Finite Group Databasebeta

← #14437781

Subgroups — #14437781

Order 1920.

800 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
1#11756447C211yesmaximal, characteristic, complemented
2#11756427C211yesmaximal, characteristic
3C3×C5×#488C211yesmaximal, characteristic, complemented
4#11751169C211yesmaximal, characteristic, complemented
5#11751157C211yesmaximal, characteristic, complemented
6#11750905C212yesmaximal, complemented
7#11750893C212yesmaximal, complemented
8#11750873C212yesmaximal, complemented
9#11750861C212yesmaximal, complemented
10#11750798C211yesmaximal, characteristic, complemented
11C4×C8×D15C211yesmaximal, characteristic, complemented
12#10613368—31nomaximal, Hall
13C2×#6821C2211yescharacteristic
14C2×#6819C2211yescharacteristic
15C3×C5×#125C2211yescharacteristic
16C3×C5×#124C2211yescharacteristic
17#91833C2211yescharacteristic
18#91829C2211yescharacteristic
19C2×C8×D15C2212yes—
20#91785—22no—
21#91781C2212yes—
22#91777C2212yes—
23#91776—22no—
24#91773—22no—
25#91770—22no—
26#91764C2211yescharacteristic
27C42×D15C2211yescharacteristic
28#91759C2211yescharacteristic
29C3×C5×#103C2212yes—
30C3×C5×#102C2212yes—
31C3×C4×C5×C8C2211yescharacteristic
32#91119C2212yes—
33#91116C2212yes—
34#91105C2212yes—
35#91100C2212yes—
36C8×Dic15C2212yes—
37#91094C2212yes—
38#91093C2212yes—
39C4×C3⋊#168C2211yescharacteristic
40#81637—51nomaximal, Hall
41#66022—31no—
42#66002—31no—
43C5×#488D311yescharacteristic, complemented
44#65357—31no—
45#65345—31no—
46#65093—32no—
47#65081—32no—
48#65061—32no—
49#65049—32no—
50#64986—31no—
51C4×C8×D5—31no—
52C2×C3×C5×Q8C2311yescharacteristic
53C2×C3×C5×D4C2311yescharacteristic
54C2×#1220—21no—
55C2×#1220—22no—
56C22×Dic15—21no—
57#6821—24no—
58#6819—24no—
59C2×D60—21no—
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×C4×D15D412yes—
63C2×C4×D15C2311yescharacteristic
64C2×Dic30—22no—
65C2×Dic30C2311yescharacteristic
66C2×C3×C5×C8C2312yes—
67C3×C5×C4⋊C4—22no—
68C3×C5×C4⋊C4C2312yes—
69C3×C5×C22⋊C4—22no—
70C3×C42×C5C2311yescharacteristic
71#6714—22no—
72#6714—22no—
73C4⋊Dic15C2312yes—
74#6712—22no—
75#6712—22no—
76#6712—22no—
77C4×Dic15—22no—
78C4×Dic15D412yes—
79C4×Dic15C2311yescharacteristic
80C2×C3⋊#168C2312yes—
81C8×D15—24no—
82#5688—51no—
83#5668—51no—
84C3×#488D511yescharacteristic, complemented
85#5068—51no—
86#5056—51no—
87#4804—52no—
88#4792—52no—
89#4772—52no—
90#4760—52no—
91#4697—51no—
92C4×D3×C8—51no—
93C2×#713—31no—
94C2×#711—31no—
95C5×#125C2×D311yescharacteristic
96C5×#124C2×D311yescharacteristic
97#4090—31no—
98#4086—31no—
99C2×C8×D5—32no—
100#4042—62no—
101#4038—32no—
102#4034—32no—
103#4033—62no—
104#4030—62no—
105#4027—62no—
106#4021—31no—
107C42×D5—31no—
108#4016—31no—
109C5×#103C2×D312yes—
110C5×#102C2×D312yes—
111C4×C5×C8C2×D311yescharacteristic
112#3967—32no—
113#3964—32no—
114#3953—32no—
115#3948—32no—
116C8×Dic5—32no—
117#3942—32no—
118#3941—32no—
119C4×#168—31no—
120#3131—151noSylow
121C23×C3×C5—21no—
122C22×D15—21no—
123C22×D15C2×D411yescharacteristic
124C3×C5×Q8—22no—
125C3×C5×D4—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5C2×D412yes—
129C2×C3×C4×C5C2411yescharacteristic
130#1220—42no—
131#1220—44no—
132C2×Dic15—22no—
133C2×Dic15—21no—
134C2×Dic15—42no—
135C2×Dic15C2×D411yescharacteristic
136C2×Dic15C2×D412yes—
137D60—22no—
138D60—42no—
139C4×D15—24no—
140C4×D15—42no—
