Finite Group Databasebeta

← C2×#10609075 #12266034

Subgroups — C2×#10609075 #12266034

Order 1280.

3002 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×#4044C211yesmaximal, characteristic, complemented
2C22×#4031C211yesmaximal, characteristic, complemented
3C2×C5×#396C211yesmaximal, characteristic, complemented
4C2×#65283C211yesmaximal, characteristic, complemented
5C2×#65280C211yesmaximal, characteristic, complemented
6C2×#65268C211yesmaximal, characteristic, complemented
7C2×#65277C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
9C2×#65248C211yesmaximal, characteristic, complemented
10C2×#65249C211yesmaximal, characteristic
11C2×#65250C211yesmaximal, characteristic, complemented
12C2×#65246C211yesmaximal, characteristic, complemented
13C2×#65240C211yesmaximal, characteristic, complemented
14#10609075C2116yesmaximal, direct product factor
15C2×#64962C211yesmaximal, characteristic, complemented
16C2×#64959C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C23×Dic10C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C2×#4044—28no—
47C2×#4044C2218yescomplemented
48C2×#4031—28no—
49C2×#4031C2218yescomplemented
50C5×#396C2218yescomplemented
51C2×C5×#95C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65283C2218yescomplemented
58#65280C2218yescomplemented
59#65277C2218yescomplemented
60#65268C2218yescomplemented
61C4⋊C4×Dic5C2218yescomplemented
62#65250C2218yescomplemented
63#65249C2218yes—
64#65248C2218yescomplemented
65#65246C2218yescomplemented
66#65240C2218yescomplemented
67#64962C2218yescomplemented
68#64959C2218yescomplemented
69C2×#2662—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C22×C22⋊D5—24no—
80C22×C22⋊D5—24no—
81C22×C22⋊D5—42no—
82C22×C22⋊D5—42no—
83C22×C22⋊D5—42no—
84C22×C22⋊D5—42no—
85C22×C22⋊D5C2314yes—
86C22×C22⋊D5C2314yes—
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C22×D20—24no—
94C22×D20—42no—
95C22×D20—42no—
96C22×D20C2314yes—
97C22×Dic10—24no—
98C22×Dic10—42no—
99C22×Dic10—42no—
100C22×Dic10C2314yes—
101C2×C5×C4⋊C4—24no—
102C2×C5×C4⋊C4—24no—
103C2×C5×C4⋊C4—42no—
104C2×C5×C4⋊C4C2314yes—
105C2×C5×C4⋊C4C2314yes—
106C2×C5×C4⋊C4C2314yes—
107C2×C5×C22⋊C4—24no—
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4—42no—
110C2×C5×C22⋊C4C2314yes—
111C2×C5×C22⋊C4C2314yes—
112C2×C5×C22⋊C4C2314yes—
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5—42no—
115C2×C22⋊Dic5C2314yes—
116C2×C22⋊Dic5C2314yes—
117C2×#685—24no—
118C2×#685—24no—
119C2×#685—24no—
120C2×#685—24no—
121C2×#685—24no—
122C2×#685—24no—
123C2×#685—42no—
124C2×#685—42no—
125C2×#685—42no—
126C2×#685—42no—
127C2×#685C2314yes—
128C2×#685C2314yes—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×C4⋊Dic5—24no—
138C2×C4⋊Dic5—24no—
139C2×C4⋊Dic5C2314yes—
140C2×C4⋊Dic5C2314yes—
141C2×#683—24no—
142C2×#683—42no—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×C4×Dic5—42no—
146C2×C4×Dic5—42no—
147C2×C4×Dic5D418yescomplemented
148C2×C4×Dic5C2314yes—
149C2×C4×Dic5C2314yes—
150C2×C4×Dic5C2314yes—
151#4044—232no—
152#4031—232no—
153C5×#95C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#126—51no—
160C22×#124—51no—
161#2662—516no—
162C2×#396—51no—
163C2×#396D511yescharacteristic, complemented
164C2×#395—51no—
165C2×#394—51no—
166C2×#394—51no—
167C2×#394—51no—
168C2×#393—51no—
169C2×#392—51no—
170C2×#390—51no—
171C2×#390—51no—
172C2×#388—51no—
173C2×#388—51no—
174C2×C4×C4⋊C4—51no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5—22no—
182C24×C5C2412yes—
183C24×C5C2411yescharacteristic
184C23×D5—22no—
