Finite Group Databasebeta

← D3×#64957 #14320233

Subgroups — D3×#64957 #14320233

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D3×D5C211yesmaximal, characteristic
2C2×D3×#685C211yesmaximal, characteristic
3C2×D3×#685C211yesmaximal, characteristic
4C2×D3×C4⋊Dic5C211yesmaximal, characteristic, complemented
5C2×D3×#683C211yesmaximal, characteristic, complemented
6#11750769C211yesmaximal, characteristic, complemented
7C5×D3×#95C211yesmaximal, characteristic, complemented
8C3×#64957C211yesmaximal, characteristic, complemented
9#11748900C211yesmaximal, characteristic, complemented
10#11748898C211yesmaximal, characteristic, complemented
11#11748895C211yesmaximal, characteristic, complemented
12#11748890C211yesmaximal, characteristic, complemented
13D3×#3963C211yesmaximal, characteristic, complemented
14#11748729C211yesmaximal, characteristic, complemented
15#11748704C211yesmaximal, characteristic, complemented
16C2×#64957—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×#1200C2211yescharacteristic
24C22×D3×Dic5C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C22×D5×Dic3C2211yescharacteristic
28C2×C4×D3×D5—24no—
29C2×C4×D3×D5—24no—
30C2×C4×D3×D5—24no—
31C2×#6714C2211yescharacteristic
32C2×#6714C2211yescharacteristic
33C2×C4⋊Dic15C2211yescharacteristic, complemented
34C2×#6712C2211yescharacteristic, complemented
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
38C2×C3×#683C2211yescharacteristic, complemented
39C2×Dic3⋊Dic5C2211yescharacteristic, complemented
40C2×Dic3⋊Dic5C2211yescharacteristic, complemented
41C2×#6669C2211yescharacteristic, complemented
42C2×#6668C2211yescharacteristic, complemented
43C2×#6667C2211yescharacteristic
44C2×#6667C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46C2×#6665C2211yescharacteristic
47D3×#685—24no—
48D3×#685C418yescomplemented
49D3×C4⋊Dic5—24no—
50D3×#683—24no—
51C3×C5×#95C2211yescharacteristic, complemented
52#91115C2211yescharacteristic, complemented
53C5×C3⋊#95C2211yescharacteristic, complemented
54C5×C3⋊#95C2211yescharacteristic, complemented
55C5×C3⋊#95C2211yescharacteristic, complemented
56C3×#3963C2211yescharacteristic, complemented
57#90994C2211yescharacteristic, complemented
58#90994C2211yescharacteristic, complemented
59D3×#385—51nomaximal, Hall
60C23×C4×D5—31no—
61C22×#685—31no—
62C22×#685—31no—
63C22×C4⋊Dic5—31no—
64C22×#683—31no—
65C2×C5×#95—31no—
66C2×#3963—31no—
67#64957—31no—
68#64957—31no—
69#64957—31no—
70#64957—31no—
71#64957—31no—
72#64957—31no—
73#64957—31no—
74#64957D311yescharacteristic, direct product factor
75C23×D15C2311yescharacteristic
76C23×C5×D3C2311yescharacteristic
77C23×C3×D5C2311yescharacteristic
78C22×D3×D5—22no—
79C22×D3×D5—22no—
80C22×D3×D5—22no—
81C22×D3×D5—22no—
82C22×D3×D5C2×C414yes—
83C22×D3×D5D414yes—
84C22×D3×D5Q814yes—
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C2×C4×D15—22no—
92C2×C4×D15—22no—
93C2×C4×D15—22no—
