Finite Group Databasebeta

← D5×#5731 #14481223

Subgroups — D5×#5731 #14481223

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756490C211yesmaximal, characteristic, complemented
2C5×#5731C211yesmaximal, characteristic, complemented
3C3×D5×C4⋊Q8C211yesmaximal, characteristic, complemented
4D5×#946C212yesmaximal
5Q8×D5×Dic3C212yesmaximal, complemented
6#11755150C212yesmaximal, complemented
7#11755143C212yesmaximal, complemented
8D5×#898C214yesmaximal
9#11753519C214yesmaximal, complemented
10D5×#889C214yesmaximal, complemented
11#11753310C214yesmaximal, complemented
12D5×#872C211yesmaximal, characteristic
13D5×#870C211yesmaximal, characteristic, complemented
14#11752485C211yesmaximal, characteristic, complemented
15#11752479C211yesmaximal, characteristic, complemented
16D5×#541—31nomaximal, Hall
17C2×C3×Q8×D5C2212yes—
18C2×C4×D3×D5C2211yescharacteristic
19C3×C5×C4⋊Q8C2211yescharacteristic, complemented
20#91835C2212yes—
21Q8×Dic15C2212yescomplemented
22#91787C2214yes—
23#91778C2214yescomplemented
24#91761C2211yescharacteristic
25#91759C2211yescharacteristic, complemented
26C5×#946C2212yes—
27C5×Q8×Dic3C2212yescomplemented
28C5×#898C2214yes—
29C5×#889C2214yescomplemented
30C5×#872C2211yescharacteristic
31C5×#870C2211yescharacteristic, complemented
32C3×#4090C2212yescomplemented
33C3×D5×C4⋊C4C2214yes—
34C3×#4034C2214yescomplemented
35C3×C42×D5C2211yescharacteristic
36C3×#4015C2211yescharacteristic, complemented
37D5×(C2×D3)⋊C4C2214yes—
38D5×(C2×D3)⋊C4C2212yes—
39D5×C4⋊Dic3C2212yes—
40D5×C4⋊Dic3C2214yes—
41#91411C2214yes—
42#91410C2214yes—
43#91402C2212yes—
44#91398C2212yes—
45D5×Dic3⋊C4C2214yes—
46D5×Dic3⋊C4C2212yes—
47D5×Dic3⋊C4C2214yes—
48C4×D5×Dic3C2211yescharacteristic
49C4×D5×Dic3C2214yes—
50#91390C2212yes—
51#91388C2212yescomplemented
52#91386C2211yescharacteristic
53#91382C2214yescomplemented
54#91380C2214yes—
55#91379C2214yescomplemented
56#91378C2214yescomplemented
57#91371C2211yescharacteristic
58#91369C2212yes—
59#91367C2214yes—
60#91346C2214yescomplemented
61#91345C2214yes—
62#91343C2214yescomplemented
63#91342C2214yes—
64#91341C2214yes—
65#91339C2214yescomplemented
66#91337C2214yes—
67#91336C2214yescomplemented
68#91331C2212yescomplemented
69#91331C2214yescomplemented
70Dic3×Dic10C2212yescomplemented
71Dic3×Dic10C2214yescomplemented
72C2×#5731—51nomaximal, Hall
73C5×#541—31no—
74#66065—31no—
