Finite Group Databasebeta

← #14458094

Subgroups — #14458094

Order 1920.

920 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#577C211yesmaximal, characteristic, complemented
2#11756596C211yesmaximal, characteristic, complemented
3#11756595C211yesmaximal, characteristic, complemented
4#11756529C211yesmaximal, characteristic, complemented
5#11751347C211yesmaximal, characteristic, complemented
6#11751342C211yesmaximal, characteristic, complemented
7#11751306C211yesmaximal, characteristic, complemented
8#11751304C211yesmaximal, characteristic, complemented
9#11751301C211yesmaximal, characteristic, complemented
10#11751299C211yesmaximal, characteristic, complemented
11#11751297C211yesmaximal, characteristic, complemented
12#11751278C211yesmaximal, characteristic, complemented
13#11751276C211yesmaximal, characteristic, complemented
14#11751245C211yesmaximal, characteristic, complemented
15#11751242C211yesmaximal, characteristic, complemented
16#10615745—31nomaximal, Hall
17C3×C5×2−1+4C2211yescharacteristic
18C3×C5×H(5,𝔽2)C2211yescharacteristic, complemented
19#92101C2211yescharacteristic
20#92100C2211yescharacteristic, complemented
21C3×C5×#137—21no—
22C3×C5×#137C2211yescharacteristic, complemented
23C3×C5×AGL(1,ℤ/8)—21no—
24C3×C5×AGL(1,ℤ/8)C2211yescharacteristic
25C3×C5×#135—21no—
26C3×C5×#135C2211yescharacteristic
27C2×C3×C5×SD16—21no—
28C2×C3×C5×SD16C2211yescharacteristic, complemented
29C3×C5×#131C2211yescharacteristic, complemented
30#91840—21no—
31#91840C2211yescharacteristic, complemented
32#91840C2211yescharacteristic, complemented
33#91839—21no—
34#91839—21no—
35#91839C2211yescharacteristic
36#91838—21no—
37#91838C2211yescharacteristic
38#91838C2211yescharacteristic
39#91837C2211yescharacteristic, complemented
40#91837C2211yescharacteristic, complemented
41#91833C2211yescharacteristic, complemented
42#91831—21no—
43#91831C2211yescharacteristic, complemented
44C2×#6717—21no—
45C2×#6717C2211yescharacteristic, complemented
46#91829C2211yescharacteristic
47C2×#6716—21no—
48C2×#6716C2211yescharacteristic, complemented
49#91821—21no—
50#91821C2211yescharacteristic
51#91807—21no—
52#91805—21no—
53SD16×D15—21no—
54#91800—21no—
55C2×#6706C2211yescharacteristic, complemented
56#91790C2211yescharacteristic, complemented
57#91121C2211yescharacteristic, complemented
58#91121C2211yescharacteristic, complemented
59#91121C2211yescharacteristic, complemented
60#91120C2211yescharacteristic, complemented
61#91117C2211yescharacteristic, complemented
62#91109C2211yescharacteristic, complemented
63#91108C2211yescharacteristic, complemented
64#91107C2211yescharacteristic, complemented
65#91106C2211yescharacteristic, complemented
