Finite Group Databasebeta

← D5×#5719 #14481112

Subgroups — D5×#5719 #14481112

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
1#11756478C211yesmaximal, characteristic, complemented
2C5×#5719C211yesmaximal, characteristic, complemented
3C3×D5×#127C211yesmaximal, characteristic, complemented
4D5×#939C214yesmaximal, complemented
5D5×#938C212yesmaximal, complemented
6#11754913C212yesmaximal, complemented
7#11754912C212yesmaximal, complemented
8#11754855C214yesmaximal, complemented
9#11754850C214yesmaximal, complemented
10D5×#935C214yesmaximal, complemented
11D4×D5×Dic3C212yesmaximal, complemented
12D5×#872C211yesmaximal, characteristic, complemented
13#11752635C211yesmaximal, characteristic, complemented
14#11752634C211yesmaximal, characteristic, complemented
15D5×#870C211yesmaximal, characteristic, complemented
16D5×#540—31nomaximal, Hall
17C2×C3×D4×D5C2212yes—
18C2×C3×D4×D5C2214yes—
19C2×D5×#67C2214yes—
20C22×D5×Dic3C2214yes—
21C2×C4×D3×D5C2211yescharacteristic
22C3×C5×#127C2211yescharacteristic, complemented
23#91828C2214yescomplemented
24#91827C2212yescomplemented
25#91824C2214yescomplemented
26D4×Dic15C2212yescomplemented
27#91761C2211yescharacteristic, complemented
28#91759C2211yescharacteristic, complemented
29C5×#939C2214yescomplemented
30C5×#938C2212yescomplemented
31C5×#935C2214yescomplemented
32C5×D4×Dic3C2212yescomplemented
33C5×#872C2211yescharacteristic, complemented
34C5×#870C2211yescharacteristic, complemented
35C3×#4086C2214yescomplemented
36C3×#4086C2212yescomplemented
37C3×#4020C2211yescharacteristic, complemented
38C3×C42×D5C2211yescharacteristic
39#91571C2214yescomplemented
40#91569C2214yescomplemented
41#91565C2214yescomplemented
42#91559C2214yescomplemented
43Dic3×C22⋊D5C2214yescomplemented
44#91550C2214yescomplemented
45#91549C2214yescomplemented
46#91548C2214yescomplemented
47#91548C2214yescomplemented
48D5×#217C2214yes—
49D5×#217C2214yes—
50#91537C2214yescomplemented
51#91536C2214yescomplemented
52#91533C2214yescomplemented
53D5×(C2×D3)⋊C4C2212yes—
54#91465C2212yescomplemented
55#91456C2212yescomplemented
56#91434C2212yescomplemented
57Dic3×D20C2212yescomplemented
58D5×C4⋊Dic3C2212yes—
59#91409C2214yescomplemented
60#91408C2214yescomplemented
61#91407C2214yescomplemented
62#91407C2214yescomplemented
63#91402C2212yescomplemented
64#91398C2212yescomplemented
65D5×Dic3⋊C4C2212yes—
66D5×Dic3⋊C4C2214yes—
67C4×D5×Dic3C2211yescharacteristic
68#91388C2212yescomplemented
69#91386C2211yescharacteristic, complemented
70#91378C2214yescomplemented
71#91371C2211yescharacteristic, complemented
72C2×#5719—51nomaximal, Hall
73C5×#540—31no—
74#66053—31no—
75D5×#127D311yescharacteristic, complemented
76#66032—31no—