75D5×C4⋊Q8D311yescharacteristic, complemented
76D5×#126—34no—
77#66035—34no—
78#66031—31no—
79#66030—34no—
80D5×#125—34no—
81D5×#125—31no—
82D5×C22⋊Q8—32no—
83#65959—32no—
84#65917—32no—
85C4×Q8×D5—32no—
86D5×#117—31no—
87#65852—31no—
88C22×D3×D5C2311yescharacteristic
89C2×C3×C5×Q8C2312yes—
90C2×C4×D15C2311yescharacteristic
91C2×C4×C5×D3C2311yescharacteristic
92C3×Q8×D5—28no—
93C2×C3×C4×D5C2312yes—
94C2×C3×C4×D5C2314yes—
95C2×C3×C4×D5C2311yescharacteristic
96C2×C3×Dic10C2312yes—
97C2×C3×Dic10C2314yes—
98C2×#1200C2311yescharacteristic
99C2×D3×Dic5C2311yescharacteristic
100C2×D5×Dic3C2311yescharacteristic
101C2×D5×Dic3C2314yes—
102C2×D5×Dic3C2312yes—
103C4×D3×D5—24no—
104C3×C5×C4⋊C4C2314yes—
105C3×C42×C5C2311yescharacteristic
106#6714C2312yes—
107#6714C2314yes—
108C4⋊Dic15C2312yes—
109C4⋊Dic15C2314yes—
110#6712C2312yes—
111#6712C2314yes—
112#6712C2314yes—
113C4×Dic15C2311yescharacteristic
114C4×Dic15C2314yes—
115C5×(C2×D3)⋊C4C2312yes—
116C5×(C2×D3)⋊C4C2314yes—
117C5×C4⋊Dic3C2312yes—
118C5×C4⋊Dic3C2314yes—
119C5×Dic3⋊C4C2312yes—
120C5×Dic3⋊C4C2314yes—
121C5×Dic3⋊C4C2314yes—
122C4×C5×Dic3C2311yescharacteristic
123C4×C5×Dic3C2314yes—
124C3×C4⋊Dic5C2314yes—
125C3×#683C2314yes—
126C3×#683C2314yes—
127C3×C4×Dic5C2312yes—
128C3×C4×Dic5C2311yescharacteristic
129Dic3⋊Dic5C2312yes—
130Dic3⋊Dic5C2314yes—
131Dic3⋊Dic5C2314yes—
132#6669C2312yes—
133#6669C2314yes—
134#6669C2314yes—
135#6668C2314yes—
136#6668C2314yes—
137#6668C2314yes—
138#6667C2312yes—
139#6667C2314yes—
140(C2×D3)⋊Dic5C2312yes—
141(C2×D3)⋊Dic5C2314yes—
142Dic3×Dic5C2312yes—
143Dic3×Dic5C2314yes—
144Dic3×Dic5C2314yes—
145C2×C3×C4⋊Q8—51no—
146C2×#946—52no—
147C2×Q8×Dic3—52no—
148#5731—51no—
149#5731—52no—
150#5731—52no—
151#5731—54no—
152#5731—54no—
153#5731—51no—
154#5731—51no—
155#5731D511yescharacteristic, direct product factor
156C2×#898—54no—
157C2×#889—54no—
158C2×#872—51no—
159C2×#870—51no—
160C2×Q8×D5C2×D312yes—
161C22×C4×D5—31no—
162C5×C4⋊Q8C2×D311yescharacteristic, complemented
163C5×#126—34no—
164C5×#125—34no—
165C5×#125—31no—
166C5×C22⋊Q8—32no—
167C4×C5×Q8—32no—
168C5×#117—31no—
169#4092—32no—
170Q8×Dic5—32no—
171#4090C2×D312yescomplemented
172#4072—31no—
173#4070—32no—
174#4044—34no—
175#4044—34no—
176#4044—34no—
177#4043—32no—
178#4042—34no—
179#4038—32no—
180D5×C4⋊C4—32no—
181D5×C4⋊C4—34no—
182D5×C4⋊C4—34no—
183D5×C4⋊C4—32no—
184D5×C4⋊C4—34no—
185D5×C4⋊C4C2×D314yes—
186#4036—34no—
