Finite Group Databasebeta

← #14472134

Subgroups — #14472134

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
1C5×#5542C211yesmaximal, characteristic
2#11752481C211yesmaximal, characteristic, complemented
3C4×#6716C211yesmaximal, characteristic
4C3×#65296C211yesmaximal, characteristic
5#11749012C212yesmaximal
6#11748942C212yesmaximal
7#11747393C212yesmaximal, complemented
8#11747275C212yesmaximal, complemented
9#11747105C211yesmaximal, characteristic, complemented
10#11746923C211yesmaximal, characteristic, complemented
11#11746857C211yesmaximal, characteristic, complemented
12#10615407—31nomaximal, Hall
13C3×C4×C5×D4C2211yescharacteristic
14C2×#6716C2211yescharacteristic
15C4×Dic30C2211yescharacteristic
16C5×#936C2212yes—
17C5×#926—21no—
18C5×#924—21no—
19C5×#887C2212yes—
20C5×#879—22no—
21C5×#869C2211yescharacteristic
22C4×C5×Dic6C2211yescharacteristic
23C3×#4015C2211yescharacteristic
24#91385—21no—
25#91381C2212yes—
26#91340C2212yes—
27#91339—22no—
28#91331—21no—
29C2×#6663C2212yes—
30#91116C2211yescharacteristic
31#91094C2211yescharacteristic
32#91092C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C3×#3964C2212yes—
35C3×#3939C2212yes—
36C3×C4⋊#168C2211yescharacteristic
37Dic3⋊#168C2212yes—
38#90973C2212yes—
39#90972C2212yes—
40#90972C2212yes—
41Dic3×#168C2212yes—
42#80994—51nomaximal, Hall
43C5×#556—31no—
44#65901—31no—
45#65379—31no—
46#65370—31no—
47#65345—32no—
48#65343—32no—
49C4×#689—32no—
50Q8×#168—31no—
51#65311—32no—
52C4×#687—31no—
53#65296D311yescharacteristic
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×Dic30C2311yescharacteristic
57C2×C5×Dic6D411yescharacteristic
58C2×C5×Dic6C2312yes—
59C2×C3×Dic10—21no—
60C3×C5×C4⋊C4C2311yescharacteristic
61C3×C5×C22⋊C4—21no—
62C3×C42×C5C2311yescharacteristic
63#6716—22no—
64C4⋊Dic15C2311yescharacteristic
65#6712—21no—
66C4×Dic15—21no—
67C2×C3⋊#168C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69C5×#217—22no—
70C5×#217—22no—
71C5×C4⋊Dic3—21no—
72C5×C4⋊Dic3—21no—
73C5×C4⋊Dic3D411yescharacteristic
74C5×Dic3⋊C4—22no—
75C5×Dic3⋊C4D412yes—
76C4×C5×Dic3—22no—
77C4×C5×Dic3C2312yes—
78C3×C4⋊Dic5—21no—
79C3×C4⋊Dic5C2312yes—
80C2×C3×#168C2312yes—
81#6669—22no—
82#6669—22no—
83#6668—22no—
84Dic3×Dic5—22no—
85#6663—24no—
86#5721—51no—
87#5542D511yescharacteristic
88C3×#474—51no—
89#5093—51no—
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×#126—62no—
99C5×#124—32no—
100C5×C22⋊Q8—61no—
101C4×C5×Q8—31no—
102C4×C5×Q8—32no—
103C4×C5×D4C2×D311yescharacteristic
104C5×#117—61no—
105#4090—61no—
106C2×#689—32no—
107C2×#687—31no—
108#4035—62no—
109#4033—61no—
110#4016—32no—
111#4015C2×D311yescharacteristic
112C4×Dic10—31no—
113C4×Dic10—32no—
114#3967—32no—
115#3967—32no—
116#3967—32no—
117#3964—31no—
118#3964C2×D312yes—
119#3942—31no—
120#3940—31no—
121#3939C2×D312yes—
122C4⋊#168—32no—
123C4⋊#168C2×D311yescharacteristic
124C4×#168—31no—
125C4×#168—32no—
126#3364—151noSylow
127C23×C3×C5—21no—
128C3×C5×D4—21no—
129C3×C5×D4—21no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—42no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—21no—
136C2×Dic15—21no—
137Dic30—21no—
138Dic30#4112yes—
139C2×C5×Dic3—22no—
140C2×C5×Dic3C2×D412yes—
141C2×C5×Dic3C2×D412yes—
142C5×Dic6—22no—
143C5×Dic6—22no—
144C5×Dic6—22no—
145C2×C3×Dic5—22no—
146C3×Dic10—42no—
