Finite Group Databasebeta

← C2×#10606506 #12269926

Subgroups — C2×#10606506 #12269926

Order 1280.

3502 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×#4072C211yesmaximal, characteristic, complemented
2C22×#4027C211yesmaximal, characteristic, complemented
3C2×C5×#386C211yesmaximal, characteristic, complemented
4C2×#65512C211yesmaximal, characteristic
5C2×#65509C211yesmaximal, characteristic, complemented
6C2×#65502C211yesmaximal, characteristic, complemented
7C2×#65245C211yesmaximal, characteristic, complemented
8C2×#65238C211yesmaximal, characteristic, complemented
9C2×#65250C211yesmaximal, characteristic, complemented
10C2×#65233C211yesmaximal, characteristic, complemented
11C2×#65239C211yesmaximal, characteristic, complemented
12#10606506C2116yesmaximal, direct product factor
13C2×#64957C211yesmaximal, characteristic, complemented
14C2×#64949C211yesmaximal, characteristic, complemented
15C2×#64959C211yesmaximal, characteristic, complemented
16C2×#64940C211yesmaximal, 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
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C2×#4072—28no—
36C2×#4072C2218yescomplemented
37C22×C4⋊Dic5C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4027—28no—
45C2×#4027C2218yescomplemented
46C5×#386C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49#65512C2218yes—
50#65509C2218yescomplemented
51#65502C2218yescomplemented
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60#65250C2218yescomplemented
61#65245C2218yescomplemented
62#65239C2218yescomplemented
63#65238C2218yescomplemented
64#65233C2218yescomplemented
65#64959C2218yescomplemented
66#64957C2218yescomplemented
67#64949C2218yescomplemented
68#64940C2218yescomplemented
69C2×#2598—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—24no—
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2314yes—
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C22×C22⋊D5—24no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—24no—
89C22×C22⋊D5—24no—
90C22×C22⋊D5—24no—
91C22×C22⋊D5—42no—
92C22×C22⋊D5C2314yes—
93C22×C22⋊D5C2314yes—
94C23×Dic5—24no—
95C23×Dic5—42no—
96C23×Dic5—42no—
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2314yes—
105C22×C4×D5—24no—
106C22×C4×D5—42no—
107C22×C4×D5—42no—
108C22×C4×D5C2314yes—
109C2×C5×C22⋊C4—24no—
110C2×C5×C22⋊C4—24no—
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—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—42no—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133#4072—232no—
134C2×C4⋊Dic5—24no—
135C2×C4⋊Dic5—24no—
136C2×C4⋊Dic5—42no—
137C2×C4⋊Dic5C2314yes—
138C2×C4⋊Dic5C2314yes—
139C2×C4⋊Dic5C2314yes—
140C2×#683—24no—
141C2×#683—42no—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×C4×Dic5—24no—
145C2×C4×Dic5D418yescomplemented
146C2×C4×Dic5C2314yes—
147C2×C4×Dic5C2314yes—
148#4027—232no—
149C5×#95C2314yes—
150C5×#95C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×C4×D4—51no—
160C22×#117—51no—
161#2598—516no—
162C2×#400—51no—
163C2×#399—51no—
164C2×#394—51no—
165C2×#392—51no—
166C2×#388—51no—
167C2×#388—51no—
168C2×#386—51no—
169C2×#386—51no—
170C2×#386—51no—
171C2×#386D511yescharacteristic, complemented
172C2×#385—51no—
173C2×#385—51no—
174C2×#383—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#4114yes—
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#4114yes—
199C23×D5C2412yes—
200C2×C5×D4—28no—
201C2×C5×D4—28no—
202C2×C5×D4—44no—
203C2×C5×D4—416no—
204C22×C4×C5—232no—
205C22×C4×C5—22no—
206C22×C4×C5—28no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—28no—
211C22×C4×C5—28no—
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—22no—
220C22×C4×C5—22no—
221C22×C4×C5C2×D414yes—
222C22×C4×C5#4114yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C2×C22⋊D5—232no—
229C2×C22⋊D5—28no—
230C2×C22⋊D5—28no—
