Finite Group Databasebeta

← C2×#11752031 #14411953

Subgroups — C2×#11752031 #14411953

Order 1920.

1576 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6780C211yesmaximal, characteristic
2C2×#91923C212yesmaximal, complemented
3C2×#91240C211yesmaximal, characteristic, complemented
4C2×C3×#4011C211yesmaximal, characteristic, complemented
5#11752031C218yesmaximal, direct product factor
6C2×#91172C212yesmaximal, complemented
7C2×#65771—31nomaximal, Hall
8C23×Dic15C411yescharacteristic, complemented
9C22×C5×#67C411yescharacteristic, complemented
10C22×C3×C22⋊D5C2211yescharacteristic
11C22×#1204C411yescharacteristic, complemented
12C22×#1201C2211yescharacteristic
13C22×D3×Dic5C411yescharacteristic, complemented
14C2×#6780—22no—
15C2×#6780—24no—
16C2×#6780—22no—
17C2×#6780C414yescomplemented
18C2×#6780C2214yes—
19C22×D5×Dic3C2211yescharacteristic
20C2×#6763C2212yes—
21C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
22C2×Dic3⋊AGL(1,𝔽5)—22no—
23#91923—24no—
24#91923C2218yescomplemented
25C2×Dic3×AGL(1,𝔽5)—22no—
26#91240C2214yescomplemented
27C3×#4011C2214yescomplemented
28#91172C2218yescomplemented
29C2×#4740—51nomaximal, Hall
30C22×#711—31no—
31C2×#4130—32no—
32C2×#4011—31no—
33C2×#4011—32no—
34C2×#4011D311yescharacteristic, complemented
35#65771—38no—
36C24×C3×C5C2×C411yescharacteristic
37C23×C5×D3C2×C411yescharacteristic
38C23×C3×D5C2311yescharacteristic
39C22×ΓL(1,𝔽16)—22no—
40C22×C3×AGL(1,𝔽5)—22no—
41C22×Dic15—22no—
42C22×Dic15—21no—
43C22×Dic15—21no—
44C22×Dic15C2×C411yescharacteristic
45C22×Dic15C2×C411yescharacteristic
46C22×Dic15C2×C414yescomplemented
47C2×C5×#67—22no—
48C2×C5×#67—22no—
49C2×C5×#67C2×C414yescomplemented
50C22×C5×Dic3C2×C411yescharacteristic
51C2×C3×C22⋊D5—22no—
52C2×C3×C22⋊D5—22no—
53C2×C3×C22⋊D5C2×C412yes—
54C2×C3×C22⋊D5C2312yes—
55C22×C3×Dic5C2×C411yescharacteristic
56C2×#1204—22no—
57C2×#1204—22no—
58C2×#1204C2×C414yescomplemented
59C2×#1201—22no—
60C2×#1201—22no—
61C2×#1201C2×C412yes—
62C2×#1201C2312yes—
63C2×D3×Dic5—22no—
64C2×D3×Dic5—21no—
65C2×D3×Dic5—21no—
66C2×D3×Dic5C2×C414yescomplemented
67#6780—28no—
68#6780—28no—
69#6780—28no—
70#6780—28no—
71C2×D5×Dic3C2×C412yes—
72C2×D5×Dic3D412yes—
73C2×D5×Dic3D414yes—
74C2×D5×Dic3D412yes—
75C2×D5×Dic3C2312yes—
76#6763—22no—
77#6763C2314yes—
78C3×C22⋊AGL(1,𝔽5)—22no—
79C3×C22⋊AGL(1,𝔽5)C2314yes—
80Dic3⋊AGL(1,𝔽5)—28no—
81Dic3×AGL(1,𝔽5)—28no—
82C22×#237—51no—
83C2×#877—52no—
84C2×C3×#99—51no—
85C2×#834—51no—
86C2×#806—52no—
87#4740—58no—
88C22×C5×D4—31no—
89C22×C22⋊D5—31no—
90C22×C22⋊D5C2×D311yescharacteristic
91C23×Dic5—31no—
92C23×Dic5—31no—
93C2×#711—34no—
94C2×#711—34no—
95C2×#711—62no—
96C2×#711—62no—
97C2×#711—64no—
98C22×C4×D5—31no—
99C22×Dic10—31no—
100C2×C22⋊AGL(1,𝔽5)—32no—
101C2×C22⋊AGL(1,𝔽5)C2×D312yes—
102#4130—38no—
