Finite Group Databasebeta

← D15×#540 #14481078

Subgroups — D15×#540 #14481078

Order 1920.

2520 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#540C211yesmaximal, characteristic, complemented
2#11756478C211yesmaximal, characteristic, complemented
3D15×#127C211yesmaximal, characteristic, complemented
4#11756456C211yesmaximal, characteristic, complemented
5D15×#125C211yesmaximal, characteristic, complemented
6#11756422C214yesmaximal, complemented
7D15×#123C214yesmaximal, complemented
8#11756378C212yesmaximal, complemented
9#11756374C214yesmaximal, complemented
10D15×#121C214yesmaximal, complemented
11D15×#121C212yesmaximal, complemented
12#11756321C212yesmaximal, complemented
13C4×D4×D15C212yesmaximal, complemented
14#11756294C211yesmaximal, characteristic, complemented
15D15×#117C211yesmaximal, characteristic, complemented
16D5×#540—31nomaximal, Hall
17C2×D4×D15C2212yes—
18C2×D4×D15C2214yes—
19C2×D4×D15C2214yes—
20C22×C4×D15C2211yescharacteristic
21C22×C4×D15C2214yes—
22C3×C5×#127C2211yescharacteristic, complemented
23C3×C5×#125C2211yescharacteristic, complemented
24C3×C5×#123C2214yescomplemented
25C3×C5×#121C2214yescomplemented
26C3×C5×#121C2212yescomplemented
27C3×C4×C5×D4C2212yescomplemented
28C3×C5×#117C2211yescharacteristic, complemented
29#91829C2212yescomplemented
30#91829C2214yescomplemented
31#91828C2214yescomplemented
32#91828C2214yescomplemented
33#91828C2214yescomplemented
34#91827C2212yescomplemented
35#91827C2214yescomplemented
36#91824C2214yescomplemented
37D4×Dic15C2212yescomplemented
38#91819C2212yescomplemented
39#91819C2214yescomplemented
40#91818C2214yescomplemented
41C4×#1220C2214yescomplemented
42#91815C2211yescharacteristic, complemented
43#91784C2212yescomplemented
44#91784C2214yescomplemented
45#91783C2214yescomplemented
46#91783C2214yescomplemented
47#91782C2212yescomplemented
48#91781C2212yescomplemented
49C4⋊C4×D15C2212yes—
50C4⋊C4×D15C2214yes—
51C4⋊C4×D15C2212yes—
52#91779C2212yescomplemented
53#91778C2214yescomplemented
54#91775C2214yescomplemented
55#91773C2214yescomplemented
56#91773C2214yescomplemented
57#91773C2214yescomplemented
58#91772C2214yescomplemented
59#91772C2214yescomplemented
60#91770C2214yescomplemented
61C22⋊C4×D15C2214yes—
62C22⋊C4×D15C2212yes—
63C22⋊C4×D15C2214yes—
64#91766C2212yescomplemented
65#91763C2211yescharacteristic, complemented
66C4×D60C2212yescomplemented
67#91761C2211yescharacteristic, complemented
68#91761C2211yescharacteristic, complemented
69C42×D15C2211yescharacteristic
70C42×D15C2211yescharacteristic
71#91759C2211yescharacteristic, complemented
72D3×#540—51nomaximal, Hall
73C5×#540D311yescharacteristic, complemented
74#66053—31no—
75D5×#127—31no—
76#66032—31no—
77D5×#125—31no—
78#65997—34no—
79D5×#123—34no—
80#65953—32no—
81#65949—34no—
82D5×#121—34no—
83D5×#121—32no—
