Subgroups — C₅×C₁₁×A₄×C₁₃⋊C₃ #38788126

Order 25740.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₁₁×C₁₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₁×A₄×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₁×C₂²⋊(C₁₃⋊C₃)	C₃	1	2	yes	maximal, complemented
4	C₃×C₅×C₁₁×C₁₃⋊C₃	—	4	1	no	maximal, Hall
5	C₁₁×A₄×C₁₃⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₁₁×C₁₃⋊C₃	—	3	1	no	—
7	C₂²×C₅×C₁₁×C₁₃	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₅×A₄×C₁₃⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₁₁×C₁₃⋊C₃	—	4	2	no	—
10	C₅×C₁₁×C₁₃⋊C₃	A₄	1	1	yes	characteristic, direct product factor
11	C₃×C₅×C₁₁×C₁₃	—	4	1	no	—
12	C₃×C₅×C₁₁×A₄	—	13	1	no	maximal, Hall
13	C₁₁×C₂²⋊(C₁₃⋊C₃)	C₃×C₅	1	2	yes	complemented
14	C₁₁×A₄×C₁₃	C₃×C₅	1	1	yes	characteristic, complemented
15	C₂²×C₁₁×C₁₃⋊C₃	C₃×C₅	1	1	yes	characteristic, complemented
16	C₂×C₅×C₁₁×C₁₃	—	3	1	no	—
17	C₃×C₁₁×C₁₃⋊C₃	—	4	1	no	Hall
18	C₂×C₁₁×C₁₃⋊C₃	—	3	1	no	—
19	C₅×C₂²⋊(C₁₃⋊C₃)	C₃×C₁₁	1	2	yes	complemented
20	C₅×A₄×C₁₃	C₃×C₁₁	1	1	yes	characteristic, complemented
21	C₂²×C₅×C₁₃⋊C₃	C₃×C₁₁	1	1	yes	characteristic, complemented
22	C₅×C₁₁×C₁₃	C₃×A₄	1	1	yes	characteristic, complemented, Hall
23	C₂²×C₃×C₅×C₁₁	—	13	1	no	—
24	C₅×C₁₁×A₄	—	13	2	no	—
25	C₅×C₁₁×A₄	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
26	C₃×C₅×C₁₃⋊C₃	—	4	1	no	Hall
27	C₂²×C₁₁×C₁₃	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
28	C₃²×C₅×C₁₁	—	52	1	no	Hall
29	A₄×C₁₃⋊C₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
30	C₃×C₁₁×C₁₃	—	4	1	no	—
31	C₁₁×C₁₃⋊C₃	—	4	2	no	—
32	C₁₁×C₁₃⋊C₃	C₅×A₄	1	1	yes	characteristic, direct product factor
33	C₃×C₁₁×A₄	—	13	1	no	Hall
34	C₂×C₅×C₁₃⋊C₃	—	3	1	no	—
35	C₂×C₃×C₅×C₁₁	—	39	1	no	—
36	C₂×C₁₁×C₁₃	—	3	1	no	—
37	C₂²×C₅×C₁₃	C₃²×C₁₁	1	1	yes	characteristic, complemented, Hall
38	C₂²×C₅×C₁₁	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅×C₁₃	—	4	1	no	—
40	C₅×C₁₃⋊C₃	—	4	2	no	—
41	C₅×C₁₃⋊C₃	C₁₁×A₄	1	1	yes	characteristic, direct product factor
42	C₃×C₅×A₄	—	13	1	no	Hall
43	C₃×C₅×C₁₁	—	4	1	no	—
44	C₃×C₅×C₁₁	—	13	1	no	—
45	C₃×C₅×C₁₁	—	52	2	no	—
46	C₂²⋊(C₁₃⋊C₃)	C₃×C₅×C₁₁	1	2	yes	complemented
47	A₄×C₁₃	C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
48	C₂²×C₁₃⋊C₃	C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
49	C₁₁×C₁₃	C₃×C₅×A₄	1	1	yes	characteristic, complemented, Hall
50	C₂²×C₃×C₁₁	—	13	1	no	—
51	C₁₁×A₄	—	13	2	no	—
52	C₁₁×A₄	C₅×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
53	C₂×C₅×C₁₃	—	3	1	no	—
54	C₃×C₁₃⋊C₃	—	4	1	no	Hall
55	C₂×C₅×C₁₁	—	3	1	no	—
56	C₃²×C₁₁	—	52	1	no	Hall
57	C₂×C₁₃⋊C₃	—	3	1	no	—
58	C₂×C₃×C₁₁	—	39	1	no	—
59	C₅×C₁₃	C₃×C₁₁×A₄	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₃×C₅	—	13	1	no	—
61	C₅×A₄	—	13	2	no	—
62	C₅×A₄	C₁₁×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
63	C₅×C₁₁	A₄×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
