Finite Group Databasebeta

← #14435451

Subgroups — #14435451

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
1C5×#5624C211yesmaximal, characteristic
2C2×#91340C211yesmaximal, characteristic, complemented
3#11751151C211yesmaximal, characteristic, complemented
4C3×#65333C211yesmaximal, characteristic, complemented
5#11749260C212yesmaximal, complemented
6#11749258C212yesmaximal, complemented
7#11748553C211yesmaximal, characteristic
8#11748385C211yesmaximal, characteristic
9#11748337C211yesmaximal, characteristic, complemented
10#11747473C212yesmaximal, complemented
11#11747290C212yesmaximal, complemented
12#10614884—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C3×C5×C22⋊Q8C2211yescharacteristic
15C2×#6718C2212yes—
16C5×#947C2211yescharacteristic
17C5×Q8×Dic3C2211yescharacteristic
18C5×#930C2211yescharacteristic
19C2×C4×C5×Dic3C2211yescharacteristic
20C5×#898—21no—
21C5×#893C2211yescharacteristic
22C5×#892—21no—
23C5×#890C2211yescharacteristic
24C5×#886—21no—
25C5×#67⋊C4—21no—
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×#6669—21no—
28C2×Dic3×Dic5—21no—
29#91340—21no—
30#91340—21no—
31#91340C2212yes—
32#91340C2212yes—
33C2×#6659C2212yes—
34#91114C2211yescharacteristic
35#91094C2212yes—
36C3×#3967C2212yes—
37C3×C22⋊#168C2211yescharacteristic
38C3×#3939C2212yes—
39#90986C2212yes—
40Dic3⋊#168C2212yes—
41#90975C2212yes—
42#90966C2212yes—
43#90953C2212yes—
44#81455—51nomaximal, Hall
45C5×#529—31no—
46C2×C4×Dic10—31no—
47#65352—32no—
48#65343—32no—
49#65339—31no—
50#65333D311yescharacteristic, complemented
51#65329—31no—
52#65323—31no—
53#65319—32no—
54#65307—32no—
55#65215—31no—
56C2×C3×C5×Q8C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×Dic15—21no—
59C2×Dic30—21no—
60C2×Dic30—24no—
61C2×Dic30C2312yes—
62C2×C5×#67—21no—
63C22×C5×Dic3D411yescharacteristic
64C22×C5×Dic3D411yescharacteristic
65C2×C5×D12C2311yescharacteristic
66C2×C4×C5×D3—21no—
67C22×C3×Dic5—21no—
68C3×C5×C4⋊C4—21no—
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C22⋊C4—21no—
71#6718—24no—
72C2×C3⋊#168C2312yes—
73C5×(C2×D3)⋊C4—21no—
74C5×(C2×D3)⋊C4—21no—
75C5×(C2×D3)⋊C4—21no—
76C5×(C2×D3)⋊C4—21no—
77C5×C4⋊Dic3—21no—
78C5×C4⋊Dic3—21no—
79C5×C4⋊Dic3C2311yescharacteristic
80C5×Dic3⋊C4—21no—
81C4×C5×Dic3—21no—
82C4×C5×Dic3D411yescharacteristic
83C4×C5×Dic3D411yescharacteristic
84C4×C5×Dic3C2311yescharacteristic
85C4×C5×Dic3C2311yescharacteristic
86C3×C4⋊Dic5—21no—
87C3×C4⋊Dic5C2312yes—
88C2×C3×#168C2312yes—
89#6669—22no—
90#6669—22no—
91Dic3×Dic5—22no—
92Dic3×Dic5—22no—
93#6659—24no—
94#5624D511yescharacteristic
95C2×#887—51no—
96C3×#484—51no—
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×#126—61no—
107C5×#125—31no—
108C5×#124—31no—
109C5×#123—61no—
110C5×C22⋊Q8C2×D311yescharacteristic
111C5×#121—31no—
112C4×C5×Q8—31no—
113C4×C5×D4—31no—
114C4×C5×D4—61no—
