Finite Group Databasebeta

← C2×#11751154 #14425629

Subgroups — C2×#11751154 #14425629

Order 1920.

1588 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92095C211yesmaximal, characteristic
2C2×C3×C5×#123C211yesmaximal, characteristic, complemented
3C2×#91818C212yesmaximal, complemented
4C2×#91118C211yesmaximal, characteristic, complemented
5#11751154C218yesmaximal, direct product factor
6C2×#91090C212yesmaximal, complemented
7C2×#65342—31nomaximal, Hall
8C22×C3×C5×D4C2211yescharacteristic
9C23×C3×C4×C5C2211yescharacteristic, complemented
10C22×#1220—21no—
11C22×#1220C2212yes—
12#92095—22no—
13#92095—24no—
14#92095C2214yes—
15C2×#6819—22no—
16C2×D4×D15—22no—
17C2×#6817—21no—
18C3×C5×#123—22no—
19C3×C5×#123C2214yescomplemented
20C2×C3×C5×C4⋊C4—21no—
21C2×C3×C5×C22⋊C4—21no—
22C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
23C2×#6719C2212yescomplemented
24#91818—24no—
25#91818C2218yescomplemented
26C2×#6714—22no—
27C2×#6712—22no—
28#91118C2214yescomplemented
29#91090C2218yescomplemented
30C2×#5053—51nomaximal, Hall
31C2×#4144—31no—
32C2×C5×#123D311yescharacteristic, complemented
33C2×#4075—32no—
34C2×#3966—31no—
35#65342—38no—
36C2×#3938—32no—
37C24×C3×C5D411yescharacteristic
38C24×C3×C5C2311yescharacteristic
39C23×D15—21no—
40C23×D15D412yes—
41C2×C3×C5×D4—22no—
42C2×C3×C5×D4—22no—
43C2×C3×C5×D4D412yes—
44C2×C3×C5×D4C2312yes—
45C22×C3×C4×C5—22no—
46C22×C3×C4×C5—22no—
47C22×C3×C4×C5—21no—
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5D411yescharacteristic
51C22×C3×C4×C5C2312yescomplemented
52C2×#1220—22no—
53C2×#1220—24no—
54C2×#1220—22no—
55C2×#1220—22no—
56C2×#1220—22no—
57C2×#1220—22no—
58C2×#1220—24no—
59C2×#1220D414yes—
60C2×#1220C2314yes—
61C22×Dic15—21no—
62C22×Dic15—22no—
63C22×Dic15D412yes—
64#6819—28no—
65#6819—28no—
66D4×D15—28no—
67D4×D15—28no—
68#6817—24no—
69#6817—24no—
70C2×D60—21no—
71C2×C4×D15—22no—
72C2×Dic30—21no—
73C3×C5×C4⋊C4—24no—
74C3×C5×C22⋊C4—24no—
75C3×C5×C22⋊C4—21no—
76C3×C5×C22⋊C4C2312yescomplemented
77#6719—22no—
78#6719C2314yescomplemented
79#6714—28no—
80#6712—28no—
81C2×#1004—51no—
82C2×C3×#123D511yescharacteristic, complemented
83C2×#929—52no—
84C2×#834—51no—
85#5053—58no—
86C2×#806—52no—
87C22×C5×D4C2×D311yescharacteristic
88C23×C4×C5C2×D311yescharacteristic, complemented
89C22×C22⋊D5—32no—
90C22×C22⋊D5—61no—
91#4144—34no—
92#4144—64no—
93#4144—62no—
94C2×#711—62no—
95C2×D4×D5—62no—
96C2×#709—61no—
97C5×#123—22no—
98C5×#123C2×D314yescomplemented
99C2×C5×C4⋊C4—21no—
100C2×C5×C22⋊C4—21no—
101C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
102C2×C22⋊Dic5—32no—
103#4075—38no—
104#4075—64no—
105C2×#685—62no—
106C2×#683—62no—
107#3966—34no—
108#3938—38no—
109C2×#458—151noSylow
110C23×C3×C5—21no—
111C23×C3×C5—21no—
112C23×C3×C5—42no—
113C23×C3×C5—42no—
114C23×C3×C5C2×D412yes—
115C23×C3×C5C2×D411yescharacteristic
116C23×C3×C5C2×D412yes—
117C23×C3×C5C2×D412yes—
118C23×C3×C5C2×D411yescharacteristic
119C23×C3×C5C2411yescharacteristic
120C22×D15—22no—
121C22×D15—24no—
122C22×D15—22no—
123C22×D15—44no—
124C22×D15—82no—
125C22×D15C2×D414yes—
126C3×C5×D4—24no—
127C3×C5×D4—24no—
128C2×C3×C4×C5—21no—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—24no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—42no—
134C2×C3×C4×C5—42no—
135C2×C3×C4×C5—41no—
136C2×C3×C4×C5—41no—
137C2×C3×C4×C5C2×D412yes—
