Finite Group Databasebeta

← D3×#65106 #14416396

Subgroups — D3×#65106 #14416396

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×Q8×Dic5C211yesmaximal, characteristic, complemented
2C2×D3×#688C211yesmaximal, characteristic
3D3×#4039C211yesmaximal, characteristic
4#11750918C211yesmaximal, characteristic, complemented
5C5×D3×#103C211yesmaximal, characteristic, complemented
6C3×#65106C211yesmaximal, characteristic, complemented
7#11749241C211yesmaximal, characteristic, complemented
8#11749225C211yesmaximal, characteristic, complemented
9D3×#3953C211yesmaximal, characteristic
10#11747748C211yesmaximal, characteristic, complemented
11#11747736C211yesmaximal, characteristic, complemented
12D3×#3947C211yesmaximal, characteristic, complemented
13#11747471C211yesmaximal, characteristic, complemented
14D3×#3939C211yesmaximal, characteristic, complemented
15#11747280C211yesmaximal, characteristic, complemented
16C2×#65106—31nomaximal, Hall
17C2×C5×D3×Q8C2211yescharacteristic
18C2×D3×D20C2211yescharacteristic
19C2×C4×D3×D5—21no—
20Q8×Dic15C2211yescharacteristic, complemented
21C2×#6717C2211yescharacteristic
22#91782C2211yescharacteristic
23C2×C5×D3×C8C2211yescharacteristic
24C5×D3×C4⋊C4C2211yescharacteristic
25C3×Q8×Dic5C2211yescharacteristic, complemented
26C2×C3×#688C2211yescharacteristic
27C3×#4039C2211yescharacteristic
28D3×#688C418yescomplemented
29D3×#685—21no—
30#91444—21no—
31#91434C2211yescharacteristic
32D3×C4⋊Dic5—21no—
33D3×C4⋊Dic5C2211yescharacteristic
34#91418C2211yescharacteristic
35C4×D3×Dic5—21no—
36C4×D3×Dic5C2211yescharacteristic
37#91396—21no—
38#91344—21no—
39#91344C2211yescharacteristic, complemented
40Dic5×Dic6—21no—
41Dic5×Dic6C2211yescharacteristic, complemented
42C2×#6660C2211yescharacteristic
43C2×#6655C2211yescharacteristic
44C2×D3×#168C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic, complemented
46#91105C2211yescharacteristic
47#91099C2211yescharacteristic, complemented
48#91091C2211yescharacteristic, complemented
49C5×#835C2211yescharacteristic, complemented
50C5×#816C2211yescharacteristic, complemented
51C5×#810C2211yescharacteristic, complemented
52C3×#3953C2211yescharacteristic
53C3×#3947C2211yescharacteristic, complemented
54C3×#3939C2211yescharacteristic, complemented
55#90989C2211yescharacteristic, complemented
56#90988C2211yescharacteristic, complemented
57#90968C2211yescharacteristic
58#90965C2211yescharacteristic
59#90954C2211yescharacteristic, complemented
60#90952C2211yescharacteristic, complemented
61D3×#440—51nomaximal, Hall
62C2×Q8×Dic5—31no—
63C22×#688—31no—
64C2×#4039—31no—
65C2×C5×#103—31no—
66C2×#3953—31no—
67C2×#3947—31no—
