Finite Group Databasebeta

← #14481116

Subgroups — #14481116

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
1D15×#125C211yesmaximal, characteristic, complemented
2C5×#5697C211yesmaximal, characteristic, complemented
3C3×#66032C211yesmaximal, characteristic, complemented
4#11753850C212yesmaximal, complemented
5#11753850C214yesmaximal, complemented
6#11753844C214yesmaximal, complemented
7#11753840C212yesmaximal, complemented
8#11753815C212yesmaximal, complemented
9#11753802C214yesmaximal, complemented
10#11753644C212yesmaximal, complemented
11#11753629C214yesmaximal, complemented
12#11752750C211yesmaximal, characteristic, complemented
13#11752723C211yesmaximal, characteristic, complemented
14#11752712C211yesmaximal, characteristic, complemented
15#11752634C211yesmaximal, characteristic, complemented
16D5×#540—31nomaximal, Hall
17C2×#6777C2212yes—
18C2×#6777C2214yes—
19C2×#6777C2214yes—
20C2×C4×D3×D5C2211yescharacteristic
21C2×C4×D3×D5C2214yes—
22C3×C5×#125C2211yescharacteristic, complemented
23C4⋊C4×D15C2212yes—
24C4⋊C4×D15C2214yes—
25#91779C2212yescomplemented
26#91778C2214yescomplemented
27C42×D15C2211yescharacteristic
28#91759C2211yescharacteristic, complemented
29C5×#895C2212yescomplemented
30C5×#895C2214yescomplemented
31C5×#894C2214yescomplemented
32C5×#893C2212yescomplemented
33C5×#874C2211yescharacteristic, complemented
34C5×#872C2211yescharacteristic, complemented
35C3×#4041C2214yescomplemented
36C3×#4041C2212yescomplemented
37C3×#4040C2214yescomplemented
38C3×#4039C2212yescomplemented
39C3×#4020C2211yescharacteristic, complemented
40C3×#4018C2211yescharacteristic, complemented
41#91473C2212yes—
42#91473C2214yes—
43#91473C2214yes—
44#91463C2214yescomplemented
45#91463C2212yescomplemented
46#91457C2214yescomplemented
47#91456C2214yescomplemented
48#91456C2212yescomplemented
49#91453C2214yescomplemented
50#91453C2214yescomplemented
51#91453C2214yescomplemented
52#91452C2214yescomplemented
53#91449C2212yescomplemented
54#91449C2214yescomplemented
55#91447C2214yescomplemented
56#91441C2214yescomplemented
57#91440C2214yescomplemented
58Dic3×D20C2212yescomplemented
59#91423C2214yescomplemented
60Dic5×D12C2212yescomplemented
61#91414C2214yescomplemented
62#91408C2214yescomplemented
63#91408C2214yescomplemented
64#91408C2214yescomplemented
65#91407C2214yescomplemented
66#91404C2212yes—
67C4×#1200C2211yescharacteristic
68#91400C2212yescomplemented
69#91394C2212yescomplemented
70#91371C2211yescharacteristic, complemented
71#91357C2211yescharacteristic, complemented
72D3×#540—51nomaximal, Hall
73C5×#540—31no—
74#66053—31no—
75D5×#127—31no—
76#66032D311yescharacteristic, complemented
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—
