Finite Group Databasebeta

← #14438706

Subgroups — #14438706

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
1C3×D5×#125C211yesmaximal, characteristic, complemented
2#11752673C211yesmaximal, characteristic
3#11751169C211yesmaximal, characteristic, complemented
4C5×#5068C211yesmaximal, characteristic, complemented
5#11747500C212yesmaximal, complemented
6#11747498C212yesmaximal, complemented
7#11747401C212yesmaximal, complemented
8#11747156C212yesmaximal, complemented
9C4×#6649C211yesmaximal, characteristic, complemented
10#11746933C211yesmaximal, characteristic, complemented
11#11746903C211yesmaximal, characteristic, complemented
12#10613372—31nomaximal, Hall
13C2×#6773C2211yescharacteristic
14C2×#6772C2211yescharacteristic
15C3×C5×#125C2211yescharacteristic
16#91764C2211yescharacteristic
17C5×#875C2211yescharacteristic
18C3×D5×C4⋊C4—22no—
19C3×D5×C4⋊C4C2212yes—
20C3×#4036C2212yes—
21C3×#4035—22no—
22C3×C42×D5C2211yescharacteristic
23C3×#4016C2211yescharacteristic
24#91451C2211yescharacteristic
25#91448—22no—
26#91405—22no—
27#91376C2211yescharacteristic
28C2×#6649C2212yes—
29#91094C2212yes—
30#91093C2212yes—
31C4×C3⋊#168C2211yescharacteristic
32C5×#810C2212yes—
33C5×#809C2212yes—
34C4×C5×C3⋊C8C2211yescharacteristic
35#90974C2212yes—
36#90972C2212yes—
37#90968C2212yes—
38#90966C2212yes—
39#90952C2212yes—
40#83012—51nomaximal, Hall
41D5×#125D311yescharacteristic, complemented
42#66002—31no—
43C5×#488—31no—
44#65357—31no—
45#65345—31no—
46#65092—32no—
47#65086—32no—
48#65060—32no—
49#65053—32no—
50#64986—31no—
51C4×#676—31no—
52C2×D60C2311yescharacteristic
53C2×Dic30C2311yescharacteristic
54C2×C5×D12C2311yescharacteristic
55C2×C5×Dic6C2311yescharacteristic
56C2×C3×C4×D5—22no—
57C2×C3×C4×D5D412yes—
58C2×C3×C4×D5C2311yescharacteristic
59C2×#1203—22no—
60C2×#1202—21no—
61C2×#1201—21no—
62C2×#1200—21no—
63C2×D3×Dic5—21no—
64#6773—24no—
65#6772—24no—
66C3×C5×C4⋊C4—22no—
67C3×C5×C4⋊C4C2312yes—
68C3×C42×C5C2311yescharacteristic
69#6714—22no—
70C2×C3⋊#168C2312yes—
71C5×(C2×D3)⋊C4—22no—
72C2×C5×C3⋊C8C2312yes—
73C3×C4⋊Dic5—22no—
74C3×C4⋊Dic5C2312yes—
75C3×#683—22no—
76C3×#683—22no—
77C3×#683—22no—
78C3×C4×Dic5D412yes—
79C3×C4×Dic5C2311yescharacteristic
80#6668—22no—
81#6649—24no—
82C2×C3×#125—51no—
83#5477—51no—
84#5069—52no—
85#5068—51no—
86#5068—51no—
87#5068—51no—
88#5068D511yescharacteristic, complemented
89#5067—52no—
90#4966—52no—
91#4966—52no—
92C4×#208—51no—
93C2×#713—31no—
94C2×#711—31no—
95C5×#125C2×D311yescharacteristic
96C5×#124—31no—
97#4090—31no—
98#4086—31no—
99C2×#676—32no—
100D5×C4⋊C4—22no—
101D5×C4⋊C4C2×D312yes—
102#4036C2×D312yes—
103#4035—22no—
104#4030—62no—
105#4027—62no—
106#4021—31no—
107C42×D5C2×D311yescharacteristic
108#4016C2×D311yescharacteristic
109C5×#103—32no—
110C5×#102—32no—
111C4×C5×C8—31no—
112#3967—32no—
113#3964—32no—
114#3953—32no—
115#3948—32no—
116#3947—32no—
117#3942—32no—
118#3941—32no—
119C4×#168—31no—
120#3142—151noSylow
121C22×D15—21no—
122C22×C5×D3—21no—
123C22×C3×D5C2×D411yescharacteristic
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5C2×D412yes—
126C2×C3×C4×C5C2411yescharacteristic
127C2×Dic15—21no—
128D60—22no—
129Dic30—22no—
130C2×C5×Dic3—21no—
131C5×D12—22no—
132C5×Dic6—22no—
133C2×C3×Dic5—22no—
