Finite Group Databasebeta

← C2×#11748883 #14320310

Subgroups — C2×#11748883 #14320310

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×#1203C211yesmaximal, characteristic
2C23×D3×Dic5C211yesmaximal, characteristic, complemented
3C22×#6714C211yesmaximal, characteristic, complemented
4C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C22×#6667C211yesmaximal, characteristic, complemented
6C2×C3×#3963C211yesmaximal, characteristic, complemented
7C2×#90994C211yesmaximal, characteristic, complemented
8#11748883C218yesmaximal, direct product factor
9C2×#65247—31nomaximal, Hall
10C24×D15C2211yescharacteristic
11C24×C5×D3C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×#1203—24no—
18C22×#1203—24no—
19C22×#1203C418yescomplemented
20C22×#1203C2214yes—
21C22×D3×Dic5—24no—
22C22×D3×Dic5—24no—
23C22×D3×Dic5—24no—
24C22×D3×Dic5C2214yescomplemented
25C2×#6714—24no—
26C2×#6714C2214yescomplemented
27C2×C5×(C2×D3)⋊C4—24no—
28C2×C5×(C2×D3)⋊C4C2214yescomplemented
29C2×#6667—24no—
30C2×#6667C2214yescomplemented
31C3×#3963C2214yescomplemented
32#90994C2214yescomplemented
33C2×#4665—51nomaximal, Hall
34C23×C22⋊D5—31no—
35C24×Dic5—31no—
36C22×C5×C22⋊C4—31no—
37C22×#685—31no—
38C22×#685—31no—
39C2×#3963—31no—
40C2×#3963D311yescharacteristic, complemented
41#65247—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×C5×D3—22no—
52C23×C5×D3—22no—
53C23×C5×D3—22no—
54C23×C5×D3—22no—
55C23×C5×D3C2×C414yes—
56C23×C5×D3D414yes—
57C23×C5×D3D414yes—
58C23×C5×D3C2312yes—
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×Dic3C2312yes—
71C22×C3×Dic5—22no—
72C22×C3×Dic5—22no—
73C22×C3×Dic5—22no—
74C22×C3×Dic5—22no—
75C22×C3×Dic5C2×C414yescomplemented
76C22×C3×Dic5D414yescomplemented
77C22×C3×Dic5C2312yes—
78C22×C3×Dic5C2312yes—
79C2×#1203—232no—
80C2×#1203—28no—
81C2×#1203—28no—
82C2×#1203C2×C4116yescomplemented
83C2×D3×Dic5—232no—
84C2×D3×Dic5—28no—
85C2×D3×Dic5—28no—
86C2×D3×Dic5—28no—
87#6714—28no—
88C5×(C2×D3)⋊C4—28no—
89#6667—28no—
90C23×D12—51no—
91C23×C4×D3—51no—
92C22×(C2×D3)⋊C4—51no—
93C22×(C2×D3)⋊C4—51no—
94C22×(C2×D3)⋊C4D511yescharacteristic, complemented
95C2×C3×#95—51no—
96C2×C3⋊#95—51no—
97#4665—58no—
98C25×C5—31no—
99C24×D5—31no—
100C23×C4×C5—31no—
101C23×C4×C5C2×D311yescharacteristic
102C22×C22⋊D5—38no—
103C22×C22⋊D5—34no—
104C22×C22⋊D5—64no—
105C22×C22⋊D5—64no—
106C23×Dic5—31no—
107C23×Dic5—34no—
108C23×Dic5—64no—
109C23×Dic5—64no—
110C23×Dic5—64no—
111C23×Dic5C2×D311yescharacteristic
112C23×Dic5C2×D311yescharacteristic
113C2×C5×C22⋊C4—34no—
114C2×C5×C22⋊C4—64no—
115C2×#685—34no—
116C2×#685—34no—
117C2×#685—64no—
118C2×#685—64no—
119#3963—34no—
120#3963C2×D314yescomplemented
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×C5×D3—28no—
145C22×C5×D3—28no—
146C22×C5×D3—28no—
147C22×C5×D3—28no—
148C22×C5×D3—28no—
149C22×C5×D3—28no—
150C22×C5×D3—22no—
151C22×C5×D3—22no—
152C22×C5×D3—22no—
153C22×C5×D3—22no—
