Finite Group Databasebeta

← #14460092

Subgroups — #14460092

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#555C211yesmaximal, characteristic, complemented
2#11756310C211yesmaximal, characteristic, complemented
3#11751194C211yesmaximal, characteristic, complemented
4#11751185C211yesmaximal, characteristic, complemented
5#11751142C212yesmaximal, complemented
6#11751138C212yesmaximal, complemented
7#11751120C211yesmaximal, characteristic, complemented
8C4×#6715C211yesmaximal, characteristic, complemented
9D4×C3⋊#168C211yesmaximal, characteristic, complemented
10#11751103C212yesmaximal, complemented
11#11751097C212yesmaximal, complemented
12#10615383—31nomaximal, Hall
13C2×#6817C2212yes—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C5×#124—22no—
16C3×C5×#121—21no—
17C3×C5×#121C2212yes—
18C3×C4×C5×D4C2211yescharacteristic
19C3×C4×C5×D4C2211yescharacteristic
20C3×C5×#117—21no—
21C3×C5×#117C2212yes—
22#91827—21no—
23C2×#6716C2212yes—
24C2×#6715C2211yescharacteristic
25#91813C2212yes—
26C22×C3⋊#168C2212yes—
27C4⋊C4×D15—21no—
28#91772—22no—
29C4×D60C2211yescharacteristic
30#91758C2211yescharacteristic
31#91116C2211yescharacteristic
32#91114C2212yes—
33#91094C2212yes—
34#91094C2212yes—
35#91094C2212yes—
36#91093C2212yes—
37#91093C2211yescharacteristic
38#91092C2212yes—
39#91091C2211yescharacteristic
40C4⋊(C3⋊#168)C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42#83652—51nomaximal, Hall
43C5×#555D311yescharacteristic, complemented
44#65885—31no—
45#65382—31no—
46#65373—31no—
47#65330—32no—
48#65326—32no—
49#65308—31no—
50C4×#686—31no—
51D4×#168—31no—
52#65291—32no—
53#65285—32no—
54C2×C3×C5×Q8—21no—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4D411yescharacteristic
57C2×C3×C5×D4C2311yescharacteristic
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5C2312yes—
60C2×#1220—22no—
61#6817—24no—
62#6817—42no—
63C2×D60C2311yescharacteristic
64C2×C4×D15—21no—
65C2×C4×D15—22no—
66C2×Dic30C2312yes—
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4D411yescharacteristic
69C3×C5×C4⋊C4C2311yescharacteristic
70C3×C5×C4⋊C4C2312yes—
71C3×C5×C22⋊C4—22no—
72C3×C5×C22⋊C4—22no—
73C3×C5×C22⋊C4—21no—
74C3×C5×C22⋊C4D412yes—
75C3×C42×C5—22no—
76C3×C42×C5C2311yescharacteristic
77#6719—22no—
78#6716—42no—
79#6715—22no—
80#6714—21no—
81C4⋊Dic15—21no—
82C4⋊Dic15—21no—
83C4⋊Dic15C2311yescharacteristic
84#6712—22no—
85C2×C3⋊#168—42no—
86C2×C3⋊#168C2311yescharacteristic
87C2×C3⋊#168C2312yes—
88C2×C3⋊#168C2311yescharacteristic
89C3×#555D511yescharacteristic, complemented
90#5551—51no—
91#5093—51no—
92#5084—51no—
93#5041—52no—
94#5037—52no—
95#5019—51no—
96C4×#213—51no—
97D4×C3⋊C8—51no—
98#5002—52no—
99#4996—52no—
100C2×#709—32no—
101C5×C4⋊Q8C2×D311yescharacteristic
102C5×#124—22no—
103C5×#121—21no—
104C5×#121C2×D312yes—
105C4×C5×D4C2×D311yescharacteristic
106C4×C5×D4C2×D311yescharacteristic
107C5×#117—21no—
108C5×#117C2×D312yes—
