Finite Group Databasebeta

← C2×#11756588 #14482480

Subgroups — C2×#11756588 #14482480

Order 1920.

3800 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
1C22×C3×C5×#41C211yesmaximal, characteristic, complemented
2C22×D4×D15C211yesmaximal, characteristic, complemented
3#11756588C2116yesmaximal, direct product factor
4C2×#91836C211yesmaximal, characteristic, complemented
5C2×#91835C211yesmaximal, characteristic, complemented
6C2×#91828C212yesmaximal, complemented
7C2×#91826C212yesmaximal, complemented
8C2×D4×Dic15C211yesmaximal, characteristic, complemented
9C2×#91819C211yesmaximal, characteristic, complemented
10C2×#91818C212yesmaximal, complemented
11C2×C4×#1220C211yesmaximal, characteristic, complemented
12C22×#6714C212yesmaximal, complemented
13C2×#66163—31nomaximal, Hall
14C24×D15C2212yes—
15C2×C3×C5×#41—28no—
16C2×C3×C5×#41C2218yescomplemented
17C22×C3×C5×Q8C2211yescharacteristic, complemented
18C22×C3×C5×D4C2211yescharacteristic
19C22×C3×C5×D4C2212yescomplemented
20C23×C3×C4×C5C2212yescomplemented
21C23×C3×C4×C5C2211yescharacteristic, complemented
22C22×#1220C2211yescharacteristic
23C22×#1220C2212yes—
24C22×#1220C2212yescomplemented
25C23×Dic15C2212yescomplemented
26C2×D4×D15—28no—
27C2×D4×D15C2218yescomplemented
28C22×D60C2211yescharacteristic
29C22×C4×D15C2211yescharacteristic
30C2×#6719C2211yescharacteristic, complemented
31C2×#6719C2212yescomplemented
32#91836C2218yescomplemented
33#91835C2218yescomplemented
34#91828C22116yescomplemented
35#91826C22116yescomplemented
36D4×Dic15C2218yescomplemented
37#91819C2218yescomplemented
38#91818C22116yescomplemented
39C4×#1220C2218yescomplemented
40C2×#6714C2211yescharacteristic
41C2×#6714C2212yes—
42C2×#6714C22116yescomplemented
43C2×#6714C2212yescomplemented
44C2×#6714C2212yescomplemented
45C2×#6714C2212yescomplemented
46C2×C4⋊Dic15C2211yescharacteristic, complemented
47C2×#6712C2211yescharacteristic, complemented
48C2×#6712C2212yescomplemented
49C2×C4×Dic15C2211yescharacteristic, complemented
50C2×#5829—51nomaximal, Hall
51C22×C5×#41D311yescharacteristic, complemented
52C22×D4×D5—31no—
53#66163—316no—
54C2×#4093—31no—
55C2×#4092—31no—
56C2×#4085—32no—
57C2×#4083—32no—
58C2×D4×Dic5—31no—
59C2×#4076—31no—
60C2×#4075—32no—
61C2×C4×C22⋊D5—31no—
62C22×#685—32no—
63C24×C3×C5C2311yescharacteristic
64C24×C3×C5C2312yes—
65C23×D15—28no—
66C23×D15—28no—
67C23×D15—44no—
68C23×D15C2312yes—
69C23×D15C2318yes—
70C23×D15C2311yescharacteristic
71C3×C5×#41—232no—
72C2×C3×C5×Q8—24no—
73C2×C3×C5×Q8C2314yescomplemented
74C2×C3×C5×D4—28no—
75C2×C3×C5×D4D418yescomplemented
76C2×C3×C5×D4C2314yes—
77C2×C3×C5×D4C2318yescomplemented
78C22×C3×C4×C5—28no—
79C22×C3×C4×C5—24no—
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2312yes—