88C22×D3×D5C2311yescharacteristic
89C22×D3×D5C2314yes—
90C2×C4×D15C2312yes—
91C2×C4×D15C2314yes—
92C2×C4×D15C2311yescharacteristic
93C2×C5×D12C2312yes—
94C2×C5×D12C2314yes—
95C2×C5×D12C2314yes—
96C2×C4×C5×D3C2311yescharacteristic
97C2×C4×C5×D3C2314yes—
98C2×C3×D20C2312yes—
99C2×C3×D20C2314yes—
100C2×C3×D20C2314yes—
101C2×C3×C4×D5C2311yescharacteristic
102C2×C3×C4×D5C2314yes—
103C2×#1201C2314yes—
104C2×#1201C2314yes—
105C2×#1201C2314yes—
106C2×#1201C2314yes—
107C2×#1201C2314yes—
108C2×#1200C2312yes—
109C2×#1200C2311yescharacteristic
110C2×D3×Dic5C2311yescharacteristic
111C2×D3×Dic5C2314yes—
112C2×D5×Dic3C2311yescharacteristic
113C2×D5×Dic3C2314yes—
114#6777—28no—
115#6777—48no—
116#6777—48no—
117C4×D3×D5—24no—
118C4×D3×D5—48no—
119C3×C5×C4⋊C4C2312yes—
120C3×C5×C4⋊C4C2314yes—
121C3×C42×C5C2311yescharacteristic
122C4⋊Dic15C2314yes—
123C4⋊Dic15C2312yes—
124#6712C2314yes—
125#6712C2314yes—
126#6712C2314yes—
127C4×Dic15C2312yes—
128C4×Dic15C2311yescharacteristic
129C5×(C2×D3)⋊C4C2312yes—
130C5×(C2×D3)⋊C4C2314yes—
131C5×(C2×D3)⋊C4C2314yes—
132C5×Dic3⋊C4C2312yes—
133C4×C5×Dic3C2311yescharacteristic
134C3×#685C2312yes—
135C3×#685C2314yes—
136C3×#685C2314yes—
137C3×#683C2312yes—
138C3×C4×Dic5C2311yescharacteristic
139Dic3⋊Dic5C2312yes—
140#6668C2312yes—
141(C2×D3)⋊Dic5C2312yes—
142(C2×D3)⋊Dic5C2314yes—
143(C2×D3)⋊Dic5C2314yes—
144#6665C2312yes—
145#6665C2314yes—
146#6665C2314yes—
147Dic3×Dic5C2312yes—
148C3×#540—51no—
149#5719—51no—
150D3×#127—51no—
151#5697D511yescharacteristic, complemented
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×#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#4041C2×D312yescomplemented
190#4041C2×D314yescomplemented
191#4040—34no—
192#4040C2×D314yescomplemented
193#4039C2×D312yescomplemented
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—32no—
208D5×C22⋊C4—34no—
209D5×C22⋊C4—34no—
210#4023—32no—
211#4020C2×D311yescharacteristic, complemented
212C4×D20—32no—
213#4018—31no—
214#4018C2×D311yescharacteristic, complemented
215C42×D5—31no—
216C42×D5—31no—
217#4016—31no—
218C2×#540—151noSylow
219C22×D15C2411yescharacteristic
220C22×C5×D3C2411yescharacteristic
221C22×C5×D3C2414yes—
222C22×C3×D5C2411yescharacteristic
223C22×C3×D5C2414yes—
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×Dic15C2414yes—
233C2×Dic15C2412yes—
234C2×Dic15C2411yescharacteristic
235C4×D15—28no—
236C4×D15—24no—
237C4×D15#4114yes—
238C2×C5×Dic3C2412yes—
239C2×C5×Dic3C2411yescharacteristic
240C5×D12—24no—
241C5×D12—44no—
242C5×D12—44no—
243C4×C5×D3—22no—
244C4×C5×D3—44no—
245C2×C3×Dic5C2412yes—
246C2×C3×Dic5C2411yescharacteristic
247C3×D20—24no—
248C3×D20—44no—
249C3×D20—44no—
250C3×C4×D5—22no—
251C3×C4×D5—44no—
252#1201—28no—
253#1201—44no—
254#1201—44no—
