Finite Group Databasebeta

← D5×#5576 #14482826

Subgroups — D5×#5576 #14482826

Order 1920.

3240 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#239C211yesmaximal, characteristic, complemented
2C2×D3×Q8×D5C211yesmaximal, characteristic, complemented
3#11756335C211yesmaximal, characteristic, complemented
4C5×#5576C211yesmaximal, characteristic, complemented
5C3×C4×Q8×D5C211yesmaximal, characteristic, complemented
6#11755134C211yesmaximal, characteristic, complemented
7#11755131C211yesmaximal, characteristic, complemented
8D5×#897C213yesmaximal, complemented
9D5×#895C213yesmaximal, complemented
10#11753437C213yesmaximal, complemented
11#11753341C213yesmaximal, complemented
12D5×#875C213yesmaximal, complemented
13C4×D5×D12C213yesmaximal, complemented
14#11752537C213yesmaximal, complemented
15#11752535C213yesmaximal, complemented
16D5×#548—31nomaximal, Hall
17C2×#6821C2211yescharacteristic, complemented
18C2×Q8×D15C2211yescharacteristic, complemented
19C2×C5×#239C2211yescharacteristic, complemented
20C2×C5×D3×Q8C2211yescharacteristic, complemented
21C2×C3×Q8×D5C2211yescharacteristic
22D5×#239—28no—
23D3×Q8×D5—28no—
24C2×D5×D12C2213yes—
25C2×D5×D12C2213yes—
26C2×C4×D3×D5C2213yes—
27C2×C4×D3×D5C2213yes—
28C2×D15⋊Q8C2213yescomplemented
29C2×#6769C2213yescomplemented
30C2×#6768C2213yescomplemented
31C2×D3×Dic10C2213yescomplemented
32C2×D5×Dic6C2213yes—
33C3×C4×C5×Q8C2211yescharacteristic, complemented
34#91786C2213yescomplemented
35#91784C2213yescomplemented
36#91764C2213yescomplemented
37C4×D60C2213yescomplemented
38C5×#897C2213yescomplemented
39C5×#895C2213yescomplemented
40C5×#875C2213yescomplemented
41C4×C5×D12C2213yescomplemented
42C3×Q8×Dic5C2211yescharacteristic, complemented
43C3×D5×C4⋊C4C2213yes—
44C3×#4033C2213yescomplemented
45C3×C42×D5C2213yes—
46C3×C4×Dic10C2213yescomplemented
47D5×(C2×D3)⋊C4C2211yescharacteristic
48D5×(C2×D3)⋊C4C2213yes—
49D5×(C2×D3)⋊C4C2216yes—
50#91466C2213yescomplemented
51#91460C2213yescomplemented
52C4×#1203C2213yescomplemented
53C4×#1203C2213yescomplemented
54#91420C2216yescomplemented
55#91419C2216yescomplemented
56#91418C2213yescomplemented
57#91417C2216yescomplemented
58#91416C2216yescomplemented
59Dic5×D12C2213yescomplemented
60D5×C4⋊Dic3C2213yes—
61#91405C2213yescomplemented
62#91405C2213yescomplemented
63#91383C2213yescomplemented
64#91375C2213yescomplemented
65#91373C2213yescomplemented
66#91365C2213yescomplemented
67#91350C2216yescomplemented
68#91350C2216yescomplemented
69C2×#5576—51nomaximal, Hall
