Finite Group Databasebeta

← C2×#10607244 #12267158

Subgroups — C2×#10607244 #12267158

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×#4043C211yesmaximal, characteristic, complemented
2C22×#4031C211yesmaximal, characteristic, complemented
3C22×#4032C211yesmaximal, characteristic, complemented
4C22×#4027C211yesmaximal, characteristic, complemented
5C2×C5×#388C211yesmaximal, characteristic, complemented
6C2×#65283C211yesmaximal, characteristic, complemented
7C2×#65249C211yesmaximal, characteristic
8C2×#65250C211yesmaximal, characteristic, complemented
9C2×#65239C211yesmaximal, characteristic, complemented
10C2×#65228C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
12#10607244C2116yesmaximal, direct product factor
13C2×#64954C211yesmaximal, characteristic, complemented
14C2×#64945C211yesmaximal, characteristic, complemented
15C2×#64959C211yesmaximal, characteristic, complemented
16C2×#64959C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C24×Dic5C2211yescharacteristic
20C23×D20C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×Dic10C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×C4⋊Dic5C2211yescharacteristic
42C22×C4⋊Dic5C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4043—28no—
47C2×#4043C2218yescomplemented
48C2×#4032—28no—
49C2×#4032C2218yescomplemented
50C2×#4031—28no—
51C2×#4031C2218yescomplemented
52C2×#4027—28no—
53C2×#4027C2218yescomplemented
54C5×#388C2218yescomplemented
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65283C2218yescomplemented
62#65250C2218yescomplemented
63#65249C2218yes—
64#65239C2218yescomplemented
65#65228C2218yescomplemented
66C4×C4⋊Dic5C2218yescomplemented
67#64959C2218yescomplemented
68#64959C2218yescomplemented
69#64954C2218yescomplemented
70#64945C2218yescomplemented
71C2×#2461—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—24no—
82C22×C22⋊D5—24no—
83C22×C22⋊D5—24no—
84C22×C22⋊D5—24no—
85C22×C22⋊D5—24no—
86C22×C22⋊D5—42no—
87C22×C22⋊D5C2314yes—
88C22×C22⋊D5C2314yes—
89C23×Dic5—24no—
90C23×Dic5—24no—
91C23×Dic5—42no—
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2314yes—
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C22×D20—24no—
100C22×D20—24no—
101C22×D20—42no—
102C22×D20C2314yes—
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—
111C2×C5×C4⋊C4—24no—
112C2×C5×C4⋊C4C2314yes—
113C2×C5×C22⋊C4—24no—
114C2×C5×C22⋊C4—24no—
115C2×C5×C22⋊C4D418yescomplemented
116C2×C5×C22⋊C4C2314yes—
117C2×C5×C22⋊C4C2314yes—
118C2×C5×C22⋊C4C2314yes—
119C2×C42×C5—24no—
120C2×C42×C5C2314yes—
121C2×C22⋊Dic5—24no—
122C2×C22⋊Dic5C2314yes—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—24no—
131C2×#685—24no—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×C4⋊Dic5—24no—
142C2×C4⋊Dic5—24no—
143C2×C4⋊Dic5—24no—
144C2×C4⋊Dic5—42no—
145C2×C4⋊Dic5D418yescomplemented
146C2×C4⋊Dic5C2314yes—
147C2×C4⋊Dic5C2314yes—
148C2×C4⋊Dic5C2314yes—
149C2×C4⋊Dic5C2314yes—
150C2×C4⋊Dic5C2314yes—
151C2×#683—24no—
152C2×#683C2314yes—
153C2×C4×Dic5—24no—
154C2×C4×Dic5—24no—
155C2×C4×Dic5C2314yes—
156C2×C4×Dic5C2314yes—
157#4043—232no—
158#4032—232no—
159#4031—232no—
160#4027—232no—
161C5×#95C2314yes—
162C5×#95C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#124—51no—
168C22×#123—51no—
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×#388D511yescharacteristic, complemented
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×C5C2×D414yes—
190C24×C5C2412yes—
191C24×C5C2411yescharacteristic
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
198C23×D5—22no—
199C23×D5—22no—
