Finite Group Databasebeta

← #14301656

Subgroups — #14301656

Order 1920.

772 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×#91818C211yesmaximal, characteristic
2#11756245C211yesmaximal, characteristic
3C3×C5×#381C211yesmaximal, characteristic, complemented
4#11751312C211yesmaximal, characteristic, complemented
5C2×#91090C211yesmaximal, characteristic
6#11746348C211yesmaximal, characteristic, complemented
7#11746347C211yesmaximal, characteristic, complemented
8#10600331—31nomaximal, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C22×#1220C2211yescharacteristic
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×C3×C5×C22⋊C4C2211yescharacteristic
13C2×#6719C2211yescharacteristic
14C2×#6719C2211yescharacteristic
15C2×#6719C2211yescharacteristic
16#91818—22no—
17#91818C414yescomplemented
18C4×#1220—22no—
19C2×#6714—21no—
20C2×#6712—21no—
21#91770—22no—
22C22⋊C4×D15—21no—
23#91766—21no—
24C3×C5×#95—22no—
25#91115—22no—
26#91090—22no—
27#69538—51nomaximal, Hall
28C2×#4075—31no—
29#65820—31no—
30C5×#381D311yescharacteristic, complemented
31#65500—31no—
32C2×#3938—31no—
33#64747—31no—
34#64746—31no—
35C24×C3×C5C2311yescharacteristic
36C23×D15D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2×C412yescomplemented
45C22×C3×C4×C5D412yes—
46C2×#1220—21no—
47C2×#1220—21no—
48C2×#1220—21no—
49C2×#1220—21no—
50C2×#1220C2×C412yes—
51C2×#1220D412yes—
52C22×Dic15—21no—
53C22×Dic15—21no—
54C22×Dic15D411yescharacteristic
55C22×Dic15D412yes—
56C2×C4×D15—22no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4—21no—
61#6719—21no—
62#6719—21no—
63#6719—21no—
64#6719—21no—
65#6719—21no—
66#6719C2×C412yescomplemented
67#6714—22no—
68#6714—24no—
69#6712—22no—
70#6712—24no—
71C4×Dic15—22no—
72C2×#929—51no—
73#5486—51no—
74C3×#381D511yescharacteristic, complemented
75#5211—51no—
76C2×#806—51no—
77#4527—51no—
78#4526—51no—
79C23×C4×C5C2×D311yescharacteristic
80C22×C22⋊D5—31no—
81C2×C5×C22⋊C4C2×D311yescharacteristic
82C2×C5×C22⋊C4C2×D311yescharacteristic
83C2×C22⋊Dic5—31no—
84C2×C22⋊Dic5—31no—
85C2×C22⋊Dic5—31no—
86#4075—34no—
87#4075—62no—
88C4×C22⋊D5—62no—
89C2×#685—61no—
90C2×#683—61no—
91#4027—62no—
92D5×C22⋊C4—61no—
93#4023—61no—
94C5×#95—22no—
95#3963—62no—
96#3938—62no—
97#1890—151noSylow
98C23×C3×C5—42no—
99C23×C3×C5C22×C411yescharacteristic
100C23×C3×C5C2×D411yescharacteristic
101C23×C3×C5C2×D411yescharacteristic
102C23×C3×C5C2×D411yescharacteristic
103C23×C3×C5C2×D411yescharacteristic
104C23×C3×C5#4111yescharacteristic
105C23×C3×C5#4111yescharacteristic
106C22×D15—21no—
107C22×D15—21no—
108C22×D15—42no—
109C22×D15C22⋊C412yes—
110C2×C3×C4×C5—22no—
111C2×C3×C4×C5—22no—
112C2×C3×C4×C5—22no—
113C2×C3×C4×C5—22no—
114C2×C3×C4×C5—41no—
115C2×C3×C4×C5—41no—
116C2×C3×C4×C5—41no—
117C2×C3×C4×C5—41no—
118C2×C3×C4×C5—42no—
119C2×C3×C4×C5—42no—
