Finite Group Databasebeta

← #14435540

Subgroups — #14435540

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×C5×#887C211yesmaximal, characteristic, complemented
2#11754422C211yesmaximal, characteristic
3#11751071C211yesmaximal, characteristic, complemented
4C3×#65257C211yesmaximal, characteristic
5#11748561C211yesmaximal, characteristic, complemented
6#11748536C211yesmaximal, characteristic
7#11748337C211yesmaximal, characteristic, complemented
8#11747396C212yesmaximal, complemented
9#11747373C212yesmaximal, complemented
10#11747276C212yesmaximal, complemented
11#11747222C212yesmaximal, complemented
12#10614176—31nomaximal, Hall
13C22×C5×Dic6C2211yescharacteristic
14C2×C3×C5×C4⋊C4C2211yescharacteristic
15#91813C2211yescharacteristic
16C2×C5×Dic3⋊C4—21no—
17C2×C4×C5×Dic3—21no—
18C2×C4×C5×Dic3C2211yescharacteristic
19C5×#887—21no—
20C5×#887—21no—
21C5×#887C2212yes—
22C5×#887C2212yes—
23C3×#4076C2211yescharacteristic
24Dic3×C22⋊D5—21no—
25#91536—21no—
26Dic3×D20C2211yescharacteristic
27#91393—21no—
28#91381C2211yescharacteristic
29#91364C2211yescharacteristic
30#91363—21no—
31#91340C2211yescharacteristic
32C2×#6663C2212yes—
33C2×#6655C2212yes—
34#91114C2211yescharacteristic
35#91094C2212yes—
36#91091C2212yes—
37C3×C22⋊#168C2211yescharacteristic
38C3×#3941C2212yes—
39C3×#3940C2212yes—
40Dic3⋊#168C2212yes—
41#90973C2212yes—
42#90972C2212yes—
43#90953C2212yes—
44#81311—51nomaximal, Hall
45C2×C4×C5×Q8—31no—
46#65813—31no—
47#65517—31no—
48#65516—31no—
49#65319—32no—
50#65317—32no—
51#65315—32no—
52#65311—32no—
53#65259—31no—
54#65257D311yescharacteristic
55#65215—31no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×Dic30C2311yescharacteristic
59C22×C5×Dic3—21no—
60C22×C5×Dic3D411yescharacteristic
61C22×C5×Dic3D411yescharacteristic
62C2×C5×Dic6—21no—
63C2×C5×Dic6—24no—
64C2×C5×Dic6C2312yes—
65C2×C3×C22⋊D5—21no—
66C2×C3×D20C2311yescharacteristic
67C2×D5×Dic3—21no—
68C3×C5×C4⋊C4—21no—
69C3×C5×C4⋊C4C2312yes—
70#6719—21no—
71C4⋊Dic15C2311yescharacteristic
72#6712—21no—
73C2×C3⋊#168C2312yes—
74C5×Dic3⋊C4—22no—
75C5×Dic3⋊C4—22no—
76C4×C5×Dic3—22no—
77C4×C5×Dic3—22no—
78C4×C5×Dic3D411yescharacteristic
79C4×C5×Dic3D411yescharacteristic
80C4×C5×Dic3C2311yescharacteristic
81C4×C5×Dic3C2311yescharacteristic
82C3×#685—21no—
83C3×C4⋊Dic5C2311yescharacteristic
84C2×C3×#168C2312yes—
85#6669—21no—
86#6669—21no—
87#6668—21no—
88#6665—21no—
89#6665—21no—
90#6665—21no—
91Dic3×Dic5—21no—
92#6663—24no—
93#6655—24no—
94#5600—51no—
95C2×#887D511yescharacteristic, complemented
96C3×#481—51no—
97#5040—51no—
98#4970—51no—
99#4857—52no—
100#4853—52no—
101#4767—52no—
102#4757—52no—
103#4739—51no—
104#4719—51no—
105C22×C5×Q8—31no—
106C4×C5×Q8—32no—
107C4×C5×Q8—32no—
108C4×C5×Q8—61no—
