Finite Group Databasebeta

← C2×#10613221 #12975693

Subgroups — C2×#10613221 #12975693

Order 1280.

2158 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65966C211yesmaximal, characteristic
2C2×#65845C211yesmaximal, characteristic
3C2×C5×#484C211yesmaximal, characteristic, complemented
4C2×#65340C211yesmaximal, characteristic, complemented
5C22×#3942C211yesmaximal, characteristic, complemented
6#10613221C2116yesmaximal, direct product factor
7C2×#65164C211yesmaximal, characteristic, complemented
8C2×#65173C211yesmaximal, characteristic, complemented
9C2×#65176C211yesmaximal, characteristic, complemented
10C2×#65162C211yesmaximal, characteristic, complemented
11C2×#65082C211yesmaximal, characteristic, complemented
12C2×#65097C211yesmaximal, characteristic, complemented
13C2×D5×#103C211yesmaximal, characteristic, complemented
14C2×#65081C211yesmaximal, characteristic, complemented
15C2×#65028C211yesmaximal, characteristic, complemented
16C2×#65014C211yesmaximal, characteristic
17C22×Q8×D5C2211yescharacteristic
18C23×Dic10C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C2×#4090C2211yescharacteristic
22C22×#689C2211yescharacteristic
23C2×C4×C22⋊D5—21no—
24C2×C4×C22⋊D5C2211yescharacteristic
25C2×#4070—21no—
26C2×#4070C2211yescharacteristic
27C23×#168C2211yescharacteristic
28C22×Dic20C2211yescharacteristic
29C22×Dic20C2211yescharacteristic
30C22×C8×D5C2211yescharacteristic
31#65966—24no—
32#65966C2218yes—
33#65845—24no—
34#65845C2218yes—
35C2×#4043C2211yescharacteristic
36C2×#4043C2211yescharacteristic
37C2×#4042—21no—
38C2×#4042—21no—
39C2×D5×C4⋊C4C2211yescharacteristic
40C2×#4035—21no—
41C2×#4034—21no—
42C2×#4034C2211yescharacteristic
43C2×#4033C2211yescharacteristic
44C2×#4033C2211yescharacteristic
45C2×#4027—21no—
46C2×#4024—21no—
47C5×#484C2218yescomplemented
48C2×C5×#107C2211yescharacteristic
49C2×C5×#107C2211yescharacteristic
50C2×C5×#103C2211yescharacteristic
51C2×C5×#103C2211yescharacteristic
52C2×C5×C22⋊C8C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3952C2211yescharacteristic
55C2×#3948C2211yescharacteristic
56C2×#3948C2211yescharacteristic
57C2×#3946C2211yescharacteristic
58C2×C8×Dic5C2211yescharacteristic
59#65340C2218yescomplemented
60C2×#3942C2211yescharacteristic
61C2×#3942C2211yescharacteristic
62C2×#3942C2211yescharacteristic
63C2×#3942C2211yescharacteristic
64C2×#3942C2211yescharacteristic
65C2×#3942C2218yescomplemented
66C2×#3939C2211yescharacteristic
67#65176C2218yescomplemented
68#65173C2218yescomplemented
69#65164C2218yescomplemented
70#65162C2218yescomplemented
71#65097C2218yescomplemented
72D5×#103C2218yescomplemented
73#65082C2218yescomplemented
74#65081C2218yescomplemented
75#65028C2218yescomplemented
76#65014C2218yes—
77C2×#3299—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C23×C4×C5—21no—
