Finite Group Databasebeta

← C2×#11748894 #14320244

Subgroups — C2×#11748894 #14320244

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1200C211yesmaximal, characteristic
2C22×#6714C211yesmaximal, characteristic
3C22×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C22×C3×#683C211yesmaximal, characteristic, complemented
5C22×#6667C211yesmaximal, characteristic
6C2×#90994C211yesmaximal, characteristic, complemented
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748894C218yesmaximal, direct product factor
9C2×#65278—31nomaximal, Hall
10C24×D15C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×Dic15C2211yescharacteristic
13C23×C5×Dic3C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×#1200—24no—
18C22×#1200—24no—
19C22×#1200—24no—
20C22×#1200C2214yes—
21C2×#6714—24no—
22C2×#6714C2214yes—
23C2×C5×Dic3⋊C4—24no—
24C2×C5×Dic3⋊C4C2214yescomplemented
25C2×C3×#683—24no—
26C2×C3×#683C2214yescomplemented
27C2×#6667C418yescomplemented
28C2×#6667C2214yes—
29#90994C2214yescomplemented
30#90994C2214yescomplemented
31C2×#4989—51nomaximal, Hall
32C23×C4×D5—31no—
33C22×C5×C4⋊C4—31no—
34C22×#685—31no—
35C22×#685—31no—
36C22×#683D311yescharacteristic, complemented
37C2×#3963—31no—
38C2×#3963—31no—
39#65278—38no—
40C24×C3×C5C2311yescharacteristic
41C23×D15—22no—
42C23×D15—22no—
43C23×D15—22no—
44C23×D15—22no—
45C23×D15C2×C414yes—
46C23×D15D414yes—
47C23×D15Q814yes—
48C23×D15C2312yes—
49C22×C3×C4×C5—22no—
50C22×C3×C4×C5—22no—
51C22×C3×C4×C5—22no—
52C22×C3×C4×C5C2312yes—
53C22×Dic15—22no—
54C22×Dic15—22no—
55C22×Dic15—22no—
56C22×Dic15C2312yes—
57C22×C5×Dic3—22no—
58C22×C5×Dic3—22no—
59C22×C5×Dic3—22no—
60C22×C5×Dic3—22no—
61C22×C5×Dic3C2×C414yescomplemented
62C22×C5×Dic3D414yes—
63C22×C5×Dic3C2312yes—
64C22×C5×Dic3C2312yes—
65C22×C3×Dic5—22no—
66C22×C3×Dic5—22no—
67C22×C3×Dic5—22no—
68C22×C3×Dic5—22no—
69C22×C3×Dic5C2×C414yescomplemented
70C22×C3×Dic5D414yes—
71C22×C3×Dic5C2312yes—
72C22×C3×Dic5C2312yes—
73C2×#1200—232no—
74C2×#1200—28no—
75C2×#1200—28no—
76C2×#1200—28no—
77#6714—28no—
78C5×Dic3⋊C4—28no—
79C3×#683—28no—
80#6667C2×C4116yescomplemented
81C23×C4×D3—51no—
82C22×C3×C4⋊C4—51no—
83C22×(C2×D3)⋊C4—51no—
84C22×(C2×D3)⋊C4—51no—
85C22×Dic3⋊C4D511yescharacteristic, complemented
86C2×C3⋊#95—51no—
87C2×C3⋊#95—51no—
88#4989—58no—
89C24×D5—31no—
90C23×C4×C5—31no—
91C23×C4×C5—31no—
92C23×C4×C5C2×D311yescharacteristic
93C23×Dic5—31no—
94C23×Dic5C2×D311yescharacteristic
95C23×Dic5C2×D311yescharacteristic
96C22×C4×D5—34no—
97C22×C4×D5—64no—
98C22×C4×D5—64no—
99C22×C4×D5—64no—
100C2×C5×C4⋊C4—34no—
101C2×C5×C4⋊C4—64no—
102C2×#685—38no—
103C2×#685—34no—
104C2×#685—34no—
105C2×#685—64no—
106C2×#683—24no—
107C2×#683C2×D314yescomplemented
108#3963—34no—
109#3963—34no—
110C2×#385—151noSylow
111C23×C3×C5C22×C412yes—
112C23×C3×C5C2×D412yes—
113C23×C3×C5C2×D412yes—
114C23×C3×C5C2×D412yes—
115C23×C3×C5C2×Q812yes—
116C23×C3×C5#4112yes—
