Finite Group Databasebeta

← #14439371

Subgroups — #14439371

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
1C5×#5716C211yesmaximal, characteristic, complemented
2C2×#91486C212yesmaximal, complemented
3C2×#91480C212yesmaximal, complemented
4D3×#4021C211yesmaximal, characteristic, complemented
5#11751175C211yesmaximal, characteristic, complemented
6C3×#65363C211yesmaximal, characteristic, complemented
7#11749078C212yesmaximal, complemented
8#11749074C212yesmaximal, complemented
9#11747097C211yesmaximal, characteristic, complemented
10#11747080C211yesmaximal, characteristic, complemented
11#11747005C211yesmaximal, characteristic, complemented
12#10615020—31nomaximal, Hall
13C2×C5×#237C2212yes—
14C2×D3×D20C2211yescharacteristic
15C2×D3×Dic10C2211yescharacteristic
16C3×C5×#127C2211yescharacteristic, complemented
17C2×#6716C2212yescomplemented
18C2×#6715C2212yes—
19#91764C2211yescharacteristic
20C5×#938—22no—
21C5×#936C2212yescomplemented
22C5×D4×Dic3—22no—
23C42×C5×D3C2211yescharacteristic
24C5×#869C2211yescharacteristic, complemented
25C2×C3×#687C2212yescomplemented
26C2×C3×#686C2212yes—
27C3×#4021C2211yescharacteristic
28#91486—28no—
29#91480—28no—
30D3×#685—22no—
31#91374C2211yescharacteristic
32#91364C2211yescharacteristic
33#91353—22no—
34C2×#6663C2212yescomplemented
35C2×#6661C2212yescomplemented
36C2×#6660C2212yes—
37C2×#6655C2212yes—
38C2×#6650C2212yes—
39#91087C2211yescharacteristic, complemented
40C3×#3935C2211yescharacteristic, complemented
41Dic3×#168C2212yescomplemented
42#81846—51nomaximal, Hall
43C5×#532—31no—
44C2×#4097—32no—
45C2×#4095—32no—
46C2×#4021—31no—
47#65375—31no—
48#65375—31no—
49#65363—31no—
50#65363D311yescharacteristic, complemented
51#65348—32no—
52#65348—32no—
53C4×#681—31no—
54C22×D3×D5—21no—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4C2312yes—
57C2×D60C2311yescharacteristic
58C2×Dic30C2311yescharacteristic
59C2×C5×#67—22no—
60C22×C5×Dic3—22no—
61C5×#237—24no—
62C5×#237—24no—
63C2×C4×C5×D3D412yes—
64C2×C4×C5×D3C2311yescharacteristic
65C2×C5×Dic6C2312yes—
66C2×C3×D20C2311yescharacteristic
67C2×C3×Dic10C2311yescharacteristic
68C2×#1204—21no—
69C2×#1202—21no—
70C2×D3×Dic5—21no—
71D3×D20—24no—
72D3×Dic10—24no—
73C3×C42×C5C2311yescharacteristic
74#6716—24no—
75#6715—24no—
76#6714—22no—
77C2×C3⋊#168C2312yes—
78C5×#217—24no—
79C5×C4⋊Dic3—22no—
80C4×C5×Dic3D412yes—
81C4×C5×Dic3C2311yescharacteristic
82C3×#687—24no—
83C3×#686—24no—
84C3×#685—22no—
85C2×C3×#168C2312yes—
86#6667—22no—
87#6665—22no—
88#6663—24no—
89#6661—24no—
90#6660—24no—
91#6655—24no—
92#6650D418yescomplemented
93C2×#915—52no—
94C2×#911—52no—
95#5716D511yescharacteristic, complemented
96D3×#124—51no—
97C3×#496—51no—
98#5168—52no—
99#5155—52no—
100#5074—51no—
101#5060—51no—
102#4715—51no—
103#4707—51no—
104C2×C5×#41—32no—
105C22×D20—31no—
106C22×Dic10—31no—
107C5×C4⋊Q8—31no—
108C5×#127C2×D311yescharacteristic, complemented
109C5×#124—32no—
110C5×#121—62no—
111C4×C5×D4—62no—
112C2×C42×C5—31no—
113#4097—68no—
114#4095—68no—
