Finite Group Databasebeta

← #14471829

Subgroups — #14471829

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756302C211yesmaximal, characteristic, complemented
2#11752636C211yesmaximal, characteristic, complemented
3C4×C5×#214C211yesmaximal, characteristic, complemented
4C3×#65304C211yesmaximal, characteristic
5#11749081C212yesmaximal, complemented
6#11748993C212yesmaximal, complemented
7#11747382C212yesmaximal, complemented
8#11747259C212yesmaximal, complemented
9#11746961C211yesmaximal, characteristic, complemented
10#11746890C211yesmaximal, characteristic, complemented
11#11746855C211yesmaximal, characteristic, complemented
12#10611352—31nomaximal, Hall
13C3×C4×C5×D4C2211yescharacteristic
14D4×Dic15C2212yes—
15C2×C4⋊Dic15—21no—
16#91813—21no—
17#91779C2212yes—
18#91767—22no—
19#91758C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C2×C5×#214C2211yescharacteristic
22C4×C5×Dic6C2211yescharacteristic
23C2×C3×#686C2212yes—
24C3×#4020C2211yescharacteristic
25#91434C2212yes—
26Dic3×D20—21no—
27#91407—22no—
28#91368C2212yes—
29#91364—21no—
30C5×#832C2211yescharacteristic
31C5×#810C2211yescharacteristic
32C5×#808C2211yescharacteristic
33C4×C5×C3⋊C8C2211yescharacteristic
34C3×#3941C2212yes—
35C3×C4⋊#168C2211yescharacteristic
36#90988C2212yes—
37#90983C2212yes—
38#90973C2212yes—
39#90965C2212yes—
40#90965C2212yes—
41#90951C2212yes—
42#80319—51nomaximal, Hall
43#65919—31no—
44#65877—31no—
45C4×C5×SD16—31no—
46#65454—32no—
47#65310—31no—
48#65304D311yescharacteristic
49#65160—32no—
50#65089—32no—
51#65045—32no—
52#64983—31no—
53C8×Dic10—31no—
54C2×C3×C5×D4C2311yescharacteristic
55C22×C3×C4×C5—21no—
56C22×Dic15—22no—
57C2×Dic30—21no—
58C2×Dic30D411yescharacteristic
59C2×C5×Dic6C2311yescharacteristic
60C2×C3×D20—21no—
61C2×C3×D20—21no—
62C2×C3×D20C2312yes—
63C2×D5×Dic3—22no—
64C3×C5×C4⋊C4C2311yescharacteristic
65C3×C5×C22⋊C4—21no—
66C3×C42×C5C2311yescharacteristic
67#6719—22no—
68C4⋊Dic15—21no—
69C4⋊Dic15—22no—
70C4⋊Dic15D411yescharacteristic
71C4⋊Dic15C2312yes—
72#6712—22no—
73#6712D412yes—
74C4×Dic15C2312yes—
75C5×#214—22no—
76C5×C4⋊Dic3C2311yescharacteristic
77C5×Dic3⋊C4—21no—
78C4×C5×Dic3—21no—
79C2×C5×C3⋊C8C2311yescharacteristic
80C2×C5×C3⋊C8C2311yescharacteristic
81C3×#686—24no—
82C2×C3×#168C2312yes—
83#6665—22no—
84#6665—22no—
85#6665—22no—
86#5713—51no—
87#5543—51no—
88C3×#459—51no—
89#5153—52no—
90Dic3×D8—52no—
91#5070—51no—
92C4×#214D511yescharacteristic, complemented
93#4850—51no—
94#4830—51no—
95#4768—52no—
96#4766—52no—
97C2×C5×SD16—31no—
98C4×C5×Q8—31no—
99C4×C5×D4C2×D311yescharacteristic
100#4093—32no—
101D4×Dic5—32no—
102C2×#686C2×D312yes—
103C2×C4⋊Dic5—61no—
104#4070—61no—
105#4040—62no—