103#4130—64no—
104C2×C4⋊AGL(1,𝔽5)—62no—
105C2×C4×AGL(1,𝔽5)—62no—
106#4011—34no—
107#4011—38no—
108#4011C2×D314yescomplemented
109C2×#410—151noSylow
110C23×C3×C5—21no—
111C23×C3×C5—21no—
112C23×C3×C5—42no—
113C23×C3×C5C22×C411yescharacteristic
114C23×C3×C5C22×C412yes—
115C22×C5×D3—21no—
116C22×C5×D3—21no—
117C22×C5×D3—42no—
118C22×C5×D3C22×C412yes—
119C22×C3×D5—42no—
120C22×C3×D5C22×C411yescharacteristic
121C22×C3×D5C2×D412yes—
122C22×C3×D5C2×D412yes—
123C22×C3×D5C2411yescharacteristic
124C2×ΓL(1,𝔽16)—24no—
125C2×ΓL(1,𝔽16)—44no—
126C2×C3×AGL(1,𝔽5)—24no—
127C2×C3×AGL(1,𝔽5)—44no—
128C2×Dic15—21no—
129C2×Dic15—21no—
130C2×Dic15—24no—
131C2×Dic15—24no—
132C2×Dic15C22⋊C412yes—
133C2×Dic15C22⋊C411yescharacteristic
134C2×Dic15C22⋊C411yescharacteristic
135C2×Dic15C22×C412yes—
136C2×Dic15C22×C412yes—
137C5×#67—28no—
138C2×C5×Dic3C22⋊C412yes—
139C2×C5×Dic3C22⋊C412yes—
140C2×C5×Dic3C22×C412yes—
141C3×C22⋊D5—24no—
142C3×C22⋊D5—24no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5C22×C412yes—
146#1204—28no—
147#1201—24no—
148#1201—24no—
149D3×Dic5—24no—
150D3×Dic5—24no—
151D5×Dic3C22⋊C414yes—
152D5×Dic3C22⋊C414yes—
153D5×Dic3C2×D414yes—
154D5×Dic3C2×D414yes—
155C22×C3×D4—51no—
156C22×#67—51no—
157C22×#67AGL(1,𝔽5)11yescharacteristic, complemented
158C23×Dic3—51no—
159C23×Dic3—51no—
160C2×#237—54no—
161C2×#237—54no—
162C2×#237—104no—
163C2×#237—102no—
164C2×#237—102no—
165C22×C4×D3—51no—
166C22×Dic6—51no—
167C2×C3×C22⋊C4—52no—
168C2×#217—52no—
169C2×Dic3⋊C4—102no—
170C2×C4×Dic3—102no—
171#877—58no—
172#877—104no—
173C3×#99—54no—
174#834—54no—
175#806—58no—
176C24×C5—31no—
177C24×C5C4×D311yescharacteristic
178C23×D5C22×D311yescharacteristic
179C22×AGL(1,𝔽5)—22no—
180C22×AGL(1,𝔽5)—62no—
181C2×C5×D4—34no—
182C2×C5×D4—62no—
183C2×C5×D4—62no—
184C22×C4×C5—31no—
185C2×C22⋊D5—22no—
186C2×C22⋊D5—22no—
187C2×C22⋊D5—32no—
188C2×C22⋊D5—32no—
189C2×C22⋊D5—62no—
190C2×C22⋊D5—62no—
191C2×C22⋊D5C4×D312yes—
192C2×C22⋊D5C22×D312yes—
193C22×Dic5—31no—
194C22×Dic5—31no—
195C22×Dic5—34no—
196C22×Dic5—34no—
197C22×Dic5—62no—
198C22×Dic5—61no—
199C22×Dic5—61no—
200C22×Dic5—62no—
201C22×Dic5—61no—
202C22×Dic5—61no—
203C22×Dic5C4×D311yescharacteristic
204#711—68no—
205#711—68no—
206#711—68no—
207#711—68no—
208C2×C4×D5—32no—
209C2×C4×D5—32no—
210C2×C4×D5—32no—
211C2×C4×D5—34no—
212C2×C4×D5—32no—
213C2×Dic10—34no—
214C2×Dic10—62no—
215C2×Dic10—62no—
216C22⋊AGL(1,𝔽5)—22no—
217C22⋊AGL(1,𝔽5)—34no—
218C22⋊AGL(1,𝔽5)—62no—
219C22⋊AGL(1,𝔽5)C22×D314yes—
220C4⋊AGL(1,𝔽5)—68no—
221C4×AGL(1,𝔽5)—68no—
222C22×#41—151no—
223C2×#117—152no—
224#410—158no—
225C2×#99—51no—
226C2×#99—152no—
227C2×#99—151no—
228C22×C3×C5—22no—
229C22×C3×C5—22no—
230C22×C3×C5—42no—
231C22×C3×C5—42no—
232C22×C3×C5—42no—
233C22×C3×C5C2×C22⋊C411yescharacteristic
