Finite Group Databasebeta

← #14325984

Subgroups — #14325984

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×D5×#217C212yesmaximal, complemented
3C2×#91434C211yesmaximal, characteristic, complemented
4C2×Dic3×D20C211yesmaximal, characteristic, complemented
5#11751322C211yesmaximal, characteristic, complemented
6C5×#5221C211yesmaximal, characteristic, complemented
7#11749518C212yesmaximal, complemented
8#11749518C212yesmaximal, complemented
9#11749488C212yesmaximal, complemented
10#11748759C211yesmaximal, characteristic, complemented
11C4×#6665C211yesmaximal, characteristic, complemented
12#10608162—31nomaximal, Hall
13C24×C3×D5C2212yes—
14C22×C3×C5×D4C2211yescharacteristic
15C22×C3×C22⋊D5C2212yes—
16C2×C3×D4×D5—24no—
17C2×C3×D4×D5—24no—
18C2×C3×D4×D5C418yescomplemented
19C22×C3×D20C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×D5×Dic3C2212yescomplemented
22C22×D5×Dic3C2212yescomplemented
23C2×#6719C2212yescomplemented
24C2×#6719C2212yescomplemented
25C2×C4⋊Dic15C2211yescharacteristic, complemented
26C2×C4×Dic15C2211yescharacteristic, complemented
27C2×C5×#217C2212yescomplemented
28C2×C5×#217C2212yescomplemented
29C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
30C2×C4×C5×Dic3C2211yescharacteristic, complemented
31D5×#217—28no—
32C2×#6665C2211yescharacteristic
33C2×#6665C2212yes—
34C2×#6665C2211yescharacteristic
35C2×#6665C2212yescomplemented
36C2×#6665C2212yescomplemented
37#91434—24no—
38Dic3×D20—24no—
39#90994C2211yescharacteristic, complemented
40#90994C2211yescharacteristic, complemented
41#90994C2212yescomplemented
42D4×#217—51nomaximal, Hall
43C22×D4×D5D311yescharacteristic
44C2×#4039—31no—
45C2×D5×C22⋊C4—32no—
46C2×C4×D20—31no—
47C5×#390—31no—
48#65510—31no—
49#65276—31no—
50#65245—32no—
51#65245—32no—
52#65244—32no—
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×D4—22no—
65C2×C3×C5×D4—22no—
66C2×C3×C5×D4C2×C414yescomplemented
67C22×C3×C4×C5C2311yescharacteristic
68C22×Dic15C2312yes—
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2311yescharacteristic
71C22×C5×Dic3C2311yescharacteristic
72C22×C5×Dic3C2312yes—
73C22×C5×Dic3C2311yescharacteristic
74C2×C3×C22⋊D5—24no—
75C2×C3×C22⋊D5—24no—
76C2×C3×C22⋊D5C2×C418yescomplemented
77C22×C3×Dic5C2311yescharacteristic
78C3×D4×D5—232no—
79C2×C3×D20C2×C414yes—
80C2×C3×D20D414yes—
81C2×C3×D20D414yes—
82C2×C3×C4×D5—22no—
83C2×C3×C4×D5—22no—
84C2×C3×C4×D5C2×C414yescomplemented
85C2×D5×Dic3—24no—
86C2×D5×Dic3—24no—
87C2×D5×Dic3—24no—
88C2×D5×Dic3—24no—
89C2×D5×Dic3—42no—
90C2×D5×Dic3—42no—
91#6719—24no—
92#6719—42no—
93C4⋊Dic15—22no—
94C4×Dic15—22no—
95C5×#217—24no—
96C5×#217—42no—
97C5×C4⋊Dic3—22no—
