Finite Group Databasebeta

← #14308928

Subgroups — #14308928

Order 1920.

564 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754619C211yesmaximal, characteristic, complemented
2#11751316C211yesmaximal, characteristic
3C5×#5221C211yesmaximal, characteristic
4C3×#65504C211yesmaximal, characteristic
5#11745986C211yesmaximal, characteristic, complemented
6#11745976C211yesmaximal, characteristic, complemented
7#11745974C211yesmaximal, characteristic, complemented
8#10600436—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10#91815C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×C5×#217—22no—
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C2×C4×C5×Dic3C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17#91575—22no—
18#91470—21no—
19#91468—21no—
20#91388—21no—
21#91384—21no—
22#91116—21no—
23#91116—21no—
24C3×#3964—21no—
25C3×#3964—21no—
26#70313—51nomaximal, Hall
27#65834—31no—
28C5×#390—31no—
29#65504—31no—
30#65504D311yescharacteristic
31#64750—31no—
32#64743—31no—
33#64743—31no—
34C24×C3×C5—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4Q812yescomplemented
41C22×C3×C4×C5C2311yescharacteristic
42C22×C5×Dic3—21no—
43C22×C5×Dic3D412yes—
44C2×#1204—22no—
45#6719—21no—
46C4⋊Dic15D411yescharacteristic
47C4⋊Dic15D411yescharacteristic
48C4×Dic15—21no—
49#6710—21no—
50#6710—21no—
51C2×C3⋊#168—21no—
52C5×#217—44no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3—21no—
55C4×C5×Dic3—21no—
56C4×C5×Dic3—21no—
57C3×C22⋊Dic5—21no—
58C3×C4⋊Dic5D411yescharacteristic
59C3×C4⋊Dic5D411yescharacteristic
60C3×C4×Dic5—21no—
61C3×#681—21no—
62C3×#681—21no—
63C2×C3×#168—21no—
64Dic3⋊Dic5—22no—
65#6669—22no—
66#6668—22no—
67#5519—51no—
68C3×#418—51no—
69#5221D511yescharacteristic
70#5215—51no—
71#4555—51no—
72#4554—51no—
73#4532—51no—
74C22×C5×D4C2×D311yescharacteristic
75C2×C5×C4⋊C4—31no—
76C2×C5×C22⋊C4—62no—
77C2×C42×C5—31no—
78#4072—31no—
79#4072C2×D311yescharacteristic
80#4070—62no—
81C2×#681—31no—
82C2×#681C2×D311yescharacteristic
83#4036—61no—
84#4036—61no—
85#4034—61no—
86#4034—61no—
87#3964—21no—
88#3964—21no—
89#3964—61no—
90#3964—61no—
91#2027—151noSylow
92C23×C3×C5—22no—
93C23×C3×C5—42no—
94C23×C3×C5—42no—
95C23×C3×C5—41no—
96C23×C3×C5—41no—
97C23×C3×C5C2×D411yescharacteristic
98C3×C5×D4—22no—
99C3×C5×D4—22no—
100C3×C5×D4—41no—
101C3×C5×D4—41no—
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×Q811yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×Dic15—21no—
109C2×Dic15—21no—
110C2×C5×Dic3—22no—
111C2×C5×Dic3—22no—
112C2×C5×Dic3—41no—
113C2×C5×Dic3—41no—
114C2×C5×Dic3—42no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—21no—
117#1204—82no—
118C3⋊#168—41no—
119C3×#168—41no—
120C22×C3×D4C2×D511yescharacteristic
121C2×C3×M16—51no—
122C3×#117—51no—
123C2×#217—22no—
124#926—51no—
125C2×C4⋊Dic3C2×D511yescharacteristic
126C2×C4×Dic3C2×D511yescharacteristic
127C2×#208—51no—
128#890—101no—
129#888—101no—
130#878—102no—
131#870—101no—
132#869—101no—
133C3×#102—101no—
134C3×#102—101no—
135#832—101no—
136#832—101no—
137C24×C5—21no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4Dic612yescomplemented
144C22×C4×C5—32no—
145C22×C4×C5—61no—
146C22×C4×C5C22×D311yescharacteristic
147C2×Dic10—62no—
148C5×C4⋊C4—61no—
149C5×C4⋊C4—61no—
150C5×C22⋊C4—124no—
151C42×C5—61no—
152C42×C5—61no—
153C22⋊Dic5—21no—
154C22⋊Dic5—61no—