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5D411yescharacteristic
82C23×Dic5—21no—
83C2×Q8×D5—22no—
84C2×Q8×D5—24no—
85C2×Q8×D5—42no—
86C2×Q8×D5C2314yes—
87C22×C4×D5—21no—
88C22×C4×D5—21no—
89C22×C4×D5C2311yescharacteristic
90C22×Dic10—24no—
91C22×Dic10—21no—
92C22×Dic10—22no—
93C22×Dic10—21no—
94C22×Dic10—21no—
95C22×Dic10—42no—
96C22×Dic10C2311yescharacteristic
97C22×Dic10C2311yescharacteristic
98C22×Dic10C2314yes—
99C22×Dic10C2311yescharacteristic
100C22×C5×C8C2311yescharacteristic
101C22×C5×C8C2311yescharacteristic
102C5×C22⋊Q8—22no—
103C5×C22⋊Q8C2314yes—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—22no—
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C4⋊C4C2311yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2314yes—
111C2×C5×C22⋊C4—21no—
112C2×C22⋊Dic5—21no—
113C2×C22⋊Dic5D411yescharacteristic
114#4090—22no—
115#4090C2314yes—
116C2×#689—42no—
117C2×#689C2314yes—
118C4×C22⋊D5—28no—
119C4×C22⋊D5D414yes—
120C4×C22⋊D5C2314yes—
121C2×#685—21no—
122C2×#685—21no—
123C2×#685D411yescharacteristic
124C2×C4⋊Dic5—21no—
125C2×C4⋊Dic5—21no—
126C2×C4⋊Dic5C2311yescharacteristic
127#4070—22no—
128#4070—28no—
129#4070C2314yes—
130C2×#683—21no—
131C2×#683—21no—
132C2×#683—21no—
133C2×#683—21no—
134C2×#683—21no—
135C2×#683—21no—
136C2×#683—21no—
137C2×#683D411yescharacteristic
138C2×C4×Dic5—21no—
139C2×C4×Dic5—21no—
140C2×C4×Dic5C2311yescharacteristic
141C22×#168—42no—
142C22×#168C2311yescharacteristic
143C22×#168C2311yescharacteristic
144C22×#168C2314yes—
145C2×Dic20—24no—
146C2×Dic20—42no—
147C2×Dic20C2314yes—
148C2×Dic20C2314yes—
149C2×C8×D5—42no—
150C2×C8×D5C2314yes—
151#4043—22no—
152#4043—22no—
153#4043C2314yes—
154#4043C2314yes—
155#4042—28no—
156#4042—28no—
157D5×C4⋊C4—22no—
158D5×C4⋊C4C2314yes—
159#4035—28no—
160#4034—28no—
161#4034—22no—
162#4034C2314yes—
163#4033—22no—
164#4033—22no—
165#4033C2314yes—
166#4033C2314yes—
167#4027—28no—
168#4024—28no—
169C5×#107C2314yes—
170C5×#107C2314yes—
171C5×#103C2314yes—
172C5×#103C2314yes—
173C5×C22⋊C8C2314yes—
174#3967C2314yes—
175#3952C2314yes—
176#3948C2314yes—
177#3948C2314yes—
178#3946C2314yes—
179C8×Dic5C2314yes—
180#3942C2314yes—
181#3942C2314yes—
182#3942C2314yes—
183#3942C2314yes—
184#3942C2314yes—
185#3939C2314yes—
186C2×#554—51no—
187C2×D4×Q8—51no—
188#3299—516no—
189C2×#487—51no—
190C2×#484—51no—
191C2×#484D511yescharacteristic, complemented
192C2×#477—51no—
193C2×#467—51no—
194C2×#467—51no—
195C2×#462—51no—
196C2×#451—51no—
197C2×#451—51no—
198C2×C4×Q16—51no—
199C2×C8×D4—51no—
200C22×#103—51no—
201C22×#103—51no—
202C24×C5C2×D411yescharacteristic
203C23×D5C2×D411yescharacteristic
204C2×C5×Q8—21no—
205C2×C5×Q8—22no—
206C2×C5×Q8—22no—
207C2×C5×Q8C2412yes—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—24no—
215C22×C4×C5—82no—
