Subgroups — C₂×C₂₃×#157 #13110286

Order 1656.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊D₃×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#157	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃²×C₂₃	C₄	1	1	yes	characteristic, complemented
4	C₃⋊D₃×C₂₃	C₄	1	1	yes	characteristic, complemented
5	C₃⋊D₃×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×D₃×C₂₃	—	6	2	no	—
7	C₃²×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×C₄×C₂₃	—	9	1	no	maximal, Hall
9	C₂×C₃×C₂₃	—	2	2	no	—
10	D₃×C₂₃	—	6	2	no	—
11	D₃×C₂₃	—	6	2	no	—
12	C₂²×C₂₃	—	9	1	no	—
13	C₄×C₂₃	—	9	2	no	—
14	C₂×#157	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₃×C₂₃	—	2	2	no	—
16	C₂×C₂₃	—	9	1	no	—
17	C₂×C₂₃	—	9	1	no	—
18	C₂×C₂₃	#157	1	1	yes	characteristic, direct product factor
19	C₂×C₃⋊D₃	C₂×C₂₃	1	1	yes	characteristic
20	#157	C₂×C₂₃	1	2	yes	direct product factor
21	C₂₃	C₂×#157	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₃²	C₄×C₂₃	1	1	yes	characteristic, complemented
23	C₃⋊D₃	C₄×C₂₃	1	1	yes	characteristic, complemented
24	C₃⋊D₃	C₂²×C₂₃	1	1	yes	characteristic
25	C₂×D₃	—	6	2	no	—
26	C₃²	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₄	—	9	1	no	Sylow
28	C₂×C₃	—	2	2	no	—
29	D₃	—	6	2	no	—
30	D₃	—	6	2	no	—
31	C₂²	—	9	1	no	—
32	C₄	—	9	2	no	—
33	C₃	—	2	2	no	—
34	C₂	—	9	1	no	—
35	C₂	—	9	1	no	—
36	C₂	C₂₃×#157	1	1	yes	characteristic, direct product factor

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.