Finite Group Databasebeta

← C2×#11748912 #14320797

Subgroups — C2×#11748912 #14320797

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×C4×C5×Dic3C211yesmaximal, characteristic, complemented
4C22×C3×#685C211yesmaximal, characteristic, complemented
5C22×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
6C22×#6667C211yesmaximal, characteristic, complemented
7C22×#6665C211yesmaximal, characteristic, complemented
8#11748912C218yesmaximal, direct product factor
9C2×#65228—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×C4×C5×Dic3—24no—
24C2×C4×C5×Dic3C2214yescomplemented
25C2×C3×#685—24no—
26C2×C3×#685C2214yescomplemented
27C2×Dic3⋊Dic5—24no—
28C2×Dic3⋊Dic5C2214yescomplemented
29C2×#6667—24no—
30C2×#6667C2214yescomplemented
31C2×#6665—24no—
32C2×#6665C2214yescomplemented
33C2×#4957—51nomaximal, Hall
34C23×D20—31no—
35C22×C42×C5—31no—
36C22×#685—31no—
37C22×#685—31no—
38C22×#685—31no—
39C22×#685D311yescharacteristic, complemented
40C22×C4⋊Dic5—31no—
41#65228—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×C5D414yescomplemented
62C22×C3×C4×C5C2312yes—
63C22×Dic15—22no—
64C22×Dic15—22no—
65C22×Dic15—22no—
66C22×Dic15C2312yes—
67C22×C5×Dic3—22no—
68C22×C5×Dic3—22no—
69C22×C5×Dic3C2×C414yes—
70C22×C5×Dic3D414yes—
71C22×C5×Dic3D414yes—
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
83#6714—28no—
84C4×C5×Dic3—28no—
85C3×#685—28no—
86Dic3⋊Dic5—28no—
87#6667—28no—
88#6665—28no—
89C23×#67—51no—
90C22×C3×C22⋊C4—51no—
91C22×#217—51no—
92C22×(C2×D3)⋊C4—51no—
93C22×(C2×D3)⋊C4—51no—
94C22×Dic3⋊C4—51no—
95C22×C4×Dic3D511yescharacteristic, complemented
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×C42×C5—34no—
109C2×C42×C5—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—28no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5C2×D414yescomplemented
161C2×Dic15—22no—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15—44no—
165C2×C5×Dic3—28no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3C22⋊C4116yescomplemented
169C2×C5×Dic3C22×C414yes—
170C2×C5×Dic3C2×D414yes—
171C2×C5×Dic3C2×D414yes—
172C2×C5×Dic3C2×D414yescomplemented
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—44no—
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—54no—
198C2×Dic3⋊C4—104no—
199C2×C4×Dic3—24no—
200C2×C4×Dic3C2×D514yescomplemented
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—34no—
221C22×C4×C5—34no—
222C22×C4×C5—34no—
223C22×C4×C5—32no—
224C22×C4×C5—34no—
225C22×C4×C5—32no—
226C22×C4×C5—62no—
227C22×C4×C5—62no—
228C22×C4×C5#6714yescomplemented
229C22×C4×C5C22×D312yes—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—32no—
234C22×Dic5—62no—
235C22×Dic5—62no—
236C22×Dic5—62no—
237C22×Dic5C22×D312yes—
238C2×D20—316no—
239C2×D20—632no—
240C2×D20—68no—
241C2×D20—68no—
242C42×C5—68no—
243#685—28no—
244#685—68no—
245#685—68no—
246#685—68no—
247C4⋊Dic5—68no—
248C23×D4—151no—
249C22×C4⋊C4—151no—
250C22×C22⋊C4—51no—
251C22×C22⋊C4—151no—
252C22×C22⋊C4—151no—
253C22×C22⋊C4—151no—
254C22×C42—31no—
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—24no—
287Dic15—42no—
288C3×Dic5—42no—
289C5×Dic3—24no—
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—52no—
311C22×C3×C4—102no—
312C22×C3×C4—102no—
313C22×C3×C4—102no—
314C22×C3×C4D2014yescomplemented
315C22×C3×C4C22×D512yes—
316C2×#67—516no—
317C2×#67—1032no—
318C2×#67—108no—
319C2×#67—108no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—52no—
323C22×Dic3—102no—
324C22×Dic3—102no—
325C22×Dic3—102no—
326C22×Dic3C4×D514yes—
327C22×Dic3D2014yes—
328C22×Dic3D2014yescomplemented
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—108no—
337C4×Dic3—28no—
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—28no—
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—34no—
382C2×C4×C5—68no—
383C2×C4×C5—62no—
384C2×C4×C5—62no—
385C2×C4×C5C2×#6714yescomplemented
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—44no—
390C2×Dic5—62no—
391C2×Dic5—62no—
392C2×Dic5—62no—
393C2×Dic5—124no—
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—154no—
407C2×C4⋊C4—304no—
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—34no—
417C2×C42—64no—
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×C3C2×D2012yes—
445C23×C3C2×D2012yes—
446C23×C3#70912yes—
447C23×C3#70912yes—
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—28no—
467C2×C3×C4—102no—
468C2×C3×C4—102no—
469C2×C3×C4—102no—
470C2×C3×C4—204no—
471C2×C3×C4C2×D2014yescomplemented
