Finite Group Databasebeta

← #14483214

Subgroups — #14483214

Order 1920.

3296 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92034C211yesmaximal, characteristic, complemented
2C2×D3×#713C211yesmaximal, characteristic, complemented
3#11756335C211yesmaximal, characteristic, complemented
4C5×#5576C211yesmaximal, characteristic, complemented
5C3×C4×#713C211yesmaximal, characteristic, complemented
6#11755245C211yesmaximal, characteristic, complemented
7Q8×#1203C211yesmaximal, characteristic, complemented
8#11753874C213yesmaximal, complemented
9#11753873C213yesmaximal, complemented
10#11753869C213yesmaximal, complemented
11#11753436C213yesmaximal, complemented
12#11752738C213yesmaximal, complemented
13#11752736C213yesmaximal, complemented
14C4×D5×D12C213yesmaximal, complemented
15#11752673C213yesmaximal, complemented
16#10618611—31nomaximal, Hall
17C2×#6821C2211yescharacteristic, complemented
18C2×Q8×D15C2211yescharacteristic, complemented
19C2×C5×#239C2211yescharacteristic, complemented
20C2×C5×D3×Q8C2211yescharacteristic, complemented
21C2×C3×#713C2211yescharacteristic
22#92034—28no—
23D3×#713—28no—
24C2×#6777C2213yescomplemented
25C2×D3×D20C2213yescomplemented
26C2×D5×D12C2213yes—
27C2×C4×D3×D5C2213yescomplemented
28C2×C4×D3×D5C2213yescomplemented
29C2×#6773C2213yescomplemented
30C2×#6772C2213yescomplemented
31C2×#6766C2213yescomplemented
32C2×#6765C2213yescomplemented
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×#4039C2213yescomplemented
44C3×#4038C2213yescomplemented
45C3×C4×D20C2213yescomplemented
46C3×C42×D5C2213yescomplemented
47#91476C2216yescomplemented
48#91475C2216yescomplemented
49D5×(C2×D3)⋊C4C2213yescomplemented
50D5×(C2×D3)⋊C4C2213yescomplemented
51#91466C2213yescomplemented
52#91460C2213yescomplemented
53#91451C2213yescomplemented
54#91448C2216yescomplemented
55#91448C2216yescomplemented
56C4×#1203C2213yes—
57C4×#1203C2213yescomplemented
58#91418C2213yescomplemented
59Dic5×D12C2213yescomplemented
60#91414C2216yescomplemented
61#91413C2216yescomplemented
62D5×C4⋊Dic3C2213yescomplemented
63#91405C2211yescharacteristic
64#91405C2213yescomplemented
65#91405C2216yescomplemented
66#91383C2213yescomplemented
67#91376C2213yescomplemented
68#91365C2213yescomplemented
69#41×D12—51nomaximal, Hall
70C2×D5×#41—31no—
71C22×#713—31no—
72C5×#548—31no—
73#66168—31no—
74Q8×C22⋊D5—31no—
75#66010—33no—
76#66002—33no—
77#65965—33no—
78#65961—33no—
79#65943—33no—
80#65940—33no—
81#65910—31no—