141C4×D15#4114yes—
142Dic30—22no—
143Dic30—44no—
144C3×C5×C8—22no—
145C3⋊#168—22no—
146C2×#239—51no—
147C2×#237—51no—
148C3×#125C2×D511yescharacteristic
149C3×#124C2×D511yescharacteristic
150#944—51no—
151#940—51no—
152C2×D3×C8—52no—
153#896—102no—
154#892—52no—
155#888—52no—
156#887—102no—
157#884—102no—
158#67⋊C4—102no—
159#875—51no—
160C42×D3—51no—
161#870—51no—
162C3×#103C2×D512yes—
163C3×#102C2×D512yes—
164C3×C4×C8C2×D511yescharacteristic
165#835—52no—
166#832—52no—
167#821—52no—
168#816—52no—
169C8×Dic3—52no—
170#810—52no—
171#809—52no—
172C4×C3⋊C8—51no—
173C2×C5×Q8C22×D311yescharacteristic
174C2×C5×D4C22×D311yescharacteristic
175C2×C22⋊D5—62no—
176C2×C22⋊D5—61no—
177C22×Dic5—61no—
178#713—64no—
179#711—64no—
180C2×D20—31no—
181C2×D20—61no—
182C2×C4×D5—31no—
183C2×C4×D5—32no—
184C2×C4×D5—61no—
185C2×Dic10—31no—
186C2×Dic10—62no—
187C2×C5×C8C22×D312yes—
188C5×C4⋊C4—22no—
189C5×C4⋊C4C22×D312yes—
190C5×C22⋊C4—22no—
191C42×C5C22×D311yescharacteristic
192#685—62no—
193#685—62no—
194C4⋊Dic5—32no—
195#683—62no—
196#683—62no—
197#683—62no—
198C4×Dic5—32no—
199C4×Dic5—31no—
200C4×Dic5—62no—
201C2×#168—32no—
202C8×D5—64no—
203#533—151no—
204#532—151no—
205#488—151no—
206#488—151no—
207#488—151no—
208#488D1511yescharacteristic, complemented
209#487—152no—
210#486—152no—
211#416—152no—
212#416—152no—
213C2×C4×C8—151no—
214C22×C3×C5—41no—
215C22×C3×C5—42no—
216C22×C3×C5C22×D411yescharacteristic
217C2×D15—22no—
218C2×D15—41no—
219C2×D15—42no—
220C2×D15#12412yes—
221C3×C4×C5—22no—
222C3×C4×C5—41no—
223C3×C4×C5—42no—
224C3×C4×C5C2×#4112yes—
225Dic15—41no—
226Dic15—42no—
227Dic15#12412yes—
228Dic15#13514yes—
229C2×C3×Q8C22×D511yescharacteristic
230C2×C3×D4C22×D511yescharacteristic
231C2×#67—102no—
232C2×#67—101no—
233C22×Dic3—101no—
234#239—104no—
235#237—104no—
236C2×D12—51no—
237C2×D12—101no—
238C2×C4×D3—51no—
239C2×C4×D3—52no—
240C2×C4×D3—101no—
241C2×Dic6—51no—
242C2×Dic6—102no—
243C2×C3×C8C22×D512yes—
244C3×C4⋊C4—22no—
245C3×C4⋊C4C22×D512yes—
246C3×C22⋊C4—22no—
247C3×C42C22×D511yescharacteristic
248(C2×D3)⋊C4—102no—
249(C2×D3)⋊C4—102no—
250C4⋊Dic3—52no—
251Dic3⋊C4—102no—
252Dic3⋊C4—102no—
253Dic3⋊C4—102no—
254C4×Dic3—52no—
255C4×Dic3—51no—
256C4×Dic3—102no—
257C2×C3⋊C8—52no—
258D3×C8—104no—
259C23×C5—21no—
260C22×D5—31no—
261C22×D5—61no—
262C5×Q8—22no—
263C5×D4—22no—
264C2×C4×C5—22no—
265C2×C4×C5—21no—
266C2×C4×C5D3×D412yes—
267C2×C4×C5C23×D311yescharacteristic
268C22⋊D5—124no—
269C22⋊D5—122no—
270C2×Dic5—31no—
271C2×Dic5—32no—
272C2×Dic5—62no—
273C2×Dic5—61no—
274C2×Dic5—122no—
275D20—62no—
276D20—122no—
277C4×D5—34no—
278C4×D5—64no—
279C4×D5—122no—
280Dic10—62no—
281Dic10—124no—
282C5×C8—22no—
283#168—62no—
284C2×#41—151no—
285C2×#41—151no—
286C22×C8—152no—
287C4⋊Q8—152no—
288C4⋊Q8—151no—
289#127—151no—
290#125—151no—
291#125C2×D1511yescharacteristic
292#124—151no—
293#124C2×D1511yescharacteristic
294C22⋊Q8—302no—
295#121—302no—
296C4×Q8—302no—
297C4×D4—302no—
298#117—152no—
299C2×C42—151no—
300#103—152no—
301#103—152no—
302#103—152no—
303#103C2×D1512yes—
304#102—152no—
305#102—152no—
306#102—152no—
307#102C2×D1512yes—
308C4×C8—152no—
309C4×C8—151no—
310C4×C8C2×D1511yescharacteristic
311C2×C3×C5—81no—
312C2×C3×C5C2×#12411yescharacteristic
313C2×C3×C5C2×#13512yes—
314D15—22no—
315D15—81no—
316C23×C3—21no—
317C22×D3—51no—
318C22×D3—101no—
319C3×Q8—22no—
