Finite Group Databasebeta

← C2×#10614811 #12267853

Subgroups — C2×#10614811 #12267853

Order 1280.

2898 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×C5×#126C211yesmaximal, characteristic, complemented
2C22×#4038C211yesmaximal, characteristic, complemented
3#10614811C2116yesmaximal, direct product factor
4C2×#65281C211yesmaximal, characteristic, complemented
5C2×#65278C211yesmaximal, characteristic, complemented
6C2×#65272C211yesmaximal, characteristic, complemented
7C2×#65262C211yesmaximal, characteristic, complemented
8C2×#65270C211yesmaximal, characteristic, complemented
9C2×#65245C211yesmaximal, characteristic
10C2×#65238C211yesmaximal, characteristic, complemented
11C2×#65250C211yesmaximal, characteristic
12C2×#65246C211yesmaximal, characteristic
13C2×#65233C211yesmaximal, characteristic, complemented
14C2×#65233C211yesmaximal, characteristic, complemented
15C2×#65229C211yesmaximal, characteristic, complemented
16C2×C4×#683C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C2×C5×#126—28no—
20C2×C5×#126C2218yescomplemented
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
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×C4×Dic5C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4038—28no—
47C2×#4038C2218yescomplemented
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56#65281C2218yescomplemented
57#65278C2218yescomplemented
58#65272C2218yescomplemented
59#65270C2218yescomplemented
60#65262C2218yescomplemented
61#65250C2218yes—
62#65246C2218yes—
63#65245C2218yes—
64#65238C2218yescomplemented
65#65233C2218yescomplemented
66#65233C2218yescomplemented
67#65229C2218yescomplemented
68C4×#683C2218yescomplemented
69C2×#2479—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—42no—
81C22×C22⋊D5C2314yes—
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C22×C4×D5—24no—
90C22×C4×D5—24no—
91C22×C4×D5—24no—
92C22×C4×D5C2314yes—
93C5×#126—232no—
94C2×C5×C4⋊C4—24no—
95C2×C5×C4⋊C4—24no—
96C2×C5×C4⋊C4D418yescomplemented
97C2×C5×C4⋊C4C2314yes—
98C2×C5×C4⋊C4C2314yes—
99C2×C5×C4⋊C4C2314yes—
100C2×C5×C22⋊C4—24no—
101C2×C5×C22⋊C4—24no—
102C2×C5×C22⋊C4—24no—
103C2×C5×C22⋊C4C2314yes—
104C2×C5×C22⋊C4C2314yes—
105C2×C5×C22⋊C4C2314yes—
106C2×C42×C5—24no—
107C2×C42×C5C2314yes—
108C2×C22⋊Dic5—24no—
109C2×C22⋊Dic5—24no—
110C2×C22⋊Dic5—42no—
111C2×C22⋊Dic5C2314yes—
112C2×C22⋊Dic5C2314yes—
113C2×C22⋊Dic5C2314yes—
114C2×#685—24no—
115C2×#685—24no—
116C2×#685—24no—
117C2×#685—24no—
118C2×#685—42no—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×#685C2314yes—
124C2×C4⋊Dic5—24no—
125C2×C4⋊Dic5—24no—
126C2×C4⋊Dic5C2314yes—
127C2×C4⋊Dic5C2314yes—
128C2×#683—24no—
129C2×#683—24no—
130C2×#683—42no—
131C2×#683—42no—
132C2×#683—42no—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×#683C2314yes—
136C2×#683C2314yes—
137C2×#683C2314yes—
138C2×C4×Dic5—24no—
139C2×C4×Dic5—24no—
140C2×C4×Dic5—24no—
141C2×C4×Dic5C2314yes—
142C2×C4×Dic5C2314yes—
143C2×C4×Dic5C2314yes—
144#4038—232no—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#126D511yescharacteristic, complemented
154C22×#117—51no—
155#2479—516no—
156C2×#399—51no—
