Subgroups — #34093261

Order 19984.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₂₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₂₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₂₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₂₄₉	C₂²	1	1	yes	characteristic
5	C₄×C₁₂₄₉	—	2	1	no	—
6	Dic₁₂₄₉	—	2	1	no	—
7	Dic₁₂₄₉	C₄	1	2	yes	complemented
8	C₂×C₁₂₄₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₂₄₉	D₄	1	1	yes	characteristic
10	C₂×C₁₂₄₉	Q₈	1	1	yes	characteristic
11	C₁₂₄₉	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
12	C₄⋊C₄	—	1249	1	no	maximal, Sylow
13	C₂×C₄	—	1249	1	no	—
14	C₂×C₄	—	1249	1	no	—
15	C₂×C₄	D₁₂₄₉	1	1	yes	characteristic
16	C₂²	C₂×D₁₂₄₉	1	1	yes	characteristic
17	C₄	—	2	1	no	—
18	C₄	—	2498	1	no	—
19	C₄	—	1249	2	no	—
20	C₂	C₄×D₁₂₄₉	1	1	yes	characteristic
21	C₂	C₂²⋊D₁₂₄₉	1	1	yes	characteristic
22	C₂	Dic₂₄₉₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. Dic₁₂₄₉	C₄	semidirect
11. C₁₂₄₉	C₄⋊C₄	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.