Finite Group Databasebeta

← #14431344

Subgroups — #14431344

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5504C211yesmaximal, characteristic
2#11754618C211yesmaximal, characteristic, complemented
3#11751065C211yesmaximal, characteristic, complemented
4C2×C3×#3940C211yesmaximal, characteristic, complemented
5#11748439C211yesmaximal, characteristic, complemented
6#11748388C211yesmaximal, characteristic
7#11748384C211yesmaximal, characteristic
8#11747419C212yesmaximal, complemented
9#11747417C212yesmaximal, complemented
10#11747396C212yesmaximal, complemented
11#11747394C212yesmaximal, complemented
12#10614291—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15#91815C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17C4×C5×#67—22no—
18C5×#926C2211yescharacteristic
19C5×#893C2212yes—
20C5×#892—21no—
21C5×D3×C4⋊C4—21no—
22C5×#887C2212yes—
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25#91574—22no—
26#91470—21no—
27#91469C2212yes—
28#91384—21no—
29#91381C2212yes—
30#91092C2212yes—
31#91091C2212yes—
32C3×#3940C2212yes—
33C3×#3940C2212yes—
34Dic3⋊#168C2212yes—
35Dic3⋊#168C2212yes—
36#90973C2211yescharacteristic
37#90973C2211yescharacteristic
38#90972C2212yes—
39#90967C2211yescharacteristic
40#90967C2211yescharacteristic
41#90966C2212yes—
42#79130—51nomaximal, Hall
43C5×#520—31no—
44#65853—31no—
45#65522—31no—
46#65521—31no—
47#65311—32no—
48#65309—32no—
49#65298—32no—
50#65297—32no—
51#65288—31no—
52#65253—31no—
53C2×#3940D311yescharacteristic, complemented
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×C5×#67—21no—
57C5×#235—22no—
58C5×#235Q814yescomplemented
59C2×C5×D12C2311yescharacteristic
60C2×C4×C5×D3—21no—
61C2×C4×C5×D3—22no—
62C2×C5×Dic6C2311yescharacteristic
63C22×C3×Dic5—21no—
64C2×#1204—22no—
65C3×C5×C4⋊C4—21no—
66C3×C5×C4⋊C4C2312yes—
67#6719—21no—
68C4⋊Dic15C2311yescharacteristic
69C4⋊Dic15C2311yescharacteristic
70C4×Dic15—21no—
71#6710—22no—
72C2×C3⋊#168C2312yes—
73C5×#217D412yes—
74C5×(C2×D3)⋊C4—22no—
75C5×C4⋊Dic3D411yescharacteristic
76C5×C4⋊Dic3D411yescharacteristic
77C5×Dic3⋊C4—22no—
78C4×C5×Dic3—22no—
79C4×C5×Dic3C2312yes—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2312yes—
82C2×C3×#168—22no—
83C2×C3×#168C2311yescharacteristic
84C2×C3×#168C2311yescharacteristic
85Dic3⋊Dic5—22no—
86#6669—22no—
87#6668—22no—
88#5504D511yescharacteristic
89#5500—51no—
90C2×C3×#106—51no—
91#5113—51no—
92#5102—51no—
93#4966—51no—
94#4964—51no—
95#4871—52no—
96#4870—52no—
97#4857—52no—
98#4854—52no—
99C2×C5×#41—31no—
100C4×C5×Q8—32no—
101C4×C5×D4—32no—
102C4×C5×D4—62no—
103C5×#117—31no—
104C5×#117—61no—
105C2×C5×C4⋊C4—61no—
106C2×C5×C4⋊C4C2×D311yescharacteristic
107#4072—31no—
108C2×C4⋊Dic5C2×D311yescharacteristic
109C2×#681—31no—
110C22×#168C2×D311yescharacteristic
