Finite Group Databasebeta

← #14416627

Subgroups — #14416627

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×#91275C211yesmaximal, characteristic
2#11753408C212yesmaximal, complemented
3#11750970C211yesmaximal, characteristic, complemented
4C5×#4860C211yesmaximal, characteristic, complemented
5C3×#65142C211yesmaximal, characteristic, complemented
6#11747884C211yesmaximal, characteristic, complemented
7#11747772C211yesmaximal, characteristic, complemented
8D3×#3947C211yesmaximal, characteristic, complemented
9#11747504C212yesmaximal, complemented
10#11747273C212yesmaximal, complemented
11#11747224C212yesmaximal, complemented
12#10610897—31nomaximal, Hall
13C2×#6769C2212yes—
14C2×D120C2211yescharacteristic
15#91782C2212yes—
16C2×C5×D3×C8C2211yescharacteristic
17C5×#892C2212yes—
18C2×C3×Dic20C2211yescharacteristic
19C3×#4033C2212yes—
20#91418C2212yes—
21#91406—22no—
22#91405—22no—
23#91403—22no—
24C4×#1200—22no—
25C4×D3×Dic5C2211yescharacteristic
26#91331C2212yes—
27C2×#6658C2212yes—
28C2×D3×#168C2211yescharacteristic
29#91275C418yescomplemented
30C3×C5×#106C2211yescharacteristic
31#91099C2211yescharacteristic
32#91093C2212yes—
33C5×#817C2211yescharacteristic
34C5×#807C2212yes—
35C3×#3947C2211yescharacteristic
36C3×#3942C2212yes—
37#90970C2212yes—
38#90969C2212yes—
39#90954C2211yescharacteristic
40#90952C2211yescharacteristic
41#79828—51nomaximal, Hall
42C2×#4050—31no—
43#65856—32no—
44C5×#427—31no—
45C2×#3947—31no—
46#65291—32no—
47#65178—32no—
48#65178—32no—
49#65158—31no—
50#65158—31no—
51#65142—31no—
52#65142D311yescharacteristic, complemented
53C2×D60C2312yes—
54C2×C4×D15—22no—
55C2×C4×C5×D3C2311yescharacteristic
56C2×C3×Dic10C2312yes—
57C2×#1203—22no—
58C2×#1200—22no—
59C2×#1200—22no—
60C2×D3×Dic5D412yes—
61#6769—24no—
62#6769C2×C418yescomplemented
63C2×C3×C5×C8C2311yescharacteristic
64C3×C5×C4⋊C4C2312yes—
65#6714—22no—
66C4×Dic15C2311yescharacteristic
67C2×C3⋊#168C2311yescharacteristic
68D120C2×C414yescomplemented
69C5×(C2×D3)⋊C4—22no—
70C5×C4⋊Dic3C2312yes—
71C4×C5×Dic3—22no—
72C2×C5×C3⋊C8C2311yescharacteristic
73C5×D3×C8C2×C414yescomplemented
74C3×#683—22no—
75C3×C4×Dic5—22no—
76C3×C4×Dic5C2311yescharacteristic
77C2×C3×#168C2311yescharacteristic
78C3×Dic20C2×C414yescomplemented
79#6668—22no—
80#6667—22no—
81Dic3×Dic5—22no—
82Dic3×Dic5D412yes—
83#6658C2×C418yescomplemented
84D3×#168—22no—
85C2×#919—51no—
86C4×#239—52no—
87C3×#441—51no—
88#5184—51no—
89#5026—52no—
90#4869—51no—
91#4860D511yescharacteristic, complemented
92#4817—52no—
93#4804—52no—
94#4711—51no—
95D3×#97—51no—
96C2×#709—32no—
97C22×C5×C8—31no—
98C5×#117—32no—