115C2×#689—32no—
116C2×#689—32no—
117C2×#688—32no—
118C2×#688—32no—
119C2×#687—32no—
120C2×#687C2×D312yescomplemented
121C2×#686—32no—
122C2×#686C2×D312yes—
123C2×#685—62no—
124C2×#681—32no—
125#4021—31no—
126#4021—31no—
127#4021—31no—
128#4021—62no—
129#4021C2×D311yescharacteristic
130#3935—31no—
131#3935C2×D311yescharacteristic, complemented
132C4×#168—32no—
133#3153—151noSylow
134C23×C3×C5—22no—
135C22×D15—21no—
136C22×C5×D3C2×D411yescharacteristic
137C22×C3×D5—21no—
138C2×D3×D5—44no—
139C2×D3×D5—42no—
140C3×C5×D4—22no—
141C3×C5×D4—22no—
142C3×C5×D4—44no—
143C2×C3×C4×C5C2×D412yes—
144C2×C3×C4×C5C2411yescharacteristic
145C2×Dic15—21no—
146D60—22no—
147Dic30—22no—
148C5×#67—44no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—44no—
151C2×C5×Dic3C2×D412yes—
152C2×C5×Dic3C2×D411yescharacteristic
153C4×C5×D3—42no—
154C4×C5×D3C2×D414yes—
155C5×Dic6—22no—
156C5×Dic6—22no—
157C2×C3×Dic5—21no—
158C3×D20—22no—
159C3×Dic10—22no—
160#1204—42no—
161#1202—42no—
162D3×Dic5—42no—
163C3⋊#168C2×D414yes—
164C3×#168C2×D414yes—
165C2×D3×Q8—51no—
166C2×#237C2×D512yes—
167C2×D3×D4—51no—
168C2×C3×SD16—52no—
169C2×C3×D8—52no—
170C3×#127C2×D511yescharacteristic, complemented
171C3×#124—51no—
172#947—51no—
173C2×#216—52no—
174#938—22no—
175#936—51no—
176#936C2×D512yescomplemented
177D4×Dic3—22no—
178C2×#214—52no—
179C2×#214—52no—
180C2×#213—52no—
181#915—108no—
182#911—108no—
183C2×Dic12—52no—
184C2×#204—52no—
185C2×ΓL(1,𝔽25)—52no—
186#885—102no—
187D3×C22⋊C4—102no—
188#875—51no—
189C42×D3C2×D511yescharacteristic
190#869C2×D511yescharacteristic, complemented
191C3×#97—51no—
192C8×Dic3—52no—
193#803—51no—
194C23×D5—61no—
195C5×#41—64no—
196C5×#41—64no—
197C2×C5×Q8—32no—
198C2×C5×D4—22no—
199C2×C5×D4—62no—
200C2×C5×D4C22×D312yes—
201C22×C4×C5—31no—
202C22×C4×C5—32no—
203C22×C4×C5—62no—
204C22×Dic5—61no—
205C2×D20—31no—
206C2×D20—64no—
207C2×D20—61no—
208C2×D20C22×D311yescharacteristic
209C2×Dic10—31no—
210C2×Dic10—64no—
211C2×Dic10—61no—
212C2×Dic10C22×D311yescharacteristic
213C5×C4⋊C4—62no—
214C5×C22⋊C4—64no—
215C42×C5—32no—
216C42×C5—31no—
217C42×C5C22×D311yescharacteristic
218#689—64no—
219#689—64no—
220#688—64no—
221#688—64no—
222#687—24no—
223#687—64no—
224#686—24no—
225#686—64no—
226#685—22no—
227#685—62no—
228#685—62no—
229#685—62no—
230#681—38no—
231C2×#168—32no—
232C2×#168C22×D312yes—
233C2×#137—152no—
234C2×AGL(1,ℤ/8)—152no—
235#532—31no—
236C2×#124—151no—
237#497—151no—
238#497—151no—
239#496—51no—
240#496—151no—
241#495—152no—
242#495—152no—
243C4×M16—151no—
244C22×C3×C5—42no—
245C22×C3×C5—44no—
246C22×C3×C5C22×D411yescharacteristic
247C2×D15—41no—
248C2×D15—42no—
249C2×C5×D3—22no—
250C2×C5×D3#12712yes—
251C2×C3×D5—41no—
252C2×C3×D5—42no—
253D3×D5—84no—
254C3×C4×C5—22no—
255C3×C4×C5C22×D412yes—
256Dic15—41no—
257C3×Dic5—41no—
258C5×Dic3—22no—
259C5×Dic3—42no—
260C5×Dic3#12712yes—
261C23×D3—101no—
262C2×C3×Q8—51no—
263C2×C3×D4—22no—
264C2×C3×D4—51no—
265C2×C3×D4C22×D512yes—
266C2×#67—22no—
267C2×#67—101no—
268C22×Dic3—22no—
