Finite Group Databasebeta

← #14301463

Subgroups — #14301463

Order 1920.

720 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 720 conjugacy classes of subgroups — too many to draw. Only its 164 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
1C2×C5×#936C211yesmaximal, characteristic
2C3×#66132C211yesmaximal, characteristic
3C2×#91117C211yesmaximal, characteristic
4#11748407C212yesmaximal, complemented
5#11745974C212yesmaximal, complemented
6#10602516—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C22×C5×Dic6C2211yescharacteristic
9C2×#6710C2212yes—
10C2×C5×#217—22no—
11C5×#936—22no—
12C5×#936C414yescomplemented
13C2×C4×C5×Dic3C2211yescharacteristic
14C2×C3×C22⋊Dic5—22no—
15C3×D4×Dic5—24no—
16C3×#4072C2212yes—
17#91117—22no—
18#90972—24no—
19#71649—51nomaximal, Hall
20C2×C5×#124—31no—
21#66132D311yescharacteristic
22#65514—32no—
23C2×#3965—31no—
24#64743—32no—
25C24×C3×C5D412yes—
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4C2×C412yes—
29C2×C3×C5×D4D412yes—
30C22×C3×C4×C5C2311yescharacteristic
31C22×C5×Dic3—21no—
32C22×C5×Dic3—21no—
33C2×C5×Dic6—22no—
34C2×C5×Dic6—22no—
35C2×C5×Dic6—21no—
36C2×C5×Dic6C2×C412yescomplemented
37C22×C3×Dic5—24no—
38#6710—22no—
39#6710—22no—
40C2×C3⋊#168—22no—
41C5×#217—28no—
42C4×C5×Dic3—21no—
43C4×C5×Dic3C2×C412yescomplemented
44C3×C22⋊Dic5—24no—
45C3×C22⋊Dic5—22no—
46C3×C4⋊Dic5D414yes—
47C3×C4×Dic5—22no—
48C3×#518—51no—
49C2×#936D511yescharacteristic
50C2×#833—51no—
51#5004—52no—
52#4532—52no—
53C22×C5×Q8—31no—
54C22×C5×D4C2×D311yescharacteristic
55C5×#124—34no—
56C5×#124—62no—
57C2×C5×C22⋊C4—62no—
58C2×C42×C5—31no—
59C2×C22⋊Dic5—22no—
60D4×Dic5—24no—
61#4072C2×D312yes—
62C2×#681—32no—
63#3967—64no—
64#3965—62no—
65#1885—151noSylow
66C23×C3×C5—22no—
67C23×C3×C5—22no—
68C23×C3×C5—44no—
69C23×C3×C5C22⋊C414yes—
70C23×C3×C5C2×D411yescharacteristic
71C3×C5×D4—24no—
72C3×C5×D4—24no—
73C2×C3×C4×C5C22×C411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4112yes—
77C2×C5×Dic3—22no—
78C2×C5×Dic3—22no—
79C2×C5×Dic3—42no—
80C2×C5×Dic3—41no—
81C2×C5×Dic3—41no—
82C5×Dic6—24no—
83C5×Dic6—42no—
84C2×C3×Dic5—24no—
85C2×C3×Dic5—84no—
86C3⋊#168—42no—
87C22×C3×D4C2×D511yescharacteristic
88C22×Dic6C2×D511yescharacteristic
89C3×C4×D4—104no—
90C3×#117—52no—
91C2×C3×C22⋊C4—102no—
92C2×#217—22no—
93#936—22no—
94#936Dic514yescomplemented
95C2×C4×Dic3C2×D511yescharacteristic
96C2×#208—52no—
97#833—102no—
98#810—104no—
99C24×C5#6712yes—
100C2×C5×Q8—32no—
101C2×C5×Q8—61no—
102C2×C5×Q8—62no—
103C2×C5×Q8—62no—
104C2×C5×D4—22no—
105C2×C5×D4—22no—