255#1201—44no—
256#1201—44no—
257#1200—22no—
258#1200—24no—
259D3×Dic5—22no—
260D3×Dic5—44no—
261D5×Dic3—22no—
262D5×Dic3—44no—
263C2×D3×D4—52no—
264C2×D3×D4—54no—
265C2×D3×D4—54no—
266C22×C4×D3—51no—
267C22×C4×D3—54no—
268C3×#127—51no—
269C3×#125C2×D511yescharacteristic, complemented
270C3×#123—54no—
271C3×#121—54no—
272C3×#121—52no—
273C3×C4×D4—52no—
274C3×#117—51no—
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#895C2×D514yescomplemented
290#895C2×D512yescomplemented
291#894—54no—
292#894C2×D514yescomplemented
293#893C2×D512yescomplemented
294#892—52no—
295D3×C4⋊C4—54no—
296D3×C4⋊C4—52no—
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#874C2×D511yescharacteristic, complemented
312C4×D12—52no—
313#872—51no—
314#872C2×D511yescharacteristic, complemented
315C42×D3—51no—
316C42×D3—51no—
317#870—51no—
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×D20C22×D312yes—
336C2×D20C22×D314yes—
337C2×D20C22×D314yes—
338C2×C4×D5—31no—
339C2×C4×D5—31no—
340C2×C4×D5—34no—
341C2×C4×D5—32no—
342C2×C4×D5—32no—
343C2×C4×D5—31no—
344C2×C4×D5—34no—
345C2×C4×D5—64no—
346C2×C4×D5—128no—
347C2×C4×D5C22×D311yescharacteristic
348C2×C4×D5C22×D314yes—
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#685C22×D312yes—
364#685C22×D314yes—
365#685C22×D314yes—
366C4⋊Dic5—32no—
367C4⋊Dic5—34no—
368C4⋊Dic5—32no—
369#683—34no—
370#683—34no—
371#683—34no—
372#683—32no—
373#683C22×D312yes—
374C4×Dic5—31no—
375C4×Dic5—32no—
376C4×Dic5—32no—
377C4×Dic5C22×D311yescharacteristic
378#540—31no—
379#540—51no—
380#540—151no—
381#540—151no—
382#540—152no—
383#540—152no—
384#540—154no—
385#540—154no—
386C2×#127—151no—
387C2×#125—151no—
388C2×#123—154no—
389C2×#121—154no—
390C2×#121—152no—
391C2×C4×D4—152no—
392C2×#117—151no—
393C22×C3×C5C2511yescharacteristic
394C2×D15C2×#4112yes—
395C2×D15H(5,𝔽2)14yes—
396C2×C5×D3—21no—
397C2×C5×D3—24no—
398C2×C5×D3—24no—
399C2×C5×D3—22no—
400C2×C5×D3—24no—
401C2×C3×D5—21no—
402C2×C3×D5—24no—
403C2×C3×D5—24no—
404C2×C3×D5—22no—
405C2×C3×D5—24no—
406D3×D5—44no—
407D3×D5—416no—
408C3×C4×C5—24no—
409C3×C4×C5—22no—
410C3×C4×C5C2×#4112yes—
411Dic15—24no—
412Dic15—22no—
413Dic15C2×#4112yes—
414C3×Dic5—21no—
415C3×Dic5—22no—
416C5×Dic3—21no—
417C5×Dic3—22no—
418C23×D3—51no—
419C23×D3—54no—
420C2×C3×D4—52no—
421C2×C3×D4—54no—
422C2×C3×D4—54no—
423C22×C3×C4—51no—
424C22×C3×C4—54no—
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×D12C22×D512yes—
436C2×D12C22×D514yes—
437C2×D12C22×D514yes—
438C2×C4×D3—51no—
439C2×C4×D3—51no—
440C2×C4×D3—52no—
441C2×C4×D3—54no—
442C2×C4×D3—52no—
443C2×C4×D3—51no—
444C2×C4×D3—54no—
445C2×C4×D3—104no—
446C2×C4×D3—208no—
447C2×C4×D3C22×D511yescharacteristic
448C2×C4×D3C22×D514yes—
449C3×C4⋊C4—52no—
450C3×C4⋊C4C22×D514yes—