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2318yescomplemented
84C22×C3×C4×C5C2314yescomplemented
85C2×#1220—28no—
86C2×#1220—24no—
87C2×#1220—44no—
88C2×#1220C2314yes—
89C2×#1220C2318yes—
90C2×#1220C2318yescomplemented
91C22×Dic15—44no—
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2312yes—
96C22×Dic15C2318yescomplemented
97D4×D15—232no—
98C2×D60—24no—
99C2×D60C2314yes—
100C2×C4×D15—24no—
101C2×C4×D15C2314yes—
102#6719C2314yescomplemented
103#6719C2318yescomplemented
104#6714C2314yes—
105#6714C2318yes—
106#6714C2318yescomplemented
107#6714C2318yescomplemented
108#6714C2318yescomplemented
109C4⋊Dic15C2314yescomplemented
110#6712C2314yescomplemented
111#6712C2318yescomplemented
112C4×Dic15C2314yescomplemented
113C22×C3×#41D511yescharacteristic, complemented
114C22×D3×D4—51no—
115#5829—516no—
116C2×#947—51no—
117C2×#946—51no—
118C2×#939—52no—
119C2×#937—52no—
120C2×D4×Dic3—51no—
121C2×#930—51no—
122C2×#929—52no—
123C2×C4×#67—51no—
124C22×(C2×D3)⋊C4—52no—
125C24×D5—32no—
126C2×C5×#41—28no—
127C2×C5×#41C2×D318yescomplemented
128C22×C5×Q8C2×D311yescharacteristic, complemented
129C22×C5×D4C2×D311yescharacteristic
130C22×C5×D4C2×D312yescomplemented
131C23×C4×C5C2×D312yescomplemented
132C23×C4×C5C2×D311yescharacteristic, complemented
133C22×C22⋊D5—31no—
134C22×C22⋊D5—32no—
135C22×C22⋊D5—32no—
136C23×Dic5—32no—
137C2×D4×D5—38no—
138C2×D4×D5—68no—
139C22×D20—31no—
140C22×C4×D5—31no—
141C2×C22⋊Dic5—31no—
142C2×C22⋊Dic5—32no—
143#4093—38no—
144#4092—38no—
145#4085—316no—
146#4083—316no—
147D4×Dic5—38no—
148#4076—38no—
149#4075—316no—
150C4×C22⋊D5—38no—
151C2×#685—31no—
152C2×#685—32no—
153C2×#685—32no—
154C2×#685—32no—
155C2×#685—32no—
156C2×#685—316no—
157C2×C4⋊Dic5—31no—
158C2×#683—31no—
159C2×#683—32no—
160C2×C4×Dic5—31no—
161C2×#546—151noSylow
162C23×C3×C5—24no—
163C23×C3×C5—24no—
164C23×C3×C5—22no—
165C23×C3×C5—22no—
166C23×C3×C5—22no—
167C23×C3×C5C2×D418yes—
168C23×C3×C5C2412yes—
169C23×C3×C5C2414yes—
170C23×C3×C5C2411yescharacteristic
171C22×D15—22no—
172C22×D15—22no—
173C22×D15—24no—
174C22×D15—216no—
175C22×D15—24no—
176C22×D15—24no—
177C22×D15—216no—
178C22×D15—48no—
179C22×D15—432no—
180C22×D15#4114yescomplemented
181C22×D15C2414yes—
182C22×D15C2412yes—
183C3×C5×Q8—28no—
184C3×C5×D4—216no—
185C3×C5×D4C2×D4116yescomplemented
186C2×C3×C4×C5—22no—
187C2×C3×C4×C5—24no—
188C2×C3×C4×C5—216no—
189C2×C3×C4×C5—28no—
190C2×C3×C4×C5C2×D414yes—
191C2×C3×C4×C5C2412yes—
192C2×C3×C4×C5C2414yes—
193C2×C3×C4×C5C2412yes—
194#1220—216no—
195#1220—28no—
196#1220—48no—
197C2×Dic15—22no—
198C2×Dic15—22no—
199C2×Dic15—22no—
200C2×Dic15—24no—
201C2×Dic15—48no—
202C2×Dic15C2412yes—
203C2×Dic15C2412yes—
204C2×Dic15C2412yes—
