Finite Group Databasebeta

← #14472162

Subgroups — #14472162

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#11752477C211yesmaximal, characteristic, complemented
3C8×Dic30C211yesmaximal, characteristic, complemented
4C5×#4681C211yesmaximal, characteristic, complemented
5C3×C4×#677C211yesmaximal, characteristic
6#11747978C212yesmaximal
7#11747885C212yesmaximal, complemented
8#11747836C212yesmaximal
9#11747828C212yesmaximal, complemented
10#11747094C211yesmaximal, characteristic, complemented
11#11746886C211yesmaximal, characteristic
12#10613356—31nomaximal, Hall
13C4×Dic30C2211yescharacteristic
14C5×#869C2211yescharacteristic
15C5×#869C2211yescharacteristic
16C2×C3×#677C2211yescharacteristic
17C3×C4×D20C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19#91384C2212yes—
20#91376—21no—
21#91368C2212yes—
22#91361—22no—
23#91360—21no—
24#91358—21no—
25#91344C2212yes—
26#91335—22no—
27Dic5×Dic6—21no—
28#91331C2212yes—
29C2×#6661C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4⋊(C3⋊#168)C2211yescharacteristic
34C5×#816C2212yes—
35C5×#816C2212yes—
36C3×#3953C2211yescharacteristic
37C3×#3949C2211yescharacteristic
38C3×#3948C2211yescharacteristic
39#90989C2212yes—
40#90972C2212yes—
41#90964C2212yes—
42#79623—51nomaximal, Hall
43#66066—31no—
44#66055—31no—
45C5×#487—31no—
46#65379—31no—
47#65376—31no—
48#65089—32no—
49#65088—32no—
50#65087—32no—
51#65079—32no—
52C4×#677D311yescharacteristic
53C8×Dic10—31no—
54C2×Dic30D411yescharacteristic
55C2×C5×Dic6—21no—
56C2×C5×Dic6C2312yes—
57C2×C3×D20C2311yescharacteristic
58C2×C3×C4×D5—21no—
59C2×C3×Dic10C2311yescharacteristic
60C2×C3×C5×C8C2311yescharacteristic
61C2×C3×C5×C8C2311yescharacteristic
62C3×C42×C5C2311yescharacteristic
63C4⋊Dic15D411yescharacteristic
64#6712D412yes—
65C4×Dic15C2312yes—
66C2×C3⋊#168C2312yes—
67C5×C4⋊Dic3—21no—
68C5×C4⋊Dic3—21no—
69C5×C4⋊Dic3—21no—
70C5×C4⋊Dic3C2312yes—
71C3×#685—21no—
72C3×C4⋊Dic5C2311yescharacteristic
73C3×C4⋊Dic5C2311yescharacteristic
74C3×#683—21no—
75C3×C4×Dic5—21no—
76C3×#677—22no—
77Dic3⋊Dic5—22no—
78Dic3⋊Dic5—22no—
79#6668—22no—
80#6668—22no—
81#6665—22no—
82#6665—22no—
83Dic3×Dic5—22no—
84Dic3×Dic5—22no—
85#6661—24no—
86#5570—51no—
87#5542—51no—
88C3×C4×SD16—51no—
89#5166—52no—
90#5031—51no—
91#5007—51no—
92#4857—52no—
93#4790—52no—
94#4768—52no—
95#4681D511yescharacteristic, complemented
96C8×Dic6—51no—
97C5×C4⋊Q8—31no—
98C5×C4⋊Q8—31no—
99#4093—32no—
100Q8×Dic5—32no—
101Q8×Dic5—61no—
102#4090—61no—
103C2×#689—32no—
104C2×#677C2×D311yescharacteristic
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×Dic10C2×D311yescharacteristic
114C5×#103—32no—
115C5×#103—32no—
116C4×C5×C8C2×D311yescharacteristic
117#3967—32no—
118#3953C2×D311yescharacteristic
119#3949C2×D311yescharacteristic
120#3948C2×D311yescharacteristic
121#3946—32no—
122C8×Dic5—32no—
123#3941—32no—
124#3939—32no—
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—22no—
135C2×C5×Dic3—22no—
136C5×Dic6—22no—
137C5×Dic6—22no—
138C5×Dic6—42no—
139C2×C3×Dic5—21no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—21no—
142C3×D20—21no—
143C3×D20—21no—
