Finite Group Databasebeta

← C2×#11748916 #14320793

Subgroups — C2×#11748916 #14320793

Order 1920.

2720 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1201C211yesmaximal, characteristic
2C22×#6712C211yesmaximal, characteristic, complemented
3C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C22×C3×#685C211yesmaximal, characteristic, complemented
5C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
6C22×#6665C211yesmaximal, characteristic, complemented
7C22×Dic3×Dic5C211yesmaximal, characteristic, complemented
8#11748916C218yesmaximal, direct product factor
9C2×#65246—31nomaximal, Hall
10C24×C5×D3C2211yescharacteristic
11C24×C3×D5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C23×Dic15C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C22×#1201—24no—
18C22×#1201—24no—
19C22×#1201C418yescomplemented
20C22×#1201C2214yes—
21C2×#6712—24no—
22C2×#6712C2214yescomplemented
23C2×C5×(C2×D3)⋊C4—24no—
24C2×C5×(C2×D3)⋊C4C2214yescomplemented
25C2×C3×#685—24no—
26C2×C3×#685C2214yescomplemented
27C2×(C2×D3)⋊Dic5—24no—
28C2×(C2×D3)⋊Dic5C2214yescomplemented
29C2×#6665—24no—
30C2×#6665C2214yescomplemented
31C2×Dic3×Dic5—24no—
32C2×Dic3×Dic5C2214yescomplemented
33C2×#4957—51nomaximal, Hall
34C23×C22⋊D5—31no—
35C22×C5×C22⋊C4—31no—
36C22×C22⋊Dic5—31no—
37C22×#685—31no—
38C22×#685D311yescharacteristic, complemented
39C22×#683—31no—
40C22×C4×Dic5—31no—
41#65246—38no—
42C24×C3×C5C2311yescharacteristic
43C23×C5×D3—22no—
44C23×C5×D3—22no—
45C23×C5×D3—22no—
46C23×C5×D3—22no—
47C23×C5×D3—22no—
48C23×C5×D3—22no—
49C23×C5×D3C2×C414yes—
50C23×C5×D3C2312yes—
51C23×C3×D5—22no—
52C23×C3×D5—22no—
53C23×C3×D5—22no—
54C23×C3×D5—22no—
55C23×C3×D5—22no—
56C23×C3×D5—22no—
57C23×C3×D5C2×C414yes—
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×Dic15—22no—
66C22×Dic15C2×C414yes—
67C22×Dic15D414yes—
68C22×Dic15D414yes—
69C22×Dic15C2312yes—
70C22×Dic15C2312yes—
71C22×C5×Dic3—22no—
72C22×C5×Dic3—22no—
73C22×C5×Dic3D414yescomplemented
74C22×C5×Dic3C2312yes—
75C22×C3×Dic5—22no—
76C22×C3×Dic5—22no—
77C22×C3×Dic5D414yescomplemented
78C22×C3×Dic5C2312yes—
79C2×#1201—232no—
80C2×#1201—28no—
81C2×#1201—28no—
82C2×#1201C2×C4116yescomplemented
83#6712—28no—
84C5×(C2×D3)⋊C4—28no—
85C3×#685—28no—
86(C2×D3)⋊Dic5—28no—
87#6665—28no—
88Dic3×Dic5—28no—
89C23×#67—51no—
90C22×C3×C22⋊C4—51no—
91C22×#217—51no—
92C22×(C2×D3)⋊C4—51no—
93C22×(C2×D3)⋊C4D511yescharacteristic, complemented
94C22×Dic3⋊C4—51no—
95C22×C4×Dic3—51no—
96#4957—58no—
97C25×C5—31no—
98C24×D5C2×D311yescharacteristic
99C23×C4×C5—31no—
100C23×C4×C5C2×D311yescharacteristic
101C22×C22⋊D5—38no—
102C22×C22⋊D5—34no—
103C22×C22⋊D5—64no—
104C22×C22⋊D5—64no—
105C23×Dic5—31no—
106C23×Dic5—31no—
107C23×Dic5C2×D311yescharacteristic
108C2×C5×C22⋊C4—34no—
109C2×C5×C22⋊C4—64no—
