Finite Group Databasebeta

← #14424498

Subgroups — #14424498

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×#92001C211yesmaximal, characteristic, complemented
2C5×#5525C211yesmaximal, characteristic, complemented
3C22×#6659C211yesmaximal, characteristic, complemented
4C2×#91299C211yesmaximal, characteristic, complemented
5#11751105C211yesmaximal, characteristic, complemented
6C3×#65291C211yesmaximal, characteristic, complemented
7#11748345C211yesmaximal, characteristic, complemented
8#11747515C214yesmaximal, complemented
9#11747494C214yesmaximal, complemented
10#10615121—31nomaximal, Hall
11C22×Dic30C2211yescharacteristic
12C2×C5×#235C2211yescharacteristic
13C22×C5×D12C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C2×#6780—22no—
16C2×#6772—21no—
17C2×D3×Dic10C2212yescomplemented
18#92001—24no—
19#92001—24no—
20C2×#6765C2212yescomplemented
21C2×D5×Dic6—21no—
22C3×C5×#117C2211yescharacteristic
23C2×#6710C2211yescharacteristic
24C5×#895C2214yes—
25C5×#882—22no—
26C5×#875—21no—
27C5×#874—21no—
28C22×C3×#168C2211yescharacteristic
29C2×#6659—24no—
30C2×#6659C2214yes—
31C2×#6656C2212yes—
32#91299—24no—
33C2×#6652C2212yes—
34#91094C2214yescomplemented
35C3×#3942C2212yescomplemented
36C3×#3941C2212yescomplemented
37(C2×D3)⋊#168C2214yescomplemented
38#78836—51nomaximal, Hall
39C2×#4150—31no—
40C5×#535—31no—
41C22×#687—31no—
42C2×#4078—31no—
43#65523—31no—
44#65329—34no—
45#65326—34no—
46#65293—31no—
47#65291D311yescharacteristic, complemented
48C23×C5×D3—21no—
49C22×C3×C4×C5C2311yescharacteristic
50C22×Dic15—21no—
51C2×Dic30—21no—
52C2×Dic30—22no—
53C2×Dic30D414yescomplemented
54C2×Dic30C2312yes—
55C2×C5×#67D412yes—
56C5×#235—22no—
57C5×#235—22no—
58C2×C5×D12—22no—
59C2×C5×D12—22no—
60C2×C5×D12—21no—
61C2×C5×D12—24no—
62C2×C5×D12D411yescharacteristic
63C2×C5×D12C2312yes—
64C2×C4×C5×D3C2312yes—
65C2×C5×Dic6D411yescharacteristic
66C2×C3×C22⋊D5—21no—
67C3×#709—22no—
68C3×#709D414yescomplemented
69C2×C3×D20C2311yescharacteristic
70C2×C3×C4×D5—21no—
71C2×C3×Dic10C2311yescharacteristic
72C2×#1204—22no—
73C2×#1201—22no—
74C2×D3×Dic5—22no—
75#6780—216no—
76C2×D5×Dic3—22no—
77#6772—28no—
78D3×Dic10—24no—
79D3×Dic10—24no—
80#6765—24no—
81#6765—24no—
82D5×Dic6—28no—
83C3×C5×C4⋊C4C2312yes—
84C3×C5×C22⋊C4—21no—
85C3×C42×C5—21no—
86#6710—22no—
87C2×C3⋊#168C2312yes—
88C5×(C2×D3)⋊C4—24no—
89C2×C3×#168—22no—
90C2×C3×#168C2312yes—
91#6659—28no—
92#6656—24no—
93#6652—24no—
94C2×#1010—51no—
95C2×#949—51no—
96C22×#204—51no—
97#5525D511yescharacteristic, complemented
98C3×#416—51no—
99#5110—51no—
100#5004—51no—
101#4806—54no—
102#4781—54no—
103C2×C5×#41—31no—
104C22×C5×D4—31no—
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×#127—61no—
115C5×#124—61no—
116C5×#121—34no—
117C5×#120—62no—
118C5×#117C2×D311yescharacteristic
119C2×#687—32no—
120C2×#687—34no—
121C2×#687—64no—
122#4078—64no—
123C2×#686—32no—
124C2×#681—31no—
125C22×#168C2×D311yescharacteristic
126C22⋊#168—34no—
127#3942—34no—
128#3942C2×D312yescomplemented
129#3941C2×D312yescomplemented
