Finite Group Databasebeta

← C11⋊C5×#5934 #72248960

Subgroups — C11⋊C5×#5934 #72248960

Order 10560.

392 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#5934C511yesmaximal, characteristic, complemented, Hall
2C2×S4×C11⋊C5—43nomaximal
3C11⋊C5×#997C211yesmaximal, characteristic, complemented
4C11⋊C5×B(4,𝔽2)—31nomaximal, Hall
5H(5,𝔽2)×C11⋊C5D311yescharacteristic, complemented
6#120×C11⋊C5—33no—
7#99×C11⋊C5—33no—
8C2×A4×C11⋊C5—43no—
9S4×C11⋊C5—46no—
10SL(2,𝔽3)×C11⋊C5—81no—
11C11×#997C2×C511yescharacteristic, complemented
12C5×#5934—111nomaximal, Hall
13C24×C11⋊C5—31no—
14#41×C11⋊C5—61no—
15C2×D4×C11⋊C5—33no—
16C2×D4×C11⋊C5—63no—
17C22⋊C4×C11⋊C5—33no—
18C22⋊C4×C11⋊C5—63no—
19C11×B(4,𝔽2)—31noHall
20C2×D3×C11⋊C5—161no—
21A4×C11⋊C5—43no—
22C2×C11×S4—43no—
23C5×#997—111no—
24C23×C11⋊C5—31no—
25C23×C11⋊C5—63no—
26C23×C11⋊C5—122no—
27C23×C11⋊C5S413yescomplemented
28Q8×C11⋊C5—21no—
29D4×C11⋊C5—63no—
30D4×C11⋊C5—126no—
31C2×C4×C11⋊C5—33no—
32C2×C4×C11⋊C5—63no—
33C11×H(5,𝔽2)C5×D311yescharacteristic, complemented
34C11×#120—33no—
35C11×#99—33no—
36C2×C3×C11⋊C5—161no—
37D3×C11⋊C5—162no—
38C5×B(4,𝔽2)—331noHall
39C2×C11×A4—43no—
40C11×S4—46no—
41C11×SL(2,𝔽3)—81no—
42C2×C5×S4—443no—
43C22×C11⋊C5—33no—
44C22×C11⋊C5—43no—
45C22×C11⋊C5—66no—
46C22×C11⋊C5—121no—
47C22×C11⋊C5—123no—
48C22×C11⋊C5—121no—
49C4×C11⋊C5—61no—
50C4×C11⋊C5—123no—
51#5934C11⋊C511yescharacteristic, direct product factor, Hall
52C24×C11—31no—
53C11×#41—61no—
54C2×D4×C11—33no—
55C2×D4×C11—63no—
56C11×C22⋊C4—33no—
57C11×C22⋊C4—63no—
58C3×C11⋊C5—161noHall
59C5×H(5,𝔽2)—111no—
60C5×#120—333no—
61C5×#99—333no—
62C2×D3×C11—161no—
63C11×A4—43no—
64C2×C5×A4—443no—
65C5×S4—446no—
66C5×SL(2,𝔽3)—881no—
67C2×C11⋊C5—63no—
68C2×C11⋊C5—122no—
69C2×C11⋊C5#102011yescharacteristic
70#997C2×C11⋊C511yescharacteristic, complemented
71C23×C11—31no—
72C23×C11—63no—
73C23×C11—122no—
74C23×C11C5×S413yescomplemented
75Q8×C11—21no—
76D4×C11—63no—
77D4×C11—126no—
78C2×C4×C11—33no—
79C2×C4×C11—63no—
80C24×C5—331no—
81C5×#41—661no—
82C2×C5×D4—333no—
83C2×C5×D4—663no—
84C5×C22⋊C4—333no—
85C5×C22⋊C4—663no—
86C2×C3×C11—161no—
87D3×C11—162no—
88B(4,𝔽2)—31noSylow
89C2×C5×D3—1761no—
90C5×A4—443no—
91C11⋊C5#593411yescharacteristic, direct product factor, Hall
92C2×S4—43no—
93C22×C11—33no—
94C22×C11—43no—
95C22×C11—66no—
96C22×C11—121no—
97C22×C11—123no—
98C22×C11—121no—
99C4×C11—61no—
100C4×C11—123no—
101C23×C5—113no—
102C23×C5—331no—
103C23×C5—663no—
104C23×C5—1322no—
105C5×Q8—221no—
106C5×D4—663no—
107C5×D4—1326no—
108C2×C4×C5—333no—
109C2×C4×C5—663no—
110C3×C11—161noHall
111H(5,𝔽2)D3×C11⋊C511yescharacteristic, complemented
112#120—33no—
113#99—33no—
114C2×C3×C5—1761no—
115C5×D3—1762no—
116C2×A4—43no—
117S4—46no—
118SL(2,𝔽3)—81no—
119C2×C11—63no—
120C2×C11—122no—
121C2×C11C5×#102011yescharacteristic
122C22×C5—333no—
123C22×C5—443no—
124C22×C5—666no—
125C22×C5—1321no—
126C22×C5—1321no—
127C22×C5—1323no—
128C4×C5—661no—
129C4×C5—1323no—
130C24—31no—
131#41—61no—
132C2×D4—33no—
133C2×D4—63no—
134C22⋊C4—33no—
135C22⋊C4—63no—
136C3×C5—1761noHall
137C2×D3—161no—
138A4—43no—
139C11C5×#593411yescharacteristic, complemented, Sylow
140C2×C5—111no—
141C2×C5—663no—
142C2×C5—1322no—
143C23—31no—
144C23—63no—
145C23—122no—
146C23S4×C11⋊C513yescomplemented
147Q8—21no—
148D4—63no—
149D4—126no—
150C2×C4—33no—
151C2×C4—63no—
152C2×C3—161no—
153D3—162no—
154C5—111noSylow
155C22—33no—
156C22—43no—
157C22—66no—
158C22—121no—
159C22—123no—
160C22—121no—
161C4—61no—
162C4—123no—
163C3—161noSylow
164C2—63no—
165C2—122no—
166C2C11⋊C5×#102011yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×#1020
commutator, cosocle, hypocenterC11×#997C2×C5
FittingC11×H(5,𝔽2)C5×D3
socleC2×C11C5×#1020
LCSG ▷ C11×#997
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C11×#5934C5semidirect
3. C11⋊C5×#997C2semidirect
5. H(5,𝔽2)×C11⋊C5D3semidirect
11. C11×#997C2×C5semidirect
27. C23×C11⋊C5S4semidirect
33. C11×H(5,𝔽2)C5×D3semidirect
51. #5934C11⋊C5direct (N × H)
70. #997C2×C11⋊C5semidirect
74. C23×C11C5×S4semidirect
91. C11⋊C5#5934direct (N × H)
111. H(5,𝔽2)D3×C11⋊C5semidirect
139. C11C5×#5934semidirect
146. C23S4×C11⋊C5semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#59345
C2×S4×C11⋊C54
C11⋊C5×#9972
C11⋊C5×B(4,𝔽2)3
C5×#593411