Finite Group Databasebeta

← #14285349

Subgroups — #14285349

Order 1920.

456 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 120 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×D5×C4⋊Q8C211yesmaximal, characteristic
2#11746871C212yesmaximal
3#11746367C211yesmaximal, characteristic, complemented
4C5×#4546C211yesmaximal, characteristic, complemented
5#11745861C212yesmaximal, complemented
6#10599280—31nomaximal, Hall
7C2×C3×Q8×D5C412yes—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×#4090C412yes—
10C3×D5×C4⋊C4—22no—
11C3×#4034—22no—
12C3×C42×D5C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14C4⋊(C3⋊#168)C2212yes—
15C5×C4⋊(C3⋊C8)C2212yes—
16#90955—22no—
17#90952—22no—
18#71777—51nomaximal, Hall
19D5×C4⋊Q8D311yescharacteristic
20#65124—32no—
21C5×#333—31no—
22#64766—31no—
23#64701—32no—
24C2×C3×C5×Q8C2×C412yes—
25C3×Q8×D5—44no—
26C2×C3×C4×D5—22no—
27C2×C3×C4×D5C2×C411yescharacteristic
28C2×C3×C4×D5D412yes—
29C2×C3×Dic10—22no—
30C2×C3×Dic10C2×C412yes—
31C3×C5×C4⋊C4—22no—
32C3×C42×C5C2311yescharacteristic
33C2×C3⋊#168—22no—
34C2×C5×C3⋊C8—22no—
35C3×C4⋊Dic5—22no—
36C3×#683—24no—
37C3×C4×Dic5C2×C411yescharacteristic
38C3×C4×Dic5D412yes—
39C2×C3×C4⋊Q8—51no—
40#4926—52no—
41#4546—51no—
42#4546—52no—
43#4546D511yescharacteristic, complemented
44C2×Q8×D5Dic312yes—
45C5×C4⋊Q8C2×D311yescharacteristic
46#4090Dic312yes—
47D5×C4⋊C4—22no—
48#4034—22no—
49C42×D5C2×D311yescharacteristic
50#4015C2×D311yescharacteristic
51C5×C4⋊C8—32no—
52#3952—62no—
53#3947—62no—
54C4⋊#168—32no—
55#1558—151noSylow
56C22×C3×D5C22⋊C411yescharacteristic
57C3×C5×Q8—42no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C22×C411yescharacteristic
60C2×C3×C4×C5C2×D412yes—
61C2×C3×Dic5—22no—
62C2×C3×Dic5C22⋊C412yes—
63C2×C3×Dic5C22⋊C411yescharacteristic
64C3×C4×D5—22no—
65C3×C4×D5—22no—
66C3×C4×D5—22no—
67C3×C4×D5—44no—
68C3×Dic10—44no—
69C3×Dic10—42no—
70C3⋊#168—42no—
71C5×C3⋊C8—42no—
72C22×C3×Q8—52no—
73C3×C4⋊Q8—52no—
74C3×C4⋊Q8—51no—
75C3×C4⋊Q8—102no—
76C3×C4⋊Q8C2×D511yescharacteristic
77C2×C3×C4⋊C4—102no—
78C2×C3×C42—51no—
79#830—102no—
80C4⋊(C3⋊C8)—52no—
81C4⋊(C3⋊C8)C2×D512yes—
82#803—102no—
83C2×C5×Q8C2×Dic312yes—
84Q8×D5—44no—
85C2×C4×D5—22no—
86C2×C4×D5C2×Dic311yescharacteristic
87C2×C4×D5#6712yes—
88C2×Dic10—22no—
89C2×Dic10C2×Dic312yes—
90C2×C5×C8—62no—
91C5×C4⋊C4—22no—
92C42×C5C22×D311yescharacteristic
93C4⋊Dic5—22no—
94#683—24no—
95C4×Dic5C2×Dic311yescharacteristic
96C4×Dic5#6712yes—
97C2×#168—62no—
98C2×C4⋊Q8—51no—
99#432—152no—
100#333—31no—
101#333—152no—
102#333—151no—
103C22×C3×C5C2×C22⋊C411yescharacteristic
104C2×C3×D5—22no—
105C2×C3×D5#10012yes—
106C3×C4×C5—21no—
107C3×C4×C5—42no—
108C3×C4×C5#13712yes—
109C3×C4×C5#13712yes—
110C3×Dic5—21no—
111C3×Dic5—22no—
112C3×Dic5—42no—
113C2×C3×Q8—52no—
114C2×C3×Q8—102no—
115C2×C3×Q8—204no—
116C2×C3×Q8C4×D512yes—
117C22×C3×C4—51no—
118C22×C3×C4—52no—
119C22×C3×C4—102no—
