Finite Group Databasebeta

← #14319926

Subgroups — #14319926

Order 1920.

2176 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
1C23×D5×Dic3C211yesmaximal, characteristic
2C2×#91766C211yesmaximal, characteristic, complemented
3C2×#91532C211yesmaximal, characteristic, complemented
4C5×#4943C211yesmaximal, characteristic, complemented
5C3×#65244C211yesmaximal, characteristic
6#11749488C211yesmaximal, characteristic
7#11749472C211yesmaximal, characteristic, complemented
8#11748885C214yesmaximal, complemented
9#11748884C214yesmaximal, complemented
10#10605781—31nomaximal, Hall
11C24×C3×D5C2211yescharacteristic
12C23×Dic15C2211yescharacteristic
13C23×C5×Dic3C2211yescharacteristic
14C22×D5×Dic3—24no—
15C22×D5×Dic3—24no—
16C22×D5×Dic3C418yescomplemented
17C22×D5×Dic3C2212yes—
18C22×D5×Dic3C2212yes—
19C2×C3×C5×C22⋊C4C2211yescharacteristic
20C2×#6719C2211yescharacteristic
21C2×#6712C2212yescomplemented
22C2×C4×Dic15C2212yescomplemented
23#91766—24no—
24C2×C5×#217C2211yescharacteristic
25C2×C3×C22⋊Dic5C2211yescharacteristic
26C2×C3×#685C2214yes—
27C2×#6669C2212yescomplemented
28C2×#6665C2214yes—
29#91532—24no—
30C2×Dic3×Dic5C2212yescomplemented
31C5×C3⋊#95C2214yescomplemented
32#90994C2214yescomplemented
33#73817—51nomaximal, Hall
34C23×C4×D5—31no—
35C2×#4023—31no—
36C2×#4023—31no—
37C5×#381—31no—
38#65500—31no—
39#65244—31no—
40#65244D311yescharacteristic
41#64956—34no—
42#64955—34no—
43C24×C3×C5C2311yescharacteristic
44C23×C3×D5—22no—
45C23×C3×D5—22no—
46C23×C3×D5—28no—
47C23×C3×D5C2×C414yes—
48C23×C3×D5C2312yes—
49C22×C3×C4×C5C2312yes—
50C22×Dic15C2×C414yes—
51C22×Dic15D414yes—
52C22×Dic15D414yes—
53C22×Dic15C2312yes—
54C22×Dic15C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×C5×Dic3—22no—
57C22×C5×Dic3—22no—
58C22×C5×Dic3C2×C414yes—
59C22×C5×Dic3C2312yes—
60C22×C5×Dic3C2312yes—
61C22×C3×Dic5C2312yes—
62C2×D5×Dic3—232no—
63C2×D5×Dic3—24no—
64C2×D5×Dic3—24no—
65C2×D5×Dic3—24no—
66C2×D5×Dic3—24no—
67C2×D5×Dic3C2×C418yes—
68C2×D5×Dic3C2×C418yes—
69C3×C5×C22⋊C4—22no—
70#6719—22no—
71#6712—24no—
72C4×Dic15—24no—
73C5×#217—22no—
74C3×C22⋊Dic5—22no—
75C3×#685—28no—
76#6669—24no—
77#6665—28no—
78Dic3×Dic5—24no—
79C24×Dic3—51no—
80C2×#877—51no—
81C2×#877—51no—
82C3×#379—51no—
83#5247—51no—
84#4943—51no—
85#4943D511yescharacteristic, complemented
86#4942—54no—
87Dic3×C22⋊C4—54no—
88C24×D5C2×D311yescharacteristic
89C23×C4×C5—31no—
90C23×Dic5—31no—
91C22×C4×D5—38no—
92C22×C4×D5—32no—
93C22×C4×D5—32no—
94C22×C4×D5—64no—
95C22×C4×D5—64no—
96C2×C5×C22⋊C4—31no—
97C2×C5×C22⋊C4C2×D311yescharacteristic
98C2×C22⋊Dic5—31no—
99C2×C22⋊Dic5C2×D311yescharacteristic
100C2×#685—34no—
101C2×#685C2×D314yes—
102C2×#683—32no—
103C2×#683—32no—
104C2×C4×Dic5—32no—
105C2×C4×Dic5—32no—
106#4023—64no—
107#4023—64no—
108C5×#95—34no—
109#3963—34no—
110#2280—151noSylow
111C23×C3×C5—24no—
112C23×C3×C5C22×C412yes—
113C23×C3×C5C2×D412yes—
114C23×C3×C5C2×D412yes—
115C23×C3×C5C2411yescharacteristic
