Finite Group Databasebeta

← #14435423

Subgroups — #14435423

Order 1920.

772 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
1C2×Q8×Dic15C211yesmaximal, characteristic, complemented
2#11756383C211yesmaximal, characteristic
3C3×C5×#451C211yesmaximal, characteristic, complemented
4#11751328C211yesmaximal, characteristic
5#11751286C212yesmaximal, complemented
6#11751285C212yesmaximal, complemented
7#11751145C211yesmaximal, characteristic, complemented
8#11750918C212yesmaximal, complemented
9#11750900C212yesmaximal, complemented
10#11750836C211yesmaximal, characteristic
11#11750820C211yesmaximal, characteristic, complemented
12#10611906—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×C3×C5×Q16C2212yes—
15C3×C5×C22⋊Q8C2211yescharacteristic
16#91836C2211yescharacteristic
17Q8×Dic15—21no—
18Q8×Dic15—21no—
19Q8×Dic15C2212yes—
20Q8×Dic15C2212yes—
21Q8×Dic15C2211yescharacteristic
22C2×#6717C2212yes—
23#91819C2211yescharacteristic
24C2×C4⋊Dic15—21no—
25C2×C4⋊Dic15C2211yescharacteristic
26C2×C4×Dic15—21no—
27C2×C4×Dic15C2211yescharacteristic
28#91787—21no—
29#91782C2211yescharacteristic
30#91781—21no—
31#91779C2211yescharacteristic
32#91775—21no—
33#91770—21no—
34C3×C5×#103C2212yes—
35C3×C5×C22⋊C8C2211yescharacteristic
36#91119C2212yes—
37#91119C2212yes—
38#91114C2211yescharacteristic
39#91105C2212yes—
40#91101C2212yes—
41#91099C2212yes—
42#91098C2212yes—
43#91091C2212yes—
44#80175—51nomaximal, Hall
45C2×Q8×Dic5—31no—
46#65958—31no—
47C5×#451D311yescharacteristic, complemented
48#65516—31no—
49#65474—32no—
50#65473—32no—
51#65333—31no—
52#65106—32no—
53#65088—32no—
54#65024—31no—
55#65008—31no—
56C2×C3×C5×Q8—24no—
57C2×C3×C5×Q8—21no—
58C2×C3×C5×Q8C2311yescharacteristic
59C2×C3×C5×Q8C2312yes—
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C2×#1220—21no—
63C22×Dic15—21no—
64C22×Dic15D411yescharacteristic
65C22×Dic15D411yescharacteristic
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C3×C5×Q16—24no—
69C2×C3×C5×C8C2312yes—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2311yescharacteristic
72C3×C5×C22⋊C4—21no—
73#6717—24no—
74#6714—21no—
75#6714—21no—
76#6714—21no—
77#6714—21no—
78C4⋊Dic15—21no—
79C4⋊Dic15—21no—
80C4⋊Dic15—21no—
81C4⋊Dic15—22no—
82C4⋊Dic15—22no—
83C4⋊Dic15C2311yescharacteristic
84C4⋊Dic15C2312yes—
85#6712—21no—
86C4×Dic15—21no—
87C4×Dic15—22no—
88C4×Dic15—22no—
89C4×Dic15D411yescharacteristic
90C4×Dic15D411yescharacteristic
91C4×Dic15C2311yescharacteristic
92C4×Dic15C2311yescharacteristic
93C2×C3⋊#168C2312yes—
94C2×Q8×Dic3—51no—
95#5624—51no—
96C3×#451D511yescharacteristic, complemented
97#5227—51no—
98#5185—52no—
99#5184—52no—
100#5044—51no—
101#4817—52no—
102#4799—52no—
103#4735—51no—
104#4719—51no—
105C22×C5×Q8C2×D311yescharacteristic
106C2×C5×Q16C2×D312yes—
107C5×C22⋊Q8C2×D311yescharacteristic
108#4093—31no—
109Q8×Dic5—32no—