110C2×C22⋊Dic5—34no—
111C2×C22⋊Dic5—64no—
112C2×#685—24no—
113C2×#685—34no—
114C2×#685—64no—
115C2×#685C2×D314yescomplemented
116C2×#683—34no—
117C2×#683—64no—
118C2×C4×Dic5—34no—
119C2×C4×Dic5—64no—
120C2×#390—151noSylow
121C23×C3×C5C22×C412yes—
122C23×C3×C5C2×D412yes—
123C23×C3×C5C2×D412yes—
124C23×C3×C5C2×D412yes—
125C23×C3×C5C2×D412yes—
126C23×C3×C5#4112yes—
127C23×C3×C5#4112yes—
128C23×C3×C5C2411yescharacteristic
129C22×C5×D3—28no—
130C22×C5×D3—28no—
131C22×C5×D3—28no—
132C22×C5×D3—22no—
133C22×C5×D3—22no—
134C22×C5×D3—22no—
135C22×C5×D3—22no—
136C22×C5×D3—22no—
137C22×C5×D3—22no—
138C22×C5×D3—44no—
139C22×C5×D3—44no—
140C22×C5×D3—44no—
141C22×C5×D3—44no—
142C22×C5×D3C22×C414yes—
143C22×C3×D5—28no—
144C22×C3×D5—28no—
145C22×C3×D5—28no—
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5—22no—
149C22×C3×D5—22no—
150C22×C3×D5—22no—
151C22×C3×D5—22no—
152C22×C3×D5—44no—
153C22×C3×D5—44no—
154C22×C3×D5—44no—
155C22×C3×D5—44no—
156C22×C3×D5C22×C414yes—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—44no—
161C2×Dic15—22no—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15—44no—
165C2×Dic15C22⋊C4116yescomplemented
166C2×Dic15C22×C414yes—
167C2×Dic15C2×D414yes—
168C2×Dic15C2×D414yes—
169C2×C5×Dic3—28no—
170C2×C5×Dic3—22no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3C2×D414yescomplemented
173C2×C3×Dic5—28no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5C2×D414yescomplemented
177#1201—232no—
178C25×C3—51no—
179C24×D3C2×D511yescharacteristic
180C23×C3×C4—51no—
181C23×C3×C4C2×D511yescharacteristic
182C22×#67—58no—
183C22×#67—54no—
184C22×#67—104no—
185C22×#67—104no—
186C23×Dic3—51no—
187C23×Dic3—51no—
188C23×Dic3C2×D511yescharacteristic
189C2×C3×C22⋊C4—54no—
190C2×C3×C22⋊C4—104no—
191C2×#217—54no—
192C2×#217—104no—
193C2×(C2×D3)⋊C4—24no—
194C2×(C2×D3)⋊C4—54no—
195C2×(C2×D3)⋊C4—104no—
196C2×(C2×D3)⋊C4C2×D514yescomplemented
197C2×Dic3⋊C4—54no—
198C2×Dic3⋊C4—104no—
199C2×C4×Dic3—54no—
200C2×C4×Dic3—104no—
201C24×C5—34no—
202C24×C5—32no—
203C24×C5—62no—
204C24×C5—62no—
205C24×C5—62no—
206C24×C5—62no—
207C24×C5—62no—
208C24×C5—62no—
209C24×C5C22×D311yescharacteristic
210C23×D5—22no—
211C23×D5—22no—
212C23×D5—22no—
213C23×D5—22no—
214C23×D5—22no—
215C23×D5—22no—
216C23×D5C4×D314yes—
217C23×D5C22×D312yes—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—34no—
222C22×C4×C5—32no—
223C22×C4×C5—62no—
224C22×C4×C5—62no—
225C22×C4×C5C22×D312yes—
226C2×C22⋊D5—316no—
227C2×C22⋊D5—632no—
228C2×C22⋊D5—68no—
229C2×C22⋊D5—68no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—34no—
233C22×Dic5—34no—
234C22×Dic5—34no—
235C22×Dic5—32no—
236C22×Dic5—32no—
237C22×Dic5—62no—
238C22×Dic5—62no—
239C22×Dic5—62no—
240C22×Dic5#6714yescomplemented
241C22×Dic5C22×D312yes—
242C5×C22⋊C4—68no—
243C22⋊Dic5—68no—