66#91103C2211yescharacteristic, complemented
67C8×Dic15C2211yescharacteristic, complemented
68#84014—51nomaximal, Hall
69C5×#577D311yescharacteristic, complemented
70#66171—31no—
71#66170—31no—
72#66104—31no—
73#65535—31no—
74#65530—31no—
75#65494—31no—
76#65492—31no—
77#65489—31no—
78#65487—31no—
79#65485—31no—
80#65466—31no—
81#65464—31no—
82#65433—31no—
83#65430—31no—
84C3×C5×#41—21no—
85C3×C5×#41—21no—
86C3×C5×#41—21no—
87C3×C5×#41—21no—
88C3×C5×#41—41no—
89C3×C5×#41C2311yescharacteristic
90C3×C5×#41C2311yescharacteristic
91C3×C5×#41C2311yescharacteristic
92C2×C3×C5×Q8—21no—
93C2×C3×C5×Q8—21no—
94C2×C3×C5×Q8C2311yescharacteristic
95C2×C3×C5×D4—21no—
96C2×C3×C5×D4—21no—
97C2×C3×C5×D4—41no—
98C2×C3×C5×D4C2311yescharacteristic
99C2×#1220—41no—
100#6821—21no—
101Q8×D15—21no—
102#6819—21no—
103#6819—41no—
104D4×D15—21no—
105D4×D15—41no—
106#6817—21no—
107#6817—21no—
108#6817C2311yescharacteristic
109C2×D60—21no—
110C2×D60C2311yescharacteristic
111C2×Dic30—21no—
112C2×Dic30C2311yescharacteristic
113C3×C5×Q16—21no—
114C3×C5×Q16D411yescharacteristic, complemented
115C3×C5×SD16—21no—
116C3×C5×SD16—21no—
117C3×C5×SD16—21no—
118C3×C5×SD16—21no—
119C3×C5×SD16D411yescharacteristic, complemented
120C3×C5×SD16D411yescharacteristic, complemented
121C3×C5×D8—21no—
122C3×C5×D8D411yescharacteristic, complemented
123C3×C5×M16—21no—
124C3×C5×M16C2311yescharacteristic
125C2×C3×C5×C8—21no—
126C2×C3×C5×C8C2311yescharacteristic
127#6718—21no—
128#6718—21no—
129#6718—21no—
130#6718D411yescharacteristic, complemented
131#6717—21no—
132#6717—21no—
133#6717—21no—
134#6717—21no—
135#6717—21no—
136#6717D411yescharacteristic, complemented
137#6716—21no—
138#6716—21no—
139#6716—21no—
140#6716—21no—
141#6716—21no—
142#6716D411yescharacteristic, complemented
143#6715—21no—
144#6715—21no—
145#6715—21no—
146#6715D411yescharacteristic, complemented
147#6712—41no—
148C4×Dic15C2311yescharacteristic
149#6710—21no—
150#6710—21no—
151#6710C2311yescharacteristic
152#6710C2311yescharacteristic
153#6710C2311yescharacteristic
154C2×C3⋊#168—21no—
155C2×C3⋊#168—21no—
156C2×C3⋊#168C2311yescharacteristic
157#6706—21no—
158#6706—21no—
159#6705—21no—
160C8×D15—21no—
161C3×#577D511yescharacteristic, complemented
162#5837—51no—
163#5836—51no—
164#5770—51no—
165#5246—51no—
166#5241—51no—
167#5205—51no—
168#5203—51no—
169#5200—51no—
170#5198—51no—
171#5196—51no—
172#5177—51no—
173#5175—51no—
174#5144—51no—
175#5141—51no—
176C5×2−1+4C2×D311yescharacteristic
177C5×H(5,𝔽2)C2×D311yescharacteristic, complemented
178#4150—31no—
179#4149—31no—
180C5×#137—21no—
181C5×#137C2×D311yescharacteristic, complemented
182C5×AGL(1,ℤ/8)—21no—
183C5×AGL(1,ℤ/8)C2×D311yescharacteristic
184C5×#135—21no—
