Finite Group Databasebeta

← #14472155

Subgroups — #14472155

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×#66066C211yesmaximal, characteristic
2#11752487C211yesmaximal, characteristic, complemented
3#11751191C211yesmaximal, characteristic, complemented
4C5×#5079C211yesmaximal, characteristic, complemented
5#11749332C212yesmaximal, complemented
6#11749331C212yesmaximal
7#11749248C212yesmaximal
8#11749244C212yesmaximal, complemented
9C4×#6657C211yesmaximal, characteristic
10#11746886C211yesmaximal, characteristic
11C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
12#10613356—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14C2×#6718C2212yes—
15C4×Dic30C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C3×#4093C2212yes—
18C3×Q8×Dic5C2212yes—
19C3×#4044—22no—
20C3×#4043—21no—
21C3×#4038—21no—
22C3×C4×D20C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic
24#91388C2212yes—
25#91385—21no—
26#91344—21no—
27#91336—22no—
28#91333C2212yes—
29C2×#6657C2211yescharacteristic
30#91119C2212yes—
31C4⋊(C3⋊#168)C2211yescharacteristic
32C5×#835C2212yes—
33C5×#835C2212yes—
34C4×C5×C3⋊C8C2211yescharacteristic
35#90989C2212yes—
36#90987C2211yescharacteristic
37#90982C2212yes—
38#90974C2211yescharacteristic
39#90965C2211yescharacteristic
40#90964C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83676—51nomaximal, Hall
43#66066D311yescharacteristic
44#66055—31no—
45C5×#487—31no—
46#65379—31no—
47#65376—31no—
48#65089—32no—
49#65088—32no—
50#65087—32no—
51#65079—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8C2312yes—
55C2×Dic30C2311yescharacteristic
56C2×C5×Dic6—21no—
57C2×C3×D20C2311yescharacteristic
58C2×C3×C4×D5—21no—
59C2×C3×Dic10D411yescharacteristic
60C3×C5×C4⋊C4—21no—
61C3×C5×C4⋊C4—21no—
62C3×C42×C5C2311yescharacteristic
63#6718—24no—
64C4⋊Dic15C2311yescharacteristic
65#6712—21no—
66C4×Dic15—21no—
67C2×C3⋊#168C2312yes—
68C5×C4⋊Dic3—21no—
69C5×C4⋊Dic3C2312yes—
70C2×C5×C3⋊C8C2311yescharacteristic
71C2×C5×C3⋊C8C2311yescharacteristic
72C3×#685—21no—
73C3×#685—22no—
74C3×#685—22no—
75C3×C4⋊Dic5—22no—
76C3×C4⋊Dic5D411yescharacteristic
77C3×C4⋊Dic5C2311yescharacteristic
78C3×#683D412yes—
79C3×C4×Dic5—22no—
80C3×C4×Dic5C2312yes—
81Dic3⋊Dic5—22no—
82#6669—22no—
83#6669—22no—
84Dic3×Dic5—22no—
85#6657—22no—
86C3×#556—51no—
87#5567—51no—
88#5090—51no—
89#5079D511yescharacteristic, complemented
90#5056—52no—
91#5054—52no—
92C4×#216—52no—
93Q8×C3⋊C8—51no—
94#5022—52no—
95C4×#214—51no—
96#5007—51no—
97C5×C4⋊Q8—31no—
98C5×C4⋊Q8C2×D311yescharacteristic
99#4093C2×D312yes—
100Q8×Dic5—61no—
101Q8×Dic5C2×D312yes—
102#4090—61no—
103C2×#689—32no—
104C2×#677—31no—
105#4044—22no—
106#4043—21no—
107#4038—21no—
108#4036—32no—
109#4035—62no—
110#4033—32no—
111C4×D20C2×D311yescharacteristic
112C4×Dic10—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×#103—32no—
115C5×#103—32no—
116C4×C5×C8—31no—
117#3967—32no—
118#3953—31no—
119#3949—31no—
120#3948—31no—
121#3946—32no—
122C8×Dic5—32no—
123#3941—32no—
124#3939—32no—
125C4⋊#168—31no—
126#3364—151noSylow
127C22×C3×D5—21no—
128C3×C5×Q8—22no—
129C3×C5×Q8—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—21no—
135C2×Dic15—21no—
136Dic30—21no—
137Dic30#4112yes—
138C2×C5×Dic3—22no—
139C5×Dic6—42no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5C2×D412yes—
142C2×C3×Dic5C2×D412yes—
