Finite Group Databasebeta

← #14471840

Subgroups — #14471840

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752662C211yesmaximal, characteristic, complemented
2#11752657C211yesmaximal, characteristic, complemented
3#11750795C211yesmaximal, characteristic, complemented
4C5×C8×Dic6C211yesmaximal, characteristic, complemented
5C3×C4×#677C211yesmaximal, characteristic, complemented
6#11747988C212yesmaximal, complemented
7#11747797C212yesmaximal, complemented
8#11747755C212yesmaximal, complemented
9#11747740C212yesmaximal, complemented
10#11747028C211yesmaximal, characteristic
11#11746916C211yesmaximal, characteristic, complemented
12#10611658—31nomaximal, Hall
13#91763C2211yescharacteristic
14#91758C2211yescharacteristic
15C4×C5×Dic6C2211yescharacteristic
16C2×C3×#677C2211yescharacteristic
17C3×C4×D20C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19#91433—22no—
20#91431—22no—
21#91428C2212yes—
22Dic3×D20C2212yes—
23#91418—21no—
24D5×C4⋊Dic3—21no—
25#91381C2212yes—
26#91375—21no—
27#91374C2212yes—
28#91359—21no—
29C2×#6653C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91105C2212yes—
32#91105C2212yes—
33C5×Dic3⋊C8C2212yes—
34C5×C8×Dic3C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×#3953C2211yescharacteristic
37C3×#3949C2211yescharacteristic
38C3×#3948C2211yescharacteristic
39#90990C2212yes—
40#90971C2212yes—
41#90968C2212yes—
42#79621—51nomaximal, Hall
43#65919—31no—
44#65913—31no—
45C5×C8×Q8—31no—
46#65139—31no—
47#65136—32no—
48#65133—32no—
49#65132—31no—
50#64986—32no—
51#64983—31no—
52C4×D40—32no—
53C4×#677D311yescharacteristic, complemented
54C2×D60—21no—
55C2×D60—21no—
56C2×D60C2312yes—
57C2×Dic30—21no—
58C2×C5×Dic6D411yescharacteristic
59C2×C3×D20C2311yescharacteristic
60C2×C3×C4×D5—21no—
61C2×C3×Dic10C2311yescharacteristic
62C2×#1200—22no—
63C2×D5×Dic3—22no—
64C2×C3×C5×C8C2311yescharacteristic
65C2×C3×C5×C8C2311yescharacteristic
66C3×C42×C5C2311yescharacteristic
67C4⋊Dic15—21no—
68C4⋊Dic15C2312yes—
69C5×C4⋊Dic3D411yescharacteristic
70C5×Dic3⋊C4D412yes—
71C4×C5×Dic3C2312yes—
72C2×C5×C3⋊C8C2312yes—
73C3×#685—21no—
74C3×C4⋊Dic5C2311yescharacteristic
75C3×C4⋊Dic5C2311yescharacteristic
76C3×#683—21no—
77C3×C4×Dic5—21no—
78C3×#677—22no—
79#6669—22no—
80#6668—22no—
81#6667—22no—
82#6667—22no—
83#6667—22no—
84#6665—22no—
85#6653—24no—
86#5585—51no—
87#5543—51no—
88C3×C4×SD16—51no—
89#5165—52no—
90#5021—51no—
91#5015—51no—
92#4871—52no—
93#4800—52no—
94#4756—52no—
95#4694—51no—
96C8×Dic6D511yescharacteristic, complemented
97C4×C5×Q8—31no—
98#4093—61no—
99#4092—61no—
100C2×D40—32no—
101C2×#677C2×D311yescharacteristic
102#4042—62no—
103#4040—62no—
104#4039—61no—
105D5×C4⋊C4—61no—
106#4021—32no—
107#4020—31no—
108C4×D20—32no—
109C4×D20—32no—
110C4×D20C2×D311yescharacteristic
111#4016—32no—
112#4015—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×C4⋊C8—32no—
115C5×C4⋊C8—31no—
116C4×C5×C8—32no—
117C4×C5×C8C2×D311yescharacteristic
118#3953—32no—
119#3953—32no—
120#3953—32no—
121#3953C2×D311yescharacteristic
122#3950—32no—
123#3949C2×D311yescharacteristic
124#3948—32no—
125#3948C2×D311yescharacteristic
126#3361—151noSylow
127C22×D15—22no—
128C22×C3×D5—21no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—22no—
133D60—22no—
134D60—22no—
135D60—42no—
136D60—81no—
137Dic30—81no—
138C2×C5×Dic3C2×D412yes—
139C2×C5×Dic3C2×D412yes—
140C5×Dic6—22no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—21no—
144C3×D20—21no—
145C3×D20#4112yes—
146C3×C4×D5—42no—
147C3×Dic10—21no—
148C3×Dic10—21no—
