Finite Group Databasebeta

← #14416624

Subgroups — #14416624

Order 1920.

984 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
1C2×#91270C211yesmaximal, characteristic
2#11753402C212yesmaximal, complemented
3#11750954C211yesmaximal, characteristic, complemented
4C5×#4869C211yesmaximal, characteristic, complemented
5C3×#65149C211yesmaximal, characteristic, complemented
6#11747876C211yesmaximal, characteristic, complemented
7#11747813C211yesmaximal, characteristic, complemented
8D5×#815C211yesmaximal, characteristic, complemented
9#11747499C212yesmaximal, complemented
10#11747473C212yesmaximal, complemented
11#11747235C212yesmaximal, complemented
12#10611595—31nomaximal, Hall
13C2×#6772C2212yes—
14C2×Dic60C2211yescharacteristic
15#91776C2212yes—
16C2×C5×D24C2211yescharacteristic
17C5×#893C2212yes—
18C2×C3×C8×D5C2211yescharacteristic
19C3×#4038C2212yes—
20#91442—22no—
21#91441—22no—
22#91435C2212yes—
23#91398—22no—
24C4×D3×Dic5—22no—
25C4×D5×Dic3C2211yescharacteristic
26#91340C2212yes—
27C2×#6659C2212yes—
28C2×D5×C3⋊C8C2211yescharacteristic
29#91270C418yescomplemented
30C3×C5×#106C2211yescharacteristic
31#91099C2211yescharacteristic
32#91094C2212yes—
33C5×#815C2211yescharacteristic
34C5×#809C2212yes—
35C3×#3949C2211yescharacteristic
36C3×#3939C2212yes—
37#90974C2212yes—
38#90966C2212yes—
39#90954C2211yescharacteristic
40#90953C2211yescharacteristic
41#79166—51nomaximal, Hall
42C2×#4058—31no—
43C4×#711—32no—
44C5×#442—31no—
45#65441—31no—
46#65307—32no—
47#65149D311yescharacteristic, complemented
48#65142—31no—
49#65061—32no—
50#65046—32no—
51#65005—31no—
52D5×#97—31no—
53C2×Dic30C2312yes—
54C2×C5×D12C2312yes—
55C2×C4×C5×D3—22no—
56C2×C3×C4×D5C2311yescharacteristic
57C2×#1201—22no—
58C2×D3×Dic5—22no—
59C2×D3×Dic5—22no—
60C2×D5×Dic3D412yes—
61#6772—24no—
62#6772C2×C418yescomplemented
63C2×C3×C5×C8C2311yescharacteristic
64C3×C5×C4⋊C4C2312yes—
65#6712—22no—
66C4×Dic15—22no—
67C4×Dic15C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69Dic60C2×C414yescomplemented
70C5×(C2×D3)⋊C4—22no—
71C4×C5×Dic3C2311yescharacteristic
72C2×C5×C3⋊C8C2311yescharacteristic
73C5×D24C2×C414yescomplemented
74C3×#685—22no—
75C3×C4⋊Dic5C2312yes—
76C3×C4×Dic5—22no—
77C2×C3×#168C2311yescharacteristic
78C3×C8×D5C2×C414yescomplemented
79#6669—22no—
80(C2×D3)⋊Dic5—22no—
81Dic3×Dic5—22no—
82Dic3×Dic5D412yes—
83#6659C2×C418yescomplemented
84D5×C3⋊C8—22no—
85C2×#904—51no—
86#5522—52no—
87C3×#427—51no—
88C2×#815—51no—
89#5002—52no—
90#4889—52no—
91#4889—52no—
92#4869—51no—
93#4869D511yescharacteristic, complemented
94#4853—51no—
95#4853—51no—
96C2×#711—32no—
97C2×C5×D8—31no—
98C4×C5×D4—32no—
