Finite Group Databasebeta

← #14425358

Subgroups — #14425358

Order 1920.

1524 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4144C211yesmaximal, characteristic, complemented
2#11756564C211yesmaximal, characteristic, complemented
3#11754154C212yesmaximal, complemented
4C2×C5×#833C211yesmaximal, characteristic, complemented
5#11749145C214yesmaximal, complemented
6#11749138C214yesmaximal, complemented
7#11748420C212yesmaximal, complemented
8#10610431—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C2×#6817C2211yescharacteristic, complemented
11C22×C3×C22⋊D5—22no—
12C3×#4144—22no—
13C3×#4144—24no—
14C3×#4144C2214yes—
15C2×C3×#711—22no—
16C2×C3×D4×D5—22no—
17C2×C3×#709C2212yes—
18#91842—22no—
19#91829C2212yescomplemented
20#91827—22no—
21#91825C2212yescomplemented
22#91815C2211yescharacteristic, complemented
23C2×C5×#208C2212yescomplemented
24#91315—22no—
25#91313C2214yescomplemented
26#91312—22no—
27#91311—24no—
28#91301C2214yescomplemented
29C5×#833C2214yescomplemented
30#90976C2218yescomplemented
31#84104—51nomaximal, Hall
32C2×#4144D311yescharacteristic, complemented
33#66139—31no—
34#66082—32no—
35C2×C5×#100—31no—
36#65428—32no—
37#65036—34no—
38#65035—34no—
39C24×C3×C5D412yes—
40C23×C3×D5—22no—
41C2×C3×C5×D4—22no—
42C2×C3×C5×D4—22no—
43C2×C3×C5×D4D412yes—
44C2×C3×C5×D4C2312yes—
45C22×C3×C4×C5C2311yescharacteristic
46C2×#1220—21no—
47C2×#1220—24no—
48#6817—22no—
49#6817—22no—
50C2×D60C2311yescharacteristic, complemented
51C2×C4×D15—21no—
52C2×Dic30C2311yescharacteristic, complemented
53C2×C3×C22⋊D5—24no—
54C2×C3×C22⋊D5—28no—
55C2×C3×C22⋊D5—22no—
56C2×C3×C22⋊D5—28no—
57C22×C3×Dic5—22no—
58C3×#711—28no—
59C3×#711—28no—
60C3×D4×D5—28no—
61C3×D4×D5—28no—
62C3×#709—22no—
63C3×#709—22no—
64C3×#709D414yescomplemented
65C3×#709C2314yes—
66C2×C3×D20D412yescomplemented
67C2×C3×C4×D5—22no—
68C2×C3×Dic10D412yescomplemented
69#6719—21no—
70#6719—24no—
71C4⋊Dic15—21no—
72C4×Dic15C2312yescomplemented
73C5×#208—22no—
74C5×#208C2314yescomplemented
75C2×C5×C3⋊C8—22no—
76#6662—24no—
77#6658—24no—
78#6657—24no—
79#6653—24no—
80C2×C3×H(5,𝔽2)—51no—
81#5822—52no—
82#5805—51no—
83#5242—54no—
84#5241—54no—
85#5236—52no—
86C2×#833D511yescharacteristic, complemented
87C22×C5×D4C2×D311yescharacteristic
88C22×C22⋊D5—22no—
89#4144—22no—
90#4144—24no—
91#4144C2×D314yes—
92C2×#711—22no—
93C2×D4×D5—22no—
94C2×#709—31no—
95C2×#709C2×D312yes—
96C2×C5×M16—32no—
97#4099—62no—
98#4086—32no—
99#4084—62no—
100#4082—32no—
101#4072—31no—
102#4055—34no—
103#4055—62no—
104#4054—34no—
105#4054—62no—
106#4050—64no—
107C5×#100—34no—
108#3957—38no—
109#3019—151noSylow
110C23×C3×C5—22no—
111C23×C3×C5—22no—
112C23×C3×C5—82no—
113C23×C3×C5C2×D414yes—
114C23×C3×C5C2×D411yescharacteristic
115C22×D15—21no—
116C22×C3×D5—22no—
117C22×C3×D5—28no—
118C22×C3×D5—84no—
119C3×C5×D4—24no—
120C3×C5×D4—24no—
121C2×C3×C4×C5C2×D411yescharacteristic
122C2×C3×C4×C5C2×D412yes—
