Finite Group Databasebeta

← C2×#10614815 #12268433

Subgroups — C2×#10614815 #12268433

Order 1280.

2726 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#126C211yesmaximal, characteristic, complemented
2C22×#4044C211yesmaximal, characteristic, complemented
3#10614815C2116yesmaximal, direct product factor
4C2×#65282C211yesmaximal, characteristic, complemented
5C2×#65283C211yesmaximal, characteristic, complemented
6C2×#65261C211yesmaximal, characteristic, complemented
7C2×#65265C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
9C2×#65242C211yesmaximal, characteristic, complemented
10C2×#65237C211yesmaximal, characteristic, complemented
11C2×#65246C211yesmaximal, characteristic
12C2×#65246C211yesmaximal, characteristic
13C2×#65246C211yesmaximal, characteristic
14C2×#65233C211yesmaximal, characteristic, complemented
15C2×#65229C211yesmaximal, characteristic, complemented
16C2×C4×#683C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C2×C5×#126—28no—
19C2×C5×#126C2218yescomplemented
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C42×C5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C22×C4×Dic5C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C2×#4044—28no—
49C2×#4044C2218yescomplemented
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56#65283C2218yescomplemented
57#65282C2218yescomplemented
58#65265C2218yescomplemented
59C4⋊C4×Dic5C2218yescomplemented
60#65261C2218yescomplemented
61#65246C2218yes—
62#65246C2218yes—
63#65246C2218yes—
64#65242C2218yescomplemented
65#65237C2218yescomplemented
66#65233C2218yescomplemented
67#65229C2218yescomplemented
68C4×#683C2218yescomplemented
69C2×#2512—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C22×C22⋊D5—24no—
79C22×C22⋊D5—24no—
80C22×C22⋊D5—24no—
81C22×C22⋊D5C2314yes—
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C5×#126—232no—
90C2×C5×C4⋊C4—24no—
91C2×C5×C4⋊C4—24no—
92C2×C5×C4⋊C4D418yescomplemented
93C2×C5×C4⋊C4C2314yes—
94C2×C5×C4⋊C4C2314yes—
95C2×C5×C4⋊C4C2314yes—
96C2×C5×C22⋊C4—24no—
97C2×C5×C22⋊C4—24no—
98C2×C5×C22⋊C4—24no—
99C2×C5×C22⋊C4C2314yes—
100C2×C5×C22⋊C4C2314yes—
101C2×C5×C22⋊C4C2314yes—
102C2×C42×C5—24no—
103C2×C42×C5C2314yes—
104C2×C22⋊Dic5—24no—
105C2×C22⋊Dic5—42no—
106C2×C22⋊Dic5—42no—
107C2×C22⋊Dic5C2314yes—
108C2×C22⋊Dic5C2314yes—
109C2×C22⋊Dic5C2314yes—
110C2×#685—24no—
111C2×#685—24no—
112C2×#685—24no—
113C2×#685—24no—
114C2×#685—42no—
115C2×#685—42no—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×C4⋊Dic5—24no—
123C2×C4⋊Dic5—24no—
124C2×C4⋊Dic5C2314yes—
125C2×C4⋊Dic5C2314yes—
126C2×#683—24no—
127C2×#683—24no—
128C2×#683—24no—
129C2×#683—24no—
130C2×#683—42no—
131C2×#683—42no—
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×#683C2314yes—
136C2×#683C2314yes—
137C2×#683C2314yes—
138C2×C4×Dic5—24no—
139C2×C4×Dic5—24no—
140C2×C4×Dic5—24no—
141C2×C4×Dic5—24no—
142C2×C4×Dic5C2314yes—
143C2×C4×Dic5C2314yes—
144C2×C4×Dic5C2314yes—
145C2×C4×Dic5C2314yes—
146#4044—232no—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#126—51no—
154C22×#126D511yescharacteristic, complemented
155#2512—516no—
156C2×#397—51no—
157C2×#397—51no—
158C2×#396—51no—
159C2×#396—51no—
160C2×#390—51no—
161C2×#390—51no—
162C2×#390—51no—
163C2×#389—51no—
164C2×#388—51no—
165C2×#388—51no—
166C2×#384—51no—
167C2×C4×C4⋊C4—51no—
168C2×C4×C4⋊C4—51no—
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5—22no—
174C24×C5—22no—
175C24×C5—22no—
176C24×C5C2412yes—
177C24×C5C2411yescharacteristic
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5—22no—
183C23×D5—22no—
