Finite Group Databasebeta

← #14424621

Subgroups — #14424621

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×#92001C211yesmaximal, characteristic
2C2×C3×#4055C211yesmaximal, characteristic, complemented
3#11754255C211yesmaximal, characteristic, complemented
4C22×#6662C211yesmaximal, characteristic, complemented
5#11751221C211yesmaximal, characteristic, complemented
6C5×#5129C211yesmaximal, characteristic, complemented
7#11748365C211yesmaximal, characteristic, complemented
8#11748147C214yesmaximal, complemented
9#11748125C214yesmaximal, complemented
10#10610410—31nomaximal, Hall
11C22×Dic30C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C2×C3×#709C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C2×#6780—22no—
16C2×#6772—21no—
17C2×D3×Dic10C2212yes—
18#92001—24no—
19#92001—24no—
20C2×#6765C2212yes—
21C2×D5×Dic6—21no—
22C2×C3×C5×M16C2211yescharacteristic
23#91815C2211yescharacteristic
24C22×C5×C3⋊C8C2211yescharacteristic
25C3×#4055—24no—
26C2×C3×Dic20C2212yes—
27C2×C3×#677C2212yes—
28#91539—22no—
29#91385—21no—
30#91370—21no—
31#91369C2214yes—
32C2×#6662—24no—
33C2×#6662C2214yes—
34#91100C2214yes—
35C5×(C2×D3)⋊C8C2214yes—
36#90971C2212yes—
37#90965C2212yes—
38#83983—51nomaximal, Hall
39C2×#4150—31no—
40#66159—31no—
41C2×#4055D311yescharacteristic, complemented
42C22×Dic20—31no—
43C5×#408—31no—
44#65409—31no—
45#65402—31no—
46#65028—34no—
47#65022—34no—
48C22×C3×C4×C5C2311yescharacteristic
49C22×Dic15—21no—
50C2×Dic30—21no—
51C2×Dic30—22no—
52C2×Dic30D414yes—
53C2×Dic30C2312yes—
54C2×C5×#67D412yes—
55C5×#235—22no—
56C5×#235—22no—
57C2×C5×D12D411yescharacteristic
58C2×C4×C5×D3C2312yes—
59C2×C5×Dic6D411yescharacteristic
60C2×C3×C22⋊D5—21no—
61C22×C3×Dic5—21no—
62C3×#709—22no—
63C3×#709D414yes—
64C2×C3×D20C2311yescharacteristic
65C2×C3×C4×D5—21no—
66C2×C3×Dic10—22no—
67C2×C3×Dic10—22no—
68C2×C3×Dic10—21no—
69C2×C3×Dic10C2312yes—
70C2×C3×Dic10C2311yescharacteristic
71C2×#1204—22no—
72C2×#1201—22no—
73C2×D3×Dic5—22no—
74#6780—216no—
75C2×D5×Dic3—22no—
76#6772—28no—
77D3×Dic10—24no—
78D3×Dic10—24no—
79#6765—24no—
80#6765—24no—
81D5×Dic6—28no—
82C3×C5×M16—22no—
83C2×C3×C5×C8C2312yes—
84#6719—21no—
85C4⋊Dic15C2312yes—
86C4×Dic15—21no—
87C2×C5×C3⋊C8—22no—
88C2×C5×C3⋊C8C2312yes—
89C3×Dic20—24no—
90C3×#677—24no—
91#6669—24no—
92(C2×D3)⋊Dic5—24no—
93#6662—28no—
94C2×#1010—51no—
95C2×C3×#137—51no—
96#5816—51no—
97C22×#216—51no—
98#5233—51no—
99#5186—54no—
100#5173—54no—
101#5129D511yescharacteristic, complemented
102#5120—51no—
103C2×C5×#41—31no—
104#4150—64no—
105#4150—64no—
106C2×Q8×D5—61no—
107C2×#711—61no—
108C2×#711—62no—
109C2×#709—32no—
110C2×#709C2×D311yescharacteristic
111C22×Dic10—31no—
112C22×Dic10—32no—
113C22×Dic10C2×D311yescharacteristic
114C2×C5×M16C2×D311yescharacteristic
115C22×C5×C8—31no—
116#4090—61no—
117#4082—61no—
118#4081—62no—
119#4072—31no—
120#4070—34no—
121#4055—24no—
122C2×Dic20—34no—
123C2×Dic20—64no—
124C2×Dic20C2×D312yes—
125C2×#677C2×D312yes—
