Finite Group Databasebeta

← #14471855

Subgroups — #14471855

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#11752651C211yesmaximal, characteristic, complemented
2#11752641C211yesmaximal, characteristic, complemented
3#11750931C211yesmaximal, characteristic, complemented
4C5×#4843C211yesmaximal, characteristic
5C3×#65139C211yesmaximal, characteristic, complemented
6#11747979C212yesmaximal, complemented
7#11747817C212yesmaximal, complemented
8#11747810C212yesmaximal, complemented
9#11747787C212yesmaximal, complemented
10C4×#6656C211yesmaximal, characteristic, complemented
11#11746901C211yesmaximal, characteristic, complemented
12#10612050—31nomaximal, Hall
13C4×Dic30C2211yescharacteristic
14C2×C5×D24C2212yes—
15C5×#874C2211yescharacteristic
16C4×C5×D12C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19#91435C2212yes—
20#91435C2212yes—
21D3×C4⋊Dic5—21no—
22#91423—22no—
23Dic5×D12—21no—
24#91410—22no—
25#91384C2212yes—
26#91373—21no—
27#91370C2212yes—
28#91365—21no—
29C2×#6656C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4×C3⋊#168C2211yescharacteristic
34C5×#821C2212yes—
35C3×#3950C2212yes—
36C3×#3948C2212yes—
37#90986C2211yescharacteristic
38#90970C2211yescharacteristic
39#90966C2212yes—
40#90966C2212yes—
41#90966C2211yescharacteristic
42#81134—51nomaximal, Hall
43#66047—31no—
44#65877—31no—
45C5×#459—31no—
46#65442—32no—
47D8×Dic5—32no—
48#65359—31no—
49C4×#687—31no—
50#65139D311yescharacteristic, complemented
51#65119—31no—
52#65057—32no—
53#65055—32no—
54C2×Dic30D411yescharacteristic
55C2×C5×D12—21no—
56C2×C5×D12—21no—
57C2×C5×D12C2312yes—
58C2×C5×D12C2311yescharacteristic
59C2×C4×C5×D3—21no—
60C2×C3×Dic10—21no—
61C2×C3×Dic10C2311yescharacteristic
62C2×D3×Dic5—22no—
63C2×D3×Dic5—22no—
64C2×C3×C5×C8C2312yes—
65C3×C42×C5C2311yescharacteristic
66C4⋊Dic15D411yescharacteristic
67#6712D412yes—
68C4×Dic15C2312yes—
69C2×C3⋊#168C2311yescharacteristic
70C2×C3⋊#168C2311yescharacteristic
71C5×(C2×D3)⋊C4—21no—
72C5×C4⋊Dic3C2311yescharacteristic
73C5×D24—24no—
74C3×C4⋊Dic5—21no—
75C3×C4⋊Dic5C2311yescharacteristic
76C3×C4⋊Dic5C2312yes—
77C3×#683—21no—
78C3×C4×Dic5—21no—
79Dic3⋊Dic5—22no—
80#6668—22no—
81(C2×D3)⋊Dic5—22no—
82(C2×D3)⋊Dic5—22no—
83(C2×D3)⋊Dic5—22no—
84(C2×D3)⋊Dic5—22no—
85#6656—22no—
86#5730—51no—
87#5585—51no—
88C3×#477—51no—
89#5088—51no—
90C4×#215—51no—
91#4891—52no—
92#4872—52no—
93#4843D511yescharacteristic
94#4830—51no—
95#4819—52no—
96#4800—52no—
97C2×C5×D8—32no—
98C5×#127—31no—
99C4×C5×D4—31no—
100#4082—32no—
101#4082—61no—
102#4081—62no—
103D4×Dic5—32no—
104D4×Dic5—32no—
105D4×Dic5—61no—
106C2×#687—31no—
107C2×C4⋊Dic5—61no—
108#4070—61no—
109#4036—32no—
110#4024—62no—
111#4015C2×D311yescharacteristic
112C4×Dic10—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×C4⋊C8C2×D311yescharacteristic
115C5×#102—32no—
116#3964—31no—
117#3964—32no—
118#3964—32no—
119#3950C2×D312yes—
120#3948C2×D312yes—
121#3946—32no—
122C8×Dic5—32no—
123#3942—31no—
124#3940—31no—
125C4×#168—31no—
126#3361—151noSylow
127C22×C5×D3—21no—
128C22×C5×D3—22no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15C2×D412yes—
133C2×Dic15C2×D412yes—
134Dic30—22no—
135C2×C5×Dic3—21no—
136C5×D12—22no—
137C5×D12—21no—
138C5×D12—22no—
139C5×D12—42no—
140C5×D12—81no—
141C5×D12#4112yes—
142C4×C5×D3—42no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—22no—
146C3×Dic10—21no—
147C3×Dic10—21no—
148C3×Dic10—81no—
