Subgroups — C₅×#16841025 #34087191

Order 19620.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₃₂₇	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅×C₁₀₉	C₄	1	1	yes	characteristic, complemented, Hall
3	#16841025	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×D₃₂₇	—	6	2	no	—
5	C₅×#89137	—	9	1	no	maximal, Hall
6	C₃⋊D₃₂₇	C₂×C₅	1	1	yes	characteristic
7	C₃×C₅×C₁₀₉	—	2	2	no	—
8	C₅×D₁₀₉	—	9	1	no	—
9	C₃²×C₁₀₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
10	D₃₂₇	—	6	2	no	—
11	C₅×C₁₀₉	#157	1	1	yes	characteristic, complemented, Hall
12	#89137	—	9	1	no	Hall
13	C₃×C₁₀₉	—	2	2	no	—
14	D₁₀₉	—	9	1	no	—
15	C₅×#157	—	109	1	no	maximal, Hall
16	C₁₀₉	C₅×#157	1	1	yes	characteristic, complemented, Sylow
17	C₅×C₃⋊D₃	—	109	1	no	—
18	C₃²×C₅	#89137	1	1	yes	characteristic, complemented, Hall
19	#157	—	109	1	no	Hall
20	C₅×D₃	—	654	2	no	—
21	C₄×C₅	—	981	1	no	Hall
22	C₃⋊D₃	—	109	1	no	—
23	C₃×C₅	—	2	2	no	—
24	C₂×C₅	—	981	1	no	—
25	C₃²	C₅×#89137	1	1	yes	characteristic, complemented, Sylow
26	D₃	—	654	2	no	—
27	C₅	#16841025	1	1	yes	characteristic, direct product factor, Sylow
28	C₄	—	981	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	981	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.