147C3⋊#168—21no—
148C3⋊#168—21no—
149C3×#168—22no—
150C3×C4⋊Q8—51no—
151C3×C4×D4C2×D511yescharacteristic
152Q8×Dic3—101no—
153#944—101no—
154#936C2×D512yes—
155C2×#214—51no—
156#926—21no—
157#924—21no—
158C2×Dic12—52no—
159#890—52no—
160#889—102no—
161#887—52no—
162#887C2×D512yes—
163#879—22no—
164#869C2×D511yescharacteristic
165C4×Dic6—51no—
166C4×Dic6C2×D511yescharacteristic
167C3×#107—52no—
168C3×C4⋊C8—51no—
169C3×#102—52no—
170#832—51no—
171#816—52no—
172Dic3⋊C8—52no—
173C8×Dic3—52no—
174#810—52no—
175#810—52no—
176#810—51no—
177#808—51no—
178C4×C3⋊C8—51no—
179C2×C5×Q8—31no—
180C2×C5×Q8—32no—
181C2×C5×D4C22×D311yescharacteristic
182C22×C4×C5—21no—
183C2×Dic10—21no—
184C2×Dic10—31no—
185C5×C4⋊C4—31no—
186C5×C4⋊C4—32no—
187C5×C4⋊C4—62no—
188C5×C4⋊C4—61no—
189C5×C4⋊C4—61no—
190C5×C4⋊C4C22×D311yescharacteristic
191C5×C22⋊C4—21no—
192C5×C22⋊C4—62no—
193C5×C22⋊C4—62no—
194C42×C5—32no—
195C42×C5—62no—
196C42×C5C22×D311yescharacteristic
197#689—64no—
198#687—62no—
199C4⋊Dic5—21no—
200C4⋊Dic5—31no—
201C4⋊Dic5C22×D312yes—
202#683—62no—
203#683—62no—
204#683—62no—
205#683—61no—
206C4×Dic5—62no—
207C4×Dic5—61no—
208C2×#168—31no—
209C2×#168—31no—
210C2×#168C22×D312yes—
211#557—151no—
212#556—31no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—51no—
217#464—152no—
218#462—151no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5—41no—
223C22×C3×C5—41no—
224C22×C3×C5—41no—
225C22×C3×C5C22×D411yescharacteristic
226C3×C4×C5—21no—
227C3×C4×C5—41no—
228C3×C4×C5#13512yes—
229C3×C4×C5C2×#4111yescharacteristic
230C3×C4×C52−1+411yescharacteristic
231Dic15—22no—
232Dic15—41no—
233C3×Dic5—42no—
234C5×Dic3—22no—
235C5×Dic3—22no—
236C5×Dic3—42no—
237C2×C3×Q8—101no—
238C2×C3×D4C22×D511yescharacteristic
239C22×C3×C4—21no—
240C2×Dic6—51no—
241C2×Dic6C22⋊D511yescharacteristic
242C2×Dic6C22×D512yes—
243C2×C3×C8—52no—
244C3×C4⋊C4—52no—
245C3×C4⋊C4—101no—
246C3×C4⋊C4C22×D511yescharacteristic
247C3×C22⋊C4—21no—
248C3×C42C22×D511yescharacteristic
249#217—22no—
250#217—22no—
251#214—102no—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3—51no—
255C4⋊Dic3—102no—
256C4⋊Dic3C22⋊D511yescharacteristic
257Dic3⋊C4—22no—
258Dic3⋊C4—101no—
259Dic3⋊C4—102no—
260Dic3⋊C4—102no—
261Dic3⋊C4C22⋊D512yes—
262C4×Dic3—22no—
263C4×Dic3—101no—
264C4×Dic3—102no—
265C4×Dic3C22×D512yes—
266C2×C3⋊C8—51no—
267C2×C3⋊C8—51no—
268Dic12—104no—
269C23×C5—21no—
270C5×Q8—62no—
271C5×Q8—62no—
272C5×Q8—62no—
273C5×D4—21no—
274C5×D4—21no—
275C2×C4×C5—21no—
276C2×C4×C5—32no—
277C2×C4×C5—32no—
278C2×C4×C5—42no—
279C2×C4×C5—62no—
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—22no—
284C2×Dic5—61no—
285C2×Dic5—61no—
286Dic10—32no—
287Dic10—42no—
288Dic10—61no—
289#168—22no—
290#168—61no—
291#168—61no—
292C2×Q16—152no—
293C2×SD16—151no—
294C4⋊Q8—31no—
295C4⋊Q8—51no—
296C4⋊Q8—301no—
297#126—62no—
298#125—152no—
299#125—302no—
300#124—32no—
301C22⋊Q8—61no—
302C4×Q8—31no—
303C4×Q8—32no—
304C4×Q8—152no—
305C4×Q8—151no—
306C4×Q8—301no—
307C4×D4D3×D511yescharacteristic
308#117—61no—
309#107—52no—
310#106—151no—
311C4⋊C8—51no—
312C4⋊C8—152no—
313#103—152no—
314#103—152no—
315#103—152no—
316#103—151no—
317#102—52no—
318#102—151no—
319C4×C8—152no—
320C4×C8—151no—
321C2×C3×C5—81no—
322C2×C3×C5#54811yescharacteristic
323C2×C3×C5C2×#13511yescharacteristic
