Finite Group Databasebeta

← C4×#65246 #12020484

Subgroups — C4×#65246 #12020484

Order 1280.

2894 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D5C211yesmaximal, characteristic
2C2×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
4C2×#65246C212yesmaximal
5C2×C4×#683C211yesmaximal, characteristic, complemented
6C2×C4×#685C211yesmaximal, characteristic, complemented
7C2×C4×#685C211yesmaximal, characteristic, complemented
8C2×C42×Dic5C211yesmaximal, characteristic, complemented
9#10602338C212yesmaximal, complemented
10#10600201C212yesmaximal, complemented
11#10600197C212yesmaximal, complemented
12C24×C4×C5C2211yescharacteristic
13C23×C22⋊D5C2211yescharacteristic
14C23×C4×D5C2211yescharacteristic
15C22×C5×C22⋊C4C2212yes—
16C22×C42×C5C2211yescharacteristic
17C22×C42×C5C2211yescharacteristic
18C22×C22⋊Dic5C2211yescharacteristic
19C22×C22⋊Dic5C2212yes—
20C2×C4×C22⋊D5—24no—
21C2×C4×C22⋊D5—24no—
22C2×C4×C22⋊D5C418yescomplemented
23C22×#685C2211yescharacteristic
24C22×#685C2212yes—
25C22×#685C2212yes—
26C22×#683C2211yescharacteristic
27C22×#683C2212yes—
28C22×C4×Dic5C2212yes—
29C22×C4×Dic5C2211yescharacteristic
30C22×C4×Dic5C2212yes—
31C22×C4×Dic5C2211yescharacteristic
32C22×C4×Dic5C2211yescharacteristic
33C4×C5×C22⋊C4—24no—
34C2×C5×#95C2212yes—
35C4×C22⋊Dic5—24no—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39C2×#3963C2212yes—
40#65246C4116yesdirect product factor
41C4×#685—24no—
42C4×#685—24no—
43C4×#683—24no—
44C42×Dic5—24no—
45C4×#390—51nomaximal, Sylow
46C25×C5C2311yescharacteristic
47C24×D5C2311yescharacteristic
48C23×C4×C5—22no—
49C23×C4×C5—22no—
50C23×C4×C5—22no—
51C23×C4×C5—22no—
52C23×C4×C5—22no—
53C23×C4×C5—22no—
54C23×C4×C5C2×C414yes—
55C23×C4×C5C2311yescharacteristic
56C23×C4×C5C2312yes—
57C23×C4×C5C2312yes—
58C23×C4×C5C2311yescharacteristic
59C22×C22⋊D5—22no—
60C22×C22⋊D5—22no—
61C22×C22⋊D5—24no—
62C22×C22⋊D5C2×C414yes—
63C22×C22⋊D5C2×C418yes—
64C23×Dic5C2312yes—
65C23×Dic5C2311yescharacteristic
66C23×Dic5C2311yescharacteristic
67C23×Dic5C2312yes—
68C23×Dic5C2311yescharacteristic
69C22×C4×D5—22no—
70C22×C4×D5—22no—
71C22×C4×D5—22no—
72C22×C4×D5—22no—
73C22×C4×D5—22no—
74C22×C4×D5—22no—
75C22×C4×D5C2×C414yes—
76C2×C5×C22⋊C4—24no—
77C2×C5×C22⋊C4—24no—
78C2×C5×C22⋊C4C2×C418yescomplemented
79C2×C42×C5—22no—
80C2×C42×C5—22no—
81C2×C42×C5—22no—
82C2×C42×C5—22no—
83C2×C42×C5—22no—
84C2×C42×C5D414yescomplemented
85C2×C22⋊Dic5—22no—
86C2×C22⋊Dic5—22no—
87C2×C22⋊Dic5—24no—
88C2×C22⋊Dic5—24no—
89C2×C22⋊Dic5C2×C414yes—