244#685—28no—
245#685—68no—
246#683—68no—
247C4×Dic5—68no—
248C23×D4—151no—
249C22×C4⋊C4—151no—
250C22×C22⋊C4—31no—
251C22×C22⋊C4—51no—
252C22×C22⋊C4—151no—
253C22×C22⋊C4—151no—
254C22×C42—151no—
255#390—158no—
256C22×C3×C5C2×C22⋊C414yes—
257C22×C3×C5C4×D414yes—
258C22×C3×C5C4×D414yes—
259C22×C3×C5#12114yes—
260C22×C3×C5#12114yes—
261C22×C3×C5#12414yes—
262C22×C3×C5#12714yes—
263C22×C3×C5C23×C411yescharacteristic
264C22×C3×C5C22×D411yescharacteristic
265C22×C3×C5C22×D411yescharacteristic
266C22×C3×C5C22×D411yescharacteristic
267C22×C3×C5C22×D411yescharacteristic
268C22×C3×C5C2×#4111yescharacteristic
269C22×C3×C5C2×#4111yescharacteristic
270C2×C5×D3—24no—
271C2×C5×D3—24no—
272C2×C5×D3—24no—
273C2×C5×D3—42no—
274C2×C5×D3—42no—
275C2×C5×D3—42no—
276C2×C5×D3—42no—
277C2×C5×D3—416no—
278C2×C3×D5—24no—
279C2×C3×D5—24no—
280C2×C3×D5—24no—
281C2×C3×D5—42no—
282C2×C3×D5—42no—
283C2×C3×D5—42no—
284C2×C3×D5—42no—
285C2×C3×D5—416no—
286C3×C4×C5—42no—
287Dic15—42no—
288Dic15C2×C22⋊C418yescomplemented
289C3×Dic5—24no—
290C5×Dic3—24no—
291C24×C3—54no—
292C24×C3—52no—
293C24×C3—102no—
294C24×C3—102no—
295C24×C3—102no—
296C24×C3—102no—
297C24×C3—102no—
298C24×C3—102no—
299C24×C3C22×D511yescharacteristic
300C23×D3—22no—
301C23×D3—22no—
302C23×D3—22no—
303C23×D3—22no—
304C23×D3—22no—
305C23×D3—22no—
306C23×D3C4×D514yes—
307C23×D3C22×D512yes—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—54no—
312C22×C3×C4—52no—
313C22×C3×C4—102no—
314C22×C3×C4—102no—
315C22×C3×C4C22×D512yes—
316C2×#67—516no—
317C2×#67—108no—
318C2×#67—108no—
319C2×#67—1032no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—54no—
323C22×Dic3—54no—
324C22×Dic3—54no—
325C22×Dic3—52no—
326C22×Dic3—52no—
327C22×Dic3—102no—
328C22×Dic3—102no—
329C22×Dic3—102no—
330C22×Dic3C22⋊D514yescomplemented
331C22×Dic3C22×D512yes—
332C3×C22⋊C4—108no—
333#217—108no—
334(C2×D3)⋊C4—28no—
335(C2×D3)⋊C4—108no—
336Dic3⋊C4—108no—
337C4×Dic3—108no—
338C23×C5—34no—
339C23×C5—68no—
340C23×C5—68no—
341C23×C5—68no—
342C23×C5—62no—
343C23×C5—62no—
344C23×C5—62no—
345C23×C5—62no—
346C23×C5—62no—
347C23×C5—62no—
348C23×C5—124no—
349C23×C5—124no—
350C23×C5—124no—
351C23×C5—124no—
352C23×C5C2×C4×D312yes—
353C23×C5#23512yes—
354C23×C5D3×D412yes—
355C23×C5D3×D412yes—
356C23×C5D3×D412yes—
357C23×C5#23712yes—
358C23×C5C2×#6712yes—
359C23×C5C23×D311yescharacteristic
360C22×D5—28no—
361C22×D5—28no—
362C22×D5—28no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—22no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5—44no—
370C22×D5—44no—
371C22×D5—44no—
372C22×D5—44no—
373C22×D5C2×C4×D314yes—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—34no—
378C2×C4×C5—44no—
379C2×C4×C5—68no—
380C2×C4×C5—62no—
381C2×C4×C5—62no—
382C22⋊D5—632no—
