Finite Group Databasebeta

← #14509976

Subgroups — #14509976

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2#11757054C211yesmaximal, characteristic, complemented
3C5×#5835C211yesmaximal, characteristic, complemented
4C3×#66169C211yesmaximal, characteristic, complemented
5#11755332C213yesmaximal, complemented
6#11755330C213yesmaximal, complemented
7#11755328C213yesmaximal, complemented
8#11755327C213yesmaximal, complemented
9#11755311C211yesmaximal, characteristic, complemented
10#11755305C211yesmaximal, characteristic, complemented
11#11755299C211yesmaximal, characteristic, complemented
12#11754704C213yesmaximal, complemented
13#11754703C213yesmaximal, complemented
14#11754701C213yesmaximal, complemented
15C2×#91481C213yesmaximal, complemented
16D5×#576—31nomaximal, Hall
17C3×C5×H(5,𝔽2)C2211yescharacteristic, complemented
18#92100—21no—
19#92100C2213yescomplemented
20#92100C2211yescharacteristic, complemented
21#41×D15—21no—
22#41×D15C2211yescharacteristic
23#41×D15C2213yescomplemented
24#92095—23no—
25#92095C2213yescomplemented
26C2×D4×D15—23no—
27C2×D4×D15C2213yescomplemented
28C5×#1009C2211yescharacteristic, complemented
29C3×#4149C2211yescharacteristic, complemented
30#92035—21no—
31#92034—21no—
32#92025—23no—
33D3×D4×D5—23no—
34#92018C2213yescomplemented
35#92017C2213yescomplemented
36#92016C2213yescomplemented
37C2×#6777C2213yescomplemented
38C5×#950C2213yescomplemented
39C5×#949C2213yescomplemented
40C5×#948C2211yescharacteristic, complemented
41C5×#932C2213yescomplemented
42C2×C5×#213C2213yescomplemented
43C3×#4096C2213yescomplemented
44C3×#4095C2213yescomplemented
45C3×#4094C2211yescharacteristic, complemented
46C3×#4078C2213yescomplemented
47C2×C3×#686C2213yescomplemented
48#91523C2213yescomplemented
49#91521C2213yescomplemented
50#91511C2211yescharacteristic, complemented
51#91506C2216yescomplemented
52#91505C2213yescomplemented
53#91500C2216yescomplemented
54#91499C2213yescomplemented
55#91498C2216yescomplemented
56#91497C2213yescomplemented
57#91487C2213yescomplemented
58#91482C2216yescomplemented
59#91481C2216yescomplemented
60#91481C2213yescomplemented
61#91481C2216yescomplemented
62#91481C2216yescomplemented
63#91312C2213yescomplemented
64#91311C2213yescomplemented
65#91305C2213yescomplemented
66#91304C2213yescomplemented
67#91303C2213yescomplemented
68C2×#6654C2213yescomplemented
69#91301C2213yescomplemented
70C2×#6653C2213yescomplemented
71#91292C2213yescomplemented
72#91291C2213yescomplemented
73#91290C2213yescomplemented
74C2×#6648C2213yescomplemented
75D3×#576—51nomaximal, Hall
76D5×H(5,𝔽2)—31no—
77D5×H(5,𝔽2)—31no—
78C5×#576—31no—
79#66169—31no—
80#66169D311yescharacteristic, complemented
81#66108—33no—
82#66108—33no—
83D5×AGL(1,ℤ/8)—33no—
84D5×AGL(1,ℤ/8)—33no—
85#66103—33no—
86D5×#135—33no—
87#66091—33no—
88C2×D5×D8—33no—
89#66086—31no—
90D5×#131—31no—
91C23×D15—23no—
92C22×D3×D5—23no—
93C3×C5×#41—21no—
94C3×C5×#41C2311yescharacteristic
95C3×C5×#41C2313yescomplemented
96C2×C3×C5×D4—23no—
97C2×C3×C5×D4C2313yescomplemented
98C2×#1220—26no—
99C2×#1220—23no—
100#6821—21no—
