Finite Group Databasebeta

← #14439365

Subgroups — #14439365

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91260C212yesmaximal, complemented
2C2×#91250C212yesmaximal, complemented
3D5×#875C211yesmaximal, characteristic, complemented
4#11752672C211yesmaximal, characteristic, complemented
5#11750816C211yesmaximal, characteristic, complemented
6C5×#4712C211yesmaximal, characteristic, complemented
7C3×#64996C211yesmaximal, characteristic, complemented
8#11747964C212yesmaximal, complemented
9#11747962C212yesmaximal, complemented
10#11747098C211yesmaximal, characteristic, complemented
11#11747031C211yesmaximal, characteristic, complemented
12#10613577—31nomaximal, Hall
13C2×D5×D12C2211yescharacteristic
14C2×#6772C2212yes—
15C2×D5×Dic6C2211yescharacteristic
16C2×Dic60C2212yescomplemented
17C2×#6706C2212yes—
18#91764C2211yescharacteristic
19#91758C2211yescharacteristic, complemented
20C2×C5×D24C2212yes—
21C2×C5×#204C2212yescomplemented
22C5×#875C2211yescharacteristic
23C5×#874C2211yescharacteristic, complemented
24C2×C3×#676C2212yes—
25C3×C42×D5C2211yescharacteristic
26D5×(C2×D3)⋊C4—22no—
27#91449—22no—
28Dic5×D12—22no—
29#91375C2211yescharacteristic
30#91373C2211yescharacteristic
31#91373C2212yescomplemented
32#91350—22no—
33C2×#6663C2212yescomplemented
34C2×#6659C2212yes—
35C2×#6659C2212yescomplemented
36C2×#6654C2212yes—
37#91260—28no—
38#91250—28no—
39C3×C5×#97C2211yescharacteristic, complemented
40C3×C8×Dic5C2212yescomplemented
41C3×#3935C2211yescharacteristic, complemented
42#78531—51nomaximal, Hall
43C2×#4061—32no—
44C2×#4057—32no—
45#66050—31no—
46D5×#124—31no—
47C5×#496—31no—
48#65457—32no—
49#65444—32no—
50#65363—31no—
51#65349—31no—
52#65004—31no—
53#64996D311yescharacteristic, complemented
54C22×D3×D5—21no—
55C2×D60C2311yescharacteristic
56C2×Dic30C2311yescharacteristic
57C2×Dic30C2312yes—
58C2×C5×D12—22no—
59C2×C5×D12C2312yes—
60C2×C5×D12C2311yescharacteristic
61C2×C5×Dic6C2311yescharacteristic
62C2×C3×C4×D5D412yes—
63C2×C3×C4×D5C2311yescharacteristic
64C2×#1204—21no—
65C2×#1203—21no—
66C2×#1201—22no—
67C2×D3×Dic5—22no—
68C2×D5×Dic3—21no—
69D5×D12—24no—
70#6772—24no—
71#6772—24no—
72D5×Dic6—24no—
73C2×C3×C5×C8C2312yes—
74C3×C42×C5C2311yescharacteristic
75#6714—22no—
76C4⋊Dic15—22no—
77Dic60—24no—
78#6706—24no—
79C5×(C2×D3)⋊C4—22no—
80C5×D24—24no—
81C5×#204—24no—
82C3×C4×Dic5D412yes—
83C3×C4×Dic5C2311yescharacteristic
84C2×C3×#168C2312yes—
85C3×#676D418yescomplemented
86#6667—22no—
87(C2×D3)⋊Dic5—24no—
88(C2×D3)⋊Dic5—22no—
89#6663—24no—
90#6659—24no—
91#6659—24no—
92#6654—24no—
93C2×#909—52no—
94C2×#908—52no—
95#5477—51no—
96C2×#875—51no—
97C3×C4×M16—51no—
98#4715—51no—
99#4715—51no—
100#4712—51no—
101#4712D511yescharacteristic, complemented
102#4696—52no—
103#4696—52no—
104C2×Q8×D5—31no—
105C2×#711—32no—
106C2×D4×D5—31no—
107C2×C5×SD16—32no—
108C2×C5×D8—32no—
109C5×#127—31no—
110C5×#124—31no—
111#4093—31no—
112C2×#689—32no—
113#4084—62no—
114#4082—32no—
115#4082—31no—
116D4×Dic5—62no—
117C2×#687—32no—
