Finite Group Databasebeta

← C2×#10606133 #12261925

Subgroups — C2×#10606133 #12261925

Order 1280.

2934 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4031C211yesmaximal, characteristic
2C2×C5×#385C211yesmaximal, characteristic, complemented
3C2×#65502C211yesmaximal, characteristic
4C2×#65499C211yesmaximal, characteristic, complemented
5C2×#65278C211yesmaximal, characteristic, complemented
6C2×#65278C211yesmaximal, characteristic, complemented
7C2×#65263C211yesmaximal, characteristic, complemented
8C2×#65266C211yesmaximal, characteristic, complemented
9C2×#65245C211yesmaximal, characteristic
10C2×#65234C211yesmaximal, characteristic, complemented
11C2×#65240C211yesmaximal, characteristic, complemented
12#10606133C2116yesmaximal, direct product factor
13C2×#64935C211yesmaximal, characteristic, complemented
14C2×#64959C211yesmaximal, characteristic, complemented
15C2×#64958C211yesmaximal, characteristic, complemented
16C2×#64939C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×Dic10C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C2×#4031C4116yescomplemented
41C2×#4031C2218yes—
42C5×#385C2218yescomplemented
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45#65502C2218yes—
46#65499C2218yescomplemented
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65278C2218yescomplemented
58#65278C2218yescomplemented
59#65266C2218yescomplemented
60#65263C2218yescomplemented
61#65245C2218yes—
62#65240C2218yescomplemented
63#65234C2218yescomplemented
64#64959C2218yescomplemented
65#64958C2218yescomplemented
66#64939C2218yescomplemented
67#64935C2218yescomplemented
68C2×#2379—51nomaximal, Sylow
69C25×C5C2311yescharacteristic
70C24×D5C2311yescharacteristic
71C23×C4×C5—42no—
72C23×C4×C5—42no—
73C23×C4×C5—42no—
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2314yes—
81C22×C22⋊D5—42no—
82C22×C22⋊D5—42no—
83C22×C22⋊D5C2×C418yes—
84C22×C22⋊D5C2314yes—
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C22×C4×D5—42no—
93C22×C4×D5—42no—
94C22×C4×D5—42no—
95C22×C4×D5C2314yes—
96C22×Dic10—42no—
97C22×Dic10—42no—
98C22×Dic10C2×C418yescomplemented
99C22×Dic10C2314yes—
100C2×C5×C4⋊C4—42no—
101C2×C5×C4⋊C4—42no—
102C2×C5×C4⋊C4C2314yes—
103C2×C5×C4⋊C4C2314yes—
104C2×C5×C22⋊C4—42no—
105C2×C5×C22⋊C4C2×C418yescomplemented
106C2×C5×C22⋊C4C2314yes—
107C2×C5×C22⋊C4C2314yes—
108C2×C22⋊Dic5—42no—
109C2×C22⋊Dic5—42no—
110C2×C22⋊Dic5C2×C418yescomplemented
111C2×C22⋊Dic5C2314yes—
112C2×C22⋊Dic5C2314yes—
113C2×C22⋊Dic5C2314yes—
114C2×#685—42no—
115C2×#685—42no—
116C2×#685—42no—
117C2×#685C2×C418yescomplemented
118C2×#685C2×C418yescomplemented
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×#685C2314yes—
124C2×C4⋊Dic5—42no—
125C2×C4⋊Dic5C2314yes—
126C2×#683—42no—
127C2×#683—42no—
128C2×#683—42no—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×C4×Dic5—42no—
133C2×C4×Dic5—42no—
134C2×C4×Dic5C2×C418yescomplemented
135C2×C4×Dic5C2314yes—
136C2×C4×Dic5C2314yes—