231C2×C22⋊D5—28no—
232C2×C22⋊D5—28no—
233C2×C22⋊D5—28no—
234C2×C22⋊D5—44no—
235C2×C22⋊D5—416no—
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—22no—
255C22×Dic5—28no—
256C22×Dic5—44no—
257C22×Dic5—44no—
258C22×Dic5—416no—
259C22×Dic5C2×D414yes—
260C22×Dic5C2×D414yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C2×C4×D5—28no—
269C2×C4×D5—44no—
270C2×C4×D5—44no—
271C2×C4×D5—416no—
272C5×C22⋊C4—28no—
273C5×C22⋊C4—28no—
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—28no—
283#685—44no—
284C4⋊Dic5—28no—
285C4⋊Dic5—28no—
286C4⋊Dic5—44no—
287#683—28no—
288#683—44no—
289C4×Dic5—28no—
290C4×Dic5C2×D4116yescomplemented
291C23×D4—51no—
292C23×D4—51no—
293C23×D4C2×D511yescharacteristic
294C24×C4—51no—
295C24×C4—51no—
296C24×C4C2×D511yescharacteristic
297C2×C4×D4—58no—
298C2×C4×D4—108no—
299C2×#117—58no—
300C2×#117—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#400—58no—
321#399—58no—
322#394—58no—
323#392—58no—
324#388—58no—
325#388—58no—
326#386—58no—
327#386—58no—
328#386—58no—
329#386C2×D518yescomplemented
330#385—58no—
331#385—58no—
332#383—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×D412yes—
370C23×C5C2×#4114yes—
371C23×C5C2×#4112yes—
372C23×C5C2×#4114yes—
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×D5C2×#4114yes—
393C5×D4—416no—
394C2×C4×C5—232no—
395C2×C4×C5—28no—
396C2×C4×C5—28no—
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—22no—
410C2×C4×C5—44no—
411C2×C4×C5—44no—
412C2×C4×C5—44no—
413C2×C4×C5C22×D414yes—
414C2×C4×C5C2×#4114yes—
415C22⋊D5—232no—
416C22⋊D5—416no—
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—22no—
437C2×Dic5—22no—
438C2×Dic5—416no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5—44no—
443C2×Dic5—44no—
444C2×Dic5C22×D414yes—
445C2×Dic5C22×D414yes—
446C4×D5—416no—
447C25—51no—
448C25C22×D511yescharacteristic
449C25C22×D511yescharacteristic
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4—54no—
454C22×D4—54no—
455C22×D4—104no—
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—24no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—51no—
472C23×C4—54no—
473C23×C4—54no—
474C23×C4—104no—
475C23×C4—104no—
476C23×C4—202no—
477C23×C4—202no—
478C23×C4—202no—
479C23×C4—202no—
480C23×C4C22×D514yes—
481C23×C4C22×D511yescharacteristic
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D511yescharacteristic
484C23×C4C22×D511yescharacteristic
485C23×C4C22×D511yescharacteristic
486C4×D4—1032no—
487#117—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—24no—
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—104no—
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—58no—
523C2×C42—54no—
524C2×C42—54no—
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—416no—
543C22×C5—416no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—42no—
552C22×C5#52514yes—
553C22×C5#52514yes—
554C22×C5#53514yes—
555C22×C5#55114yes—
556C22×C5#55114yes—
557C22×C5#55314yes—
558C22×C5#55314yes—
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—416no—
570C2×D5—42no—
571C2×D5—42no—
572C2×D5—42no—
573C2×D5—42no—
574C4×C5—24no—
575C4×C5—24no—
576C4×C5—42no—
577C4×C5—42no—
578C4×C5—42no—
579Dic5—24no—
580Dic5—24no—
581Dic5—42no—
582Dic5—42no—
583Dic5—42no—
584Dic5—42no—
585Dic5—42no—
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—
607C24#71114yes—
608C24C23×D512yes—
609C24C23×D512yes—
610C24C23×D511yescharacteristic
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—44no—
614C2×D4—416no—
615C2×D4—108no—
616C2×D4—108no—
617C2×D4—1032no—
618C2×D4—108no—
619C2×D4—108no—
620C2×D4—108no—
621C2×D4—204no—
622C2×D4—2016no—
623C22×C4—232no—
624C22×C4—22no—
625C22×C4—28no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—28no—
630C22×C4—28no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—54no—
