Finite Group Databasebeta

← #14439330

Subgroups — #14439330

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91821C211yesmaximal, characteristic, complemented
2C2×C5×#932C211yesmaximal, characteristic, complemented
3C2×C3×#4082C211yesmaximal, characteristic, complemented
4#11754572C211yesmaximal, characteristic, complemented
5C2×#91315C211yesmaximal, characteristic, complemented
6C2×#91309C211yesmaximal, characteristic, complemented
7#11749107C212yesmaximal, complemented
8#11749094C212yesmaximal, complemented
9#11749070C212yesmaximal, complemented
10#11749067C212yesmaximal, complemented
11Dic5×#208C211yesmaximal, characteristic, complemented
12#10615669—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17C2×#6716C2212yes—
18#91821—24no—
19C2×#6715C2212yes—
20C2×#6710C2211yescharacteristic
21C2×C5×#214C2212yes—
22C5×#932—24no—
23C2×C5×#213C2212yes—
24C2×C5×#208C2211yescharacteristic
25C2×C3×C22⋊Dic5—22no—
26C3×#4082—22no—
27C3×#4082C2212yes—
28C3×#4082C2212yes—
29C2×C3×C4×Dic5C2211yescharacteristic
30#91566—22no—
31#91451C2211yescharacteristic, complemented
32C4×#1203—22no—
33#91376C2211yescharacteristic, complemented
34#91375C2211yescharacteristic, complemented
35#91373C2211yescharacteristic, complemented
36C2×#6662C2212yescomplemented
37C2×#6661C2212yescomplemented
38#91315—24no—
39C2×#6658C2212yescomplemented
40#91309—24no—
41C2×#6656C2212yescomplemented
42#90952C2212yescomplemented
43Dic5×C3⋊C8C2212yescomplemented
44#82943—51nomaximal, Hall
45C2×C5×AGL(1,ℤ/8)—31no—
46#66166—31no—
47C2×#4097—31no—
48C2×#4082D311yescharacteristic, complemented
49C2×#4078—31no—
50C2×#4055—31no—
51#65457—32no—
52#65456—32no—
53#65444—32no—
54#65443—32no—
55M16×Dic5—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
62C2×#1220—21no—
63#6817—22no—
64#6817—22no—
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C2×Dic30C2311yescharacteristic
68C2×C5×#67—21no—
69C5×#235—22no—
70C5×#235—22no—
71C2×C5×D12C2311yescharacteristic
72C2×C4×C5×D3—21no—
73C2×C5×Dic6C2311yescharacteristic
74C22×C3×Dic5—21no—
75C22×C3×Dic5D412yes—
76C2×C3×Dic10—22no—
77C2×C3×Dic10—22no—
78C2×C3×Dic10—21no—
79C2×C3×Dic10C2312yes—
80C2×#1203—22no—
81#6716—24no—
82#6715—24no—
83#6710D414yescomplemented
84C2×C3⋊#168C2312yes—
85C5×#214—24no—
86C5×#213—24no—
87C5×#208D414yescomplemented
88C2×C5×C3⋊C8C2312yes—
89C3×C22⋊Dic5—24no—
90C3×C22⋊Dic5—24no—
91C3×C4×Dic5D412yes—
92C3×C4×Dic5C2311yescharacteristic
93C3×C4×Dic5C2311yescharacteristic
94#6668—22no—
95#6667—22no—
96(C2×D3)⋊Dic5—22no—
97#6662—24no—
98#6661—24no—
99#6658—24no—
