Finite Group Databasebeta

← #14439687

Subgroups — #14439687

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
1C2×#91831C211yesmaximal, characteristic, complemented
2C22×C5×#216C211yesmaximal, characteristic, complemented
3C3×#66150C211yesmaximal, characteristic, complemented
4#11754270C211yesmaximal, characteristic, complemented
5C2×#91311C211yesmaximal, characteristic
6C2×#91307C211yesmaximal, characteristic, complemented
7#11749353C212yesmaximal, complemented
8#11749347C212yesmaximal, complemented
9#11749316C212yesmaximal, complemented
10#11749315C212yesmaximal, complemented
11#11748318C211yesmaximal, characteristic, complemented
12#10615612—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17C2×#6718C2212yes—
18#91831—24no—
19C2×#6717C2212yes—
20C2×#6710C2211yescharacteristic
21C2×C5×#216—24no—
22C2×C5×#216C2212yes—
23C2×C5×#216C2212yes—
24C22×C5×C3⋊C8C2211yescharacteristic
25C3×#4093C2212yes—
26C3×#4092—22no—
27C3×#4090C2212yes—
28C3×#4075—22no—
29C3×#4072C2211yescharacteristic
30#91542—22no—
31#91383—22no—
32#91376C2212yes—
33#91375C2212yes—
34C2×#6662C2211yescharacteristic
35C2×#6661C2212yes—
36C2×#6658C2211yescharacteristic
37#91311—24no—
38C2×#6657C2211yescharacteristic
39#91307—24no—
40C2×#6655C2212yes—
41C2×#6653C2211yescharacteristic
42#90952C2212yes—
43Dic5×C3⋊C8C2212yes—
44#83403—51nomaximal, Hall
45C22×C5×Q16—31no—
46#66150—31no—
47#66150D311yescharacteristic, complemented
48C2×#4088—31no—
49C2×#4088—31no—
50C2×#4050—31no—
51#65480—32no—
52#65479—32no—
53#65479—32no—
54#65470—32no—
55#65390—31no—
56C2×C3×C5×Q8—21no—
57C2×C3×C5×Q8—22no—
58C2×C3×C5×Q8—22no—
59C2×C3×C5×Q8C2312yes—
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2311yescharacteristic
62C2×#1220—21no—
63#6817—22no—
64#6817—22no—
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C2×Dic30C2311yescharacteristic
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#6718—24no—
80#6717—24no—
81#6710D414yes—
82C2×C3⋊#168C2312yes—
83C5×#216—24no—
84C5×#216—24no—
85C2×C5×C3⋊C8D414yes—
86C2×C5×C3⋊C8C2311yescharacteristic
87C2×C5×C3⋊C8C2311yescharacteristic
88C3×C22⋊Dic5D412yes—
89C3×#685—24no—
90C3×C4⋊Dic5D412yes—
91C3×#683—24no—
92C3×C4×Dic5C2312yes—
93#6668—24no—
94#6667—24no—
95#6662—22no—
96#6661—24no—
97#6658—22no—
98#6657—22no—
99#6655—24no—
100#6653—22no—
101C3×#536—51no—
102C2×#951—51no—
103C2×#950—51no—
104C22×#216D511yescharacteristic, complemented
105C2×#942—51no—
106#5526—51no—
107#5092—52no—
108#5086—52no—
109#5060—52no—
110#5059—52no—
111#4997—51no—
112C22×C5×Q8—31no—
113C22×C5×Q8C2×D311yescharacteristic
114C2×#709—31no—
115C2×#709C2×D311yescharacteristic
116C2×C5×Q16—32no—
117C2×C5×Q16—32no—
118C2×C5×Q16—64no—
119C22×C5×C8—31no—
120#4093—32no—
121#4093C2×D312yes—
122#4092—22no—
123#4092—62no—
124#4090—32no—
125#4090C2×D312yes—
126C2×#689—32no—
127C2×#689—32no—
128#4088—64no—
129#4088—64no—
130C2×#688—32no—
131C2×#688—32no—
132#4075—22no—
133#4075—62no—
134#4072C2×D311yescharacteristic
