Finite Group Databasebeta

← D5×#5697 #14481115

Subgroups — D5×#5697 #14481115

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#11756456C211yesmaximal, characteristic, complemented
2C5×#5697C211yesmaximal, characteristic, complemented
3C3×D5×#125C211yesmaximal, characteristic, complemented
4D5×#895C212yesmaximal, complemented
5D5×#895C214yesmaximal, complemented
6D5×#894C214yesmaximal, complemented
7D5×#893C212yesmaximal, complemented
8#11753823C212yesmaximal, complemented
9#11753661C212yesmaximal, complemented
10#11753553C214yesmaximal, complemented
11#11753539C214yesmaximal, complemented
12D5×#874C211yesmaximal, characteristic, complemented
13D5×#872C211yesmaximal, characteristic, complemented
14#11752663C211yesmaximal, characteristic, complemented
15#11752652C211yesmaximal, characteristic, complemented
16D5×#540—31nomaximal, Hall
17C2×D5×D12C2212yes—
18C2×D5×D12C2214yes—
19C2×D5×D12C2214yes—
20C2×C4×D3×D5C2211yescharacteristic
21C2×C4×D3×D5C2214yes—
22C3×C5×#125C2211yescharacteristic, complemented
23#91784C2214yescomplemented
24#91784C2212yescomplemented
25#91783C2214yescomplemented
26#91782C2212yescomplemented
27#91763C2211yescharacteristic, complemented
28#91761C2211yescharacteristic, complemented
29C5×#895C2214yescomplemented
30C5×#895C2212yescomplemented
31C5×#894C2214yescomplemented
32C5×#893C2212yescomplemented
33C5×#874C2211yescharacteristic, complemented
34C5×#872C2211yescharacteristic, complemented
35C3×D5×C4⋊C4C2212yes—
36C3×D5×C4⋊C4C2214yes—
37C3×#4036C2212yescomplemented
38C3×#4035C2214yescomplemented
39C3×C42×D5C2211yescharacteristic
40C3×#4016C2211yescharacteristic, complemented
41D5×(C2×D3)⋊C4C2212yes—
42D5×(C2×D3)⋊C4C2214yes—
43D5×(C2×D3)⋊C4C2214yes—
44#91466C2214yescomplemented
45#91466C2212yescomplemented
46#91460C2214yescomplemented
47#91460C2212yescomplemented
48#91451C2214yescomplemented
49#91451C2212yescomplemented
50#91446C2214yescomplemented
51#91438C2214yescomplemented
52#91435C2212yescomplemented
53#91433C2214yescomplemented
54#91428C2212yescomplemented
55#91427C2214yescomplemented
56#91423C2214yescomplemented
57#91420C2214yescomplemented
58#91420C2214yescomplemented
59#91420C2214yescomplemented
60#91416C2214yescomplemented
61#91416C2214yescomplemented
62#91416C2214yescomplemented
63#91406C2214yescomplemented
64#91402C2212yescomplemented
65#91398C2212yescomplemented
66D5×Dic3⋊C4C2212yes—
67C4×D5×Dic3C2211yescharacteristic
68#91386C2211yescharacteristic, complemented
69#91371C2211yescharacteristic, complemented
70#91355C2214yescomplemented
71#91351C2214yescomplemented
