Finite Group Databasebeta

← #14472167

Subgroups — #14472167

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756480C211yesmaximal, characteristic, complemented
2#11752508C211yesmaximal, characteristic
3C5×#5093C211yesmaximal, characteristic, complemented
4C3×#65376C211yesmaximal, characteristic
5#11747382C212yesmaximal
6#11747381C212yesmaximal
7#11747298C212yesmaximal, complemented
8#11747278C212yesmaximal, complemented
9#11747105C211yesmaximal, characteristic, complemented
10C4×#6657C211yesmaximal, characteristic
11#11746855C211yesmaximal, characteristic, complemented
12#10613356—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14Q8×Dic15—21no—
15#91833—21no—
16#91779C2212yes—
17#91778—22no—
18#91776C2212yes—
19C4×Dic30C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C5×#869C2211yescharacteristic
22C3×C4×D20C2211yescharacteristic
23#91368C2212yes—
24#91361—22no—
25#91360—21no—
26#91358—21no—
27#91344C2212yes—
28C2×#6663C2212yes—
29C2×#6657C2211yescharacteristic
30C5×#810C2212yes—
31C5×#810C2212yes—
32C4×C5×C3⋊C8C2211yescharacteristic
33C3×#3941C2212yes—
34C3×#3939C2212yes—
35C3×C4⋊#168C2211yescharacteristic
36#90987C2211yescharacteristic
37#90983C2212yes—
38#90974C2211yescharacteristic
39#90973C2212yes—
40#90965C2211yescharacteristic
41#90951C2212yes—
42#80994—51nomaximal, Hall
43#66066—31no—
44#66055—31no—
45C5×#487—31no—
46#65379—31no—
47#65376D311yescharacteristic
48#65089—32no—
49#65088—32no—
50#65087—32no—
51#65079—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8—21no—
55C2×Dic30D411yescharacteristic
56C2×Dic30C2311yescharacteristic
57C2×C5×Dic6C2312yes—
58C2×C3×D20C2311yescharacteristic
59C2×C3×C4×D5—21no—
60C3×C5×C4⋊C4—21no—
61C3×C5×C4⋊C4C2312yes—
62C3×C42×C5C2311yescharacteristic
63C4⋊Dic15—22no—
64C4⋊Dic15D411yescharacteristic
65C4⋊Dic15C2311yescharacteristic
66#6712—21no—
67#6712—22no—
68#6712—22no—
69#6712D412yes—
70C4×Dic15—21no—
71C4×Dic15—22no—
72C4×Dic15C2312yes—
73C5×C4⋊Dic3—21no—
74C5×C4⋊Dic3—21no—
75C2×C5×C3⋊C8C2311yescharacteristic
76C2×C5×C3⋊C8C2311yescharacteristic
77C3×#685—21no—
78C3×C4⋊Dic5C2311yescharacteristic
79C2×C3×#168C2312yes—
80Dic3⋊Dic5—22no—
81#6665—22no—
82#6665—22no—
83Dic3×Dic5—22no—
84#6663—24no—
85#6657—22no—
86#5721—51no—
87#5542—51no—
88C3×#474—51no—
89#5093D511yescharacteristic, complemented
90C4×#214—51no—
91#4877—52no—
92#4873—52no—
93#4849—51no—
94#4830—51no—
95#4768—52no—
96#4767—52no—
97C5×C4⋊Q8—31no—
98C5×C4⋊Q8C2×D311yescharacteristic
99#4093—32no—
100Q8×Dic5—32no—
101Q8×Dic5—61no—
102#4090—61no—
103C2×#689—32no—
104C2×#677—31no—
105#4044—62no—
106#4043—61no—
107#4038—61no—
108#4036—32no—
109#4035—62no—
110#4033—32no—
111C4×D20C2×D311yescharacteristic
112C4×Dic10—31no—
113C4×Dic10—31no—
114C5×#103—32no—
115C5×#103—32no—
116C4×C5×C8—31no—
117#3967—32no—
118#3953—31no—
119#3949—31no—
120#3948—31no—
121#3946—32no—
122C8×Dic5—32no—
123#3941C2×D312yes—
124#3939C2×D312yes—
125C4⋊#168C2×D311yescharacteristic
126#3364—151noSylow
127C22×C3×D5—21no—
128C3×C5×Q8—42no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2411yescharacteristic
133C2×Dic15—21no—
134C2×Dic15—21no—
135C2×Dic15C2×D412yes—
136C2×Dic15C2×D412yes—
137Dic30—22no—
138Dic30—21no—
139Dic30#4112yes—
140C2×C5×Dic3—22no—
141C5×Dic6—22no—
142C5×Dic6—22no—
143C2×C3×Dic5—21no—
144C3×D20—21no—
