Subgroups — C₂×C₃⋊#1035 #10597057

Order 600.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₂₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#1035	C₂	1	2	yes	maximal, direct product factor
3	C₂×#1035	—	3	1	no	maximal, Hall
4	C₂×C₃×C₂₅	C₄	1	1	yes	characteristic, complemented
5	C₃×D₂₅	C₄	1	1	yes	characteristic, complemented
6	C₃×D₂₅	C₂²	1	1	yes	characteristic
7	C₂×ΓL(1,𝔽₁₆)	—	5	1	no	maximal
8	C₂×D₂₅	D₃	1	1	yes	characteristic
9	#1035	—	3	2	no	—
10	C₃×C₂₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×D₅	—	5	1	no	—
12	ΓL(1,𝔽₁₆)	—	5	2	no	—
13	C₂×C₂₅	Dic₃	1	1	yes	characteristic, complemented
14	D₂₅	Dic₃	1	1	yes	characteristic, complemented
15	D₂₅	C₂×D₃	1	1	yes	characteristic
16	C₂×AGL(1,𝔽₅)	—	15	1	no	—
17	C₂×C₃×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
18	C₃×D₅	—	5	1	no	—
19	C₃×D₅	—	5	1	no	—
20	C₂₅	C₂×Dic₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×Dic₃	—	25	1	no	Hall
22	C₂×D₅	—	5	1	no	—
23	AGL(1,𝔽₅)	—	15	2	no	—
24	C₃×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
25	C₂²×C₃	—	25	1	no	—
26	Dic₃	—	25	2	no	—
27	C₂×C₅	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
28	D₅	—	5	1	no	—
29	D₅	—	5	1	no	—
30	C₂×C₄	—	75	1	no	Sylow
31	C₂×C₃	—	25	1	no	—
32	C₂×C₃	—	25	1	no	—
33	C₂×C₃	#1035	1	1	yes	characteristic, complemented
34	C₅	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
35	C₂²	—	25	1	no	—
36	C₄	—	75	2	no	—
37	C₃	C₂×#1035	1	1	yes	characteristic, complemented, Sylow
38	C₂	—	25	1	no	—
39	C₂	—	25	1	no	—
40	C₂	C₃⋊#1035	1	1	yes	characteristic, direct product factor

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.