Finite Group Databasebeta

← D15×#539 #14480913

Subgroups — D15×#539 #14480913

Order 1920.

2288 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#539C211yesmaximal, characteristic, complemented
2#11756466C212yesmaximal, complemented
3D15×#126C212yesmaximal, complemented
4#11756451C212yesmaximal, complemented
5D15×#125C212yesmaximal, complemented
6#11756424C212yesmaximal, complemented
7#11756419C212yesmaximal, complemented
8D15×#123C212yesmaximal, complemented
9D15×#123C212yesmaximal, complemented
10#11756404C211yesmaximal, characteristic, complemented
11#11756397C212yesmaximal, complemented
12D15×C22⋊Q8C211yesmaximal, characteristic, complemented
13D15×C22⋊Q8C212yesmaximal, complemented
14D15×#121C211yesmaximal, characteristic
15#11756361C211yesmaximal, characteristic, complemented
16#11756323C212yesmaximal, complemented
17C4×D4×D15C212yesmaximal, complemented
18#11756274C211yesmaximal, characteristic, complemented
19C2×C4⋊C4×D15C211yesmaximal, characteristic, complemented
20D5×#539—31nomaximal, Hall
21C2×Q8×D15C2211yescharacteristic
22C2×D4×D15C2212yes—
23C2×D4×D15C2211yescharacteristic
24C22×C4×D15C2211yescharacteristic
25C22×C4×D15C2211yescharacteristic
26C22×C4×D15C2212yes—
27C22×C4×D15C2211yescharacteristic
28C3×C5×#126C2212yescomplemented
29C3×C5×#125C2212yescomplemented
30C3×C5×#123C2212yescomplemented
31C3×C5×#123C2212yescomplemented
32C3×C5×C22⋊Q8C2212yescomplemented
33C3×C5×C22⋊Q8C2211yescharacteristic, complemented
34C3×C5×#121C2211yescharacteristic
35C3×C4×C5×D4C2212yescomplemented
36C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
37#91835C2211yescharacteristic, complemented
38#91835C2212yescomplemented
39#91828C2212yes—
40#91827C2211yescharacteristic
41#91824C2212yescomplemented
42#91824C2212yescomplemented
43D4×Dic15C2212yescomplemented
44#91819C2211yescharacteristic
45#91818C2212yescomplemented
46#91818C2212yescomplemented
47C4×#1220C2212yescomplemented
48C4×#1220C2212yescomplemented
49C2×C4⋊Dic15C2211yescharacteristic, complemented
50#91813C2212yescomplemented
51#91813C2211yescharacteristic, complemented
52C2×#6712C2211yescharacteristic, complemented
53C2×#6712C2211yescharacteristic, complemented
54#91787C2212yescomplemented
55#91787C2212yescomplemented
56#91787C2212yescomplemented
57#91786C2212yescomplemented
58#91786C2211yescharacteristic, complemented
59#91785C2212yescomplemented
60#91785C2212yescomplemented
61#91785C2212yescomplemented
62#91784C2211yescharacteristic
63#91783C2212yescomplemented
64#91783C2212yescomplemented
65#91783C2212yescomplemented
66#91783C2212yescomplemented
67#91782C2212yescomplemented
68C4⋊C4×D15C2212yes—
69C4⋊C4×D15C2211yescharacteristic
70C4⋊C4×D15C2212yes—
71C4⋊C4×D15C2212yes—
72C4⋊C4×D15C2211yescharacteristic
73C4⋊C4×D15C2212yes—
74C4⋊C4×D15C2212yes—
75C4⋊C4×D15C2212yes—
76C4⋊C4×D15C2212yescomplemented
77C4⋊C4×D15C2212yescomplemented
78#91779C2212yescomplemented
79#91779C2212yescomplemented
80#91778C2212yescomplemented
81#91778C2212yescomplemented
82#91778C2212yescomplemented
83#91778C2212yescomplemented
84#91775C2212yescomplemented
85#91775C2212yescomplemented
86#91773C2212yes—
87#91772C2212yescomplemented
88#91772C2212yescomplemented
89#91772C2212yescomplemented
90#91772C2212yescomplemented
91#91770C2212yescomplemented
92#91770C2212yescomplemented
93C22⋊C4×D15C2212yes—
94C22⋊C4×D15C2212yes—
95C22⋊C4×D15C2212yes—
96C22⋊C4×D15C2212yes—
97C22⋊C4×D15C2212yes—
98#91768C2212yescomplemented
99#91768C2212yescomplemented
100#91768C2212yescomplemented
