Subgroups — C₂₅×D₂₆₇ #27211162

Order 13350.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₅×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₅×D₈₉	—	3	1	no	maximal, Hall
3	C₅×D₂₆₇	C₅	1	1	yes	maximal, characteristic
4	C₂₅×C₈₉	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₈₉	C₂×C₅	1	1	yes	characteristic
6	C₅×D₈₉	—	3	1	no	—
7	D₂₆₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₈₉	C₅×D₃	1	1	yes	characteristic
9	C₃×C₈₉	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
10	D₈₉	—	3	1	no	Hall
11	D₃×C₂₅	—	89	1	no	maximal, Hall
12	C₈₉	D₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₂₅	D₈₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₂₅	—	267	1	no	Hall
15	C₅×D₃	—	89	1	no	—
16	C₂₅	D₂₆₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅	C₅×D₈₉	1	1	yes	characteristic
18	C₂×C₅	—	267	1	no	—
19	D₃	—	89	1	no	Hall
20	C₅	C₅×D₂₆₇	1	1	yes	characteristic
21	C₃	C₂₅×D₈₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	267	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.