205C2×Dic15C2414yes—
206D60—28no—
207C4×D15—28no—
208C24×D3—52no—
209C2×C3×#41—28no—
210C2×C3×#41C2×D518yescomplemented
211C22×C3×Q8C2×D511yescharacteristic, complemented
212C22×C3×D4C2×D511yescharacteristic
213C22×C3×D4C2×D512yescomplemented
214C23×C3×C4C2×D512yescomplemented
215C23×C3×C4C2×D511yescharacteristic, complemented
216C22×#67—52no—
217C22×#67—51no—
218C22×#67—52no—
219C23×Dic3—52no—
220C2×D3×D4—58no—
221C2×D3×D4—108no—
222C22×D12—51no—
223C22×C4×D3—51no—
224C2×#217—51no—
225C2×#217—52no—
226#947—58no—
227#946—58no—
228#939—516no—
229#937—516no—
230D4×Dic3—58no—
231#930—58no—
232#929—516no—
233C4×#67—58no—
234C2×(C2×D3)⋊C4—51no—
235C2×(C2×D3)⋊C4—52no—
236C2×(C2×D3)⋊C4—52no—
237C2×(C2×D3)⋊C4—52no—
238C2×(C2×D3)⋊C4—52no—
239C2×(C2×D3)⋊C4—516no—
240C2×C4⋊Dic3—51no—
241C2×Dic3⋊C4—51no—
242C2×Dic3⋊C4—52no—
243C2×C4×Dic3—51no—
244C24×C5C22×D311yescharacteristic
245C24×C5C22×D312yes—
246C23×D5—31no—
247C23×D5—32no—
248C23×D5—38no—
249C23×D5—68no—
250C23×D5—68no—
251C23×D5—124no—
252C5×#41—232no—
253C2×C5×Q8—24no—
254C2×C5×Q8C22×D314yescomplemented
255C2×C5×D4—28no—
256C2×C5×D4#6718yescomplemented
257C2×C5×D4C22×D314yes—
258C2×C5×D4C22×D318yescomplemented
259C22×C4×C5—28no—
260C22×C4×C5—24no—
261C22×C4×C5C22×D311yescharacteristic
262C22×C4×C5C22×D312yes—
263C22×C4×C5C22×D311yescharacteristic
264C22×C4×C5C22×D318yescomplemented
265C22×C4×C5C22×D314yescomplemented
266C2×C22⋊D5—38no—
267C2×C22⋊D5—34no—
268C2×C22⋊D5—38no—
269C2×C22⋊D5—64no—
270C2×C22⋊D5—68no—
271C2×C22⋊D5—124no—
272C22×Dic5—31no—
273C22×Dic5—31no—
274C22×Dic5—31no—
275C22×Dic5—32no—
276C22×Dic5—38no—
277C22×Dic5—124no—
278D4×D5—632no—
279C2×D20—34no—
280C2×D20—64no—
281C2×C4×D5—34no—
282C2×C4×D5—64no—
283C22⋊Dic5—34no—
284C22⋊Dic5—38no—
285#685—34no—
286#685—38no—
287#685—38no—
288#685—38no—
289#685—38no—
290C4⋊Dic5—34no—
291#683—34no—
292#683—38no—
293C4×Dic5—34no—
294C22×#41D1511yescharacteristic, complemented
295C23×D4—151no—
296#546—1516no—
297C2×#124—151no—
298C2×#123—152no—
299C2×C22⋊Q8—151no—
300C2×#121—152no—
301C2×#121—151no—
302C2×#120—152no—
303C2×C4×D4—151no—
304C2×C4×D4—151no—
305C22×C22⋊C4—152no—
306C22×C3×C5—216no—
307C22×C3×C5—24no—
308C22×C3×C5—24no—
309C22×C3×C5—22no—
310C22×C3×C5—22no—
311C22×C3×C5—22no—
312C22×C3×C5—44no—
313C22×C3×C5C22×D418yes—
314C22×C3×C5C22×D412yes—
315C22×C3×C5C2×#4112yes—
316C22×C3×C5H(5,𝔽2)12yes—
317C22×C3×C5C2511yescharacteristic
318C2×D15—28no—
319C2×D15—22no—
320C2×D15—22no—
321C2×D15—24no—
322C2×D15—24no—
323C2×D15—24no—
324C2×D15—432no—
325C2×D15—48no—
326C2×D15C2×#4114yescomplemented
327C3×C4×C5—22no—
328C3×C4×C5—24no—
329C3×C4×C5C22×D414yes—
330Dic15—22no—
331Dic15—22no—
332Dic15—22no—
333Dic15—24no—
334C24×C3C22×D511yescharacteristic
