Finite Group Databasebeta

← #14424485

Subgroups — #14424485

Order 1920.

1464 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1010C211yesmaximal, characteristic, complemented
2C3×#66164C211yesmaximal, characteristic, complemented
3C22×#6655C211yesmaximal, characteristic, complemented
4C2×#91298C211yesmaximal, characteristic, complemented
5#11751335C211yesmaximal, characteristic, complemented
6#11748536C214yesmaximal, complemented
7#11748517C214yesmaximal, complemented
8#11748407C211yesmaximal, characteristic, complemented
9#11748382C211yesmaximal, characteristic, complemented
10#10615844—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12C5×#1010—24no—
13C5×#1010—24no—
14C2×C5×D3×Q8—21no—
15C2×C5×#237—21no—
16C2×C5×#237—22no—
17C2×C5×#235C2211yescharacteristic
18C2×C5×#235C2212yescomplemented
19C22×C5×Dic6C2211yescharacteristic
20C22×C5×Dic6C2212yescomplemented
21C22×C3×D20C2211yescharacteristic
22C2×#6710C2211yescharacteristic
23C22×C3⋊#168C2211yescharacteristic
24C3×#4093—21no—
25C3×#4086—21no—
26C3×#4083—22no—
27C3×#4076C2214yes—
28C3×#4072C2211yescharacteristic
29C2×#6655—24no—
30C2×#6655C2212yes—
31C2×#6655C2214yes—
32#91298—24no—
33C2×#6652C2212yes—
34#91114C2214yescomplemented
35#90972C2212yescomplemented
36#90972C2214yescomplemented
37#90966C2212yescomplemented
38#83390—51nomaximal, Hall
39C2×C5×2−1+4—31no—
40#66164D311yescharacteristic, complemented
41C2×#4095—31no—
42C22×#688—31no—
43#65527—34no—
44#65523—31no—
45#65522—31no—
46#65516—34no—
47#65514—31no—
48C23×C3×D5—21no—
49C3×C5×#41—22no—
50C3×C5×#41—22no—
51C2×C3×C5×Q8D411yescharacteristic
52C2×C3×C5×D4D412yes—
53C2×C3×C5×D4D411yescharacteristic
54C22×C3×C4×C5C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C2×C5×#67—21no—
57C2×C5×#67—22no—
58C22×C5×Dic3—21no—
59C22×C5×Dic3—22no—
60C5×D3×Q8—28no—
61C5×#237—216no—
62C5×#237—28no—
63C5×#235—22no—
64C5×#235—24no—
65C5×#235—24no—
66C5×#235D414yescomplemented
67C2×C5×D12C2311yescharacteristic
68C2×C4×C5×D3—21no—
69C2×C4×C5×D3—22no—
70C2×C5×Dic6—21no—
71C2×C5×Dic6—22no—
72C2×C5×Dic6—22no—
73C2×C5×Dic6—24no—
74C2×C5×Dic6—24no—
75C2×C5×Dic6D414yescomplemented
76C2×C5×Dic6C2312yes—
77C2×C5×Dic6C2311yescharacteristic
78C2×C3×C22⋊D5—24no—
79C2×C3×D20—22no—
80C2×C3×D20—22no—
81C2×C3×D20—21no—
82C2×C3×D20C2312yes—
83#6710—22no—
84C2×C3⋊#168—22no—
85C2×C3⋊#168C2312yes—
86C2×C3⋊#168C2312yes—
87C3×C22⋊Dic5—21no—
88C3×#685—24no—
89C3×C4⋊Dic5C2312yes—
90C3×C4×Dic5—21no—
91#6655—24no—
92#6655—28no—
93#6652—24no—
94C2×#1010D511yescharacteristic, complemented
95C3×#535—51no—
96C22×#214—51no—
97C2×#932—51no—
98#5234—51no—
99#5040—54no—
100#5037—54no—
101#5004—51no—
102#5002—51no—
103C5×2−1+4—64no—
104C5×2−1+4—64no—
105C2×C5×#41—31no—
106C2×C5×#41—32no—
107C2×C5×#41—62no—
108C2×C5×#41—61no—
109C2×C5×#41C2×D311yescharacteristic
110C22×C5×Q8—31no—
111C22×C5×Q8—32no—
112C22×C5×Q8—61no—
113C22×D20C2×D311yescharacteristic
114#4095—64no—
115#4093—21no—
116C2×#688—34no—
117C2×#688—32no—
118C2×#688—64no—
119#4086—21no—
120#4083—22no—
121C2×#686—32no—
122#4076C2×D314yes—
123#4072C2×D311yescharacteristic
124C2×#681—31no—
125C22×#168—31no—
126#3967—34no—
127#3967—32no—
