Finite Group Databasebeta

← #14325935

Subgroups — #14325935

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1202C211yesmaximal, characteristic
2C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×#91561C211yesmaximal, characteristic, complemented
4C2×#91444C212yesmaximal, complemented
5#11751056C211yesmaximal, characteristic, complemented
6C5×#4942C211yesmaximal, characteristic, complemented
7#11749488C211yesmaximal, characteristic, complemented
8Dic3×C22⋊Dic5C211yesmaximal, characteristic, complemented
9#11748913C212yesmaximal, complemented
10#11748907C212yesmaximal, complemented
11#11748700C212yesmaximal, complemented
12#10605738—31nomaximal, Hall
13C24×D15C2211yescharacteristic
14C24×C3×D5C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C22×C3×C4×D5C2212yescomplemented
17C22×#1202—28no—
18C22×#1202C418yescomplemented
19C22×#1202C2211yescharacteristic
20C22×#1202C2211yescharacteristic
21C22×#1202C2211yescharacteristic
22C22×#1202C2211yescharacteristic
23C22×#1200C2212yescomplemented
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6714C2212yescomplemented
27C2×#6714C2212yescomplemented
28C2×C5×#217C2211yescharacteristic
29C2×C5×Dic3⋊C4C2212yescomplemented
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×#685C2212yescomplemented
32C3×D5×C22⋊C4—24no—
33#91561—24no—
34C2×#6667C2212yescomplemented
35C2×#6665C2212yescomplemented
36C2×#6665C2212yescomplemented
37C2×Dic3×Dic5C2212yescomplemented
38#91444—28no—
39C5×C3⋊#95C2212yescomplemented
40#90994C2212yescomplemented
41C22⋊C4×#67—51nomaximal, Hall
42C23×D20—31no—
43C2×#4039—32no—
44C2×D5×C22⋊C4—31no—
45C2×D5×C22⋊C4D311yescharacteristic, complemented
46C5×#380—31no—
47C4×C22⋊Dic5—31no—
48#65277—32no—
49#65244—31no—
50#65244—31no—
51#64954—32no—
52#64954—32no—
53C24×C3×C5C2311yescharacteristic
54C23×D15—22no—
55C23×D15—22no—
56C23×D15—24no—
57C23×D15—42no—
58C23×D15C2×C414yescomplemented
59C23×D15C2311yescharacteristic
60C23×D15C2311yescharacteristic
61C23×C3×D5—22no—
62C23×C3×D5—22no—
63C23×C3×D5—24no—
64C23×C3×D5—42no—
65C23×C3×D5C2×C414yescomplemented
66C23×C3×D5C2311yescharacteristic
67C23×C3×D5C2311yescharacteristic
68C22×C3×C4×C5C2312yes—
69C22×Dic15C2312yes—
70C22×C5×Dic3—24no—
71C22×C5×Dic3C2×C414yescomplemented
72C22×C5×Dic3C2312yes—
73C22×C5×Dic3C2311yescharacteristic
74C22×C5×Dic3C2311yescharacteristic
75C22×C3×Dic5C2312yes—
76C2×C3×C4×D5—24no—
77C2×C3×C4×D5—24no—
78C2×C3×C4×D5—42no—
79C2×#1202—24no—
80C2×#1202—24no—
81C2×#1202—24no—
82C2×#1202—232no—
83C2×#1202C2×C414yes—
84C2×#1202C2×C414yescomplemented
