Finite Group Databasebeta

← #14439458

Subgroups — #14439458

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6716C211yesmaximal, characteristic, complemented
2C2×C5×#932C211yesmaximal, characteristic, complemented
3C3×#66139C211yesmaximal, characteristic, complemented
4#11754271C211yesmaximal, characteristic, complemented
5C2×#91313C211yesmaximal, characteristic, complemented
6C2×#91297C211yesmaximal, characteristic, complemented
7#11749107C212yesmaximal, complemented
8#11749106C212yesmaximal, complemented
9#11749067C212yesmaximal, complemented
10#11749066C212yesmaximal, complemented
11#11748320C211yesmaximal, characteristic, complemented
12#10615670—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17C2×#6716—24no—
18C2×#6716C2212yes—
19C2×#6716C2212yes—
20C22×C3⋊#168C2211yescharacteristic
21C2×C5×#214C2212yes—
22C5×#932—24no—
23C2×C5×#213C2212yes—
24C2×C5×#208C2211yescharacteristic
25C3×#4099—22no—
26C3×#4086C2212yes—
27C3×#4084—22no—
28C3×#4082C2212yes—
29C3×#4072C2211yescharacteristic
30#91543—22no—
31#91376C2212yescomplemented
32#91373C2212yescomplemented
33#91365—22no—
34C2×#6662C2212yescomplemented
35C2×#6661C2211yescharacteristic, complemented
36#91313—24no—
37C2×#6657C2212yescomplemented
38C2×#6656C2211yescharacteristic, complemented
39C2×#6655C2211yescharacteristic, complemented
40#91297—24no—
41C2×#6652C2211yescharacteristic, complemented
42#90952C2212yescomplemented
43Dic5×C3⋊C8C2212yescomplemented
44#83381—51nomaximal, Hall
45C2×C5×AGL(1,ℤ/8)—31no—
46#66159—31no—
47C2×#4096—31no—
48#66139D311yescharacteristic, complemented
49C22×#687—31no—
50C2×#4055—31no—
51#65464—32no—
52#65456—32no—
53#65444—32no—
54#65443—32no—
55#65411—31no—
56C24×C3×C5—21no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4—22no—
59C2×C3×C5×D4—21no—
60C2×C3×C5×D4C2312yes—
61C22×C3×C4×C5C2311yescharacteristic
62C22×Dic15—21no—
63C2×Dic30—22no—
64C2×Dic30—22no—
65C2×Dic30—21no—
66C2×Dic30C2312yes—
67C2×C5×#67—21no—
68C5×#235—22no—
69C5×#235—22no—
70C2×C5×D12C2311yescharacteristic
71C2×C4×C5×D3—21no—
72C2×C5×Dic6C2311yescharacteristic
73C2×C3×C22⋊D5—21no—
74C2×C3×C22⋊D5—24no—
75C3×#709—22no—
76C3×#709—22no—
77C2×C3×D20C2311yescharacteristic
78C2×C3×C4×D5—21no—
79C2×C3×Dic10C2311yescharacteristic
80#6716—24no—
81#6716—24no—
82C2×C3⋊#168D414yescomplemented
83C2×C3⋊#168C2311yescharacteristic
84C2×C3⋊#168C2311yescharacteristic
85C5×#214—24no—
86C5×#213—24no—
87C5×#208D414yescomplemented
88C2×C5×C3⋊C8C2312yes—
89C3×C22⋊Dic5—24no—
90C3×C22⋊Dic5D412yes—
91C3×C4⋊Dic5D412yes—
92C3×C4×Dic5C2312yes—
93#6668—24no—
94(C2×D3)⋊Dic5—24no—
