Finite Group Databasebeta

← C2×#10606426 #12267429

Subgroups — C2×#10606426 #12267429

Order 1280.

3438 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4085C211yesmaximal, characteristic
2C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×C5×#386C211yesmaximal, characteristic, complemented
4C2×#65511C211yesmaximal, characteristic, complemented
5C2×#65500C211yesmaximal, characteristic, complemented
6C2×#65245C211yesmaximal, characteristic, complemented
7C2×#65242C211yesmaximal, characteristic, complemented
8C2×#65250C211yesmaximal, characteristic, complemented
9C2×#65246C211yesmaximal, characteristic, complemented
10C2×#65231C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
12#10606426C2116yesmaximal, direct product factor
13C2×#64964C211yesmaximal, characteristic, complemented
14C2×#64953C211yesmaximal, characteristic, complemented
15C2×#64936C211yesmaximal, characteristic, complemented
16C2×#64939C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C2×#4085—28no—
32C2×#4085C2218yes—
33C2×C4×C22⋊D5—28no—
34C2×C4×C22⋊D5C2218yescomplemented
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C5×#386C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49#65511C2218yescomplemented
50#65500C2218yescomplemented
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59#65250C2218yescomplemented
60#65246C2218yescomplemented
61#65245C2218yescomplemented
62#65242C2218yescomplemented
63#65231C2218yescomplemented
64C22⋊C4×Dic5C2218yescomplemented
65#64964C2218yescomplemented
66#64953C2218yescomplemented
67#64939C2218yescomplemented
68#64936C2218yescomplemented
69C2×#2420—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×C5—24no—
78C23×C4×C5—24no—
79C23×C4×C5—42no—
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2314yes—
85C23×C4×C5C2311yescharacteristic
86C22×C22⋊D5—24no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—24no—
89C22×C22⋊D5—24no—
90C22×C22⋊D5—42no—
91C22×C22⋊D5D418yes—
92C22×C22⋊D5C2314yes—
93C22×C22⋊D5C2314yes—
94C23×Dic5—24no—
95C23×Dic5—24no—
96C23×Dic5—24no—
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2314yes—
104C23×Dic5C2311yescharacteristic
105C22×C4×D5—24no—
106C22×C4×D5—24no—
107C22×C4×D5—42no—
108C22×C4×D5C2314yes—
109C2×C5×C22⋊C4—24no—
110C2×C5×C22⋊C4—42no—
111C2×C5×C22⋊C4—42no—
112C2×C5×C22⋊C4C2314yes—
113C2×C5×C22⋊C4C2314yes—
114C2×C5×C22⋊C4C2314yes—
115C2×C22⋊Dic5—24no—
116C2×C22⋊Dic5—24no—
117C2×C22⋊Dic5—24no—
118C2×C22⋊Dic5—42no—
119C2×C22⋊Dic5—42no—
120C2×C22⋊Dic5C2314yes—
121C2×C22⋊Dic5C2314yes—
122C2×C22⋊Dic5C2314yes—
123C2×C22⋊Dic5C2314yes—
124C2×C22⋊Dic5C2314yes—
125#4085—232no—
126C4×C22⋊D5—232no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—42no—
130C2×#685—42no—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×C4⋊Dic5—42no—
136C2×C4⋊Dic5C2314yes—
137C2×#683—24no—
138C2×#683—24no—
139C2×#683—24no—
140C2×#683—42no—
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×C4×Dic5—24no—
146C2×C4×Dic5—24no—
147C2×C4×Dic5C2314yes—
148C2×C4×Dic5C2314yes—
149C5×#95C2314yes—
150C5×#95C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#121—51no—
160C22×C4×D4—51no—
161#2420—516no—
162C2×#397—51no—
163C2×#397—51no—
164C2×#394—51no—
165C2×#394—51no—
166C2×#390—51no—
167C2×#389—51no—
168C2×#386—51no—
169C2×#386D511yescharacteristic, complemented
170C2×#382—51no—
171C2×#381—51no—
172C2×#381—51no—
173C2×#380—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×D5C2×D414yes—
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—28no—
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—22no—
