Finite Group Databasebeta

← #14319504

Subgroups — #14319504

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×#91393C212yesmaximal
2C2×C4×D5×Dic3C211yesmaximal, characteristic
3#11750750C211yesmaximal, characteristic, complemented
4C5×#4648C211yesmaximal, characteristic, complemented
5C3×#64955C211yesmaximal, characteristic
6#11748884C212yesmaximal
7#11748702C211yesmaximal, characteristic
8#11748663C211yesmaximal, characteristic, complemented
9#11748643C211yesmaximal, characteristic, complemented
10#11748640C212yesmaximal, complemented
11C4×Dic3×Dic5C212yesmaximal, complemented
12#10605113—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C22×D5×Dic3C2211yescharacteristic
15C22×D5×Dic3C2211yescharacteristic
16C2×#6712C2212yes—
17C2×C4×Dic15C2212yes—
18C2×C4×Dic15C2211yescharacteristic
19C2×C4×C5×Dic3C2211yescharacteristic
20C2×C4×C5×Dic3C2212yes—
21C2×C3×#685C2212yes—
22C2×C3×C4×Dic5C2212yes—
23C2×#6669C2212yes—
24C2×#6665C2212yes—
25C2×Dic3×Dic5C2212yes—
26C2×Dic3×Dic5C2212yes—
27C2×Dic3×Dic5C2211yescharacteristic
28C2×Dic3×Dic5C2211yescharacteristic
29C2×Dic3×Dic5C2212yes—
30#91393C4116yescomplemented
31C4×D5×Dic3C418yescomplemented
32C3×C5×#95C2211yescharacteristic
33#91115C2211yescharacteristic
34C5×C3⋊#95C2212yes—
35C5×C3⋊#95C2211yescharacteristic
36C3×#3963C2211yescharacteristic
37#90994C2212yes—
38C4×#877—51nomaximal, Hall
39C2×#4018—32no—
40C2×C42×D5—31no—
41C5×#376—31no—
42#65221—31no—
43C42×Dic5—32no—
44#64955—32no—
45#64955—31no—
46#64955D311yescharacteristic
47#64938—32no—
48#64938—31no—
49#64938—31no—
50C23×C3×D5C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×Dic15C2312yes—
54C22×Dic15C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×C5×Dic3C2311yescharacteristic
57C22×C5×Dic3C2312yes—
58C22×C5×Dic3C2311yescharacteristic
59C22×C3×Dic5C2312yes—
60C22×C3×Dic5C2311yescharacteristic
61C2×C3×C4×D5—24no—
62C2×C3×C4×D5C2×C414yes—
63C2×D5×Dic3—22no—
64C2×D5×Dic3—22no—
65C2×D5×Dic3C2×C414yes—
66C2×D5×Dic3C2×C418yes—
67C2×D5×Dic3C2×C414yes—
68#6712C2×C418yescomplemented
69C4×Dic15—24no—
70C4×Dic15C2×C414yes—
71C4×C5×Dic3C2×C414yes—
72C4×C5×Dic3C2×C418yescomplemented
73C3×#685C2×C418yes—
74C3×C4×Dic5—24no—
75#6669C2×C418yescomplemented
76#6665C2×C418yes—
77Dic3×Dic5—24no—
78Dic3×Dic5—24no—
79Dic3×Dic5C2×C414yes—
80Dic3×Dic5C2×C414yes—
81Dic3×Dic5C2×C418yescomplemented
82C22×C4×Dic3—51no—
83C2×#877—52no—
84C3×C4×C22⋊C4—51no—
85C4×#217—51no—
86Dic3×C22⋊C4—52no—
87C4×Dic3⋊C4—52no—
88C42×Dic3—52no—
89#4649—51no—
90#4649—51no—
91#4648—51no—
92#4648D511yescharacteristic, complemented
93C22×C4×D5—31no—
94C22×C4×D5—31no—
95C22×C4×D5C2×D311yescharacteristic
96C2×C42×C5—31no—
97C2×C42×C5—32no—
98C2×#685—32no—
99C2×#685C2×D312yes—
100C2×#683—32no—
101C2×#683—32no—
102C2×C4×Dic5—31no—
103C2×C4×Dic5—31no—
104C2×C4×Dic5—31no—
105C2×C4×Dic5—32no—
106C2×C4×Dic5—32no—
107C2×C4×Dic5—32no—
108C2×C4×Dic5—32no—
109C2×C4×Dic5C2×D312yes—