77D5×#125—31no—
78#65997—34no—
79D5×#123—34no—
80#65953—32no—
81#65949—34no—
82D5×#121—32no—
83D5×#121—34no—
84#65896—32no—
85C4×D4×D5—32no—
86#65869—31no—
87D5×#117—31no—
88C23×C3×D5C2314yes—
89C22×D3×D5C2311yescharacteristic
90C2×C3×C5×D4C2312yes—
91C2×C3×C5×D4C2314yes—
92C2×#1220C2314yes—
93C22×Dic15C2314yes—
94C2×C4×D15C2311yescharacteristic
95C2×C5×#67C2314yes—
96C22×C5×Dic3C2314yes—
97C2×C4×C5×D3C2311yescharacteristic
98C2×C3×C22⋊D5C2314yes—
99C2×C3×C22⋊D5C2314yes—
100C2×C3×C22⋊D5C2314yes—
101C3×D4×D5—28no—
102C3×D4×D5—48no—
103C2×C3×D20C2312yes—
104C2×C3×D20C2314yes—
105C2×C3×C4×D5C2312yes—
106C2×C3×C4×D5C2311yescharacteristic
107D5×#67—48no—
108C2×#1202C2314yes—
109C2×#1201C2314yes—
110C2×#1200C2311yescharacteristic
111C2×D3×Dic5C2311yescharacteristic
112C2×D5×Dic3—48no—
113C2×D5×Dic3C2314yes—
114C2×D5×Dic3C2311yescharacteristic
115C2×D5×Dic3C2312yes—
116C2×D5×Dic3C2314yes—
117C2×D5×Dic3C2314yes—
118C4×D3×D5—24no—
119C3×C42×C5C2311yescharacteristic
120#6719C2314yes—
121#6719C2314yes—
122#6714C2312yes—
123C4⋊Dic15C2312yes—
124#6712C2312yes—
125#6712C2314yes—
126C4×Dic15C2311yescharacteristic
127C5×#217C2314yes—
128C5×#217C2314yes—
129C5×(C2×D3)⋊C4C2312yes—
130C5×C4⋊Dic3C2312yes—
131C5×Dic3⋊C4C2312yes—
132C5×Dic3⋊C4C2314yes—
133C4×C5×Dic3C2311yescharacteristic
134C3×C4×Dic5C2312yes—
135C3×C4×Dic5C2311yescharacteristic
136Dic3⋊Dic5C2312yes—
137Dic3⋊Dic5C2314yes—
138#6669C2312yes—
139#6669C2314yes—
140#6668C2314yes—
141#6667C2312yes—
142(C2×D3)⋊Dic5C2312yes—
143#6665C2314yes—
144#6665C2314yes—
145#6665C2314yes—
146#6665C2314yes—
147Dic3×Dic5C2312yes—
148C2×C3×#127—51no—
149C2×#939—54no—
150C2×#938—52no—
151C2×#935—54no—
152C2×D4×Dic3—52no—
153#5719—51no—
154#5719—54no—
155#5719—52no—
156#5719—54no—
157#5719—52no—
158#5719—51no—
159#5719—51no—
160#5719D511yescharacteristic, direct product factor
161C2×#872—51no—
162C2×#870—51no—
163C2×D4×D5—34no—
164C2×D4×D5C2×D312yes—
165C2×D4×D5C2×D314yes—
166C22×C4×D5—34no—
167C22×C4×D5—31no—
168C5×#127C2×D311yescharacteristic, complemented
169C5×#125—31no—
170C5×#123—34no—
171C5×#121—32no—
172C5×#121—34no—
173C4×C5×D4—32no—
174C5×#117—31no—
175#4086C2×D312yescomplemented
176#4086C2×D314yescomplemented
177#4085—34no—
178#4085—34no—
179#4085—34no—
180#4084—32no—
181#4084—34no—
182#4081—34no—
183D4×Dic5—32no—
184#4076—34no—
185#4076—32no—
186#4075—34no—
187C4×C22⋊D5—34no—
188#4072—31no—
189#4041—34no—
190#4041—32no—
191#4040—34no—
192#4040—34no—
193#4039—32no—
194#4038—32no—
195D5×C4⋊C4—32no—
196D5×C4⋊C4—34no—
197D5×C4⋊C4—32no—
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—34no—
208D5×C22⋊C4—34no—
209D5×C22⋊C4—32no—
210#4023—32no—
211#4020C2×D311yescharacteristic, complemented
212C4×D20—32no—