85C2×#1202C2×C414yescomplemented
86C2×#1202C2×C414yescomplemented
87C2×#1202D418yes—
88C2×#1200—24no—
89C2×#1200—24no—
90C2×#1200—42no—
91C3×C5×C22⋊C4—22no—
92#6719—22no—
93#6714—24no—
94#6714—42no—
95C5×#217—22no—
96C5×Dic3⋊C4—24no—
97C3×C22⋊Dic5D414yescomplemented
98C3×#685—24no—
99#6667—24no—
100#6665—24no—
101#6665—42no—
102Dic3×Dic5—24no—
103C23×#67—51no—
104C22×C3×C22⋊C4—51no—
105C2×C4×#67—52no—
106C2×D3×C22⋊C4—51no—
107#5247—51no—
108#5213—52no—
109#4957—52no—
110#4956—52no—
111#4955—51no—
112#4942D511yescharacteristic, complemented
113Dic3×C22⋊C4—51no—
114C24×D5—31no—
115C24×D5C2×D311yescharacteristic
116C23×C4×C5—31no—
117C22×D20—31no—
118C22×D20—38no—
119C22×D20—31no—
120C22×D20—31no—
121C22×D20—31no—
122C22×D20—68no—
123C22×C4×D5—32no—
124C22×C4×D5C2×D312yescomplemented
125C2×C5×C4⋊C4—32no—
126C2×C5×C22⋊C4—31no—
127C2×C5×C22⋊C4C2×D311yescharacteristic
128C2×C22⋊Dic5—31no—
129C2×C22⋊Dic5C2×D311yescharacteristic
130C2×#685—32no—
131C2×#685—32no—
132C2×#685—32no—
133C2×#685—32no—
134C2×#685—32no—
135C2×#685C2×D312yescomplemented
136C2×C4×Dic5—32no—
137#4039—68no—
138D5×C22⋊C4—24no—
139D5×C22⋊C4—64no—
140C5×#95—32no—
141#3963—32no—
142D4×C22⋊C4—151noSylow
143C23×C3×C5—22no—
144C23×C3×C5—22no—
145C23×C3×C5C22×C412yes—
146C23×C3×C5C2×D412yes—
147C23×C3×C5#4112yes—
148C23×C3×C5C2411yescharacteristic
149C22×D15—21no—
150C22×D15—21no—
151C22×D15—22no—
152C22×D15—28no—
153C22×D15—21no—
154C22×D15—22no—
155C22×D15—21no—
156C22×D15—22no—
157C22×D15—28no—
158C22×D15—44no—
159C22×D15—48no—
160C22×D15—48no—
161C22×D15C22×C412yes—
162C22×D15C22×C412yes—
163C22×D15C2×D414yes—
164C22×C3×D5—21no—
165C22×C3×D5—21no—
166C22×C3×D5—22no—
167C22×C3×D5—28no—
168C22×C3×D5—21no—
169C22×C3×D5—22no—
170C22×C3×D5—21no—
171C22×C3×D5—22no—
172C22×C3×D5—28no—
173C22×C3×D5—44no—
174C22×C3×D5—48no—
175C22×C3×D5—48no—
176C22×C3×D5C22×C412yes—
177C22×C3×D5C22×C412yes—
178C22×C3×D5C2×D414yes—
179C2×C3×C4×C5—22no—
180C2×C3×C4×C5—22no—
181C2×C3×C4×C5—22no—
182C2×Dic15—22no—
183C2×Dic15—22no—
184C2×Dic15—22no—
185C2×C5×Dic3—22no—
186C2×C5×Dic3—28no—
187C2×C5×Dic3—22no—
188C2×C5×Dic3—22no—
189C2×C5×Dic3—22no—
190C2×C5×Dic3C22×C412yes—
191C2×C5×Dic3C22×C412yes—
192C2×C5×Dic3C2×D414yes—
193C2×C3×Dic5—22no—
194C2×C3×Dic5—22no—
195C2×C3×Dic5C2×D414yescomplemented
196C3×C4×D5—48no—
197#1202—28no—
198#1202—28no—
199#1202—28no—
200#1202C22⋊C4116yescomplemented
201#1200—48no—
202C25×C3—51no—
203C24×D3—51no—
204C23×C3×C4—52no—
205C22×#67—58no—
206C22×#67—51no—
207C22×#67—51no—
208C22×#67—51no—
