Finite Group Databasebeta

← #14471851

Subgroups — #14471851

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×#66064C211yesmaximal, characteristic, complemented
2#11752651C211yesmaximal, characteristic, complemented
3#11751192C211yesmaximal, characteristic, complemented
4C5×#5088C211yesmaximal, characteristic, complemented
5#11747368C212yesmaximal, complemented
6#11747241C212yesmaximal, complemented
7#11747216C212yesmaximal, complemented
8#11747142C212yesmaximal, complemented
9C4×#6657C211yesmaximal, characteristic, complemented
10#11747026C211yesmaximal, characteristic
11C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
12#10613316—31nomaximal, Hall
13C3×C5×C4⋊Q8C2211yescharacteristic
14C4×Dic30C2211yescharacteristic
15C5×#874C2211yescharacteristic
16C3×#4092—22no—
17C3×#4043—21no—
18C3×#4039C2212yes—
19C3×D5×C4⋊C4—21no—
20C3×#4036C2212yes—
21C3×C4×D20C2211yescharacteristic
22C3×C4×Dic10C2211yescharacteristic
23#91435—21no—
24#91423—22no—
25Dic5×D12C2212yes—
26#91373C2212yes—
27#91370—21no—
28C2×#6657C2211yescharacteristic
29C2×#6652C2212yes—
30#91094C2212yes—
31#91091C2212yes—
32C4⋊(C3⋊#168)C2211yescharacteristic
33C5×#809C2212yes—
34C5×#809C2212yes—
35C4×C5×C3⋊C8C2211yescharacteristic
36#90987C2211yescharacteristic
37#90982C2212yes—
38#90974C2211yescharacteristic
39#90966C2212yes—
40#90965C2211yescharacteristic
41Dic5×C3⋊C8C2212yes—
42#83643—51nomaximal, Hall
43#66064D311yescharacteristic, complemented
44#66047—31no—
45C5×#486—31no—
46#65380—31no—
47#65361—31no—
48#65076—32no—
49#65057—32no—
50#65052—32no—
51#65045—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8—21no—
55C2×Dic30C2311yescharacteristic
56C2×C5×D12—21no—
57C2×C5×D12—21no—
58C2×C5×D12C2312yes—
59C2×C3×D20C2311yescharacteristic
60C2×C3×C4×D5—21no—
61C2×C3×C4×D5—22no—
62C2×C3×Dic10D411yescharacteristic
63C2×D3×Dic5—22no—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4C2312yes—
66C3×C42×C5C2311yescharacteristic
67C4⋊Dic15C2311yescharacteristic
68#6712—21no—
69C4×Dic15—21no—
70C2×C3⋊#168C2312yes—
71C2×C5×C3⋊C8C2311yescharacteristic
72C2×C5×C3⋊C8C2311yescharacteristic
73C3×#685—21no—
74C3×#685—22no—
75C3×C4⋊Dic5—22no—
76C3×C4⋊Dic5D411yescharacteristic
77C3×C4⋊Dic5C2311yescharacteristic
78C3×#683—22no—
79C3×#683D412yes—
80C3×C4×Dic5C2312yes—
81(C2×D3)⋊Dic5—22no—
82(C2×D3)⋊Dic5—22no—
83(C2×D3)⋊Dic5—22no—
84#6657—22no—
85#6652—24no—
86C3×#554—51no—
87#5585—51no—
88#5091—51no—
89#5088D511yescharacteristic, complemented
90#5068—52no—
91#5066—52no—
92Q8×C3⋊C8—51no—
93C4×#214—51no—
94#5016—52no—
95#5015—51no—
96C4×#213—52no—
97C5×C4⋊Q8C2×D311yescharacteristic
98C5×#127—31no—
99#4092—22no—
100#4082—32no—
101#4082—61no—
102#4081—62no—
103D4×Dic5—32no—
