Finite Group Databasebeta

← #14439350

Subgroups — #14439350

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×#91838C211yesmaximal, characteristic, complemented
2C2×C5×#951C211yesmaximal, characteristic, complemented
3C3×#66166C211yesmaximal, characteristic, complemented
4C2×#91375C211yesmaximal, characteristic, complemented
5C2×#91307C211yesmaximal, characteristic, complemented
6C2×#91301C211yesmaximal, characteristic, complemented
7#11749316C212yesmaximal, complemented
8#11749315C212yesmaximal, complemented
9#11749070C212yesmaximal, complemented
10#11749069C212yesmaximal, complemented
11Dic5×#208C211yesmaximal, characteristic, complemented
12#10615704—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C2×C3×#709C2211yescharacteristic
17#91838—24no—
18C2×#6717C2212yes—
19C2×#6715C2212yes—
20C2×#6710C2211yescharacteristic
21C5×#951—24no—
22C2×C5×#216C2212yescomplemented
23C2×C5×#214C2212yescomplemented
24C2×C5×#208C2211yescharacteristic
25C3×#4093C2211yescharacteristic, complemented
26C3×#4090C2211yescharacteristic, complemented
27C3×#4086C2211yescharacteristic, complemented
28C3×#4085—22no—
29C3×#4082C2211yescharacteristic, complemented
30C3×C4×C22⋊D5—22no—
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×#6667—22no—
33#91375—22no—
34#91375C2212yes—
35#91375C2212yes—
36C2×#6661C2212yescomplemented
37C2×#6658C2212yes—
38#91307—24no—
39C2×#6655C2212yescomplemented
40#91301—24no—
41C2×#6653C2212yes—
42#90952C2212yescomplemented
43Dic5×C3⋊C8C2212yescomplemented
44#83289—51nomaximal, Hall
45C2×C5×#137—31no—
46#66166D311yescharacteristic, complemented
47C2×#4095—31no—
48C2×#4093—31no—
49C2×#4088—31no—
50C2×#4054—31no—
51#65480—32no—
52#65479—32no—
53#65465—32no—
54#65457—32no—
55M16×Dic5—31no—
56C23×D15—21no—
57C3×C5×#41—22no—
58C3×C5×#41—22no—
59C2×C3×C5×Q8C2311yescharacteristic
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2311yescharacteristic
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5C2311yescharacteristic
64C2×D60—22no—
65C2×D60—22no—
66C2×D60—21no—
67C2×D60C2312yes—
68C22×C5×Dic3—21no—
69C2×C5×Dic6—22no—
70C2×C5×Dic6—22no—
71C2×C5×Dic6—21no—
72C2×C5×Dic6C2312yes—
73C2×C3×C22⋊D5—21no—
74C2×C3×C22⋊D5—22no—
75C22×C3×Dic5D412yes—
76C3×#709—22no—
77C3×#709—22no—
78C2×C3×D20C2311yescharacteristic
79C2×C3×C4×D5—21no—
80C2×C3×Dic10C2311yescharacteristic
81#6717—24no—
82#6715—24no—
83#6710D414yescomplemented
84C2×C3⋊#168C2312yes—
85C5×#216—24no—
86C5×#214—24no—
87C5×#208D414yescomplemented
88C2×C5×C3⋊C8C2312yes—
89C3×C22⋊Dic5—22no—
90C3×#685—22no—
91C3×#683—22no—
92C3×C4×Dic5D412yes—
93C3×C4×Dic5C2311yescharacteristic
94C3×C4×Dic5C2311yescharacteristic
95#6667—24no—
96#6667—24no—
97#6661—24no—
98#6658—24no—
