Finite Group Databasebeta

← C2×#11755435 #14480344

Subgroups — C2×#11755435 #14480344

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×D5×#67C211yesmaximal, characteristic, complemented
3C2×#91842C211yesmaximal, characteristic, complemented
4C2×C5×#953C211yesmaximal, characteristic, complemented
5#11755435C2116yesmaximal, direct product factor
6C2×#91577C212yesmaximal, complemented
7C2×#91550C212yesmaximal, complemented
8C2×#91549C212yesmaximal, complemented
9C2×#91548C212yesmaximal, complemented
10C2×D5×#217C211yesmaximal, characteristic, complemented
11C2×#91546C211yesmaximal, characteristic, complemented
12C2×#91539C211yesmaximal, characteristic, complemented
13C2×#65923—31nomaximal, Hall
14C25×C3×C5C2211yescharacteristic, complemented
15C24×C3×D5C2211yescharacteristic
16C23×D3×D5C2211yescharacteristic, complemented
17C22×#1220C2211yescharacteristic
18C22×#1220C2212yescomplemented
19C22×C5×#67C2211yescharacteristic
20C22×C5×#67C2212yescomplemented
21C22×C3×C22⋊D5—28no—
22C22×C3×C22⋊D5C2212yes—
23C22×C3×C22⋊D5C2212yescomplemented
24C22×C3×C22⋊D5C2218yescomplemented
25C23×C3×Dic5C2211yescharacteristic, complemented
26C2×D5×#67—28no—
27C2×D5×#67C2218yescomplemented
28C22×#1202C2211yescharacteristic, complemented
29C22×#1201C2211yescharacteristic, complemented
30C22×D5×Dic3C2211yescharacteristic, complemented
31C22×D5×Dic3C2212yescomplemented
32#91842C2218yescomplemented
33C2×#6719C2211yescharacteristic, complemented
34C2×#6719C2212yescomplemented
35C5×#953C2218yescomplemented
36C2×C5×#217C2211yescharacteristic, complemented
37C2×C5×#217C2212yescomplemented
38#91577C22116yescomplemented
39#91550C22116yescomplemented
40#91549C22116yescomplemented
41#91548C22116yescomplemented
42D5×#217C2218yescomplemented
43#91546C2218yescomplemented
44C2×Dic3⋊Dic5C2212yescomplemented
45C2×#6669C2212yescomplemented
46C2×#6667C2212yescomplemented
47#91539C2218yescomplemented
48C2×(C2×D3)⋊Dic5C2212yescomplemented
49C2×#6665C2212yescomplemented
50C2×#5804—51nomaximal, Hall
51C23×C22⋊D5D311yescharacteristic, complemented
52C22×D4×D5—31no—
53C2×C5×#120—31no—
54C2×#4099—31no—
55C2×#4084—32no—
56C2×#4083—32no—
57C2×#4081—31no—
58#65923—316no—
59C2×#4032—31no—
60C2×#4030—32no—
61C2×#4029—32no—
62C2×D5×C22⋊C4—31no—
63C24×C3×C5—24no—
64C24×C3×C5—44no—
65C24×C3×C5C2312yes—
66C24×C3×C5C2311yescharacteristic
67C24×C3×C5C2314yescomplemented
68C23×D15C2311yescharacteristic
69C23×C5×D3C2311yescharacteristic
70C23×C3×D5—44no—
71C23×C3×D5D418yescomplemented
72C23×C3×D5C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C23×C3×D5C2314yes—
75C22×D3×D5—24no—
76C22×D3×D5—44no—
77C22×D3×D5C2314yescomplemented
78C2×#1220—24no—
79C2×#1220—44no—
