Finite Group Databasebeta

← #14471818

Subgroups — #14471818

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
1C3×#65919C211yesmaximal, characteristic, complemented
2#11752660C211yesmaximal, characteristic, complemented
3#11751122C211yesmaximal, characteristic, complemented
4C4×C5×#215C211yesmaximal, characteristic, complemented
5#11749331C212yesmaximal, complemented
6#11749224C212yesmaximal, complemented
7#11747392C212yesmaximal, complemented
8#11747216C212yesmaximal, complemented
9#11747033C211yesmaximal, characteristic
10#11746890C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
12#10611352—31nomaximal, Hall
13C3×C4×C5×Q8C2211yescharacteristic
14#91758C2211yescharacteristic
15C2×C5×#215C2211yescharacteristic
16C4×C5×D12C2211yescharacteristic
17C3×#4093C2212yes—
18C3×#4040—22no—
19C3×#4039C2212yes—
20C3×#4021—21no—
21C3×#4020C2211yescharacteristic
22C3×C4×D20—21no—
23C3×C4×Dic10C2211yescharacteristic
24#91432—22no—
25D3×C4⋊Dic5—21no—
26Dic5×D12C2212yes—
27#91388C2212yes—
28#91369—21no—
29C2×#6652C2212yes—
30#91119C2212yes—
31#91091C2212yes—
32C4⋊(C3⋊#168)C2211yescharacteristic
33C5×#835C2211yescharacteristic
34C5×#809C2211yescharacteristic
35C5×#808C2211yescharacteristic
36C4×C5×C3⋊C8C2211yescharacteristic
37#90982C2212yes—
38#90965C2212yes—
39#90965C2212yes—
40#90964C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83713—51nomaximal, Hall
43#65919D311yescharacteristic, complemented
44#65877—31no—
45C4×C5×SD16—31no—
46#65454—32no—
47#65310—31no—
48#65304—31no—
49#65160—32no—
50#65089—32no—
51#65045—32no—
52#64983—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×Dic30—21no—
56C2×C5×D12C2311yescharacteristic
57C2×C4×C5×D3—21no—
58C2×C3×D20—21no—
59C2×C3×D20—21no—
60C2×C3×D20C2312yes—
61C2×C3×C4×D5—22no—
62C2×C3×Dic10D411yescharacteristic
63C2×D3×Dic5—22no—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4C2311yescharacteristic
66C3×C42×C5—21no—
67C3×C42×C5C2311yescharacteristic
68C4⋊Dic15—21no—
69C4⋊Dic15C2312yes—
70C2×C3⋊#168C2312yes—
71C5×#215—22no—
72C5×(C2×D3)⋊C4—21no—
73C5×C4⋊Dic3C2311yescharacteristic
74C2×C5×C3⋊C8C2311yescharacteristic
75C2×C5×C3⋊C8C2311yescharacteristic
76C3×#685—22no—
77C3×#685—22no—
78C3×#685—22no—
79C3×C4⋊Dic5D411yescharacteristic
80C3×#683D412yes—
81C3×C4×Dic5C2312yes—
82Dic3⋊Dic5—22no—
83#6669—22no—
84(C2×D3)⋊Dic5—22no—
85#6652—24no—
86C3×#559—51no—
87#5579—51no—
88#5072—51no—
89#5070—51no—
90#5057—52no—
91#5056—52no—
92C4×#215D511yescharacteristic, complemented
93Q8×C3⋊C8—51no—
94#5021—51no—
95C4×#213—52no—
96#5009—52no—
97C2×C5×SD16—31no—
98C4×C5×Q8C2×D311yescharacteristic
99C4×C5×D4—31no—
100#4093C2×D312yes—
101D4×Dic5—32no—
102C2×#686—32no—
103C2×C4⋊Dic5—61no—
