Subgroups — C₂×C₇²×D₁₃⋊C₉ #37524504

Order 22932.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×D₁₃⋊C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₇²×D₁₃	C₃	1	1	yes	maximal, characteristic
4	C₇²×C₁₃⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇²×D₁₃	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic
7	C₂×C₇×D₁₃⋊C₉	C₇	1	8	yes	maximal, direct product factor
8	C₂×C₇²×D₁₃	C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic
10	C₂²×C₇²×C₉	—	13	1	no	maximal, Hall
11	C₂×C₇×C₁₃⋊C₉	C₂×C₇	1	8	yes	complemented
12	C₇×D₁₃⋊C₉	C₂×C₇	1	16	yes	direct product factor
13	C₂×C₇²×C₁₃	C₂×C₉	1	1	yes	characteristic, complemented
14	C₇²×D₁₃	C₂×C₉	1	2	yes	complemented
15	C₂×C₃×C₇×D₁₃	C₃×C₇	1	8	yes	—
16	C₂×C₇²×C₉	—	13	2	no	—
17	C₂×C₇²×C₉	—	13	1	no	—
18	C₇×C₁₃⋊C₉	C₂²×C₇	1	8	yes	complemented
19	C₇²×C₁₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₃×C₇²	—	13	1	no	—
21	C₂×C₃×C₇×C₁₃	C₂×C₃×C₇	1	8	yes	—
22	C₃×C₇×D₁₃	C₂×C₃×C₇	1	16	yes	—
23	C₂×D₁₃⋊C₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
24	C₇²×C₉	—	13	1	no	Hall
25	C₂×C₇×D₁₃	C₇×C₉	1	8	yes	complemented
26	C₂×C₃×C₇²	—	13	2	no	—
27	C₂×C₃×C₇²	D₁₃⋊C₃	1	1	yes	characteristic
28	C₃×C₇×C₁₃	C₂²×C₃×C₇	1	8	yes	—
29	C₂²×C₇×C₉	—	13	8	no	—
30	C₂×C₁₃⋊C₉	C₂×C₇²	1	1	yes	characteristic, complemented
31	D₁₃⋊C₉	C₂×C₇²	1	2	yes	direct product factor
32	C₂²×C₇²	—	13	1	no	Hall
33	C₂×C₇×C₁₃	C₂×C₇×C₉	1	8	yes	complemented
34	C₇×D₁₃	C₂×C₇×C₉	1	16	yes	complemented
35	C₂×C₃×D₁₃	C₃×C₇²	1	1	yes	characteristic
36	C₃×C₇²	C₂×D₁₃⋊C₃	1	1	yes	characteristic
37	C₂×C₇×C₉	—	13	16	no	—
38	C₂×C₇×C₉	—	13	8	no	—
39	C₁₃⋊C₉	C₂²×C₇²	1	1	yes	characteristic, complemented, Hall
40	C₂×C₇²	—	13	2	no	—
41	C₂×C₇²	D₁₃⋊C₉	1	1	yes	characteristic, direct product factor
42	C₇×C₁₃	C₂²×C₇×C₉	1	8	yes	complemented
43	C₂²×C₃×C₇	—	13	8	no	—
44	C₂×C₃×C₁₃	C₂×C₃×C₇²	1	1	yes	characteristic
45	C₃×D₁₃	C₂×C₃×C₇²	1	2	yes	—
46	C₇×C₉	—	13	8	no	—
47	C₂×D₁₃	C₇²×C₉	1	1	yes	characteristic, complemented, Hall
48	C₇²	C₂×D₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
49	C₂×C₃×C₇	—	13	16	no	—
50	C₂×C₃×C₇	C₇×D₁₃⋊C₃	1	8	yes	—
51	C₃×C₁₃	C₂²×C₃×C₇²	1	1	yes	characteristic
52	C₂²×C₉	—	13	1	no	Hall
53	C₂²×C₇	—	13	8	no	—
54	C₂×C₁₃	C₂×C₇²×C₉	1	1	yes	characteristic, complemented
55	D₁₃	C₂×C₇²×C₉	1	2	yes	complemented
56	C₃×C₇	C₂×C₇×D₁₃⋊C₃	1	8	yes	—
57	C₂×C₉	—	13	2	no	—
58	C₂×C₉	—	13	1	no	—
59	C₂×C₇	—	13	16	no	—
60	C₂×C₇	C₇×D₁₃⋊C₉	1	8	yes	direct product factor
61	C₁₃	C₂²×C₇²×C₉	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₃	—	13	1	no	—
63	C₉	—	13	1	no	Sylow
64	C₇	C₂×C₇×D₁₃⋊C₉	1	8	yes	direct product factor
65	C₂×C₃	—	13	2	no	—
66	C₂×C₃	C₇²×D₁₃⋊C₃	1	1	yes	characteristic
67	C₂²	—	13	1	no	Sylow
68	C₃	C₂×C₇²×D₁₃⋊C₃	1	1	yes	characteristic
69	C₂	—	13	2	no	—
70	C₂	C₇²×D₁₃⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇²	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂²×C₇²×C₉
Frattini	C₃	C₂×C₇²×D₁₃⋊C₃
Fitting, socle	C₂×C₃×C₇²×C₁₃	C₂×C₃
prime radical	C₂×C₃×C₇²×D₁₃	C₃
cosocle	C₃×C₁₃	C₂²×C₃×C₇²
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₇²