145C3×D20—21no—
146C3×C4×D5—42no—
147C3×#168—22no—
148C5×C3⋊C8—21no—
149C5×C3⋊C8—21no—
150C3×C4⋊Q8C2×D511yescharacteristic
151C3×C4×D4—51no—
152Q8×Dic3—101no—
153#944—101no—
154#936—52no—
155C2×#214—51no—
156#926—101no—
157#924—101no—
158C2×Dic12—52no—
159#890—52no—
160#889—102no—
161#887—52no—
162#887—52no—
163#879—102no—
164#869C2×D511yescharacteristic
165C4×Dic6—51no—
166C4×Dic6—51no—
167C3×#107—52no—
168C3×C4⋊C8—51no—
169C3×#102—52no—
170#832—51no—
171#816—52no—
172Dic3⋊C8—52no—
173C8×Dic3—52no—
174#810—51no—
175#810C2×D512yes—
176#810C2×D512yes—
177#808—51no—
178C4×C3⋊C8C2×D511yescharacteristic
179C2×C5×Q8—21no—
180C2×C5×Q8—32no—
181C2×D20C22×D311yescharacteristic
182C2×C4×D5—21no—
183C2×Dic10—31no—
184C2×Dic10—31no—
185C2×C5×C8—31no—
186C2×C5×C8—31no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—61no—
189C5×C4⋊C4—61no—
190C5×C4⋊C4C22×D312yes—
191C42×C5C22×D311yescharacteristic
192#689—64no—
193#685—21no—
194#685—62no—
195#685—62no—
196C4⋊Dic5—31no—
197C4⋊Dic5—31no—
198C4⋊Dic5—62no—
199C4⋊Dic5—62no—
200C4⋊Dic5C22×D311yescharacteristic
201#683—32no—
202#683—62no—
203#683—62no—
204#683—61no—
205C4×Dic5—32no—
206C4×Dic5—62no—
207C4×Dic5—62no—
208C4×Dic5—61no—
209C2×#168C22×D312yes—
210#677—62no—
211#557—151no—
212#556—151no—
213#488—152no—
214#487—31no—
215#479—152no—
216#474—51no—
217#464—152no—
218#462—151no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×C3×D5—41no—
224C2×C3×D5—41no—
225C2×C3×D5—41no—
226C3×C4×C5—21no—
227C3×C4×C5—42no—
228C3×C4×C5#13512yes—
229C3×C4×C5C2×#4111yescharacteristic
230C3×C4×C52−1+411yescharacteristic
231Dic15—22no—
232Dic15—22no—
233Dic15—22no—
234Dic15—41no—
235C3×Dic5—41no—
236C5×Dic3—42no—
237C2×C3×Q8—21no—
238C2×C3×D4—51no—
239C22×C3×C4—101no—
240C2×Dic6—51no—
241C2×Dic6—51no—
242C2×Dic6C22×D512yes—
243C2×C3×C8—52no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—51no—
246C3×C4⋊C4C22×D512yes—
247C3×C22⋊C4—101no—
248C3×C42C22×D511yescharacteristic
249#217—102no—
250#217—102no—
251#214—102no—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3—51no—
255C4⋊Dic3—51no—
256C4⋊Dic3—102no—
257Dic3⋊C4—52no—
258Dic3⋊C4—102no—
259Dic3⋊C4—102no—
260Dic3⋊C4—102no—
261Dic3⋊C4—101no—
262C4×Dic3—52no—
263C4×Dic3—102no—
264C4×Dic3—102no—
265C4×Dic3—101no—
266C2×C3⋊C8C22×D511yescharacteristic
267C2×C3⋊C8C22×D511yescharacteristic
268Dic12—104no—
269C22×D5—21no—
270C5×Q8—42no—
271C5×Q8—62no—
272C5×Q8—62no—
273C2×C4×C5—22no—
274C2×C4×C5—62no—
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5D3×D411yescharacteristic
277C2×C4×C5C23×D311yescharacteristic
278C2×Dic5—21no—
279C2×Dic5—32no—
280C2×Dic5—32no—
281C2×Dic5—61no—
282C2×Dic5—61no—
283D20—21no—
284D20—21no—
285C4×D5—42no—
286Dic10—32no—
287Dic10—62no—
288Dic10—61no—
289C5×C8—61no—
290C5×C8—61no—
291#168—22no—
292C2×Q16—152no—
293C2×SD16—151no—
294C4⋊Q8—31no—
295C4⋊Q8—301no—
296C4⋊Q8D3×D511yescharacteristic
297#126—302no—
298#125—152no—
299#125—302no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—151no—
303C4×Q8—152no—
304C4×Q8—152no—
305C4×Q8—151no—
306C4×Q8—301no—
307C4×D4—51no—
308#117—301no—
309#107—52no—
310#106—151no—
311C4⋊C8—51no—
312C4⋊C8—152no—
313#103—32no—
314#103—32no—
315#103—151no—
316#103—152no—
317#102—52no—
318#102—151no—
319C4×C8—31no—
320C4×C8—152no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324C3×D5—81no—
