Finite Group Databasebeta

← #14471667

Subgroups — #14471667

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756338C211yesmaximal, characteristic, complemented
2C3×#65918C211yesmaximal, characteristic, complemented
3C5×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4#11747085C211yesmaximal, characteristic, complemented
5C4×#6658C212yesmaximal, complemented
6#11747044C212yesmaximal
7C4×#6653C211yesmaximal, characteristic
8#11746944C212yesmaximal, complemented
9#11746920C211yesmaximal, characteristic, complemented
10#11746891C212yesmaximal, complemented
11#11746881C211yesmaximal, characteristic, complemented
12#10611657—31nomaximal, Hall
13C3×C4×C5×Q8C2211yescharacteristic
14#91835—21no—
15#91785—22no—
16C4⋊C4×D15—21no—
17C4×D60C2211yescharacteristic
18C4×D60C2212yes—
19#91759C2212yes—
20#91758C2211yescharacteristic
21C3×#4092—21no—
22C3×#4044—22no—
23C3×#4038—21no—
24C3×#4021C2212yes—
25C3×C4×D20C2211yescharacteristic
26C3×#4015C2211yescharacteristic
27C3×C4×Dic10C2212yes—
28C2×#6658C2212yes—
29C2×#6653C2211yescharacteristic
30C5×C4⋊(C3⋊C8)C2211yescharacteristic
31C5×C4⋊(C3⋊C8)C2212yes—
32C4×C5×C3⋊C8C2212yes—
33C4×C5×C3⋊C8C2211yescharacteristic
34#90990C2211yescharacteristic
35#90987C2212yes—
36#90971C2212yes—
37#90971C2212yes—
38#90971C2212yes—
39#90968C2211yescharacteristic
40#90965C2212yes—
41#90965C2211yescharacteristic
42#83667—51nomaximal, Hall
43#65918D311yescharacteristic, complemented
44#65913—31no—
45C5×C8×Q8—31no—
46#65133—32no—
47#65131—31no—
48#65130—31no—
49#65118—32no—
50#64986—32no—
51C4×D40—31no—
52C4×#677—32no—
53#64970—31no—
54C2×C3×C5×Q8D411yescharacteristic
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×C4×D15—22no—
58C2×Dic30—21no—
59C2×C3×D20C2311yescharacteristic
60C2×C3×C4×D5—21no—
61C2×C3×Dic10C2312yes—
62C3×C5×C4⋊C4D411yescharacteristic
63C3×C5×C4⋊C4D412yes—
64C3×C42×C5C2311yescharacteristic
65C3×C42×C5C2312yes—
66#6714—21no—
67#6714—22no—
68C4⋊Dic15—21no—
69C4⋊Dic15C2312yes—
70C4⋊Dic15C2311yescharacteristic
71#6712—22no—
72#6712—22no—
73C2×C5×C3⋊C8C2311yescharacteristic
74C2×C5×C3⋊C8C2312yes—
75C2×C5×C3⋊C8C2311yescharacteristic
76C3×#685—22no—
77C3×#685—21no—
78C3×#685—22no—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×#683—22no—
83C3×C4×Dic5—22no—
84#6658—24no—
85#6653—22no—
86C3×#556—51no—
87#5579—51no—
88#5083—51no—
89#5079—51no—
90#5057—52no—
91#5056—52no—
92C4×#215—52no—
93Q8×C3⋊C8D511yescharacteristic, complemented
94#5022—52no—
95C4×#213—51no—
96#5008—51no—
97C4×C5×Q8C2×D311yescharacteristic
98#4092—21no—
99#4092—61no—
100C2×D40—31no—
101C2×#677—32no—
102#4044—22no—
103#4042—62no—
104#4038—21no—
105D5×C4⋊C4—61no—