70C2×D5×#41—31no—
71C22×Q8×D5—31no—
72C5×#548—31no—
73#66165—31no—
74#66151—31no—
75#66011—33no—
76D5×#124—33no—
77#65967—33no—
78D5×C22⋊Q8—33no—
79D5×#121—33no—
80#65932—33no—
81#65910—31no—
82C4×Q8×D5D311yescharacteristic, complemented
83#65886—33no—
84C4×D4×D5—33no—
85C22×D3×D5C2313yes—
86C22×D3×D5C2311yescharacteristic
87C2×C3×C5×Q8C2311yescharacteristic
88#6821—24no—
89Q8×D15—24no—
90C2×D60C2313yes—
91C2×D60C2313yes—
92C2×C4×D15C2313yes—
93C2×C4×D15C2313yes—
94C2×Dic30C2313yes—
95C5×#239—24no—
96C5×D3×Q8—24no—
97C2×C5×D12C2313yes—
98C2×C5×D12C2313yes—
99C2×C4×C5×D3C2313yes—
100C2×C4×C5×D3C2313yes—
101C2×C5×Dic6C2313yes—
102C3×Q8×D5D418yescomplemented
103C2×C3×C4×D5C2313yes—
104C2×C3×C4×D5C2311yescharacteristic
105C2×C3×C4×D5C2313yes—
106C2×C3×Dic10C2313yes—
107C2×#1204C2316yes—
108C2×#1203C2313yes—
109C2×#1203C2313yes—
110C2×#1203C2316yes—
111C2×#1200C2313yes—
112C2×#1200C2313yes—
113C2×D3×Dic5C2313yes—
114C2×D3×Dic5C2313yes—
115C2×D5×Dic3C2311yescharacteristic
116C2×D5×Dic3C2313yes—
117D5×D12—212no—
118D5×D12—212no—
119C4×D3×D5—212no—
120C4×D3×D5—212no—
121D15⋊Q8—212no—
122#6769—212no—
123#6768—212no—
124D3×Dic10—212no—
125D5×Dic6—212no—
126C3×C5×C4⋊C4C2313yes—
127C3×C42×C5C2313yes—
128#6714C2311yescharacteristic
129#6714C2313yes—
130#6714C2316yes—
131C4⋊Dic15C2313yes—
132C5×(C2×D3)⋊C4C2311yescharacteristic
133C5×(C2×D3)⋊C4C2313yes—
134C5×(C2×D3)⋊C4C2316yes—
135C5×C4⋊Dic3C2313yes—
136C3×C4⋊Dic5C2313yes—
137C3×#683C2316yes—
138C3×C4×Dic5C2313yes—
139C3×C4×Dic5C2313yes—
140C3×C4×Dic5C2313yes—
141#6668C2313yes—
142#6668C2313yes—
143#6667C2311yescharacteristic
144#6667C2313yes—
145#6667C2316yes—
146(C2×D3)⋊Dic5C2311yescharacteristic
147(C2×D3)⋊Dic5C2313yes—
148(C2×D3)⋊Dic5C2316yes—
149C22×#239—51no—
150C22×D3×Q8—51no—
151C2×C3×C4×Q8—51no—
152#5576—51no—
153#5576—51no—
154#5576—51no—
155#5576—53no—
156#5576—53no—
157#5576—53no—
158#5576—53no—
159#5576D511yescharacteristic, direct product factor
160C2×#897—53no—
161C2×#895—53no—
162C2×#875—53no—
163C2×C4×D12—53no—
164C2×C5×#41—31no—
165C22×C5×Q8—31no—
166D5×#41—68no—
167C2×#713—31no—
168C2×Q8×D5—31no—
169C2×Q8×D5—33no—
170C2×Q8×D5—33no—
171C2×Q8×D5—68no—
172C2×Q8×D5C2×D311yescharacteristic
173C2×#711—33no—
174C2×D4×D5—33no—
175C2×D4×D5—33no—
176C2×#709—33no—
177C22×C4×D5—33no—
178C22×C4×D5—33no—
179C22×Dic10—33no—
180C5×#124—33no—
181C5×C22⋊Q8—33no—
182C5×#121—33no—
183C4×C5×Q8C2×D311yescharacteristic, complemented
184C4×C5×D4—33no—
185#4093—33no—
186#4092—33no—
187Q8×Dic5C2×D311yescharacteristic, complemented
