Finite Group Databasebeta

← #14471822

Subgroups — #14471822

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
1C5×#5585C211yesmaximal, characteristic, complemented
2C3×#65913C211yesmaximal, characteristic, complemented
3Q8×C3⋊#168C211yesmaximal, characteristic, complemented
4C4×#6655C211yesmaximal, characteristic, complemented
5#11747027C212yesmaximal, complemented
6#11747026C211yesmaximal, characteristic
7C4×#6652C212yesmaximal, complemented
8#11746959C211yesmaximal, characteristic, complemented
9#11746903C212yesmaximal, complemented
10#11746902C212yesmaximal, complemented
11#11746901C211yesmaximal, characteristic, complemented
12#10615444—31nomaximal, Hall
13C3×C4×C5×Q8C2211yescharacteristic
14C5×#947—21no—
15C5×#894—22no—
16C5×#893—21no—
17C5×#875C2212yes—
18C5×#874C2211yescharacteristic
19C4×C5×D12C2212yes—
20C4×C5×Dic6C2211yescharacteristic
21C3×#4092—21no—
22C3×#4042—22no—
23C3×D5×C4⋊C4—21no—
24C3×C4×D20C2212yes—
25C3×C4×D20C2211yescharacteristic
26C3×#4016C2212yes—
27C3×#4015C2211yescharacteristic
28C2×#6655C2211yescharacteristic
29C2×#6652C2212yes—
30C4⋊(C3⋊#168)C2212yes—
31C4⋊(C3⋊#168)C2211yescharacteristic
32C4×C3⋊#168C2211yescharacteristic
33C4×C3⋊#168C2212yes—
34#90989C2212yes—
35#90986C2211yescharacteristic
36#90972C2211yescharacteristic
37#90972C2212yes—
38#90966C2212yes—
39#90966C2212yes—
40#90966C2212yes—
41#90964C2211yescharacteristic
42#83643—51nomaximal, Hall
43C5×#559—31no—
44#65913D311yescharacteristic, complemented
45#65361—31no—
46#65359—31no—
47#65346—32no—
48#65345—32no—
49C4×#688—31no—
50Q8×#168—31no—
51#65310—31no—
52C4×#686—32no—
53#65298—32no—
54C2×C3×C5×Q8D411yescharacteristic
55C2×C5×D12—21no—
56C2×C5×D12—21no—
57C2×C5×D12C2312yes—
58C2×C4×C5×D3—22no—
59C2×C5×Dic6C2311yescharacteristic
60C2×C3×D20C2311yescharacteristic
61C2×C3×C4×D5—21no—
62C2×C3×C4×D5—22no—
63C2×C3×Dic10—21no—
64C3×C5×C4⋊C4D411yescharacteristic
65C3×C5×C4⋊C4D412yes—
66C3×C42×C5C2311yescharacteristic
67C3×C42×C5C2312yes—
68C2×C3⋊#168C2311yescharacteristic
69C2×C3⋊#168C2311yescharacteristic
70C2×C3⋊#168C2312yes—
71C5×(C2×D3)⋊C4—22no—
72C5×(C2×D3)⋊C4—22no—
73C5×(C2×D3)⋊C4—22no—
74C5×C4⋊Dic3C2311yescharacteristic
75C5×Dic3⋊C4—21no—
76C4×C5×Dic3—21no—
77C3×#685—22no—
78C3×#685—21no—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5C2311yescharacteristic
81C3×C4⋊Dic5C2312yes—
82C3×#683—22no—
83C3×#683—22no—
84#6655—22no—
85#6652—24no—
86C3×#554—51no—
87#5585D511yescharacteristic, complemented
88#5091—51no—
89#5088—51no—
90#5068—52no—
91#5066—52no—
92Q8×C3⋊C8—51no—
93C4×#214—51no—
94#5016—52no—
95#5015—51no—
96C4×#213—52no—
97C5×#127—31no—
98C5×#124—32no—
99C5×#124—61no—
100C5×#123—62no—
101C4×C5×Q8—31no—
