Finite Group Databasebeta

← C2×#10614576 #12267169

Subgroups — C2×#10614576 #12267169

Order 1280.

3830 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#123C211yesmaximal, characteristic, complemented
2C22×#4085C211yesmaximal, characteristic
3C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4C22×#4029C211yesmaximal, characteristic, complemented
5C2×#65511C211yesmaximal, characteristic, complemented
6C2×#65499C211yesmaximal, characteristic, complemented
7#10614576C2116yesmaximal, direct product factor
8C2×#65282C211yesmaximal, characteristic, complemented
9C2×#65278C211yesmaximal, characteristic, complemented
10C2×#65261C211yesmaximal, characteristic, complemented
11C2×#65265C211yesmaximal, characteristic, complemented
12C2×#65248C211yesmaximal, characteristic, complemented
13C2×#65242C211yesmaximal, characteristic, complemented
14C2×#65246C211yesmaximal, characteristic, complemented
15C2×#65231C211yesmaximal, characteristic, complemented
16C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C2×C5×#123—28no—
24C2×C5×#123C2218yescomplemented
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×C22⋊Dic5C2211yescharacteristic
35C2×#4085—28no—
36C2×#4085C2218yes—
37C2×C4×C22⋊D5—28no—
38C2×C4×C22⋊D5C2218yescomplemented
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×#685C2211yescharacteristic
42C22×#685C2211yescharacteristic
43C22×C4⋊Dic5C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×#683C2211yescharacteristic
49C22×#683C2211yescharacteristic
50C22×C4×Dic5C2211yescharacteristic
51C22×C4×Dic5C2211yescharacteristic
52C2×#4029—28no—
53C2×#4029C2218yescomplemented
54#65511C2218yescomplemented
55#65499C2218yescomplemented
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#65282C2218yescomplemented
63#65278C2218yescomplemented
64#65265C2218yescomplemented
65#65261C2218yescomplemented
66#65248C2218yescomplemented
67#65246C2218yescomplemented
68#65242C2218yescomplemented
69#65231C2218yescomplemented
70C22⋊C4×Dic5C2218yescomplemented
71C2×#2422—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C25×C5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—42no—
78C22×C5×D4C2314yes—
79C23×C4×C5—24no—
80C23×C4×C5—24no—
81C23×C4×C5—42no—
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2314yes—
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C22×C22⋊D5—24no—
89C22×C22⋊D5—24no—
90C22×C22⋊D5—24no—
91C22×C22⋊D5—24no—
92C22×C22⋊D5—42no—
93C22×C22⋊D5D418yes—
94C22×C22⋊D5C2314yes—
95C22×C22⋊D5C2314yes—
96C23×Dic5—24no—
97C23×Dic5—24no—
98C23×Dic5—24no—
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2314yes—
105C23×Dic5C2311yescharacteristic
106C23×Dic5C2311yescharacteristic
107C22×C4×D5—24no—
108C22×C4×D5—24no—
109C22×C4×D5—42no—
110C22×C4×D5C2314yes—
111C5×#123—232no—
112C2×C5×C4⋊C4—24no—
113C2×C5×C4⋊C4—24no—
114C2×C5×C4⋊C4C2314yes—
115C2×C5×C4⋊C4C2314yes—
116C2×C5×C22⋊C4—24no—
117C2×C5×C22⋊C4—24no—
118C2×C5×C22⋊C4D418yescomplemented
119C2×C5×C22⋊C4C2314yes—
120C2×C5×C22⋊C4C2314yes—
121C2×C5×C22⋊C4C2314yes—
122C2×C22⋊Dic5—24no—
123C2×C22⋊Dic5—24no—
124C2×C22⋊Dic5—24no—
125C2×C22⋊Dic5—24no—
126C2×C22⋊Dic5—24no—
127C2×C22⋊Dic5C2314yes—
128C2×C22⋊Dic5C2314yes—
129C2×C22⋊Dic5C2314yes—
130C2×C22⋊Dic5C2314yes—
131C2×C22⋊Dic5C2314yes—
132#4085—232no—
133C4×C22⋊D5—232no—
