Finite Group Databasebeta

← #14313431

Subgroups — #14313431

Order 1920.

516 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66166C211yesmaximal, characteristic
2#11751341C211yesmaximal, characteristic, complemented
3C5×#5240C211yesmaximal, characteristic, complemented
4#11746009C212yesmaximal, complemented
5#11746006C212yesmaximal, complemented
6#10600853—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C2×C3×#709C411yescharacteristic, complemented
9#91815—21no—
10C5×#926—21no—
11C3×#4093C411yescharacteristic, complemented
12C3×#4090C411yescharacteristic, complemented
13C3×#4086C2211yescharacteristic
14C3×#4085—21no—
15C3×#4085—21no—
16C3×#4082C2211yescharacteristic
17C3×C4×C22⋊D5—21no—
18C3×C4×C22⋊D5—21no—
19C2×C3×C4×Dic5C411yescharacteristic, complemented
20#91118—21no—
21#91118C2212yes—
22C5×#834—21no—
23C5×#834C2212yes—
24#71819—51nomaximal, Hall
25#66166D311yescharacteristic
26C5×#410—31no—
27#65529—31no—
28#64694—32no—
29#64693—32no—
30C3×C5×#41—41no—
31C3×C5×#41—41no—
32C2×C3×C5×Q8C2×C411yescharacteristic
33C2×C3×C5×D4D411yescharacteristic
34C2×C3×C5×D4D411yescharacteristic
35C2×C3×C5×D4C2311yescharacteristic
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—21no—
42C22×C3×Dic5—21no—
43C3×#709—41no—
44C3×#709—41no—
45C2×C3×D20C2×C411yescharacteristic
46C2×C3×C4×D5—21no—
47C2×C3×Dic10C2×C411yescharacteristic
48#6719—22no—
49C4⋊Dic15—41no—
50C4×Dic15—41no—
51C5×#217—22no—
52C5×C4⋊Dic3—41no—
53C4×C5×Dic3—41no—
54C3×C22⋊Dic5—21no—
55C3×C22⋊Dic5—21no—
56C3×#685—21no—
57C3×#685—21no—
58C3×#683—21no—
59C3×#683—21no—
60C3×C4×Dic5—21no—
61C3×C4×Dic5C2×C411yescharacteristic
62C3×C4×Dic5C2×C411yescharacteristic
63C3×#532—51no—
64#5240—51no—
65#5240D511yescharacteristic, complemented
66#4545—52no—
67#4541—52no—
68C2×C5×#41C2×D311yescharacteristic
69C2×#709Dic311yescharacteristic, complemented
70C5×#117—61no—
71#4093Dic311yescharacteristic, complemented
72#4090Dic311yescharacteristic, complemented
73#4086C2×D311yescharacteristic
74#4085—21no—
75#4085—21no—
76#4082C2×D311yescharacteristic
77C4×C22⋊D5—21no—
78C4×C22⋊D5—21no—
79#4072—61no—
80C2×C4×Dic5Dic311yescharacteristic, complemented
81C5×#99—32no—
82C5×#99—61no—
83#3966—32no—
84#3966—61no—
85#2126—151noSylow
86C23×C3×C5C22⋊C411yescharacteristic
87C23×C3×C5C2×D411yescharacteristic
88C23×C3×C5C2×D411yescharacteristic
89C22×C3×D5—21no—
90C3×C5×Q8—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5C22⋊C411yescharacteristic
101C2×C3×C4×C5C22⋊C411yescharacteristic
102C2×C3×C4×C5C22⋊C411yescharacteristic
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×Dic15—42no—
105C2×C5×Dic3—42no—
106C3×C22⋊D5—42no—
107C3×C22⋊D5—42no—
108C3×C22⋊D5—42no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—42no—
113C3×D20—41no—
114C3×C4×D5—41no—
115C3×C4×D5—41no—
116C3×Dic10—41no—
117C2×C3×#41—51no—
118C2×C3×#41C2×D511yescharacteristic
119C3×C4⋊Q8—51no—
120C3×#127—51no—
121C3×#124—51no—
122C3×#124—51no—
123C3×#121—101no—
124C3×#121—101no—
125C3×C4×D4—101no—
126C3×C4×D4—101no—
127C2×C3×C42—51no—
128#926—21no—
129#926—101no—
130#834—21no—
131#834—52no—
132#834—101no—
133#834C2×D512yes—
134C5×#41—41no—
135C5×#41—41no—
136C2×C5×Q8C2×Dic311yescharacteristic
137C2×C5×D4#6711yescharacteristic
138C2×C5×D4#6711yescharacteristic
139C2×C5×D4C22×D311yescharacteristic
140C22×C4×C5C2×Dic311yescharacteristic
141C22×C4×C5#6711yescharacteristic
142C22×C4×C5#6711yescharacteristic
