Subgroups — C₇×C₉×C₁₃×Dic₇ #37524389

Order 22932.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₉×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×C₁₃×Dic₇	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₉×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic
5	C₉×C₁₃×Dic₇	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₄×C₇×C₉×C₁₃	—	7	1	no	maximal
7	C₇×C₁₃×Dic₇	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic
9	C₇×C₉×Dic₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₇×C₉×C₁₃	—	2	3	no	—
11	C₂×C₇×C₉×C₁₃	D₇	1	1	yes	characteristic
12	C₂×C₇×C₉×C₁₃	C₂×C₇	1	1	yes	characteristic
13	C₂×C₇²×C₁₃	C₂×C₉	1	1	yes	characteristic
14	C₃×C₄×C₇×C₁₃	—	7	1	no	—
15	C₃×C₁₃×Dic₇	C₃×C₇	1	1	yes	characteristic
16	C₂×C₇²×C₉	C₂×C₁₃	1	1	yes	characteristic
17	C₇×C₉×C₁₃	—	2	3	no	—
18	C₇×C₉×C₁₃	Dic₇	1	1	yes	characteristic, direct product factor
19	C₇×C₉×C₁₃	C₄×C₇	1	1	yes	characteristic, complemented
20	C₇²×C₁₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
21	C₃×C₇×Dic₇	C₃×C₁₃	1	1	yes	characteristic
22	C₂×C₃×C₇×C₁₃	—	2	3	no	—
23	C₂×C₃×C₇×C₁₃	C₃×D₇	1	1	yes	characteristic
24	C₂×C₃×C₇×C₁₃	C₂×C₃×C₇	1	1	yes	characteristic
25	C₄×C₉×C₁₃	—	7	1	no	Hall
26	C₇²×C₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
27	C₄×C₇×C₁₃	—	7	1	no	—
28	C₁₃×Dic₇	C₇×C₉	1	1	yes	characteristic, direct product factor
29	C₂×C₃×C₇²	C₂×C₃×C₁₃	1	1	yes	characteristic
30	C₃×C₇×C₁₃	—	2	3	no	—
31	C₃×C₇×C₁₃	C₃×Dic₇	1	1	yes	characteristic
32	C₃×C₇×C₁₃	C₃×C₄×C₇	1	1	yes	characteristic
33	C₄×C₇×C₉	—	7	1	no	—
34	C₉×Dic₇	C₇×C₁₃	1	1	yes	characteristic, direct product factor
35	C₂×C₉×C₁₃	C₇×D₇	1	1	yes	characteristic
36	C₇×Dic₇	C₉×C₁₃	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₇×C₁₃	—	2	3	no	—
38	C₂×C₇×C₁₃	C₉×D₇	1	1	yes	characteristic
39	C₂×C₇×C₁₃	C₂×C₇×C₉	1	1	yes	characteristic
40	C₃×C₄×C₁₃	—	7	1	no	—
41	C₃×C₇²	C₃×C₄×C₁₃	1	1	yes	characteristic
42	C₂×C₇×C₉	—	2	3	no	—
43	C₂×C₇×C₉	C₁₃×D₇	1	1	yes	characteristic
44	C₂×C₇×C₉	C₂×C₇×C₁₃	1	1	yes	characteristic
45	C₉×C₁₃	C₇×Dic₇	1	1	yes	characteristic, direct product factor, Hall
46	C₂×C₇²	C₂×C₉×C₁₃	1	1	yes	characteristic
47	C₇×C₁₃	—	2	3	no	—
48	C₇×C₁₃	C₉×Dic₇	1	1	yes	characteristic, direct product factor
49	C₇×C₁₃	C₄×C₇×C₉	1	1	yes	characteristic, complemented
50	C₃×C₄×C₇	—	7	1	no	—
51	C₃×Dic₇	C₃×C₇×C₁₃	1	1	yes	characteristic
52	C₂×C₃×C₁₃	C₃×C₇×D₇	1	1	yes	characteristic
53	C₇×C₉	—	2	3	no	—
54	C₇×C₉	C₁₃×Dic₇	1	1	yes	characteristic, direct product factor
