Finite Group Databasebeta

← #14308992

Subgroups — #14308992

Order 1920.

932 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11755432C211yesmaximal, characteristic, complemented
2#11751348C211yesmaximal, characteristic
3C5×#5247C211yesmaximal, characteristic
4C3×#65536C211yesmaximal, characteristic
5#11746020C211yesmaximal, characteristic, complemented
6#11746019C211yesmaximal, characteristic, complemented
7#11746018C211yesmaximal, characteristic, complemented
8#10600290—31nomaximal, Hall
9C25×C3×C5C2211yescharacteristic
10C2×#6719—22no—
11C2×#6719C2211yescharacteristic
12C2×#6719C2211yescharacteristic
13C2×C5×#217—22no—
14C2×C5×#217C2211yescharacteristic
15C2×C5×#217C2211yescharacteristic
16C2×C3×C22⋊Dic5—22no—
17C2×C3×C22⋊Dic5C2211yescharacteristic
18C2×C3×C22⋊Dic5C2211yescharacteristic
19#91576—22no—
20#91575—22no—
21#91574—22no—
22#69497—51nomaximal, Hall
23#65817—31no—
24C5×#379—31no—
25#65536—31no—
26#65536D311yescharacteristic
27#64747—31no—
28#64747—31no—
29#64746—31no—
30C24×C3×C5—21no—
31C24×C3×C5—21no—
32C24×C3×C5—21no—
33C24×C3×C5—21no—
34C24×C3×C5—21no—
35C24×C3×C5—21no—
36C24×C3×C5—44no—
37C24×C3×C5Q812yescomplemented
38C24×C3×C5C2311yescharacteristic
39C22×Dic15—21no—
40C22×Dic15D412yes—
41C22×C5×Dic3—21no—
42C22×C5×Dic3D412yes—
43C22×C3×Dic5—21no—
44C22×C3×Dic5D412yes—
45C2×#1204—22no—
46#6719—21no—
47#6719—21no—
48#6719—21no—
49#6719—21no—
50#6719—44no—
51C5×#217—21no—
52C5×#217—21no—
53C5×#217—21no—
54C5×#217—21no—
55C5×#217—44no—
56C3×C22⋊Dic5—21no—
57C3×C22⋊Dic5—21no—
58C3×C22⋊Dic5—21no—
59C3×C22⋊Dic5—21no—
60C3×C22⋊Dic5—44no—
61Dic3⋊Dic5—22no—
62#6669—22no—
63#6668—22no—
64#5483—51no—
65C3×#379—51no—
66#5247—51no—
67#5247D511yescharacteristic
68#4527—51no—
69#4527—51no—
70#4526—51no—
71C25×C5C2×D311yescharacteristic
72C2×C5×C22⋊C4—31no—
73C2×C5×C22⋊C4—31no—
74C2×C5×C22⋊C4—62no—
75C2×C22⋊Dic5—22no—
76C2×C22⋊Dic5—31no—
77C2×C22⋊Dic5—31no—
78C2×C22⋊Dic5—62no—
79C2×C22⋊Dic5C2×D311yescharacteristic
80C2×C22⋊Dic5C2×D311yescharacteristic
81#4070—62no—
82#4024—62no—
83#4024—62no—
84#2029—151noSylow
85C23×C3×C5—24no—
86C23×C3×C5—24no—
87C23×C3×C5—24no—
88C23×C3×C5—22no—
89C23×C3×C5—22no—
90C23×C3×C5—22no—
91C23×C3×C5—44no—
92C23×C3×C5—42no—
93C23×C3×C5—42no—
94C23×C3×C5—42no—
95C23×C3×C5—42no—
96C23×C3×C5—44no—
97C23×C3×C5—44no—
98C23×C3×C5—44no—
99C23×C3×C5—41no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5C2×D411yescharacteristic
104C23×C3×C5C2×D411yescharacteristic
105C23×C3×C5C2×D411yescharacteristic
106C23×C3×C5C2×Q811yescharacteristic
107C23×C3×C5#4111yescharacteristic
108C23×C3×C5#4111yescharacteristic
109C23×C3×C5#4111yescharacteristic
110C2×Dic15—22no—
111C2×Dic15—42no—
112C2×Dic15—42no—
113C2×Dic15—41no—
114C2×C5×Dic3—22no—
115C2×C5×Dic3—42no—
116C2×C5×Dic3—42no—
117C2×C5×Dic3—41no—
118C2×C3×Dic5—22no—
119C2×C3×Dic5—42no—
120C2×C3×Dic5—42no—
