Finite Group Databasebeta

← C2×#10607219 #12259014

Subgroups — C2×#10607219 #12259014

Order 1280.

3094 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4032C211yesmaximal, characteristic
2C2×C5×#388C211yesmaximal, characteristic, complemented
3C2×#65279C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
5C2×#65245C211yesmaximal, characteristic
6C2×#65246C211yesmaximal, characteristic
7C2×#65240C211yesmaximal, characteristic, complemented
8C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
9C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
10C2×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
11C2×C4×#685C211yesmaximal, characteristic, complemented
12#10607219C2116yesmaximal, direct product factor
13C2×#64959C211yesmaximal, characteristic, complemented
14C2×#64943C211yesmaximal, characteristic, complemented
15C2×#64942C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C24×Dic5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×C4×Dic5C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4032C4116yescomplemented
43C2×#4032C2218yes—
44C5×#388C2218yescomplemented
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55#65279C2218yescomplemented
56C4⋊C4×Dic5C2218yescomplemented
57#65246C2218yes—
58#65245C2218yes—
59#65240C2218yescomplemented
60C22⋊C4×Dic5C2218yescomplemented
61C22⋊C4×Dic5C2218yescomplemented
62C4×#685C2218yescomplemented
63C4×C4⋊Dic5C2218yescomplemented
64#64959C2218yescomplemented
65#64955C2218yescomplemented
66#64943C2218yescomplemented
67#64942C2218yescomplemented
68C2×#2374—51nomaximal, Sylow
69C25×C5C2311yescharacteristic
70C24×D5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C22×C22⋊D5—42no—
78C22×C22⋊D5—42no—
79C22×C22⋊D5C2×C418yes—
80C22×C22⋊D5C2314yes—
81C23×Dic5—42no—
82C23×Dic5—42no—
83C23×Dic5C2×C418yescomplemented
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2314yes—
92C22×C4×D5—24no—
93C22×C4×D5—24no—
94C22×C4×D5—42no—
95C22×C4×D5C2314yes—
96C2×C5×C4⋊C4—24no—
97C2×C5×C4⋊C4C2314yes—
98C2×C5×C22⋊C4—24no—
99C2×C5×C22⋊C4—24no—
100C2×C5×C22⋊C4C2×C418yescomplemented
101C2×C5×C22⋊C4C2314yes—
102C2×C5×C22⋊C4C2314yes—
103C2×C5×C22⋊C4C2314yes—
104C2×C42×C5—24no—
105C2×C42×C5C2314yes—
106C2×C22⋊Dic5—24no—
107C2×C22⋊Dic5—24no—
108C2×C22⋊Dic5C2314yes—
109C2×C22⋊Dic5C2314yes—
110C2×#685—24no—
111C2×#685—24no—
112C2×#685—42no—
113C2×#685C2×C418yes—
114C2×#685C2×C418yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×C4⋊Dic5—24no—
121C2×C4⋊Dic5C2×C418yescomplemented
122C2×C4⋊Dic5C2×C418yescomplemented
123C2×C4⋊Dic5C2314yes—
124C2×C4⋊Dic5C2314yes—
125C2×C4⋊Dic5C2314yes—
126C2×#683—42no—
127C2×#683C2314yes—
128C2×C4×Dic5—24no—
129C2×C4×Dic5—42no—
130C2×C4×Dic5—42no—
131C2×C4×Dic5—42no—
132C2×C4×Dic5—42no—
133C2×C4×Dic5—42no—
134C2×C4×Dic5C2314yes—
135C2×C4×Dic5C2314yes—
136C2×C4×Dic5C2314yes—
137C2×C4×Dic5C2314yes—
138C2×C4×Dic5C2314yes—
139C2×C4×Dic5C2314yes—