84#65896—32no—
85C4×D4×D5—32no—
86#65869—31no—
87D5×#117—31no—
88C23×D15C2311yescharacteristic
89C23×D15C2314yes—
90C2×C3×C5×D4C2312yes—
91C2×C3×C5×D4C2314yes—
92C2×C3×C5×D4C2314yes—
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2314yes—
95C2×#1220C2314yes—
96C2×#1220C2314yes—
97C2×#1220C2314yes—
98C2×#1220C2314yes—
99C2×#1220C2314yes—
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2314yes—
102D4×D15—28no—
103D4×D15—48no—
104D4×D15—48no—
105C2×D60C2312yes—
106C2×D60C2314yes—
107C2×D60C2314yes—
108C2×C4×D15—24no—
109C2×C4×D15—48no—
110C2×C4×D15C2312yes—
111C2×C4×D15C2312yes—
112C2×C4×D15C2311yescharacteristic
113C2×C4×D15C2311yescharacteristic
114C2×C4×D15C2314yes—
115C2×C4×D15C2311yescharacteristic
116C2×C4×D15C2314yes—
117C2×C4×D15C2314yes—
118C2×C4×D15C2311yescharacteristic
119C3×C5×C4⋊C4C2314yes—
120C3×C5×C4⋊C4C2312yes—
121C3×C5×C4⋊C4C2312yes—
122C3×C5×C22⋊C4C2312yes—
123C3×C5×C22⋊C4C2314yes—
124C3×C5×C22⋊C4C2314yes—
125C3×C42×C5C2311yescharacteristic
126C3×C42×C5C2311yescharacteristic
127#6719C2312yes—
128#6719C2314yes—
129#6719C2314yes—
130#6714C2312yes—
131#6714C2312yes—
132#6714C2314yes—
133#6714C2314yes—
134#6714C2314yes—
135#6714C2314yes—
136C4⋊Dic15C2312yes—
137C4⋊Dic15C2312yes—
138C4⋊Dic15C2314yes—
139#6712C2314yes—
140#6712C2312yes—
141#6712C2312yes—
142#6712C2314yes—
143#6712C2314yes—
144C4×Dic15C2311yescharacteristic
145C4×Dic15C2311yescharacteristic
146C4×Dic15C2312yes—
147C4×Dic15C2312yes—
148C3×#540D511yescharacteristic, complemented
149#5719—51no—
150D3×#127—51no—
151#5697—51no—
152D3×#125—51no—
153#5663—54no—
154D3×#123—54no—
155#5619—52no—
156#5615—54no—
157D3×#121—52no—
158D3×#121—54no—
159#5562—52no—
160C4×D3×D4—52no—
161#5535—51no—
162D3×#117—51no—
163C2×D4×D5—32no—
164C2×D4×D5—34no—
165C2×D4×D5—34no—
166C22×C4×D5—31no—
167C22×C4×D5—34no—
168C5×#127C2×D311yescharacteristic, complemented
169C5×#125C2×D311yescharacteristic, complemented
170C5×#123C2×D314yescomplemented
171C5×#121C2×D314yescomplemented
172C5×#121C2×D312yescomplemented
173C4×C5×D4C2×D312yescomplemented
174C5×#117C2×D311yescharacteristic, complemented
175#4086—32no—
176#4086—34no—
177#4085—34no—
178#4085—34no—
179#4085—34no—
180#4084—32no—
181#4084—34no—
182#4081—34no—
183D4×Dic5—32no—
184#4076—32no—
185#4076—34no—
186#4075—34no—
187C4×C22⋊D5—34no—
188#4072—31no—
189#4041—32no—
190#4041—34no—
191#4040—34no—
192#4040—34no—
193#4039—32no—
194#4038—32no—
195D5×C4⋊C4—32no—
196D5×C4⋊C4—32no—
197D5×C4⋊C4—34no—
198#4036—32no—
199#4035—34no—
200#4032—34no—
201#4030—34no—
202#4030—34no—
203#4030—34no—
204#4029—34no—
205#4029—34no—
206#4027—34no—
207D5×C22⋊C4—32no—
208D5×C22⋊C4—34no—
209D5×C22⋊C4—34no—
210#4023—32no—
211#4020—31no—
212C4×D20—32no—
213#4018—31no—
214#4018—31no—
215C42×D5—31no—
216C42×D5—31no—
217#4016—31no—
218C2×#540—151noSylow
