Finite Group Databasebeta

← #14439706

Subgroups — #14439706

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×#951C211yesmaximal, characteristic, complemented
3C2×C3×#4096C211yesmaximal, characteristic
4#11754251C211yesmaximal, characteristic, complemented
5C22×#6663C211yesmaximal, characteristic, complemented
6C2×#91313C211yesmaximal, characteristic, complemented
7#11749355C212yesmaximal, complemented
8#11749320C212yesmaximal, complemented
9#11749111C212yesmaximal, complemented
10#11749072C212yesmaximal, complemented
11#11748324C211yesmaximal, characteristic, complemented
12#10615706—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17#91833C2212yes—
18#91825C2212yes—
19#91824—22no—
20#91815C2211yescharacteristic
21#91813—22no—
22C5×#951—24no—
23C2×C5×#216C2212yes—
24C2×C5×#214C2212yes—
25C2×C5×#208C2211yescharacteristic
26C3×#4096—24no—
27C2×C3×#689C2211yescharacteristic
28C2×C3×#688C2211yescharacteristic
29C2×C3×#687C2211yescharacteristic
30C2×C3×#686C2211yescharacteristic
31C22×C3×#168C2211yescharacteristic
32#91536—22no—
33#91385C2212yes—
34#91368C2212yes—
35#91359—22no—
36C2×#6663—24no—
37C2×#6663C2212yes—
38C2×#6663C2212yes—
39C2×#6662C2212yes—
40#91313—24no—
41C2×#6657C2212yes—
42#90954C2212yes—
43#90951C2212yes—
44#83907—51nomaximal, Hall
45C2×C5×#137—31no—
46#66159—31no—
47C2×#4096D311yescharacteristic
48#66150—31no—
49C22×#689—31no—
50C2×#4055—31no—
51#65479—32no—
52#65470—32no—
53#65457—32no—
54#65456—32no—
55#65411—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—
68C22×C5×Dic3—21no—
69C2×C5×Dic6—22no—
70C2×C5×Dic6—22no—
71C2×C5×Dic6—21no—
72C2×C5×Dic6C2312yes—
73C2×C3×C22⋊D5—21no—
74C3×#709—22no—
75C3×#709—22no—
76C2×C3×D20C2311yescharacteristic
77C2×C3×C4×D5—21no—
78C2×C3×Dic10C2311yescharacteristic
79#6719—24no—
80#6719D412yes—
81C4⋊Dic15D412yes—
82#6712—24no—
83C4×Dic15C2312yes—
84C5×#216—24no—
85C5×#214—24no—
86C5×#208D414yes—
87C2×C5×C3⋊C8C2312yes—
88C3×#689—22no—
89C3×#688—22no—
90C3×#687—22no—
91C3×#686—22no—
92C2×C3×#168D414yes—
93C2×C3×#168C2311yescharacteristic
94C2×C3×#168C2311yescharacteristic
95#6669—24no—
96#6665—24no—
97#6663—24no—
98#6663—24no—
99#6662—24no—
100#6657—24no—
101C2×C3×#135—51no—
102#5825—51no—
103#5825—51no—
104C2×#951—51no—
105C2×#951D511yescharacteristic, complemented
106C22×Dic12—51no—
107#5183—52no—
108#5167—52no—
109#5167—52no—
110#5155—52no—
111#5101—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×Q8—31no—
114C2×#709C2×D311yescharacteristic
115C22×Dic10—31no—
116C5×#137—64no—
117C2×C5×Q16—32no—
118C2×C5×SD16—32no—
119C2×C5×M16—31no—
120#4096—24no—
121#4093—32no—
122#4092—62no—
123#4090—32no—
124#4090—32no—
125C2×#689—32no—
126C2×#689—32no—
127C2×#689—64no—