188#4085—36no—
189#4084—33no—
190#4082—33no—
191D4×Dic5—33no—
192#4076—33no—
193C4×C22⋊D5—33no—
194C4×C22⋊D5—33no—
195#4070—33no—
196#4043—33no—
197#4042—36no—
198#4041—33no—
199#4039—33no—
200D5×C4⋊C4—33no—
201D5×C4⋊C4C2×D313yes—
202#4033C2×D313yescomplemented
203#4031—36no—
204#4031—36no—
205#4030—36no—
206#4027—33no—
207#4027—33no—
208D5×C22⋊C4—31no—
209D5×C22⋊C4—33no—
210D5×C22⋊C4—36no—
211#4024—36no—
212#4021—33no—
213C4×D20—33no—
214C42×D5C2×D313yes—
215C4×Dic10C2×D313yescomplemented
216C2×#548—151noSylow
217C22×D15C2413yes—
218C22×D15C2411yescharacteristic
219C22×C5×D3C2413yes—
220C22×C5×D3C2411yescharacteristic
221C22×C3×D5C2411yescharacteristic
222C2×D3×D5—22no—
223C2×D3×D5—22no—
224C2×D3×D5—26no—
225C2×D3×D5—26no—
226C2×D3×D5—26no—
227C2×D3×D5#4114yescomplemented
228C3×C5×Q8C2×D414yescomplemented
229C2×C3×C4×C5C2411yescharacteristic
230C2×C3×C4×C5C2413yes—
231C2×C3×C4×C5C2413yes—
232C2×Dic15C2413yes—
233C2×Dic15C2411yescharacteristic
234D60—26no—
235D60—26no—
236C4×D15—26no—
237C4×D15—26no—
238Dic30—26no—
239C2×C5×Dic3C2413yes—
240C2×C5×Dic3C2411yescharacteristic
241C5×D12—26no—
242C5×D12—26no—
243C4×C5×D3—26no—
244C4×C5×D3—26no—
245C5×Dic6—26no—
246C2×C3×Dic5C2411yescharacteristic
247C2×C3×Dic5C2413yes—
248C2×C3×Dic5C2413yes—
249C3×C4×D5—26no—
250C3×C4×D5—22no—
251C3×C4×D5C2×D4112yes—
252C3×Dic10C2×D4112yescomplemented
253#1204—212no—
254#1203—26no—
255#1203—26no—
256#1203—212no—
257#1200—26no—
258#1200—26no—
259D3×Dic5—26no—
260D3×Dic5—26no—
261D5×Dic3—26no—
262D5×Dic3—22no—
263C22×C3×Q8—51no—
264C2×#239—51no—
265C2×#239—53no—
266C2×#239—53no—
267C2×#239—108no—
268C2×#239C2×D511yescharacteristic, complemented
269C2×D3×Q8—51no—
270C2×D3×Q8—53no—
271C2×D3×Q8—53no—
272C2×D3×Q8—108no—
273C2×D3×Q8C2×D511yescharacteristic, complemented
274C22×D12—53no—
275C22×D12—53no—
276C22×C4×D3—53no—
277C22×C4×D3—53no—
278C22×Dic6—53no—
279C3×C4×Q8—51no—
280C3×C4×Q8—53no—
281C3×C4×Q8—53no—
282C3×C4×Q8C2×D511yescharacteristic, complemented
283C2×C3×C4⋊C4—53no—
284C2×C3×C42—53no—
285C2×(C2×D3)⋊C4—51no—
286C2×(C2×D3)⋊C4—53no—
287C2×(C2×D3)⋊C4—56no—
288C2×C4⋊Dic3—53no—
289#897—53no—
290#897—53no—
291#897—53no—
292#897—56no—
293#897—56no—
294#897C2×D513yescomplemented
295#895—56no—
296#895—53no—
297#895—53no—
298#895—53no—
299#895—56no—
300#895C2×D513yescomplemented
301#875—53no—
302#875—53no—
303#875—53no—
304#875—56no—
305#875—56no—
306#875C2×D513yescomplemented
307C4×D12—53no—
308C4×D12—53no—
309C4×D12—53no—
310C4×D12—53no—
