Finite Group Databasebeta

← #14472135

Subgroups — #14472135

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
1C3×#65876C211yesmaximal, characteristic
2#11752490C211yesmaximal, characteristic, complemented
3#11751108C211yesmaximal, characteristic
4C4×C5×#214C211yesmaximal, characteristic
5#11749085C212yesmaximal
6#11749003C212yesmaximal
7#11747390C212yesmaximal, complemented
8#11747263C212yesmaximal, complemented
9#11747099C211yesmaximal, characteristic, complemented
10#11746920C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
12#10611354—31nomaximal, Hall
13C3×C4×C5×D4C2211yescharacteristic
14#91758C2211yescharacteristic
15C2×C5×#214C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C3×#4082C2212yes—
18C3×#4072—21no—
19C3×#4070—21no—
20C3×#4033C2212yes—
21C3×#4025—22no—
22C3×#4015C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic
24#91389—21no—
25#91388C2212yes—
26#91343—22no—
27#91340—21no—
28Dic5×Dic6C2212yes—
29C2×#6661C2212yes—
30#91116C2212yes—
31#91091C2212yes—
32C4⋊(C3⋊#168)C2211yescharacteristic
33C5×#832C2211yescharacteristic
34C5×#810C2211yescharacteristic
35C5×#808C2211yescharacteristic
36C4×C5×C3⋊C8C2211yescharacteristic
37#90982C2212yes—
38#90971C2212yes—
39#90971C2212yes—
40#90970C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83676—51nomaximal, Hall
43#65904—31no—
44#65876D311yescharacteristic
45C4×C5×SD16—31no—
46#65455—32no—
47#65320—31no—
48#65296—31no—
49#65146—32no—
50#65079—32no—
51#65057—32no—
52#64970—31no—
53C8×Dic10—31no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×Dic30—21no—
57C2×C5×Dic6C2311yescharacteristic
58C2×C3×Dic10D411yescharacteristic
59C2×C3×Dic10C2312yes—
60C3×C5×C4⋊C4C2311yescharacteristic
61C3×C5×C22⋊C4—21no—
62C3×C42×C5C2311yescharacteristic
63C4⋊Dic15—21no—
64C4⋊Dic15C2312yes—
65C2×C3⋊#168C2312yes—
66C5×#214—22no—
67C5×C4⋊Dic3C2311yescharacteristic
68C5×Dic3⋊C4—21no—
69C4×C5×Dic3—21no—
70C2×C5×C3⋊C8C2311yescharacteristic
71C2×C5×C3⋊C8C2311yescharacteristic
72C3×C22⋊Dic5—22no—
73C3×C22⋊Dic5—22no—
74C3×C4⋊Dic5—21no—
75C3×C4⋊Dic5—21no—
76C3×C4⋊Dic5D411yescharacteristic
77C3×#683—22no—
78C3×#683D412yes—
79C3×C4×Dic5—22no—
80C3×C4×Dic5C2312yes—
81Dic3⋊Dic5—22no—
82Dic3⋊Dic5—22no—
83#6669—22no—
84Dic3×Dic5—22no—
85#6661—24no—
86C3×#556—51no—
87#5567—51no—
88#5090—51no—
89#5079—51no—
90#5056—52no—
91#5054—52no—
92C4×#216—52no—
93Q8×C3⋊C8—51no—
94#5022—52no—
95C4×#214D511yescharacteristic
96#5007—51no—
97C2×C5×SD16—31no—
98C4×C5×Q8—31no—
99C4×C5×D4C2×D311yescharacteristic
100Q8×Dic5—32no—
101C2×#689—32no—
102#4082C2×D312yes—
103#4072—21no—
104#4070—21no—
105#4036—32no—
106#4036—62no—
107#4033C2×D312yes—
108#4025—22no—
109#4015—31no—
110#4015—61no—
111#4015C2×D311yescharacteristic
112C4×Dic10—61no—
113C4×Dic10C2×D311yescharacteristic
114C5×#106—31no—
115C5×#103—31no—
116C5×#102—31no—
117C4×C5×C8—31no—
118#3964—32no—
119#3948—32no—
120#3948—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3942—32no—
124#3939—32no—
125C4⋊#168—31no—
126#3364—151noSylow
127C23×C3×C5—21no—
128C3×C5×D4—21no—
129C3×C5×D4—21no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—42no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—22no—
136Dic30—42no—
137C2×C5×Dic3—21no—
138C2×C5×Dic3—21no—
139C5×Dic6—21no—
140C5×Dic6#4112yes—
141C2×C3×Dic5—22no—
142C2×C3×Dic5C2×D412yes—
143C2×C3×Dic5C2×D412yes—
144C3×Dic10—22no—
145C3×Dic10—22no—