128C2×#689C2×D311yescharacteristic
129C2×#688C2×D311yescharacteristic
130#4082—32no—
131#4081—62no—
132C2×#687C2×D311yescharacteristic
133C2×#686C2×D311yescharacteristic
134#4075—62no—
135#4072—31no—
136#4070—62no—
137C22×#168C2×D311yescharacteristic
138#4055—64no—
139C2×Dic20—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3156—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×C3×D5—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—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—42no—
166C5×Dic6—22no—
167C5×Dic6—22no—
168C5×Dic6—42no—
169C3×C22⋊D5—42no—
170C2×C3×Dic5—21no—
171C3×D20—21no—
172C3×D20—21no—
173C3×C4×D5—42no—
174C3×Dic10—21no—
175C3×Dic10—21no—
176C3×#168C2×D412yes—
177C3×#168C2×D412yes—
178C5×C3⋊C8C2×D414yes—
179C2×C3×#41—51no—
180C2×C3×#41C2×D511yescharacteristic
181C22×Dic6—51no—
182C22×Dic6C2×D511yescharacteristic
183C3×#135—104no—
184C2×C3×Q16—51no—
185C2×C3×SD16—51no—
186C2×C3×SD16—51no—
187C2×C3×D8—51no—
188C22×C3×C8—51no—
189#951—24no—
190#951—104no—
191#944—52no—
192#944—52no—
193C2×#216—52no—
194C2×#216C2×D512yes—
195#936—52no—
196#936—52no—
197#935—102no—
198#935—102no—
199C2×#214—52no—
200C2×#214C2×D512yes—
201#926—51no—
202#924—102no—
203#924—102no—
204C2×#208C2×D511yescharacteristic
205C2×Dic12—52no—
206C2×Dic12—52no—
207C2×Dic12—104no—
208#815—52no—
209C8×Dic3—52no—
210C5×#41—22no—
211C5×#41—22no—
212C2×C5×Q8—32no—
213C2×C5×Q8—61no—
214C2×C5×Q8—62no—
215C2×C5×Q8—62no—
216C2×C5×Q8C22×D311yescharacteristic
217C2×C5×D4—21no—
218C2×C5×D4C22×D311yescharacteristic
219C22×C4×C5—21no—
220C22×C4×C5—61no—
221C22×C4×C5C22×D311yescharacteristic
222C2×C22⋊D5—21no—
223C22×Dic5—61no—
224#709—22no—
225#709—22no—
226C2×D20C22×D311yescharacteristic
227C2×C4×D5—21no—
228C2×Dic10—32no—
229C2×Dic10—62no—
230C2×Dic10—62no—
231C2×Dic10—61no—
232C2×Dic10C22×D311yescharacteristic
233C5×Q16—64no—
234C5×SD16—64no—
235C5×M16—34no—
236C2×C5×C8—32no—
237C22⋊Dic5—32no—
238C22⋊Dic5—64no—
239#689—22no—
240#689—64no—
241#689—64no—
242#688—22no—
243#687—22no—
244#686—22no—
245#685—64no—
246C4⋊Dic5—32no—
247#683—64no—
248#683—64no—
249C4×Dic5—32no—
250C2×#168#6714yes—
251C2×#168C22×D311yescharacteristic
252C2×#168C22×D311yescharacteristic
253Dic20—64no—
254#677—64no—
255C2×#137—31no—
256C2×#137—151no—
257C2×#135—51no—
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×C3×D5—41no—
272C2×C3×D5—42no—
273C3×C4×C5—41no—
274C3×C4×C5#12712yes—
275C3×C4×C5C22×D411yescharacteristic
276C3×C4×C5C22×D411yescharacteristic
277Dic15—24no—
278Dic15—42no—
279C3×Dic5—41no—
280C5×Dic3—42no—
281C3×#41—22no—
282C3×#41—22no—
283C3×#41—102no—
284C3×#41—102no—
285C2×C3×Q8—51no—
286C2×C3×Q8C22×D511yescharacteristic
287C2×C3×D4—21no—
288C2×C3×D4—51no—