100#6656—24no—
101C2×C3×#124—51no—
102C2×#942—51no—
103C2×#942—51no—
104C2×#932—51no—
105C2×#932D511yescharacteristic, complemented
106#5477—51no—
107#5060—52no—
108#5059—52no—
109#5059—52no—
110#5058—52no—
111C4×#208—51no—
112C2×C5×#41—31no—
113C22×C5×D4C2×D311yescharacteristic
114C2×#709—31no—
115C22×Dic10C2×D311yescharacteristic
116C5×AGL(1,ℤ/8)—64no—
117C2×C5×SD16—32no—
118C2×C5×D8—32no—
119C2×C5×M16—31no—
120C2×C22⋊Dic5—22no—
121#4097—64no—
122#4093—31no—
123#4090—31no—
124C2×#689—32no—
125#4086—31no—
126#4085—62no—
127#4082—22no—
128#4082—31no—
129#4082C2×D312yes—
130#4082C2×D312yes—
131C2×#687—32no—
132C2×#687—32no—
133#4078—64no—
134C2×#686—32no—
135C4×C22⋊D5—62no—
136C2×C4×Dic5C2×D311yescharacteristic
137C2×#681—31no—
138#4055—64no—
139C2×Dic20—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3153—151noSylow
144C23×C3×C5—22no—
145C23×C3×C5—44no—
146C23×C3×C5—42no—
147C23×C3×C5C2×D411yescharacteristic
148C22×D15—21no—
149C22×C5×D3—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
157#1220—42no—
158C2×Dic15—21no—
159D60—21no—
160D60—21no—
161C4×D15—42no—
162Dic30—21no—
163Dic30—21no—
164C5×#67—42no—
165C2×C5×Dic3—21no—
166C5×D12—21no—
167C5×D12—21no—
168C4×C5×D3—42no—
169C5×Dic6—21no—
170C5×Dic6—21no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—42no—
173C2×C3×Dic5—42no—
174C2×C3×Dic5C2×D412yes—
175C2×C3×Dic5C2×D412yes—
176C3×Dic10—22no—
177C3×Dic10—22no—
178C3×Dic10—42no—
179#1203—44no—
180C3⋊#168C2×D414yes—
181C5×C3⋊C8C2×D414yes—
182C22×C3×Q8—51no—
183C22×C3×D4C2×D511yescharacteristic
184C2×#235—51no—
185C2×#235C2×D511yescharacteristic
186C3×#124—52no—
187C3×#124—52no—
188C3×#124—102no—
189C2×C3×C22⋊C4—102no—
190C2×C3×C42—51no—
191C2×#216—52no—
192C2×#216—52no—
193#942—104no—
194#942—104no—
195C2×#215—52no—
196C2×#215—52no—
197C2×#214—52no—
198C2×#214C2×D512yes—
199#932—24no—
200#932—104no—
201C2×#213—52no—
202C2×#213C2×D512yes—
203#930—102no—
204C2×#208—51no—
205C2×#208C2×D511yescharacteristic
206#875—51no—
207#875—51no—
208#874—51no—
209C4×D12—102no—
210#869—51no—
211#803—52no—
212C4×C3⋊C8—52no—
213C24×C5—21no—
214C5×#41—62no—
215C5×#41—62no—
216C2×C5×Q8—31no—
217C2×C5×D4—22no—
218C2×C5×D4—22no—
219C2×C5×D4—21no—
220C2×C5×D4—31no—
221C2×C5×D4—61no—
222C2×C5×D4C22×D312yes—
223C22×C4×C5—61no—
224C22×C4×C5C22×D311yescharacteristic
225C2×C22⋊D5—61no—
226C2×C22⋊D5—62no—
227C22×Dic5—21no—
228C22×Dic5#6712yes—
229#709—62no—
230#709—62no—
231C2×D20—31no—
232C2×C4×D5—61no—
233C2×Dic10—22no—
234C2×Dic10—22no—
235C2×Dic10—21no—
236C2×Dic10—31no—
237C2×Dic10C22×D312yes—
238C5×SD16—64no—
