Finite Group Databasebeta

← C2×#10615284 #12975922

Subgroups — C2×#10615284 #12975922

Order 1280.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D4×Q8C211yesmaximal, characteristic, complemented
2C2×#65899C211yesmaximal, characteristic
3C2×#65516C211yesmaximal, characteristic, complemented
4C2×#65516C211yesmaximal, characteristic, complemented
5C2×#65514C211yesmaximal, characteristic, complemented
6C22×#3967C211yesmaximal, characteristic, complemented
7#10615284C2116yesmaximal, direct product factor
8C2×#65372C211yesmaximal, characteristic, complemented
9C2×#65371C211yesmaximal, characteristic, complemented
10C2×#65338C211yesmaximal, characteristic, complemented
11C2×#65337C211yesmaximal, characteristic, complemented
12C2×#65333C211yesmaximal, characteristic, complemented
13C2×#65334C211yesmaximal, characteristic, complemented
14C2×#65315C211yesmaximal, characteristic, complemented
15C2×#65311C211yesmaximal, characteristic, complemented
16C2×#65300C211yesmaximal, characteristic, complemented
17C23×C5×Q8C2211yescharacteristic
18C23×C5×Q8C2211yescharacteristic
19C5×D4×Q8—24no—
20C5×D4×Q8C2218yescomplemented
21C2×C5×C4⋊Q8—21no—
22C2×C5×C4⋊Q8C2211yescharacteristic
23C2×C5×C22⋊Q8—21no—
24C2×C5×C22⋊Q8—21no—
25C2×C5×C22⋊Q8C2211yescharacteristic
26C2×C5×C22⋊Q8C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4—21no—
29C2×C4×C5×D4C2211yescharacteristic
30C22×#688C2211yescharacteristic
31C22×#688C2211yescharacteristic
32C22×#688C2211yescharacteristic
33C2×#4085—21no—
34C2×#4076C2211yescharacteristic
35C2×#4076C2211yescharacteristic
36C2×#4072C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×#681C2211yescharacteristic
39C23×#168C2211yescharacteristic
40#65899—24no—
41#65899C2218yes—
42C2×#4044—21no—
43C2×#4029—21no—
44C2×#4027—21no—
45C2×C4×D20C2211yescharacteristic
46C2×#4016C2211yescharacteristic
47#65516C2218yescomplemented
48#65516C2218yescomplemented
49#65514C2218yescomplemented
50C2×#3967C2211yescharacteristic
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3967C2211yescharacteristic
55C2×#3967C2211yescharacteristic
56C2×#3967C2211yescharacteristic
57C2×#3967C2211yescharacteristic
58C2×#3967C2211yescharacteristic
59C2×#3967C2218yescomplemented
60C2×C22⋊#168C2211yescharacteristic
61C2×C22⋊#168C2211yescharacteristic
62#65372C2218yescomplemented
63#65371C2218yescomplemented
64#65338C2218yescomplemented
65#65337C2218yescomplemented
66#65334C2218yescomplemented
67#65333C2218yescomplemented
68#65315C2218yescomplemented
69#65311C2218yescomplemented
70#65300C2218yescomplemented
71C2×#3941C2211yescharacteristic
72C2×#3940C2211yescharacteristic
73C2×#3939C2211yescharacteristic
74C2×#3939C2211yescharacteristic
75C2×C4⋊#168C2211yescharacteristic
76C2×#3935C2211yescharacteristic
77C2×#3320—51nomaximal, Sylow
78C22×C5×Q8—21no—
79C22×C5×Q8—21no—
