Finite Group Databasebeta

← #14439703

Subgroups — #14439703

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756584C211yesmaximal, characteristic, complemented
2C2×C5×#950C211yesmaximal, characteristic
3C2×C3×#4097C211yesmaximal, characteristic, complemented
4#11754255C211yesmaximal, characteristic, complemented
5C2×#91322C211yesmaximal, characteristic, complemented
6C22×#6662C211yesmaximal, characteristic, complemented
7#11749355C212yesmaximal, complemented
8#11749322C212yesmaximal, complemented
9#11749111C212yesmaximal, complemented
10#11749075C212yesmaximal, complemented
11#11748326C211yesmaximal, characteristic, complemented
12#10615638—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17#91833C2212yes—
18#91825C2212yes—
19#91824—22no—
20#91815C2211yescharacteristic
21#91813—22no—
22C5×#950—24no—
23C2×C5×#216C2211yescharacteristic
24C2×C5×#215C2211yescharacteristic
25C2×C5×#214C2211yescharacteristic
26C2×C5×#213C2211yescharacteristic
27C22×C5×C3⋊C8C2211yescharacteristic
28C3×#4097—24no—
29C2×C3×#689C2212yes—
30C2×C3×#687C2212yes—
31C2×C3×#681C2211yescharacteristic
32#91539—22no—
33#91385C2212yes—
34#91370C2212yes—
35#91369—22no—
36#91322—24no—
37C2×#6663C2212yes—
38C2×#6662—24no—
39C2×#6662C2212yes—
40C2×#6662C2212yes—
41C2×#6659C2212yes—
42#90954C2212yes—
43#90951C2212yes—
44#83975—51nomaximal, Hall
45C2×C5×#135—31no—
46#66159—31no—
47#66159—31no—
48C2×#4097—31no—
49C2×#4097D311yescharacteristic, complemented
50C22×Dic20—31no—
51#65470—32no—
52#65456—32no—
53#65456—32no—
54#65444—32no—
55#65390—31no—
56C3×C5×#41—22no—
57C3×C5×#41—22no—
58C2×C3×C5×Q8C2311yescharacteristic
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2311yescharacteristic
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5C2311yescharacteristic
63C22×Dic15—21no—
64C2×Dic30—22no—
65C2×Dic30—22no—
66C2×Dic30—21no—
67C2×Dic30C2312yes—
68C2×C5×#67—21no—
69C5×#235—22no—
70C5×#235—22no—
71C2×C5×D12C2311yescharacteristic
72C2×C4×C5×D3—21no—
73C2×C5×Dic6C2311yescharacteristic
74C22×C3×Dic5—21no—
75C2×C3×Dic10—22no—
76C2×C3×Dic10—22no—
77C2×C3×Dic10—21no—
78C2×C3×Dic10C2312yes—
79#6719—24no—
80#6719D412yes—
81C4⋊Dic15D412yes—
82#6712—24no—
83C4×Dic15C2312yes—
84C5×#216—22no—
85C5×#215—22no—
86C5×#214—22no—
87C5×#213—22no—
88C2×C5×C3⋊C8D414yes—
89C2×C5×C3⋊C8C2311yescharacteristic
90C2×C5×C3⋊C8C2311yescharacteristic
91C3×#689—24no—
92C3×#687—24no—
93C3×#681D414yes—
94C2×C3×#168C2312yes—
95#6669—24no—
96(C2×D3)⋊Dic5—24no—
97#6663—24no—
98#6662—24no—
99#6662—24no—
100#6659—24no—
101C2×C3×#137—51no—
102#5825—51no—
103C2×#950D511yescharacteristic
104#5816—51no—
105C22×#216—51no—
106C2×#909—51no—
107#5190—52no—
108#5183—52no—
109#5168—52no—
110#5167—52no—
111#5122—51no—
112C2×C5×#41—31no—
113C2×C5×#41C2×D311yescharacteristic
114C22×Dic10—31no—
115C22×Dic10C2×D311yescharacteristic
116C5×#135—64no—
117C2×C5×Q16—31no—
118C2×C5×SD16—31no—
119C2×C5×SD16—31no—
120C2×C5×D8—31no—
121C22×C5×C8—31no—
122#4097—24no—
123#4097—64no—
124#4090—32no—
125#4090—32no—
126C2×#689—32no—
127C2×#689C2×D312yes—
128#4082—32no—