102C4×C5×Q8C2×D311yescharacteristic
103C4×C5×D4—32no—
104C4×C5×D4—61no—
105#4092—21no—
106C2×#688—31no—
107C2×#686—32no—
108#4042—22no—
109D5×C4⋊C4—21no—
110C4×D20C2×D312yes—
111C4×D20C2×D311yescharacteristic
112#4016C2×D312yes—
113#4015C2×D311yescharacteristic
114#3967—32no—
115#3967—31no—
116#3964—32no—
117#3964—32no—
118#3964—32no—
119#3941—31no—
120#3940—31no—
121#3939—32no—
122C4⋊#168—32no—
123C4⋊#168—31no—
124C4×#168—32no—
125C4×#168—31no—
126#3361—151noSylow
127C22×C5×D3—22no—
128C22×C3×D5—21no—
129C3×C5×Q8—22no—
130C2×C3×C4×C5C2×D412yes—
131C2×C3×C4×C5C2×D412yes—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×C5×Dic3—21no—
136C2×C5×Dic3—21no—
137C5×D12—22no—
138C5×D12—22no—
139C5×D12—42no—
140C5×D12—81no—
141C4×C5×D3—82no—
142C5×Dic6—21no—
143C5×Dic6—21no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—22no—
146C3×D20—21no—
147C3×D20#4112yes—
148C3×C4×D5—42no—
149C3×C4×D5—82no—
150C3×Dic10—81no—
151C3⋊#168—22no—
152C3⋊#168—21no—
153C3⋊#168—21no—
154C3×C4⋊Q8—51no—
155C3×#125—52no—
156C3×C22⋊Q8—101no—
157C3×C22⋊Q8—102no—
158C3×C4×Q8C2×D511yescharacteristic
159C3×C4×D4—52no—
160C3×C4×D4—51no—
161C2×C3×C4⋊C4—101no—
162#947—21no—
163C2×#214—51no—
164C2×#213—52no—
165#894—22no—
166#893—21no—
167#875C2×D512yes—
168#874C2×D511yescharacteristic
169C4×D12C2×D512yes—
170C4×Dic6C2×D511yescharacteristic
171#832—51no—
172#810—52no—
173#810—51no—
174#809—52no—
175#809—52no—
176#809—52no—
177#808—51no—
178#807—52no—
179C4⋊(C3⋊C8)—51no—
180C4⋊(C3⋊C8)—52no—
181C4×C3⋊C8—52no—
182C4×C3⋊C8—51no—
183C2×C5×Q8—31no—
184C2×C5×Q8#6711yescharacteristic
185C2×C5×D4—32no—
186C2×C5×D4—61no—
187C2×C5×D4—61no—
188C22×C4×C5—62no—
189C2×D20C22×D311yescharacteristic
190C2×C4×D5—21no—
191C2×C4×D5—22no—
192C2×Dic10—21no—
193C5×C4⋊C4—31no—
194C5×C4⋊C4—61no—
195C5×C4⋊C4#6711yescharacteristic
196C5×C4⋊C4#6712yes—
197C5×C22⋊C4—62no—
198C5×C22⋊C4—62no—
199C5×C22⋊C4—62no—
200C42×C5—61no—
201C42×C5C22×D312yes—
202C42×C5C22×D311yescharacteristic
203#688—62no—
204#686—64no—
205#685—21no—
206#685—22no—
207C4⋊Dic5—21no—
208C4⋊Dic5C22×D312yes—
209C4⋊Dic5C22×D311yescharacteristic
210#683—22no—
211#683—22no—
212C2×#168—31no—
213C2×#168—32no—
214C2×#168—31no—
215#559—31no—
216#554—51no—
217#488—152no—
218#486—151no—
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—22no—
234C3×C4×C5—21no—
235C3×C4×C5—22no—
236C3×C4×C5#13512yes—
237C3×C4×C5C2×#4111yescharacteristic
238C3×C4×C52−1+411yescharacteristic
239C3×Dic5—41no—
240C3×Dic5—42no—
241C5×Dic3—41no—
242C5×Dic3—41no—
243C2×C3×Q8—101no—
244C2×C3×Q8C22⋊D511yescharacteristic
245C2×C3×D4—51no—
246C22×C3×C4—101no—
247C22×C3×C4—102no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12C22×D512yes—