149D3×Dic5—82no—
150D3×Dic5—82no—
151C3×C5×C8—22no—
152C3⋊#168—21no—
153C3⋊#168—21no—
154C3×C4⋊Q8—51no—
155C3×C4×Q8—51no—
156#947—52no—
157#946—102no—
158C2×#215—51no—
159C2×D24C2×D512yes—
160#897—101no—
161#894—102no—
162#893—52no—
163#893—52no—
164D3×C4⋊C4—101no—
165#890—52no—
166#875—101no—
167#874C2×D511yescharacteristic
168C4×D12—101no—
169C4×D12C2×D511yescharacteristic
170C4×Dic6—51no—
171C3×#107—52no—
172C3×C4⋊C8C2×D511yescharacteristic
173C3×#103—52no—
174#835—51no—
175#821C2×D512yes—
176Dic3⋊C8—52no—
177C8×Dic3—52no—
178#809—51no—
179#809—52no—
180#809—52no—
181#808—51no—
182C4×C3⋊C8—51no—
183C2×C5×D4—31no—
184C2×C5×D4—32no—
185C2×C5×D4—61no—
186C2×C5×D4—61no—
187C22×C4×C5—61no—
188C22×Dic5—62no—
189C22×Dic5—62no—
190C2×Dic10—21no—
191C2×Dic10—31no—
192C2×Dic10C22×D311yescharacteristic
193C5×D8—64no—
194C2×C5×C8C22×D312yes—
195C5×C4⋊C4—31no—
196C5×C22⋊C4—61no—
197C42×C5C22×D311yescharacteristic
198C22⋊Dic5—62no—
199C22⋊Dic5—62no—
200C22⋊Dic5—62no—
201C22⋊Dic5—62no—
202#687—62no—
203C4⋊Dic5—21no—
204C4⋊Dic5—31no—
205C4⋊Dic5—62no—
206C4⋊Dic5C22×D311yescharacteristic
207C4⋊Dic5C22×D312yes—
208#683—21no—
209#683—32no—
210#683—62no—
211C4×Dic5—21no—
212C4×Dic5—32no—
213C2×#168—31no—
214C2×#168—31no—
215#559—151no—
216#554—151no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477—51no—
221#463—152no—
222#459—31no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C5×D3—22no—
228C2×C5×D3—41no—
229C2×C5×D3—41no—
230C2×C5×D3—42no—
231C2×C5×D3—42no—
232C2×C5×D3—42no—
233C3×C4×C5—21no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—22no—
238Dic15—22no—
239C3×Dic5—41no—
240C3×Dic5—41no—
241C3×Dic5—42no—
242C5×Dic3—41no—
243C2×C3×Q8—51no—
244C2×C3×Q8—101no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12C22×D512yes—
248C2×D12C22×D511yescharacteristic
249C2×C4×D3—21no—
250C2×C4×D3—102no—
251C2×C4×D3—102no—
252C2×Dic6—51no—
253C2×C3×C8C22×D512yes—
254C3×C4⋊C4—51no—
255C3×C4⋊C4—52no—
256C3×C4⋊C4—101no—
257C3×C4⋊C4—101no—
258C3×C42—101no—
259C3×C42C22×D511yescharacteristic
260#215—102no—
261(C2×D3)⋊C4—21no—
262(C2×D3)⋊C4—102no—
263(C2×D3)⋊C4—102no—
264(C2×D3)⋊C4—102no—
265(C2×D3)⋊C4—102no—
266C4⋊Dic3—51no—
267C4⋊Dic3—102no—
268C4⋊Dic3C22×D511yescharacteristic
269Dic3⋊C4—52no—
270Dic3⋊C4—102no—
271C4×Dic3—52no—
272C2×C3⋊C8—51no—
273C2×C3⋊C8—51no—
274D24—24no—
275C23×C5—61no—
276C23×C5—62no—
277C5×D4—32no—
278C5×D4—61no—
279C5×D4—62no—
280C5×D4—62no—
281C5×D4—122no—
282C5×D4—241no—
283C2×C4×C5—61no—
284C2×C4×C5—122no—
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—22no—
291C2×Dic5—32no—
292C2×Dic5—32no—
293C2×Dic5—242no—
294C2×Dic5—242no—
295Dic10—21no—
296Dic10—21no—
297Dic10—62no—
298Dic10—81no—
299C5×C8—22no—
300#168—61no—
301#168—61no—
302C2×SD16—151no—
303C2×D8—32no—
304C4⋊Q8—51no—
305#127—31no—
306#125—152no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—51no—
313C4×Q8—151no—
314C4×D4—31no—
315C4×D4—152no—
316C4×D4—152no—
317C4×D4—301no—
318C2×C4⋊C4—301no—
319#107—52no—
320#106—151no—
321C4⋊C8—152no—
322C4⋊C8D3×D511yescharacteristic
323#103—52no—
324#103—151no—
325#102—32no—
326#102—151no—
327#102—152no—
328#102—152no—
329C4×C8—152no—
330C4×C8—151no—
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334C5×D3—42no—
335C5×D3—82no—
336C22×D3—21no—
337C22×D3—22no—
338C3×Q8—101no—
339C3×Q8—101no—
340C3×Q8—401no—
341C2×C3×C4—102no—
342C2×C3×C4—101no—
343C2×C3×C4—101no—