134C2×C3×Dic5C2×D412yes—
135C2×C3×Dic5C2×D411yescharacteristic
136C3×C4×D5—42no—
137C3×C4×D5—44no—
138C3×C4×D5#4114yes—
139#1203—44no—
140#1202—42no—
141#1201—42no—
142#1200—42no—
143D3×Dic5—42no—
144C3⋊#168—22no—
145C5×C3⋊C8—22no—
146C2×#235—51no—
147C2×#235—51no—
148C3×#125—52no—
149C3×#125—51no—
150C3×#125—102no—
151C3×#125C2×D511yescharacteristic
152C2×C3×C4⋊C4—52no—
153C2×C3×C4⋊C4—102no—
154C2×C3×C42—51no—
155#930—102no—
156C2×#208—52no—
157#875—51no—
158#875C2×D511yescharacteristic
159#874—51no—
160C4×D12—102no—
161#869—51no—
162#810—52no—
163#810—52no—
164#810—52no—
165#810C2×D512yes—
166#809—52no—
167#809—52no—
168#809—52no—
169#809C2×D512yes—
170#803—52no—
171C4×C3⋊C8—51no—
172C4×C3⋊C8C2×D511yescharacteristic
173C2×C5×Q8—31no—
174C2×C5×D4—31no—
175C2×C22⋊D5—61no—
176C2×C22⋊D5—62no—
177C22×Dic5—61no—
178#713—64no—
179#711—64no—
180C2×D20—31no—
181C2×D20—61no—
182C2×C4×D5—22no—
183C2×C4×D5—61no—
184C2×C4×D5#6712yes—
185C2×C4×D5C22×D311yescharacteristic
186C2×Dic10—31no—
187C2×C5×C8—32no—
188C5×C4⋊C4—22no—
189C5×C4⋊C4C22×D312yes—
190C5×C22⋊C4—62no—
191C42×C5C22×D311yescharacteristic
192#685—62no—
193C4⋊Dic5—22no—
194C4⋊Dic5C22×D312yes—
195#683—22no—
196#683—22no—
197#683—22no—
198#683—62no—
199C4×Dic5#6712yes—
200C4×Dic5C22×D311yescharacteristic
201C2×#168—32no—
202#676—64no—
203#532—151no—
204C2×#125—51no—
205#491—152no—
206#490—152no—
207#488—31no—
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—41no—
218C2×C5×D3—42no—
219C2×C3×D5—22no—
220C2×C3×D5#12412yes—
221C3×C4×C5—22no—
222C3×C4×C5—42no—
223C3×C4×C5C2×#4112yes—
224Dic15—41no—
225C3×Dic5—22no—
226C3×Dic5—42no—
227C3×Dic5#12412yes—
228C5×Dic3—41no—
229C22×C3×C4—51no—
230C22×C3×C4—52no—
231C22×C3×C4—102no—
232C2×#67—101no—
233C2×#67—101no—
234#235—104no—
235#235—104no—
236C2×D12—51no—
237C2×D12—102no—
238C2×D12C22×D511yescharacteristic
239C2×C4×D3—101no—
240C2×C4×D3—101no—
241C2×Dic6—51no—
242C2×Dic6C22×D511yescharacteristic
243C3×C4⋊C4—22no—
244C3×C4⋊C4—52no—
245C3×C4⋊C4—102no—
246C3×C4⋊C4—102no—
247C3×C4⋊C4—102no—
248C3×C4⋊C4—102no—
249C3×C4⋊C4C22×D512yes—
250C3×C42—52no—
251C3×C42—51no—
252C3×C42C22×D511yescharacteristic
253(C2×D3)⋊C4—22no—
254(C2×D3)⋊C4—102no—
255C4⋊Dic3—102no—
256#208—104no—
257C2×C3⋊C8—52no—
258C2×C3⋊C8C22×D512yes—
259C23×C5—61no—
260C22×D5—61no—
261C22×D5C2×#6711yescharacteristic
262C5×Q8—62no—
263C5×D4—62no—
264C2×C4×C5—22no—
265C2×C4×C5—61no—
266C2×C4×C5C2×#6712yes—
267C2×C4×C5C23×D311yescharacteristic
268C22⋊D5—124no—
269C22⋊D5—122no—
270C2×Dic5—22no—
271C2×Dic5—61no—
272C2×Dic5—122no—
273C2×Dic5C2×#6712yes—
274C2×Dic5C2×#6711yescharacteristic
275D20—62no—
276D20—122no—
277C4×D5—42no—
278C4×D5—44no—
279C4×D5—122no—
280C4×D5#23914yes—
281Dic10—62no—
282C5×C8—62no—
283#168—62no—
284C2×#41—151no—
285C2×#41—151no—
286C2×M16—152no—
287C4⋊Q8—151no—
288#127—151no—
289#125—52no—
290#125—51no—
291#125—102no—
292#125D3×D511yescharacteristic
293#124—31no—
294#124—151no—
295#121—302no—
296C4×D4—302no—
297C2×C4⋊C4—52no—
298C2×C4⋊C4—102no—
299C2×C42—51no—
300#103—32no—
301#103—152no—
302#103—152no—
303#103—152no—
304#102—32no—
305#102—152no—
306#102—152no—
307#102—152no—
308#97—152no—
309C4×C8—31no—
310C4×C8—151no—
311C2×C3×C5C2×#12411yescharacteristic
312C2×C3×C5#57512yes—
313D15—81no—
