Finite Group Databasebeta

← #14439707

Subgroups — #14439707

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×#91839C211yesmaximal, characteristic
2C2×C5×#951C211yesmaximal, characteristic, complemented
3C3×#66159C211yesmaximal, characteristic, complemented
4#11754270C211yesmaximal, characteristic, complemented
5C22×#6661C211yesmaximal, characteristic, complemented
6C2×#91315C211yesmaximal, characteristic, complemented
7#11749347C212yesmaximal, complemented
8#11749315C212yesmaximal, complemented
9#11749107C212yesmaximal, complemented
10#11749070C212yesmaximal, complemented
11#11748320C211yesmaximal, characteristic, complemented
12#10615706—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17#91839—24no—
18C2×#6718C2211yescharacteristic
19C2×#6717C2211yescharacteristic
20C2×#6716C2211yescharacteristic
21C2×#6715C2211yescharacteristic
22C22×C3⋊#168C2211yescharacteristic
23C5×#951—24no—
24C2×C5×#216C2212yes—
25C2×C5×#214C2212yes—
26C2×C5×#208C2211yescharacteristic
27C3×#4090C2212yes—
28C3×#4082C2212yes—
29C3×#4081—22no—
30C3×#4072C2211yescharacteristic
31C3×#4070—22no—
32#91542—22no—
33#91383—22no—
34#91376C2212yes—
35#91375C2212yes—
36C2×#6662C2212yes—
37C2×#6661—24no—
38C2×#6661C2212yes—
39C2×#6661C2212yes—
40#91315—24no—
41C2×#6658C2212yes—
42#90952C2212yes—
43Dic5×C3⋊C8C2212yes—
44#83403—51nomaximal, Hall
45C2×C5×#137—31no—
46#66159D311yescharacteristic, complemented
47C2×#4096—31no—
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
63C2×#1220—21no—
64#6817—22no—
65#6817—22no—
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C22×C5×Dic3—21no—
70C2×C5×Dic6—22no—
71C2×C5×Dic6—22no—
72C2×C5×Dic6—21no—
73C2×C5×Dic6C2312yes—
74C22×C3×Dic5—21no—
75C2×C3×Dic10—22no—
76C2×C3×Dic10—22no—
77C2×C3×Dic10—21no—
78C2×C3×Dic10C2312yes—
79#6718—22no—
80#6717—22no—
81#6716—22no—
82#6715—22no—
83C2×C3⋊#168D414yes—
84C2×C3⋊#168C2311yescharacteristic
85C2×C3⋊#168C2311yescharacteristic
86C5×#216—24no—
87C5×#214—24no—
88C5×#208D414yes—
89C2×C5×C3⋊C8C2312yes—
90C3×C22⋊Dic5—24no—
91C3×C22⋊Dic5D412yes—
92C3×C4⋊Dic5D412yes—
93C3×#683—24no—
94C3×C4×Dic5C2312yes—
95#6668—24no—
96#6667—24no—
97#6662—24no—
98#6661—24no—
99#6661—24no—
100#6658—24no—
101C3×#536—51no—
102C2×#951D511yescharacteristic, complemented
103C2×#950—51no—
104C22×#216—51no—
105C2×#942—51no—
106#5526—51no—
107#5092—52no—
108#5086—52no—
109#5060—52no—
110#5059—52no—
111#4997—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×Q8—31no—
114C2×#709—31no—
115C22×Dic10C2×D311yescharacteristic
116C5×#137—64no—
117C2×C5×Q16—32no—
118C2×C5×SD16—32no—
119C2×C5×M16—31no—
120#4096—64no—
121#4093—32no—
122#4092—62no—
123#4090—32no—
124#4090C2×D312yes—
125C2×#689—31no—
126C2×#689—32no—
127C2×#689—32no—
128C2×#689—64no—
129C2×#688—31no—
130#4082C2×D312yes—
131#4081—22no—
132C2×#687—31no—
133C2×#686—31no—
134#4075—62no—
135#4072C2×D311yescharacteristic
136#4070—22no—
137C22×#168—31no—
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×D15—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
158#1220—42no—
159C2×Dic15—21no—
160D60—21no—
161D60—21no—
162C4×D15—42no—
163Dic30—21no—
164Dic30—21no—
165C2×C5×Dic3—22no—
166C2×C5×Dic3—42no—
167C5×Dic6—22no—
168C5×Dic6—22no—
169C5×Dic6—42no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—42no—