101#91767C2212yescomplemented
102#91767C2212yescomplemented
103#91767C2212yescomplemented
104#91765C2212yescomplemented
105C4×D60C2212yescomplemented
106C42×D15C2212yes—
107#91759C2212yescomplemented
108D3×#539—51nomaximal, Hall
109C5×#539D311yescharacteristic, complemented
110#66041—32no—
111D5×#126—32no—
112#66026—32no—
113D5×#125—32no—
114#65999—32no—
115#65994—32no—
116D5×#123—32no—
117D5×#123—32no—
118#65979—31no—
119#65972—32no—
120D5×C22⋊Q8—32no—
121D5×C22⋊Q8—31no—
122D5×#121—31no—
123#65936—31no—
124#65898—32no—
125C4×D4×D5—32no—
126#65849—31no—
127C2×D5×C4⋊C4—31no—
128C23×D15C2312yes—
129C23×D15C2311yescharacteristic
130C2×C3×C5×Q8C2311yescharacteristic
131C2×C3×C5×D4C2312yes—
132C2×C3×C5×D4C2311yescharacteristic
133C22×C3×C4×C5C2311yescharacteristic
134C22×C3×C4×C5C2311yescharacteristic
135C22×C3×C4×C5C2311yescharacteristic
136C22×C3×C4×C5C2312yes—
137C2×#1220C2312yes—
138C2×#1220C2312yes—
139C2×#1220C2312yes—
140C22×Dic15C2311yescharacteristic
141C22×Dic15C2312yes—
142C22×Dic15C2311yescharacteristic
143C22×Dic15C2311yescharacteristic
144Q8×D15—42no—
145D4×D15—28no—
146D4×D15—42no—
147C2×D60C2312yes—
148C2×D60C2311yescharacteristic
149C2×C4×D15—24no—
150C2×C4×D15—42no—
151C2×C4×D15—44no—
152C2×C4×D15—42no—
153C2×C4×D15C2312yes—
154C2×C4×D15C2312yes—
155C2×C4×D15C2312yes—
156C2×C4×D15C2312yes—
157C2×C4×D15C2312yes—
158C2×C4×D15C2311yescharacteristic
159C2×C4×D15C2312yes—
160C2×C4×D15C2311yescharacteristic
161C2×C4×D15C2312yes—
162C2×C4×D15C2312yes—
163C2×C4×D15C2312yes—
164C2×C4×D15C2311yescharacteristic
165C2×C4×D15C2311yescharacteristic
166C2×Dic30C2312yes—
167C2×Dic30C2311yescharacteristic
168C3×C5×C4⋊C4C2311yescharacteristic
169C3×C5×C4⋊C4C2312yes—
170C3×C5×C4⋊C4C2312yes—
171C3×C5×C4⋊C4C2312yes—
172C3×C5×C4⋊C4C2312yes—
173C3×C5×C4⋊C4C2312yes—
174C3×C5×C4⋊C4C2312yes—
175C3×C5×C4⋊C4C2311yescharacteristic
176C3×C5×C22⋊C4C2312yes—
177C3×C5×C22⋊C4C2312yes—
178C3×C5×C22⋊C4C2312yes—
179C3×C5×C22⋊C4C2312yes—
180C3×C5×C22⋊C4C2312yes—
181C3×C42×C5C2312yes—
182#6719C2312yes—
183#6719C2312yes—
184#6719C2312yes—
185#6719C2312yes—
186#6719C2312yes—
187#6714C2312yes—
188#6714C2312yes—
189#6714C2312yes—
190#6714C2312yes—
191#6714C2312yes—
192#6714C2312yes—
193#6714C2312yes—
194#6714C2312yes—
195#6714C2312yes—
196#6714C2312yes—
197C4⋊Dic15C2312yes—
198C4⋊Dic15C2312yes—
199C4⋊Dic15C2312yes—
200C4⋊Dic15C2312yes—
201C4⋊Dic15C2311yescharacteristic
202C4⋊Dic15C2312yes—
203C4⋊Dic15C2312yes—
204C4⋊Dic15C2311yescharacteristic
205#6712C2312yes—
206#6712C2312yes—
207#6712C2312yes—
208#6712C2312yes—
209#6712C2312yes—
210#6712C2312yes—
211#6712C2312yes—
212#6712C2312yes—
213#6712C2312yes—
214#6712C2312yes—
215#6712C2312yes—
216#6712C2312yes—
217#6712C2312yes—
218#6712C2312yes—
219C4×Dic15C2312yes—
220C4×Dic15C2312yes—
221C4×Dic15C2312yes—
222C3×#539D511yescharacteristic, complemented
223#5707—52no—
224D3×#126—52no—
225#5692—52no—
226D3×#125—52no—
227#5665—52no—
228#5660—52no—
229D3×#123—52no—
230D3×#123—52no—
231#5645—51no—
232#5638—52no—
233D3×C22⋊Q8—52no—
234D3×C22⋊Q8—51no—
235D3×#121—51no—
236#5602—51no—
237#5564—52no—
238C4×D3×D4—52no—
239#5515—51no—
240C2×D3×C4⋊C4—51no—
241C2×Q8×D5—31no—
242C2×D4×D5—32no—
243C2×D4×D5—31no—
244C22×C4×D5—31no—
245C22×C4×D5—31no—
246C22×C4×D5—31no—
247C22×C4×D5—32no—
248C5×#126C2×D312yescomplemented
249C5×#125C2×D312yescomplemented
250C5×#123C2×D312yescomplemented
251C5×#123C2×D312yescomplemented
252C5×C22⋊Q8C2×D312yescomplemented
253C5×C22⋊Q8C2×D311yescharacteristic, complemented
254C5×#121C2×D311yescharacteristic