115C5×#117—61no—
116C2×C42×C5—31no—
117C2×#689—32no—
118C2×#687—32no—
119C2×C4⋊Dic5C2×D311yescharacteristic
120C2×#683—61no—
121C2×C4×Dic5—61no—
122C4×Dic10—32no—
123C4×Dic10—32no—
124C4×Dic10—61no—
125C4×Dic10—61no—
126#3967C2×D312yes—
127#3964—32no—
128C22⋊#168—31no—
129C22⋊#168C2×D311yescharacteristic
130#3942—32no—
131#3942—32no—
132#3940—32no—
133#3939C2×D312yes—
134C4⋊#168—32no—
135#3935—32no—
136#3117—151noSylow
137C23×C3×C5C2×D411yescharacteristic
138C22×C5×D3—21no—
139C3×C5×Q8—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2411yescharacteristic
145C2×Dic15—24no—
146C2×Dic15—22no—
147Dic30—24no—
148Dic30—22no—
149Dic30#4114yes—
150C5×#67—42no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—21no—
153C2×C5×Dic3—41no—
154C2×C5×Dic3C2×D411yescharacteristic
155C2×C5×Dic3C2×D411yescharacteristic
156C2×C5×Dic3C2×D411yescharacteristic
157C2×C5×Dic3C2×D411yescharacteristic
158C5×D12—22no—
159C4×C5×D3—42no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—42no—
162C3⋊#168—22no—
163C3×#168—22no—
164C22×Dic6—51no—
165C3×C22⋊Q8C2×D511yescharacteristic
166C2×C3×C4⋊C4—51no—
167#947C2×D511yescharacteristic
168Q8×Dic3C2×D511yescharacteristic
169C2×#216—52no—
170#930C2×D511yescharacteristic
171C2×Dic3⋊C4—101no—
172C2×C4×Dic3—101no—
173C2×C4×Dic3C2×D511yescharacteristic
174C2×#204—52no—
175#898—21no—
176#893C2×D511yescharacteristic
177#892—21no—
178#890C2×D511yescharacteristic
179#887—52no—
180#887—52no—
181#887—101no—
182#887—101no—
183#886—21no—
184#67⋊C4—21no—
185C3×#107—52no—
186C3×#103—52no—
187C3×C22⋊C8—51no—
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
196C2×C5×D4—31no—
197C2×C5×D4—61no—
198C22×C4×C5—31no—
199C22×C4×C5—31no—
200C22×C4×C5—61no—
201C22×C4×C5C22×D311yescharacteristic
202C22×Dic5—21no—
203C22×Dic5—61no—
204C2×Dic10—32no—
205C2×Dic10—64no—
206C2×Dic10—61no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—31no—
209C5×C4⋊C4—61no—
210C5×C4⋊C4—61no—
211C5×C4⋊C4—61no—
212C5×C4⋊C4C22×D311yescharacteristic
213C5×C22⋊C4—21no—
214C5×C22⋊C4—61no—
215C5×C22⋊C4—61no—
216C5×C22⋊C4—61no—
217C5×C22⋊C4—61no—
218C42×C5—31no—
219C42×C5—31no—
220C42×C5—31no—
221C42×C5—31no—
222C42×C5—61no—
223#689—64no—
224#687—64no—
225C4⋊Dic5—21no—
226C4⋊Dic5C22×D312yes—
227#683—62no—
228#683—62no—
229C4×Dic5—62no—
230C4×Dic5—62no—
231C2×#168—32no—
232C2×#168C22×D312yes—
233#529—31no—
234C2×C4×Q8—151no—
235#484—51no—
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×C5×D3—41no—
249C2×C5×D3—41no—
250C2×C5×D3—41no—
251C3×C4×C5—21no—
252C3×C4×C5—41no—
253C3×C4×C5—41no—
254C3×C4×C5C2×#4112yes—
255Dic15—24no—
256C3×Dic5—42no—
257C5×Dic3—21no—
258C5×Dic3—21no—
259C5×Dic3—21no—
260C5×Dic3—21no—
261C5×Dic3—41no—
262C2×C3×Q8C22×D511yescharacteristic
263C22×C3×C4—101no—
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—21no—
266C22×Dic3—101no—
