Finite Group Databasebeta

← #14472149

Subgroups — #14472149

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#11756329C211yesmaximal, characteristic, complemented
2#11752508C211yesmaximal, characteristic
3C5×#5031C211yesmaximal, characteristic, complemented
4C3×C4×#688C211yesmaximal, characteristic
5#11749327C212yesmaximal
6#11749265C212yesmaximal, complemented
7#11747382C212yesmaximal
8#11747299C212yesmaximal, complemented
9#11746929C211yesmaximal, characteristic, complemented
10#11746889C211yesmaximal, characteristic
11#11746851C211yesmaximal, characteristic, complemented
12#10612194—31nomaximal, Hall
13C3×C4×C5×Q8C2211yescharacteristic
14Q8×Dic15C2212yes—
15#91779—22no—
16#91779C2212yes—
17#91758—21no—
18#91758C2211yescharacteristic
19C4×Dic30—21no—
20C4×Dic30C2211yescharacteristic
21C2×C5×#216C2212yes—
22C5×#869C2211yescharacteristic
23C2×C3×#688C2211yescharacteristic
24C3×C4×D20C2211yescharacteristic
25#91368C2212yes—
26#91361—22no—
27#91360—21no—
28#91358—21no—
29#91344C2212yes—
30C5×#810C2212yes—
31C5×C4⋊(C3⋊C8)C2211yescharacteristic
32C3×#3967C2211yescharacteristic
33C3×#3941C2211yescharacteristic
34C3×#3940C2211yescharacteristic
35C3×C4×#168C2211yescharacteristic
36#90990C2212yes—
37#90983C2212yes—
38#90973C2212yes—
39#90973C2212yes—
40#90965C2212yes—
41#90951C2212yes—
42#79623—51nomaximal, Hall
43#66066—31no—
44#65904—31no—
45C5×#462—31no—
46#65474—32no—
47Q16×Dic5—32no—
48#65370—31no—
49C4×#688D311yescharacteristic
50#65135—31no—
51#65119—31no—
52#65089—32no—
53#65085—32no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×Dic30—21no—
56C2×Dic30D411yescharacteristic
57C2×C5×Dic6C2312yes—
58C2×C3×D20C2311yescharacteristic
59C2×C3×C4×D5—21no—
60C3×C5×C4⋊C4—21no—
61C3×C5×C4⋊C4C2311yescharacteristic
62C3×C42×C5—21no—
63C3×C42×C5C2311yescharacteristic
64C4⋊Dic15—21no—
65C4⋊Dic15—22no—
66C4⋊Dic15—22no—
67C4⋊Dic15D411yescharacteristic
68C4⋊Dic15C2312yes—
69#6712—22no—
70#6712D412yes—
71C4×Dic15—22no—
72C4×Dic15C2312yes—
73C5×#216—24no—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3—21no—
76C2×C5×C3⋊C8C2312yes—
77C3×#688—22no—
78C3×#685—21no—
79C3×C4⋊Dic5C2311yescharacteristic
80C2×C3×#168C2311yescharacteristic
81C2×C3×#168C2311yescharacteristic
82Dic3⋊Dic5—22no—
83#6665—22no—
84#6665—22no—
85Dic3×Dic5—22no—
86#5570—51no—
87#5542—51no—
88C3×C4×SD16—51no—
89#5166—52no—
90#5031D511yescharacteristic, complemented
91#5007—51no—
92#4857—52no—
93#4790—52no—
94#4768—52no—
95#4681—51no—
96C8×Dic6—51no—
97C2×C5×Q16—32no—
98C5×C4⋊Q8—31no—
99C4×C5×Q8C2×D311yescharacteristic
100#4093—32no—
101Q8×Dic5—32no—
102Q8×Dic5—32no—
103C2×#688C2×D311yescharacteristic
104#4044—62no—
105#4043—61no—
106#4038—61no—
107#4036—32no—
108#4036—62no—
109C4×D20C2×D311yescharacteristic
110#4015—31no—
111#4015—61no—
112C4×Dic10—31no—
113C4×Dic10—61no—
114C5×C4⋊C8—31no—
115C5×#103—32no—
116#3967—32no—
117#3967—32no—
118#3967C2×D311yescharacteristic
119#3953—32no—
120#3950—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3941C2×D311yescharacteristic
124#3940C2×D311yescharacteristic
125C4×#168C2×D311yescharacteristic
126#3364—151noSylow
127C22×C3×D5—21no—
128C3×C5×Q8—21no—
129C3×C5×Q8#4112yes—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—22no—
