Finite Group Databasebeta

← D4×#6667 #14325955

Subgroups — D4×#6667 #14325955

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×D4×D15C211yesmaximal, characteristic
2C2×C5×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
4C22×#6667C212yesmaximal, complemented
5#11749502C212yesmaximal, complemented
6#11749498C212yesmaximal, complemented
7#11749494C212yesmaximal, complemented
8#11748799C211yesmaximal, characteristic, complemented
9#11748789C211yesmaximal, characteristic, complemented
10#11748768C211yesmaximal, characteristic, complemented
11C4×#6667C211yesmaximal, characteristic, complemented
12D4×#685—31nomaximal, Hall
13C24×D15C2212yes—
14C22×C3×C5×D4C2211yescharacteristic
15C22×#1220C2212yes—
16C2×D4×D15—24no—
17C2×D4×D15—24no—
18C2×D4×D15C418yescomplemented
19C22×D60C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C23×C5×Dic3C2212yescomplemented
22C23×C3×Dic5C2212yescomplemented
23C2×C5×#217C2212yescomplemented
24C5×D4×Dic3—24no—
25C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
26C2×C4×C5×Dic3C2211yescharacteristic, complemented
27C2×C3×C22⋊Dic5C2212yescomplemented
28C3×D4×Dic5—24no—
29C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
30C2×C3×C4×Dic5C2211yescharacteristic, complemented
31C2×#6667—28no—
32C2×#6667C2212yes—
33C2×#6667C2211yescharacteristic
34C2×#6667C2211yescharacteristic
35C2×#6667C2212yescomplemented
36C2×#6667C2212yescomplemented
37C2×#6667C2212yescomplemented
38C2×#6667C2212yescomplemented
39#90994C2211yescharacteristic, complemented
40#90994C2211yescharacteristic, complemented
41#90994C2212yescomplemented
42D4×(C2×D3)⋊C4—51nomaximal, Hall
43C22×D4×D5—31no—
44C2×C4×C5×D4—31no—
45C2×D4×Dic5D311yescharacteristic, complemented
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×D15—24no—
56C23×D15—24no—
57C23×D15—24no—
58C23×D15—24no—
59C23×D15—42no—
60C23×D15—42no—
61C23×D15C2×C418yescomplemented
62C23×D15C2312yes—
63C23×D15C2311yescharacteristic
64C2×C3×C5×D4C2×C414yes—
65C2×C3×C5×D4D414yes—
66C2×C3×C5×D4D414yes—
67C22×C3×C4×C5C2311yescharacteristic
68C2×#1220—24no—
69C2×#1220—24no—
70C2×#1220C2×C418yescomplemented
71C22×Dic15C2311yescharacteristic
72D4×D15—232no—
73C2×D60—22no—
74C2×D60—22no—
75C2×D60C2×C414yescomplemented
76C2×C4×D15—22no—
77C2×C4×D15—22no—
78C2×C4×D15C2×C414yescomplemented
79C22×C5×Dic3—24no—
80C22×C5×Dic3—24no—
81C22×C5×Dic3—42no—
82C22×C5×Dic3C2311yescharacteristic
83C22×C5×Dic3C2312yes—
84C22×C5×Dic3C2311yescharacteristic
85C22×C3×Dic5—24no—
86C22×C3×Dic5—24no—
87C22×C3×Dic5—42no—
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2312yes—
90C22×C3×Dic5C2311yescharacteristic
91C5×#217—24no—
92C5×C4⋊Dic3—22no—
93C4×C5×Dic3—22no—
94C3×C22⋊Dic5—24no—
95C3×C4⋊Dic5—22no—
96C3×C4×Dic5—22no—
97#6667—24no—
98#6667—22no—
99#6667—24no—
100#6667—24no—
101#6667—42no—
102#6667—42no—
103#6667D414yesdirect product factor
104C22×D3×D4—51no—
105C2×C3×C4×D4—51no—