116C22×C3×D5—216no—
117C22×C3×D5—216no—
118C22×C3×D5—28no—
119C22×C3×D5—22no—
120C22×C3×D5—22no—
121C22×C3×D5—24no—
122C22×C3×D5—216no—
123C22×C3×D5C22×C414yes—
124C22×C3×D5#4118yes—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—24no—
127C2×Dic15—22no—
128C2×Dic15—24no—
129C2×Dic15C22⋊C4116yescomplemented
130C2×Dic15C22×C412yes—
131C2×Dic15C22×C412yes—
132C2×Dic15C2×D412yes—
133C2×Dic15C2×D412yes—
134C2×Dic15C2×D412yes—
135C2×Dic15C2×D412yes—
136C2×C5×Dic3—28no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—24no—
141C2×C5×Dic3C22×C414yes—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—24no—
144D5×Dic3—216no—
145D5×Dic3—216no—
146C25×C3—51no—
147C23×Dic3—51no—
148C23×Dic3—58no—
149C23×Dic3—52no—
150C23×Dic3—52no—
151C23×Dic3—104no—
152C23×Dic3—104no—
153C23×Dic3C2×D511yescharacteristic
154C2×C3×C22⋊C4—51no—
155C2×C3×C22⋊C4—54no—
156C2×C3×C22⋊C4C2×D511yescharacteristic
157C2×#217—51no—
158C2×#217—54no—
159C2×#217C2×D511yescharacteristic
160C2×Dic3⋊C4—52no—
161C2×Dic3⋊C4—52no—
162C2×C4×Dic3—52no—
163C2×C4×Dic3—52no—
164#877—104no—
165#877—104no—
166C3⋊#95—54no—
167C3⋊#95C2×D514yescomplemented
168C24×C5C22×D311yescharacteristic
169C23×D5—22no—
170C23×D5—22no—
171C23×D5—28no—
172C23×D5C4×D314yes—
173C23×D5C22×D312yes—
174C22×C4×C5—34no—
175C22×C4×C5—32no—
176C22×C4×C5—32no—
177C22×C4×C5—62no—
178C22×C4×C5—62no—
179C22×C4×C5C22×D312yes—
180C22×Dic5—34no—
181C22×Dic5—34no—
182C22×Dic5—34no—
183C22×Dic5—31no—
184C22×Dic5—31no—
185C22×Dic5—32no—
186C22×Dic5C22×D312yes—
187C2×C4×D5—38no—
188C2×C4×D5—38no—
189C2×C4×D5—632no—
190C2×C4×D5—64no—
191C2×C4×D5—64no—
192C2×C4×D5—64no—
193C2×C4×D5—64no—
194C5×C22⋊C4—22no—
195C5×C22⋊C4—62no—
196C22⋊Dic5—22no—
197C22⋊Dic5—62no—
198#685—28no—
199#685—68no—
200#683—64no—
201#683—64no—
202C4×Dic5—64no—
203C4×Dic5—64no—
204C24×C4—151no—
205C2×#117—151no—
206C2×#117—151no—
207#381—31no—
208#381—151no—
209#380—154no—
210#379—51no—
211#379—151no—
212C4×C22⋊C4—154no—
213C22×C3×C5—24no—
214C22×C3×C5—24no—
215C22×C3×C5—24no—
216C22×C3×C5C2×C22⋊C414yes—
217C22×C3×C5C23×C411yescharacteristic
218C22×C3×C5C22×D411yescharacteristic
219C22×C3×C5C22×D411yescharacteristic
220C22×C3×C5C2×#4114yes—
221C2×C3×D5—232no—
222C2×C3×D5—24no—
223C2×C3×D5—24no—
224C2×C3×D5—28no—
225C2×C3×D5—28no—
226C2×C3×D5#11718yescomplemented
227C3×C4×C5—42no—
228Dic15—42no—
229Dic15C2×C22⋊C414yes—
230Dic15C2×C22⋊C414yes—
231C3×Dic5—42no—
232C5×Dic3—24no—
233C5×Dic3—42no—
234C24×C3—52no—
235C24×C3—54no—
236C24×C3—108no—
237C24×C3—102no—
238C24×C3—102no—
239C24×C3C22×D511yescharacteristic
240C22×C3×C4—52no—
241C22×C3×C4C22×D512yes—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—54no—
245C22×Dic3—54no—
246C22×Dic3—54no—
247C22×Dic3—51no—
248C22×Dic3—51no—
249C22×Dic3—58no—
250C22×Dic3—58no—
251C22×Dic3—52no—
252C22×Dic3—104no—
253C22×Dic3—104no—
254C22×Dic3—104no—
255C22×Dic3—104no—
256C22×Dic3—1032no—
257C22×Dic3C4×D514yes—
