Finite Group Databasebeta

← C2×#11748730 #14320482

Subgroups — C2×#11748730 #14320482

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6714C211yesmaximal, characteristic
2C22×C4×C5×Dic3C211yesmaximal, characteristic, complemented
3C22×#6668C211yesmaximal, characteristic, complemented
4C22×#6667C211yesmaximal, characteristic
5C22×#6667C211yesmaximal, characteristic
6C2×C3×#3963C211yesmaximal, characteristic, complemented
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748730C218yesmaximal, direct product factor
9C2×#65229—31nomaximal, Hall
10C24×D15C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×Dic15C2211yescharacteristic
13C23×C5×Dic3C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C2×#6714—24no—
18C2×#6714C2214yes—
19C2×C4×C5×Dic3—24no—
20C2×C4×C5×Dic3C2214yescomplemented
21C2×#6668—24no—
22C2×#6668C2214yescomplemented
23C2×#6667—24no—
24C2×#6667C418yescomplemented
25C2×#6667C2214yes—
26C2×#6667C2214yes—
27C3×#3963C2214yescomplemented
28#90994C2214yescomplemented
29C2×#4670—51nomaximal, Hall
30C22×C42×C5—31no—
31C22×#685—31no—
32C22×#685—31no—
33C22×#685—31no—
34C22×#683—31no—
35C2×#3963—31no—
36C2×#3963D311yescharacteristic, complemented
37#65229—38no—
38C24×C3×C5C2311yescharacteristic
39C23×D15—22no—
40C23×D15—22no—
41C23×D15—22no—
42C23×D15—22no—
43C23×D15—22no—
44C23×D15—22no—
45C23×D15C2×C414yes—
46C23×D15C2312yes—
47C22×C3×C4×C5—22no—
48C22×C3×C4×C5—22no—
49C22×C3×C4×C5D414yes—
50C22×C3×C4×C5C2312yes—
51C22×Dic15—22no—
52C22×Dic15—22no—
53C22×Dic15—22no—
54C22×Dic15C2312yes—
55C22×C5×Dic3—22no—
56C22×C5×Dic3—22no—
57C22×C5×Dic3—22no—
58C22×C5×Dic3—22no—
59C22×C5×Dic3C2×C414yes—
60C22×C5×Dic3D414yes—
61C22×C5×Dic3C2312yes—
62C22×C5×Dic3C2312yes—
63C22×C3×Dic5—22no—
64C22×C3×Dic5—22no—
65C22×C3×Dic5—22no—
66C22×C3×Dic5—22no—
67C22×C3×Dic5—22no—
68C22×C3×Dic5C2×C414yes—
69C22×C3×Dic5C2312yes—
70C22×C3×Dic5C2312yes—
71#6714—28no—
72C4×C5×Dic3—28no—
73#6668—28no—
74#6667—28no—
75#6667C2×C4116yescomplemented
76C22×(C2×D3)⋊C4—51no—
77C22×(C2×D3)⋊C4—51no—
78C22×(C2×D3)⋊C4—51no—
79C22×C4⋊Dic3—51no—
80C22×C4×Dic3D511yescharacteristic, complemented
81C2×C3×#95—51no—
82C2×C3⋊#95—51no—
83#4670—58no—
84C24×D5—31no—
85C23×C4×C5—31no—
86C23×C4×C5—31no—
87C23×C4×C5C2×D311yescharacteristic
88C23×Dic5—31no—
89C23×Dic5C2×D311yescharacteristic
90C23×Dic5C2×D311yescharacteristic
91C2×C42×C5—34no—
92C2×C42×C5—64no—
93C2×#685—38no—
94C2×#685—34no—
95C2×#685—34no—
96C2×#685—34no—
97C2×#685—64no—
98C2×#685—64no—
99C2×#683—34no—
100C2×#683—64no—
101#3963—34no—
102#3963C2×D314yescomplemented
103C2×#388—151noSylow
104C23×C3×C5C22×C412yes—
105C23×C3×C5C2×D412yes—
106C23×C3×C5C2×D412yes—
107C23×C3×C5#4112yes—
108C23×C3×C5#4112yes—
109C23×C3×C5#4112yes—