106C2×D4×Dic3D511yescharacteristic, complemented
107C22×(C2×D3)⋊C4—52no—
108#5213—52no—
109#4988—51no—
110#4987—51no—
111#4958—52no—
112#4955—52no—
113#4939—51no—
114C4×(C2×D3)⋊C4—51no—
115C24×D5—32no—
116C22×C5×D4C2×D311yescharacteristic
117C23×C4×C5—32no—
118C22×C22⋊D5—32no—
119C23×Dic5C2×D312yescomplemented
120C2×D4×D5—38no—
121C2×D4×D5—64no—
122C2×D4×D5—64no—
123C22×D20—31no—
124C22×C4×D5—31no—
125C4×C5×D4—64no—
126C2×C5×C4⋊C4—31no—
127C2×C5×C22⋊C4—32no—
128C2×C42×C5—31no—
129C2×C22⋊Dic5C2×D312yescomplemented
130D4×Dic5—24no—
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⋊Dic5C2×D311yescharacteristic, complemented
140C2×C4×Dic5C2×D311yescharacteristic, complemented
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×D15—21no—
154C22×D15—21no—
155C22×D15—21no—
156C22×D15—21no—
157C22×D15—216no—
158C22×D15—22no—
159C22×D15—22no—
160C22×D15—22no—
161C22×D15—22no—
162C22×D15—22no—
163C22×D15—22no—
164C22×D15—216no—
165C22×D15—48no—
166C22×D15—48no—
167C22×D15—48no—
168C22×D15—48no—
169C22×D15—48no—
170C22×D15C22×C414yes—
171C22×D15C22×C412yes—
172C22×D15C2×D412yes—
173C22×D15#4112yes—
174C3×C5×D4C22⋊C4116yescomplemented
175C2×C3×C4×C5C22×C412yes—
176C2×C3×C4×C5C2×D412yes—
177C2×C3×C4×C5C2×D412yes—
178#1220—216no—
179C2×Dic15—21no—
180C2×Dic15—21no—
181C2×Dic15C22×C412yes—
182D60—28no—
183C4×D15—28no—
184C2×C5×Dic3—21no—
185C2×C5×Dic3—21no—
186C2×C5×Dic3—22no—
187C2×C5×Dic3—21no—
188C2×C5×Dic3—22no—
189C2×C5×Dic3—21no—
190C2×C5×Dic3—21no—
191C2×C5×Dic3—22no—
192C2×C5×Dic3—48no—
193C2×C5×Dic3C2×D412yescomplemented
194C2×C3×Dic5—21no—
195C2×C3×Dic5—21no—
196C2×C3×Dic5—22no—
197C2×C3×Dic5—21no—
198C2×C3×Dic5—22no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—22no—
202C2×C3×Dic5—48no—
203C2×C3×Dic5C2×D412yescomplemented
204C24×D3—52no—
205C22×C3×D4C2×D511yescharacteristic
206C23×C3×C4—52no—
207C22×#67—52no—
208C23×Dic3C2×D512yescomplemented
209C2×D3×D4—58no—
210C2×D3×D4—104no—
211C2×D3×D4—104no—
212C22×D12—51no—
213C22×C4×D3—51no—
214C3×C4×D4—104no—
215C2×C3×C4⋊C4—51no—
216C2×C3×C22⋊C4—52no—
217C2×C3×C42—51no—
218C2×#217C2×D512yescomplemented
219D4×Dic3—24no—
220C2×(C2×D3)⋊C4—51no—
221C2×(C2×D3)⋊C4—51no—
222C2×(C2×D3)⋊C4—52no—
223C2×(C2×D3)⋊C4—52no—
224C2×(C2×D3)⋊C4—52no—
225C2×(C2×D3)⋊C4—52no—
226C2×(C2×D3)⋊C4—52no—
227C2×(C2×D3)⋊C4—108no—
228C2×C4⋊Dic3C2×D511yescharacteristic, complemented
229C2×C4×Dic3C2×D511yescharacteristic, complemented
230C3⋊#95—51no—
231C3⋊#95—51no—
232C3⋊#95—52no—
233C24×C5C22×D312yes—
234C23×D5—31no—
235C23×D5—32no—
236C23×D5—38no—
237C23×D5—64no—
238C23×D5—64no—
239C23×D5—64no—
240C23×D5—64no—
241C23×D5—122no—
242C23×D5—122no—
243C2×C5×D4C4×D314yes—
244C2×C5×D4D1214yes—
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—38no—
254C2×C22⋊D5—64no—
255C2×C22⋊D5—64no—
256C22×Dic5—24no—
257C22×Dic5—24no—
258C22×Dic5—31no—
259C22×Dic5—42no—
260C22×Dic5C22×D311yescharacteristic
