Subgroups — C₇₉×#90646 #48001200

Order 35550.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₅×C₇₉	—	3	1	no	maximal
3	C₃×C₅²×C₇₉	D₃	1	1	yes	characteristic
4	C₅×D₅×C₇₉	—	9	1	no	Hall
5	D₁₅×C₇₉	—	3	1	no	—
6	C₅×D₃×C₇₉	—	15	1	no	—
7	C₅²×C₇₉	D₉	1	1	yes	characteristic, complemented, Hall
8	D₉×C₇₉	—	25	1	no	maximal, Hall
9	C₃×C₅×C₇₉	—	3	1	no	—
10	C₃×C₅×C₇₉	—	3	1	no	—
11	C₂×C₅×C₇₉	—	45	1	no	—
12	D₅×C₇₉	—	9	1	no	—
13	C₉×C₇₉	—	25	1	no	Hall
14	D₃×C₇₉	—	15	1	no	—
15	#90646	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₅×C₇₉	—	3	1	no	—
17	C₅×C₇₉	—	3	1	no	—
18	C₃×C₇₉	#3874	1	1	yes	characteristic
19	C₅²⋊C₉	C₂×C₇₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₇₉	—	45	1	no	Hall
21	C₅×D₁₅	—	3	1	no	—
22	C₇₉	#90646	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×C₅²	D₃×C₇₉	1	1	yes	characteristic
24	C₅×D₅	—	9	1	no	Hall
25	D₁₅	—	3	1	no	—
26	C₅×D₃	—	15	1	no	—
27	C₅²	D₉×C₇₉	1	1	yes	characteristic, complemented, Sylow
28	D₉	—	25	1	no	Hall
29	C₃×C₅	—	3	1	no	—
30	C₃×C₅	—	3	1	no	—
31	C₂×C₅	—	45	1	no	—
32	D₅	—	9	1	no	—
33	C₉	—	25	1	no	Sylow
34	D₃	—	15	1	no	—
35	C₅	—	3	1	no	—
36	C₅	—	3	1	no	—
37	C₃	C₇₉×#3874	1	1	yes	characteristic
38	C₂	—	45	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₉	#90646
commutator, cosocle, hypocenter	C₅²⋊C₉	C₂×C₇₉
Frattini	C₃	C₇₉×#3874
Fitting, socle	C₃×C₅²×C₇₉	D₃
LCS	G ▷ C₅²⋊C₉
UCS	C₁ ◁ C₇₉

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.