Finite Group Databasebeta

← C2×#10614635 #12265677

Subgroups — C2×#10614635 #12265677

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×C5×#123C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×#65512C211yesmaximal, characteristic
4C2×#65511C211yesmaximal, characteristic, complemented
5C2×#65501C211yesmaximal, characteristic, complemented
6#10614635C2116yesmaximal, direct product factor
7C2×#65283C211yesmaximal, characteristic, complemented
8C2×#65278C211yesmaximal, characteristic, complemented
9C2×#65273C211yesmaximal, characteristic, complemented
10C2×#65267C211yesmaximal, characteristic, complemented
11C2×#65248C211yesmaximal, characteristic, complemented
12C2×#65245C211yesmaximal, characteristic, complemented
13C2×#65241C211yesmaximal, characteristic, complemented
14C2×#65237C211yesmaximal, characteristic, complemented
15C2×#65250C211yesmaximal, characteristic, complemented
16C2×#65233C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C2×C5×#123—28no—
23C2×C5×#123C2218yescomplemented
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×C22⋊Dic5C2211yescharacteristic
35C2×C4×C22⋊D5—28no—
36C2×C4×C22⋊D5C2218yescomplemented
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×C4⋊Dic5C2211yescharacteristic
42C22×C4⋊Dic5C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48#65512C2218yes—
49#65511C2218yescomplemented
50#65501C2218yescomplemented
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59#65283C2218yescomplemented
60#65278C2218yescomplemented
61#65273C2218yescomplemented
62#65267C2218yescomplemented
63#65250C2218yescomplemented
64#65248C2218yescomplemented
65#65245C2218yescomplemented
66#65241C2218yescomplemented
67#65237C2218yescomplemented
68#65233C2218yescomplemented
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—42no—
78C23×C4×C5—42no—
79C23×C4×C5D418yescomplemented
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—
105C5×#123—232no—
106C2×C5×C4⋊C4—24no—
107C2×C5×C4⋊C4—24no—
108C2×C5×C4⋊C4C2314yes—
109C2×C5×C4⋊C4C2314yes—
110C2×C5×C22⋊C4—24no—
111C2×C5×C22⋊C4—24no—
112C2×C5×C22⋊C4—24no—
113C2×C5×C22⋊C4C2314yes—
114C2×C5×C22⋊C4C2314yes—
115C2×C5×C22⋊C4C2314yes—
116C2×C22⋊Dic5—24no—
117C2×C22⋊Dic5—24no—
118C2×C22⋊Dic5—42no—
119C2×C22⋊Dic5—42no—
120C2×C22⋊Dic5—42no—
121C2×C22⋊Dic5—42no—
122C2×C22⋊Dic5C2314yes—
123C2×C22⋊Dic5C2314yes—
124C2×C22⋊Dic5C2314yes—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127C2×C22⋊Dic5C2314yes—
128C4×C22⋊D5—232no—
129C2×#685—24no—
130C2×#685—24no—
131C2×#685—42no—
132C2×#685—42no—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×C4⋊Dic5—42no—
138C2×C4⋊Dic5—42no—
139C2×C4⋊Dic5C2314yes—
140C2×C4⋊Dic5C2314yes—
141C2×#683—24no—
142C2×#683—24no—
143C2×#683—42no—
144C2×#683—42no—
145C2×#683C2314yes—
146C2×#683C2314yes—
147C2×#683C2314yes—
148C2×#683C2314yes—
149C2×C4×Dic5—24no—
150C2×C4×Dic5C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#123D511yescharacteristic, complemented
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×#386—51no—
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×C5C2×D414yes—
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—416no—
218C22×C4×C5—44no—
219C22×C4×C5—44no—
220C22×C4×C5C2×D414yes—
221C22×C4×C5C2×D414yes—
222C22×C4×C5C2×D4116yescomplemented
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×Dic5—22no—
256C22×Dic5#4114yes—
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×C4⋊C4—28no—
269C5×C4⋊C4—28no—
270C5×C22⋊C4—28no—
271C5×C22⋊C4—28no—
272C5×C22⋊C4—28no—
273C22⋊Dic5—28no—
274C22⋊Dic5—28no—
275C22⋊Dic5—44no—
276C22⋊Dic5—44no—
277C22⋊Dic5—44no—
278C22⋊Dic5—44no—
279#685—28no—
280#685—28no—
281#685—44no—
282#685—44no—
283C4⋊Dic5—44no—
284C4⋊Dic5—44no—
285#683—28no—
286#683—28no—
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—28no—
296C2×#123C2×D518yescomplemented
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⋊C4C2×D511yescharacteristic
306C22×C4⋊C4C2×D511yescharacteristic
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#386—58no—
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×#95—51no—
341C2×#95—51no—
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×D414yes—
370C23×C5C22×D412yes—
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—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—416no—
409C2×C4×C5—44no—
410C2×C4×C5—44no—
411C2×C4×C5—44no—
412C2×C4×C5C22×D414yes—
413C2×C4×C5C22×D414yes—
414C22⋊D5—232no—
415C22⋊D5—416no—
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—22no—
436C2×Dic5—22no—
437C2×Dic5—44no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5—44no—
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—42no—
461C23×C4—42no—
462C23×C4—51no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—54no—
470C23×C4—104no—
471C23×C4—202no—
472C23×C4—202no—
473C23×C4C22⋊D518yescomplemented