80C2×#1220C2314yes—
81C2×#1220C2318yescomplemented
82C22×Dic15C2311yescharacteristic
83C22×Dic15C2312yes—
84C2×C5×#67—24no—
85C2×C5×#67—44no—
86C2×C5×#67C2314yes—
87C2×C5×#67C2318yescomplemented
88C22×C5×Dic3C2311yescharacteristic
89C22×C5×Dic3C2312yes—
90C2×C3×C22⋊D5—28no—
91C2×C3×C22⋊D5—28no—
92C2×C3×C22⋊D5—232no—
93C2×C3×C22⋊D5C2318yes—
94C2×C3×C22⋊D5C2318yescomplemented
95C22×C3×Dic5—24no—
96C22×C3×Dic5C2312yes—
97C22×C3×Dic5C2314yescomplemented
98D5×#67—232no—
99C2×#1202—24no—
100C2×#1202C2314yescomplemented
101C2×#1201—24no—
102C2×#1201C2314yescomplemented
103C2×D5×Dic3—24no—
104C2×D5×Dic3—44no—
105C2×D5×Dic3C2314yescomplemented
106C2×D5×Dic3C2318yescomplemented
107#6719C2314yescomplemented
108#6719C2318yescomplemented
109C5×#217C2314yescomplemented
110C5×#217C2318yescomplemented
111Dic3⋊Dic5C2318yescomplemented
112#6669C2318yescomplemented
113#6667C2318yescomplemented
114(C2×D3)⋊Dic5C2318yescomplemented
115#6665C2318yescomplemented
116C23×C3×D4—51no—
117C23×#67—51no—
118C2×#953—51no—
119C2×#953D511yescharacteristic, complemented
120C22×#217—51no—
121#5804—516no—
122C2×#939—52no—
123C2×#939—52no—
124C2×#937—52no—
125C2×#935—52no—
126C2×#929—51no—
127C2×#929—51no—
128C25×C5C2×D311yescharacteristic, complemented
129C24×D5—31no—
130C24×D5C2×D311yescharacteristic
131C22×C5×D4—31no—
132C22×C5×D4—32no—
133C22×C22⋊D5—28no—
134C22×C22⋊D5—31no—
135C22×C22⋊D5—31no—
136C22×C22⋊D5—32no—
137C22×C22⋊D5C2×D312yes—
138C22×C22⋊D5C2×D312yescomplemented
139C22×C22⋊D5C2×D318yescomplemented
140C23×Dic5C2×D311yescharacteristic, complemented
141C2×D4×D5—38no—
142C2×D4×D5—68no—
143C22×D20—31no—
144C22×C4×D5—31no—
145C22×C4×D5—32no—
146C5×#120—38no—
147C2×C5×C22⋊C4—31no—
148C2×C5×C22⋊C4—32no—
149#4099—38no—
150C2×C22⋊Dic5—31no—
151C2×C22⋊Dic5—32no—
152C2×C22⋊Dic5—32no—
153#4084—316no—
154#4083—316no—
155#4081—38no—
156C2×#685—32no—
157C2×#685—32no—
158C2×C4⋊Dic5—32no—
159C2×#683—32no—
160#4032—38no—
161#4030—316no—
162#4029—316no—
163D5×C22⋊C4—38no—
164C2×#534—151noSylow
165C23×C3×C5—24no—
166C23×C3×C5—24no—
167C23×C3×C5—28no—
168C23×C3×C5—24no—
169C23×C3×C5—24no—
170C23×C3×C5—48no—
171C23×C3×C5—416no—
172C23×C3×C5C2×D414yes—
173C23×C3×C5C2414yes—
174C23×C3×C5C2412yes—
175C23×C3×C5C2411yescharacteristic
176C22×D15—22no—
177C22×D15—24no—
178C22×D15C2412yes—
179C22×C5×D3—22no—
180C22×C5×D3—24no—
181C22×C5×D3C2412yes—
182C22×C3×D5—24no—
183C22×C3×D5—24no—
184C22×C3×D5—416no—
185C22×C3×D5—48no—
186C22×C3×D5C2×D414yes—
187C22×C3×D5C2×D414yes—
188C22×C3×D5C2×D4116yescomplemented
189C22×C3×D5C2412yes—
190C22×C3×D5C2412yes—
191C2×D3×D5—28no—
192C2×D3×D5—48no—
193C2×D3×D5—416no—
194#1220—28no—
195#1220—48no—
196C2×Dic15—22no—