82C4×#713D311yescharacteristic, complemented
83#65884—33no—
84C4×D4×D5—33no—
85C22×D3×D5C2313yes—
86C22×D3×D5C2313yes—
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×#713D418yescomplemented
103C2×C3×D20C2313yes—
104C2×C3×C4×D5C2313yes—
105C2×C3×C4×D5C2313yes—
106C2×C3×C4×D5C2313yes—
107C2×#1203C2313yes—
108C2×#1203C2316yes—
109C2×#1203C2311yescharacteristic
110C2×#1202C2316yes—
111C2×#1201C2316yes—
112C2×#1200C2311yescharacteristic
113C2×#1200C2313yes—
114C2×D3×Dic5C2311yescharacteristic
115C2×D3×Dic5C2313yes—
116C2×D5×Dic3C2313yes—
117C2×D5×Dic3C2313yes—
118#6777—212no—
119D3×D20—212no—
120D5×D12—212no—
121C4×D3×D5—212no—
122C4×D3×D5—212no—
123#6773—212no—
124#6772—212no—
125#6766—212no—
126#6765—212no—
127C3×C5×C4⋊C4C2313yes—
128C3×C42×C5C2313yes—
129#6714C2311yescharacteristic
130#6714C2316yes—
131#6714C2313yes—
132C4⋊Dic15C2313yes—
133C5×(C2×D3)⋊C4C2311yescharacteristic
134C5×(C2×D3)⋊C4C2316yes—
135C5×(C2×D3)⋊C4C2313yes—
136C5×C4⋊Dic3C2313yes—
137C3×#685C2316yes—
138C3×C4⋊Dic5C2313yes—
139C3×C4×Dic5C2311yescharacteristic
140C3×C4×Dic5C2313yes—
141C3×C4×Dic5C2313yes—
142#6668C2311yescharacteristic
143#6668C2313yes—
144#6668C2316yes—
145#6667C2313yes—
146#6667C2313yes—
147(C2×D3)⋊Dic5C2313yes—
148(C2×D3)⋊Dic5C2313yes—
149C2×D3×#41—51no—
150C2×D3×#41—51no—
151C3×C4×#41—51no—
152#5577—51no—
153#5576—51no—
154#5576D511yescharacteristic, complemented
155Q8×D12—51no—
156#5555—53no—
157#5554—53no—
158#5554—53no—
159D4×D12—53no—
160#5524—53no—
161#5524—53no—
162#5477—53no—
163C2×C4×D12—53no—
164C2×C5×#41—31no—
165C22×C5×Q8—31no—
166D5×#41—68no—
167C2×#713—31no—
168C2×#713—33no—
169C2×#713—33no—
170C2×#713—68no—
171C2×#713C2×D311yescharacteristic
172C2×Q8×D5—31no—
173C2×#711—33no—
174C2×D4×D5—33no—
175C2×D4×D5—33no—
176C2×#709—33no—
177C22×D20—33no—
178C22×C4×D5—33no—
179C22×C4×D5—33no—
180C5×#124—33no—
181C5×C22⋊Q8—33no—
182C5×#121—33no—
183C4×C5×Q8C2×D311yescharacteristic, complemented
184C4×C5×D4—33no—
185#4092—33no—
186Q8×Dic5C2×D311yescharacteristic, complemented
187#4090—33no—
188#4086—33no—
189#4084—33no—
190#4083—36no—
191D4×Dic5—33no—
192#4076—33no—
193C4×C22⋊D5—33no—
194C4×C22⋊D5—33no—
195#4070—33no—
196#4043—33no—
197#4041—33no—
198#4040—36no—
199#4039—33no—
200#4039C2×D313yescomplemented
201#4038C2×D313yescomplemented
202D5×C4⋊C4—33no—
203#4030—36no—
204#4030—36no—
205#4029—36no—
206#4028—36no—
207#4027—31no—
208#4027—33no—
209#4027—36no—
210D5×C22⋊C4—33no—
211D5×C22⋊C4—33no—