267C22×Dic3C22⋊D511yescharacteristic
268C22×Dic3C22⋊D511yescharacteristic
269C2×D12C22×D511yescharacteristic
270C2×C4×D3—21no—
271C2×Dic6—52no—
272C2×Dic6—104no—
273C2×Dic6—101no—
274C2×C3×C8—52no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—52no—
277C3×C4⋊C4—101no—
278C3×C4⋊C4C22×D511yescharacteristic
279C3×C22⋊C4—21no—
280#216—104no—
281(C2×D3)⋊C4—21no—
282(C2×D3)⋊C4—21no—
283(C2×D3)⋊C4—21no—
284(C2×D3)⋊C4—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287C4⋊Dic3C22×D511yescharacteristic
288Dic3⋊C4—21no—
289Dic3⋊C4—102no—
290Dic3⋊C4—102no—
291C4×Dic3—21no—
292C4×Dic3—102no—
293C4×Dic3—102no—
294C4×Dic3C22⋊D511yescharacteristic
295C4×Dic3C22⋊D511yescharacteristic
296C4×Dic3C22×D511yescharacteristic
297C4×Dic3C22×D511yescharacteristic
298C2×C3⋊C8—52no—
299#204—104no—
300C23×C5—61no—
301C23×C5D3×D411yescharacteristic
302C5×Q8—22no—
303C5×D4—62no—
304C5×D4—122no—
305C2×C4×C5—22no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—31no—
309C2×C4×C5—31no—
310C2×C4×C5—31no—
311C2×C4×C5—31no—
312C2×C4×C5—62no—
313C2×C4×C5—61no—
314C2×C4×C5—122no—
315C2×C4×C5—121no—
316C2×C4×C5D3×D411yescharacteristic
317C2×C4×C5C23×D311yescharacteristic
318C2×Dic5—22no—
319C2×Dic5—42no—
320C2×Dic5—64no—
321C2×Dic5—62no—
322Dic10—34no—
323Dic10—64no—
324Dic10—62no—
325#168—22no—
326#168—62no—
327C22×Q8—151no—
328C2×Q16—152no—
329C2×SD16—152no—
330#126—61no—
331#125—31no—
332#124—31no—
333#123—61no—
334C22⋊Q8D3×D511yescharacteristic
335#121—31no—
336C4×Q8—31no—
337C4×Q8—152no—
338C4×Q8—152no—
339C4×Q8—301no—
340C4×Q8—301no—
341C4×D4—31no—
342C4×D4—61no—
343#117—61no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—301no—
346C2×C42—31no—
347C2×C42—301no—
348#107—52no—
349#106—152no—
350C4⋊C8—152no—
351#103—52no—
352#103—152no—
353#103—152no—
354#102—152no—
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
362C5×D3—81no—
363C23×C3C2×C22⋊D511yescharacteristic
364C22×D3—21no—
365C3×Q8—22no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—102no—
370C2×C3×C4—202no—
371C2×C3×C4C2×C22⋊D511yescharacteristic
372C2×C3×C4C23×D511yescharacteristic
373#67—42no—
374C2×Dic3—22no—
375C2×Dic3—21no—
376C2×Dic3—41no—
377C2×Dic3—104no—
378C2×Dic3—102no—
379C2×Dic3C2×C22⋊D511yescharacteristic
380C2×Dic3C2×C22⋊D511yescharacteristic
381C2×Dic3C2×C22⋊D511yescharacteristic
382C2×Dic3C2×C22⋊D511yescharacteristic
383D12—22no—
384C4×D3—42no—
385Dic6—54no—
386Dic6—104no—
387Dic6—102no—
388C3×C8—102no—
389C3⋊C8—102no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—121no—
393C22×C5—121no—
394C22×C5—121no—
395C22×C5#91812yes—
396C22×C5C2×D3×D411yescharacteristic
397C4×C5—21no—
398C4×C5—41no—
399C4×C5—41no—
400C4×C5—61no—
401C4×C5—61no—
402C4×C5—61no—
403C4×C5—61no—
404C4×C5—121no—
405C4×C5D3×#4112yes—
406Dic5—42no—
407Dic5—64no—
408C2×Q8—152no—
409C2×Q8—304no—
410C2×Q8—301no—