255C4×C5×D4C2×D312yescomplemented
256C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
257#4092—31no—
258#4092—32no—
259#4085—32no—
260#4084—31no—
261#4081—32no—
262#4081—32no—
263D4×Dic5—32no—
264#4076—31no—
265#4075—32no—
266#4075—32no—
267C4×C22⋊D5—32no—
268C4×C22⋊D5—32no—
269C2×C4⋊Dic5—31no—
270#4070—31no—
271#4070—32no—
272C2×#683—31no—
273C2×#683—31no—
274#4044—32no—
275#4044—32no—
276#4044—32no—
277#4043—32no—
278#4043—31no—
279#4042—32no—
280#4042—32no—
281#4042—32no—
282#4041—31no—
283#4040—32no—
284#4040—32no—
285#4040—32no—
286#4040—32no—
287#4039—32no—
288D5×C4⋊C4—32no—
289D5×C4⋊C4—32no—
290D5×C4⋊C4—32no—
291D5×C4⋊C4—32no—
292D5×C4⋊C4—32no—
293D5×C4⋊C4—31no—
294D5×C4⋊C4—32no—
295D5×C4⋊C4—32no—
296D5×C4⋊C4—31no—
297D5×C4⋊C4—32no—
298#4036—32no—
299#4036—32no—
300#4035—32no—
301#4035—32no—
302#4035—32no—
303#4035—32no—
304#4032—32no—
305#4032—32no—
306#4030—32no—
307#4029—32no—
308#4029—32no—
309#4029—32no—
310#4029—32no—
311#4027—32no—
312#4027—32no—
313D5×C22⋊C4—32no—
314D5×C22⋊C4—32no—
315D5×C22⋊C4—32no—
316D5×C22⋊C4—32no—
317D5×C22⋊C4—32no—
318#4025—32no—
319#4025—32no—
320#4025—32no—
321#4024—32no—
322#4024—32no—
323#4024—32no—
324#4022—32no—
325C4×D20—32no—
326C42×D5—32no—
327#4016—32no—
328C2×#539—151noSylow
329C23×C3×C5C2412yes—
330C23×C3×C5C2411yescharacteristic
331C22×D15—22no—
332C22×D15—22no—
333C22×D15—24no—
334C22×D15—24no—
335C22×D15—24no—
336C22×D15#4114yes—
337C22×D15C2412yes—
338C22×D15C2411yescharacteristic
339C22×D15C2411yescharacteristic
340C3×C5×Q8—41no—
341C3×C5×D4—24no—
342C3×C5×D4—41no—
343C2×C3×C4×C5—22no—
344C2×C3×C4×C5—42no—
345C2×C3×C4×C5—41no—
346C2×C3×C4×C5—41no—
347C2×C3×C4×C5C2412yes—
348C2×C3×C4×C5C2412yes—
349C2×C3×C4×C5C2412yes—
350C2×C3×C4×C5C2411yescharacteristic
351C2×C3×C4×C5C2412yes—
352C2×C3×C4×C5C2411yescharacteristic
353C2×C3×C4×C5C2412yes—
354#1220—24no—
355#1220—24no—
356#1220—42no—
357C2×Dic15—22no—
358C2×Dic15—42no—
359C2×Dic15—41no—
360C2×Dic15—41no—
361C2×Dic15C2412yes—
362C2×Dic15C2412yes—
363C2×Dic15C2412yes—
364C2×Dic15C2411yescharacteristic
365C2×Dic15C2412yes—
366C2×Dic15C2412yes—
367C2×Dic15C2411yescharacteristic
368D60—24no—
369D60—41no—
370C4×D15—24no—
371C4×D15—24no—
372C4×D15—24no—
373C4×D15—24no—
374C4×D15—22no—
375C4×D15—24no—
376C4×D15—22no—
377C4×D15—24no—
378C4×D15—42no—
379C4×D15—41no—
380C4×D15—42no—
381C4×D15—42no—
382C4×D15—41no—
383Dic30—42no—
384Dic30—41no—
385C2×D3×Q8—51no—
386C2×D3×D4—52no—
387C2×D3×D4—51no—
388C22×C4×D3—51no—
389C22×C4×D3—52no—
390C22×C4×D3—51no—
391C22×C4×D3—51no—
392C3×#126C2×D512yescomplemented
393C3×#125C2×D512yescomplemented
394C3×#123C2×D512yescomplemented
395C3×#123C2×D512yescomplemented
396C3×C22⋊Q8C2×D512yescomplemented
397C3×C22⋊Q8C2×D511yescharacteristic, complemented
398C3×#121C2×D511yescharacteristic
399C3×C4×D4C2×D512yescomplemented
400C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
401#946—51no—
402#946—52no—
403#939—52no—
404#938—51no—
405#935—52no—
406#935—52no—
407D4×Dic3—52no—
408#930—51no—
409#929—52no—
410#929—52no—
411C4×#67—52no—
412C4×#67—52no—
413C2×C4⋊Dic3—51no—
414#924—52no—
415#924—51no—
416C2×Dic3⋊C4—51no—
417C2×Dic3⋊C4—51no—
418#898—52no—
419#898—52no—
420#898—52no—
421#897—52no—
422#897—51no—
423#896—52no—
424#896—52no—
425#896—52no—
426#895—51no—
427#894—52no—
428#894—52no—
429#894—52no—
430#894—52no—
431#893—52no—
432D3×C4⋊C4—52no—
433D3×C4⋊C4—52no—
434D3×C4⋊C4—52no—
435D3×C4⋊C4—52no—
436D3×C4⋊C4—52no—
437D3×C4⋊C4—52no—
438D3×C4⋊C4—51no—
439D3×C4⋊C4—52no—
