Subgroups — #44566002

Order 32192.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅₀₃⋊C₈	C₂	1	2	yes	maximal
2	C₄×C₈×C₅₀₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₀₃⋊C₈	C₄	1	4	yes	—
4	C₂×C₈×C₅₀₃	C₄	1	2	yes	—
5	C₄²×C₅₀₃	C₂²	1	1	yes	characteristic
6	C₅₀₃⋊C₈	—	2	4	no	—
7	C₂×C₄×C₅₀₃	C₂×C₄	1	2	yes	—
8	C₂×C₄×C₅₀₃	C₂×C₄	1	1	yes	characteristic
9	C₈×C₅₀₃	C₈	1	4	yes	complemented
10	C₂²×C₅₀₃	C₄²	1	1	yes	characteristic
11	C₄×C₅₀₃	C₂×C₈	1	2	yes	—
12	C₄×C₅₀₃	M₁₆	1	4	yes	—
13	C₂×C₅₀₃	C₄×C₈	1	1	yes	characteristic
14	C₂×C₅₀₃	#97	1	2	yes	—
15	C₅₀₃	#322	1	1	yes	characteristic, complemented, Sylow
16	#322	—	503	1	no	maximal, Sylow
17	C₄×C₈	—	503	2	no	—
18	C₄×C₈	D₅₀₃	1	1	yes	characteristic
19	C₂×C₈	—	503	4	no	—
20	C₂×C₈	Dic₅₀₃	1	2	yes	—
21	C₄²	C₂×D₅₀₃	1	1	yes	characteristic
22	C₂×C₄	C₄×D₅₀₃	1	2	yes	—
23	C₂×C₄	C₂×Dic₅₀₃	1	1	yes	characteristic
24	C₈	—	1006	4	no	—
25	C₈	C₅₀₃⋊C₈	1	4	yes	complemented
26	C₂²	C₄×Dic₅₀₃	1	1	yes	characteristic
27	C₄	C₂×C₅₀₃⋊C₈	1	2	yes	—
28	C₄	#22548866	1	4	yes	—
29	C₂	C₄×C₅₀₃⋊C₈	1	1	yes	characteristic
30	C₂	#30632774	1	2	yes	—

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

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