Subgroups — C₇×D₂₉×D₁₃⋊C₃ #44539811

Order 31668.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₉⋊(D₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₂₉×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₃⋊C₃×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₁₃×D₂₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇×C₂₉×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×D₃₇₇	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₁₃×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×C₁₃×D₂₉	C₂×C₃	1	1	yes	characteristic, complemented
9	D₂₉×D₁₃⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₇×C₁₃×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇×D₂₉	—	13	1	no	maximal, Hall
12	C₂₉⋊(D₁₃⋊C₃)	C₂×C₇	1	1	yes	characteristic, complemented
13	C₂₉×D₁₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
14	C₁₃⋊C₃×D₂₉	C₂×C₇	1	1	yes	characteristic, complemented
15	D₁₃×D₂₉	C₃×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₇×C₂₉	—	13	1	no	—
17	C₃×C₇×D₂₉	—	13	1	no	—
18	C₃×C₇×D₂₉	—	13	1	no	—
19	C₂₉×C₁₃⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₇×D₁₃⋊C₃	—	29	1	no	maximal, Hall
21	C₂×C₇×D₂₉	—	13	1	no	Hall
22	D₃₇₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
23	C₁₃×D₂₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
24	D₁₃×C₂₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
25	C₃×C₇×C₂₉	—	13	1	no	Hall
26	C₂×C₇×C₁₃⋊C₃	—	29	1	no	—
27	C₇×D₁₃⋊C₃	—	29	1	no	—
28	C₇×D₁₃⋊C₃	D₂₉	1	1	yes	characteristic, direct product factor
29	C₂×C₇×C₂₉	—	13	1	no	—
30	C₇×D₂₉	—	13	1	no	—
31	C₇×D₂₉	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
32	C₁₃×C₂₉	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₇×D₁₃	—	29	1	no	Hall
34	C₂×C₃×D₂₉	—	13	1	no	Hall
35	C₇×C₁₃⋊C₃	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
36	C₇×C₂₉	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
37	C₂×C₇×C₁₃	—	29	1	no	—
38	C₇×D₁₃	—	29	1	no	—
39	C₇×D₁₃	C₃×D₂₉	1	1	yes	characteristic, complemented
40	C₂×C₃×C₂₉	—	13	1	no	—
41	C₃×D₂₉	—	13	1	no	—
42	C₃×D₂₉	—	13	1	no	—
43	C₂×D₁₃⋊C₃	—	29	1	no	Hall
44	C₂×D₂₉	—	13	1	no	Hall
45	C₇×C₁₃	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
46	C₃×C₂₉	—	13	1	no	Hall
47	C₂²×C₃×C₇	—	377	1	no	Hall
48	C₂×C₁₃⋊C₃	—	29	1	no	—
49	D₁₃⋊C₃	—	29	1	no	—
50	D₁₃⋊C₃	C₇×D₂₉	1	1	yes	characteristic, direct product factor
51	C₂×C₂₉	—	13	1	no	—
52	D₂₉	—	13	1	no	—
53	D₂₉	C₇×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
54	C₂×D₁₃	—	29	1	no	Hall
55	C₂×C₃×C₇	—	13	1	no	—
56	C₂×C₃×C₇	—	377	1	no	—
57	C₂×C₃×C₇	—	377	1	no	—
58	C₁₃⋊C₃	C₂×C₇×D₂₉	1	1	yes	characteristic, complemented, Hall
59	C₂₉	C₂×C₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₇	—	377	1	no	Hall
61	C₂×C₁₃	—	29	1	no	—
62	D₁₃	—	29	1	no	—
63	D₁₃	C₃×C₇×D₂₉	1	1	yes	characteristic, complemented
64	C₃×C₇	—	13	1	no	Hall
65	C₂×C₇	—	13	1	no	—
66	C₂×C₇	—	29	1	no	—
67	C₂×C₇	—	377	1	no	—
68	C₁₃	C₂×C₃×C₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₃	—	377	1	no	Hall
70	C₇	D₂₉×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₃	—	13	1	no	—
72	C₂×C₃	—	377	1	no	—
73	C₂×C₃	—	377	1	no	—
74	C₂²	—	377	1	no	Sylow
75	C₃	—	13	1	no	Sylow
76	C₂	—	13	1	no	—
77	C₂	—	29	1	no	—
78	C₂	—	377	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₂₉×D₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃×C₂₉	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₂₉	C₂²×C₃
LCS	G ▷ C₁₃×C₂₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₉⋊(D₁₃⋊C₃)	C₂	semidirect
2. C₇×C₂₉×D₁₃⋊C₃	C₂	semidirect
3. C₇×C₁₃⋊C₃×D₂₉	C₂	semidirect
4. C₇×D₁₃×D₂₉	C₃	semidirect
5. C₇×C₂₉×C₁₃⋊C₃	C₂²	semidirect
6. C₇×D₃₇₇	C₂×C₃	semidirect
7. C₇×D₁₃×C₂₉	C₂×C₃	semidirect
8. C₇×C₁₃×D₂₉	C₂×C₃	semidirect
9. D₂₉×D₁₃⋊C₃	C₇	direct (N × H)
10. C₇×C₁₃×C₂₉	C₂²×C₃	semidirect
12. C₂₉⋊(D₁₃⋊C₃)	C₂×C₇	semidirect
13. C₂₉×D₁₃⋊C₃	C₂×C₇	semidirect
14. C₁₃⋊C₃×D₂₉	C₂×C₇	semidirect
15. D₁₃×D₂₉	C₃×C₇	semidirect
19. C₂₉×C₁₃⋊C₃	C₂²×C₇	semidirect
22. D₃₇₇	C₂×C₃×C₇	semidirect
23. C₁₃×D₂₉	C₂×C₃×C₇	semidirect
24. D₁₃×C₂₉	C₂×C₃×C₇	semidirect
28. C₇×D₁₃⋊C₃	D₂₉	direct (N × H)
31. C₇×D₂₉	D₁₃⋊C₃	direct (N × H)
32. C₁₃×C₂₉	C₂²×C₃×C₇	semidirect
35. C₇×C₁₃⋊C₃	C₂×D₂₉	semidirect
36. C₇×C₂₉	C₂×D₁₃⋊C₃	semidirect
39. C₇×D₁₃	C₃×D₂₉	semidirect
45. C₇×C₁₃	C₂×C₃×D₂₉	semidirect
50. D₁₃⋊C₃	C₇×D₂₉	direct (N × H)
53. D₂₉	C₇×D₁₃⋊C₃	direct (N × H)
58. C₁₃⋊C₃	C₂×C₇×D₂₉	semidirect
59. C₂₉	C₂×C₇×D₁₃⋊C₃	semidirect
63. D₁₃	C₃×C₇×D₂₉	semidirect
68. C₁₃	C₂×C₃×C₇×D₂₉	semidirect
70. C₇	D₂₉×D₁₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₂₉⋊(D₁₃⋊C₃)	2
C₇×C₂₉×D₁₃⋊C₃	2
C₇×C₁₃⋊C₃×D₂₉	2
C₇×D₁₃×D₂₉	3
D₂₉×D₁₃⋊C₃	7
C₂×C₃×C₇×D₂₉	13
C₂×C₇×D₁₃⋊C₃	29

Subgroups — C7×D29×D13⋊C3 #44539811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₂₉×D₁₃⋊C₃ #44539811