154C22×C5×D3C22⋊C4116yescomplemented
155C22×C5×D3C22×C414yes—
156C22×C5×D3C2×D414yes—
157C22×C5×D3C2×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—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—44no—
170C2×C3×Dic5—28no—
171C2×C3×Dic5—28no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5C22×C414yescomplemented
177C2×C3×Dic5C2×D414yescomplemented
178#1203—232no—
179D3×Dic5—232no—
180C24×D3—51no—
181C24×D3C2×D511yescharacteristic
182C23×C3×C4—51no—
183C23×C3×C4—51no—
184C23×C3×C4C2×D511yescharacteristic
185C23×Dic3—51no—
186C23×Dic3C2×D511yescharacteristic
187C22×D12—58no—
188C22×D12—54no—
189C22×D12—104no—
190C22×D12—104no—
191C22×C4×D3—54no—
192C22×C4×D3—104no—
193C22×C4×D3—104no—
194C22×C4×D3—104no—
195C2×(C2×D3)⋊C4—24no—
196C2×(C2×D3)⋊C4—54no—
197C2×(C2×D3)⋊C4—54no—
198C2×(C2×D3)⋊C4—104no—
199C2×(C2×D3)⋊C4—104no—
200C2×(C2×D3)⋊C4C2×D514yescomplemented
201C3×#95—54no—
202C3⋊#95—54no—
203C24×C5—34no—
204C24×C5—34no—
205C24×C5—34no—
206C24×C5—32no—
207C24×C5—62no—
208C24×C5—62no—
209C24×C5—62no—
210C24×C5—62no—
211C24×C5C22×D311yescharacteristic
212C23×D5—34no—
213C23×D5—32no—
214C23×D5—62no—
215C23×D5—62no—
216C23×D5—62no—
217C23×D5—62no—
218C23×D5—62no—
219C23×D5—62no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—32no—
224C22×C4×C5—62no—
225C22×C4×C5—62no—
226C22×C4×C5—62no—
227C22×C4×C5C22×D312yes—
228C2×C22⋊D5—316no—
229C2×C22⋊D5—632no—
230C2×C22⋊D5—68no—
231C2×C22⋊D5—68no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—34no—
237C22×Dic5—32no—
238C22×Dic5—68no—
239C22×Dic5—68no—
240C22×Dic5—632no—
241C22×Dic5—62no—
242C22×Dic5—62no—
243C22×Dic5—68no—
244C22×Dic5C4×D314yescomplemented
245C22×Dic5D1214yescomplemented
246C22×Dic5C22×D312yes—
247C22×Dic5C22×D312yes—
248C5×C22⋊C4—68no—
249#685—68no—
250#685—68no—
251C23×D4—151no—
252C24×C4—151no—
253C22×C22⋊C4—31no—
254C22×C22⋊C4—151no—
255C22×C22⋊C4—151no—
256#386—158no—
257C2×#95—51no—
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×C5×D3—24no—
282C2×C5×D3—24no—
283C2×C5×D3—24no—
284C2×C5×D3—24no—
285C2×C5×D3—24no—
286C2×C5×D3—24no—
287C2×C5×D3—232no—
288C2×C5×D3C2×C22⋊C418yescomplemented
289C3×C4×C5—42no—
290Dic15—24no—
291C3×Dic5—24no—
292C3×Dic5—24no—
293C5×Dic3—42no—
294C24×C3C22×D511yescharacteristic
295C23×D3—22no—
296C23×D3—22no—
297C23×D3—22no—
298C23×D3—22no—
299C23×D3—54no—
300C23×D3—52no—
301C23×D3—102no—
302C23×D3—102no—
303C23×D3—102no—
304C23×D3—102no—
305C23×D3—102no—
306C23×D3—102no—
307C23×D3C4×D514yes—
308C23×D3D2014yes—
309C23×D3C22⋊D514yes—
310C23×D3C22×D512yes—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—22no—
314C22×C3×C4—54no—
315C22×C3×C4—54no—
316C22×C3×C4—52no—
317C22×C3×C4—52no—
318C22×C3×C4—102no—
319C22×C3×C4—102no—
320C22×C3×C4—102no—
321C22×C3×C4—102no—
322C22×C3×C4C22×D512yes—
323C22×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3—54no—
327C22×Dic3—52no—
328C22×Dic3—102no—
329C22×Dic3—102no—