261C22×Dic5C22×D312yes—
262C22×Dic5C22×D311yescharacteristic
263D4×D5—632no—
264C2×D20—34no—
265C2×D20—62no—
266C2×D20—62no—
267C2×C4×D5—34no—
268C2×C4×D5—62no—
269C2×C4×D5—62no—
270C5×C4⋊C4—62no—
271C5×C22⋊C4—64no—
272C42×C5—62no—
273C22⋊Dic5—24no—
274#685—34no—
275#685—64no—
276#685—62no—
277#685—64no—
278#685—64no—
279#685—122no—
280#685—122no—
281C4⋊Dic5—22no—
282C4×Dic5—22no—
283C23×D4—151no—
284C2×C4×D4—31no—
285C2×C4×D4—51no—
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×D15—22no—
309C2×D15—22no—
310C2×D15—22no—
311C2×D15—22no—
312C2×D15—22no—
313C2×D15—22no—
314C2×D15—24no—
315C2×D15—24no—
316C2×D15—24no—
317C2×D15—432no—
318C2×D15—42no—
319C2×D15—42no—
320C2×D15—42no—
321C2×D15—42no—
322C2×D15C4×D414yescomplemented
323C3×C4×C5C2×C22⋊C414yescomplemented
324Dic15—22no—
325C3×Dic5—22no—
326C3×Dic5—42no—
327C3×Dic5—41no—
328C5×Dic3—22no—
329C5×Dic3—42no—
330C5×Dic3—41no—
331C24×C3C22×D512yes—
332C23×D3—51no—
333C23×D3—52no—
334C23×D3—58no—
335C23×D3—104no—
336C23×D3—104no—
337C23×D3—104no—
338C23×D3—104no—
339C23×D3—202no—
340C23×D3—202no—
341C2×C3×D4C4×D514yes—
342C2×C3×D4D2014yes—
343C2×C3×D4C22⋊D514yes—
344C22×C3×C4—51no—
345C22×C3×C4—51no—
346C22×C3×C4—52no—
347C22×C3×C4—104no—
348C22×C3×C4—104no—
349C22×C3×C4—202no—
350C22×C3×C4C22×D511yescharacteristic
351C2×#67—58no—
352C2×#67—104no—
353C2×#67—104no—
354C22×Dic3—24no—
355C22×Dic3—24no—
356C22×Dic3—42no—
357C22×Dic3—51no—
358C22×Dic3C22×D511yescharacteristic
359C22×Dic3C22×D512yes—
360C22×Dic3C22×D511yescharacteristic
361D3×D4—1032no—
362C2×D12—54no—
363C2×D12—102no—
364C2×D12—102no—
365C2×C4×D3—54no—
366C2×C4×D3—102no—
367C2×C4×D3—102no—
368C3×C4⋊C4—102no—
369C3×C22⋊C4—104no—
370C3×C42—102no—
371#217—24no—
372(C2×D3)⋊C4—54no—
373(C2×D3)⋊C4—104no—
374(C2×D3)⋊C4—102no—
375(C2×D3)⋊C4—104no—
376(C2×D3)⋊C4—104no—
377(C2×D3)⋊C4—202no—
378(C2×D3)⋊C4—202no—
379C4⋊Dic3—22no—
380C4×Dic3—22no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5C2×C4×D314yes—
386C23×C5C2×D1214yes—
387C23×C5C2×#6714yes—
388C23×C5C23×D311yescharacteristic
389C22×D5—32no—
390C22×D5—32no—
391C22×D5—32no—
392C22×D5—34no—
393C22×D5—616no—
394C22×D5—61no—
395C22×D5—61no—
396C22×D5—61no—
397C22×D5—61no—
398C22×D5—616no—
399C22×D5—62no—
400C22×D5—62no—
401C22×D5—62no—
402C22×D5—62no—
403C22×D5—62no—
404C22×D5—62no—
405C22×D5—128no—
406C22×D5—128no—
407C22×D5—128no—
408C22×D5—128no—
409C22×D5—128no—
410C5×D4(C2×D3)⋊C4116yescomplemented
411C2×C4×C5—32no—
412C2×C4×C5—61no—
413C2×C4×C5—61no—
414C2×C4×C5—61no—
415C2×C4×C5—62no—
416C2×C4×C5—62no—
417C2×C4×C5—61no—
418C2×C4×C5—61no—
419C2×C4×C5—62no—
420C2×C4×C5—128no—
421C2×C4×C5C2×C4×D312yes—
422C2×C4×C5C2×D1212yes—
423C2×C4×C5C2×#6712yes—
424C22⋊D5—616no—
425C2×Dic5—21no—
426C2×Dic5—21no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—21no—
430C2×Dic5—21no—
431C2×Dic5—21no—
432C2×Dic5—22no—
433C2×Dic5—32no—
434C2×Dic5—48no—
435C2×Dic5—61no—