239C5×D8—64no—
240C5×M16—34no—
241C2×C5×C8—32no—
242C22⋊Dic5—24no—
243C22⋊Dic5—24no—
244C22⋊Dic5—62no—
245#689—64no—
246#687—64no—
247#687—64no—
248#686—64no—
249#685—62no—
250#683—62no—
251C4×Dic5#6712yes—
252C4×Dic5C22×D311yescharacteristic
253C4×Dic5C22×D311yescharacteristic
254#681—34no—
255C2×#168—32no—
256Dic20—64no—
257#677—64no—
258C2×#137—151no—
259C2×#137—151no—
260C2×AGL(1,ℤ/8)—31no—
261C2×AGL(1,ℤ/8)—151no—
262#532—151no—
263C2×#124—51no—
264#497—152no—
265#496—152no—
266#495—152no—
267#495—152no—
268C4×M16—151no—
269C22×C3×C5—22no—
270C22×C3×C5—42no—
271C22×C3×C5—44no—
272C22×C3×C5—84no—
273C22×C3×C5#12712yes—
274C22×C3×C5C22×D411yescharacteristic
275C2×D15—41no—
276C2×D15—42no—
277C2×C5×D3—41no—
278C2×C5×D3—42no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—41no—
283C3×Dic5—22no—
284C3×Dic5—22no—
285C3×Dic5—42no—
286C5×Dic3—41no—
287C24×C3—21no—
288C2×C3×Q8—52no—
289C2×C3×Q8—101no—
290C2×C3×Q8—102no—
291C2×C3×Q8—102no—
292C2×C3×D4—22no—
293C2×C3×D4—21no—
294C2×C3×D4—22no—
295C2×C3×D4C22×D512yes—
296C22×C3×C4—52no—
297C22×C3×C4—101no—
298C22×C3×C4C22×D511yescharacteristic
299C2×#67—21no—
300C2×#67—101no—
301#235—22no—
302#235—22no—
303#235—102no—
304#235—102no—
305C2×D12—51no—
306C2×D12—102no—
307C2×D12C22×D511yescharacteristic
308C2×C4×D3—21no—
309C2×C4×D3—101no—
310C2×Dic6—51no—
311C2×Dic6C22×D511yescharacteristic
312C3×C22⋊C4—104no—
313C3×C22⋊C4—104no—
314C3×C42—52no—
315C3×C42—51no—
316C3×C42—51no—
317#216—104no—
318#216—104no—
319#215—104no—
320#215—104no—
321#214—24no—
322#214—104no—
323#213—24no—
324#213—104no—
325(C2×D3)⋊C4—102no—
326(C2×D3)⋊C4—102no—
327C4⋊Dic3—102no—
328#208—54no—
329#208C22⋊D514yescomplemented
330C2×C3⋊C8—52no—
331C2×C3⋊C8C22×D512yes—
332C23×C5—22no—
333C23×C5—44no—
334C23×C5—42no—
335C23×C5—61no—
336C23×C5C2×#6711yescharacteristic
337C22×D5—61no—
338C5×Q8—61no—
339C5×Q8—61no—
340C5×D4—22no—
341C5×D4—22no—
342C5×D4—42no—
343C5×D4—61no—
344C5×D4—61no—
345C5×D4—122no—
346C2×C4×C5—61no—
347C2×C4×C5—122no—
348C2×C4×C5D3×D412yes—
349C2×C4×C5D3×D412yes—
350C2×C4×C5C2×#6711yescharacteristic
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—124no—
353C22⋊D5—122no—
354C2×Dic5—22no—
355C2×Dic5—42no—
356C2×Dic5—42no—
357C2×Dic5—61no—
358C2×Dic5C2×#6712yes—
359C2×Dic5C2×#6712yes—
360D20—61no—
361D20—61no—
362C4×D5—122no—
363Dic10—22no—
364Dic10—22no—
365Dic10—42no—
366Dic10—61no—
367Dic10—61no—
368C5×C8—34no—
369#168—34no—
370C2×#41—31no—
371C2×#41—151no—
372C22×Q8—51no—
373C22×D4D3×D511yescharacteristic
374#137—304no—
375#137—304no—
376AGL(1,ℤ/8)—64no—