143C2×C22⋊D5—21no—
144C2×C22⋊D5—21no—
145C2×C22⋊D5—21no—
146C22×Dic5—21no—
147#709—41no—
148#709—41no—
149C2×D20C2×Dic311yescharacteristic
150C2×C4×D5—21no—
151C2×Dic10C2×Dic311yescharacteristic
152C5×C4⋊C4—121no—
153C5×C22⋊C4—62no—
154C42×C5—121no—
155C22⋊Dic5—21no—
156C22⋊Dic5—21no—
157C22⋊Dic5—62no—
158#685—21no—
159#685—21no—
160C4⋊Dic5—121no—
161#683—21no—
162#683—21no—
163C4×Dic5—21no—
164C4×Dic5—121no—
165C4×Dic5C2×Dic311yescharacteristic
166C4×Dic5C2×Dic311yescharacteristic
167#532—51no—
168#410—31no—
169#410—151no—
170#354—152no—
171#353—152no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—41no—
176C22×C3×C5—41no—
177C22×C3×C5—41no—
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C2×C3×D5—41no—
180C2×C3×D5—41no—
181C2×C3×D5—41no—
182C3×C4×C5—21no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5#9911yescharacteristic
186C3×C4×C5#9911yescharacteristic
187Dic15—82no—
188C3×Dic5—22no—
189C3×Dic5—41no—
190C3×Dic5—41no—
191C5×Dic3—82no—
192C3×#41—41no—
193C3×#41—41no—
194C3×#41—201no—
195C3×#41—201no—
196C2×C3×Q8—51no—
197C2×C3×Q8C4×D511yescharacteristic
198C2×C3×D4—51no—
199C2×C3×D4—101no—
200C2×C3×D4—101no—
201C2×C3×D4—101no—
202C2×C3×D4D2011yescharacteristic
203C2×C3×D4C22⋊D511yescharacteristic
204C2×C3×D4C22×D511yescharacteristic
205C22×C3×C4—101no—
206C22×C3×C4—101no—
207C22×C3×C4C4×D511yescharacteristic
208C22×C3×C4D2011yescharacteristic
209C22×C3×C4C22⋊D511yescharacteristic
210C3×C4⋊C4—101no—
211C3×C4⋊C4—101no—
212C3×C22⋊C4—101no—
213C3×C22⋊C4—101no—
214C3×C22⋊C4—101no—
215C3×C22⋊C4—101no—
216C3×C42—51no—
217C3×C42—51no—
218C3×C42—101no—
219#217—22no—
220#217—102no—
221C4⋊Dic3—41no—
222C4⋊Dic3—201no—
223C4×Dic3—41no—
224C4×Dic3—201no—
225C23×C5#21711yescharacteristic
226C23×C5C2×#6711yescharacteristic
227C23×C5C2×#6711yescharacteristic
228C22×D5—21no—
229C5×Q8—41no—
230C5×D4—41no—
231C5×D4—41no—
232C5×D4—41no—
233C2×C4×C5—21no—
234C2×C4×C5—21no—
235C2×C4×C5—21no—
236C2×C4×C5—21no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—122no—
240C2×C4×C5#21711yescharacteristic
241C2×C4×C5#21711yescharacteristic
242C2×C4×C5#21711yescharacteristic
243C2×C4×C5C22×Dic311yescharacteristic
244C22⋊D5—42no—
245C22⋊D5—42no—
246C22⋊D5—42no—
247C2×Dic5—21no—
248C2×Dic5—21no—
249C2×Dic5—21no—
250C2×Dic5—42no—
251C2×Dic5—122no—
252D20—41no—
253C4×D5—41no—
254C4×D5—41no—
255Dic10—41no—
256C2×#41—51no—
257C2×#41D3×D511yescharacteristic
258C4⋊Q8—51no—
259#127—51no—
260#124—51no—
261#124—51no—
262#121—101no—
263#121—101no—
264C4×D4—101no—
265C4×D4—101no—
266#117—61no—
267#117—301no—
268C2×C42—51no—
269#99—32no—
270#99—61no—
271#99—152no—
272#99—301no—
273C2×C3×C5—21no—
274C2×C3×C5—41no—
275C2×C3×C5—41no—
276C2×C3×C5—41no—
277C2×C3×C5C2×#9911yescharacteristic
278C3×D5—81no—
279C23×C3—101no—
280C23×C3#68511yescharacteristic
281C23×C3C2×D2011yescharacteristic
282C23×C3C2×C22⋊D511yescharacteristic
283C3×Q8—41no—
284C3×Q8—201no—
285C3×D4—41no—
286C3×D4—41no—
287C3×D4—41no—
288C3×D4—201no—
289C3×D4—202no—
290C3×D4—202no—
291C3×D4—202no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—101no—
299C2×C3×C4—101no—
300C2×C3×C4—101no—
301C2×C3×C4—202no—
302C2×C3×C4—201no—
303C2×C3×C4—201no—
304C2×C3×C4#68511yescharacteristic
305C2×C3×C4#68511yescharacteristic
306C2×C3×C4#68511yescharacteristic
307C2×C3×C4C2×C4×D511yescharacteristic
308C2×Dic3—42no—
309C2×Dic3—202no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—41no—