213#4018—31no—
214#4018—31no—
215C42×D5—31no—
216C42×D5C2×D311yescharacteristic
217#4016—31no—
218C2×#540—151noSylow
219C23×C3×C5C2414yes—
220C22×D15C2411yescharacteristic
221C22×C5×D3C2411yescharacteristic
222C22×C3×D5—28no—
223C22×C3×D5—28no—
224C22×C3×D5—28no—
225C22×C3×D5C2414yes—
226C22×C3×D5C2411yescharacteristic
227C2×D3×D5—22no—
228C2×D3×D5—24no—
229C3×C5×D4—24no—
230C3×C5×D4—44no—
231C2×C3×C4×C5C2412yes—
232C2×C3×C4×C5C2411yescharacteristic
233#1220—44no—
234C2×Dic15—44no—
235C2×Dic15C2412yes—
236C2×Dic15C2411yescharacteristic
237C2×Dic15C2414yes—
238C4×D15—22no—
239C5×#67—44no—
240C2×C5×Dic3—44no—
241C2×C5×Dic3C2412yes—
242C2×C5×Dic3C2411yescharacteristic
243C2×C5×Dic3C2414yes—
244C4×C5×D3—22no—
245C3×C22⋊D5—28no—
246C3×C22⋊D5—44no—
247C3×C22⋊D5—44no—
248C2×C3×Dic5C2412yes—
249C2×C3×Dic5C2411yescharacteristic
250C3×D20—24no—
251C3×D20—44no—
252C3×C4×D5—24no—
253C3×C4×D5#4114yes—
254#1202—44no—
255#1201—44no—
256#1200—22no—
257D3×Dic5—22no—
258D5×Dic3—22no—
259D5×Dic3—24no—
260D5×Dic3—28no—
261D5×Dic3—44no—
262D5×Dic3—44no—
263C22×C3×D4—52no—
264C22×C3×D4—54no—
265C22×#67—54no—
266C23×Dic3—54no—
267C22×C4×D3—51no—
268C3×#127—54no—
269C3×#127—52no—
270C3×#127—51no—
271C3×#127C2×D511yescharacteristic, complemented
272C2×C3×C42—51no—
273C2×#217—54no—
274C2×#217—54no—
275#939—54no—
276#939—54no—
277#939—54no—
278#939—54no—
279#939—54no—
280#939—54no—
281#939—54no—
282#939C2×D514yescomplemented
283#938—52no—
284#938—54no—
285#938—52no—
286#938—54no—
287#938—52no—
288#938C2×D512yescomplemented
289#935—54no—
290#935—54no—
291#935—54no—
292#935—54no—
293#935—54no—
294#935—54no—
295#935—54no—
296#935C2×D514yescomplemented
297D4×Dic3—52no—
298D4×Dic3—54no—
299D4×Dic3—54no—
300D4×Dic3—52no—
301D4×Dic3—52no—
302D4×Dic3C2×D512yescomplemented
303C2×(C2×D3)⋊C4—52no—
304C2×C4⋊Dic3—52no—
305C2×Dic3⋊C4—54no—
306C2×Dic3⋊C4—52no—
307C2×C4×Dic3—51no—
308#872—51no—
309#872—51no—
310#872—52no—
311#872—52no—
312#872—51no—
313#872C2×D511yescharacteristic, complemented
314#870—51no—
315#870—52no—
316#870—54no—
317#870C2×D511yescharacteristic, complemented
318C23×D5—31no—
319C23×D5C22×D314yes—
320C2×C5×D4—34no—
321C2×C5×D4C22×D312yes—
322C2×C5×D4C22×D314yes—
323C22×C4×C5—34no—
324C22×C4×C5—31no—
325C2×C22⋊D5—34no—
326C2×C22⋊D5—34no—
327C2×C22⋊D5C22×D314yes—
328C2×C22⋊D5C22×D314yes—
329C2×C22⋊D5C22×D314yes—
330C22×Dic5—34no—
331C22×Dic5—31no—
332D4×D5—28no—
333D4×D5—48no—
334D4×D5—128no—
335C2×D20—34no—
336C2×D20C22×D312yes—
337C2×D20C22×D314yes—
338C2×C4×D5—32no—
339C2×C4×D5—34no—
340C2×C4×D5—31no—
341C2×C4×D5—31no—
342C2×C4×D5—31no—
343C2×C4×D5—34no—
344C2×C4×D5—34no—
345C2×C4×D5—64no—
346C2×C4×D5—128no—
347C2×C4×D5C22×D312yes—
348C2×C4×D5C22×D311yescharacteristic