185C5×#135C2×D311yescharacteristic
186C2×C5×SD16—21no—
187C2×C5×SD16C2×D311yescharacteristic, complemented
188C5×#131C2×D311yescharacteristic, complemented
189#4097—31no—
190#4097—31no—
191#4097—61no—
192#4096—31no—
193#4096—61no—
194#4096—61no—
195#4095—31no—
196#4095—31no—
197#4095—61no—
198#4094—31no—
199#4094—31no—
200#4090—31no—
201#4088—31no—
202#4088—61no—
203C2×#688—31no—
204C2×#688—61no—
205#4086—31no—
206C2×#687—31no—
207C2×#687—61no—
208#4078—31no—
209#4078—61no—
210#4064—61no—
211#4062—61no—
212D5×SD16—61no—
213#4057—61no—
214C2×#677—31no—
215#4047—31no—
216#3969—31no—
217#3969—31no—
218#3969—31no—
219#3968—31no—
220#3965—31no—
221#3957—31no—
222#3956—31no—
223#3955—31no—
224#3954—31no—
225#3951—31no—
226C8×Dic5—31no—
227#3291—151noSylow
228C23×C3×C5—21no—
229C23×C3×C5—41no—
230C22×D15—21no—
231C22×D15—41no—
232C3×C5×Q8—21no—
233C3×C5×Q8—21no—
234C3×C5×Q8—41no—
235C3×C5×Q8C2×D411yescharacteristic
236C3×C5×Q8C2×D411yescharacteristic
237C3×C5×Q8C2×D411yescharacteristic
238C3×C5×D4—21no—
239C3×C5×D4—21no—
240C3×C5×D4—21no—
241C3×C5×D4—21no—
242C3×C5×D4—21no—
243C3×C5×D4—41no—
244C3×C5×D4—41no—
245C3×C5×D4—41no—
246C3×C5×D4C2×D411yescharacteristic
247C3×C5×D4C2×D411yescharacteristic
248C3×C5×D4C2×D411yescharacteristic
249C2×C3×C4×C5—21no—
250C2×C3×C4×C5—21no—
251C2×C3×C4×C5—21no—
252C2×C3×C4×C5—21no—
253C2×C3×C4×C5—41no—
254C2×C3×C4×C5—41no—
255C2×C3×C4×C5—41no—
256C2×C3×C4×C5C2411yescharacteristic
257#1220—21no—
258#1220—41no—
259#1220—41no—
260#1220—82no—
261C2×Dic15—21no—
262C2×Dic15—21no—
263C2×Dic15—41no—
264D60—21no—
265D60—21no—
266D60—41no—
267D60C2×D411yescharacteristic
268C4×D15—21no—
269C4×D15—41no—
270C4×D15—41no—
271Dic30—21no—
272Dic30—21no—
273Dic30—41no—
274Dic30C2×D411yescharacteristic
275C3×C5×C8—21no—
276C3×C5×C8C2×D411yescharacteristic
277C3×C5×C8C2×D411yescharacteristic
278C3⋊#168—21no—
279C3⋊#168—21no—
280C3⋊#168—21no—
281C3⋊#168C2×D411yescharacteristic
282C3⋊#168C2×D411yescharacteristic
283C3×2−1+4C2×D511yescharacteristic
284C3×H(5,𝔽2)C2×D511yescharacteristic, complemented
285#1010—51no—
286#1009—51no—
287C3×#137—21no—
288C3×#137C2×D511yescharacteristic, complemented
289C3×AGL(1,ℤ/8)—21no—
290C3×AGL(1,ℤ/8)C2×D511yescharacteristic
291C3×#135—21no—
292C3×#135C2×D511yescharacteristic
293C2×C3×SD16—21no—
294C2×C3×SD16C2×D511yescharacteristic, complemented
295C3×#131C2×D511yescharacteristic, complemented
296#951—51no—
297#951—51no—
298#951—101no—
299#950—51no—
300#950—101no—
301#950—101no—
302#949—51no—
303#949—51no—
304#949—101no—
305#948—51no—
306#948—51no—
307#944—51no—
308#942—51no—
309#942—101no—
310C2×#215—51no—
311C2×#215—101no—
312#940—51no—
313C2×#214—51no—
314C2×#214—101no—
315#932—51no—
