Finite Group Databasebeta

← C2×#11748872 #14320312

Subgroups — C2×#11748872 #14320312

Order 1920.

3152 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1202C211yesmaximal, characteristic
2C23×D5×Dic3C211yesmaximal, characteristic, complemented
3C22×#6714C211yesmaximal, characteristic, complemented
4C22×C3×#685C211yesmaximal, characteristic, complemented
5C22×#6667C211yesmaximal, characteristic, complemented
6C2×C5×C3⋊#95C211yesmaximal, characteristic, complemented
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748872C218yesmaximal, direct product factor
9C2×#64954—31nomaximal, Hall
10C24×D15C2211yescharacteristic
11C24×C3×D5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×#1202—24no—
18C22×#1202—24no—
19C22×#1202C418yescomplemented
20C22×#1202C2214yes—
21C22×D5×Dic3—24no—
22C22×D5×Dic3—24no—
23C22×D5×Dic3—24no—
24C22×D5×Dic3C2214yescomplemented
25C2×#6714—24no—
26C2×#6714C2214yescomplemented
27C2×C3×#685—24no—
28C2×C3×#685C2214yescomplemented
29C2×#6667—24no—
30C2×#6667C2214yescomplemented
31C5×C3⋊#95C2214yescomplemented
32#90994C2214yescomplemented
33C2×#4958—51nomaximal, Hall
34C23×D20—31no—
35C23×C4×D5—31no—
36C22×#685—31no—
37C22×#685—31no—
38C22×#685D311yescharacteristic, complemented
39C2×C5×#95—31no—
40C2×#3963—31no—
41#64954—38no—
42C24×C3×C5C2311yescharacteristic
43C23×D15—22no—
44C23×D15—22no—
45C23×D15—22no—
46C23×D15—22no—
47C23×D15—22no—
48C23×D15—22no—
49C23×D15C2×C414yescomplemented
50C23×D15C2312yes—
51C23×C3×D5—22no—
52C23×C3×D5—22no—
53C23×C3×D5—22no—
54C23×C3×D5—22no—
55C23×C3×D5C2×C414yes—
56C23×C3×D5D414yes—
57C23×C3×D5D414yes—
58C23×C3×D5C2312yes—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5C2312yes—
63C22×Dic15—22no—
64C22×Dic15—22no—
65C22×Dic15D414yescomplemented
66C22×Dic15C2312yes—
67C22×C5×Dic3—22no—
68C22×C5×Dic3—22no—
69C22×C5×Dic3—22no—
70C22×C5×Dic3—22no—
71C22×C5×Dic3C2×C414yescomplemented
72C22×C5×Dic3D414yescomplemented
73C22×C5×Dic3C2312yes—
74C22×C5×Dic3C2312yes—
75C22×C3×Dic5—22no—
76C22×C3×Dic5—22no—
77C22×C3×Dic5—22no—
78C22×C3×Dic5C2312yes—
79C2×#1202—232no—
80C2×#1202—28no—
81C2×#1202—28no—
82C2×#1202C2×C4116yescomplemented
83C2×D5×Dic3—232no—
84C2×D5×Dic3—28no—
85C2×D5×Dic3—28no—
86C2×D5×Dic3—28no—
87#6714—28no—
88C3×#685—28no—
89#6667—28no—
90C23×#67—51no—
91C24×Dic3—51no—
92C22×C3×C22⋊C4—51no—
93C22×(C2×D3)⋊C4—51no—
94C22×(C2×D3)⋊C4—51no—
95C2×C3⋊#95—51no—
96C2×C3⋊#95D511yescharacteristic, complemented
97#4958—58no—
98C24×D5—31no—
99C24×D5C2×D311yescharacteristic
100C23×C4×C5—31no—
101C23×C4×C5—31no—
102C23×C4×C5C2×D311yescharacteristic
103C23×Dic5—31no—
104C23×Dic5C2×D311yescharacteristic
105C22×D20—38no—
106C22×D20—34no—
107C22×D20—64no—
108C22×D20—64no—
109C22×C4×D5—34no—
110C22×C4×D5—64no—
111C22×C4×D5—64no—
112C22×C4×D5—64no—
113C2×#685—24no—
