Subgroups — #67040⋊C₅ #13183286

Order 1760.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	#4343⋊C₅	C₂	1	4	yes	maximal, complemented
3	Q₈×AGL(1,𝔽₁₁)	C₂	1	4	yes	maximal, complemented
4	#4339⋊C₅	C₂	1	6	yes	maximal, complemented
5	Q₈×C₁₁⋊C₅	C₂²	1	4	yes	—
6	C₂×C₄×C₁₁⋊C₅	C₂²	1	3	yes	—
7	C₂²⋊AGL(1,𝔽₁₁)	C₂²	1	4	yes	—
8	C₄⋊AGL(1,𝔽₁₁)	C₂²	1	6	yes	—
9	C₄×AGL(1,𝔽₁₁)	C₂²	1	12	yes	—
10	(C₁₁⋊C₅)⋊Q₈	C₂²	1	6	yes	—
11	#67040	C₅	1	1	yes	maximal, characteristic, complemented, Hall
12	C₂²×C₁₁⋊C₅	C₂³	1	1	yes	characteristic
13	C₂×AGL(1,𝔽₁₁)	C₂³	1	4	yes	—
14	C₄×C₁₁⋊C₅	C₂³	1	6	yes	—
15	Dic₁₁⋊C₅	C₂³	1	4	yes	—
16	C₂×Q₈×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
17	#4343	C₂×C₅	1	4	yes	complemented
18	Q₈×D₁₁	C₂×C₅	1	4	yes	complemented
19	#4339	C₂×C₅	1	6	yes	complemented
20	C₅×2₋¹⁺⁴	—	11	1	no	maximal, Hall
21	C₂×C₁₁⋊C₅	—	2	1	no	—
22	C₂×C₁₁⋊C₅	C₂⁴	1	1	yes	characteristic
23	AGL(1,𝔽₁₁)	—	2	4	no	—
24	Q₈×C₁₁	C₂²×C₅	1	4	yes	—
25	C₂×C₄×C₁₁	C₂²×C₅	1	3	yes	—
26	C₂²⋊D₁₁	C₂²×C₅	1	4	yes	—
27	D₄₄	C₂²×C₅	1	6	yes	—
28	C₄×D₁₁	C₂²×C₅	1	12	yes	—
29	Dic₂₂	C₂²×C₅	1	6	yes	—
30	C₅×#41	—	11	6	no	—
31	C₅×#41	—	11	4	no	—
32	C₂×C₅×Q₈	—	11	4	no	—
33	C₂×C₅×Q₈	—	11	1	no	—
34	C₁₁⋊C₅	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₁₁	C₂³×C₅	1	1	yes	characteristic
36	C₂×D₁₁	C₂³×C₅	1	4	yes	—
37	C₄×C₁₁	C₂³×C₅	1	6	yes	—
38	Dic₁₁	C₂³×C₅	1	4	yes	—
39	C₅×Q₈	—	11	6	no	—
40	C₅×Q₈	—	11	4	no	—
41	C₅×D₄	—	11	6	no	—
42	C₅×D₄	—	11	4	no	—
43	C₂×C₄×C₅	—	11	12	no	—
44	C₂×C₄×C₅	—	11	3	no	—
45	2₋¹⁺⁴	—	11	1	no	Sylow
46	C₂×C₁₁	—	2	1	no	—
47	C₂×C₁₁	C₂⁴×C₅	1	1	yes	characteristic
48	D₁₁	—	2	4	no	—
49	C₂²×C₅	—	11	4	no	—
50	C₂²×C₅	—	11	1	no	—
51	C₄×C₅	—	11	4	no	—
52	C₄×C₅	—	11	6	no	—
53	#41	—	11	4	no	—
54	#41	—	11	6	no	—
55	C₂×Q₈	—	11	4	no	—
56	C₂×Q₈	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
57	C₁₁	C₅×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₅	—	11	1	no	—
59	C₂×C₅	—	22	1	no	—
60	C₂×C₅	—	22	4	no	—
61	Q₈	—	11	6	no	—
62	Q₈	C₂×AGL(1,𝔽₁₁)	1	4	yes	—
63	D₄	—	11	4	no	—
64	D₄	—	11	6	no	—
65	C₂×C₄	—	11	12	no	—
66	C₂×C₄	C₂×AGL(1,𝔽₁₁)	1	3	yes	—
67	C₅	—	11	1	no	Sylow
68	C₂²	—	11	4	no	—
69	C₂²	C₂²×AGL(1,𝔽₁₁)	1	1	yes	characteristic
70	C₄	—	11	4	no	—
71	C₄	C₂²×AGL(1,𝔽₁₁)	1	6	yes	—
72	C₂	—	2	1	no	—
73	C₂	—	22	4	no	—
74	C₂	C₂³×AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×AGL(1,𝔽₁₁)
commutator, socle, cosocle	C₂×C₁₁	C₂⁴×C₅
Fitting	C₂×Q₈×C₁₁	C₂×C₅
hypercenter	C₂×Q₈	AGL(1,𝔽₁₁)
hypocenter	C₁₁	C₅×2₋¹⁺⁴
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₁₁⋊C₅	C₂	semidirect
2. #4343⋊C₅	C₂	semidirect
3. Q₈×AGL(1,𝔽₁₁)	C₂	semidirect
4. #4339⋊C₅	C₂	semidirect
11. #67040	C₅	semidirect
16. C₂×Q₈×C₁₁	C₂×C₅	semidirect
17. #4343	C₂×C₅	semidirect
18. Q₈×D₁₁	C₂×C₅	semidirect
19. #4339	C₂×C₅	semidirect
34. C₁₁⋊C₅	2₋¹⁺⁴	semidirect
56. C₂×Q₈	AGL(1,𝔽₁₁)	semidirect
57. C₁₁	C₅×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₁₁⋊C₅	2
#4343⋊C₅	2
Q₈×AGL(1,𝔽₁₁)	2
#4339⋊C₅	2
#67040	5
C₅×2₋¹⁺⁴	11

Subgroups — #67040⋊C5 #13183286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #67040⋊C₅ #13183286