Subgroups — C₃×AGL(1,𝔽₂₅) #14268372

Order 1800.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#1043⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×#6053	C₃	1	1	yes	maximal, characteristic, complemented
3	AGL(1,𝔽₂₅)	C₃	1	3	yes	maximal, direct product factor
4	C₃×(C₅⋊D₅)⋊C₃	C₄	1	1	yes	characteristic
5	C₃×#1043	C₂×C₃	1	1	yes	characteristic
6	#1043⋊C₃	C₂×C₃	1	3	yes	—
7	C₃×C₅²⋊C₃	C₈	1	1	yes	characteristic, complemented, Hall
8	#6053	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅⋊D₅	C₃×C₄	1	1	yes	characteristic
10	(C₅⋊D₅)⋊C₃	C₃×C₄	1	3	yes	—
11	#1043	C₂×C₃²	1	1	yes	characteristic
12	C₃×C₅²	C₃×C₈	1	1	yes	characteristic, complemented
13	C₅²⋊C₃	C₃×C₈	1	3	yes	complemented
14	C₃²×C₈	—	25	1	no	maximal, Hall
15	C₃×AGL(1,𝔽₅)	—	30	1	no	—
16	C₅⋊D₅	C₃²×C₄	1	1	yes	characteristic
17	C₃²×C₄	—	25	1	no	—
18	C₃×D₅	—	30	1	no	—
19	C₅²	C₃²×C₈	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₈	—	25	3	no	—
21	C₃×C₈	—	25	1	no	—
22	AGL(1,𝔽₅)	—	30	1	no	—
23	C₂×C₃²	—	25	1	no	—
24	C₃×C₅	—	6	1	no	—
25	C₃×C₄	—	25	1	no	—
26	C₃×C₄	—	25	3	no	—
27	D₅	—	30	1	no	—
28	C₃²	—	25	1	no	Sylow
29	C₈	—	25	1	no	Sylow
30	C₂×C₃	—	25	3	no	—
31	C₂×C₃	—	25	1	no	—
32	C₅	—	6	1	no	—
33	C₄	—	25	1	no	—
34	C₃	—	25	3	no	—
35	C₃	AGL(1,𝔽₂₅)	1	1	yes	characteristic, direct product factor
36	C₂	—	25	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.