Finite Group Databasebeta

← #14424585

Subgroups — #14424585

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
2C22×#6718C211yesmaximal, characteristic, complemented
3C5×#5816C211yesmaximal, characteristic, complemented
4C2×C3×#4088C211yesmaximal, characteristic, complemented
5#11749403C214yesmaximal, complemented
6#11749401C214yesmaximal, complemented
7#11748417C211yesmaximal, characteristic, complemented
8#11748364C211yesmaximal, characteristic, complemented
9#11748347C211yesmaximal, characteristic, complemented
10#10615142—31nomaximal, Hall
11C22×C3×C5×Q8C2211yescharacteristic
12C22×Dic30C2211yescharacteristic
13C2×C5×#235C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C2×#6780—22no—
16C2×#6772—21no—
17C2×D3×Dic10C2212yes—
18#92001—24no—
19#92001—24no—
20C2×#6765C2212yes—
21C2×D5×Dic6—21no—
22C2×#6718—24no—
23C2×#6718C2214yes—
24C22×C3⋊#168C2211yescharacteristic
25C5×#947—21no—
26C5×#946C2214yes—
27C5×#944—21no—
28C5×#929—22no—
29C5×#926C2211yescharacteristic
30C2×C3×#689C2212yes—
31C3×#4088—24no—
32C2×C3×#688C2212yes—
33C2×C3×#681C2211yescharacteristic
34#90975C2214yes—
35#90970C2212yes—
36#90964C2212yes—
37(C2×D3)⋊#168C2214yes—
38#83983—51nomaximal, Hall
39C2×#4150—31no—
40C5×#536—31no—
41C22×#689—31no—
42C2×#4088D311yescharacteristic, complemented
43#65523—31no—
44#65339—34no—
45#65336—34no—
46#65293—31no—
47#65291—31no—
48C2×C3×C5×Q8—21no—
49C2×C3×C5×Q8—22no—
50C2×C3×C5×Q8—22no—
51C2×C3×C5×Q8C2312yes—
52C22×C3×C4×C5—21no—
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15—21no—
55C2×Dic30—21no—
56C2×Dic30—22no—
57C2×Dic30D414yes—
58C2×Dic30C2312yes—
59C2×C5×#67D412yes—
60C5×#235—22no—
61C5×#235—22no—
62C2×C5×D12D411yescharacteristic
63C2×C4×C5×D3C2312yes—
64C2×C5×Dic6D411yescharacteristic
65C2×C3×C22⋊D5—21no—
66C3×#709—22no—
67C3×#709D414yes—
68C2×C3×D20C2311yescharacteristic
69C2×C3×C4×D5—21no—
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—
82#6718—28no—
83C2×C3⋊#168—22no—
84C2×C3⋊#168C2312yes—
85C5×#217—21no—
86C5×(C2×D3)⋊C4—24no—
87C5×C4⋊Dic3C2312yes—
88C5×Dic3⋊C4—24no—
89C4×C5×Dic3—21no—
90C3×#689—24no—
91C3×#688—24no—
92C3×#681—22no—
93C2×C3×#168C2312yes—
94C2×#1010—51no—
95C2×C3×#137—51no—
96#5816D511yescharacteristic, complemented
97C22×#216—51no—
98#5233—51no—
99#5186—54no—
100#5173—54no—
101#5129—51no—
102#5120—51no—
103C2×C5×#41—31no—
104C22×C5×Q8C2×D311yescharacteristic
105#4150—64no—
106#4150—64no—
107C2×Q8×D5—61no—
108C2×#711—61no—
109C2×#711—62no—
110C2×#709—32no—
111C2×#709C2×D311yescharacteristic
112C22×Dic10—31no—
113C22×Dic10—32no—
114C5×C4⋊Q8—61no—
115C5×#124—61no—
116C5×#123—62no—
117C5×C22⋊Q8—34no—
118C5×#117—31no—
119C2×#689—34no—
120C2×#689—64no—
121C2×#689C2×D312yes—
122#4088—24no—
123C2×#688C2×D312yes—
124C2×#681C2×D311yescharacteristic
