Subgroups — C₃×C₁₃⋊C₃×C₁₁⋊AGL(1,𝔽₅) #38788066

Order 25740.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₁₁×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₁₁⋊AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₃⋊C₃×C₁₁⋊AGL(1,𝔽₅)	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₅×C₁₁×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃⋊C₃×Dic₁₁	—	5	1	no	maximal, Hall
6	D₅×C₁₁×C₁₃⋊C₃	C₂×C₃	1	3	yes	—
7	C₃×D₅×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic
8	C₁₃×C₁₁⋊AGL(1,𝔽₅)	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₁₁×C₁₃⋊C₃	—	5	1	no	—
10	C₃×AGL(1,𝔽₅)×C₁₃⋊C₃	—	11	1	no	maximal, Hall
11	C₅×C₁₁×C₁₃⋊C₃	C₃×C₄	1	3	yes	complemented
12	C₃×C₅×C₁₁×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
13	C₃²×C₁₁⋊AGL(1,𝔽₅)	—	13	1	no	maximal, Hall
14	C₃×C₁₃×Dic₁₁	—	5	1	no	—
15	C₁₃⋊C₃×Dic₁₁	—	5	3	no	—
16	D₅×C₁₁×C₁₃	C₂×C₃²	1	1	yes	characteristic
17	C₃×C₁₁×C₁₃⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
18	C₃×D₅×C₁₃⋊C₃	D₁₁	1	1	yes	characteristic
19	C₃²×D₅×C₁₁	—	13	1	no	—
20	C₂×C₃×C₁₁×C₁₃	—	5	1	no	—
21	C₂×C₁₁×C₁₃⋊C₃	—	5	3	no	—
22	C₃×C₁₃×AGL(1,𝔽₅)	—	11	1	no	—
23	AGL(1,𝔽₅)×C₁₃⋊C₃	—	11	3	no	—
24	C₅×C₁₁×C₁₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₁⋊AGL(1,𝔽₅)	—	13	3	no	—
26	C₃×C₁₁⋊AGL(1,𝔽₅)	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
27	C₃×C₅×C₁₃⋊C₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
28	C₁₃×Dic₁₁	—	5	1	no	Hall
29	C₃²×C₅×C₁₁	—	13	1	no	Hall
30	C₃×C₄×C₁₃⋊C₃	—	55	1	no	Hall
31	C₃×C₁₁×C₁₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
32	C₁₁×C₁₃⋊C₃	C₃×AGL(1,𝔽₅)	1	3	yes	complemented
33	C₃²×Dic₁₁	—	65	1	no	Hall
34	C₃×D₅×C₁₃	C₃×D₁₁	1	1	yes	characteristic
35	D₅×C₁₃⋊C₃	C₃×D₁₁	1	3	yes	—
36	C₃×D₅×C₁₁	—	13	3	no	—
37	C₃×D₅×C₁₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic
38	C₂×C₁₁×C₁₃	—	5	1	no	—
39	C₁₃×AGL(1,𝔽₅)	—	11	1	no	Hall
40	C₂×C₃×C₁₃⋊C₃	—	5	1	no	—
41	C₁₁⋊AGL(1,𝔽₅)	C₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
42	C₂×C₃²×C₁₁	—	65	1	no	—
43	C₃×C₅×C₁₃	C₃×Dic₁₁	1	1	yes	characteristic, complemented
44	C₅×C₁₃⋊C₃	C₃×Dic₁₁	1	3	yes	complemented
45	C₃²×AGL(1,𝔽₅)	—	143	1	no	Hall
46	C₃×C₅×C₁₁	—	13	3	no	—
47	C₃×C₅×C₁₁	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
48	C₃×C₄×C₁₃	—	55	1	no	—
49	C₄×C₁₃⋊C₃	—	55	3	no	—
50	C₁₁×C₁₃	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
51	C₃×Dic₁₁	—	5	1	no	—
52	C₃×Dic₁₁	—	65	3	no	—
53	D₅×C₁₃	C₃²×D₁₁	1	1	yes	characteristic
54	C₃×C₁₃⋊C₃	C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
55	D₅×C₁₁	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic
56	C₃²×C₁₁	—	13	1	no	Hall
57	C₃²×D₅	—	13	1	no	—
58	C₂×C₃×C₁₃	—	5	1	no	—
59	C₂×C₁₃⋊C₃	—	5	3	no	—
60	C₂×C₃×C₁₁	—	5	1	no	—
61	C₂×C₃×C₁₁	—	65	3	no	—
62	C₅×C₁₃	C₃²×Dic₁₁	1	1	yes	characteristic, complemented, Hall
63	C₃×AGL(1,𝔽₅)	—	11	1	no	—
