Finite Group Databasebeta

← C2×#10608682 #12269430

Subgroups — C2×#10608682 #12269430

Order 1280.

3266 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4085C211yesmaximal, characteristic
2C22×#4025C211yesmaximal, characteristic, complemented
3C2×C5×#394C211yesmaximal, characteristic, complemented
4C2×#65509C211yesmaximal, characteristic, complemented
5C2×#65262C211yesmaximal, characteristic, complemented
6C2×#65279C211yesmaximal, characteristic, complemented
7C2×#65248C211yesmaximal, characteristic, complemented
8C2×#65250C211yesmaximal, characteristic, complemented
9C2×#65246C211yesmaximal, characteristic, complemented
10C2×#65247C211yesmaximal, characteristic, complemented
11C2×#65239C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
14#10608682C2116yesmaximal, direct product factor
15C2×#64947C211yesmaximal, characteristic, complemented
16C2×#64959C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C2×#4085—28no—
32C2×#4085C2218yes—
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4025—28no—
47C2×#4025C2218yescomplemented
48C5×#394C2218yescomplemented
49C2×C5×#95C2211yescharacteristic
50#65509C2218yescomplemented
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58#65279C2218yescomplemented
59#65262C2218yescomplemented
60#65250C2218yescomplemented
61#65248C2218yescomplemented
62#65247C2218yescomplemented
63#65246C2218yescomplemented
64#65239C2218yescomplemented
65C22⋊C4×Dic5C2218yescomplemented
66C22⋊C4×Dic5C2218yescomplemented
67#64959C2218yescomplemented
68#64947C2218yescomplemented
69C2×#2559—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C25×C5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C22×C5×D4—24no—
74C22×C5×D4—24no—
75C22×C5×D4—42no—
76C22×C5×D4C2314yes—
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—24no—
83C22×C22⋊D5—24no—
84C22×C22⋊D5—24no—
85C22×C22⋊D5—24no—
86C22×C22⋊D5—42no—
87C22×C22⋊D5—42no—
88C22×C22⋊D5C2314yes—
89C22×C22⋊D5C2314yes—
90C23×Dic5—24no—
91C23×Dic5—24no—
92C23×Dic5—24no—
93C23×Dic5—42no—
94C23×Dic5—42no—
95C23×Dic5—42no—
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2314yes—
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2314yes—
105C2×C5×C4⋊C4—42no—
106C2×C5×C4⋊C4C2314yes—
107C2×C5×C22⋊C4—24no—
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4—24no—
110C2×C5×C22⋊C4—24no—
111C2×C5×C22⋊C4C2314yes—
112C2×C5×C22⋊C4C2314yes—
113C2×C5×C22⋊C4C2314yes—
114C2×C5×C22⋊C4C2314yes—
115C2×C22⋊Dic5—24no—
116C2×C22⋊Dic5—24no—
117C2×C22⋊Dic5—42no—
118C2×C22⋊Dic5D418yes—
119C2×C22⋊Dic5C2314yes—
120C2×C22⋊Dic5C2314yes—
121C2×C22⋊Dic5C2314yes—
122C2×C22⋊Dic5C2314yes—
123#4085—232no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—42no—
128C2×#685—42no—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×C4⋊Dic5—24no—
135C2×C4⋊Dic5—24no—
136C2×C4⋊Dic5C2314yes—
137C2×C4⋊Dic5C2314yes—
138C2×#683—24no—
139C2×#683—24no—
140C2×#683—24no—
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×C4×Dic5—24no—
145C2×C4×Dic5—42no—
146C2×C4×Dic5—42no—
147C2×C4×Dic5C2314yes—
148C2×C4×Dic5C2314yes—
149C2×C4×Dic5C2314yes—
150#4025—232no—
151C5×#95C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#126—51no—
160C22×#121—51no—
161#2559—516no—
162C2×#400—51no—
163C2×#394—51no—
164C2×#394—51no—
165C2×#394D511yescharacteristic, complemented
166C2×#390—51no—
167C2×#389—51no—
168C2×#388—51no—
169C2×#388—51no—
170C2×#386—51no—
171C2×#386—51no—
172C2×#385—51no—
173C2×C4×C22⋊C4—51no—
174C2×C4×C22⋊C4—51no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5—22no—
182C24×C5—22no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5C2×D414yes—
188C24×C5#4114yes—
189C24×C5C2412yes—
190C24×C5C2412yes—
191C24×C5C2411yescharacteristic