209C22×#67—51no—
210C22×#67—108no—
211C23×Dic3C2×D511yescharacteristic
212C22×C4×D3—52no—
213C2×C3×C22⋊C4—51no—
214C2×C3×C22⋊C4—52no—
215C2×C3×C22⋊C4—104no—
216C2×C3×C22⋊C4C2×D511yescharacteristic
217C2×#217—51no—
218C2×#217—52no—
219C2×#217—52no—
220C2×#217C2×D511yescharacteristic
221C4×#67—108no—
222C2×(C2×D3)⋊C4—52no—
223C2×(C2×D3)⋊C4—52no—
224C2×(C2×D3)⋊C4—52no—
225C2×Dic3⋊C4C2×D512yescomplemented
226C2×C4×Dic3—52no—
227D3×C22⋊C4—104no—
228C3⋊#95—52no—
229C3⋊#95C2×D512yescomplemented
230C24×C5C22×D311yescharacteristic
231C23×D5—22no—
232C23×D5—22no—
233C23×D5—24no—
234C23×D5—31no—
235C23×D5—31no—
236C23×D5—34no—
237C23×D5—42no—
238C23×D5—64no—
239C23×D5—62no—
240C23×D5—62no—
241C23×D5—122no—
242C23×D5C4×D314yescomplemented
243C23×D5C22×D311yescharacteristic
244C23×D5C22×D311yescharacteristic
245C22×C4×C5—31no—
246C22×C4×C5—34no—
247C22×C4×C5—31no—
248C22×C4×C5—32no—
249C22×C4×C5—64no—
250C22×C4×C5C22×D312yes—
251C22×Dic5—32no—
252C22×Dic5C22×D312yes—
253C2×D20—34no—
254C2×D20—38no—
255C2×D20—34no—
256C2×D20—34no—
257C2×D20—34no—
258C2×D20—632no—
259C2×D20—64no—
260C2×D20—64no—
261C2×D20—64no—
262C2×C4×D5—24no—
263C2×C4×D5—24no—
264C2×C4×D5—42no—
265C2×C4×D5—64no—
266C2×C4×D5—64no—
267C2×C4×D5—122no—
268C5×C4⋊C4—64no—
269C5×C22⋊C4—22no—
270C5×C22⋊C4—62no—
271C22⋊Dic5—62no—
272C22⋊Dic5#6714yescomplemented
273#685—24no—
274#685—64no—
275#685—64no—
276#685—64no—
277#685—122no—
278#685—122no—
279C4×Dic5—64no—
280C23×D4—151no—
281C2×C4×D4—152no—
282C22×C22⋊C4—51no—
283C22×C22⋊C4—151no—
284#390—152no—
285#386—152no—
286#386—152no—
287#380—31no—
288#379—151no—
289#379—151no—
290C4×C22⋊C4—151no—
291C22×C3×C5—22no—
292C22×C3×C5—22no—
293C22×C3×C5—24no—
294C22×C3×C5—24no—
295C22×C3×C5C4×D414yescomplemented
296C22×C3×C5C23×C411yescharacteristic
297C22×C3×C5C22×D412yes—
298C22×C3×C5C22×D411yescharacteristic
299C22×C3×C5C2×#4111yescharacteristic
300C22×C3×C5H(5,𝔽2)12yes—
301C2×D15—22no—
302C2×D15—22no—
303C2×D15—24no—
304C2×D15—24no—
305C2×D15—22no—
306C2×D15—22no—
307C2×D15—22no—
308C2×D15—416no—
309C2×D15—42no—
310C2×D15—42no—
311C2×D15C2×C22⋊C414yescomplemented
312C2×C3×D5—22no—
313C2×C3×D5—22no—
314C2×C3×D5—24no—
315C2×C3×D5—24no—
316C2×C3×D5—22no—
317C2×C3×D5—22no—
318C2×C3×D5—22no—
319C2×C3×D5—416no—
320C2×C3×D5—42no—
321C2×C3×D5—42no—
322C2×C3×D5C2×C22⋊C414yescomplemented
323C3×C4×C5—42no—
324Dic15—42no—
325C3×Dic5—24no—
326C5×Dic3—22no—
327C5×Dic3—42no—
328C5×Dic3C2×C22⋊C414yescomplemented
329C24×C3—51no—
330C24×C3—51no—
331C24×C3—54no—
332C24×C3—104no—
333C24×C3—102no—
