Finite Group Databasebeta

← C2×#11751095 #14331688

Subgroups — C2×#11751095 #14331688

Order 1920.

1816 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×#6714C211yesmaximal, characteristic
3C22×#6714C211yesmaximal, characteristic
4C22×#6714C211yesmaximal, characteristic
5C22×C4⋊Dic15C211yesmaximal, characteristic, complemented
6C22×#6712C211yesmaximal, characteristic, complemented
7C2×#91115C211yesmaximal, characteristic, complemented
8#11751095C218yesmaximal, direct product factor
9C2×#65283—31nomaximal, Hall
10C24×D15C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C3×C4×C5C2211yescharacteristic
14C23×Dic15C2211yescharacteristic
15C23×Dic15C2211yescharacteristic
16C23×Dic15C2211yescharacteristic
17C2×C3×C5×C4⋊C4—24no—
18C2×C3×C5×C4⋊C4C2214yescomplemented
19C2×#6714—24no—
20C2×#6714—24no—
21C2×#6714—24no—
22C2×#6714C2214yes—
23C2×#6714C2214yes—
24C2×#6714C2214yes—
25C2×C4⋊Dic15—24no—
26C2×C4⋊Dic15C2214yescomplemented
27C2×#6712—24no—
28C2×#6712C2214yescomplemented
29#91115C2214yescomplemented
30C2×#4994—51nomaximal, Hall
31C22×C5×C4⋊C4D311yescharacteristic, complemented
32C22×#685—31no—
33C22×#685—31no—
34C22×#685—31no—
35C22×C4⋊Dic5—31no—
36C22×#683—31no—
37C2×#3963—31no—
38#65283—38no—
39C24×C3×C5C2311yescharacteristic
40C23×D15—22no—
41C23×D15—22no—
42C23×D15—22no—
43C23×D15—22no—
44C23×D15—22no—
45C23×D15—22no—
46C23×D15Q814yes—
47C23×D15C2312yes—
48C22×C3×C4×C5—22no—
49C22×C3×C4×C5—22no—
50C22×C3×C4×C5—22no—
51C22×C3×C4×C5—22no—
52C22×C3×C4×C5—22no—
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5D414yes—
56C22×C3×C4×C5D414yes—
57C22×C3×C4×C5C2312yes—
58C22×C3×C4×C5C2312yes—
59C22×C3×C4×C5C2312yes—
60C22×Dic15—22no—
61C22×Dic15—22no—
62C22×Dic15—22no—
63C22×Dic15—22no—
64C22×Dic15—22no—
65C22×Dic15—22no—
66C22×Dic15—22no—
67C22×Dic15—22no—
68C22×Dic15D414yes—
69C22×Dic15C2312yes—
70C22×Dic15C2312yes—
71C22×Dic15C2312yes—
72C3×C5×C4⋊C4—28no—
73#6714—28no—
74#6714—28no—
75#6714—28no—
76C4⋊Dic15—28no—
77#6712—28no—
78C22×C3×C4⋊C4D511yescharacteristic, complemented
79C22×(C2×D3)⋊C4—51no—
80C22×(C2×D3)⋊C4—51no—
81C22×(C2×D3)⋊C4—51no—
82C22×C4⋊Dic3—51no—
83C22×Dic3⋊C4—51no—
84C2×C3⋊#95—51no—
85#4994—58no—
86C24×D5—31no—
87C23×C4×C5C2×D311yescharacteristic
88C23×C4×C5C2×D311yescharacteristic
89C23×C4×C5C2×D311yescharacteristic
90C23×Dic5—31no—
91C23×Dic5—31no—
92C23×Dic5—31no—
93C2×C5×C4⋊C4—24no—
94C2×C5×C4⋊C4C2×D314yescomplemented
95C2×#685—34no—
96C2×#685—34no—
97C2×#685—34no—
98C2×#685—64no—
99C2×#685—64no—
100C2×#685—64no—
101C2×C4⋊Dic5—34no—
102C2×C4⋊Dic5—64no—
103C2×#683—34no—
104C2×#683—64no—
105#3963—34no—
106C2×#396—151noSylow
107C23×C3×C5C2×D412yes—
108C23×C3×C5C2×D412yes—
109C23×C3×C5C2×D412yes—
110C23×C3×C5C2×Q812yes—
