Finite Group Databasebeta

← #14481110

Subgroups — #14481110

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×#117C211yesmaximal, characteristic, complemented
2C5×#5535C211yesmaximal, characteristic, complemented
3C3×#65869C211yesmaximal, characteristic, complemented
4#11754670C212yesmaximal, complemented
5#11754601C212yesmaximal, complemented
6#11753844C214yesmaximal, complemented
7#11753785C214yesmaximal, complemented
8#11753219C214yesmaximal, complemented
9#11753146C214yesmaximal, complemented
10#11752750C211yesmaximal, characteristic, complemented
11C4×#6777C212yesmaximal, complemented
12#11752707C212yesmaximal, complemented
13#11752652C211yesmaximal, characteristic, complemented
14#11752635C211yesmaximal, characteristic, complemented
15#11752631C211yesmaximal, characteristic, complemented
16D5×#540—31nomaximal, Hall
17C22×C4×D15C2211yescharacteristic
18C2×#6790C2214yes—
19C2×#6777C2212yes—
20C2×#6777C2214yes—
21C2×C4×D3×D5C2214yes—
22C3×C5×#117C2211yescharacteristic, complemented
23#91815C2211yescharacteristic, complemented
24#91781C2212yescomplemented
25C4⋊C4×D15C2212yes—
26C22⋊C4×D15C2212yes—
27#91766C2212yescomplemented
28#91761C2211yescharacteristic, complemented
29#91761C2211yescharacteristic, complemented
30C42×D15C2211yescharacteristic
31C42×D15C2211yescharacteristic
32C5×#930C2212yescomplemented
33C5×#894C2214yescomplemented
34C5×#884C2214yescomplemented
35C5×#874C2211yescharacteristic, complemented
36C4×C5×D12C2212yescomplemented
37C5×#870C2211yescharacteristic, complemented
38C3×#4076C2212yescomplemented
39C3×#4040C2214yescomplemented
40C3×#4030C2214yescomplemented
41C3×#4020C2211yescharacteristic, complemented
42C3×C4×D20C2212yescomplemented
43C3×#4016C2211yescharacteristic, complemented
44#91571C2214yescomplemented
45#91565C2214yescomplemented
46#91549C2214yescomplemented
47#91473C2214yes—
48#91473C2214yes—
49#91466C2212yescomplemented
50#91465C2212yescomplemented
51#91463C2212yescomplemented
52#91463C2214yescomplemented
53#91461C2214yescomplemented
54#91457C2214yescomplemented
55#91454C2214yescomplemented
56#91452C2214yescomplemented
57#91448C2214yescomplemented
58#91447C2214yescomplemented
59#91442C2214yescomplemented
60C4×#1201C2214yescomplemented
61#91437C2212yes—
62#91435C2212yescomplemented
63#91434C2212yescomplemented
64#91423C2214yescomplemented
65#91416C2214yescomplemented
66#91414C2214yescomplemented
67#91409C2214yescomplemented
68#91407C2214yescomplemented
69#91404C2214yes—
70#91384C2212yescomplemented
71#91382C2214yescomplemented
72D3×#540—51nomaximal, Hall
73C5×#540—31no—
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—32no—