234C22×C3×C5C2×C22⋊C411yescharacteristic
235C22×C3×C5C23×C411yescharacteristic
236C2×C5×D3—22no—
237C2×C5×D3—42no—
238C2×C5×D3—42no—
239C2×C5×D3—42no—
240C2×C3×D5—24no—
241C2×C3×D5—41no—
242C2×C3×D5—42no—
243C2×C3×D5—41no—
244C2×C3×D5C2×C22⋊C412yes—
245C2×C3×D5C22×D412yes—
246ΓL(1,𝔽16)—44no—
247C3×AGL(1,𝔽5)—44no—
248Dic15—22no—
249Dic15C2×C22⋊C412yes—
250Dic15C2×C22⋊C412yes—
251C3×Dic5—22no—
252C5×Dic3C2×C22⋊C414yes—
253C24×C3—51no—
254C24×C3C2×AGL(1,𝔽5)11yescharacteristic
255C23×D3C2×AGL(1,𝔽5)11yescharacteristic
256C2×C3×D4—52no—
257C2×C3×D4—52no—
258C2×C3×D4—102no—
259C2×C3×D4—102no—
260C22×C3×C4—51no—
261C22×C3×C4—102no—
262C2×#67—22no—
263C2×#67—22no—
264C2×#67—52no—
265C2×#67—52no—
266C2×#67—102no—
267C2×#67—102no—
268C2×#67C2×AGL(1,𝔽5)14yescomplemented
269C22×Dic3—51no—
270C22×Dic3—54no—
271C22×Dic3—52no—
272C22×Dic3—52no—
273C22×Dic3—52no—
274C22×Dic3—52no—
275C22×Dic3—51no—
276C22×Dic3—54no—
277C22×Dic3—102no—
278C22×Dic3—101no—
279C22×Dic3—101no—
280C22×Dic3—102no—
281C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
282#237—108no—
283#237—108no—
284#237—108no—
285#237—108no—
286C2×C4×D3—54no—
287C2×C4×D3—102no—
288C2×C4×D3—101no—
289C2×C4×D3—101no—
290C2×Dic6—54no—
291C2×Dic6—102no—
292C2×Dic6—102no—
293C3×C22⋊C4—54no—
294C3×C22⋊C4—102no—
295#217—54no—
296#217—102no—
297Dic3⋊C4—108no—
298C4×Dic3—108no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—32no—
302C23×C5—42no—
303C23×C5—61no—
304C23×C5—61no—
305C23×C5—122no—
306C23×C5C2×C4×D312yes—
307C23×C5C2×C4×D311yescharacteristic
308C22×D5—42no—
309C22×D5C2×C4×D311yescharacteristic
310C22×D5D3×D412yes—
311C22×D5D3×D412yes—
312C22×D5C23×D311yescharacteristic
313C2×AGL(1,𝔽5)—24no—
314C2×AGL(1,𝔽5)—44no—
315C2×AGL(1,𝔽5)—64no—
316C2×AGL(1,𝔽5)—124no—
317C5×D4—68no—
318C2×C4×C5—32no—
319C2×C4×C5—32no—
320C2×C4×C5—32no—
321C22⋊D5—24no—
322C22⋊D5—24no—
323C22⋊D5—64no—
324C22⋊D5—64no—
325C2×Dic5—21no—
326C2×Dic5—21no—
327C2×Dic5—32no—
328C2×Dic5—31no—
329C2×Dic5—31no—
330C2×Dic5—32no—
331C2×Dic5—32no—
332C2×Dic5—64no—
333C2×Dic5—64no—
334C2×Dic5—64no—
335C2×Dic5—64no—
336C2×Dic5—61no—
337C2×Dic5—61no—
338C2×Dic5C2×C4×D312yes—
339C4×D5—34no—
340C4×D5—34no—
341C4×D5—34no—
342C4×D5—34no—
343Dic10—68no—
344C2×#41—154no—
345C2×#41—154no—
346C2×#41—302no—
347C2×#41—302no—
348C2×#41—304no—
349C22×Q8—151no—
350C22×D4—31no—
351C22×D4—51no—
352C22×D4—151no—
353C23×C4—151no—
354C23×C4—151no—
355C23×C4—151no—
356#117—158no—
357#117—304no—
358C2×C4⋊C4—302no—
359C2×C22⋊C4—52no—
360C2×C22⋊C4—152no—
361C2×C42—302no—
362#99—54no—
363#99—158no—
364#99—154no—
365C2×C3×C5—21no—
366C2×C3×C5—21no—
367C2×C3×C5—42no—
368C2×C3×C5#41012yescomplemented
369C2×C3×C5C22×C22⋊C411yescharacteristic
370C3×D5—22no—
371C3×D5—22no—
372C5×D3—42no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—42no—