219C23×C3×C5C2411yescharacteristic
220C23×C3×C5C2414yes—
221C22×D15—22no—
222C22×D15—28no—
223C22×D15—28no—
224C22×D15—24no—
225C22×D15—28no—
226C22×D15C2411yescharacteristic
227C22×D15C2414yes—
228C22×D15C2411yescharacteristic
229C3×C5×D4—24no—
230C3×C5×D4—44no—
231C3×C5×D4—44no—
232C2×C3×C4×C5—22no—
233C2×C3×C4×C5—44no—
234C2×C3×C4×C5C2412yes—
235C2×C3×C4×C5C2412yes—
236C2×C3×C4×C5C2414yes—
237C2×C3×C4×C5C2411yescharacteristic
238C2×C3×C4×C5C2411yescharacteristic
239#1220—28no—
240#1220—44no—
241#1220—44no—
242#1220—44no—
243#1220—44no—
244C2×Dic15—22no—
245C2×Dic15—44no—
246C2×Dic15C2412yes—
247C2×Dic15C2412yes—
248C2×Dic15C2414yes—
249C2×Dic15C2411yescharacteristic
250C2×Dic15C2411yescharacteristic
251D60—24no—
252D60—44no—
253D60—44no—
254C4×D15—22no—
255C4×D15—24no—
256C4×D15—28no—
257C4×D15—24no—
258C4×D15—22no—
259C4×D15—22no—
260C4×D15—44no—
261C4×D15—44no—
262C4×D15#4114yes—
263C2×D3×D4—52no—
264C2×D3×D4—54no—
265C2×D3×D4—54no—
266C22×C4×D3—51no—
267C22×C4×D3—54no—
268C3×#127C2×D511yescharacteristic, complemented
269C3×#125C2×D511yescharacteristic, complemented
270C3×#123C2×D514yescomplemented
271C3×#121C2×D514yescomplemented
272C3×#121C2×D512yescomplemented
273C3×C4×D4C2×D512yescomplemented
274C3×#117C2×D511yescharacteristic, complemented
275#940—54no—
276#940—52no—
277#939—54no—
278#939—54no—
279#939—54no—
280#938—52no—
281#938—54no—
282#935—54no—
283D4×Dic3—52no—
284#930—54no—
285#930—52no—
286#929—54no—
287C4×#67—54no—
288#926—51no—
289#895—54no—
290#895—52no—
291#894—54no—
292#894—54no—
293#893—52no—
294#892—52no—
295D3×C4⋊C4—52no—
296D3×C4⋊C4—54no—
297D3×C4⋊C4—52no—
298#890—52no—
299#889—54no—
300#886—54no—
301#884—54no—
302#884—54no—
303#884—54no—
304#883—54no—
305#883—54no—
306#67⋊C4—54no—
307D3×C22⋊C4—54no—
308D3×C22⋊C4—54no—
309D3×C22⋊C4—52no—
310#877—52no—
311#874—51no—
312C4×D12—52no—
313#872—51no—
314#872—51no—
315C42×D3—51no—
316C42×D3—51no—
317#870—51no—
318C23×D5—31no—
319C23×D5—34no—
320C2×C5×D4C22×D312yes—
321C2×C5×D4C22×D314yes—
322C2×C5×D4C22×D314yes—
323C22×C4×C5C22×D311yescharacteristic
324C22×C4×C5C22×D314yes—
325C2×C22⋊D5—34no—
326C2×C22⋊D5—34no—
327C2×C22⋊D5—34no—
328C2×C22⋊D5—34no—
329C2×C22⋊D5—34no—
330C22×Dic5—31no—
331C22×Dic5—34no—
332D4×D5—68no—
333D4×D5—128no—
334D4×D5—128no—
335C2×D20—32no—
336C2×D20—34no—
337C2×D20—34no—
338C2×C4×D5—31no—
339C2×C4×D5—32no—
340C2×C4×D5—34no—
341C2×C4×D5—31no—
342C2×C4×D5—31no—
343C2×C4×D5—31no—
344C2×C4×D5—32no—
345C2×C4×D5—34no—
346C2×C4×D5—34no—
347C2×C4×D5—64no—
348C2×C4×D5—128no—
349C5×C4⋊C4C22×D312yes—
350C5×C4⋊C4C22×D312yes—
351C5×C4⋊C4C22×D314yes—
352C5×C22⋊C4C22×D312yes—
353C5×C22⋊C4C22×D314yes—
354C5×C22⋊C4C22×D314yes—
355C42×C5C22×D311yescharacteristic
356C42×C5C22×D311yescharacteristic
357C22⋊Dic5—32no—
358C22⋊Dic5—34no—
359C22⋊Dic5—34no—
360#685—32no—
