Finite Group Databasebeta

← #14279408

Subgroups — #14279408

Order 1920.

216 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 34 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#11747036C211yesmaximal, characteristic
2#11746725C211yesmaximal, characteristic, complemented
3C3×#64856C211yesmaximal, characteristic, complemented
4#10598540—31nomaximal, Hall
5#91763C411yescharacteristic, complemented
6C3×#4021C2211yescharacteristic
7C2×#6658—21no—
8C2×#6653—21no—
9#91228—21no—
10C3×#4005—21no—
11C5×#803C411yescharacteristic, complemented
12#67548—51nomaximal, Hall
13#65001—31no—
14#64856D311yescharacteristic, complemented
15#64854—31no—
16C2×D60—21no—
17C2×D60—41no—
18C2×C3×D20D411yescharacteristic
19C2×C3×Dic10D411yescharacteristic
20#6763—41no—
21C3×#704—41no—
22C3×C42×C5C2×C411yescharacteristic
23C2×C5×C3⋊C8—21no—
24C3×#685—41no—
25#6658—42no—
26#6653—42no—
27#5058—51no—
28C3×#355—51no—
29#4541—51no—
30C2×D40—61no—
31C2×#677—61no—
32#4021C2×D311yescharacteristic
33#4020—31no—
34#4005—21no—
35#3999—61no—
36C5×#97—31no—
37#1406—151noSylow
38C22×D15—41no—
39C22×C3×D5—21no—
40C2×ΓL(1,𝔽16)—81no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5C22⋊C411yescharacteristic
43D60—41no—
44D60—41no—
45D60—82no—
46C2×C3×Dic5—21no—
47C3×D20—41no—
48C3×Dic10—41no—
49C3×#170—81no—
50C5×C3⋊C8—22no—
51C3×#124—51no—
52C2×#215—101no—
53C2×#213—101no—
54#874—51no—
55C3×#101—101no—
56#834—101no—
57#803AGL(1,𝔽5)11yescharacteristic, complemented
58C2×D20—61no—
59C2×D20—121no—
60C2×D20D1211yescharacteristic
61C2×Dic10#6711yescharacteristic
62C22⋊AGL(1,𝔽5)—121no—
63#704—41no—
64C2×C5×C8—61no—
65C42×C5C4×D311yescharacteristic
66#685—41no—
67D40—122no—
68#677—122no—
69#496—151no—
70#355—51no—
71#354—151no—
72C22×C3×C5#9911yescharacteristic
73C2×D15—82no—
74C2×D15—81no—
75C2×C3×D5—41no—
76C2×C3×D5—81no—
77ΓL(1,𝔽16)—161no—
78C3×C4×C5—21no—
79C3×C4×C5—41no—
80C3×Dic5—41no—
81C2×C3×Q8—51no—
82C2×C3×D4—51no—
83C2×D12—101no—
84C2×D12—201no—
85C3×M16—201no—
86C3×C22⋊C4—201no—
87C3×C42C2×AGL(1,𝔽5)11yescharacteristic
88#217—201no—
89#215—202no—
90#213—202no—
91C2×C3⋊C8—21no—
92C22×D5—21no—
93C22×D5—121no—
94C2×AGL(1,𝔽5)—241no—
95C2×C4×C5—21no—
96C2×C4×C5(C2×D3)⋊C411yescharacteristic
97C2×Dic5—21no—
98D20—41no—
99D20—121no—
100D20—121no—
101D20—242no—
102Dic10—41no—
103#170—81no—
104C5×C8—62no—
105C2×SD16—301no—
106C2×D8—301no—
107#127—151no—
108#124—51no—
109#101—101no—
110#99—301no—
111#97—31no—
112C2×C3×C5—21no—
113C2×C3×C5#35311yescharacteristic
114D15—161no—
115C3×D5—81no—
116C23×C3—101no—
117C22×D3—201no—
118C3×Q8—201no—
119C3×D4—201no—
120C2×C3×C4—21no—
121C2×C3×C4—101no—
122C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
123C2×Dic3—401no—
124D12—201no—
125D12—201no—
126D12—402no—
127C3×C8—401no—
128C3⋊C8—22no—
129C22×C5#80611yescharacteristic
130C2×D5—41no—
131C2×D5—81no—
132C2×D5—242no—
133C2×D5—241no—
134AGL(1,𝔽5)—481no—
135C4×C5—21no—
136C4×C5—41no—
137Dic5—41no—
138C2×Q8—51no—
139C2×D4—51no—
140C2×D4—301no—
141C2×D4—601no—
142SD16—602no—
143D8—602no—
144M16—201no—
145C2×C8—61no—
146C22⋊C4—201no—
147C22⋊C4—601no—
148C42D3×AGL(1,𝔽5)11yescharacteristic
149C3×C5#140611yescharacteristic, complemented, Hall
150C22×C3—201no—
151C22×C3—401no—
152C22×C3#399911yescharacteristic
153C2×D3—402no—
154C2×D3—401no—
155C3×C4—21no—
156C3×C4—41no—
157C3×C4—201no—
158Dic3—801no—
159C2×C5—21no—
160C2×C5#447411yescharacteristic
161D5—81no—
162D5—481no—
163C23—101no—
164C23—601no—
165Q8—201no—
166D4—201no—
167D4—601no—
168D4—601no—
169D4—1202no—
170C2×C4—21no—
171C2×C4—101no—
172C2×C4—1201no—
173C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
174C8—62no—
175C8—401no—
176C2×C3—21no—
177C2×C3—401no—
178C2×C3#6485311yescharacteristic
179D3—801no—
180C5#6754811yescharacteristic, complemented, Sylow
181C22—201no—
182C22—401no—
183C22—1202no—
184C22—1201no—
185C22#9117311yescharacteristic
186C4—21no—
187C4—41no—
188C4—201no—
189C4—2401no—
190C3#1059854011yescharacteristic, complemented, Sylow
191C2—21no—
192C2—401no—
193C2—2401no—
194C2#1174655511yescharacteristic
subgroupG/H
centerC2#11746555
commutator, FittingC3×C42×C5C2×C4
Frattini, hypercenterC42D3×AGL(1,𝔽5)
socleC2×C3×C5#353
prime radical#11747036C2
cosocleC3×#4021C22
hypocenterC3×C5#1406
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #11746725C2semidirect
3. C3×#64856C2semidirect
5. #91763C4semidirect
11. C5×#803C4semidirect
14. #64856D3semidirect
57. #803AGL(1,𝔽5)semidirect
149. C3×C5#1406semidirect
180. C5#67548semidirect
190. C3#10598540semidirect

Maximal subgroups

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

subgroupindex
#117470362
#117467252
C3×#648562
#105985403
#675485