Finite Group Databasebeta

← #14284729

Subgroups — #14284729

Order 1920.

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

normal subgroups only

This group has 492 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
1C5×#5725C211yesmaximal, characteristic
2#11746853C212yesmaximal, complemented
3#11746367C211yesmaximal, characteristic, complemented
4C3×#64766C211yesmaximal, characteristic, complemented
5#11745853C212yesmaximal, complemented
6#10602598—31nomaximal, Hall
7C2×C5×#239C412yes—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C5×#947C412yes—
10C5×#895—22no—
11C5×#893—22no—
12C5×#874C2211yescharacteristic
13C42×C5×D3C2211yescharacteristic
14C4⋊(C3⋊#168)C2212yes—
15C3×C4⋊#168C2212yes—
16(C2×D3)⋊#168—22no—
17Dic3×#168—22no—
18#68482—51nomaximal, Hall
19C5×#532—31no—
20#65214—32no—
21#64766—31no—
22#64766D311yescharacteristic, complemented
23#64764—32no—
24C2×C3×C5×Q8C2×C412yes—
25C5×#239—44no—
26C2×C5×D12—22no—
27C2×C5×D12—22no—
28C2×C5×D12C2×C412yes—
29C2×C4×C5×D3—22no—
30C2×C4×C5×D3C2×C411yescharacteristic
31C2×C4×C5×D3D412yes—
32C3×C5×C4⋊C4—22no—
33C3×C42×C5C2311yescharacteristic
34C2×C3⋊#168—22no—
35C5×(C2×D3)⋊C4—24no—
36C4×C5×Dic3C2×C411yescharacteristic
37C4×C5×Dic3D412yes—
38C2×C3×#168—22no—
39#5725D511yescharacteristic
40#4833—52no—
41C3×#333—51no—
42#4546—51no—
43#4485—52no—
44C2×C5×#41—32no—
45C5×C4⋊Q8C2×D311yescharacteristic
46C5×#127—31no—
47C5×#124—32no—
48C5×#121—62no—
49C4×C5×D4—62no—
50C2×C42×C5—31no—
51C22⋊#168—62no—
52C4⋊#168—32no—
53C4⋊#168C2×D312yes—
54C4×#168—62no—
55#1543—151noSylow
56C22×C5×D3—22no—
57C22×C5×D3C22⋊C411yescharacteristic
58C3×C5×Q8—42no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5C22×C411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×C5×Dic3C22⋊C412yes—
63C2×C5×Dic3C22⋊C411yescharacteristic
64C5×D12—42no—
65C5×D12—44no—
66C5×D12—42no—
67C5×D12—42no—
68C4×C5×D3—22no—
69C4×C5×D3—22no—
70C4×C5×D3—22no—
71C4×C5×D3—44no—
72C3⋊#168—42no—
73C3×#168—42no—
74C2×#239Dic512yes—
75C3×C4⋊Q8C2×D511yescharacteristic
76#947Dic512yes—
77#895—22no—
78#893—22no—
79#874C2×D511yescharacteristic
80C42×D3C2×D511yescharacteristic
81C3×C4⋊C8—52no—
82(C2×D3)⋊C8—102no—
83C8×Dic3—102no—
84C4⋊(C3⋊C8)—52no—
85C5×#41—124no—
86C2×C5×Q8C4×D312yes—
87C2×C5×D4—32no—
88C2×C5×D4—62no—
89C2×C5×D4—62no—
90C22×C4×C5—31no—
91C22×C4×C5—32no—
92C22×C4×C5—62no—
93C5×C4⋊C4—22no—
94C5×C22⋊C4—64no—
95C42×C5—31no—
96C42×C5—32no—
97C42×C5C22×D311yescharacteristic
98C2×#168—22no—
99C2×#168—62no—
100#532—31no—
101#431—152no—
102#333—51no—
103#333—151no—
104#331—152no—
105C22×C3×C5C2×C22⋊C411yescharacteristic
106C2×C5×D3—21no—
107C2×C5×D3—22no—
108C2×C5×D3—42no—
109C2×C5×D3—44no—
110C3×C4×C5—21no—
111C3×C4×C5—42no—
112C3×C4×C5#13512yes—
113C3×C4×C5#13512yes—
114C5×Dic3—22no—
115C5×Dic3#10012yes—
116C2×C3×Q8C2×Dic512yes—
117#239—44no—
118C2×D12—22no—
119C2×D12—22no—
120C2×D12C2×Dic512yes—
121C2×C4×D3—22no—
122C2×C4×D3C2×Dic511yescharacteristic
123C2×C4×D3C22⋊D512yes—
124C2×C3×C8—102no—
125C3×C4⋊C4—22no—
126C3×C42C22×D511yescharacteristic
127(C2×D3)⋊C4—24no—
128C4×Dic3C2×Dic511yescharacteristic