121C2×C3×Dic5—41no—
122#1204—82no—
123C25×C3C2×D511yescharacteristic
124C2×C3×C22⋊C4—51no—
125C2×C3×C22⋊C4—51no—
126C2×C3×C22⋊C4—102no—
127C2×#217—22no—
128C2×#217—51no—
129C2×#217—51no—
130C2×#217—102no—
131C2×#217C2×D511yescharacteristic
132C2×#217C2×D511yescharacteristic
133#924—102no—
134#878—102no—
135#878—102no—
136C24×C5—21no—
137C24×C5—21no—
138C24×C5—21no—
139C24×C5—21no—
140C24×C5—21no—
141C24×C5—21no—
142C24×C5—44no—
143C24×C5Dic612yescomplemented
144C24×C5C22×D311yescharacteristic
145C22×C4×C5—32no—
146C22×C4×C5—61no—
147C22×Dic5—21no—
148C22×Dic5—32no—
149C22×Dic5—61no—
150C22×Dic5#6712yes—
151C2×Dic10—62no—
152C5×C22⋊C4—61no—
153C5×C22⋊C4—61no—
154C5×C22⋊C4—61no—
155C5×C22⋊C4—61no—
156C5×C22⋊C4—124no—
157C22⋊Dic5—21no—
158C22⋊Dic5—21no—
159C22⋊Dic5—21no—
160C22⋊Dic5—21no—
161C22⋊Dic5—44no—
162C22⋊Dic5—61no—
163C22⋊Dic5—61no—
164C22⋊Dic5—61no—
165C22⋊Dic5—61no—
166C22⋊Dic5—124no—
167C4⋊Dic5—62no—
168#683—62no—
169#683—62no—
170#543—151no—
171#379—31no—
172#379—51no—
173#379—151no—
174#342—151no—
175#342—151no—
176#342—151no—
177C22×C3×C5—22no—
178C22×C3×C5—22no—
179C22×C3×C5—22no—
180C22×C3×C5—24no—
181C22×C3×C5—24no—
182C22×C3×C5—24no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5—41no—
187C22×C3×C5—44no—
188C22×C3×C5—44no—
189C22×C3×C5—44no—
190C22×C3×C5—42no—
191C22×C3×C5—42no—
192C22×C3×C5—42no—
193C22×C3×C5—42no—
194C22×C3×C5—44no—
195C22×C3×C5#12011yescharacteristic
196C22×C3×C5C22⋊Q811yescharacteristic
197C22×C3×C5C22⋊Q811yescharacteristic
198C22×C3×C5C22⋊Q811yescharacteristic
199C22×C3×C5#12411yescharacteristic
200C22×C3×C5#12411yescharacteristic
201C22×C3×C5#12411yescharacteristic
202Dic15—42no—
203Dic15—81no—
204C3×Dic5—42no—
205C3×Dic5—81no—
206C5×Dic3—42no—
207C5×Dic3—81no—
208C24×C3—21no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3—21no—
214C24×C3—44no—
215C24×C3Dic1012yescomplemented
216C24×C3C22×D511yescharacteristic
217C22×C3×C4—52no—
218C22×C3×C4—101no—
219C22×Dic3—21no—
220C22×Dic3—52no—
221C22×Dic3—101no—
222C22×Dic3C22⋊D512yes—
223C2×Dic6—102no—
224C3×C22⋊C4—101no—
225C3×C22⋊C4—101no—
226C3×C22⋊C4—101no—
227C3×C22⋊C4—101no—
228C3×C22⋊C4—204no—
229#217—21no—
230#217—21no—
231#217—21no—
232#217—21no—
233#217—44no—
234#217—101no—
235#217—101no—
236#217—101no—
237#217—101no—
238#217—204no—
239C4⋊Dic3—102no—
240Dic3⋊C4—102no—
241Dic3⋊C4—102no—
242C23×C5—24no—
243C23×C5—24no—
244C23×C5—24no—
245C23×C5—22no—
246C23×C5—22no—
247C23×C5—22no—
248C23×C5—44no—
249C23×C5—42no—
250C23×C5—42no—
251C23×C5—42no—
252C23×C5—42no—
253C23×C5—44no—
254C23×C5—44no—
255C23×C5—44no—
256C23×C5—41no—
257C23×C5—41no—
258C23×C5—41no—
259C23×C5—41no—
260C23×C5C2×Dic611yescharacteristic
261C23×C5#23511yescharacteristic
262C23×C5D3×D411yescharacteristic
263C23×C5D3×D411yescharacteristic
264C23×C5#23711yescharacteristic
265C23×C5#23711yescharacteristic
266C23×C5C2×#6711yescharacteristic