117C23×C3×C5#4112yes—
118C23×C3×C5C2411yescharacteristic
119C22×D15—28no—
120C22×D15—28no—
121C22×D15—28no—
122C22×D15—28no—
123C22×D15—28no—
124C22×D15—28no—
125C22×D15—22no—
126C22×D15—22no—
127C22×D15—22no—
128C22×D15—22no—
129C22×D15C4⋊C4116yescomplemented
130C22×D15C22×C414yes—
131C22×D15C2×D414yes—
132C22×D15C2×Q814yes—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—44no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—44no—
141C2×C5×Dic3—28no—
142C2×C5×Dic3—28no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3C22×C414yescomplemented
148C2×C5×Dic3C2×D414yes—
149C2×C3×Dic5—28no—
150C2×C3×Dic5—28no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5C22×C414yescomplemented
156C2×C3×Dic5C2×D414yes—
157#1200—232no—
158C24×D3—51no—
159C23×C3×C4—51no—
160C23×C3×C4—51no—
161C23×C3×C4C2×D511yescharacteristic
162C23×Dic3—51no—
163C23×Dic3C2×D511yescharacteristic
164C23×Dic3C2×D511yescharacteristic
165C22×C4×D3—54no—
166C22×C4×D3—104no—
167C22×C4×D3—104no—
168C22×C4×D3—104no—
169C2×C3×C4⋊C4—54no—
170C2×C3×C4⋊C4—104no—
171C2×(C2×D3)⋊C4—58no—
172C2×(C2×D3)⋊C4—54no—
173C2×(C2×D3)⋊C4—54no—
174C2×(C2×D3)⋊C4—104no—
175C2×Dic3⋊C4—24no—
176C2×Dic3⋊C4C2×D514yescomplemented
177C3⋊#95—54no—
178C3⋊#95—54no—
179C24×C5C22×D311yescharacteristic
180C23×D5—34no—
181C23×D5—34no—
182C23×D5—34no—
183C23×D5—32no—
184C23×D5—62no—
185C23×D5—62no—
186C23×D5—62no—
187C23×D5—62no—
188C22×C4×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5—34no—
192C22×C4×C5—34no—
193C22×C4×C5—32no—
194C22×C4×C5—32no—
195C22×C4×C5—62no—
196C22×C4×C5—62no—
197C22×C4×C5—62no—
198C22×C4×C5—62no—
199C22×C4×C5C22×D312yes—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—32no—
205C22×Dic5—62no—
206C22×Dic5—62no—
207C22×Dic5—62no—
208C22×Dic5C4×D314yescomplemented
209C22×Dic5#6714yes—
210C22×Dic5C22×D312yes—
211C22×Dic5C22×D312yes—
212C2×C4×D5—68no—
213C2×C4×D5—68no—
214C2×C4×D5—632no—
215C2×C4×D5—68no—
216C5×C4⋊C4—68no—
217#685—316no—
218#685—68no—
219#683—28no—
220C24×C4—151no—
221C22×C4⋊C4—31no—
222C22×C4⋊C4—51no—
223C22×C22⋊C4—151no—
224C22×C22⋊C4—151no—
225#385—158no—
226C2×#95—151no—
227C2×#95—151no—
228C22×C3×C5C2×C4⋊C414yes—
229C22×C3×C5C4×D414yes—
230C22×C3×C5C4×D414yes—
231C22×C3×C5#12014yes—
232C22×C3×C5C22⋊Q814yes—
233C22×C3×C5C22⋊Q814yes—
234C22×C3×C5#12314yes—
235C22×C3×C5C23×C411yescharacteristic
236C22×C3×C5C22×D411yescharacteristic
237C22×C3×C5C22×D411yescharacteristic
238C22×C3×C5C22×D411yescharacteristic
239C22×C3×C5C22×Q811yescharacteristic
240C22×C3×C5C2×#4111yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C2×D15—24no—
243C2×D15—24no—
244C2×D15—24no—
245C2×D15—24no—
246C2×D15—24no—
247C2×D15—24no—
248C2×D15—232no—
249C2×D15C2×C4⋊C418yescomplemented
250C3×C4×C5—42no—
251Dic15—42no—
252C3×Dic5—24no—
253C3×Dic5—24no—
254C5×Dic3—24no—
255C5×Dic3—24no—
256C24×C3C22×D511yescharacteristic
257C23×D3—54no—
258C23×D3—54no—
259C23×D3—54no—
260C23×D3—52no—