109#4084—61no—
110C2×#687—32no—
111C2×#686—31no—
112#4070—32no—
113C22×#168—32no—
114D5×C4⋊C4—61no—
115#4029—62no—
116C4×D20—31no—
117#4015—31no—
118#3964—31no—
119C22⋊#168—32no—
120#3942—32no—
121#3942—32no—
122#3942—32no—
123#3941—31no—
124#3941—32no—
125#3940—32no—
126#3939—31no—
127C4⋊#168—31no—
128C4×#168—31no—
129#3303—151noSylow
130C23×C3×C5—21no—
131C23×C3×C5C2×D412yes—
132C22×D15—21no—
133C3×C5×Q8—81no—
134C3×C5×D4—22no—
135C3×C5×D4—21no—
136C3×C5×D4—21no—
137C3×C5×D4—82no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—42no—
143C2×C3×C4×C5C2×D412yes—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2411yescharacteristic
147#1220—44no—
148C2×Dic15—21no—
149C2×Dic15—22no—
150D60—21no—
151D60#4112yes—
152C4×D15—44no—
153C4×D15—42no—
154Dic30—22no—
155Dic30—22no—
156C3⋊#168—21no—
157C3⋊#168—21no—
158C3⋊#168—22no—
159C2×#235—52no—
160C3×C4⋊Q8C2×D511yescharacteristic
161C3×#124—22no—
162C3×#121—21no—
163C3×#121C2×D512yes—
164C3×C4×D4C2×D511yescharacteristic
165C3×C4×D4C2×D511yescharacteristic
166C3×#117—21no—
167C3×#117C2×D512yes—
168#938—101no—
169C2×#214—52no—
170C2×#213—51no—
171#924—52no—
172C22×C3⋊C8—52no—
173D3×C4⋊C4—101no—
174#883—102no—
175C4×D12—51no—
176#869—51no—
177#832—51no—
178#830—52no—
179#810—52no—
180#810—52no—
181#810—52no—
182#809—51no—
183#809—52no—
184#808—52no—
185#807—51no—
186C4⋊(C3⋊C8)—51no—
187C4×C3⋊C8—51no—
188C2×C5×Q8—21no—
189C2×C5×D4—22no—
190C2×C5×D4#6711yescharacteristic
191C2×C5×D4C22×D311yescharacteristic
192C22×C4×C5—21no—
193C22×C4×C5C22×D312yes—
194C2×C22⋊D5—62no—
195#709—64no—
196#709—122no—
197C2×D20—31no—
198C2×C4×D5—62no—
199C2×C4×D5—61no—
200C2×Dic10—32no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4#6711yescharacteristic
203C5×C4⋊C4C22×D311yescharacteristic
204C5×C4⋊C4C22×D312yes—
205C5×C22⋊C4—22no—
206C5×C22⋊C4—22no—
207C5×C22⋊C4—21no—
208C5×C22⋊C4#6712yes—
209C42×C5—22no—
210C42×C5C22×D311yescharacteristic
211C22⋊Dic5—62no—
212#687—122no—
213#686—62no—
214#685—61no—
215C4⋊Dic5—31no—
216C4⋊Dic5—61no—
217C4⋊Dic5—61no—
218#683—62no—
219C2×#168—31no—
220C2×#168—31no—
221C2×#168—32no—
222C2×#168—122no—
223#555D1511yescharacteristic, complemented
224#547—151no—
225#487—151no—
226#485—152no—
227#476—151no—
228#465—152no—
229#461—151no—
230#449—152no—
231C4×D8—151no—
232C8×D4—151no—
233#416—152no—
234C22×C3×C5—22no—
235C22×C3×C5—22no—
236C22×C3×C5—22no—
237C22×C3×C5—41no—
238C22×C3×C5—41no—
239C22×C3×C5—41no—
240C22×C3×C5C22×D411yescharacteristic
241C2×D15—22no—
242C2×D15—41no—
243C2×D15—41no—
244C3×C4×C5—22no—
245C3×C4×C5—21no—
246C3×C4×C5—41no—
247C3×C4×C5—42no—
248C3×C4×C5#13512yes—
249C3×C4×C5C2×#4111yescharacteristic
250C3×C4×C5H(5,𝔽2)11yescharacteristic
251Dic15—42no—
252Dic15—41no—
253C2×C3×Q8—21no—
254C2×C3×D4—22no—
255C2×C3×D4C22⋊D511yescharacteristic
256C2×C3×D4C22×D511yescharacteristic
257C22×C3×C4—21no—
258C22×C3×C4C22×D512yes—
259C2×#67—102no—
260#235—104no—
