Subgroups — C₇₉×#6893 #34063111

Order 19197.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×3₋¹⁺²×C₇₉	C₃	1	2	yes	maximal, complemented
2	C₃×H(3,𝔽₃)×C₇₉	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₉×C₇₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₇₉×C₃²⋊C₉	C₃	1	9	yes	maximal, complemented
5	C₃³×C₇₉	C₃²	1	3	yes	—
6	C₃³×C₇₉	C₃²	1	1	yes	characteristic
7	3₋¹⁺²×C₇₉	—	3	6	no	—
8	H(3,𝔽₃)×C₇₉	—	3	3	no	—
9	C₃×C₉×C₇₉	—	3	3	no	—
10	C₃×C₉×C₇₉	C₃²	1	3	yes	—
11	C₃×C₉×C₇₉	C₃²	1	6	yes	—
12	C₃²×C₇₉	—	3	3	no	—
13	C₃²×C₇₉	—	3	3	no	—
14	C₃²×C₇₉	—	3	9	no	—
15	C₃²×C₇₉	H(3,𝔽₃)	1	3	yes	—
16	C₃²×C₇₉	C₃³	1	1	yes	characteristic
17	C₉×C₇₉	—	3	3	no	—
18	C₉×C₇₉	—	3	6	no	—
19	#6893	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₃×C₇₉	—	3	3	no	—
21	C₃×C₇₉	—	9	3	no	—
22	C₃×C₇₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
23	C₃×C₇₉	#737	1	3	yes	—
24	C₃×3₋¹⁺²	C₃×C₇₉	1	2	yes	complemented
25	C₃×H(3,𝔽₃)	C₃×C₇₉	1	1	yes	characteristic
26	C₃²×C₉	C₃×C₇₉	1	1	yes	characteristic, complemented
27	C₃²⋊C₉	C₃×C₇₉	1	9	yes	complemented
28	C₇₉	#6893	1	1	yes	characteristic, direct product factor, Sylow
29	C₃³	C₃²×C₇₉	1	3	yes	—
30	C₃³	C₃²×C₇₉	1	1	yes	characteristic
31	3₋¹⁺²	—	3	6	no	—
32	H(3,𝔽₃)	—	3	3	no	—
33	C₃×C₉	—	3	3	no	—
34	C₃×C₉	C₃²×C₇₉	1	3	yes	—
35	C₃×C₉	C₃²×C₇₉	1	6	yes	—
36	C₃²	—	3	3	no	—
37	C₃²	—	3	3	no	—
38	C₃²	—	3	9	no	—
39	C₃²	H(3,𝔽₃)×C₇₉	1	3	yes	—
40	C₃²	C₃³×C₇₉	1	1	yes	characteristic
41	C₉	—	3	3	no	—
42	C₉	—	3	6	no	—
43	C₃	—	3	3	no	—
44	C₃	—	9	3	no	—
45	C₃	C₃×H(3,𝔽₃)×C₇₉	1	1	yes	characteristic
46	C₃	C₇₉×#737	1	3	yes	—

	subgroup	G/H
center, socle	C₃²×C₇₉	C₃³
commutator, Frattini, cosocle	C₃²	C₃³×C₇₉
prime radical	C₃×H(3,𝔽₃)×C₇₉	C₃
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×3₋¹⁺²×C₇₉	C₃	semidirect
3. C₃²×C₉×C₇₉	C₃	semidirect
4. C₇₉×C₃²⋊C₉	C₃	semidirect
19. #6893	C₇₉	direct (N × H)
24. C₃×3₋¹⁺²	C₃×C₇₉	semidirect
26. C₃²×C₉	C₃×C₇₉	semidirect
27. C₃²⋊C₉	C₃×C₇₉	semidirect
28. C₇₉	#6893	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×3₋¹⁺²×C₇₉	3
C₃×H(3,𝔽₃)×C₇₉	3
C₃²×C₉×C₇₉	3
C₇₉×C₃²⋊C₉	3
#6893	79

Subgroups — C79×#6893 #34063111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#6893 #34063111