68C2×#3939—31no—
69#65106—31no—
70#65106—31no—
71#65106—31no—
72#65106—31no—
73#65106—31no—
74#65106—31no—
75#65106—31no—
76#65106D311yescharacteristic, direct product factor
77C22×D3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×D60C2311yescharacteristic
80C2×C4×D15—21no—
81C5×D3×Q8—22no—
82C5×D3×Q8C2×C414yescomplemented
83C2×C4×C5×D3—21no—
84C2×C4×C5×D3—21no—
85C2×C4×C5×D3C2311yescharacteristic
86C2×C5×Dic6—21no—
87C2×C5×Dic6C2311yescharacteristic
88C2×C3×D20C2311yescharacteristic
89C2×C3×C4×D5—21no—
90C2×#1202—21no—
91C2×#1200—21no—
92C2×D3×Dic5—21no—
93C2×D3×Dic5D411yescharacteristic
94C2×D3×Dic5D411yescharacteristic
95C2×D5×Dic3—21no—
96D3×D20—22no—
97D3×D20C2×C414yes—
98C4×D3×D5—44no—
99C2×C3×C5×C8C2311yescharacteristic
100C3×C5×C4⋊C4C2311yescharacteristic
101#6717C2×C414yescomplemented
102#6714—21no—
103C4⋊Dic15—21no—
104C4⋊Dic15C2311yescharacteristic
105C4×Dic15—21no—
106C4×Dic15C2311yescharacteristic
107C2×C3⋊#168C2311yescharacteristic
108C5×C4⋊Dic3C2311yescharacteristic
109C5×Dic3⋊C4—21no—
110C2×C5×C3⋊C8C2311yescharacteristic
111C5×D3×C8—22no—
112C3×#688C2×C414yescomplemented
113C3×#685—21no—
114C3×C4⋊Dic5—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4×Dic5—21no—
117C3×C4×Dic5C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119Dic3⋊Dic5—21no—
120Dic3⋊Dic5—21no—
121Dic3⋊Dic5—21no—
122#6667—21no—
123#6665—21no—
124Dic3×Dic5—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5D411yescharacteristic
127Dic3×Dic5D411yescharacteristic
128#6660C2×C414yescomplemented
129#6655C2×C414yescomplemented
130D3×#168C2×C414yescomplemented
131C2×D3×SD16—51no—
132C4×D3×Q8—51no—
133C4×D3×D4—51no—
134C3×#440—51no—
135#5164—51no—
136#5026—51no—
137#5018—51no—
138#4889—51no—
139D3×#107—51no—
140#4817—51no—
141D3×#103D511yescharacteristic, complemented
142D3×#102—51no—
143#4757—51no—
144#4710—51no—
145D3×#97—51no—
146C22×C5×Q8—31no—
147C22×D20—31no—
148C22×C4×D5—61no—
149C22×C5×C8—31no—
150C2×C5×C4⋊C4—31no—
151Q8×Dic5—31no—
152Q8×Dic5—31no—
153Q8×Dic5—31no—
154Q8×Dic5—61no—
155Q8×Dic5—61no—
156Q8×Dic5C2×D311yescharacteristic, complemented
157C2×#688—31no—
158C2×#688—31no—
159C2×#688—38no—
160C2×#688—31no—
161C2×#688C2×D311yescharacteristic
162C2×#685—61no—
163C2×C4⋊Dic5—31no—
164C2×C4⋊Dic5—61no—
165C2×C4×Dic5—31no—
166C2×C4×Dic5—61no—
167C22×#168—31no—
168#4039—31no—
169#4039—31no—
170#4039—31no—
171#4039—61no—
172#4039—61no—
173#4039C2×D311yescharacteristic
174C5×#103—31no—
175C5×#103—31no—
176C5×#103—31no—
177C5×#103C2×D311yescharacteristic, complemented
178#3953—31no—
179#3953—31no—
180#3953—31no—
181#3953C2×D311yescharacteristic
182#3947—31no—
183#3947—31no—