106C2×C5×D4C4×D312yes—
107C2×C5×D4D1212yes—
108C22×C4×C5—61no—
109C22×C4×C5—61no—
110C22×C4×C5C22×D311yescharacteristic
111C22×Dic5—24no—
112C5×C22⋊C4—68no—
113C42×C5—32no—
114C42×C5—61no—
115C22⋊Dic5—24no—
116C22⋊Dic5—22no—
117C4⋊Dic5#6714yes—
118C4×Dic5—22no—
119#681—62no—
120#681—62no—
121C2×#168—62no—
122C2×#124—31no—
123#518—51no—
124#419—152no—
125C2×#100—151no—
126#339—152no—
127C22×C3×C5—22no—
128C22×C3×C5—24no—
129C22×C3×C5—44no—
130C22×C3×C5—44no—
131C22×C3×C5—82no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C22×C3×C5#12011yescharacteristic
134C22×C3×C5#12311yescharacteristic
135C3×C4×C5C4×D412yes—
136C3×C4×C5#12112yes—
137C3×Dic5—44no—
138C5×Dic3—42no—
139C5×Dic3—42no—
140C24×C3C22⋊D512yes—
141C2×C3×D4—22no—
142C2×C3×D4—22no—
143C2×C3×D4C2×Dic512yes—
144C2×C3×D4C22⋊D512yes—
145C22×C3×C4—104no—
146C22×C3×C4C22×D511yescharacteristic
147C22×Dic3—21no—
148C22×Dic3—21no—
149C2×Dic6—22no—
150C2×Dic6—22no—
151C2×Dic6—21no—
152C2×Dic6C2×Dic512yescomplemented
153C3×C4⋊C4—54no—
154C3×C22⋊C4—104no—
155C3×C22⋊C4—102no—
156C3×C42—102no—
157#217—28no—
158C4×Dic3—21no—
159C4×Dic3C2×Dic512yescomplemented
160#208—102no—
161#208—102no—
162C2×C3⋊C8—102no—
163C23×C5—22no—
164C23×C5—22no—
165C23×C5—44no—
166C23×C5(C2×D3)⋊C414yes—
167C23×C5C2×#6711yescharacteristic
168C5×Q8—64no—
169C5×Q8—122no—
170C5×D4—24no—
171C5×D4—24no—
172C2×C4×C5—62no—
173C2×C4×C5—62no—
174C2×C4×C5—122no—
175C2×C4×C5—121no—
176C2×C4×C5—121no—
177C2×C4×C5C2×C4×D311yescharacteristic
178C2×C4×C5C2×D1211yescharacteristic
179C2×C4×C5#23512yes—
180C2×C4×C5C2×#6712yes—
181C2×Dic5—24no—
182C2×Dic5—84no—
183#168—122no—
184C22×Q8—31no—
185C22×D4D3×D511yescharacteristic
186C2×M16—152no—
187#124—34no—
188#124—62no—
189C4×D4—104no—
190#117—52no—
191C2×C22⋊C4—62no—
192C2×C22⋊C4—102no—
193C2×C42—31no—
194#103—304no—
195#100—302no—
196C2×C3×C5—21no—
197C2×C3×C5—21no—
198C2×C3×C5—44no—
199C2×C3×C5#38611yescharacteristic
200C2×C3×C5#45512yes—
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—44no—
204C23×C3C22⋊Dic514yes—
205C23×C3C2×C22⋊D511yescharacteristic
206C3×D4—24no—
207C3×D4—24no—
208C2×C3×C4—104no—
209C2×C3×C4—404no—
210C2×C3×C4D4×D512yes—
211C2×C3×C4#71112yes—
212C2×C3×C4C22×Dic511yescharacteristic
213C2×C3×C4C2×C22⋊D511yescharacteristic
214C2×Dic3—22no—
215C2×Dic3—22no—
216C2×Dic3—42no—
217C2×Dic3—41no—
218C2×Dic3—41no—
219Dic6—24no—
220Dic6—42no—
221C3⋊C8—202no—
222C22×C5—22no—
223C22×C5—24no—
224C22×C5—44no—
225C22×C5—44no—
226C22×C5—82no—
227C22×C5C2×(C2×D3)⋊C411yescharacteristic