106#4039—32no—
107#4036—32no—
108#4024—62no—
109#4021—61no—
110#4020C2×D311yescharacteristic
111C4×D20—61no—
112#4015—31no—
113C4×Dic10—31no—
114C5×#106—31no—
115C5×#103—31no—
116C5×#102—31no—
117C4×C5×C8—31no—
118#3967—32no—
119#3953—32no—
120#3953—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3941C2×D312yes—
124#3939—32no—
125C4⋊#168C2×D311yescharacteristic
126#3361—151noSylow
127C23×C3×C5—21no—
128C22×C3×D5—22no—
129C3×C5×D4—21no—
130C3×C5×D4#4112yes—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—42no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—22no—
137C2×Dic15—82no—
138C2×Dic15C2×D412yes—
139C2×Dic15C2×D412yes—
140Dic30—22no—
141Dic30—81no—
142C2×C5×Dic3—21no—
143C2×C5×Dic3—21no—
144C5×Dic6—21no—
145C5×Dic6—21no—
146C3×D20—22no—
147C3×D20—22no—
148C3×D20—42no—
149C3×D20—81no—
150D5×Dic3—82no—
151C3×#168—22no—
152C5×C3⋊C8—21no—
153C5×C3⋊C8—21no—
154C2×C3×D8—52no—
155C3×#127—51no—
156C3×C4×D4C2×D511yescharacteristic
157#936—52no—
158#936—101no—
159#935—102no—
160D4×Dic3—52no—
161D4×Dic3—52no—
162D4×Dic3—101no—
163C2×#214C2×D511yescharacteristic
164C2×C4⋊Dic3—101no—
165#924—101no—
166#890—52no—
167#878—102no—
168#869—51no—
169C4×Dic6—51no—
170C4×Dic6C2×D511yescharacteristic
171C3×C4⋊C8—51no—
172C3×#102—52no—
173#832—52no—
174#832—52no—
175#832C2×D511yescharacteristic
176#818—52no—
177#816—52no—
178Dic3⋊C8—52no—
179C8×Dic3—52no—
180#810C2×D511yescharacteristic
181#808C2×D511yescharacteristic
182C4×C3⋊C8C2×D511yescharacteristic
183C2×C5×Q8—31no—
184C2×C5×D4C22×D311yescharacteristic
185C22×C4×C5—21no—
186C22×Dic5—62no—
187C2×D20—21no—
188C2×D20—21no—
189C2×D20C22×D312yes—
190C2×C4×D5—62no—
191C2×Dic10—31no—
192C2×Dic10—61no—
193C5×SD16—62no—
194C2×C5×C8—31no—
195C2×C5×C8—31no—
196C5×C4⋊C4—31no—
197C5×C4⋊C4—61no—
198C5×C4⋊C4C22×D311yescharacteristic
199C5×C22⋊C4—21no—
200C42×C5—61no—
201C42×C5C22×D311yescharacteristic
202C22⋊Dic5—62no—
203#686—24no—
204#685—62no—
205#685—62no—
206#685—62no—
207C4⋊Dic5—31no—
208C4⋊Dic5—32no—
209C4⋊Dic5—62no—
210C4⋊Dic5—61no—
211#683—32no—
212#683—62no—
213C4×Dic5—32no—
214C2×#168C22×D312yes—
215#559—151no—
216#554—151no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—51no—
223C8×Q8—151no—
224C4×SD16—31no—
225C4×D8—152no—
226C22×C3×C5—22no—
227C22×C3×C5—41no—
228C22×C3×C5—41no—
229C22×C3×C5C22×D411yescharacteristic
230C2×C3×D5—42no—
231C2×C3×D5—42no—
232C2×C3×D5—42no—
233C3×C4×C5—21no—
234C3×C4×C5—41no—
235C3×C4×C5#13512yes—
236C3×C4×C5C2×#4111yescharacteristic
237C3×C4×C52−1+411yescharacteristic
238Dic15—22no—
239Dic15—22no—
240Dic15—42no—
241C5×Dic3—41no—
242C5×Dic3—41no—
243C2×C3×D4—52no—
244C2×C3×D4—101no—
245C2×C3×D4—101no—
246C2×C3×D4C22×D511yescharacteristic