316#932—101no—
317#918—101no—
318#916—101no—
319D3×SD16—101no—
320#911—101no—
321C2×#204—51no—
322#901—51no—
323#837—51no—
324#837—51no—
325#837—51no—
326#836—51no—
327#833—51no—
328#825—51no—
329#824—51no—
330#823—51no—
331#822—51no—
332#819—51no—
333C8×Dic3—51no—
334C5×#41—21no—
335C5×#41—21no—
336C5×#41—21no—
337C5×#41—21no—
338C5×#41—41no—
339C5×#41C22×D311yescharacteristic
340C5×#41C22×D311yescharacteristic
341C5×#41C22×D311yescharacteristic
342C2×C5×Q8—21no—
343C2×C5×Q8—21no—
344C2×C5×Q8C22×D311yescharacteristic
345C2×C5×D4—21no—
346C2×C5×D4—21no—
347C2×C5×D4—41no—
348C2×C5×D4C22×D311yescharacteristic
349C2×C22⋊D5—121no—
350#713—61no—
351Q8×D5—61no—
352#711—61no—
353#711—121no—
354D4×D5—61no—
355D4×D5—121no—
356#709—31no—
357#709—61no—
358#709—61no—
359C2×D20—31no—
360C2×D20—61no—
361C2×Dic10—31no—
362C2×Dic10—61no—
363C5×Q16—21no—
364C5×Q16#6711yescharacteristic, complemented
365C5×SD16—21no—
366C5×SD16—21no—
367C5×SD16—21no—
368C5×SD16—21no—
369C5×SD16#6711yescharacteristic, complemented
370C5×SD16#6711yescharacteristic, complemented
371C5×D8—21no—
372C5×D8#6711yescharacteristic, complemented
373C5×M16—21no—
374C5×M16C22×D311yescharacteristic
375C2×C5×C8—21no—
376C2×C5×C8C22×D311yescharacteristic
377#689—31no—
378#689—61no—
379#689—61no—
380#689—61no—
381#688—31no—
382#688—61no—
383#688—61no—
384#688—61no—
385#688—61no—
386#688—61no—
387#687—31no—
388#687—61no—
389#687—61no—
390#687—61no—
391#687—61no—
392#687—61no—
393#686—31no—
394#686—61no—
395#686—61no—
396#686—61no—
397#683—121no—
398C4×Dic5—31no—
399#681—31no—
400#681—31no—
401#681—31no—
402#681—61no—
403#681—61no—
404C2×#168—31no—
405C2×#168—61no—
406C2×#168—61no—
407#677—61no—
408#677—61no—
409#676—61no—
410C8×D5—61no—
411#577—151no—
412#577—151no—
413#577—151no—
414#577D1511yescharacteristic, complemented
415#492—151no—
416#471—151no—
417#471—151no—
418#471—151no—
419#471—151no—
420#456—151no—
421#456—151no—
422#453—151no—
423#453—151no—
424#443—151no—
425#443—151no—
426C22×C3×C5—21no—
427C22×C3×C5—21no—
428C22×C3×C5—21no—
429C22×C3×C5—41no—
430C22×C3×C5—81no—
431C22×C3×C5—161no—
432C22×C3×C5H(5,𝔽2)11yescharacteristic
433C2×D15—21no—
434C2×D15—41no—
435C2×D15—81no—
436C2×D15—161no—
437C3×C4×C5—21no—
438C3×C4×C5—21no—
439C3×C4×C5—21no—
440C3×C4×C5—41no—
441C3×C4×C5C22×D411yescharacteristic
442C3×C4×C5C22×D411yescharacteristic
443Dic15—22no—
444Dic15—21no—
445Dic15—41no—
446C3×#41—21no—
447C3×#41—21no—
448C3×#41—21no—
449C3×#41—21no—
450C3×#41—41no—
451C3×#41C22×D511yescharacteristic
452C3×#41C22×D511yescharacteristic
453C3×#41C22×D511yescharacteristic
454C2×C3×Q8—21no—
455C2×C3×Q8—21no—
456C2×C3×Q8C22×D511yescharacteristic
457C2×C3×D4—21no—
458C2×C3×D4—21no—