172C2×C3×Dic5C2×D414yes—
173C3×Dic10—22no—
174C3×Dic10—22no—
175C3×Dic10—42no—
176C3⋊#168C2×D412yes—
177C3⋊#168C2×D412yes—
178C5×C3⋊C8C2×D414yes—
179C2×C3×#41C2×D511yescharacteristic
180C22×C3×Q8—51no—
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—24no—
189#950—104no—
190C2×#216—51no—
191C2×#216—52no—
192C2×#216—52no—
193C2×#216—52no—
194C2×#216—104no—
195C2×#216C2×D512yes—
196#942—104no—
197C2×#215—51no—
198C2×#215—52no—
199C2×#214—51no—
200C2×#214C2×D512yes—
201C2×#213—51no—
202C2×#208C2×D511yescharacteristic
203C22×C3⋊C8—51no—
204#897—102no—
205#886—102no—
206#875—52no—
207#869—52no—
208#803—52no—
209C4×C3⋊C8—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—61no—
223C22×Dic5—21no—
224#709—62no—
225#709—62no—
226C2×D20—31no—
227C2×C4×D5—61no—
228C2×Dic10—22no—
229C2×Dic10—22no—
230C2×Dic10—21no—
231C2×Dic10—31no—
232C2×Dic10C22×D312yes—
233C5×Q16—64no—
234C5×SD16—64no—
235C5×M16—34no—
236C2×C5×C8—32no—
237C22⋊Dic5—24no—
238C22⋊Dic5#6712yes—
239#689—64no—
240#689—64no—
241#689—62no—
242#688—62no—
243#687—62no—
244#686—62no—
245#685—64no—
246C4⋊Dic5#6712yes—
247#683—24no—
248#683—64no—
249C4×Dic5C22×D312yes—
250C2×#168—34no—
251C2×#168—31no—
252C2×#168—31no—
253Dic20—64no—
254#677—64no—
255C2×#137—31no—
256C2×#137—151no—
257C2×#135—151no—
258C22×Q16—151no—
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—41no—
268C22×C3×C5—42no—
269C22×C3×C5#12712yes—
270C22×C3×C5C22×D411yescharacteristic
271C2×D15—41no—
272C2×D15—42no—
273C3×C4×C5—41no—
274C3×C4×C5#12712yes—
275C3×C4×C5C22×D411yescharacteristic
276C3×C4×C5C22×D411yescharacteristic
277Dic15—41no—
278C3×Dic5—24no—
279C3×Dic5—42no—
280C5×Dic3—42no—
281C3×#41—22no—
282C3×#41—22no—
283C2×C3×Q8—52no—
284C2×C3×Q8—101no—
285C2×C3×Q8—102no—
286C2×C3×Q8—102no—
287C2×C3×Q8C22×D511yescharacteristic
288C2×C3×D4—21no—
289C2×C3×D4C22×D511yescharacteristic
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—104no—
311#216—104no—
312#216—102no—
313#216—104no—
314#215—102no—
315#215—104no—
316#214—24no—
317#214—102no—
318#213—102no—
319(C2×D3)⋊C4—104no—
320C4⋊Dic3—104no—
321#208C22⋊D514yes—
322C2×C3⋊C8—54no—
323C2×C3⋊C8—51no—
324C2×C3⋊C8—51no—
325C2×C3⋊C8C22×D512yes—
326C23×C5—21no—
327C23×C5C2×#6711yescharacteristic
328C22×D5—61no—
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×D412yes—
343C2×C4×C5C2×#6711yescharacteristic
344C2×C4×C5C23×D311yescharacteristic
345C22⋊D5—122no—
346C2×Dic5—22no—
347C2×Dic5—42no—
348C2×Dic5—61no—
349C2×Dic5C2×#6714yes—
350D20—61no—
351D20—61no—
352C4×D5—122no—
353Dic10—22no—
354Dic10—22no—
355Dic10—42no—
356Dic10—61no—
357Dic10—61no—
358C5×C8—34no—
359#168—32no—
360#168—32no—
361C2×#41—151no—
362C2×#41D3×D511yescharacteristic
363C22×Q8—31no—
364C22×Q8—51no—
365#137—64no—
366#137—304no—
367#135—304no—
368C2×Q16—32no—
369C2×Q16—152no—
370C2×Q16—152no—
371C2×Q16—152no—
372C2×Q16—151no—
373C2×Q16—304no—
374C2×SD16—32no—
375C2×SD16—152no—
376C2×SD16—151no—
377C2×SD16—151no—
378C2×D8—151no—
379C2×M16—31no—
380C22×C8—151no—
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×C5—81no—
394C2×C3×C5C2×#12711yescharacteristic
395C2×C3×C5#57812yes—
396D15—81no—
397C23×C3—21no—
398C23×C3D4×D511yescharacteristic
399C22×D3—101no—
400C3×Q8—21no—
401C3×Q8—21no—
402C3×Q8—102no—
403C3×Q8—102no—
404C3×Q8—202no—
405C3×D4—21no—
406C3×D4—21no—