324C2×C3×C5#57811yescharacteristic
325C23×C3—21no—
326C3×Q8—202no—
327C3×D4—21no—
328C3×D4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—42no—
331C2×C3×C4—102no—
332C2×C3×C4C2×C22⋊D511yescharacteristic
333C2×C3×C4C2×C22⋊D511yescharacteristic
334C2×C3×C4C23×D511yescharacteristic
335C2×Dic3—22no—
336C2×Dic3—101no—
337C2×Dic3—101no—
338C2×Dic3C2×C22⋊D512yes—
339C2×Dic3C2×C22⋊D512yes—
340Dic6—22no—
341Dic6—22no—
342Dic6—22no—
343Dic6—52no—
344Dic6—101no—
345C3×C8—102no—
346C3⋊C8—101no—
347C3⋊C8—101no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—41no—
351C22×C5C2×D3×D411yescharacteristic
352C4×C5—21no—
353C4×C5—41no—
354C4×C5—62no—
355C4×C5—62no—
356C4×C5—122no—
357C4×C5#91212yes—
358C4×C5#100711yescharacteristic
359C4×C5D3×#4111yescharacteristic
360Dic5—42no—
361Dic5—62no—
362Dic5—121no—
363C2×Q8—31no—
364C2×Q8—32no—
365C2×Q8—101no—
366C2×Q8—151no—
367C2×D4C2×D3×D511yescharacteristic
368C22×C4—21no—
369Q16—304no—
370SD16—302no—
371C2×C8—52no—
372C2×C8—151no—
373C2×C8—151no—
374C4⋊C4—31no—
375C4⋊C4—32no—
376C4⋊C4—52no—
377C4⋊C4—62no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—101no—
381C4⋊C4—151no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—301no—
386C4⋊C4C2×D3×D511yescharacteristic
387C22⋊C4—21no—
388C22⋊C4—62no—
389C22⋊C4—62no—
390C42—32no—
391C42—62no—
392C42—302no—
393C42—301no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3C22×C22⋊D511yescharacteristic
400C3×C4—21no—
401C3×C4—41no—
402C3×C4—202no—
403C3×C4#409612yes—
404C3×C4D5×#4111yescharacteristic
405C3×C4#415011yescharacteristic
406Dic3—22no—
407Dic3—22no—
408Dic3—42no—
409Dic3—102no—
410Dic3—201no—
411C2×C5—81no—
412C2×C5#563311yescharacteristic
413C2×C5C2×#91211yescharacteristic
414C2×C5#577911yescharacteristic
415C23—21no—
416Q8—62no—
417Q8—62no—
418Q8—62no—
419Q8—152no—
420Q8—202no—
421Q8—301no—
422D4—21no—
423D4—21no—
424C2×C4—21no—
425C2×C4—32no—
426C2×C4—32no—
427C2×C4—42no—
428C2×C4—62no—
429C2×C4—102no—
430C2×C4—301no—
431C2×C4—301no—
432C2×C4D3×C22⋊D511yescharacteristic
433C2×C4D3×C22⋊D511yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—102no—
436C8—301no—
437C8—301no—
438C2×C3—81no—
439C2×C3C2×#409611yescharacteristic
440C2×C3#6616511yescharacteristic
441C2×C3#6617211yescharacteristic
442C5#8099411yescharacteristic, complemented, Sylow
443C22—41no—
444C22—41no—
445C22—41no—
446C22C2×D3×C22⋊D511yescharacteristic
447C4—21no—
448C4—41no—
449C4—62no—
450C4—62no—
451C4—122no—
452C4—202no—
453C4—302no—
454C4—601no—
455C4#9149312yes—
456C4#9200411yescharacteristic
457C4#9201611yescharacteristic
458C3#1061540711yescharacteristic, complemented, Sylow
459C2—81no—
460C2#1175454611yescharacteristic
461C2C2×#9149311yescharacteristic
462C2#1175534111yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×C5×D4C23
hypercenterC4×D4D3×D5
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #11752481C2semidirect
7. #11747393C2semidirect
8. #11747275C2semidirect
9. #11747105C2semidirect
10. #11746923C2semidirect
11. #11746857C2semidirect
395. C3×C5#3364semidirect
442. C5#80994semidirect
458. C3#10615407semidirect

Maximal subgroups

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

subgroupindex
C5×#55422
#117524812
C4×#67162
C3×#652962
#117490122
#117489422
#117473932
#117472752
#117471052
#117469232
#117468572
#106154073
#809945