Finite Group Databasebeta

← #14319503

Subgroups — #14319503

Order 1920.

1504 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91400C212yesmaximal
2C2×C4×D3×Dic5C211yesmaximal, characteristic
3#11750749C211yesmaximal, characteristic, complemented
4C5×#4666C211yesmaximal, characteristic
5C3×#64938C211yesmaximal, characteristic, complemented
6Dic5×(C2×D3)⋊C4C212yesmaximal
7#11748719C211yesmaximal, characteristic
8#11748653C211yesmaximal, characteristic, complemented
9#11748638C211yesmaximal, characteristic, complemented
10Dic3×#683C212yesmaximal, complemented
11C4×Dic3×Dic5C212yesmaximal, complemented
12C4×#4023—31nomaximal, Hall
13C22×C4×C5×D3C2211yescharacteristic
14C22×D3×Dic5C2211yescharacteristic
15C22×D3×Dic5C2211yescharacteristic
16C2×C4×Dic15C2211yescharacteristic
17C2×C4×Dic15C2212yes—
18C2×C5×(C2×D3)⋊C4C2212yes—
19C2×C4×C5×Dic3C2212yes—
20C2×C3×#683C2212yes—
21C2×C3×C4×Dic5C2212yes—
22C2×C3×C4×Dic5C2211yescharacteristic
23C2×#6668C2212yes—
24C2×(C2×D3)⋊Dic5C2212yes—
25C2×Dic3×Dic5C2212yes—
26C2×Dic3×Dic5C2212yes—
27C2×Dic3×Dic5C2211yescharacteristic
28C2×Dic3×Dic5C2211yescharacteristic
29C2×Dic3×Dic5C2212yes—
30#91400C4116yescomplemented
31C4×D3×Dic5C418yescomplemented
32C3×C5×#95C2211yescharacteristic
33#91115C2212yes—
34#91115C2211yescharacteristic
35C5×C3⋊#95C2211yescharacteristic
36C3×#3963C2211yescharacteristic
37#90994C2212yes—
38C4×#892—51nomaximal, Hall
39C22×C4×Dic5—31no—
40C2×#4023—32no—
41C4×C5×C22⋊C4—31no—
42C4×C22⋊Dic5—31no—
43C22⋊C4×Dic5—32no—
44C4×#683—32no—
45C42×Dic5—32no—
46#64938—31no—
47#64938D311yescharacteristic, complemented
48#64937—31no—
49#64937—31no—
50C23×C5×D3C2311yescharacteristic
51C22×C3×C4×C5C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2311yescharacteristic
54C22×Dic15C2312yes—
55C22×Dic15C2311yescharacteristic
56C22×C5×Dic3C2312yes—
57C22×C5×Dic3C2311yescharacteristic
58C2×C4×C5×D3—24no—
59C2×C4×C5×D3C2×C414yes—
60C22×C3×Dic5C2312yes—
61C22×C3×Dic5C2311yescharacteristic
62C22×C3×Dic5C2311yescharacteristic
63C2×D3×Dic5—22no—
64C2×D3×Dic5—22no—
65C2×D3×Dic5C2×C414yes—
66C2×D3×Dic5C2×C414yes—
67C2×D3×Dic5C2×C418yes—
68C4×Dic15C2×C414yes—
69C4×Dic15C2×C418yescomplemented
70C5×(C2×D3)⋊C4C2×C418yes—
71C4×C5×Dic3—24no—
72C3×#683C2×C418yescomplemented
73C3×C4×Dic5—24no—
74C3×C4×Dic5C2×C414yes—
75#6668C2×C418yescomplemented
76(C2×D3)⋊Dic5C2×C418yes—
77Dic3×Dic5—24no—
78Dic3×Dic5—24no—
79Dic3×Dic5C2×C414yes—
80Dic3×Dic5C2×C414yes—
81Dic3×Dic5C2×C418yescomplemented
