Finite Group Databasebeta

← #14471832

Subgroups — #14471832

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#11756302C211yesmaximal, characteristic, complemented
2#11752651C211yesmaximal, characteristic, complemented
3C5×#5015C211yesmaximal, characteristic
4C3×C4×#687C211yesmaximal, characteristic, complemented
5#11749082C212yesmaximal, complemented
6#11748994C212yesmaximal, complemented
7#11747387C212yesmaximal, complemented
8#11747260C212yesmaximal, complemented
9#11746916C211yesmaximal, characteristic, complemented
10#11746906C211yesmaximal, characteristic, complemented
11#11746851C211yesmaximal, characteristic, complemented
12#10612050—31nomaximal, Hall
13C3×C4×C5×D4C2211yescharacteristic
14D4×Dic15C2212yes—
15C2×C4⋊Dic15—21no—
16#91813—21no—
17#91779C2212yes—
18#91767—22no—
19#91758C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C2×C5×#213C2212yes—
22C5×#874C2211yescharacteristic
23C2×C3×#687C2211yescharacteristic
24C3×C4×Dic10C2211yescharacteristic
25#91435C2212yes—
26#91423—22no—
27Dic5×D12—21no—
28#91373—21no—
29#91370C2212yes—
30C5×#809C2212yes—
31C5×C4⋊(C3⋊C8)C2211yescharacteristic
32C3×#3964C2211yescharacteristic
33C3×#3942C2211yescharacteristic
34C3×#3940C2211yescharacteristic
35C3×C4×#168C2211yescharacteristic
36#90990C2212yes—
37#90983C2212yes—
38#90971C2212yes—
39#90967C2212yes—
40#90967C2212yes—
41#90951C2212yes—
42#79621—51nomaximal, Hall
43#66047—31no—
44#65877—31no—
45C5×#459—31no—
46#65442—32no—
47D8×Dic5—32no—
48#65359—31no—
49C4×#687D311yescharacteristic, complemented
50#65139—31no—
51#65119—31no—
52#65057—32no—
53#65055—32no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C22×Dic15—22no—
57C2×Dic30—21no—
58C2×Dic30D411yescharacteristic
59C2×C5×D12—21no—
60C2×C5×D12—21no—
61C2×C5×D12C2312yes—
62C2×C3×Dic10C2311yescharacteristic
63C2×D3×Dic5—22no—
64C3×C5×C4⋊C4C2311yescharacteristic
65C3×C5×C22⋊C4—21no—
66C3×C42×C5C2311yescharacteristic
67#6719—22no—
68C4⋊Dic15—21no—
69C4⋊Dic15—22no—
70C4⋊Dic15D411yescharacteristic
71C4⋊Dic15C2312yes—
72#6712—22no—
73#6712D412yes—
74C4×Dic15C2312yes—
75C5×#213—24no—
76C2×C5×C3⋊C8C2312yes—
77C3×#687—22no—
78C3×C4⋊Dic5C2311yescharacteristic
79C3×#683—21no—
80C3×C4×Dic5—21no—
81C2×C3×#168C2311yescharacteristic
82C2×C3×#168C2311yescharacteristic
83(C2×D3)⋊Dic5—22no—
84(C2×D3)⋊Dic5—22no—
85(C2×D3)⋊Dic5—22no—
86#5585—51no—
87#5543—51no—
88C3×C4×SD16—51no—
89#5165—52no—
90#5021—51no—
91#5015D511yescharacteristic
92#4871—52no—
93#4800—52no—
94#4756—52no—
95#4694—51no—
96C8×Dic6—51no—
97C2×C5×D8—32no—
98C5×#127—31no—
99C4×C5×D4C2×D311yescharacteristic
100#4082—32no—
101#4082—61no—
102#4081—62no—
103D4×Dic5—32no—
104D4×Dic5—32no—
105D4×Dic5—61no—
106C2×#687C2×D311yescharacteristic
107C2×C4⋊Dic5—61no—
108#4070—61no—
109#4036—32no—
110#4024—62no—
111#4015—31no—
112C4×Dic10—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×C4⋊C8—31no—
115C5×#102—32no—
116#3964—32no—
117#3964—32no—
118#3964C2×D311yescharacteristic
119#3950—32no—
120#3948—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3942C2×D311yescharacteristic
124#3940C2×D311yescharacteristic
125C4×#168C2×D311yescharacteristic
126#3361—151noSylow
127C23×C3×C5—21no—
128C22×C5×D3—22no—
129C3×C5×D4—21no—
130C3×C5×D4#4112yes—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—42no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—22no—
137C2×Dic15—82no—
138C2×Dic15C2×D412yes—
139C2×Dic15C2×D412yes—
140Dic30—22no—
141Dic30—81no—
142C5×D12—22no—
143C5×D12—22no—
144C5×D12—42no—