251C2×C4×D3—22no—
252C2×Dic6C22×D511yescharacteristic
253C3×C4⋊C4—52no—
254C3×C4⋊C4—51no—
255C3×C4⋊C4—102no—
256C3×C4⋊C4—102no—
257C3×C4⋊C4—101no—
258C3×C4⋊C4C22⋊D511yescharacteristic
259C3×C4⋊C4C22⋊D512yes—
260C3×C22⋊C4—101no—
261C3×C22⋊C4—102no—
262C3×C42C22×D511yescharacteristic
263C3×C42C22×D512yes—
264#214—102no—
265#213—104no—
266(C2×D3)⋊C4—22no—
267(C2×D3)⋊C4—22no—
268(C2×D3)⋊C4—22no—
269C4⋊Dic3C22×D511yescharacteristic
270Dic3⋊C4—21no—
271C4×Dic3—21no—
272C2×C3⋊C8—51no—
273C2×C3⋊C8—52no—
274C2×C3⋊C8—51no—
275C23×C5—62no—
276C22×D5—21no—
277C5×Q8—22no—
278C5×Q8—61no—
279C5×Q8—61no—
280C5×D4—62no—
281C5×D4—62no—
282C5×D4—122no—
283C5×D4—241no—
284C2×C4×C5—61no—
285C2×C4×C5—61no—
286C2×C4×C5—242no—
287C2×C4×C5C2×#6712yes—
288C2×C4×C5C2×#6712yes—
289C2×C4×C5C2×#6711yescharacteristic
290C2×C4×C5C2×#6711yescharacteristic
291C2×C4×C5C23×D311yescharacteristic
292C2×Dic5—21no—
293C2×Dic5—22no—
294D20—21no—
295D20#23912yes—
296C4×D5—42no—
297C4×D5—82no—
298Dic10—81no—
299#168—62no—
300#168—61no—
301#168—61no—
302C2×SD16—151no—
303C2×D8—152no—
304C4⋊Q8—51no—
305#127—31no—
306#125—52no—
307#124—32no—
308#124—61no—
309#123—62no—
310C22⋊Q8—101no—
311C22⋊Q8—102no—
312C4×Q8—31no—
313C4×Q8D3×D511yescharacteristic
314C4×D4—32no—
315C4×D4—52no—
316C4×D4—51no—
317C4×D4—61no—
318C2×C4⋊C4—101no—
319#107—152no—
320#106—151no—
321C4⋊C8—151no—
322C4⋊C8—152no—
323#103—151no—
324#103—152no—
325#102—151no—
326#102—152no—
327#102—152no—
328#102—152no—
329C4×C8—152no—
330C4×C8—151no—
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—22no—
339C3×Q8—401no—
340C3×D4—52no—
341C3×D4—101no—
342C2×C3×C4—101no—
343C2×C3×C4—102no—
344C2×C3×C4—202no—
345C2×C3×C4—402no—
346C2×C3×C4C2×C22⋊D511yescharacteristic
347C2×C3×C4C2×C22⋊D512yes—
348C2×C3×C4C2×C22⋊D512yes—
349C2×C3×C4C2×C22⋊D511yescharacteristic
350C2×C3×C4C23×D511yescharacteristic
351C2×Dic3—21no—
352C2×Dic3—21no—
353D12—22no—
354D12—22no—
355D12—42no—
356D12—81no—
357C4×D3—82no—
358Dic6—21no—
359Dic6—21no—
360C3⋊C8—102no—
361C3⋊C8—101no—
362C3⋊C8—101no—
363C22×C5—122no—
364C22×C5—122no—
365C22×C5—122no—
366C22×C5C22×#6711yescharacteristic
367C2×D5—22no—
368C2×D5—41no—
369C2×D5—41no—
370C4×C5—22no—
371C4×C5—21no—
372C4×C5—22no—
373C4×C5—121no—
374C4×C5—121no—
375C4×C5#95012yes—
376C4×C5C2×#23911yescharacteristic
377C4×C5#100711yescharacteristic
378Dic5—41no—
379Dic5—42no—
380C2×Q8—31no—
381C2×Q8—101no—
382C2×Q8#120111yescharacteristic
383C2×D4—32no—
384C2×D4—51no—
385C2×D4—61no—
386C2×D4—61no—
387C22×C4—62no—
388C22×C4—101no—
389C22×C4—102no—
390SD16—302no—
391D8—304no—
392C2×C8—151no—
393C2×C8—151no—
394C2×C8—152no—
395C4⋊C4—31no—
396C4⋊C4—51no—
397C4⋊C4—52no—
398C4⋊C4—61no—
399C4⋊C4—102no—