311C4×D12—53no—
312C4×D12—53no—
313C4×D12—53no—
314C4×D12C2×D513yescomplemented
315C23×D5—31no—
316C23×D5—33no—
317C5×#41—64no—
318C2×C5×Q8—33no—
319C2×C5×Q8—64no—
320C2×C5×Q8C22×D311yescharacteristic
321C2×C5×D4—33no—
322C2×C5×D4—33no—
323C22×C4×C5—33no—
324C22×C4×C5—33no—
325C2×C22⋊D5—36no—
326C2×C22⋊D5—33no—
327C2×C22⋊D5—33no—
328C22×Dic5—33no—
329C22×Dic5—33no—
330#713—64no—
331Q8×D5—64no—
332Q8×D5—612no—
333Q8×D5—612no—
334Q8×D5D1218yescomplemented
335#711—612no—
336D4×D5—612no—
337D4×D5—612no—
338#709—612no—
339C2×D20—33no—
340C2×D20—33no—
341C2×C4×D5—31no—
342C2×C4×D5—33no—
343C2×C4×D5—33no—
344C2×C4×D5—33no—
345C2×C4×D5—33no—
346C2×C4×D5—33no—
347C2×C4×D5—612no—
348C2×C4×D5—612no—
349C2×C4×D5C22×D313yes—
350C2×C4×D5C22×D311yescharacteristic
351C2×C4×D5C22×D313yes—
352C2×Dic10—33no—
353C2×Dic10—36no—
354C2×Dic10—612no—
355C2×Dic10C22×D313yes—
356C5×C4⋊C4—33no—
357C5×C4⋊C4C22×D313yes—
358C5×C22⋊C4—31no—
359C5×C22⋊C4—33no—
360C5×C22⋊C4—36no—
361C42×C5C22×D313yes—
362C22⋊Dic5—36no—
363C22⋊Dic5—33no—
364C22⋊Dic5—31no—
365#685—31no—
366#685—33no—
367#685—36no—
368#685—36no—
369#685—33no—
370#685—31no—
371C4⋊Dic5—33no—
372C4⋊Dic5C22×D313yes—
373#683—33no—
374#683—33no—
375#683C22×D316yes—
376C4×Dic5C22×D313yes—
377C4×Dic5C22×D313yes—
378C4×Dic5C22×D313yes—
379C22×#41—151no—
380C23×Q8—151no—
381#548—31no—
382#548—153no—
383#548—153no—
384#548—153no—
385#548—153no—
386#548—151no—
387#548—151no—
388#548—151no—
389C2×#124—153no—
390C2×C22⋊Q8—153no—
391C2×#121—153no—
392C2×C4×Q8—51no—
393C2×C4×D4—153no—
394C22×C3×C5C2511yescharacteristic
395C2×D15—21no—
396C2×D15—21no—
397C2×D15—23no—
398C2×D15—23no—
399C2×D15—23no—
400C2×D15C2×#4112yescomplemented
401C2×C5×D3—21no—
402C2×C5×D3—21no—
403C2×C5×D3—23no—
404C2×C5×D3—23no—
405C2×C5×D3—23no—
406C2×C5×D3C2×#4112yescomplemented
407C2×C3×D5C22×D412yes—
408C2×C3×D5C2×#4112yes—
409C2×C3×D52−1+412yes—
410D3×D5—28no—
411D3×D5—412no—
412C3×C4×C5—23no—
413C3×C4×C5—21no—
414C3×C4×C5C22×D416yes—
415Dic15—21no—
416Dic15—23no—
417C3×Dic5—23no—
418C3×Dic5—21no—
419C3×Dic5C22×D416yes—
420C5×Dic3—21no—
421C5×Dic3—23no—
422C23×D3—51no—
423C23×D3—53no—
424C2×C3×Q8—58no—
425C2×C3×Q8—53no—
426C2×C3×Q8C22×D511yescharacteristic
427C22×C3×C4—53no—
428C22×C3×C4—53no—
429C22×C3×C4—51no—
430C22×Dic3—51no—
431C22×Dic3—53no—
432#239—24no—
433#239—1012no—
434#239—1012no—
435#239—104no—
436D3×Q8—24no—
437D3×Q8—1012no—
438D3×Q8—1012no—
439D3×Q8—104no—
440C2×D12—53no—
441C2×D12—53no—
442C2×D12—56no—
443C2×D12—53no—
444C2×D12—53no—