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C2×C4×C5×D3—22no—
98C2×C4×C5×D3—22no—
99C2×C4×C5×D3—22no—
100C2×C4×C5×D3—22no—
101C2×C4×C5×D3—22no—
102C2×C4×C5×D3—22no—
103C2×C4×C5×D3—22no—
104C2×C4×C5×D3C2×C414yescomplemented
105C2×C4×C5×D3D414yes—
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C2×C3×C4×D5—22no—
110C2×C3×C4×D5—22no—
111C2×C3×C4×D5—22no—
112C2×#1200—22no—
113C2×#1200—22no—
114C2×#1200—22no—
115C2×D3×Dic5—22no—
116C2×D3×Dic5—22no—
117C2×D3×Dic5—22no—
118C2×D3×Dic5—22no—
119C2×D3×Dic5—22no—
120C2×D3×Dic5—22no—
121C2×D3×Dic5—22no—
122C2×D3×Dic5C2×C414yescomplemented
123C2×D3×Dic5D414yes—
124C2×D5×Dic3—22no—
125C2×D5×Dic3—22no—
126C2×D5×Dic3—22no—
127C4×D3×D5—232no—
128#6714—22no—
129#6714C2×C414yescomplemented
130C4⋊Dic15—22no—
131#6712—22no—
132C3×#685—22no—
133C3×#685C2×C414yescomplemented
134C3×C4⋊Dic5—22no—
135C3×#683—22no—
136Dic3⋊Dic5—22no—
137Dic3⋊Dic5—22no—
138#6669—22no—
139#6668—22no—
140#6667—22no—
141#6667C2×C414yescomplemented
142#6665—22no—
143#6665C2×C414yescomplemented
144C23×C4×D3—51no—
145C2×D3×C4⋊C4—51no—
146C2×D3×C4⋊C4—51no—
147C2×D3×C22⋊C4—51no—
148C2×D3×C22⋊C4—51no—
149C3×#385—51no—
150#5210—51no—
151#4989—51no—
152#4989—51no—
153#4950—51no—
154#4946—51no—
155#4668—51no—
156#4668—51no—
157D3×#95—51no—
158D3×#95D511yescharacteristic, complemented
159C24×D5—31no—
160C23×C4×C5—31no—
161C23×C4×C5—31no—
162C23×C4×C5—31no—
163C23×Dic5—31no—
164C23×Dic5—31no—
165C23×Dic5—31no—
166C22×C4×D5—31no—
167C22×C4×D5—31no—
168C22×C4×D5—31no—
169C22×C4×D5—64no—
170C22×C4×D5—64no—
171C22×C4×D5—64no—
172C22×C4×D5C2×D311yescharacteristic
173C2×#685—31no—
174C2×#685—31no—
175C2×#685—31no—
176C2×#685—38no—
177C2×#685—31no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685—64no—
181C2×#685C2×D311yescharacteristic
182C2×#685C2×D311yescharacteristic
183C2×C4⋊Dic5—31no—
184C2×C4⋊Dic5—31no—
185C2×C4⋊Dic5—31no—
186C2×C4⋊Dic5—64no—
187C2×C4⋊Dic5C2×D311yescharacteristic, complemented
188C2×#683—31no—
189C2×#683—31no—
190C2×#683—31no—
191C2×#683—64no—
192C2×#683C2×D311yescharacteristic, complemented
193C5×#95—31no—
194C5×#95—31no—
195C5×#95—31no—
196C5×#95C2×D311yescharacteristic, complemented
197#3963—31no—
198#3963—31no—
199#3963—31no—
200#3963C2×D311yescharacteristic, complemented
201C2×#385—151noSylow
202C23×C3×C5C2411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—21no—
206C22×D15—21no—
207C22×D15C22×C412yes—
208C22×D15C2×D412yes—
209C22×D15C2×Q812yes—
210C22×C5×D3C22×C412yes—
211C22×C5×D3C2×D412yes—
212C22×C5×D3C2×D412yes—
213C22×C5×D3C2×D412yes—
214C22×C5×D3C2×Q812yes—
215C22×C5×D3#4112yes—
216C22×C5×D3#4112yes—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×D5C22×C412yes—
222C22×C3×D5C2×D412yes—
223C22×C3×D5C2×Q812yes—
224C2×D3×D5—28no—
225C2×D3×D5—28no—
226C2×D3×D5—28no—
227C2×D3×D5—28no—
228C2×D3×D5—28no—
229C2×D3×D5—28no—
230C2×D3×D5C4⋊C4116yescomplemented