335C24×C3C22×D512yes—
336C23×D3—51no—
337C23×D3—52no—
338C23×D3—58no—
339C23×D3—108no—
340C23×D3—108no—
341C23×D3—204no—
342C3×#41—232no—
343C2×C3×Q8—24no—
344C2×C3×Q8C22×D514yescomplemented
345C2×C3×D4—28no—
346C2×C3×D4C22⋊D518yescomplemented
347C2×C3×D4C22×D514yes—
348C2×C3×D4C22×D518yescomplemented
349C22×C3×C4—28no—
350C22×C3×C4—24no—
351C22×C3×C4C22×D511yescharacteristic
352C22×C3×C4C22×D512yes—
353C22×C3×C4C22×D511yescharacteristic
354C22×C3×C4C22×D518yescomplemented
355C22×C3×C4C22×D514yescomplemented
356C2×#67—54no—
357C2×#67—58no—
358C2×#67—58no—
359C2×#67—104no—
360C2×#67—108no—
361C2×#67—204no—
362C22×Dic3—51no—
363C22×Dic3—51no—
364C22×Dic3—51no—
365C22×Dic3—52no—
366C22×Dic3—58no—
367C22×Dic3—204no—
368D3×D4—1032no—
369C2×D12—54no—
370C2×D12—104no—
371C2×C4×D3—54no—
372C2×C4×D3—104no—
373#217—54no—
374#217—58no—
375(C2×D3)⋊C4—54no—
376(C2×D3)⋊C4—58no—
377(C2×D3)⋊C4—58no—
378(C2×D3)⋊C4—58no—
379(C2×D3)⋊C4—58no—
380C4⋊Dic3—54no—
381Dic3⋊C4—54no—
382Dic3⋊C4—58no—
383C4×Dic3—54no—
384C23×C5—24no—
385C23×C5—24no—
386C23×C5—22no—
387C23×C5—22no—
388C23×C5—22no—
389C23×C5C2×#6718yes—
390C23×C5C23×D312yes—
391C23×C5C23×D314yes—
392C23×C5C23×D311yescharacteristic
393C22×D5—34no—
394C22×D5—32no—
395C22×D5—34no—
396C22×D5—616no—
397C22×D5—62no—
398C22×D5—62no—
399C22×D5—64no—
400C22×D5—64no—
401C22×D5—64no—
402C22×D5—616no—
403C22×D5—128no—
404C22×D5—1232no—
405C5×Q8—28no—
406C5×D4—216no—
407C5×D4C2×#67116yescomplemented
408C2×C4×C5—22no—
409C2×C4×C5—24no—
410C2×C4×C5—216no—
411C2×C4×C5—28no—
412C2×C4×C5C2×#6714yes—
413C2×C4×C5C23×D312yes—
414C2×C4×C5C23×D314yes—
415C2×C4×C5C23×D312yes—
416C22⋊D5—68no—
417C22⋊D5—616no—
418C22⋊D5—128no—
419C2×Dic5—32no—
420C2×Dic5—32no—
421C2×Dic5—32no—
422C2×Dic5—34no—
423C2×Dic5—62no—
424C2×Dic5—62no—
425C2×Dic5—64no—
426C2×Dic5—62no—
427C2×Dic5—128no—
428D20—68no—
429C4×D5—68no—
430C25—152no—
431C2×#41—28no—
432C2×#41C2×D1518yescomplemented
433C22×Q8C2×D1511yescharacteristic, complemented
434C22×D4—151no—
435C22×D4—152no—
436C22×D4—152no—
437C22×D4—158no—
438C22×D4—151no—
439C22×D4—308no—
440C22×D4C2×D1511yescharacteristic
441C22×D4C2×D1512yescomplemented
442C23×C4—152no—
443C23×C4—151no—
444C23×C4C2×D1512yescomplemented
445C23×C4C2×D1511yescharacteristic, complemented
446#124—158no—
447#123—1516no—
448C22⋊Q8—158no—
449#121—1516no—
450#121—158no—
451#120—1516no—
452C4×D4—158no—
453C4×D4—158no—
454C2×C4⋊C4—151no—
455C2×C4⋊C4—151no—
456C2×C4⋊C4—152no—
457C2×C22⋊C4—152no—
458C2×C22⋊C4—151no—
459C2×C22⋊C4—151no—
460C2×C22⋊C4—152no—
461C2×C22⋊C4—152no—
462C2×C22⋊C4—152no—
463C2×C22⋊C4—152no—
464C2×C22⋊C4—1516no—
465C2×C42—151no—
466C2×C3×C5—28no—
467C2×C3×C5—42no—
468C2×C3×C5#54614yescomplemented