137C2×C4×Dic5C2314yes—
138#4031C2×C4164yescomplemented
139C5×#95C2314yes—
140C5×#95C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151C22×#124—51no—
152#2379—516no—
153C2×#391—51no—
154C2×#391—51no—
155C2×#388—51no—
156C2×#388—51no—
157C2×#388—51no—
158C2×#388—51no—
159C2×#386—51no—
160C2×#386—51no—
161C2×#385—51no—
162C2×#385—51no—
163C2×#385—51no—
164C2×#385D511yescharacteristic, complemented
165C2×#382—51no—
166C2×#382—51no—
167C24×C5—22no—
168C24×C5—22no—
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5C22×C414yes—
174C24×C5C2412yes—
175C24×C5C2411yescharacteristic
176C23×D5—22no—
177C23×D5—22no—
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5C22×C414yes—
183C23×D5C2412yes—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—44no—
201C22×C4×C5—44no—
202C22×C4×C5—44no—
203C22×C4×C5—416no—
204C22×C4×C5C22×C414yes—
205C22×C4×C5C22×C414yes—
206C22×C4×C5C2412yes—
207C22×C4×C5C2412yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
210C22×C4×C5C2412yes—
211C22×C4×C5C2412yes—
212C2×C22⋊D5—416no—
213C2×C22⋊D5—44no—
214C2×C22⋊D5—44no—
215C2×C22⋊D5C22×C4116yes—
216C22×Dic5—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5—22no—
220C22×Dic5—22no—
221C22×Dic5—22no—
222C22×Dic5—22no—
223C22×Dic5—22no—
224C22×Dic5—22no—
225C22×Dic5—22no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5C22×C414yes—
235C22×Dic5C22×C414yes—
236C22×Dic5C22×C414yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C2×C4×D5—44no—
245C2×C4×D5—44no—
246C2×C4×D5—44no—
247C2×C4×D5—416no—
248C2×Dic10—416no—
249C2×Dic10—44no—
250C2×Dic10—44no—
251C2×Dic10C22×C4116yescomplemented
252C5×C4⋊C4—44no—
253C5×C4⋊C4—44no—
254C5×C22⋊C4—44no—
255C5×C22⋊C4C22×C4116yescomplemented
256C22⋊Dic5—44no—
257C22⋊Dic5—44no—
258C22⋊Dic5C22×C4116yescomplemented
259#685—44no—
260#685—44no—
261#685—44no—
262#685C22×C4116yescomplemented
263#685C22×C4116yescomplemented
264C4⋊Dic5—44no—
265#683—44no—
266#683—44no—
267#683—44no—
268C4×Dic5—44no—
269C4×Dic5—44no—
270C4×Dic5C22×C4116yescomplemented
271C23×Q8—51no—
272C23×D4—51no—
273C24×C4—51no—
274C24×C4C2×D511yescharacteristic
275C2×#124—516no—
276C2×#124—58no—
277C22×C4⋊C4—51no—
278C22×C4⋊C4—51no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4C2×D511yescharacteristic
282C22×C4⋊C4C2×D511yescharacteristic
283C22×C22⋊C4—51no—
284C22×C22⋊C4—51no—
285C22×C22⋊C4—51no—
286C22×C22⋊C4—51no—
287C22×C22⋊C4—51no—
288C22×C22⋊C4—51no—
289C22×C22⋊C4—51no—
290C22×C22⋊C4—51no—
291C22×C22⋊C4C2×D511yescharacteristic
292C22×C22⋊C4C2×D511yescharacteristic
293C22×C42—51no—
294C22×C42—51no—
295C22×C42—51no—
296#391—58no—
297#391—58no—
298#388—58no—
299#388—58no—
300#388—58no—
301#388—58no—
302#386—58no—
303#386—58no—
304#385—58no—
305#385—58no—
306#385—58no—
307#385C2×D518yescomplemented
308#382—58no—
309#382—58no—
310C2×#95—51no—
311C2×#95—51no—
312C2×#95—51no—
313C2×#95—51no—
314C2×#95—51no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95C2×D511yescharacteristic
