Finite Group Databasebeta

← #14471836

Subgroups — #14471836

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
1C3×#66047C211yesmaximal, characteristic, complemented
2#11752660C211yesmaximal, characteristic, complemented
3#11751171C211yesmaximal, characteristic, complemented
4C5×#5072C211yesmaximal, characteristic
5#11749086C212yesmaximal, complemented
6#11749085C212yesmaximal, complemented
7#11748978C212yesmaximal, complemented
8Dic5×#213C212yesmaximal, complemented
9C4×#6656C211yesmaximal, characteristic, complemented
10#11746916C211yesmaximal, characteristic, complemented
11#11746846C211yesmaximal, characteristic, complemented
12#10612050—31nomaximal, Hall
13C3×C5×#127C2211yescharacteristic
14#91758C2211yescharacteristic
15C2×C5×#213C2212yes—
16C4×C5×D12C2211yescharacteristic
17C3×#4082—21no—
18C3×#4082C2212yes—
19C3×#4081—22no—
20C3×D4×Dic5—21no—
21C3×D4×Dic5C2212yes—
22C3×C4×Dic10C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic
24#91432—22no—
25D3×C4⋊Dic5—21no—
26Dic5×D12C2212yes—
27#91388C2212yes—
28#91369—21no—
29C2×#6656C2211yescharacteristic
30#91116C2212yes—
31#91116C2212yes—
32C4×C3⋊#168C2211yescharacteristic
33C5×#832C2212yes—
34C5×C4⋊(C3⋊C8)C2211yescharacteristic
35#90990C2212yes—
36#90986C2211yescharacteristic
37#90982C2212yes—
38#90971C2212yes—
39#90970C2211yescharacteristic
40#90966C2211yescharacteristic
41Dic5×C3⋊C8C2212yes—
42#83713—51nomaximal, Hall
43#66047D311yescharacteristic, complemented
44#65877—31no—
45C5×#459—31no—
46#65442—32no—
47D8×Dic5—32no—
48#65359—31no—
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—
57C2×Dic30—21no—
58C2×C5×D12C2311yescharacteristic
59C2×C4×C5×D3—21no—
60C22×C3×Dic5—22no—
61C2×C3×Dic10D411yescharacteristic
62C2×C3×Dic10C2311yescharacteristic
63C2×D3×Dic5—22no—
64C3×C42×C5C2311yescharacteristic
65C4⋊Dic15—21no—
66C4⋊Dic15C2312yes—
67C2×C3⋊#168C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69C5×#213—24no—
70C5×(C2×D3)⋊C4—21no—
71C5×C4⋊Dic3C2311yescharacteristic
72C2×C5×C3⋊C8C2312yes—
73C3×C22⋊Dic5—22no—
74C3×C22⋊Dic5—22no—
75C3×C22⋊Dic5—22no—
76C3×C4⋊Dic5D411yescharacteristic
77C3×C4⋊Dic5C2311yescharacteristic
78C3×#683—21no—
79C3×#683D412yes—
80C3×C4×Dic5—21no—
81C3×C4×Dic5C2312yes—
82Dic3⋊Dic5—22no—
83#6669—22no—
84(C2×D3)⋊Dic5—22no—
85#6656—22no—
86C3×#559—51no—
87#5579—51no—
88#5072D511yescharacteristic
89#5070—51no—
90#5057—52no—
91#5056—52no—
92C4×#215—51no—
93Q8×C3⋊C8—51no—
94#5021—51no—
95C4×#213—52no—
96#5009—52no—
97C2×C5×D8—32no—
98C5×#127C2×D311yescharacteristic
99C4×C5×D4—31no—
100#4082—21no—
101#4082C2×D312yes—
102#4081—22no—
103D4×Dic5—21no—
104D4×Dic5—32no—
105D4×Dic5C2×D312yes—
106C2×#687—31no—
107C2×C4⋊Dic5—61no—
108#4070—61no—
109#4036—32no—
110#4024—62no—
111#4015—31no—
112C4×Dic10C2×D311yescharacteristic
113C4×Dic10C2×D311yescharacteristic
114C5×C4⋊C8—31no—
115C5×#102—32no—
116#3964—32no—
117#3964—32no—
118#3964—31no—
119#3950—32no—
120#3948—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3942—31no—
124#3940—31no—
125C4×#168—31no—
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—22no—
137Dic30—81no—
138C2×C5×Dic3—21no—
139C5×D12—21no—
140C5×D12#4112yes—
141C4×C5×D3—42no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—82no—
145C2×C3×Dic5C2×D412yes—