99#6655—24no—
100#6653—24no—
101C3×#532—51no—
102C2×#951—51no—
103C2×#951D511yescharacteristic, complemented
104C2×#949—51no—
105C2×#949—51no—
106C2×#875—51no—
107#5086—52no—
108#5074—52no—
109#5059—52no—
110#5059—52no—
111C4×#208—51no—
112C2×C5×#41C2×D311yescharacteristic
113C22×C5×Q8—31no—
114C2×#709C2×D311yescharacteristic
115C22×D20—31no—
116C5×#137—64no—
117C2×C5×Q16—32no—
118C2×C5×SD16—32no—
119C2×C5×M16—31no—
120#4095—64no—
121#4093—32no—
122#4093—32no—
123#4093—62no—
124#4093C2×D311yescharacteristic, complemented
125#4090C2×D311yescharacteristic, complemented
126C2×#689—32no—
127#4088—64no—
128C2×#688—32no—
129C2×#688—32no—
130#4086C2×D311yescharacteristic, complemented
131#4085—22no—
132#4082C2×D311yescharacteristic, complemented
133C2×#686—32no—
134C4×C22⋊D5—22no—
135C2×#685—62no—
136C2×C4×Dic5C2×D311yescharacteristic
137C2×#681—31no—
138#4054—64no—
139C2×D40—32no—
140C2×#677—32no—
141#3947—32no—
142C8×Dic5—32no—
143#3153—151noSylow
144C23×C3×C5—21no—
145C23×C3×C5C2×D411yescharacteristic
146C22×D15—22no—
147C22×D15—44no—
148C22×D15—42no—
149C22×C3×D5—21no—
150C3×C5×Q8—21no—
151C3×C5×Q8—21no—
152C3×C5×D4—21no—
153C3×C5×D4—21no—
154C3×C5×D4—42no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—42no—
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5C2411yescharacteristic
161D60—22no—
162D60—22no—
163D60—42no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3—42no—
166C5×Dic6—22no—
167C5×Dic6—22no—
168C5×Dic6—42no—
169C3×C22⋊D5—44no—
170C3×C22⋊D5—42no—
171C2×C3×Dic5—21no—
172C2×C3×Dic5—42no—
173C2×C3×Dic5C2×D412yes—
174C2×C3×Dic5C2×D412yes—
175C3×D20—21no—
176C3×D20—21no—
177C3×C4×D5—42no—
178C3×Dic10—21no—
179C3×Dic10—21no—
180C3⋊#168C2×D414yes—
181C5×C3⋊C8C2×D414yes—
182C2×C3×#41—51no—
183C2×C3×#41C2×D511yescharacteristic
184C22×D12—51no—
185C22×Dic6C2×D511yescharacteristic
186C3×C4⋊Q8—51no—
187C3×#127—51no—
188C3×#124—51no—
189C3×#124—51no—
190C3×#121—102no—
191C3×C4×D4—102no—
192C2×C3×C42—51no—
193#951—24no—
194#951—104no—
195#949—104no—
196#949—104no—
197C2×#216—52no—
198C2×#216C2×D512yescomplemented
199C2×#215—52no—
200C2×#215—52no—
201C2×#214—52no—
202C2×#214C2×D512yescomplemented
203C2×#213—52no—
204C2×#213—52no—
205C2×(C2×D3)⋊C4—102no—
206C2×#208—51no—
207C2×#208C2×D511yescharacteristic
208#875—52no—
209#875—52no—
210#875—102no—
211#803—52no—
212C4×C3⋊C8—52no—
213C23×D5—61no—
214C5×#41—22no—
215C5×#41—22no—
216C2×C5×Q8—32no—
217C2×C5×Q8—61no—
218C2×C5×Q8—62no—
219C2×C5×Q8—62no—
220C2×C5×Q8C22×D311yescharacteristic
221C2×C5×D4—21no—
222C2×C5×D4C22×D311yescharacteristic
223C22×C4×C5—21no—
224C22×C4×C5—61no—
225C22×C4×C5C22×D311yescharacteristic
226C2×C22⋊D5—21no—
227C2×C22⋊D5—22no—
228C22×Dic5#6712yes—