80C22×C5×Q8—22no—
81C22×C5×Q8—22no—
82C22×C5×Q8—24no—
83C22×C5×Q8—24no—
84C22×C5×Q8—42no—
85C22×C5×Q8—42no—
86C22×C5×Q8C2311yescharacteristic
87C22×C5×Q8C2311yescharacteristic
88C22×C5×Q8C2314yes—
89C22×C5×Q8C2314yes—
90C22×C5×Q8C2311yescharacteristic
91C22×C5×D4D411yescharacteristic
92C23×C4×C5—21no—
93C23×C4×C5—21no—
94C23×C4×C5C2311yescharacteristic
95C23×C4×C5C2311yescharacteristic
96C22×C22⋊D5—21no—
97C22×C22⋊D5—21no—
98C23×Dic5—21no—
99C22×D20C2311yescharacteristic
100C22×C4×D5—21no—
101C5×C4⋊Q8—28no—
102C5×C4⋊Q8—22no—
103C5×C4⋊Q8C2314yes—
104C5×C22⋊Q8—22no—
105C5×C22⋊Q8—22no—
106C5×C22⋊Q8—28no—
107C5×C22⋊Q8—28no—
108C5×C22⋊Q8C2314yes—
109C5×C22⋊Q8C2314yes—
110C4×C5×Q8—22no—
111C4×C5×Q8C2314yes—
112C4×C5×D4—28no—
113C4×C5×D4D414yes—
114C4×C5×D4C2314yes—
115C2×C5×C4⋊C4—21no—
116C2×C5×C4⋊C4—21no—
117C2×C5×C4⋊C4—21no—
118C2×C5×C4⋊C4—21no—
119C2×C5×C4⋊C4—21no—
120C2×C5×C4⋊C4D411yescharacteristic
121C2×C5×C4⋊C4C2311yescharacteristic
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—21no—
124C2×C5×C22⋊C4D411yescharacteristic
125C2×C5×C22⋊C4D411yescharacteristic
126C2×C42×C5—21no—
127C2×C42×C5C2311yescharacteristic
128C2×C22⋊Dic5—21no—
129C2×#688—24no—
130C2×#688—42no—
131C2×#688—42no—
132C2×#688C2314yes—
133C2×#688C2314yes—
134C2×#688C2314yes—
135#4085—28no—
136#4076—22no—
137#4076—22no—
138#4076C2314yes—
139#4076C2314yes—
140C2×#685—21no—
141C2×#685—21no—
142C2×#685—21no—
143#4072—22no—
144#4072C2314yes—
145C2×C4⋊Dic5—21no—
146C2×C4⋊Dic5—22no—
147C2×C4⋊Dic5C2311yescharacteristic
148C2×C4⋊Dic5C2311yescharacteristic
149C2×C4⋊Dic5C2311yescharacteristic
150C2×C4⋊Dic5C2314yes—
151C2×#683—21no—
152C2×#683—21no—
153C2×C4×Dic5—21no—
154C2×#681—42no—
155C2×#681C2314yes—
156C22×#168—42no—
157C22×#168C2311yescharacteristic
158C22×#168C2311yescharacteristic
159C22×#168C2311yescharacteristic
160C22×#168C2311yescharacteristic
161C22×#168C2314yes—
162#4044—28no—
163#4029—28no—
164#4027—28no—
165C4×D20—22no—
166C4×D20C2314yes—
167#4016—22no—
168#4016C2314yes—
169#3967C2314yes—
170#3967C2314yes—
171#3967C2314yes—
172#3967C2314yes—
173#3967C2314yes—
174#3967C2314yes—
175#3967C2314yes—
176#3967C2314yes—
177#3967C2314yes—
178C22⋊#168C2314yes—
179C22⋊#168C2314yes—
180#3941C2314yes—
181#3940C2314yes—
182#3939C2314yes—
183#3939C2314yes—
184C4⋊#168C2314yes—
185#3935C2314yes—
186C2×#553—51no—
187C2×D4×Q8D511yescharacteristic, complemented
188#3320—516no—
189C2×#491—51no—
190C2×#484—51no—
191C2×#485—51no—
192C2×#479—51no—
193C2×#468—51no—
194C2×#465—51no—
195C2×#461—51no—
196C2×#448—51no—
197C2×#448—51no—
198C2×#440—51no—
199C2×#435—51no—
200C2×#419—51no—
201C22×#103—51no—
202C24×C5C2×D411yescharacteristic
203C24×C5C2×D411yescharacteristic
204C23×D5—21no—
205C2×C5×Q8—21no—
206C2×C5×Q8—24no—
207C2×C5×Q8—24no—
208C2×C5×Q8—21no—
209C2×C5×Q8—21no—
210C2×C5×Q8—22no—
211C2×C5×Q8—28no—
