Finite Group Databasebeta

← #14425777

Subgroups — #14425777

Order 1920.

1432 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11757146C211yesmaximal, characteristic
2C3×C5×#536C211yesmaximal, characteristic, complemented
3#11756575C212yesmaximal, complemented
4#11751341C211yesmaximal, characteristic, complemented
5#11751154C218yesmaximal, complemented
6#11751107C212yesmaximal, complemented
7#10615148—31nomaximal, Hall
8C2×C3×C5×#41C2211yescharacteristic
9C22×C3×C5×Q8C2211yescharacteristic, complemented
10#92101—22no—
11#92100—22no—
12#41×D15—24no—
13#92098—21no—
14#92095—21no—
15#92095C2214yes—
16C2×#6817—22no—
17C2×#6817C2212yes—
18C3×C5×C4⋊Q8—21no—
19C3×C5×#124—21no—
20C3×C5×#123C2214yescomplemented
21C3×C5×C22⋊Q8—22no—
22C3×C5×#117C2211yescharacteristic, complemented
23#91836—22no—
24#91835—24no—
25#91833—22no—
26#91818C2218yescomplemented
27#91815C2212yescomplemented
28#91118C2214yescomplemented
29#91090C2218yescomplemented
30#83417—51nomaximal, Hall
31#66283—31no—
32C5×#536D311yescharacteristic, complemented
33#66150—32no—
34#65529—31no—
35#65342—38no—
36#65295—32no—
37C3×C5×#41—22no—
38C3×C5×#41—22no—
39C2×C3×C5×Q8—22no—
40C2×C3×C5×Q8—22no—
41C2×C3×C5×Q8—21no—
42C2×C3×C5×Q8—21no—
43C2×C3×C5×Q8D411yescharacteristic
44C2×C3×C5×D4D411yescharacteristic
45C2×C3×C5×D4C2312yes—
46C22×C3×C4×C5D412yes—
47C22×C3×C4×C5C2312yes—
48C22×C3×C4×C5C2311yescharacteristic
49C2×#1220—24no—
50C2×#1220C2314yes—
51#6821—24no—
52Q8×D15—24no—
53#6819—24no—
54#6819—28no—
55D4×D15—24no—
56D4×D15—28no—
57#6817—24no—
58#6817—24no—
59#6817—22no—
60#6817—24no—
61#6817—22no—
62#6817—22no—
63#6817—22no—
64C2×D60—22no—
65C2×D60D412yes—
66C2×C4×D15—24no—
67C2×C4×D15D414yes—
68C2×Dic30—22no—
69C2×Dic30D412yes—
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4—24no—
72C3×C5×C22⋊C4—24no—
73C3×C5×C22⋊C4C2312yes—
74C3×C42×C5—21no—
75#6719C2314yes—
76#6714—28no—
77C4⋊Dic15—22no—
78#6712—28no—
79C4×Dic15—22no—
80#5964—51no—
81C3×#536D511yescharacteristic, complemented
82#5816—52no—
83#5240—51no—
84#5053—58no—
85#5006—52no—
86C2×C5×#41C2×D311yescharacteristic
87C22×C5×Q8C2×D311yescharacteristic, complemented
88#4150—62no—
89#4149—62no—
90D5×#41—64no—
91#4147—61no—
92#4144—34no—
93#4144—61no—
94C2×#709—32no—
95C2×#709—62no—
96C5×C4⋊Q8—21no—
97C5×#124—21no—
98C5×#123C2×D314yescomplemented
99C5×C22⋊Q8—22no—
100C5×#117C2×D311yescharacteristic, complemented
101#4093—62no—
102#4092—64no—
103#4090—62no—
104#4075—38no—
105#4072—32no—
106#3966—34no—
107#3938—38no—
108#3028—151noSylow
109C23×C3×C5C2×D412yes—
110C23×C3×C5C2411yescharacteristic
111C22×D15—24no—
112C22×D15C2×D414yes—
113C3×C5×Q8—22no—
114C3×C5×Q8—41no—
115C3×C5×Q8—42no—
116C3×C5×Q8—41no—
117C3×C5×D4—24no—
118C3×C5×D4—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—24no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5C2×D412yes—
