Subgroups — C₂×C₄⋊(Dic₁₁⋊C₅) #13182526

Order 1760.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₁₁⋊C₅	C₂	1	2	yes	maximal
3	C₄⋊(Dic₁₁⋊C₅)	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₁₁⋊C₅	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₁₁⋊C₅	C₄	1	4	yes	complemented
6	C₂×C₄×C₁₁⋊C₅	C₂²	1	2	yes	—
7	C₂×Dic₁₁⋊C₅	—	2	4	no	—
8	C₂×Dic₁₁⋊C₅	C₂²	1	4	yes	—
9	C₂×C₄⋊Dic₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
10	C₂²×C₁₁⋊C₅	C₂×C₄	1	2	yes	—
11	C₂²×C₁₁⋊C₅	D₄	1	2	yes	—
12	C₂²×C₁₁⋊C₅	Q₈	1	2	yes	—
13	C₂²×C₁₁⋊C₅	C₂³	1	1	yes	characteristic
14	C₄×C₁₁⋊C₅	C₂×C₄	1	4	yes	complemented
15	Dic₁₁⋊C₅	—	2	4	no	—
16	C₂²×C₄×C₁₁	C₂×C₅	1	1	yes	characteristic
17	C₂²×Dic₁₁	C₂×C₅	1	2	yes	—
18	C₄⋊Dic₁₁	C₂×C₅	1	4	yes	complemented
19	C₂×C₅×C₄⋊C₄	—	11	1	no	maximal, Hall
20	C₂×C₁₁⋊C₅	C₄⋊C₄	1	4	yes	complemented
21	C₂×C₁₁⋊C₅	C₂²×C₄	1	1	yes	characteristic
22	C₂×C₁₁⋊C₅	C₂×D₄	1	1	yes	characteristic
23	C₂×C₁₁⋊C₅	C₂×Q₈	1	1	yes	characteristic
24	C₂³×C₁₁	C₂²×C₅	1	1	yes	characteristic
25	C₂×C₄×C₁₁	C₄×C₅	1	4	yes	complemented
26	C₂×C₄×C₁₁	C₂²×C₅	1	2	yes	—
27	C₂×Dic₁₁	—	2	4	no	—
28	C₂×Dic₁₁	C₂²×C₅	1	4	yes	—
29	C₂²×C₄×C₅	—	11	2	no	—
30	C₂²×C₄×C₅	—	11	1	no	—
31	C₅×C₄⋊C₄	—	11	4	no	—
32	C₁₁⋊C₅	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
33	C₂²×C₁₁	C₂×C₄×C₅	1	2	yes	—
34	C₂²×C₁₁	C₅×D₄	1	2	yes	—
35	C₂²×C₁₁	C₅×Q₈	1	2	yes	—
36	C₂²×C₁₁	C₂³×C₅	1	1	yes	characteristic
37	C₄×C₁₁	C₂×C₄×C₅	1	4	yes	complemented
38	Dic₁₁	—	2	4	no	—
39	C₂³×C₅	—	11	1	no	—
40	C₂×C₄×C₅	—	11	4	no	—
41	C₂×C₄×C₅	—	11	4	no	—
42	C₂×C₄×C₅	—	11	2	no	—
43	C₂×C₄×C₅	—	22	4	no	—
44	C₂×C₄⋊C₄	—	11	1	no	Sylow
45	C₂×C₁₁	C₅×C₄⋊C₄	1	4	yes	complemented
46	C₂×C₁₁	C₂²×C₄×C₅	1	1	yes	characteristic
47	C₂×C₁₁	C₂×C₅×D₄	1	1	yes	characteristic
48	C₂×C₁₁	C₂×C₅×Q₈	1	1	yes	characteristic
49	C₂²×C₅	—	11	2	no	—
50	C₂²×C₅	—	11	2	no	—
51	C₂²×C₅	—	11	2	no	—
52	C₂²×C₅	—	11	1	no	—
53	C₄×C₅	—	11	4	no	—
54	C₄×C₅	—	22	4	no	—
55	C₂²×C₄	—	11	2	no	—
56	C₂²×C₄	AGL(1,𝔽₁₁)	1	1	yes	characteristic
57	C₄⋊C₄	—	11	4	no	—
58	C₁₁	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₅	—	11	4	no	—
60	C₂×C₅	—	11	1	no	—
61	C₂×C₅	—	11	1	no	—
62	C₂×C₅	—	11	1	no	—
63	C₂³	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic
64	C₂×C₄	—	11	4	no	—
65	C₂×C₄	—	22	4	no	—
66	C₂×C₄	Dic₁₁⋊C₅	1	4	yes	complemented
67	C₂×C₄	C₂×AGL(1,𝔽₁₁)	1	2	yes	—
68	C₅	—	11	1	no	Sylow
69	C₂²	(C₁₁⋊C₅)⋊Q₈	1	2	yes	—
70	C₂²	C₄⋊AGL(1,𝔽₁₁)	1	2	yes	—
71	C₂²	C₂×Dic₁₁⋊C₅	1	2	yes	—
72	C₂²	C₂²×AGL(1,𝔽₁₁)	1	1	yes	characteristic
73	C₄	—	22	4	no	—
74	C₄	C₂×Dic₁₁⋊C₅	1	4	yes	complemented
75	C₂	C₄⋊(Dic₁₁⋊C₅)	1	4	yes	direct product factor
76	C₂	C₂×(C₁₁⋊C₅)⋊Q₈	1	1	yes	characteristic
77	C₂	C₂×C₄⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
78	C₂	C₂²×Dic₁₁⋊C₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₄⋊(Dic₁₁⋊C₅)	C₂	direct (N × H)
5. C₂×C₄×C₁₁⋊C₅	C₄	semidirect
9. C₂×C₄⋊Dic₁₁	C₅	semidirect
14. C₄×C₁₁⋊C₅	C₂×C₄	semidirect
18. C₄⋊Dic₁₁	C₂×C₅	semidirect
20. C₂×C₁₁⋊C₅	C₄⋊C₄	semidirect
25. C₂×C₄×C₁₁	C₄×C₅	semidirect
32. C₁₁⋊C₅	C₂×C₄⋊C₄	semidirect
37. C₄×C₁₁	C₂×C₄×C₅	semidirect
45. C₂×C₁₁	C₅×C₄⋊C₄	semidirect
58. C₁₁	C₂×C₅×C₄⋊C₄	semidirect
66. C₂×C₄	Dic₁₁⋊C₅	semidirect
74. C₄	C₂×Dic₁₁⋊C₅	semidirect
75. C₂	C₄⋊(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
C₂²×C₄×C₁₁⋊C₅	2
C₂²×Dic₁₁⋊C₅	2
C₄⋊(Dic₁₁⋊C₅)	2
C₂×C₄⋊Dic₁₁	5
C₂×C₅×C₄⋊C₄	11

Subgroups — C2×C4⋊(Dic11⋊C5) #13182526

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊(Dic₁₁⋊C₅) #13182526