440D3×C4⋊C4—51no—
441D3×C4⋊C4—52no—
442#890—52no—
443#890—52no—
444#889—52no—
445#889—52no—
446#889—52no—
447#889—52no—
448#886—52no—
449#886—52no—
450#884—52no—
451#883—52no—
452#883—52no—
453#883—52no—
454#883—52no—
455#67⋊C4—52no—
456#67⋊C4—52no—
457D3×C22⋊C4—52no—
458D3×C22⋊C4—52no—
459D3×C22⋊C4—52no—
460D3×C22⋊C4—52no—
461D3×C22⋊C4—52no—
462#879—52no—
463#879—52no—
464#879—52no—
465#878—52no—
466#878—52no—
467#878—52no—
468#876—52no—
469C4×D12—52no—
470C42×D3—52no—
471#870—52no—
472C23×D5—31no—
473C23×D5—32no—
474C2×C5×Q8C22×D311yescharacteristic
475C2×C5×D4C22×D312yes—
476C2×C5×D4C22×D311yescharacteristic
477C22×C4×C5C22×D311yescharacteristic
478C22×C4×C5C22×D311yescharacteristic
479C22×C4×C5C22×D311yescharacteristic
480C22×C4×C5C22×D312yes—
481C2×C22⋊D5—32no—
482C2×C22⋊D5—32no—
483C2×C22⋊D5—32no—
484C22×Dic5—31no—
485C22×Dic5—32no—
486C22×Dic5—31no—
487C22×Dic5—31no—
488Q8×D5—122no—
489D4×D5—68no—
490D4×D5—122no—
491C2×D20—32no—
492C2×D20—31no—
493C2×C4×D5—32no—
494C2×C4×D5—31no—
495C2×C4×D5—31no—
496C2×C4×D5—32no—
497C2×C4×D5—32no—
498C2×C4×D5—32no—
499C2×C4×D5—32no—
500C2×C4×D5—32no—
501C2×C4×D5—32no—
502C2×C4×D5—32no—
503C2×C4×D5—32no—
504C2×C4×D5—31no—
505C2×C4×D5—31no—
506C2×C4×D5—64no—
507C2×C4×D5—122no—
508C2×C4×D5—124no—
509C2×C4×D5—122no—
510C2×Dic10—32no—
511C2×Dic10—31no—
512C5×C4⋊C4C22×D312yes—
513C5×C4⋊C4C22×D312yes—
514C5×C4⋊C4C22×D312yes—
515C5×C4⋊C4C22×D311yescharacteristic
516C5×C4⋊C4C22×D312yes—
517C5×C4⋊C4C22×D312yes—
518C5×C4⋊C4C22×D311yescharacteristic
519C5×C4⋊C4C22×D312yes—
520C5×C22⋊C4C22×D312yes—
521C5×C22⋊C4C22×D312yes—
522C5×C22⋊C4C22×D312yes—
523C5×C22⋊C4C22×D312yes—
524C5×C22⋊C4C22×D312yes—
525C42×C5C22×D312yes—
526C22⋊Dic5—32no—
527C22⋊Dic5—32no—
528C22⋊Dic5—32no—
529C22⋊Dic5—32no—
530C22⋊Dic5—32no—
531#685—32no—
532#685—32no—
533#685—32no—
534#685—32no—
535#685—32no—
536#685—32no—
537#685—32no—
538#685—32no—
539#685—32no—
540#685—32no—
541C4⋊Dic5—32no—
542C4⋊Dic5—32no—
543C4⋊Dic5—32no—
544C4⋊Dic5—32no—
545C4⋊Dic5—31no—
546C4⋊Dic5—32no—
547C4⋊Dic5—32no—
548C4⋊Dic5—31no—
549#683—32no—
550#683—32no—
551#683—32no—
552#683—32no—
553#683—32no—
554#683—32no—
555#683—32no—
556#683—32no—
557#683—32no—
558#683—32no—
559#683—32no—
560#683—32no—
561#683—32no—
562#683—32no—
563C4×Dic5—32no—
564C4×Dic5—32no—
565C4×Dic5—32no—
566#539—152no—
567#539—152no—
568#539—152no—
569#539—152no—
570#539—152no—
571#539—151no—
572#539—151no—
573#539—152no—
574#539—151no—
575#539D1511yescharacteristic, direct product factor
576C2×#126—152no—
577C2×#125—152no—
578C2×#123—152no—
579C2×#123—152no—
580C2×C22⋊Q8—151no—
581C2×C22⋊Q8—152no—
582C2×#121—151no—
583C2×C4×D4—152no—
584C22×C4⋊C4—151no—
585C22×C3×C5—21no—
586C22×C3×C5—21no—
587C22×C3×C5—22no—
588C22×C3×C5—22no—
589C22×C3×C5—22no—
590C22×C3×C5C2×#4112yes—
591C22×C3×C5C2511yescharacteristic
592C2×D15—21no—
593C2×D15—21no—
594C2×D15—28no—
595C2×D15—22no—
596C2×D15—22no—
597C2×D15—22no—
598C2×D15—48no—
599C2×D15C2×#4112yes—
600C2×D15C2×#4112yes—
601C2×D15H(5,𝔽2)12yes—
602C2×D152−1+412yes—
603C3×C4×C5—22no—
604C3×C4×C5—22no—
605C3×C4×C5—22no—
606C3×C4×C5—21no—
607C3×C4×C5—22no—
608C3×C4×C5—21no—
609C3×C4×C5—22no—
610Dic15—22no—
611Dic15—22no—
612Dic15—22no—
613Dic15—21no—
614Dic15—22no—
615Dic15—21no—
616Dic15—22no—
617C23×D3—51no—
618C23×D3—52no—
619C2×C3×Q8C22×D511yescharacteristic
620C2×C3×D4C22×D512yes—
621C2×C3×D4C22×D511yescharacteristic
622C22×C3×C4C22×D511yescharacteristic
623C22×C3×C4C22×D511yescharacteristic
624C22×C3×C4C22×D511yescharacteristic
