Finite Group Databasebeta

← #14471758

Subgroups — #14471758

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#554C211yesmaximal, characteristic, complemented
2#11756344C211yesmaximal, characteristic, complemented
3#11751192C211yesmaximal, characteristic, complemented
4#11751189C211yesmaximal, characteristic, complemented
5#11751169C212yesmaximal, complemented
6#11751167C212yesmaximal, complemented
7Q8×C3⋊#168C211yesmaximal, characteristic, complemented
8C4×#6716C211yesmaximal, characteristic, complemented
9#11751117C212yesmaximal, complemented
10#11751116C211yesmaximal, characteristic
11C4×#6715C212yesmaximal, complemented
12#10615374—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14C3×C5×#125C2212yes—
15C3×C5×C22⋊Q8—21no—
16C3×C5×C22⋊Q8—22no—
17C3×C4×C5×Q8C2211yescharacteristic
18C3×C4×C5×D4C2212yes—
19C3×C4×C5×D4C2211yescharacteristic
20C2×C3×C5×C4⋊C4—21no—
21#91836—21no—
22C2×#6716C2211yescharacteristic
23C2×#6715C2212yes—
24#91783—22no—
25#91782—21no—
26#91764C2212yes—
27#91763C2211yescharacteristic
28C4×D60C2212yes—
29C4×Dic30C2211yescharacteristic
30#91116C2211yescharacteristic
31#91094C2211yescharacteristic
32#91094C2212yes—
33#91093C2212yes—
34#91093C2212yes—
35#91093C2212yes—
36#91092C2211yescharacteristic
37#91091C2212yes—
38C4⋊(C3⋊#168)C2211yescharacteristic
39C4⋊(C3⋊#168)C2212yes—
40C4×C3⋊#168C2212yes—
41C4×C3⋊#168C2211yescharacteristic
42#83643—51nomaximal, Hall
43C5×#554D311yescharacteristic, complemented
44#65919—31no—
45#65380—31no—
46#65377—31no—
47#65357—32no—
48#65355—32no—
49Q8×#168—31no—
50C4×#687—31no—
51#65305—32no—
52#65304—31no—
53C4×#686—32no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×Q8D411yescharacteristic
56C2×C3×C5×D4C2311yescharacteristic
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5—22no—
59C2×D60—21no—
60C2×D60—21no—
61C2×D60C2312yes—
62C2×C4×D15—22no—
63C2×Dic30C2311yescharacteristic
64C3×C5×C4⋊C4—22no—
65C3×C5×C4⋊C4—21no—
66C3×C5×C4⋊C4—22no—
67C3×C5×C4⋊C4D411yescharacteristic
68C3×C5×C4⋊C4D412yes—
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C4⋊C4C2312yes—
71C3×C5×C22⋊C4—21no—
72C3×C5×C22⋊C4—22no—
73C3×C42×C5C2311yescharacteristic
74C3×C42×C5C2312yes—
75#6716—22no—
76#6715—24no—
77#6714—22no—
78#6714—22no—
79#6714—22no—
80C4⋊Dic15C2311yescharacteristic
81#6712—21no—
82C4×Dic15—21no—
83C2×C3⋊#168C2312yes—
84C2×C3⋊#168C2311yescharacteristic
85C2×C3⋊#168C2311yescharacteristic
86C3×#554D511yescharacteristic, complemented
87#5585—51no—
88#5091—51no—
89#5088—51no—
90#5068—52no—
91#5066—52no—
92Q8×C3⋊C8—51no—
93C4×#214—51no—
94#5016—52no—
95#5015—51no—
96C4×#213—52no—
97C5×C4⋊Q8C2×D311yescharacteristic
98C5×#125C2×D312yes—
99C5×C22⋊Q8—21no—
100C5×C22⋊Q8—22no—
101C4×C5×Q8C2×D311yescharacteristic
102C4×C5×D4C2×D312yes—
103C4×C5×D4C2×D311yescharacteristic