361#685—32no—
362#685—34no—
363#685—34no—
364#685—34no—
365#685—34no—
366C4⋊Dic5—32no—
367C4⋊Dic5—32no—
368C4⋊Dic5—34no—
369#683—34no—
370#683—32no—
371#683—32no—
372#683—34no—
373#683—34no—
374C4×Dic5—31no—
375C4×Dic5—31no—
376C4×Dic5—32no—
377C4×Dic5—32no—
378#540—151no—
379#540—151no—
380#540—154no—
381#540—154no—
382#540—152no—
383#540—152no—
384#540—151no—
385#540D1511yescharacteristic, direct product factor
386C2×#127—151no—
387C2×#125—151no—
388C2×#123—154no—
389C2×#121—154no—
390C2×#121—152no—
391C2×C4×D4—152no—
392C2×#117—151no—
393C22×C3×C5—21no—
394C22×C3×C5—24no—
395C22×C3×C5—24no—
396C22×C3×C5—22no—
397C22×C3×C5—24no—
398C22×C3×C5C2511yescharacteristic
399C2×D15—21no—
400C2×D15—24no—
401C2×D15—24no—
402C2×D15—22no—
403C2×D15—24no—
404C2×D15—44no—
405C2×D15—416no—
406C2×D15C2×#4112yes—
407C2×D15H(5,𝔽2)14yes—
408C3×C4×C5—21no—
409C3×C4×C5—22no—
410C3×C4×C5—24no—
411C3×C4×C5—22no—
412C3×C4×C5C2×#4112yes—
413Dic15—21no—
414Dic15—22no—
415Dic15—24no—
416Dic15—22no—
417Dic15C2×#4112yes—
418C23×D3—51no—
419C23×D3—54no—
420C2×C3×D4C22×D512yes—
421C2×C3×D4C22×D514yes—
422C2×C3×D4C22×D514yes—
423C22×C3×C4C22×D511yescharacteristic
424C22×C3×C4C22×D514yes—
425C2×#67—54no—
426C2×#67—54no—
427C2×#67—54no—
428C2×#67—54no—
429C2×#67—54no—
430C22×Dic3—51no—
431C22×Dic3—54no—
432D3×D4—108no—
433D3×D4—208no—
434D3×D4—208no—
435C2×D12—52no—
436C2×D12—54no—
437C2×D12—54no—
438C2×C4×D3—51no—
439C2×C4×D3—52no—
440C2×C4×D3—52no—
441C2×C4×D3—51no—
442C2×C4×D3—51no—
443C2×C4×D3—54no—
444C2×C4×D3—51no—
445C2×C4×D3—54no—
446C2×C4×D3—54no—
447C2×C4×D3—104no—
448C2×C4×D3—208no—
449C3×C4⋊C4C22×D514yes—
450C3×C4⋊C4C22×D512yes—
451C3×C4⋊C4C22×D512yes—
452C3×C22⋊C4C22×D512yes—
453C3×C22⋊C4C22×D514yes—
454C3×C22⋊C4C22×D514yes—
455C3×C42C22×D511yescharacteristic
456C3×C42C22×D511yescharacteristic
457#217—52no—
458#217—54no—
459#217—54no—
460(C2×D3)⋊C4—52no—
461(C2×D3)⋊C4—52no—
462(C2×D3)⋊C4—54no—
463(C2×D3)⋊C4—54no—
464(C2×D3)⋊C4—54no—
465(C2×D3)⋊C4—54no—
466C4⋊Dic3—52no—
467C4⋊Dic3—52no—
468C4⋊Dic3—54no—
469Dic3⋊C4—54no—
470Dic3⋊C4—52no—
471Dic3⋊C4—52no—
472Dic3⋊C4—54no—
473Dic3⋊C4—54no—
474C4×Dic3—51no—
475C4×Dic3—51no—
476C4×Dic3—52no—
477C4×Dic3—52no—
478C23×C5C23×D311yescharacteristic
479C23×C5C23×D314yes—
480C22×D5—31no—
481C22×D5—31no—
482C22×D5—34no—
483C22×D5—62no—
484C22×D5—68no—
485C22×D5—68no—
486C22×D5—64no—
487C22×D5—68no—
488C5×D4—24no—
489C5×D4—44no—
490C5×D4—44no—
491C2×C4×C5—22no—
492C2×C4×C5—44no—
493C2×C4×C5C23×D312yes—
494C2×C4×C5C23×D312yes—
495C2×C4×C5C23×D314yes—
496C2×C4×C5C23×D311yescharacteristic
497C2×C4×C5C23×D311yescharacteristic
498C22⋊D5—68no—
499C22⋊D5—124no—
500C22⋊D5—124no—
501C22⋊D5—124no—
502C22⋊D5—124no—
503C2×Dic5—31no—
504C2×Dic5—32no—
505C2×Dic5—32no—
506C2×Dic5—34no—
507C2×Dic5—31no—
508C2×Dic5—62no—
509C2×Dic5—124no—