472#67—1032no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—28no—
476C2×Dic3—102no—
477C2×Dic3—102no—
478C2×Dic3—102no—
479C2×Dic3—204no—
480C2×Dic3#685116yescomplemented
481C2×Dic3C2×C4×D514yes—
482C2×Dic3C2×D2014yes—
483C2×Dic3C2×D2014yescomplemented
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—24no—
516C4×C5—38no—
517C4×C5—64no—
518Dic5—42no—
519Dic5—122no—
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—34no—
544C22×C4—34no—
545C22×C4—34no—
546C22×C4—32no—
547C22×C4—34no—
548C22×C4—32no—
549C22×C4—52no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—102no—
553C22×C4—102no—
554C22×C4—102no—
555C22×C4—152no—
556C22×C4—302no—
557C22×C4—302no—
558C22×C4—302no—
559C22×C4#120214yescomplemented
560C22×C4C2×D3×D512yes—
561C4⋊C4—308no—
562C22⋊C4—108no—
563C22⋊C4—308no—
564C22⋊C4—308no—
565C22⋊C4—308no—
566C42—68no—
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×C3C4×D2014yes—
577C22×C3C4×D2014yes—
578C22×C3#402014yes—
579C22×C3#402114yes—
580C22×C3C2×#68514yes—
581C22×C3#407614yes—
582C22×C3#407614yes—
583C22×C3C22×C4×D511yescharacteristic
584C22×C3C22×D2011yescharacteristic
585C22×C3C22×D2011yescharacteristic
586C22×C3C22×D2011yescharacteristic
587C22×C3C2×#70911yescharacteristic
588C22×C3C2×#70911yescharacteristic
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—24no—
599C3×C4—202no—
600Dic3—24no—
601Dic3—202no—
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#677112yes—
642C23C4×D3×D512yes—
643C23D3×D2012yes—
644C23D3×D2012yes—
645C23#677912yes—
646C23C2×#120212yes—
647C23D3×C22⋊D512yes—
648C23C22×D3×D511yescharacteristic
649D4—3032no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—28no—
653C2×C4—316no—
654C2×C4—34no—
655C2×C4—34no—
656C2×C4—34no—
657C2×C4—34no—
658C2×C4—68no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—102no—
662C2×C4—102no—
663C2×C4—102no—
664C2×C4—204no—
665C2×C4—302no—
666C2×C4—302no—
667C2×C4—302no—
668C2×C4—604no—
669C2×C4C2×#120214yescomplemented
670C2×C3—204no—
671C2×C3#6522818yescomplemented
672C2×C3C2×C4×D2011yescharacteristic
673C2×C3C2×C4×D2011yescharacteristic
674C2×C3C2×#402011yescharacteristic
675C2×C3C2×#402111yescharacteristic
676C2×C3C22×#68511yescharacteristic
677C2×C3C2×#407611yescharacteristic
678C2×C3C2×#407611yescharacteristic
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#9135314yes—
698C22#9139514yes—
699C22C4×#120214yes—
700C22#9145414yes—
701C22#9145814yes—
702C22D3×#68514yes—
703C22#9156914yes—
704C22C2×#677111yescharacteristic
705C22C2×C4×D3×D511yescharacteristic
706C22C2×D3×D2011yescharacteristic
707C22C2×D3×D2011yescharacteristic
708C22C2×#677911yescharacteristic
709C22C22×#120211yescharacteristic
710C22C2×D3×C22⋊D511yescharacteristic
711C4—24no—
712C4—38no—
713C4—64no—
714C4—202no—
715C4—602no—
716C3C2×#6522811yescharacteristic, complemented, Sylow
717C2—204no—
718C2—604no—
719C2#1174891218yesdirect product factor
720C2C2×#9135311yescharacteristic
721C2C2×#9139511yescharacteristic
722C2C2×C4×#120211yescharacteristic
723C2C2×#9145411yescharacteristic
724C2C2×#9145811yescharacteristic
725C2C2×D3×#68511yescharacteristic
726C2C2×#9156911yescharacteristic
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×C4×C5×Dic3C2semidirect
4. C22×C3×#685C2semidirect
5. C22×Dic3⋊Dic5C2semidirect
6. C22×#6667C2semidirect
7. C22×#6665C2semidirect
8. #11748912C2direct (N × H)
19. C22×#1202C4semidirect
22. C2×#6714C22semidirect
24. C2×C4×C5×Dic3C22semidirect
26. C2×C3×#685C22semidirect
28. C2×Dic3⋊Dic5C22semidirect
30. C2×#6667C22semidirect
32. C2×#6665C22semidirect
39. C22×#685D3semidirect
61. C22×C3×C4×C5D4semidirect
72. C22×C5×Dic3D4semidirect
82. C2×#1202C2×C4semidirect
95. C22×C4×Dic3D5semidirect
117. C2×#685C2×D3semidirect
160. C2×C3×C4×C5C2×D4semidirect
168. C2×C5×Dic3C22⋊C4semidirect
172. C2×C5×Dic3C2×D4semidirect
200. C2×C4×Dic3C2×D5semidirect
228. C22×C4×C5#67semidirect
290. C5×Dic3C2×C22⋊C4semidirect
314. C22×C3×C4D20semidirect
328. C22×Dic3D20semidirect
385. C2×C4×C5C2×#67semidirect
418. C2×C3×C5#390semidirect
471. C2×C3×C4C2×D20semidirect
480. C2×Dic3#685semidirect
483. C2×Dic3C2×D20semidirect
559. C22×C4#1202semidirect
567. C3×C5C2×#390semidirect
602. Dic3C2×#685semidirect
603. C2×C5#4957semidirect
669. C2×C4C2×#1202semidirect
671. C2×C3#65228semidirect
680. C5C2×#4957semidirect
716. C3C2×#65228semidirect
719. C2#11748912direct (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×C4×C5×Dic32
C22×C3×#6852
C22×Dic3⋊Dic52
C22×#66672
C22×#66652
#117489122
C2×#652283
C2×#49575