Finite Group Databasebeta

← #14424591

Subgroups — #14424591

Order 1920.

1400 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1007C211yesmaximal, characteristic
2C22×#6718C211yesmaximal, characteristic, complemented
3#11754271C211yesmaximal, characteristic, complemented
4C2×#91322C211yesmaximal, characteristic, complemented
5C3×#65514C211yesmaximal, characteristic, complemented
6#11749302C214yesmaximal, complemented
7#11749300C214yesmaximal, complemented
8#11748382C211yesmaximal, characteristic, complemented
9#11748347C211yesmaximal, characteristic, complemented
10#10615848—31nomaximal, Hall
11C22×C3×C5×Q8C2211yescharacteristic
12C22×Dic30C2211yescharacteristic
13C5×#1007—24no—
14C5×#1007—24no—
15C2×C5×#239—21no—
16C2×C5×#239C2212yes—
17C2×C5×D3×Q8—21no—
18C2×C5×D3×Q8C2212yes—
19C2×C5×#235—22no—
20C2×C5×#235C2211yescharacteristic
21C2×C5×#235C2211yescharacteristic
22C2×#6718—24no—
23C2×#6718C2214yes—
24C22×C3⋊#168C2211yescharacteristic
25C3×#4072C2211yescharacteristic
26C2×C3×#681C2211yescharacteristic
27#91543—22no—
28#91376—21no—
29#91373—21no—
30#91365C2214yes—
31#91322—24no—
32C2×#6663C2212yes—
33C2×#6659C2212yes—
34C3×#3967C2214yes—
35#90972C2212yes—
36#90966C2212yes—
37(C2×D3)⋊#168C2214yes—
38#78961—51nomaximal, Hall
39C2×C5×2−1+4—31no—
40#66159—31no—
41C2×#4097—31no—
42C22×#689—31no—
43#65528—34no—
44#65523—31no—
45#65522—31no—
46#65517—34no—
47#65514D311yescharacteristic, complemented
48C2×C3×C5×Q8—21no—
49C2×C3×C5×Q8—22no—
50C2×C3×C5×Q8D414yes—
51C2×C3×C5×Q8C2312yes—
52C22×C3×C4×C5—21no—
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15—21no—
55C2×Dic30—22no—
56C2×Dic30—22no—
57C2×Dic30—21no—
58C2×Dic30C2312yes—
59C2×C5×#67—21no—
60C2×C5×#67D412yes—
61C5×#239—28no—
62C5×#239—24no—
63C5×#239—24no—
64C5×D3×Q8—28no—
65C5×D3×Q8—24no—
66C5×D3×Q8—24no—
67C5×#235—216no—
68C5×#235—22no—
69C5×#235—22no—
70C5×#235—22no—
71C5×#235D414yes—
72C2×C5×D12—22no—
73C2×C5×D12D411yescharacteristic
74C2×C5×D12C2311yescharacteristic
75C2×C4×C5×D3—22no—
76C2×C4×C5×D3—21no—
77C2×C4×C5×D3—22no—
78C2×C4×C5×D3C2312yes—
79C2×C5×Dic6—22no—
80C2×C5×Dic6D411yescharacteristic
81C2×C5×Dic6C2311yescharacteristic
82#6718—28no—
83C2×C3⋊#168—22no—
84C2×C3⋊#168C2312yes—
85C3×C22⋊Dic5—21no—
86C3×C4⋊Dic5C2312yes—
87C3×C4×Dic5—21no—
88C3×#681—22no—
89C2×C3×#168C2312yes—
90#6668—24no—
91(C2×D3)⋊Dic5—24no—
92#6663—24no—
93#6659—24no—
94C2×#1007D511yescharacteristic
95C22×#216—51no—
96C2×#909—51no—
97#5526—51no—
98C3×#419—51no—
99#5129—51no—
100#5002—51no—
101#4809—54no—
102#4808—54no—
103C5×2−1+4—64no—
104C5×2−1+4—64no—
105C2×C5×#41—31no—
106C2×C5×#41—32no—
107C2×C5×#41—31no—
108C2×C5×#41—62no—
109C2×C5×#41—61no—
110C22×C5×Q8—32no—
111C22×C5×Q8—61no—
112C22×C5×Q8C2×D311yescharacteristic
113C22×Dic10—31no—
114#4097—64no—
115#4090—61no—
116C2×#689—34no—
117C2×#689—32no—
118C2×#689—64no—
119#4082—61no—
120#4081—62no—
121C2×#687—32no—
122#4072C2×D311yescharacteristic
123#4070—34no—
