Finite Group Databasebeta

← C2×#10613253 #12969856

Subgroups — C2×#10613253 #12969856

Order 1280.

2374 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#65858C211yesmaximal, characteristic
3C2×C5×#485C211yesmaximal, characteristic, complemented
4C2×#65336C211yesmaximal, characteristic, complemented
5C2×#65285C211yesmaximal, characteristic, complemented
6#10613253C2116yesmaximal, direct product factor
7C2×#65171C211yesmaximal, characteristic, complemented
8C2×#65176C211yesmaximal, characteristic, complemented
9C2×#65151C211yesmaximal, characteristic, complemented
10C2×#65153C211yesmaximal, characteristic, complemented
11C2×#65102C211yesmaximal, characteristic, complemented
12C2×#65096C211yesmaximal, characteristic, complemented
13C2×#65097C211yesmaximal, characteristic, complemented
14C2×#65095C211yesmaximal, characteristic, complemented
15C2×#65022C211yesmaximal, characteristic, complemented
16C2×D5×C22⋊C8C211yesmaximal, characteristic, complemented
17C22×Q8×D5C2211yescharacteristic
18C22×#709C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C2×#4092C2211yescharacteristic
23C22×#689C2211yescharacteristic, complemented
24C22×#688C2211yescharacteristic, complemented
25C2×#4070C2211yescharacteristic
26C22×Dic20C2211yescharacteristic, complemented
27C22×#677C2211yescharacteristic, complemented
28C22×C8×D5C2211yescharacteristic
29C22×C8×D5C2211yescharacteristic
30D5×C22⋊Q8—24no—
31D5×C22⋊Q8C2218yescomplemented
32#65858—24no—
33#65858C2218yes—
34C2×#4043C2211yescharacteristic
35C2×#4043C2211yescharacteristic
36C2×#4043C2211yescharacteristic
37C2×#4042—21no—
38C2×#4041C2211yescharacteristic
39C2×#4041C2211yescharacteristic
40C2×D5×C4⋊C4—21no—
41C2×D5×C4⋊C4C2211yescharacteristic
42C2×#4032—21no—
43C2×#4028—21no—
44C2×D5×C22⋊C4—21no—
45C2×#4024—21no—
46C2×C4×D20—21no—
47C2×C4×D20—21no—
48C5×#485C2218yescomplemented
49C2×C5×#107C2211yescharacteristic, complemented
50C2×C5×#106C2211yescharacteristic, complemented
51C2×C5×#103C2211yescharacteristic, complemented
52C2×C5×#103C2211yescharacteristic, complemented
53C2×C5×C22⋊C8C2211yescharacteristic
54C2×C22⋊#168C2211yescharacteristic
55C2×#3953C2211yescharacteristic, complemented
56C2×#3952C2211yescharacteristic
57C2×#3952C2211yescharacteristic
58C2×#3948C2211yescharacteristic, complemented
59#65336C2218yescomplemented
60#65285C2218yescomplemented
61C2×#3942C2211yescharacteristic, complemented
62C2×#3942C2211yescharacteristic, complemented
63C2×#3942C2211yescharacteristic, complemented
64C2×#3941C2211yescharacteristic, complemented
65C2×#3940C2211yescharacteristic, complemented
66C2×#3939C2211yescharacteristic, complemented
67#65176C2218yescomplemented
68#65171C2218yescomplemented
69#65153C2218yescomplemented
70#65151C2218yescomplemented