64	C₂²×C₁₃	C₃²×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
65	C₃²×C₅	—	52	1	no	Hall
66	C₂²×C₁₁	C₃×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
67	C₃×C₁₃	—	4	1	no	—
68	C₁₃⋊C₃	—	4	2	no	—
69	C₁₃⋊C₃	C₅×C₁₁×A₄	1	1	yes	characteristic, direct product factor
70	C₃×A₄	—	13	1	no	Hall
71	C₃×C₁₁	—	4	1	no	—
72	C₃×C₁₁	—	13	1	no	—
73	C₃×C₁₁	—	52	2	no	—
74	C₂×C₃×C₅	—	39	1	no	—
75	C₂×C₁₃	—	3	1	no	—
76	C₂×C₁₁	—	3	1	no	—
77	C₂²×C₅	C₃×C₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
78	C₃×C₅	—	4	1	no	—
79	C₃×C₅	—	13	1	no	—
80	C₃×C₅	—	52	2	no	—
81	C₁₃	C₃×C₅×C₁₁×A₄	1	1	yes	characteristic, complemented, Sylow
82	C₂²×C₃	—	13	1	no	—
83	A₄	—	13	2	no	—
84	A₄	C₅×C₁₁×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
85	C₁₁	C₅×A₄×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
86	C₂×C₅	—	3	1	no	—
87	C₃²	—	52	1	no	Sylow
88	C₂×C₃	—	39	1	no	—
89	C₅	C₁₁×A₄×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
90	C₂²	C₃×C₅×C₁₁×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
91	C₃	—	4	1	no	—
92	C₃	—	13	1	no	—
93	C₃	—	52	2	no	—
94	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₁	A₄×C₁₃⋊C₃
commutator, cosocle, hypocenter	C₂²×C₁₃	C₃²×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₁₁×C₁₃	C₃²
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₁₁×C₁₃⋊C₃	C₃	semidirect
2. C₅×C₁₁×A₄×C₁₃	C₃	semidirect
3. C₅×C₁₁×C₂²⋊(C₁₃⋊C₃)	C₃	semidirect
5. C₁₁×A₄×C₁₃⋊C₃	C₅	direct (N × H)
7. C₂²×C₅×C₁₁×C₁₃	C₃²	semidirect
8. C₅×A₄×C₁₃⋊C₃	C₁₁	direct (N × H)
10. C₅×C₁₁×C₁₃⋊C₃	A₄	direct (N × H)
13. C₁₁×C₂²⋊(C₁₃⋊C₃)	C₃×C₅	semidirect
14. C₁₁×A₄×C₁₃	C₃×C₅	semidirect
15. C₂²×C₁₁×C₁₃⋊C₃	C₃×C₅	semidirect
19. C₅×C₂²⋊(C₁₃⋊C₃)	C₃×C₁₁	semidirect
20. C₅×A₄×C₁₃	C₃×C₁₁	semidirect
21. C₂²×C₅×C₁₃⋊C₃	C₃×C₁₁	semidirect
22. C₅×C₁₁×C₁₃	C₃×A₄	semidirect
25. C₅×C₁₁×A₄	C₁₃⋊C₃	direct (N × H)
27. C₂²×C₁₁×C₁₃	C₃²×C₅	semidirect
29. A₄×C₁₃⋊C₃	C₅×C₁₁	direct (N × H)
32. C₁₁×C₁₃⋊C₃	C₅×A₄	direct (N × H)
37. C₂²×C₅×C₁₃	C₃²×C₁₁	semidirect
38. C₂²×C₅×C₁₁	C₃×C₁₃⋊C₃	semidirect
41. C₅×C₁₃⋊C₃	C₁₁×A₄	direct (N × H)
46. C₂²⋊(C₁₃⋊C₃)	C₃×C₅×C₁₁	semidirect
47. A₄×C₁₃	C₃×C₅×C₁₁	semidirect
48. C₂²×C₁₃⋊C₃	C₃×C₅×C₁₁	semidirect
49. C₁₁×C₁₃	C₃×C₅×A₄	semidirect
52. C₁₁×A₄	C₅×C₁₃⋊C₃	direct (N × H)
59. C₅×C₁₃	C₃×C₁₁×A₄	semidirect
62. C₅×A₄	C₁₁×C₁₃⋊C₃	direct (N × H)
63. C₅×C₁₁	A₄×C₁₃⋊C₃	direct (N × H)
64. C₂²×C₁₃	C₃²×C₅×C₁₁	semidirect
66. C₂²×C₁₁	C₃×C₅×C₁₃⋊C₃	semidirect
69. C₁₃⋊C₃	C₅×C₁₁×A₄	direct (N × H)
77. C₂²×C₅	C₃×C₁₁×C₁₃⋊C₃	semidirect
81. C₁₃	C₃×C₅×C₁₁×A₄	semidirect
84. A₄	C₅×C₁₁×C₁₃⋊C₃	direct (N × H)
85. C₁₁	C₅×A₄×C₁₃⋊C₃	direct (N × H)
89. C₅	C₁₁×A₄×C₁₃⋊C₃	direct (N × H)
90. C₂²	C₃×C₅×C₁₁×C₁₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₁₁×C₁₃⋊C₃	3
C₅×C₁₁×A₄×C₁₃	3
C₅×C₁₁×C₂²⋊(C₁₃⋊C₃)	3
C₃×C₅×C₁₁×C₁₃⋊C₃	4
C₁₁×A₄×C₁₃⋊C₃	5
C₅×A₄×C₁₃⋊C₃	11
C₃×C₅×C₁₁×A₄	13

Subgroups — C5×C11×A4×C13⋊C3 #38788126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×A₄×C₁₃⋊C₃ #38788126