125C22×#168—31no—
126C22⋊#168—34no—
127#3942—32no—
128#3942—34no—
129#3941—32no—
130#3011—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×C5×D3C2×D412yes—
133C22×C3×D5—21no—
134C3×C5×Q8—22no—
135C3×C5×Q8—22no—
136C3×C5×Q8—42no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—42no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2411yescharacteristic
143C2×Dic15—24no—
144C2×Dic15—22no—
145Dic30—24no—
146Dic30—22no—
147Dic30C2×D414yes—
148C5×#67—24no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3C2×D412yes—
151C5×D12—22no—
152C4×C5×D3—22no—
153C4×C5×D3—22no—
154C5×Dic6—22no—
155C3×C22⋊D5—24no—
156C2×C3×Dic5—21no—
157C3×D20—21no—
158C3×D20C2×D412yes—
159C3×C4×D5—24no—
160C3×Dic10—21no—
161C3×Dic10C2×D412yes—
162#1204—28no—
163#1201—28no—
164D3×Dic5—28no—
165D5×Dic3—28no—
166C3⋊#168—22no—
167C3×#168—22no—
168C2×C3×#41—51no—
169C22×C3×Q8C2×D511yescharacteristic
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×M16—51no—
183#947—21no—
184#946C2×D514yes—
185#944—21no—
186C2×#216—54no—
187C2×#216—104no—
188#929—22no—
189#926C2×D511yescharacteristic
190C22×C3⋊C8—51no—
191#835—52no—
192#832—52no—
193(C2×D3)⋊C8—54no—
194#816—54no—
195C5×#41—62no—
196C5×#41—62no—
197C2×C5×Q8—21no—
198C2×C5×Q8—22no—
199C2×C5×Q8—22no—
200C2×C5×Q8—31no—
201C2×C5×Q8C22×D312yes—
202C2×C5×D4—32no—
203C2×C5×D4—31no—
204C22×C4×C5—21no—
205C22×C4×C5—32no—
206C22×C4×C5C22×D311yescharacteristic
207C2×C22⋊D5—21no—
208C2×C22⋊D5—62no—
209C22×Dic5—62no—
210C22×Dic5—61no—
211Q8×D5—68no—
212#711—68no—
213#711—616no—
214#709—22no—
215#709—64no—
216#709—64no—
217#709#6714yes—
218C2×D20C22×D311yescharacteristic
219C2×C4×D5—21no—
220C2×C4×D5—62no—
221C2×Dic10—34no—
222C2×Dic10—32no—
223C2×Dic10—64no—
224C2×Dic10—62no—
225C2×Dic10—61no—
226C2×Dic10—62no—
227C2×Dic10—64no—
228C2×Dic10C22×D311yescharacteristic
229C5×C4⋊C4—32no—
230C5×C4⋊C4—64no—
231C5×C22⋊C4—64no—
232C5×C22⋊C4—61no—
233C42×C5—61no—
234#689—24no—
235#689—68no—
236#688—24no—
237#681—22no—
238C2×#168—32no—
239C2×#168—62no—
240C2×#168C22×D312yes—
241C2×2−1+4—151no—
242C2×#137—51no—
243C22×Q16—151no—
244#536—31no—
245#452—154no—
246#451—154no—
247#419—151no—
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—24no—
255C2×C3×D5—22no—
256C2×C3×D5—42no—
257C3×C4×C5—42no—
258C3×C4×C5#12012yes—
259C3×C4×C5C22×D411yescharacteristic
260C3×C4×C5C22×D411yescharacteristic
261Dic15—24no—
262C3×Dic5—22no—
263C5×Dic3—22no—
264C5×Dic3—42no—
265C3×#41—54no—
266C3×#41—102no—
267C2×C3×Q8—21no—
268C2×C3×Q8—22no—
269C2×C3×Q8—22no—
270C2×C3×Q8—51no—
271C2×C3×Q8C22×D512yes—
272C2×C3×D4—51no—
273C2×C3×D4—101no—
274C22×C3×C4—21no—
275C22×C3×C4—101no—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—102no—
278C2×#67C22⋊D512yes—
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×D12C22⋊D511yescharacteristic
