Finite Group Databasebeta

← C2×#10614101 #12266986

Subgroups — C2×#10614101 #12266986

Order 1280.

3330 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×C5×D4C211yesmaximal, characteristic, complemented
2C22×#4044C211yesmaximal, characteristic, complemented
3C2×#65512C211yesmaximal, characteristic
4C2×#65511C211yesmaximal, characteristic, complemented
5C2×#65502C211yesmaximal, characteristic, complemented
6C2×#65502C211yesmaximal, characteristic, complemented
7C2×#65501C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
9#10614101C2116yesmaximal, direct product factor
10C2×#65270C211yesmaximal, characteristic, complemented
11C2×#65238C211yesmaximal, characteristic, complemented
12C2×#65250C211yesmaximal, characteristic, complemented
13C2×#65246C211yesmaximal, characteristic, complemented
14C2×#65233C211yesmaximal, characteristic, complemented
15C2×#65229C211yesmaximal, characteristic, complemented
16C2×#65222C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C22⋊D5C2211yescharacteristic
22C2×C4×C5×D4—28no—
23C2×C4×C5×D4C2218yescomplemented
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C42×C5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4044—28no—
47C2×#4044C2218yescomplemented
48#65512C2218yes—
49#65511C2218yescomplemented
50#65502C2218yescomplemented
51#65502C2218yescomplemented
52#65501C2218yescomplemented
53C4×C22⋊Dic5C2218yescomplemented
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#65270C2218yescomplemented
63#65250C2218yescomplemented
64#65246C2218yescomplemented
65#65238C2218yescomplemented
66#65233C2218yescomplemented
67#65229C2218yescomplemented
68#65222C2218yescomplemented
69C2×#2467—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C25×C5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C22×C5×D4—24no—
74C22×C5×D4—24no—
75C22×C5×D4—24no—
76C22×C5×D4C2314yes—
77C23×C4×C5—24no—
78C23×C4×C5—24no—
79C23×C4×C5—24no—
80C23×C4×C5—24no—
81C23×C4×C5—42no—
82C23×C4×C5—42no—
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2314yes—
85C23×C4×C5C2314yes—
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C22×C22⋊D5—24no—
91C22×C22⋊D5—24no—
92C22×C22⋊D5—24no—
93C22×C22⋊D5—42no—
94C22×C22⋊D5—42no—
95C22×C22⋊D5—42no—
96C22×C22⋊D5C2314yes—
97C22×C22⋊D5C2314yes—
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2311yescharacteristic
105C4×C5×D4—232no—
106C2×C5×C4⋊C4D418yescomplemented
107C2×C5×C4⋊C4C2314yes—
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4—24no—
110C2×C5×C22⋊C4C2314yes—
111C2×C5×C22⋊C4C2314yes—
112C2×C42×C5—24no—
113C2×C42×C5C2314yes—
114C2×C22⋊Dic5—24no—
115C2×C22⋊Dic5—24no—
116C2×C22⋊Dic5—24no—
117C2×C22⋊Dic5—42no—
118C2×C22⋊Dic5—42no—
119C2×C22⋊Dic5—42no—
120C2×C22⋊Dic5C2314yes—
121C2×C22⋊Dic5C2314yes—
122C2×C22⋊Dic5C2314yes—
123C2×C22⋊Dic5C2314yes—
124C2×C22⋊Dic5C2314yes—
125C2×C22⋊Dic5C2314yes—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—42no—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×C4⋊Dic5—24no—
137C2×C4⋊Dic5—42no—
138C2×C4⋊Dic5C2314yes—
139C2×C4⋊Dic5C2314yes—
140C2×#683—24no—
141C2×#683—24no—
142C2×#683—42no—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×#683C2314yes—
146C2×C4×Dic5—24no—
147C2×C4×Dic5—42no—
148C2×C4×Dic5C2314yes—
149C2×C4×Dic5C2314yes—
150#4044—232no—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#126—51no—
160C22×C4×D4D511yescharacteristic, complemented
161#2467—516no—
162C2×#399—51no—