129#4082—32no—
130#4081—62no—
131#4081—62no—
132C2×#687—32no—
133C2×#687C2×D312yes—
134#4072—31no—
135#4070—62no—
136#4070—62no—
137C2×#681C2×D311yescharacteristic
138C2×Dic20—32no—
139C2×Dic20—32no—
140C2×Dic20—64no—
141#3947—32no—
142C8×Dic5—32no—
143#3156—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×C5×D3—21no—
147C3×C5×Q8—21no—
148C3×C5×Q8—21no—
149C3×C5×D4—21no—
150C3×C5×D4—21no—
151C3×C5×D4—42no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—42no—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5C2×D412yes—
157C2×C3×C4×C5C2411yescharacteristic
158C2×Dic15—22no—
159C2×Dic15—42no—
160C2×Dic15C2×D414yes—
161Dic30—22no—
162Dic30—22no—
163Dic30—42no—
164C5×#67—42no—
165C2×C5×Dic3—21no—
166C5×D12—21no—
167C5×D12—21no—
168C4×C5×D3—42no—
169C5×Dic6—21no—
170C5×Dic6—21no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—42no—
173C3×Dic10—22no—
174C3×Dic10—22no—
175C3×Dic10—42no—
176C3×#168C2×D414yes—
177C5×C3⋊C8C2×D412yes—
178C5×C3⋊C8C2×D412yes—
179C2×C3×#41C2×D511yescharacteristic
180C22×C3×Q8—51no—
181C2×#235C2×D511yescharacteristic
182C22×Dic6—51no—
183C3×#137—104no—
184C2×C3×Q16—52no—
185C2×C3×SD16—52no—
186C2×C3×M16—51no—
187#950—24no—
188#947—52no—
189#946—102no—
190#944—52no—
191#944—52no—
192C2×#216—52no—
193C2×#216—52no—
194C2×#216—104no—
195C2×#216C2×D511yescharacteristic
196C2×#215C2×D511yescharacteristic
197#936—52no—
198#935—102no—
199C2×#214C2×D511yescharacteristic
200C2×#213C2×D511yescharacteristic
201#929—102no—
202#926—51no—
203#924—102no—
204C22×C3⋊C8C2×D511yescharacteristic
205#909—104no—
206C2×Dic12—52no—
207C2×#204—52no—
208#815—52no—
209C8×Dic3—52no—
210C5×#41—22no—
211C5×#41—22no—
212C5×#41—62no—
213C5×#41—62no—
214C2×C5×Q8—31no—
215C2×C5×Q8C22×D311yescharacteristic
216C2×C5×D4—21no—
217C2×C5×D4—31no—
218C2×C5×D4—61no—
219C2×C5×D4C22×D311yescharacteristic
220C22×C4×C5—21no—
221C22×C4×C5—61no—
222C22×C4×C5C22×D311yescharacteristic
223C22×Dic5—21no—
224C22×Dic5—61no—
225C2×Dic10—22no—
226C2×Dic10—22no—
227C2×Dic10—21no—
228C2×Dic10—32no—
229C2×Dic10—62no—
230C2×Dic10—62no—
231C2×Dic10—61no—
232C2×Dic10C22×D312yes—
233C5×Q16—62no—
234C5×SD16—62no—
235C5×SD16—62no—
236C5×D8—62no—
237C2×C5×C8—34no—
238C2×C5×C8—31no—
239C2×C5×C8—31no—
240C22⋊Dic5—32no—
241C22⋊Dic5—64no—
242C22⋊Dic5—64no—
243#689—24no—
244#689—64no—
245#687—24no—
246#687—64no—
247C4⋊Dic5—32no—
248#683—64no—
249#683—64no—
250C4×Dic5—32no—
251#681#6714yes—
252C2×#168C22×D312yes—
253Dic20—64no—
254Dic20—64no—
255C2×#137—51no—
256C2×#137—151no—
257C2×#135—31no—
258C22×Q16—151no—
259#536—151no—
260#536—151no—
261#497—152no—
262#497—152no—
263#495—152no—
264#494—152no—
265#405—151no—
266C22×C3×C5—22no—
267C22×C3×C5—41no—
268C22×C3×C5—42no—
269C22×C3×C5#12712yes—
270C22×C3×C5C22×D411yescharacteristic
271C2×C5×D3—41no—
272C2×C5×D3—42no—
273C3×C4×C5—41no—
274C3×C4×C5#12712yes—
275C3×C4×C5C22×D411yescharacteristic
276C3×C4×C5C22×D411yescharacteristic
277Dic15—24no—
278Dic15—42no—
279C3×Dic5—42no—
280C5×Dic3—41no—
281C3×#41—22no—
282C3×#41—22no—
283C2×C3×Q8—52no—
284C2×C3×Q8—101no—
285C2×C3×Q8—102no—