90C2×C22⋊Dic5C2×C418yescomplemented
91C4×C22⋊D5—232no—
92C2×#685—24no—
93C2×#685—24no—
94C2×#685—22no—
95C2×#685—22no—
96C2×#685—24no—
97C2×#685—24no—
98C2×#685C2×C414yes—
99C2×#685C2×C418yescomplemented
100C2×#685C2×C418yescomplemented
101C2×#683—22no—
102C2×#683—22no—
103C2×#683—24no—
104C2×#683—24no—
105C2×#683C2×C414yes—
106C2×#683C2×C418yescomplemented
107C2×C4×Dic5—22no—
108C2×C4×Dic5—24no—
109C2×C4×Dic5—22no—
110C2×C4×Dic5—24no—
111C2×C4×Dic5—24no—
112C2×C4×Dic5—24no—
113C2×C4×Dic5—24no—
114C2×C4×Dic5—22no—
115C2×C4×Dic5—22no—
116C2×C4×Dic5—22no—
117C2×C4×Dic5C2×C414yes—
118C2×C4×Dic5C2×C418yescomplemented
119C2×C4×Dic5D414yes—
120C2×C4×Dic5D414yes—
121C2×C4×Dic5D414yescomplemented
122C5×#95—24no—
123#3963—24no—
124#3963—24no—
125#3963—24no—
126#3963—24no—
127C22×C4×D4—51no—
128C2×#390—52no—
129C2×C4×C4⋊C4—51no—
130C2×C4×C22⋊C4—51no—
131C2×C4×C22⋊C4—51no—
132C2×C4×C22⋊C4—51no—
133C2×C4×C22⋊C4D511yescharacteristic, complemented
134C2×C43—51no—
135#1437—52no—
136#1437—52no—
137C4⋊#95—52no—
138C24×C5—21no—
139C24×C5—21no—
140C24×C5—21no—
141C24×C5—21no—
142C24×C5—22no—
143C24×C5—22no—
144C24×C5—22no—
145C24×C5—21no—
146C24×C5—21no—
147C24×C5C22×C412yes—
148C24×C5C22×C414yes—
149C24×C5C2411yescharacteristic
150C23×D5—21no—
151C23×D5—21no—
152C23×D5—21no—
153C23×D5—21no—
154C23×D5—21no—
155C23×D5—21no—
156C23×D5—22no—
157C23×D5—22no—
158C23×D5—22no—
159C23×D5C22×C412yes—
160C23×D5C22×C414yes—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—22no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—28no—
178C22×C4×C5—28no—
179C22×C4×C5—28no—
180C22×C4×C5—44no—
181C22×C4×C5—44no—
182C22×C4×C5—44no—
183C22×C4×C5—44no—
184C22×C4×C5C22×C414yes—
185C22×C4×C5C22×C412yes—
186C22×C4×C5C22×C414yes—
187C22×C4×C5C22×C412yes—
188C22×C4×C5C2×D412yes—
189C22×C4×C5C2×D412yes—
190C22×C4×C5C2×D412yes—
191C22×C4×C5C2×D414yes—
192C22×C4×C5C2×D412yes—
193C22×C4×C5#4114yes—
194C22×C4×C5#4112yes—
195C22×C4×C5#4112yes—
196C2×C22⋊D5—28no—
197C2×C22⋊D5—28no—
198C2×C22⋊D5—216no—
199C2×C22⋊D5—216no—
200C2×C22⋊D5C42116yescomplemented
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5—22no—
207C22×Dic5—21no—
208C22×Dic5—21no—
209C22×Dic5—22no—
210C22×Dic5—21no—
211C22×Dic5—21no—
212C22×Dic5—22no—
213C22×Dic5—22no—
214C22×Dic5—22no—
215C22×Dic5—21no—
216C22×Dic5—21no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5C22×C412yes—
220C22×Dic5C22×C414yes—
221C22×Dic5C22×C412yes—
222C22×Dic5C22×C414yes—
223C22×Dic5C22×C412yes—
224C22×Dic5C22×C414yes—
225C22×Dic5C2×D412yes—
