Finite Group Databasebeta

← D4×#6665 #14325954

Subgroups — D4×#6665 #14325954

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D4×D5C211yesmaximal, characteristic
2C2×D4×Dic15C211yesmaximal, characteristic, complemented
3C2×C5×D4×Dic3C211yesmaximal, characteristic, complemented
4C22×#6665C212yesmaximal, complemented
5#11749500C212yesmaximal, complemented
6#11749495C212yesmaximal, complemented
7#11749488C212yesmaximal, complemented
8#11748796C211yesmaximal, characteristic, complemented
9#11748785C211yesmaximal, characteristic, complemented
10#11748759C211yesmaximal, characteristic, complemented
11C4×#6665C211yesmaximal, characteristic, complemented
12D4×#685—31nomaximal, Hall
13C24×C3×D5C2212yes—
14C22×C3×C5×D4C2211yescharacteristic
15C23×Dic15C2212yescomplemented
16C23×C5×Dic3C2212yescomplemented
17C22×C3×C22⋊D5C2212yes—
18C2×C3×D4×D5—24no—
19C2×C3×D4×D5—24no—
20C2×C3×D4×D5C418yescomplemented
21C22×C3×D20C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C2×#6719C2212yescomplemented
24D4×Dic15—24no—
25C2×C4⋊Dic15C2211yescharacteristic, complemented
26C2×C4×Dic15C2211yescharacteristic, complemented
27C2×C5×#217C2212yescomplemented
28C5×D4×Dic3—24no—
29C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
30C2×C4×C5×Dic3C2211yescharacteristic, complemented
31C2×#6665—28no—
32C2×#6665C2211yescharacteristic
33C2×#6665C2212yes—
34C2×#6665C2211yescharacteristic
35C2×#6665C2212yescomplemented
36C2×#6665C2212yescomplemented
37C2×#6665C2212yescomplemented
38C2×#6665C2212yescomplemented
39#90994C2211yescharacteristic, complemented
40#90994C2211yescharacteristic, complemented
41#90994C2212yescomplemented
42D4×#217—51nomaximal, Hall
43C22×D4×D5D311yescharacteristic
44C2×C4×C5×D4—31no—
45C2×D4×Dic5—31no—
46C22×#685—32no—
47#65502—32no—
48#65277—31no—
49#65276—31no—
50#65247—32no—
51#65244—32no—
52#65228—31no—
53C4×#685—31no—
54C24×C3×C5C2312yes—
55C23×C3×D5—24no—
56C23×C3×D5—24no—
57C23×C3×D5—24no—
58C23×C3×D5—24no—
59C23×C3×D5—42no—
60C23×C3×D5—42no—
61C23×C3×D5C2×C418yescomplemented
62C23×C3×D5C2312yes—
63C23×C3×D5C2311yescharacteristic
64C2×C3×C5×D4C2×C414yes—
65C2×C3×C5×D4D414yes—
66C2×C3×C5×D4D414yes—
67C22×C3×C4×C5C2311yescharacteristic
68C22×Dic15—24no—
69C22×Dic15—24no—
70C22×Dic15—42no—
71C22×Dic15C2311yescharacteristic
72C22×Dic15C2312yes—
73C22×Dic15C2311yescharacteristic
74C22×C5×Dic3—24no—
75C22×C5×Dic3—24no—
76C22×C5×Dic3—42no—
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2312yes—
79C22×C5×Dic3C2311yescharacteristic
80C2×C3×C22⋊D5—24no—
81C2×C3×C22⋊D5—24no—
82C2×C3×C22⋊D5C2×C418yescomplemented
83C22×C3×Dic5C2311yescharacteristic
84C3×D4×D5—232no—
85C2×C3×D20—22no—
86C2×C3×D20—22no—
87C2×C3×D20C2×C414yescomplemented
