Finite Group Databasebeta

← C2×#11749172 #14411944

Subgroups — C2×#11749172 #14411944

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×C3×#711C211yesmaximal, characteristic
2C2×#91528C212yesmaximal, complemented
3C2×#91118C211yesmaximal, characteristic, complemented
4C2×C5×#834C211yesmaximal, characteristic, complemented
5C2×#90995C212yesmaximal, complemented
6#11749172C218yesmaximal, direct product factor
7C2×#65029—31nomaximal, Hall
8C22×C3×C5×D4C2211yescharacteristic
9C22×C3×C22⋊D5C411yescharacteristic, complemented
10C22×C3×C22⋊D5C2211yescharacteristic
11C23×C3×Dic5C411yescharacteristic, complemented
12C23×C3×Dic5C2211yescharacteristic
13C2×C3×#711—22no—
14C2×C3×#711—24no—
15C2×C3×#711—22no—
16C2×C3×#711C414yescomplemented
17C2×C3×#711C2214yes—
18C22×C3×C4×D5C411yescharacteristic, complemented
19C22×C3×Dic10C411yescharacteristic, complemented
20C2×#6719C2212yes—
21C2×C5×#217C2212yes—
22C2×#6668—22no—
23#91528—24no—
24#91528C2218yescomplemented
25C2×Dic3×Dic5—22no—
26#91118C2214yescomplemented
27C5×#834C2214yescomplemented
28#90995C2218yescomplemented
29C2×#5240—51nomaximal, Hall
30C22×#711D311yescharacteristic
31C2×#4023—32no—
32C2×C5×#99—31no—
33C2×#3966—31no—
34C2×#3938—32no—
35#65029—38no—
36C24×C3×C5C2×C411yescharacteristic
37C24×C3×C5C2311yescharacteristic
38C23×C3×D5C2×C411yescharacteristic
39C2×C3×C5×D4—22no—
40C2×C3×C5×D4—22no—
41C2×C3×C5×D4C2×C412yes—
42C2×C3×C5×D4C2312yes—
43C22×C3×C4×C5C2×C411yescharacteristic
44C22×Dic15—22no—
45C22×C5×Dic3—22no—
46C2×C3×C22⋊D5—22no—
47C2×C3×C22⋊D5—22no—
48C2×C3×C22⋊D5—22no—
49C2×C3×C22⋊D5—22no—
50C2×C3×C22⋊D5C2×C412yes—
51C2×C3×C22⋊D5C2×C414yescomplemented
52C2×C3×C22⋊D5C2312yes—
53C22×C3×Dic5—22no—
54C22×C3×Dic5—21no—
55C22×C3×Dic5—21no—
56C22×C3×Dic5C2×C411yescharacteristic
57C22×C3×Dic5C2×C411yescharacteristic
58C22×C3×Dic5C2×C411yescharacteristic
59C22×C3×Dic5C2×C412yes—
60C22×C3×Dic5C2×C414yescomplemented
61C22×C3×Dic5D412yes—
62C22×C3×Dic5D414yes—
63C22×C3×Dic5D412yes—
64C22×C3×Dic5C2312yes—
65C3×#711—28no—
66C3×#711—28no—
67C3×#711—28no—
68C3×#711—28no—
69C2×C3×C4×D5—22no—
70C2×C3×C4×D5—21no—
71C2×C3×C4×D5—21no—
72C2×C3×C4×D5C2×C414yescomplemented
73C2×C3×Dic10—22no—
74C2×C3×Dic10—22no—
75C2×C3×Dic10C2×C414yescomplemented
76#6719—22no—
77#6719C2314yes—
78C5×#217—22no—
79C5×#217C2314yes—
80#6668—28no—
81Dic3×Dic5—28no—
82C22×C3×#41—51no—
83C2×#926—52no—
84#5240—58no—
85C2×#834—51no—
86C2×#834—52no—
87C2×#834D511yescharacteristic, complemented
88C22×C5×D4C2×D311yescharacteristic
89C22×C22⋊D5Dic311yescharacteristic, complemented
90C22×C22⋊D5C2×D311yescharacteristic
91C23×Dic5Dic311yescharacteristic, complemented
92C23×Dic5C2×D311yescharacteristic
93C2×#711—24no—
94C2×#711—22no—
95C2×#711—22no—
96C2×#711Dic314yescomplemented
97C2×#711C2×D314yes—
98C22×C4×D5Dic311yescharacteristic, complemented
99C22×Dic10Dic311yescharacteristic, complemented
100C2×C5×C22⋊C4—32no—
