Finite Group Databasebeta

← D3×#65901 #14484530

Subgroups — D3×#65901 #14484530

Order 1920.

2096 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756326C211yesmaximal, characteristic, complemented
2C4×C5×D3×Q8C211yesmaximal, characteristic
3C3×#65901C211yesmaximal, characteristic, complemented
4#11755265C212yesmaximal, complemented
5D3×#4090C212yesmaximal
6#11753827C214yesmaximal, complemented
7#11753825C212yesmaximal, complemented
8D3×#4035C214yesmaximal
9D3×#4033C212yesmaximal
10D3×#4016C212yesmaximal
11D3×#4015C211yesmaximal, characteristic
12C4×D3×Dic10C211yesmaximal, characteristic
13C4×D3×Dic10C212yesmaximal
14#11752481C211yesmaximal, characteristic, complemented
15#11752476C211yesmaximal, characteristic, complemented
16#11752467C212yesmaximal, complemented
17#11752465C212yesmaximal, complemented
18C2×#65901—31nomaximal, Hall
19C2×C5×D3×Q8C2211yescharacteristic
20C2×D3×Dic10C2212yes—
21C2×D3×Dic10C2211yescharacteristic
22C3×C4×C5×Q8C2211yescharacteristic
23#91833C2212yes—
24#91778C2214yes—
25#91776C2212yes—
26#91759C2212yes—
27#91758C2211yescharacteristic
28C4×Dic30C2212yes—
29C4×Dic30C2211yescharacteristic
30C5×Q8×Dic3C2211yescharacteristic
31C5×D3×C4⋊C4C2211yescharacteristic
32C5×D3×C4⋊C4C2212yes—
33C5×#887C2211yescharacteristic
34C5×#887C2212yes—
35C42×C5×D3C2211yescharacteristic
36C42×C5×D3C2212yes—
37C4×C5×Dic6C2212yes—
38C4×C5×Dic6C2211yescharacteristic
39C3×#4090C2212yes—
40C3×#4035C2214yes—
41C3×#4033C2212yes—
42C3×#4016C2212yes—
43C3×#4015C2211yescharacteristic
44C3×C4×Dic10C2212yes—
45C3×C4×Dic10C2211yescharacteristic
46#91469C2212yes—
47#91469C2212yes—
48C4×#1204C2212yes—
49C4×#1204C2214yes—
50D3×C4⋊Dic5C2212yes—
51D3×C4⋊Dic5C2211yescharacteristic
52D3×C4⋊Dic5C2212yes—
53D3×#683C2214yes—
54D3×#683C2212yes—
55D3×#683C2214yes—
56D3×#683C2214yes—
57C4×D3×Dic5C2212yes—
58C4×D3×Dic5C2214yes—
59#91389C2212yes—
60#91385C2212yes—
61#91382C2214yes—
62#91381C2212yes—
63#91381C2212yes—
64#91379C2214yes—
65#91379C2214yes—
66#91378C2214yes—
67#91376C2212yes—
68#91340C2211yescharacteristic
69#91340C2212yes—
70#91339C2214yes—
71#91336C2214yes—
72#91335C2214yes—
73#91334C2214yes—
74#91333C2212yes—
75#91331C2212yes—
76Dic3×Dic10C2211yescharacteristic
77Dic3×Dic10C2212yes—
78#91329C2214yes—
79#91329C2214yes—
80#91325C2214yes—
81#91324C2214yes—
82#91324C2212yes—
83#91323C2214yes—
84D3×#557—51nomaximal, Hall
85C2×C4×C5×Q8—31no—
86C2×#4090—32no—
87#65901—32no—
88#65901—34no—
89#65901—32no—
90#65901—32no—
91#65901—31no—
92#65901—32no—
93#65901—31no—
94#65901—31no—
95#65901D311yescharacteristic, direct product factor
96C2×#4035—34no—
