Subgroups — A₅×C₂₉⋊C₇ #27131831

Order 12180.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×C₂₉⋊C₇	—	5	1	no	maximal, Hall
2	D₅×C₂₉⋊C₇	—	6	1	no	maximal
3	C₂₉×A₅	C₇	1	1	yes	maximal, characteristic, complemented, Hall
4	D₃×C₂₉⋊C₇	—	10	1	no	maximal
5	C₅×C₂₉⋊C₇	—	6	1	no	Hall
6	C₂²×C₂₉⋊C₇	—	5	1	no	Hall
7	C₃×C₂₉⋊C₇	—	10	1	no	Hall
8	C₇×A₅	—	29	1	no	maximal, Hall
9	C₂×C₂₉⋊C₇	—	15	1	no	—
10	A₄×C₂₉	—	5	1	no	Hall
11	D₅×C₂₉	—	6	1	no	—
12	C₂₉⋊C₇	A₅	1	1	yes	maximal normal, characteristic, direct product factor, Hall
13	D₃×C₂₉	—	10	1	no	—
14	C₅×C₂₉	—	6	1	no	Hall
15	C₂²×C₂₉	—	5	1	no	Hall
16	C₃×C₂₉	—	10	1	no	Hall
17	C₇×A₄	—	145	1	no	Hall
18	C₇×D₅	—	174	1	no	—
19	A₅	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₂₉	—	15	1	no	—
21	D₃×C₇	—	290	1	no	—
22	C₅×C₇	—	174	1	no	Hall
23	C₂₉	C₇×A₅	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₇	—	145	1	no	Hall
25	C₃×C₇	—	290	1	no	Hall
26	C₂×C₇	—	435	1	no	—
27	A₄	—	5	1	no	Hall
28	D₅	—	6	1	no	—
29	C₇	—	29	1	no	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	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, hypocenter	C₂₉×A₅	C₇
Fitting	C₂₉	C₇×A₅
LCS	G ▷ C₂₉×A₅
UCS	C₁

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