212#4021—33no—
213C4×D20—33no—
214C4×D20C2×D313yescomplemented
215C42×D5C2×D313yescomplemented
216D4×#41—151noSylow
217C22×D15C2413yes—
218C22×D15C2411yescharacteristic
219C22×C5×D3C2413yes—
220C22×C5×D3C2411yescharacteristic
221C22×C3×D5C2413yes—
222C2×D3×D5—26no—
223C2×D3×D5—26no—
224C2×D3×D5—26no—
225C2×D3×D5—26no—
226C2×D3×D5—43no—
227C2×D3×D5—43no—
228C3×C5×Q8C2×D414yescomplemented
229C2×C3×C4×C5C2413yes—
230C2×C3×C4×C5C2411yescharacteristic
231C2×C3×C4×C5C2413yes—
232C2×Dic15C2411yescharacteristic
233C2×Dic15C2413yes—
234D60—26no—
235D60—26no—
236C4×D15—26no—
237C4×D15—26no—
238Dic30—26no—
239C2×C5×Dic3C2411yescharacteristic
240C2×C5×Dic3C2413yes—
241C5×D12—26no—
242C5×D12—26no—
243C4×C5×D3—26no—
244C4×C5×D3—26no—
245C5×Dic6—26no—
246C2×C3×Dic5C2413yes—
247C2×C3×Dic5C2411yescharacteristic
248C2×C3×Dic5C2411yescharacteristic
249C3×D20C2×D4112yescomplemented
250C3×C4×D5—26no—
251C3×C4×D5—43no—
252C3×C4×D5C2×D4112yescomplemented
253#1203—26no—
254#1203—46no—
255#1203#4114yescomplemented
256#1202—212no—
257#1201—212no—
258#1200—26no—
259#1200—22no—
260D3×Dic5—26no—
261D3×Dic5—22no—
262D5×Dic3—26no—
263D5×Dic3—26no—
264C2×C3×#41—51no—
265D3×#41—108no—
266D3×#41—108no—
267C2×#239—51no—
268C2×#239C2×D511yescharacteristic, complemented
269C2×D3×Q8—51no—
270C2×D3×Q8C2×D511yescharacteristic, complemented
271C2×#237—53no—
272C2×#237—53no—
273C2×D3×D4—53no—
274C2×D3×D4—53no—
275C2×#235—53no—
276C2×#235—53no—
277C22×D12—53no—
278C22×C4×D3—53no—
279C22×C4×D3—53no—
280C3×C4×Q8—51no—
281C3×C4×Q8C2×D511yescharacteristic, complemented
282C3×C4×D4—53no—
283C3×C4×D4—53no—
284C3×#117—53no—
285C2×C3×C42—53no—
286#930—56no—
287#930—56no—
288C2×(C2×D3)⋊C4—53no—
289C2×(C2×D3)⋊C4—53no—
290C2×C4⋊Dic3—53no—
291#897—53no—
292#897—53no—
293#897—53no—
294#897C2×D513yescomplemented
295#895—53no—
296#895—53no—
297#895—53no—
298#895C2×D513yescomplemented
299#886—56no—
300#886—56no—
301#882—56no—
302#882—56no—
303#875—53no—
304#875C2×D513yescomplemented
305#874—53no—
306C4×D12—53no—
307C4×D12—53no—
308C4×D12—53no—
309C4×D12—53no—
310C4×D12—51no—
311C4×D12—53no—
312C4×D12—56no—
313C4×D12—53no—
314C4×D12C2×D513yescomplemented
315#869—53no—
316C23×D5—33no—
317C23×D5—33no—
318C5×#41—64no—
319C2×C5×Q8—33no—
320C2×C5×Q8—64no—
321C2×C5×Q8C22×D311yescharacteristic
322C2×C5×D4—33no—
323C2×C5×D4—33no—
324C22×C4×C5—33no—
325C22×C4×C5—33no—
326C2×C22⋊D5—36no—
327C2×C22⋊D5—31no—
328C2×C22⋊D5—33no—
329C2×C22⋊D5—36no—
330C22×Dic5—31no—