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5—21no—
238C2×C3×C4×C5C22×C412yescomplemented
239C2×C3×C4×C5C2×D412yes—
240C2×Dic15—21no—
241C2×Dic15—21no—
242C2×Dic15—21no—
243C2×Dic15—21no—
244C2×Dic15—21no—
245C2×Dic15—21no—
246C2×Dic15—21no—
247C2×Dic15C22×C412yescomplemented
248C2×Dic15C2×D412yes—
249C4×D15—28no—
250C2×C5×Dic3—21no—
251C2×C5×Dic3—21no—
252C2×C5×Dic3—21no—
253C2×C5×Dic3—21no—
254C2×C5×Dic3—21no—
255C2×C5×Dic3—21no—
256C2×C5×Dic3—21no—
257C2×C5×Dic3C22×C412yescomplemented
258C2×C5×Dic3C2×D412yes—
259C4×C5×D3—28no—
260C4×C5×D3—28no—
261C4×C5×D3—44no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5—21no—
266C2×C3×Dic5—21no—
267C2×C3×Dic5—21no—
268C2×C3×Dic5—21no—
269C2×C3×Dic5C22×C412yescomplemented
270C2×C3×Dic5C2×D412yes—
271C3×C4×D5—28no—
272#1200—28no—
273D3×Dic5—28no—
274D3×Dic5—28no—
275D3×Dic5—44no—
276D5×Dic3—28no—
277C24×D3—51no—
278C23×C3×C4—51no—
279C23×Dic3—51no—
280C22×C4×D3—51no—
281C22×C4×D3—51no—
282C22×C4×D3—51no—
283C22×C4×D3—51no—
284C22×C4×D3—51no—
285C22×C4×D3—104no—
286C22×C4×D3—104no—
287C22×C4×D3—104no—
288C22×C4×D3C2×D511yescharacteristic
289C22×C4×D3C2×D511yescharacteristic
290C22×C4×D3C2×D511yescharacteristic
291C2×C3×C4⋊C4—51no—
292C2×C3×C4⋊C4—51no—
293C2×C3×C22⋊C4—51no—
294C2×C3×C22⋊C4—51no—
295C2×#217—51no—
296C2×#217—51no—
297C2×(C2×D3)⋊C4—51no—
298C2×(C2×D3)⋊C4—51no—
299C2×(C2×D3)⋊C4—51no—
300C2×(C2×D3)⋊C4—51no—
301C2×C4⋊Dic3—51no—
302C2×C4⋊Dic3—51no—
303C2×Dic3⋊C4—51no—
304C2×Dic3⋊C4—51no—
305C2×Dic3⋊C4—51no—
306C2×Dic3⋊C4—51no—
307D3×C4⋊C4—104no—
308D3×C4⋊C4—104no—
309D3×C22⋊C4—58no—
310D3×C22⋊C4—104no—
311C3×#95—51no—
312C3×#95C2×D511yescharacteristic, complemented
313C3⋊#95—51no—
314C3⋊#95—51no—
315C3⋊#95—51no—
316C3⋊#95C2×D511yescharacteristic, complemented
317C3⋊#95C2×D511yescharacteristic, complemented
318C3⋊#95C2×D511yescharacteristic, complemented
319C24×C5—31no—
320C23×D5—31no—
321C23×D5—34no—
322C23×D5—34no—
323C23×D5—34no—
324C23×D5—62no—
325C23×D5—62no—
326C23×D5—62no—
327C23×D5—62no—
328C23×D5C22×D311yescharacteristic
329C22×C4×C5—31no—
330C22×C4×C5—31no—
331C22×C4×C5—34no—
332C22×C4×C5—34no—
333C22×C4×C5—31no—
334C22×C4×C5—62no—
335C22×C4×C5—62no—
336C22×C4×C5—62no—
337C22×C4×C5—62no—
338C22×C4×C5—62no—
339C22×C4×C5—62no—
340C22×C4×C5—62no—
341C22×C4×C5C22×D311yescharacteristic
342C22×C4×C5C22×D311yescharacteristic
343C22×C4×C5C22×D311yescharacteristic
344C22×Dic5—31no—
345C22×Dic5—31no—
346C22×Dic5—34no—
347C22×Dic5—34no—
348C22×Dic5—31no—
349C22×Dic5—62no—
350C22×Dic5—62no—
351C22×Dic5—62no—
352C22×Dic5—62no—
353C22×Dic5—62no—
354C22×Dic5—62no—
355C22×Dic5—62no—
356C22×Dic5C22×D311yescharacteristic
357C22×Dic5C22×D311yescharacteristic
358C22×Dic5C22×D311yescharacteristic
359C2×C4×D5—22no—
360C2×C4×D5—22no—
361C2×C4×D5—22no—
362C2×C4×D5—632no—
363C2×C4×D5—62no—
364C2×C4×D5—62no—
365C2×C4×D5—62no—
366C2×C4×D5—62no—
367C2×C4×D5—62no—
368C2×C4×D5—62no—
369C2×C4×D5—62no—
370C2×C4×D5—62no—