321C2×#95C2×D511yescharacteristic
322C23×C5—28no—
323C23×C5—28no—
324C23×C5—28no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—44no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5C23×C414yes—
336C23×C5C23×C412yes—
337C23×C5H(5,𝔽2)12yes—
338C23×C5H(5,𝔽2)12yes—
339C23×C5H(5,𝔽2)12yes—
340C23×C5H(5,𝔽2)12yes—
341C23×C52−1+412yes—
342C23×C52−1+412yes—
343C23×C5C2511yescharacteristic
344C22×D5—28no—
345C22×D5—28no—
346C22×D5—28no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—44no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5C23×C414yes—
358C2×C4×C5—28no—
359C2×C4×C5—28no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—416no—
377C2×C4×C5—44no—
378C2×C4×C5—44no—
379C2×C4×C5—44no—
380C2×C4×C5—44no—
381C2×C4×C5C23×C414yes—
382C2×C4×C5C23×C414yes—
383C22⋊D5—416no—
384C2×Dic5—28no—
385C2×Dic5—28no—
386C2×Dic5—28no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—44no—
406C2×Dic5—44no—
407C2×Dic5—44no—
408C2×Dic5—44no—
409C2×Dic5C23×C414yes—
410C2×Dic5C23×C414yes—
411C2×Dic5C23×C414yes—
412C4×D5—416no—
413Dic10—416no—
414C25—51no—
415C25C22×D511yescharacteristic
416C22×Q8—58no—
417C22×Q8—54no—
418C22×Q8—202no—
419C22×Q8—202no—
420C22×D4—58no—
421C22×D4—54no—
422C22×D4—202no—
423C22×D4—202no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—51no—
428C23×C4—51no—
429C23×C4—51no—
430C23×C4—51no—
431C23×C4—51no—
432C23×C4—51no—
433C23×C4—51no—
434C23×C4—54no—
435C23×C4—202no—
436C23×C4—202no—
437C23×C4—202no—
438C23×C4C22×D511yescharacteristic
439C23×C4C22×D511yescharacteristic
440C23×C4C22×D511yescharacteristic
441C23×C4C22×D511yescharacteristic
442C23×C4C22×D511yescharacteristic
443C23×C4C22×D511yescharacteristic
444C23×C4C22×D514yes—
445#124—564no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—54no—
449C2×C4⋊C4—54no—
450C2×C4⋊C4—54no—
451C2×C4⋊C4—54no—
452C2×C4⋊C4—202no—
453C2×C4⋊C4—202no—
454C2×C4⋊C4—202no—
455C2×C4⋊C4—202no—
456C2×C4⋊C4C22×D514yes—
457C2×C4⋊C4C22×D514yes—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—58no—
460C2×C22⋊C4—54no—
461C2×C22⋊C4—58no—
462C2×C22⋊C4—58no—
463C2×C22⋊C4—54no—
464C2×C22⋊C4—54no—
465C2×C22⋊C4—54no—
466C2×C22⋊C4—54no—
467C2×C22⋊C4—54no—
468C2×C22⋊C4—54no—
469C2×C22⋊C4—54no—
470C2×C22⋊C4—202no—
471C2×C22⋊C4—202no—
472C2×C22⋊C4—202no—
473C2×C22⋊C4—202no—
474C2×C22⋊C4—202no—
475C2×C22⋊C4C4×D518yescomplemented
476C2×C22⋊C4C22×D514yes—
477C2×C22⋊C4C22×D514yes—
478C2×C42—58no—
479C2×C42—54no—
480C2×C42—54no—
481C2×C42—54no—
482C2×C42—202no—
483C2×C42—202no—
484#95—54no—
485#95—54no—
486#95—54no—
487#95—54no—
488#95—54no—
489#95—54no—
490#95—54no—
491#95—54no—
492#95—54no—
493#95—54no—
494#95C22×D514yes—
495#95C22×D514yes—
496C22×C5—24no—
497C22×C5—24no—
498C22×C5—24no—
499C22×C5—416no—
500C22×C5—42no—
501C22×C5—42no—
502C22×C5—42no—
503C22×C5—42no—
504C22×C5#51814yes—
505C22×C5#52014yes—
506C22×C5#52014yes—
507C22×C5H(3,𝔽4)14yes—
508C22×C5#56214yes—