126C5×C22⋊C8—34no—
127#3953—32no—
128#3948—32no—
129#3948—34no—
130#3011—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×C5×D3C2×D412yes—
133C22×C3×D5—21no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D412yes—
137C2×C3×C4×C5C2411yescharacteristic
138C2×Dic15—24no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141Dic30—24no—
142Dic30—22no—
143Dic30C2×D414yes—
144C5×#67—24no—
145C2×C5×Dic3C2×D412yes—
146C5×D12—22no—
147C4×C5×D3—22no—
148C4×C5×D3—22no—
149C5×Dic6—22no—
150C3×C22⋊D5—24no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—42no—
154C3×D20—21no—
155C3×D20C2×D412yes—
156C3×C4×D5—24no—
157C3×Dic10—21no—
158C3×Dic10—22no—
159C3×Dic10—22no—
160C3×Dic10—42no—
161C3×Dic10C2×D412yes—
162#1204—28no—
163#1201—28no—
164D3×Dic5—28no—
165D5×Dic3—28no—
166C3×C5×C8—22no—
167C5×C3⋊C8—22no—
168C2×C3×#41—51no—
169C22×C3×Q8—51no—
170#1010—104no—
171#1010—104no—
172C2×D3×Q8—52no—
173C2×#237—52no—
174C2×#237—102no—
175C2×#235—101no—
176C2×#235C2×D511yescharacteristic
177C22×Dic6—51no—
178C22×Dic6—101no—
179C3×#137—104no—
180C2×C3×Q16—52no—
181C2×C3×SD16—52no—
182C2×C3×M16C2×D511yescharacteristic
183#947—101no—
184#946—54no—
185#944—101no—
186C2×#216—54no—
187C2×#216—104no—
188#929—102no—
189#926—51no—
190C22×C3⋊C8C2×D511yescharacteristic
191#835—52no—
192#832—52no—
193(C2×D3)⋊C8C2×D514yes—
194#816—54no—
195C5×#41—62no—
196C5×#41—62no—
197C2×C5×Q8—31no—
198C2×C5×D4—32no—
199C2×C5×D4—31no—
200C22×C4×C5—32no—
201C22×C4×C5C22×D311yescharacteristic
202C2×C22⋊D5—21no—
203C2×C22⋊D5—62no—
204C22×Dic5—21no—
205C22×Dic5—62no—
206C22×Dic5—61no—
207Q8×D5—68no—
208#711—68no—
209#711—616no—
210#709—22no—
211#709—64no—
212#709—64no—
213#709#6714yes—
214C2×D20C22×D311yescharacteristic
215C2×C4×D5—21no—
216C2×C4×D5—62no—
217C2×Dic10—22no—
218C2×Dic10—22no—
219C2×Dic10—21no—
220C2×Dic10—34no—
221C2×Dic10—32no—
222C2×Dic10—64no—
223C2×Dic10—62no—
224C2×Dic10—61no—
225C2×Dic10—62no—
226C2×Dic10—64no—
227C2×Dic10C22×D312yes—
228C2×Dic10C22×D311yescharacteristic
229C5×M16—22no—
230C2×C5×C8—32no—
231C2×C5×C8—62no—
232C2×C5×C8C22×D312yes—
233C22⋊Dic5—64no—
234C22⋊Dic5—61no—
235C4⋊Dic5—32no—
236#683—64no—
237C4×Dic5—61no—
238Dic20—24no—
239Dic20—68no—
240#677—24no—
241C2×2−1+4—151no—
242C2×#137—51no—
243C22×Q16—151no—
244#536—151no—
245#452—154no—
246#451—154no—
247#419—151no—
248#416—151no—
249#408—31no—
250C22×C3×C5—22no—
251C22×C3×C5#12012yes—
252C22×C3×C5C22×D411yescharacteristic
253C2×C5×D3—22no—
254C2×C5×D3—24no—
255C2×C3×D5—22no—
256C2×C3×D5—42no—
257C3×C4×C5#12012yes—
258C3×C4×C5C22×D411yescharacteristic
259C3×C4×C5C22×D411yescharacteristic
260Dic15—24no—
261Dic15—42no—
262C3×Dic5—22no—
263C3×Dic5—42no—
264C5×Dic3—22no—
265C3×#41—54no—
266C3×#41—102no—
267C2×C3×Q8—51no—
268C2×C3×Q8—52no—
269C2×C3×Q8—101no—
270C2×C3×Q8—102no—
271C2×C3×Q8—102no—
272C2×C3×D4—51no—
273C2×C3×D4—101no—
274C22×C3×C4—101no—
275C22×C3×C4—101no—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—102no—