114C2×#685—34no—
115C2×#685—34no—
116C2×#685—64no—
117C2×#685—64no—
118C2×#685C2×D314yescomplemented
119C5×#95—34no—
120#3963—34no—
121C2×#386—151noSylow
122C23×C3×C5C22×C412yes—
123C23×C3×C5C2×D412yes—
124C23×C3×C5C2×D412yes—
125C23×C3×C5C2×D412yes—
126C23×C3×C5C2×D412yes—
127C23×C3×C5#4112yes—
128C23×C3×C5#4112yes—
129C23×C3×C5C2411yescharacteristic
130C22×D15—28no—
131C22×D15—28no—
132C22×D15—28no—
133C22×D15—22no—
134C22×D15—22no—
135C22×D15—22no—
136C22×D15—22no—
137C22×D15—22no—
138C22×D15—22no—
139C22×D15—44no—
140C22×D15—44no—
141C22×D15—44no—
142C22×D15—44no—
143C22×D15C22×C414yescomplemented
144C22×C3×D5—28no—
145C22×C3×D5—28no—
146C22×C3×D5—28no—
147C22×C3×D5—28no—
148C22×C3×D5—28no—
149C22×C3×D5—28no—
150C22×C3×D5—22no—
151C22×C3×D5—22no—
152C22×C3×D5—22no—
153C22×C3×D5—22no—
154C22×C3×D5C22⋊C4116yescomplemented
155C22×C3×D5C22×C414yes—
156C22×C3×D5C2×D414yes—
157C22×C3×D5C2×D414yes—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—44no—
162C2×Dic15—28no—
163C2×Dic15—22no—
164C2×Dic15—22no—
165C2×Dic15C2×D414yescomplemented
166C2×C5×Dic3—28no—
167C2×C5×Dic3—28no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—22no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3C22×C414yescomplemented
173C2×C5×Dic3C2×D414yescomplemented
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—22no—
177C2×C3×Dic5—44no—
178#1202—232no—
179D5×Dic3—232no—
180C25×C3—51no—
181C24×D3—51no—
182C23×C3×C4—51no—
183C23×C3×C4C2×D511yescharacteristic
184C22×#67—58no—
185C22×#67—54no—
186C22×#67—104no—
187C22×#67—104no—
188C23×Dic3—51no—
189C23×Dic3—54no—
190C23×Dic3—104no—
191C23×Dic3—104no—
192C23×Dic3—104no—
193C23×Dic3C2×D511yescharacteristic
194C23×Dic3C2×D511yescharacteristic
195C2×C3×C22⋊C4—54no—
196C2×C3×C22⋊C4—104no—
197C2×(C2×D3)⋊C4—54no—
198C2×(C2×D3)⋊C4—54no—
199C2×(C2×D3)⋊C4—104no—
200C2×(C2×D3)⋊C4—104no—
201C3⋊#95—54no—
202C3⋊#95C2×D514yescomplemented
203C24×C5C22×D311yescharacteristic
204C23×D5—22no—
205C23×D5—22no—
206C23×D5—22no—
207C23×D5—22no—
208C23×D5—34no—
209C23×D5—32no—
210C23×D5—62no—
211C23×D5—62no—
212C23×D5—62no—
213C23×D5—62no—
214C23×D5—62no—
215C23×D5—62no—
216C23×D5C4×D314yes—
217C23×D5D1214yes—
218C23×D5#6714yes—
219C23×D5C22×D312yes—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—34no—
224C22×C4×C5—34no—
225C22×C4×C5—32no—
226C22×C4×C5—32no—
227C22×C4×C5—62no—
228C22×C4×C5—62no—
229C22×C4×C5—62no—
230C22×C4×C5—62no—
231C22×C4×C5C22×D312yes—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—34no—
236C22×Dic5—32no—
237C22×Dic5—62no—
238C22×Dic5—62no—
239C22×Dic5C22×D312yes—
240C2×D20—316no—
241C2×D20—632no—
242C2×D20—68no—
243C2×D20—68no—
244C2×C4×D5—68no—
245C2×C4×D5—68no—
246C2×C4×D5—632no—
247C2×C4×D5—68no—
248#685—28no—
249#685—68no—
250#685—68no—
251C23×D4—151no—
252C24×C4—151no—
253C22×C22⋊C4—51no—