104D4×Dic5—61no—
105C2×#686—32no—
106C2×#677—31no—
107#4043—21no—
108#4039C2×D312yes—
109D5×C4⋊C4—21no—
110#4036C2×D312yes—
111C4×D20C2×D311yescharacteristic
112C4×Dic10—31no—
113C4×Dic10C2×D311yescharacteristic
114C5×#102—32no—
115C5×#102—32no—
116C4×C5×C8—31no—
117#3964—32no—
118#3953—31no—
119#3949—31no—
120#3948—31no—
121#3946—32no—
122C8×Dic5—32no—
123#3942—32no—
124#3939—32no—
125C4⋊#168—31no—
126#3361—151noSylow
127C22×C5×D3—22no—
128C22×C3×D5—21no—
129C3×C5×Q8—81no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—21no—
135C2×Dic15—21no—
136Dic30—21no—
137Dic30—21no—
138C5×D12—22no—
139C5×D12—22no—
140C5×D12—42no—
141C5×D12—81no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5C2×D412yes—
144C2×C3×Dic5C2×D412yes—
145C3×D20—21no—
146C3×D20#4112yes—
147C3×C4×D5—42no—
148C3×C4×D5—82no—
149C3×Dic10—22no—
150D3×Dic5—82no—
151C3⋊#168—22no—
152C5×C3⋊C8—21no—
153C5×C3⋊C8—21no—
154C3×C4⋊Q8C2×D511yescharacteristic
155C3×#125—52no—
156C3×C22⋊Q8—101no—
157C3×C22⋊Q8—102no—
158C3×C4×Q8—51no—
159C3×C4×D4—52no—
160C3×C4×D4—51no—
161C2×C3×C4⋊C4—101no—
162#947—101no—
163C2×#214—51no—
164C2×#213—52no—
165#894—102no—
166#893—101no—
167#875—52no—
168#874C2×D511yescharacteristic
169C4×D12—52no—
170C4×Dic6—51no—
171#832—51no—
172#810—52no—
173#810—51no—
174#809—52no—
175#809C2×D512yes—
176#809C2×D512yes—
177#808—51no—
178#807—52no—
179C4⋊(C3⋊C8)—51no—
180C4⋊(C3⋊C8)—52no—
181C4×C3⋊C8—52no—
182C4×C3⋊C8C2×D511yescharacteristic
183C2×C5×Q8—21no—
184C2×C5×D4—32no—
185C2×C5×D4—61no—
186C2×C5×D4—61no—
187C22×Dic5—62no—
188C2×D20C22×D311yescharacteristic
189C2×C4×D5—21no—
190C2×C4×D5—22no—
191C2×Dic10—31no—
192C2×Dic10#6711yescharacteristic
193C2×C5×C8—31no—
194C2×C5×C8—31no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4C22×D312yes—
197C42×C5C22×D311yescharacteristic
198C22⋊Dic5—62no—
199C22⋊Dic5—62no—
200C22⋊Dic5—62no—
201#686—64no—
202#685—21no—
203#685—22no—
204C4⋊Dic5—22no—
205C4⋊Dic5—31no—
206C4⋊Dic5#6711yescharacteristic
207C4⋊Dic5C22×D311yescharacteristic
208#683—22no—
209#683—61no—
210#683#6712yes—
211C4×Dic5—61no—
212C4×Dic5C22×D312yes—
213C2×#168—32no—
214#677—62no—
215#559—151no—
216#554—51no—
217#488—152no—
218#486—31no—
219#478—152no—
220#477—151no—
221#463—152no—
222#459—151no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×D8—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C5×D3—42no—
228C2×C5×D3—42no—
229C2×C5×D3—42no—
230C2×C3×D5—22no—
231C2×C3×D5—41no—
232C2×C3×D5—41no—
233C3×C4×C5—21no—
234C3×C4×C5—42no—
235C3×C4×C5#13512yes—
236C3×C4×C5C2×#4111yescharacteristic
237C3×C4×C52−1+411yescharacteristic
238Dic15—41no—
239Dic15—41no—
240C3×Dic5—22no—
241C3×Dic5—22no—
242C3×Dic5—41no—
243C2×C3×Q8—21no—
244C2×C3×Q8—51no—
