₁₁)
commutator	C₂×C₁₁	C₂²×C₄×C₅
Frattini	C₂²	C₂²×AGL(1,𝔽₁₁)
Fitting	C₂⁴×C₁₁	C₂×C₅
socle	C₂³×C₁₁	C₂²×C₅
prime radical	C₂⁴×C₁₁⋊C₅	C₂
cosocle	C₂²×C₁₁	C₂³×C₅
hypercenter	C₂⁴	AGL(1,𝔽₁₁)
hypocenter	C₁₁	C₂×C₅×C₂²⋊C₄
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₁₁⋊C₅	C₂	semidirect
3. C₂²⋊(Dic₁₁⋊C₅)	C₂	direct (N × H)
5. C₂³×C₁₁⋊C₅	C₄	semidirect
9. C₂×Dic₁₁⋊C₅	C₂²	semidirect
10. C₂×C₂²⋊Dic₁₁	C₅	semidirect
14. C₂²×C₁₁⋊C₅	C₂×C₄	semidirect
19. C₂²×Dic₁₁	C₂×C₅	semidirect
20. C₂²⋊Dic₁₁	C₂×C₅	semidirect
23. C₂×C₁₁⋊C₅	C₂²⋊C₄	semidirect
27. C₂³×C₁₁	C₄×C₅	semidirect
31. C₂×Dic₁₁	C₂²×C₅	semidirect
35. C₁₁⋊C₅	C₂×C₂²⋊C₄	semidirect
39. C₂²×C₁₁	C₂×C₄×C₅	semidirect
51. C₂×C₁₁	C₅×C₂²⋊C₄	semidirect
64. C₁₁	C₂×C₅×C₂²⋊C₄	semidirect
70. C₂³	Dic₁₁⋊C₅	semidirect
79. C₂²	C₂×Dic₁₁⋊C₅	semidirect
84. C₂	C₂²⋊(Dic₁₁⋊C₅)	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×C₁₁⋊C₅	2
C₂²×Dic₁₁⋊C₅	2
C₂²⋊(Dic₁₁⋊C₅)	2
C₂×C₂²⋊Dic₁₁	5
C₂×C₅×C₂²⋊C₄	11

Subgroups — C2×C22⋊(Dic11⋊C5) #13182553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂²⋊(Dic₁₁⋊C₅) #13182553