Finite Group Databasebeta

← #14471837

Subgroups — #14471837

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#11756472C211yesmaximal, characteristic, complemented
2#11752641C211yesmaximal, characteristic, complemented
3C5×#5072C211yesmaximal, characteristic
4C3×#65359C211yesmaximal, characteristic, complemented
5#11749091C212yesmaximal, complemented
6#11748994C212yesmaximal, complemented
7#11748992C212yesmaximal, complemented
8#11748944C212yesmaximal, complemented
9C4×#6659C211yesmaximal, characteristic, complemented
10#11746917C211yesmaximal, characteristic, complemented
11#11746851C211yesmaximal, characteristic, complemented
12#10612050—31nomaximal, Hall
13C3×C5×#127C2211yescharacteristic
14#91825—21no—
15#91825C2212yes—
16#91824—22no—
17D4×Dic15—21no—
18D4×Dic15C2212yes—
19C4×Dic30C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C2×C5×#213C2212yes—
22C4×C5×D12C2211yescharacteristic
23C3×#4015C2211yescharacteristic
24#91435C2212yes—
25D3×C4⋊Dic5—21no—
26#91410—22no—
27#91384C2212yes—
28#91365—21no—
29C2×#6659C2211yescharacteristic
30C5×#832C2212yes—
31C5×C4⋊(C3⋊C8)C2211yescharacteristic
32C3×#3964C2212yes—
33C3×#3964C2212yes—
34C3×C4×#168C2211yescharacteristic
35#90990C2212yes—
36#90985C2211yescharacteristic
37#90983C2212yes—
38#90975C2211yescharacteristic
39#90974C2212yes—
40#90967C2211yescharacteristic
41#90951C2212yes—
42#81585—51nomaximal, Hall
43#66047—31no—
44#65877—31no—
45C5×#459—31no—
46#65442—32no—
47D8×Dic5—32no—
48#65359D311yescharacteristic, complemented
49C4×#687—31no—
50#65139—31no—
51#65119—31no—
52#65057—32no—
53#65055—32no—
54C2×C3×C5×D4—21no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4C2312yes—
57C22×Dic15—22no—
58C2×Dic30D411yescharacteristic
59C2×Dic30C2311yescharacteristic
60C2×C5×D12C2311yescharacteristic
61C2×C4×C5×D3—21no—
62C2×C3×Dic10—21no—
63C2×D3×Dic5—22no—
64C3×C42×C5C2311yescharacteristic
65#6719—22no—
66#6719—22no—
67#6719—22no—
68C4⋊Dic15D411yescharacteristic
69C4⋊Dic15C2311yescharacteristic
70#6712—21no—
71#6712D412yes—
72C4×Dic15—21no—
73C4×Dic15C2312yes—
74C5×#213—24no—
75C5×(C2×D3)⋊C4—21no—
76C5×C4⋊Dic3C2311yescharacteristic
77C2×C5×C3⋊C8C2312yes—
78C3×C4⋊Dic5—21no—
79C3×C4⋊Dic5C2312yes—
80C2×C3×#168C2311yescharacteristic
81C2×C3×#168C2311yescharacteristic
82Dic3⋊Dic5—22no—
83#6668—22no—
84(C2×D3)⋊Dic5—22no—
85#6659—22no—
86#5730—51no—
87#5713—51no—
88C3×#486—51no—
89#5091—51no—
90#5072D511yescharacteristic
91#4787—52no—
92#4768—52no—
93#4763—52no—
94#4756—52no—
95C4×#204—51no—
96C8×Dic6—51no—
97C2×C5×D8—32no—
98C5×#127C2×D311yescharacteristic
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×Dic10—31no—
114C5×C4⋊C8—31no—
115C5×#102—32no—
116#3964—31no—
117#3964C2×D312yes—
118#3964C2×D312yes—
119#3950—32no—
120#3948—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3942—31no—
124#3940—31no—
125C4×#168C2×D311yescharacteristic
126#3361—151noSylow
127C23×C3×C5—22no—
128C22×C5×D3—21no—
129C3×C5×D4—22no—
130C3×C5×D4—22no—
131C3×C5×D4—42no—
132C3×C5×D4—81no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—21no—
137C2×Dic15—21no—
138C2×Dic15—82no—
139C2×Dic15C2×D412yes—
140C2×Dic15C2×D412yes—
141Dic30—22no—
142Dic30—21no—
143Dic30—21no—
144C2×C5×Dic3—21no—
145C5×D12—21no—
146C5×D12#4112yes—
147C4×C5×D3—42no—
148C2×C3×Dic5—22no—
149C3×Dic10—81no—
150D3×Dic5—82no—
151C3×#168—21no—
152C3×#168—21no—