111#4036—61no—
112#4034—61no—
113#4024—62no—
114#4016—32no—
115#4015—32no—
116#3967—32no—
117#3967—31no—
118#3967—31no—
119#3964—32no—
120#3964—31no—
121#3964—31no—
122#3940—32no—
123#3940C2×D312yes—
124#3940C2×D312yes—
125#3939—32no—
126C4⋊#168—32no—
127C4⋊#168—32no—
128#3084—151noSylow
129C23×C3×C5C2×D411yescharacteristic
130C22×C5×D3—21no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—81no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×Q812yes—
135C2×C3×C4×C5#4112yes—
136C2×C3×C4×C5C2411yescharacteristic
137C2×Dic15—21no—
138C2×Dic15—21no—
139C5×#67—24no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3C2×D412yes—
142C2×C5×Dic3C2×D412yes—
143C5×D12—21no—
144C5×D12C2×Q812yes—
145C4×C5×D3—24no—
146C4×C5×D3—82no—
147C5×Dic6—21no—
148C5×Dic6C2×Q812yes—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—81no—
151#1204—82no—
152C3⋊#168—22no—
153C3×#168—21no—
154C3×#168—21no—
155C2×#235C2×D511yescharacteristic
156C22×C3×C8—51no—
157C2×C3×C4⋊C4—51no—
158C2×C3×C4⋊C4C2×D511yescharacteristic
159C4×#67—22no—
160#926—51no—
161#926C2×D511yescharacteristic
162#924—102no—
163C2×#208—51no—
164#893C2×D512yes—
165#892—21no—
166D3×C4⋊C4—21no—
167#890—52no—
168#890—101no—
169#888—52no—
170#888—101no—
171#887C2×D512yes—
172C3×#106—52no—
173C3×#106—52no—
174#821—51no—
175#821—51no—
176#816—51no—
177#816—51no—
178Dic3⋊C8—52no—
179Dic3⋊C8—52no—
180#810—52no—
181#809—52no—
182#808—52no—
183#807—52no—
184C5×#41—34no—
185C5×#41—62no—
186C2×C5×Q8—31no—
187C2×C5×D4—31no—
188C2×C5×D4—61no—
189C22×C4×C5—21no—
190C22×C4×C5—62no—
191C22×C4×C5—61no—
192C22×C4×C5C22×D311yescharacteristic
193C22×Dic5—21no—
194C2×Dic10—62no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—31no—
197C5×C4⋊C4—31no—
198C5×C4⋊C4—62no—
199C5×C4⋊C4C22×D312yes—
200C5×C22⋊C4—32no—
201C5×C22⋊C4—62no—
202C42×C5—32no—
203C42×C5—62no—
204C22⋊Dic5—61no—
205C4⋊Dic5—21no—
206C4⋊Dic5—31no—
207C4⋊Dic5—31no—
208C4⋊Dic5—62no—
209C4⋊Dic5C22×D312yes—
210#683—62no—
211#683—62no—
212C4×Dic5—61no—
213#681—62no—
214C2×#168—22no—
215C2×#168—32no—
216C2×#168C22×D311yescharacteristic
217C2×#168C22×D311yescharacteristic
218#544—151no—
219#520—31no—
220#479—152no—
221#478—152no—
222#476—152no—
223#475—152no—
224#428—151no—
225C2×#106—51no—
226#424—151no—
227#417—151no—
228#416—151no—
229C22×C3×C5—21no—
230C22×C3×C5—21no—
231C22×C3×C5C22⋊Q812yes—
232C22×C3×C5C22×D411yescharacteristic
233C2×C5×D3—22no—
234C2×C5×D3—41no—
235C2×C5×D3—41no—
236C3×C4×C5—42no—
237C3×C4×C5C22⋊Q812yes—
238C3×C4×C5C22×Q811yescharacteristic
239C3×C4×C5C2×#4111yescharacteristic
240Dic15—41no—
241Dic15—41no—
242C3×Dic5—42no—
243C5×Dic3—22no—
244C5×Dic3—22no—
245C5×Dic3—22no—
246C22×C3×C4—21no—
247C22×C3×C4—101no—
248C22×C3×C4C22×D511yescharacteristic
249C2×#67—21no—