436C2×Dic5—61no—
437C2×Dic5D3×D412yescomplemented
438D20—68no—
439C4×D5—68no—
440C25—152no—
441C22×D4—152no—
442C22×D4—158no—
443C22×D4—151no—
444C22×D4—304no—
445C22×D4—304no—
446C22×D4D3×D511yescharacteristic
447C23×C4—32no—
448C23×C4—52no—
449C23×C4—151no—
450C4×D4—64no—
451C4×D4—104no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—51no—
454C2×C22⋊C4—32no—
455C2×C22⋊C4—52no—
456C2×C22⋊C4—151no—
457C2×C22⋊C4—152no—
458C2×C22⋊C4—152no—
459C2×C22⋊C4—152no—
460C2×C22⋊C4—151no—
461C2×C22⋊C4—152no—
462C2×C22⋊C4—152no—
463C2×C22⋊C4—308no—
464C2×C42—31no—
465C2×C42—51no—
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
477D15—24no—
478D15—44no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3C2×C4×D514yes—
484C23×C3C2×D2014yes—
485C23×C3C2×C22⋊D514yes—
486C23×C3C23×D511yescharacteristic
487C22×D3—52no—
488C22×D3—52no—
489C22×D3—52no—
490C22×D3—54no—
491C22×D3—1016no—
492C22×D3—101no—
493C22×D3—101no—
494C22×D3—101no—
495C22×D3—101no—
496C22×D3—102no—
497C22×D3—102no—
498C22×D3—102no—
499C22×D3—102no—
500C22×D3—102no—
501C22×D3—102no—
502C22×D3—1016no—
503C22×D3—208no—
504C22×D3—208no—
505C22×D3—208no—
506C22×D3—208no—
507C22×D3—208no—
508C3×D4#685116yescomplemented
509C2×C3×C4—52no—
510C2×C3×C4—101no—
511C2×C3×C4—101no—
512C2×C3×C4—101no—
513C2×C3×C4—102no—
514C2×C3×C4—102no—
515C2×C3×C4—101no—
516C2×C3×C4—101no—
517C2×C3×C4—102no—
518C2×C3×C4—208no—
519C2×C3×C4C2×C4×D512yes—
520C2×C3×C4C2×D2012yes—
521C2×C3×C4C2×C22⋊D512yes—
522#67—1016no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—22no—
531C2×Dic3—48no—
532C2×Dic3—52no—
533C2×Dic3—101no—
534C2×Dic3—101no—
535C2×Dic3D4×D512yescomplemented
536D12—108no—
537C4×D3—108no—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—24no—
541C22×C5—24no—
542C22×C5—24no—
543C22×C5—24no—
544C22×C5C2×(C2×D3)⋊C418yescomplemented
545C22×C5C22×C4×D311yescharacteristic
546C22×C5C22×D1211yescharacteristic
547C22×C5C2×D3×D411yescharacteristic
548C22×C5#100411yescharacteristic
549C22×C5D3×#4111yescharacteristic
550C22×C5#100911yescharacteristic
551C22×C5C22×#6711yescharacteristic
552C2×D5—34no—
553C2×D5—62no—
554C2×D5—62no—
555C2×D5—62no—
556C2×D5—62no—
557C2×D5—62no—
558C2×D5—62no—
559C2×D5—64no—
560C2×D5—64no—
561C2×D5—64no—
562C2×D5—1232no—
563C2×D5—122no—
564C2×D5—122no—
565C2×D5—122no—
566C2×D5—122no—
567C4×C5—62no—
568C4×C5—122no—
569C4×C5—121no—
570C4×C5C2×(C2×D3)⋊C414yescomplemented
571Dic5—22no—
572Dic5—42no—
573Dic5—41no—
574Dic5—62no—
575C24—151no—
576C24—152no—
577C24—158no—
578C24—304no—
579C24—304no—
580C24—304no—
581C24—304no—
582C24—602no—
583C24—602no—
584C24C2×D3×D512yes—
585C2×D4—158no—
586C2×D4—154no—
587C2×D4—304no—
588C2×D4—304no—
589C2×D4—3032no—
590C2×D4—302no—
591C2×D4—302no—
592C2×D4#120014yes—
593C2×D4#120214yes—
594C2×D4#120314yes—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—32no—
598C22×C4—51no—
599C22×C4—51no—
600C22×C4—52no—