71#65102C2218yescomplemented
72#65097C2218yescomplemented
73#65096C2218yescomplemented
74#65095C2218yescomplemented
75#65022C2218yescomplemented
76D5×C22⋊C8C2218yescomplemented
77C2×#3190—51nomaximal, Sylow
78C24×D5D411yescharacteristic
79C22×C5×Q8C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—21no—
82C23×Dic5D411yescharacteristic
83C2×Q8×D5—22no—
84C2×Q8×D5—42no—
85C2×Q8×D5—42no—
86C2×Q8×D5C2314yes—
87C2×#709—22no—
88C2×#709—42no—
89C2×#709—42no—
90C2×#709C2314yes—
91C22×D20—21no—
92C22×D20—21no—
93C22×D20C2311yescharacteristic
94C22×C4×D5—21no—
95C22×C4×D5—21no—
96C22×C4×D5—21no—
97C22×C4×D5—42no—
98C22×C4×D5—42no—
99C22×C4×D5D411yescharacteristic
100C22×C4×D5D411yescharacteristic
101C22×C4×D5D414yes—
102C22×C4×D5C2311yescharacteristic
103C22×C4×D5C2311yescharacteristic
104C22×C4×D5C2314yes—
105C22×Dic10—21no—
106C22×Dic10C2311yescharacteristic
107C22×Dic10C2311yescharacteristic
108C22×C5×C8C2311yescharacteristic
109C22×C5×C8C2311yescharacteristic
110C5×C22⋊Q8—22no—
111C5×C22⋊Q8C2314yes—
112C5×#117—22no—
113C5×#117C2314yes—
114C2×C5×C4⋊C4—21no—
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C4⋊C4C2311yescharacteristic
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C42×C5—21no—
121C2×C22⋊Dic5—21no—
122#4092—22no—
123#4092C2314yes—
124C2×#689—42no—
125C2×#689C2314yescomplemented
126C2×#688—42no—
127C2×#688C2314yescomplemented
128C2×#685—21no—
129C2×#685—21no—
130C2×#685—21no—
131C2×#685—21no—
132C2×#685—21no—
133C2×#685—21no—
134C2×C4⋊Dic5—21no—
135C2×C4⋊Dic5—21no—
136C2×C4⋊Dic5—21no—
137C2×C4⋊Dic5C2311yescharacteristic
138#4070—22no—
139#4070C2314yes—
140C2×#683—21no—
141C2×#683—21no—
142C2×#683—21no—
143C22×#168C2311yescharacteristic
144C22×#168C2311yescharacteristic
145C2×Dic20—42no—
146C2×Dic20C2314yescomplemented
147C2×#677—42no—
148C2×#677C2314yescomplemented
149C2×C8×D5—42no—
150C2×C8×D5—42no—
151C2×C8×D5C2314yes—
152C2×C8×D5C2314yes—
153#4043—22no—
154#4043—22no—
155#4043—22no—
156#4043C2314yes—
157#4043C2314yes—
158#4043C2314yes—
159#4042—28no—
160#4041—22no—
161#4041—22no—
162#4041C2314yes—
163#4041C2314yes—
164D5×C4⋊C4—28no—
165D5×C4⋊C4—22no—
166D5×C4⋊C4C2314yes—
167#4032—28no—
168#4028—28no—
169D5×C22⋊C4—28no—
170#4024—28no—
171C4×D20—28no—
172C4×D20—28no—
173C5×#107C2314yescomplemented
174C5×#106C2314yescomplemented
175C5×#103C2314yescomplemented
176C5×#103C2314yescomplemented
177C5×C22⋊C8C2314yes—
178C22⋊#168C2314yes—
179#3953C2314yescomplemented
180#3952C2314yes—
181#3952C2314yes—
182#3948C2314yescomplemented
183#3942C2314yescomplemented
184#3942C2314yescomplemented
185#3942C2314yescomplemented
186#3941C2314yescomplemented
187#3940C2314yescomplemented
188#3939C2314yescomplemented
189C2×#525—51no—
190C22×C22⋊Q8—51no—
191#3190—516no—