110Q8×Dic5—32no—
111Q8×Dic5—31no—
112Q8×Dic5—61no—
113Q8×Dic5—61no—
114C2×#688—32no—
115#4076—31no—
116C2×C4⋊Dic5—31no—
117C2×C4⋊Dic5—61no—
118C2×C4×Dic5—31no—
119C2×C4×Dic5—61no—
120#4044—61no—
121#4039—31no—
122#4038—61no—
123#4036—31no—
124#4032—61no—
125#4027—61no—
126C5×#103C2×D312yes—
127C5×C22⋊C8C2×D311yescharacteristic
128#3967—32no—
129#3967—32no—
130C22⋊#168—31no—
131#3953—32no—
132#3949—32no—
133#3947—32no—
134#3946—32no—
135#3939—32no—
136#3117—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×D15—21no—
139C3×C5×Q8—24no—
140C3×C5×Q8—22no—
141C3×C5×Q8—22no—
142C3×C5×Q8#4114yes—
143C2×C3×C4×C5—24no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2411yescharacteristic
150#1220—42no—
151C2×Dic15—22no—
152C2×Dic15—22no—
153C2×Dic15—21no—
154C2×Dic15—41no—
155C2×Dic15—42no—
156C2×Dic15C2×D411yescharacteristic
157C2×Dic15C2×D411yescharacteristic
158C2×Dic15C2×D411yescharacteristic
159C2×Dic15C2×D411yescharacteristic
160D60—22no—
161C4×D15—42no—
162C3×C5×C8—22no—
163C3⋊#168—22no—
164C22×C3×Q8C2×D511yescharacteristic
165C2×C3×Q16C2×D512yes—
166C3×C22⋊Q8C2×D511yescharacteristic
167#947—51no—
168Q8×Dic3—51no—
169Q8×Dic3—52no—
170Q8×Dic3—52no—
171Q8×Dic3—101no—
172Q8×Dic3—101no—
173C2×#215—52no—
174#930—51no—
175C2×C4⋊Dic3—51no—
176C2×C4⋊Dic3—101no—
177C2×C4×Dic3—51no—
178C2×C4×Dic3—101no—
179#898—101no—
180#893—51no—
181#892—101no—
182#890—51no—
183#886—101no—
184#67⋊C4—101no—
185C3×#103C2×D512yes—
186C3×C22⋊C8C2×D511yescharacteristic
187#835—52no—
188#835—52no—
189#830—51no—
190#821—52no—
191#817—52no—
192#815—52no—
193Dic3⋊C8—52no—
194#807—52no—
195C2×C5×Q8—24no—
196C2×C5×Q8—21no—
197C2×C5×Q8C22×D311yescharacteristic
198C2×C5×Q8C22×D312yes—
199C22×C4×C5—21no—
200C22×C4×C5C22×D311yescharacteristic
201C2×C22⋊D5—61no—
202C22×Dic5—31no—
203C22×Dic5—31no—
204C22×Dic5—61no—
205C2×D20—31no—
206C2×C4×D5—61no—
207C5×Q16—24no—
208C2×C5×C8C22×D312yes—
209C5×C4⋊C4—21no—
210C5×C4⋊C4C22×D311yescharacteristic
211C5×C22⋊C4—21no—
212#688—64no—
213#685—61no—
214#685—61no—
215#685—61no—
216#685—61no—
217C4⋊Dic5—32no—
218C4⋊Dic5—31no—
219C4⋊Dic5—61no—
220C4⋊Dic5—61no—
221C4⋊Dic5—62no—
222C4⋊Dic5—62no—
223C4⋊Dic5—61no—
224#683—61no—
225C4×Dic5—31no—
226C4×Dic5—31no—
227C4×Dic5—31no—
228C4×Dic5—31no—
229C4×Dic5—61no—
230C4×Dic5—62no—
231C4×Dic5—62no—
232C2×#168—32no—
233#529—151no—
234C2×C4×Q8—151no—
235#484—151no—
236#481—151no—
237#479—152no—
238#464—152no—
239#451D1511yescharacteristic, complemented
240#448—151no—
241#441—152no—
242#440—152no—
243#432—151no—
244C22×C3×C5—21no—
245C22×C3×C5—21no—
246C22×C3×C5#13712yes—
247C22×C3×C5C22×D411yescharacteristic
248C2×D15—41no—
249C2×D15—41no—
250C2×D15—41no—
251C3×C4×C5—24no—
252C3×C4×C5—21no—
253C3×C4×C5—41no—
254C3×C4×C5—41no—
255C3×C4×C5C2×#4112yes—
256Dic15—21no—
257Dic15—21no—
258Dic15—21no—
259Dic15—21no—