72C2×#5697—51nomaximal, Hall
73C5×#540—31no—
74#66053—31no—
75D5×#127—31no—
76#66032—31no—
77D5×#125D311yescharacteristic, complemented
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—
88C22×D3×D5C2311yescharacteristic
89C22×D3×D5C2314yes—
90C2×D60C2312yes—
91C2×D60C2314yes—
92C2×D60C2314yes—
93C2×C4×D15C2311yescharacteristic
94C2×C4×D15C2314yes—
95C2×C5×D12C2312yes—
96C2×C5×D12C2314yes—
97C2×C5×D12C2314yes—
98C2×C4×C5×D3C2311yescharacteristic
99C2×C4×C5×D3C2314yes—
100C2×C3×C4×D5C2312yes—
101C2×C3×C4×D5C2314yes—
102C2×C3×C4×D5C2311yescharacteristic
103C2×#1203C2314yes—
104C2×#1203C2314yes—
105C2×#1203C2314yes—
106C2×#1203C2314yes—
107C2×#1203C2314yes—
108C2×#1200C2311yescharacteristic
109C2×#1200C2314yes—
110C2×D3×Dic5C2311yescharacteristic
111C2×D3×Dic5C2314yes—
112C2×D5×Dic3C2311yescharacteristic
113C2×D5×Dic3C2312yes—
114D5×D12—28no—
115D5×D12—48no—
116D5×D12—48no—
117C4×D3×D5—24no—
118C4×D3×D5—48no—
119C3×C5×C4⋊C4C2312yes—
120C3×C5×C4⋊C4C2314yes—
121C3×C42×C5C2311yescharacteristic
122#6714C2312yes—
123#6714C2314yes—
124#6714C2314yes—
125#6712C2312yes—
126C4×Dic15C2311yescharacteristic
127C5×(C2×D3)⋊C4C2312yes—
128C5×(C2×D3)⋊C4C2314yes—
129C5×(C2×D3)⋊C4C2314yes—
130C5×Dic3⋊C4C2312yes—
131C4×C5×Dic3C2311yescharacteristic
132C3×C4⋊Dic5C2314yes—
133C3×C4⋊Dic5C2312yes—
134C3×#683C2314yes—
135C3×#683C2314yes—
136C3×#683C2314yes—
137C3×C4×Dic5C2312yes—
138C3×C4×Dic5C2311yescharacteristic
139Dic3⋊Dic5C2312yes—
140#6669C2312yes—
141#6667C2312yes—
142#6667C2314yes—
143#6667C2314yes—
144(C2×D3)⋊Dic5C2312yes—
145(C2×D3)⋊Dic5C2314yes—
146(C2×D3)⋊Dic5C2314yes—
147Dic3×Dic5C2312yes—
148C2×C3×#125—51no—
149#5697—51no—
150#5697—54no—
151#5697—52no—
152#5697—54no—
153#5697—52no—
154#5697—51no—
155#5697—51no—
156#5697D511yescharacteristic, direct product factor
157C2×#895—54no—
158C2×#895—52no—
159C2×#894—54no—
160C2×#893—52no—
161C2×#874—51no—
162C2×#872—51no—
163C2×D4×D5—32no—
164C2×D4×D5—34no—
165C2×D4×D5—34no—
166C22×C4×D5—31no—
167C22×C4×D5—34no—
168C5×#127—31no—
169C5×#125C2×D311yescharacteristic, complemented
170C5×#123—34no—
171C5×#121—34no—
172C5×#121—32no—
173C4×C5×D4—32no—
174C5×#117—31no—
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⋊C4C2×D312yes—
197D5×C4⋊C4C2×D314yes—
198#4036C2×D312yescomplemented
199#4035C2×D314yescomplemented
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×D5C2×D311yescharacteristic
217#4016C2×D311yescharacteristic, complemented
218C2×#540—151noSylow
219C22×D15C2411yescharacteristic
220C22×D15C2414yes—
221C22×C5×D3C2411yescharacteristic
