Subgroups — C₅×(C₇⋊D₇)⋊D₂₉ #43249332

Order 28420.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₂₀₃	C₂	1	2	yes	maximal, complemented
2	C₅×C₂₉×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇²×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	(C₇⋊D₇)⋊D₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×D₇×D₂₉	—	7	2	no	maximal
6	C₂₉×C₇⋊D₇	C₂×C₅	1	1	yes	characteristic, complemented
7	C₇×D₂₀₃	C₂×C₅	1	2	yes	complemented
8	C₅×D₂₀₃	D₇	1	2	yes	complemented
9	C₅×D₇×C₂₉	—	7	2	no	—
10	C₅×D₇×C₂₉	—	14	3	no	—
11	C₅×C₇×D₂₉	—	7	2	no	—
12	C₇²×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
13	C₅×C₇×C₂₉	—	2	3	no	—
14	C₅×C₇×C₂₉	C₂×D₇	1	2	yes	complemented
15	C₅×D₇²	—	29	1	no	maximal, Hall
16	D₇×D₂₉	—	7	2	no	—
17	C₂×C₅×D₂₉	—	49	1	no	Hall
18	C₅×C₇⋊D₇	D₂₉	1	1	yes	characteristic, complemented
19	C₅×C₇×D₇	—	29	2	no	—
20	D₂₀₃	C₅×D₇	1	2	yes	complemented
21	C₇×D₂₉	—	7	2	no	—
22	D₇×C₂₉	—	7	2	no	—
23	D₇×C₂₉	—	14	3	no	—
24	C₂×C₅×C₂₉	—	49	1	no	—
25	C₅×D₂₉	—	7	2	no	—
26	C₅×C₇²	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
27	C₇×C₂₉	—	2	3	no	—
28	C₇×C₂₉	C₂×C₅×D₇	1	2	yes	complemented
29	D₇²	—	29	1	no	Hall
30	C₅×C₂₉	D₇²	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅×D₇	—	203	2	no	—
32	C₂×D₂₉	—	49	1	no	Hall
33	C₇⋊D₇	C₅×D₂₉	1	1	yes	characteristic, complemented
34	C₇×D₇	—	29	2	no	—
35	C₂×C₅×C₇	—	203	2	no	—
36	C₅×D₇	—	7	2	no	—
37	C₅×D₇	—	14	3	no	—
38	C₅×D₇	—	29	2	no	—
39	C₂×C₂₉	—	49	1	no	—
40	D₂₉	—	7	2	no	—
41	C₇²	C₂×C₅×D₂₉	1	1	yes	characteristic, complemented, Sylow
42	C₅×C₇	—	2	3	no	—
43	C₅×C₇	D₇×D₂₉	1	2	yes	complemented
44	C₂₉	C₅×D₇²	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₇	—	203	2	no	—
46	C₂²×C₅	—	1421	1	no	Hall
47	C₂×C₇	—	203	2	no	—
48	D₇	—	7	2	no	—
49	D₇	—	14	3	no	—
50	D₇	—	29	2	no	—
51	C₂×C₅	—	49	1	no	—
52	C₂×C₅	—	203	2	no	—
53	C₇	—	2	3	no	—
54	C₇	C₅×D₇×D₂₉	1	2	yes	complemented
55	C₅	(C₇⋊D₇)⋊D₂₉	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²	—	1421	1	no	Sylow
57	C₂	—	49	1	no	—
58	C₂	—	203	2	no	—

	subgroup	G/H
center, hypercenter	C₅	(C₇⋊D₇)⋊D₂₉
commutator, cosocle, hypocenter	C₇²×C₂₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₂₉	C₂²
LCS	G ▷ C₇²×C₂₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₂₀₃	C₂	semidirect
2. C₅×C₂₉×C₇⋊D₇	C₂	semidirect
3. C₅×C₇²×C₂₉	C₂²	semidirect
4. (C₇⋊D₇)⋊D₂₉	C₅	direct (N × H)
6. C₂₉×C₇⋊D₇	C₂×C₅	semidirect
7. C₇×D₂₀₃	C₂×C₅	semidirect
8. C₅×D₂₀₃	D₇	semidirect
12. C₇²×C₂₉	C₂²×C₅	semidirect
14. C₅×C₇×C₂₉	C₂×D₇	semidirect
18. C₅×C₇⋊D₇	D₂₉	semidirect
20. D₂₀₃	C₅×D₇	semidirect
26. C₅×C₇²	C₂×D₂₉	semidirect
28. C₇×C₂₉	C₂×C₅×D₇	semidirect
30. C₅×C₂₉	D₇²	semidirect
33. C₇⋊D₇	C₅×D₂₉	semidirect
41. C₇²	C₂×C₅×D₂₉	semidirect
43. C₅×C₇	D₇×D₂₉	semidirect
44. C₂₉	C₅×D₇²	semidirect
54. C₇	C₅×D₇×D₂₉	semidirect
55. C₅	(C₇⋊D₇)⋊D₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×D₂₀₃	2
C₅×C₂₉×C₇⋊D₇	2
(C₇⋊D₇)⋊D₂₉	5
C₅×D₇×D₂₉	7
C₅×D₇²	29

Subgroups — C5×(C7⋊D7)⋊D29 #43249332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×(C₇⋊D₇)⋊D₂₉ #43249332