Subgroups — C₇×C₂₉×#157 #20300671

Order 7308.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₃×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₇×C₂₉	—	6	2	no	—
4	C₂₉×#157	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₄×C₇×C₂₉	—	9	1	no	maximal, Hall
6	C₃×C₇×C₂₉	—	2	2	no	—
7	C₃⋊D₃×C₂₉	C₂×C₇	1	1	yes	characteristic
8	C₂×C₇×C₂₉	—	9	1	no	—
9	C₃²×C₂₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
10	C₇×#157	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₇×C₂₉	#157	1	1	yes	characteristic, direct product factor, Hall
12	D₃×C₂₉	—	6	2	no	—
13	C₇×C₃⋊D₃	C₂×C₂₉	1	1	yes	characteristic
14	C₄×C₂₉	—	9	1	no	Hall
15	C₃×C₂₉	—	2	2	no	—
16	C₃²×C₇	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₂₉	—	9	1	no	—
18	D₃×C₇	—	6	2	no	—
19	#157	C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
20	C₂₉	C₇×#157	1	1	yes	characteristic, direct product factor, Sylow
21	C₄×C₇	—	9	1	no	Hall
22	C₃×C₇	—	2	2	no	—
23	C₃⋊D₃	C₂×C₇×C₂₉	1	1	yes	characteristic
24	C₂×C₇	—	9	1	no	—
25	C₃²	C₄×C₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
26	C₇	C₂₉×#157	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.