Finite Group Databasebeta

← C2×#10606638 #12265679

Subgroups — C2×#10606638 #12265679

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×#4029C211yesmaximal, characteristic, complemented
3C2×C5×#386C211yesmaximal, characteristic, complemented
4C2×#65512C211yesmaximal, characteristic
5C2×#65511C211yesmaximal, characteristic, complemented
6C2×#65499C211yesmaximal, characteristic, complemented
7C2×#65248C211yesmaximal, characteristic, complemented
8C2×#65237C211yesmaximal, characteristic, complemented
9C2×#65237C211yesmaximal, characteristic, complemented
10C2×#65250C211yesmaximal, characteristic, complemented
11C2×#65233C211yesmaximal, characteristic, complemented
12#10606638C2116yesmaximal, direct product factor
13C2×#64964C211yesmaximal, characteristic, complemented
14C2×#64956C211yesmaximal, characteristic, complemented
15C2×#64946C211yesmaximal, characteristic, complemented
16C2×#64942C211yesmaximal, 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×#4029—28no—
47C2×#4029C2218yescomplemented
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#65237C2218yescomplemented
63#65237C2218yescomplemented
64#65233C2218yescomplemented
65#64964C2218yescomplemented
66#64956C2218yescomplemented
67#64946C2218yescomplemented
68#64942C2218yescomplemented
69C2×#2630—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—42no—
102C22×C4×D5—42no—
103C22×C4×D5D418yescomplemented
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—24no—
134C2×C4⋊Dic5C2314yes—
135C2×C4⋊Dic5C2314yes—
136C2×#683—24no—
137C2×#683—24no—
138C2×#683—42no—
139C2×#683—42no—
140C2×#683—42no—
141C2×#683—42no—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×#683C2314yes—
146C2×#683C2314yes—
147C2×#683C2314yes—
148C2×C4×Dic5—24no—
149C2×C4×Dic5C2314yes—
150#4029—232no—
151C5×#95C2314yes—
152C5×#95C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#123—51no—
160C22×C4×D4—51no—
161#2630—516no—
162C2×#398—51no—
163C2×#397—51no—
164C2×#396—51no—
165C2×#396—51no—
166C2×#394—51no—
167C2×#394—51no—
168C2×#394—51no—
169C2×#392—51no—
170C2×#388—51no—
171C2×#387—51no—
172C2×#386D511yescharacteristic, complemented
173C2×#385—51no—
174C2×#380—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×D5C2×D414yes—
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×Dic5#4114yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C2×C4×D5—416no—
265C2×C4×D5—44no—
266C2×C4×D5—44no—
267C2×C4×D5C2×D4116yescomplemented
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—28no—
283#683—28no—
284#683—28no—
285#683—44no—
286#683—44no—
287#683—44no—
288#683—44no—
289C4×Dic5—28no—
290C23×D4—51no—
291C23×D4—51no—
292C23×D4C2×D511yescharacteristic
293C24×C4—51no—
294C24×C4C2×D511yescharacteristic
295C2×#123—58no—
296C2×#123—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#398—58no—
322#397—58no—
323#396—58no—
324#396—58no—
325#394—58no—
326#394—58no—
327#394—58no—
328#392—58no—
329#388—58no—
330#387—58no—
331#386C2×D518yescomplemented
332#385—58no—
333#380—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×D5C22×D414yes—
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×Dic5C2×#4114yes—
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—58no—
466C23×C4—54no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—51no—
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#123—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—54no—
525C2×C42—104no—
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#53414yes—
552C22×C5#53714yes—
553C22×C5#53814yes—
554C22×C5#53914yes—
555C22×C5#54014yes—
556C22×C5#54214yes—
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—516no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—52no—
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—102no—
668C22×C4—2016no—
669C22×C4—204no—
670C22×C4—204no—
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—108no—
699C2×C5—44no—
700C2×C5—82no—
701C2×C5#263018yescomplemented
702C2×C5C2×#52511yescharacteristic
703C2×C5C2×#53411yescharacteristic
704C2×C5C2×#53711yescharacteristic
705C2×C5C2×#53811yescharacteristic
706C2×C5C2×#53911yescharacteristic
707C2×C5C2×#54011yescharacteristic
708C2×C5C2×#54211yescharacteristic
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×#263011yescharacteristic, 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#6592314yes—
842C22#6594214yes—
843C22#6594914yes—
844C22#6599614yes—
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#1060663818yesdirect product factor
868C2C2×#6582811yescharacteristic
869C2C2×#6589811yescharacteristic
870C2C2×#6588111yescharacteristic
871C2C2×#6592311yescharacteristic
872C2C2×#6594911yescharacteristic
873C2C2×#6594211yescharacteristic
874C2C2×#6599611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#386C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC2×#386D5
hypocenterC5C2×#2630
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×#4029C2semidirect
3. C2×C5×#386C2semidirect
5. C2×#65511C2semidirect
6. C2×#65499C2semidirect
7. C2×#65248C2semidirect
8. C2×#65237C2semidirect
9. C2×#65237C2semidirect
10. C2×#65250C2semidirect
11. C2×#65233C2semidirect
12. #10606638C2direct (N × H)
13. C2×#64964C2semidirect
14. C2×#64956C2semidirect
15. C2×#64946C2semidirect
16. C2×#64942C2semidirect
32. C2×C4×C22⋊D5C22semidirect
47. C2×#4029C22semidirect
48. C5×#386C22semidirect
52. #65511C22semidirect
53. #65499C22semidirect
60. #65250C22semidirect
61. #65248C22semidirect
62. #65237C22semidirect
63. #65237C22semidirect
64. #65233C22semidirect
65. #64964C22semidirect
66. #64956C22semidirect
67. #64946C22semidirect
68. #64942C22semidirect
103. C22×C4×D5D4semidirect
172. C2×#386D5semidirect
267. C2×C4×D5C2×D4semidirect
331. #386C2×D5semidirect
701. C2×C5#2630semidirect
813. C5C2×#2630semidirect
867. C2#10606638direct (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×#40292
C2×C5×#3862
C2×#655122
C2×#655112
C2×#654992
C2×#652482
C2×#652372
C2×#652502
C2×#652332
#106066382
C2×#649642
C2×#649562
C2×#649462
C2×#649422
C2×#26305