226C22×Dic5C2×D412yes—
227C22×Dic5C2×D414yes—
228C22×Dic5C2×D412yes—
229C22×Dic5C2×D412yes—
230C22×Dic5#4114yes—
231C22×Dic5#4114yes—
232C2×C4×D5—28no—
233C2×C4×D5—28no—
234C2×C4×D5—28no—
235C2×C4×D5—44no—
236C2×C4×D5—44no—
237C2×C4×D5—44no—
238C2×C4×D5—44no—
239C5×C22⋊C4—216no—
240C42×C5—28no—
241C42×C5—44no—
242C22⋊Dic5—28no—
243C22⋊Dic5—216no—
244#685—216no—
245#685—28no—
246#685—216no—
247#683—28no—
248#683—216no—
249C4×Dic5—216no—
250C4×Dic5—28no—
251C4×Dic5—216no—
252C4×Dic5—44no—
253C4×Dic5C22⋊C4116yescomplemented
254C23×D4—51no—
255C24×C4—51no—
256C24×C4C2×D511yescharacteristic
257C2×C4×D4—58no—
258C2×C4×D4—104no—
259C2×C4×D4—104no—
260C22×C4⋊C4—51no—
261C22×C4⋊C4—52no—
262C22×C22⋊C4—51no—
263C22×C22⋊C4—52no—
264C22×C22⋊C4—51no—
265C22×C22⋊C4—52no—
266C22×C22⋊C4—52no—
267C22×C22⋊C4C2×D512yes—
268C22×C42—51no—
269C22×C42—52no—
270C22×C42—51no—
271C22×C42—52no—
272C22×C42—51no—
273C22×C42C2×D511yescharacteristic
274C22×C42C2×D511yescharacteristic
275#390—516no—
276C4×C4⋊C4—104no—
277C4×C22⋊C4—24no—
278C4×C22⋊C4—104no—
279C4×C22⋊C4—104no—
280C4×C22⋊C4—104no—
281C2×#95—52no—
282C2×#95—52no—
283C2×#95—52no—
284C2×#95—52no—
285C2×#95C2×D512yes—
286C43—104no—
287C23×C5—22no—
288C23×C5—22no—
289C23×C5—24no—
290C23×C5—24no—
291C23×C5—24no—
292C23×C5—24no—
293C23×C5—22no—
294C23×C5—22no—
295C23×C5—22no—
296C23×C5—24no—
297C23×C5—22no—
298C23×C5—24no—
299C23×C5—41no—
300C23×C5—41no—
301C23×C5—42no—
302C23×C5—41no—
303C23×C5—42no—
304C23×C5—42no—
305C23×C5—41no—
306C23×C5—42no—
307C23×C5—42no—
308C23×C5—42no—
309C23×C5C2×C4214yes—
310C23×C5C23×C411yescharacteristic
311C23×C5C23×C412yes—
312C23×C5C22×D411yescharacteristic
313C23×C5C22×D411yescharacteristic
314C23×C5C22×D411yescharacteristic
315C23×C5C22×D411yescharacteristic
316C23×C5C2×#4111yescharacteristic
317C23×C5C2×#4112yes—
318C23×C5C2×#4111yescharacteristic
319C23×C5C2×#4112yes—
320C23×C5C2×#4112yes—
321C22×D5—22no—
322C22×D5—22no—
323C22×D5—24no—
324C22×D5—24no—
325C22×D5—22no—
326C22×D5—22no—
327C22×D5—24no—
328C22×D5—24no—
329C22×D5—22no—
330C22×D5—24no—
331C22×D5—22no—
332C22×D5—24no—
333C22×D5—41no—
334C22×D5—41no—
335C22×D5—42no—
336C22×D5—41no—
337C22×D5—42no—
338C22×D5—42no—
339C22×D5—41no—
340C22×D5—42no—
341C22×D5—42no—
342C22×D5—42no—
343C22×D5C2×C4214yes—
344C2×C4×C5—24no—
345C2×C4×C5—24no—
346C2×C4×C5—24no—
347C2×C4×C5—24no—
348C2×C4×C5—24no—
349C2×C4×C5—24no—
350C2×C4×C5—22no—
351C2×C4×C5—24no—
352C2×C4×C5—24no—
353C2×C4×C5—24no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—42no—