106#4021C2×D312yes—
107C4×D20—31no—
108C4×D20—32no—
109C4×D20C2×D311yescharacteristic
110#4016—32no—
111#4015—31no—
112#4015C2×D311yescharacteristic
113C4×Dic10C2×D312yes—
114C5×C4⋊C8—32no—
115C5×C4⋊C8—31no—
116C4×C5×C8—31no—
117C4×C5×C8—32no—
118#3953—32no—
119#3953—31no—
120#3953—31no—
121#3950—31no—
122#3949—32no—
123#3948—32no—
124#3948—32no—
125#3948—32no—
126#3360—151noSylow
127C22×D15—21no—
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×Dic15—21no—
136C2×Dic15—22no—
137D60—21no—
138D60#4112yes—
139C4×D15—42no—
140C4×D15—82no—
141Dic30—81no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—22no—
144C3×D20—21no—
145C3×D20—21no—
146C3×C4×D5—42no—
147C3×Dic10—22no—
148C3×Dic10—22no—
149C5×C3⋊C8—22no—
150C5×C3⋊C8—21no—
151C5×C3⋊C8—21no—
152C3×C4⋊Q8—51no—
153C3×#126—102no—
154C3×#124—52no—
155C3×C22⋊Q8—101no—
156C3×C4×Q8—52no—
157C3×C4×Q8C2×D511yescharacteristic
158C3×C4×D4—51no—
159C3×#117—101no—
160#946—101no—
161C2×#215—52no—
162C2×#213—51no—
163#896—102no—
164D3×C4⋊C4—101no—
165C4×D12—51no—
166C4×D12—52no—
167#870—52no—
168#869—51no—
169#835—52no—
170#835—52no—
171#835—52no—
172#832—52no—
173#832—51no—
174#809—51no—
175#808—52no—
176#807—51no—
177C4⋊(C3⋊C8)C2×D511yescharacteristic
178C4⋊(C3⋊C8)C2×D512yes—
179C4×C3⋊C8C2×D511yescharacteristic
180C4×C3⋊C8C2×D512yes—
181C2×C5×Q8#6711yescharacteristic
182C2×D20—31no—
183C2×D20C22×D311yescharacteristic
184C2×C4×D5—21no—
185C2×C4×D5—61no—
186C2×C4×D5—62no—
187C2×Dic10—61no—
188C2×Dic10C22×D312yes—
189C2×C5×C8—31no—
190C2×C5×C8—31no—
191C2×C5×C8—32no—
192C5×C4⋊C4#6711yescharacteristic
193C5×C4⋊C4#6712yes—
194C42×C5C22×D312yes—
195C42×C5C22×D311yescharacteristic
196#685—21no—
197#685—22no—
198#685—22no—
199#685—61no—
200#685—62no—
201C4⋊Dic5—21no—
202C4⋊Dic5—21no—
203C4⋊Dic5—32no—
204C4⋊Dic5—31no—
205C4⋊Dic5—61no—
206C4⋊Dic5C22×D311yescharacteristic
207#683—22no—
208#683—62no—
209#683—62no—
210C4×Dic5—22no—
211D40—62no—
212#677—64no—
213#556—51no—
214#554—151no—
215#488—152no—
216#487—151no—
217#479—152no—
218#476—151no—
219#463—152no—
220#461—151no—
221C8×Q8—31no—
222C4×SD16—152no—
223C4×D8—151no—
224C22×C3×C5C22×D411yescharacteristic
225C2×D15—22no—
226C2×D15—41no—
227C2×D15—41no—
228C2×C3×D5—41no—
229C2×C3×D5—41no—
230C2×C3×D5—41no—
231C3×C4×C5—22no—
232C3×C4×C5—21no—
233C3×C4×C5—22no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—41no—
238Dic15—42no—
239C3×Dic5—42no—
240C3×Dic5—41no—
241C2×C3×Q8—52no—
242C2×C3×Q8D2011yescharacteristic
243C2×C3×D4—51no—
244C22×C3×C4—101no—
245C2×D12—51no—
246C2×C4×D3—101no—
247C2×C4×D3—102no—
248C2×Dic6—101no—
249C3×C4⋊C4—51no—
250C3×C4⋊C4—102no—
251C3×C4⋊C4—101no—