98C4×C5×Dic3—22no—
99#6665—24no—
100#6665—24no—
101#6665—24no—
102#6665—22no—
103#6665D414yescomplemented
104C23×C3×D4—51no—
105C22×#217—52no—
106C2×D4×Dic3—51no—
107C2×D4×Dic3—51no—
108#5247—52no—
109#5221—51no—
110#5221D511yescharacteristic, complemented
111#5220—52no—
112#5220—52no—
113#5212—51no—
114C4×#217—51no—
115C24×D5C2×D312yes—
116C22×C5×D4C2×D311yescharacteristic
117C22×C22⋊D5C2×D312yes—
118C2×D4×D5—24no—
119C2×D4×D5—24no—
120C2×D4×D5Dic318yescomplemented
121C22×D20C2×D311yescharacteristic
122C22×C4×D5—32no—
123C22×C4×D5—32no—
124C22×C4×D5C2×D311yescharacteristic
125C2×C5×C4⋊C4—31no—
126C2×C5×C22⋊C4—32no—
127C2×C5×C22⋊C4—32no—
128C2×C42×C5—31no—
129C2×C22⋊Dic5—32no—
130C2×C22⋊Dic5—32no—
131C2×#685—31no—
132C2×#685—32no—
133C2×#685—32no—
134C2×#685—32no—
135C2×#685—31no—
136C2×C4⋊Dic5—31no—
137C2×C4×Dic5—31no—
138#4039—64no—
139D5×C22⋊C4—68no—
140C4×D20—64no—
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×C5—22no—
150C23×C3×C5—22no—
151C23×C3×C5C22×C414yes—
152C23×C3×C5C2411yescharacteristic
153C22×C3×D5—22no—
154C22×C3×D5—21no—
155C22×C3×D5—21no—
156C22×C3×D5—22no—
157C22×C3×D5—22no—
158C22×C3×D5—22no—
159C22×C3×D5—21no—
160C22×C3×D5—21no—
161C22×C3×D5—216no—
162C22×C3×D5—216no—
163C22×C3×D5—48no—
164C22×C3×D5—48no—
165C22×C3×D5—48no—
166C22×C3×D5—48no—
167C22×C3×D5—48no—
168C22×C3×D5C22×C414yes—
169C22×C3×D5C22×C412yes—
170C22×C3×D5C2×D414yes—
171C22×C3×D5C2×D414yes—
172C22×C3×D5C2×D412yes—
173C22×C3×D5#4112yes—
174C3×C5×D4—28no—
175C2×C3×C4×C5C22×C412yes—
176C2×C3×C4×C5C2×D412yes—
177C2×C3×C4×C5C2×D412yes—
178C2×Dic15—21no—
179C2×Dic15—21no—
180C2×Dic15—21no—
181C2×Dic15—22no—
182C2×Dic15—22no—
183C2×Dic15—21no—
184C2×Dic15—21no—
185C2×Dic15—22no—
186C2×Dic15C2×D412yescomplemented
187C2×C5×Dic3—21no—
188C2×C5×Dic3—21no—
189C2×C5×Dic3—21no—
190C2×C5×Dic3—22no—
191C2×C5×Dic3—22no—
192C2×C5×Dic3—21no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—22no—
195C2×C5×Dic3C2×D412yescomplemented
196C3×C22⋊D5—216no—
197C2×C3×Dic5—21no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5C22×C412yes—
200C3×D20C22⋊C4116yescomplemented
201C3×C4×D5—28no—
202D5×Dic3—48no—
203D5×Dic3—48no—
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×Dic3—52no—
214C2×#217—51no—
215C2×#217—52no—
216C2×#217—51no—
217C2×#217—52no—
218C2×#217—52no—
219C2×#217—52no—
220C2×#217—52no—
221C2×#217—108no—
222C2×#217C2×D512yescomplemented
223C2×#217C2×D512yescomplemented
224D4×Dic3—104no—
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×D311yescharacteristic
242C23×D5C22×D312yes—
243C2×C5×D4—22no—
244C2×C5×D4—22no—
245C2×C5×D4C2×Dic314yescomplemented
246C22×C4×C5—31no—
247C22×C4×C5—31no—
