Finite Group Databasebeta

← C2×#11749182 #14425651

Subgroups — C2×#11749182 #14425651

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×C3×#4144C211yesmaximal, characteristic
2C2×#91824C211yesmaximal, characteristic, complemented
3C2×#91537C212yesmaximal, complemented
4C2×C5×#834C211yesmaximal, characteristic, complemented
5C2×#90995C212yesmaximal, complemented
6#11749182C218yesmaximal, direct product factor
7C2×#65031—31nomaximal, Hall
8C22×C3×C5×D4C2211yescharacteristic
9C23×Dic15C2211yescharacteristic, complemented
10C22×C3×C22⋊D5—21no—
11C22×C3×C22⋊D5C2212yes—
12C3×#4144—22no—
13C3×#4144—24no—
14C3×#4144C2214yes—
15C2×C3×#711—22no—
16C2×C3×D4×D5—22no—
17C2×C3×#709—21no—
18C2×#6719—21no—
19C2×#6719C2211yescharacteristic, complemented
20#91824—22no—
21#91824C2214yescomplemented
22C2×#6712—21no—
23C2×C5×#217C2212yescomplemented
24C2×Dic3⋊Dic5—22no—
25#91537—24no—
26#91537C2218yescomplemented
27C2×#6665—22no—
28C5×#834C2214yescomplemented
29#90995C2218yescomplemented
30C2×#5243—51nomaximal, Hall
31C2×#4144D311yescharacteristic
32C2×#4081—31no—
33C2×#4032—32no—
34C2×C5×#99—31no—
35C2×#3938—32no—
36#65031—38no—
37C24×C3×C5D411yescharacteristic
38C24×C3×C5C2311yescharacteristic
39C23×C3×D5—21no—
40C23×C3×D5D412yes—
41C2×C3×C5×D4—22no—
42C2×C3×C5×D4—22no—
43C2×C3×C5×D4D412yes—
44C2×C3×C5×D4C2312yes—
45C22×C3×C4×C5D411yescharacteristic
46C22×Dic15—22no—
47C22×Dic15—22no—
48C22×Dic15—21no—
49C22×Dic15—21no—
50C22×Dic15—21no—
51C22×Dic15C2312yescomplemented
52C22×C5×Dic3—22no—
53C2×C3×C22⋊D5—22no—
54C2×C3×C22⋊D5—24no—
55C2×C3×C22⋊D5—22no—
56C2×C3×C22⋊D5—22no—
57C2×C3×C22⋊D5—22no—
58C2×C3×C22⋊D5—22no—
59C2×C3×C22⋊D5—24no—
60C2×C3×C22⋊D5D414yes—
61C2×C3×C22⋊D5C2314yes—
62C22×C3×Dic5—21no—
63C22×C3×Dic5D412yes—
64C3×#711—28no—
65C3×#711—28no—
66C3×D4×D5—28no—
67C3×D4×D5—28no—
68C3×#709—24no—
69C3×#709—24no—
70C2×C3×D20—21no—
71C2×C3×C4×D5—22no—
72C2×C3×Dic10—21no—
73#6719—21no—
74#6719—24no—
75#6719C2312yescomplemented
76#6712—24no—
77C5×#217—22no—
78C5×#217C2314yescomplemented
79Dic3⋊Dic5—28no—
80#6665—28no—
81C2×C3×H(5,𝔽2)—51no—
82C2×#935—51no—
83C2×#935—52no—
84#5243—58no—
85C2×#834—52no—
86C2×#834D511yescharacteristic, complemented
87C22×C5×D4C2×D311yescharacteristic
88C22×C22⋊D5—21no—
89C22×C22⋊D5C2×D312yes—
90C23×Dic5—31no—
91#4144—22no—
92#4144—24no—
93#4144C2×D314yes—
94C2×#711—22no—
95C2×D4×D5—22no—
96C2×#709—21no—
97C2×C5×C22⋊C4—32no—
98C2×C22⋊Dic5—31no—
99C2×C22⋊Dic5—61no—
100#4081—34no—
101#4081—62no—
102C2×#685—62no—
103C2×C4⋊Dic5—62no—
104C2×#683—61no—
105#4032—38no—
106#4032—64no—
107C5×#99—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×D411yescharacteristic
115C23×C3×C5C2×D412yes—
116C23×C3×C5C2×D412yes—
117C23×C3×C5C2×D411yescharacteristic
118C23×C3×C5C2×D412yes—
119C23×C3×C5C2411yescharacteristic
120C22×C3×D5—22no—
121C22×C3×D5—24no—
122C22×C3×D5—22no—
123C22×C3×D5—44no—
124C22×C3×D5—82no—
125C22×C3×D5C2×D414yes—
126C3×C5×D4—24no—
127C3×C5×D4—24no—
128C2×C3×C4×C5—21no—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5C2×D412yes—
131C2×Dic15—24no—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—42no—
135C2×Dic15—42no—
136C2×Dic15—41no—
137C2×Dic15—41no—