120C3×C4⋊C4—22no—
121C3×C4⋊C4—104no—
122C3×C4⋊C4—102no—
123C3×C42—51no—
124C3×C42—52no—
125C3×C42C22×D511yescharacteristic
126C2×C3⋊C8—22no—
127C2×C3⋊C8—102no—
128C22×D5#21711yescharacteristic
129C5×Q8—42no—
130C2×C4×C5—22no—
131C2×C4×C5C22×Dic311yescharacteristic
132C2×C4×C5C2×#6712yes—
133C2×Dic5—22no—
134C2×Dic5#21712yes—
135C2×Dic5#21711yescharacteristic
136C4×D5—22no—
137C4×D5—22no—
138C4×D5—22no—
139C4×D5—44no—
140Dic10—44no—
141Dic10—42no—
142C5×C8—122no—
143#168—122no—
144C22×Q8—52no—
145C4⋊Q8—52no—
146C4⋊Q8—51no—
147C4⋊Q8—102no—
148C4⋊Q8D3×D511yescharacteristic
149C2×C4⋊C4—102no—
150C2×C42—51no—
151C4⋊C8—32no—
152C4⋊C8—152no—
153C22⋊C8—302no—
154#97—302no—
155C2×C3×C5C2×#10011yescharacteristic
156C2×C3×C5#41912yes—
157C3×D5—22no—
158C23×C3—51no—
159C3×Q8—42no—
160C3×Q8—202no—
161C3×Q8—204no—
162C2×C3×C4—22no—
163C2×C3×C4—52no—
164C2×C3×C4—51no—
165C2×C3×C4—102no—
166C2×C3×C4—102no—
167C2×C3×C4—102no—
168C2×C3×C4—102no—
169C2×C3×C4—204no—
170C2×C3×C4C2×C4×D511yescharacteristic
171C2×C3×C4D4×D512yes—
172C3⋊C8—42no—
173C3⋊C8—202no—
174C22×C5C2×#21711yescharacteristic
175C2×D5—22no—
176C2×D5#83312yes—
177C4×C5—21no—
178C4×C5—42no—
179C4×C5#94212yes—
180C4×C5#94212yes—
181Dic5—21no—
182Dic5—22no—
183Dic5—42no—
184C2×Q8—52no—
185C2×Q8—102no—
186C2×Q8—204no—
187C2×Q8D5×Dic312yes—
188C22×C4—51no—
189C22×C4—52no—
190C22×C4—102no—
191C2×C8—62no—
192C2×C8—302no—
193C4⋊C4—22no—
194C4⋊C4—104no—
195C4⋊C4—102no—
196C42—51no—
197C42—52no—
198C42C2×D3×D511yescharacteristic
199C3×C5#155811yescharacteristic, complemented, Hall
200C22×C3—52no—
201C22×C3—102no—
202C22×C3D5×C22⋊C411yescharacteristic
203C3×C4—21no—
204C3×C4—42no—
205C3×C4—101no—
206C3×C4—102no—
207C3×C4—202no—
208C3×C4#406112yes—
209C3×C4#406412yes—
210C2×C5C2×#83311yescharacteristic
211C2×C5#522512yes—
212D5—22no—
213C23—51no—
214Q8—42no—
215Q8—202no—
216Q8—204no—
217C2×C4—22no—
218C2×C4—52no—
219C2×C4—51no—
220C2×C4—102no—
221C2×C4—102no—
222C2×C4—102no—
223C2×C4—102no—
224C2×C4—204no—
225C2×C4C2×D5×Dic311yescharacteristic
226C2×C4D5×#6712yes—
227C8—122no—
228C8—602no—
229C2×C3—102no—
230C2×C3D5×#10011yescharacteristic
231C2×C3#6509112yes—
232C5#7177711yescharacteristic, complemented, Sylow
233C22—52no—
234C22—102no—
235C22D5×#21711yescharacteristic
236C4—21no—
237C4—42no—
238C4—101no—
239C4—102no—
240C4—202no—
241C4#9151312yes—
242C4#9151512yes—
243C3#1059928011yescharacteristic, complemented, Sylow
244C2—102no—
245C2D5×#83311yescharacteristic
246C2#1174920812yes—
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1558
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #11746367C2semidirect
4. C5×#4546C2semidirect
5. #11745861C2semidirect
43. #4546D5semidirect
199. C3×C5#1558semidirect
232. C5#71777semidirect
243. C3#10599280semidirect

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
#117468712
#117463672
C5×#45462
#117458612
#105992803
#717775