192C2×#485—51no—
193C2×#485D511yescharacteristic, complemented
194C2×#483—51no—
195C2×#480—51no—
196C2×#467—51no—
197C2×#467—51no—
198C2×#465—51no—
199C2×#465—51no—
200C2×#452—51no—
201C2×#452—51no—
202C2×#451—51no—
203C2×#448—51no—
204C22×C22⋊C8—51no—
205C24×C5C2×D411yescharacteristic
206C23×D5—24no—
207C23×D5—24no—
208C23×D5—21no—
209C23×D5—42no—
210C23×D5C2×D414yes—
211C23×D5C2×D411yescharacteristic
212C23×D5C2×D411yescharacteristic
213C2×C5×Q8—21no—
214C2×C5×Q8—22no—
215C2×C5×Q8—22no—
216C2×C5×Q8C2412yes—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2411yescharacteristic
227C2×C22⋊D5—24no—
228C2×C22⋊D5—44no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—42no—
233C22×Dic5C2×D411yescharacteristic
234C22×Dic5C2×D411yescharacteristic
235C22×Dic5C2×D414yes—
236Q8×D5—44no—
237Q8×D5—44no—
238Q8×D5—48no—
239#709—44no—
240#709—44no—
241#709—48no—
242C2×D20—22no—
243C2×D20—22no—
244C2×D20—24no—
245C2×D20—24no—
246C2×D20—21no—
247C2×D20—44no—
248C2×D20—44no—
249C2×D20C2412yes—
250C2×C4×D5—22no—
251C2×C4×D5—22no—
252C2×C4×D5—22no—
253C2×C4×D5—22no—
254C2×C4×D5—24no—
255C2×C4×D5—24no—
256C2×C4×D5—24no—
257C2×C4×D5—48no—
258C2×C4×D5—44no—
259C2×C4×D5—44no—
260C2×C4×D5—42no—
261C2×C4×D5—42no—
262C2×C4×D5—44no—
263C2×C4×D5—44no—
264C2×C4×D5—44no—
265C2×C4×D5C2×D412yes—
266C2×C4×D5C2×D412yes—
267C2×C4×D5C2×D414yes—
268C2×C4×D5C2×D414yes—
269C2×C4×D5C2412yes—
270C2×C4×D5C2412yes—
271C2×Dic10—22no—
272C2×Dic10—22no—
273C2×Dic10—22no—
274C2×Dic10—22no—
275C2×Dic10—21no—
276C2×Dic10—21no—
277C2×Dic10—24no—
278C2×Dic10—44no—
279C2×Dic10C2412yes—
280C2×Dic10C2412yes—
281C2×C5×C8—22no—
282C2×C5×C8—22no—
283C2×C5×C8C2412yes—
284C2×C5×C8C2412yes—
285C5×C4⋊C4—24no—
286C5×C4⋊C4—21no—
287C5×C4⋊C4—21no—
288C5×C4⋊C4—21no—
289C5×C4⋊C4C2412yes—
290C5×C4⋊C4C2412yes—
291C5×C4⋊C4C2412yes—
292C5×C22⋊C4—24no—
293C5×C22⋊C4—24no—
294C42×C5—24no—
295C22⋊Dic5—24no—
296#689—44no—
297#688—44no—
298#685—24no—
299#685—24no—
300#685—24no—
301#685—24no—
302#685—24no—
303#685—24no—
304C4⋊Dic5—21no—
305C4⋊Dic5—24no—
306C4⋊Dic5—24no—
307C4⋊Dic5—24no—
308C4⋊Dic5C2412yes—
309#683—24no—
310#683—24no—
311#683—24no—
312C2×#168—22no—
313C2×#168—22no—
314C2×#168C2412yes—
315C2×#168C2412yes—
316Dic20—44no—
317#677—44no—
318C8×D5—44no—
319C8×D5—44no—
320C22×#41—51no—
321C23×Q8—51no—
322C24×C4—51no—
323C22×Q16—51no—
324C22×Q16—51no—
325C22×SD16—51no—
326C22×SD16—51no—
327C23×C8—51no—
328C23×C8—51no—
329#525—58no—
330#525—104no—
331C2×#123—101no—
332C2×C22⋊Q8—51no—
333C2×C22⋊Q8—51no—
334C2×C22⋊Q8—58no—
335C2×C22⋊Q8—51no—
336C2×C22⋊Q8—51no—
337C2×C22⋊Q8—51no—
338C2×C22⋊Q8—101no—
339C2×C22⋊Q8—101no—
340C2×C22⋊Q8—104no—
341C2×C22⋊Q8C2×D511yescharacteristic
342C2×#121—51no—
343C2×#121—51no—
344C2×#120—101no—
