Finite Group Databasebeta

← #14438708

Subgroups — #14438708

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D3×#125C211yesmaximal, characteristic, complemented
2#11752543C211yesmaximal, characteristic
3#11751169C211yesmaximal, characteristic, complemented
4C3×#65357C211yesmaximal, characteristic, complemented
5#11747505C212yesmaximal, complemented
6#11747503C212yesmaximal, complemented
7#11747423C212yesmaximal, complemented
8#11747405C212yesmaximal, complemented
9C4×#6650C211yesmaximal, characteristic, complemented
10#11746913C211yesmaximal, characteristic, complemented
11#11746896C211yesmaximal, characteristic, complemented
12#10614743—31nomaximal, Hall
13C2×#6769C2211yescharacteristic
14C2×#6765C2211yescharacteristic
15C3×C5×#125C2211yescharacteristic
16#91764C2211yescharacteristic
17C5×D3×C4⋊C4—22no—
18C5×D3×C4⋊C4C2212yes—
19C5×#890C2212yes—
20C5×#889—22no—
21C42×C5×D3C2211yescharacteristic
22C5×#870C2211yescharacteristic
23C3×#4021C2211yescharacteristic
24#91458C2211yescharacteristic
25#91454—22no—
26#91395—22no—
27#91389C2211yescharacteristic
28C2×#6650C2212yes—
29#91094C2212yes—
30#91093C2212yes—
31C4×C3⋊#168C2211yescharacteristic
32C3×#3942C2212yes—
33C3×#3941C2212yes—
34C3×C4×#168C2211yescharacteristic
35#90975C2212yes—
36#90970C2212yes—
37#90969C2212yes—
38#90964C2212yes—
39#90953C2212yes—
40#81641—51nomaximal, Hall
41C2×C5×#125—31no—
42#65811—31no—
43#65358—32no—
44#65357—31no—
45#65357—31no—
46#65357—31no—
47#65357D311yescharacteristic, complemented
48#65356—32no—
49#65255—32no—
50#65255—32no—
51C4×#681—31no—
52C2×D60C2311yescharacteristic
53C2×Dic30C2311yescharacteristic
54C2×C4×C5×D3—22no—
55C2×C4×C5×D3D412yes—
56C2×C4×C5×D3C2311yescharacteristic
57C2×C3×D20C2311yescharacteristic
58C2×C3×Dic10C2311yescharacteristic
59C2×#1203—21no—
60C2×#1202—22no—
61C2×#1201—21no—
62C2×#1200—21no—
63C2×D5×Dic3—21no—
64#6769—24no—
65#6765—24no—
66C3×C5×C4⋊C4—22no—
67C3×C5×C4⋊C4C2312yes—
68C3×C42×C5C2311yescharacteristic
69#6714—22no—
70C2×C3⋊#168C2312yes—
71C5×C4⋊Dic3—22no—
72C5×C4⋊Dic3C2312yes—
73C5×Dic3⋊C4—22no—
74C5×Dic3⋊C4—22no—
75C5×Dic3⋊C4—22no—
76C4×C5×Dic3D412yes—
77C4×C5×Dic3C2311yescharacteristic
78C3×#685—22no—
79C2×C3×#168C2312yes—
80Dic3⋊Dic5—22no—
81#6650—24no—
82D3×#125D511yescharacteristic, complemented
83#5668—51no—
84C3×#488—51no—
85#5068—51no—
86#5056—51no—
87#4803—52no—
88#4797—52no—
89#4771—52no—
90#4764—52no—
91#4697—51no—
92C4×ΓL(1,𝔽25)—51no—
93C2×#709—31no—
94C2×#709—31no—
95C5×#125—32no—
96C5×#125—31no—