383C2×Dic5—28no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—316no—
387C2×Dic5—34no—
388C2×Dic5—34no—
389C2×Dic5—34no—
390C2×Dic5—62no—
391C2×Dic5—62no—
392C2×Dic5—62no—
393C2×Dic5—124no—
394C2×Dic5C2×#6714yescomplemented
395C25—31no—
396C25—51no—
397C22×D4—154no—
398C22×D4—158no—
399C22×D4—304no—
400C22×D4—304no—
401C23×C4—31no—
402C23×C4—51no—
403C23×C4—151no—
404C23×C4—151no—
405C23×C4D3×D511yescharacteristic
406C2×C4⋊C4—154no—
407C2×C4⋊C4—304no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—54no—
410C2×C22⋊C4—64no—
411C2×C22⋊C4—104no—
412C2×C22⋊C4—154no—
413C2×C22⋊C4—154no—
414C2×C22⋊C4—304no—
415C2×C22⋊C4—304no—
416C2×C42—154no—
417C2×C42—304no—
418C2×C3×C5#39018yescomplemented
419C2×C3×C5C22×C22⋊C411yescharacteristic
420C2×C3×C5C2×C4×D411yescharacteristic
421C2×C3×C5C2×C4×D411yescharacteristic
422C2×C3×C5C2×#12111yescharacteristic
423C2×C3×C5C2×#12111yescharacteristic
424C2×C3×C5C2×#12411yescharacteristic
425C2×C3×C5C2×#12711yescharacteristic
426C3×D5—44no—
427C5×D3—44no—
428C23×C3—54no—
429C23×C3—102no—
430C23×C3—102no—
431C23×C3—102no—
432C23×C3—102no—
433C23×C3—102no—
434C23×C3—102no—
435C23×C3—108no—
436C23×C3—108no—
437C23×C3—108no—
438C23×C3—204no—
439C23×C3—204no—
440C23×C3—204no—
441C23×C3—204no—
442C23×C3C2×C4×D512yes—
443C23×C3#70912yes—
444C23×C3D4×D512yes—
445C23×C3D4×D512yes—
446C23×C3D4×D512yes—
447C23×C3#71112yes—
448C23×C3C2×C22⋊D512yes—
449C23×C3C23×D511yescharacteristic
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—28no—
457C22×D3—28no—
458C22×D3—28no—
459C22×D3—44no—
460C22×D3—44no—
461C22×D3—44no—
462C22×D3—44no—
463C22×D3C2×C4×D514yes—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—44no—
468C2×C3×C4—54no—
469C2×C3×C4—102no—
470C2×C3×C4—102no—
471C2×C3×C4—108no—
472#67—1032no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—28no—
476C2×Dic3—54no—
477C2×Dic3—54no—
478C2×Dic3—54no—
479C2×Dic3—516no—
480C2×Dic3—102no—
481C2×Dic3—102no—
482C2×Dic3—102no—
483C2×Dic3—204no—
484C2×Dic3C2×C22⋊D514yescomplemented
485C22×C5—64no—
486C22×C5—64no—
487C22×C5—64no—
488C22×C5—1216no—
489C22×C5—122no—
490C22×C5—122no—
491C22×C5—122no—
492C22×C5—122no—
493C22×C5D3×C22⋊C414yes—
494C22×C5#67⋊C414yes—
495C22×C5#88414yes—
496C22×C5#88514yes—
497C22×C5C4×#6714yes—
498C22×C5#93914yes—
499C22×C5#94014yes—
500C22×C5C22×C4×D311yescharacteristic
501C22×C5C2×#23511yescharacteristic
502C22×C5C2×D3×D411yescharacteristic
503C22×C5C2×D3×D411yescharacteristic
504C22×C5C2×D3×D411yescharacteristic
505C22×C5C2×#23711yescharacteristic
506C22×C5C22×#6711yescharacteristic
507C2×D5—24no—
508C2×D5—24no—
509C2×D5—24no—
510C2×D5—416no—
511C2×D5—42no—
512C2×D5—42no—
513C2×D5—42no—
514C2×D5—42no—
515C4×C5—42no—
516C4×C5—64no—
517Dic5—24no—
518Dic5—38no—
519Dic5—122no—
520C24—34no—
521C24—32no—
522C24—54no—
523C24—52no—