120C2×C3×C4×C5—41no—
121#1220—22no—
122#1220—22no—
123#1220—22no—
124#1220—22no—
125C2×Dic15—21no—
126C2×Dic15—21no—
127C2×Dic15—22no—
128C2×Dic15—22no—
129C2×Dic15—42no—
130C2×Dic15—42no—
131C2×Dic15—42no—
132C2×Dic15—41no—
133C2×Dic15C22⋊C412yes—
134C4×D15—82no—
135C23×C3×C4C2×D511yescharacteristic
136C22×#67—51no—
137C2×C3×C22⋊C4C2×D511yescharacteristic
138C2×C3×C22⋊C4C2×D511yescharacteristic
139C2×#217—51no—
140C2×#217—51no—
141C2×#217—51no—
142#929—54no—
143#929—102no—
144C4×#67—102no—
145C2×(C2×D3)⋊C4—101no—
146C2×Dic3⋊C4—101no—
147#67⋊C4—102no—
148D3×C22⋊C4—101no—
149#877—101no—
150C3×#95—22no—
151C3⋊#95—102no—
152#806—102no—
153C24×C5C22×D311yescharacteristic
154C23×D5—31no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5C4×D312yescomplemented
163C22×C4×C5#6712yes—
164C2×C22⋊D5—32no—
165C2×C22⋊D5—32no—
166C2×C22⋊D5—61no—
167C2×C22⋊D5—61no—
168C2×C22⋊D5—61no—
169C2×C22⋊D5—61no—
170C22×Dic5—31no—
171C22×Dic5—32no—
172C22×Dic5—61no—
173C22×Dic5—61no—
174C2×C4×D5—62no—
175C5×C22⋊C4—21no—
176C5×C22⋊C4—21no—
177C5×C22⋊C4—21no—
178C5×C22⋊C4—21no—
179C22⋊Dic5—32no—
180C22⋊Dic5—61no—
181C22⋊Dic5—61no—
182C22⋊Dic5—61no—
183C22⋊Dic5—61no—
184C22⋊Dic5—61no—
185#685—64no—
186#685—62no—
187#683—64no—
188#683—62no—
189C4×Dic5—62no—
190C2×#123—151no—
191#518—151no—
192C2×#99—151no—
193#381—151no—
194#381D1511yescharacteristic, complemented
195#342—151no—
196#342—151no—
197C22×C3×C5—22no—
198C22×C3×C5—22no—
199C22×C3×C5—22no—
200C22×C3×C5—41no—
201C22×C3×C5—41no—
202C22×C3×C5—41no—
203C22×C3×C5—41no—
204C22×C3×C5C2×C22⋊C411yescharacteristic
205C22×C3×C5C4×D411yescharacteristic
206C22×C3×C5C4×D411yescharacteristic
207C22×C3×C5#12011yescharacteristic
208C22×C3×C5#12111yescharacteristic
209C22×C3×C5#12111yescharacteristic
210C22×C3×C5#12311yescharacteristic
211C2×D15—22no—
212C2×D15—42no—
213C2×D15—42no—
214C2×D15—81no—
215C3×C4×C5—42no—
216C3×C4×C5—42no—
217C3×C4×C5—81no—
218Dic15—22no—
219Dic15—42no—
220Dic15—42no—
221Dic15—81no—
222C24×C3C22×D511yescharacteristic
223C23×D3—51no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4C4×D512yescomplemented
232C22×C3×C4C22⋊D512yes—
233C2×#67—52no—
234C2×#67—52no—
235C2×#67—101no—
236C2×#67—101no—
237C2×#67—101no—
238C2×#67—101no—
239C22×Dic3—51no—
240C22×Dic3—52no—
241C22×Dic3—101no—
242C22×Dic3—101no—
243C2×C4×D3—102no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—21no—
246C3×C22⋊C4—21no—
247C3×C22⋊C4—21no—
248#217—52no—
249#217—101no—
250#217—101no—
251#217—101no—
252#217—101no—
253#217—101no—
254(C2×D3)⋊C4—104no—
255(C2×D3)⋊C4—102no—
256Dic3⋊C4—104no—
257Dic3⋊C4—102no—
258C4×Dic3—102no—
259C23×C5—42no—
260C23×C5C2×C4×D311yescharacteristic
261C23×C5#23511yescharacteristic
262C23×C5D3×D411yescharacteristic
263C23×C5D3×D411yescharacteristic
264C23×C5D3×D411yescharacteristic
265C23×C5#23711yescharacteristic
