Finite Group Databasebeta

← C2×#10608186 #12269385

Subgroups — C2×#10608186 #12269385

Order 1280.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4029C211yesmaximal, characteristic, complemented
2C22×#4025C211yesmaximal, characteristic, complemented
3C2×C5×#390C211yesmaximal, characteristic, complemented
4C2×#65512C211yesmaximal, characteristic
5C2×#65511C211yesmaximal, characteristic, complemented
6C2×#65283C211yesmaximal, characteristic, complemented
7C2×#65273C211yesmaximal, characteristic, complemented
8C2×#65245C211yesmaximal, characteristic, complemented
9C2×#65246C211yesmaximal, characteristic, complemented
10C2×#65246C211yesmaximal, characteristic, complemented
11C2×#65233C211yesmaximal, characteristic, complemented
12C2×#65240C211yesmaximal, characteristic, complemented
13C2×#65240C211yesmaximal, characteristic, complemented
14C2×C4×#683C211yesmaximal, characteristic, complemented
15C2×C4×#685C211yesmaximal, characteristic, complemented
16#10608186C2116yesmaximal, direct product factor
17C23×C5×D4C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C42×C5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4029—28no—
47C2×#4029C2218yescomplemented
48C2×#4025—28no—
49C2×#4025C2218yescomplemented
50C5×#390C2218yescomplemented
51#65512C2218yes—
52#65511C2218yescomplemented
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59#65283C2218yescomplemented
60#65273C2218yescomplemented
61#65246C2218yescomplemented
62#65246C2218yescomplemented
63#65245C2218yescomplemented
64#65240C2218yescomplemented
65#65240C2218yescomplemented
66#65233C2218yescomplemented
67C4×#685C2218yescomplemented
68C4×#683C2218yescomplemented
69C2×#2554—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—24no—
85C22×C22⋊D5—24no—
86C22×C22⋊D5—42no—
87C22×C22⋊D5—42no—
88C22×C22⋊D5C2314yes—
89C22×C22⋊D5C2314yes—
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C22×C4×D5—24no—
98C22×C4×D5—24no—
99C22×C4×D5—42no—
100C22×C4×D5C2314yes—
101C2×C5×C4⋊C4—42no—
102C2×C5×C4⋊C4C2314yes—
103C2×C5×C22⋊C4—24no—
104C2×C5×C22⋊C4—24no—
105C2×C5×C22⋊C4—24no—
106C2×C5×C22⋊C4—24no—
107C2×C5×C22⋊C4C2314yes—
108C2×C5×C22⋊C4C2314yes—
109C2×C5×C22⋊C4C2314yes—
110C2×C5×C22⋊C4C2314yes—
111C2×C42×C5—42no—
112C2×C42×C5C2314yes—
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⋊Dic5C2314yes—
120C2×C22⋊Dic5C2314yes—
121C2×C22⋊Dic5C2314yes—
122C2×C22⋊Dic5C2314yes—
123C2×C22⋊Dic5C2314yes—
124C2×C22⋊Dic5C2314yes—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—42no—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×C4⋊Dic5—24no—
134C2×C4⋊Dic5—24no—
135C2×C4⋊Dic5C2314yes—
136C2×C4⋊Dic5C2314yes—
137C2×#683—24no—
138C2×#683—24no—
139C2×#683—42no—
140C2×#683D418yescomplemented
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×C4×Dic5—24no—
146C2×C4×Dic5—24no—
147C2×C4×Dic5—42no—
148C2×C4×Dic5C2314yes—
149C2×C4×Dic5C2314yes—
150C2×C4×Dic5C2314yes—
151#4029—232no—
152#4025—232no—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#126—51no—
160C22×#123—51no—
161#2554—516no—
162C2×#398—51no—
163C2×#396—51no—
164C2×#394—51no—
165C2×#392—51no—
166C2×#390—51no—
167C2×#390—51no—
168C2×#390D511yescharacteristic, complemented
169C2×#388—51no—
170C2×#388—51no—
171C2×#388—51no—
172C2×#386—51no—
173C2×C4×C4⋊C4—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—22no—