157C2×#399—51no—
158C2×#398—51no—
159C2×#394—51no—
160C2×#390—51no—
161C2×#389—51no—
162C2×#388—51no—
163C2×#388—51no—
164C2×#388—51no—
165C2×#387—51no—
166C2×#386—51no—
167C2×#385—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#4114yes—
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—44no—
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—22no—
232C22×Dic5#4114yes—
233C22×Dic5#4114yes—
234C22×Dic5#4114yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C2×C4×D5—232no—
243C2×C4×D5—28no—
244C2×C4×D5—28no—
245C2×C4×D5—28no—
246C5×C4⋊C4—28no—
247C5×C4⋊C4—28no—
248C5×C4⋊C4C2×D4116yescomplemented
249C5×C22⋊C4—28no—
250C5×C22⋊C4—28no—
251C5×C22⋊C4—28no—
252C42×C5—28no—
253C22⋊Dic5—28no—
254C22⋊Dic5—28no—
255C22⋊Dic5—44no—
256#685—28no—
257#685—28no—
258#685—28no—
259#685—28no—
260#685—44no—
261C4⋊Dic5—28no—
262C4⋊Dic5—28no—
263#683—28no—
264#683—28no—
265#683—44no—
266#683—44no—
267#683—44no—
268C4×Dic5—28no—
269C4×Dic5—28no—
270C4×Dic5—28no—
271C23×D4—51no—
272C24×C4—51no—
273C2×#126—28no—
274C2×#126C2×D518yescomplemented
275C2×#117—58no—
276C2×#117—108no—
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⋊C4—51no—
284C22×C4⋊C4C2×D511yescharacteristic
285C22×C4⋊C4C2×D511yescharacteristic
286C22×C4⋊C4C2×D511yescharacteristic
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×C42C2×D511yescharacteristic
302#399—58no—
303#399—58no—
304#398—58no—
305#394—58no—
306#390—58no—
307#389—58no—
308#388—58no—
309#388—58no—
310#388—58no—
311#387—58no—
312#386—58no—
313#385—58no—
314C4×C4⋊C4—58no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95—51no—
323C23×C5—22no—
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×C5—44no—
335C23×C5—44no—
336C23×C5—44no—
337C23×C5C22×D412yes—
338C23×C5C2×#4112yes—
339C23×C5C2×#4112yes—
340C23×C5C2×#4112yes—
341C23×C5C2×#4112yes—
342C23×C5H(5,𝔽2)12yes—
343C23×C52−1+412yes—
344C23×C5C2511yescharacteristic
345C22×D5—28no—
346C22×D5—28no—
347C22×D5—28no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—22no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5—44no—
358C22×D5C2×#4114yes—
359C2×C4×C5—28no—
360C2×C4×C5—28no—
361C2×C4×C5—28no—
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—22no—
377C2×C4×C5—44no—
378C2×C4×C5—44no—
379C2×C4×C5—44no—
380C2×C4×C5C22×D414yes—
381C2×C4×C5C22×D414yes—
382C2×C4×C5C22×D414yes—
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×Dic5C2×#4114yes—
410C2×Dic5C2×#4114yes—
411C2×Dic5C2×#4114yes—
412C4×D5—232no—
413C25—51no—
414C25C22×D511yescharacteristic
415C22×D4—54no—
416C22×D4—104no—
417C22×D4—104no—
418C22×D4—202no—
419C23×C4—51no—
420C23×C4—51no—
421C23×C4—51no—
422C23×C4—51no—
423C23×C4—51no—
424C23×C4—51no—
425C23×C4—51no—
426C23×C4—54no—
427C23×C4—104no—
428C23×C4—104no—
429C23×C4—104no—
430C23×C4C22×D511yescharacteristic
431C23×C4C22×D511yescharacteristic
432C23×C4C22×D511yescharacteristic
433C23×C4C22×D511yescharacteristic
434C23×C4C22×D511yescharacteristic
435C23×C4C22×D511yescharacteristic
436#126—232no—
437#117—1032no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—54no—
441C2×C4⋊C4—54no—
442C2×C4⋊C4—54no—
443C2×C4⋊C4—54no—