125C2×C3×C4×C5C2×D412yes—
126C2×C3×C4×C5C2×D412yes—
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129#1220—28no—
130#1220—24no—
131#1220—24no—
132C2×Dic15—24no—
133C2×Dic15—24no—
134C2×Dic15C2×D414yes—
135D60—24no—
136D60—22no—
137D60—22no—
138C4×D15—28no—
139C4×D15—24no—
140C4×D15—24no—
141Dic30—24no—
142Dic30—22no—
143Dic30—22no—
144C2×C3×#41C2×D511yescharacteristic
145C22×C3×Q8C2×D511yescharacteristic, complemented
146#1010—102no—
147#1009—102no—
148D3×#41—104no—
149#1007—101no—
150#1004—54no—
151#1004—101no—
152C2×#235—52no—
153C2×#235—102no—
154C3×C4⋊Q8—21no—
155C3×#124—21no—
156C3×#123C2×D514yescomplemented
157C3×C22⋊Q8—22no—
158C3×#117C2×D511yescharacteristic, complemented
159#947—102no—
160#946—104no—
161#944—102no—
162#929—58no—
163#926—52no—
164#834—54no—
165#806—58no—
166C5×#41—22no—
167C5×#41—22no—
168C2×C5×Q8—22no—
169C2×C5×Q8—22no—
170C2×C5×Q8—21no—
171C2×C5×Q8—21no—
172C2×C5×Q8#6711yescharacteristic
173C2×C5×D4#6711yescharacteristic
174C2×C5×D4C22×D312yes—
175C22×C4×C5#6712yes—
176C22×C4×C5C22×D312yes—
177C22×C4×C5C22×D311yescharacteristic
178C2×C22⋊D5—34no—
179C2×C22⋊D5—64no—
180#713—64no—
181Q8×D5—64no—
182#711—68no—
183#711—64no—
184D4×D5—68no—
185D4×D5—64no—
186#709—64no—
187#709—64no—
188#709—62no—
189#709—62no—
190#709—62no—
191#709—62no—
192#709—64no—
193C2×D20—32no—
194C2×D20—62no—
195C2×C4×D5—34no—
196C2×C4×D5—64no—
197C2×Dic10—32no—
198C2×Dic10—62no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—24no—
201C5×C22⋊C4—24no—
202C5×C22⋊C4C22×D312yes—
203C42×C5—21no—
204C22⋊Dic5—34no—
205#685—68no—
206C4⋊Dic5—62no—
207#683—68no—
208C4×Dic5—62no—
209#585—151no—
210#536—152no—
211#536D1511yescharacteristic, complemented
212#458—158no—
213#410—151no—
214#410—152no—
215C22×C3×C5—22no—
216C22×C3×C5—41no—
217C22×C3×C5—42no—
218C22×C3×C5C22×D412yes—
219C22×C3×C5C22×D411yescharacteristic
220C2×D15—24no—
221C2×D15—44no—
222C2×D15—84no—
223C3×C4×C5—22no—
224C3×C4×C5—42no—
225C3×C4×C5—42no—
226C3×C4×C5#12011yescharacteristic
227C3×C4×C5#12012yes—
228C3×C4×C5#12011yescharacteristic
229Dic15—24no—
230Dic15—44no—
231C3×#41—22no—
232C3×#41—22no—
233C2×C3×Q8—22no—
234C2×C3×Q8—22no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8C22⋊D511yescharacteristic
238C2×C3×D4C22⋊D511yescharacteristic
239C2×C3×D4C22×D512yes—
240C22×C3×C4C22⋊D512yes—
241C22×C3×C4C22×D512yes—
242C22×C3×C4C22×D511yescharacteristic
243C2×#67—54no—
244C2×#67—104no—
245#239—104no—
246D3×Q8—104no—
247#237—108no—
248#237—104no—
249D3×D4—108no—
250D3×D4—104no—
251#235—104no—
252#235—104no—
253#235—102no—
254#235—102no—
255#235—102no—
256#235—102no—
257#235—104no—
258C2×D12—52no—
259C2×D12—102no—
260C2×C4×D3—54no—
261C2×C4×D3—104no—
262C2×Dic6—52no—
263C2×Dic6—102no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—24no—
266C3×C22⋊C4—24no—
267C3×C22⋊C4C22×D512yes—
268C3×C42—21no—
269#217—54no—