101C2×C22⋊Dic5—32no—
102C2×#683—62no—
103C2×C4×Dic5—62no—
104#4023—38no—
105#4023—64no—
106C5×#99—34no—
107#3966—34no—
108#3938—38no—
109C2×#410—151noSylow
110C23×C3×C5—21no—
111C23×C3×C5—21no—
112C23×C3×C5—42no—
113C23×C3×C5—42no—
114C23×C3×C5C22×C411yescharacteristic
115C23×C3×C5C22×C412yes—
116C23×C3×C5C22×C411yescharacteristic
117C23×C3×C5C2×D412yes—
118C23×C3×C5C2×D412yes—
119C23×C3×C5C2411yescharacteristic
120C22×C3×D5—21no—
121C22×C3×D5—21no—
122C22×C3×D5—42no—
123C22×C3×D5C22×C412yes—
124C3×C5×D4—24no—
125C3×C5×D4—24no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5C22×C412yes—
129C2×Dic15—24no—
130C2×Dic15—44no—
131C2×C5×Dic3—24no—
132C2×C5×Dic3—44no—
133C3×C22⋊D5—24no—
134C3×C22⋊D5—24no—
135C3×C22⋊D5—28no—
136C2×C3×Dic5—21no—
137C2×C3×Dic5—21no—
138C2×C3×Dic5—24no—
139C2×C3×Dic5—24no—
140C2×C3×Dic5C22⋊C412yes—
141C2×C3×Dic5C22⋊C412yes—
142C2×C3×Dic5C22⋊C412yes—
143C2×C3×Dic5C22⋊C411yescharacteristic
144C2×C3×Dic5C22⋊C411yescharacteristic
145C2×C3×Dic5C22⋊C414yes—
146C2×C3×Dic5C22⋊C414yes—
147C2×C3×Dic5C22×C412yes—
148C2×C3×Dic5C22×C412yes—
149C2×C3×Dic5C22×C412yes—
150C2×C3×Dic5C2×D414yes—
151C2×C3×Dic5C2×D414yes—
152C3×C4×D5—24no—
153C3×C4×D5—24no—
154C3×Dic10—28no—
155C2×C3×#41—54no—
156C2×C3×#41—54no—
157C2×C3×#41—102no—
158C2×C3×#41—102no—
159C2×C3×#41—104no—
160C22×C3×Q8—51no—
161C22×C3×D4—51no—
162C22×C3×D4—51no—
163C22×C3×D4C2×D511yescharacteristic
164C23×C3×C4—51no—
165C23×C3×C4—51no—
166C23×C3×C4—51no—
167C2×#217—52no—
168C2×#217C2×D512yes—
169#926—58no—
170#926—104no—
171C2×C4⋊Dic3—102no—
172C2×C4×Dic3—102no—
173#834—54no—
174#834—58no—
175#834C2×D514yescomplemented
176C24×C5C2×Dic311yescharacteristic
177C24×C5C22×D311yescharacteristic
178C23×D5C2×Dic311yescharacteristic
179C2×C5×D4—22no—
180C2×C5×D4—22no—
181C2×C5×D4C2×Dic312yes—
182C2×C5×D4C22×D312yes—
183C22×C4×C5—62no—
184C22×C4×C5C2×Dic311yescharacteristic
185C2×C22⋊D5—22no—
186C2×C22⋊D5—22no—
187C2×C22⋊D5—22no—
188C2×C22⋊D5—22no—
189C2×C22⋊D5C2×Dic312yes—
190C2×C22⋊D5C2×Dic314yescomplemented
191C2×C22⋊D5C22×D312yes—
192C22×Dic5—22no—
193C22×Dic5—21no—
194C22×Dic5—21no—
195C22×Dic5—62no—
196C22×Dic5C2×Dic311yescharacteristic
197C22×Dic5C2×Dic311yescharacteristic
198C22×Dic5C2×Dic311yescharacteristic
199C22×Dic5C2×Dic312yes—
200C22×Dic5C2×Dic314yescomplemented
201C22×Dic5#6714yes—
202C22×Dic5#6712yes—
203C22×Dic5#6712yes—
204C22×Dic5C22×D312yes—
205#711—28no—
206#711—28no—
207#711—28no—
208#711—28no—
209C2×C4×D5—22no—
210C2×C4×D5—21no—
211C2×C4×D5—21no—
212C2×C4×D5C2×Dic314yescomplemented
213C2×Dic10—22no—
214C2×Dic10—22no—
215C2×Dic10C2×Dic314yescomplemented
216C5×C22⋊C4—34no—
217C5×C22⋊C4—62no—
218C22⋊Dic5—34no—
219C22⋊Dic5—62no—
220#683—68no—
221C4×Dic5—68no—
222C22×#41—51no—
223C2×#117—152no—
224#410—158no—
225C2×#99—31no—
226C2×#99—152no—
227C2×#99—151no—
228C22×C3×C5—24no—
229C22×C3×C5—22no—
230C22×C3×C5—22no—
231C22×C3×C5—41no—