124C2×#681C2×D311yescharacteristic
125C22×#168—31no—
126#3967—32no—
127#3967C2×D314yes—
128#3964—32no—
129C22⋊#168—34no—
130#3011—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×C5×D3—21no—
133C22×C5×D3C2×D412yes—
134C3×C5×Q8—24no—
135C3×C5×Q8—22no—
136C3×C5×Q8C2×D414yes—
137C2×C3×C4×C5—24no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2411yescharacteristic
143C2×Dic15—22no—
144C2×Dic15—42no—
145Dic30—22no—
146Dic30—22no—
147Dic30—42no—
148C5×#67—24no—
149C5×#67—24no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3C2×D412yes—
152C5×D12—28no—
153C5×D12—22no—
154C5×D12—21no—
155C5×D12C2×D412yes—
156C4×C5×D3—28no—
157C4×C5×D3—28no—
158C4×C5×D3—24no—
159C4×C5×D3—22no—
160C4×C5×D3—22no—
161C5×Dic6—28no—
162C5×Dic6—22no—
163C5×Dic6—21no—
164C5×Dic6C2×D412yes—
165C2×C3×Dic5—22no—
166C3⋊#168—22no—
167C3×#168—22no—
168C22×C3×Q8C2×D511yescharacteristic
169#1007—24no—
170#1007—24no—
171C2×#239—21no—
172C2×#239C2×D512yes—
173C2×D3×Q8—21no—
174C2×D3×Q8C2×D512yes—
175C2×#235—22no—
176C2×#235C2×D511yescharacteristic
177C2×#235C2×D511yescharacteristic
178C22×Dic6—51no—
179C2×C3×M16—51no—
180C3×#117—51no—
181C2×#216—54no—
182C2×#216—104no—
183C22×C3⋊C8—51no—
184#909—104no—
185C2×Dic12—52no—
186C2×#204—52no—
187#897—54no—
188#886—102no—
189#875—101no—
190#869—101no—
191C3×#103—54no—
192(C2×D3)⋊C8—54no—
193#810—52no—
194#809—52no—
195C5×#41—34no—
196C5×#41—616no—
197C5×#41—64no—
198C5×#41—68no—
199C5×#41—64no—
200C5×#41—62no—
201C5×#41—62no—
202C5×#41—62no—
203C2×C5×Q8—21no—
204C2×C5×Q8—22no—
205C2×C5×Q8—31no—
206C2×C5×Q8—31no—
207C2×C5×Q8—62no—
208C2×C5×Q8—64no—
209C2×C5×Q8—68no—
210C2×C5×Q8—64no—
211C2×C5×Q8D1214yes—
212C2×C5×Q8C22×D312yes—
213C2×C5×D4—32no—
214C2×C5×D4—31no—
215C2×C5×D4—31no—
216C2×C5×D4—62no—
217C2×C5×D4—61no—
218C22×C4×C5—21no—
219C22×C4×C5—32no—
220C22×C4×C5—62no—
221C22×C4×C5—62no—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C22×Dic5—61no—
225C2×Dic10—32no—
226C2×Dic10—62no—
227C2×Dic10—62no—
228C2×Dic10—61no—
229C22⋊Dic5—21no—
230C22⋊Dic5—64no—
231#689—64no—
232#689—68no—
233#687—64no—
234C4⋊Dic5C22×D312yes—
235#683—64no—
236C4×Dic5—21no—
237#681—22no—
238C2×#168—32no—
239C2×#168—62no—
240C2×#168C22×D312yes—
241C2×2−1+4—31no—
242C2×#137—151no—
243C22×Q16—151no—
244#536—151no—
245#452—154no—
246#451—154no—
247#419—51no—
248#416—151no—
249#408—151no—
250C22×C3×C5—22no—
251C22×C3×C5#12012yes—
252C22×C3×C5C22×D411yescharacteristic
253C2×C5×D3—22no—
254C2×C5×D3—22no—
255C2×C5×D3—24no—
256C2×C5×D3—42no—
257C3×C4×C5—24no—
258C3×C4×C5#12012yes—
259C3×C4×C5C22×D411yescharacteristic
260C3×C4×C5C22×D411yescharacteristic
261Dic15—42no—
262C3×Dic5—42no—
263C5×Dic3—22no—
264C5×Dic3—22no—
265C2×C3×Q8—21no—
266C2×C3×Q8—22no—
267C2×C3×Q8C22⋊D514yes—
268C2×C3×Q8C22×D512yes—
269C22×C3×C4—21no—
270C22×C3×C4C22×D511yescharacteristic
271C2×#67—21no—
272C2×#67C22⋊D512yes—
273C22×Dic3—101no—
274#239—28no—
275#239—24no—
276#239—24no—
277D3×Q8—28no—
278D3×Q8—24no—
279D3×Q8—24no—