187#4036—34no—
188#4036—32no—
189#4035—34no—
190#4035—34no—
191#4035—34no—
192#4035—34no—
193#4035—34no—
194#4034C2×D314yescomplemented
195#4033—32no—
196#4033—34no—
197D5×C22⋊C4—32no—
198D5×C22⋊C4—34no—
199#4025—34no—
200#4025—34no—
201#4025—34no—
202#4024—34no—
203#4023—32no—
204#4022—34no—
205#4018—31no—
206#4018—31no—
207C42×D5—31no—
208C42×D5—34no—
209C42×D5C2×D311yescharacteristic
210#4016—31no—
211#4016—34no—
212#4015C2×D311yescharacteristic, complemented
213C4×Dic10—32no—
214C4×Dic10—34no—
215C2×#541—151noSylow
216C22×D15C2411yescharacteristic
217C22×C5×D3C2411yescharacteristic
218C22×C3×D5C2411yescharacteristic
219C2×D3×D5—22no—
220C2×D3×D5—24no—
221C3×C5×Q8—24no—
222C2×C3×C4×C5C2412yes—
223C2×C3×C4×C5C2414yes—
224C2×C3×C4×C5C2411yescharacteristic
225C2×Dic15C2412yes—
226C2×Dic15C2414yes—
227C2×Dic15C2411yescharacteristic
228C4×D15—22no—
229C2×C5×Dic3C2412yes—
230C2×C5×Dic3C2414yes—
231C2×C5×Dic3C2411yescharacteristic
232C4×C5×D3—22no—
233C2×C3×Dic5C2414yes—
234C2×C3×Dic5C2412yes—
235C2×C3×Dic5C2411yescharacteristic
236C3×C4×D5—28no—
237C3×C4×D5—24no—
238C3×C4×D5#4114yes—
239C3×Dic10—24no—
240C3×Dic10—28no—
241#1200—22no—
242D3×Dic5—22no—
243D5×Dic3—22no—
244D5×Dic3—28no—
245D5×Dic3—24no—
246C22×C3×Q8—52no—
247C22×C4×D3—51no—
248C3×C4⋊Q8—52no—
249C3×C4⋊Q8—54no—
250C3×C4⋊Q8—51no—
251C3×C4⋊Q8C2×D511yescharacteristic, complemented
252C2×C3×C4⋊C4—54no—
253C2×C3×C42—51no—
254#946—52no—
255#946—52no—
256#946—54no—
257#946—52no—
258#946—54no—
259#946C2×D512yes—
260Q8×Dic3—52no—
261Q8×Dic3—52no—
262Q8×Dic3—54no—
263Q8×Dic3—54no—
264Q8×Dic3—52no—
265Q8×Dic3C2×D512yescomplemented
266C2×(C2×D3)⋊C4—52no—
267C2×(C2×D3)⋊C4—54no—
268C2×C4⋊Dic3—52no—
269C2×C4⋊Dic3—54no—
270C2×Dic3⋊C4—54no—
271C2×Dic3⋊C4—52no—
272C2×Dic3⋊C4—54no—
273C2×C4×Dic3—51no—
274C2×C4×Dic3—54no—
275#898—54no—
276#898—54no—
277#898—54no—
278#898—54no—
279#898—54no—
280#898—54no—
281#898—54no—
282#898C2×D514yes—
283#889—54no—
284#889—54no—
285#889—54no—
286#889—54no—
287#889—54no—
288#889—54no—
289#889—54no—
290#889C2×D514yescomplemented
291#872—51no—
292#872—51no—
293#872—52no—
294#872—52no—
295#872—51no—
296#872C2×D511yescharacteristic
297#870—51no—
298#870—52no—
299#870—54no—
300#870C2×D511yescharacteristic, complemented
301C23×D5—31no—
302C2×C5×Q8C22×D312yes—
303C22×C4×C5—31no—
304C22×Dic5—31no—
305Q8×D5—28no—
306C2×C4×D5—31no—
307C2×C4×D5—32no—
308C2×C4×D5—34no—
