Finite Group Databasebeta

← #14424611

Subgroups — #14424611

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
2C3×#65860C211yesmaximal, characteristic, complemented
3C22×#6662C211yesmaximal, characteristic, complemented
4C2×#91309C211yesmaximal, characteristic, complemented
5#11751105C211yesmaximal, characteristic, complemented
6C5×#5002C211yesmaximal, characteristic, complemented
7#11748342C211yesmaximal, characteristic, complemented
8#11747511C214yesmaximal, complemented
9#11747492C214yesmaximal, complemented
10#10610568—31nomaximal, Hall
11C22×Dic30C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C2×C3×#709C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C2×#6780—22no—
16C2×#6772C2212yes—
17C2×D3×Dic10—21no—
18#92001—24no—
19#92001—24no—
20C2×#6765—21no—
21C2×D5×Dic6C2212yes—
22C3×C5×#117C2211yescharacteristic
23C2×#6710C2211yescharacteristic
24C22×C5×C3⋊C8C2211yescharacteristic
25C3×#4043C2214yes—
26C3×#4032—22no—
27C3×#4021—21no—
28C3×#4015—21no—
29C2×#6662—24no—
30C2×#6662C2214yes—
31C2×#6661C2212yes—
32#91309—24no—
33C2×#6656C2212yes—
34#91094C2214yes—
35C5×#810C2212yes—
36C5×#809C2212yes—
37#90955C2214yes—
38#83411—51nomaximal, Hall
39C2×#4150—31no—
40C2×#4097—31no—
41C22×Dic20—31no—
42#65860D311yescharacteristic, complemented
43C5×#416—31no—
44#65399—31no—
45#65293—31no—
46#65097—34no—
47#65072—34no—
48C22×C3×C4×C5C2311yescharacteristic
49C22×Dic15—21no—
50C2×Dic30—21no—
51C2×Dic30—22no—
52C2×Dic30D414yes—
53C2×Dic30C2312yes—
54C2×C5×#67—21no—
55C5×#235—22no—
56C5×#235D414yes—
57C2×C5×D12C2311yescharacteristic
58C2×C4×C5×D3—21no—
59C2×C5×Dic6C2311yescharacteristic
60C2×C3×C22⋊D5D412yes—
61C22×C3×Dic5—21no—
62C3×#709—22no—
63C3×#709—22no—
64C2×C3×D20D411yescharacteristic
65C2×C3×C4×D5C2312yes—
66C2×C3×Dic10—22no—
67C2×C3×Dic10—22no—
68C2×C3×Dic10—21no—
69C2×C3×Dic10D411yescharacteristic
70C2×C3×Dic10C2312yes—
71C2×#1204—22no—
72C2×#1201—22no—
73C2×D3×Dic5—22no—
74#6780—216no—
75C2×D5×Dic3—22no—
76#6772—24no—
77#6772—24no—
78D3×Dic10—28no—
79#6765—28no—
80D5×Dic6—24no—
81D5×Dic6—24no—
82C3×C5×C4⋊C4C2312yes—
83C3×C5×C22⋊C4—21no—
84C3×C42×C5—21no—
85#6710—22no—
86C2×C3⋊#168C2312yes—
87C2×C5×C3⋊C8—22no—
88C2×C5×C3⋊C8C2312yes—
89C3×#685—24no—
90C3×C4⋊Dic5—24no—
91#6662—28no—
92#6661—24no—
93#6656—24no—
94C2×#1010—51no—
95C3×#536—51no—
96C22×#216—51no—
97C2×#942—51no—
98#5234—51no—
99#5050—54no—
100#5047—54no—
101#5004—51no—
102#5002D511yescharacteristic, complemented
103C2×C5×#41—31no—
104#4150—64no—
105#4150—64no—
106C2×Q8×D5—32no—
107C2×#711—32no—
108C2×#711—62no—
109C2×#709—61no—
110C2×#709C2×D311yescharacteristic
111C22×Dic10—31no—
112C22×Dic10—61no—
113C22×Dic10C2×D311yescharacteristic
114C22×C5×C8—31no—
115C5×#117C2×D311yescharacteristic
116#4097—64no—
117C2×#689—32no—
118C2×#687—32no—
119C2×#681—31no—
120C2×Dic20—34no—
121C2×Dic20—64no—
122#4043C2×D314yes—
123#4032—22no—
