Finite Group Databasebeta

← #14303013

Subgroups — #14303013

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5804C211yesmaximal, characteristic
2C3×#66132C211yesmaximal, characteristic, complemented
3C2×#91118C211yesmaximal, characteristic, complemented
4C2×#90996C212yesmaximal, complemented
5#11746020C212yesmaximal, complemented
6#10602641—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C22×C5×#67C2211yescharacteristic
9C2×#6719C2212yes—
10C5×#953—21no—
11C2×C5×#217C2211yescharacteristic
12C5×#939—22no—
13C5×#937C412yescomplemented
14C5×#935C412yescomplemented
15C5×#929—21no—
16C2×C3×C22⋊Dic5—21no—
17C2×C3×C22⋊Dic5C2212yes—
18C3×D4×Dic5—24no—
19C3×#4072—21no—
20#91118—22no—
21#90996—24no—
22#71656—51nomaximal, Hall
23C5×#534—31no—
24#66132D311yescharacteristic, complemented
25C2×#3966—31no—
26C2×#3966—32no—
27#64747—32no—
28C24×C3×C5D411yescharacteristic
29C24×C3×C5C2311yescharacteristic
30C23×C5×D3C2×C411yescharacteristic, complemented
31C2×C3×C5×D4—22no—
32C2×C3×C5×D4—22no—
33C2×C3×C5×D4C2×C412yes—
34C2×C3×C5×D4D412yes—
35C22×C3×C4×C5D411yescharacteristic
36C22×Dic15—22no—
37C2×C5×#67—21no—
38C2×C5×#67—21no—
39C2×C5×#67—22no—
40C2×C5×#67—22no—
41C2×C5×#67—22no—
42C22×C5×Dic3—21no—
43C22×C5×Dic3C2×C411yescharacteristic, complemented
44C22×C3×Dic5—22no—
45C22×C3×Dic5—22no—
46#6719—22no—
47#6719—22no—
48C5×#217—22no—
49C5×#217—21no—
50C5×#217C2×C412yescomplemented
51C5×(C2×D3)⋊C4—22no—
52C5×Dic3⋊C4—22no—
53C3×C22⋊Dic5—22no—
54C3×C22⋊Dic5—22no—
55C3×C22⋊Dic5D414yescomplemented
56C3×C4⋊Dic5—22no—
57C3×C4×Dic5—22no—
58C3×#518—51no—
59#5804D511yescharacteristic
60C2×#834—51no—
61C2×#806—52no—
62#4527—52no—
63C22×C5×D4—31no—
64C22×C5×D4C2×D311yescharacteristic
65C5×#123—32no—
66C5×#123—61no—
67C5×#121—62no—
68C5×#120—32no—
69C5×#120—61no—
70C2×C5×C22⋊C4—31no—
71C2×C22⋊Dic5—21no—
72C2×C22⋊Dic5—32no—
73C2×C22⋊Dic5C2×D312yes—
74D4×Dic5—24no—
75#4072—21no—
76#3966—62no—
77#3966—64no—
78#1913—151noSylow
79C23×C3×C5—21no—
80C23×C3×C5—21no—
81C23×C3×C5—81no—
82C23×C3×C5—81no—
83C23×C3×C5C22⋊C412yes—
84C23×C3×C5C22×C411yescharacteristic
85C23×C3×C5C2×D411yescharacteristic
86C23×C3×C5C2×D411yescharacteristic
87C23×C3×C5C2×D412yes—
88C23×C3×C5#4112yes—
89C22×C5×D3—21no—
90C22×C5×D3—22no—
91C22×C5×D3—81no—
92C3×C5×D4—24no—
93C3×C5×D4—24no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22⋊C412yes—
97C2×Dic15—42no—
98C2×Dic15—82no—
99C5×#67—41no—
100C5×#67—42no—
101C5×#67—41no—
102C5×#67—82no—
103C2×C5×Dic3—21no—
104C2×C5×Dic3—22no—
105C2×C5×Dic3—22no—
106C2×C5×Dic3—81no—
107C2×C3×Dic5—24no—
