Finite Group Databasebeta

← C2×#11751058 #14320768

Subgroups — C2×#11751058 #14320768

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×#1220C211yesmaximal, characteristic
2C22×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
3C22×#6719C211yesmaximal, characteristic, complemented
4C22×#6714C211yesmaximal, characteristic, complemented
5C22×#6714C211yesmaximal, characteristic, complemented
6C22×#6712C211yesmaximal, characteristic, complemented
7C22×C4×Dic15C211yesmaximal, characteristic, complemented
8#11751058C218yesmaximal, direct product factor
9C2×#65246—31nomaximal, Hall
10C25×C3×C5C2211yescharacteristic
11C24×D15C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C3×C4×C5C2211yescharacteristic
14C22×#1220—24no—
15C22×#1220—24no—
16C22×#1220C418yescomplemented
17C22×#1220C2214yes—
18C23×Dic15C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C23×Dic15C2211yescharacteristic
21C2×C3×C5×C22⋊C4—24no—
22C2×C3×C5×C22⋊C4C2214yescomplemented
23C2×#6719—24no—
24C2×#6719C2214yescomplemented
25C2×#6714—24no—
26C2×#6714—24no—
27C2×#6714C2214yescomplemented
28C2×#6714C2214yescomplemented
29C2×#6712—24no—
30C2×#6712C2214yescomplemented
31C2×C4×Dic15—24no—
32C2×C4×Dic15C2214yescomplemented
33C2×#4957—51nomaximal, Hall
34C23×C22⋊D5—31no—
35C22×C5×C22⋊C4D311yescharacteristic, complemented
36C22×C22⋊Dic5—31no—
37C22×#685—31no—
38C22×#685—31no—
39C22×#683—31no—
40C22×C4×Dic5—31no—
41#65246—38no—
42C24×C3×C5—22no—
43C24×C3×C5—22no—
44C24×C3×C5—22no—
45C24×C3×C5—22no—
46C24×C3×C5—22no—
47C24×C3×C5—22no—
48C24×C3×C5C2×C414yes—
49C24×C3×C5C2312yes—
50C24×C3×C5C2311yescharacteristic
51C23×D15—22no—
52C23×D15—22no—
53C23×D15—22no—
54C23×D15—22no—
55C23×D15—22no—
56C23×D15—22no—
57C23×D15C2×C414yes—
58C23×D15C2312yes—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5—22no—
64C22×C3×C4×C5D414yescomplemented
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2312yes—
67C2×#1220—232no—
68C2×#1220—28no—
69C2×#1220—28no—
70C2×#1220C2×C4116yescomplemented
71C22×Dic15—22no—
72C22×Dic15—22no—
73C22×Dic15—22no—
74C22×Dic15—22no—
75C22×Dic15—22no—
76C22×Dic15C2×C414yes—
77C22×Dic15D414yes—
78C22×Dic15D414yes—
79C22×Dic15D414yescomplemented
80C22×Dic15C2312yes—
81C22×Dic15C2312yes—
82C22×Dic15C2312yes—
83C3×C5×C22⋊C4—28no—
84#6719—28no—
85#6714—28no—
86#6714—28no—
87#6712—28no—
88C4×Dic15—28no—
89C23×#67—51no—
90C22×C3×C22⋊C4D511yescharacteristic, complemented
91C22×#217—51no—
92C22×(C2×D3)⋊C4—51no—
93C22×(C2×D3)⋊C4—51no—
94C22×Dic3⋊C4—51no—
95C22×C4×Dic3—51no—
96#4957—58no—
97C25×C5C2×D311yescharacteristic
98C24×D5—31no—
99C23×C4×C5C2×D311yescharacteristic
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×Dic5—31no—
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4C2×D314yescomplemented
110C2×C22⋊Dic5—34no—
111C2×C22⋊Dic5—64no—
112C2×#685—34no—
113C2×#685—34no—