625C22×C3×C4C22×D512yes—
626C2×#67—52no—
627C2×#67—52no—
628C2×#67—52no—
629C22×Dic3—51no—
630C22×Dic3—52no—
631C22×Dic3—51no—
632C22×Dic3—51no—
633D3×Q8—202no—
634D3×D4—108no—
635D3×D4—202no—
636C2×D12—52no—
637C2×D12—51no—
638C2×C4×D3—52no—
639C2×C4×D3—52no—
640C2×C4×D3—52no—
641C2×C4×D3—52no—
642C2×C4×D3—52no—
643C2×C4×D3—51no—
644C2×C4×D3—52no—
645C2×C4×D3—51no—
646C2×C4×D3—52no—
647C2×C4×D3—52no—
648C2×C4×D3—52no—
649C2×C4×D3—51no—
650C2×C4×D3—51no—
651C2×C4×D3—104no—
652C2×C4×D3—202no—
653C2×C4×D3—204no—
654C2×C4×D3—202no—
655C2×Dic6—52no—
656C2×Dic6—51no—
657C3×C4⋊C4C22×D511yescharacteristic
658C3×C4⋊C4C22×D512yes—
659C3×C4⋊C4C22×D512yes—
660C3×C4⋊C4C22×D512yes—
661C3×C4⋊C4C22×D512yes—
662C3×C4⋊C4C22×D512yes—
663C3×C4⋊C4C22×D512yes—
664C3×C4⋊C4C22×D511yescharacteristic
665C3×C22⋊C4C22×D512yes—
666C3×C22⋊C4C22×D512yes—
667C3×C22⋊C4C22×D512yes—
668C3×C22⋊C4C22×D512yes—
669C3×C22⋊C4C22×D512yes—
670C3×C42C22×D512yes—
671#217—52no—
672#217—52no—
673#217—52no—
674#217—52no—
675#217—52no—
676(C2×D3)⋊C4—52no—
677(C2×D3)⋊C4—52no—
678(C2×D3)⋊C4—52no—
679(C2×D3)⋊C4—52no—
680(C2×D3)⋊C4—52no—
681(C2×D3)⋊C4—52no—
682(C2×D3)⋊C4—52no—
683(C2×D3)⋊C4—52no—
684(C2×D3)⋊C4—52no—
685(C2×D3)⋊C4—52no—
686C4⋊Dic3—52no—
687C4⋊Dic3—52no—
688C4⋊Dic3—52no—
689C4⋊Dic3—52no—
690C4⋊Dic3—51no—
691C4⋊Dic3—52no—
692C4⋊Dic3—52no—
693C4⋊Dic3—51no—
694Dic3⋊C4—52no—
695Dic3⋊C4—52no—
696Dic3⋊C4—52no—
697Dic3⋊C4—52no—
698Dic3⋊C4—52no—
699Dic3⋊C4—52no—
700Dic3⋊C4—52no—
701Dic3⋊C4—52no—
702Dic3⋊C4—52no—
703Dic3⋊C4—52no—
704Dic3⋊C4—52no—
705Dic3⋊C4—52no—
706Dic3⋊C4—52no—
707Dic3⋊C4—52no—
708C4×Dic3—52no—
709C4×Dic3—52no—
710C4×Dic3—52no—
711C23×C5C23×D312yes—
712C23×C5C23×D311yescharacteristic
713C22×D5—31no—
714C22×D5—34no—
715C22×D5—31no—
716C22×D5—32no—
717C22×D5—62no—
718C22×D5—62no—
719C22×D5—64no—
720C22×D5—64no—
721C22×D5—64no—
722C5×Q8—41no—
723C5×D4—24no—
724C5×D4—41no—
725C2×C4×C5—22no—
726C2×C4×C5—42no—
727C2×C4×C5—41no—
728C2×C4×C5—41no—
729C2×C4×C5C23×D312yes—
730C2×C4×C5C23×D312yes—
731C2×C4×C5C23×D312yes—
732C2×C4×C5C23×D311yescharacteristic
733C2×C4×C5C23×D312yes—
734C2×C4×C5C23×D311yescharacteristic
735C2×C4×C5C23×D312yes—
736C22⋊D5—64no—
737C22⋊D5—64no—
738C22⋊D5—122no—
739C2×Dic5—32no—
740C2×Dic5—32no—
741C2×Dic5—32no—
742C2×Dic5—31no—
743C2×Dic5—32no—
744C2×Dic5—32no—
745C2×Dic5—31no—
746C2×Dic5—62no—
747C2×Dic5—122no—
748C2×Dic5—121no—
749C2×Dic5—121no—
750D20—64no—
751D20—121no—
752C4×D5—64no—
753C4×D5—64no—
754C4×D5—64no—
755C4×D5—64no—
756C4×D5—62no—
757C4×D5—62no—
758C4×D5—64no—
759C4×D5—64no—
760C4×D5—122no—
761C4×D5—121no—
762C4×D5—122no—
763C4×D5—122no—
764C4×D5—121no—
765Dic10—122no—
766Dic10—121no—
767C22×Q8—151no—
768C22×D4—152no—
769C22×D4—151no—
770C23×C4—151no—
771C23×C4—151no—
772C23×C4—151no—
773C23×C4—152no—
774#126—152no—
775#126—152no—
776#126—152no—
777#126—152no—
778#126—152no—
779#126—152no—
780#126—152no—
781#126C2×D1512yescomplemented
782#125—152no—
783#125—152no—
784#125—152no—
785#125—152no—
786#125—152no—
787#125—152no—
788#125—152no—
789#125C2×D1512yescomplemented
790#123—152no—
791#123—152no—
792#123—152no—
793#123—152no—
794#123—152no—
795#123—152no—
796#123—152no—
797#123—152no—
798#123—152no—
799#123—152no—
800#123—152no—
801#123—152no—
802#123—152no—
803#123—152no—
804#123C2×D1512yescomplemented
805#123C2×D1512yescomplemented
806C22⋊Q8—151no—
807C22⋊Q8—152no—
808C22⋊Q8—151no—
809C22⋊Q8—152no—
810C22⋊Q8—152no—
811C22⋊Q8—152no—
812C22⋊Q8—152no—
813C22⋊Q8—151no—
814C22⋊Q8—152no—
815C22⋊Q8—152no—
816C22⋊Q8—152no—
