Finite Group Databasebeta

← C2×#10608817 #12305429

Subgroups — C2×#10608817 #12305429

Order 1280.

2998 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×#4085C211yesmaximal, characteristic
2C22×#4024C211yesmaximal, characteristic, complemented
3C2×C5×#394C211yesmaximal, characteristic, complemented
4C2×#65511C211yesmaximal, characteristic, complemented
5C2×#65281C211yesmaximal, characteristic, complemented
6C2×#65273C211yesmaximal, characteristic, complemented
7C2×#65248C211yesmaximal, characteristic, complemented
8C2×#65248C211yesmaximal, characteristic, complemented
9C2×#65238C211yesmaximal, characteristic, complemented
10C2×#65250C211yesmaximal, characteristic, complemented
11C2×#65250C211yesmaximal, characteristic, complemented
12C2×#65236C211yesmaximal, characteristic, complemented
13C2×#65232C211yesmaximal, characteristic, complemented
14#10608817C2116yesmaximal, direct product factor
15C2×#64962C211yesmaximal, characteristic, complemented
16C2×#64946C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C23×Dic10C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C2×#4085—28no—
33C2×#4085C2218yes—
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C2×#4024—28no—
47C2×#4024C2218yescomplemented
48C5×#394C2218yescomplemented
49C2×C5×#95C2211yescharacteristic
50#65511C2218yescomplemented
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58#65281C2218yescomplemented
59#65273C2218yescomplemented
60#65250C2218yescomplemented
61#65250C2218yescomplemented
62#65248C2218yescomplemented
63#65248C2218yescomplemented
64#65238C2218yescomplemented
65#65236C2218yescomplemented
66#65232C2218yescomplemented
67#64962C2218yescomplemented
68#64946C2218yescomplemented
69C2×#2816—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×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—24no—
83C22×C22⋊D5—24no—
84C22×C22⋊D5—42no—
85C22×C22⋊D5—42no—
86C22×C22⋊D5—42no—
87C22×C22⋊D5—42no—
88C22×C22⋊D5C2314yes—
89C22×C22⋊D5C2314yes—
90C23×Dic5—42no—
91C23×Dic5—42no—
92C23×Dic5D418yes—
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2314yes—
101C22×Dic10—24no—
102C22×Dic10—42no—
103C22×Dic10—42no—
104C22×Dic10C2314yes—
105C2×C5×C4⋊C4—42no—
106C2×C5×C4⋊C4C2314yes—
107C2×C5×C22⋊C4—24no—
108C2×C5×C22⋊C4—42no—
109C2×C5×C22⋊C4—42no—
110C2×C5×C22⋊C4—42no—
111C2×C5×C22⋊C4C2314yes—
112C2×C5×C22⋊C4C2314yes—
113C2×C5×C22⋊C4C2314yes—
114C2×C5×C22⋊C4C2314yes—
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—
125#4085—232no—
126C2×#685—24no—
127C2×#685—42no—
128C2×#685—42no—
129C2×#685—42no—
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—24no—
143C2×#683—42no—
144C2×#683—42no—
145C2×#683C2314yes—
146C2×#683C2314yes—
147C2×#683C2314yes—
148C2×#683C2314yes—
149C2×#683C2314yes—
150#4024—232no—
151C5×#95C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×C22⋊Q8—51no—
160C22×#121—51no—
161#2816—516no—
162C2×#399—51no—
163C2×#399—51no—
164C2×#398—51no—
165C2×#398—51no—
166C2×#394—51no—
167C2×#394—51no—
168C2×#394—51no—
169C2×#394—51no—
170C2×#394—51no—
171C2×#394D511yescharacteristic, complemented
172C2×#393—51no—
173C2×#393—51no—
174C2×#381—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—22no—
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—22no—
219C22×C4×C5C2412yes—
220C22×C4×C5C2412yes—
221C22×C4×C5C2412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2412yes—
224C2×C22⋊D5—28no—
225C2×C22⋊D5—28no—
226C2×C22⋊D5—44no—
227C2×C22⋊D5—44no—
228C2×C22⋊D5—44no—
229C2×C22⋊D5—44no—
230C2×C22⋊D5—416no—
231C2×C22⋊D5—416no—
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—22no—
251C22×Dic5—416no—
252C22×Dic5—44no—
253C22×Dic5—44no—
254C22×Dic5C2×D414yes—
255C22×Dic5C2×D414yes—
256C22×Dic5C2×D4116yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C2×Dic10—28no—
265C2×Dic10—44no—
266C2×Dic10—44no—
267C2×Dic10—416no—
268C5×C4⋊C4—44no—
269C5×C22⋊C4—28no—
270C5×C22⋊C4—44no—
271C5×C22⋊C4—44no—
