Finite Group Databasebeta

← #14297812

Subgroups — #14297812

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756281C211yesmaximal, characteristic
2C2×#91109C211yesmaximal, characteristic
3#11751219C211yesmaximal, characteristic, complemented
4C4×#6712C211yesmaximal, characteristic, complemented
5C2×#91089C211yesmaximal, characteristic
6C3×C5×#339C211yesmaximal, characteristic, complemented
7#11746353C211yesmaximal, characteristic, complemented
8#10599563—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C2×#6712—21no—
14C2×C4×Dic15C2211yescharacteristic
15C2×C4×Dic15C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17#91782C411yescharacteristic, complemented
18#91782C411yescharacteristic, complemented
19#91776C411yescharacteristic, complemented
20#91776C411yescharacteristic, complemented
21#91770—21no—
22#91770—21no—
23#91761—21no—
24C42×D15—21no—
25#91115—21no—
26#91109—22no—
27#91098—21no—
28#91098—21no—
29#91089—22no—
30#68770—51nomaximal, Hall
31#65856—31no—
32C2×#3957—31no—
33#65407—31no—
34C4×#683—31no—
35C2×#3937—31no—
36C5×#339D311yescharacteristic, complemented
37#64752—31no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×#1220—21no—
41C22×Dic15—21no—
42C22×Dic15D411yescharacteristic
43C22×Dic15D411yescharacteristic
44#6817—21no—
45#6817—21no—
46#6817D412yes—
47#6817Q812yes—
48C2×D60C2×C411yescharacteristic
49C2×C4×D15—21no—
50C2×C4×D15—21no—
51C2×C4×D15—21no—
52C2×Dic30C2×C411yescharacteristic
53C3×C5×M16—21no—
54C3×C5×M16—21no—
55C2×C3×C5×C8—21no—
56C3×C5×C4⋊C4C2×C411yescharacteristic
57C3×C5×C4⋊C4C2×C411yescharacteristic
58C3×C5×C22⋊C4—21no—
59C3×C42×C5—21no—
60C3×C42×C5—21no—
61C3×C42×C5—21no—
62#6714—21no—
63#6714—21no—
64#6712—24no—
65#6712—21no—
66#6712—21no—
67C4×Dic15—21no—
68C4×Dic15—21no—
69C4×Dic15—21no—
70C4×Dic15—21no—
71C4×Dic15C2×C411yescharacteristic
72C4×Dic15C2×C411yescharacteristic
73C4×Dic15D411yescharacteristic
74C4×Dic15D411yescharacteristic
75#6710—21no—
76#6710—21no—
77C2×C3⋊#168—21no—
78#5522—51no—
79C2×#825—51no—
80#5118—51no—
81C4×Dic3⋊C4—51no—
82C2×#805—51no—
83C3×#339D511yescharacteristic, complemented
84#4532—51no—
85C2×#709—31no—
86C2×C5×M16C2×D311yescharacteristic
87C5×#117C2×D311yescharacteristic
88C2×C42×C5C2×D311yescharacteristic
89C2×#683—61no—
90C2×C4×Dic5—31no—
91C2×C4×Dic5—31no—
92C2×#681—31no—
93#4039—31no—
94#4039—31no—
95#4033—31no—
96#4033—31no—
97#4027—61no—
98#4027—61no—
99#4018—61no—
100C42×D5—61no—
101#3963—61no—
102#3957—62no—
103#3946—61no—
104#3946—61no—
105#3937—62no—
106#1806—151noSylow
107C23×C3×C5C2×D411yescharacteristic
108C22×D15—21no—
109C2×C3×C4×C5—22no—
110C2×C3×C4×C5—21no—
111C2×C3×C4×C5—21no—
112C2×C3×C4×C5—41no—
113C2×C3×C4×C5—41no—
114C2×C3×C4×C5C22×C411yescharacteristic
115C2×C3×C4×C5C2×D411yescharacteristic
116C2×C3×C4×C5C2×D411yescharacteristic
117C2×C3×C4×C5C2×Q811yescharacteristic
118C2×C3×C4×C5#4111yescharacteristic
119C2×C3×C4×C5#4111yescharacteristic
120#1220—22no—
121#1220—22no—