371C2×C4×D5—62no—
372#685—22no—
373#685—34no—
374#685—34no—
375#685—34no—
376#685—62no—
377#685—62no—
378#685—62no—
379#685C4×D314yescomplemented
380C4⋊Dic5—22no—
381C4⋊Dic5—62no—
382C4⋊Dic5—62no—
383C4⋊Dic5—62no—
384#683—22no—
385#683—62no—
386#683—62no—
387#683—62no—
388C24×C4—151no—
389C22×C4⋊C4—151no—
390C22×C4⋊C4—151no—
391C22×C22⋊C4—151no—
392C22×C22⋊C4—151no—
393#385—51no—
394#385—151no—
395#385—151no—
396#385—151no—
397#385—151no—
398#385—151no—
399#385—151no—
400#385—151no—
401C2×#95—31no—
402C2×#95—151no—
403C22×C3×C5C23×C411yescharacteristic
404C22×C3×C5C22×D411yescharacteristic
405C22×C3×C5C22×D411yescharacteristic
406C22×C3×C5C22×D411yescharacteristic
407C22×C3×C5C22×Q811yescharacteristic
408C22×C3×C5C2×#4111yescharacteristic
409C22×C3×C5C2×#4111yescharacteristic
410C2×D15—22no—
411C2×D15—22no—
412C2×D15—22no—
413C2×D15—22no—
414C2×D15—22no—
415C2×D15—22no—
416C2×D15C2×C4⋊C414yescomplemented
417C2×C5×D3C2×C4⋊C414yes—
418C2×C5×D3C4×D414yes—
419C2×C5×D3C4×D414yes—
420C2×C5×D3#12014yes—
421C2×C5×D3C22⋊Q814yes—
422C2×C5×D3C22⋊Q814yes—
423C2×C5×D3#12314yes—
424C2×C3×D5—22no—
425C2×C3×D5—22no—
426C2×C3×D5—22no—
427C2×C3×D5—22no—
428C2×C3×D5—22no—
429C2×C3×D5—22no—
430C2×C3×D5C2×C4⋊C414yescomplemented
431D3×D5—232no—
432C3×C4×C5—22no—
433C3×C4×C5—22no—
434C3×C4×C5—41no—
435Dic15—22no—
436Dic15—22no—
437Dic15—41no—
438C3×Dic5—22no—
439C3×Dic5—22no—
440C3×Dic5—41no—
441C5×Dic3—22no—
442C5×Dic3—22no—
443C5×Dic3—41no—
444C24×C3—51no—
445C23×D3—51no—
446C23×D3—54no—
447C23×D3—54no—
448C23×D3—54no—
449C23×D3—102no—
450C23×D3—102no—
451C23×D3—102no—
452C23×D3—102no—
453C23×D3C22×D511yescharacteristic
454C22×C3×C4—51no—
455C22×C3×C4—51no—
456C22×C3×C4—51no—
457C22×C3×C4—102no—
458C22×C3×C4—102no—
459C22×C3×C4—102no—
460C22×C3×C4C22×D511yescharacteristic
461C22×C3×C4C22×D511yescharacteristic
462C22×C3×C4C22×D511yescharacteristic
463C22×Dic3—51no—
464C22×Dic3—51no—
465C22×Dic3—51no—
466C22×Dic3—102no—
467C22×Dic3—102no—
468C22×Dic3—102no—
469C22×Dic3C22×D511yescharacteristic
470C22×Dic3C22×D511yescharacteristic
471C22×Dic3C22×D511yescharacteristic
472C2×C4×D3—22no—
473C2×C4×D3—22no—
474C2×C4×D3—22no—
475C2×C4×D3—22no—
476C2×C4×D3—22no—
477C2×C4×D3—22no—
478C2×C4×D3—22no—
479C2×C4×D3—54no—
480C2×C4×D3—54no—
481C2×C4×D3—1032no—
482C2×C4×D3—102no—
483C2×C4×D3—102no—
484C2×C4×D3—102no—
485C2×C4×D3—102no—
486C2×C4×D3—102no—
487C2×C4×D3—102no—
488C2×C4×D3—102no—
489C2×C4×D3—102no—
490C2×C4×D3—102no—
491C2×C4×D3—102no—
492C2×C4×D3—102no—
493C2×C4×D3—102no—
494C2×C4×D3—102no—
495C2×C4×D3C4×D514yescomplemented
496C2×C4×D3D2014yes—
497C3×C4⋊C4—102no—
498C3×C4⋊C4—102no—
499C3×C22⋊C4—54no—
500C3×C22⋊C4—102no—
501#217—54no—
502#217—102no—
503(C2×D3)⋊C4—54no—
504(C2×D3)⋊C4—54no—
505(C2×D3)⋊C4—102no—
506(C2×D3)⋊C4—102no—
507C4⋊Dic3—102no—
508C4⋊Dic3—102no—
509Dic3⋊C4—102no—
510Dic3⋊C4—102no—
511Dic3⋊C4—102no—
512Dic3⋊C4—102no—
513C23×C5—32no—