245C2×C3×D4—51no—
246C22×C3×C4—102no—
247C22×C3×C4—101no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12C22×D512yes—
251C2×C4×D3—102no—
252C2×Dic6—51no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—52no—
255C3×C4⋊C4—51no—
256C3×C4⋊C4—51no—
257C3×C4⋊C4—102no—
258C3×C4⋊C4—102no—
259C3×C4⋊C4C22×D512yes—
260C3×C22⋊C4—102no—
261C3×C22⋊C4—101no—
262C3×C42—52no—
263C3×C42C22×D511yescharacteristic
264#214—102no—
265#213—104no—
266(C2×D3)⋊C4—102no—
267(C2×D3)⋊C4—102no—
268(C2×D3)⋊C4—102no—
269C4⋊Dic3—51no—
270Dic3⋊C4—101no—
271C4×Dic3—101no—
272C2×C3⋊C8—52no—
273C2×C3⋊C8C22×D511yescharacteristic
274C2×C3⋊C8C22×D511yescharacteristic
275C23×C5—62no—
276C22×D5—21no—
277C5×Q8—81no—
278C5×D4—62no—
279C5×D4—62no—
280C5×D4—122no—
281C5×D4—241no—
282C2×C4×C5—22no—
283C2×C4×C5C2×#6711yescharacteristic
284C2×C4×C5C2×#6711yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C2×Dic5—21no—
287C2×Dic5—61no—
288C2×Dic5—61no—
289C2×Dic5—242no—
290C2×Dic5C2×#6712yes—
291C2×Dic5C2×#6712yes—
292D20—21no—
293D20#23912yes—
294C4×D5—42no—
295C4×D5—82no—
296Dic10—22no—
297Dic10—61no—
298Dic10—61no—
299C5×C8—61no—
300C5×C8—61no—
301#168—62no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8D3×D511yescharacteristic
305#127—31no—
306#125—52no—
307#124—152no—
308#124—301no—
309#123—302no—
310C22⋊Q8—101no—
311C22⋊Q8—102no—
312C4×Q8—51no—
313C4×Q8—151no—
314C4×D4—52no—
315C4×D4—51no—
316C4×D4—152no—
317C4×D4—301no—
318C2×C4⋊C4—101no—
319#107—152no—
320#106—151no—
321C4⋊C8—152no—
322C4⋊C8—151no—
323#103—151no—
324#103—152no—
325#102—32no—
326#102—32no—
327#102—152no—
328#102—151no—
329C4×C8—31no—
330C4×C8—152no—
331C2×C3×C5#54811yescharacteristic
332C2×C3×C5C2×#13511yescharacteristic
333C2×C3×C5#57611yescharacteristic
334C3×D5—42no—
335C5×D3—82no—
336C23×C3—101no—
337C22×D3—22no—
338C3×Q8—81no—
339C3×Q8—102no—
340C3×D4—52no—
341C3×D4—101no—
342C2×C3×C4—22no—
343C2×C3×C4—52no—
344C2×C3×C4—52no—
345C2×C3×C4—101no—
346C2×C3×C4—202no—
347C2×C3×C4—402no—
348C2×C3×C4D4×D511yescharacteristic
349C2×C3×C4D4×D511yescharacteristic
350C2×C3×C4C23×D511yescharacteristic
351C2×Dic3—101no—
352C2×Dic3—101no—
353D12—22no—
354D12—22no—
355D12—42no—
356D12—81no—
357C4×D3—402no—
358Dic6—101no—
359Dic6—101no—
360C3⋊C8—21no—
361C3⋊C8—21no—
362C3⋊C8—102no—
363C22×C5—122no—
364C22×C5—122no—
365C22×C5—122no—
366C22×C5C22×#6711yescharacteristic
367C2×D5—22no—
368C2×D5—41no—
369C2×D5—41no—
370C4×C5—21no—
371C4×C5—42no—
372C4×C5#95012yes—
373C4×C5C2×#23911yescharacteristic
374C4×C5#100711yescharacteristic
375Dic5—22no—
376Dic5—22no—
377Dic5—41no—
378Dic5—121no—
379Dic5—121no—
380C2×Q8—21no—
381C2×Q8—51no—
382C2×Q8—151no—
383C2×D4—32no—
384C2×D4—51no—
385C2×D4—61no—
386C2×D4—61no—
387C22×C4—102no—