184#3947—31no—
185#3947C2×D311yescharacteristic, complemented
186#3939—31no—
187#3939—31no—
188#3939—31no—
189#3939C2×D311yescharacteristic, complemented
190C2×#440—151noSylow
191C22×D15—21no—
192C22×C5×D3C2×D411yescharacteristic
193C22×C3×D5—21no—
194C2×D3×D5—24no—
195C2×D3×D5—42no—
196C2×D3×D5—42no—
197C3×C5×Q8—21no—
198C3×C5×Q8C22×C412yescomplemented
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5C2411yescharacteristic
202C2×Dic15—21no—
203C2×Dic15C2×D411yescharacteristic
204C2×Dic15C2×D411yescharacteristic
205D60—21no—
206D60C22×C412yes—
207C4×D15—42no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3C2×D411yescharacteristic
211C4×C5×D3—24no—
212C4×C5×D3—42no—
213C4×C5×D3C22×C412yes—
214C4×C5×D3#4112yes—
215C5×Dic6—21no—
216C5×Dic6—24no—
217C5×Dic6C22×C412yescomplemented
218C2×C3×Dic5—21no—
219C2×C3×Dic5C2×D411yescharacteristic
220C2×C3×Dic5C2×D411yescharacteristic
221C3×D20—21no—
222C3×D20C22×C412yes—
223C3×C4×D5—42no—
224#1202—24no—
225#1200—42no—
226D3×Dic5—22no—
227D3×Dic5—22no—
228D3×Dic5—42no—
229D5×Dic3—42no—
230C3×C5×C8—21no—
231C3⋊#168C22×C412yescomplemented
232C3×#168C22×C412yescomplemented
233C5×C3⋊C8—21no—
234C2×D3×Q8C2×D511yescharacteristic
235C2×D3×D4—51no—
236C22×C4×D3—101no—
237C2×C3×SD16—51no—
238C3×C4×Q8—51no—
239C3×C4×D4—51no—
240Q8×Dic3—51no—
241C2×#215—51no—
242D4×Dic3—51no—
243C2×#214—51no—
244C4×#67—101no—
245D3×SD16—58no—
246C2×#204—51no—
247C2×D3×C8—51no—
248C2×D3×C8C2×D511yescharacteristic
249#893—51no—
250D3×C4⋊C4—51no—
251D3×C4⋊C4—101no—
252D3×C4⋊C4C2×D511yescharacteristic
253#887—51no—
254#887—101no—
255#67⋊C4—101no—
256D3×C22⋊C4—101no—
257C4×D12—51no—
258C42×D3—51no—
259C42×D3—101no—
260C4×Dic6—51no—
261C4×Dic6—101no—
262C3×#107—51no—
263C3×#103C2×D511yescharacteristic, complemented
264C3×#102—51no—
265C3×#97—51no—
266#835C2×D511yescharacteristic, complemented
267#832—51no—
268#821—51no—
269#818—51no—
270#816C2×D511yescharacteristic, complemented
271#815—51no—
272#815—51no—
273#810C2×D511yescharacteristic, complemented
274#809—51no—
275#807—51no—
276#807—51no—
277#803—51no—
278C23×D5—61no—
279C2×C5×Q8—34no—
280C2×C5×Q8—31no—
281C2×C5×Q8—61no—
282C2×C5×Q8—62no—
283C2×C5×Q8C22×D311yescharacteristic
284C22×C4×C5—31no—
285C22×C4×C5—61no—
286C22×C4×C5—61no—
287C22×Dic5—31no—
288C22×Dic5—31no—
289C22×Dic5—61no—
290C2×D20—31no—
291C2×D20—34no—
292C2×D20—62no—
293C2×D20—61no—
294C2×D20C22×D311yescharacteristic
295C2×C4×D5—21no—
296C2×C4×D5—61no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5—124no—
300C2×C5×C8—31no—
301C2×C5×C8—62no—
302C2×C5×C8C22×D311yescharacteristic
303C5×C4⋊C4—31no—
304C5×C4⋊C4—61no—