184C23×D5—22no—
185C23×D5C2412yes—
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—22no—
201C22×C4×C5C2×D414yes—
202C22×C4×C5C2×D414yes—
203C22×C4×C5C2×D414yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×C4×C5C2412yes—
207C22×C4×C5C2412yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
210C2×C22⋊D5—28no—
211C2×C22⋊D5—28no—
212C2×C22⋊D5—28no—
213C2×C22⋊D5—416no—
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—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5#4114yes—
232C22×Dic5#4114yes—
233C22×Dic5#4114yes—
234C22×Dic5#4114yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C5×C4⋊C4—28no—
243C5×C4⋊C4—28no—
244C5×C4⋊C4C2×D4116yescomplemented
245C5×C22⋊C4—28no—
246C5×C22⋊C4—28no—
247C5×C22⋊C4—28no—
248C42×C5—28no—
249C22⋊Dic5—28no—
250C22⋊Dic5—44no—
251C22⋊Dic5—44no—
252#685—28no—
253#685—28no—
254#685—28no—
255#685—28no—
256#685—44no—
257#685—44no—
258C4⋊Dic5—28no—
259C4⋊Dic5—28no—
260#683—28no—
261#683—28no—
262#683—28no—
263#683—28no—
264#683—44no—
265#683—44no—
266C4×Dic5—28no—
267C4×Dic5—28no—
268C4×Dic5—28no—
269C4×Dic5—28no—
270C23×D4—51no—
271C2×#126—28no—
272C2×#126—58no—
273C2×#126—108no—
274C2×#126C2×D518yescomplemented
275C22×C4⋊C4—51no—
276C22×C4⋊C4—51no—
277C22×C4⋊C4—51no—
278C22×C4⋊C4—51no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4C2×D511yescharacteristic
284C22×C4⋊C4C2×D511yescharacteristic
285C22×C4⋊C4C2×D511yescharacteristic
286C22×C22⋊C4—51no—
287C22×C22⋊C4—51no—
288C22×C22⋊C4—51no—
289C22×C22⋊C4—51no—
290C22×C22⋊C4—51no—
291C22×C22⋊C4—51no—
292C22×C22⋊C4—51no—
293C22×C22⋊C4—51no—
294C22×C22⋊C4—51no—
295C22×C22⋊C4C2×D511yescharacteristic
296C22×C22⋊C4C2×D511yescharacteristic
297C22×C22⋊C4C2×D511yescharacteristic
298C22×C42—51no—
299C22×C42—51no—
300C22×C42—51no—
301C22×C42—51no—
302C22×C42C2×D511yescharacteristic
303#397—58no—
304#397—58no—
305#396—58no—
306#396—58no—
307#390—58no—
308#390—58no—
309#390—58no—
310#389—58no—
311#388—58no—
312#388—58no—
313#384—58no—
314C4×C4⋊C4—58no—
315C4×C4⋊C4—58no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C23×C5—22no—
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—44no—
330C23×C5—44no—
331C23×C5—44no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5—44no—
336C23×C5C22×D412yes—
337C23×C5C2×#4112yes—
338C23×C5C2×#4112yes—
339C23×C5C2×#4112yes—
340C23×C5C2×#4112yes—
341C23×C5H(5,𝔽2)12yes—
342C23×C52−1+412yes—
343C23×C5C2511yescharacteristic
344C22×D5—22no—
345C22×D5—22no—
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—44no—
352C22×D5—44no—
353C22×D5—44no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5—44no—
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—22no—
376C2×C4×C5—44no—
377C2×C4×C5—44no—
378C2×C4×C5—44no—
379C2×C4×C5C22×D414yes—
380C2×C4×C5C22×D414yes—
381C2×C4×C5C22×D414yes—
382C22⋊D5—416no—
383C2×Dic5—28no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
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—44no—
402C2×Dic5—44no—
403C2×Dic5—44no—
404C2×Dic5—44no—
405C2×Dic5—44no—
406C2×Dic5#126116yescomplemented
407C2×Dic5C2×#4114yes—
408C2×Dic5C2×#4114yes—
409C2×Dic5C2×#4114yes—
410C2×Dic5C2×#4114yes—
411C25—51no—
412C25C22×D511yescharacteristic
413C22×D4—54no—
414C22×D4—104no—
415C22×D4—104no—
416C22×D4—104no—
417C23×C4—51no—
418C23×C4—51no—
419C23×C4—51no—
420C23×C4—51no—
421C23×C4—51no—
422C23×C4—51no—
423C23×C4—51no—
424C23×C4C22×D511yescharacteristic
425C23×C4C22×D511yescharacteristic
426C23×C4C22×D511yescharacteristic
427C23×C4C22×D511yescharacteristic
428C23×C4C22×D511yescharacteristic
429C23×C4C22×D511yescharacteristic
