Finite Group Databasebeta

← #14323197

Subgroups — #14323197

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2#11751313C211yesmaximal, characteristic, complemented
3C5×#5211C211yesmaximal, characteristic, complemented
4#11749489C212yesmaximal
5#11749486C212yesmaximal, complemented
6#11748772C212yesmaximal, complemented
7#11748738C211yesmaximal, characteristic, complemented
8#11748737C211yesmaximal, characteristic, complemented
9#11748680C212yesmaximal, complemented
10#11748638C211yesmaximal, characteristic, complemented
11#11748635C211yesmaximal, characteristic, complemented
12#10605786—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C2×#6719C2212yes—
17C2×C4⋊Dic15C2212yes—
18C2×C5×#217C2212yes—
19C2×C3×C22⋊Dic5C2211yescharacteristic
20C3×C4×C22⋊D5C418yescomplemented
21C2×C3×#685C2211yescharacteristic
22C2×C3×#683C2211yescharacteristic
23C2×C3×C4×Dic5C2211yescharacteristic
24C2×#6668C2212yes—
25C2×#6668C2212yes—
26C2×#6665C2212yes—
27C2×#6665C2212yes—
28C2×Dic3×Dic5C2212yes—
29C2×Dic3×Dic5C2212yes—
30#91115C2211yescharacteristic
31#91115C2211yescharacteristic
32C5×C3⋊#95C2211yescharacteristic
33C5×C3⋊#95C2211yescharacteristic
34C5×C3⋊#95C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#82325—51nomaximal, Hall
38C2×C4×C22⋊D5D311yescharacteristic
39C5×#381—31no—
40#65501—31no—
41#65246—32no—
42#65234—32no—
43#64959—32no—
44#64956—31no—
45#64953—31no—
46#64938—31no—
47#64937—31no—
48#64936—32no—
49C24×C3×C5C2311yescharacteristic
50C23×C3×D5C2311yescharacteristic
51C22×C3×C4×C5—42no—
52C22×C3×C4×C5C2×C414yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2312yes—
57C22×C5×Dic3C2312yes—
58C22×C5×Dic3C2312yes—
59C2×C3×C22⋊D5—24no—
60C2×C3×C22⋊D5C2×C414yes—
61C22×C3×Dic5C2311yescharacteristic
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C2×C3×C4×D5—42no—
65C2×C3×C4×D5C2×C414yes—
66#6719—42no—
67C4⋊Dic15—42no—
68C5×#217—42no—
69C3×C22⋊Dic5C2×C414yes—
70C3×#685C2×C414yes—
71C3×#683C2×C414yes—
72C3×C4×Dic5C2×C414yes—
73#6668—24no—
74#6668—42no—
75#6665—42no—
76#6665—42no—
77Dic3×Dic5—24no—
78Dic3×Dic5—42no—
79C2×C3×C4×D4—51no—
80#5221—52no—
81#5212—51no—
82#5212—51no—
83#5211—51no—
84#5211D511yescharacteristic, complemented
85#4984—52no—
86#4951—52no—
87#4951—52no—
88C4×C4⋊Dic3—51no—
89#4932—51no—
90C23×C4×C5C2×D311yescharacteristic
91C22×C22⋊D5C2×D311yescharacteristic
92C22×C4×D5C2×D311yescharacteristic
93C2×C5×C22⋊C4—32no—
94C2×C22⋊Dic5—32no—
95C2×C22⋊Dic5C2×D311yescharacteristic
96C4×C22⋊D5Dic318yescomplemented
97C2×#685—32no—
98C2×#685—32no—
99C2×#685C2×D311yescharacteristic
100C2×C4⋊Dic5—32no—
101C2×#683—32no—
102C2×#683—32no—
103C2×#683C2×D311yescharacteristic
104C2×C4×Dic5—32no—
105C2×C4×Dic5—32no—
106C2×C4×Dic5C2×D311yescharacteristic
107C5×#95—32no—
108C5×#95—31no—
109C5×#95—31no—
110#3963—31no—
111#3963—31no—
112#3963—32no—
113#3963—32no—
114#2319—151noSylow
115C23×C3×C5—22no—
116C23×C3×C5—22no—
117C23×C3×C5—21no—
