Finite Group Databasebeta

← #14509973

Subgroups — #14509973

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11757054C212yesmaximal, complemented
2D15×#135C211yesmaximal, characteristic, complemented
3C5×#5769C211yesmaximal, characteristic, complemented
4C3×#66103C211yesmaximal, characteristic, complemented
5#11755327C212yesmaximal, complemented
6#11755323C212yesmaximal, complemented
7#11755316C212yesmaximal, complemented
8#11754115C212yesmaximal, complemented
9#11754105C212yesmaximal, complemented
10#11754083C214yesmaximal, complemented
11#11754067C214yesmaximal, complemented
12#11754054C212yesmaximal, complemented
13D3×D5×D8C212yesmaximal, complemented
14C2×#91256C211yesmaximal, characteristic, complemented
15#11753971C211yesmaximal, characteristic, complemented
16#11753961C211yesmaximal, characteristic, complemented
17#11753952C211yesmaximal, characteristic, complemented
18D5×#576—31nomaximal, Hall
19#41×D15C2212yescomplemented
20C5×#1009C2212yescomplemented
21C3×#4149C2212yescomplemented
22#92035C2214yescomplemented
23#92034C2214yescomplemented
24#92025—24no—
25#92025C2214yescomplemented
26D3×D4×D5—24no—
27D3×D4×D5C2214yescomplemented
28#92018—22no—
29#92018C2212yescomplemented
30#92017—22no—
31#92017C2212yescomplemented
32#92016—22no—
33#92016C2211yescharacteristic
34C2×#6777—22no—
35C2×#6777C2212yescomplemented
36C3×C5×#135C2211yescharacteristic, complemented
37#91839C2212yescomplemented
38#91808C2211yescharacteristic, complemented
39Q16×D15C2211yescharacteristic, complemented
40#91805C2212yescomplemented
41SD16×D15C2212yescomplemented
42#91801C2211yescharacteristic, complemented
43D8×D15C2211yescharacteristic, complemented
44#91793C2211yescharacteristic, complemented
45C2×C8×D15C2211yescharacteristic, complemented
46C5×#949C2212yescomplemented
47C5×#919C2212yescomplemented
48C5×#914C2214yescomplemented
49C5×D3×D8C2212yescomplemented
50C2×C5×D24C2211yescharacteristic, complemented
51C5×#901C2211yescharacteristic, complemented
52C3×#4095C2212yescomplemented
53C3×#4065C2212yescomplemented
54C3×#4060C2214yescomplemented
55C3×D5×D8C2212yescomplemented
56C2×C3×D40C2211yescharacteristic, complemented
57C3×#4047C2211yescharacteristic, complemented
58#91517C2214yescomplemented
59#91514C2214yescomplemented
60#91506C2214yescomplemented
61#91505C2214yescomplemented
62#91504C2214yescomplemented
63#91502C2214yescomplemented
64#91494C2214yescomplemented
65#91489C2214yescomplemented
66#91482C2214yescomplemented
67#91481C2214yescomplemented
68D3×#686C2214yescomplemented
69D5×#213C2214yescomplemented
70#91312C2212yescomplemented
71#91304C2212yescomplemented
72C2×#6652C2212yescomplemented
73#91292C2211yescharacteristic, complemented
74#91288C2211yescharacteristic, complemented
75#91284C2211yescharacteristic, complemented
76#91273C2212yescomplemented
77#91270C2212yescomplemented
78#91268C2212yescomplemented
79#91265C2212yescomplemented
80#91256C2212yescomplemented
81#91256C2212yescomplemented
82#91256C2212yescomplemented
83#91256C2212yescomplemented
84#91254C2214yescomplemented
85D3×D40C2212yescomplemented
86#91250C2214yescomplemented
87D5×D24C2212yescomplemented
88#91246C2212yescomplemented
89D3×C8×D5C2212yescomplemented
90D3×#576—51nomaximal, Hall
91D5×H(5,𝔽2)—32no—
92C5×#576—31no—
93#66169—32no—
94#66108—34no—
95#66108—32no—
96D5×AGL(1,ℤ/8)—32no—
97D5×AGL(1,ℤ/8)—34no—
98#66103—32no—
99#66103D311yescharacteristic, complemented
100D5×#135—32no—
101D5×#135—31no—
102#66091—32no—
103#66091—31no—
104C2×D5×D8—32no—
105C2×D5×D8—31no—
106#66086—31no—
107D5×#131—31no—
108C22×D3×D5—22no—
109C22×D3×D5—24no—
110C3×C5×#41C2312yescomplemented
111#6821C2312yescomplemented
112Q8×D15C2312yes—
113#6819—22no—
114#6819C2312yescomplemented
115D4×D15—22no—
116D4×D15C2312yes—
117#6817—22no—
118#6817C2312yescomplemented
119C2×C4×D15—22no—