459C2×C3×D4—41no—
460C2×C3×D4C22×D511yescharacteristic
461C2×#67—201no—
462#239—101no—
463D3×Q8—101no—
464#237—101no—
465#237—201no—
466D3×D4—101no—
467D3×D4—201no—
468#235—51no—
469#235—101no—
470#235—101no—
471C2×D12—51no—
472C2×D12—101no—
473C2×Dic6—51no—
474C2×Dic6—101no—
475C3×Q16—21no—
476C3×Q16C22⋊D511yescharacteristic, complemented
477C3×SD16—21no—
478C3×SD16—21no—
479C3×SD16—21no—
480C3×SD16—21no—
481C3×SD16C22⋊D511yescharacteristic, complemented
482C3×SD16C22⋊D511yescharacteristic, complemented
483C3×D8—21no—
484C3×D8C22⋊D511yescharacteristic, complemented
485C3×M16—21no—
486C3×M16C22×D511yescharacteristic
487C2×C3×C8—21no—
488C2×C3×C8C22×D511yescharacteristic
489#216—51no—
490#216—101no—
491#216—101no—
492#216—101no—
493#215—51no—
494#215—101no—
495#215—101no—
496#215—101no—
497#215—101no—
498#215—101no—
499#214—51no—
500#214—101no—
501#214—101no—
502#214—101no—
503#214—101no—
504#214—101no—
505#213—51no—
506#213—101no—
507#213—101no—
508#213—101no—
509Dic3⋊C4—201no—
510C4×Dic3—51no—
511#208—51no—
512#208—51no—
513#208—51no—
514#208—101no—
515#208—101no—
516C2×C3⋊C8—51no—
517C2×C3⋊C8—101no—
518C2×C3⋊C8—101no—
519#204—101no—
520#204—101no—
521ΓL(1,𝔽25)—101no—
522D3×C8—101no—
523C23×C5—21no—
524C23×C5—41no—
525C22×D5—61no—
526C22×D5—121no—
527C5×Q8—21no—
528C5×Q8—21no—
529C5×Q8—41no—
530C5×Q8D3×D411yescharacteristic
531C5×Q8C2×#6711yescharacteristic
532C5×Q8C2×#6711yescharacteristic
533C5×D4—21no—
534C5×D4—21no—
535C5×D4—21no—
536C5×D4—21no—
537C5×D4—21no—
538C5×D4—41no—
539C5×D4—41no—
540C5×D4—41no—
541C5×D4D3×D411yescharacteristic
542C5×D4C2×#6711yescharacteristic
543C5×D4C2×#6711yescharacteristic
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—21no—
548C2×C4×C5—41no—
549C2×C4×C5—41no—
550C2×C4×C5—41no—
551C2×C4×C5C23×D311yescharacteristic
552C22⋊D5—61no—
553C22⋊D5—121no—
554C22⋊D5—121no—
555C22⋊D5—242no—
556C2×Dic5—61no—
557C2×Dic5—61no—
558C2×Dic5—121no—
559D20—31no—
560D20—61no—
561D20—61no—
562D20—121no—
563C4×D5—61no—
564C4×D5—121no—
565C4×D5—121no—
566Dic10—31no—
567Dic10—61no—
568Dic10—61no—
569Dic10—121no—
570C5×C8—21no—
571C5×C8C2×#6711yescharacteristic
572C5×C8C2×#6711yescharacteristic
573#168—31no—
574#168—31no—
575#168—61no—
576#168—61no—
577#168—61no—
5782−1+4—151no—
5792−1+4C2×D1511yescharacteristic
580H(5,𝔽2)—151no—
581H(5,𝔽2)C2×D1511yescharacteristic, complemented
582#137—21no—
583#137—151no—
584#137—151no—
585#137—151no—
586#137—301no—
587#137—301no—
588#137—301no—
589#137C2×D1511yescharacteristic, complemented
590AGL(1,ℤ/8)—21no—
591AGL(1,ℤ/8)—151no—
592AGL(1,ℤ/8)—151no—
593AGL(1,ℤ/8)—151no—
594AGL(1,ℤ/8)—301no—
595AGL(1,ℤ/8)—301no—
596AGL(1,ℤ/8)—301no—
597AGL(1,ℤ/8)C2×D1511yescharacteristic
598#135—21no—