82C2×#892—52no—
83C2×C42×D3—51no—
84C3×C4×C4⋊C4—51no—
85Dic3×C4⋊C4—52no—
86C4×(C2×D3)⋊C4—52no—
87C4×C4⋊Dic3—51no—
88C42×Dic3—52no—
89#4666—51no—
90#4666D511yescharacteristic
91#4648—51no—
92#4648—51no—
93C23×C4×C5—31no—
94C23×Dic5—31no—
95C23×Dic5—31no—
96C2×C5×C22⋊C4—32no—
97C2×C42×C5—32no—
98C2×C22⋊Dic5—32no—
99C2×#683—32no—
100C2×#683C2×D312yes—
101C2×C4×Dic5—32no—
102C2×C4×Dic5—31no—
103C2×C4×Dic5—32no—
104C2×C4×Dic5—31no—
105C2×C4×Dic5—31no—
106C2×C4×Dic5—38no—
107C2×C4×Dic5—32no—
108C2×C4×Dic5—32no—
109C2×C4×Dic5C2×D312yes—
110C2×C4×Dic5C2×D311yescharacteristic
111#4023—316no—
112C5×#95—31no—
113C5×#95C2×D311yescharacteristic
114#3963—31no—
115#3963—32no—
116#3963—32no—
117#3963C2×D311yescharacteristic
118C4×#117—151noSylow
119C23×C3×C5C2411yescharacteristic
120C22×C5×D3—21no—
121C22×C5×D3—21no—
122C22×C5×D3—22no—
123C22×C5×D3C22×C414yes—
124C22×C5×D3C22×C412yes—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5C22×C412yes—
129C2×C3×C4×C5C22×C414yes—
130C2×Dic15—22no—
131C2×Dic15—22no—
132C2×Dic15—21no—
133C2×Dic15—21no—
134C2×Dic15C22×C412yes—
135C2×Dic15C22×C414yes—
136C2×Dic15C22×C412yes—
137C2×Dic15C22×C414yes—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3C22×C414yes—
141C2×C5×Dic3C22×C412yes—
142C2×C5×Dic3#4114yes—
143C4×C5×D3—28no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5C22×C414yes—
147C2×C3×Dic5C22×C412yes—
148C2×C3×Dic5C22×C414yes—
149C2×C3×Dic5C22×C412yes—
150C2×C3×Dic5#4112yes—
151C2×C3×Dic5#4112yes—
152D3×Dic5—28no—
153D3×Dic5C42116yescomplemented
154C22×C4×D3—51no—
155C22×C4×D3—51no—
156C22×C4×D3C2×D511yescharacteristic
157C2×C3×C4⋊C4—52no—
158C2×C3×C42—51no—
159C2×C3×C42—52no—
160C2×(C2×D3)⋊C4—52no—
161C2×(C2×D3)⋊C4C2×D512yes—
162C2×C4⋊Dic3—52no—
163C2×C4×Dic3—51no—
164C2×C4×Dic3—52no—
165C2×C4×Dic3—52no—
166C2×C4×Dic3—51no—
167C2×C4×Dic3—51no—
168C2×C4×Dic3—52no—
169C2×C4×Dic3—52no—
170C2×C4×Dic3C2×D512yes—
171#892—516no—
172C42×D3—58no—
173C3×#95—51no—
174C3×#95C2×D511yescharacteristic
175C3⋊#95—51no—
176C3⋊#95—52no—
177C3⋊#95—52no—
178C3⋊#95C2×D511yescharacteristic
179C24×C5—31no—
180C22×C4×C5—31no—
181C22×C4×C5—32no—
182C22×C4×C5—34no—
183C22×C4×C5—64no—
184C22×C4×C5C22×D312yes—
185C22×C4×C5C22×D311yescharacteristic
186C22×Dic5—31no—
187C22×Dic5—38no—
188C22×Dic5—34no—
189C22×Dic5—32no—
190C22×Dic5—31no—
191C22×Dic5—34no—
192C22×Dic5—62no—
193C22×Dic5—62no—
194C22×Dic5C22×D312yes—
195C22×Dic5C22×D311yescharacteristic
196C22×Dic5C22×D311yescharacteristic
197C5×C22⋊C4—38no—
