Finite Group Databasebeta

← C2×#10608727 #12266028

Subgroups — C2×#10608727 #12266028

Order 1280.

3002 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4025C211yesmaximal, characteristic, complemented
2C22×#4031C211yesmaximal, characteristic, complemented
3C2×C5×#394C211yesmaximal, characteristic, complemented
4C2×#65512C211yesmaximal, characteristic
5C2×#65510C211yesmaximal, characteristic, complemented
6C2×#65283C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
8C2×#65237C211yesmaximal, characteristic, complemented
9C2×#65250C211yesmaximal, characteristic, complemented
10C2×#65250C211yesmaximal, characteristic, complemented
11C2×#65236C211yesmaximal, characteristic, complemented
12C2×#65246C211yesmaximal, characteristic, complemented
13C2×#65233C211yesmaximal, characteristic, complemented
14#10608727C2116yesmaximal, direct product factor
15C2×#64945C211yesmaximal, characteristic, complemented
16C2×#64958C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×Dic10C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
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
31C22×C22⋊Dic5C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4031—28no—
47C2×#4031C2218yescomplemented
48C2×#4025—28no—
49C2×#4025C2218yescomplemented
50C5×#394C2218yescomplemented
51C2×C5×#95C2211yescharacteristic
52#65512C2218yes—
53#65510C2218yescomplemented
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59#65283C2218yescomplemented
60C4⋊C4×Dic5C2218yescomplemented
61#65250C2218yescomplemented
62#65250C2218yescomplemented
63#65246C2218yescomplemented
64#65237C2218yescomplemented
65#65236C2218yescomplemented
66#65233C2218yescomplemented
67#64958C2218yescomplemented
68#64945C2218yescomplemented
69C2×#2662—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C25×C5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C22×C5×D4—24no—
74C22×C5×D4—42no—
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—42no—
85C22×C22⋊D5—42no—
86C22×C22⋊D5—42no—
87C22×C22⋊D5—42no—
88C22×C22⋊D5C2314yes—
89C22×C22⋊D5C2314yes—
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C22×Dic10—24no—
98C22×Dic10—42no—
99C22×Dic10—42no—
100C22×Dic10C2314yes—
101C2×C5×C4⋊C4—24no—
102C2×C5×C4⋊C4C2314yes—
103C2×C5×C22⋊C4—24no—
104C2×C5×C22⋊C4—24no—
105C2×C5×C22⋊C4—42no—
106C2×C5×C22⋊C4—42no—
107C2×C5×C22⋊C4C2314yes—
108C2×C5×C22⋊C4C2314yes—
109C2×C5×C22⋊C4C2314yes—
110C2×C5×C22⋊C4C2314yes—
111C2×C22⋊Dic5—24no—
112C2×C22⋊Dic5—24no—
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5—24no—
115C2×C22⋊Dic5—42no—
116C2×C22⋊Dic5—42no—
117C2×C22⋊Dic5C2314yes—
118C2×C22⋊Dic5C2314yes—
119C2×C22⋊Dic5C2314yes—
120C2×C22⋊Dic5C2314yes—
121C2×C22⋊Dic5C2314yes—
122C2×C22⋊Dic5C2314yes—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—42no—
127C2×#685—42no—
128C2×#685C2314yes—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×C4⋊Dic5—24no—
134C2×C4⋊Dic5—24no—
135C2×C4⋊Dic5—42no—
136C2×C4⋊Dic5C2314yes—
137C2×C4⋊Dic5C2314yes—
138C2×C4⋊Dic5C2314yes—
139C2×#683—24no—
140C2×#683—24no—
141C2×#683—42no—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×C4×Dic5—42no—
146C2×C4×Dic5—42no—
147C2×C4×Dic5D418yescomplemented
148C2×C4×Dic5C2314yes—
149C2×C4×Dic5C2314yes—
150C2×C4×Dic5C2314yes—
151#4031—232no—
152#4025—232no—
153C5×#95C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#126—51no—
160C22×#124—51no—
161#2662—516no—
162C2×#396—51no—