445C2×D12—1012no—
446C2×D12—1012no—
447C2×D12C22×D513yes—
448C2×D12C22×D513yes—
449C2×C4×D3—53no—
450C2×C4×D3—53no—
451C2×C4×D3—53no—
452C2×C4×D3—53no—
453C2×C4×D3—53no—
454C2×C4×D3—53no—
455C2×C4×D3—1012no—
456C2×C4×D3—1012no—
457C2×C4×D3C22×D513yes—
458C2×C4×D3C22×D513yes—
459C2×Dic6—53no—
460C2×Dic6—56no—
461C2×Dic6—1012no—
462C2×Dic6C22×D513yes—
463C3×C4⋊C4—56no—
464C3×C4⋊C4—53no—
465C3×C4⋊C4C22×D513yes—
466C3×C42—53no—
467C3×C42—53no—
468C3×C42—53no—
469C3×C42C22×D513yes—
470(C2×D3)⋊C4—51no—
471(C2×D3)⋊C4—53no—
472(C2×D3)⋊C4—56no—
473(C2×D3)⋊C4—51no—
474(C2×D3)⋊C4—53no—
475(C2×D3)⋊C4—56no—
476(C2×D3)⋊C4—51no—
477(C2×D3)⋊C4—53no—
478(C2×D3)⋊C4—56no—
479(C2×D3)⋊C4C22×D511yescharacteristic
480(C2×D3)⋊C4C22×D513yes—
481(C2×D3)⋊C4C22×D516yes—
482C4⋊Dic3—53no—
483C4⋊Dic3—53no—
484C4⋊Dic3—53no—
485C4⋊Dic3C22×D513yes—
486C23×C5—31no—
487C23×C5—33no—
488C22×D5—31no—
489C22×D5—34no—
490C22×D5—33no—
491C22×D5—62no—
492C22×D5—62no—
493C22×D5—66no—
494C22×D5—66no—
495C22×D5—66no—
496C22×D5C23×D311yescharacteristic
497C5×Q8—66no—
498C5×Q8C2×D1214yescomplemented
499C5×D4—66no—
500C5×D4—66no—
501C2×C4×C5—31no—
502C2×C4×C5—33no—
503C2×C4×C5—66no—
504C2×C4×C5—66no—
505C2×C4×C5C23×D311yescharacteristic
506C2×C4×C5C23×D313yes—
507C2×C4×C5C23×D313yes—
508C22⋊D5—66no—
509C22⋊D5—66no—
510C22⋊D5—612no—
511C2×Dic5—31no—
512C2×Dic5—33no—
513C2×Dic5—66no—
514C2×Dic5—66no—
515C2×Dic5C23×D311yescharacteristic
516C2×Dic5C23×D313yes—
517C2×Dic5C23×D313yes—
518D20—66no—
519D20—66no—
520C4×D5—22no—
521C4×D5—26no—
522C4×D5—62no—
523C4×D5—66no—
524C4×D5—66no—
525C4×D5—66no—
526C4×D5—66no—
527C4×D5—66no—
528C4×D5C2×D12112yes—
529Dic10—66no—
530Dic10—612no—
531Dic10C2×D12112yescomplemented
532C2×#41—31no—
533C2×#41—153no—
534C2×#41—153no—
535C2×#41—151no—
536C2×#41—308no—
537C22×Q8—31no—
538C22×Q8—51no—
539C22×Q8—153no—
540C22×Q8—153no—
541C22×Q8—153no—
542C22×Q8—151no—
543C22×Q8—308no—
544C22×D4—153no—
545C22×D4—153no—
546C23×C4—153no—
547C23×C4—153no—
548#124—33no—
549#124—156no—
550#124—156no—
551#124—153no—
552#124—153no—
553#124—153no—
554C22⋊Q8—33no—
555C22⋊Q8—156no—
556C22⋊Q8—156no—
557C22⋊Q8—153no—
558C22⋊Q8—153no—
559C22⋊Q8—153no—
560#121—33no—
561#121—156no—
562#121—153no—
563#121—153no—
564#121—156no—
565#121—153no—
566C4×Q8—51no—
567C4×Q8—53no—
568C4×Q8—53no—
569C4×Q8D3×D511yescharacteristic, complemented
570C4×D4—33no—
571C4×D4—153no—
572C4×D4—153no—
573C4×D4—153no—
574C4×D4—153no—
575C4×D4—153no—
576C4×D4—153no—
577C4×D4—153no—
578C2×C4⋊C4—53no—
579C2×C4⋊C4—153no—