118C23×C3×C5—21no—
119C23×C3×C5C22×C412yes—
120C23×C3×C5C2411yescharacteristic
121C22×C3×D5—22no—
122C22×C3×D5—21no—
123C22×C3×D5—22no—
124C22×C3×D5—21no—
125C22×C3×D5C22×C412yes—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—44no—
129C2×C3×C4×C5C22×C412yes—
130C2×C3×C4×C5C22×C412yes—
131C2×Dic15—22no—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—22no—
143C3×C22⋊D5—28no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5C22×C412yes—
148C2×C3×Dic5C22×C412yes—
149C2×C3×Dic5C22×C412yes—
150C2×C3×Dic5#4114yes—
151C3×C4×D5—44no—
152C22×C3×D4—51no—
153C23×C3×C4—51no—
154C23×C3×C4C2×D511yescharacteristic
155C3×C4×D4—58no—
156C2×C3×C4⋊C4—51no—
157C2×C3×C22⋊C4—51no—
158C2×C3×C22⋊C4—51no—
159C2×C3×C42—51no—
160C2×#217—52no—
161C2×#217—52no—
162C2×#217—52no—
163C2×#217C2×D512yes—
164C2×C4⋊Dic3—52no—
165C2×C4⋊Dic3—52no—
166C2×C4⋊Dic3—52no—
167C2×C4×Dic3—52no—
168C2×C4×Dic3—52no—
169C3⋊#95—51no—
170C3⋊#95—51no—
171C3⋊#95—52no—
172C3⋊#95—52no—
173C3⋊#95C2×D511yescharacteristic
174C3⋊#95C2×D511yescharacteristic
175C3⋊#95C2×D512yes—
176C24×C5C22×D311yescharacteristic
177C23×D5C22×D311yescharacteristic
178C22×C4×C5—32no—
179C22×C4×C5—32no—
180C22×C4×C5—42no—
181C22×C4×C5C2×Dic314yes—
182C22×C4×C5C22×D311yescharacteristic
183C22×C4×C5C22×D311yescharacteristic
184C2×C22⋊D5—24no—
185C2×C22⋊D5C2×Dic314yes—
186C22×Dic5—32no—
187C22×Dic5—32no—
188C22×Dic5C22×D311yescharacteristic
189C22×Dic5C22×D311yescharacteristic
190C22×Dic5C22×D311yescharacteristic
191C2×C4×D5—42no—
192C2×C4×D5C2×Dic314yes—
193C5×C22⋊C4—122no—
194C22⋊Dic5—122no—
195C22⋊Dic5C2×Dic314yes—
196#685—122no—
197#685—122no—
198#685C2×Dic314yes—
199C4⋊Dic5—122no—
200#683—64no—
201#683—122no—
202#683C2×Dic314yes—
203C4×Dic5—64no—
204C4×Dic5—122no—
205C4×Dic5C2×Dic314yes—
206C2×C4×D4—51no—
207#390—152no—
208#389—152no—
209#388—152no—
210#388—152no—
211#381—31no—
212#381—151no—
213#380—151no—
214#380—151no—
215C4×C4⋊C4—151no—
216#376—151no—
217C22×C3×C5—22no—
218C22×C3×C5—22no—
219C22×C3×C5—22no—
220C22×C3×C5—42no—
221C22×C3×C5—42no—
222C22×C3×C5C23×C411yescharacteristic
223C22×C3×C5C2×#4112yes—
224C22×C3×C5H(5,𝔽2)12yes—
225C22×C3×C5H(5,𝔽2)11yescharacteristic
226C22×C3×C52−1+411yescharacteristic
227C2×C3×D5—22no—
228C2×C3×D5—22no—
229C2×C3×D5—22no—
230C2×C3×D5—42no—
231C2×C3×D5—42no—
232C3×C4×C5—22no—
233C3×C4×C5—22no—
234Dic15—42no—
235Dic15—42no—
236C3×Dic5—22no—
237C3×Dic5—22no—
238C3×Dic5#11714yes—
239C5×Dic3—42no—
240C5×Dic3—42no—
241C24×C3—51no—
242C24×C3C22×D511yescharacteristic
243C2×C3×D4—54no—
244C2×C3×D4—104no—
245C22×C3×C4—42no—
246C22×C3×C4—51no—
247C22×C3×C4—51no—
248C22×C3×C4—51no—
249C22×C3×C4—54no—
250C22×C3×C4—202no—
251C22×C3×C4C4×D514yes—
252C22×C3×C4C22×D511yescharacteristic
253C22×C3×C4C22×D511yescharacteristic
254C22×Dic3—52no—
255C22×Dic3—52no—
256C22×Dic3C22×D512yes—
257C22×Dic3C22×D512yes—
258C3×C4⋊C4—54no—
259C3×C22⋊C4—54no—
260C3×C22⋊C4—54no—