136C2×Dic15C2×D412yes—
137C2×Dic15C2×D412yes—
138Dic30—22no—
139Dic30—42no—
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—21no—
148C3×#168—21no—
149C5×C3⋊C8—22no—
150C2×C3×SD16—51no—
151C3×C4×Q8C2×D511yescharacteristic
152C3×C4×D4—51no—
153Q8×Dic3—52no—
154C2×#216C2×D512yes—
155#936—52no—
156#926—101no—
157#924—101no—
158#890—52no—
159#890—102no—
160#887—52no—
161#879—102no—
162#869—51no—
163#869—101no—
164#869C2×D511yescharacteristic
165C4×Dic6—51no—
166C4×Dic6—101no—
167C3×#106—51no—
168C3×#103—51no—
169C3×#102—51no—
170C3×C4×C8—51no—
171#832—52no—
172#816—52no—
173#816—52no—
174Dic3⋊C8—52no—
175C8×Dic3—52no—
176#810C2×D512yes—
177#807—52no—
178C4⋊(C3⋊C8)C2×D511yescharacteristic
179C2×C5×Q8—32no—
180C2×C5×Q8C22×D311yescharacteristic
181C2×D20C22×D311yescharacteristic
182C2×C4×D5—21no—
183C2×Dic10—31no—
184C2×Dic10—61no—
185C5×Q16—64no—
186C2×C5×C8—32no—
187C5×C4⋊C4—21no—
188C5×C4⋊C4—61no—
189C5×C4⋊C4—61no—
190C5×C4⋊C4C22×D311yescharacteristic
191C42×C5—21no—
192C42×C5C22×D311yescharacteristic
193#688—22no—
194#685—21no—
195#685—62no—
196#685—62no—
197C4⋊Dic5—31no—
198C4⋊Dic5—32no—
199C4⋊Dic5—62no—
200C4⋊Dic5—62no—
201C4⋊Dic5—62no—
202C4⋊Dic5—61no—
203C4⋊Dic5C22×D311yescharacteristic
204#683—32no—
205#683—62no—
206C4×Dic5—32no—
207C4×Dic5—62no—
208C4×Dic5—62no—
209C2×#168C22×D311yescharacteristic
210C2×#168C22×D311yescharacteristic
211#557—151no—
212#556—151no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—151no—
217#464—152no—
218#462—31no—
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—22no—
227C3×C4×C5—21no—
228C3×C4×C5—41no—
229C3×C4×C5#13512yes—
230C3×C4×C5C2×#4111yescharacteristic
231C3×C4×C52−1+411yescharacteristic
232Dic15—22no—
233Dic15—22no—
234Dic15—42no—
235C3×Dic5—41no—
236C5×Dic3—42no—
237C2×C3×Q8C22×D511yescharacteristic
238C2×C3×D4—51no—
239C22×C3×C4—101no—
240C2×Dic6—51no—
241C2×Dic6—101no—
242C2×Dic6C22×D512yes—
243C3×SD16—102no—
244C2×C3×C8—51no—
245C2×C3×C8—51no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—51no—
248C3×C4⋊C4C22×D511yescharacteristic
249C3×C22⋊C4—101no—
250C3×C42—21no—
251C3×C42C22×D511yescharacteristic
252#217—102no—
253#217—102no—
254#216—24no—
255C4⋊Dic3—21no—
256C4⋊Dic3—21no—
257C4⋊Dic3—51no—
258C4⋊Dic3—52no—
259C4⋊Dic3—102no—
260C4⋊Dic3—102no—
261C4⋊Dic3—101no—
262Dic3⋊C4—52no—
263Dic3⋊C4—102no—
264Dic3⋊C4—102no—
265C4×Dic3—52no—
266C4×Dic3—102no—
267C4×Dic3—102no—
268C2×C3⋊C8C22×D512yes—
269C22×D5—21no—
270C5×Q8—21no—
271C5×Q8—62no—
272C5×Q8—62no—
273C5×Q8#23512yes—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—62no—
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5C23×D311yescharacteristic
280C2×Dic5—21no—
281C2×Dic5—32no—
282C2×Dic5—32no—
283C2×Dic5—62no—
284D20—21no—
285D20—21no—
286C4×D5—42no—
287Dic10—62no—
288Dic10—122no—
289C5×C8—62no—
290#168—21no—
291#168—21no—
292C2×Q16—32no—
293C2×SD16—51no—
294C4⋊Q8—31no—
295C4⋊Q8—151no—
296C4⋊Q8—301no—
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—301no—
306C4×Q8D3×D511yescharacteristic
307C4×D4—51no—
308#117—301no—
309#107—152no—
310#106—51no—
311C4⋊C8—31no—
312C4⋊C8—152no—
313#103—32no—
314#103—51no—
315#103—152no—
316#103—152no—