430#126—232no—
431#126—1032no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—54no—
435C2×C4⋊C4—54no—
436C2×C4⋊C4—54no—
437C2×C4⋊C4—54no—
438C2×C4⋊C4—54no—
439C2×C4⋊C4—54no—
440C2×C4⋊C4—54no—
441C2×C4⋊C4—54no—
442C2×C4⋊C4—104no—
443C2×C4⋊C4—104no—
444C2×C4⋊C4—104no—
445C2×C4⋊C4—104no—
446C2×C4⋊C4—104no—
447C2×C4⋊C4—104no—
448C2×C4⋊C4—202no—
449C2×C4⋊C4—202no—
450C2×C4⋊C4C22⋊D518yescomplemented
451C2×C4⋊C4C22×D514yes—
452C2×C4⋊C4C22×D514yes—
453C2×C4⋊C4C22×D514yes—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—54no—
458C2×C22⋊C4—54no—
459C2×C22⋊C4—54no—
460C2×C22⋊C4—54no—
461C2×C22⋊C4—54no—
462C2×C22⋊C4—54no—
463C2×C22⋊C4—54no—
464C2×C22⋊C4—54no—
465C2×C22⋊C4—54no—
466C2×C22⋊C4—104no—
467C2×C22⋊C4—104no—
468C2×C22⋊C4—104no—
469C2×C22⋊C4—104no—
470C2×C22⋊C4—104no—
471C2×C22⋊C4—202no—
472C2×C22⋊C4—202no—
473C2×C22⋊C4—202no—
474C2×C22⋊C4—202no—
475C2×C22⋊C4C22×D514yes—
476C2×C22⋊C4C22×D514yes—
477C2×C22⋊C4C22×D514yes—
478C2×C42—24no—
479C2×C42—54no—
480C2×C42—54no—
481C2×C42—54no—
482C2×C42—54no—
483C2×C42—104no—
484C2×C42—104no—
485C2×C42—104no—
486C2×C42—104no—
487C2×C42C22×D514yes—
488#95—54no—
489#95—54no—
490#95—54no—
491#95—54no—
492#95—54no—
493#95—54no—
494C22×C5—42no—
495C22×C5—42no—
496C22×C5—42no—
497C22×C5—42no—
498C22×C5—42no—
499C22×C5—42no—
500C22×C5—42no—
501C22×C5—88no—
502C22×C5C2×#12614yes—
503C22×C5#53214yes—
504C22×C5#54214yes—
505C22×C5#54714yes—
506C22×C5#55014yes—
507C22×C5#55314yes—
508C22×C5#55614yes—
509C22×C5C23×D411yescharacteristic
510C22×C5C22×#4111yescharacteristic
511C22×C5C22×#4111yescharacteristic
512C22×C5C22×#4111yescharacteristic
513C22×C5C22×#4111yescharacteristic
514C22×C5C2×H(5,𝔽2)11yescharacteristic
515C22×C5C2×2−1+411yescharacteristic
516C2×D5—42no—
517C2×D5—42no—
518C2×D5—42no—
519C2×D5—42no—
520C2×D5—42no—
521C2×D5—42no—
522C2×D5—42no—
523C2×D5—88no—
524C4×C5—24no—
525C4×C5—24no—
526C4×C5—24no—
527C4×C5—42no—
528C4×C5—42no—
529C4×C5—42no—
530Dic5—24no—
531Dic5—42no—
532Dic5—42no—
533Dic5—42no—
534Dic5—42no—
535Dic5—42no—
536Dic5C2×#12618yescomplemented
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—52no—
545C24—102no—
546C24—102no—
547C24—102no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24C23×D512yes—
553C24C23×D511yescharacteristic
554C2×D4—108no—
555C2×D4—108no—
556C2×D4—108no—
557C2×D4—2016no—
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—22no—
573C22×C4—54no—
574C22×C4—54no—
575C22×C4—54no—
576C22×C4—52no—
577C22×C4—54no—
578C22×C4—52no—
579C22×C4—52no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—102no—
585C22×C4—102no—
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×C4C2×C22⋊D514yes—
602C22×C4C2×C22⋊D514yes—
603C22×C4C2×C22⋊D514yes—
604C22×C4C23×D512yes—
605C22×C4C23×D512yes—
606C22×C4C23×D512yes—
607C22×C4C23×D512yes—
608C22×C4C23×D512yes—
609C22×C4C23×D512yes—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—108no—
613C4⋊C4—108no—
614C4⋊C4—108no—
615C4⋊C4—108no—
616C4⋊C4—108no—
617C4⋊C4—108no—
618C4⋊C4—204no—
619C4⋊C4—204no—
620C4⋊C4C2×C22⋊D5116yescomplemented
621C22⋊C4—28no—
622C22⋊C4—28no—
623C22⋊C4—28no—
624C22⋊C4—108no—
625C22⋊C4—108no—
626C22⋊C4—108no—
627C22⋊C4—108no—
628C22⋊C4—108no—
629C22⋊C4—204no—
630C22⋊C4—204no—
631C22⋊C4—204no—
632C22⋊C4—204no—
633C42—28no—
634C42—108no—
635C42—108no—
636C42—108no—
637C42—108no—
638C2×C5—82no—
639C2×C5#251218yescomplemented
640C2×C5C22×#12611yescharacteristic
641C2×C5C2×#53211yescharacteristic
642C2×C5C2×#54211yescharacteristic
643C2×C5C2×#54711yescharacteristic
644C2×C5C2×#55011yescharacteristic