120C2×C4×D15C2311yescharacteristic
121C5×#239C2314yescomplemented
122C5×D3×D4—24no—
123C5×D3×D4C2314yescomplemented
124C5×#235—22no—
125C5×#235C2311yescharacteristic
126C2×C5×D12—22no—
127C2×C5×D12C2312yescomplemented
128C3×#713C2314yescomplemented
129C3×D4×D5—24no—
130C3×D4×D5C2314yescomplemented
131C3×#709—22no—
132C3×#709C2311yescharacteristic
133C2×C3×D20—22no—
134C2×C3×D20C2312yescomplemented
135#6790—24no—
136#6790D412yes—
137D3×C22⋊D5—24no—
138D3×C22⋊D5—24no—
139D3×C22⋊D5—24no—
140D5×#67—24no—
141D5×#67—24no—
142D5×#67—24no—
143C2×#1201—22no—
144C2×#1201—24no—
145#6780—24no—
146#6780D412yes—
147#6777—24no—
148#6777—22no—
149#6777—22no—
150#6777—22no—
151#6777—22no—
152#6777—24no—
153#6777D411yescharacteristic
154#6777C2314yes—
155#6777C2314yescomplemented
156D3×D20—24no—
157D3×D20C2314yescomplemented
158D5×D12—24no—
159D5×D12C2314yescomplemented
160C4×D3×D5—24no—
161C4×D3×D5C2312yes—
162#6772—24no—
163#6772C2314yescomplemented
164#6771—24no—
165#6771C2312yes—
166D15⋊Q8D411yescharacteristic
167#6768—22no—
168#6768D411yescharacteristic
169#6766—22no—
170#6766D411yescharacteristic
171#6765—24no—
172#6765C2314yescomplemented
173C3×C5×Q16C2311yescharacteristic, complemented
174C3×C5×SD16C2312yescomplemented
175C3×C5×D8C2311yescharacteristic, complemented
176C2×C3×C5×C8C2311yescharacteristic, complemented
177#6718C2312yescomplemented
178#6717C2312yescomplemented
179#6716C2312yescomplemented
180#6715C2312yescomplemented
181C2×C3⋊#168C2311yescharacteristic, complemented
182Dic60C2311yescharacteristic, complemented
183D120C2311yescharacteristic, complemented
184#6706C2312yescomplemented
185C8×D15C2311yescharacteristic
186C8×D15C2311yescharacteristic
187C8×D15C2311yescharacteristic, complemented
188C8×D15C2311yescharacteristic, complemented
189C5×#215C2314yescomplemented
190C5×#213C2314yescomplemented
191C5×#208C2311yescharacteristic, complemented
192C5×D24C2312yescomplemented
193C5×D24C2312yescomplemented
194C5×ΓL(1,𝔽25)C2312yescomplemented
195C5×D3×C8C2312yescomplemented
196C3×#688C2314yescomplemented
197C3×#686C2314yescomplemented
198C3×#681C2311yescharacteristic, complemented
199C3×D40C2312yescomplemented
200C3×D40C2312yescomplemented
201C3×#676C2312yescomplemented
202C3×C8×D5C2312yescomplemented
203#6659C2314yescomplemented
204#6657C2314yescomplemented
205#6654C2314yescomplemented
206#6653C2314yescomplemented
207#6652C2314yescomplemented
208#6652C2314yescomplemented
209#6651C2312yescomplemented
210#6650C2312yescomplemented
211#6649C2312yescomplemented
212#6648C2312yes—
213D3×#168C2312yescomplemented
214D5×C3⋊C8C2312yescomplemented
215D3×H(5,𝔽2)—52no—
216C3×#576—51no—
217#5835—52no—
218#5774—52no—
219#5774—54no—
220D3×AGL(1,ℤ/8)—52no—
221D3×AGL(1,ℤ/8)—54no—
222#5769—52no—
223#5769D511yescharacteristic, complemented
224D3×#135—51no—
225D3×#135—52no—
226#5757—52no—
227#5757—51no—
228C2×D3×D8—52no—
229C2×D3×D8—51no—
230#5752—51no—
231D3×#131—51no—
232C5×H(5,𝔽2)—32no—
233#4149—32no—
234#4149—34no—
235#4149—62no—
236#4149C2×D312yescomplemented
237D5×#41—31no—
238D5×#41—32no—
239D5×#41—34no—
240D5×#41—62no—
241#4144—34no—
242#4144—32no—
243#4144—62no—
244#4144—64no—
245C2×D4×D5—34no—
246C2×D4×D5—32no—
247C2×D4×D5—62no—
248C2×D4×D5—64no—
249C5×AGL(1,ℤ/8)—32no—
250C5×AGL(1,ℤ/8)—34no—
251C5×#135—32no—
252C5×#135C2×D311yescharacteristic, complemented
253C2×C5×D8—32no—
254C2×C5×D8—31no—
255C5×#131—31no—
256#4096—32no—
257#4096—34no—
258#4095—34no—
259#4095C2×D312yescomplemented
260#4094—31no—
261#4078—34no—
262#4078—32no—
263C2×#686—32no—
264C2×#686—34no—
265#4065—31no—
266#4065C2×D312yescomplemented
267D5×Q16—31no—
268#4062—34no—
269#4062—32no—
270#4060—34no—
271#4060—34no—
272#4060C2×D314yescomplemented
273D5×SD16—32no—
274D5×SD16—34no—
275#4058—31no—
276#4058—32no—
277#4057—34no—
278#4057—34no—
279#4057—34no—