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2×D412yes—
218C22×C4×C5C2412yes—
219C22×C4×C5C2411yescharacteristic
220C2×C22⋊D5Q1618yescomplemented
221C2×C22⋊D5C2×D414yes—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—24no—
226C22×Dic5—21no—
227C22×Dic5—44no—
228C22×Dic5C2×D411yescharacteristic
229C22×Dic5C2×D411yescharacteristic
230C22×Dic5C2×D411yescharacteristic
231Q8×D5—28no—
232Q8×D5—44no—
233Q8×D5—48no—
234C2×C4×D5—22no—
235C2×C4×D5—22no—
236C2×C4×D5—24no—
237C2×C4×D5—24no—
238C2×C4×D5—44no—
239C2×C4×D5—82no—
240C2×C4×D5C2×D412yes—
241C2×C4×D5C2412yes—
242C2×Dic10—21no—
243C2×Dic10—22no—
244C2×Dic10—22no—
245C2×Dic10—22no—
246C2×Dic10—22no—
247C2×Dic10—22no—
248C2×Dic10—28no—
249C2×Dic10—24no—
250C2×Dic10—21no—
251C2×Dic10—21no—
252C2×Dic10—24no—
253C2×Dic10—24no—
254C2×Dic10—44no—
255C2×Dic10—48no—
256C2×Dic10—44no—
257C2×Dic10—44no—
258C2×Dic10—82no—
259C2×Dic10#4114yes—
260C2×Dic10C2412yes—
261C2×Dic10C2412yes—
262C2×Dic10C2412yes—
263C2×C5×C8—22no—
264C2×C5×C8—22no—
265C2×C5×C8C2412yes—
266C2×C5×C8C2412yes—
267C5×C4⋊C4—21no—
268C5×C4⋊C4—21no—
269C5×C4⋊C4—24no—
270C5×C4⋊C4—24no—
271C5×C4⋊C4—21no—
272C5×C4⋊C4C2412yes—
273C5×C4⋊C4C2412yes—
274C5×C4⋊C4C2412yes—
275C5×C22⋊C4—24no—
276C22⋊Dic5—24no—
277C22⋊Dic5C2×D414yes—
278#689—44no—
279#685—24no—
280#685—24no—
281#685C2×D414yes—
282C4⋊Dic5—21no—
283C4⋊Dic5—24no—
284C4⋊Dic5—24no—
285C4⋊Dic5C2412yes—
286#683—24no—
287#683—24no—
288#683—24no—
289#683—24no—
290#683—24no—
291#683—24no—
292#683—24no—
293#683C2×D414yes—
294C4×Dic5—24no—
295C4×Dic5—24no—
296C4×Dic5C2×D412yes—
297C4×Dic5C2412yes—
298C2×#168—22no—
299C2×#168—22no—
300C2×#168—44no—
301C2×#168C2412yes—
302C2×#168C2412yes—
303Dic20—28no—
304Dic20—44no—
305C8×D5—44no—
306C23×Q8—51no—
307C23×Q8—51no—
308C22×Q16—51no—
309C22×Q16—51no—
310C22×Q16—51no—
311C23×C8—51no—
312C23×C8—51no—
313#554—58no—
314#554—104no—
315D4×Q8—58no—
316D4×Q8—104no—
317C2×C4⋊Q8—51no—
318C2×C4⋊Q8—51no—
319C2×C4⋊Q8—101no—
320C2×#125—101no—
321C2×C22⋊Q8—51no—
322C2×C22⋊Q8—51no—
323C2×C22⋊Q8—51no—
324C2×C22⋊Q8—101no—
325C2×C22⋊Q8—101no—
326C2×C22⋊Q8—101no—
327C2×C22⋊Q8—101no—
328C2×C22⋊Q8C2×D511yescharacteristic
329C2×C4×Q8—51no—
330C2×C4×Q8—51no—
331C2×C4×D4—51no—
332C2×C4×D4—101no—
333C2×C4×D4—101no—
334C22×C4⋊C4—51no—
335C22×C4⋊C4C2×D511yescharacteristic
336#487—58no—
337#484—58no—
338#484C2×D518yescomplemented
339#477—58no—
340#467—58no—
341#467—58no—
342#462—58no—
343#451—58no—
344#451—58no—
345C4×Q16—58no—
346C8×D4—58no—
347C2×#107—51no—
348C2×#107C2×D511yescharacteristic
349C2×#107C2×D511yescharacteristic
350C2×C4⋊C8—51no—
351C2×#103—51no—
352C2×#103—51no—
353C2×#103—51no—
354C2×#103—51no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#103—58no—
359C2×#103—51no—
360C2×#103—58no—
361C2×#103C2×D511yescharacteristic