254C22×C22⋊C4—151no—
255C22×C22⋊C4—151no—
256#386—158no—
257C2×#95—31no—
258C2×#95—151no—
259C22×C3×C5C2×C22⋊C414yes—
260C22×C3×C5C4×D414yes—
261C22×C3×C5C4×D414yes—
262C22×C3×C5#12014yes—
263C22×C3×C5#12114yes—
264C22×C3×C5#12114yes—
265C22×C3×C5#12314yes—
266C22×C3×C5C23×C411yescharacteristic
267C22×C3×C5C22×D411yescharacteristic
268C22×C3×C5C22×D411yescharacteristic
269C22×C3×C5C22×D411yescharacteristic
270C22×C3×C5C22×D411yescharacteristic
271C22×C3×C5C2×#4111yescharacteristic
272C22×C3×C5C2×#4111yescharacteristic
273C2×D15—24no—
274C2×D15—24no—
275C2×D15—24no—
276C2×D15—42no—
277C2×D15—42no—
278C2×D15—42no—
279C2×D15—42no—
280C2×D15—416no—
281C2×C3×D5—24no—
282C2×C3×D5—24no—
283C2×C3×D5—24no—
284C2×C3×D5—24no—
285C2×C3×D5—24no—
286C2×C3×D5—24no—
287C2×C3×D5—232no—
288C2×C3×D5C2×C22⋊C418yescomplemented
289C3×C4×C5—42no—
290Dic15—24no—
291C3×Dic5—42no—
292C5×Dic3—24no—
293C5×Dic3—24no—
294C24×C3—54no—
295C24×C3—54no—
296C24×C3—54no—
297C24×C3—52no—
298C24×C3—102no—
299C24×C3—102no—
300C24×C3—102no—
301C24×C3—102no—
302C24×C3C22×D511yescharacteristic
303C23×D3—54no—
304C23×D3—52no—
305C23×D3—102no—
306C23×D3—102no—
307C23×D3—102no—
308C23×D3—102no—
309C23×D3—102no—
310C23×D3—102no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—22no—
314C22×C3×C4—52no—
315C22×C3×C4—102no—
316C22×C3×C4—102no—
317C22×C3×C4—102no—
318C22×C3×C4C22×D512yes—
319C2×#67—516no—
320C2×#67—108no—
321C2×#67—108no—
322C2×#67—1032no—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3—22no—
327C22×Dic3—54no—
328C22×Dic3—52no—
329C22×Dic3—108no—
330C22×Dic3—108no—
331C22×Dic3—1032no—
332C22×Dic3—102no—
333C22×Dic3—102no—
334C22×Dic3—108no—
335C22×Dic3C4×D514yescomplemented
336C22×Dic3D2014yescomplemented
337C22×Dic3C22×D512yes—
338C22×Dic3C22×D512yes—
339C3×C22⋊C4—108no—
340(C2×D3)⋊C4—108no—
341(C2×D3)⋊C4—108no—
342C23×C5C2×C4×D312yes—
343C23×C5C2×D1212yes—
344C23×C5D3×D412yes—
345C23×C5D3×D412yes—
346C23×C5#23712yes—
347C23×C5#23712yes—
348C23×C5C2×#6712yes—
349C23×C5C23×D311yescharacteristic
350C22×D5—28no—
351C22×D5—28no—
352C22×D5—28no—
353C22×D5—28no—
354C22×D5—28no—
355C22×D5—28no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5—22no—
359C22×D5—22no—
360C22×D5—34no—
361C22×D5—68no—
362C22×D5—68no—
363C22×D5—68no—
364C22×D5—62no—
365C22×D5—62no—
366C22×D5—62no—
367C22×D5—62no—
368C22×D5—62no—
369C22×D5—62no—
370C22×D5—124no—
371C22×D5—124no—
372C22×D5—124no—
373C22×D5—124no—
374C22×D5(C2×D3)⋊C4116yescomplemented
375C22×D5C2×C4×D314yes—
376C22×D5C2×D1214yes—
377C22×D5C2×#6714yes—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—34no—
382C2×C4×C5—34no—
383C2×C4×C5—44no—
384C2×C4×C5—68no—
385C2×C4×C5—68no—
386C2×C4×C5—62no—
387C2×C4×C5—62no—
388C2×C4×C5—62no—
389C2×C4×C5—62no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—34no—