108C2×C3×Dic5—82no—
109C2×C3×Dic5—82no—
110C22×C3×D4C2×D511yescharacteristic
111C22×#67C2×D511yescharacteristic
112C3×C4×D4—104no—
113C3×#117—101no—
114C2×C3×C22⋊C4—52no—
115C2×C3×C22⋊C4—101no—
116#953—21no—
117C2×#217—52no—
118C2×#217C2×D511yescharacteristic
119#939—22no—
120#937Dic512yescomplemented
121#935Dic512yescomplemented
122#929—21no—
123#834—102no—
124#806—104no—
125C24×C5—31no—
126C24×C5#6711yescharacteristic
127C24×C5C22×D311yescharacteristic
128C2×C5×D4—22no—
129C2×C5×D4—22no—
130C2×C5×D4—61no—
131C2×C5×D4—62no—
132C2×C5×D4—61no—
133C2×C5×D4—62no—
134C2×C5×D4—62no—
135C2×C5×D4C4×D312yes—
136C2×C5×D4D1212yes—
137C22×C4×C5—31no—
138C22×C4×C5—61no—
139C22×C4×C5#6711yescharacteristic
140C22×Dic5—22no—
141C22×Dic5—22no—
142C22×Dic5—62no—
143C5×C4⋊C4—62no—
144C5×C22⋊C4—32no—
145C5×C22⋊C4—62no—
146C5×C22⋊C4—61no—
147C5×C22⋊C4—62no—
148C22⋊Dic5—22no—
149C22⋊Dic5—22no—
150C22⋊Dic5—62no—
151C22⋊Dic5—62no—
152C22⋊Dic5#6714yescomplemented
153C4⋊Dic5—22no—
154C4×Dic5—22no—
155#534—31no—
156#518—51no—
157C2×#99—152no—
158C2×#99—151no—
159#342—152no—
160C22×C3×C5—22no—
161C22×C3×C5—42no—
162C22×C3×C5—41no—
163C22×C3×C5—42no—
164C22×C3×C5—41no—
165C22×C3×C5—41no—
166C22×C3×C5—42no—
167C22×C3×C5—42no—
168C22×C3×C5—81no—
169C22×C3×C5C2×C22⋊C411yescharacteristic
170C22×C3×C5C4×D412yes—
171C22×C3×C5#12011yescharacteristic
172C22×C3×C5#12112yes—
173C22×C3×C5#12311yescharacteristic
174C2×C5×D3—42no—
175C2×C5×D3—41no—
176C2×C5×D3—82no—
177C3×C4×C5—22no—
178Dic15—82no—
179C3×Dic5—44no—
180C5×Dic3—42no—
181C5×Dic3—41no—
182C24×C3C22⋊D511yescharacteristic
183C24×C3C22×D511yescharacteristic
184C23×D3C2×Dic511yescharacteristic, complemented
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4C2×Dic512yes—
188C2×C3×D4C22⋊D512yes—
189C22×C3×C4—102no—
190C22×C3×C4—102no—
191C22×C3×C4C22⋊D511yescharacteristic
192C2×#67—22no—
193C2×#67—22no—
194C2×#67—21no—
195C2×#67—21no—
196C2×#67—22no—
197C22×Dic3—21no—
198C22×Dic3—102no—
199C22×Dic3C2×Dic511yescharacteristic, complemented
200C3×C4⋊C4—102no—
201C3×C22⋊C4—54no—
202C3×C22⋊C4—102no—
203C3×C22⋊C4—102no—
204C3×C42—102no—
205#217—22no—
206#217—21no—
207#217—102no—
208#217—102no—
209#217C2×Dic512yescomplemented
210(C2×D3)⋊C4—22no—
211Dic3⋊C4—22no—
212C23×C5—21no—
213C23×C5—21no—
214C23×C5—61no—
215C23×C5—62no—
216C23×C5—81no—
217C23×C5—81no—
218C23×C5—241no—
219C23×C5(C2×D3)⋊C412yes—
220C23×C5C2×C4×D311yescharacteristic
221C23×C5C2×D1211yescharacteristic
222C23×C5#23512yes—
223C23×C5C2×#6711yescharacteristic
224C23×C5C2×#6712yes—
225C5×D4—24no—
226C5×D4—24no—
227C5×D4—121no—
