Subgroups — C₂×C₁₁×#713 #13183433

Order 1760.

328 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#713	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₁₁×D₂₀	C₂	1	3	yes	maximal, complemented
4	C₂×C₄×D₅×C₁₁	C₂	1	3	yes	maximal, complemented
5	C₂²×D₅×C₁₁	C₂²	1	3	yes	—
6	C₅×Q₈×C₁₁	C₂²	1	4	yes	complemented
7	C₂×C₄×C₅×C₁₁	C₂²	1	3	yes	—
8	C₂×C₁₁×Dic₅	C₂²	1	1	yes	characteristic
9	C₁₁×D₂₀	C₂²	1	12	yes	complemented
10	C₄×D₅×C₁₁	C₂²	1	12	yes	complemented
11	C₂×C₁₁×#41	—	5	1	no	maximal, Hall
12	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
13	C₂×D₅×C₁₁	—	2	6	no	—
14	C₂×D₅×C₁₁	C₂³	1	6	yes	—
15	C₄×C₅×C₁₁	C₂³	1	6	yes	—
16	C₁₁×Dic₅	C₂³	1	2	yes	—
17	C₁₁×#41	—	5	8	no	—
18	C₂×Q₈×C₁₁	D₅	1	1	yes	characteristic, complemented
19	C₂×D₄×C₁₁	—	5	3	no	—
20	C₂²×C₄×C₁₁	—	5	3	no	—
21	C₂×#713	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×C₁₁	#41	1	2	yes	complemented
23	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
24	D₅×C₁₁	—	2	6	no	—
25	C₂³×C₁₁	—	5	3	no	—
26	Q₈×C₁₁	C₂×D₅	1	4	yes	complemented
27	D₄×C₁₁	—	5	12	no	—
28	C₂×C₄×C₁₁	—	5	1	no	—
29	C₂×C₄×C₁₁	—	5	12	no	—
30	C₂×C₄×C₁₁	C₂×D₅	1	3	yes	—
31	C₂×C₅×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
32	#713	C₂×C₁₁	1	8	yes	direct product factor
33	C₂×D₂₀	C₂×C₁₁	1	3	yes	complemented
34	C₂×C₄×D₅	C₂×C₁₁	1	3	yes	complemented
35	C₅×C₁₁	C₂×#41	1	1	yes	characteristic, complemented, Hall
36	C₂²×C₁₁	—	5	6	no	—
37	C₂²×C₁₁	—	10	6	no	—
38	C₂²×C₁₁	C₂²×D₅	1	1	yes	characteristic
39	C₄×C₁₁	—	5	2	no	—
40	C₄×C₁₁	C₂²×D₅	1	6	yes	—
41	C₂²×D₅	C₂²×C₁₁	1	3	yes	—
42	C₅×Q₈	C₂²×C₁₁	1	4	yes	complemented
43	C₂×C₄×C₅	C₂²×C₁₁	1	3	yes	—
44	C₂×Dic₅	C₂²×C₁₁	1	1	yes	characteristic
45	D₂₀	C₂²×C₁₁	1	12	yes	complemented
46	C₄×D₅	C₂²×C₁₁	1	12	yes	complemented
47	C₂×#41	—	5	1	no	Sylow
48	C₂×C₁₁	—	10	6	no	—
49	C₂×C₁₁	#713	1	2	yes	direct product factor
50	C₂×C₁₁	C₂³×D₅	1	1	yes	characteristic
51	C₂²×C₅	C₂³×C₁₁	1	1	yes	characteristic
52	C₂×D₅	—	2	6	no	—
53	C₂×D₅	C₂³×C₁₁	1	6	yes	—
54	C₄×C₅	C₂³×C₁₁	1	6	yes	—
55	Dic₅	C₂³×C₁₁	1	2	yes	—
56	#41	—	5	8	no	—
57	C₂×Q₈	D₅×C₁₁	1	1	yes	characteristic, complemented
58	C₂×D₄	—	5	3	no	—
59	C₂²×C₄	—	5	3	no	—
60	C₁₁	C₂×#713	1	1	yes	characteristic, direct product factor, Sylow
61	C₂×C₅	C₁₁×#41	1	2	yes	complemented
62	C₂×C₅	C₂⁴×C₁₁	1	1	yes	characteristic
63	D₅	—	2	6	no	—
64	C₂³	—	5	3	no	—
65	Q₈	C₂×D₅×C₁₁	1	4	yes	complemented
66	D₄	—	5	12	no	—
67	C₂×C₄	—	5	1	no	—
68	C₂×C₄	—	5	12	no	—
69	C₂×C₄	C₂×D₅×C₁₁	1	3	yes	—
70	C₅	C₂×C₁₁×#41	1	1	yes	characteristic, complemented, Sylow
71	C₂²	—	5	6	no	—
72	C₂²	—	10	6	no	—
73	C₂²	C₂²×D₅×C₁₁	1	1	yes	characteristic
74	C₄	—	5	2	no	—
75	C₄	C₂²×D₅×C₁₁	1	6	yes	—
76	C₂	—	10	6	no	—
77	C₂	C₁₁×#713	1	2	yes	direct product factor
78	C₂	C₂³×D₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₁	C₂²×D₅
commutator, cosocle	C₂×C₅	C₂⁴×C₁₁
Frattini	C₂	C₂³×D₅×C₁₁
Fitting	C₂×C₅×Q₈×C₁₁	C₂
socle	C₂²×C₅×C₁₁	C₂³
hypercenter	C₂×Q₈×C₁₁	D₅
hypocenter	C₅	C₂×C₁₁×#41
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×Q₈×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×Q₈×C₁₁	C₂	semidirect
2. C₁₁×#713	C₂	direct (N × H)
3. C₂×C₁₁×D₂₀	C₂	semidirect
4. C₂×C₄×D₅×C₁₁	C₂	semidirect
6. C₅×Q₈×C₁₁	C₂²	semidirect
9. C₁₁×D₂₀	C₂²	semidirect
10. C₄×D₅×C₁₁	C₂²	semidirect
18. C₂×Q₈×C₁₁	D₅	semidirect
21. C₂×#713	C₁₁	direct (N × H)
22. C₂×C₅×C₁₁	#41	semidirect
26. Q₈×C₁₁	C₂×D₅	semidirect
31. C₂×C₅×Q₈	C₂×C₁₁	semidirect
32. #713	C₂×C₁₁	direct (N × H)
33. C₂×D₂₀	C₂×C₁₁	semidirect
34. C₂×C₄×D₅	C₂×C₁₁	semidirect
35. C₅×C₁₁	C₂×#41	semidirect
42. C₅×Q₈	C₂²×C₁₁	semidirect
45. D₂₀	C₂²×C₁₁	semidirect
46. C₄×D₅	C₂²×C₁₁	semidirect
49. C₂×C₁₁	#713	direct (N × H)
57. C₂×Q₈	D₅×C₁₁	semidirect
60. C₁₁	C₂×#713	direct (N × H)
61. C₂×C₅	C₁₁×#41	semidirect
65. Q₈	C₂×D₅×C₁₁	semidirect
70. C₅	C₂×C₁₁×#41	semidirect
77. C₂	C₁₁×#713	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×C₅×Q₈×C₁₁	2
C₁₁×#713	2
C₂×C₁₁×D₂₀	2
C₂×C₄×D₅×C₁₁	2
C₂×C₁₁×#41	5
C₂×#713	11

Subgroups — C2×C11×#713 #13183433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#713 #13183433