290C2×C4×D3—102no—
291C2×C4×D3C22×D512yes—
292C2×Dic6—54no—
293C2×Dic6—52no—
294C2×Dic6—108no—
295C2×Dic6—102no—
296C2×Dic6—101no—
297C2×Dic6—102no—
298C2×Dic6C22⋊D511yescharacteristic
299C3×Q16—104no—
300C3×SD16—104no—
301C3×M16—102no—
302C2×C3×C8—52no—
303#217—21no—
304#216—108no—
305(C2×D3)⋊C4—24no—
306C4⋊Dic3C22×D512yes—
307Dic3⋊C4—24no—
308C4×Dic3—21no—
309C2×C3⋊C8—52no—
310C2×C3⋊C8—102no—
311C23×C5—32no—
312C23×C5D3×D411yescharacteristic
313C22×D5—21no—
314C5×Q8—22no—
315C5×Q8—22no—
316C5×Q8—42no—
317C5×Q8—62no—
318C5×D4—64no—
319C5×D4—62no—
320C2×C4×C5—22no—
321C2×C4×C5—32no—
322C2×C4×C5—42no—
323C2×C4×C5—62no—
324C2×C4×C5—62no—
325C2×C4×C5—62no—
326C2×C4×C5D3×D411yescharacteristic
327C2×C4×C5D3×D412yes—
328C2×C4×C5C2×#6712yes—
329C2×C4×C5C23×D311yescharacteristic
330C22⋊D5—24no—
331C22⋊D5—68no—
332C2×Dic5—21no—
333C2×Dic5—68no—
334C2×Dic5—64no—
335C2×Dic5—62no—
336D20—21no—
337D20C2×#6712yes—
338C4×D5—24no—
339C4×D5—68no—
340Dic10—21no—
341Dic10—34no—
342Dic10—68no—
343Dic10—64no—
344Dic10—62no—
345Dic10C2×#6712yes—
346#168—22no—
347#168—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—152no—
356C22×Q8—151no—
357C22×Q8—301no—
358C22×Q8D3×D511yescharacteristic
359#137—104no—
360C2×Q16—52no—
361C2×Q16—154no—
362C2×Q16—304no—
363C2×SD16—52no—
364C2×M16—51no—
365C22×C8—151no—
366C4⋊Q8—61no—
367#124—61no—
368#123—62no—
369C22⋊Q8—34no—
370#117—31no—
371#103—154no—
372#103—152no—
373#102—152no—
374C22⋊C8—154no—
375C2×C3×C5—22no—
376C2×C3×C5C2×#12011yescharacteristic
377C2×C3×C5#57812yes—
378C3×D5—42no—
379C5×D3—42no—
380C23×C3—101no—
381C23×C3C2×C22⋊D511yescharacteristic
382C22×D3C2×C22⋊D512yes—
383C3×Q8—22no—
384C3×Q8—22no—
385C3×Q8—42no—
386C3×Q8—52no—
387C3×Q8—101no—
388C3×D4—52no—
389C3×D4—104no—
390C3×D4—101no—
391C2×C3×C4—22no—
392C2×C3×C4—42no—
393C2×C3×C4—101no—
394C2×C3×C4—104no—
395C2×C3×C4D4×D512yes—
396C2×C3×C4D4×D512yes—
397C2×C3×C4C2×C22⋊D511yescharacteristic
398C2×C3×C4C23×D511yescharacteristic
399#67—24no—
400#67—108no—
401C2×Dic3—22no—
402C2×Dic3—108no—
403C2×Dic3—102no—
404C2×Dic3—104no—
405C2×Dic3C2×C22⋊D512yes—
406D12—22no—
407C4×D3—22no—
408C4×D3—22no—
409C4×D3—108no—
410Dic6—22no—
411Dic6—54no—
412Dic6—108no—
413Dic6—102no—
414Dic6—104no—
415C3×C8—102no—
416C3⋊C8—102no—
417C22×C5—22no—
418C22×C5—64no—
419C22×C5—62no—
420C22×C5#93712yes—
421C22×C5C2×D3×D411yescharacteristic
422C2×D5—22no—
423C2×D5—42no—
424C4×C5—42no—
425C4×C5—62no—
426C4×C5—122no—
427C4×C5#93712yes—
428C4×C5C2×D3×D411yescharacteristic
429C4×C5C22×#6711yescharacteristic
430Dic5—22no—
431Dic5—64no—
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—21no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—31no—
444C2×Q8—51no—
445C2×Q8—154no—
446C2×Q8—152no—
447C2×Q8—302no—
