Subgroups — C₇×#157×C₄₁ #23780228

Order 10332.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₃×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₇×C₄₁	—	6	2	no	—
4	#157×C₄₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₄×C₇×C₄₁	—	9	1	no	maximal, Hall
6	C₃×C₇×C₄₁	—	2	2	no	—
7	C₃⋊D₃×C₄₁	C₂×C₇	1	1	yes	characteristic
8	C₂×C₇×C₄₁	—	9	1	no	—
9	C₃²×C₄₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₄₁	#157	1	1	yes	characteristic, direct product factor, Hall
11	C₇×#157	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	D₃×C₄₁	—	6	2	no	—
13	C₄×C₄₁	—	9	1	no	Hall
14	C₇×C₃⋊D₃	C₂×C₄₁	1	1	yes	characteristic
15	C₃×C₄₁	—	2	2	no	—
16	C₂×C₄₁	—	9	1	no	—
17	C₃²×C₇	C₄×C₄₁	1	1	yes	characteristic, complemented, Hall
18	D₃×C₇	—	6	2	no	—
19	C₄₁	C₇×#157	1	1	yes	characteristic, direct product factor, Sylow
20	#157	C₇×C₄₁	1	1	yes	characteristic, direct product factor, Hall
21	C₄×C₇	—	9	1	no	Hall
22	C₃×C₇	—	2	2	no	—
23	C₃⋊D₃	C₂×C₇×C₄₁	1	1	yes	characteristic
24	C₂×C₇	—	9	1	no	—
25	C₃²	C₄×C₇×C₄₁	1	1	yes	characteristic, complemented, Sylow
26	C₇	#157×C₄₁	1	1	yes	characteristic, direct product factor, Sylow
27	D₃	—	6	2	no	—
28	C₄	—	9	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	9	1	no	—

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