212C2×C5×Q8—28no—
213C2×C5×Q8—22no—
214C2×C5×Q8—22no—
215C2×C5×Q8—22no—
216C2×C5×Q8—22no—
217C2×C5×Q8—44no—
218C2×C5×Q8—44no—
219C2×C5×Q8—44no—
220C2×C5×Q8—44no—
221C2×C5×Q8—48no—
222C2×C5×Q8—48no—
223C2×C5×Q8#4114yes—
224C2×C5×Q8C2412yes—
225C2×C5×Q8C2412yes—
226C2×C5×Q8C2412yes—
227C2×C5×D4—24no—
228C2×C5×D4C2×D414yes—
229C22×C4×C5—21no—
230C22×C4×C5—22no—
231C22×C4×C5—22no—
232C22×C4×C5—22no—
233C22×C4×C5—22no—
234C22×C4×C5—21no—
235C22×C4×C5—21no—
236C22×C4×C5—21no—
237C22×C4×C5—24no—
238C22×C4×C5—24no—
239C22×C4×C5—44no—
240C22×C4×C5—44no—
241C22×C4×C5C2×D411yescharacteristic
242C22×C4×C5C2×D411yescharacteristic
243C22×C4×C5C2×D411yescharacteristic
244C22×C4×C5C2×D411yescharacteristic
245C22×C4×C5C2×D412yes—
246C22×C4×C5C2×D412yes—
247C22×C4×C5C2412yes—
248C22×C4×C5C2412yes—
249C22×C4×C5C2411yescharacteristic
250C2×C22⋊D5—24no—
251C2×C22⋊D5—24no—
252C2×C22⋊D5—44no—
253C2×C22⋊D5—82no—
254C22×Dic5—21no—
255C22×Dic5—21no—
256C22×Dic5—21no—
257C22×Dic5—24no—
258C22×Dic5—82no—
259C2×D20—22no—
260C2×D20—22no—
261C2×D20—21no—
262C2×D20C2412yes—
263C2×C4×D5—24no—
264C2×C4×D5—82no—
265C5×C4⋊C4—24no—
266C5×C4⋊C4—24no—
267C5×C4⋊C4—24no—
268C5×C4⋊C4—24no—
269C5×C4⋊C4—24no—
270C5×C4⋊C4—21no—
271C5×C4⋊C4C2×D414yes—
272C5×C4⋊C4C2412yes—
273C5×C22⋊C4—24no—
274C5×C22⋊C4—24no—
275C5×C22⋊C4C2×D414yes—
276C5×C22⋊C4C2×D414yes—
277C42×C5—24no—
278C42×C5C2×D412yes—
279C42×C5C2412yes—
280C22⋊Dic5—24no—
281#688—28no—
282#688—44no—
283#688—44no—
284#685—24no—
285#685—24no—
286#685—24no—
287C4⋊Dic5—21no—
288C4⋊Dic5—21no—
289C4⋊Dic5—21no—
290C4⋊Dic5—24no—
291C4⋊Dic5C2412yes—
292C4⋊Dic5C2412yes—
293C4⋊Dic5C2412yes—
294#683—24no—
295#683—24no—
296C4×Dic5—24no—
297#681—44no—
298C2×#168—22no—
299C2×#168—22no—
300C2×#168—22no—
301C2×#168—22no—
302C2×#168—44no—
303C2×#168C2412yes—
304C2×#168C2412yes—
305C2×#168C2412yes—
306C2×#168C2412yes—
307C23×Q8C2×D511yescharacteristic
308C23×Q8C2×D511yescharacteristic
309C22×SD16—51no—
310C22×SD16—51no—
311C22×SD16—51no—
312C22×M16—51no—
313C23×C8—51no—
314#553—58no—
315#553—104no—
316D4×Q8—24no—
317D4×Q8C2×D518yescomplemented
318C2×C4⋊Q8—21no—
319C2×C4⋊Q8C2×D511yescharacteristic
320C2×#126—101no—
321C2×#125—51no—
322C2×#123—101no—
323C2×C22⋊Q8—21no—
324C2×C22⋊Q8—21no—
325C2×C22⋊Q8C2×D511yescharacteristic
326C2×C22⋊Q8C2×D511yescharacteristic
327C2×#121—51no—
328C2×#121—51no—
329C2×#121—101no—
330C2×C4×Q8C2×D511yescharacteristic
331C2×C4×D4—21no—
332C2×C4×D4—51no—
333C2×C4×D4—101no—
334C2×C4×D4C2×D511yescharacteristic
335C2×#117—51no—
336C22×C4⋊C4—51no—
337#491—58no—
338#485—58no—
339#484—58no—
340#479—58no—
341#468—58no—
342#465—58no—
343#461—58no—
344#448—58no—
345#448—58no—
346#440—58no—
347#435—58no—
348C2×#107—51no—
349C2×#107—51no—
350C2×#106—51no—
351C2×C4⋊C8—51no—
352#419—58no—
353C2×#103—51no—
354C2×#103—51no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103—51no—
