Subgroups — C₇₉×#6895 #34063113

Order 19197.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉×C₇₉	C₃	1	1	yes	maximal, characteristic
2	C₇₉×C₉⋊C₉	C₃	1	9	yes	maximal, complemented
3	C₇₉×C₃²⋊C₉	C₃	1	3	yes	maximal
4	C₃³×C₇₉	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₇₉	—	3	3	no	—
6	C₃×C₉×C₇₉	C₃²	1	9	yes	—
7	C₃×C₉×C₇₉	C₃²	1	3	yes	—
8	C₃²×C₇₉	—	3	3	no	—
9	C₃²×C₇₉	3₋¹⁺²	1	3	yes	—
10	C₃²×C₇₉	C₃³	1	1	yes	characteristic
11	C₉×C₇₉	—	3	3	no	—
12	C₉×C₇₉	—	3	9	no	—
13	#6895	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃×C₇₉	—	3	3	no	—
15	C₃×C₇₉	C₃×3₋¹⁺²	1	1	yes	characteristic
16	C₃×C₇₉	#737	1	3	yes	—
17	C₃²×C₉	C₃×C₇₉	1	1	yes	characteristic
18	C₉⋊C₉	C₃×C₇₉	1	9	yes	complemented
19	C₃²⋊C₉	C₃×C₇₉	1	3	yes	—
20	C₇₉	#6895	1	1	yes	characteristic, direct product factor, Sylow
21	C₃³	C₃²×C₇₉	1	1	yes	characteristic
22	C₃×C₉	—	3	3	no	—
23	C₃×C₉	C₃²×C₇₉	1	9	yes	—
24	C₃×C₉	C₃²×C₇₉	1	3	yes	—
25	C₃²	—	3	3	no	—
26	C₃²	3₋¹⁺²×C₇₉	1	3	yes	—
27	C₃²	C₃³×C₇₉	1	1	yes	characteristic
28	C₉	—	3	3	no	—
29	C₉	—	3	9	no	—
30	C₃	—	3	3	no	—
31	C₃	C₃×3₋¹⁺²×C₇₉	1	1	yes	characteristic
32	C₃	C₇₉×#737	1	3	yes	—

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

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.