Subgroups — D₇×C₂₉×D₁₃⋊C₃ #44539876

Order 31668.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×(C₁₃⋊C₃)⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×C₂₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂₉×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₁₃×C₂₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₇×C₂₉×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂₉×D₉₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃×D₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₁₃×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×C₂₉×D₁₃⋊C₃	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×D₇×C₂₉	—	13	1	no	maximal, Hall
12	C₂₉×D₁₃⋊C₃	—	7	1	no	—
13	C₂₉×D₁₃⋊C₃	D₇	1	1	yes	characteristic, direct product factor
14	C₂×C₂₉×C₁₃⋊C₃	—	7	1	no	—
15	C₂×D₁₃×C₂₉	—	7	1	no	Hall
16	C₂×C₃×C₇×C₂₉	—	13	1	no	—
17	C₃×D₇×C₂₉	—	13	1	no	—
18	C₃×D₇×C₂₉	—	13	1	no	—
19	C₂₉×C₁₃⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	D₇×D₁₃⋊C₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×D₇×C₂₉	—	13	1	no	Hall
22	C₂×C₁₃×C₂₉	—	7	1	no	—
23	D₁₃×C₂₉	—	7	1	no	—
24	D₁₃×C₂₉	C₃×D₇	1	1	yes	characteristic, complemented
25	C₃×C₇×C₂₉	—	13	1	no	Hall
26	(C₁₃⋊C₃)⋊D₇	C₂×C₂₉	1	1	yes	characteristic, complemented
27	D₇×C₁₃⋊C₃	C₂×C₂₉	1	1	yes	characteristic, complemented
28	C₇×D₁₃⋊C₃	C₂×C₂₉	1	1	yes	characteristic, complemented
29	C₂×C₇×C₂₉	—	13	1	no	—
30	D₇×C₂₉	—	13	1	no	—
31	D₇×C₂₉	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
32	C₁₃×C₂₉	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
33	D₇×D₁₃	C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
34	C₂²×C₃×C₂₉	—	91	1	no	Hall
35	C₇×C₁₃⋊C₃	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
36	C₇×C₂₉	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
37	D₉₁	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
38	C₇×D₁₃	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
39	C₁₃×D₇	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented
40	C₂×C₃×C₂₉	—	13	1	no	—
41	C₂×C₃×C₂₉	—	91	1	no	—
42	C₂×C₃×C₂₉	—	91	1	no	—
43	C₂×D₁₃⋊C₃	—	7	1	no	Hall
44	C₂²×C₂₉	—	91	1	no	Hall
45	C₇×C₁₃	C₂²×C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
46	C₃×C₂₉	—	13	1	no	Hall
47	C₂×C₃×D₇	—	13	1	no	Hall
48	C₂×C₁₃⋊C₃	—	7	1	no	—
49	D₁₃⋊C₃	—	7	1	no	—
50	D₁₃⋊C₃	D₇×C₂₉	1	1	yes	characteristic, direct product factor
51	C₂×C₂₉	—	7	1	no	—
52	C₂×C₂₉	—	13	1	no	—
53	C₂×C₂₉	—	91	1	no	—
54	C₂×D₁₃	—	7	1	no	Hall
55	C₂×C₃×C₇	—	13	1	no	—
56	C₃×D₇	—	13	1	no	—
57	C₃×D₇	—	13	1	no	—
58	C₁₃⋊C₃	C₂×D₇×C₂₉	1	1	yes	characteristic, complemented, Hall
59	C₂₉	D₇×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×D₇	—	13	1	no	Hall
61	C₂×C₁₃	—	7	1	no	—
62	D₁₃	—	7	1	no	—
63	D₁₃	C₃×D₇×C₂₉	1	1	yes	characteristic, complemented
64	C₃×C₇	—	13	1	no	Hall
65	C₂×C₇	—	13	1	no	—
66	D₇	—	13	1	no	—
67	D₇	C₂₉×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
68	C₁₃	C₂×C₃×D₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₃	—	91	1	no	Hall
70	C₇	C₂×C₂₉×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	13	1	no	—
72	C₂×C₃	—	91	1	no	—
73	C₂×C₃	—	91	1	no	—
74	C₂²	—	91	1	no	Sylow
75	C₃	—	13	1	no	Sylow
76	C₂	—	7	1	no	—
77	C₂	—	13	1	no	—
78	C₂	—	91	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	D₇×D₁₃⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₃	C₂²×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₂₉	C₂²×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₉×(C₁₃⋊C₃)⋊D₇	C₂	semidirect
2. D₇×C₂₉×C₁₃⋊C₃	C₂	semidirect
3. C₇×C₂₉×D₁₃⋊C₃	C₂	semidirect
4. D₇×D₁₃×C₂₉	C₃	semidirect
5. C₇×C₂₉×C₁₃⋊C₃	C₂²	semidirect
6. C₂₉×D₉₁	C₂×C₃	semidirect
7. C₁₃×D₇×C₂₉	C₂×C₃	semidirect
8. C₇×D₁₃×C₂₉	C₂×C₃	semidirect
10. C₇×C₁₃×C₂₉	C₂²×C₃	semidirect
13. C₂₉×D₁₃⋊C₃	D₇	direct (N × H)
19. C₂₉×C₁₃⋊C₃	C₂×D₇	semidirect
20. D₇×D₁₃⋊C₃	C₂₉	direct (N × H)
24. D₁₃×C₂₉	C₃×D₇	semidirect
26. (C₁₃⋊C₃)⋊D₇	C₂×C₂₉	semidirect
27. D₇×C₁₃⋊C₃	C₂×C₂₉	semidirect
28. C₇×D₁₃⋊C₃	C₂×C₂₉	semidirect
31. D₇×C₂₉	D₁₃⋊C₃	direct (N × H)
32. C₁₃×C₂₉	C₂×C₃×D₇	semidirect
33. D₇×D₁₃	C₃×C₂₉	semidirect
35. C₇×C₁₃⋊C₃	C₂²×C₂₉	semidirect
36. C₇×C₂₉	C₂×D₁₃⋊C₃	semidirect
37. D₉₁	C₂×C₃×C₂₉	semidirect
38. C₇×D₁₃	C₂×C₃×C₂₉	semidirect
39. C₁₃×D₇	C₂×C₃×C₂₉	semidirect
45. C₇×C₁₃	C₂²×C₃×C₂₉	semidirect
50. D₁₃⋊C₃	D₇×C₂₉	direct (N × H)
58. C₁₃⋊C₃	C₂×D₇×C₂₉	semidirect
59. C₂₉	D₇×D₁₃⋊C₃	direct (N × H)
63. D₁₃	C₃×D₇×C₂₉	semidirect
67. D₇	C₂₉×D₁₃⋊C₃	direct (N × H)
68. C₁₃	C₂×C₃×D₇×C₂₉	semidirect
70. C₇	C₂×C₂₉×D₁₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×(C₁₃⋊C₃)⋊D₇	2
D₇×C₂₉×C₁₃⋊C₃	2
C₇×C₂₉×D₁₃⋊C₃	2
D₇×D₁₃×C₂₉	3
C₂×C₂₉×D₁₃⋊C₃	7
C₂×C₃×D₇×C₂₉	13
D₇×D₁₃⋊C₃	29

Subgroups — D7×C29×D13⋊C3 #44539876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₂₉×D₁₃⋊C₃ #44539876