Finite Group Databasebeta

← D3×#66032 #14481117

Subgroups — D3×#66032 #14481117

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×D3×#125C211yesmaximal, characteristic, complemented
3C3×#66032C211yesmaximal, characteristic, complemented
4D3×#4041C212yesmaximal, complemented
5D3×#4041C214yesmaximal, complemented
6D3×#4040C214yesmaximal, complemented
7D3×#4039C212yesmaximal, complemented
8#11753821C212yesmaximal, complemented
9#11753782C214yesmaximal, complemented
10#11753772C214yesmaximal, complemented
11#11753649C212yesmaximal, complemented
12D3×#4020C211yesmaximal, characteristic, complemented
13D3×#4018C211yesmaximal, characteristic, complemented
14#11752719C211yesmaximal, characteristic, complemented
15#11752635C211yesmaximal, characteristic, complemented
16C2×#66032—31nomaximal, Hall
17C2×D3×D20C2212yes—
18C2×D3×D20C2214yes—
19C2×D3×D20C2214yes—
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×D3×C4⋊C4C2212yes—
30C5×D3×C4⋊C4C2214yes—
31C5×#890C2212yescomplemented
32C5×#889C2214yescomplemented
33C42×C5×D3C2211yescharacteristic
34C5×#870C2211yescharacteristic, complemented
35C3×#4041C2214yescomplemented
36C3×#4041C2212yescomplemented
37C3×#4040C2214yescomplemented
38C3×#4039C2212yescomplemented
39C3×#4020C2211yescharacteristic, complemented
40C3×#4018C2211yescharacteristic, complemented
41D3×#685C2212yes—
42D3×#685C2214yes—
43D3×#685C2214yes—
44#91465C2214yescomplemented
45#91465C2212yescomplemented
46#91459C2214yescomplemented
47#91459C2214yescomplemented
48#91459C2214yescomplemented
49#91458C2214yescomplemented
50#91458C2212yescomplemented
51#91450C2212yescomplemented
52#91450C2214yescomplemented
53#91444C2214yescomplemented
54#91434C2212yescomplemented
55#91433C2214yescomplemented
56#91418C2212yescomplemented
57#91413C2214yescomplemented
58#91409C2214yescomplemented
59#91409C2214yescomplemented
60#91409C2214yescomplemented
61#91407C2214yescomplemented
62#91403C2212yescomplemented
63D3×#683C2212yes—
64C4×D3×Dic5C2211yescharacteristic
65#91396C2214yescomplemented
66#91393C2212yescomplemented
67#91386C2211yescharacteristic, complemented
68#91357C2211yescharacteristic, complemented
69#91356C2214yescomplemented
70#91354C2214yescomplemented
71#91348C2214yescomplemented
72D3×#540—51nomaximal, Hall
73C2×C5×#125—31no—
74#66032—34no—
75#66032—32no—
76#66032—34no—
77#66032—32no—
78#66032—31no—
79#66032—31no—
80#66032—31no—
81#66032D311yescharacteristic, direct product factor
82C2×#4041—32no—
83C2×#4041—34no—
84C2×#4040—34no—
85C2×#4039—32no—
86C2×#4020—31no—
87C2×#4018—31no—
88C22×D3×D5C2311yescharacteristic
89C22×D3×D5C2314yes—
90C2×D60C2312yes—
91C2×D60C2314yes—
92C2×D60C2314yes—
93C2×C4×D15C2311yescharacteristic
94C2×C4×D15C2314yes—
95C2×C4×C5×D3C2312yes—
96C2×C4×C5×D3C2314yes—
97C2×C4×C5×D3C2311yescharacteristic
98C2×C3×D20C2312yes—
99C2×C3×D20C2314yes—
100C2×C3×D20C2314yes—
101C2×C3×C4×D5C2311yescharacteristic
102C2×C3×C4×D5C2314yes—
103C2×#1202C2314yes—
104C2×#1202C2314yes—
105C2×#1202C2314yes—
106C2×#1202C2314yes—
107C2×#1202C2314yes—
108C2×#1200C2311yescharacteristic
109C2×#1200C2314yes—
110C2×D3×Dic5C2312yes—
111C2×D3×Dic5C2311yescharacteristic