138#1220—28no—
139#1220—24no—
140#1220—24no—
141#1220—24no—
142#1220—24no—
143C2×Dic15—24no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—24no—
147C2×Dic15—44no—
148C2×Dic15C2×D414yes—
149D60—24no—
150C4×D15—28no—
151Dic30—24no—
152C22×C3×D4C2×D511yescharacteristic
153C23×C3×C4C2×D511yescharacteristic, complemented
154C22×#67—52no—
155C22×#67—101no—
156#1004—54no—
157#1004—104no—
158#1004—102no—
159C2×#237—102no—
160C2×D3×D4—102no—
161C2×#235—101no—
162C3×#123—22no—
163C3×#123C2×D514yescomplemented
164C2×C3×C4⋊C4—21no—
165C2×C3×C22⋊C4—21no—
166C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
167C2×#217—52no—
168#929—58no—
169#929—104no—
170C2×(C2×D3)⋊C4—102no—
171C2×Dic3⋊C4—102no—
172#834—54no—
173#806—58no—
174C24×C5#6711yescharacteristic
175C24×C5C22×D311yescharacteristic
176C23×D5—32no—
177C23×D5—61no—
178C2×C5×D4—22no—
179C2×C5×D4—22no—
180C2×C5×D4#6712yes—
181C2×C5×D4C22×D312yes—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5#6711yescharacteristic
188C22×C4×C5C22×D312yescomplemented
189C2×C22⋊D5—34no—
190C2×C22⋊D5—34no—
191C2×C22⋊D5—62no—
192C2×C22⋊D5—64no—
193C2×C22⋊D5—62no—
194C2×C22⋊D5—62no—
195C2×C22⋊D5—62no—
196C2×C22⋊D5—64no—
197C2×C22⋊D5—62no—
198C22×Dic5—32no—
199C22×Dic5—61no—
200C22×Dic5—62no—
201#711—68no—
202#711—68no—
203D4×D5—68no—
204D4×D5—68no—
205#709—64no—
206#709—64no—
207C2×D20—61no—
208C2×C4×D5—62no—
209C2×Dic10—61no—
210C5×C4⋊C4—24no—
211C5×C22⋊C4—24no—
212C5×C22⋊C4—21no—
213C5×C22⋊C4C22×D312yescomplemented
214C22⋊Dic5—34no—
215C22⋊Dic5—62no—
216#685—68no—
217#683—68no—
218C2×H(5,𝔽2)—151no—
219C2×#123—152no—
220C2×#123D1511yescharacteristic, complemented
221#458—158no—
222C2×#99—151no—
223C2×#99—152no—
224C22×C3×C5—24no—
225C22×C3×C5—22no—
226C22×C3×C5—22no—
227C22×C3×C5—42no—
228C22×C3×C5—41no—
229C22×C3×C5—41no—
230C22×C3×C5—42no—
231C22×C3×C5—42no—
232C22×C3×C5—81no—
233C22×C3×C5#12012yes—
234C22×C3×C5#12011yescharacteristic
235C22×C3×C5#12011yescharacteristic
236C22×C3×C5C22×D412yes—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—24no—
239C2×D15—44no—
240C2×D15—44no—
241C2×D15—82no—
242C2×D15—84no—
243C3×C4×C5—22no—
244C3×C4×C5—42no—
245C3×C4×C5—42no—
246Dic15—24no—
247Dic15—44no—
248C24×C3C22⋊D511yescharacteristic
249C24×C3C22×D511yescharacteristic
250C23×D3—52no—
251C23×D3—101no—
252C2×C3×D4—22no—
253C2×C3×D4—22no—
254C2×C3×D4C22⋊D512yes—
255C2×C3×D4C22×D512yes—
256C22×C3×C4—22no—
257C22×C3×C4—22no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4C22⋊D511yescharacteristic
262C22×C3×C4C22×D512yescomplemented
263C2×#67—54no—
264C2×#67—54no—
265C2×#67—102no—
266C2×#67—104no—
267C2×#67—102no—
268C2×#67—102no—
269C2×#67—102no—
270C2×#67—104no—
271C2×#67—102no—
272C22×Dic3—52no—
273C22×Dic3—101no—
274C22×Dic3—102no—
275#237—108no—
276#237—108no—
277D3×D4—108no—
278D3×D4—108no—
279#235—104no—
280#235—104no—
281C2×D12—101no—
282C2×C4×D3—102no—
283C2×Dic6—101no—
284C3×C4⋊C4—24no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—21no—
287C3×C22⋊C4C22×D512yescomplemented
288#217—54no—
289#217—102no—
290(C2×D3)⋊C4—108no—
291Dic3⋊C4—108no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5—42no—
295C23×C5—42no—
296C23×C5D3×D412yes—
297C23×C5D3×D412yes—
298C23×C5C2×#6711yescharacteristic
299C23×C5C2×#6712yes—
300C23×C5C2×#6711yescharacteristic
301C23×C5C23×D311yescharacteristic
302C22×D5—34no—