219C22×C4×C5—28no—
220C22×C4×C5—44no—
221C22×C4×C5—416no—
222C22×C4×C5#4114yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C2×C22⋊D5—28no—
229C2×C22⋊D5—28no—
230C2×C22⋊D5—232no—
231C2×C22⋊D5—28no—
232C2×C22⋊D5—28no—
233C2×C22⋊D5—44no—
234C2×C22⋊D5—416no—
235C2×C22⋊D5C2×D4116yes—
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—22no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—28no—
255C22×Dic5—28no—
256C22×Dic5—28no—
257C22×Dic5—416no—
258C22×Dic5C2×D414yes—
259C22×Dic5#4114yes—
260C22×Dic5#4114yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C2×C4×D5—28no—
269C2×C4×D5—28no—
270C2×C4×D5—44no—
271C2×C4×D5—416no—
272C5×C22⋊C4—28no—
273C5×C22⋊C4—44no—
274C5×C22⋊C4—44no—
275C22⋊Dic5—28no—
276C22⋊Dic5—28no—
277C22⋊Dic5—28no—
278C22⋊Dic5—44no—
279C22⋊Dic5—44no—
280#685—28no—
281#685—28no—
282#685—44no—
283#685—44no—
284C4⋊Dic5—44no—
285#683—28no—
286#683—28no—
287#683—28no—
288#683—44no—
289C4×Dic5—28no—
290C4×Dic5—28no—
291C23×D4—51no—
292C23×D4—51no—
293C23×D4C2×D511yescharacteristic
294C24×C4—51no—
295C24×C4—51no—
296C24×C4C2×D511yescharacteristic
297C2×#121—58no—
298C2×#121—108no—
299C2×C4×D4—58no—
300C2×C4×D4—108no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4—51no—
305C22×C4⋊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⋊C4—51no—
315C22×C22⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42—51no—
320#397—58no—
321#397—58no—
322#394—58no—
323#394—58no—
324#390—58no—
325#389—58no—
326#386—58no—
327#386C2×D518yescomplemented
328#382—58no—
329#381—58no—
330#381—58no—
331#380—58no—
332C4×C22⋊C4—58no—
333C2×#95—51no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C2×#95C2×D511yescharacteristic
342C2×#95C2×D511yescharacteristic
343C23×C5—28no—
344C23×C5—28no—
345C23×C5—28no—
346C23×C5—28no—
347C23×C5—28no—
348C23×C5—28no—
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—22no—
361C23×C5—44no—
362C23×C5—44no—
363C23×C5—44no—
364C23×C5—44no—
365C23×C5—44no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5C22×D414yes—
370C23×C5C22×D412yes—
371C23×C5C2×#4114yes—
372C23×C5C2×#4112yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5C2×#4112yes—
376C23×C5H(5,𝔽2)12yes—
377C23×C5H(5,𝔽2)12yes—
378C23×C5C2511yescharacteristic
379C22×D5—28no—
380C22×D5—28no—
381C22×D5—28no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5—44no—
391C22×D5—44no—
392C22×D5C22×D414yes—
393C5×D4—416no—
394C2×C4×C5—28no—
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—22no—
409C2×C4×C5—416no—
410C2×C4×C5—44no—
411C2×C4×C5—44no—
412C2×C4×C5—44no—
413C2×C4×C5—44no—
414C2×C4×C5C2×#4114yes—
415C22⋊D5—232no—
416C22⋊D5—416no—
417C2×Dic5—22no—
418C2×Dic5—22no—
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—44no—
436C2×Dic5—44no—
437C2×Dic5—44no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—416no—
442C2×Dic5#123116yes—
443C2×Dic5C22×D414yes—
444C2×Dic5C2×#4114yes—
445C2×Dic5C2×#4114yes—
446C4×D5—416no—
447C25—51no—
448C25C22×D511yescharacteristic
449C25C22×D511yescharacteristic
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4—58no—
454C22×D4—54no—
455C22×D4—54no—
456C22×D4—104no—
457C22×D4—104no—
458C22×D4—104no—
459C22×D4—104no—
460C22×D4—202no—
461C22×D4C22×D514yes—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—42no—
465C23×C4—51no—
466C23×C4—54no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—51no—
472C23×C4—51no—
473C23×C4—54no—
474C23×C4—104no—
475C23×C4—104no—
476C23×C4—104no—
477C23×C4—104no—
478C23×C4—104no—
479C23×C4—202no—
480C23×C4C22×D511yescharacteristic
481C23×C4C22×D511yescharacteristic