376C23×C3—52no—
377C23×C3—52no—
378C23×C3—51no—
379C23×C3—51no—
380C23×C3—202no—
381C23×C3C22×AGL(1,𝔽5)12yes—
382C23×C3C22×AGL(1,𝔽5)11yescharacteristic
383C22×D3—21no—
384C22×D3—21no—
385C22×D3—42no—
386C22×D3C22×AGL(1,𝔽5)12yes—
387C3×D4—104no—
388C3×D4—104no—
389C2×C3×C4—52no—
390C2×C3×C4—101no—
391C2×C3×C4—101no—
392C2×C3×C4—104no—
393C2×C3×C4—204no—
394#67—28no—
395#67—104no—
396#67—104no—
397C2×Dic3—52no—
398C2×Dic3—51no—
399C2×Dic3—51no—
400C2×Dic3—52no—
401C2×Dic3—54no—
402C2×Dic3—54no—
403C2×Dic3—54no—
404C2×Dic3—54no—
405C2×Dic3—52no—
406C2×Dic3—104no—
407C2×Dic3—104no—
408C2×Dic3—101no—
409C2×Dic3—101no—
410C2×Dic3—104no—
411C2×Dic3—204no—
412C2×Dic3C22⋊AGL(1,𝔽5)12yes—
413C2×Dic3C22⋊AGL(1,𝔽5)12yes—
414C2×Dic3C22×AGL(1,𝔽5)12yes—
415C4×D3—104no—
416C4×D3—104no—
417Dic6—108no—
418C22×C5—22no—
419C22×C5—22no—
420C22×C5—42no—
421C22×C5—42no—
422C22×C5—42no—
423C22×C5—62no—
424C22×C5—122no—
425C22×C5—122no—
426C22×C5—122no—
427C22×C5D3×C22⋊C411yescharacteristic
428C22×C5D3×C22⋊C411yescharacteristic
429C22×C5C22×C4×D311yescharacteristic
430C2×D5—24no—
431C2×D5—41no—
432C2×D5—42no—
433C2×D5—41no—
434C2×D5D3×C22⋊C412yes—
435C2×D5C2×D3×D412yes—
436AGL(1,𝔽5)—44no—
437AGL(1,𝔽5)—124no—
438C4×C5—34no—
439Dic5—22no—
440Dic5—32no—
441Dic5—32no—
442Dic5—62no—
443C24—31no—
444C24—51no—
445C24D3×AGL(1,𝔽5)11yescharacteristic
446#41—308no—
447#41—308no—
448#41—308no—
449#41—308no—
450C2×Q8—154no—
451C2×Q8—302no—
452C2×Q8—302no—
453C2×D4—34no—
454C2×D4—52no—
455C2×D4—52no—
456C2×D4—62no—
457C2×D4—62no—
458C2×D4—102no—
459C2×D4—102no—
460C2×D4—152no—
461C2×D4—152no—
462C2×D4—302no—
463C2×D4—302no—
464C22×C4—31no—
465C22×C4—51no—
466C22×C4—102no—
467C22×C4—152no—
468C22×C4—152no—
469C22×C4—152no—
470C22×C4—154no—
471C22×C4—152no—
472C22×C4—154no—
473C22×C4—151no—
474C22×C4—154no—
475C22×C4—151no—
476C22×C4—302no—
477C22×C4—301no—
478C22×C4—301no—
479C22×C4—302no—
480C22×C4—301no—
481C22×C4—301no—
482C22×C4—302no—
483C4⋊C4—308no—
484C22⋊C4—54no—
485C22⋊C4—102no—
486C22⋊C4—154no—
487C22⋊C4—302no—
488C42—308no—
489C3×C5C2×#41011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—52no—
496C22×C3—52no—
497C22×C3—104no—
498C22×C3—202no—
499C22×C3—201no—
500C22×C3—201no—
501C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
502C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
503C22×C3C23×AGL(1,𝔽5)11yescharacteristic
504C2×D3—22no—
505C2×D3—42no—
506C2×D3—42no—
507C2×D3—42no—
508C3×C4—102no—
509C3×C4—204no—
510Dic3—52no—
511Dic3—52no—
512Dic3—102no—
513Dic3—204no—
514Dic3C2×C22⋊AGL(1,𝔽5)14yes—
515C2×C5—21no—
516C2×C5—21no—
517C2×C5—42no—
518C2×C5—122no—
519C2×C5#474012yescomplemented
520C2×C5C2×D3×C22⋊C411yescharacteristic
521D5—22no—
522D5—22no—
523C23—21no—
524C23—21no—
525C23—32no—
526C23—42no—