407C3×D4—42no—
408C2×C3×C4—21no—
409C2×C3×C4—42no—
410C2×C3×C4—54no—
411C2×C3×C4—102no—
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—52no—
430C3⋊C8—52no—
431C3⋊C8C2×C22⋊D514yes—
432C22×C5—22no—
433C22×C5—41no—
434C22×C5—42no—
435C22×C5#94012yes—
436C22×C5C22×#6711yescharacteristic
437C2×D5—121no—
438C2×D5—122no—
439C4×C5—41no—
440C4×C5—122no—
441C4×C5#94012yes—
442C4×C5C2×D3×D411yescharacteristic
443C4×C5C2×D3×D411yescharacteristic
444Dic5—24no—
445Dic5—42no—
446Dic5—121no—
447#41—22no—
448#41—22no—
449#41—302no—
450#41—302no—
451C2×Q8—32no—
452C2×Q8—52no—
453C2×Q8—61no—
454C2×Q8—62no—
455C2×Q8—62no—
456C2×Q8—101no—
457C2×Q8—102no—
458C2×Q8—102no—
459C2×Q8—151no—
460C2×Q8C2×D3×D511yescharacteristic
461C2×D4—21no—
462C2×D4—151no—
463C2×D4—301no—
464C2×D4C2×D3×D511yescharacteristic
465C22×C4—21no—
466C22×C4—61no—
467C22×C4—101no—
468C22×C4—301no—
469C22×C4C2×D3×D511yescharacteristic
470Q16—64no—
471Q16—304no—
472Q16—302no—
473Q16—304no—
474Q16—304no—
475SD16—64no—
476SD16—304no—
477SD16—302no—
478SD16—302no—
479D8—302no—
480M16—34no—
481C2×C8—32no—
482C2×C8—154no—
483C2×C8—151no—
484C2×C8—151no—
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—42no—
495C22×C3—41no—
496C22×C3#408612yes—
497C22×C3C2×D4×D511yescharacteristic
498C2×D3—202no—
499C2×D3—201no—
500C3×C4—41no—
501C3×C4—104no—
502C3×C4—202no—
503C3×C4#408612yes—
504C3×C4C2×D4×D511yescharacteristic
505C3×C4C22×C22⋊D511yescharacteristic
506Dic3—42no—
507Dic3—201no—
508C2×C5—22no—
509C2×C5—81no—
510C2×C5C2×#94011yescharacteristic
511C2×C5#583812yes—
512D5—241no—
513C23—21no—
514C23—301no—
515C23D5×#6711yescharacteristic
516Q8—21no—
517Q8—21no—
518Q8—62no—
519Q8—62no—
520Q8—102no—
521Q8—102no—
522Q8—122no—
523Q8—202no—
524Q8—301no—
525Q8—301no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4—301no—
530D4—301no—
531D4—602no—
532C2×C4—21no—
533C2×C4—42no—
534C2×C4—54no—
535C2×C4—62no—
536C2×C4—102no—
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—34no—
546C8—152no—
547C8—152no—
548C2×C3—22no—
549C2×C3—81no—
550C2×C3#6611312yes—
551C2×C3C2×#408611yescharacteristic
552D3—401no—
553C5#8340311yescharacteristic, complemented, Sylow
554C22—22no—
555C22—42no—
556C22—41no—
557C22—602no—
558C22—601no—
559C22#9156712yes—
560C22C2×D5×#6711yescharacteristic
561C4—41no—
562C4—104no—
563C4—122no—
564C4—202no—
565C4—601no—
566C4#9156712yes—
567C4C2×D3×C22⋊D511yescharacteristic
568C4C2×#679011yescharacteristic
569C3#1061570611yescharacteristic, complemented, Sylow
570C2—22no—
571C2—81no—
572C2—1201no—
573C2#1175533612yes—
574C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×#91839C2
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
2. C2×C5×#951C2semidirect
3. C3×#66159C2semidirect
4. #11754270C2semidirect
5. C22×#6661C2semidirect
6. C2×#91315C2semidirect
7. #11749347C2semidirect
8. #11749315C2semidirect
9. #11749107C2semidirect
10. #11749070C2semidirect
11. #11748320C2semidirect
46. #66159D3semidirect
102. C2×#951D5semidirect
492. C3×C5#3156semidirect
553. C5#83403semidirect
569. C3#10615706semidirect

Maximal subgroups

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

subgroupindex
C2×#918392
C2×C5×#9512
C3×#661592
#117542702
C22×#66612
C2×#913152
#117493472
#117493152
#117491072
#117490702
#117483202
#106157063
#834035