Finite Group Databasebeta

← #14472138

Subgroups — #14472138

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#11756301C211yesmaximal, characteristic
2#11752477C211yesmaximal, characteristic, complemented
3C5×#5007C211yesmaximal, characteristic
4C3×C4×#687C211yesmaximal, characteristic
5#11749007C212yesmaximal
6#11748944C212yesmaximal
7#11747271C212yesmaximal, complemented
8#11747187C212yesmaximal, complemented
9#11747095C211yesmaximal, characteristic, complemented
10#11746930C211yesmaximal, characteristic, complemented
11#11746851C211yesmaximal, characteristic, complemented
12#10612725—31nomaximal, Hall
13C3×C4×C5×D4C2211yescharacteristic
14#91825C2212yes—
15#91815—21no—
16#91813—21no—
17#91776C2212yes—
18#91768—22no—
19#91758C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C5×#869C2211yescharacteristic
22C2×C3×#687C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic
24#91384C2212yes—
25#91376—21no—
26#91335—22no—
27Dic5×Dic6—21no—
28#91331C2212yes—
29C2×#6662C2212yes—
30C5×#832C2212yes—
31C5×#807C2212yes—
32C5×C4⋊(C3⋊C8)C2211yescharacteristic
33C3×#3964C2211yescharacteristic
34C3×#3942C2211yescharacteristic
35C3×#3940C2211yescharacteristic
36C3×C4×#168C2211yescharacteristic
37#90983C2212yes—
38#90975C2212yes—
39#90975C2212yes—
40#90974C2212yes—
41#90951C2212yes—
42#79623—51nomaximal, Hall
43#66055—31no—
44#65876—31no—
45C5×#474—31no—
46#65382—31no—
47C4×#687D311yescharacteristic
48#65166—32no—
49#65162—32no—
50#65138—31no—
51#65119—31no—
52#65057—32no—
53#65056—32no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×Dic30D411yescharacteristic
57C2×Dic30C2312yes—
58C2×C5×Dic6—21no—
59C2×C3×Dic10C2311yescharacteristic
60C3×C5×C4⋊C4C2311yescharacteristic
61C3×C5×C22⋊C4—21no—
62C3×C42×C5C2311yescharacteristic
63#6719—22no—
64#6719—22no—
65C4⋊Dic15—21no—
66C4⋊Dic15—21no—
67C4⋊Dic15D411yescharacteristic
68#6712—22no—
69#6712D412yes—
70C4×Dic15—22no—
71C4×Dic15C2312yes—
72C5×C4⋊Dic3—21no—
73C5×C4⋊Dic3C2312yes—
74C2×C5×C3⋊C8C2312yes—
75C3×#687—22no—
76C3×C4⋊Dic5C2311yescharacteristic
77C3×#683—21no—
78C3×C4×Dic5—21no—
79C2×C3×#168C2311yescharacteristic
80C2×C3×#168C2311yescharacteristic
81Dic3⋊Dic5—22no—
82#6668—22no—
83#6668—22no—
84Dic3×Dic5—22no—
85#6662—24no—
86#5570—51no—
87#5542—51no—
88C3×C4×SD16—51no—
89#5166—52no—
90#5031—51no—
91#5007D511yescharacteristic
92#4857—52no—
93#4790—52no—
94#4768—52no—
95#4681—51no—
96C8×Dic6—51no—
97C5×C4⋊Q8—31no—
98C4×C5×D4C2×D311yescharacteristic
99Q8×Dic5—61no—
100#4090—61no—
101#4082—32no—
102C2×#687C2×D311yescharacteristic
103#4072—61no—
104#4070—61no—
105C2×Dic20—32no—
106#4036—32no—
107#4035—62no—
108#4033—32no—
109#4033—32no—
110#4025—62no—
111#4015—31no—
112C4×Dic10—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×#107—32no—
115C5×C4⋊C8—31no—
116C5×#102—32no—
117#3964C2×D311yescharacteristic
118#3948—32no—
119#3946—32no—
120C8×Dic5—32no—
121#3942—32no—
122#3942—32no—
123#3942C2×D311yescharacteristic
124#3940C2×D311yescharacteristic
125C4×#168C2×D311yescharacteristic
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—22no—
136C2×Dic15C2×D412yes—
137C2×Dic15C2×D412yes—