451C3×C4⋊C4C22×D512yes—
452C3×C22⋊C4—52no—
453C3×C22⋊C4—54no—
454C3×C22⋊C4—54no—
455C3×C42—51no—
456C3×C42C22×D511yescharacteristic
457#217—52no—
458#217—54no—
459#217—54no—
460(C2×D3)⋊C4—52no—
461(C2×D3)⋊C4—54no—
462(C2×D3)⋊C4—54no—
463(C2×D3)⋊C4C22×D512yes—
464(C2×D3)⋊C4C22×D514yes—
465(C2×D3)⋊C4C22×D514yes—
466C4⋊Dic3—52no—
467C4⋊Dic3—54no—
468C4⋊Dic3—52no—
469Dic3⋊C4—54no—
470Dic3⋊C4—54no—
471Dic3⋊C4—54no—
472Dic3⋊C4—52no—
473Dic3⋊C4C22×D512yes—
474C4×Dic3—51no—
475C4×Dic3—52no—
476C4×Dic3—52no—
477C4×Dic3C22×D511yescharacteristic
478C23×C5—31no—
479C23×C5—34no—
480C22×D5—31no—
481C22×D5—62no—
482C22×D5—68no—
483C22×D5—68no—
484C22×D5—64no—
485C22×D5—68no—
486C22×D5C23×D311yescharacteristic
487C22×D5C23×D314yes—
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—31no—
504C2×Dic5—32no—
505C2×Dic5—34no—
506C2×Dic5—62no—
507C2×Dic5—124no—
508C2×Dic5C23×D312yes—
509C2×Dic5C23×D311yescharacteristic
510D20—24no—
511D20—44no—
512D20—44no—
513C4×D5—22no—
514C4×D5—34no—
515C4×D5—44no—
516C4×D5—62no—
517C4×D5—64no—
518C4×D5—62no—
519C4×D5—68no—
520C4×D5—64no—
521C4×D5—124no—
522C22×D4—152no—
523C22×D4—154no—
524C22×D4—154no—
525C23×C4—151no—
526C23×C4—154no—
527#127—31no—
528#127—51no—
529#127—152no—
530#127—154no—
531#125—154no—
532#125—152no—
533#125—151no—
534#125D3×D511yescharacteristic, complemented
535#123—34no—
536#123—54no—
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—54no—
546#121—52no—
547#121—154no—
548#121—154no—
549#121—154no—
550#121—154no—
551#121—154no—
552#121—154no—
553#121—154no—
554#121—152no—
555#121—154no—
556#121—152no—
557C4×D4—32no—
558C4×D4—52no—
559C4×D4—152no—
560C4×D4—152no—
561C4×D4—154no—
562C4×D4—154no—
563#117—31no—
564#117—51no—
565#117—151no—
566#117—151no—
567#117—152no—
568#117—152no—
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×C5C22×#4111yescharacteristic
578C2×C3×C5C2×H(5,𝔽2)12yes—
579D15#54014yescomplemented
580C3×D5—41no—
581C3×D5—44no—
582C5×D3—41no—
583C5×D3—44no—
584C23×C3—51no—
585C23×C3—54no—
586C22×D3—51no—
587C22×D3—102no—
588C22×D3—108no—
589C22×D3—108no—
590C22×D3—104no—
591C22×D3—108no—
592C22×D3C23×D511yescharacteristic
593C22×D3C23×D514yes—
594C3×D4—104no—
595C3×D4—204no—
596C3×D4—204no—
597C2×C3×C4—52no—
598C2×C3×C4—51no—
599C2×C3×C4—102no—
600C2×C3×C4—204no—
601C2×C3×C4C23×D512yes—
602C2×C3×C4C23×D514yes—
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—54no—
612C2×Dic3—102no—
613C2×Dic3—204no—
614C2×Dic3C23×D512yes—
615C2×Dic3C23×D511yescharacteristic
616D12—24no—
617D12—44no—
618D12—44no—
619C4×D3—22no—
620C4×D3—44no—
621C4×D3—54no—
622C4×D3—102no—
623C4×D3—104no—
624C4×D3—102no—
625C4×D3—108no—
626C4×D3—104no—
627C4×D3—204no—
628C22×C5—61no—
629C22×C5—64no—