514C23×C5—32no—
515C23×C5—32no—
516C23×C5—32no—
517C23×C5—32no—
518C23×C5—32no—
519C23×C5—32no—
520C23×C5C23×D311yescharacteristic
521C22×D5—21no—
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—21no—
525C22×D5—32no—
526C22×D5—32no—
527C22×D5—32no—
528C22×D5—316no—
529C22×D5—68no—
530C22×D5—68no—
531C22×D5—68no—
532C22×D5—68no—
533C22×D5—68no—
534C22×D5—68no—
535C22×D5—61no—
536C22×D5—61no—
537C22×D5—61no—
538C22×D5—61no—
539C22×D5C2×C4×D312yes—
540C22×D5D3×D412yes—
541C22×D5D3×Q812yes—
542C2×C4×C5—21no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—21no—
548C2×C4×C5—21no—
549C2×C4×C5—32no—
550C2×C4×C5—32no—
551C2×C4×C5—68no—
552C2×C4×C5—68no—
553C2×C4×C5—61no—
554C2×C4×C5—61no—
555C2×C4×C5—61no—
556C2×C4×C5—61no—
557C2×C4×C5—61no—
558C2×C4×C5—61no—
559C2×C4×C5—61no—
560C2×C4×C5—124no—
561C2×C4×C5C2×C4×D312yescomplemented
562C2×C4×C5D3×D412yes—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—21no—
567C2×Dic5—21no—
568C2×Dic5—21no—
569C2×Dic5—21no—
570C2×Dic5—32no—
571C2×Dic5—32no—
572C2×Dic5—68no—
573C2×Dic5—68no—
574C2×Dic5—61no—
575C2×Dic5—61no—
576C2×Dic5—61no—
577C2×Dic5—61no—
578C2×Dic5—61no—
579C2×Dic5—61no—
580C2×Dic5—61no—
581C2×Dic5—124no—
582C2×Dic5C2×C4×D312yescomplemented
583C2×Dic5D3×D412yes—
584C4×D5—28no—
585C4×D5—68no—
586C4×D5—68no—
587C4×D5—68no—
588C25—151no—
589C23×C4—31no—
590C23×C4—31no—
591C23×C4—31no—
592C23×C4—51no—
593C23×C4—151no—
594C23×C4—151no—
595C23×C4—151no—
596C23×C4—151no—
597C23×C4—151no—
598C23×C4—151no—
599C23×C4—304no—
600C23×C4—304no—
601C23×C4—304no—
602C2×C4⋊C4—51no—
603C2×C4⋊C4—51no—
604C2×C4⋊C4—151no—
605C2×C4⋊C4—151no—
606C2×C4⋊C4—151no—
607C2×C4⋊C4—151no—
608C2×C4⋊C4—151no—
609C2×C4⋊C4—151no—
610C2×C4⋊C4—304no—
611C2×C4⋊C4—304no—
612C2×C22⋊C4—51no—
613C2×C22⋊C4—51no—
614C2×C22⋊C4—158no—
615C2×C22⋊C4—151no—
616C2×C22⋊C4—151no—
617C2×C22⋊C4—151no—
618C2×C22⋊C4—151no—
619C2×C22⋊C4—151no—
620C2×C22⋊C4—151no—
621C2×C22⋊C4—304no—
622#95—31no—
623#95—31no—
624#95—31no—
625#95—51no—
626#95—151no—
627#95—151no—
628#95—151no—
629#95D3×D511yescharacteristic, complemented
630C2×C3×C5C22×C4⋊C411yescharacteristic
631C2×C3×C5C2×C4×D411yescharacteristic
632C2×C3×C5C2×C4×D411yescharacteristic
633C2×C3×C5C2×#12011yescharacteristic
634C2×C3×C5C2×C22⋊Q811yescharacteristic
635C2×C3×C5C2×C22⋊Q811yescharacteristic
636C2×C3×C5C2×#12311yescharacteristic
637D15—24no—
638C3×D5—24no—
639C5×D3#38518yescomplemented
640C23×C3—52no—
641C23×C3—52no—
642C23×C3—52no—
643C23×C3—101no—
644C23×C3—101no—
645C23×C3—101no—
646C23×C3—101no—
647C23×C3C23×D511yescharacteristic
648C22×D3—52no—
649C22×D3—52no—
650C22×D3—52no—
651C22×D3—516no—
652C22×D3—101no—
653C22×D3—101no—
654C22×D3—101no—
655C22×D3—101no—
656C22×D3—108no—
657C22×D3—108no—
658C22×D3—108no—
659C22×D3—108no—
660C22×D3—108no—
661C22×D3—108no—
662C22×D3C2×C4×D512yes—
663C22×D3C2×D2012yes—
664C22×D3#70912yes—
665C22×D3D4×D512yes—
666C22×D3D4×D512yes—