641C22×C4—54no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—108no—
650C22×C4—108no—
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—102no—
667C22×C4—102no—
668C22×C4—102no—
669C22×C4—102no—
670C22×C4—204no—
671C22×C4—204no—
672C22×C4—2016no—
673C22×C4—204no—
674C22×C4—204no—
675C22×C4—2016no—
676C22×C4D4×D514yes—
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—28no—
690C22⋊C4—44no—
691C22⋊C4—108no—
692C22⋊C4—108no—
693C22⋊C4—108no—
694C22⋊C4—108no—
695C22⋊C4—108no—
696C22⋊C4—108no—
697C22⋊C4—204no—
698C22⋊C4—204no—
699C22⋊C4—204no—
700C42—516no—
701C42—108no—
702C2×C5—44no—
703C2×C5—44no—
704C2×C5#259818yescomplemented
705C2×C5C2×#52511yescharacteristic
706C2×C5C2×#52511yescharacteristic
707C2×C5C2×#53511yescharacteristic
708C2×C5C2×#55111yescharacteristic
709C2×C5C2×#55111yescharacteristic
710C2×C5C2×#55311yescharacteristic
711C2×C5C2×#55311yescharacteristic
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×D512yes—
756C23C2×#71114yes—
757C23C2×#71112yes—
758C23C2×#71112yes—
759C23#414412yes—
760C23D5×#4112yes—
761C23#414912yes—
762C23C24×D511yescharacteristic
763D4—416no—
764D4—1032no—
765D4—2016no—
766C2×C4—232no—
767C2×C4—28no—
768C2×C4—28no—
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—22no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—54no—
786C2×C4—54no—
787C2×C4—108no—
788C2×C4—108no—
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—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×C4C2×D4×D514yes—
816C2×C4C2×#71114yes—
817C5C2×#259811yescharacteristic, 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—2016no—
839C22—202no—
840C22—202no—
841C22—202no—
842C22#6582914yes—
843C22#6588114yes—
844C22#6589914yes—
845C22#6592014yes—
846C22#6594114yes—
847C22#6594814yes—
848C22#6599214yes—
849C22C22×#70911yescharacteristic
850C22C22×D4×D511yescharacteristic
851C22C22×#71111yescharacteristic
852C22C22×#71111yescharacteristic
853C22C2×#414411yescharacteristic
854C22C2×D5×#4111yescharacteristic
855C22C2×#414911yescharacteristic
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—104no—
862C4—104no—
863C4—202no—
864C4—202no—
865C4—202no—
866C4—202no—
867C4—202no—
868C2—44no—
869C2—44no—
870C2—204no—
871C2#1060650618yesdirect product factor
872C2C2×#6582911yescharacteristic
873C2C2×#6589911yescharacteristic
874C2C2×#6588111yescharacteristic
875C2C2×#6592011yescharacteristic
876C2C2×#6594111yescharacteristic
877C2C2×#6594811yescharacteristic
878C2C2×#6599211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#386C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC2×#386D5
hypocenterC5C2×#2598
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#4072C2semidirect
2. C22×#4027C2semidirect
3. C2×C5×#386C2semidirect
5. C2×#65509C2semidirect
6. C2×#65502C2semidirect
7. C2×#65245C2semidirect
8. C2×#65238C2semidirect
9. C2×#65250C2semidirect
10. C2×#65233C2semidirect
11. C2×#65239C2semidirect
12. #10606506C2direct (N × H)
13. C2×#64957C2semidirect
14. C2×#64949C2semidirect
15. C2×#64959C2semidirect
16. C2×#64940C2semidirect
36. C2×#4072C22semidirect
45. C2×#4027C22semidirect
46. C5×#386C22semidirect
50. #65509C22semidirect
51. #65502C22semidirect
60. #65250C22semidirect
61. #65245C22semidirect
62. #65239C22semidirect
63. #65238C22semidirect
64. #65233C22semidirect
65. #64959C22semidirect
66. #64957C22semidirect
67. #64949C22semidirect
68. #64940C22semidirect
145. C2×C4×Dic5D4semidirect
171. C2×#386D5semidirect
290. C4×Dic5C2×D4semidirect
329. #386C2×D5semidirect
704. C2×C5#2598semidirect
817. C5C2×#2598semidirect
871. C2#10606506direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40722
C22×#40272
C2×C5×#3862
C2×#655122
C2×#655092
C2×#655022
C2×#652452
C2×#652382
C2×#652502
C2×#652332
C2×#652392
#106065062
C2×#649572
C2×#649492
C2×#649592
C2×#649402
C2×#25985