83D5×#121—34no—
84#65896—32no—
85C4×D4×D5—32no—
86#65869D311yescharacteristic, complemented
87D5×#117—31no—
88C23×D15C2311yescharacteristic
89C22×D3×D5C2314yes—
90C22×C3×C4×C5C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C2×C4×D15—24no—
93C2×C4×D15C2312yes—
94C2×C4×D15C2311yescharacteristic
95C2×C4×D15C2311yescharacteristic
96C2×C4×D15C2311yescharacteristic
97C2×C4×D15C2312yes—
98C2×C4×D15C2311yescharacteristic
99C2×C5×#67C2314yes—
100C2×C5×D12C2312yes—
101C2×C5×D12C2314yes—
102C2×C4×C5×D3C2314yes—
103C2×C3×C22⋊D5C2314yes—
104C2×C3×D20C2312yes—
105C2×C3×D20C2314yes—
106C2×C3×C4×D5C2314yes—
107#6790—48no—
108C2×#1203C2314yes—
109C2×#1202C2314yes—
110C2×#1201C2314yes—
111C2×#1201C2314yes—
112C2×#1201C2314yes—
113C2×#1200C2314yes—
114C2×D3×Dic5C2314yes—
115C2×D5×Dic3C2314yes—
116#6777—28no—
117#6777—48no—
118C4×D3×D5—48no—
119C3×C5×C4⋊C4C2312yes—
120C3×C5×C22⋊C4C2312yes—
121C3×C42×C5C2311yescharacteristic
122C3×C42×C5C2311yescharacteristic
123#6719C2312yes—
124#6714C2312yes—
125#6714C2312yes—
126C4⋊Dic15C2312yes—
127#6712C2312yes—
128#6712C2312yes—
129C4×Dic15C2311yescharacteristic
130C4×Dic15C2312yes—
131C4×Dic15C2311yescharacteristic
132C4×Dic15C2312yes—
133C5×(C2×D3)⋊C4C2314yes—
134C5×(C2×D3)⋊C4C2314yes—
135C5×C4⋊Dic3C2312yes—
136C5×Dic3⋊C4C2314yes—
137C3×#685C2314yes—
138C3×#685C2314yes—
139C3×C4⋊Dic5C2312yes—
140C3×#683C2314yes—
141Dic3⋊Dic5C2314yes—
142#6669C2314yes—
143#6668C2314yes—
144(C2×D3)⋊Dic5C2314yes—
145(C2×D3)⋊Dic5C2314yes—
146#6665C2314yes—
147#6665C2314yes—
148C3×#540—51no—
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#5535D511yescharacteristic, complemented
162D3×#117—51no—
163C2×D4×D5—34no—
164C2×D4×D5—32no—
165C2×D4×D5—34no—
166C22×C4×D5—31no—
167C22×C4×D5—34no—
168C5×#127—31no—
169C5×#125—31no—
170C5×#123—34no—
171C5×#121—32no—
172C5×#121—34no—
173C4×C5×D4—32no—
174C5×#117C2×D311yescharacteristic, complemented
175#4086—32no—
176#4086—34no—
177#4085—34no—
178#4085—34no—
179#4085—34no—
180#4084—34no—
181#4084—32no—
182#4081—34no—
183D4×Dic5—32no—
184#4076—34no—
185#4076C2×D312yescomplemented
186#4075—34no—
187C4×C22⋊D5—34no—
188#4072—31no—
189#4041—34no—
190#4041—32no—
191#4040—34no—
192#4040C2×D314yescomplemented
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#4030C2×D314yescomplemented
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×D20C2×D312yescomplemented
213#4018—31no—
214#4018—31no—
215C42×D5—31no—
216C42×D5—31no—
217#4016C2×D311yescharacteristic, complemented
218C2×#540—151noSylow
219C23×C3×C5C2411yescharacteristic
220C22×D15—22no—
221C22×D15—24no—