360C2×C4×C5—41no—
361C2×C4×C5—42no—
362C2×C4×C5—42no—
363C2×C4×C5—42no—
364C2×C4×C5—416no—
365C2×C4×C5C2×C22⋊C414yes—
366C2×C4×C5C4×D414yes—
367C2×C4×C5C4×D414yes—
368C2×C4×C5C4×D418yescomplemented
369C2×C4×C5#12114yes—
370C2×C4×C5#12114yes—
371C2×C4×C5#12414yes—
372C2×C4×C5#12714yes—
373C22⋊D5—232no—
374C2×Dic5—24no—
375C2×Dic5—22no—
376C2×Dic5—24no—
377C2×Dic5—22no—
378C2×Dic5—24no—
379C2×Dic5—24no—
380C2×Dic5—24no—
381C2×Dic5—24no—
382C2×Dic5—24no—
383C2×Dic5—24no—
384C2×Dic5—22no—
385C2×Dic5—24no—
386C2×Dic5—24no—
387C2×Dic5—24no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—41no—
391C2×Dic5—41no—
392C2×Dic5—41no—
393C2×Dic5—42no—
394C2×Dic5—41no—
395C2×Dic5—42no—
396C2×Dic5—42no—
397C2×Dic5—42no—
398C2×Dic5C2×C4214yes—
399C2×Dic5C2×C22⋊C414yes—
400C2×Dic5C2×C22⋊C414yes—
401C2×Dic5#11714yes—
402C2×Dic5C4×D418yes—
403C2×Dic5C4×D418yes—
404C2×Dic5C4×D418yescomplemented
405C4×D5—416no—
406C25—51no—
407C25C22×D511yescharacteristic
408C22×D4—54no—
409C22×D4—58no—
410C22×D4—102no—
411C22×D4—102no—
412C22×D4—104no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—22no—
419C23×C4—51no—
420C23×C4—51no—
421C23×C4—52no—
422C23×C4—52no—
423C23×C4—51no—
424C23×C4—54no—
425C23×C4—102no—
426C23×C4—102no—
427C23×C4—102no—
428C23×C4—102no—
429C23×C4—102no—
430C23×C4—102no—
431C23×C4C4×D514yes—
432C23×C4C22×D512yes—
433C23×C4C22×D511yescharacteristic
434C23×C4C22×D512yes—
435C23×C4C22×D511yescharacteristic
436C4×D4—1032no—
437C2×C4⋊C4—54no—
438C2×C4⋊C4—58no—
439C2×C4⋊C4—102no—
440C2×C4⋊C4—102no—
441C2×C4⋊C4—104no—
442C2×C4⋊C4—104no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—54no—
446C2×C22⋊C4—58no—
447C2×C22⋊C4—54no—
448C2×C22⋊C4—58no—
449C2×C22⋊C4—58no—
450C2×C22⋊C4—102no—
451C2×C22⋊C4—102no—
452C2×C22⋊C4—104no—
453C2×C22⋊C4—104no—
454C2×C22⋊C4—104no—
455C2×C22⋊C4—102no—
456C2×C22⋊C4—102no—
457C2×C22⋊C4—104no—
458C2×C22⋊C4—104no—
459C2×C22⋊C4—104no—
460C2×C22⋊C4C4×D518yescomplemented
461C2×C42—22no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—54no—
467C2×C42—54no—
468C2×C42—54no—
469C2×C42—58no—
470C2×C42—54no—
471C2×C42—104no—
472C2×C42—104no—
473C2×C42—104no—
474C2×C42—104no—
475C2×C42—104no—
476C2×C42—102no—
477C2×C42—102no—
478C2×C42—102no—
479C2×C42—102no—
480C2×C42—102no—
481C2×C42C22⋊D514yescomplemented
482#95—24no—
483#95—104no—
484#95—104no—
485#95—104no—
486#95—104no—
487C22×C5—24no—
488C22×C5—24no—
489C22×C5—24no—
490C22×C5—44no—
491C22×C5—42no—
492C22×C5—42no—
493C22×C5—42no—
494C22×C5—42no—