101#6821D411yescharacteristic
102#6821C2313yescomplemented
103Q8×D15D411yescharacteristic
104Q8×D15C2311yescharacteristic
105#6819—23no—
106#6819—23no—
107#6819D413yes—
108#6819C2313yescomplemented
109D4×D15—23no—
110D4×D15—23no—
111D4×D15—26no—
112D4×D15—23no—
113D4×D15—23no—
114D4×D15—23no—
115D4×D15D413yes—
116D4×D15C2313yes—
117D4×D15C2316yescomplemented
118#6817—23no—
119#6817—23no—
120#6817C2313yes—
121#6817C2313yescomplemented
122C2×D60—23no—
123C2×D60C2313yescomplemented
124C2×C4×D15—23no—
125C2×C4×D15C2313yes—
126C5×#239—21no—
127C5×D3×D4—23no—
128C5×#235C2313yescomplemented
129C2×C5×D12C2313yescomplemented
130C3×#713—21no—
131C3×D4×D5—23no—
132C3×#709C2313yescomplemented
133C2×C3×D20C2313yescomplemented
134#6790—23no—
135D3×C22⋊D5—26no—
136D5×#67—26no—
137C2×#1201—23no—
138#6780—23no—
139#6777—23no—
140#6777—23no—
141#6777C2313yes—
142#6777C2316yescomplemented
143D3×D20—23no—
144D5×D12—23no—
145C4×D3×D5—23no—
146#6772—23no—
147#6771—23no—
148D15⋊Q8C2311yescharacteristic
149#6768C2313yescomplemented
150#6766C2313yescomplemented
151#6765—23no—
152C5×#216C2311yescharacteristic, complemented
153C5×#215C2313yescomplemented
154C5×#214C2313yescomplemented
155C5×#213C2313yescomplemented
156C5×#213C2316yescomplemented
157C5×#208C2313yescomplemented
158C2×C5×C3⋊C8C2313yescomplemented
159C3×#689C2311yescharacteristic, complemented
160C3×#688C2313yescomplemented
161C3×#687C2313yescomplemented
162C3×#686C2313yescomplemented
163C3×#686C2316yescomplemented
164C3×#681C2313yescomplemented
165C2×C3×#168C2313yescomplemented
166#6663C2311yescharacteristic, complemented
167#6662C2311yescharacteristic, complemented
168#6660C2313yescomplemented
169#6659C2313yescomplemented
170#6658C2313yescomplemented
171#6657C2313yescomplemented
172#6654C2313yescomplemented
173#6654C2316yescomplemented
174#6653C2313yescomplemented
175#6653C2316yescomplemented
176#6651C2316yescomplemented
177#6648C2311yescharacteristic
178#6648C2313yes—
179#6648C2313yescomplemented
180#6648C2313yescomplemented
181D3×H(5,𝔽2)—51no—
182D3×H(5,𝔽2)—51no—
183C3×#576—51no—
184#5835—51no—
185#5835D511yescharacteristic, complemented
186#5774—53no—
187#5774—53no—
188D3×AGL(1,ℤ/8)—53no—
189D3×AGL(1,ℤ/8)—53no—
190#5769—53no—
191D3×#135—53no—
192#5757—53no—
193C2×D3×D8—53no—
194#5752—51no—
195D3×#131—51no—
196C5×H(5,𝔽2)—31no—
197C5×H(5,𝔽2)C2×D311yescharacteristic, complemented
198#4149—31no—
199#4149—33no—
200#4149—33no—
201#4149—61no—
202#4149—61no—
203#4149C2×D311yescharacteristic, complemented
204D5×#41—31no—
205D5×#41—33no—
206D5×#41—33no—
207D5×#41—61no—
208D5×#41—61no—
209#4144—33no—
210#4144—33no—
211#4144—63no—
212#4144—63no—
213C2×D4×D5—33no—
214C2×D4×D5—33no—
215C2×D4×D5—63no—
216C2×D4×D5—63no—
217C5×AGL(1,ℤ/8)—33no—
218C5×AGL(1,ℤ/8)—33no—
219C5×#135—33no—
220C2×C5×D8—33no—
221C5×#131—31no—
222#4096—33no—
223#4096C2×D313yescomplemented
224#4095—33no—
225#4095C2×D313yescomplemented
226#4094C2×D311yescharacteristic, complemented
227#4078—33no—
228#4078C2×D313yescomplemented
229C2×#686—33no—
230C2×#686C2×D313yescomplemented
231#4065—33no—