599#135—151no—
600#135—301no—
601#135—301no—
602#135—301no—
603#135C2×D1511yescharacteristic
604C2×SD16—21no—
605C2×SD16—151no—
606C2×SD16—151no—
607C2×SD16—151no—
608C2×SD16—301no—
609C2×SD16—301no—
610C2×SD16—301no—
611C2×SD16C2×D1511yescharacteristic, complemented
612#131—151no—
613#131—151no—
614#131—151no—
615#131C2×D1511yescharacteristic, complemented
616C4⋊Q8—151no—
617#127—151no—
618#108—151no—
619#108—151no—
620#104—151no—
621#104—151no—
622#104—151no—
623#104—151no—
624#101—151no—
625#101—151no—
626#100—151no—
627#100—151no—
628C4×C8—151no—
629C2×C3×C5—21no—
630C2×C3×C5—41no—
631C2×C3×C5—41no—
632C2×C3×C5—41no—
633C2×C3×C5—81no—
634C2×C3×C5D4211yescharacteristic
635D15—41no—
636D15—81no—
637C23×C3—21no—
638C23×C3—41no—
639C22×D3—101no—
640C22×D3—201no—
641C3×Q8—21no—
642C3×Q8—21no—
643C3×Q8—41no—
644C3×Q8D4×D511yescharacteristic
645C3×Q8C2×C22⋊D511yescharacteristic
646C3×Q8C2×C22⋊D511yescharacteristic
647C3×D4—21no—
648C3×D4—21no—
649C3×D4—21no—
650C3×D4—21no—
651C3×D4—21no—
652C3×D4—41no—
653C3×D4—41no—
654C3×D4—41no—
655C3×D4D4×D511yescharacteristic
656C3×D4C2×C22⋊D511yescharacteristic
657C3×D4C2×C22⋊D511yescharacteristic
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4C23×D511yescharacteristic
666#67—101no—
667#67—201no—
668#67—201no—
669#67—402no—
670C2×Dic3—101no—
671C2×Dic3—101no—
672C2×Dic3—201no—
673D12—51no—
674D12—101no—
675D12—101no—
676D12—201no—
677C4×D3—101no—
678C4×D3—201no—
679C4×D3—201no—
680Dic6—51no—
681Dic6—101no—
682Dic6—101no—
683Dic6—201no—
684C3×C8—21no—
685C3×C8C2×C22⋊D511yescharacteristic
686C3×C8C2×C22⋊D511yescharacteristic
687C3⋊C8—51no—
688C3⋊C8—51no—
689C3⋊C8—101no—
690C3⋊C8—101no—
691C3⋊C8—101no—
692C22×C5—21no—
693C22×C5—21no—
694C22×C5—21no—
695C22×C5—41no—
696C22×C5—81no—
697C22×C5—161no—
698C22×C5#100411yescharacteristic
699C2×D5—61no—
700C2×D5—121no—
701C2×D5—241no—
702C2×D5—481no—
703C4×C5—21no—
704C4×C5—21no—
705C4×C5—21no—
706C4×C5—41no—
707C4×C5C2×D3×D411yescharacteristic
708C4×C5C22×#6711yescharacteristic
709Dic5—62no—
710Dic5—61no—
711Dic5—121no—
712#41—21no—
713#41—21no—
714#41—21no—
715#41—21no—
716#41—41no—
717#41—151no—
718#41—301no—
719#41—301no—
720#41—301no—
721#41—301no—
722#41—601no—
723#41C22×D1511yescharacteristic
724#41C22×D1511yescharacteristic
725#41C22×D1511yescharacteristic
726C2×Q8—21no—
727C2×Q8—21no—
728C2×Q8—151no—
729C2×Q8—301no—
730C2×Q8—301no—
731C2×Q8C22×D1511yescharacteristic
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—41no—
735C2×D4—151no—
736C2×D4—301no—
737C2×D4—301no—
738C2×D4—601no—
739C2×D4—601no—
740C2×D4C22×D1511yescharacteristic
741Q16—21no—
742Q16—151no—
743Q16—301no—
744Q16—301no—
745Q16—301no—
746Q16#122011yescharacteristic, complemented
