Finite Group Databasebeta

← C2×#10606515 #12266017

Subgroups — C2×#10606515 #12266017

Order 1280.

3218 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×C4×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×#4025C211yesmaximal, characteristic, complemented
3C2×C5×#386C211yesmaximal, characteristic, complemented
4C2×#65512C211yesmaximal, characteristic
5C2×#65511C211yesmaximal, characteristic, complemented
6C2×#65499C211yesmaximal, characteristic, complemented
7C2×#65248C211yesmaximal, characteristic, complemented
8C2×#65245C211yesmaximal, characteristic, complemented
9C2×#65238C211yesmaximal, characteristic, complemented
10C2×#65237C211yesmaximal, characteristic, complemented
11C2×#65250C211yesmaximal, characteristic, complemented
12#10606515C2116yesmaximal, direct product factor
13C2×#64965C211yesmaximal, characteristic, complemented
14C2×#64957C211yesmaximal, characteristic, complemented
15C2×#64949C211yesmaximal, characteristic, complemented
16C2×#64939C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C2×C4×C22⋊D5—28no—
32C2×C4×C22⋊D5C2218yescomplemented
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4025—28no—
47C2×#4025C2218yescomplemented
48C5×#386C2218yescomplemented
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51#65512C2218yes—
52#65511C2218yescomplemented
53#65499C2218yescomplemented
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60#65250C2218yescomplemented
61#65248C2218yescomplemented
62#65245C2218yescomplemented
63#65238C2218yescomplemented
64#65237C2218yescomplemented
65#64965C2218yescomplemented
66#64957C2218yescomplemented
67#64949C2218yescomplemented
68#64939C2218yescomplemented
69C2×#2636—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×C5—24no—
78C23×C4×C5—42no—
79C23×C4×C5—42no—
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2314yes—
86C22×C22⋊D5—24no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—24no—
89C22×C22⋊D5—24no—
90C22×C22⋊D5—42no—
91C22×C22⋊D5—42no—
92C22×C22⋊D5C2314yes—
93C22×C22⋊D5C2314yes—
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C22×C4×D5—24no—
102C22×C4×D5—42no—
103C22×C4×D5—42no—
104C22×C4×D5C2314yes—
105C2×C5×C22⋊C4—24no—
106C2×C5×C22⋊C4—42no—
107C2×C5×C22⋊C4—42no—
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—
123C4×C22⋊D5—232no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—42no—
127C2×#685—42no—
128C2×#685C2314yes—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×C4⋊Dic5—24no—
133C2×C4⋊Dic5—42no—
134C2×C4⋊Dic5C2314yes—
135C2×C4⋊Dic5C2314yes—
136C2×#683—24no—
137C2×#683—24no—
138C2×#683—24no—
139C2×#683—42no—
140C2×#683—42no—
141C2×#683—42no—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×#683C2314yes—
146C2×#683C2314yes—
147C2×#683C2314yes—
148C2×C4×Dic5D418yescomplemented
149C2×C4×Dic5C2314yes—
150#4025—232no—
151C5×#95C2314yes—
152C5×#95C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#126—51no—
160C22×C4×D4—51no—
161#2636—516no—
162C2×#400—51no—
163C2×#399—51no—
164C2×#396—51no—
165C2×#396—51no—
166C2×#394—51no—
167C2×#394—51no—
168C2×#394—51no—
169C2×#392—51no—
170C2×#386—51no—
171C2×#386D511yescharacteristic, complemented
172C2×#385—51no—
173C2×#385—51no—