99C2×C4×Dic5—31no—
100C22×#168—31no—
101C2×Dic20C2×D311yescharacteristic
102#4050—38no—
103C2×D40—31no—
104C2×#677—32no—
105#4039—32no—
106#4039—32no—
107#4033—32no—
108#4033C2×D312yes—
109#4027—62no—
110#4027—62no—
111#4018—62no—
112C42×D5—62no—
113C5×#107—32no—
114C5×#106—31no—
115C5×#106C2×D311yescharacteristic
116#3947—31no—
117#3947—31no—
118#3947—31no—
119#3947C2×D311yescharacteristic
120#3942—32no—
121#3942C2×D312yes—
122#3941—32no—
123#3941—32no—
124#2943—151noSylow
125C22×D15—22no—
126C22×C5×D3C2×D411yescharacteristic
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5C2411yescharacteristic
129C2×Dic15C2×D412yes—
130D60—22no—
131D60C22×C414yes—
132C4×D15—44no—
133C2×C5×Dic3—22no—
134C2×C5×Dic3C2×D411yescharacteristic
135C4×C5×D3C22×C412yes—
136C4×C5×D3#4112yes—
137C2×C3×Dic5—22no—
138C2×C3×Dic5C2×D412yes—
139C3×Dic10—22no—
140C3×Dic10C22×C414yes—
141#1203—28no—
142#1200—28no—
143#1200—44no—
144D3×Dic5—42no—
145C3×C5×C8C22×C412yes—
146C3⋊#168—21no—
147C3×#168—21no—
148C5×C3⋊C8C22×C412yes—
149C2×#239—52no—
150C2×C3×Q16—51no—
151C3×C4×Q8—52no—
152Q8×Dic3—52no—
153C2×#215—52no—
154#919—58no—
155C2×D24—51no—
156C2×D3×C8—51no—
157C2×D3×C8C2×D511yescharacteristic
158#893—52no—
159#893—102no—
160#892—102no—
161#892C2×D512yes—
162C4×D12—52no—
163C4×D12—102no—
164C42×D3—51no—
165C42×D3—102no—
166C3×#106C2×D511yescharacteristic
167C3×#103—52no—
168C3×#97—51no—
169#835—52no—
170#821—52no—
171#817C2×D511yescharacteristic
172#815—51no—
173#815—51no—
174#809—52no—
175#807C2×D512yes—
176#803—51no—
177C22×C4×C5—31no—
178C2×C22⋊D5—62no—
179C22×Dic5—32no—
180#709—38no—
181#709—64no—
182C2×D20—32no—
183C2×C4×D5—62no—
184C2×C4×D5—62no—
185C2×C4×D5—62no—
186C2×Dic10C22×D312yes—
187C2×C5×C8—31no—
188C2×C5×C8—34no—
189C2×C5×C8C22×D311yescharacteristic
190C5×C4⋊C4—32no—
191C5×C4⋊C4C22×D312yes—
192C5×C22⋊C4—62no—
193C42×C5—62no—
194#685—62no—
195#685—62no—
196#683—22no—
197#683—62no—
198C4×Dic5—22no—
199C4×Dic5—31no—
200C4×Dic5—32no—
201C4×Dic5—62no—
202C4×Dic5C22×D311yescharacteristic
203C2×#168—31no—
204C2×#168—62no—
205C2×#168C22×D311yescharacteristic
206Dic20C4×D314yescomplemented
207D40—34no—
208#677—38no—
209C2×#135—151no—
210C4×#41—152no—
211#442—151no—
212#442—151no—
213#441—51no—
214#441—151no—
215#440—152no—
216#440—152no—
217#427—31no—
218#416—152no—
219C2×#97—151no—
220C22×C3×C5C22×D411yescharacteristic
221C2×D15—24no—
222C2×D15—42no—
223C2×D15—42no—
224C2×C5×D3—22no—
225C2×C5×D3C4×D412yes—
226C3×C4×C5—42no—
227C3×C4×C5C23×C411yescharacteristic
228C3×C4×C5C2×#4111yescharacteristic
229Dic15—22no—
230C3×Dic5—24no—
231C3×Dic5—22no—
232C5×Dic3—42no—