140#4032C2×C4164yescomplemented
141C5×#95C2314yes—
142C5×#95C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151C22×#123—51no—
152#2374—516no—
153C2×#390—51no—
154C2×#388—51no—
155C2×#388—51no—
156C2×#388—51no—
157C2×#388D511yescharacteristic, complemented
158C2×#387—51no—
159C2×#387—51no—
160C2×#386—51no—
161C2×C4×C4⋊C4—51no—
162C2×C4×C4⋊C4—51no—
163C2×C4×C22⋊C4—51no—
164C2×C4×C22⋊C4—51no—
165C2×C4×C22⋊C4—51no—
166C2×C4×C22⋊C4—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×C5C22×C414yes—
199C22×C4×C5C22×C414yes—
200C22×C4×C5#4114yes—
201C22×C4×C5#4114yes—
202C22×C4×C5C2412yes—
203C22×C4×C5C2412yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×C4×C5C2412yes—
207C22×C4×C5C2412yes—
208C2×C22⋊D5—416no—
209C2×C22⋊D5—44no—
210C2×C22⋊D5—44no—
211C2×C22⋊D5C22×C4116yes—
212C22×Dic5—22no—
213C22×Dic5—22no—
214C22×Dic5—22no—
215C22×Dic5—22no—
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—416no—
229C22×Dic5—44no—
230C22×Dic5—44no—
231C22×Dic5C22×C414yes—
232C22×Dic5C22×C414yes—
233C22×Dic5C22×C414yes—
234C22×Dic5C22×C4116yescomplemented
235C22×Dic5#4114yes—
236C22×Dic5#4114yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C2×C4×D5—28no—
245C2×C4×D5—28no—
246C2×C4×D5—44no—
247C2×C4×D5—416no—
248C5×C4⋊C4—28no—
249C5×C22⋊C4—28no—
250C5×C22⋊C4—28no—
251C5×C22⋊C4C22×C4116yescomplemented
252C42×C5—28no—
253C22⋊Dic5—28no—
254C22⋊Dic5—28no—
255#685—28no—
256#685—28no—
257#685—44no—
258#685C22×C4116yes—
259#685C22×C4116yes—
260C4⋊Dic5—28no—
261C4⋊Dic5C22×C4116yescomplemented
262C4⋊Dic5C22×C4116yescomplemented
263#683—44no—
264C4×Dic5—28no—
265C4×Dic5—44no—
266C4×Dic5—44no—
267C4×Dic5—44no—
268C4×Dic5—44no—
269C4×Dic5—44no—
270C23×D4—51no—
271C24×C4—51no—
272C24×C4—51no—
273C2×#123—516no—
274C2×#123—58no—
275C22×C4⋊C4—51no—
276C22×C4⋊C4—51no—
277C22×C4⋊C4—51no—
278C22×C4⋊C4—51no—
279C22×C4⋊C4C2×D511yescharacteristic
280C22×C22⋊C4—51no—
281C22×C22⋊C4—51no—
282C22×C22⋊C4—51no—
283C22×C22⋊C4—51no—
284C22×C22⋊C4—51no—
285C22×C22⋊C4—51no—
286C22×C22⋊C4—51no—
287C22×C22⋊C4C2×D511yescharacteristic
288C22×C22⋊C4C2×D511yescharacteristic
289C22×C22⋊C4C2×D511yescharacteristic
290C22×C42—51no—
291C22×C42—51no—
292C22×C42—51no—
293C22×C42—51no—
294C22×C42—51no—
295C22×C42—51no—
296C22×C42C2×D511yescharacteristic
297#390—58no—
298#388—58no—
299#388—58no—
300#388—58no—
301#388C2×D518yescomplemented
302#387—58no—
303#387—58no—
304#386—58no—
305C4×C4⋊C4—58no—
306C4×C4⋊C4—58no—
307C4×C22⋊C4—58no—
308C4×C22⋊C4—58no—
309C4×C22⋊C4—58no—
310C4×C22⋊C4—58no—
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×#95C2×D511yescharacteristic
320C2×#95C2×D511yescharacteristic
321C23×C5—28no—
322C23×C5—28no—
323C23×C5—28no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—44no—
331C23×C5—44no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5C23×C414yes—
335C23×C5C23×C412yes—
336C23×C5C2×#4112yes—
337C23×C5C2×#4112yes—
338C23×C5C2×#4112yes—