345C2×C4×D4—101no—
346C2×C4×D4—101no—
347C2×#117C2×D511yescharacteristic
348C22×C4⋊C4—51no—
349C22×C4⋊C4—101no—
350C22×C22⋊C4—101no—
351#485—58no—
352#485C2×D518yescomplemented
353#483—58no—
354#480—58no—
355#467—58no—
356#467—58no—
357#465—58no—
358#465—58no—
359#452—58no—
360#452—58no—
361#451—58no—
362#448—58no—
363C2×#107—51no—
364C2×#107C2×D511yescharacteristic, complemented
365C2×#106—51no—
366C2×#106C2×D511yescharacteristic, complemented
367C2×#103—51no—
368C2×#103—51no—
369C2×#103—51no—
370C2×#103—51no—
371C2×#103C2×D511yescharacteristic, complemented
372C2×#103C2×D511yescharacteristic, complemented
373C2×#102—51no—
374C2×#102—51no—
375C2×C22⋊C8—51no—
376C2×C22⋊C8—51no—
377C2×C22⋊C8—51no—
378C2×C22⋊C8—58no—
379C2×C22⋊C8C2×D511yescharacteristic
380C23×C5—22no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5C22×D412yes—
384C23×C5C22×D411yescharacteristic
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—28no—
390C22×D5—28no—
391C22×D5—22no—
392C22×D5—44no—
393C22×D5—416no—
394C22×D5—42no—
395C22×D5—42no—
396C22×D5—42no—
397C22×D5#13514yes—
398C22×D5#13714yes—
399C22×D5C22×D412yes—
400C22×D5C22×D412yes—
401C5×Q8—22no—
402C5×Q8—22no—
403C5×Q8—42no—
404C2×C4×C5—22no—
405C2×C4×C5—24no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—42no—
413C2×C4×C5—42no—
414C2×C4×C5—42no—
415C2×C4×C5—42no—
416C2×C4×C5C22×D412yes—
417C2×C4×C5C22×D411yescharacteristic
418C2×C4×C5H(5,𝔽2)12yes—
419C2×C4×C5H(5,𝔽2)12yes—
420C2×C4×C5C2511yescharacteristic
421C22⋊D5—48no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—44no—
428C2×Dic5—42no—
429C2×Dic5—42no—
430C2×Dic5—42no—
431C2×Dic5C22×D412yes—
432C2×Dic5C22×D412yes—
433D20—22no—
434D20—22no—
435D20—48no—
436D20—48no—
437D20—42no—
438C4×D5—24no—
439C4×D5—24no—
440C4×D5—22no—
441C4×D5—22no—
442C4×D5—22no—
443C4×D5—22no—
444C4×D5—44no—
445C4×D5—44no—
446C4×D5—48no—
447C4×D5—48no—
448C4×D5—48no—
449Dic10—22no—
450Dic10—22no—
451Dic10—22no—
452Dic10—22no—
453Dic10—48no—
454Dic10—42no—
455Dic10—42no—
456C5×C8—22no—
457C5×C8—22no—
458#168—22no—
459#168—22no—
460C25—51no—
461C2×#41—54no—
462C2×#41—102no—
463C2×#41—202no—
464C2×#41—202no—
465C22×Q8—54no—
466C22×Q8—51no—
467C22×Q8—51no—
468C22×Q8—101no—
469C22×Q8—102no—
470C22×Q8—202no—
471C22×Q8—202no—
472C22×Q8C22×D511yescharacteristic
473C22×D4—51no—
474C22×D4—101no—
475C22×D4—101no—
476C22×D4—101no—
477C23×C4—51no—
478C23×C4—51no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—54no—
483C23×C4—54no—
484C23×C4—101no—
485C23×C4—101no—
486C23×C4—101no—
487C23×C4—202no—
488C23×C4—202no—
489C23×C4C22×D511yescharacteristic
490C2×Q16—54no—
491C2×Q16—54no—
492C2×Q16—202no—
493C2×Q16—202no—
494C2×SD16—54no—
495C2×SD16—54no—
496C2×SD16—202no—
497C2×SD16—202no—
498C22×C8—51no—
499C22×C8—51no—
