Finite Group Databasebeta

← C2×#10608631 #12267168

Subgroups — C2×#10608631 #12267168

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×#4081C211yesmaximal, characteristic, complemented
2C22×#4085C211yesmaximal, characteristic
3C22×#4029C211yesmaximal, characteristic, complemented
4C22×#4027C211yesmaximal, characteristic, complemented
5C2×C5×#394C211yesmaximal, characteristic, complemented
6C2×#65278C211yesmaximal, characteristic, complemented
7C2×#65265C211yesmaximal, characteristic, complemented
8C2×#65241C211yesmaximal, characteristic, complemented
9C2×#65250C211yesmaximal, characteristic, complemented
10C2×#65246C211yesmaximal, characteristic, complemented
11C2×#65239C211yesmaximal, characteristic, complemented
12C2×#65231C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
14#10608631C2116yesmaximal, direct product factor
15C2×#64964C211yesmaximal, characteristic, complemented
16C2×#64936C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C2×#4085—28no—
33C2×#4085C2218yes—
34C2×#4081—28no—
35C2×#4081C2218yescomplemented
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×C4⋊Dic5C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×C4×Dic5C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C2×#4029—28no—
51C2×#4029C2218yescomplemented
52C2×#4027—28no—
53C2×#4027C2218yescomplemented
54C5×#394C2218yescomplemented
55C2×C5×#95C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65278C2218yescomplemented
62#65265C2218yescomplemented
63#65250C2218yescomplemented
64#65246C2218yescomplemented
65#65241C2218yescomplemented
66#65239C2218yescomplemented
67#65231C2218yescomplemented
68C22⋊C4×Dic5C2218yescomplemented
69#64964C2218yescomplemented
70#64936C2218yescomplemented
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×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C22×C22⋊D5—24no—
85C22×C22⋊D5—24no—
86C22×C22⋊D5—24no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—42no—
89C22×C22⋊D5D418yes—
90C22×C22⋊D5C2314yes—
91C22×C22⋊D5C2314yes—
92C23×Dic5—24no—
93C23×Dic5—24no—
94C23×Dic5—24no—
95C23×Dic5—24no—
96C23×Dic5—24no—
97C23×Dic5—42no—
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2314yes—
103C23×Dic5C2314yes—
104C23×Dic5C2311yescharacteristic
105C23×Dic5C2311yescharacteristic
106C23×Dic5C2311yescharacteristic
107C22×C4×D5—24no—
108C22×C4×D5—24no—
109C22×C4×D5—42no—
110C22×C4×D5C2314yes—
111C2×C5×C4⋊C4—42no—
112C2×C5×C4⋊C4C2314yes—
113C2×C5×C22⋊C4—24no—
114C2×C5×C22⋊C4—24no—
115C2×C5×C22⋊C4—24no—
116C2×C5×C22⋊C4—24no—
117C2×C5×C22⋊C4C2314yes—
118C2×C5×C22⋊C4C2314yes—
119C2×C5×C22⋊C4C2314yes—
120C2×C5×C22⋊C4C2314yes—
121C2×C22⋊Dic5—24no—
122C2×C22⋊Dic5—24no—
123C2×C22⋊Dic5—24no—
124C2×C22⋊Dic5D418yescomplemented
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127C2×C22⋊Dic5C2314yes—
128C2×C22⋊Dic5C2314yes—
129#4085—232no—
130#4081—232no—
131C2×#685—24no—
132C2×#685—24no—
133C2×#685—24no—
134C2×#685—24no—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×C4⋊Dic5—24no—
140C2×C4⋊Dic5—42no—
141C2×C4⋊Dic5C2314yes—
142C2×C4⋊Dic5C2314yes—
143C2×#683—24no—
144C2×#683—24no—
145C2×#683—24no—
146C2×#683—24no—
147C2×#683—24no—
148C2×#683—24no—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×C4×Dic5—24no—
156C2×C4×Dic5—24no—
157C2×C4×Dic5C2314yes—
158C2×C4×Dic5C2314yes—
159#4029—232no—
160#4027—232no—
161C5×#95C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#123—51no—
168C22×#123—51no—
169C22×#121—51no—
170C22×C4×D4—51no—
171#2422—516no—
172C2×#397—51no—
173C2×#397—51no—
174C2×#394—51no—
175C2×#394D511yescharacteristic, complemented
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—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5#4114yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C2×C22⋊D5—28no—