163C2×#396—51no—
164C2×#395—51no—
165C2×#394—51no—
166C2×#394—51no—
167C2×#394D511yescharacteristic, complemented
168C2×#393—51no—
169C2×#392—51no—
170C2×#390—51no—
171C2×#390—51no—
172C2×#388—51no—
173C2×#388—51no—
174C2×C4×C4⋊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×C5—22no—
188C24×C5—22no—
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—44no—
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×C5C2×D414yes—
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—44no—
227C2×C22⋊D5—44no—
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—22no—
250C22×Dic5C2×D414yes—
251C22×Dic5C2×D414yes—
252C22×Dic5#4114yes—
253C22×Dic5C2412yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C22×Dic5C2412yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C2×Dic10—28no—
261C2×Dic10—44no—
262C2×Dic10—44no—
263C2×Dic10—416no—
264C5×C4⋊C4—28no—
265C5×C22⋊C4—28no—
266C5×C22⋊C4—28no—
267C5×C22⋊C4—44no—
268C5×C22⋊C4—44no—
269C22⋊Dic5—28no—
270C22⋊Dic5—28no—
271C22⋊Dic5—28no—
272C22⋊Dic5—28no—
273C22⋊Dic5—44no—
274C22⋊Dic5—44no—
275#685—28no—
276#685—28no—
277#685—28no—
278#685—44no—
279#685—44no—
280C4⋊Dic5—28no—
281C4⋊Dic5—28no—
282C4⋊Dic5—44no—
283#683—28no—
284#683—28no—
285#683—44no—
286C4×Dic5—44no—
287C4×Dic5—44no—
288C4×Dic5C2×D4116yescomplemented
289C23×Q8—51no—
290C23×D4—51no—
291C23×D4—51no—
292C23×D4C2×D511yescharacteristic
293C2×#126—58no—
294C2×#126—108no—
295C2×#124—58no—
296C2×#124—108no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4C2×D511yescharacteristic
304C22×C22⋊C4—51no—
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⋊C4—51no—
315C22×C22⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C22⋊C4C2×D511yescharacteristic
319C22×C42—51no—
320C22×C42—51no—
321C22×C42—51no—
322#396—58no—
323#396—58no—
324#395—58no—
325#394—58no—
326#394—58no—
327#394C2×D518yescomplemented
328#393—58no—
329#392—58no—
330#390—58no—
331#390—58no—
332#388—58no—
333#388—58no—
334C4×C4⋊C4—58no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95C2×D511yescharacteristic
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—44no—
356C23×C5—44no—
357C23×C5—44no—
358C23×C5—44no—
359C23×C5—44no—
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×C5—44no—
369C23×C5C22×D412yes—
370C23×C5C2×#4112yes—
371C23×C5C2×#4112yes—
372C23×C5H(5,𝔽2)12yes—
373C23×C5H(5,𝔽2)12yes—
374C23×C5H(5,𝔽2)12yes—
375C23×C52−1+412yes—
376C23×C5C2511yescharacteristic
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—44no—
385C22×D5—44no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5—44no—
391C5×D4—416no—
392C2×C4×C5—28no—
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—44no—
408C2×C4×C5—44no—
409C2×C4×C5—44no—
410C2×C4×C5C22×D414yes—
411C2×C4×C5C2×#4114yes—
412C22⋊D5—416no—
413C22⋊D5—416no—
414C2×Dic5—28no—
415C2×Dic5—28no—
416C2×Dic5—28no—
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×Dic5C22×D414yes—
440C2×Dic5C22×D414yes—
441C2×Dic5C2×#4114yes—
442Dic10—416no—
443C25—51no—
444C25C22×D511yescharacteristic
445C25C22×D511yescharacteristic
446C22×Q8—54no—
447C22×Q8—104no—
448C22×Q8—202no—
449C22×Q8—202no—
450C22×D4—24no—
451C22×D4—42no—
452C22×D4—42no—
453C22×D4—54no—
454C22×D4—54no—
455C22×D4—104no—
456C22×D4—104no—
457C22×D4—202no—
458C22×D4—202no—
459C22×D4—202no—
460C22×D4—202no—
461C22×D4C22×D514yes—
462C23×C4—51no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4C22×D511yescharacteristic
