Subgroups — C₂×C₇×C₂₉⋊(D₁₃⋊C₃) #44539884

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	2	yes	maximal, direct product factor
2	C₂×C₇×C₂₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₃₇₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇×C₂₉×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₃₇₇	C₂×C₃	1	2	yes	complemented
6	C₂×C₇×C₁₃×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₂₉⋊(D₁₃⋊C₃)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₁₃×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₇×D₂₉	—	13	1	no	maximal, Hall
10	C₂₉⋊(D₁₃⋊C₃)	C₂×C₇	1	2	yes	direct product factor
11	C₂×C₂₉×C₁₃⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
12	C₂×D₃₇₇	C₃×C₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₇×C₂₉	—	13	1	no	—
14	C₃×C₇×D₂₉	—	13	2	no	—
15	C₂₉×C₁₃⋊C₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇×D₁₃⋊C₃	—	29	1	no	maximal, Hall
17	C₂×C₇×D₂₉	—	13	1	no	Hall
18	C₂×C₁₃×C₂₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
19	D₃₇₇	C₂×C₃×C₇	1	2	yes	complemented
20	C₃×C₇×C₂₉	—	13	1	no	Hall
21	C₂×C₇×C₁₃⋊C₃	D₂₉	1	1	yes	characteristic, complemented
22	C₇×D₁₃⋊C₃	—	29	2	no	—
23	C₂×C₇×C₂₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented
24	C₇×D₂₉	—	13	2	no	—
25	C₁₃×C₂₉	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇×D₁₃	—	29	1	no	Hall
27	C₂×C₃×D₂₉	—	13	1	no	Hall
28	C₇×C₁₃⋊C₃	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
29	C₇×C₂₉	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₇×C₁₃	C₃×D₂₉	1	1	yes	characteristic, complemented
31	C₇×D₁₃	—	29	2	no	—
32	C₂×C₃×C₂₉	—	13	1	no	—
33	C₃×D₂₉	—	13	2	no	—
34	C₂×D₁₃⋊C₃	—	29	1	no	Hall
35	C₂×D₂₉	—	13	1	no	Hall
36	C₇×C₁₃	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
37	C₃×C₂₉	—	13	1	no	Hall
38	C₂²×C₃×C₇	—	377	1	no	Hall
39	C₂×C₁₃⋊C₃	C₇×D₂₉	1	1	yes	characteristic, complemented
40	D₁₃⋊C₃	—	29	2	no	—
41	C₂×C₂₉	C₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented
42	D₂₉	—	13	2	no	—
43	C₂×D₁₃	—	29	1	no	Hall
44	C₂×C₃×C₇	—	13	1	no	—
45	C₂×C₃×C₇	—	377	2	no	—
46	C₁₃⋊C₃	C₂×C₇×D₂₉	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	C₃×C₇×D₂₉	1	1	yes	characteristic, complemented
50	D₁₃	—	29	2	no	—
51	C₃×C₇	—	13	1	no	Hall
52	C₂×C₇	—	377	2	no	—
53	C₂×C₇	C₂₉⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
54	C₁₃	C₂×C₃×C₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₃	—	377	1	no	Hall
56	C₇	C₂×C₂₉⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₃	—	13	1	no	—
58	C₂×C₃	—	377	2	no	—
59	C₂²	—	377	1	no	Sylow
60	C₃	—	13	1	no	Sylow
61	C₂	—	377	2	no	—
62	C₂	C₇×C₂₉⋊(D₁₃⋊C₃)	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₉⋊(D₁₃⋊C₃)	C₂	direct (N × H)
2. C₂×C₇×C₂₉×C₁₃⋊C₃	C₂	semidirect
3. C₂×C₇×D₃₇₇	C₃	semidirect
4. C₇×C₂₉×C₁₃⋊C₃	C₂²	semidirect
5. C₇×D₃₇₇	C₂×C₃	semidirect
6. C₂×C₇×C₁₃×C₂₉	C₂×C₃	semidirect
7. C₂×C₂₉⋊(D₁₃⋊C₃)	C₇	direct (N × H)
8. C₇×C₁₃×C₂₉	C₂²×C₃	semidirect
10. C₂₉⋊(D₁₃⋊C₃)	C₂×C₇	direct (N × H)
11. C₂×C₂₉×C₁₃⋊C₃	C₂×C₇	semidirect
12. C₂×D₃₇₇	C₃×C₇	semidirect
15. C₂₉×C₁₃⋊C₃	C₂²×C₇	semidirect
18. C₂×C₁₃×C₂₉	C₂×C₃×C₇	semidirect
19. D₃₇₇	C₂×C₃×C₇	semidirect
21. C₂×C₇×C₁₃⋊C₃	D₂₉	semidirect
23. C₂×C₇×C₂₉	D₁₃⋊C₃	semidirect
25. C₁₃×C₂₉	C₂²×C₃×C₇	semidirect
28. C₇×C₁₃⋊C₃	C₂×D₂₉	semidirect
29. C₇×C₂₉	C₂×D₁₃⋊C₃	semidirect
30. C₂×C₇×C₁₃	C₃×D₂₉	semidirect
36. C₇×C₁₃	C₂×C₃×D₂₉	semidirect
39. C₂×C₁₃⋊C₃	C₇×D₂₉	semidirect
41. C₂×C₂₉	C₇×D₁₃⋊C₃	semidirect
46. C₁₃⋊C₃	C₂×C₇×D₂₉	semidirect
47. C₂₉	C₂×C₇×D₁₃⋊C₃	semidirect
49. C₂×C₁₃	C₃×C₇×D₂₉	semidirect
53. C₂×C₇	C₂₉⋊(D₁₃⋊C₃)	direct (N × H)
54. C₁₃	C₂×C₃×C₇×D₂₉	semidirect
56. C₇	C₂×C₂₉⋊(D₁₃⋊C₃)	direct (N × H)
62. C₂	C₇×C₂₉⋊(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
C₂×C₇×C₂₉×C₁₃⋊C₃	2
C₂×C₇×D₃₇₇	3
C₂×C₂₉⋊(D₁₃⋊C₃)	7
C₂×C₃×C₇×D₂₉	13
C₂×C₇×D₁₃⋊C₃	29

Subgroups — C2×C7×C29⋊(D13⋊C3) #44539884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₂₉⋊(D₁₃⋊C₃) #44539884