Finite Group Databasebeta

← #14435429

Subgroups — #14435429

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
1#11756383C211yesmaximal, characteristic
2C2×#91776C211yesmaximal, characteristic, complemented
3C3×C5×#484C211yesmaximal, characteristic, complemented
4#11751151C211yesmaximal, characteristic, complemented
5#11751069C211yesmaximal, characteristic
6#11750990C212yesmaximal, complemented
7#11750978C212yesmaximal, complemented
8#11750899C212yesmaximal, complemented
9#11750890C212yesmaximal, complemented
10#11750839C211yesmaximal, characteristic
11#11750820C211yesmaximal, characteristic, complemented
12#10613186—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C3×C5×C22⋊Q8C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16#91836C2211yescharacteristic
17Q8×Dic15C2211yescharacteristic
18C2×#6718C2212yes—
19#91819C2211yescharacteristic
20C2×#6712—21no—
21C2×C4×Dic15—21no—
22C2×C4×Dic15C2211yescharacteristic
23C2×#6706C2212yes—
24#91787—21no—
25#91782C2211yescharacteristic
26#91781—21no—
27#91779C2211yescharacteristic
28#91776—21no—
29#91776—21no—
30#91776C2212yes—
31#91776C2212yes—
32#91775—21no—
33#91770—21no—
34C3×C5×#107C2212yes—
35C3×C5×#103C2212yes—
36C3×C5×C22⋊C8C2211yescharacteristic
37#91114C2211yescharacteristic
38#91100C2212yes—
39#91099C2212yes—
40#91098C2212yes—
41#91094C2212yes—
42#91093C2212yes—
43#91092C2212yes—
44#81455—51nomaximal, Hall
45#65958—31no—
46C2×#4033—31no—
47C5×#484D311yescharacteristic, complemented
48#65339—31no—
49#65257—31no—
50#65178—32no—
51#65166—32no—
52#65087—32no—
53#65078—32no—
54#65027—31no—
55#65008—31no—
56C2×C3×C5×Q8C2311yescharacteristic
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×#1220—21no—
60C22×Dic15—21no—
61C22×Dic15D411yescharacteristic
62C22×Dic15D411yescharacteristic
63C2×D60C2311yescharacteristic
64C2×C4×D15—21no—
65C2×Dic30—21no—
66C2×Dic30—24no—
67C2×Dic30C2312yes—
68C2×C3×C5×C8C2312yes—
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2312yes—
72C3×C5×C4⋊C4C2311yescharacteristic
73C3×C5×C22⋊C4—21no—
74#6718—24no—
75#6714—21no—
76#6714—21no—
77#6714—21no—
78#6714—21no—
79C4⋊Dic15—21no—
80C4⋊Dic15—21no—
81C4⋊Dic15C2311yescharacteristic
82#6712—21no—
83#6712—22no—
84#6712—22no—
85C4×Dic15—21no—
86C4×Dic15—22no—
87C4×Dic15—22no—
88C4×Dic15D411yescharacteristic
89C4×Dic15D411yescharacteristic
90C4×Dic15C2311yescharacteristic
91C4×Dic15C2311yescharacteristic
92C2×C3⋊#168C2312yes—
93#6706—24no—
94#5624—51no—
95C2×#887—51no—
96C3×#484D511yescharacteristic, complemented
97#5050—51no—
98#4968—51no—
99#4889—52no—
100#4877—52no—
101#4798—52no—
102#4789—52no—
103#4738—51no—
104#4719—51no—
105C22×Dic10—31no—
106C5×C22⋊Q8C2×D311yescharacteristic
107C2×C5×C4⋊C4C2×D311yescharacteristic
108#4093—31no—
109Q8×Dic5—31no—
110C2×#689—32no—
111#4076—31no—
112C2×#683—61no—
113C2×C4×Dic5—31no—
114C2×C4×Dic5—61no—
115C2×#677—32no—
116#4044—61no—
117#4039—31no—
118#4038—61no—
119#4036—31no—
120#4033—32no—
121#4033—32no—
122#4033—61no—
123#4033—61no—
124#4032—61no—
125#4027—61no—
126C5×#107C2×D312yes—
127C5×#103C2×D312yes—
128C5×C22⋊C8C2×D311yescharacteristic
129C22⋊#168—31no—
130#3948—32no—
131#3947—32no—
132#3946—32no—
133#3942—32no—
134#3941—32no—
135#3940—32no—
136#3117—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×D15—21no—
139C3×C5×Q8—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—42no—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2411yescharacteristic