104C2×C5×C4⋊C4—21no—
105#4093—61no—
106C2×#687—31no—
107C2×#686—32no—
108#4040—62no—
109#4039—61no—
110#4021—32no—
111#4020—31no—
112C4×D20—32no—
113C4×Dic10—31no—
114#3964—31no—
115#3942—32no—
116#3942—31no—
117#3941—32no—
118#3941—32no—
119#3941—32no—
120#3940—31no—
121#3939—32no—
122C4⋊#168—31no—
123C4⋊#168—32no—
124C4×#168—32no—
125C4×#168—31no—
126#3361—151noSylow
127C23×C3×C5—21no—
128C22×D15—22no—
129C3×C5×Q8—22no—
130C3×C5×Q8—81no—
131C3×C5×D4—21no—
132C3×C5×D4#4112yes—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—42no—
136C2×C3×C4×C5—82no—
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D412yes—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—21no—
143C2×Dic15—21no—
144D60—22no—
145D60—22no—
146D60—42no—
147D60—81no—
148C4×D15—82no—
149Dic30—21no—
150Dic30—21no—
151C3⋊#168—22no—
152C3⋊#168—21no—
153C3⋊#168—21no—
154C3×C4⋊Q8C2×D511yescharacteristic
155C3×#125C2×D512yes—
156C3×C22⋊Q8—21no—
157C3×C22⋊Q8—22no—
158C3×C4×Q8C2×D511yescharacteristic
159C3×C4×D4C2×D512yes—
160C3×C4×D4C2×D511yescharacteristic
161C2×C3×C4⋊C4—21no—
162#947—101no—
163C2×#214—51no—
164C2×#213—52no—
165#894—102no—
166#893—101no—
167#875—52no—
168#874—51no—
169C4×D12—52no—
170C4×Dic6—51no—
171#832—51no—
172#810—52no—
173#810—51no—
174#809—52no—
175#809—52no—
176#809—52no—
177#808—51no—
178#807—52no—
179C4⋊(C3⋊C8)—51no—
180C4⋊(C3⋊C8)—52no—
181C4×C3⋊C8—52no—
182C4×C3⋊C8—51no—
183C2×C5×Q8—21no—
184C2×C5×Q8#6711yescharacteristic
185C2×C5×D4C22×D311yescharacteristic
186C22×C4×C5—21no—
187C22×C4×C5—22no—
188C2×D20—32no—
189C2×D20—61no—
190C2×D20—61no—
191C2×C4×D5—62no—
192C2×Dic10—31no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—22no—
196C5×C4⋊C4#6711yescharacteristic
197C5×C4⋊C4#6712yes—
198C5×C4⋊C4C22×D311yescharacteristic
199C5×C4⋊C4C22×D312yes—
200C5×C22⋊C4—21no—
201C5×C22⋊C4—22no—
202C42×C5C22×D312yes—
203C42×C5C22×D311yescharacteristic
204#687—62no—
205#686—64no—
206#685—62no—
207#685—62no—
208#685—62no—
209C4⋊Dic5—31no—
210#683—61no—
211C4×Dic5—61no—
212C2×#168—31no—
213C2×#168—32no—
214C2×#168—31no—
215#559—151no—
216#554D1511yescharacteristic, complemented
217#488—152no—
218#486—151no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—151no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5—22no—
227C22×C3×C5—41no—
228C22×C3×C5—41no—
229C22×C3×C5C22×D411yescharacteristic
230C2×D15—42no—
231C2×D15—42no—
232C2×D15—42no—
233C3×C4×C5—22no—
234C3×C4×C5—22no—
235C3×C4×C5—21no—
236C3×C4×C5—41no—
237C3×C4×C5—42no—
238C3×C4×C5#13512yes—
239C3×C4×C5C2×#4111yescharacteristic
240C3×C4×C52−1+411yescharacteristic
241Dic15—41no—
242Dic15—41no—
243C2×C3×Q8—21no—
244C2×C3×Q8C22⋊D511yescharacteristic
245C2×C3×D4C22×D511yescharacteristic
246C22×C3×C4—21no—
247C22×C3×C4—22no—
248C2×D12—52no—
249C2×D12—101no—
