Finite Group Databasebeta

← #14430865

Subgroups — #14430865

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756557C211yesmaximal, characteristic
2#11754619C211yesmaximal, characteristic, complemented
3C2×C5×#832C211yesmaximal, characteristic
4C3×#65504C211yesmaximal, characteristic
5#11749116C212yesmaximal, complemented
6#11749115C212yesmaximal, complemented
7#11749091C212yesmaximal, complemented
8#11749089C212yesmaximal, complemented
9#11748459C211yesmaximal, characteristic, complemented
10#11748451C211yesmaximal, characteristic, complemented
11#11748436C211yesmaximal, characteristic, complemented
12#10610462—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×#6719—22no—
15D4×Dic15—21no—
16D4×Dic15—21no—
17D4×Dic15C2212yes—
18D4×Dic15C2212yes—
19#91815C2211yescharacteristic
20#91815C2211yescharacteristic
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C3×#4072C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25#91575—22no—
26#91470C2212yescomplemented
27#91468—21no—
28#91388—21no—
29#91384C2212yescomplemented
30C5×#832C2212yes—
31C5×#832C2212yes—
32C3×#3964C2212yes—
33C3×#3964C2212yes—
34#90990C2211yescharacteristic, complemented
35#90990C2211yescharacteristic, complemented
36#90988C2212yescomplemented
37#90987C2211yescharacteristic, complemented
38#90987C2211yescharacteristic, complemented
39#90985C2212yescomplemented
40#90983C2212yescomplemented
41#90983C2212yescomplemented
42#78918—51nomaximal, Hall
43#66132—31no—
44#65834—31no—
45C2×C5×#102—31no—
46#65504D311yescharacteristic
47#65395—31no—
48#65391—31no—
49#65253—31no—
50#65055—32no—
51#65052—32no—
52#65050—32no—
53#65048—32no—
54C24×C3×C5—21no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4Q814yescomplemented
58C2×C3×C5×D4C2312yes—
59C22×C3×C4×C5C2311yescharacteristic
60C22×Dic15—22no—
61C22×Dic15—22no—
62C22×C5×Dic3—21no—
63C2×#1204—22no—
64#6719—21no—
65#6719—22no—
66#6719—22no—
67#6719D412yes—
68C4⋊Dic15D411yescharacteristic
69C4⋊Dic15D411yescharacteristic
70C4⋊Dic15C2311yescharacteristic
71C4⋊Dic15C2311yescharacteristic
72C4×Dic15—21no—
73C4×Dic15C2312yes—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2312yes—
76C2×C5×C3⋊C8—22no—
77C2×C5×C3⋊C8C2311yescharacteristic
78C2×C5×C3⋊C8C2311yescharacteristic
79C3×C22⋊Dic5—21no—
80C3×C4⋊Dic5C2311yescharacteristic
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4×Dic5—21no—
83C3×#681—22no—
84C2×C3×#168C2312yes—
85Dic3⋊Dic5—22no—
86#6669—22no—
87#6668—22no—
88#5798—51no—
89#5519—51no—
90C3×#418—51no—
91C2×#832D511yescharacteristic
92#5121—51no—
93#5119—51no—
94#4998—51no—
95#4766—52no—
96#4763—52no—
97#4761—52no—
98#4759—52no—
99C22×C5×D4C2×D311yescharacteristic
100C22×C5×C8—31no—
101C2×C5×C4⋊C4—31no—
102C2×C22⋊Dic5—62no—
103D4×Dic5—32no—
104D4×Dic5—32no—
105D4×Dic5—61no—
106D4×Dic5—61no—
107#4072—31no—
108#4072—31no—
109#4072C2×D311yescharacteristic
110#4070—62no—