448C2×Q8—304no—
449C2×Q8—304no—
450C2×Q8—308no—
451C2×Q8—302no—
452C2×Q8—301no—
453C2×Q8C2×D3×D512yes—
454C2×D4—32no—
455C2×D4—31no—
456C2×D4—51no—
457C2×D4—101no—
458C2×D4—302no—
459C22×C4—21no—
460C22×C4—32no—
461C22×C4—101no—
462C22×C4—302no—
463C22×C4—302no—
464C22×C4—301no—
465C22×C4C2×D3×D511yescharacteristic
466Q16—104no—
467Q16—308no—
468SD16—104no—
469M16—102no—
470C2×C8—52no—
471C2×C8—152no—
472C2×C8—302no—
473C4⋊C4—32no—
474C4⋊C4—64no—
475C22⋊C4—64no—
476C22⋊C4—61no—
477C42—61no—
478C3×C5#301111yescharacteristic, complemented, Hall
479C22×C3—22no—
480C22×C3—102no—
481C22×C3—202no—
482C22×C3#408312yes—
483C22×C3C22×C22⋊D511yescharacteristic
484C2×D3—22no—
485C2×D3—24no—
486C3×C4—42no—
487C3×C4—102no—
488C3×C4#408312yes—
489C3×C4C2×D4×D511yescharacteristic
490C3×C4C2×D4×D511yescharacteristic
491Dic3—22no—
492Dic3—42no—
493Dic3—104no—
494C2×C5—22no—
495C2×C5—122no—
496C2×C5#577912yes—
497C2×C5C2×#93711yescharacteristic
498D5—42no—
499C23—32no—
500C23—101no—
501C23D3×C22⋊D511yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—42no—
505Q8—52no—
506Q8—62no—
507Q8—101no—
508Q8—154no—
509Q8—308no—
510Q8—302no—
511Q8—304no—
512D4—52no—
513D4—64no—
514D4—62no—
515D4—104no—
516D4—101no—
517D4—308no—
518C2×C4—22no—
519C2×C4—32no—
520C2×C4—42no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—101no—
525C2×C4—104no—
526C2×C4—308no—
527C2×C4—308no—
528C2×C4—302no—
529C2×C4—304no—
530C2×C4D5×#6712yes—
531C2×C4D3×C22⋊D511yescharacteristic
532C2×C4#679012yes—
533C2×C4C22×D3×D511yescharacteristic
534C8—102no—
535C8—302no—
536C2×C3—22no—
537C2×C3—202no—
538C2×C3C2×#408311yescharacteristic
539C2×C3#6617212yes—
540D3—42no—
541C5#8398311yescharacteristic, complemented, Sylow
542C22—22no—
543C22—64no—
544C22—62no—
545C22—102no—
546C22—202no—
547C22#9157712yes—
548C22C2×D3×C22⋊D511yescharacteristic
549C4—42no—
550C4—62no—
551C4—102no—
552C4—122no—
553C4—304no—
554C4#9157712yes—
555C4C2×D5×#6711yescharacteristic
556C4C2×#679011yescharacteristic
557C3#1061514211yescharacteristic, complemented, Sylow
558C2—22no—
559C2—122no—
560C2—202no—
561C2#1175511412yes—
562C2C2×#9157711yescharacteristic
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×#92001C2
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. C5×#5816C2semidirect
4. C2×C3×#4088C2semidirect
5. #11749403C2semidirect
6. #11749401C2semidirect
7. #11748417C2semidirect
8. #11748364C2semidirect
9. #11748347C2semidirect
42. C2×#4088D3semidirect
96. #5816D5semidirect
478. C3×C5#3011semidirect
541. C5#83983semidirect
557. C3#10615142semidirect

Maximal subgroups

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

subgroupindex
C2×#920012
C22×#67182
C5×#58162
C2×C3×#40882
#117494032
#117494012
#117484172
#117483642
#117483472
#106151423
#839835