330C22×Dic3C22×D512yes—
331C2×D12—516no—
332C2×D12—1032no—
333C2×D12—108no—
334C2×D12—108no—
335C2×C4×D3—108no—
336C2×C4×D3—108no—
337C2×C4×D3—1032no—
338C2×C4×D3—108no—
339(C2×D3)⋊C4—28no—
340(C2×D3)⋊C4—108no—
341(C2×D3)⋊C4—108no—
342C23×C5—316no—
343C23×C5—34no—
344C23×C5—34no—
345C23×C5—34no—
346C23×C5—68no—
347C23×C5—68no—
348C23×C5—68no—
349C23×C5—68no—
350C23×C5—68no—
351C23×C5—68no—
352C23×C5—62no—
353C23×C5—62no—
354C23×C5—62no—
355C23×C5—62no—
356C23×C5C2×C4×D312yes—
357C23×C5C2×D1212yes—
358C23×C5#23512yes—
359C23×C5D3×D412yes—
360C23×C5D3×D412yes—
361C23×C5D3×D412yes—
362C23×C5#23912yes—
363C23×C5C23×D311yescharacteristic
364C22×D5—34no—
365C22×D5—68no—
366C22×D5—68no—
367C22×D5—68no—
368C22×D5—62no—
369C22×D5—62no—
370C22×D5—62no—
371C22×D5—62no—
372C22×D5—62no—
373C22×D5—62no—
374C22×D5—124no—
375C22×D5—124no—
376C22×D5—124no—
377C22×D5—124no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—44no—
382C2×C4×C5—62no—
383C2×C4×C5—62no—
384C2×C4×C5—62no—
385C2×C4×C5—124no—
386C22⋊D5—632no—
387C2×Dic5—28no—
388C2×Dic5—28no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—34no—
394C2×Dic5—632no—
395C2×Dic5—68no—
396C2×Dic5—62no—
397C2×Dic5—62no—
398C2×Dic5C2×C4×D314yescomplemented
399C2×Dic5C2×D1214yescomplemented
400C25—31no—
401C25—151no—
402C22×D4—154no—
403C22×D4—158no—
404C22×D4—304no—
405C22×D4—304no—
406C23×C4—31no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—154no—
410C23×C4—151no—
411C23×C4—304no—
412C23×C4—304no—
413C23×C4—304no—
414C23×C4D3×D511yescharacteristic
415C2×C22⋊C4—34no—
416C2×C22⋊C4—64no—
417C2×C22⋊C4—154no—
418C2×C22⋊C4—154no—
419C2×C22⋊C4—304no—
420C2×C22⋊C4—304no—
421#95—54no—
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—
432C5×D3—28no—
433C23×C3C2×C4×D512yes—
434C23×C3C2×D2012yes—
435C23×C3D4×D512yes—
436C23×C3D4×D512yes—
437C23×C3#71112yes—
438C23×C3#71112yes—
439C23×C3C2×C22⋊D512yes—
440C23×C3C23×D511yescharacteristic
441C22×D3—22no—
442C22×D3—22no—
443C22×D3—22no—
444C22×D3—22no—
445C22×D3—28no—
446C22×D3—28no—
447C22×D3—28no—
448C22×D3—28no—
449C22×D3—28no—
450C22×D3—28no—
451C22×D3—54no—
452C22×D3—102no—
453C22×D3—102no—
454C22×D3—102no—
455C22×D3—102no—
456C22×D3—102no—
457C22×D3—102no—
458C22×D3—108no—
459C22×D3—108no—
460C22×D3—108no—
461C22×D3—204no—
462C22×D3—204no—
463C22×D3—204no—
464C22×D3—204no—
465C22×D3#685116yescomplemented
466C22×D3C2×C4×D514yes—
467C22×D3C2×D2014yes—
468C22×D3C2×C22⋊D514yes—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—44no—
473C2×C3×C4—54no—
474C2×C3×C4—54no—
475C2×C3×C4—102no—
476C2×C3×C4—102no—
477C2×C3×C4—102no—
478C2×C3×C4—102no—
479C2×C3×C4—108no—
480C2×C3×C4—108no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—44no—
485C2×Dic3—54no—
486C2×Dic3—102no—
487C2×Dic3—102no—
488C2×Dic3—108no—
489D12—1032no—
490C4×D3—1032no—
491C22×C5—38no—
492C22×C5—632no—
493C22×C5—64no—
494C22×C5—64no—
495C22×C5—64no—