135C2×#681—31no—
136C2×Dic20—31no—
137#4050—64no—
138C2×D40—31no—
139C2×#677—31no—
140C2×#677—31no—
141#3947—32no—
142C8×Dic5—32no—
143#3156—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C22×C3×D5—21no—
147C3×C5×Q8—22no—
148C3×C5×Q8—22no—
149C3×C5×Q8—42no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—42no—
152C2×C3×C4×C5C2×D411yescharacteristic
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2×D412yes—
155C2×C3×C4×C5C2411yescharacteristic
156#1220—42no—
157C2×Dic15—21no—
158D60—21no—
159D60—21no—
160C4×D15—42no—
161Dic30—21no—
162Dic30—21no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—42no—
165C5×Dic6—22no—
166C5×Dic6—22no—
167C5×Dic6—42no—
168C3×C22⋊D5—42no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5C2×D414yes—
171C3×D20—21no—
172C3×D20—21no—
173C3×C4×D5—42no—
174C3×Dic10—21no—
175C3×Dic10—21no—
176C3⋊#168C2×D414yes—
177C5×C3⋊C8C2×D412yes—
178C5×C3⋊C8C2×D412yes—
179C2×C3×#41—51no—
180C22×C3×Q8C2×D511yescharacteristic
181C2×#235—51no—
182C22×Dic6C2×D511yescharacteristic
183C3×C4⋊Q8—52no—
184C3×#124—52no—
185C3×#123—102no—
186C3×C22⋊Q8—102no—
187C3×#117—51no—
188#951—104no—
189#950—104no—
190C2×#216—24no—
191C2×#216—52no—
192C2×#216—52no—
193C2×#216—51no—
194C2×#216C2×D512yes—
195C2×#216C2×D512yes—
196#942—104no—
197C2×#215—52no—
198C2×#215—51no—
199C2×#214—52no—
200C2×#214—51no—
201C2×#213—51no—
202C2×#208—51no—
203C22×C3⋊C8C2×D511yescharacteristic
204#897—102no—
205#886—102no—
206#875—52no—
207#869—52no—
208#803—52no—
209C4×C3⋊C8—52no—
210C2×C5×Q8—21no—
211C2×C5×Q8—22no—
212C2×C5×Q8—22no—
213C2×C5×Q8—32no—
214C2×C5×Q8—61no—
215C2×C5×Q8—62no—
216C2×C5×Q8—62no—
217C2×C5×Q8C22×D312yes—
218C22×C4×C5—21no—
219C22×C4×C5—61no—
220C22×C4×C5C22×D311yescharacteristic
221C2×C22⋊D5—21no—
222C2×C22⋊D5—61no—
223#709—22no—
224#709—22no—
225#709—62no—
226#709—62no—
227C2×D20—31no—
228C2×D20C22×D311yescharacteristic
229C2×C4×D5—21no—
230C2×C4×D5—61no—
231C2×Dic10—31no—
232C2×Dic10C22×D311yescharacteristic
233C5×Q16—64no—
234C5×Q16—64no—
235C2×C5×C8—34no—
236C2×C5×C8—31no—
237C2×C5×C8—31no—
238C22⋊Dic5#6712yes—
239#689—64no—
240#689—64no—
241#688—64no—
242#688—64no—
243#685—24no—
244#685—64no—
245C4⋊Dic5#6712yes—
246#683—24no—
247#683—64no—
248C4×Dic5C22×D312yes—
249#681—34no—
250C2×#168—32no—
251Dic20—62no—
252D40—62no—
253#677—62no—
254#677—62no—
255C2×#137—151no—
256C2×#137—151no—
257C2×#135—151no—
258C22×Q16—31no—
259#536—51no—
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#12712yes—
268C22×C3×C5C22×D411yescharacteristic
269C2×D15—41no—
270C2×D15—42no—
271C2×C3×D5—41no—
272C2×C3×D5—42no—
273C3×C4×C5—42no—
274C3×C4×C5#12712yes—
275C3×C4×C5C22×D411yescharacteristic
276C3×C4×C5C22×D411yescharacteristic
277Dic15—41no—
278C3×Dic5—24no—
279C3×Dic5—41no—
280C5×Dic3—42no—
281C3×#41—102no—
282C3×#41—102no—
283C2×C3×Q8—21no—
284C2×C3×Q8—22no—
285C2×C3×Q8—22no—
286C2×C3×Q8—51no—
287C2×C3×Q8C22×D512yes—
288C2×C3×D4—51no—
289C2×C3×D4—101no—
290C22×C3×C4—21no—
291C22×C3×C4—101no—