110C23×C3×C5#4112yes—
111C23×C3×C5C2411yescharacteristic
112C22×D15—28no—
113C22×D15—28no—
114C22×D15—28no—
115C22×D15—22no—
116C22×D15—22no—
117C22×D15—22no—
118C22×D15—22no—
119C22×D15—22no—
120C22×D15—22no—
121C22×D15—44no—
122C22×D15—44no—
123C22×D15—44no—
124C22×D15—44no—
125C22×D15C22×C414yes—
126C2×C3×C4×C5—28no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5C2×D414yes—
130C2×Dic15—22no—
131C2×Dic15—22no—
132C2×Dic15—22no—
133C2×Dic15—44no—
134C2×C5×Dic3—28no—
135C2×C5×Dic3—28no—
136C2×C5×Dic3—22no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3C22×C414yes—
141C2×C5×Dic3C2×D414yes—
142C2×C3×Dic5—28no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—44no—
149C2×C3×Dic5C22×C414yes—
150C24×D3—51no—
151C23×C3×C4—51no—
152C23×C3×C4—51no—
153C23×C3×C4C2×D511yescharacteristic
154C23×Dic3—51no—
155C23×Dic3C2×D511yescharacteristic
156C23×Dic3C2×D511yescharacteristic
157C2×(C2×D3)⋊C4—58no—
158C2×(C2×D3)⋊C4—54no—
159C2×(C2×D3)⋊C4—54no—
160C2×(C2×D3)⋊C4—54no—
161C2×(C2×D3)⋊C4—104no—
162C2×(C2×D3)⋊C4—104no—
163C2×C4⋊Dic3—54no—
164C2×C4⋊Dic3—104no—
165C2×C4×Dic3—24no—
166C2×C4×Dic3C2×D514yescomplemented
167C3×#95—54no—
168C3⋊#95—54no—
169C24×C5C22×D311yescharacteristic
170C23×D5—34no—
171C23×D5—32no—
172C23×D5—62no—
173C23×D5—62no—
174C23×D5—62no—
175C23×D5—62no—
176C23×D5—62no—
177C23×D5—62no—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—34no—
181C22×C4×C5—34no—
182C22×C4×C5—32no—
183C22×C4×C5—32no—
184C22×C4×C5—62no—
185C22×C4×C5—62no—
186C22×C4×C5—62no—
187C22×C4×C5—62no—
188C22×C4×C5D1214yes—
189C22×C4×C5C22×D312yes—
190C22×Dic5—22no—
191C22×Dic5—22no—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—22no—
195C22×Dic5—32no—
196C22×Dic5—62no—
197C22×Dic5—62no—
198C22×Dic5—62no—
199C22×Dic5C4×D314yes—
200C22×Dic5C22×D312yes—
201C22×Dic5C22×D312yes—
202C42×C5—68no—
203#685—316no—
204#685—68no—
205#685—68no—
206#683—68no—
207C22×C4⋊C4—151no—
208C22×C22⋊C4—151no—
209C22×C22⋊C4—151no—
210C22×C22⋊C4—151no—
211C22×C42—31no—
212#388—158no—
213C2×#95—51no—
214C2×#95—151no—
215C22×C3×C5#11714yes—
216C22×C3×C5C4×D414yes—
217C22×C3×C5C4×D414yes—
218C22×C3×C5#12114yes—
219C22×C3×C5#12314yes—
220C22×C3×C5#12414yes—
221C22×C3×C5#12614yes—
222C22×C3×C5C23×C411yescharacteristic
223C22×C3×C5C22×D411yescharacteristic
224C22×C3×C5C22×D411yescharacteristic
225C22×C3×C5C2×#4111yescharacteristic
226C22×C3×C5C2×#4111yescharacteristic
227C22×C3×C5C2×#4111yescharacteristic
228C22×C3×C5C2×#4111yescharacteristic
229C2×D15—24no—
230C2×D15—24no—
231C2×D15—24no—
232C2×D15—42no—
233C2×D15—42no—
234C2×D15—42no—
235C2×D15—42no—
236C2×D15—416no—
237C3×C4×C5—24no—
238Dic15—42no—
239C3×Dic5—24no—
240C3×Dic5—42no—
241C5×Dic3—24no—
242C5×Dic3—24no—
243C24×C3C22×D511yescharacteristic
