Subgroups — C₅×C₂₉×Dic₄₉ #43249229

Order 28420.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₉×C₄₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₂₉×C₄₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₉×Dic₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×Dic₇×C₂₉	—	7	1	no	maximal
5	C₂×C₂₉×C₄₉	C₂×C₅	1	1	yes	characteristic
6	C₂×C₅×C₇×C₂₉	D₇	1	1	yes	characteristic
7	C₂₉×C₄₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇×C₂₉	Dic₇	1	1	yes	characteristic
9	C₅×Dic₄₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	Dic₇×C₂₉	—	7	1	no	—
11	C₄×C₅×C₂₉	—	49	1	no	Hall
12	C₂×C₅×C₄₉	C₂×C₂₉	1	1	yes	characteristic
13	C₂×C₇×C₂₉	C₅×D₇	1	1	yes	characteristic
14	C₂×C₅×C₂₉	D₄₉	1	1	yes	characteristic
15	C₅×C₄₉	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
16	C₇×C₂₉	C₅×Dic₇	1	1	yes	characteristic
17	Dic₄₉	C₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₂₉	Dic₄₉	1	1	yes	characteristic, direct product factor, Hall
19	C₅×Dic₇	—	7	1	no	—
20	C₄×C₂₉	—	49	1	no	Hall
21	C₂×C₄₉	C₂×C₅×C₂₉	1	1	yes	characteristic
22	C₂×C₅×C₇	D₇×C₂₉	1	1	yes	characteristic
23	C₂×C₂₉	C₅×D₄₉	1	1	yes	characteristic
24	C₄₉	C₄×C₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
25	C₅×C₇	Dic₇×C₂₉	1	1	yes	characteristic
26	C₂₉	C₅×Dic₄₉	1	1	yes	characteristic, direct product factor, Sylow
27	Dic₇	—	7	1	no	—
28	C₄×C₅	—	49	1	no	Hall
29	C₂×C₇	C₅×D₇×C₂₉	1	1	yes	characteristic
30	C₂×C₅	C₂₉×D₄₉	1	1	yes	characteristic
31	C₇	C₅×Dic₇×C₂₉	1	1	yes	characteristic
32	C₅	C₂₉×Dic₄₉	1	1	yes	characteristic, direct product factor, Sylow
33	C₄	—	49	1	no	Sylow
34	C₂	C₅×C₂₉×D₄₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₂₉	D₄₉
commutator, hypocenter	C₄₉	C₄×C₅×C₂₉
Frattini	C₂×C₇	C₅×D₇×C₂₉
Fitting	C₂×C₅×C₂₉×C₄₉	C₂
socle, prime radical	C₂×C₅×C₇×C₂₉	D₇
cosocle	C₂×C₄₉	C₂×C₅×C₂₉
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₂×C₅×C₂₉

Complements

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

N	H ≅ G/N	type
2. C₅×C₂₉×C₄₉	C₄	semidirect
3. C₂₉×Dic₄₉	C₅	direct (N × H)
7. C₂₉×C₄₉	C₄×C₅	semidirect
9. C₅×Dic₄₉	C₂₉	direct (N × H)
15. C₅×C₄₉	C₄×C₂₉	semidirect
17. Dic₄₉	C₅×C₂₉	direct (N × H)
18. C₅×C₂₉	Dic₄₉	direct (N × H)
24. C₄₉	C₄×C₅×C₂₉	semidirect
26. C₂₉	C₅×Dic₄₉	direct (N × H)
32. C₅	C₂₉×Dic₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₂₉×C₄₉	2
C₂₉×Dic₄₉	5
C₅×Dic₇×C₂₉	7
C₅×Dic₄₉	29

Subgroups — C5×C29×Dic49 #43249229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂₉×Dic₄₉ #43249229