109C4×C5×Q8—61no—
110C2×C5×C4⋊C4—61no—
111C2×C5×C4⋊C4C2×D311yescharacteristic
112C2×C42×C5—31no—
113C2×C42×C5—61no—
114C2×#689—32no—
115C2×#688—32no—
116#4076C2×D311yescharacteristic
117#4075—61no—
118C4×C22⋊D5—61no—
119#4070—31no—
120#4022—61no—
121#4021—31no—
122C4×D20—31no—
123#4018—61no—
124#4016—31no—
125C4×Dic10—31no—
126#3967—32no—
127#3967—32no—
128C22⋊#168—31no—
129C22⋊#168C2×D311yescharacteristic
130#3942—32no—
131#3941C2×D312yes—
132#3940C2×D312yes—
133#3939—32no—
134C4⋊#168—32no—
135#3935—32no—
136#3117—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×C3×D5—21no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—42no—
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—21no—
145C2×Dic15—21no—
146Dic30—22no—
147C2×C5×Dic3—24no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—41no—
151C2×C5×Dic3C2×D411yescharacteristic
152C2×C5×Dic3C2×D411yescharacteristic
153C2×C5×Dic3C2×D411yescharacteristic
154C2×C5×Dic3C2×D411yescharacteristic
155C5×Dic6—24no—
156C5×Dic6—22no—
157C5×Dic6#4114yes—
158C3×C22⋊D5—42no—
159C2×C3×Dic5—21no—
160C3×D20—22no—
161D5×Dic3—42no—
162C3⋊#168—22no—
163C3×#168—22no—
164C22×Dic6C2×D511yescharacteristic
165C3×#121—51no—
166C2×C3×C4⋊C4C2×D511yescharacteristic
167#936—51no—
168#935—101no—
169D4×Dic3—51no—
170D4×Dic3—101no—
171C2×#214—52no—
172#924—51no—
173C2×Dic3⋊C4—21no—
174C2×C4×Dic3—21no—
175C2×C4×Dic3C2×D511yescharacteristic
176C2×Dic12—52no—
177#890—51no—
178#887—21no—
179#887—21no—
180#887—51no—
181#887C2×D512yes—
182#887C2×D512yes—
183#879—101no—
184#877—101no—
185C3×#106—52no—
186C3×#102—52no—
187C3×C22⋊C8—51no—
188#830—51no—
189#816—52no—
190#815—52no—
191Dic3⋊C8—52no—
192#810—52no—
193#810—52no—
194#807—52no—
195C2×C5×Q8—32no—
196C2×C5×Q8—64no—
197C2×C5×Q8—61no—
198C22×C4×C5—21no—
199C22×C4×C5—31no—
200C22×C4×C5—31no—
201C22×C4×C5—61no—
202C22×C4×C5C22×D311yescharacteristic
203C2×C22⋊D5—21no—
204C2×D20C22×D311yescharacteristic
205C2×C4×D5—61no—
206C2×Dic10—31no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—62no—
209C5×C4⋊C4—62no—
210C5×C4⋊C4C22×D312yes—
211C42×C5—31no—
212C42×C5—31no—
213C42×C5—31no—
214C42×C5—31no—
215C42×C5—62no—
216C42×C5—62no—
217C22⋊Dic5—61no—
218#689—64no—
219#688—64no—
220#685—21no—
221#685—61no—
222#685—61no—
223#685—61no—
224C4⋊Dic5—31no—
225C4⋊Dic5C22×D311yescharacteristic
226#683—61no—
227#683—61no—
228#683—61no—
229#683—61no—
230C4×Dic5—61no—
231C2×#168—32no—
232C2×#168C22×D312yes—
233#529—151no—
234C2×C4×Q8—31no—
235#484—151no—
236#481—51no—
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×C3×D5—41no—
249C2×C3×D5—41no—
250C2×C3×D5—41no—
251C3×C4×C5—21no—
252C3×C4×C5—42no—
253C3×C4×C5C2×#4112yes—
254Dic15—41no—
255Dic15—41no—
256C3×Dic5—41no—
257C5×Dic3—24no—
258C5×Dic3—21no—