147#1220—42no—
148C2×Dic15—24no—
149C2×Dic15—22no—
150C2×Dic15—22no—
151C2×Dic15—21no—
152C2×Dic15—41no—
153C2×Dic15C2×D411yescharacteristic
154C2×Dic15C2×D411yescharacteristic
155C2×Dic15C2×D411yescharacteristic
156C2×Dic15C2×D411yescharacteristic
157D60—22no—
158C4×D15—42no—
159Dic30—24no—
160Dic30—22no—
161Dic30#4114yes—
162C3×C5×C8—22no—
163C3⋊#168—22no—
164C22×Dic6—51no—
165C3×C22⋊Q8C2×D511yescharacteristic
166C2×C3×C4⋊C4C2×D511yescharacteristic
167#947—51no—
168Q8×Dic3—51no—
169C2×#216—52no—
170#930—51no—
171C2×Dic3⋊C4—101no—
172C2×C4×Dic3—51no—
173C2×C4×Dic3—101no—
174C2×#204—52no—
175#898—101no—
176#893—51no—
177#892—101no—
178#890—51no—
179#887—52no—
180#887—52no—
181#887—101no—
182#887—101no—
183#886—101no—
184#67⋊C4—101no—
185C3×#107C2×D512yes—
186C3×#103C2×D512yes—
187C3×C22⋊C8C2×D511yescharacteristic
188#830—51no—
189#816—52no—
190#815—52no—
191Dic3⋊C8—52no—
192#810—52no—
193#809—52no—
194#808—52no—
195C2×C5×Q8C22×D311yescharacteristic
196C22×C4×C5—21no—
197C22×C4×C5C22×D311yescharacteristic
198C2×C22⋊D5—61no—
199C22×Dic5—31no—
200C22×Dic5—31no—
201C22×Dic5—61no—
202C2×D20—31no—
203C2×C4×D5—61no—
204C2×Dic10—32no—
205C2×Dic10—64no—
206C2×Dic10—61no—
207C2×C5×C8C22×D312yes—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4C22×D312yes—
211C5×C4⋊C4C22×D311yescharacteristic
212C5×C22⋊C4—21no—
213#689—64no—
214#685—61no—
215#685—61no—
216#685—61no—
217#685—61no—
218C4⋊Dic5—31no—
219C4⋊Dic5—61no—
220C4⋊Dic5—61no—
221#683—61no—
222#683—62no—
223#683—62no—
224C4×Dic5—31no—
225C4×Dic5—31no—
226C4×Dic5—31no—
227C4×Dic5—31no—
228C4×Dic5—61no—
229C4×Dic5—62no—
230C4×Dic5—62no—
231C2×#168—32no—
232#677—64no—
233#529—151no—
234C2×C4×Q8—151no—
235#484D1511yescharacteristic, complemented
236#481—151no—
237#479—152no—
238#464—152no—
239#451—151no—
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—21no—
252C3×C4×C5—41no—
253C3×C4×C5—41no—
254C3×C4×C5—42no—
255C3×C4×C5C2×#4112yes—
256Dic15—24no—
257Dic15—21no—
258Dic15—21no—
259Dic15—21no—
260Dic15—21no—
261Dic15—41no—
262C2×C3×Q8C22×D511yescharacteristic
263C22×C3×C4—21no—
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—101no—
266C22×Dic3—51no—
267C22×Dic3—51no—
268C22×Dic3—101no—
269C2×D12—51no—
270C2×C4×D3—101no—
271C2×Dic6—52no—
272C2×Dic6—104no—
273C2×Dic6—101no—
274C2×C3×C8C22×D512yes—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4C22×D512yes—
278C3×C4⋊C4C22×D511yescharacteristic
279C3×C22⋊C4—21no—
280#216—104no—
281(C2×D3)⋊C4—101no—
282(C2×D3)⋊C4—101no—
283(C2×D3)⋊C4—101no—
284(C2×D3)⋊C4—101no—
285C4⋊Dic3—51no—
286C4⋊Dic3—101no—
287C4⋊Dic3—101no—
288Dic3⋊C4—101no—
289Dic3⋊C4—102no—
290Dic3⋊C4—102no—
291C4×Dic3—51no—
292C4×Dic3—51no—
293C4×Dic3—51no—
294C4×Dic3—51no—
295C4×Dic3—101no—
296C4×Dic3—102no—
297C4×Dic3—102no—
298C2×C3⋊C8—52no—
299#204—104no—
300C23×C5D3×D411yescharacteristic
301C22×D5—61no—
302C5×Q8—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—42no—
308C2×C4×C5D3×D411yescharacteristic
309C2×C4×C5C23×D311yescharacteristic
310C22⋊D5—122no—
311C2×Dic5—31no—
312C2×Dic5—31no—
313C2×Dic5—31no—
314C2×Dic5—31no—
315C2×Dic5—64no—
316C2×Dic5—62no—
317C2×Dic5—62no—
318C2×Dic5—61no—
319C2×Dic5—121no—
320D20—62no—
321C4×D5—122no—
322Dic10—34no—
323Dic10—64no—
324Dic10—62no—
325C5×C8—22no—
326#168—62no—
327C22×Q8—151no—
328C2×Q16—152no—
329C2×SD16—152no—
330#126—301no—
331#125—151no—
332#124—151no—
333#123—301no—
334C22⋊Q8C2×D1511yescharacteristic