359C2×#103—51no—
360C2×#103—51no—
361C2×#103—51no—
362C2×#103—58no—
363C2×#102—51no—
364C2×C22⋊C8—51no—
365C2×C22⋊C8—51no—
366C2×#97—51no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5#13714yes—
373C23×C5C22×D412yes—
374C23×C5C22×D412yes—
375C23×C5C22×D411yescharacteristic
376C22×D5—22no—
377C22×D5—42no—
378C22×D5—42no—
379C22×D5—42no—
380C5×Q8—24no—
381C5×Q8—22no—
382C5×Q8—22no—
383C5×Q8—22no—
384C5×Q8—22no—
385C5×Q8—22no—
386C5×Q8—48no—
387C5×Q8—48no—
388C5×Q8—42no—
389C5×Q8—42no—
390C5×Q8C2×#4114yes—
391C5×D4—28no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5—24no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—24no—
399C2×C4×C5—24no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—48no—
408C2×C4×C5—48no—
409C2×C4×C5—42no—
410C2×C4×C5—42no—
411C2×C4×C5—42no—
412C2×C4×C5C22×D412yes—
413C2×C4×C5C22×D412yes—
414C2×C4×C5C22×D412yes—
415C2×C4×C5C22×D412yes—
416C2×C4×C5C22×D411yescharacteristic
417C2×C4×C5C2×#4112yes—
418C2×C4×C5H(5,𝔽2)12yes—
419C2×C4×C5C2511yescharacteristic
420C22⋊D5—48no—
421C22⋊D5—84no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—42no—
426C2×Dic5—42no—
427C2×Dic5—42no—
428C2×Dic5—84no—
429D20—22no—
430D20—22no—
431D20—42no—
432C4×D5—84no—
433#168—22no—
434#168—22no—
435#168—22no—
436#168—22no—
437C22×Q8—21no—
438C22×Q8—21no—
439C22×Q8—22no—
440C22×Q8—22no—
441C22×Q8—24no—
442C22×Q8—24no—
443C22×Q8—42no—
444C22×Q8—42no—
445C22×Q8C22×D511yescharacteristic
446C22×Q8C22×D511yescharacteristic
447C22×Q8C22×D514yes—
448C22×Q8C22×D514yes—
449C22×Q8C22×D511yescharacteristic
450C22×D4—51no—
451C22×D4—101no—
452C22×D4—101no—
453C22×D4C22⋊D511yescharacteristic
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—101no—
457C23×C4—101no—
458C23×C4C22×D511yescharacteristic
459C23×C4C22×D511yescharacteristic
460C2×SD16—54no—
461C2×SD16—54no—
462C2×SD16—54no—
463C2×SD16—104no—
464C2×SD16—202no—
465C2×SD16—202no—
466C2×M16—54no—
467C2×M16—202no—
468C22×C8—51no—
469C22×C8—51no—
470C22×C8—51no—
471C22×C8—51no—
472C22×C8—54no—
473C22×C8—202no—
474C4⋊Q8—28no—
475C4⋊Q8—22no—
476C4⋊Q8C22×D514yes—
477#126—108no—
478#125—54no—
479#125—102no—
480#123—108no—
481C22⋊Q8—22no—
482C22⋊Q8—22no—
483C22⋊Q8—28no—
484C22⋊Q8—28no—
485C22⋊Q8C22×D514yes—
486C22⋊Q8C22×D514yes—
487#121—54no—
488#121—54no—
489#121—108no—
490#121—102no—
491#121—102no—
492C4×Q8—22no—
493C4×Q8C22×D514yes—
494C4×D4—28no—
495C4×D4—54no—
496C4×D4—108no—
497C4×D4—102no—
498C4×D4C22⋊D514yes—
499C4×D4C22×D514yes—
500#117—54no—
501#117—102no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—51no—
508C2×C4⋊C4—51no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—51no—
511C2×C4⋊C4—101no—
512C2×C4⋊C4—102no—
513C2×C4⋊C4—101no—
514C2×C4⋊C4—101no—
515C2×C4⋊C4C22⋊D511yescharacteristic
516C2×C4⋊C4C22×D511yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—101no—