114C2×#685—64no—
115C2×#685—64no—
116C2×#683—34no—
117C2×#683—64no—
118C2×C4×Dic5—34no—
119C2×C4×Dic5—64no—
120C2×#390—151noSylow
121C23×C3×C5—28no—
122C23×C3×C5—28no—
123C23×C3×C5—28no—
124C23×C3×C5—22no—
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—22no—
128C23×C3×C5—22no—
129C23×C3×C5—22no—
130C23×C3×C5—44no—
131C23×C3×C5—44no—
132C23×C3×C5—44no—
133C23×C3×C5—44no—
134C23×C3×C5C22×C414yes—
135C23×C3×C5C22×C412yes—
136C23×C3×C5C2×D412yes—
137C23×C3×C5C2×D412yes—
138C23×C3×C5C2×D412yes—
139C23×C3×C5C2×D412yes—
140C23×C3×C5#4112yes—
141C23×C3×C5#4112yes—
142C23×C3×C5C2411yescharacteristic
143C22×D15—28no—
144C22×D15—28no—
145C22×D15—28no—
146C22×D15—22no—
147C22×D15—22no—
148C22×D15—22no—
149C22×D15—22no—
150C22×D15—22no—
151C22×D15—22no—
152C22×D15—44no—
153C22×D15—44no—
154C22×D15—44no—
155C22×D15—44no—
156C22×D15C22×C414yes—
157C2×C3×C4×C5—28no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—44no—
164C2×C3×C4×C5C2×D414yescomplemented
165#1220—232no—
166C2×Dic15—28no—
167C2×Dic15—22no—
168C2×Dic15—22no—
169C2×Dic15—22no—
170C2×Dic15—22no—
171C2×Dic15—22no—
172C2×Dic15—44no—
173C2×Dic15C22⋊C4116yescomplemented
174C2×Dic15C22×C414yes—
175C2×Dic15C2×D414yes—
176C2×Dic15C2×D414yes—
177C2×Dic15C2×D414yescomplemented
178C25×C3C2×D511yescharacteristic
179C24×D3—51no—
180C23×C3×C4C2×D511yescharacteristic
181C23×C3×C4C2×D511yescharacteristic
182C22×#67—58no—
183C22×#67—54no—
184C22×#67—104no—
185C22×#67—104no—
186C23×Dic3—51no—
187C23×Dic3—51no—
188C23×Dic3—51no—
189C2×C3×C22⋊C4—24no—
190C2×C3×C22⋊C4C2×D514yescomplemented
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—54no—
200C2×C4×Dic3—104no—
201C24×C5—22no—
202C24×C5—22no—
203C24×C5—22no—
204C24×C5—22no—
205C24×C5—22no—
206C24×C5—22no—
207C24×C5C4×D314yes—
208C24×C5C22×D312yes—
209C24×C5C22×D311yescharacteristic
210C23×D5—34no—
211C23×D5—32no—
212C23×D5—62no—
213C23×D5—62no—
214C23×D5—62no—
215C23×D5—62no—
216C23×D5—62no—
217C23×D5—62no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5#6714yescomplemented
224C22×C4×C5C22×D312yes—
225C22×C4×C5C22×D312yes—
226C2×C22⋊D5—316no—
227C2×C22⋊D5—632no—
228C2×C22⋊D5—68no—
229C2×C22⋊D5—68no—
230C22×Dic5—34no—
231C22×Dic5—34no—
232C22×Dic5—34no—
233C22×Dic5—32no—
234C22×Dic5—34no—
235C22×Dic5—32no—
236C22×Dic5—32no—
237C22×Dic5—62no—
238C22×Dic5—62no—
239C22×Dic5—62no—
240C22×Dic5—62no—
241C22×Dic5—62no—
242C5×C22⋊C4—28no—
243C22⋊Dic5—68no—
244#685—68no—
245#685—68no—
246#683—68no—
247C4×Dic5—68no—
248C23×D4—151no—
249C22×C4⋊C4—151no—
250C22×C22⋊C4—151no—
251C22×C22⋊C4—151no—
252C22×C22⋊C4—151no—
253C22×C22⋊C4D1511yescharacteristic, complemented
254C22×C42—151no—
255#390—158no—
256C22×C3×C5—24no—
257C22×C3×C5—24no—
258C22×C3×C5—24no—
259C22×C3×C5—42no—
260C22×C3×C5—42no—
261C22×C3×C5—42no—
262C22×C3×C5—42no—
263C22×C3×C5—416no—
264C22×C3×C5C2×C22⋊C414yes—
