Finite Group Databasebeta

← #14472072

Subgroups — #14472072

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756480C211yesmaximal, characteristic, complemented
2#11756301C211yesmaximal, characteristic
3C3×C5×#474C211yesmaximal, characteristic
4#11751194C211yesmaximal, characteristic, complemented
5C4×#6716C211yesmaximal, characteristic
6#11750978C212yesmaximal, complemented
7#11750974C212yesmaximal, complemented
8#11750950C211yesmaximal, characteristic, complemented
9#11750931C211yesmaximal, characteristic, complemented
10#11750869C212yesmaximal
11#11750868C212yesmaximal
12#10612725—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14C3×C4×C5×D4C2211yescharacteristic
15Q8×Dic15—21no—
16#91833—21no—
17#91825C2212yes—
18C2×#6716C2211yescharacteristic
19#91815—21no—
20#91813—21no—
21C2×Dic60C2212yes—
22#91779C2212yes—
23#91778—22no—
24#91776C2212yes—
25#91776C2212yes—
26#91768—22no—
27#91758C2211yescharacteristic
28C4×Dic30C2211yescharacteristic
29C4×Dic30C2211yescharacteristic
30C3×C5×#107C2212yes—
31C3×C5×C4⋊C8C2211yescharacteristic
32C3×C5×#102C2212yes—
33#91116C2211yescharacteristic
34#91100C2212yes—
35#91098C2212yes—
36C8×Dic15C2212yes—
37#91094C2212yes—
38#91094C2212yes—
39#91094C2211yescharacteristic
40#91092C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42#80994—51nomaximal, Hall
43#66055—31no—
44#65876—31no—
45C5×#474D311yescharacteristic
46#65382—31no—
47C4×#687—31no—
48#65166—32no—
49#65162—32no—
50#65138—31no—
51#65119—31no—
52#65057—32no—
53#65056—32no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C2×Dic30D411yescharacteristic
58C2×Dic30C2312yes—
59C2×Dic30C2311yescharacteristic
60C2×C3×C5×C8C2312yes—
61C3×C5×C4⋊C4—21no—
62C3×C5×C4⋊C4C2311yescharacteristic
63C3×C5×C4⋊C4C2312yes—
64C3×C5×C22⋊C4—21no—
65C3×C42×C5C2311yescharacteristic
66#6719—22no—
67#6719—22no—
68#6716—22no—
69C4⋊Dic15—21no—
70C4⋊Dic15—21no—
71C4⋊Dic15—22no—
72C4⋊Dic15D411yescharacteristic
73C4⋊Dic15C2311yescharacteristic
74#6712—21no—
75#6712—22no—
76#6712—22no—
77#6712—22no—
78#6712D412yes—
79C4×Dic15—21no—
80C4×Dic15—22no—
81C4×Dic15—22no—
82C4×Dic15C2312yes—
83C2×C3⋊#168C2311yescharacteristic
84C2×C3⋊#168C2311yescharacteristic
85Dic60—24no—
86#5721—51no—
87#5542—51no—
88C3×#474D511yescharacteristic
89#5093—51no—
90C4×#214—51no—
91#4877—52no—
92#4873—52no—
93#4849—51no—
94#4830—51no—
95#4768—52no—
96#4767—52no—
97C5×C4⋊Q8C2×D311yescharacteristic
98C4×C5×D4C2×D311yescharacteristic
99Q8×Dic5—61no—
100#4090—61no—
101#4082—32no—
102C2×#687—31no—
103#4072—61no—
104#4070—61no—
105C2×Dic20—32no—
106#4036—32no—
107#4035—62no—
108#4033—32no—
109#4033—32no—
110#4025—62no—
111#4015—31no—
112C4×Dic10—31no—
113C4×Dic10—31no—
114C5×#107C2×D312yes—
115C5×C4⋊C8C2×D311yescharacteristic
116C5×#102C2×D312yes—
117#3964—31no—
118#3948—32no—
119#3946—32no—
120C8×Dic5—32no—
121#3942—31no—
122#3942—32no—
123#3942—32no—
124#3940—31no—
125C4×#168—31no—
126#3364—151noSylow
127C23×C3×C5—21no—
128C3×C5×Q8—42no—
129C3×C5×D4—21no—
130C3×C5×D4—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—42no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2411yescharacteristic
137C2×Dic15—21no—
138C2×Dic15—21no—
139C2×Dic15—22no—
140C2×Dic15C2×D412yes—
141C2×Dic15C2×D412yes—
142Dic30—22no—
143Dic30—21no—
144Dic30—22no—
145Dic30—22no—
146Dic30#4112yes—
147C3×C5×C8—22no—
148C3⋊#168—21no—