197C2×Dic15—24no—
198C2×Dic15C2414yes—
199C2×Dic15C2412yes—
200C5×#67—28no—
201C5×#67—48no—
202C2×C5×Dic3—22no—
203C2×C5×Dic3—24no—
204C2×C5×Dic3C2414yes—
205C2×C5×Dic3C2412yes—
206C3×C22⋊D5—216no—
207C3×C22⋊D5—216no—
208C2×C3×Dic5—24no—
209C2×C3×Dic5—28no—
210C2×C3×Dic5C2414yes—
211#1202—28no—
212#1201—28no—
213D5×Dic3—28no—
214D5×Dic3—48no—
215C25×C3—51no—
216C25×C3C2×D511yescharacteristic, complemented
217C24×D3—51no—
218C22×C3×D4—52no—
219C22×C3×D4—52no—
220C22×C3×D4—58no—
221C22×C3×D4—108no—
222C23×C3×C4—51no—
223C22×#67—51no—
224C22×#67—51no—
225C22×#67—52no—
226C22×#67—58no—
227C22×#67—51no—
228C22×#67—108no—
229C22×#67C2×D511yescharacteristic
230C22×#67C2×D512yescomplemented
231C23×Dic3—51no—
232C23×Dic3—52no—
233#953—58no—
234#953C2×D518yescomplemented
235C2×#217—51no—
236C2×#217—52no—
237C2×#217—52no—
238C2×#217—58no—
239C2×#217C2×D511yescharacteristic, complemented
240C2×#217C2×D512yescomplemented
241#939—516no—
242#939—516no—
243#937—516no—
244#935—516no—
245#929—58no—
246#929—58no—
247C2×(C2×D3)⋊C4—52no—
248C2×(C2×D3)⋊C4—52no—
249C2×Dic3⋊C4—52no—
250C2×Dic3⋊C4—52no—
251C24×C5—24no—
252C24×C5—31no—
253C24×C5—44no—
254C24×C5C22×D312yes—
255C24×C5C22×D311yescharacteristic
256C24×C5C22×D314yescomplemented
257C23×D5—31no—
258C23×D5—34no—
259C23×D5—44no—
260C23×D5—64no—
261C23×D5—124no—
262C23×D5#6718yescomplemented
263C23×D5C22×D311yescharacteristic
264C23×D5C22×D311yescharacteristic
265C23×D5C22×D314yes—
266C2×C5×D4—34no—
267C2×C5×D4—38no—
268C2×C5×D4—64no—
269C2×C5×D4—124no—
270C22×C4×C5—31no—
271C22×C4×C5—32no—
272C2×C22⋊D5—28no—
273C2×C22⋊D5—28no—
274C2×C22⋊D5—232no—
275C2×C22⋊D5—34no—
276C2×C22⋊D5—34no—
277C2×C22⋊D5—38no—
278C2×C22⋊D5—64no—
279C2×C22⋊D5—64no—
280C2×C22⋊D5—124no—
281C2×C22⋊D5C22×D318yes—
282C2×C22⋊D5C22×D318yescomplemented
283C22×Dic5—24no—
284C22×Dic5—32no—
285C22×Dic5—31no—
286C22×Dic5C22×D312yes—
287C22×Dic5C22×D314yescomplemented
288D4×D5—632no—
289C2×D20—34no—
290C2×D20—64no—
291C2×C4×D5—34no—
292C2×C4×D5—38no—
293C2×C4×D5—64no—
294C2×C4×D5—124no—
295C5×C22⋊C4—34no—
296C5×C22⋊C4—38no—
297C22⋊Dic5—34no—
298C22⋊Dic5—38no—
299C22⋊Dic5—38no—
300#685—38no—
301#685—38no—
302C4⋊Dic5—38no—
303#683—38no—
304C23×D4—51no—
305C23×D4—151no—
306#534—1516no—
307C2×#123—151no—
308C2×#123—152no—
309C2×#123—151no—
310C2×#121—152no—
311C2×#121—152no—
312C2×#120—31no—
313C2×#120—152no—
314C2×#120—151no—
315C22×C22⋊C4—151no—
316C22×C3×C5—28no—
317C22×C3×C5—24no—
318C22×C3×C5—24no—
319C22×C3×C5—24no—
320C22×C3×C5—24no—
321C22×C3×C5—416no—
322C22×C3×C5—48no—
323C22×C3×C5C22×D414yes—
324C22×C3×C5C22×D412yes—
325C22×C3×C5H(5,𝔽2)14yes—
326C22×C3×C5C2511yescharacteristic
327C2×D15—22no—
328C2×D15—24no—
