Subgroups — C₃×C₇×H(5,𝔽₃) #19100350

Order 5103.

6776 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×H(5,𝔽₃)	C₃	1	81	yes	maximal, direct product factor
2	C₃²×C₇×H(3,𝔽₃)	C₃	1	40	yes	maximal, complemented
3	C₃×H(5,𝔽₃)	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₃⁴×C₇	C₃²	1	40	yes	complemented
5	C₃×C₇×H(3,𝔽₃)	C₃²	1	90	yes	complemented
6	C₃×C₇×H(3,𝔽₃)	C₃²	1	1080	yes	complemented
7	H(5,𝔽₃)	C₃×C₇	1	81	yes	direct product factor
8	C₃²×H(3,𝔽₃)	C₃×C₇	1	40	yes	complemented
9	C₃³×C₇	—	9	120	no	—
10	C₃³×C₇	C₃³	1	40	yes	—
11	C₃³×C₇	C₃³	1	360	yes	complemented
12	C₇×H(3,𝔽₃)	C₃³	1	810	yes	complemented
13	C₃⁴	C₃²×C₇	1	40	yes	complemented
14	C₃×H(3,𝔽₃)	C₃²×C₇	1	90	yes	complemented
15	C₃×H(3,𝔽₃)	C₃²×C₇	1	1080	yes	complemented
16	C₃²×C₇	—	3	120	no	—
17	C₃²×C₇	—	9	360	no	—
18	C₃²×C₇	C₃⁴	1	120	yes	—
19	C₃²×C₇	C₃⁴	1	1	yes	characteristic
20	C₃³	—	9	120	no	—
21	C₃³	C₃³×C₇	1	40	yes	—
22	C₃³	C₃³×C₇	1	360	yes	complemented
23	H(3,𝔽₃)	C₃³×C₇	1	810	yes	complemented
24	C₃×C₇	—	3	120	no	—
25	C₃×C₇	H(5,𝔽₃)	1	3	yes	direct product factor
26	C₃×C₇	C₃⁵	1	1	yes	characteristic
27	C₃²	—	3	120	no	—
28	C₃²	—	9	360	no	—
29	C₃²	C₃⁴×C₇	1	120	yes	—
30	C₃²	C₃⁴×C₇	1	1	yes	characteristic
31	C₇	C₃×H(5,𝔽₃)	1	1	yes	characteristic, direct product factor, Sylow
32	C₃	—	3	120	no	—
33	C₃	C₇×H(5,𝔽₃)	1	3	yes	direct product factor
34	C₃	C₃⁵×C₇	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.