130#3010—151noSylow
131C23×C3×C5C2×D411yescharacteristic
132C22×C5×D3—22no—
133C22×C5×D3—42no—
134C22×C5×D3—82no—
135C22×C5×D3C2×D412yes—
136C22×C3×D5—21no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—24no—
143C2×Dic15—22no—
144Dic30—24no—
145Dic30—22no—
146Dic30C2×D414yes—
147C5×#67—24no—
148C2×C5×Dic3C2×D412yes—
149C5×D12—22no—
150C5×D12—22no—
151C5×D12—22no—
152C5×D12—42no—
153C5×D12—84no—
154C4×C5×D3—22no—
155C4×C5×D3—22no—
156C5×Dic6—22no—
157C3×C22⋊D5—24no—
158C2×C3×Dic5—21no—
159C3×D20—21no—
160C3×D20C2×D412yes—
161C3×C4×D5—24no—
162C3×Dic10—21no—
163C3×Dic10C2×D412yes—
164#1204—28no—
165#1201—28no—
166D3×Dic5—28no—
167D5×Dic3—28no—
168C3⋊#168—22no—
169C3×#168—22no—
170C2×C3×#41—51no—
171#1010—104no—
172#1010—104no—
173C2×D3×Q8—52no—
174C2×#237—52no—
175C2×#237—102no—
176C2×#235—101no—
177C2×#235C2×D511yescharacteristic
178C22×D12C2×D511yescharacteristic
179C22×Dic6—51no—
180C22×Dic6—101no—
181C22×C3×C8—51no—
182C3×#117C2×D511yescharacteristic
183#949—104no—
184C2×#215—52no—
185C2×#213—52no—
186C2×#208—51no—
187C2×#204—54no—
188C2×#204—104no—
189#895C2×D514yes—
190#882—22no—
191#875—21no—
192#874—21no—
193C3×#103—52no—
194C3×#102—52no—
195(C2×D3)⋊C8—54no—
196#810—54no—
197C24×C5—61no—
198C5×#41—62no—
199C5×#41—62no—
200C2×C5×Q8—31no—
201C2×C5×D4—32no—
202C2×C5×D4—31no—
203C2×C5×D4—32no—
204C2×C5×D4—64no—
205C2×C5×D4—62no—
206C2×C5×D4—62no—
207C2×C5×D4—61no—
208C22×C4×C5—32no—
209C22×C4×C5C22×D311yescharacteristic
210C2×C22⋊D5—21no—
211C2×C22⋊D5—62no—
212C22×Dic5—62no—
213C22×Dic5—61no—
214Q8×D5—68no—
215#711—68no—
216#711—616no—
217#709—22no—
218#709—64no—
219#709—64no—
220#709D1214yescomplemented
221C2×D20C22×D311yescharacteristic
222C2×C4×D5—21no—
223C2×C4×D5—62no—
224C2×Dic10—34no—
225C2×Dic10—32no—
226C2×Dic10—64no—
227C2×Dic10—62no—
228C2×Dic10—62no—
229C2×Dic10—61no—
230C2×Dic10—64no—
231C2×Dic10C22×D311yescharacteristic
232C5×C4⋊C4C22×D312yes—
233C5×C22⋊C4—21no—
234C5×C22⋊C4—64no—
235C42×C5—21no—
236#687—68no—
237#687—64no—
238#686—64no—
239#681—62no—
240C2×#168—22no—
241C2×#168—32no—
242C2×#168C22×D312yes—
243C2×2−1+4—151no—
244C2×AGL(1,ℤ/8)—151no—
245C22×SD16—151no—
246#535—31no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—51no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5#12012yes—
254C22×C3×C5C22×D411yescharacteristic
255C2×C5×D3—22no—
256C2×C5×D3—24no—
257C2×C5×D3—42no—
258C2×C5×D3—44no—
259C2×C5×D3—84no—
260C2×C3×D5—22no—
261C2×C3×D5—42no—
262C3×C4×C5—42no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—24no—
267C3×Dic5—22no—
268C5×Dic3—22no—
269C23×D3—21no—
270C3×#41—54no—
271C3×#41—102no—
272C2×C3×Q8—51no—
273C2×C3×D4—51no—
274C2×C3×D4—101no—
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×D12—22no—
290C2×D12—22no—
291C2×D12—21no—
292C2×D12—24no—
293C2×D12C22⋊D511yescharacteristic
294C2×D12C22×D512yes—
295C2×C4×D3—102no—
296C2×C4×D3C22×D512yes—
297C2×Dic6—54no—
298C2×Dic6—52no—
299C2×Dic6—108no—
300C2×Dic6—102no—
301C2×Dic6—101no—
302C2×Dic6—102no—
303C2×Dic6C22⋊D511yescharacteristic