222C22×C5×D3C2414yes—
223C22×C3×D5C2411yescharacteristic
224C2×D3×D5—22no—
225C2×D3×D5—28no—
226C2×D3×D5—28no—
227C2×D3×D5—24no—
228C2×D3×D5—28no—
229C2×C3×C4×C5C2412yes—
230C2×C3×C4×C5C2414yes—
231C2×C3×C4×C5C2411yescharacteristic
232C2×Dic15C2412yes—
233C2×Dic15C2411yescharacteristic
234D60—24no—
235D60—44no—
236D60—44no—
237C4×D15—22no—
238C4×D15—44no—
239C2×C5×Dic3C2412yes—
240C2×C5×Dic3C2411yescharacteristic
241C5×D12—24no—
242C5×D12—44no—
243C5×D12—44no—
244C4×C5×D3—22no—
245C4×C5×D3—44no—
246C2×C3×Dic5C2414yes—
247C2×C3×Dic5C2412yes—
248C2×C3×Dic5C2411yescharacteristic
249C3×C4×D5—28no—
250C3×C4×D5—24no—
251C3×C4×D5#4114yes—
252#1203—28no—
253#1203—44no—
254#1203—44no—
255#1203—44no—
256#1203—44no—
257#1200—22no—
258#1200—44no—
259D3×Dic5—22no—
260D3×Dic5—44no—
261D5×Dic3—22no—
262D5×Dic3—24no—
263C22×D12—52no—
264C22×D12—54no—
265C22×D12—54no—
266C22×C4×D3—51no—
267C22×C4×D3—54no—
268C3×#125—54no—
269C3×#125—52no—
270C3×#125—51no—
271C3×#125C2×D511yescharacteristic, complemented
272C2×C3×C4⋊C4—52no—
273C2×C3×C4⋊C4—54no—
274C2×C3×C42—51no—
275C2×(C2×D3)⋊C4—52no—
276C2×(C2×D3)⋊C4—54no—
277C2×(C2×D3)⋊C4—54no—
278C2×Dic3⋊C4—52no—
279C2×C4×Dic3—51no—
280#895—54no—
281#895—54no—
282#895—54no—
283#895—54no—
284#895—52no—
285#895—54no—
286#895—52no—
287#895—54no—
288#895—52no—
289#895—54no—
290#895—54no—
291#895—54no—
292#895C2×D514yescomplemented
293#895C2×D512yescomplemented
294#894—54no—
295#894—54no—
296#894—54no—
297#894—54no—
298#894—54no—
299#894—54no—
300#894—54no—
301#894C2×D514yescomplemented
302#893—52no—
303#893—54no—
304#893—52no—
305#893—54no—
306#893—52no—
307#893C2×D512yescomplemented
308#874—54no—
309#874—52no—
310#874—51no—
311#874C2×D511yescharacteristic, complemented
312#872—51no—
313#872—51no—
314#872—52no—
315#872—52no—
316#872—51no—
317#872C2×D511yescharacteristic, complemented
318C23×D5—31no—
319C23×D5—34no—
320C2×C5×D4—32no—
321C2×C5×D4—34no—
322C2×C5×D4—34no—
323C22×C4×C5—31no—
324C22×C4×C5—34no—
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—32no—
339C2×C4×D5—31no—
340C2×C4×D5—31no—
341C2×C4×D5—31no—
342C2×C4×D5—34no—
343C2×C4×D5—34no—
344C2×C4×D5—64no—
345C2×C4×D5—128no—
346C2×C4×D5C22×D314yes—
347C2×C4×D5C22×D312yes—
348C2×C4×D5C22×D311yescharacteristic
349C5×C4⋊C4—32no—
350C5×C4⋊C4C22×D312yes—
351C5×C4⋊C4C22×D314yes—
352C5×C22⋊C4—32no—
353C5×C22⋊C4—34no—
354C5×C22⋊C4—34no—
355C42×C5—31no—
356C42×C5C22×D311yescharacteristic
357C22⋊Dic5—32no—
358C22⋊Dic5—34no—
359C22⋊Dic5—34no—
360#685—32no—
361#685—34no—
362#685—34no—
363#685—32no—
364#685—34no—
365#685—34no—