377AGL(1,ℤ/8)—304no—
378C2×Q16—152no—
379C2×Q16—152no—
380C2×SD16—32no—
381C2×SD16—152no—
382C2×SD16—152no—
383C2×SD16—152no—
384C2×D8—32no—
385C2×D8—152no—
386C2×M16—31no—
387C2×M16—151no—
388C4⋊Q8—151no—
389#127—151no—
390#124—52no—
391#124—52no—
392#124—102no—
393#124—151no—
394#124—151no—
395#121—302no—
396C4×D4—302no—
397C2×C22⋊C4—102no—
398C2×C42—51no—
399#97—152no—
400C4×C8—152no—
401C2×C3×C5—22no—
402C2×C3×C5—82no—
403C2×C3×C5C2×#12711yescharacteristic
404C2×C3×C5#57512yes—
405D15—81no—
406C5×D3—81no—
407C23×C3—22no—
408C23×C3—44no—
409C23×C3—42no—
410C23×C3D4×D511yescharacteristic
411C22×D3—21no—
412C22×D3—101no—
413C3×Q8—102no—
414C3×Q8—102no—
415C3×Q8—202no—
416C3×D4—22no—
417C3×D4—22no—
418C3×D4—42no—
419C2×C3×C4—52no—
420C2×C3×C4—52no—
421C2×C3×C4—102no—
422C2×C3×C4—202no—
423C2×C3×C4—202no—
424C2×C3×C4D4×D511yescharacteristic
425C2×C3×C4D4×D512yes—
426C2×C3×C4C2×C22⋊D512yes—
427C2×C3×C4C23×D511yescharacteristic
428#67—42no—
429#67—202no—
430C2×Dic3—21no—
431C2×Dic3—101no—
432D12—21no—
433D12—21no—
434D12—101no—
435D12—101no—
436D12—204no—
437C4×D3—42no—
438C4×D3—202no—
439Dic6—21no—
440Dic6—21no—
441Dic6—101no—
442Dic6—101no—
443C3⋊C8—54no—
444C3⋊C8C2×C22⋊D514yes—
445C22×C5—22no—
446C22×C5—42no—
447C22×C5—44no—
448C22×C5—84no—
449C22×C5—121no—
450C22×C5—122no—
451C22×C5#94012yes—
452C22×C5C22×#6711yescharacteristic
453C2×D5—121no—
454C2×D5—122no—
455C4×C5—121no—
456C4×C5#94012yes—
457C4×C5C2×D3×D411yescharacteristic
458C4×C5C2×D3×D411yescharacteristic
459Dic5—22no—
460Dic5—22no—
461Dic5—42no—
462Dic5—121no—
463C24—21no—
464#41—62no—
465#41—62no—
466#41—302no—
467#41—302no—
468C2×Q8—31no—
469C2×Q8—52no—
470C2×Q8—101no—
471C2×Q8—102no—
472C2×Q8—102no—
473C2×Q8—151no—
474C2×D4—21no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—31no—
478C2×D4—61no—
479C2×D4—151no—
480C2×D4—302no—
481C2×D4—301no—
482C2×D4C2×D3×D512yes—
483C22×C4—52no—
484C22×C4—61no—
485C22×C4—101no—
486C22×C4—301no—
487C22×C4C2×D3×D511yescharacteristic
488Q16—304no—
489Q16—304no—
490SD16—64no—
491SD16—304no—
492SD16—304no—
493SD16—304no—
494D8—64no—
495D8—304no—
496M16—34no—
497M16—154no—
498C2×C8—32no—
499C2×C8—152no—
500C4⋊C4—302no—
501C22⋊C4—104no—
502C22⋊C4—104no—
503C22⋊C4—302no—
504C22⋊C4—302no—
505C42—52no—
506C42—51no—
507C42—51no—
508C3×C5#315311yescharacteristic, complemented, Hall
509C22×C3—22no—
510C22×C3—44no—
511C22×C3—42no—
512C22×C3—84no—
513C22×C3#408612yes—
514C22×C3C2×D4×D511yescharacteristic
515C2×D3—42no—
516C2×D3—41no—
517C2×D3—202no—
518C2×D3—201no—
519C3×C4—102no—
520C3×C4—102no—