118C2×#687—32no—
119C2×#686—32no—
120#4061—68no—
121#4057—68no—
122C2×Dic20—32no—
123C2×#677—32no—
124C2×#676C2×D312yes—
125#4031—62no—
126D5×C22⋊C4—62no—
127#4021—31no—
128C42×D5C2×D311yescharacteristic
129#4015—31no—
130C5×#97C2×D311yescharacteristic, complemented
131C8×Dic5C2×D312yescomplemented
132#3935C2×D311yescharacteristic, complemented
133#3153—151noSylow
134C22×D15—21no—
135C22×C5×D3—21no—
136C22×C5×D3—22no—
137C22×C3×D5C2×D411yescharacteristic
138C2×D3×D5—44no—
139C2×D3×D5—42no—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—22no—
143C2×Dic15—21no—
144D60—22no—
145Dic30—22no—
146Dic30—22no—
147Dic30—22no—
148C2×C5×Dic3—21no—
149C5×D12—22no—
150C5×D12—22no—
151C5×D12—22no—
152C5×D12—44no—
153C5×Dic6—22no—
154C2×C3×Dic5C2×D412yes—
155C2×C3×Dic5C2×D411yescharacteristic
156C3×C4×D5—42no—
157C3×C4×D5C2×D414yes—
158#1204—42no—
159#1203—42no—
160#1201—44no—
161D3×Dic5—44no—
162D5×Dic3—42no—
163C3×C5×C8C2×D414yes—
164C3×#168C2×D414yes—
165C2×#235—52no—
166C22×D12—51no—
167C22×Dic6—51no—
168C2×C3×M16—52no—
169C2×C3×C42—51no—
170#930—102no—
171C2×(C2×D3)⋊C4—102no—
172#909—108no—
173#908—108no—
174C2×Dic12—52no—
175C2×Dic12—52no—
176C2×D24—52no—
177C2×D24C2×D512yes—
178C2×#204—52no—
179C2×#204—52no—
180C2×#204—52no—
181C2×#204C2×D512yescomplemented
182#875—51no—
183#875—52no—
184#875—51no—
185#875—51no—
186#875—102no—
187#875C2×D511yescharacteristic
188#874C2×D511yescharacteristic, complemented
189C4×D12—102no—
190#869—51no—
191C3×#97—51no—
192C3×#97C2×D511yescharacteristic, complemented
193C3×C4×C8—52no—
194C23×D5—61no—
195C2×C5×Q8—31no—
196C2×C5×D4—31no—
197C2×C5×D4—32no—
198C2×C5×D4—62no—
199C2×C22⋊D5—62no—
200C2×C22⋊D5—61no—
201C22×Dic5—62no—
202Q8×D5—64no—
203#711—64no—
204#711—64no—
205D4×D5—64no—
206C2×D20—31no—
207C2×C4×D5—61no—
208C2×C4×D5D1212yes—
209C2×C4×D5C22×D311yescharacteristic
210C2×Dic10—32no—
211C2×Dic10—31no—
212C2×Dic10—61no—
213C5×SD16—64no—
214C5×D8—64no—
215C2×C5×C8C22×D312yes—
216C5×C22⋊C4—62no—
217C42×C5C22×D311yescharacteristic
218C22⋊Dic5—62no—
219C22⋊Dic5—64no—
220#689—64no—
221#687—64no—
222#687—64no—
223#686—64no—
224#685—62no—
225#685—62no—
226C4⋊Dic5—62no—
227C4×Dic5D1212yes—
228C4×Dic5C22×D311yescharacteristic
229C2×#168C22×D312yes—
230Dic20—64no—
231#677—64no—
232#676D1218yescomplemented
233C2×#137—152no—
234C2×AGL(1,ℤ/8)—152no—
235#532—151no—
236C2×#124—151no—
237#497—151no—
238#497—151no—
239#496—31no—
240#496—151no—
241#495—152no—
242#495—152no—
243C4×M16—51no—
244C22×C3×C5C22×D411yescharacteristic
245C2×D15—41no—
246C2×D15—42no—
247C2×C5×D3—42no—
248C2×C5×D3—41no—
249C2×C5×D3—44no—
250C2×C5×D3—42no—
251C2×C3×D5—22no—
252C2×C3×D5#12712yes—
253D3×D5—84no—
254C3×C4×C5—22no—
255C3×C4×C5C22×D412yes—
256Dic15—41no—
257Dic15—42no—
258C3×Dic5—22no—
259C3×Dic5#12712yes—
260C5×Dic3—41no—
261C23×D3—101no—
262C22×C3×C4—51no—
263C22×C3×C4—52no—
264C2×#67—102no—
265C22×Dic3—101no—
266#235—104no—
267#235—104no—
268C2×D12—22no—
269C2×D12—51no—
270C2×D12—104no—
271C2×D12—101no—
272C2×D12C22×D512yes—