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D511yescharacteristic
484C23×C4C22×D514yes—
485C23×C4C22×D511yescharacteristic
486#121—1032no—
487C4×D4—1032no—
488C2×C4⋊C4—54no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—54no—
492C2×C4⋊C4—54no—
493C2×C4⋊C4—104no—
494C2×C4⋊C4—104no—
495C2×C4⋊C4—104no—
496C2×C4⋊C4—202no—
497C2×C4⋊C4—202no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
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—54no—
509C2×C22⋊C4—54no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—104no—
513C2×C22⋊C4—104no—
514C2×C22⋊C4—104no—
515C2×C22⋊C4—202no—
516C2×C22⋊C4—202no—
517C2×C22⋊C4—202no—
518C2×C22⋊C4—202no—
519C2×C22⋊C4C22×D514yes—
520C2×C22⋊C4C22×D514yes—
521C2×C22⋊C4C22×D514yes—
522C2×C42—54no—
523C2×C42—54no—
524C2×C42—104no—
525C2×C42—104no—
526#95—54no—
527#95—54no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532#95—54no—
533#95—54no—
534#95C22×D514yes—
535#95C22×D514yes—
536C22×C5—24no—
537C22×C5—24no—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—24no—
541C22×C5—24no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—416no—
545C22×C5—416no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—42no—
552C22×C5C2×#12314yes—
553C22×C5#52914yes—
554C22×C5#54014yes—
555C22×C5#54614yes—
556C22×C5#54614yes—
557C22×C5#55314yes—
558C22×C5#55514yes—
559C22×C5C23×D411yescharacteristic
560C22×C5C22×#4111yescharacteristic
561C22×C5C22×#4111yescharacteristic
562C22×C5C22×#4111yescharacteristic
563C22×C5C22×#4111yescharacteristic
564C22×C5C2×H(5,𝔽2)11yescharacteristic
565C22×C5C2×H(5,𝔽2)11yescharacteristic
566C2×D5—24no—
567C2×D5—24no—
568C2×D5—24no—
569C2×D5—42no—
570C2×D5—416no—
571C2×D5—42no—
572C2×D5—42no—
573C2×D5—42no—
574C4×C5—24no—
575C4×C5—42no—
576C4×C5—42no—
577C4×C5—42no—
578C4×C5—42no—
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582Dic5—42no—
583Dic5—42no—
584Dic5—42no—
585Dic5C2×#12318yes—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—54no—
599C24—52no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24—102no—
606C24#70914yes—
607C24D4×D514yes—
608C24C23×D512yes—
609C24C23×D512yes—
610C24C23×D511yescharacteristic
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—44no—
614C2×D4—416no—
615C2×D4—516no—
616C2×D4—1032no—
617C2×D4—108no—
618C2×D4—108no—
619C2×D4—108no—
620C2×D4—108no—
621C2×D4—204no—
622C2×D4—2016no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—28no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—28no—
639C22×C4—44no—
640C22×C4—416no—
641C22×C4—54no—
642C22×C4—54no—
643C22×C4—54no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—52no—
650C22×C4—52no—
651C22×C4—108no—
652C22×C4—108no—
653C22×C4—108no—
654C22×C4—108no—
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—102no—
667C22×C4—102no—
668C22×C4—102no—
669C22×C4—102no—
670C22×C4—102no—
671C22×C4—102no—
672C22×C4—102no—
673C22×C4—108no—
674C22×C4—204no—
675C22×C4—2016no—
676C22×C4—2016no—
677C22×C4#71114yes—
678C22×C4C23×D512yes—
679C22×C4C23×D512yes—
680C22×C4C23×D512yes—
681C22×C4C23×D512yes—
682C22×C4C23×D512yes—
683C4⋊C4—108no—
684C4⋊C4—108no—
685C4⋊C4—108no—
686C4⋊C4—204no—
687C4⋊C4—204no—
688C22⋊C4—28no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—108no—
692C22⋊C4—108no—
693C22⋊C4—108no—
694C22⋊C4—108no—
695C22⋊C4—108no—
696C22⋊C4—204no—
697C22⋊C4—204no—
698C22⋊C4—204no—
699C22⋊C4—204no—
700C42—108no—
701C42—108no—
702C2×C5—44no—
703C2×C5—44no—
704C2×C5#242018yescomplemented
705C2×C5C22×#12311yescharacteristic
706C2×C5C2×#52911yescharacteristic
