Finite Group Databasebeta

← #14278024

Subgroups — #14278024

Order 1920.

208 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 46 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
1#11747944C211yesmaximal, characteristic
2#11746766C211yesmaximal, characteristic
3C3×#64891C211yesmaximal, characteristic
4#10598600—31nomaximal, Hall
5#91989—21no—
6C2×Dic60C411yescharacteristic, complemented
7C2×C3×#676C2211yescharacteristic
8#91360—21no—
9C3×#3998—21no—
10C5×#817C411yescharacteristic, complemented
11#90975—21no—
12#67536—51nomaximal, Hall
13#65157—31no—
14#64895—31no—
15#64891D311yescharacteristic
16C2×Dic30—21no—
17C2×C3×C4×D5D411yescharacteristic
18#6763—41no—
19C4⋊ΓL(1,𝔽16)—41no—
20C4×ΓL(1,𝔽16)—22no—
21C2×C3×C5×C8C2×C411yescharacteristic
22Dic60—41no—
23C5×C4⋊Dic3—21no—
24C2×C3×#168D411yescharacteristic
25C3×#676—41no—
26Dic3⋊Dic5—41no—
27#6665—41no—
28C3×#674—41no—
29#5137—51no—
30C3×#349—51no—
31#4557—51no—
32#4130—61no—
33C2×Dic20—31no—
34C2×#676C2×D311yescharacteristic
35#4043—61no—
36#3998—21no—
37C5×#106—31no—
38#3942—61no—
39#1340—151noSylow
40C22×C3×D5D811yescharacteristic
41C2×ΓL(1,𝔽16)—42no—
42C2×C3×C4×C5C22⋊C411yescharacteristic
43C2×Dic15—41no—
44Dic30—41no—
45Dic30—41no—
46C2×C5×Dic3—41no—
47C2×C3×Dic5SD1611yescharacteristic
48C3×C4×D5—21no—
49C3×C4×D5—21no—
50C3×C5×C8—21no—
51C3×#168—21no—
52C2×C3×M16—51no—
53#926—101no—
54#924—101no—
55C2×Dic12—51no—
56C3×M32—101no—
57#817AGL(1,𝔽5)11yescharacteristic, complemented
58#816—101no—
59C2×C4×D5D1211yescharacteristic
60C2×Dic10—61no—
61C22⋊AGL(1,𝔽5)—121no—
62C4⋊AGL(1,𝔽5)—121no—
63C4×AGL(1,𝔽5)—62no—
64C2×C5×C8C4×D311yescharacteristic
65C5×C4⋊C4—61no—
66#685—121no—
67C4⋊Dic5—121no—
68C2×#168#6711yescharacteristic
69Dic20—121no—
70#676—41no—
71#674—41no—
72#470—151no—
73#349—51no—
74H(3,ℤ/4)—151no—
75C22×C3×C5#10211yescharacteristic
76C2×C3×D5—21no—
77C2×C3×D5—41no—
78ΓL(1,𝔽16)—82no—
79C3×C4×C5#9911yescharacteristic
80C3×C4×C5#10411yescharacteristic
81Dic15—81no—
82C3×Dic5—21no—
83C5×Dic3—81no—
84C22×C3×C4—51no—
85C2×Dic6—101no—
86C3×M16—201no—
87C2×C3×C8—51no—
88C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
89#217—201no—
90#217—201no—
91C4⋊Dic3—21no—
92C4⋊Dic3—201no—
93Dic3⋊C4—201no—
94C4×Dic3—102no—
95Dic12—201no—
96C3×C16—201no—
97C22×D5D2411yescharacteristic
98C2×AGL(1,𝔽5)—122no—
99C2×C4×C5—121no—
100C2×C4×C5(C2×D3)⋊C411yescharacteristic
101C2×Dic5—121no—
102C2×Dic5#20411yescharacteristic
103C4×D5—21no—
104C4×D5—21no—
105Dic10—121no—
106Dic10—121no—
107C5×C8—21no—
108#168—21no—
109C2×Q16—151no—
110C2×M16—51no—
111C22⋊Q8—301no—
112#117—301no—
113M32—101no—
114#106—31no—
115#103—301no—
116C2×C3×C5—21no—
117C2×C3×C5#32711yescharacteristic
118C3×D5—41no—
119C23×C3—51no—
120C2×C3×C4—51no—
121C2×C3×C4—101no—
122C2×C3×C4—101no—
123C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
124C2×Dic3—41no—
125C2×Dic3—202no—
126C2×Dic3—201no—
127Dic6—201no—
128Dic6—201no—
129C3×C8—21no—
130C3×C8—101no—
131C22×C5#82111yescharacteristic
132C2×D5—21no—
133C2×D5—41no—
134AGL(1,𝔽5)—242no—
135C4×C5—241no—
136C4×C5#80611yescharacteristic
137C4×C5#82511yescharacteristic
138Dic5—21no—
139Dic5—241no—
140C2×Q8—301no—
141C22×C4—51no—
142Q16—601no—
143M16—201no—
144C2×C8—51no—
145C2×C8D3×AGL(1,𝔽5)11yescharacteristic
146C4⋊C4—61no—
147C4⋊C4—601no—
148C4⋊C4—601no—
149C22⋊C4—601no—
150C22⋊C4—601no—
151C42—302no—
152C16—201no—
153C3×C5#134011yescharacteristic, complemented, Hall
154C22×C3—101no—
155C22×C3—201no—
156C22×C3#400711yescharacteristic
157C3×C4—101no—
158C3×C4#399911yescharacteristic
159C3×C4#401011yescharacteristic
160Dic3—81no—
161Dic3—402no—
162Dic3—401no—
163C2×C5—21no—
164C2×C5#447011yescharacteristic
165D5—41no—
166C23—51no—
167Q8—601no—
168Q8—601no—
169C2×C4—51no—
170C2×C4—101no—
171C2×C4—101no—
172C2×C4—121no—
173C2×C4—602no—
174C2×C4—601no—
175C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
176C8—21no—
177C8—101no—
178C2×C3—21no—
179C2×C3—201no—
180C2×C3#6486811yescharacteristic
181C5#6753611yescharacteristic, complemented, Sylow
182C22—101no—
183C22—201no—
184C22#9115211yescharacteristic
185C4—101no—
186C4—241no—
187C4—1202no—
188C4—1201no—
189C4#9115711yescharacteristic
190C4#9117311yescharacteristic
191C3#1059860011yescharacteristic, complemented, Sylow
192C2—21no—
193C2—201no—
194C2#1174649911yescharacteristic
subgroupG/H
centerC2#11746499
commutator, FittingC2×C3×C5×C8C2×C4
Frattini, hypercenterC2×C8D3×AGL(1,𝔽5)
socleC2×C3×C5#327
prime radicalC22×C3×D5D8
cosocleC2×C3×#676C22
hypocenterC3×C5#1340
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
6. C2×Dic60C4semidirect
10. C5×#817C4semidirect
57. #817AGL(1,𝔽5)semidirect
153. C3×C5#1340semidirect
181. C5#67536semidirect
191. C3#10598600semidirect

Maximal subgroups

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

subgroupindex
#117479442
#117467662
C3×#648912
#105986003
#675365