97C2×#4033—32no—
98C2×#4016—32no—
99C2×#4015—31no—
100C2×C4×Dic10—31no—
101C2×C4×Dic10—32no—
102C2×C3×C5×Q8C2311yescharacteristic
103C2×Dic30C2312yes—
104C2×Dic30C2311yescharacteristic
105C5×D3×Q8—24no—
106C2×C4×C5×D3C2312yes—
107C2×C4×C5×D3C2312yes—
108C2×C4×C5×D3C2311yescharacteristic
109C2×C4×C5×D3C2311yescharacteristic
110C2×C4×C5×D3C2311yescharacteristic
111C2×C5×Dic6C2312yes—
112C2×C5×Dic6C2311yescharacteristic
113C2×C3×Dic10C2312yes—
114C2×C3×Dic10C2311yescharacteristic
115C2×#1204C2314yes—
116C2×#1204C2312yes—
117C2×D3×Dic5C2312yes—
118C2×D3×Dic5C2314yes—
119C2×D3×Dic5C2312yes—
120D3×Dic10—28no—
121D3×Dic10Q818yescomplemented
122C3×C5×C4⋊C4C2311yescharacteristic
123C3×C5×C4⋊C4C2312yes—
124C3×C42×C5C2311yescharacteristic
125C3×C42×C5C2312yes—
126C4⋊Dic15C2312yes—
127C4⋊Dic15C2312yes—
128C4⋊Dic15C2311yescharacteristic
129#6712C2312yes—
130#6712C2314yes—
131#6712C2314yes—
132#6712C2314yes—
133C4×Dic15C2314yes—
134C4×Dic15C2312yes—
135C5×C4⋊Dic3C2311yescharacteristic
136C5×C4⋊Dic3C2312yes—
137C5×Dic3⋊C4C2312yes—
138C5×Dic3⋊C4C2312yes—
139C5×Dic3⋊C4C2312yes—
140C4×C5×Dic3C2311yescharacteristic
141C4×C5×Dic3C2312yes—
142C4×C5×Dic3C2312yes—
143C4×C5×Dic3C2311yescharacteristic
144C4×C5×Dic3C2311yescharacteristic
145C4×C5×Dic3C2312yes—
146C3×C4⋊Dic5C2312yes—
147C3×C4⋊Dic5C2312yes—
148C3×C4⋊Dic5C2311yescharacteristic
149C3×#683C2314yes—
150C3×#683C2314yes—
151C3×#683C2312yes—
152C3×#683C2314yes—
153C3×C4×Dic5C2312yes—
154C3×C4×Dic5C2314yes—
155Dic3⋊Dic5C2314yes—
156Dic3⋊Dic5C2312yes—
157Dic3⋊Dic5C2314yes—
158#6669C2314yes—
159#6669C2312yes—
160#6669C2314yes—
161#6669C2314yes—
162#6668C2314yes—
163#6668C2312yes—
164#6668C2314yes—
165#6668C2314yes—
166Dic3×Dic5C2312yes—
167Dic3×Dic5C2314yes—
168Dic3×Dic5C2312yes—
169Dic3×Dic5C2314yes—
170C3×#557—51no—
171D3×C4⋊Q8—52no—
172D3×C4⋊Q8—51no—
173#5721—52no—
174#5721—51no—
175D3×#125—54no—
176D3×#125—52no—
177#5685—54no—
178#5685—52no—
179C4×D3×Q8—52no—
180C4×D3×Q8—52no—
181C4×D3×Q8—51no—
182C4×D3×Q8D511yescharacteristic
183#5570—51no—
184#5569—52no—
185#5567—51no—
186#5567—52no—
187C22×C5×Q8—31no—
188C22×Dic10—31no—
189C22×Dic10—32no—
190C4×C5×Q8—31no—
191C4×C5×Q8—32no—
192C4×C5×Q8—31no—
193C4×C5×Q8—32no—
194C4×C5×Q8—31no—
195C4×C5×Q8C2×D311yescharacteristic
196C2×C5×C4⋊C4—31no—
197C2×C5×C4⋊C4—32no—
198C2×C42×C5—31no—
199C2×C42×C5—32no—
200#4090—32no—
201#4090—32no—
202#4090—34no—
203#4090—34no—
204#4090—32no—
205#4090C2×D312yes—
206C2×C4⋊Dic5—32no—
207C2×C4⋊Dic5—31no—
208C2×C4⋊Dic5—32no—
209C2×#683—32no—
210C2×#683—34no—
211C2×#683—34no—
212C2×#683—34no—
213C2×C4×Dic5—34no—
214C2×C4×Dic5—32no—