331C22×Dic5—33no—
332#713—64no—
333#713—612no—
334#713—612no—
335#713D1218yescomplemented
336Q8×D5—64no—
337#711—612no—
338D4×D5—612no—
339D4×D5—612no—
340#709—612no—
341C2×D20—36no—
342C2×D20—33no—
343C2×D20—33no—
344C2×D20—612no—
345C2×D20C22×D313yes—
346C2×C4×D5—33no—
347C2×C4×D5—33no—
348C2×C4×D5—33no—
349C2×C4×D5—33no—
350C2×C4×D5—31no—
351C2×C4×D5—33no—
352C2×C4×D5—612no—
353C2×C4×D5—612no—
354C2×C4×D5C22×D313yes—
355C2×C4×D5C22×D313yes—
356C2×C4×D5C22×D313yes—
357C2×Dic10—33no—
358C5×C4⋊C4—33no—
359C5×C4⋊C4C22×D313yes—
360C5×C22⋊C4—31no—
361C5×C22⋊C4—33no—
362C5×C22⋊C4—36no—
363C42×C5C22×D313yes—
364C22⋊Dic5—33no—
365C22⋊Dic5—33no—
366#685—31no—
367#685—33no—
368#685—36no—
369#685—33no—
370#685—33no—
371#685C22×D316yes—
372C4⋊Dic5—33no—
373C4⋊Dic5C22×D313yes—
374#683—36no—
375#683—33no—
376#683—31no—
377C4×Dic5C22×D311yescharacteristic
378C4×Dic5C22×D313yes—
379C4×Dic5C22×D313yes—
380C22×#41—151no—
381C22×#41—151no—
382#550—151no—
383D4×Q8—151no—
384#548—31no—
385#548—151no—
386#547—153no—
387#546—153no—
388#546—153no—
389D42—153no—
390#532—153no—
391#525—153no—
392#525—153no—
393C4×#41—51no—
394C2×C4×D4—153no—
395C22×C3×C5C2511yescharacteristic
396C2×D15—21no—
397C2×D15—21no—
398C2×D15—23no—
399C2×D15—23no—
400C2×D15—23no—
401C2×D15C2×#4112yescomplemented
402C2×C5×D3—21no—
403C2×C5×D3—21no—
404C2×C5×D3—23no—
405C2×C5×D3—23no—
406C2×C5×D3—23no—
407C2×C5×D3C2×#4112yescomplemented
408C2×C3×D5—23no—
409C2×C3×D5—23no—
410C2×C3×D5C22×D416yes—
411D3×D5—412no—
412D3×D5—412no—
413C3×C4×C5—23no—
414C3×C4×C5—21no—
415C3×C4×C5C22×D416yes—
416Dic15—21no—
417Dic15—23no—
418C3×Dic5—23no—
419C3×Dic5C22×D412yes—
420C3×Dic5C2×#4112yescomplemented
421C5×Dic3—21no—
422C5×Dic3—23no—
423C23×D3—53no—
424C23×D3—53no—
425C3×#41—58no—
426C2×C3×Q8C22×D511yescharacteristic
427C2×C3×D4—53no—
428C22×C3×C4—53no—
429C22×C3×C4—53no—
430C22×C3×C4—53no—
431C2×#67—56no—
432C2×#67—56no—
433C22×Dic3—53no—
434C22×Dic3—53no—
435#239—24no—
436#239—104no—
437D3×Q8—24no—
438D3×Q8—104no—
439#237—1012no—
440#237—1012no—
441D3×D4—1012no—
442D3×D4—1012no—
443#235—1012no—
444#235—1012no—
445C2×D12—51no—
446C2×D12—53no—
447C2×D12—53no—
448C2×D12—53no—
449C2×D12—56no—
450C2×D12—1012no—
451C2×D12C22×D513yes—
452C2×D12C22×D513yes—
453C2×C4×D3—51no—
454C2×C4×D3—53no—
455C2×C4×D3—53no—
456C2×C4×D3—53no—
457C2×C4×D3—51no—
458C2×C4×D3—53no—
459C2×C4×D3—1012no—
460C2×C4×D3—1012no—
461C2×C4×D3C22×D513yes—
462C2×C4×D3C22×D513yes—
463C2×Dic6—53no—
