Finite Group Databasebeta

← C2×#10614583 #12267153

Subgroups — C2×#10614583 #12267153

Order 1280.

3786 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×#4082C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4C22×#4042C211yesmaximal, characteristic, complemented
5C2×#65512C211yesmaximal, characteristic
6C2×#65499C211yesmaximal, characteristic, complemented
7#10614583C2116yesmaximal, direct product factor
8C2×#65268C211yesmaximal, characteristic, complemented
9C2×#65279C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
11C2×#65245C211yesmaximal, characteristic, complemented
12C2×#65237C211yesmaximal, characteristic, complemented
13C2×#65250C211yesmaximal, characteristic, complemented
14C2×#65246C211yesmaximal, characteristic, complemented
15C2×#65234C211yesmaximal, characteristic, complemented
16C2×#65234C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×Dic10C2211yescharacteristic
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
35C22×C22⋊Dic5C2211yescharacteristic
36C2×#4082—28no—
37C2×#4082C2218yescomplemented
38C2×C4×C22⋊D5—28no—
39C2×C4×C22⋊D5C2218yescomplemented
40C22×#685C2211yescharacteristic
41C22×#685C2211yescharacteristic
42C22×#685C2211yescharacteristic
43C22×#685C2211yescharacteristic
44C22×C4⋊Dic5C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×#683C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C22×C4×Dic5C2211yescharacteristic
51C22×C4×Dic5C2211yescharacteristic
52C2×#4042—28no—
53C2×#4042C2218yescomplemented
54#65512C2218yes—
55#65499C2218yescomplemented
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#65279C2218yescomplemented
63#65268C2218yescomplemented
64C4⋊C4×Dic5C2218yescomplemented
65#65250C2218yescomplemented
66#65246C2218yescomplemented
67#65245C2218yescomplemented
68#65237C2218yescomplemented
69#65234C2218yescomplemented
70#65234C2218yescomplemented
71C2×#2461—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×C5C2314yes—
85C23×C4×C5C2311yescharacteristic
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—24no—
93C22×C22⋊D5—42no—
94C22×C22⋊D5C2314yes—
95C22×C22⋊D5C2314yes—
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—42no—
106C22×C4×D5C2314yes—
107C22×Dic10—24no—
108C22×Dic10—24no—
109C22×Dic10—42no—
110C22×Dic10C2314yes—
111C5×#123—232no—
112C2×C5×C4⋊C4—24no—
113C2×C5×C4⋊C4D418yescomplemented
114C2×C5×C4⋊C4C2314yes—
115C2×C5×C4⋊C4C2314yes—
116C2×C5×C22⋊C4—24no—
117C2×C5×C22⋊C4—24no—
118C2×C5×C22⋊C4—24no—
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⋊Dic5D418yescomplemented
128C2×C22⋊Dic5C2314yes—
129C2×C22⋊Dic5C2314yes—
130C2×C22⋊Dic5C2314yes—
131C2×C22⋊Dic5C2314yes—
132C2×C22⋊Dic5C2314yes—
133C2×C22⋊Dic5C2314yes—
134#4082—232no—
135C4×C22⋊D5—232no—
136C2×#685—24no—
137C2×#685—24no—
138C2×#685—24no—
139C2×#685—24no—
140C2×#685C2314yes—
141C2×#685C2314yes—
142C2×#685C2314yes—
143C2×#685C2314yes—
144C2×C4⋊Dic5—24no—
145C2×C4⋊Dic5C2314yes—
146C2×#683—24no—
147C2×#683—24no—
148C2×#683—24no—
149C2×#683—42no—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×C4×Dic5—24no—
155C2×C4×Dic5—24no—
156C2×C4×Dic5—24no—
157C2×C4×Dic5C2314yes—
158C2×C4×Dic5C2314yes—
159C2×C4×Dic5C2314yes—
160#4042—232no—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#124—51no—
168C22×#123D511yescharacteristic, complemented
169C22×C22⋊Q8—51no—
170C22×C4×D4—51no—
171#2461—516no—
172C2×#396—51no—