233C5×Dic3C4×D412yes—
234C2×C3×Q8—52no—
235#239—58no—
236#239—104no—
237C2×D12—52no—
238C2×D12—102no—
239C2×C4×D3—52no—
240C2×C4×D3—102no—
241C2×C4×D3—102no—
242C2×C4×D3—102no—
243C2×C4×D3C22×D511yescharacteristic
244C3×Q16—54no—
245C2×C3×C8—51no—
246C2×C3×C8C22×D511yescharacteristic
247C3×C4⋊C4—102no—
248C3×C4⋊C4C22×D512yes—
249C3×C42—51no—
250C3×C42—102no—
251#215—58no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—102no—
254(C2×D3)⋊C4—102no—
255C4⋊Dic3—102no—
256C4⋊Dic3C22×D512yes—
257C4×Dic3—22no—
258C4×Dic3—51no—
259C4×Dic3—52no—
260C4×Dic3—102no—
261C2×C3⋊C8—51no—
262C2×C3⋊C8C22×D511yescharacteristic
263D24—54no—
264D3×C8—102no—
265D3×C8C4×D514yescomplemented
266C23×C5—31no—
267C22×D5—62no—
268C2×C4×C5—22no—
269C2×C4×C5—31no—
270C2×C4×C5—32no—
271C2×C4×C5—32no—
272C2×C4×C5—62no—
273C2×C4×C5C23×D311yescharacteristic
274C22⋊D5—68no—
275C2×Dic5—22no—
276C2×Dic5—32no—
277C2×Dic5—122no—
278C2×Dic5D3×D412yes—
279D20—34no—
280D20—62no—
281C4×D5—68no—
282C4×D5—124no—
283C4×D5—124no—
284Dic10—22no—
285Dic10C2×C4×D314yes—
286C5×C8—32no—
287C5×C8C2×C4×D312yes—
288#168—21no—
289#168—61no—
290C2×#41—152no—
291#135—158no—
292C2×Q16—51no—
293C2×SD16—152no—
294C2×D8—151no—
295C22×C8—31no—
296C22×C8—151no—
297C4×Q8—52no—
298C4×Q8—152no—
299C4×D4—152no—
300C4×D4—152no—
301C4×D4—302no—
302C4×D4—302no—
303#117—32no—
304#117—302no—
305C2×C42—151no—
306C2×C42—302no—
307#107—32no—
308#106—31no—
309#106D3×D511yescharacteristic
310#103—52no—
311#103—152no—
312#102—152no—
313#102—152no—
314#97—51no—
315#97—151no—
316#97—151no—
317#97—151no—
318C2×C3×C5C2×C4×D411yescharacteristic
319C2×C3×C5#57512yes—
320D15—44no—
321C5×D3—22no—
322C22×D3—102no—
323C22×D3D4×D511yescharacteristic
324C3×Q8—54no—
325C3×Q8—102no—
326C2×C3×C4—22no—
327C2×C3×C4—52no—
328C2×C3×C4—102no—
329C2×C3×C4C23×D511yescharacteristic
330C2×Dic3—22no—
331C2×Dic3—52no—
332C2×Dic3D4×D511yescharacteristic
333D12—54no—
334D12—108no—
335D12—102no—
336C4×D3—108no—
337C4×D3—204no—
338C4×D3—204no—
339C4×D3—202no—
340C4×D3C2×C4×D512yes—
341C4×D3#71312yes—
342C3×C8—101no—
343C3×C8C2×C4×D512yes—
344C3⋊C8—101no—
345C3⋊C8C2×C4×D512yes—
346C22×C5—32no—
347C22×C5—62no—
348C22×C5C2×D3×D411yescharacteristic
349C2×D5—64no—
350C2×D5—122no—
351C2×D5—122no—
352C4×C5—32no—
353C4×C5—42no—
354C4×C5—122no—
355C4×C5C22×C4×D311yescharacteristic
356C4×C5D3×#4111yescharacteristic
357Dic5—22no—
358Dic5—24no—
359Dic5—62no—
360#41—158no—
361#41—304no—
362C2×Q8—52no—
363C2×D4—152no—
364C2×D4—302no—
365C22×C4—31no—
366C22×C4—152no—
367C22×C4—302no—
368C22×C4—302no—
369C22×C4—302no—
370Q16—54no—
371SD16—158no—
372D8—154no—