524C24—62no—
525C24—62no—
526C24—62no—
527C24—62no—
528C24—62no—
529C24—62no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24—102no—
535C24—102no—
536C24C2×D3×D511yescharacteristic
537C2×D4—1516no—
538C2×D4—3032no—
539C2×D4—308no—
540C2×D4—308no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—34no—
545C22×C4—32no—
546C22×C4—54no—
547C22×C4—52no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—102no—
551C22×C4—102no—
552C22×C4—154no—
553C22×C4—154no—
554C22×C4—154no—
555C22×C4—152no—
556C22×C4—152no—
557C22×C4—302no—
558C22×C4—302no—
559C22×C4—302no—
560C22×C4C2×D3×D512yes—
561C4⋊C4—308no—
562C22⋊C4—68no—
563C22⋊C4—108no—
564C22⋊C4—308no—
565C22⋊C4—308no—
566C42—308no—
567C3×C5C2×#39011yescharacteristic, complemented, Hall
568C22×C3—104no—
569C22×C3—104no—
570C22×C3—104no—
571C22×C3—202no—
572C22×C3—202no—
573C22×C3—202no—
574C22×C3—202no—
575C22×C3—2016no—
576C22×C3D5×C22⋊C414yes—
577C22×C3#402714yes—
578C22×C3#403014yes—
579C22×C3#403114yes—
580C22×C3C4×C22⋊D514yes—
581C22×C3#408514yes—
582C22×C3#408614yes—
583C22×C3C22×C4×D511yescharacteristic
584C22×C3C2×#70911yescharacteristic
585C22×C3C2×D4×D511yescharacteristic
586C22×C3C2×D4×D511yescharacteristic
587C22×C3C2×D4×D511yescharacteristic
588C22×C3C2×#71111yescharacteristic
589C22×C3C22×C22⋊D511yescharacteristic
590C2×D3—24no—
591C2×D3—24no—
592C2×D3—24no—
593C2×D3—42no—
594C2×D3—42no—
595C2×D3—42no—
596C2×D3—42no—
597C2×D3—416no—
598C3×C4—42no—
599C3×C4—104no—
600Dic3—24no—
601Dic3—58no—
602Dic3—202no—
603C2×C5—124no—
604C2×C5#495718yescomplemented
605C2×C5C2×D3×C22⋊C411yescharacteristic
606C2×C5C2×#67⋊C411yescharacteristic
607C2×C5C2×#88411yescharacteristic
608C2×C5C2×#88511yescharacteristic
609C2×C5C2×C4×#6711yescharacteristic
610C2×C5C2×#93911yescharacteristic
611C2×C5C2×#94011yescharacteristic
612D5—44no—
613C23—34no—
614C23—54no—
615C23—68no—
616C23—68no—
617C23—68no—
618C23—62no—
619C23—62no—
620C23—62no—
621C23—62no—
622C23—62no—
623C23—62no—
624C23—108no—
625C23—108no—
626C23—108no—
627C23—102no—
628C23—102no—
629C23—102no—
630C23—102no—
631C23—102no—
632C23—102no—
633C23—124no—
634C23—124no—
635C23—124no—
636C23—124no—
637C23—204no—
638C23—204no—
639C23—204no—
640C23—204no—
641C23#676512yes—
642C23#677212yes—
643C23C4×D3×D512yes—
644C23#677712yes—
645C23D5×#6712yes—
646C23D3×C22⋊D512yes—
647C23#679012yes—
648C23C22×D3×D511yescharacteristic
649D4—3032no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—34no—
654C2×C4—44no—
655C2×C4—54no—
656C2×C4—68no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—108no—
660C2×C4—102no—
661C2×C4—102no—
662C2×C4—1516no—
663C2×C4—154no—
664C2×C4—154no—
665C2×C4—154no—
666C2×C4—302no—
667C2×C4—302no—
668C2×C4—302no—
669C2×C4—604no—
670C2×C3—204no—
671C2×C3#6524618yescomplemented