495C22×C5—44no—
496C22×C5—44no—
497C22×C5—44no—
498C22×C5C22×C4211yescharacteristic
499C22×C5C22×C22⋊C411yescharacteristic
500C22×C5C2×#11711yescharacteristic
501C22×C5C2×C4×D411yescharacteristic
502C22×C5C2×C4×D412yes—
503C22×C5C2×C4×D411yescharacteristic
504C22×C5C2×C4×D412yes—
505C22×C5C2×C4×D412yes—
506C22×C5C2×C4×D412yes—
507C22×C5C4×#4111yescharacteristic
508C22×C5C4×#4112yes—
509C22×C5C4×#4111yescharacteristic
510C22×C5C4×#4112yes—
511C22×C5C2×#12111yescharacteristic
512C22×C5C2×#12111yescharacteristic
513C22×C5#52512yes—
514C22×C5C2×#12411yescharacteristic
515C22×C5#52912yes—
516C22×C5#52912yes—
517C22×C5C2×#12711yescharacteristic
518C22×C5#53212yes—
519C22×C5#53212yes—
520C22×C5#53212yes—
521C2×D5—24no—
522C2×D5—24no—
523C2×D5—24no—
524C2×D5—44no—
525C2×D5—42no—
526C2×D5—42no—
527C2×D5—42no—
528C2×D5—42no—
529C2×D5—44no—
530C2×D5—44no—
531C2×D5—44no—
532C4×C5—28no—
533C4×C5—44no—
534C4×C5—42no—
535C4×C5#39018yescomplemented
536Dic5—24no—
537Dic5—28no—
538Dic5—44no—
539Dic5—42no—
540Dic5C4×C22⋊C418yescomplemented
541C24—22no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—22no—
548C24—22no—
549C24—21no—
550C24—54no—
551C24—52no—
552C24—102no—
553C24—101no—
554C24—101no—
555C24—101no—
556C24—101no—
557C24—101no—
558C24—102no—
559C24—102no—
560C24—101no—
561C24C2×C4×D514yes—
562C24C2×C4×D512yes—
563C24C23×D511yescharacteristic
564C2×D4—516no—
565C2×D4—108no—
566C2×D4—108no—
567C2×D4—1016no—
568C2×D4—1016no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—28no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—52no—
593C22×C4—54no—
594C22×C4—52no—
595C22×C4—52no—
596C22×C4—54no—
597C22×C4—52no—
598C22×C4—54no—
599C22×C4—52no—
600C22×C4—54no—
601C22×C4—52no—
602C22×C4—54no—
603C22×C4—54no—
604C22×C4—52no—
605C22×C4—102no—
606C22×C4—102no—
607C22×C4—102no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—102no—
612C22×C4—101no—
613C22×C4—101no—
614C22×C4—102no—
615C22×C4—102no—
616C22×C4—101no—
617C22×C4—101no—
618C22×C4—101no—
619C22×C4—102no—
620C22×C4—102no—
621C22×C4—101no—
622C22×C4—102no—
623C22×C4—108no—
624C22×C4—108no—
625C22×C4—108no—
626C22×C4—204no—
627C22×C4—204no—
628C22×C4—204no—
629C22×C4—204no—
630C22×C4C2×C4×D514yes—
631C22×C4C2×C4×D512yes—
632C22×C4C2×C4×D514yes—
633C22×C4C2×C4×D512yes—
634C22×C4#70914yes—
635C22×C4#70912yes—
636C22×C4D4×D512yes—
637C22×C4D4×D512yes—
638C22×C4D4×D512yes—
639C22×C4#71112yes—
640C22×C4C2×C22⋊D514yes—
641C22×C4C2×C22⋊D512yes—
642C4⋊C4—108no—
643C4⋊C4—1016no—
644C22⋊C4—216no—