394C2×Dic5—44no—
395C2×Dic5—68no—
396C2×Dic5—62no—
397C2×Dic5—62no—
398D20—632no—
399C4×D5—632no—
400C25—51no—
401C25—151no—
402C22×D4—154no—
403C22×D4—158no—
404C22×D4—304no—
405C22×D4—304no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—51no—
409C23×C4—154no—
410C23×C4—151no—
411C23×C4—304no—
412C23×C4—304no—
413C23×C4—304no—
414C23×C4D3×D511yescharacteristic
415C2×C22⋊C4—54no—
416C2×C22⋊C4—104no—
417C2×C22⋊C4—154no—
418C2×C22⋊C4—154no—
419C2×C22⋊C4—304no—
420C2×C22⋊C4—304no—
421#95—34no—
422#95—154no—
423C2×C3×C5#38618yescomplemented
424C2×C3×C5C22×C22⋊C411yescharacteristic
425C2×C3×C5C2×C4×D411yescharacteristic
426C2×C3×C5C2×C4×D411yescharacteristic
427C2×C3×C5C2×#12011yescharacteristic
428C2×C3×C5C2×#12111yescharacteristic
429C2×C3×C5C2×#12111yescharacteristic
430C2×C3×C5C2×#12311yescharacteristic
431D15—44no—
432C3×D5—28no—
433C23×C3—54no—
434C23×C3—54no—
435C23×C3—54no—
436C23×C3—516no—
437C23×C3—102no—
438C23×C3—102no—
439C23×C3—102no—
440C23×C3—102no—
441C23×C3—108no—
442C23×C3—108no—
443C23×C3—108no—
444C23×C3—108no—
445C23×C3—108no—
446C23×C3—108no—
447C23×C3C2×C4×D512yes—
448C23×C3C2×D2012yes—
449C23×C3#70912yes—
450C23×C3D4×D512yes—
451C23×C3D4×D512yes—
452C23×C3D4×D512yes—
453C23×C3#71312yes—
454C23×C3C23×D511yescharacteristic
455C22×D3—54no—
456C22×D3—102no—
457C22×D3—102no—
458C22×D3—102no—
459C22×D3—102no—
460C22×D3—102no—
461C22×D3—102no—
462C22×D3—108no—
463C22×D3—108no—
464C22×D3—108no—
465C22×D3—204no—
466C22×D3—204no—
467C22×D3—204no—
468C22×D3—204no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—44no—
473C2×C3×C4—102no—
474C2×C3×C4—102no—
475C2×C3×C4—102no—
476C2×C3×C4—204no—
477#67—1032no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—28no—
483C2×Dic3—28no—
484C2×Dic3—54no—
485C2×Dic3—1032no—
486C2×Dic3—102no—
487C2×Dic3—102no—
488C2×Dic3—108no—
489C2×Dic3C2×C4×D514yescomplemented
490C2×Dic3C2×D2014yescomplemented
491C22×C5#67⋊C414yes—
492C22×C5#67⋊C414yes—
493C22×C5#88214yes—
494C22×C5#88614yes—
495C22×C5C2×(C2×D3)⋊C414yes—
496C22×C5#93914yes—
497C22×C5#93914yes—
498C22×C5C22×C4×D311yescharacteristic
499C22×C5C22×D1211yescharacteristic
500C22×C5C2×D3×D411yescharacteristic
501C22×C5C2×D3×D411yescharacteristic
502C22×C5C2×#23711yescharacteristic
503C22×C5C2×#23711yescharacteristic
504C22×C5C22×#6711yescharacteristic
505C2×D5—232no—
506C2×D5—24no—
507C2×D5—24no—
508C2×D5—24no—
509C2×D5—24no—
510C2×D5—24no—
511C2×D5—24no—
512C2×D5—64no—
513C2×D5—64no—
514C2×D5—64no—
515C2×D5—1216no—
516C2×D5—122no—
517C2×D5—122no—
518C2×D5—122no—
519C2×D5—122no—
520C2×D5C2×(C2×D3)⋊C418yescomplemented
521C4×C5—42no—
522C4×C5—64no—
523C4×C5—64no—
524Dic5—42no—
525Dic5—64no—
526C24—54no—
527C24—54no—
528C24—54no—
529C24—52no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24—154no—
535C24—152no—
536C24—302no—
