Finite Group Databasebeta

← C2×#10609026 #12267164

Subgroups — C2×#10609026 #12267164

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×#4039C211yesmaximal, characteristic, complemented
3C22×#4029C211yesmaximal, characteristic, complemented
4C22×#4031C211yesmaximal, characteristic, complemented
5C2×C5×#396C211yesmaximal, characteristic, complemented
6C2×#65280C211yesmaximal, characteristic, complemented
7C2×#65268C211yesmaximal, characteristic, complemented
8C2×#65279C211yesmaximal, characteristic, complemented
9C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
10C2×#65249C211yesmaximal, characteristic
11C2×#65245C211yesmaximal, characteristic, complemented
12C2×#65246C211yesmaximal, characteristic, complemented
13C2×#65240C211yesmaximal, characteristic, complemented
14#10609026C2116yesmaximal, direct product factor
15C2×#64957C211yesmaximal, characteristic, complemented
16C2×#64958C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×Dic10C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4043—28no—
47C2×#4043C2218yescomplemented
48C2×#4039—28no—
49C2×#4039C2218yescomplemented
50C2×#4031—28no—
51C2×#4031C2218yescomplemented
52C2×#4029—28no—
53C2×#4029C2218yescomplemented
54C5×#396C2218yescomplemented
55C2×C5×#95C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65280C2218yescomplemented
62#65279C2218yescomplemented
63#65268C2218yescomplemented
64C4⋊C4×Dic5C2218yescomplemented
65#65249C2218yes—
66#65246C2218yescomplemented
67#65245C2218yescomplemented
68#65240C2218yescomplemented
69#64958C2218yescomplemented
70#64957C2218yescomplemented
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—42no—
86C22×C22⋊D5—42no—
87C22×C22⋊D5C2314yes—
88C22×C22⋊D5C2314yes—
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C22×D20—24no—
96C22×D20—24no—
97C22×D20—24no—
98C22×D20C2314yes—
99C22×C4×D5—24no—
100C22×C4×D5—24no—
101C22×C4×D5—24no—
102C22×C4×D5—24no—
103C22×C4×D5—42no—
104C22×C4×D5—42no—
105C22×C4×D5C2314yes—
106C22×C4×D5C2314yes—
107C22×Dic10—24no—
108C22×Dic10—24no—
109C22×Dic10—42no—
110C22×Dic10C2314yes—
111C2×C5×C4⋊C4—24no—
112C2×C5×C4⋊C4—24no—
113C2×C5×C4⋊C4—24no—
114C2×C5×C4⋊C4C2314yes—
115C2×C5×C4⋊C4C2314yes—
116C2×C5×C4⋊C4C2314yes—
117C2×C5×C22⋊C4—24no—
118C2×C5×C22⋊C4—24no—
119C2×C5×C22⋊C4—24no—
120C2×C5×C22⋊C4C2314yes—
121C2×C5×C22⋊C4C2314yes—
122C2×C5×C22⋊C4C2314yes—
123C2×C22⋊Dic5—24no—
124C2×C22⋊Dic5—24no—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—24no—
131C2×#685—24no—
132C2×#685—24no—
133C2×#685—24no—
134C2×#685D418yescomplemented
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×#685C2314yes—
142C2×#685C2314yes—
143C2×C4⋊Dic5—24no—
144C2×C4⋊Dic5D418yescomplemented
145C2×C4⋊Dic5C2314yes—
146C2×C4⋊Dic5C2314yes—
147C2×#683—24no—
148C2×#683—42no—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×C4×Dic5—24no—
152C2×C4×Dic5—24no—
153C2×C4×Dic5—24no—
154C2×C4×Dic5C2314yes—
155C2×C4×Dic5C2314yes—
156C2×C4×Dic5C2314yes—
157#4043—232no—
158#4039—232no—
159#4031—232no—
160#4029—232no—
161C5×#95C2314yes—
162#3963C2314yes—
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×#396D511yescharacteristic, complemented
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×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×D5C2×D414yes—
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×C5—22no—
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—28no—
233C2×C22⋊D5—28no—
234C2×C22⋊D5—28no—
235C2×C22⋊D5—28no—
236C2×C22⋊D5—44no—
237C2×C22⋊D5—44no—
238C2×C22⋊D5—416no—
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—22no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5C2×D414yes—
255C22×Dic5C2×D414yes—
