Subgroups — C₁₉⋊#11725071 #30660613

Order 16758.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#89205	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₃₉₉	—	3	1	no	maximal
3	C₃×C₇²×C₁₉	D₃	1	1	yes	characteristic
4	C₇×D₁₃₃	—	9	1	no	Hall
5	C₁₉×C₇⋊C₉	—	14	1	no	—
6	C₇²×C₁₉	D₉	1	1	yes	characteristic, complemented, Hall
7	#11725071	—	19	1	no	maximal, Hall
8	D₃₉₉	—	3	1	no	—
9	C₇×D₅₇	—	21	1	no	—
10	#89205	D₁₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₁₉	—	2	1	no	—
12	C₃×C₇×C₁₉	—	3	1	no	—
13	C₃×C₇×C₁₉	—	6	1	no	—
14	D₁₇₁	—	49	1	no	maximal, Hall
15	C₇×D₂₁	—	57	1	no	—
16	D₁₃₃	—	9	1	no	—
17	C₇×D₁₉	—	63	1	no	—
18	C₉×C₁₉	—	98	1	no	Hall
19	C₃×C₇²	D₅₇	1	1	yes	characteristic
20	C₇×C₁₉	—	2	1	no	—
21	C₇×C₁₉	—	3	1	no	—
22	C₇×C₁₉	—	6	1	no	—
23	D₅₇	—	21	1	no	—
24	C₇×D₇	—	171	1	no	Hall
25	C₇⋊C₉	—	14	1	no	—
26	C₃×C₁₉	#64418	1	1	yes	characteristic
27	C₇²	D₁₇₁	1	1	yes	characteristic, complemented, Sylow
28	D₂₁	—	57	1	no	—
29	D₃×C₇	—	399	1	no	—
30	D₁₉	—	63	1	no	Hall
31	C₃×C₇	—	2	1	no	—
32	C₃×C₇	—	6	1	no	—
33	C₃×C₇	—	6	1	no	—
34	C₁₉	#11725071	1	1	yes	characteristic, complemented, Sylow
35	D₉	—	931	1	no	Hall
36	C₂×C₇	—	1197	1	no	—
37	D₇	—	171	1	no	—
38	C₉	—	98	1	no	Sylow
39	C₇	—	2	1	no	—
40	C₇	—	6	1	no	—
41	C₇	—	6	1	no	—
42	D₃	—	399	1	no	—
43	C₃	C₁₉⋊#64418	1	1	yes	characteristic
44	C₂	—	1197	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₁₉×#89205	C₂
Frattini	C₃	C₁₉⋊#64418
Fitting, socle	C₃×C₇²×C₁₉	D₃
LCS	G ▷ C₁₉×#89205
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.