339C23×C5C2×#4112yes—
340C23×C5H(5,𝔽2)12yes—
341C23×C5H(5,𝔽2)12yes—
342C23×C5C2511yescharacteristic
343C22×D5—28no—
344C22×D5—28no—
345C22×D5—28no—
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—44no—
353C22×D5—44no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5C23×C414yes—
357C2×C4×C5—28no—
358C2×C4×C5—28no—
359C2×C4×C5—28no—
360C2×C4×C5—28no—
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—44no—
376C2×C4×C5—44no—
377C2×C4×C5C23×C414yes—
378C2×C4×C5C23×C414yes—
379C2×C4×C5C2×#4114yes—
380C2×C4×C5C2×#4114yes—
381C22⋊D5—416no—
382C2×Dic5—28no—
383C2×Dic5—28no—
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—416no—
404C2×Dic5—44no—
405C2×Dic5—44no—
406C2×Dic5C23×C414yes—
407C2×Dic5C23×C414yes—
408C2×Dic5C23×C414yes—
409C2×Dic5C2×#4114yes—
410C2×Dic5C2×#4114yes—
411C4×D5—416no—
412C25—51no—
413C25C22×D511yescharacteristic
414C22×D4—58no—
415C22×D4—54no—
416C22×D4—202no—
417C22×D4—202no—
418C23×C4—51no—
419C23×C4—51no—
420C23×C4—51no—
421C23×C4—51no—
422C23×C4—51no—
423C23×C4—58no—
424C23×C4—54no—
425C23×C4—51no—
426C23×C4—51no—
427C23×C4—54no—
428C23×C4—104no—
429C23×C4—104no—
430C23×C4—202no—
431C23×C4—202no—
432C23×C4—202no—
433C23×C4C22×D511yescharacteristic
434C23×C4C22×D511yescharacteristic
435C23×C4C22×D511yescharacteristic
436C23×C4C22×D511yescharacteristic
437C23×C4C22×D511yescharacteristic
438C23×C4C22×D511yescharacteristic
439#123—564no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—58no—
442C2×C4⋊C4—58no—
443C2×C4⋊C4—54no—
444C2×C4⋊C4—54no—
445C2×C4⋊C4—54no—
446C2×C4⋊C4—54no—
447C2×C4⋊C4—104no—
448C2×C4⋊C4—202no—
449C2×C4⋊C4C22×D514yes—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—58no—
453C2×C22⋊C4—58no—
454C2×C22⋊C4—54no—
455C2×C22⋊C4—54no—
456C2×C22⋊C4—54no—
457C2×C22⋊C4—54no—
458C2×C22⋊C4—54no—
459C2×C22⋊C4—54no—
460C2×C22⋊C4—54no—
461C2×C22⋊C4—104no—
462C2×C22⋊C4—104no—
463C2×C22⋊C4—104no—
464C2×C22⋊C4—104no—
465C2×C22⋊C4—202no—
466C2×C22⋊C4C4×D518yescomplemented
467C2×C22⋊C4C22×D514yes—
468C2×C22⋊C4C22×D514yes—
469C2×C22⋊C4C22×D514yes—
470C2×C42—24no—
471C2×C42—54no—
472C2×C42—54no—
473C2×C42—54no—
474C2×C42—54no—
475C2×C42—54no—
476C2×C42—54no—
477C2×C42—104no—
478C2×C42—202no—
479C2×C42—202no—
480C2×C42—202no—
481C2×C42—202no—
482C2×C42—202no—
483C2×C42C22×D514yes—
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#95C22×D514yes—
493#95C22×D514yes—
494C22×C5—24no—
495C22×C5—24no—
496C22×C5—24no—
497C22×C5—416no—
498C22×C5—42no—
499C22×C5—42no—
500C22×C5—42no—
501C22×C5—42no—
502C22×C5C4×#4114yes—
503C22×C5C4×#4114yes—
504C22×C5#51814yes—
505C22×C5#55114yes—
506C22×C5#55314yes—
507C22×C5#55314yes—
508C22×C5#55914yes—
509C22×C5C24×C411yescharacteristic
510C22×C5C22×#4111yescharacteristic
511C22×C5C22×#4111yescharacteristic
512C22×C5C22×#4111yescharacteristic
513C22×C5C22×#4111yescharacteristic
514C22×C5C2×H(5,𝔽2)11yescharacteristic
515C22×C5C2×H(5,𝔽2)11yescharacteristic