153C5×C3⋊C8—22no—
154C3×C4⋊Q8—51no—
155C3×#127C2×D511yescharacteristic
156#946—102no—
157#936—52no—
158#936—101no—
159#935—102no—
160D4×Dic3—52no—
161D4×Dic3—101no—
162C2×#213C2×D512yes—
163C2×#204—51no—
164#897—101no—
165#893—52no—
166D3×C4⋊C4—101no—
167#890—52no—
168C4×D12C2×D511yescharacteristic
169C4×Dic6—51no—
170C4×Dic6—51no—
171C3×#102—52no—
172C3×#102—52no—
173C3×C4×C8—51no—
174#832C2×D512yes—
175#821—51no—
176#817—51no—
177#816—51no—
178Dic3⋊C8—52no—
179C8×Dic3—52no—
180#810—52no—
181#807—52no—
182C4⋊(C3⋊C8)C2×D511yescharacteristic
183C2×C5×D4—21no—
184C2×C5×D4—21no—
185C2×C5×D4—31no—
186C2×C5×D4C22×D312yes—
187C22×C4×C5—61no—
188C22×Dic5—62no—
189C22×Dic5—62no—
190C2×Dic10—21no—
191C2×Dic10—31no—
192C2×Dic10—31no—
193C5×D8—64no—
194C2×C5×C8—32no—
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—31no—
206C4⋊Dic5—62no—
207C4⋊Dic5C22×D312yes—
208#683—32no—
209#683—62no—
210#683—61no—
211C4×Dic5—32no—
212C4×Dic5—61no—
213C2×#168C22×D311yescharacteristic
214C2×#168C22×D311yescharacteristic
215#559—151no—
216#554—151no—
217#488—152no—
218#486—51no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—31no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5—42no—
227C22×C3×C5—42no—
228C22×C3×C5—42no—
229C22×C3×C5C22×D411yescharacteristic
230C2×C5×D3—22no—
231C2×C5×D3—41no—
232C2×C5×D3—41no—
233C3×C4×C5—21no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—22no—
238Dic15—22no—
239Dic15—41no—
240Dic15—41no—
241C3×Dic5—42no—
242C5×Dic3—41no—
243C2×C3×Q8—101no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4C22×D512yes—
247C22×Dic3—102no—
248C2×D12C22×D511yescharacteristic
249C2×C4×D3—21no—
250C2×C4×D3—102no—
251C2×Dic6—51no—
252C2×Dic6—51no—
253C2×C3×C8—51no—
254C2×C3×C8—51no—
255C3×C4⋊C4—52no—
256C3×C4⋊C4—101no—
257C3×C42C22×D511yescharacteristic
258#217—102no—
259#217—102no—
260#217—102no—
261#213—24no—
262(C2×D3)⋊C4—21no—
263(C2×D3)⋊C4—102no—
264C4⋊Dic3—51no—
265C4⋊Dic3—51no—
266C4⋊Dic3—102no—
267C4⋊Dic3C22×D511yescharacteristic
268Dic3⋊C4—52no—
269Dic3⋊C4—102no—
270Dic3⋊C4—101no—
271C4×Dic3—52no—
272C4×Dic3—101no—
273C2×C3⋊C8C22×D512yes—
274#204—102no—
275C23×C5—22no—
276C23×C5—61no—
277C5×D4—22no—
278C5×D4—22no—
279C5×D4—32no—
280C5×D4—42no—
281C5×D4—61no—
282C5×D4—81no—
283C2×C4×C5—61no—
284C2×C4×C5—122no—
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—22no—
289C2×Dic5—32no—
290C2×Dic5—32no—
291C2×Dic5—61no—
292C2×Dic5—61no—
293C2×Dic5—242no—
294C2×Dic5—242no—
295Dic10—62no—
296Dic10—61no—
297Dic10—61no—
298Dic10—81no—
299C5×C8—62no—
300#168—21no—
301#168—21no—
302C2×SD16—151no—
303C2×D8—32no—
304C4⋊Q8—51no—
305#127D3×D511yescharacteristic
306#125—152no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—151no—
313C4×Q8—151no—
314C4×D4—31no—
315C4×D4—152no—
316C4×D4—152no—
317C4×D4—301no—
318C2×C4⋊C4—301no—
319#107—152no—
320#106—151no—
321C4⋊C8—31no—
322C4⋊C8—152no—
323#103—151no—
324#103—152no—
325#102—32no—
326#102—52no—
327#102—52no—
328#102—151no—
329C4×C8—51no—
330C4×C8—152no—
331C2×C3×C5—82no—
332C2×C3×C5#54811yescharacteristic
333C2×C3×C5C2×#13511yescharacteristic
334C2×C3×C5#57611yescharacteristic
335C5×D3—42no—
336C23×C3—22no—
337C22×D3—21no—
338C3×Q8—401no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—42no—
342C3×D4—81no—
343C2×C3×C4—102no—
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4D4×D511yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—21no—