314C3×D5—22no—
315C5×D3—81no—
316C23×C3—51no—
317C22×D3—21no—
318C22×D3—101no—
319C2×C3×C4—22no—
320C2×C3×C4—51no—
321C2×C3×C4—54no—
322C2×C3×C4—52no—
323C2×C3×C4—102no—
324C2×C3×C4—202no—
325C2×C3×C4—204no—
326C2×C3×C4D4×D512yes—
327C2×C3×C4C23×D511yescharacteristic
328#67—202no—
329#67—202no—
330C2×Dic3—21no—
331C2×Dic3—101no—
332D12—22no—
333D12—102no—
334D12—204no—
335C4×D3—202no—
336C4×D3—202no—
337Dic6—22no—
338Dic6—102no—
339C3⋊C8—22no—
340C3⋊C8—102no—
341C22×C5—121no—
342C22×C5—122no—
343C22×C5C22×#6711yescharacteristic
344C2×D5—22no—
345C2×D5—121no—
346C2×D5—122no—
347C2×D5#94712yes—
348C4×C5—22no—
349C4×C5—42no—
350C4×C5—121no—
351C4×C5C2×#23912yes—
352Dic5—22no—
353Dic5—42no—
354Dic5—121no—
355Dic5#94712yes—
356#41—304no—
357#41—304no—
358C2×Q8—31no—
359C2×Q8—151no—
360C2×D4—31no—
361C2×D4—151no—
362C2×D4—302no—
363C2×D4—301no—
364C2×D4—301no—
365C22×C4—51no—
366C22×C4—52no—
367C22×C4—102no—
368C22×C4—301no—
369C22×C4—301no—
370M16—304no—
371C2×C8—32no—
372C2×C8—152no—
373C4⋊C4—22no—
374C4⋊C4—52no—
375C4⋊C4—102no—
376C4⋊C4—102no—
377C4⋊C4—102no—
378C4⋊C4—102no—
379C4⋊C4—302no—
380C4⋊C4C2×D3×D512yes—
381C22⋊C4—62no—
382C22⋊C4—302no—
383C42—52no—
384C42—51no—
385C42C2×D3×D511yescharacteristic
386C3×C5#314211yescharacteristic, complemented, Hall
387C22×C3—52no—
388C22×C3—102no—
389C22×C3C2×D4×D511yescharacteristic
390C2×D3—42no—
391C2×D3—41no—
392C2×D3—202no—
393C2×D3—201no—
394C3×C4—22no—
395C3×C4—42no—
396C3×C4—52no—
397C3×C4—102no—
398C3×C4—202no—
399C3×C4D5×#4112yes—
400Dic3—41no—
401Dic3—201no—
402C2×C5—241no—
403C2×C5C2×#94711yescharacteristic
404C2×C5#582212yes—
405D5—22no—
406D5—241no—
407C23—51no—
408C23—61no—
409C23—301no—
410Q8—62no—
411Q8—302no—
412D4—62no—
413D4—302no—
414D4—604no—
415D4—602no—
416D4—602no—
417C2×C4—22no—
418C2×C4—51no—
419C2×C4—54no—
420C2×C4—52no—
421C2×C4—61no—
422C2×C4—102no—
423C2×C4—202no—
424C2×C4—204no—
425C2×C4—301no—
426C2×C4—602no—
427C2×C4—602no—
428C2×C4D5×#6712yes—
429C2×C4C22×D3×D511yescharacteristic
430C8—62no—
431C8—302no—
432C2×C3—102no—
433C2×C3D5×#12411yescharacteristic
434C2×C3#6610212yes—
435D3—81no—
436D3—401no—
437C5#8301211yescharacteristic, complemented, Sylow
438C22—52no—
439C22—102no—
440C22—121no—
441C22—122no—
442C22—601no—
443C22—602no—
444C22C2×D5×#6711yescharacteristic
445C4—22no—
446C4—42no—
447C4—52no—
448C4—102no—
449C4—121no—
450C4—202no—
451C4—601no—
452C4D5×#23912yes—
453C3#1061337211yescharacteristic, complemented, Sylow
454C2—102no—
455C2—241no—
456C2—1201no—
457C2D5×#94711yescharacteristic
458C2#1175531512yes—
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
prime radical#11752673C2
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. C3×D5×#125C2semidirect
3. #11751169C2semidirect
4. C5×#5068C2semidirect
5. #11747500C2semidirect
6. #11747498C2semidirect
7. #11747401C2semidirect
8. #11747156C2semidirect
9. C4×#6649C2semidirect
10. #11746933C2semidirect
11. #11746903C2semidirect
41. D5×#125D3semidirect
88. #5068D5semidirect
386. C3×C5#3142semidirect
437. C5#83012semidirect
453. C3#10613372semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1252
#117526732
#117511692
C5×#50682
#117475002
#117474982
#117474012
#117471562
C4×#66492
#117469332
#117469032
#106133723
#830125