111C23×C3×C5#4112yes—
112C23×C3×C5#4112yes—
113C23×C3×C5#4112yes—
114C23×C3×C5C2411yescharacteristic
115C22×D15—28no—
116C22×D15—28no—
117C22×D15—28no—
118C22×D15—22no—
119C22×D15—22no—
120C22×D15—22no—
121C22×D15—22no—
122C22×D15—22no—
123C22×D15—22no—
124C22×D15—44no—
125C22×D15—44no—
126C22×D15—44no—
127C22×D15—44no—
128C22×D15C2×Q814yes—
129C2×C3×C4×C5—28no—
130C2×C3×C4×C5—28no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—44no—
139C2×C3×C4×C5C2×D414yes—
140C2×C3×C4×C5C2×D414yes—
141C2×Dic15—28no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15—22no—
148C2×Dic15—22no—
149C2×Dic15—22no—
150C2×Dic15—44no—
151C2×Dic15—44no—
152C2×Dic15C2×D414yes—
153C24×D3—51no—
154C23×C3×C4C2×D511yescharacteristic
155C23×C3×C4C2×D511yescharacteristic
156C23×C3×C4C2×D511yescharacteristic
157C23×Dic3—51no—
158C23×Dic3—51no—
159C23×Dic3—51no—
160C2×C3×C4⋊C4—24no—
161C2×C3×C4⋊C4C2×D514yescomplemented
162C2×(C2×D3)⋊C4—54no—
163C2×(C2×D3)⋊C4—54no—
164C2×(C2×D3)⋊C4—54no—
165C2×(C2×D3)⋊C4—104no—
166C2×(C2×D3)⋊C4—104no—
167C2×(C2×D3)⋊C4—104no—
168C2×C4⋊Dic3—54no—
169C2×C4⋊Dic3—104no—
170C2×Dic3⋊C4—54no—
171C2×Dic3⋊C4—104no—
172C3⋊#95—54no—
173C24×C5C22×D311yescharacteristic
174C23×D5—34no—
175C23×D5—32no—
176C23×D5—62no—
177C23×D5—62no—
178C23×D5—62no—
179C23×D5—62no—
180C23×D5—62no—
181C23×D5—62no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5D1214yes—
190C22×C4×C5#6714yes—
191C22×C4×C5C22×D312yes—
192C22×C4×C5C22×D312yes—
193C22×C4×C5C22×D312yes—
194C22×Dic5—34no—
195C22×Dic5—32no—
196C22×Dic5—32no—
197C22×Dic5—32no—
198C22×Dic5—62no—
199C22×Dic5—62no—
200C22×Dic5—62no—
201C22×Dic5—62no—
202C22×Dic5—62no—
203C22×Dic5—62no—
204C22×Dic5—62no—
205C22×Dic5—62no—
206C5×C4⋊C4—28no—
207#685—68no—
208#685—68no—
209#685—68no—
210C4⋊Dic5—68no—
211#683—68no—
212C22×C4⋊C4—151no—
213C22×C4⋊C4—151no—
214C22×C4⋊C4D1511yescharacteristic, complemented
215C22×C22⋊C4—151no—
216C22×C22⋊C4—151no—
217C22×C22⋊C4—151no—
218#396—158no—
219C2×#95—151no—
220C22×C3×C5#12114yes—
221C22×C3×C5#12114yes—
222C22×C3×C5#12114yes—
223C22×C3×C5C22⋊Q814yes—
224C22×C3×C5C22⋊Q814yes—
225C22×C3×C5C22⋊Q814yes—
226C22×C3×C5#12614yes—
227C22×C3×C5C22×D411yescharacteristic
228C22×C3×C5C22×D411yescharacteristic
229C22×C3×C5C22×D411yescharacteristic
230C22×C3×C5C22×Q811yescharacteristic
231C22×C3×C5C2×#4111yescharacteristic
232C22×C3×C5C2×#4111yescharacteristic
233C22×C3×C5C2×#4111yescharacteristic
234C2×D15—24no—
235C2×D15—24no—
236C2×D15—24no—
237C2×D15—42no—
238C2×D15—42no—
239C2×D15—42no—
240C2×D15—42no—
241C2×D15—416no—
242C3×C4×C5—24no—
243C3×C4×C5—24no—
244C3×C4×C5—42no—
245Dic15—24no—
246Dic15—42no—
247Dic15—42no—
248C24×C3C22×D511yescharacteristic
249C23×D3—54no—
