Subgroups — D₂₉×D₂₉⋊C₇ #37555412

Order 23548.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₂₉⋊C₇)⋊D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×D₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×C₂₉⋊C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₉²	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂₉⋊D₂₉	C₂×C₇	1	1	yes	characteristic, complemented
7	C₂₉×D₂₉	C₂×C₇	1	1	yes	characteristic, complemented
8	C₂₉×D₂₉	C₂×C₇	1	1	yes	characteristic, complemented
9	C₂₉²	C₂²×C₇	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₇×D₂₉	—	29	1	no	maximal
11	C₂×D₂₉⋊C₇	—	29	1	no	maximal
12	C₂×C₇×C₂₉	—	29	1	no	—
13	C₇×D₂₉	—	29	1	no	—
14	C₇×D₂₉	—	29	1	no	—
15	C₂×C₂₉⋊C₇	—	29	1	no	—
16	D₂₉⋊C₇	—	29	1	no	—
17	D₂₉⋊C₇	D₂₉	1	1	yes	characteristic, direct product factor
18	C₇×C₂₉	—	29	1	no	—
19	C₂₉⋊C₇	C₂×D₂₉	1	1	yes	characteristic, complemented
20	C₂×D₂₉	—	29	1	no	—
21	C₂×D₂₉	—	203	1	no	—
22	C₂×C₂₉	—	29	1	no	—
23	C₂×C₂₉	—	203	1	no	—
24	D₂₉	—	29	1	no	—
25	D₂₉	—	29	1	no	—
26	D₂₉	—	406	2	no	—
27	D₂₉	D₂₉⋊C₇	1	1	yes	characteristic, direct product factor
28	D₂₉	C₇×D₂₉	1	1	yes	characteristic, complemented
29	C₂₉	—	14	2	no	—
30	C₂₉	C₂×D₂₉⋊C₇	1	1	yes	characteristic, complemented
31	C₂₉	C₂×C₇×D₂₉	1	1	yes	characteristic, complemented
32	C₂²×C₇	—	841	1	no	Hall
33	C₂×C₇	—	29	1	no	—
34	C₂×C₇	—	841	1	no	—
35	C₂×C₇	—	841	1	no	—
36	C₇	—	29	1	no	Sylow
37	C₂²	—	5887	1	no	Sylow
38	C₂	—	29	1	no	—
39	C₂	—	203	1	no	—
40	C₂	—	5887	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂₉²	C₂²×C₇
LCS	G ▷ C₂₉²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₂₉×C₂₉⋊C₇	C₂	semidirect
2. (C₂₉⋊C₇)⋊D₂₉	C₂	semidirect
3. C₂₉×D₂₉⋊C₇	C₂	semidirect
4. C₂₉×C₂₉⋊C₇	C₂²	semidirect
5. D₂₉²	C₇	semidirect
6. C₂₉⋊D₂₉	C₂×C₇	semidirect
7. C₂₉×D₂₉	C₂×C₇	semidirect
8. C₂₉×D₂₉	C₂×C₇	semidirect
9. C₂₉²	C₂²×C₇	semidirect
17. D₂₉⋊C₇	D₂₉	direct (N × H)
19. C₂₉⋊C₇	C₂×D₂₉	semidirect
27. D₂₉	D₂₉⋊C₇	direct (N × H)
28. D₂₉	C₇×D₂₉	semidirect
30. C₂₉	C₂×D₂₉⋊C₇	semidirect
31. C₂₉	C₂×C₇×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
D₂₉×C₂₉⋊C₇	2
(C₂₉⋊C₇)⋊D₂₉	2
C₂₉×D₂₉⋊C₇	2
D₂₉²	7
C₂×C₇×D₂₉	29
C₂×D₂₉⋊C₇	29

Subgroups — D29×D29⋊C7 #37555412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉×D₂₉⋊C₇ #37555412