349C5×C4⋊C4—32no—
350C5×C4⋊C4—32no—
351C5×C4⋊C4—34no—
352C5×C22⋊C4—34no—
353C5×C22⋊C4—34no—
354C5×C22⋊C4—32no—
355C42×C5—31no—
356C42×C5C22×D311yescharacteristic
357C22⋊Dic5—34no—
358C22⋊Dic5—34no—
359C22⋊Dic5—32no—
360#685—34no—
361#685—34no—
362#685—34no—
363#685—34no—
364#685—32no—
365#685—32no—
366C4⋊Dic5—32no—
367C4⋊Dic5—32no—
368C4⋊Dic5—34no—
369#683—34no—
370#683—32no—
371#683—34no—
372#683—32no—
373#683—34no—
374C4×Dic5—31no—
375C4×Dic5—32no—
376C4×Dic5C22×D311yescharacteristic
377C4×Dic5C22×D312yes—
378#540—31no—
379#540—151no—
380#540—152no—
381#540—154no—
382#540—152no—
383#540—154no—
384#540—151no—
385#540—151no—
386C2×#127—51no—
387C2×#125—151no—
388C2×#123—154no—
389C2×#121—152no—
390C2×#121—154no—
391C2×C4×D4—152no—
392C2×#117—151no—
393C22×C3×C5—24no—
394C22×C3×C5—24no—
395C22×C3×C5—24no—
396C22×C3×C5C2511yescharacteristic
397C2×D15—21no—
398C2×D15—22no—
399C2×C5×D3—21no—
400C2×C5×D3—22no—
401C2×C3×D5—24no—
402C2×C3×D5—24no—
403C2×C3×D5—24no—
404C2×C3×D5—416no—
405C2×C3×D5C2×#4112yes—
406C2×C3×D5H(5,𝔽2)14yes—
407D3×D5—44no—
408C3×C4×C5—22no—
409C3×C4×C5C2×#4112yes—
410Dic15—21no—
411Dic15—22no—
412Dic15—24no—
413C3×Dic5—22no—
414C3×Dic5C2×#4112yes—
415C5×Dic3—21no—
416C5×Dic3—22no—
417C5×Dic3—24no—
418C24×C3—54no—
419C23×D3—51no—
420C2×C3×D4—54no—
421C2×C3×D4—54no—
422C2×C3×D4—54no—
423C2×C3×D4—52no—
424C2×C3×D4—54no—
425C2×C3×D4—108no—
426C2×C3×D4—208no—
427C2×C3×D4C22×D512yes—
428C2×C3×D4C22×D514yes—
429C22×C3×C4—51no—
430C22×C3×C4—52no—
431C2×#67—54no—
432C2×#67—54no—
433C2×#67—54no—
434C2×#67—208no—
435C2×#67C22×D514yes—
436C22×Dic3—54no—
437C22×Dic3—52no—
438C22×Dic3—54no—
439C22×Dic3—51no—
440C22×Dic3—54no—
441C22×Dic3—54no—
442C22×Dic3—208no—
443C22×Dic3C22×D514yes—
444C2×C4×D3—51no—
445C2×C4×D3—51no—
446C2×C4×D3—51no—
447C2×C4×D3—104no—
448C2×C4×D3C22×D511yescharacteristic
449C3×C42—52no—
450C3×C42—51no—
451C3×C42C22×D511yescharacteristic
452#217—54no—
453#217—54no—
454#217—54no—
455#217—54no—
456#217—54no—
457#217—54no—
458#217C22×D514yes—
459#217C22×D514yes—
460(C2×D3)⋊C4—52no—
461(C2×D3)⋊C4—52no—
462(C2×D3)⋊C4—52no—
463(C2×D3)⋊C4C22×D512yes—
464C4⋊Dic3—52no—
465C4⋊Dic3—54no—
466C4⋊Dic3C22×D512yes—
467Dic3⋊C4—54no—
468Dic3⋊C4—52no—
469Dic3⋊C4—54no—
470Dic3⋊C4—52no—
471Dic3⋊C4—54no—
472Dic3⋊C4—52no—
473Dic3⋊C4C22×D514yes—
474Dic3⋊C4C22×D512yes—
475C4×Dic3—51no—
476C4×Dic3—52no—
477C4×Dic3C22×D511yescharacteristic
478C23×C5—31no—
479C23×C5C23×D314yes—
480C22×D5—28no—
481C22×D5—28no—
482C22×D5—28no—
483C22×D5—31no—
484C22×D5—62no—
485C22×D5—64no—
486C22×D5C23×D314yes—
487C22×D5C23×D311yescharacteristic
488C5×D4—24no—
489C5×D4—44no—
490C5×D4—124no—
491C2×C4×C5—32no—
492C2×C4×C5—34no—
493C2×C4×C5—31no—
