Subgroups — C₂×C₅×C₇×C₁₃×C₃⋊D₃ #30655786

Order 16380.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₃×C₃⋊D₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₃×C₇×C₁₃	—	3	4	no	maximal
4	C₃²×C₅×C₇×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₁₃×C₃⋊D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₃×C₇×C₁₃	—	3	8	no	—
7	C₂×C₃×C₅×C₇×C₁₃	D₃	1	4	yes	complemented
8	C₂×C₅×C₁₃×C₃⋊D₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₅×C₇×C₁₃	—	9	1	no	Hall
10	C₂×C₃²×C₇×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented
11	C₇×C₁₃×C₃⋊D₃	C₂×C₅	1	2	yes	direct product factor
12	C₃×C₅×C₇×C₁₃	C₂×D₃	1	4	yes	complemented
13	C₂×C₅×C₇×C₃⋊D₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃²×C₅×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented
15	C₅×C₁₃×C₃⋊D₃	C₂×C₇	1	2	yes	direct product factor
16	C₂×D₃×C₇×C₁₃	—	3	4	no	—
17	C₂×C₅×C₇×C₁₃	—	9	2	no	—
18	C₂×C₅×C₇×C₁₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
19	C₃²×C₇×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×D₃×C₁₃	—	3	4	no	—
21	C₂×C₃²×C₅×C₇	C₂×C₁₃	1	1	yes	characteristic, complemented
22	C₅×C₇×C₃⋊D₃	C₂×C₁₃	1	2	yes	direct product factor
23	C₃²×C₅×C₁₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₇×C₁₃	C₅×D₃	1	4	yes	complemented
25	D₃×C₇×C₁₃	—	3	8	no	—
26	C₂×C₁₃×C₃⋊D₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
27	C₅×C₇×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₅×D₃×C₇	—	3	4	no	—
29	C₂×C₃×C₅×C₁₃	D₃×C₇	1	4	yes	complemented
30	C₅×D₃×C₁₃	—	3	8	no	—
31	C₂²×C₇×C₁₃	—	9	1	no	Hall
32	C₃²×C₅×C₇	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
33	C₃×C₇×C₁₃	C₂×C₅×D₃	1	4	yes	complemented
34	C₂²×C₅×C₁₃	—	9	1	no	Hall
35	C₂×C₇×C₃⋊D₃	C₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₃²×C₁₃	C₂×C₅×C₇	1	1	yes	characteristic, complemented
37	C₁₃×C₃⋊D₃	C₂×C₅×C₇	1	2	yes	direct product factor
38	C₂×C₃×C₅×C₇	D₃×C₁₃	1	4	yes	complemented
39	C₅×D₃×C₇	—	3	8	no	—
40	C₃×C₅×C₁₃	C₂×D₃×C₇	1	4	yes	complemented
41	C₂×C₇×C₁₃	—	9	2	no	—
42	C₂×C₇×C₁₃	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor
43	C₂×C₅×C₃⋊D₃	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
44	C₂×D₃×C₁₃	—	3	4	no	—
45	C₂²×C₅×C₇	—	9	1	no	Hall
46	C₂×C₅×C₁₃	—	9	2	no	—
47	C₂×C₅×C₁₃	C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
48	C₂×C₃²×C₇	C₂×C₅×C₁₃	1	1	yes	characteristic, complemented
49	C₇×C₃⋊D₃	C₂×C₅×C₁₃	1	2	yes	direct product factor