305C5×C4⋊C4C22×D311yescharacteristic
306#688—34no—
307#688—34no—
308#688—34no—
309#688C4×D314yescomplemented
310#685—21no—
311#685—61no—
312#685—61no—
313#685—61no—
314C4⋊Dic5—21no—
315C4⋊Dic5—31no—
316C4⋊Dic5—61no—
317C4⋊Dic5—61no—
318C4⋊Dic5—61no—
319C4⋊Dic5—61no—
320C4⋊Dic5C22×D311yescharacteristic
321C4×Dic5—21no—
322C4×Dic5—31no—
323C4×Dic5—31no—
324C4×Dic5—31no—
325C4×Dic5—61no—
326C4×Dic5—61no—
327C4×Dic5—61no—
328C4×Dic5C22×D311yescharacteristic
329C2×#168—31no—
330C2×#168—34no—
331C2×#168C22×D311yescharacteristic
332C22×SD16—151no—
333C2×C4×Q8—151no—
334C2×C4×D4—151no—
335#440—51no—
336#440—151no—
337#440—151no—
338#440—151no—
339#440—151no—
340#440—151no—
341#440—151no—
342#440—151no—
343C2×#107—151no—
344C2×#103—31no—
345C2×#102—151no—
346C2×#97—151no—
347C22×C3×C5C22×D411yescharacteristic
348C2×D15—22no—
349C2×D15—41no—
350C2×D15—41no—
351C2×C5×D3C4×D412yes—
352C2×C5×D3AGL(1,ℤ/8)12yes—
353C2×C5×D3#13712yes—
354C2×C3×D5—22no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357D3×D5—48no—
358C3×C4×C5—22no—
359C3×C4×C5—41no—
360C3×C4×C5C23×C411yescharacteristic
361C3×C4×C5C2×#4111yescharacteristic
362Dic15—21no—
363Dic15—21no—
364Dic15—41no—
365C3×Dic5—21no—
366C3×Dic5—21no—
367C3×Dic5—41no—
368C5×Dic3—22no—
369C5×Dic3—41no—
370C5×Dic3C4×D412yes—
371C23×D3—101no—
372C2×C3×Q8C22×D511yescharacteristic
373C2×C3×D4—51no—
374C22×C3×C4—101no—
375C2×#67—101no—
376C22×Dic3—101no—
377D3×Q8—22no—
378D3×Q8C4×D514yescomplemented
379D3×D4—54no—
380D3×D4—102no—
381C2×D12—51no—
382C2×C4×D3—21no—
383C2×C4×D3—21no—
384C2×C4×D3—51no—
385C2×C4×D3—51no—
386C2×C4×D3—101no—
387C2×C4×D3—101no—
388C2×C4×D3—101no—
389C2×C4×D3—204no—
390C2×C4×D3C22×D511yescharacteristic
391C2×Dic6—21no—
392C2×Dic6C22×D511yescharacteristic
393C3×SD16—54no—
394C2×C3×C8—51no—
395C2×C3×C8C22×D511yescharacteristic
396C3×C4⋊C4—51no—
397C3×C4⋊C4—101no—
398C3×C4⋊C4C22×D511yescharacteristic
399C3×C22⋊C4—101no—
400C3×C42—51no—
401C3×C42—101no—
402#217—101no—
403#215—54no—
404#214—54no—
405(C2×D3)⋊C4—101no—
406(C2×D3)⋊C4—101no—
407C4⋊Dic3—51no—
408C4⋊Dic3—101no—
409C4⋊Dic3C22×D511yescharacteristic
410Dic3⋊C4—21no—
411Dic3⋊C4—101no—
412Dic3⋊C4—101no—
413Dic3⋊C4—101no—
414C4×Dic3—51no—
415C4×Dic3—51no—
416C4×Dic3—51no—
417C4×Dic3—101no—
418C4×Dic3—101no—
419C4×Dic3—101no—
420C2×C3⋊C8—51no—
421C2×C3⋊C8C22×D511yescharacteristic
422#204—54no—
423D3×C8—22no—
424D3×C8—54no—
425C23×C5—31no—
426C22×D5—21no—
427C22×D5—64no—
428C22×D5—61no—
429C22×D5—122no—
430C22×D5—122no—
431C5×Q8—21no—
432C5×Q8—32no—
433C5×Q8—64no—
434C5×Q8—61no—
435C5×Q8C2×C4×D312yescomplemented
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—31no—
439C2×C4×C5—32no—