173C2×#395—51no—
174C2×#394—51no—
175C2×#392—51no—
176C2×#390—51no—
177C2×#388—51no—
178C2×#388—51no—
179C2×#388—51no—
180C2×#386—51no—
181C2×#385—51no—
182C2×C4×C4⋊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×C5—22no—
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×D5#4114yes—
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—22no—
221C22×C4×C5—28no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—28no—
226C22×C4×C5—44no—
227C22×C4×C5—416no—
228C22×C4×C5C2×D414yes—
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—232no—
237C2×C22⋊D5—28no—
238C2×C22⋊D5—28no—
239C2×C22⋊D5—28no—
240C2×C22⋊D5—28no—
241C2×C22⋊D5—28no—
242C2×C22⋊D5—44no—
243C2×C22⋊D5—416no—
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×Dic5C2×D414yes—
262C22×Dic5C2×D414yes—
263C22×Dic5#4114yes—
264C22×Dic5#4114yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C22×Dic5C2412yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C2×C4×D5—28no—
273C2×C4×D5—28no—
274C2×C4×D5—44no—
275C2×C4×D5—416no—
276C2×Dic10—28no—
277C2×Dic10—28no—
278C2×Dic10—44no—
279C2×Dic10—416no—
280C5×C4⋊C4—28no—
281C5×C4⋊C4C2×D4116yescomplemented
282C5×C22⋊C4—28no—
283C5×C22⋊C4—28no—
284C5×C22⋊C4—28no—
285C22⋊Dic5—28no—
286C22⋊Dic5—28no—
287C22⋊Dic5—28no—
288C22⋊Dic5—28no—
289C22⋊Dic5—28no—
290C22⋊Dic5C2×D4116yescomplemented
291#685—28no—
292#685—28no—
293#685—28no—
294#685—28no—
295C4⋊Dic5—28no—
296#683—28no—
297#683—28no—
298#683—28no—
299#683—44no—
300C4×Dic5—28no—
301C4×Dic5—28no—
302C4×Dic5—28no—
303C23×Q8—51no—
304C23×D4—51no—
305C23×D4—51no—
306C23×D4C2×D511yescharacteristic
307C24×C4—51no—
308C24×C4C2×D511yescharacteristic
309C2×#124—58no—
310C2×#124—108no—
311C2×#123—28no—
312C2×#123C2×D518yescomplemented
313C2×C22⋊Q8—58no—
314C2×C22⋊Q8—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⋊C4C2×D511yescharacteristic
323C22×C4⋊C4C2×D511yescharacteristic
324C22×C22⋊C4—51no—
325C22×C22⋊C4—51no—
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⋊C4C2×D511yescharacteristic
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C42—51no—
338C22×C42—51no—
339C22×C42—51no—
340#396—58no—
341#395—58no—
342#394—58no—
343#392—58no—
344#390—58no—
345#388—58no—
346#388—58no—
347#388—58no—
348#386—58no—
349#385—58no—
350C4×C4⋊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—22no—
361C23×C5—22no—
362C23×C5—22no—
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—44no—
374C23×C5—44no—
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×C5—44no—
384C23×C5C22×D414yes—
385C23×C5C22×D412yes—
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×D5C2×#4114yes—
407C5×D4—416no—
408C2×C4×C5—28no—
409C2×C4×C5—28no—
410C2×C4×C5—28no—
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×C5C22×D414yes—
427C2×C4×C5C22×D414yes—
428C2×C4×C5C22×D414yes—
429C22⋊D5—232no—
430C22⋊D5—416no—
431C2×Dic5—28no—
432C2×Dic5—28no—
433C2×Dic5—28no—
434C2×Dic5—28no—
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—22no—
450C2×Dic5—22no—
451C2×Dic5—22no—
452C2×Dic5—44no—
453C2×Dic5—44no—
454C2×Dic5—44no—
455C2×Dic5C22×D414yes—
456C2×Dic5C22×D414yes—
457C2×Dic5C2×#4114yes—
458C2×Dic5C2×#4114yes—
459C4×D5—416no—
460Dic10—416no—
461C25—51no—
462C25C22×D511yescharacteristic
463C25C22×D511yescharacteristic
464C22×Q8—54no—
465C22×Q8—104no—
466C22×Q8—104no—
467C22×Q8—202no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—42no—