233C2×C22⋊D5—28no—
234C2×C22⋊D5—232no—
235C2×C22⋊D5—28no—
236C2×C22⋊D5—28no—
237C2×C22⋊D5—44no—
238C2×C22⋊D5—416no—
239C2×C22⋊D5C2×D4116yes—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—22no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—28no—
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—28no—
258C22×Dic5—28no—
259C22×Dic5—28no—
260C22×Dic5—28no—
261C22×Dic5—44no—
262C22×Dic5—416no—
263C22×Dic5—416no—
264C22×Dic5C2×D414yes—
265C22×Dic5C2×D414yes—
266C22×Dic5C2×D414yes—
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—44no—
281C5×C22⋊C4—28no—
282C5×C22⋊C4—28no—
283C5×C22⋊C4—28no—
284C5×C22⋊C4—28no—
285C22⋊Dic5—28no—
286C22⋊Dic5—28no—
287C22⋊Dic5—28no—
288C22⋊Dic5C2×D4116yescomplemented
289#685—28no—
290#685—28no—
291#685—28no—
292#685—28no—
293C4⋊Dic5—28no—
294C4⋊Dic5—44no—
295#683—28no—
296#683—28no—
297#683—28no—
298#683—28no—
299#683—28no—
300#683—28no—
301C4×Dic5—28no—
302C4×Dic5—28no—
303C23×D4—51no—
304C23×D4—51no—
305C23×D4C2×D511yescharacteristic
306C24×C4—51no—
307C24×C4—51no—
308C24×C4—51no—
309C2×#123—58no—
310C2×#123—58no—
311C2×#123—108no—
312C2×#123—108no—
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⋊C4—51no—
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⋊C4C2×D511yescharacteristic
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#394C2×D518yescomplemented
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×#95C2×D511yescharacteristic
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×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×D5C22×D414yes—
407C5×D4—416no—
408C2×C4×C5—28no—
409C2×C4×C5—22no—
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—44no—
424C2×C4×C5—44no—
425C2×C4×C5—44no—
426C2×C4×C5—44no—
427C2×C4×C5C2×#4114yes—
428C22⋊D5—232no—
429C22⋊D5—416no—
430C2×Dic5—28no—
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—416no—
449C2×Dic5—44no—
450C2×Dic5—44no—
451C2×Dic5—44no—
452C2×Dic5—44no—
453C2×Dic5—416no—
454C2×Dic5#123116yescomplemented
455C2×Dic5C22×D414yes—
456C2×Dic5C22×D414yes—
457C2×Dic5C22×D414yes—
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—51no—
477C23×C4—51no—
478C23×C4—51no—
479C23×C4—54no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—54no—
485C23×C4—54no—
486C23×C4—104no—
487C23×C4—104no—
488C23×C4—104no—
489C23×C4—104no—
490C23×C4—104no—
491C23×C4—104no—
492C23×C4—104no—
493C23×C4—202no—
494C23×C4—202no—
495C23×C4C22×D511yescharacteristic
496C23×C4C22×D511yescharacteristic
497C23×C4C22×D511yescharacteristic
498C23×C4C22×D511yescharacteristic
499C23×C4C22×D511yescharacteristic
500#123—1032no—
501#123—1032no—
502#121—1032no—
503C4×D4—1032no—
504C2×C4⋊C4—42no—
505C2×C4⋊C4—54no—
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—104no—
519C2×C4⋊C4—104no—
520C2×C4⋊C4—202no—
521C2×C4⋊C4C22×D514yes—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—58no—
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—54no—
534C2×C22⋊C4—54no—
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×D514yes—
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#95C22×D514yes—
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—42no—
596C4×C5—42no—
597C4×C5—42no—
598C4×C5—42no—
599Dic5—24no—
600Dic5—24no—
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—
627C24D4×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—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—54no—
658C22×C4—54no—
659C22×C4—54no—
660C22×C4—52no—
661C22×C4—54no—
662C22×C4—54no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—108no—
670C22×C4—108no—
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—108no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—102no—