128#3964—32no—
129C22⋊#168—34no—
130#3010—151noSylow
131C23×C3×C5C2×D412yes—
132C23×C3×C5C2×D411yescharacteristic
133C22×C5×D3—21no—
134C22×C3×D5—22no—
135C22×C3×D5—42no—
136C22×C3×D5—82no—
137C3×C5×Q8—22no—
138C3×C5×D4—24no—
139C3×C5×D4—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2411yescharacteristic
147C5×#67—28no—
148C5×#67—24no—
149C2×C5×Dic3—28no—
150C2×C5×Dic3—24no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—21no—
153C5×D12—21no—
154C5×D12C2×D412yes—
155C4×C5×D3—28no—
156C4×C5×D3—24no—
157C5×Dic6—28no—
158C5×Dic6—24no—
159C5×Dic6—22no—
160C5×Dic6—21no—
161C5×Dic6C2×D412yes—
162C5×Dic6C2×D414yes—
163C3×C22⋊D5—84no—
164C2×C3×Dic5—22no—
165C3×D20—22no—
166C3×D20—22no—
167C3×D20—42no—
168C3⋊#168—22no—
169C3⋊#168—22no—
170C2×C3×#41C2×D511yescharacteristic
171C22×C3×D4—51no—
172#1010—24no—
173#1010—24no—
174C2×D3×Q8—21no—
175C2×#237—21no—
176C2×#237—22no—
177C2×#235C2×D511yescharacteristic
178C2×#235C2×D512yescomplemented
179C22×Dic6C2×D511yescharacteristic
180C22×Dic6C2×D512yescomplemented
181C3×#127—101no—
182C3×#124—101no—
183C3×#121—54no—
184C3×#120—102no—
185C3×#117—51no—
186C2×#214—52no—
187C2×#214—54no—
188C2×#214—104no—
189#932—104no—
190C2×#213—52no—
191C2×#208—51no—
192C22×C3⋊C8—51no—
193#830—54no—
194#810—52no—
195#810—54no—
196#809—52no—
197C23×D5—21no—
198C5×#41—22no—
199C5×#41—22no—
200C5×#41—34no—
201C5×#41—64no—
202C5×#41—64no—
203C5×#41—616no—
204C5×#41—68no—
205C5×#41—62no—
206C2×C5×Q8—34no—
207C2×C5×Q8—32no—
208C2×C5×Q8—31no—
209C2×C5×Q8—64no—
210C2×C5×Q8—64no—
211C2×C5×Q8—68no—
212C2×C5×Q8—62no—
213C2×C5×Q8—62no—
214C2×C5×Q8—61no—
215C2×C5×Q8#6711yescharacteristic
216C2×C5×D4—31no—
217C2×C5×D4—62no—
218C2×C5×D4—61no—
219C2×C5×D4#6712yes—
220C2×C5×D4#6711yescharacteristic
221C22×C4×C5—62no—
222C22×C4×C5—61no—
223C22×C4×C5—62no—
224C22×C4×C5—61no—
225C22×C4×C5C22×D312yes—
226C22×C4×C5C22×D311yescharacteristic
227C2×C22⋊D5—24no—
228C2×D20—22no—
229C2×D20—22no—
230C2×D20—21no—
231C2×D20C22×D312yes—
232C22⋊Dic5—21no—
233#688—68no—
234#688—64no—
235#686—64no—
236#685—24no—
237C4⋊Dic5C22×D312yes—
238C4×Dic5—21no—
239#681—62no—
240C2×#168—32no—
241C2×#168—32no—
242C2×#168—62no—
243C2×2−1+4—31no—
244C2×AGL(1,ℤ/8)—151no—
245C22×SD16—151no—
246#535—51no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—151no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5—22no—
254C22×C3×C5—24no—
255C22×C3×C5#12012yes—
256C22×C3×C5C22×D411yescharacteristic
257C2×C5×D3—22no—
258C2×C5×D3—42no—
259C2×C3×D5—42no—
260C2×C3×D5—44no—
261C2×C3×D5—84no—
262C3×C4×C5—22no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266C3×Dic5—42no—
267C5×Dic3—22no—
268C5×Dic3—24no—
269C24×C3—101no—
270C3×#41—22no—
271C3×#41—22no—
272C2×C3×Q8C22⋊D511yescharacteristic
273C2×C3×D4—52no—
274C2×C3×D4—104no—
275C2×C3×D4—102no—
276C2×C3×D4—102no—
277C2×C3×D4—101no—
278C2×C3×D4C22⋊D512yes—
279C2×C3×D4C22⋊D511yescharacteristic
280C22×C3×C4C22×D512yes—
281C22×C3×C4C22×D511yescharacteristic
282C2×#67—21no—
283C2×#67—22no—
284C22×Dic3—21no—
285C22×Dic3—22no—
286D3×Q8—28no—
287#237—216no—
288#237—28no—
289#235—22no—
290#235—24no—
291#235—24no—
292#235C22⋊D514yescomplemented
