Finite Group Databasebeta

← #14430866

Subgroups — #14430866

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
1C5×#5798C211yesmaximal, characteristic
2#11754618C211yesmaximal, characteristic, complemented
3#11751316C211yesmaximal, characteristic
4C2×C3×#3964C211yesmaximal, characteristic
5#11749113C212yesmaximal, complemented
6#11749112C212yesmaximal, complemented
7#11749088C212yesmaximal, complemented
8#11749087C212yesmaximal, complemented
9#11748470C211yesmaximal, characteristic, complemented
10#11748458C211yesmaximal, characteristic, complemented
11#11748439C211yesmaximal, characteristic, complemented
12#10614270—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14#91815C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16C2×C5×#217—22no—
17C5×D4×Dic3—21no—
18C5×D4×Dic3—21no—
19C5×D4×Dic3C2212yes—
20C5×D4×Dic3C2212yes—
21C5×#926C2211yescharacteristic
22C5×#926C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25#91574—22no—
26#91470—21no—
27#91469C2212yescomplemented
28#91384—21no—
29#91381C2212yescomplemented
30#91116C2212yes—
31#91116C2212yes—
32C3×#3964C2212yes—
33C3×#3964C2212yes—
34#90989C2212yescomplemented
35#90988C2211yescharacteristic, complemented
36#90988C2211yescharacteristic, complemented
37#90986C2212yescomplemented
38#90985C2211yescharacteristic, complemented
39#90985C2211yescharacteristic, complemented
40Dic3⋊#168C2212yescomplemented
41Dic3⋊#168C2212yescomplemented
42#78731—51nomaximal, Hall
43C5×#518—31no—
44#65853—31no—
45#65504—31no—
46C2×#3964D311yescharacteristic
47#65298—32no—
48#65298—32no—
49#65297—32no—
50#65296—32no—
51#65288—31no—
52#65287—31no—
53#65284—31no—
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×C5×Dic3—22no—
61C22×C5×Dic3—22no—
62C22×C3×Dic5—21no—
63C2×#1204—22no—
64#6719—21no—
65C4⋊Dic15C2311yescharacteristic
66C4⋊Dic15C2311yescharacteristic
67C4×Dic15—21no—
68#6710—22no—
69C2×C3⋊#168C2312yes—
70C5×#217—21no—
71C5×#217—22no—
72C5×#217—22no—
73C5×#217D412yes—
74C5×C4⋊Dic3D411yescharacteristic
75C5×C4⋊Dic3D411yescharacteristic
76C5×C4⋊Dic3C2311yescharacteristic
77C5×C4⋊Dic3C2311yescharacteristic
78C4×C5×Dic3—21no—
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#5798D511yescharacteristic
89#5500—51no—
90C2×C3×#102—51no—
91#5215—51no—
92#5106—51no—
93#5102—51no—
94#4964—51no—
95#4766—52no—
96#4763—52no—
97#4761—52no—
98#4759—52no—
99C22×C5×D4C2×D311yescharacteristic
100C4×C5×D4—32no—
101C4×C5×D4—32no—
102C4×C5×D4—61no—
103C4×C5×D4—61no—
104C5×#117—31no—
105C5×#117—31no—
106C2×C5×C22⋊C4—62no—
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#3964—32no—
117#3964—32no—
118#3964C2×D312yes—
119#3964C2×D312yes—
120#3940—32no—
121#3940—31no—
122#3940—31no—
123#3939—32no—
124#3939—31no—
125#3939—31no—
126C4⋊#168—32no—
127C4⋊#168—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×C5×Dic3—21no—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—82no—
146C2×C5×Dic3—82no—
147C2×C5×Dic3C2×D412yes—
148C2×C5×Dic3C2×D412yes—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—81no—
151#1204—82no—
152C3⋊#168—22no—
153C3×#168—21no—
154C3×#168—21no—
155C22×C3×D4C2×D511yescharacteristic
156C22×C3×C8—51no—
157C2×C3×C4⋊C4—51no—
158C2×#217—22no—
159D4×Dic3—21no—
160D4×Dic3—21no—
161D4×Dic3C2×D512yes—
162D4×Dic3C2×D512yes—