500C22×C8—54no—
501C22×C8—54no—
502C22×C8—202no—
503C22×C8—202no—
504C22×C8C22×D511yescharacteristic
505C22×C8C22×D511yescharacteristic
506#123—108no—
507C22⋊Q8—22no—
508C22⋊Q8—54no—
509C22⋊Q8—54no—
510C22⋊Q8—54no—
511C22⋊Q8—54no—
512C22⋊Q8—54no—
513C22⋊Q8—108no—
514C22⋊Q8—108no—
515C22⋊Q8—102no—
516C22⋊Q8—102no—
517C22⋊Q8—102no—
518C22⋊Q8—102no—
519C22⋊Q8—102no—
520C22⋊Q8C22×D514yes—
521#121—54no—
522#121—54no—
523#121—102no—
524#121—102no—
525#120—108no—
526C4×D4—108no—
527C4×D4—108no—
528#117—22no—
529#117C22×D514yes—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—51no—
532C2×C4⋊C4—54no—
533C2×C4⋊C4—102no—
534C2×C4⋊C4—108no—
535C2×C4⋊C4—101no—
536C2×C4⋊C4—101no—
537C2×C4⋊C4—101no—
538C2×C4⋊C4—101no—
539C2×C4⋊C4—101no—
540C2×C4⋊C4—101no—
541C2×C4⋊C4C22×D511yescharacteristic
542C2×C4⋊C4C22×D511yescharacteristic
543C2×C4⋊C4C22×D511yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—108no—
547C2×C22⋊C4—101no—
548C2×C22⋊C4—101no—
549C2×C22⋊C4—101no—
550C2×C22⋊C4—101no—
551C2×C22⋊C4—101no—
552C2×C22⋊C4—101no—
553C2×C22⋊C4—101no—
554C2×C42—21no—
555#107—54no—
556#107C22×D514yescomplemented
557#106—54no—
558#106C22×D514yescomplemented
559#103—54no—
560#103—54no—
561#103—54no—
562#103—54no—
563#103C22×D514yescomplemented
564#103C22×D514yescomplemented
565#102—54no—
566#102—54no—
567C22⋊C8—54no—
568C22⋊C8—54no—
569C22⋊C8—54no—
570C22⋊C8C22×D514yes—
571C22×C5—22no—
572C22×C5—22no—
573C22×C5—22no—
574C22×C5—44no—
575C22×C5#53412yes—
576C22×C5C2×#13512yes—
577C22×C5C2×#13712yes—
578C22×C5C23×D411yescharacteristic
579C2×D5—22no—
580C2×D5—22no—
581C2×D5—28no—
582C2×D5—28no—
583C2×D5—22no—
584C2×D5—22no—
585C2×D5—416no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—84no—
590C2×D5C2×#13514yes—
591C2×D5C2×#13714yes—
592C4×C5—22no—
593C4×C5—42no—
594C4×C5—42no—
595C4×C5—42no—
596C4×C5—42no—
597C4×C5#53412yes—
598C4×C5C2×H(5,𝔽2)11yescharacteristic
599C4×C5C2×H(5,𝔽2)11yescharacteristic
600Dic5—22no—
601Dic5—22no—
602Dic5—42no—
603Dic5—42no—
604Dic5—42no—
605C24—51no—
606C24—51no—
607C24—54no—
608C24—104no—
609C24—104no—
610C24—101no—
611C24—202no—
612C24D4×D511yescharacteristic
613#41—204no—
614#41—204no—
615#41—208no—
616C2×Q8—21no—
617C2×Q8—22no—
618C2×Q8—22no—
619C2×Q8—52no—
620C2×Q8—52no—
621C2×Q8—104no—
622C2×Q8—101no—
623C2×Q8—101no—
624C2×Q8—102no—
625C2×Q8—102no—
626C2×Q8—102no—
627C2×Q8—102no—
628C2×Q8—204no—
629C2×Q8—204no—
630C2×Q8—204no—
631C2×Q8—208no—
632C2×Q8C23×D512yes—
633C2×D4—52no—
634C2×D4—104no—
635C2×D4—104no—
636C2×D4—104no—
637C2×D4—101no—
638C2×D4—102no—
639C2×D4—102no—
640C2×D4—204no—
641C2×D4—204no—
642C2×D4—204no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—51no—
650C22×C4—51no—
651C22×C4—54no—
652C22×C4—52no—
653C22×C4—52no—
654C22×C4—52no—
