Subgroups — C₅²×C₃⋊D₃₉ #19154396

Order 5850.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×D₃₉	—	3	4	no	maximal
3	C₅×C₃⋊D₃₉	C₅	1	6	yes	maximal, direct product factor
4	C₃×C₅²×C₁₃	D₃	1	4	yes	complemented
5	C₅²×D₁₃	—	9	1	no	Hall
6	C₃²×C₅×C₁₃	C₂×C₅	1	6	yes	complemented
7	C₅²×C₃⋊D₃	—	13	1	no	maximal, Hall
8	C₅×D₃₉	—	3	24	no	—
9	C₅²×C₁₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	C₃⋊D₃₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₃²×C₅²	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×C₁₃	C₅×D₃	1	24	yes	complemented
13	C₅²×D₃	—	39	4	no	—
14	C₅×D₁₃	—	9	6	no	—
15	C₃²×C₁₃	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
16	C₅×C₃⋊D₃	—	13	6	no	—
17	D₃₉	—	3	4	no	—
18	C₃×C₅²	D₃₉	1	4	yes	complemented
19	C₅×C₁₃	C₅×C₃⋊D₃	1	6	yes	complemented
20	C₂×C₅²	—	117	1	no	Hall
21	C₃²×C₅	C₅×D₁₃	1	6	yes	complemented
22	C₃×C₁₃	C₅²×D₃	1	4	yes	complemented
23	C₅×D₃	—	39	24	no	—
24	D₁₃	—	9	1	no	Hall
25	C₅²	C₃⋊D₃₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₃⋊D₃	—	13	1	no	Hall
27	C₃×C₅	C₅×D₃₉	1	24	yes	complemented
28	C₁₃	C₅²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅	—	117	6	no	—
30	C₃²	C₅²×D₁₃	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	39	4	no	—
32	C₅	C₅×C₃⋊D₃₉	1	6	yes	direct product factor
33	C₃	C₅²×D₃₉	1	4	yes	complemented
34	C₂	—	117	1	no	Sylow

Splittings G = N ⋊ H with N normal; H ≅ G/N.