95#6662—24no—
96#6661—22no—
97#6657—24no—
98#6656—22no—
99#6655—22no—
100#6652—22no—
101C3×#535—51no—
102C2×#951—51no—
103C2×#950—51no—
104C22×#214—51no—
105C2×#932D511yescharacteristic, complemented
106#5526—51no—
107#5076—52no—
108#5074—52no—
109#5060—52no—
110#5059—52no—
111#4997—51no—
112C2×C5×#41—31no—
113C22×C5×D4C2×D311yescharacteristic
114C2×#709C2×D311yescharacteristic
115C22×Dic10—31no—
116C5×AGL(1,ℤ/8)—64no—
117C2×C5×SD16—32no—
118C2×C5×D8—32no—
119C2×C5×M16—31no—
120#4099—22no—
121#4096—64no—
122#4090—32no—
123C2×#689—31no—
124C2×#688—31no—
125#4086C2×D312yes—
126#4084—22no—
127#4082—32no—
128#4082C2×D312yes—
129#4081—62no—
130C2×#687—32no—
131C2×#687—32no—
132C2×#687—31no—
133C2×#687—64no—
134C2×#686—31no—
135#4072C2×D311yescharacteristic
136#4070—62no—
137C22×#168—31no—
138#4055—64no—
139C2×Dic20—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3154—151noSylow
144C23×C3×C5—22no—
145C23×C3×C5—42no—
146C23×C3×C5—82no—
147C23×C3×C5C2×D411yescharacteristic
148C22×C5×D3—21no—
149C22×C3×D5—21no—
150C3×C5×D4—22no—
151C3×C5×D4—22no—
152C3×C5×D4—42no—
153C2×C3×C4×C5C2×D411yescharacteristic
154C2×C3×C4×C5C2×D412yes—
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5C2411yescharacteristic
157C2×Dic15—22no—
158C2×Dic15—42no—
159Dic30—22no—
160Dic30—22no—
161Dic30—42no—
162C5×#67—42no—
163C2×C5×Dic3—21no—
164C5×D12—21no—
165C5×D12—21no—
166C4×C5×D3—42no—
167C5×Dic6—21no—
168C5×Dic6—21no—
169C3×C22⋊D5—42no—
170C3×C22⋊D5—84no—
171C2×C3×Dic5—21no—
172C2×C3×Dic5C2×D414yes—
173C3×D20—21no—
174C3×D20—21no—
175C3×C4×D5—42no—
176C3×Dic10—21no—
177C3×Dic10—21no—
178C3⋊#168C2×D412yes—
179C3⋊#168C2×D412yes—
180C5×C3⋊C8C2×D414yes—
181C2×C3×#41—51no—
182C22×C3×D4C2×D511yescharacteristic
183C2×#235C2×D511yescharacteristic
184C22×Dic6—51no—
185C3×#127—52no—
186C3×#124—52no—
187C3×#121—102no—
188C3×#120—102no—
189C3×#117—51no—
190#951—104no—
191#950—104no—
192C2×#216—51no—
193C2×#216—52no—
194C2×#215—51no—
195C2×#214—52no—
196C2×#214—52no—
197C2×#214—51no—
198C2×#214—52no—
199C2×#214—104no—
200C2×#214C2×D512yes—
201#932—24no—
202C2×#213—51no—
203C2×#213C2×D512yes—
204C2×#208C2×D511yescharacteristic
205C22×C3⋊C8—51no—
206#897—102no—
207#886—102no—
208#875—52no—
209#869—52no—
210#803—52no—
211C4×C3⋊C8—52no—
212C24×C5—21no—
213C5×#41—62no—
214C5×#41—62no—
215C2×C5×Q8—31no—
216C2×C5×D4—22no—
217C2×C5×D4—22no—
218C2×C5×D4—21no—
219C2×C5×D4—31no—
220C2×C5×D4—61no—
221C2×C5×D4C22×D312yes—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—21no—
225C2×C22⋊D5—24no—
226C22×Dic5—61no—
227#709—22no—
228#709—22no—