143C3×D20—21no—
144C3×D20—21no—
145C3×C4×D5—42no—
146C3×Dic10—22no—
147C3⋊#168—22no—
148C5×C3⋊C8—21no—
149C5×C3⋊C8—21no—
150C3×C4⋊Q8C2×D511yescharacteristic
151C3×#126—102no—
152C3×#124—52no—
153C3×C22⋊Q8—101no—
154C3×C4×Q8—51no—
155C3×C4×Q8—52no—
156C3×C4×D4—51no—
157C3×#117—101no—
158#944—101no—
159C2×#216—52no—
160C2×#214—51no—
161#889—102no—
162#887—101no—
163#870—52no—
164#869C2×D511yescharacteristic
165C4×Dic6—51no—
166C4×Dic6—52no—
167#835—52no—
168#835C2×D512yes—
169#835C2×D512yes—
170#832—52no—
171#832—51no—
172#810—51no—
173#808—51no—
174#807—52no—
175C4⋊(C3⋊C8)—51no—
176C4⋊(C3⋊C8)—52no—
177C4×C3⋊C8—52no—
178C4×C3⋊C8C2×D511yescharacteristic
179C2×C5×Q8—61no—
180C2×C5×Q8C22×D312yes—
181C2×D20C22×D311yescharacteristic
182C2×C4×D5—21no—
183C2×Dic10—31no—
184C2×Dic10#6711yescharacteristic
185C2×C5×C8—31no—
186C2×C5×C8—31no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—21no—
189C5×C4⋊C4—32no—
190C5×C4⋊C4—61no—
191C42×C5C22×D311yescharacteristic
192#689—64no—
193#685—21no—
194#685—22no—
195#685—22no—
196C4⋊Dic5—22no—
197C4⋊Dic5—31no—
198C4⋊Dic5—62no—
199C4⋊Dic5#6711yescharacteristic
200C4⋊Dic5C22×D311yescharacteristic
201#683—61no—
202#683—62no—
203#683—62no—
204#683#6712yes—
205C4×Dic5—22no—
206C4×Dic5—61no—
207C4×Dic5—62no—
208C4×Dic5C22×D312yes—
209C2×#168—32no—
210#677—62no—
211#557—151no—
212#556—51no—
213#488—152no—
214#487—31no—
215#479—152no—
216#474—151no—
217#464—152no—
218#462—151no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×C3×D5—41no—
224C2×C3×D5—41no—
225C2×C3×D5—41no—
226C3×C4×C5—21no—
227C3×C4×C5—42no—
228C3×C4×C5#13512yes—
229C3×C4×C5C2×#4111yescharacteristic
230C3×C4×C52−1+411yescharacteristic
231Dic15—22no—
232Dic15—41no—
233C3×Dic5—22no—
234C3×Dic5—22no—
235C3×Dic5—41no—
236C5×Dic3—42no—
237C2×C3×Q8—51no—
238C2×C3×Q8C22×D512yes—
239C2×C3×D4—51no—
240C22×C3×C4—101no—
241C2×Dic6—21no—
242C2×Dic6—51no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—52no—
246C3×C4⋊C4—51no—
247C3×C4⋊C4—51no—
248C3×C4⋊C4—102no—
249C3×C22⋊C4—102no—
250C3×C22⋊C4—102no—
251C3×C22⋊C4—101no—
252C3×C42—52no—
253C3×C42—102no—
254C3×C42C22×D511yescharacteristic
255#216—104no—
256#214—102no—
257C4⋊Dic3—21no—
258C4⋊Dic3—51no—
259C4⋊Dic3C22×D512yes—
260Dic3⋊C4—102no—
261Dic3⋊C4—102no—
262Dic3⋊C4—102no—
263Dic3⋊C4—101no—
264C4×Dic3—102no—
265C4×Dic3—101no—
266C2×C3⋊C8—52no—
267C2×C3⋊C8C22×D511yescharacteristic
268C2×C3⋊C8C22×D511yescharacteristic
269C22×D5—21no—
270C5×Q8—22no—
271C5×Q8—22no—
272C5×Q8—122no—
273C2×C4×C5—22no—
274C2×C4×C5—62no—
275C2×C4×C5C2×#6711yescharacteristic
276C2×C4×C5C2×#6711yescharacteristic
277C2×C4×C5C23×D311yescharacteristic
278C2×Dic5—21no—
279C2×Dic5—61no—
280C2×Dic5—61no—
281C2×Dic5C2×#6712yes—
282C2×Dic5C2×#6712yes—
283D20—21no—
284D20—21no—
285C4×D5—42no—
286Dic10—22no—
287Dic10—32no—
288Dic10—61no—
289C5×C8—61no—
290C5×C8—61no—
291#168—62no—
292C2×Q16—152no—
293C2×SD16—151no—
294C4⋊Q8—31no—
295C4⋊Q8—301no—
296C4⋊Q8D3×D511yescharacteristic
297#126—102no—
298#125—152no—
299#125—302no—
300#124—52no—
301C22⋊Q8—101no—
302C4×Q8—51no—
303C4×Q8—52no—
304C4×Q8—152no—
305C4×Q8—151no—
306C4×Q8—301no—
307C4×D4—51no—
308#117—101no—
309#107—152no—
310#106—151no—
311C4⋊C8—152no—
312C4⋊C8—151no—
313#103—32no—
314#103—32no—
315#103—151no—
316#103—152no—
317#102—152no—
318#102—151no—
319C4×C8—31no—