267C2×C4×C5—62no—
268C2×C4×C5—122no—
269C2×C4×C5—122no—
270C2×C4×C5—121no—
271C2×Dic5—22no—
272C2×Dic5—42no—
273C2×Dic5—42no—
274C2×Dic5—41no—
275C2×Dic5—62no—
276C2×Dic5—122no—
277C2×Dic5—122no—
278C2×Dic5—121no—
279Dic10—242no—
280C25D3×D511yescharacteristic
281C22⋊Q8—302no—
282C22⋊Q8—302no—
283C22⋊Q8—302no—
284C2×C22⋊C4—31no—
285C2×C22⋊C4—31no—
286C2×C22⋊C4—51no—
287C2×C22⋊C4—51no—
288C2×C22⋊C4—62no—
289C2×C22⋊C4—102no—
290C2×C22⋊C4—151no—
291C2×C22⋊C4—151no—
292C2×C22⋊C4—302no—
293C2×C3×C5—21no—
294C2×C3×C5—21no—
295C2×C3×C5—21no—
296C2×C3×C5—21no—
297C2×C3×C5—21no—
298C2×C3×C5—21no—
299C2×C3×C5—44no—
300C2×C3×C5#39311yescharacteristic
301C2×C3×C5B(4,𝔽2)12yes—
302C23×C3—24no—
303C23×C3—24no—
304C23×C3—24no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—44no—
309C23×C3—42no—
310C23×C3—42no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—44no—
314C23×C3—44no—
315C23×C3—44no—
316C23×C3—41no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3C2×Dic1011yescharacteristic
321C23×C3#70911yescharacteristic
322C23×C3D4×D511yescharacteristic
323C23×C3D4×D511yescharacteristic
324C23×C3#71111yescharacteristic
325C23×C3#71111yescharacteristic
326C23×C3C2×C22⋊D511yescharacteristic
327C2×C3×C4—102no—
328C2×C3×C4—202no—
329C2×C3×C4—202no—
330C2×C3×C4—201no—
331C2×Dic3—22no—
332C2×Dic3—42no—
333C2×Dic3—42no—
334C2×Dic3—41no—
335C2×Dic3—102no—
336C2×Dic3—202no—
337C2×Dic3—202no—
338C2×Dic3—201no—
339Dic6—402no—
340C22×C5—22no—
341C22×C5—22no—
342C22×C5—22no—
343C22×C5—24no—
344C22×C5—24no—
345C22×C5—24no—
346C22×C5—41no—
347C22×C5—41no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—44no—
351C22×C5—44no—
352C22×C5—44no—
353C22×C5—42no—
354C22×C5—42no—
355C22×C5—42no—
356C22×C5—42no—
357C22×C5—44no—
358C22×C5#87811yescharacteristic
359C22×C5#87811yescharacteristic
360C22×C5#88511yescharacteristic
361C22×C5#88511yescharacteristic
362C22×C5#92411yescharacteristic
363C22×C5#93611yescharacteristic
364C22×C5#93711yescharacteristic
365C4×C5—122no—
366C4×C5—241no—
367Dic5—42no—
368Dic5—81no—
369Dic5—122no—
370Dic5—241no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—44no—
378C24#120412yescomplemented
379C24C2×D3×D511yescharacteristic
380C2×Q8—302no—
381C22×C4—32no—
382C22×C4—52no—
383C22×C4—61no—
384C22×C4—101no—
385C22×C4—152no—
386C22×C4—301no—
387C4⋊C4—302no—
388C4⋊C4—302no—
389C4⋊C4—302no—
390C22⋊C4—61no—
391C22⋊C4—61no—
392C22⋊C4—61no—
393C22⋊C4—61no—
394C22⋊C4—101no—
395C22⋊C4—101no—
396C22⋊C4—101no—
397C22⋊C4—101no—
398C22⋊C4—124no—
399C22⋊C4—204no—
400C22⋊C4—301no—
401C22⋊C4—301no—
402C22⋊C4—301no—
403C22⋊C4—301no—
404C22⋊C4—604no—
405C3×C5#202911yescharacteristic, complemented, Hall
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—22no—
409C22×C3—24no—
410C22×C3—24no—
411C22×C3—24no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—44no—
417C22×C3—44no—
