Subgroups — C₂²×C₇×C₁₃×C₇⋊C₉ #37524608

Order 22932.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₃×C₇⋊C₉	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₇²×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₃×C₇⋊C₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇²×C₁₃	C₂×C₃	1	3	yes	—
5	C₂²×C₁₃×C₇⋊C₉	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₇×C₉×C₁₃	—	7	1	no	maximal
7	C₂²×C₇²×C₁₃	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic
9	C₂²×C₇×C₇⋊C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₇×C₉×C₁₃	—	7	3	no	—
11	C₂×C₁₃×C₇⋊C₉	C₂×C₇	1	3	yes	direct product factor
12	C₂×C₇²×C₁₃	C₂×C₉	1	3	yes	complemented
13	C₂²×C₃×C₇×C₁₃	—	3	2	no	—
14	C₂²×C₃×C₇×C₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₂²×C₃×C₇×C₁₃	C₃×C₇	1	1	yes	characteristic
16	C₂×C₇×C₇⋊C₉	C₂×C₁₃	1	3	yes	direct product factor
17	C₇×C₉×C₁₃	—	7	1	no	—
18	C₁₃×C₇⋊C₉	C₂²×C₇	1	1	yes	characteristic, direct product factor
19	C₇²×C₁₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₃×C₇²	C₃×C₁₃	1	1	yes	characteristic
21	C₂×C₃×C₇×C₁₃	—	3	6	no	—
22	C₂×C₃×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	3	yes	—
23	C₂×C₃×C₇×C₁₃	C₂×C₃×C₇	1	3	yes	—
24	C₂²×C₉×C₁₃	—	7	1	no	Hall
25	C₇×C₇⋊C₉	C₂²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
26	C₂²×C₇×C₁₃	—	3	2	no	—
27	C₂²×C₇×C₁₃	C₇⋊C₉	1	1	yes	characteristic, direct product factor
28	C₂²×C₇×C₁₃	C₇×C₉	1	1	yes	characteristic, complemented
29	C₂×C₃×C₇²	C₂×C₃×C₁₃	1	3	yes	—
30	C₃×C₇×C₁₃	—	3	2	no	—
31	C₃×C₇×C₁₃	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic
32	C₃×C₇×C₁₃	C₂²×C₃×C₇	1	1	yes	characteristic
33	C₂²×C₇×C₉	—	7	1	no	—
34	C₂²×C₇⋊C₉	C₇×C₁₃	1	1	yes	characteristic, direct product factor
35	C₂×C₉×C₁₃	—	7	3	no	—
36	C₂²×C₇²	C₉×C₁₃	1	1	yes	characteristic, complemented, Hall
37	C₂×C₇×C₁₃	—	3	6	no	—
38	C₂×C₇×C₁₃	C₂×C₇⋊C₉	1	3	yes	direct product factor
39	C₂×C₇×C₁₃	C₂×C₇×C₉	1	3	yes	complemented
40	C₂²×C₃×C₁₃	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
41	C₃×C₇²	C₂²×C₃×C₁₃	1	1	yes	characteristic
42	C₂×C₇×C₉	—	7	3	no	—
43	C₂×C₇⋊C₉	C₂×C₇×C₁₃	1	3	yes	direct product factor
44	C₉×C₁₃	—	7	1	no	Hall
45	C₂×C₇²	C₂×C₉×C₁₃	1	3	yes	complemented
46	C₇×C₁₃	—	3	2	no	—
47	C₇×C₁₃	C₂²×C₇⋊C₉	1	1	yes	characteristic, direct product factor
48	C₇×C₁₃	C₂²×C₇×C₉	1	1	yes	characteristic, complemented
49	C₂²×C₃×C₇	—	3	2	no	—
50	C₂²×C₃×C₇	C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
51	C₂²×C₃×C₇	C₃×C₇×C₁₃	1	1	yes	characteristic
52	C₂×C₃×C₁₃	C₂×C₇×ΓL(1,𝔽₈)	1	3	yes	—
53	C₇×C₉	—	7	1	no	—
54	C₇⋊C₉	C₂²×C₇×C₁₃	1	1	yes	characteristic, direct product factor
55	C₂²×C₁₃	C₇×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
56	C₇²	C₂²×C₉×C₁₃	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃×C₇	—	3	6	no	—
58	C₂×C₃×C₇	C₂×C₁₃×ΓL(1,𝔽₈)	1	3	yes	—
59	C₂×C₃×C₇	C₂×C₃×C₇×C₁₃	1	3	yes	—