250C23×D3—52no—
251C23×D3—102no—
252C23×D3—102no—
253C23×D3—102no—
254C23×D3—102no—
255C23×D3—102no—
256C23×D3—102no—
257C22×C3×C4—22no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4D2014yes—
265C22×C3×C4C22⋊D514yes—
266C22×C3×C4C22×D512yes—
267C22×C3×C4C22×D512yes—
268C22×C3×C4C22×D512yes—
269C22×Dic3—54no—
270C22×Dic3—52no—
271C22×Dic3—52no—
272C22×Dic3—52no—
273C22×Dic3—102no—
274C22×Dic3—102no—
275C22×Dic3—102no—
276C22×Dic3—102no—
277C22×Dic3—102no—
278C22×Dic3—102no—
279C22×Dic3—102no—
280C22×Dic3—102no—
281C3×C4⋊C4—28no—
282(C2×D3)⋊C4—108no—
283(C2×D3)⋊C4—108no—
284(C2×D3)⋊C4—108no—
285C4⋊Dic3—108no—
286Dic3⋊C4—108no—
287C23×C5C2×D1212yes—
288C23×C5#23512yes—
289C23×C5D3×D412yes—
290C23×C5#23712yes—
291C23×C5D3×Q812yes—
292C23×C5#23912yes—
293C23×C5C2×#6712yes—
294C23×C5C23×D311yescharacteristic
295C22×D5—34no—
296C22×D5—68no—
297C22×D5—68no—
298C22×D5—68no—
299C22×D5—62no—
300C22×D5—62no—
301C22×D5—62no—
302C22×D5—62no—
303C22×D5—62no—
304C22×D5—62no—
305C22×D5—124no—
306C22×D5—124no—
307C22×D5—124no—
308C22×D5—124no—
309C2×C4×C5—28no—
310C2×C4×C5—28no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—44no—
319C2×C4×C5C2×D1214yes—
320C2×C4×C5C2×#6714yes—
321C2×Dic5—34no—
322C2×Dic5—68no—
323C2×Dic5—62no—
324C2×Dic5—62no—
325C2×Dic5—62no—
326C2×Dic5—62no—
327C2×Dic5—62no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5—124no—
332C2×Dic5—124no—
333C25—151no—
334C23×C4—151no—
335C23×C4—151no—
336C23×C4—151no—
337C23×C4C2×D1511yescharacteristic
338C23×C4C2×D1511yescharacteristic
339C23×C4C2×D1511yescharacteristic
340C2×C4⋊C4—24no—
341C2×C4⋊C4—154no—
342C2×C4⋊C4—154no—
343C2×C4⋊C4—304no—
344C2×C4⋊C4—304no—
345C2×C4⋊C4C2×D1514yescomplemented
346C2×C22⋊C4—154no—
347C2×C22⋊C4—154no—
348C2×C22⋊C4—154no—
349C2×C22⋊C4—304no—
350C2×C22⋊C4—304no—
351C2×C22⋊C4—304no—
352#95—154no—
353C2×C3×C5#39618yescomplemented
354C2×C3×C5C2×#12111yescharacteristic
355C2×C3×C5C2×#12111yescharacteristic
356C2×C3×C5C2×#12111yescharacteristic
357C2×C3×C5C2×C22⋊Q811yescharacteristic
358C2×C3×C5C2×C22⋊Q811yescharacteristic
359C2×C3×C5C2×C22⋊Q811yescharacteristic
360C2×C3×C5C2×#12611yescharacteristic
361D15—44no—
362C23×C3C2×D2012yes—
363C23×C3#70912yes—
364C23×C3D4×D512yes—
365C23×C3#71112yes—
366C23×C3Q8×D512yes—
367C23×C3#71312yes—
368C23×C3C2×C22⋊D512yes—
369C23×C3C23×D511yescharacteristic
370C22×D3—54no—
371C22×D3—102no—
372C22×D3—102no—
373C22×D3—102no—
374C22×D3—102no—
375C22×D3—102no—
376C22×D3—102no—
377C22×D3—108no—
378C22×D3—108no—
379C22×D3—108no—
380C22×D3—204no—
381C22×D3—204no—
382C22×D3—204no—
383C22×D3—204no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—28no—
389C2×C3×C4—28no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—44no—