645C22⋊C4—108no—
646C22⋊C4—1016no—
647C22⋊C4—108no—
648C22⋊C4—1016no—
649C22⋊C4—1016no—
650C42—28no—
651C42—44no—
652C42—516no—
653C42—1016no—
654C42—1016no—
655C42—108no—
656C42—204no—
657C2×C5—44no—
658C2×C5C2×C4×C22⋊C411yescharacteristic
659C2×C5C42×D411yescharacteristic
660C2×C5C42×D411yescharacteristic
661C2×C5C2×#39011yescharacteristic
662C2×C5#229311yescharacteristic
663C2×C5#229311yescharacteristic
664C2×C5#229711yescharacteristic
665C2×C5C4×#12112yes—
666C2×C5C4×#12112yes—
667C2×C5C4×#12412yes—
668C2×C5C4×#12712yes—
669D5—44no—
670C23—22no—
671C23—24no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—24no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—41no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—41no—
687C23—42no—
688C23—41no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—54no—
693C23—102no—
694C23—104no—
695C23—102no—
696C23—102no—
697C23—102no—
698C23—102no—
699C23—104no—
700C23—102no—
701C23—104no—
702C23—104no—
703C23—104no—
704C23—104no—
705C23—201no—
706C23—201no—
707C23—202no—
708C23—202no—
709C23—201no—
710C23—202no—
711C23—201no—
712C23—202no—
713C23—202no—
714C23—202no—
715C23C42×D514yes—
716C23C22×C4×D511yescharacteristic
717C23C22×C4×D512yes—
718C23C2×#70911yescharacteristic
719C23C2×#70912yes—
720C23C2×D4×D511yescharacteristic
721C23C2×D4×D511yescharacteristic
722C23C2×D4×D511yescharacteristic
723C23C2×#71111yescharacteristic
724C23D5×#4112yes—
725C23D5×#4112yes—
726C23C22×C22⋊D511yescharacteristic
727D4—1032no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—416no—
749C2×C4—54no—
750C2×C4—54no—
751C2×C4—54no—
752C2×C4—58no—
753C2×C4—58no—
754C2×C4—54no—
755C2×C4—58no—
756C2×C4—102no—
757C2×C4—104no—
758C2×C4—104no—
759C2×C4—102no—
760C2×C4—104no—
761C2×C4—104no—
762C2×C4—104no—
763C2×C4—104no—
764C2×C4—104no—
765C2×C4—104no—
766C2×C4—102no—
767C2×C4—102no—
768C2×C4—104no—
769C2×C4—102no—
770C2×C4—104no—
771C2×C4—104no—
772C2×C4—201no—
773C2×C4—201no—
774C2×C4—201no—
775C2×C4—202no—
776C2×C4—201no—
777C2×C4—202no—
778C2×C4—202no—
779C2×C4—202no—
780C2×C4—2016no—
781C2×C4D5×C22⋊C414yes—
782C2×C4#402714yes—
783C2×C4#403014yes—
784C2×C4#403114yes—
785C2×C4C4×C22⋊D514yes—
786C2×C4C4×C22⋊D518yescomplemented
787C2×C4#408514yes—
788C2×C4#408614yes—
789C5C4×#39011yescharacteristic, complemented, Sylow
790C22—24no—
791C22—24no—
792C22—24no—
793C22—44no—
794C22—44no—
795C22—42no—
796C22—42no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—44no—
801C22—104no—
802C22—104no—
803C22—104no—
804C22—204no—