645C2×C5C2×#55311yescharacteristic
646C2×C5C2×#55611yescharacteristic
647D5—82no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—102no—
663C23—102no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—102no—
668C23—102no—
669C23—204no—
670C23—204no—
671C23—204no—
672C23—204no—
673C23—204no—
674C23—204no—
675C23—204no—
676C23D5×#4112yes—
677C23D5×#4112yes—
678C23D5×#4112yes—
679C23D5×#4112yes—
680C23#414912yes—
681C23#415012yes—
682C23C22×C22⋊D512yes—
683C23C24×D511yescharacteristic
684D4—2016no—
685C2×C4—28no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
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—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—54no—
707C2×C4—54no—
708C2×C4—54no—
709C2×C4—516no—
710C2×C4—54no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—108no—
714C2×C4—102no—
715C2×C4—102no—
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—102no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—204no—
730C2×C4—204no—
731C2×C4—204no—
732C2×C4—204no—
733C2×C4—204no—
734C2×C4C22×C22⋊D514yes—
735C2×C4C22×C22⋊D514yes—
736C2×C4C22×C22⋊D514yes—
737C5C2×#251211yescharacteristic, complemented, Sylow
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—88no—
746C22—202no—
747C22—202no—
748C22—202no—
749C22—202no—
750C22—202no—
751C22—202no—
752C22—202no—
753C22—408no—
754C22#6603614yes—
755C22D5×#12614yes—
756C22#6604314yes—
757C22#6604414yes—
758C22#6615814yes—
759C22#6616614yes—
760C22#6616814yes—
761C22C2×D5×#4111yescharacteristic
762C22C2×D5×#4111yescharacteristic
763C22C2×D5×#4111yescharacteristic
764C22C2×D5×#4111yescharacteristic
765C22C2×#414911yescharacteristic
766C22C2×#415011yescharacteristic
767C22C23×C22⋊D511yescharacteristic
768C4—24no—
769C4—24no—
770C4—24no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—58no—
775C4—104no—
776C4—202no—
777C4—202no—
778C4—202no—
779C4—202no—
780C4—202no—
781C2—82no—
782C2—402no—
783C2#1061481518yesdirect product factor
784C2C2×#6604411yescharacteristic
785C2C2×#6604311yescharacteristic
786C2C2×#6603611yescharacteristic
787C2C2×D5×#12611yescharacteristic
788C2C2×#6616611yescharacteristic
789C2C2×#6615811yescharacteristic
790C2C2×#6616811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#126C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC22×#126D5
hypocenterC5C2×#2512
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×C5×#126C2semidirect
2. C22×#4044C2semidirect
3. #10614815C2direct (N × H)
4. C2×#65282C2semidirect
5. C2×#65283C2semidirect
6. C2×#65261C2semidirect
7. C2×#65265C2semidirect
8. C2×C4⋊C4×Dic5C2semidirect
9. C2×#65242C2semidirect
10. C2×#65237C2semidirect
14. C2×#65233C2semidirect
15. C2×#65229C2semidirect
16. C2×C4×#683C2semidirect
19. C2×C5×#126C22semidirect
49. C2×#4044C22semidirect
56. #65283C22semidirect
57. #65282C22semidirect
58. #65265C22semidirect
59. C4⋊C4×Dic5C22semidirect
60. #65261C22semidirect
64. #65242C22semidirect
65. #65237C22semidirect
66. #65233C22semidirect
67. #65229C22semidirect
68. C4×#683C22semidirect
92. C2×C5×C4⋊C4D4semidirect
154. C22×#126D5semidirect
244. C5×C4⋊C4C2×D4semidirect
274. C2×#126C2×D5semidirect
406. C2×Dic5#126semidirect
450. C2×C4⋊C4C22⋊D5semidirect
536. Dic5C2×#126semidirect
620. C4⋊C4C2×C22⋊D5semidirect
639. C2×C5#2512semidirect
737. C5C2×#2512semidirect
783. C2#10614815direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1262
C22×#40442
#106148152
C2×#652822
C2×#652832
C2×#652612
C2×#652652
C2×C4⋊C4×Dic52
C2×#652422
C2×#652372
C2×#652462
C2×#652332
C2×#652292
C2×C4×#6832
C2×#25125