134C2×#685—24no—
135C2×#685—24no—
136C2×#685—24no—
137C2×#685—24no—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×#685C2314yes—
142C2×C4⋊Dic5—24no—
143C2×C4⋊Dic5C2314yes—
144C2×#683—24no—
145C2×#683—24no—
146C2×#683—24no—
147C2×#683—24no—
148C2×#683—42no—
149C2×#683—42no—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×#683C2314yes—
156C2×C4×Dic5—24no—
157C2×C4×Dic5—24no—
158C2×C4×Dic5C2314yes—
159C2×C4×Dic5C2314yes—
160#4029—232no—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#123—51no—
168C22×#123D511yescharacteristic, complemented
169C22×#121—51no—
170C22×C4×D4—51no—
171#2422—516no—
172C2×#397—51no—
173C2×#397—51no—
174C2×#394—51no—
175C2×#394—51no—
176C2×#390—51no—
177C2×#389—51no—
178C2×#385—51no—
179C2×#385—51no—
180C2×#384—51no—
181C2×#380—51no—
182C2×C4×C22⋊C4—51no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5—22no—
190C24×C5—22no—
191C24×C5—22no—
192C24×C5—22no—
193C24×C5—22no—
194C24×C5—22no—
195C24×C5C2×D414yes—
196C24×C5C2×D414yes—
197C24×C5C2412yes—
198C24×C5C2412yes—
199C24×C5C2411yescharacteristic
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5—22no—
205C23×D5—22no—
206C23×D5C2×D414yes—
207C23×D5C2412yes—
208C2×C5×D4—28no—
209C2×C5×D4—28no—
210C2×C5×D4—44no—
211C2×C5×D4—416no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—28no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5—28no—
227C22×C4×C5—44no—
228C22×C4×C5—416no—
229C22×C4×C5C2×D414yes—
230C22×C4×C5C2×D414yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C2×C22⋊D5—28no—
237C2×C22⋊D5—28no—
238C2×C22⋊D5—232no—
239C2×C22⋊D5—28no—
240C2×C22⋊D5—28no—
241C2×C22⋊D5—44no—
242C2×C22⋊D5—416no—
243C2×C22⋊D5C2×D4116yes—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5—22no—
257C22×Dic5—22no—
258C22×Dic5—22no—
259C22×Dic5—22no—
260C22×Dic5—22no—
261C22×Dic5—28no—
262C22×Dic5—28no—
263C22×Dic5—28no—
264C22×Dic5—416no—
265C22×Dic5C2×D414yes—
266C22×Dic5#4114yes—
267C22×Dic5#4114yes—
268C22×Dic5#4114yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C22×Dic5C2412yes—
273C22×Dic5C2412yes—
274C22×Dic5C2412yes—
275C22×Dic5C2412yes—
276C2×C4×D5—28no—
277C2×C4×D5—28no—
278C2×C4×D5—44no—
279C2×C4×D5—416no—
280C5×C4⋊C4—28no—
281C5×C4⋊C4—28no—
282C5×C22⋊C4—28no—
283C5×C22⋊C4—28no—
284C5×C22⋊C4C2×D4116yescomplemented
285C22⋊Dic5—28no—
286C22⋊Dic5—28no—
287C22⋊Dic5—28no—
288C22⋊Dic5—28no—
289C22⋊Dic5—28no—
290#685—28no—
291#685—28no—
292#685—28no—
293#685—28no—
294C4⋊Dic5—28no—
295#683—28no—
296#683—28no—
297#683—28no—
298#683—28no—
299#683—44no—
300#683—44no—
301C4×Dic5—28no—
302C4×Dic5—28no—
303C23×D4—51no—
304C23×D4—51no—
305C23×D4C2×D511yescharacteristic
306C24×C4—51no—
307C24×C4—51no—
308C24×C4C2×D511yescharacteristic
309C2×#123—28no—
310C2×#123—58no—
311C2×#123—108no—
312C2×#123C2×D518yescomplemented
313C2×#121—58no—
314C2×#121—108no—
315C2×C4×D4—58no—
316C2×C4×D4—108no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—51no—
323C22×C4⋊C4—51no—
324C22×C4⋊C4C2×D511yescharacteristic
325C22×C4⋊C4C2×D511yescharacteristic
326C22×C22⋊C4—51no—
327C22×C22⋊C4—51no—
328C22×C22⋊C4—51no—
329C22×C22⋊C4—51no—
330C22×C22⋊C4—51no—
331C22×C22⋊C4—51no—
332C22×C22⋊C4—51no—
333C22×C22⋊C4—51no—
334C22×C22⋊C4—51no—
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C22⋊C4C2×D511yescharacteristic
