Finite Group Databasebeta

← #14438636

Subgroups — #14438636

Order 1920.

848 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×C4⋊Q8C211yesmaximal, characteristic, complemented
2#11752674C211yesmaximal, characteristic
3#11751189C211yesmaximal, characteristic, complemented
4C5×#5093C211yesmaximal, characteristic, complemented
5#11747500C214yesmaximal, complemented
6#11747159C214yesmaximal, complemented
7C4×#6649C211yesmaximal, characteristic, complemented
8#11746923C211yesmaximal, characteristic, complemented
9#11746910C211yesmaximal, characteristic, complemented
10#10613332—31nomaximal, Hall
11C2×C3×Q8×D5—21no—
12C2×#6773C2212yes—
13C3×C5×C4⋊Q8C2211yescharacteristic
14#91763C2211yescharacteristic
15C5×#869C2211yescharacteristic
16C3×#4090—21no—
17C3×D5×C4⋊C4—21no—
18C3×D5×C4⋊C4C2212yes—
19C3×#4034—21no—
20C3×#4034C2212yes—
21C3×C42×D5C2211yescharacteristic
22C3×#4015C2211yescharacteristic
23#91450—21no—
24#91450—21no—
25#91418—21no—
26#91418—21no—
27#91375C2212yes—
28C2×#6649C2212yes—
29#91093C2214yes—
30C4×C3⋊#168C2211yescharacteristic
31C5×#810C2214yes—
32C4×C5×C3⋊C8C2211yescharacteristic
33#90972C2214yes—
34#90968C2214yes—
35#90952C2212yes—
36#83199—51nomaximal, Hall
37#66059—31no—
38D5×C4⋊Q8D311yescharacteristic, complemented
39C5×#487—31no—
40#65377—31no—
41#65370—31no—
42#65092—34no—
43#65084—34no—
44#64983—31no—
45C4×#676—31no—
46C2×C3×C5×Q8—21no—
47C2×D60—21no—
48C2×D60—21no—
49C2×D60C2312yes—
50C2×C5×Dic6C2312yes—
51C3×Q8×D5—44no—
52C2×C3×C4×D5—22no—
53C2×C3×C4×D5D411yescharacteristic
54C2×C3×C4×D5D411yescharacteristic
55C2×C3×C4×D5C2311yescharacteristic
56C2×C3×Dic10—21no—
57C2×C3×Dic10—22no—
58C2×#1202—22no—
59C2×#1200—22no—
60#6773—28no—
61C3×C5×C4⋊C4—21no—
62C3×C5×C4⋊C4C2312yes—
63C3×C42×C5C2311yescharacteristic
64C2×C3⋊#168C2312yes—
65C5×C4⋊Dic3—21no—
66C5×C4⋊Dic3—21no—
67C2×C5×C3⋊C8C2312yes—
68C3×C4⋊Dic5—21no—
69C3×C4⋊Dic5C2312yes—
70C3×#683—22no—
71C3×#683—22no—
72C3×C4×Dic5D411yescharacteristic
73C3×C4×Dic5D411yescharacteristic
74C3×C4×Dic5C2311yescharacteristic
75#6667—22no—
76#6667—22no—
77#6649—24no—
78C2×C3×C4⋊Q8—51no—
79#5477—51no—
80#5093—51no—
81#5093D511yescharacteristic, complemented
82#5089—54no—
83#5088—51no—
84#5088—51no—
85#4966—54no—
86C4×#208—51no—
87C2×#713—32no—
88C2×Q8×D5—21no—
89C5×C4⋊Q8—31no—
90C5×C4⋊Q8C2×D311yescharacteristic
91#4093—32no—
92#4090—21no—
93C2×#676—32no—
94#4041—61no—
95#4041—61no—
96#4039—61no—
97#4039—61no—
98D5×C4⋊C4—21no—
99D5×C4⋊C4C2×D312yes—
100#4034—21no—
101#4034C2×D312yes—
102#4020—31no—
103C42×D5C2×D311yescharacteristic