537C24—302no—
538C24—302no—
539C24—302no—
540C24—302no—
541C24—302no—
542C24C2×D3×D511yescharacteristic
543C2×D4—1516no—
544C2×D4—3032no—
545C2×D4—308no—
546C2×D4—308no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—34no—
551C22×C4—34no—
552C22×C4—32no—
553C22×C4—32no—
554C22×C4—52no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—102no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—154no—
563C22×C4—152no—
564C22×C4—308no—
565C22×C4—308no—
566C22×C4—308no—
567C22×C4—3032no—
568C22×C4—302no—
569C22×C4—302no—
570C22×C4C2×D3×D512yes—
571C22⋊C4—108no—
572C22⋊C4—308no—
573C22⋊C4—308no—
574C3×C5C2×#38611yescharacteristic, complemented, Hall
575C22×C3—58no—
576C22×C3—104no—
577C22×C3—104no—
578C22×C3—104no—
579C22×C3—104no—
580C22×C3—104no—
581C22×C3—104no—
582C22×C3—1032no—
583C22×C3C4×D2014yes—
584C22×C3D5×C22⋊C414yes—
585C22×C3#402814yes—
586C22×C3#403014yes—
587C22×C3#403914yes—
588C22×C3#404014yes—
589C22×C3#404114yes—
590C22×C3C22×C4×D511yescharacteristic
591C22×C3C22×D2011yescharacteristic
592C22×C3C2×#70911yescharacteristic
593C22×C3C2×D4×D511yescharacteristic
594C22×C3C2×D4×D511yescharacteristic
595C22×C3C2×D4×D511yescharacteristic
596C22×C3C2×#71311yescharacteristic
597C2×D3—104no—
598C2×D3—104no—
599C2×D3—104no—
600C2×D3—202no—
601C2×D3—202no—
602C2×D3—202no—
603C2×D3—202no—
604C2×D3—2016no—
605C3×C4—42no—
606C3×C4—202no—
607Dic3—24no—
608Dic3—24no—
609Dic3—104no—
610C2×C5#495818yescomplemented
611C2×C5C2×#67⋊C411yescharacteristic
612C2×C5C2×#67⋊C411yescharacteristic
613C2×C5C2×#88211yescharacteristic
614C2×C5C2×#88611yescharacteristic
615C2×C5C22×(C2×D3)⋊C411yescharacteristic
616C2×C5C2×#93911yescharacteristic
617C2×C5C2×#93911yescharacteristic
618D5—28no—
619D5—124no—
620C23—516no—
621C23—54no—
622C23—54no—
623C23—54no—
624C23—108no—
625C23—108no—
626C23—108no—
627C23—108no—
628C23—108no—
629C23—102no—
630C23—102no—
631C23—102no—
632C23—102no—
633C23—108no—
634C23—154no—
635C23—308no—
636C23—308no—
637C23—308no—
638C23—302no—
639C23—302no—
640C23—302no—
641C23—302no—
642C23—302no—
643C23—302no—
644C23—604no—
645C23—604no—
646C23—604no—
647C23—604no—
648C23#676612yes—
649C23C4×D3×D512yes—
650C23D5×D1212yes—
651C23D3×D2012yes—
652C23#677912yes—
653C23D5×#6712yes—
654C23#679012yes—
655C23C22×D3×D511yescharacteristic
656D4—3032no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—34no—
661C2×C4—34no—
662C2×C4—44no—
663C2×C4—68no—
664C2×C4—68no—
665C2×C4—62no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—102no—
670C2×C4—102no—
671C2×C4—102no—
672C2×C4—154no—
673C2×C4—204no—
674C2×C4—3032no—
675C2×C4—308no—
676C2×C4—302no—
677C2×C4—302no—
678C2×C3—108no—
679C2×C3#6495418yescomplemented
680C2×C3C2×C4×D2011yescharacteristic
681C2×C3C2×D5×C22⋊C411yescharacteristic
682C2×C3C2×#402811yescharacteristic