260Dic15—41no—
261Dic15—42no—
262C2×C3×Q8—24no—
263C2×C3×Q8—21no—
264C2×C3×Q8C22×D511yescharacteristic
265C2×C3×Q8C22×D512yes—
266C22×C3×C4—21no—
267C22×C3×C4C22×D511yescharacteristic
268C2×#67—101no—
269C22×Dic3—51no—
270C22×Dic3—51no—
271C22×Dic3—101no—
272C2×D12—51no—
273C2×C4×D3—101no—
274C3×Q16—24no—
275C2×C3×C8C22×D512yes—
276C3×C4⋊C4—21no—
277C3×C4⋊C4C22×D511yescharacteristic
278C3×C22⋊C4—21no—
279#215—104no—
280(C2×D3)⋊C4—101no—
281(C2×D3)⋊C4—101no—
282(C2×D3)⋊C4—101no—
283(C2×D3)⋊C4—101no—
284C4⋊Dic3—52no—
285C4⋊Dic3—51no—
286C4⋊Dic3—101no—
287C4⋊Dic3—101no—
288C4⋊Dic3—102no—
289C4⋊Dic3—102no—
290C4⋊Dic3—101no—
291Dic3⋊C4—101no—
292C4×Dic3—51no—
293C4×Dic3—51no—
294C4×Dic3—51no—
295C4×Dic3—51no—
296C4×Dic3—101no—
297C4×Dic3—102no—
298C4×Dic3—102no—
299C2×C3⋊C8—52no—
300C23×C5D3×D411yescharacteristic
301C22×D5—61no—
302C5×Q8—24no—
303C5×Q8—22no—
304C5×Q8—22no—
305C5×Q8#23714yes—
306C2×C4×C5—24no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5D3×D411yescharacteristic
312C2×C4×C5C23×D311yescharacteristic
313C22⋊D5—122no—
314C2×Dic5—31no—
315C2×Dic5—31no—
316C2×Dic5—31no—
317C2×Dic5—31no—
318C2×Dic5—62no—
319C2×Dic5—62no—
320C2×Dic5—61no—
321C2×Dic5—121no—
322C2×Dic5—122no—
323D20—62no—
324C4×D5—122no—
325C5×C8—22no—
326#168—62no—
327C22×Q8C2×D1511yescharacteristic
328C2×Q16C2×D1512yes—
329C2×SD16—152no—
330#126—301no—
331#125—151no—
332#124—151no—
333#123—301no—
334C22⋊Q8C2×D1511yescharacteristic
335#121—151no—
336C4×Q8—152no—
337C4×Q8—152no—
338C4×Q8—151no—
339C4×Q8—301no—
340C4×Q8—301no—
341C4×D4—151no—
342C4×D4—301no—
343#117—301no—
344C2×C4⋊C4—151no—
345C2×C4⋊C4—301no—
346C2×C42—151no—
347C2×C42—301no—
348#107—152no—
349#106—152no—
350C4⋊C8—152no—
351#103—152no—
352#103—152no—
353#103C2×D1512yes—
354#102—152no—
355C22⋊C8—151no—
356C22⋊C8C2×D1511yescharacteristic
357#97—152no—
358C2×C3×C5—22no—
359C2×C3×C5#52511yescharacteristic
360C2×C3×C5C2×#13711yescharacteristic
361C2×C3×C5#57511yescharacteristic
362D15—81no—
363C23×C3D4×D511yescharacteristic
364C22×D3—101no—
365C3×Q8—24no—
366C3×Q8—22no—
367C3×Q8—22no—
368C3×Q8#71114yes—
369C2×C3×C4—24no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4D4×D511yescharacteristic
375C2×C3×C4C23×D511yescharacteristic
376#67—202no—
377C2×Dic3—51no—
378C2×Dic3—51no—
379C2×Dic3—51no—
380C2×Dic3—51no—
381C2×Dic3—102no—
382C2×Dic3—102no—
383C2×Dic3—101no—
384C2×Dic3—201no—
385C2×Dic3—202no—
386D12—102no—
387C4×D3—202no—
388C3×C8—22no—
389C3⋊C8—102no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5#91812yes—
393C22×C5C2×D3×D411yescharacteristic
394C2×D5—121no—
395C2×D5—121no—
396C2×D5—121no—
397C4×C5—24no—
398C4×C5—21no—
399C4×C5—41no—
400C4×C5—41no—
401C4×C5C2×#23712yes—
402Dic5—61no—
403Dic5—61no—
404Dic5—61no—
405Dic5—61no—
406Dic5—121no—
407Dic5—122no—
408C2×Q8—24no—
409C2×Q8—21no—
