Subgroups — C₄×C₅×C₂₃²⋊C₃ #44540697

Order 31740.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₂₃²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₂₃²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₂₃²⋊C₃	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₄×C₂₃²⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₅×C₂₃²	C₂×C₃	1	1	yes	characteristic
6	C₂×C₂₃²⋊C₃	C₂×C₅	1	1	yes	characteristic
7	C₅×C₂₃²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₄×C₂₃²	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂₃²⋊C₃	C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₂₃²	C₂×C₃×C₅	1	1	yes	characteristic
11	C₂₃²	C₃×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
12	C₄×C₅×C₂₃	—	3	8	no	—
13	C₂×C₅×C₂₃	—	3	8	no	—
14	C₅×C₂₃	—	3	8	no	—
15	C₄×C₂₃	—	3	8	no	—
16	C₃×C₄×C₅	—	529	1	no	maximal, Hall
17	C₂×C₂₃	—	3	8	no	—
18	C₂×C₃×C₅	—	529	1	no	—
19	C₂₃	—	3	8	no	—
20	C₄×C₅	C₂₃²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₅	—	529	1	no	Hall
22	C₃×C₄	—	529	1	no	Hall
23	C₂×C₅	C₂×C₂₃²⋊C₃	1	1	yes	characteristic
24	C₂×C₃	—	529	1	no	—
25	C₅	C₄×C₂₃²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₄	C₅×C₂₃²⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₃	—	529	1	no	Sylow
28	C₂	C₂×C₅×C₂₃²⋊C₃	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.