138Dic30—22no—
139Dic30—22no—
140Dic30—22no—
141C2×C5×Dic3—22no—
142C5×Dic6—42no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C3×Dic10—21no—
146C3×Dic10#4112yes—
147C3×#168—21no—
148C3×#168—21no—
149C5×C3⋊C8—22no—
150C2×C3×SD16—51no—
151C3×C4×Q8—51no—
152C3×C4×D4C2×D511yescharacteristic
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—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#832C2×D512yes—
172#816—52no—
173#816—52no—
174Dic3⋊C8—52no—
175C8×Dic3—52no—
176#810—52no—
177#807C2×D512yes—
178C4⋊(C3⋊C8)C2×D511yescharacteristic
179C2×C5×Q8—61no—
180C2×C5×D4C22×D311yescharacteristic
181C22×C4×C5—21no—
182C2×Dic10—31no—
183C2×Dic10—32no—
184C2×Dic10C22×D311yescharacteristic
185C2×C5×C8—32no—
186C5×C4⋊C4—32no—
187C5×C4⋊C4—61no—
188C5×C4⋊C4C22×D311yescharacteristic
189C5×C22⋊C4—21no—
190C42×C5C22×D311yescharacteristic
191C22⋊Dic5—62no—
192C22⋊Dic5—62no—
193#687—22no—
194C4⋊Dic5—31no—
195C4⋊Dic5—62no—
196C4⋊Dic5—61no—
197C4⋊Dic5—61no—
198C4⋊Dic5C22×D311yescharacteristic
199#683—21no—
200#683—32no—
201#683—62no—
202#683—62no—
203#683—62no—
204C4×Dic5—21no—
205C4×Dic5—32no—
206C4×Dic5—62no—
207C4×Dic5—62no—
208C2×#168C22×D311yescharacteristic
209C2×#168C22×D311yescharacteristic
210Dic20—64no—
211#557—151no—
212#556—151no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—31no—
217#464—152no—
218#462—151no—
219C8×Q8—151no—
220C4×Q16—152no—
221C4×SD16—51no—
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—22no—
233Dic15—42no—
234C3×Dic5—22no—
235C3×Dic5—41no—
236C5×Dic3—42no—
237C2×C3×Q8—51no—
238C2×C3×D4C22×D511yescharacteristic
239C22×C3×C4—21no—
240C2×Dic6—21no—
241C2×Dic6—51no—
242C2×Dic6—52no—
243C3×SD16—102no—
244C2×C3×C8—51no—
245C2×C3×C8—51no—
246C3×C4⋊C4—51no—
247C3×C4⋊C4—101no—
248C3×C4⋊C4C22×D511yescharacteristic
249C3×C22⋊C4—21no—
250C3×C42—101no—
251C3×C42C22×D511yescharacteristic
252#217—102no—
253#217—102no—
254#216—104no—
255C4⋊Dic3—21no—
256C4⋊Dic3—51no—
257C4⋊Dic3—102no—
258C4⋊Dic3—102no—
259C4⋊Dic3—101no—
260C4⋊Dic3—101no—
261C4⋊Dic3C22×D512yes—
262Dic3⋊C4—52no—
263Dic3⋊C4—102no—
264Dic3⋊C4—102no—
265C4×Dic3—52no—
266C4×Dic3—102no—
267C4×Dic3—102no—
268C2×C3⋊C8C22×D512yes—
269C23×C5—21no—
270C5×Q8—122no—
271C5×D4—21no—
272C5×D4—21no—
273C2×C4×C5—21no—
274C2×C4×C5—42no—
275C2×C4×C5—62no—
276C2×C4×C5D3×D411yescharacteristic
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5C23×D311yescharacteristic
279C2×Dic5—21no—
280C2×Dic5—21no—
281C2×Dic5—32no—
282C2×Dic5—32no—
283C2×Dic5—62no—
284Dic10—21no—
285Dic10—62no—
286Dic10—62no—
287Dic10—62no—
288Dic10#23512yes—
289C5×C8—62no—
290#168—21no—
291#168—21no—
292C2×Q16—152no—
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—51no—
303C4×Q8—151no—
304C4×Q8—152no—
305C4×Q8—152no—
306C4×Q8—301no—
307C4×D4D3×D511yescharacteristic
308#117—301no—
309#107—32no—
310#106—51no—
311C4⋊C8—31no—
312C4⋊C8—152no—
313#103—51no—
314#103—152no—
315#103—152no—
316#103—152no—
317#102—32no—
318#102—51no—
319C4×C8—51no—
320C4×C8—152no—
321C2×C3×C5—81no—
322C2×C3×C5#54811yescharacteristic
323C2×C3×C5C2×#13511yescharacteristic
324C2×C3×C5#57811yescharacteristic