252C3×C4⋊C4—101no—
253C3×C4⋊C4D2011yescharacteristic
254C3×C4⋊C4D2012yes—
255C3×C22⋊C4—102no—
256C3×C22⋊C4—101no—
257C3×C22⋊C4—102no—
258C3×C42—102no—
259C3×C42C22×D511yescharacteristic
260C3×C42C22×D512yes—
261#215—104no—
262#213—102no—
263(C2×D3)⋊C4—101no—
264(C2×D3)⋊C4—102no—
265C4⋊Dic3—51no—
266C4⋊Dic3—52no—
267C4⋊Dic3—101no—
268Dic3⋊C4—102no—
269Dic3⋊C4—102no—
270C2×C3⋊C8C22×D511yescharacteristic
271C2×C3⋊C8C22×D511yescharacteristic
272C2×C3⋊C8C22×D512yes—
273C22×D5—21no—
274C22×D5—61no—
275C5×Q8—22no—
276C2×C4×C5C2×#6712yes—
277C2×C4×C5C2×#6712yes—
278C2×C4×C5C2×#6711yescharacteristic
279C2×C4×C5C2×#6711yescharacteristic
280C2×C4×C5C23×D311yescharacteristic
281C2×Dic5—21no—
282C2×Dic5—22no—
283C2×Dic5—61no—
284C2×Dic5—62no—
285D20—21no—
286D20—21no—
287D20—32no—
288D20—61no—
289C4×D5—42no—
290C4×D5—122no—
291C4×D5—242no—
292Dic10—22no—
293Dic10—22no—
294Dic10—241no—
295C5×C8—62no—
296C5×C8—61no—
297C5×C8—61no—
298C2×SD16—152no—
299C2×D8—151no—
300C4⋊Q8—51no—
301C4⋊Q8—151no—
302#126—102no—
303#125—152no—
304#124—52no—
305C22⋊Q8—101no—
306C22⋊Q8—301no—
307C22⋊Q8—302no—
308C4×Q8—52no—
309C4×Q8D3×D511yescharacteristic
310C4×D4—51no—
311C4×D4—151no—
312C4×D4—152no—
313#117—101no—
314C2×C4⋊C4—301no—
315#107—151no—
316#106—152no—
317C4⋊C8—31no—
318C4⋊C8—32no—
319#103—152no—
320#103—152no—
321#103—152no—
322#102—151no—
323#102—151no—
324#102—152no—
325C4×C8—31no—
326C4×C8—32no—
327C2×C3×C5#54811yescharacteristic
328C2×C3×C5C2×#13511yescharacteristic
329C2×C3×C5#57711yescharacteristic
330D15—42no—
331C3×D5—81no—
332C23×C3—101no—
333C22×D3—101no—
334C3×Q8—22no—
335C3×Q8—102no—
336C3×Q8—102no—
337C3×D4—101no—
338C3×D4—101no—
339C2×C3×C4—101no—
340C2×C3×C4—102no—
341C2×C3×C4—202no—
342C2×C3×C4C2×D2012yes—
343C2×C3×C4C2×D2012yes—
344C2×C3×C4C2×D2011yescharacteristic
345C2×C3×C4C2×D2011yescharacteristic
346C2×C3×C4C23×D511yescharacteristic
347C2×Dic3—101no—
348C2×Dic3—102no—
349D12—52no—
350D12—101no—
351C4×D3—202no—
352C4×D3—402no—
353Dic6—401no—
354C3⋊C8—21no—
355C3⋊C8—21no—
356C3⋊C8—22no—
357C22×C5C22×#6711yescharacteristic
358C2×D5—41no—
359C2×D5—41no—
360C2×D5—41no—
361C2×D5—62no—
362C2×D5—121no—
363C2×D5—121no—
364C4×C5—22no—
365C4×C5—21no—
366C4×C5—22no—
367C4×C5#95012yes—
368C4×C5D3×#4111yescharacteristic
369C4×C5#101011yescharacteristic
370Dic5—41no—
371Dic5—42no—
372Dic5—121no—
373Dic5—122no—
374C2×Q8—52no—
375C2×Q8—301no—
376C2×Q8#120211yescharacteristic
377C2×D4—51no—
378C2×D4—151no—
379C22×C4—101no—
380C22×C4—301no—
381C22×C4—302no—
382SD16—304no—
383D8—302no—
384C2×C8—31no—
385C2×C8—32no—
386C2×C8—31no—
387C4⋊C4—51no—
388C4⋊C4—101no—
389C4⋊C4—102no—
390C4⋊C4—101no—