474C23×C4C22×D511yescharacteristic
475C23×C4C22×D511yescharacteristic
476C23×C4C22×D511yescharacteristic
477C23×C4C22×D511yescharacteristic
478C23×C4C22×D511yescharacteristic
479C23×C4C22×D514yes—
480#123—232no—
481C4×D4—1032no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
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—202no—
493C2×C4⋊C4—202no—
494C2×C4⋊C4—202no—
495C2×C4⋊C4—202no—
496C2×C4⋊C4C22×D514yes—
497C2×C4⋊C4C22×D514yes—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
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—202no—
516C2×C22⋊C4—202no—
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#95—54no—
533#95—54no—
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—24no—
574C4×C5—42no—
575C4×C5—42no—
576C4×C5—42no—
577Dic5—24no—
578Dic5—42no—
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—
605C24C2×C22⋊D514yes—
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—416no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—54no—
638C22×C4—52no—
639C22×C4—52no—
640C22×C4—52no—
641C22×C4—52no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—52no—
645C22×C4—102no—
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×C4—102no—
665C22×C4—108no—
666C22×C4—204no—
667C22×C4—204no—
668C22×C4—2016no—
669C22×C4C2×C22⋊D514yes—
670C22×C4C2×C22⋊D514yes—
671C22×C4C2×C22⋊D5116yescomplemented
672C22×C4C23×D512yes—
673C22×C4C23×D512yes—
674C22×C4C23×D512yes—
675C22×C4C23×D512yes—
676C22×C4C23×D512yes—
677C4⋊C4—28no—
678C4⋊C4—28no—
679C4⋊C4—108no—
680C4⋊C4—108no—
681C4⋊C4—204no—
682C4⋊C4—204no—
683C4⋊C4—204no—
684C4⋊C4—204no—
685C22⋊C4—28no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—108no—
689C22⋊C4—108no—
690C22⋊C4—108no—
691C22⋊C4—108no—
692C22⋊C4—204no—
693C22⋊C4—204no—
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—
751C23#414412yes—
752C23#414412yes—
753C23D5×#4112yes—
754C23D5×#4112yes—
755C23#414912yes—
756C23#415012yes—
757C23C22×C22⋊D514yes—
758C23C22×C22⋊D512yes—
759C23C24×D511yescharacteristic
760D4—416no—
761D4—1032no—
762D4—2016no—
763C2×C4—28no—
764C2×C4—28no—
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—54no—
783C2×C4—108no—
784C2×C4—102no—
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—102no—
804C2×C4—2016no—
805C2×C4—204no—
806C2×C4—204no—
807C2×C4—204no—
808C2×C4—204no—
809C2×C4—204no—
810C2×C4—204no—
811C2×C4C22×C22⋊D514yes—
812C2×C4C22×C22⋊D514yes—
813C5C2×#263011yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—416no—
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—202no—
835C22—202no—
836C22—202no—
837C22—2016no—
838C22#6599114yes—
839C22#6599414yes—
840C22#6599614yes—
841C22#6599714yes—
842C22#6613814yes—
843C22#6616214yes—
844C22#6616714yes—
845C22C2×#414411yescharacteristic
846C22C2×#414411yescharacteristic
847C22C2×D5×#4111yescharacteristic
848C22C2×D5×#4111yescharacteristic
849C22C2×#414911yescharacteristic
850C22C2×#415011yescharacteristic
851C22C23×C22⋊D511yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—104no—
858C4—202no—
859C4—202no—
860C4—202no—
861C4—202no—
862C4—202no—
863C4—202no—
864C2—44no—
865C2—82no—
866C2—204no—
867C2#1061463518yesdirect product factor
868C2C2×#6599711yescharacteristic
869C2C2×#6599611yescharacteristic
870C2C2×#6599111yescharacteristic
871C2C2×#6599411yescharacteristic
872C2C2×#6613811yescharacteristic
873C2C2×#6616211yescharacteristic
874C2C2×#6616711yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#123C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC22×#123D5
hypocenterC5C2×#2630
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C5×#123C2semidirect
2. C22×C4×C22⋊D5C2semidirect
4. C2×#65511C2semidirect
5. C2×#65501C2semidirect
6. #10614635C2direct (N × H)
7. C2×#65283C2semidirect
8. C2×#65278C2semidirect
9. C2×#65273C2semidirect
10. C2×#65267C2semidirect
11. C2×#65248C2semidirect
12. C2×#65245C2semidirect
13. C2×#65241C2semidirect
14. C2×#65237C2semidirect
15. C2×#65250C2semidirect
16. C2×#65233C2semidirect
23. C2×C5×#123C22semidirect
36. C2×C4×C22⋊D5C22semidirect
49. #65511C22semidirect
50. #65501C22semidirect
59. #65283C22semidirect
60. #65278C22semidirect
61. #65273C22semidirect
62. #65267C22semidirect
63. #65250C22semidirect
64. #65248C22semidirect
65. #65245C22semidirect
66. #65241C22semidirect
67. #65237C22semidirect
68. #65233C22semidirect
79. C23×C4×C5D4semidirect
159. C22×#123D5semidirect
222. C22×C4×C5C2×D4semidirect
296. C2×#123C2×D5semidirect
473. C23×C4C22⋊D5semidirect
671. C22×C4C2×C22⋊D5semidirect
701. C2×C5#2630semidirect
813. C5C2×#2630semidirect
867. C2#10614635direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1232
C22×C4×C22⋊D52
C2×#655122
C2×#655112
C2×#655012
#106146352
C2×#652832
C2×#652782
C2×#652732
C2×#652672
C2×#652482
C2×#652452
C2×#652412
C2×#652372
C2×#652502
C2×#652332
C2×#26305