464C2×Dic6C22×D513yes—
465C3×C4⋊C4—53no—
466C3×C4⋊C4C22×D513yes—
467C3×C22⋊C4—56no—
468C3×C42—53no—
469C3×C42—51no—
470C3×C42—53no—
471C3×C42C22×D513yes—
472(C2×D3)⋊C4—53no—
473(C2×D3)⋊C4—53no—
474(C2×D3)⋊C4—51no—
475(C2×D3)⋊C4—53no—
476(C2×D3)⋊C4—56no—
477(C2×D3)⋊C4—53no—
478(C2×D3)⋊C4—53no—
479(C2×D3)⋊C4C22×D511yescharacteristic
480(C2×D3)⋊C4C22×D513yes—
481(C2×D3)⋊C4C22×D516yes—
482C4⋊Dic3—53no—
483C4⋊Dic3—53no—
484C4⋊Dic3—56no—
485C4⋊Dic3—51no—
486C4⋊Dic3C22×D513yes—
487C23×C5—31no—
488C23×C5—33no—
489C22×D5—31no—
490C22×D5—33no—
491C22×D5—66no—
492C22×D5—66no—
493C22×D5—66no—
494C22×D5—66no—
495C22×D5—123no—
496C22×D5—123no—
497C22×D5C23×D313yes—
498C5×Q8—66no—
499C5×Q8C2×D1214yescomplemented
500C5×D4—66no—
501C5×D4—66no—
502C2×C4×C5—33no—
503C2×C4×C5—31no—
504C2×C4×C5—66no—
505C2×C4×C5—66no—
506C2×C4×C5C23×D313yes—
507C2×C4×C5C23×D311yescharacteristic
508C2×C4×C5C23×D313yes—
509C22⋊D5—34no—
510C22⋊D5—612no—
511C22⋊D5—66no—
512C22⋊D5—126no—
513C2×Dic5—33no—
514C2×Dic5—31no—
515C2×Dic5—62no—
516C2×Dic5—66no—
517C2×Dic5C23×D313yes—
518C2×Dic5C23×D311yescharacteristic
519C2×Dic5C23×D311yescharacteristic
520D20—66no—
521D20—612no—
522D20—66no—
523D20C2×D12112yescomplemented
524C4×D5—26no—
525C4×D5—43no—
526C4×D5—66no—
527C4×D5—66no—
528C4×D5—66no—
529C4×D5—66no—
530C4×D5—62no—
531C4×D5—66no—
532C4×D5C2×D12112yescomplemented
533Dic10—66no—
534C2×#41—31no—
535C2×#41—51no—
536C2×#41—153no—
537C2×#41—153no—
538C2×#41—153no—
539C2×#41—153no—
540C2×#41—151no—
541C2×#41—308no—
542C2×#41—308no—
543C22×Q8—31no—
544C22×Q8—151no—
545C22×D4—153no—
546C22×D4—153no—
547C22×D4—153no—
548C23×C4—153no—
549C23×C4—153no—
550C4⋊Q8—153no—
551#127—153no—
552#124—33no—
553#124—153no—
554#123—156no—
555#123—156no—
556C22⋊Q8—33no—
557C22⋊Q8—153no—
558C22⋊Q8—153no—
559C22⋊Q8—153no—
560#121—33no—
561#121—156no—
562#121—156no—
563#121—153no—
564#121—153no—
565#121—153no—
566#120—156no—
567#120—156no—
568C4×Q8—51no—
569C4×Q8D3×D511yescharacteristic, complemented
570C4×D4—33no—
571C4×D4—53no—
572C4×D4—53no—
573C4×D4—151no—
574C4×D4—153no—
575C4×D4—156no—
576C4×D4—153no—
577C4×D4—153no—
578C4×D4—153no—
579C4×D4—153no—
580C4×D4—153no—
581#117—53no—
582C2×C4⋊C4—153no—
583C2×C22⋊C4—153no—
584C2×C22⋊C4—153no—
585C2×C42—53no—
586C2×C3×C5C23×D411yescharacteristic
587C2×C3×C5C22×#4111yescharacteristic
588C2×C3×C5#58511yescharacteristic
589D15—22no—
590D15—43no—
591C3×D5—26no—
592C5×D3—22no—
593C5×D3—43no—
594C23×C3—53no—
595C22×D3—51no—