265C22×C3×C5C4×D414yes—
266C22×C3×C5C4×D414yes—
267C22×C3×C5#12114yes—
268C22×C3×C5#12114yes—
269C22×C3×C5#12414yes—
270C22×C3×C5#12714yes—
271C22×C3×C5C23×C411yescharacteristic
272C22×C3×C5C22×D411yescharacteristic
273C22×C3×C5C22×D411yescharacteristic
274C22×C3×C5C22×D411yescharacteristic
275C22×C3×C5C22×D411yescharacteristic
276C22×C3×C5C2×#4111yescharacteristic
277C22×C3×C5C2×#4111yescharacteristic
278C2×D15—24no—
279C2×D15—24no—
280C2×D15—24no—
281C2×D15—42no—
282C2×D15—42no—
283C2×D15—42no—
284C2×D15—42no—
285C2×D15—416no—
286C3×C4×C5—24no—
287C3×C4×C5—42no—
288Dic15—24no—
289Dic15—42no—
290Dic15C2×C22⋊C418yescomplemented
291C24×C3—22no—
292C24×C3—22no—
293C24×C3—22no—
294C24×C3—22no—
295C24×C3—22no—
296C24×C3—22no—
297C24×C3C4×D514yes—
298C24×C3C22×D512yes—
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—22no—
312C22×C3×C4—22no—
313C22×C3×C4C22⋊D514yescomplemented
314C22×C3×C4C22×D512yes—
315C22×C3×C4C22×D512yes—
316C2×#67—516no—
317C2×#67—108no—
318C2×#67—108no—
319C2×#67—1032no—
320C22×Dic3—54no—
321C22×Dic3—54no—
322C22×Dic3—54no—
323C22×Dic3—52no—
324C22×Dic3—54no—
325C22×Dic3—52no—
326C22×Dic3—52no—
327C22×Dic3—102no—
328C22×Dic3—102no—
329C22×Dic3—102no—
330C22×Dic3—102no—
331C22×Dic3—102no—
332C3×C22⋊C4—28no—
333#217—108no—
334(C2×D3)⋊C4—108no—
335(C2×D3)⋊C4—108no—
336Dic3⋊C4—108no—
337C4×Dic3—108no—
338C23×C5—28no—
339C23×C5—28no—
340C23×C5—28no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—44no—
348C23×C5—44no—
349C23×C5—44no—
350C23×C5—44no—
351C23×C5C2×C4×D314yes—
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—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—
374C2×C4×C5—28no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—44no—
381C2×C4×C5C2×#6714yescomplemented
382C22⋊D5—632no—
383C2×Dic5—316no—
384C2×Dic5—34no—
385C2×Dic5—34no—
386C2×Dic5—34no—
387C2×Dic5—34no—
388C2×Dic5—68no—
389C2×Dic5—62no—
390C2×Dic5—62no—
391C2×Dic5—62no—
392C2×Dic5—62no—
393C2×Dic5—62no—
394C2×Dic5—124no—
395C25—151no—
396C25C2×D1511yescharacteristic
397C22×D4—158no—
398C22×D4—154no—
399C22×D4—304no—
400C22×D4—304no—
401C23×C4—151no—
402C23×C4—151no—
403C23×C4—151no—
404C23×C4C2×D1511yescharacteristic
405C23×C4C2×D1511yescharacteristic
406C2×C4⋊C4—154no—
407C2×C4⋊C4—304no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—154no—
410C2×C22⋊C4—154no—
411C2×C22⋊C4—154no—
412C2×C22⋊C4—304no—
413C2×C22⋊C4—304no—
414C2×C22⋊C4—304no—
415C2×C22⋊C4C2×D1514yescomplemented
416C2×C42—154no—
417C2×C42—304no—
418C2×C3×C5—44no—
419C2×C3×C5#39018yescomplemented
420C2×C3×C5C22×C22⋊C411yescharacteristic
421C2×C3×C5C2×C4×D411yescharacteristic
422C2×C3×C5C2×C4×D411yescharacteristic
423C2×C3×C5C2×#12111yescharacteristic
424C2×C3×C5C2×#12111yescharacteristic
425C2×C3×C5C2×#12411yescharacteristic
426C2×C3×C5C2×#12711yescharacteristic