667C22×D3#71112yes—
668C22×D3Q8×D512yes—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—52no—
677C2×C3×C4—52no—
678C2×C3×C4—108no—
679C2×C3×C4—101no—
680C2×C3×C4—101no—
681C2×C3×C4—101no—
682C2×C3×C4—101no—
683C2×C3×C4—101no—
684C2×C3×C4—101no—
685C2×C3×C4—101no—
686C2×C3×C4C2×C4×D512yescomplemented
687C2×C3×C4C2×D2012yes—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—21no—
692C2×Dic3—21no—
693C2×Dic3—21no—
694C2×Dic3—21no—
695C2×Dic3—52no—
696C2×Dic3—52no—
697C2×Dic3—108no—
698C2×Dic3—101no—
699C2×Dic3—101no—
700C2×Dic3—101no—
701C2×Dic3—101no—
702C2×Dic3—101no—
703C2×Dic3—101no—
704C2×Dic3—101no—
705C2×Dic3C2×C4×D512yescomplemented
706C2×Dic3C2×D2012yes—
707C4×D3—28no—
708C4×D3—28no—
709C4×D3—44no—
710C4×D3—108no—
711C4×D3—108no—
712C4×D3—108no—
713C4×D3—108no—
714C4×D3—204no—
715C22×C5—34no—
716C22×C5—34no—
717C22×C5—34no—
718C22×C5—34no—
719C22×C5—34no—
720C22×C5—34no—
721C22×C5—34no—
722C22×C5C22×C4×D311yescharacteristic
723C22×C5C2×D3×D411yescharacteristic
724C22×C5C2×D3×D411yescharacteristic
725C22×C5C2×D3×D411yescharacteristic
726C22×C5C2×D3×Q811yescharacteristic
727C22×C5D3×#4111yescharacteristic
728C22×C5D3×#4111yescharacteristic
729C2×D5—22no—
730C2×D5—22no—
731C2×D5—22no—
732C2×D5—22no—
733C2×D5—22no—
734C2×D5—22no—
735C2×D5—34no—
736C2×D5—632no—
737C2×D5—62no—
738C2×D5—62no—
739C2×D5—62no—
740C2×D5—62no—
741C2×D5—62no—
742C2×D5—62no—
743C2×D5D3×C4⋊C414yescomplemented
744C4×C5—22no—
745C4×C5—22no—
746C4×C5—41no—
747C4×C5—62no—
748C4×C5—62no—
749C4×C5—121no—
750Dic5—22no—
751Dic5—22no—
752Dic5—41no—
753Dic5—62no—
754Dic5—62no—
755Dic5—121no—
756C24—31no—
757C24—51no—
758C24—154no—
759C24—154no—
760C24—154no—
761C24—151no—
762C24—302no—
763C24—302no—
764C24—302no—
765C24—302no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—34no—
769C22×C4—34no—
770C22×C4—31no—
771C22×C4—51no—
772C22×C4—51no—
773C22×C4—51no—
774C22×C4—62no—
775C22×C4—62no—
776C22×C4—62no—
777C22×C4—62no—
778C22×C4—62no—
779C22×C4—62no—
780C22×C4—62no—
781C22×C4—102no—
782C22×C4—102no—
783C22×C4—102no—
784C22×C4—154no—
785C22×C4—154no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—151no—
789C22×C4—302no—
790C22×C4—302no—
791C22×C4—302no—
792C22×C4—302no—
793C22×C4—302no—
794C22×C4—302no—
795C22×C4—3032no—
796C22×C4—302no—
797C22×C4—302no—
798C22×C4—302no—
799C22×C4—302no—
800C22×C4—302no—
801C22×C4—302no—
802C22×C4—302no—
803C22×C4—302no—
804C22×C4—302no—
805C22×C4—302no—
806C22×C4C2×D3×D511yescharacteristic
807C22×C4C2×D3×D511yescharacteristic
808C22×C4C2×D3×D511yescharacteristic
809C4⋊C4—102no—
810C4⋊C4—102no—
811C4⋊C4—302no—
812C4⋊C4—302no—
813C4⋊C4—302no—
814C4⋊C4—302no—
815C4⋊C4—302no—
816C4⋊C4—302no—
817C22⋊C4—54no—
818C22⋊C4—102no—
819C22⋊C4—154no—
820C22⋊C4—154no—
821C22⋊C4—154no—
822C22⋊C4—302no—
823C22⋊C4—302no—
824C22⋊C4—302no—
825C3×C5C2×#38511yescharacteristic, complemented, Hall
826C22×C3—54no—
827C22×C3—102no—