50	C₃²×C₁₃	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
51	C₃×C₅×C₇	C₂×D₃×C₁₃	1	4	yes	complemented
52	C₇×C₁₃	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
53	C₂×C₃²×C₅	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
54	C₅×C₃⋊D₃	C₂×C₇×C₁₃	1	2	yes	direct product factor
55	C₂×D₃×C₇	—	3	4	no	—
56	C₂×C₃×C₁₃	C₅×D₃×C₇	1	4	yes	complemented
57	D₃×C₁₃	—	3	8	no	—
58	C₂×C₅×C₇	—	9	2	no	—
59	C₂×C₅×C₇	C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
60	C₅×C₁₃	C₂×C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
61	C₃²×C₇	C₂²×C₅×C₁₃	1	1	yes	characteristic, complemented, Hall
62	C₂×C₅×D₃	—	3	4	no	—
63	C₂²×C₁₃	—	9	1	no	Hall
64	C₃²×C₅	C₂²×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
65	C₂×C₃×C₇	C₅×D₃×C₁₃	1	4	yes	complemented
66	D₃×C₇	—	3	8	no	—
67	C₃×C₁₃	C₂×C₅×D₃×C₇	1	4	yes	complemented
68	C₂×C₃⋊D₃	C₅×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
69	C₅×C₇	C₂×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
70	C₂×C₃×C₅	D₃×C₇×C₁₃	1	4	yes	complemented
71	C₅×D₃	—	3	8	no	—
72	C₂²×C₇	—	9	1	no	Hall
73	C₂×C₁₃	—	9	2	no	—
74	C₂×C₁₃	C₅×C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor
75	C₃×C₇	C₂×C₅×D₃×C₁₃	1	4	yes	complemented
76	C₂²×C₅	—	9	1	no	Hall
77	C₂×C₃²	C₂×C₅×C₇×C₁₃	1	1	yes	characteristic, complemented
78	C₃⋊D₃	C₂×C₅×C₇×C₁₃	1	2	yes	direct product factor
79	C₃×C₅	C₂×D₃×C₇×C₁₃	1	4	yes	complemented
80	C₂×C₇	—	9	2	no	—
81	C₂×C₇	C₅×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
82	C₁₃	C₂×C₅×C₇×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
83	C₂×D₃	—	3	4	no	—
84	C₂×C₅	—	9	2	no	—
85	C₂×C₅	C₇×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
86	C₃²	C₂²×C₅×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
87	C₇	C₂×C₅×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×C₃	C₅×D₃×C₇×C₁₃	1	4	yes	complemented
89	D₃	—	3	8	no	—
90	C₅	C₂×C₇×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	9	1	no	Sylow
92	C₃	C₂×C₅×D₃×C₇×C₁₃	1	4	yes	complemented
93	C₂	—	9	2	no	—
94	C₂	C₅×C₇×C₁₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇×C₁₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₅×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₁₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₅×C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₃×C₃⋊D₃	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₁₃	C₂	semidirect
4. C₃²×C₅×C₇×C₁₃	C₂²	semidirect
5. C₂×C₇×C₁₃×C₃⋊D₃	C₅	direct (N × H)
