Finite Group Databasebeta

← C2×#11748913 #14320794

Subgroups — C2×#11748913 #14320794

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×#1202C211yesmaximal, characteristic
2C22×#6714C211yesmaximal, characteristic, complemented
3C22×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C22×C3×#685C211yesmaximal, characteristic, complemented
5C22×#6667C211yesmaximal, characteristic, complemented
6C22×#6665C211yesmaximal, characteristic, complemented
7C22×Dic3×Dic5C211yesmaximal, characteristic, complemented
8#11748913C218yesmaximal, direct product factor
9C2×#65277—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—
21C2×#6714—24no—
22C2×#6714C2214yescomplemented
23C2×C5×Dic3⋊C4—24no—
24C2×C5×Dic3⋊C4C2214yescomplemented
25C2×C3×#685—24no—
26C2×C3×#685C2214yescomplemented
27C2×#6667—24no—
28C2×#6667C2214yescomplemented
29C2×#6665—24no—
30C2×#6665C2214yescomplemented
31C2×Dic3×Dic5—24no—
32C2×Dic3×Dic5C2214yescomplemented
33C2×#4957—51nomaximal, Hall
34C23×D20—31no—
35C22×C5×C4⋊C4—31no—
36C22×#685—31no—
37C22×#685—31no—
38C22×#685—31no—
39C22×#685D311yescharacteristic, complemented
40C22×C4×Dic5—31no—
41#65277—38no—
42C24×C3×C5C2311yescharacteristic
43C23×D15—22no—
44C23×D15—22no—
45C23×D15—22no—
46C23×D15—22no—
47C23×D15—22no—
48C23×D15—22no—
49C23×D15C2×C414yes—
50C23×D15C2312yes—
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×Dic15D414yescomplemented
66C22×Dic15C2312yes—
67C22×C5×Dic3—22no—
68C22×C5×Dic3—22no—
69C22×C5×Dic3—22no—
70C22×C5×Dic3C2×C414yes—
71C22×C5×Dic3D414yes—
72C22×C5×Dic3D414yes—
73C22×C5×Dic3C2312yes—
74C22×C5×Dic3C2312yes—
75C22×C3×Dic5—22no—
76C22×C3×Dic5—22no—
77C22×C3×Dic5D414yescomplemented
78C22×C3×Dic5C2312yes—
79C2×#1202—232no—
80C2×#1202—28no—
81C2×#1202—28no—
82C2×#1202C2×C4116yescomplemented
83#6714—28no—
84C5×Dic3⋊C4—28no—
85C3×#685—28no—
86#6667—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)⋊C4—51no—
94C22×Dic3⋊C4D511yescharacteristic, complemented
95C22×C4×Dic3—51no—
96#4957—58no—
97C24×D5—31no—
98C24×D5C2×D311yescharacteristic
99C23×C4×C5—31no—
100C23×C4×C5—31no—
101C23×C4×C5C2×D311yescharacteristic
102C23×Dic5—31no—
103C23×Dic5C2×D311yescharacteristic
104C22×D20—38no—
105C22×D20—34no—
106C22×D20—64no—
107C22×D20—64no—
108C2×C5×C4⋊C4—34no—
109C2×C5×C4⋊C4—64no—
110C2×#685—24no—
111C2×#685—34no—
112C2×#685—34no—
113C2×#685—34no—
114C2×#685—64no—
115C2×#685—64no—
116C2×#685—64no—
117C2×#685C2×D314yescomplemented
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×D15—28no—
130C22×D15—28no—
131C22×D15—28no—
132C22×D15—22no—
133C22×D15—22no—
134C22×D15—22no—
135C22×D15—22no—
136C22×D15—22no—
137C22×D15—22no—
138C22×D15—44no—
139C22×D15—44no—
140C22×D15—44no—
141C22×D15—44no—
142C22×D15C22×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—28no—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15C2×D414yescomplemented
165C2×C5×Dic3—22no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—44no—
169C2×C5×Dic3C22⋊C4116yescomplemented
170C2×C5×Dic3C22×C414yes—
171C2×C5×Dic3C2×D414yes—
172C2×C5×Dic3C2×D414yes—
173C2×C3×Dic5—28no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5C2×D414yescomplemented
177#1202—232no—
178C25×C3—51no—
179C24×D3—51no—
180C23×C3×C4—51no—
181C23×C3×C4C2×D511yescharacteristic
182C22×#67—58no—
183C22×#67—54no—
184C22×#67—104no—
185C22×#67—104no—
186C23×Dic3—51no—
187C23×Dic3C2×D511yescharacteristic
