Subgroups — C₂×C₁₃×C₃⋊(C₅⋊(C₇⋊D₇)) #50304531

Order 38220.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊(C₅⋊(C₇⋊D₇))	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₇²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×C₅⋊(C₇⋊D₇)	—	3	1	no	maximal, Hall
4	C₃×C₅×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₃⋊(C₇⋊D₇)	—	5	1	no	maximal, Hall
6	C₁₃×C₅⋊(C₇⋊D₇)	—	3	2	no	—
7	C₂×C₅×C₇²×C₁₃	D₃	1	1	yes	characteristic, complemented
8	C₂×C₁₃×D₁₀₅	—	7	8	no	maximal
9	C₁₃×C₃⋊(C₇⋊D₇)	—	5	2	no	—
10	C₂×C₃×C₇²×C₁₃	D₅	1	1	yes	characteristic, complemented
11	C₅×C₇²×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃⋊(C₅⋊(C₇⋊D₇))	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₁₃×D₁₀₅	—	7	16	no	—
14	C₂×C₃×C₅×C₇×C₁₃	D₇	1	8	yes	complemented
15	C₂×C₁₃×C₇⋊D₇	—	15	1	no	Hall
16	C₃×C₇²×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₃×D₃₅	—	21	8	no	—
18	C₂×C₃×C₅×C₇²	C₂×C₁₃	1	1	yes	characteristic, complemented
19	C₃⋊(C₅⋊(C₇⋊D₇))	C₂×C₁₃	1	2	yes	direct product factor
20	C₃×C₅×C₇×C₁₃	C₂×D₇	1	8	yes	complemented
21	C₂×C₇²×C₁₃	D₁₅	1	1	yes	characteristic, complemented
22	C₁₃×C₇⋊D₇	—	15	2	no	—
23	C₂×C₁₃×D₂₁	—	35	8	no	—
24	C₂×C₅⋊(C₇⋊D₇)	—	3	1	no	Hall
25	C₂×C₅×C₇×C₁₃	D₂₁	1	8	yes	complemented
26	C₁₃×D₃₅	—	21	16	no	—
27	C₂×C₁₃×D₁₅	—	49	1	no	Hall
28	C₃×C₅×C₇²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
29	C₇²×C₁₃	C₂×D₁₅	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃⋊(C₇⋊D₇)	—	5	1	no	Hall
31	C₂×C₃×C₇×C₁₃	D₃₅	1	8	yes	complemented
32	C₁₃×D₂₁	—	35	16	no	—
33	C₂×C₅×C₇²	D₃×C₁₃	1	1	yes	characteristic, complemented
34	C₅⋊(C₇⋊D₇)	—	3	2	no	—
35	C₅×C₇×C₁₃	C₂×D₂₁	1	8	yes	complemented
36	C₂×D₁₀₅	—	7	8	no	—
37	C₂×C₃×C₅×C₁₃	C₇⋊D₇	1	1	yes	characteristic, complemented
38	C₁₃×D₁₅	—	49	2	no	—
39	C₂×C₁₃×D₇	—	105	8	no	—
40	C₂×C₃×C₇²	D₅×C₁₃	1	1	yes	characteristic, complemented
41	C₃⋊(C₇⋊D₇)	—	5	2	no	—
42	C₃×C₇×C₁₃	C₂×D₃₅	1	8	yes	complemented
43	C₂×D₅×C₁₃	—	147	1	no	Hall
44	C₅×C₇²	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented, Hall
45	C₂×C₃×C₅×C₇	C₁₃×D₇	1	8	yes	complemented
46	D₁₀₅	—	7	16	no	—
47	C₂×C₇⋊D₇	—	15	1	no	Hall