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
198C23×D5—22no—
199C23×D5C2412yes—
200C2×C5×D4—28no—
201C2×C5×D4—28no—
202C2×C5×D4—44no—
203C2×C5×D4—416no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5#4114yes—
219C22×C4×C5C2412yes—
220C22×C4×C5C2412yes—
221C22×C4×C5C2412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2412yes—
224C2×C22⋊D5—28no—
225C2×C22⋊D5—28no—
226C2×C22⋊D5—28no—
227C2×C22⋊D5—28no—
228C2×C22⋊D5—44no—
229C2×C22⋊D5—44no—
230C2×C22⋊D5—416no—
231C2×C22⋊D5—416no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—22no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5—28no—
250C22×Dic5—28no—
251C22×Dic5—28no—
252C22×Dic5—44no—
253C22×Dic5—44no—
254C22×Dic5—44no—
255C22×Dic5—416no—
256C22×Dic5—416no—
257C22×Dic5C2×D414yes—
258C22×Dic5C2×D414yes—
259C22×Dic5#4114yes—
260C22×Dic5#4114yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C5×C4⋊C4—44no—
269C5×C22⋊C4—28no—
270C5×C22⋊C4—28no—
271C5×C22⋊C4—28no—
272C5×C22⋊C4—28no—
273C22⋊Dic5—28no—
274C22⋊Dic5—28no—
275C22⋊Dic5—44no—
276C22⋊Dic5C2×D4116yes—
277#685—28no—
278#685—28no—
279#685—28no—
280#685—44no—
281#685—44no—
282C4⋊Dic5—28no—
283C4⋊Dic5—28no—
284#683—28no—
285#683—28no—
286#683—28no—
287C4×Dic5—28no—
288C4×Dic5—44no—
289C4×Dic5—44no—
290C23×D4—51no—
291C23×D4—51no—
292C23×D4C2×D511yescharacteristic
293C24×C4—51no—
294C24×C4—51no—
295C2×#126—58no—
296C2×#126—108no—
297C2×#121—58no—
298C2×#121—108no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4C2×D511yescharacteristic
305C22×C22⋊C4—51no—
306C22×C22⋊C4—51no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4—51no—
310C22×C22⋊C4—51no—
311C22×C22⋊C4—51no—
312C22×C22⋊C4—51no—
313C22×C22⋊C4—51no—
314C22×C22⋊C4C2×D511yescharacteristic
315C22×C22⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42—51no—
320C22×C42—51no—
321#400—58no—
322#394—58no—
323#394—58no—
324#394C2×D518yescomplemented
325#390—58no—
326#389—58no—
327#388—58no—
328#388—58no—
329#386—58no—
330#386—58no—
331#385—58no—
332C4×C22⋊C4—58no—
333C4×C22⋊C4—58no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C2×#95C2×D511yescharacteristic
342C23×C5—28no—
343C23×C5—28no—
344C23×C5—28no—
345C23×C5—28no—
346C23×C5—28no—
347C23×C5—28no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—44no—
361C23×C5—44no—
362C23×C5—44no—
363C23×C5—44no—
364C23×C5—44no—
365C23×C5—44no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5C22×D414yes—
369C23×C5C22×D412yes—
370C23×C5C2×#4114yes—
371C23×C5C2×#4112yes—
372C23×C5C2×#4112yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5H(5,𝔽2)12yes—
376C23×C5H(5,𝔽2)12yes—
377C23×C5C2511yescharacteristic
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—44no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5—44no—
391C22×D5—44no—
392C5×D4—416no—
393C2×C4×C5—28no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—44no—
409C2×C4×C5—44no—
410C2×C4×C5—44no—
411C2×C4×C5—44no—
412C2×C4×C5C2×#4114yes—
413C22⋊D5—416no—
414C22⋊D5—416no—
415C2×Dic5—28no—
416C2×Dic5—28no—
417C2×Dic5—28no—
418C2×Dic5—28no—
419C2×Dic5—22no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—22no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—416no—
437C2×Dic5—416no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5C22×D414yes—
442C2×Dic5C22×D414yes—
443C2×Dic5C2×#4114yes—
444C2×Dic5C2×#4114yes—
445C25—51no—
446C25C22×D511yescharacteristic
447C25C22×D511yescharacteristic
448C22×D4—24no—
449C22×D4—24no—
450C22×D4—42no—
451C22×D4—54no—
452C22×D4—54no—
453C22×D4—104no—
454C22×D4—104no—
455C22×D4—104no—
456C22×D4—104no—
457C22×D4—202no—
458C22×D4—202no—
459C22×D4C22×D514yes—
460C23×C4—51no—
461C23×C4—51no—
462C23×C4—51no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—54no—