88C2×C3×C4×D5—22no—
89C2×C3×C4×D5—22no—
90C2×C3×C4×D5C2×C414yescomplemented
91#6719—24no—
92C4⋊Dic15—22no—
93C4×Dic15—22no—
94C5×#217—24no—
95C5×C4⋊Dic3—22no—
96C4×C5×Dic3—22no—
97#6665—24no—
98#6665—22no—
99#6665—24no—
100#6665—24no—
101#6665—42no—
102#6665—42no—
103#6665D414yesdirect product factor
104C23×C3×D4—51no—
105C22×#217—52no—
106C2×D4×Dic3—51no—
107C2×D4×Dic3D511yescharacteristic, complemented
108#5247—52no—
109#5221—51no—
110#5221—51no—
111#5220—52no—
112#5220—52no—
113#5212—51no—
114C4×#217—51no—
115C24×D5C2×D312yes—
116C22×C5×D4C2×D311yescharacteristic
117C23×C4×C5—32no—
118C22×C22⋊D5C2×D312yes—
119C23×Dic5—32no—
120C2×D4×D5—24no—
121C2×D4×D5—24no—
122C2×D4×D5Dic318yescomplemented
123C22×D20C2×D311yescharacteristic
124C22×C4×D5C2×D311yescharacteristic
125C4×C5×D4—64no—
126C2×C5×C4⋊C4—31no—
127C2×C5×C22⋊C4—32no—
128C2×C42×C5—31no—
129C2×C22⋊Dic5—32no—
130D4×Dic5—64no—
131C2×#685—31no—
132C2×#685—32no—
133C2×#685—32no—
134C2×#685—32no—
135C2×#685—31no—
136C2×#685—32no—
137C2×#685—32no—
138C2×#685—68no—
139C2×C4⋊Dic5—31no—
140C2×C4×Dic5—31no—
141#3963—31no—
142#3963—31no—
143#3963—32no—
144D4×C22⋊C4—151noSylow
145C23×C3×C5—22no—
146C23×C3×C5—22no—
147C23×C3×C5—22no—
148C23×C3×C5—22no—
149C23×C3×C5C22×C414yes—
150C23×C3×C5C2×D414yes—
151C23×C3×C5C2×D414yes—
152C23×C3×C5C2411yescharacteristic
153C22×C3×D5—21no—
154C22×C3×D5—21no—
155C22×C3×D5—21no—
156C22×C3×D5—21no—
157C22×C3×D5—216no—
158C22×C3×D5—22no—
159C22×C3×D5—22no—
160C22×C3×D5—22no—
161C22×C3×D5—22no—
162C22×C3×D5—22no—
163C22×C3×D5—22no—
164C22×C3×D5—216no—
165C22×C3×D5—48no—
166C22×C3×D5—48no—
167C22×C3×D5—48no—
168C22×C3×D5—48no—
169C22×C3×D5—48no—
170C22×C3×D5C22×C414yes—
171C22×C3×D5C22×C412yes—
172C22×C3×D5C2×D412yes—
173C22×C3×D5#4112yes—
174C3×C5×D4C22⋊C4116yescomplemented
175C2×C3×C4×C5C22×C412yes—
176C2×C3×C4×C5C2×D412yes—
177C2×C3×C4×C5C2×D412yes—
178C2×Dic15—21no—
179C2×Dic15—21no—
180C2×Dic15—22no—
181C2×Dic15—21no—
182C2×Dic15—22no—
183C2×Dic15—21no—
184C2×Dic15—21no—
185C2×Dic15—22no—
186C2×Dic15—48no—
187C2×Dic15C2×D412yescomplemented
188C2×C5×Dic3—21no—
189C2×C5×Dic3—21no—
190C2×C5×Dic3—22no—
191C2×C5×Dic3—21no—
192C2×C5×Dic3—22no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—22no—
196C2×C5×Dic3—48no—
197C2×C5×Dic3C2×D412yescomplemented
198C3×C22⋊D5—216no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5C22×C412yes—
202C3×D20—28no—
203C3×C4×D5—28no—
204C25×C3—52no—
205C22×C3×D4—52no—
206C22×C3×D4—58no—
207C22×C3×D4—51no—
208C22×C3×D4—104no—
209C22×C3×D4—104no—
210C22×C3×D4C2×D511yescharacteristic
211C23×C3×C4—51no—
212C23×Dic3—52no—
213C23×Dic3C2×D512yescomplemented
214C2×#217—51no—
215C2×#217—52no—
216C2×#217—51no—