250#235—22no—
251#235Dic1014yescomplemented
252C2×D12C22×D511yescharacteristic
253C2×C4×D3—21no—
254C2×C4×D3—22no—
255C2×Dic6—102no—
256C2×Dic6C22×D511yescharacteristic
257C2×C3×C8—51no—
258C2×C3×C8—51no—
259C2×C3×C8—102no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—52no—
262C3×C4⋊C4—101no—
263C3×C4⋊C4C22×D512yes—
264#217—101no—
265#217C22⋊D512yes—
266(C2×D3)⋊C4—22no—
267C4⋊Dic3—51no—
268C4⋊Dic3—51no—
269C4⋊Dic3—102no—
270C4⋊Dic3C22⋊D511yescharacteristic
271C4⋊Dic3C22⋊D511yescharacteristic
272Dic3⋊C4—22no—
273Dic3⋊C4—102no—
274Dic3⋊C4—102no—
275C4×Dic3—22no—
276C4×Dic3—101no—
277C4×Dic3C22×D512yes—
278#208—102no—
279C2×C3⋊C8—52no—
280C23×C5—61no—
281C23×C5D3×D411yescharacteristic
282C5×Q8—32no—
283C5×Q8—61no—
284C5×D4—32no—
285C5×D4—64no—
286C5×D4—61no—
287C2×C4×C5—22no—
288C2×C4×C5—32no—
289C2×C4×C5—32no—
290C2×C4×C5—61no—
291C2×C4×C5—64no—
292C2×C4×C5—81no—
293C2×C4×C5—242no—
294C2×C4×C5#23512yes—
295C2×C4×C5D3×D411yescharacteristic
296C2×C4×C5D3×Q812yes—
297C2×C4×C5C23×D311yescharacteristic
298C2×Dic5—22no—
299C2×Dic5—61no—
300C2×Dic5—61no—
301C2×Dic5—81no—
302Dic10—242no—
303#168—21no—
304#168—21no—
305#168—62no—
306C2×#41—31no—
307C2×M16—151no—
308C22×C8—51no—
309C4⋊Q8—152no—
310C4⋊Q8—301no—
311#125—152no—
312#125—301no—
313C22⋊Q8—302no—
314C4×Q8—32no—
315C4×D4—32no—
316C4×D4—62no—
317#117—31no—
318#117—61no—
319#117—151no—
320C2×C4⋊C4—51no—
321C2×C4⋊C4—61no—
322C2×C4⋊C4D3×D511yescharacteristic
323#107—152no—
324#106—52no—
325#106—52no—
326#106—152no—
327C4⋊C8—152no—
328C4⋊C8—152no—
329#103—152no—
330#103—151no—
331#103—151no—
332#102—152no—
333#102—151no—
334#102—151no—
335C2×C3×C5—22no—
336C2×C3×C5C2×C22⋊Q811yescharacteristic
337C2×C3×C5#57711yescharacteristic
338C2×C3×C5#57711yescharacteristic
339C5×D3—42no—
340C23×C3C2×C22⋊D511yescharacteristic
341C22×D3—21no—
342C2×C3×C4—22no—
343C2×C3×C4—81no—
344C2×C3×C4—102no—
345C2×C3×C4—401no—
346C2×C3×C4C2×Dic1012yes—
347C2×C3×C4#70912yes—
348C2×C3×C4C2×C22⋊D511yescharacteristic
349C2×C3×C4C23×D511yescharacteristic
350#67—24no—
351C2×Dic3—21no—
352C2×Dic3—101no—
353C2×Dic3—101no—
354C2×Dic3C2×C22⋊D512yes—
355C2×Dic3C2×C22⋊D512yes—
356D12—21no—
357D12C2×Dic1012yes—
358C4×D3—24no—
359C4×D3—82no—
360Dic6—21no—
361Dic6—402no—
362Dic6C2×Dic1012yes—
363C3×C8—101no—
364C3×C8—101no—
365C3⋊C8—102no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5—62no—
369C22×C5—121no—
370C22×C5—121no—
371C22×C5#89612yes—
372C22×C5C2×D3×D411yescharacteristic
373C4×C5—42no—
374C4×C5—62no—
375C4×C5—62no—
376C4×C5—62no—
377C4×C5#89612yes—
378C4×C5C2×#23511yescharacteristic
379C4×C5C2×D3×Q811yescharacteristic
380Dic5—42no—
381Dic5—121no—
382Dic5—121no—
383#41—34no—
384#41—62no—
385C2×Q8—31no—
386C2×Q8—302no—
387C2×D4—31no—
388C2×D4—61no—
389C22×C4—21no—
390C22×C4—62no—