314C22×C5—41no—
315C22×C5—41no—
316C22×C5C2×#21711yescharacteristic
317C2×D5—41no—
318C2×D5—41no—
319C2×D5—41no—
320C4×C5—21no—
321C4×C5—21no—
322C4×C5—21no—
323C4×C5—242no—
324C4×C5#83411yescharacteristic
325C4×C5#83411yescharacteristic
326Dic5—22no—
327Dic5—41no—
328Dic5—41no—
329Dic5—242no—
330#41—41no—
331#41—41no—
332#41—201no—
333#41—201no—
334C2×Q8—51no—
335C2×Q8D5×Dic311yescharacteristic
336C2×D4—51no—
337C2×D4—101no—
338C2×D4—101no—
339C2×D4—101no—
340C2×D4#120111yescharacteristic
341C2×D4#120211yescharacteristic
342C2×D4C2×D3×D511yescharacteristic
343C22×C4—101no—
344C22×C4—101no—
345C22×C4D5×Dic311yescharacteristic
346C22×C4#120111yescharacteristic
347C22×C4#120211yescharacteristic
348C4⋊C4—101no—
349C4⋊C4—101no—
350C4⋊C4—121no—
351C4⋊C4—601no—
352C22⋊C4—62no—
353C22⋊C4—101no—
354C22⋊C4—101no—
355C22⋊C4—101no—
356C22⋊C4—101no—
357C22⋊C4—302no—
358C42—51no—
359C42—51no—
360C42—101no—
361C42—121no—
362C42—601no—
363C3×C5#212611yescharacteristic, complemented, Hall
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—201no—
371C22×C3—201no—
372C22×C3—201no—
373C22×C3C2×#68511yescharacteristic
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—102no—
378C3×C4—201no—
379C3×C4—201no—
380C3×C4#393811yescharacteristic
381C3×C4#393811yescharacteristic
382Dic3—82no—
383Dic3—402no—
384C2×C5—21no—
385C2×C5—41no—
386C2×C5—41no—
387C2×C5—41no—
388C2×C5C2×#83411yescharacteristic
389D5—81no—
390C23—101no—
391C23#666511yescharacteristic
392C23C2×#120111yescharacteristic
393C23C2×#120211yescharacteristic
394Q8—41no—
395Q8—201no—
396D4—41no—
397D4—41no—
398D4—41no—
399D4—201no—
400D4—202no—
401D4—202no—
402D4—202no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—101no—
410C2×C4—101no—
411C2×C4—101no—
412C2×C4—122no—
413C2×C4—202no—
414C2×C4—201no—
415C2×C4—201no—
416C2×C4—602no—
417C2×C4#666511yescharacteristic
418C2×C4#666511yescharacteristic
419C2×C4#666511yescharacteristic
420C2×C4C2×D5×Dic311yescharacteristic
421C2×C3—21no—
422C2×C3—41no—
423C2×C3—41no—
424C2×C3—41no—
425C2×C3—401no—
426C2×C3C2×#393811yescharacteristic
427C5#7181911yescharacteristic, complemented, Sylow
428C22—21no—
429C22—21no—
430C22—21no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—201no—
435C22—201no—
436C22—201no—
437C22C2×#666511yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—102no—
442C4—201no—
443C4—201no—
444C4—242no—
445C4—1202no—
446C4#9099511yescharacteristic
447C4#9099511yescharacteristic
448C3#1060085311yescharacteristic, complemented, Sylow
449C2—21no—
450C2—41no—
451C2—41no—
452C2—41no—
453C2—401no—
454C2C2×#9099511yescharacteristic
subgroupG/H
centerC4#90995
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5C2×#99
prime radicalC3×#66166C2
cosocleC2×C3×C5×D4C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#2126
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11751341C2semidirect
3. C5×#5240C2semidirect
4. #11746009C2semidirect
5. #11746006C2semidirect
8. C2×C3×#709C4semidirect
11. C3×#4093C4semidirect
12. C3×#4090C4semidirect
19. C2×C3×C4×Dic5C4semidirect
65. #5240D5semidirect
69. C2×#709Dic3semidirect
71. #4093Dic3semidirect
72. #4090Dic3semidirect
80. C2×C4×Dic5Dic3semidirect
363. C3×C5#2126semidirect
427. C5#71819semidirect
448. C3#10600853semidirect

Maximal subgroups

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

subgroupindex
C3×#661662
#117513412
C5×#52402
#117460092
#117460062
#106008533
#718195