248C22×C4×C5—32no—
249C22×C4×C5C22×D311yescharacteristic
250C2×C22⋊D5—24no—
251C2×C22⋊D5—24no—
252C2×C22⋊D5C2×Dic318yescomplemented
253C22×Dic5—31no—
254C22×Dic5—32no—
255C22×Dic5—31no—
256C22×Dic5C22×D311yescharacteristic
257D4×D5—232no—
258C2×D20C2×Dic314yes—
259C2×D20#6714yes—
260C2×D20#6714yes—
261C2×C4×D5—22no—
262C2×C4×D5—22no—
263C2×C4×D5—64no—
264C2×C4×D5—64no—
265C2×C4×D5—64no—
266C2×C4×D5—64no—
267C2×C4×D5—122no—
268C2×C4×D5—122no—
269C2×C4×D5C2×Dic314yescomplemented
270C5×C4⋊C4—62no—
271C5×C22⋊C4—64no—
272C5×C22⋊C4—122no—
273C42×C5—62no—
274C22⋊Dic5—64no—
275C22⋊Dic5—122no—
276#685—34no—
277#685—64no—
278#685—62no—
279#685—64no—
280#685—64no—
281C4⋊Dic5—62no—
282C4×Dic5—62no—
283C23×D4—51no—
284C2×C4×D4—151no—
285C2×C4×D4—151no—
286C22×C22⋊C4—152no—
287#390—31no—
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—42no—
298C22×C3×C5—42no—
299C22×C3×C5—42no—
300C22×C3×C5—42no—
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—24no—
310C2×C3×D5—22no—
311C2×C3×D5—24no—
312C2×C3×D5—24no—
313C2×C3×D5—24no—
314C2×C3×D5—22no—
315C2×C3×D5—22no—
316C2×C3×D5—22no—
317C2×C3×D5—22no—
318C2×C3×D5—24no—
319C2×C3×D5—24no—
320C2×C3×D5—432no—
321C2×C3×D5C2×C22⋊C418yescomplemented
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—22no—
342C2×C3×D4—22no—
343C2×C3×D4—58no—
344C2×C3×D4—54no—
345C2×C3×D4—54no—
346C2×C3×D4—54no—
347C2×C3×D4—1032no—
348C2×C3×D4—104no—
349C2×C3×D4—104no—
350C2×C3×D4C4×D514yescomplemented
351C22×C3×C4—51no—
352C22×C3×C4—54no—
353C22×C3×C4—102no—
354C22×C3×C4—102no—
355C22×C3×C4C22×D511yescharacteristic
356C22×Dic3—51no—
357C22×Dic3—51no—
358C22×Dic3—52no—
359C22×Dic3—104no—
360C22×Dic3—104no—
361C22×Dic3—104no—
362C22×Dic3—104no—
363C22×Dic3—202no—
364C22×Dic3—202no—
365C22×Dic3C22×D511yescharacteristic
366C22×Dic3C22×D512yes—
367C22×Dic3C22×D511yescharacteristic
368#217—24no—
369#217—42no—
370#217—54no—
371#217—104no—
372#217—104no—
373#217—102no—
374#217—104no—
375#217—104no—
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×C5—22no—
386C23×C5—22no—
387C23×C5C22×Dic314yes—
388C23×C5C23×D311yescharacteristic
389C22×D5—22no—
390C22×D5—22no—
391C22×D5—22no—
392C22×D5—22no—
393C22×D5—21no—
394C22×D5—21no—
395C22×D5—21no—
396C22×D5—21no—
397C22×D5—216no—
398C22×D5—216no—
399C22×D5—48no—
400C22×D5—48no—
401C22×D5—48no—
402C22×D5—48no—
403C22×D5—48no—
404C22×D5D3×D412yes—
405C22×D5#23712yes—
406C22×D5C22×Dic312yes—
407C22×D5C22×Dic314yes—
408C22×D5C2×#6714yes—
409C22×D5C2×#6714yes—
410C5×D4—28no—
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×C5C22×Dic312yes—
421C2×C4×C5C2×#6712yes—
422C2×C4×C5C2×#6712yes—
423C22⋊D5—216no—
424C2×Dic5—21no—
425C2×Dic5—21no—