259C5×Dic3—21no—
260C5×Dic3—21no—
261C5×Dic3—21no—
262C2×C3×D4—51no—
263C2×C3×D4—101no—
264C22×C3×C4—21no—
265C22×C3×C4C22×D511yescharacteristic
266C22×Dic3—21no—
267C22×Dic3—101no—
268C22×Dic3C22⋊D511yescharacteristic
269C22×Dic3C22⋊D511yescharacteristic
270C2×Dic6—21no—
271C2×Dic6—24no—
272C2×Dic6—51no—
273C2×Dic6C22×D512yes—
274C2×C3×C8—52no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—51no—
277C3×C4⋊C4C22×D512yes—
278C3×C22⋊C4—101no—
279#217—101no—
280#217—101no—
281#217—101no—
282#217—101no—
283#214—104no—
284C4⋊Dic3—51no—
285C4⋊Dic3—101no—
286Dic3⋊C4—22no—
287Dic3⋊C4—22no—
288Dic3⋊C4—101no—
289Dic3⋊C4—101no—
290Dic3⋊C4—101no—
291C4×Dic3—22no—
292C4×Dic3—22no—
293C4×Dic3—101no—
294C4×Dic3C22⋊D511yescharacteristic
295C4×Dic3C22⋊D511yescharacteristic
296C4×Dic3C22×D511yescharacteristic
297C4×Dic3C22×D511yescharacteristic
298C2×C3⋊C8—52no—
299Dic12—104no—
300C23×C5D3×D411yescharacteristic
301C22×D5—21no—
302C5×Q8—34no—
303C5×Q8—64no—
304C5×Q8—62no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—31no—
308C2×C4×C5—31no—
309C2×C4×C5—31no—
310C2×C4×C5—31no—
311C2×C4×C5—42no—
312C2×C4×C5—64no—
313C2×C4×C5—62no—
314C2×C4×C5—62no—
315C2×C4×C5—121no—
316C2×C4×C5D3×D411yescharacteristic
317C2×C4×C5C23×D311yescharacteristic
318C22⋊D5—42no—
319C2×Dic5—21no—
320C2×Dic5—61no—
321C2×Dic5—61no—
322D20—22no—
323C4×D5—122no—
324Dic10—62no—
325#168—22no—
326#168—62no—
327C22×Q8—31no—
328C2×Q16—152no—
329C2×SD16—152no—
330#126—301no—
331#125—151no—
332#124—151no—
333#123—301no—
334C22⋊Q8—151no—
335#121—51no—
336C4×Q8—32no—
337C4×Q8—32no—
338C4×Q8—61no—
339C4×Q8—61no—
340C4×Q8—151no—
341C4×D4—151no—
342C4×D4—301no—
343#117—301no—
344C2×C4⋊C4—61no—
345C2×C4⋊C4D3×D511yescharacteristic
346C2×C42—31no—
347C2×C42—61no—
348#107—152no—
349#106—52no—
350C4⋊C8—152no—
351#103—152no—
352#103—152no—
353#103—152no—
354#102—52no—
355C22⋊C8—51no—
356C22⋊C8—151no—
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×C3C2×C22⋊D511yescharacteristic
365C3×D4—102no—
366C3×D4—202no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—42no—
370C2×C3×C4—101no—
371C2×C3×C4C2×C22⋊D511yescharacteristic
372C2×C3×C4C23×D511yescharacteristic
373C2×Dic3—24no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—41no—
377C2×Dic3—101no—
378C2×Dic3—101no—
379C2×Dic3—202no—
380C2×Dic3C2×C22⋊D511yescharacteristic
381C2×Dic3C2×C22⋊D511yescharacteristic
382C2×Dic3C2×C22⋊D511yescharacteristic
383C2×Dic3C2×C22⋊D511yescharacteristic
384Dic6—24no—
385Dic6—22no—
386Dic6—102no—
387Dic6#70914yes—
388C3×C8—102no—
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—42no—
399C4×C5—64no—
400C4×C5—61no—
401C4×C5—61no—
402C4×C5—61no—
403C4×C5—61no—
404C4×C5D3×#4112yes—
405Dic5—41no—
406Dic5—121no—
407Dic5—121no—