261C23×D3—102no—
262C23×D3—102no—
263C23×D3—102no—
264C23×D3—102no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—54no—
269C22×C3×C4—54no—
270C22×C3×C4—52no—
271C22×C3×C4—52no—
272C22×C3×C4—102no—
273C22×C3×C4—102no—
274C22×C3×C4—102no—
275C22×C3×C4—102no—
276C22×C3×C4C22×D512yes—
277C22×Dic3—22no—
278C22×Dic3—22no—
279C22×Dic3—22no—
280C22×Dic3—22no—
281C22×Dic3—52no—
282C22×Dic3—102no—
283C22×Dic3—102no—
284C22×Dic3—102no—
285C22×Dic3C4×D514yescomplemented
286C22×Dic3C22⋊D514yes—
287C22×Dic3C22×D512yes—
288C22×Dic3C22×D512yes—
289C2×C4×D3—108no—
290C2×C4×D3—108no—
291C2×C4×D3—1032no—
292C2×C4×D3—108no—
293C3×C4⋊C4—108no—
294(C2×D3)⋊C4—516no—
295(C2×D3)⋊C4—108no—
296Dic3⋊C4—28no—
297C23×C5C2×C4×D312yes—
298C23×C5#23512yes—
299C23×C5D3×D412yes—
300C23×C5D3×D412yes—
301C23×C5D3×Q812yes—
302C23×C5#23912yes—
303C23×C5C2×#6712yes—
304C23×C5C23×D311yescharacteristic
305C22×D5—316no—
306C22×D5—34no—
307C22×D5—34no—
308C22×D5—34no—
309C22×D5—68no—
310C22×D5—68no—
311C22×D5—68no—
312C22×D5—68no—
313C22×D5—68no—
314C22×D5—68no—
315C22×D5—62no—
316C22×D5—62no—
317C22×D5—62no—
318C22×D5—62no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—34no—
323C2×C4×C5—34no—
324C2×C4×C5—44no—
325C2×C4×C5—68no—
326C2×C4×C5—68no—
327C2×C4×C5—62no—
328C2×C4×C5—62no—
329C2×C4×C5—62no—
330C2×C4×C5—62no—
331C2×Dic5—28no—
332C2×Dic5—28no—
333C2×Dic5—22no—
334C2×Dic5—22no—
335C2×Dic5—22no—
336C2×Dic5—22no—
337C2×Dic5—62no—
338C2×Dic5—62no—
339C2×Dic5—62no—
340C2×Dic5—124no—
341C2×Dic5C2×C4×D314yescomplemented
342C2×Dic5C2×#6714yes—
343C4×D5—632no—
344C25—151no—
345C23×C4—31no—
346C23×C4—31no—
347C23×C4—51no—
348C23×C4—51no—
349C23×C4—154no—
350C23×C4—151no—
351C23×C4—304no—
352C23×C4—304no—
353C23×C4—304no—
354C23×C4D3×D511yescharacteristic
355C2×C4⋊C4—34no—
356C2×C4⋊C4—54no—
357C2×C4⋊C4—64no—
358C2×C4⋊C4—104no—
359C2×C22⋊C4—154no—
360C2×C22⋊C4—158no—
361C2×C22⋊C4—154no—
362C2×C22⋊C4—304no—
363#95—154no—
364#95—154no—
365C2×C3×C5#38518yescomplemented
366C2×C3×C5C22×C4⋊C411yescharacteristic
367C2×C3×C5C2×C4×D411yescharacteristic
368C2×C3×C5C2×C4×D411yescharacteristic
369C2×C3×C5C2×#12011yescharacteristic
370C2×C3×C5C2×C22⋊Q811yescharacteristic
371C2×C3×C5C2×C22⋊Q811yescharacteristic
372C2×C3×C5C2×#12311yescharacteristic
373D15—28no—
374C23×C3C2×C4×D512yes—
375C23×C3#70912yes—
376C23×C3D4×D512yes—
377C23×C3D4×D512yes—
378C23×C3Q8×D512yes—
379C23×C3#71312yes—
380C23×C3C2×C22⋊D512yes—
381C23×C3C23×D511yescharacteristic
382C22×D3—54no—
383C22×D3—54no—
384C22×D3—54no—
385C22×D3—516no—
386C22×D3—102no—
387C22×D3—102no—
388C22×D3—102no—
389C22×D3—102no—
390C22×D3—108no—
391C22×D3—108no—
392C22×D3—108no—
393C22×D3—108no—
394C22×D3—108no—
395C22×D3—108no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—44no—
400C2×C3×C4—54no—
401C2×C3×C4—54no—
402C2×C3×C4—102no—
403C2×C3×C4—102no—
404C2×C3×C4—102no—
405C2×C3×C4—102no—
406C2×C3×C4—108no—