655C22×C4—52no—
656C22×C4—54no—
657C22×C4—54no—
658C22×C4—104no—
659C22×C4—104no—
660C22×C4—102no—
661C22×C4—102no—
662C22×C4—102no—
663C22×C4—102no—
664C22×C4—101no—
665C22×C4—101no—
666C22×C4—101no—
667C22×C4—104no—
668C22×C4—208no—
669C22×C4—204no—
670C22×C4—204no—
671C22×C4—202no—
672C22×C4—202no—
673C22×C4—204no—
674C22×C4—204no—
675C22×C4—204no—
676C22×C4—202no—
677C22×C4D4×D512yes—
678C22×C4D4×D511yescharacteristic
679C22×C4C23×D512yes—
680C22×C4C23×D511yescharacteristic
681Q16—204no—
682Q16—204no—
683SD16—204no—
684SD16—204no—
685C2×C8—22no—
686C2×C8—22no—
687C2×C8—52no—
688C2×C8—52no—
689C2×C8—102no—
690C2×C8—102no—
691C2×C8—204no—
692C2×C8—204no—
693C2×C8C23×D512yes—
694C2×C8C23×D512yes—
695C4⋊C4—24no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—52no—
700C4⋊C4—104no—
701C4⋊C4—104no—
702C4⋊C4—104no—
703C4⋊C4—104no—
704C4⋊C4—104no—
705C4⋊C4—101no—
706C4⋊C4—104no—
707C4⋊C4C23×D512yes—
708C4⋊C4C23×D512yes—
709C4⋊C4C23×D512yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—104no—
713C22⋊C4—104no—
714C22⋊C4—104no—
715C22⋊C4—104no—
716C22⋊C4—104no—
717C22⋊C4—104no—
718C22⋊C4—104no—
719C42—24no—
720C2×C5—42no—
721C2×C5#319014yescomplemented
722C2×C5C2×#53411yescharacteristic
723C2×C5C22×#13511yescharacteristic
724C2×C5C22×#13711yescharacteristic
725D5—24no—
726D5—24no—
727D5—82no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—54no—
732C23—54no—
733C23—52no—
734C23—52no—
735C23—108no—
736C23—108no—
737C23—102no—
738C23—102no—
739C23—102no—
740C23—102no—
741C23—102no—
742C23—204no—
743C23—2016no—
744C23—202no—
745C23—202no—
746C23—202no—
747C23C2×D4×D512yes—
748C23C2×D4×D511yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—42no—
752Q8—102no—
753Q8—102no—
754Q8—102no—
755Q8—102no—
756Q8—208no—
757Q8—202no—
758Q8—202no—
759D4—102no—
760D4—102no—
761D4—208no—
762D4—208no—
763D4—208no—
764D4—202no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—52no—
778C2×C4—52no—
779C2×C4—102no—
780C2×C4—102no—
781C2×C4—104no—
782C2×C4—104no—
783C2×C4—102no—
784C2×C4—102no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—204no—
791C2×C4—204no—
792C2×C4—208no—
793C2×C4—208no—
794C2×C4—208no—
795C2×C4—204no—
796C2×C4—202no—
797C2×C4—202no—
798C2×C4—202no—
799C2×C4C2×D4×D512yes—
800C2×C4C2×D4×D511yescharacteristic
801C2×C4#414912yes—
802C2×C4#414912yes—
803C2×C4C24×D511yescharacteristic
804C8—22no—
805C8—22no—
806C8—102no—
807C8—102no—
808C5C2×#319011yescharacteristic, complemented, Sylow
809C22—22no—
810C22—22no—
811C22—22no—
812C22—44no—
813C22—54no—
814C22—54no—
815C22—108no—
816C22—108no—
817C22—102no—
818C22—102no—
819C22—102no—
820C22—102no—
821C22—2016no—
822C22—202no—
823C22—202no—
824C22—202no—
825C22—404no—
826C22#6598712yes—
827C22D5×#13512yes—
828C22D5×#13712yes—