426C2×Dic5—32no—
427C2×Dic5—61no—
428C2×Dic5—61no—
429C2×Dic5—62no—
430C2×Dic5—61no—
431C2×Dic5—61no—
432C2×Dic5—62no—
433C2×Dic5—61no—
434C2×Dic5—62no—
435C2×Dic5C22×Dic312yes—
436D20#217116yescomplemented
437C4×D5—28no—
438C4×D5—128no—
439C4×D5—128no—
440C25—52no—
441C22×D4—52no—
442C22×D4—58no—
443C22×D4—51no—
444C22×D4—104no—
445C22×D4—104no—
446C22×D4D3×D511yescharacteristic
447C23×C4—51no—
448C23×C4—152no—
449C23×C4—152no—
450C4×D4—304no—
451C4×D4—304no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—151no—
454C2×C22⋊C4—32no—
455C2×C22⋊C4—32no—
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—151no—
466#95—151no—
467#95—151no—
468#95—152no—
469C2×C3×C5—44no—
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—28no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—52no—
486C23×C3—54no—
487C23×C3—52no—
488C23×C3—54no—
489C23×C3—54no—
490C23×C3—52no—
491C23×C3—1016no—
492C23×C3—1016no—
493C23×C3—102no—
494C23×C3—101no—
495C23×C3—101no—
496C23×C3—102no—
497C23×C3—101no—
498C23×C3—102no—
499C23×C3—102no—
500C23×C3—101no—
501C23×C3—208no—
502C23×C3—208no—
503C23×C3—208no—
504C23×C3—208no—
505C23×C3—208no—
506C23×C3C2×C4×D514yes—
507C23×C3C23×D511yescharacteristic
508C3×D4—28no—
509C3×D4—516no—
510C3×D4—1016no—
511C2×C3×C4—52no—
512C2×C3×C4—101no—
513C2×C3×C4—101no—
514C2×C3×C4—108no—
515C2×C3×C4C2×C4×D512yes—
516C2×C3×C4D4×D512yes—
517C2×C3×C4D4×D512yes—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—21no—
524C2×Dic3—22no—
525C2×Dic3—21no—
526C2×Dic3—52no—
527C2×Dic3—101no—
528C2×Dic3—101no—
529C2×Dic3—101no—
530C2×Dic3—102no—
531C2×Dic3—102no—
532C2×Dic3—101no—
533C2×Dic3—101no—
534C2×Dic3—102no—
535C2×Dic3—208no—
536C2×Dic3—208no—
537C2×Dic3D4×D512yescomplemented
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—24no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5C2×D3×D411yescharacteristic
546C22×C5C2×#23711yescharacteristic
547C22×C5#100411yescharacteristic
548C22×C5#100411yescharacteristic
549C22×C5C23×Dic311yescharacteristic
550C22×C5C22×#6711yescharacteristic
551C22×C5C22×#6711yescharacteristic
552C2×D5—24no—
553C2×D5—22no—
554C2×D5—24no—
555C2×D5—24no—
556C2×D5—24no—
557C2×D5—22no—
558C2×D5—22no—
559C2×D5—22no—
560C2×D5—22no—
561C2×D5—24no—
562C2×D5—24no—
563C2×D5—22no—
564C2×D5—432no—
565C2×D5D4×Dic314yescomplemented
566C2×D5C2×#21718yescomplemented
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—22no—
586C2×D4—22no—
587C2×D4—58no—
588C2×D4—54no—
589C2×D4—54no—
590C2×D4—54no—
591C2×D4—1032no—
592C2×D4—104no—
593C2×D4—104no—
594C2×D4D5×Dic314yescomplemented
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—32no—
598C22×C4—51no—