155C4⋊Dic5—31no—
156C4⋊Dic5—31no—
157C4⋊Dic5—62no—
158C4⋊Dic5#6711yescharacteristic
159C4⋊Dic5#6711yescharacteristic
160#683—62no—
161#683—62no—
162C4×Dic5—21no—
163C4×Dic5—61no—
164#681—21no—
165#681—21no—
166#681—61no—
167#681—61no—
168C2×#168—21no—
169C2×#168—61no—
170#544—151no—
171#418—51no—
172#418—151no—
173#390—31no—
174#343—151no—
175#339—151no—
176#339—151no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5—44no—
180C22×C3×C5—42no—
181C22×C3×C5—82no—
182C22×C3×C5—81no—
183C22×C3×C5—81no—
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5C22⋊Q811yescharacteristic
186C22×C3×C5#12411yescharacteristic
187C3×C4×C5C22⋊Q811yescharacteristic
188C3×C4×C5C22⋊Q811yescharacteristic
189C3×C4×C5#12411yescharacteristic
190C3×C4×C5#12411yescharacteristic
191Dic15—41no—
192Dic15—41no—
193C3×Dic5—41no—
194C3×Dic5—41no—
195C5×Dic3—42no—
196C5×Dic3—42no—
197C24×C3—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4Dic1012yescomplemented
204C22×C3×C4C22×D511yescharacteristic
205C22×Dic3—21no—
206C22×Dic3C22⋊D512yes—
207C2×Dic6—102no—
208C3×M16—101no—
209C3×M16—101no—
210C2×C3×C8—101no—
211C3×C4⋊C4—51no—
212C3×C4⋊C4—51no—
213C3×C22⋊C4—101no—
214C3×C42—101no—
215#217—44no—
216#217—101no—
217C4⋊Dic3—21no—
218C4⋊Dic3—21no—
219C4⋊Dic3—51no—
220C4⋊Dic3—51no—
221C4⋊Dic3—102no—
222Dic3⋊C4—102no—
223Dic3⋊C4—102no—
224C4×Dic3—21no—
225C4×Dic3—21no—
226C4×Dic3—101no—
227#208—101no—
228#208—101no—
229C2×C3⋊C8—101no—
230C23×C5—22no—
231C23×C5—42no—
232C23×C5—42no—
233C23×C5—41no—
234C23×C5—41no—
235C23×C5D3×D411yescharacteristic
236C5×D4—22no—
237C5×D4—22no—
238C5×D4—41no—
239C5×D4—41no—
240C2×C4×C5—62no—
241C2×C4×C5—62no—
242C2×C4×C5—121no—
243C2×C4×C5—121no—
244C2×C4×C5—122no—
245C2×C4×C5C2×Dic611yescharacteristic
246C2×C4×C5#23511yescharacteristic
247C2×C4×C5D3×D411yescharacteristic
248C2×C4×C5#23711yescharacteristic
249C2×C4×C5#23711yescharacteristic
250C2×C4×C5C2×#6711yescharacteristic
251C2×Dic5—21no—
252C2×Dic5—21no—
253C2×Dic5—61no—
254C2×Dic5—61no—
255Dic10—242no—
256#168—41no—
257#168—121no—
258C22×D4D3×D511yescharacteristic
259C2×M16—51no—
260C2×M16—151no—
261C4⋊Q8—301no—
262C4⋊Q8—301no—
263#125—301no—
264#125—301no—
265C22⋊Q8—302no—
266#117—51no—
267#117—151no—
268C2×C4⋊C4—31no—
269C2×C22⋊C4—62no—
270C2×C42—31no—
271#102—101no—
272#102—101no—
273#102—301no—
274#102—301no—
275C2×C3×C5—21no—
276C2×C3×C5—21no—
277C2×C3×C5—82no—
278C2×C3×C5#39311yescharacteristic
279C2×C3×C5#45311yescharacteristic
280C2×C3×C5#45411yescharacteristic
281C23×C3—22no—
282C23×C3—42no—
283C23×C3—42no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3C2×C22⋊D511yescharacteristic
287C3×D4—22no—
288C3×D4—22no—
289C3×D4—41no—
290C3×D4—41no—
291C2×C3×C4—101no—
292C2×C3×C4—101no—
293C2×C3×C4C2×Dic1011yescharacteristic
294C2×C3×C4#70911yescharacteristic
295C2×C3×C4D4×D511yescharacteristic
296C2×C3×C4D4×D511yescharacteristic
297C2×C3×C4#71111yescharacteristic
298C2×C3×C4#71111yescharacteristic
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—41no—
302C2×Dic3—41no—
303C2×Dic3—42no—
304C2×Dic3—101no—
305C2×Dic3—101no—
306Dic6—402no—
307C3×C8—201no—
308C3⋊C8—201no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—44no—
312C22×C5—42no—
313C22×C5—82no—
314C22×C5—81no—
315C22×C5—81no—
316C22×C5#87811yescharacteristic
317C22×C5#88511yescharacteristic
318C22×C5#93711yescharacteristic