123C2×C3×C4×C5C2×D412yes—
124C2×C3×C4×C5C2411yescharacteristic
125#1220—41no—
126#1220—41no—
127#1220—84no—
128C2×Dic15—22no—
129C2×Dic15—21no—
130D60—22no—
131C4×D15—42no—
132Dic30—22no—
133C3×C22⋊D5—216no—
134C3×C22⋊D5—24no—
135C3×C22⋊D5—24no—
136C2×C3×Dic5—28no—
137C2×C3×Dic5—22no—
138C3×D20—22no—
139C3×D20C2×D414yes—
140C3×C4×D5—24no—
141C3×C4×D5—24no—
142C3×Dic10—22no—
143C3×Dic10C2×D414yes—
144C5×C3⋊C8—24no—
145C3×H(5,𝔽2)—54no—
146C3×H(5,𝔽2)—104no—
147C3×H(5,𝔽2)—102no—
148C2×C3×#41—52no—
149C2×C3×#41—102no—
150C22×C3×D4—102no—
151C22×C3×D4—102no—
152C22×C3×D4C2×D511yescharacteristic
153C2×#235—51no—
154#953—102no—
155#951—54no—
156#950—104no—
157#949—54no—
158#942—102no—
159#940—52no—
160#938—102no—
161#936—52no—
162#932—102no—
163#926—51no—
164C2×#208C2×D512yescomplemented
165#837—58no—
166#833C2×D514yescomplemented
167C24×C5#6712yes—
168C23×D5—22no—
169C2×C5×D4—22no—
170C2×C5×D4—22no—
171C2×C5×D4#6712yes—
172C2×C5×D4C22×D312yes—
173C22×C4×C5C22×D311yescharacteristic
174C2×C22⋊D5—24no—
175C2×C22⋊D5—28no—
176C2×C22⋊D5—22no—
177C2×C22⋊D5—28no—
178C2×C22⋊D5—61no—
179C2×C22⋊D5—64no—
180C22×Dic5—22no—
181#711—28no—
182#711—28no—
183D4×D5—28no—
184D4×D5—28no—
185#709—22no—
186#709—22no—
187#709—62no—
188#709—62no—
189#709#6714yescomplemented
190#709C22×D314yes—
191C2×D20—31no—
192C2×D20#6712yescomplemented
193C2×C4×D5—22no—
194C2×C4×D5—61no—
195C2×Dic10—31no—
196C2×Dic10#6712yescomplemented
197C5×M16—34no—
198C5×M16—62no—
199C2×C5×C8—62no—
200C22⋊Dic5—61no—
201C22⋊Dic5—64no—
202C4⋊Dic5—61no—
203C4×Dic5—32no—
204Dic20—64no—
205D40—64no—
206#677—64no—
207#677—64no—
208C2×H(5,𝔽2)—51no—
209#575—152no—
210#535—151no—
211#455—154no—
212#453—154no—
213#421—152no—
214C2×#100—31no—
215C22×C3×C5—24no—
216C22×C3×C5—41no—
217C22×C3×C5—44no—
218C22×C3×C5—44no—
219C22×C3×C5—82no—
220C22×C3×C5#12011yescharacteristic
221C22×C3×C5#12011yescharacteristic
222C22×C3×C5C22×D411yescharacteristic
223C2×D15—42no—
224C2×D15—41no—
225C2×C3×D5—24no—
226C2×C3×D5—44no—
227C2×C3×D5—88no—
228C3×C4×C5#12012yes—
229C3×C4×C5C22×D412yes—
230Dic15—42no—
231Dic15—41no—
232C3×Dic5—24no—
233C24×C3—102no—
234C24×C3D2012yes—
235C3×#41—54no—
236C3×#41—54no—
237C3×#41—108no—
238C3×#41—108no—
239C3×#41—102no—
240C3×#41—102no—
241C2×C3×Q8—52no—
242C2×C3×D4—22no—
243C2×C3×D4—22no—
244C2×C3×D4—52no—
245C2×C3×D4—108no—
246C2×C3×D4—108no—
247C2×C3×D4—104no—
248C2×C3×D4—108no—
249C2×C3×D4—102no—
250C2×C3×D4—108no—
251C2×C3×D4D2012yes—
252C2×C3×D4C22×D512yes—
253C22×C3×C4—102no—
254C22×C3×C4—102no—
255C22×C3×C4C22×D511yescharacteristic
256C2×#67—101no—
257C2×#67—104no—
258#235—102no—
259#235—102no—
260C2×D12—51no—
261C2×C4×D3—101no—
262C2×Dic6—51no—
263#217—101no—
264#217—104no—
265#216—104no—
266#215—104no—
267#214—104no—
268#213—104no—
269C4⋊Dic3—101no—
270C4×Dic3—52no—
271#208—22no—
272#208C22×D514yescomplemented
273C2×C3⋊C8—22no—
274C23×C5—22no—
275C23×C5—22no—