99D4×Dic5—32no—
100C2×#687—32no—
101C4×C22⋊D5—62no—
102C2×C4×Dic5—62no—
103#4058—38no—
104C2×Dic20—31no—
105C2×C8×D5—31no—
106C2×C8×D5C2×D311yescharacteristic
107#4038C2×D312yes—
108#4033—32no—
109#4027—62no—
110#4023—62no—
111C42×D5—31no—
112C4×Dic10—32no—
113C5×#106C2×D311yescharacteristic
114C5×#102—32no—
115C5×#97—31no—
116#3964—32no—
117#3949C2×D311yescharacteristic
118#3948—32no—
119#3947—31no—
120#3947—31no—
121#3942—32no—
122#3939C2×D312yes—
123#3935—31no—
124#2943—151noSylow
125C22×C5×D3—22no—
126C22×C3×D5C2×D411yescharacteristic
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5C2411yescharacteristic
129C2×Dic15—22no—
130C2×Dic15C2×D412yes—
131Dic30—22no—
132Dic30C22×C414yes—
133C2×C5×Dic3C2×D412yes—
134C5×D12—22no—
135C5×D12C22×C414yes—
136C4×C5×D3—44no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5C2×D411yescharacteristic
139C3×C4×D5C22×C412yes—
140C3×C4×D5#4112yes—
141#1201—28no—
142D3×Dic5—28no—
143D3×Dic5—44no—
144D5×Dic3—42no—
145C3×C5×C8C22×C412yes—
146C3⋊#168—21no—
147C3×#168C22×C412yes—
148C5×C3⋊C8—21no—
149C2×#235—52no—
150C22×C3×C8—51no—
151C3×#117—52no—
152C2×C4×Dic3—51no—
153C22×C3⋊C8—51no—
154C2×Dic12—51no—
155#904—58no—
156C2×D24C2×D511yescharacteristic
157C2×#204—52no—
158#893—52no—
159#893C2×D512yes—
160#887—52no—
161#887—52no—
162#67⋊C4—102no—
163#67⋊C4—102no—
164#872—102no—
165C42×D3—102no—
166C3×#107—52no—
167C3×#106—51no—
168C3×#106C2×D511yescharacteristic
169#815—51no—
170#815—51no—
171#815—51no—
172#815C2×D511yescharacteristic
173#810—52no—
174#810—52no—
175#809—52no—
176#809C2×D512yes—
177C2×C5×D4—32no—
178C22×C4×C5—62no—
179C2×C22⋊D5—62no—
180C22×Dic5—62no—
181C22×Dic5—62no—
182#711—38no—
183#711—64no—
184C2×C4×D5—32no—
185C2×C4×D5C22×D311yescharacteristic
186C2×Dic10—32no—
187C5×D8—34no—
188C2×C5×C8—31no—
189C2×C5×C8C22×D311yescharacteristic
190C5×C4⋊C4C22×D312yes—
191C5×C22⋊C4—62no—
192C42×C5—31no—
193C22⋊Dic5—62no—
194#687—38no—
195#685—22no—
196C4⋊Dic5C22×D312yes—
197#683—62no—
198#683—62no—
199C4×Dic5—22no—
200C4×Dic5—31no—
201C4×Dic5—32no—
202C4×Dic5—62no—
203C4×Dic5—62no—
204C2×#168—31no—
205C2×#168C22×D311yescharacteristic
206Dic20—34no—
207C8×D5—62no—
208C8×D5C4×D314yescomplemented
209C2×#135—151no—
210C4×#41—152no—
211#442—31no—
212#442—151no—
213#441—151no—
214#441—151no—
215#440—152no—
216#440—152no—
217#427—51no—
218#416—152no—
219C2×#97—151no—
220C22×C3×C5C22×D411yescharacteristic
221C2×C5×D3—24no—
222C2×C5×D3—42no—
223C2×C5×D3—42no—
224C2×C3×D5—22no—
225C2×C3×D5C4×D412yes—
226C3×C4×C5—42no—
227C3×C4×C5C23×C411yescharacteristic
228C3×C4×C5C2×#4111yescharacteristic
229Dic15—24no—
230Dic15—22no—
231C3×Dic5—42no—