185C23×D5—22no—
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—22no—
189C23×D5—22no—
190C23×D5—22no—
191C23×D5—22no—
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
198C23×D5C2412yes—
199C23×D5C2412yes—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
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×C5C2412yes—
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×Dic5C2×D414yes—
248C22×Dic5C2×D414yes—
249C22×Dic5#4114yes—
250C22×Dic5C2412yes—
251C22×Dic5C2412yes—
252C22×Dic5C2412yes—
253C22×Dic5C2412yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C2×D20—28no—
257C2×D20—44no—
258C2×D20—44no—
259C2×D20—416no—
260C2×Dic10—28no—
261C2×Dic10—44no—
262C2×Dic10—44no—
263C2×Dic10—416no—
264C5×C4⋊C4—28no—
265C5×C4⋊C4—28no—
266C5×C4⋊C4—44no—
267C5×C22⋊C4—28no—
268C5×C22⋊C4—28no—
269C5×C22⋊C4—44no—
270C22⋊Dic5—28no—
271C22⋊Dic5—44no—
272#685—28no—
273#685—28no—
274#685—28no—
275#685—28no—
276#685—28no—
277#685—28no—
278#685—44no—
279#685—44no—
280#685—44no—
281#685—44no—
282C4⋊Dic5—28no—
283C4⋊Dic5—28no—
284#683—28no—
285#683—44no—
286C4×Dic5—44no—
287C4×Dic5—44no—
288C4×Dic5C2×D4116yescomplemented
289C23×Q8—51no—
290C23×D4—51no—
291C23×D4—51no—
292C23×D4—51no—
293C2×#126—58no—
294C2×#126—108no—
295C2×#124—58no—
296C2×#124—108no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4C2×D511yescharacteristic
302C22×C4⋊C4C2×D511yescharacteristic
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⋊C4—51no—
315C22×C22⋊C4—51no—
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C22⋊C4C2×D511yescharacteristic
319C22×C42—51no—
320C22×C42—51no—
321C22×C42—51no—
322#396—58no—
323#396C2×D518yescomplemented
324#395—58no—
325#394—58no—
326#394—58no—
327#394—58no—
328#393—58no—
329#392—58no—
330#390—58no—
331#390—58no—
332#388—58no—
333#388—58no—
334C4×C4⋊C4—58no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95C2×D511yescharacteristic
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—44no—
349C23×C5—44no—
350C23×C5—44no—
351C23×C5—44no—
352C23×C5—44no—
353C23×C5—44no—
354C23×C5—44no—
355C23×C5C22×D412yes—
356C23×C5C2×#4112yes—
357C23×C5C2×#4112yes—
358C23×C5H(5,𝔽2)12yes—
359C23×C5H(5,𝔽2)12yes—
360C23×C5H(5,𝔽2)12yes—
361C23×C52−1+412yes—
362C23×C5C2511yescharacteristic
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—22no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5—22no—
370C22×D5—22no—
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—44no—
378C22×D5—44no—
379C22×D5—44no—
380C22×D5—44no—
381C22×D5—44no—
382C22×D5—44no—
383C22×D5—44no—
384C22×D5—44no—
385C22×D5—44no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5—44no—
391C2×C4×C5—28no—
392C2×C4×C5—28no—
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—22no—
409C2×C4×C5—44no—
410C2×C4×C5—44no—
411C2×C4×C5—44no—
412C2×C4×C5—44no—
413C2×C4×C5C22×D414yes—
414C2×C4×C5C2×#4114yes—
415C22⋊D5—416no—
416C22⋊D5—416no—
417C2×Dic5—28no—
418C2×Dic5—28no—
419C2×Dic5—28no—
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×Dic5C22×D414yes—
439C2×Dic5C22×D414yes—
440C2×Dic5C2×#4114yes—
441D20—416no—
442Dic10—416no—
443C25—51no—
444C25—51no—
445C25C22×D511yescharacteristic
446C22×Q8—54no—
447C22×Q8—104no—
448C22×Q8—202no—
449C22×Q8—202no—
450C22×D4—54no—
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×D4—202no—
460C22×D4—202no—
461C22×D4—202no—
462C23×C4—51no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4C22×D511yescharacteristic
469C23×C4C22×D511yescharacteristic
470C23×C4C22×D511yescharacteristic