247C22×C3×C4—21no—
248C22×Dic3—102no—
249C22×Dic3—102no—
250C2×Dic6—51no—
251C2×Dic6—101no—
252C2×Dic6C22×D511yescharacteristic
253C3×D8—104no—
254C2×C3×C8—52no—
255C3×C4⋊C4C22×D511yescharacteristic
256C3×C22⋊C4—21no—
257C3×C42C22×D511yescharacteristic
258#217—102no—
259#217—102no—
260#217—102no—
261#217—102no—
262#214—22no—
263C4⋊Dic3—51no—
264C4⋊Dic3—52no—
265C4⋊Dic3—102no—
266C4⋊Dic3—101no—
267C4⋊Dic3C22×D511yescharacteristic
268Dic3⋊C4—21no—
269Dic3⋊C4—52no—
270Dic3⋊C4—102no—
271C4×Dic3—21no—
272C4×Dic3—52no—
273C2×C3⋊C8C22×D511yescharacteristic
274C2×C3⋊C8C22×D511yescharacteristic
275C23×C5—21no—
276C22×D5—22no—
277C5×Q8—61no—
278C5×Q8—61no—
279C5×D4—21no—
280C5×D4#23712yes—
281C2×C4×C5—21no—
282C2×C4×C5—42no—
283C2×C4×C5—61no—
284C2×C4×C5—61no—
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—32no—
289C2×Dic5—32no—
290C2×Dic5—62no—
291C2×Dic5—242no—
292D20—22no—
293D20—22no—
294D20—42no—
295D20—81no—
296C4×D5—242no—
297Dic10—62no—
298Dic10—241no—
299C5×C8—61no—
300C5×C8—61no—
301#168—22no—
302C2×SD16—31no—
303C2×D8—52no—
304C4⋊Q8—151no—
305#127—51no—
306#125—152no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—31no—
313C4×Q8—151no—
314C4×D4—152no—
315C4×D4—152no—
316C4×D4—301no—
317C4×D4D3×D511yescharacteristic
318C2×C4⋊C4—301no—
319#107—152no—
320#106—31no—
321C4⋊C8—51no—
322C4⋊C8—152no—
323#103—31no—
324#103—152no—
325#102—31no—
326#102—52no—
327#102—152no—
328#102—152no—
329C4×C8—31no—
330C4×C8—152no—
331C2×C3×C5—42no—
332C2×C3×C5#54811yescharacteristic
333C2×C3×C5C2×#13511yescharacteristic
334C2×C3×C5#57611yescharacteristic
335C3×D5—82no—
336C23×C3—21no—
337C23×C3—102no—
338C3×D4—21no—
339C3×D4—102no—
340C3×D4—102no—
341C3×D4—202no—
342C3×D4—401no—
343C3×D4#70912yes—
344C2×C3×C4—21no—
345C2×C3×C4—42no—
346C2×C3×C4D4×D511yescharacteristic
347C2×C3×C4D4×D511yescharacteristic
348C2×C3×C4C23×D511yescharacteristic
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—52no—
352C2×Dic3—52no—
353C2×Dic3—102no—
354C2×Dic3—402no—
355C2×Dic3—402no—
356Dic6—21no—
357Dic6—21no—
358Dic6—102no—
359Dic6—401no—
360C3×C8—102no—
361C3⋊C8—21no—
362C3⋊C8—21no—
363C22×C5—22no—
364C22×C5—41no—
365C22×C5—41no—
366C22×C5C2×D3×D411yescharacteristic
367C2×D5—42no—
368C2×D5—42no—
369C2×D5—42no—
370C4×C5—21no—
371C4×C5—41no—
372C4×C5—121no—
373C4×C5—121no—
374C4×C5#91212yes—
375C4×C5C2×#23711yescharacteristic
376C4×C5#101011yescharacteristic
377Dic5—62no—
378Dic5—62no—
379Dic5—122no—
380C2×Q8—31no—
381C2×Q8—151no—
382C2×Q8—301no—
383C2×D4—52no—
384C2×D4—101no—
385C2×D4—101no—
386C2×D4C2×D3×D511yescharacteristic
387C22×C4—21no—
388C22×C4—302no—
389C22×C4—302no—
390SD16—62no—
391D8—104no—
392C2×C8—31no—
