Finite Group Databasebeta

← #14435446

Subgroups — #14435446

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#11754451C211yesmaximal, characteristic
2C2×#91331C211yesmaximal, characteristic, complemented
3#11750820C211yesmaximal, characteristic, complemented
4C5×#4722C211yesmaximal, characteristic, complemented
5C3×#65027C211yesmaximal, characteristic
6#11748555C211yesmaximal, characteristic, complemented
7#11748372C211yesmaximal, characteristic
8#11747878C212yesmaximal, complemented
9#11747836C212yesmaximal, complemented
10#11747829C212yesmaximal, complemented
11#11747812C212yesmaximal, complemented
12#10613186—31nomaximal, Hall
13C22×C3×Dic10C2211yescharacteristic
14C2×C4×Dic15C2211yescharacteristic
15C2×C5×C4⋊Dic3C2211yescharacteristic
16C5×#924C2211yescharacteristic
17C3×#4076C2211yescharacteristic
18C2×C3×#677C2212yes—
19#91559—21no—
20C2×#6668—21no—
21#91537—21no—
22C2×Dic3×Dic5—21no—
23#91434C2211yescharacteristic
24#91394—21no—
25#91384C2211yescharacteristic
26#91368C2211yescharacteristic
27#91366—21no—
28#91344C2211yescharacteristic
29#91331—21no—
30#91331—21no—
31#91331C2212yes—
32#91331C2212yes—
33C2×#6661C2212yes—
34C3×C5×C22⋊C8C2211yescharacteristic
35#91114C2211yescharacteristic
36#91099C2212yes—
37#91098C2212yes—
38C5×#818C2212yes—
39C5×#816C2212yes—
40C3×#3948C2212yes—
41#90986C2212yes—
42#90970C2212yes—
43#90964C2212yes—
44#80031—51nomaximal, Hall
45#65958—31no—
46C2×#4033—31no—
47C5×#484—31no—
48#65339—31no—
49#65257—31no—
50#65178—32no—
51#65166—32no—
52#65087—32no—
53#65078—32no—
54#65027D311yescharacteristic
55#65008—31no—
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15D411yescharacteristic
58C22×Dic15D411yescharacteristic
59C22×C5×Dic3—21no—
60C2×C5×Dic6C2311yescharacteristic
61C2×C3×C22⋊D5—21no—
62C22×C3×Dic5—21no—
63C2×C3×D20C2311yescharacteristic
64C2×C3×Dic10—21no—
65C2×C3×Dic10—24no—
66C2×C3×Dic10C2312yes—
67C2×D5×Dic3—21no—
68C2×C3×C5×C8C2312yes—
69C4×Dic15D411yescharacteristic
70C4×Dic15D411yescharacteristic
71C4×Dic15C2311yescharacteristic
72C4×Dic15C2311yescharacteristic
73C2×C3⋊#168C2312yes—
74C5×#217—21no—
75C5×C4⋊Dic3—21no—
76C5×C4⋊Dic3C2311yescharacteristic
77C5×C4⋊Dic3C2312yes—
78C5×Dic3⋊C4—21no—
79C3×#685—21no—
80C3×C4⋊Dic5C2311yescharacteristic
81C3×#677—24no—
82Dic3⋊Dic5—21no—
83Dic3⋊Dic5—21no—
84#6668—22no—
85#6668—22no—
86#6668—21no—
87#6665—21no—
88#6665—21no—
89#6665—21no—
90Dic3×Dic5—21no—
91Dic3×Dic5—22no—
92Dic3×Dic5—22no—
93#6661—24no—
94C2×Q8×Dic3—51no—
95#5600—51no—
96C3×#448—51no—
97#5228—51no—
98#5166—52no—
99#5164—52no—
100#5034—51no—
101#4796—52no—
102#4789—52no—
103#4722D511yescharacteristic, complemented
104#4719—51no—
105C22×Dic10C2×D311yescharacteristic
106C5×C22⋊Q8—31no—
107C2×C5×C4⋊C4—31no—
108#4093—31no—
109Q8×Dic5—31no—
110C2×#689—32no—
111#4076C2×D311yescharacteristic
112C2×#683—61no—
113C2×C4×Dic5—31no—
114C2×C4×Dic5—61no—
115C2×#677C2×D312yes—
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×#107—32no—
127C5×#103—32no—
128C5×C22⋊C8C2×D311yescharacteristic
129C22⋊#168—31no—
130#3948C2×D312yes—
131#3947—32no—
132#3946—32no—
133#3942—32no—
134#3941—32no—
135#3940—32no—
136#3117—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×C3×D5—21no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—22no—
143C2×Dic15—41no—
144C2×Dic15C2×D411yescharacteristic
145C2×Dic15C2×D411yescharacteristic
146C2×Dic15C2×D411yescharacteristic
147C2×Dic15C2×D411yescharacteristic
148C2×C5×Dic3—22no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—42no—
