Finite Group Databasebeta

← #14472172

Subgroups — #14472172

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#11752508C211yesmaximal, characteristic
2#11752482C211yesmaximal, characteristic, complemented
3#11750931C211yesmaximal, characteristic, complemented
4C5×#4849C211yesmaximal, characteristic, complemented
5C3×#65135C211yesmaximal, characteristic
6#11747978C212yesmaximal
7#11747966C212yesmaximal
8#11747887C212yesmaximal, complemented
9#11747886C212yesmaximal, complemented
10C4×#6655C211yesmaximal, characteristic
11#11746923C211yesmaximal, characteristic, complemented
12#10612194—31nomaximal, Hall
13C4×Dic30C2211yescharacteristic
14C2×C5×Dic12C2212yes—
15C5×#869C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C3×C4×D20C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19#91389—21no—
20#91384C2212yes—
21#91368C2212yes—
22#91361—22no—
23#91360—21no—
24#91358—21no—
25#91346—22no—
26#91344C2212yes—
27#91344C2212yes—
28Dic3×Dic10—21no—
29C2×#6655C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4×C3⋊#168C2211yescharacteristic
34C5×#816C2212yes—
35C3×#3953C2212yes—
36C3×#3950C2212yes—
37#90986C2211yescharacteristic
38#90972C2211yescharacteristic
39#90972C2212yes—
40#90972C2212yes—
41#90964C2211yescharacteristic
42#80994—51nomaximal, Hall
43#66066—31no—
44#65904—31no—
45C5×#462—31no—
46#65474—32no—
47Q16×Dic5—32no—
48#65370—31no—
49C4×#688—31no—
50#65135D311yescharacteristic
51#65119—31no—
52#65089—32no—
53#65085—32no—
54C2×Dic30D411yescharacteristic
55C2×C5×Dic6C2312yes—
56C2×C5×Dic6C2311yescharacteristic
57C2×C3×D20C2311yescharacteristic
58C2×C3×C4×D5—21no—
59C2×C3×Dic10—21no—
60C2×C3×C5×C8C2312yes—
61C3×C42×C5C2311yescharacteristic
62C4⋊Dic15D411yescharacteristic
63#6712D412yes—
64C4×Dic15C2312yes—
65C2×C3⋊#168C2311yescharacteristic
66C2×C3⋊#168C2311yescharacteristic
67C5×C4⋊Dic3—21no—
68C5×C4⋊Dic3—21no—
69C5×C4⋊Dic3C2311yescharacteristic
70C5×Dic3⋊C4—21no—
71C4×C5×Dic3—21no—
72C5×Dic12—24no—
73C3×#685—21no—
74C3×C4⋊Dic5—21no—
75C3×C4⋊Dic5C2312yes—
76C3×C4⋊Dic5C2311yescharacteristic
77Dic3⋊Dic5—22no—
78Dic3⋊Dic5—22no—
79Dic3⋊Dic5—22no—
80#6668—22no—
81#6665—22no—
82#6665—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85#6655—22no—
86#5721—51no—
87#5542—51no—
88C3×#474—51no—
89#5093—51no—
90C4×#214—51no—
91#4877—52no—
92#4873—52no—
93#4849D511yescharacteristic, complemented
94#4830—51no—
95#4768—52no—
96#4767—52no—
97C2×C5×Q16—32no—
98C5×C4⋊Q8—31no—
99C4×C5×Q8—31no—
100#4093—32no—
101Q8×Dic5—32no—
102Q8×Dic5—32no—
103C2×#688—31no—
104#4044—62no—
105#4043—61no—
106#4038—61no—
107#4036—32no—
108#4036—62no—
109C4×D20C2×D311yescharacteristic
110#4015—61no—
111#4015C2×D311yescharacteristic
112C4×Dic10—31no—
113C4×Dic10—61no—
114C5×C4⋊C8C2×D311yescharacteristic
115C5×#103—32no—
116#3967—31no—
117#3967—32no—
118#3967—32no—
119#3953C2×D312yes—
120#3950C2×D312yes—
121#3946—32no—
122C8×Dic5—32no—
123#3941—31no—
124#3940—31no—
125C4×#168—31no—
126#3364—151noSylow
127C22×C3×D5—21no—
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15C2×D412yes—
132C2×Dic15C2×D412yes—
133Dic30—22no—
134C2×C5×Dic3—21no—
135C2×C5×Dic3—22no—
136C2×C5×Dic3—21no—
137C5×Dic6—21no—