309C2×C4×D5—31no—
310C2×C4×D5—31no—
311C2×C4×D5—64no—
312C2×C4×D5C22×D314yes—
313C2×C4×D5C22×D312yes—
314C2×C4×D5C22×D311yescharacteristic
315C2×Dic10C22×D312yes—
316C2×Dic10C22×D314yes—
317C5×C4⋊C4—32no—
318C5×C4⋊C4—32no—
319C5×C4⋊C4—34no—
320C5×C4⋊C4—34no—
321C5×C4⋊C4—34no—
322C5×C4⋊C4C22×D314yes—
323C5×C22⋊C4—32no—
324C5×C22⋊C4—34no—
325C42×C5—31no—
326C42×C5—34no—
327C42×C5C22×D311yescharacteristic
328C22⋊Dic5—32no—
329C22⋊Dic5—34no—
330#685—32no—
331#685—34no—
332#685—32no—
333#685—34no—
334C4⋊Dic5—32no—
335C4⋊Dic5—34no—
336C4⋊Dic5—34no—
337C4⋊Dic5—34no—
338C4⋊Dic5—32no—
339C4⋊Dic5C22×D314yes—
340#683—34no—
341#683—34no—
342#683—32no—
343#683—34no—
344#683—34no—
345#683—34no—
346#683—32no—
347#683—34no—
348#683—34no—
349#683C22×D314yes—
350#683C22×D314yes—
351C4×Dic5—31no—
352C4×Dic5—34no—
353C4×Dic5—32no—
354C4×Dic5—34no—
355C4×Dic5—34no—
356C4×Dic5C22×D311yescharacteristic
357C4×Dic5C22×D312yes—
358#541—31no—
359#541—151no—
360#541—152no—
361#541—152no—
362#541—154no—
363#541—151no—
364#541—154no—
365#541—151no—
366C2×C4⋊Q8—51no—
367C2×#126—154no—
368C2×#125—151no—
369C2×#125—154no—
370C2×C22⋊Q8—152no—
371C2×C4×Q8—152no—
372C2×#117—151no—
373C22×C3×C5C2511yescharacteristic
374C2×D15—21no—
375C2×D15—22no—
376C2×C5×D3—21no—
377C2×C5×D3—22no—
378C2×C3×D5C2×#4112yes—
379C2×C3×D52−1+414yes—
380D3×D5—44no—
381C3×C4×C5—24no—
382C3×C4×C5—22no—
383C3×C4×C5C2×#4112yes—
384Dic15—21no—
385Dic15—22no—
386Dic15—24no—
387C3×Dic5—24no—
388C3×Dic5—22no—
389C3×Dic5C2×#4112yes—
390C5×Dic3—21no—
391C5×Dic3—22no—
392C5×Dic3—24no—
393C23×D3—51no—
394C2×C3×Q8—54no—
395C2×C3×Q8—52no—
396C2×C3×Q8—108no—
397C2×C3×Q8C22×D512yes—
398C22×C3×C4—51no—
399C22×C3×C4—54no—
400C22×C3×C4—52no—
401C22×Dic3—52no—
402C22×Dic3—54no—
403C22×Dic3—51no—
404C2×C4×D3—51no—
405C2×C4×D3—51no—
406C2×C4×D3—51no—
407C2×C4×D3—104no—
408C2×C4×D3C22×D511yescharacteristic
409C3×C4⋊C4—54no—
410C3×C4⋊C4—54no—
411C3×C4⋊C4—54no—
412C3×C4⋊C4C22×D514yes—
413C3×C42—52no—
414C3×C42—51no—
415C3×C42C22×D511yescharacteristic
416(C2×D3)⋊C4—52no—
417(C2×D3)⋊C4—54no—
418(C2×D3)⋊C4—52no—
419(C2×D3)⋊C4—54no—
420(C2×D3)⋊C4—52no—
421(C2×D3)⋊C4—54no—
422(C2×D3)⋊C4C22×D512yes—
423(C2×D3)⋊C4C22×D514yes—
424C4⋊Dic3—52no—
425C4⋊Dic3—54no—
426C4⋊Dic3—54no—
427C4⋊Dic3—54no—
428C4⋊Dic3—54no—
429C4⋊Dic3C22×D512yes—
430C4⋊Dic3C22×D514yes—
431Dic3⋊C4—54no—
432Dic3⋊C4—52no—
433Dic3⋊C4—54no—