280D5×D8—34no—
281D5×D8—31no—
282D5×D8—34no—
283D5×D8—32no—
284D5×D8—32no—
285D5×D8—32no—
286D5×D8—32no—
287D5×D8—32no—
288D5×D8C2×D312yescomplemented
289#4054—32no—
290#4054—34no—
291#4053—31no—
292#4053—32no—
293D5×M16—31no—
294D5×M16—32no—
295#4050—31no—
296#4050—32no—
297C2×D40—32no—
298C2×D40C2×D311yescharacteristic, complemented
299#4047—32no—
300#4047C2×D311yescharacteristic, complemented
301C2×C8×D5—31no—
302C2×C8×D5—32no—
303C2×#576—151noSylow
304C22×D15—22no—
305C22×D15C2×D411yescharacteristic
306C22×C5×D3—22no—
307C22×C5×D3—24no—
308C22×C3×D5—22no—
309C22×C3×D5—24no—
310C2×D3×D5—24no—
311C2×D3×D5—24no—
312C2×D3×D5—24no—
313C2×D3×D5—24no—
314C2×D3×D5—88no—
315C2×D3×D5—84no—
316C2×D3×D5C2×D412yes—
317C3×C5×Q8C2412yes—
318C3×C5×D4—22no—
319C3×C5×D4C2412yes—
320C2×C3×C4×C5—22no—
321C2×C3×C4×C5C2411yescharacteristic
322#1220—22no—
323#1220—22no—
324#1220—22no—
325C2×Dic15—22no—
326C2×Dic15C2×D411yescharacteristic
327D60—22no—
328D60C2412yes—
329C4×D15—22no—
330C4×D15—22no—
331C4×D15—22no—
332C4×D15C2×D411yescharacteristic
333C4×D15C2×D411yescharacteristic
334C4×D15C2411yescharacteristic
335C4×D15C2411yescharacteristic
336Dic30—22no—
337Dic30C2412yes—
338C5×#67—24no—
339C5×#67C2×D412yes—
340C5×D12—24no—
341C5×D12—22no—
342C5×D12C2×D411yescharacteristic
343C5×D12C2414yes—
344C4×C5×D3—24no—
345C4×C5×D3C2412yes—
346C5×Dic6C2×D411yescharacteristic
347C3×C22⋊D5—24no—
348C3×C22⋊D5C2×D412yes—
349C3×D20—24no—
350C3×D20—22no—
351C3×D20C2×D411yescharacteristic
352C3×D20C2414yes—
353C3×C4×D5—24no—
354C3×C4×D5C2412yes—
355C3×Dic10C2×D411yescharacteristic
356#1204C2×D412yes—
357#1203—24no—
358#1203C2×D412yes—
359#1202—24no—
360#1202C2×D412yes—
361#1201—24no—
362#1201—24no—
363#1201—24no—
364#1201—24no—
365#1201C2×D412yes—
366#1200C2×D412yes—
367D3×Dic5—24no—
368D3×Dic5C2×D412yes—
369D5×Dic3—24no—
370D5×Dic3C2×D412yes—
371C3×C5×C8C2411yescharacteristic
372C3×C5×C8C2411yescharacteristic
373C3⋊#168C2411yescharacteristic
374C3⋊#168C2411yescharacteristic
375C3×#168C2412yes—
376C5×C3⋊C8C2412yes—
377C3×H(5,𝔽2)—52no—
378#1009—52no—
379#1009—54no—
380#1009—102no—
381#1009C2×D512yescomplemented
382D3×#41—51no—
383D3×#41—52no—
384D3×#41—54no—
385D3×#41—102no—
386#1004—54no—
387#1004—52no—
388#1004—102no—
389#1004—104no—
390C2×D3×D4—54no—
391C2×D3×D4—52no—
392C2×D3×D4—102no—
393C2×D3×D4—104no—
394C3×AGL(1,ℤ/8)—52no—
395C3×AGL(1,ℤ/8)—54no—
396C3×#135—52no—
397C3×#135C2×D511yescharacteristic, complemented
398C2×C3×D8—52no—
399C2×C3×D8—51no—
400C3×#131—51no—
401#950—52no—
402#950—54no—
403#949—54no—
404#949C2×D512yescomplemented
405#948—51no—
406#932—54no—
407#932—52no—
408C2×#213—52no—
409C2×#213—54no—
410#919—51no—
411#919C2×D512yescomplemented
412D3×Q16—51no—
413#916—54no—
414#916—52no—
415#914—54no—
416#914—54no—
417#914C2×D514yescomplemented
418D3×SD16—52no—
419D3×SD16—54no—
420#912—51no—
421#912—52no—
422#911—54no—
423#911—54no—
424#911—54no—
425D3×D8—54no—
426D3×D8—51no—
427D3×D8—54no—
428D3×D8—52no—
429D3×D8—52no—
430D3×D8—52no—
431D3×D8—52no—
432D3×D8—52no—
433D3×D8C2×D512yescomplemented
434#908—52no—
435#908—54no—
436#907—51no—
437#907—52no—
438D3×M16—51no—
439D3×M16—52no—
440#904—51no—
441#904—52no—
442C2×D24—52no—
443C2×D24C2×D511yescharacteristic, complemented
444#901—52no—
445#901C2×D511yescharacteristic, complemented
446C2×D3×C8—51no—
447C2×D3×C8—52no—
448C23×D5—62no—
449C23×D5—64no—
450C5×#41—31no—
451C5×#41—34no—
452C5×#41—62no—
453C5×#41C22×D312yescomplemented
454C2×C5×D4—34no—
455C2×C5×D4—32no—
456C2×C5×D4—62no—
457C2×C5×D4—64no—
458C2×C22⋊D5—64no—
459C2×C22⋊D5—62no—
460C2×C22⋊D5—64no—
461C2×C22⋊D5—64no—
462C2×C22⋊D5—64no—
463#713—31no—
464#713—32no—
465#713—62no—
466#713C22×D314yescomplemented
467Q8×D5—31no—
468Q8×D5—32no—
469#711—32no—
470#711—32no—
471#711—34no—
472#711—31no—
473#711—64no—
474#711—64no—
475#711—62no—
