Subgroups — C₁₉×#6875 #17987261

Order 4617.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₂₇⋊C₃	C₃	1	2	yes	maximal
2	C₁₉×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₁₉×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₃×C₉×C₁₉	—	3	1	no	—
5	C₃×C₉×C₁₉	C₃²	1	1	yes	characteristic
6	C₁₉×C₂₇	—	3	2	no	—
7	C₁₉×C₂₇	C₉	1	3	yes	complemented
8	#6875	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₃²×C₁₉	3₋¹⁺²	1	1	yes	characteristic
10	C₉×C₁₉	—	9	1	no	—
11	C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
12	C₉×C₁₉	3₋¹⁺²	1	2	yes	—
13	C₂₇⋊C₃	C₃×C₁₉	1	2	yes	—
14	C₂₇⋊C₃	C₃×C₁₉	1	1	yes	characteristic
15	C₉⋊C₉	C₃×C₁₉	1	1	yes	characteristic
16	C₃×C₁₉	—	3	1	no	—
17	C₃×C₁₉	C₉⋊C₉	1	1	yes	characteristic
18	C₃×C₉	—	3	1	no	—
19	C₃×C₉	C₃²×C₁₉	1	1	yes	characteristic
20	C₂₇	—	3	2	no	—
21	C₂₇	C₉×C₁₉	1	3	yes	complemented
22	C₁₉	#6875	1	1	yes	characteristic, direct product factor, Sylow
23	C₃²	C₁₉×3₋¹⁺²	1	1	yes	characteristic
24	C₉	—	9	1	no	—
25	C₉	C₃×C₉×C₁₉	1	1	yes	characteristic
26	C₉	C₁₉×3₋¹⁺²	1	2	yes	—
27	C₃	—	3	1	no	—
28	C₃	C₁₉×C₉⋊C₉	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.