261C3×C42—54no—
262#217—42no—
263#217—202no—
264#217—202no—
265#217—202no—
266C4⋊Dic3—104no—
267C4⋊Dic3—202no—
268C4⋊Dic3—202no—
269C4×Dic3—104no—
270C4×Dic3—202no—
271C23×C5—22no—
272C23×C5—22no—
273C23×C5—21no—
274C23×C5—21no—
275C23×C5C22×Dic312yes—
276C23×C5C23×D311yescharacteristic
277C22×D5—22no—
278C22×D5—22no—
279C22×D5—21no—
280C22×D5—21no—
281C22×D5C22×Dic312yes—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—44no—
285C2×C4×C5—62no—
286C2×C4×C5—62no—
287C2×C4×C5—62no—
288C2×C4×C5—62no—
289C2×C4×C5—62no—
290C2×C4×C5—62no—
291C2×C4×C5C22×Dic312yes—
292C2×C4×C5C22×Dic312yes—
293C22⋊D5—28no—
294C2×Dic5—22no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—62no—
298C2×Dic5—62no—
299C2×Dic5—62no—
300C2×Dic5—62no—
301C2×Dic5—62no—
302C2×Dic5—62no—
303C2×Dic5#23514yes—
304C2×Dic5C22×Dic312yes—
305C2×Dic5C22×Dic312yes—
306C2×Dic5C22×Dic312yes—
307C4×D5—44no—
308C22×D4—51no—
309C23×C4—51no—
310C23×C4D3×D511yescharacteristic
311C4×D4—58no—
312C2×C4⋊C4—51no—
313C2×C4⋊C4—152no—
314C2×C4⋊C4—152no—
315C2×C4⋊C4—152no—
316C2×C22⋊C4—32no—
317C2×C22⋊C4—51no—
318C2×C22⋊C4—51no—
319C2×C22⋊C4—152no—
320C2×C22⋊C4—152no—
321C2×C22⋊C4—152no—
322C2×C42—51no—
323C2×C42—152no—
324C2×C42—152no—
325#95—31no—
326#95—31no—
327#95—32no—
328#95—152no—
329#95—152no—
330#95—151no—
331#95—151no—
332C2×C3×C5—42no—
333C2×C3×C5C2×#11711yescharacteristic
334C2×C3×C5#51811yescharacteristic
335C2×C3×C5#52011yescharacteristic
336C2×C3×C5#54012yes—
337C2×C3×C5#54212yes—
338C3×D5—42no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—52no—
344C23×C3—102no—
345C23×C3—102no—
346C23×C3—101no—
347C23×C3—101no—
348C23×C3C2×C4×D512yes—
349C23×C3C23×D511yescharacteristic
350C3×D4—108no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—44no—
354C2×C3×C4—52no—
355C2×C3×C4—54no—
356C2×C3×C4—52no—
357C2×C3×C4—52no—
358C2×C3×C4—102no—
359C2×C3×C4—101no—
360C2×C3×C4—101no—
361C2×C3×C4—204no—
362C2×C3×C4C2×C4×D512yes—
363C2×C3×C4C2×C4×D512yes—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—102no—
371C2×Dic3—102no—
372C2×Dic3—102no—
373C2×Dic3—102no—
374C2×Dic3—102no—
375C2×Dic3—102no—
376C22×C5—22no—
377C22×C5—22no—
378C22×C5—22no—
379C22×C5—42no—
380C22×C5—42no—
381C22×C5C2×#23512yes—
382C22×C5#100412yes—
383C22×C5#100911yescharacteristic
384C22×C5#101011yescharacteristic
385C22×C5C23×Dic311yescharacteristic
386C2×D5—22no—
387C2×D5—22no—
388C2×D5—22no—
389C2×D5—42no—
390C2×D5—42no—
391C4×C5—22no—
392C4×C5—22no—
393C4×C5—122no—
394C4×C5—122no—
395Dic5—22no—
396Dic5—22no—
397Dic5—122no—
398Dic5—122no—
399Dic5#92614yes—
400C24—51no—
401C24C2×D3×D511yescharacteristic
402C2×D4—54no—
403C2×D4—104no—
404C22×C4—32no—
405C22×C4—32no—
406C22×C4—42no—
407C22×C4—51no—
408C22×C4—51no—
409C22×C4—51no—
410C22×C4—54no—
411C22×C4—152no—
412C22×C4—152no—
413C22×C4—202no—
414C22×C4D5×Dic314yes—
415C22×C4C2×D3×D511yescharacteristic
416C22×C4C2×D3×D511yescharacteristic
417C4⋊C4—54no—
