Subgroups — #20258975

Order 6084.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₃×D₃₉	—	6	2	no	—
4	#10621730	—	9	1	no	maximal, Hall
5	C₃×C₁₃²	—	2	2	no	—
6	#90866	—	13	1	no	maximal
7	#90865	—	13	1	no	maximal
8	C₁₃×D₁₃	—	9	1	no	—
9	C₃⋊D₃₉	D₁₃	1	1	yes	characteristic
10	C₁₃×C₃⋊D₃	—	13	1	no	—
11	C₁₃²	#157	1	1	yes	characteristic, complemented, Sylow
12	C₃²×C₁₃	—	4	3	no	—
13	C₃²×C₁₃	Dic₁₃	1	1	yes	characteristic, complemented
14	C₃²×C₁₃	#261	1	1	yes	characteristic, complemented
15	D₃₉	—	6	2	no	—
16	D₃×C₁₃	—	78	2	no	—
17	#261	—	117	1	no	—
18	Dic₁₃	—	117	1	no	—
19	C₃×C₁₃	—	2	2	no	—
20	C₃×C₁₃	—	2	2	no	—
21	C₃×C₁₃	—	4	12	no	—
22	#157	—	169	1	no	Hall
23	C₂×C₁₃	—	117	1	no	—
24	D₁₃	—	9	1	no	—
25	C₃⋊D₃	—	13	1	no	—
26	C₁₃	—	4	3	no	—
27	C₁₃	#90865	1	1	yes	characteristic, complemented
28	C₁₃	#90866	1	1	yes	characteristic, complemented
29	C₃²	#10621730	1	1	yes	characteristic, complemented, Sylow
30	D₃	—	78	2	no	—
31	C₄	—	1521	1	no	Sylow
32	C₃	—	2	2	no	—
33	C₂	—	117	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₃²	C₄
LCS	G ▷ C₃²×C₁₃²
UCS	C₁

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