122C2×Dic15—21no—
123C2×Dic15—22no—
124C2×Dic15—22no—
125C2×Dic15—41no—
126C2×Dic15—41no—
127C2×Dic15—41no—
128C2×Dic15C22⋊C411yescharacteristic
129C2×Dic15C22⋊C411yescharacteristic
130C2×Dic15C22⋊C411yescharacteristic
131C2×Dic15C22⋊C411yescharacteristic
132D60—21no—
133D60C4⋊C412yescomplemented
134C4×D15—22no—
135C4×D15—22no—
136C4×D15—42no—
137C4×D15—42no—
138Dic30—21no—
139Dic30C4⋊C412yescomplemented
140C3×C5×C8—41no—
141C3⋊#168—41no—
142C2×#235—51no—
143C2×C3×M16C2×D511yescharacteristic
144C3×#117C2×D511yescharacteristic
145C2×C3×C42C2×D511yescharacteristic
146C2×Dic3⋊C4—101no—
147C2×C4×Dic3—51no—
148C2×C4×Dic3—51no—
149C2×#208—51no—
150#893—51no—
151#893—51no—
152#887—51no—
153#887—51no—
154#67⋊C4—101no—
155#67⋊C4—101no—
156#872—101no—
157C42×D3—101no—
158C3⋊#95—101no—
159#825—102no—
160Dic3⋊C8—101no—
161Dic3⋊C8—101no—
162#805—102no—
163C22×C4×C5—21no—
164C22×C4×C5C22×D311yescharacteristic
165C2×C22⋊D5—61no—
166C22×Dic5—31no—
167C22×Dic5—31no—
168C22×Dic5—61no—
169#709—32no—
170#709—32no—
171#709—61no—
172#709—61no—
173C2×D20—31no—
174C2×C4×D5—61no—
175C2×C4×D5—61no—
176C2×C4×D5—61no—
177C2×Dic10—31no—
178C5×M16—21no—
179C5×M16—21no—
180C2×C5×C8—21no—
181C5×C4⋊C4C4×D311yescharacteristic
182C5×C4⋊C4C4×D311yescharacteristic
183C5×C22⋊C4—21no—
184C42×C5—21no—
185C42×C5—21no—
186C42×C5—21no—
187#685—61no—
188#685—61no—
189#683—61no—
190#683—61no—
191#683—64no—
192C4×Dic5—31no—
193C4×Dic5—31no—
194C4×Dic5—31no—
195C4×Dic5—31no—
196C4×Dic5—61no—
197C4×Dic5—61no—
198C4×Dic5—61no—
199C4×Dic5—61no—
200#681—61no—
201#681—61no—
202C2×#168—61no—
203C4×#41—151no—
204#423—151no—
205C2×#104—151no—
206C2×#104—151no—
207C4×C4⋊C4—151no—
208#339—151no—
209#339D1511yescharacteristic, complemented
210C22×C3×C5—21no—
211C22×C3×C5—21no—
212C22×C3×C5C2×C22⋊C411yescharacteristic
213C22×C3×C5#12111yescharacteristic
214C22×C3×C5C22⋊Q811yescharacteristic
215C2×D15—22no—
216C2×D15—41no—
217C2×D15—41no—
218C3×C4×C5—42no—
219C3×C4×C5—41no—
220C3×C4×C5—41no—
221C3×C4×C5C2×C4⋊C411yescharacteristic
222C3×C4×C5#11711yescharacteristic
223C3×C4×C5#12111yescharacteristic
224C3×C4×C5C22⋊Q811yescharacteristic
225Dic15—22no—
226Dic15—21no—
227Dic15—21no—
228Dic15—21no—
229Dic15—42no—
230Dic15#10412yescomplemented
231C22×C3×C4—21no—
232C22×C3×C4C22×D511yescharacteristic
233C2×#67—101no—
234C22×Dic3—51no—
235C22×Dic3—51no—
236C22×Dic3—101no—
237#235—52no—
238#235—52no—
239#235—101no—
240#235—101no—
241C2×D12—51no—
242C2×C4×D3—101no—
243C2×C4×D3—101no—
244C2×C4×D3—101no—
245C2×Dic6—51no—
246C3×M16—21no—
247C3×M16—21no—
248C2×C3×C8—21no—
249C3×C4⋊C4C4×D511yescharacteristic
250C3×C4⋊C4C4×D511yescharacteristic
251C3×C22⋊C4—21no—
252C3×C42—21no—
253C3×C42—21no—
254C3×C42—21no—
255(C2×D3)⋊C4—101no—
256(C2×D3)⋊C4—101no—
257Dic3⋊C4—101no—
258Dic3⋊C4—101no—
259Dic3⋊C4—104no—
260C4×Dic3—51no—
261C4×Dic3—51no—
262C4×Dic3—51no—
263C4×Dic3—51no—
264C4×Dic3—101no—
265C4×Dic3—101no—
266C4×Dic3—101no—
267C4×Dic3—101no—
268#208—101no—
269#208—101no—