817C22⋊Q8—152no—
818C22⋊Q8C2×D1511yescharacteristic, complemented
819C22⋊Q8C2×D1512yescomplemented
820#121—151no—
821#121—152no—
822#121—151no—
823#121—151no—
824#121—152no—
825#121C2×D1511yescharacteristic
826C4×D4—152no—
827C4×D4—152no—
828C4×D4—152no—
829C4×D4—152no—
830C4×D4—152no—
831C4×D4—152no—
832C4×D4—152no—
833C4×D4C2×D1512yescomplemented
834C2×C4⋊C4—151no—
835C2×C4⋊C4—151no—
836C2×C4⋊C4—151no—
837C2×C4⋊C4—152no—
838C2×C4⋊C4—152no—
839C2×C4⋊C4—152no—
840C2×C4⋊C4—152no—
841C2×C4⋊C4—152no—
842C2×C4⋊C4—151no—
843C2×C4⋊C4—152no—
844C2×C4⋊C4—152no—
845C2×C4⋊C4—151no—
846C2×C4⋊C4—152no—
847C2×C4⋊C4C2×D1511yescharacteristic, complemented
848C2×C22⋊C4—152no—
849C2×C22⋊C4—152no—
850C2×C22⋊C4—152no—
851C2×C22⋊C4—152no—
852C2×C22⋊C4—152no—
853C2×C42—152no—
854C2×C3×C5—22no—
855C2×C3×C5—42no—
856C2×C3×C5C22×#4111yescharacteristic
857C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
858C2×C3×C5C2×2−1+411yescharacteristic
859D15—22no—
860D15—42no—
861D15#53914yesdirect product factor
862C23×C3C23×D512yes—
863C23×C3C23×D511yescharacteristic
864C22×D3—51no—
865C22×D3—54no—
866C22×D3—51no—
867C22×D3—52no—
868C22×D3—102no—
869C22×D3—102no—
870C22×D3—104no—
871C22×D3—104no—
872C22×D3—104no—
873C3×Q8—41no—
874C3×D4—24no—
875C3×D4—41no—
876C2×C3×C4—22no—
877C2×C3×C4—42no—
878C2×C3×C4—41no—
879C2×C3×C4—41no—
880C2×C3×C4C23×D512yes—
881C2×C3×C4C23×D512yes—
882C2×C3×C4C23×D512yes—
883C2×C3×C4C23×D511yescharacteristic
884C2×C3×C4C23×D512yes—
885C2×C3×C4C23×D511yescharacteristic
886C2×C3×C4C23×D512yes—
887#67—104no—
888#67—104no—
889#67—202no—
890C2×Dic3—52no—
891C2×Dic3—52no—
892C2×Dic3—52no—
893C2×Dic3—51no—
894C2×Dic3—52no—
895C2×Dic3—52no—
896C2×Dic3—51no—
897C2×Dic3—102no—
898C2×Dic3—202no—
899C2×Dic3—201no—
900C2×Dic3—201no—
901D12—104no—
902D12—201no—
903C4×D3—104no—
904C4×D3—104no—
905C4×D3—104no—
906C4×D3—104no—
907C4×D3—102no—
908C4×D3—104no—
909C4×D3—102no—
910C4×D3—104no—
911C4×D3—202no—
912C4×D3—201no—
913C4×D3—202no—
914C4×D3—202no—
915C4×D3—201no—
916Dic6—202no—
917Dic6—201no—
918C22×C5—21no—
919C22×C5—21no—
920C22×C5—22no—
921C22×C5—22no—
922C22×C5—22no—
923C22×C5D3×#4112yes—
924C22×C5C24×D311yescharacteristic
925C2×D5—32no—
926C2×D5—32no—
927C2×D5—32no—
928C2×D5—32no—
929C2×D5—68no—
930C2×D5—61no—
931C2×D5—61no—
932C2×D5—62no—
933C2×D5—62no—
934C2×D5—62no—
935C2×D5—128no—
936C4×C5—22no—
937C4×C5—22no—
938C4×C5—22no—
939C4×C5—21no—
940C4×C5—22no—
941C4×C5—21no—
942C4×C5—22no—
943Dic5—62no—
944Dic5—62no—
945Dic5—62no—
946Dic5—61no—
947Dic5—62no—
948Dic5—61no—
949Dic5—62no—
950C24—151no—
951C24—152no—
952C2×Q8—151no—
953C2×Q8—152no—
954C2×Q8—602no—
955C2×Q8C22×D1511yescharacteristic
956C2×D4—152no—
957C2×D4—152no—
958C2×D4—152no—
959C2×D4—152no—
960C2×D4—151no—
961C2×D4—308no—
962C2×D4—602no—
963C2×D4C22×D1512yes—
964C2×D4C22×D1511yescharacteristic
965C22×C4—151no—
966C22×C4—151no—
967C22×C4—151no—
968C22×C4—152no—
969C22×C4—152no—
970C22×C4—152no—
971C22×C4—152no—
972C22×C4—152no—
973C22×C4—152no—
974C22×C4—151no—
975C22×C4—151no—
976C22×C4—152no—
977C22×C4—152no—
978C22×C4—151no—
979C22×C4—151no—
980C22×C4—152no—
981C22×C4—152no—
982C22×C4—304no—
983C22×C4—602no—
984C22×C4—604no—
985C22×C4—602no—
986C22×C4C22×D1511yescharacteristic
987C22×C4C22×D1511yescharacteristic
988C22×C4C22×D1511yescharacteristic
989C22×C4C22×D1512yes—
990C4⋊C4—152no—
991C4⋊C4—152no—
992C4⋊C4—152no—
993C4⋊C4—152no—
994C4⋊C4—152no—
995C4⋊C4—152no—
996C4⋊C4—152no—
997C4⋊C4—152no—
998C4⋊C4—152no—
999C4⋊C4—152no—
1000C4⋊C4—151no—