434Dic3⋊C4—54no—
435Dic3⋊C4—52no—
436Dic3⋊C4—54no—
437Dic3⋊C4—54no—
438Dic3⋊C4—52no—
439Dic3⋊C4—54no—
440Dic3⋊C4C22×D514yes—
441Dic3⋊C4C22×D512yes—
442Dic3⋊C4C22×D514yes—
443C4×Dic3—51no—
444C4×Dic3—54no—
445C4×Dic3—52no—
446C4×Dic3—54no—
447C4×Dic3—54no—
448C4×Dic3C22×D511yescharacteristic
449C4×Dic3C22×D514yes—
450C23×C5—31no—
451C22×D5—31no—
452C22×D5—62no—
453C22×D5—64no—
454C22×D5C23×D311yescharacteristic
455C5×Q8—24no—
456C2×C4×C5—32no—
457C2×C4×C5—34no—
458C2×C4×C5—31no—
459C2×C4×C5—62no—
460C2×C4×C5C23×D314yes—
461C2×C4×C5C23×D312yes—
462C2×C4×C5C23×D311yescharacteristic
463C2×Dic5—32no—
464C2×Dic5—34no—
465C2×Dic5—31no—
466C2×Dic5—62no—
467C2×Dic5C23×D314yes—
468C2×Dic5C23×D312yes—
469C2×Dic5C23×D311yescharacteristic
470C4×D5—28no—
471C4×D5—24no—
472C4×D5—62no—
473C4×D5—64no—
474C4×D5—68no—
475C4×D5—62no—
476C4×D5—62no—
477C4×D5#23714yes—
478Dic10—24no—
479Dic10—28no—
480C22×Q8—52no—
481C23×C4—151no—
482C4⋊Q8—52no—
483C4⋊Q8—54no—
484C4⋊Q8—51no—
485C4⋊Q8D3×D511yescharacteristic, complemented
486#126—34no—
487#126—154no—
488#126—154no—
489#126—154no—
490#126—154no—
491#126—154no—
492#126—154no—
493#126—154no—
494#125—34no—
495#125—31no—
496#125—154no—
497#125—154no—
498#125—152no—
499#125—154no—
500#125—154no—
501#125—154no—
502#125—154no—
503#125—154no—
504#125—154no—
505#125—151no—
506C22⋊Q8—32no—
507C22⋊Q8—154no—
508C22⋊Q8—154no—
509C22⋊Q8—152no—
510C22⋊Q8—152no—
511C22⋊Q8—152no—
512C4×Q8—32no—
513C4×Q8—152no—
514C4×Q8—154no—
515C4×Q8—154no—
516C4×Q8—152no—
517C4×Q8—152no—
518#117—31no—
519#117—151no—
520#117—152no—
521#117—152no—
522#117—151no—
523#117—151no—
524C2×C4⋊C4—54no—
525C2×C4⋊C4—152no—
526C2×C4⋊C4—152no—
527C2×C4⋊C4—154no—
528C2×C4⋊C4—154no—
529C2×C4⋊C4—154no—
530C2×C22⋊C4—152no—
531C2×C22⋊C4—154no—
532C2×C42—51no—
533C2×C42—151no—
534C2×C42—154no—
535C2×C3×C5C22×#4111yescharacteristic
536C2×C3×C5C2×2−1+412yes—
537D15—41no—
538C3×D5#54114yescomplemented
539C5×D3—41no—
540C23×C3—51no—
541C22×D3—51no—
542C22×D3—102no—
543C22×D3—104no—
544C22×D3C23×D511yescharacteristic
545C3×Q8—24no—
546C3×Q8—108no—
547C3×Q8—104no—
548C2×C3×C4—51no—
549C2×C3×C4—54no—
550C2×C3×C4—54no—
551C2×C3×C4—52no—
552C2×C3×C4—104no—
553C2×C3×C4—108no—
554C2×C3×C4C23×D514yes—
555C2×C3×C4C23×D512yes—
556C2×C3×C4C23×D511yescharacteristic
557C2×Dic3—52no—
558C2×Dic3—54no—
559C2×Dic3—51no—
560C2×Dic3—102no—
561C2×Dic3—104no—
562C2×Dic3—108no—