244C23×D3—54no—
245C23×D3—52no—
246C23×D3—102no—
247C23×D3—102no—
248C23×D3—102no—
249C23×D3—102no—
250C23×D3—102no—
251C23×D3—102no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—54no—
255C22×C3×C4—52no—
256C22×C3×C4—52no—
257C22×C3×C4—102no—
258C22×C3×C4—102no—
259C22×C3×C4—102no—
260C22×C3×C4—102no—
261C22×C3×C4—102no—
262C22×C3×C4C22⋊D514yes—
263C22×C3×C4C22×D512yes—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—52no—
269C22×Dic3—102no—
270C22×Dic3—102no—
271C22×Dic3—102no—
272C22×Dic3C4×D514yes—
273C22×Dic3D2014yes—
274C22×Dic3C22×D512yes—
275C22×Dic3C22×D512yes—
276(C2×D3)⋊C4—516no—
277(C2×D3)⋊C4—108no—
278(C2×D3)⋊C4—108no—
279C4⋊Dic3—108no—
280C4×Dic3—28no—
281C23×C5C2×C4×D312yes—
282C23×C5C2×D1212yes—
283C23×C5#23512yes—
284C23×C5D3×D412yes—
285C23×C5#23712yes—
286C23×C5#23712yes—
287C23×C5#23912yes—
288C23×C5C23×D311yescharacteristic
289C22×D5—34no—
290C22×D5—68no—
291C22×D5—68no—
292C22×D5—68no—
293C22×D5—62no—
294C22×D5—62no—
295C22×D5—62no—
296C22×D5—62no—
297C22×D5—62no—
298C22×D5—62no—
299C22×D5—124no—
300C22×D5—124no—
301C22×D5—124no—
302C22×D5—124no—
303C2×C4×C5—28no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—34no—
307C2×C4×C5—34no—
308C2×C4×C5—68no—
309C2×C4×C5—68no—
310C2×C4×C5—62no—
311C2×C4×C5—62no—
312C2×C4×C5—62no—
313C2×C4×C5—62no—
314C2×C4×C5C2×D1214yes—
315C2×Dic5—28no—
316C2×Dic5—22no—
317C2×Dic5—22no—
318C2×Dic5—22no—
319C2×Dic5—22no—
320C2×Dic5—22no—
321C2×Dic5—44no—
322C2×Dic5—62no—
323C2×Dic5—62no—
324C2×Dic5—62no—
325C2×Dic5—124no—
326C2×Dic5C2×C4×D314yes—
327C25—151no—
328C23×C4—31no—
329C23×C4—31no—
330C23×C4—51no—
331C23×C4—51no—
332C23×C4—151no—
333C23×C4D3×D511yescharacteristic
334C2×C4⋊C4—154no—
335C2×C4⋊C4—304no—
336C2×C22⋊C4—154no—
337C2×C22⋊C4—158no—
338C2×C22⋊C4—154no—
339C2×C22⋊C4—154no—
340C2×C22⋊C4—304no—
341C2×C22⋊C4—304no—
342C2×C42—34no—
343C2×C42—64no—
344#95—54no—
345#95—154no—
346C2×C3×C5#38818yescomplemented
347C2×C3×C5C2×#11711yescharacteristic
348C2×C3×C5C2×C4×D411yescharacteristic
349C2×C3×C5C2×C4×D411yescharacteristic
350C2×C3×C5C2×#12111yescharacteristic
351C2×C3×C5C2×#12311yescharacteristic
352C2×C3×C5C2×#12411yescharacteristic
353C2×C3×C5C2×#12611yescharacteristic
354D15—44no—
355C23×C3C2×C4×D512yes—
356C23×C3C2×D2012yes—
357C23×C3#70912yes—
358C23×C3#70912yes—
359C23×C3#70912yes—
360C23×C3#70912yes—
361C23×C3C2×C22⋊D512yes—
362C23×C3C23×D511yescharacteristic
363C22×D3—54no—
364C22×D3—102no—
365C22×D3—102no—
366C22×D3—102no—
367C22×D3—102no—
368C22×D3—102no—
369C22×D3—102no—
370C22×D3—108no—
371C22×D3—108no—
372C22×D3—108no—
373C22×D3—204no—
374C22×D3—204no—
375C22×D3—204no—
376C22×D3—204no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—28no—
380C2×C3×C4—54no—
381C2×C3×C4—102no—
