Subgroups — C₅²⋊C₃×D₂₀₃ #44478573

Order 30450.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×D₂₀₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₂₉×C₅²⋊C₃	—	7	1	no	maximal, Hall
5	C₂₉×C₅²⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
6	C₅×D₂₀₃	—	3	2	no	—
7	C₅²×D₂₉	—	7	1	no	Hall
8	C₃×D₂₀₃	—	25	1	no	maximal, Hall
9	D₇×C₅²⋊C₃	—	29	1	no	maximal, Hall
10	C₅×C₇×C₂₉	—	3	2	no	—
11	C₅²×C₂₉	C₃×D₇	1	1	yes	characteristic, complemented, Hall
12	C₃×C₇×C₂₉	—	25	1	no	Hall
13	C₇×C₅²⋊C₃	D₂₉	1	1	yes	characteristic, complemented, Hall
14	D₂₀₃	C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
15	C₅²×D₇	—	29	1	no	Hall
16	C₅×D₂₉	—	21	2	no	—
17	C₇×C₂₉	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₅²×C₇	C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
19	C₃×D₂₉	—	175	1	no	Hall
20	C₂×C₅²⋊C₃	—	203	1	no	Hall
21	C₅×C₂₉	—	3	2	no	—
22	C₃×C₂₉	—	25	1	no	Hall
23	C₅²⋊C₃	D₂₀₃	1	1	yes	characteristic, direct product factor, Hall
24	C₅×D₇	—	87	2	no	—
25	D₂₉	—	7	1	no	Hall
26	C₂×C₅²	—	203	1	no	Hall
27	C₃×D₇	—	725	1	no	Hall
28	C₅×C₇	—	3	2	no	—
29	C₂₉	D₇×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₅²	C₃×D₂₀₃	1	1	yes	characteristic, complemented, Sylow
31	C₃×C₇	—	25	1	no	Hall
32	D₇	—	29	1	no	Hall
33	C₂×C₅	—	609	2	no	—
34	C₇	D₂₉×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃	—	5075	1	no	Hall
36	C₅	—	3	2	no	—
37	C₃	—	25	1	no	Sylow
38	C₂	—	203	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₇×C₂₉	C₂×C₃
LCS	G ▷ C₅²×C₇×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₉×C₅²⋊C₃	C₂	semidirect
2. C₅²×D₂₀₃	C₃	semidirect
3. C₅²×C₇×C₂₉	C₂×C₃	semidirect
5. C₂₉×C₅²⋊C₃	D₇	semidirect
11. C₅²×C₂₉	C₃×D₇	semidirect
13. C₇×C₅²⋊C₃	D₂₉	semidirect
14. D₂₀₃	C₅²⋊C₃	direct (N × H)
17. C₇×C₂₉	C₂×C₅²⋊C₃	semidirect
18. C₅²×C₇	C₃×D₂₉	semidirect
23. C₅²⋊C₃	D₂₀₃	direct (N × H)
29. C₂₉	D₇×C₅²⋊C₃	semidirect
30. C₅²	C₃×D₂₀₃	semidirect
34. C₇	D₂₉×C₅²⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₂₉×C₅²⋊C₃	2
C₅²×D₂₀₃	3
D₂₉×C₅²⋊C₃	7
C₃×D₂₀₃	25
D₇×C₅²⋊C₃	29

Subgroups — C52⋊C3×D203 #44478573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²⋊C₃×D₂₀₃ #44478573