Finite Group Databasebeta

← #14471953

Subgroups — #14471953

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×Dic10C211yesmaximal, characteristic, complemented
2#11752538C211yesmaximal, characteristic
3#11751128C211yesmaximal, characteristic, complemented
4C4×C5×#215C211yesmaximal, characteristic, complemented
5#11749338C212yesmaximal, complemented
6#11749221C212yesmaximal, complemented
7#11747240C212yesmaximal, complemented
8#11747138C212yesmaximal, complemented
9#11746910C211yesmaximal, characteristic, complemented
10#11746882C211yesmaximal, characteristic, complemented
11C3⋊C8×Dic10C211yesmaximal, characteristic, complemented
12#10611353—31nomaximal, Hall
13C2×#6769—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15C2×#6717C2212yes—
16#91763C2211yescharacteristic
17C2×C5×#215C2211yescharacteristic
18C4×C5×D12C2211yescharacteristic
19C3×Q8×Dic5C2212yes—
20C3×#4034—22no—
21C3×#4034C2212yes—
22C3×#4015—21no—
23C3×#4015C2211yescharacteristic
24C3×C4×Dic10—21no—
25C3×C4×Dic10C2211yescharacteristic
26#91460—21no—
27#91451C2212yes—
28#91420—22no—
29#91418C2212yes—
30#91093C2212yes—
31C4⋊(C3⋊#168)C2211yescharacteristic
32C5×#835C2211yescharacteristic
33C5×#809C2211yescharacteristic
34C5×#808C2211yescharacteristic
35C4×C5×C3⋊C8C2211yescharacteristic
36#90986C2212yes—
37#90982C2212yes—
38#90968C2212yes—
39#90968C2212yes—
40#90966C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83703—51nomaximal, Hall
43Q8×Dic10D311yescharacteristic, complemented
44#65887—31no—
45C4×C5×SD16—31no—
46#65452—32no—
47#65316—31no—
48#65297—31no—
49#65159—32no—
50#65077—32no—
51#65049—32no—
52#64983—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×D60—21no—
56C2×D60—21no—
57C2×D60C2312yes—
58C2×C5×D12C2311yescharacteristic
59C2×C4×C5×D3—21no—
60C2×C3×Dic10—21no—
61C2×C3×Dic10—22no—
62C2×C3×Dic10D411yescharacteristic
63C2×#1203—22no—
64C2×#1203—22no—
65C2×#1200—22no—
66#6769—44no—
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4C2311yescharacteristic
69C3×C42×C5—21no—
70C3×C42×C5C2311yescharacteristic
71#6717—24no—
72C2×C3⋊#168C2312yes—
73C5×#215—22no—
74C5×(C2×D3)⋊C4—21no—
75C5×C4⋊Dic3C2311yescharacteristic
76C2×C5×C3⋊C8C2311yescharacteristic
77C2×C5×C3⋊C8C2311yescharacteristic
78C3×C4⋊Dic5—21no—
79C3×C4⋊Dic5—22no—
80C3×C4⋊Dic5D411yescharacteristic
81C3×C4⋊Dic5C2312yes—
82C3×#683—22no—
83C3×#683D412yes—
84C3×C4×Dic5—22no—
85C3×C4×Dic5C2312yes—
86#6667—22no—
87C3×Q82—51no—
88#5577—51no—
89#5088—52no—
90#5088—51no—
91#5084—51no—
92#5084—52no—
93#5027—51no—
94#5027—52no—
95C4×#215—52no—
96C4×#215D511yescharacteristic, complemented
97Q8×C3⋊C8—51no—
98C2×#709—61no—
99C2×C5×SD16—31no—
100C4×C5×Q8C2×D311yescharacteristic
101C4×C5×D4—31no—
102Q8×Dic5C2×D312yes—
103C2×#688—32no—
104#4086—32no—
105#4076—61no—
106#4039—32no—
107#4034—22no—
108#4034C2×D312yes—
109#4030—62no—
110#4020—31no—