303C22×D5—62no—
304C22×D5—64no—
305C22×D5—62no—
306C22×D5—124no—
307C22×D5—242no—
308C5×D4—24no—
309C5×D4—24no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—24no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—42no—
316C2×C4×C5—42no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5C2×#6712yes—
320C22⋊D5—68no—
321C22⋊D5—64no—
322C22⋊D5—64no—
323C22⋊D5—64no—
324C22⋊D5—64no—
325C2×Dic5—34no—
326C2×Dic5—64no—
327C2×Dic5—62no—
328C2×Dic5—62no—
329C2×Dic5—64no—
330C2×Dic5—124no—
331D20—64no—
332C4×D5—68no—
333Dic10—64no—
334H(5,𝔽2)—154no—
335H(5,𝔽2)—304no—
336H(5,𝔽2)—302no—
337C2×#41—302no—
338C2×#41—301no—
339C22×D4—152no—
340C22×D4—302no—
341C22×D4—301no—
342C22×D4C2×D1511yescharacteristic
343C23×C4C2×D1511yescharacteristic, complemented
344#123—22no—
345#123—158no—
346#123—304no—
347#123C2×D1514yescomplemented
348C2×C4⋊C4—21no—
349C2×C4⋊C4—302no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—152no—
352C2×C22⋊C4—302no—
353C2×C22⋊C4C2×D1511yescharacteristic, complemented
354#99—154no—
355#99—158no—
356C2×C3×C5—22no—
357C2×C3×C5—21no—
358C2×C3×C5—22no—
359C2×C3×C5—21no—
360C2×C3×C5—42no—
361C2×C3×C5#45812yescomplemented
362C2×C3×C5C2×#12011yescharacteristic
363D15—44no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3D4×D512yes—
369C23×C3D4×D512yes—
370C23×C3C2×C22⋊D511yescharacteristic
371C23×C3C2×C22⋊D512yes—
372C23×C3C2×C22⋊D511yescharacteristic
373C23×C3C23×D511yescharacteristic
374C22×D3—54no—
375C22×D3—102no—
376C22×D3—104no—
377C22×D3—102no—
378C22×D3—204no—
379C22×D3—402no—
380C3×D4—24no—
381C3×D4—24no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4C2×C22⋊D512yes—
392#67—108no—
393#67—104no—
394#67—104no—
395#67—104no—
396#67—104no—
397C2×Dic3—54no—
398C2×Dic3—104no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401C2×Dic3—104no—
402C2×Dic3—204no—
403D12—104no—
404C4×D3—108no—
405Dic6—104no—
406C22×C5—24no—
407C22×C5—22no—
408C22×C5—22no—
409C22×C5—42no—
410C22×C5—41no—
411C22×C5—41no—
412C22×C5—42no—
413C22×C5—42no—
414C22×C5—81no—
415C22×C5#93712yes—
416C22×C5#93711yescharacteristic
417C22×C5#93711yescharacteristic
418C22×C5C2×D3×D412yes—
419C22×C5C22×#6711yescharacteristic
420C2×D5—64no—
421C2×D5—124no—
422C2×D5—124no—
423C2×D5—242no—
424C2×D5—244no—
425C4×C5—22no—
426C4×C5—42no—
427C4×C5—42no—
428Dic5—64no—
429Dic5—124no—
430C24—152no—
431C24—301no—
432C24#122011yescharacteristic
433C24C22×D1511yescharacteristic
434#41—304no—
435#41—308no—
436#41—308no—
437#41—304no—
438C2×Q8—301no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—154no—
442C2×D4—154no—
443C2×D4—301no—
444C2×D4—308no—
445C2×D4—308no—
446C2×D4—302no—
447C2×D4—304no—
448C2×D4—302no—
449C2×D4—302no—
450C2×D4—302no—
451C2×D4—302no—
452C2×D4—304no—
453C2×D4#122012yes—
454C2×D4C22×D1512yes—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—152no—
461C22×C4—302no—
462C22×C4—301no—
463C22×C4—302no—
464C22×C4#122011yescharacteristic
465C22×C4C22×D1512yescomplemented
466C4⋊C4—24no—
467C4⋊C4—308no—
468C22⋊C4—24no—
469C22⋊C4—21no—
470C22⋊C4—154no—
471C22⋊C4—308no—
472C22⋊C4—302no—
473C22⋊C4C22×D1512yescomplemented
474C3×C5C2×#45811yescharacteristic, complemented, Hall
475C22×C3—24no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—42no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—81no—
484C22×C3#408312yes—
485C22×C3#408311yescharacteristic