520C2×C22⋊C4—101no—
521C2×C22⋊C4—101no—
522C2×C22⋊C4—101no—
523C2×C22⋊C4C22⋊D511yescharacteristic
524C2×C22⋊C4C22⋊D511yescharacteristic
525C2×C42—21no—
526C2×C42—101no—
527C2×C42C22×D511yescharacteristic
528#107—54no—
529#107—54no—
530#106—54no—
531C4⋊C8—54no—
532#103—54no—
533#103—54no—
534#103—54no—
535#103—54no—
536#103—54no—
537#103—54no—
538#103—54no—
539#103—54no—
540#103—54no—
541#102—54no—
542C22⋊C8—54no—
543C22⋊C8—54no—
544#97—54no—
545C22×C5—22no—
546C22×C5—28no—
547C22×C5—22no—
548C22×C5—22no—
549C22×C5—22no—
550C22×C5—22no—
551C22×C5—44no—
552C22×C5#54612yes—
553C22×C5C2×#13714yes—
554C22×C5C2×#13712yes—
555C22×C5#57712yes—
556C22×C5C23×D411yescharacteristic
557C2×D5—42no—
558C2×D5—42no—
559C2×D5—42no—
560C2×D5—84no—
561C4×C5—22no—
562C4×C5—22no—
563C4×C5—24no—
564C4×C5—22no—
565C4×C5—22no—
566C4×C5—42no—
567C4×C5—42no—
568C4×C5—42no—
569C4×C5#54612yes—
570C4×C5C22×#4111yescharacteristic
571C4×C5C2×H(5,𝔽2)11yescharacteristic
572Dic5—42no—
573Dic5—42no—
574Dic5—42no—
575C24—101no—
576C24C2×C22⋊D511yescharacteristic
577C24C2×C22⋊D511yescharacteristic
578C2×Q8—22no—
579C2×Q8—21no—
580C2×Q8—24no—
581C2×Q8—24no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—28no—
585C2×Q8—28no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—44no—
591C2×Q8—44no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—48no—
595C2×Q8—48no—
596C2×Q8#71114yes—
597C2×Q8C23×D512yes—
598C2×Q8C23×D512yes—
599C2×Q8C23×D512yes—
600C2×D4—24no—
601C2×D4—52no—
602C2×D4—104no—
603C2×D4—104no—
604C2×D4—102no—
605C2×D4—102no—
606C2×D4—101no—
607C2×D4—204no—
608C2×D4—402no—
609C2×D4C2×C22⋊D514yes—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—101no—
623C22×C4—101no—
624C22×C4—101no—
625C22×C4—104no—
626C22×C4—104no—
627C22×C4—402no—
628C22×C4—402no—
629C22×C4C2×C22⋊D512yes—
630C22×C4C2×C22⋊D512yes—
631C22×C4C2×C22⋊D511yescharacteristic
632C22×C4C2×C22⋊D511yescharacteristic
633C22×C4C2×C22⋊D511yescharacteristic
634C22×C4C2×C22⋊D511yescharacteristic
635C22×C4C23×D512yes—
636C22×C4C23×D512yes—
637C22×C4C23×D511yescharacteristic
638SD16—108no—
639SD16—204no—
640SD16—204no—
641M16—204no—
642C2×C8—52no—
643C2×C8—52no—
644C2×C8—52no—
645C2×C8—52no—
646C2×C8—102no—
647C2×C8—102no—
648C2×C8—102no—
649C2×C8—102no—
650C2×C8—204no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—21no—
657C4⋊C4—52no—
658C4⋊C4—52no—
659C4⋊C4—52no—
660C4⋊C4—101no—
661C4⋊C4—101no—
662C4⋊C4—104no—
663C4⋊C4—101no—
664C4⋊C4—104no—
665C4⋊C4—104no—
666C4⋊C4C2×C22⋊D514yes—
667C4⋊C4C23×D512yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—104no—
671C22⋊C4—104no—
672C22⋊C4—104no—
673C22⋊C4—104no—
674C22⋊C4C2×C22⋊D514yes—
675C22⋊C4C2×C22⋊D514yes—
676C42—24no—
677C42—104no—
678C42C2×C22⋊D512yes—
679C42C23×D512yes—
680C2×C5—24no—
681C2×C5—42no—
682C2×C5#332014yescomplemented