276C23×C5—82no—
277C23×C5C2×#6714yes—
278C23×C5C2×#6711yescharacteristic
279C22×D5—22no—
280C22×D5—28no—
281C22×D5—61no—
282C22×D5—84no—
283C5×D4—24no—
284C5×D4—24no—
285C2×C4×C5C2×#6711yescharacteristic
286C2×C4×C5C2×#6712yes—
287C2×C4×C5C2×#6712yes—
288C2×C4×C5C23×D311yescharacteristic
289C22⋊D5—216no—
290C22⋊D5—24no—
291C22⋊D5—24no—
292C22⋊D5—121no—
293C22⋊D5—121no—
294C22⋊D5—244no—
295C2×Dic5—28no—
296C2×Dic5—22no—
297C2×Dic5—62no—
298C2×Dic5—61no—
299D20—22no—
300D20—62no—
301D20C2×#6714yes—
302C4×D5—24no—
303C4×D5—24no—
304C4×D5—122no—
305Dic10—22no—
306Dic10—62no—
307Dic10C2×#6714yes—
308C5×C8—64no—
309H(5,𝔽2)—54no—
310H(5,𝔽2)—104no—
311H(5,𝔽2)—102no—
312C2×#41—52no—
313C2×#41—102no—
314C2×#41—151no—
315C22×D4—102no—
316C22×D4—102no—
317C22×D4D3×D511yescharacteristic
318#137—154no—
319#137—302no—
320AGL(1,ℤ/8)—154no—
321AGL(1,ℤ/8)—302no—
322#135—304no—
323C2×M16—32no—
324#127—152no—
325#124—152no—
326#121—302no—
327#120—302no—
328#117—151no—
329#104—158no—
330#100—34no—
331C2×C3×C5—21no—
332C2×C3×C5—21no—
333C2×C3×C5—21no—
334C2×C3×C5—44no—
335C2×C3×C5C2×#12011yescharacteristic
336D15—81no—
337C3×D5—44no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—82no—
341C23×C3—108no—
342C23×C3—102no—
343C23×C3—404no—
344C23×C3C2×D2014yes—
345C23×C3C2×D2011yescharacteristic
346C22×D3—101no—
347C3×Q8—54no—
348C3×Q8—102no—
349C3×D4—24no—
350C3×D4—24no—
351C3×D4—54no—
352C3×D4—1016no—
353C3×D4—104no—
354C3×D4—104no—
355C3×D4—102no—
356C2×C3×C4—108no—
357C2×C3×C4—102no—
358C2×C3×C4—104no—
359C2×C3×C4—104no—
360C2×C3×C4C2×D2011yescharacteristic
361C2×C3×C4D4×D512yes—
362C2×C3×C4D4×D512yes—
363C2×C3×C4C23×D511yescharacteristic
364#67—201no—
365#67—201no—
366#67—404no—
367C2×Dic3—102no—
368C2×Dic3—101no—
369D12—102no—
370C4×D3—202no—
371Dic6—102no—
372C3⋊C8—24no—
373C22×C5—24no—
374C22×C5—41no—
375C22×C5—44no—
376C22×C5—44no—
377C22×C5—82no—
378C22×C5#95311yescharacteristic
379C22×C5#95311yescharacteristic
380C22×C5C22×#6711yescharacteristic
381C2×D5—24no—
382C2×D5—44no—
383C2×D5—88no—
384C2×D5—122no—
385C2×D5—121no—
386C4×C5#95312yes—
387C4×C5C22×#6712yes—
388Dic5—24no—
389Dic5—122no—
390Dic5—121no—
391C24—102no—
392C24#120212yes—
393#41—54no—
394#41—54no—
395#41—108no—
396#41—108no—
397#41—102no—
398#41—102no—
399#41—302no—
400#41—302no—
401C2×Q8—52no—
402C2×Q8—151no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—52no—
406C2×D4—108no—
407C2×D4—108no—
408C2×D4—104no—
409C2×D4—108no—
410C2×D4—102no—
411C2×D4—108no—
412C2×D4—151no—
413C2×D4—301no—
414C2×D4—304no—
415C2×D4#120212yes—
416C2×D4C2×D3×D512yes—
417C22×C4—102no—
418C22×C4—102no—
419C22×C4—301no—
420C22×C4C2×D3×D511yescharacteristic
421Q16—304no—
422SD16—304no—
423SD16—304no—
424D8—304no—
425M16—34no—
426M16—62no—
427C2×C8—62no—
428C4⋊C4—301no—
429C22⋊C4—301no—
430C22⋊C4—304no—
431C42—152no—
432C3×C5#301911yescharacteristic, complemented, Hall
433C22×C3—24no—