270(C2×D3)⋊C4—108no—
271C4⋊Dic3—102no—
272Dic3⋊C4—108no—
273C4×Dic3—102no—
274C23×C5C2×#6712yes—
275C23×C5C23×D311yescharacteristic
276C22×D5—34no—
277C22×D5—64no—
278C5×Q8—22no—
279C5×Q8—41no—
280C5×Q8—42no—
281C5×Q8—41no—
282C5×D4—24no—
283C5×D4—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—24no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5D3×D412yes—
290C2×C4×C5D3×D412yes—
291C2×C4×C5C2×#6712yes—
292C2×C4×C5C2×#6711yescharacteristic
293C2×C4×C5C2×#6711yescharacteristic
294C22⋊D5—68no—
295C22⋊D5—64no—
296C22⋊D5—64no—
297C2×Dic5—34no—
298C2×Dic5—64no—
299C2×Dic5—64no—
300D20—64no—
301D20—62no—
302D20—62no—
303C4×D5—68no—
304C4×D5—64no—
305C4×D5—64no—
306Dic10—64no—
307Dic10—62no—
308Dic10—62no—
3092−1+4—302no—
3102−1+4—301no—
311H(5,𝔽2)—154no—
312H(5,𝔽2)—302no—
313H(5,𝔽2)—301no—
314C2×#41—152no—
315C2×#41—304no—
316C2×#41—302no—
317C2×#41C2×D1511yescharacteristic
318C22×Q8C2×D1511yescharacteristic, complemented
319C4⋊Q8—21no—
320C4⋊Q8—302no—
321#124—21no—
322#124—302no—
323#123—158no—
324#123C2×D1514yescomplemented
325C22⋊Q8—22no—
326C22⋊Q8—304no—
327#117—152no—
328#117C2×D1511yescharacteristic, complemented
329#99—154no—
330#99—158no—
331C2×C3×C5—22no—
332C2×C3×C5—21no—
333C2×C3×C5—42no—
334C2×C3×C5C2×#12011yescharacteristic
335D15—44no—
336C23×C3C2×C22⋊D512yes—
337C23×C3C23×D511yescharacteristic
338C22×D3—54no—
339C22×D3—104no—
340C3×Q8—22no—
341C3×Q8—41no—
342C3×Q8—42no—
343C3×Q8—41no—
344C3×D4—24no—
345C3×D4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—24no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4D4×D512yes—
352C2×C3×C4D4×D512yes—
353C2×C3×C4C2×C22⋊D512yes—
354C2×C3×C4C2×C22⋊D511yescharacteristic
355C2×C3×C4C2×C22⋊D511yescharacteristic
356#67—108no—
357#67—104no—
358#67—104no—
359C2×Dic3—54no—
360C2×Dic3—104no—
361C2×Dic3—104no—
362D12—104no—
363D12—102no—
364D12—102no—
365C4×D3—108no—
366C4×D3—104no—
367C4×D3—104no—
368Dic6—104no—
369Dic6—102no—
370Dic6—102no—
371C22×C5—22no—
372C22×C5—41no—
373C22×C5—42no—
374C22×C5C2×D3×D412yes—
375C22×C5C22×#6711yescharacteristic
376C2×D5—64no—
377C2×D5—124no—
378C2×D5—244no—
379C4×C5—22no—
380C4×C5—42no—
381C4×C5—42no—
382C4×C5#93711yescharacteristic
383C4×C5#93712yes—
384C4×C5#93711yescharacteristic
385Dic5—64no—
386Dic5—124no—
387#41—22no—
388#41—22no—
389#41—304no—
390#41—304no—
391#41—308no—
392#41—304no—
393#41—304no—
394#41—302no—
395#41—302no—
396#41—302no—
397#41—302no—
398#41—304no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—152no—
404C2×Q8—302no—
405C2×Q8—304no—
406C2×Q8#122011yescharacteristic
407C2×D4—154no—
408C2×D4—152no—
409C2×D4—302no—
410C2×D4—308no—
411C2×D4—304no—
412C2×D4—304no—
413C2×D4#122011yescharacteristic
414C2×D4C22×D1512yes—
415C22×C4—154no—
416C22×C4—304no—
417C22×C4#122012yes—
418C22×C4C22×D1512yes—
419C22×C4C22×D1511yescharacteristic
420C4⋊C4—21no—
421C4⋊C4—24no—
