Subgroups — C₇×C₂₃×A₅ #23751659

Order 9660.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×A₄×C₂₃	—	5	1	no	maximal, Hall
2	C₇×D₅×C₂₃	—	6	1	no	maximal
3	C₂₃×A₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	D₃×C₇×C₂₃	—	10	1	no	maximal
5	C₅×C₇×C₂₃	—	6	1	no	Hall
6	C₂²×C₇×C₂₃	—	5	1	no	Hall
7	C₃×C₇×C₂₃	—	10	1	no	Hall
8	C₇×A₅	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₇×C₂₃	—	15	1	no	—
10	A₄×C₂₃	—	5	1	no	Hall
11	D₅×C₂₃	—	6	1	no	—
12	C₇×C₂₃	A₅	1	1	yes	maximal normal, characteristic, direct product factor, Hall
13	D₃×C₂₃	—	10	1	no	—
14	C₅×C₂₃	—	6	1	no	Hall
15	C₂²×C₂₃	—	5	1	no	Hall
16	C₇×A₄	—	5	1	no	Hall
17	C₇×D₅	—	6	1	no	—
18	C₃×C₂₃	—	10	1	no	Hall
19	A₅	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₂₃	—	15	1	no	—
21	D₃×C₇	—	10	1	no	—
22	C₅×C₇	—	6	1	no	Hall
23	C₂²×C₇	—	5	1	no	Hall
24	C₂₃	C₇×A₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₇	—	10	1	no	Hall
26	C₂×C₇	—	15	1	no	—
27	A₄	—	5	1	no	Hall
28	D₅	—	6	1	no	—
29	C₇	C₂₃×A₅	1	1	yes	characteristic, direct product factor, Sylow
30	D₃	—	10	1	no	—
31	C₅	—	6	1	no	Sylow
32	C₂²	—	5	1	no	Sylow
33	C₃	—	10	1	no	Sylow
34	C₂	—	15	1	no	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.