Subgroups — C₇×C₄₇×A₅ #34089552

Order 19740.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×A₄×C₄₇	—	5	1	no	maximal, Hall
2	C₇×D₅×C₄₇	—	6	1	no	maximal
3	C₄₇×A₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	D₃×C₇×C₄₇	—	10	1	no	maximal
5	C₅×C₇×C₄₇	—	6	1	no	Hall
6	C₂²×C₇×C₄₇	—	5	1	no	Hall
7	C₃×C₇×C₄₇	—	10	1	no	Hall
8	C₂×C₇×C₄₇	—	15	1	no	—
9	A₄×C₄₇	—	5	1	no	Hall
10	D₅×C₄₇	—	6	1	no	—
11	C₇×A₅	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₄₇	A₅	1	1	yes	maximal normal, characteristic, direct product factor, Hall
13	D₃×C₄₇	—	10	1	no	—
14	C₅×C₄₇	—	6	1	no	Hall
15	C₂²×C₄₇	—	5	1	no	Hall
16	C₃×C₄₇	—	10	1	no	Hall
17	C₂×C₄₇	—	15	1	no	—
18	C₇×A₄	—	5	1	no	Hall
19	C₇×D₅	—	6	1	no	—
20	A₅	C₇×C₄₇	1	1	yes	characteristic, direct product factor, Hall
21	C₄₇	C₇×A₅	1	1	yes	characteristic, direct product factor, Sylow
22	D₃×C₇	—	10	1	no	—
23	C₅×C₇	—	6	1	no	Hall
24	C₂²×C₇	—	5	1	no	Hall
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	C₄₇×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.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.