599C22×C4—54no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—151no—
603C22×C4—151no—
604C22×C4—152no—
605C22×C4—304no—
606C22×C4—304no—
607C22×C4—304no—
608C22×C4—304no—
609C22×C4—602no—
610C22×C4—602no—
611C22×C4C2×D3×D511yescharacteristic
612C4⋊C4—62no—
613C4⋊C4—302no—
614C22⋊C4—64no—
615C22⋊C4—122no—
616C22⋊C4—154no—
617C22⋊C4—304no—
618C22⋊C4—304no—
619C22⋊C4—304no—
620C22⋊C4—302no—
621C22⋊C4—304no—
622C22⋊C4—602no—
623C42—62no—
624C42—302no—
625C3×C5D4×C22⋊C411yescharacteristic, complemented, Hall
626C22×C3—24no—
627C22×C3—24no—
628C22×C3—24no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—42no—
633C22×C3—58no—
634C22×C3—54no—
635C22×C3—104no—
636C22×C3—102no—
637C22×C3—102no—
638C22×C3—104no—
639C22×C3—104no—
640C22×C3—102no—
641C22×C3—104no—
642C22×C3—102no—
643C22×C3—104no—
644C22×C3—102no—
645C22×C3—104no—
646C22×C3—102no—
647C22×C3—2032no—
648C22×C3C22×C4×D511yescharacteristic
649C22×C3C2×D4×D511yescharacteristic
650C22×C3C2×D4×D511yescharacteristic
651C22×C3C2×D4×D511yescharacteristic
652C22×C3#414411yescharacteristic
653C22×C3D5×#4111yescharacteristic
654C22×C3#414911yescharacteristic
655C3×C4—102no—
656C3×C4D5×C22⋊C414yescomplemented
657Dic3—22no—
658Dic3—42no—
659Dic3—41no—
660Dic3—102no—
661Dic3—202no—
662Dic3—201no—
663C2×C5—44no—
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—28no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—52no—
680C23—52no—
681C23—52no—
682C23—54no—
683C23—54no—
684C23—54no—
685C23—1016no—
686C23—1016no—
687C23—102no—
688C23—102no—
689C23—102no—
690C23—101no—
691C23—102no—
692C23—101no—
693C23—101no—
694C23—101no—
695C23—208no—
696C23—208no—
697C23—208no—
698C23—208no—
699C23—208no—
700C23C2×D5×Dic314yes—
701C23C22×D3×D511yescharacteristic
702D4—28no—
703D4—516no—
704D4—1016no—
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—108no—
718C2×C4—152no—
719C2×C4—301no—
720C2×C4—301no—
721C2×C4—302no—
722C2×C4—301no—
723C2×C4—301no—
724C2×C4—302no—
725C2×C4—301no—
726C2×C4—302no—
727C2×C4—608no—
728C2×C4—608no—
729C2×C4C2×D5×Dic312yes—
730C2×C4D5×#6712yes—
731C2×C4D5×#6712yes—
732C2×C3—44no—
733C2×C3—104no—
734C2×C3—108no—
735C2×C3C2×D5×C22⋊C411yescharacteristic
736C2×C3C4×D4×D511yescharacteristic
737C2×C3#6587911yescharacteristic
738C2×C3#6594311yescharacteristic
739C2×C3#6594611yescharacteristic
740C2×C3#6601011yescharacteristic
741C2×C3#6605111yescharacteristic
742C5D4×#21711yescharacteristic, complemented, Sylow
743C22—24no—
744C22—24no—
745C22—24no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—54no—
751C22—58no—
752C22—104no—
753C22—104no—
754C22—102no—
755C22—104no—
756C22—102no—
757C22—102no—
758C22—102no—