146C3×Dic10—22no—
147C3⋊#168—22no—
148C5×C3⋊C8—21no—
149C5×C3⋊C8—21no—
150C3×C4⋊Q8—51no—
151C3×#126—102no—
152C3×#124—52no—
153C3×C22⋊Q8—101no—
154C3×C4×Q8—51no—
155C3×C4×Q8—52no—
156C3×C4×D4C2×D511yescharacteristic
157C3×#117—101no—
158#944—101no—
159C2×#216—52no—
160C2×#214C2×D511yescharacteristic
161#889—102no—
162#887—101no—
163#870—52no—
164#869—51no—
165C4×Dic6—52no—
166C4×Dic6C2×D511yescharacteristic
167#835—52no—
168#835—52no—
169#835—52no—
170#832—52no—
171#832C2×D511yescharacteristic
172#810C2×D511yescharacteristic
173#808C2×D511yescharacteristic
174#807—52no—
175C4⋊(C3⋊C8)—51no—
176C4⋊(C3⋊C8)—52no—
177C4×C3⋊C8—52no—
178C4×C3⋊C8C2×D511yescharacteristic
179C2×C5×Q8—31no—
180C2×C5×D4C22×D311yescharacteristic
181C22×C4×C5—21no—
182C2×Dic10—61no—
183C2×Dic10#6711yescharacteristic
184C2×Dic10C22×D312yes—
185C5×SD16—62no—
186C2×C5×C8—31no—
187C2×C5×C8—31no—
188C5×C4⋊C4—31no—
189C5×C4⋊C4—61no—
190C5×C4⋊C4C22×D311yescharacteristic
191C5×C22⋊C4—21no—
192C42×C5—61no—
193C42×C5C22×D311yescharacteristic
194C22⋊Dic5—22no—
195C22⋊Dic5—22no—
196#689—64no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—32no—
200C4⋊Dic5—61no—
201C4⋊Dic5—62no—
202C4⋊Dic5—62no—
203C4⋊Dic5#6711yescharacteristic
204#683—22no—
205#683—62no—
206#683#6712yes—
207C4×Dic5—22no—
208C4×Dic5—62no—
209C4×Dic5C22×D312yes—
210C2×#168—32no—
211#557—151no—
212#556—51no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—151no—
217#464—152no—
218#462—151no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—31no—
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#13512yes—
229C3×C4×C5C2×#4111yescharacteristic
230C3×C4×C52−1+411yescharacteristic
231Dic15—42no—
232C3×Dic5—22no—
233C3×Dic5—22no—
234C3×Dic5—42no—
235C5×Dic3—22no—
236C5×Dic3—41no—
237C2×C3×Q8—51no—
238C2×C3×Q8—52no—
239C2×C3×D4C22×D511yescharacteristic
240C22×C3×C4—21no—
241C2×Dic6—101no—
242C2×Dic6C22×D511yescharacteristic
243C3×C4⋊C4—52no—
244C3×C4⋊C4—51no—
245C3×C4⋊C4—102no—
246C3×C4⋊C4—101no—
247C3×C4⋊C4—101no—
248C3×C4⋊C4C22×D511yescharacteristic
249C3×C22⋊C4—21no—
250C3×C22⋊C4—102no—
251C3×C22⋊C4—102no—
252C3×C42—52no—
253C3×C42—102no—
254C3×C42C22×D511yescharacteristic
255#216—104no—
256#214—22no—
257C4⋊Dic3—52no—
258C4⋊Dic3—101no—
259C4⋊Dic3C22×D511yescharacteristic
260Dic3⋊C4—21no—
261Dic3⋊C4—102no—
262Dic3⋊C4—102no—
263Dic3⋊C4—102no—
264C4×Dic3—21no—
265C4×Dic3—102no—
266C2×C3⋊C8—52no—
267C2×C3⋊C8C22×D511yescharacteristic
268C2×C3⋊C8C22×D511yescharacteristic
269C23×C5—21no—
270C5×Q8—32no—
271C5×Q8—61no—
272C5×D4—21no—
273C5×D4—21no—
274C2×C4×C5—21no—
275C2×C4×C5—42no—
276C2×C4×C5—61no—
277C2×C4×C5—61no—
278C2×C4×C5C2×#6711yescharacteristic
279C2×C4×C5C2×#6711yescharacteristic
280C2×C4×C5C23×D311yescharacteristic
281C2×Dic5—22no—
282C2×Dic5—62no—
283C2×Dic5C2×#6712yes—
284C2×Dic5C2×#6712yes—
285Dic10—22no—
286Dic10—22no—
287Dic10—22no—
288Dic10—122no—
289C5×C8—61no—
290C5×C8—61no—
291#168—62no—
292C2×Q16—152no—
293C2×SD16—31no—
294C4⋊Q8—51no—
295C4⋊Q8—151no—
296C4⋊Q8—301no—
297#126—102no—
298#125—152no—
299#125—302no—
300#124—52no—
301C22⋊Q8—101no—
302C4×Q8—31no—
303C4×Q8—51no—
304C4×Q8—52no—
305C4×Q8—152no—
306C4×Q8—301no—
307C4×D4D3×D511yescharacteristic
308#117—101no—
309#107—152no—
310#106—31no—
311C4⋊C8—152no—
312C4⋊C8—151no—
313#103—31no—
314#103—152no—
315#103—152no—
316#103—152no—
317#102—31no—
318#102—152no—
319C4×C8—31no—