215#4035—34no—
216#4035—34no—
217#4035—34no—
218#4035—34no—
219#4035—34no—
220#4035—34no—
221#4035—34no—
222#4035C2×D314yes—
223#4033—32no—
224#4033—32no—
225#4033—34no—
226#4033—34no—
227#4033—32no—
228#4033C2×D312yes—
229#4016—32no—
230#4016—32no—
231#4016—32no—
232#4016—34no—
233#4016—34no—
234#4016C2×D312yes—
235#4015—32no—
236#4015—31no—
237#4015—32no—
238#4015—32no—
239#4015C2×D311yescharacteristic
240C4×Dic10—32no—
241C4×Dic10—31no—
242C4×Dic10—32no—
243C4×Dic10—31no—
244C4×Dic10—32no—
245C4×Dic10—31no—
246C4×Dic10—34no—
247C4×Dic10—32no—
248C4×Dic10—34no—
249C4×Dic10—32no—
250C4×Dic10C2×D312yes—
251C4×Dic10C2×D311yescharacteristic
252C2×#557—151noSylow
253C22×C5×D3C2411yescharacteristic
254C3×C5×Q8—22no—
255C2×C3×C4×C5C2412yes—
256C2×C3×C4×C5C2412yes—
257C2×C3×C4×C5C2411yescharacteristic
258C2×C3×C4×C5C2411yescharacteristic
259C2×C3×C4×C5C2411yescharacteristic
260C2×Dic15C2412yes—
261C2×Dic15C2414yes—
262C2×Dic15C2412yes—
263Dic30—24no—
264Dic30C2×Q814yescomplemented
265C2×C5×Dic3C2412yes—
266C2×C5×Dic3C2412yes—
267C2×C5×Dic3C2411yescharacteristic
268C2×C5×Dic3C2411yescharacteristic
269C2×C5×Dic3C2411yescharacteristic
270C4×C5×D3—24no—
271C4×C5×D3—24no—
272C4×C5×D3—22no—
273C4×C5×D3C2×Q814yes—
274C4×C5×D3#4114yes—
275C5×Dic6—22no—
276C5×Dic6—24no—
277C2×C3×Dic5C2412yes—
278C2×C3×Dic5C2414yes—
279C2×C3×Dic5C2412yes—
280C3×Dic10—24no—
281C3×Dic10C2×Q814yescomplemented
282#1204—28no—
283#1204C2×Q818yescomplemented
284D3×Dic5—28no—
285D3×Dic5—24no—
286D3×Dic5C2×Q818yes—
287C2×D3×Q8—51no—
288C2×D3×Q8—52no—
289C2×D3×Q8C2×D511yescharacteristic
290C3×C4⋊Q8—52no—
291C3×C4⋊Q8—51no—
292C3×#125—54no—
293C3×#125—52no—
294C3×C4×Q8—52no—
295C3×C4×Q8—52no—
296C3×C4×Q8—51no—
297C3×C4×Q8C2×D511yescharacteristic
298Q8×Dic3—52no—
299Q8×Dic3—51no—
300Q8×Dic3—52no—
301Q8×Dic3C2×D511yescharacteristic
302#944—52no—
303#944—52no—
304#944—52no—
305D3×C4⋊C4—54no—
306D3×C4⋊C4—54no—
307D3×C4⋊C4—52no—
308D3×C4⋊C4—54no—
309D3×C4⋊C4—52no—
310D3×C4⋊C4—51no—
311D3×C4⋊C4—52no—
312D3×C4⋊C4C2×D512yes—
313D3×C4⋊C4C2×D511yescharacteristic
314#890—54no—
315#890—54no—
316#890—52no—
317#890—52no—
318#889—54no—
319#889—54no—
320#889—54no—
321#889—54no—
322#889—54no—
323#889—54no—
324#888—54no—
325#888—54no—
326#888—52no—
327#888—52no—
328#887—52no—
329#887—54no—
330#887—52no—
331#887—51no—
332#887—54no—
333#887—52no—
334#887C2×D512yes—
335#887C2×D511yescharacteristic
336C42×D3—54no—
337C42×D3—52no—
338C42×D3C2×D512yes—
339C42×D3C2×D511yescharacteristic
340#870—52no—
341#870—54no—
342#869—52no—
343#869—51no—
344C4×Dic6—52no—
345C4×Dic6—51no—
346C4×Dic6—52no—
347C4×Dic6—54no—