149C3⋊#168—21no—
150C3×C4⋊Q8C2×D511yescharacteristic
151C3×C4×D4C2×D511yescharacteristic
152Q8×Dic3—101no—
153#944—101no—
154#936—52no—
155C2×#214—51no—
156#926—101no—
157#924—101no—
158C2×Dic12—52no—
159#890—52no—
160#889—102no—
161#887—52no—
162#887—52no—
163#879—102no—
164#869—51no—
165C4×Dic6—51no—
166C4×Dic6—51no—
167C3×#107C2×D512yes—
168C3×C4⋊C8C2×D511yescharacteristic
169C3×#102C2×D512yes—
170#832—51no—
171#816—52no—
172Dic3⋊C8—52no—
173C8×Dic3—52no—
174#810—51no—
175#810—52no—
176#810—52no—
177#808—51no—
178C4×C3⋊C8—51no—
179C2×C5×Q8—21no—
180C2×C5×D4C22×D311yescharacteristic
181C22×C4×C5—21no—
182C2×Dic10—31no—
183C2×Dic10—31no—
184C2×Dic10—32no—
185C2×C5×C8C22×D312yes—
186C5×C4⋊C4—21no—
187C5×C4⋊C4C22×D311yescharacteristic
188C5×C4⋊C4C22×D312yes—
189C5×C22⋊C4—21no—
190C42×C5C22×D311yescharacteristic
191C22⋊Dic5—62no—
192C22⋊Dic5—62no—
193#687—62no—
194C4⋊Dic5—31no—
195C4⋊Dic5—31no—
196C4⋊Dic5—62no—
197C4⋊Dic5—61no—
198C4⋊Dic5—61no—
199#683—32no—
200#683—62no—
201#683—62no—
202#683—62no—
203#683—61no—
204C4×Dic5—32no—
205C4×Dic5—62no—
206C4×Dic5—62no—
207C4×Dic5—61no—
208C2×#168—31no—
209C2×#168—31no—
210Dic20—64no—
211#557—151no—
212#556—151no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474D1511yescharacteristic
217#464—152no—
218#462—151no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5—41no—
223C22×C3×C5—41no—
224C22×C3×C5—41no—
225C22×C3×C5C22×D411yescharacteristic
226C3×C4×C5—21no—
227C3×C4×C5—41no—
228C3×C4×C5—42no—
229C3×C4×C5#13512yes—
230C3×C4×C5C2×#4111yescharacteristic
231C3×C4×C52−1+411yescharacteristic
232Dic15—22no—
233Dic15—22no—
234Dic15—22no—
235Dic15—42no—
236Dic15—41no—
237C2×C3×Q8—21no—
238C2×C3×D4C22×D511yescharacteristic
239C22×C3×C4—21no—
240C2×Dic6—51no—
241C2×Dic6—51no—
242C2×Dic6—52no—
243C2×C3×C8C22×D512yes—
244C3×C4⋊C4—21no—
245C3×C4⋊C4C22×D511yescharacteristic
246C3×C4⋊C4C22×D512yes—
247C3×C22⋊C4—21no—
248C3×C42C22×D511yescharacteristic
249#217—102no—
250#217—102no—
251#214—102no—
252C4⋊Dic3—51no—
253C4⋊Dic3—51no—
254C4⋊Dic3—102no—
255C4⋊Dic3—101no—
256C4⋊Dic3—101no—
257Dic3⋊C4—52no—
258Dic3⋊C4—102no—
259Dic3⋊C4—102no—
260Dic3⋊C4—102no—
261Dic3⋊C4—101no—
262C4×Dic3—52no—
263C4×Dic3—102no—
264C4×Dic3—102no—
265C4×Dic3—101no—
266C2×C3⋊C8—51no—
267C2×C3⋊C8—51no—
268Dic12—104no—
269C23×C5—21no—
270C5×Q8—42no—
271C5×D4—21no—
272C5×D4—21no—
273C2×C4×C5—21no—
274C2×C4×C5—22no—
275C2×C4×C5—42no—
276C2×C4×C5D3×D411yescharacteristic
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5C23×D311yescharacteristic
279C2×Dic5—32no—
280C2×Dic5—32no—
281C2×Dic5—61no—
282C2×Dic5—61no—
283C2×Dic5—62no—
284Dic10—32no—
285Dic10—62no—
286Dic10—61no—
287Dic10—62no—
288Dic10—62no—
289C5×C8—22no—
290#168—61no—
291#168—61no—
292C2×Q16—152no—
293C2×SD16—151no—
294C4⋊Q8—151no—
295C4⋊Q8—301no—
296C4⋊Q8C2×D1511yescharacteristic
297#126—302no—
298#125—152no—
299#125—302no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—151no—
303C4×Q8—152no—
304C4×Q8—152no—
305C4×Q8—151no—
306C4×Q8—301no—
307C4×D4C2×D1511yescharacteristic
308#117—301no—
309#107C2×D1512yes—
310#106—151no—
311C4⋊C8—152no—
312C4⋊C8C2×D1511yescharacteristic
313#103—152no—
314#103—151no—
315#103—152no—
316#103—152no—
317#102—151no—
318#102C2×D1512yes—
319C4×C8—152no—
320C4×C8—151no—
321C2×C3×C5—81no—
322C2×C3×C5#54811yescharacteristic
323C2×C3×C5C2×#13511yescharacteristic