444C2×C4⋊C4—54no—
445C2×C4⋊C4—54no—
446C2×C4⋊C4—54no—
447C2×C4⋊C4—104no—
448C2×C4⋊C4—104no—
449C2×C4⋊C4—104no—
450C2×C4⋊C4—104no—
451C2×C4⋊C4—202no—
452C2×C4⋊C4—202no—
453C2×C4⋊C4—202no—
454C2×C4⋊C4C22⋊D518yescomplemented
455C2×C4⋊C4C22×D514yes—
456C2×C4⋊C4C22×D514yes—
457C2×C4⋊C4C22×D514yes—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—54no—
462C2×C22⋊C4—54no—
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—104no—
470C2×C22⋊C4—104no—
471C2×C22⋊C4—104no—
472C2×C22⋊C4—104no—
473C2×C22⋊C4—104no—
474C2×C22⋊C4—104no—
475C2×C22⋊C4—202no—
476C2×C22⋊C4—202no—
477C2×C22⋊C4C22×D514yes—
478C2×C22⋊C4C22×D514yes—
479C2×C22⋊C4C22×D514yes—
480C2×C42—24no—
481C2×C42—54no—
482C2×C42—54no—
483C2×C42—54no—
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—
494#95—54no—
495#95—54no—
496C22×C5—42no—
497C22×C5—42no—
498C22×C5—42no—
499C22×C5—42no—
500C22×C5—42no—
501C22×C5—42no—
502C22×C5—42no—
503C22×C5—88no—
504C22×C5#52514yes—
505C22×C5#52914yes—
506C22×C5#54214yes—
507C22×C5#54714yes—
508C22×C5#55014yes—
509C22×C5#55114yes—
510C22×C5#55214yes—
511C22×C5C23×D411yescharacteristic
512C22×C5C22×#4111yescharacteristic
513C22×C5C22×#4111yescharacteristic
514C22×C5C22×#4111yescharacteristic
515C22×C5C22×#4111yescharacteristic
516C22×C5C2×H(5,𝔽2)11yescharacteristic
517C22×C5C2×2−1+411yescharacteristic
518C2×D5—24no—
519C2×D5—24no—
520C2×D5—24no—
521C2×D5—42no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—416no—
526C4×C5—24no—
527C4×C5—24no—
528C4×C5—24no—
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—22no—
546C24—54no—
547C24—52no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24C23×D512yes—
555C24C23×D511yescharacteristic
556C2×D4—108no—
557C2×D4—108no—
558C2×D4—204no—
559C2×D4—2016no—
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—22no—
574C22×C4—22no—
575C22×C4—54no—
576C22×C4—54no—
577C22×C4—54no—
578C22×C4—52no—
579C22×C4—52no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—108no—
586C22×C4—108no—
587C22×C4—1032no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—108no—
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×C4C2×C22⋊D514yes—
608C22×C4C2×C22⋊D514yes—
609C22×C4C2×C22⋊D514yes—
610C22×C4C23×D512yes—
611C22×C4C23×D512yes—
612C22×C4C23×D512yes—
613C22×C4C23×D512yes—
614C22×C4C23×D512yes—
615C22×C4C23×D512yes—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—108no—
619C4⋊C4—108no—
620C4⋊C4—108no—
621C4⋊C4—108no—
622C4⋊C4—204no—
623C4⋊C4—204no—
624C4⋊C4—204no—
625C4⋊C4C2×C22⋊D5116yescomplemented
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—28no—
629C22⋊C4—108no—
630C22⋊C4—108no—
631C22⋊C4—108no—
632C22⋊C4—108no—
633C22⋊C4—108no—
634C22⋊C4—108no—
635C22⋊C4—204no—
636C22⋊C4—204no—
637C42—28no—
638C42—108no—
639C42—108no—
640C42—108no—
641C2×C5—82no—
642C2×C5#247918yescomplemented
643C2×C5C2×#52511yescharacteristic
644C2×C5C2×#52911yescharacteristic
645C2×C5C2×#54211yescharacteristic
646C2×C5C2×#54711yescharacteristic
647C2×C5C2×#55011yescharacteristic
648C2×C5C2×#55111yescharacteristic
649C2×C5C2×#55211yescharacteristic
650D5—44no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—54no—