174C2×#382—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#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—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×C5—22no—
218C22×C4×C5—28no—
219C22×C4×C5—44no—
220C22×C4×C5—44no—
221C22×C4×C5—416no—
222C22×C4×C5C2×D414yes—
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—44no—
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×Dic5C2×D414yes—
256C22×Dic5C2×D414yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C2×C4×D5—28no—
265C2×C4×D5—44no—
266C2×C4×D5—44no—
267C2×C4×D5—416no—
268C5×C22⋊C4—28no—
269C5×C22⋊C4—44no—
270C5×C22⋊C4—44no—
271C22⋊Dic5—28no—
272C22⋊Dic5—28no—
273C22⋊Dic5—28no—
274C22⋊Dic5—28no—
275C22⋊Dic5—44no—
276C22⋊Dic5—44no—
277#685—28no—
278#685—28no—
279#685—44no—
280#685—44no—
281C4⋊Dic5—28no—
282C4⋊Dic5—44no—
283#683—28no—
284#683—28no—
285#683—28no—
286#683—44no—
287#683—44no—
288#683—44no—
289C4×Dic5C2×D4116yescomplemented
290C23×D4—51no—
291C23×D4—51no—
292C23×D4C2×D511yescharacteristic
293C24×C4—51no—
294C24×C4C2×D511yescharacteristic
295C2×#126—58no—
296C2×#126—108no—
297C2×C4×D4—58no—
298C2×C4×D4—108no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4—51no—
305C22×C4⋊C4—51no—
306C22×C4⋊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⋊C4—51no—
316C22×C22⋊C4—51no—
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C22⋊C4C2×D511yescharacteristic
319C22×C22⋊C4C2×D511yescharacteristic
320C22×C42—51no—
321#400—58no—
322#399—58no—
323#396—58no—
324#396—58no—
325#394—58no—
326#394—58no—
327#394—58no—
328#392—58no—
329#386—58no—
330#386C2×D518yescomplemented
331#385—58no—
332#385—58no—
333#382—58no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95C2×D511yescharacteristic
341C2×#95C2×D511yescharacteristic
342C23×C5—28no—
343C23×C5—28no—
344C23×C5—28no—
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—22no—
356C23×C5—22no—
357C23×C5—22no—
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×#4114yes—
371C23×C5C2×#4112yes—
372C23×C5C2×#4112yes—
373C23×C5H(5,𝔽2)12yes—
374C23×C5H(5,𝔽2)12yes—
375C23×C5H(5,𝔽2)12yes—
376C23×C52−1+412yes—
377C23×C5C2511yescharacteristic
378C22×D5—28no—
379C22×D5—28no—
380C22×D5—28no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5—44no—
391C22×D5C2×#4114yes—
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—416no—
409C2×C4×C5—44no—
410C2×C4×C5—44no—
411C2×C4×C5—44no—
412C2×C4×C5—44no—
413C2×C4×C5C22×D414yes—
414C22⋊D5—232no—
415C22⋊D5—416no—
416C2×Dic5—28no—
417C2×Dic5—28no—
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—22no—
436C2×Dic5—22no—
437C2×Dic5—44no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5C22×D414yes—
443C2×Dic5C22×D414yes—
444C4×D5—416no—
445C25—51no—
446C25C22×D511yescharacteristic
447C25C22×D511yescharacteristic
448C22×D4—24no—
449C22×D4—42no—
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—24no—
461C23×C4—42no—
462C23×C4—42no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—54no—
471C23×C4—104no—
472C23×C4—202no—
473C23×C4—202no—
474C23×C4C22×D511yescharacteristic
475C23×C4C22×D511yescharacteristic
476C23×C4C22×D511yescharacteristic
477C23×C4C22×D511yescharacteristic
478C23×C4C22×D511yescharacteristic
479C23×C4C22×D514yes—
480#126—1032no—
481C4×D4—1032no—
482C2×C4⋊C4—54no—
483C2×C4⋊C4—54no—
484C2×C4⋊C4—54no—
485C2×C4⋊C4—54no—
