Subgroups — C₁₉×#11924776 #36384457

Order 22743.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₉²	C₃	1	1	yes	maximal, characteristic
2	C₁₉×#4294	—	7	1	no	maximal, Hall
3	C₇×C₁₉²	C₉	1	1	yes	characteristic, complemented, Hall
4	#11924776	C₁₉	1	1	yes	maximal, characteristic, direct product factor
5	C₁₉×C₇⋊C₉	—	19	1	no	maximal
6	C₃×C₁₉²	ΓL(1,𝔽₈)	1	1	yes	characteristic
7	C₃×C₇×C₁₉	—	3	6	no	—
8	C₃×C₇×C₁₉	C₁₉⋊C₃	1	1	yes	characteristic
9	C₃×C₇×C₁₉	C₃×C₁₉	1	1	yes	characteristic
10	C₁₉²	C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
11	C₉×C₁₉	—	133	1	no	—
12	#4294	—	7	1	no	—
13	C₇×C₁₉	—	3	6	no	—
14	C₇×C₁₉	#4294	1	1	yes	characteristic, complemented
15	C₇×C₁₉	C₉×C₁₉	1	1	yes	characteristic, complemented
16	C₇⋊C₉	—	19	1	no	Hall
17	C₃×C₁₉	—	3	6	no	—
18	C₃×C₁₉	C₁₉×ΓL(1,𝔽₈)	1	1	yes	characteristic
19	C₃×C₁₉	#87704	1	1	yes	characteristic
20	C₃×C₇	C₁₉×C₁₉⋊C₃	1	1	yes	characteristic
21	C₁₉	—	3	6	no	—
22	C₁₉	C₁₉×C₇⋊C₉	1	1	yes	characteristic, complemented
23	C₁₉	#11924776	1	1	yes	characteristic, direct product factor
24	C₉	—	133	1	no	Sylow
25	C₇	C₁₉×#4294	1	1	yes	characteristic, complemented, Sylow
26	C₃	C₁₉×#87704	1	1	yes	characteristic

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.