198C42×C5—64no—
199C22⋊Dic5—38no—
200#683—38no—
201#683C4×D318yescomplemented
202C4×Dic5—24no—
203C4×Dic5—34no—
204C4×Dic5—38no—
205C4×Dic5—34no—
206C4×Dic5—34no—
207C4×Dic5—38no—
208C4×Dic5—64no—
209C4×Dic5—64no—
210C4×Dic5C4×D314yes—
211C2×#117—152no—
212C22×C42—151no—
213C4×C4⋊C4—51no—
214C4×C4⋊C4—151no—
215C4×C4⋊C4—152no—
216C4×C22⋊C4—31no—
217C4×C22⋊C4—151no—
218C4×C22⋊C4—152no—
219#376—151no—
220#376—151no—
221C43—152no—
222C22×C3×C5C23×C411yescharacteristic
223C22×C3×C5C23×C412yes—
224C22×C3×C5C2×#4112yes—
225C22×C3×C5C2×#4111yescharacteristic
226C22×C3×C5C2×#4111yescharacteristic
227C2×C5×D3—22no—
228C2×C5×D3—22no—
229C2×C5×D3—24no—
230C2×C5×D3—24no—
231C2×C5×D3C2×C4214yes—
232C3×C4×C5—22no—
233C3×C4×C5—24no—
234Dic15—22no—
235Dic15—24no—
236Dic15C2×C4214yes—
237C3×Dic5—24no—
238C3×Dic5C2×C4214yes—
239C3×Dic5#11714yescomplemented
240C5×Dic3—24no—
241C5×Dic3#11714yescomplemented
242C23×D3C22×D511yescharacteristic
243C22×C3×C4—51no—
244C22×C3×C4—51no—
245C22×C3×C4—52no—
246C22×C3×C4C22×D511yescharacteristic
247C22×C3×C4C22×D512yes—
248C22×Dic3—51no—
249C22×Dic3—51no—
250C22×Dic3—52no—
251C22×Dic3C22×D512yes—
252C22×Dic3C22×D511yescharacteristic
253C2×C4×D3—24no—
254C2×C4×D3—54no—
255C2×C4×D3—58no—
256C2×C4×D3—54no—
257C2×C4×D3—102no—
258C2×C4×D3—102no—
259C2×C4×D3C4×D514yes—
260C3×C4⋊C4—58no—
261C3×C42—54no—
262C3×C42—104no—
263(C2×D3)⋊C4—58no—
264(C2×D3)⋊C4C4×D518yes—
265C4⋊Dic3—58no—
266C4×Dic3—24no—
267C4×Dic3—54no—
268C4×Dic3—58no—
269C4×Dic3—54no—
270C4×Dic3—54no—
271C4×Dic3—58no—
272C4×Dic3—104no—
273C4×Dic3—104no—
274C23×C5—34no—
275C23×C5—32no—
276C23×C5—61no—
277C23×C5—61no—
278C23×C5—62no—
279C23×C5C23×D311yescharacteristic
280C2×C4×C5—22no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—32no—
284C2×C4×C5—34no—
285C2×C4×C5—34no—
286C2×C4×C5—68no—
287C2×C4×C5—62no—
288C2×C4×C5—62no—
289C2×C4×C5C2×C4×D312yes—
290C2×C4×C5C2×C4×D314yes—
291C2×Dic5—22no—
292C2×Dic5—22no—
293C2×Dic5—32no—
294C2×Dic5—34no—
295C2×Dic5—316no—
296C2×Dic5—32no—
297C2×Dic5—34no—
298C2×Dic5—61no—
299C2×Dic5—62no—
300C2×Dic5—61no—
301C2×Dic5—62no—
302C2×Dic5—68no—
303C2×Dic5C2×C4×D314yes—
304C2×Dic5C2×C4×D312yes—
305C2×Dic5C2×C4×D314yes—
306C2×Dic5C2×C4×D312yes—
307C2×Dic5#23712yes—
308C2×Dic5#23912yes—
309C23×C4—31no—
310C23×C4—151no—
311C23×C4—151no—
312#117—1516no—
313C2×C4⋊C4—52no—
314C2×C4⋊C4—152no—
315C2×C22⋊C4—32no—
316C2×C22⋊C4—152no—
317C2×C42—32no—
318C2×C42—51no—
319C2×C42—52no—
320C2×C42—158no—
321C2×C42—152no—
322C2×C42—151no—