325C23×C3—101no—
326C3×Q8—42no—
327C3×D4—101no—
328C3×D4—101no—
329C2×C3×C4—22no—
330C2×C3×C4—101no—
331C2×C3×C4—202no—
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4C23×D511yescharacteristic
335C2×Dic3—22no—
336C2×Dic3—52no—
337C2×Dic3—52no—
338C2×Dic3—101no—
339C2×Dic3—101no—
340Dic6—22no—
341Dic6—22no—
342Dic6—52no—
343Dic6—101no—
344Dic6—102no—
345C3×C8—102no—
346C3⋊C8—21no—
347C3⋊C8—21no—
348C22×C5C2×D3×D411yescharacteristic
349C2×D5—41no—
350C2×D5—41no—
351C2×D5—41no—
352C4×C5—21no—
353C4×C5—42no—
354C4×C5—122no—
355C4×C5#91212yes—
356C4×C5#100711yescharacteristic
357C4×C5D3×#4111yescharacteristic
358Dic5—41no—
359Dic5—62no—
360Dic5—62no—
361Dic5—62no—
362Dic5—121no—
363C2×Q8—21no—
364C2×Q8—32no—
365C2×Q8—151no—
366C2×Q8—151no—
367C2×D4—51no—
368C22×C4—101no—
369Q16—304no—
370SD16—302no—
371C2×C8—31no—
372C2×C8—31no—
373C2×C8—52no—
374C4⋊C4—21no—
375C4⋊C4—51no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4—151no—
379C4⋊C4—152no—
380C4⋊C4—151no—
381C4⋊C4—302no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—301no—
386C4⋊C4C2×D3×D512yes—
387C22⋊C4—101no—
388C22⋊C4—302no—
389C22⋊C4—302no—
390C42—152no—
391C42—302no—
392C42—302no—
393C42—301no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3—201no—
397C22×C3—201no—
398C22×C3—201no—
399C22×C3C2×D4×D511yescharacteristic
400C3×C4—21no—
401C3×C4—42no—
402C3×C4—201no—
403C3×C4#406212yes—
404C3×C4D5×#4111yescharacteristic
405C3×C4#415011yescharacteristic
406Dic3—42no—
407Dic3—102no—
408Dic3—102no—
409Dic3—102no—
410Dic3—201no—
411C2×C5#563311yescharacteristic
412C2×C5C2×#91211yescharacteristic
413C2×C5#577911yescharacteristic
414D5—81no—
415C23—101no—
416Q8—42no—
417Q8—62no—
418Q8—62no—
419Q8—152no—
420Q8—302no—
421Q8—301no—
422D4—101no—
423D4—101no—
424C2×C4—22no—
425C2×C4—62no—
426C2×C4—101no—
427C2×C4—152no—
428C2×C4—152no—
429C2×C4—202no—
430C2×C4—301no—
431C2×C4—301no—
432C2×C4#679011yescharacteristic
433C2×C4#679011yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—61no—
436C8—61no—
437C8—102no—
438C2×C3—401no—
439C2×C3#6601111yescharacteristic
440C2×C3C2×#406211yescharacteristic
441C2×C3#6610011yescharacteristic
442C5#8099411yescharacteristic, complemented, Sylow
443C22—201no—
444C22—201no—
445C22—201no—
446C22C2×#679011yescharacteristic
447C4—21no—
448C4—42no—
449C4—122no—
450C4—201no—
451C4—302no—
452C4—302no—
453C4—302no—
454C4—601no—
455C4#9149712yes—
456C4#9203011yescharacteristic
457C4#9203411yescharacteristic
458C3#1061335611yescharacteristic, complemented, Sylow
459C2—401no—
460C2C2×#9149711yescharacteristic
461C2#1175511911yescharacteristic
462C2#1175523811yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D20C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3364
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. #11756480C2semidirect
3. C5×#5093C2semidirect
7. #11747298C2semidirect
8. #11747278C2semidirect
9. #11747105C2semidirect
11. #11746855C2semidirect
89. #5093D5semidirect
395. C3×C5#3364semidirect
442. C5#80994semidirect
458. C3#10613356semidirect

Maximal subgroups

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

subgroupindex
#117564802
#117525082
C5×#50932
C3×#653762
#117473822
#117473812
#117472982
#117472782
#117471052
C4×#66572
#117468552
#106133563
#809945