232C22×C3×C5—42no—
233C22×C3×C5—41no—
234C22×C3×C5—42no—
235C22×C3×C5—42no—
236C22×C3×C5—42no—
237C22×C3×C5C2×C22⋊C411yescharacteristic
238C22×C3×C5C2×C22⋊C412yes—
239C22×C3×C5C2×C22⋊C411yescharacteristic
240C22×C3×C5C23×C411yescharacteristic
241C22×C3×C5C22×D412yes—
242C2×C3×D5—22no—
243C2×C3×D5—42no—
244C2×C3×D5—42no—
245C2×C3×D5—42no—
246C3×C4×C5—22no—
247Dic15—44no—
248C3×Dic5—22no—
249C3×Dic5C2×C22⋊C414yes—
250C3×Dic5C2×C22⋊C412yes—
251C3×Dic5C2×C22⋊C412yes—
252C5×Dic3—44no—
253C24×C3—51no—
254C24×C3C4×D511yescharacteristic
255C24×C3C22×D511yescharacteristic
256C3×#41—108no—
257C3×#41—108no—
258C3×#41—108no—
259C3×#41—108no—
260C2×C3×Q8—54no—
261C2×C3×Q8—102no—
262C2×C3×Q8—102no—
263C2×C3×D4—22no—
264C2×C3×D4—22no—
265C2×C3×D4—52no—
266C2×C3×D4—54no—
267C2×C3×D4—52no—
268C2×C3×D4—102no—
269C2×C3×D4—102no—
270C2×C3×D4—102no—
271C2×C3×D4—102no—
272C2×C3×D4C4×D512yes—
273C2×C3×D4C22×D512yes—
274C22×C3×C4—51no—
275C22×C3×C4—51no—
276C22×C3×C4—52no—
277C22×C3×C4—52no—
278C22×C3×C4—52no—
279C22×C3×C4—54no—
280C22×C3×C4—52no—
281C22×C3×C4—51no—
282C22×C3×C4—54no—
283C22×C3×C4—54no—
284C22×C3×C4—102no—
285C22×C3×C4—101no—
286C22×C3×C4—101no—
287C22×C3×C4—102no—
288C22×C3×C4—101no—
289C22×C3×C4—101no—
290C22×C3×C4C4×D511yescharacteristic
291C22×Dic3—22no—
292C22×Dic3—102no—
293#217—22no—
294#217—54no—
295#217—102no—
296#217C22×D514yes—
297C4⋊Dic3—108no—
298C4×Dic3—108no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—42no—
302C23×C5—42no—
303C23×C5C22×Dic311yescharacteristic
304C23×C5C22×Dic312yes—
305C23×C5C22×Dic311yescharacteristic
306C23×C5C2×#6712yes—
307C23×C5C2×#6712yes—
308C23×C5C23×D311yescharacteristic
309C22×D5—21no—
310C22×D5—21no—
311C22×D5—42no—
312C22×D5C22×Dic312yes—
313C5×D4—24no—
314C5×D4—24no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—64no—
318C2×C4×C5—124no—
319C2×C4×C5C22×Dic312yes—
320C22⋊D5—24no—
321C22⋊D5—24no—
322C22⋊D5—28no—
323C2×Dic5—21no—
324C2×Dic5—21no—
325C2×Dic5—24no—
326C2×Dic5—24no—
327C2×Dic5—64no—
328C2×Dic5—124no—
329C2×Dic5#21712yes—
330C2×Dic5#21712yes—
331C2×Dic5#21712yes—
332C2×Dic5#21711yescharacteristic
333C2×Dic5#21711yescharacteristic
334C2×Dic5#21714yes—
335C2×Dic5#21714yes—
336C2×Dic5C22×Dic312yes—
337C2×Dic5C22×Dic312yes—
338C2×Dic5C22×Dic312yes—
339C2×Dic5C2×#6714yes—
340C2×Dic5C2×#6714yes—
341C4×D5—24no—
342C4×D5—24no—
343Dic10—28no—
344C2×#41—54no—
345C2×#41—54no—
346C2×#41—102no—
347C2×#41—102no—
348C2×#41—104no—
349C22×Q8—51no—
350C22×D4—51no—
351C22×D4—51no—
352C22×D4D3×D511yescharacteristic
353C23×C4—51no—
354C23×C4—51no—
355C23×C4—51no—
356#117—158no—
357#117—304no—
358C2×C4⋊C4—302no—
359C2×C22⋊C4—32no—
360C2×C22⋊C4—152no—
361C2×C42—302no—
362#99—34no—
363#99—158no—
364#99—154no—
365C2×C3×C5—22no—
366C2×C3×C5—21no—
367C2×C3×C5—21no—
368C2×C3×C5—22no—
369C2×C3×C5—42no—
370C2×C3×C5#41012yescomplemented
371C2×C3×C5C22×C22⋊C411yescharacteristic