273C2×D12C22×D511yescharacteristic
274C2×C4×D3—102no—
275C2×Dic6—52no—
276C2×Dic6—51no—
277C2×Dic6—104no—
278C2×Dic6—101no—
279C2×Dic6C22×D511yescharacteristic
280C3×M16—58no—
281C2×C3×C8—52no—
282C2×C3×C8C22×D512yes—
283C3×C42—52no—
284C3×C42—51no—
285C3×C42C22×D511yescharacteristic
286(C2×D3)⋊C4—22no—
287(C2×D3)⋊C4—102no—
288(C2×D3)⋊C4—104no—
289(C2×D3)⋊C4—102no—
290(C2×D3)⋊C4—102no—
291C4⋊Dic3—102no—
292Dic12—104no—
293Dic12—104no—
294D24—24no—
295D24—104no—
296#204—24no—
297#204—104no—
298#204—104no—
299#204—104no—
300C23×C5—61no—
301C23×C5—62no—
302C22×D5—61no—
303C22×D5—124no—
304C22×D5—122no—
305C22×D5C2×D1211yescharacteristic
306C5×Q8—62no—
307C5×D4—62no—
308C5×D4—62no—
309C5×D4—62no—
310C5×D4—124no—
311C2×C4×C5—61no—
312C2×C4×C5C2×D1212yes—
313C2×C4×C5C23×D311yescharacteristic
314C22⋊D5—124no—
315C22⋊D5—122no—
316C2×Dic5—62no—
317C2×Dic5—61no—
318C2×Dic5—124no—
319C2×Dic5C2×D1212yes—
320C2×Dic5C2×D1211yescharacteristic
321D20—62no—
322C4×D5—42no—
323C4×D5—122no—
324C4×D5C2×D1214yes—
325Dic10—62no—
326Dic10—62no—
327Dic10—62no—
328Dic10—122no—
329C5×C8C2×D1214yes—
330#168C2×D1214yes—
331C2×#41—152no—
332C22×Q8—151no—
333C22×D4—151no—
334#137—308no—
335AGL(1,ℤ/8)—308no—
336C2×Q16—152no—
337C2×Q16—152no—
338C2×SD16—32no—
339C2×SD16—152no—
340C2×SD16—152no—
341C2×SD16—152no—
342C2×D8—32no—
343C2×D8—152no—
344C2×M16—52no—
345C4⋊Q8—151no—
346#127—31no—
347#124—31no—
348#124—151no—
349#124—152no—
350#124—151no—
351#124—151no—
352#124—302no—
353#121—302no—
354C4×D4—302no—
355C2×C22⋊C4—302no—
356C2×C42—51no—
357#97—51no—
358#97D3×D511yescharacteristic, complemented
359C4×C8—52no—
360C2×C3×C5C2×#12711yescharacteristic
361C2×C3×C5#57512yes—
362D15—81no—
363C3×D5—22no—
364C5×D3—81no—
365C5×D3—82no—
366C23×C3—51no—
367C22×D3—21no—
368C22×D3—22no—
369C22×D3—101no—
370C22×D3—202no—
371C22×D3—204no—
372C2×C3×C4—51no—
373C2×C3×C4—54no—
374C2×C3×C4—52no—
375C2×C3×C4—202no—
376C2×C3×C4D4×D512yes—
377C2×C3×C4C23×D511yescharacteristic
378#67—204no—
379C2×Dic3—21no—
380C2×Dic3—102no—
381C2×Dic3—101no—
382C2×Dic3—202no—
383D12—22no—
384D12—22no—
385D12—22no—
386D12—44no—
387D12—102no—
388D12—202no—
389C4×D3—204no—
390Dic6—22no—
391Dic6—102no—
392Dic6—102no—
393Dic6—102no—
394Dic6—202no—
395C3×C8—54no—
396C3×C8D4×D514yes—
397C22×C5—122no—
398C22×C5—121no—
399C22×C5—124no—
400C22×C5—122no—
401C22×C5C22×D1211yescharacteristic
402C2×D5—22no—
403C2×D5—121no—
404C2×D5—122no—
405C2×D5—244no—
406C2×D5#87412yes—
407C4×C5—22no—
408C4×C5—121no—
409C4×C5C22×D1212yes—
410Dic5—22no—
411Dic5—121no—
412Dic5—122no—
413Dic5#87412yes—
414C24—301no—
415#41—304no—
416#41—304no—
417C2×Q8—31no—
418C2×Q8—151no—
419C2×Q8—152no—
420C2×Q8—301no—
421C2×Q8—304no—
422C2×D4—31no—
423C2×D4—32no—
424C2×D4—62no—
425C2×D4—151no—
426C2×D4—304no—
427C2×D4—301no—
428C2×D4—302no—
429C22×C4—51no—
430C22×C4—52no—
431C22×C4—302no—
432C22×C4—301no—
433Q16—304no—
434Q16—304no—
435SD16—64no—
436SD16—304no—
437SD16—304no—
438SD16—304no—
439D8—64no—
440D8—304no—