391C22×C4—61no—
392C22×C4—101no—
393C22×C4C2×D3×D511yescharacteristic
394M16—302no—
395C2×C8—51no—
396C2×C8—51no—
397C2×C8—102no—
398C2×C8—152no—
399C4⋊C4—21no—
400C4⋊C4—31no—
401C4⋊C4—31no—
402C4⋊C4—52no—
403C4⋊C4—62no—
404C4⋊C4—101no—
405C4⋊C4—151no—
406C4⋊C4—151no—
407C4⋊C4—302no—
408C4⋊C4—302no—
409C4⋊C4—302no—
410C4⋊C4C2×D3×D512yes—
411C22⋊C4—32no—
412C22⋊C4—62no—
413C22⋊C4—301no—
414C42—32no—
415C42—62no—
416C42—301no—
417C3×C5#308411yescharacteristic, complemented, Hall
418C22×C3—21no—
419C22×C3—21no—
420C22×C3#407012yes—
421C22×C3C22×C22⋊D511yescharacteristic
422C2×D3—22no—
423C2×D3—41no—
424C2×D3—41no—
425C3×C4—42no—
426C3×C4—202no—
427C3×C4#407012yes—
428C3×C4C22×Dic1011yescharacteristic
429C3×C4C2×#70911yescharacteristic
430Dic3—22no—
431Dic3—22no—
432Dic3—22no—
433Dic3—201no—
434Dic3—201no—
435C2×C5—22no—
436C2×C5—122no—
437C2×C5C2×#89611yescharacteristic
438C2×C5#576211yescharacteristic
439C2×C5#576211yescharacteristic
440C23—61no—
441C23D3×C22⋊D511yescharacteristic
442Q8—32no—
443Q8—61no—
444Q8—1202no—
445D4—32no—
446D4—64no—
447D4—61no—
448C2×C4—22no—
449C2×C4—32no—
450C2×C4—32no—
451C2×C4—61no—
452C2×C4—64no—
453C2×C4—81no—
454C2×C4—102no—
455C2×C4—242no—
456C2×C4—301no—
457C2×C4—301no—
458C2×C4—401no—
459C2×C4D3×Dic1012yes—
460C2×C4#677112yes—
461C2×C4D3×C22⋊D511yescharacteristic
462C2×C4C22×D3×D511yescharacteristic
463C8—101no—
464C8—101no—
465C8—302no—
466C2×C3—22no—
467C2×C3C2×#407011yescharacteristic
468C2×C3#6617011yescharacteristic
469C2×C3#6617111yescharacteristic
470D3—42no—
471C5#7913011yescharacteristic, complemented, Sylow
472C22—21no—
473C22—21no—
474C22—62no—
475C22—121no—
476C22—121no—
477C22#9135212yes—
478C22C2×D3×C22⋊D511yescharacteristic
479C4—42no—
480C4—62no—
481C4—62no—
482C4—62no—
483C4—202no—
484C4—601no—
485C4—601no—
486C4#9135212yes—
487C4C2×D3×Dic1011yescharacteristic
488C4C2×#677111yescharacteristic
489C3#1061429111yescharacteristic, complemented, Sylow
490C2—22no—
491C2—122no—
492C2C2×#9135211yescharacteristic
493C2#1175471111yescharacteristic
494C2#1175509111yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3084
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11754618C2semidirect
3. #11751065C2semidirect
4. C2×C3×#3940C2semidirect
5. #11748439C2semidirect
8. #11747419C2semidirect
9. #11747417C2semidirect
10. #11747396C2semidirect
11. #11747394C2semidirect
53. C2×#3940D3semidirect
58. C5×#235Q8semidirect
251. #235Dic10semidirect
417. C3×C5#3084semidirect
471. C5#79130semidirect
489. C3#10614291semidirect

Maximal subgroups

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

subgroupindex
C5×#55042
#117546182
#117510652
C2×C3×#39402
#117484392
#117483882
#117483842
#117474192
#117474172
#117473962
#117473942
#106142913
#791305