Finite Group Databasebeta

← C2×#10609181 #12305833

Subgroups — C2×#10609181 #12305833

Order 1280.

2502 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×#4044C211yesmaximal, characteristic, complemented
2C22×#4025C211yesmaximal, characteristic, complemented
3C2×C5×#396C211yesmaximal, characteristic, complemented
4C2×#65283C211yesmaximal, characteristic, complemented
5C2×#65283C211yesmaximal, characteristic, complemented
6C2×#65269C211yesmaximal, characteristic, complemented
7C2×#65273C211yesmaximal, characteristic, complemented
8C2×#65265C211yesmaximal, characteristic, complemented
9C2×#65248C211yesmaximal, characteristic
10C2×#65248C211yesmaximal, characteristic
11C2×#65237C211yesmaximal, characteristic, complemented
12C2×#65237C211yesmaximal, characteristic, complemented
13C2×#65250C211yesmaximal, characteristic
14#10609181C2116yesmaximal, direct product factor
15C2×#64965C211yesmaximal, characteristic, complemented
16C2×#64950C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4044—28no—
47C2×#4044C2218yescomplemented
48C2×#4025—28no—
49C2×#4025C2218yescomplemented
50C5×#396C2218yescomplemented
51C2×C5×#95C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65283C2218yescomplemented
58#65283C2218yescomplemented
59#65273C2218yescomplemented
60#65269C2218yescomplemented
61#65265C2218yescomplemented
62#65250C2218yes—
63#65248C2218yes—
64#65248C2218yes—
65#65237C2218yescomplemented
66#65237C2218yescomplemented
67#64965C2218yescomplemented
68#64950C2218yescomplemented
69C2×#2823—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—42no—
79C22×C22⋊D5—42no—
80C22×C22⋊D5—42no—
81C22×C22⋊D5C2314yes—
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C2×C5×C4⋊C4—24no—
90C2×C5×C4⋊C4—42no—
91C2×C5×C4⋊C4—42no—
92C2×C5×C4⋊C4C2314yes—
93C2×C5×C4⋊C4C2314yes—
94C2×C5×C4⋊C4C2314yes—
95C2×C5×C22⋊C4—24no—
96C2×C5×C22⋊C4—42no—
97C2×C5×C22⋊C4—42no—
98C2×C5×C22⋊C4C2314yes—
99C2×C5×C22⋊C4C2314yes—
100C2×C5×C22⋊C4C2314yes—
101C2×C22⋊Dic5—24no—
102C2×C22⋊Dic5—24no—
103C2×C22⋊Dic5—42no—
104C2×C22⋊Dic5C2314yes—
105C2×C22⋊Dic5C2314yes—
106C2×C22⋊Dic5C2314yes—
107C2×#685—24no—
108C2×#685—24no—
109C2×#685—24no—
110C2×#685—42no—
111C2×#685—42no—
112C2×#685—42no—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×C4⋊Dic5—24no—
120C2×C4⋊Dic5—24no—
121C2×C4⋊Dic5—42no—
122C2×C4⋊Dic5—42no—
123C2×C4⋊Dic5C2314yes—
124C2×C4⋊Dic5C2314yes—
125C2×C4⋊Dic5C2314yes—
126C2×C4⋊Dic5C2314yes—
127C2×#683—24no—
128C2×#683—24no—
129C2×#683—24no—
130C2×#683—42no—
131C2×#683—42no—
132C2×#683—42no—
133C2×#683—42no—
134C2×#683—42no—
135C2×#683C2314yes—
136C2×#683C2314yes—
137C2×#683C2314yes—
138C2×#683C2314yes—
139C2×#683C2314yes—
140C2×#683C2314yes—
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×C4×Dic5D418yescomplemented
144C2×C4×Dic5C2314yes—
145#4044—232no—
146#4025—232no—
147C5×#95C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#126—51no—
154C22×#126—51no—
155#2823—516no—
156C2×#398—51no—
157C2×#398—51no—
158C2×#398—51no—
159C2×#396—51no—
160C2×#396—51no—
161C2×#396—51no—
162C2×#396—51no—
163C2×#396—51no—
164C2×#396D511yescharacteristic, complemented
165C2×#394—51no—
166C2×#394—51no—
167C2×#394—51no—
168C2×#384—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×C5—22no—
202C22×C4×C5—22no—
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—44no—
211C2×C22⋊D5—44no—
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—22no—
233C22×Dic5C2×D414yes—
234C22×Dic5C2×D414yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C5×C4⋊C4—28no—
243C5×C4⋊C4—44no—
244C5×C4⋊C4—44no—
245C5×C22⋊C4—28no—
246C5×C22⋊C4—44no—
247C5×C22⋊C4—44no—
248C22⋊Dic5—28no—
249C22⋊Dic5—28no—
250C22⋊Dic5—44no—
251#685—28no—
252#685—28no—
253#685—28no—
254#685—44no—
255#685—44no—
256#685—44no—
257C4⋊Dic5—28no—