338C22×C42—51no—
339C22×C42—51no—
340#397—58no—
341#397—58no—
342#394—58no—
343#394—58no—
344#390—58no—
345#389—58no—
346#385—58no—
347#385—58no—
348#384—58no—
349#380—58no—
350C4×C22⋊C4—58no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95—51no—
356C2×#95—51no—
357C23×C5—28no—
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—28no—
361C23×C5—28no—
362C23×C5—28no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—44no—
376C23×C5—44no—
377C23×C5—44no—
378C23×C5—44no—
379C23×C5—44no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5—44no—
383C23×C5C22×D414yes—
384C23×C5C22×D412yes—
385C23×C5C22×D414yes—
386C23×C5C22×D412yes—
387C23×C5C2×#4112yes—
388C23×C5C2×#4112yes—
389C23×C5C2×#4112yes—
390C23×C5H(5,𝔽2)12yes—
391C23×C52−1+412yes—
392C23×C5C2511yescharacteristic
393C22×D5—28no—
394C22×D5—28no—
395C22×D5—28no—
396C22×D5—22no—
397C22×D5—22no—
398C22×D5—22no—
399C22×D5—22no—
400C22×D5—22no—
401C22×D5—22no—
402C22×D5—44no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5—44no—
406C22×D5C22×D414yes—
407C5×D4—416no—
408C2×C4×C5—28no—
409C2×C4×C5—28no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—416no—
424C2×C4×C5—44no—
425C2×C4×C5—44no—
426C2×C4×C5—44no—
427C2×C4×C5C22×D414yes—
428C2×C4×C5C22×D414yes—
429C22⋊D5—232no—
430C22⋊D5—416no—
431C2×Dic5—28no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—22no—
441C2×Dic5—22no—
442C2×Dic5—22no—
443C2×Dic5—22no—
444C2×Dic5—22no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—22no—
448C2×Dic5—22no—
449C2×Dic5—44no—
450C2×Dic5—44no—
451C2×Dic5—44no—
452C2×Dic5—44no—
453C2×Dic5—44no—
454C2×Dic5—416no—
455C2×Dic5#123116yescomplemented
456C2×Dic5C22×D414yes—
457C2×Dic5C2×#4114yes—
458C2×Dic5C2×#4114yes—
459C2×Dic5C2×#4114yes—
460C4×D5—416no—
461C25—51no—
462C25C22×D511yescharacteristic
463C25C22×D511yescharacteristic
464C22×D4—24no—
465C22×D4—24no—
466C22×D4—42no—
467C22×D4—58no—
468C22×D4—54no—
469C22×D4—54no—
470C22×D4—104no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—202no—
475C22×D4C22×D514yes—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—42no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—54no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—54no—
488C23×C4—104no—
489C23×C4—104no—
490C23×C4—104no—
491C23×C4—104no—
492C23×C4—104no—
493C23×C4—202no—
494C23×C4C22×D511yescharacteristic
495C23×C4C22×D511yescharacteristic
496C23×C4C22×D511yescharacteristic
497C23×C4C22×D514yes—
498C23×C4C22×D511yescharacteristic
499C23×C4C22×D511yescharacteristic
500#123—232no—
501#123—1032no—
502#121—1032no—
503C4×D4—1032no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—54no—
507C2×C4⋊C4—54no—
508C2×C4⋊C4—54no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—54no—
511C2×C4⋊C4—54no—
512C2×C4⋊C4—54no—
513C2×C4⋊C4—104no—
514C2×C4⋊C4—104no—
515C2×C4⋊C4—104no—
516C2×C4⋊C4—104no—
517C2×C4⋊C4—104no—
518C2×C4⋊C4—202no—
519C2×C4⋊C4—202no—
520C2×C4⋊C4C22×D514yes—
521C2×C4⋊C4C22×D514yes—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—54no—
525C2×C22⋊C4—54no—
526C2×C22⋊C4—54no—
527C2×C22⋊C4—54no—
528C2×C22⋊C4—54no—
529C2×C22⋊C4—54no—
530C2×C22⋊C4—54no—
531C2×C22⋊C4—54no—
532C2×C22⋊C4—54no—
533C2×C22⋊C4—104no—
534C2×C22⋊C4—104no—
535C2×C22⋊C4—104no—
536C2×C22⋊C4—104no—
537C2×C22⋊C4—104no—