471C22×D4—54no—
472C22×D4—54no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4—104no—
478C22×D4—202no—
479C22×D4C22×D514yes—
480C23×C4—24no—
481C23×C4—24no—
482C23×C4—42no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—51no—
488C23×C4—51no—
489C23×C4—51no—
490C23×C4—54no—
491C23×C4—104no—
492C23×C4—104no—
493C23×C4—202no—
494C23×C4C22×D511yescharacteristic
495C23×C4C22×D511yescharacteristic
496C23×C4C22×D514yes—
497C23×C4C22×D511yescharacteristic
498C23×C4C22×D511yescharacteristic
499C23×C4C22×D511yescharacteristic
500#124—1032no—
501#123—232no—
502C22⋊Q8—1032no—
503C4×D4—1032no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—54no—
506C2×C4⋊C4—54no—
507C2×C4⋊C4—54no—
508C2×C4⋊C4—54no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—104no—
511C2×C4⋊C4—104no—
512C2×C4⋊C4—104no—
513C2×C4⋊C4—104no—
514C2×C4⋊C4—202no—
515C2×C4⋊C4C22⋊D518yescomplemented
516C2×C4⋊C4C22×D514yes—
517C2×C4⋊C4C22×D514yes—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—58no—
522C2×C22⋊C4—54no—
523C2×C22⋊C4—54no—
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—104no—
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⋊C4C22×D514yes—
542C2×C22⋊C4C22×D514yes—
543C2×C22⋊C4C22×D514yes—
544C2×C42—54no—
545C2×C42—54no—
546C2×C42—54no—
547C2×C42—104no—
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—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—416no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—88no—
572C22×C5#52514yes—
573C22×C5#53214yes—
574C22×C5#54214yes—
575C22×C5D4214yes—
576C22×C5#54714yes—
577C22×C5#54814yes—
578C22×C5#55114yes—
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—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—416no—
594C4×C5—24no—
595C4×C5—24no—
596C4×C5—24no—
597C4×C5—42no—
598C4×C5—42no—
599Dic5—24no—
600Dic5—24no—
601Dic5—24no—
602Dic5—24no—
603Dic5—42no—
604Dic5—42no—
605Dic5—42no—
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—22no—
619C24—54no—
620C24—52no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24D4×D514yes—
628C24C23×D512yes—
629C24C23×D512yes—
630C24C23×D511yescharacteristic
631C2×Q8—108no—
632C2×Q8—108no—
633C2×Q8—204no—
634C2×Q8—2016no—
635C2×D4—28no—
636C2×D4—28no—
637C2×D4—44no—
638C2×D4—416no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—1032no—
643C2×D4—108no—
644C2×D4—108no—
645C2×D4—204no—
646C2×D4—2016no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—28no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—28no—
661C22×C4—44no—
662C22×C4—416no—
663C22×C4—54no—
664C22×C4—54no—
665C22×C4—54no—
666C22×C4—54no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—52no—
671C22×C4—52no—
672C22×C4—52no—
673C22×C4—52no—
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×C4C2×C22⋊D514yes—
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—108no—
705C4⋊C4—108no—
706C4⋊C4—108no—
707C4⋊C4—108no—
708C4⋊C4—204no—
709C4⋊C4C2×C22⋊D5116yescomplemented
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—28no—
713C22⋊C4—516no—
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—
723C42—108no—
724C42—108no—
725C42—108no—
726C2×C5—44no—
727C2×C5—82no—
728C2×C5#246118yescomplemented
729C2×C5C2×#52511yescharacteristic
730C2×C5C2×#53211yescharacteristic
731C2×C5C2×#54211yescharacteristic
732C2×C5C2×D4211yescharacteristic
733C2×C5C2×#54711yescharacteristic
734C2×C5C2×#54811yescharacteristic