111C2×#681C2×D311yescharacteristic
112#4036—32no—
113#4036—61no—
114#4034—32no—
115#4034—61no—
116C5×#102—32no—
117C5×#102—32no—
118#3964C2×D312yes—
119#3964C2×D312yes—
120#3950—31no—
121#3950—31no—
122#3949—31no—
123#3949—31no—
124#3946—32no—
125#3946—32no—
126#3940—32no—
127#3939—32no—
128#3081—151noSylow
129C23×C3×C5—22no—
130C23×C3×C5—24no—
131C23×C3×C5—81no—
132C23×C3×C5—81no—
133C23×C3×C5C2×D411yescharacteristic
134C3×C5×D4—24no—
135C3×C5×D4—22no—
136C3×C5×D4C2×Q814yes—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×Q812yes—
139C2×C3×C4×C5#4112yes—
140C2×C3×C4×C5C2411yescharacteristic
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15—82no—
144C2×Dic15—82no—
145C2×Dic15C2×D412yes—
146C2×Dic15C2×D412yes—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—81no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—21no—
151#1204—82no—
152C3×#168—22no—
153C5×C3⋊C8—21no—
154C5×C3⋊C8—21no—
155C22×C3×D4C2×D511yescharacteristic
156C2×C3×M16—51no—
157C3×#117—51no—
158C2×#217—102no—
159D4×Dic3—52no—
160D4×Dic3—52no—
161D4×Dic3—101no—
162D4×Dic3—101no—
163#926—51no—
164#926—51no—
165C2×C4⋊Dic3C2×D511yescharacteristic
166C22×C3⋊C8C2×D511yescharacteristic
167#890—52no—
168#888—52no—
169#878—102no—
170#870—101no—
171#869—101no—
172C3×#102—52no—
173C3×#102—52no—
174#832C2×D512yes—
175#832C2×D512yes—
176#818—52no—
177#817—52no—
178Dic3⋊C8—52no—
179Dic3⋊C8—52no—
180#808—51no—
181#808—51no—
182#807—51no—
183#807—51no—
184C24×C5—21no—
185C2×C5×D4—21no—
186C2×C5×D4—22no—
187C2×C5×D4Dic614yescomplemented
188C2×C5×D4C22×D312yes—
189C22×C4×C5—61no—
190C22×C4×C5C22×D311yescharacteristic
191C22×Dic5—62no—
192C22×Dic5—62no—
193C2×Dic10—62no—
194C2×C5×C8—31no—
195C2×C5×C8—31no—
196C2×C5×C8—62no—
197C5×C4⋊C4—32no—
198C5×C4⋊C4—61no—
199C22⋊Dic5—21no—
200C22⋊Dic5—32no—
201C22⋊Dic5—62no—
202C22⋊Dic5—62no—
203C22⋊Dic5—61no—
204C4⋊Dic5—31no—
205C4⋊Dic5—31no—
206C4⋊Dic5—31no—
207C4⋊Dic5—31no—
208C4⋊Dic5—62no—
209C4⋊Dic5C22×D311yescharacteristic
210C4⋊Dic5C22×D311yescharacteristic
211#683—62no—
212#683—62no—
213C4×Dic5—21no—
214C4×Dic5—32no—
215C4×Dic5—61no—
216#681—22no—
217C2×#168C22×D312yes—
218#544—151no—
219#518—151no—
220#478—152no—
221#478—152no—
222#476—152no—
223#474—152no—
224#428—151no—
225#427—151no—
226#424—151no—
227#418—51no—
228C2×#102—31no—
229C22×C3×C5—21no—
230C22×C3×C5—21no—
231C22×C3×C5—24no—
232C22×C3×C5—42no—
233C22×C3×C5—42no—
234C22×C3×C5—84no—
235C22×C3×C5C22⋊Q812yes—
236C22×C3×C5C22×D411yescharacteristic
237C3×C4×C5C22⋊Q812yes—
238C3×C4×C5C22×Q811yescharacteristic
239C3×C4×C5C2×#4111yescharacteristic
240Dic15—22no—
241Dic15—22no—
242Dic15—41no—
243Dic15—41no—
244C3×Dic5—41no—
245C3×Dic5—41no—
246C5×Dic3—42no—
247C24×C3—21no—
248C2×C3×D4—21no—
249C2×C3×D4—22no—
250C2×C3×D4Dic1014yescomplemented
251C2×C3×D4C22×D512yes—
252C22×C3×C4C22×D511yescharacteristic
253C22×Dic3—21no—
254C22×Dic3—102no—