683C2×C3C2×#403011yescharacteristic
684C2×C3C2×#403911yescharacteristic
685C2×C3C2×#404011yescharacteristic
686C2×C3C2×#404111yescharacteristic
687D3—204no—
688C5C2×#495811yescharacteristic, complemented, Sylow
689C22—58no—
690C22—1032no—
691C22—104no—
692C22—104no—
693C22—104no—
694C22—104no—
695C22—104no—
696C22—104no—
697C22—304no—
698C22—304no—
699C22—304no—
700C22—6016no—
701C22—602no—
702C22—602no—
703C22—602no—
704C22—602no—
705C22#9139514yes—
706C22#9139614yes—
707C22#9140914yes—
708C22#9141314yes—
709C22D5×(C2×D3)⋊C414yes—
710C22#9147614yes—
711C22#9155014yes—
712C22C2×#676611yescharacteristic
713C22C2×C4×D3×D511yescharacteristic
714C22C2×D5×D1211yescharacteristic
715C22C2×D3×D2011yescharacteristic
716C22C2×#677911yescharacteristic
717C22C2×D5×#6711yescharacteristic
718C22C2×#679011yescharacteristic
719C4—42no—
720C4—64no—
721C4—64no—
722C4—202no—
723C4—304no—
724C3C2×#6495411yescharacteristic, complemented, Sylow
725C2—108no—
726C2—604no—
727C2#1174887218yesdirect product factor
728C2C2×#9139511yescharacteristic
729C2C2×#9139611yescharacteristic
730C2C2×#9140911yescharacteristic
731C2C2×#9141311yescharacteristic
732C2C2×D5×(C2×D3)⋊C411yescharacteristic
733C2C2×#9147611yescharacteristic
734C2C2×#9155011yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socleC24×C3×C5C23
prime radicalC23×#1202C2
cosocleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#386
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. C23×D5×Dic3C2semidirect
3. C22×#6714C2semidirect
4. C22×C3×#685C2semidirect
5. C22×#6667C2semidirect
6. C2×C5×C3⋊#95C2semidirect
7. C2×#90994C2semidirect
8. #11748872C2direct (N × H)
19. C22×#1202C4semidirect
24. C22×D5×Dic3C22semidirect
26. C2×#6714C22semidirect
28. C2×C3×#685C22semidirect
30. C2×#6667C22semidirect
31. C5×C3⋊#95C22semidirect
32. #90994C22semidirect
38. C22×#685D3semidirect
49. C23×D15C2×C4semidirect
65. C22×Dic15D4semidirect
71. C22×C5×Dic3C2×C4semidirect
72. C22×C5×Dic3D4semidirect
82. C2×#1202C2×C4semidirect
96. C2×C3⋊#95D5semidirect
118. C2×#685C2×D3semidirect
143. C22×D15C22×C4semidirect
154. C22×C3×D5C22⋊C4semidirect
165. C2×Dic15C2×D4semidirect
172. C2×C5×Dic3C22×C4semidirect
173. C2×C5×Dic3C2×D4semidirect
202. C3⋊#95C2×D5semidirect
288. C2×C3×D5C2×C22⋊C4semidirect
335. C22×Dic3C4×D5semidirect
336. C22×Dic3D20semidirect
374. C22×D5(C2×D3)⋊C4semidirect
423. C2×C3×C5#386semidirect
489. C2×Dic3C2×C4×D5semidirect
490. C2×Dic3C2×D20semidirect
520. C2×D5C2×(C2×D3)⋊C4semidirect
574. C3×C5C2×#386semidirect
610. C2×C5#4958semidirect
679. C2×C3#64954semidirect
688. C5C2×#4958semidirect
724. C3C2×#64954semidirect
727. C2#11748872direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#12022
C23×D5×Dic32
C22×#67142
C22×C3×#6852
C22×#66672
C2×C5×C3⋊#952
C2×#909942
#117488722
C2×#649543
C2×#49585