486C2×C4⋊C4—54no—
487C2×C4⋊C4—54no—
488C2×C4⋊C4—54no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—104no—
491C2×C4⋊C4—104no—
492C2×C4⋊C4—104no—
493C2×C4⋊C4—104no—
494C2×C4⋊C4—202no—
495C2×C4⋊C4—202no—
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—54no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—104no—
513C2×C22⋊C4—104no—
514C2×C22⋊C4—104no—
515C2×C22⋊C4—104no—
516C2×C22⋊C4—104no—
517C2×C22⋊C4—202no—
518C2×C22⋊C4—202no—
519C2×C22⋊C4—202no—
520C2×C22⋊C4—202no—
521C2×C22⋊C4C22×D514yes—
522C2×C22⋊C4C22×D514yes—
523C2×C22⋊C4C22×D514yes—
524C2×C42—58no—
525C2×C42—54no—
526#95—54no—
527#95—54no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532#95C22×D514yes—
533#95C22×D514yes—
534C22×C5—24no—
535C22×C5—24no—
536C22×C5—24no—
537C22×C5—416no—
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—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—88no—
550C22×C5#52514yes—
551C22×C5#53514yes—
552C22×C5#53714yes—
553C22×C5#53814yes—
554C22×C5#53814yes—
555C22×C5#53914yes—
556C22×C5#53914yes—
557C22×C5C23×D411yescharacteristic
558C22×C5C22×#4111yescharacteristic
559C22×C5C22×#4111yescharacteristic
560C22×C5C2×H(5,𝔽2)11yescharacteristic
561C22×C5C2×H(5,𝔽2)11yescharacteristic
562C22×C5C2×H(5,𝔽2)11yescharacteristic
563C22×C5C2×2−1+411yescharacteristic
564C2×D5—24no—
565C2×D5—24no—
566C2×D5—24no—
567C2×D5—416no—
568C2×D5—42no—
569C2×D5—42no—
570C2×D5—42no—
571C2×D5—42no—
572C4×C5—24no—
573C4×C5—42no—
574C4×C5—42no—
575C4×C5—42no—
576C4×C5—42no—
577Dic5—24no—
578Dic5—24no—
579Dic5—42no—
580Dic5—42no—
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—22no—
597C24—54no—
598C24—52no—
599C24—102no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24#70914yes—
606C24C23×D512yes—
607C24C23×D512yes—
608C24C23×D511yescharacteristic
609C2×D4—28no—
610C2×D4—44no—
611C2×D4—44no—
612C2×D4—416no—
613C2×D4—108no—
614C2×D4—108no—
615C2×D4—1032no—
616C2×D4—108no—
617C2×D4—108no—
618C2×D4—204no—
619C2×D4—204no—
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—28no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—416no—
639C22×C4—54no—
640C22×C4—54no—
641C22×C4—52no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
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×C4—102no—
665C22×C4—102no—
666C22×C4—102no—
667C22×C4—108no—
668C22×C4—204no—
669C22×C4—204no—
670C22×C4—2016no—
671C22×C4D4×D514yes—
672C22×C4C23×D512yes—
673C22×C4C23×D512yes—
674C22×C4C23×D512yes—
675C22×C4C23×D512yes—
676C22×C4C23×D512yes—
677C4⋊C4—108no—
678C4⋊C4—108no—
679C4⋊C4—108no—
680C4⋊C4—108no—
681C4⋊C4—204no—
682C4⋊C4—204no—
683C4⋊C4—204no—
684C4⋊C4—204no—
685C22⋊C4—28no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—108no—
689C22⋊C4—108no—
690C22⋊C4—108no—
691C22⋊C4—108no—
692C22⋊C4—108no—
693C22⋊C4—108no—
694C22⋊C4—204no—
695C22⋊C4—204no—
696C22⋊C4—204no—
697C22⋊C4—204no—
698C42—516no—
699C2×C5—44no—
700C2×C5—82no—
701C2×C5#263618yescomplemented
702C2×C5C2×#52511yescharacteristic
703C2×C5C2×#53511yescharacteristic
704C2×C5C2×#53711yescharacteristic
705C2×C5C2×#53811yescharacteristic
706C2×C5C2×#53811yescharacteristic
707C2×C5C2×#53911yescharacteristic
708C2×C5C2×#53911yescharacteristic
709D5—44no—
710C23—28no—
711C23—28no—