325C23×C3—21no—
326C3×Q8—52no—
327C3×Q8—101no—
328C3×D4—21no—
329C3×D4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—42no—
332C2×C3×C4—101no—
333C2×C3×C4—101no—
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—42no—
342Dic6—102no—
343Dic6—102no—
344Dic6—102no—
345C3×C8—101no—
346C3×C8—101no—
347C3⋊C8—22no—
348C22×C5—41no—
349C22×C5—41no—
350C22×C5—41no—
351C22×C5C2×D3×D411yescharacteristic
352C4×C5—21no—
353C4×C5—41no—
354C4×C5—122no—
355C4×C5#91612yes—
356C4×C5C2×#23511yescharacteristic
357C4×C5#101011yescharacteristic
358Dic5—22no—
359Dic5—41no—
360Dic5—62no—
361Dic5—62no—
362Dic5—122no—
363C2×Q8—51no—
364C2×Q8—61no—
365C2×Q8—151no—
366C2×Q8—152no—
367C2×D4C2×D3×D511yescharacteristic
368C22×C4—21no—
369Q16—304no—
370SD16—102no—
371C2×C8—32no—
372C2×C8—51no—
373C2×C8—51no—
374C4⋊C4—32no—
375C4⋊C4—51no—
376C4⋊C4—61no—
377C4⋊C4—101no—
378C4⋊C4—151no—
379C4⋊C4—152no—
380C4⋊C4—302no—
381C4⋊C4—302no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—301no—
385C4⋊C4—301no—
386C4⋊C4C2×D3×D511yescharacteristic
387C22⋊C4—21no—
388C22⋊C4—302no—
389C22⋊C4—302no—
390C42—101no—
391C42—152no—
392C42—302no—
393C42—302no—
394C42C2×D3×D511yescharacteristic
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3C2×D4×D511yescharacteristic
400C3×C4—21no—
401C3×C4—41no—
402C3×C4—102no—
403C3×C4—201no—
404C3×C4#405812yes—
405C3×C4#414711yescharacteristic
406C3×C4D5×#4111yescharacteristic
407Dic3—42no—
408Dic3—102no—
409Dic3—102no—
410Dic3—202no—
411C2×C5—81no—
412C2×C5#555211yescharacteristic
413C2×C5C2×#91611yescharacteristic
414C2×C5#577111yescharacteristic
415C23—21no—
416Q8—52no—
417Q8—101no—
418Q8—122no—
419Q8—302no—
420Q8—302no—
421Q8—302no—
422D4—21no—
423D4—21no—
424C2×C4—21no—
425C2×C4—42no—
426C2×C4—62no—
427C2×C4—101no—
428C2×C4—101no—
429C2×C4—152no—
430C2×C4—152no—
431C2×C4—302no—
432C2×C4#679011yescharacteristic
433C2×C4#679011yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—62no—
436C8—101no—
437C8—101no—
438C2×C3—81no—
439C2×C3#6596711yescharacteristic
440C2×C3C2×#405811yescharacteristic
441C2×C3#6611311yescharacteristic
442C5#7962311yescharacteristic, complemented, Sylow
443C22—41no—
444C22—41no—
445C22—41no—
446C22C2×#679011yescharacteristic
447C4—21no—
448C4—41no—
449C4—102no—
450C4—122no—
451C4—201no—
452C4—302no—
453C4—302no—
454C4—602no—
455C4#9149912yes—
456C4#9200011yescharacteristic
457C4D5×#23511yescharacteristic
458C3#1061272511yescharacteristic, complemented, Sylow
459C2—81no—
460C2#1175436711yescharacteristic
461C2C2×#9149911yescharacteristic
462C2#1175535011yescharacteristic
subgroupG/H
centerC22C2×#6790
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. #11752477C2semidirect
7. #11747271C2semidirect
8. #11747187C2semidirect
9. #11747095C2semidirect
10. #11746930C2semidirect
11. #11746851C2semidirect
395. C3×C5#3364semidirect
442. C5#79623semidirect
458. C3#10612725semidirect

Maximal subgroups

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

subgroupindex
#117563012
#117524772
C5×#50072
C3×C4×#6872
#117490072
#117489442
#117472712
#117471872
#117470952
#117469302
#117468512
#106127253
#796235