272C5×C22⋊C4—44no—
273C22⋊Dic5—28no—
274C22⋊Dic5—28no—
275C22⋊Dic5—44no—
276C22⋊Dic5—44no—
277C22⋊Dic5—44no—
278#685—28no—
279#685—44no—
280#685—44no—
281#685—44no—
282#685—44no—
283C4⋊Dic5—28no—
284C4⋊Dic5—44no—
285#683—28no—
286#683—28no—
287#683—28no—
288#683—44no—
289#683—44no—
290C23×Q8—51no—
291C23×D4—51no—
292C23×D4—51no—
293C23×D4C2×D511yescharacteristic
294C24×C4—51no—
295C2×C22⋊Q8—58no—
296C2×C22⋊Q8—108no—
297C2×#121—58no—
298C2×#121—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⋊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×C22⋊C4C2×D511yescharacteristic
321#399—58no—
322#399—58no—
323#398—58no—
324#398—58no—
325#394—58no—
326#394—58no—
327#394—58no—
328#394—58no—
329#394—58no—
330#394C2×D518yescomplemented
331#393—58no—
332#393—58no—
333#381—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—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×C5H(5,𝔽2)12yes—
372C23×C5H(5,𝔽2)12yes—
373C23×C5H(5,𝔽2)12yes—
374C23×C5H(5,𝔽2)12yes—
375C23×C52−1+412yes—
376C23×C52−1+412yes—
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—416no—
393C2×C4×C5—22no—
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—44no—
409C2×C4×C5—44no—
410C2×C4×C5—44no—
411C2×C4×C5—44no—
412C2×C4×C5—44no—
413C22⋊D5—416no—
414C22⋊D5—416no—
415C2×Dic5—28no—
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—416no—
437C2×Dic5—44no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5—44no—
441C2×Dic5—44no—
442C2×Dic5C22×D414yes—
443C2×Dic5C22×D414yes—
444Dic10—416no—
445C25—51no—
446C25C22×D511yescharacteristic
447C25C22×D511yescharacteristic
448C22×Q8—54no—
449C22×Q8—104no—
450C22×Q8—202no—
451C22×Q8—202no—
452C22×D4—24no—
453C22×D4—42no—
454C22×D4—42no—
455C22×D4—54no—
456C22×D4—54no—
457C22×D4—104no—
458C22×D4—104no—
459C22×D4—202no—
460C22×D4—202no—
461C22×D4—202no—
462C22×D4—202no—
463C22×D4C22×D514yes—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—58no—
467C23×C4—54no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—51no—
472C23×C4—51no—
473C23×C4—202no—
474C23×C4—202no—
475C23×C4C22×D511yescharacteristic
476C23×C4C22×D511yescharacteristic
477C23×C4C22×D511yescharacteristic
478C23×C4C22×D511yescharacteristic
479C23×C4C22×D511yescharacteristic
480C22⋊Q8—1032no—
481#121—1032no—
482C2×C4⋊C4—42no—
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⋊C4C22×D514yes—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
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—54no—
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⋊C4—202no—
522C2×C22⋊C4C22×D514yes—
523C2×C22⋊C4C22×D514yes—
524C2×C22⋊C4C22×D514yes—
525C2×C22⋊C4C22×D514yes—
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—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#53414yes—
551C22×C5#53514yes—
552C22×C5#53614yes—
553C22×C5#56214yes—
554C22×C5#56214yes—
555C22×C5#56214yes—
556C22×C5#56214yes—
557C22×C5C23×D411yescharacteristic
558C22×C5C2×H(5,𝔽2)11yescharacteristic
559C22×C5C2×H(5,𝔽2)11yescharacteristic
560C22×C5C2×H(5,𝔽2)11yescharacteristic
561C22×C5C2×H(5,𝔽2)11yescharacteristic
562C22×C5C2×2−1+411yescharacteristic
563C22×C5C2×2−1+411yescharacteristic
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—42no—
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—52no—
598C24—102no—
599C24—102no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24D4×D514yes—
606C24C23×D512yes—
607C24C23×D512yes—
608C24C23×D511yescharacteristic
609C2×Q8—108no—
610C2×Q8—204no—
611C2×Q8—204no—
612C2×Q8—2016no—
613C2×D4—28no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—416no—
617C2×D4—108no—
618C2×D4—108no—
619C2×D4—204no—
620C2×D4—204no—
621C2×D4—204no—
622C2×D4—204no—
623C2×D4—2016no—
624C2×D4—2016no—
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—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—54no—
641C22×C4—54no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—516no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—52no—
