Subgroups — ((C₁₃⋊C₃)⋊D₇)⋊D₂₉ #44539879

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	C₁₃⋊C₃×D₂₀₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂₉⋊(D₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₉₁⋊D₂₉	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×D₂₀₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₃₇₇	C₂×C₃	1	1	yes	characteristic, complemented
9	D₂₉×D₁₃⋊C₃	—	7	1	no	maximal, Hall
10	C₇×C₁₃×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₃×D₇×D₂₉	—	13	1	no	maximal, Hall
12	C₂₉⋊(D₁₃⋊C₃)	D₇	1	1	yes	characteristic, complemented
13	C₂₉×D₁₃⋊C₃	—	7	1	no	—
14	C₁₃⋊C₃×D₂₉	—	7	1	no	—
15	D₁₃×D₂₉	—	7	1	no	Hall
16	C₃×D₂₀₃	—	13	1	no	—
17	C₃×D₇×C₂₉	—	13	1	no	—
18	C₃×C₇×D₂₉	—	13	1	no	—
19	C₂₉×C₁₃⋊C₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
20	D₇×D₁₃⋊C₃	—	29	1	no	maximal, Hall
21	D₇×D₂₉	—	13	1	no	Hall
22	D₃₇₇	C₃×D₇	1	1	yes	characteristic, complemented
23	C₁₃×D₂₉	—	7	1	no	—
24	D₁₃×C₂₉	—	7	1	no	—
25	C₃×C₇×C₂₉	—	13	1	no	Hall
26	(C₁₃⋊C₃)⋊D₇	D₂₉	1	1	yes	characteristic, complemented
27	D₇×C₁₃⋊C₃	—	29	1	no	—
28	C₇×D₁₃⋊C₃	—	29	1	no	—
29	D₂₀₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented
30	C₇×D₂₉	—	13	1	no	—
31	D₇×C₂₉	—	13	1	no	—
32	C₁₃×C₂₉	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
33	D₇×D₁₃	—	29	1	no	Hall
34	C₂×C₃×D₂₉	—	91	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	D₉₁	C₃×D₂₉	1	1	yes	characteristic, complemented
38	C₇×D₁₃	—	29	1	no	—
39	C₁₃×D₇	—	29	1	no	—
40	C₂×C₃×C₂₉	—	91	1	no	—
41	C₃×D₂₉	—	13	1	no	—
42	C₃×D₂₉	—	91	1	no	—
43	C₂×D₁₃⋊C₃	—	203	1	no	Hall
44	C₂×D₂₉	—	91	1	no	Hall
45	C₇×C₁₃	C₂×C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
46	C₃×C₂₉	—	13	1	no	Hall
47	C₂×C₃×D₇	—	377	1	no	Hall
48	C₂×C₁₃⋊C₃	—	203	1	no	—
49	D₁₃⋊C₃	—	7	1	no	—
50	D₁₃⋊C₃	—	29	1	no	—
51	C₂×C₂₉	—	91	1	no	—
52	D₂₉	—	7	1	no	—
53	D₂₉	—	13	1	no	—
54	C₂×D₁₃	—	203	1	no	Hall
55	C₂×C₃×C₇	—	377	1	no	—
56	C₃×D₇	—	13	1	no	—
57	C₃×D₇	—	377	1	no	—
58	C₁₃⋊C₃	D₇×D₂₉	1	1	yes	characteristic, complemented, Hall
59	C₂₉	D₇×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
60	C₂×D₇	—	377	1	no	Hall
61	C₂×C₁₃	—	203	1	no	—
62	D₁₃	—	7	1	no	—
63	D₁₃	—	29	1	no	—
64	C₃×C₇	—	13	1	no	Hall
65	C₂×C₇	—	377	1	no	—
66	D₇	—	13	1	no	—
67	D₇	—	29	1	no	—
68	C₁₃	C₃×D₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₃	—	2639	1	no	Hall
70	C₇	D₂₉×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₃	—	2639	1	no	—
72	C₂×C₃	—	91	1	no	—
73	C₂×C₃	—	377	1	no	—
74	C₂²	—	2639	1	no	Sylow
75	C₃	—	13	1	no	Sylow
76	C₂	—	91	1	no	—
77	C₂	—	377	1	no	—
78	C₂	—	203	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₂₉×(C₁₃⋊C₃)⋊D₇	C₂	semidirect
2. C₁₃⋊C₃×D₂₀₃	C₂	semidirect
3. C₇×C₂₉⋊(D₁₃⋊C₃)	C₂	semidirect
4. D₉₁⋊D₂₉	C₃	semidirect
5. C₇×C₂₉×C₁₃⋊C₃	C₂²	semidirect
6. C₂₉×D₉₁	C₂×C₃	semidirect
7. C₁₃×D₂₀₃	C₂×C₃	semidirect
8. C₇×D₃₇₇	C₂×C₃	semidirect
10. C₇×C₁₃×C₂₉	C₂²×C₃	semidirect
12. C₂₉⋊(D₁₃⋊C₃)	D₇	semidirect
19. C₂₉×C₁₃⋊C₃	C₂×D₇	semidirect
22. D₃₇₇	C₃×D₇	semidirect
26. (C₁₃⋊C₃)⋊D₇	D₂₉	semidirect
29. D₂₀₃	D₁₃⋊C₃	semidirect
32. C₁₃×C₂₉	C₂×C₃×D₇	semidirect
35. C₇×C₁₃⋊C₃	C₂×D₂₉	semidirect
36. C₇×C₂₉	C₂×D₁₃⋊C₃	semidirect
37. D₉₁	C₃×D₂₉	semidirect
45. C₇×C₁₃	C₂×C₃×D₂₉	semidirect
58. C₁₃⋊C₃	D₇×D₂₉	semidirect
59. C₂₉	D₇×D₁₃⋊C₃	semidirect
68. C₁₃	C₃×D₇×D₂₉	semidirect
70. C₇	D₂₉×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
C₁₃⋊C₃×D₂₀₃	2
C₇×C₂₉⋊(D₁₃⋊C₃)	2
D₉₁⋊D₂₉	3
D₂₉×D₁₃⋊C₃	7
C₃×D₇×D₂₉	13
D₇×D₁₃⋊C₃	29

Subgroups — ((C13⋊C3)⋊D7)⋊D29 #44539879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — ((C₁₃⋊C₃)⋊D₇)⋊D₂₉ #44539879