759C22—104no—
760C22—102no—
761C22—104no—
762C22—102no—
763C22—104no—
764C22—2032no—
765C22D3×D4×D511yescharacteristic
766C22D5×#23711yescharacteristic
767C22#9202511yescharacteristic
768C22#9202611yescharacteristic
769C22C22×D5×Dic311yescharacteristic
770C22C2×D5×#6711yescharacteristic
771C22C2×D5×#6711yescharacteristic
772C4—62no—
773C4—102no—
774C4—122no—
775C4—121no—
776C4—302no—
777C4—602no—
778C4—601no—
779C4D5×#21714yescomplemented
780C3#1060816211yescharacteristic, complemented, Sylow
781C2—44no—
782C2—104no—
783C2—108no—
784C2D4×D5×Dic311yescharacteristic
785C2#1175491011yescharacteristic
786C2#1175493011yescharacteristic
787C2#1175493111yescharacteristic
788C2#1175503311yescharacteristic
789C2#1175504011yescharacteristic
790C2C2×D5×#21711yescharacteristic
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×D5×#217C2semidirect
3. C2×#91434C2semidirect
4. C2×Dic3×D20C2semidirect
5. #11751322C2semidirect
6. C5×#5221C2semidirect
7. #11749518C2semidirect
8. #11749518C2semidirect
9. #11749488C2semidirect
10. #11748759C2semidirect
11. C4×#6665C2semidirect
18. C2×C3×D4×D5C4semidirect
21. C22×D5×Dic3C22semidirect
22. C22×D5×Dic3C22semidirect
23. C2×#6719C22semidirect
24. C2×#6719C22semidirect
25. C2×C4⋊Dic15C22semidirect
26. C2×C4×Dic15C22semidirect
27. C2×C5×#217C22semidirect
28. C2×C5×#217C22semidirect
29. C2×C5×C4⋊Dic3C22semidirect
30. C2×C4×C5×Dic3C22semidirect
35. C2×#6665C22semidirect
36. C2×#6665C22semidirect
39. #90994C22semidirect
40. #90994C22semidirect
41. #90994C22semidirect
61. C23×C3×D5C2×C4semidirect
66. C2×C3×C5×D4C2×C4semidirect
76. C2×C3×C22⋊D5C2×C4semidirect
84. C2×C3×C4×D5C2×C4semidirect
103. #6665D4semidirect
110. #5221D5semidirect
120. C2×D4×D5Dic3semidirect
186. C2×Dic15C2×D4semidirect
195. C2×C5×Dic3C2×D4semidirect
200. C3×D20C22⋊C4semidirect
222. C2×#217C2×D5semidirect
223. C2×#217C2×D5semidirect
227. C2×C4⋊Dic3C2×D5semidirect
229. C2×C4×Dic3C2×D5semidirect
240. C23×D5C2×Dic3semidirect
245. C2×C5×D4C2×Dic3semidirect
252. C2×C22⋊D5C2×Dic3semidirect
269. C2×C4×D5C2×Dic3semidirect
321. C2×C3×D5C2×C22⋊C4semidirect
322. C2×C3×D5C4×D4semidirect
323. C3×C4×C5C2×C22⋊C4semidirect
350. C2×C3×D4C4×D5semidirect
436. D20#217semidirect
537. C2×Dic3D4×D5semidirect
565. C2×D5D4×Dic3semidirect
566. C2×D5C2×#217semidirect
570. C4×C5C2×#217semidirect
594. C2×D4D5×Dic3semidirect
625. C3×C5D4×C22⋊C4semidirect
656. C3×C4D5×C22⋊C4semidirect
742. C5D4×#217semidirect
779. C4D5×#217semidirect
780. C3#10608162semidirect

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×D5×#2172
C2×#914342
C2×Dic3×D202
#117513222
C5×#52212
#117495182
#117494882
#117487592
C4×#66652
#106081623
D4×#2175