278C2×#67D2012yes—
279C22×Dic3—101no—
280C22×Dic3—102no—
281D3×Q8—104no—
282D3×Q8—104no—
283#237—104no—
284#237—104no—
285#237—1016no—
286#235—22no—
287#235—22no—
288#235—108no—
289C2×D12D2011yescharacteristic
290C2×C4×D3—102no—
291C2×C4×D3C22×D512yes—
292C2×Dic6—54no—
293C2×Dic6—52no—
294C2×Dic6—108no—
295C2×Dic6—101no—
296C2×Dic6—102no—
297C2×Dic6—102no—
298C2×Dic6D2011yescharacteristic
299C3×Q16—104no—
300C3×SD16—104no—
301C3×M16—22no—
302C2×C3×C8C22×D512yes—
303#217—101no—
304#216—108no—
305(C2×D3)⋊C4—104no—
306C4⋊Dic3—52no—
307Dic3⋊C4—104no—
308C4×Dic3—101no—
309C2×C3⋊C8—22no—
310C2×C3⋊C8C22×D512yes—
311C23×C5—32no—
312C23×C5D3×D411yescharacteristic
313C22×D5—21no—
314C5×Q8—62no—
315C5×D4—64no—
316C5×D4—62no—
317C2×C4×C5—32no—
318C2×C4×C5—62no—
319C2×C4×C5—62no—
320C2×C4×C5D3×D411yescharacteristic
321C2×C4×C5D3×D412yes—
322C2×C4×C5C2×#6712yes—
323C2×C4×C5C23×D311yescharacteristic
324C22⋊D5—24no—
325C22⋊D5—68no—
326C2×Dic5—21no—
327C2×Dic5—22no—
328C2×Dic5—42no—
329C2×Dic5—68no—
330C2×Dic5—64no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333D20—21no—
334D20C2×#6712yes—
335C4×D5—24no—
336C4×D5—68no—
337Dic10—21no—
338Dic10—22no—
339Dic10—22no—
340Dic10—34no—
341Dic10—42no—
342Dic10—68no—
343Dic10—64no—
344Dic10—62no—
345Dic10C2×#6712yes—
346C5×C8—22no—
347C5×C8—62no—
3482−1+4—304no—
3492−1+4—304no—
350C2×#41—31no—
351C2×#41—51no—
352C2×#41—152no—
353C2×#41—301no—
354C2×#41—302no—
355C22×Q8—51no—
356C22×Q8—152no—
357C22×Q8—151no—
358C22×Q8—301no—
359#137—104no—
360C2×Q16—52no—
361C2×Q16—154no—
362C2×Q16—304no—
363C2×SD16—52no—
364C2×M16D3×D511yescharacteristic
365C22×C8—31no—
366C4⋊Q8—301no—
367#124—301no—
368#123—302no—
369C22⋊Q8—154no—
370#117—151no—
371#103—152no—
372#103—154no—
373#102—152no—
374C22⋊C8—34no—
375C2×C3×C5—22no—
376C2×C3×C5C2×#12011yescharacteristic
377C2×C3×C5#57812yes—
378C3×D5—42no—
379C5×D3—42no—
380C23×C3—101no—
381C23×C3C2×D2011yescharacteristic
382C22×D3C2×D2012yes—
383C3×Q8—52no—
384C3×Q8—101no—
385C3×Q8—102no—
386C3×Q8—102no—
387C3×Q8—202no—
388C3×D4—52no—
389C3×D4—104no—
390C3×D4—101no—
391C2×C3×C4—101no—
392C2×C3×C4—104no—
393C2×C3×C4—102no—
394C2×C3×C4—202no—
395C2×C3×C4C2×D2011yescharacteristic
396C2×C3×C4D4×D512yes—
397C2×C3×C4D4×D512yes—
398C2×C3×C4C23×D511yescharacteristic
399#67—24no—
400#67—108no—
401C2×Dic3—108no—
402C2×Dic3—102no—
403C2×Dic3—104no—
404C2×Dic3—102no—
405C2×Dic3C2×D2012yes—
406D12—22no—
407C4×D3—22no—
408C4×D3—22no—
409C4×D3—108no—
410Dic6—22no—
411Dic6—54no—
412Dic6—108no—
413Dic6—102no—
414Dic6—104no—
415C3×C8—22no—
416C3⋊C8—22no—
417C22×C5—22no—
418C22×C5—64no—
419C22×C5—62no—
420C22×C5#93712yes—
421C22×C5C2×D3×D411yescharacteristic
422C2×D5—22no—
423C2×D5—42no—
424C4×C5—62no—
425C4×C5#93712yes—
426C4×C5C2×D3×D411yescharacteristic
427C4×C5C22×#6711yescharacteristic
428Dic5—22no—
429Dic5—42no—
430Dic5—64no—
431Dic5—122no—
432#41—54no—
433#41—62no—
434#41—62no—
435#41—102no—
436#41—304no—
437#41—304no—
438#41—308no—