217C2×#217—52no—
218C2×#217—52no—
219C2×#217—52no—
220C2×#217—52no—
221C2×#217—52no—
222C2×#217—108no—
223C2×#217C2×D512yescomplemented
224D4×Dic3—24no—
225D4×Dic3—104no—
226C2×C4⋊Dic3—51no—
227C2×C4⋊Dic3C2×D511yescharacteristic, complemented
228C2×C4×Dic3—51no—
229C2×C4×Dic3C2×D511yescharacteristic, complemented
230C3⋊#95—51no—
231C3⋊#95—51no—
232C3⋊#95—52no—
233C24×C5C22×D312yes—
234C23×D5—24no—
235C23×D5—24no—
236C23×D5—24no—
237C23×D5—24no—
238C23×D5—42no—
239C23×D5—42no—
240C23×D5C2×Dic318yescomplemented
241C23×D5C22×D312yes—
242C23×D5C22×D311yescharacteristic
243C2×C5×D4C2×Dic314yes—
244C2×C5×D4#6714yes—
245C2×C5×D4#6714yes—
246C22×C4×C5—31no—
247C22×C4×C5—31no—
248C22×C4×C5—32no—
249C22×C4×C5—64no—
250C22×C4×C5—64no—
251C22×C4×C5—122no—
252C22×C4×C5C22×D311yescharacteristic
253C2×C22⋊D5—24no—
254C2×C22⋊D5—24no—
255C2×C22⋊D5C2×Dic318yescomplemented
256C22×Dic5—31no—
257C22×Dic5—31no—
258C22×Dic5—32no—
259C22×Dic5—64no—
260C22×Dic5—64no—
261C22×Dic5—122no—
262C22×Dic5C22×D311yescharacteristic
263D4×D5—232no—
264C2×D20—22no—
265C2×D20—22no—
266C2×D20C2×Dic314yescomplemented
267C2×C4×D5—22no—
268C2×C4×D5—22no—
269C2×C4×D5C2×Dic314yescomplemented
270C5×C4⋊C4—62no—
271C5×C22⋊C4—64no—
272C42×C5—62no—
273C22⋊Dic5—64no—
274#685—34no—
275#685—64no—
276#685—64no—
277#685—64no—
278#685—62no—
279#685—122no—
280#685—122no—
281C4⋊Dic5—62no—
282C4×Dic5—62no—
283C23×D4—51no—
284C2×C4×D4—31no—
285C2×C4×D4—151no—
286C22×C22⋊C4—152no—
287#390—151no—
288#390—151no—
289#386—152no—
290#386—152no—
291#380—151no—
292#379—152no—
293C4×C22⋊C4—151no—
294C22×C3×C5—24no—
295C22×C3×C5—24no—
296C22×C3×C5—24no—
297C22×C3×C5—24no—
298C22×C3×C5—24no—
299C22×C3×C5—24no—
300C22×C3×C5C2×C22⋊C418yescomplemented
301C22×C3×C5C23×C411yescharacteristic
302C22×C3×C5C22×D411yescharacteristic
303C22×C3×C5C22×D411yescharacteristic
304C22×C3×C5C22×D411yescharacteristic
305C22×C3×C5C2×#4111yescharacteristic
306C22×C3×C5H(5,𝔽2)11yescharacteristic
307C22×C3×C5H(5,𝔽2)11yescharacteristic
308C2×C3×D5—22no—
309C2×C3×D5—22no—
310C2×C3×D5—22no—
311C2×C3×D5—22no—
312C2×C3×D5—22no—
313C2×C3×D5—22no—
314C2×C3×D5—24no—
315C2×C3×D5—24no—
316C2×C3×D5—24no—
317C2×C3×D5—432no—
318C2×C3×D5—42no—
319C2×C3×D5—42no—
320C2×C3×D5—42no—
321C2×C3×D5—42no—
322C2×C3×D5C4×D414yescomplemented
323C3×C4×C5C2×C22⋊C414yescomplemented
324Dic15—22no—
325Dic15—42no—
326Dic15—41no—
327C3×Dic5—22no—
328C5×Dic3—22no—
329C5×Dic3—42no—
330C5×Dic3—41no—
331C24×C3—51no—
332C24×C3—52no—
333C24×C3—58no—
334C24×C3—104no—
335C24×C3—104no—
336C24×C3—104no—
337C24×C3—104no—
338C24×C3—202no—
339C24×C3—202no—
340C24×C3C22×D512yes—
341C2×C3×D4—58no—
342C2×C3×D4—54no—
343C2×C3×D4—104no—
344C2×C3×D4—104no—
345C2×C3×D4—1032no—