149#1200—82no—
150D5×Dic3—82no—
151C3×C5×C8—21no—
152C3×C5×C8—21no—
153C5×C3⋊C8—22no—
154C2×C3×SD16—51no—
155C3×C4×Q8—51no—
156C3×C4×D4—51no—
157#947—52no—
158D4×Dic3—52no—
159C2×#213—52no—
160C2×C4⋊Dic3—101no—
161#924—101no—
162#894—102no—
163#893—52no—
164#890—52no—
165#878—102no—
166#875—101no—
167#874—51no—
168C4×D12—101no—
169#869—51no—
170C4×Dic6C2×D511yescharacteristic
171C3×#106—51no—
172C3×#103—51no—
173C3×#102—51no—
174C3×C4×C8C2×D511yescharacteristic
175#835—52no—
176#821—52no—
177#821—52no—
178Dic3⋊C8C2×D512yes—
179C8×Dic3C2×D512yes—
180#809—52no—
181#807—52no—
182C4⋊(C3⋊C8)C2×D511yescharacteristic
183C2×C5×Q8—31no—
184C2×D20—32no—
185C2×D20—61no—
186C2×D20—61no—
187C2×D20C22×D311yescharacteristic
188C2×C4×D5—21no—
189C2×C4×D5—62no—
190C2×C4×D5—62no—
191C2×Dic10—61no—
192C2×Dic10C22×D311yescharacteristic
193C2×C5×C8—32no—
194C2×C5×C8C22×D311yescharacteristic
195C2×C5×C8C22×D311yescharacteristic
196C5×C4⋊C4—32no—
197C5×C4⋊C4—31no—
198C42×C5—32no—
199C42×C5C22×D311yescharacteristic
200#685—21no—
201#685—62no—
202#685—62no—
203#685—62no—
204#685—62no—
205C4⋊Dic5—32no—
206C4⋊Dic5—61no—
207C4⋊Dic5C22×D311yescharacteristic
208C4⋊Dic5C22×D311yescharacteristic
209#683—21no—
210#683—62no—
211#683—62no—
212C4×Dic5—21no—
213D40—64no—
214#677—22no—
215#559—151no—
216#554—151no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—151no—
223C8×Q8—31no—
224C4×SD16—51no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—42no—
228C2×D15—42no—
229C2×D15—42no—
230C2×C3×D5—22no—
231C2×C3×D5—41no—
232C2×C3×D5—41no—
233C3×C4×C5—21no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—42no—
238C3×Dic5—41no—
239C3×Dic5—41no—
240C3×Dic5—41no—
241C5×Dic3—22no—
242C5×Dic3—22no—
243C2×C3×Q8—51no—
244C2×C3×D4—51no—
245C22×C3×C4—101no—
246C22×Dic3—102no—
247C2×D12—52no—
248C2×D12—101no—
249C2×D12—101no—
250C2×C4×D3—102no—
251C2×Dic6—101no—
252C2×Dic6D2011yescharacteristic
253C3×SD16—102no—
254C2×C3×C8C22×D511yescharacteristic
255C2×C3×C8C22×D511yescharacteristic
256C3×C4⋊C4—51no—
257C3×C4⋊C4—51no—
258C3×C4⋊C4—101no—
259C3×C22⋊C4—101no—
260C3×C42—101no—
261C3×C42C22×D511yescharacteristic
262#217—102no—
263#213—104no—
264(C2×D3)⋊C4—102no—
265(C2×D3)⋊C4—102no—
266(C2×D3)⋊C4—102no—
267C4⋊Dic3—52no—
268C4⋊Dic3—101no—
269C4⋊Dic3—102no—
270C4⋊Dic3D2011yescharacteristic
271Dic3⋊C4—102no—
272Dic3⋊C4D2012yes—
273C4×Dic3C22×D512yes—
274C2×C3⋊C8C22×D512yes—
275C22×D5—21no—
276C22×D5—62no—
277C5×Q8—62no—
278C2×C4×C5—32no—
279C2×C4×C5—32no—
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—21no—
284C2×Dic5—21no—
285C2×Dic5—21no—
286C2×Dic5—62no—
287D20—21no—
288D20—62no—
289D20—62no—
290D20—122no—
291D20—241no—
292D20#23512yes—
293C4×D5—42no—
294C4×D5—242no—
295C4×D5—242no—
296Dic10—21no—
297Dic10—21no—
298Dic10—241no—
299C5×C8—21no—
300C5×C8—21no—
301C5×C8—62no—
302C2×SD16—51no—
303C2×D8—152no—
304C4⋊Q8—151no—
305#127—151no—
306#125—152no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—31no—
313C4×Q8—51no—
314C4×D4—51no—
315C4×D4—152no—
316C4×D4—152no—
317C4×D4—301no—
318C2×C4⋊C4—301no—
319#107—152no—
320#106—51no—
321C4⋊C8—32no—
322C4⋊C8—31no—
323#103—51no—
324#103—152no—
325#102—51no—
326#102—152no—
327#102—152no—
328#102—152no—
329C4×C8—32no—
330C4×C8D3×D511yescharacteristic
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334D15—82no—
335C3×D5—42no—
336C23×C3—101no—
337C22×D3—102no—
338C3×Q8—101no—
339C3×Q8—101no—
340C3×D4—52no—
341C3×D4—101no—
342C2×C3×C4—101no—
343C2×C3×C4—101no—
344C2×C3×C4—101no—
345C2×C3×C4—202no—