232D5×Q16—31no—
233#4062—33no—
234#4062—33no—
235#4060—36no—
236#4060—36no—
237D5×SD16—33no—
238D5×SD16—33no—
239#4058—33no—
240#4057—36no—
241#4057—36no—
242D5×D8—33no—
243D5×D8—36no—
244D5×D8—36no—
245D5×D8—36no—
246#4054—33no—
247#4054—33no—
248#4053—33no—
249D5×M16—33no—
250#4050—33no—
251C2×D40—33no—
252#4047—33no—
253C2×C8×D5—33no—
254C2×#576—151noSylow
255C23×C3×C5—23no—
256C22×D15—23no—
257C22×D15—23no—
258C22×D15—26no—
259C22×D15—86no—
260C22×D15C2×D413yes—
261C22×C5×D3—23no—
262C22×C3×D5—23no—
263C2×D3×D5—23no—
264C2×D3×D5—26no—
265C2×D3×D5—86no—
266C3×C5×Q8C2×D411yescharacteristic
267C3×C5×Q8C2411yescharacteristic
268C3×C5×D4—23no—
269C3×C5×D4—23no—
270C3×C5×D4C2×D413yes—
271C3×C5×D4C2413yes—
272C2×C3×C4×C5—23no—
273C2×C3×C4×C5C2413yes—
274#1220—23no—
275#1220—23no—
276#1220—23no—
277#1220—26no—
278#1220C2×D416yes—
279C2×Dic15—23no—
280C2×Dic15C2×D413yes—
281D60—23no—
282D60—23no—
283D60C2×D413yes—
284D60C2413yes—
285C4×D15—21no—
286C4×D15—23no—
287C4×D15—23no—
288C4×D15C2×D413yes—
289C4×D15C2×D413yes—
290C4×D15C2413yes—
291C4×D15C2411yescharacteristic
292Dic30—21no—
293Dic30C2×D413yes—
294Dic30C2411yescharacteristic
295C5×#67—23no—
296C5×D12—23no—
297C5×D12C2413yes—
298C4×C5×D3—23no—
299C5×Dic6C2411yescharacteristic
300C3×C22⋊D5—23no—
301C3×D20—23no—
302C3×D20C2413yes—
303C3×C4×D5—23no—
304C3×Dic10C2411yescharacteristic
305#1204—21no—
306#1203—23no—
307#1202—23no—
308#1201—26no—
309#1201—23no—
310#1200—21no—
311D3×Dic5—23no—
312D5×Dic3—23no—
313C3×#168C2413yes—
314C3×#168C2411yescharacteristic
315C5×C3⋊C8C2413yes—
316C5×C3⋊C8C2411yescharacteristic
317C3×H(5,𝔽2)—51no—
318C3×H(5,𝔽2)C2×D511yescharacteristic, complemented
319#1009—51no—
320#1009—53no—
321#1009—53no—
322#1009—101no—
323#1009—101no—
324#1009C2×D511yescharacteristic, complemented
325D3×#41—51no—
326D3×#41—53no—
327D3×#41—53no—
328D3×#41—101no—
329D3×#41—101no—
330#1004—53no—
331#1004—53no—
332#1004—103no—
333#1004—103no—
334C2×D3×D4—53no—
335C2×D3×D4—53no—
336C2×D3×D4—103no—
337C2×D3×D4—103no—
338C3×AGL(1,ℤ/8)—53no—
339C3×AGL(1,ℤ/8)—53no—
340C3×#135—53no—
341C2×C3×D8—53no—
342C3×#131—51no—
343#950—53no—
344#950C2×D513yescomplemented
345#949—53no—
346#949C2×D513yescomplemented
347#948C2×D511yescharacteristic, complemented
348#932—53no—
349#932C2×D513yescomplemented
350C2×#213—53no—
351C2×#213C2×D513yescomplemented
352#919—53no—
353D3×Q16—51no—
354#916—53no—
355#916—53no—
356#914—56no—
357#914—56no—
358D3×SD16—53no—
359D3×SD16—53no—
360#912—53no—
361#911—56no—
362#911—56no—
363D3×D8—53no—
364D3×D8—56no—
365D3×D8—56no—
366D3×D8—56no—
367#908—53no—
368#908—53no—
369#907—53no—
370D3×M16—53no—
371#904—53no—
372C2×D24—53no—
373#901—53no—
374C2×D3×C8—53no—
375C23×D5—63no—
376C23×D5—63no—
377C5×#41—21no—
378C5×#41—33no—
379C5×#41—61no—
380C5×#41C22×D311yescharacteristic
381C5×#41C22×D313yescomplemented
382C2×C5×D4—23no—
383C2×C5×D4—33no—
384C2×C5×D4—63no—
385C2×C5×D4C22×D313yescomplemented
386C2×C22⋊D5—63no—
387C2×C22⋊D5—63no—
388C2×C22⋊D5—66no—
389C2×C22⋊D5—66no—
390#713—21no—
391#713—31no—
392#713—33no—
393#713—33no—
394#713—61no—
