Subgroups — #30632872

Order 16096.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22548883	C₂	1	1	yes	maximal, characteristic
2	#22548866	C₂	1	2	yes	maximal, complemented
3	C₂×C₅₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₅₀₃	C₂	1	2	yes	maximal, complemented
5	M₁₆×C₅₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₁₀₀₆	C₄	1	1	yes	characteristic
7	D₂₀₁₂	C₄	1	1	yes	characteristic
8	C₂²⋊D₅₀₃	C₄	1	2	yes	—
9	C₄×D₅₀₃	C₂²	1	2	yes	—
10	C₅₀₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₅₀₃⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅₀₃	C₂²	1	1	yes	characteristic
13	C₈×C₅₀₃	C₂²	1	2	yes	—
14	C₂²×C₅₀₃	C₂×C₄	1	1	yes	characteristic
15	C₂×D₅₀₃	C₂×C₄	1	2	yes	—
16	C₄×C₅₀₃	C₂×C₄	1	1	yes	characteristic
17	C₄×C₅₀₃	C₂³	1	1	yes	characteristic
18	Dic₅₀₃	C₂×C₄	1	2	yes	—
19	C₂×C₅₀₃	—	2	1	no	—
20	C₂×C₅₀₃	C₂²×C₄	1	1	yes	characteristic
21	D₅₀₃	—	2	2	no	—
22	C₅₀₃	#131	1	1	yes	characteristic, complemented, Sylow
23	#131	—	503	1	no	maximal, Sylow
24	#41	—	503	1	no	—
25	M₁₆	—	503	2	no	—
26	M₁₆	D₅₀₃	1	1	yes	characteristic, complemented
27	C₂×C₈	—	503	1	no	—
28	C₂×C₈	—	503	2	no	—
29	Q₈	—	503	1	no	—
30	D₄	—	503	2	no	—
31	D₄	—	503	1	no	—
32	C₂×C₄	—	503	2	no	—
33	C₂×C₄	C₂×D₅₀₃	1	1	yes	characteristic
34	C₈	—	503	1	no	—
35	C₈	—	503	1	no	—
36	C₈	C₂×D₅₀₃	1	2	yes	—
37	C₂²	—	503	2	no	—
38	C₂²	C₄×D₅₀₃	1	1	yes	characteristic
39	C₄	—	503	2	no	—
40	C₄	C₄×D₅₀₃	1	1	yes	characteristic
41	C₄	C₂²×D₅₀₃	1	1	yes	characteristic
42	C₂	—	2	1	no	—
43	C₂	—	1006	2	no	—
44	C₂	C₂×C₄×D₅₀₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×D₅₀₃
commutator, socle	C₂×C₅₀₃	C₂²×C₄
Fitting	M₁₆×C₅₀₃	C₂
prime radical	#22548883	C₂
cosocle	C₄×C₅₀₃	C₂³
hypercenter	M₁₆	D₅₀₃
hypocenter	C₅₀₃	#131
LCS	G ▷ C₂×C₅₀₃ ▷ C₅₀₃
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. #22548866	C₂	semidirect
3. C₂×C₅₀₃⋊C₈	C₂	semidirect
4. C₈×D₅₀₃	C₂	semidirect
5. M₁₆×C₅₀₃	C₂	semidirect
22. C₅₀₃	#131	semidirect
26. M₁₆	D₅₀₃	semidirect

Maximal subgroups

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

subgroup	index
#22548883	2
#22548866	2
C₂×C₅₀₃⋊C₈	2
C₈×D₅₀₃	2
M₁₆×C₅₀₃	2
#131	503