476#711—62no—
477D4×D5—24no—
478D4×D5—32no—
479D4×D5—32no—
480D4×D5—31no—
481D4×D5—34no—
482D4×D5—34no—
483D4×D5—34no—
484D4×D5—64no—
485D4×D5—62no—
486D4×D5—62no—
487D4×D5—64no—
488D4×D5—64no—
489D4×D5—64no—
490D4×D5—62no—
491D4×D5—64no—
492D4×D5—64no—
493D4×D5—62no—
494D4×D5—64no—
495D4×D5—62no—
496D4×D5C22×D314yescomplemented
497#709—22no—
498#709—32no—
499#709—32no—
500#709—34no—
501#709—64no—
502#709—64no—
503#709—62no—
504#709C22×D311yescharacteristic
505C2×D20—22no—
506C2×D20—34no—
507C2×D20—64no—
508C2×D20C22×D312yescomplemented
509C2×C4×D5—31no—
510C2×C4×D5—32no—
511C2×C4×D5—64no—
512C2×C4×D5—62no—
513C5×Q16C22×D311yescharacteristic, complemented
514C5×SD16—34no—
515C5×SD16C22×D312yescomplemented
516C5×D8—34no—
517C5×D8—32no—
518C5×D8—32no—
519C5×D8C22×D311yescharacteristic, complemented
520C5×M16—31no—
521C5×M16—32no—
522C2×C5×C8—32no—
523C2×C5×C8C22×D311yescharacteristic, complemented
524#689—32no—
525#688—32no—
526#688C22×D314yescomplemented
527#687—32no—
528#687—34no—
529#686—32no—
530#686—34no—
531#686—34no—
532#686—34no—
533#686C22×D314yescomplemented
534#681—32no—
535#681C22×D311yescharacteristic, complemented
536C2×#168—31no—
537C2×#168—32no—
538Dic20—31no—
539D40—34no—
540D40—31no—
541D40C22×D312yescomplemented
542D40C22×D312yescomplemented
543#677—34no—
544#677—32no—
545#676—32no—
546#676—32no—
547#676C22×D312yescomplemented
548C8×D5—32no—
549C8×D5—31no—
550C8×D5—31no—
551C8×D5—31no—
552C8×D5—31no—
553C8×D5—32no—
554C8×D5C22×D312yescomplemented
555C2×H(5,𝔽2)—152no—
556#576—31no—
557#576—51no—
558#576—151no—
559#576—151no—
560#576—152no—
561#576—152no—
562#576—154no—
563#576—152no—
564#576—152no—
565C2×AGL(1,ℤ/8)—152no—
566C2×AGL(1,ℤ/8)—154no—
567C2×#135—152no—
568C2×#135—151no—
569C22×D8—152no—
570C22×D8—151no—
571C2×#131—151no—
572C22×C3×C5—22no—
573C22×C3×C5C22×D411yescharacteristic
574C2×D15—22no—
575C2×D15—22no—
576C2×D15—44no—
577C2×D15C22×D411yescharacteristic
578C2×D15C22×D411yescharacteristic
579C2×C5×D3—24no—
580C2×C5×D3—84no—
581C2×C5×D3—82no—
582C2×C5×D3C22×D412yes—
583C2×C3×D5—24no—
584C2×C3×D5—84no—
585C2×C3×D5—82no—
586C2×C3×D5C22×D412yes—
587D3×D5—24no—
588D3×D5—48no—
589D3×D5—84no—
590D3×D5—84no—
591D3×D5—84no—
592C3×C4×C5—22no—
593C3×C4×C5C22×D411yescharacteristic
594C3×C4×C5C2511yescharacteristic
595Dic15—22no—
596Dic15C22×D411yescharacteristic
597Dic15C22×D411yescharacteristic
598C3×Dic5C22×D412yes—
599C5×Dic3C22×D412yes—
600C23×D3—102no—
601C23×D3—104no—
602C3×#41—51no—
603C3×#41—54no—
604C3×#41—102no—
605C3×#41C22×D512yescomplemented
606C2×C3×D4—54no—
607C2×C3×D4—52no—
608C2×C3×D4—102no—
609C2×C3×D4—104no—
610C2×#67—104no—
611C2×#67—102no—
612C2×#67—104no—
613C2×#67—104no—
614C2×#67—104no—
615#239—51no—
616#239—52no—
617#239—102no—
618#239C22×D514yescomplemented
619D3×Q8—51no—
620D3×Q8—52no—
621#237—52no—
622#237—52no—
623#237—54no—
624#237—51no—
625#237—104no—
626#237—104no—
627#237—102no—
628#237—102no—
629D3×D4—24no—
630D3×D4—52no—
631D3×D4—52no—
632D3×D4—51no—
633D3×D4—54no—
634D3×D4—54no—
635D3×D4—54no—
636D3×D4—104no—
637D3×D4—102no—
638D3×D4—102no—
639D3×D4—104no—
640D3×D4—104no—
641D3×D4—104no—
642D3×D4—102no—
643D3×D4—104no—
644D3×D4—104no—
645D3×D4—102no—
646D3×D4—104no—
647D3×D4—102no—
648D3×D4C22×D514yescomplemented
649#235—22no—
650#235—52no—
651#235—52no—
652#235—54no—
653#235—104no—
654#235—104no—
655#235—102no—
656#235C22×D511yescharacteristic
657C2×D12—22no—
658C2×D12—54no—
659C2×D12—104no—
660C2×D12C22×D512yescomplemented
661C2×C4×D3—51no—
662C2×C4×D3—52no—
663C2×C4×D3—104no—
664C2×C4×D3—102no—
665C3×Q16C22×D511yescharacteristic, complemented
666C3×SD16—54no—
667C3×SD16C22×D512yescomplemented
668C3×D8—54no—
669C3×D8—52no—
670C3×D8—52no—
671C3×D8C22×D511yescharacteristic, complemented
672C3×M16—51no—
673C3×M16—52no—
674C2×C3×C8—52no—