188C23×Dic3C2×D511yescharacteristic
189C2×C3×C22⋊C4—54no—
190C2×C3×C22⋊C4—104no—
191C2×#217—54no—
192C2×#217—104no—
193C2×(C2×D3)⋊C4—54no—
194C2×(C2×D3)⋊C4—54no—
195C2×(C2×D3)⋊C4—104no—
196C2×(C2×D3)⋊C4—104no—
197C2×Dic3⋊C4—24no—
198C2×Dic3⋊C4C2×D514yescomplemented
199C2×C4×Dic3—54no—
200C2×C4×Dic3—104no—
201C24×C5C22×D311yescharacteristic
202C23×D5—22no—
203C23×D5—22no—
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×D5C22×D312yes—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—34no—
222C22×C4×C5—34no—
223C22×C4×C5—34no—
224C22×C4×C5—32no—
225C22×C4×C5—32no—
226C22×C4×C5—62no—
227C22×C4×C5—62no—
228C22×C4×C5—62no—
229C22×C4×C5C22×D312yes—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—34no—
233C22×Dic5—32no—
234C22×Dic5—62no—
235C22×Dic5—62no—
236C22×Dic5#6714yescomplemented
237C22×Dic5C22×D312yes—
238C2×D20—316no—
239C2×D20—632no—
240C2×D20—68no—
241C2×D20—68no—
242C5×C4⋊C4—68no—
243#685—28no—
244#685—68no—
245#685—68no—
246#685—68no—
247C4×Dic5—68no—
248C23×D4—151no—
249C22×C4⋊C4—31no—
250C22×C22⋊C4—51no—
251C22×C22⋊C4—151no—
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×D15—24no—
271C2×D15—24no—
272C2×D15—24no—
273C2×D15—42no—
274C2×D15—42no—
275C2×D15—42no—
276C2×D15—42no—
277C2×D15—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—24no—
288C3×Dic5—24no—
289C5×Dic3—42no—
290C5×Dic3C2×C22⋊C418yescomplemented
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—54no—
301C23×D3—52no—
302C23×D3—102no—
303C23×D3—102no—
304C23×D3—102no—
305C23×D3—102no—
306C23×D3—102no—
307C23×D3—102no—
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—1032no—
318C2×#67—108no—
319C2×#67—108no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3—54no—
324C22×Dic3—52no—
325C22×Dic3—102no—
326C22×Dic3—102no—
327C22×Dic3C4×D514yes—
328C22×Dic3D2014yes—
329C22×Dic3C22⋊D514yes—
330C22×Dic3C22×D512yes—
331C22×Dic3C22×D512yes—
332C3×C22⋊C4—108no—
333#217—108no—
334(C2×D3)⋊C4—108no—
335(C2×D3)⋊C4—108no—
336Dic3⋊C4—28no—
337C4×Dic3—108no—
338C23×C5C2×C4×D312yes—
339C23×C5#23512yes—
340C23×C5D3×D412yes—
341C23×C5D3×D412yes—
342C23×C5D3×D412yes—
343C23×C5#23712yes—
344C23×C5C2×#6712yes—
345C23×C5C23×D311yescharacteristic
346C22×D5—28no—
347C22×D5—28no—
348C22×D5—28no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—22no—
354C22×D5—22no—
355C22×D5—34no—
356C22×D5—44no—
357C22×D5—44no—
358C22×D5—44no—
359C22×D5—44no—
360C22×D5—68no—
361C22×D5—68no—
362C22×D5—68no—
363C22×D5—62no—
364C22×D5—62no—
365C22×D5—62no—
366C22×D5—62no—
367C22×D5—62no—
368C22×D5—62no—
369C22×D5—124no—
370C22×D5—124no—
371C22×D5—124no—
372C22×D5—124no—
373C22×D5C2×C4×D314yes—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—316no—
378C2×C4×C5—34no—
379C2×C4×C5—34no—
380C2×C4×C5—34no—
381C2×C4×C5—44no—
382C2×C4×C5—62no—
383C2×C4×C5—62no—
384C2×C4×C5—62no—
385C2×C4×C5—124no—
386C2×Dic5—28no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—34no—
390C2×Dic5—68no—
391C2×Dic5—62no—
392C2×Dic5—62no—
393C2×Dic5C2×#6714yescomplemented
394D20—632no—
395C25—51no—
396C25—151no—
397C22×D4—154no—
398C22×D4—158no—
399C22×D4—304no—
400C22×D4—304no—
401C23×C4—31no—
402C23×C4—31no—
403C23×C4—51no—
404C23×C4—151no—
405C23×C4D3×D511yescharacteristic
406C2×C4⋊C4—34no—
407C2×C4⋊C4—64no—
408C2×C22⋊C4—54no—
409C2×C22⋊C4—104no—
410C2×C22⋊C4—154no—
411C2×C22⋊C4—154no—
412C2×C22⋊C4—154no—
