Subgroups — #34093290

Order 19984.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23756088	C₂	1	2	yes	maximal, complemented
2	C₄×D₁₂₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂×D₁₂₄₉	C₄	1	1	yes	characteristic
4	C₄×C₁₂₄₉	C₄	1	1	yes	characteristic
5	Dic₁₂₄₉	C₂²	1	1	yes	characteristic
6	C₂×C₁₂₄₉	C₂×C₄	1	1	yes	characteristic
7	D₁₂₄₉	C₈	1	2	yes	complemented
8	C₁₂₄₉	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₈	—	1249	1	no	maximal, Sylow
10	C₂×C₄	—	1249	1	no	—
11	C₈	—	1249	2	no	—
12	C₂²	—	1249	1	no	—
13	C₄	—	1249	1	no	—
14	C₄	#19097413	1	1	yes	characteristic
15	C₂	—	1249	2	no	—
16	C₂	C₂×#19097413	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.