Complements

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

N	H ≅ G/N	type
1. C₂×C₇²×C₁₃⋊C₉	C₂	semidirect
2. C₇²×D₁₃⋊C₉	C₂	direct (N × H)
4. C₇²×C₁₃⋊C₉	C₂²	semidirect
7. C₂×C₇×D₁₃⋊C₉	C₇	direct (N × H)
8. C₂×C₇²×D₁₃	C₉	semidirect
11. C₂×C₇×C₁₃⋊C₉	C₂×C₇	semidirect
12. C₇×D₁₃⋊C₉	C₂×C₇	direct (N × H)
13. C₂×C₇²×C₁₃	C₂×C₉	semidirect
14. C₇²×D₁₃	C₂×C₉	semidirect
18. C₇×C₁₃⋊C₉	C₂²×C₇	semidirect
19. C₇²×C₁₃	C₂²×C₉	semidirect
23. C₂×D₁₃⋊C₉	C₇²	direct (N × H)
25. C₂×C₇×D₁₃	C₇×C₉	semidirect
30. C₂×C₁₃⋊C₉	C₂×C₇²	semidirect
31. D₁₃⋊C₉	C₂×C₇²	direct (N × H)
33. C₂×C₇×C₁₃	C₂×C₇×C₉	semidirect
34. C₇×D₁₃	C₂×C₇×C₉	semidirect
39. C₁₃⋊C₉	C₂²×C₇²	semidirect
41. C₂×C₇²	D₁₃⋊C₉	direct (N × H)
42. C₇×C₁₃	C₂²×C₇×C₉	semidirect
47. C₂×D₁₃	C₇²×C₉	semidirect
48. C₇²	C₂×D₁₃⋊C₉	direct (N × H)
54. C₂×C₁₃	C₂×C₇²×C₉	semidirect
55. D₁₃	C₂×C₇²×C₉	semidirect
60. C₂×C₇	C₇×D₁₃⋊C₉	direct (N × H)
61. C₁₃	C₂²×C₇²×C₉	semidirect
64. C₇	C₂×C₇×D₁₃⋊C₉	direct (N × H)
70. C₂	C₇²×D₁₃⋊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×C₇²×C₁₃⋊C₉	2
C₇²×D₁₃⋊C₉	2
C₂×C₃×C₇²×D₁₃	3
C₂×C₇×D₁₃⋊C₉	7
C₂²×C₇²×C₉	13

Subgroups — C2×C72×D13⋊C9 #37524504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇²×D₁₃⋊C₉ #37524504