Subgroups — D₄×D₁₂₈₉ #35207409

Order 20624.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₂₈₉	C₂	1	2	yes	maximal, complemented
2	D₅₁₅₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊D₁₂₈₉	C₂	1	2	yes	maximal, complemented
4	C₄×D₁₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₁₂₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₂₈₉	C₂²	1	2	yes	complemented
7	C₂×D₁₂₈₉	—	2	4	no	—
8	C₂×D₁₂₈₉	C₂²	1	1	yes	characteristic
9	C₂×D₁₂₈₉	C₂²	1	2	yes	complemented
10	C₄×C₁₂₈₉	C₂²	1	1	yes	characteristic, complemented
11	Dic₁₂₈₉	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₁₂₈₉	—	2	2	no	—
13	C₂×C₁₂₈₉	C₂³	1	1	yes	characteristic
14	D₁₂₈₉	—	2	2	no	—
15	D₁₂₈₉	D₄	1	2	yes	direct product factor
16	C₁₂₈₉	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
17	C₂×D₄	—	1289	1	no	maximal, Sylow
18	C₂³	—	1289	2	no	—
19	D₄	—	1289	2	no	—
20	D₄	—	1289	1	no	—
21	D₄	D₁₂₈₉	1	1	yes	characteristic, direct product factor
22	C₂×C₄	—	1289	1	no	—
23	C₂²	—	1289	1	no	—
24	C₂²	—	1289	2	no	—
25	C₂²	—	2578	4	no	—
26	C₂²	C₂×D₁₂₈₉	1	2	yes	complemented
27	C₄	—	1289	1	no	—
28	C₄	C₂×D₁₂₈₉	1	1	yes	characteristic, complemented
29	C₂	—	2	2	no	—
30	C₂	—	1289	2	no	—
31	C₂	—	2578	2	no	—
32	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.