601C22×C4—64no—
602C22×C4—64no—
603C22×C4—104no—
604C22×C4—104no—
605C22×C4—122no—
606C22×C4—151no—
607C22×C4—154no—
608C22×C4—202no—
609C22×C4—302no—
610C22×C4—302no—
611C22×C4C2×D3×D511yescharacteristic
612C4⋊C4—62no—
613C4⋊C4—102no—
614C22⋊C4—64no—
615C22⋊C4—104no—
616C22⋊C4—154no—
617C22⋊C4—304no—
618C22⋊C4—304no—
619C22⋊C4—304no—
620C22⋊C4—302no—
621C22⋊C4—602no—
622C22⋊C4—602no—
623C42—62no—
624C42—102no—
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×C3C2×#68518yescomplemented
633C22×C3C22×C4×D511yescharacteristic
634C22×C3C22×D2011yescharacteristic
635C22×C3C2×D4×D511yescharacteristic
636C22×C3#414411yescharacteristic
637C22×C3D5×#4111yescharacteristic
638C22×C3#414911yescharacteristic
639C22×C3C22×C22⋊D511yescharacteristic
640C2×D3—54no—
641C2×D3—102no—
642C2×D3—102no—
643C2×D3—102no—
644C2×D3—102no—
645C2×D3—102no—
646C2×D3—102no—
647C2×D3—104no—
648C2×D3—104no—
649C2×D3—104no—
650C2×D3—2032no—
651C2×D3—202no—
652C2×D3—202no—
653C2×D3—202no—
654C2×D3—202no—
655C3×C4—102no—
656C3×C4—202no—
657C3×C4—201no—
658C3×C4C2×#68514yescomplemented
659Dic3—22no—
660Dic3—42no—
661Dic3—41no—
662Dic3—102no—
663C2×C5—28no—
664C2×C5C4×D3×D411yescharacteristic
665C2×C5#554511yescharacteristic
666C2×C5D4×D1211yescharacteristic
667C2×C5#555411yescharacteristic
668C2×C5C22×(C2×D3)⋊C411yescharacteristic
669C2×C5D4×#6711yescharacteristic
670C2×C5#582911yescharacteristic
671D5—64no—
672D5—124no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—152no—
678C23—152no—
679C23—152no—
680C23—154no—
681C23—3016no—
682C23—301no—
683C23—301no—
684C23—301no—
685C23—301no—
686C23—302no—
687C23—302no—
688C23—302no—
689C23—302no—
690C23—302no—
691C23—302no—
692C23—3016no—
693C23—608no—
694C23—608no—
695C23—608no—
696C23—608no—
697C23—608no—
698C23C2×#120014yes—
699C23C2×#120214yes—
700C23C2×#120314yes—
701C23C22×D3×D511yescharacteristic
702D4—3016no—
703D4—308no—
704D4#6667116yesdirect product factor
705C2×C4—32no—
706C2×C4—52no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—62no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—62no—
713C2×C4—61no—
714C2×C4—62no—
715C2×C4—101no—
716C2×C4—101no—
717C2×C4—102no—
718C2×C4—101no—
719C2×C4—102no—
720C2×C4—101no—
721C2×C4—101no—
722C2×C4—102no—
723C2×C4—128no—
724C2×C4—152no—
725C2×C4—208no—
726C2×C4—301no—
727C2×C4—301no—
728C2×C4—308no—
729C2×C4C2×#120012yes—
730C2×C4C2×#120212yes—
731C2×C4C2×#120312yes—
732C2×C3—28no—
733C2×C3C4×D4×D511yescharacteristic
734C2×C3#6587911yescharacteristic
735C2×C3D4×D2011yescharacteristic
736C2×C3#6588811yescharacteristic
737C2×C3C22×#68511yescharacteristic
738C2×C3D4×C22⋊D511yescharacteristic
739C2×C3#6616311yescharacteristic
740D3—104no—
741D3—204no—
742C5D4×(C2×D3)⋊C411yescharacteristic, complemented, Sylow
743C22—24no—
744C22—24no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—154no—
750C22—302no—
751C22—302no—
752C22—302no—
753C22—302no—