395Q8×D5—31no—
396Q8×D5—31no—
397Q8×D5—31no—
398#711—33no—
399#711—33no—
400#711—33no—
401#711—63no—
402#711—63no—
403#711—63no—
404#711—63no—
405D4×D5—23no—
406D4×D5—33no—
407D4×D5—33no—
408D4×D5—36no—
409D4×D5—33no—
410D4×D5—36no—
411D4×D5—63no—
412D4×D5—63no—
413D4×D5—63no—
414D4×D5—63no—
415D4×D5—63no—
416D4×D5—63no—
417D4×D5—63no—
418D4×D5—66no—
419D4×D5—66no—
420D4×D5—63no—
421D4×D5—63no—
422#709—33no—
423#709—33no—
424#709—63no—
425#709—63no—
426#709—63no—
427#709—63no—
428#709C22×D313yescomplemented
429C2×D20—33no—
430C2×D20—63no—
431C2×D20—63no—
432C2×D20C22×D313yescomplemented
433C2×C4×D5—33no—
434C2×C4×D5—63no—
435C2×C4×D5—63no—
436C5×Q16—31no—
437C5×SD16—33no—
438C5×SD16—33no—
439C5×D8—33no—
440C5×D8—36no—
441C5×M16—33no—
442C2×C5×C8—33no—
443#689—31no—
444#689C22×D311yescharacteristic, complemented
445#688—33no—
446#688C22×D313yescomplemented
447#687—33no—
448#687C22×D313yescomplemented
449#686—33no—
450#686—36no—
451#686C22×D313yescomplemented
452#686C22×D316yescomplemented
453#681C22×D313yescomplemented
454C2×#168C22×D313yescomplemented
455Dic20—31no—
456D40—33no—
457D40—36no—
458#677—33no—
459#677—33no—
460#676—36no—
461C8×D5—31no—
462C8×D5—33no—
463C8×D5—33no—
464C8×D5—33no—
465C2×H(5,𝔽2)—151no—
466C2×H(5,𝔽2)—151no—
467#576—31no—
468#576—51no—
469#576—151no—
470#576—151no—
471#576—153no—
472#576—153no—
473#576—153no—
474#576—153no—
475C2×AGL(1,ℤ/8)—153no—
476C2×AGL(1,ℤ/8)—153no—
477C2×#135—153no—
478C22×D8—153no—
479C2×#131—151no—
480C22×C3×C5—23no—
481C22×C3×C5—83no—
482C22×C3×C5C22×D413yes—
483C2×D15—26no—
484C2×D15—23no—
485C2×D15—46no—
486C2×D15—86no—
487C2×D15—83no—
488C2×D15C22×D413yes—
489C2×D15C22×D411yescharacteristic
490C2×C5×D3—23no—
491C2×C5×D3—83no—
492C2×C3×D5—23no—
493C2×C3×D5—83no—
494D3×D5—46no—
495D3×D5—86no—
496C3×C4×C5—21no—
497C3×C4×C5C22×D413yes—
498C3×C4×C5C2511yescharacteristic
499Dic15—21no—
500Dic15C22×D413yes—
501Dic15C22×D411yescharacteristic
502C3×Dic5—21no—
503C5×Dic3—21no—
504C23×D3—103no—
505C23×D3—103no—
506C3×#41—21no—
507C3×#41—53no—
508C3×#41—101no—
509C3×#41C22×D511yescharacteristic
510C3×#41C22×D513yescomplemented
511C2×C3×D4—23no—
512C2×C3×D4—53no—
513C2×C3×D4—103no—
514C2×C3×D4C22×D513yescomplemented
515C2×#67—103no—
516C2×#67—103no—
517C2×#67—106no—
518C2×#67—106no—
519#239—21no—
520#239—51no—
521#239—53no—
522#239—53no—
523#239—101no—
524D3×Q8—51no—
525D3×Q8—51no—
526D3×Q8—51no—
527#237—53no—
528#237—53no—
529#237—53no—
530#237—103no—
531#237—103no—
532#237—103no—
533#237—103no—
534D3×D4—23no—
535D3×D4—53no—
536D3×D4—53no—
537D3×D4—56no—
538D3×D4—53no—
539D3×D4—56no—
540D3×D4—103no—
541D3×D4—103no—
542D3×D4—103no—
543D3×D4—103no—
544D3×D4—103no—
545D3×D4—103no—
546D3×D4—103no—
547D3×D4—106no—
548D3×D4—106no—
549D3×D4—103no—
550D3×D4—103no—
551#235—53no—
552#235—53no—
553#235—103no—
554#235—103no—
555#235—103no—
556#235—103no—
557#235C22×D513yescomplemented
558C2×D12—53no—
559C2×D12—103no—
560C2×D12—103no—
561C2×D12C22×D513yescomplemented
562C2×C4×D3—53no—
563C2×C4×D3—103no—
564C2×C4×D3—103no—
565C3×Q16—51no—
566C3×SD16—53no—
567C3×SD16—53no—