348C4×Dic6—54no—
349C4×Dic6—52no—
350C4×Dic6C2×D512yes—
351C4×Dic6C2×D511yescharacteristic
352C2×C5×Q8—32no—
353C2×C5×Q8—31no—
354C2×C5×Q8—64no—
355C2×C5×Q8C22×D311yescharacteristic
356C22×C4×C5—31no—
357C22×C4×C5—31no—
358C22×C4×C5—32no—
359C22×C4×C5—31no—
360C22×C4×C5—32no—
361C22×Dic5—32no—
362C22×Dic5—34no—
363C22×Dic5—32no—
364C2×Dic10—31no—
365C2×Dic10—32no—
366C2×Dic10—38no—
367C2×Dic10—32no—
368C2×Dic10—34no—
369C2×Dic10—68no—
370C2×Dic10C22×D312yes—
371C2×Dic10C22×D311yescharacteristic
372C5×C4⋊C4—32no—
373C5×C4⋊C4—32no—
374C5×C4⋊C4—32no—
375C5×C4⋊C4—31no—
376C5×C4⋊C4—32no—
377C5×C4⋊C4C22×D311yescharacteristic
378C5×C4⋊C4C22×D312yes—
379C42×C5—31no—
380C42×C5—31no—
381C42×C5—31no—
382C42×C5—32no—
383C42×C5—32no—
384C42×C5—32no—
385C42×C5C22×D311yescharacteristic
386C42×C5C22×D312yes—
387C4⋊Dic5—32no—
388C4⋊Dic5—31no—
389C4⋊Dic5—32no—
390C4⋊Dic5—34no—
391C4⋊Dic5—32no—
392C4⋊Dic5—34no—
393C4⋊Dic5C22×D312yes—
394C4⋊Dic5C22×D311yescharacteristic
395C4⋊Dic5C22×D312yes—
396#683—32no—
397#683—34no—
398#683—34no—
399#683—34no—
400#683—32no—
401#683—34no—
402#683—34no—
403#683—34no—
404#683—32no—
405#683—34no—
406#683—34no—
407#683—34no—
408#683C22×D312yes—
409#683C22×D314yes—
410#683C22×D314yes—
411#683C22×D314yes—
412C4×Dic5—34no—
413C4×Dic5—32no—
414C4×Dic5—34no—
415C4×Dic5—34no—
416C4×Dic5—32no—
417C4×Dic5—32no—
418C4×Dic5C22×D314yes—
419C4×Dic5C22×D312yes—
420#557—51no—
421#557—152no—
422#557—152no—
423#557—151no—
424#557—154no—
425#557—152no—
426#557—152no—
427#557—151no—
428#557—151no—
429C2×C4⋊Q8—151no—
430C2×C4⋊Q8—152no—
431C2×#125—152no—
432C2×#125—154no—
433C2×C4×Q8—31no—
434C2×C4×Q8—152no—
435C2×C4×Q8—151no—
436C2×C4×Q8—152no—
437C22×C3×C5C2511yescharacteristic
438C2×C5×D3C22×Q812yes—
439C2×C5×D3C2×#4112yes—
440C2×C5×D32−1+412yes—
441C3×C4×C5—22no—
442C3×C4×C5—22no—
443C3×C4×C5—21no—
444C3×C4×C5C22×Q812yes—
445C3×C4×C5C2×#4112yes—
446Dic15—24no—
447Dic15—22no—
448Dic15C22×Q814yes—
449C3×Dic5—24no—
450C3×Dic5—22no—
451C3×Dic5C22×Q814yes—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C5×Dic3—21no—
455C5×Dic3C22×Q812yes—
456C5×Dic3C2×#4112yes—
457C2×C3×Q8—51no—
458C2×C3×Q8—52no—
459C2×C3×Q8C22×D511yescharacteristic
460D3×Q8—24no—
461D3×Q8—58no—
462D3×Q8—108no—
463C2×C4×D3—52no—
464C2×C4×D3—52no—
465C2×C4×D3—54no—
466C2×C4×D3C22×D512yes—
467C2×C4×D3C22×D511yescharacteristic
468C2×C4×D3C22×D512yes—
469C2×C4×D3C22×D511yescharacteristic
470C2×C4×D3C22×D511yescharacteristic
471C2×Dic6—51no—
472C2×Dic6—52no—
473C2×Dic6—52no—
474C2×Dic6—54no—
475C2×Dic6C22×D511yescharacteristic
476C2×Dic6C22×D512yes—
477C3×C4⋊C4—54no—
478C3×C4⋊C4—54no—