280#235—216no—
281#235—22no—
282#235—22no—
283#235—22no—
284#235C22⋊D514yes—
285C2×D12—22no—
286C2×D12C22⋊D511yescharacteristic
287C2×D12C22×D511yescharacteristic
288C2×C4×D3—22no—
289C2×C4×D3—21no—
290C2×C4×D3—22no—
291C2×C4×D3C22×D512yes—
292C2×Dic6—22no—
293C2×Dic6—52no—
294C2×Dic6—102no—
295C2×Dic6—102no—
296C2×Dic6—101no—
297C2×Dic6C22⋊D511yescharacteristic
298C2×Dic6C22×D511yescharacteristic
299C3×M16—102no—
300C2×C3×C8—52no—
301C3×C4⋊C4—52no—
302C3×C22⋊C4—101no—
303C3×C42—101no—
304#216—108no—
305(C2×D3)⋊C4—104no—
306C4⋊Dic3—104no—
307C2×C3⋊C8—52no—
308C2×C3⋊C8—102no—
309Dic12—104no—
310#204—104no—
311C23×C5—32no—
312C23×C5—61no—
313C23×C5D3×D411yescharacteristic
314C5×Q8—24no—
315C5×Q8—22no—
316C5×Q8—32no—
317C5×Q8—68no—
318C5×Q8—62no—
319C5×Q8—61no—
320C5×Q8C2×D1214yes—
321C5×D4—32no—
322C5×D4—68no—
323C5×D4—64no—
324C5×D4—64no—
325C5×D4—62no—
326C5×D4—61no—
327C2×C4×C5—24no—
328C2×C4×C5—22no—
329C2×C4×C5—32no—
330C2×C4×C5—68no—
331C2×C4×C5—68no—
332C2×C4×C5—61no—
333C2×C4×C5—64no—
334C2×C4×C5—62no—
335C2×C4×C5—62no—
336C2×C4×C5C2×D1212yes—
337C2×C4×C5D3×D411yescharacteristic
338C2×C4×C5D3×D412yes—
339C2×C4×C5C23×D311yescharacteristic
340C2×Dic5—22no—
341C2×Dic5—62no—
342C2×Dic5—122no—
343Dic10—62no—
344Dic10—62no—
345Dic10—122no—
346#168—22no—
347#168—62no—
3482−1+4—64no—
3492−1+4—64no—
350C2×#41—31no—
351C2×#41—32no—
352C2×#41—31no—
353C2×#41—62no—
354C2×#41—61no—
355C22×Q8—32no—
356C22×Q8—61no—
357C22×Q8—151no—
358C22×Q8D3×D511yescharacteristic
359#137—304no—
360C2×Q16—152no—
361C2×Q16—154no—
362C2×Q16—304no—
363C2×SD16—152no—
364C2×M16—51no—
365C22×C8—151no—
366C4⋊Q8—301no—
367#124—301no—
368#123—302no—
369C22⋊Q8—154no—
370#117—51no—
371#103—54no—
372#103—152no—
373#102—152no—
374C22⋊C8—154no—
375C2×C3×C5—22no—
376C2×C3×C5C2×#12011yescharacteristic
377C2×C3×C5#57812yes—
378C5×D3—42no—
379C5×D3—42no—
380C23×C3C2×C22⋊D511yescharacteristic
381C22×D3—21no—
382C22×D3C2×C22⋊D512yes—
383C3×Q8—24no—
384C3×Q8—22no—
385C3×Q8C2×C22⋊D514yes—
386C2×C3×C4—24no—
387C2×C3×C4—22no—
388C2×C3×C4—102no—
389C2×C3×C4C2×C22⋊D512yes—
390C2×C3×C4C2×C22⋊D511yescharacteristic
391C2×C3×C4C2×C22⋊D512yes—
392C2×C3×C4C23×D511yescharacteristic
393#67—24no—
394#67—24no—
395C2×Dic3—21no—
396C2×Dic3—102no—
397C2×Dic3—202no—
398C2×Dic3C2×C22⋊D512yes—
399D12—28no—
400D12—22no—
401D12—21no—
402D12C2×C22⋊D512yes—
403C4×D3—28no—
404C4×D3—28no—
405C4×D3—24no—
406C4×D3—22no—
407C4×D3—22no—
408Dic6—28no—
409Dic6—22no—
410Dic6—21no—
411Dic6—102no—
412Dic6—102no—
413Dic6—202no—
414Dic6C2×C22⋊D512yes—
415C3×C8—102no—
416C3⋊C8—102no—
417C22×C5—22no—
418C22×C5—62no—
419C22×C5—62no—
420C22×C5—64no—
421C22×C5—122no—
422C22×C5#88212yes—
423C22×C5C2×D3×D411yescharacteristic
424C4×C5—24no—
425C4×C5—62no—
426C4×C5—62no—
427C4×C5#88212yes—
428C4×C5C22×D1211yescharacteristic
429C4×C5C2×D3×D411yescharacteristic
430Dic5—42no—
431Dic5—122no—
432#41—34no—
433#41—616no—
434#41—64no—
435#41—68no—
436#41—64no—
437#41—62no—