258C22×Dic3C22×D512yes—
259C22×Dic3C22×D512yes—
260C3×C22⋊C4—22no—
261C3×C22⋊C4—108no—
262C3×C22⋊C4—102no—
263#217—22no—
264#217—108no—
265#217—102no—
266Dic3⋊C4—104no—
267Dic3⋊C4—104no—
268C4×Dic3—104no—
269C4×Dic3—104no—
270C23×C5—24no—
271C23×C5C2×C4×D312yes—
272C23×C5D3×D412yes—
273C23×C5D3×D412yes—
274C23×C5C23×D311yescharacteristic
275C22×D5—216no—
276C22×D5—216no—
277C22×D5—28no—
278C22×D5—22no—
279C22×D5—22no—
280C22×D5—24no—
281C22×D5—216no—
282C22×D5C2×C4×D314yes—
283C22×D5#23718yes—
284C2×C4×C5—22no—
285C2×C4×C5—24no—
286C2×C4×C5—34no—
287C2×C4×C5—68no—
288C2×C4×C5—62no—
289C2×C4×C5—62no—
290C2×C4×C5—62no—
291C2×C4×C5—64no—
292C2×Dic5—22no—
293C2×Dic5—24no—
294C2×Dic5—316no—
295C2×Dic5—32no—
296C2×Dic5—32no—
297C2×Dic5—32no—
298C2×Dic5—32no—
299C2×Dic5—32no—
300C2×Dic5—32no—
301C2×Dic5—62no—
302C2×Dic5—64no—
303C4×D5—616no—
304C4×D5—616no—
305C25—51no—
306C23×C4—31no—
307C23×C4—152no—
308C23×C4—152no—
309C23×C4—158no—
310C23×C4—151no—
311C23×C4—304no—
312C23×C4—304no—
313#117—304no—
314#117—304no—
315C2×C4⋊C4—152no—
316C2×C4⋊C4—152no—
317C2×C22⋊C4—31no—
318C2×C22⋊C4—51no—
319C2×C22⋊C4—54no—
320C2×C22⋊C4—154no—
321C2×C22⋊C4—151no—
322C2×C22⋊C4D3×D511yescharacteristic
323C2×C42—152no—
324C2×C42—152no—
325#95—34no—
326#95—154no—
327C2×C3×C5—24no—
328C2×C3×C5C22×C22⋊C411yescharacteristic
329C2×C3×C5C2×#11712yes—
330C2×C3×C5#52512yes—
331C2×C3×C5#52512yes—
332C3×D5—28no—
333C23×C3—24no—
334C23×C3—54no—
335C23×C3—58no—
336C23×C3—1016no—
337C23×C3—1016no—
338C23×C3—1016no—
339C23×C3—102no—
340C23×C3—102no—
341C23×C3—104no—
342C23×C3—108no—
343C23×C3C2×C4×D512yes—
344C23×C3D4×D512yes—
345C23×C3D4×D512yes—
346C23×C3C23×D511yescharacteristic
347C2×C3×C4—22no—
348C2×C3×C4—24no—
349C2×C3×C4—102no—
350C2×C3×C4—104no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—28no—
354C2×Dic3—22no—
355C2×Dic3—24no—
356C2×Dic3—52no—
357C2×Dic3—52no—
358C2×Dic3—52no—
359C2×Dic3—52no—
360C2×Dic3—52no—
361C2×Dic3—52no—
362C2×Dic3—516no—
363C2×Dic3—1016no—
364C2×Dic3—1016no—
365C2×Dic3—102no—
366C2×Dic3—104no—
367C2×Dic3C2×C4×D514yes—
368C22×C5—24no—
369C22×C5—24no—
370C22×C5—24no—
371C22×C5D3×C22⋊C414yes—
372C22×C5C22×C4×D311yescharacteristic
373C22×C5C2×D3×D411yescharacteristic
374C22×C5C2×D3×D411yescharacteristic
375C22×C5C2×#23714yes—
376C2×D5—232no—
377C2×D5—24no—
378C2×D5—24no—
379C2×D5—28no—
380C2×D5—28no—
381C2×D5#87718yescomplemented
382C4×C5—42no—
383C4×C5—64no—
384C4×C5—122no—
385Dic5—34no—
386Dic5—34no—
387Dic5—42no—
388Dic5—122no—
389C24—52no—
390C24—54no—
391C24—108no—
392C24—102no—
393C24—102no—
394C24C2×D3×D511yescharacteristic
395C22×C4—34no—
396C22×C4—32no—
397C22×C4—32no—
398C22×C4—52no—
399C22×C4—62no—
400C22×C4—62no—
401C22×C4—158no—
402C22×C4—158no—
403C22×C4—154no—
404C22×C4—154no—
405C22×C4—154no—
406C22×C4—151no—
407C22×C4—151no—
408C22×C4—152no—
409C22×C4—3032no—
410C22×C4—304no—
411C22×C4—304no—
412C22×C4—304no—
413C22×C4—304no—
414C22×C4C2×D3×D512yes—