329C2×D15—44no—
330C2×C5×D3—22no—
331C2×C5×D3—24no—
332C2×C5×D3—44no—
333C2×C3×D5—28no—
334C2×C3×D5—28no—
335C2×C3×D5—24no—
336C2×C3×D5—24no—
337C2×C3×D5—416no—
338C2×C3×D5C22×D414yes—
339C2×C3×D5C22×D414yes—
340D3×D5—416no—
341Dic15—22no—
342Dic15—24no—
343C3×Dic5—24no—
344C5×Dic3—22no—
345C5×Dic3—24no—
346C24×C3—24no—
347C24×C3—44no—
348C24×C3—51no—
349C24×C3—51no—
350C24×C3—58no—
351C24×C3—54no—
352C24×C3—204no—
353C24×C3C22×D512yes—
354C24×C3C22×D511yescharacteristic
355C24×C3C22×D514yescomplemented
356C23×D3—51no—
357C23×D3—54no—
358C23×D3—104no—
359C23×D3—204no—
360C23×D3C22×D511yescharacteristic
361C2×C3×D4—58no—
362C2×C3×D4—58no—
363C2×C3×D4—108no—
364C2×C3×D4—108no—
365C2×C3×D4—1032no—
366C22×C3×C4—52no—
367C22×C3×C4—54no—
368C22×C3×C4—104no—
369C2×#67—24no—
370C2×#67—44no—
371C2×#67—54no—
372C2×#67—54no—
373C2×#67—58no—
374C2×#67—54no—
375C2×#67—104no—
376C2×#67—1032no—
377C2×#67—104no—
378C2×#67—104no—
379C2×#67—204no—
380C2×#67C22×D514yes—
381C2×#67C22×D518yescomplemented
382C22×Dic3—51no—
383C22×Dic3—52no—
384C22×Dic3—54no—
385C22×Dic3—58no—
386C22×Dic3—104no—
387C22×Dic3—204no—
388C22×Dic3C22×D511yescharacteristic
389C22×Dic3C22×D512yes—
390#217—54no—
391#217—58no—
392#217—58no—
393#217C22×D514yescomplemented
394#217C22×D518yescomplemented
395(C2×D3)⋊C4—58no—
396(C2×D3)⋊C4—58no—
397Dic3⋊C4—58no—
398Dic3⋊C4—58no—
399C23×C5—24no—
400C23×C5—24no—
401C23×C5—24no—
402C23×C5—24no—
403C23×C5—28no—
404C23×C5—32no—
405C23×C5—48no—
406C23×C5—416no—
407C23×C5—64no—
408C23×C5—62no—
409C23×C5C2×#6714yes—
410C23×C5C23×D314yes—
411C23×C5C23×D312yes—
412C23×C5C23×D311yescharacteristic
413C22×D5—24no—
414C22×D5—24no—
415C22×D5—32no—
416C22×D5—416no—
417C22×D5—48no—
418C22×D5—64no—
419C22×D5—62no—
420C22×D5—68no—
421C22×D5—128no—
422C22×D5—1216no—
423C22×D5C2×#6714yes—
424C22×D5C2×#6714yes—
425C22×D5C2×#67116yescomplemented
426C22×D5C23×D312yes—
427C22×D5C23×D312yes—
428C5×D4—68no—
429C5×D4—128no—
430C2×C4×C5—32no—
431C2×C4×C5—34no—
432C2×C4×C5—64no—
433C2×C4×C5—62no—
434C22⋊D5—216no—
435C22⋊D5—216no—
436C22⋊D5—68no—
437C22⋊D5—68no—
438C22⋊D5—128no—
439C2×Dic5—24no—
440C2×Dic5—28no—
441C2×Dic5—34no—
442C2×Dic5—32no—
443C2×Dic5—64no—
444C2×Dic5—62no—
445C2×Dic5C23×D314yes—
446D20—68no—
447C4×D5—68no—
448C4×D5—128no—
449C25—51no—
450C25—151no—
451C25D3×D511yescharacteristic, complemented
452C22×D4—31no—
453C22×D4—32no—
454C22×D4—52no—
455C22×D4—52no—
456C22×D4—58no—
457C22×D4—108no—
458C22×D4—151no—
459C22×D4—158no—
460C22×D4—151no—
461C22×D4—151no—
462C22×D4—152no—
463C22×D4—308no—
464C23×C4—51no—
465C23×C4—151no—
466C23×C4—152no—
467#123—158no—
468#123—1516no—
469#123—158no—
470#121—1516no—
471#121—1516no—