470C23×C4C22×D511yescharacteristic
471C23×C4C22×D511yescharacteristic
472C23×C4C22×D511yescharacteristic
473C23×C4C22×D511yescharacteristic
474#126—1032no—
475#124—1032no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—54no—
478C2×C4⋊C4—54no—
479C2×C4⋊C4—54no—
480C2×C4⋊C4—54no—
481C2×C4⋊C4—54no—
482C2×C4⋊C4—54no—
483C2×C4⋊C4—104no—
484C2×C4⋊C4—104no—
485C2×C4⋊C4—104no—
486C2×C4⋊C4—104no—
487C2×C4⋊C4—202no—
488C2×C4⋊C4—202no—
489C2×C4⋊C4C22×D514yes—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—54no—
495C2×C22⋊C4—54no—
496C2×C22⋊C4—54no—
497C2×C22⋊C4—54no—
498C2×C22⋊C4—54no—
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—104no—
506C2×C22⋊C4—104no—
507C2×C22⋊C4—104no—
508C2×C22⋊C4—104no—
509C2×C22⋊C4—104no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—202no—
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—58no—
521C2×C42—54no—
522C2×C42—54no—
523C2×C42—54no—
524C2×C42—202no—
525C2×C42—202no—
526#95—54no—
527#95—54no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95C22×D514yes—
532C22×C5—42no—
533C22×C5—42no—
534C22×C5—42no—
535C22×C5—42no—
536C22×C5—42no—
537C22×C5—42no—
538C22×C5—42no—
539C22×C5—42no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—88no—
547C22×C5—88no—
548C22×C5#53214yes—
549C22×C5#53514yes—
550C22×C5#53714yes—
551C22×C5#53814yes—
552C22×C5#53814yes—
553C22×C5#54214yes—
554C22×C5#54214yes—
555C22×C5C23×D411yescharacteristic
556C22×C5C22×#4111yescharacteristic
557C22×C5C22×#4111yescharacteristic
558C22×C5C2×H(5,𝔽2)11yescharacteristic
559C22×C5C2×H(5,𝔽2)11yescharacteristic
560C22×C5C2×H(5,𝔽2)11yescharacteristic
561C22×C5C2×2−1+411yescharacteristic
562C2×D5—42no—
563C2×D5—42no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—42no—
569C2×D5—88no—
570C4×C5—24no—
571C4×C5—24no—
572C4×C5—42no—
573C4×C5—42no—
574C4×C5—42no—
575Dic5—24no—
576Dic5—24no—
577Dic5—24no—
578Dic5—42no—
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582C24—22no—
583C24—22no—
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—
604C24C23×D512yes—
605C24C23×D512yes—
606C24C23×D511yescharacteristic
607C2×Q8—108no—
608C2×Q8—204no—
609C2×Q8—204no—
610C2×Q8—2016no—
611C2×D4—28no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—416no—
615C2×D4—108no—
616C2×D4—108no—
617C2×D4—204no—
618C2×D4—204no—
619C2×D4—204no—
620C2×D4—204no—
621C2×D4—2016no—
622C2×D4—2016no—
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—22no—
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—102no—
647C22×C4—102no—
648C22×C4—102no—
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×C4D4×D514yes—
665C22×C4#71114yes—
666C22×C4C23×D512yes—
667C22×C4C23×D512yes—
668C22×C4C23×D512yes—
669C22×C4C23×D512yes—
670C22×C4C23×D512yes—
671C4⋊C4—28no—
672C4⋊C4—108no—
673C4⋊C4—108no—
674C4⋊C4—108no—
675C4⋊C4—108no—
676C4⋊C4—204no—
677C4⋊C4—204no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—108no—
683C22⋊C4—108no—
684C22⋊C4—108no—
685C22⋊C4—108no—
686C22⋊C4—108no—
687C22⋊C4—108no—
688C22⋊C4—108no—
689C22⋊C4—204no—
690C22⋊C4—204no—
691C22⋊C4—204no—
692C22⋊C4—204no—
693C42—516no—
694C42—204no—
695C42—204no—
696C2×C5—82no—
697C2×C5—82no—
698C2×C5#266218yescomplemented
699C2×C5C2×#53211yescharacteristic
700C2×C5C2×#53511yescharacteristic
701C2×C5C2×#53711yescharacteristic
702C2×C5C2×#53811yescharacteristic
703C2×C5C2×#53811yescharacteristic
704C2×C5C2×#54211yescharacteristic
