Finite Group Databasebeta

← C2×#10608430 #12265676

Subgroups — C2×#10608430 #12265676

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×#4081C211yesmaximal, characteristic, complemented
2C22×D4×Dic5C211yesmaximal, characteristic, complemented
3C2×C5×#392C211yesmaximal, characteristic
4C2×#65511C211yesmaximal, characteristic, complemented
5C2×#65511C211yesmaximal, characteristic, complemented
6C2×#65511C211yesmaximal, characteristic, complemented
7C2×#65509C211yesmaximal, characteristic, complemented
8C2×#65242C211yesmaximal, characteristic, complemented
9C2×#65237C211yesmaximal, characteristic, complemented
10C2×#65237C211yesmaximal, characteristic, complemented
11C2×#65240C211yesmaximal, characteristic, complemented
12C2×#65235C211yesmaximal, characteristic, complemented
13C2×#65231C211yesmaximal, characteristic, complemented
14#10608430C2116yesmaximal, direct product factor
15C2×#64946C211yesmaximal, characteristic, complemented
16C2×#64941C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C23×C5×D4C2211yescharacteristic
19C23×C5×D4C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
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
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×C22⋊Dic5C2211yescharacteristic
35C2×#4081—28no—
36C2×#4081C2218yescomplemented
37C2×D4×Dic5—28no—
38C2×D4×Dic5C2218yescomplemented
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C5×#392C2218yes—
49C2×C5×#95C2211yescharacteristic
50#65511C2218yescomplemented
51#65511C2218yescomplemented
52#65511C2218yescomplemented
53#65509C2218yescomplemented
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65242C2218yescomplemented
62#65240C2218yescomplemented
63#65237C2218yescomplemented
64#65237C2218yescomplemented
65#65235C2218yescomplemented
66#65231C2218yescomplemented
67#64946C2218yescomplemented
68#64941C2218yescomplemented
69C2×#2630—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C25×C5C2311yescharacteristic
72C25×C5C2311yescharacteristic
73C22×C5×D4—24no—
74C22×C5×D4—24no—
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—24no—
78C22×C5×D4—42no—
79C22×C5×D4—42no—
80C22×C5×D4—42no—
81C22×C5×D4—42no—
82C22×C5×D4C2314yes—
83C22×C5×D4C2314yes—
84C22×C5×D4C2314yes—
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×Dic5—24no—
90C23×Dic5—42no—
91C23×Dic5—42no—
92C23×Dic5—42no—
93C23×Dic5—42no—
94C23×Dic5D418yescomplemented
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2314yes—
104C23×Dic5C2314yes—
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—24no—
116C2×C22⋊Dic5—24no—
117C2×C22⋊Dic5—42no—
118C2×C22⋊Dic5—42no—
119C2×C22⋊Dic5—42no—
120C2×C22⋊Dic5—42no—
121C2×C22⋊Dic5C2314yes—
122C2×C22⋊Dic5C2314yes—
123C2×C22⋊Dic5C2314yes—
124C2×C22⋊Dic5C2314yes—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127C2×C22⋊Dic5C2314yes—
128C2×C22⋊Dic5C2314yes—
129C2×C22⋊Dic5C2314yes—
130C2×C22⋊Dic5C2314yes—
131#4081—232no—
132D4×Dic5—232no—
133C2×C4⋊Dic5—24no—
134C2×C4⋊Dic5—42no—
135C2×C4⋊Dic5C2314yes—
136C2×C4⋊Dic5C2314yes—
137C2×#683—24no—
138C2×#683—24no—
139C2×#683—24no—
140C2×#683—42no—
141C2×#683—42no—
142C2×#683—42no—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×#683C2314yes—
146C2×#683C2314yes—
147C2×#683C2314yes—
148C2×#683C2314yes—
149C2×C4×Dic5—24no—
150C2×C4×Dic5C2314yes—
151C5×#95C2314yes—
152#3963C2314yes—
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×#392D511yescharacteristic
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×C5—22no—
189C24×C5—22no—
190C24×C5—22no—
191C24×C5—22no—
192C24×C5—22no—
193C24×C5—22no—
194C24×C5C2×D414yes—
195C24×C5#4114yes—
196C24×C5C2412yes—
197C24×C5C2412yes—
198C24×C5C2412yes—
199C24×C5C2411yescharacteristic
200C2×C5×D4—232no—
201C2×C5×D4—28no—
202C2×C5×D4—28no—
203C2×C5×D4—28no—
204C2×C5×D4—28no—
205C2×C5×D4—28no—
206C2×C5×D4—44no—
207C2×C5×D4—44no—
208C2×C5×D4—44no—
