Finite Group Databasebeta

← #14288151

Subgroups — #14288151

Order 1920.

476 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 91 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#11756259C211yesmaximal, characteristic
2#11751080C211yesmaximal, characteristic
3#11750840C212yesmaximal
4C3×C5×#324C211yesmaximal, characteristic
5#11746288C212yesmaximal
6#10598932—31nomaximal, Hall
7C22×Dic30C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9#91815—21no—
10#91813—21no—
11#91813C2212yes—
12C2×#6712—21no—
13C2×Dic60—22no—
14#91779—22no—
15#91777—22no—
16C3×C5×C22⋊C8C2212yes—
17#91115—21no—
18#91115C2211yescharacteristic
19#91100—22no—
20#68139—51nomaximal, Hall
21#65834—31no—
22#65268—31no—
23#65028—32no—
24C5×#324D311yescharacteristic
25#64687—32no—
26C22×C3×C4×C5D411yescharacteristic
27C22×C3×C4×C5D411yescharacteristic
28C22×C3×C4×C5C2311yescharacteristic
29C22×Dic15—21no—
30C22×Dic15—21no—
31C2×Dic30—22no—
32C2×Dic30—21no—
33C2×Dic30—42no—
34C2×Dic30D412yes—
35C2×C3×C5×C8—22no—
36C3×C5×C4⋊C4—22no—
37#6719—22no—
38C4⋊Dic15—21no—
39C4⋊Dic15—21no—
40C4⋊Dic15—21no—
41C4⋊Dic15D412yes—
42#6712—22no—
43#6712—22no—
44#6712—42no—
45C4×Dic15—22no—
46Dic60—44no—
47#5500—51no—
48#4979—51no—
49#4739—52no—
50C3×#324D511yescharacteristic
51#4467—52no—
52C22×Dic10—31no—
53C2×C5×C4⋊C4C2×D311yescharacteristic
54#4072—61no—
55#4070—32no—
56#4070—61no—
57C2×#683—61no—
58C2×Dic20—62no—
59#4036—62no—
60#4034—62no—
61C5×C22⋊C8C2×D312yes—
62#3963—31no—
63#3963—61no—
64#3948—62no—
65#1605—151noSylow
66C23×C3×C5C2×D411yescharacteristic
67C2×C3×C4×C5—21no—
68C2×C3×C4×C5—21no—
69C2×C3×C4×C5—21no—
70C2×C3×C4×C5—41no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5Q1612yescomplemented
73C2×C3×C4×C5C2×D412yes—
74C2×Dic15—22no—
75C2×Dic15—22no—
76C2×Dic15—22no—
77C2×Dic15—22no—
78C2×Dic15—41no—
79C2×Dic15—41no—
80C2×Dic15—41no—
81C2×Dic15—41no—
82Dic30—24no—
83Dic30—42no—
84Dic30—42no—
85Dic30—81no—
86C3×C5×C8—42no—
87C22×Dic6—51no—
88C2×C3×C4⋊C4C2×D511yescharacteristic
89#926—101no—
90#924—52no—
91#924—101no—
92C2×Dic3⋊C4—101no—
93C2×Dic12—102no—
94#890—102no—
95#888—102no—
96C3×C22⋊C8C2×D512yes—
97C3⋊#95—51no—
98C3⋊#95—101no—
99#816—102no—
100C22×C4×C5D1211yescharacteristic
101C22×C4×C5D1211yescharacteristic
102C22×C4×C5C22×D311yescharacteristic
103C22×Dic5—61no—
104C22×Dic5—61no—
105C2×Dic10—32no—
106C2×Dic10—62no—
107C2×Dic10—61no—
108C2×Dic10—122no—
109C2×C5×C8—22no—
110C5×C4⋊C4—22no—
111C22⋊Dic5—62no—
112C4⋊Dic5—32no—
113C4⋊Dic5—61no—
114C4⋊Dic5—61no—
115C4⋊Dic5—61no—
116#683—62no—
117#683—62no—
118#683—122no—
119C4×Dic5—62no—
120Dic20—124no—
121#544—151no—
122#451—152no—
123#395—151no—
124#328—152no—
125#324D1511yescharacteristic
126C22×C3×C5—21no—
127C22×C3×C5—21no—
128C22×C3×C5#12011yescharacteristic
129C22×C3×C5C2×Q1611yescharacteristic
130C22×C3×C5#13711yescharacteristic
131C3×C4×C5—22no—
132C3×C4×C5—22no—
133C3×C4×C5—41no—
134Dic15—42no—
135Dic15—42no—
136Dic15—42no—
137Dic15—42no—
138C22×C3×C4D2011yescharacteristic
139C22×C3×C4D2011yescharacteristic
140C22×C3×C4C22×D511yescharacteristic
141C22×Dic3—101no—
142C22×Dic3—101no—
143C2×Dic6—52no—
144C2×Dic6—102no—
145C2×Dic6—101no—
146C2×Dic6—202no—
147C2×C3×C8—22no—
148C3×C4⋊C4—22no—
149#217—102no—
150C4⋊Dic3—52no—
151C4⋊Dic3—101no—
152C4⋊Dic3—101no—
153C4⋊Dic3—101no—
154Dic3⋊C4—102no—
155Dic3⋊C4—102no—
156Dic3⋊C4—202no—
157C4×Dic3—102no—
158Dic12—204no—
159C23×C5C2×D1211yescharacteristic
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5Dic1212yescomplemented
166C2×C4×C5D3×D412yes—