516C2×D5—24no—
517C2×D5—24no—
518C2×D5—24no—
519C2×D5—416no—
520C2×D5—42no—
521C2×D5—42no—
522C2×D5—42no—
523C2×D5—42no—
524C4×C5—24no—
525C4×C5—24no—
526C4×C5—24no—
527C4×C5—24no—
528C4×C5—42no—
529C4×C5—42no—
530Dic5—24no—
531Dic5—24no—
532Dic5—24no—
533Dic5—24no—
534Dic5—24no—
535Dic5—42no—
536Dic5—42no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—54no—
544C24—52no—
545C24—102no—
546C24—102no—
547C24—102no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24C2×C4×D514yes—
552C24C23×D512yes—
553C24C23×D511yescharacteristic
554C2×D4—516no—
555C2×D4—2016no—
556C2×D4—204no—
557C2×D4—204no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
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—54no—
573C22×C4—54no—
574C22×C4—54no—
575C22×C4—54no—
576C22×C4—54no—
577C22×C4—52no—
578C22×C4—52no—
579C22×C4—52no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—516no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—108no—
586C22×C4—102no—
587C22×C4—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
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—108no—
603C22×C4—204no—
604C22×C4—2016no—
605C22×C4—2016no—
606C22×C4—204no—
607C22×C4—204no—
608C22×C4C2×C4×D514yes—
609C22×C4C2×C4×D514yes—
610C22×C4#71114yes—
611C22×C4#71114yes—
612C22×C4C23×D512yes—
613C22×C4C23×D512yes—
614C22×C4C23×D512yes—
615C22×C4C23×D512yes—
616C22×C4C23×D512yes—
617C22×C4C23×D512yes—
618C4⋊C4—28no—
619C4⋊C4—516no—
620C4⋊C4—516no—
621C4⋊C4—108no—
622C4⋊C4—204no—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—516no—
626C22⋊C4—516no—
627C22⋊C4—108no—
628C22⋊C4—108no—
629C22⋊C4—108no—
630C22⋊C4—108no—
631C22⋊C4—204no—
632C22⋊C4C2×C4×D5116yescomplemented
633C42—28no—
634C42—108no—
635C42—204no—
636C42—204no—
637C42—204no—
638C42—204no—
639C42—204no—
640C2×C5—44no—
641C2×C5#237418yescomplemented
642C2×C5C2×C4×#4111yescharacteristic
643C2×C5C2×C4×#4111yescharacteristic
644C2×C5C2×#51811yescharacteristic
645C2×C5C2×#55111yescharacteristic
646C2×C5C2×#55311yescharacteristic
647C2×C5C2×#55311yescharacteristic
648C2×C5C2×#55911yescharacteristic
649D5—44no—
650C23—28no—
651C23—28no—
652C23—28no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—54no—
664C23—108no—
665C23—108no—
666C23—108no—
667C23—102no—
668C23—102no—
669C23—102no—
670C23—102no—
671C23—102no—
672C23—102no—
673C23—204no—
674C23—204no—
675C23—204no—
676C23—204no—
677C23C22×C4×D514yes—
678C23C22×C4×D512yes—
679C23C2×#71112yes—
680C23C2×#71112yes—
681C23D5×#4112yes—
682C23D5×#4112yes—
683C23#414912yes—
684C23#414912yes—
685C23C24×D511yescharacteristic
686D4—2016no—
687C2×C4—28no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
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—44no—
706C2×C4—44no—
707C2×C4—54no—
708C2×C4—54no—
709C2×C4—54no—
710C2×C4—54no—
711C2×C4—54no—
712C2×C4—108no—
713C2×C4—108no—
714C2×C4—108no—