596C22×D3—53no—
597C22×D3—106no—
598C22×D3—106no—
599C22×D3—106no—
600C22×D3—106no—
601C22×D3—203no—
602C22×D3—203no—
603C22×D3C23×D513yes—
604C22×D3C23×D511yescharacteristic
605C3×Q8D4×D514yescomplemented
606C3×D4—512no—
607C2×C3×C4—51no—
608C2×C3×C4—51no—
609C2×C3×C4—512no—
610C2×C3×C4—53no—
611C2×C3×C4—106no—
612C2×C3×C4—203no—
613C2×C3×C4C23×D513yes—
614C2×C3×C4C23×D511yescharacteristic
615C2×C3×C4C23×D513yes—
616#67—1012no—
617#67—1012no—
618C2×Dic3—53no—
619C2×Dic3—51no—
620C2×Dic3—106no—
621C2×Dic3—106no—
622C2×Dic3C23×D513yes—
623C2×Dic3C23×D511yescharacteristic
624D12—26no—
625D12—26no—
626D12—54no—
627D12—106no—
628D12—106no—
629D12—106no—
630D12—206no—
631C4×D3—26no—
632C4×D3—26no—
633C4×D3—102no—
634C4×D3—106no—
635C4×D3—102no—
636C4×D3—106no—
637C4×D3—106no—
638C4×D3—106no—
639Dic6—26no—
640Dic6—106no—
641C22×C5—32no—
642C22×C5—61no—
643C22×C5—61no—
644C22×C5—63no—
645C22×C5—63no—
646C22×C5—63no—
647C22×C5C24×D311yescharacteristic
648C2×D5—23no—
649C2×D5—23no—
650C2×D5—32no—
651C2×D5—61no—
652C2×D5—61no—
653C2×D5—63no—
654C2×D5—63no—
655C2×D5—63no—
656C2×D5—1212no—
657C2×D5—1212no—
658C2×D5C22×D1216yes—
659C4×C5—23no—
660C4×C5—21no—
661C4×C5—61no—
662C4×C5—63no—
663C4×C5C22×D1216yes—
664Dic5—23no—
665Dic5—63no—
666Dic5—61no—
667Dic5C22×D1212yes—
668Dic5D3×#4112yescomplemented
669C24—153no—
670C24—153no—
671#41—58no—
672#41—64no—
673#41—3012no—
674#41—3012no—
675#41—3012no—
676#41—3012no—
677#41—304no—
678C2×Q8—33no—
679C2×Q8—64no—
680C2×Q8—153no—
681C2×Q8—304no—
682C2×Q8C2×D3×D511yescharacteristic
683C2×D4—33no—
684C2×D4—33no—
685C2×D4—53no—
686C2×D4—156no—
687C2×D4—151no—
688C2×D4—153no—
689C2×D4—156no—
690C2×D4—156no—
691C2×D4—153no—
692C2×D4—153no—
693C2×D4—3012no—
694C2×D4—3012no—
695C2×D4—3012no—
696C22×C4—33no—
697C22×C4—33no—
698C22×C4—53no—
699C22×C4—53no—
700C22×C4—53no—
701C22×C4—151no—
702C22×C4—153no—
703C22×C4—153no—
704C22×C4—153no—
705C22×C4—151no—
706C22×C4—153no—
707C22×C4—153no—
708C22×C4—153no—
709C22×C4—3012no—
710C22×C4—3012no—
711C4⋊C4—33no—
712C4⋊C4—53no—
713C4⋊C4—151no—
714C4⋊C4—153no—
715C4⋊C4—156no—
716C4⋊C4—153no—
717C4⋊C4C2×D3×D513yes—
718C22⋊C4—31no—
719C22⋊C4—33no—
720C22⋊C4—36no—
721C22⋊C4—56no—
722C22⋊C4—153no—
723C22⋊C4—153no—
724C22⋊C4—153no—
725C22⋊C4—153no—
726C22⋊C4—151no—
727C22⋊C4—153no—
728C22⋊C4—156no—
729C42—51no—
730C42—53no—
731C42—53no—
732C42C2×D3×D513yes—
733C3×C5D4×#4111yescharacteristic, complemented, Hall
734C22×C3—56no—
735C22×C3—103no—