468C23×C4—54no—
469C23×C4—104no—
470C23×C4—104no—
471C23×C4—104no—
472C23×C4—202no—
473C23×C4—202no—
474C23×C4—202no—
475C23×C4C22×D511yescharacteristic
476C23×C4C22×D511yescharacteristic
477C23×C4C22×D511yescharacteristic
478C23×C4C22×D511yescharacteristic
479C23×C4C22×D511yescharacteristic
480#126—1032no—
481#121—1032no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—54no—
484C2×C4⋊C4—54no—
485C2×C4⋊C4—54no—
486C2×C4⋊C4—54no—
487C2×C4⋊C4—54no—
488C2×C4⋊C4—104no—
489C2×C4⋊C4—104no—
490C2×C4⋊C4—104no—
491C2×C4⋊C4—104no—
492C2×C4⋊C4—104no—
493C2×C4⋊C4C22×D514yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—58no—
499C2×C22⋊C4—54no—
500C2×C22⋊C4—54no—
501C2×C22⋊C4—54no—
502C2×C22⋊C4—54no—
503C2×C22⋊C4—54no—
504C2×C22⋊C4—54no—
505C2×C22⋊C4—54no—
506C2×C22⋊C4—54no—
507C2×C22⋊C4—54no—
508C2×C22⋊C4—104no—
509C2×C22⋊C4—104no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—104no—
513C2×C22⋊C4—202no—
514C2×C22⋊C4—202no—
515C2×C22⋊C4—202no—
516C2×C22⋊C4C22×D514yes—
517C2×C22⋊C4C22×D514yes—
518C2×C22⋊C4C22×D514yes—
519C2×C22⋊C4C22×D514yes—
520C2×C42—54no—
521C2×C42—54no—
522C2×C42—54no—
523C2×C42—104no—
524C2×C42—202no—
525C2×C42—202no—
526#95—54no—
527#95—54no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532#95—54no—
533#95C22×D514yes—
534C22×C5—24no—
535C22×C5—24no—
536C22×C5—24no—
537C22×C5—24no—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—416no—
549C22×C5—416no—
550C22×C5#52914yes—
551C22×C5#53214yes—
552C22×C5#53814yes—
553C22×C5#54614yes—
554C22×C5#54614yes—
555C22×C5#55314yes—
556C22×C5#55314yes—
557C22×C5C23×D411yescharacteristic
558C22×C5C22×#4111yescharacteristic
559C22×C5C22×#4111yescharacteristic
560C22×C5C22×#4111yescharacteristic
561C22×C5C22×#4111yescharacteristic
562C22×C5C2×H(5,𝔽2)11yescharacteristic
563C22×C5C2×H(5,𝔽2)11yescharacteristic
564C2×D5—42no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—42no—
569C2×D5—42no—
570C2×D5—42no—
571C2×D5—88no—
572C4×C5—24no—
573C4×C5—42no—
574C4×C5—42no—
575C4×C5—42no—
576C4×C5—42no—
577Dic5—24no—
578Dic5—24no—
579Dic5—24no—
580Dic5—24no—
581Dic5—42no—
582Dic5—42no—
583Dic5—42no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—52no—
597C24—102no—
598C24—102no—
599C24—102no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24D4×D514yes—
605C24#71114yes—
606C24C23×D512yes—
607C24C23×D512yes—
608C24C23×D511yescharacteristic
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—44no—
612C2×D4—416no—
613C2×D4—108no—
614C2×D4—108no—
615C2×D4—108no—
616C2×D4—108no—
617C2×D4—204no—
618C2×D4—204no—
619C2×D4—2016no—
620C2×D4—2016no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—54no—
636C22×C4—54no—
637C22×C4—54no—
638C22×C4—54no—
639C22×C4—52no—
640C22×C4—52no—
641C22×C4—52no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—108no—
647C22×C4—108no—
648C22×C4—108no—
649C22×C4—102no—
650C22×C4—102no—
651C22×C4—102no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—102no—
659C22×C4—102no—
660C22×C4—102no—
661C22×C4—102no—
662C22×C4—102no—
663C22×C4—102no—
664C22×C4—102no—
665C22×C4—102no—
666C22×C4—204no—
667C22×C4—204no—
668C22×C4—204no—
669C22×C4—2016no—
670C22×C4—2016no—
671C22×C4#71114yes—
672C22×C4C23×D512yes—
673C22×C4C23×D512yes—
674C22×C4C23×D512yes—
675C22×C4C23×D512yes—
676C22×C4C23×D512yes—
677C4⋊C4—44no—
678C4⋊C4—108no—
679C4⋊C4—108no—
680C4⋊C4—108no—
681C4⋊C4—108no—
682C4⋊C4—108no—
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—516no—
688C22⋊C4—108no—
689C22⋊C4—108no—
690C22⋊C4—108no—
691C22⋊C4—108no—
692C22⋊C4—108no—
693C22⋊C4—204no—
694C22⋊C4—204no—
695C22⋊C4—204no—
696C42—108no—
697C42—204no—
698C42—204no—
699C2×C5—44no—
700C2×C5—44no—
701C2×C5#255918yescomplemented