346C2×C3×D4—102no—
347C2×C3×D4—102no—
348C2×C3×D4C4×D514yes—
349C2×C3×D4D2014yes—
350C2×C3×D4C22⋊D514yes—
351C22×C3×C4—51no—
352C22×C3×C4—54no—
353C22×C3×C4—102no—
354C22×C3×C4—102no—
355C22×C3×C4C22×D511yescharacteristic
356C22×Dic3—24no—
357C22×Dic3—24no—
358C22×Dic3—42no—
359C22×Dic3—51no—
360C22×Dic3—51no—
361C22×Dic3—52no—
362C22×Dic3—104no—
363C22×Dic3—104no—
364C22×Dic3—202no—
365C22×Dic3C22×D511yescharacteristic
366C22×Dic3C22×D512yes—
367C22×Dic3C22×D511yescharacteristic
368#217—24no—
369#217—54no—
370#217—104no—
371#217—102no—
372#217—104no—
373#217—104no—
374#217—104no—
375#217—202no—
376#217—202no—
377C4⋊Dic3—22no—
378C4⋊Dic3—102no—
379C4×Dic3—22no—
380C4×Dic3—102no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5C22×Dic314yes—
386C23×C5C2×#6714yes—
387C23×C5C2×#6714yes—
388C23×C5C23×D311yescharacteristic
389C22×D5—21no—
390C22×D5—21no—
391C22×D5—21no—
392C22×D5—21no—
393C22×D5—216no—
394C22×D5—22no—
395C22×D5—22no—
396C22×D5—22no—
397C22×D5—22no—
398C22×D5—22no—
399C22×D5—22no—
400C22×D5—216no—
401C22×D5—48no—
402C22×D5—48no—
403C22×D5—48no—
404C22×D5—48no—
405C22×D5—48no—
406C22×D5D3×D412yes—
407C22×D5#23712yes—
408C22×D5C22×Dic314yes—
409C22×D5C22×Dic312yes—
410C5×D4#217116yescomplemented
411C2×C4×C5—32no—
412C2×C4×C5—61no—
413C2×C4×C5—61no—
414C2×C4×C5—62no—
415C2×C4×C5—61no—
416C2×C4×C5—61no—
417C2×C4×C5—62no—
418C2×C4×C5—61no—
419C2×C4×C5—62no—
420C2×C4×C5—128no—
421C2×C4×C5C22×Dic312yes—
422C2×C4×C5C2×#6712yes—
423C2×C4×C5C2×#6712yes—
424C22⋊D5—216no—
425C2×Dic5—21no—
426C2×Dic5—21no—
427C2×Dic5—32no—
428C2×Dic5—61no—
429C2×Dic5—61no—
430C2×Dic5—62no—
431C2×Dic5—61no—
432C2×Dic5—61no—
433C2×Dic5—62no—
434C2×Dic5—61no—
435C2×Dic5—62no—
436C2×Dic5—128no—
437C2×Dic5C22×Dic312yes—
438D20—28no—
439C4×D5—28no—
440C25—52no—
441C22×D4—52no—
442C22×D4—58no—
443C22×D4—51no—
444C22×D4—104no—
445C22×D4—104no—
446C22×D4D3×D511yescharacteristic
447C23×C4—32no—
448C23×C4—51no—
449C23×C4—152no—
450C4×D4—64no—
451C4×D4—304no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—151no—
454C2×C22⋊C4—32no—
455C2×C22⋊C4—151no—
456C2×C22⋊C4—152no—
457C2×C22⋊C4—152no—
458C2×C22⋊C4—152no—
459C2×C22⋊C4—151no—
460C2×C22⋊C4—152no—
461C2×C22⋊C4—152no—
462C2×C22⋊C4—152no—
463C2×C22⋊C4—308no—
464C2×C42—31no—
465C2×C42—151no—
466#95—151no—
467#95—151no—
468#95—152no—
469C2×C3×C5—28no—
470C2×C3×C5C22×C22⋊C411yescharacteristic
471C2×C3×C5C2×C4×D411yescharacteristic
472C2×C3×C5#51811yescharacteristic
473C2×C3×C5D4211yescharacteristic
474C2×C3×C5D4211yescharacteristic
475C2×C3×C5#54611yescharacteristic
476C2×C3×C5#54611yescharacteristic
477C3×D5—24no—
478C3×D5—44no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—52no—
484C23×C3—52no—