163C2×#394—51no—
164C2×#394—51no—
165C2×#392—51no—
166C2×#390—51no—
167C2×#388—51no—
168C2×#388—51no—
169C2×#387—51no—
170C2×#387—51no—
171C2×#386—51no—
172C2×#386—51no—
173C2×#380—51no—
174C2×C4×C22⋊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#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—22no—
199C23×D5C2412yes—
200C2×C5×D4—232no—
201C2×C5×D4—28no—
202C2×C5×D4—28no—
203C2×C5×D4—28no—
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—28no—
216C22×C4×C5—28no—
217C22×C4×C5—28no—
218C22×C4×C5—28no—
219C22×C4×C5—44no—
220C22×C4×C5—44no—
221C22×C4×C5—416no—
222C22×C4×C5—416no—
223C22×C4×C5C2×D414yes—
224C22×C4×C5C2×D414yes—
225C22×C4×C5C2×D414yes—
226C22×C4×C5#4114yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C2×C22⋊D5—28no—
233C2×C22⋊D5—28no—
234C2×C22⋊D5—28no—
235C2×C22⋊D5—44no—
236C2×C22⋊D5—44no—
237C2×C22⋊D5—44no—
238C2×C22⋊D5—416no—
239C2×C22⋊D5—416no—
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—22no—
257C22×Dic5—22no—
258C22×Dic5—22no—
259C22×Dic5—22no—
260C22×Dic5#4114yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C5×C4⋊C4C2×D4116yescomplemented
269C5×C22⋊C4—28no—
270C5×C22⋊C4—28no—
271C42×C5—28no—
272C22⋊Dic5—28no—
273C22⋊Dic5—28no—
274C22⋊Dic5—28no—
275C22⋊Dic5—44no—
276C22⋊Dic5—44no—
277C22⋊Dic5—44no—
278#685—28no—
279#685—28no—
280#685—28no—
281#685—28no—
282#685—44no—
283C4⋊Dic5—28no—
284C4⋊Dic5—44no—
285#683—28no—
286#683—28no—
287#683—44no—
288C4×Dic5—28no—
289C4×Dic5—44no—
290C23×D4—51no—
291C23×D4—51no—
292C23×D4C2×D511yescharacteristic
293C24×C4C2×D511yescharacteristic
294C24×C4C2×D511yescharacteristic
295C2×#126—58no—
296C2×#126—108no—
297C2×C4×D4—28no—
298C2×C4×D4C2×D518yescomplemented
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4C2×D511yescharacteristic
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⋊C4—51no—
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42—51no—
320C22×C42C2×D511yescharacteristic
321#399—58no—
322#394—58no—
323#394—58no—
324#392—58no—
325#390—58no—
326#388—58no—
327#388—58no—
328#387—58no—
329#387—58no—
330#386—58no—
331#386—58no—
332#380—58no—
333C4×C22⋊C4—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—28no—
346C23×C5—28no—
347C23×C5—28no—
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—22no—
359C23×C5—22no—
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×C5C22×D412yes—
369C23×C5C2×#4114yes—
370C23×C5C2×#4114yes—
371C23×C5C2×#4112yes—
372C23×C5C2×#4112yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5H(5,𝔽2)12yes—
376C23×C5H(5,𝔽2)12yes—
377C23×C5C2511yescharacteristic
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—44no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5—44no—
391C22×D5—44no—
392C5×D4—232no—
393C2×C4×C5—28no—
394C2×C4×C5—28no—
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—416no—
409C2×C4×C5—416no—
410C2×C4×C5—44no—
411C2×C4×C5C22×D414yes—
412C2×C4×C5C22×D414yes—
413C2×C4×C5C22×D414yes—
414C2×C4×C5C2×#4114yes—
415C22⋊D5—416no—
416C22⋊D5—416no—
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—22no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5—44no—
443C2×Dic5—44no—
444C2×Dic5C2×#4114yes—
445C25—51no—
446C25C22×D511yescharacteristic
447C25C22×D511yescharacteristic
448C22×D4—24no—
449C22×D4—24no—
450C22×D4—24no—
451C22×D4—54no—
452C22×D4—54no—
453C22×D4—104no—
454C22×D4—104no—
455C22×D4—104no—
456C22×D4—202no—
457C22×D4—202no—
458C22×D4—202no—