104#4070—61no—
105#4040—22no—
106#4039C2×D312yes—
107#4036—32no—
108#4024—62no—
109#4021—21no—
110#4020C2×D311yescharacteristic
111C4×D20—21no—
112#4015—31no—
113C4×Dic10C2×D311yescharacteristic
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#3941—32no—
124#3939—32no—
125C4⋊#168—31no—
126#3361—151noSylow
127C22×C5×D3—21no—
128C22×C3×D5—22no—
129C3×C5×Q8—21no—
130C3×C5×Q8—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—22no—
137Dic30—81no—
138C2×C5×Dic3—21no—
139C5×D12—21no—
140C5×D12#4112yes—
141C4×C5×D3—42no—
142C2×C3×Dic5C2×D412yes—
143C2×C3×Dic5C2×D412yes—
144C3×D20—22no—
145C3×D20—22no—
146C3×D20—42no—
147C3×D20—81no—
148C3×C4×D5—82no—
149C3×Dic10—22no—
150D3×Dic5—82no—
151C3⋊#168—22no—
152C5×C3⋊C8—21no—
153C5×C3⋊C8—21no—
154C3×#127—51no—
155C3×#124—52no—
156C3×#124—101no—
157C3×#123—102no—
158C3×C4×Q8—51no—
159C3×C4×Q8C2×D511yescharacteristic
160C3×C4×D4—52no—
161C3×C4×D4—101no—
162#946—101no—
163C2×#215C2×D511yescharacteristic
164C2×#213—52no—
165#896—102no—
166D3×C4⋊C4—101no—
167C4×D12—52no—
168C4×D12C2×D511yescharacteristic
169#870—52no—
170#869—51no—
171#835—52no—
172#835C2×D511yescharacteristic
173#832—52no—
174#832—52no—
175#832—52no—
176#809C2×D511yescharacteristic
177#808C2×D511yescharacteristic
178#807—52no—
179C4⋊(C3⋊C8)—51no—
180C4⋊(C3⋊C8)—52no—
181C4×C3⋊C8—52no—
182C4×C3⋊C8C2×D511yescharacteristic
183C2×C5×Q8C22×D311yescharacteristic
184C2×C5×D4—31no—
185C22×C4×C5—61no—
186C22×Dic5—62no—
187C2×D20—21no—
188C2×D20—21no—
189C2×D20C22×D312yes—
190C2×C4×D5—22no—
191C2×Dic10—61no—
192C2×Dic10#6711yescharacteristic
193C5×SD16—62no—
194C2×C5×C8—31no—
195C2×C5×C8—31no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—31no—
198C5×C4⋊C4C22×D311yescharacteristic
199C5×C22⋊C4—61no—
200C42×C5—21no—
201C42×C5C22×D311yescharacteristic
202C22⋊Dic5—62no—
203#686—64no—
204#685—22no—
205#685—22no—
206#685—22no—
207C4⋊Dic5—32no—
208C4⋊Dic5—61no—
209C4⋊Dic5—62no—
210C4⋊Dic5#6711yescharacteristic
211#683—62no—
212#683#6712yes—
213C4×Dic5C22×D312yes—
214C2×#168—32no—
215#559—51no—
216#554—151no—
217#488—152no—
218#486—151no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—151no—
223C8×Q8—151no—
224C4×SD16—31no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C5×D3—22no—
228C2×C5×D3—41no—
229C2×C5×D3—41no—
230C2×C3×D5—42no—
231C2×C3×D5—42no—
232C2×C3×D5—42no—
233C3×C4×C5—21no—
234C3×C4×C5—41no—
235C3×C4×C5—41no—
236C3×C4×C5#13512yes—
237C3×C4×C5C2×#4111yescharacteristic
238C3×C4×C52−1+411yescharacteristic
239Dic15—42no—
240C3×Dic5—22no—
241C3×Dic5—22no—
242C5×Dic3—41no—
243C2×C3×Q8—51no—
244C2×C3×Q8C22×D511yescharacteristic
245C2×C3×D4—52no—
246C2×C3×D4—101no—
247C2×C3×D4—101no—
248C22×C3×C4—102no—