434C22×C3—41no—
435C22×C3—44no—
436C22×C3—44no—
437C22×C3—82no—
438C22×C3—104no—
439C22×C3—204no—
440C22×C3—408no—
441C22×C3#402811yescharacteristic
442C22×C3#402811yescharacteristic
443C22×C3C22×D2011yescharacteristic
444C2×D3—202no—
445C2×D3—201no—
446C3×C4—104no—
447C3×C4#402812yes—
448C3×C4C2×D4×D512yes—
449Dic3—202no—
450Dic3—201no—
451C2×C5—21no—
452C2×C5—21no—
453C2×C5—21no—
454C2×C5—44no—
455C2×C5C2×#95311yescharacteristic
456D5—44no—
457D5—241no—
458C23—22no—
459C23—22no—
460C23—82no—
461C23—108no—
462C23—102no—
463C23—301no—
464C23—404no—
465C23C2×#120214yes—
466C23C2×#120211yescharacteristic
467Q8—54no—
468Q8—102no—
469Q8—302no—
470D4—24no—
471D4—24no—
472D4—54no—
473D4—1016no—
474D4—104no—
475D4—104no—
476D4—102no—
477D4—302no—
478D4—601no—
479D4—601no—
480D4—1204no—
481C2×C4—108no—
482C2×C4—102no—
483C2×C4—104no—
484C2×C4—104no—
485C2×C4—302no—
486C2×C4—301no—
487C2×C4—602no—
488C2×C4C2×#120211yescharacteristic
489C2×C4D5×#6712yes—
490C2×C4D5×#6712yes—
491C2×C4C22×D3×D511yescharacteristic
492C8—64no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—44no—
497C2×C3—204no—
498C2×C3C2×#402811yescharacteristic
499D3—401no—
500C5#8410411yescharacteristic, complemented, Sylow
501C22—24no—
502C22—41no—
503C22—44no—
504C22—44no—
505C22—82no—
506C22—104no—
507C22—204no—
508C22—408no—
509C22—602no—
510C22—601no—
511C22#9156411yescharacteristic
512C22#9156411yescharacteristic
513C22C22×#120211yescharacteristic
514C4—104no—
515C4—602no—
516C4—601no—
517C4#9156412yes—
518C4C2×D5×#6712yes—
519C3#1061043111yescharacteristic, complemented, Sylow
520C2—21no—
521C2—21no—
522C2—21no—
523C2—44no—
524C2—204no—
525C2—1201no—
526C2C2×#9156411yescharacteristic
subgroupG/H
centerC2C2×#91564
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC2×C3×C5C2×#120
hypercenterC22×D4D3×D5
hypocenterC3×C5#3019
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4144C2semidirect
2. #11756564C2semidirect
3. #11754154C2semidirect
4. C2×C5×#833C2semidirect
5. #11749145C2semidirect
6. #11749138C2semidirect
7. #11748420C2semidirect
10. C2×#6817C22semidirect
19. #91829C22semidirect
21. #91825C22semidirect
22. #91815C22semidirect
23. C2×C5×#208C22semidirect
25. #91313C22semidirect
28. #91301C22semidirect
29. C5×#833C22semidirect
30. #90976C22semidirect
32. C2×#4144D3semidirect
50. C2×D60C23semidirect
52. C2×Dic30C23semidirect
64. C3×#709D4semidirect
66. C2×C3×D20D4semidirect
68. C2×C3×Dic10D4semidirect
72. C4×Dic15C23semidirect
74. C5×#208C23semidirect
86. C2×#833D5semidirect
164. C2×#208C2×D5semidirect
166. #833C2×D5semidirect
189. #709#67semidirect
192. C2×D20#67semidirect
196. C2×Dic10#67semidirect
272. #208C22×D5semidirect
432. C3×C5#3019semidirect
500. C5#84104semidirect
519. C3#10610431semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41442
#117565642
#117541542
C2×C5×#8332
#117491452
#117491382
#117484202
#106104313
#841045