111#4015—21no—
112#4015C2×D311yescharacteristic
113C4×Dic10—21no—
114C4×Dic10C2×D311yescharacteristic
115C5×#106—31no—
116C5×#103—31no—
117C5×#102—31no—
118C4×C5×C8—31no—
119#3964—32no—
120#3953—32no—
121#3953—32no—
122#3946—32no—
123C8×Dic5—32no—
124#3941—32no—
125#3940—32no—
126C4⋊#168—31no—
127#3362—151noSylow
128C22×D15—22no—
129C22×C5×D3—21no—
130C3×C5×Q8—21no—
131C3×C5×Q8#4112yescomplemented
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2411yescharacteristic
137D60—22no—
138D60—22no—
139D60—42no—
140D60—81no—
141C2×C5×Dic3—21no—
142C5×D12—21no—
143C5×D12—21no—
144C4×C5×D3—42no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5C2×D412yes—
147C2×C3×Dic5C2×D412yes—
148C3×Dic10—82no—
149C3×Dic10—81no—
150C3×Dic10SD1614yescomplemented
151#1203—44no—
152#1203—82no—
153#1200—44no—
154C3⋊#168—22no—
155C5×C3⋊C8—21no—
156C5×C3⋊C8—21no—
157C2×#239—101no—
158C3×C4⋊Q8—52no—
159C3×C4⋊Q8—51no—
160C3×C4⋊Q8—101no—
161C3×C4⋊Q8—102no—
162C3×C4×Q8—51no—
163C3×C4×Q8—52no—
164C3×C4×Q8—101no—
165C3×C4×Q8C2×D511yescharacteristic
166C2×#215—52no—
167C2×#215C2×D511yescharacteristic
168#895—102no—
169#895—101no—
170#874—52no—
171#874—51no—
172C4×D12—52no—
173C4×D12C2×D511yescharacteristic
174#835C2×D511yescharacteristic
175#809—52no—
176#809—52no—
177#809—52no—
178#809—52no—
179#809C2×D511yescharacteristic
180#808—52no—
181#808C2×D511yescharacteristic
182C4⋊(C3⋊C8)—51no—
183C4⋊(C3⋊C8)—52no—
184C4×C3⋊C8—52no—
185C4×C3⋊C8C2×D511yescharacteristic
186C2×C5×Q8C22×D311yescharacteristic
187C2×C5×D4—31no—
188C22×C4×C5—61no—
189C2×C22⋊D5—62no—
190C2×C22⋊D5—62no—
191#709—124no—
192C2×D20—32no—
193C2×D20—61no—
194C2×D20—61no—
195C2×C4×D5—62no—
196C2×Dic10—21no—
197C2×Dic10—22no—
198C2×Dic10#6711yescharacteristic
199C5×SD16—62no—
200C2×C5×C8—31no—
201C2×C5×C8—31no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—31no—
204C5×C4⋊C4C22×D311yescharacteristic
205C5×C22⋊C4—61no—
206C42×C5—21no—
207C42×C5C22×D311yescharacteristic
208#688—64no—
209#685—62no—
210C4⋊Dic5—21no—
211C4⋊Dic5—22no—
212C4⋊Dic5#6711yescharacteristic
213C4⋊Dic5C22×D312yes—
214#683—22no—
215#683#6712yes—
216C4×Dic5—22no—
217C4×Dic5C22×D312yes—
218C2×#168—32no—
219Q82—51no—
220#550—151no—
221#486—151no—
222#486—152no—
223#476—152no—
224#476—151no—
225#460—152no—
226#460—151no—
227C8×Q8—151no—
228C4×SD16—31no—
229C4×SD16—152no—
230C22×C3×C5C22×D411yescharacteristic
231C2×D15—42no—
232C2×D15—42no—
233C2×D15—42no—
234C2×C5×D3—41no—
235C2×C5×D3—41no—
236C2×C5×D3—41no—
237C3×C4×C5—22no—
238C3×C4×C5—21no—
239C3×C4×C5—41no—
240C3×C4×C5C2×SD1612yes—
241C3×C4×C5C2×#4111yescharacteristic
242C3×C4×C52−1+411yescharacteristic
243C3×Dic5—22no—
244C3×Dic5—42no—
245C3×Dic5C2×SD1614yes—
246C5×Dic3—41no—
247C2×C3×Q8—51no—
248C2×C3×Q8—102no—
249C2×C3×Q8—101no—
250C2×C3×Q8C22×D511yescharacteristic
251#239—204no—
252C2×D12—52no—
253C2×D12—102no—
254C2×D12—101no—