129C4×Dic3C22⋊D512yes—
130C2×C3⋊C8—102no—
131C23×C5—31no—
132C23×C5—62no—
133C5×Q8—42no—
134C5×D4—122no—
135C5×D4—124no—
136C5×D4—122no—
137C5×D4—122no—
138C2×C4×C5—22no—
139C2×C4×C5—31no—
140C2×C4×C5—32no—
141C2×C4×C5—62no—
142C2×C4×C5—62no—
143C2×C4×C5—62no—
144C2×C4×C5—124no—
145C2×C4×C5C2×C4×D311yescharacteristic
146C2×C4×C5D3×D412yes—
147#168—42no—
148#168—122no—
149C2×#41—32no—
150C4⋊Q8D3×D511yescharacteristic
151#127—31no—
152#124—32no—
153#121—62no—
154C4×D4—62no—
155C2×C42—31no—
156C4⋊C8—52no—
157C4⋊C8—152no—
158C22⋊C8—302no—
159C4×C8—302no—
160C2×C3×C5C2×#10011yescharacteristic
161C2×C3×C5#41612yes—
162C5×D3—41no—
163C5×D3—82no—
164C22×D3—22no—
165C22×D3C22⋊Dic511yescharacteristic
166C3×Q8—42no—
167C2×C3×C4—22no—
168C2×C3×C4C22×Dic511yescharacteristic
169C2×C3×C4C2×C22⋊D512yes—
170C2×Dic3C22⋊Dic512yes—
171C2×Dic3C22⋊Dic511yescharacteristic
172D12—42no—
173D12—44no—
174D12—42no—
175D12—42no—
176C4×D3—22no—
177C4×D3—22no—
178C4×D3—22no—
179C4×D3—44no—
180C3×C8—202no—
181C3⋊C8—202no—
182C22×C5—61no—
183C22×C5—62no—
184C22×C5—122no—
185C22×C5—124no—
186C22×C5D3×C22⋊C411yescharacteristic
187C4×C5—21no—
188C4×C5—32no—
189C4×C5—42no—
190C4×C5—62no—
191C4×C5#91612yes—
192C4×C5#91912yes—
193#41—124no—
194C2×Q8D3×Dic512yes—
195C2×D4—32no—
196C2×D4—62no—
197C2×D4—62no—
198C22×C4—31no—
199C22×C4—32no—
200C22×C4—62no—
201C2×C8—102no—
202C2×C8—302no—
203C4⋊C4—22no—
204C22⋊C4—64no—
205C42—31no—
206C42—32no—
207C42C2×D3×D511yescharacteristic
208C3×C5#154311yescharacteristic, complemented, Hall
209C22×C3C2×C22⋊Dic511yescharacteristic
210C2×D3—21no—
211C2×D3—22no—
212C2×D3—42no—
213C2×D3—44no—
214C3×C4—21no—
215C3×C4—42no—
216C3×C4#409612yes—
217C3×C4#409612yes—
218Dic3—22no—
219Dic3#396512yes—
220C2×C5—121no—
221C2×C5—242no—
222C2×C5D3×#10011yescharacteristic
223C2×C5#480412yes—
224C23—31no—
225C23—62no—
226Q8—42no—
227D4—122no—
228D4—124no—
229D4—122no—
230D4—122no—
231C2×C4—22no—
232C2×C4—31no—
233C2×C4—32no—
234C2×C4—62no—
235C2×C4—62no—
236C2×C4—62no—
237C2×C4—124no—
238C2×C4C2×D3×Dic511yescharacteristic
239C2×C4D3×C22⋊D512yes—
240C8—202no—
241C8—602no—
242C2×C3C2×#396511yescharacteristic
243C2×C3#6552212yes—
244D3—41no—
245D3—82no—
246C5#6848211yescharacteristic, complemented, Sylow
247C22—61no—
248C22—62no—
249C22—122no—
250C22—124no—
251C22D3×C22⋊Dic511yescharacteristic
252C4—21no—
253C4—32no—
254C4—42no—
255C4—62no—
256C4#9151712yes—
257C4#9151912yes—
258C3#1060259811yescharacteristic, complemented, Sylow
259C2—121no—
260C2—242no—
261C2D3×#396511yescharacteristic
262C2#1174921112yes—
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5725C2
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1543
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
2. #11746853C2semidirect
3. #11746367C2semidirect
4. C3×#64766C2semidirect
5. #11745853C2semidirect
22. #64766D3semidirect
208. C3×C5#1543semidirect
246. C5#68482semidirect
258. C3#10602598semidirect

Maximal subgroups

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

subgroupindex
C5×#57252
#117468532
#117463672
C3×#647662
#117458532
#106025983
#684825