471C23×C4C22×D511yescharacteristic
472C23×C4C22×D511yescharacteristic
473C23×C4C22×D511yescharacteristic
474#126—1032no—
475#124—1032no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—54no—
480C2×C4⋊C4—54no—
481C2×C4⋊C4—54no—
482C2×C4⋊C4—54no—
483C2×C4⋊C4—104no—
484C2×C4⋊C4—104no—
485C2×C4⋊C4—104no—
486C2×C4⋊C4—202no—
487C2×C4⋊C4C22×D514yes—
488C2×C4⋊C4C22×D514yes—
489C2×C4⋊C4C22×D514yes—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—54no—
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—54no—
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—104no—
512C2×C22⋊C4—202no—
513C2×C22⋊C4—202no—
514C2×C22⋊C4—202no—
515C2×C22⋊C4—202no—
516C2×C22⋊C4—202no—
517C2×C22⋊C4C22×D514yes—
518C2×C22⋊C4C22×D514yes—
519C2×C22⋊C4C22×D514yes—
520C2×C42—58no—
521C2×C42—54no—
522C2×C42—54no—
523C2×C42—54no—
524C2×C42—202no—
525C2×C42—202no—
526#95—54no—
527#95—54no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95C22×D514yes—
532C22×C5—42no—
533C22×C5—42no—
534C22×C5—42no—
535C22×C5—42no—
536C22×C5—42no—
537C22×C5—42no—
538C22×C5—42no—
539C22×C5—88no—
540C22×C5#53214yes—
541C22×C5#53514yes—
542C22×C5#53714yes—
543C22×C5#53814yes—
544C22×C5#53814yes—
545C22×C5#54214yes—
546C22×C5#54214yes—
547C22×C5C23×D411yescharacteristic
548C22×C5C22×#4111yescharacteristic
549C22×C5C22×#4111yescharacteristic
550C22×C5C2×H(5,𝔽2)11yescharacteristic
551C22×C5C2×H(5,𝔽2)11yescharacteristic
552C22×C5C2×H(5,𝔽2)11yescharacteristic
553C22×C5C2×2−1+411yescharacteristic
554C2×D5—42no—
555C2×D5—42no—
556C2×D5—42no—
557C2×D5—42no—
558C2×D5—42no—
559C2×D5—42no—
560C2×D5—42no—
561C2×D5—42no—
562C2×D5—42no—
563C2×D5—42no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—88no—
569C2×D5—88no—
570C4×C5—24no—
571C4×C5—24no—
572C4×C5—42no—
573C4×C5—42no—
574C4×C5—42no—
575C4×C5—42no—
576Dic5—24no—
577Dic5—24no—
578Dic5—24no—
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—52no—
590C24—52no—
591C24—102no—
592C24—102no—
593C24—102no—
594C24—102no—
595C24—102no—
596C24—102no—
597C24—102no—
598C24—102no—
599C24—102no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24C23×D512yes—
606C24C23×D511yescharacteristic
607C2×Q8—108no—
608C2×Q8—204no—
609C2×Q8—204no—
610C2×Q8—2016no—
611C2×D4—108no—
612C2×D4—108no—
613C2×D4—108no—
614C2×D4—204no—
615C2×D4—204no—
616C2×D4—2016no—
617C2×D4—204no—
618C2×D4—204no—
619C2×D4—204no—
620C2×D4—204no—
621C2×D4—2016no—
622C2×D4—2016no—
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—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—54no—
640C22×C4—54no—
641C22×C4—54no—
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×C4D4×D514yes—
664C22×C4#71114yes—
665C22×C4C23×D512yes—
666C22×C4C23×D512yes—
667C22×C4C23×D512yes—
668C22×C4C23×D512yes—
669C22×C4C23×D512yes—
670C22×C4C23×D512yes—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—44no—
674C4⋊C4—108no—
675C4⋊C4—108no—
676C4⋊C4—108no—
677C4⋊C4—204no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—44no—
681C22⋊C4—108no—
682C22⋊C4—108no—
683C22⋊C4—108no—
684C22⋊C4—108no—
685C22⋊C4—108no—
686C22⋊C4—108no—
687C22⋊C4—108no—
688C22⋊C4—204no—
689C22⋊C4—204no—
690C22⋊C4—204no—
691C22⋊C4—204no—
692C22⋊C4—204no—
693C42—516no—
694C42—204no—
695C42—204no—
696C2×C5—82no—
697C2×C5#266218yescomplemented
698C2×C5C2×#53211yescharacteristic
699C2×C5C2×#53511yescharacteristic
700C2×C5C2×#53711yescharacteristic
701C2×C5C2×#53811yescharacteristic
702C2×C5C2×#53811yescharacteristic
703C2×C5C2×#54211yescharacteristic
704C2×C5C2×#54211yescharacteristic
705D5—82no—