112C2×D5×Dic3C2311yescharacteristic
113C2×D5×Dic3C2314yes—
114D3×D20—28no—
115D3×D20—48no—
116D3×D20—48no—
117C4×D3×D5—24no—
118C4×D3×D5—48no—
119C3×C5×C4⋊C4C2314yes—
120C3×C5×C4⋊C4C2312yes—
121C3×C42×C5C2311yescharacteristic
122#6714C2312yes—
123#6714C2314yes—
124#6714C2314yes—
125#6712C2312yes—
126C4×Dic15C2311yescharacteristic
127C5×C4⋊Dic3C2314yes—
128C5×C4⋊Dic3C2312yes—
129C5×Dic3⋊C4C2314yes—
130C5×Dic3⋊C4C2314yes—
131C5×Dic3⋊C4C2314yes—
132C4×C5×Dic3C2312yes—
133C4×C5×Dic3C2311yescharacteristic
134C3×#685C2312yes—
135C3×#685C2314yes—
136C3×#685C2314yes—
137C3×#683C2312yes—
138C3×C4×Dic5C2311yescharacteristic
139#6669C2312yes—
140#6668C2312yes—
141#6667C2314yes—
142#6667C2312yes—
143#6667C2314yes—
144#6665C2312yes—
145#6665C2314yes—
146#6665C2314yes—
147Dic3×Dic5C2312yes—
148C3×#540—51no—
149#5719—51no—
150D3×#127—51no—
151#5697—51no—
152D3×#125D511yescharacteristic, complemented
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—
163C22×D20—32no—
164C22×D20—34no—
165C22×D20—34no—
166C22×C4×D5—31no—
167C22×C4×D5—34no—
168C5×#125—34no—
169C5×#125—32no—
170C5×#125—31no—
171C5×#125C2×D311yescharacteristic, complemented
172C2×C5×C4⋊C4—32no—
173C2×C5×C4⋊C4—34no—
174C2×C42×C5—31no—
175C2×#685—32no—
176C2×#685—34no—
177C2×#685—34no—
178C2×#683—32no—
179C2×C4×Dic5—31no—
180#4041—34no—
181#4041—34no—
182#4041—34no—
183#4041—34no—
184#4041—32no—
185#4041—34no—
186#4041—32no—
187#4041—34no—
188#4041—32no—
189#4041—34no—
190#4041—34no—
191#4041—34no—
192#4041C2×D314yescomplemented
193#4041C2×D312yescomplemented
194#4040—34no—
195#4040—34no—
196#4040—34no—
197#4040—34no—
198#4040—34no—
199#4040—34no—
200#4040—34no—
201#4040C2×D314yescomplemented
202#4039—32no—
203#4039—34no—
204#4039—32no—
205#4039—34no—
206#4039—32no—
207#4039C2×D312yescomplemented
208#4020—34no—
209#4020—32no—
210#4020—31no—
211#4020C2×D311yescharacteristic, complemented
212#4018—31no—
213#4018—31no—
214#4018—32no—
215#4018—32no—
216#4018—31no—
217#4018C2×D311yescharacteristic, complemented
218C2×#540—151noSylow
219C22×D15C2411yescharacteristic
220C22×D15C2414yes—
221C22×C5×D3C2411yescharacteristic
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×Dic15C2412yes—
233C2×Dic15C2411yescharacteristic
234D60—24no—
235D60—44no—
236D60—44no—
237C4×D15—22no—
238C4×D15—44no—
239C2×C5×Dic3C2414yes—
240C2×C5×Dic3C2412yes—
241C2×C5×Dic3C2411yescharacteristic
242C4×C5×D3—28no—
243C4×C5×D3—24no—
244C4×C5×D3#4114yes—
245C2×C3×Dic5C2412yes—
246C2×C3×Dic5C2411yescharacteristic
247C3×D20—24no—
248C3×D20—44no—
249C3×D20—44no—
250C3×C4×D5—22no—
251C3×C4×D5—44no—
252#1202—28no—
253#1202—44no—
254#1202—44no—
255#1202—44no—
256#1202—44no—
257#1200—22no—
258#1200—44no—
259D3×Dic5—22no—
260D3×Dic5—24no—
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#895—54no—
290#895—52no—
291#894—54no—
292#894—54no—
293#893—52no—
294#892—52no—
295D3×C4⋊C4—52no—
296D3×C4⋊C4C2×D514yes—
297D3×C4⋊C4C2×D512yes—
298#890C2×D512yescomplemented
299#889C2×D514yescomplemented
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×D3C2×D511yescharacteristic
317#870C2×D511yescharacteristic, complemented
318C23×D5—31no—
319C23×D5—34no—