323C2×C42—151no—
324C2×C42—152no—
325C2×C42—151no—
326C2×C42—152no—
327C2×C42—152no—
328#95—31no—
329#95—51no—
330#95—152no—
331#95—152no—
332#95—151no—
333#95D3×D511yescharacteristic
334C2×C3×C5C22×C4211yescharacteristic
335C2×C3×C5C2×#11711yescharacteristic
336C2×C3×C5C2×#11711yescharacteristic
337C2×C3×C5C4×#4112yes—
338C2×C3×C5C4×#4112yes—
339C5×D3—24no—
340C23×C3C23×D511yescharacteristic
341C22×D3—22no—
342C22×D3—21no—
343C22×D3—21no—
344C22×D3C2×C4×D514yes—
345C22×D3C2×C4×D512yes—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—52no—
350C2×C3×C4—52no—
351C2×C3×C4—54no—
352C2×C3×C4—52no—
353C2×C3×C4—52no—
354C2×C3×C4—54no—
355C2×C3×C4—102no—
356C2×C3×C4—102no—
357C2×C3×C4C2×C4×D514yes—
358C2×C3×C4C2×C4×D512yes—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—52no—
362C2×Dic3—54no—
363C2×Dic3—52no—
364C2×Dic3—54no—
365C2×Dic3—102no—
366C2×Dic3—102no—
367C2×Dic3—101no—
368C2×Dic3—101no—
369C2×Dic3C2×C4×D514yes—
370C2×Dic3C2×C4×D512yes—
371C2×Dic3#71114yes—
372C4×D3—28no—
373C4×D3—516no—
374C4×D3—108no—
375C22×C5—34no—
376C22×C5—62no—
377C22×C5—62no—
378C22×C5—64no—
379C22×C5—64no—
380C22×C5C22×C4×D311yescharacteristic
381C22×C5C22×C4×D312yes—
382C22×C5C2×#23711yescharacteristic
383C22×C5C2×#23911yescharacteristic
384C22×C5D3×#4112yes—
385C4×C5—22no—
386C4×C5—24no—
387C4×C5—34no—
388C4×C5—64no—
389Dic5—24no—
390Dic5—34no—
391Dic5—62no—
392Dic5—64no—
393Dic5C42×D314yes—
394Dic5#89214yescomplemented
395C24—31no—
396C22×C4—31no—
397C22×C4—32no—
398C22×C4—34no—
399C22×C4—51no—
400C22×C4—51no—
401C22×C4—52no—
402C22×C4—64no—
403C22×C4—154no—
404C22×C4—158no—
405C22×C4—154no—
406C22×C4—151no—
407C22×C4—151no—
408C22×C4—152no—
409C22×C4—302no—
410C22×C4—302no—
411C22×C4C2×D3×D511yescharacteristic
412C22×C4C2×D3×D512yes—
413C4⋊C4—58no—
414C4⋊C4—158no—
415C22⋊C4—38no—
416C22⋊C4—158no—
417C42—54no—
418C42—64no—
419C42—104no—
420C42—154no—
421C42—154no—
422C42—158no—
423C42—154no—
424C42—158no—
425C42—304no—
426C42—304no—
427C3×C5C4×#11711yescharacteristic, complemented, Hall
428C22×C3C22×C4×D511yescharacteristic
429C22×C3C22×C4×D512yes—
430C22×C3C2×#71112yes—
431C22×C3D5×#4111yescharacteristic
432C22×C3D5×#4111yescharacteristic
433C2×D3—22no—
434C2×D3—22no—
435C2×D3—24no—
436C2×D3—24no—
437C2×D3C42×D514yes—
438C3×C4—22no—
439C3×C4—24no—
440C3×C4—54no—
441C3×C4—54no—
442C3×C4—104no—
443Dic3—24no—
444Dic3—54no—
445Dic3—102no—
446Dic3—104no—
447Dic3#402314yescomplemented
448C2×C5—64no—
449C2×C5C2×C42×D311yescharacteristic