372C3×D5—42no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—52no—
378C23×C3—101no—
379C23×C3—101no—
380C23×C3—202no—
381C23×C3C2×C4×D511yescharacteristic
382C23×C3C2×C4×D512yes—
383C23×C3C2×C4×D511yescharacteristic
384C23×C3D4×D512yes—
385C23×C3D4×D512yes—
386C23×C3C23×D511yescharacteristic
387C3×Q8—108no—
388C3×D4—24no—
389C3×D4—24no—
390C3×D4—108no—
391C3×D4—104no—
392C3×D4—104no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—52no—
396C2×C3×C4—52no—
397C2×C3×C4—54no—
398C2×C3×C4—54no—
399C2×C3×C4—52no—
400C2×C3×C4—51no—
401C2×C3×C4—51no—
402C2×C3×C4—52no—
403C2×C3×C4—52no—
404C2×C3×C4—54no—
405C2×C3×C4—54no—
406C2×C3×C4—52no—
407C2×C3×C4—104no—
408C2×C3×C4—104no—
409C2×C3×C4—104no—
410C2×C3×C4—104no—
411C2×C3×C4—101no—
412C2×C3×C4—101no—
413C2×C3×C4C2×C4×D512yes—
414C2×Dic3—24no—
415C2×Dic3—44no—
416C2×Dic3—104no—
417C2×Dic3—204no—
418C22×C5—24no—
419C22×C5—22no—
420C22×C5—22no—
421C22×C5—41no—
422C22×C5—42no—
423C22×C5—41no—
424C22×C5—42no—
425C22×C5—42no—
426C22×C5—42no—
427C22×C5C2×#21711yescharacteristic
428C22×C5C2×#21712yes—
429C22×C5C2×#21711yescharacteristic
430C22×C5C23×Dic311yescharacteristic
431C22×C5C22×#6712yes—
432C2×D5—22no—
433C2×D5—42no—
434C2×D5—42no—
435C2×D5—42no—
436C4×C5—22no—
437C4×C5—124no—
438Dic5—22no—
439Dic5—124no—
440Dic5C2×#21714yes—
441Dic5C2×#21712yes—
442Dic5C2×#21712yes—
443C24—51no—
444C24D5×Dic311yescharacteristic
445C24C2×D3×D511yescharacteristic
446#41—108no—
447#41—108no—
448#41—108no—
449#41—108no—
450C2×Q8—54no—
451C2×Q8—102no—
452C2×Q8—102no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—52no—
456C2×D4—54no—
457C2×D4—52no—
458C2×D4—102no—
459C2×D4—102no—
460C2×D4—102no—
461C2×D4—102no—
462C2×D4D5×Dic312yes—
463C2×D4C2×D3×D512yes—
464C22×C4—51no—
465C22×C4—51no—
466C22×C4—52no—
467C22×C4—52no—
468C22×C4—52no—
469C22×C4—54no—
470C22×C4—52no—
471C22×C4—51no—
472C22×C4—54no—
473C22×C4—54no—
474C22×C4—62no—
475C22×C4—102no—
476C22×C4—101no—
477C22×C4—101no—
478C22×C4—102no—
479C22×C4—101no—
480C22×C4—101no—
481C22×C4—302no—
482C22×C4D5×Dic311yescharacteristic
483C4⋊C4—308no—
484C22⋊C4—34no—
485C22⋊C4—62no—
486C22⋊C4—154no—
487C22⋊C4—302no—
488C42—308no—
489C3×C5C2×#41011yescharacteristic, complemented, Hall
490C22×C3—24no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—41no—
494C22×C3—42no—
495C22×C3—41no—
496C22×C3—42no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3—102no—
500C22×C3—202no—
501C22×C3—202no—
502C22×C3—202no—
503C22×C3D5×C22⋊C411yescharacteristic
504C22×C3D5×C22⋊C412yes—
505C22×C3D5×C22⋊C411yescharacteristic
506C22×C3C22×C4×D511yescharacteristic
507C22×C3C2×D4×D512yes—
508C3×C4—22no—
509C3×C4—52no—
510C3×C4—52no—
511C3×C4—54no—
512C3×C4—102no—
513Dic3—44no—
514Dic3—204no—
515C2×C5—22no—
516C2×C5—21no—
517C2×C5—21no—
518C2×C5—22no—
519C2×C5—42no—
520C2×C5#524012yescomplemented
521C2×C5C22×#21711yescharacteristic
522D5—42no—
523C23—21no—
524C23—21no—