229C2×D20C22×D311yescharacteristic
230C2×C4×D5—21no—
231C2×Dic10—32no—
232C2×Dic10—62no—
233C2×Dic10—62no—
234C2×Dic10—61no—
235C2×Dic10C22×D311yescharacteristic
236C5×SD16—64no—
237C5×D8—64no—
238C5×M16—34no—
239C2×C5×C8—32no—
240C22⋊Dic5—24no—
241C22⋊Dic5—64no—
242C22⋊Dic5#6712yes—
243#689—62no—
244#688—62no—
245#687—62no—
246#687—64no—
247#687—64no—
248#686—62no—
249C4⋊Dic5#6712yes—
250#683—64no—
251C4×Dic5C22×D312yes—
252C2×#168—34no—
253C2×#168—31no—
254C2×#168—31no—
255Dic20—64no—
256#677—64no—
257C2×#137—151no—
258C2×AGL(1,ℤ/8)—31no—
259C2×#135—151no—
260C22×SD16—151no—
261#536—151no—
262#535—51no—
263#497—152no—
264#496—152no—
265#495—152no—
266#492—152no—
267#405—151no—
268C22×C3×C5—22no—
269C22×C3×C5—42no—
270C22×C3×C5—44no—
271C22×C3×C5—84no—
272C22×C3×C5#12712yes—
273C22×C3×C5C22×D411yescharacteristic
274C2×C5×D3—41no—
275C2×C5×D3—42no—
276C2×C3×D5—41no—
277C2×C3×D5—42no—
278C3×C4×C5#12712yes—
279C3×C4×C5C22×D411yescharacteristic
280C3×C4×C5C22×D411yescharacteristic
281Dic15—42no—
282C3×Dic5—24no—
283C3×Dic5—41no—
284C5×Dic3—41no—
285C24×C3—21no—
286C3×#41—102no—
287C3×#41—102no—
288C2×C3×Q8—51no—
289C2×C3×D4—22no—
290C2×C3×D4—21no—
291C2×C3×D4—22no—
292C2×C3×D4—51no—
293C2×C3×D4—104no—
294C2×C3×D4—101no—
295C2×C3×D4C22×D512yes—
296C22×C3×C4—101no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—21no—
299C22×Dic3—101no—
300#235—22no—
301#235—22no—
302C2×D12C22×D511yescharacteristic
303C2×C4×D3—21no—
304C2×Dic6—52no—
305C2×Dic6—102no—
306C2×Dic6—102no—
307C2×Dic6—101no—
308C2×Dic6C22×D511yescharacteristic
309C3×C4⋊C4—52no—
310C3×C22⋊C4—52no—
311C3×C22⋊C4—104no—
312C3×C42—52no—
313#216—102no—
314#216—104no—
315#215—102no—
316#214—24no—
317#214—102no—
318#214—104no—
319#214—104no—
320#214—104no—
321#213—24no—
322#213—102no—
323(C2×D3)⋊C4—104no—
324C4⋊Dic3—104no—
325#208C22⋊D514yescomplemented
326C2×C3⋊C8—54no—
327C2×C3⋊C8—51no—
328C2×C3⋊C8—51no—
329C2×C3⋊C8C22×D512yes—
330C23×C5—22no—
331C23×C5—42no—
332C23×C5—61no—
333C23×C5—82no—
334C23×C5C2×#6711yescharacteristic
335C22×D5—21no—
336C5×Q8—61no—
337C5×Q8—61no—
338C5×D4—22no—
339C5×D4—22no—
340C5×D4—42no—
341C5×D4—61no—
342C5×D4—61no—
343C5×D4—122no—
344C2×C4×C5—61no—
345C2×C4×C5—122no—
346C2×C4×C5D3×D412yes—
347C2×C4×C5D3×D412yes—
348C2×C4×C5C2×#6711yescharacteristic
349C2×C4×C5C23×D311yescharacteristic
350C22⋊D5—42no—
351C22⋊D5—84no—
352C2×Dic5—21no—
353C2×Dic5—62no—
354C2×Dic5—122no—
355C2×Dic5C2×#6714yes—
356D20—21no—
357D20—21no—
358C4×D5—42no—
359Dic10—21no—
360Dic10—21no—
361Dic10—62no—
362Dic10—62no—
363Dic10—122no—
364C5×C8—34no—
365#168—32no—
366#168—32no—