293C2×D12C22×D511yescharacteristic
294C2×C4×D3—21no—
295C2×C4×D3—22no—
296C2×Dic6—21no—
297C2×Dic6—22no—
298C2×Dic6—22no—
299C2×Dic6—24no—
300C2×Dic6—24no—
301C2×Dic6C22⋊D514yescomplemented
302C2×Dic6C22×D512yes—
303C2×Dic6C22×D511yescharacteristic
304C3×C4⋊C4—52no—
305C3×C22⋊C4—101no—
306C3×C22⋊C4—104no—
307C3×C42—101no—
308#214—104no—
309#214—108no—
310#213—104no—
311#208—102no—
312C2×C3⋊C8—52no—
313C2×C3⋊C8—52no—
314C2×C3⋊C8—102no—
315C23×C5—61no—
316C23×C5C2×#6712yes—
317C23×C5C2×#6711yescharacteristic
318C22×D5—22no—
319C22×D5—42no—
320C22×D5—82no—
321C5×Q8—22no—
322C5×Q8—34no—
323C5×Q8—32no—
324C5×Q8—68no—
325C5×Q8—64no—
326C5×Q8—62no—
327C5×Q8—61no—
328C5×D4—24no—
329C5×D4—22no—
330C5×D4—32no—
331C5×D4—68no—
332C5×D4—64no—
333C5×D4—61no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—68no—
337C2×C4×C5—68no—
338C2×C4×C5—64no—
339C2×C4×C5—62no—
340C2×C4×C5—61no—
341C2×C4×C5—64no—
342C2×C4×C5D3×D412yes—
343C2×C4×C5D3×D412yes—
344C2×C4×C5C2×#6712yes—
345C2×C4×C5C2×#6711yescharacteristic
346C2×C4×C5C23×D311yescharacteristic
347C22⋊D5—84no—
348C2×Dic5—22no—
349D20—22no—
350D20—22no—
351D20—42no—
352#168—62no—
353#168—62no—
3542−1+4—64no—
3552−1+4—64no—
356C2×#41—31no—
357C2×#41—32no—
358C2×#41—62no—
359C2×#41—61no—
360C2×#41D3×D511yescharacteristic
361C22×Q8—31no—
362C22×Q8—32no—
363C22×Q8—61no—
364C22×D4—51no—
365AGL(1,ℤ/8)—304no—
366C2×SD16—154no—
367C2×SD16—152no—
368C2×SD16—304no—
369C2×D8—152no—
370C2×M16—151no—
371C22×C8—151no—
372#127—101no—
373#124—101no—
374#121—54no—
375#120—102no—
376#117—51no—
377#103—152no—
378#103—154no—
379#102—152no—
380C22⋊C8—154no—
381C2×C3×C5—22no—
382C2×C3×C5—42no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385C3×D5—82no—
386C5×D3—42no—
387C23×C3—102no—
388C23×C3—202no—
389C23×C3—402no—
390C23×C3C2×C22⋊D512yes—
391C23×C3C2×C22⋊D511yescharacteristic
392C22×D3—21no—
393C3×Q8—22no—
394C3×D4—24no—
395C3×D4—22no—
396C3×D4—102no—
397C3×D4—102no—
398C3×D4—202no—
399C3×D4—404no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—102no—
403C2×C3×C4C2×C22⋊D512yes—
404C2×C3×C4C2×C22⋊D511yescharacteristic
405C2×C3×C4C2×C22⋊D512yes—
406C2×C3×C4C2×C22⋊D512yes—
407C2×C3×C4C23×D511yescharacteristic
408#67—28no—
409#67—24no—
410C2×Dic3—28no—
411C2×Dic3—24no—
412C2×Dic3—22no—
413C2×Dic3—21no—
414D12—21no—
415D12C2×C22⋊D512yes—
416C4×D3—28no—
417C4×D3—24no—
418Dic6—28no—
419Dic6—24no—
420Dic6—22no—
421Dic6—21no—
422Dic6C2×C22⋊D512yes—
423Dic6C2×C22⋊D514yes—
424C3⋊C8—102no—
425C3⋊C8—102no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—24no—
429C22×C5—62no—
430C22×C5—122no—
431C22×C5#93712yes—
432C22×C5C22×#6711yescharacteristic
433C2×D5—42no—
434C2×D5—44no—
435C2×D5—84no—
436C4×C5—22no—
437C4×C5—64no—
438C4×C5—62no—
439C4×C5#93712yes—
440C4×C5C2×D3×D411yescharacteristic
441C4×C5C2×D3×D411yescharacteristic
442Dic5—42no—
443C24—101no—
444#41—22no—
445#41—22no—
446#41—34no—
447#41—64no—
448#41—64no—
449#41—616no—
450#41—68no—
451#41—62no—
452C2×Q8—34no—
453C2×Q8—32no—
454C2×Q8—31no—
455C2×Q8—64no—
456C2×Q8—64no—
457C2×Q8—68no—
458C2×Q8—62no—
459C2×Q8—61no—
460C2×Q8—62no—
461C2×Q8#120111yescharacteristic
462C2×D4—31no—