222C22×D15C2411yescharacteristic
223C22×D15C2411yescharacteristic
224C22×C5×D3C2414yes—
225C22×C3×D5C2414yes—
226C2×D3×D5—28no—
227C2×D3×D5—28no—
228C2×D3×D5—28no—
229C2×C3×C4×C5—22no—
230C2×C3×C4×C5C2412yes—
231C2×C3×C4×C5C2411yescharacteristic
232C2×C3×C4×C5C2412yes—
233C2×C3×C4×C5C2411yescharacteristic
234C2×Dic15—22no—
235C2×Dic15C2411yescharacteristic
236C2×Dic15C2412yes—
237C2×Dic15C2412yes—
238C2×Dic15C2411yescharacteristic
239C4×D15—22no—
240C4×D15—24no—
241C4×D15—24no—
242C4×D15—22no—
243C4×D15—22no—
244C4×D15#4114yes—
245C5×#67—44no—
246C2×C5×Dic3C2414yes—
247C5×D12—24no—
248C5×D12—44no—
249C4×C5×D3—44no—
250C3×C22⋊D5—44no—
251C2×C3×Dic5C2414yes—
252C3×D20—24no—
253C3×D20—44no—
254C3×C4×D5—44no—
255#1203—44no—
256#1202—44no—
257#1201—28no—
258#1201—44no—
259#1201—44no—
260#1200—28no—
261D3×Dic5—44no—
262D5×Dic3—44no—
263C2×D3×D4—54no—
264C2×D3×D4—52no—
265C2×D3×D4—54no—
266C22×C4×D3—51no—
267C22×C4×D3—54no—
268C3×#127—51no—
269C3×#125—51no—
270C3×#123—54no—
271C3×#121—52no—
272C3×#121—54no—
273C3×C4×D4—52no—
274C3×#117C2×D511yescharacteristic, complemented
275#940—54no—
276#940—52no—
277#939—54no—
278#939—54no—
279#939—54no—
280#938—54no—
281#938—52no—
282#935—54no—
283D4×Dic3—52no—
284#930—54no—
285#930C2×D512yescomplemented
286#929—54no—
287C4×#67—54no—
288#926—51no—
289#895—54no—
290#895—52no—
291#894—54no—
292#894C2×D514yescomplemented
293#893—52no—
294#892—52no—
295D3×C4⋊C4—52no—
296D3×C4⋊C4—52no—
297D3×C4⋊C4—54no—
298#890—52no—
299#889—54no—
300#886—54no—
301#884—54no—
302#884—54no—
303#884C2×D514yescomplemented
304#883—54no—
305#883—54no—
306#67⋊C4—54no—
307D3×C22⋊C4—52no—
308D3×C22⋊C4—54no—
309D3×C22⋊C4—54no—
310#877—52no—
311#874C2×D511yescharacteristic, complemented
312C4×D12C2×D512yescomplemented
313#872—51no—
314#872—51no—
315C42×D3—51no—
316C42×D3—51no—
317#870C2×D511yescharacteristic, complemented
318C23×D5—31no—
319C23×D5—34no—
320C2×C5×D4—34no—
321C2×C5×D4—32no—
322C2×C5×D4—34no—
323C22×C4×C5—34no—
324C22×C4×C5C22×D311yescharacteristic
325C2×C22⋊D5—34no—
326C2×C22⋊D5—34no—
327C2×C22⋊D5—34no—
328C2×C22⋊D5—34no—
329C2×C22⋊D5C22×D314yes—
330C22×Dic5—31no—
331C22×Dic5—34no—
332D4×D5—68no—
333D4×D5—128no—
334D4×D5—128no—
335C2×D20—34no—
336C2×D20C22×D312yes—
337C2×D20C22×D314yes—
338C2×C4×D5—31no—
339C2×C4×D5—32no—
340C2×C4×D5—31no—
341C2×C4×D5—31no—
342C2×C4×D5—31no—
343C2×C4×D5—32no—
344C2×C4×D5—34no—
345C2×C4×D5—34no—
346C2×C4×D5—64no—
347C2×C4×D5—128no—
348C2×C4×D5C22×D314yes—
349C5×C4⋊C4—32no—
350C5×C4⋊C4—34no—
351C5×C4⋊C4C22×D312yes—
352C5×C22⋊C4—34no—
353C5×C22⋊C4—34no—
354C5×C22⋊C4C22×D312yes—
355C42×C5C22×D311yescharacteristic