146C2×C3×Dic5C2×D412yes—
147C3×Dic10—22no—
148C3×Dic10—21no—
149C3×Dic10—21no—
150D3×Dic5—82no—
151C3⋊#168—21no—
152C3⋊#168—21no—
153C5×C3⋊C8—22no—
154C3×#127C2×D511yescharacteristic
155C3×#124—52no—
156C3×#124—101no—
157C3×#123—102no—
158C3×C4×Q8—51no—
159C3×C4×Q8—51no—
160C3×C4×D4—52no—
161C3×C4×D4—101no—
162#946—101no—
163C2×#215—51no—
164C2×#213C2×D512yes—
165#896—102no—
166D3×C4⋊C4—101no—
167C4×D12—52no—
168C4×D12C2×D511yescharacteristic
169#870—52no—
170#869—51no—
171#835—51no—
172#835—52no—
173#832—52no—
174#832—52no—
175#832C2×D512yes—
176#809—51no—
177#808—51no—
178#807—52no—
179C4⋊(C3⋊C8)—52no—
180C4⋊(C3⋊C8)C2×D511yescharacteristic
181C4×C3⋊C8—51no—
182C4×C3⋊C8—52no—
183C2×C5×D4—21no—
184C2×C5×D4—21no—
185C2×C5×D4—31no—
186C2×C5×D4C22×D312yes—
187C22×C4×C5—61no—
188C22×Dic5—22no—
189C22×Dic5—62no—
190C2×Dic10—61no—
191C2×Dic10#6711yescharacteristic
192C2×Dic10C22×D311yescharacteristic
193C5×D8—64no—
194C2×C5×C8—32no—
195C5×C4⋊C4—31no—
196C5×C22⋊C4—61no—
197C42×C5C22×D311yescharacteristic
198C22⋊Dic5—22no—
199C22⋊Dic5—22no—
200C22⋊Dic5—22no—
201C22⋊Dic5—62no—
202#687—62no—
203C4⋊Dic5—32no—
204C4⋊Dic5—61no—
205C4⋊Dic5—62no—
206C4⋊Dic5#6711yescharacteristic
207C4⋊Dic5C22×D311yescharacteristic
208#683—21no—
209#683—62no—
210#683#6712yes—
211C4×Dic5—21no—
212C4×Dic5C22×D312yes—
213C2×#168—31no—
214C2×#168—31no—
215#559—51no—
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—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—42no—
238C3×Dic5—22no—
239C3×Dic5—22no—
240C3×Dic5—41no—
241C3×Dic5—41no—
242C5×Dic3—41no—
243C2×C3×Q8—51no—
244C2×C3×Q8—51no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4C22×D512yes—
248C22×C3×C4—102no—
249C2×D12C22×D511yescharacteristic
250C2×C4×D3—21no—
251C2×C4×D3—102no—
252C2×Dic6—101no—
253C3×C4⋊C4—52no—
254C3×C4⋊C4—51no—
255C3×C4⋊C4—51no—
256C3×C4⋊C4—101no—
257C3×C22⋊C4—102no—
258C3×C22⋊C4—102no—
259C3×C22⋊C4—102no—
260C3×C42—52no—
261C3×C42—101no—
262C3×C42C22×D511yescharacteristic
263#215—102no—
264#213—24no—
265(C2×D3)⋊C4—21no—
266(C2×D3)⋊C4—102no—
267C4⋊Dic3—52no—
268C4⋊Dic3—101no—
269C4⋊Dic3C22×D511yescharacteristic
270Dic3⋊C4—102no—
271Dic3⋊C4—102no—
272C2×C3⋊C8—51no—
273C2×C3⋊C8—51no—
274C2×C3⋊C8C22×D512yes—
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×C5C2×#6711yescharacteristic
286C2×C4×C5C2×#6711yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—21no—
289C2×Dic5—21no—
290C2×Dic5—62no—
291C2×Dic5—82no—
292C2×Dic5—242no—
293C2×Dic5C2×#6712yes—
294C2×Dic5C2×#6712yes—
295Dic10—22no—
296Dic10—21no—
297Dic10—21no—
298Dic10—241no—
299C5×C8—62no—
300#168—61no—
301#168—61no—
302C2×SD16—151no—
303C2×D8—32no—
304C4⋊Q8—151no—
305#127D3×D511yescharacteristic
306#125—152no—
307#124—52no—
308#124—101no—
309#123—102no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—51no—
313C4×Q8—51no—
314C4×D4—31no—
315C4×D4—52no—
316C4×D4—101no—
317C4×D4—152no—
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—151no—
327#102—152no—
328#102—152no—
329C4×C8—152no—
330C4×C8—151no—
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—102no—
339C3×Q8—101no—
340C3×Q8—101no—
341C3×D4—22no—
342C3×D4—22no—
343C3×D4—42no—
344C3×D4—81no—
345C2×C3×C4—52no—
346C2×C3×C4—52no—
347C2×C3×C4—101no—
348C2×C3×C4—101no—