525C23—42no—
526C23—42no—
527C23—52no—
528C23—101no—
529C23—101no—
530C23—202no—
531C23C2×D5×Dic311yescharacteristic
532C23C2×D5×Dic312yes—
533C23C2×D5×Dic311yescharacteristic
534C23D5×#6712yes—
535C23D5×#6712yes—
536C23C22×D3×D511yescharacteristic
537Q8—108no—
538D4—24no—
539D4—24no—
540D4—108no—
541D4—104no—
542D4—104no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—52no—
546C2×C4—52no—
547C2×C4—54no—
548C2×C4—54no—
549C2×C4—52no—
550C2×C4—52no—
551C2×C4—54no—
552C2×C4—54no—
553C2×C4—51no—
554C2×C4—51no—
555C2×C4—52no—
556C2×C4—52no—
557C2×C4—64no—
558C2×C4—104no—
559C2×C4—104no—
560C2×C4—104no—
561C2×C4—104no—
562C2×C4—101no—
563C2×C4—101no—
564C2×C4—124no—
565C2×C4—304no—
566C2×C4—604no—
567C2×C4C2×D5×Dic312yes—
568C2×C3—22no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—22no—
572C2×C3—42no—
573C2×C3—202no—
574C2×C3#6502912yescomplemented
575C2×C3C2×D5×C22⋊C411yescharacteristic
576C5C2×#524011yescharacteristic, complemented, Sylow
577C22—24no—
578C22—22no—
579C22—22no—
580C22—41no—
581C22—42no—
582C22—41no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—102no—
587C22—202no—
588C22—202no—
589C22—202no—
590C22D5×#21711yescharacteristic
591C22D5×#21712yes—
592C22D5×#21711yescharacteristic
593C22C22×D5×Dic311yescharacteristic
594C22C2×D5×#6712yes—
595C4—22no—
596C4—52no—
597C4—52no—
598C4—54no—
599C4—102no—
600C4—124no—
601C4—604no—
602C3C2×#6502911yescharacteristic, complemented, Sylow
603C2—22no—
604C2—21no—
605C2—21no—
606C2—22no—
607C2—42no—
608C2—202no—
609C2#1174917212yesdirect product factor
610C2C2×D5×#21711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×#711C2
cosocleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#410
LCSG ▷ C22×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×#91528C2semidirect
3. C2×#91118C2semidirect
4. C2×C5×#834C2semidirect
5. C2×#90995C2semidirect
6. #11749172C2direct (N × H)
9. C22×C3×C22⋊D5C4semidirect
11. C23×C3×Dic5C4semidirect
16. C2×C3×#711C4semidirect
18. C22×C3×C4×D5C4semidirect
19. C22×C3×Dic10C4semidirect
24. #91528C22semidirect
26. #91118C22semidirect
27. C5×#834C22semidirect
28. #90995C22semidirect
51. C2×C3×C22⋊D5C2×C4semidirect
60. C22×C3×Dic5C2×C4semidirect
72. C2×C3×C4×D5C2×C4semidirect
75. C2×C3×Dic10C2×C4semidirect
87. C2×#834D5semidirect
89. C22×C22⋊D5Dic3semidirect
91. C23×Dic5Dic3semidirect
96. C2×#711Dic3semidirect
98. C22×C4×D5Dic3semidirect
99. C22×Dic10Dic3semidirect
175. #834C2×D5semidirect
190. C2×C22⋊D5C2×Dic3semidirect
200. C22×Dic5C2×Dic3semidirect
212. C2×C4×D5C2×Dic3semidirect
215. C2×Dic10C2×Dic3semidirect
370. C2×C3×C5#410semidirect
489. C3×C5C2×#410semidirect
520. C2×C5#5240semidirect
574. C2×C3#65029semidirect
576. C5C2×#5240semidirect
602. C3C2×#65029semidirect
609. C2#11749172direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7112
C2×#915282
C2×#911182
C2×C5×#8342
C2×#909952
#117491722
C2×#650293
C2×#52405