485C23×C3—52no—
486C23×C3—54no—
487C23×C3—1016no—
488C23×C3—101no—
489C23×C3—101no—
490C23×C3—101no—
491C23×C3—101no—
492C23×C3—102no—
493C23×C3—102no—
494C23×C3—102no—
495C23×C3—102no—
496C23×C3—102no—
497C23×C3—102no—
498C23×C3—1016no—
499C23×C3—208no—
500C23×C3—208no—
501C23×C3—208no—
502C23×C3—208no—
503C23×C3—208no—
504C23×C3C2×C4×D514yes—
505C23×C3C2×D2014yes—
506C23×C3C2×C22⋊D514yes—
507C23×C3C23×D511yescharacteristic
508C3×D4—1016no—
509C3×D4—108no—
510C3×D4#685116yescomplemented
511C2×C3×C4—52no—
512C2×C3×C4—101no—
513C2×C3×C4—101no—
514C2×C3×C4—108no—
515C2×C3×C4C2×C4×D512yes—
516C2×C3×C4C2×D2012yes—
517C2×C3×C4C2×C22⋊D512yes—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—22no—
526C2×Dic3—48no—
527C2×Dic3—52no—
528C2×Dic3—101no—
529C2×Dic3—101no—
530C2×Dic3—101no—
531C2×Dic3—102no—
532C2×Dic3—102no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535C2×Dic3—102no—
536C2×Dic3—208no—
537C2×Dic3D4×D512yescomplemented
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—24no—
541C22×C5—24no—
542C22×C5—24no—
543C22×C5—24no—
544C22×C5C2×#21718yescomplemented
545C22×C5C2×D3×D411yescharacteristic
546C22×C5C2×#23711yescharacteristic
547C22×C5#100411yescharacteristic
548C22×C5#100411yescharacteristic
549C22×C5C23×Dic311yescharacteristic
550C22×C5C22×#6711yescharacteristic
551C22×C5C22×#6711yescharacteristic
552C2×D5—22no—
553C2×D5—22no—
554C2×D5—22no—
555C2×D5—22no—
556C2×D5—22no—
557C2×D5—22no—
558C2×D5—24no—
559C2×D5—24no—
560C2×D5—24no—
561C2×D5—432no—
562C2×D5—42no—
563C2×D5—42no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5D4×Dic314yescomplemented
567C4×C5—62no—
568C4×C5—122no—
569C4×C5—121no—
570C4×C5C2×#21714yescomplemented
571Dic5—22no—
572Dic5—62no—
573Dic5—122no—
574Dic5—121no—
575C24—51no—
576C24—52no—
577C24—58no—
578C24—104no—
579C24—104no—
580C24—104no—
581C24—104no—
582C24—202no—
583C24—202no—
584C24C2×D3×D512yes—
585C2×D4—58no—
586C2×D4—54no—
587C2×D4—104no—
588C2×D4—104no—
589C2×D4—1032no—
590C2×D4—102no—
591C2×D4—102no—
592C2×D4D5×Dic314yes—
593C2×D4#120114yes—
594C2×D4#120214yes—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—32no—
598C22×C4—51no—
599C22×C4—54no—
600C22×C4—64no—
601C22×C4—64no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—122no—
605C22×C4—151no—
606C22×C4—151no—
607C22×C4—152no—
608C22×C4—304no—
609C22×C4—304no—
610C22×C4—602no—
611C22×C4C2×D3×D511yescharacteristic
612C4⋊C4—62no—
613C4⋊C4—302no—
614C22⋊C4—64no—
615C22⋊C4—154no—
616C22⋊C4—304no—
617C22⋊C4—304no—
618C22⋊C4—304no—
619C22⋊C4—302no—
620C22⋊C4—304no—
621C22⋊C4—602no—
622C22⋊C4—602no—
623C42—62no—
624C42—302no—
625C3×C5D4×C22⋊C411yescharacteristic, complemented, Hall
626C22×C3—24no—
627C22×C3—24no—