261#235—202no—
262C2×D12—51no—
263C2×C4×D3—101no—
264C2×C4×D3—102no—
265C2×Dic6—52no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4C22⋊D511yescharacteristic
268C3×C4⋊C4C22×D511yescharacteristic
269C3×C4⋊C4C22×D512yes—
270C3×C22⋊C4—22no—
271C3×C22⋊C4—22no—
272C3×C22⋊C4—21no—
273C3×C22⋊C4C22⋊D512yes—
274C3×C42—22no—
275C3×C42C22×D511yescharacteristic
276#217—102no—
277#214—202no—
278#213—102no—
279(C2×D3)⋊C4—101no—
280C4⋊Dic3—51no—
281C4⋊Dic3—101no—
282C4⋊Dic3—101no—
283Dic3⋊C4—102no—
284C2×C3⋊C8—51no—
285C2×C3⋊C8—51no—
286C2×C3⋊C8—52no—
287C2×C3⋊C8—202no—
288C23×C5—21no—
289C23×C5C2×#6712yes—
290C22×D5—61no—
291C5×Q8—81no—
292C5×D4—22no—
293C5×D4—21no—
294C5×D4—21no—
295C5×D4—82no—
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5—21no—
299C2×C4×C5—22no—
300C2×C4×C5—42no—
301C2×C4×C5C2×#6712yes—
302C2×C4×C5C2×#6711yescharacteristic
303C2×C4×C5C2×#6711yescharacteristic
304C2×C4×C5C23×D311yescharacteristic
305C22⋊D5—124no—
306C2×Dic5—61no—
307C2×Dic5—62no—
308D20—32no—
309D20—61no—
310C4×D5—124no—
311C4×D5—122no—
312Dic10—62no—
313Dic10—62no—
314#168—61no—
315#168—61no—
316#168—62no—
317C2×#41—152no—
318C2×SD16—152no—
319C2×D8—151no—
320C22×C8—152no—
321C4⋊Q8—151no—
322C4⋊Q8C2×D1511yescharacteristic
323#124—22no—
324#123—302no—
325C22⋊Q8—152no—
326#121—21no—
327#121—301no—
328#121C2×D1512yes—
329C4×D4—151no—
330C4×D4C2×D1511yescharacteristic
331C4×D4C2×D1511yescharacteristic
332#117—21no—
333#117C2×D1512yes—
334C2×C4⋊C4—301no—
335#107—151no—
336#106—152no—
337C4⋊C8—151no—
338#103—152no—
339#103—152no—
340#103—152no—
341#102—151no—
342#102—151no—
343#102—152no—
344C22⋊C8—152no—
345C4×C8—151no—
346C2×C3×C5—42no—
347C2×C3×C5—81no—
348C2×C3×C5#54611yescharacteristic
349C2×C3×C5C2×#13511yescharacteristic
350C2×C3×C5#57711yescharacteristic
351D15—42no—
352C23×C3—21no—
353C23×C3C2×C22⋊D512yes—
354C22×D3—101no—
355C3×Q8—81no—
356C3×D4—22no—
357C3×D4—21no—
358C3×D4—21no—
359C3×D4—82no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—42no—
365C2×C3×C4C2×C22⋊D512yes—
366C2×C3×C4C2×C22⋊D511yescharacteristic
367C2×C3×C4C2×C22⋊D511yescharacteristic
368C2×C3×C4C23×D511yescharacteristic
369#67—204no—
370C2×Dic3—101no—
371C2×Dic3—102no—
372D12—52no—
373D12—101no—
374C4×D3—204no—
375C4×D3—202no—
376Dic6—102no—
377Dic6—102no—
378C3⋊C8—101no—
379C3⋊C8—101no—
380C3⋊C8—102no—
381C22×C5—22no—
382C22×C5—22no—
383C22×C5—22no—
384C22×C5—41no—
385C22×C5—41no—
386C22×C5—41no—
387C22×C5C22×#6711yescharacteristic
388C2×D5—62no—
389C2×D5—121no—
390C2×D5—121no—
391C4×C5—22no—
392C4×C5—21no—
393C4×C5—41no—
394C4×C5—42no—
395C4×C5#95012yes—
396C4×C5D3×#4111yescharacteristic
397C4×C5#100911yescharacteristic
398Dic5—121no—
399Dic5—122no—
400#41—304no—
401#41—602no—
402C2×Q8—21no—
403C2×Q8—152no—
404C2×D4—22no—
405C2×D4—151no—
406C2×D4—302no—
407C2×D4#122011yescharacteristic
408C2×D4C22×D1511yescharacteristic
409C22×C4—21no—
410C22×C4—301no—
411C22×C4—302no—