394C2×C3×C4C2×D2014yes—
395C2×C3×C4C2×C22⋊D514yes—
396C2×Dic3—54no—
397C2×Dic3—102no—
398C2×Dic3—102no—
399C2×Dic3—108no—
400C2×Dic3—102no—
401C2×Dic3—102no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405C2×Dic3—102no—
406C2×Dic3—204no—
407C2×Dic3—204no—
408C22×C5#89514yes—
409C22×C5#89614yes—
410C22×C5#89714yes—
411C22×C5#89814yes—
412C22×C5#93014yes—
413C22×C5#93914yes—
414C22×C5#94614yes—
415C22×C5C22×D1211yescharacteristic
416C22×C5C2×#23511yescharacteristic
417C22×C5C2×D3×D411yescharacteristic
418C22×C5C2×#23711yescharacteristic
419C22×C5C2×D3×Q811yescharacteristic
420C22×C5C2×#23911yescharacteristic
421C22×C5C22×#6711yescharacteristic
422C2×D5—64no—
423C2×D5—64no—
424C2×D5—64no—
425C2×D5—1216no—
426C2×D5—122no—
427C2×D5—122no—
428C2×D5—122no—
429C2×D5—122no—
430C4×C5—24no—
431C4×C5—24no—
432C4×C5—42no—
433Dic5—64no—
434Dic5—122no—
435Dic5—122no—
436C24—154no—
437C24—152no—
438C24—302no—
439C24—302no—
440C24—302no—
441C24—302no—
442C24—302no—
443C24—302no—
444C24C22×D1511yescharacteristic
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—154no—
453C22×C4—152no—
454C22×C4—152no—
455C22×C4—152no—
456C22×C4—302no—
457C22×C4—302no—
458C22×C4—302no—
459C22×C4—302no—
460C22×C4—302no—
461C22×C4—302no—
462C22×C4—302no—
463C22×C4—302no—
464C22×C4D6014yes—
465C22×C4#122014yes—
466C22×C4C22×D1512yes—
467C22×C4C22×D1512yes—
468C22×C4C22×D1512yes—
469C4⋊C4—28no—
470C4⋊C4—308no—
471C4⋊C4—308no—
472C22⋊C4—308no—
473C22⋊C4—308no—
474C22⋊C4—308no—
475C3×C5C2×#39611yescharacteristic, complemented, Hall
476C22×C3#404114yes—
477C22×C3#404214yes—
478C22×C3#404314yes—
479C22×C3#404414yes—
480C22×C3#407614yes—
481C22×C3#408514yes—
482C22×C3#409214yes—
483C22×C3C22×D2011yescharacteristic
484C22×C3C2×#70911yescharacteristic
485C22×C3C2×D4×D511yescharacteristic
486C22×C3C2×#71111yescharacteristic
487C22×C3C2×Q8×D511yescharacteristic
488C22×C3C2×#71311yescharacteristic
489C22×C3C22×C22⋊D511yescharacteristic
490C2×D3—104no—
491C2×D3—104no—
492C2×D3—104no—
493C2×D3—2016no—
494C2×D3—202no—
495C2×D3—202no—
496C2×D3—202no—
497C2×D3—202no—
498C3×C4—24no—
499C3×C4—24no—
500C3×C4—42no—
501Dic3—104no—
502Dic3—202no—
503Dic3—202no—
504C2×C5#499418yescomplemented
505C2×C5C2×#89511yescharacteristic
506C2×C5C2×#89611yescharacteristic
507C2×C5C2×#89711yescharacteristic
508C2×C5C2×#89811yescharacteristic
509C2×C5C2×#93011yescharacteristic
510C2×C5C2×#93911yescharacteristic
511C2×C5C2×#94611yescharacteristic
512D5—124no—
513C23—154no—
514C23—308no—
515C23—308no—
516C23—308no—
517C23—302no—
518C23—302no—
519C23—302no—
520C23—302no—
521C23—302no—
522C23—302no—
523C23—604no—
524C23—604no—
525C23—604no—
526C23—604no—
527C23C2×D6012yes—
528C23#681712yes—
