Subgroups — C₃×C₁₁×#63118⋊C₃ #38788067

Order 25740.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₁×#63118	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#63118⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₅×C₁₁×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×AGL(1,𝔽₁₃)	—	5	1	no	maximal, Hall
6	C₅×C₁₁×D₁₃⋊C₃	C₂×C₃	1	3	yes	—
7	C₃×C₅×C₁₁×D₁₃	C₂×C₃	1	1	yes	characteristic
8	C₁₁×#63118	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₁×D₁₃⋊C₃	D₅	1	1	yes	characteristic
10	C₃×#63118⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, 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×Dic₅	—	13	1	no	maximal, Hall
14	C₃×C₁₁×#261	—	5	1	no	—
15	C₁₁×AGL(1,𝔽₁₃)	—	5	3	no	—
16	C₅×C₁₁×D₁₃	C₂×C₃²	1	1	yes	characteristic
17	C₃×C₁₁×C₁₃⋊C₃	Dic₅	1	1	yes	characteristic, complemented, Hall
18	C₃×C₅×D₁₃⋊C₃	C₂×C₁₁	1	1	yes	characteristic
19	C₂×C₃²×C₅×C₁₁	—	13	1	no	—
20	C₃×C₁₁×D₁₃	C₃×D₅	1	1	yes	characteristic
21	C₁₁×D₁₃⋊C₃	C₃×D₅	1	3	yes	—
22	C₃×#63118	C₃×C₁₁	1	1	yes	characteristic, complemented
23	#63118⋊C₃	C₃×C₁₁	1	3	yes	direct product factor
24	C₅×C₁₁×C₁₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
25	C₃×C₁₁×Dic₅	—	13	1	no	—
26	C₃×C₁₁×Dic₅	—	13	3	no	—
27	C₃×C₅×C₁₃⋊C₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
28	C₁₁×#261	—	5	1	no	Hall
29	C₃²×C₅×C₁₁	—	13	1	no	Hall
30	C₃×AGL(1,𝔽₁₃)	—	5	1	no	Hall
31	C₃×C₁₁×C₁₃	C₃×Dic₅	1	1	yes	characteristic, complemented
32	C₁₁×C₁₃⋊C₃	C₃×Dic₅	1	3	yes	complemented
33	C₃²×C₄×C₁₁	—	65	1	no	Hall
34	C₃×C₅×D₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic
35	C₅×D₁₃⋊C₃	C₂×C₃×C₁₁	1	3	yes	—
36	C₂×C₃×C₅×C₁₁	—	13	3	no	—
37	C₂×C₃×C₅×C₁₁	—	13	1	no	—
38	C₁₁×D₁₃	C₃²×D₅	1	1	yes	characteristic
39	#63118	C₃²×C₁₁	1	1	yes	characteristic, complemented, Hall
40	C₃×D₁₃⋊C₃	D₅×C₁₁	1	1	yes	characteristic
41	C₁₁×Dic₅	—	13	1	no	Hall
42	C₂×C₃²×C₁₁	—	13	1	no	—
43	C₃×C₅×C₁₃	C₃×C₄×C₁₁	1	1	yes	characteristic, complemented
44	C₅×C₁₃⋊C₃	C₃×C₄×C₁₁	1	3	yes	complemented
45	C₃²×Dic₅	—	13	1	no	Hall
46	C₃×C₅×C₁₁	—	13	3	no	—
47	C₃×C₅×C₁₁	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
48	C₃×#261	—	5	1	no	—
49	AGL(1,𝔽₁₃)	—	5	3	no	—
50	C₁₁×C₁₃	C₃²×Dic₅	1	1	yes	characteristic, complemented, Hall
51	C₃×C₄×C₁₁	—	65	3	no	—
52	C₃×C₄×C₁₁	—	65	1	no	—
53	C₅×D₁₃	C₂×C₃²×C₁₁	1	1	yes	characteristic
54	C₃×C₁₃⋊C₃	C₁₁×Dic₅	1	1	yes	characteristic, complemented, Hall
55	C₂×C₅×C₁₁	—	13	1	no	—
56	C₃²×C₁₁	—	13	1	no	Hall
57	C₂×C₃²×C₅	—	13	1	no	—
58	C₃×D₁₃	C₃×D₅×C₁₁	1	1	yes	characteristic
59	D₁₃⋊C₃	C₃×D₅×C₁₁	1	3	yes	—
60	C₂×C₃×C₁₁	—	13	3	no	—
61	C₂×C₃×C₁₁	—	13	1	no	—
62	C₅×C₁₃	C₃²×C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
63	C₃×Dic₅	—	13	3	no	—
64	C₃×Dic₅	—	13	1	no	—