675C2×C3×C8C22×D511yescharacteristic, complemented
676#216—52no—
677#215—52no—
678#215C22×D514yescomplemented
679#214—52no—
680#214—54no—
681#213—52no—
682#213—54no—
683#213—54no—
684#213—54no—
685#213C22×D514yescomplemented
686#208—52no—
687#208C22×D511yescharacteristic, complemented
688C2×C3⋊C8—51no—
689C2×C3⋊C8—52no—
690Dic12—51no—
691D24—54no—
692D24—51no—
693D24C22×D512yescomplemented
694D24C22×D512yescomplemented
695#204—54no—
696#204—52no—
697ΓL(1,𝔽25)—52no—
698ΓL(1,𝔽25)—52no—
699ΓL(1,𝔽25)C22×D512yescomplemented
700D3×C8—52no—
701D3×C8—51no—
702D3×C8—51no—
703D3×C8—51no—
704D3×C8—51no—
705D3×C8—52no—
706D3×C8C22×D512yescomplemented
707C23×C5—64no—
708C23×C5—62no—
709C22×D5—22no—
710C22×D5—24no—
711C22×D5—31no—
712C22×D5—32no—
713C22×D5—64no—
714C22×D5—64no—
715C22×D5—64no—
716C22×D5—62no—
717C22×D5—64no—
718C22×D5—248no—
719C22×D5—244no—
720C5×Q8—31no—
721C5×Q8C23×D312yes—
722C5×D4—22no—
723C5×D4—32no—
724C5×D4—31no—
725C5×D4—34no—
726C5×D4—64no—
727C5×D4—64no—
728C5×D4—62no—
729C5×D4C23×D312yes—
730C2×C4×C5—22no—
731C2×C4×C5—32no—
732C2×C4×C5—64no—
733C2×C4×C5C23×D311yescharacteristic
734C22⋊D5—24no—
735C22⋊D5—32no—
736C22⋊D5—32no—
737C22⋊D5—64no—
738C22⋊D5—64no—
739C22⋊D5—62no—
740C22⋊D5—64no—
741C22⋊D5—62no—
742C22⋊D5—62no—
743C22⋊D5—64no—
744C22⋊D5—64no—
745C22⋊D5D3×D412yes—
746C2×Dic5—31no—
747C2×Dic5—32no—
748C2×Dic5—62no—
749C2×Dic5—64no—
750D20—24no—
751D20—22no—
752D20—32no—
753D20—32no—
754D20—62no—
755D20—64no—
756D20D3×D411yescharacteristic
757D20C23×D314yes—
758C4×D5—24no—
759C4×D5—32no—
760C4×D5—31no—
761C4×D5—31no—
762C4×D5—31no—
763C4×D5—31no—
764C4×D5—32no—
765C4×D5—62no—
766C4×D5—62no—
767C4×D5—64no—
768C4×D5—62no—
769C4×D5C23×D312yes—
770Dic10—32no—
771Dic10—32no—
772Dic10—62no—
773Dic10D3×D411yescharacteristic
774C5×C8—32no—
775C5×C8C23×D311yescharacteristic
776C5×C8C23×D311yescharacteristic
777#168—31no—
778#168—31no—
779#168C23×D312yes—
780H(5,𝔽2)—32no—
781H(5,𝔽2)—52no—
782H(5,𝔽2)—154no—
783H(5,𝔽2)—152no—
784H(5,𝔽2)—152no—
785H(5,𝔽2)—154no—
786H(5,𝔽2)—304no—
787H(5,𝔽2)—302no—
788H(5,𝔽2)—302no—
789C2×#41—151no—
790C2×#41—154no—
791C2×#41—152no—
792C2×#41—302no—
793C22×D4—154no—
794C22×D4—152no—
795C22×D4—302no—
796C22×D4—304no—
797AGL(1,ℤ/8)—32no—
798AGL(1,ℤ/8)—34no—
799AGL(1,ℤ/8)—52no—
800AGL(1,ℤ/8)—54no—
801AGL(1,ℤ/8)—154no—
802AGL(1,ℤ/8)—152no—
803AGL(1,ℤ/8)—154no—
804AGL(1,ℤ/8)—152no—
805AGL(1,ℤ/8)—154no—
806AGL(1,ℤ/8)—154no—
807AGL(1,ℤ/8)—154no—
808AGL(1,ℤ/8)—154no—
809AGL(1,ℤ/8)—154no—
810AGL(1,ℤ/8)—154no—
811#135—32no—
812#135—52no—
813#135—152no—
814#135—152no—
815#135—154no—
816#135—154no—
817#135—152no—
818#135—151no—
819#135—152no—
820#135—151no—
821#135—151no—
822#135D3×D511yescharacteristic, complemented
823C2×Q16—151no—
824C2×SD16—154no—
825C2×SD16—152no—
826C2×D8—32no—
827C2×D8—31no—
828C2×D8—52no—
829C2×D8—51no—
830C2×D8—152no—
831C2×D8—152no—
832C2×D8—152no—
833C2×D8—154no—
834C2×D8—152no—
835C2×D8—152no—
836C2×D8—152no—
837C2×D8—154no—
838C2×D8—154no—
839C2×D8—152no—
840C2×D8—151no—
841#131—31no—
842#131—51no—
843#131—152no—
844#131—152no—
845#131—151no—
846#131—151no—
847C2×M16—151no—
848C2×M16—152no—
849C22×C8—152no—
850C22×C8—151no—
851C2×C3×C5—21no—
852C2×C3×C5—42no—
853C2×C3×C5C23×D411yescharacteristic
854D15—21no—
855D15—42no—
856D15#57612yescomplemented
857C3×D5—22no—
858C3×D5—44no—
859C5×D3—22no—
860C5×D3—44no—
861C23×C3—104no—
862C23×C3—102no—
863C22×D3—22no—
864C22×D3—24no—
865C22×D3—51no—
866C22×D3—52no—
867C22×D3—104no—
868C22×D3—104no—
869C22×D3—104no—
870C22×D3—102no—
871C22×D3—104no—
872C22×D3—408no—
873C22×D3—404no—
874C3×Q8—51no—
875C3×Q8C23×D512yes—
876C3×D4—22no—
877C3×D4—52no—
878C3×D4—51no—
879C3×D4—54no—
880C3×D4—104no—
881C3×D4—104no—
882C3×D4—102no—
883C3×D4C23×D512yes—
884C2×C3×C4—22no—
885C2×C3×C4—52no—
886C2×C3×C4—104no—
887C2×C3×C4C23×D511yescharacteristic