258C4⋊Dic5—28no—
259C4⋊Dic5—44no—
260C4⋊Dic5—44no—
261#683—28no—
262#683—28no—
263#683—28no—
264#683—44no—
265#683—44no—
266#683—44no—
267#683—44no—
268#683—44no—
269C4×Dic5C2×D4116yescomplemented
270C23×D4—51no—
271C2×#126—58no—
272C2×#126—58no—
273C2×#126—108no—
274C2×#126—108no—
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⋊C4—51no—
284C22×C4⋊C4—51no—
285C22×C4⋊C4—51no—
286C22×C4⋊C4—51no—
287C22×C4⋊C4C2×D511yescharacteristic
288C22×C4⋊C4C2×D511yescharacteristic
289C22×C4⋊C4C2×D511yescharacteristic
290C22×C22⋊C4—51no—
291C22×C22⋊C4—51no—
292C22×C22⋊C4—51no—
293C22×C22⋊C4—51no—
294C22×C22⋊C4—51no—
295C22×C22⋊C4—51no—
296C22×C22⋊C4—51no—
297C22×C22⋊C4—51no—
298C22×C22⋊C4—51no—
299C22×C22⋊C4C2×D511yescharacteristic
300C22×C22⋊C4C2×D511yescharacteristic
301C22×C22⋊C4C2×D511yescharacteristic
302C22×C42—51no—
303#398—58no—
304#398—58no—
305#398—58no—
306#396—58no—
307#396—58no—
308#396—58no—
309#396—58no—
310#396—58no—
311#396C2×D518yescomplemented
312#394—58no—
313#394—58no—
314#394—58no—
315#384—58no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95C2×D511yescharacteristic
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×C5H(5,𝔽2)12yes—
338C23×C5H(5,𝔽2)12yes—
339C23×C5H(5,𝔽2)12yes—
340C23×C52−1+412yes—
341C23×C52−1+412yes—
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—22no—
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—44no—
377C2×C4×C5—44no—
378C2×C4×C5—44no—
379C2×C4×C5—44no—
380C2×C4×C5—44no—
381C2×C4×C5C22×D414yes—
382C22⋊D5—416no—
383C2×Dic5—28no—
384C2×Dic5—28no—
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—22no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—44no—
405C2×Dic5—44no—
406C2×Dic5—44no—
407C2×Dic5—44no—
408C2×Dic5—44no—
409C2×Dic5C22×D414yes—
410C2×Dic5C22×D414yes—
411C25—51no—
412C25C22×D511yescharacteristic
413C22×D4—54no—
414C22×D4—202no—
415C22×D4—202no—
416C22×D4—202no—
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—1032no—
431#126—1032no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
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—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—104no—
452C2×C4⋊C4—202no—
453C2×C4⋊C4—202no—
454C2×C4⋊C4—202no—
455C2×C4⋊C4—202no—
456C2×C4⋊C4—202no—
457C2×C4⋊C4—202no—
458C2×C4⋊C4—202no—
459C2×C4⋊C4C22×D514yes—
460C2×C4⋊C4C22×D514yes—
461C2×C4⋊C4C22×D514yes—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—54no—
466C2×C22⋊C4—54no—
467C2×C22⋊C4—54no—
468C2×C22⋊C4—54no—
469C2×C22⋊C4—54no—
470C2×C22⋊C4—54no—
471C2×C22⋊C4—54no—
472C2×C22⋊C4—54no—
473C2×C22⋊C4—54no—
474C2×C22⋊C4—104no—
475C2×C22⋊C4—104no—
476C2×C22⋊C4—104no—
477C2×C22⋊C4—104no—
478C2×C22⋊C4—104no—
479C2×C22⋊C4—202no—
480C2×C22⋊C4—202no—
481C2×C22⋊C4—202no—
482C2×C22⋊C4—202no—
483C2×C22⋊C4C22×D514yes—
484C2×C22⋊C4C22×D514yes—
485C2×C22⋊C4C22×D514yes—
486C2×C42—58no—
487C2×C42—54no—
488#95—54no—
489#95—54no—
490#95—54no—
491#95—54no—
492#95—54no—
493#95C22×D514yes—
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×C5#53714yes—
503C22×C5#53714yes—
504C22×C5#53714yes—
505C22×C5#56014yes—
506C22×C5#56314yes—
507C22×C5#56314yes—
508C22×C5#56314yes—
509C22×C5C23×D411yescharacteristic
510C22×C5C2×H(5,𝔽2)11yescharacteristic
511C22×C5C2×H(5,𝔽2)11yescharacteristic
512C22×C5C2×H(5,𝔽2)11yescharacteristic
513C22×C5C2×2−1+411yescharacteristic
514C22×C5C2×2−1+411yescharacteristic
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—42no—
526C4×C5—42no—
527C4×C5—42no—
528C4×C5—42no—
529C4×C5—42no—
530Dic5—24no—
531Dic5—24no—
532Dic5—42no—
533Dic5—42no—
534Dic5—42no—
535Dic5—42no—
536Dic5—42no—
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—204no—
555C2×D4—204no—
556C2×D4—204no—
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—22no—
574C22×C4—22no—
575C22×C4—54no—
576C22×C4—54no—