55	C₇×C₉	C₄×C₇×C₁₃	1	1	yes	characteristic, complemented
56	C₄×C₁₃	—	7	1	no	Hall
57	C₇²	C₄×C₉×C₁₃	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃×C₇	—	2	3	no	—
59	C₂×C₃×C₇	C₃×C₁₃×D₇	1	1	yes	characteristic
60	C₂×C₃×C₇	C₂×C₃×C₇×C₁₃	1	1	yes	characteristic
61	C₃×C₁₃	C₃×C₇×Dic₇	1	1	yes	characteristic
62	C₄×C₉	—	7	1	no	Hall
63	C₄×C₇	—	7	1	no	—
64	Dic₇	C₇×C₉×C₁₃	1	1	yes	characteristic, direct product factor
65	C₂×C₁₃	C₇×C₉×D₇	1	1	yes	characteristic
66	C₃×C₇	—	2	3	no	—
67	C₃×C₇	C₃×C₁₃×Dic₇	1	1	yes	characteristic
68	C₃×C₇	C₃×C₄×C₇×C₁₃	1	1	yes	characteristic
69	C₂×C₉	C₇×C₁₃×D₇	1	1	yes	characteristic
70	C₂×C₇	—	2	3	no	—
71	C₂×C₇	C₉×C₁₃×D₇	1	1	yes	characteristic
72	C₂×C₇	C₂×C₇×C₉×C₁₃	1	1	yes	characteristic
73	C₁₃	C₇×C₉×Dic₇	1	1	yes	characteristic, direct product factor, Sylow
74	C₃×C₄	—	7	1	no	—
75	C₉	C₇×C₁₃×Dic₇	1	1	yes	characteristic, direct product factor, Sylow
76	C₇	—	2	3	no	—
77	C₇	C₄×C₇×C₉×C₁₃	1	1	yes	characteristic, complemented
78	C₇	C₉×C₁₃×Dic₇	1	1	yes	characteristic, direct product factor
79	C₂×C₃	C₃×C₇×C₁₃×D₇	1	1	yes	characteristic
80	C₄	—	7	1	no	Sylow
81	C₃	C₃×C₇×C₁₃×Dic₇	1	1	yes	characteristic
82	C₂	C₇×C₉×C₁₃×D₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇×C₉×C₁₃	D₇
commutator, hypocenter	C₇	C₄×C₇×C₉×C₁₃
Frattini	C₂×C₃	C₃×C₇×C₁₃×D₇
Fitting	C₂×C₇²×C₉×C₁₃	C₂
socle, prime radical	C₂×C₃×C₇²×C₁₃	C₂×C₃
cosocle	C₂×C₃×C₇	C₂×C₃×C₇×C₁₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₇×C₉×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₇²×C₉×C₁₃	C₄	semidirect
5. C₉×C₁₃×Dic₇	C₇	direct (N × H)
7. C₇×C₁₃×Dic₇	C₉	direct (N × H)
9. C₇×C₉×Dic₇	C₁₃	direct (N × H)
18. C₇×C₉×C₁₃	Dic₇	direct (N × H)
19. C₇×C₉×C₁₃	C₄×C₇	semidirect
20. C₇²×C₁₃	C₄×C₉	semidirect
26. C₇²×C₉	C₄×C₁₃	semidirect
28. C₁₃×Dic₇	C₇×C₉	direct (N × H)
34. C₉×Dic₇	C₇×C₁₃	direct (N × H)
36. C₇×Dic₇	C₉×C₁₃	direct (N × H)
45. C₉×C₁₃	C₇×Dic₇	direct (N × H)
48. C₇×C₁₃	C₉×Dic₇	direct (N × H)
49. C₇×C₁₃	C₄×C₇×C₉	semidirect
54. C₇×C₉	C₁₃×Dic₇	direct (N × H)
55. C₇×C₉	C₄×C₇×C₁₃	semidirect
57. C₇²	C₄×C₉×C₁₃	semidirect
64. Dic₇	C₇×C₉×C₁₃	direct (N × H)
73. C₁₃	C₇×C₉×Dic₇	direct (N × H)
75. C₉	C₇×C₁₃×Dic₇	direct (N × H)
77. C₇	C₄×C₇×C₉×C₁₃	semidirect
78. C₇	C₉×C₁₃×Dic₇	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×C₉×C₁₃	2
C₃×C₇×C₁₃×Dic₇	3
C₉×C₁₃×Dic₇	7
C₄×C₇×C₉×C₁₃	7
C₇×C₉×Dic₇	13

Subgroups — C7×C9×C13×Dic7 #37524389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₉×C₁₃×Dic₇ #37524389