356C42×C5C22×D311yescharacteristic
357C22⋊Dic5—32no—
358C22⋊Dic5—34no—
359C22⋊Dic5—34no—
360#685—34no—
361#685—34no—
362#685—32no—
363#685—32no—
364#685C22×D314yes—
365#685C22×D314yes—
366C4⋊Dic5—32no—
367C4⋊Dic5—34no—
368C4⋊Dic5C22×D312yes—
369#683—32no—
370#683—32no—
371#683—34no—
372#683—34no—
373#683C22×D314yes—
374C4×Dic5—31no—
375C4×Dic5—31no—
376C4×Dic5—32no—
377C4×Dic5—32no—
378#540—31no—
379#540—51no—
380#540—152no—
381#540—154no—
382#540—152no—
383#540—154no—
384#540—151no—
385#540—151no—
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—22no—
395C22×C3×C5C2511yescharacteristic
396C2×D15—21no—
397C2×D15—22no—
398C2×D15—44no—
399C2×D15C2×#4112yes—
400C2×D15H(5,𝔽2)14yes—
401C2×C5×D3—24no—
402C2×C5×D3—24no—
403C2×C5×D3—24no—
404C2×C3×D5—24no—
405C2×C3×D5—24no—
406C2×C3×D5—24no—
407D3×D5—416no—
408C3×C4×C5—21no—
409C3×C4×C5—22no—
410C3×C4×C5—22no—
411C3×C4×C5C2×#4112yes—
412Dic15—21no—
413Dic15—22no—
414Dic15—22no—
415Dic15C2×#4112yes—
416C3×Dic5—24no—
417C5×Dic3—24no—
418C23×D3—51no—
419C23×D3—54no—
420C2×C3×D4—54no—
421C2×C3×D4—52no—
422C2×C3×D4—54no—
423C22×C3×C4—54no—
424C22×C3×C4C22×D511yescharacteristic
425C2×#67—54no—
426C2×#67—54no—
427C2×#67—54no—
428C2×#67—54no—
429C2×#67C22×D514yes—
430C22×Dic3—51no—
431C22×Dic3—54no—
432D3×D4—108no—
433D3×D4—208no—
434D3×D4—208no—
435C2×D12—54no—
436C2×D12C22×D512yes—
437C2×D12C22×D514yes—
438C2×C4×D3—51no—
439C2×C4×D3—52no—
440C2×C4×D3—52no—
441C2×C4×D3—51no—
442C2×C4×D3—51no—
443C2×C4×D3—51no—
444C2×C4×D3—54no—
445C2×C4×D3—54no—
446C2×C4×D3—104no—
447C2×C4×D3—208no—
448C2×C4×D3C22×D514yes—
449C3×C4⋊C4—54no—
450C3×C4⋊C4—52no—
451C3×C4⋊C4C22×D512yes—
452C3×C22⋊C4—54no—
453C3×C22⋊C4—54no—
454C3×C22⋊C4C22×D512yes—
455C3×C42C22×D511yescharacteristic
456C3×C42C22×D511yescharacteristic
457#217—52no—
458#217—54no—
459#217—54no—
460(C2×D3)⋊C4—54no—
461(C2×D3)⋊C4—54no—
462(C2×D3)⋊C4—52no—
463(C2×D3)⋊C4—52no—
464(C2×D3)⋊C4C22×D514yes—
465(C2×D3)⋊C4C22×D514yes—
466C4⋊Dic3—52no—
467C4⋊Dic3—54no—
468C4⋊Dic3C22×D512yes—
469Dic3⋊C4—52no—
470Dic3⋊C4—52no—
471Dic3⋊C4—54no—
472Dic3⋊C4—54no—
473Dic3⋊C4C22×D514yes—
474C4×Dic3—51no—
475C4×Dic3—51no—
476C4×Dic3—52no—
477C4×Dic3—52no—
478C23×C5—34no—
479C23×C5C23×D311yescharacteristic
480C22×D5—31no—
481C22×D5—31no—
482C22×D5—68no—
483C22×D5—68no—
484C22×D5—68no—
485C22×D5—62no—
486C22×D5—64no—
487C22×D5C23×D314yes—
488C5×D4—64no—
489C5×D4—124no—
490C5×D4—124no—
491C2×C4×C5—22no—
492C2×C4×C5—34no—
493C2×C4×C5—124no—
494C2×C4×C5C23×D312yes—
495C2×C4×C5C23×D312yes—
496C2×C4×C5C23×D311yescharacteristic
497C2×C4×C5C23×D311yescharacteristic
498C22⋊D5—44no—