270C2×C3⋊C8—101no—
271C23×C5D3×D411yescharacteristic
272C22×D5—61no—
273C2×C4×C5—22no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5C2×C4×D311yescharacteristic
279C2×C4×C5#23511yescharacteristic
280C2×C4×C5#23511yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5D3×Q811yescharacteristic
284C22⋊D5—62no—
285C22⋊D5—62no—
286C2×Dic5—31no—
287C2×Dic5—31no—
288C2×Dic5—31no—
289C2×Dic5—31no—
290C2×Dic5—62no—
291C2×Dic5—61no—
292C2×Dic5—62no—
293C2×Dic5—121no—
294C2×Dic5—121no—
295C2×Dic5—121no—
296D20—32no—
297D20—61no—
298C4×D5—62no—
299C4×D5—62no—
300C4×D5—122no—
301C4×D5—122no—
302Dic10—32no—
303Dic10—61no—
304C5×C8—41no—
305#168—121no—
306C2×#41—151no—
307C2×M16—151no—
308C2×M16C2×D1511yescharacteristic
309C4×Q8—151no—
310C4×Q8—151no—
311C4×D4—151no—
312C4×D4—151no—
313C4×D4—301no—
314C4×D4—301no—
315#117—301no—
316#117C2×D1511yescharacteristic
317C2×C4⋊C4—301no—
318C2×C42—151no—
319C2×C42—151no—
320C2×C42—301no—
321C2×C42C2×D1511yescharacteristic
322C4⋊C8—301no—
323C4⋊C8—301no—
324#104—302no—
325#104—302no—
326#95—301no—
327C2×C3×C5—21no—
328C2×C3×C5—21no—
329C2×C3×C5#38011yescharacteristic
330C2×C3×C5C2×#10411yescharacteristic
331C2×C3×C5#42111yescharacteristic
332D15—42no—
333C23×C3D4×D511yescharacteristic
334C22×D3—101no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4C2×C4×D511yescharacteristic
341C2×C3×C4#70911yescharacteristic
342C2×C3×C4#70911yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4D4×D511yescharacteristic
345C2×C3×C4Q8×D511yescharacteristic
346#67—102no—
347#67—102no—
348C2×Dic3—51no—
349C2×Dic3—51no—
350C2×Dic3—51no—
351C2×Dic3—51no—
352C2×Dic3—102no—
353C2×Dic3—101no—
354C2×Dic3—102no—
355C2×Dic3—201no—
356C2×Dic3—201no—
357C2×Dic3—201no—
358D12—52no—
359D12—101no—
360C4×D3—102no—
361C4×D3—102no—
362C4×D3—202no—
363C4×D3—202no—
364Dic6—52no—
365Dic6—101no—
366C3×C8—41no—
367C3⋊C8—201no—
368C22×C5—21no—
369C22×C5—21no—
370C22×C5D3×C22⋊C411yescharacteristic
371C22×C5#88411yescharacteristic
372C22×C5#89611yescharacteristic
373C2×D5—62no—
374C2×D5—121no—
375C2×D5—121no—
376C4×C5—42no—
377C4×C5—41no—
378C4×C5—41no—
379C4×C5#87211yescharacteristic
380C4×C5#88411yescharacteristic
381C4×C5D3×C4⋊C411yescharacteristic
382C4×C5#89611yescharacteristic
383Dic5—32no—
384Dic5—62no—
385Dic5—61no—
386Dic5—61no—
387Dic5—61no—
388Dic5—122no—
389#41—152no—
390#41—152no—
391#41—301no—
392#41—301no—
393C2×Q8—151no—
394C2×D4—151no—
395C2×D4—301no—
396C22×C4—21no—
397C22×C4—151no—
398C22×C4—151no—
399C22×C4—301no—
400C22×C4—301no—
401C22×C4—301no—
402C22×C4—301no—
403C22×C4C22×D1511yescharacteristic
404M16—21no—
405M16—21no—
406M16—301no—
407M16—301no—
408C2×C8—21no—
409C2×C8—301no—
410C4⋊C4—301no—
411C4⋊C4—301no—
412C4⋊C4—304no—
413C4⋊C4C4×D1511yescharacteristic
414C4⋊C4C4×D1511yescharacteristic
415C22⋊C4—21no—
416C22⋊C4—301no—
417C22⋊C4—301no—
418C42—21no—
419C42—21no—
420C42—21no—
421C42—151no—
422C42—151no—
423C42—151no—
424C42—151no—
425C42—301no—
426C42—301no—