735C2×C5C2×#55111yescharacteristic
736D5—44no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—54no—
765C23—108no—
766C23—108no—
767C23—108no—
768C23—102no—
769C23—102no—
770C23—102no—
771C23—102no—
772C23—102no—
773C23—102no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23C2×D4×D514yes—
779C23C2×D4×D512yes—
780C23#414412yes—
781C23D5×#4112yes—
782C23D5×#4112yes—
783C23D5×#4112yes—
784C23#415012yes—
785C23C22×C22⋊D512yes—
786C23C24×D511yescharacteristic
787Q8—2016no—
788D4—416no—
789D4—1032no—
790D4—2016no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
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—22no—
806C2×C4—416no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—54no—
810C2×C4—54no—
811C2×C4—54no—
812C2×C4—54no—
813C2×C4—108no—
814C2×C4—108no—
815C2×C4—108no—
816C2×C4—108no—
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—102no—
833C2×C4—102no—
834C2×C4—2016no—
835C2×C4—204no—
836C2×C4—204no—
837C2×C4—204no—
838C2×C4C22×C22⋊D514yes—
839C2×C4C22×C22⋊D514yes—
840C2×C4C22×C22⋊D514yes—
841C5C2×#246111yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—416no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—88no—
858C22—104no—
859C22—104no—
860C22—104no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—2016no—
866C22#6598914yes—
867C22#6599014yes—
868C22#6599314yes—
869C22#6599614yes—
870C22D4×C22⋊D514yes—
871C22#6616514yes—
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—24no—
883C4—42no—
884C4—42no—
885C4—104no—
886C4—104no—
887C4—104no—
888C4—104no—
889C4—202no—
890C4—202no—
891C4—202no—
892C2—44no—
893C2—82no—
894C2—204no—
895C2#1061458318yesdirect product factor
896C2C2×#6599011yescharacteristic
897C2C2×#6599611yescharacteristic
898C2C2×#6598911yescharacteristic
899C2C2×#6599311yescharacteristic
900C2C2×D4×C22⋊D511yescharacteristic
901C2C2×#6616611yescharacteristic
902C2C2×#6616511yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#123C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC22×#123D5
hypocenterC5C2×#2461
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
2. C22×#4082C2semidirect
3. C22×C4×C22⋊D5C2semidirect
4. C22×#4042C2semidirect
6. C2×#65499C2semidirect
7. #10614583C2direct (N × H)
8. C2×#65268C2semidirect
9. C2×#65279C2semidirect
10. C2×C4⋊C4×Dic5C2semidirect
11. C2×#65245C2semidirect
12. C2×#65237C2semidirect
13. C2×#65250C2semidirect
14. C2×#65246C2semidirect
15. C2×#65234C2semidirect
16. C2×#65234C2semidirect
24. C2×C5×#123C22semidirect
37. C2×#4082C22semidirect
39. C2×C4×C22⋊D5C22semidirect
53. C2×#4042C22semidirect
55. #65499C22semidirect
62. #65279C22semidirect
63. #65268C22semidirect
64. C4⋊C4×Dic5C22semidirect
65. #65250C22semidirect
66. #65246C22semidirect
67. #65245C22semidirect
68. #65237C22semidirect
69. #65234C22semidirect
70. #65234C22semidirect
113. C2×C5×C4⋊C4D4semidirect
127. C2×C22⋊Dic5D4semidirect
168. C22×#123D5semidirect
281. C5×C4⋊C4C2×D4semidirect
290. C22⋊Dic5C2×D4semidirect
312. C2×#123C2×D5semidirect
515. C2×C4⋊C4C22⋊D5semidirect
709. C4⋊C4C2×C22⋊D5semidirect
728. C2×C5#2461semidirect
841. C5C2×#2461semidirect
895. C2#10614583direct (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×#40822
C22×C4×C22⋊D52
C22×#40422
C2×#655122
C2×#654992
#106145832
C2×#652682
C2×#652792
C2×C4⋊C4×Dic52
C2×#652452
C2×#652372
C2×#652502
C2×#652462
C2×#652342
C2×#24615