7. C₂×C₃×C₅×C₇×C₁₃	D₃	semidirect
8. C₂×C₅×C₁₃×C₃⋊D₃	C₇	direct (N × H)
10. C₂×C₃²×C₇×C₁₃	C₂×C₅	semidirect
11. C₇×C₁₃×C₃⋊D₃	C₂×C₅	direct (N × H)
12. C₃×C₅×C₇×C₁₃	C₂×D₃	semidirect
13. C₂×C₅×C₇×C₃⋊D₃	C₁₃	direct (N × H)
14. C₂×C₃²×C₅×C₁₃	C₂×C₇	semidirect
15. C₅×C₁₃×C₃⋊D₃	C₂×C₇	direct (N × H)
18. C₂×C₅×C₇×C₁₃	C₃⋊D₃	direct (N × H)
19. C₃²×C₇×C₁₃	C₂²×C₅	semidirect
21. C₂×C₃²×C₅×C₇	C₂×C₁₃	semidirect
22. C₅×C₇×C₃⋊D₃	C₂×C₁₃	direct (N × H)
23. C₃²×C₅×C₁₃	C₂²×C₇	semidirect
24. C₂×C₃×C₇×C₁₃	C₅×D₃	semidirect
26. C₂×C₁₃×C₃⋊D₃	C₅×C₇	direct (N × H)
27. C₅×C₇×C₁₃	C₂×C₃⋊D₃	direct (N × H)
29. C₂×C₃×C₅×C₁₃	D₃×C₇	semidirect
32. C₃²×C₅×C₇	C₂²×C₁₃	semidirect
33. C₃×C₇×C₁₃	C₂×C₅×D₃	semidirect
35. C₂×C₇×C₃⋊D₃	C₅×C₁₃	direct (N × H)
36. C₂×C₃²×C₁₃	C₂×C₅×C₇	semidirect
37. C₁₃×C₃⋊D₃	C₂×C₅×C₇	direct (N × H)
38. C₂×C₃×C₅×C₇	D₃×C₁₃	semidirect
40. C₃×C₅×C₁₃	C₂×D₃×C₇	semidirect
42. C₂×C₇×C₁₃	C₅×C₃⋊D₃	direct (N × H)
43. C₂×C₅×C₃⋊D₃	C₇×C₁₃	direct (N × H)
47. C₂×C₅×C₁₃	C₇×C₃⋊D₃	direct (N × H)
48. C₂×C₃²×C₇	C₂×C₅×C₁₃	semidirect
49. C₇×C₃⋊D₃	C₂×C₅×C₁₃	direct (N × H)
50. C₃²×C₁₃	C₂²×C₅×C₇	semidirect
51. C₃×C₅×C₇	C₂×D₃×C₁₃	semidirect
52. C₇×C₁₃	C₂×C₅×C₃⋊D₃	direct (N × H)
53. C₂×C₃²×C₅	C₂×C₇×C₁₃	semidirect
54. C₅×C₃⋊D₃	C₂×C₇×C₁₃	direct (N × H)
56. C₂×C₃×C₁₃	C₅×D₃×C₇	semidirect
59. C₂×C₅×C₇	C₁₃×C₃⋊D₃	direct (N × H)
60. C₅×C₁₃	C₂×C₇×C₃⋊D₃	direct (N × H)
61. C₃²×C₇	C₂²×C₅×C₁₃	semidirect
64. C₃²×C₅	C₂²×C₇×C₁₃	semidirect
65. C₂×C₃×C₇	C₅×D₃×C₁₃	semidirect
67. C₃×C₁₃	C₂×C₅×D₃×C₇	semidirect
68. C₂×C₃⋊D₃	C₅×C₇×C₁₃	direct (N × H)
69. C₅×C₇	C₂×C₁₃×C₃⋊D₃	direct (N × H)
70. C₂×C₃×C₅	D₃×C₇×C₁₃	semidirect
74. C₂×C₁₃	C₅×C₇×C₃⋊D₃	direct (N × H)
75. C₃×C₇	C₂×C₅×D₃×C₁₃	semidirect
77. C₂×C₃²	C₂×C₅×C₇×C₁₃	semidirect
78. C₃⋊D₃	C₂×C₅×C₇×C₁₃	direct (N × H)
79. C₃×C₅	C₂×D₃×C₇×C₁₃	semidirect
81. C₂×C₇	C₅×C₁₃×C₃⋊D₃	direct (N × H)
82. C₁₃	C₂×C₅×C₇×C₃⋊D₃	direct (N × H)
85. C₂×C₅	C₇×C₁₃×C₃⋊D₃	direct (N × H)
86. C₃²	C₂²×C₅×C₇×C₁₃	semidirect
87. C₇	C₂×C₅×C₁₃×C₃⋊D₃	direct (N × H)
88. C₂×C₃	C₅×D₃×C₇×C₁₃	semidirect
90. C₅	C₂×C₇×C₁₃×C₃⋊D₃	direct (N × H)
92. C₃	C₂×C₅×D₃×C₇×C₁₃	semidirect
94. C₂	C₅×C₇×C₁₃×C₃⋊D₃	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×C₇×C₁₃×C₃⋊D₃	2
C₂×C₃²×C₅×C₇×C₁₃	2
C₂×C₅×D₃×C₇×C₁₃	3
C₂×C₇×C₁₃×C₃⋊D₃	5
C₂×C₅×C₁₃×C₃⋊D₃	7
C₂×C₅×C₇×C₃⋊D₃	13

Subgroups — C2×C5×C7×C13×C3⋊D3 #30655786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₇×C₁₃×C₃⋊D₃ #30655786