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—102no—
669C22×C4—2016no—
670C22×C4—204no—
671C22×C4—204no—
672C22×C4C23×D512yes—
673C22×C4C23×D512yes—
674C22×C4C23×D512yes—
675C22×C4C23×D512yes—
676C22×C4C23×D512yes—
677C4⋊C4—44no—
678C4⋊C4—108no—
679C4⋊C4—108no—
680C4⋊C4—108no—
681C4⋊C4—108no—
682C4⋊C4—204no—
683C4⋊C4—204no—
684C4⋊C4—204no—
685C22⋊C4—28no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—44no—
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—
698C22⋊C4—204no—
699C2×C5—44no—
700C2×C5—82no—
701C2×C5#281618yescomplemented
702C2×C5C2×#53411yescharacteristic
703C2×C5C2×#53511yescharacteristic
704C2×C5C2×#53611yescharacteristic
705C2×C5C2×#56211yescharacteristic
706C2×C5C2×#56211yescharacteristic
707C2×C5C2×#56211yescharacteristic
708C2×C5C2×#56211yescharacteristic
709D5—82no—
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—102no—
738C23—102no—
739C23—102no—
740C23—102no—
741C23—102no—
742C23—102no—
743C23—102no—
744C23—204no—
745C23—204no—
746C23—204no—
747C23—204no—
748C23—204no—
749C23—204no—
750C23—204no—
751C23C2×D4×D514yes—
752C23C2×D4×D512yes—
753C23#414412yes—
754C23#414412yes—
755C23#414412yes—
756C23#414912yes—
757C23#415012yes—
758C23#415012yes—
759C23C24×D511yescharacteristic
760Q8—2016no—
761D4—416no—
762D4—2016no—
763D4—2016no—
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—22no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—54no—
785C2×C4—54no—
786C2×C4—108no—
787C2×C4—108no—
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—102no—
807C2×C4—2016no—
808C2×C4—204no—
809C2×C4—204no—
810C2×C4—204no—
811C2×C4—204no—
812C2×C4—204no—
813C5C2×#281611yescharacteristic, complemented, Sylow
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—416no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—88no—
830C22—202no—
831C22—202no—
832C22—202no—
833C22—202no—
834C22—202no—
835C22—202no—
836C22—202no—
837C22—408no—
838C22#6592614yes—
839C22#6593914yes—
840C22#6595514yes—
841C22#6595514yes—
842C22#6598214yes—
843C22#6600114yes—
844C22#6601814yes—
845C22C22×D4×D511yescharacteristic
846C22C2×#414411yescharacteristic
847C22C2×#414411yescharacteristic
848C22C2×#414411yescharacteristic
849C22C2×#414911yescharacteristic
850C22C2×#415011yescharacteristic
851C22C2×#415011yescharacteristic
852C4—42no—
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—402no—
867C2#1060881718yesdirect product factor
868C2C2×#6592611yescharacteristic
869C2C2×#6593911yescharacteristic
870C2C2×#6595511yescharacteristic
871C2C2×#6595511yescharacteristic
872C2C2×#6598211yescharacteristic
873C2C2×#6600111yescharacteristic
874C2C2×#6601811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#394C2
socleC24×C5C24
prime radicalC22×#4085C2
hypercenterC2×#394D5
hypocenterC5C2×#2816
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#4024C2semidirect
3. C2×C5×#394C2semidirect
4. C2×#65511C2semidirect
5. C2×#65281C2semidirect
6. C2×#65273C2semidirect
7. C2×#65248C2semidirect
8. C2×#65248C2semidirect
9. C2×#65238C2semidirect
10. C2×#65250C2semidirect
11. C2×#65250C2semidirect
12. C2×#65236C2semidirect
13. C2×#65232C2semidirect
14. #10608817C2direct (N × H)
15. C2×#64962C2semidirect
16. C2×#64946C2semidirect
47. C2×#4024C22semidirect
48. C5×#394C22semidirect
50. #65511C22semidirect
58. #65281C22semidirect
59. #65273C22semidirect
60. #65250C22semidirect
61. #65250C22semidirect
62. #65248C22semidirect
63. #65248C22semidirect
64. #65238C22semidirect
65. #65236C22semidirect
66. #65232C22semidirect
67. #64962C22semidirect
68. #64946C22semidirect
171. C2×#394D5semidirect
330. #394C2×D5semidirect
701. C2×C5#2816semidirect
813. C5C2×#2816semidirect
867. C2#10608817direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40852
C22×#40242
C2×C5×#3942
C2×#655112
C2×#652812
C2×#652732
C2×#652482
C2×#652382
C2×#652502
C2×#652362
C2×#652322
#106088172
C2×#649622
C2×#649462
C2×#28165