580C2×C22⋊C4—151no—
581C2×C22⋊C4—153no—
582C2×C22⋊C4—156no—
583C2×C42—53no—
584C2×C3×C5C23×D411yescharacteristic
585C2×C3×C5C22×#4111yescharacteristic
586C2×C3×C5C2×2−1+411yescharacteristic
587D15—22no—
588D15—43no—
589C3×D5#54814yescomplemented
590C5×D3—22no—
591C5×D3—43no—
592C23×C3—51no—
593C22×D3—51no—
594C22×D3—54no—
595C22×D3—53no—
596C22×D3—102no—
597C22×D3—102no—
598C22×D3—106no—
599C22×D3—106no—
600C22×D3—106no—
601C22×D3C23×D513yes—
602C22×D3C23×D511yescharacteristic
603C3×Q8—512no—
604C3×Q8D4×D514yescomplemented
605C2×C3×C4—53no—
606C2×C3×C4—512no—
607C2×C3×C4—53no—
608C2×C3×C4—51no—
609C2×C3×C4—106no—
610C2×C3×C4—102no—
611C2×C3×C4C23×D513yes—
612C2×C3×C4C23×D511yescharacteristic
613C2×C3×C4C23×D513yes—
614C2×Dic3—51no—
615C2×Dic3—53no—
616C2×Dic3—106no—
617C2×Dic3—102no—
618C2×Dic3C23×D511yescharacteristic
619C2×Dic3C23×D513yes—
620D12—26no—
621D12—26no—
622D12—106no—
623D12—1012no—
624D12—106no—
625D12—106no—
626D12—106no—
627C4×D3—26no—
628C4×D3—26no—
629C4×D3—106no—
630C4×D3—106no—
631C4×D3—106no—
632C4×D3—106no—
633C4×D3—106no—
634C4×D3—106no—
635Dic6—26no—
636Dic6—1012no—
637Dic6—106no—
638C22×C5—32no—
639C22×C5—61no—
640C22×C5—61no—
641C22×C5—63no—
642C22×C5—63no—
643C22×C5—63no—
644C22×C5C24×D311yescharacteristic
645C2×D5—32no—
646C2×D5—61no—
647C2×D5—61no—
648C2×D5—68no—
649C2×D5—63no—
650C2×D5—63no—
651C2×D5—63no—
652C2×D5—1212no—
653C2×D5C22×D1212yes—
654C2×D5#100712yes—
655C2×D5D3×#4112yes—
656C4×C5—21no—
657C4×C5—23no—
658C4×C5—63no—
659C4×C5—61no—
660C4×C5C22×D1216yes—
661Dic5—21no—
662Dic5—23no—
663Dic5—63no—
664Dic5—61no—
665Dic5C22×D1216yes—
666C24—151no—
667C24—153no—
668#41—64no—
669#41—3012no—
670#41—3012no—
671#41—304no—
672C2×Q8—33no—
673C2×Q8—58no—
674C2×Q8—53no—
675C2×Q8—64no—
676C2×Q8—156no—
677C2×Q8—153no—
678C2×Q8—3012no—
679C2×Q8—3012no—
680C2×Q8—3012no—
681C2×Q8—304no—
682C2×Q8C2×D3×D511yescharacteristic
683C2×D4—33no—
684C2×D4—33no—
685C2×D4—153no—
686C2×D4—153no—
687C2×D4—156no—
688C2×D4—153no—
689C2×D4—153no—
690C2×D4—3012no—
691C2×D4—3012no—
692C22×C4—33no—
693C22×C4—33no—
694C22×C4—53no—
695C22×C4—51no—
696C22×C4—53no—
697C22×C4—153no—
698C22×C4—153no—
699C22×C4—153no—
700C22×C4—151no—
701C22×C4—153no—
702C22×C4—153no—
703C22×C4—153no—
704C22×C4—153no—
705C22×C4—3012no—
706C22×C4—3012no—
707C4⋊C4—33no—
708C4⋊C4—56no—
709C4⋊C4—53no—
710C4⋊C4—153no—
711C4⋊C4—153no—
712C4⋊C4—153no—
713C4⋊C4C2×D3×D513yes—
714C22⋊C4—31no—
715C22⋊C4—33no—
716C22⋊C4—36no—
717C22⋊C4—151no—
718C22⋊C4—153no—
719C22⋊C4—156no—