320C22×C4×C5—31no—
321C22×C4×C5—32no—
322C22×C4×C5—34no—
323C22×Dic5—32no—
324C22×Dic5—31no—
325C2×D20—34no—
326C2×D20—32no—
327C2×D20—34no—
328C2×D20—34no—
329C2×D20—34no—
330C2×D20—34no—
331C2×D20—34no—
332C2×D20—34no—
333C2×D20—68no—
334C2×D20—128no—
335C2×D20—128no—
336C2×D20C22×D312yes—
337C2×D20C22×D314yes—
338C2×D20C22×D314yes—
339C2×C4×D5—31no—
340C2×C4×D5—31no—
341C2×C4×D5—31no—
342C2×C4×D5—34no—
343C2×C4×D5—34no—
344C2×C4×D5—34no—
345C2×C4×D5—64no—
346C2×C4×D5—128no—
347C2×C4×D5C22×D311yescharacteristic
348C2×C4×D5C22×D314yes—
349C5×C4⋊C4—34no—
350C5×C4⋊C4—34no—
351C5×C4⋊C4—34no—
352C5×C4⋊C4—32no—
353C5×C4⋊C4—34no—
354C5×C4⋊C4C22×D312yes—
355C5×C4⋊C4C22×D314yes—
356C42×C5—32no—
357C42×C5—31no—
358C42×C5C22×D311yescharacteristic
359#685—32no—
360#685—34no—
361#685—34no—
362#685—32no—
363#685—34no—
364#685—34no—
365#685—32no—
366#685—34no—
367#685—34no—
368#685C22×D312yes—
369#685C22×D314yes—
370#685C22×D314yes—
371#683—32no—
372#683—32no—
373#683—32no—
374#683C22×D312yes—
375C4×Dic5—31no—
376C4×Dic5—32no—
377C4×Dic5C22×D311yescharacteristic
378#540—51no—
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—31no—
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×D3C2×#4112yes—
400C2×C5×D3H(5,𝔽2)14yes—
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—21no—
412Dic15—22no—
413C3×Dic5—21no—
414C3×Dic5—22no—
415C5×Dic3—24no—
416C5×Dic3—22no—
417C5×Dic3C2×#4112yes—
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×D12—52no—
436C2×D12—54no—
437C2×D12—54no—
438C2×C4×D3—52no—
439C2×C4×D3—51no—
440C2×C4×D3—51no—
441C2×C4×D3—51no—
442C2×C4×D3—54no—
443C2×C4×D3—54no—
444C2×C4×D3—104no—
445C2×C4×D3—208no—
446C2×C4×D3C22×D512yes—
447C2×C4×D3C22×D514yes—
448C2×C4×D3C22×D511yescharacteristic
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)⋊C4—52no—
464(C2×D3)⋊C4—54no—
465(C2×D3)⋊C4—54no—
466C4⋊Dic3—52no—
467C4⋊Dic3C22×D512yes—
468C4⋊Dic3C22×D514yes—
469Dic3⋊C4—52no—
470Dic3⋊C4—52no—
471Dic3⋊C4C22×D514yes—
472Dic3⋊C4C22×D514yes—
473Dic3⋊C4C22×D514yes—
474C4×Dic3—51no—
475C4×Dic3—52no—
476C4×Dic3C22×D511yescharacteristic
477C4×Dic3C22×D512yes—
478C23×C5—31no—
479C22×D5—31no—
480C22×D5—34no—
481C22×D5—62no—
482C22×D5—68no—
483C22×D5—68no—
484C22×D5—64no—
485C22×D5—68no—
486C22×D5C23×D311yescharacteristic
487C22×D5C23×D314yes—
488C2×C4×C5—31no—
489C2×C4×C5—34no—
490C2×C4×C5—32no—
491C2×C4×C5—34no—
492C2×C4×C5—68no—
493C2×C4×C5—64no—
494C2×C4×C5C23×D312yes—
495C2×C4×C5C23×D314yes—
496C2×C4×C5C23×D311yescharacteristic
497C2×Dic5—32no—
498C2×Dic5—31no—
499C2×Dic5—62no—
500C2×Dic5—64no—
501C2×Dic5C23×D312yes—
502C2×Dic5C23×D311yescharacteristic
503D20—24no—
504D20—44no—
505D20—44no—
506D20—68no—
507D20—64no—
508D20—124no—
509D20—124no—
510D20—124no—
511D20—124no—
512D20—124no—
513D20—124no—
514C4×D5—22no—
515C4×D5—44no—
516C4×D5—62no—
517C4×D5—62no—
518C4×D5—62no—
519C4×D5—124no—
520C4×D5—124no—
521C4×D5—124no—
522C22×D4—152no—
523C22×D4—154no—
524C22×D4—154no—
525C23×C4—151no—
526C23×C4—154no—
527#127—51no—
528#127—152no—
529#127—154no—
530#127—151no—
531#125—34no—
532#125—32no—
533#125—31no—
534#125D3×D511yescharacteristic, complemented
535#123—54no—