672C2×C3C2×D5×C22⋊C411yescharacteristic
673C2×C3C2×#402711yescharacteristic
674C2×C3C2×#403011yescharacteristic
675C2×C3C2×#403111yescharacteristic
676C2×C3C2×C4×C22⋊D511yescharacteristic
677C2×C3C2×#408511yescharacteristic
678C2×C3C2×#408611yescharacteristic
679D3—44no—
680C5C2×#495711yescharacteristic, complemented, Sylow
681C22—64no—
682C22—64no—
683C22—64no—
684C22—104no—
685C22—104no—
686C22—104no—
687C22—122no—
688C22—1216no—
689C22—122no—
690C22—122no—
691C22—122no—
692C22—202no—
693C22—2016no—
694C22—202no—
695C22—202no—
696C22—202no—
697C22#9140814yes—
698C22#9144014yes—
699C22#9144114yes—
700C22#9145314yes—
701C22#9146214yes—
702C22#9147314yes—
703C22#9156714yes—
704C22C2×#676511yescharacteristic
705C22C2×#677211yescharacteristic
706C22C2×C4×D3×D511yescharacteristic
707C22C2×#677711yescharacteristic
708C22C2×D5×#6711yescharacteristic
709C22C2×D3×C22⋊D511yescharacteristic
710C22C2×#679011yescharacteristic
711C4—42no—
712C4—64no—
713C4—104no—
714C4—158no—
715C4—602no—
716C3C2×#6524611yescharacteristic, complemented, Sylow
717C2—124no—
718C2—204no—
719C2#1174891618yesdirect product factor
720C2C2×#9140811yescharacteristic
721C2C2×#9144011yescharacteristic
722C2C2×#9144111yescharacteristic
723C2C2×#9145311yescharacteristic
724C2C2×#9146211yescharacteristic
725C2C2×#9147311yescharacteristic
726C2C2×#9156711yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socleC24×C3×C5C23
prime radicalC23×#1201C2
cosocleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#390
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×#6712C2semidirect
3. C22×C5×(C2×D3)⋊C4C2semidirect
4. C22×C3×#685C2semidirect
5. C22×(C2×D3)⋊Dic5C2semidirect
6. C22×#6665C2semidirect
7. C22×Dic3×Dic5C2semidirect
8. #11748916C2direct (N × H)
19. C22×#1201C4semidirect
22. C2×#6712C22semidirect
24. C2×C5×(C2×D3)⋊C4C22semidirect
26. C2×C3×#685C22semidirect
28. C2×(C2×D3)⋊Dic5C22semidirect
30. C2×#6665C22semidirect
32. C2×Dic3×Dic5C22semidirect
38. C22×#685D3semidirect
73. C22×C5×Dic3D4semidirect
77. C22×C3×Dic5D4semidirect
82. C2×#1201C2×C4semidirect
93. C22×(C2×D3)⋊C4D5semidirect
115. C2×#685C2×D3semidirect
165. C2×Dic15C22⋊C4semidirect
172. C2×C5×Dic3C2×D4semidirect
176. C2×C3×Dic5C2×D4semidirect
196. C2×(C2×D3)⋊C4C2×D5semidirect
240. C22×Dic5#67semidirect
288. Dic15C2×C22⋊C4semidirect
330. C22×Dic3C22⋊D5semidirect
394. C2×Dic5C2×#67semidirect
418. C2×C3×C5#390semidirect
484. C2×Dic3C2×C22⋊D5semidirect
567. C3×C5C2×#390semidirect
604. C2×C5#4957semidirect
671. C2×C3#65246semidirect
680. C5C2×#4957semidirect
716. C3C2×#65246semidirect
719. C2#11748916direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#12012
C22×#67122
C22×C5×(C2×D3)⋊C42
C22×C3×#6852
C22×(C2×D3)⋊Dic52
C22×#66652
C22×Dic3×Dic52
#117489162
C2×#652463
C2×#49575