Subgroups — C₅×#67001 #13183075

Order 1760.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×#41	C₂	1	1	yes	maximal, characteristic
2	C₅×#4318	C₂	1	3	yes	maximal, complemented
3	C₂×C₅×C₁₁⋊C₈	C₂	1	3	yes	maximal, complemented
4	C₅×Q₈×C₁₁	C₄	1	1	yes	characteristic
5	C₅×D₄×C₁₁	C₄	1	3	yes	—
6	C₂×C₄×C₅×C₁₁	C₂²	1	3	yes	—
7	C₅×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
8	C₅×C₁₁⋊C₈	C₂²	1	3	yes	—
9	#67001	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₅×C₁₁	C₂×C₄	1	3	yes	—
11	C₄×C₅×C₁₁	C₂×C₄	1	3	yes	—
12	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
13	C₁₁×#41	C₂×C₅	1	1	yes	characteristic
14	#4318	C₂×C₅	1	3	yes	complemented
15	C₂×C₁₁⋊C₈	C₂×C₅	1	3	yes	complemented
16	C₅×#131	—	11	1	no	maximal, Hall
17	C₂×C₅×C₁₁	—	2	3	no	—
18	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
19	Q₈×C₁₁	C₄×C₅	1	1	yes	characteristic
20	D₄×C₁₁	C₄×C₅	1	3	yes	—
21	C₂×C₄×C₁₁	C₂²×C₅	1	3	yes	—
22	C₁₁⋊C₈	C₂²×C₅	1	1	yes	characteristic
23	C₁₁⋊C₈	C₂²×C₅	1	3	yes	—
24	C₅×#41	D₁₁	1	1	yes	characteristic
25	C₅×M₁₆	—	11	3	no	—
26	C₂×C₅×C₈	—	11	3	no	—
27	C₅×C₁₁	#131	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₁₁	C₂×C₄×C₅	1	3	yes	—
29	C₄×C₁₁	C₂×C₄×C₅	1	3	yes	—
30	C₄×C₁₁	C₂³×C₅	1	1	yes	characteristic
31	C₅×Q₈	Dic₁₁	1	1	yes	characteristic
32	C₅×D₄	Dic₁₁	1	3	yes	—
33	C₂×C₄×C₅	C₂×D₁₁	1	3	yes	—
34	C₅×C₈	—	11	1	no	—
35	C₅×C₈	—	11	3	no	—
36	#131	—	11	1	no	Sylow
37	C₂×C₁₁	—	2	3	no	—
38	C₂×C₁₁	C₂²×C₄×C₅	1	1	yes	characteristic
39	C₂²×C₅	C₂×Dic₁₁	1	3	yes	—
40	C₄×C₅	C₂×Dic₁₁	1	3	yes	—
41	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
42	#41	C₅×D₁₁	1	1	yes	characteristic
43	M₁₆	—	11	3	no	—
44	C₂×C₈	—	11	3	no	—
45	C₁₁	C₅×#131	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₅	—	2	3	no	—
47	C₂×C₅	C₂²×Dic₁₁	1	1	yes	characteristic
48	Q₈	C₅×Dic₁₁	1	1	yes	characteristic
49	D₄	C₅×Dic₁₁	1	3	yes	—
50	C₂×C₄	C₂×C₅×D₁₁	1	3	yes	—
51	C₈	—	11	1	no	—
52	C₈	—	11	3	no	—
53	C₅	#67001	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²	C₂×C₅×Dic₁₁	1	3	yes	—
55	C₄	C₂×C₅×Dic₁₁	1	3	yes	—
56	C₄	C₂²×C₅×D₁₁	1	1	yes	characteristic
57	C₂	—	2	3	no	—
58	C₂	C₂²×C₅×Dic₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂²×D₁₁
commutator	C₂×C₁₁	C₂²×C₄×C₅
Frattini	C₄	C₂²×C₅×D₁₁
Fitting, prime radical	C₅×C₁₁×#41	C₂
socle	C₂×C₅×C₁₁	C₂²×C₄
cosocle	C₄×C₁₁	C₂³×C₅
hypercenter	C₅×#41	D₁₁
hypocenter	C₁₁	C₅×#131
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄×C₅ ◁ C₅×#41

Complements

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

N	H ≅ G/N	type
2. C₅×#4318	C₂	semidirect
3. C₂×C₅×C₁₁⋊C₈	C₂	semidirect
9. #67001	C₅	direct (N × H)
14. #4318	C₂×C₅	semidirect
15. C₂×C₁₁⋊C₈	C₂×C₅	semidirect
27. C₅×C₁₁	#131	semidirect
45. C₁₁	C₅×#131	semidirect
53. C₅	#67001	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
C₅×#4318	2
C₂×C₅×C₁₁⋊C₈	2
#67001	5
C₅×#131	11

Subgroups — C5×#67001 #13183075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#67001 #13183075