228C5×D4—122no—
229C5×D4—121no—
230C5×D4—242no—
231C2×C4×C5—21no—
232C2×C4×C5—21no—
233C2×C4×C5—62no—
234C2×C4×C5—61no—
235C2×C4×C5—62no—
236C2×C4×C5—241no—
237C2×C4×C5(C2×D3)⋊C412yes—
238C2×Dic5—24no—
239C2×Dic5—82no—
240C2×Dic5—82no—
241C2×Dic5—122no—
242C2×Dic5—242no—
243C22×D4—31no—
244C22×D4D3×D511yescharacteristic
245#123—32no—
246#123—61no—
247#121—62no—
248#120—32no—
249#120—61no—
250C4×D4—104no—
251#117—101no—
252C2×C22⋊C4—31no—
253C2×C22⋊C4—52no—
254C2×C22⋊C4—101no—
255C2×C22⋊C4—152no—
256#99—304no—
257#99—302no—
258C2×C3×C5—21no—
259C2×C3×C5—21no—
260C2×C3×C5—22no—
261C2×C3×C5—22no—
262C2×C3×C5—21no—
263C2×C3×C5—42no—
264C2×C3×C5#38611yescharacteristic
265C5×D3—81no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—81no—
269C23×C3—81no—
270C23×C3C22⋊Dic512yes—
271C23×C3D4×D512yes—
272C23×C3#71112yes—
273C23×C3C22×Dic511yescharacteristic
274C23×C3C2×C22⋊D511yescharacteristic
275C23×C3C2×C22⋊D511yescharacteristic
276C22×D3—21no—
277C22×D3—22no—
278C22×D3—81no—
279C3×D4—24no—
280C3×D4—24no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—104no—
284C2×C3×C4—402no—
285C2×C3×C4—402no—
286C2×C3×C4C22⋊Dic512yes—
287#67—41no—
288#67—41no—
289#67—42no—
290#67—82no—
291C2×Dic3—21no—
292C2×Dic3—22no—
293C2×Dic3—22no—
294C2×Dic3—81no—
295C2×Dic3—202no—
296C2×Dic3—402no—
297C22×C5—22no—
298C22×C5—42no—
299C22×C5—42no—
300C22×C5—41no—
301C22×C5—41no—
302C22×C5—41no—
303C22×C5—42no—
304C22×C5—42no—
305C22×C5—81no—
306C22×C5—122no—
307C22×C5—121no—
308C22×C5—242no—
309C22×C5C2×(C2×D3)⋊C411yescharacteristic
310C22×C5C4×#6712yes—
311C22×C5#92911yescharacteristic
312C22×C5#93012yes—
313C22×C5#95311yescharacteristic
314C4×C5—22no—
315C4×C5—122no—
316C4×C5—121no—
317Dic5—44no—
318Dic5—242no—
319C24—31no—
320C24#120111yescharacteristic
321C24C2×D3×D511yescharacteristic
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—62no—
325C2×D4—61no—
326C2×D4—61no—
327C2×D4—62no—
328C2×D4—62no—
329C2×D4D3×Dic512yes—
330C2×D4#120312yes—
331C22×C4—31no—
332C22×C4—61no—
333C22×C4—102no—
334C22×C4—102no—
335C22×C4—302no—
336C22×C4#120111yescharacteristic
337C4⋊C4—62no—
338C4⋊C4—102no—
339C22⋊C4—32no—
340C22⋊C4—54no—
341C22⋊C4—62no—
342C22⋊C4—61no—
343C22⋊C4—62no—
344C22⋊C4—102no—
345C22⋊C4—102no—
346C22⋊C4—302no—
347C22⋊C4—302no—
348C42—102no—
349C3×C5#191311yescharacteristic, complemented, Hall
350C22×C3—22no—
351C22×C3—41no—
352C22×C3—42no—
353C22×C3—42no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—81no—
359C22×C3D4×Dic512yes—
360C22×C3#408111yescharacteristic
361C22×C3#408311yescharacteristic