209C2×C5×D4—44no—
210C2×C5×D4—416no—
211C2×C5×D4—416no—
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×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5#4114yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
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—28no—
251C22×Dic5—416no—
252C22×Dic5—44no—
253C22×Dic5—44no—
254C22×Dic5—44no—
255C22×Dic5—44no—
256C22×Dic5—416no—
257C22×Dic5C2×D414yes—
258C22×Dic5C2×D414yes—
259C22×Dic5C2×D4116yescomplemented
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
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—28no—
276C22⋊Dic5—28no—
277C22⋊Dic5—44no—
278C22⋊Dic5—44no—
279C22⋊Dic5—44no—
280C22⋊Dic5—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×Dic5—28no—
290C23×D4C2×D511yescharacteristic
291C23×D4C2×D511yescharacteristic
292C23×D4C2×D511yescharacteristic
293C24×C4—51no—
294C24×C4—51no—
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#392C2×D518yes—
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×#95C2×D511yescharacteristic
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—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5—44no—
371C23×C5—44no—
372C23×C5—44no—
373C23×C5—44no—
374C23×C5—44no—
375C23×C5—44no—
376C23×C5—44no—
377C23×C5—44no—
378C23×C5—44no—
379C23×C5—44no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5C22×D414yes—
383C23×C5C22×D412yes—
384C23×C5C2×#4114yes—
385C23×C5C2×#4112yes—
386C23×C5C2×#4112yes—
387C23×C5H(5,𝔽2)12yes—
388C23×C5H(5,𝔽2)12yes—
389C23×C5H(5,𝔽2)12yes—
390C23×C52−1+412yes—
391C23×C5C2511yescharacteristic
392C5×D4—232no—
393C5×D4—416no—
394C5×D4—416no—
395C2×C4×C5—28no—
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—44no—
408C2×C4×C5—44no—
409C2×C4×C5—44no—
410C2×C4×C5C2×#4114yes—
411C2×Dic5—28no—
412C2×Dic5—28no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—22no—
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—416no—
436C2×Dic5—416no—
437C2×Dic5—44no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5—44no—
443C2×Dic5C22×D414yes—
444C2×Dic5C22×D414yes—
445C25C22×D511yescharacteristic
446C25C22×D511yescharacteristic
447C25C22×D511yescharacteristic
448C22×D4—24no—
449C22×D4—24no—
450C22×D4—24no—
451C22×D4—24no—
452C22×D4—24no—
453C22×D4—42no—
454C22×D4—42no—
455C22×D4—42no—
456C22×D4—42no—
457C22×D4C22×D514yes—
458C22×D4C22×D514yes—
459C22×D4C22×D514yes—
460C23×C4—51no—
461C23×C4—51no—
462C23×C4—58no—
463C23×C4—54no—
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×C4—202no—
475C23×C4—202no—
476C23×C4C22×D511yescharacteristic
477C23×C4C22×D511yescharacteristic
478C23×C4C22×D511yescharacteristic
479C23×C4C22×D511yescharacteristic
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#95—54no—
533#95C22×D514yes—
534C22×C5—24no—
535C22×C5—24no—
536C22×C5—24no—
537C22×C5—24no—
538C22×C5—24no—
539C22×C5—24no—
540C22×C5—416no—
541C22×C5—416no—
542C22×C5—42no—
543C22×C5—42no—
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—42no—
553C22×C5—42no—
554C22×C5—42no—
555C22×C5—42no—
556C22×C5—42no—
557C22×C5—88no—
558C22×C5#52514yes—
559C22×C5#53414yes—
560C22×C5#53714yes—
561C22×C5#53814yes—
562C22×C5#53914yes—
563C22×C5#54014yes—
564C22×C5#54214yes—
565C22×C5C23×D411yescharacteristic
566C22×C5C22×#4111yescharacteristic
567C22×C5C22×#4111yescharacteristic
568C22×C5C2×H(5,𝔽2)11yescharacteristic
569C22×C5C2×H(5,𝔽2)11yescharacteristic
570C22×C5C2×H(5,𝔽2)11yescharacteristic
571C22×C5C2×2−1+411yescharacteristic
572C4×C5—24no—
573C4×C5—42no—
574C4×C5—42no—
575C4×C5—42no—
576Dic5—24no—
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—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24D4×D514yes—
604C24#71114yes—
605C24C23×D512yes—
606C24C23×D512yes—
607C24C23×D512yes—
608C24C23×D511yescharacteristic
609C2×D4—232no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—28no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—44no—