334C24×C3—102no—
335C24×C3—202no—
336C24×C3C22×D511yescharacteristic
337C23×D3—51no—
338C23×D3—51no—
339C23×D3—54no—
340C23×D3—104no—
341C23×D3—102no—
342C23×D3—102no—
343C23×D3—202no—
344C22×C3×C4—52no—
345C22×C3×C4—104no—
346C22×C3×C4—104no—
347C22×C3×C4—202no—
348C22×C3×C4C22×D512yes—
349C2×#67—54no—
350C2×#67—54no—
351C2×#67—54no—
352C2×#67—54no—
353C2×#67—58no—
354C2×#67—1032no—
355C2×#67—104no—
356C2×#67—104no—
357C2×#67—104no—
358C22×Dic3—24no—
359C22×Dic3—52no—
360C22×Dic3C4×D514yescomplemented
361C22×Dic3C22×D512yes—
362C22×Dic3C22×D511yescharacteristic
363C22×Dic3C22×D511yescharacteristic
364C2×C4×D3—104no—
365C2×C4×D3—104no—
366C2×C4×D3—202no—
367C3×C22⋊C4—22no—
368C3×C22⋊C4—54no—
369C3×C22⋊C4—104no—
370#217—22no—
371#217—104no—
372#217—102no—
373#217—202no—
374(C2×D3)⋊C4—104no—
375(C2×D3)⋊C4—104no—
376(C2×D3)⋊C4—202no—
377Dic3⋊C4—24no—
378C4×Dic3—104no—
379C23×C5—22no—
380C23×C5—22no—
381C23×C5C2×C4×D312yes—
382C23×C5#23512yes—
383C23×C5C2×#6712yes—
384C23×C5C23×D311yescharacteristic
385C22×D5—21no—
386C22×D5—22no—
387C22×D5—21no—
388C22×D5—28no—
389C22×D5—21no—
390C22×D5—22no—
391C22×D5—22no—
392C22×D5—21no—
393C22×D5—28no—
394C22×D5—32no—
395C22×D5—34no—
396C22×D5—32no—
397C22×D5—44no—
398C22×D5—48no—
399C22×D5—48no—
400C22×D5—68no—
401C22×D5—61no—
402C22×D5—62no—
403C22×D5—61no—
404C22×D5—68no—
405C22×D5—61no—
406C22×D5—62no—
407C22×D5—62no—
408C22×D5—61no—
409C22×D5—124no—
410C22×D5—128no—
411C22×D5—128no—
412C22×D5C2×C4×D312yes—
413C22×D5C2×C4×D312yes—
414C22×D5D3×D414yes—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—32no—
419C2×C4×C5—34no—
420C2×C4×C5—32no—
421C2×C4×C5—68no—
422C2×C4×C5—62no—
423C2×C4×C5—62no—
424C2×C4×C5—62no—
425C2×C4×C5—62no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—62no—
429C2×Dic5—62no—
430C2×Dic5—62no—
431C2×Dic5C2×#6714yescomplemented
432D20—316no—
433D20—68no—
434D20—68no—
435D20—68no—
436C4×D5—48no—
437C4×D5—128no—
438C25—51no—
439C25—151no—
440C22×D4—151no—
441C22×D4—151no—
442C22×D4—151no—
443C22×D4—151no—
444C22×D4—158no—
445C22×D4—308no—
446C23×C4—31no—
447C23×C4—52no—
448C23×C4—152no—
449C4×D4—308no—
450C2×C4⋊C4—32no—
451C2×C22⋊C4—31no—
452C2×C22⋊C4—51no—
453C2×C22⋊C4—52no—
454C2×C22⋊C4—104no—
455C2×C22⋊C4—152no—
456C2×C22⋊C4—152no—
457C2×C22⋊C4—151no—
458C2×C22⋊C4—152no—
459C2×C22⋊C4—152no—
460C2×C22⋊C4—152no—
461C2×C22⋊C4—304no—
462C2×C22⋊C4D3×D511yescharacteristic
463C2×C42—152no—
464#95—32no—
465#95—152no—
466C2×C3×C5—24no—
467C2×C3×C5C22×C22⋊C411yescharacteristic
468C2×C3×C5C2×C4×D411yescharacteristic