469C2×C3×C5C23×D411yescharacteristic
470C2×C3×C5C22×#4111yescharacteristic
471C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
472D15—24no—
473D15—44no—
474C23×C3—24no—
475C23×C3—24no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3C2×C22⋊D518yes—
480C23×C3C23×D512yes—
481C23×C3C23×D514yes—
482C23×C3C23×D511yescharacteristic
483C22×D3—54no—
484C22×D3—52no—
485C22×D3—54no—
486C22×D3—1016no—
487C22×D3—102no—
488C22×D3—102no—
489C22×D3—104no—
490C22×D3—104no—
491C22×D3—104no—
492C22×D3—1016no—
493C22×D3—208no—
494C22×D3—2032no—
495C3×Q8—28no—
496C3×D4—216no—
497C3×D4C2×C22⋊D5116yescomplemented
498C2×C3×C4—22no—
499C2×C3×C4—24no—
500C2×C3×C4—216no—
501C2×C3×C4—28no—
502C2×C3×C4C2×C22⋊D514yes—
503C2×C3×C4C23×D512yes—
504C2×C3×C4C23×D514yes—
505C2×C3×C4C23×D512yes—
506#67—108no—
507#67—1016no—
508#67—208no—
509C2×Dic3—52no—
510C2×Dic3—52no—
511C2×Dic3—52no—
512C2×Dic3—54no—
513C2×Dic3—102no—
514C2×Dic3—102no—
515C2×Dic3—104no—
516C2×Dic3—102no—
517C2×Dic3—208no—
518D12—108no—
519C4×D3—108no—
520C22×C5—24no—
521C22×C5—24no—
522C22×C5—216no—
523C22×C5—22no—
524C22×C5—22no—
525C22×C5—22no—
526C22×C5—44no—
527C22×C5D3×#4112yes—
528C22×C5#100912yes—
529C22×C5C22×#6718yes—
530C22×C5C22×#6712yes—
531C22×C5C24×D311yescharacteristic
532C2×D5—34no—
533C2×D5—62no—
534C2×D5—62no—
535C2×D5—68no—
536C2×D5—64no—
537C2×D5—64no—
538C2×D5—64no—
539C2×D5—1232no—
540C2×D5—128no—
541C4×C5—22no—
542C4×C5—24no—
543C4×C5C22×#6714yes—
544Dic5—62no—
545Dic5—62no—
546Dic5—64no—
547Dic5—62no—
548C24—151no—
549C24—152no—
550C24—158no—
551C24—308no—
552C24—308no—
553C24—604no—
554C24C22×D1511yescharacteristic
555C24C22×D1512yes—
556#41—232no—
557C2×Q8—24no—
558C2×Q8C22×D1514yescomplemented
559C2×D4—28no—
560C2×D4—154no—
561C2×D4—158no—
562C2×D4—158no—
563C2×D4—154no—
564C2×D4—304no—
565C2×D4—308no—
566C2×D4—3032no—
567C2×D4—304no—
568C2×D4—604no—
569C2×D4#122018yescomplemented
570C2×D4C22×D1514yes—
571C2×D4C22×D1518yescomplemented
572C22×C4—28no—
573C22×C4—24no—
574C22×C4—151no—
575C22×C4—151no—
576C22×C4—152no—
577C22×C4—151no—
578C22×C4—158no—
579C22×C4—154no—
580C22×C4—304no—
581C22×C4—604no—
582C22×C4C22×D1511yescharacteristic
583C22×C4C22×D1512yes—
584C22×C4C22×D1511yescharacteristic
585C22×C4C22×D1518yescomplemented
586C22×C4C22×D1514yescomplemented
587C4⋊C4—154no—
588C4⋊C4—154no—
589C4⋊C4—158no—
590C22⋊C4—158no—
591C22⋊C4—154no—
592C22⋊C4—154no—
593C22⋊C4—158no—
594C22⋊C4—158no—
595C22⋊C4—158no—
596C22⋊C4—158no—
597C42—154no—
598C3×C5C2×#54611yescharacteristic, complemented, Hall
599C22×C3—216no—
600C22×C3—24no—
601C22×C3—24no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—44no—
606C22×C3D5×#4112yes—
607C22×C3#414912yes—
608C22×C3C22×C22⋊D518yes—