228C22×C5#92911yescharacteristic
229C22×C5#95311yescharacteristic
230C4×C5—122no—
231C4×C5—122no—
232C4×C5C4×#6712yes—
233C4×C5#93012yes—
234Dic5—44no—
235C24#120112yes—
236C2×Q8—32no—
237C2×Q8—61no—
238C2×Q8—62no—
239C2×Q8—62no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4D3×Dic512yes—
243C2×D4#120312yes—
244C22×C4—61no—
245C22×C4—61no—
246C22×C4—104no—
247C22×C4C2×D3×D511yescharacteristic
248M16—302no—
249M16—302no—
250C2×C8—302no—
251C4⋊C4—54no—
252C22⋊C4—68no—
253C22⋊C4—104no—
254C22⋊C4—102no—
255C42—32no—
256C42—61no—
257C42—102no—
258C3×C5#188511yescharacteristic, complemented, Hall
259C22×C3—22no—
260C22×C3—24no—
261C22×C3—44no—
262C22×C3—44no—
263C22×C3—82no—
264C22×C3#408111yescharacteristic
265C22×C3#408311yescharacteristic
266C22×C3C2×C22⋊Dic511yescharacteristic
267C3×C4—204no—
268C3×C4D4×Dic512yes—
269C3×C4#408512yes—
270Dic3—42no—
271Dic3—42no—
272C2×C5—21no—
273C2×C5—21no—
274C2×C5—44no—
275C2×C5#521311yescharacteristic
276C2×C5#524212yes—
277C23—22no—
278C23—22no—
279C23—44no—
280C23(C2×D3)⋊Dic514yes—
281C23C2×#120111yescharacteristic
282Q8—64no—
283Q8—122no—
284D4—24no—
285D4—24no—
286C2×C4—62no—
287C2×C4—62no—
288C2×C4—104no—
289C2×C4—122no—
290C2×C4—121no—
291C2×C4—121no—
292C2×C4—404no—
293C2×C4C2×D3×Dic511yescharacteristic
294C2×C4#678212yes—
295C2×C4C2×#120311yescharacteristic
296C2×C4D5×#6712yes—
297C8—602no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—44no—
301C2×C3#6535012yes—
302C2×C3#6550911yescharacteristic
303C5#7164911yescharacteristic, complemented, Sylow
304C22—22no—
305C22—24no—
306C22—44no—
307C22—44no—
308C22—82no—
309C22C2×(C2×D3)⋊Dic511yescharacteristic
310C22#9153911yescharacteristic
311C22#9156311yescharacteristic
312C4—122no—
313C4—122no—
314C4—204no—
315C4Dic5×#6712yes—
316C4#9156612yes—
317C3#1060251611yescharacteristic, complemented, Sylow
318C2—21no—
319C2—21no—
320C2—44no—
321C2#1174914412yes—
322C2#1174949211yescharacteristic
subgroupG/H
centerC22#91563
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC22×C3×C5#120
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1885
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #11748407C2semidirect
5. #11745974C2semidirect
12. C5×#936C4semidirect
36. C2×C5×Dic6C2×C4semidirect
43. C4×C5×Dic3C2×C4semidirect
94. #936Dic5semidirect
152. C2×Dic6C2×Dic5semidirect
159. C4×Dic3C2×Dic5semidirect
258. C3×C5#1885semidirect
303. C5#71649semidirect
317. C3#10602516semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9362
C3×#661322
C2×#911172
#117484072
#117459742
#106025163
#716495