Subgroups — #66943⋊C₅ #13182492

Order 1760.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊C₄×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(Dic₁₁⋊C₅)	C₂	1	2	yes	maximal
3	C₄⋊(Dic₁₁⋊C₅)	C₂	1	1	yes	maximal, characteristic
4	(Dic₁₁⋊C₄)⋊C₅	C₂	1	2	yes	maximal
5	C₄×Dic₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₁₁⋊C₅	C₂²	1	2	yes	—
7	C₂×C₄×C₁₁⋊C₅	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₁⋊C₅	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₁⋊C₅	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₁⋊C₅	C₂²	1	2	yes	—
11	#66943	C₅	1	1	yes	maximal, characteristic, complemented, Hall
12	C₂²×C₁₁⋊C₅	C₂³	1	1	yes	characteristic
13	C₄×C₁₁⋊C₅	—	2	2	no	—
14	C₄×C₁₁⋊C₅	Q₈	1	2	yes	—
15	Dic₁₁⋊C₅	—	2	1	no	—
16	Dic₁₁⋊C₅	—	2	2	no	—
17	Dic₁₁⋊C₅	—	2	1	no	—
18	C₁₁×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
19	C₄⋊Dic₁₁	C₂×C₅	1	2	yes	—
20	C₄⋊Dic₁₁	C₂×C₅	1	1	yes	characteristic
21	Dic₁₁⋊C₄	C₂×C₅	1	2	yes	—
22	C₄×Dic₁₁	C₂×C₅	1	1	yes	characteristic
23	C₅×#125	—	11	1	no	maximal, Hall
24	C₂×C₁₁⋊C₅	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₁₁⋊C₅	#41	1	1	yes	characteristic
26	C₂×C₁₁⋊C₅	#41	1	1	yes	characteristic
27	C₂×C₄×C₁₁	C₂²×C₅	1	2	yes	—
28	C₂×C₄×C₁₁	C₂²×C₅	1	1	yes	characteristic
29	C₂×Dic₁₁	C₂²×C₅	1	1	yes	characteristic
30	C₂×Dic₁₁	C₂²×C₅	1	1	yes	characteristic
31	C₂×Dic₁₁	C₂²×C₅	1	2	yes	—
32	C₅×C₄⋊C₄	—	11	2	no	—
33	C₅×C₄⋊C₄	—	11	2	no	—
34	C₅×C₄⋊C₄	—	11	1	no	—
35	C₅×C₄⋊C₄	—	11	1	no	—
36	C₄²×C₅	—	11	1	no	—
37	C₁₁⋊C₅	#125	1	1	yes	characteristic, complemented, Hall
38	C₂²×C₁₁	C₂³×C₅	1	1	yes	characteristic
39	C₄×C₁₁	—	2	2	no	—
40	C₄×C₁₁	C₅×Q₈	1	2	yes	—
41	Dic₁₁	—	2	1	no	—
42	Dic₁₁	—	2	1	no	—
43	Dic₁₁	—	2	2	no	—
44	C₂×C₄×C₅	—	11	1	no	—
45	C₂×C₄×C₅	—	11	1	no	—
46	C₂×C₄×C₅	—	11	2	no	—
47	C₂×C₄×C₅	—	11	1	no	—
48	C₂×C₄×C₅	—	11	2	no	—
49	#125	—	11	1	no	Sylow
50	C₂×C₁₁	C₂×C₅×Q₈	1	1	yes	characteristic
51	C₂×C₁₁	C₅×#41	1	1	yes	characteristic
52	C₂×C₁₁	C₅×#41	1	1	yes	characteristic
53	C₂²×C₅	—	11	1	no	—
54	C₄×C₅	—	11	2	no	—
55	C₄×C₅	—	22	2	no	—
56	C₄×C₅	—	22	1	no	—
57	C₄×C₅	—	22	1	no	—
58	C₄×C₅	—	22	2	no	—
59	C₄⋊C₄	—	11	2	no	—
60	C₄⋊C₄	—	11	2	no	—
61	C₄⋊C₄	—	11	1	no	—
62	C₄⋊C₄	AGL(1,𝔽₁₁)	1	1	yes	characteristic
63	C₄²	—	11	1	no	—
64	C₁₁	C₅×#125	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₅	—	11	1	no	—
66	C₂×C₅	—	11	1	no	—
67	C₂×C₅	—	11	1	no	—
68	C₂×C₄	—	11	1	no	—
69	C₂×C₄	—	11	1	no	—
70	C₂×C₄	—	11	2	no	—
71	C₂×C₄	C₂×AGL(1,𝔽₁₁)	1	2	yes	—
72	C₂×C₄	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic
73	C₅	—	11	1	no	Sylow
74	C₂²	C₂²×AGL(1,𝔽₁₁)	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	22	1	no	—
77	C₄	—	22	1	no	—
78	C₄	—	22	2	no	—
79	C₄	(C₁₁⋊C₅)⋊Q₈	1	2	yes	—
80	C₂	C₂×(C₁₁⋊C₅)⋊Q₈	1	1	yes	characteristic
81	C₂	#4341⋊C₅	1	1	yes	characteristic
82	C₂	#4343⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×AGL(1,𝔽₁₁)
commutator, socle, cosocle	C₂²×C₁₁	C₂³×C₅
Fitting	C₁₁×C₄⋊C₄	C₂×C₅
prime radical	C₂²×C₁₁⋊C₅	C₂³
hypercenter	C₄⋊C₄	AGL(1,𝔽₁₁)
hypocenter	C₁₁	C₅×#125
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
11. #66943	C₅	semidirect
37. C₁₁⋊C₅	#125	semidirect
64. C₁₁	C₅×#125	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊C₄×C₁₁⋊C₅	2
C₄⋊(Dic₁₁⋊C₅)	2
(Dic₁₁⋊C₄)⋊C₅	2
C₄×Dic₁₁⋊C₅	2
#66943	5
C₅×#125	11

Subgroups — #66943⋊C5 #13182492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #66943⋊C₅ #13182492