440C2×C4×C5—32no—
441C2×C4×C5—64no—
442C2×C4×C5—61no—
443C2×C4×C5—61no—
444C2×C4×C5—122no—
445C2×C4×C5C23×D311yescharacteristic
446C2×Dic5—21no—
447C2×Dic5—31no—
448C2×Dic5—31no—
449C2×Dic5—62no—
450C2×Dic5—62no—
451C2×Dic5—61no—
452C2×Dic5—122no—
453C2×Dic5D3×D411yescharacteristic
454C2×Dic5D3×D411yescharacteristic
455D20—21no—
456D20—32no—
457D20—64no—
458D20—61no—
459D20C2×C4×D312yes—
460C4×D5—42no—
461C4×D5—122no—
462C4×D5—122no—
463C4×D5—122no—
464C5×C8—21no—
465C5×C8—61no—
466#168—32no—
467#168C2×C4×D312yescomplemented
468C22×Q8—31no—
469C22×D4—151no—
470C23×C4—301no—
471C2×SD16—51no—
472C2×SD16—151no—
473C2×SD16—158no—
474C2×SD16—151no—
475C2×SD16—151no—
476C22×C8—31no—
477C22×C8—151no—
478C4×Q8—51no—
479C4×Q8—151no—
480C4×Q8—151no—
481C4×Q8—151no—
482C4×Q8—301no—
483C4×Q8—301no—
484C4×D4—51no—
485C4×D4—151no—
486C4×D4—151no—
487C4×D4—151no—
488C4×D4—301no—
489C4×D4—301no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—151no—
492C2×C4⋊C4—301no—
493C2×C22⋊C4—301no—
494C2×C42—151no—
495C2×C42—301no—
496#107—51no—
497#107—151no—
498#107—151no—
499#107—151no—
500#103—31no—
501#103—31no—
502#103—31no—
503#103D3×D511yescharacteristic, complemented
504#102—51no—
505#102—151no—
506#102—151no—
507#102—151no—
508#97—51no—
509#97—151no—
510#97—151no—
511#97—151no—
512C2×C3×C5C2×C4×D411yescharacteristic
513C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
514C2×C3×C5C2×#13711yescharacteristic
515D15—42no—
516C3×D5—42no—
517C5×D3#44014yescomplemented
518C23×C3—101no—
519C22×D3—101no—
520C22×D3—104no—
521C22×D3—202no—
522C22×D3—202no—
523C22×D3D4×D511yescharacteristic
524C3×Q8—21no—
525C3×Q8C2×C4×D512yescomplemented
526C3×D4—52no—
527C3×D4—101no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—51no—
531C2×C3×C4—51no—
532C2×C3×C4—101no—
533C2×C3×C4—202no—
534C2×C3×C4C23×D511yescharacteristic
535#67—104no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—51no—
539C2×Dic3—51no—
540C2×Dic3—101no—
541C2×Dic3—202no—
542C2×Dic3D4×D511yescharacteristic
543D12—52no—
544D12—101no—
545C4×D3—24no—
546C4×D3—42no—
547C4×D3—102no—
548C4×D3—102no—
549C4×D3—202no—
550C4×D3—202no—
551C4×D3—202no—
552C4×D3C2×C4×D512yes—
553C4×D3#71112yes—
554Dic6—21no—
555Dic6—24no—
556Dic6C2×C4×D512yescomplemented
557C3×C8—21no—
558C3×C8—52no—
559C3⋊C8—21no—
560C3⋊C8—52no—
561C22×C5—32no—
562C22×C5—32no—
563C22×C5—32no—
564C22×C5C2×D3×D411yescharacteristic
565C2×D5—22no—
566C2×D5—41no—
567C2×D5—41no—
568C2×D5—62no—
569C2×D5—128no—
570C2×D5—121no—
571C2×D5—121no—
572C4×C5—22no—
573C4×C5—32no—
574C4×C5—41no—
575C4×C5—62no—
576C4×C5—121no—
577C4×C5C22×C4×D311yescharacteristic