422C4⋊C4—308no—
423C4⋊C4—302no—
424C22⋊C4—24no—
425C22⋊C4—154no—
426C22⋊C4—308no—
427C22⋊C4C22×D1512yes—
428C42—21no—
429C42—302no—
430C3×C5#302811yescharacteristic, complemented, Hall
431C22×C3—22no—
432C22×C3—41no—
433C22×C3—42no—
434C22×C3C2×D4×D512yes—
435C22×C3C22×C22⋊D511yescharacteristic
436C2×D3—104no—
437C2×D3—204no—
438C2×D3—404no—
439C3×C4—22no—
440C3×C4—42no—
441C3×C4—42no—
442C3×C4#408311yescharacteristic
443C3×C4#408312yes—
444C3×C4#408311yescharacteristic
445Dic3—104no—
446Dic3—204no—
447C2×C5—22no—
448C2×C5—21no—
449C2×C5—42no—
450C2×C5C2×#93711yescharacteristic
451D5—124no—
452C23—154no—
453C23—304no—
454C23C2×#122012yes—
455C23C23×D1511yescharacteristic
456Q8—22no—
457Q8—41no—
458Q8—41no—
459Q8—42no—
460Q8—304no—
461Q8—302no—
462Q8—302no—
463D4—24no—
464D4—22no—
465D4—304no—
466D4—308no—
467D4—304no—
468D4—304no—
469D4—302no—
470D4—302no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—154no—
477C2×C4—308no—
478C2×C4—304no—
479C2×C4—304no—
480C2×C4—304no—
481C2×C4—304no—
482C2×C4D4×D1512yes—
483C2×C4D4×D1512yes—
484C2×C4C2×#122012yes—
485C2×C4C2×#122011yescharacteristic
486C2×C4C2×#122011yescharacteristic
487C2×C3—22no—
488C2×C3—21no—
489C2×C3—42no—
490C2×C3C2×#408311yescharacteristic
491D3—204no—
492C5#8341711yescharacteristic, complemented, Sylow
493C22—22no—
494C22—41no—
495C22—42no—
496C22—304no—
497C22—604no—
498C22—1204no—
499C22C2×D4×D1512yes—
500C22C22×#122011yescharacteristic
501C4—22no—
502C4—42no—
503C4—42no—
504C4—304no—
505C4—604no—
506C4#9182611yescharacteristic
507C4#9182611yescharacteristic
508C4#9182612yes—
509C3#1061514811yescharacteristic, complemented, Sylow
510C2—21no—
511C2—22no—
512C2—42no—
513C2—604no—
514C2C2×#9182611yescharacteristic
subgroupG/H
centerC2C2×#91826
commutator, cosocleC23×C3×C5C24
FrattiniC23C23×D15
FittingC3×C5×#536C2
socleC2×C3×C5C2×#120
prime radical#11757146C2
hypercenter#536D15
hypocenterC3×C5#3028
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C3×C5×#536C2semidirect
3. #11756575C2semidirect
4. #11751341C2semidirect
5. #11751154C2semidirect
6. #11751107C2semidirect
9. C22×C3×C5×Q8C22semidirect
20. C3×C5×#123C22semidirect
22. C3×C5×#117C22semidirect
26. #91818C22semidirect
27. #91815C22semidirect
28. #91118C22semidirect
29. #91090C22semidirect
32. C5×#536D3semidirect
81. C3×#536D5semidirect
87. C22×C5×Q8C2×D3semidirect
98. C5×#123C2×D3semidirect
100. C5×#117C2×D3semidirect
145. C22×C3×Q8C2×D5semidirect
156. C3×#123C2×D5semidirect
158. C3×#117C2×D5semidirect
211. #536D15semidirect
318. C22×Q8C2×D15semidirect
324. #123C2×D15semidirect
328. #117C2×D15semidirect
430. C3×C5#3028semidirect
492. C5#83417semidirect
509. C3#10615148semidirect

Maximal subgroups

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

subgroupindex
#117571462
C3×C5×#5362
#117565752
#117513412
#117511542
#117511072
#106151483
#834175