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5—22no—
205C23×D5#4114yes—
206C23×D5C2412yes—
207C23×D5C2412yes—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
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×C5C2×D414yes—
223C22×C4×C5C2×D414yes—
224C22×C4×C5C2×D414yes—
225C22×C4×C5#4114yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C2×C22⋊D5—232no—
233C2×C22⋊D5—28no—
234C2×C22⋊D5—28no—
235C2×C22⋊D5—28no—
236C2×C22⋊D5—28no—
237C2×C22⋊D5—28no—
238C2×C22⋊D5—44no—
239C2×C22⋊D5—416no—
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—22no—
249C22×Dic5—28no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5—28no—
257C22×Dic5—44no—
258C22×Dic5—416no—
259C22×Dic5C2×D414yes—
260C22×Dic5C2×D414yes—
261C22×Dic5#4114yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C2×D20—28no—
269C2×D20—28no—
270C2×D20—44no—
271C2×D20—416no—
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×C22⋊C4—28no—
282C5×C22⋊C4—28no—
283C5×C22⋊C4C2×D4116yescomplemented
284C42×C5—28no—
285C22⋊Dic5—28no—
286#685—28no—
287#685—28no—
288#685—28no—
289#685—28no—
290#685—28no—
291#685—28no—
292#685—28no—
293#685—28no—
294#685—28no—
295C4⋊Dic5—28no—
296C4⋊Dic5—28no—
297C4⋊Dic5—28no—
298C4⋊Dic5—44no—
299C4⋊Dic5C2×D4116yescomplemented
300#683—28no—
301C4×Dic5—28no—
302C4×Dic5—28no—
303C23×Q8—51no—
304C23×D4—51no—
305C23×D4—51no—
306C23×D4—51no—
307C24×C4—51no—
308C24×C4—51no—
309C2×#124—58no—
310C2×#124—108no—
311C2×#123—58no—
312C2×#123—108no—
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⋊C4—51no—
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×C42C2×D511yescharacteristic
340#396—58no—
341#395—58no—
342#394—58no—
343#392—58no—
344#390—58no—
345#388—58no—
346#388—58no—
347#388C2×D518yescomplemented
348#386—58no—
349#385—58no—
350C4×C4⋊C4—58no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95C2×D511yescharacteristic
356C2×#95C2×D511yescharacteristic
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—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5C22×D414yes—
371C23×C5C22×D412yes—
372C23×C5C22×D412yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5C2×#4112yes—
376C23×C5H(5,𝔽2)12yes—
377C23×C52−1+412yes—
378C23×C5C2511yescharacteristic
379C22×D5—28no—
380C22×D5—28no—
381C22×D5—28no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—22no—
391C22×D5—22no—
392C22×D5—22no—
393C22×D5—22no—
394C22×D5—22no—
395C22×D5—44no—
396C22×D5—44no—
397C22×D5—44no—
398C22×D5—44no—
399C22×D5—44no—
400C22×D5—44no—
401C22×D5—44no—
402C22×D5—44no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5—44no—
406C22×D5C2×#4114yes—
407C2×C4×C5—28no—
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—22no—
424C2×C4×C5—22no—
425C2×C4×C5—44no—
426C2×C4×C5—44no—
427C2×C4×C5C22×D414yes—
428C2×C4×C5C22×D414yes—
429C2×C4×C5C22×D414yes—
430C2×C4×C5C2×#4114yes—
431C22⋊D5—232no—
432C22⋊D5—416no—
433C2×Dic5—28no—
434C2×Dic5—28no—
435C2×Dic5—28no—
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—416no—
452C2×Dic5—44no—
453C2×Dic5—44no—
454C2×Dic5—44no—
455C2×Dic5C22×D414yes—
456C2×Dic5C22×D414yes—
457C2×Dic5C2×#4114yes—
458D20—416no—
459C4×D5—416no—
460Dic10—416no—
461C25—51no—
462C25—51no—
463C25C22×D511yescharacteristic
464C22×Q8—54no—
465C22×Q8—104no—
466C22×Q8—104no—
467C22×Q8—202no—
468C22×D4—54no—
469C22×D4—54no—
470C22×D4—54no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4—104no—
478C22×D4—202no—
479C22×D4—202no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—54no—
487C23×C4—54no—
488C23×C4—104no—
489C23×C4—104no—
490C23×C4—104no—
491C23×C4—104no—
492C23×C4—202no—
