Subgroups — #20265001

Order 6464.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692195	C₂	1	1	yes	maximal, characteristic
2	#15692187	C₂	1	1	yes	maximal, characteristic
3	#108×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₁₀₁	—	2	1	no	—
5	#13108049	C₄	1	2	yes	complemented
6	M₁₆×C₁₀₁	—	2	1	no	—
7	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
9	C₂×Dic₁₀₁	—	4	1	no	—
10	C₈×C₁₀₁	—	4	1	no	—
11	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₀₁	Q₈	1	1	yes	characteristic
13	C₂²×C₁₀₁	SD₁₆	1	1	yes	characteristic
14	C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₀₁	SD₁₆	1	1	yes	characteristic
16	Dic₁₀₁	—	8	1	no	—
17	C₂×C₁₀₁	—	2	1	no	—
18	C₂×C₁₀₁	#106	1	1	yes	characteristic
19	C₁₀₁	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	101	1	no	maximal, Sylow
21	M₃₂	—	101	1	no	—
22	#108	D₁₀₁	1	1	yes	characteristic
23	#106	—	101	1	no	—
24	M₁₆	—	2	1	no	—
25	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
26	C₄⋊C₄	—	202	1	no	—
27	C₁₆	—	101	2	no	—
28	C₂×C₄	—	404	1	no	—
29	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
30	C₈	—	4	1	no	—
31	C₈	Dic₂₀₂	1	1	yes	characteristic
32	C₈	C₄×D₁₀₁	1	1	yes	characteristic
33	C₂²	#13108061	1	1	yes	characteristic
34	C₄	—	808	1	no	—
35	C₄	#13108053	1	1	yes	characteristic
36	C₄	#13108062	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#15692186	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. #13108049	C₄	semidirect
19. C₁₀₁	#365	semidirect