Subgroups — C₃×C₅×C₁₃×C₂²⋊(C₁₃⋊C₃) #44478331

Order 30420.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×C₂²⋊(C₁₃⋊C₃)	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₅×C₁₃²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₁₃×C₁₃⋊C₃	—	4	1	no	maximal, Hall
4	C₃×C₁₃×C₂²⋊(C₁₃⋊C₃)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₁₃²	—	3	1	no	—
6	C₂²×C₅×C₁₃²	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₅×C₁₃×C₁₃⋊C₃	—	4	3	no	—
8	C₃×C₅×C₁₃²	A₄	1	1	yes	characteristic, complemented
9	C₃×C₅×A₄×C₁₃	—	13	1	no	maximal
10	C₃×C₅×C₂²⋊(C₁₃⋊C₃)	C₁₃	1	1	yes	maximal, characteristic, direct product factor
11	C₁₃×C₂²⋊(C₁₃⋊C₃)	C₃×C₅	1	3	yes	direct product factor
12	C₂²×C₃×C₁₃²	C₃×C₅	1	1	yes	characteristic, complemented
13	C₂×C₅×C₁₃²	—	3	1	no	—
14	C₃×C₁₃×C₁₃⋊C₃	—	4	1	no	Hall
15	C₂×C₃×C₁₃²	—	3	1	no	—
16	C₅×C₁₃²	C₃×A₄	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₃×C₅×C₁₃	—	3	4	no	—
18	C₂²×C₃×C₅×C₁₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₅×C₁₃	C₃×C₁₃	1	1	yes	characteristic, complemented
20	C₅×C₂²⋊(C₁₃⋊C₃)	C₃×C₁₃	1	3	yes	direct product factor
21	C₅×A₄×C₁₃	—	13	3	no	—
22	C₂²×C₁₃²	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
23	C₃²×C₅×C₁₃	—	52	1	no	—
24	C₃×C₅×C₁₃⋊C₃	—	4	1	no	—
25	C₃×C₁₃²	C₅×A₄	1	1	yes	characteristic, complemented
26	C₁₃×C₁₃⋊C₃	—	4	3	no	—
27	C₃×C₂²⋊(C₁₃⋊C₃)	C₅×C₁₃	1	1	yes	characteristic, direct product factor
28	C₃×A₄×C₁₃	—	13	1	no	—
29	C₂×C₃×C₅×C₁₃	—	3	12	no	—
30	C₂×C₃×C₅×C₁₃	—	3	1	no	—
31	C₂×C₃×C₅×C₁₃	—	3	1	no	—
32	C₂×C₁₃²	—	3	1	no	—
33	C₂²×C₅×C₁₃	—	3	4	no	—
34	C₂²×C₅×C₁₃	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
35	C₂²×C₅×C₁₃	C₃²×C₁₃	1	1	yes	characteristic, complemented
36	C₃×C₅×C₁₃	—	3	4	no	—
37	C₃×C₅×C₁₃	—	52	3	no	—
38	C₃×C₅×C₁₃	A₄×C₁₃	1	1	yes	characteristic, complemented
39	C₃×C₅×C₁₃	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
40	C₅×C₁₃⋊C₃	—	4	3	no	—
41	C₃×C₅×A₄	—	13	1	no	Hall
42	C₁₃²	C₃×C₅×A₄	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₃×C₁₃	—	3	4	no	—
44	C₂²×C₃×C₁₃	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented
45	C₂²×C₃×C₁₃	C₃×C₅×C₁₃	1	1	yes	characteristic, complemented
46	C₂²⋊(C₁₃⋊C₃)	C₃×C₅×C₁₃	1	3	yes	direct product factor
47	A₄×C₁₃	—	13	3	no	—
48	C₂×C₅×C₁₃	—	3	12	no	—
49	C₂×C₅×C₁₃	—	3	1	no	—
50	C₂×C₅×C₁₃	—	3	1	no	—
51	C₃²×C₁₃	—	52	1	no	—
52	C₃×C₁₃⋊C₃	—	4	1	no	—
53	C₂×C₃×C₁₃	—	3	12	no	—
54	C₂×C₃×C₁₃	—	3	1	no	—
55	C₂×C₃×C₁₃	—	3	1	no	—
56	C₅×C₁₃	—	3	4	no	—
57	C₅×C₁₃	C₃×A₄×C₁₃	1	1	yes	characteristic, complemented
58	C₅×C₁₃	C₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
59	C₂²×C₃×C₅	C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
60	C₅×A₄	—	13	3	no	—
61	C₂²×C₁₃	—	3	4	no	—
62	C₂²×C₁₃	C₃×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented
63	C₂²×C₁₃	C₃²×C₅×C₁₃	1	1	yes	characteristic, complemented
64	C₃²×C₅	—	52	1	no	Hall
65	C₃×C₁₃	—	3	4	no	—
66	C₃×C₁₃	—	52	3	no	—