494C2×C4×C5—62no—
495C2×C4×C5—124no—
496C2×C4×C5C23×D312yes—
497C2×C4×C5C23×D311yescharacteristic
498C22⋊D5—28no—
499C22⋊D5—44no—
500C22⋊D5—44no—
501C22⋊D5—124no—
502C22⋊D5—124no—
503C2×Dic5—32no—
504C2×Dic5—34no—
505C2×Dic5—31no—
506C2×Dic5—62no—
507C2×Dic5—124no—
508C2×Dic5C23×D312yes—
509C2×Dic5C23×D311yescharacteristic
510D20—24no—
511D20—44no—
512D20—124no—
513C4×D5—24no—
514C4×D5—62no—
515C4×D5—64no—
516C4×D5—68no—
517C4×D5—62no—
518C4×D5—62no—
519C4×D5—124no—
520C4×D5—124no—
521C4×D5#23714yes—
522C22×D4—52no—
523C22×D4—54no—
524C22×D4—154no—
525C23×C4—151no—
526C23×C4—154no—
527#127—54no—
528#127—52no—
529#127—51no—
530#127D3×D511yescharacteristic, complemented
531#125—31no—
532#125—154no—
533#125—152no—
534#125—151no—
535#123—34no—
536#123—154no—
537#123—154no—
538#123—154no—
539#123—154no—
540#123—154no—
541#123—154no—
542#123—154no—
543#121—32no—
544#121—34no—
545#121—154no—
546#121—154no—
547#121—154no—
548#121—152no—
549#121—154no—
550#121—152no—
551#121—154no—
552#121—154no—
553#121—154no—
554#121—154no—
555#121—152no—
556#121—154no—
557C4×D4—32no—
558C4×D4—152no—
559C4×D4—154no—
560C4×D4—152no—
561C4×D4—154no—
562C4×D4—152no—
563#117—31no—
564#117—151no—
565#117—152no—
566#117—152no—
567#117—151no—
568#117—151no—
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—51no—
576C2×C42—151no—
577C2×C3×C5—44no—
578C2×C3×C5C22×#4111yescharacteristic
579C2×C3×C5C2×H(5,𝔽2)12yes—
580D15—41no—
581C3×D5—44no—
582C3×D5#54014yescomplemented
583C5×D3—41no—
584C23×C3—51no—
585C23×C3—54no—
586C23×C3—108no—
587C23×C3—108no—
588C23×C3—108no—
589C23×C3C23×D514yes—
590C22×D3—51no—
591C22×D3—102no—
592C22×D3—104no—
593C22×D3C23×D511yescharacteristic
594C3×D4—24no—
595C3×D4—44no—
596C3×D4—108no—
597C3×D4—104no—
598C3×D4—204no—
599C3×D4—204no—
600C3×D4—204no—
601C2×C3×C4—51no—
602C2×C3×C4—54no—
603C2×C3×C4—52no—
604C2×C3×C4—104no—
605C2×C3×C4C23×D512yes—
606C2×C3×C4C23×D511yescharacteristic
607#67—44no—
608#67—204no—
609#67—204no—
610#67—204no—
611C2×Dic3—44no—
612C2×Dic3—52no—
613C2×Dic3—54no—
614C2×Dic3—51no—
615C2×Dic3—102no—
616C2×Dic3—104no—
617C2×Dic3—108no—
618C2×Dic3—204no—
619C2×Dic3—204no—
620C2×Dic3—204no—
621C2×Dic3C23×D512yes—
622C2×Dic3C23×D514yes—
623C2×Dic3C23×D511yescharacteristic
624C4×D3—22no—
625C4×D3—102no—
626C4×D3—102no—
627C4×D3—102no—
628C22×C5—24no—
629C22×C5—24no—
630C22×C5—24no—
631C22×C5—61no—
632C22×C5—62no—
633C22×C5C24×D311yescharacteristic
634C2×D5—24no—
635C2×D5—24no—
636C2×D5—24no—
637C2×D5—416no—
638C2×D5—61no—
639C2×D5—62no—
640C2×D5—124no—
641C2×D5C2×#23712yes—
642C2×D5#100414yes—
643C4×C5—22no—
644C4×C5—61no—
645C4×C5—62no—
646C4×C5—64no—
647C4×C5C2×#23712yes—
648Dic5—22no—
649Dic5—61no—