367C2×#41—31no—
368C2×#41—51no—
369C22×Q8—151no—
370C22×D4D3×D511yescharacteristic
371#137—304no—
372AGL(1,ℤ/8)—64no—
373#135—304no—
374C2×Q16—152no—
375C2×Q16—151no—
376C2×SD16—32no—
377C2×SD16—152no—
378C2×SD16—151no—
379C2×SD16—151no—
380C2×SD16—152no—
381C2×SD16—152no—
382C2×SD16—304no—
383C2×D8—32no—
384C2×D8—151no—
385C2×M16—31no—
386C22×C8—151no—
387C4⋊Q8—152no—
388#127—52no—
389#124—52no—
390#124—152no—
391#123—302no—
392C22⋊Q8—302no—
393#121—102no—
394#120—102no—
395#117—51no—
396#97—152no—
397C4×C8—152no—
398C2×C3×C5—22no—
399C2×C3×C5—82no—
400C2×C3×C5C2×#12711yescharacteristic
401C2×C3×C5#57712yes—
402C3×D5—81no—
403C5×D3—81no—
404C23×C3—22no—
405C23×C3—42no—
406C23×C3—82no—
407C23×C3—101no—
408C23×C3D4×D511yescharacteristic
409C22×D3—21no—
410C3×Q8—101no—
411C3×Q8—101no—
412C3×D4—22no—
413C3×D4—22no—
414C3×D4—42no—
415C3×D4—101no—
416C3×D4—101no—
417C3×D4—202no—
418C3×D4—404no—
419C2×C3×C4—54no—
420C2×C3×C4—101no—
421C2×C3×C4—202no—
422C2×C3×C4D4×D511yescharacteristic
423C2×C3×C4D4×D512yes—
424C2×C3×C4C2×C22⋊D512yes—
425C2×C3×C4C23×D511yescharacteristic
426#67—42no—
427C2×Dic3—21no—
428C2×Dic3—102no—
429C2×Dic3—202no—
430D12—21no—
431D12—21no—
432C4×D3—42no—
433Dic6—21no—
434Dic6—21no—
435Dic6—102no—
436Dic6—102no—
437Dic6—202no—
438C3⋊C8—52no—
439C3⋊C8—52no—
440C3⋊C8C2×C22⋊D514yes—
441C22×C5—22no—
442C22×C5—42no—
443C22×C5—44no—
444C22×C5—84no—
445C22×C5—121no—
446C22×C5—122no—
447C22×C5#94012yes—
448C22×C5C22×#6711yescharacteristic
449C2×D5—41no—
450C2×D5—42no—
451C4×C5—121no—
452C4×C5#94012yes—
453C4×C5C2×D3×D411yescharacteristic
454C4×C5C2×D3×D411yescharacteristic
455Dic5—24no—
456Dic5—41no—
457Dic5—122no—
458C24—21no—
459#41—62no—
460#41—62no—
461#41—102no—
462#41—102no—
463C2×Q8—31no—
464C2×Q8—51no—
465C2×Q8—152no—
466C2×Q8—301no—
467C2×Q8—302no—
468C2×Q8—302no—
469C2×D4—21no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—31no—
473C2×D4—51no—
474C2×D4—61no—
475C2×D4—104no—
476C2×D4—101no—
477C2×D4C2×D3×D512yes—
478C22×C4—61no—
479C22×C4—101no—
480C22×C4—301no—
481C22×C4C2×D3×D511yescharacteristic
482Q16—304no—
483Q16—302no—
484SD16—64no—
485SD16—304no—
486SD16—304no—
487SD16—304no—
488SD16—302no—
489SD16—302no—
490D8—64no—
491D8—302no—
492M16—34no—
493C2×C8—32no—
494C2×C8—154no—
495C2×C8—151no—
496C2×C8—151no—
497C4⋊C4—52no—
498C4⋊C4—304no—
499C22⋊C4—52no—
500C22⋊C4—104no—
501C22⋊C4—304no—
502C42—52no—
503C3×C5#315411yescharacteristic, complemented, Hall
504C22×C3—22no—
505C22×C3—44no—
506C22×C3—42no—
507C22×C3—84no—
508C22×C3—202no—
509C22×C3—201no—
510C22×C3#408612yes—