754C22—302no—
755C22—302no—
756C22—304no—
757C22—304no—
758C22—304no—
759C22—6032no—
760C22—602no—
761C22—602no—
762C22—602no—
763C22—602no—
764C22C2×#666718yescomplemented
765C22D3×D4×D511yescharacteristic
766C22#9202411yescharacteristic
767C22#9202611yescharacteristic
768C22#9202711yescharacteristic
769C22C22×#120011yescharacteristic
770C22C22×#120211yescharacteristic
771C22C22×#120311yescharacteristic
772C4—62no—
773C4—102no—
774C4—122no—
775C4—121no—
776C4—202no—
777C4—201no—
778C4—302no—
779C4C2×#666714yescomplemented
780C3D4×#68511yescharacteristic, complemented, Sylow
781C2—28no—
782C2—304no—
783C2—604no—
784C2D4×#120011yescharacteristic
785C2#1175492211yescharacteristic
786C2D4×#120211yescharacteristic
787C2D4×#120311yescharacteristic
788C2#1175498011yescharacteristic
789C2#1175498211yescharacteristic
790C2C22×#666711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D4×D15C2
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×C5×D4×Dic3C2semidirect
3. C2×C3×D4×Dic5C2semidirect
4. C22×#6667C2semidirect
5. #11749502C2semidirect
6. #11749498C2semidirect
7. #11749494C2semidirect
8. #11748799C2semidirect
9. #11748789C2semidirect
10. #11748768C2semidirect
11. C4×#6667C2semidirect
18. C2×D4×D15C4semidirect
21. C23×C5×Dic3C22semidirect
22. C23×C3×Dic5C22semidirect
23. C2×C5×#217C22semidirect
25. C2×C5×C4⋊Dic3C22semidirect
26. C2×C4×C5×Dic3C22semidirect
27. C2×C3×C22⋊Dic5C22semidirect
29. C2×C3×C4⋊Dic5C22semidirect
30. C2×C3×C4×Dic5C22semidirect
35. C2×#6667C22semidirect
36. C2×#6667C22semidirect
37. C2×#6667C22semidirect
38. C2×#6667C22semidirect
39. #90994C22semidirect
40. #90994C22semidirect
41. #90994C22semidirect
45. C2×D4×Dic5D3semidirect
61. C23×D15C2×C4semidirect
70. C2×#1220C2×C4semidirect
75. C2×D60C2×C4semidirect
78. C2×C4×D15C2×C4semidirect
103. #6667D4direct (N × H)
106. C2×D4×Dic3D5semidirect
119. C23×Dic5C2×D3semidirect
129. C2×C22⋊Dic5C2×D3semidirect
139. C2×C4⋊Dic5C2×D3semidirect
140. C2×C4×Dic5C2×D3semidirect
174. C3×C5×D4C22⋊C4semidirect
193. C2×C5×Dic3C2×D4semidirect
203. C2×C3×Dic5C2×D4semidirect
208. C23×Dic3C2×D5semidirect
218. C2×#217C2×D5semidirect
228. C2×C4⋊Dic3C2×D5semidirect
229. C2×C4×Dic3C2×D5semidirect
300. C22×C3×C5C2×C22⋊C4semidirect
322. C2×D15C4×D4semidirect
323. C3×C4×C5C2×C22⋊C4semidirect
410. C5×D4(C2×D3)⋊C4semidirect
437. C2×Dic5D3×D4semidirect
508. C3×D4#685semidirect
535. C2×Dic3D4×D5semidirect
544. C22×C5C2×(C2×D3)⋊C4semidirect
570. C4×C5C2×(C2×D3)⋊C4semidirect
625. C3×C5D4×C22⋊C4semidirect
632. C22×C3C2×#685semidirect
658. C3×C4C2×#685semidirect
704. D4#6667direct (N × H)
742. C5D4×(C2×D3)⋊C4semidirect
764. C22C2×#6667semidirect
779. C4C2×#6667semidirect
780. C3D4×#685semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D152
C2×C5×D4×Dic32
C2×C3×D4×Dic52
C22×#66672
#117495022
#117494982
#117494942
#117487992
#117487892
#117487682
C4×#66672
D4×#6853
D4×(C2×D3)⋊C45