Finite Group Databasebeta

← #14313457

Subgroups — #14313457

Order 1920.

572 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 81 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#11756433C211yesmaximal, characteristic
2D15×#99C212yesmaximal, complemented
3C3×C5×#354C211yesmaximal, characteristic, complemented
4#11746362C211yesmaximal, characteristic, complemented
5#11746295C212yesmaximal, complemented
6#10599950—31nomaximal, Hall
7C2×#6821C411yescharacteristic, complemented
8C2×D4×D15C2211yescharacteristic
9C3×C5×#124C2211yescharacteristic
10#91836C411yescharacteristic, complemented
11#91829C2211yescharacteristic
12#91773—22no—
13#91771—22no—
14C22⋊C4×D15—22no—
15#91763C411yescharacteristic, complemented
16#91761C411yescharacteristic, complemented
17C3×C5×#99C2212yes—
18#91118C2212yes—
19#91090—22no—
20#69157—51nomaximal, Hall
21#66008—31no—
22D5×#99—32no—
23C5×#354D311yescharacteristic, complemented
24#64761—31no—
25#64694—32no—
26C23×D15D412yes—
27C2×C3×C5×Q8C2×C411yescharacteristic, complemented
28C2×C3×C5×D4C2311yescharacteristic
29C2×#1220—22no—
30C2×#1220D412yes—
31#6821—42no—
32D4×D15—42no—
33C2×D60—21no—
34C2×D60—22no—
35C2×D60C2×C411yescharacteristic
36C2×D60C2×C411yescharacteristic, complemented
37C2×C4×D15—21no—
38C2×C4×D15—42no—
39C2×C4×D15C2×C411yescharacteristic
40C3×C5×C22⋊C4—22no—
41C3×C5×C22⋊C4—22no—
42C3×C42×C5C2×C411yescharacteristic, complemented
43#6719—22no—
44#6714—21no—
45#6714—22no—
46#6714—42no—
47#6712—21no—
48C4×Dic15C2×C411yescharacteristic, complemented
49#5674—51no—
50D3×#99—52no—
51C3×#354D511yescharacteristic, complemented
52#4541—51no—
53#4474—52no—
54C2×#713—31no—
55C2×D4×D5—31no—
56C5×#124C2×D311yescharacteristic
57#4093—31no—
58#4086—31no—
59#4030—62no—
60#4028—62no—
61D5×C22⋊C4—62no—
62#4020—31no—
63#4018—31no—
64C5×#99C2×D312yes—
65#3966—32no—
66#3938—62no—
67#2127—151noSylow
68C23×C3×C5C2×D412yes—
69C22×D15—22no—
70C22×D15—22no—
71C22×D15—21no—
72C22×D15—82no—
73C22×D15C22⋊C412yes—
74C22×D15C22⋊C411yescharacteristic
75C3×C5×Q8—41no—
76C3×C5×D4—41no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—42no—
80C2×C3×C4×C5C22×C411yescharacteristic
81#1220—42no—
82#1220—82no—
83C2×Dic15—21no—
84C2×Dic15—42no—
85C2×Dic15C22⋊C411yescharacteristic
86D60—41no—
87D60—41no—
88D60—42no—
89D60—82no—
90C4×D15—22no—
91C4×D15—42no—
92C4×D15—84no—
93C2×#239—51no—
94C2×D3×D4—51no—
95C3×#124C2×D511yescharacteristic
96#947—51no—
97#940—51no—
98#884—102no—
99#882—102no—
100D3×C22⋊C4—102no—
101#874—51no—
102#872—51no—
103C3×#99C2×D512yes—
104#834—52no—
105#806—102no—
106C23×D5—32no—
107C2×C5×Q8C4×D311yescharacteristic, complemented
108C2×C5×D4C22×D311yescharacteristic
109C2×C22⋊D5—32no—
110C2×C22⋊D5—62no—
111#713—122no—
112D4×D5—122no—
113C2×D20—31no—
114C2×D20—31no—
115C2×D20—61no—
116C2×D20—62no—
