Subgroups — #41008259

Order 26973.

5490 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582680	C₃	1	80	yes	maximal, complemented
2	C₃×#15688530	C₃	1	40	yes	maximal, complemented
3	C₃₇×H(5,𝔽₃)	C₃	1	1	yes	maximal, characteristic
4	#15688530	C₃²	1	90	yes	complemented
5	#15688530	C₃²	1	720	yes	complemented
6	C₃×#11758608	C₃²	1	320	yes	complemented
7	C₃²×#66524	C₃²	1	40	yes	complemented
8	C₃×H(3,𝔽₃)×C₃₇	C₃²	1	40	yes	—
9	C₃³×C₃₇	C₃³	1	40	yes	—
10	H(3,𝔽₃)×C₃₇	C₃³	1	90	yes	—
11	#11758608	C₃³	1	720	yes	—
12	C₃×#66524	C₃³	1	40	yes	—
13	C₃×#66524	C₃³	1	320	yes	—
14	#10624943	—	37	1	no	maximal, Sylow
15	C₃²×C₃₇	—	9	40	no	—
16	C₃²×C₃₇	C₃⁴	1	40	yes	—
17	#66524	C₃⁴	1	1	yes	characteristic
18	#66524	C₃⁴	1	80	yes	—
19	3₋¹⁺⁴	—	37	80	no	—
20	H(5,𝔽₃)	C₃₇⋊C₃	1	1	yes	characteristic
21	C₃×#737	—	37	40	no	—
22	C₃×C₃₇	—	3	40	no	—
23	C₃×C₃₇	C₃⁵	1	1	yes	characteristic
24	#737	—	37	90	no	—
25	#737	—	37	720	no	—
26	C₃×3₋¹⁺²	—	37	320	no	—
27	C₃×H(3,𝔽₃)	C₃×C₃₇⋊C₃	1	40	yes	—
28	C₃²×C₉	—	37	40	no	—
29	C₃₇	#10624943	1	1	yes	characteristic, complemented, Sylow
30	C₃³	C₃²×C₃₇⋊C₃	1	40	yes	—
31	3₋¹⁺²	—	37	720	no	—
32	H(3,𝔽₃)	C₃²×C₃₇⋊C₃	1	90	yes	—
33	C₃×C₉	—	37	40	no	—
34	C₃×C₉	—	37	320	no	—
35	C₃²	—	9	40	no	—
36	C₃²	C₃³×C₃₇⋊C₃	1	40	yes	—
37	C₉	—	37	1	no	—
38	C₉	—	37	80	no	—
39	C₃	—	3	40	no	—
40	C₃	C₃⁴×C₃₇⋊C₃	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.