Finite Group Databasebeta

← #14278019

Subgroups — #14278019

Order 1920.

208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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#11751238C211yesmaximal, characteristic
2C5×#4553C211yesmaximal, characteristic
3C3×#64777C211yesmaximal, characteristic
4#10598027—31nomaximal, Hall
5C2×C3×C5×M16C2211yescharacteristic
6#91813—21no—
7C2×Dic60C411yescharacteristic, complemented
8C3×#4072—21no—
9#91101C411yescharacteristic, complemented
10#91100—21no—
11C5×#812—21no—
12#67482—51nomaximal, Hall
13#65426—31no—
14C5×#349—31no—
15#64777D311yescharacteristic
16C22×C3×C4×C5D411yescharacteristic
17C2×Dic30—21no—
18C3×C5×M16—41no—
19C2×C3×C5×C8C2×C411yescharacteristic
20C2×C3×C5×C8D411yescharacteristic
21#6719—41no—
22C4⋊Dic15—21no—
23#6712—41no—
24Dic60—41no—
25C3×C22⋊Dic5—41no—
26C3×C4⋊Dic5—41no—
27C3×C4×Dic5—22no—
28C5×C3⋊C16—41no—
29#5137—51no—
30C3×H(3,ℤ/4)—51no—
31#4553D511yescharacteristic
32C2×C5×M16C2×D311yescharacteristic
33#4072—21no—
34#4070—61no—
35C2×Dic20—31no—
36C5×M32—61no—
37#3949—31no—
38#3948—61no—
39#1340—151noSylow
40C23×C3×C5D811yescharacteristic
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C2×C3×C4×C5SD1611yescharacteristic
45C2×Dic15—41no—
46C2×Dic15—41no—
47Dic30—41no—
48Dic30—41no—
49C2×C3×Dic5—42no—
50C3×C5×C8—21no—
51C3×C5×C8—21no—
52C2×C3×M16C2×D511yescharacteristic
53C3×#117—101no—
54#924—101no—
55C2×Dic12—51no—
56#817—51no—
57#816—101no—
58#812—21no—
59C22×C4×C5#6711yescharacteristic
60C2×Dic10—61no—
61C5×M16—41no—
62C2×C5×C8C4×D311yescharacteristic
63C2×C5×C8D1211yescharacteristic
64C22⋊Dic5—41no—
65C22⋊Dic5—121no—
66C4⋊Dic5—41no—
67C4⋊Dic5—61no—
68#683—121no—
69C4×Dic5—22no—
70Dic20—121no—
71C5×C16—121no—
72#470—151no—
73#349—31no—
74H(3,ℤ/4)—51no—
75C22×C3×C5—21no—
76C22×C3×C5—41no—
77C22×C3×C5#10211yescharacteristic
78C3×C4×C5—21no—
79C3×C4×C5#9911yescharacteristic
80C3×C4×C5#10411yescharacteristic
81Dic15—81no—
82Dic15—81no—
83C3×Dic5—82no—
84C22×C3×C4D2011yescharacteristic
85C2×Dic6—101no—
86C3×M16—41no—
87C2×C3×C8C4×D511yescharacteristic
88C2×C3×C8C22⋊D511yescharacteristic
89C3×C4⋊C4—201no—
90C3×C22⋊C4—201no—
91C3×C42—102no—
92#217—201no—
93C4⋊Dic3—101no—
94Dic3⋊C4—201no—
95Dic12—201no—
96C3⋊C16—41no—
97C23×C5#21311yescharacteristic
98C2×C4×C5—21no—
99C2×C4×C5—21no—
100C2×C4×C5(C2×D3)⋊C411yescharacteristic
101C2×C4×C5#21511yescharacteristic
102C2×Dic5—42no—
103C2×Dic5—121no—
104C2×Dic5—121no—
105Dic10—121no—
106Dic10—121no—
107C5×C8—21no—
108C5×C8—21no—
109C2×Q16—151no—
110C2×M16D3×D511yescharacteristic
111C22⋊Q8—301no—
112#117—101no—
113M32—61no—
114#106—151no—
115#103—301no—
116C2×C3×C5—21no—
117C2×C3×C5—41no—
118C2×C3×C5#32711yescharacteristic
119C23×C3D4011yescharacteristic
120C2×C3×C4—21no—
121C2×C3×C4—21no—
122C2×C3×C4—202no—
123C2×C3×C4#67711yescharacteristic
124C2×C3×C4#68511yescharacteristic
125C2×Dic3—201no—
126C2×Dic3—201no—
127Dic6—201no—
128Dic6—201no—
129C3×C8—21no—
130C3×C8—21no—
131C22×C5—21no—
132C22×C5—41no—
133C22×C5#80911yescharacteristic
134C4×C5—21no—
135C4×C5#80511yescharacteristic
136C4×C5#80611yescharacteristic
137Dic5—82no—
138Dic5—241no—
139Dic5—241no—
140C2×Q8—301no—
141C22×C4#120211yescharacteristic
142Q16—601no—
143M16—41no—
144C2×C8#120011yescharacteristic
145C2×C8#120311yescharacteristic
146C4⋊C4—201no—
147C4⋊C4—301no—
148C4⋊C4—601no—
149C22⋊C4—201no—
150C22⋊C4—601no—
151C42—102no—
152C16—121no—
153C3×C5#134011yescharacteristic, complemented, Hall
154C22×C3—21no—
155C22×C3—41no—
156C22×C3#395311yescharacteristic
157C3×C4—21no—
158C3×C4—402no—
159C3×C4#393811yescharacteristic
160C3×C4#395711yescharacteristic
161Dic3—401no—
162Dic3—401no—
163C2×C5—21no—
164C2×C5—41no—
165C2×C5#445111yescharacteristic
166C23#665311yescharacteristic
167Q8—601no—
168Q8—601no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—202no—
172C2×C4—601no—
173C2×C4—601no—
174C2×C4#665811yescharacteristic
175C2×C4#666711yescharacteristic
176C8—21no—
177C8—21no—
178C2×C3—21no—
179C2×C3—41no—
180C2×C3#6469011yescharacteristic
181C5#6748211yescharacteristic, complemented, Sylow
182C22—21no—
183C22—41no—
184C22#9096811yescharacteristic
185C4—21no—
186C4—402no—
187C4—1201no—
188C4—1201no—
189C4#9098111yescharacteristic
190C4#9099711yescharacteristic
191C3#1059802711yescharacteristic, complemented, Sylow
192C2—21no—
193C2—41no—
194C2#1174595811yescharacteristic
subgroupG/H
centerC2#11745958
commutatorC2×C3×C5×C8C2×C4
Frattini, hypercenterC2×M16D3×D5
Fitting, cosocleC2×C3×C5×M16C22
socleC2×C3×C5#327
prime radicalC23×C3×C5D8
hypocenterC3×C5#1340
LCSG ▷ C2×C3×C5×C8 ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
7. C2×Dic60C4semidirect
9. #91101C4semidirect
153. C3×C5#1340semidirect
181. C5#67482semidirect
191. C3#10598027semidirect

Maximal subgroups

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

subgroupindex
#117512382
C5×#45532
C3×#647772
#105980273
#674825