255C22×Dic3—102no—
256C2×Dic6—102no—
257C3×M16—102no—
258C2×C3×C8—52no—
259C3×C4⋊C4—51no—
260C3×C4⋊C4—51no—
261C3×C22⋊C4—101no—
262C3×C42—101no—
263#217—52no—
264#217—102no—
265#217—102no—
266#217—101no—
267C4⋊Dic3—21no—
268C4⋊Dic3—51no—
269C4⋊Dic3—51no—
270C4⋊Dic3—51no—
271C4⋊Dic3—51no—
272C4⋊Dic3—102no—
273C4⋊Dic3C22×D512yes—
274Dic3⋊C4—102no—
275Dic3⋊C4—102no—
276C4×Dic3—52no—
277C4×Dic3—101no—
278C2×C3⋊C8—22no—
279C2×C3⋊C8C22×D511yescharacteristic
280C2×C3⋊C8C22×D511yescharacteristic
281C23×C5—22no—
282C23×C5—24no—
283C23×C5—81no—
284C23×C5—81no—
285C23×C5D3×D411yescharacteristic
286C5×D4—24no—
287C5×D4—22no—
288C5×D4C2×Dic614yes—
289C2×C4×C5—62no—
290C2×C4×C5—241no—
291C2×C4×C5C2×Dic612yes—
292C2×C4×C5D3×D411yescharacteristic
293C2×C4×C5#23712yes—
294C2×C4×C5C23×D311yescharacteristic
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—32no—
298C2×Dic5—32no—
299C2×Dic5—61no—
300C2×Dic5—61no—
301C2×Dic5—242no—
302C2×Dic5—242no—
303Dic10—242no—
304C5×C8—61no—
305C5×C8—61no—
306#168—22no—
307C22×D4D3×D511yescharacteristic
308C2×M16—51no—
309C22×C8—31no—
310C4⋊Q8—152no—
311C4⋊Q8—301no—
312#125—152no—
313#125—301no—
314C22⋊Q8—302no—
315C4×D4—152no—
316C4×D4—152no—
317C4×D4—301no—
318C4×D4—301no—
319#117—51no—
320#117—151no—
321#117—151no—
322C2×C4⋊C4—31no—
323C2×C22⋊C4—302no—
324#107—152no—
325#107—151no—
326#107—151no—
327#106—152no—
328#106—151no—
329#106—151no—
330C4⋊C8—152no—
331C4⋊C8—152no—
332#102—32no—
333#102—32no—
334#102—52no—
335#102—52no—
336C2×C3×C5—22no—
337C2×C3×C5—44no—
338C2×C3×C5C2×C22⋊Q811yescharacteristic
339C2×C3×C5#57611yescharacteristic
340C2×C3×C5#57711yescharacteristic
341C23×C3—22no—
342C23×C3—24no—
343C23×C3—81no—
344C23×C3—81no—
345C23×C3D4×D511yescharacteristic
346C3×D4—22no—
347C3×D4—24no—
348C3×D4C2×Dic1014yes—
349C2×C3×C4—101no—
350C2×C3×C4—101no—
351C2×C3×C4C2×Dic1012yes—
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4#71112yes—
354C2×C3×C4C23×D511yescharacteristic
355C2×Dic3—22no—
356C2×Dic3—52no—
357C2×Dic3—52no—
358C2×Dic3—81no—
359C2×Dic3—101no—
360C2×Dic3—101no—
361C2×Dic3—402no—
362C2×Dic3—402no—
363Dic6—402no—
364C3×C8—102no—
365C3⋊C8—21no—
366C3⋊C8—21no—
367C22×C5—21no—
368C22×C5—21no—
369C22×C5—24no—
370C22×C5—42no—
371C22×C5—42no—
372C22×C5—84no—
373C22×C5#87812yes—
374C22×C5C2×D3×D411yescharacteristic
375C4×C5—122no—
376C4×C5#87812yes—
377C4×C5C22×Dic611yescharacteristic
378C4×C5C2×#23711yescharacteristic
379Dic5—41no—
380Dic5—41no—
381Dic5—62no—
382Dic5—62no—
383Dic5—121no—
384Dic5—121no—
385C24—21no—
386C2×Q8—302no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4#120414yescomplemented
390C2×D4C2×D3×D512yes—
391C22×C4—61no—
392C22×C4—302no—
393C22×C4—302no—
394C22×C4C2×D3×D511yescharacteristic
395M16—102no—
396C2×C8—31no—
397C2×C8—31no—
398C2×C8—52no—
399C2×C8—62no—
400C4⋊C4—32no—
401C4⋊C4—51no—
402C4⋊C4—51no—
403C4⋊C4—61no—