250C2×D12—101no—
251C2×C4×D3—102no—
252C2×Dic6—51no—
253C3×C4⋊C4—22no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4C22⋊D511yescharacteristic
257C3×C4⋊C4C22⋊D512yes—
258C3×C4⋊C4C22×D512yes—
259C3×C4⋊C4C22×D511yescharacteristic
260C3×C22⋊C4—21no—
261C3×C22⋊C4—22no—
262C3×C42C22×D511yescharacteristic
263C3×C42C22×D512yes—
264#214—102no—
265#213—104no—
266(C2×D3)⋊C4—102no—
267(C2×D3)⋊C4—102no—
268(C2×D3)⋊C4—102no—
269C4⋊Dic3—51no—
270Dic3⋊C4—101no—
271C4×Dic3—101no—
272C2×C3⋊C8—51no—
273C2×C3⋊C8—52no—
274C2×C3⋊C8—51no—
275C23×C5—21no—
276C22×D5—62no—
277C5×Q8—22no—
278C5×Q8—81no—
279C5×D4—21no—
280C5×D4#23912yes—
281C2×C4×C5—21no—
282C2×C4×C5—22no—
283C2×C4×C5—42no—
284C2×C4×C5—82no—
285C2×C4×C5C2×#6711yescharacteristic
286C2×C4×C5C2×#6712yes—
287C2×C4×C5C2×#6712yes—
288C2×C4×C5C2×#6711yescharacteristic
289C2×C4×C5C23×D311yescharacteristic
290C2×Dic5—61no—
291C2×Dic5—61no—
292D20—62no—
293D20—62no—
294D20—122no—
295D20—241no—
296C4×D5—242no—
297Dic10—61no—
298Dic10—61no—
299#168—62no—
300#168—61no—
301#168—61no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8C2×D1511yescharacteristic
305#127—151no—
306#125C2×D1512yes—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—21no—
311C22⋊Q8—22no—
312C4×Q8—151no—
313C4×Q8C2×D1511yescharacteristic
314C4×D4—152no—
315C4×D4—301no—
316C4×D4C2×D1512yes—
317C4×D4C2×D1511yescharacteristic
318C2×C4⋊C4—21no—
319#107—152no—
320#106—151no—
321C4⋊C8—151no—
322C4⋊C8—152no—
323#103—151no—
324#103—152no—
325#102—151no—
326#102—152no—
327#102—152no—
328#102—152no—
329C4×C8—152no—
330C4×C8—151no—
331C2×C3×C5—42no—
332C2×C3×C5#54811yescharacteristic
333C2×C3×C5C2×#13511yescharacteristic
334C2×C3×C5#57611yescharacteristic
335D15—82no—
336C23×C3—21no—
337C22×D3—102no—
338C3×Q8—22no—
339C3×Q8—81no—
340C3×D4—21no—
341C3×D4#71312yes—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—42no—
345C2×C3×C4—82no—
346C2×C3×C4C2×C22⋊D511yescharacteristic
347C2×C3×C4C2×C22⋊D512yes—
348C2×C3×C4C2×C22⋊D512yes—
349C2×C3×C4C2×C22⋊D511yescharacteristic
350C2×C3×C4C23×D511yescharacteristic
351C2×Dic3—101no—
352C2×Dic3—101no—
353D12—102no—
354D12—102no—
355D12—202no—
356D12—401no—
357C4×D3—402no—
358Dic6—101no—
359Dic6—101no—
360C3⋊C8—102no—
361C3⋊C8—101no—
362C3⋊C8—101no—
363C22×C5—22no—
364C22×C5—41no—
365C22×C5—41no—
366C22×C5C22×#6711yescharacteristic
367C2×D5—122no—
368C2×D5—122no—
369C2×D5—122no—
370C4×C5—22no—
371C4×C5—22no—
372C4×C5—21no—
373C4×C5—41no—
374C4×C5—42no—
375C4×C5#95012yes—
376C4×C5C2×#23911yescharacteristic
377C4×C5#100711yescharacteristic
378Dic5—121no—
379Dic5—121no—
380C2×Q8—21no—
381C2×Q8—151no—
382C2×Q8#122011yescharacteristic
383C2×D4—152no—
384C2×D4—301no—
385C2×D4—301no—
386C2×D4C22×D1511yescharacteristic
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—302no—