578C4×C5D3×#4111yescharacteristic
579Dic5—21no—
580Dic5—21no—
581Dic5—41no—
582Dic5—61no—
583Dic5—61no—
584Dic5—121no—
585C24—301no—
586C2×Q8—34no—
587C2×Q8—31no—
588C2×Q8—61no—
589C2×Q8—62no—
590C2×Q8C2×D3×D511yescharacteristic
591C2×D4—51no—
592C2×D4—154no—
593C2×D4—151no—
594C2×D4—302no—
595C2×D4—301no—
596C22×C4—31no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—101no—
600C22×C4—151no—
601C22×C4—151no—
602C22×C4—301no—
603C22×C4—301no—
604C22×C4—301no—
605C22×C4—301no—
606C22×C4—604no—
607SD16—54no—
608SD16—154no—
609SD16—154no—
610SD16—154no—
611C2×C8—31no—
612C2×C8—51no—
613C2×C8—62no—
614C2×C8—154no—
615C2×C8—151no—
616C2×C8C2×D3×D511yescharacteristic
617C4⋊C4—31no—
618C4⋊C4—51no—
619C4⋊C4—61no—
620C4⋊C4—101no—
621C4⋊C4—151no—
622C4⋊C4—301no—
623C4⋊C4—301no—
624C4⋊C4—301no—
625C4⋊C4—301no—
626C4⋊C4C2×D3×D511yescharacteristic
627C22⋊C4—101no—
628C22⋊C4—301no—
629C22⋊C4—301no—
630C22⋊C4—301no—
631C42—51no—
632C42—101no—
633C42—151no—
634C42—151no—
635C42—151no—
636C42—301no—
637C42—301no—
638C42—301no—
639C3×C5C2×#44011yescharacteristic, complemented, Hall
640C22×C3—102no—
641C22×C3—201no—
642C22×C3—201no—
643C22×C3C2×D4×D511yescharacteristic
644C2×D3—102no—
645C2×D3—201no—
646C2×D3—201no—
647C2×D3—208no—
648C2×D3#402712yes—
649C2×D3#406012yes—
650C2×D3#406412yes—
651C3×C4—22no—
652C3×C4—41no—
653C3×C4—101no—
654C3×C4—101no—
655C3×C4—201no—
656C3×C4C22×C4×D511yescharacteristic
657C3×C4C2×#71111yescharacteristic
658Dic3—22no—
659Dic3—41no—
660Dic3—101no—
661Dic3—101no—
662Dic3—201no—
663Dic3#402712yes—
664C2×C5—34no—
665C2×C5C4×D3×D411yescharacteristic
666C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
667C2×C5D3×#13711yescharacteristic
668D5—42no—
669D5—122no—
670C23—31no—
671C23—101no—
672C23—304no—
673C23—301no—
674C23—602no—
675C23—602no—
676Q8—21no—
677Q8—32no—
678Q8—64no—
679Q8—61no—
680Q8C4×D3×D512yescomplemented
681D4—52no—
682D4—101no—
683D4—152no—
684D4—304no—
685D4—301no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—31no—
689C2×C4—32no—
690C2×C4—32no—
691C2×C4—51no—
692C2×C4—51no—
693C2×C4—64no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—101no—
697C2×C4—122no—
698C2×C4—151no—
699C2×C4—151no—
700C2×C4—202no—
701C2×C4—302no—
702C2×C4—302no—
703C2×C4—301no—
704C2×C4—602no—
705C2×C4—602no—
706C2×C4—602no—
707C2×C4—602no—
708C2×C4C22×D3×D511yescharacteristic
709C8—21no—
710C8—52no—
711C8—61no—
712C8—152no—
713C2×C3—202no—
714C2×C3C2×#402711yescharacteristic
715C2×C3C2×#406011yescharacteristic
716C2×C3C2×#406411yescharacteristic
717D3—202no—
718D3#6510614yesdirect product factor
719C5D3×#44011yescharacteristic, complemented, Sylow
720C22—32no—