266C23×C5C2×#6711yescharacteristic
267C22×D5—32no—
268C22×D5—61no—
269C22×D5—61no—
270C22×D5—122no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5—42no—
280C2×C4×C5—42no—
281C2×C4×C5—41no—
282C22⋊D5—62no—
283C22⋊D5—62no—
284C22⋊D5—62no—
285C22⋊D5—62no—
286C2×Dic5—32no—
287C2×Dic5—61no—
288C2×Dic5—61no—
289C2×Dic5—62no—
290C2×Dic5—62no—
291C2×Dic5—122no—
292C2×Dic5—122no—
293C2×Dic5—122no—
294C2×Dic5—121no—
295C4×D5—242no—
296C22×D4—151no—
297C23×C4C2×D1511yescharacteristic
298#123—154no—
299#123—302no—
300C4×D4—302no—
301C4×D4—302no—
302#117—301no—
303C2×C4⋊C4—301no—
304C2×C22⋊C4—151no—
305C2×C22⋊C4—151no—
306C2×C22⋊C4—151no—
307C2×C22⋊C4—301no—
308C2×C22⋊C4—301no—
309C2×C22⋊C4C2×D1511yescharacteristic
310C2×C22⋊C4C2×D1511yescharacteristic
311#99—302no—
312#95—22no—
313#95—302no—
314C2×C3×C5—21no—
315C2×C3×C5—21no—
316C2×C3×C5—21no—
317C2×C3×C5—21no—
318C2×C3×C5—21no—
319C2×C3×C5—21no—
320C2×C3×C5#38611yescharacteristic
321C2×C3×C5#45812yes—
322D15—42no—
323C23×C3—42no—
324C23×C3C2×C4×D511yescharacteristic
325C23×C3#70911yescharacteristic
326C23×C3D4×D511yescharacteristic
327C23×C3D4×D511yescharacteristic
328C23×C3D4×D511yescharacteristic
329C23×C3#71111yescharacteristic
330C23×C3C2×C22⋊D511yescharacteristic
331C22×D3—52no—
332C22×D3—101no—
333C22×D3—101no—
334C22×D3—202no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—41no—
346#67—102no—
347#67—102no—
348#67—102no—
349#67—102no—
350C2×Dic3—52no—
351C2×Dic3—101no—
352C2×Dic3—101no—
353C2×Dic3—102no—
354C2×Dic3—102no—
355C2×Dic3—202no—
356C2×Dic3—202no—
357C2×Dic3—202no—
358C2×Dic3—201no—
359C4×D3—402no—
360C22×C5—22no—
361C22×C5—22no—
362C22×C5—22no—
363C22×C5—41no—
364C22×C5—41no—
365C22×C5—41no—
366C22×C5—41no—
367C22×C5D3×C22⋊C411yescharacteristic
368C22×C5#67⋊C411yescharacteristic
369C22×C5#88311yescharacteristic
370C22×C5#88411yescharacteristic
371C22×C5C4×#6711yescharacteristic
372C22×C5#93711yescharacteristic
373C22×C5#93811yescharacteristic
374C2×D5—62no—
375C2×D5—122no—
376C2×D5—122no—
377C2×D5—241no—
378C4×C5—42no—
379C4×C5—42no—
380C4×C5—81no—
381Dic5—62no—
382Dic5—122no—
383Dic5—122no—
384Dic5—241no—
385C24—151no—
386C24C22×D1511yescharacteristic
387C2×D4—152no—
388C2×D4—152no—
389C2×D4—301no—
390C2×D4—301no—
391C2×D4—301no—
392C2×D4—301no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—151no—
401C22×C4—152no—
402C22×C4—302no—
403C22×C4—301no—
404C22×C4—301no—
405C22×C4C4×D1512yescomplemented
406C22×C4#122012yes—
407C4⋊C4—304no—
408C4⋊C4—302no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—152no—
414C22⋊C4—304no—
415C22⋊C4—302no—
416C22⋊C4—301no—
417C22⋊C4—301no—
418C22⋊C4—301no—
419C22⋊C4—301no—
420C22⋊C4—301no—
421C42—302no—
422C3×C5#189011yescharacteristic, complemented, Hall
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3D5×C22⋊C411yescharacteristic