317#102—51no—
318#102—152no—
319C4×C8—51no—
320C4×C8—152no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324C3×D5—81no—
325C23×C3—101no—
326C3×Q8—21no—
327C3×Q8#71112yes—
328C3×D4—101no—
329C3×D4—101no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
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—52no—
339C2×Dic3—52no—
340C2×Dic3—102no—
341Dic6—22no—
342Dic6—22no—
343Dic6—102no—
344Dic6—202no—
345C3×C8—101no—
346C3×C8—101no—
347C3⋊C8—22no—
348C22×C5C2×D3×D411yescharacteristic
349C2×D5—41no—
350C2×D5—41no—
351C2×D5—41no—
352C4×C5—21no—
353C4×C5—22no—
354C4×C5—41no—
355C4×C5—122no—
356C4×C5#91612yes—
357C4×C5C2×#23511yescharacteristic
358C4×C5#101011yescharacteristic
359Dic5—41no—
360Dic5—62no—
361Dic5—62no—
362Dic5—122no—
363C2×Q8—32no—
364C2×Q8—151no—
365C2×Q8—301no—
366C2×Q8C2×D3×D511yescharacteristic
367C2×D4—51no—
368C22×C4—101no—
369Q16—64no—
370SD16—102no—
371C2×C8—32no—
372C2×C8—51no—
373C2×C8—51no—
374C4⋊C4—21no—
375C4⋊C4—51no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4—151no—
379C4⋊C4—152no—
380C4⋊C4—152no—
381C4⋊C4—302no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—302no—
385C4⋊C4—301no—
386C4⋊C4C2×D3×D511yescharacteristic
387C22⋊C4—101no—
388C22⋊C4—302no—
389C22⋊C4—302no—
390C42—21no—
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—22no—
402C3×C4—41no—
403C3×C4—201no—
404C3×C4#406512yes—
405C3×C4C2×#71111yescharacteristic
406C3×C4#415011yescharacteristic
407Dic3—42no—
408Dic3—102no—
409Dic3—102no—
410Dic3—202no—
411C2×C5#555211yescharacteristic
412C2×C5C2×#91611yescharacteristic
413C2×C5#577111yescharacteristic
414D5—81no—
415C23—101no—
416Q8—21no—
417Q8—62no—
418Q8—62no—
419Q8—302no—
420Q8—602no—
421Q8#677212yes—
422D4—101no—
423D4—101no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—62no—
427C2×C4—101no—
428C2×C4—152no—
429C2×C4—152no—
430C2×C4—202no—
431C2×C4—302no—
432C2×C4#679011yescharacteristic
433C2×C4#679011yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—62no—
436C8—101no—
437C8—101no—
438C2×C3—401no—
439C2×C3#6593211yescharacteristic
440C2×C3C2×#406511yescharacteristic
441C2×C3#6611311yescharacteristic
442C5#7962311yescharacteristic, complemented, Sylow
443C22—201no—
444C22—201no—
445C22—201no—
446C22C2×#679011yescharacteristic
447C4—22no—
448C4—21no—
449C4—41no—
450C4—122no—
451C4—201no—
452C4—302no—
453C4—302no—
454C4—602no—
455C4#9152112yes—
456C4#9200111yescharacteristic
457C4C2×#677211yescharacteristic
458C3#1061219411yescharacteristic, complemented, Sylow
459C2—401no—
460C2#1175455611yescharacteristic
461C2C2×#9152111yescharacteristic
462C2#1175535011yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×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. #11756329C2semidirect
3. C5×#5031C2semidirect
6. #11749265C2semidirect
8. #11747299C2semidirect
9. #11746929C2semidirect
11. #11746851C2semidirect
90. #5031D5semidirect
395. C3×C5#3364semidirect
442. C5#79623semidirect
458. C3#10612194semidirect

Maximal subgroups

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

subgroupindex
#117563292
#117525082
C5×#50312
C3×C4×#6882
#117493272
#117492652
#117473822
#117472992
#117469292
#117468892
#117468512
#106121943
#796235