144C3×C4×D5—42no—
145C3×Dic10—21no—
146C3×Dic10#4112yes—
147C3×C5×C8—21no—
148C3×C5×C8—21no—
149C3⋊#168—22no—
150C2×C3×SD16—51no—
151C3×C4×Q8—51no—
152C3×C4×D4—51no—
153Q8×Dic3—52no—
154C2×#216—52no—
155#936—52no—
156#926—101no—
157#924—101no—
158#890—52no—
159#890—102no—
160#887—52no—
161#879—102no—
162#869—101no—
163#869C2×D511yescharacteristic
164#869C2×D511yescharacteristic
165C4×Dic6—51no—
166C4×Dic6—101no—
167C3×#106—51no—
168C3×#103—51no—
169C3×#102—51no—
170C3×C4×C8C2×D511yescharacteristic
171#832—52no—
172#816C2×D512yes—
173#816C2×D512yes—
174Dic3⋊C8—52no—
175C8×Dic3—52no—
176#810—52no—
177#807—52no—
178C4⋊(C3⋊C8)—51no—
179C2×C5×Q8—32no—
180C2×C5×Q8—61no—
181C2×D20C22×D311yescharacteristic
182C2×C4×D5—21no—
183C2×Dic10—31no—
184C2×Dic10C22×D311yescharacteristic
185C2×C5×C8C22×D311yescharacteristic
186C2×C5×C8C22×D311yescharacteristic
187C5×C4⋊C4—32no—
188C5×C4⋊C4—61no—
189C5×C4⋊C4—61no—
190C5×C4⋊C4—61no—
191C42×C5C22×D311yescharacteristic
192#689—64no—
193#685—21no—
194#685—62no—
195#685—62no—
196C4⋊Dic5—31no—
197C4⋊Dic5—62no—
198C4⋊Dic5—62no—
199C4⋊Dic5C22×D311yescharacteristic
200C4⋊Dic5C22×D311yescharacteristic
201#683—21no—
202#683—32no—
203#683—62no—
204#683—62no—
205C4×Dic5—21no—
206C4×Dic5—32no—
207C4×Dic5—62no—
208C4×Dic5—62no—
209C2×#168—32no—
210#677—22no—
211#557—151no—
212#556—151no—
213#488—152no—
214#487—31no—
215#479—152no—
216#474—151no—
217#464—152no—
218#462—151no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—51no—
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—22no—
233C3×Dic5—41no—
234C3×Dic5—41no—
235C5×Dic3—42no—
236C5×Dic3—42no—
237C2×C3×Q8—51no—
238C2×C3×D4—51no—
239C22×C3×C4—101no—
240C2×Dic6—21no—
241C2×Dic6—51no—
242C2×Dic6C22×D512yes—
243C3×SD16—102no—
244C2×C3×C8C22×D511yescharacteristic
245C2×C3×C8C22×D511yescharacteristic
246C3×C4⋊C4—51no—
247C3×C4⋊C4—51no—
248C3×C4⋊C4—101no—
249C3×C22⋊C4—101no—
250C3×C42—101no—
251C3×C42C22×D511yescharacteristic
252#217—102no—
253#217—102no—
254#216—104no—
255C4⋊Dic3—21no—
256C4⋊Dic3—21no—
257C4⋊Dic3—21no—
258C4⋊Dic3—51no—
259C4⋊Dic3—102no—
260C4⋊Dic3—102no—
261C4⋊Dic3C22×D512yes—
262Dic3⋊C4—52no—
263Dic3⋊C4—102no—
264Dic3⋊C4—102no—
265C4×Dic3—52no—
266C4×Dic3—102no—
267C4×Dic3—102no—
268C2×C3⋊C8—52no—
269C22×D5—21no—
270C5×Q8—62no—
271C5×Q8—62no—
272C5×Q8—122no—
273C2×C4×C5—62no—
274C2×C4×C5—62no—
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5D3×D411yescharacteristic
277C2×C4×C5C23×D311yescharacteristic
278C2×Dic5—21no—
279C2×Dic5—21no—
280C2×Dic5—21no—
281C2×Dic5—32no—
282C2×Dic5—32no—
283D20—21no—
284D20—21no—
285C4×D5—42no—
286Dic10—21no—
287Dic10—62no—
288Dic10#23512yes—
289C5×C8—21no—
290C5×C8—21no—
291#168—62no—
292C2×Q16—152no—
293C2×SD16—51no—
294C4⋊Q8—31no—
295C4⋊Q8—31no—
296C4⋊Q8—301no—
297#126—302no—
298#125—152no—
299#125—302no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—51no—
303C4×Q8—151no—
304C4×Q8—152no—
305C4×Q8—152no—
306C4×Q8—301no—
307C4×D4—51no—
308#117—301no—
309#107—152no—
310#106—51no—
311C4⋊C8—152no—
312C4⋊C8—151no—
313#103—32no—
314#103—32no—
315#103—51no—
316#103—152no—
317#102—51no—