97C5×#125—62no—
98C5×#125C2×D311yescharacteristic
99C2×C5×C4⋊C4—32no—
100C2×C5×C4⋊C4—62no—
101C2×C42×C5—31no—
102#4076—62no—
103C2×#681—32no—
104#4021—31no—
105#4021C2×D311yescharacteristic
106#4020—31no—
107C4×D20—62no—
108#4015—31no—
109#3942—32no—
110#3942—32no—
111#3942—32no—
112#3942C2×D312yes—
113#3941—32no—
114#3941—32no—
115#3941—32no—
116#3941C2×D312yes—
117#3935—32no—
118C4×#168—31no—
119C4×#168C2×D311yescharacteristic
120#3142—151noSylow
121C22×D15—21no—
122C22×C5×D3C2×D411yescharacteristic
123C22×C3×D5—21no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5C2×D412yes—
126C2×C3×C4×C5C2411yescharacteristic
127C2×Dic15—21no—
128D60—22no—
129Dic30—22no—
130C2×C5×Dic3—22no—
131C2×C5×Dic3C2×D412yes—
132C2×C5×Dic3C2×D411yescharacteristic
133C4×C5×D3—42no—
134C4×C5×D3—44no—
135C4×C5×D3#4114yes—
136C2×C3×Dic5—21no—
137C3×D20—22no—
138C3×Dic10—22no—
139#1203—42no—
140#1202—44no—
141#1201—42no—
142#1200—42no—
143D5×Dic3—42no—
144C3⋊#168—22no—
145C3×#168—22no—
146C2×#239—51no—
147C2×#237—51no—
148C3×#125C2×D511yescharacteristic
149C3×#124—51no—
150#944—51no—
151#940—51no—
152C2×ΓL(1,𝔽25)—52no—
153D3×C4⋊C4—22no—
154D3×C4⋊C4C2×D512yes—
155#890C2×D512yes—
156#889—22no—
157#884—102no—
158#67⋊C4—102no—
159#875—51no—
160C42×D3C2×D511yescharacteristic
161#870C2×D511yescharacteristic
162C3×#103—52no—
163C3×#102—52no—
164C3×C4×C8—51no—
165#835—52no—
166#832—52no—
167#821—52no—
168#816—52no—
169#815—52no—
170#810—52no—
171#809—52no—
172C4×C3⋊C8—51no—
173C22×C4×C5—31no—
174C22×C4×C5—32no—
175C22×C4×C5—62no—
176C2×C22⋊D5—61no—
177C2×C22⋊D5—61no—
178#709—64no—
179#709—64no—
180C2×D20—31no—
181C2×D20—62no—
182C2×D20C22×D311yescharacteristic
183C2×C4×D5—61no—
184C2×C4×D5—61no—
185C2×Dic10—31no—
186C2×Dic10C22×D311yescharacteristic
187C5×C4⋊C4—22no—
188C5×C4⋊C4—32no—
189C5×C4⋊C4—62no—
190C5×C4⋊C4—62no—
191C5×C4⋊C4—62no—
192C5×C4⋊C4—62no—
193C5×C4⋊C4C22×D312yes—
194C42×C5—32no—
195C42×C5—31no—
196C42×C5C22×D311yescharacteristic
197#685—22no—
198#685—62no—
199C4⋊Dic5—62no—
200#681—64no—
201C2×#168—32no—
202C2×#168C22×D312yes—
203#532—151no—
204C2×#125—31no—
205#491—152no—
206#490—152no—
207#488—51no—
208#488—151no—
209#488—151no—
210#488—151no—
211#417—152no—
212#417—152no—
213C4×M16—151no—
214C22×C3×C5C22×D411yescharacteristic
215C2×D15—41no—
216C2×D15—42no—
217C2×C5×D3—22no—
218C2×C5×D3#12412yes—
219C2×C3×D5—41no—
220C2×C3×D5—42no—
221C3×C4×C5—22no—
222C3×C4×C5—42no—
223C3×C4×C5C2×#4112yes—
224Dic15—41no—
225C3×Dic5—41no—
226C5×Dic3—22no—
227C5×Dic3—42no—