145C5×D12—81no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—21no—
148C3×Dic10—21no—
149C3×Dic10—21no—
150D3×Dic5—82no—
151C3×#168—21no—
152C3×#168—21no—
153C5×C3⋊C8—22no—
154C2×C3×SD16—51no—
155C3×C4×Q8—51no—
156C3×C4×D4C2×D511yescharacteristic
157#947—52no—
158D4×Dic3—52no—
159C2×#213C2×D512yes—
160C2×C4⋊Dic3—101no—
161#924—101no—
162#894—102no—
163#893—52no—
164#890—52no—
165#878—102no—
166#875—101no—
167#874C2×D511yescharacteristic
168C4×D12—101no—
169#869—51no—
170C4×Dic6—51no—
171C3×#106—51no—
172C3×#103—51no—
173C3×#102—51no—
174C3×C4×C8—51no—
175#835—52no—
176#821—52no—
177#821—52no—
178Dic3⋊C8—52no—
179C8×Dic3—52no—
180#809C2×D512yes—
181#807—52no—
182C4⋊(C3⋊C8)C2×D511yescharacteristic
183C2×C5×D4—32no—
184C2×C5×D4—61no—
185C2×C5×D4—61no—
186C2×C5×D4C22×D311yescharacteristic
187C22×C4×C5—21no—
188C22×Dic5—62no—
189C22×Dic5—62no—
190C2×Dic10—31no—
191C2×Dic10—61no—
192C2×Dic10C22×D311yescharacteristic
193C5×D8—64no—
194C2×C5×C8—32no—
195C5×C4⋊C4C22×D311yescharacteristic
196C5×C22⋊C4—21no—
197C42×C5C22×D311yescharacteristic
198C22⋊Dic5—62no—
199C22⋊Dic5—62no—
200C22⋊Dic5—62no—
201C22⋊Dic5—62no—
202#687—22no—
203C4⋊Dic5—31no—
204C4⋊Dic5—32no—
205C4⋊Dic5—62no—
206C4⋊Dic5—61no—
207C4⋊Dic5C22×D311yescharacteristic
208#683—21no—
209#683—32no—
210#683—62no—
211C4×Dic5—21no—
212C4×Dic5—32no—
213C2×#168C22×D311yescharacteristic
214C2×#168C22×D311yescharacteristic
215#559—151no—
216#554—151no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—31no—
223C8×Q8—151no—
224C4×SD16—51no—
225C4×D8—152no—
226C22×C3×C5—22no—
227C22×C3×C5—41no—
228C22×C3×C5—41no—
229C22×C3×C5C22×D411yescharacteristic
230C2×C5×D3—42no—
231C2×C5×D3—42no—
232C2×C5×D3—42no—
233C3×C4×C5—21no—
234C3×C4×C5—41no—
235C3×C4×C5#13512yes—
236C3×C4×C5C2×#4111yescharacteristic
237C3×C4×C52−1+411yescharacteristic
238Dic15—22no—
239Dic15—22no—
240Dic15—42no—
241C3×Dic5—41no—
242C3×Dic5—41no—
243C2×C3×Q8—51no—
244C2×C3×D4C22×D511yescharacteristic
245C22×C3×C4—21no—
246C22×Dic3—102no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12C22×D512yes—
250C2×C4×D3—102no—
251C2×Dic6—51no—
252C2×Dic6—101no—
253C3×SD16—102no—
254C2×C3×C8—51no—
255C2×C3×C8—51no—
256C3×C4⋊C4—51no—
257C3×C4⋊C4—101no—
258C3×C4⋊C4C22×D511yescharacteristic
259C3×C22⋊C4—21no—
260C3×C42—101no—
261C3×C42C22×D511yescharacteristic
262#217—102no—
263#213—24no—
264(C2×D3)⋊C4—102no—
265(C2×D3)⋊C4—102no—
266(C2×D3)⋊C4—102no—
267C4⋊Dic3—51no—
268C4⋊Dic3—52no—
269C4⋊Dic3—102no—
270C4⋊Dic3—101no—
271Dic3⋊C4—52no—
272Dic3⋊C4—102no—
273C4×Dic3—52no—
274C2×C3⋊C8C22×D512yes—
275C23×C5—21no—
276C23×C5—62no—
277C5×D4—21no—
278C5×D4—62no—
279C5×D4—62no—
280C5×D4—122no—
281C5×D4—241no—
282C5×D4#23512yes—
283C2×C4×C5—21no—
284C2×C4×C5—42no—
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—32no—
291C2×Dic5—32no—
292C2×Dic5—62no—
293C2×Dic5—242no—
294C2×Dic5—242no—
295Dic10—21no—
296Dic10—21no—
297Dic10—62no—
298Dic10—241no—
299C5×C8—62no—
300#168—21no—
301#168—21no—
302C2×SD16—51no—
303C2×D8—32no—
304C4⋊Q8—151no—
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—152no—
315C4×D4—152no—
316C4×D4—301no—
317C4×D4D3×D511yescharacteristic
318C2×C4⋊C4—301no—
319#107—152no—
320#106—51no—
321C4⋊C8—31no—
322C4⋊C8—152no—
323#103—51no—
324#103—152no—
325#102—32no—
326#102—51no—
327#102—152no—
328#102—152no—
329C4×C8—51no—
330C4×C8—152no—
331C2×C3×C5—42no—
332C2×C3×C5#54811yescharacteristic
333C2×C3×C5C2×#13511yescharacteristic
334C2×C3×C5#57611yescharacteristic
335C5×D3—82no—
336C23×C3—21no—
337C22×D3—22no—
338C3×Q8—101no—
339C3×Q8—101no—