255C2×D12—102no—
256C2×D12—101no—
257C2×D12C22×D511yescharacteristic
258C2×C4×D3—21no—
259C2×C4×D3—102no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—52no—
262C3×C4⋊C4—51no—
263C3×C4⋊C4—52no—
264C3×C4⋊C4—102no—
265C3×C4⋊C4—102no—
266C3×C4⋊C4—101no—
267C3×C4⋊C4C22×D511yescharacteristic
268C3×C42—21no—
269C3×C42—52no—
270C3×C42—102no—
271C3×C42C22×D511yescharacteristic
272#215—22no—
273#215—104no—
274(C2×D3)⋊C4—21no—
275(C2×D3)⋊C4—102no—
276C4⋊Dic3C22×D511yescharacteristic
277C2×C3⋊C8—52no—
278C2×C3⋊C8C22×D511yescharacteristic
279C2×C3⋊C8C22×D511yescharacteristic
280C23×C5—61no—
281C22×D5—62no—
282C5×Q8—21no—
283C5×Q8#23912yescomplemented
284C5×D4—61no—
285C5×D4—61no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—61no—
289C2×C4×C5—122no—
290C2×C4×C5C2×#6711yescharacteristic
291C2×C4×C5C2×#6711yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—124no—
294C22⋊D5—242no—
295C2×Dic5—22no—
296C2×Dic5C2×#6712yes—
297C2×Dic5C2×#6712yes—
298D20—62no—
299D20—62no—
300D20—122no—
301D20—241no—
302C4×D5—124no—
303Dic10—82no—
304Dic10—81no—
305Dic10#21514yescomplemented
306C5×C8—61no—
307C5×C8—61no—
308#168—62no—
309C2×#41—301no—
310C2×SD16—31no—
311C2×SD16—152no—
312C4⋊Q8—52no—
313C4⋊Q8—51no—
314C4⋊Q8—101no—
315C4⋊Q8—102no—
316#127—152no—
317#127—151no—
318#121—302no—
319#121—301no—
320C4×Q8—51no—
321C4×Q8—52no—
322C4×Q8—101no—
323C4×Q8D3×D511yescharacteristic
324C4×D4—31no—
325C4×D4—152no—
326#106—31no—
327#106—152no—
328C4⋊C8—152no—
329C4⋊C8—151no—
330#103—31no—
331#102—31no—
332#102—152no—
333#102—152no—
334#102—152no—
335#102—152no—
336C4×C8—31no—
337C4×C8—152no—
338C2×C3×C5#54811yescharacteristic
339C2×C3×C5C22×SD1611yescharacteristic
340C2×C3×C5#57611yescharacteristic
341D15—82no—
342C5×D3—81no—
343C22×D3—21no—
344C22×D3—102no—
345C3×Q8—21no—
346C3×Q8—54no—
347C3×Q8—401no—
348C3×Q8—402no—
349C3×Q8#70912yescomplemented
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—52no—
353C2×C3×C4—52no—
354C2×C3×C4—102no—
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4D4×D511yescharacteristic
357C2×C3×C4C23×D511yescharacteristic
358C2×Dic3—21no—
359D12—21no—
360D12—21no—
361D12—102no—
362D12—102no—
363D12—204no—
364D12—202no—
365D12—401no—
366D12—402no—
367C4×D3—42no—
368C4×D3—204no—
369C3⋊C8—21no—
370C3⋊C8—21no—
371C3⋊C8—102no—
372C22×C5—121no—
373C22×C5—121no—
374C22×C5—121no—
375C22×C5C22×#6711yescharacteristic
376C2×D5—122no—
377C2×D5—122no—
378C2×D5—122no—
379C4×C5—22no—
380C4×C5—21no—
381C4×C5—41no—
382C4×C5—121no—
383C4×C5C2×#21512yes—
384C4×C5C2×#23911yescharacteristic
385C4×C5#100711yescharacteristic
386Dic5—22no—
387Dic5—42no—
388Dic5C2×#21514yes—
389#41—604no—
390C2×Q8—51no—
391C2×Q8—102no—
392C2×Q8—101no—
393C2×Q8C2×D3×D511yescharacteristic
394C2×D4—31no—
395C2×D4—152no—
396C2×D4—302no—
397C2×D4—302no—
398C2×D4—301no—
399C2×D4—301no—
400C22×C4—61no—
