Subgroups — C₂₅×C₂²⋊(C₄₃⋊C₃) #27166364

Order 12900.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₅×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₅×C₄₃⋊C₃	—	4	1	no	maximal, Hall
3	C₅×C₂²⋊(C₄₃⋊C₃)	C₅	1	1	yes	maximal, characteristic
4	C₂×C₂₅×C₄₃	—	3	1	no	—
5	C₂₅×C₄₃	A₄	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₅×C₄₃	C₃×C₅	1	1	yes	characteristic
7	C₅×C₄₃⋊C₃	—	4	1	no	—
8	C₂²⋊(C₄₃⋊C₃)	C₂₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₄₃	—	3	1	no	—
10	A₄×C₂₅	—	43	1	no	maximal, Hall
11	C₅×C₄₃	C₅×A₄	1	1	yes	characteristic
12	C₂²×C₄₃	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
13	C₄₃⋊C₃	—	4	1	no	Hall
14	C₂²×C₂₅	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₄₃	—	3	1	no	—
16	C₃×C₂₅	—	172	1	no	Hall
17	C₅×A₄	—	43	1	no	—
18	C₂×C₂₅	—	3	1	no	—
19	C₄₃	A₄×C₂₅	1	1	yes	characteristic, complemented, Sylow
20	C₂₅	C₂²⋊(C₄₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
21	C₂²×C₅	C₅×C₄₃⋊C₃	1	1	yes	characteristic
22	C₃×C₅	—	172	1	no	—
23	A₄	—	43	1	no	Hall
24	C₂×C₅	—	3	1	no	—
25	C₅	C₅×C₂²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
26	C₂²	C₂₅×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	172	1	no	Sylow
28	C₂	—	3	1	no	—

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.