Subgroups — #20265557

Order 6464.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₀₄	C₂	1	4	yes	maximal
2	#15692255	C₂	1	2	yes	maximal
3	C₄×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₀₂	C₂²	1	4	yes	—
5	Dic₄₀₄	—	2	8	no	—
6	C₄⋊Dic₁₀₁	—	2	4	no	—
7	C₂×C₈×C₁₀₁	C₂²	1	2	yes	—
8	C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₀₁	D₄	1	2	yes	—
10	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
11	C₂×Dic₁₀₁	—	2	4	no	—
12	Dic₂₀₂	—	2	8	no	—
13	C₈×C₁₀₁	D₄	1	4	yes	—
14	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
15	C₄×C₁₀₁	Q₁₆	1	4	yes	complemented
16	C₄×C₁₀₁	C₂×D₄	1	2	yes	—
17	Dic₁₀₁	—	4	4	no	—
18	C₂×C₁₀₁	#127	1	1	yes	characteristic
19	C₂×C₁₀₁	C₂×Q₁₆	1	2	yes	—
20	C₁₀₁	#494	1	1	yes	characteristic, complemented, Sylow
21	#494	—	101	1	no	maximal, Sylow
22	C₂×Q₁₆	—	101	4	no	—
23	C₄⋊Q₈	—	101	2	no	—
24	C₄×C₈	D₁₀₁	1	1	yes	characteristic
25	C₂×Q₈	—	101	4	no	—
26	Q₁₆	—	202	8	no	—
27	C₂×C₈	C₂×D₁₀₁	1	2	yes	—
28	C₄⋊C₄	—	202	4	no	—
29	C₄²	C₂×D₁₀₁	1	1	yes	characteristic
30	Q₈	—	202	8	no	—
31	C₂×C₄	—	202	4	no	—
32	C₂×C₄	D₄₀₄	1	2	yes	—
33	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
34	C₈	D₄₀₄	1	4	yes	—
35	C₂²	C₂×D₄₀₄	1	1	yes	characteristic
36	C₄	—	404	4	no	—
37	C₄	Dic₄₀₄	1	4	yes	complemented
38	C₄	C₂×D₄₀₄	1	2	yes	—
39	C₂	#15692252	1	1	yes	characteristic
40	C₂	C₂×Dic₄₀₄	1	2	yes	—

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