415C4⋊C4—304no—
416C4⋊C4—304no—
417C22⋊C4—22no—
418C22⋊C4—62no—
419C22⋊C4—108no—
420C22⋊C4—102no—
421C22⋊C4—308no—
422C22⋊C4—302no—
423C42—304no—
424C42—304no—
425C3×C5#228011yescharacteristic, complemented, Hall
426C22×C3—24no—
427C22×C3—24no—
428C22×C3—24no—
429C22×C3—58no—
430C22×C3—1032no—
431C22×C3—104no—
432C22×C3—104no—
433C22×C3—108no—
434C22×C3—108no—
435C22×C3D5×C22⋊C414yes—
436C22×C3C22×C4×D511yescharacteristic
437C22×C3C2×D4×D511yescharacteristic
438C22×C3C2×D4×D511yescharacteristic
439C22×C3D5×#4114yes—
440C3×C4—42no—
441C3×C4—202no—
442Dic3—24no—
443Dic3—42no—
444Dic3—54no—
445Dic3—54no—
446Dic3—202no—
447C2×C5—24no—
448C2×C5C2×#87712yes—
449C2×C5C2×D3×C22⋊C411yescharacteristic
450C2×C5#558612yes—
451C2×C5#558612yes—
452D5—28no—
453C23—24no—
454C23—54no—
455C23—58no—
456C23—1016no—
457C23—1016no—
458C23—1016no—
459C23—108no—
460C23—102no—
461C23—104no—
462C23—102no—
463C23C4×D3×D512yes—
464C23#677712yes—
465C23#679012yes—
466C23C22×D3×D511yescharacteristic
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—34no—
470C2×C4—68no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—64no—
475C2×C4—102no—
476C2×C4—104no—
477C2×C4—1516no—
478C2×C4—152no—
479C2×C4—152no—
480C2×C4—152no—
481C2×C4—152no—
482C2×C4—152no—
483C2×C4—152no—
484C2×C4—3016no—
485C2×C4—3016no—
486C2×C4—304no—
487C2×C4—302no—
488C2×C3—24no—
489C2×C3—108no—
490C2×C3C2×D5×C22⋊C411yescharacteristic
491C2×C3D5×#11712yes—
492C2×C3#6599012yes—
493C2×C3#6599012yes—
494C5#7381711yescharacteristic, complemented, Sylow
495C22—24no—
496C22—24no—
497C22—24no—
498C22—58no—
499C22—1032no—
500C22—108no—
501C22—104no—
502C22—104no—
503C22—108no—
504C22#9147314yes—
505C22C2×C4×D3×D511yescharacteristic
506C22C2×#677711yescharacteristic
507C22D5×#23714yes—
508C22C2×#679011yescharacteristic
509C4—42no—
510C4—64no—
511C4—122no—
512C4—154no—
513C4—154no—
514C4—202no—
515C4—602no—
516C3#1060578111yescharacteristic, complemented, Sylow
517C2—24no—
518C2—108no—
519C2D5×#87712yes—
520C2#1175288012yes—
521C2C2×#9147311yescharacteristic
522C2#1175481512yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2280
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91766C2semidirect
3. C2×#91532C2semidirect
4. C5×#4943C2semidirect
7. #11749472C2semidirect
8. #11748885C2semidirect
9. #11748884C2semidirect
16. C22×D5×Dic3C4semidirect
21. C2×#6712C22semidirect
22. C2×C4×Dic15C22semidirect
27. C2×#6669C22semidirect
30. C2×Dic3×Dic5C22semidirect
31. C5×C3⋊#95C22semidirect
32. #90994C22semidirect
85. #4943D5semidirect
129. C2×Dic15C22⋊C4semidirect
167. C3⋊#95C2×D5semidirect
226. C2×C3×D5#117semidirect
381. C2×D5#877semidirect
425. C3×C5#2280semidirect
494. C5#73817semidirect
516. C3#10605781semidirect

Maximal subgroups

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

subgroupindex
C23×D5×Dic32
C2×#917662
C2×#915322
C5×#49432
C3×#652442
#117494882
#117494722
#117488852
#117488842
#106057813
#738175