538C2×C22⋊C4—104no—
539C2×C22⋊C4—104no—
540C2×C22⋊C4—104no—
541C2×C22⋊C4—104no—
542C2×C22⋊C4C22⋊D518yescomplemented
543C2×C22⋊C4C22×D514yes—
544C2×C22⋊C4C22×D514yes—
545C2×C22⋊C4C22×D514yes—
546C2×C42—54no—
547C2×C42—54no—
548C2×C42—104no—
549C2×C42—104no—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95—54no—
555#95—54no—
556C22×C5—24no—
557C22×C5—24no—
558C22×C5—24no—
559C22×C5—24no—
560C22×C5—24no—
561C22×C5—24no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—416no—
565C22×C5—416no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5C2×#12314yes—
573C22×C5#53214yes—
574C22×C5#54214yes—
575C22×C5D4214yes—
576C22×C5#54714yes—
577C22×C5#54714yes—
578C22×C5#55314yes—
579C22×C5C23×D411yescharacteristic
580C22×C5C23×D411yescharacteristic
581C22×C5C22×#4111yescharacteristic
582C22×C5C22×#4111yescharacteristic
583C22×C5C22×#4111yescharacteristic
584C22×C5C2×H(5,𝔽2)11yescharacteristic
585C22×C5C2×2−1+411yescharacteristic
586C2×D5—24no—
587C2×D5—24no—
588C2×D5—24no—
589C2×D5—42no—
590C2×D5—416no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—42no—
594C4×C5—24no—
595C4×C5—24no—
596C4×C5—42no—
597C4×C5—42no—
598C4×C5—42no—
599Dic5—24no—
600Dic5—42no—
601Dic5—42no—
602Dic5—42no—
603Dic5—42no—
604Dic5—42no—
605Dic5C2×#12318yescomplemented
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—54no—
619C24—52no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24D4×D514yes—
627C24C2×C22⋊D514yes—
628C24C23×D512yes—
629C24C23×D512yes—
630C24C23×D511yescharacteristic
631C2×D4—28no—
632C2×D4—28no—
633C2×D4—44no—
634C2×D4—416no—
635C2×D4—516no—
636C2×D4—1032no—
637C2×D4—108no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—204no—
642C2×D4—2016no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—28no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—28no—
658C22×C4—44no—
659C22×C4—416no—
660C22×C4—54no—
661C22×C4—54no—
662C22×C4—54no—
663C22×C4—52no—
664C22×C4—54no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—52no—
671C22×C4—108no—
672C22×C4—108no—
673C22×C4—108no—
674C22×C4—108no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—102no—
690C22×C4—102no—
691C22×C4—102no—
692C22×C4—108no—
693C22×C4—204no—
694C22×C4—2016no—
695C22×C4—2016no—
696C22×C4C2×C22⋊D514yes—
697C22×C4C2×C22⋊D514yes—
698C22×C4C23×D512yes—
699C22×C4C23×D512yes—
700C22×C4C23×D512yes—
701C22×C4C23×D512yes—
702C22×C4C23×D512yes—
703C4⋊C4—28no—
704C4⋊C4—28no—
705C4⋊C4—108no—
706C4⋊C4—108no—
707C4⋊C4—108no—
708C4⋊C4—108no—
709C4⋊C4—108no—
710C4⋊C4—204no—
711C4⋊C4—204no—
712C22⋊C4—28no—
713C22⋊C4—28no—
714C22⋊C4—108no—
715C22⋊C4—108no—
716C22⋊C4—108no—
717C22⋊C4—108no—
718C22⋊C4—108no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C22⋊C4C2×C22⋊D5116yescomplemented
724C42—108no—
725C42—108no—
726C2×C5—44no—
727C2×C5—44no—
728C2×C5#242218yescomplemented
729C2×C5C22×#12311yescharacteristic
730C2×C5C2×#53211yescharacteristic
731C2×C5C2×#54211yescharacteristic
732C2×C5C2×D4211yescharacteristic
733C2×C5C2×#54711yescharacteristic
734C2×C5C2×#54711yescharacteristic
735C2×C5C2×#55311yescharacteristic
736D5—44no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—54no—
764C23—108no—
765C23—108no—
766C23—108no—
767C23—102no—
768C23—102no—
769C23—102no—
770C23—102no—
771C23—102no—