441M16—58no—
442C2×C8—52no—
443C2×C8C2×D3×D512yes—
444C4⋊C4—302no—
445C22⋊C4—62no—
446C22⋊C4—302no—
447C22⋊C4—302no—
448C22⋊C4—304no—
449C22⋊C4—302no—
450C42—52no—
451C42—51no—
452C42C2×D3×D511yescharacteristic
453C3×C5#315311yescharacteristic, complemented, Hall
454C22×C3—52no—
455C22×C3—102no—
456C22×C3C2×D4×D511yescharacteristic
457C2×D3—42no—
458C2×D3—41no—
459C2×D3—44no—
460C2×D3—42no—
461C2×D3—201no—
462C2×D3—202no—
463C2×D3—404no—
464C3×C4—22no—
465C3×C4—52no—
466C3×C4—102no—
467C3×C4C2×D4×D512yes—
468Dic3—41no—
469Dic3—201no—
470Dic3—202no—
471C2×C5—241no—
472C2×C5—242no—
473C2×C5C2×#87411yescharacteristic
474C2×C5#574812yes—
475D5—22no—
476D5—241no—
477C23—51no—
478C23—61no—
479C23—62no—
480C23—301no—
481C23—602no—
482C23—604no—
483Q8—62no—
484Q8—302no—
485Q8—302no—
486Q8—302no—
487Q8—602no—
488D4—62no—
489D4—62no—
490D4—62no—
491D4—124no—
492D4—302no—
493D4—602no—
494D4—604no—
495C2×C4—51no—
496C2×C4—54no—
497C2×C4—52no—
498C2×C4—61no—
499C2×C4—202no—
500C2×C4—301no—
501C2×C4—302no—
502C2×C4—604no—
503C2×C4—602no—
504C2×C4D5×D1212yes—
505C2×C4C22×D3×D511yescharacteristic
506C8—54no—
507C8D5×D1214yes—
508C2×C3—102no—
509C2×C3D5×#12711yescharacteristic
510C2×C3#6610712yes—
511D3—81no—
512D3—82no—
513D3—401no—
514C5#7853111yescharacteristic, complemented, Sylow
515C22—52no—
516C22—102no—
517C22—122no—
518C22—121no—
519C22—124no—
520C22—122no—
521C22—601no—
522C22—602no—
523C22—1204no—
524C22C2×D5×D1211yescharacteristic
525C4—22no—
526C4—52no—
527C4—102no—
528C4—121no—
529C4—602no—
530C4—601no—
531C4C2×D5×D1212yes—
532C3#1061357711yescharacteristic, complemented, Sylow
533C2—102no—
534C2—241no—
535C2—242no—
536C2—1201no—
537C2D5×#87411yescharacteristic
538C2#1175402212yes—
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C22×D4
hypercenter#97D3×D5
hypocenterC3×C5#3153
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
1. C2×#91260C2semidirect
2. C2×#91250C2semidirect
3. D5×#875C2semidirect
4. #11752672C2semidirect
5. #11750816C2semidirect
6. C5×#4712C2semidirect
7. C3×#64996C2semidirect
8. #11747964C2semidirect
9. #11747962C2semidirect
10. #11747098C2semidirect
11. #11747031C2semidirect
16. C2×Dic60C22semidirect
19. #91758C22semidirect
21. C2×C5×#204C22semidirect
23. C5×#874C22semidirect
31. #91373C22semidirect
33. C2×#6663C22semidirect
35. C2×#6659C22semidirect
39. C3×C5×#97C22semidirect
40. C3×C8×Dic5C22semidirect
41. C3×#3935C22semidirect
53. #64996D3semidirect
85. C3×#676D4semidirect
101. #4712D5semidirect
130. C5×#97C2×D3semidirect
131. C8×Dic5C2×D3semidirect
132. #3935C2×D3semidirect
181. C2×#204C2×D5semidirect
188. #874C2×D5semidirect
192. C3×#97C2×D5semidirect
232. #676D12semidirect
358. #97D3×D5semidirect
453. C3×C5#3153semidirect
514. C5#78531semidirect
532. C3#10613577semidirect

Maximal subgroups

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

subgroupindex
C2×#912602
C2×#912502
D5×#8752
#117526722
#117508162
C5×#47122
C3×#649962
#117479642
#117479622
#117470982
#117470312
#106135773
#785315