382C2×C3×C4—102no—
383C2×C3×C4—108no—
384C2×C3×C4—102no—
385C2×C3×C4—102no—
386C2×C3×C4—102no—
387C2×C3×C4—204no—
388C2×C3×C4C2×C22⋊D514yes—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—28no—
394C2×Dic3—28no—
395C2×Dic3—102no—
396C2×Dic3—102no—
397C2×Dic3—102no—
398C2×Dic3—204no—
399C2×Dic3C2×C4×D514yes—
400C2×Dic3C2×D2014yes—
401C22×C5C4×D1214yes—
402C22×C5#67⋊C414yes—
403C22×C5#88514yes—
404C22×C5#88614yes—
405C22×C5#89214yes—
406C22×C5#89514yes—
407C22×C5#89814yes—
408C22×C5C22×C4×D311yescharacteristic
409C22×C5C22×D1211yescharacteristic
410C22×C5C2×#23511yescharacteristic
411C22×C5C2×D3×D411yescharacteristic
412C22×C5C2×#23711yescharacteristic
413C22×C5C2×#23711yescharacteristic
414C22×C5C2×#23911yescharacteristic
415C2×D5—64no—
416C2×D5—64no—
417C2×D5—64no—
418C2×D5—1216no—
419C2×D5—122no—
420C2×D5—122no—
421C2×D5—122no—
422C2×D5—122no—
423C4×C5—24no—
424C4×C5—64no—
425C4×C5—64no—
426Dic5—24no—
427Dic5—42no—
428Dic5—122no—
429C24—154no—
430C24—152no—
431C24—302no—
432C24—302no—
433C24—302no—
434C24—302no—
435C24—302no—
436C24—302no—
437C24C2×D3×D511yescharacteristic
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—34no—
441C22×C4—34no—
442C22×C4—32no—
443C22×C4—32no—
444C22×C4—54no—
445C22×C4—52no—
446C22×C4—52no—
447C22×C4—62no—
448C22×C4—62no—
449C22×C4—62no—
450C22×C4—62no—
451C22×C4—102no—
452C22×C4—102no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—102no—
456C22×C4—152no—
457C22×C4—302no—
458C22×C4—302no—
459C22×C4—302no—
460C22×C4#120314yes—
461C22×C4C2×D3×D512yes—
462C4⋊C4—308no—
463C22⋊C4—1516no—
464C22⋊C4—308no—
465C22⋊C4—308no—
466C42—68no—
467C3×C5C2×#38811yescharacteristic, complemented, Hall
468C22×C3#401814yes—
469C22×C3C4×D2014yes—
470C22×C3#402114yes—
471C22×C3#402214yes—
472C22×C3C4×C22⋊D514yes—
473C22×C3#407514yes—
474C22×C3#407614yes—
475C22×C3C22×C4×D511yescharacteristic
476C22×C3C22×D2011yescharacteristic
477C22×C3C2×#70911yescharacteristic
478C22×C3C2×#70911yescharacteristic
479C22×C3C2×#70911yescharacteristic
480C22×C3C2×#70911yescharacteristic
481C22×C3C22×C22⋊D511yescharacteristic
482C2×D3—104no—
483C2×D3—104no—
484C2×D3—104no—
485C2×D3—202no—
486C2×D3—202no—
487C2×D3—202no—
488C2×D3—202no—
489C2×D3—2016no—
490C3×C4—24no—
491C3×C4—104no—
492C3×C4—202no—
493Dic3—24no—
494Dic3—24no—
495Dic3—202no—
496C2×C5#467018yescomplemented
497C2×C5C2×C4×D1211yescharacteristic
498C2×C5C2×#67⋊C411yescharacteristic
499C2×C5C2×#88511yescharacteristic
500C2×C5C2×#88611yescharacteristic
501C2×C5C2×#89211yescharacteristic
502C2×C5C2×#89511yescharacteristic
503C2×C5C2×#89811yescharacteristic
504D5—124no—
505C23—154no—
506C23—308no—
507C23—308no—
508C23—308no—
509C23—302no—
510C23—302no—
511C23—302no—
512C23—302no—
513C23—302no—
514C23—302no—