438#41—62no—
439#41—62no—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—31no—
443C2×Q8—31no—
444C2×Q8—62no—
445C2×Q8—64no—
446C2×Q8—68no—
447C2×Q8—64no—
448C2×Q8—152no—
449C2×Q8—301no—
450C2×Q8—302no—
451C2×Q8—302no—
452C2×Q8#120314yes—
453C2×Q8C2×D3×D512yes—
454C2×D4—32no—
455C2×D4—31no—
456C2×D4—31no—
457C2×D4—62no—
458C2×D4—61no—
459C22×C4—21no—
460C22×C4—32no—
461C22×C4—62no—
462C22×C4—62no—
463C22×C4—61no—
464C22×C4—301no—
465C22×C4C2×D3×D511yescharacteristic
466Q16—304no—
467Q16—308no—
468SD16—304no—
469M16—102no—
470C2×C8—52no—
471C2×C8—152no—
472C2×C8—302no—
473C4⋊C4—52no—
474C4⋊C4—304no—
475C22⋊C4—101no—
476C22⋊C4—304no—
477C42—101no—
478C3×C5#301111yescharacteristic, complemented, Hall
479C22×C3—22no—
480C22×C3#409912yes—
481C22×C3C22×C22⋊D511yescharacteristic
482C2×D3—24no—
483C2×D3—22no—
484C2×D3—22no—
485C2×D3—42no—
486C3×C4—24no—
487C3×C4—202no—
488C3×C4#409912yes—
489C3×C4C22×C22⋊D511yescharacteristic
490C3×C4C22×C22⋊D511yescharacteristic
491Dic3—22no—
492Dic3—22no—
493Dic3—202no—
494C2×C5—22no—
495C2×C5—122no—
496C2×C5—122no—
497C2×C5C2×#88211yescharacteristic
498C2×C5#577912yes—
499C23—32no—
500C23—61no—
501C23D3×C22⋊D511yescharacteristic
502Q8—22no—
503Q8—24no—
504Q8—32no—
505Q8—68no—
506Q8—61no—
507Q8—62no—
508Q8—302no—
509Q8—302no—
510Q8—602no—
511Q8C2×#120314yes—
512D4—32no—
513D4—68no—
514D4—64no—
515D4—64no—
516D4—61no—
517D4—62no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—32no—
521C2×C4—68no—
522C2×C4—68no—
523C2×C4—61no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—64no—
527C2×C4—102no—
528C2×C4—302no—
529C2×C4—602no—
530C2×C4C2×#120312yes—
531C2×C4D3×C22⋊D512yes—
532C2×C4D3×C22⋊D511yescharacteristic
533C2×C4C22×D3×D511yescharacteristic
534C8—102no—
535C8—302no—
536C2×C3—22no—
537C2×C3#6617212yes—
538C2×C3C2×#409911yescharacteristic
539D3—42no—
540D3—42no—
541C5#7896111yescharacteristic, complemented, Sylow
542C22—22no—
543C22—64no—
544C22—62no—
545C22—62no—
546C22—122no—
547C22#9157012yes—
548C22C2×D3×C22⋊D511yescharacteristic
549C4—24no—
550C4—62no—
551C4—62no—
552C4—202no—
553C4—602no—
554C4#9157012yes—
555C4C22×#120311yescharacteristic
556C4C2×D3×C22⋊D511yescharacteristic
557C3#1061584811yescharacteristic, complemented, Sylow
558C2—22no—
559C2—122no—
560C2—122no—
561C2#1175511412yes—
562C2C2×#9157011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#1007C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3011
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. C22×#6718C2semidirect
3. #11754271C2semidirect
4. C2×#91322C2semidirect
5. C3×#65514C2semidirect
6. #11749302C2semidirect
7. #11749300C2semidirect
8. #11748382C2semidirect
9. #11748347C2semidirect
47. #65514D3semidirect
478. C3×C5#3011semidirect
541. C5#78961semidirect
557. C3#10615848semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10072
C22×#67182
#117542712
C2×#913222
C3×#655142
#117493022
#117493002
#117483822
#117483472
#106158483
#789615