138C5×Dic6—22no—
139C5×Dic6—22no—
140C5×Dic6#4112yes—
141C2×C3×Dic5—21no—
142C2×C3×Dic5—22no—
143C3×D20—21no—
144C3×D20—21no—
145C3×C4×D5—42no—
146C3×Dic10—42no—
147C3×C5×C8—22no—
148C3⋊#168—21no—
149C3⋊#168—21no—
150C3×C4⋊Q8—51no—
151C3×C4×D4—51no—
152Q8×Dic3—101no—
153#944—101no—
154#936—52no—
155C2×#214—51no—
156#926—101no—
157#924—101no—
158C2×Dic12C2×D512yes—
159#890—52no—
160#889—102no—
161#887—52no—
162#887—52no—
163#879—102no—
164#869C2×D511yescharacteristic
165C4×Dic6—51no—
166C4×Dic6C2×D511yescharacteristic
167C3×#107—52no—
168C3×C4⋊C8C2×D511yescharacteristic
169C3×#102—52no—
170#832—51no—
171#816C2×D512yes—
172Dic3⋊C8—52no—
173C8×Dic3—52no—
174#810—51no—
175#810—52no—
176#810—52no—
177#808—51no—
178C4×C3⋊C8—51no—
179C2×C5×Q8—31no—
180C2×C5×Q8—32no—
181C2×D20C22×D311yescharacteristic
182C2×C4×D5—21no—
183C2×Dic10—21no—
184C2×Dic10—31no—
185C5×Q16—64no—
186C2×C5×C8C22×D312yes—
187C5×C4⋊C4—31no—
188C5×C4⋊C4—61no—
189C5×C4⋊C4—61no—
190C5×C4⋊C4—61no—
191C42×C5—61no—
192C42×C5C22×D311yescharacteristic
193#688—62no—
194#685—21no—
195#685—62no—
196#685—62no—
197C4⋊Dic5—21no—
198C4⋊Dic5—31no—
199C4⋊Dic5—62no—
200C4⋊Dic5—62no—
201C4⋊Dic5—62no—
202C4⋊Dic5C22×D311yescharacteristic
203C4⋊Dic5C22×D312yes—
204#683—32no—
205#683—62no—
206C4×Dic5—32no—
207C4×Dic5—62no—
208C4×Dic5—62no—
209C2×#168—31no—
210C2×#168—31no—
211#557—151no—
212#556—151no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—51no—
217#464—152no—
218#462—31no—
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#13512yes—
228C3×C4×C5C2×#4111yescharacteristic
229C3×C4×C52−1+411yescharacteristic
230Dic15—22no—
231Dic15—22no—
232C3×Dic5—42no—
233C3×Dic5—41no—
234C5×Dic3—22no—
235C5×Dic3—42no—
236C5×Dic3—41no—
237C2×C3×Q8—101no—
238C2×C3×D4—51no—
239C22×C3×C4—101no—
240C2×Dic6—51no—
241C2×Dic6C22×D512yes—
242C2×Dic6C22×D511yescharacteristic
243C2×C3×C8C22×D512yes—
244C3×C4⋊C4—51no—
245C3×C4⋊C4—52no—
246C3×C4⋊C4—101no—
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—102no—
256C4⋊Dic3C22×D511yescharacteristic
257Dic3⋊C4—21no—
258Dic3⋊C4—52no—
259Dic3⋊C4—102no—
260Dic3⋊C4—102no—
261Dic3⋊C4—102no—
262C4×Dic3—21no—
263C4×Dic3—52no—
264C4×Dic3—102no—
265C4×Dic3—102no—
266C2×C3⋊C8—51no—
267C2×C3⋊C8—51no—
268Dic12—24no—
269C22×D5—21no—
270C5×Q8—32no—
271C5×Q8—61no—
272C5×Q8—62no—
273C5×Q8—62no—
274C2×C4×C5—61no—
275C2×C4×C5—62no—
276C2×C4×C5—61no—
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5C23×D311yescharacteristic
280C2×Dic5—21no—
281C2×Dic5—22no—
282C2×Dic5—32no—
283C2×Dic5—32no—
284D20—21no—
285D20—21no—
286C4×D5—42no—
287Dic10—42no—
288Dic10—62no—
289C5×C8—22no—
290#168—61no—
291#168—61no—
292C2×Q16—32no—
293C2×SD16—151no—
294C4⋊Q8—31no—
295C4⋊Q8—51no—
296C4⋊Q8—301no—
297#126—302no—
298#125—152no—
299#125—302no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—31no—
303C4×Q8—151no—
304C4×Q8—152no—
305C4×Q8—152no—
306C4×Q8—301no—
307C4×D4—51no—
308#117—301no—
309#107—52no—
310#106—151no—
311C4⋊C8—152no—
312C4⋊C8D3×D511yescharacteristic
313#103—32no—
314#103—151no—
315#103—152no—
316#103—152no—
317#102—52no—
318#102—151no—
319C4×C8—152no—
320C4×C8—151no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324C3×D5—81no—