486C22×C3#408311yescharacteristic
487C22×C3C2×D4×D512yes—
488C22×C3C22×C22⋊D511yescharacteristic
489C2×D3—104no—
490C2×D3—204no—
491C2×D3—204no—
492C2×D3—402no—
493C2×D3—404no—
494C3×C4—22no—
495C3×C4—42no—
496C3×C4—42no—
497Dic3—104no—
498Dic3—204no—
499C2×C5—22no—
500C2×C5—21no—
501C2×C5—22no—
502C2×C5—21no—
503C2×C5—42no—
504C2×C5#505312yescomplemented
505C2×C5C2×#93711yescharacteristic
506D5—124no—
507C23—21no—
508C23—21no—
509C23—42no—
510C23—42no—
511C23—154no—
512C23—304no—
513C23—302no—
514C23—302no—
515C23—604no—
516C23—1202no—
517C23D4×D1512yes—
518C23D4×D1512yes—
519C23C2×#122011yescharacteristic
520C23C2×#122012yes—
521C23C2×#122011yescharacteristic
522C23C23×D1511yescharacteristic
523Q8—304no—
524D4—24no—
525D4—24no—
526D4—304no—
527D4—308no—
528D4—304no—
529D4—304no—
530D4—304no—
531D4—304no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—154no—
542C2×C4—308no—
543C2×C4—304no—
544C2×C4—302no—
545C2×C4—302no—
546C2×C4—304no—
547C2×C4—604no—
548C2×C4C2×#122012yes—
549C2×C3—22no—
550C2×C3—21no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—42no—
554C2×C3#6534212yescomplemented
555C2×C3C2×#408311yescharacteristic
556D3—204no—
557C5C2×#505311yescharacteristic, complemented, Sylow
558C22—22no—
559C22—24no—
560C22—22no—
561C22—42no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22—42no—
566C22—81no—
567C22—304no—
568C22—604no—
569C22—604no—
570C22—1202no—
571C22—1204no—
572C22#9182611yescharacteristic
573C22#9182612yes—
574C22#9182611yescharacteristic
575C22C2×D4×D1512yes—
576C22C22×#122011yescharacteristic
577C4—22no—
578C4—42no—
579C4—42no—
580C4—304no—
581C4—604no—
582C3C2×#6534211yescharacteristic, complemented, Sylow
583C2—21no—
584C2—22no—
585C2—21no—
586C2—22no—
587C2—42no—
588C2—604no—
589C2#1175115412yesdirect product factor
590C2C2×#9182611yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC23×C3×C5C24
FrattiniC23C23×D15
FittingC2×C3×C5×#123C2
socleC22×C3×C5#120
prime radicalC2×#92095C2
hypercenterC2×#123D15
hypocenterC3×C5C2×#458
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#123C2semidirect
3. C2×#91818C2semidirect
4. C2×#91118C2semidirect
5. #11751154C2direct (N × H)
6. C2×#91090C2semidirect
9. C23×C3×C4×C5C22semidirect
19. C3×C5×#123C22semidirect
22. C2×C3×C5×C22⋊C4C22semidirect
23. C2×#6719C22semidirect
25. #91818C22semidirect
28. #91118C22semidirect
29. #91090C22semidirect
32. C2×C5×#123D3semidirect
51. C22×C3×C4×C5C23semidirect
76. C3×C5×C22⋊C4C23semidirect
78. #6719C23semidirect
82. C2×C3×#123D5semidirect
88. C23×C4×C5C2×D3semidirect
98. C5×#123C2×D3semidirect
101. C2×C5×C22⋊C4C2×D3semidirect
153. C23×C3×C4C2×D5semidirect
163. C3×#123C2×D5semidirect
166. C2×C3×C22⋊C4C2×D5semidirect
188. C22×C4×C5C22×D3semidirect
213. C5×C22⋊C4C22×D3semidirect
220. C2×#123D15semidirect
262. C22×C3×C4C22×D5semidirect
287. C3×C22⋊C4C22×D5semidirect
343. C23×C4C2×D15semidirect
347. #123C2×D15semidirect
353. C2×C22⋊C4C2×D15semidirect
361. C2×C3×C5#458semidirect
465. C22×C4C22×D15semidirect
473. C22⋊C4C22×D15semidirect
474. C3×C5C2×#458semidirect
504. C2×C5#5053semidirect
554. C2×C3#65342semidirect
557. C5C2×#5053semidirect
582. C3C2×#65342semidirect
589. C2#11751154direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#920952
C2×C3×C5×#1232
C2×#918182
C2×#911182
#117511542
C2×#910902
C2×#653423
C2×#50535