1001C4⋊C4—152no—
1002C4⋊C4—152no—
1003C4⋊C4—152no—
1004C4⋊C4—152no—
1005C4⋊C4—152no—
1006C4⋊C4—152no—
1007C4⋊C4—152no—
1008C4⋊C4—151no—
1009C4⋊C4—152no—
1010C4⋊C4—152no—
1011C4⋊C4—152no—
1012C4⋊C4C22×D1512yes—
1013C4⋊C4C22×D1512yes—
1014C4⋊C4C22×D1512yes—
1015C4⋊C4C22×D1511yescharacteristic
1016C4⋊C4C22×D1512yes—
1017C4⋊C4C22×D1512yes—
1018C4⋊C4C22×D1511yescharacteristic
1019C4⋊C4C22×D1512yes—
1020C22⋊C4—152no—
1021C22⋊C4—152no—
1022C22⋊C4—152no—
1023C22⋊C4—152no—
1024C22⋊C4—152no—
1025C22⋊C4—152no—
1026C22⋊C4—152no—
1027C22⋊C4—152no—
1028C22⋊C4—152no—
1029C22⋊C4—152no—
1030C22⋊C4—152no—
1031C22⋊C4—152no—
1032C22⋊C4—152no—
1033C22⋊C4—152no—
1034C22⋊C4—152no—
1035C22⋊C4C22×D1512yes—
1036C22⋊C4C22×D1512yes—
1037C22⋊C4C22×D1512yes—
1038C22⋊C4C22×D1512yes—
1039C22⋊C4C22×D1512yes—
1040C42—152no—
1041C42—152no—
1042C42—152no—
1043C42C22×D1512yes—
1044C3×C5C2×#53911yescharacteristic, complemented, Hall
1045C22×C3—21no—
1046C22×C3—21no—
1047C22×C3—22no—
1048C22×C3—22no—
1049C22×C3—22no—
1050C22×C3D5×#4112yes—
1051C22×C3C24×D511yescharacteristic
1052C2×D3—52no—
1053C2×D3—52no—
1054C2×D3—52no—
1055C2×D3—52no—
1056C2×D3—108no—
1057C2×D3—101no—
1058C2×D3—101no—
1059C2×D3—102no—
1060C2×D3—102no—
1061C2×D3—102no—
1062C2×D3—208no—
1063C3×C4—22no—
1064C3×C4—22no—
1065C3×C4—22no—
1066C3×C4—21no—
1067C3×C4—22no—
1068C3×C4—21no—
1069C3×C4—22no—
1070Dic3—102no—
1071Dic3—102no—
1072Dic3—102no—
1073Dic3—101no—
1074Dic3—102no—
1075Dic3—101no—
1076Dic3—102no—
1077C2×C5—22no—
1078C2×C5—42no—
1079C2×C5C2×D3×#4111yescharacteristic
1080C2×C5D3×H(5,𝔽2)11yescharacteristic
1081C2×C5D3×2−1+411yescharacteristic
1082D5—34no—
1083D5—62no—
1084D5—122no—
1085C23—151no—
1086C23—154no—
1087C23—151no—
1088C23—152no—
1089C23—302no—
1090C23—302no—
1091C23—304no—
1092C23—304no—
1093C23—304no—
1094C23C23×D1512yes—
1095C23C23×D1511yescharacteristic
1096Q8—41no—
1097Q8—602no—
1098Q8—601no—
1099D4—24no—
1100D4—41no—
1101D4—304no—
1102D4—304no—
1103D4—304no—
1104D4—601no—
1105D4—602no—
1106C2×C4—22no—
1107C2×C4—41no—
1108C2×C4—42no—
1109C2×C4—41no—
1110C2×C4—152no—
1111C2×C4—152no—
1112C2×C4—152no—
1113C2×C4—152no—
1114C2×C4—152no—
1115C2×C4—151no—
1116C2×C4—151no—
1117C2×C4—304no—
1118C2×C4—304no—
1119C2×C4—304no—
1120C2×C4—302no—
1121C2×C4—304no—
1122C2×C4—302no—
1123C2×C4—304no—
1124C2×C4—304no—
1125C2×C4—302no—
1126C2×C4—602no—
1127C2×C4—602no—
1128C2×C4—601no—
1129C2×C4—602no—
1130C2×C4—601no—
1131C2×C4—601no—
1132C2×C4—602no—
1133C2×C4—601no—
1134C2×C4C23×D1512yes—
1135C2×C4C23×D1512yes—
1136C2×C4C23×D1512yes—
1137C2×C4C23×D1512yes—
1138C2×C4C23×D1512yes—
1139C2×C4C23×D1511yescharacteristic
1140C2×C4C23×D1511yescharacteristic
1141C2×C3—22no—
1142C2×C3—42no—
1143C2×C3C2×D5×#4111yescharacteristic
1144C2×C3D5×H(5,𝔽2)11yescharacteristic
1145C2×C3D5×2−1+411yescharacteristic
1146D3—54no—
1147D3—102no—
1148D3—202no—
1149C5D3×#53911yescharacteristic, complemented, Sylow
1150C22—21no—
1151C22—21no—
1152C22—22no—
1153C22—22no—
1154C22—22no—
1155C22—152no—
1156C22—152no—
1157C22—152no—
1158C22—152no—
1159C22—308no—
1160C22—301no—
1161C22—301no—
1162C22—302no—
1163C22—302no—
1164C22—302no—
1165C22—608no—
1166C22#41×D1512yes—
1167C22C24×D1511yescharacteristic
1168C4—22no—
1169C4—22no—
1170C4—22no—
1171C4—21no—
1172C4—22no—
1173C4—21no—
1174C4—22no—
1175C4—302no—
1176C4—302no—
1177C4—302no—
1178C4—301no—
1179C4—302no—
1180C4—301no—
1181C4—302no—
1182C3D5×#53911yescharacteristic, complemented, Sylow
1183C2—22no—
1184C2—42no—
1185C2—154no—
1186C2—302no—
1187C2—602no—