138C2×C5×Dic3—24no—
139C2×C5×Dic3—44no—
140C3×C22⋊D5—28no—
141C3×C22⋊D5—24no—
142C3×C22⋊D5—24no—
143C3×C22⋊D5—24no—
144C3×C22⋊D5—24no—
145C2×C3×Dic5—24no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5C2×D414yes—
149C3×D20—24no—
150C3×C4×D5—28no—
151C3×Dic10—24no—
152C3×H(5,𝔽2)—54no—
153C3×H(5,𝔽2)—104no—
154C3×H(5,𝔽2)—102no—
155C2×C3×#41—102no—
156C2×C3×#41—101no—
157C22×C3×D4—52no—
158C22×C3×D4—102no—
159C22×C3×D4—101no—
160C22×C3×D4C2×D511yescharacteristic
161C23×Dic3—51no—
162C2×#217—51no—
163C2×#217—102no—
164C2×#217—101no—
165C2×#217C2×D512yescomplemented
166#935—54no—
167#935—58no—
168#935—104no—
169#935—102no—
170C2×Dic3⋊C4—102no—
171C2×Dic3⋊C4—101no—
172#834—58no—
173#834C2×D514yescomplemented
174C24×C5#6711yescharacteristic
175C24×C5C22×D311yescharacteristic
176C23×D5—21no—
177C23×D5#6712yes—
178C2×C5×D4—22no—
179C2×C5×D4—22no—
180C2×C5×D4#6712yes—
181C2×C5×D4C22×D312yes—
182C22×C4×C5—62no—
183C22×C4×C5#6711yescharacteristic
184C2×C22⋊D5—22no—
185C2×C22⋊D5—24no—
186C2×C22⋊D5—22no—
187C2×C22⋊D5—22no—
188C2×C22⋊D5—22no—
189C2×C22⋊D5—22no—
190C2×C22⋊D5—24no—
191C2×C22⋊D5#6714yes—
192C2×C22⋊D5C22×D314yes—
193C22×Dic5—21no—
194C22×Dic5—32no—
195C22×Dic5—61no—
196C22×Dic5—61no—
197C22×Dic5—62no—
198C22×Dic5—62no—
199C22×Dic5—61no—
200C22×Dic5#6712yes—
201#711—28no—
202#711—28no—
203D4×D5—28no—
204D4×D5—28no—
205#709—24no—
206#709—24no—
207C2×D20—21no—
208C2×C4×D5—22no—
209C2×Dic10—21no—
210C5×C22⋊C4—34no—
211C5×C22⋊C4—62no—
212C22⋊Dic5—32no—
213C22⋊Dic5—61no—
214C22⋊Dic5—64no—
215#685—68no—
216C4⋊Dic5—68no—
217#683—64no—
218C2×H(5,𝔽2)—51no—
219C2×#123—152no—
220C2×#123—151no—
221#458—158no—
222C2×#99—31no—
223C2×#99—152no—
224C22×C3×C5—24no—
225C22×C3×C5—22no—
226C22×C3×C5—22no—
227C22×C3×C5—41no—
228C22×C3×C5—42no—
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×D411yescharacteristic
237C22×C3×C5C22×D412yes—
238C2×C3×D5—24no—
239C2×C3×D5—44no—
240C2×C3×D5—44no—
241C2×C3×D5—82no—
242C2×C3×D5—84no—
243C3×C4×C5—22no—
244Dic15—42no—
245Dic15—42no—
246C3×Dic5—24no—
247C5×Dic3—44no—
248C24×C3—52no—
249C24×C3—101no—
250C24×C3D2011yescharacteristic
251C24×C3C22×D511yescharacteristic
252C3×#41—104no—
253C3×#41—108no—
254C3×#41—108no—
255C3×#41—104no—
256C2×C3×Q8—101no—
257C2×C3×D4—22no—
258C2×C3×D4—22no—
259C2×C3×D4—54no—
260C2×C3×D4—54no—
261C2×C3×D4—101no—
262C2×C3×D4—108no—
263C2×C3×D4—108no—
264C2×C3×D4—102no—
265C2×C3×D4—104no—
266C2×C3×D4—102no—
267C2×C3×D4—102no—
268C2×C3×D4—104no—
269C2×C3×D4—102no—
270C2×C3×D4—102no—
271C2×C3×D4D2012yes—
272C2×C3×D4C22×D512yes—
273C22×C3×C4—52no—
274C22×C3×C4—102no—
275C22×C3×C4—101no—
276C22×C3×C4D2011yescharacteristic
277C22×Dic3—22no—
278C22×Dic3—52no—
279C22×Dic3—101no—
280C22×Dic3—101no—
281C22×Dic3—101no—
282C22×Dic3—102no—
283C22×Dic3—102no—
284#217—22no—
285#217—52no—
286#217—108no—
287#217—104no—
288#217—101no—
289#217C22×D514yescomplemented
290Dic3⋊C4—108no—
291Dic3⋊C4—104no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5—42no—
295C23×C5—42no—
296C23×C5C2×#6711yescharacteristic
297C23×C5C2×#6712yes—
298C23×C5C2×#6711yescharacteristic
299C23×C5C2×#6712yes—
300C23×C5C2×#6712yes—
301C23×C5C23×D311yescharacteristic