472#120—38no—
473#120—1516no—
474#120—158no—
475C2×C4⋊C4—152no—
476C2×C4⋊C4—152no—
477C2×C22⋊C4—31no—
478C2×C22⋊C4—32no—
479C2×C22⋊C4—158no—
480C2×C22⋊C4—152no—
481C2×C22⋊C4—152no—
482C2×C22⋊C4—152no—
483C2×C22⋊C4—151no—
484C2×C22⋊C4—152no—
485C2×C3×C5—24no—
486C2×C3×C5—44no—
487C2×C3×C5#53414yescomplemented
488C2×C3×C5C23×D411yescharacteristic
489C2×C3×C5C2×H(5,𝔽2)12yes—
490D15—42no—
491C3×D5—24no—
492C3×D5—24no—
493C5×D3—42no—
494C23×C3—24no—
495C23×C3—24no—
496C23×C3—28no—
497C23×C3—24no—
498C23×C3—24no—
499C23×C3—48no—
500C23×C3—416no—
501C23×C3—54no—
502C23×C3—54no—
503C23×C3—52no—
504C23×C3—52no—
505C23×C3—516no—
506C23×C3—104no—
507C23×C3—104no—
508C23×C3—2016no—
509C23×C3—208no—
510C23×C3D4×D514yes—
511C23×C3C23×D514yes—
512C23×C3C23×D512yes—
513C23×C3C23×D511yescharacteristic
514C22×D3—22no—
515C22×D3—24no—
516C22×D3—52no—
517C22×D3—108no—
518C22×D3—102no—
519C22×D3—104no—
520C22×D3—208no—
521C22×D3—2016no—
522C22×D3C23×D512yes—
523C3×D4—1016no—
524C3×D4—1016no—
525C2×C3×C4—54no—
526C2×C3×C4—108no—
527C2×C3×C4—104no—
528#67—28no—
529#67—48no—
530#67—108no—
531#67—108no—
532#67—108no—
533#67—208no—
534C2×Dic3—22no—
535C2×Dic3—24no—
536C2×Dic3—52no—
537C2×Dic3—54no—
538C2×Dic3—108no—
539C2×Dic3—102no—
540C2×Dic3—104no—
541C2×Dic3—208no—
542C2×Dic3C23×D512yes—
543C2×Dic3C23×D514yes—
544C22×C5—24no—
545C22×C5—28no—
546C22×C5—24no—
547C22×C5—24no—
548C22×C5—24no—
549C22×C5—416no—
550C22×C5—48no—
551C22×C5—64no—
552C22×C5—62no—
553C22×C5—124no—
554C22×C5#100414yes—
555C22×C5C22×#6714yes—
556C22×C5C22×#6712yes—
557C22×C5C24×D311yescharacteristic
558C2×D5—24no—
559C2×D5—24no—
560C2×D5—28no—
561C2×D5—28no—
562C2×D5—416no—
563C2×D5—64no—
564C2×D5—62no—
565C2×D5—1216no—
566C2×D5—124no—
567C2×D5C22×#6714yes—
568C2×D5C22×#6714yes—
569C4×C5—64no—
570C4×C5—62no—
571Dic5—24no—
572Dic5—64no—
573Dic5—62no—
574C24—24no—
575C24—31no—
576C24—44no—
577C24—51no—
578C24—51no—
579C24—58no—
580C24—54no—
581C24—154no—
582C24—151no—
583C24—204no—
584C24—304no—
585C24—604no—
586C24C2×D3×D512yes—
587C24C2×D3×D511yescharacteristic
588C24C2×D3×D514yescomplemented
589C2×D4—34no—
590C2×D4—38no—
591C2×D4—58no—
592C2×D4—58no—
593C2×D4—64no—
594C2×D4—108no—
595C2×D4—108no—
596C2×D4—1032no—
597C2×D4—124no—
598C2×D4—154no—
599C2×D4—154no—
600C2×D4—154no—
601C2×D4—158no—
602C2×D4—304no—
603C2×D4—3032no—
604C2×D4—304no—
605C2×D4—304no—
606C2×D4—604no—
607C22×C4—32no—
608C22×C4—31no—
609C22×C4—54no—
610C22×C4—52no—
611C22×C4—104no—
612C22×C4—154no—
613C22×C4—158no—
614C22×C4—152no—
615C22×C4—151no—
616C22×C4—304no—
617C22×C4—604no—
618C4⋊C4—158no—
619C4⋊C4—158no—
620C22⋊C4—34no—
621C22⋊C4—38no—
622C22⋊C4—158no—
623C22⋊C4—158no—
