Subgroups — C₂×C₃×D₆₁₃⋊C₃ #36348192

Order 22068.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₆₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₆₁₃⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₆₁₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×D₆₁₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₆₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₆₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×D₆₁₃	C₂×C₃	1	2	yes	complemented
8	C₂×C₆₁₃⋊C₃	C₂×C₃	1	3	yes	complemented
9	D₆₁₃⋊C₃	C₂×C₃	1	6	yes	direct product factor
10	C₂×D₆₁₃	C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×C₆₁₃	C₂²×C₃	1	1	yes	characteristic, complemented
12	C₆₁₃⋊C₃	C₂²×C₃	1	3	yes	complemented
13	C₂×C₆₁₃	C₂×C₃²	1	1	yes	characteristic, complemented
14	D₆₁₃	C₂×C₃²	1	2	yes	complemented
15	C₆₁₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₃²	—	613	1	no	maximal, Hall
17	C₂×C₃²	—	613	2	no	—
18	C₂×C₃²	—	613	1	no	—
19	C₂²×C₃	—	1839	1	no	—
20	C₂²×C₃	—	613	3	no	—
21	C₃²	—	613	1	no	Sylow
22	C₂×C₃	—	1839	2	no	—
23	C₂×C₃	—	613	6	no	—
24	C₂×C₃	—	613	3	no	—
25	C₂×C₃	D₆₁₃⋊C₃	1	1	yes	characteristic, direct product factor
26	C₂²	—	1839	1	no	Sylow
27	C₃	—	613	3	no	—
28	C₃	C₂×D₆₁₃⋊C₃	1	1	yes	characteristic, direct product factor
29	C₂	—	1839	2	no	—
30	C₂	C₃×D₆₁₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₆₁₃⋊C₃
commutator, cosocle, hypocenter	C₆₁₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₆₁₃	C₂×C₃
LCS	G ▷ C₆₁₃
UCS	C₁ ◁ C₂×C₃

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.