Subgroups — C₂×C₅×C₁₁×#41 #13183458

Order 1760.

328 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂×C₄×C₅×C₁₁	C₂²
commutator, Frattini, cosocle	C₂	C₂⁴×C₅×C₁₁
socle	C₂²×C₅×C₁₁	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×#41	C₂	direct (N × H)
2. C₂×C₅×Q₈×C₁₁	C₂	semidirect
3. C₂×C₅×D₄×C₁₁	C₂	semidirect
4. C₂²×C₄×C₅×C₁₁	C₂	semidirect
6. C₅×Q₈×C₁₁	C₂²	semidirect
7. C₅×D₄×C₁₁	C₂²	semidirect
10. C₂×C₄×C₅×C₁₁	C₂²	semidirect
11. C₂×C₁₁×#41	C₅	direct (N × H)
17. C₁₁×#41	C₂×C₅	direct (N × H)
18. C₂×Q₈×C₁₁	C₂×C₅	semidirect
19. C₂×D₄×C₁₁	C₂×C₅	semidirect
20. C₂²×C₄×C₁₁	C₂×C₅	semidirect
21. C₂×C₅×#41	C₁₁	direct (N × H)
23. C₂×C₅×C₁₁	#41	direct (N × H)
26. Q₈×C₁₁	C₂²×C₅	semidirect
27. D₄×C₁₁	C₂²×C₅	semidirect
30. C₂×C₄×C₁₁	C₂²×C₅	semidirect
31. C₅×#41	C₂×C₁₁	direct (N × H)
32. C₂×C₅×Q₈	C₂×C₁₁	semidirect
33. C₂×C₅×D₄	C₂×C₁₁	semidirect
34. C₂²×C₄×C₅	C₂×C₁₁	semidirect
35. C₅×C₁₁	C₂×#41	direct (N × H)
42. C₅×Q₈	C₂²×C₁₁	semidirect
43. C₅×D₄	C₂²×C₁₁	semidirect
46. C₂×C₄×C₅	C₂²×C₁₁	semidirect
47. C₂×#41	C₅×C₁₁	direct (N × H)
49. C₂×C₁₁	C₅×#41	direct (N × H)
56. #41	C₂×C₅×C₁₁	direct (N × H)
57. C₂×Q₈	C₂×C₅×C₁₁	semidirect
58. C₂×D₄	C₂×C₅×C₁₁	semidirect
59. C₂²×C₄	C₂×C₅×C₁₁	semidirect
60. C₁₁	C₂×C₅×#41	direct (N × H)
62. C₂×C₅	C₁₁×#41	direct (N × H)
65. Q₈	C₂²×C₅×C₁₁	semidirect
66. D₄	C₂²×C₅×C₁₁	semidirect
69. C₂×C₄	C₂²×C₅×C₁₁	semidirect
70. C₅	C₂×C₁₁×#41	direct (N × H)
77. C₂	C₅×C₁₁×#41	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₁×#41	2
C₂×C₅×Q₈×C₁₁	2
C₂×C₅×D₄×C₁₁	2
C₂²×C₄×C₅×C₁₁	2
C₂×C₁₁×#41	5
C₂×C₅×#41	11

Subgroups — C2×C5×C11×#41 #13183458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₁₁×#41 #13183458