493C23×C4—202no—
494C23×C4C22×D511yescharacteristic
495C23×C4C22×D511yescharacteristic
496C23×C4C22×D511yescharacteristic
497C23×C4C22×D511yescharacteristic
498C23×C4C22×D511yescharacteristic
499C23×C4C22×D511yescharacteristic
500#124—1032no—
501#123—1032no—
502C22⋊Q8—1032no—
503C4×D4—1032no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—58no—
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—104no—
513C2×C4⋊C4—104no—
514C2×C4⋊C4—104no—
515C2×C4⋊C4—104no—
516C2×C4⋊C4—202no—
517C2×C4⋊C4C22×D514yes—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—54no—
521C2×C22⋊C4—54no—
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—104no—
531C2×C22⋊C4—104no—
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⋊C4D2018yescomplemented
541C2×C22⋊C4C22×D514yes—
542C2×C22⋊C4C22×D514yes—
543C2×C22⋊C4C22×D514yes—
544C2×C42—24no—
545C2×C42—54no—
546C2×C42—54no—
547C2×C42—104no—
548C2×C42—104no—
549C2×C42C22×D514yes—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95C22×D514yes—
555#95C22×D514yes—
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#52514yes—
565C22×C5#53214yes—
566C22×C5#54214yes—
567C22×C5D4214yes—
568C22×C5#54714yes—
569C22×C5#54814yes—
570C22×C5#55114yes—
571C22×C5C23×D411yescharacteristic
572C22×C5C23×D411yescharacteristic
573C22×C5C22×#4111yescharacteristic
574C22×C5C22×#4111yescharacteristic
575C22×C5C22×#4111yescharacteristic
576C22×C5C2×H(5,𝔽2)11yescharacteristic
577C22×C5C2×2−1+411yescharacteristic
578C2×D5—24no—
579C2×D5—24no—
580C2×D5—24no—
581C2×D5—42no—
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—416no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—88no—
594C4×C5—24no—
595C4×C5—24no—
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—42no—
599C4×C5—42no—
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—54no—
613C24—52no—
614C24—52no—
615C24—102no—
616C24—102no—
617C24—102no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24C2×D2014yes—
629C24C23×D512yes—
630C24C23×D511yescharacteristic
631C2×Q8—108no—
632C2×Q8—108no—
633C2×Q8—204no—
634C2×Q8—2016no—
635C2×D4—108no—
636C2×D4—108no—
637C2×D4—108no—
638C2×D4—108no—
639C2×D4—1032no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—108no—
643C2×D4—204no—
644C2×D4—2016no—
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—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—54no—
662C22×C4—54no—
663C22×C4—54no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—108no—
671C22×C4—108no—
672C22×C4—102no—
673C22×C4—102no—
674C22×C4—102no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—108no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—108no—
689C22×C4—204no—
690C22×C4—2016no—
691C22×C4—204no—
692C22×C4—2016no—
693C22×C4C2×D2014yes—
694C22×C4C2×D2014yes—
695C22×C4D4×D514yes—
696C22×C4#71114yes—
697C22×C4C23×D512yes—
698C22×C4C23×D512yes—
699C22×C4C23×D512yes—
700C22×C4C23×D512yes—
701C22×C4C23×D512yes—
702C22×C4C23×D512yes—
703C4⋊C4—28no—
704C4⋊C4—516no—
705C4⋊C4—108no—
706C4⋊C4—108no—
707C4⋊C4—108no—
708C4⋊C4—108no—
709C4⋊C4—204no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—108no—
713C22⋊C4—108no—
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⋊C4C2×D20116yescomplemented
723C42—28no—
724C42—108no—
725C42—108no—
726C2×C5—44no—
727C2×C5#246118yescomplemented
728C2×C5C2×#52511yescharacteristic
729C2×C5C2×#53211yescharacteristic
730C2×C5C2×#54211yescharacteristic
731C2×C5C2×D4211yescharacteristic
732C2×C5C2×#54711yescharacteristic
733C2×C5C2×#54811yescharacteristic
734C2×C5C2×#55111yescharacteristic
735D5—44no—