427D15—44no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—28no—
435C23×C3—28no—
436C23×C3—28no—
437C23×C3—44no—
438C23×C3—44no—
439C23×C3—44no—
440C23×C3—44no—
441C23×C3C2×C4×D514yes—
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—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—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—44no—
471C2×C3×C4C2×C22⋊D514yescomplemented
472#67—1032no—
473C2×Dic3—54no—
474C2×Dic3—54no—
475C2×Dic3—54no—
476C2×Dic3—516no—
477C2×Dic3—54no—
478C2×Dic3—102no—
479C2×Dic3—102no—
480C2×Dic3—108no—
481C2×Dic3—102no—
482C2×Dic3—102no—
483C2×Dic3—102no—
484C2×Dic3—204no—
485C22×C5—24no—
486C22×C5—24no—
487C22×C5—24no—
488C22×C5—416no—
489C22×C5—42no—
490C22×C5—42no—
491C22×C5—42no—
492C22×C5—42no—
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—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—42no—
517Dic5—38no—
518Dic5—64no—
519Dic5—122no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—154no—
527C24—152no—
528C24—302no—
529C24—302no—
530C24—302no—
531C24—302no—
532C24—302no—
533C24—302no—
534C24C4×D1514yes—
535C24C22×D1512yes—
536C24C22×D1511yescharacteristic
537C2×D4—1516no—
538C2×D4—3032no—
539C2×D4—308no—
540C2×D4—308no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—154no—
547C22×C4—154no—
548C22×C4—154no—
549C22×C4—152no—
550C22×C4—154no—
551C22×C4—152no—
552C22×C4—152no—
553C22×C4—302no—
554C22×C4—302no—
555C22×C4—302no—
556C22×C4—302no—
557C22×C4—302no—
558C22×C4#122014yescomplemented
559C22×C4C22×D1512yes—
560C22×C4C22×D1512yes—
561C4⋊C4—308no—
562C22⋊C4—28no—
563C22⋊C4—308no—
564C22⋊C4—308no—
565C22⋊C4—308no—
566C42—308no—
567C3×C5C2×#39011yescharacteristic, complemented, Hall
568C22×C3—24no—
569C22×C3—24no—
570C22×C3—24no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—416no—
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—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—42no—
600Dic3—58no—
601Dic3—104no—
602Dic3—202no—
603C2×C5—44no—
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—124no—
613C23—28no—
614C23—28no—
615C23—28no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—44no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—154no—
627C23—308no—
628C23—308no—
629C23—308no—
630C23—302no—
631C23—302no—
632C23—302no—
633C23—302no—
634C23—302no—
635C23—302no—
636C23—604no—
637C23—604no—
638C23—604no—
639C23—604no—
640C23C2×C4×D1514yes—
641C23C2×C4×D1512yes—
642C23#681712yes—
643C23D4×D1512yes—
644C23D4×D1512yes—
645C23D4×D1512yes—
646C23#681912yes—
647C23C2×#122012yes—
648C23C23×D1511yescharacteristic
649D4—3032no—
650C2×C4—28no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—44no—
657C2×C4—1516no—
658C2×C4—154no—
659C2×C4—154no—
660C2×C4—154no—
661C2×C4—154no—
662C2×C4—308no—
663C2×C4—302no—
664C2×C4—302no—
665C2×C4—302no—
666C2×C4—302no—
667C2×C4—302no—