349C2×C3×C4—402no—
350C2×C3×C4D4×D511yescharacteristic
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4C23×D511yescharacteristic
353C2×Dic3—21no—
354C2×Dic3—102no—
355D12—21no—
356D12#71112yes—
357C4×D3—42no—
358C4×D3—402no—
359Dic6—401no—
360C3⋊C8—22no—
361C3⋊C8—101no—
362C3⋊C8—101no—
363C22×C5—42no—
364C22×C5—42no—
365C22×C5—42no—
366C22×C5—62no—
367C22×C5—121no—
368C22×C5—121no—
369C22×C5C22×#6711yescharacteristic
370C4×C5—21no—
371C4×C5—121no—
372C4×C5#95012yes—
373C4×C5D3×#4111yescharacteristic
374C4×C5#101011yescharacteristic
375Dic5—22no—
376Dic5—22no—
377Dic5—41no—
378Dic5—41no—
379Dic5—122no—
380C2×Q8—51no—
381C2×Q8—51no—
382C2×Q8—301no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—31no—
386C2×D4C2×D3×D512yes—
387C22×C4—61no—
388C22×C4—102no—
389C22×C4—302no—
390SD16—302no—
391D8—64no—
392C2×C8—32no—
393C2×C8—151no—
394C2×C8—151no—
395C4⋊C4—31no—
396C4⋊C4—51no—
397C4⋊C4—52no—
398C4⋊C4—51no—
399C4⋊C4—101no—
400C4⋊C4—152no—
401C4⋊C4—302no—
402C4⋊C4—302no—
403C4⋊C4—301no—
404C22⋊C4—61no—
405C22⋊C4—102no—
406C22⋊C4—102no—
407C22⋊C4—102no—
408C22⋊C4—302no—
409C42—52no—
410C42—101no—
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—102no—
422C3×C4—102no—
423C3×C4—201no—
424C3×C4—201no—
425C3×C4#405812yes—
426C3×C4C2×#71111yescharacteristic
427C3×C4#415011yescharacteristic
428Dic3—41no—
429Dic3—202no—
430C2×C5—82no—
431C2×C5—122no—
432C2×C5C2×#95011yescharacteristic
433C2×C5#583111yescharacteristic
434C2×C5#583511yescharacteristic
435C23—22no—
436C23—61no—
437Q8—102no—
438Q8—101no—
439Q8—101no—
440Q8—1201no—
441D4—22no—
442D4—22no—
443D4—32no—
444D4—42no—
445D4—61no—
446D4—81no—
447C2×C4—52no—
448C2×C4—52no—
449C2×C4—61no—
450C2×C4—101no—
451C2×C4—101no—
452C2×C4—122no—
453C2×C4—302no—
454C2×C4—402no—
455C2×C4—1202no—
456C2×C4D5×#6711yescharacteristic
457C2×C4D5×#6711yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—62no—
460C8—301no—
461C8—301no—
462C2×C3—82no—
463C2×C3#6593211yescharacteristic
464C2×C3C2×#405811yescharacteristic
465C2×C3#6610811yescharacteristic
466D3—42no—
467C5#8371311yescharacteristic, complemented, Sylow
468C22—42no—
469C22—42no—
470C22—42no—
471C22—62no—
472C22—121no—
473C22—121no—
474C22C2×D5×#6711yescharacteristic
475C4—21no—
476C4—102no—
477C4—102no—
478C4—121no—
479C4—201no—
480C4—201no—
481C4—602no—
482C4#9149012yes—
483C4#9202011yescharacteristic
484C4D3×#71111yescharacteristic
485C3#1061205011yescharacteristic, complemented, Sylow
486C2—82no—
487C2—122no—
488C2#1175469211yescharacteristic
489C2C2×#9149011yescharacteristic
490C2#1175479811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
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. C3×#66047C2semidirect
2. #11752660C2semidirect
3. #11751171C2semidirect
5. #11749086C2semidirect
6. #11749085C2semidirect
7. #11748978C2semidirect
8. Dic5×#213C2semidirect
9. C4×#6656C2semidirect
10. #11746916C2semidirect
11. #11746846C2semidirect
43. #66047D3semidirect
412. C3×C5#3361semidirect
467. C5#83713semidirect
485. C3#10612050semidirect

Maximal subgroups

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

subgroupindex
C3×#660472
#117526602
#117511712
C5×#50722
#117490862
#117490852
#117489782
Dic5×#2132
C4×#66562
#117469162
#117468462
#106120503
#837135