619C2×D4—416no—
620C2×D4—416no—
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—54no—
633C22×C4—54no—
634C22×C4—52no—
635C22×C4—52no—
636C22×C4—516no—
637C22×C4—52no—
638C22×C4—52no—
639C22×C4—52no—
640C22×C4—52no—
641C22×C4—52no—
642C22×C4—52no—
643C22×C4—108no—
644C22×C4—102no—
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—102no—
666C22×C4—2016no—
667C22×C4—204no—
668C22×C4—204no—
669C22×C4—204no—
670C22×C4—204no—
671C22×C4—2016no—
672C22×C4#71114yes—
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—44no—
701C2×C5—82no—
702C2×C5#263018yescomplemented
703C2×C5C2×#52511yescharacteristic
704C2×C5C2×#53411yescharacteristic
705C2×C5C2×#53711yescharacteristic
706C2×C5C2×#53811yescharacteristic
707C2×C5C2×#53911yescharacteristic
708C2×C5C2×#54011yescharacteristic
709C2×C5C2×#54211yescharacteristic
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—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23C2×D4×D514yes—
751C23C2×D4×D512yes—
752C23C2×#71114yes—
753C23C2×#71112yes—
754C23C2×#71112yes—
755C23#414412yes—
756C23#414412yes—
757C23#414412yes—
758C23#415012yes—
759C23C24×D511yescharacteristic
760D4—232no—
761D4—416no—
762D4—416no—
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—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—54no—
779C2×C4—54no—
780C2×C4—108no—
781C2×C4—108no—
782C2×C4—102no—
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—102no—
804C2×C4—2016no—
805C2×C4—2016no—
806C2×C4—204no—
807C2×C4—204no—
808C2×C4—204no—
809C2×C4—204no—
810C2×C4—204no—
811C2×C4—204no—
812C2×C4C2×#71114yes—
813C5C2×#263011yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—416no—
821C22—416no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—88no—
838C22#6592014yes—
839C22#6592314yes—
840C22#6592714yes—
841C22#6593114yes—
842C22#6593614yes—
843C22#6593714yes—
844C22#6605314yes—
845C22C22×D4×D511yescharacteristic
846C22C22×#71111yescharacteristic
847C22C22×#71111yescharacteristic
848C22C2×#414411yescharacteristic
849C22C2×#414411yescharacteristic
850C22C2×#414411yescharacteristic
851C22C2×#415011yescharacteristic
852C4—24no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—104no—
857C4—104no—
858C4—202no—
859C4—202no—
860C4—202no—
861C4—202no—
862C4—202no—
863C4—202no—
864C2—44no—
865C2—44no—
866C2—82no—
867C2#1060843018yesdirect product factor
868C2C2×#6592011yescharacteristic
869C2C2×#6592711yescharacteristic
870C2C2×#6592311yescharacteristic
871C2C2×#6593111yescharacteristic
872C2C2×#6593611yescharacteristic
873C2C2×#6593711yescharacteristic
874C2C2×#6605311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
Fitting, prime radicalC2×C5×#392C2
socleC24×C5C24
hypercenterC2×#392D5
hypocenterC5C2×#2630
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#4081C2semidirect
2. C22×D4×Dic5C2semidirect
4. C2×#65511C2semidirect
5. C2×#65511C2semidirect
6. C2×#65511C2semidirect
7. C2×#65509C2semidirect
8. C2×#65242C2semidirect
9. C2×#65237C2semidirect
10. C2×#65237C2semidirect
11. C2×#65240C2semidirect
12. C2×#65235C2semidirect
13. C2×#65231C2semidirect
14. #10608430C2direct (N × H)
15. C2×#64946C2semidirect
16. C2×#64941C2semidirect
36. C2×#4081C22semidirect
38. C2×D4×Dic5C22semidirect
50. #65511C22semidirect
51. #65511C22semidirect
52. #65511C22semidirect
53. #65509C22semidirect
61. #65242C22semidirect
62. #65240C22semidirect
63. #65237C22semidirect
64. #65237C22semidirect
65. #65235C22semidirect
66. #65231C22semidirect
67. #64946C22semidirect
68. #64941C22semidirect
94. C23×Dic5D4semidirect
259. C22×Dic5C2×D4semidirect
702. C2×C5#2630semidirect
813. C5C2×#2630semidirect
867. C2#10608430direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40812
C22×D4×Dic52
C2×C5×#3922
C2×#655112
C2×#655092
C2×#652422
C2×#652372
C2×#652402
C2×#652352
C2×#652312
#106084302
C2×#649462
C2×#649412
C2×#26305