413C2×C22⋊C4—304no—
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
426D15—44no—
427C3×D5—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×C3C2×D2012yes—
444C23×C3D4×D512yes—
445C23×C3D4×D512yes—
446C23×C3#71312yes—
447C23×C3#71312yes—
448C23×C3C2×C22⋊D512yes—
449C23×C3C23×D511yescharacteristic
450C22×D3—54no—
451C22×D3—102no—
452C22×D3—102no—
453C22×D3—102no—
454C22×D3—102no—
455C22×D3—102no—
456C22×D3—102no—
457C22×D3—108no—
458C22×D3—108no—
459C22×D3—108no—
460C22×D3—204no—
461C22×D3—204no—
462C22×D3—204no—
463C22×D3—204no—
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—22no—
476C2×Dic3—44no—
477C2×Dic3—54no—
478C2×Dic3—102no—
479C2×Dic3—102no—
480C2×Dic3—108no—
481C2×Dic3#685116yescomplemented
482C2×Dic3C2×C4×D514yes—
483C2×Dic3C2×D2014yes—
484C2×Dic3C2×C22⋊D514yes—
485C22×C5D3×C22⋊C414yes—
486C22×C5#67⋊C414yes—
487C22×C5#88414yes—
488C22×C5#88514yes—
489C22×C5C4×#6714yes—
490C22×C5#93914yes—
491C22×C5#94014yes—
492C22×C5C22×C4×D311yescharacteristic
493C22×C5C2×#23511yescharacteristic
494C22×C5C2×D3×D411yescharacteristic
495C22×C5C2×D3×D411yescharacteristic
496C22×C5C2×D3×D411yescharacteristic
497C22×C5C2×#23711yescharacteristic
498C22×C5C22×#6711yescharacteristic
499C2×D5—24no—
500C2×D5—24no—
501C2×D5—24no—
502C2×D5—416no—
503C2×D5—42no—
504C2×D5—42no—
505C2×D5—42no—
506C2×D5—42no—
507C2×D5—64no—
508C2×D5—64no—
509C2×D5—64no—
510C2×D5—1216no—
511C2×D5—122no—
512C2×D5—122no—
513C2×D5—122no—
514C2×D5—122no—
515C4×C5—38no—
516C4×C5—42no—
517C4×C5—122no—
518Dic5—24no—
519Dic5—64no—
520C24—54no—
521C24—52no—
522C24—102no—
523C24—102no—
524C24—102no—
525C24—102no—
526C24—102no—
527C24—102no—
528C24—154no—
529C24—152no—
530C24—302no—
531C24—302no—
532C24—302no—
533C24—302no—
534C24—302no—
535C24—302no—
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—34no—
546C22×C4—34no—
547C22×C4—32no—
548C22×C4—32no—
549C22×C4—54no—
550C22×C4—52no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—102no—
555C22×C4—102no—
556C22×C4—154no—
557C22×C4—152no—
558C22×C4—302no—
559C22×C4—302no—
560C22×C4C2×D3×D512yes—
561C4⋊C4—68no—
562C22⋊C4—108no—
563C22⋊C4—308no—
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×C3#403914yes—
577C22×C3#403914yes—
578C22×C3#404114yes—
579C22×C3#404114yes—
580C22×C3C2×#68514yes—
581C22×C3#408614yes—
582C22×C3#409314yes—
583C22×C3C22×C4×D511yescharacteristic
584C22×C3C22×D2011yescharacteristic
585C22×C3C2×D4×D511yescharacteristic
586C22×C3C2×D4×D511yescharacteristic
587C22×C3C2×#71311yescharacteristic
588C22×C3C2×#71311yescharacteristic
589C22×C3C22×C22⋊D511yescharacteristic
590C2×D3—104no—
591C2×D3—104no—
592C2×D3—104no—
593C2×D3—202no—
594C2×D3—202no—
595C2×D3—202no—
596C2×D3—202no—
597C2×D3—2016no—
598C3×C4—42no—
599C3×C4—104no—
600Dic3—42no—
601Dic3—104no—
602Dic3C2×#68518yescomplemented
603C2×C5#495718yescomplemented
604C2×C5C2×D3×C22⋊C411yescharacteristic
605C2×C5C2×#67⋊C411yescharacteristic
606C2×C5C2×#88411yescharacteristic
607C2×C5C2×#88511yescharacteristic
608C2×C5C2×C4×#6711yescharacteristic
609C2×C5C2×#93911yescharacteristic
610C2×C5C2×#94011yescharacteristic
611D5—44no—
612D5—124no—
613C23—54no—
614C23—108no—
615C23—108no—
616C23—108no—
617C23—102no—
618C23—102no—
619C23—102no—
620C23—102no—
621C23—102no—
622C23—102no—
623C23—154no—
624C23—204no—
625C23—204no—
626C23—204no—
627C23—204no—
628C23—308no—
629C23—308no—