459C22×D4C22×D514yes—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—42no—
465C23×C4—42no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—51no—
472C23×C4—51no—
473C23×C4C22×D511yescharacteristic
474C23×C4C22×D514yes—
475C23×C4C22×D514yes—
476C23×C4C22×D511yescharacteristic
477C23×C4C22×D511yescharacteristic
478C23×C4C22×D511yescharacteristic
479C23×C4C22×D511yescharacteristic
480#126—1032no—
481C4×D4—232no—
482C2×C4⋊C4—54no—
483C2×C4⋊C4—54no—
484C2×C4⋊C4—54no—
485C2×C4⋊C4—54no—
486C2×C4⋊C4—54no—
487C2×C4⋊C4—104no—
488C2×C4⋊C4—104no—
489C2×C4⋊C4—104no—
490C2×C4⋊C4—202no—
491C2×C4⋊C4—202no—
492C2×C4⋊C4C22⋊D518yescomplemented
493C2×C4⋊C4C22×D514yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
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—54no—
506C2×C22⋊C4—54no—
507C2×C22⋊C4—104no—
508C2×C22⋊C4—104no—
509C2×C22⋊C4—104no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—104no—
513C2×C22⋊C4—104no—
514C2×C22⋊C4—202no—
515C2×C22⋊C4—202no—
516C2×C22⋊C4—202no—
517C2×C22⋊C4—202no—
518C2×C22⋊C4C22×D514yes—
519C2×C22⋊C4C22×D514yes—
520C2×C42—24no—
521C2×C42—54no—
522C2×C42—54no—
523C2×C42—104no—
524C2×C42—202no—
525C2×C42C22×D514yes—
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—24no—
538C22×C5—24no—
539C22×C5—24no—
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—416no—
549C22×C5—416no—
550C22×C5#52514yes—
551C22×C5#52914yes—
552C22×C5#53814yes—
553C22×C5#54614yes—
554C22×C5#55014yes—
555C22×C5#55114yes—
556C22×C5#55314yes—
557C22×C5C23×D411yescharacteristic
558C22×C5C22×#4111yescharacteristic
559C22×C5C22×#4111yescharacteristic
560C22×C5C22×#4111yescharacteristic
561C22×C5C22×#4111yescharacteristic
562C22×C5C2×H(5,𝔽2)11yescharacteristic
563C22×C5C2×H(5,𝔽2)11yescharacteristic
564C2×D5—42no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—42no—
569C2×D5—42no—
570C2×D5—42no—
571C2×D5—88no—
572C4×C5—24no—
573C4×C5—24no—
574C4×C5—24no—
575C4×C5—24no—
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—52no—
597C24—102no—
598C24—102no—
599C24—102no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24#70914yes—
605C24#70914yes—
606C24C23×D512yes—
607C24C23×D512yes—
608C24C23×D511yescharacteristic
609C2×D4—232no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—108no—
614C2×D4—108no—
615C2×D4—108no—
616C2×D4—204no—
617C2×D4—204no—
618C2×D4—204no—
619C2×D4—2016no—
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—28no—
633C22×C4—28no—
634C22×C4—28no—
635C22×C4—28no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—416no—
639C22×C4—416no—
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—102no—
668C22×C4#71114yes—
669C22×C4C2×C22⋊D514yes—
670C22×C4C2×C22⋊D514yes—
671C22×C4C2×C22⋊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—204no—
681C4⋊C4—204no—
682C4⋊C4C2×C22⋊D5116yescomplemented
683C22⋊C4—28no—
684C22⋊C4—28no—
685C22⋊C4—108no—
686C22⋊C4—108no—
687C22⋊C4—108no—
688C22⋊C4—108no—
689C22⋊C4—108no—
690C22⋊C4—108no—
691C22⋊C4—108no—
692C22⋊C4—204no—
693C22⋊C4—204no—
694C22⋊C4—204no—
695C22⋊C4—204no—
696C42—28no—
697C42—108no—
698C42—204no—
699C2×C5—44no—
700C2×C5—44no—
701C2×C5#246718yescomplemented
702C2×C5C2×#52511yescharacteristic
703C2×C5C2×#52911yescharacteristic
704C2×C5C2×#53811yescharacteristic
705C2×C5C2×#54611yescharacteristic
706C2×C5C2×#55011yescharacteristic
707C2×C5C2×#55111yescharacteristic
708C2×C5C2×#55311yescharacteristic
709D5—82no—