228C5×Dic3#12412yes—
229C2×C3×Q8—51no—
230C2×C3×D4—51no—
231C2×#67—101no—
232C2×#67—102no—
233C22×Dic3—101no—
234#239—104no—
235#237—104no—
236C2×D12—51no—
237C2×D12—101no—
238C2×C4×D3—22no—
239C2×C4×D3—101no—
240C2×C4×D3C22⋊D512yes—
241C2×C4×D3C22×D511yescharacteristic
242C2×Dic6—51no—
243C2×C3×C8—52no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4C22×D512yes—
246C3×C22⋊C4—102no—
247C3×C42C22×D511yescharacteristic
248(C2×D3)⋊C4—102no—
249C4⋊Dic3—22no—
250C4⋊Dic3C22×D512yes—
251Dic3⋊C4—22no—
252Dic3⋊C4—22no—
253Dic3⋊C4—22no—
254Dic3⋊C4—102no—
255C4×Dic3C22⋊D512yes—
256C4×Dic3C22×D511yescharacteristic
257C2×C3⋊C8—52no—
258ΓL(1,𝔽25)—104no—
259C23×C5—31no—
260C22×D5—21no—
261C22×D5—61no—
262C2×C4×C5—22no—
263C2×C4×C5—31no—
264C2×C4×C5—34no—
265C2×C4×C5—32no—
266C2×C4×C5—62no—
267C2×C4×C5—122no—
268C2×C4×C5—124no—
269C2×C4×C5D3×D412yes—
270C2×C4×C5C23×D311yescharacteristic
271C22⋊D5—122no—
272C22⋊D5—122no—
273C2×Dic5—21no—
274C2×Dic5—61no—
275D20—22no—
276D20—62no—
277D20—124no—
278C4×D5—122no—
279C4×D5—122no—
280Dic10—22no—
281Dic10—62no—
282#168—22no—
283#168—62no—
284C2×#41—151no—
285C2×#41—151no—
286C2×M16—152no—
287C4⋊Q8—151no—
288#127—151no—
289#125—32no—
290#125—31no—
291#125—62no—
292#125D3×D511yescharacteristic
293#124—51no—
294#124—151no—
295#121—302no—
296C4×D4—302no—
297C2×C4⋊C4—32no—
298C2×C4⋊C4—62no—
299C2×C42—31no—
300#103—52no—
301#103—152no—
302#103—152no—
303#103—152no—
304#102—52no—
305#102—152no—
306#102—152no—
307#102—152no—
308#97—152no—
309C4×C8—51no—
310C4×C8—151no—
311C2×C3×C5C2×#12411yescharacteristic
312C2×C3×C5#57512yes—
313D15—81no—
314C3×D5—81no—
315C5×D3—22no—
316C23×C3—101no—
317C22×D3—101no—
318C22×D3C2×C22⋊D511yescharacteristic
319C3×Q8—102no—
320C3×D4—102no—
321C2×C3×C4—22no—
322C2×C3×C4—101no—
323C2×C3×C4C2×C22⋊D512yes—
324C2×C3×C4C23×D511yescharacteristic
325#67—204no—
326#67—202no—
327C2×Dic3—22no—
328C2×Dic3—101no—
329C2×Dic3—202no—
330C2×Dic3C2×C22⋊D512yes—
331C2×Dic3C2×C22⋊D511yescharacteristic
332D12—102no—
333D12—202no—
334C4×D3—42no—
335C4×D3—44no—
336C4×D3—202no—
337C4×D3#71314yes—
338Dic6—102no—
339C3×C8—102no—
340C3⋊C8—102no—
341C22×C5—32no—
342C22×C5—62no—
343C22×C5C2×D3×D411yescharacteristic
344C2×D5—41no—
345C2×D5—42no—
346C2×D5—121no—
347C2×D5—122no—
348C4×C5—22no—
349C4×C5—32no—
350C4×C5—42no—
351C4×C5—62no—
352C4×C5—122no—
353C4×C5D3×#4112yes—
354Dic5—41no—
355Dic5—121no—
356#41—304no—
357#41—304no—
358C2×Q8—51no—
359C2×Q8—151no—
360C2×D4—51no—
361C2×D4—151no—
362C2×D4—302no—