439#41—3016no—
440C2×Q8—31no—
441C2×Q8—51no—
442C2×Q8—52no—
443C2×Q8—101no—
444C2×Q8—102no—
445C2×Q8—102no—
446C2×Q8—154no—
447C2×Q8—152no—
448C2×Q8—302no—
449C2×Q8—304no—
450C2×Q8—304no—
451C2×Q8—308no—
452C2×Q8—301no—
453C2×Q8—302no—
454C2×D4—32no—
455C2×D4—31no—
456C2×D4—51no—
457C2×D4—101no—
458C2×D4—302no—
459C22×C4—32no—
460C22×C4—101no—
461C22×C4—101no—
462C22×C4—302no—
463C22×C4—302no—
464C22×C4—301no—
465C22×C4C2×D3×D511yescharacteristic
466Q16—104no—
467Q16—308no—
468SD16—104no—
469M16—22no—
470C2×C8—32no—
471C2×C8—62no—
472C2×C8C2×D3×D512yes—
473C4⋊C4—152no—
474C4⋊C4—304no—
475C22⋊C4—304no—
476C22⋊C4—301no—
477C42—301no—
478C3×C5#301111yescharacteristic, complemented, Hall
479C22×C3—22no—
480C22×C3—102no—
481C22×C3—202no—
482C22×C3#402812yes—
483C22×C3C22×D2011yescharacteristic
484C2×D3—22no—
485C2×D3—24no—
486C3×C4—102no—
487C3×C4—202no—
488C3×C4#402812yes—
489C3×C4C2×D4×D511yescharacteristic
490C3×C4C2×D4×D511yescharacteristic
491Dic3—22no—
492Dic3—104no—
493Dic3—202no—
494C2×C5—22no—
495C2×C5—122no—
496C2×C5#577912yes—
497C2×C5C2×#93711yescharacteristic
498D5—42no—
499C23—32no—
500C23—101no—
501C23D3×D2011yescharacteristic
502Q8—52no—
503Q8—62no—
504Q8—101no—
505Q8—102no—
506Q8—102no—
507Q8—154no—
508Q8—202no—
509Q8—308no—
510Q8—304no—
511Q8—302no—
512D4—52no—
513D4—64no—
514D4—62no—
515D4—104no—
516D4—101no—
517D4—308no—
518C2×C4—32no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—101no—
522C2×C4—104no—
523C2×C4—102no—
524C2×C4—202no—
525C2×C4—308no—
526C2×C4—308no—
527C2×C4—304no—
528C2×C4—302no—
529C2×C4—302no—
530C2×C4D3×D2011yescharacteristic
531C2×C4#677712yes—
532C2×C4D5×#6712yes—
533C2×C4C22×D3×D511yescharacteristic
534C8—22no—
535C8—62no—
536C2×C3—22no—
537C2×C3—202no—
538C2×C3C2×#402811yescharacteristic
539C2×C3#6608712yes—
540D3—42no—
541C5#8398311yescharacteristic, complemented, Sylow
542C22—22no—
543C22—64no—
544C22—62no—
545C22—102no—
546C22—202no—
547C22#9147412yes—
548C22C2×D3×D2011yescharacteristic
549C4—62no—
550C4—102no—
551C4—202no—
552C4—304no—
553C4—602no—
554C4#9147412yes—
555C4C2×#677711yescharacteristic
556C4C2×D5×#6711yescharacteristic
557C3#1061041011yescharacteristic, complemented, Sylow
558C2—22no—
559C2—122no—
560C2—202no—
561C2#1175404212yes—
562C2C2×#9147411yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×#92001C2
hypercenterC2×M16D3×D5
hypocenterC3×C5#3011
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4055C2semidirect
3. #11754255C2semidirect
4. C22×#6662C2semidirect
5. #11751221C2semidirect
6. C5×#5129C2semidirect
7. #11748365C2semidirect
8. #11748147C2semidirect
9. #11748125C2semidirect
41. C2×#4055D3semidirect
101. #5129D5semidirect
478. C3×C5#3011semidirect
541. C5#83983semidirect
557. C3#10610410semidirect

Maximal subgroups

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

subgroupindex
C2×#920012
C2×C3×#40552
#117542552
C22×#66622
#117512212
C5×#51292
#117483652
#117481472
#117481252
#106104103
#839835