Subgroups — C₂×C₁₁×#700 #13183332

Order 1760.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#170	C₂	1	2	yes	maximal, complemented
3	C₁₁×#700	C₂	1	4	yes	maximal, direct product factor
4	C₂²×D₅×C₁₁	C₄	1	1	yes	characteristic
5	C₂×C₄×C₅×C₁₁	C₄	1	1	yes	characteristic
6	C₂×C₁₁×Dic₅	C₂²	1	1	yes	characteristic
7	C₄×D₅×C₁₁	C₄	1	2	yes	—
8	C₄×D₅×C₁₁	C₂²	1	2	yes	—
9	C₁₁×#170	C₂²	1	4	yes	complemented
10	C₂×C₁₁×M₁₆	—	5	1	no	maximal, Hall
11	C₂²×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₂×D₅×C₁₁	—	2	2	no	—
13	C₂×D₅×C₁₁	C₂×C₄	1	2	yes	—
14	C₄×C₅×C₁₁	C₂×C₄	1	2	yes	—
15	C₁₁×Dic₅	C₂×C₄	1	1	yes	characteristic
16	C₁₁×Dic₅	C₂³	1	1	yes	characteristic
17	C₂²×C₄×C₁₁	—	5	1	no	—
18	C₁₁×M₁₆	—	5	4	no	—
19	C₂×C₈×C₁₁	—	5	2	no	—
20	C₂×#700	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₅×C₁₁	M₁₆	1	2	yes	complemented
22	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
23	D₅×C₁₁	—	2	2	no	—
24	C₂³×C₁₁	—	5	1	no	—
25	C₂×C₄×C₁₁	—	5	1	no	—
26	C₂×C₄×C₁₁	—	5	2	no	—
27	C₂×C₄×C₁₁	—	5	2	no	—
28	C₂×C₄×C₁₁	AGL(1,𝔽₅)	1	1	yes	characteristic
29	C₈×C₁₁	—	5	4	no	—
30	C₂×C₄×D₅	C₂×C₁₁	1	1	yes	characteristic
31	C₂×#170	C₂×C₁₁	1	2	yes	complemented
32	#700	C₂×C₁₁	1	4	yes	direct product factor
33	C₅×C₁₁	C₂×M₁₆	1	1	yes	characteristic, complemented, Hall
34	C₂²×C₁₁	—	5	2	no	—
35	C₂²×C₁₁	—	10	2	no	—
36	C₂²×C₁₁	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
37	C₄×C₁₁	—	5	1	no	—
38	C₄×C₁₁	—	5	1	no	—
39	C₄×C₁₁	C₂×AGL(1,𝔽₅)	1	2	yes	—
40	C₂²×D₅	C₄×C₁₁	1	1	yes	characteristic
41	C₂×C₄×C₅	C₄×C₁₁	1	1	yes	characteristic
42	C₂×Dic₅	C₂²×C₁₁	1	1	yes	characteristic
43	C₄×D₅	C₄×C₁₁	1	2	yes	—
44	C₄×D₅	C₂²×C₁₁	1	2	yes	—
45	#170	C₂²×C₁₁	1	4	yes	complemented
46	C₂×M₁₆	—	5	1	no	Sylow
47	C₂×C₁₁	—	10	2	no	—
48	C₂×C₁₁	#700	1	2	yes	direct product factor
49	C₂×C₁₁	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
50	C₂²×C₅	C₂×C₄×C₁₁	1	1	yes	characteristic
51	C₂×D₅	—	2	2	no	—
52	C₂×D₅	C₂×C₄×C₁₁	1	2	yes	—
53	C₄×C₅	C₂×C₄×C₁₁	1	2	yes	—
54	Dic₅	C₂×C₄×C₁₁	1	1	yes	characteristic
55	Dic₅	C₂³×C₁₁	1	1	yes	characteristic
56	C₂²×C₄	—	5	1	no	—
57	M₁₆	—	5	4	no	—
58	C₂×C₈	—	5	2	no	—
59	C₁₁	C₂×#700	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×C₅	C₁₁×M₁₆	1	2	yes	complemented
61	C₂×C₅	C₂²×C₄×C₁₁	1	1	yes	characteristic
62	D₅	—	2	2	no	—
63	C₂³	—	5	1	no	—
64	C₂×C₄	—	5	1	no	—
65	C₂×C₄	—	5	2	no	—
66	C₂×C₄	—	5	2	no	—
67	C₂×C₄	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic
68	C₈	—	5	4	no	—
69	C₅	C₂×C₁₁×M₁₆	1	1	yes	characteristic, complemented, Sylow
70	C₂²	—	5	2	no	—
71	C₂²	—	10	2	no	—
72	C₂²	C₂×C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic
73	C₄	—	5	1	no	—
74	C₄	—	5	1	no	—
75	C₄	C₂×C₁₁×AGL(1,𝔽₅)	1	2	yes	—
76	C₂	—	10	2	no	—
77	C₂	C₁₁×#700	1	2	yes	direct product factor
78	C₂	C₂²×C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₁	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₄×C₁₁
Frattini	C₂	C₂²×C₁₁×AGL(1,𝔽₅)
Fitting	C₂×C₄×C₅×C₁₁	C₄
socle	C₂²×C₅×C₁₁	C₂×C₄
prime radical	C₂²×D₅×C₁₁	C₄
cosocle	Dic₅	C₂³×C₁₁
hypercenter	C₂×C₄×C₁₁	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₁₁×M₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#170	C₂	semidirect
3. C₁₁×#700	C₂	direct (N × H)
9. C₁₁×#170	C₂²	semidirect
20. C₂×#700	C₁₁	direct (N × H)
21. C₂×C₅×C₁₁	M₁₆	semidirect
31. C₂×#170	C₂×C₁₁	semidirect
32. #700	C₂×C₁₁	direct (N × H)
33. C₅×C₁₁	C₂×M₁₆	semidirect
45. #170	C₂²×C₁₁	semidirect
48. C₂×C₁₁	#700	direct (N × H)
59. C₁₁	C₂×#700	direct (N × H)
60. C₂×C₅	C₁₁×M₁₆	semidirect
69. C₅	C₂×C₁₁×M₁₆	semidirect
77. C₂	C₁₁×#700	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×C₄×D₅×C₁₁	2
C₂×C₁₁×#170	2
C₁₁×#700	2
C₂×C₁₁×M₁₆	5
C₂×#700	11

Subgroups — C2×C11×#700 #13183332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#700 #13183332