Subgroups — C₂×D₁₃⋊C₃×C₂₉⋊C₇ #44539775

Order 31668.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂	D₁₃⋊C₃×C₂₉⋊C₇
commutator, cosocle, hypocenter	C₁₃×C₂₉	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₂₉	C₂×C₃×C₇
LCS	G ▷ C₁₃×C₂₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₁₃⋊C₃×C₂₉⋊C₇	C₂	direct (N × H)
2. C₂×C₁₃⋊C₃×C₂₉⋊C₇	C₂	semidirect
3. C₂×D₁₃×C₂₉⋊C₇	C₃	semidirect
4. C₁₃⋊C₃×C₂₉⋊C₇	C₂²	semidirect
5. D₁₃×C₂₉⋊C₇	C₂×C₃	semidirect
6. C₂×C₁₃×C₂₉⋊C₇	C₂×C₃	semidirect
7. C₂×C₂₉×D₁₃⋊C₃	C₇	semidirect
8. C₁₃×C₂₉⋊C₇	C₂²×C₃	semidirect
10. C₂₉×D₁₃⋊C₃	C₂×C₇	semidirect
11. C₂×C₂₉×C₁₃⋊C₃	C₂×C₇	semidirect
12. C₂×D₁₃×C₂₉	C₃×C₇	semidirect
15. C₂₉×C₁₃⋊C₃	C₂²×C₇	semidirect
18. C₂×C₁₃×C₂₉	C₂×C₃×C₇	semidirect
19. D₁₃×C₂₉	C₂×C₃×C₇	semidirect
24. C₂×C₂₉⋊C₇	D₁₃⋊C₃	direct (N × H)
25. C₁₃×C₂₉	C₂²×C₃×C₇	semidirect
29. C₂₉⋊C₇	C₂×D₁₃⋊C₃	direct (N × H)
34. C₂×D₁₃⋊C₃	C₂₉⋊C₇	direct (N × H)
39. C₂×C₁₃⋊C₃	C₂×C₂₉⋊C₇	semidirect
40. D₁₃⋊C₃	C₂×C₂₉⋊C₇	direct (N × H)
42. C₂×C₂₉	C₇×D₁₃⋊C₃	semidirect
43. C₂×D₁₃	C₃×C₂₉⋊C₇	semidirect
46. C₁₃⋊C₃	C₂²×C₂₉⋊C₇	semidirect
47. C₂₉	C₂×C₇×D₁₃⋊C₃	semidirect
49. C₂×C₁₃	C₂×C₃×C₂₉⋊C₇	semidirect
50. D₁₃	C₂×C₃×C₂₉⋊C₇	semidirect
54. C₁₃	C₂²×C₃×C₂₉⋊C₇	semidirect
62. C₂	D₁₃⋊C₃×C₂₉⋊C₇	direct (N × H)

Maximal subgroups

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

subgroup	index
D₁₃⋊C₃×C₂₉⋊C₇	2
C₂×C₁₃⋊C₃×C₂₉⋊C₇	2
C₂×D₁₃×C₂₉⋊C₇	3
C₂×C₂₉×D₁₃⋊C₃	7
C₂²×C₃×C₂₉⋊C₇	13
C₂×C₇×D₁₃⋊C₃	29

Subgroups — C2×D13⋊C3×C29⋊C7 #44539775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃⋊C₃×C₂₉⋊C₇ #44539775