536#123—154no—
537#123—154no—
538#123—154no—
539#123—154no—
540#123—154no—
541#123—154no—
542#123—154no—
543#121—54no—
544#121—52no—
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—52no—
558C4×D4—152no—
559C4×D4—154no—
560C4×D4—154no—
561C4×D4—152no—
562C4×D4—152no—
563#117—51no—
564#117—151no—
565#117—152no—
566#117—152no—
567#117—151no—
568#117—151no—
569C2×C4⋊C4—32no—
570C2×C4⋊C4—34no—
571C2×C4⋊C4—152no—
572C2×C22⋊C4—152no—
573C2×C22⋊C4—154no—
574C2×C22⋊C4—154no—
575C2×C42—31no—
576C2×C42—151no—
577C2×C3×C5C22×#4111yescharacteristic
578C2×C3×C5C2×H(5,𝔽2)12yes—
579D15—41no—
580D15—44no—
581C3×D5—41no—
582C3×D5—44no—
583C5×D3#54014yescomplemented
584C23×C3—51no—
585C23×C3—54no—
586C22×D3—51no—
587C22×D3—54no—
588C22×D3—102no—
589C22×D3—108no—
590C22×D3—108no—
591C22×D3—104no—
592C22×D3—108no—
593C22×D3C23×D511yescharacteristic
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—52no—
610C2×Dic3—51no—
611C2×Dic3—102no—
612C2×Dic3—204no—
613C2×Dic3C23×D512yes—
614C2×Dic3C23×D514yes—
615C2×Dic3C23×D511yescharacteristic
616D12—104no—
617D12—204no—
618D12—204no—
619C4×D3—28no—
620C4×D3—24no—
621C4×D3—102no—
622C4×D3—104no—
623C4×D3—102no—
624C4×D3—102no—
625C4×D3—204no—
626C4×D3—204no—
627C4×D3#71314yes—
628C22×C5—32no—
629C22×C5—34no—
630C22×C5C24×D311yescharacteristic
631C2×D5—21no—
632C2×D5—24no—
633C2×D5—24no—
634C2×D5—22no—
635C2×D5—24no—
636C2×D5—61no—
637C2×D5—64no—
638C2×D5—64no—
639C2×D5—62no—
640C2×D5—64no—
641C2×D5—124no—
642C2×D5—1216no—
643C4×C5—24no—
644C4×C5—22no—
645C4×C5—32no—
646C4×C5—64no—
647C4×C5—62no—
648C4×C5D3×#4112yes—
649Dic5—21no—
650Dic5—22no—
651Dic5—61no—
652Dic5—62no—
653C24—151no—
654C24—154no—
655C2×D4—52no—
656C2×D4—54no—
657C2×D4—54no—
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—32no—
671C22×C4—34no—
672C22×C4—51no—
673C22×C4—54no—
674C22×C4—151no—
675C22×C4—154no—
676C22×C4—151no—
677C22×C4—154no—
678C22×C4—152no—
679C22×C4—151no—
680C22×C4—151no—
681C22×C4—154no—
682C22×C4—304no—
683C22×C4—608no—
684C4⋊C4—34no—
685C4⋊C4—32no—
686C4⋊C4—34no—
687C4⋊C4—34no—
688C4⋊C4—34no—
689C4⋊C4—52no—
690C4⋊C4—152no—
691C4⋊C4—152no—
692C4⋊C4—152no—
693C4⋊C4C2×D3×D512yes—
694C4⋊C4C2×D3×D514yes—
695C22⋊C4—52no—
696C22⋊C4—54no—
697C22⋊C4—54no—
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—32no—
708C42—31no—
709C42—51no—
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—101no—
721C2×D3—104no—
722C2×D3—104no—
723C2×D3—102no—
724C2×D3—104no—
725C2×D3—204no—
726C2×D3—2016no—
727C2×D3C2×#71312yes—
728C2×D3#414914yes—
729C3×C4—24no—
730C3×C4—22no—
731C3×C4—101no—
732C3×C4—102no—
733C3×C4C2×#71312yes—
734Dic3—24no—
735Dic3—22no—
736Dic3—101no—
737Dic3—102no—
738Dic3C2×#71312yes—
739C2×C5—34no—
740C2×C5C2×D3×#4111yescharacteristic
741C2×C5D3×H(5,𝔽2)12yes—
742D5—41no—
743D5—44no—
744D5—121no—
745D5—124no—
746C23—31no—
747C23—51no—
748C23—54no—
749C23—151no—
750C23—154no—
751C23—302no—
752C23—308no—
753C23—308no—
754C23—304no—
755C23—308no—
756D4—104no—
757D4—204no—
758D4—204no—
759D4—308no—
760D4—304no—
761D4—604no—
762D4—604no—
763D4—604no—
764D4—604no—
765D4—604no—
766D4—604no—
767C2×C4—31no—
768C2×C4—34no—
769C2×C4—32no—