515C23—604no—
516C23—604no—
517C23—604no—
518C23—604no—
519C23#676912yes—
520C23#677112yes—
521C23C4×D3×D512yes—
522C23D3×D2012yes—
523C23#677912yes—
524C23#677912yes—
525C23C2×#120312yes—
526C23C22×D3×D511yescharacteristic
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—28no—
530C2×C4—34no—
531C2×C4—34no—
532C2×C4—54no—
533C2×C4—68no—
534C2×C4—68no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—108no—
540C2×C4—102no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—102no—
545C2×C4—204no—
546C2×C4—302no—
547C2×C4—302no—
548C2×C4—302no—
549C2×C4—604no—
550C2×C4C2×#120314yes—
551C2×C3#6522918yescomplemented
552C2×C3C2×#401811yescharacteristic
553C2×C3C2×C4×D2011yescharacteristic
554C2×C3C2×#402111yescharacteristic
555C2×C3C2×#402211yescharacteristic
556C2×C3C2×C4×C22⋊D511yescharacteristic
557C2×C3C2×#407511yescharacteristic
558C2×C3C2×#407611yescharacteristic
559D3—204no—
560C5C2×#467011yescharacteristic, complemented, Sylow
561C22—304no—
562C22—304no—
563C22—304no—
564C22—602no—
565C22—602no—
566C22—602no—
567C22—6016no—
568C22—602no—
569C22#9135314yes—
570C22#9138014yes—
571C22#9139514yes—
572C22#9140314yes—
573C22C4×#120314yes—
574C22#9146014yes—
575C22#9154214yes—
576C22C2×#676911yescharacteristic
577C22C2×#677111yescharacteristic
578C22C2×C4×D3×D511yescharacteristic
579C22C2×D3×D2011yescharacteristic
580C22C2×#677911yescharacteristic
581C22C2×#677911yescharacteristic
582C22C22×#120311yescharacteristic
583C4—24no—
584C4—64no—
585C4—64no—
586C4—104no—
587C4—202no—
588C4—602no—
589C3C2×#6522911yescharacteristic, complemented, Sylow
590C2—604no—
591C2#1174873018yesdirect product factor
592C2C2×#9135311yescharacteristic
593C2C2×#9138011yescharacteristic
594C2C2×#9139511yescharacteristic
595C2C2×#9140311yescharacteristic
596C2C2×C4×#120311yescharacteristic
597C2C2×#9146011yescharacteristic
598C2C2×#9154211yescharacteristic
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×#388
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C5×Dic3C2semidirect
3. C22×#6668C2semidirect
6. C2×C3×#3963C2semidirect
7. C2×#90994C2semidirect
8. #11748730C2direct (N × H)
20. C2×C4×C5×Dic3C22semidirect
22. C2×#6668C22semidirect
24. C2×#6667C4semidirect
27. C3×#3963C22semidirect
28. #90994C22semidirect
36. C2×#3963D3semidirect
75. #6667C2×C4semidirect
80. C22×C4×Dic3D5semidirect
102. #3963C2×D3semidirect
166. C2×C4×Dic3C2×D5semidirect
346. C2×C3×C5#388semidirect
467. C3×C5C2×#388semidirect
496. C2×C5#4670semidirect
551. C2×C3#65229semidirect
560. C5C2×#4670semidirect
589. C3C2×#65229semidirect
591. C2#11748730direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67142
C22×C4×C5×Dic32
C22×#66682
C22×#66672
C2×C3×#39632
C2×#909942
#117487302
C2×#652293
C2×#46705