348C2×Dic3—52no—
349C2×Dic3—52no—
350C2×Dic3—101no—
351C2×Dic3—101no—
352C2×Dic3—402no—
353D12—21no—
354D12#71112yes—
355C4×D3—42no—
356C4×D3—402no—
357Dic6—102no—
358Dic6—101no—
359Dic6—101no—
360C3×C8—101no—
361C3×C8—101no—
362C3⋊C8—22no—
363C22×C5—42no—
364C22×C5—42no—
365C22×C5—42no—
366C22×C5—62no—
367C22×C5—121no—
368C22×C5—121no—
369C22×C5C2×D3×D411yescharacteristic
370C4×C5—21no—
371C4×C5—121no—
372C4×C5#91612yes—
373C4×C5D3×#4111yescharacteristic
374C4×C5#101011yescharacteristic
375Dic5—42no—
376Dic5—62no—
377Dic5—62no—
378Dic5—121no—
379Dic5—121no—
380C2×Q8—101no—
381C2×Q8—151no—
382C2×Q8—151no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—31no—
386C2×D4C2×D3×D512yes—
387C22×C4—61no—
388C22×C4—302no—
389C22×C4—302no—
390SD16—302no—
391D8—64no—
392C2×C8—32no—
393C2×C8—51no—
394C2×C8—51no—
395C4⋊C4—31no—
396C4⋊C4—52no—
397C4⋊C4—101no—
398C4⋊C4—151no—
399C4⋊C4—152no—
400C4⋊C4—151no—
401C4⋊C4—302no—
402C4⋊C4—302no—
403C4⋊C4—301no—
404C22⋊C4—61no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—152no—
410C42—301no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3C2×D4×D511yescharacteristic
417C2×D3—22no—
418C2×D3—41no—
419C2×D3—41no—
420C3×C4—21no—
421C3×C4—202no—
422C3×C4#405812yes—
423C3×C4C2×#71111yescharacteristic
424C3×C4#415011yescharacteristic
425Dic3—41no—
426Dic3—102no—
427Dic3—102no—
428Dic3—201no—
429Dic3—201no—
430C2×C5—82no—
431C2×C5—122no—
432C2×C5#567711yescharacteristic
433C2×C5#575711yescharacteristic
434C2×C5C2×#91611yescharacteristic
435C23—22no—
436C23—61no—
437Q8—302no—
438Q8—301no—
439Q8—301no—
440Q8—401no—
441D4—22no—
442D4—22no—
443D4—32no—
444D4—42no—
445D4—61no—
446D4—81no—
447C2×C4—61no—
448C2×C4—102no—
449C2×C4—122no—
450C2×C4—152no—
451C2×C4—152no—
452C2×C4—301no—
453C2×C4—301no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4#679011yescharacteristic
457C2×C4#679011yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—62no—
460C8—101no—
461C8—101no—
462C2×C3—82no—
463C2×C3#6593211yescharacteristic
464C2×C3C2×#405811yescharacteristic
465C2×C3#6610811yescharacteristic
466D3—42no—
467C5#8158511yescharacteristic, complemented, Sylow
468C22—42no—
469C22—42no—
470C22—42no—
471C22—62no—
472C22—121no—
473C22—121no—
474C22C2×#679011yescharacteristic
475C4—21no—
476C4—121no—
477C4—202no—
478C4—302no—
479C4—302no—
480C4—601no—
481C4—601no—
482C4#9149912yes—
483C4#9202011yescharacteristic
484C4D3×#71111yescharacteristic
485C3#1061205011yescharacteristic, complemented, Sylow
486C2—82no—
487C2—122no—
488C2#1175470311yescharacteristic
489C2C2×#9149911yescharacteristic
490C2#1175482711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
prime radicalC5×#5072C2
hypercenter#127D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #11756472C2semidirect
2. #11752641C2semidirect
4. C3×#65359C2semidirect
5. #11749091C2semidirect
6. #11748994C2semidirect
7. #11748992C2semidirect
8. #11748944C2semidirect
9. C4×#6659C2semidirect
10. #11746917C2semidirect
11. #11746851C2semidirect
48. #65359D3semidirect
412. C3×C5#3361semidirect
467. C5#81585semidirect
485. C3#10612050semidirect

Maximal subgroups

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

subgroupindex
#117564722
#117526412
C5×#50722
C3×#653592
#117490912
#117489942
#117489922
#117489442
C4×#66592
#117469172
#117468512
#106120503
#815855