529C23D4×D1512yes—
530C23#681912yes—
531C23Q8×D1512yes—
532C23#682112yes—
533C23C2×#122012yes—
534C23C23×D1511yescharacteristic
535C2×C4—28no—
536C2×C4—28no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—44no—
545C2×C4—154no—
546C2×C4—308no—
547C2×C4—302no—
548C2×C4—302no—
549C2×C4—302no—
550C2×C4—302no—
551C2×C4—302no—
552C2×C4—302no—
553C2×C4—302no—
554C2×C4—302no—
555C2×C4—604no—
556C2×C4—604no—
557C2×C4C2×D6014yes—
558C2×C4C2×#122014yes—
559C2×C3#6528318yescomplemented
560C2×C3C2×#404111yescharacteristic
561C2×C3C2×#404211yescharacteristic
562C2×C3C2×#404311yescharacteristic
563C2×C3C2×#404411yescharacteristic
564C2×C3C2×#407611yescharacteristic
565C2×C3C2×#408511yescharacteristic
566C2×C3C2×#409211yescharacteristic
567D3—204no—
568C5C2×#499411yescharacteristic, complemented, Sylow
569C22—304no—
570C22—304no—
571C22—304no—
572C22—602no—
573C22—602no—
574C22—6016no—
575C22—602no—
576C22—602no—
577C22#9178414yes—
578C22#9178514yes—
579C22#9178614yes—
580C22#9178714yes—
581C22#9181914yes—
582C22#9182814yes—
583C22#9183514yes—
584C22C22×D6011yescharacteristic
585C22C2×#681711yescharacteristic
586C22C2×D4×D1511yescharacteristic
587C22C2×#681911yescharacteristic
588C22C2×Q8×D1511yescharacteristic
589C22C2×#682111yescharacteristic
590C22C22×#122011yescharacteristic
591C4—24no—
592C4—24no—
593C4—42no—
594C4—304no—
595C4—602no—
596C4—602no—
597C3C2×#6528311yescharacteristic, complemented, Sylow
598C2—604no—
599C2#1175109518yesdirect product factor
600C2C2×#9178411yescharacteristic
601C2C2×#9178511yescharacteristic
602C2C2×#9178611yescharacteristic
603C2C2×#9178711yescharacteristic
604C2C2×#9181911yescharacteristic
605C2C2×#9182811yescharacteristic
606C2C2×#9183511yescharacteristic
subgroupG/H
centerC24C22×D15
commutator, cosocleC23×C3×C5C24
FrattiniC23C23×D15
FittingC22×C3×C5×C4⋊C4C2
socleC24×C3×C5C23
prime radicalC24×D15C22
hypercenterC22×C4⋊C4D15
hypocenterC3×C5C2×#396
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×C4⋊C4C2semidirect
5. C22×C4⋊Dic15C2semidirect
6. C22×#6712C2semidirect
7. C2×#91115C2semidirect
8. #11751095C2direct (N × H)
18. C2×C3×C5×C4⋊C4C22semidirect
26. C2×C4⋊Dic15C22semidirect
28. C2×#6712C22semidirect
29. #91115C22semidirect
31. C22×C5×C4⋊C4D3semidirect
78. C22×C3×C4⋊C4D5semidirect
94. C2×C5×C4⋊C4C2×D3semidirect
161. C2×C3×C4⋊C4C2×D5semidirect
214. C22×C4⋊C4D15semidirect
345. C2×C4⋊C4C2×D15semidirect
353. C2×C3×C5#396semidirect
475. C3×C5C2×#396semidirect
504. C2×C5#4994semidirect
559. C2×C3#65283semidirect
568. C5C2×#4994semidirect
597. C3C2×#65283semidirect
599. C2#11751095direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×C4⋊C42
C22×#67142
C22×C4⋊Dic152
C22×#67122
C2×#911152
#117510952
C2×#652833
C2×#49945