805C22—204no—
806C22—202no—
807C22—202no—
808C22—204no—
809C22—202no—
810C22—202no—
811C22—204no—
812C22C2×C42×D511yescharacteristic
813C22C4×#70911yescharacteristic
814C22C4×#70912yes—
815C22C2×D5×C22⋊C411yescharacteristic
816C22C2×#402711yescharacteristic
817C22C2×#403011yescharacteristic
818C22C2×#403111yescharacteristic
819C22D5×#11711yescharacteristic
820C22#6585611yescharacteristic
821C22#6586212yes—
822C22C4×#71112yes—
823C22#6587212yes—
824C22C4×D4×D512yes—
825C22C4×D4×D512yes—
826C22C4×D4×D512yes—
827C22#6588112yes—
828C22#6588212yes—
829C22#6588212yes—
830C22C2×C4×C22⋊D512yes—
831C22C2×C4×C22⋊D511yescharacteristic
832C22C2×#408511yescharacteristic
833C22C2×#408611yescharacteristic
834C22#6616612yes—
835C4—28no—
836C4—44no—
837C4—42no—
838C4—58no—
839C4—104no—
840C4—108no—
841C4—204no—
842C4—202no—
843C4#6524618yesdirect product factor
844C2—44no—
845C2—204no—
846C2C4×#402711yescharacteristic
847C2#1060517011yescharacteristic
848C2C4×#403112yes—
849C2C4×D5×C22⋊C411yescharacteristic
850C2#1060529411yescharacteristic
851C2C4×#403012yes—
852C2C42×C22⋊D511yescharacteristic
853C2C2×#6524611yescharacteristic
854C2#1061395611yescharacteristic
855C2C4×#408512yes—
856C2C4×#408612yes—
subgroupG/H
centerC23×C4C22×D5
commutatorC22×C5C22×C42
FrattiniC24C23×D5
FittingC2×C4×C5×C22⋊C4C2
socle, cosocleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×C4×C22⋊C4D5
hypocenterC5C4×#390
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C5×C22⋊C4C2semidirect
3. C2×C4×C22⋊Dic5C2semidirect
5. C2×C4×#683C2semidirect
6. C2×C4×#685C2semidirect
7. C2×C4×#685C2semidirect
8. C2×C42×Dic5C2semidirect
9. #10602338C2semidirect
10. #10600201C2semidirect
11. #10600197C2semidirect
22. C2×C4×C22⋊D5C4semidirect
40. #65246C4direct (N × H)
78. C2×C5×C22⋊C4C2×C4semidirect
84. C2×C42×C5D4semidirect
90. C2×C22⋊Dic5C2×C4semidirect
99. C2×#685C2×C4semidirect
100. C2×#685C2×C4semidirect
106. C2×#683C2×C4semidirect
118. C2×C4×Dic5C2×C4semidirect
121. C2×C4×Dic5D4semidirect
133. C2×C4×C22⋊C4D5semidirect
200. C2×C22⋊D5C42semidirect
253. C4×Dic5C22⋊C4semidirect
368. C2×C4×C5C4×D4semidirect
404. C2×Dic5C4×D4semidirect
460. C2×C22⋊C4C4×D5semidirect
481. C2×C42C22⋊D5semidirect
535. C4×C5#390semidirect
540. Dic5C4×C22⋊C4semidirect
786. C2×C4C4×C22⋊D5semidirect
789. C5C4×#390semidirect
843. C4#65246direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D52
C2×C4×C5×C22⋊C42
C2×C4×C22⋊Dic52
C2×#652462
C2×C4×#6832
C2×C4×#6852
C2×C42×Dic52
#106023382
#106002012
#106001972
C4×#3905