48	C₃×C₅×C₁₃	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
49	C₂×C₇×C₁₃	D₁₀₅	1	8	yes	complemented
50	C₁₃×D₇	—	105	16	no	—
51	C₂×D₃×C₁₃	—	245	1	no	Hall
52	C₃×C₇²	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented, Hall
53	C₂×D₃₅	—	21	8	no	—
54	C₂×C₅×C₁₃	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented
55	D₅×C₁₃	—	147	2	no	—
56	C₃×C₅×C₇	C₂×C₁₃×D₇	1	8	yes	complemented
57	C₂×C₇²	C₁₃×D₁₅	1	1	yes	characteristic, complemented
58	C₇⋊D₇	—	15	2	no	—
59	C₇×C₁₃	C₂×D₁₀₅	1	8	yes	complemented
60	C₂×D₂₁	—	35	8	no	—
61	C₂×C₃×C₁₃	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented
62	D₃×C₁₃	—	245	2	no	—
63	C₂×C₅×C₇	C₁₃×D₂₁	1	8	yes	complemented
64	D₃₅	—	21	16	no	—
65	C₅×C₁₃	C₂×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Hall
66	C₂×D₁₅	—	49	1	no	Hall
67	C₂²×C₁₃	—	735	1	no	Hall
68	C₇²	C₂×C₁₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
69	C₂×C₃×C₇	C₁₃×D₃₅	1	8	yes	complemented
70	D₂₁	—	35	16	no	—
71	C₃×C₁₃	C₂×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Hall
72	C₅×C₇	C₂×C₁₃×D₂₁	1	8	yes	complemented
73	C₂×C₃×C₅	C₁₃×C₇⋊D₇	1	1	yes	characteristic, complemented
74	D₁₅	—	49	2	no	—
75	C₂×D₇	—	105	8	no	—
76	C₂×C₁₃	—	735	2	no	—
77	C₂×C₁₃	C₃⋊(C₅⋊(C₇⋊D₇))	1	1	yes	characteristic, direct product factor
78	C₃×C₇	C₂×C₁₃×D₃₅	1	8	yes	complemented
79	C₂×D₅	—	147	1	no	Hall
80	C₃×C₅	C₂×C₁₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
81	C₂×C₇	C₁₃×D₁₀₅	1	8	yes	complemented
82	D₇	—	105	16	no	—
83	C₁₃	C₂×C₃⋊(C₅⋊(C₇⋊D₇))	1	1	yes	characteristic, direct product factor, Sylow
84	C₂×D₃	—	245	1	no	Hall
85	C₂×C₅	C₁₃×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented
86	D₅	—	147	2	no	—
87	C₇	C₂×C₁₃×D₁₀₅	1	8	yes	complemented
88	C₂×C₃	C₁₃×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented
89	D₃	—	245	2	no	—
90	C₅	C₂×C₁₃×C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	735	1	no	Sylow
92	C₃	C₂×C₁₃×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	735	2	no	—
94	C₂	C₁₃×C₃⋊(C₅⋊(C₇⋊D₇))	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₃⋊(C₅⋊(C₇⋊D₇))
commutator, cosocle, hypocenter	C₃×C₅×C₇²	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇²×C₁₃	C₂