408C2×Q8—32no—
409C2×Q8—64no—
410C2×Q8—61no—
411C2×Q8—151no—
412C2×D4—51no—
413C2×D4—101no—
414C22×C4—21no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—61no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—304no—
422C2×C8—52no—
423C2×C8—152no—
424C4⋊C4—21no—
425C4⋊C4—51no—
426C4⋊C4—62no—
427C4⋊C4—62no—
428C4⋊C4—151no—
429C4⋊C4—301no—
430C4⋊C4—301no—
431C4⋊C4—301no—
432C4⋊C4—301no—
433C4⋊C4C2×D3×D512yes—
434C22⋊C4—101no—
435C22⋊C4—301no—
436C22⋊C4—301no—
437C22⋊C4—301no—
438C22⋊C4—301no—
439C42—31no—
440C42—31no—
441C42—31no—
442C42—31no—
443C42—62no—
444C42—62no—
445C42—301no—
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—201no—
450C22×C3—201no—
451C22×C3—201no—
452C22×C3#408812yes—
453C22×C3C22×C22⋊D511yescharacteristic
454C3×C4—21no—
455C3×C4—42no—
456C3×C4—201no—
457C3×C4C2×#70912yes—
458Dic3—24no—
459Dic3—21no—
460Dic3—21no—
461Dic3—21no—
462Dic3—21no—
463Dic3—201no—
464Dic3—201no—
465C2×C5—22no—
466C2×C5#565611yescharacteristic
467C2×C5C2×#91511yescharacteristic
468C2×C5#577311yescharacteristic
469D5—81no—
470C23—101no—
471C23D3×C22⋊D511yescharacteristic
472Q8—34no—
473Q8—64no—
474Q8—62no—
475Q8—302no—
476D4—102no—
477D4—202no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—31no—
481C2×C4—31no—
482C2×C4—31no—
483C2×C4—31no—
484C2×C4—42no—
485C2×C4—64no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—101no—
489C2×C4—121no—
490C2×C4—301no—
491C2×C4—301no—
492C2×C4—602no—
493C2×C4D3×C22⋊D511yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—102no—
496C8—302no—
497C2×C3—22no—
498C2×C3—401no—
499C2×C3#6612511yescharacteristic
500C2×C3C2×#408811yescharacteristic
501C2×C3#6615611yescharacteristic
502C5#8131111yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—201no—
506C22—201no—
507C22—201no—
508C22#9151812yes—
509C22C2×D3×C22⋊D511yescharacteristic
510C4—21no—
511C4—42no—
512C4—64no—
513C4—61no—
514C4—61no—
515C4—61no—
516C4—61no—
517C4—201no—
518C4—601no—
519C4—601no—
520C4D3×#70912yes—
521C3#1061417611yescharacteristic, complemented, Sylow
522C2—22no—
523C2—401no—
524C2#1175433911yescharacteristic
525C2#1175469611yescharacteristic
526C2C2×#9151811yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC3×#4076C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#887C2semidirect
3. #11751071C2semidirect
5. #11748561C2semidirect
7. #11748337C2semidirect
8. #11747396C2semidirect
9. #11747373C2semidirect
10. #11747276C2semidirect
11. #11747222C2semidirect
95. C2×#887D5semidirect
446. C3×C5#3117semidirect
502. C5#81311semidirect
521. C3#10614176semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8872
#117544222
#117510712
C3×#652572
#117485612
#117485362
#117483372
#117473962
#117473732
#117472762
#117472222
#106141763
#813115