366C4⋊Dic5—32no—
367C4⋊Dic5C22×D312yes—
368C4⋊Dic5C22×D314yes—
369#683—32no—
370#683—32no—
371#683C22×D314yes—
372#683C22×D314yes—
373#683C22×D314yes—
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—151no—
387C2×#125—51no—
388C2×#123—154no—
389C2×#121—154no—
390C2×#121—152no—
391C2×C4×D4—152no—
392C2×#117—151no—
393C22×C3×C5C2511yescharacteristic
394C2×D15—21no—
395C2×D15—24no—
396C2×D15—24no—
397C2×D15—22no—
398C2×D15—24no—
399C2×C5×D3—21no—
400C2×C5×D3—24no—
401C2×C5×D3—24no—
402C2×C5×D3—22no—
403C2×C5×D3—24no—
404C2×C3×D5C2×#4112yes—
405C2×C3×D5H(5,𝔽2)14yes—
406D3×D5—44no—
407D3×D5—416no—
408C3×C4×C5—24no—
409C3×C4×C5—22no—
410C3×C4×C5C2×#4112yes—
411Dic15—21no—
412Dic15—22no—
413C3×Dic5—24no—
414C3×Dic5—22no—
415C3×Dic5C2×#4112yes—
416C5×Dic3—21no—
417C5×Dic3—22no—
418C23×D3—51no—
419C23×D3—54no—
420C22×C3×C4—51no—
421C22×C3×C4—52no—
422C22×C3×C4—54no—
423C22×Dic3—52no—
424C22×Dic3—51no—
425C2×D12—54no—
426C2×D12—52no—
427C2×D12—54no—
428C2×D12—54no—
429C2×D12—54no—
430C2×D12—54no—
431C2×D12—54no—
432C2×D12—54no—
433C2×D12—108no—
434C2×D12—208no—
435C2×D12—208no—
436C2×D12C22×D512yes—
437C2×D12C22×D514yes—
438C2×D12C22×D514yes—
439C2×C4×D3—51no—
440C2×C4×D3—51no—
441C2×C4×D3—51no—
442C2×C4×D3—54no—
443C2×C4×D3—54no—
444C2×C4×D3—54no—
445C2×C4×D3—104no—
446C2×C4×D3—208no—
447C2×C4×D3C22×D511yescharacteristic
448C2×C4×D3C22×D514yes—
449C3×C4⋊C4—54no—
450C3×C4⋊C4—54no—
451C3×C4⋊C4—54no—
452C3×C4⋊C4—52no—
453C3×C4⋊C4—54no—
454C3×C4⋊C4C22×D512yes—
455C3×C4⋊C4C22×D514yes—
456C3×C42—52no—
457C3×C42—51no—
458C3×C42C22×D511yescharacteristic
459(C2×D3)⋊C4—52no—
460(C2×D3)⋊C4—54no—
461(C2×D3)⋊C4—54no—
462(C2×D3)⋊C4—52no—
463(C2×D3)⋊C4—54no—
464(C2×D3)⋊C4—54no—
465(C2×D3)⋊C4—52no—
466(C2×D3)⋊C4—54no—
467(C2×D3)⋊C4—54no—
468(C2×D3)⋊C4C22×D512yes—
469(C2×D3)⋊C4C22×D514yes—
470(C2×D3)⋊C4C22×D514yes—
471Dic3⋊C4—52no—
472Dic3⋊C4—52no—
473Dic3⋊C4—52no—
474Dic3⋊C4C22×D512yes—
475C4×Dic3—51no—
476C4×Dic3—52no—
477C4×Dic3C22×D511yescharacteristic
478C23×C5—31no—
479C23×C5—34no—
480C22×D5—31no—
481C22×D5—34no—
482C22×D5—62no—
483C22×D5—68no—
484C22×D5—68no—
485C22×D5—64no—
486C22×D5—68no—
487C22×D5C23×D311yescharacteristic
488C5×D4—64no—
489C5×D4—124no—
490C5×D4—124no—
491C2×C4×C5—32no—
492C2×C4×C5—31no—
493C2×C4×C5—62no—
494C2×C4×C5—124no—
495C2×C4×C5C23×D312yes—
496C2×C4×C5C23×D314yes—
497C2×C4×C5C23×D311yescharacteristic
498C22⋊D5—68no—
499C22⋊D5—124no—
500C22⋊D5—124no—
501C22⋊D5—124no—
502C22⋊D5—124no—
503C2×Dic5—32no—
504C2×Dic5—31no—
505C2×Dic5—62no—
506C2×Dic5—124no—
507C2×Dic5C23×D312yes—