320C3×D4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—21no—
323C2×C3×C4D4×D512yes—
324C2×C3×C4C23×D511yescharacteristic
325#67—204no—
326#67—202no—
327C2×Dic3—51no—
328C2×Dic3—52no—
329C2×Dic3—102no—
330C2×Dic3—101no—
331C2×Dic3—202no—
332D12—102no—
333D12—202no—
334C4×D3—54no—
335C4×D3—104no—
336C4×D3—202no—
337Dic6—102no—
338Dic6—204no—
339C3×C8—22no—
340C3⋊C8—102no—
341C22×C5—41no—
342C22×C5—42no—
343C22×C5C2×D3×D411yescharacteristic
344C2×D5—32no—
345C2×D5—62no—
346C2×D5—121no—
347C2×D5—122no—
348C4×C5—22no—
349C4×C5—41no—
350C4×C5—42no—
351C4×C5D3×#4112yes—
352Dic5—32no—
353Dic5—34no—
354Dic5—121no—
355Dic5—122no—
356#41—304no—
357#41—304no—
358C2×Q8—151no—
359C2×Q8—302no—
360C2×Q8C22×D1511yescharacteristic
361C2×D4—151no—
362C2×D4—301no—
363C2×D4—302no—
364C2×D4—301no—
365C2×D4C22×D1511yescharacteristic
366C22×C4—151no—
367C22×C4—152no—
368C22×C4—301no—
369C22×C4—301no—
370C2×C8—152no—
371C2×C8—304no—
372C2×C8C22×D1512yes—
373C4⋊C4—22no—
374C4⋊C4—152no—
375C4⋊C4—302no—
376C4⋊C4—302no—
377C4⋊C4—302no—
378C4⋊C4C22×D1512yes—
379C22⋊C4—22no—
380C22⋊C4—302no—
381C22⋊C4—302no—
382C42—152no—
383C42—151no—
384C42—302no—
385C42C22×D1511yescharacteristic
386C3×C5#313111yescharacteristic, complemented, Hall
387C22×C3—42no—
388C22×C3—41no—
389C22×C3C2×D4×D511yescharacteristic
390C2×D3—52no—
391C2×D3—102no—
392C2×D3—202no—
393C2×D3—201no—
394C3×C4—22no—
395C3×C4—42no—
396C3×C4—41no—
397C3×C4D5×#4112yes—
398Dic3—54no—
399Dic3—52no—
400Dic3—202no—
401Dic3—201no—
402C2×C5—81no—
403C2×C5D3×#12411yescharacteristic
404C2×C5D3×#13512yes—
405D5—62no—
406D5—241no—
407C23—21no—
408C23—151no—
409C23—301no—
410Q8—22no—
411Q8—302no—
412Q8—604no—
413D4—22no—
414D4—302no—
415D4—602no—
416D4—604no—
417D4—602no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—151no—
421C2×C4—152no—
422C2×C4—154no—
423C2×C4—304no—
424C2×C4—302no—
425C2×C4—301no—
426C2×C4—602no—
427C2×C4—602no—
428C2×C4D4×D1512yes—
429C2×C4C23×D1511yescharacteristic
430C8—22no—
431C8—302no—
432C2×C3—81no—
433C2×C3D5×#12411yescharacteristic
434C2×C3D5×#13512yes—
435D3—102no—
436D3—401no—
437C5#8163711yescharacteristic, complemented, Sylow
438C22—41no—
439C22—42no—
440C22—152no—
441C22—302no—
442C22—601no—
443C22—602no—
444C22C2×D4×D1511yescharacteristic
445C4—22no—
446C4—41no—
447C4—42no—
448C4—152no—
449C4—154no—
450C4—601no—
451C4—602no—
452C4#41×D1512yes—
453C3#1061336811yescharacteristic, complemented, Sylow
454C2—81no—
455C2—302no—
456C2—1201no—
457C2D15×#12411yescharacteristic
458C2D15×#13512yes—
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#488C2
socleC22×C3×C5C22×D4
prime radical#11756427C2
hypercenter#488D15
hypocenterC3×C5#3131
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #11756447C2semidirect
3. C3×C5×#488C2semidirect
4. #11751169C2semidirect
5. #11751157C2semidirect
6. #11750905C2semidirect
7. #11750893C2semidirect
8. #11750873C2semidirect
9. #11750861C2semidirect
10. #11750798C2semidirect
11. C4×C8×D15C2semidirect
43. C5×#488D3semidirect
84. C3×#488D5semidirect
208. #488D15semidirect
386. C3×C5#3131semidirect
437. C5#81637semidirect
453. C3#10613368semidirect

Maximal subgroups

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

subgroupindex
#117564472
#117564272
C3×C5×#4882
#117511692
#117511572
#117509052
#117508932
#117508732
#117508612
#117507982
C4×C8×D152
#106133683
#816375