117C2×C4×D5—31no—
118C2×C4×D5—61no—
119C2×C4×D5—122no—
120C5×C22⋊C4—22no—
121C5×C22⋊C4—22no—
122C42×C5C4×D311yescharacteristic, complemented
123C22⋊Dic5—62no—
124#685—61no—
125#685—62no—
126#685—122no—
127#683—61no—
128C4×Dic5—31no—
129#535—151no—
130C2×#99—152no—
131#354—151no—
132#354D1511yescharacteristic, complemented
133#353—152no—
134C22×C3×C5—22no—
135C22×C3×C5—42no—
136C22×C3×C5C2×C22⋊C411yescharacteristic
137C2×D15—22no—
138C2×D15—41no—
139C2×D15—44no—
140C2×D15—42no—
141C2×D15—42no—
142C2×D15—41no—
143C2×D15—82no—
144C2×D15#9912yes—
145C3×C4×C5—21no—
146C3×C4×C5—41no—
147C3×C4×C5—41no—
148C3×C4×C5—82no—
149Dic15—21no—
150Dic15—41no—
151Dic15—82no—
152C23×D3—52no—
153C2×C3×Q8C4×D511yescharacteristic, complemented
154C2×C3×D4C22×D511yescharacteristic
155C2×#67—52no—
156C2×#67—102no—
157#239—202no—
158D3×D4—202no—
159C2×D12—51no—
160C2×D12—51no—
161C2×D12—101no—
162C2×D12—102no—
163C2×C4×D3—51no—
164C2×C4×D3—101no—
165C2×C4×D3—202no—
166C3×C22⋊C4—22no—
167C3×C22⋊C4—22no—
168C3×C42C4×D511yescharacteristic, complemented
169#217—102no—
170(C2×D3)⋊C4—101no—
171(C2×D3)⋊C4—102no—
172(C2×D3)⋊C4—202no—
173Dic3⋊C4—101no—
174C4×Dic3—51no—
175C23×C5D3×D412yes—
176C22×D5—31no—
177C22×D5—32no—
178C22×D5—62no—
179C22×D5—62no—
180C22×D5—61no—
181C22×D5—242no—
182C5×Q8—41no—
183C5×D4—41no—
184C2×C4×C5—21no—
185C2×C4×C5—21no—
186C2×C4×C5—42no—
187C2×C4×C5C2×C4×D311yescharacteristic
188C22⋊D5—122no—
189C22⋊D5—242no—
190C2×Dic5—31no—
191C2×Dic5—61no—
192C2×Dic5—122no—
193D20—121no—
194D20—121no—
195D20—122no—
196D20—242no—
197C4×D5—62no—
198C4×D5—122no—
199C4×D5—244no—
200C2×#41—151no—
201C22×D4—151no—
202#127—151no—
203#127—151no—
204#124—151no—
205#124C2×D1511yescharacteristic
206#121—302no—
207#120—302no—
208#117—151no—
209C2×C22⋊C4—302no—
210#99—152no—
211#99—302no—
212#99C2×D1512yes—
213C2×C3×C5—21no—
214C2×C3×C5—42no—
215C2×C3×C5C2×#9911yescharacteristic
216D15—22no—
217D15—42no—
218D15—81no—
219C23×C3D4×D512yes—
220C22×D3—51no—
221C22×D3—52no—
222C22×D3—102no—
223C22×D3—102no—
224C22×D3—101no—
225C22×D3—402no—
226C3×Q8—41no—
227C3×D4—41no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—42no—
231C2×C3×C4C2×C4×D511yescharacteristic
232#67—202no—
233#67—402no—
234C2×Dic3—51no—
235C2×Dic3—101no—
236C2×Dic3—202no—
237D12—201no—
238D12—201no—
239D12—202no—
240D12—402no—
241C4×D3—102no—
242C4×D3—202no—
243C4×D3—404no—
244C22×C5—22no—
245C22×C5—42no—
246C22×C5D3×C22⋊C411yescharacteristic
247C2×D5—32no—
248C2×D5—62no—
249C2×D5—121no—
250C2×D5—124no—
251C2×D5—122no—
252C2×D5—122no—
253C2×D5—121no—
254C2×D5—242no—
255C4×C5—21no—
256C4×C5—41no—
257C4×C5—41no—
258C4×C5—82no—
259Dic5—61no—
260Dic5—121no—
261Dic5—242no—
262C24—152no—
263#41—602no—
264C2×Q8C4×D1511yescharacteristic, complemented
265C2×D4—152no—
266C2×D4—151no—
267C2×D4—151no—
268C2×D4—301no—