65	C₅×C₁₁	C₃×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Hall
66	#261	—	5	1	no	Hall
67	C₃²×C₅	—	13	1	no	Hall
68	C₄×C₁₁	—	65	1	no	Hall
69	C₃×C₁₃	C₃×C₁₁×Dic₅	1	1	yes	characteristic, complemented
70	C₁₃⋊C₃	C₃×C₁₁×Dic₅	1	3	yes	complemented
71	C₃²×C₄	—	65	1	no	Hall
72	C₃×C₁₁	—	13	3	no	—
73	C₃×C₁₁	#63118⋊C₃	1	1	yes	characteristic, direct product factor
74	C₂×C₃×C₅	—	13	3	no	—
75	C₂×C₃×C₅	—	13	1	no	—
76	D₁₃	C₃²×D₅×C₁₁	1	1	yes	characteristic
77	C₂×C₁₁	—	13	1	no	—
78	Dic₅	—	13	1	no	Hall
79	C₂×C₃²	—	13	1	no	—
80	C₃×C₅	—	13	3	no	—
81	C₃×C₅	C₁₁×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
82	C₁₃	C₃²×C₁₁×Dic₅	1	1	yes	characteristic, complemented, Sylow
83	C₃×C₄	—	65	3	no	—
84	C₃×C₄	—	65	1	no	—
85	C₁₁	C₃×#63118⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
86	C₂×C₅	—	13	1	no	—
87	C₃²	—	13	1	no	Sylow
88	C₂×C₃	—	13	3	no	—
89	C₂×C₃	—	13	1	no	—
90	C₅	C₃×C₁₁×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
91	C₄	—	65	1	no	Sylow
92	C₃	—	13	3	no	—
93	C₃	C₁₁×#63118⋊C₃	1	1	yes	characteristic, direct product factor
94	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₁	#63118⋊C₃
commutator, hypocenter	C₅×C₁₃	C₃²×C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₃	C₃×C₄
prime radical	C₃×C₅×C₁₁×D₁₃⋊C₃	C₂
cosocle	C₅×D₁₃	C₂×C₃²×C₁₁
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₃×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₁×#63118	C₃	semidirect
3. C₁₁×#63118⋊C₃	C₃	direct (N × H)
4. C₃×C₅×C₁₁×C₁₃⋊C₃	C₄	semidirect
8. C₁₁×#63118	C₃²	semidirect
10. C₃×#63118⋊C₃	C₁₁	direct (N × H)
11. C₅×C₁₁×C₁₃⋊C₃	C₃×C₄	semidirect
12. C₃×C₅×C₁₁×C₁₃	C₃×C₄	semidirect
17. C₃×C₁₁×C₁₃⋊C₃	Dic₅	semidirect
22. C₃×#63118	C₃×C₁₁	semidirect
23. #63118⋊C₃	C₃×C₁₁	direct (N × H)
24. C₅×C₁₁×C₁₃	C₃²×C₄	semidirect
27. C₃×C₅×C₁₃⋊C₃	C₄×C₁₁	semidirect
31. C₃×C₁₁×C₁₃	C₃×Dic₅	semidirect
32. C₁₁×C₁₃⋊C₃	C₃×Dic₅	semidirect
39. #63118	C₃²×C₁₁	semidirect
43. C₃×C₅×C₁₃	C₃×C₄×C₁₁	semidirect
44. C₅×C₁₃⋊C₃	C₃×C₄×C₁₁	semidirect
47. C₃×C₅×C₁₁	AGL(1,𝔽₁₃)	semidirect
50. C₁₁×C₁₃	C₃²×Dic₅	semidirect
54. C₃×C₁₃⋊C₃	C₁₁×Dic₅	semidirect
62. C₅×C₁₃	C₃²×C₄×C₁₁	semidirect
65. C₅×C₁₁	C₃×AGL(1,𝔽₁₃)	semidirect
69. C₃×C₁₃	C₃×C₁₁×Dic₅	semidirect
70. C₁₃⋊C₃	C₃×C₁₁×Dic₅	semidirect
73. C₃×C₁₁	#63118⋊C₃	direct (N × H)
81. C₃×C₅	C₁₁×AGL(1,𝔽₁₃)	semidirect
82. C₁₃	C₃²×C₁₁×Dic₅	semidirect
85. C₁₁	C₃×#63118⋊C₃	direct (N × H)
90. C₅	C₃×C₁₁×AGL(1,𝔽₁₃)	semidirect
93. C₃	C₁₁×#63118⋊C₃	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×C₅×C₁₁×D₁₃⋊C₃	2
C₃×C₁₁×#63118	3
C₁₁×#63118⋊C₃	3
C₃×C₁₁×AGL(1,𝔽₁₃)	5
C₃×#63118⋊C₃	11
C₃²×C₁₁×Dic₅	13

Subgroups — C3×C11×#63118⋊C3 #38788067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×#63118⋊C₃ #38788067