Subgroups — C₂×C₇×#11762245 #29503152

Order 15162.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#11762245	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₁₉²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×#11762245	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	#11762245	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₇×C₁₉⋊C₃	—	19	20	no	maximal
7	C₂×C₁₉²	C₃×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×C₁₉⋊C₃	—	19	20	no	—
9	C₁₉²	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₇×C₁₉	C₁₉⋊C₃	1	20	yes	complemented
11	C₇×C₁₉	C₂×C₁₉⋊C₃	1	20	yes	complemented
12	C₂×C₁₉⋊C₃	—	19	20	no	—
13	C₁₉⋊C₃	—	19	20	no	—
14	C₂×C₃×C₇	—	361	1	no	Hall
15	C₂×C₁₉	C₇×C₁₉⋊C₃	1	20	yes	complemented
16	C₃×C₇	—	361	1	no	Hall
17	C₁₉	C₂×C₇×C₁₉⋊C₃	1	20	yes	complemented
18	C₂×C₇	#11762245	1	1	yes	characteristic, direct product factor, Hall
19	C₇	C₂×#11762245	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	361	1	no	Hall
21	C₃	—	361	1	no	Sylow
22	C₂	C₇×#11762245	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₇	#11762245
commutator, cosocle, hypocenter	C₁₉²	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₉²	C₃
LCS	G ▷ C₁₉²
UCS	C₁ ◁ C₂×C₇

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.