362C2×#103C2×D511yescharacteristic
363C2×C22⋊C8—51no—
364C2×C22⋊C8C2×D511yescharacteristic
365C2×C4×C8—51no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5C2×Q1614yes—
369C23×C5C22×D412yes—
370C23×C5C22×D411yescharacteristic
371C22×D5—22no—
372C22×D5—22no—
373C22×D5C2×Q1614yes—
374C22×D5C22×D412yes—
375C5×Q8—22no—
376C5×Q8—22no—
377C5×Q8—42no—
378C2×C4×C5—22no—
379C2×C4×C5—24no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—42no—
387C2×C4×C5—42no—
388C2×C4×C5—42no—
389C2×C4×C5—42no—
390C2×C4×C5—84no—
391C2×C4×C5C22×D412yes—
392C2×C4×C5C22×D411yescharacteristic
393C2×C4×C5C2×#4112yes—
394C2×C4×C5H(5,𝔽2)12yes—
395C2×C4×C5C2511yescharacteristic
396C22⋊D5C2×Q16116yescomplemented
397C2×Dic5—24no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—48no—
405C2×Dic5—42no—
406C2×Dic5—42no—
407C2×Dic5—42no—
408C2×Dic5C2×Q1614yes—
409C2×Dic5C22×D412yes—
410C2×Dic5C22×D412yes—
411C2×Dic5C22×D412yes—
412C4×D5—24no—
413C4×D5—22no—
414C4×D5—22no—
415C4×D5—48no—
416C4×D5—84no—
417Dic10—24no—
418Dic10—22no—
419Dic10—22no—
420Dic10—22no—
421Dic10—22no—
422Dic10—22no—
423Dic10—48no—
424Dic10—48no—
425Dic10—42no—
426Dic10—42no—
427Dic10—84no—
428Dic10C2×#4114yes—
429C5×C8—22no—
430C5×C8—22no—
431#168—22no—
432#168—22no—
433C22×Q8—54no—
434C22×Q8—51no—
435C22×Q8—51no—
436C22×Q8—51no—
437C22×Q8—54no—
438C22×Q8—101no—
439C22×Q8—101no—
440C22×Q8—104no—
441C22×Q8—102no—
442C22×Q8—101no—
443C22×Q8—102no—
444C22×Q8—104no—
445C22×Q8—202no—
446C22×Q8—202no—
447C22×Q8C22×D511yescharacteristic
448C22×D4—51no—
449C23×C4—21no—
450C23×C4—51no—
451C23×C4—101no—
452C23×C4—101no—
453C23×C4—101no—
454C23×C4C22×D511yescharacteristic
455C2×Q16—54no—
456C2×Q16—54no—
457C2×Q16—54no—
458C2×Q16—104no—
459C2×Q16—202no—
460C2×Q16—202no—
461C22×C8—51no—
462C22×C8—51no—
463C22×C8—54no—
464C22×C8—54no—
465C22×C8—202no—
466C22×C8—202no—
467C22×C8C22×D511yescharacteristic
468C22×C8C22×D511yescharacteristic
469C4⋊Q8—54no—
470C4⋊Q8—54no—
471C4⋊Q8—102no—
472C4⋊Q8—102no—
473C4⋊Q8—108no—
474#125—108no—
475C22⋊Q8—22no—
476C22⋊Q8—54no—
477C22⋊Q8—54no—
478C22⋊Q8—54no—
479C22⋊Q8—108no—
480C22⋊Q8—108no—
481C22⋊Q8—108no—
482C22⋊Q8—108no—
483C22⋊Q8—102no—
484C22⋊Q8—102no—
485C22⋊Q8—102no—
486C22⋊Q8C22×D514yes—
487C4×Q8—54no—
488C4×Q8—54no—
489C4×Q8—102no—
490C4×Q8—102no—
491C4×D4—54no—
492C4×D4—54no—
493C4×D4—108no—
494C4×D4—108no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—51no—
499C2×C4⋊C4—51no—
500C2×C4⋊C4—54no—
501C2×C4⋊C4—102no—
502C2×C4⋊C4—101no—
503C2×C4⋊C4—101no—
504C2×C4⋊C4—101no—
505C2×C4⋊C4—101no—
506C2×C4⋊C4—101no—
507C2×C4⋊C4—101no—
508C2×C4⋊C4—101no—
509C2×C4⋊C4—101no—
510C2×C4⋊C4—101no—
511C2×C4⋊C4C22×D511yescharacteristic
512C2×C4⋊C4C22×D511yescharacteristic
513C2×C4⋊C4C22×D514yes—
514C2×C4⋊C4C22×D511yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—51no—