496C22×C5—64no—
497C22×C5—64no—
498C22×C5—64no—
499C22×C5C4×D1214yes—
500C22×C5D3×C22⋊C414yes—
501C22×C5#88214yes—
502C22×C5#88414yes—
503C22×C5#89314yes—
504C22×C5#89414yes—
505C22×C5#89514yes—
506C22×C5C22×C4×D311yescharacteristic
507C22×C5C22×D1211yescharacteristic
508C22×C5C2×#23511yescharacteristic
509C22×C5C2×D3×D411yescharacteristic
510C22×C5C2×D3×D411yescharacteristic
511C22×C5C2×D3×D411yescharacteristic
512C22×C5C2×#23911yescharacteristic
513C2×D5—64no—
514C2×D5—64no—
515C2×D5—64no—
516C2×D5—1216no—
517C2×D5—122no—
518C2×D5—122no—
519C2×D5—122no—
520C2×D5—122no—
521C4×C5—42no—
522C4×C5—122no—
523Dic5—24no—
524Dic5—24no—
525Dic5—64no—
526C24—34no—
527C24—34no—
528C24—34no—
529C24—32no—
530C24—62no—
531C24—62no—
532C24—62no—
533C24—62no—
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—32no—
551C22×C4—54no—
552C22×C4—54no—
553C22×C4—52no—
554C22×C4—52no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—102no—
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—68no—
572C22⋊C4—308no—
573C22⋊C4—308no—
574C3×C5C2×#38611yescharacteristic, complemented, Hall
575C22×C3#402714yes—
576C22×C3#402714yes—
577C22×C3#402814yes—
578C22×C3#403214yes—
579C22×C3C2×#68514yes—
580C22×C3#408514yes—
581C22×C3#408514yes—
582C22×C3C22×C4×D511yescharacteristic
583C22×C3C22×D2011yescharacteristic
584C22×C3C2×D4×D511yescharacteristic
585C22×C3C2×D4×D511yescharacteristic
586C22×C3C2×#71111yescharacteristic
587C22×C3C2×#71111yescharacteristic
588C22×C3C22×C22⋊D511yescharacteristic
589C2×D3—24no—
590C2×D3—24no—
591C2×D3—24no—
592C2×D3—24no—
593C2×D3—24no—
594C2×D3—24no—
595C2×D3—232no—
596C2×D3—104no—
597C2×D3—104no—
598C2×D3—104no—
599C2×D3—202no—
600C2×D3—202no—
601C2×D3—202no—
602C2×D3—202no—
603C2×D3—2016no—
604C2×D3C2×#68518yescomplemented
605C3×C4—42no—
606C3×C4—104no—
607C3×C4—104no—
608Dic3—42no—
609Dic3—104no—
610C2×C5—68no—
611C2×C5#466518yescomplemented
612C2×C5C2×C4×D1211yescharacteristic
613C2×C5C2×D3×C22⋊C411yescharacteristic
614C2×C5C2×#88211yescharacteristic
615C2×C5C2×#88411yescharacteristic
616C2×C5C2×#89311yescharacteristic
617C2×C5C2×#89411yescharacteristic
618C2×C5C2×#89511yescharacteristic
619D5—124no—
620C23—316no—
621C23—34no—
622C23—34no—
623C23—34no—
624C23—68no—
625C23—68no—
626C23—68no—
627C23—68no—
628C23—68no—
629C23—62no—
630C23—62no—
631C23—62no—
632C23—62no—
633C23—68no—
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#676812yes—
649C23C4×D3×D512yes—
650C23D5×D1212yes—
651C23D3×D2012yes—
652C23#678212yes—
653C23D3×C22⋊D512yes—
654C23#679012yes—
655C23C22×D3×D511yescharacteristic
656D4—3032no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—44no—
661C2×C4—54no—
662C2×C4—54no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—108no—
667C2×C4—108no—
668C2×C4—102no—
669C2×C4—102no—
670C2×C4—102no—
671C2×C4—102no—
672C2×C4—124no—
673C2×C4—154no—
674C2×C4—3032no—
675C2×C4—308no—
676C2×C4—302no—