721C22—32no—
722C22—32no—
723C22—102no—
724C22—201no—
725C22—201no—
726C22—302no—
727C22—608no—
728C22—601no—
729C22—601no—
730C22D3×D4×D511yescharacteristic
731C4—22no—
732C4—32no—
733C4—41no—
734C4—62no—
735C4—101no—
736C4—101no—
737C4—121no—
738C4—201no—
739C4—301no—
740C4—301no—
741C4—601no—
742C4C2×C4×D3×D511yescharacteristic
743C4D3×#71111yescharacteristic
744C3C2×#6510611yescharacteristic, complemented, Sylow
745C2—34no—
746C2—202no—
747C2—602no—
748C2D3×#402711yescharacteristic
749C2D3×#406011yescharacteristic
750C2D3×#406411yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC2×D3×D20C22
cosocleC2×C3×C4×C5C24
hypercenter#103D3×D5
hypocenterC3×C5C2×#440
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. D3×Q8×Dic5C2semidirect
4. #11750918C2semidirect
5. C5×D3×#103C2semidirect
6. C3×#65106C2semidirect
7. #11749241C2semidirect
8. #11749225C2semidirect
10. #11747748C2semidirect
11. #11747736C2semidirect
12. D3×#3947C2semidirect
13. #11747471C2semidirect
14. D3×#3939C2semidirect
15. #11747280C2semidirect
20. Q8×Dic15C22semidirect
25. C3×Q8×Dic5C22semidirect
28. D3×#688C4semidirect
39. #91344C22semidirect
41. Dic5×Dic6C22semidirect
45. C3×C5×#103C22semidirect
47. #91099C22semidirect
48. #91091C22semidirect
49. C5×#835C22semidirect
50. C5×#816C22semidirect
51. C5×#810C22semidirect
53. C3×#3947C22semidirect
54. C3×#3939C22semidirect
55. #90989C22semidirect
56. #90988C22semidirect
59. #90954C22semidirect
60. #90952C22semidirect
76. #65106D3direct (N × H)
82. C5×D3×Q8C2×C4semidirect
101. #6717C2×C4semidirect
112. C3×#688C2×C4semidirect
128. #6660C2×C4semidirect
129. #6655C2×C4semidirect
130. D3×#168C2×C4semidirect
141. D3×#103D5semidirect
156. Q8×Dic5C2×D3semidirect
177. C5×#103C2×D3semidirect
185. #3947C2×D3semidirect
189. #3939C2×D3semidirect
198. C3×C5×Q8C22×C4semidirect
217. C5×Dic6C22×C4semidirect
231. C3⋊#168C22×C4semidirect
232. C3×#168C22×C4semidirect
263. C3×#103C2×D5semidirect
266. #835C2×D5semidirect
270. #816C2×D5semidirect
273. #810C2×D5semidirect
309. #688C4×D3semidirect
378. D3×Q8C4×D5semidirect
435. C5×Q8C2×C4×D3semidirect
467. #168C2×C4×D3semidirect
503. #103D3×D5semidirect
517. C5×D3#440semidirect
525. C3×Q8C2×C4×D5semidirect
556. Dic6C2×C4×D5semidirect
639. C3×C5C2×#440semidirect
680. Q8C4×D3×D5semidirect
718. D3#65106direct (N × H)
719. C5D3×#440semidirect
744. C3C2×#65106semidirect

Maximal subgroups

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

subgroupindex
D3×Q8×Dic52
C2×D3×#6882
D3×#40392
#117509182
C5×D3×#1032
C3×#651062
#117492412
#117492252
D3×#39532
#117477482
#117477362
D3×#39472
#117474712
D3×#39392
#117472802
C2×#651063
D3×#4405