232C3×Dic5C4×D412yes—
233C5×Dic3—22no—
234C22×C3×C4—51no—
235C2×#67—102no—
236C22×Dic3—52no—
237#235—58no—
238#235—104no—
239C2×D12C22×D512yes—
240C2×C4×D3—22no—
241C2×C4×D3—102no—
242C2×C4×D3—102no—
243C2×Dic6—52no—
244C2×C3×C8—51no—
245C2×C3×C8—54no—
246C2×C3×C8C22×D511yescharacteristic
247C3×C4⋊C4—52no—
248C3×C4⋊C4C22×D512yes—
249C3×C22⋊C4—102no—
250C3×C42—102no—
251(C2×D3)⋊C4—22no—
252(C2×D3)⋊C4—102no—
253Dic3⋊C4—102no—
254Dic3⋊C4—102no—
255C4×Dic3—51no—
256C4×Dic3—52no—
257C4×Dic3—102no—
258C4×Dic3—102no—
259C4×Dic3C22×D511yescharacteristic
260C2×C3⋊C8—51no—
261C2×C3⋊C8—102no—
262C2×C3⋊C8C22×D511yescharacteristic
263Dic12—54no—
264D24C4×D514yescomplemented
265#204—58no—
266C23×C5—62no—
267C22×D5D3×D411yescharacteristic
268C5×D4—34no—
269C5×D4—62no—
270C2×C4×C5—22no—
271C2×C4×C5—32no—
272C2×C4×C5—124no—
273C2×C4×C5C23×D311yescharacteristic
274C22⋊D5—68no—
275C2×Dic5—22no—
276C2×Dic5—32no—
277C2×Dic5—62no—
278C2×Dic5—68no—
279C2×Dic5—124no—
280C2×Dic5D3×D411yescharacteristic
281C4×D5—122no—
282C4×D5C2×C4×D312yes—
283C4×D5#23912yes—
284Dic10—34no—
285Dic10—62no—
286C5×C8—61no—
287C5×C8C2×C4×D312yes—
288#168—61no—
289#168C2×C4×D312yes—
290C2×#41—152no—
291#135—158no—
292C2×Q16—151no—
293C2×SD16—152no—
294C2×D8—31no—
295C22×C8—51no—
296C22×C8—151no—
297C4×Q8—152no—
298C4×Q8—152no—
299C4×D4—32no—
300C4×D4—152no—
301C4×D4—302no—
302C4×D4—302no—
303#117—52no—
304#117—302no—
305C2×C42—151no—
306C2×C42—302no—
307#107—52no—
308#106—51no—
309#106D3×D511yescharacteristic
310#103—152no—
311#103—152no—
312#102—32no—
313#102—152no—
314#97—31no—
315#97—151no—
316#97—151no—
317#97—151no—
318C2×C3×C5C2×C4×D411yescharacteristic
319C2×C3×C5#57512yes—
320C3×D5—22no—
321C5×D3—44no—
322C23×C3—51no—
323C22×D3—22no—
324C2×C3×C4—22no—
325C2×C3×C4—51no—
326C2×C3×C4—52no—
327C2×C3×C4—52no—
328C2×C3×C4—102no—
329C2×C3×C4C23×D511yescharacteristic
330#67—108no—
331C2×Dic3—52no—
332C2×Dic3—102no—
333C2×Dic3—202no—
334C2×Dic3D4×D512yes—
335D12—22no—
336D12C2×C4×D514yes—
337C4×D3—44no—
338C4×D3—108no—
339C4×D3—204no—
340Dic6—54no—
341Dic6—102no—
342C3×C8—52no—
343C3×C8C2×C4×D512yes—
344C3⋊C8—21no—
345C3⋊C8—101no—
346C22×C5—64no—
347C22×C5—122no—
348C22×C5—122no—
349C22×C5C2×D3×D411yescharacteristic
350C2×D5—22no—
351C2×D5#89312yes—
352C4×C5—42no—
353C4×C5—62no—
354C4×C5C22×C4×D311yescharacteristic
355C4×C5C2×#23911yescharacteristic
356Dic5—42no—
357Dic5—64no—
358Dic5—62no—
359Dic5#89312yes—
360#41—158no—
361#41—304no—
362C2×Q8—152no—
363C2×D4—32no—
364C2×D4—302no—
365C22×C4—51no—
366C22×C4—62no—
367C22×C4—152no—
368C22×C4—302no—
369C22×C4—302no—
370Q16—154no—
371SD16—158no—
372D8—34no—
373C2×C8—31no—