249C2×D12C22×D511yescharacteristic
250C2×C4×D3—21no—
251C2×C4×D3—102no—
252C2×Dic6—101no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—52no—
255C3×C4⋊C4—51no—
256C3×C4⋊C4C22×D511yescharacteristic
257C3×C22⋊C4—102no—
258C3×C22⋊C4—102no—
259C3×C22⋊C4—102no—
260C3×C42—21no—
261C3×C42—52no—
262C3×C42C22×D511yescharacteristic
263#215—22no—
264#213—104no—
265(C2×D3)⋊C4—21no—
266(C2×D3)⋊C4—102no—
267C4⋊Dic3—52no—
268C4⋊Dic3—101no—
269C4⋊Dic3C22×D511yescharacteristic
270Dic3⋊C4—102no—
271Dic3⋊C4—102no—
272C2×C3⋊C8—52no—
273C2×C3⋊C8C22×D511yescharacteristic
274C2×C3⋊C8C22×D511yescharacteristic
275C23×C5—61no—
276C22×D5—22no—
277C5×Q8—21no—
278C5×Q8—21no—
279C5×D4—32no—
280C5×D4—61no—
281C2×C4×C5—21no—
282C2×C4×C5—21no—
283C2×C4×C5—61no—
284C2×C4×C5—122no—
285C2×C4×C5C2×#6711yescharacteristic
286C2×C4×C5C2×#6711yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—62no—
289C2×Dic5—242no—
290C2×Dic5C2×#6712yes—
291C2×Dic5C2×#6712yes—
292D20—22no—
293D20—22no—
294D20—42no—
295D20—81no—
296C4×D5—82no—
297Dic10—22no—
298Dic10—241no—
299C5×C8—61no—
300C5×C8—61no—
301#168—62no—
302C2×SD16—31no—
303C2×D8—152no—
304C4⋊Q8—151no—
305#127—51no—
306#125—152no—
307#124—52no—
308#124—101no—
309#123—102no—
310C22⋊Q8—302no—
311C22⋊Q8—301no—
312C4×Q8—51no—
313C4×Q8D3×D511yescharacteristic
314C4×D4—31no—
315C4×D4—52no—
316C4×D4—101no—
317C4×D4—152no—
318C2×C4⋊C4—301no—
319#107—152no—
320#106—31no—
321C4⋊C8—152no—
322C4⋊C8—151no—
323#103—31no—
324#103—152no—
325#102—31no—
326#102—152no—
327#102—152no—
328#102—152no—
329C4×C8—31no—
330C4×C8—152no—
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334C3×D5—82no—
335C5×D3—42no—
336C23×C3—102no—
337C22×D3—21no—
338C3×Q8—21no—
339C3×Q8—21no—
340C3×Q8—102no—
341C3×D4—102no—
342C3×D4—102no—
343C3×D4—202no—
344C3×D4—401no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—52no—
348C2×C3×C4—52no—
349C2×C3×C4—402no—
350C2×C3×C4D4×D511yescharacteristic
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4C23×D511yescharacteristic
353C2×Dic3—21no—
354C2×Dic3—102no—
355D12—21no—
356D12#70912yes—
357C4×D3—42no—
358C4×D3—402no—
359Dic6—401no—
360C3⋊C8—21no—
361C3⋊C8—21no—
362C3⋊C8—102no—
363C22×C5—62no—
364C22×C5—121no—
365C22×C5—121no—
366C22×C5C22×#6711yescharacteristic
367C2×D5—42no—
368C2×D5—42no—
369C2×D5—42no—
370C4×C5—21no—
371C4×C5—41no—
372C4×C5—41no—
373C4×C5—121no—
374C4×C5#95012yes—
375C4×C5D3×#4111yescharacteristic
376C4×C5#101011yescharacteristic
377Dic5—22no—
378Dic5—22no—
379Dic5—122no—
380C2×Q8—51no—
381C2×Q8—301no—
382C2×Q8C2×D3×D511yescharacteristic
383C2×D4—31no—
384C2×D4—52no—
385C2×D4—101no—
386C2×D4—101no—
387C22×C4—61no—
388C22×C4—102no—
389C22×C4—302no—
390SD16—62no—
391D8—304no—