64	C₃×AGL(1,𝔽₅)	—	143	3	no	—
65	C₅×C₁₁	C₃×C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
66	C₄×C₁₃	—	55	1	no	Hall
67	C₃²×C₅	—	13	1	no	Hall
68	Dic₁₁	—	5	1	no	Hall
69	C₃×C₁₃	C₃×C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
70	C₁₃⋊C₃	C₃×C₁₁⋊AGL(1,𝔽₅)	1	3	yes	direct product factor
71	C₃²×C₄	—	715	1	no	Hall
72	C₃×C₁₁	—	13	3	no	—
73	C₃×C₁₁	AGL(1,𝔽₅)×C₁₃⋊C₃	1	1	yes	characteristic, complemented
74	C₃×D₅	—	13	3	no	—
75	C₃×D₅	D₁₁×C₁₃⋊C₃	1	1	yes	characteristic
76	C₂×C₁₃	—	5	1	no	—
77	C₂×C₁₁	—	5	1	no	—
78	AGL(1,𝔽₅)	—	11	1	no	Hall
79	C₂×C₃²	—	65	1	no	—
80	C₃×C₅	—	13	3	no	—
81	C₃×C₅	C₁₃⋊C₃×Dic₁₁	1	1	yes	characteristic, complemented
82	C₁₃	C₃²×C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
83	C₃×C₄	—	55	1	no	—
84	C₃×C₄	—	715	3	no	—
85	C₁₁	C₃×AGL(1,𝔽₅)×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
86	D₅	C₃×D₁₁×C₁₃⋊C₃	1	1	yes	characteristic
87	C₃²	—	13	1	no	Sylow
88	C₂×C₃	—	5	1	no	—
89	C₂×C₃	—	65	3	no	—
90	C₅	C₃×C₁₃⋊C₃×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
91	C₄	—	55	1	no	Sylow
92	C₃	—	13	3	no	—
93	C₃	C₁₃⋊C₃×C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
94	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₁₃⋊C₃×C₁₁⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₁₁×C₁₃	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₃	C₃×C₄
prime radical	C₃×D₅×C₁₁×C₁₃⋊C₃	C₂
cosocle	D₅×C₁₁×C₁₃	C₂×C₃²
LCS	G ▷ C₅×C₁₁×C₁₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×C₁₁⋊AGL(1,𝔽₅)	C₃	semidirect
3. C₁₃⋊C₃×C₁₁⋊AGL(1,𝔽₅)	C₃	direct (N × H)
4. C₃×C₅×C₁₁×C₁₃⋊C₃	C₄	semidirect
8. C₁₃×C₁₁⋊AGL(1,𝔽₅)	C₃²	semidirect
11. C₅×C₁₁×C₁₃⋊C₃	C₃×C₄	semidirect
12. C₃×C₅×C₁₁×C₁₃	C₃×C₄	semidirect
17. C₃×C₁₁×C₁₃⋊C₃	AGL(1,𝔽₅)	semidirect
24. C₅×C₁₁×C₁₃	C₃²×C₄	semidirect
26. C₃×C₁₁⋊AGL(1,𝔽₅)	C₁₃⋊C₃	direct (N × H)
27. C₃×C₅×C₁₃⋊C₃	Dic₁₁	semidirect
31. C₃×C₁₁×C₁₃	C₃×AGL(1,𝔽₅)	semidirect
32. C₁₁×C₁₃⋊C₃	C₃×AGL(1,𝔽₅)	semidirect
41. C₁₁⋊AGL(1,𝔽₅)	C₃×C₁₃⋊C₃	direct (N × H)
43. C₃×C₅×C₁₃	C₃×Dic₁₁	semidirect
44. C₅×C₁₃⋊C₃	C₃×Dic₁₁	semidirect
47. C₃×C₅×C₁₁	C₄×C₁₃⋊C₃	semidirect
50. C₁₁×C₁₃	C₃²×AGL(1,𝔽₅)	semidirect
54. C₃×C₁₃⋊C₃	C₁₁⋊AGL(1,𝔽₅)	direct (N × H)
62. C₅×C₁₃	C₃²×Dic₁₁	semidirect
65. C₅×C₁₁	C₃×C₄×C₁₃⋊C₃	semidirect
69. C₃×C₁₃	C₃×C₁₁⋊AGL(1,𝔽₅)	semidirect
70. C₁₃⋊C₃	C₃×C₁₁⋊AGL(1,𝔽₅)	direct (N × H)
73. C₃×C₁₁	AGL(1,𝔽₅)×C₁₃⋊C₃	semidirect
81. C₃×C₅	C₁₃⋊C₃×Dic₁₁	semidirect
82. C₁₃	C₃²×C₁₁⋊AGL(1,𝔽₅)	semidirect
85. C₁₁	C₃×AGL(1,𝔽₅)×C₁₃⋊C₃	semidirect
90. C₅	C₃×C₁₃⋊C₃×Dic₁₁	semidirect
93. C₃	C₁₃⋊C₃×C₁₁⋊AGL(1,𝔽₅)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₅×C₁₁×C₁₃⋊C₃	2
C₃×C₁₃×C₁₁⋊AGL(1,𝔽₅)	3
C₁₃⋊C₃×C₁₁⋊AGL(1,𝔽₅)	3
C₃×C₁₃⋊C₃×Dic₁₁	5
C₃×AGL(1,𝔽₅)×C₁₃⋊C₃	11
C₃²×C₁₁⋊AGL(1,𝔽₅)	13

Subgroups — C3×C13⋊C3×C11⋊AGL(1,𝔽5) #38788066

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃⋊C₃×C₁₁⋊AGL(1,𝔽₅) #38788066