104#4015C2×D311yescharacteristic
105C5×#103—34no—
106C4×C5×C8—31no—
107#3967—34no—
108#3953—34no—
109#3947—32no—
110#3941—34no—
111C4×#168—31no—
112#3141—151noSylow
113C22×D15—22no—
114C22×C3×D5C2×D411yescharacteristic
115C3×C5×Q8—42no—
116C2×C3×C4×C5—22no—
117C2×C3×C4×C5C2×D411yescharacteristic
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2411yescharacteristic
120D60—24no—
121D60—42no—
122D60—42no—
123C2×C5×Dic3—22no—
124C5×Dic6—24no—
125C2×C3×Dic5—22no—
126C2×C3×Dic5C2×D411yescharacteristic
127C2×C3×Dic5C2×D411yescharacteristic
128C2×C3×Dic5C2×D411yescharacteristic
129C3×C4×D5—22no—
130C3×C4×D5—22no—
131C3×C4×D5—44no—
132C3×C4×D5#4114yes—
133C3×Dic10—44no—
134C3×Dic10—42no—
135#1202—44no—
136#1200—44no—
137C3⋊#168—22no—
138C5×C3⋊C8—22no—
139C22×C3×Q8—101no—
140C2×#235—52no—
141C3×C4⋊Q8—52no—
142C3×C4⋊Q8—51no—
143C3×C4⋊Q8—101no—
144C3×C4⋊Q8—101no—
145C3×C4⋊Q8C2×D511yescharacteristic
146C2×C3×C4⋊C4—52no—
147C2×C3×C4⋊C4—101no—
148C2×C3×C42—51no—
149#930—101no—
150#930—101no—
151C2×#208—52no—
152#875—52no—
153#874—51no—
154C4×D12—101no—
155C4×D12—101no—
156#869C2×D511yescharacteristic
157#810—54no—
158#810C2×D514yes—
159#809—54no—
160#809—54no—
161#803—52no—
162C4×C3⋊C8—51no—
163C4×C3⋊C8C2×D511yescharacteristic
164C2×C5×Q8—21no—
165C2×C5×Q8—32no—
166#713—68no—
167Q8×D5—44no—
168C2×D20—32no—
169C2×D20—62no—
170C2×D20—61no—
171C2×D20—61no—
172C2×C4×D5—22no—
173C2×C4×D5—62no—
174C2×C4×D5#6711yescharacteristic
175C2×C4×D5#6711yescharacteristic
176C2×C4×D5C22×D311yescharacteristic
177C2×Dic10—21no—
178C2×Dic10—22no—
179C2×C5×C8—32no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—61no—
182C5×C4⋊C4—61no—
183C5×C4⋊C4C22×D312yes—
184C42×C5C22×D311yescharacteristic
185#685—62no—
186#685—62no—
187C4⋊Dic5—21no—
188C4⋊Dic5C22×D312yes—
189#683—22no—
190#683—22no—
191C4×Dic5#6711yescharacteristic
192C4×Dic5#6711yescharacteristic
193C4×Dic5C22×D311yescharacteristic
194C2×#168—32no—
195#676—64no—
196#532—151no—
197C2×C4⋊Q8—51no—
198#489—154no—
199#487—31no—
200#487—151no—
201#486—151no—
202#486—151no—
203#417—154no—
204C4×M16—151no—
205C22×C3×C5C22×D411yescharacteristic
206C2×D15—42no—
207C2×D15—42no—
208C2×D15—42no—
209C2×C3×D5—21no—
210C2×C3×D5—21no—
211C2×C3×D5#12412yes—
212C3×C4×C5—42no—
213C3×C4×C5AGL(1,ℤ/8)12yes—
214C3×C4×C5#13712yes—
215C3×C4×C5C2×#4112yes—
216C3×Dic5—21no—
217C3×Dic5—21no—
218C3×Dic5—42no—
219C3×Dic5#12412yes—
220C5×Dic3—42no—
221C2×C3×Q8—21no—
222C2×C3×Q8—102no—
223C2×C3×Q8—101no—
224C2×C3×Q8—204no—
225C22×C3×C4—51no—
226C22×C3×C4—51no—
227C22×C3×C4—51no—
228C22×C3×C4—102no—