609C22×C3C22×C22⋊D512yes—
610C22×C3C24×D511yescharacteristic
611C2×D3—54no—
612C2×D3—108no—
613C2×D3—102no—
614C2×D3—102no—
615C2×D3—104no—
616C2×D3—104no—
617C2×D3—104no—
618C2×D3—2032no—
619C2×D3—208no—
620C3×C4—22no—
621C3×C4—24no—
622C3×C4C22×C22⋊D514yes—
623Dic3—102no—
624Dic3—102no—
625Dic3—104no—
626Dic3—102no—
627C2×C5—28no—
628C2×C5—42no—
629C2×C5#582914yescomplemented
630C2×C5C2×D3×#4111yescharacteristic
631C2×C5C2×#100911yescharacteristic
632C2×C5C23×#6711yescharacteristic
633D5—64no—
634D5—124no—
635C23—24no—
636C23—24no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—154no—
641C23—152no—
642C23—154no—
643C23—3016no—
644C23—302no—
645C23—302no—
646C23—304no—
647C23—304no—
648C23—3016no—
649C23—304no—
650C23—608no—
651C23—6032no—
652C23C2×#122018yes—
653C23C23×D1512yes—
654C23C23×D1514yes—
655C23C23×D1511yescharacteristic
656Q8—28no—
657D4—216no—
658D4—308no—
659D4—3016no—
660D4—308no—
661D4—608no—
662D4C2×#1220116yescomplemented
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—216no—
666C2×C4—28no—
667C2×C4—152no—
668C2×C4—152no—
669C2×C4—154no—
670C2×C4—152no—
671C2×C4—302no—
672C2×C4—302no—
673C2×C4—304no—
674C2×C4—302no—
675C2×C4—308no—
676C2×C4—608no—
677C2×C4C2×#122014yes—
678C2×C4C23×D1512yes—
679C2×C4C23×D1514yes—
680C2×C4C23×D1512yes—
681C2×C3—28no—
682C2×C3—42no—
683C2×C3#6616314yescomplemented
684C2×C3C2×D5×#4111yescharacteristic
685C2×C3C2×#414911yescharacteristic
686C2×C3C23×C22⋊D511yescharacteristic
687D3—104no—
688D3—204no—
689C5C2×#582911yescharacteristic, complemented, Sylow
690C22—216no—
691C22—24no—
692C22—24no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—44no—
697C22—154no—
698C22—308no—
699C22—302no—
700C22—302no—
701C22—304no—
702C22—304no—
703C22—304no—
704C22—6032no—
705C22—608no—
706C22#41×D1512yes—
707C22#9210012yes—
708C22C22×#122018yes—
709C22C22×#122012yes—
710C22C24×D1511yescharacteristic
711C4—22no—
712C4—24no—
713C4—302no—
714C4—302no—
715C4—304no—
716C4—302no—
717C4C22×#122014yes—
718C3C2×#6616311yescharacteristic, complemented, Sylow
719C2—28no—
720C2—42no—
721C2—304no—
722C2—604no—
723C2#1175658814yesdirect product factor
724C2C2×#41×D1511yescharacteristic
725C2C2×#9210011yescharacteristic
726C2C23×#122011yescharacteristic
subgroupG/H
centerC23C23×D15
commutator, cosocleC22×C3×C5C25
FrattiniC22C24×D15
FittingC22×C3×C5×#41C2
socleC23×C3×C5C24
hypercenterC22×#41D15
hypocenterC3×C5C2×#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×#41C2semidirect
2. C22×D4×D15C2semidirect
3. #11756588C2direct (N × H)
4. C2×#91836C2semidirect
5. C2×#91835C2semidirect
6. C2×#91828C2semidirect
7. C2×#91826C2semidirect
8. C2×D4×Dic15C2semidirect
9. C2×#91819C2semidirect
10. C2×#91818C2semidirect