LCS	G ▷ C₃×C₅×C₇²
UCS	C₁ ◁ C₂×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊(C₅⋊(C₇⋊D₇))	C₂	direct (N × H)
2. C₂×C₃×C₅×C₇²×C₁₃	C₂	semidirect
4. C₃×C₅×C₇²×C₁₃	C₂²	semidirect
7. C₂×C₅×C₇²×C₁₃	D₃	semidirect
10. C₂×C₃×C₇²×C₁₃	D₅	semidirect
11. C₅×C₇²×C₁₃	C₂×D₃	semidirect
12. C₂×C₃⋊(C₅⋊(C₇⋊D₇))	C₁₃	direct (N × H)
14. C₂×C₃×C₅×C₇×C₁₃	D₇	semidirect
16. C₃×C₇²×C₁₃	C₂×D₅	semidirect
18. C₂×C₃×C₅×C₇²	C₂×C₁₃	semidirect
19. C₃⋊(C₅⋊(C₇⋊D₇))	C₂×C₁₃	direct (N × H)
20. C₃×C₅×C₇×C₁₃	C₂×D₇	semidirect
21. C₂×C₇²×C₁₃	D₁₅	semidirect
25. C₂×C₅×C₇×C₁₃	D₂₁	semidirect
28. C₃×C₅×C₇²	C₂²×C₁₃	semidirect
29. C₇²×C₁₃	C₂×D₁₅	semidirect
31. C₂×C₃×C₇×C₁₃	D₃₅	semidirect
33. C₂×C₅×C₇²	D₃×C₁₃	semidirect
35. C₅×C₇×C₁₃	C₂×D₂₁	semidirect
37. C₂×C₃×C₅×C₁₃	C₇⋊D₇	semidirect
40. C₂×C₃×C₇²	D₅×C₁₃	semidirect
42. C₃×C₇×C₁₃	C₂×D₃₅	semidirect
44. C₅×C₇²	C₂×D₃×C₁₃	semidirect
45. C₂×C₃×C₅×C₇	C₁₃×D₇	semidirect
48. C₃×C₅×C₁₃	C₂×C₇⋊D₇	semidirect
49. C₂×C₇×C₁₃	D₁₀₅	semidirect
52. C₃×C₇²	C₂×D₅×C₁₃	semidirect
54. C₂×C₅×C₁₃	C₃⋊(C₇⋊D₇)	semidirect
56. C₃×C₅×C₇	C₂×C₁₃×D₇	semidirect
57. C₂×C₇²	C₁₃×D₁₅	semidirect
59. C₇×C₁₃	C₂×D₁₀₅	semidirect
61. C₂×C₃×C₁₃	C₅⋊(C₇⋊D₇)	semidirect
63. C₂×C₅×C₇	C₁₃×D₂₁	semidirect
65. C₅×C₁₃	C₂×C₃⋊(C₇⋊D₇)	semidirect
68. C₇²	C₂×C₁₃×D₁₅	semidirect
69. C₂×C₃×C₇	C₁₃×D₃₅	semidirect
71. C₃×C₁₃	C₂×C₅⋊(C₇⋊D₇)	semidirect
72. C₅×C₇	C₂×C₁₃×D₂₁	semidirect
73. C₂×C₃×C₅	C₁₃×C₇⋊D₇	semidirect
77. C₂×C₁₃	C₃⋊(C₅⋊(C₇⋊D₇))	direct (N × H)
78. C₃×C₇	C₂×C₁₃×D₃₅	semidirect
80. C₃×C₅	C₂×C₁₃×C₇⋊D₇	semidirect
81. C₂×C₇	C₁₃×D₁₀₅	semidirect
83. C₁₃	C₂×C₃⋊(C₅⋊(C₇⋊D₇))	direct (N × H)
85. C₂×C₅	C₁₃×C₃⋊(C₇⋊D₇)	semidirect
87. C₇	C₂×C₁₃×D₁₀₅	semidirect
88. C₂×C₃	C₁₃×C₅⋊(C₇⋊D₇)	semidirect
90. C₅	C₂×C₁₃×C₃⋊(C₇⋊D₇)	semidirect
92. C₃	C₂×C₁₃×C₅⋊(C₇⋊D₇)	semidirect
94. C₂	C₁₃×C₃⋊(C₅⋊(C₇⋊D₇))	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₃⋊(C₅⋊(C₇⋊D₇))	2
C₂×C₃×C₅×C₇²×C₁₃	2
C₂×C₁₃×C₅⋊(C₇⋊D₇)	3
C₂×C₁₃×C₃⋊(C₇⋊D₇)	5
C₂×C₁₃×D₁₀₅	7
C₂×C₃⋊(C₅⋊(C₇⋊D₇))	13

Subgroups — C2×C13×C3⋊(C5⋊(C7⋊D7)) #50304531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×C₃⋊(C₅⋊(C₇⋊D₇)) #50304531