Subgroups — C₅×#67006 #13183080

Order 1760.

260 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×C₂²⋊D₁₁	C₂	1	3	yes	maximal, complemented
3	C₅×C₂²⋊Dic₁₁	C₂	1	3	yes	maximal, complemented
4	C₂³×C₅×C₁₁	—	2	6	no	—
5	C₂³×C₅×C₁₁	C₂²	1	3	yes	—
6	C₂²×C₅×D₁₁	C₂²	1	1	yes	characteristic, complemented
7	C₅×C₂²⋊D₁₁	—	2	6	no	—
8	C₂×C₅×Dic₁₁	C₂²	1	3	yes	complemented
9	#67006	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₅×C₁₁	—	2	8	no	—
11	C₂²×C₅×C₁₁	—	2	6	no	—
12	C₂²×C₅×C₁₁	D₄	1	6	yes	complemented
13	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
14	C₂×C₅×D₁₁	—	2	3	no	—
15	C₅×Dic₁₁	—	2	3	no	—
16	C₂⁴×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
17	C₂×C₂²⋊D₁₁	C₂×C₅	1	3	yes	complemented
18	C₂²⋊Dic₁₁	C₂×C₅	1	3	yes	complemented
19	C₅×#120	—	11	1	no	maximal, Hall
20	C₂×C₅×C₁₁	—	2	6	no	—
21	C₂×C₅×C₁₁	C₂×D₄	1	3	yes	—
22	C₅×D₁₁	—	4	1	no	—
23	C₂³×C₁₁	—	2	6	no	—
24	C₂³×C₁₁	C₂²×C₅	1	3	yes	—
25	C₂²×D₁₁	C₂²×C₅	1	1	yes	characteristic, complemented
26	C₂²⋊D₁₁	—	2	6	no	—
27	C₂×Dic₁₁	C₂²×C₅	1	3	yes	complemented
28	C₂⁴×C₅	D₁₁	1	1	yes	characteristic, complemented
29	C₂×C₅×D₄	—	11	3	no	—
30	C₅×C₂²⋊C₄	—	11	3	no	—
31	C₅×C₁₁	#120	1	1	yes	characteristic, complemented, Hall
32	C₂²×C₁₁	—	2	8	no	—
33	C₂²×C₁₁	—	2	6	no	—
34	C₂²×C₁₁	C₅×D₄	1	6	yes	complemented
35	C₂²×C₁₁	C₂³×C₅	1	1	yes	characteristic
36	C₂×D₁₁	—	2	3	no	—
37	Dic₁₁	—	2	3	no	—
38	C₂³×C₅	—	2	6	no	—
39	C₂³×C₅	—	11	1	no	—
40	C₂³×C₅	C₂×D₁₁	1	3	yes	—
41	C₅×D₄	—	22	6	no	—
42	C₂×C₄×C₅	—	11	3	no	—
43	#120	—	11	1	no	Sylow
44	C₂×C₁₁	—	2	6	no	—
45	C₂×C₁₁	C₂×C₅×D₄	1	3	yes	—
46	D₁₁	—	4	1	no	—
47	C₂²×C₅	—	2	8	no	—
48	C₂²×C₅	—	2	6	no	—
49	C₂²×C₅	—	22	3	no	—
50	C₂²×C₅	C₂²⋊D₁₁	1	6	yes	complemented
51	C₂²×C₅	C₂²×D₁₁	1	1	yes	characteristic
52	C₄×C₅	—	22	3	no	—
53	C₂⁴	C₅×D₁₁	1	1	yes	characteristic, complemented
54	C₂×D₄	—	11	3	no	—
55	C₂²⋊C₄	—	11	3	no	—
56	C₁₁	C₅×#120	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₅	—	2	6	no	—
58	C₂×C₅	—	44	1	no	—
59	C₂×C₅	C₂×C₂²⋊D₁₁	1	3	yes	—
60	C₂³	—	2	6	no	—
61	C₂³	—	11	1	no	—
62	C₂³	C₂×C₅×D₁₁	1	3	yes	—
63	D₄	—	22	6	no	—
64	C₂×C₄	—	11	3	no	—
65	C₅	#67006	1	1	yes	characteristic, direct product factor, Sylow
66	C₂²	—	2	8	no	—
67	C₂²	—	2	6	no	—
68	C₂²	—	22	3	no	—
69	C₂²	C₅×C₂²⋊D₁₁	1	6	yes	complemented
70	C₂²	C₂²×C₅×D₁₁	1	1	yes	characteristic
71	C₄	—	22	3	no	—
72	C₂	—	2	6	no	—
73	C₂	—	44	1	no	—
74	C₂	C₂×C₅×C₂²⋊D₁₁	1	3	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₁
commutator, cosocle	C₂²×C₁₁	C₂³×C₅
Frattini	C₂²	C₂²×C₅×D₁₁
Fitting	C₂⁴×C₅×C₁₁	C₂
socle	C₂²×C₅×C₁₁	C₂³
hypercenter	C₂⁴×C₅	D₁₁
hypocenter	C₁₁	C₅×#120
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂⁴×C₅

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₅×C₁₁	C₂	semidirect
2. C₂×C₅×C₂²⋊D₁₁	C₂	semidirect
3. C₅×C₂²⋊Dic₁₁	C₂	semidirect
6. C₂²×C₅×D₁₁	C₂²	semidirect
8. C₂×C₅×Dic₁₁	C₂²	semidirect
9. #67006	C₅	direct (N × H)
12. C₂²×C₅×C₁₁	D₄	semidirect
16. C₂⁴×C₁₁	C₂×C₅	semidirect
17. C₂×C₂²⋊D₁₁	C₂×C₅	semidirect
18. C₂²⋊Dic₁₁	C₂×C₅	semidirect
25. C₂²×D₁₁	C₂²×C₅	semidirect
27. C₂×Dic₁₁	C₂²×C₅	semidirect
28. C₂⁴×C₅	D₁₁	semidirect
31. C₅×C₁₁	#120	semidirect
34. C₂²×C₁₁	C₅×D₄	semidirect
50. C₂²×C₅	C₂²⋊D₁₁	semidirect
53. C₂⁴	C₅×D₁₁	semidirect
56. C₁₁	C₅×#120	semidirect
65. C₅	#67006	direct (N × H)
69. C₂²	C₅×C₂²⋊D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×C₅×C₁₁	2
C₂×C₅×C₂²⋊D₁₁	2
C₅×C₂²⋊Dic₁₁	2
#67006	5
C₅×#120	11

Subgroups — C5×#67006 #13183080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#67006 #13183080