Subgroups — C₆₄×D₆₁ #21444027

Order 7808.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₂×D₆₁	C₂	1	1	yes	maximal, characteristic
2	#16839481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₆₁	C₄	1	1	yes	characteristic
5	#14519683	C₄	1	1	yes	characteristic
6	C₃₂×C₆₁	C₂²	1	1	yes	characteristic
7	C₈×D₆₁	C₈	1	1	yes	characteristic
8	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
9	#11758185	C₈	1	1	yes	characteristic
10	C₄×D₆₁	C₁₆	1	1	yes	characteristic
11	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
12	#92418	C₁₆	1	1	yes	characteristic
13	C₂×D₆₁	C₃₂	1	1	yes	characteristic
14	C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
15	Dic₆₁	C₃₂	1	1	yes	characteristic
16	C₂×C₆₄	—	61	1	no	maximal, Sylow
17	C₂×C₆₁	C₂×C₃₂	1	1	yes	characteristic
18	D₆₁	C₆₄	1	2	yes	direct product factor
19	C₂×C₃₂	—	61	1	no	—
20	C₆₄	—	61	1	no	—
21	C₆₄	D₆₁	1	1	yes	characteristic, direct product factor
22	C₆₁	C₂×C₆₄	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	—	61	1	no	—
24	C₃₂	—	61	1	no	—
25	C₃₂	C₂×D₆₁	1	1	yes	characteristic
26	C₂×C₈	—	61	1	no	—
27	C₁₆	—	61	1	no	—
28	C₁₆	C₄×D₆₁	1	1	yes	characteristic
29	C₂×C₄	—	61	1	no	—
30	C₈	—	61	1	no	—
31	C₈	C₈×D₆₁	1	1	yes	characteristic
32	C₂²	—	61	1	no	—
33	C₄	—	61	1	no	—
34	C₄	C₁₆×D₆₁	1	1	yes	characteristic
35	C₂	—	61	2	no	—
36	C₂	C₃₂×D₆₁	1	1	yes	characteristic

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