152C5×Dic6—22no—
153C3×C22⋊D5—42no—
154C2×C3×Dic5—24no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—21no—
157C3×D20—22no—
158C3×Dic10—24no—
159C3×Dic10—22no—
160C3×Dic10#4114yes—
161D5×Dic3—42no—
162C3×C5×C8—22no—
163C3⋊#168—22no—
164C22×C3×Q8—51no—
165C2×C3×SD16—52no—
166C3×#121—51no—
167Q8×Dic3—52no—
168Q8×Dic3—52no—
169Q8×Dic3—101no—
170Q8×Dic3—101no—
171C2×#216—52no—
172#936—51no—
173#935—101no—
174D4×Dic3—51no—
175D4×Dic3—101no—
176C2×C4⋊Dic3—101no—
177C2×C4⋊Dic3C2×D511yescharacteristic
178#924C2×D511yescharacteristic
179C2×C4×Dic3—51no—
180C2×C4×Dic3—101no—
181#890—51no—
182#887—51no—
183#879—101no—
184#877—101no—
185C3×#103—52no—
186C3×C22⋊C8C2×D511yescharacteristic
187#835—52no—
188#832—52no—
189#830—51no—
190#818C2×D512yes—
191#816C2×D512yes—
192#815—52no—
193Dic3⋊C8—52no—
194#808—52no—
195C2×C5×Q8—31no—
196C22×C4×C5—61no—
197C22×C4×C5C22×D311yescharacteristic
198C2×C22⋊D5—21no—
199C22×Dic5—21no—
200C22×Dic5—31no—
201C22×Dic5—31no—
202C2×D20C22×D311yescharacteristic
203C2×C4×D5—61no—
204C2×Dic10—21no—
205C2×Dic10—24no—
206C2×Dic10C22×D312yes—
207C2×C5×C8C22×D312yes—
208C5×C4⋊C4—32no—
209C5×C4⋊C4—31no—
210C5×C4⋊C4—61no—
211C5×C4⋊C4—61no—
212C5×C22⋊C4—61no—
213#689—64no—
214#685—21no—
215#685—61no—
216#685—61no—
217#685—61no—
218C4⋊Dic5—61no—
219C4⋊Dic5—61no—
220C4⋊Dic5C22×D311yescharacteristic
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—24no—
233#529—151no—
234C2×C4×Q8—151no—
235#484—31no—
236#481—151no—
237#479—152no—
238#464—152no—
239#451—151no—
240#448—51no—
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×C3×D5—41no—
249C2×C3×D5—41no—
250C2×C3×D5—41no—
251C3×C4×C5—21no—
252C3×C4×C5C2×#4112yes—
253Dic15—21no—
254Dic15—21no—
255Dic15—21no—
256Dic15—21no—
257C3×Dic5—24no—
258C3×Dic5—41no—
259C5×Dic3—41no—
260C5×Dic3—41no—
261C5×Dic3—42no—
262C2×C3×Q8—52no—
263C2×C3×Q8—104no—
264C2×C3×Q8—101no—
265C2×C3×D4—51no—
266C2×C3×D4—101no—
267C22×C3×C4—101no—
268C22×C3×C4C22×D511yescharacteristic
269C22×Dic3—21no—
270C22×Dic3—51no—
271C22×Dic3—51no—
272C22×Dic3—101no—
273C2×Dic6C22×D511yescharacteristic
274C3×SD16—104no—
275C2×C3×C8C22×D512yes—
276C3×C4⋊C4—51no—
277C3×C22⋊C4—101no—
278#217—21no—
279#217—101no—
280#217—101no—
281#217—101no—
282#216—104no—
283C4⋊Dic3—21no—
284C4⋊Dic3—101no—
285C4⋊Dic3—102no—
286C4⋊Dic3—102no—
287C4⋊Dic3C22×D512yes—
288C4⋊Dic3C22×D511yescharacteristic
289Dic3⋊C4—21no—
290Dic3⋊C4—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—21no—
302C5×Q8—62no—
303C2×C4×C5—22no—
304C2×C4×C5—62no—
305C2×C4×C5—61no—
306C2×C4×C5—61no—
307C2×C4×C5—122no—
308C2×C4×C5D3×D411yescharacteristic
309C2×C4×C5C23×D311yescharacteristic
310C22⋊D5—42no—
311C2×Dic5—24no—
312C2×Dic5—22no—
313C2×Dic5—21no—
314C2×Dic5—31no—
315C2×Dic5—31no—
316C2×Dic5—31no—
317C2×Dic5—31no—
318C2×Dic5—62no—
319C2×Dic5—121no—
320D20—22no—
321C4×D5—122no—
322Dic10—24no—
323Dic10—22no—
324Dic10#23714yes—
325C5×C8—22no—
326#168—62no—
327C22×Q8—51no—
328C2×Q16—152no—
329C2×SD16—52no—
330#126—301no—
331#125—151no—
332#124—151no—
333#123—301no—
334C22⋊Q8—31no—
335#121—51no—
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—31no—
345C2×C4⋊C4—301no—
346C2×C42—151no—
347C2×C42—301no—
348#107—32no—
349#106—152no—
350C4⋊C8—152no—
351#103—32no—
352#103—52no—
353#103—152no—
354#102—152no—
355C22⋊C8—151no—
356C22⋊C8D3×D511yescharacteristic
357#97—152no—
358C2×C3×C5—22no—
359C2×C3×C5#52511yescharacteristic
360C2×C3×C5C2×#13711yescharacteristic
361C2×C3×C5#57511yescharacteristic
