Subgroups — C₆₇×D₁₁⋊C₂₅ #49145995

Order 36850.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×C₁₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₁×C₆₇	C₅	1	1	yes	maximal, characteristic
3	C₅×C₁₁×C₆₇	C₂×C₅	1	1	yes	characteristic
4	C₂×C₂₅×C₆₇	—	11	1	no	maximal, Hall
5	C₂₅×C₆₇	—	11	1	no	Hall
6	D₁₁×C₆₇	C₂₅	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₆₇	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅×C₆₇	—	11	1	no	—
9	D₁₁⋊C₂₅	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅×C₆₇	AGL(1,𝔽₁₁)	1	1	yes	characteristic
11	C₁₁⋊C₂₅	C₂×C₆₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₆₇	—	11	1	no	Hall
13	C₅×D₁₁	C₅×C₆₇	1	1	yes	characteristic
14	C₆₇	D₁₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow
15	C₅×C₁₁	C₂×C₅×C₆₇	1	1	yes	characteristic
16	C₂×C₂₅	—	11	1	no	Hall
17	C₂₅	—	11	1	no	Sylow
18	D₁₁	C₂₅×C₆₇	1	1	yes	characteristic, complemented, Hall
19	C₁₁	C₂×C₂₅×C₆₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₅	—	11	1	no	—
21	C₅	C₆₇×AGL(1,𝔽₁₁)	1	1	yes	characteristic
22	C₂	—	11	1	no	Sylow

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.