630C22×C5—64no—
631C22×C5—62no—
632C22×C5—64no—
633C22×C5C24×D311yescharacteristic
634C2×D5—21no—
635C2×D5—24no—
636C2×D5—24no—
637C2×D5—22no—
638C2×D5—24no—
639C2×D5—32no—
640C2×D5—34no—
641C2×D5—124no—
642C2×D5—1216no—
643C4×C5—24no—
644C4×C5—22no—
645C4×C5—61no—
646C4×C5—62no—
647C4×C5D3×#4112yes—
648Dic5—21no—
649Dic5—22no—
650Dic5—32no—
651Dic5—64no—
652Dic5—62no—
653C24—151no—
654C24—154no—
655C2×D4—32no—
656C2×D4—34no—
657C2×D4—34no—
658C2×D4—52no—
659C2×D4—54no—
660C2×D4—54no—
661C2×D4—154no—
662C2×D4—154no—
663C2×D4—154no—
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—54no—
673C22×C4—152no—
674C22×C4—151no—
675C22×C4—151no—
676C22×C4—154no—
677C22×C4—151no—
678C22×C4—154no—
679C22×C4—151no—
680C22×C4—152no—
681C22×C4—154no—
682C22×C4—304no—
683C22×C4—608no—
684C4⋊C4—32no—
685C4⋊C4—52no—
686C4⋊C4—152no—
687C4⋊C4—152no—
688C4⋊C4—154no—
689C4⋊C4—152no—
690C4⋊C4—154no—
691C4⋊C4—154no—
692C4⋊C4—154no—
693C4⋊C4C2×D3×D512yes—
694C4⋊C4C2×D3×D514yes—
695C22⋊C4—32no—
696C22⋊C4—34no—
697C22⋊C4—34no—
698C22⋊C4—52no—
699C22⋊C4—54no—
700C22⋊C4—54no—
701C22⋊C4—152no—
702C22⋊C4—154no—
703C22⋊C4—154no—
704C22⋊C4—152no—
705C22⋊C4—154no—
706C22⋊C4—154no—
707C42—31no—
708C42—51no—
709C42—152no—
710C42—152no—
711C42—151no—
712C42C2×D3×D511yescharacteristic
713C3×C5C2×#54011yescharacteristic, complemented, Hall
714C22×C3—101no—
715C22×C3—104no—
716C22×C3—104no—
717C22×C3—102no—
718C22×C3—104no—
719C22×C3C24×D511yescharacteristic
720C2×D3—21no—
721C2×D3—24no—
722C2×D3—24no—
723C2×D3—22no—
724C2×D3—24no—
725C2×D3—52no—
726C2×D3—54no—
727C2×D3—204no—
728C2×D3—2016no—
729C3×C4—24no—
730C3×C4—22no—
731C3×C4—101no—
732C3×C4—102no—
733C3×C4D5×#4112yes—
734Dic3—21no—
735Dic3—22no—
736Dic3—52no—
737Dic3—104no—
738Dic3—102no—
739C2×C5—121no—
740C2×C5—124no—
741C2×C5C2×D3×#4111yescharacteristic
742C2×C5D3×H(5,𝔽2)12yes—
743D5—34no—
744D5—41no—
745D5—44no—
746C23—31no—
747C23—34no—
748C23—51no—
749C23—54no—
750C23—151no—
751C23—302no—
752C23—308no—
753C23—308no—
754C23—304no—
755C23—308no—
756D4—64no—
757D4—104no—
758D4—124no—
759D4—124no—
760D4—204no—
761D4—204no—
762D4—308no—
763D4—604no—
764D4—604no—
765D4—604no—
766D4—604no—
767C2×C4—32no—
768C2×C4—31no—
769C2×C4—52no—
770C2×C4—51no—
771C2×C4—62no—
772C2×C4—102no—
773C2×C4—124no—
774C2×C4—151no—
775C2×C4—154no—
776C2×C4—152no—
777C2×C4—154no—
778C2×C4—204no—
779C2×C4—308no—
780C2×C4—304no—
781C2×C4—302no—
782C2×C4—304no—
783C2×C4—302no—
784C2×C4—302no—
785C2×C4—604no—
786C2×C4—604no—
787C2×C4C22×D3×D512yes—
788C2×C4C22×D3×D514yes—
789C2×C4C22×D3×D511yescharacteristic
790C2×C3—201no—
791C2×C3—204no—
792C2×C3C2×D5×#4111yescharacteristic
793C2×C3D5×H(5,𝔽2)12yes—
794D3—41no—
795D3—44no—
796D3—54no—
797C5D3×#54011yescharacteristic, complemented, Sylow