510D20—64no—
511D20—124no—
512D20—124no—
513C4×D5—34no—
514C4×D5—62no—
515C4×D5—62no—
516C4×D5—64no—
517C4×D5—68no—
518C4×D5—64no—
519C4×D5—62no—
520C4×D5—124no—
521C4×D5—124no—
522C22×D4—152no—
523C22×D4—154no—
524C22×D4—154no—
525C23×C4—151no—
526C23×C4—154no—
527#127—154no—
528#127—152no—
529#127—151no—
530#127C2×D1511yescharacteristic, complemented
531#125—154no—
532#125—152no—
533#125—151no—
534#125C2×D1511yescharacteristic, complemented
535#123—154no—
536#123—154no—
537#123—154no—
538#123—154no—
539#123—154no—
540#123—154no—
541#123—154no—
542#123C2×D1514yescomplemented
543#121—154no—
544#121—152no—
545#121—154no—
546#121—154no—
547#121—154no—
548#121—154no—
549#121—152no—
550#121—154no—
551#121—152no—
552#121—154no—
553#121—154no—
554#121—154no—
555#121C2×D1514yescomplemented
556#121C2×D1512yescomplemented
557C4×D4—152no—
558C4×D4—154no—
559C4×D4—152no—
560C4×D4—154no—
561C4×D4—152no—
562C4×D4C2×D1512yescomplemented
563#117—151no—
564#117—152no—
565#117—152no—
566#117—151no—
567#117—151no—
568#117C2×D1511yescharacteristic, complemented
569C2×C4⋊C4—152no—
570C2×C4⋊C4—152no—
571C2×C4⋊C4—154no—
572C2×C22⋊C4—152no—
573C2×C22⋊C4—154no—
574C2×C22⋊C4—154no—
575C2×C42—151no—
576C2×C42—151no—
577C2×C3×C5—41no—
578C2×C3×C5—44no—
579C2×C3×C5C22×#4111yescharacteristic
580C2×C3×C5C2×H(5,𝔽2)12yes—
581D15—41no—
582D15—44no—
583D15#54014yesdirect product factor
584C23×C3C23×D511yescharacteristic
585C23×C3C23×D514yes—
586C22×D3—51no—
587C22×D3—51no—
588C22×D3—54no—
589C22×D3—102no—
590C22×D3—108no—
591C22×D3—108no—
592C22×D3—104no—
593C22×D3—108no—
594C3×D4—24no—
595C3×D4—44no—
596C3×D4—44no—
597C2×C3×C4—22no—
598C2×C3×C4—44no—
599C2×C3×C4C23×D512yes—
600C2×C3×C4C23×D512yes—
601C2×C3×C4C23×D514yes—
602C2×C3×C4C23×D511yescharacteristic
603C2×C3×C4C23×D511yescharacteristic
604#67—108no—
605#67—204no—
606#67—204no—
607#67—204no—
608#67—204no—
609C2×Dic3—51no—
610C2×Dic3—52no—
611C2×Dic3—52no—
612C2×Dic3—54no—
613C2×Dic3—51no—
614C2×Dic3—102no—
615C2×Dic3—204no—
616D12—104no—
617D12—204no—
618D12—204no—
619C4×D3—54no—
620C4×D3—102no—
621C4×D3—102no—
622C4×D3—104no—
623C4×D3—108no—
624C4×D3—104no—
625C4×D3—102no—
626C4×D3—204no—
627C4×D3—204no—
628C22×C5—21no—
629C22×C5—24no—
630C22×C5—24no—
631C22×C5—22no—
632C22×C5—24no—
633C22×C5C24×D311yescharacteristic
634C2×D5—32no—
635C2×D5—34no—
636C2×D5—61no—
637C2×D5—64no—
638C2×D5—64no—
639C2×D5—62no—
640C2×D5—64no—
641C2×D5—124no—
642C2×D5—1216no—
643C4×C5—21no—
644C4×C5—22no—
645C4×C5—24no—
646C4×C5—22no—
647C4×C5D3×#4112yes—
648Dic5—32no—
649Dic5—61no—
650Dic5—62no—
651Dic5—64no—
652Dic5—62no—
653C24—151no—
654C24—154no—
655C2×D4—154no—
656C2×D4—154no—
657C2×D4—154no—
658C2×D4—154no—
659C2×D4—154no—
660C2×D4—152no—
661C2×D4—154no—
662C2×D4—154no—
663C2×D4—308no—
664C2×D4—608no—
665C2×D4—608no—