736C22×C3—103no—
737C22×C3C24×D511yescharacteristic
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—23no—
741C2×D3—23no—
742C2×D3—23no—
743C2×D3—52no—
744C2×D3—101no—
745C2×D3—101no—
746C2×D3—103no—
747C2×D3—103no—
748C2×D3—103no—
749C2×D3—2012no—
750C2×D3—2012no—
751C2×D3D5×#4112yescomplemented
752C3×C4—23no—
753C3×C4—21no—
754C3×C4—52no—
755C3×C4—52no—
756C3×C4—103no—
757C3×C4C2×D4×D516yes—
758Dic3—23no—
759Dic3—21no—
760Dic3—103no—
761Dic3—101no—
762C2×C5—62no—
763C2×C5—123no—
764C2×C5C23×D1211yescharacteristic
765C2×C5C2×D3×#4111yescharacteristic
766C2×C5#596411yescharacteristic
767D5—26no—
768D5—62no—
769D5—123no—
770C23—31no—
771C23—33no—
772C23—53no—
773C23—151no—
774C23—153no—
775C23—306no—
776C23—306no—
777C23—306no—
778C23—306no—
779C23—603no—
780C23—603no—
781Q8—66no—
782Q8—306no—
783Q8D5×D1214yescomplemented
784D4—512no—
785D4—66no—
786D4—66no—
787D4—154no—
788D4—306no—
789D4—306no—
790D4—3012no—
791D4—3012no—
792D4—306no—
793D4—606no—
794C2×C4—33no—
795C2×C4—31no—
796C2×C4—51no—
797C2×C4—51no—
798C2×C4—512no—
799C2×C4—53no—
800C2×C4—66no—
801C2×C4—66no—
802C2×C4—106no—
803C2×C4—151no—
804C2×C4—153no—
805C2×C4—203no—
806C2×C4—302no—
807C2×C4—306no—
808C2×C4—302no—
809C2×C4—306no—
810C2×C4—306no—
811C2×C4—306no—
812C2×C4—306no—
813C2×C4—306no—
814C2×C4C22×D3×D511yescharacteristic
815C2×C4C22×D3×D513yes—
816C2×C4C22×D3×D513yes—
817C2×C3—106no—
818C2×C3C22×D4×D511yescharacteristic
819C2×C3C2×D5×#4111yescharacteristic
820C2×C3#6628711yescharacteristic
821D3—22no—
822D3—43no—
823D3—102no—
824D3—203no—
825C5#41×D1211yescharacteristic, complemented, Sylow
826C22—32no—
827C22—56no—
828C22—61no—
829C22—61no—
830C22—63no—
831C22—63no—
832C22—63no—
833C22—103no—
834C22—103no—
835C22—152no—
836C22—301no—
837C22—301no—
838C22—303no—
839C22—303no—
840C22—303no—
841C22—6012no—
842C22—6012no—
843C22C23×D3×D511yescharacteristic
844C4—21no—
845C4—23no—
846C4—52no—
847C4—52no—
848C4—61no—
849C4—63no—
850C4—103no—
851C4—301no—
852C4—303no—
853C4C2×D5×D1216yes—
854C3#1061861111yescharacteristic, complemented, Sylow
855C2—62no—
856C2—106no—
857C2—123no—
858C2—302no—
859C2—603no—
860C2C22×D5×D1211yescharacteristic
861C2#1175704811yescharacteristic
862C2D3×D5×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5D4×#41
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×#92034C2semidirect
2. C2×D3×#713C2semidirect
3. #11756335C2semidirect
4. C5×#5576C2semidirect
5. C3×C4×#713C2semidirect