324C2×C3×C5#57811yescharacteristic
325C23×C3—21no—
326C3×Q8—42no—
327C3×D4—21no—
328C3×D4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—42no—
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4C23×D511yescharacteristic
335C2×Dic3—52no—
336C2×Dic3—52no—
337C2×Dic3—101no—
338C2×Dic3—101no—
339C2×Dic3—102no—
340Dic6—52no—
341Dic6—101no—
342Dic6—102no—
343Dic6—102no—
344Dic6—102no—
345C3×C8—22no—
346C3⋊C8—101no—
347C3⋊C8—101no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—41no—
351C22×C5C2×D3×D411yescharacteristic
352C4×C5—21no—
353C4×C5—41no—
354C4×C5—42no—
355C4×C5#91212yes—
356C4×C5#100711yescharacteristic
357C4×C5D3×#4111yescharacteristic
358Dic5—62no—
359Dic5—62no—
360Dic5—62no—
361Dic5—122no—
362Dic5—121no—
363C2×Q8—21no—
364C2×Q8—151no—
365C2×Q8—151no—
366C2×Q8—152no—
367C2×D4C22×D1511yescharacteristic
368C22×C4—21no—
369Q16—304no—
370SD16—302no—
371C2×C8—151no—
372C2×C8—151no—
373C2×C8C22×D1512yes—
374C4⋊C4—21no—
375C4⋊C4—151no—
376C4⋊C4—152no—
377C4⋊C4—151no—
378C4⋊C4—302no—
379C4⋊C4—302no—
380C4⋊C4—302no—
381C4⋊C4—302no—
382C4⋊C4—301no—
383C4⋊C4—301no—
384C4⋊C4—301no—
385C4⋊C4C22×D1512yes—
386C4⋊C4C22×D1511yescharacteristic
387C22⋊C4—21no—
388C22⋊C4—302no—
389C22⋊C4—302no—
390C42—152no—
391C42—302no—
392C42—302no—
393C42—301no—
394C42C22×D1511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3C2×D4×D511yescharacteristic
400C3×C4—21no—
401C3×C4—41no—
402C3×C4—42no—
403C3×C4#405812yes—
404C3×C4#414711yescharacteristic
405C3×C4D5×#4111yescharacteristic
406Dic3—102no—
407Dic3—102no—
408Dic3—102no—
409Dic3—201no—
410Dic3—202no—
411C2×C5—81no—
412C2×C5#563311yescharacteristic
413C2×C5C2×#91211yescharacteristic
414C2×C5#577911yescharacteristic
415C23—21no—
416Q8—42no—
417Q8—152no—
418Q8—302no—
419Q8—301no—
420Q8—302no—
421Q8—302no—
422D4—21no—
423D4—21no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—42no—
427C2×C4—152no—
428C2×C4—152no—
429C2×C4—301no—
430C2×C4—302no—
431C2×C4—301no—
432C2×C4D4×D1511yescharacteristic
433C2×C4D4×D1511yescharacteristic
434C2×C4C23×D1511yescharacteristic
435C8—22no—
436C8—301no—
437C8—301no—
438C2×C3—81no—
439C2×C3#6596711yescharacteristic
440C2×C3C2×#405811yescharacteristic
441C2×C3#6611311yescharacteristic
442C5#8099411yescharacteristic, complemented, Sylow
443C22—41no—
444C22—41no—
445C22—41no—
446C22C2×D4×D1511yescharacteristic
447C4—21no—
448C4—41no—
449C4—42no—
450C4—302no—
451C4—302no—
452C4—302no—
453C4—602no—
454C4—601no—
455C4#9180112yes—
456C4#9209811yescharacteristic
457C4#41×D1511yescharacteristic
458C3#1061272511yescharacteristic, complemented, Sylow
459C2—81no—
460C2#1175639211yescharacteristic
461C2C2×#9180111yescharacteristic
462C2#1175653811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#474C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×D4C23
hypercenter#474D15
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11756480C2semidirect
4. #11751194C2semidirect
6. #11750978C2semidirect
7. #11750974C2semidirect
8. #11750950C2semidirect
9. #11750931C2semidirect
395. C3×C5#3364semidirect
442. C5#80994semidirect
458. C3#10612725semidirect

Maximal subgroups

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

subgroupindex
#117564802
#117563012
C3×C5×#4742
#117511942
C4×#67162
#117509782
#117509742
#117509502
#117509312
#117508692
#117508682
#106127253
#809945