Subgroups — C₁₃×#157×C₅₉ #42120237

Order 27612.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₃×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₃×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₁₃×C₅₉	—	6	2	no	—
4	C₄×C₁₃×C₅₉	—	9	1	no	maximal, Hall
5	C₃×C₁₃×C₅₉	—	2	2	no	—
6	#157×C₅₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₃×C₅₉	—	9	1	no	—
8	C₃⋊D₃×C₅₉	C₂×C₁₃	1	1	yes	characteristic
9	C₁₃×C₅₉	#157	1	1	yes	characteristic, direct product factor, Hall
10	C₃²×C₅₉	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
11	C₁₃×#157	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	D₃×C₅₉	—	6	2	no	—
13	C₄×C₅₉	—	9	1	no	Hall
14	C₁₃×C₃⋊D₃	C₂×C₅₉	1	1	yes	characteristic
15	C₃×C₅₉	—	2	2	no	—
16	C₂×C₅₉	—	9	1	no	—
17	C₃²×C₁₃	C₄×C₅₉	1	1	yes	characteristic, complemented, Hall
18	D₃×C₁₃	—	6	2	no	—
19	C₅₉	C₁₃×#157	1	1	yes	characteristic, direct product factor, Sylow
20	C₄×C₁₃	—	9	1	no	Hall
21	C₃×C₁₃	—	2	2	no	—
22	#157	C₁₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₃	—	9	1	no	—
24	C₃⋊D₃	C₂×C₁₃×C₅₉	1	1	yes	characteristic
25	C₁₃	#157×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₃²	C₄×C₁₃×C₅₉	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	6	2	no	—
28	C₄	—	9	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	9	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.