188C24×C5—22no—
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×C5C2×D414yes—
217C22×C4×C5#4114yes—
218C22×C4×C5#4114yes—
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—28no—
227C2×C22⋊D5—28no—
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×Dic5C2×D414yes—
251C22×Dic5C2×D414yes—
252C22×Dic5#4114yes—
253C22×Dic5C2412yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C22×Dic5C2412yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C2×C4×D5—28no—
261C2×C4×D5—28no—
262C2×C4×D5—44no—
263C2×C4×D5—416no—
264C5×C4⋊C4—44no—
265C5×C22⋊C4—28no—
266C5×C22⋊C4—28no—
267C5×C22⋊C4—28no—
268C5×C22⋊C4—28no—
269C42×C5—44no—
270C22⋊Dic5—28no—
271C22⋊Dic5—28no—
272C22⋊Dic5—28no—
273C22⋊Dic5—28no—
274C22⋊Dic5—44no—
275C22⋊Dic5—44no—
276#685—28no—
277#685—28no—
278#685—28no—
279#685—44no—
280C4⋊Dic5—28no—
281C4⋊Dic5—28no—
282#683—28no—
283#683—28no—
284#683—44no—
285#683C2×D4116yescomplemented
286C4×Dic5—28no—
287C4×Dic5—28no—
288C4×Dic5—44no—
289C23×D4—51no—
290C23×D4—51no—
291C23×D4C2×D511yescharacteristic
292C24×C4—51no—
293C2×#126—58no—
294C2×#126—108no—
295C2×#123—58no—
296C2×#123—108no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4C2×D511yescharacteristic
304C22×C22⋊C4—51no—
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⋊C4C2×D511yescharacteristic
315C22×C22⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42—51no—
320C22×C42—51no—
321C22×C42C2×D511yescharacteristic
322#398—58no—
323#396—58no—
324#394—58no—
325#392—58no—
326#390—58no—
327#390—58no—
328#390C2×D518yescomplemented
329#388—58no—
330#388—58no—
331#388—58no—
332#386—58no—
333C4×C4⋊C4—58no—
334C4×C22⋊C4—58no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
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—44no—
356C23×C5—44no—
357C23×C5—44no—
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×#4112yes—
371C23×C5C2×#4112yes—
372C23×C5C2×#4112yes—
373C23×C5C2×#4112yes—
374C23×C5H(5,𝔽2)12yes—
375C23×C5H(5,𝔽2)12yes—
376C23×C5C2511yescharacteristic
377C22×D5—28no—
378C22×D5—28no—
379C22×D5—28no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5C2×#4114yes—
391C5×D4—416no—
392C2×C4×C5—28no—
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—44no—
408C2×C4×C5—44no—
409C2×C4×C5C22×D414yes—
410C2×C4×C5C2×#4114yes—
411C2×C4×C5C2×#4114yes—
412C22⋊D5—416no—
413C22⋊D5—416no—
414C2×Dic5—28no—
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—44no—
436C2×Dic5—44no—
437C2×Dic5—44no—
438C2×Dic5—44no—
439C2×Dic5C22×D414yes—
440C2×Dic5C22×D414yes—
441C2×Dic5C2×#4114yes—
442C4×D5—416no—
443C25—51no—
444C25C22×D511yescharacteristic
445C25C22×D511yescharacteristic
446C22×D4—24no—
447C22×D4—42no—
448C22×D4—42no—
449C22×D4—54no—
450C22×D4—54no—
451C22×D4—104no—
452C22×D4—104no—
453C22×D4—104no—
454C22×D4—104no—
455C22×D4—202no—
456C22×D4—202no—
457C22×D4C22×D514yes—
458C23×C4—51no—
459C23×C4—51no—
460C23×C4—51no—
461C23×C4—51no—
462C23×C4—51no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—54no—
466C23×C4—104no—
467C23×C4—104no—
468C23×C4—202no—
469C23×C4C22×D511yescharacteristic
470C23×C4C22×D511yescharacteristic
471C23×C4C22×D511yescharacteristic
472C23×C4C22×D511yescharacteristic
473C23×C4C22×D511yescharacteristic
474#126—1032no—
475#123—1032no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—58no—