292C22×C3×C4C22×D511yescharacteristic
293C2×#67—101no—
294C22×Dic3—21no—
295#235—102no—
296#235—102no—
297C2×D12—51no—
298C2×C4×D3—101no—
299C2×Dic6—22no—
300C2×Dic6—22no—
301C2×Dic6—21no—
302C2×Dic6—51no—
303C2×Dic6C22×D512yes—
304C3×C4⋊C4—52no—
305C3×C4⋊C4—104no—
306C3×C22⋊C4—52no—
307C3×C22⋊C4—104no—
308C3×C42—52no—
309#216—24no—
310#216—24no—
311#216—104no—
312#216—104no—
313#216—102no—
314#215—104no—
315#215—102no—
316#214—104no—
317#214—102no—
318#213—102no—
319(C2×D3)⋊C4—104no—
320C4⋊Dic3—104no—
321#208—54no—
322C2×C3⋊C8—52no—
323C2×C3⋊C8C22⋊D514yes—
324C2×C3⋊C8C22×D511yescharacteristic
325C2×C3⋊C8C22×D511yescharacteristic
326C23×C5C2×#6711yescharacteristic
327C22×D5—21no—
328C22×D5—61no—
329C5×Q8—22no—
330C5×Q8—22no—
331C5×Q8—42no—
332C5×Q8—62no—
333C5×Q8—62no—
334C5×Q8—122no—
335C2×C4×C5—22no—
336C2×C4×C5—42no—
337C2×C4×C5—62no—
338C2×C4×C5—122no—
339C2×C4×C5D3×D412yes—
340C2×C4×C5D3×D412yes—
341C2×C4×C5C2×#6711yescharacteristic
342C2×C4×C5C23×D311yescharacteristic
343C22⋊D5—42no—
344C22⋊D5—122no—
345C2×Dic5—21no—
346C2×Dic5—61no—
347C2×Dic5C2×#6714yes—
348D20—21no—
349D20—21no—
350D20—61no—
351D20—61no—
352C4×D5—42no—
353C4×D5—122no—
354Dic10—21no—
355Dic10—21no—
356Dic10—61no—
357Dic10—61no—
358C5×C8—32no—
359C5×C8—32no—
360#168—34no—
361C2×#41—51no—
362C2×#41—151no—
363C22×Q8—31no—
364C22×Q8D3×D511yescharacteristic
365#137—304no—
366#137—304no—
367#135—304no—
368C2×Q16—32no—
369C2×Q16—32no—
370C2×Q16—64no—
371C2×Q16—151no—
372C2×Q16—152no—
373C2×Q16—152no—
374C2×SD16—151no—
375C2×SD16—151no—
376C2×SD16—152no—
377C2×SD16—152no—
378C2×D8—151no—
379C2×M16—151no—
380C22×C8—31no—
381C4⋊Q8—52no—
382C4⋊Q8—152no—
383#124—52no—
384#124—152no—
385#123—102no—
386#123—302no—
387C22⋊Q8—102no—
388C22⋊Q8—302no—
389#117—51no—
390#97—152no—
391C4×C8—152no—
392C2×C3×C5—22no—
393C2×C3×C5C2×#12711yescharacteristic
394C2×C3×C5#57812yes—
395D15—81no—
396C3×D5—81no—
397C23×C3—101no—
398C23×C3D4×D511yescharacteristic
399C22×D3—101no—
400C3×Q8—22no—
401C3×Q8—22no—
402C3×Q8—42no—
403C3×Q8—101no—
404C3×Q8—101no—
405C3×D4—101no—
406C3×D4—101no—
407C3×D4—202no—
408C2×C3×C4—22no—
409C2×C3×C4—42no—
410C2×C3×C4—54no—
411C2×C3×C4—101no—
412C2×C3×C4—202no—
413C2×C3×C4D4×D511yescharacteristic
414C2×C3×C4D4×D512yes—
415C2×C3×C4C2×C22⋊D512yes—
416C2×C3×C4C23×D511yescharacteristic
417#67—202no—
418C2×Dic3—22no—
419C2×Dic3—42no—
420C2×Dic3—101no—
421D12—101no—
422D12—101no—
423C4×D3—202no—
424Dic6—22no—
425Dic6—22no—
426Dic6—42no—
427Dic6—101no—
428Dic6—101no—
429C3⋊C8—54no—
430C3⋊C8C2×C22⋊D512yes—
431C3⋊C8C2×C22⋊D512yes—
432C22×C5—22no—
433C22×C5#94012yes—
434C22×C5C22×#6711yescharacteristic
435C2×D5—41no—
436C2×D5—42no—
437C2×D5—121no—
438C2×D5—122no—
439C4×C5—42no—
440C4×C5—122no—
441C4×C5#94012yes—
442C4×C5C2×D3×D411yescharacteristic
443C4×C5C2×D3×D411yescharacteristic
444Dic5—24no—
445Dic5—41no—
446Dic5—121no—
447#41—102no—
448#41—102no—
449#41—302no—
450#41—302no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—32no—