666C23—108no—
667C23—102no—
668C23—102no—
669C23—102no—
670C23—102no—
671C23—102no—
672C23—102no—
673C23—108no—
674C23—108no—
675C23—204no—
676C23—204no—
677C23—204no—
678C23—204no—
679C23D5×#4112yes—
680C23D5×#4112yes—
681C23D5×#4112yes—
682C23D5×#4112yes—
683C23#414912yes—
684C23#415012yes—
685C23C22×C22⋊D512yes—
686C23C24×D511yescharacteristic
687D4—2016no—
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—22no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—54no—
710C2×C4—54no—
711C2×C4—54no—
712C2×C4—1032no—
713C2×C4—108no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—108no—
721C2×C4—108no—
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—204no—
735C2×C4—204no—
736C2×C4—204no—
737C2×C4—204no—
738C2×C4C22×C22⋊D514yes—
739C2×C4C22×C22⋊D514yes—
740C2×C4C22×C22⋊D514yes—
741C5C2×#247911yescharacteristic, complemented, Sylow
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—88no—
750C22—104no—
751C22—104no—
752C22—104no—
753C22—2016no—
754C22—202no—
755C22—202no—
756C22—202no—
757C22—202no—
758C22#6603914yes—
759C22#6604014yes—
760C22#6604214yes—
761C22#6604414yes—
762C22#6615814yes—
763C22#6616214yes—
764C22#6616814yes—
765C22C2×D5×#4111yescharacteristic
766C22C2×D5×#4111yescharacteristic
767C22C2×D5×#4111yescharacteristic
768C22C2×D5×#4111yescharacteristic
769C22C2×#414911yescharacteristic
770C22C2×#415011yescharacteristic
771C22C23×C22⋊D511yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—104no—
779C4—104no—
780C4—104no—
781C4—202no—
782C4—202no—
783C4—202no—
784C4—202no—
785C2—82no—
786C2—204no—
787C2#1061481118yesdirect product factor
788C2C2×#6604011yescharacteristic
789C2C2×#6604411yescharacteristic
790C2C2×#6603911yescharacteristic
791C2C2×#6604211yescharacteristic
792C2C2×#6615811yescharacteristic
793C2C2×#6616211yescharacteristic
794C2C2×#6616811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#126C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC22×#126D5
hypocenterC5C2×#2479
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×#4038C2semidirect
3. #10614811C2direct (N × H)
4. C2×#65281C2semidirect
5. C2×#65278C2semidirect
6. C2×#65272C2semidirect
7. C2×#65262C2semidirect
8. C2×#65270C2semidirect
10. C2×#65238C2semidirect
13. C2×#65233C2semidirect
14. C2×#65233C2semidirect
15. C2×#65229C2semidirect
16. C2×C4×#683C2semidirect
20. C2×C5×#126C22semidirect
47. C2×#4038C22semidirect
56. #65281C22semidirect
57. #65278C22semidirect
58. #65272C22semidirect
59. #65270C22semidirect
60. #65262C22semidirect
64. #65238C22semidirect
65. #65233C22semidirect
66. #65233C22semidirect
67. #65229C22semidirect
68. C4×#683C22semidirect
96. C2×C5×C4⋊C4D4semidirect
153. C22×#126D5semidirect
248. C5×C4⋊C4C2×D4semidirect
274. C2×#126C2×D5semidirect
454. C2×C4⋊C4C22⋊D5semidirect
625. C4⋊C4C2×C22⋊D5semidirect
642. C2×C5#2479semidirect
741. C5C2×#2479semidirect
787. C2#10614811direct (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×#40382
#106148112
C2×#652812
C2×#652782
C2×#652722
C2×#652622
C2×#652702
C2×#652452
C2×#652382
C2×#652502
C2×#652462
C2×#652332
C2×#652292
C2×C4×#6832
C2×#24795