710C23—28no—
711C23—28no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—102no—
737C23—102no—
738C23—102no—
739C23—102no—
740C23—102no—
741C23—102no—
742C23—102no—
743C23—204no—
744C23—204no—
745C23—204no—
746C23—204no—
747C23—204no—
748C23—204no—
749C23—204no—
750C23C2×#70914yes—
751C23C2×#70914yes—
752C23C2×#70912yes—
753C23C2×#70912yes—
754C23C2×#71112yes—
755C23#414412yes—
756C23D5×#4112yes—
757C23#414912yes—
758C23C22×C22⋊D512yes—
759C23C24×D511yescharacteristic
760D4—232no—
761D4—2016no—
762D4—2016no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
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—416no—
780C2×C4—44no—
781C2×C4—54no—
782C2×C4—108no—
783C2×C4—102no—
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—204no—
804C2×C4—204no—
805C2×C4—204no—
806C2×C4—204no—
807C2×C4—204no—
808C2×C4—204no—
809C2×C4C2×#71114yes—
810C2×C4C22×C22⋊D514yes—
811C2×C4C22×C22⋊D514yes—
812C2×C4C22×C22⋊D514yes—
813C5C2×#246711yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—416no—
827C22—416no—
828C22—42no—
829C22—42no—
830C22—202no—
831C22—202no—
832C22—202no—
833C22—202no—
834C22—202no—
835C22—202no—
836C22—202no—
837C22—408no—
838C22#6587214yes—
839C22#6589014yes—
840C22#6589414yes—
841C22#6589914yes—
842C22#6612514yes—
843C22#6614014yes—
844C22#6616814yes—
845C22C22×#70911yescharacteristic
846C22C22×#70911yescharacteristic
847C22C22×#71111yescharacteristic
848C22C2×#414411yescharacteristic
849C22C2×D5×#4111yescharacteristic
850C22C2×#414911yescharacteristic
851C22C23×C22⋊D511yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—42no—
857C4—104no—
858C4—202no—
859C4—202no—
860C4—202no—
861C4—202no—
862C4—202no—
863C4—202no—
864C2—44no—
865C2—44no—
866C2—402no—
867C2#1061410118yesdirect product factor
868C2C2×#6587211yescharacteristic
869C2C2×#6589911yescharacteristic
870C2C2×#6589411yescharacteristic
871C2C2×#6589011yescharacteristic
872C2C2×#6612511yescharacteristic
873C2C2×#6614011yescharacteristic
874C2C2×#6616811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C4×C5×D4C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC22×C4×D4D5
hypocenterC5C2×#2467
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×D4C2semidirect
2. C22×#4044C2semidirect
4. C2×#65511C2semidirect
5. C2×#65502C2semidirect
6. C2×#65502C2semidirect
7. C2×#65501C2semidirect
8. C2×C4×C22⋊Dic5C2semidirect
9. #10614101C2direct (N × H)
10. C2×#65270C2semidirect
11. C2×#65238C2semidirect
12. C2×#65250C2semidirect
13. C2×#65246C2semidirect
14. C2×#65233C2semidirect
15. C2×#65229C2semidirect
16. C2×#65222C2semidirect
23. C2×C4×C5×D4C22semidirect
47. C2×#4044C22semidirect
49. #65511C22semidirect
50. #65502C22semidirect
51. #65502C22semidirect
52. #65501C22semidirect
53. C4×C22⋊Dic5C22semidirect
62. #65270C22semidirect
63. #65250C22semidirect
64. #65246C22semidirect
65. #65238C22semidirect
66. #65233C22semidirect
67. #65229C22semidirect
68. #65222C22semidirect
106. C2×C5×C4⋊C4D4semidirect
160. C22×C4×D4D5semidirect
268. C5×C4⋊C4C2×D4semidirect
298. C2×C4×D4C2×D5semidirect
492. C2×C4⋊C4C22⋊D5semidirect
682. C4⋊C4C2×C22⋊D5semidirect
701. C2×C5#2467semidirect
813. C5C2×#2467semidirect
867. C2#10614101direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×D42
C22×#40442
C2×#655122
C2×#655112
C2×#655022
C2×#655012
C2×C4×C22⋊Dic52
#106141012
C2×#652702
C2×#652382
C2×#652502
C2×#652462
C2×#652332
C2×#652292
C2×#652222
C2×#24675