Subgroups — #23780607

Order 10374.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#10625203	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₉₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#13093365	—	7	1	no	maximal, Hall
5	D₇×C₁₉⋊C₃	—	13	1	no	maximal, Hall
6	#10625203	D₇	1	1	yes	characteristic, complemented, Hall
7	(C₁₃⋊C₃)⋊D₇	—	19	1	no	maximal, Hall
8	C₁₉×D₁₃	—	7	1	no	Hall
9	C₇×C₁₉⋊C₃	—	13	1	no	Hall
10	C₇×C₁₃⋊C₃	—	19	1	no	Hall
11	D₇×C₁₉	—	13	1	no	Hall
12	C₁₃×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented, Hall
13	D₉₁	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₇×C₁₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₉⋊C₃	—	91	1	no	Hall
16	C₇×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
17	D₁₃⋊C₃	—	133	1	no	Hall
18	C₁₉⋊C₃	—	13	1	no	Hall
19	C₃×D₇	—	247	1	no	Hall
20	C₁₃⋊C₃	—	19	1	no	Hall
21	C₂×C₁₉	—	91	1	no	Hall
22	D₁₃	—	7	1	no	Hall
23	C₃×C₇	—	247	1	no	Hall
24	C₁₉	(C₁₃⋊C₃)⋊D₇	1	1	yes	characteristic, complemented, Sylow
25	D₇	—	13	1	no	Hall
26	C₁₃	D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₇	#13093365	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	1729	1	no	Hall
29	C₃	—	247	1	no	Sylow
30	C₂	—	91	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₁₉
UCS	C₁

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