289C2×C3×D4—101no—
290C2×C3×D4C22×D511yescharacteristic
291C22×C3×C4—21no—
292C22×C3×C4—101no—
293C22×C3×C4C22×D511yescharacteristic
294C22×Dic3—21no—
295C22×Dic3—101no—
296C2×Dic6—22no—
297C2×Dic6—22no—
298C2×Dic6—21no—
299C2×Dic6—52no—
300C2×Dic6—102no—
301C2×Dic6—102no—
302C2×Dic6—101no—
303C2×Dic6C22×D512yes—
304C3×Q16—102no—
305C3×SD16—102no—
306C3×SD16—102no—
307C3×D8—102no—
308C2×C3×C8—54no—
309C2×C3×C8—51no—
310C2×C3×C8—51no—
311#217—52no—
312#217—104no—
313#217—104no—
314#216—24no—
315#216—104no—
316#214—24no—
317#214—104no—
318C4⋊Dic3—52no—
319Dic3⋊C4—104no—
320Dic3⋊C4—104no—
321C4×Dic3—52no—
322#208C22⋊D514yes—
323C2×C3⋊C8C22×D512yes—
324Dic12—104no—
325Dic12—104no—
326C23×C5—21no—
327C23×C5D3×D411yescharacteristic
328C22×D5—21no—
329C5×Q8—21no—
330C5×Q8—21no—
331C5×Q8—62no—
332C5×Q8—62no—
333C5×Q8—122no—
334C5×D4—21no—
335C5×D4—21no—
336C5×D4—42no—
337C2×C4×C5—21no—
338C2×C4×C5—42no—
339C2×C4×C5—62no—
340C2×C4×C5—122no—
341C2×C4×C5D3×D412yes—
342C2×C4×C5D3×D411yescharacteristic
343C2×C4×C5C2×#6712yes—
344C2×C4×C5C23×D311yescharacteristic
345C22⋊D5—42no—
346C2×Dic5—21no—
347C2×Dic5—34no—
348C2×Dic5—62no—
349C2×Dic5—122no—
350D20—21no—
351D20—21no—
352C4×D5—42no—
353Dic10—21no—
354Dic10—21no—
355Dic10—62no—
356Dic10—62no—
357Dic10—122no—
358C5×C8—34no—
359#168C2×#6712yes—
360#168C2×#6712yes—
361C2×#41—51no—
362C2×#41D3×D511yescharacteristic
363C22×Q8—31no—
364C22×Q8—151no—
365#137—64no—
366#137—304no—
367#135—104no—
368C2×Q16—32no—
369C2×Q16—51no—
370C2×Q16—152no—
371C2×Q16—152no—
372C2×Q16—152no—
373C2×Q16—304no—
374C2×SD16—32no—
375C2×SD16—51no—
376C2×SD16—51no—
377C2×SD16—152no—
378C2×D8—51no—
379C2×M16—31no—
380C22×C8—51no—
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—
396C3×D5—81no—
397C23×C3—21no—
398C23×C3—101no—
399C23×C3D4×D511yescharacteristic
400C3×Q8—21no—
401C3×Q8—21no—
402C3×Q8—101no—
403C3×Q8—101no—
404C3×D4—21no—
405C3×D4—21no—
406C3×D4—42no—
407C3×D4—101no—
408C3×D4—101no—
409C3×D4—202no—
410C2×C3×C4—21no—
411C2×C3×C4—42no—
412C2×C3×C4—101no—
413C2×C3×C4—202no—
414C2×C3×C4D4×D512yes—
415C2×C3×C4D4×D511yescharacteristic
416C2×C3×C4C2×C22⋊D512yes—
417C2×C3×C4C23×D511yescharacteristic
418C2×Dic3—22no—
419C2×Dic3—42no—
420C2×Dic3—54no—
421C2×Dic3—102no—
422C2×Dic3—202no—
423Dic6—22no—
424Dic6—22no—
425Dic6—42no—
426Dic6—102no—
427Dic6—102no—
428Dic6—202no—
429C3×C8—52no—
430C3×C8—52no—
431C3⋊C8C2×C22⋊D514yes—
432C22×C5—22no—
433C22×C5—42no—
434C22×C5—41no—
435C22×C5#94012yes—
436C22×C5C2×D3×D411yescharacteristic
437C2×D5—42no—
438C2×D5—41no—
439C4×C5—41no—
440C4×C5—122no—
441C4×C5#94012yes—
442C4×C5C2×D3×D411yescharacteristic
443C4×C5C22×#6711yescharacteristic
444Dic5—41no—
445Dic5—64no—