335#121—151no—
336C4×Q8—151no—
337C4×Q8—152no—
338C4×Q8—152no—
339C4×Q8—301no—
340C4×Q8—301no—
341C4×D4—151no—
342C4×D4—301no—
343#117—301no—
344C2×C4⋊C4—301no—
345C2×C4⋊C4C2×D1511yescharacteristic
346C2×C42—151no—
347C2×C42—301no—
348#107C2×D1512yes—
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—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—42no—
371C2×C3×C4D4×D511yescharacteristic
372C2×C3×C4C23×D511yescharacteristic
373#67—202no—
374C2×Dic3—51no—
375C2×Dic3—51no—
376C2×Dic3—51no—
377C2×Dic3—51no—
378C2×Dic3—104no—
379C2×Dic3—102no—
380C2×Dic3—102no—
381C2×Dic3—101no—
382C2×Dic3—201no—
383D12—102no—
384C4×D3—202no—
385Dic6—54no—
386Dic6—104no—
387Dic6—102no—
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—21no—
398C4×C5—41no—
399C4×C5—41no—
400C4×C5—42no—
401C4×C5D3×#4112yes—
402Dic5—64no—
403Dic5—61no—
404Dic5—61no—
405Dic5—61no—
406Dic5—61no—
407Dic5—121no—
408C2×Q8—152no—
409C2×Q8—304no—
410C2×Q8—301no—
411C2×Q8C22×D1511yescharacteristic
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—304no—
421SD16—304no—
422C2×C8—152no—
423C2×C8C22×D1512yes—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—151no—
427C4⋊C4—302no—
428C4⋊C4—302no—
429C4⋊C4—301no—
430C4⋊C4—301no—
431C4⋊C4—301no—
432C4⋊C4C22×D1512yes—
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—21no—
455C3×C4—41no—
456C3×C4—42no—
457C3×C4—41no—
458C3×C4D5×#4112yes—
459Dic3—101no—
460Dic3—101no—
461Dic3—101no—
462Dic3—101no—
463Dic3—104no—
464Dic3—201no—
465C2×C5—22no—
466C2×C5#565611yescharacteristic
467C2×C5C2×#91811yescharacteristic
468C2×C5#577311yescharacteristic
469D5—241no—
470C23—301no—
471C23D4×D1511yescharacteristic
472Q8—22no—
473Q8—154no—
474Q8—304no—
475Q8—302no—
476D4—302no—
477D4—602no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—42no—
483C2×C4—151no—
484C2×C4—151no—
485C2×C4—151no—
486C2×C4—151no—
487C2×C4—304no—
488C2×C4—302no—
489C2×C4—302no—
490C2×C4—301no—
491C2×C4—602no—
492C2×C4—601no—
493C2×C4D4×D1511yescharacteristic
494C2×C4C23×D1511yescharacteristic
495C8—22no—
496C8—302no—
497C2×C3—22no—
498C2×C3#6599011yescharacteristic
499C2×C3C2×#406411yescharacteristic
500C2×C3#6610711yescharacteristic
501D3—401no—
502C5#8145511yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—601no—
506C22—601no—
507C22—601no—
508C22#9180712yes—
509C22C2×D4×D1511yescharacteristic
510C4—21no—
511C4—41no—
512C4—42no—
513C4—41no—
514C4—304no—
515C4—301no—
516C4—301no—
517C4—301no—
518C4—301no—
519C4—601no—
520C4#41×D1512yes—
521C3#1061318611yescharacteristic, complemented, Sylow
522C2—22no—
523C2—1201no—
524C2#1175641511yescharacteristic
525C2C2×#9180711yescharacteristic
526C2#1175653211yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#484C2
socleC22×C3×C5C22×D4
prime radical#91819C22
hypercenter#484D15
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#91776C2semidirect
3. C3×C5×#484C2semidirect
4. #11751151C2semidirect
6. #11750990C2semidirect
7. #11750978C2semidirect
8. #11750899C2semidirect
9. #11750890C2semidirect
11. #11750820C2semidirect
47. C5×#484D3semidirect
96. C3×#484D5semidirect
235. #484D15semidirect
446. C3×C5#3117semidirect
502. C5#81455semidirect
521. C3#10613186semidirect

Maximal subgroups

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

subgroupindex
#117563832
C2×#917762
C3×C5×#4842
#117511512
#117510692
#117509902
#117509782
#117508992
#117508902
#117508392
#117508202
#106131863
#814555