479C3×C4⋊C4—52no—
480C3×C4⋊C4—54no—
481C3×C4⋊C4—52no—
482C3×C4⋊C4—51no—
483C3×C4⋊C4—52no—
484C3×C4⋊C4C22×D511yescharacteristic
485C3×C4⋊C4C22×D512yes—
486C3×C42—52no—
487C3×C42—54no—
488C3×C42C22×D511yescharacteristic
489C3×C42C22×D512yes—
490C4⋊Dic3—52no—
491C4⋊Dic3—51no—
492C4⋊Dic3—52no—
493C4⋊Dic3—54no—
494C4⋊Dic3—52no—
495C4⋊Dic3—54no—
496C4⋊Dic3—54no—
497C4⋊Dic3C22×D511yescharacteristic
498C4⋊Dic3C22×D512yes—
499Dic3⋊C4—54no—
500Dic3⋊C4—54no—
501Dic3⋊C4—52no—
502Dic3⋊C4—54no—
503Dic3⋊C4—54no—
504Dic3⋊C4—52no—
505Dic3⋊C4—54no—
506Dic3⋊C4—54no—
507Dic3⋊C4—54no—
508Dic3⋊C4—52no—
509Dic3⋊C4—54no—
510Dic3⋊C4C22×D512yes—
511Dic3⋊C4C22×D512yes—
512Dic3⋊C4C22×D512yes—
513C4×Dic3—54no—
514C4×Dic3—52no—
515C4×Dic3—52no—
516C4×Dic3—54no—
517C4×Dic3—52no—
518C4×Dic3—54no—
519C4×Dic3C22×D512yes—
520C4×Dic3C22×D511yescharacteristic
521C4×Dic3C22×D511yescharacteristic
522C4×Dic3C22×D512yes—
523C4×Dic3C22×D511yescharacteristic
524C4×Dic3C22×D512yes—
525C23×C5—31no—
526C5×Q8—22no—
527C5×Q8—64no—
528C5×Q8—62no—
529C2×C4×C5—31no—
530C2×C4×C5—31no—
531C2×C4×C5—34no—
532C2×C4×C5—34no—
533C2×C4×C5—32no—
534C2×C4×C5—32no—
535C2×C4×C5—31no—
536C2×C4×C5—64no—
537C2×C4×C5—62no—
538C2×C4×C5—64no—
539C2×C4×C5C23×D312yes—
540C2×C4×C5C23×D312yes—
541C2×C4×C5C23×D311yescharacteristic
542C2×C4×C5C23×D311yescharacteristic
543C2×C4×C5C23×D311yescharacteristic
544C2×Dic5—32no—
545C2×Dic5—38no—
546C2×Dic5—32no—
547C2×Dic5—34no—
548C2×Dic5—68no—
549C2×Dic5—64no—
550C2×Dic5C23×D312yes—
551C2×Dic5C23×D314yes—
552C2×Dic5C23×D312yes—
553Dic10—24no—
554Dic10—34no—
555Dic10—38no—
556Dic10—68no—
557Dic10—64no—
558Dic10D3×Q814yescomplemented
559C22×Q8—31no—
560C22×Q8—151no—
561C22×Q8—152no—
562C4⋊Q8—52no—
563C4⋊Q8—51no—
564C4⋊Q8—152no—
565C4⋊Q8—152no—
566C4⋊Q8—152no—
567C4⋊Q8—152no—
568C4⋊Q8—154no—
569C4⋊Q8—154no—
570C4⋊Q8—152no—
571C4⋊Q8—152no—
572C4⋊Q8—151no—
573#125—54no—
574#125—52no—
575#125—154no—
576#125—154no—
577#125—152no—
578#125—152no—
579#125—154no—
580#125—154no—
581#125—154no—
582#125—154no—
583#125—154no—
584#125—154no—
585#125—154no—
586#125—152no—
587C4×Q8—31no—
588C4×Q8—32no—
589C4×Q8—31no—
590C4×Q8—31no—
591C4×Q8—32no—
592C4×Q8—52no—
593C4×Q8—52no—
594C4×Q8—51no—
595C4×Q8—154no—
596C4×Q8—152no—
597C4×Q8—154no—
598C4×Q8—152no—
599C4×Q8—152no—
600C4×Q8—151no—
601C4×Q8—152no—
602C4×Q8—151no—
603C4×Q8—154no—
604C4×Q8—152no—
605C4×Q8—154no—
606C4×Q8—152no—
607C4×Q8—152no—
608C4×Q8—152no—
609C4×Q8—151no—
610C4×Q8D3×D511yescharacteristic
611C2×C4⋊C4—31no—
612C2×C4⋊C4—32no—
613C2×C4⋊C4—154no—
614C2×C4⋊C4—152no—
615C2×C4⋊C4—151no—
616C2×C4⋊C4—154no—
617C2×C4⋊C4—152no—
