Finite Group Databasebeta

← #14278015

Subgroups — #14278015

Order 1920.

208 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C3×#65426C211yesmaximal, characteristic
2#11746374C211yesmaximal, characteristic
3C5×#4557C211yesmaximal, characteristic
4#10597973—31nomaximal, Hall
5C2×C3×C5×M16C2211yescharacteristic
6C5×#926—21no—
7C3×#4070—21no—
8C2×C3×Dic20C411yescharacteristic, complemented
9#91096—21no—
10C3×#3949C411yescharacteristic, complemented
11C3×#3948—21no—
12#67780—51nomaximal, Hall
13#65426D311yescharacteristic
14C5×H(3,ℤ/4)—31no—
15#64773—31no—
16C22×C3×C4×C5D411yescharacteristic
17C2×C3×Dic10—21no—
18C3×C5×M16—41no—
19C2×C3×C5×C8C2×C411yescharacteristic
20C2×C3×C5×C8D411yescharacteristic
21C5×#217—41no—
22C5×C4⋊Dic3—41no—
23C4×C5×Dic3—22no—
24C3×C22⋊Dic5—41no—
25C3×C4⋊Dic5—21no—
26C3×#683—41no—
27C3×Dic20—41no—
28C3⋊#672—41no—
29C3×#470—51no—
30#4557D511yescharacteristic
31#4553—51no—
32C2×C5×M16C2×D311yescharacteristic
33C5×#117—61no—
34#4070—21no—
35C2×Dic20Dic311yescharacteristic, complemented
36#3949Dic311yescharacteristic, complemented
37#3948—21no—
38#3944—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×C5×Dic3—42no—
46C2×C3×Dic5—41no—
47C2×C3×Dic5—41no—
48C3×Dic10—41no—
49C3×Dic10—41no—
50C3×C5×C8—21no—
51C3×C5×C8—21no—
52C2×C3×Q16—51no—
53C2×C3×M16C2×D511yescharacteristic
54C3×C22⋊Q8—101no—
55#926—21no—
56C3×#106—51no—
57C3×#103—101no—
58#812—101no—
59C22×C4×C5#6711yescharacteristic
60C2×Dic10—21no—
61C5×M16—41no—
62C2×C5×C8C2×Dic311yescharacteristic
63C2×C5×C8#6711yescharacteristic
64C5×C4⋊C4—121no—
65C5×C22⋊C4—121no—
66C42×C5—62no—
67C22⋊Dic5—41no—
68C4⋊Dic5—21no—
69#683—41no—
70Dic20—41no—
71#672—121no—
72#470—51no—
73#349—151no—
74H(3,ℤ/4)—31no—
75C22×C3×C5—21no—
76C22×C3×C5—41no—
77C22×C3×C5#10211yescharacteristic
78C3×C4×C5—21no—
79C3×C4×C5#9911yescharacteristic
80C3×C4×C5#10411yescharacteristic
81C3×Dic5—81no—
82C3×Dic5—81no—
83C5×Dic3—82no—
84C2×C3×Q8—101no—
85C22×C3×C4C22⋊D511yescharacteristic
86C3×Q16—201no—
87C3×M16—41no—
88C2×C3×C8C4×D511yescharacteristic
89C2×C3×C8D2011yescharacteristic
90C3×C4⋊C4—101no—
91C3×C4⋊C4—201no—
92C3×C22⋊C4—201no—
93#217—41no—
94C4⋊Dic3—41no—
95C4×Dic3—22no—
96C3⋊C16—201no—
97C23×C5#21311yescharacteristic
98C2×C4×C5—21no—
99C2×C4×C5—21no—
100C2×C4×C5—122no—
101C2×C4×C5#21411yescharacteristic
102C2×C4×C5#21711yescharacteristic
103C2×Dic5—41no—
104C2×Dic5—41no—
105Dic10—41no—
106Dic10—41no—
107C5×C8—21no—
108C5×C8—21no—
109C2×Q16—51no—
110C2×M16D3×D511yescharacteristic
111C22⋊Q8—101no—
112#117—61no—
113M32—301no—
114#106—51no—
115#103—101no—
116C2×C3×C5—21no—
117C2×C3×C5—41no—
118C2×C3×C5#32711yescharacteristic
119C23×C3#68611yescharacteristic
120C3×Q8—201no—
121C3×Q8—201no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—201no—
125C2×C3×C4—201no—
126C2×C3×C4#68511yescharacteristic
127C2×C3×C4#68811yescharacteristic
128C2×Dic3—42no—
129C3×C8—21no—
130C3×C8—21no—
131C22×C5—21no—
132C22×C5—41no—
133C22×C5#83211yescharacteristic
134C4×C5—21no—
135C4×C5—242no—
136C4×C5#83411yescharacteristic
137C4×C5#83711yescharacteristic
138Dic5—81no—
139Dic5—81no—
140C2×Q8—101no—
141C22×C4#120111yescharacteristic
142Q16—201no—
143M16—41no—
144C2×C8D5×Dic311yescharacteristic
145C2×C8#120211yescharacteristic
146C4⋊C4—101no—
147C4⋊C4—121no—
148C4⋊C4—201no—
149C22⋊C4—121no—
150C22⋊C4—201no—
151C42—62no—
152C16—601no—
153C3×C5#134011yescharacteristic, complemented, Hall
154C22×C3—21no—
155C22×C3—41no—
156C22×C3#394111yescharacteristic
157C3×C4—21no—
158C3×C4—401no—
159C3×C4—401no—
160C3×C4#393711yescharacteristic
161C3×C4#393811yescharacteristic
162Dic3—82no—
163C2×C5—21no—
164C2×C5—41no—
165C2×C5#453711yescharacteristic
166C23#665211yescharacteristic
167Q8—201no—
168Q8—201no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—122no—
172C2×C4—201no—
173C2×C4—201no—
174C2×C4#665511yescharacteristic
175C2×C4#666511yescharacteristic
176C8—21no—
177C8—21no—
178C2×C3—21no—
179C2×C3—41no—
180C2×C3#6467111yescharacteristic
181C5#6778011yescharacteristic, complemented, Sylow
182C22—21no—
183C22—41no—
184C22#9096411yescharacteristic
185C4—21no—
186C4—242no—
187C4—401no—
188C4—401no—
189C4#9097711yescharacteristic
190C4#9099511yescharacteristic
191C3#1059797311yescharacteristic, complemented, Sylow
192C2—21no—
193C2—41no—
194C2#1174595411yescharacteristic
subgroupG/H
centerC2#11745954
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
8. C2×C3×Dic20C4semidirect
10. C3×#3949C4semidirect
35. C2×Dic20Dic3semidirect
36. #3949Dic3semidirect
153. C3×C5#1340semidirect
181. C5#67780semidirect
191. C3#10597973semidirect

Maximal subgroups

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

subgroupindex
C3×#654262
#117463742
C5×#45572
#105979733
#677805