304C2×C3×C8—52no—
305C2×C3×C8—102no—
306C3×C4⋊C4C22×D512yes—
307C3×C22⋊C4—21no—
308C3×C42—21no—
309#215—104no—
310#213—104no—
311(C2×D3)⋊C4—24no—
312#208—102no—
313C2×C3⋊C8—52no—
314#204—108no—
315C23×C5—32no—
316C23×C5—62no—
317C23×C5—122no—
318C23×C5—242no—
319C23×C5D3×D411yescharacteristic
320C22×D5—21no—
321C5×Q8—62no—
322C5×D4—64no—
323C5×D4—62no—
324C5×D4—62no—
325C5×D4—62no—
326C5×D4—122no—
327C5×D4—244no—
328C2×C4×C5—22no—
329C2×C4×C5—32no—
330C2×C4×C5—62no—
331C2×C4×C5—62no—
332C2×C4×C5C2×D1212yes—
333C2×C4×C5D3×D412yes—
334C2×C4×C5D3×D411yescharacteristic
335C2×C4×C5C23×D311yescharacteristic
336C22⋊D5—24no—
337C22⋊D5—68no—
338C2×Dic5—21no—
339C2×Dic5—68no—
340C2×Dic5—64no—
341C2×Dic5—62no—
342D20—21no—
343D20C2×D1212yes—
344C4×D5—24no—
345C4×D5—68no—
346Dic10—21no—
347Dic10—34no—
348Dic10—68no—
349Dic10—64no—
350Dic10—62no—
351Dic10C2×D1212yes—
352#168—22no—
353#168—62no—
3542−1+4—304no—
3552−1+4—304no—
356C2×#41—31no—
357C2×#41—51no—
358C2×#41—152no—
359C2×#41—301no—
360C2×#41—302no—
361C22×Q8—152no—
362C22×Q8—151no—
363C22×Q8—301no—
364C22×D4—31no—
365AGL(1,ℤ/8)—304no—
366C2×SD16—154no—
367C2×SD16—152no—
368C2×SD16—304no—
369C2×D8—152no—
370C2×M16—151no—
371C22×C8—51no—
372#127—61no—
373#124—61no—
374#121—34no—
375#120—62no—
376#117D3×D511yescharacteristic
377#103—52no—
378#103—154no—
379#102—52no—
380C22⋊C8—154no—
381C2×C3×C5—22no—
382C2×C3×C5C2×#12011yescharacteristic
383C2×C3×C5#57712yes—
384C3×D5—42no—
385C5×D3—42no—
386C5×D3—82no—
387C23×C3—101no—
388C23×C3C2×C22⋊D511yescharacteristic
389C22×D3—22no—
390C22×D3—42no—
391C22×D3—82no—
392C22×D3C2×C22⋊D512yes—
393C3×Q8—52no—
394C3×Q8—101no—
395C3×D4—52no—
396C3×D4—104no—
397C3×D4—101no—
398C2×C3×C4—22no—
399C2×C3×C4—101no—
400C2×C3×C4—104no—
401C2×C3×C4D4×D512yes—
402C2×C3×C4D4×D512yes—
403C2×C3×C4C2×C22⋊D511yescharacteristic
404C2×C3×C4C23×D511yescharacteristic
405#67—24no—
406#67—108no—
407C2×Dic3—108no—
408C2×Dic3—102no—
409C2×Dic3—104no—
410C2×Dic3C2×C22⋊D512yes—
411D12—22no—
412D12—22no—
413D12—22no—
414D12—42no—
415D12—84no—
416C4×D3—22no—
417C4×D3—22no—
418C4×D3—108no—
419Dic6—22no—
420Dic6—54no—
421Dic6—108no—
422Dic6—102no—
423Dic6—104no—
424C3×C8—102no—
425C3⋊C8—102no—
426C22×C5—22no—
427C22×C5—62no—
428C22×C5—64no—
429C22×C5—122no—
430C22×C5—124no—
431C22×C5—244no—
432C22×C5#88212yes—
433C22×C5C2×D3×D411yescharacteristic
434C2×D5—22no—
435C2×D5—42no—
436C4×C5—42no—
437C4×C5—62no—
438C4×C5#88212yes—
439C4×C5C22×D1211yescharacteristic
440C4×C5C2×D3×D411yescharacteristic
441Dic5—22no—
442Dic5—64no—
443C24—61no—
444#41—54no—
445#41—62no—
446#41—62no—
447#41—102no—
448#41—304no—
449#41—304no—
450#41—308no—
451#41—3016no—
452C2×Q8—31no—
453C2×Q8—51no—
454C2×Q8—154no—
455C2×Q8—152no—
456C2×Q8—302no—
457C2×Q8—304no—
458C2×Q8—304no—
459C2×Q8—308no—
460C2×Q8—302no—
461C2×Q8—301no—
462C2×D4—32no—
463C2×D4—31no—
464C2×D4—32no—
465C2×D4—51no—
466C2×D4—64no—
467C2×D4—62no—
468C2×D4—62no—
469C2×D4—61no—
470C2×D4—101no—
471C2×D4—302no—
472C22×C4—32no—