650Dic5—62no—
651Dic5—64no—
652Dic5C2×#23712yes—
653C24—54no—
654C24—151no—
655C2×D4—34no—
656C2×D4—54no—
657C2×D4—54no—
658C2×D4—54no—
659C2×D4—52no—
660C2×D4—54no—
661C2×D4—108no—
662C2×D4—154no—
663C2×D4—154no—
664C2×D4—154no—
665C2×D4—208no—
666C2×D4—608no—
667C2×D4C2×D3×D512yes—
668C2×D4C2×D3×D514yes—
669C22×C4—34no—
670C22×C4—31no—
671C22×C4—51no—
672C22×C4—52no—
673C22×C4—151no—
674C22×C4—152no—
675C22×C4—151no—
676C22×C4—154no—
677C22×C4—154no—
678C22×C4—154no—
679C22×C4—151no—
680C22×C4—154no—
681C22×C4—151no—
682C22×C4—304no—
683C22×C4—608no—
684C4⋊C4—32no—
685C4⋊C4—32no—
686C4⋊C4—34no—
687C4⋊C4—152no—
688C4⋊C4—152no—
689C4⋊C4—154no—
690C4⋊C4—154no—
691C4⋊C4—154no—
692C4⋊C4—152no—
693C4⋊C4—152no—
694C4⋊C4—154no—
695C22⋊C4—34no—
696C22⋊C4—34no—
697C22⋊C4—32no—
698C22⋊C4—152no—
699C22⋊C4—154no—
700C22⋊C4—154no—
701C22⋊C4—154no—
702C22⋊C4—154no—
703C22⋊C4—152no—
704C22⋊C4—154no—
705C22⋊C4—154no—
706C22⋊C4—152no—
707C42—31no—
708C42—52no—
709C42—51no—
710C42—152no—
711C42—151no—
712C42C2×D3×D511yescharacteristic
713C3×C5C2×#54011yescharacteristic, complemented, Hall
714C22×C3—24no—
715C22×C3—24no—
716C22×C3—24no—
717C22×C3—52no—
718C22×C3—54no—
719C22×C3—104no—
720C22×C3—104no—
721C22×C3—104no—
722C22×C3—2016no—
723C22×C3C24×D511yescharacteristic
724C2×D3—21no—
725C2×D3—22no—
726C2×D3—101no—
727C2×D3—102no—
728C2×D3—204no—
729C3×C4—22no—
730C3×C4—52no—
731C3×C4—102no—
732C3×C4D5×#4112yes—
733Dic3—21no—
734Dic3—22no—
735Dic3—24no—
736Dic3—101no—
737Dic3—102no—
738Dic3—104no—
739C2×C5—44no—
740C2×C5—121no—
741C2×C5C22×#23711yescharacteristic
742C2×C5C2×#100412yes—
743D5—44no—
744D5—121no—
745D5#571914yesdirect product factor
746C23—31no—
747C23—51no—
748C23—54no—
749C23—108no—
750C23—108no—
751C23—108no—
752C23—151no—
753C23—302no—
754C23—304no—
755C23C22×D3×D514yes—
756D4—24no—
757D4—44no—
758D4—108no—
759D4—104no—
760D4—124no—
761D4—204no—
762D4—204no—
763D4—204no—
764D4—604no—
765D4—604no—
766D4—604no—
767C2×C4—32no—
768C2×C4—31no—
769C2×C4—34no—
770C2×C4—51no—
771C2×C4—54no—
772C2×C4—52no—
773C2×C4—62no—
774C2×C4—104no—
775C2×C4—124no—
776C2×C4—152no—
777C2×C4—151no—
778C2×C4—154no—
779C2×C4—302no—
780C2×C4—302no—
781C2×C4—302no—
782C2×C4—304no—
783C2×C4—308no—
784C2×C4—302no—
785C2×C4—604no—
786C2×C4—604no—
787C2×C4—604no—
788C2×C4C22×D3×D512yes—
789C2×C4C22×D3×D511yescharacteristic
790C2×C3—44no—
791C2×C3—54no—
792C2×C3—204no—
793C2×C3C2×D5×#4111yescharacteristic
794C2×C3D5×H(5,𝔽2)12yes—
795D3—41no—
796D3—201no—
797C5C2×#571911yescharacteristic, complemented, Sylow
798C22—24no—
799C22—24no—
800C22—24no—
801C22—52no—
802C22—54no—
803C22—61no—
804C22—62no—
805C22—104no—
806C22—104no—
807C22—104no—
808C22—2016no—
809C22—301no—