400C4⋊C4—101no—
401C4⋊C4—102no—
402C4⋊C4#120111yescharacteristic
403C4⋊C4#120112yes—
404C22⋊C4—62no—
405C22⋊C4—62no—
406C22⋊C4—62no—
407C22⋊C4—101no—
408C22⋊C4—102no—
409C42—61no—
410C42C2×D3×D512yes—
411C42C2×D3×D511yescharacteristic
412C3×C5#336111yescharacteristic, complemented, Hall
413C22×C3—102no—
414C22×C3—201no—
415C22×C3—201no—
416C22×C3C22×C22⋊D511yescharacteristic
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—42no—
420C3×C4—22no—
421C3×C4—22no—
422C3×C4—21no—
423C3×C4—201no—
424C3×C4—202no—
425C3×C4#409612yes—
426C3×C4D5×#4111yescharacteristic
427C3×C4#415011yescharacteristic
428Dic3—41no—
429Dic3—41no—
430C2×C5—242no—
431C2×C5#581711yescharacteristic
432C2×C5C2×#95011yescharacteristic
433C2×C5#583511yescharacteristic
434D5—42no—
435C23—62no—
436C23—101no—
437Q8—22no—
438Q8—61no—
439Q8—61no—
440Q8—401no—
441D4—52no—
442D4—62no—
443D4—62no—
444D4—101no—
445D4—122no—
446D4—241no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—101no—
450C2×C4—102no—
451C2×C4—202no—
452C2×C4—242no—
453C2×C4—402no—
454C2×C4C2×#120112yes—
455C2×C4C2×#120112yes—
456C2×C4C2×#120111yescharacteristic
457C2×C4C2×#120111yescharacteristic
458C2×C4C22×D3×D511yescharacteristic
459C8—301no—
460C8—302no—
461C8—301no—
462C2×C3—202no—
463C2×C3C2×#409611yescharacteristic
464C2×C3#6616511yescharacteristic
465C2×C3#6616911yescharacteristic
466D3—82no—
467C5#8364311yescharacteristic, complemented, Sylow
468C22—102no—
469C22—122no—
470C22—122no—
471C22—122no—
472C22—201no—
473C22—201no—
474C22C22×#120111yescharacteristic
475C4—22no—
476C4—21no—
477C4—22no—
478C4—121no—
479C4—121no—
480C4—202no—
481C4—201no—
482C4#9129712yes—
483C4#9203011yescharacteristic
484C4D5×#23911yescharacteristic
485C3#1061544411yescharacteristic, complemented, Sylow
486C2—202no—
487C2—242no—
488C2C2×#9129711yescharacteristic
489C2#1175524411yescharacteristic
490C2#1175530111yescharacteristic
subgroupG/H
centerC22C22×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×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 ◁ C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C5×#5585C2semidirect
2. C3×#65913C2semidirect
3. Q8×C3⋊#168C2semidirect
4. C4×#6655C2semidirect
5. #11747027C2semidirect
7. C4×#6652C2semidirect
8. #11746959C2semidirect
9. #11746903C2semidirect
10. #11746902C2semidirect
11. #11746901C2semidirect
44. #65913D3semidirect
87. #5585D5semidirect
412. C3×C5#3361semidirect
467. C5#83643semidirect
485. C3#10615444semidirect

Maximal subgroups

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

subgroupindex
C5×#55852
C3×#659132
Q8×C3⋊#1682
C4×#66552
#117470272
#117470262
C4×#66522
#117469592
#117469032
#117469022
#117469012
#106154443
#836435