Subgroups — C₃²×#13184069 #30630849

Order 16020.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₅×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₃×#13184069	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×Dic₈₉	—	5	1	no	maximal, Hall
5	C₃×D₅×C₈₉	C₂×C₃	1	4	yes	—
6	#13184069	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₈₉	—	5	1	no	—
8	C₃×C₅×C₈₉	C₃×C₄	1	4	yes	complemented
9	C₃×Dic₈₉	—	5	4	no	—
10	D₅×C₈₉	C₂×C₃²	1	1	yes	characteristic
11	C₃²×C₈₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₈₉	—	5	4	no	—
13	C₅×C₈₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	Dic₈₉	—	5	1	no	Hall
15	C₃×C₈₉	C₃×AGL(1,𝔽₅)	1	4	yes	complemented
16	C₃²×AGL(1,𝔽₅)	—	89	1	no	maximal, Hall
17	C₂×C₈₉	—	5	1	no	—
18	C₃²×D₅	D₈₉	1	1	yes	characteristic
19	C₈₉	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
20	C₃×AGL(1,𝔽₅)	—	89	4	no	—
21	C₃²×C₅	Dic₈₉	1	1	yes	characteristic, complemented, Hall
22	C₃²×C₄	—	445	1	no	Hall
23	C₃×D₅	C₃×D₈₉	1	4	yes	—
24	AGL(1,𝔽₅)	—	89	1	no	Hall
25	C₂×C₃²	—	5	1	no	—
26	C₃×C₅	C₃×Dic₈₉	1	4	yes	complemented
27	C₃×C₄	—	445	4	no	—
28	D₅	C₃²×D₈₉	1	1	yes	characteristic
29	C₃²	#13184069	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	—	5	4	no	—
31	C₅	C₃²×Dic₈₉	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	445	1	no	Sylow
33	C₃	C₃×#13184069	1	4	yes	direct product factor
34	C₂	—	5	1	no	—

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.