563C2×Dic3C23×D512yes—
564C2×Dic3C23×D514yes—
565C2×Dic3C23×D511yescharacteristic
566C4×D3—22no—
567C4×D3—102no—
568C4×D3—102no—
569C4×D3—102no—
570C22×C5—61no—
571C22×C5—62no—
572C22×C5C24×D311yescharacteristic
573C2×D5—61no—
574C2×D5—62no—
575C2×D5—124no—
576C2×D5C2×#23712yes—
577C2×D5#100714yes—
578C4×C5—24no—
579C4×C5—22no—
580C4×C5—61no—
581C4×C5—62no—
582C4×C5—64no—
583C4×C5C2×#23712yes—
584Dic5—24no—
585Dic5—22no—
586Dic5—61no—
587Dic5—62no—
588Dic5—64no—
589Dic5C2×#23712yes—
590C24—151no—
591C2×Q8—54no—
592C2×Q8—52no—
593C2×Q8—108no—
594C2×Q8C2×D3×D512yes—
595C22×C4—31no—
596C22×C4—51no—
597C22×C4—52no—
598C22×C4—54no—
599C22×C4—151no—
600C22×C4—152no—
601C22×C4—154no—
602C22×C4—151no—
603C22×C4—151no—
604C22×C4—151no—
605C22×C4—304no—
606C4⋊C4—32no—
607C4⋊C4—32no—
608C4⋊C4—34no—
609C4⋊C4—34no—
610C4⋊C4—34no—
611C4⋊C4—54no—
612C4⋊C4—54no—
613C4⋊C4—54no—
614C4⋊C4—152no—
615C4⋊C4—152no—
616C4⋊C4—154no—
617C4⋊C4—154no—
618C4⋊C4—154no—
619C4⋊C4—154no—
620C4⋊C4—154no—
621C4⋊C4—154no—
622C4⋊C4—154no—
623C4⋊C4—152no—
624C4⋊C4—152no—
625C4⋊C4—154no—
626C4⋊C4—154no—
627C4⋊C4—154no—
628C4⋊C4C2×D3×D514yes—
629C22⋊C4—32no—
630C22⋊C4—34no—
631C22⋊C4—152no—
632C22⋊C4—154no—
633C22⋊C4—152no—
634C22⋊C4—154no—
635C22⋊C4—152no—
636C22⋊C4—154no—
637C42—31no—
638C42—34no—
639C42—52no—
640C42—51no—
641C42—152no—
642C42—154no—
643C42—154no—
644C42—151no—
645C42—154no—
646C42C2×D3×D511yescharacteristic
647C3×C5C2×#54111yescharacteristic, complemented, Hall
648C22×C3—52no—
649C22×C3—54no—
650C22×C3C24×D511yescharacteristic
651C2×D3—21no—
652C2×D3—22no—
653C2×D3—101no—
654C2×D3—102no—
655C2×D3—204no—
656C3×C4—24no—
657C3×C4—22no—
658C3×C4—52no—
659C3×C4—104no—
660C3×C4—102no—
661C3×C4D5×#4112yes—
662Dic3—21no—
663Dic3—22no—
664Dic3—24no—
665Dic3—101no—
666Dic3—102no—
667Dic3—104no—
668C2×C5—121no—
669C2×C5C22×#23711yescharacteristic
670C2×C5C2×#100712yes—
671D5—121no—
672D5#573114yesdirect product factor
673C23—31no—
674C23—51no—
675C23—151no—
676C23—302no—
677C23—304no—
678Q8—24no—
679Q8—108no—
680Q8—104no—
681C2×C4—32no—
682C2×C4—34no—
683C2×C4—31no—
684C2×C4—51no—
685C2×C4—54no—
686C2×C4—52no—
687C2×C4—54no—
688C2×C4—62no—
689C2×C4—108no—
690C2×C4—104no—
691C2×C4—152no—
692C2×C4—154no—
693C2×C4—151no—
694C2×C4—302no—
695C2×C4—302no—
696C2×C4—302no—
697C2×C4—304no—
698C2×C4—308no—
699C2×C4—302no—
700C2×C4C22×D3×D514yes—
701C2×C4C22×D3×D512yes—