418C22×C3—44no—
419C22×C3—42no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—44no—
423C22×C3—42no—
424C22×C3#402411yescharacteristic
425C22×C3#402411yescharacteristic
426C22×C3#403111yescharacteristic
427C22×C3#403111yescharacteristic
428C22×C3#407011yescharacteristic
429C22×C3#408211yescharacteristic
430C22×C3#408311yescharacteristic
431C3×C4—202no—
432C3×C4—401no—
433Dic3—42no—
434Dic3—81no—
435Dic3—202no—
436Dic3—401no—
437C2×C5—21no—
438C2×C5—21no—
439C2×C5—21no—
440C2×C5—21no—
441C2×C5—21no—
442C2×C5—21no—
443C2×C5—44no—
444C2×C5#494711yescharacteristic
445C2×C5#503212yes—
446C23—24no—
447C23—24no—
448C23—24no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—44no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—44no—
458C23—44no—
459C23—44no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23#677911yescharacteristic
465C23#678011yescharacteristic
466C23#678211yescharacteristic
467C23C2×#120411yescharacteristic
468C23D5×#6711yescharacteristic
469C23D3×C22⋊D511yescharacteristic
470C23#679011yescharacteristic
471Q8—1202no—
472C2×C4—62no—
473C2×C4—102no—
474C2×C4—122no—
475C2×C4—122no—
476C2×C4—121no—
477C2×C4—202no—
478C2×C4—202no—
479C2×C4—201no—
480C2×C4—302no—
481C2×C4—602no—
482C2×C4—602no—
483C2×C4—601no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—44no—
491C2×C3#6523611yescharacteristic
492C2×C3#6532112yes—
493C5#6949711yescharacteristic, complemented, Sylow
494C22—22no—
495C22—22no—
496C22—22no—
497C22—24no—
498C22—24no—
499C22—24no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—44no—
505C22—44no—
506C22—44no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—44no—
512C22#9152511yescharacteristic
513C22#9152611yescharacteristic
514C22#9153411yescharacteristic
515C22#9157411yescharacteristic
516C22#9157511yescharacteristic
517C22#9157611yescharacteristic
518C22#9157711yescharacteristic
519C4—122no—
520C4—202no—
521C4—241no—
522C4—401no—
523C4—602no—
524C4—1201no—
525C3#1060029011yescharacteristic, complemented, Sylow
526C2—21no—
527C2—21no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—44no—
533C2#1174952411yescharacteristic
534C2#1174952512yes—
subgroupG/H
centerC22#91577
commutator, cosocleC24×C3×C5C23
FrattiniC24C2×D3×D5
Fitting, prime radicalC25×C3×C5C22
socleC22×C3×C5#120
hypercenterC25D3×D5
hypocenterC3×C5#2029
LCSG ▷ C24×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
1. #11755432C2semidirect
5. #11746020C2semidirect
6. #11746019C2semidirect
7. #11746018C2semidirect
37. C24×C3×C5Q8semidirect
143. C24×C5Dic6semidirect
215. C24×C3Dic10semidirect
378. C24#1204semidirect
405. C3×C5#2029semidirect
493. C5#69497semidirect
525. C3#10600290semidirect

Maximal subgroups

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

subgroupindex
#117554322
#117513482
C5×#52472
C3×#655362
#117460202
#117460192
#117460182
#106002903
#694975