373C2×C8—31no—
374C2×C8—34no—
375C2×C8—51no—
376C2×C8—151no—
377C2×C8—302no—
378C2×C8C2×D3×D511yescharacteristic
379C4⋊C4—32no—
380C4⋊C4—102no—
381C4⋊C4—302no—
382C4⋊C4C2×D3×D512yes—
383C22⋊C4—62no—
384C22⋊C4—302no—
385C22⋊C4—302no—
386C42—51no—
387C42—62no—
388C42—102no—
389C42—152no—
390C42—151no—
391C42—302no—
392C3×C5#294311yescharacteristic, complemented, Hall
393C22×C3C2×D4×D511yescharacteristic
394C2×D3—22no—
395C2×D3—104no—
396C2×D3—202no—
397C2×D3—202no—
398C2×D3#403912yes—
399C3×C4—42no—
400C3×C4—104no—
401C3×C4—102no—
402C3×C4C22×C4×D511yescharacteristic
403C3×C4C2×#71311yescharacteristic
404Dic3—42no—
405Dic3—102no—
406Dic3#403912yes—
407C2×C5—62no—
408C2×C5C4×D3×D411yescharacteristic
409C2×C5#577712yes—
410D5—124no—
411C23—31no—
412C23—302no—
413Q8—54no—
414Q8—102no—
415D4—154no—
416D4—308no—
417D4—302no—
418C2×C4—22no—
419C2×C4—31no—
420C2×C4—32no—
421C2×C4—32no—
422C2×C4—52no—
423C2×C4—62no—
424C2×C4—102no—
425C2×C4—152no—
426C2×C4—308no—
427C2×C4—604no—
428C2×C4—604no—
429C2×C4—602no—
430C2×C4C22×D3×D511yescharacteristic
431C8—32no—
432C8—101no—
433C8—301no—
434C8C4×D3×D512yes—
435C2×C3C2×#403911yescharacteristic
436C2×C3#6610212yes—
437D3—22no—
438D3—204no—
439C5#7982811yescharacteristic, complemented, Sylow
440C22—32no—
441C22—62no—
442C22—304no—
443C22—602no—
444C22—602no—
445C22D3×D4×D511yescharacteristic
446C4—32no—
447C4—42no—
448C4—102no—
449C4—104no—
450C4—122no—
451C4—302no—
452C4C2×C4×D3×D511yescharacteristic
453C4D3×#71311yescharacteristic
454C3#1061089711yescharacteristic, complemented, Sylow
455C2—62no—
456C2—604no—
457C2D3×#403911yescharacteristic
458C2#1175407512yes—
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#106C22
socleC22×C3×C5C22×D4
prime radicalC2×#91275C2
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. #11753408C2semidirect
3. #11750970C2semidirect
4. C5×#4860C2semidirect
5. C3×#65142C2semidirect
6. #11747884C2semidirect
7. #11747772C2semidirect
8. D3×#3947C2semidirect
9. #11747504C2semidirect
10. #11747273C2semidirect
11. #11747224C2semidirect
29. #91275C4semidirect
52. #65142D3semidirect
62. #6769C2×C4semidirect
68. D120C2×C4semidirect
73. C5×D3×C8C2×C4semidirect
78. C3×Dic20C2×C4semidirect
83. #6658C2×C4semidirect
91. #4860D5semidirect
206. Dic20C4×D3semidirect
265. D3×C8C4×D5semidirect
392. C3×C5#2943semidirect
439. C5#79828semidirect
454. C3#10610897semidirect

Maximal subgroups

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

subgroupindex
C2×#912752
#117534082
#117509702
C5×#48602
C3×#651422
#117478842
#117477722
D3×#39472
#117475042
#117472732
#117472242
#106108973
#798285