363C2×D4—301no—
364C2×D4—301no—
365C22×C4—31no—
366C22×C4—32no—
367C22×C4—62no—
368C22×C4—301no—
369C22×C4—301no—
370M16—304no—
371C2×C8—52no—
372C2×C8—152no—
373C4⋊C4—22no—
374C4⋊C4—32no—
375C4⋊C4—62no—
376C4⋊C4—62no—
377C4⋊C4—62no—
378C4⋊C4—62no—
379C4⋊C4—302no—
380C4⋊C4C2×D3×D512yes—
381C22⋊C4—102no—
382C22⋊C4—302no—
383C42—32no—
384C42—31no—
385C42C2×D3×D511yescharacteristic
386C3×C5#314211yescharacteristic, complemented, Hall
387C22×C3—201no—
388C22×C3—202no—
389C22×C3C22×C22⋊D511yescharacteristic
390C2×D3—22no—
391C2×D3—201no—
392C2×D3—202no—
393C2×D3#409312yes—
394C3×C4—22no—
395C3×C4—42no—
396C3×C4—201no—
397C3×C4C2×#71312yes—
398Dic3—22no—
399Dic3—42no—
400Dic3—201no—
401Dic3#409312yes—
402C2×C5—62no—
403C2×C5D3×#12411yescharacteristic
404C2×C5#576812yes—
405D5—81no—
406D5—241no—
407C23—31no—
408C23—101no—
409C23—301no—
410Q8—102no—
411Q8—302no—
412D4—102no—
413D4—302no—
414D4—604no—
415D4—602no—
416D4—602no—
417C2×C4—22no—
418C2×C4—31no—
419C2×C4—34no—
420C2×C4—32no—
421C2×C4—62no—
422C2×C4—101no—
423C2×C4—122no—
424C2×C4—124no—
425C2×C4—301no—
426C2×C4—602no—
427C2×C4—602no—
428C2×C4D3×C22⋊D512yes—
429C2×C4C22×D3×D511yescharacteristic
430C8—102no—
431C8—302no—
432C2×C3—401no—
433C2×C3C2×#409311yescharacteristic
434C2×C3#6615612yes—
435D3—22no—
436D3—401no—
437C5#8164111yescharacteristic, complemented, Sylow
438C22—32no—
439C22—62no—
440C22—201no—
441C22—202no—
442C22—601no—
443C22—602no—
444C22C2×D3×C22⋊D511yescharacteristic
445C4—22no—
446C4—32no—
447C4—42no—
448C4—62no—
449C4—122no—
450C4—201no—
451C4—601no—
452C4D3×#71312yes—
453C3#1061474311yescharacteristic, complemented, Sylow
454C2—62no—
455C2—401no—
456C2—1201no—
457C2D3×#409311yescharacteristic
458C2#1175532212yes—
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
prime radical#11752543C2
hypercenter#125D3×D5
hypocenterC3×C5#3142
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C5×D3×#125C2semidirect
3. #11751169C2semidirect
4. C3×#65357C2semidirect
5. #11747505C2semidirect
6. #11747503C2semidirect
7. #11747423C2semidirect
8. #11747405C2semidirect
9. C4×#6650C2semidirect
10. #11746913C2semidirect
11. #11746896C2semidirect
47. #65357D3semidirect
82. D3×#125D5semidirect
386. C3×C5#3142semidirect
437. C5#81641semidirect
453. C3#10614743semidirect

Maximal subgroups

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

subgroupindex
C5×D3×#1252
#117525432
#117511692
C3×#653572
#117475052
#117475032
#117474232
#117474052
C4×#66502
#117469132
#117468962
#106147433
#816415