888#67—24no—
889#67—52no—
890#67—52no—
891#67—104no—
892#67—104no—
893#67—102no—
894#67—104no—
895#67—102no—
896#67—102no—
897#67—104no—
898#67—104no—
899#67D4×D512yes—
900C2×Dic3—51no—
901C2×Dic3—52no—
902C2×Dic3—102no—
903C2×Dic3—104no—
904D12—24no—
905D12—22no—
906D12—52no—
907D12—52no—
908D12—102no—
909D12—104no—
910D12D4×D511yescharacteristic
911D12C23×D514yes—
912C4×D3—24no—
913C4×D3—52no—
914C4×D3—51no—
915C4×D3—51no—
916C4×D3—51no—
917C4×D3—51no—
918C4×D3—52no—
919C4×D3—102no—
920C4×D3—102no—
921C4×D3—104no—
922C4×D3—102no—
923C4×D3C23×D512yes—
924Dic6—52no—
925Dic6—52no—
926Dic6—102no—
927Dic6D4×D511yescharacteristic
928C3×C8—52no—
929C3×C8C23×D511yescharacteristic
930C3×C8C23×D511yescharacteristic
931C3⋊C8—51no—
932C3⋊C8—51no—
933C3⋊C8C23×D512yes—
934C22×C5—22no—
935C22×C5—32no—
936C22×C5—64no—
937C22×C5—242no—
938C22×C5—244no—
939C22×C5C2×D3×D411yescharacteristic
940C2×D5—24no—
941C2×D5—31no—
942C2×D5—31no—
943C2×D5—64no—
944C2×D5—62no—
945C2×D5—62no—
946C2×D5—84no—
947C2×D5—82no—
948C2×D5—128no—
949C2×D5—124no—
950C2×D5—244no—
951C2×D5—244no—
952C2×D5—244no—
953C2×D5C2×D3×D412yes—
954C4×C5—22no—
955C4×C5—32no—
956C4×C5C2×D3×D411yescharacteristic
957C4×C5C24×D311yescharacteristic
958Dic5—31no—
959Dic5—31no—
960Dic5—62no—
961Dic5C2×D3×D412yes—
962C24—304no—
963C24—302no—
964#41—31no—
965#41—34no—
966#41—51no—
967#41—54no—
968#41—62no—
969#41—102no—
970#41—152no—
971#41—154no—
972#41—154no—
973#41—152no—
974#41—151no—
975#41—151no—
976#41—152no—
977#41—152no—
978#41—152no—
979#41—302no—
980#41—304no—
981#41—304no—
982#41—304no—
983#41—302no—
984#41—304no—
985#41—302no—
986#41—302no—
987#41C2×D3×D512yescomplemented
988C2×Q8—151no—
989C2×Q8—152no—
990C2×D4—34no—
991C2×D4—32no—
992C2×D4—54no—
993C2×D4—52no—
994C2×D4—62no—
995C2×D4—64no—
996C2×D4—102no—
997C2×D4—104no—
998C2×D4—154no—
999C2×D4—154no—
1000C2×D4—152no—
1001C2×D4—151no—
1002C2×D4—154no—
1003C2×D4—154no—
1004C2×D4—152no—
1005C2×D4—304no—
1006C2×D4—304no—
1007C2×D4—304no—
1008C2×D4—302no—
1009C2×D4—302no—
1010C2×D4—304no—
1011C2×D4—304no—
1012C2×D4—302no—
1013C2×D4—302no—
1014C2×D4—302no—
1015C2×D4—304no—
1016C2×D4—302no—
1017C2×D4—304no—
1018C2×D4—304no—
1019C2×D4—304no—
1020C2×D4—304no—
1021C2×D4—304no—
1022C2×D4—304no—
1023C22×C4—152no—
1024C22×C4—151no—
1025C22×C4—302no—
1026C22×C4—304no—
1027Q16—152no—
1028Q16—151no—
1029Q16C2×D3×D511yescharacteristic, complemented
1030SD16—34no—
1031SD16—54no—
1032SD16—154no—
1033SD16—154no—
1034SD16—152no—
1035SD16—152no—
1036SD16—152no—
1037SD16C2×D3×D512yescomplemented
1038D8—34no—
1039D8—32no—
1040D8—32no—
1041D8—54no—
1042D8—52no—
1043D8—52no—
1044D8—154no—
1045D8—154no—
1046D8—154no—
1047D8—154no—
1048D8—152no—
1049D8—151no—
1050D8C2×D3×D511yescharacteristic, complemented
1051M16—31no—
1052M16—32no—
1053M16—51no—
1054M16—52no—
1055M16—152no—
1056M16—152no—
1057M16—152no—
1058C2×C8—32no—
1059C2×C8—52no—
1060C2×C8—152no—
1061C2×C8—152no—
1062C2×C8—152no—
1063C2×C8—151no—
1064C2×C8—151no—
1065C2×C8—151no—
1066C2×C8—151no—
1067C2×C8—151no—
1068C2×C8C2×D3×D511yescharacteristic, complemented
1069C3×C5C2×#57611yescharacteristic, complemented, Hall
1070C22×C3—22no—
1071C22×C3—52no—
1072C22×C3—104no—
1073C22×C3—402no—
1074C22×C3—404no—
1075C22×C3C2×D4×D511yescharacteristic
1076C2×D3—24no—
1077C2×D3—51no—
1078C2×D3—51no—
1079C2×D3—84no—
1080C2×D3—82no—
1081C2×D3—104no—
1082C2×D3—102no—
1083C2×D3—102no—
1084C2×D3—208no—
1085C2×D3—204no—
1086C2×D3—404no—
1087C2×D3—404no—
1088C2×D3—404no—
1089C2×D3C2×D4×D512yes—
1090C3×C4—22no—
1091C3×C4—52no—
1092C3×C4C2×D4×D511yescharacteristic
1093C3×C4C24×D511yescharacteristic
1094Dic3—51no—
1095Dic3—51no—
1096Dic3—102no—
1097Dic3C2×D4×D512yes—
1098C2×C5—21no—
1099C2×C5—42no—
1100C2×C5—62no—
1101C2×C5—124no—
1102C2×C5C22×D3×D411yescharacteristic
1103D5—22no—