6. #11755245C2semidirect
7. Q8×#1203C2semidirect
8. #11753874C2semidirect
9. #11753873C2semidirect
10. #11753869C2semidirect
11. #11753436C2semidirect
12. #11752738C2semidirect
13. #11752736C2semidirect
14. C4×D5×D12C2semidirect
15. #11752673C2semidirect
17. C2×#6821C22semidirect
18. C2×Q8×D15C22semidirect
19. C2×C5×#239C22semidirect
20. C2×C5×D3×Q8C22semidirect
24. C2×#6777C22semidirect
25. C2×D3×D20C22semidirect
27. C2×C4×D3×D5C22semidirect
28. C2×C4×D3×D5C22semidirect
29. C2×#6773C22semidirect
30. C2×#6772C22semidirect
31. C2×#6766C22semidirect
32. C2×#6765C22semidirect
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
43. C3×#4039C22semidirect
44. C3×#4038C22semidirect
45. C3×C4×D20C22semidirect
46. C3×C42×D5C22semidirect
47. #91476C22semidirect
48. #91475C22semidirect
49. D5×(C2×D3)⋊C4C22semidirect
50. D5×(C2×D3)⋊C4C22semidirect
51. #91466C22semidirect
52. #91460C22semidirect
53. #91451C22semidirect
54. #91448C22semidirect
55. #91448C22semidirect
57. C4×#1203C22semidirect
58. #91418C22semidirect
59. Dic5×D12C22semidirect
60. #91414C22semidirect
61. #91413C22semidirect
62. D5×C4⋊Dic3C22semidirect
64. #91405C22semidirect
65. #91405C22semidirect
66. #91383C22semidirect
67. #91376C22semidirect
68. #91365C22semidirect
82. C4×#713D3semidirect
102. C3×#713D4semidirect
154. #5576D5semidirect
183. C4×C5×Q8C2×D3semidirect
186. Q8×Dic5C2×D3semidirect
200. #4039C2×D3semidirect
201. #4038C2×D3semidirect
214. C4×D20C2×D3semidirect
215. C42×D5C2×D3semidirect
228. C3×C5×Q8C2×D4semidirect
249. C3×D20C2×D4semidirect
252. C3×C4×D5C2×D4semidirect
255. #1203#41semidirect
268. C2×#239C2×D5semidirect
270. C2×D3×Q8C2×D5semidirect
281. C3×C4×Q8C2×D5semidirect
294. #897C2×D5semidirect
298. #895C2×D5semidirect
304. #875C2×D5semidirect
314. C4×D12C2×D5semidirect
335. #713D12semidirect
401. C2×D15C2×#41semidirect
407. C2×C5×D3C2×#41semidirect
420. C3×Dic5C2×#41semidirect
499. C5×Q8C2×D12semidirect
523. D20C2×D12semidirect
532. C4×D5C2×D12semidirect
569. C4×Q8D3×D5semidirect
605. C3×Q8D4×D5semidirect
668. Dic5D3×#41semidirect
733. C3×C5D4×#41semidirect
751. C2×D3D5×#41semidirect
783. Q8D5×D12semidirect
825. C5#41×D12semidirect
854. C3#10618611semidirect

Maximal subgroups

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

subgroupindex
C2×#920342
C2×D3×#7132
#117563352
C5×#55762
C3×C4×#7132
#117552452
Q8×#12032
#117538742
#117538732
#117538692
#117534362
#117527382
#117527362
C4×D5×D122
#117526732
#106186113
#41×D125