302C22×D5—22no—
303C22×D5—24no—
304C22×D5—22no—
305C22×D5—44no—
306C22×D5—82no—
307C22×D5C2×#6714yes—
308C5×D4—24no—
309C5×D4—24no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—64no—
313C2×C4×C5—124no—
314C2×C4×C5C2×#6712yes—
315C22⋊D5—28no—
316C22⋊D5—24no—
317C22⋊D5—24no—
318C22⋊D5—24no—
319C22⋊D5—24no—
320C2×Dic5—24no—
321C2×Dic5—22no—
322C2×Dic5—22no—
323C2×Dic5—62no—
324C2×Dic5—62no—
325C2×Dic5—64no—
326C2×Dic5—122no—
327C2×Dic5—122no—
328C2×Dic5—121no—
329C2×Dic5—121no—
330C2×Dic5C2×#6714yes—
331D20—24no—
332C4×D5—28no—
333Dic10—24no—
334H(5,𝔽2)—54no—
335H(5,𝔽2)—104no—
336H(5,𝔽2)—102no—
337C2×#41—102no—
338C2×#41—101no—
339C22×D4—52no—
340C22×D4—102no—
341C22×D4—101no—
342C22×D4D3×D511yescharacteristic
343C23×C4—151no—
344#123—158no—
345#123—154no—
346#123—304no—
347#123—302no—
348C2×C4⋊C4—302no—
349C2×C4⋊C4—301no—
350C2×C22⋊C4—32no—
351C2×C22⋊C4—151no—
352C2×C22⋊C4—302no—
353C2×C22⋊C4—301no—
354#99—34no—
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
363C3×D5—44no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—54no—
369C23×C3—104no—
370C23×C3—102no—
371C23×C3—102no—
372C23×C3—204no—
373C23×C3—402no—
374C23×C3C2×D2011yescharacteristic
375C23×C3C2×D2012yes—
376C23×C3C2×D2011yescharacteristic
377C23×C3D4×D512yes—
378C23×C3D4×D512yes—
379C23×C3C23×D511yescharacteristic
380C3×Q8—104no—
381C3×D4—24no—
382C3×D4—24no—
383C3×D4—104no—
384C3×D4—108no—
385C3×D4—104no—
386C3×D4—104no—
387C3×D4—104no—
388C3×D4—104no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—54no—
392C2×C3×C4—108no—
393C2×C3×C4—104no—
394C2×C3×C4—102no—
395C2×C3×C4—102no—
396C2×C3×C4C2×D2012yes—
397C2×Dic3—24no—
398C2×Dic3—44no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401C2×Dic3—104no—
402C2×Dic3—202no—
403C2×Dic3—201no—
404C2×Dic3—202no—
405C2×Dic3—201no—
406C22×C5—22no—
407C22×C5—24no—
408C22×C5—22no—
409C22×C5—41no—
410C22×C5—42no—
411C22×C5—41no—
412C22×C5—42no—
413C22×C5—42no—
414C22×C5—81no—
415C22×C5#95312yes—
416C22×C5#95311yescharacteristic
417C22×C5#95311yescharacteristic
418C22×C5C22×#6711yescharacteristic
419C22×C5C22×#6712yes—
420C2×D5—24no—
421C2×D5—44no—
422C2×D5—44no—
423C2×D5—82no—
424C2×D5—84no—
425C4×C5—22no—
426C4×C5—124no—
427Dic5—24no—
428Dic5—122no—
429Dic5—122no—
430C24—52no—
431C24—101no—
432C24#120211yescharacteristic
433C24C2×D3×D511yescharacteristic
434#41—104no—
435#41—108no—
436#41—108no—
437#41—104no—
438C2×Q8—101no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—54no—
442C2×D4—54no—
443C2×D4—101no—
444C2×D4—108no—
445C2×D4—108no—
446C2×D4—102no—
447C2×D4—104no—
448C2×D4—102no—
449C2×D4—102no—
450C2×D4—104no—
451C2×D4—102no—
452C2×D4—102no—
453C2×D4#120212yes—
454C2×D4C2×D3×D512yes—
455C22×C4—52no—
456C22×C4—62no—
457C22×C4—102no—
458C22×C4—101no—
459C22×C4—152no—
460C22×C4—301no—
461C22×C4—301no—
462C22×C4—301no—
463C22×C4—302no—
464C22×C4—302no—
465C22×C4#120211yescharacteristic
466C4⋊C4—308no—
467C4⋊C4—304no—
468C22⋊C4—34no—
469C22⋊C4—62no—
470C22⋊C4—152no—
471C22⋊C4—308no—
472C22⋊C4—301no—
473C22⋊C4—304no—
474C3×C5C2×#45811yescharacteristic, complemented, Hall
475C22×C3—24no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—41no—