463C2×D4—52no—
464C2×D4—62no—
465C2×D4—61no—
466C2×D4—104no—
467C2×D4—101no—
468C2×D4—102no—
469C2×D4—102no—
470C2×D4#120112yes—
471C2×D4#120111yescharacteristic
472C22×C4—62no—
473C22×C4—61no—
474C22×C4—62no—
475C22×C4—61no—
476C22×C4C2×D3×D512yes—
477C22×C4C2×D3×D511yescharacteristic
478SD16—308no—
479SD16—304no—
480D8—304no—
481M16—302no—
482C2×C8—152no—
483C2×C8—152no—
484C2×C8—302no—
485C4⋊C4—52no—
486C22⋊C4—101no—
487C22⋊C4—104no—
488C42—101no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—24no—
492C22×C3—22no—
493C22×C3—204no—
494C22×C3—202no—
495C22×C3—404no—
496C22×C3#409912yes—
497C22×C3C22×C22⋊D511yescharacteristic
498C2×D3—22no—
499C2×D3—42no—
500C3×C4—22no—
501C3×C4—202no—
502C3×C4#409912yes—
503C3×C4C22×C22⋊D511yescharacteristic
504C3×C4C22×C22⋊D511yescharacteristic
505Dic3—22no—
506Dic3—24no—
507C2×C5—22no—
508C2×C5—42no—
509C2×C5—122no—
510C2×C5C2×#93711yescharacteristic
511C2×C5#583612yes—
512D5—82no—
513C23—61no—
514C23—102no—
515C23—202no—
516C23—402no—
517C23C2×#120112yes—
518C23C2×#120111yescharacteristic
519Q8—22no—
520Q8—34no—
521Q8—32no—
522Q8—68no—
523Q8—62no—
524Q8—61no—
525Q8—64no—
526D4—24no—
527D4—22no—
528D4—32no—
529D4—68no—
530D4—64no—
531D4—61no—
532D4—102no—
533D4—102no—
534D4—202no—
535D4—404no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—68no—
539C2×C4—68no—
540C2×C4—62no—
541C2×C4—61no—
542C2×C4—64no—
543C2×C4—64no—
544C2×C4—102no—
545C2×C4C2×#120112yes—
546C2×C4C2×#120111yescharacteristic
547C2×C4D3×C22⋊D512yes—
548C2×C4D3×C22⋊D512yes—
549C2×C4C22×D3×D511yescharacteristic
550C8—302no—
551C8—302no—
552C2×C3—22no—
553C2×C3—42no—
554C2×C3—402no—
555C2×C3#6617112yes—
556C2×C3C2×#409911yescharacteristic
557D3—42no—
558C5#8339011yescharacteristic, complemented, Sylow
559C22—22no—
560C22—24no—
561C22—22no—
562C22—62no—
563C22—122no—
564C22—204no—
565C22—202no—
566C22—404no—
567C22#9156812yes—
568C22C22×#120111yescharacteristic
569C4—22no—
570C4—64no—
571C4—62no—
572C4—202no—
573C4#9156812yes—
574C4C2×D3×C22⋊D511yescharacteristic
575C4C2×D3×C22⋊D511yescharacteristic
576C3#1061584411yescharacteristic, complemented, Sylow
577C2—22no—
578C2—42no—
579C2—122no—
580C2—402no—
581C2#1175530312yes—
582C2C2×#9156811yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3010
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C5×#1010C2semidirect
2. C3×#66164C2semidirect
3. C22×#6655C2semidirect
4. C2×#91298C2semidirect
5. #11751335C2semidirect
6. #11748536C2semidirect
7. #11748517C2semidirect
8. #11748407C2semidirect
9. #11748382C2semidirect
18. C2×C5×#235C22semidirect
20. C22×C5×Dic6C22semidirect
34. #91114C22semidirect
35. #90972C22semidirect
36. #90972C22semidirect
37. #90966C22semidirect
40. #66164D3semidirect
66. C5×#235D4semidirect
75. C2×C5×Dic6D4semidirect
94. C2×#1010D5semidirect
178. C2×#235C2×D5semidirect
180. C22×Dic6C2×D5semidirect
292. #235C22⋊D5semidirect
301. C2×Dic6C22⋊D5semidirect
489. C3×C5#3010semidirect
558. C5#83390semidirect
576. C3#10615844semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10102
C3×#661642
C22×#66552
C2×#912982
#117513352
#117485362
#117485172
#117484072
#117483822
#106158443
#833905