499C22⋊D5—68no—
500C22⋊D5—124no—
501C22⋊D5—124no—
502C22⋊D5—124no—
503C2×Dic5—31no—
504C2×Dic5—32no—
505C2×Dic5—32no—
506C2×Dic5—31no—
507C2×Dic5—62no—
508C2×Dic5—124no—
509C2×Dic5C23×D314yes—
510D20—24no—
511D20—44no—
512D20—124no—
513C4×D5—34no—
514C4×D5—44no—
515C4×D5—68no—
516C4×D5—62no—
517C4×D5—62no—
518C4×D5—64no—
519C4×D5—64no—
520C4×D5—62no—
521C4×D5—124no—
522C22×D4—152no—
523C22×D4—154no—
524C22×D4—154no—
525C23×C4—154no—
526C23×C4—151no—
527#127—31no—
528#127—51no—
529#127—152no—
530#127—154no—
531#125—31no—
532#125—51no—
533#125—154no—
534#125—152no—
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—32no—
544#121—34no—
545#121—52no—
546#121—54no—
547#121—154no—
548#121—154no—
549#121—154no—
550#121—152no—
551#121—154no—
552#121—152no—
553#121—154no—
554#121—154no—
555#121—154no—
556#121—154no—
557C4×D4—32no—
558C4×D4—52no—
559C4×D4—154no—
560C4×D4—152no—
561C4×D4—152no—
562C4×D4—154no—
563#117—151no—
564#117—152no—
565#117—152no—
566#117—151no—
567#117—151no—
568#117D3×D511yescharacteristic, complemented
569C2×C4⋊C4—152no—
570C2×C4⋊C4—154no—
571C2×C4⋊C4—152no—
572C2×C22⋊C4—154no—
573C2×C22⋊C4—154no—
574C2×C22⋊C4—152no—
575C2×C42—151no—
576C2×C42—151no—
577C2×C3×C5—41no—
578C2×C3×C5C22×#4111yescharacteristic
579C2×C3×C5C2×H(5,𝔽2)12yes—
580D15—41no—
581D15#54014yescomplemented
582C3×D5—44no—
583C5×D3—44no—
584C23×C3—54no—
585C23×C3C23×D511yescharacteristic
586C22×D3—51no—
587C22×D3—51no—
588C22×D3—108no—
589C22×D3—108no—
590C22×D3—108no—
591C22×D3—102no—
592C22×D3—104no—
593C22×D3C23×D514yes—
594C3×D4—104no—
595C3×D4—204no—
596C3×D4—204no—
597C2×C3×C4—22no—
598C2×C3×C4—54no—
599C2×C3×C4—204no—
600C2×C3×C4C23×D512yes—
601C2×C3×C4C23×D512yes—
602C2×C3×C4C23×D511yescharacteristic
603C2×C3×C4C23×D511yescharacteristic
604#67—44no—
605#67—108no—
606#67—204no—
607#67—204no—
608#67—204no—
609C2×Dic3—51no—
610C2×Dic3—52no—
611C2×Dic3—52no—
612C2×Dic3—51no—
613C2×Dic3—102no—
614C2×Dic3—204no—
615C2×Dic3C23×D514yes—
616D12—24no—
617D12—44no—
618D12—204no—
619C4×D3—44no—
620C4×D3—54no—
621C4×D3—108no—
622C4×D3—102no—
623C4×D3—102no—
624C4×D3—104no—
625C4×D3—104no—
626C4×D3—102no—
627C4×D3—204no—
628C22×C5—21no—
629C22×C5—22no—
630C22×C5—64no—
631C22×C5—64no—
632C22×C5—64no—
633C22×C5C24×D311yescharacteristic
634C2×D5—24no—
635C2×D5—24no—
636C2×D5—24no—
637C2×D5—32no—
638C2×D5—34no—
639C2×D5—61no—
640C2×D5—62no—
641C2×D5—1216no—
642C2×D5—124no—
643C4×C5—21no—
644C4×C5—22no—
645C4×C5—22no—
646C4×C5—64no—
647C4×C5D3×#4112yes—
648Dic5—24no—
649Dic5—32no—
650Dic5—61no—
651Dic5—62no—
652Dic5—62no—
653C24—154no—
654C24—151no—
655C2×D4—34no—