325C23×C3—101no—
326C3×Q8—202no—
327C3×D4—101no—
328C3×D4—101no—
329C2×C3×C4—101no—
330C2×C3×C4—102no—
331C2×C3×C4—202no—
332C2×C3×C4D4×D511yescharacteristic
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4C23×D511yescharacteristic
335C2×Dic3—21no—
336C2×Dic3—21no—
337C2×Dic3—22no—
338C2×Dic3—52no—
339C2×Dic3—52no—
340Dic6—21no—
341Dic6—22no—
342Dic6—22no—
343Dic6—102no—
344Dic6#71112yes—
345C3×C8—22no—
346C3⋊C8—101no—
347C3⋊C8—101no—
348C22×C5C2×D3×D411yescharacteristic
349C2×D5—41no—
350C2×D5—41no—
351C2×D5—41no—
352C4×C5—21no—
353C4×C5—62no—
354C4×C5—122no—
355C4×C5—121no—
356C4×C5#91212yes—
357C4×C5#100711yescharacteristic
358C4×C5D3×#4111yescharacteristic
359Dic5—42no—
360Dic5—41no—
361Dic5—62no—
362Dic5—62no—
363C2×Q8—31no—
364C2×Q8—32no—
365C2×Q8—101no—
366C2×Q8—151no—
367C2×D4—51no—
368C22×C4—101no—
369Q16—64no—
370SD16—302no—
371C2×C8—151no—
372C2×C8—151no—
373C2×C8C2×D3×D512yes—
374C4⋊C4—31no—
375C4⋊C4—52no—
376C4⋊C4—51no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—101no—
381C4⋊C4—151no—
382C4⋊C4—152no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—302no—
386C4⋊C4—302no—
387C22⋊C4—101no—
388C22⋊C4—302no—
389C22⋊C4—302no—
390C42—61no—
391C42—152no—
392C42—302no—
393C42—302no—
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—201no—
402C3×C4—202no—
403C3×C4#406512yes—
404C3×C4C2×#71111yescharacteristic
405C3×C4#415011yescharacteristic
406Dic3—22no—
407Dic3—41no—
408Dic3—42no—
409Dic3—102no—
410Dic3—102no—
411C2×C5#563311yescharacteristic
412C2×C5C2×#91211yescharacteristic
413C2×C5#577911yescharacteristic
414D5—81no—
415C23—101no—
416Q8—32no—
417Q8—61no—
418Q8—62no—
419Q8—62no—
420Q8—202no—
421Q8—302no—
422D4—101no—
423D4—101no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—62no—
427C2×C4—101no—
428C2×C4—102no—
429C2×C4—152no—
430C2×C4—152no—
431C2×C4—202no—
432C2×C4#677711yescharacteristic
433C2×C4#677711yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—22no—
436C8—301no—
437C8—301no—
438C2×C3—401no—
439C2×C3#6593211yescharacteristic
440C2×C3C2×#406511yescharacteristic
441C2×C3#6611311yescharacteristic
442C5#8099411yescharacteristic, complemented, Sylow
443C22—201no—
444C22—201no—
445C22—201no—
446C22C2×#677711yescharacteristic
447C4—21no—
448C4—62no—
449C4—121no—
450C4—122no—
451C4—201no—
452C4—202no—
453C4—302no—
454C4—302no—
455C4#9127712yes—
456C4D3×#71111yescharacteristic
457C4#9203011yescharacteristic
458C3#1061219411yescharacteristic, complemented, Sylow
459C2—401no—
460C2#1175370311yescharacteristic
461C2C2×#9127711yescharacteristic
462C2#1175404311yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D20C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11752482C2semidirect
3. #11750931C2semidirect
4. C5×#4849C2semidirect
8. #11747887C2semidirect
9. #11747886C2semidirect
11. #11746923C2semidirect
93. #4849D5semidirect
395. C3×C5#3364semidirect
442. C5#80994semidirect
458. C3#10612194semidirect

Maximal subgroups

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

subgroupindex
#117525082
#117524822
#117509312
C5×#48492
C3×#651352
#117479782
#117479662
#117478872
#117478862
C4×#66552
#117469232
#106121943
#809945