521C3×C4—202no—
522C3×C4#408612yes—
523C3×C4C2×D4×D511yescharacteristic
524C3×C4C22×C22⋊D511yescharacteristic
525Dic3—41no—
526Dic3—201no—
527C2×C5—22no—
528C2×C5—82no—
529C2×C5—241no—
530C2×C5C2×#94011yescharacteristic
531C2×C5#582212yes—
532D5—241no—
533C23—22no—
534C23—44no—
535C23—42no—
536C23—61no—
537C23—301no—
538C23D5×#6711yescharacteristic
539Q8—61no—
540Q8—61no—
541Q8—102no—
542Q8—102no—
543Q8—202no—
544Q8—301no—
545Q8—301no—
546D4—22no—
547D4—22no—
548D4—42no—
549D4—61no—
550D4—61no—
551D4—122no—
552D4—301no—
553D4—301no—
554D4—604no—
555D4—602no—
556C2×C4—52no—
557C2×C4—52no—
558C2×C4—61no—
559C2×C4—102no—
560C2×C4—122no—
561C2×C4—202no—
562C2×C4—202no—
563C2×C4—301no—
564C2×C4—602no—
565C2×C4D5×#6711yescharacteristic
566C2×C4D3×C22⋊D512yes—
567C2×C4#679012yes—
568C2×C4C22×D3×D511yescharacteristic
569C8—34no—
570C8—154no—
571C2×C3—22no—
572C2×C3—82no—
573C2×C3#6610712yes—
574C2×C3C2×#408611yescharacteristic
575D3—81no—
576D3—401no—
577C5#8294311yescharacteristic, complemented, Sylow
578C22—22no—
579C22—42no—
580C22—44no—
581C22—84no—
582C22—121no—
583C22—122no—
584C22—601no—
585C22—602no—
586C22#9156712yes—
587C22C2×D5×#6711yescharacteristic
588C4—102no—
589C4—102no—
590C4—121no—
591C4—202no—
592C4—601no—
593C4#9156712yes—
594C4C2×D3×C22⋊D511yescharacteristic
595C4C2×#679011yescharacteristic
596C3#1061566911yescharacteristic, complemented, Sylow
597C2—22no—
598C2—82no—
599C2—241no—
600C2—1201no—
601C2#1175469012yes—
602C2C2×#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#3153
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. C2×#91821C2semidirect
2. C2×C5×#932C2semidirect
3. C2×C3×#4082C2semidirect
4. #11754572C2semidirect
5. C2×#91315C2semidirect
6. C2×#91309C2semidirect
7. #11749107C2semidirect
8. #11749094C2semidirect
9. #11749070C2semidirect
10. #11749067C2semidirect
11. Dic5×#208C2semidirect
31. #91451C22semidirect
33. #91376C22semidirect
34. #91375C22semidirect
35. #91373C22semidirect
36. C2×#6662C22semidirect
37. C2×#6661C22semidirect
39. C2×#6658C22semidirect
41. C2×#6656C22semidirect
42. #90952C22semidirect
43. Dic5×C3⋊C8C22semidirect
48. C2×#4082D3semidirect
83. #6710D4semidirect
87. C5×#208D4semidirect
105. C2×#932D5semidirect
329. #208C22⋊D5semidirect
508. C3×C5#3153semidirect
577. C5#82943semidirect
596. C3#10615669semidirect

Maximal subgroups

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

subgroupindex
C2×#918212
C2×C5×#9322
C2×C3×#40822
#117545722
C2×#913152
C2×#913092
#117491072
#117490942
#117490702
#117490672
Dic5×#2082
#106156693
#829435