392C2×C8—31no—
393C2×C8—31no—
394C2×C8—152no—
395C4⋊C4—21no—
396C4⋊C4—31no—
397C4⋊C4—51no—
398C4⋊C4—52no—
399C4⋊C4—152no—
400C4⋊C4—302no—
401C4⋊C4—302no—
402C4⋊C4—301no—
403C4⋊C4C2×D3×D511yescharacteristic
404C22⋊C4—61no—
405C22⋊C4—102no—
406C22⋊C4—102no—
407C22⋊C4—102no—
408C22⋊C4—302no—
409C42—21no—
410C42—52no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—202no—
414C22×C3—202no—
415C22×C3—202no—
416C22×C3C2×D4×D511yescharacteristic
417C2×D3—22no—
418C2×D3—41no—
419C2×D3—41no—
420C3×C4—21no—
421C3×C4—41no—
422C3×C4—41no—
423C3×C4—102no—
424C3×C4—102no—
425C3×C4#406212yes—
426C3×C4C2×#70911yescharacteristic
427C3×C4#415011yescharacteristic
428Dic3—41no—
429Dic3—202no—
430C2×C5—122no—
431C2×C5C2×#95011yescharacteristic
432C2×C5#583111yescharacteristic
433C2×C5#583511yescharacteristic
434D5—82no—
435C23—61no—
436C23—102no—
437Q8—21no—
438Q8—21no—
439Q8—102no—
440Q8—1201no—
441D4—32no—
442D4—61no—
443D4—102no—
444D4—102no—
445D4—202no—
446D4—401no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—52no—
450C2×C4—52no—
451C2×C4—61no—
452C2×C4—122no—
453C2×C4—302no—
454C2×C4—402no—
455C2×C4—1202no—
456C2×C4D5×#6711yescharacteristic
457C2×C4D5×#6711yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—61no—
460C8—61no—
461C8—302no—
462C2×C3—402no—
463C2×C3#6588611yescharacteristic
464C2×C3C2×#406211yescharacteristic
465C2×C3#6610311yescharacteristic
466D3—42no—
467C5#8371311yescharacteristic, complemented, Sylow
468C22—62no—
469C22—121no—
470C22—121no—
471C22—202no—
472C22—202no—
473C22—202no—
474C22C2×D5×#6711yescharacteristic
475C4—21no—
476C4—41no—
477C4—41no—
478C4—102no—
479C4—102no—
480C4—121no—
481C4—602no—
482C4#9151412yes—
483C4#9200111yescharacteristic
484C4D3×#70911yescharacteristic
485C3#1061135211yescharacteristic, complemented, Sylow
486C2—122no—
487C2—402no—
488C2#1175452811yescharacteristic
489C2C2×#9151411yescharacteristic
490C2#1175531811yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11747033C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3361
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. C3×#65919C2semidirect
2. #11752660C2semidirect
3. #11751122C2semidirect
4. C4×C5×#215C2semidirect
5. #11749331C2semidirect
6. #11749224C2semidirect
7. #11747392C2semidirect
8. #11747216C2semidirect
10. #11746890C2semidirect
11. C3⋊C8×Dic10C2semidirect
43. #65919D3semidirect
92. C4×#215D5semidirect
412. C3×C5#3361semidirect
467. C5#83713semidirect
485. C3#10611352semidirect

Maximal subgroups

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

subgroupindex
C3×#659192
#117526602
#117511222
C4×C5×#2152
#117493312
#117492242
#117473922
#117472162
#117470332
#117468902
C3⋊C8×Dic102
#106113523
#837135