362C22×C3#408512yes—
363C22×C3C2×C22⋊Dic511yescharacteristic
364C2×D3—42no—
365C2×D3—41no—
366C2×D3—82no—
367C3×C4—22no—
368C3×C4—204no—
369Dic3—42no—
370Dic3—41no—
371Dic3—402no—
372C2×C5—21no—
373C2×C5—22no—
374C2×C5—21no—
375C2×C5—21no—
376C2×C5—22no—
377C2×C5—42no—
378C2×C5—241no—
379C2×C5#521311yescharacteristic
380C23—21no—
381C23—21no—
382C23—61no—
383C23—62no—
384C23—81no—
385C23—81no—
386C23—241no—
387C23(C2×D3)⋊Dic512yes—
388C23C2×D3×Dic511yescharacteristic
389C23#678212yes—
390C23C2×#120111yescharacteristic
391C23C2×#120311yescharacteristic
392C23D5×#6712yes—
393D4—24no—
394D4—24no—
395D4—121no—
396D4—121no—
397D4—122no—
398D4—242no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—62no—
402C2×C4—61no—
403C2×C4—62no—
404C2×C4—104no—
405C2×C4—241no—
406C2×C4—402no—
407C2×C4—402no—
408C2×C4—602no—
409C2×C4—1202no—
410C2×C4(C2×D3)⋊Dic512yes—
411C2×C3—21no—
412C2×C3—22no—
413C2×C3—21no—
414C2×C3—22no—
415C2×C3—21no—
416C2×C3—42no—
417C2×C3#6550911yescharacteristic
418D3—81no—
419C5#7165611yescharacteristic, complemented, Sylow
420C22—22no—
421C22—41no—
422C22—42no—
423C22—42no—
424C22—41no—
425C22—41no—
426C22—42no—
427C22—42no—
428C22—81no—
429C22—122no—
430C22—121no—
431C22—242no—
432C22C2×(C2×D3)⋊Dic511yescharacteristic
433C22#9153911yescharacteristic
434C22Dic5×#6712yes—
435C22#9156311yescharacteristic
436C22#9156612yes—
437C4—22no—
438C4—122no—
439C4—121no—
440C4—204no—
441C4—1202no—
442C3#1060264111yescharacteristic, complemented, Sylow
443C2—21no—
444C2—21no—
445C2—22no—
446C2—21no—
447C2—22no—
448C2—42no—
449C2—241no—
450C2#1174949211yescharacteristic
subgroupG/H
centerC2#11749492
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC22×C3×C5×D4C22
socleC2×C3×C5#386
prime radicalC5×#5804C2
cosocleC24×C3×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1913
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C3×#66132C2semidirect
3. C2×#91118C2semidirect
4. C2×#90996C2semidirect
5. #11746020C2semidirect
13. C5×#937C4semidirect
14. C5×#935C4semidirect
24. #66132D3semidirect
30. C23×C5×D3C2×C4semidirect
43. C22×C5×Dic3C2×C4semidirect
50. C5×#217C2×C4semidirect
55. C3×C22⋊Dic5D4semidirect
120. #937Dic5semidirect
121. #935Dic5semidirect
152. C22⋊Dic5#67semidirect
184. C23×D3C2×Dic5semidirect
199. C22×Dic3C2×Dic5semidirect
209. #217C2×Dic5semidirect
349. C3×C5#1913semidirect
419. C5#71656semidirect
442. C3#10602641semidirect

Maximal subgroups

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

subgroupindex
C5×#58042
C3×#661322
C2×#911182
C2×#909962
#117460202
#106026413
#716565