508C2×Dic5C23×D314yes—
509C2×Dic5C23×D311yescharacteristic
510D20—64no—
511D20—124no—
512D20—124no—
513C4×D5—28no—
514C4×D5—24no—
515C4×D5—62no—
516C4×D5—64no—
517C4×D5—62no—
518C4×D5—62no—
519C4×D5—124no—
520C4×D5—124no—
521C4×D5#23914yes—
522C22×D4—152no—
523C22×D4—154no—
524C22×D4—154no—
525C23×C4—151no—
526C23×C4—154no—
527#127—31no—
528#127—152no—
529#127—154no—
530#127—151no—
531#125—54no—
532#125—52no—
533#125—51no—
534#125D3×D511yescharacteristic, complemented
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—34no—
544#121—32no—
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#121—154no—
556#121—152no—
557C4×D4—32no—
558C4×D4—152no—
559C4×D4—154no—
560C4×D4—154no—
561C4×D4—152no—
562C4×D4—152no—
563#117—31no—
564#117—151no—
565#117—152no—
566#117—152no—
567#117—151no—
568#117—151no—
569C2×C4⋊C4—52no—
570C2×C4⋊C4—54no—
571C2×C4⋊C4—152no—
572C2×C22⋊C4—152no—
573C2×C22⋊C4—154no—
574C2×C22⋊C4—154no—
575C2×C42—51no—
576C2×C42—151no—
577C2×C3×C5C22×#4111yescharacteristic
578C2×C3×C5C2×H(5,𝔽2)12yes—
579D15—41no—
580D15—44no—
581C3×D5#54014yescomplemented
582C5×D3—41no—
583C5×D3—44no—
584C23×C3—51no—
585C22×D3—51no—
586C22×D3—54no—
587C22×D3—102no—
588C22×D3—108no—
589C22×D3—108no—
590C22×D3—104no—
591C22×D3—108no—
592C22×D3C23×D511yescharacteristic
593C22×D3C23×D514yes—
594C2×C3×C4—51no—
595C2×C3×C4—54no—
596C2×C3×C4—52no—
597C2×C3×C4—54no—
598C2×C3×C4—108no—
599C2×C3×C4—104no—
600C2×C3×C4C23×D512yes—
601C2×C3×C4C23×D514yes—
602C2×C3×C4C23×D511yescharacteristic
603C2×Dic3—52no—
604C2×Dic3—51no—
605C2×Dic3—102no—
606C2×Dic3—104no—
607C2×Dic3C23×D512yes—
608C2×Dic3C23×D511yescharacteristic
609D12—24no—
610D12—44no—
611D12—44no—
612D12—108no—
613D12—104no—
614D12—204no—
615D12—204no—
616D12—204no—
617D12—204no—
618D12—204no—
619D12—204no—
620C4×D3—22no—
621C4×D3—44no—
622C4×D3—102no—
623C4×D3—102no—
624C4×D3—102no—
625C4×D3—204no—
626C4×D3—204no—
627C4×D3—204no—
628C22×C5—61no—
629C22×C5—64no—
630C22×C5—64no—
631C22×C5—62no—
632C22×C5—64no—
633C22×C5C24×D311yescharacteristic
634C2×D5—61no—
635C2×D5—64no—
636C2×D5—64no—
637C2×D5—62no—
638C2×D5—64no—
639C2×D5—124no—
640C2×D5—1216no—
641C2×D5C2×#23912yes—
642C2×D5#100914yes—
643C4×C5—24no—
644C4×C5—22no—
645C4×C5—61no—
646C4×C5—62no—
647C4×C5C2×#23912yes—
648Dic5—24no—
649Dic5—22no—
650Dic5—61no—
651Dic5—62no—
652Dic5C2×#23912yes—
653C24—151no—
654C24—154no—
655C2×D4—32no—
656C2×D4—34no—
657C2×D4—34no—
658C2×D4—154no—
659C2×D4—154no—
660C2×D4—154no—
661C2×D4—154no—
662C2×D4—154no—
663C2×D4—152no—
664C2×D4—154no—
665C2×D4—154no—
666C2×D4—308no—