624C22⋊C4—158no—
625C22⋊C4—154no—
626C22⋊C4—158no—
627C3×C5C2×#53411yescharacteristic, complemented, Hall
628C22×C3—28no—
629C22×C3—24no—
630C22×C3—24no—
631C22×C3—24no—
632C22×C3—24no—
633C22×C3—416no—
634C22×C3—48no—
635C22×C3—54no—
636C22×C3—54no—
637C22×C3—108no—
638C22×C3—108no—
639C22×C3—104no—
640C22×C3—104no—
641C22×C3—2016no—
642C22×C3C2×D4×D514yes—
643C22×C3C2×D4×D512yes—
644C22×C3#414414yes—
645C22×C3C24×D511yescharacteristic
646C2×D3—22no—
647C2×D3—24no—
648C2×D3—44no—
649C2×D3—102no—
650C2×D3—104no—
651C2×D3—2016no—
652C2×D3—204no—
653C3×C4—104no—
654Dic3—22no—
655Dic3—24no—
656Dic3—102no—
657Dic3—104no—
658C2×C5—24no—
659C2×C5—44no—
660C2×C5—122no—
661C2×C5#580414yescomplemented
662C2×C5C2×#100412yes—
663C2×C5C23×#6711yescharacteristic
664D5—24no—
665D5—24no—
666D5—122no—
667C23—24no—
668C23—24no—
669C23—28no—
670C23—24no—
671C23—24no—
672C23—32no—
673C23—48no—
674C23—416no—
675C23—54no—
676C23—54no—
677C23—52no—
678C23—52no—
679C23—516no—
680C23—62no—
681C23—64no—
682C23—104no—
683C23—104no—
684C23—152no—
685C23—208no—
686C23—2016no—
687C23—308no—
688C23—302no—
689C23—304no—
690C23—608no—
691C23—6016no—
692C23D5×#6714yes—
693C23C22×D3×D514yes—
694C23C22×D3×D512yes—
695C23C22×D3×D511yescharacteristic
696D4—68no—
697D4—1016no—
698D4—1016no—
699D4—128no—
700D4—308no—
701D4—308no—
702D4—308no—
703D4—608no—
704C2×C4—34no—
705C2×C4—32no—
706C2×C4—54no—
707C2×C4—62no—
708C2×C4—64no—
709C2×C4—108no—
710C2×C4—104no—
711C2×C4—154no—
712C2×C4—152no—
713C2×C4—308no—
714C2×C4—302no—
715C2×C4—304no—
716C2×C4—608no—
717C2×C3—24no—
718C2×C3—44no—
719C2×C3—104no—
720C2×C3—104no—
721C2×C3#6592314yescomplemented
722C2×C3C22×D4×D511yescharacteristic
723C2×C3C2×#414412yes—
724D3—42no—
725D3—202no—
726C5C2×#580411yescharacteristic, complemented, Sylow
727C22—24no—
728C22—28no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—416no—
733C22—48no—
734C22—54no—
735C22—54no—
736C22—62no—
737C22—64no—
738C22—104no—
739C22—104no—
740C22—108no—
741C22—108no—
742C22—124no—
743C22—2016no—
744C22—302no—
745C22—304no—
746C22—6016no—
747C22—604no—
748C22C2×D5×#6714yes—
749C22C2×D5×#6712yes—
750C22#9204914yes—
751C22C23×D3×D511yescharacteristic
752C4—62no—
753C4—64no—
754C4—104no—
755C4—302no—
756C4—304no—
757C3C2×#6592311yescharacteristic, complemented, Sylow
758C2—24no—
759C2—44no—
760C2—104no—
761C2—104no—
762C2—122no—
763C2—602no—
764C2#1175543514yesdirect product factor
765C2C22×D5×#6711yescharacteristic
766C2C2×#9204912yes—
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC25×C3×C5C22
socleC23×C3×C5C24
hypercenterC25D3×D5
hypocenterC3×C5C2×#534
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C23×C3×C22⋊D5C2semidirect