666C2×D4C22×D1512yes—
667C2×D4C22×D1514yes—
668C2×D4C22×D1514yes—
669C22×C4—151no—
670C22×C4—151no—
671C22×C4—154no—
672C22×C4—152no—
673C22×C4—152no—
674C22×C4—151no—
675C22×C4—154no—
676C22×C4—151no—
677C22×C4—151no—
678C22×C4—154no—
679C22×C4—154no—
680C22×C4—304no—
681C22×C4—608no—
682C22×C4C22×D1511yescharacteristic
683C22×C4C22×D1514yes—
684C4⋊C4—152no—
685C4⋊C4—152no—
686C4⋊C4—152no—
687C4⋊C4—154no—
688C4⋊C4—152no—
689C4⋊C4—154no—
690C4⋊C4—154no—
691C4⋊C4—154no—
692C4⋊C4C22×D1512yes—
693C4⋊C4C22×D1512yes—
694C4⋊C4C22×D1514yes—
695C22⋊C4—152no—
696C22⋊C4—154no—
697C22⋊C4—154no—
698C22⋊C4—152no—
699C22⋊C4—152no—
700C22⋊C4—154no—
701C22⋊C4—154no—
702C22⋊C4—154no—
703C22⋊C4—154no—
704C22⋊C4C22×D1512yes—
705C22⋊C4C22×D1514yes—
706C22⋊C4C22×D1514yes—
707C42—152no—
708C42—151no—
709C42—152no—
710C42—151no—
711C42C22×D1511yescharacteristic
712C42C22×D1511yescharacteristic
713C3×C5C2×#54011yescharacteristic, complemented, Hall
714C22×C3—21no—
715C22×C3—24no—
716C22×C3—24no—
717C22×C3—22no—
718C22×C3—24no—
719C22×C3C24×D511yescharacteristic
720C2×D3—52no—
721C2×D3—54no—
722C2×D3—101no—
723C2×D3—104no—
724C2×D3—104no—
725C2×D3—102no—
726C2×D3—104no—
727C2×D3—204no—
728C2×D3—2016no—
729C3×C4—21no—
730C3×C4—22no—
731C3×C4—24no—
732C3×C4—22no—
733C3×C4D5×#4112yes—
734Dic3—52no—
735Dic3—101no—
736Dic3—102no—
737Dic3—104no—
738Dic3—102no—
739C2×C5—41no—
740C2×C5—44no—
741C2×C5C2×D3×#4111yescharacteristic
742C2×C5D3×H(5,𝔽2)12yes—
743D5—34no—
744D5—121no—
745D5—124no—
746C23—151no—
747C23—151no—
748C23—154no—
749C23—302no—
750C23—308no—
751C23—308no—
752C23—304no—
753C23—308no—
754C23C23×D1511yescharacteristic
755C23C23×D1514yes—
756D4—24no—
757D4—44no—
758D4—44no—
759D4—308no—
760D4—304no—
761D4—604no—
762D4—604no—
763D4—604no—
764D4—604no—
765D4—604no—
766D4—604no—
767C2×C4—22no—
768C2×C4—44no—
769C2×C4—151no—
770C2×C4—154no—
771C2×C4—152no—
772C2×C4—152no—
773C2×C4—151no—
774C2×C4—154no—
775C2×C4—302no—
776C2×C4—302no—
777C2×C4—304no—
778C2×C4—308no—
779C2×C4—304no—
780C2×C4—302no—
781C2×C4—302no—
782C2×C4—604no—
783C2×C4—604no—
784C2×C4—604no—
785C2×C4C23×D1512yes—
786C2×C4C23×D1512yes—
787C2×C4C23×D1511yescharacteristic
788C2×C4C23×D1514yes—
789C2×C4C23×D1511yescharacteristic
790C2×C3—41no—
791C2×C3—44no—
792C2×C3C2×D5×#4111yescharacteristic
793C2×C3D5×H(5,𝔽2)12yes—
794D3—54no—
795D3—201no—
796D3—204no—
797C5D3×#54011yescharacteristic, complemented, Sylow
798C22—21no—
799C22—24no—
800C22—24no—
801C22—22no—
802C22—24no—
803C22—152no—
804C22—154no—
805C22—301no—
806C22—304no—
807C22—304no—
808C22—302no—
809C22—304no—
810C22—604no—
811C22—6016no—
812C22C24×D1511yescharacteristic
813C4—21no—
814C4—22no—
815C4—24no—
816C4—22no—
817C4—152no—
818C4—301no—
819C4—302no—
820C4—304no—
821C4—302no—
822C4#41×D1512yes—
823C3D5×#54011yescharacteristic, complemented, Sylow