517C2×C22⋊C4—51no—
518C2×C22⋊C4—101no—
519C2×C22⋊C4—101no—
520C2×C22⋊C4—101no—
521C2×C42—51no—
522C2×C42—101no—
523C2×C42—101no—
524#107—54no—
525#107C22×D514yes—
526#107C22×D514yes—
527C4⋊C8—54no—
528#103—54no—
529#103—54no—
530#103—54no—
531#103—54no—
532#103—54no—
533#103—54no—
534#103—54no—
535#103—54no—
536#103C22×D514yes—
537#103C22×D514yes—
538C22⋊C8—54no—
539C22⋊C8C22×D514yes—
540C4×C8—54no—
541C22×C5—22no—
542C22×C5—28no—
543C22×C5—22no—
544C22×C5#54612yes—
545C22×C5C22×Q1614yes—
546C22×C5C22×Q1612yes—
547C22×C5#57712yes—
548C22×C5C23×D411yescharacteristic
549C2×D5—22no—
550C2×D5—28no—
551C2×D5—22no—
552C2×D5C22×Q1614yes—
553C4×C5—22no—
554C4×C5—42no—
555C4×C5—42no—
556C4×C5—42no—
557C4×C5—42no—
558C4×C5#54612yes—
559C4×C5C22×#4111yescharacteristic
560C4×C5C2×H(5,𝔽2)11yescharacteristic
561Dic5—24no—
562Dic5—22no—
563Dic5—22no—
564Dic5—42no—
565Dic5—42no—
566Dic5—42no—
567Dic5C22×Q1614yes—
568C24—51no—
569C24D4×D511yescharacteristic
570C2×Q8—21no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—54no—
574C2×Q8—52no—
575C2×Q8—52no—
576C2×Q8—52no—
577C2×Q8—104no—
578C2×Q8—104no—
579C2×Q8—108no—
580C2×Q8—101no—
581C2×Q8—101no—
582C2×Q8—104no—
583C2×Q8—101no—
584C2×Q8—102no—
585C2×Q8—108no—
586C2×Q8—102no—
587C2×Q8—102no—
588C2×Q8—102no—
589C2×Q8—102no—
590C2×Q8—204no—
591C2×Q8—204no—
592C2×Q8—208no—
593C2×Q8—204no—
594C2×Q8—204no—
595C2×Q8—208no—
596C2×Q8—402no—
597C2×Q8C23×D512yes—
598C2×D4—54no—
599C2×D4—58no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—51no—
608C22×C4—51no—
609C22×C4—51no—
610C22×C4—52no—
611C22×C4—52no—
612C22×C4—82no—
613C22×C4—104no—
614C22×C4—104no—
615C22×C4—101no—
616C22×C4—102no—
617C22×C4—102no—
618C22×C4—104no—
619C22×C4—101no—
620C22×C4—101no—
621C22×C4—101no—
622C22×C4—204no—
623C22×C4—204no—
624C22×C4—402no—
625C22×C4D4×D512yes—
626C22×C4D4×D511yescharacteristic
627C22×C4C23×D512yes—
628C22×C4C23×D511yescharacteristic
629Q16—108no—
630Q16—204no—
631Q16—204no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—52no—
635C2×C8—52no—
636C2×C8—102no—
637C2×C8—102no—
638C2×C8—204no—
639C2×C8—204no—
640C2×C8C23×D512yes—
641C2×C8C23×D512yes—
642C4⋊C4—21no—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—54no—
648C4⋊C4—52no—
649C4⋊C4—104no—
650C4⋊C4—104no—
651C4⋊C4—104no—
652C4⋊C4—104no—
653C4⋊C4—104no—
654C4⋊C4—104no—
655C4⋊C4—104no—
656C4⋊C4—104no—
657C4⋊C4—101no—
658C4⋊C4—104no—
659C4⋊C4C23×D512yes—
660C4⋊C4C23×D512yes—
661C4⋊C4C23×D512yes—
662C22⋊C4—24no—
663C22⋊C4—54no—
664C22⋊C4—54no—
665C22⋊C4—104no—
666C22⋊C4—104no—
667C22⋊C4—104no—
668C42—52no—
669C42—52no—
670C42—104no—
671C42—104no—
672C2×C5—24no—
673C2×C5#329914yescomplemented
674C2×C5C2×#54611yescharacteristic
675C2×C5C23×Q1611yescharacteristic
676C2×C5C2×#57711yescharacteristic
677D5—24no—
678C23—22no—