450C2×C5C2×#89211yescharacteristic
451C2×C5D3×#11711yescharacteristic
452C2×C5C4×#23712yes—
453C2×C5C4×#23912yes—
454C23—34no—
455C23—32no—
456C23—61no—
457C23—62no—
458C23—61no—
459C23C22×D3×D511yescharacteristic
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—32no—
464C2×C4—34no—
465C2×C4—34no—
466C2×C4—52no—
467C2×C4—52no—
468C2×C4—54no—
469C2×C4—52no—
470C2×C4—52no—
471C2×C4—54no—
472C2×C4—68no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—102no—
476C2×C4—102no—
477C2×C4—1516no—
478C2×C4—152no—
479C2×C4—154no—
480C2×C4—152no—
481C2×C4—154no—
482C2×C4—308no—
483C2×C4—301no—
484C2×C4—302no—
485C2×C4—302no—
486C2×C4—301no—
487C2×C4C4×D3×D512yes—
488C2×C4C4×D3×D514yes—
489C2×C3C2×C42×D511yescharacteristic
490C2×C3C2×#402311yescharacteristic
491C2×C3D5×#11711yescharacteristic
492C2×C3C4×#71112yes—
493C2×C3C4×#71112yes—
494D3—24no—
495C5C4×#89211yescharacteristic, complemented, Sylow
496C22—34no—
497C22—62no—
498C22—64no—
499C22—62no—
500C22—64no—
501C22C2×C4×D3×D511yescharacteristic
502C22C2×C4×D3×D512yes—
503C22D5×#23711yescharacteristic
504C22D3×#71112yes—
505C22D5×#23911yescharacteristic
506C4—24no—
507C4—22no—
508C4—34no—
509C4—54no—
510C4—54no—
511C4—64no—
512C4—104no—
513C4—154no—
514C4—302no—
515C4—304no—
516C3C4×#402311yescharacteristic, complemented, Sylow
517C2—64no—
518C2C42×D3×D511yescharacteristic
519C2#1175282012yes—
520C2D3×#402311yescharacteristic
521C2#1175340612yes—
522C2D5×#89211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC2×C3×C5C22×C42
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenter#95D3×D5
hypocenterC3×C5C4×#117
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. #11750749C2semidirect
5. C3×#64938C2semidirect
8. #11748653C2semidirect
9. #11748638C2semidirect
10. Dic3×#683C2semidirect
11. C4×Dic3×Dic5C2semidirect
30. #91400C4semidirect
31. C4×D3×Dic5C4semidirect
47. #64938D3semidirect
69. C4×Dic15C2×C4semidirect
72. C3×#683C2×C4semidirect
75. #6668C2×C4semidirect
81. Dic3×Dic5C2×C4semidirect
153. D3×Dic5C42semidirect
201. #683C4×D3semidirect
239. C3×Dic5#117semidirect
241. C5×Dic3#117semidirect
394. Dic5#892semidirect
427. C3×C5C4×#117semidirect
447. Dic3#4023semidirect
495. C5C4×#892semidirect
516. C3C4×#4023semidirect

Maximal subgroups

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

subgroupindex
C2×#914002
C2×C4×D3×Dic52
#117507492
C5×#46662
C3×#649382
Dic5×(C2×D3)⋊C42
#117487192
#117486532
#117486382
Dic3×#6832
C4×Dic3×Dic52
C4×#40233
C4×#8925