829C22C22×D4×D511yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—102no—
836C4—102no—
837C4—202no—
838C4—202no—
839C4—202no—
840C4#6598712yes—
841C4C2×#414911yescharacteristic
842C4C2×#414911yescharacteristic
843C2—42no—
844C2—104no—
845C2—104no—
846C2—402no—
847C2#1061325314yesdirect product factor
848C2C2×#6598711yescharacteristic
849C2C2×D5×#13511yescharacteristic
850C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#485C2
socleC23×C5C22×D4
prime radicalC2×#65858C2
hypercenterC2×#485D5
hypocenterC5C2×#3190
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×D5×C22⋊Q8C2semidirect
3. C2×C5×#485C2semidirect
4. C2×#65336C2semidirect
5. C2×#65285C2semidirect
6. #10613253C2direct (N × H)
7. C2×#65171C2semidirect
8. C2×#65176C2semidirect
9. C2×#65151C2semidirect
10. C2×#65153C2semidirect
11. C2×#65102C2semidirect
12. C2×#65096C2semidirect
13. C2×#65097C2semidirect
14. C2×#65095C2semidirect
15. C2×#65022C2semidirect
16. C2×D5×C22⋊C8C2semidirect
23. C22×#689C22semidirect
24. C22×#688C22semidirect
26. C22×Dic20C22semidirect
27. C22×#677C22semidirect
31. D5×C22⋊Q8C22semidirect
48. C5×#485C22semidirect
49. C2×C5×#107C22semidirect
50. C2×C5×#106C22semidirect
51. C2×C5×#103C22semidirect
52. C2×C5×#103C22semidirect
55. C2×#3953C22semidirect
58. C2×#3948C22semidirect
59. #65336C22semidirect
60. #65285C22semidirect
61. C2×#3942C22semidirect
62. C2×#3942C22semidirect
63. C2×#3942C22semidirect
64. C2×#3941C22semidirect
65. C2×#3940C22semidirect
66. C2×#3939C22semidirect
67. #65176C22semidirect
68. #65171C22semidirect
69. #65153C22semidirect
70. #65151C22semidirect
71. #65102C22semidirect
72. #65097C22semidirect
73. #65096C22semidirect
74. #65095C22semidirect
75. #65022C22semidirect
76. D5×C22⋊C8C22semidirect
125. C2×#689C23semidirect
127. C2×#688C23semidirect
146. C2×Dic20C23semidirect
148. C2×#677C23semidirect
173. C5×#107C23semidirect
174. C5×#106C23semidirect
175. C5×#103C23semidirect
176. C5×#103C23semidirect
179. #3953C23semidirect
182. #3948C23semidirect
183. #3942C23semidirect
184. #3942C23semidirect
185. #3942C23semidirect
186. #3941C23semidirect
187. #3940C23semidirect
188. #3939C23semidirect
193. C2×#485D5semidirect
352. #485C2×D5semidirect
364. C2×#107C2×D5semidirect
366. C2×#106C2×D5semidirect
371. C2×#103C2×D5semidirect
372. C2×#103C2×D5semidirect
556. #107C22×D5semidirect
558. #106C22×D5semidirect
563. #103C22×D5semidirect
564. #103C22×D5semidirect
721. C2×C5#3190semidirect
808. C5C2×#3190semidirect
847. C2#10613253direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×C22⋊Q82
C2×#658582
C2×C5×#4852
C2×#653362
C2×#652852
#106132532
C2×#651712
C2×#651762
C2×#651512
C2×#651532
C2×#651022
C2×#650962
C2×#650972
C2×#650952
C2×#650222
C2×D5×C22⋊C82
C2×#31905