Subgroups — C₂×C₄×Dic₁₁⋊C₅ #13182523

Order 1760.

216 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	C₄	1	8	yes	direct product factor
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	4	yes	—
11	C₂²×C₁₁⋊C₅	C₂×C₄	1	2	yes	—
12	C₂²×C₁₁⋊C₅	C₂³	1	1	yes	characteristic
13	C₄×C₁₁⋊C₅	C₂×C₄	1	4	yes	complemented
14	Dic₁₁⋊C₅	C₂×C₄	1	8	yes	direct product factor
15	C₂²×C₄×C₁₁	C₂×C₅	1	1	yes	characteristic
16	C₂²×Dic₁₁	C₂×C₅	1	2	yes	—
17	C₄×Dic₁₁	C₂×C₅	1	4	yes	complemented
18	C₂×C₄²×C₅	—	11	1	no	maximal, Hall
19	C₂×C₁₁⋊C₅	C₄²	1	4	yes	complemented
20	C₂×C₁₁⋊C₅	C₂²×C₄	1	2	yes	—
21	C₂×C₁₁⋊C₅	C₂²×C₄	1	1	yes	characteristic
22	C₂³×C₁₁	C₂²×C₅	1	1	yes	characteristic
23	C₂×C₄×C₁₁	C₄×C₅	1	4	yes	complemented
24	C₂×C₄×C₁₁	C₂²×C₅	1	2	yes	—
25	C₂×Dic₁₁	C₄×C₅	1	8	yes	complemented
26	C₂×Dic₁₁	C₂²×C₅	1	4	yes	—
27	C₂²×C₄×C₅	—	11	2	no	—
28	C₂²×C₄×C₅	—	11	1	no	—
29	C₄²×C₅	—	11	4	no	—
30	C₁₁⋊C₅	C₂×C₄²	1	1	yes	characteristic, complemented, Hall
31	C₂²×C₁₁	C₂×C₄×C₅	1	4	yes	—
32	C₂²×C₁₁	C₂×C₄×C₅	1	2	yes	—
33	C₂²×C₁₁	C₂³×C₅	1	1	yes	characteristic
34	C₄×C₁₁	C₂×C₄×C₅	1	4	yes	complemented
35	Dic₁₁	C₂×C₄×C₅	1	8	yes	complemented
36	C₂³×C₅	—	11	1	no	—
37	C₂×C₄×C₅	—	11	8	no	—
38	C₂×C₄×C₅	—	11	4	no	—
39	C₂×C₄×C₅	—	11	4	no	—
40	C₂×C₄×C₅	—	11	2	no	—
41	C₂×C₄²	—	11	1	no	Sylow
42	C₂×C₁₁	C₄²×C₅	1	4	yes	complemented
43	C₂×C₁₁	C₂²×C₄×C₅	1	2	yes	—
44	C₂×C₁₁	C₂²×C₄×C₅	1	1	yes	characteristic
45	C₂²×C₅	—	11	4	no	—
46	C₂²×C₅	—	11	2	no	—
47	C₂²×C₅	—	11	1	no	—
48	C₄×C₅	—	11	8	no	—
49	C₄×C₅	—	11	4	no	—
50	C₂²×C₄	—	11	2	no	—
51	C₂²×C₄	AGL(1,𝔽₁₁)	1	1	yes	characteristic
52	C₄²	—	11	4	no	—
53	C₁₁	C₂×C₄²×C₅	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₅	—	11	4	no	—
55	C₂×C₅	—	11	2	no	—
56	C₂×C₅	—	11	1	no	—
57	C₂³	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic
58	C₂×C₄	—	11	8	no	—
59	C₂×C₄	—	11	4	no	—
60	C₂×C₄	Dic₁₁⋊C₅	1	4	yes	direct product factor
61	C₂×C₄	C₂×AGL(1,𝔽₁₁)	1	2	yes	—
62	C₅	—	11	1	no	Sylow
63	C₂²	C₄×AGL(1,𝔽₁₁)	1	4	yes	—
64	C₂²	C₂×Dic₁₁⋊C₅	1	2	yes	—
65	C₂²	C₂²×AGL(1,𝔽₁₁)	1	1	yes	characteristic
66	C₄	—	11	8	no	—
67	C₄	C₂×Dic₁₁⋊C₅	1	4	yes	direct product factor
68	C₂	C₄×Dic₁₁⋊C₅	1	4	yes	direct product factor
69	C₂	C₂×C₄×AGL(1,𝔽₁₁)	1	2	yes	—
70	C₂	C₂²×Dic₁₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	AGL(1,𝔽₁₁)
commutator, hypocenter	C₁₁	C₂×C₄²×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
LCS	G ▷ C₁₁
UCS	C₁ ◁ 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
7. C₂×Dic₁₁⋊C₅	C₄	direct (N × H)
9. C₂×C₄×Dic₁₁	C₅	semidirect
13. C₄×C₁₁⋊C₅	C₂×C₄	semidirect
14. Dic₁₁⋊C₅	C₂×C₄	direct (N × H)
17. C₄×Dic₁₁	C₂×C₅	semidirect
19. C₂×C₁₁⋊C₅	C₄²	semidirect
23. C₂×C₄×C₁₁	C₄×C₅	semidirect
25. C₂×Dic₁₁	C₄×C₅	semidirect
30. C₁₁⋊C₅	C₂×C₄²	semidirect
34. C₄×C₁₁	C₂×C₄×C₅	semidirect
35. Dic₁₁	C₂×C₄×C₅	semidirect
42. C₂×C₁₁	C₄²×C₅	semidirect
53. C₁₁	C₂×C₄²×C₅	semidirect
60. C₂×C₄	Dic₁₁⋊C₅	direct (N × H)
67. C₄	C₂×Dic₁₁⋊C₅	direct (N × H)
68. 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×C₄²×C₅	11

Subgroups — C2×C4×Dic11⋊C5 #13182523

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×Dic₁₁⋊C₅ #13182523