163#926—51no—
164#926C2×D511yescharacteristic
165#926C2×D511yescharacteristic
166#924—102no—
167C2×#208—51no—
168#890—52no—
169#890—101no—
170#888—52no—
171#888—101no—
172C3×#102—52no—
173C3×#102—52no—
174#832—52no—
175#832—52no—
176#818—51no—
177#818—51no—
178#817—51no—
179#817—51no—
180Dic3⋊C8—52no—
181Dic3⋊C8—52no—
182#808—52no—
183#807—52no—
184C24×C5—21no—
185C2×C5×D4—21no—
186C2×C5×D4—22no—
187C2×C5×D4Dic614yescomplemented
188C2×C5×D4C22×D312yes—
189C22×C4×C5—62no—
190C22×C4×C5—62no—
191C22×C4×C5C22×D311yescharacteristic
192C22×Dic5—21no—
193C2×Dic10—62no—
194C5×C4⋊C4—31no—
195C5×C4⋊C4—31no—
196C5×C4⋊C4—31no—
197C5×C4⋊C4—31no—
198C5×C22⋊C4—32no—
199C5×C22⋊C4—62no—
200C5×C22⋊C4—62no—
201C5×C22⋊C4—61no—
202C42×C5—32no—
203C42×C5—61no—
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#518—31no—
220#478—152no—
221#478—152no—
222#476—152no—
223#474—152no—
224#428—151no—
225#427—151no—
226#424—151no—
227#418—151no—
228C2×#102—51no—
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—41no—
241Dic15—41no—
242C3×Dic5—42no—
243C5×Dic3—22no—
244C5×Dic3—22no—
245C5×Dic3—41no—
246C5×Dic3—41no—
247C24×C3—21no—
248C2×C3×D4—22no—
249C2×C3×D4—21no—
250C2×C3×D4Dic1014yescomplemented
251C2×C3×D4C22×D512yes—
252C22×C3×C4—101no—
253C22×C3×C4C22×D511yescharacteristic
254C22×Dic3—22no—
255C22×Dic3—22no—
256C2×Dic6—102no—
257C2×C3×C8—51no—
258C2×C3×C8—51no—
259C2×C3×C8—102no—
260C3×C4⋊C4—52no—
261C3×C4⋊C4—101no—
262#217—21no—
263#217—22no—
264#217—22no—
265#217—101no—
266#217C22⋊D512yes—
267C4⋊Dic3—51no—
268C4⋊Dic3—51no—
269C4⋊Dic3—102no—
270C4⋊Dic3C22⋊D511yescharacteristic
271C4⋊Dic3C22⋊D511yescharacteristic
272C4⋊Dic3C22×D511yescharacteristic
273C4⋊Dic3C22×D511yescharacteristic
274Dic3⋊C4—102no—
275Dic3⋊C4—102no—
276C4×Dic3—21no—
277C4×Dic3—101no—
278C4×Dic3C22×D512yes—
279#208—102no—
280C2×C3⋊C8—52no—
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—32no—
290C2×C4×C5—32no—
291C2×C4×C5—61no—
292C2×C4×C5—61no—
293C2×C4×C5—242no—
294C2×C4×C5—242no—
295C2×C4×C5C2×Dic612yes—
296C2×C4×C5D3×D411yescharacteristic
297C2×C4×C5#23712yes—
298C2×C4×C5C23×D311yescharacteristic
299C2×Dic5—22no—
300C2×Dic5—61no—
301C2×Dic5—61no—
302C2×Dic5—81no—
303Dic10—242no—
304#168—21no—
305#168—21no—
306#168—62no—
307C22×D4D3×D511yescharacteristic
308C2×M16—151no—
309C22×C8—51no—
310C4⋊Q8—152no—
311C4⋊Q8—301no—
312#125—152no—
313#125—301no—
314C22⋊Q8—302no—
315C4×D4—32no—
316C4×D4—32no—
317C4×D4—61no—
318C4×D4—61no—
319#117—31no—
320#117—31no—
321#117—151no—
322C2×C4⋊C4—51no—
323C2×C22⋊C4—62no—
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—52no—
333#102—52no—
334#102—152no—
335#102—152no—
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×C3C2×C22⋊D511yescharacteristic
346C3×D4—22no—
347C3×D4—24no—
348C3×D4C2×Dic1014yes—
349C2×C3×C4—102no—
350C2×C3×C4—401no—
351C2×C3×C4C2×Dic1012yes—
352C2×C3×C4#70912yes—
353C2×C3×C4C2×C22⋊D511yescharacteristic
354C2×C3×C4C23×D511yescharacteristic
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—82no—
358C2×Dic3—82no—
359C2×Dic3—101no—
360C2×Dic3—101no—
361C2×Dic3C2×C22⋊D512yes—
362C2×Dic3C2×C22⋊D512yes—
363Dic6—402no—
364C3×C8—101no—
365C3×C8—101no—
366C3⋊C8—102no—
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—62no—
376C4×C5—62no—
377C4×C5—121no—