628C22×C3—24no—
629C22×C3—24no—
630C22×C3—24no—
631C22×C3—24no—
632C22×C3—54no—
633C22×C3—102no—
634C22×C3—102no—
635C22×C3—102no—
636C22×C3—102no—
637C22×C3—102no—
638C22×C3—102no—
639C22×C3—104no—
640C22×C3—104no—
641C22×C3—104no—
642C22×C3—2032no—
643C22×C3—202no—
644C22×C3—202no—
645C22×C3—202no—
646C22×C3—202no—
647C22×C3C2×#68518yescomplemented
648C22×C3C22×C4×D511yescharacteristic
649C22×C3C22×D2011yescharacteristic
650C22×C3C2×D4×D511yescharacteristic
651C22×C3#414411yescharacteristic
652C22×C3D5×#4111yescharacteristic
653C22×C3#414911yescharacteristic
654C22×C3C22×C22⋊D511yescharacteristic
655C3×C4—102no—
656C3×C4C2×#68514yescomplemented
657Dic3—22no—
658Dic3—42no—
659Dic3—41no—
660Dic3—102no—
661Dic3—202no—
662Dic3—201no—
663C2×C5—28no—
664C2×C5C2×D4×Dic311yescharacteristic
665C2×C5#579811yescharacteristic
666C2×C5D4×#6711yescharacteristic
667C2×C5D4×#6711yescharacteristic
668C2×C5#580611yescharacteristic
669C2×C5#580611yescharacteristic
670C2×C5C22×#21711yescharacteristic
671D5—24no—
672D5—44no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—52no—
678C23—52no—
679C23—52no—
680C23—54no—
681C23—1016no—
682C23—101no—
683C23—101no—
684C23—101no—
685C23—101no—
686C23—102no—
687C23—102no—
688C23—102no—
689C23—102no—
690C23—102no—
691C23—102no—
692C23—1016no—
693C23—208no—
694C23—208no—
695C23—208no—
696C23—208no—
697C23—208no—
698C23C2×D5×Dic314yes—
699C23C2×#120114yes—
700C23C2×#120214yes—
701C23C22×D3×D511yescharacteristic
702D4—1016no—
703D4—108no—
704D4#6665116yesdirect product factor
705C2×C4—32no—
706C2×C4—52no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—62no—
710C2×C4—61no—
711C2×C4—62no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—62no—
715C2×C4—101no—
716C2×C4—101no—
717C2×C4—108no—
718C2×C4—128no—
719C2×C4—152no—
720C2×C4—301no—
721C2×C4—301no—
722C2×C4—302no—
723C2×C4—301no—
724C2×C4—301no—
725C2×C4—302no—
726C2×C4—301no—
727C2×C4—302no—
728C2×C4—608no—
729C2×C4C2×D5×Dic312yes—
730C2×C4C2×#120112yes—
731C2×C4C2×#120212yes—
732C2×C3—28no—
733C2×C3—104no—
734C2×C3—204no—
735C2×C3C4×D4×D511yescharacteristic
736C2×C3#6587911yescharacteristic
737C2×C3D4×D2011yescharacteristic
738C2×C3#6588811yescharacteristic
739C2×C3C22×#68511yescharacteristic
740C2×C3D4×C22⋊D511yescharacteristic
741C2×C3#6616311yescharacteristic
742C5D4×#21711yescharacteristic, complemented, Sylow
743C22—24no—
744C22—24no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—54no—
750C22—102no—
751C22—102no—
752C22—102no—
753C22—102no—
754C22—102no—
755C22—102no—
756C22—104no—
757C22—104no—
758C22—104no—
759C22—2032no—
760C22—202no—
761C22—202no—
762C22—202no—
763C22—202no—
764C22C2×#666518yescomplemented
765C22D3×D4×D511yescharacteristic