319C4×C5—122no—
320C4×C5—122no—
321C4×C5#87811yescharacteristic
322C4×C5#88511yescharacteristic
323C4×C5#92411yescharacteristic
324C4×C5#93611yescharacteristic
325Dic5—41no—
326Dic5—41no—
327Dic5—121no—
328Dic5—121no—
329C24—21no—
330C2×Q8—302no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4#120412yescomplemented
337C22×C4—32no—
338C22×C4—61no—
339C22×C4C2×D3×D511yescharacteristic
340M16—101no—
341M16—101no—
342M16—301no—
343M16—301no—
344C2×C8—101no—
345C2×C8—301no—
346C4⋊C4—51no—
347C4⋊C4—51no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4—151no—
351C4⋊C4—151no—
352C4⋊C4—302no—
353C4⋊C4—302no—
354C4⋊C4—302no—
355C22⋊C4—101no—
356C22⋊C4—124no—
357C22⋊C4—301no—
358C42—61no—
359C42—61no—
360C42—101no—
361C42—301no—
362C3×C5#202711yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—44no—
366C22×C3—42no—
367C22×C3—82no—
368C22×C3—81no—
369C22×C3—81no—
370C22×C3#407011yescharacteristic
371C22×C3#408211yescharacteristic
372C22×C3#408311yescharacteristic
373C3×C4—201no—
374C3×C4—201no—
375C3×C4#402411yescharacteristic
376C3×C4#402411yescharacteristic
377C3×C4#403111yescharacteristic
378C3×C4#403111yescharacteristic
379Dic3—42no—
380Dic3—42no—
381Dic3—201no—
382Dic3—201no—
383C2×C5—21no—
384C2×C5—21no—
385C2×C5—82no—
386C2×C5#494711yescharacteristic
387C2×C5#519811yescharacteristic
388C2×C5#520111yescharacteristic
389C23—22no—
390C23—42no—
391C23—42no—
392C23—41no—
393C23—41no—
394C23D3×C22⋊D511yescharacteristic
395Q8—1202no—
396D4—22no—
397D4—22no—
398D4—41no—
399D4—41no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—101no—
403C2×C4—101no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—122no—
407C2×C4—301no—
408C2×C4—301no—
409C2×C4#677911yescharacteristic
410C2×C4#678011yescharacteristic
411C2×C4#678211yescharacteristic
412C2×C4C2×#120411yescharacteristic
413C2×C4D5×#6711yescharacteristic
414C2×C4#679011yescharacteristic
415C8—201no—
416C8—601no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—82no—
420C2×C3#6523611yescharacteristic
421C2×C3#6535111yescharacteristic
422C2×C3#6536611yescharacteristic
423C5#7031311yescharacteristic, complemented, Sylow
424C22—21no—
425C22—21no—
426C22—44no—
427C22—42no—
428C22—82no—
429C22—81no—
430C22—81no—
431C22#9152511yescharacteristic
432C22#9157511yescharacteristic
433C22#9157711yescharacteristic
434C4—122no—
435C4—122no—
436C4—201no—
437C4—201no—
438C4—601no—
439C4—601no—
440C4#9152611yescharacteristic
441C4#9153411yescharacteristic
442C4#9157411yescharacteristic
443C4#9157611yescharacteristic
444C3#1060043611yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—82no—
448C2#1174916511yescharacteristic
449C2#1174916711yescharacteristic
450C2#1174952411yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC22×C3×C5#120
hypercenterC22×D4D3×D5
hypocenterC3×C5#2027
LCSG ▷ C22×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
1. #11754619C2semidirect
5. #11745986C2semidirect
6. #11745976C2semidirect
7. #11745974C2semidirect
40. C2×C3×C5×D4Q8semidirect
143. C2×C5×D4Dic6semidirect
203. C2×C3×D4Dic10semidirect
336. C2×D4#1204semidirect
362. C3×C5#2027semidirect
423. C5#70313semidirect
444. C3#10600436semidirect

Maximal subgroups

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

subgroupindex
#117546192
#117513162
C5×#52212
C3×#655042
#117459862
#117459762
#117459742
#106004363
#703135