824C2—41no—
825C2—44no—
826C2—154no—
827C2—601no—
828C2—604no—
829C2C2×#41×D1511yescharacteristic
830C2D15×H(5,𝔽2)12yes—
subgroupG/H
center, FrattiniC22C24×D15
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#540C2
hypercenter#540D15
hypocenterC3×C5C2×#540
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #540

Complements

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

NH ≅ G/Ntype
1. C3×C5×#540C2semidirect
2. #11756478C2semidirect
3. D15×#127C2semidirect
4. #11756456C2semidirect
5. D15×#125C2semidirect
6. #11756422C2semidirect
7. D15×#123C2semidirect
8. #11756378C2semidirect
9. #11756374C2semidirect
10. D15×#121C2semidirect
11. D15×#121C2semidirect
12. #11756321C2semidirect
13. C4×D4×D15C2semidirect
14. #11756294C2semidirect
15. D15×#117C2semidirect
22. C3×C5×#127C22semidirect
23. C3×C5×#125C22semidirect
24. C3×C5×#123C22semidirect
25. C3×C5×#121C22semidirect
26. C3×C5×#121C22semidirect
27. C3×C4×C5×D4C22semidirect
28. C3×C5×#117C22semidirect
29. #91829C22semidirect
30. #91829C22semidirect
31. #91828C22semidirect
32. #91828C22semidirect
33. #91828C22semidirect
34. #91827C22semidirect
35. #91827C22semidirect
36. #91824C22semidirect
37. D4×Dic15C22semidirect
38. #91819C22semidirect
39. #91819C22semidirect
40. #91818C22semidirect
41. C4×#1220C22semidirect
42. #91815C22semidirect
43. #91784C22semidirect
44. #91784C22semidirect
45. #91783C22semidirect
46. #91783C22semidirect
47. #91782C22semidirect
48. #91781C22semidirect
52. #91779C22semidirect
53. #91778C22semidirect
54. #91775C22semidirect
55. #91773C22semidirect
56. #91773C22semidirect
57. #91773C22semidirect
58. #91772C22semidirect
59. #91772C22semidirect
60. #91770C22semidirect
64. #91766C22semidirect
65. #91763C22semidirect
66. C4×D60C22semidirect
67. #91761C22semidirect
68. #91761C22semidirect
71. #91759C22semidirect
73. C5×#540D3semidirect
148. C3×#540D5semidirect
168. C5×#127C2×D3semidirect
169. C5×#125C2×D3semidirect
170. C5×#123C2×D3semidirect
171. C5×#121C2×D3semidirect
172. C5×#121C2×D3semidirect
173. C4×C5×D4C2×D3semidirect
174. C5×#117C2×D3semidirect
268. C3×#127C2×D5semidirect
269. C3×#125C2×D5semidirect
270. C3×#123C2×D5semidirect
271. C3×#121C2×D5semidirect
272. C3×#121C2×D5semidirect
273. C3×C4×D4C2×D5semidirect
274. C3×#117C2×D5semidirect
385. #540D15direct (N × H)
530. #127C2×D15semidirect
534. #125C2×D15semidirect
542. #123C2×D15semidirect
555. #121C2×D15semidirect
556. #121C2×D15semidirect
562. C4×D4C2×D15semidirect
568. #117C2×D15semidirect
583. D15#540direct (N × H)
713. C3×C5C2×#540semidirect
797. C5D3×#540semidirect
823. C3D5×#540semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5402
#117564782
D15×#1272
#117564562
D15×#1252
#117564222
D15×#1232
#117563782
#117563742
D15×#1212
#117563212
C4×D4×D152
#117562942
D15×#1172
D5×#5403
D3×#5405