269D3×Q8—104no—
270#237—24no—
271#237—24no—
272D3×D4—104no—
273C2×D12—51no—
274C2×C4×D3—101no—
275C2×C4×D3C22⋊D512yes—
276C2×C4×D3C22×D511yescharacteristic
277C2×Dic6—51no—
278C2×Dic6—101no—
279C2×Dic6C22×D512yes—
280C3×SD16—104no—
281C3×D8—104no—
282C2×C3×C8—52no—
283C3×C22⋊C4—102no—
284C3×C42C22×D511yescharacteristic
285#217—24no—
286#217—102no—
287#216—104no—
288#214—104no—
289#214—104no—
290#213—104no—
291(C2×D3)⋊C4—102no—
292(C2×D3)⋊C4—102no—
293C4⋊Dic3—22no—
294C4×Dic3C22⋊D512yes—
295C4×Dic3C22×D511yescharacteristic
296C2×C3⋊C8—52no—
297Dic12—104no—
298#204—104no—
299ΓL(1,𝔽25)—58no—
300C23×C5—22no—
301C23×C5—31no—
302C22×D5—21no—
303C22×D5—61no—
304C22×D5—122no—
305C22×D5—124no—
306C5×Q8—62no—
307C5×Q8—62no—
308C5×D4—22no—
309C5×D4—22no—
310C5×D4—44no—
311C5×D4—124no—
312C2×C4×C5—31no—
313C2×C4×C5—34no—
314C2×C4×C5—32no—
315C2×C4×C5—62no—
316C2×C4×C5—122no—
317C2×C4×C5—124no—
318C2×C4×C5D3×D412yes—
319C2×C4×C5C23×D311yescharacteristic
320C2×Dic5—21no—
321C2×Dic5—61no—
322C2×Dic5—122no—
323D20—22no—
324D20—62no—
325D20—122no—
326Dic10—22no—
327Dic10—62no—
328Dic10—122no—
329#168—34no—
330#168D3×D414yes—
331C2×#41—32no—
332C22×Q8—151no—
333C22×D4—151no—
334#137—308no—
335AGL(1,ℤ/8)—308no—
336C2×Q16—152no—
337C2×Q16—152no—
338C2×SD16—52no—
339C2×SD16—152no—
340C2×SD16—152no—
341C2×SD16—152no—
342C2×D8—52no—
343C2×D8—152no—
344C2×M16—152no—
345C4⋊Q8—31no—
346#127D3×D511yescharacteristic, complemented
347#124—32no—
348#124—51no—
349#124—151no—
350#124—151no—
351#124—151no—
352#124—302no—
353#121—62no—
354C4×D4—62no—
355C2×C22⋊C4—302no—
356C2×C42—31no—
357#97—51no—
358#97—151no—
359C4×C8—152no—
360C2×C3×C5—82no—
361C2×C3×C5C2×#12711yescharacteristic
362C2×C3×C5#57512yes—
363D15—81no—
364C3×D5—81no—
365C5×D3—22no—
366C23×C3—22no—
367C23×C3—101no—
368C22×D3—101no—
369C22×D3—204no—
370C22×D3—202no—
371C22×D3C2×C22⋊D511yescharacteristic
372C3×Q8—102no—
373C3×D4—22no—
374C3×D4—22no—
375C3×D4—44no—
376C3×D4—102no—
377C2×C3×C4—101no—
378C2×C3×C4C2×C22⋊D512yes—
379C2×C3×C4C23×D511yescharacteristic
380#67—44no—
381#67—202no—
382C2×Dic3—22no—
383C2×Dic3—44no—
384C2×Dic3—101no—
385C2×Dic3C2×C22⋊D512yes—
386C2×Dic3C2×C22⋊D511yescharacteristic
387D12—102no—
388C4×D3—42no—
389C4×D3—202no—
390C4×D3D4×D514yes—
391Dic6—22no—
392Dic6—22no—
393Dic6—102no—
394Dic6—202no—
395C3×C8—54no—
396C3⋊C8—54no—
397C22×C5—32no—
398C22×C5—42no—
399C22×C5—44no—
400C22×C5—62no—
401C22×C5C2×D3×D411yescharacteristic
402C2×D5—41no—
403C2×D5—42no—
404C2×D5—121no—
405C2×D5—122no—
406C2×D5—244no—
407C4×C5—22no—
408C4×C5—32no—
409C4×C5—62no—
410C4×C5—122no—
411C4×C5C2×D3×D412yes—
412Dic5—41no—
413Dic5—121no—
414C24—301no—
415#41—64no—
416#41—64no—
417C2×Q8—32no—
418C2×Q8—51no—
419C2×Q8—151no—
420C2×Q8—301no—
421C2×Q8—304no—
422C2×D4—22no—
423C2×D4—51no—
424C2×D4—62no—
425C2×D4—151no—
426C2×D4—304no—
427C2×D4—301no—
428C2×D4C2×D3×D512yes—
429C22×C4—31no—
430C22×C4—32no—
431C22×C4—62no—
432C22×C4—301no—
433Q16—304no—
434Q16—304no—
435SD16—104no—
436SD16—304no—
437SD16—304no—