407C2×C3×C4—108no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—28no—
413C2×Dic3—28no—
414C2×Dic3—102no—
415C2×Dic3—102no—
416C2×Dic3—102no—
417C2×Dic3—204no—
418C2×Dic3C2×C4×D514yescomplemented
419C2×Dic3C2×C22⋊D514yes—
420C4×D3—1032no—
421C22×C5D3×C4⋊C414yes—
422C22×C5#89314yes—
423C22×C5#89414yes—
424C22×C5#89614yes—
425C22×C5C4×#6714yes—
426C22×C5#93714yes—
427C22×C5#94614yes—
428C22×C5C22×C4×D311yescharacteristic
429C22×C5C2×#23511yescharacteristic
430C22×C5C2×D3×D411yescharacteristic
431C22×C5C2×D3×D411yescharacteristic
432C22×C5C2×D3×Q811yescharacteristic
433C22×C5C2×#23911yescharacteristic
434C22×C5C22×#6711yescharacteristic
435C2×D5—38no—
436C2×D5—632no—
437C2×D5—64no—
438C2×D5—64no—
439C2×D5—64no—
440C2×D5—64no—
441C2×D5—64no—
442C2×D5—64no—
443C4×C5—42no—
444C4×C5—64no—
445C4×C5—64no—
446Dic5—24no—
447Dic5—24no—
448Dic5—122no—
449C24—154no—
450C24—154no—
451C24—154no—
452C24—152no—
453C24—302no—
454C24—302no—
455C24—302no—
456C24—302no—
457C24C2×D3×D511yescharacteristic
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—34no—
462C22×C4—34no—
463C22×C4—32no—
464C22×C4—32no—
465C22×C4—54no—
466C22×C4—54no—
467C22×C4—52no—
468C22×C4—52no—
469C22×C4—62no—
470C22×C4—62no—
471C22×C4—62no—
472C22×C4—62no—
473C22×C4—102no—
474C22×C4—102no—
475C22×C4—102no—
476C22×C4—102no—
477C22×C4—152no—
478C22×C4—308no—
479C22×C4—308no—
480C22×C4—308no—
481C22×C4—3032no—
482C22×C4—302no—
483C22×C4—302no—
484C22×C4—302no—
485C22×C4C2×D3×D512yes—
486C4⋊C4—68no—
487C4⋊C4—108no—
488C22⋊C4—1516no—
489C22⋊C4—308no—
490C3×C5C2×#38511yescharacteristic, complemented, Hall
491C22×C3D5×C4⋊C414yes—
492C22×C3#403914yes—
493C22×C3#404014yes—
494C22×C3#404214yes—
495C22×C3C4×C22⋊D514yes—
496C22×C3#408314yes—
497C22×C3#409214yes—
498C22×C3C22×C4×D511yescharacteristic
499C22×C3C2×#70911yescharacteristic
500C22×C3C2×D4×D511yescharacteristic
501C22×C3C2×D4×D511yescharacteristic
502C22×C3C2×Q8×D511yescharacteristic
503C22×C3C2×#71311yescharacteristic
504C22×C3C22×C22⋊D511yescharacteristic
505C2×D3—58no—
506C2×D3—104no—
507C2×D3—104no—
508C2×D3—104no—
509C2×D3—104no—
510C2×D3—104no—
511C2×D3—104no—
512C2×D3—1032no—
513C3×C4—42no—
514C3×C4—104no—
515C3×C4—104no—
516Dic3—24no—
517Dic3—24no—
518Dic3—202no—
519C2×C5#498918yescomplemented
520C2×C5C2×D3×C4⋊C411yescharacteristic
521C2×C5C2×#89311yescharacteristic
522C2×C5C2×#89411yescharacteristic
523C2×C5C2×#89611yescharacteristic
524C2×C5C2×C4×#6711yescharacteristic
525C2×C5C2×#93711yescharacteristic
526C2×C5C2×#94611yescharacteristic
527D5—68no—
528C23—1516no—
529C23—154no—
530C23—154no—
531C23—154no—
532C23—308no—
533C23—308no—
534C23—308no—
535C23—308no—
536C23—308no—
537C23—302no—
538C23—302no—
539C23—302no—
540C23—302no—
541C23—308no—
542C23#676912yes—
543C23D15⋊Q812yes—
544C23#677312yes—
545C23C4×D3×D512yes—
546C23D5×#6712yes—
547C23D3×C22⋊D512yes—
548C23#679012yes—
549C23C22×D3×D511yescharacteristic