229#709—22no—
230#709—22no—
231C2×D20—32no—
232C2×D20—62no—
233C2×D20—62no—
234C2×D20—61no—
235C2×D20C22×D311yescharacteristic
236C2×C4×D5—21no—
237C2×Dic10C22×D311yescharacteristic
238C5×Q16—64no—
239C5×SD16—64no—
240C5×M16—34no—
241C2×C5×C8—32no—
242C22⋊Dic5—22no—
243#689—64no—
244#688—64no—
245#688—64no—
246#686—64no—
247#685—22no—
248#685—64no—
249#685—64no—
250#683—22no—
251C4×Dic5#6712yes—
252C4×Dic5C22×D311yescharacteristic
253C4×Dic5C22×D311yescharacteristic
254#681—34no—
255C2×#168—32no—
256D40—64no—
257#677—64no—
258C2×#137—31no—
259C2×#137—151no—
260C2×AGL(1,ℤ/8)—151no—
261C2×AGL(1,ℤ/8)—151no—
262#532—51no—
263C2×#124—151no—
264#497—152no—
265#496—152no—
266#495—152no—
267#495—152no—
268C4×M16—151no—
269C22×C3×C5—22no—
270C22×C3×C5—41no—
271C22×C3×C5—42no—
272C22×C3×C5#12712yes—
273C22×C3×C5C22×D411yescharacteristic
274C2×D15—42no—
275C2×D15—44no—
276C2×D15—84no—
277C2×C3×D5—41no—
278C2×C3×D5—42no—
279C3×C4×C5—41no—
280C3×C4×C5#12712yes—
281C3×C4×C5C22×D411yescharacteristic
282C3×C4×C5C22×D411yescharacteristic
283C3×Dic5—22no—
284C3×Dic5—22no—
285C3×Dic5—41no—
286C5×Dic3—42no—
287C23×D3—101no—
288C3×#41—22no—
289C3×#41—22no—
290C3×#41—102no—
291C3×#41—102no—
292C2×C3×Q8—51no—
293C2×C3×Q8C22×D511yescharacteristic
294C2×C3×D4—21no—
295C2×C3×D4—51no—
296C2×C3×D4—102no—
297C2×C3×D4—101no—
298C2×C3×D4C22×D511yescharacteristic
299C22×C3×C4—21no—
300C22×C3×C4—52no—
301C22×C3×C4—101no—
302C22×C3×C4C22×D511yescharacteristic
303C22×Dic3—21no—
304C2×D12—52no—
305C2×D12—102no—
306C2×D12—102no—
307C2×D12—101no—
308C2×Dic6—22no—
309C2×Dic6—22no—
310C2×Dic6—21no—
311C2×Dic6C22×D512yes—
312C3×C4⋊C4—102no—
313C3×C22⋊C4—102no—
314C3×C22⋊C4—102no—
315C3×C42—52no—
316C3×C42—51no—
317C3×C42—51no—
318#216—24no—
319#216—104no—
320#215—104no—
321#215—104no—
322#214—24no—
323#214—104no—
324#213—104no—
325#213—104no—
326(C2×D3)⋊C4—104no—
327(C2×D3)⋊C4—104no—
328#208—54no—
329#208C22⋊D514yescomplemented
330C2×C3⋊C8—52no—
331C2×C3⋊C8C22×D512yes—
332C23×C5—21no—
333C23×C5C2×#6711yescharacteristic
334C22×D5—21no—
335C22×D5—62no—
336C22×D5—124no—
337C22×D5—122no—
338C5×Q8—21no—
339C5×Q8—21no—
340C5×Q8—62no—
341C5×Q8—62no—
342C5×Q8—122no—
343C5×D4—21no—
344C5×D4—21no—
345C5×D4—42no—
346C2×C4×C5—21no—
347C2×C4×C5—42no—
348C2×C4×C5—62no—
349C2×C4×C5—122no—
350C2×C4×C5D3×D412yes—
351C2×C4×C5D3×D412yes—
352C2×C4×C5C2×#6711yescharacteristic
353C2×C4×C5C23×D311yescharacteristic
354C22⋊D5—44no—
355C22⋊D5—42no—
356C2×Dic5—21no—
357C2×Dic5—42no—
358C2×Dic5C2×#6712yes—
359C2×Dic5C2×#6712yes—
360D20—21no—
361D20—21no—
362D20—62no—
363D20—62no—
364D20—122no—
365C4×D5—42no—
366Dic10—21no—
367Dic10—21no—
368C5×C8—34no—
369#168—34no—
370C2×#41—51no—
371C2×#41D3×D511yescharacteristic
