Subgroups — C₂×D₁₁×#170 #13183312

Order 1760.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅×D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁⋊#170	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#170	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₁×#170	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅×D₁₁	C₄	1	1	yes	characteristic
6	C₂×Dic₅₅	C₄	1	1	yes	characteristic
7	C₂×C₁₁×Dic₅	C₂²	1	1	yes	characteristic
8	Dic₅×D₁₁	C₄	1	2	yes	—
9	Dic₅×D₁₁	C₂²	1	2	yes	—
10	C₁₁⋊#170	C₂²	1	2	yes	complemented
11	C₁₁×#170	C₂²	1	2	yes	complemented
12	C₂×C₈×D₁₁	—	5	1	no	maximal, Hall
13	C₂²×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₅×D₁₁	C₈	1	4	yes	complemented
15	C₂×C₅×D₁₁	C₂×C₄	1	2	yes	—
16	Dic₅₅	C₂×C₄	1	2	yes	—
17	C₁₁×Dic₅	C₂×C₄	1	1	yes	characteristic
18	C₁₁×Dic₅	C₂³	1	1	yes	characteristic
19	C₂×C₄×D₁₁	—	5	1	no	—
20	C₂×C₈×C₁₁	—	5	1	no	—
21	C₂×C₁₁⋊C₈	—	5	1	no	—
22	C₈×D₁₁	—	5	4	no	—
23	C₂²×#170	—	11	1	no	maximal, Hall
24	C₂×C₅×C₁₁	C₂×C₈	1	2	yes	complemented
25	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
26	C₅×D₁₁	C₂×C₈	1	4	yes	complemented
27	C₂²×D₁₁	AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₂×C₄×C₁₁	—	5	1	no	—
29	C₂×Dic₁₁	—	5	1	no	—
30	C₄×D₁₁	—	5	2	no	—
31	C₄×D₁₁	—	5	2	no	—
32	C₈×C₁₁	—	5	2	no	—
33	C₁₁⋊C₈	—	5	2	no	—
34	C₂²×Dic₅	—	11	1	no	—
35	C₂×#170	—	11	1	no	—
36	C₂×#170	—	11	4	no	—
37	C₂×#170	D₁₁	1	1	yes	characteristic, direct product factor
38	C₅×C₁₁	C₂²×C₈	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₁₁	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
40	C₂×D₁₁	#170	1	4	yes	direct product factor
41	C₂×D₁₁	C₂×AGL(1,𝔽₅)	1	2	yes	—
42	C₄×C₁₁	—	5	1	no	—
43	C₄×C₁₁	—	5	1	no	—
44	Dic₁₁	—	5	2	no	—
45	C₂³×C₅	—	11	1	no	—
46	C₂×Dic₅	—	11	1	no	—
47	C₂×Dic₅	—	11	2	no	—
48	C₂×Dic₅	—	11	2	no	—
49	C₂×Dic₅	C₂×D₁₁	1	1	yes	characteristic
50	#170	—	11	2	no	—
51	#170	C₂×D₁₁	1	2	yes	direct product factor
52	C₂²×C₈	—	55	1	no	Sylow
53	C₂×C₁₁	C₂×#170	1	2	yes	complemented
54	C₂×C₁₁	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
55	D₁₁	C₂×#170	1	4	yes	direct product factor
56	C₂²×C₅	—	11	4	no	—
57	C₂²×C₅	—	11	2	no	—
58	C₂²×C₅	C₄×D₁₁	1	1	yes	characteristic
59	Dic₅	—	11	2	no	—
60	Dic₅	C₄×D₁₁	1	1	yes	characteristic
61	Dic₅	C₂²×D₁₁	1	1	yes	characteristic
62	C₂²×C₄	—	55	1	no	—
63	C₂×C₈	—	5	1	no	—
64	C₂×C₈	—	55	4	no	—
65	C₂×C₈	—	55	1	no	—
66	C₁₁	C₂²×#170	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₅	—	11	4	no	—
68	C₂×C₅	C₈×D₁₁	1	2	yes	complemented
69	C₂×C₅	C₂×C₄×D₁₁	1	1	yes	characteristic
70	C₂³	—	11	1	no	—
71	C₂×C₄	—	5	1	no	—
72	C₂×C₄	—	55	2	no	—
73	C₂×C₄	—	55	2	no	—
74	C₂×C₄	—	55	1	no	—
75	C₈	—	5	2	no	—
76	C₈	—	55	2	no	—
77	C₅	C₂×C₈×D₁₁	1	1	yes	characteristic, complemented, Sylow
78	C₂²	—	11	4	no	—
79	C₂²	—	11	2	no	—
80	C₂²	AGL(1,𝔽₅)×D₁₁	1	1	yes	characteristic
81	C₄	—	5	1	no	—
82	C₄	—	5	1	no	—
83	C₄	—	55	2	no	—
84	C₂	—	11	4	no	—
85	C₂	D₁₁×#170	1	2	yes	direct product factor
86	C₂	C₂×AGL(1,𝔽₅)×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	AGL(1,𝔽₅)×D₁₁
commutator, hypocenter	C₅×C₁₁	C₂²×C₈
Frattini	C₂	C₂×AGL(1,𝔽₅)×D₁₁
Fitting, socle	C₂²×C₅×C₁₁	C₂×C₄
prime radical	C₂²×C₅×D₁₁	C₄
cosocle	C₁₁×Dic₅	C₂³
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁⋊#170	C₂	semidirect
3. C₂×C₁₁×#170	C₂	semidirect
4. D₁₁×#170	C₂	direct (N × H)
10. C₁₁⋊#170	C₂²	semidirect
11. C₁₁×#170	C₂²	semidirect
14. C₂×C₅×D₁₁	C₈	semidirect
24. C₂×C₅×C₁₁	C₂×C₈	semidirect
26. C₅×D₁₁	C₂×C₈	semidirect
37. C₂×#170	D₁₁	direct (N × H)
38. C₅×C₁₁	C₂²×C₈	semidirect
40. C₂×D₁₁	#170	direct (N × H)
51. #170	C₂×D₁₁	direct (N × H)
53. C₂×C₁₁	C₂×#170	semidirect
55. D₁₁	C₂×#170	direct (N × H)
66. C₁₁	C₂²×#170	semidirect
68. C₂×C₅	C₈×D₁₁	semidirect
77. C₅	C₂×C₈×D₁₁	semidirect
85. C₂	D₁₁×#170	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₅×D₁₁	2
C₂×C₁₁⋊#170	2
C₂×C₁₁×#170	2
D₁₁×#170	2
C₂×C₈×D₁₁	5
C₂²×#170	11

Subgroups — C2×D11×#170 #13183312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₁×#170 #13183312