Subgroups — C₇₉×#6903 #34063121

Order 19197.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#737	C₃	1	1	yes	maximal, characteristic
2	C₇₉×C₂₇⋊C₃	C₃	1	8	yes	maximal, complemented
3	C₃×C₂₇×C₇₉	C₃	1	4	yes	maximal, complemented
4	3₋¹⁺²×C₇₉	C₉	1	8	yes	—
5	H(3,𝔽₃)×C₇₉	C₉	1	1	yes	characteristic
6	C₃×C₉×C₇₉	C₃²	1	4	yes	—
7	C₂₇×C₇₉	C₃²	1	8	yes	—
8	C₂₇×C₇₉	C₃²	1	1	yes	characteristic
9	C₃²×C₇₉	C₃×C₉	1	4	yes	—
10	C₉×C₇₉	C₃×C₉	1	8	yes	—
11	C₉×C₇₉	C₃³	1	1	yes	characteristic
12	#6903	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃×C₇₉	—	3	4	no	—
14	C₃×C₇₉	C₃²×C₉	1	1	yes	characteristic
15	#737	C₃×C₇₉	1	1	yes	characteristic
16	C₂₇⋊C₃	C₃×C₇₉	1	8	yes	complemented
17	C₃×C₂₇	C₃×C₇₉	1	4	yes	complemented
18	C₇₉	#6903	1	1	yes	characteristic, direct product factor, Sylow
19	3₋¹⁺²	C₉×C₇₉	1	8	yes	—
20	H(3,𝔽₃)	C₉×C₇₉	1	1	yes	characteristic
21	C₃×C₉	C₃²×C₇₉	1	4	yes	—
22	C₂₇	C₃²×C₇₉	1	8	yes	—
23	C₂₇	C₃²×C₇₉	1	1	yes	characteristic
24	C₃²	C₃×C₉×C₇₉	1	4	yes	—
25	C₉	C₃×C₉×C₇₉	1	8	yes	—
26	C₉	C₃³×C₇₉	1	1	yes	characteristic
27	C₃	—	3	4	no	—
28	C₃	C₃²×C₉×C₇₉	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.