473C22×C4—101no—
474C22×C4—302no—
475C22×C4—302no—
476C22×C4—301no—
477C22×C4C2×D3×D511yescharacteristic
478SD16—308no—
479SD16—304no—
480D8—304no—
481M16—302no—
482C2×C8—52no—
483C2×C8—102no—
484C2×C8—152no—
485C4⋊C4C2×D3×D512yes—
486C22⋊C4—21no—
487C22⋊C4—64no—
488C42—21no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—102no—
492C22×C3—202no—
493C22×C3#408312yes—
494C22×C3C22×C22⋊D511yescharacteristic
495C2×D3—22no—
496C2×D3—24no—
497C2×D3—42no—
498C2×D3—44no—
499C2×D3—84no—
500C3×C4—42no—
501C3×C4—102no—
502C3×C4#408312yes—
503C3×C4C2×D4×D511yescharacteristic
504C3×C4C2×D4×D511yescharacteristic
505Dic3—22no—
506Dic3—104no—
507C2×C5—22no—
508C2×C5—122no—
509C2×C5—242no—
510C2×C5C2×#88211yescharacteristic
511C2×C5#577012yes—
512D5—42no—
513C23—32no—
514C23—62no—
515C23—101no—
516C23—122no—
517C23—242no—
518C23D3×C22⋊D511yescharacteristic
519Q8—52no—
520Q8—62no—
521Q8—101no—
522Q8—154no—
523Q8—308no—
524Q8—304no—
525Q8—302no—
526D4—52no—
527D4—64no—
528D4—62no—
529D4—62no—
530D4—62no—
531D4—104no—
532D4—101no—
533D4—122no—
534D4—244no—
535D4—308no—
536C2×C4—22no—
537C2×C4—32no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—101no—
541C2×C4—104no—
542C2×C4—308no—
543C2×C4—308no—
544C2×C4—304no—
545C2×C4—302no—
546C2×C4D5×D1212yes—
547C2×C4#677712yes—
548C2×C4D3×C22⋊D511yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—102no—
551C8—302no—
552C2×C3—22no—
553C2×C3—202no—
554C2×C3C2×#408311yescharacteristic
555C2×C3#6617012yes—
556D3—42no—
557D3—82no—
558C5#7883611yescharacteristic, complemented, Sylow
559C22—22no—
560C22—64no—
561C22—62no—
562C22—102no—
563C22—124no—
564C22—122no—
565C22—202no—
566C22—244no—
567C22#9147512yes—
568C22C2×D3×C22⋊D511yescharacteristic
569C4—42no—
570C4—62no—
571C4—102no—
572C4—304no—
573C4#9147512yes—
574C4C2×D5×D1211yescharacteristic
575C4C2×#677711yescharacteristic
576C3#1061512111yescharacteristic, complemented, Sylow
577C2—22no—
578C2—122no—
579C2—202no—
580C2—242no—
581C2C2×#9147511yescharacteristic
582C2#1175534712yes—
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
hypercenter#117D3×D5
hypocenterC3×C5#3010
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
1. C2×#92001C2semidirect
2. C5×#5525C2semidirect
3. C22×#6659C2semidirect
4. C2×#91299C2semidirect
5. #11751105C2semidirect
6. C3×#65291C2semidirect
7. #11748345C2semidirect
8. #11747515C2semidirect
9. #11747494C2semidirect
17. C2×D3×Dic10C22semidirect
20. C2×#6765C22semidirect
34. #91094C22semidirect
35. C3×#3942C22semidirect
36. C3×#3941C22semidirect
37. (C2×D3)⋊#168C22semidirect
47. #65291D3semidirect
53. C2×Dic30D4semidirect
68. C3×#709D4semidirect
97. #5525D5semidirect
128. #3942C2×D3semidirect
129. #3941C2×D3semidirect
220. #709D12semidirect
489. C3×C5#3010semidirect
558. C5#78836semidirect
576. C3#10615121semidirect

Maximal subgroups

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

subgroupindex
C2×#920012
C5×#55252
C22×#66592
C2×#912992
#117511052
C3×#652912
#117483452
#117475152
#117474942
#106151213
#788365