Subgroups — #30632804

Order 16096.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₀₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
2	C₂×C₈×C₅₀₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅₀₃	C₄	1	1	yes	characteristic
4	C₈×C₅₀₃	C₄	1	1	yes	characteristic
5	C₈×C₅₀₃	C₂²	1	1	yes	characteristic
6	C₂²×C₅₀₃	C₈	1	1	yes	characteristic
7	C₄×C₅₀₃	C₈	1	1	yes	characteristic
8	C₄×C₅₀₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₅₀₃	—	2	1	no	—
10	C₂×C₅₀₃	C₂×C₈	1	1	yes	characteristic
11	C₅₀₃	M₃₂	1	1	yes	characteristic, complemented, Sylow
12	M₃₂	—	503	1	no	maximal, Sylow
13	C₂×C₈	D₅₀₃	1	1	yes	characteristic
14	C₁₆	—	503	2	no	—
15	C₂×C₄	Dic₅₀₃	1	1	yes	characteristic
16	C₈	Dic₅₀₃	1	1	yes	characteristic
17	C₈	C₂×D₅₀₃	1	1	yes	characteristic
18	C₂²	C₅₀₃⋊C₈	1	1	yes	characteristic
19	C₄	C₅₀₃⋊C₈	1	1	yes	characteristic
20	C₄	C₂×Dic₅₀₃	1	1	yes	characteristic
21	C₂	—	2	1	no	—
22	C₂	C₂×C₅₀₃⋊C₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. C₅₀₃⋊C₁₆	C₂	semidirect
11. C₅₀₃	M₃₂	semidirect

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