286C2×C3×Q8—102no—
287C2×C3×Q8C22×D511yescharacteristic
288C2×C3×D4—21no—
289C2×C3×D4C22×D511yescharacteristic
290C22×C3×C4—21no—
291C22×C3×C4—101no—
292C22×C3×C4C22×D511yescharacteristic
293C2×#67—21no—
294C22×Dic3—101no—
295#235—22no—
296#235—22no—
297C2×D12C22×D511yescharacteristic
298C2×C4×D3—21no—
299C2×Dic6—52no—
300C2×Dic6—102no—
301C2×Dic6—102no—
302C2×Dic6—101no—
303C2×Dic6C22×D511yescharacteristic
304C3×Q16—104no—
305C3×SD16—104no—
306C3×M16—54no—
307C2×C3×C8—52no—
308#217—52no—
309#217—104no—
310#216—22no—
311#216—104no—
312#216—104no—
313#215—22no—
314#214—22no—
315#213—22no—
316(C2×D3)⋊C4—104no—
317C4⋊Dic3—52no—
318Dic3⋊C4—104no—
319Dic3⋊C4—104no—
320C4×Dic3—52no—
321C2×C3⋊C8C22⋊D514yes—
322C2×C3⋊C8C22×D511yescharacteristic
323C2×C3⋊C8C22×D511yescharacteristic
324Dic12—104no—
325#204—104no—
326C23×C5—21no—
327C23×C5—61no—
328C23×C5D3×D411yescharacteristic
329C5×Q8—21no—
330C5×Q8—21no—
331C5×Q8—61no—
332C5×Q8—61no—
333C5×D4—21no—
334C5×D4—21no—
335C5×D4—42no—
336C5×D4—61no—
337C5×D4—61no—
338C5×D4—122no—
339C2×C4×C5—21no—
340C2×C4×C5—42no—
341C2×C4×C5—61no—
342C2×C4×C5—122no—
343C2×C4×C5D3×D412yes—
344C2×C4×C5D3×D411yescharacteristic
345C2×C4×C5C2×#6712yes—
346C2×C4×C5C23×D311yescharacteristic
347C2×Dic5—22no—
348C2×Dic5—34no—
349C2×Dic5—42no—
350C2×Dic5—62no—
351C2×Dic5—122no—
352Dic10—22no—
353Dic10—22no—
354Dic10—42no—
355Dic10—62no—
356Dic10—62no—
357Dic10—122no—
358C5×C8—32no—
359C5×C8—32no—
360#168C2×#6714yes—
361C2×#41—31no—
362C2×#41D3×D511yescharacteristic
363C22×Q8—51no—
364C22×Q8—151no—
365#137—104no—
366#137—304no—
367#135—64no—
368C2×Q16—31no—
369C2×Q16—52no—
370C2×Q16—152no—
371C2×Q16—152no—
372C2×Q16—152no—
373C2×Q16—304no—
374C2×SD16—31no—
375C2×SD16—31no—
376C2×SD16—52no—
377C2×SD16—152no—
378C2×D8—31no—
379C2×M16—51no—
380C22×C8—31no—
381C4⋊Q8—152no—
382C4⋊Q8—152no—
383#124—152no—
384#124—152no—
385#123—302no—
386#123—302no—
387C22⋊Q8—302no—
388C22⋊Q8—302no—
389#117—151no—
390#97—152no—
391C4×C8—152no—
392C2×C3×C5—22no—
393C2×C3×C5—81no—
394C2×C3×C5C2×#12711yescharacteristic
395C2×C3×C5#57812yes—
396C5×D3—81no—
397C23×C3—21no—
398C23×C3D4×D511yescharacteristic
399C22×D3—21no—
400C3×Q8—21no—
401C3×Q8—21no—
402C3×Q8—102no—
403C3×Q8—102no—
404C3×Q8—202no—
405C3×D4—21no—
406C3×D4—21no—
407C3×D4—42no—
408C2×C3×C4—21no—
409C2×C3×C4—42no—
410C2×C3×C4—102no—
411C2×C3×C4—202no—
412C2×C3×C4D4×D512yes—
413C2×C3×C4D4×D511yescharacteristic
414C2×C3×C4C2×C22⋊D512yes—
415C2×C3×C4C23×D511yescharacteristic
416#67—42no—
417C2×Dic3—21no—
418C2×Dic3—54no—
419C2×Dic3—102no—
420C2×Dic3—202no—
421D12—21no—
422D12—21no—
423C4×D3—42no—
424Dic6—21no—
425Dic6—21no—
426Dic6—102no—
427Dic6—102no—
428Dic6—202no—
429C3×C8—54no—
430C3⋊C8C2×C22⋊D512yes—
431C3⋊C8C2×C22⋊D512yes—
432C22×C5—22no—
433C22×C5—42no—
434C22×C5—41no—
435C22×C5—122no—
436C22×C5—121no—
437C22×C5#94012yes—
438C22×C5C2×D3×D411yescharacteristic
439C4×C5—41no—
440C4×C5—121no—
441C4×C5#94012yes—
442C4×C5C2×D3×D411yescharacteristic
443C4×C5C22×#6711yescharacteristic
444Dic5—42no—
445Dic5—64no—
446Dic5—122no—
447#41—22no—