401C22×C4—302no—
402SD16—62no—
403SD16—304no—
404C2×C8—31no—
405C2×C8—31no—
406C2×C8—152no—
407C4⋊C4—21no—
408C4⋊C4—31no—
409C4⋊C4—52no—
410C4⋊C4—51no—
411C4⋊C4—52no—
412C4⋊C4—102no—
413C4⋊C4—102no—
414C4⋊C4—101no—
415C4⋊C4C2×D3×D511yescharacteristic
416C22⋊C4—61no—
417C22⋊C4—302no—
418C42—21no—
419C42—52no—
420C42—102no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3C2×D4×D511yescharacteristic
424C2×D3—41no—
425C2×D3—41no—
426C2×D3—41no—
427C2×D3—202no—
428C2×D3—202no—
429C2×D3—202no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—41no—
433C3×C4—54no—
434C3×C4—102no—
435C3×C4—202no—
436C3×C4D5×SD1612yes—
437C3×C4C2×#70911yescharacteristic
438C3×C4#415011yescharacteristic
439Dic3—41no—
440C2×C5—241no—
441C2×C5C22×#21511yescharacteristic
442C2×C5#581711yescharacteristic
443C2×C5#583511yescharacteristic
444D5—242no—
445C23—61no—
446C23—302no—
447Q8—21no—
448Q8—54no—
449Q8—401no—
450Q8—402no—
451Q8#676912yescomplemented
452D4—61no—
453D4—61no—
454D4—302no—
455D4—302no—
456D4—604no—
457D4—602no—
458D4—1201no—
459D4—1202no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—52no—
463C2×C4—52no—
464C2×C4—61no—
465C2×C4—102no—
466C2×C4—122no—
467C2×C4—604no—
468C2×C4D5×#6711yescharacteristic
469C2×C4D5×#6711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—61no—
472C8—61no—
473C8—302no—
474C2×C3#6588611yescharacteristic
475C2×C3C2×D5×SD1611yescharacteristic
476C2×C3#6610311yescharacteristic
477D3—81no—
478D3—402no—
479C5#8370311yescharacteristic, complemented, Sylow
480C22—121no—
481C22—121no—
482C22—121no—
483C22—602no—
484C22—602no—
485C22—602no—
486C22C2×D5×#6711yescharacteristic
487C4—21no—
488C4—22no—
489C4—41no—
490C4—54no—
491C4—102no—
492C4—121no—
493C4—202no—
494C4D5×#21512yes—
495C4#9200411yescharacteristic
496C4C2×#676911yescharacteristic
497C3#1061135311yescharacteristic, complemented, Sylow
498C2—241no—
499C2—1202no—
500C2#1175432111yescharacteristic
501C2C2×D5×#21511yescharacteristic
502C2#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#11752538C2
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3362
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×Q8×Dic10C2semidirect
3. #11751128C2semidirect
4. C4×C5×#215C2semidirect
5. #11749338C2semidirect
6. #11749221C2semidirect
7. #11747240C2semidirect
8. #11747138C2semidirect
9. #11746910C2semidirect
10. #11746882C2semidirect
11. C3⋊C8×Dic10C2semidirect
43. Q8×Dic10D3semidirect
96. C4×#215D5semidirect
131. C3×C5×Q8#41semidirect
150. C3×Dic10SD16semidirect
283. C5×Q8#239semidirect
305. Dic10#215semidirect
349. C3×Q8#709semidirect
422. C3×C5#3362semidirect
451. Q8#6769semidirect
479. C5#83703semidirect
497. C3#10611353semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic102
#117525382
#117511282
C4×C5×#2152
#117493382
#117492212
#117472402
#117471382
#117469102
#117468822
C3⋊C8×Dic102
#106113533
#837035