Subgroups — C₃²×#16812340 #44528175

Order 31140.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×D₁₇₃	C₂	1	1	yes	maximal, characteristic
2	C₃×#16812340	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅×C₁₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×#10621924	—	5	1	no	maximal, Hall
5	C₃×C₅×D₁₇₃	C₂×C₃	1	4	yes	—
6	#16812340	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×D₁₇₃	D₅	1	1	yes	characteristic
8	C₃×C₅×C₁₇₃	C₃×C₄	1	4	yes	complemented
9	C₃×#10621924	—	5	4	no	—
10	C₅×D₁₇₃	C₂×C₃²	1	1	yes	characteristic
11	C₃²×C₁₇₃	Dic₅	1	1	yes	characteristic, complemented, Hall
12	C₃×D₁₇₃	C₃×D₅	1	4	yes	—
13	C₅×C₁₇₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	#10621924	—	5	1	no	Hall
15	C₃×C₁₇₃	C₃×Dic₅	1	4	yes	complemented
16	D₁₇₃	C₃²×D₅	1	1	yes	characteristic
17	C₃²×Dic₅	—	173	1	no	maximal, Hall
18	C₁₇₃	C₃²×Dic₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃²×C₅	—	173	1	no	—
20	C₃×Dic₅	—	173	4	no	—
21	C₃²×C₅	#10621924	1	1	yes	characteristic, complemented, Hall
22	C₃²×C₄	—	865	1	no	Hall
23	C₂×C₃×C₅	—	173	4	no	—
24	Dic₅	—	173	1	no	Hall
25	C₂×C₃²	—	173	1	no	—
26	C₃×C₅	C₃×#10621924	1	4	yes	complemented
27	C₃×C₄	—	865	4	no	—
28	C₂×C₅	—	173	1	no	—
29	C₃²	#16812340	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	—	173	4	no	—
31	C₅	C₃²×#10621924	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	865	1	no	Sylow
33	C₃	C₃×#16812340	1	4	yes	direct product factor
34	C₂	—	173	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.