736D5—82no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—54no—
751C23—108no—
752C23—108no—
753C23—108no—
754C23—102no—
755C23—102no—
756C23—102no—
757C23—102no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—102no—
765C23—102no—
766C23—102no—
767C23—204no—
768C23—204no—
769C23—204no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23C22×D2014yes—
779C23C22×D2012yes—
780C23C2×D4×D512yes—
781C23C2×#71112yes—
782C23D5×#4112yes—
783C23D5×#4112yes—
784C23#414912yes—
785C23#415012yes—
786C23C24×D511yescharacteristic
787Q8—2016no—
788D4—1032no—
789D4—2016no—
790D4—2016no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
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—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—54no—
812C2×C4—54no—
813C2×C4—54no—
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—2016no—
833C2×C4—2016no—
834C2×C4—204no—
835C2×C4—204no—
836C2×C4—204no—
837C2×C4C22×D2014yes—
838C2×C4C22×D2014yes—
839C2×C4C2×D4×D514yes—
840C2×C4C2×#71114yes—
841C5C2×#246111yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—416no—
848C22—42no—
849C22—42no—
850C22—104no—
851C22—104no—
852C22—104no—
853C22—202no—
854C22—202no—
855C22—2016no—
856C22—202no—
857C22—202no—
858C22—202no—
859C22—202no—
860C22—202no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—408no—
866C22#6585814yes—
867C22D4×D2014yes—
868C22#6588914yes—
869C22#6593014yes—
870C22#6599214yes—
871C22#6601114yes—
872C22#6604414yes—
873C22C23×D2011yescharacteristic
874C22C22×D4×D511yescharacteristic
875C22C22×#71111yescharacteristic
876C22C2×D5×#4111yescharacteristic
877C22C2×D5×#4111yescharacteristic
878C22C2×#414911yescharacteristic
879C22C2×#415011yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—42no—
886C4—104no—
887C4—104no—
888C4—104no—
889C4—202no—
890C4—202no—
891C4—202no—
892C2—44no—
893C2—204no—
894C2—402no—
895C2#1060724418yesdirect product factor
896C2C2×#6585811yescharacteristic
897C2C2×#6588911yescharacteristic
898C2C2×D4×D2011yescharacteristic
899C2C2×#6593011yescharacteristic
900C2C2×#6599211yescharacteristic
901C2C2×#6601111yescharacteristic
902C2C2×#6604411yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC2×#65249C2
hypercenterC2×#388D5
hypocenterC5C2×#2461
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#4043C2semidirect
2. C22×#4031C2semidirect
3. C22×#4032C2semidirect
4. C22×#4027C2semidirect
5. C2×C5×#388C2semidirect
6. C2×#65283C2semidirect
8. C2×#65250C2semidirect
9. C2×#65239C2semidirect
10. C2×#65228C2semidirect
11. C2×C4×C4⋊Dic5C2semidirect
12. #10607244C2direct (N × H)
13. C2×#64954C2semidirect
14. C2×#64945C2semidirect
15. C2×#64959C2semidirect
16. C2×#64959C2semidirect
47. C2×#4043C22semidirect
49. C2×#4032C22semidirect
51. C2×#4031C22semidirect
53. C2×#4027C22semidirect
54. C5×#388C22semidirect
61. #65283C22semidirect
62. #65250C22semidirect
64. #65239C22semidirect
65. #65228C22semidirect
66. C4×C4⋊Dic5C22semidirect
67. #64959C22semidirect
68. #64959C22semidirect
69. #64954C22semidirect
70. #64945C22semidirect
115. C2×C5×C22⋊C4D4semidirect
145. C2×C4⋊Dic5D4semidirect
179. C2×#388D5semidirect
283. C5×C22⋊C4C2×D4semidirect
299. C4⋊Dic5C2×D4semidirect
347. #388C2×D5semidirect
540. C2×C22⋊C4D20semidirect
722. C22⋊C4C2×D20semidirect
727. C2×C5#2461semidirect
841. C5C2×#2461semidirect
895. C2#10607244direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40432
C22×#40312
C22×#40322
C22×#40272
C2×C5×#3882
C2×#652832
C2×#652492
C2×#652502
C2×#652392
C2×#652282
C2×C4×C4⋊Dic52
#106072442
C2×#649542
C2×#649452
C2×#649592
C2×#24615