747SD16—21no—
748SD16—21no—
749SD16—21no—
750SD16—21no—
751SD16—151no—
752SD16—151no—
753SD16—301no—
754SD16—301no—
755SD16—301no—
756SD16—301no—
757SD16—301no—
758SD16—301no—
759SD16—301no—
760SD16—301no—
761SD16—301no—
762SD16—301no—
763SD16—301no—
764SD16—301no—
765SD16#122011yescharacteristic, complemented
766SD16#122011yescharacteristic, complemented
767D8—21no—
768D8—151no—
769D8—301no—
770D8—301no—
771D8—301no—
772D8#122011yescharacteristic, complemented
773M16—21no—
774M16—151no—
775M16—151no—
776M16—151no—
777M16—301no—
778M16—301no—
779M16—301no—
780M16C22×D1511yescharacteristic
781C2×C8—21no—
782C2×C8—151no—
783C2×C8—301no—
784C2×C8—301no—
785C2×C8—301no—
786C2×C8C22×D1511yescharacteristic
787C4⋊C4—601no—
788C42—151no—
789C3×C5#329111yescharacteristic, complemented, Hall
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—41no—
794C22×C3—81no—
795C22×C3—161no—
796C22×C3#414411yescharacteristic
797C2×D3—101no—
798C2×D3—201no—
799C2×D3—401no—
800C2×D3—801no—
801C3×C4—21no—
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—41no—
805C3×C4C2×D4×D511yescharacteristic
806C3×C4C22×C22⋊D511yescharacteristic
807Dic3—102no—
808Dic3—101no—
809Dic3—201no—
810C2×C5—21no—
811C2×C5—41no—
812C2×C5—41no—
813C2×C5—41no—
814C2×C5—81no—
815C2×C5D4×#6711yescharacteristic
816D5—121no—
817D5—241no—
818C23—21no—
819C23—41no—
820C23—301no—
821C23—601no—
822Q8—21no—
823Q8—21no—
824Q8—41no—
825Q8—151no—
826Q8—301no—
827Q8—301no—
828Q8—601no—
829Q8D4×D1511yescharacteristic
830Q8C2×#122011yescharacteristic
831Q8C2×#122011yescharacteristic
832D4—21no—
833D4—21no—
834D4—21no—
835D4—21no—
836D4—21no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—151no—
841D4—301no—
842D4—301no—
843D4—301no—
844D4—601no—
845D4—601no—
846D4—601no—
847D4—1202no—
848D4D4×D1511yescharacteristic
849D4C2×#122011yescharacteristic
850D4C2×#122011yescharacteristic
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—301no—
859C2×C4—301no—
860C2×C4—301no—
861C2×C4—601no—
862C2×C4—601no—
863C2×C4—601no—
864C2×C4C23×D1511yescharacteristic
865C8—21no—
866C8—151no—
867C8—151no—
868C8—301no—
869C8—301no—
870C8—301no—
871C8C2×#122011yescharacteristic
872C8C2×#122011yescharacteristic
873C2×C3—21no—
874C2×C3—41no—
875C2×C3—41no—
876C2×C3—41no—
877C2×C3—81no—
878C2×C3D4×C22⋊D511yescharacteristic
879D3—201no—
880D3—401no—
881C5#8401411yescharacteristic, complemented, Sylow
882C22—21no—
883C22—21no—
884C22—21no—
885C22—41no—
886C22—81no—
887C22—161no—
888C22—301no—
889C22—601no—
890C22—1201no—
891C22—2401no—
892C22#9209511yescharacteristic
893C4—21no—
894C4—21no—
895C4—21no—
896C4—41no—
897C4—302no—
898C4—301no—
899C4—601no—
900C4C2×D4×D1511yescharacteristic