706D5—82no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—102no—
722C23—102no—
723C23—102no—
724C23—102no—
725C23—102no—
726C23—102no—
727C23—102no—
728C23—102no—
729C23—102no—
730C23—102no—
731C23—102no—
732C23—102no—
733C23—102no—
734C23—102no—
735C23—204no—
736C23—204no—
737C23—204no—
738C23—204no—
739C23—204no—
740C23—204no—
741C23—204no—
742C23—204no—
743C23—204no—
744C23—204no—
745C23—204no—
746C23—204no—
747C23—204no—
748C23—204no—
749C23C2×D4×D512yes—
750C23C2×#71112yes—
751C23#414412yes—
752C23#414712yes—
753C23D5×#4112yes—
754C23#414912yes—
755C23#414912yes—
756C23C24×D511yescharacteristic
757Q8—2016no—
758D4—2016no—
759D4—2016no—
760D4—2016no—
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—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—54no—
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—108no—
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—204no—
805C2×C4—204no—
806C2×C4—204no—
807C2×C4C2×D4×D514yes—
808C2×C4C2×#71114yes—
809C5C2×#266211yescharacteristic, complemented, Sylow
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—88no—
818C22—202no—
819C22—202no—
820C22—202no—
821C22—202no—
822C22—202no—
823C22—202no—
824C22—202no—
825C22—202no—
826C22—202no—
827C22—202no—
828C22—202no—
829C22—202no—
830C22—202no—
831C22—202no—
832C22—408no—
833C22—408no—
834C22#6593014yes—
835C22#6594114yes—
836C22#6595114yes—
837C22#6596314yes—
838C22#6597414yes—
839C22#6597714yes—
840C22#6603814yes—
841C22C22×D4×D511yescharacteristic
842C22C22×#71111yescharacteristic
843C22C2×#414411yescharacteristic
844C22C2×#414711yescharacteristic
845C22C2×D5×#4111yescharacteristic
846C22C2×#414911yescharacteristic
847C22C2×#414911yescharacteristic
848C4—24no—
849C4—24no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—104no—
855C4—104no—
856C4—104no—
857C4—202no—
858C4—202no—
859C4—202no—
860C2—82no—
861C2—402no—
862C2—402no—
863C2#1060907518yesdirect product factor
864C2C2×#6593011yescharacteristic
865C2C2×#6594111yescharacteristic
866C2C2×#6595111yescharacteristic
867C2C2×#6597711yescharacteristic
868C2C2×#6597411yescharacteristic
869C2C2×#6596311yescharacteristic
870C2C2×#6603811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#396C2
socleC24×C5C24
prime radicalC2×#65249C2
hypercenterC2×#396D5
hypocenterC5C2×#2662
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#4044C2semidirect
2. C22×#4031C2semidirect
3. C2×C5×#396C2semidirect
4. C2×#65283C2semidirect
5. C2×#65280C2semidirect
6. C2×#65268C2semidirect
7. C2×#65277C2semidirect
8. C2×C4⋊C4×Dic5C2semidirect
9. C2×#65248C2semidirect
11. C2×#65250C2semidirect
12. C2×#65246C2semidirect
13. C2×#65240C2semidirect
14. #10609075C2direct (N × H)
15. C2×#64962C2semidirect
16. C2×#64959C2semidirect
47. C2×#4044C22semidirect
49. C2×#4031C22semidirect
50. C5×#396C22semidirect
57. #65283C22semidirect
58. #65280C22semidirect
59. #65277C22semidirect
60. #65268C22semidirect
61. C4⋊C4×Dic5C22semidirect
62. #65250C22semidirect
64. #65248C22semidirect
65. #65246C22semidirect
66. #65240C22semidirect
67. #64962C22semidirect
68. #64959C22semidirect
147. C2×C4×Dic5D4semidirect
163. C2×#396D5semidirect
288. C4×Dic5C2×D4semidirect
323. #396C2×D5semidirect
697. C2×C5#2662semidirect
809. C5C2×#2662semidirect
863. C2#10609075direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40442
C22×#40312
C2×C5×#3962
C2×#652832
C2×#652802
C2×#652682
C2×#652772
C2×C4⋊C4×Dic52
C2×#652482
C2×#652492
C2×#652502
C2×#652462
C2×#652402
#106090752
C2×#649622
C2×#649592
C2×#26625