715C2×C4—108no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—108no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—2016no—
734C2×C4—2016no—
735C2×C4—204no—
736C2×C4—204no—
737C2×C4C22×C4×D514yes—
738C2×C4C22×C4×D514yes—
739C2×C4C2×#71114yes—
740C2×C4C2×#71114yes—
741C5C2×#237411yescharacteristic, complemented, Sylow
742C22—24no—
743C22—24no—
744C22—24no—
745C22—42no—
746C22—42no—
747C22—416no—
748C22—42no—
749C22—42no—
750C22—104no—
751C22—104no—
752C22—104no—
753C22—202no—
754C22—202no—
755C22—2016no—
756C22—202no—
757C22—202no—
758C22#6585514yes—
759C22C4×#71114yes—
760C22C4×#71114yes—
761C22#6595214yes—
762C22#6599214yes—
763C22#6601514yes—
764C22#6604314yes—
765C22C23×C4×D511yescharacteristic
766C22C22×#71111yescharacteristic
767C22C22×#71111yescharacteristic
768C22C2×D5×#4111yescharacteristic
769C22C2×D5×#4111yescharacteristic
770C22C2×#414911yescharacteristic
771C22C2×#414911yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—104no—
779C4—104no—
780C4—104no—
781C4—104no—
782C4—104no—
783C4—202no—
784C4—202no—
785C2—44no—
786C2—204no—
787C2#1060721918yesdirect product factor
788C2C2×#6585511yescharacteristic
789C2C2×C4×#71111yescharacteristic
790C2C2×C4×#71111yescharacteristic
791C2C2×#6595211yescharacteristic
792C2C2×#6599211yescharacteristic
793C2C2×#6601511yescharacteristic
794C2C2×#6604311yescharacteristic
subgroupG/H
centerC24C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
cosocleC23×C5C25
hypercenterC2×#388D5
hypocenterC5C2×#2374
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×C5×#388C2semidirect
3. C2×#65279C2semidirect
4. C2×C4⋊C4×Dic5C2semidirect
7. C2×#65240C2semidirect
8. C2×C22⋊C4×Dic5C2semidirect
9. C2×C22⋊C4×Dic5C2semidirect
10. C2×C4×C4⋊Dic5C2semidirect
11. C2×C4×#685C2semidirect
12. #10607219C2direct (N × H)
13. C2×#64959C2semidirect
14. C2×#64943C2semidirect
15. C2×#64942C2semidirect
16. C2×#64955C2semidirect
42. C2×#4032C4semidirect
44. C5×#388C22semidirect
55. #65279C22semidirect
56. C4⋊C4×Dic5C22semidirect
59. #65240C22semidirect
60. C22⋊C4×Dic5C22semidirect
61. C22⋊C4×Dic5C22semidirect
62. C4×#685C22semidirect
63. C4×C4⋊Dic5C22semidirect
64. #64959C22semidirect
65. #64955C22semidirect
66. #64943C22semidirect
67. #64942C22semidirect
83. C23×Dic5C2×C4semidirect
100. C2×C5×C22⋊C4C2×C4semidirect
121. C2×C4⋊Dic5C2×C4semidirect
122. C2×C4⋊Dic5C2×C4semidirect
140. #4032C2×C4semidirect
157. C2×#388D5semidirect
234. C22×Dic5C22×C4semidirect
251. C5×C22⋊C4C22×C4semidirect
261. C4⋊Dic5C22×C4semidirect
262. C4⋊Dic5C22×C4semidirect
301. #388C2×D5semidirect
466. C2×C22⋊C4C4×D5semidirect
632. C22⋊C4C2×C4×D5semidirect
641. C2×C5#2374semidirect
741. C5C2×#2374semidirect
787. C2#10607219direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40322
C2×C5×#3882
C2×#652792
C2×C4⋊C4×Dic52
C2×#652452
C2×#652462
C2×#652402
C2×C22⋊C4×Dic52
C2×C4×C4⋊Dic52
C2×C4×#6852
#106072192
C2×#649592
C2×#649432
C2×#649422
C2×#649552
C2×#23745