Subgroups — #34063253

Order 19197.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14523840	C₃	1	3	yes	maximal, complemented
2	C₃²⋊(C₇₉⋊C₉)	C₃	1	9	yes	maximal, complemented
3	C₃⁴×C₇₉	C₃	1	1	yes	maximal, characteristic
4	#14523840	—	3	9	no	—
5	C₃×C₇₉⋊C₉	C₃²	1	9	yes	complemented
6	C₃³×C₇₉	—	3	3	no	—
7	C₃³×C₇₉	—	3	9	no	—
8	C₃³×C₇₉	C₃²	1	1	yes	characteristic
9	C₃³×C₇₉	C₃²	1	3	yes	—
10	C₃²×C₇₉	—	3	27	no	—
11	C₃²×C₇₉	—	3	3	no	—
12	C₃²×C₇₉	—	3	3	no	—
13	C₃²×C₇₉	—	3	6	no	—
14	C₃²×C₇₉	H(3,𝔽₃)	1	3	yes	—
15	C₃²×C₇₉	3₋¹⁺²	1	9	yes	complemented
16	C₃²×C₇₉	C₃³	1	1	yes	characteristic
17	C₇₉⋊C₉	—	3	9	no	—
18	#6891	—	79	1	no	maximal, Sylow
19	C₃×C₇₉	—	3	3	no	—
20	C₃×C₇₉	—	3	9	no	—
21	C₃×C₇₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
22	C₃×C₇₉	C₃×3₋¹⁺²	1	3	yes	—
23	C₃⁴	C₇₉⋊C₃	1	1	yes	characteristic
24	C₃×3₋¹⁺²	—	79	3	no	—
25	C₃²⋊C₉	—	79	9	no	—
26	C₇₉	#6891	1	1	yes	characteristic, complemented, Sylow
27	C₃³	—	3	3	no	—
28	C₃³	—	3	9	no	—
29	C₃³	C₃×C₇₉⋊C₃	1	1	yes	characteristic
30	C₃³	C₃×C₇₉⋊C₃	1	3	yes	—
31	3₋¹⁺²	—	237	9	no	—
32	C₃×C₉	—	79	9	no	—
33	C₃²	—	3	27	no	—
34	C₃²	—	3	3	no	—
35	C₃²	—	3	3	no	—
36	C₃²	—	3	6	no	—
37	C₃²	C₃²⋊(C₇₉⋊C₃)	1	3	yes	—
38	C₃²	#14523840	1	9	yes	complemented
39	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
40	C₉	—	237	9	no	—
41	C₃	—	3	3	no	—
42	C₃	—	3	9	no	—
43	C₃	C₃×C₃²⋊(C₇₉⋊C₃)	1	1	yes	characteristic
44	C₃	C₃×#14523840	1	3	yes	—

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.