705C2×C5C2×#54211yescharacteristic
706D5—82no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—102no—
736C23—102no—
737C23—102no—
738C23—102no—
739C23—102no—
740C23—102no—
741C23—102no—
742C23—204no—
743C23—204no—
744C23—204no—
745C23—204no—
746C23—204no—
747C23—204no—
748C23—204no—
749C23C2×D4×D512yes—
750C23C2×#71112yes—
751C23#414412yes—
752C23#414412yes—
753C23D5×#4112yes—
754C23#414912yes—
755C23#415012yes—
756C23C24×D511yescharacteristic
757Q8—2016no—
758D4—416no—
759D4—2016no—
760D4—2016no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—22no—
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—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—54no—
780C2×C4—54no—
781C2×C4—54no—
782C2×C4—108no—
783C2×C4—108no—
784C2×C4—108no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
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—204no—
804C2×C4—204no—
805C2×C4—204no—
806C2×C4—204no—
807C2×C4C2×D4×D514yes—
808C2×C4C2×#71114yes—
809C5C2×#266211yescharacteristic, complemented, Sylow
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—88no—
825C22—88no—
826C22—202no—
827C22—202no—
828C22—202no—
829C22—202no—
830C22—202no—
831C22—202no—
832C22—202no—
833C22—408no—
834C22#6592714yes—
835C22#6593014yes—
836C22#6594114yes—
837C22#6594214yes—
838C22#6599114yes—
839C22#6599614yes—
840C22#6601614yes—
841C22C22×D4×D511yescharacteristic
842C22C22×#71111yescharacteristic
843C22C2×#414411yescharacteristic
844C22C2×#414411yescharacteristic
845C22C2×D5×#4111yescharacteristic
846C22C2×#414911yescharacteristic
847C22C2×#415011yescharacteristic
848C4—24no—
849C4—24no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—104no—
854C4—104no—
855C4—104no—
856C4—202no—
857C4—202no—
858C4—202no—
859C4—202no—
860C2—82no—
861C2—82no—
862C2—402no—
863C2#1060872718yesdirect product factor
864C2C2×#6592711yescharacteristic
865C2C2×#6593011yescharacteristic
866C2C2×#6594111yescharacteristic
867C2C2×#6594211yescharacteristic
868C2C2×#6599611yescharacteristic
869C2C2×#6599111yescharacteristic
870C2C2×#6601611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#394C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC2×#394D5
hypocenterC5C2×#2662
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#4025C2semidirect
2. C22×#4031C2semidirect
3. C2×C5×#394C2semidirect
5. C2×#65510C2semidirect
6. C2×#65283C2semidirect
7. C2×C4⋊C4×Dic5C2semidirect
8. C2×#65237C2semidirect
9. C2×#65250C2semidirect
10. C2×#65250C2semidirect
11. C2×#65236C2semidirect
12. C2×#65246C2semidirect
13. C2×#65233C2semidirect
14. #10608727C2direct (N × H)
15. C2×#64945C2semidirect
16. C2×#64958C2semidirect
47. C2×#4031C22semidirect
49. C2×#4025C22semidirect
50. C5×#394C22semidirect
53. #65510C22semidirect
59. #65283C22semidirect
60. C4⋊C4×Dic5C22semidirect
61. #65250C22semidirect
62. #65250C22semidirect
63. #65246C22semidirect
64. #65237C22semidirect
65. #65236C22semidirect
66. #65233C22semidirect
67. #64958C22semidirect
68. #64945C22semidirect
147. C2×C4×Dic5D4semidirect
167. C2×#394D5semidirect
288. C4×Dic5C2×D4semidirect
327. #394C2×D5semidirect
698. C2×C5#2662semidirect
809. C5C2×#2662semidirect
863. C2#10608727direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40252
C22×#40312
C2×C5×#3942
C2×#655122
C2×#655102
C2×#652832
C2×C4⋊C4×Dic52
C2×#652372
C2×#652502
C2×#652362
C2×#652462
C2×#652332
#106087272
C2×#649452
C2×#649582
C2×#26625