667C2×D4—608no—
668C2×D4—608no—
669C22×C4—31no—
670C22×C4—34no—
671C22×C4—51no—
672C22×C4—52no—
673C22×C4—54no—
674C22×C4—151no—
675C22×C4—154no—
676C22×C4—152no—
677C22×C4—151no—
678C22×C4—151no—
679C22×C4—154no—
680C22×C4—151no—
681C22×C4—154no—
682C22×C4—304no—
683C22×C4—608no—
684C4⋊C4—32no—
685C4⋊C4—54no—
686C4⋊C4—52no—
687C4⋊C4—54no—
688C4⋊C4—54no—
689C4⋊C4—54no—
690C4⋊C4—152no—
691C4⋊C4—152no—
692C4⋊C4—152no—
693C4⋊C4C2×D3×D512yes—
694C4⋊C4C2×D3×D514yes—
695C22⋊C4—32no—
696C22⋊C4—34no—
697C22⋊C4—34no—
698C22⋊C4—152no—
699C22⋊C4—154no—
700C22⋊C4—154no—
701C22⋊C4—152no—
702C22⋊C4—154no—
703C22⋊C4—154no—
704C22⋊C4—152no—
705C22⋊C4—154no—
706C22⋊C4—154no—
707C42—31no—
708C42—52no—
709C42—51no—
710C42—152no—
711C42—151no—
712C42C2×D3×D511yescharacteristic
713C3×C5C2×#54011yescharacteristic, complemented, Hall
714C22×C3—52no—
715C22×C3—54no—
716C22×C3C24×D511yescharacteristic
717C2×D3—21no—
718C2×D3—24no—
719C2×D3—24no—
720C2×D3—22no—
721C2×D3—24no—
722C2×D3—101no—
723C2×D3—104no—
724C2×D3—104no—
725C2×D3—102no—
726C2×D3—104no—
727C2×D3—204no—
728C2×D3—2016no—
729C3×C4—24no—
730C3×C4—22no—
731C3×C4—52no—
732C3×C4—104no—
733C3×C4—102no—
734C3×C4D5×#4112yes—
735Dic3—21no—
736Dic3—22no—
737Dic3—101no—
738Dic3—102no—
739C2×C5—121no—
740C2×C5—124no—
741C2×C5C22×#23911yescharacteristic
742C2×C5C2×#100912yes—
743D5—121no—
744D5—124no—
745D5#569714yesdirect product factor
746C23—31no—
747C23—34no—
748C23—51no—
749C23—151no—
750C23—154no—
751C23—302no—
752C23—308no—
753C23—308no—
754C23—304no—
755C23—308no—
756D4—64no—
757D4—124no—
758D4—124no—
759D4—308no—
760D4—304no—
761D4—604no—
762D4—604no—
763D4—604no—
764D4—604no—
765D4—604no—
766D4—604no—
767C2×C4—32no—
768C2×C4—31no—
769C2×C4—51no—
770C2×C4—54no—
771C2×C4—52no—
772C2×C4—54no—
773C2×C4—62no—
774C2×C4—108no—
775C2×C4—104no—
776C2×C4—124no—
777C2×C4—152no—
778C2×C4—151no—
779C2×C4—302no—
780C2×C4—302no—
781C2×C4—302no—
782C2×C4—304no—
783C2×C4—302no—
784C2×C4—604no—
785C2×C4—604no—
786C2×C4—604no—
787C2×C4C22×D3×D512yes—
788C2×C4C22×D3×D514yes—
789C2×C4C22×D3×D511yescharacteristic
790C2×C3—54no—
791C2×C3C2×D5×#4111yescharacteristic
792C2×C3D5×H(5,𝔽2)12yes—
793D3—41no—
794D3—44no—
795D3—201no—
796D3—204no—
797C5C2×#569711yescharacteristic, complemented, Sylow
798C22—52no—
799C22—54no—
800C22—61no—
801C22—64no—
802C22—64no—
803C22—62no—
804C22—64no—
805C22—301no—
806C22—304no—
807C22—304no—
808C22—302no—
809C22—304no—
810C22—604no—
811C22—6016no—
812C22C23×D3×D511yescharacteristic
813C4—24no—
814C4—22no—
815C4—52no—
816C4—61no—
817C4—62no—