509C22×C5#56214yes—
510C22×C5#56314yes—
511C22×C5C24×C411yescharacteristic
512C22×C5C2×H(5,𝔽2)11yescharacteristic
513C22×C5C2×H(5,𝔽2)11yescharacteristic
514C22×C5C2×H(5,𝔽2)11yescharacteristic
515C22×C5C2×H(5,𝔽2)11yescharacteristic
516C22×C5C2×2−1+411yescharacteristic
517C22×C5C2×2−1+411yescharacteristic
518C2×D5—24no—
519C2×D5—24no—
520C2×D5—24no—
521C2×D5—416no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C4×C5—24no—
527C4×C5—24no—
528C4×C5—42no—
529C4×C5—42no—
530C4×C5—42no—
531C4×C5—42no—
532Dic5—24no—
533Dic5—24no—
534Dic5—24no—
535Dic5—42no—
536Dic5—42no—
537Dic5—42no—
538Dic5—42no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—54no—
546C24—52no—
547C24—102no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24C2×C4×D514yes—
554C24C23×D512yes—
555C24C23×D511yescharacteristic
556C2×Q8—516no—
557C2×Q8—2016no—
558C2×Q8—204no—
559C2×Q8—204no—
560C2×D4—516no—
561C2×D4—2016no—
562C2×D4—204no—
563C2×D4—204no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—416no—
584C22×C4—54no—
585C22×C4—54no—
586C22×C4—54no—
587C22×C4—52no—
588C22×C4—52no—
589C22×C4—52no—
590C22×C4—52no—
591C22×C4—52no—
592C22×C4—52no—
593C22×C4—52no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—102no—
606C22×C4—102no—
607C22×C4—102no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—102no—
612C22×C4—204no—
613C22×C4—204no—
614C22×C4—204no—
615C22×C4—2016no—
616C22×C4C2×C4×D514yes—
617C22×C4C2×C4×D514yes—
618C22×C4C23×D512yes—
619C22×C4C23×D512yes—
620C22×C4C23×D512yes—
621C22×C4C23×D512yes—
622C22×C4C23×D512yes—
623C22×C4C23×D512yes—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—204no—
627C4⋊C4—204no—
628C4⋊C4—204no—
629C4⋊C4—204no—
630C22⋊C4—44no—
631C22⋊C4—516no—
632C22⋊C4—516no—
633C22⋊C4—516no—
634C22⋊C4—204no—
635C22⋊C4—204no—
636C22⋊C4—204no—
637C22⋊C4—204no—
638C22⋊C4—204no—
639C22⋊C4C2×C4×D5116yescomplemented
640C42—516no—
641C42—204no—
642C42—204no—
643C2×C5—44no—
644C2×C5#237918yescomplemented
645C2×C5C2×#51811yescharacteristic
646C2×C5C2×#52011yescharacteristic
647C2×C5C2×#52011yescharacteristic
648C2×C5C2×H(3,𝔽4)11yescharacteristic
649C2×C5C2×#56211yescharacteristic
650C2×C5C2×#56211yescharacteristic
651C2×C5C2×#56311yescharacteristic
652D5—44no—
653C23—28no—
654C23—28no—
655C23—28no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—54no—
667C23—108no—
668C23—108no—
669C23—108no—
670C23—102no—
671C23—102no—
672C23—102no—
673C23—102no—
674C23—102no—
675C23—102no—
676C23—204no—
677C23—204no—
678C23—204no—
679C23—204no—
680C23C22×C4×D514yes—
681C23C22×C4×D512yes—
682C23#414412yes—
683C23#414412yes—
684C23#414412yes—
685C23#414712yes—
686C23#414912yes—
687C23#415012yes—
688C23C24×D511yescharacteristic
689Q8—2016no—
690D4—2016no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—416no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—54no—
715C2×C4—54no—
716C2×C4—54no—
717C2×C4—108no—
718C2×C4—108no—