320C4×C8—152no—
321C2×C3×C5—81no—
322C2×C3×C5#54811yescharacteristic
323C2×C3×C5C2×#13511yescharacteristic
324C2×C3×C5#57811yescharacteristic
325C23×C3—21no—
326C3×Q8—102no—
327C3×Q8—102no—
328C3×Q8—102no—
329C3×D4—21no—
330C3×D4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—42no—
333C2×C3×C4—52no—
334C2×C3×C4—52no—
335C2×C3×C4—102no—
336C2×C3×C4D4×D511yescharacteristic
337C2×C3×C4D4×D511yescharacteristic
338C2×C3×C4C23×D511yescharacteristic
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—102no—
342Dic6—21no—
343Dic6—202no—
344Dic6#70912yes—
345C3⋊C8—21no—
346C3⋊C8—21no—
347C3⋊C8—102no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—41no—
351C22×C5C22×#6711yescharacteristic
352C4×C5—21no—
353C4×C5—41no—
354C4×C5—62no—
355C4×C5—121no—
356C4×C5#95012yes—
357C4×C5D3×#4111yescharacteristic
358C4×C5#101011yescharacteristic
359Dic5—22no—
360Dic5—22no—
361Dic5—42no—
362Dic5—122no—
363C2×Q8—31no—
364C2×Q8—51no—
365C2×Q8—52no—
366C2×Q8—301no—
367C2×D4C2×D3×D511yescharacteristic
368C22×C4—21no—
369Q16—304no—
370SD16—62no—
371C2×C8—31no—
372C2×C8—31no—
373C2×C8—152no—
374C4⋊C4—31no—
375C4⋊C4—51no—
376C4⋊C4—52no—
377C4⋊C4—61no—
378C4⋊C4—102no—
379C4⋊C4—101no—
380C4⋊C4—101no—
381C4⋊C4—152no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—301no—
386C4⋊C4C2×D3×D511yescharacteristic
387C22⋊C4—21no—
388C22⋊C4—102no—
389C22⋊C4—102no—
390C42—52no—
391C42—61no—
392C42—102no—
393C42—302no—
394C42C2×D3×D511yescharacteristic
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—102no—
403C3×C4—102no—
404C3×C4—202no—
405C3×C4#406212yes—
406C3×C4C2×#70911yescharacteristic
407C3×C4#415011yescharacteristic
408Dic3—22no—
409Dic3—41no—
410Dic3—202no—
411C2×C5—81no—
412C2×C5C2×#95011yescharacteristic
413C2×C5#583111yescharacteristic
414C2×C5#583811yescharacteristic
415C23—21no—
416Q8—32no—
417Q8—61no—
418Q8—102no—
419Q8—102no—
420Q8—102no—
421Q8—602no—
422D4—21no—
423D4—21no—
424C2×C4—21no—
425C2×C4—42no—
426C2×C4—52no—
427C2×C4—52no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—102no—
431C2×C4—302no—
432C2×C4D5×#6711yescharacteristic
433C2×C4D5×#6711yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—61no—
436C8—61no—
437C8—302no—
438C2×C3—81no—
439C2×C3#6588611yescharacteristic
440C2×C3C2×#406211yescharacteristic
441C2×C3#6610511yescharacteristic
442C5#8367611yescharacteristic, complemented, Sylow
443C22—41no—
444C22—41no—
445C22—41no—
446C22C2×D5×#6711yescharacteristic
447C4—21no—
448C4—41no—
449C4—62no—
450C4—102no—
451C4—102no—
452C4—121no—
453C4—202no—
454C4—602no—
455C4#9149212yes—
456C4#9200111yescharacteristic
457C4D3×#70911yescharacteristic
458C3#1061135411yescharacteristic, complemented, Sylow
459C2—81no—
460C2#1175452811yescharacteristic
461C2C2×#9149211yescharacteristic
462C2#1175533811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×D4C23
hypercenterC4×D4D3×D5
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11752490C2semidirect
7. #11747390C2semidirect
8. #11747263C2semidirect
9. #11747099C2semidirect
10. #11746920C2semidirect
11. C3⋊C8×Dic10C2semidirect
395. C3×C5#3364semidirect
442. C5#83676semidirect
458. C3#10611354semidirect

Maximal subgroups

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

subgroupindex
C3×#658762
#117524902
#117511082
C4×C5×#2142
#117490852
#117490032
#117473902
#117472632
#117470992
#117469202
C3⋊C8×Dic102
#106113543
#836765