1104D5—32no—
1105D5—44no—
1106D5—61no—
1107D5—122no—
1108C23—64no—
1109C23—62no—
1110C23—104no—
1111C23—102no—
1112C23—152no—
1113C23—151no—
1114C23—302no—
1115C23—304no—
1116C23—304no—
1117C23—304no—
1118C23—304no—
1119C23—1204no—
1120C23—1208no—
1121Q8—31no—
1122Q8—51no—
1123Q8—152no—
1124Q8—152no—
1125Q8—302no—
1126Q8C22×D3×D512yes—
1127D4—22no—
1128D4—32no—
1129D4—31no—
1130D4—34no—
1131D4—52no—
1132D4—51no—
1133D4—54no—
1134D4—64no—
1135D4—64no—
1136D4—62no—
1137D4—104no—
1138D4—104no—
1139D4—102no—
1140D4—152no—
1141D4—152no—
1142D4—152no—
1143D4—152no—
1144D4—302no—
1145D4—304no—
1146D4—304no—
1147D4—302no—
1148D4—304no—
1149D4—304no—
1150D4—302no—
1151D4—304no—
1152D4—304no—
1153D4—302no—
1154D4C22×D3×D512yes—
1155C2×C4—22no—
1156C2×C4—32no—
1157C2×C4—52no—
1158C2×C4—64no—
1159C2×C4—104no—
1160C2×C4—152no—
1161C2×C4—152no—
1162C2×C4—152no—
1163C2×C4—151no—
1164C2×C4—151no—
1165C2×C4—151no—
1166C2×C4—151no—
1167C2×C4—151no—
1168C2×C4—302no—
1169C2×C4—302no—
1170C2×C4—304no—
1171C2×C4—304no—
1172C2×C4—302no—
1173C2×C4—302no—
1174C2×C4C22×D3×D511yescharacteristic
1175C8—32no—
1176C8—52no—
1177C8—151no—
1178C8—151no—
1179C8C22×D3×D511yescharacteristic
1180C8C22×D3×D511yescharacteristic
1181C2×C3—21no—
1182C2×C3—42no—
1183C2×C3—102no—
1184C2×C3—204no—
1185C2×C3C22×D4×D511yescharacteristic
1186D3—22no—
1187D3—44no—
1188D3—52no—
1189D3—101no—
1190D3—202no—
1191C5D3×#57611yescharacteristic, complemented, Sylow
1192C22—22no—
1193C22—32no—
1194C22—52no—
1195C22—64no—
1196C22—104no—
1197C22—151no—
1198C22—151no—
1199C22—242no—
1200C22—244no—
1201C22—302no—
1202C22—304no—
1203C22—302no—
1204C22—402no—
1205C22—404no—
1206C22—604no—
1207C22—608no—
1208C22—1204no—
1209C22—1204no—
1210C22—1204no—
1211C22D3×D4×D511yescharacteristic
1212C4—22no—
1213C4—32no—
1214C4—52no—
1215C4—151no—
1216C4—151no—
1217C4—302no—
1218C4D3×D4×D511yescharacteristic
1219C4C23×D3×D511yescharacteristic
1220C3D5×#57611yescharacteristic, complemented, Sylow
1221C2—21no—
1222C2—42no—
1223C2—62no—
1224C2—102no—
1225C2—124no—
1226C2—152no—
1227C2—204no—
1228C2—301no—
1229C2—602no—
1230C2C2×D3×D4×D511yescharacteristic
subgroupG/H
centerC2C2×D3×D4×D5
commutator, cosocleC3×C4×C5C25
FrattiniC4C23×D3×D5
FittingC3×C5×#135C22
socleC2×C3×C5C23×D4
hypercenter#135D3×D5
hypocenterC3×C5C2×#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #11757054C2semidirect
2. D15×#135C2semidirect
3. C5×#5769C2semidirect
4. C3×#66103C2semidirect
5. #11755327C2semidirect
6. #11755323C2semidirect
7. #11755316C2semidirect
8. #11754115C2semidirect
9. #11754105C2semidirect
10. #11754083C2semidirect
11. #11754067C2semidirect
12. #11754054C2semidirect
13. D3×D5×D8C2semidirect
14. C2×#91256C2semidirect
15. #11753971C2semidirect
16. #11753961C2semidirect
17. #11753952C2semidirect
19. #41×D15C22semidirect
20. C5×#1009C22semidirect
21. C3×#4149C22semidirect
22. #92035C22semidirect
23. #92034C22semidirect
25. #92025C22semidirect
27. D3×D4×D5C22semidirect
29. #92018C22semidirect
31. #92017C22semidirect
35. C2×#6777C22semidirect
36. C3×C5×#135C22semidirect
37. #91839C22semidirect
38. #91808C22semidirect
39. Q16×D15C22semidirect
40. #91805C22semidirect
41. SD16×D15C22semidirect
42. #91801C22semidirect
43. D8×D15C22semidirect
44. #91793C22semidirect
45. C2×C8×D15C22semidirect
46. C5×#949C22semidirect
47. C5×#919C22semidirect
48. C5×#914C22semidirect
49. C5×D3×D8C22semidirect
50. C2×C5×D24C22semidirect
51. C5×#901C22semidirect
52. C3×#4095C22semidirect
53. C3×#4065C22semidirect
54. C3×#4060C22semidirect
55. C3×D5×D8C22semidirect
56. C2×C3×D40C22semidirect
57. C3×#4047C22semidirect
58. #91517C22semidirect
59. #91514C22semidirect
60. #91506C22semidirect
61. #91505C22semidirect
62. #91504C22semidirect
63. #91502C22semidirect
64. #91494C22semidirect
65. #91489C22semidirect
66. #91482C22semidirect