818C4—104no—
819C4—102no—
820C4—301no—
821C4—302no—
822C4D5×#23912yes—
823C3D5×#54011yescharacteristic, complemented, Sylow
824C2—54no—
825C2—121no—
826C2—124no—
827C2—601no—
828C2—604no—
829C2C2×D5×#23911yescharacteristic
830C2D5×#100912yes—
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#125C22
hypercenter#125D3×D5
hypocenterC3×C5C2×#540
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #11756456C2semidirect
2. C5×#5697C2semidirect
3. C3×D5×#125C2semidirect
4. D5×#895C2semidirect
5. D5×#895C2semidirect
6. D5×#894C2semidirect
7. D5×#893C2semidirect
8. #11753823C2semidirect
9. #11753661C2semidirect
10. #11753553C2semidirect
11. #11753539C2semidirect
12. D5×#874C2semidirect
13. D5×#872C2semidirect
14. #11752663C2semidirect
15. #11752652C2semidirect
22. C3×C5×#125C22semidirect
23. #91784C22semidirect
24. #91784C22semidirect
25. #91783C22semidirect
26. #91782C22semidirect
27. #91763C22semidirect
28. #91761C22semidirect
29. C5×#895C22semidirect
30. C5×#895C22semidirect
31. C5×#894C22semidirect
32. C5×#893C22semidirect
33. C5×#874C22semidirect
34. C5×#872C22semidirect
37. C3×#4036C22semidirect
38. C3×#4035C22semidirect
40. C3×#4016C22semidirect
44. #91466C22semidirect
45. #91466C22semidirect
46. #91460C22semidirect
47. #91460C22semidirect
48. #91451C22semidirect
49. #91451C22semidirect
50. #91446C22semidirect
51. #91438C22semidirect
52. #91435C22semidirect
53. #91433C22semidirect
54. #91428C22semidirect
55. #91427C22semidirect
56. #91423C22semidirect
57. #91420C22semidirect
58. #91420C22semidirect
59. #91420C22semidirect
60. #91416C22semidirect
61. #91416C22semidirect
62. #91416C22semidirect
63. #91406C22semidirect
64. #91402C22semidirect
65. #91398C22semidirect
68. #91386C22semidirect
69. #91371C22semidirect
70. #91355C22semidirect
71. #91351C22semidirect
77. D5×#125D3semidirect
156. #5697D5direct (N × H)
169. C5×#125C2×D3semidirect
198. #4036C2×D3semidirect
199. #4035C2×D3semidirect
217. #4016C2×D3semidirect
271. C3×#125C2×D5semidirect
292. #895C2×D5semidirect
293. #895C2×D5semidirect
301. #894C2×D5semidirect
307. #893C2×D5semidirect
311. #874C2×D5semidirect
317. #872C2×D5semidirect
534. #125D3×D5semidirect
581. C3×D5#540semidirect
713. C3×C5C2×#540semidirect
745. D5#5697direct (N × H)
797. C5C2×#5697semidirect
823. C3D5×#540semidirect

Maximal subgroups

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

subgroupindex
#117564562
C5×#56972
C3×D5×#1252
D5×#8952
D5×#8942
D5×#8932
#117538232
#117536612
#117535532
#117535392
D5×#8742
D5×#8722
#117526632
#117526522
D5×#5403
C2×#56975