720C22⋊C4—151no—
721C22⋊C4—153no—
722C22⋊C4—156no—
723C22⋊C4—151no—
724C22⋊C4—153no—
725C22⋊C4—156no—
726C42—53no—
727C42—53no—
728C42—53no—
729C42C2×D3×D513yes—
730C3×C5C2×#54811yescharacteristic, complemented, Hall
731C22×C3—52no—
732C22×C3—52no—
733C22×C3—52no—
734C22×C3C24×D511yescharacteristic
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—23no—
738C2×D3—23no—
739C2×D3—23no—
740C2×D3—52no—
741C2×D3—108no—
742C2×D3—101no—
743C2×D3—101no—
744C2×D3—103no—
745C2×D3—103no—
746C2×D3—103no—
747C2×D3—2012no—
748C2×D3D5×#4112yescomplemented
749C3×C4—23no—
750C3×C4—21no—
751C3×C4—56no—
752C3×C4—103no—
753C3×C4—101no—
754C3×C4C2×D4×D516yes—
755Dic3—23no—
756Dic3—21no—
757Dic3—103no—
758Dic3—101no—
759C2×C5—62no—
760C2×C5—123no—
761C2×C5C23×D1211yescharacteristic
762C2×C5C2×#100711yescharacteristic
763C2×C5C2×D3×#4111yescharacteristic
764D5—62no—
765D5—123no—
766D5#557614yesdirect product factor
767C23—31no—
768C23—33no—
769C23—51no—
770C23—154no—
771C23—151no—
772C23—153no—
773C23—302no—
774C23—302no—
775C23—306no—
776C23—306no—
777C23—306no—
778Q8—512no—
779Q8—66no—
780Q8—3012no—
781Q8—306no—
782Q8D5×D1214yescomplemented
783D4—66no—
784D4—66no—
785D4—306no—
786D4—3012no—
787D4—306no—
788D4—306no—
789D4—306no—
790C2×C4—33no—
791C2×C4—31no—
792C2×C4—53no—
793C2×C4—512no—
794C2×C4—51no—
795C2×C4—53no—
796C2×C4—66no—
797C2×C4—66no—
798C2×C4—106no—
799C2×C4—102no—
800C2×C4—153no—
801C2×C4—151no—
802C2×C4—306no—
803C2×C4—306no—
804C2×C4—306no—
805C2×C4—306no—
806C2×C4—302no—
807C2×C4—306no—
808C2×C4—306no—
809C2×C4—306no—
810C2×C4C22×D3×D511yescharacteristic
811C2×C4C22×D3×D513yes—
812C2×C4C22×D3×D513yes—
813C2×C3—54no—
814C2×C3C22×D4×D511yescharacteristic
815C2×C3C2×D5×#4111yescharacteristic
816C2×C3D5×2−1+411yescharacteristic
817D3—22no—
818D3—43no—
819D3—102no—
820D3—203no—
821C5C2×#557611yescharacteristic, complemented, Sylow
822C22—32no—
823C22—52no—
824C22—52no—
825C22—52no—
826C22—61no—
827C22—61no—
828C22—63no—
829C22—63no—
830C22—63no—
831C22—152no—
832C22—308no—
833C22—301no—
834C22—301no—
835C22—303no—
836C22—303no—
837C22—303no—
838C22—6012no—
839C22C23×D3×D511yescharacteristic
840C4—21no—
841C4—23no—
842C4—56no—
843C4—61no—
844C4—63no—
845C4—101no—
846C4—103no—
847C4—301no—
848C4—303no—
849C4C2×D5×D1216yes—
850C3D5×#54811yescharacteristic, complemented, Sylow
851C2—54no—
852C2—62no—
853C2—123no—
854C2—302no—
855C2—603no—
856C2C22×D5×D1211yescharacteristic
857C2D5×#100711yescharacteristic
858C2D3×D5×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5C2×#548