656C2×D4—32no—
657C2×D4—34no—
658C2×D4—54no—
659C2×D4—52no—
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—34no—
670C22×C4—54no—
671C22×C4—154no—
672C22×C4—154no—
673C22×C4—154no—
674C22×C4—151no—
675C22×C4—151no—
676C22×C4—152no—
677C22×C4—152no—
678C22×C4—151no—
679C22×C4—151no—
680C22×C4—151no—
681C22×C4—304no—
682C22×C4—608no—
683C22×C4C2×D3×D511yescharacteristic
684C4⋊C4—32no—
685C4⋊C4—34no—
686C4⋊C4—52no—
687C4⋊C4—54no—
688C4⋊C4—154no—
689C4⋊C4—154no—
690C4⋊C4—154no—
691C4⋊C4—152no—
692C4⋊C4—152no—
693C4⋊C4—152no—
694C4⋊C4C2×D3×D512yes—
695C22⋊C4—34no—
696C22⋊C4—34no—
697C22⋊C4—54no—
698C22⋊C4—54no—
699C22⋊C4—154no—
700C22⋊C4—154no—
701C22⋊C4—154no—
702C22⋊C4—154no—
703C22⋊C4—152no—
704C22⋊C4—152no—
705C22⋊C4—152no—
706C22⋊C4C2×D3×D512yes—
707C42—152no—
708C42—151no—
709C42—152no—
710C42—151no—
711C42C2×D3×D511yescharacteristic
712C42C2×D3×D511yescharacteristic
713C3×C5C2×#54011yescharacteristic, complemented, Hall
714C22×C3—21no—
715C22×C3—22no—
716C22×C3—104no—
717C22×C3—104no—
718C22×C3—104no—
719C22×C3C24×D511yescharacteristic
720C2×D3—24no—
721C2×D3—24no—
722C2×D3—24no—
723C2×D3—52no—
724C2×D3—54no—
725C2×D3—101no—
726C2×D3—102no—
727C2×D3—2016no—
728C2×D3—204no—
729C3×C4—21no—
730C3×C4—22no—
731C3×C4—22no—
732C3×C4—104no—
733C3×C4D5×#4112yes—
734Dic3—24no—
735Dic3—52no—
736Dic3—101no—
737Dic3—102no—
738Dic3—102no—
739C2×C5—41no—
740C2×C5—124no—
741C2×C5C2×D3×#4111yescharacteristic
742C2×C5D3×H(5,𝔽2)12yes—
743D5—34no—
744D5—44no—
745D5—121no—
746C23—34no—
747C23—54no—
748C23—151no—
749C23—151no—
750C23—302no—
751C23—304no—
752C23—308no—
753C23—308no—
754C23—308no—
755C23C22×D3×D511yescharacteristic
756D4—64no—
757D4—104no—
758D4—124no—
759D4—124no—
760D4—204no—
761D4—204no—
762D4—308no—
763D4—604no—
764D4—604no—
765D4—604no—
766D4—604no—
767C2×C4—22no—
768C2×C4—34no—
769C2×C4—54no—
770C2×C4—124no—
771C2×C4—151no—
772C2×C4—154no—
773C2×C4—152no—
774C2×C4—152no—
775C2×C4—151no—
776C2×C4—204no—
777C2×C4—302no—
778C2×C4—302no—
779C2×C4—304no—
780C2×C4—304no—
781C2×C4—308no—
782C2×C4—302no—
783C2×C4—302no—
784C2×C4—604no—
785C2×C4—604no—
786C2×C4C22×D3×D512yes—
787C2×C4C22×D3×D512yes—
788C2×C4C22×D3×D511yescharacteristic
789C2×C4C22×D3×D511yescharacteristic
790C2×C3—41no—
791C2×C3—204no—
792C2×C3C2×D5×#4111yescharacteristic
793C2×C3D5×H(5,𝔽2)12yes—
794D3—44no—
795D3—54no—
796D3—201no—
797C5D3×#54011yescharacteristic, complemented, Sylow
798C22—21no—
799C22—22no—
800C22—64no—
801C22—64no—
802C22—64no—
803C22—104no—
804C22—104no—
805C22—104no—
806C22—152no—
807C22—154no—
808C22—301no—
809C22—302no—
810C22—604no—
811C22—6016no—