2. C22×D5×#67C2semidirect
3. C2×#91842C2semidirect
4. C2×C5×#953C2semidirect
5. #11755435C2direct (N × H)
6. C2×#91577C2semidirect
7. C2×#91550C2semidirect
8. C2×#91549C2semidirect
9. C2×#91548C2semidirect
10. C2×D5×#217C2semidirect
11. C2×#91546C2semidirect
12. C2×#91539C2semidirect
14. C25×C3×C5C22semidirect
16. C23×D3×D5C22semidirect
18. C22×#1220C22semidirect
20. C22×C5×#67C22semidirect
23. C22×C3×C22⋊D5C22semidirect
24. C22×C3×C22⋊D5C22semidirect
25. C23×C3×Dic5C22semidirect
27. C2×D5×#67C22semidirect
28. C22×#1202C22semidirect
29. C22×#1201C22semidirect
30. C22×D5×Dic3C22semidirect
31. C22×D5×Dic3C22semidirect
32. #91842C22semidirect
33. C2×#6719C22semidirect
34. C2×#6719C22semidirect
35. C5×#953C22semidirect
36. C2×C5×#217C22semidirect
37. C2×C5×#217C22semidirect
38. #91577C22semidirect
39. #91550C22semidirect
40. #91549C22semidirect
41. #91548C22semidirect
42. D5×#217C22semidirect
43. #91546C22semidirect
44. C2×Dic3⋊Dic5C22semidirect
45. C2×#6669C22semidirect
46. C2×#6667C22semidirect
47. #91539C22semidirect
48. C2×(C2×D3)⋊Dic5C22semidirect
49. C2×#6665C22semidirect
51. C23×C22⋊D5D3semidirect
67. C24×C3×C5C23semidirect
71. C23×C3×D5D4semidirect
77. C22×D3×D5C23semidirect
81. C2×#1220C23semidirect
87. C2×C5×#67C23semidirect
94. C2×C3×C22⋊D5C23semidirect
97. C22×C3×Dic5C23semidirect
100. C2×#1202C23semidirect
102. C2×#1201C23semidirect
105. C2×D5×Dic3C23semidirect
106. C2×D5×Dic3C23semidirect
107. #6719C23semidirect
108. #6719C23semidirect
109. C5×#217C23semidirect
110. C5×#217C23semidirect
111. Dic3⋊Dic5C23semidirect
112. #6669C23semidirect
113. #6667C23semidirect
114. (C2×D3)⋊Dic5C23semidirect
115. #6665C23semidirect
119. C2×#953D5semidirect
128. C25×C5C2×D3semidirect
138. C22×C22⋊D5C2×D3semidirect
139. C22×C22⋊D5C2×D3semidirect
140. C23×Dic5C2×D3semidirect
188. C22×C3×D5C2×D4semidirect
216. C25×C3C2×D5semidirect
230. C22×#67C2×D5semidirect
234. #953C2×D5semidirect
239. C2×#217C2×D5semidirect
240. C2×#217C2×D5semidirect
256. C24×C5C22×D3semidirect
262. C23×D5#67semidirect
282. C2×C22⋊D5C22×D3semidirect
287. C22×Dic5C22×D3semidirect
355. C24×C3C22×D5semidirect
381. C2×#67C22×D5semidirect
393. #217C22×D5semidirect
394. #217C22×D5semidirect
425. C22×D5C2×#67semidirect
451. C25D3×D5semidirect
487. C2×C3×C5#534semidirect
588. C24C2×D3×D5semidirect
627. C3×C5C2×#534semidirect
661. C2×C5#5804semidirect
721. C2×C3#65923semidirect
726. C5C2×#5804semidirect
757. C3C2×#65923semidirect
764. C2#11755435direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C22⋊D52
C22×D5×#672
C2×#918422
C2×C5×#9532
#117554352
C2×#915772
C2×#915502
C2×#915492
C2×#915482
C2×D5×#2172
C2×#915462
C2×#915392
C2×#659233
C2×#58045