479C22×C3—42no—
480C22×C3—41no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—81no—
484C22×C3—104no—
485C22×C3—204no—
486C22×C3—204no—
487C22×C3—402no—
488C22×C3—404no—
489C22×C3#402811yescharacteristic
490C22×C3#402812yes—
491C22×C3#402811yescharacteristic
492C22×C3C22×D2011yescharacteristic
493C22×C3C2×D4×D512yes—
494C3×C4—22no—
495C3×C4—104no—
496Dic3—44no—
497Dic3—202no—
498Dic3—202no—
499C2×C5—21no—
500C2×C5—22no—
501C2×C5—22no—
502C2×C5—21no—
503C2×C5—42no—
504C2×C5#524312yescomplemented
505C2×C5C2×#95311yescharacteristic
506D5—44no—
507C23—21no—
508C23—21no—
509C23—42no—
510C23—42no—
511C23—54no—
512C23—104no—
513C23—102no—
514C23—102no—
515C23—204no—
516C23—402no—
517C23C2×#120211yescharacteristic
518C23C2×#120212yes—
519C23C2×#120211yescharacteristic
520C23D5×#6712yes—
521C23D5×#6712yes—
522C23C22×D3×D511yescharacteristic
523Q8—104no—
524D4—24no—
525D4—24no—
526D4—104no—
527D4—108no—
528D4—104no—
529D4—104no—
530D4—104no—
531D4—104no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—54no—
535C2×C4—64no—
536C2×C4—108no—
537C2×C4—104no—
538C2×C4—102no—
539C2×C4—102no—
540C2×C4—124no—
541C2×C4—302no—
542C2×C4—302no—
543C2×C4—304no—
544C2×C4—602no—
545C2×C4—601no—
546C2×C4—602no—
547C2×C4—601no—
548C2×C4C2×#120212yes—
549C2×C3—22no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—22no—
553C2×C3—42no—
554C2×C3—204no—
555C2×C3#6503112yescomplemented
556C2×C3C2×#402811yescharacteristic
557C5C2×#524311yescharacteristic, complemented, Sylow
558C22—24no—
559C22—22no—
560C22—22no—
561C22—41no—
562C22—42no—
563C22—41no—
564C22—42no—
565C22—42no—
566C22—81no—
567C22—104no—
568C22—204no—
569C22—204no—
570C22—402no—
571C22—404no—
572C22#9156411yescharacteristic
573C22#9156412yes—
574C22#9156411yescharacteristic
575C22C22×#120211yescharacteristic
576C22C2×D5×#6712yes—
577C4—22no—
578C4—104no—
579C4—124no—
580C4—602no—
581C4—602no—
582C3C2×#6503111yescharacteristic, complemented, Sylow
583C2—22no—
584C2—21no—
585C2—21no—
586C2—22no—
587C2—42no—
588C2—204no—
589C2#1174918212yesdirect product factor
590C2C2×#9156411yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC23×C3×C5C24
FrattiniC23C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5#120
prime radicalC2×C3×#4144C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#458
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91824C2semidirect
3. C2×#91537C2semidirect
4. C2×C5×#834C2semidirect
5. C2×#90995C2semidirect
6. #11749182C2direct (N × H)
9. C23×Dic15C22semidirect
19. C2×#6719C22semidirect
21. #91824C22semidirect
23. C2×C5×#217C22semidirect
26. #91537C22semidirect
28. C5×#834C22semidirect
29. #90995C22semidirect
51. C22×Dic15C23semidirect
75. #6719C23semidirect
78. C5×#217C23semidirect
86. C2×#834D5semidirect
165. C2×#217C2×D5semidirect
173. #834C2×D5semidirect
289. #217C22×D5semidirect
361. C2×C3×C5#458semidirect
474. C3×C5C2×#458semidirect
504. C2×C5#5243semidirect
555. C2×C3#65031semidirect
557. C5C2×#5243semidirect
582. C3C2×#65031semidirect
589. C2#11749182direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41442
C2×#918242
C2×#915372
C2×C5×#8342
C2×#909952
#117491822
C2×#650313
C2×#52435