630C23—308no—
631C23—302no—
632C23—302no—
633C23—302no—
634C23—302no—
635C23—302no—
636C23—302no—
637C23—604no—
638C23—604no—
639C23—604no—
640C23—604no—
641C23#676612yes—
642C23#677312yes—
643C23C4×D3×D512yes—
644C23D3×D2012yes—
645C23D5×#6712yes—
646C23D3×C22⋊D512yes—
647C23#679012yes—
648C23C22×D3×D511yescharacteristic
649D4—3032no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—316no—
654C2×C4—34no—
655C2×C4—34no—
656C2×C4—34no—
657C2×C4—44no—
658C2×C4—54no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—62no—
662C2×C4—108no—
663C2×C4—102no—
664C2×C4—102no—
665C2×C4—124no—
666C2×C4—154no—
667C2×C4—308no—
668C2×C4—302no—
669C2×C4—302no—
670C2×C3—204no—
671C2×C3#6527718yescomplemented
672C2×C3C2×#403911yescharacteristic
673C2×C3C2×#403911yescharacteristic
674C2×C3C2×#404111yescharacteristic
675C2×C3C2×#404111yescharacteristic
676C2×C3C22×#68511yescharacteristic
677C2×C3C2×#408611yescharacteristic
678C2×C3C2×#409311yescharacteristic
679D3—204no—
680C5C2×#495711yescharacteristic, complemented, Sylow
681C22—104no—
682C22—104no—
683C22—104no—
684C22—202no—
685C22—2016no—
686C22—202no—
687C22—202no—
688C22—202no—
689C22—304no—
690C22—304no—
691C22—304no—
692C22—602no—
693C22—6016no—
694C22—602no—
695C22—602no—
696C22—602no—
697C22#9139614yes—
698C22#9140914yes—
699C22#9144414yes—
700C22#9145514yes—
701C22#9145914yes—
702C22D3×#68514yes—
703C22#9156714yes—
704C22C2×#676611yescharacteristic
705C22C2×#677311yescharacteristic
706C22C2×C4×D3×D511yescharacteristic
707C22C2×D3×D2011yescharacteristic
708C22C2×D5×#6711yescharacteristic
709C22C2×D3×C22⋊D511yescharacteristic
710C22C2×#679011yescharacteristic
711C4—38no—
712C4—42no—
713C4—104no—
714C4—122no—
715C4—304no—
716C3C2×#6527711yescharacteristic, complemented, Sylow
717C2—204no—
718C2—604no—
719C2#1174891318yesdirect product factor
720C2C2×#9139611yescharacteristic
721C2C2×#9140911yescharacteristic
722C2C2×#9144411yescharacteristic
723C2C2×#9145511yescharacteristic
724C2C2×#9145911yescharacteristic
725C2C2×D3×#68511yescharacteristic
726C2C2×#9156711yescharacteristic
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×#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×#6714C2semidirect
3. C22×C5×Dic3⋊C4C2semidirect
4. C22×C3×#685C2semidirect
5. C22×#6667C2semidirect
6. C22×#6665C2semidirect
7. C22×Dic3×Dic5C2semidirect
8. #11748913C2direct (N × H)
19. C22×#1202C4semidirect
22. C2×#6714C22semidirect
24. C2×C5×Dic3⋊C4C22semidirect
26. C2×C3×#685C22semidirect
28. C2×#6667C22semidirect
30. C2×#6665C22semidirect
32. C2×Dic3×Dic5C22semidirect
39. C22×#685D3semidirect
65. C22×Dic15D4semidirect
77. C22×C3×Dic5D4semidirect
82. C2×#1202C2×C4semidirect
94. C22×Dic3⋊C4D5semidirect
117. C2×#685C2×D3semidirect
164. C2×Dic15C2×D4semidirect
169. C2×C5×Dic3C22⋊C4semidirect
176. C2×C3×Dic5C2×D4semidirect
198. C2×Dic3⋊C4C2×D5semidirect
236. C22×Dic5#67semidirect
290. C5×Dic3C2×C22⋊C4semidirect
393. C2×Dic5C2×#67semidirect
418. C2×C3×C5#390semidirect
481. C2×Dic3#685semidirect
567. C3×C5C2×#390semidirect
602. Dic3C2×#685semidirect
603. C2×C5#4957semidirect
671. C2×C3#65277semidirect
680. C5C2×#4957semidirect
716. C3C2×#65277semidirect
719. C2#11748913direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#12022
C22×#67142
C22×C5×Dic3⋊C42
C22×C3×#6852
C22×#66672
C22×#66652
C22×Dic3×Dic52
#117489132
C2×#652773
C2×#49575