256C22×Dic5C2×D414yes—
257C22×Dic5#4114yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C2×D20—232no—
265C2×D20—28no—
266C2×D20—28no—
267C2×D20—28no—
268C2×C4×D5—28no—
269C2×C4×D5—28no—
270C2×C4×D5—28no—
271C2×C4×D5—28no—
272C2×C4×D5—44no—
273C2×C4×D5—44no—
274C2×C4×D5—416no—
275C2×C4×D5—416no—
276C2×Dic10—28no—
277C2×Dic10—28no—
278C2×Dic10—44no—
279C2×Dic10—416no—
280C5×C4⋊C4—28no—
281C5×C4⋊C4—28no—
282C5×C4⋊C4—28no—
283C5×C22⋊C4—28no—
284C5×C22⋊C4—28no—
285C5×C22⋊C4—28no—
286C22⋊Dic5—28no—
287C22⋊Dic5—28no—
288#685—28no—
289#685—28no—
290#685—28no—
291#685—28no—
292#685—28no—
293#685—28no—
294#685—28no—
295#685C2×D4116yescomplemented
296C4⋊Dic5—28no—
297C4⋊Dic5C2×D4116yescomplemented
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×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⋊C4C2×D511yescharacteristic
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#396C2×D518yescomplemented
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×#95C2×D511yescharacteristic
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—44no—
365C23×C5—44no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5—44no—
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—28no—
383C22×D5—28no—
384C22×D5—28no—
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—22no—
396C22×D5—22no—
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×D5C22×D414yes—
406C22×D5C2×#4114yes—
407C2×C4×C5—28no—
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—22no—
424C2×C4×C5—22no—
425C2×C4×C5—44no—
426C2×C4×C5—44no—
427C2×C4×C5—44no—
428C2×C4×C5C22×D414yes—
429C2×C4×C5C22×D414yes—
430C2×C4×C5C2×#4114yes—
431C22⋊D5—416no—
432C22⋊D5—416no—
433C2×Dic5—28no—
434C2×Dic5—28no—
435C2×Dic5—28no—
436C2×Dic5—28no—
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—44no—
452C2×Dic5—44no—
453C2×Dic5C22×D414yes—
454C2×Dic5C22×D414yes—
455C2×Dic5C22×D414yes—
456C2×Dic5C2×#4114yes—
457D20—232no—
458C4×D5—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—24no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—58no—
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—202no—
515C2×C4⋊C4C22×D514yes—
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#95C22×D514yes—
556C22×C5—42no—
557C22×C5—42no—
558C22×C5—42no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—88no—
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—24no—
582C2×D5—24no—
583C2×D5—24no—
584C2×D5—42no—
585C2×D5—42no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—416no—
593C2×D5—416no—
594C4×C5—24no—
595C4×C5—24no—
596C4×C5—24no—
597C4×C5—42no—
598C4×C5—42no—
599C4×C5—42no—
600Dic5—24no—
601Dic5—24no—
602Dic5—24no—
603Dic5—24no—
604Dic5—42no—
605Dic5—42no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—54no—
614C24—54no—
615C24—52no—
616C24—52no—
617C24—102no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24—102no—
629C24C23×D512yes—
630C24C23×D511yescharacteristic
631C2×Q8—108no—
632C2×Q8—108no—
633C2×Q8—204no—
634C2×Q8—2016no—
635C2×D4—108no—
636C2×D4—108no—
637C2×D4—1032no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—108no—
643C2×D4—204no—
644C2×D4—204no—
645C2×D4—2016no—
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—22no—
662C22×C4—54no—
663C22×C4—54no—
664C22×C4—54no—
665C22×C4—54no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—52no—
671C22×C4—52no—
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—108no—
690C22×C4—204no—
691C22×C4—204no—
692C22×C4—2016no—
693C22×C4—2016no—
694C22×C4D4×D514yes—
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—28no—
705C4⋊C4—28no—
706C4⋊C4—516no—
707C4⋊C4—108no—
708C4⋊C4—108no—
709C4⋊C4—204no—
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—82no—