229C2×#67—102no—
230#235—108no—
231C2×D12—52no—
232C2×D12—101no—
233C2×D12—101no—
234C2×C4×D3—102no—
235C2×Dic6C22×D512yes—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—52no—
238C3×C4⋊C4—102no—
239C3×C4⋊C4—102no—
240C3×C4⋊C4—101no—
241C3×C4⋊C4C22×D512yes—
242C3×C42—51no—
243C3×C42—51no—
244C3×C42—51no—
245C3×C42C22×D511yescharacteristic
246(C2×D3)⋊C4—102no—
247(C2×D3)⋊C4—102no—
248C4⋊Dic3—21no—
249C4⋊Dic3—21no—
250#208—104no—
251C2×C3⋊C8—52no—
252C2×C3⋊C8C22×D512yes—
253C22×D5—62no—
254C22×D5C2×#6711yescharacteristic
255C5×Q8—42no—
256C5×Q8—64no—
257C2×C4×C5—22no—
258C2×C4×C5—62no—
259C2×C4×C5C2×#6711yescharacteristic
260C2×C4×C5C2×#6711yescharacteristic
261C2×C4×C5C23×D311yescharacteristic
262C2×Dic5—22no—
263C2×Dic5C2×#6711yescharacteristic
264C2×Dic5C2×#6711yescharacteristic
265C2×Dic5C2×#6711yescharacteristic
266D20—64no—
267D20—124no—
268D20—122no—
269D20—122no—
270C4×D5—22no—
271C4×D5—22no—
272C4×D5—44no—
273C4×D5—124no—
274C4×D5#23914yes—
275Dic10—44no—
276Dic10—42no—
277C5×C8—62no—
278#168—62no—
279C2×#41—152no—
280C22×Q8—101no—
281C2×M16—152no—
282C4⋊Q8—31no—
283C4⋊Q8—52no—
284C4⋊Q8—51no—
285C4⋊Q8—101no—
286C4⋊Q8—101no—
287C4⋊Q8D3×D511yescharacteristic
288#127—151no—
289#124—152no—
290#121—301no—
291#121—301no—
292C4×D4—301no—
293C4×D4—301no—
294C2×C4⋊C4—52no—
295C2×C4⋊C4—101no—
296C2×C42—51no—
297#103—34no—
298#103—154no—
299#102—154no—
300#102—154no—
301#97—152no—
302C4×C8—31no—
303C4×C8—151no—
304C2×C3×C5C2×#12411yescharacteristic
305C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
306C2×C3×C5C2×#13711yescharacteristic
307D15—82no—
308C3×D5—22no—
309C23×C3—51no—
310C22×D3—102no—
311C3×Q8—42no—
312C3×Q8—204no—
313C3×Q8—202no—
314C2×C3×C4—22no—
315C2×C3×C4—51no—
316C2×C3×C4—54no—
317C2×C3×C4—51no—
318C2×C3×C4—51no—
319C2×C3×C4—102no—
320C2×C3×C4—102no—
321C2×C3×C4—102no—
322C2×C3×C4—204no—
323C2×C3×C4D4×D511yescharacteristic
324C2×C3×C4D4×D511yescharacteristic
325C2×C3×C4C23×D511yescharacteristic
326#67—204no—
327C2×Dic3—22no—
328D12—104no—
329D12—202no—
330D12—202no—
331C4×D3—204no—
332Dic6—24no—
333C3⋊C8—22no—
334C3⋊C8—102no—
335C22×C5C22×#6711yescharacteristic
336C2×D5—21no—
337C2×D5—21no—
338C2×D5—122no—
339C2×D5—122no—
340C2×D5—122no—
341C2×D5#94712yes—
342C4×C5—42no—
343C4×C5—122no—
344C4×C5#93212yes—
345C4×C5#94212yes—
346C4×C5C2×#23912yes—
347Dic5—21no—
348Dic5—21no—
349Dic5—42no—
350Dic5#94712yes—
351#41—308no—
352C2×Q8—21no—
353C2×Q8—32no—
354C2×Q8—102no—
355C2×Q8—101no—
356C2×Q8—204no—
357C2×D4—152no—
358C2×D4—302no—
359C2×D4—301no—
360C2×D4—301no—
361C22×C4—51no—
