Subgroups — C₅×#67043 #13183422

Order 1760.

292 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, complemented
2	C₅×Q₈×D₁₁	C₂	1	2	yes	maximal, complemented
3	C₅×#4341	C₂	1	6	yes	maximal, complemented
4	C₅×#4339	C₂	1	3	yes	maximal, complemented
5	C₂×C₅×Dic₂₂	C₂	1	3	yes	maximal, complemented
6	C₅×Q₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₅×D₄×C₁₁	C₂²	1	3	yes	—
8	C₂×C₄×C₅×C₁₁	C₂²	1	3	yes	—
9	C₅×C₂²⋊D₁₁	C₂²	1	6	yes	—
10	C₂×C₅×Dic₁₁	C₂²	1	6	yes	—
11	C₅×D₄₄	C₂²	1	1	yes	characteristic
12	C₄×C₅×D₁₁	C₂²	1	6	yes	—
13	C₅×Dic₂₂	C₂²	1	3	yes	—
14	C₅×Dic₂₂	C₂²	1	6	yes	—
15	#67043	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂²×C₅×C₁₁	C₂³	1	3	yes	—
17	C₂×C₅×D₁₁	C₂³	1	2	yes	—
18	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
19	C₄×C₅×C₁₁	C₂³	1	3	yes	—
20	C₅×Dic₁₁	C₂³	1	6	yes	—
21	C₁₁×#41	C₂×C₅	1	1	yes	characteristic, complemented
22	Q₈×D₁₁	C₂×C₅	1	2	yes	complemented
23	#4341	C₂×C₅	1	6	yes	complemented
24	#4339	C₂×C₅	1	3	yes	complemented
25	C₂×Dic₂₂	C₂×C₅	1	3	yes	complemented
26	C₅×2₋¹⁺⁴	—	11	1	no	maximal, Hall
27	C₂×C₅×C₁₁	—	2	3	no	—
28	C₂×C₅×C₁₁	C₂⁴	1	1	yes	characteristic
29	C₅×D₁₁	—	2	2	no	—
30	Q₈×C₁₁	C₂²×C₅	1	1	yes	characteristic
31	D₄×C₁₁	C₂²×C₅	1	3	yes	—
32	C₂×C₄×C₁₁	C₂²×C₅	1	3	yes	—
33	C₂²⋊D₁₁	C₂²×C₅	1	6	yes	—
34	C₂×Dic₁₁	C₂²×C₅	1	6	yes	—
35	D₄₄	C₂²×C₅	1	1	yes	characteristic
36	C₄×D₁₁	C₂²×C₅	1	6	yes	—
37	Dic₂₂	C₂²×C₅	1	3	yes	—
38	Dic₂₂	C₂²×C₅	1	6	yes	—
39	C₅×#41	—	11	6	no	—
40	C₅×#41	—	11	3	no	—
41	C₅×#41	D₁₁	1	1	yes	characteristic, complemented
42	C₂×C₅×Q₈	—	11	2	no	—
43	C₂×C₅×Q₈	—	11	3	no	—
44	C₅×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₁₁	C₂³×C₅	1	3	yes	—
46	C₂×D₁₁	C₂³×C₅	1	2	yes	—
47	C₄×C₁₁	C₂³×C₅	1	1	yes	characteristic
48	C₄×C₁₁	C₂³×C₅	1	3	yes	—
49	Dic₁₁	C₂³×C₅	1	6	yes	—
50	C₅×Q₈	—	11	6	no	—
51	C₅×Q₈	—	11	3	no	—
52	C₅×Q₈	C₂×D₁₁	1	1	yes	characteristic
53	C₅×D₄	—	11	6	no	—
54	C₅×D₄	—	11	1	no	—
55	C₅×D₄	C₂×D₁₁	1	3	yes	—
56	C₂×C₄×C₅	—	11	6	no	—
57	C₂×C₄×C₅	—	11	6	no	—
58	C₂×C₄×C₅	C₂×D₁₁	1	3	yes	—
59	2₋¹⁺⁴	—	11	1	no	Sylow
60	C₂×C₁₁	—	2	3	no	—
61	C₂×C₁₁	C₂⁴×C₅	1	1	yes	characteristic
62	D₁₁	—	2	2	no	—
63	C₂²×C₅	—	11	2	no	—
64	C₂²×C₅	C₂²×D₁₁	1	3	yes	—
65	C₄×C₅	—	11	6	no	—
66	C₄×C₅	C₂²×D₁₁	1	3	yes	—
67	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
68	#41	—	11	6	no	—
69	#41	—	11	3	no	—
70	#41	C₅×D₁₁	1	1	yes	characteristic, complemented
71	C₂×Q₈	—	11	2	no	—
72	C₂×Q₈	—	11	3	no	—
73	C₁₁	C₅×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
74	C₂×C₅	—	2	3	no	—
75	C₂×C₅	—	22	2	no	—
76	C₂×C₅	C₂³×D₁₁	1	1	yes	characteristic
77	Q₈	—	11	6	no	—
78	Q₈	—	11	3	no	—
79	Q₈	C₂×C₅×D₁₁	1	1	yes	characteristic
80	D₄	—	11	6	no	—
81	D₄	—	11	1	no	—
82	D₄	C₂×C₅×D₁₁	1	3	yes	—
83	C₂×C₄	—	11	6	no	—
84	C₂×C₄	—	11	6	no	—
85	C₂×C₄	C₂×C₅×D₁₁	1	3	yes	—
86	C₅	#67043	1	1	yes	characteristic, direct product factor, Sylow
87	C₂²	—	11	2	no	—
88	C₂²	C₂²×C₅×D₁₁	1	3	yes	—
89	C₄	—	11	6	no	—
90	C₄	C₂²×C₅×D₁₁	1	3	yes	—
91	C₄	C₂²×C₅×D₁₁	1	1	yes	characteristic
92	C₂	—	2	3	no	—
93	C₂	—	22	2	no	—
94	C₂	C₂³×C₅×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂³×D₁₁
commutator, cosocle	C₂×C₁₁	C₂⁴×C₅
Frattini	C₂	C₂³×C₅×D₁₁
Fitting	C₅×C₁₁×#41	C₂
socle	C₂×C₅×C₁₁	C₂⁴
hypercenter	C₅×#41	D₁₁
hypocenter	C₁₁	C₅×2₋¹⁺⁴
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₅ ◁ C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×#41	C₂	semidirect
2. C₅×Q₈×D₁₁	C₂	semidirect
3. C₅×#4341	C₂	semidirect
4. C₅×#4339	C₂	semidirect
5. C₂×C₅×Dic₂₂	C₂	semidirect
15. #67043	C₅	direct (N × H)
21. C₁₁×#41	C₂×C₅	semidirect
22. Q₈×D₁₁	C₂×C₅	semidirect
23. #4341	C₂×C₅	semidirect
24. #4339	C₂×C₅	semidirect
25. C₂×Dic₂₂	C₂×C₅	semidirect
41. C₅×#41	D₁₁	semidirect
44. C₅×C₁₁	2₋¹⁺⁴	semidirect
70. #41	C₅×D₁₁	semidirect
73. C₁₁	C₅×2₋¹⁺⁴	semidirect
86. C₅	#67043	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×Q₈×D₁₁	2
C₅×#4341	2
C₅×#4339	2
C₂×C₅×Dic₂₂	2
#67043	5
C₅×2₋¹⁺⁴	11

Subgroups — C5×#67043 #13183422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#67043 #13183422