362C3×D5—81no—
363C23×C3—101no—
364C23×C3D4×D511yescharacteristic
365C3×Q8—54no—
366C3×Q8—104no—
367C3×Q8—102no—
368C3×D4—102no—
369C3×D4—202no—
370C2×C3×C4—22no—
371C2×C3×C4—104no—
372C2×C3×C4—102no—
373C2×C3×C4—101no—
374C2×C3×C4D4×D511yescharacteristic
375C2×C3×C4C23×D511yescharacteristic
376C2×Dic3—22no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—42no—
380C2×Dic3—51no—
381C2×Dic3—51no—
382C2×Dic3—51no—
383C2×Dic3—51no—
384C2×Dic3—102no—
385C2×Dic3—202no—
386C2×Dic3—201no—
387Dic6—22no—
388C3×C8—22no—
389C3⋊C8—102no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5#91512yes—
393C22×C5C2×D3×D411yescharacteristic
394C2×D5—41no—
395C2×D5—41no—
396C2×D5—41no—
397C4×C5—21no—
398C4×C5—121no—
399C4×C5—122no—
400C4×C5—121no—
401C4×C5C2×#23712yes—
402Dic5—24no—
403Dic5—41no—
404Dic5—61no—
405Dic5—61no—
406Dic5—61no—
407Dic5—61no—
408C2×Q8—31no—
409C2×Q8—52no—
410C2×Q8—104no—
411C2×Q8—101no—
412C2×D4—51no—
413C2×D4—101no—
414C22×C4—61no—
415C22×C4—101no—
416C22×C4—151no—
417C22×C4—151no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—104no—
422C2×C8—152no—
423C2×C8C2×D3×D512yes—
424C4⋊C4—32no—
425C4⋊C4—31no—
426C4⋊C4—51no—
427C4⋊C4—61no—
428C4⋊C4—61no—
429C4⋊C4—302no—
430C4⋊C4—302no—
431C4⋊C4—301no—
432C4⋊C4—301no—
433C4⋊C4—301no—
434C22⋊C4—61no—
435C22⋊C4—101no—
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—201no—
450C22×C3—201no—
451C22×C3—201no—
452C22×C3#406412yes—
453C22×C3C2×D4×D511yescharacteristic
454C3×C4—21no—
455C3×C4—104no—
456C3×C4—201no—
457C3×C4D5×#4112yes—
458Dic3—42no—
459Dic3—41no—
460Dic3—41no—
461Dic3—101no—
462Dic3—101no—
463Dic3—101no—
464Dic3—101no—
465C2×C5—22no—
466C2×C5#558611yescharacteristic
467C2×C5C2×#91511yescharacteristic
468C2×C5#577711yescharacteristic
469D5—81no—
470C23—101no—
471C23#677711yescharacteristic
472Q8—54no—
473Q8—62no—
474Q8—104no—
475Q8—102no—
476D4—102no—
477D4—202no—
478C2×C4—22no—
479C2×C4—62no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—104no—
483C2×C4—102no—
484C2×C4—101no—
485C2×C4—122no—
486C2×C4—151no—
487C2×C4—151no—
488C2×C4—151no—
489C2×C4—151no—
490C2×C4—302no—
491C2×C4—602no—
492C2×C4—601no—
493C2×C4#677711yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—22no—
496C8—302no—
497C2×C3—22no—
498C2×C3—401no—
499C2×C3#6599011yescharacteristic
500C2×C3C2×#406411yescharacteristic
501C2×C3#6610711yescharacteristic
502C5#8003111yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—201no—
506C22—201no—
507C22—201no—
508C22#9127812yes—
509C22C2×#677711yescharacteristic
510C4—21no—
511C4—104no—
512C4—122no—
513C4—121no—
514C4—121no—
515C4—201no—
516C4—301no—
517C4—301no—
518C4—301no—
519C4—301no—
520C4D5×#23712yes—
521C3#1061318611yescharacteristic, complemented, Sylow
522C2—22no—
523C2—401no—
524C2#1175288011yescharacteristic
525C2C2×#9127811yescharacteristic
526C2#1175403511yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC3×#4076C22
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#91331C2semidirect
3. #11750820C2semidirect
4. C5×#4722C2semidirect
6. #11748555C2semidirect
8. #11747878C2semidirect
9. #11747836C2semidirect
10. #11747829C2semidirect
11. #11747812C2semidirect
103. #4722D5semidirect
446. C3×C5#3117semidirect
502. C5#80031semidirect
521. C3#10613186semidirect

Maximal subgroups

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

subgroupindex
#117544512
C2×#913312
#117508202
C5×#47222
C3×#650272
#117485552
#117483722
#117478782
#117478362
#117478292
#117478122
#106131863
#800315