511C22×C3C2×D4×D511yescharacteristic
512C2×D3—42no—
513C2×D3—41no—
514C3×C4—104no—
515C3×C4—201no—
516C3×C4#408612yes—
517C3×C4C2×D4×D511yescharacteristic
518C3×C4C22×C22⋊D511yescharacteristic
519Dic3—41no—
520Dic3—202no—
521C2×C5—22no—
522C2×C5—82no—
523C2×C5—241no—
524C2×C5C2×#94011yescharacteristic
525C2×C5#583612yes—
526D5—81no—
527C23—22no—
528C23—42no—
529C23—61no—
530C23—82no—
531C23—101no—
532C23D5×#6711yescharacteristic
533Q8—61no—
534Q8—61no—
535Q8—101no—
536Q8—101no—
537Q8—302no—
538Q8—302no—
539Q8—602no—
540D4—22no—
541D4—22no—
542D4—42no—
543D4—61no—
544D4—61no—
545D4—101no—
546D4—101no—
547D4—122no—
548D4—202no—
549D4—404no—
550C2×C4—54no—
551C2×C4—61no—
552C2×C4—101no—
553C2×C4—122no—
554C2×C4—202no—
555C2×C4—302no—
556C2×C4—602no—
557C2×C4D5×#6711yescharacteristic
558C2×C4D3×C22⋊D512yes—
559C2×C4#679012yes—
560C2×C4C22×D3×D511yescharacteristic
561C8—34no—
562C8—152no—
563C8—152no—
564C2×C3—22no—
565C2×C3—82no—
566C2×C3—401no—
567C2×C3#6610912yes—
568C2×C3C2×#408611yescharacteristic
569D3—81no—
570C5#8338111yescharacteristic, complemented, Sylow
571C22—22no—
572C22—42no—
573C22—44no—
574C22—84no—
575C22—121no—
576C22—122no—
577C22—201no—
578C22—202no—
579C22#9156712yes—
580C22C2×D5×#6711yescharacteristic
581C4—104no—
582C4—121no—
583C4—201no—
584C4—602no—
585C4#9156712yes—
586C4C2×D3×C22⋊D511yescharacteristic
587C4C2×#679011yescharacteristic
588C3#1061567011yescharacteristic, complemented, Sylow
589C2—22no—
590C2—82no—
591C2—241no—
592C2—401no—
593C2#1175470812yes—
594C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3154
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6716C2semidirect
2. C2×C5×#932C2semidirect
3. C3×#66139C2semidirect
4. #11754271C2semidirect
5. C2×#91313C2semidirect
6. C2×#91297C2semidirect
7. #11749107C2semidirect
8. #11749106C2semidirect
9. #11749067C2semidirect
10. #11749066C2semidirect
11. #11748320C2semidirect
31. #91376C22semidirect
32. #91373C22semidirect
34. C2×#6662C22semidirect
35. C2×#6661C22semidirect
37. C2×#6657C22semidirect
38. C2×#6656C22semidirect
39. C2×#6655C22semidirect
41. C2×#6652C22semidirect
42. #90952C22semidirect
43. Dic5×C3⋊C8C22semidirect
48. #66139D3semidirect
82. C2×C3⋊#168D4semidirect
87. C5×#208D4semidirect
105. C2×#932D5semidirect
325. #208C22⋊D5semidirect
503. C3×C5#3154semidirect
570. C5#83381semidirect
588. C3#10615670semidirect

Maximal subgroups

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

subgroupindex
C22×#67162
C2×C5×#9322
C3×#661392
#117542712
C2×#913132
C2×#912972
#117491072
#117491062
#117490672
#117490662
#117483202
#106156703
#833815