110#4018—316no—
111C42×D5—38no—
112C5×#95—32no—
113C5×#95—31no—
114C5×#95C2×D311yescharacteristic
115#3963—31no—
116#3963—32no—
117#3963C2×D311yescharacteristic
118C4×#117—151noSylow
119C23×C3×C5C2411yescharacteristic
120C22×C3×D5—21no—
121C22×C3×D5—21no—
122C22×C3×D5—22no—
123C22×C3×D5C22×C414yes—
124C22×C3×D5C22×C412yes—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5C22×C414yes—
129C2×C3×C4×C5C22×C412yes—
130C2×Dic15—22no—
131C2×Dic15—22no—
132C2×Dic15C22×C414yes—
133C2×Dic15C22×C412yes—
134C2×Dic15C22×C414yes—
135C2×Dic15C22×C412yes—
136C2×Dic15#4112yes—
137C2×Dic15#4112yes—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—21no—
142C2×C5×Dic3C22×C412yes—
143C2×C5×Dic3C22×C414yes—
144C2×C5×Dic3C22×C412yes—
145C2×C5×Dic3C22×C414yes—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5C22×C414yes—
149C2×C3×Dic5C22×C412yes—
150C2×C3×Dic5#4114yes—
151C3×C4×D5—28no—
152D5×Dic3—28no—
153D5×Dic3C42116yescomplemented
154C23×C3×C4—51no—
155C23×Dic3—51no—
156C23×Dic3—51no—
157C2×C3×C22⋊C4—52no—
158C2×C3×C42—52no—
159C2×#217—52no—
160C2×Dic3⋊C4—52no—
161C2×Dic3⋊C4—52no—
162C2×C4×Dic3—51no—
163C2×C4×Dic3—52no—
164C2×C4×Dic3—51no—
165C2×C4×Dic3—51no—
166C2×C4×Dic3—58no—
167C2×C4×Dic3—52no—
168C2×C4×Dic3—52no—
169C2×C4×Dic3—52no—
170C2×C4×Dic3C2×D511yescharacteristic
171C2×C4×Dic3C2×D512yes—
172#877—516no—
173C3×#95—51no—
174C3×#95C2×D511yescharacteristic
175C3⋊#95—51no—
176C3⋊#95—52no—
177C3⋊#95C2×D511yescharacteristic
178C3⋊#95C2×D512yes—
179C23×D5C22×D311yescharacteristic
180C22×C4×C5—31no—
181C22×C4×C5—31no—
182C22×C4×C5—32no—
183C22×C4×C5C22×D311yescharacteristic
184C22×C4×C5C22×D312yes—
185C22×Dic5—31no—
186C22×Dic5—31no—
187C22×Dic5—32no—
188C22×Dic5C22×D312yes—
189C22×Dic5C22×D311yescharacteristic
190C2×C4×D5—24no—
191C2×C4×D5—34no—
192C2×C4×D5—38no—
193C2×C4×D5—34no—
194C2×C4×D5—62no—
195C2×C4×D5—62no—
196C2×C4×D5C4×D314yes—
197C42×C5—34no—
198C42×C5—38no—
199#685—38no—
200#685C4×D318yes—
201#683—38no—
202#683—38no—
203C4×Dic5—24no—
204C4×Dic5—34no—
205C4×Dic5—34no—
206C4×Dic5—34no—
207C4×Dic5—38no—
208C4×Dic5—64no—
209C4×Dic5—64no—
210C4×Dic5—64no—
211C2×#117—152no—
212C22×C42—151no—
213C4×C4⋊C4—151no—
214C4×C4⋊C4—152no—
215C4×C4⋊C4—151no—
216C4×C22⋊C4—51no—
217C4×C22⋊C4—152no—
218C4×C22⋊C4—151no—
219#376—31no—
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×C3×D5—22no—
228C2×C3×D5—22no—
229C2×C3×D5—24no—
230C2×C3×D5—24no—
231C2×C3×D5C2×C4214yes—
232C3×C4×C5—22no—
233C3×C4×C5—24no—
234Dic15—24no—
235Dic15C2×C4214yes—
236Dic15#11714yescomplemented
237C3×Dic5—24no—
238C3×Dic5#11714yescomplemented
239C5×Dic3—22no—
240C5×Dic3—24no—
241C5×Dic3C2×C4214yes—
242C24×C3—51no—
243C22×C3×C4—51no—
244C22×C3×C4—52no—
245C22×C3×C4—54no—
246C22×C3×C4—104no—
247C22×C3×C4C22×D511yescharacteristic
248C22×C3×C4C22×D512yes—
249C22×Dic3—51no—
250C22×Dic3—51no—
251C22×Dic3—58no—
252C22×Dic3—54no—
253C22×Dic3—52no—
254C22×Dic3—54no—
255C22×Dic3—102no—