828C22×C3—102no—
829C22×C3—102no—
830C22×C3—102no—
831C22×C3—102no—
832C22×C3—102no—
833C22×C3C22×C4×D511yescharacteristic
834C22×C3C22×D2011yescharacteristic
835C22×C3C2×#70911yescharacteristic
836C22×C3C2×D4×D511yescharacteristic
837C22×C3C2×D4×D511yescharacteristic
838C22×C3C2×#71111yescharacteristic
839C22×C3C2×Q8×D511yescharacteristic
840C2×D3—54no—
841C2×D3—102no—
842C2×D3—102no—
843C2×D3—102no—
844C2×D3—102no—
845C2×D3—102no—
846C2×D3—102no—
847C2×D3—1032no—
848C2×D3C4×D2014yes—
849C2×D3#402714yes—
850C2×D3#402814yes—
851C2×D3#402914yes—
852C2×D3D5×C4⋊C414yes—
853C2×D3#404214yes—
854C2×D3#404314yes—
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—41no—
858C3×C4—102no—
859C3×C4—102no—
860C3×C4—201no—
861Dic3—22no—
862Dic3—22no—
863Dic3—41no—
864Dic3—102no—
865Dic3—102no—
866Dic3—201no—
867C2×C5—38no—
868C2×C5C2×D3×C4⋊C411yescharacteristic
869C2×C5C4×D3×D411yescharacteristic
870C2×C5C4×D3×D411yescharacteristic
871C2×C5D3×#12011yescharacteristic
872C2×C5D3×C22⋊Q811yescharacteristic
873C2×C5D3×C22⋊Q811yescharacteristic
874C2×C5D3×#12311yescharacteristic
875D5—24no—
876D5—64no—
877C23—32no—
878C23—32no—
879C23—32no—
880C23—32no—
881C23—32no—
882C23—32no—
883C23—32no—
884C23—52no—
885C23—52no—
886C23—52no—
887C23—101no—
888C23—101no—
889C23—101no—
890C23—101no—
891C23—1516no—
892C23—152no—
893C23—152no—
894C23—152no—
895C23—308no—
896C23—308no—
897C23—308no—
898C23—308no—
899C23—308no—
900C23—308no—
901C23—301no—
902C23—301no—
903C23—301no—
904C23—301no—
905C23C22×D3×D511yescharacteristic
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—32no—
914C2×C4—32no—
915C2×C4—52no—
916C2×C4—52no—
917C2×C4—68no—
918C2×C4—68no—
919C2×C4—61no—
920C2×C4—61no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—61no—
926C2×C4—108no—
927C2×C4—101no—
928C2×C4—101no—
929C2×C4—101no—
930C2×C4—101no—
931C2×C4—101no—
932C2×C4—101no—
933C2×C4—101no—
934C2×C4—124no—
935C2×C4—152no—
936C2×C4—152no—
937C2×C4—308no—
938C2×C4—308no—
939C2×C4—308no—
940C2×C4—308no—
941C2×C4—308no—
942C2×C4—301no—
943C2×C4—301no—
944C2×C4—301no—
945C2×C4—301no—
946C2×C4—301no—
947C2×C4—301no—
948C2×C4—301no—
949C2×C4—604no—
950C2×C4C4×D3×D512yescomplemented
951C2×C4D3×D2012yes—
952C2×C3—104no—
953C2×C3C2×C4×D2011yescharacteristic
954C2×C3C2×#402711yescharacteristic
955C2×C3C2×#402811yescharacteristic
956C2×C3C2×#402911yescharacteristic
957C2×C3C2×D5×C4⋊C411yescharacteristic
958C2×C3C2×#404211yescharacteristic
959C2×C3C2×#404311yescharacteristic
960D3—104no—
961D3#6495718yesdirect product factor
962C5D3×#38511yescharacteristic, complemented, Sylow
963C22—34no—
964C22—34no—
965C22—34no—
966C22—34no—
967C22—34no—
968C22—34no—
969C22—34no—
970C22—54no—
971C22—102no—
972C22—102no—
973C22—102no—
974C22—102no—
975C22—102no—
976C22—102no—
977C22—154no—
978C22—3032no—
979C22—302no—
980C22—302no—
981C22—302no—
982C22—302no—
983C22—302no—
984C22—302no—