618C2×C4⋊C4—154no—
619C2×C4⋊C4—152no—
620C2×C42—32no—
621C2×C42—31no—
622C2×C42—154no—
623C2×C42—152no—
624C2×C3×C5C23×Q811yescharacteristic
625C2×C3×C5C22×#4111yescharacteristic
626C2×C3×C5C2×2−1+411yescharacteristic
627C5×D3#55714yescomplemented
628C22×D3C23×D511yescharacteristic
629C3×Q8—22no—
630C3×Q8—54no—
631C3×Q8—104no—
632C2×C3×C4—52no—
633C2×C3×C4—52no—
634C2×C3×C4—54no—
635C2×C3×C4C23×D512yes—
636C2×C3×C4C23×D512yes—
637C2×C3×C4C23×D511yescharacteristic
638C2×C3×C4C23×D511yescharacteristic
639C2×C3×C4C23×D511yescharacteristic
640C2×Dic3—52no—
641C2×Dic3—52no—
642C2×Dic3—54no—
643C2×Dic3C23×D512yes—
644C2×Dic3C23×D511yescharacteristic
645C2×Dic3C23×D512yes—
646C2×Dic3C23×D511yescharacteristic
647C2×Dic3C23×D511yescharacteristic
648C4×D3—24no—
649C4×D3—24no—
650C4×D3—22no—
651C4×D3—58no—
652C4×D3—108no—
653C4×D3—104no—
654C4×D3#70914yes—
655C4×D3Q8×D514yes—
656Dic6—22no—
657Dic6—24no—
658Dic6—54no—
659Dic6—58no—
660Dic6—104no—
661Dic6—108no—
662C22×C5—32no—
663C22×C5—32no—
664C22×C5—32no—
665C22×C5C24×D311yescharacteristic
666C4×C5—22no—
667C4×C5—22no—
668C4×C5—21no—
669C4×C5—32no—
670C4×C5—32no—
671C4×C5—62no—
672C4×C5—62no—
673C4×C5—61no—
674C4×C5C2×D3×Q812yes—
675C4×C5D3×#4112yes—
676Dic5—24no—
677Dic5—22no—
678Dic5—34no—
679Dic5—64no—
680Dic5—62no—
681Dic5C2×D3×Q814yes—
682C2×Q8—32no—
683C2×Q8—31no—
684C2×Q8—51no—
685C2×Q8—52no—
686C2×Q8—64no—
687C2×Q8—152no—
688C2×Q8—154no—
689C2×Q8—158no—
690C2×Q8—151no—
691C2×Q8—152no—
692C2×Q8—308no—
693C2×Q8C2×D3×D511yescharacteristic
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—32no—
697C22×C4—31no—
698C22×C4—32no—
699C22×C4—152no—
700C22×C4—152no—
701C22×C4—154no—
702C4⋊C4—32no—
703C4⋊C4—31no—
704C4⋊C4—32no—
705C4⋊C4—32no—
706C4⋊C4—32no—
707C4⋊C4—52no—
708C4⋊C4—54no—
709C4⋊C4—51no—
710C4⋊C4—54no—
711C4⋊C4—52no—
712C4⋊C4—54no—
713C4⋊C4—52no—
714C4⋊C4—154no—
715C4⋊C4—152no—
716C4⋊C4—154no—
717C4⋊C4—152no—
718C4⋊C4—152no—
719C4⋊C4—154no—
720C4⋊C4—154no—
721C4⋊C4—154no—
722C4⋊C4—154no—
723C4⋊C4—154no—
724C4⋊C4—154no—
725C4⋊C4—152no—
726C4⋊C4—154no—
727C4⋊C4—151no—
728C4⋊C4—154no—
729C4⋊C4—152no—
730C4⋊C4—154no—
731C4⋊C4—152no—
732C4⋊C4C2×D3×D511yescharacteristic
733C4⋊C4C2×D3×D512yes—
734C42—32no—
735C42—32no—
736C42—32no—
737C42—31no—
738C42—31no—
739C42—31no—
740C42—54no—
741C42—52no—
742C42—154no—
743C42—154no—
744C42—152no—
745C42—152no—
746C42—154no—
747C42—152no—
748C42C2×D3×D512yes—
749C42C2×D3×D511yescharacteristic
750C3×C5C2×#55711yescharacteristic, complemented, Hall
751C22×C3C24×D511yescharacteristic
752C2×D3C2×#70912yes—
753C2×D3C2×Q8×D512yes—
754C2×D3#415012yes—