478C2×C4⋊C4—54no—
479C2×C4⋊C4—54no—
480C2×C4⋊C4—54no—
481C2×C4⋊C4—54no—
482C2×C4⋊C4—54no—
483C2×C4⋊C4—54no—
484C2×C4⋊C4—104no—
485C2×C4⋊C4—104no—
486C2×C4⋊C4—104no—
487C2×C4⋊C4—104no—
488C2×C4⋊C4—202no—
489C2×C4⋊C4C22×D514yes—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—54no—
495C2×C22⋊C4—54no—
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—104no—
505C2×C22⋊C4—104no—
506C2×C22⋊C4—104no—
507C2×C22⋊C4—104no—
508C2×C22⋊C4—104no—
509C2×C22⋊C4—104no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—202no—
512C2×C22⋊C4—202no—
513C2×C22⋊C4—202no—
514C2×C22⋊C4C22×D514yes—
515C2×C22⋊C4C22×D514yes—
516C2×C22⋊C4C22×D514yes—
517C2×C22⋊C4C22×D514yes—
518C2×C42—42no—
519C2×C42—54no—
520C2×C42—54no—
521C2×C42—54no—
522C2×C42—104no—
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—
532C22×C5—42no—
533C22×C5—42no—
534C22×C5—42no—
535C22×C5—42no—
536C22×C5—42no—
537C22×C5—42no—
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—88no—
547C22×C5—88no—
548C22×C5#52914yes—
549C22×C5#53214yes—
550C22×C5#53814yes—
551C22×C5#54614yes—
552C22×C5#55014yes—
553C22×C5#55114yes—
554C22×C5#55314yes—
555C22×C5C23×D411yescharacteristic
556C22×C5C22×#4111yescharacteristic
557C22×C5C22×#4111yescharacteristic
558C22×C5C22×#4111yescharacteristic
559C22×C5C22×#4111yescharacteristic
560C22×C5C2×H(5,𝔽2)11yescharacteristic
561C22×C5C2×H(5,𝔽2)11yescharacteristic
562C2×D5—24no—
563C2×D5—24no—
564C2×D5—24no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—42no—
569C2×D5—416no—
570C4×C5—24no—
571C4×C5—24no—
572C4×C5—24no—
573C4×C5—42no—
574C4×C5—42no—
575Dic5—24no—
576Dic5—24no—
577Dic5—24no—
578Dic5—42no—
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582C24—22no—
583C24—22no—
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—54no—
597C24—52no—
598C24—102no—
599C24—102no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24C23×D512yes—
605C24C23×D512yes—
606C24C23×D511yescharacteristic
607C2×D4—28no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—416no—
611C2×D4—108no—
612C2×D4—108no—
613C2×D4—108no—
614C2×D4—108no—
615C2×D4—204no—
616C2×D4—204no—
617C2×D4—2016no—
618C2×D4—2016no—
619C22×C4—22no—
620C22×C4—22no—
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—54no—
632C22×C4—54no—
633C22×C4—54no—
634C22×C4—52no—
635C22×C4—52no—
636C22×C4—52no—
637C22×C4—52no—
638C22×C4—52no—
639C22×C4—52no—
640C22×C4—52no—
641C22×C4—108no—
642C22×C4—102no—
643C22×C4—102no—
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—108no—
661C22×C4—204no—
662C22×C4—2016no—
663C22×C4#70914yes—
664C22×C4D4×D514yes—
665C22×C4#71114yes—
666C22×C4C23×D512yes—
667C22×C4C23×D512yes—
668C22×C4C23×D512yes—
669C22×C4C23×D512yes—
670C22×C4C23×D512yes—
671C4⋊C4—44no—
672C4⋊C4—516no—
673C4⋊C4—108no—
674C4⋊C4—108no—
675C4⋊C4—108no—
676C4⋊C4—108no—
677C4⋊C4—204no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—28no—
682C22⋊C4—108no—
683C22⋊C4—108no—
684C22⋊C4—108no—
685C22⋊C4—108no—
686C22⋊C4—108no—
687C22⋊C4—108no—
688C22⋊C4—108no—
689C22⋊C4—204no—
690C22⋊C4—204no—
691C22⋊C4—204no—
692C42—44no—
693C42—108no—
694C42—108no—
695C42—204no—
696C2×C5—82no—
697C2×C5—82no—
698C2×C5#255418yescomplemented
699C2×C5C2×#52911yescharacteristic
700C2×C5C2×#53211yescharacteristic
701C2×C5C2×#53811yescharacteristic
702C2×C5C2×#54611yescharacteristic