712C23—28no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—54no—
738C23—108no—
739C23—108no—
740C23—108no—
741C23—102no—
742C23—102no—
743C23—102no—
744C23—102no—
745C23—102no—
746C23—102no—
747C23—204no—
748C23—204no—
749C23—204no—
750C23—204no—
751C23C2×#70914yes—
752C23C2×#70912yes—
753C23C2×D4×D512yes—
754C23#414412yes—
755C23#414412yes—
756C23#414412yes—
757C23D5×#4112yes—
758C23#415012yes—
759C23C24×D511yescharacteristic
760D4—416no—
761D4—1032no—
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—416no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—54no—
784C2×C4—54no—
785C2×C4—108no—
786C2×C4—108no—
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—102no—
804C2×C4—102no—
805C2×C4—102no—
806C2×C4—2016no—
807C2×C4—204no—
808C2×C4—204no—
809C2×C4—204no—
810C2×C4—204no—
811C2×C4—204no—
812C2×C4C2×D4×D514yes—
813C5C2×#263611yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—416no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—88no—
830C22—104no—
831C22—104no—
832C22—104no—
833C22—202no—
834C22—2016no—
835C22—202no—
836C22—202no—
837C22—202no—
838C22#6582814yes—
839C22#6588114yes—
840C22#6589814yes—
841C22#6592614yes—
842C22#6594214yes—
843C22#6594714yes—
844C22#6599414yes—
845C22C22×#70911yescharacteristic
846C22C22×D4×D511yescharacteristic
847C22C2×#414411yescharacteristic
848C22C2×#414411yescharacteristic
849C22C2×#414411yescharacteristic
850C22C2×D5×#4111yescharacteristic
851C22C2×#415011yescharacteristic
852C4—24no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—104no—
858C4—104no—
859C4—202no—
860C4—202no—
861C4—202no—
862C4—202no—
863C4—202no—
864C2—44no—
865C2—82no—
866C2—204no—
867C2#1060651518yesdirect product factor
868C2C2×#6582811yescharacteristic
869C2C2×#6589811yescharacteristic
870C2C2×#6588111yescharacteristic
871C2C2×#6592611yescharacteristic
872C2C2×#6594211yescharacteristic
873C2C2×#6594711yescharacteristic
874C2C2×#6599411yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#386C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC2×#386D5
hypocenterC5C2×#2636
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊D5C2semidirect
2. C22×#4025C2semidirect
3. C2×C5×#386C2semidirect
5. C2×#65511C2semidirect
6. C2×#65499C2semidirect
7. C2×#65248C2semidirect
8. C2×#65245C2semidirect
9. C2×#65238C2semidirect
10. C2×#65237C2semidirect
11. C2×#65250C2semidirect
12. #10606515C2direct (N × H)
13. C2×#64965C2semidirect
14. C2×#64957C2semidirect
15. C2×#64949C2semidirect
16. C2×#64939C2semidirect
32. C2×C4×C22⋊D5C22semidirect
47. C2×#4025C22semidirect
48. C5×#386C22semidirect
52. #65511C22semidirect
53. #65499C22semidirect
60. #65250C22semidirect
61. #65248C22semidirect
62. #65245C22semidirect
63. #65238C22semidirect
64. #65237C22semidirect
65. #64965C22semidirect
66. #64957C22semidirect
67. #64949C22semidirect
68. #64939C22semidirect
148. C2×C4×Dic5D4semidirect
171. C2×#386D5semidirect
289. C4×Dic5C2×D4semidirect
330. #386C2×D5semidirect
701. C2×C5#2636semidirect
813. C5C2×#2636semidirect
867. C2#10606515direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D52
C22×#40252
C2×C5×#3862
C2×#655122
C2×#655112
C2×#654992
C2×#652482
C2×#652452
C2×#652382
C2×#652372
C2×#652502
#106065152
C2×#649652
C2×#649572
C2×#649492
C2×#649392
C2×#26365