668C2×C4—604no—
669C2×C4C2×#122014yescomplemented
670C2×C3—44no—
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—204no—
680C5C2×#495711yescharacteristic, complemented, Sylow
681C22—24no—
682C22—24no—
683C22—24no—
684C22—42no—
685C22—42no—
686C22—416no—
687C22—42no—
688C22—42no—
689C22—304no—
690C22—304no—
691C22—304no—
692C22—602no—
693C22—602no—
694C22—6016no—
695C22—602no—
696C22—602no—
697C22C22⋊C4×D1514yes—
698C22#9177014yes—
699C22#9177314yes—
700C22#9177414yes—
701C22C4×#122014yes—
702C22#9182814yes—
703C22#9182914yes—
704C22C22×C4×D1511yescharacteristic
705C22C2×#681711yescharacteristic
706C22C2×D4×D1511yescharacteristic
707C22C2×D4×D1511yescharacteristic
708C22C2×D4×D1511yescharacteristic
709C22C2×#681911yescharacteristic
710C22C22×#122011yescharacteristic
711C4—24no—
712C4—42no—
713C4—158no—
714C4—304no—
715C4—602no—
716C3C2×#6524611yescharacteristic, complemented, Sylow
717C2—44no—
718C2—604no—
719C2#1175105818yesdirect product factor
720C2C2×C22⋊C4×D1511yescharacteristic
721C2C2×#9177011yescharacteristic
722C2C2×#9177311yescharacteristic
723C2C2×#9177411yescharacteristic
724C2C2×C4×#122011yescharacteristic
725C2C2×#9182811yescharacteristic
726C2C2×#9182911yescharacteristic
subgroupG/H
centerC24C22×D15
commutatorC22×C3×C5C23×C4
FrattiniC23C23×D15
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC23×#1220C2
cosocleC23×C3×C5C24
hypercenterC22×C22⋊C4D15
hypocenterC3×C5C2×#390
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C22×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×C3×C5×C22⋊C4C2semidirect
3. C22×#6719C2semidirect
4. C22×#6714C2semidirect
5. C22×#6714C2semidirect
6. C22×#6712C2semidirect
7. C22×C4×Dic15C2semidirect
8. #11751058C2direct (N × H)
16. C22×#1220C4semidirect
22. C2×C3×C5×C22⋊C4C22semidirect
24. C2×#6719C22semidirect
27. C2×#6714C22semidirect
28. C2×#6714C22semidirect
30. C2×#6712C22semidirect
32. C2×C4×Dic15C22semidirect
35. C22×C5×C22⋊C4D3semidirect
64. C22×C3×C4×C5D4semidirect
70. C2×#1220C2×C4semidirect
79. C22×Dic15D4semidirect
90. C22×C3×C22⋊C4D5semidirect
109. C2×C5×C22⋊C4C2×D3semidirect
164. C2×C3×C4×C5C2×D4semidirect
173. C2×Dic15C22⋊C4semidirect
177. C2×Dic15C2×D4semidirect
190. C2×C3×C22⋊C4C2×D5semidirect
223. C22×C4×C5#67semidirect
253. C22×C22⋊C4D15semidirect
290. Dic15C2×C22⋊C4semidirect
313. C22×C3×C4C22⋊D5semidirect
381. C2×C4×C5C2×#67semidirect
415. C2×C22⋊C4C2×D15semidirect
419. C2×C3×C5#390semidirect
471. C2×C3×C4C2×C22⋊D5semidirect
558. C22×C4#1220semidirect
567. C3×C5C2×#390semidirect
604. C2×C5#4957semidirect
669. C2×C4C2×#1220semidirect
671. C2×C3#65246semidirect
680. C5C2×#4957semidirect
716. C3C2×#65246semidirect
719. C2#11751058direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#12202
C22×C3×C5×C22⋊C42
C22×#67192
C22×#67142
C22×#67122
C22×C4×Dic152
#117510582
C2×#652463
C2×#49575