455C2×Q8—51no—
456C2×Q8—61no—
457C2×Q8—62no—
458C2×Q8—62no—
459C2×Q8—151no—
460C2×Q8C2×D3×D512yes—
461C2×D4—51no—
462C2×D4—101no—
463C2×D4—151no—
464C2×D4—301no—
465C22×C4—21no—
466C22×C4—61no—
467C22×C4—101no—
468C22×C4—301no—
469C22×C4C2×D3×D511yescharacteristic
470Q16—64no—
471Q16—64no—
472Q16—302no—
473Q16—304no—
474Q16—304no—
475SD16—302no—
476SD16—302no—
477SD16—304no—
478SD16—304no—
479D8—302no—
480M16—154no—
481C2×C8—34no—
482C2×C8—31no—
483C2×C8—31no—
484C2×C8—152no—
485C4⋊C4—52no—
486C4⋊C4—104no—
487C4⋊C4—304no—
488C22⋊C4—52no—
489C22⋊C4—104no—
490C22⋊C4—304no—
491C42—52no—
492C3×C5#315611yescharacteristic, complemented, Hall
493C22×C3—22no—
494C22×C3—202no—
495C22×C3—201no—
496C22×C3#408612yes—
497C22×C3C2×D4×D511yescharacteristic
498C2×D3—202no—
499C2×D3—201no—
500C3×C4—42no—
501C3×C4—104no—
502C3×C4—201no—
503C3×C4#408612yes—
504C3×C4C2×D4×D511yescharacteristic
505C3×C4C22×C22⋊D511yescharacteristic
506Dic3—42no—
507Dic3—201no—
508C2×C5—22no—
509C2×C5C2×#94011yescharacteristic
510C2×C5#583812yes—
511D5—81no—
512D5—241no—
513C23—101no—
514C23—301no—
515C23D5×#6711yescharacteristic
516Q8—22no—
517Q8—22no—
518Q8—42no—
519Q8—62no—
520Q8—62no—
521Q8—101no—
522Q8—101no—
523Q8—122no—
524Q8—301no—
525Q8—301no—
526D4—101no—
527D4—101no—
528D4—202no—
529D4—301no—
530D4—301no—
531D4—602no—
532C2×C4—22no—
533C2×C4—42no—
534C2×C4—54no—
535C2×C4—62no—
536C2×C4—101no—
537C2×C4—122no—
538C2×C4—202no—
539C2×C4—301no—
540C2×C4—602no—
541C2×C4D5×#6711yescharacteristic
542C2×C4D3×C22⋊D512yes—
543C2×C4#679012yes—
544C2×C4C22×D3×D511yescharacteristic
545C8—32no—
546C8—32no—
547C8—154no—
548C2×C3—22no—
549C2×C3—401no—
550C2×C3#6610012yes—
551C2×C3C2×#408611yescharacteristic
552D3—401no—
553C5#8340311yescharacteristic, complemented, Sylow
554C22—22no—
555C22—202no—
556C22—201no—
557C22—602no—
558C22—601no—
559C22#9156712yes—
560C22C2×D5×#6711yescharacteristic
561C4—42no—
562C4—104no—
563C4—122no—
564C4—201no—
565C4—601no—
566C4#9156712yes—
567C4C2×D3×C22⋊D511yescharacteristic
568C4C2×#679011yescharacteristic
569C3#1061561211yescharacteristic, complemented, Sylow
570C2—22no—
571C2—401no—
572C2—1201no—
573C2#1175510112yes—
574C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91311C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5#3156
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
1. C2×#91831C2semidirect
2. C22×C5×#216C2semidirect
3. C3×#66150C2semidirect
4. #11754270C2semidirect
6. C2×#91307C2semidirect
7. #11749353C2semidirect
8. #11749347C2semidirect
9. #11749316C2semidirect
10. #11749315C2semidirect
11. #11748318C2semidirect
47. #66150D3semidirect
104. C22×#216D5semidirect
492. C3×C5#3156semidirect
553. C5#83403semidirect
569. C3#10615612semidirect

Maximal subgroups

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

subgroupindex
C2×#918312
C22×C5×#2162
C3×#661502
#117542702
C2×#913112
C2×#913072
#117493532
#117493472
#117493162
#117493152
#117483182
#106156123
#834035