391C4⋊C4—152no—
392C4⋊C4—151no—
393C4⋊C4—302no—
394C4⋊C4—301no—
395C4⋊C4—302no—
396C4⋊C4#120211yescharacteristic
397C4⋊C4#120212yes—
398C22⋊C4—102no—
399C22⋊C4—101no—
400C22⋊C4—102no—
401C22⋊C4—301no—
402C22⋊C4—302no—
403C42—102no—
404C42C2×D3×D511yescharacteristic
405C42C2×D3×D512yes—
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3—201no—
408C22×C3—201no—
409C22×C3—201no—
410C22×C3C22×D2011yescharacteristic
411C2×D3—102no—
412C2×D3—201no—
413C2×D3—201no—
414C3×C4—22no—
415C3×C4—21no—
416C3×C4—22no—
417C3×C4—201no—
418C3×C4—202no—
419C3×C4#405012yes—
420C3×C4#414711yescharacteristic
421C3×C4D5×#4111yescharacteristic
422Dic3—201no—
423Dic3—202no—
424C2×C5C2×#95011yescharacteristic
425C2×C5#583111yescharacteristic
426C2×C5#583711yescharacteristic
427D5—81no—
428D5—122no—
429C23—101no—
430C23—301no—
431Q8—22no—
432Q8—102no—
433Q8—102no—
434Q8—1201no—
435D4—101no—
436D4—101no—
437D4—152no—
438D4—301no—
439C2×C4—101no—
440C2×C4—102no—
441C2×C4—202no—
442C2×C4—301no—
443C2×C4—302no—
444C2×C4—602no—
445C2×C4—1202no—
446C2×C4C2×#120212yes—
447C2×C4C2×#120212yes—
448C2×C4C2×#120211yescharacteristic
449C2×C4C2×#120211yescharacteristic
450C2×C4C22×D3×D511yescharacteristic
451C8—61no—
452C8—61no—
453C8—62no—
454C2×C3—401no—
455C2×C3#6591011yescharacteristic
456C2×C3C2×#405011yescharacteristic
457C2×C3#6608511yescharacteristic
458D3—202no—
459C5#8366711yescharacteristic, complemented, Sylow
460C22—201no—
461C22—201no—
462C22—201no—
463C22—302no—
464C22—601no—
465C22—601no—
466C22C22×#120211yescharacteristic
467C4—22no—
468C4—21no—
469C4—22no—
470C4—201no—
471C4—202no—
472C4—602no—
473C4—601no—
474C4#9131112yes—
475C4#9202811yescharacteristic
476C4#9203411yescharacteristic
477C3#1061165711yescharacteristic, complemented, Sylow
478C2—401no—
479C2—602no—
480C2C2×#9131111yescharacteristic
481C2#1175525711yescharacteristic
482C2#1175531011yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6653C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3360
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. #11756338C2semidirect
2. C3×#65918C2semidirect
3. C5×Q8×C3⋊C8C2semidirect
4. #11747085C2semidirect
5. C4×#6658C2semidirect
8. #11746944C2semidirect
9. #11746920C2semidirect
10. #11746891C2semidirect
11. #11746881C2semidirect
43. #65918D3semidirect
93. Q8×C3⋊C8D5semidirect
406. C3×C5#3360semidirect
459. C5#83667semidirect
477. C3#10611657semidirect

Maximal subgroups

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

subgroupindex
#117563382
C3×#659182
C5×Q8×C3⋊C82
#117470852
C4×#66582
#117470442
C4×#66532
#117469442
#117469202
#117468912
#117468812
#106116573
#836675