372C22×Q8—31no—
373C22×D4—151no—
374#137—64no—
375#137—304no—
376AGL(1,ℤ/8)—304no—
377AGL(1,ℤ/8)—304no—
378C2×Q16—32no—
379C2×Q16—152no—
380C2×SD16—32no—
381C2×SD16—152no—
382C2×SD16—152no—
383C2×SD16—152no—
384C2×D8—152no—
385C2×D8—152no—
386C2×M16—31no—
387C2×M16—151no—
388C4⋊Q8—51no—
389#127—51no—
390#124—51no—
391#124—51no—
392#124—152no—
393#124—152no—
394#124—302no—
395#121—102no—
396C4×D4—102no—
397C2×C22⋊C4—302no—
398C2×C42—51no—
399#97—152no—
400C4×C8—152no—
401C2×C3×C5—22no—
402C2×C3×C5—81no—
403C2×C3×C5C2×#12711yescharacteristic
404C2×C3×C5#57512yes—
405D15—82no—
406C3×D5—81no—
407C23×C3—21no—
408C23×C3—101no—
409C23×C3D4×D511yescharacteristic
410C22×D3—102no—
411C22×D3—204no—
412C22×D3—202no—
413C3×Q8—21no—
414C3×Q8—21no—
415C3×Q8—101no—
416C3×Q8—101no—
417C3×D4—21no—
418C3×D4—21no—
419C3×D4—42no—
420C3×D4—101no—
421C3×D4—101no—
422C3×D4—204no—
423C3×D4—202no—
424C2×C3×C4—21no—
425C2×C3×C4—42no—
426C2×C3×C4—52no—
427C2×C3×C4—52no—
428C2×C3×C4—101no—
429C2×C3×C4—202no—
430C2×C3×C4—202no—
431C2×C3×C4D4×D511yescharacteristic
432C2×C3×C4D4×D512yes—
433C2×C3×C4C2×C22⋊D512yes—
434C2×C3×C4C23×D511yescharacteristic
435C2×Dic3—22no—
436C2×Dic3—42no—
437D12—102no—
438D12—102no—
439D12—202no—
440Dic6—22no—
441Dic6—22no—
442Dic6—42no—
443C3⋊C8—54no—
444C3⋊C8C2×C22⋊D514yes—
445C22×C5—22no—
446C22×C5—41no—
447C22×C5—42no—
448C22×C5#94012yes—
449C22×C5C22×#6711yescharacteristic
450C2×D5—41no—
451C2×D5—42no—
452C2×D5—122no—
453C2×D5—124no—
454C2×D5—244no—
455C4×C5—41no—
456C4×C5—122no—
457C4×C5#94012yes—
458C4×C5C2×D3×D411yescharacteristic
459C4×C5C2×D3×D411yescharacteristic
460Dic5—22no—
461Dic5—22no—
462Dic5—41no—
463C24—301no—
464#41—22no—
465#41—22no—
466#41—102no—
467#41—102no—
468C2×Q8—32no—
469C2×Q8—51no—
470C2×Q8—61no—
471C2×Q8—62no—
472C2×Q8—62no—
473C2×Q8C2×D3×D511yescharacteristic
474C2×D4—21no—
475C2×D4—51no—
476C2×D4—102no—
477C2×D4—101no—
478C2×D4—152no—
479C2×D4—301no—
480C2×D4—302no—
481C2×D4—302no—
482C2×D4C2×D3×D511yescharacteristic
483C22×C4—21no—
484C22×C4—52no—
485C22×C4—61no—
486C22×C4—101no—
487C22×C4C2×D3×D511yescharacteristic
488Q16—64no—
489Q16—304no—
490SD16—64no—
491SD16—304no—
492SD16—304no—
493SD16—304no—
494D8—304no—
495D8—304no—
496M16—34no—
497M16—154no—
498C2×C8—32no—
499C2×C8—152no—
500C4⋊C4—102no—
501C22⋊C4—102no—
502C22⋊C4—102no—
503C22⋊C4—304no—
504C22⋊C4—304no—
505C42—52no—
506C42—51no—
507C42—51no—
508C3×C5#315311yescharacteristic, complemented, Hall
509C22×C3—22no—
510C22×C3—42no—
511C22×C3—41no—
512C22×C3—202no—
513C22×C3—201no—
514C22×C3#408612yes—
515C22×C3C2×D4×D511yescharacteristic
516C2×D3—204no—
517C2×D3—202no—
518C2×D3—404no—
519C3×C4—41no—
520C3×C4—102no—
521C3×C4—102no—