448#41—22no—
449#41—62no—
450#41—62no—
451C2×Q8—31no—
452C2×Q8—52no—
453C2×Q8—101no—
454C2×Q8—102no—
455C2×Q8—102no—
456C2×Q8—152no—
457C2×Q8—301no—
458C2×Q8—302no—
459C2×Q8—302no—
460C2×Q8C2×D3×D511yescharacteristic
461C2×D4—21no—
462C2×D4—31no—
463C2×D4—61no—
464C2×D4C2×D3×D511yescharacteristic
465C22×C4—21no—
466C22×C4—61no—
467C22×C4—101no—
468C22×C4—301no—
469C22×C4C2×D3×D511yescharacteristic
470Q16—62no—
471Q16—104no—
472Q16—304no—
473Q16—304no—
474Q16—304no—
475SD16—62no—
476SD16—62no—
477SD16—104no—
478SD16—304no—
479D8—62no—
480M16—54no—
481C2×C8—34no—
482C2×C8—31no—
483C2×C8—31no—
484C2×C8—52no—
485C4⋊C4—152no—
486C4⋊C4—304no—
487C4⋊C4—304no—
488C22⋊C4—152no—
489C22⋊C4—304no—
490C22⋊C4—304no—
491C42—152no—
492C3×C5#315611yescharacteristic, complemented, Hall
493C22×C3—22no—
494C22×C3—42no—
495C22×C3—41no—
496C22×C3#408612yes—
497C22×C3C2×D4×D511yescharacteristic
498C2×D3—42no—
499C2×D3—41no—
500C3×C4—41no—
501C3×C4—202no—
502C3×C4#408612yes—
503C3×C4C2×D4×D511yescharacteristic
504C3×C4C22×C22⋊D511yescharacteristic
505Dic3—41no—
506Dic3—104no—
507Dic3—202no—
508C2×C5—22no—
509C2×C5—81no—
510C2×C5—241no—
511C2×C5#577912yes—
512C2×C5C2×#94011yescharacteristic
513C23—21no—
514C23—61no—
515C23#679011yescharacteristic
516Q8—21no—
517Q8—21no—
518Q8—61no—
519Q8—61no—
520Q8—102no—
521Q8—102no—
522Q8—202no—
523Q8—302no—
524Q8—302no—
525Q8—602no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4—61no—
530D4—61no—
531D4—122no—
532C2×C4—21no—
533C2×C4—42no—
534C2×C4—61no—
535C2×C4—102no—
536C2×C4—122no—
537C2×C4—154no—
538C2×C4—202no—
539C2×C4—302no—
540C2×C4—602no—
541C2×C4D5×#6712yes—
542C2×C4D3×C22⋊D512yes—
543C2×C4#679011yescharacteristic
544C2×C4C22×D3×D511yescharacteristic
545C8—32no—
546C8—32no—
547C8—54no—
548C2×C3—22no—
549C2×C3—81no—
550C2×C3#6610512yes—
551C2×C3C2×#408611yescharacteristic
552D3—81no—
553C5#8397511yescharacteristic, complemented, Sylow
554C22—22no—
555C22—42no—
556C22—41no—
557C22—122no—
558C22—121no—
559C22#9156712yes—
560C22C2×#679011yescharacteristic
561C4—41no—
562C4—121no—
563C4—202no—
564C4—304no—
565C4—602no—
566C4#9156712yes—
567C4C2×D5×#6711yescharacteristic
568C4C2×D3×C22⋊D511yescharacteristic
569C3#1061563811yescharacteristic, complemented, Sylow
570C2—22no—
571C2—81no—
572C2—241no—
573C2#1175535312yes—
574C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#950C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3156
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11756584C2semidirect
3. C2×C3×#4097C2semidirect
4. #11754255C2semidirect
5. C2×#91322C2semidirect
6. C22×#6662C2semidirect
7. #11749355C2semidirect
8. #11749322C2semidirect
9. #11749111C2semidirect
10. #11749075C2semidirect
11. #11748326C2semidirect
49. C2×#4097D3semidirect
492. C3×C5#3156semidirect
553. C5#83975semidirect
569. C3#10615638semidirect

Maximal subgroups

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

subgroupindex
#117565842
C2×C5×#9502
C2×C3×#40972
#117542552
C2×#913222
C22×#66622
#117493552
#117493222
#117491112
#117490752
#117483262
#106156383
#839755