707C2×C5C2×#54011yescharacteristic
708C2×C5C2×#54611yescharacteristic
709C2×C5C2×#54611yescharacteristic
710C2×C5C2×#55311yescharacteristic
711C2×C5C2×#55511yescharacteristic
712D5—44no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—54no—
740C23—108no—
741C23—108no—
742C23—108no—
743C23—102no—
744C23—102no—
745C23—102no—
746C23—102no—
747C23—102no—
748C23—102no—
749C23—204no—
750C23—204no—
751C23—204no—
752C23—204no—
753C23C2×#70914yes—
754C23C2×#70912yes—
755C23C2×D4×D514yes—
756C23C2×D4×D512yes—
757C23C2×#71112yes—
758C23#414412yes—
759C23#414412yes—
760C23D5×#4112yes—
761C23D5×#4112yes—
762C23C24×D511yescharacteristic
763D4—416no—
764D4—1032no—
765D4—2016no—
766C2×C4—28no—
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—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—416no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—516no—
787C2×C4—54no—
788C2×C4—54no—
789C2×C4—54no—
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—102no—
808C2×C4—2016no—
809C2×C4—2016no—
810C2×C4—204no—
811C2×C4—204no—
812C2×C4—204no—
813C2×C4—204no—
814C2×C4—204no—
815C2×C4—204no—
816C2×C4C2×#71114yes—
817C5C2×#242011yescharacteristic, complemented, Sylow
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—416no—
828C22—416no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—104no—
835C22—104no—
836C22—104no—
837C22—202no—
838C22—202no—
839C22—2016no—
840C22—202no—
841C22—202no—
842C22#6582414yes—
843C22#6587214yes—
844C22#6587414yes—
845C22#6592514yes—
846C22#6594914yes—
847C22#6595014yes—
848C22D5×#12314yes—
849C22C22×#70911yescharacteristic
850C22C22×D4×D511yescharacteristic
851C22C22×#71111yescharacteristic
852C22C2×#414411yescharacteristic
853C22C2×#414411yescharacteristic
854C22C2×D5×#4111yescharacteristic
855C22C2×D5×#4111yescharacteristic
856C4—24no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—58no—
862C4—202no—
863C4—202no—
864C4—202no—
865C4—202no—
866C4—202no—
867C4—202no—
868C2—44no—
869C2—44no—
870C2—204no—
871C2#1060642618yesdirect product factor
872C2C2×#6582411yescharacteristic
873C2C2×#6587211yescharacteristic
874C2C2×#6587411yescharacteristic
875C2C2×#6592511yescharacteristic
876C2C2×#6594911yescharacteristic
877C2C2×#6595011yescharacteristic
878C2C2×D5×#12311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#386C2
socleC24×C5C24
prime radicalC22×#4085C2
hypercenterC2×#386D5
hypocenterC5C2×#2420
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D5C2semidirect
3. C2×C5×#386C2semidirect
4. C2×#65511C2semidirect
5. C2×#65500C2semidirect
6. C2×#65245C2semidirect
7. C2×#65242C2semidirect
8. C2×#65250C2semidirect
9. C2×#65246C2semidirect
10. C2×#65231C2semidirect
11. C2×C22⋊C4×Dic5C2semidirect
12. #10606426C2direct (N × H)
13. C2×#64964C2semidirect
14. C2×#64953C2semidirect
15. C2×#64936C2semidirect
16. C2×#64939C2semidirect
34. C2×C4×C22⋊D5C22semidirect
46. C5×#386C22semidirect
49. #65511C22semidirect
50. #65500C22semidirect
59. #65250C22semidirect
60. #65246C22semidirect
61. #65245C22semidirect
62. #65242C22semidirect
63. #65231C22semidirect
64. C22⋊C4×Dic5C22semidirect
65. #64964C22semidirect
66. #64953C22semidirect
67. #64939C22semidirect
68. #64936C22semidirect
169. C2×#386D5semidirect
327. #386C2×D5semidirect
704. C2×C5#2420semidirect
817. C5C2×#2420semidirect
871. C2#10606426direct (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×C4×C22⋊D52
C2×C5×#3862
C2×#655112
C2×#655002
C2×#652452
C2×#652422
C2×#652502
C2×#652462
C2×#652312
C2×C22⋊C4×Dic52
#106064262
C2×#649642
C2×#649532
C2×#649362
C2×#649392
C2×#24205