438SD16—304no—
439D8—104no—
440D8—304no—
441M16—158no—
442C2×C8—52no—
443C2×C8—152no—
444C4⋊C4—62no—
445C22⋊C4—64no—
446C22⋊C4—102no—
447C22⋊C4—302no—
448C22⋊C4—302no—
449C22⋊C4—302no—
450C42—32no—
451C42—31no—
452C42C2×D3×D511yescharacteristic
453C3×C5#315311yescharacteristic, complemented, Hall
454C22×C3—42no—
455C22×C3—44no—
456C22×C3—201no—
457C22×C3—202no—
458C22×C3C22×C22⋊D511yescharacteristic
459C2×D3—22no—
460C2×D3—201no—
461C2×D3—202no—
462C2×D3—404no—
463C2×D3#408612yes—
464C3×C4—22no—
465C3×C4—201no—
466C3×C4C2×D4×D512yes—
467Dic3—22no—
468Dic3—42no—
469Dic3—201no—
470Dic3#408612yes—
471C2×C5—62no—
472C2×C5—82no—
473C2×C5D3×#12711yescharacteristic
474C2×C5#577312yes—
475D5—81no—
476D5—241no—
477C23—22no—
478C23—31no—
479C23—101no—
480C23—301no—
481C23—602no—
482C23—604no—
483Q8—62no—
484Q8—62no—
485Q8—102no—
486Q8—302no—
487Q8—602no—
488D4—22no—
489D4—22no—
490D4—44no—
491D4—102no—
492D4—124no—
493D4—302no—
494D4—602no—
495C2×C4—31no—
496C2×C4—34no—
497C2×C4—32no—
498C2×C4—62no—
499C2×C4—101no—
500C2×C4—122no—
501C2×C4—124no—
502C2×C4—301no—
503C2×C4—602no—
504C2×C4D3×C22⋊D512yes—
505C2×C4C22×D3×D511yescharacteristic
506C8—54no—
507C8—154no—
508C2×C3—82no—
509C2×C3—401no—
510C2×C3C2×#408611yescharacteristic
511C2×C3#6615612yes—
512D3—22no—
513D3—401no—
514C5#8184611yescharacteristic, complemented, Sylow
515C22—32no—
516C22—42no—
517C22—44no—
518C22—62no—
519C22—201no—
520C22—202no—
521C22—601no—
522C22—602no—
523C22—1204no—
524C22C2×D3×C22⋊D511yescharacteristic
525C4—22no—
526C4—32no—
527C4—62no—
528C4—122no—
529C4—201no—
530C4—601no—
531C4D3×D4×D512yes—
532C3#1061502011yescharacteristic, complemented, Sylow
533C2—62no—
534C2—82no—
535C2—401no—
536C2—1201no—
537C2#1175469612yes—
538C2D3×#408611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C22×D4
hypercenter#127D3×D5
hypocenterC3×C5#3153
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C5×#5716C2semidirect
2. C2×#91486C2semidirect
3. C2×#91480C2semidirect
4. D3×#4021C2semidirect
5. #11751175C2semidirect
6. C3×#65363C2semidirect
7. #11749078C2semidirect
8. #11749074C2semidirect
9. #11747097C2semidirect
10. #11747080C2semidirect
11. #11747005C2semidirect
16. C3×C5×#127C22semidirect
17. C2×#6716C22semidirect
21. C5×#936C22semidirect
24. C5×#869C22semidirect
25. C2×C3×#687C22semidirect
34. C2×#6663C22semidirect
35. C2×#6661C22semidirect
39. #91087C22semidirect
40. C3×#3935C22semidirect
41. Dic3×#168C22semidirect
50. #65363D3semidirect
92. #6650D4semidirect
95. #5716D5semidirect
108. C5×#127C2×D3semidirect
120. C2×#687C2×D3semidirect
131. #3935C2×D3semidirect
170. C3×#127C2×D5semidirect
176. #936C2×D5semidirect
190. #869C2×D5semidirect
346. #127D3×D5semidirect
453. C3×C5#3153semidirect
514. C5#81846semidirect
532. C3#10615020semidirect

Maximal subgroups

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

subgroupindex
C5×#57162
C2×#914862
C2×#914802
D3×#40212
#117511752
C3×#653632
#117490782
#117490742
#117470972
#117470802
#117470052
#106150203
#818465