410C2×Q8C22×D1511yescharacteristic
411C2×Q8C22×D1512yes—
412C2×D4—151no—
413C2×D4—301no—
414C22×C4—21no—
415C22×C4—151no—
416C22×C4—151no—
417C22×C4—301no—
418C22×C4—301no—
419C22×C4C22×D1511yescharacteristic
420Q16—24no—
421SD16—304no—
422C2×C8—152no—
423C2×C8C22×D1512yes—
424C4⋊C4—21no—
425C4⋊C4—152no—
426C4⋊C4—151no—
427C4⋊C4—302no—
428C4⋊C4—302no—
429C4⋊C4—301no—
430C4⋊C4—301no—
431C4⋊C4—301no—
432C4⋊C4—301no—
433C4⋊C4C22×D1511yescharacteristic
434C22⋊C4—21no—
435C22⋊C4—301no—
436C22⋊C4—301no—
437C22⋊C4—301no—
438C22⋊C4—301no—
439C42—151no—
440C42—151no—
441C42—151no—
442C42—151no—
443C42—302no—
444C42—302no—
445C42—301no—
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3#406412yes—
450C22×C3C2×D4×D511yescharacteristic
451C2×D3—201no—
452C2×D3—201no—
453C2×D3—201no—
454C3×C4—24no—
455C3×C4—21no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4C2×#71112yes—
459Dic3—101no—
460Dic3—101no—
461Dic3—101no—
462Dic3—101no—
463Dic3—201no—
464Dic3—202no—
465C2×C5—22no—
466C2×C5#558611yescharacteristic
467C2×C5C2×#91811yescharacteristic
468C2×C5#577711yescharacteristic
469D5—241no—
470C23—301no—
471C23D4×D1511yescharacteristic
472Q8—24no—
473Q8—22no—
474Q8—22no—
475Q8#681914yes—
476D4—302no—
477D4—602no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—151no—
484C2×C4—151no—
485C2×C4—151no—
486C2×C4—151no—
487C2×C4—302no—
488C2×C4—302no—
489C2×C4—301no—
490C2×C4—602no—
491C2×C4—601no—
492C2×C4—602no—
493C2×C4D4×D1511yescharacteristic
494C2×C4C23×D1511yescharacteristic
495C8—22no—
496C8—302no—
497C2×C3—22no—
498C2×C3#6592011yescharacteristic
499C2×C3C2×#406411yescharacteristic
500C2×C3#6611111yescharacteristic
501D3—401no—
502C5#8017511yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—601no—
506C22—601no—
507C22—601no—
508C22#9180712yes—
509C22C2×D4×D1511yescharacteristic
510C4—24no—
511C4—21no—
512C4—41no—
513C4—41no—
514C4—301no—
515C4—301no—
516C4—301no—
517C4—301no—
518C4—601no—
519C4—602no—
520C4C2×#681912yes—
521C3#1061190611yescharacteristic, complemented, Sylow
522C2—22no—
523C2—1201no—
524C2#1175634511yescharacteristic
525C2C2×#9180711yescharacteristic
526C2#1175653611yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#451C2
socleC22×C3×C5C22×D4
prime radical#91819C22
hypercenter#451D15
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic15C2semidirect
3. C3×C5×#451C2semidirect
5. #11751286C2semidirect
6. #11751285C2semidirect
7. #11751145C2semidirect
8. #11750918C2semidirect
9. #11750900C2semidirect
11. #11750820C2semidirect
47. C5×#451D3semidirect
96. C3×#451D5semidirect
239. #451D15semidirect
446. C3×C5#3117semidirect
502. C5#80175semidirect
521. C3#10611906semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic152
#117563832
C3×C5×#4512
#117513282
#117512862
#117512852
#117511452
#117509182
#117509002
#117508362
#117508202
#106119063
#801755