446Dic5—122no—
447#41—22no—
448#41—22no—
449#41—102no—
450#41—102no—
451C2×Q8—32no—
452C2×Q8—51no—
453C2×Q8—61no—
454C2×Q8—62no—
455C2×Q8—62no—
456C2×Q8—152no—
457C2×Q8—301no—
458C2×Q8—302no—
459C2×Q8—302no—
460C2×Q8C2×D3×D511yescharacteristic
461C2×D4—21no—
462C2×D4—51no—
463C2×D4—101no—
464C2×D4C2×D3×D511yescharacteristic
465C22×C4—21no—
466C22×C4—61no—
467C22×C4—101no—
468C22×C4—301no—
469C22×C4C2×D3×D511yescharacteristic
470Q16—64no—
471Q16—102no—
472Q16—304no—
473Q16—304no—
474Q16—304no—
475SD16—64no—
476SD16—102no—
477SD16—102no—
478SD16—304no—
479D8—102no—
480M16—34no—
481C2×C8—32no—
482C2×C8—54no—
483C2×C8—51no—
484C2×C8—51no—
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—202no—
497C22×C3—201no—
498C22×C3#408612yes—
499C22×C3C2×D4×D511yescharacteristic
500C3×C4—41no—
501C3×C4—201no—
502C3×C4#408612yes—
503C3×C4C2×D4×D511yescharacteristic
504C3×C4C22×C22⋊D511yescharacteristic
505Dic3—42no—
506Dic3—104no—
507Dic3—202no—
508C2×C5—22no—
509C2×C5—81no—
510C2×C5#577112yes—
511C2×C5C2×#94011yescharacteristic
512D5—81no—
513C23—21no—
514C23—101no—
515C23#679011yescharacteristic
516Q8—21no—
517Q8—21no—
518Q8—62no—
519Q8—62no—
520Q8—101no—
521Q8—101no—
522Q8—122no—
523Q8—302no—
524Q8—302no—
525Q8—602no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4—101no—
530D4—101no—
531D4—202no—
532C2×C4—21no—
533C2×C4—42no—
534C2×C4—62no—
535C2×C4—101no—
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—34no—
546C8—52no—
547C8—52no—
548C2×C3—22no—
549C2×C3—81no—
550C2×C3—401no—
551C2×C3#6611312yes—
552C2×C3C2×#408611yescharacteristic
553C5#8390711yescharacteristic, complemented, Sylow
554C22—22no—
555C22—42no—
556C22—41no—
557C22—202no—
558C22—201no—
559C22#9156712yes—
560C22C2×#679011yescharacteristic
561C4—41no—
562C4—122no—
563C4—201no—
564C4—304no—
565C4—602no—
566C4#9156712yes—
567C4C2×D5×#6711yescharacteristic
568C4C2×D3×C22⋊D511yescharacteristic
569C3#1061570611yescharacteristic, complemented, Sylow
570C2—22no—
571C2—81no—
572C2—401no—
573C2#1175535012yes—
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×C3×#4096C2
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
2. C2×C5×#951C2semidirect
4. #11754251C2semidirect
5. C22×#6663C2semidirect
6. C2×#91313C2semidirect
7. #11749355C2semidirect
8. #11749320C2semidirect
9. #11749111C2semidirect
10. #11749072C2semidirect
11. #11748324C2semidirect
105. C2×#951D5semidirect
492. C3×C5#3156semidirect
553. C5#83907semidirect
569. C3#10615706semidirect

Maximal subgroups

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

subgroupindex
#117565842
C2×C5×#9512
C2×C3×#40962
#117542512
C22×#66632
C2×#913132
#117493552
#117493202
#117491112
#117490722
#117483242
#106157063
#839075