755C3×C4—22no—
756C3×C4—22no—
757C3×C4—21no—
758C3×C4—54no—
759C3×C4—104no—
760C3×C4—102no—
761C3×C4C2×#70912yes—
762C3×C4C2×Q8×D512yes—
763Dic3—22no—
764Dic3—22no—
765Dic3—21no—
766Dic3—54no—
767Dic3—104no—
768Dic3—102no—
769Dic3C2×#70912yes—
770Dic3C2×Q8×D512yes—
771C2×C5—34no—
772C2×C5C22×D3×Q811yescharacteristic
773C2×C5C2×D3×#4111yescharacteristic
774C2×C5D3×2−1+411yescharacteristic
775C23—31no—
776Q8—22no—
777Q8—54no—
778Q8—64no—
779Q8—62no—
780Q8—104no—
781Q8—158no—
782Q8—154no—
783Q8—308no—
784Q8—304no—
785C2×C4—31no—
786C2×C4—31no—
787C2×C4—34no—
788C2×C4—34no—
789C2×C4—32no—
790C2×C4—31no—
791C2×C4—32no—
792C2×C4—52no—
793C2×C4—52no—
794C2×C4—54no—
795C2×C4—64no—
796C2×C4—64no—
797C2×C4—62no—
798C2×C4—158no—
799C2×C4—152no—
800C2×C4—152no—
801C2×C4—154no—
802C2×C4—308no—
803C2×C4—304no—
804C2×C4C22×D3×D512yes—
805C2×C4C22×D3×D511yescharacteristic
806C2×C4C22×D3×D512yes—
807C2×C4C22×D3×D511yescharacteristic
808C2×C4C22×D3×D511yescharacteristic
809C2×C3C22×#70911yescharacteristic
810C2×C3C22×Q8×D511yescharacteristic
811C2×C3C2×#415011yescharacteristic
812D3#6590114yesdirect product factor
813C5D3×#55711yescharacteristic, complemented, Sylow
814C22—32no—
815C22—32no—
816C22—32no—
817C22C23×D3×D511yescharacteristic
818C4—22no—
819C4—21no—
820C4—22no—
821C4—32no—
822C4—32no—
823C4—54no—
824C4—62no—
825C4—61no—
826C4—62no—
827C4—102no—
828C4—104no—
829C4—154no—
830C4—302no—
831C4—304no—
832C4D3×#70912yes—
833C4D3×Q8×D512yes—
834C3C2×#6590111yescharacteristic, complemented, Sylow
835C2—34no—
836C2C2×D3×#70911yescharacteristic
837C2C2×D3×Q8×D511yescharacteristic
838C2D3×#415011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
prime radicalC22×C5×D3C24
hypercenterC4×Q8D3×D5
hypocenterC3×C5C2×#557
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756326C2semidirect
3. C3×#65901C2semidirect
4. #11755265C2semidirect
6. #11753827C2semidirect
7. #11753825C2semidirect
14. #11752481C2semidirect
15. #11752476C2semidirect
16. #11752467C2semidirect
17. #11752465C2semidirect
95. #65901D3direct (N × H)
121. D3×Dic10Q8semidirect
264. Dic30C2×Q8semidirect
281. C3×Dic10C2×Q8semidirect
283. #1204C2×Q8semidirect
558. Dic10D3×Q8semidirect
627. C5×D3#557semidirect
750. C3×C5C2×#557semidirect
812. D3#65901direct (N × H)
813. C5D3×#557semidirect
834. C3C2×#65901semidirect

Maximal subgroups

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

subgroupindex
#117563262
C4×C5×D3×Q82
C3×#659012
#117552652
D3×#40902
#117538272
#117538252
D3×#40352
D3×#40332
D3×#40162
D3×#40152
C4×D3×Dic102
#117524812
#117524762
#117524672
#117524652
C2×#659013
D3×#5575