393C2×C8—31no—
394C2×C8—52no—
395C4⋊C4—31no—
396C4⋊C4—61no—
397C4⋊C4—151no—
398C4⋊C4—152no—
399C4⋊C4—152no—
400C4⋊C4—302no—
401C4⋊C4—302no—
402C4⋊C4—301no—
403C4⋊C4C2×D3×D511yescharacteristic
404C22⋊C4—21no—
405C22⋊C4—302no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—61no—
410C42—152no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—22no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—202no—
417C22×C3—202no—
418C22×C3—202no—
419C22×C3C2×D4×D511yescharacteristic
420C3×C4—21no—
421C3×C4—41no—
422C3×C4#406212yes—
423C3×C4C2×#70911yescharacteristic
424C3×C4#415011yescharacteristic
425Dic3—41no—
426Dic3—41no—
427Dic3—102no—
428Dic3—102no—
429Dic3—202no—
430C2×C5—42no—
431C2×C5#559811yescharacteristic
432C2×C5C2×#91211yescharacteristic
433C2×C5#577411yescharacteristic
434D5—82no—
435C23—21no—
436C23—102no—
437Q8—61no—
438Q8—61no—
439Q8—302no—
440Q8—1201no—
441D4—21no—
442D4—102no—
443D4—102no—
444D4—202no—
445D4—401no—
446D4#676512yes—
447C2×C4—21no—
448C2×C4—42no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—152no—
452C2×C4—152no—
453C2×C4—302no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4#679011yescharacteristic
457C2×C4#679011yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—61no—
460C8—61no—
461C8—102no—
462C2×C3—42no—
463C2×C3—402no—
464C2×C3#6588611yescharacteristic
465C2×C3C2×#406211yescharacteristic
466C2×C3#6610311yescharacteristic
467C5#8031911yescharacteristic, complemented, Sylow
468C22—22no—
469C22—41no—
470C22—41no—
471C22—202no—
472C22—202no—
473C22—202no—
474C22C2×#679011yescharacteristic
475C4—21no—
476C4—41no—
477C4—121no—
478C4—121no—
479C4—302no—
480C4—302no—
481C4—602no—
482C4#9149712yes—
483C4C2×#676511yescharacteristic
484C4#9200111yescharacteristic
485C3#1061135211yescharacteristic, complemented, Sylow
486C2—42no—
487C2—402no—
488C2#1175436911yescharacteristic
489C2C2×#9149711yescharacteristic
490C2#1175533011yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC3×#65304C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3361
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
1. #11756302C2semidirect
2. #11752636C2semidirect
3. C4×C5×#214C2semidirect
5. #11749081C2semidirect
6. #11748993C2semidirect
7. #11747382C2semidirect
8. #11747259C2semidirect
9. #11746961C2semidirect
10. #11746890C2semidirect
11. #11746855C2semidirect
92. C4×#214D5semidirect
412. C3×C5#3361semidirect
467. C5#80319semidirect
485. C3#10611352semidirect

Maximal subgroups

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

subgroupindex
#117563022
#117526362
C4×C5×#2142
C3×#653042
#117490812
#117489932
#117473822
#117472592
#117469612
#117468902
#117468552
#106113523
#803195