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—34no—
554C2×C4—34no—
555C2×C4—44no—
556C2×C4—54no—
557C2×C4—54no—
558C2×C4—68no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—62no—
563C2×C4—68no—
564C2×C4—108no—
565C2×C4—102no—
566C2×C4—102no—
567C2×C4—102no—
568C2×C4—102no—
569C2×C4—108no—
570C2×C4—3032no—
571C2×C4—302no—
572C2×C4—302no—
573C2×C4—302no—
574C2×C4—604no—
575C2×C3#6527818yescomplemented
576C2×C3C2×D5×C4⋊C411yescharacteristic
577C2×C3C2×#403911yescharacteristic
578C2×C3C2×#404011yescharacteristic
579C2×C3C2×#404211yescharacteristic
580C2×C3C2×C4×C22⋊D511yescharacteristic
581C2×C3C2×#408311yescharacteristic
582C2×C3C2×#409211yescharacteristic
583D3—108no—
584C5C2×#498911yescharacteristic, complemented, Sylow
585C22—158no—
586C22—304no—
587C22—304no—
588C22—3032no—
589C22—304no—
590C22—304no—
591C22—304no—
592C22—304no—
593C22#9140414yes—
594C22#9141114yes—
595C22#9142414yes—
596C22#9143314yes—
597C22#9144414yes—
598C22#9144614yes—
599C22#9157714yes—
600C22C2×#676911yescharacteristic
601C22C2×D15⋊Q811yescharacteristic
602C22C2×#677311yescharacteristic
603C22C2×C4×D3×D511yescharacteristic
604C22C2×D5×#6711yescharacteristic
605C22C2×D3×C22⋊D511yescharacteristic
606C22C2×#679011yescharacteristic
607C4—42no—
608C4—64no—
609C4—64no—
610C4—104no—
611C4—104no—
612C4—602no—
613C3C2×#6527811yescharacteristic, complemented, Sylow
614C2—308no—
615C2#1174889418yesdirect product factor
616C2C2×#9140411yescharacteristic
617C2C2×#9141111yescharacteristic
618C2C2×#9142411yescharacteristic
619C2C2×#9143311yescharacteristic
620C2C2×#9144411yescharacteristic
621C2C2×#9144611yescharacteristic
622C2C2×#9157711yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socleC24×C3×C5C23
prime radicalC24×D15C22
cosocleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#385
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C22×C5×Dic3⋊C4C2semidirect
4. C22×C3×#683C2semidirect
6. C2×#90994C2semidirect
7. C2×#90994C2semidirect
8. #11748894C2direct (N × H)
24. C2×C5×Dic3⋊C4C22semidirect
26. C2×C3×#683C22semidirect
27. C2×#6667C4semidirect
29. #90994C22semidirect
30. #90994C22semidirect
36. C22×#683D3semidirect
61. C22×C5×Dic3C2×C4semidirect
69. C22×C3×Dic5C2×C4semidirect
80. #6667C2×C4semidirect
85. C22×Dic3⋊C4D5semidirect
107. C2×#683C2×D3semidirect
129. C22×D15C4⋊C4semidirect
147. C2×C5×Dic3C22×C4semidirect
155. C2×C3×Dic5C22×C4semidirect
176. C2×Dic3⋊C4C2×D5semidirect
208. C22×Dic5C4×D3semidirect
249. C2×D15C2×C4⋊C4semidirect
285. C22×Dic3C4×D5semidirect
341. C2×Dic5C2×C4×D3semidirect
365. C2×C3×C5#385semidirect
418. C2×Dic3C2×C4×D5semidirect
490. C3×C5C2×#385semidirect
519. C2×C5#4989semidirect
575. C2×C3#65278semidirect
584. C5C2×#4989semidirect
613. C3C2×#65278semidirect
615. C2#11748894direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#12002
C22×#67142
C22×C5×Dic3⋊C42
C22×C3×#6832
C22×#66672
C2×#909942
#117488942
C2×#652783
C2×#49895