Subgroups — #20258962

Order 6084.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₃₉	C₂	1	2	yes	maximal, complemented
2	C₃²×C₁₃⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃₉⋊D₁₃	—	3	4	no	maximal
4	C₃²×C₁₃²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₃×D₃₉	—	3	8	no	—
6	C₃×C₁₃⋊D₁₃	D₃	1	4	yes	complemented
7	D₁₃²	—	9	1	no	Hall
8	C₃×C₁₃²	C₂×D₃	1	4	yes	complemented
9	C₃⋊D₃×D₁₃	—	13	2	no	maximal
10	C₁₃⋊D₁₃	C₃⋊D₃	1	1	yes	characteristic, complemented
11	C₁₃×D₁₃	—	9	2	no	—
12	C₃⋊D₃₉	D₁₃	1	2	yes	complemented
13	C₁₃×C₃⋊D₃	—	13	2	no	—
14	C₃²×D₁₃	—	13	2	no	—
15	C₃²×D₁₃	—	26	6	no	—
16	C₁₃²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
17	D₃×D₁₃	—	39	8	no	—
18	C₃²×C₁₃	—	2	6	no	—
19	C₃²×C₁₃	C₂×D₁₃	1	2	yes	complemented
20	D₃₉	—	3	8	no	—
21	C₃×D₁₃	—	13	8	no	—
22	C₃×D₁₃	—	26	24	no	—
23	D₃×C₁₃	—	39	8	no	—
24	C₂×D₁₃	—	117	2	no	—
25	C₃×C₁₃	—	2	24	no	—
26	C₃×C₁₃	D₃×D₁₃	1	8	yes	complemented
27	C₂×C₃⋊D₃	—	169	1	no	Hall
28	C₂×C₁₃	—	117	2	no	—
29	D₁₃	—	9	2	no	—
30	D₁₃	—	13	2	no	—
31	D₁₃	—	26	6	no	—
32	C₂×C₃²	—	169	1	no	—
33	C₃⋊D₃	—	13	2	no	—
34	C₁₃	—	2	6	no	—
35	C₁₃	C₃⋊D₃×D₁₃	1	2	yes	complemented
36	C₂×D₃	—	507	4	no	—
37	C₃²	D₁₃²	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃	—	169	4	no	—
39	D₃	—	39	8	no	—
40	C₂²	—	1521	1	no	Sylow
41	C₃	D₃₉⋊D₁₃	1	4	yes	complemented
42	C₂	—	117	2	no	—
43	C₂	—	169	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₃²	C₂²
LCS	G ▷ C₃²×C₁₃²
UCS	C₁

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