901C4C22×#122011yescharacteristic
902C3#1061574511yescharacteristic, complemented, Sylow
903C2—21no—
904C2—41no—
905C2—41no—
906C2—41no—
907C2—81no—
908C2—601no—
909C2—1201no—
910C2D4×#122011yescharacteristic
subgroupG/H
centerC2D4×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#577C2
socleC2×C3×C5D42
hypercenter#577D15
hypocenterC3×C5#3291
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. C3×C5×#577C2semidirect
2. #11756596C2semidirect
3. #11756595C2semidirect
4. #11756529C2semidirect
5. #11751347C2semidirect
6. #11751342C2semidirect
7. #11751306C2semidirect
8. #11751304C2semidirect
9. #11751301C2semidirect
10. #11751299C2semidirect
11. #11751297C2semidirect
12. #11751278C2semidirect
13. #11751276C2semidirect
14. #11751245C2semidirect
15. #11751242C2semidirect
18. C3×C5×H(5,𝔽2)C22semidirect
20. #92100C22semidirect
22. C3×C5×#137C22semidirect
28. C2×C3×C5×SD16C22semidirect
29. C3×C5×#131C22semidirect
31. #91840C22semidirect
32. #91840C22semidirect
39. #91837C22semidirect
40. #91837C22semidirect
41. #91833C22semidirect
43. #91831C22semidirect
45. C2×#6717C22semidirect
48. C2×#6716C22semidirect
55. C2×#6706C22semidirect
56. #91790C22semidirect
57. #91121C22semidirect
58. #91121C22semidirect
59. #91121C22semidirect
60. #91120C22semidirect
61. #91117C22semidirect
62. #91109C22semidirect
63. #91108C22semidirect
64. #91107C22semidirect
65. #91106C22semidirect
66. #91103C22semidirect
67. C8×Dic15C22semidirect
69. C5×#577D3semidirect
114. C3×C5×Q16D4semidirect
119. C3×C5×SD16D4semidirect
120. C3×C5×SD16D4semidirect
122. C3×C5×D8D4semidirect
130. #6718D4semidirect
136. #6717D4semidirect
142. #6716D4semidirect
146. #6715D4semidirect
161. C3×#577D5semidirect
177. C5×H(5,𝔽2)C2×D3semidirect
181. C5×#137C2×D3semidirect
187. C2×C5×SD16C2×D3semidirect
188. C5×#131C2×D3semidirect
284. C3×H(5,𝔽2)C2×D5semidirect
288. C3×#137C2×D5semidirect
294. C2×C3×SD16C2×D5semidirect
295. C3×#131C2×D5semidirect
364. C5×Q16#67semidirect
369. C5×SD16#67semidirect
370. C5×SD16#67semidirect
372. C5×D8#67semidirect
414. #577D15semidirect
476. C3×Q16C22⋊D5semidirect
481. C3×SD16C22⋊D5semidirect
482. C3×SD16C22⋊D5semidirect
484. C3×D8C22⋊D5semidirect
581. H(5,𝔽2)C2×D15semidirect
589. #137C2×D15semidirect
611. C2×SD16C2×D15semidirect
615. #131C2×D15semidirect
746. Q16#1220semidirect
765. SD16#1220semidirect
766. SD16#1220semidirect
772. D8#1220semidirect
789. C3×C5#3291semidirect
881. C5#84014semidirect
902. C3#10615745semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5772
#117565962
#117565952
#117565292
#117513472
#117513422
#117513062
#117513042
#117513012
#117512992
#117512972
#117512782
#117512762
#117512452
#117512422
#106157453
#840145