766C22D5×#23711yescharacteristic
767C22#9202511yescharacteristic
768C22#9202611yescharacteristic
769C22C22×D5×Dic311yescharacteristic
770C22C22×#120111yescharacteristic
771C22C22×#120211yescharacteristic
772C4—62no—
773C4—102no—
774C4—122no—
775C4—121no—
776C4—302no—
777C4—602no—
778C4—601no—
779C4C2×#666514yescomplemented
780C3D4×#68511yescharacteristic, complemented, Sylow
781C2—28no—
782C2—104no—
783C2—204no—
784C2D4×D5×Dic311yescharacteristic
785C2#1175491011yescharacteristic
786C2D4×#120111yescharacteristic
787C2D4×#120211yescharacteristic
788C2#1175496111yescharacteristic
789C2#1175496311yescharacteristic
790C2C22×#666511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×D4×D5C2
hypercenterC22×D4D3×D5
hypocenterC3×C5D4×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic15C2semidirect
3. C2×C5×D4×Dic3C2semidirect
4. C22×#6665C2semidirect
5. #11749500C2semidirect
6. #11749495C2semidirect
7. #11749488C2semidirect
8. #11748796C2semidirect
9. #11748785C2semidirect
10. #11748759C2semidirect
11. C4×#6665C2semidirect
15. C23×Dic15C22semidirect
16. C23×C5×Dic3C22semidirect
20. C2×C3×D4×D5C4semidirect
23. C2×#6719C22semidirect
25. C2×C4⋊Dic15C22semidirect
26. C2×C4×Dic15C22semidirect
27. C2×C5×#217C22semidirect
29. C2×C5×C4⋊Dic3C22semidirect
30. C2×C4×C5×Dic3C22semidirect
35. C2×#6665C22semidirect
36. C2×#6665C22semidirect
37. C2×#6665C22semidirect
38. C2×#6665C22semidirect
39. #90994C22semidirect
40. #90994C22semidirect
41. #90994C22semidirect
61. C23×C3×D5C2×C4semidirect
82. C2×C3×C22⋊D5C2×C4semidirect
87. C2×C3×D20C2×C4semidirect
90. C2×C3×C4×D5C2×C4semidirect
103. #6665D4direct (N × H)
107. C2×D4×Dic3D5semidirect
122. C2×D4×D5Dic3semidirect
174. C3×C5×D4C22⋊C4semidirect
187. C2×Dic15C2×D4semidirect
197. C2×C5×Dic3C2×D4semidirect
213. C23×Dic3C2×D5semidirect
223. C2×#217C2×D5semidirect
227. C2×C4⋊Dic3C2×D5semidirect
229. C2×C4×Dic3C2×D5semidirect
240. C23×D5C2×Dic3semidirect
255. C2×C22⋊D5C2×Dic3semidirect
266. C2×D20C2×Dic3semidirect
269. C2×C4×D5C2×Dic3semidirect
300. C22×C3×C5C2×C22⋊C4semidirect
322. C2×C3×D5C4×D4semidirect
323. C3×C4×C5C2×C22⋊C4semidirect
410. C5×D4#217semidirect
510. C3×D4#685semidirect
537. C2×Dic3D4×D5semidirect
544. C22×C5C2×#217semidirect
566. C2×D5D4×Dic3semidirect
570. C4×C5C2×#217semidirect
625. C3×C5D4×C22⋊C4semidirect
647. C22×C3C2×#685semidirect
656. C3×C4C2×#685semidirect
704. D4#6665direct (N × H)
742. C5D4×#217semidirect
764. C22C2×#6665semidirect
779. C4C2×#6665semidirect
780. C3D4×#685semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D4×D52
C2×D4×Dic152
C2×C5×D4×Dic32
C22×#66652
#117495002
#117494952
#117494882
#117487962
#117487852
#117487592
C4×#66652
D4×#6853
D4×#2175