67. #91481C22semidirect
68. D3×#686C22semidirect
69. D5×#213C22semidirect
70. #91312C22semidirect
71. #91304C22semidirect
72. C2×#6652C22semidirect
73. #91292C22semidirect
74. #91288C22semidirect
75. #91284C22semidirect
76. #91273C22semidirect
77. #91270C22semidirect
78. #91268C22semidirect
79. #91265C22semidirect
80. #91256C22semidirect
81. #91256C22semidirect
82. #91256C22semidirect
83. #91256C22semidirect
84. #91254C22semidirect
85. D3×D40C22semidirect
86. #91250C22semidirect
87. D5×D24C22semidirect
88. #91246C22semidirect
89. D3×C8×D5C22semidirect
99. #66103D3semidirect
110. C3×C5×#41C23semidirect
111. #6821C23semidirect
114. #6819C23semidirect
118. #6817C23semidirect
121. C5×#239C23semidirect
123. C5×D3×D4C23semidirect
127. C2×C5×D12C23semidirect
128. C3×#713C23semidirect
130. C3×D4×D5C23semidirect
134. C2×C3×D20C23semidirect
155. #6777C23semidirect
157. D3×D20C23semidirect
159. D5×D12C23semidirect
163. #6772C23semidirect
172. #6765C23semidirect
173. C3×C5×Q16C23semidirect
174. C3×C5×SD16C23semidirect
175. C3×C5×D8C23semidirect
176. C2×C3×C5×C8C23semidirect
177. #6718C23semidirect
178. #6717C23semidirect
179. #6716C23semidirect
180. #6715C23semidirect
181. C2×C3⋊#168C23semidirect
182. Dic60C23semidirect
183. D120C23semidirect
184. #6706C23semidirect
187. C8×D15C23semidirect
188. C8×D15C23semidirect
189. C5×#215C23semidirect
190. C5×#213C23semidirect
191. C5×#208C23semidirect
192. C5×D24C23semidirect
193. C5×D24C23semidirect
194. C5×ΓL(1,𝔽25)C23semidirect
195. C5×D3×C8C23semidirect
196. C3×#688C23semidirect
197. C3×#686C23semidirect
198. C3×#681C23semidirect
199. C3×D40C23semidirect
200. C3×D40C23semidirect
201. C3×#676C23semidirect
202. C3×C8×D5C23semidirect
203. #6659C23semidirect
204. #6657C23semidirect
205. #6654C23semidirect
206. #6653C23semidirect
207. #6652C23semidirect
208. #6652C23semidirect
209. #6651C23semidirect
210. #6650C23semidirect
211. #6649C23semidirect
213. D3×#168C23semidirect
214. D5×C3⋊C8C23semidirect
223. #5769D5semidirect
236. #4149C2×D3semidirect
252. C5×#135C2×D3semidirect
259. #4095C2×D3semidirect
266. #4065C2×D3semidirect
272. #4060C2×D3semidirect
288. D5×D8C2×D3semidirect
298. C2×D40C2×D3semidirect
300. #4047C2×D3semidirect
381. #1009C2×D5semidirect
397. C3×#135C2×D5semidirect
404. #949C2×D5semidirect
411. #919C2×D5semidirect
417. #914C2×D5semidirect
433. D3×D8C2×D5semidirect
443. C2×D24C2×D5semidirect
445. #901C2×D5semidirect
453. C5×#41C22×D3semidirect
466. #713C22×D3semidirect
496. D4×D5C22×D3semidirect
508. C2×D20C22×D3semidirect
513. C5×Q16C22×D3semidirect
515. C5×SD16C22×D3semidirect
519. C5×D8C22×D3semidirect
523. C2×C5×C8C22×D3semidirect
526. #688C22×D3semidirect
533. #686C22×D3semidirect
535. #681C22×D3semidirect
541. D40C22×D3semidirect
542. D40C22×D3semidirect
547. #676C22×D3semidirect
554. C8×D5C22×D3semidirect
605. C3×#41C22×D5semidirect
618. #239C22×D5semidirect
648. D3×D4C22×D5semidirect
660. C2×D12C22×D5semidirect
665. C3×Q16C22×D5semidirect
667. C3×SD16C22×D5semidirect
671. C3×D8C22×D5semidirect
675. C2×C3×C8C22×D5semidirect
678. #215C22×D5semidirect
685. #213C22×D5semidirect
687. #208C22×D5semidirect
693. D24C22×D5semidirect
694. D24C22×D5semidirect
699. ΓL(1,𝔽25)C22×D5semidirect
706. D3×C8C22×D5semidirect
822. #135D3×D5semidirect
856. D15#576semidirect
987. #41C2×D3×D5semidirect
1029. Q16C2×D3×D5semidirect
1037. SD16C2×D3×D5semidirect
1050. D8C2×D3×D5semidirect
1068. C2×C8C2×D3×D5semidirect
1069. C3×C5C2×#576semidirect
1191. C5D3×#576semidirect
1220. C3D5×#576semidirect

Maximal subgroups

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

subgroupindex
#117570542
D15×#1352
C5×#57692
C3×#661032
#117553272
#117553232
#117553162
#117541152
#117541052
#117540832
#117540672
#117540542
D3×D5×D82
C2×#912562
#117539712
#117539612
#117539522
D5×#5763
D3×#5765