469C2×C3×C5#51811yescharacteristic
470C2×C3×C5D4212yes—
471C2×C3×C5#54612yes—
472D15—24no—
473D15—42no—
474C3×D5—24no—
475C3×D5—42no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—52no—
479C23×C3—54no—
480C23×C3—52no—
481C23×C3—108no—
482C23×C3—101no—
483C23×C3—101no—
484C23×C3—102no—
485C23×C3—101no—
486C23×C3—102no—
487C23×C3—101no—
488C23×C3—102no—
489C23×C3—108no—
490C23×C3—204no—
491C23×C3—208no—
492C23×C3—208no—
493C23×C3C2×C4×D512yes—
494C23×C3D4×D512yes—
495C23×C3#71312yes—
496C23×C3C23×D511yescharacteristic
497C22×D3—52no—
498C22×D3—54no—
499C22×D3—52no—
500C22×D3—108no—
501C22×D3—101no—
502C22×D3—101no—
503C22×D3—102no—
504C22×D3—101no—
505C22×D3—102no—
506C22×D3—101no—
507C22×D3—102no—
508C22×D3—108no—
509C22×D3—204no—
510C22×D3—208no—
511C22×D3—208no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—54no—
516C2×C3×C4—102no—
517C2×C3×C4—102no—
518C2×C3×C4—208no—
519#67—516no—
520#67—108no—
521#67—108no—
522#67—108no—
523C2×Dic3—22no—
524C2×Dic3—28no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—102no—
529C2×Dic3—102no—
530C2×Dic3—102no—
531C2×Dic3C2×C4×D512yes—
532C2×Dic3C2×C4×D512yes—
533C2×Dic3D4×D514yes—
534C4×D3—208no—
535C22×C5—22no—
536C22×C5—22no—
537C22×C5—24no—
538C22×C5—24no—
539C22×C5C4×#6714yescomplemented
540C22×C5C22×C4×D311yescharacteristic
541C22×C5C2×#23511yescharacteristic
542C22×C5C2×D3×D412yes—
543C22×C5#100412yes—
544C22×C5C22×#6711yescharacteristic
545C2×D5—22no—
546C2×D5—24no—
547C2×D5—22no—
548C2×D5—24no—
549C2×D5—22no—
550C2×D5—22no—
551C2×D5—22no—
552C2×D5—34no—
553C2×D5—416no—
554C2×D5—42no—
555C2×D5—42no—
556C2×D5—62no—
557C2×D5—64no—
558C2×D5—62no—
559C2×D5—64no—
560C2×D5—62no—
561C2×D5—62no—
562C2×D5—62no—
563C2×D5—1216no—
564C2×D5—122no—
565C2×D5—122no—
566C2×D5D3×C22⋊C414yescomplemented
567C4×C5—34no—
568C4×C5—42no—
569C4×C5—62no—
570C4×C5—122no—
571Dic5—24no—
572Dic5—122no—
573C24—51no—
574C24—51no—
575C24—54no—
576C24—104no—
577C24—102no—
578C24—102no—
579C24—151no—
580C24—151no—
581C24—154no—
582C24—202no—
583C24—304no—
584C24—302no—
585C24—302no—
586C24—602no—
587C24C2×D3×D511yescharacteristic
588C2×D4—158no—
589C2×D4—154no—
590C2×D4—154no—
591C2×D4—154no—
592C2×D4—154no—
593C2×D4—304no—
594C2×D4—3032no—
595C2×D4—304no—
596C2×D4—304no—
597C22×C4—31no—
598C22×C4—34no—
599C22×C4—31no—
600C22×C4—32no—
601C22×C4—52no—
602C22×C4—64no—
603C22×C4—104no—
604C22×C4—104no—
605C22×C4—152no—
606C22×C4—202no—
607C22×C4—304no—
608C22×C4—304no—
609C22×C4—602no—
610C22×C4C2×D3×D512yes—
611C4⋊C4—64no—
612C22⋊C4—22no—
613C22⋊C4—54no—
