Subgroups — #35207402

Order 20624.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₁₅₆	C₂	1	1	yes	maximal, characteristic
2	#23780025	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₁₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₂₈₉	—	2	1	no	—
5	C₄×C₁₂₈₉	—	2	1	no	—
6	C₄×C₁₂₈₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₂₈₉	D₄	1	1	yes	characteristic
8	D₁₂₈₉	—	4	1	no	—
9	C₁₂₈₉	SD₁₆	1	1	yes	characteristic, complemented, Sylow
10	SD₁₆	—	1289	1	no	maximal, Sylow
11	Q₈	D₁₂₈₉	1	1	yes	characteristic, complemented
12	D₄	—	1289	1	no	—
13	C₈	—	1289	1	no	—
14	C₂²	—	2578	1	no	—
15	C₄	—	2	1	no	—
16	C₄	C₂×D₁₂₈₉	1	1	yes	characteristic
17	C₂	—	5156	1	no	—
18	C₂	C₂²⋊D₁₂₈₉	1	1	yes	characteristic

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.