568C3×D8—53no—
569C3×D8—56no—
570C3×M16—53no—
571C2×C3×C8—53no—
572#216—51no—
573#216C22×D511yescharacteristic, complemented
574#215—53no—
575#215C22×D513yescomplemented
576#214—53no—
577#214C22×D513yescomplemented
578#213—53no—
579#213—56no—
580#213C22×D513yescomplemented
581#213C22×D516yescomplemented
582#208C22×D513yescomplemented
583C2×C3⋊C8C22×D513yescomplemented
584Dic12—51no—
585D24—53no—
586D24—56no—
587#204—53no—
588#204—53no—
589ΓL(1,𝔽25)—56no—
590D3×C8—51no—
591D3×C8—53no—
592D3×C8—53no—
593D3×C8—53no—
594C23×C5—23no—
595C23×C5—63no—
596C22×D5—23no—
597C22×D5—33no—
598C22×D5—63no—
599C22×D5—66no—
600C22×D5—63no—
601C22×D5—66no—
602C22×D5—63no—
603C22×D5—246no—
604C22×D5—246no—
605C5×Q8—31no—
606C5×Q8D3×D411yescharacteristic
607C5×Q8C23×D311yescharacteristic
608C5×D4—23no—
609C5×D4—23no—
610C5×D4—33no—
611C5×D4—63no—
612C5×D4—63no—
613C5×D4D3×D413yes—
614C5×D4C23×D313yes—
615C2×C4×C5—23no—
616C2×C4×C5—63no—
617C2×C4×C5C23×D313yes—
618C22⋊D5—23no—
619C22⋊D5—36no—
620C22⋊D5—63no—
621C22⋊D5—66no—
622C22⋊D5—63no—
623C22⋊D5—66no—
624C22⋊D5—63no—
625C22⋊D5—63no—
626C22⋊D5—63no—
627C2×Dic5—33no—
628C2×Dic5—63no—
629C2×Dic5—63no—
630D20—23no—
631D20—33no—
632D20—33no—
633D20—63no—
634D20—63no—
635D20—63no—
636D20C23×D313yes—
637C4×D5—23no—
638C4×D5—33no—
639C4×D5—33no—
640C4×D5—31no—
641C4×D5—33no—
642C4×D5—61no—
643C4×D5—63no—
644C4×D5—63no—
645C4×D5—61no—
646C4×D5—63no—
647Dic10—33no—
648Dic10—31no—
649Dic10—61no—
650Dic10—61no—
651Dic10C23×D311yescharacteristic
652C5×C8—31no—
653C5×C8—33no—
654#168C23×D311yescharacteristic
655#168C23×D313yes—
656H(5,𝔽2)—31no—
657H(5,𝔽2)—51no—
658H(5,𝔽2)—153no—
659H(5,𝔽2)—153no—
660H(5,𝔽2)—151no—
661H(5,𝔽2)—153no—
662H(5,𝔽2)—153no—
663H(5,𝔽2)—303no—
664H(5,𝔽2)—303no—
665H(5,𝔽2)—301no—
666H(5,𝔽2)—301no—
667H(5,𝔽2)D3×D511yescharacteristic, complemented
668C2×#41—151no—
669C2×#41—153no—
670C2×#41—153no—
671C2×#41—301no—
672C2×#41—301no—
673C22×D4—153no—
674C22×D4—153no—
675C22×D4—303no—
676C22×D4—303no—
677AGL(1,ℤ/8)—33no—
678AGL(1,ℤ/8)—33no—
679AGL(1,ℤ/8)—53no—
680AGL(1,ℤ/8)—53no—
681AGL(1,ℤ/8)—153no—
682AGL(1,ℤ/8)—153no—
683AGL(1,ℤ/8)—153no—
684AGL(1,ℤ/8)—153no—
685AGL(1,ℤ/8)—156no—
686AGL(1,ℤ/8)—156no—
687AGL(1,ℤ/8)—156no—
688AGL(1,ℤ/8)—156no—
689#135—33no—
690#135—53no—
691#135—153no—
692#135—153no—
693#135—153no—
694#135—153no—
695#135—153no—
696#135—153no—
697C2×Q16—151no—
698C2×SD16—153no—
699C2×SD16—153no—
700C2×D8—33no—
701C2×D8—53no—
702C2×D8—153no—
703C2×D8—153no—
704C2×D8—153no—
705C2×D8—156no—
706C2×D8—156no—
707C2×D8—156no—
708#131—31no—
709#131—51no—
710#131—153no—
711#131—153no—
712C2×M16—153no—
713C22×C8—153no—
714C2×C3×C5—23no—
715C2×C3×C5—43no—
716C2×C3×C5C23×D411yescharacteristic
717D15—23no—
718D15—43no—
719D15#57612yescomplemented
720C3×D5—43no—
721C5×D3—43no—
722C23×C3—23no—
723C23×C3—103no—
724C22×D3—23no—
725C22×D3—53no—
726C22×D3—103no—
727C22×D3—106no—
728C22×D3—103no—
729C22×D3—106no—
730C22×D3—103no—
731C22×D3—406no—
732C22×D3—406no—
733C3×Q8—51no—
734C3×Q8D4×D511yescharacteristic
735C3×Q8C23×D511yescharacteristic
736C3×D4—23no—