810C22—302no—
811C22—604no—
812C22C23×D3×D511yescharacteristic
813C4—22no—
814C4—52no—
815C4—61no—
816C4—62no—
817C4—64no—
818C4—102no—
819C4—301no—
820C4—302no—
821C4—304no—
822C4D5×#23712yes—
823C3D5×#54011yescharacteristic, complemented, Sylow
824C2—44no—
825C2—54no—
826C2—121no—
827C2—204no—
828C2—601no—
829C2C2×D5×#23711yescharacteristic
830C2D5×#100412yes—
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#127C22
hypercenter#127D3×D5
hypocenterC3×C5C2×#540
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #11756478C2semidirect
2. C5×#5719C2semidirect
3. C3×D5×#127C2semidirect
4. D5×#939C2semidirect
5. D5×#938C2semidirect
6. #11754913C2semidirect
7. #11754912C2semidirect
8. #11754855C2semidirect
9. #11754850C2semidirect
10. D5×#935C2semidirect
11. D4×D5×Dic3C2semidirect
12. D5×#872C2semidirect
13. #11752635C2semidirect
14. #11752634C2semidirect
15. D5×#870C2semidirect
22. C3×C5×#127C22semidirect
23. #91828C22semidirect
24. #91827C22semidirect
25. #91824C22semidirect
26. D4×Dic15C22semidirect
27. #91761C22semidirect
28. #91759C22semidirect
29. C5×#939C22semidirect
30. C5×#938C22semidirect
31. C5×#935C22semidirect
32. C5×D4×Dic3C22semidirect
33. C5×#872C22semidirect
34. C5×#870C22semidirect
35. C3×#4086C22semidirect
36. C3×#4086C22semidirect
37. C3×#4020C22semidirect
39. #91571C22semidirect
40. #91569C22semidirect
41. #91565C22semidirect
42. #91559C22semidirect
43. Dic3×C22⋊D5C22semidirect
44. #91550C22semidirect
45. #91549C22semidirect
46. #91548C22semidirect
47. #91548C22semidirect
50. #91537C22semidirect
51. #91536C22semidirect
52. #91533C22semidirect
54. #91465C22semidirect
55. #91456C22semidirect
56. #91434C22semidirect
57. Dic3×D20C22semidirect
59. #91409C22semidirect
60. #91408C22semidirect
61. #91407C22semidirect
62. #91407C22semidirect
63. #91402C22semidirect
64. #91398C22semidirect
68. #91388C22semidirect
69. #91386C22semidirect
70. #91378C22semidirect
71. #91371C22semidirect
75. D5×#127D3semidirect
160. #5719D5direct (N × H)
168. C5×#127C2×D3semidirect
175. #4086C2×D3semidirect
176. #4086C2×D3semidirect
211. #4020C2×D3semidirect
271. C3×#127C2×D5semidirect
282. #939C2×D5semidirect
288. #938C2×D5semidirect
296. #935C2×D5semidirect
302. D4×Dic3C2×D5semidirect
313. #872C2×D5semidirect
317. #870C2×D5semidirect
530. #127D3×D5semidirect
582. C3×D5#540semidirect
713. C3×C5C2×#540semidirect
745. D5#5719direct (N × H)
797. C5C2×#5719semidirect
823. C3D5×#540semidirect

Maximal subgroups

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

subgroupindex
#117564782
C5×#57192
C3×D5×#1272
D5×#9392
D5×#9382
#117549132
#117549122
#117548552
#117548502
D5×#9352
D4×D5×Dic32
D5×#8722
#117526352
#117526342
D5×#8702
D5×#5403
C2×#57195