985C22C2×C4×D3×D511yescharacteristic
986C22C2×D3×D2011yescharacteristic
987C22D3×#70911yescharacteristic
988C22D3×D4×D511yescharacteristic
989C22D3×D4×D511yescharacteristic
990C22D3×#71111yescharacteristic
991C22D3×Q8×D511yescharacteristic
992C4—22no—
993C4—22no—
994C4—41no—
995C4—62no—
996C4—62no—
997C4—102no—
998C4—102no—
999C4—121no—
1000C4—201no—
1001C4—302no—
1002C4—302no—
1003C4—601no—
1004C3C2×#6495711yescharacteristic, complemented, Sylow
1005C2—38no—
1006C2—104no—
1007C2—304no—
1008C2C4×D3×D2011yescharacteristic
1009C2D3×#402711yescharacteristic
1010C2D3×#402811yescharacteristic
1011C2D3×#402911yescharacteristic
1012C2D3×D5×C4⋊C411yescharacteristic
1013C2D3×#404211yescharacteristic
1014C2D3×#404311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenter#95D3×D5
hypocenterC3×C5C2×#385
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C2×D3×C4⋊Dic5C2semidirect
5. C2×D3×#683C2semidirect
6. #11750769C2semidirect
7. C5×D3×#95C2semidirect
8. C3×#64957C2semidirect
9. #11748900C2semidirect
10. #11748898C2semidirect
11. #11748895C2semidirect
12. #11748890C2semidirect
13. D3×#3963C2semidirect
14. #11748729C2semidirect
15. #11748704C2semidirect
33. C2×C4⋊Dic15C22semidirect
34. C2×#6712C22semidirect
37. C2×C3×C4⋊Dic5C22semidirect
38. C2×C3×#683C22semidirect
39. C2×Dic3⋊Dic5C22semidirect
40. C2×Dic3⋊Dic5C22semidirect
41. C2×#6669C22semidirect
42. C2×#6668C22semidirect
48. D3×#685C4semidirect
51. C3×C5×#95C22semidirect
52. #91115C22semidirect
53. C5×C3⋊#95C22semidirect
54. C5×C3⋊#95C22semidirect
55. C5×C3⋊#95C22semidirect
56. C3×#3963C22semidirect
57. #90994C22semidirect
58. #90994C22semidirect
74. #64957D3direct (N × H)
104. C2×C4×C5×D3C2×C4semidirect
122. C2×D3×Dic5C2×C4semidirect
129. #6714C2×C4semidirect
133. C3×#685C2×C4semidirect
141. #6667C2×C4semidirect
143. #6665C2×C4semidirect
158. D3×#95D5semidirect
187. C2×C4⋊Dic5C2×D3semidirect
192. C2×#683C2×D3semidirect
196. C5×#95C2×D3semidirect
200. #3963C2×D3semidirect
230. C2×D3×D5C4⋊C4semidirect
238. C2×C3×C4×C5C22×C4semidirect
247. C2×Dic15C22×C4semidirect
257. C2×C5×Dic3C22×C4semidirect
269. C2×C3×Dic5C22×C4semidirect
312. C3×#95C2×D5semidirect
316. C3⋊#95C2×D5semidirect
317. C3⋊#95C2×D5semidirect
318. C3⋊#95C2×D5semidirect
379. #685C4×D3semidirect
416. C2×D15C2×C4⋊C4semidirect
430. C2×C3×D5C2×C4⋊C4semidirect
495. C2×C4×D3C4×D5semidirect
561. C2×C4×C5C2×C4×D3semidirect
582. C2×Dic5C2×C4×D3semidirect
629. #95D3×D5semidirect
639. C5×D3#385semidirect
686. C2×C3×C4C2×C4×D5semidirect
705. C2×Dic3C2×C4×D5semidirect
743. C2×D5D3×C4⋊C4semidirect
825. C3×C5C2×#385semidirect
950. C2×C4C4×D3×D5semidirect
961. D3#64957direct (N × H)
962. C5D3×#385semidirect
1004. C3C2×#64957semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D3×D52
C2×D3×#6852
C2×D3×C4⋊Dic52
C2×D3×#6832
#117507692
C5×D3×#952
C3×#649572
#117489002
#117488982
#117488952
#117488902
D3×#39632
#117487292
#117487042
C2×#649573
D3×#3855