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—21no—
348C2×Dic3—52no—
349C2×Dic3—52no—
350D12—22no—
351D12—21no—
352D12—22no—
353D12—42no—
354D12—81no—
355D12#71112yes—
356C4×D3—42no—
357C4×D3—402no—
358C4×D3—402no—
359Dic6—102no—
360C3×C8—22no—
361C3⋊C8—101no—
362C3⋊C8—101no—
363C22×C5—62no—
364C22×C5—121no—
365C22×C5—121no—
366C22×C5—122no—
367C22×C5—122no—
368C22×C5—122no—
369C22×C5C2×D3×D411yescharacteristic
370C4×C5—21no—
371C4×C5—121no—
372C4×C5#91912yes—
373C4×C5#100711yescharacteristic
374C4×C5D3×#4111yescharacteristic
375Dic5—41no—
376Dic5—42no—
377Dic5—41no—
378Dic5—62no—
379Dic5—62no—
380C2×Q8—51no—
381C2×Q8—101no—
382C2×Q8—151no—
383C2×D4—31no—
384C2×D4—32no—
385C2×D4—61no—
386C2×D4—61no—
387C22×C4—61no—
388C22×C4—302no—
389C22×C4—302no—
390SD16—302no—
391D8—64no—
392C2×C8—151no—
393C2×C8—151no—
394C2×C8C2×D3×D512yes—
395C4⋊C4—31no—
396C4⋊C4—52no—
397C4⋊C4—51no—
398C4⋊C4—101no—
399C4⋊C4—101no—
400C4⋊C4—151no—
401C4⋊C4—152no—
402C4⋊C4—302no—
403C4⋊C4—302no—
404C22⋊C4—61no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—101no—
410C42—152no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3C2×D4×D511yescharacteristic
414C2×D3—22no—
415C2×D3—41no—
416C2×D3—41no—
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—42no—
420C3×C4—21no—
421C3×C4—201no—
422C3×C4—202no—
423C3×C4—201no—
424C3×C4#405812yes—
425C3×C4C2×#71111yescharacteristic
426C3×C4#415011yescharacteristic
427Dic3—41no—
428Dic3—102no—
429Dic3—102no—
430C2×C5—122no—
431C2×C5—242no—
432C2×C5#563311yescharacteristic
433C2×C5C2×#91911yescharacteristic
434C2×C5#577411yescharacteristic
435C23—61no—
436C23—62no—
437Q8—101no—
438Q8—101no—
439Q8—302no—
440Q8—401no—
441D4—32no—
442D4—62no—
443D4—61no—
444D4—62no—
445D4—122no—
446D4—241no—
447C2×C4—61no—
448C2×C4—101no—
449C2×C4—101no—
450C2×C4—102no—
451C2×C4—122no—
452C2×C4—152no—
453C2×C4—152no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4#677711yescharacteristic
457C2×C4#677711yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—22no—
460C8—301no—
461C8—301no—
462C2×C3#6593211yescharacteristic
463C2×C3C2×#405811yescharacteristic
464C2×C3#6610811yescharacteristic
465D3—42no—
466D3—82no—
467C5#8113411yescharacteristic, complemented, Sylow
468C22—62no—
469C22—121no—
470C22—121no—
471C22—122no—
472C22—122no—
473C22—122no—
474C22C2×#677711yescharacteristic
475C4—21no—
476C4—121no—
477C4—201no—
478C4—202no—
479C4—201no—
480C4—302no—
481C4—302no—
482C4#9127912yes—
483C4D3×#71111yescharacteristic
484C4#9203011yescharacteristic
485C3#1061205011yescharacteristic, complemented, Sylow
486C2—122no—
487C2—242no—
488C2#1175370311yescharacteristic
489C2C2×#9127911yescharacteristic
490C2#1175403811yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC5×#4843C2
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. #11752651C2semidirect
2. #11752641C2semidirect
3. #11750931C2semidirect
5. C3×#65139C2semidirect
6. #11747979C2semidirect
7. #11747817C2semidirect
8. #11747810C2semidirect
9. #11747787C2semidirect
10. C4×#6656C2semidirect
11. #11746901C2semidirect
50. #65139D3semidirect
412. C3×C5#3361semidirect
467. C5#81134semidirect
485. C3#10612050semidirect

Maximal subgroups

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

subgroupindex
#117526512
#117526412
#117509312
C5×#48432
C3×#651392
#117479792
#117478172
#117478102
#117477872
C4×#66562
#117469012
#106120503
#811345