737C3×D4—23no—
738C3×D4—53no—
739C3×D4—103no—
740C3×D4—103no—
741C3×D4D4×D513yes—
742C3×D4C23×D513yes—
743C2×C3×C4—23no—
744C2×C3×C4—103no—
745C2×C3×C4C23×D513yes—
746#67—23no—
747#67—56no—
748#67—103no—
749#67—106no—
750#67—103no—
751#67—106no—
752#67—103no—
753#67—103no—
754#67—103no—
755C2×Dic3—53no—
756C2×Dic3—103no—
757C2×Dic3—103no—
758D12—23no—
759D12—53no—
760D12—53no—
761D12—103no—
762D12—103no—
763D12—103no—
764D12C23×D513yes—
765C4×D3—23no—
766C4×D3—53no—
767C4×D3—53no—
768C4×D3—51no—
769C4×D3—53no—
770C4×D3—101no—
771C4×D3—103no—
772C4×D3—103no—
773C4×D3—101no—
774C4×D3—103no—
775Dic6—53no—
776Dic6—51no—
777Dic6—101no—
778Dic6—101no—
779Dic6C23×D511yescharacteristic
780C3×C8—51no—
781C3×C8—53no—
782C3⋊C8C23×D511yescharacteristic
783C3⋊C8C23×D513yes—
784C22×C5—23no—
785C22×C5—63no—
786C22×C5—83no—
787C22×C5—243no—
788C22×C5C2×D3×D413yes—
789C2×D5—23no—
790C2×D5—31no—
791C2×D5—33no—
792C2×D5—66no—
793C2×D5—63no—
794C2×D5—83no—
795C2×D5—126no—
796C2×D5—126no—
797C2×D5—246no—
798C2×D5—246no—
799C2×D5—243no—
800C4×C5—21no—
801C4×C5—61no—
802C4×C5C2×D3×D413yes—
803C4×C5C24×D311yescharacteristic
804Dic5—21no—
805Dic5—33no—
806Dic5—31no—
807Dic5—61no—
808C24—303no—
809C24—303no—
810#41—21no—
811#41—33no—
812#41—53no—
813#41—61no—
814#41—101no—
815#41—151no—
816#41—153no—
817#41—153no—
818#41—153no—
819#41—153no—
820#41—153no—
821#41—153no—
822#41—153no—
823#41—303no—
824#41—303no—
825#41—303no—
826#41—303no—
827#41—303no—
828#41—303no—
829#41—303no—
830#41—303no—
831#41—301no—
832#41C2×D3×D511yescharacteristic
833#41C2×D3×D513yescomplemented
834C2×Q8—151no—
835C2×Q8—151no—
836C2×Q8—151no—
837C2×D4—23no—
838C2×D4—33no—
839C2×D4—53no—
840C2×D4—63no—
841C2×D4—103no—
842C2×D4—153no—
843C2×D4—156no—
844C2×D4—153no—
845C2×D4—153no—
846C2×D4—156no—
847C2×D4—153no—
848C2×D4—303no—
849C2×D4—303no—
850C2×D4—303no—
851C2×D4—303no—
852C2×D4—303no—
853C2×D4—303no—
854C2×D4—303no—
855C2×D4—303no—
856C2×D4—303no—
857C2×D4—306no—
858C2×D4—303no—
859C2×D4—303no—
860C2×D4—303no—
861C2×D4—306no—
862C2×D4—306no—
863C2×D4—306no—
864C2×D4—303no—
865C2×D4C2×D3×D513yescomplemented
866C22×C4—153no—
867C22×C4—303no—
868C22×C4—303no—
869Q16—31no—
870Q16—51no—
871Q16—151no—
872Q16—151no—
873SD16—33no—
874SD16—33no—
875SD16—53no—
876SD16—53no—
877SD16—153no—
878SD16—153no—
879SD16—153no—
880SD16—153no—
881D8—33no—
882D8—36no—
883D8—53no—
884D8—56no—
885D8—153no—
886D8—156no—
887D8—153no—
888D8—156no—
889M16—33no—
890M16—53no—
891M16—156no—
892C2×C8—33no—
893C2×C8—53no—
894C2×C8—151no—
895C2×C8—153no—
896C2×C8—153no—
897C2×C8—153no—
898C3×C5C2×#57611yescharacteristic, complemented, Hall
899C22×C3—23no—
900C22×C3—83no—
901C22×C3—103no—
902C22×C3—403no—
903C22×C3C2×D4×D513yes—
904C2×D3—23no—
905C2×D3—51no—
906C2×D3—53no—
907C2×D3—83no—
908C2×D3—106no—
909C2×D3—103no—
910C2×D3—206no—
911C2×D3—206no—
912C2×D3—406no—
913C2×D3—406no—
914C2×D3—403no—
915C3×C4—21no—
916C3×C4—101no—
917C3×C4C2×D4×D513yes—
918C3×C4C24×D511yescharacteristic
919Dic3—21no—
920Dic3—53no—
921Dic3—51no—
922Dic3—101no—
923C2×C5—23no—
924C2×C5—43no—