269C2×D4—302no—
270C2×D4—302no—
271C2×D4—602no—
272C2×D4C22×D1511yescharacteristic
273C22×C4—151no—
274C22×C4—301no—
275C22×C4—602no—
276C4⋊C4—301no—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—301no—
280C22⋊C4—302no—
281C22⋊C4—302no—
282C22⋊C4—602no—
283C42—151no—
284C42C4×D1511yescharacteristic, complemented
285C3×C5#212711yescharacteristic, complemented, Hall
286C22×C3—22no—
287C22×C3—42no—
288C22×C3D5×C22⋊C411yescharacteristic
289C2×D3—52no—
290C2×D3—102no—
291C2×D3—201no—
292C2×D3—204no—
293C2×D3—202no—
294C2×D3—202no—
295C2×D3—201no—
296C2×D3—402no—
297C3×C4—21no—
298C3×C4—41no—
299C3×C4—41no—
300C3×C4—82no—
301Dic3—101no—
302Dic3—201no—
303Dic3—402no—
304C2×C5—21no—
305C2×C5—42no—
306C2×C5D3×#9911yescharacteristic
307D5—62no—
308D5—122no—
309D5—241no—
310C23—151no—
311C23—152no—
312C23—302no—
313C23—302no—
314C23—301no—
315C23—1202no—
316C23D4×D1512yes—
317Q8—41no—
318D4—41no—
319D4—601no—
320D4—601no—
321D4—602no—
322D4—602no—
323D4—1202no—
324D4—1202no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—151no—
329C2×C4—302no—
330C2×C4—301no—
331C2×C4—602no—
332C2×C4—602no—
333C2×C4—1204no—
334C2×C4C2×C4×D1511yescharacteristic
335C2×C3—21no—
336C2×C3—42no—
337C2×C3D5×#9911yescharacteristic
338D3—102no—
339D3—202no—
340D3—401no—
341C5#6915711yescharacteristic, complemented, Sylow
342C22—22no—
343C22—42no—
344C22—152no—
345C22—302no—
346C22—601no—
347C22—602no—
348C22—602no—
349C22—604no—
350C22—601no—
351C22—1202no—
352C22C22⋊C4×D1511yescharacteristic
353C4—21no—
354C4—41no—
355C4—41no—
356C4—82no—
357C4—301no—
358C4—601no—
359C4—1202no—
360C3#1059995011yescharacteristic, complemented, Sylow
361C2—21no—
362C2—42no—
363C2—302no—
364C2—602no—
365C2—1201no—
366C2D15×#9911yescharacteristic
subgroupG/H
centerC2D15×#99
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×D4C22×D15
FittingC3×C5×#354C2
socleC2×C3×C5C2×#99
prime radical#11756433C2
cosocleC2×C3×C5×D4C23
hypercenter#354D15
hypocenterC3×C5#2127
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. D15×#99C2semidirect
3. C3×C5×#354C2semidirect
4. #11746362C2semidirect
5. #11746295C2semidirect
7. C2×#6821C4semidirect
10. #91836C4semidirect
15. #91763C4semidirect
16. #91761C4semidirect
23. C5×#354D3semidirect
27. C2×C3×C5×Q8C2×C4semidirect
36. C2×D60C2×C4semidirect
42. C3×C42×C5C2×C4semidirect
48. C4×Dic15C2×C4semidirect
51. C3×#354D5semidirect
107. C2×C5×Q8C4×D3semidirect
122. C42×C5C4×D3semidirect
132. #354D15semidirect
153. C2×C3×Q8C4×D5semidirect
168. C3×C42C4×D5semidirect
264. C2×Q8C4×D15semidirect
284. C42C4×D15semidirect
285. C3×C5#2127semidirect
341. C5#69157semidirect
360. C3#10599950semidirect

Maximal subgroups

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

subgroupindex
#117564332
D15×#992
C3×C5×#3542
#117463622
#117462952
#105999503
#691575