Subgroups — D₁₃×C₃⋊(D₂₉⋊C₇) #44539792

Order 31668.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₁₃⋊(D₂₉⋊C₇))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₃⋊(D₂₉⋊C₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₃×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₂₉⋊C₇	—	3	1	no	maximal, Hall
5	C₃×C₁₃×C₂₉⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₃⋊(D₂₉⋊C₇)	—	3	1	no	—
7	D₁₃×C₂₉⋊C₇	D₃	1	1	yes	characteristic, complemented
8	C₁₃×D₂₉⋊C₇	—	3	1	no	—
9	D₁₃×D₈₇	C₇	1	1	yes	maximal, characteristic, complemented, Hall
10	C₁₃×C₂₉⋊C₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃⋊(D₂₉⋊C₇)	—	13	1	no	maximal, Hall
12	D₁₁₃₁	C₂×C₇	1	1	yes	characteristic, complemented
13	C₁₃×D₈₇	C₂×C₇	1	1	yes	characteristic, complemented
14	C₃×D₁₃×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
15	D₁₃×D₂₉	—	3	1	no	Hall
16	C₂×C₃×C₂₉⋊C₇	—	13	1	no	—
17	C₃⋊(D₂₉⋊C₇)	—	13	1	no	—
18	C₃⋊(D₂₉⋊C₇)	D₁₃	1	1	yes	characteristic, direct product factor
19	C₃×C₁₃×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
20	D₃×C₇×D₁₃	—	29	1	no	maximal, Hall
21	C₂×D₂₉⋊C₇	—	39	1	no	Hall
22	D₃₇₇	—	3	1	no	—
23	C₁₃×D₂₉	—	3	1	no	—
24	D₁₃×C₂₉	D₃×C₇	1	1	yes	characteristic, complemented
25	C₃×C₂₉⋊C₇	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
26	C₇×D₃₉	—	29	1	no	—
27	D₃×C₇×C₁₃	—	29	1	no	—
28	C₃×C₇×D₁₃	—	29	1	no	—
29	C₂×C₂₉⋊C₇	—	13	1	no	—
30	D₂₉⋊C₇	—	3	1	no	—
31	D₂₉⋊C₇	—	39	1	no	—
32	C₁₃×C₂₉	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₇×D₁₃	—	87	1	no	Hall
34	C₂×D₈₇	—	13	1	no	Hall
35	C₃×C₇×C₁₃	—	29	1	no	Hall
36	C₂₉⋊C₇	D₃×D₁₃	1	1	yes	characteristic, complemented, Hall
37	C₂×C₇×C₁₃	—	87	1	no	—
38	C₇×D₁₃	—	29	1	no	—
39	C₇×D₁₃	—	87	1	no	—
40	C₂×C₃×C₂₉	—	13	1	no	—
41	D₈₇	—	13	1	no	—
42	D₈₇	C₇×D₁₃	1	1	yes	characteristic, complemented
43	D₃×D₁₃	—	29	1	no	Hall
44	C₂×D₂₉	—	39	1	no	Hall
45	C₇×C₁₃	—	29	1	no	Hall
46	C₃×C₂₉	C₂×C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
47	C₂×D₃×C₇	—	377	1	no	Hall
48	D₃₉	—	29	1	no	—
49	C₃×D₁₃	D₂₉⋊C₇	1	1	yes	characteristic, complemented
50	D₃×C₁₃	—	29	1	no	—
51	C₂×C₂₉	—	13	1	no	—
52	D₂₉	—	3	1	no	—
53	D₂₉	—	39	1	no	—
54	C₂×D₁₃	—	87	1	no	Hall
55	C₂×C₃×C₇	—	377	1	no	—
56	D₃×C₇	—	29	1	no	—
57	D₃×C₇	—	377	1	no	—
58	C₃×C₁₃	C₂×D₂₉⋊C₇	1	1	yes	characteristic, complemented, Hall
59	C₂₉	D₃×C₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₇	—	1131	1	no	Hall
61	C₂×C₁₃	—	87	1	no	—
62	D₁₃	—	87	1	no	—
63	D₁₃	C₃⋊(D₂₉⋊C₇)	1	1	yes	characteristic, direct product factor
64	C₃×C₇	—	29	1	no	Hall
65	C₂×C₇	—	87	1	no	—
66	C₂×C₇	—	1131	1	no	—
67	C₂×C₇	—	377	1	no	—
68	C₁₃	C₂×C₃⋊(D₂₉⋊C₇)	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	377	1	no	Hall
70	C₇	—	29	1	no	Sylow
71	C₂×C₃	—	13	1	no	—
72	D₃	—	29	1	no	—
73	D₃	—	377	1	no	—
74	C₂²	—	1131	1	no	Sylow
75	C₃	D₁₃×D₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	13	1	no	—
77	C₂	—	87	1	no	—
78	C₂	—	1131	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₁₃⋊(D₂₉⋊C₇))	C₂	semidirect
2. C₁₃×C₃⋊(D₂₉⋊C₇)	C₂	semidirect
3. C₃×D₁₃×C₂₉⋊C₇	C₂	semidirect
5. C₃×C₁₃×C₂₉⋊C₇	C₂²	semidirect
7. D₁₃×C₂₉⋊C₇	D₃	semidirect
9. D₁₃×D₈₇	C₇	semidirect
10. C₁₃×C₂₉⋊C₇	C₂×D₃	semidirect
12. D₁₁₃₁	C₂×C₇	semidirect
13. C₁₃×D₈₇	C₂×C₇	semidirect
14. C₃×D₁₃×C₂₉	C₂×C₇	semidirect
18. C₃⋊(D₂₉⋊C₇)	D₁₃	direct (N × H)
19. C₃×C₁₃×C₂₉	C₂²×C₇	semidirect
24. D₁₃×C₂₉	D₃×C₇	semidirect
25. C₃×C₂₉⋊C₇	C₂×D₁₃	semidirect
32. C₁₃×C₂₉	C₂×D₃×C₇	semidirect
36. C₂₉⋊C₇	D₃×D₁₃	semidirect
42. D₈₇	C₇×D₁₃	semidirect
46. C₃×C₂₉	C₂×C₇×D₁₃	semidirect
49. C₃×D₁₃	D₂₉⋊C₇	semidirect
58. C₃×C₁₃	C₂×D₂₉⋊C₇	semidirect
59. C₂₉	D₃×C₇×D₁₃	semidirect
63. D₁₃	C₃⋊(D₂₉⋊C₇)	direct (N × H)
68. C₁₃	C₂×C₃⋊(D₂₉⋊C₇)	semidirect
75. C₃	D₁₃×D₂₉⋊C₇	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₁₃⋊(D₂₉⋊C₇))	2
C₁₃×C₃⋊(D₂₉⋊C₇)	2
C₃×D₁₃×C₂₉⋊C₇	2
D₁₃×D₂₉⋊C₇	3
D₁₃×D₈₇	7
C₂×C₃⋊(D₂₉⋊C₇)	13
D₃×C₇×D₁₃	29

Subgroups — D13×C3⋊(D29⋊C7) #44539792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×C₃⋊(D₂₉⋊C₇) #44539792