404C4⋊C4—151no—
405C4⋊C4—151no—
406C4⋊C4—151no—
407C4⋊C4—151no—
408C4⋊C4—302no—
409C4⋊C4—302no—
410C4⋊C4—302no—
411C22⋊C4—101no—
412C22⋊C4—152no—
413C22⋊C4—302no—
414C22⋊C4—302no—
415C22⋊C4—301no—
416C42—101no—
417C42—152no—
418C42—301no—
419C3×C5#308111yescharacteristic, complemented, Hall
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—24no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—84no—
426C22×C3#402412yes—
427C22×C3C2×D4×D511yescharacteristic
428C3×C4—201no—
429C3×C4—201no—
430C3×C4#402412yes—
431C3×C4C22×Dic1011yescharacteristic
432C3×C4C2×#71111yescharacteristic
433Dic3—42no—
434Dic3—102no—
435Dic3—102no—
436Dic3—201no—
437Dic3—201no—
438C2×C5—22no—
439C2×C5—44no—
440C2×C5C2×#87811yescharacteristic
441C2×C5#577411yescharacteristic
442C2×C5#577511yescharacteristic
443C23—22no—
444C23—24no—
445C23—81no—
446C23—81no—
447C23#679011yescharacteristic
448Q8—1202no—
449D4—22no—
450D4—24no—
451D4C2×#120414yes—
452C2×C4—62no—
453C2×C4—101no—
454C2×C4—101no—
455C2×C4—152no—
456C2×C4—152no—
457C2×C4—241no—
458C2×C4—301no—
459C2×C4—301no—
460C2×C4—1202no—
461C2×C4—1202no—
462C2×C4#678012yes—
463C2×C4C2×#120412yes—
464C2×C4#679011yescharacteristic
465C2×C4C22×D3×D511yescharacteristic
466C8—61no—
467C8—61no—
468C8—102no—
469C2×C3—22no—
470C2×C3—44no—
471C2×C3C2×#402411yescharacteristic
472C2×C3#6609111yescharacteristic
473C2×C3#6609611yescharacteristic
474C5#7891811yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—24no—
478C22—42no—
479C22—42no—
480C22—84no—
481C22#9157612yes—
482C22C2×#679011yescharacteristic
483C4—122no—
484C4—201no—
485C4—201no—
486C4—302no—
487C4—302no—
488C4—601no—
489C4—601no—
490C4#9157612yes—
491C4C2×#678011yescharacteristic
492C4C22×#120411yescharacteristic
493C3#1061046211yescharacteristic, complemented, Sylow
494C2—22no—
495C2—44no—
496C2#1175470411yescharacteristic
497C2#1175472511yescharacteristic
498C2C2×#9157611yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3081
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11754619C2semidirect
5. #11749116C2semidirect
6. #11749115C2semidirect
7. #11749091C2semidirect
8. #11749089C2semidirect
9. #11748459C2semidirect
10. #11748451C2semidirect
11. #11748436C2semidirect
26. #91470C22semidirect
29. #91384C22semidirect
34. #90990C22semidirect
35. #90990C22semidirect
36. #90988C22semidirect
37. #90987C22semidirect
38. #90987C22semidirect
39. #90985C22semidirect
40. #90983C22semidirect
41. #90983C22semidirect
57. C2×C3×C5×D4Q8semidirect
187. C2×C5×D4Dic6semidirect
250. C2×C3×D4Dic10semidirect
389. C2×D4#1204semidirect
419. C3×C5#3081semidirect
474. C5#78918semidirect
493. C3#10610462semidirect

Maximal subgroups

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

subgroupindex
#117565572
#117546192
C2×C5×#8322
C3×#655042
#117491162
#117491152
#117490912
#117490892
#117484592
#117484512
#117484362
#106104623
#789185