256C22×Dic3—102no—
257C22×Dic3C22×D511yescharacteristic
258C22×Dic3C22×D512yes—
259C22×Dic3C22×D511yescharacteristic
260C3×C22⋊C4—58no—
261C3×C42—104no—
262#217—58no—
263Dic3⋊C4—58no—
264Dic3⋊C4—58no—
265C4×Dic3—54no—
266C4×Dic3—54no—
267C4×Dic3—54no—
268C4×Dic3—58no—
269C4×Dic3—104no—
270C4×Dic3—104no—
271C4×Dic3—104no—
272C4×Dic3C4×D514yes—
273C4×Dic3C4×D518yescomplemented
274C23×C5C23×D311yescharacteristic
275C22×D5—22no—
276C22×D5—21no—
277C22×D5—21no—
278C22×D5C2×C4×D314yes—
279C22×D5C2×C4×D312yes—
280C2×C4×C5—22no—
281C2×C4×C5—22no—
282C2×C4×C5—22no—
283C2×C4×C5—32no—
284C2×C4×C5—34no—
285C2×C4×C5—32no—
286C2×C4×C5—34no—
287C2×C4×C5—62no—
288C2×C4×C5—62no—
289C2×C4×C5—61no—
290C2×C4×C5—61no—
291C2×C4×C5C2×C4×D312yes—
292C2×C4×C5C2×C4×D314yes—
293C2×Dic5—22no—
294C2×Dic5—22no—
295C2×Dic5—32no—
296C2×Dic5—32no—
297C2×Dic5—34no—
298C2×Dic5—32no—
299C2×Dic5—32no—
300C2×Dic5—34no—
301C2×Dic5—62no—
302C2×Dic5—62no—
303C2×Dic5C2×C4×D314yes—
304C2×Dic5C2×C4×D312yes—
305C2×Dic5#23714yes—
306C4×D5—28no—
307C4×D5—316no—
308C4×D5—68no—
309C23×C4—51no—
310C23×C4—151no—
311C23×C4—151no—
312#117—1516no—
313C2×C4⋊C4—152no—
314C2×C4⋊C4—152no—
315C2×C22⋊C4—52no—
316C2×C22⋊C4—152no—
317C2×C42—32no—
318C2×C42—31no—
319C2×C42—52no—
320C2×C42—158no—
321C2×C42—152no—
322C2×C42—151no—
323C2×C42—151no—
324C2×C42—151no—
325C2×C42—152no—
326C2×C42—152no—
327C2×C42—152no—
328#95—32no—
329#95—31no—
330#95—51no—
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—
339C3×D5—24no—
340C23×C3—54no—
341C23×C3—52no—
342C23×C3—101no—
343C23×C3—101no—
344C23×C3—102no—
345C23×C3C23×D511yescharacteristic
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—52no—
350C2×C3×C4—54no—
351C2×C3×C4—54no—
352C2×C3×C4—108no—
353C2×C3×C4—102no—
354C2×C3×C4—102no—
355C2×C3×C4C2×C4×D512yes—
356C2×C3×C4C2×C4×D514yes—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—52no—
362C2×Dic3—52no—
363C2×Dic3—54no—
364C2×Dic3—52no—
365C2×Dic3—52no—
366C2×Dic3—516no—
367C2×Dic3—54no—
368C2×Dic3—108no—
369C2×Dic3—102no—
370C2×Dic3—102no—
371C2×Dic3C2×C4×D512yes—
372C2×Dic3C2×C4×D514yes—
373C2×Dic3C2×C4×D512yes—
374C2×Dic3C2×C4×D514yes—
375C22×C5C22×C4×D311yescharacteristic
376C22×C5C22×C4×D312yes—
377C22×C5C2×#23712yes—
378C22×C5D3×#4111yescharacteristic
379C22×C5D3×#4111yescharacteristic
380C2×D5—22no—
381C2×D5—22no—
382C2×D5—24no—
383C2×D5—24no—
384C2×D5C42×D314yes—
385C4×C5—22no—
386C4×C5—24no—
387C4×C5—34no—
388C4×C5—62no—
389C4×C5—64no—
390Dic5—24no—
391Dic5—34no—
392Dic5—34no—
393Dic5—64no—
394Dic5#87714yescomplemented
395C24—51no—
396C22×C4—31no—
397C22×C4—31no—
398C22×C4—32no—
399C22×C4—51no—
400C22×C4—52no—
401C22×C4—54no—
402C22×C4—104no—
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—158no—
414C4⋊C4—158no—
415C22⋊C4—58no—
416C22⋊C4—158no—
417C42—34no—
418C42—38no—
419C42—104no—
420C42—154no—
421C42—154no—
422C42—158no—
423C42—154no—
424C42—304no—
425C42—304no—
