Subgroups — C₁₃⋊C₃×D₂₁₉ #30685205

Order 17082.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃⋊C₃×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃⋊C₃×D₇₃	—	3	1	no	maximal
3	C₁₃×D₂₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₃⋊C₃×C₇₃	—	2	1	no	—
6	C₁₃⋊C₃×C₇₃	D₃	1	1	yes	characteristic, complemented
7	C₁₃×D₇₃	—	3	1	no	Hall
8	C₃×D₂₁₉	—	13	1	no	maximal, Hall
9	C₁₃×C₇₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
10	C₃²×C₇₃	—	13	1	no	Hall
11	D₂₁₉	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
12	C₃×D₇₃	—	39	1	no	—
13	D₃×C₁₃⋊C₃	—	73	1	no	maximal, Hall
14	C₃×C₇₃	—	13	1	no	—
15	C₃×C₇₃	—	26	1	no	—
16	C₃×C₇₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
17	D₇₃	—	3	1	no	Hall
18	C₃×C₁₃⋊C₃	D₇₃	1	1	yes	characteristic, complemented, Hall
19	D₃×C₁₃	—	73	1	no	—
20	C₂×C₁₃⋊C₃	—	219	1	no	—
21	C₇₃	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
22	C₃×C₁₃	C₃×D₇₃	1	1	yes	characteristic, complemented
23	C₁₃⋊C₃	—	2	1	no	—
24	C₁₃⋊C₃	D₂₁₉	1	1	yes	characteristic, direct product factor
25	C₂×C₁₃	—	219	1	no	Hall
26	C₃×D₃	—	949	1	no	Hall
27	C₁₃	C₃×D₂₁₉	1	1	yes	characteristic, complemented, Sylow
28	C₃²	—	13	1	no	Sylow
29	C₂×C₃	—	2847	1	no	—
30	D₃	—	73	1	no	—
31	C₃	—	13	1	no	—
32	C₃	—	26	1	no	—
33	C₃	C₁₃⋊C₃×D₇₃	1	1	yes	characteristic, complemented
34	C₂	—	219	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₇₃	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₇₃
UCS	C₁

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.