677C2×C4—302no—
678C2×C3#6524718yescomplemented
679C2×C3C2×#402711yescharacteristic
680C2×C3C2×#402711yescharacteristic
681C2×C3C2×#402811yescharacteristic
682C2×C3C2×#403211yescharacteristic
683C2×C3C22×#68511yescharacteristic
684C2×C3C2×#408511yescharacteristic
685C2×C3C2×#408511yescharacteristic
686D3—28no—
687D3—204no—
688C5C2×#466511yescharacteristic, complemented, Sylow
689C22—38no—
690C22—632no—
691C22—64no—
692C22—64no—
693C22—64no—
694C22—64no—
695C22—64no—
696C22—64no—
697C22—304no—
698C22—304no—
699C22—304no—
700C22—6016no—
701C22—602no—
702C22—602no—
703C22—602no—
704C22—602no—
705C22#9140514yes—
706C22#9140614yes—
707C22#9141614yes—
708C22#9142714yes—
709C22D3×#68514yes—
710C22#9147614yes—
711C22#9155814yes—
712C22C2×#676811yescharacteristic
713C22C2×C4×D3×D511yescharacteristic
714C22C2×D5×D1211yescharacteristic
715C22C2×D3×D2011yescharacteristic
716C22C2×#678211yescharacteristic
717C22C2×D3×C22⋊D511yescharacteristic
718C22C2×#679011yescharacteristic
719C4—42no—
720C4—104no—
721C4—104no—
722C4—122no—
723C4—304no—
724C3C2×#6524711yescharacteristic, complemented, Sylow
725C2—68no—
726C2—604no—
727C2#1174888318yesdirect product factor
728C2C2×#9140511yescharacteristic
729C2C2×#9140611yescharacteristic
730C2C2×#9141611yescharacteristic
731C2C2×#9142711yescharacteristic
732C2C2×D3×#68511yescharacteristic
733C2C2×#9147611yescharacteristic
734C2C2×#9155811yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socleC24×C3×C5C23
prime radicalC23×#1203C2
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×D3×Dic5C2semidirect
3. C22×#6714C2semidirect
4. C22×C5×(C2×D3)⋊C4C2semidirect
5. C22×#6667C2semidirect
6. C2×C3×#3963C2semidirect
7. C2×#90994C2semidirect
8. #11748883C2direct (N × H)
19. C22×#1203C4semidirect
24. C22×D3×Dic5C22semidirect
26. C2×#6714C22semidirect
28. C2×C5×(C2×D3)⋊C4C22semidirect
30. C2×#6667C22semidirect
31. C3×#3963C22semidirect
32. #90994C22semidirect
40. C2×#3963D3semidirect
49. C23×D15C2×C4semidirect
65. C22×Dic15D4semidirect
75. C22×C3×Dic5C2×C4semidirect
76. C22×C3×Dic5D4semidirect
82. C2×#1203C2×C4semidirect
94. C22×(C2×D3)⋊C4D5semidirect
120. #3963C2×D3semidirect
143. C22×D15C22×C4semidirect
154. C22×C5×D3C22⋊C4semidirect
165. C2×Dic15C2×D4semidirect
176. C2×C3×Dic5C22×C4semidirect
177. C2×C3×Dic5C2×D4semidirect
200. C2×(C2×D3)⋊C4C2×D5semidirect
244. C22×Dic5C4×D3semidirect
245. C22×Dic5D12semidirect
288. C2×C5×D3C2×C22⋊C4semidirect
398. C2×Dic5C2×C4×D3semidirect
399. C2×Dic5C2×D12semidirect
423. C2×C3×C5#386semidirect
465. C22×D3#685semidirect
574. C3×C5C2×#386semidirect
604. C2×D3C2×#685semidirect
611. C2×C5#4665semidirect
678. C2×C3#65247semidirect
688. C5C2×#4665semidirect
724. C3C2×#65247semidirect
727. C2#11748883direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#12032
C23×D3×Dic52
C22×#67142
C22×C5×(C2×D3)⋊C42
C22×#66672
C2×C3×#39632
C2×#909942
#117488832
C2×#652473
C2×#46655