346C2×C3×C4C2×D2011yescharacteristic
347C2×C3×C4C2×D2011yescharacteristic
348C2×C3×C4C23×D511yescharacteristic
349C2×Dic3—102no—
350C2×Dic3—402no—
351C2×Dic3C2×D2012yes—
352C2×Dic3C2×D2012yes—
353D12—102no—
354D12—102no—
355D12—202no—
356D12—401no—
357C4×D3—402no—
358Dic6—22no—
359Dic6—401no—
360C3×C8—21no—
361C3×C8—21no—
362C3⋊C8—22no—
363C22×C5C2×D3×D411yescharacteristic
364C2×D5—22no—
365C2×D5—41no—
366C2×D5—41no—
367C2×D5—122no—
368C2×D5—122no—
369C2×D5—122no—
370C4×C5—21no—
371C4×C5—62no—
372C4×C5—62no—
373C4×C5#91612yes—
374C4×C5C2×#23511yescharacteristic
375C4×C5#101011yescharacteristic
376Dic5—41no—
377Dic5—41no—
378Dic5—41no—
379Dic5—122no—
380C2×Q8—31no—
381C2×Q8—51no—
382C2×Q8—301no—
383C2×D4—51no—
384C2×D4—152no—
385C2×D4—301no—
386C2×D4—301no—
387C22×C4—101no—
388C22×C4—302no—
389C22×C4—302no—
390SD16—102no—
391D8—304no—
392C2×C8—32no—
393C2×C8C2×D3×D511yescharacteristic
394C2×C8C2×D3×D511yescharacteristic
395C4⋊C4—31no—
396C4⋊C4—32no—
397C4⋊C4—51no—
398C4⋊C4—51no—
399C4⋊C4—101no—
400C4⋊C4—152no—
401C4⋊C4—302no—
402C4⋊C4—302no—
403C4⋊C4—301no—
404C22⋊C4—101no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—32no—
410C42—101no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—102no—
414C22×C3—201no—
415C22×C3—201no—
416C22×C3C22×D2011yescharacteristic
417C2×D3—202no—
418C2×D3—202no—
419C2×D3—202no—
420C3×C4—21no—
421C3×C4—201no—
422C3×C4—201no—
423C3×C4—201no—
424C3×C4#405012yes—
425C3×C4#414711yescharacteristic
426C3×C4D5×#4111yescharacteristic
427Dic3—22no—
428Dic3—22no—
429Dic3—202no—
430C2×C5#555211yescharacteristic
431C2×C5C2×#91611yescharacteristic
432C2×C5#576911yescharacteristic
433D5—42no—
434D5—242no—
435C23—101no—
436C23—302no—
437Q8—62no—
438Q8—101no—
439Q8—101no—
440Q8—1201no—
441D4—52no—
442D4—101no—
443D4—302no—
444D4—302no—
445D4—602no—
446D4—1201no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—101no—
450C2×C4—101no—
451C2×C4—101no—
452C2×C4—202no—
453C2×C4—302no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4D3×D2011yescharacteristic
457C2×C4D3×D2011yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—21no—
460C8—21no—
461C8—62no—
462C2×C3—202no—
463C2×C3#6591011yescharacteristic
464C2×C3C2×#405011yescharacteristic
465C2×C3#6608611yescharacteristic
466D3—402no—
467C5#7962111yescharacteristic, complemented, Sylow
468C22—102no—
469C22—201no—
470C22—201no—
471C22—602no—
472C22—602no—
473C22—602no—
474C22C2×D3×D2011yescharacteristic
475C4—21no—
476C4—62no—
477C4—62no—
478C4—201no—
479C4—201no—
480C4—201no—
481C4—602no—
482C4#9127212yes—
483C4#9200011yescharacteristic
484C4D5×#23511yescharacteristic
485C3#1061165811yescharacteristic, complemented, Sylow
486C2—202no—
487C2—1202no—
488C2#1175254111yescharacteristic
489C2#1175397311yescharacteristic
490C2C2×#9127211yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11747028C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #11752662C2semidirect
2. #11752657C2semidirect
3. #11750795C2semidirect
4. C5×C8×Dic6C2semidirect
5. C3×C4×#677C2semidirect
6. #11747988C2semidirect
7. #11747797C2semidirect
8. #11747755C2semidirect
9. #11747740C2semidirect
11. #11746916C2semidirect
53. C4×#677D3semidirect
96. C8×Dic6D5semidirect
412. C3×C5#3361semidirect
467. C5#79621semidirect
485. C3#10611658semidirect

Maximal subgroups

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

subgroupindex
#117526622
#117526572
#117507952
C5×C8×Dic62
C3×C4×#6772
#117479882
#117477972
#117477552
#117477402
#117470282
#117469162
#106116583
#796215