418C4⋊C4—304no—
419C4⋊C4—602no—
420C4⋊C4—602no—
421C22⋊C4—54no—
422C22⋊C4—54no—
423C22⋊C4—122no—
424C22⋊C4—602no—
425C22⋊C4—602no—
426C22⋊C4—602no—
427C42—54no—
428C42—304no—
429C42—602no—
430C3×C5#231911yescharacteristic, complemented, Hall
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—102no—
437C22×C3—102no—
438C22×C3—102no—
439C22×C3—202no—
440C22×C3—202no—
441C22×C3C22×C4×D511yescharacteristic
442C22×C3#414412yes—
443C22×C3D5×#4112yes—
444C22×C3#414911yescharacteristic
445C22×C3#415011yescharacteristic
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—54no—
449C3×C4—102no—
450C3×C4—102no—
451Dic3—42no—
452Dic3—42no—
453Dic3—202no—
454Dic3—202no—
455C2×C5—42no—
456C2×C5#556112yes—
457C2×C5#556212yes—
458C2×C5C2×#92611yescharacteristic
459C2×C5#579811yescharacteristic
460C2×C5#582711yescharacteristic
461D5—42no—
462C23—21no—
463C23—22no—
464C23—21no—
465C23—22no—
466C23—52no—
467C23—101no—
468C23—102no—
469C23—101no—
470C23—102no—
471C23C2×D5×Dic312yes—
472C23C22×D3×D511yescharacteristic
473D4—108no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—44no—
477C2×C4—54no—
478C2×C4—52no—
479C2×C4—52no—
480C2×C4—52no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—101no—
488C2×C4—101no—
489C2×C4—102no—
490C2×C4—204no—
491C2×C4—302no—
492C2×C4—302no—
493C2×C4—302no—
494C2×C4—302no—
495C2×C4—302no—
496C2×C4—302no—
497C2×C4C2×D5×Dic312yes—
498C2×C4C2×D5×Dic312yes—
499C2×C3—42no—
500C2×C3—202no—
501C2×C3#6582011yescharacteristic
502C2×C3D5×#11711yescharacteristic
503C2×C3#6585711yescharacteristic
504C2×C3#6599612yes—
505C2×C3#6599712yes—
506C5#8232511yescharacteristic, complemented, Sylow
507C22—22no—
508C22—22no—
509C22—22no—
510C22—42no—
511C22—42no—
512C22—102no—
513C22—102no—
514C22—102no—
515C22—202no—
516C22—202no—
517C22#9200111yescharacteristic
518C22D5×#23512yes—
519C22#9201911yescharacteristic
520C22C22×D5×Dic311yescharacteristic
521C22#9204912yes—
522C4—22no—
523C4—22no—
524C4—54no—
525C4—102no—
526C4—102no—
527C4—122no—
528C4—122no—
529C4—602no—
530C4—602no—
531C3#1060578611yescharacteristic, complemented, Sylow
532C2—42no—
533C2—202no—
534C2D5×#92611yescharacteristic
535C2#1175450911yescharacteristic
536C2#1175456612yes—
537C2#1175457112yes—
538C2#1175540611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2319
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #11751313C2semidirect
3. C5×#5211C2semidirect
5. #11749486C2semidirect
6. #11748772C2semidirect
7. #11748738C2semidirect
8. #11748737C2semidirect
9. #11748680C2semidirect
10. #11748638C2semidirect
11. #11748635C2semidirect
20. C3×C4×C22⋊D5C4semidirect
84. #5211D5semidirect
96. C4×C22⋊D5Dic3semidirect
430. C3×C5#2319semidirect
506. C5#82325semidirect
531. C3#10605786semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
#117513132
C5×#52112
#117494892
#117494862
#117487722
#117487382
#117487372
#117486802
#117486382
#117486352
#106057863
#823255