702C2×C5C2×#52911yescharacteristic
703C2×C5C2×#53211yescharacteristic
704C2×C5C2×#53811yescharacteristic
705C2×C5C2×#54611yescharacteristic
706C2×C5C2×#54611yescharacteristic
707C2×C5C2×#55311yescharacteristic
708C2×C5C2×#55311yescharacteristic
709D5—82no—
710C23—28no—
711C23—28no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—102no—
737C23—102no—
738C23—102no—
739C23—102no—
740C23—102no—
741C23—102no—
742C23—102no—
743C23—204no—
744C23—204no—
745C23—204no—
746C23—204no—
747C23—204no—
748C23—204no—
749C23—204no—
750C23C2×D4×D514yes—
751C23C2×D4×D512yes—
752C23C2×#71114yes—
753C23C2×#71112yes—
754C23C2×#71112yes—
755C23#414412yes—
756C23D5×#4112yes—
757C23D5×#4112yes—
758C23#414912yes—
759C23C24×D511yescharacteristic
760D4—416no—
761D4—2016no—
762D4—2016no—
763C2×C4—28no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—54no—
783C2×C4—54no—
784C2×C4—54no—
785C2×C4—54no—
786C2×C4—108no—
787C2×C4—108no—
788C2×C4—108no—
789C2×C4—108no—
790C2×C4—102no—
791C2×C4—102no—
792C2×C4—102no—
793C2×C4—102no—
794C2×C4—102no—
795C2×C4—102no—
796C2×C4—102no—
797C2×C4—102no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—102no—
802C2×C4—102no—
803C2×C4—102no—
804C2×C4—102no—
805C2×C4—102no—
806C2×C4—102no—
807C2×C4—2016no—
808C2×C4—2016no—
809C2×C4—204no—
810C2×C4—204no—
811C2×C4—204no—
812C2×C4C2×#71114yes—
813C5C2×#255911yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—416no—
822C22—416no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—202no—
831C22—202no—
832C22—202no—
833C22—202no—
834C22—202no—
835C22—202no—
836C22—202no—
837C22—408no—
838C22#6592514yes—
839C22#6593014yes—
840C22#6593514yes—
841C22#6595214yes—
842C22#6598314yes—
843C22#6598814yes—
844C22#6601214yes—
845C22C22×D4×D511yescharacteristic
846C22C22×#71111yescharacteristic
847C22C22×#71111yescharacteristic
848C22C2×#414411yescharacteristic
849C22C2×D5×#4111yescharacteristic
850C22C2×D5×#4111yescharacteristic
851C22C2×#414911yescharacteristic
852C4—24no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—104no—
858C4—104no—
859C4—104no—
860C4—104no—
861C4—202no—
862C4—202no—
863C4—202no—
864C2—44no—
865C2—44no—
866C2—402no—
867C2#1060868218yesdirect product factor
868C2C2×#6592511yescharacteristic
869C2C2×#6593011yescharacteristic
870C2C2×#6595211yescharacteristic
871C2C2×#6593511yescharacteristic
872C2C2×#6598311yescharacteristic
873C2C2×#6598811yescharacteristic
874C2C2×#6601211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#394C2
socleC24×C5C24
prime radicalC22×#4085C2
hypercenterC2×#394D5
hypocenterC5C2×#2559
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#4025C2semidirect
3. C2×C5×#394C2semidirect
4. C2×#65509C2semidirect
5. C2×#65262C2semidirect
6. C2×#65279C2semidirect
7. C2×#65248C2semidirect
8. C2×#65250C2semidirect
9. C2×#65246C2semidirect
10. C2×#65247C2semidirect
11. C2×#65239C2semidirect
12. C2×C22⋊C4×Dic5C2semidirect
13. C2×C22⋊C4×Dic5C2semidirect
14. #10608682C2direct (N × H)
15. C2×#64947C2semidirect
16. C2×#64959C2semidirect
47. C2×#4025C22semidirect
48. C5×#394C22semidirect
50. #65509C22semidirect
58. #65279C22semidirect
59. #65262C22semidirect
60. #65250C22semidirect
61. #65248C22semidirect
62. #65247C22semidirect
63. #65246C22semidirect
64. #65239C22semidirect
65. C22⋊C4×Dic5C22semidirect
66. C22⋊C4×Dic5C22semidirect
67. #64959C22semidirect
68. #64947C22semidirect
165. C2×#394D5semidirect
324. #394C2×D5semidirect
701. C2×C5#2559semidirect
813. C5C2×#2559semidirect
867. C2#10608682direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40852
C22×#40252
C2×C5×#3942
C2×#655092
C2×#652622
C2×#652792
C2×#652482
C2×#652502
C2×#652462
C2×#652472
C2×#652392
C2×C22⋊C4×Dic52
#106086822
C2×#649472
C2×#649592
C2×#25595