Subgroups — C₁₉⋊C₃×D₇₇ #22578639

Order 8778.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₇₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	D₁₁×C₁₉⋊C₃	—	7	1	no	maximal, Hall
5	D₇×C₁₉⋊C₃	—	11	1	no	maximal, Hall
6	C₁₁×C₁₉⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
7	C₃×D₇₇	—	19	1	no	maximal, Hall
8	C₁₉×D₁₁	—	7	1	no	Hall
9	C₇×C₁₉⋊C₃	D₁₁	1	1	yes	characteristic, complemented, Hall
10	D₇×C₁₉	—	11	1	no	Hall
11	C₃×C₇×C₁₁	—	19	1	no	Hall
12	C₁₁×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented, Hall
13	D₇₇	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
14	C₇×C₁₉	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₉⋊C₃	—	77	1	no	Hall
16	C₇×C₁₁	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₃×D₁₁	—	133	1	no	Hall
18	C₁₉⋊C₃	D₇₇	1	1	yes	characteristic, direct product factor, Hall
19	C₃×D₇	—	209	1	no	Hall
20	C₂×C₁₉	—	77	1	no	Hall
21	C₃×C₁₁	—	19	1	no	Hall
22	D₁₁	—	7	1	no	Hall
23	C₃×C₇	—	19	1	no	Hall
24	C₁₉	C₃×D₇₇	1	1	yes	characteristic, complemented, Sylow
25	D₇	—	11	1	no	Hall
26	C₁₁	D₇×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₇	D₁₁×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	1463	1	no	Hall
29	C₃	—	19	1	no	Sylow
30	C₂	—	77	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₁₁×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₁×C₁₉
UCS	C₁

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