772C23—102no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23C2×D4×D514yes—
778C23C2×D4×D512yes—
779C23#414412yes—
780C23D5×#4112yes—
781C23D5×#4112yes—
782C23D5×#4112yes—
783C23#415012yes—
784C23C22×C22⋊D514yes—
785C23C22×C22⋊D512yes—
786C23C24×D511yescharacteristic
787D4—416no—
788D4—1032no—
789D4—2016no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—416no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—516no—
810C2×C4—54no—
811C2×C4—54no—
812C2×C4—54no—
813C2×C4—54no—
814C2×C4—108no—
815C2×C4—102no—
816C2×C4—102no—
817C2×C4—102no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—2016no—
833C2×C4—2016no—
834C2×C4—204no—
835C2×C4—204no—
836C2×C4—204no—
837C2×C4—204no—
838C2×C4—204no—
839C2×C4C22×C22⋊D514yes—
840C2×C4C22×C22⋊D514yes—
841C5C2×#242211yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—416no—
855C22—416no—
856C22—42no—
857C22—42no—
858C22—104no—
859C22—104no—
860C22—104no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—2016no—
866C22D5×#12314yes—
867C22#6598914yes—
868C22#6599514yes—
869C22#6599614yes—
870C22D4×C22⋊D514yes—
871C22#6615814yes—
872C22#6616614yes—
873C22C22×D4×D511yescharacteristic
874C22C2×#414411yescharacteristic
875C22C2×D5×#4111yescharacteristic
876C22C2×D5×#4111yescharacteristic
877C22C2×D5×#4111yescharacteristic
878C22C2×#415011yescharacteristic
879C22C23×C22⋊D511yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—58no—
886C4—104no—
887C4—202no—
888C4—202no—
889C4—202no—
890C4—202no—
891C4—202no—
892C2—44no—
893C2—44no—
894C2—204no—
895C2#1061457618yesdirect product factor
896C2C2×#6599611yescharacteristic
897C2C2×#6599511yescharacteristic
898C2C2×D5×#12311yescharacteristic
899C2C2×#6598911yescharacteristic
900C2C2×D4×C22⋊D511yescharacteristic
901C2C2×#6616611yescharacteristic
902C2C2×#6615811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#123C2
socleC24×C5C24
prime radicalC22×#4085C2
hypercenterC22×#123D5
hypocenterC5C2×#2422
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C5×#123C2semidirect
3. C22×C4×C22⋊D5C2semidirect
4. C22×#4029C2semidirect
5. C2×#65511C2semidirect
6. C2×#65499C2semidirect
7. #10614576C2direct (N × H)
8. C2×#65282C2semidirect
9. C2×#65278C2semidirect
10. C2×#65261C2semidirect
11. C2×#65265C2semidirect
12. C2×#65248C2semidirect
13. C2×#65242C2semidirect
14. C2×#65246C2semidirect
15. C2×#65231C2semidirect
16. C2×C22⋊C4×Dic5C2semidirect
24. C2×C5×#123C22semidirect
38. C2×C4×C22⋊D5C22semidirect
53. C2×#4029C22semidirect
54. #65511C22semidirect
55. #65499C22semidirect
62. #65282C22semidirect
63. #65278C22semidirect
64. #65265C22semidirect
65. #65261C22semidirect
66. #65248C22semidirect
67. #65246C22semidirect
68. #65242C22semidirect
69. #65231C22semidirect
70. C22⋊C4×Dic5C22semidirect
118. C2×C5×C22⋊C4D4semidirect
168. C22×#123D5semidirect
284. C5×C22⋊C4C2×D4semidirect
312. C2×#123C2×D5semidirect
455. C2×Dic5#123semidirect
542. C2×C22⋊C4C22⋊D5semidirect
605. Dic5C2×#123semidirect
723. C22⋊C4C2×C22⋊D5semidirect
728. C2×C5#2422semidirect
841. C5C2×#2422semidirect
895. C2#10614576direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1232
C22×#40852
C22×C4×C22⋊D52
C22×#40292
C2×#655112
C2×#654992
#106145762
C2×#652822
C2×#652782
C2×#652612
C2×#652652
C2×#652482
C2×#652422
C2×#652462
C2×#652312
C2×C22⋊C4×Dic52
C2×#24225