124#4021—21no—
125#4015—21no—
126C5×#103—32no—
127C5×#102—32no—
128#3952—34no—
129#3942—34no—
130#3011—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×C5×D3—21no—
133C22×C3×D5C2×D412yes—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D412yes—
137C2×C3×C4×C5C2×D412yes—
138C2×C3×C4×C5C2411yescharacteristic
139C2×Dic15—24no—
140C2×Dic15—22no—
141Dic30—24no—
142Dic30—22no—
143Dic30C2×D414yes—
144C5×#67—24no—
145C2×C5×Dic3—21no—
146C5×D12—21no—
147C5×D12C2×D412yes—
148C4×C5×D3—24no—
149C5×Dic6—21no—
150C5×Dic6C2×D412yes—
151C3×C22⋊D5—24no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—42no—
154C2×C3×Dic5C2×D412yes—
155C3×D20—22no—
156C3×C4×D5—22no—
157C3×C4×D5—22no—
158C3×Dic10—22no—
159C3×Dic10—22no—
160C3×Dic10—22no—
161C3×Dic10—42no—
162#1204—28no—
163#1201—28no—
164D3×Dic5—28no—
165D5×Dic3—28no—
166C3⋊#168—22no—
167C5×C3⋊C8—22no—
168C2×C3×#41—51no—
169C22×C3×Q8—51no—
170#1010—104no—
171#1010—104no—
172C2×D3×Q8—101no—
173C2×#237—101no—
174C2×#237—102no—
175C2×#235—52no—
176C2×#235C2×D511yescharacteristic
177C22×Dic6—51no—
178C22×Dic6—52no—
179C3×C4⋊Q8—101no—
180C3×#124—101no—
181C3×#123—102no—
182C3×C22⋊Q8—54no—
183C3×#117C2×D511yescharacteristic
184C2×#216—52no—
185C2×#216—54no—
186C2×#216—104no—
187#942—104no—
188C2×#215—52no—
189C2×#208—51no—
190C22×C3⋊C8C2×D511yescharacteristic
191#830—54no—
192#810—54no—
193#810C2×D512yes—
194#809C2×D512yes—
195C5×#41—34no—
196C5×#41—62no—
197C2×C5×Q8—31no—
198C2×C5×D4—31no—
199C2×C5×D4—61no—
200C22×C4×C5—61no—
201C22×C4×C5C22×D311yescharacteristic
202C2×C22⋊D5—62no—
203C2×C22⋊D5#6712yes—
204C22×Dic5—21no—
205C22×Dic5—61no—
206C22×Dic5—62no—
207Q8×D5—64no—
208Q8×D5—64no—
209#711—64no—
210#711—64no—
211#711—616no—
212#709—22no—
213#709—22no—
214#709—68no—
215C2×D20#6711yescharacteristic
216C2×C4×D5—62no—
217C2×C4×D5C22×D312yes—
218C2×Dic10—22no—
219C2×Dic10—22no—
220C2×Dic10—21no—
221C2×Dic10—34no—
222C2×Dic10—32no—
223C2×Dic10—68no—
224C2×Dic10—62no—
225C2×Dic10—61no—
226C2×Dic10—62no—
227C2×Dic10#6711yescharacteristic
228C2×Dic10C22×D312yes—
229C2×C5×C8—32no—
230C2×C5×C8—62no—
231C5×C4⋊C4C22×D312yes—
232C5×C22⋊C4—21no—
233C42×C5—21no—
234#689—64no—
235#687—64no—
236#685—24no—
237C4⋊Dic5—24no—
238#681—62no—
239C2×#168—32no—
240Dic20—68no—
241C2×2−1+4—151no—
242C2×#137—151no—
243C22×Q16—151no—
244#536—51no—
245#452—154no—
246#451—154no—
247#419—151no—
248#416—31no—
249#408—151no—
250C22×C3×C5—22no—
251C22×C3×C5#12012yes—
252C22×C3×C5C22×D411yescharacteristic
253C2×C5×D3—22no—
254C2×C5×D3—42no—
255C2×C3×D5—22no—
256C2×C3×D5—24no—
257C3×C4×C5—42no—
258C3×C4×C5#12012yes—
259C3×C4×C5C22×D411yescharacteristic
260C3×C4×C5C22×D411yescharacteristic
261Dic15—24no—
262C3×Dic5—22no—
263C3×Dic5—42no—
264C5×Dic3—22no—
265C3×#41—102no—
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—52no—
273C2×C3×D4—51no—
274C22×C3×C4—52no—