320C4×C8—152no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324C3×D5—81no—
325C23×C3—101no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—102no—
329C3×D4—101no—
330C3×D4—101no—
331C2×C3×C4—22no—
332C2×C3×C4—52no—
333C2×C3×C4—52no—
334C2×C3×C4—101no—
335C2×C3×C4—202no—
336C2×C3×C4D4×D511yescharacteristic
337C2×C3×C4D4×D511yescharacteristic
338C2×C3×C4C23×D511yescharacteristic
339C2×Dic3—22no—
340C2×Dic3—101no—
341C2×Dic3—101no—
342Dic6—42no—
343Dic6—52no—
344Dic6—101no—
345C3⋊C8—21no—
346C3⋊C8—21no—
347C3⋊C8—102no—
348C22×C5C22×#6711yescharacteristic
349C2×D5—41no—
350C2×D5—41no—
351C2×D5—41no—
352C4×C5—21no—
353C4×C5—42no—
354C4×C5—122no—
355C4×C5#95012yes—
356C4×C5D3×#4111yescharacteristic
357C4×C5#101011yescharacteristic
358Dic5—22no—
359Dic5—22no—
360Dic5—41no—
361Dic5—62no—
362Dic5—121no—
363C2×Q8—51no—
364C2×Q8—61no—
365C2×Q8—151no—
366C2×Q8C2×D3×D512yes—
367C2×D4—51no—
368C22×C4—101no—
369Q16—304no—
370SD16—302no—
371C2×C8—31no—
372C2×C8—31no—
373C2×C8—152no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—32no—
377C4⋊C4—51no—
378C4⋊C4—52no—
379C4⋊C4—51no—
380C4⋊C4—61no—
381C4⋊C4—102no—
382C4⋊C4—151no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—302no—
386C4⋊C4—301no—
387C22⋊C4—102no—
388C22⋊C4—102no—
389C22⋊C4—101no—
390C42—52no—
391C42—102no—
392C42—302no—
393C42—301no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3—201no—
397C22×C3—201no—
398C22×C3—201no—
399C22×C3C2×D4×D511yescharacteristic
400C3×C4—21no—
401C3×C4—42no—
402C3×C4—102no—
403C3×C4—102no—
404C3×C4—201no—
405C3×C4#406212yes—
406C3×C4D5×#4111yescharacteristic
407C3×C4#415011yescharacteristic
408Dic3—42no—
409Dic3—102no—
410Dic3—201no—
411C2×C5C2×#95011yescharacteristic
412C2×C5#583111yescharacteristic
413C2×C5#583811yescharacteristic
414D5—81no—
415C23—101no—
416Q8—22no—
417Q8—22no—
418Q8—102no—
419Q8—122no—
420Q8—152no—
421Q8—301no—
422D4—101no—
423D4—101no—
424C2×C4—22no—
425C2×C4—52no—
426C2×C4—52no—
427C2×C4—62no—
428C2×C4—101no—
429C2×C4—202no—
430C2×C4—301no—
431C2×C4—301no—
432C2×C4D5×#6711yescharacteristic
433C2×C4D5×#6711yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—61no—
436C8—61no—
437C8—302no—
438C2×C3—401no—
439C2×C3#6601111yescharacteristic
440C2×C3C2×#406211yescharacteristic
441C2×C3#6610011yescharacteristic
442C5#8367611yescharacteristic, complemented, Sylow
443C22—201no—
444C22—201no—
445C22—201no—
446C22C2×D5×#6711yescharacteristic
447C4—21no—
448C4—42no—
449C4—102no—
450C4—102no—
451C4—122no—
452C4—201no—
453C4—302no—
454C4—601no—
455C4#9151412yes—
456C4#9202011yescharacteristic
457C4#9202411yescharacteristic
458C3#1061335611yescharacteristic, complemented, Sylow
459C2—401no—
460C2#1175493911yescharacteristic
461C2#1175510111yescharacteristic
462C2C2×#9151411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D20C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11752487C2semidirect
3. #11751191C2semidirect
4. C5×#5079C2semidirect
5. #11749332C2semidirect
8. #11749244C2semidirect
11. C3⋊C8×Dic10C2semidirect
89. #5079D5semidirect
395. C3×C5#3364semidirect
442. C5#83676semidirect
458. C3#10613356semidirect

Maximal subgroups

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

subgroupindex
C3×#660662
#117524872
#117511912
C5×#50792
#117493322
#117493312
#117492482
#117492442
C4×#66572
#117468862
C3⋊C8×Dic102
#106133563
#836765