679C23—22no—
680C23—54no—
681C23—52no—
682C23—102no—
683C23—102no—
684C23D5×Q1614yes—
685C23C2×D4×D512yes—
686C23C2×D4×D511yescharacteristic
687Q8—22no—
688Q8—22no—
689Q8—42no—
690Q8—54no—
691Q8—104no—
692Q8—102no—
693Q8—102no—
694Q8—102no—
695Q8—102no—
696Q8—102no—
697Q8—208no—
698Q8—208no—
699Q8—202no—
700Q8—202no—
701Q8—404no—
702D4—516no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—54no—
716C2×C4—52no—
717C2×C4—52no—
718C2×C4—52no—
719C2×C4—84no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—104no—
723C2×C4—102no—
724C2×C4—104no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—208no—
731C2×C4—208no—
732C2×C4—202no—
733C2×C4—202no—
734C2×C4—202no—
735C2×C4—404no—
736C2×C4C2×D4×D512yes—
737C2×C4C2×D4×D511yescharacteristic
738C2×C4D5×#4112yes—
739C2×C4#414912yes—
740C2×C4C24×D511yescharacteristic
741C8—22no—
742C8—22no—
743C8—102no—
744C8—102no—
745C5C2×#329911yescharacteristic, complemented, Sylow
746C22—22no—
747C22—22no—
748C22—28no—
749C22—54no—
750C22—102no—
751C22—102no—
752C22—108no—
753C22#6598812yes—
754C22C2×D5×Q1614yes—
755C22C2×D5×Q1612yes—
756C22#6610912yes—
757C22C22×D4×D511yescharacteristic
758C4—22no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—54no—
764C4—102no—
765C4—104no—
766C4—102no—
767C4—202no—
768C4—202no—
769C4—202no—
770C4#6598812yes—
771C4C2×D5×#4111yescharacteristic
772C4C2×#414911yescharacteristic
773C2—24no—
774C2—104no—
775C2#1061322114yesdirect product factor
776C2C2×#6598811yescharacteristic
777C2C22×D5×Q1611yescharacteristic
778C2C2×#6610911yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#484C2
socleC23×C5C22×D4
prime radicalC22×C22⋊D5D4
hypercenterC2×#484D5
hypocenterC5C2×#3299
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. C2×C5×#484C2semidirect
4. C2×#65340C2semidirect
5. C22×#3942C2semidirect
6. #10613221C2direct (N × H)
7. C2×#65164C2semidirect
8. C2×#65173C2semidirect
9. C2×#65176C2semidirect
10. C2×#65162C2semidirect
11. C2×#65082C2semidirect
12. C2×#65097C2semidirect
13. C2×D5×#103C2semidirect
14. C2×#65081C2semidirect
15. C2×#65028C2semidirect
47. C5×#484C22semidirect
59. #65340C22semidirect
65. C2×#3942C22semidirect
67. #65176C22semidirect
68. #65173C22semidirect
69. #65164C22semidirect
70. #65162C22semidirect
71. #65097C22semidirect
72. D5×#103C22semidirect
73. #65082C22semidirect
74. #65081C22semidirect
75. #65028C22semidirect
191. C2×#484D5semidirect
220. C2×C22⋊D5Q16semidirect
338. #484C2×D5semidirect
396. C22⋊D5C2×Q16semidirect
673. C2×C5#3299semidirect
745. C5C2×#3299semidirect
775. C2#10613221direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659662
C2×#658452
C2×C5×#4842
C2×#653402
C22×#39422
#106132212
C2×#651642
C2×#651732
C2×#651762
C2×#651622
C2×#650822
C2×#650972
C2×D5×#1032
C2×#650812
C2×#650282
C2×#650142
C2×#32995