770C2×C4—34no—
771C2×C4—52no—
772C2×C4—51no—
773C2×C4—68no—
774C2×C4—64no—
775C2×C4—102no—
776C2×C4—152no—
777C2×C4—151no—
778C2×C4—204no—
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—201no—
791C2×C3—204no—
792C2×C3C22×#71311yescharacteristic
793C2×C3C2×#414912yes—
794D3—201no—
795D3—204no—
796D3#6603214yesdirect product factor
797C5D3×#54011yescharacteristic, complemented, Sylow
798C22—32no—
799C22—34no—
800C22—101no—
801C22—104no—
802C22—104no—
803C22—102no—
804C22—104no—
805C22—301no—
806C22—304no—
807C22—304no—
808C22—302no—
809C22—304no—
810C22—604no—
811C22—6016no—
812C22C23×D3×D511yescharacteristic
813C4—24no—
814C4—22no—
815C4—32no—
816C4—64no—
817C4—62no—
818C4—101no—
819C4—102no—
820C4—301no—
821C4—302no—
822C4D3×#71312yes—
823C3C2×#6603211yescharacteristic, complemented, Sylow
824C2—34no—
825C2—201no—
826C2—204no—
827C2—601no—
828C2—604no—
829C2C2×D3×#71311yescharacteristic
830C2D3×#414912yes—
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×D3×#125C2semidirect
3. C3×#66032C2semidirect
4. D3×#4041C2semidirect
5. D3×#4041C2semidirect
6. D3×#4040C2semidirect
7. D3×#4039C2semidirect
8. #11753821C2semidirect
9. #11753782C2semidirect
10. #11753772C2semidirect
11. #11753649C2semidirect
12. D3×#4020C2semidirect
13. D3×#4018C2semidirect
14. #11752719C2semidirect
15. #11752635C2semidirect
22. C3×C5×#125C22semidirect
23. #91784C22semidirect
24. #91784C22semidirect
25. #91783C22semidirect
26. #91782C22semidirect
27. #91763C22semidirect
28. #91761C22semidirect
31. C5×#890C22semidirect
32. C5×#889C22semidirect
34. C5×#870C22semidirect
35. C3×#4041C22semidirect
36. C3×#4041C22semidirect
37. C3×#4040C22semidirect
38. C3×#4039C22semidirect
39. C3×#4020C22semidirect
40. C3×#4018C22semidirect
44. #91465C22semidirect
45. #91465C22semidirect
46. #91459C22semidirect
47. #91459C22semidirect
48. #91459C22semidirect
49. #91458C22semidirect
50. #91458C22semidirect
51. #91450C22semidirect
52. #91450C22semidirect
53. #91444C22semidirect
54. #91434C22semidirect
55. #91433C22semidirect
56. #91418C22semidirect
57. #91413C22semidirect
58. #91409C22semidirect
59. #91409C22semidirect
60. #91409C22semidirect
61. #91407C22semidirect
62. #91403C22semidirect
65. #91396C22semidirect
66. #91393C22semidirect
67. #91386C22semidirect
68. #91357C22semidirect
69. #91356C22semidirect
70. #91354C22semidirect
71. #91348C22semidirect
81. #66032D3direct (N × H)
152. D3×#125D5semidirect
171. C5×#125C2×D3semidirect
192. #4041C2×D3semidirect
193. #4041C2×D3semidirect
201. #4040C2×D3semidirect
207. #4039C2×D3semidirect
211. #4020C2×D3semidirect
217. #4018C2×D3semidirect
269. C3×#125C2×D5semidirect
298. #890C2×D5semidirect
299. #889C2×D5semidirect
317. #870C2×D5semidirect
534. #125D3×D5semidirect
583. C5×D3#540semidirect
713. C3×C5C2×#540semidirect
796. D3#66032direct (N × H)
797. C5D3×#540semidirect
823. C3C2×#66032semidirect

Maximal subgroups

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

subgroupindex
#117564562
C5×D3×#1252
C3×#660322
D3×#40412
D3×#40402
D3×#40392
#117538212
#117537822
#117537722
#117536492
D3×#40202
D3×#40182
#117527192
#117526352
C2×#660323
D3×#5405