812C22C23×D3×D511yescharacteristic
813C4—21no—
814C4—22no—
815C4—22no—
816C4—64no—
817C4—104no—
818C4—152no—
819C4—301no—
820C4—302no—
821C4—302no—
822C4#9201612yes—
823C3D5×#54011yescharacteristic, complemented, Sylow
824C2—41no—
825C2—124no—
826C2—154no—
827C2—204no—
828C2—601no—
829C2C2×#9201611yescharacteristic
830C2#1175705412yes—
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#117C22
hypercenter#117D3×D5
hypocenterC3×C5C2×#540
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. D15×#117C2semidirect
2. C5×#5535C2semidirect
3. C3×#65869C2semidirect
4. #11754670C2semidirect
5. #11754601C2semidirect
6. #11753844C2semidirect
7. #11753785C2semidirect
8. #11753219C2semidirect
9. #11753146C2semidirect
10. #11752750C2semidirect
11. C4×#6777C2semidirect
12. #11752707C2semidirect
13. #11752652C2semidirect
14. #11752635C2semidirect
15. #11752631C2semidirect
22. C3×C5×#117C22semidirect
23. #91815C22semidirect
24. #91781C22semidirect
27. #91766C22semidirect
28. #91761C22semidirect
29. #91761C22semidirect
32. C5×#930C22semidirect
33. C5×#894C22semidirect
34. C5×#884C22semidirect
35. C5×#874C22semidirect
36. C4×C5×D12C22semidirect
37. C5×#870C22semidirect
38. C3×#4076C22semidirect
39. C3×#4040C22semidirect
40. C3×#4030C22semidirect
41. C3×#4020C22semidirect
42. C3×C4×D20C22semidirect
43. C3×#4016C22semidirect
44. #91571C22semidirect
45. #91565C22semidirect
46. #91549C22semidirect
49. #91466C22semidirect
50. #91465C22semidirect
51. #91463C22semidirect
52. #91463C22semidirect
53. #91461C22semidirect
54. #91457C22semidirect
55. #91454C22semidirect
56. #91452C22semidirect
57. #91448C22semidirect
58. #91447C22semidirect
59. #91442C22semidirect
60. C4×#1201C22semidirect
62. #91435C22semidirect
63. #91434C22semidirect
64. #91423C22semidirect
65. #91416C22semidirect
66. #91414C22semidirect
67. #91409C22semidirect
68. #91407C22semidirect
70. #91384C22semidirect
71. #91382C22semidirect
86. #65869D3semidirect
161. #5535D5semidirect
174. C5×#117C2×D3semidirect
185. #4076C2×D3semidirect
192. #4040C2×D3semidirect
203. #4030C2×D3semidirect
211. #4020C2×D3semidirect
212. C4×D20C2×D3semidirect
217. #4016C2×D3semidirect
274. C3×#117C2×D5semidirect
285. #930C2×D5semidirect
292. #894C2×D5semidirect
303. #884C2×D5semidirect
311. #874C2×D5semidirect
312. C4×D12C2×D5semidirect
317. #870C2×D5semidirect
568. #117D3×D5semidirect
581. 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×#1172
C5×#55352
C3×#658692
#117546702
#117546012
#117538442
#117537852
#117532192
#117531462
#117527502
C4×#67772
#117527072
#117526522
#117526352
#117526312
D5×#5403
D3×#5405