Finite Group Databasebeta

← #14472133

Subgroups — #14472133

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#11752476C211yesmaximal, characteristic, complemented
3#11751108C211yesmaximal, characteristic
4C3×C4×#687C211yesmaximal, characteristic
5#11749006C212yesmaximal
6#11748942C212yesmaximal
7#11747396C212yesmaximal, complemented
8#11747266C212yesmaximal, complemented
9#11747094C211yesmaximal, characteristic, complemented
10#11746929C211yesmaximal, characteristic, complemented
11Dic6×#168C211yesmaximal, characteristic, complemented
12#10615407—31nomaximal, Hall
13C3×C4×C5×D4C2211yescharacteristic
14#91758C2211yescharacteristic
15C5×#936C2212yes—
16C5×#926—21no—
17C5×#924—21no—
18C5×#887C2212yes—
19C5×#879—22no—
20C5×#869C2211yescharacteristic
21C4×C5×Dic6C2211yescharacteristic
22C2×C3×#687C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic
24#91381C2212yes—
25#91376—21no—
26#91334—22no—
27#91333—21no—
28Dic3×Dic10C2212yes—
29C2×#6661C2212yes—
30#91116C2212yes—
31#91091C2212yes—
32C4⋊(C3⋊#168)C2211yescharacteristic
33C3×#3964C2211yescharacteristic
34C3×#3942C2211yescharacteristic
35C3×#3940C2211yescharacteristic
36C3×C4×#168C2211yescharacteristic
37Dic3⋊#168C2212yes—
38#90973C2212yes—
39#90973C2212yes—
40#90972C2212yes—
41Dic3×#168C2212yes—
42#79623—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×#687D311yescharacteristic
53#65296—31no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C2×Dic30—21no—
57C2×C5×Dic6D411yescharacteristic
58C2×C5×Dic6C2312yes—
59C2×C3×Dic10C2311yescharacteristic
60C3×C5×C4⋊C4C2311yescharacteristic
61C3×C5×C22⋊C4—21no—
62C3×C42×C5C2311yescharacteristic
63C4⋊Dic15—21no—
64C4⋊Dic15C2312yes—
65C2×C3⋊#168C2312yes—
66C5×#217—22no—
67C5×#217—22no—
68C5×C4⋊Dic3—21no—
69C5×C4⋊Dic3—21no—
70C5×C4⋊Dic3D411yescharacteristic
71C5×Dic3⋊C4—22no—
72C5×Dic3⋊C4D412yes—
73C4×C5×Dic3—22no—
74C4×C5×Dic3C2312yes—
75C3×#687—22no—
76C3×C4⋊Dic5C2311yescharacteristic
77C3×#683—21no—
78C3×C4×Dic5—21no—
79C2×C3×#168C2311yescharacteristic
80C2×C3×#168C2311yescharacteristic
81#6669—22no—
82#6668—22no—
83#6668—22no—
84Dic3×Dic5—22no—
85#6661—24no—
86#5570—51no—
87#5542D511yescharacteristic
88C3×C4×SD16—51no—
89#5166—52no—
90#5031—51no—
91#5007—51no—
92#4857—52no—
93#4790—52no—
94#4768—52no—
95#4681—51no—
96C8×Dic6—51no—
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×#687C2×D311yescharacteristic
108#4035—62no—
109#4033—61no—
110#4016—32no—
111#4015—31no—
112C4×Dic10—32no—
113C4×Dic10C2×D311yescharacteristic
114#3967—32no—
115#3967—32no—
116#3967—32no—
117#3964—32no—
118#3964C2×D311yescharacteristic
119#3942C2×D311yescharacteristic
120#3940C2×D311yescharacteristic
121#3939—32no—
122C4⋊#168—31no—
123C4⋊#168—32no—
124C4×#168—32no—
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—
136Dic30—42no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3C2×D412yes—
139C2×C5×Dic3C2×D412yes—
140C5×Dic6—22no—
141C5×Dic6—22no—
142C5×Dic6—22no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C3×Dic10—21no—
146C3×Dic10#4112yes—
147C3⋊#168—22no—
148C3×#168—21no—
149C3×#168—21no—
150C2×C3×SD16—51no—
151C3×C4×Q8—51no—
152C3×C4×D4C2×D511yescharacteristic
153Q8×Dic3—52no—
154C2×#216—52no—
155#936C2×D512yes—
156#926—21no—
157#924—21no—
158#890—52no—
159#890—102no—
160#887C2×D512yes—
161#879—22no—
162#869—51no—
163#869—101no—
164#869C2×D511yescharacteristic
165C4×Dic6—101no—
166C4×Dic6C2×D511yescharacteristic
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#810—52no—
177#807—52no—
178C4⋊(C3⋊C8)—51no—
179C2×C5×Q8—31no—
180C2×C5×Q8—32no—
181C2×C5×D4C22×D311yescharacteristic
182C22×C4×C5—21no—
183C2×Dic10—61no—
184C2×Dic10C22×D311yescharacteristic
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—22no—
199C4⋊Dic5—32no—
200C4⋊Dic5—61no—
201C4⋊Dic5C22×D311yescharacteristic
202#683—21no—
203#683—62no—
204#683—62no—
205#683—62no—
206C4×Dic5—21no—
207C4×Dic5—62no—
208C2×#168—32no—
209C2×#168C22×D311yescharacteristic
210C2×#168C22×D311yescharacteristic
211#557—151no—