411C2×Q8C2×D3×D511yescharacteristic
412C2×D4—31no—
413C2×D4—61no—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—61no—
417C22×C4—101no—
418C22×C4—301no—
419C22×C4C2×D3×D511yescharacteristic
420Q16—304no—
421SD16—304no—
422C2×C8—52no—
423C2×C8—152no—
424C4⋊C4—21no—
425C4⋊C4—31no—
426C4⋊C4—52no—
427C4⋊C4—61no—
428C4⋊C4—61no—
429C4⋊C4—61no—
430C4⋊C4—101no—
431C4⋊C4—302no—
432C4⋊C4—302no—
433C4⋊C4C2×D3×D511yescharacteristic
434C22⋊C4—21no—
435C22⋊C4—61no—
436C22⋊C4—61no—
437C22⋊C4—61no—
438C22⋊C4—61no—
439C42—31no—
440C42—31no—
441C42—31no—
442C42—31no—
443C42—61no—
444C42—302no—
445C42—302no—
446C3×C5#311711yescharacteristic, complemented, Hall
447C22×C3—21no—
448C22×C3—21no—
449C22×C3#409712yes—
450C22×C3C22×C22⋊D511yescharacteristic
451C2×D3—41no—
452C2×D3—41no—
453C2×D3—41no—
454C3×C4—21no—
455C3×C4—41no—
456C3×C4—41no—
457C3×C4—202no—
458C3×C4D5×#4112yes—
459Dic3—21no—
460Dic3—21no—
461Dic3—21no—
462Dic3—21no—
463Dic3—41no—
464Dic3—104no—
465C2×C5—22no—
466C2×C5—241no—
467C2×C5#565611yescharacteristic
468C2×C5C2×#91811yescharacteristic
469C2×C5#577311yescharacteristic
470C23—61no—
471C23D3×C22⋊D511yescharacteristic
472Q8—22no—
473Q8—154no—
474Q8—304no—
475Q8—302no—
476D4—62no—
477D4—122no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—31no—
482C2×C4—31no—
483C2×C4—31no—
484C2×C4—31no—
485C2×C4—62no—
486C2×C4—61no—
487C2×C4—102no—
488C2×C4—122no—
489C2×C4—121no—
490C2×C4—202no—
491C2×C4—304no—
492C2×C4—302no—
493C2×C4D3×C22⋊D511yescharacteristic
494C2×C4C22×D3×D511yescharacteristic
495C8—102no—
496C8—302no—
497C2×C3—22no—
498C2×C3#6615611yescharacteristic
499C2×C3C2×#409711yescharacteristic
500C2×C3#6616211yescharacteristic
501D3—81no—
502C5#8145511yescharacteristic, complemented, Sylow
503C22—21no—
504C22—21no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22#9151012yes—
509C22C2×D3×C22⋊D511yescharacteristic
510C4—21no—
511C4—41no—
512C4—41no—
513C4—61no—
514C4—61no—
515C4—61no—
516C4—61no—
517C4—121no—
518C4—202no—
519C4—304no—
520C4#9202412yes—
521C3#1061488411yescharacteristic, complemented, Sylow
522C2—22no—
523C2—241no—
524C2#1175481311yescharacteristic
525C2C2×#9151011yescharacteristic
526C2#1175534511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC5×#930C22
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#91340C2semidirect
3. #11751151C2semidirect
4. C3×#65333C2semidirect
5. #11749260C2semidirect
6. #11749258C2semidirect
9. #11748337C2semidirect
10. #11747473C2semidirect
11. #11747290C2semidirect
50. #65333D3semidirect
446. C3×C5#3117semidirect
502. C5#81455semidirect
521. C3#10614884semidirect

Maximal subgroups

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

subgroupindex
C5×#56242
C2×#913402
#117511512
C3×#653332
#117492602
#117492582
#117485532
#117483852
#117483372
#117474732
#117472902
#106148843
#814555