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. C2×D5×#239C2semidirect
2. C2×D3×Q8×D5C2semidirect
3. #11756335C2semidirect
4. C5×#5576C2semidirect
5. C3×C4×Q8×D5C2semidirect
6. #11755134C2semidirect
7. #11755131C2semidirect
8. D5×#897C2semidirect
9. D5×#895C2semidirect
10. #11753437C2semidirect
11. #11753341C2semidirect
12. D5×#875C2semidirect
13. C4×D5×D12C2semidirect
14. #11752537C2semidirect
15. #11752535C2semidirect
17. C2×#6821C22semidirect
18. C2×Q8×D15C22semidirect
19. C2×C5×#239C22semidirect
20. C2×C5×D3×Q8C22semidirect
28. C2×D15⋊Q8C22semidirect
29. C2×#6769C22semidirect
30. C2×#6768C22semidirect
31. C2×D3×Dic10C22semidirect
33. C3×C4×C5×Q8C22semidirect
34. #91786C22semidirect
35. #91784C22semidirect
36. #91764C22semidirect
37. C4×D60C22semidirect
38. C5×#897C22semidirect
39. C5×#895C22semidirect
40. C5×#875C22semidirect
41. C4×C5×D12C22semidirect
42. C3×Q8×Dic5C22semidirect
44. C3×#4033C22semidirect
46. C3×C4×Dic10C22semidirect
50. #91466C22semidirect
51. #91460C22semidirect
52. C4×#1203C22semidirect
53. C4×#1203C22semidirect
54. #91420C22semidirect
55. #91419C22semidirect
56. #91418C22semidirect
57. #91417C22semidirect
58. #91416C22semidirect
59. Dic5×D12C22semidirect
61. #91405C22semidirect
62. #91405C22semidirect
63. #91383C22semidirect
64. #91375C22semidirect
65. #91373C22semidirect
66. #91365C22semidirect
67. #91350C22semidirect
68. #91350C22semidirect
82. C4×Q8×D5D3semidirect
102. C3×Q8×D5D4semidirect
159. #5576D5direct (N × H)
183. C4×C5×Q8C2×D3semidirect
187. Q8×Dic5C2×D3semidirect
202. #4033C2×D3semidirect
215. C4×Dic10C2×D3semidirect
227. C2×D3×D5#41semidirect
228. C3×C5×Q8C2×D4semidirect
252. C3×Dic10C2×D4semidirect
268. C2×#239C2×D5semidirect
273. C2×D3×Q8C2×D5semidirect
282. C3×C4×Q8C2×D5semidirect
294. #897C2×D5semidirect
300. #895C2×D5semidirect
306. #875C2×D5semidirect
314. C4×D12C2×D5semidirect
334. Q8×D5D12semidirect
400. C2×D15C2×#41semidirect
406. C2×C5×D3C2×#41semidirect
498. C5×Q8C2×D12semidirect
531. Dic10C2×D12semidirect
569. C4×Q8D3×D5semidirect
589. C3×D5#548semidirect
604. C3×Q8D4×D5semidirect
730. C3×C5C2×#548semidirect
748. C2×D3D5×#41semidirect
766. D5#5576direct (N × H)
782. Q8D5×D12semidirect
821. C5C2×#5576semidirect
850. C3D5×#548semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#2392
C2×D3×Q8×D52
#117563352
C5×#55762
C3×C4×Q8×D52
#117551342
#117551312
D5×#8972
D5×#8952
#117534372
#117533412
D5×#8752
C4×D5×D122
#117525372
#117525352
D5×#5483
C2×#55765