390SD16—302no—
391D8—304no—
392C2×C8—151no—
393C2×C8—151no—
394C2×C8—152no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—151no—
399C4⋊C4—301no—
400C4⋊C4#122011yescharacteristic
401C4⋊C4#122012yes—
402C4⋊C4C22×D1511yescharacteristic
403C4⋊C4C22×D1512yes—
404C22⋊C4—21no—
405C22⋊C4—22no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—301no—
410C42C22×D1512yes—
411C42C22×D1511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—22no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3C22×C22⋊D511yescharacteristic
417C2×D3—202no—
418C2×D3—202no—
419C2×D3—202no—
420C3×C4—22no—
421C3×C4—22no—
422C3×C4—21no—
423C3×C4—41no—
424C3×C4—42no—
425C3×C4#409612yes—
426C3×C4C2×#71311yescharacteristic
427C3×C4#414711yescharacteristic
428Dic3—201no—
429Dic3—201no—
430C2×C5—42no—
431C2×C5#581711yescharacteristic
432C2×C5C2×#95011yescharacteristic
433C2×C5#583511yescharacteristic
434D5—242no—
435C23—21no—
436C23—302no—
437Q8—22no—
438Q8—81no—
439Q8—301no—
440Q8—301no—
441D4—21no—
442D4—302no—
443D4—302no—
444D4—602no—
445D4—1201no—
446D4#682112yes—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—42no—
450C2×C4—82no—
451C2×C4—301no—
452C2×C4—301no—
453C2×C4—1202no—
454C2×C4C2×#122012yes—
455C2×C4C2×#122011yescharacteristic
456C2×C4C2×#122012yes—
457C2×C4C2×#122011yescharacteristic
458C2×C4C23×D1511yescharacteristic
459C8—302no—
460C8—301no—
461C8—301no—
462C2×C3—42no—
463C2×C3#6615111yescharacteristic
464C2×C3C2×#409611yescharacteristic
465C2×C3#6616911yescharacteristic
466D3—402no—
467C5#8364311yescharacteristic, complemented, Sylow
468C22—22no—
469C22—41no—
470C22—41no—
471C22—602no—
472C22—602no—
473C22—602no—
474C22C22×#122011yescharacteristic
475C4—22no—
476C4—22no—
477C4—21no—
478C4—41no—
479C4—42no—
480C4—601no—
481C4—601no—
482C4#9183912yes—
483C4C2×#682111yescharacteristic
484C4#9209811yescharacteristic
485C3#1061537411yescharacteristic, complemented, Sylow
486C2—42no—
487C2—1202no—
488C2#1175657611yescharacteristic
489C2C2×#9183911yescharacteristic
490C2#1175659411yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#554C2
socleC22×C3×C5C22×D4
prime radical#11751116C2
hypercenter#554D15
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C3×C5×#554C2semidirect
2. #11756344C2semidirect
3. #11751192C2semidirect
4. #11751189C2semidirect
5. #11751169C2semidirect
6. #11751167C2semidirect
7. Q8×C3⋊#168C2semidirect
8. C4×#6716C2semidirect
9. #11751117C2semidirect
11. C4×#6715C2semidirect
43. C5×#554D3semidirect
86. C3×#554D5semidirect
216. #554D15semidirect
412. C3×C5#3361semidirect
467. C5#83643semidirect
485. C3#10615374semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5542
#117563442
#117511922
#117511892
#117511692
#117511672
Q8×C3⋊#1682
C4×#67162
#117511172
#117511162
C4×#67152
#106153743
#836435