412C22×C4C22×D1512yes—
413SD16—602no—
414D8—302no—
415C2×C8—151no—
416C2×C8—151no—
417C2×C8—152no—
418C2×C8—602no—
419C4⋊C4—21no—
420C4⋊C4—151no—
421C4⋊C4—301no—
422C4⋊C4—302no—
423C4⋊C4—301no—
424C4⋊C4#122011yescharacteristic
425C4⋊C4C22×D1512yes—
426C4⋊C4C22×D1511yescharacteristic
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—21no—
430C22⋊C4—302no—
431C22⋊C4—301no—
432C22⋊C4#122012yes—
433C42—22no—
434C42C22×D1511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—22no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3C22×C22⋊D511yescharacteristic
443C2×D3—102no—
444C2×D3—201no—
445C2×D3—201no—
446C3×C4—22no—
447C3×C4—21no—
448C3×C4—41no—
449C3×C4—42no—
450C3×C4#409612yes—
451C3×C4D5×#4111yescharacteristic
452C3×C4#414911yescharacteristic
453Dic3—201no—
454Dic3—202no—
455C2×C5—42no—
456C2×C5—81no—
457C2×C5C2×#95011yescharacteristic
458C2×C5#582911yescharacteristic
459C2×C5#583611yescharacteristic
460D5—122no—
461C23—21no—
462C23—301no—
463C23C2×#122012yes—
464Q8—81no—
465Q8—302no—
466Q8—302no—
467D4—22no—
468D4—21no—
469D4—21no—
470D4—82no—
471D4—152no—
472D4—301no—
473D4—604no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—42no—
479C2×C4—301no—
480C2×C4—302no—
481C2×C4—604no—
482C2×C4—602no—
483C2×C4C2×#122012yes—
484C2×C4C2×#122011yescharacteristic
485C2×C4C2×#122011yescharacteristic
486C2×C4C23×D1511yescharacteristic
487C8—301no—
488C8—301no—
489C8—302no—
490C2×C3—42no—
491C2×C3—81no—
492C2×C3C2×#409611yescharacteristic
493C2×C3#6616311yescharacteristic
494C2×C3#6617011yescharacteristic
495D3—202no—
496C5#8365211yescharacteristic, complemented, Sylow
497C22—22no—
498C22—22no—
499C22—22no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—302no—
504C22—601no—
505C22—601no—
506C22C22×#122011yescharacteristic
507C4—22no—
508C4—21no—
509C4—41no—
510C4—42no—
511C4—601no—
512C4—602no—
513C4#9183912yes—
514C4#41×D1511yescharacteristic
515C4#9210011yescharacteristic
516C3#1061538311yescharacteristic, complemented, Sylow
517C2—42no—
518C2—81no—
519C2—602no—
520C2C2×#9183911yescharacteristic
521C2#1175658811yescharacteristic
522C2#1175659511yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#555C2
socleC22×C3×C5C22×D4
hypercenter#555D15
hypocenterC3×C5#3303
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. C3×C5×#555C2semidirect
2. #11756310C2semidirect
3. #11751194C2semidirect
4. #11751185C2semidirect
5. #11751142C2semidirect
6. #11751138C2semidirect
7. #11751120C2semidirect
8. C4×#6715C2semidirect
9. D4×C3⋊#168C2semidirect
10. #11751103C2semidirect
11. #11751097C2semidirect
43. C5×#555D3semidirect
89. C3×#555D5semidirect
223. #555D15semidirect
435. C3×C5#3303semidirect
496. C5#83652semidirect
516. C3#10615383semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5552
#117563102
#117511942
#117511852
#117511422
#117511382
#117511202
C4×#67152
D4×C3⋊#1682
#117511032
#117510972
#106153833
#836525