60	C₃×C₁₃	C₂²×C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
61	C₂²×C₉	—	7	1	no	Hall
62	C₂²×C₇	—	3	2	no	—
63	C₂²×C₇	C₁₃×C₇⋊C₉	1	1	yes	characteristic, direct product factor
64	C₂²×C₇	C₇×C₉×C₁₃	1	1	yes	characteristic, complemented
65	C₂×C₁₃	C₂×C₇×C₇⋊C₉	1	3	yes	direct product factor
66	C₃×C₇	—	3	2	no	—
67	C₃×C₇	C₂²×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
68	C₃×C₇	C₂²×C₃×C₇×C₁₃	1	1	yes	characteristic
69	C₂×C₉	—	7	3	no	—
70	C₂×C₇	—	3	6	no	—
71	C₂×C₇	C₂×C₁₃×C₇⋊C₉	1	3	yes	direct product factor
72	C₂×C₇	C₂×C₇×C₉×C₁₃	1	3	yes	complemented
73	C₁₃	C₂²×C₇×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²×C₃	C₇×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
75	C₉	—	7	1	no	Sylow
76	C₇	—	3	2	no	—
77	C₇	C₂²×C₇×C₉×C₁₃	1	1	yes	characteristic, complemented
78	C₇	C₂²×C₁₃×C₇⋊C₉	1	1	yes	characteristic, direct product factor
79	C₂×C₃	C₂×C₇×C₁₃×ΓL(1,𝔽₈)	1	3	yes	—
80	C₂²	C₇×C₁₃×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
81	C₃	C₂²×C₇×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
82	C₂	C₂×C₇×C₁₃×C₇⋊C₉	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₇×C₁₃	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₂²×C₇×C₉×C₁₃
Frattini	C₃	C₂²×C₇×C₁₃×ΓL(1,𝔽₈)
Fitting, socle, prime radical	C₂²×C₃×C₇²×C₁₃	C₃
cosocle	C₃×C₇	C₂²×C₃×C₇×C₁₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂²×C₃×C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×C₁₃×C₇⋊C₉	C₂	direct (N × H)
3. C₇×C₁₃×C₇⋊C₉	C₂²	direct (N × H)
5. C₂²×C₁₃×C₇⋊C₉	C₇	direct (N × H)
7. C₂²×C₇²×C₁₃	C₉	semidirect
9. C₂²×C₇×C₇⋊C₉	C₁₃	direct (N × H)
11. C₂×C₁₃×C₇⋊C₉	C₂×C₇	direct (N × H)
12. C₂×C₇²×C₁₃	C₂×C₉	semidirect
16. C₂×C₇×C₇⋊C₉	C₂×C₁₃	direct (N × H)
18. C₁₃×C₇⋊C₉	C₂²×C₇	direct (N × H)
19. C₇²×C₁₃	C₂²×C₉	semidirect
25. C₇×C₇⋊C₉	C₂²×C₁₃	direct (N × H)
27. C₂²×C₇×C₁₃	C₇⋊C₉	direct (N × H)
28. C₂²×C₇×C₁₃	C₇×C₉	semidirect
34. C₂²×C₇⋊C₉	C₇×C₁₃	direct (N × H)
36. C₂²×C₇²	C₉×C₁₃	semidirect
38. C₂×C₇×C₁₃	C₂×C₇⋊C₉	direct (N × H)
39. C₂×C₇×C₁₃	C₂×C₇×C₉	semidirect
43. C₂×C₇⋊C₉	C₂×C₇×C₁₃	direct (N × H)
45. C₂×C₇²	C₂×C₉×C₁₃	semidirect
47. C₇×C₁₃	C₂²×C₇⋊C₉	direct (N × H)
48. C₇×C₁₃	C₂²×C₇×C₉	semidirect
54. C₇⋊C₉	C₂²×C₇×C₁₃	direct (N × H)
55. C₂²×C₁₃	C₇×C₇⋊C₉	direct (N × H)
56. C₇²	C₂²×C₉×C₁₃	semidirect
63. C₂²×C₇	C₁₃×C₇⋊C₉	direct (N × H)
64. C₂²×C₇	C₇×C₉×C₁₃	semidirect
65. C₂×C₁₃	C₂×C₇×C₇⋊C₉	direct (N × H)
71. C₂×C₇	C₂×C₁₃×C₇⋊C₉	direct (N × H)
72. C₂×C₇	C₂×C₇×C₉×C₁₃	semidirect
73. C₁₃	C₂²×C₇×C₇⋊C₉	direct (N × H)
77. C₇	C₂²×C₇×C₉×C₁₃	semidirect
78. C₇	C₂²×C₁₃×C₇⋊C₉	direct (N × H)
80. C₂²	C₇×C₁₃×C₇⋊C₉	direct (N × H)
82. C₂	C₂×C₇×C₁₃×C₇⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×C₁₃×C₇⋊C₉	2
C₂²×C₃×C₇²×C₁₃	3
C₂²×C₁₃×C₇⋊C₉	7
C₂²×C₇×C₉×C₁₃	7
C₂²×C₇×C₇⋊C₉	13

Subgroups — C22×C7×C13×C7⋊C9 #37524608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×C₁₃×C₇⋊C₉ #37524608