67	C₃×C₁₃	C₅×A₄×C₁₃	1	1	yes	characteristic, complemented
68	C₃×C₁₃	C₅×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
69	C₁₃⋊C₃	—	4	3	no	—
70	C₃×A₄	—	13	1	no	Hall
71	C₂×C₃×C₅	—	3	1	no	—
72	C₂×C₁₃	—	3	12	no	—
73	C₂×C₁₃	—	3	1	no	—
74	C₂×C₁₃	—	3	1	no	—
75	C₂²×C₅	C₃×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
76	C₃×C₅	—	52	3	no	—
77	C₃×C₅	C₁₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
78	C₁₃	—	3	4	no	—
79	C₁₃	C₃×C₅×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
80	C₁₃	C₃×C₅×A₄×C₁₃	1	1	yes	characteristic, complemented
81	C₂²×C₃	C₅×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented
82	A₄	—	13	3	no	—
83	C₂×C₅	—	3	1	no	—
84	C₃²	—	52	1	no	Sylow
85	C₂×C₃	—	3	1	no	—
86	C₅	C₃×C₁₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
87	C₂²	C₃×C₅×C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
88	C₃	—	52	3	no	—
89	C₃	C₅×C₁₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
90	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₃	C₂²⋊(C₁₃⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₃	C₃²×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₅×C₁₃²	C₃
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₃×C₅×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×C₂²⋊(C₁₃⋊C₃)	C₃	direct (N × H)
2. C₂²×C₃×C₅×C₁₃²	C₃	semidirect
4. C₃×C₁₃×C₂²⋊(C₁₃⋊C₃)	C₅	direct (N × H)
6. C₂²×C₅×C₁₃²	C₃²	semidirect
8. C₃×C₅×C₁₃²	A₄	semidirect
10. C₃×C₅×C₂²⋊(C₁₃⋊C₃)	C₁₃	direct (N × H)
11. C₁₃×C₂²⋊(C₁₃⋊C₃)	C₃×C₅	direct (N × H)
12. C₂²×C₃×C₁₃²	C₃×C₅	semidirect
16. C₅×C₁₃²	C₃×A₄	semidirect
18. C₂²×C₃×C₅×C₁₃	C₁₃⋊C₃	semidirect
19. C₂²×C₃×C₅×C₁₃	C₃×C₁₃	semidirect
20. C₅×C₂²⋊(C₁₃⋊C₃)	C₃×C₁₃	direct (N × H)
22. C₂²×C₁₃²	C₃²×C₅	semidirect
25. C₃×C₁₃²	C₅×A₄	semidirect
27. C₃×C₂²⋊(C₁₃⋊C₃)	C₅×C₁₃	direct (N × H)
34. C₂²×C₅×C₁₃	C₃×C₁₃⋊C₃	semidirect
35. C₂²×C₅×C₁₃	C₃²×C₁₃	semidirect
38. C₃×C₅×C₁₃	A₄×C₁₃	semidirect
39. C₃×C₅×C₁₃	C₂²⋊(C₁₃⋊C₃)	direct (N × H)
42. C₁₃²	C₃×C₅×A₄	semidirect
44. C₂²×C₃×C₁₃	C₅×C₁₃⋊C₃	semidirect
45. C₂²×C₃×C₁₃	C₃×C₅×C₁₃	semidirect
46. C₂²⋊(C₁₃⋊C₃)	C₃×C₅×C₁₃	direct (N × H)
57. C₅×C₁₃	C₃×A₄×C₁₃	semidirect
58. C₅×C₁₃	C₃×C₂²⋊(C₁₃⋊C₃)	direct (N × H)
59. C₂²×C₃×C₅	C₁₃×C₁₃⋊C₃	semidirect
62. C₂²×C₁₃	C₃×C₅×C₁₃⋊C₃	semidirect
63. C₂²×C₁₃	C₃²×C₅×C₁₃	semidirect
67. C₃×C₁₃	C₅×A₄×C₁₃	semidirect
68. C₃×C₁₃	C₅×C₂²⋊(C₁₃⋊C₃)	direct (N × H)
75. C₂²×C₅	C₃×C₁₃×C₁₃⋊C₃	semidirect
77. C₃×C₅	C₁₃×C₂²⋊(C₁₃⋊C₃)	direct (N × H)
79. C₁₃	C₃×C₅×C₂²⋊(C₁₃⋊C₃)	direct (N × H)
80. C₁₃	C₃×C₅×A₄×C₁₃	semidirect
81. C₂²×C₃	C₅×C₁₃×C₁₃⋊C₃	semidirect
86. C₅	C₃×C₁₃×C₂²⋊(C₁₃⋊C₃)	direct (N × H)
87. C₂²	C₃×C₅×C₁₃×C₁₃⋊C₃	semidirect
89. C₃	C₅×C₁₃×C₂²⋊(C₁₃⋊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
C₅×C₁₃×C₂²⋊(C₁₃⋊C₃)	3
C₂²×C₃×C₅×C₁₃²	3
C₃×C₅×C₁₃×C₁₃⋊C₃	4
C₃×C₁₃×C₂²⋊(C₁₃⋊C₃)	5
C₃×C₅×A₄×C₁₃	13
C₃×C₅×C₂²⋊(C₁₃⋊C₃)	13

Subgroups — C3×C5×C13×C22⋊(C13⋊C3) #44478331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₃×C₂²⋊(C₁₃⋊C₃) #44478331