11. C2×C4×#1220C2semidirect
12. C22×#6714C2semidirect
16. C2×C3×C5×#41C22semidirect
17. C22×C3×C5×Q8C22semidirect
19. C22×C3×C5×D4C22semidirect
20. C23×C3×C4×C5C22semidirect
21. C23×C3×C4×C5C22semidirect
24. C22×#1220C22semidirect
25. C23×Dic15C22semidirect
27. C2×D4×D15C22semidirect
30. C2×#6719C22semidirect
31. C2×#6719C22semidirect
32. #91836C22semidirect
33. #91835C22semidirect
34. #91828C22semidirect
35. #91826C22semidirect
36. D4×Dic15C22semidirect
37. #91819C22semidirect
38. #91818C22semidirect
39. C4×#1220C22semidirect
42. C2×#6714C22semidirect
43. C2×#6714C22semidirect
44. C2×#6714C22semidirect
45. C2×#6714C22semidirect
46. C2×C4⋊Dic15C22semidirect
47. C2×#6712C22semidirect
48. C2×#6712C22semidirect
49. C2×C4×Dic15C22semidirect
51. C22×C5×#41D3semidirect
73. C2×C3×C5×Q8C23semidirect
75. C2×C3×C5×D4D4semidirect
77. C2×C3×C5×D4C23semidirect
83. C22×C3×C4×C5C23semidirect
84. C22×C3×C4×C5C23semidirect
90. C2×#1220C23semidirect
96. C22×Dic15C23semidirect
102. #6719C23semidirect
103. #6719C23semidirect
106. #6714C23semidirect
107. #6714C23semidirect
108. #6714C23semidirect
109. C4⋊Dic15C23semidirect
110. #6712C23semidirect
111. #6712C23semidirect
112. C4×Dic15C23semidirect
113. C22×C3×#41D5semidirect
127. C2×C5×#41C2×D3semidirect
128. C22×C5×Q8C2×D3semidirect
130. C22×C5×D4C2×D3semidirect
131. C23×C4×C5C2×D3semidirect
132. C23×C4×C5C2×D3semidirect
180. C22×D15#41semidirect
185. C3×C5×D4C2×D4semidirect
210. C2×C3×#41C2×D5semidirect
211. C22×C3×Q8C2×D5semidirect
213. C22×C3×D4C2×D5semidirect
214. C23×C3×C4C2×D5semidirect
215. C23×C3×C4C2×D5semidirect
254. C2×C5×Q8C22×D3semidirect
256. C2×C5×D4#67semidirect
258. C2×C5×D4C22×D3semidirect
264. C22×C4×C5C22×D3semidirect
265. C22×C4×C5C22×D3semidirect
294. C22×#41D15semidirect
326. C2×D15C2×#41semidirect
344. C2×C3×Q8C22×D5semidirect
346. C2×C3×D4C22⋊D5semidirect
348. C2×C3×D4C22×D5semidirect
354. C22×C3×C4C22×D5semidirect
355. C22×C3×C4C22×D5semidirect
407. C5×D4C2×#67semidirect
432. C2×#41C2×D15semidirect
433. C22×Q8C2×D15semidirect
441. C22×D4C2×D15semidirect
444. C23×C4C2×D15semidirect
445. C23×C4C2×D15semidirect
468. C2×C3×C5#546semidirect
497. C3×D4C2×C22⋊D5semidirect
558. C2×Q8C22×D15semidirect
569. C2×D4#1220semidirect
571. C2×D4C22×D15semidirect
585. C22×C4C22×D15semidirect
586. C22×C4C22×D15semidirect
598. C3×C5C2×#546semidirect
629. C2×C5#5829semidirect
662. D4C2×#1220semidirect
683. C2×C3#66163semidirect
689. C5C2×#5829semidirect
718. C3C2×#66163semidirect
723. C2#11756588direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×#412
C22×D4×D152
#117565882
C2×#918362
C2×#918352
C2×#918282
C2×#918262
C2×D4×Dic152
C2×#918192
C2×#918182
C2×C4×#12202
C22×#67142
C2×#661633
C2×#58295