925C2×C5—123no—
926C2×C5C22×D3×D411yescharacteristic
927D5—32no—
928D5—43no—
929D5—63no—
930D5—123no—
931C23—23no—
932C23—63no—
933C23—103no—
934C23—153no—
935C23—303no—
936C23—306no—
937C23—303no—
938C23—306no—
939C23—303no—
940C23—1206no—
941C23—1206no—
942Q8—31no—
943Q8—51no—
944Q8—153no—
945Q8—151no—
946Q8—301no—
947Q8—301no—
948Q8#679011yescharacteristic
949Q8C22×D3×D511yescharacteristic
950D4—23no—
951D4—23no—
952D4—33no—
953D4—53no—
954D4—63no—
955D4—63no—
956D4—103no—
957D4—103no—
958D4—156no—
959D4—153no—
960D4—153no—
961D4—303no—
962D4—303no—
963D4—303no—
964D4—303no—
965D4—306no—
966D4—303no—
967D4—306no—
968D4—303no—
969D4—303no—
970D4—303no—
971D4#679013yes—
972D4C22×D3×D513yes—
973C2×C4—23no—
974C2×C4—63no—
975C2×C4—103no—
976C2×C4—153no—
977C2×C4—153no—
978C2×C4—153no—
979C2×C4—151no—
980C2×C4—153no—
981C2×C4—303no—
982C2×C4—301no—
983C2×C4—301no—
984C2×C4—303no—
985C2×C4—303no—
986C2×C4—303no—
987C2×C4—303no—
988C2×C4C22×D3×D513yes—
989C8—31no—
990C8—33no—
991C8—51no—
992C8—53no—
993C2×C3—23no—
994C2×C3—43no—
995C2×C3—203no—
996C2×C3C22×D4×D511yescharacteristic
997D3—43no—
998D3—52no—
999D3—103no—
1000D3—203no—
1001C5D3×#57611yescharacteristic, complemented, Sylow
1002C22—23no—
1003C22—63no—
1004C22—83no—
1005C22—103no—
1006C22—151no—
1007C22—153no—
1008C22—243no—
1009C22—306no—
1010C22—303no—
1011C22—403no—
1012C22—606no—
1013C22—606no—
1014C22—1203no—
1015C22—1206no—
1016C22—1206no—
1017C22C2×#679013yes—
1018C4—21no—
1019C4—61no—
1020C4—101no—
1021C4—151no—
1022C4—153no—
1023C4—301no—
1024C4C2×#679013yes—
1025C4C23×D3×D511yescharacteristic
1026C3D5×#57611yescharacteristic, complemented, Sylow
1027C2—23no—
1028C2—43no—
1029C2—123no—
1030C2—152no—
1031C2—203no—
1032C2—303no—
1033C2—603no—
1034C2C22×#679011yescharacteristic
subgroupG/H
centerC2C22×#6790
commutator, cosocleC3×C4×C5C25
FrattiniC4C23×D3×D5
FittingC3×C5×H(5,𝔽2)C22
socleC2×C3×C5C23×D4
hypercenterH(5,𝔽2)D3×D5
hypocenterC3×C5C2×#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. D15×H(5,𝔽2)C2semidirect
2. #11757054C2semidirect
3. C5×#5835C2semidirect
4. C3×#66169C2semidirect
5. #11755332C2semidirect
6. #11755330C2semidirect
7. #11755328C2semidirect
8. #11755327C2semidirect
9. #11755311C2semidirect
10. #11755305C2semidirect
11. #11755299C2semidirect
12. #11754704C2semidirect
13. #11754703C2semidirect
14. #11754701C2semidirect
15. C2×#91481C2semidirect
17. C3×C5×H(5,𝔽2)C22semidirect
19. #92100C22semidirect
20. #92100C22semidirect
23. #41×D15C22semidirect
25. #92095C22semidirect
27. C2×D4×D15C22semidirect
28. C5×#1009C22semidirect
29. C3×#4149C22semidirect
34. #92018C22semidirect
35. #92017C22semidirect
36. #92016C22semidirect
37. C2×#6777C22semidirect
38. C5×#950C22semidirect
39. C5×#949C22semidirect
40. C5×#948C22semidirect
41. C5×#932C22semidirect
42. C2×C5×#213C22semidirect
43. C3×#4096C22semidirect
44. C3×#4095C22semidirect
45. C3×#4094C22semidirect
46. C3×#4078C22semidirect
47. C2×C3×#686C22semidirect
48. #91523C22semidirect
49. #91521C22semidirect
50. #91511C22semidirect
51. #91506C22semidirect
52. #91505C22semidirect
