Subgroups — C₂×C₇⋊D₇×C₁₃⋊C₉ #37524556

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	C₇⋊D₇×C₁₃⋊C₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₁₃×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic
4	C₇²×C₁₃⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×C₇⋊D₇	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic
7	C₂×D₇×C₁₃⋊C₉	—	7	8	no	maximal
8	C₂×C₁₃×C₇⋊D₇	C₉	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇²×C₁₃	C₂²×C₃	1	1	yes	characteristic
10	C₂×C₉×C₇⋊D₇	—	13	1	no	maximal, Hall
11	C₂×C₇×C₁₃⋊C₉	D₇	1	8	yes	complemented
12	D₇×C₁₃⋊C₉	—	7	16	no	—
13	C₂×C₇²×C₁₃	C₂×C₉	1	1	yes	characteristic, complemented
14	C₁₃×C₇⋊D₇	C₂×C₉	1	2	yes	complemented
15	C₂×C₃×C₁₃×D₇	—	7	8	no	—
16	C₂×C₇²×C₉	—	13	1	no	—
17	C₉×C₇⋊D₇	—	13	2	no	—
18	C₇×C₁₃⋊C₉	C₂×D₇	1	8	yes	complemented
19	C₇²×C₁₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₇⋊D₇	C₁₃⋊C₃	1	1	yes	characteristic
21	C₂×C₃×C₇×C₁₃	C₃×D₇	1	8	yes	—
22	C₃×C₁₃×D₇	—	7	16	no	—
23	C₂²×C₁₃⋊C₉	—	49	1	no	Hall
24	C₇²×C₉	—	13	1	no	Hall
25	C₂×C₁₃×D₇	—	7	8	no	—
26	C₂×C₃×C₇²	C₂×C₁₃⋊C₃	1	1	yes	characteristic
27	C₃×C₇⋊D₇	C₂×C₁₃⋊C₃	1	2	yes	—
28	C₃×C₇×C₁₃	C₂×C₃×D₇	1	8	yes	—
29	C₂×C₉×D₇	—	91	8	no	—
30	C₂×C₁₃⋊C₉	—	49	2	no	—
31	C₂×C₁₃⋊C₉	C₇⋊D₇	1	1	yes	characteristic, direct product factor
32	C₂×C₇⋊D₇	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₇×C₁₃	C₉×D₇	1	8	yes	complemented
34	C₁₃×D₇	—	7	16	no	—
35	C₂²×C₃×C₁₃	—	49	1	no	—
36	C₃×C₇²	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
37	C₂×C₇×C₉	—	13	8	no	—
38	C₉×D₇	—	91	16	no	—
39	C₁₃⋊C₉	C₂×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
40	C₂×C₇²	C₂×C₁₃⋊C₉	1	1	yes	characteristic, complemented
41	C₇⋊D₇	C₂×C₁₃⋊C₉	1	2	yes	direct product factor
42	C₇×C₁₃	C₂×C₉×D₇	1	8	yes	complemented
43	C₂×C₃×D₇	—	7	8	no	—
44	C₂×C₃×C₁₃	—	49	2	no	—
45	C₂×C₃×C₁₃	C₃×C₇⋊D₇	1	1	yes	characteristic
46	C₇×C₉	—	13	8	no	—
47	C₂²×C₁₃	—	49	1	no	Hall
48	C₇²	C₂²×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃×C₇	D₇×C₁₃⋊C₃	1	8	yes	—
50	C₃×D₇	—	7	16	no	—
51	C₃×C₁₃	C₂×C₃×C₇⋊D₇	1	1	yes	characteristic
52	C₂²×C₉	—	637	1	no	Hall
53	C₂×D₇	—	7	8	no	—
54	C₂×C₁₃	—	49	2	no	—
55	C₂×C₁₃	C₉×C₇⋊D₇	1	1	yes	characteristic, complemented
56	C₃×C₇	C₂×D₇×C₁₃⋊C₃	1	8	yes	—
57	C₂×C₉	—	13	1	no	—
58	C₂×C₉	—	637	2	no	—
59	C₂×C₇	D₇×C₁₃⋊C₉	1	8	yes	complemented
60	D₇	—	7	16	no	—
61	C₁₃	C₂×C₉×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₃	—	49	1	no	—
63	C₉	—	13	1	no	Sylow
64	C₇	C₂×D₇×C₁₃⋊C₉	1	8	yes	complemented
65	C₂×C₃	—	49	2	no	—
66	C₂×C₃	C₁₃⋊C₃×C₇⋊D₇	1	1	yes	characteristic
67	C₂²	—	49	1	no	Sylow
68	C₃	C₂×C₁₃⋊C₃×C₇⋊D₇	1	1	yes	characteristic
69	C₂	—	49	2	no	—
70	C₂	C₇⋊D₇×C₁₃⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₃⋊C₃×C₇⋊D₇
commutator, hypocenter	C₇²×C₁₃	C₂²×C₉
Frattini	C₃	C₂×C₁₃⋊C₃×C₇⋊D₇
Fitting, socle	C₂×C₃×C₇²×C₁₃	C₂×C₃
prime radical	C₂×C₃×C₁₃×C₇⋊D₇	C₃
cosocle	C₃×C₇²×C₁₃	C₂²×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₇²×C₁₃⋊C₉	C₂	semidirect
2. C₇⋊D₇×C₁₃⋊C₉	C₂	direct (N × H)
4. C₇²×C₁₃⋊C₉	C₂²	semidirect
8. C₂×C₁₃×C₇⋊D₇	C₉	semidirect
11. C₂×C₇×C₁₃⋊C₉	D₇	semidirect
13. C₂×C₇²×C₁₃	C₂×C₉	semidirect
14. C₁₃×C₇⋊D₇	C₂×C₉	semidirect
18. C₇×C₁₃⋊C₉	C₂×D₇	semidirect
19. C₇²×C₁₃	C₂²×C₉	semidirect
31. C₂×C₁₃⋊C₉	C₇⋊D₇	direct (N × H)
32. C₂×C₇⋊D₇	C₁₃⋊C₉	direct (N × H)
33. C₂×C₇×C₁₃	C₉×D₇	semidirect
39. C₁₃⋊C₉	C₂×C₇⋊D₇	direct (N × H)
40. C₂×C₇²	C₂×C₁₃⋊C₉	semidirect
41. C₇⋊D₇	C₂×C₁₃⋊C₉	direct (N × H)
42. C₇×C₁₃	C₂×C₉×D₇	semidirect
48. C₇²	C₂²×C₁₃⋊C₉	semidirect
55. C₂×C₁₃	C₉×C₇⋊D₇	semidirect
59. C₂×C₇	D₇×C₁₃⋊C₉	semidirect
61. C₁₃	C₂×C₉×C₇⋊D₇	semidirect
64. C₇	C₂×D₇×C₁₃⋊C₉	semidirect
70. C₂	C₇⋊D₇×C₁₃⋊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
C₇⋊D₇×C₁₃⋊C₉	2
C₂×C₃×C₁₃×C₇⋊D₇	3
C₂×D₇×C₁₃⋊C₉	7
C₂×C₉×C₇⋊D₇	13

Subgroups — C2×C7⋊D7×C13⋊C9 #37524556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇⋊D₇×C₁₃⋊C₉ #37524556