683C2×C5C2×#54611yescharacteristic
684C2×C5C22×#13711yescharacteristic
685C2×C5C2×#57711yescharacteristic
686D5—82no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—102no—
693C23—202no—
694C23—202no—
695C23—202no—
696C23#408814yes—
697C23C22×C22⋊D512yes—
698C23C22×C22⋊D512yes—
699C23C22×C22⋊D511yescharacteristic
700Q8—24no—
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—22no—
706Q8—48no—
707Q8—48no—
708Q8—42no—
709Q8—42no—
710Q8C2×#71114yes—
711D4—28no—
712D4—102no—
713D4—102no—
714D4—208no—
715D4—202no—
716D4—404no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—202no—
741C2×C4—202no—
742C2×C4—202no—
743C2×C4—404no—
744C2×C4—404no—
745C2×C4C2×#71112yes—
746C2×C4#414412yes—
747C2×C4C22×C22⋊D512yes—
748C2×C4C22×C22⋊D512yes—
749C2×C4C22×C22⋊D512yes—
750C2×C4C22×C22⋊D512yes—
751C2×C4C22×C22⋊D511yescharacteristic
752C2×C4C24×D511yescharacteristic
753C8—102no—
754C8—102no—
755C8—102no—
756C8—102no—
757C5C2×#332011yescharacteristic, complemented, Sylow
758C22—22no—
759C22—28no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—202no—
766C22—202no—
767C22—202no—
768C22—404no—
769C22#6614012yes—
770C22C2×#408814yes—
771C22C2×#408812yes—
772C22#6617112yes—
773C22C23×C22⋊D511yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—202no—
783C4—202no—
784C4—202no—
785C4#6614012yes—
786C4C22×#71111yescharacteristic
787C4C2×#414411yescharacteristic
788C2—24no—
789C2—42no—
790C2—402no—
791C2#1061528414yesdirect product factor
792C2C2×#6614011yescharacteristic
793C2C22×#408811yescharacteristic
794C2C2×#6617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×D4×Q8C2
socleC23×C5C22×D4
prime radicalC2×#65899C2
hypercenterC2×D4×Q8D5
hypocenterC5C2×#3320
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C5×D4×Q8C2semidirect
3. C2×#65516C2semidirect
4. C2×#65516C2semidirect
5. C2×#65514C2semidirect
6. C22×#3967C2semidirect
7. #10615284C2direct (N × H)
8. C2×#65372C2semidirect
9. C2×#65371C2semidirect
10. C2×#65338C2semidirect
11. C2×#65337C2semidirect
12. C2×#65333C2semidirect
13. C2×#65334C2semidirect
14. C2×#65315C2semidirect
15. C2×#65311C2semidirect
16. C2×#65300C2semidirect
20. C5×D4×Q8C22semidirect
47. #65516C22semidirect
48. #65516C22semidirect
49. #65514C22semidirect
59. C2×#3967C22semidirect
62. #65372C22semidirect
63. #65371C22semidirect
64. #65338C22semidirect
65. #65337C22semidirect
66. #65334C22semidirect
67. #65333C22semidirect
68. #65315C22semidirect
69. #65311C22semidirect
70. #65300C22semidirect
187. C2×D4×Q8D5semidirect
317. D4×Q8C2×D5semidirect
682. C2×C5#3320semidirect
757. C5C2×#3320semidirect
791. C2#10615284direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×D4×Q82
C2×#658992
C2×#655162
C2×#655142
C22×#39672
#106152842
C2×#653722
C2×#653712
C2×#653382
C2×#653372
C2×#653332
C2×#653342
C2×#653152
C2×#653112
C2×#653002
C2×#33205