703C2×C5C2×#55011yescharacteristic
704C2×C5C2×#55111yescharacteristic
705C2×C5C2×#55311yescharacteristic
706D5—44no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—54no—
736C23—108no—
737C23—108no—
738C23—108no—
739C23—102no—
740C23—102no—
741C23—102no—
742C23—102no—
743C23—102no—
744C23—102no—
745C23—204no—
746C23—204no—
747C23—204no—
748C23—204no—
749C23C2×#70912yes—
750C23C2×D4×D512yes—
751C23C2×#71112yes—
752C23#414412yes—
753C23#414412yes—
754C23D5×#4112yes—
755C23D5×#4112yes—
756C23C24×D511yescharacteristic
757D4—416no—
758D4—2016no—
759D4—2016no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—22no—
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—54no—
778C2×C4—54no—
779C2×C4—54no—
780C2×C4—108no—
781C2×C4—108no—
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—2016no—
802C2×C4—204no—
803C2×C4—204no—
804C2×C4—204no—
805C2×C4—204no—
806C2×C4C2×#70914yes—
807C2×C4C2×D4×D514yes—
808C2×C4C2×#71114yes—
809C5C2×#255411yescharacteristic, complemented, Sylow
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—88no—
825C22—88no—
826C22—104no—
827C22—104no—
828C22—104no—
829C22—2016no—
830C22—202no—
831C22—202no—
832C22—202no—
833C22—202no—
834C22#6582814yes—
835C22#6588214yes—
836C22#6589114yes—
837C22#6593514yes—
838C22#6594414yes—
839C22#6601314yes—
840C22#6605214yes—
841C22C22×#70911yescharacteristic
842C22C22×D4×D511yescharacteristic
843C22C22×#71111yescharacteristic
844C22C2×#414411yescharacteristic
845C22C2×#414411yescharacteristic
846C22C2×D5×#4111yescharacteristic
847C22C2×D5×#4111yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—104no—
854C4—104no—
855C4—104no—
856C4—202no—
857C4—202no—
858C4—202no—
859C4—202no—
860C2—82no—
861C2—82no—
862C2—204no—
863C2#1060818618yesdirect product factor
864C2C2×#6582811yescharacteristic
865C2C2×#6589111yescharacteristic
866C2C2×#6588211yescharacteristic
867C2C2×#6593511yescharacteristic
868C2C2×#6594411yescharacteristic
869C2C2×#6601311yescharacteristic
870C2C2×#6605211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#390C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC2×#390D5
hypocenterC5C2×#2554
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#4029C2semidirect
2. C22×#4025C2semidirect
3. C2×C5×#390C2semidirect
5. C2×#65511C2semidirect
6. C2×#65283C2semidirect
7. C2×#65273C2semidirect
8. C2×#65245C2semidirect
9. C2×#65246C2semidirect
10. C2×#65246C2semidirect
11. C2×#65233C2semidirect
12. C2×#65240C2semidirect
13. C2×#65240C2semidirect
14. C2×C4×#683C2semidirect
15. C2×C4×#685C2semidirect
16. #10608186C2direct (N × H)
47. C2×#4029C22semidirect
49. C2×#4025C22semidirect
50. C5×#390C22semidirect
52. #65511C22semidirect
59. #65283C22semidirect
60. #65273C22semidirect
61. #65246C22semidirect
62. #65246C22semidirect
63. #65245C22semidirect
64. #65240C22semidirect
65. #65240C22semidirect
66. #65233C22semidirect
67. C4×#685C22semidirect
68. C4×#683C22semidirect
140. C2×#683D4semidirect
168. C2×#390D5semidirect
285. #683C2×D4semidirect
328. #390C2×D5semidirect
698. C2×C5#2554semidirect
809. C5C2×#2554semidirect
863. C2#10608186direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40292
C22×#40252
C2×C5×#3902
C2×#655122
C2×#655112
C2×#652832
C2×#652732
C2×#652452
C2×#652462
C2×#652332
C2×#652402
C2×C4×#6832
C2×C4×#6852
#106081862
C2×#25545