719C2×C4—108no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—2016no—
739C2×C4—204no—
740C2×C4—204no—
741C2×C4—204no—
742C2×C4—204no—
743C2×C4C22×C4×D514yes—
744C2×C4C22×C4×D514yes—
745C5C2×#237911yescharacteristic, complemented, Sylow
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—416no—
752C22—42no—
753C22—42no—
754C22—104no—
755C22—104no—
756C22—104no—
757C22—202no—
758C22—202no—
759C22—2016no—
760C22—202no—
761C22—202no—
762C22#6583814yes—
763C22#6587914yes—
764C22#6588014yes—
765C22#6592814yes—
766C22#6598014yes—
767C22#6598114yes—
768C22#6600114yes—
769C22C23×C4×D511yescharacteristic
770C22C2×#414411yescharacteristic
771C22C2×#414411yescharacteristic
772C22C2×#414411yescharacteristic
773C22C2×#414711yescharacteristic
774C22C2×#414911yescharacteristic
775C22C2×#415011yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—104no—
783C4—104no—
784C4—104no—
785C4—202no—
786C4—202no—
787C4—202no—
788C4—202no—
789C2—44no—
790C2—204no—
791C2#1060613318yesdirect product factor
792C2C2×#6583811yescharacteristic
793C2C2×#6588011yescharacteristic
794C2C2×#6587911yescharacteristic
795C2C2×#6592811yescharacteristic
796C2C2×#6598011yescharacteristic
797C2C2×#6598111yescharacteristic
798C2C2×#6600111yescharacteristic
subgroupG/H
centerC24C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC2×C5×#385C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
cosocleC23×C5C25
hypercenterC2×#385D5
hypocenterC5C2×#2379
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×C5×#385C2semidirect
4. C2×#65499C2semidirect
5. C2×#65278C2semidirect
6. C2×#65278C2semidirect
7. C2×#65263C2semidirect
8. C2×#65266C2semidirect
10. C2×#65234C2semidirect
11. C2×#65240C2semidirect
12. #10606133C2direct (N × H)
13. C2×#64935C2semidirect
14. C2×#64959C2semidirect
15. C2×#64958C2semidirect
16. C2×#64939C2semidirect
40. C2×#4031C4semidirect
42. C5×#385C22semidirect
46. #65499C22semidirect
57. #65278C22semidirect
58. #65278C22semidirect
59. #65266C22semidirect
60. #65263C22semidirect
62. #65240C22semidirect
63. #65234C22semidirect
64. #64959C22semidirect
65. #64958C22semidirect
66. #64939C22semidirect
67. #64935C22semidirect
98. C22×Dic10C2×C4semidirect
105. C2×C5×C22⋊C4C2×C4semidirect
110. C2×C22⋊Dic5C2×C4semidirect
117. C2×#685C2×C4semidirect
118. C2×#685C2×C4semidirect
134. C2×C4×Dic5C2×C4semidirect
138. #4031C2×C4semidirect
164. C2×#385D5semidirect
251. C2×Dic10C22×C4semidirect
255. C5×C22⋊C4C22×C4semidirect
258. C22⋊Dic5C22×C4semidirect
262. #685C22×C4semidirect
263. #685C22×C4semidirect
270. C4×Dic5C22×C4semidirect
307. #385C2×D5semidirect
475. C2×C22⋊C4C4×D5semidirect
639. C22⋊C4C2×C4×D5semidirect
644. C2×C5#2379semidirect
745. C5C2×#2379semidirect
791. C2#10606133direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40312
C2×C5×#3852
C2×#655022
C2×#654992
C2×#652782
C2×#652632
C2×#652662
C2×#652452
C2×#652342
C2×#652402
#106061332
C2×#649352
C2×#649592
C2×#649582
C2×#649392
C2×#23795