577C22×C4—52no—
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×C4—102no—
602C22×C4—102no—
603C22×C4D4×D514yes—
604C22×C4C23×D512yes—
605C22×C4C23×D512yes—
606C22×C4C23×D512yes—
607C22×C4C23×D512yes—
608C22×C4C23×D512yes—
609C22×C4C23×D512yes—
610C4⋊C4—28no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—108no—
614C4⋊C4—108no—
615C4⋊C4—108no—
616C4⋊C4—108no—
617C4⋊C4—108no—
618C4⋊C4—204no—
619C4⋊C4—204no—
620C4⋊C4—204no—
621C4⋊C4—204no—
622C4⋊C4—204no—
623C4⋊C4—204no—
624C4⋊C4—204no—
625C22⋊C4—28no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—108no—
629C22⋊C4—108no—
630C22⋊C4—108no—
631C22⋊C4—108no—
632C22⋊C4—108no—
633C22⋊C4—204no—
634C22⋊C4—204no—
635C22⋊C4—204no—
636C22⋊C4—204no—
637C42—516no—
638C2×C5—82no—
639C2×C5#282318yescomplemented
640C2×C5C2×#53711yescharacteristic
641C2×C5C2×#53711yescharacteristic
642C2×C5C2×#53711yescharacteristic
643C2×C5C2×#56011yescharacteristic
644C2×C5C2×#56311yescharacteristic
645C2×C5C2×#56311yescharacteristic
646C2×C5C2×#56311yescharacteristic
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—
676C23C2×D4×D512yes—
677C23#414412yes—
678C23#414412yes—
679C23#414712yes—
680C23#414912yes—
681C23#415012yes—
682C23#415012yes—
683C23C24×D511yescharacteristic
684D4—2016no—
685C2×C4—28no—
686C2×C4—22no—
687C2×C4—22no—
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—44no—
707C2×C4—44no—
708C2×C4—54no—
709C2×C4—54no—
710C2×C4—108no—
711C2×C4—108no—
712C2×C4—102no—
713C2×C4—102no—
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—102no—
730C2×C4—102no—
731C2×C4—204no—
732C2×C4—204no—
733C2×C4—204no—
734C2×C4—204no—
735C2×C4—204no—
736C2×C4C2×D4×D514yes—
737C5C2×#282311yescharacteristic, 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#6593114yes—
755C22#6594214yes—
756C22#6595414yes—
757C22#6596314yes—
758C22#6598014yes—
759C22#6598014yes—
760C22#6604614yes—
761C22C22×D4×D511yescharacteristic
762C22C2×#414411yescharacteristic
763C22C2×#414411yescharacteristic
764C22C2×#414711yescharacteristic
765C22C2×#414911yescharacteristic
766C22C2×#415011yescharacteristic
767C22C2×#415011yescharacteristic
768C4—24no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—104no—
775C4—104no—
776C4—202no—
777C4—202no—
778C4—202no—
779C4—202no—
780C4—202no—
781C2—82no—
782C2—402no—
783C2#1060918118yesdirect product factor
784C2C2×#6593111yescharacteristic
785C2C2×#6594211yescharacteristic
786C2C2×#6595411yescharacteristic
787C2C2×#6598011yescharacteristic
788C2C2×#6598011yescharacteristic
789C2C2×#6596311yescharacteristic
790C2C2×#6604611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#396C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#396D5
hypocenterC5C2×#2823
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#4044C2semidirect
2. C22×#4025C2semidirect
3. C2×C5×#396C2semidirect
4. C2×#65283C2semidirect
5. C2×#65283C2semidirect
6. C2×#65269C2semidirect
7. C2×#65273C2semidirect
8. C2×#65265C2semidirect
11. C2×#65237C2semidirect
12. C2×#65237C2semidirect
14. #10609181C2direct (N × H)
15. C2×#64965C2semidirect
16. C2×#64950C2semidirect
47. C2×#4044C22semidirect
49. C2×#4025C22semidirect
50. C5×#396C22semidirect
57. #65283C22semidirect
58. #65283C22semidirect
59. #65273C22semidirect
60. #65269C22semidirect
61. #65265C22semidirect
65. #65237C22semidirect
66. #65237C22semidirect
67. #64965C22semidirect
68. #64950C22semidirect
143. C2×C4×Dic5D4semidirect
164. C2×#396D5semidirect
269. C4×Dic5C2×D4semidirect
311. #396C2×D5semidirect
639. C2×C5#2823semidirect
737. C5C2×#2823semidirect
783. C2#10609181direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40442
C22×#40252
C2×C5×#3962
C2×#652832
C2×#652692
C2×#652732
C2×#652652
C2×#652482
C2×#652372
C2×#652502
#106091812
C2×#649652
C2×#649502
C2×#28235