431C22×C3#402711yescharacteristic
432C22×C3#402911yescharacteristic
433C22×C3#403011yescharacteristic
434C22×C3C4×C22⋊D511yescharacteristic
435C22×C3#408311yescharacteristic
436C22×C3#408411yescharacteristic
437C2×D3—102no—
438C2×D3—202no—
439C2×D3—202no—
440C2×D3—401no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—81no—
444Dic3—102no—
445Dic3—202no—
446Dic3—202no—
447Dic3—401no—
448C2×C5—21no—
449C2×C5—21no—
450C2×C5—21no—
451C2×C5—21no—
452C2×C5—21no—
453C2×C5—21no—
454C2×C5#495611yescharacteristic
455C2×C5#505312yes—
456D5—122no—
457C23—42no—
458C23—152no—
459C23—301no—
460C23—301no—
461C23—602no—
462C23C2×C4×D1511yescharacteristic
463C23#681711yescharacteristic
464C23D4×D1511yescharacteristic
465C23D4×D1511yescharacteristic
466C23D4×D1511yescharacteristic
467C23#681911yescharacteristic
468C23C2×#122011yescharacteristic
469D4—302no—
470D4—302no—
471D4—302no—
472D4—302no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—152no—
485C2×C4—301no—
486C2×C4—301no—
487C2×C4—302no—
488C2×C4—302no—
489C2×C4—602no—
490C2×C4—602no—
491C2×C4—602no—
492C2×C4—601no—
493C2×C4—1202no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3#6524511yescharacteristic
501C2×C3#6534212yes—
502D3—202no—
503C5#6953811yescharacteristic, complemented, Sylow
504C22—22no—
505C22—22no—
506C22—22no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—302no—
512C22—602no—
513C22—602no—
514C22—1201no—
515C22C22⋊C4×D1511yescharacteristic
516C22#9177011yescharacteristic
517C22#9177211yescharacteristic
518C22#9177311yescharacteristic
519C22C4×#122011yescharacteristic
520C22#9182611yescharacteristic
521C22#9182711yescharacteristic
522C4—42no—
523C4—42no—
524C4—81no—
525C4—302no—
526C4—602no—
527C4—602no—
528C4—1201no—
529C3#1060033111yescharacteristic, complemented, Sylow
530C2—21no—
531C2—21no—
532C2—21no—
533C2—21no—
534C2—21no—
535C2—21no—
536C2—602no—
537C2#1175105711yescharacteristic
538C2#1175115412yes—
subgroupG/H
centerC22#91826
commutatorC23×C3×C5C22×C4
FrattiniC24C22×D15
FittingC3×C5×#381C2
socleC22×C3×C5#120
prime radicalC22×#1220C22
cosocleC24×C3×C5C23
hypercenter#381D15
hypocenterC3×C5#1890
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
3. C3×C5×#381C2semidirect
4. #11751312C2semidirect
6. #11746348C2semidirect
7. #11746347C2semidirect
17. #91818C4semidirect
30. C5×#381D3semidirect
44. C22×C3×C4×C5C2×C4semidirect
66. #6719C2×C4semidirect
74. C3×#381D5semidirect
162. C22×C4×C5C4×D3semidirect
194. #381D15semidirect
231. C22×C3×C4C4×D5semidirect
405. C22×C4C4×D15semidirect
422. C3×C5#1890semidirect
503. C5#69538semidirect
529. C3#10600331semidirect

Maximal subgroups

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

subgroupindex
C2×#918182
#117562452
C3×C5×#3812
#117513122
C2×#910902
#117463482
#117463472
#106003313
#695385