167C2×Dic5—62no—
168C2×Dic5—62no—
169C2×Dic5—62no—
170C2×Dic5—62no—
171C2×Dic5—121no—
172C2×Dic5—121no—
173C2×Dic5—121no—
174C2×Dic5—121no—
175Dic10—64no—
176Dic10—122no—
177Dic10—122no—
178Dic10—241no—
179C5×C8—42no—
180C22×Q8—151no—
181C2×Q16—302no—
182C4⋊Q8—302no—
183#125—302no—
184C22⋊Q8—152no—
185C22⋊Q8—301no—
186#117—301no—
187C2×C4⋊C4—301no—
188C2×C4⋊C4C2×D1511yescharacteristic
189#103—302no—
190C22⋊C8C2×D1512yes—
191#95—151no—
192#95—301no—
193C2×C3×C5—21no—
194C2×C3×C5—21no—
195C2×C3×C5#45111yescharacteristic
196C2×C3×C5#45611yescharacteristic
197C2×C3×C5B(4,𝔽2)11yescharacteristic
198C23×C3C2×D2011yescharacteristic
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—41no—
203C2×C3×C4—41no—
204C2×C3×C4Dic2012yescomplemented
205C2×C3×C4D4×D512yes—
206C2×Dic3—102no—
207C2×Dic3—102no—
208C2×Dic3—102no—
209C2×Dic3—102no—
210C2×Dic3—201no—
211C2×Dic3—201no—
212C2×Dic3—201no—
213C2×Dic3—201no—
214Dic6—104no—
215Dic6—202no—
216Dic6—202no—
217Dic6—401no—
218C3×C8—42no—
219C22×C5—21no—
220C22×C5—21no—
221C22×C5#88211yescharacteristic
222C22×C5C2×Dic1211yescharacteristic
223C22×C5#90911yescharacteristic
224C4×C5—22no—
225C4×C5—22no—
226C4×C5—41no—
227Dic5—122no—
228Dic5—122no—
229Dic5—122no—
230Dic5—122no—
231C2×Q8—152no—
232C2×Q8—301no—
233C2×Q8—302no—
234C2×Q8—602no—
235C22×C4—301no—
236C22×C4—301no—
237C22×C4D6011yescharacteristic
238C22×C4D6011yescharacteristic
239C22×C4C22×D1511yescharacteristic
240Q16—604no—
241C2×C8—22no—
242C4⋊C4—22no—
243C4⋊C4—152no—
244C4⋊C4—301no—
245C4⋊C4—301no—
246C4⋊C4—301no—
247C4⋊C4—302no—
248C4⋊C4—302no—
249C4⋊C4—602no—
250C22⋊C4—302no—
251C42—302no—
252C3×C5#160511yescharacteristic, complemented, Hall
253C22×C3—21no—
254C22×C3—21no—
255C22×C3#402811yescharacteristic
256C22×C3C2×Dic2011yescharacteristic
257C22×C3#405511yescharacteristic
258C3×C4—22no—
259C3×C4—22no—
260C3×C4—41no—
261Dic3—202no—
262Dic3—202no—
263Dic3—202no—
264Dic3—202no—
265C2×C5—21no—
266C2×C5—21no—
267C2×C5#473911yescharacteristic
268C2×C5#474111yescharacteristic
269C2×C5#475211yescharacteristic
270C23C2×D6011yescharacteristic
271Q8—304no—
272Q8—602no—
273Q8—602no—
274Q8—1201no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—302no—
281C2×C4—302no—
282C2×C4—302no—
283C2×C4—302no—
284C2×C4—601no—
285C2×C4—601no—
286C2×C4—601no—
287C2×C4—601no—
288C2×C4Dic6012yescomplemented
289C2×C4D4×D1512yes—
290C8—42no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3#6502811yescharacteristic
294C2×C3#6503011yescharacteristic
295C2×C3#6504111yescharacteristic
296C5#6813911yescharacteristic, complemented, Sylow
297C22—21no—
298C22—21no—
299C22#9177111yescharacteristic
300C22C2×Dic6011yescharacteristic
301C22#9179811yescharacteristic
302C4—22no—
303C4—22no—
304C4—41no—
305C4—602no—
306C4—602no—
307C4—602no—
308C4—602no—
309C3#1059893211yescharacteristic, complemented, Sylow
310C2—21no—
311C2—21no—
312C2#1175084011yescharacteristic
313C2#1175084211yescharacteristic
314C2#1175085311yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#324C2
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
hypercenter#324D15
hypocenterC3×C5#1605
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
72. C2×C3×C4×C5Q16semidirect
165. C2×C4×C5Dic12semidirect
204. C2×C3×C4Dic20semidirect
252. C3×C5#1605semidirect
288. C2×C4Dic60semidirect
296. C5#68139semidirect
309. C3#10598932semidirect

Maximal subgroups

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

subgroupindex
#117562592
#117510802
#117508402
C3×C5×#3242
#117462882
#105989323
#681395