374C2×C8—51no—
375C2×C8—54no—
376C2×C8—151no—
377C2×C8—302no—
378C2×C8C2×D3×D511yescharacteristic
379C4⋊C4—52no—
380C4⋊C4—302no—
381C4⋊C4—302no—
382C4⋊C4C2×D3×D512yes—
383C22⋊C4—62no—
384C22⋊C4—102no—
385C22⋊C4—302no—
386C42—31no—
387C42—102no—
388C42—152no—
389C42—151no—
390C42—302no—
391C42—302no—
392C3×C5#294311yescharacteristic, complemented, Hall
393C22×C3—52no—
394C22×C3—102no—
395C22×C3C2×D4×D511yescharacteristic
396C2×D3—24no—
397C2×D3—42no—
398C2×D3—42no—
399C3×C4—42no—
400C3×C4—52no—
401C3×C4—202no—
402C3×C4C22×C4×D511yescharacteristic
403C3×C4D5×#4111yescharacteristic
404Dic3—22no—
405Dic3—102no—
406Dic3—104no—
407C2×C5—124no—
408C2×C5C2×#89311yescharacteristic
409C2×C5#576812yes—
410D5—22no—
411C23—51no—
412C23—62no—
413Q8—154no—
414Q8—302no—
415D4—34no—
416D4—62no—
417D4—308no—
418C2×C4—22no—
419C2×C4—32no—
420C2×C4—51no—
421C2×C4—52no—
422C2×C4—52no—
423C2×C4—102no—
424C2×C4—124no—
425C2×C4—152no—
426C2×C4—308no—
427C2×C4—302no—
428C2×C4—602no—
429C2×C4—604no—
430C2×C4C22×D3×D511yescharacteristic
431C8—52no—
432C8—61no—
433C8—301no—
434C8C4×D3×D512yes—
435C2×C3—102no—
436C2×C3C4×D4×D511yescharacteristic
437C2×C3#6610712yes—
438D3—44no—
439C5#7916611yescharacteristic, complemented, Sylow
440C22—52no—
441C22—64no—
442C22—102no—
443C22—122no—
444C22—122no—
445C22D3×D4×D511yescharacteristic
446C4—42no—
447C4—52no—
448C4—62no—
449C4—202no—
450C4—302no—
451C4—304no—
452C4C2×C4×D3×D511yescharacteristic
453C4D5×#23911yescharacteristic
454C3#1061159511yescharacteristic, complemented, Sylow
455C2—102no—
456C2—124no—
457C2D5×#89311yescharacteristic
458C2#1175407712yes—
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#106C22
socleC22×C3×C5C22×D4
prime radicalC2×#91270C2
cosocleC2×C3×C4×C5C24
hypercenter#106D3×D5
hypocenterC3×C5#2943
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #11753402C2semidirect
3. #11750954C2semidirect
4. C5×#4869C2semidirect
5. C3×#65149C2semidirect
6. #11747876C2semidirect
7. #11747813C2semidirect
8. D5×#815C2semidirect
9. #11747499C2semidirect
10. #11747473C2semidirect
11. #11747235C2semidirect
29. #91270C4semidirect
47. #65149D3semidirect
62. #6772C2×C4semidirect
69. Dic60C2×C4semidirect
73. C5×D24C2×C4semidirect
78. C3×C8×D5C2×C4semidirect
83. #6659C2×C4semidirect
93. #4869D5semidirect
208. C8×D5C4×D3semidirect
264. D24C4×D5semidirect
392. C3×C5#2943semidirect
439. C5#79166semidirect
454. C3#10611595semidirect

Maximal subgroups

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

subgroupindex
C2×#912702
#117534022
#117509542
C5×#48692
C3×#651492
#117478762
#117478132
D5×#8152
#117474992
#117474732
#117472352
#106115953
#791665