362C22×C4—51no—
363C22×C4—51no—
364C22×C4—102no—
365C22×C4—302no—
366M16—304no—
367C2×C8—32no—
368C2×C8—152no—
369C4⋊C4—21no—
370C4⋊C4—52no—
371C4⋊C4—61no—
372C4⋊C4—61no—
373C4⋊C4—102no—
374C4⋊C4—102no—
375C4⋊C4—101no—
376C4⋊C4C2×D3×D512yes—
377C22⋊C4—302no—
378C22⋊C4—302no—
379C42—51no—
380C42—51no—
381C42—51no—
382C42C2×D3×D511yescharacteristic
383C3×C5#314111yescharacteristic, complemented, Hall
384C22×C3—52no—
385C22×C3—101no—
386C22×C3—101no—
387C22×C3C2×D4×D511yescharacteristic
388C2×D3—202no—
389C2×D3—202no—
390C2×D3—202no—
391C3×C4—42no—
392C3×C4—52no—
393C3×C4—101no—
394C3×C4—101no—
395C3×C4—202no—
396C3×C4#406012yes—
397C3×C4#406412yes—
398C3×C4D5×#4112yes—
399Dic3—42no—
400C2×C5C2×#93211yescharacteristic
401C2×C5C2×#94211yescharacteristic
402C2×C5C2×#94711yescharacteristic
403D5—22no—
404D5—242no—
405C23—51no—
406C23—302no—
407Q8—42no—
408Q8—64no—
409Q8—204no—
410Q8—202no—
411D4—304no—
412D4—604no—
413D4—602no—
414D4—602no—
415C2×C4—22no—
416C2×C4—51no—
417C2×C4—54no—
418C2×C4—51no—
419C2×C4—51no—
420C2×C4—62no—
421C2×C4—102no—
422C2×C4—102no—
423C2×C4—102no—
424C2×C4—204no—
425C2×C4—604no—
426C2×C4D5×#6711yescharacteristic
427C2×C4D5×#6711yescharacteristic
428C2×C4C22×D3×D511yescharacteristic
429C8—62no—
430C8—302no—
431C2×C3—102no—
432C2×C3D5×#12411yescharacteristic
433C2×C3C2×#406011yescharacteristic
434C2×C3C2×#406411yescharacteristic
435D3—402no—
436C5#8319911yescharacteristic, complemented, Sylow
437C22—52no—
438C22—101no—
439C22—101no—
440C22—602no—
441C22—602no—
442C22—602no—
443C22C2×D5×#6711yescharacteristic
444C4—42no—
445C4—52no—
446C4—101no—
447C4—101no—
448C4—122no—
449C4—202no—
450C4#9149112yes—
451C4#9151512yes—
452C4D5×#23912yes—
453C3#1061333211yescharacteristic, complemented, Sylow
454C2—102no—
455C2—1202no—
456C2C2×#9149111yescharacteristic
457C2C2×#9151511yescharacteristic
458C2D5×#94711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11752674C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3141
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×D5×C4⋊Q8C2semidirect
3. #11751189C2semidirect
4. C5×#5093C2semidirect
5. #11747500C2semidirect
6. #11747159C2semidirect
7. C4×#6649C2semidirect
8. #11746923C2semidirect
9. #11746910C2semidirect
38. D5×C4⋊Q8D3semidirect
81. #5093D5semidirect
383. C3×C5#3141semidirect
436. C5#83199semidirect
453. C3#10613332semidirect

Maximal subgroups

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

subgroupindex
C3×D5×C4⋊Q82
#117526742
#117511892
C5×#50932
#117475002
#117471592
C4×#66492
#117469232
#117469102
#106133323
#831995