340C3×D4—21no—
341C3×D4#71112yes—
342C2×C3×C4—21no—
343C2×C3×C4—42no—
344C2×C3×C4—101no—
345C2×C3×C4—101no—
346C2×C3×C4D4×D511yescharacteristic
347C2×C3×C4D4×D511yescharacteristic
348C2×C3×C4C23×D511yescharacteristic
349C2×Dic3—52no—
350C2×Dic3—52no—
351C2×Dic3—102no—
352C2×Dic3—402no—
353D12—22no—
354D12—22no—
355D12—42no—
356D12—81no—
357C4×D3—402no—
358Dic6—102no—
359Dic6—401no—
360C3×C8—101no—
361C3×C8—101no—
362C3⋊C8—22no—
363C22×C5—22no—
364C22×C5—41no—
365C22×C5—41no—
366C22×C5—122no—
367C22×C5—122no—
368C22×C5—122no—
369C22×C5C2×D3×D411yescharacteristic
370C4×C5—21no—
371C4×C5—41no—
372C4×C5#91612yes—
373C4×C5C2×#23511yescharacteristic
374C4×C5#101011yescharacteristic
375Dic5—41no—
376Dic5—41no—
377Dic5—62no—
378Dic5—62no—
379Dic5—122no—
380C2×Q8—51no—
381C2×Q8—151no—
382C2×Q8—301no—
383C2×D4—32no—
384C2×D4—61no—
385C2×D4—61no—
386C2×D4C2×D3×D511yescharacteristic
387C22×C4—21no—
388C22×C4—302no—
389C22×C4—302no—
390SD16—102no—
391D8—64no—
392C2×C8—32no—
393C2×C8—51no—
394C2×C8—51no—
395C4⋊C4—51no—
396C4⋊C4—101no—
397C4⋊C4—151no—
398C4⋊C4—152no—
399C4⋊C4—152no—
400C4⋊C4—302no—
401C4⋊C4—302no—
402C4⋊C4—301no—
403C4⋊C4C2×D3×D511yescharacteristic
404C22⋊C4—21no—
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×C3—22no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3C2×D4×D511yescharacteristic
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—42no—
420C3×C4—21no—
421C3×C4—41no—
422C3×C4—201no—
423C3×C4—201no—
424C3×C4#405812yes—
425C3×C4C2×#71111yescharacteristic
426C3×C4#415011yescharacteristic
427Dic3—102no—
428Dic3—102no—
429Dic3—202no—
430C2×C5—42no—
431C2×C5—242no—
432C2×C5#555211yescharacteristic
433C2×C5C2×#91611yescharacteristic
434C2×C5#576911yescharacteristic
435C23—21no—
436C23—62no—
437Q8—101no—
438Q8—101no—
439Q8—302no—
440Q8—1201no—
441D4—21no—
442D4—62no—
443D4—62no—
444D4—122no—
445D4—241no—
446D4#677212yes—
447C2×C4—21no—
448C2×C4—42no—
449C2×C4—101no—
450C2×C4—101no—
451C2×C4—152no—
452C2×C4—152no—
453C2×C4—302no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4#679011yescharacteristic
457C2×C4#679011yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—62no—
460C8—101no—
461C8—101no—
462C2×C3—42no—
463C2×C3#6593211yescharacteristic
464C2×C3C2×#405811yescharacteristic
465C2×C3#6610811yescharacteristic
466D3—82no—
467C5#7962111yescharacteristic, complemented, Sylow
468C22—22no—
469C22—41no—
470C22—41no—
471C22—122no—
472C22—122no—
473C22—122no—
474C22C2×#679011yescharacteristic
475C4—21no—
476C4—41no—
477C4—201no—
478C4—201no—
479C4—302no—
480C4—302no—
481C4—602no—
482C4#9149912yes—
483C4#9200111yescharacteristic
484C4C2×#677211yescharacteristic
485C3#1061205011yescharacteristic, complemented, Sylow
486C2—42no—
487C2—242no—
488C2#1175455611yescharacteristic
489C2C2×#9149911yescharacteristic
490C2#1175533211yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC5×#5015C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #11756302C2semidirect
2. #11752651C2semidirect
4. C3×C4×#687C2semidirect
5. #11749082C2semidirect
6. #11748994C2semidirect
7. #11747387C2semidirect
8. #11747260C2semidirect
9. #11746916C2semidirect
10. #11746906C2semidirect
11. #11746851C2semidirect
49. C4×#687D3semidirect
412. C3×C5#3361semidirect
467. C5#79621semidirect
485. C3#10612050semidirect

Maximal subgroups

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

subgroupindex
#117563022
#117526512
C5×#50152
C3×C4×#6872
#117490822
#117489942
#117473872
#117472602
#117469162
#117469062
#117468512
#106120503
#796215