690C22×C4—102no—
691C22×C4—102no—
692C22×C4—204no—
693C22×C4—2016no—
694C22×C4—2016no—
695C22×C4—204no—
696C22×C4—2016no—
697C22×C4#71114yes—
698C22×C4C23×D512yes—
699C22×C4C23×D512yes—
700C22×C4C23×D512yes—
701C22×C4C23×D512yes—
702C22×C4C23×D512yes—
703C4⋊C4—44no—
704C4⋊C4—108no—
705C4⋊C4—108no—
706C4⋊C4—108no—
707C4⋊C4—108no—
708C4⋊C4—108no—
709C4⋊C4—108no—
710C4⋊C4—108no—
711C4⋊C4—204no—
712C22⋊C4—28no—
713C22⋊C4—28no—
714C22⋊C4—28no—
715C22⋊C4—28no—
716C22⋊C4—516no—
717C22⋊C4—108no—
718C22⋊C4—108no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C22⋊C4—108no—
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×D514yes—
779C23C2×D4×D512yes—
780C23C2×D4×D512yes—
781C23C2×#71112yes—
782C23#414412yes—
783C23D5×#4112yes—
784C23D5×#4112yes—
785C23#415012yes—
786C23C24×D511yescharacteristic
787D4—416no—
788D4—1032no—
789D4—2016no—
790C2×C4—28no—
791C2×C4—22no—
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—44no—
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—54no—
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—2016no—
834C2×C4—2016no—
835C2×C4—2016no—
836C2×C4—204no—
837C2×C4—204no—
838C2×C4—204no—
839C2×C4—204no—
840C2×C4C2×#71114yes—
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—42no—
855C22—42no—
856C22—416no—
857C22—416no—
858C22—104no—
859C22—104no—
860C22—104no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—2016no—
866C22#6592414yes—
867C22#6593014yes—
868C22#6593514yes—
869C22#6594514yes—
870C22D5×#12314yes—
871C22#6598914yes—
872C22#6600314yes—
873C22C22×D4×D511yescharacteristic
874C22C22×D4×D511yescharacteristic
875C22C22×#71111yescharacteristic
876C22C2×#414411yescharacteristic
877C22C2×D5×#4111yescharacteristic
878C22C2×D5×#4111yescharacteristic
879C22C2×#415011yescharacteristic
880C4—24no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—58no—
886C4—104no—
887C4—104no—
888C4—202no—
889C4—202no—
890C4—202no—
891C4—202no—
892C2—44no—
893C2—44no—
894C2—204no—
895C2#1060863118yesdirect product factor
896C2C2×#6592411yescharacteristic
897C2C2×#6593011yescharacteristic
898C2C2×#6594511yescharacteristic
899C2C2×#6593511yescharacteristic
900C2C2×D5×#12311yescharacteristic
901C2C2×#6598911yescharacteristic
902C2C2×#6600311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#394C2
socleC24×C5C24
prime radicalC22×#4085C2
hypercenterC2×#394D5
hypocenterC5C2×#2422
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#4081C2semidirect
3. C22×#4029C2semidirect
4. C22×#4027C2semidirect
5. C2×C5×#394C2semidirect
6. C2×#65278C2semidirect
7. C2×#65265C2semidirect
8. C2×#65241C2semidirect
9. C2×#65250C2semidirect
10. C2×#65246C2semidirect
11. C2×#65239C2semidirect
12. C2×#65231C2semidirect
13. C2×C22⋊C4×Dic5C2semidirect
14. #10608631C2direct (N × H)
15. C2×#64964C2semidirect
16. C2×#64936C2semidirect
35. C2×#4081C22semidirect
51. C2×#4029C22semidirect
53. C2×#4027C22semidirect
54. C5×#394C22semidirect
61. #65278C22semidirect
62. #65265C22semidirect
63. #65250C22semidirect
64. #65246C22semidirect
65. #65241C22semidirect
66. #65239C22semidirect
67. #65231C22semidirect
68. C22⋊C4×Dic5C22semidirect
69. #64964C22semidirect
70. #64936C22semidirect
124. C2×C22⋊Dic5D4semidirect
175. C2×#394D5semidirect
288. C22⋊Dic5C2×D4semidirect
343. #394C2×D5semidirect
454. C2×Dic5#123semidirect
605. Dic5C2×#123semidirect
728. C2×C5#2422semidirect
841. C5C2×#2422semidirect
895. C2#10608631direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40812
C22×#40852
C22×#40292
C22×#40272
C2×C5×#3942
C2×#652782
C2×#652652
C2×#652412
C2×#652502
C2×#652462
C2×#652392
C2×#652312
C2×C22⋊C4×Dic52
#106086312
C2×#649642
C2×#649362
C2×#24225