427C42—301no—
428C42—301no—
429C3×C5#180611yescharacteristic, complemented, Hall
430C22×C3—21no—
431C22×C3—21no—
432C22×C3D5×C22⋊C411yescharacteristic
433C22×C3#403011yescharacteristic
434C22×C3#404211yescharacteristic
435C2×D3—102no—
436C2×D3—201no—
437C2×D3—201no—
438C3×C4—42no—
439C3×C4—41no—
440C3×C4—41no—
441C3×C4#401811yescharacteristic
442C3×C4#403011yescharacteristic
443C3×C4D5×C4⋊C411yescharacteristic
444C3×C4#404211yescharacteristic
445Dic3—52no—
446Dic3—101no—
447Dic3—101no—
448Dic3—101no—
449Dic3—102no—
450Dic3—202no—
451C2×C5—21no—
452C2×C5—21no—
453C2×C5#466711yescharacteristic
454C2×C5D3×#10411yescharacteristic
455C2×C5#482111yescharacteristic
456D5—122no—
457C23—301no—
458C23D4×D1511yescharacteristic
459Q8—152no—
460Q8—301no—
461D4—152no—
462D4—302no—
463D4—302no—
464D4—301no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—151no—
471C2×C4—151no—
472C2×C4—151no—
473C2×C4—151no—
474C2×C4—302no—
475C2×C4—301no—
476C2×C4—302no—
477C2×C4—302no—
478C2×C4—302no—
479C2×C4—602no—
480C2×C4—602no—
481C2×C4—601no—
482C2×C4—601no—
483C2×C4—601no—
484C2×C4C2×C4×D1511yescharacteristic
485C2×C4#681711yescharacteristic
486C2×C4#681711yescharacteristic
487C2×C4D4×D1511yescharacteristic
488C2×C4D4×D1511yescharacteristic
489C2×C4Q8×D1511yescharacteristic
490C8—41no—
491C8—601no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3#6495611yescharacteristic
495C2×C3D5×#10411yescharacteristic
496C2×C3#6511011yescharacteristic
497D3—202no—
498C5#6877011yescharacteristic, complemented, Sylow
499C22—21no—
500C22—21no—
501C22—302no—
502C22—601no—
503C22—601no—
504C22C22⋊C4×D1511yescharacteristic
505C22#9177311yescharacteristic
506C22#9178511yescharacteristic
507C4—42no—
508C4—41no—
509C4—41no—
510C4—152no—
511C4—301no—
512C4—301no—
513C4—301no—
514C4—302no—
515C4—602no—
516C4#9176111yescharacteristic
517C4#9177311yescharacteristic
518C4C4⋊C4×D1511yescharacteristic
519C4#9178511yescharacteristic
520C3#1059956311yescharacteristic, complemented, Sylow
521C2—21no—
522C2—21no—
523C2—602no—
524C2#1175076811yescharacteristic
525C2D15×#10411yescharacteristic
526C2#1175092211yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#339C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#6817C22
cosocleC22×C3×C4×C5C23
hypercenter#339D15
hypocenterC3×C5#1806
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
3. #11751219C2semidirect
4. C4×#6712C2semidirect
6. C3×C5×#339C2semidirect
7. #11746353C2semidirect
17. #91782C4semidirect
18. #91782C4semidirect
19. #91776C4semidirect
20. #91776C4semidirect
36. C5×#339D3semidirect
83. C3×#339D5semidirect
133. D60C4⋊C4semidirect
139. Dic30C4⋊C4semidirect
209. #339D15semidirect
230. Dic15#104semidirect
429. C3×C5#1806semidirect
498. C5#68770semidirect
520. C3#10599563semidirect

Maximal subgroups

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

subgroupindex
#117562812
C2×#911092
#117512192
C4×#67122
C2×#910892
C3×C5×#3392
#117463532
#105995633
#687705