275C22×C3×C4—101no—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—21no—
278C2×#67—102no—
279C22×Dic3—102no—
280C22×Dic3—101no—
281D3×Q8—108no—
282#237—108no—
283#237—1016no—
284#235—22no—
285#235—104no—
286#235—104no—
287#235D2014yes—
288C2×D12C22×D511yescharacteristic
289C2×C4×D3—21no—
290C2×C4×D3—102no—
291C2×Dic6—54no—
292C2×Dic6—52no—
293C2×Dic6—104no—
294C2×Dic6—102no—
295C2×Dic6—102no—
296C2×Dic6—101no—
297C2×Dic6—104no—
298C2×Dic6C22×D511yescharacteristic
299C3×C4⋊C4—104no—
300C3×C4⋊C4C22×D512yes—
301C3×C22⋊C4—21no—
302C3×C22⋊C4—104no—
303C3×C42—21no—
304#216—108no—
305#216—104no—
306#215—104no—
307#208—102no—
308C2×C3⋊C8—22no—
309C2×C3⋊C8—52no—
310C2×C3⋊C8C22×D512yes—
311C23×C5—61no—
312C23×C5C2×#6711yescharacteristic
313C22×D5C2×#6712yes—
314C5×Q8—32no—
315C5×Q8—61no—
316C5×D4—32no—
317C5×D4—64no—
318C5×D4—61no—
319C2×C4×C5—22no—
320C2×C4×C5—61no—
321C2×C4×C5—64no—
322C2×C4×C5D3×D412yes—
323C2×C4×C5D3×D412yes—
324C2×C4×C5C2×#6711yescharacteristic
325C2×C4×C5C23×D311yescharacteristic
326C22⋊D5—24no—
327C22⋊D5—68no—
328C2×Dic5—22no—
329C2×Dic5—42no—
330C2×Dic5—68no—
331C2×Dic5—64no—
332C2×Dic5—62no—
333C2×Dic5C2×#6712yes—
334D20—22no—
335C4×D5—22no—
336C4×D5—22no—
337C4×D5—68no—
338Dic10—22no—
339Dic10—22no—
340Dic10—22no—
341Dic10—34no—
342Dic10—42no—
343Dic10—68no—
344Dic10—64no—
345Dic10—62no—
346C5×C8—62no—
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—51no—
356C22×Q8—152no—
357C22×Q8—151no—
358C22×Q8—301no—
359#137—304no—
360C2×Q16—154no—
361C2×Q16—152no—
362C2×Q16—304no—
363C2×SD16—152no—
364C2×M16—151no—
365C22×C8—31no—
366C4⋊Q8—101no—
367#124—101no—
368#123—102no—
369C22⋊Q8—54no—
370#117D3×D511yescharacteristic
371#103—32no—
372#103—154no—
373#102—32no—
374C22⋊C8—154no—
375C2×C3×C5—22no—
376C2×C3×C5C2×#12011yescharacteristic
377C2×C3×C5#57812yes—
378C3×D5—42no—
379C5×D3—42no—
380C23×C3—52no—
381C23×C3D4×D511yescharacteristic
382C22×D3—21no—
383C3×Q8—102no—
384C3×Q8—102no—
385C3×Q8—102no—
386C3×Q8—202no—
387C3×D4—104no—
388C3×D4—102no—
389C2×C3×C4—22no—
390C2×C3×C4—52no—
391C2×C3×C4—102no—
392C2×C3×C4—102no—
393C2×C3×C4—102no—
394C2×C3×C4—202no—
395C2×C3×C4C2×D2012yes—
396C2×C3×C4D4×D512yes—
397C2×C3×C4D4×D511yescharacteristic
398C2×C3×C4C23×D511yescharacteristic
399#67—24no—
400#67—108no—
401C2×Dic3—21no—
402C2×Dic3—108no—
403C2×Dic3—102no—
404C2×Dic3—104no—
405D12—21no—
406D12C2×D2012yes—
407C4×D3—24no—
408C4×D3—108no—
409Dic6—21no—
410Dic6—54no—
411Dic6—108no—
412Dic6—102no—
413Dic6—104no—
414Dic6C2×D2012yes—
415C3⋊C8—22no—
416C3⋊C8—102no—
417C22×C5—22no—
418C22×C5—62no—
419C22×C5—122no—
420C22×C5#93712yes—
421C22×C5C22×#6711yescharacteristic
422C2×D5—22no—
423C2×D5—24no—
424C4×C5—42no—
425C4×C5—62no—
426C4×C5#93712yes—
427C4×C5C2×D3×D411yescharacteristic
428C4×C5C2×D3×D411yescharacteristic
429Dic5—22no—
430Dic5—42no—
431Dic5—64no—
432#41—34no—
433#41—62no—
434#41—102no—
435#41—102no—
436#41—308no—