378C4×C5—121no—
379C4×C5#87812yes—
380C4×C5C22×Dic611yescharacteristic
381C4×C5C2×#23711yescharacteristic
382Dic5—42no—
383Dic5—121no—
384Dic5—121no—
385C24—21no—
386C2×Q8—302no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4#120414yescomplemented
390C2×D4C2×D3×D512yes—
391C22×C4—62no—
392C22×C4—62no—
393C22×C4—101no—
394C22×C4C2×D3×D511yescharacteristic
395M16—302no—
396C2×C8—51no—
397C2×C8—51no—
398C2×C8—102no—
399C2×C8—152no—
400C4⋊C4—31no—
401C4⋊C4—31no—
402C4⋊C4—31no—
403C4⋊C4—31no—
404C4⋊C4—52no—
405C4⋊C4—101no—
406C4⋊C4—151no—
407C4⋊C4—151no—
408C4⋊C4—302no—
409C4⋊C4—302no—
410C4⋊C4—302no—
411C22⋊C4—32no—
412C22⋊C4—62no—
413C22⋊C4—62no—
414C22⋊C4—61no—
415C22⋊C4—301no—
416C42—32no—
417C42—61no—
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#407012yes—
427C22×C3C22×C22⋊D511yescharacteristic
428C3×C4—202no—
429C3×C4#407012yes—
430C3×C4C22×Dic1011yescharacteristic
431C3×C4C2×#70911yescharacteristic
432Dic3—22no—
433Dic3—22no—
434Dic3—41no—
435Dic3—41no—
436Dic3—201no—
437Dic3—201no—
438C2×C5—22no—
439C2×C5—44no—
440C2×C5C2×#87811yescharacteristic
441C2×C5#575711yescharacteristic
442C2×C5#576211yescharacteristic
443C23—22no—
444C23—24no—
445C23—81no—
446C23—81no—
447C23D3×C22⋊D511yescharacteristic
448Q8—1202no—
449D4—22no—
450D4—24no—
451D4C2×#120414yes—
452C2×C4—32no—
453C2×C4—32no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—102no—
457C2×C4—242no—
458C2×C4—242no—
459C2×C4—301no—
460C2×C4—301no—
461C2×C4—401no—
462C2×C4#677912yes—
463C2×C4C2×#120412yes—
464C2×C4D3×C22⋊D511yescharacteristic
465C2×C4C22×D3×D511yescharacteristic
466C8—101no—
467C8—101no—
468C8—302no—
469C2×C3—22no—
470C2×C3—44no—
471C2×C3C2×#407011yescharacteristic
472C2×C3#6616911yescharacteristic
473C2×C3#6617011yescharacteristic
474C5#7873111yescharacteristic, complemented, Sylow
475C22—21no—
476C22—21no—
477C22—24no—
478C22—42no—
479C22—42no—
480C22—84no—
481C22#9157512yes—
482C22C2×D3×C22⋊D511yescharacteristic
483C4—62no—
484C4—62no—
485C4—121no—
486C4—121no—
487C4—202no—
488C4—601no—
489C4—601no—
490C4#9157512yes—
491C4C2×#677911yescharacteristic
492C4C22×#120411yescharacteristic
493C3#1061427011yescharacteristic, complemented, Sylow
494C2—22no—
495C2—44no—
496C2#1175469711yescharacteristic
497C2#1175471111yescharacteristic
498C2C2×#9157511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
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. #11754618C2semidirect
5. #11749113C2semidirect
6. #11749112C2semidirect
7. #11749088C2semidirect
8. #11749087C2semidirect
9. #11748470C2semidirect
10. #11748458C2semidirect
11. #11748439C2semidirect
27. #91469C22semidirect
29. #91381C22semidirect
34. #90989C22semidirect
35. #90988C22semidirect
36. #90988C22semidirect
37. #90986C22semidirect
38. #90985C22semidirect
39. #90985C22semidirect
40. Dic3⋊#168C22semidirect
41. Dic3⋊#168C22semidirect
57. C2×C3×C5×D4Q8semidirect
187. C2×C5×D4Dic6semidirect
250. C2×C3×D4Dic10semidirect
389. C2×D4#1204semidirect
419. C3×C5#3081semidirect
474. C5#78731semidirect
493. C3#10614270semidirect

Maximal subgroups

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

subgroupindex
C5×#57982
#117546182
#117513162
C2×C3×#39642
#117491132
#117491122
#117490882
#117490872
#117484702
#117484582
#117484392
#106142703
#787315