Subgroups — #66972⋊C₅ #13182520

Order 1760.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4343⋊C₅	C₂	1	2	yes	maximal, complemented
2	Q₁₆×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	#4325⋊C₅	C₂	1	2	yes	maximal, complemented
4	D₈₈⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×C₁₁⋊C₅	C₂²	1	2	yes	—
7	C₄⋊AGL(1,𝔽₁₁)	—	2	2	no	—
8	C₄⋊AGL(1,𝔽₁₁)	C₂²	1	2	yes	—
9	C₄×AGL(1,𝔽₁₁)	—	2	2	no	—
10	C₄×AGL(1,𝔽₁₁)	C₂²	1	1	yes	characteristic
11	C₈×C₁₁⋊C₅	C₂²	1	1	yes	characteristic
12	(C₁₁⋊C₅)⋊C₈	C₂²	1	1	yes	characteristic
13	#66972	C₅	1	1	yes	maximal, characteristic, complemented, Hall
14	C₂×AGL(1,𝔽₁₁)	—	2	2	no	—
15	C₂×AGL(1,𝔽₁₁)	D₄	1	1	yes	characteristic
16	C₄×C₁₁⋊C₅	—	2	2	no	—
17	C₄×C₁₁⋊C₅	C₂³	1	1	yes	characteristic
18	Dic₁₁⋊C₅	D₄	1	1	yes	characteristic
19	#4343	C₂×C₅	1	2	yes	complemented
20	C₁₁×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
21	#4325	C₂×C₅	1	2	yes	complemented
22	D₈₈	C₂×C₅	1	1	yes	characteristic, complemented
23	C₈×D₁₁	C₂×C₅	1	1	yes	characteristic, complemented
24	C₅×#135	—	11	1	no	maximal, Hall
25	C₂×C₁₁⋊C₅	C₂×D₄	1	1	yes	characteristic
26	AGL(1,𝔽₁₁)	—	2	1	no	—
27	AGL(1,𝔽₁₁)	—	4	2	no	—
28	Q₈×C₁₁	C₂²×C₅	1	2	yes	—
29	D₄₄	—	2	2	no	—
30	D₄₄	C₂²×C₅	1	2	yes	—
31	C₄×D₁₁	—	2	2	no	—
32	C₄×D₁₁	C₂²×C₅	1	1	yes	characteristic
33	C₈×C₁₁	C₂²×C₅	1	1	yes	characteristic
34	C₁₁⋊C₈	C₂²×C₅	1	1	yes	characteristic
35	C₅×#41	—	11	2	no	—
36	C₅×Q₁₆	—	11	1	no	—
37	C₅×SD₁₆	—	11	2	no	—
38	C₅×D₈	—	11	1	no	—
39	C₂×C₅×C₈	—	11	1	no	—
40	C₁₁⋊C₅	#135	1	1	yes	characteristic, complemented, Hall
41	C₂×D₁₁	—	2	2	no	—
42	C₂×D₁₁	C₅×D₄	1	1	yes	characteristic
43	C₄×C₁₁	—	2	2	no	—
44	C₄×C₁₁	C₂³×C₅	1	1	yes	characteristic
45	Dic₁₁	C₅×D₄	1	1	yes	characteristic
46	C₅×Q₈	—	11	2	no	—
47	C₅×D₄	—	11	2	no	—
48	C₅×D₄	—	22	2	no	—
49	C₂×C₄×C₅	—	11	1	no	—
50	C₂×C₄×C₅	—	22	2	no	—
51	C₅×C₈	—	11	1	no	—
52	C₅×C₈	—	11	1	no	—
53	#135	—	11	1	no	Sylow
54	C₂×C₁₁	C₂×C₅×D₄	1	1	yes	characteristic
55	D₁₁	—	2	1	no	—
56	D₁₁	—	4	2	no	—
57	C₂²×C₅	—	11	1	no	—
58	C₂²×C₅	—	22	2	no	—
59	C₄×C₅	—	11	1	no	—
60	C₄×C₅	—	11	1	no	—
61	C₄×C₅	—	22	2	no	—
62	#41	—	11	2	no	—
63	Q₁₆	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
64	SD₁₆	—	11	2	no	—
65	D₈	—	11	1	no	—
66	C₂×C₈	—	11	1	no	—
67	C₁₁	C₅×#135	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₅	—	11	1	no	—
69	C₂×C₅	—	22	1	no	—
70	C₂×C₅	—	44	2	no	—
71	Q₈	C₂×AGL(1,𝔽₁₁)	1	2	yes	—
72	D₄	—	11	2	no	—
73	D₄	—	22	2	no	—
74	C₂×C₄	—	11	1	no	—
75	C₂×C₄	—	22	2	no	—
76	C₈	—	11	1	no	—
77	C₈	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic
78	C₅	—	11	1	no	Sylow
79	C₂²	—	11	1	no	—
80	C₂²	—	22	2	no	—
81	C₄	—	2	2	no	—
82	C₄	—	11	1	no	—
83	C₄	C₂²×AGL(1,𝔽₁₁)	1	1	yes	characteristic
84	C₂	—	22	1	no	—
85	C₂	—	44	2	no	—
86	C₂	D₄×AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×AGL(1,𝔽₁₁)
commutator, cosocle	C₄×C₁₁	C₂³×C₅
Frattini	C₄	C₂²×AGL(1,𝔽₁₁)
Fitting	C₁₁×Q₁₆	C₂×C₅
socle	C₂×C₁₁	C₂×C₅×D₄
hypercenter	Q₁₆	AGL(1,𝔽₁₁)
hypocenter	C₁₁	C₅×#135
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #4343⋊C₅	C₂	semidirect
2. Q₁₆×C₁₁⋊C₅	C₂	semidirect
3. #4325⋊C₅	C₂	semidirect
4. D₈₈⋊C₅	C₂	semidirect
5. C₈×AGL(1,𝔽₁₁)	C₂	semidirect
13. #66972	C₅	semidirect
19. #4343	C₂×C₅	semidirect
20. C₁₁×Q₁₆	C₂×C₅	semidirect
21. #4325	C₂×C₅	semidirect
22. D₈₈	C₂×C₅	semidirect
23. C₈×D₁₁	C₂×C₅	semidirect
40. C₁₁⋊C₅	#135	semidirect
63. Q₁₆	AGL(1,𝔽₁₁)	semidirect
67. C₁₁	C₅×#135	semidirect

Maximal subgroups

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

subgroup	index
#4343⋊C₅	2
Q₁₆×C₁₁⋊C₅	2
#4325⋊C₅	2
D₈₈⋊C₅	2
C₈×AGL(1,𝔽₁₁)	2
#66972	5
C₅×#135	11

Subgroups — #66972⋊C5 #13182520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #66972⋊C₅ #13182520