426C42—304no—
427C3×C5C4×#11711yescharacteristic, complemented, Hall
428C22×C3—54no—
429C22×C3—102no—
430C22×C3—102no—
431C22×C3—104no—
432C22×C3—104no—
433C22×C3C22×C4×D511yescharacteristic
434C22×C3C22×C4×D512yes—
435C22×C3D5×#4112yes—
436C22×C3D5×#4111yescharacteristic
437C22×C3D5×#4111yescharacteristic
438C3×C4—22no—
439C3×C4—24no—
440C3×C4—54no—
441C3×C4—104no—
442Dic3—22no—
443Dic3—24no—
444Dic3—54no—
445Dic3—54no—
446Dic3—104no—
447Dic3C42×D514yes—
448C2×C5C2×C42×D311yescharacteristic
449C2×C5C2×#87711yescharacteristic
450C2×C5D3×#11711yescharacteristic
451C2×C5C4×#23712yes—
452C2×C5C4×#23712yes—
453D5—24no—
454C23—54no—
455C23—52no—
456C23—102no—
457C23—101no—
458C23—101no—
459C23C22×D3×D511yescharacteristic
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—32no—
464C2×C4—34no—
465C2×C4—32no—
466C2×C4—34no—
467C2×C4—52no—
468C2×C4—54no—
469C2×C4—54no—
470C2×C4—62no—
471C2×C4—61no—
472C2×C4—62no—
473C2×C4—61no—
474C2×C4—108no—
475C2×C4—102no—
476C2×C4—102no—
477C2×C4—1516no—
478C2×C4—152no—
479C2×C4—152no—
480C2×C4—154no—
481C2×C4—152no—
482C2×C4—152no—
483C2×C4—154no—
484C2×C4—308no—
485C2×C4—302no—
486C2×C4—302no—
487C2×C4C4×D3×D512yes—
488C2×C4C4×D3×D514yes—
489C2×C3—104no—
490C2×C3C2×C42×D511yescharacteristic
491C2×C3D5×#11711yescharacteristic
492C2×C3D5×#11711yescharacteristic
493C2×C3#6585612yes—
494C2×C3#6585612yes—
495C5C4×#87711yescharacteristic, complemented, Sylow
496C22—54no—
497C22—102no—
498C22—102no—
499C22—104no—
500C22—104no—
501C22C2×C4×D3×D511yescharacteristic
502C22C2×C4×D3×D512yes—
503C22D5×#23712yes—
504C22#9202411yescharacteristic
505C22#9203411yescharacteristic
506C4—22no—
507C4—24no—
508C4—34no—
509C4—54no—
510C4—62no—
511C4—64no—
512C4—104no—
513C4—154no—
514C4—154no—
515C4—304no—
516C3#1060511311yescharacteristic, complemented, Sylow
517C2—104no—
518C2C42×D3×D511yescharacteristic
519C2D5×#87711yescharacteristic
520C2#1175281812yes—
521C2#1175339812yes—
522C2#1175383511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC2×C3×C5C22×C42
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
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. #11750750C2semidirect
4. C5×#4648C2semidirect
8. #11748663C2semidirect
9. #11748643C2semidirect
10. #11748640C2semidirect
11. C4×Dic3×Dic5C2semidirect
30. #91393C4semidirect
31. C4×D5×Dic3C4semidirect
68. #6712C2×C4semidirect
72. C4×C5×Dic3C2×C4semidirect
75. #6669C2×C4semidirect
81. Dic3×Dic5C2×C4semidirect
92. #4648D5semidirect
153. D5×Dic3C42semidirect
236. Dic15#117semidirect
238. C3×Dic5#117semidirect
273. C4×Dic3C4×D5semidirect
394. Dic5#877semidirect
427. C3×C5C4×#117semidirect
495. C5C4×#877semidirect
516. C3#10605113semidirect

Maximal subgroups

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

subgroupindex
C2×#913932
C2×C4×D5×Dic32
#117507502
C5×#46482
C3×#649552
#117488842
#117487022
#117486632
#117486432
#117486402
C4×Dic3×Dic52
#106051133
C4×#8775