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—44no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—54no—
752C23—54no—
753C23—108no—
754C23—108no—
755C23—108no—
756C23—108no—
757C23—108no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—102no—
765C23—102no—
766C23—102no—
767C23—102no—
768C23—102no—
769C23—102no—
770C23—108no—
771C23—204no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23—204no—
779C23C2×D4×D512yes—
780C23C2×D4×D512yes—
781C23C2×#71112yes—
782C23#414712yes—
783C23D5×#4112yes—
784C23D5×#4112yes—
785C23#414912yes—
786C23C24×D511yescharacteristic
787Q8—2016no—
788D4—1032no—
789D4—2016no—
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—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—54no—
813C2×C4—54no—
814C2×C4—54no—
815C2×C4—54no—
816C2×C4—108no—
817C2×C4—108no—
818C2×C4—108no—
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—108no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—102no—
834C2×C4—2016no—
835C2×C4—2016no—
836C2×C4—204no—
837C2×C4—204no—
838C2×C4C2×D4×D514yes—
839C2×C4C2×D4×D514yes—
840C2×C4C2×#71114yes—
841C5C2×#246111yescharacteristic, complemented, Sylow
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—88no—
850C22—104no—
851C22—104no—
852C22—104no—
853C22—104no—
854C22—104no—
855C22—104no—
856C22—202no—
857C22—202no—
858C22—202no—
859C22—202no—
860C22—2016no—
861C22—2016no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—202no—
866C22#6593014yes—
867C22#6594014yes—
868C22#6594314yes—
869C22#6596514yes—
870C22#6596714yes—
871C22#6597714yes—
872C22#6603914yes—
873C22C22×D4×D511yescharacteristic
874C22C22×D4×D511yescharacteristic
875C22C22×#71111yescharacteristic
876C22C2×#414711yescharacteristic
877C22C2×D5×#4111yescharacteristic
878C22C2×D5×#4111yescharacteristic
879C22C2×#414911yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—104no—
887C4—104no—
888C4—104no—
889C4—104no—
890C4—202no—
891C4—202no—
892C2—82no—
893C2—204no—
894C2—204no—
895C2#1060902618yesdirect product factor
896C2C2×#6594011yescharacteristic
897C2C2×#6593011yescharacteristic
898C2C2×#6594311yescharacteristic
899C2C2×#6597711yescharacteristic
900C2C2×#6596511yescharacteristic
901C2C2×#6596711yescharacteristic
902C2C2×#6603911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#396C2
socleC24×C5C24
prime radicalC2×#65249C2
hypercenterC2×#396D5
hypocenterC5C2×#2461
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#4043C2semidirect
2. C22×#4039C2semidirect
3. C22×#4029C2semidirect
4. C22×#4031C2semidirect
5. C2×C5×#396C2semidirect
6. C2×#65280C2semidirect
7. C2×#65268C2semidirect
8. C2×#65279C2semidirect
9. C2×C4⋊C4×Dic5C2semidirect
11. C2×#65245C2semidirect
12. C2×#65246C2semidirect
13. C2×#65240C2semidirect
14. #10609026C2direct (N × H)
15. C2×#64957C2semidirect
16. C2×#64958C2semidirect
47. C2×#4043C22semidirect
49. C2×#4039C22semidirect
51. C2×#4031C22semidirect
53. C2×#4029C22semidirect
54. C5×#396C22semidirect
61. #65280C22semidirect
62. #65279C22semidirect
63. #65268C22semidirect
64. C4⋊C4×Dic5C22semidirect
66. #65246C22semidirect
67. #65245C22semidirect
68. #65240C22semidirect
69. #64958C22semidirect
70. #64957C22semidirect
134. C2×#685D4semidirect
144. C2×C4⋊Dic5D4semidirect
172. C2×#396D5semidirect
295. #685C2×D4semidirect
297. C4⋊Dic5C2×D4semidirect
340. #396C2×D5semidirect
727. C2×C5#2461semidirect
841. C5C2×#2461semidirect
895. C2#10609026direct (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×#40392
C22×#40292
C22×#40312
C2×C5×#3962
C2×#652802
C2×#652682
C2×#652792
C2×C4⋊C4×Dic52
C2×#652492
C2×#652452
C2×#652462
C2×#652402
#106090262
C2×#649572
C2×#649582
C2×#24615