Subgroups — C₇₉⋊H(5,𝔽₃) #34063375

Order 19197.

586 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₇₉⋊C₃)	C₃	1	12	yes	maximal, complemented
2	H(3,𝔽₃)×C₇₉⋊C₃	C₃	1	27	yes	maximal, complemented
3	C₃×H(3,𝔽₃)×C₇₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₇₉⋊C₃	C₃²	1	36	yes	complemented
5	C₃²⋊(C₇₉⋊C₃)	C₃²	1	72	yes	complemented
6	C₃²⋊(C₇₉⋊C₃)	C₃²	1	9	yes	complemented
7	C₃³×C₇₉	C₃²	1	4	yes	complemented
8	H(3,𝔽₃)×C₇₉	C₃²	1	9	yes	complemented
9	C₃²×C₇₉	—	9	4	no	—
10	C₃²×C₇₉	C₃³	1	12	yes	—
11	C₃²×C₇₉	C₃³	1	1	yes	characteristic
12	C₃×C₇₉⋊C₃	—	9	36	no	—
13	C₃×C₇₉⋊C₃	C₃³	1	27	yes	—
14	H(5,𝔽₃)	—	79	1	no	maximal, Sylow
15	C₃×C₇₉	—	3	12	no	—
16	C₃×C₇₉	—	3	1	no	—
17	C₃×C₇₉	C₃⁴	1	1	yes	characteristic
18	C₇₉⋊C₃	—	3	27	no	—
19	C₃×H(3,𝔽₃)	—	79	12	no	—
20	C₃×H(3,𝔽₃)	—	79	27	no	—
21	C₃×H(3,𝔽₃)	C₇₉⋊C₃	1	1	yes	characteristic, complemented
22	C₇₉	H(5,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
23	C₃³	—	79	36	no	—
24	C₃³	C₃×C₇₉⋊C₃	1	4	yes	complemented
25	H(3,𝔽₃)	—	79	9	no	—
26	H(3,𝔽₃)	—	79	72	no	—
27	H(3,𝔽₃)	C₃×C₇₉⋊C₃	1	9	yes	complemented
28	C₃²	—	9	4	no	—
29	C₃²	—	79	27	no	—
30	C₃²	—	711	36	no	—
31	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
32	C₃²	C₃²×C₇₉⋊C₃	1	12	yes	—
33	C₃	—	3	1	no	—
34	C₃	—	3	12	no	—
35	C₃	—	237	27	no	—
36	C₃	C₃³×C₇₉⋊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.