53. #91500C22semidirect
54. #91499C22semidirect
55. #91498C22semidirect
56. #91497C22semidirect
57. #91487C22semidirect
58. #91482C22semidirect
59. #91481C22semidirect
60. #91481C22semidirect
61. #91481C22semidirect
62. #91481C22semidirect
63. #91312C22semidirect
64. #91311C22semidirect
65. #91305C22semidirect
66. #91304C22semidirect
67. #91303C22semidirect
68. C2×#6654C22semidirect
69. #91301C22semidirect
70. C2×#6653C22semidirect
71. #91292C22semidirect
72. #91291C22semidirect
73. #91290C22semidirect
74. C2×#6648C22semidirect
80. #66169D3semidirect
95. C3×C5×#41C23semidirect
97. C2×C3×C5×D4C23semidirect
102. #6821C23semidirect
108. #6819C23semidirect
117. D4×D15C23semidirect
121. #6817C23semidirect
123. C2×D60C23semidirect
128. C5×#235C23semidirect
129. C2×C5×D12C23semidirect
132. C3×#709C23semidirect
133. C2×C3×D20C23semidirect
142. #6777C23semidirect
149. #6768C23semidirect
150. #6766C23semidirect
152. C5×#216C23semidirect
153. C5×#215C23semidirect
154. C5×#214C23semidirect
155. C5×#213C23semidirect
156. C5×#213C23semidirect
157. C5×#208C23semidirect
158. C2×C5×C3⋊C8C23semidirect
159. C3×#689C23semidirect
160. C3×#688C23semidirect
161. C3×#687C23semidirect
162. C3×#686C23semidirect
163. C3×#686C23semidirect
164. C3×#681C23semidirect
165. C2×C3×#168C23semidirect
166. #6663C23semidirect
167. #6662C23semidirect
168. #6660C23semidirect
169. #6659C23semidirect
170. #6658C23semidirect
171. #6657C23semidirect
172. #6654C23semidirect
173. #6654C23semidirect
174. #6653C23semidirect
175. #6653C23semidirect
176. #6651C23semidirect
179. #6648C23semidirect
180. #6648C23semidirect
185. #5835D5semidirect
197. C5×H(5,𝔽2)C2×D3semidirect
203. #4149C2×D3semidirect
223. #4096C2×D3semidirect
225. #4095C2×D3semidirect
226. #4094C2×D3semidirect
228. #4078C2×D3semidirect
230. C2×#686C2×D3semidirect
318. C3×H(5,𝔽2)C2×D5semidirect
324. #1009C2×D5semidirect
344. #950C2×D5semidirect
346. #949C2×D5semidirect
347. #948C2×D5semidirect
349. #932C2×D5semidirect
351. C2×#213C2×D5semidirect
381. C5×#41C22×D3semidirect
385. C2×C5×D4C22×D3semidirect
428. #709C22×D3semidirect
432. C2×D20C22×D3semidirect
444. #689C22×D3semidirect
446. #688C22×D3semidirect
448. #687C22×D3semidirect
451. #686C22×D3semidirect
452. #686C22×D3semidirect
453. #681C22×D3semidirect
454. C2×#168C22×D3semidirect
510. C3×#41C22×D5semidirect
514. C2×C3×D4C22×D5semidirect
557. #235C22×D5semidirect
561. C2×D12C22×D5semidirect
573. #216C22×D5semidirect
575. #215C22×D5semidirect
577. #214C22×D5semidirect
580. #213C22×D5semidirect
581. #213C22×D5semidirect
582. #208C22×D5semidirect
583. C2×C3⋊C8C22×D5semidirect
667. H(5,𝔽2)D3×D5semidirect
719. D15#576semidirect
833. #41C2×D3×D5semidirect
865. C2×D4C2×D3×D5semidirect
898. C3×C5C2×#576semidirect
1001. C5D3×#576semidirect
1026. C3D5×#576semidirect

Maximal subgroups

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

subgroupindex
D15×H(5,𝔽2)2
#117570542
C5×#58352
C3×#661692
#117553322
#117553302
#117553282
#117553272
#117553112
#117553052
#117552992
#117547042
#117547032
#117547012
C2×#914812
D5×#5763
D3×#5765