437#41—304no—
438#41—304no—
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—308no—
450C2×Q8—304no—
451C2×Q8—304no—
452C2×Q8—302no—
453C2×Q8—301no—
454C2×D4—31no—
455C2×D4—52no—
456C2×D4—51no—
457C2×D4—61no—
458C2×D4—302no—
459C22×C4—52no—
460C22×C4—61no—
461C22×C4—101no—
462C22×C4—302no—
463C22×C4—302no—
464C22×C4—301no—
465C22×C4C2×D3×D511yescharacteristic
466Q16—308no—
467Q16—304no—
468SD16—304no—
469M16—302no—
470C2×C8—32no—
471C2×C8—62no—
472C2×C8—152no—
473C4⋊C4—104no—
474C4⋊C4C2×D3×D512yes—
475C22⋊C4—21no—
476C22⋊C4—104no—
477C42—21no—
478C3×C5#301111yescharacteristic, complemented, Hall
479C22×C3—22no—
480C22×C3—102no—
481C22×C3—104no—
482C22×C3#402812yes—
483C22×C3C2×D4×D511yescharacteristic
484C2×D3—22no—
485C2×D3—42no—
486C3×C4—42no—
487C3×C4—102no—
488C3×C4—202no—
489C3×C4#402812yes—
490C3×C4C22×D2011yescharacteristic
491C3×C4C2×D4×D511yescharacteristic
492Dic3—22no—
493Dic3—104no—
494C2×C5—22no—
495C2×C5—122no—
496C2×C5C2×#93711yescharacteristic
497C2×C5#583812yes—
498D5—42no—
499C23—52no—
500C23—61no—
501C23D5×#6711yescharacteristic
502Q8—32no—
503Q8—61no—
504Q8—102no—
505Q8—102no—
506Q8—102no—
507Q8—154no—
508Q8—202no—
509Q8—308no—
510Q8—304no—
511Q8—302no—
512D4—32no—
513D4—64no—
514D4—61no—
515D4—104no—
516D4—102no—
517D4—308no—
518C2×C4—22no—
519C2×C4—52no—
520C2×C4—61no—
521C2×C4—64no—
522C2×C4—102no—
523C2×C4—102no—
524C2×C4—102no—
525C2×C4—202no—
526C2×C4—308no—
527C2×C4—308no—
528C2×C4—304no—
529C2×C4—302no—
530C2×C4D3×D2012yes—
531C2×C4#677712yes—
532C2×C4D5×#6711yescharacteristic
533C2×C4C22×D3×D511yescharacteristic
534C8—62no—
535C8—302no—
536C2×C3—22no—
537C2×C3—202no—
538C2×C3C2×#402811yescharacteristic
539C2×C3#6610512yes—
540D3—42no—
541C5#8341111yescharacteristic, complemented, Sylow
542C22—22no—
543C22—62no—
544C22—104no—
545C22—102no—
546C22—122no—
547C22#9147412yes—
548C22C2×D5×#6711yescharacteristic
549C4—42no—
550C4—62no—
551C4—102no—
552C4—202no—
553C4—304no—
554C4#9147412yes—
555C4C2×D3×D2011yescharacteristic
556C4C2×#677711yescharacteristic
557C3#1061056811yescharacteristic, complemented, Sylow
558C2—22no—
559C2—122no—
560C2—202no—
561C2C2×#9147411yescharacteristic
562C2#1175533812yes—
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#92001C2
hypercenter#117D3×D5
hypocenterC3×C5#3011
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#65860C2semidirect
3. C22×#6662C2semidirect
4. C2×#91309C2semidirect
5. #11751105C2semidirect
6. C5×#5002C2semidirect
7. #11748342C2semidirect
8. #11747511C2semidirect
9. #11747492C2semidirect
42. #65860D3semidirect
102. #5002D5semidirect
478. C3×C5#3011semidirect
541. C5#83411semidirect
557. C3#10610568semidirect

Maximal subgroups

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

subgroupindex
C2×#920012
C3×#658602
C22×#66622
C2×#913092
#117511052
C5×#50022
#117483422
#117475112
#117474922
#106105683
#834115