527C23—52no—
528C23—52no—
529C23—51no—
530C23—51no—
531C23—61no—
532C23—61no—
533C23—122no—
534C23—202no—
535C23C2×D3×AGL(1,𝔽5)12yes—
536C23C2×D3×AGL(1,𝔽5)11yescharacteristic
537Q8—308no—
538D4—68no—
539D4—104no—
540D4—104no—
541D4—304no—
542D4—304no—
543C2×C4—32no—
544C2×C4—32no—
545C2×C4—32no—
546C2×C4—52no—
547C2×C4—101no—
548C2×C4—101no—
549C2×C4—104no—
550C2×C4—154no—
551C2×C4—154no—
552C2×C4—154no—
553C2×C4—154no—
554C2×C4—152no—
555C2×C4—151no—
556C2×C4—151no—
557C2×C4—152no—
558C2×C4—152no—
559C2×C4—204no—
560C2×C4—304no—
561C2×C4—304no—
562C2×C4—304no—
563C2×C4—304no—
564C2×C4—301no—
565C2×C4—301no—
566C2×C4—304no—
567C2×C4—604no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—42no—
571C2×C3—102no—
572C2×C3—102no—
573C2×C3#6577112yescomplemented
574C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
575D3—42no—
576C5C2×#474011yescharacteristic, complemented, Sylow
577C22—22no—
578C22—22no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—52no—
583C22—52no—
584C22—62no—
585C22—104no—
586C22—122no—
587C22—122no—
588C22—122no—
589C22—202no—
590C22—201no—
591C22—201no—
592C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
593C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
594C22C22×D3×AGL(1,𝔽5)11yescharacteristic
595C4—34no—
596C4—102no—
597C4—152no—
598C4—152no—
599C4—204no—
600C4—302no—
601C4—604no—
602C3C2×#6577111yescharacteristic, complemented, Sylow
603C2—21no—
604C2—21no—
605C2—42no—
606C2—102no—
607C2—102no—
608C2—122no—
609C2#1175203112yesdirect product factor
610C2C2×D3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC22×C3×C5C23×C4
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC24×C3×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#6780C2
cosocleC22×C3×D5C24
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#410
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×#91923C2semidirect
3. C2×#91240C2semidirect
4. C2×C3×#4011C2semidirect
5. #11752031C2direct (N × H)
6. C2×#91172C2semidirect
8. C23×Dic15C4semidirect
9. C22×C5×#67C4semidirect
11. C22×#1204C4semidirect
13. C22×D3×Dic5C4semidirect
17. C2×#6780C4semidirect
24. #91923C22semidirect
26. #91240C22semidirect
27. C3×#4011C22semidirect
28. #91172C22semidirect
34. C2×#4011D3semidirect
46. C22×Dic15C2×C4semidirect
49. C2×C5×#67C2×C4semidirect
58. C2×#1204C2×C4semidirect
66. C2×D3×Dic5C2×C4semidirect
108. #4011C2×D3semidirect
157. C22×#67AGL(1,𝔽5)semidirect
268. C2×#67C2×AGL(1,𝔽5)semidirect
368. C2×C3×C5#410semidirect
489. C3×C5C2×#410semidirect
519. C2×C5#4740semidirect
573. C2×C3#65771semidirect
576. C5C2×#4740semidirect
602. C3C2×#65771semidirect
609. C2#11752031direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67802
C2×#919232
C2×#912402
C2×C3×#40112
#117520312
C2×#911722
C2×#657713
C2×#47405