798C22—61no—
799C22—64no—
800C22—64no—
801C22—62no—
802C22—64no—
803C22—101no—
804C22—104no—
805C22—104no—
806C22—102no—
807C22—104no—
808C22—152no—
809C22—154no—
810C22—604no—
811C22—6016no—
812C22C23×D3×D511yescharacteristic
813C4—24no—
814C4—22no—
815C4—61no—
816C4—62no—
817C4—101no—
818C4—102no—
819C4—152no—
820C4—304no—
821C4—302no—
822C4#9203412yes—
823C3D5×#54011yescharacteristic, complemented, Sylow
824C2—121no—
825C2—124no—
826C2—154no—
827C2—201no—
828C2—204no—
829C2C2×#9203411yescharacteristic
830C2#1175705412yes—
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. D15×#125C2semidirect
2. C5×#5697C2semidirect
3. C3×#66032C2semidirect
4. #11753850C2semidirect
5. #11753850C2semidirect
6. #11753844C2semidirect
7. #11753840C2semidirect
8. #11753815C2semidirect
9. #11753802C2semidirect
10. #11753644C2semidirect
11. #11753629C2semidirect
12. #11752750C2semidirect
13. #11752723C2semidirect
14. #11752712C2semidirect
15. #11752634C2semidirect
22. C3×C5×#125C22semidirect
25. #91779C22semidirect
26. #91778C22semidirect
28. #91759C22semidirect
29. C5×#895C22semidirect
30. C5×#895C22semidirect
31. C5×#894C22semidirect
32. C5×#893C22semidirect
33. C5×#874C22semidirect
34. C5×#872C22semidirect
35. C3×#4041C22semidirect
36. C3×#4041C22semidirect
37. C3×#4040C22semidirect
38. C3×#4039C22semidirect
39. C3×#4020C22semidirect
40. C3×#4018C22semidirect
44. #91463C22semidirect
45. #91463C22semidirect
46. #91457C22semidirect
47. #91456C22semidirect
48. #91456C22semidirect
49. #91453C22semidirect
50. #91453C22semidirect
51. #91453C22semidirect
52. #91452C22semidirect
53. #91449C22semidirect
54. #91449C22semidirect
55. #91447C22semidirect
56. #91441C22semidirect
57. #91440C22semidirect
58. Dic3×D20C22semidirect
59. #91423C22semidirect
60. Dic5×D12C22semidirect
61. #91414C22semidirect
62. #91408C22semidirect
63. #91408C22semidirect
64. #91408C22semidirect
65. #91407C22semidirect
68. #91400C22semidirect
69. #91394C22semidirect
70. #91371C22semidirect
71. #91357C22semidirect
76. #66032D3semidirect
151. #5697D5semidirect
169. C5×#125C2×D3semidirect
189. #4041C2×D3semidirect
190. #4041C2×D3semidirect
192. #4040C2×D3semidirect
193. #4039C2×D3semidirect
211. #4020C2×D3semidirect
214. #4018C2×D3semidirect
269. C3×#125C2×D5semidirect
289. #895C2×D5semidirect
290. #895C2×D5semidirect
292. #894C2×D5semidirect
293. #893C2×D5semidirect
311. #874C2×D5semidirect
314. #872C2×D5semidirect
534. #125D3×D5semidirect
579. D15#540semidirect
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
D15×#1252
C5×#56972
C3×#660322
#117538502
#117538442
#117538402
#117538152
#117538022
#117536442
#117536292
#117527502
#117527232
#117527122
#117526342
D5×#5403
D3×#5405