614C22⋊C4—62no—
615C22⋊C4—104no—
616C22⋊C4—304no—
617C22⋊C4—304no—
618C22⋊C4—304no—
619C22⋊C4—302no—
620C22⋊C4—602no—
621C22⋊C4—602no—
622C42—304no—
623C3×C5D4×C22⋊C411yescharacteristic, complemented, Hall
624C22×C3—22no—
625C22×C3—22no—
626C22×C3—24no—
627C22×C3—24no—
628C22×C3—54no—
629C22×C3—102no—
630C22×C3—102no—
631C22×C3—104no—
632C22×C3—104no—
633C22×C3—102no—
634C22×C3—102no—
635C22×C3—102no—
636C22×C3—2016no—
637C22×C3—202no—
638C22×C3—202no—
639C22×C3#403914yescomplemented
640C22×C3C22×C4×D511yescharacteristic
641C22×C3C2×D4×D512yes—
642C22×C3C2×D4×D511yescharacteristic
643C22×C3C2×#71311yescharacteristic
644C22×C3#414912yes—
645C2×D3—54no—
646C2×D3—102no—
647C2×D3—102no—
648C2×D3—104no—
649C2×D3—104no—
650C2×D3—102no—
651C2×D3—102no—
652C2×D3—102no—
653C2×D3—2016no—
654C2×D3—202no—
655C2×D3—202no—
656C3×C4—42no—
657C3×C4—104no—
658Dic3—22no—
659Dic3—42no—
660Dic3—202no—
661Dic3D5×C22⋊C414yescomplemented
662C2×C5—24no—
663C2×C5C2×D3×C22⋊C411yescharacteristic
664C2×C5#548611yescharacteristic
665C2×C5#549012yes—
666C2×C5C2×C4×#6711yescharacteristic
667C2×C5D4×#6712yes—
668D5—24no—
669D5—42no—
670D5—64no—
671D5—122no—
672C23—22no—
673C23—22no—
674C23—52no—
675C23—54no—
676C23—52no—
677C23—108no—
678C23—101no—
679C23—102no—
680C23—101no—
681C23—108no—
682C23—101no—
683C23—102no—
684C23—102no—
685C23—101no—
686C23—152no—
687C23—154no—
688C23—152no—
689C23—204no—
690C23—208no—
691C23—208no—
692C23—308no—
693C23—301no—
694C23—302no—
695C23—301no—
696C23—308no—
697C23—301no—
698C23—302no—
699C23—302no—
700C23—301no—
701C23—604no—
702C23—608no—
703C23—608no—
704C23#677312yes—
705C23C4×D3×D512yes—
706C23D5×#6712yes—
707C23C22×D3×D511yescharacteristic
708D4—1516no—
709D4—308no—
710D4—308no—
711D4—308no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—32no—
716C2×C4—34no—
717C2×C4—32no—
718C2×C4—54no—
719C2×C4—68no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—208no—
727C2×C4—302no—
728C2×C4—302no—
729C2×C4—302no—
730C2×C4—608no—
731C2×C3—24no—
732C2×C3—104no—
733C2×C3—202no—
734C2×C3C2×D5×C22⋊C411yescharacteristic
735C2×C3C2×#403911yescharacteristic
736C2×C3#6585511yescharacteristic
737C2×C3#6594312yes—
738C2×C3#6596412yes—
739D3—104no—
740D3—202no—
741C5C22⋊C4×#6711yescharacteristic, complemented, Sylow
742C22—24no—
743C22—22no—
744C22—24no—
745C22—22no—
746C22—54no—
747C22—102no—
748C22—104no—
749C22—102no—
750C22—104no—
751C22—102no—
752C22—102no—
753C22—102no—
754C22—154no—
755C22—2016no—
756C22—202no—
757C22—202no—
758C22—302no—
759C22—304no—
760C22—302no—