702C2×C4C22×D3×D511yescharacteristic
703C2×C3—54no—
704C2×C3C2×D5×#4111yescharacteristic
705C2×C3D5×2−1+412yes—
706D3—41no—
707D3—201no—
708C5C2×#573111yescharacteristic, complemented, Sylow
709C22—52no—
710C22—54no—
711C22—61no—
712C22—62no—
713C22—301no—
714C22—302no—
715C22—604no—
716C22C23×D3×D511yescharacteristic
717C4—24no—
718C4—22no—
719C4—52no—
720C4—61no—
721C4—62no—
722C4—64no—
723C4—104no—
724C4—102no—
725C4—301no—
726C4—302no—
727C4—304no—
728C4D5×#23712yes—
729C3D5×#54111yescharacteristic, complemented, Sylow
730C2—54no—
731C2—121no—
732C2—601no—
733C2C2×D5×#23711yescharacteristic
734C2D5×#100712yes—
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×C4⋊Q8C22
prime radicalC22×D3×D5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5C2×#541
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #11756490C2semidirect
2. C5×#5731C2semidirect
3. C3×D5×C4⋊Q8C2semidirect
5. Q8×D5×Dic3C2semidirect
6. #11755150C2semidirect
7. #11755143C2semidirect
9. #11753519C2semidirect
10. D5×#889C2semidirect
11. #11753310C2semidirect
13. D5×#870C2semidirect
14. #11752485C2semidirect
15. #11752479C2semidirect
19. C3×C5×C4⋊Q8C22semidirect
21. Q8×Dic15C22semidirect
23. #91778C22semidirect
25. #91759C22semidirect
27. C5×Q8×Dic3C22semidirect
29. C5×#889C22semidirect
31. C5×#870C22semidirect
32. C3×#4090C22semidirect
34. C3×#4034C22semidirect
36. C3×#4015C22semidirect
51. #91388C22semidirect
53. #91382C22semidirect
55. #91379C22semidirect
56. #91378C22semidirect
60. #91346C22semidirect
62. #91343C22semidirect
65. #91339C22semidirect
67. #91336C22semidirect
68. #91331C22semidirect
69. #91331C22semidirect
70. Dic3×Dic10C22semidirect
71. Dic3×Dic10C22semidirect
75. D5×C4⋊Q8D3semidirect
155. #5731D5direct (N × H)
162. C5×C4⋊Q8C2×D3semidirect
171. #4090C2×D3semidirect
194. #4034C2×D3semidirect
212. #4015C2×D3semidirect
251. C3×C4⋊Q8C2×D5semidirect
265. Q8×Dic3C2×D5semidirect
290. #889C2×D5semidirect
300. #870C2×D5semidirect
485. C4⋊Q8D3×D5semidirect
538. C3×D5#541semidirect
647. C3×C5C2×#541semidirect
672. D5#5731direct (N × H)
708. C5C2×#5731semidirect
729. C3D5×#541semidirect

Maximal subgroups

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

subgroupindex
#117564902
C5×#57312
C3×D5×C4⋊Q82
D5×#9462
Q8×D5×Dic32
#117551502
#117551432
D5×#8982
#117535192
D5×#8892
#117533102
D5×#8722
D5×#8702
#117524852
#117524792
D5×#5413
C2×#57315