212#556—31no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—151no—
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—42no—
232C3×Dic5—22no—
233C3×Dic5—41no—
234C5×Dic3—22no—
235C5×Dic3—22no—
236C5×Dic3—42no—
237C2×C3×Q8—51no—
238C2×C3×D4C22×D511yescharacteristic
239C22×C3×C4—21no—
240C2×Dic6—101no—
241C2×Dic6C22⋊D511yescharacteristic
242C2×Dic6C22×D512yes—
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—22no—
253#217—22no—
254#216—104no—
255C4⋊Dic3—21no—
256C4⋊Dic3—21no—
257C4⋊Dic3—52no—
258C4⋊Dic3—101no—
259C4⋊Dic3—102no—
260C4⋊Dic3—102no—
261C4⋊Dic3C22⋊D511yescharacteristic
262Dic3⋊C4—22no—
263Dic3⋊C4—102no—
264Dic3⋊C4C22⋊D512yes—
265C4×Dic3—22no—
266C4×Dic3—102no—
267C4×Dic3C22×D512yes—
268C2×C3⋊C8—52no—
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—21no—
284C2×Dic5—21no—
285C2×Dic5—62no—
286Dic10—21no—
287Dic10—122no—
288Dic10#23512yes—
289#168—21no—
290#168—21no—
291#168—62no—
292C2×Q16—152no—
293C2×SD16—51no—
294C4⋊Q8—31no—
295C4⋊Q8—151no—
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—51no—
305C4×Q8—152no—
306C4×Q8—301no—
307C4×D4D3×D511yescharacteristic
308#117—61no—
309#107—152no—
310#106—51no—
311C4⋊C8—152no—
312C4⋊C8—151no—
313#103—51no—
314#103—152no—
315#103—152no—
316#103—152no—
317#102—51no—
318#102—152no—
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×C4C2×C22⋊D511yescharacteristic
335C2×C3×C4C2×C22⋊D511yescharacteristic
336C2×C3×C4C23×D511yescharacteristic
337C2×Dic3—22no—
338C2×Dic3—102no—
339C2×Dic3C2×C22⋊D512yes—
340C2×Dic3C2×C22⋊D512yes—
341Dic6—22no—
342Dic6—22no—
343Dic6—22no—
344Dic6—202no—
345C3×C8—101no—
346C3×C8—101no—
347C3⋊C8—102no—
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#91612yes—
358C4×C5C2×#23511yescharacteristic
359C4×C5#101011yescharacteristic
360Dic5—22no—
361Dic5—41no—
362Dic5—122no—
363C2×Q8—31no—
364C2×Q8—32no—
365C2×Q8—51no—
366C2×Q8—301no—
367C2×D4C2×D3×D511yescharacteristic
368C22×C4—21no—
369Q16—304no—
370SD16—102no—
371C2×C8—51no—
372C2×C8—51no—
373C2×C8—152no—
374C4⋊C4—31no—
375C4⋊C4—32no—
376C4⋊C4—51no—
377C4⋊C4—62no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—101no—
381C4⋊C4—152no—
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—101no—
393C42—302no—
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—102no—
403C3×C4—201no—
404C3×C4#409612yes—
405C3×C4D5×#4111yescharacteristic
406C3×C4#415011yescharacteristic
407Dic3—22no—
408Dic3—22no—
409Dic3—42no—
410Dic3—202no—
411C2×C5—81no—
412C2×C5#555211yescharacteristic
413C2×C5C2×#91611yescharacteristic
414C2×C5#577111yescharacteristic
415C23—21no—
416Q8—52no—
417Q8—62no—
418Q8—62no—
419Q8—62no—
420Q8—101no—
421Q8—602no—
422D4—21no—
423D4—21no—
424C2×C4—21no—
425C2×C4—32no—
426C2×C4—32no—
427C2×C4—42no—
428C2×C4—62no—
429C2×C4—101no—
430C2×C4—101no—
431C2×C4—302no—
432C2×C4D3×C22⋊D511yescharacteristic
433C2×C4D3×C22⋊D511yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—101no—
436C8—101no—
437C8—302no—
438C2×C3—81no—
439C2×C3C2×#409611yescharacteristic
440C2×C3#6616511yescharacteristic
441C2×C3#6617211yescharacteristic
442C5#7962311yescharacteristic, complemented, Sylow
443C22—41no—
444C22—41no—
445C22—41no—
446C22C2×D3×C22⋊D511yescharacteristic
447C4—21no—
448C4—41no—
449C4—62no—
450C4—62no—
451C4—102no—
452C4—122no—
453C4—201no—
454C4—602no—
455C4#9149512yes—
456C4#9200111yescharacteristic
457C4D5×#23511yescharacteristic
458C3#1061540711yescharacteristic, complemented, Sylow
459C2—81no—
460C2#1175433811yescharacteristic
461C2C2×#9149511yescharacteristic
462C2#1175534611yescharacteristic
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. #11752476C2semidirect
7. #11747396C2semidirect
8. #11747266C2semidirect
9. #11747094C2semidirect
10. #11746929C2semidirect
11. Dic6×#168C2semidirect
395. C3×C5#3364semidirect
442. C5#79623semidirect
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
#117524762
#117511082
C3×C4×#6872
#117490062
#117489422
#117473962
#117472662
#117470942
#117469292
Dic6×#1682
#106154073
#796235