522C3×C4—201no—
523C3×C4#408612yes—
524C3×C4C2×D4×D511yescharacteristic
525C3×C4C22×C22⋊D511yescharacteristic
526Dic3—42no—
527C2×C5—22no—
528C2×C5—81no—
529C2×C5C2×#94011yescharacteristic
530C2×C5#582212yes—
531D5—81no—
532D5—242no—
533C23—21no—
534C23—101no—
535C23—302no—
536C23—604no—
537C23—602no—
538C23D5×#6711yescharacteristic
539Q8—21no—
540Q8—21no—
541Q8—62no—
542Q8—62no—
543Q8—101no—
544Q8—101no—
545Q8—122no—
546D4—21no—
547D4—21no—
548D4—42no—
549D4—101no—
550D4—101no—
551D4—204no—
552D4—202no—
553D4—302no—
554D4—302no—
555D4—602no—
556C2×C4—21no—
557C2×C4—42no—
558C2×C4—52no—
559C2×C4—52no—
560C2×C4—62no—
561C2×C4—101no—
562C2×C4—122no—
563C2×C4—202no—
564C2×C4—202no—
565C2×C4D5×#6711yescharacteristic
566C2×C4D3×C22⋊D512yes—
567C2×C4#679012yes—
568C2×C4C22×D3×D511yescharacteristic
569C8—34no—
570C8—154no—
571C2×C3—22no—
572C2×C3—81no—
573C2×C3—401no—
574C2×C3#6611112yes—
575C2×C3C2×#408611yescharacteristic
576D3—402no—
577C5#8328911yescharacteristic, complemented, Sylow
578C22—22no—
579C22—42no—
580C22—41no—
581C22—202no—
582C22—201no—
583C22—604no—
584C22—602no—
585C22—1204no—
586C22#9156712yes—
587C22C2×D5×#6711yescharacteristic
588C4—41no—
589C4—102no—
590C4—102no—
591C4—122no—
592C4—201no—
593C4#9156712yes—
594C4C2×D3×C22⋊D511yescharacteristic
595C4C2×#679011yescharacteristic
596C3#1061570411yescharacteristic, complemented, Sylow
597C2—22no—
598C2—81no—
599C2—401no—
600C2—1202no—
601C2#1175534412yes—
602C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3153
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
1. C2×#91838C2semidirect
2. C2×C5×#951C2semidirect
3. C3×#66166C2semidirect
4. C2×#91375C2semidirect
5. C2×#91307C2semidirect
6. C2×#91301C2semidirect
7. #11749316C2semidirect
8. #11749315C2semidirect
9. #11749070C2semidirect
10. #11749069C2semidirect
11. Dic5×#208C2semidirect
22. C2×C5×#216C22semidirect
23. C2×C5×#214C22semidirect
25. C3×#4093C22semidirect
26. C3×#4090C22semidirect
27. C3×#4086C22semidirect
29. C3×#4082C22semidirect
36. C2×#6661C22semidirect
39. C2×#6655C22semidirect
42. #90952C22semidirect
43. Dic5×C3⋊C8C22semidirect
46. #66166D3semidirect
83. #6710D4semidirect
87. C5×#208D4semidirect
103. C2×#951D5semidirect
124. #4093C2×D3semidirect
125. #4090C2×D3semidirect
130. #4086C2×D3semidirect
132. #4082C2×D3semidirect
198. C2×#216C2×D5semidirect
202. C2×#214C2×D5semidirect
329. #208C22⋊D5semidirect
508. C3×C5#3153semidirect
577. C5#83289semidirect
596. C3#10615704semidirect

Maximal subgroups

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

subgroupindex
C2×#918382
C2×C5×#9512
C3×#661662
C2×#913752
C2×#913072
C2×#913012
#117493162
#117493152
#117490702
#117490692
Dic5×#2082
#106157043
#832895