761C22—304no—
762C22—302no—
763C22—302no—
764C22—302no—
765C22—6016no—
766C22—602no—
767C22—602no—
768C22#9144414yescomplemented
769C22C2×#677311yescharacteristic
770C22C2×C4×D3×D511yescharacteristic
771C22D3×D4×D512yes—
772C22#9202612yes—
773C22C2×D5×#6711yescharacteristic
774C4—34no—
775C4—42no—
776C4—62no—
777C4—104no—
778C4—122no—
779C4—602no—
780C3#1060573811yescharacteristic, complemented, Sylow
781C2—24no—
782C2—104no—
783C2—202no—
784C2—304no—
785C2—602no—
786C2#1175306611yescharacteristic
787C2#1175307312yes—
788C2D3×D5×C22⋊C411yescharacteristic
789C2C2×#9144411yescharacteristic
790C2#1175503812yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×#1202C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5D4×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D5×C22⋊C4C2semidirect
3. C2×#91561C2semidirect
4. C2×#91444C2semidirect
5. #11751056C2semidirect
6. C5×#4942C2semidirect
7. #11749488C2semidirect
8. Dic3×C22⋊Dic5C2semidirect
9. #11748913C2semidirect
10. #11748907C2semidirect
11. #11748700C2semidirect
16. C22×C3×C4×D5C22semidirect
18. C22×#1202C4semidirect
23. C22×#1200C22semidirect
26. C2×#6714C22semidirect
27. C2×#6714C22semidirect
29. C2×C5×Dic3⋊C4C22semidirect
31. C2×C3×#685C22semidirect
34. C2×#6667C22semidirect
35. C2×#6665C22semidirect
36. C2×#6665C22semidirect
37. C2×Dic3×Dic5C22semidirect
39. C5×C3⋊#95C22semidirect
40. #90994C22semidirect
45. C2×D5×C22⋊C4D3semidirect
58. C23×D15C2×C4semidirect
65. C23×C3×D5C2×C4semidirect
71. C22×C5×Dic3C2×C4semidirect
84. C2×#1202C2×C4semidirect
85. C2×#1202C2×C4semidirect
86. C2×#1202C2×C4semidirect
97. C3×C22⋊Dic5D4semidirect
112. #4942D5semidirect
124. C22×C4×D5C2×D3semidirect
135. C2×#685C2×D3semidirect
195. C2×C3×Dic5C2×D4semidirect
200. #1202C22⋊C4semidirect
225. C2×Dic3⋊C4C2×D5semidirect
229. C3⋊#95C2×D5semidirect
242. C23×D5C4×D3semidirect
272. C22⋊Dic5#67semidirect
295. C22×C3×C5C4×D4semidirect
311. C2×D15C2×C22⋊C4semidirect
322. C2×C3×D5C2×C22⋊C4semidirect
328. C5×Dic3C2×C22⋊C4semidirect
360. C22×Dic3C4×D5semidirect
431. C2×Dic5C2×#67semidirect
539. C22×C5C4×#67semidirect
566. C2×D5D3×C22⋊C4semidirect
623. C3×C5D4×C22⋊C4semidirect
639. C22×C3#4039semidirect
661. Dic3D5×C22⋊C4semidirect
741. C5C22⋊C4×#67semidirect
768. C22#91444semidirect
780. C3#10605738semidirect

Maximal subgroups

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

subgroupindex
C23×#12022
C2×C3×D5×C22⋊C42
C2×#915612
C2×#914442
#117510562
C5×#49422
#117494882
Dic3×C22⋊Dic52
#117489132
#117489072
#117487002
#106057383
C22⋊C4×#675