388C22×C4—101no—
389C22×C4—302no—
390SD16—302no—
391D8—304no—
392C2×C8—31no—
393C2×C8—31no—
394C2×C8—152no—
395C4⋊C4—21no—
396C4⋊C4—51no—
397C4⋊C4—52no—
398C4⋊C4—51no—
399C4⋊C4—102no—
400C4⋊C4—102no—
401C4⋊C4—151no—
402C4⋊C4—301no—
403C4⋊C4C2×D3×D512yes—
404C22⋊C4—102no—
405C22⋊C4—101no—
406C22⋊C4—302no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—52no—
410C42—301no—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—102no—
414C22×C3—201no—
415C22×C3—201no—
416C22×C3C2×D4×D511yescharacteristic
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—42no—
420C3×C4—21no—
421C3×C4—42no—
422C3×C4—102no—
423C3×C4—102no—
424C3×C4—201no—
425C3×C4#406212yes—
426C3×C4D5×#4111yescharacteristic
427C3×C4#415011yescharacteristic
428Dic3—201no—
429Dic3—201no—
430C2×C5—242no—
431C2×C5#581711yescharacteristic
432C2×C5C2×#95011yescharacteristic
433C2×C5#583511yescharacteristic
434D5—42no—
435C23—62no—
436C23—101no—
437Q8—81no—
438Q8—102no—
439Q8—301no—
440Q8—301no—
441D4—52no—
442D4—62no—
443D4—62no—
444D4—101no—
445D4—122no—
446D4—241no—
447C2×C4—22no—
448C2×C4—52no—
449C2×C4—52no—
450C2×C4—101no—
451C2×C4—202no—
452C2×C4—301no—
453C2×C4—301no—
454C2×C4—402no—
455C2×C4—1202no—
456C2×C4D5×#6711yescharacteristic
457C2×C4D5×#6711yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—61no—
460C8—61no—
461C8—302no—
462C2×C3—202no—
463C2×C3#6601111yescharacteristic
464C2×C3#6609111yescharacteristic
465C2×C3C2×#406211yescharacteristic
466D3—82no—
467C5#8364311yescharacteristic, complemented, Sylow
468C22—102no—
469C22—122no—
470C22—122no—
471C22—122no—
472C22—201no—
473C22—201no—
474C22C2×D5×#6711yescharacteristic
475C4—21no—
476C4—42no—
477C4—102no—
478C4—102no—
479C4—201no—
480C4—601no—
481C4—601no—
482C4#9151412yes—
483C4#9203011yescharacteristic
484C4D5×#23911yescharacteristic
485C3#1061331611yescharacteristic, complemented, Sylow
486C2—202no—
487C2—242no—
488C2#1175469111yescharacteristic
489C2C2×#9151411yescharacteristic
490C2#1175522611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11747026C2
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×#66064C2semidirect
2. #11752651C2semidirect
3. #11751192C2semidirect
4. C5×#5088C2semidirect
5. #11747368C2semidirect
6. #11747241C2semidirect
7. #11747216C2semidirect
8. #11747142C2semidirect
9. C4×#6657C2semidirect
11. C3⋊C8×Dic10C2semidirect
43. #66064D3semidirect
89. #5088D5semidirect
412. C3×C5#3361semidirect
467. C5#83643semidirect
485. C3#10613316semidirect

Maximal subgroups

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

subgroupindex
C3×#660642
#117526512
#117511922
C5×#50882
#117473682
#117472412
#117472162
#117471422
C4×#66572
#117470262
C3⋊C8×Dic102
#106133163
#836435