1188C2C2×#41×D1511yescharacteristic
1189C2D15×H(5,𝔽2)11yescharacteristic
1190C2D15×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D15
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#539C2
prime radicalD15×#121C2
hypercenter#539D15
hypocenterC3×C5C2×#539
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #539

Complements

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

NH ≅ G/Ntype
1. C3×C5×#539C2semidirect
2. #11756466C2semidirect
3. D15×#126C2semidirect
4. #11756451C2semidirect
5. D15×#125C2semidirect
6. #11756424C2semidirect
7. #11756419C2semidirect
8. D15×#123C2semidirect
9. D15×#123C2semidirect
10. #11756404C2semidirect
11. #11756397C2semidirect
12. D15×C22⋊Q8C2semidirect
13. D15×C22⋊Q8C2semidirect
15. #11756361C2semidirect
16. #11756323C2semidirect
17. C4×D4×D15C2semidirect
18. #11756274C2semidirect
19. C2×C4⋊C4×D15C2semidirect
28. C3×C5×#126C22semidirect
29. C3×C5×#125C22semidirect
30. C3×C5×#123C22semidirect
31. C3×C5×#123C22semidirect
32. C3×C5×C22⋊Q8C22semidirect
33. C3×C5×C22⋊Q8C22semidirect
35. C3×C4×C5×D4C22semidirect
36. C2×C3×C5×C4⋊C4C22semidirect
37. #91835C22semidirect
38. #91835C22semidirect
41. #91824C22semidirect
42. #91824C22semidirect
43. D4×Dic15C22semidirect
45. #91818C22semidirect
46. #91818C22semidirect
47. C4×#1220C22semidirect
48. C4×#1220C22semidirect
49. C2×C4⋊Dic15C22semidirect
50. #91813C22semidirect
51. #91813C22semidirect
52. C2×#6712C22semidirect
53. C2×#6712C22semidirect
54. #91787C22semidirect
55. #91787C22semidirect
56. #91787C22semidirect
57. #91786C22semidirect
58. #91786C22semidirect
59. #91785C22semidirect
60. #91785C22semidirect
61. #91785C22semidirect
63. #91783C22semidirect
64. #91783C22semidirect
65. #91783C22semidirect
66. #91783C22semidirect
67. #91782C22semidirect
76. C4⋊C4×D15C22semidirect
77. C4⋊C4×D15C22semidirect
78. #91779C22semidirect
79. #91779C22semidirect
80. #91778C22semidirect
81. #91778C22semidirect
82. #91778C22semidirect
83. #91778C22semidirect
84. #91775C22semidirect
85. #91775C22semidirect
87. #91772C22semidirect
88. #91772C22semidirect
89. #91772C22semidirect
90. #91772C22semidirect
91. #91770C22semidirect
92. #91770C22semidirect
98. #91768C22semidirect
99. #91768C22semidirect
100. #91768C22semidirect
101. #91767C22semidirect
102. #91767C22semidirect
103. #91767C22semidirect
104. #91765C22semidirect
105. C4×D60C22semidirect
107. #91759C22semidirect
109. C5×#539D3semidirect
222. C3×#539D5semidirect
248. C5×#126C2×D3semidirect
249. C5×#125C2×D3semidirect
250. C5×#123C2×D3semidirect
251. C5×#123C2×D3semidirect
252. C5×C22⋊Q8C2×D3semidirect
253. C5×C22⋊Q8C2×D3semidirect
255. C4×C5×D4C2×D3semidirect
256. C2×C5×C4⋊C4C2×D3semidirect
392. C3×#126C2×D5semidirect
393. C3×#125C2×D5semidirect
394. C3×#123C2×D5semidirect
395. C3×#123C2×D5semidirect
396. C3×C22⋊Q8C2×D5semidirect
397. C3×C22⋊Q8C2×D5semidirect
399. C3×C4×D4C2×D5semidirect
400. C2×C3×C4⋊C4C2×D5semidirect
575. #539D15direct (N × H)
781. #126C2×D15semidirect
789. #125C2×D15semidirect
804. #123C2×D15semidirect
805. #123C2×D15semidirect
818. C22⋊Q8C2×D15semidirect
819. C22⋊Q8C2×D15semidirect
833. C4×D4C2×D15semidirect
847. C2×C4⋊C4C2×D15semidirect
861. D15#539direct (N × H)
1044. C3×C5C2×#539semidirect
1149. C5D3×#539semidirect
1182. C3D5×#539semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5392
#117564662
D15×#1262
#117564512
D15×#1252
#117564242
#117564192
D15×#1232
#117564042
#117563972
D15×C22⋊Q82
D15×#1212
#117563612
#117563232
C4×D4×D152
#117562742
C2×C4⋊C4×D152
D5×#5393
D3×#5395