318#102—152no—
319C4×C8—152no—
320C4×C8D3×D511yescharacteristic
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324C3×D5—81no—
325C23×C3—101no—
326C3×Q8—52no—
327C3×Q8—101no—
328C3×D4—101no—
329C3×D4—101no—
330C2×C3×C4—101no—
331C2×C3×C4—101no—
332C2×C3×C4—101no—
333C2×C3×C4—202no—
334C2×C3×C4D4×D511yescharacteristic
335C2×C3×C4D4×D511yescharacteristic
336C2×C3×C4C23×D511yescharacteristic
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—52no—
340C2×Dic3—52no—
341Dic6—22no—
342Dic6—22no—
343Dic6—42no—
344Dic6—102no—
345C3×C8—21no—
346C3×C8—21no—
347C3⋊C8—102no—
348C22×C5C2×D3×D411yescharacteristic
349C2×D5—41no—
350C2×D5—41no—
351C2×D5—41no—
352C4×C5—21no—
353C4×C5—122no—
354C4×C5—122no—
355C4×C5#91612yes—
356C4×C5C2×#23511yescharacteristic
357C4×C5#101011yescharacteristic
358Dic5—22no—
359Dic5—41no—
360Dic5—41no—
361Dic5—62no—
362Dic5—62no—
363C2×Q8—32no—
364C2×Q8—51no—
365C2×Q8—61no—
366C2×Q8—151no—
367C2×D4—51no—
368C22×C4—101no—
369Q16—304no—
370SD16—102no—
371C2×C8—152no—
372C2×C8C2×D3×D511yescharacteristic
373C2×C8C2×D3×D511yescharacteristic
374C4⋊C4—32no—
375C4⋊C4—51no—
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—101no—
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—102no—
402C3×C4—201no—
403C3×C4—201no—
404C3×C4#406212yes—
405C3×C4D5×#4111yescharacteristic
406C3×C4#415011yescharacteristic
407Dic3—42no—
408Dic3—42no—
409Dic3—102no—
410Dic3—102no—
411C2×C5#555211yescharacteristic
412C2×C5C2×#91611yescharacteristic
413C2×C5#577111yescharacteristic
414D5—81no—
415C23—101no—
416Q8—52no—
417Q8—62no—
418Q8—62no—
419Q8—101no—
420Q8—122no—
421Q8—302no—
422D4—101no—
423D4—101no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—101no—
427C2×C4—101no—
428C2×C4—101no—
429C2×C4—152no—
430C2×C4—152no—
431C2×C4—202no—
432C2×C4#677711yescharacteristic
433C2×C4#677711yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—21no—
436C8—21no—
437C8—302no—
438C2×C3—401no—
439C2×C3#6601111yescharacteristic
440C2×C3C2×#406211yescharacteristic
441C2×C3#6610011yescharacteristic
442C5#7962311yescharacteristic, complemented, Sylow
443C22—201no—
444C22—201no—
445C22—201no—
446C22C2×#677711yescharacteristic
447C4—21no—
448C4—102no—
449C4—122no—
450C4—122no—
451C4—201no—
452C4—201no—
453C4—302no—
454C4—302no—
455C4#9127612yes—
456C4#9200111yescharacteristic
457C4D5×#23511yescharacteristic
458C3#1061335611yescharacteristic, complemented, Sylow
459C2—401no—
460C2#1175255311yescharacteristic
461C2C2×#9127611yescharacteristic
462C2#1175400811yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×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. #11752477C2semidirect
3. C8×Dic30C2semidirect
4. C5×#4681C2semidirect
7. #11747885C2semidirect
9. #11747828C2semidirect
10. #11747094C2semidirect
95. #4681D5semidirect
395. C3×C5#3364semidirect
442. C5#79623semidirect
458. C3#10613356semidirect

Maximal subgroups

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

subgroupindex
#117525082
#117524772
C8×Dic302
C5×#46812
C3×C4×#6772
#117479782
#117478852
#117478362
#117478282
#117470942
#117468862
#106133563
#796235