Finite Group Databasebeta

← C2×#10607230 #12267548

Subgroups — C2×#10607230 #12267548

Order 1280.

3678 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4042C211yesmaximal, characteristic, complemented
2C22×#4030C211yesmaximal, characteristic
3C22×#4031C211yesmaximal, characteristic, complemented
4C22×C4×Dic10C211yesmaximal, characteristic, complemented
5C2×C5×#388C211yesmaximal, characteristic, complemented
6C2×#65283C211yesmaximal, characteristic, complemented
7C2×#65237C211yesmaximal, characteristic, complemented
8C2×#65250C211yesmaximal, characteristic, complemented
9C2×#65246C211yesmaximal, characteristic, complemented
10C2×#65246C211yesmaximal, characteristic, complemented
11C2×#65228C211yesmaximal, characteristic, complemented
12#10607230C2116yesmaximal, direct product factor
13C2×#64961C211yesmaximal, characteristic, complemented
14C2×#64936C211yesmaximal, characteristic, complemented
15C2×#64958C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×Dic10C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C42×C5C2211yescharacteristic
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×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C22×C4×Dic5C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C2×#4042—28no—
49C2×#4042C2218yescomplemented
50C2×#4031—28no—
51C2×#4031C2218yescomplemented
52C2×#4030—28no—
53C2×#4030C2218yes—
54C2×C4×Dic10—28no—
55C2×C4×Dic10C2218yescomplemented
56C5×#388C2218yescomplemented
57C2×C5×#95C2211yescharacteristic
58C2×C5×#95C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65283C2218yescomplemented
62#65250C2218yescomplemented
63#65246C2218yescomplemented
64#65246C2218yescomplemented
65#65237C2218yescomplemented
66#65228C2218yescomplemented
67#64961C2218yescomplemented
68#64958C2218yescomplemented
69#64955C2218yescomplemented
70#64936C2218yescomplemented
71C2×#2426—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—24no—
82C22×C22⋊D5—24no—
83C22×C22⋊D5—24no—
84C22×C22⋊D5—24no—
85C22×C22⋊D5—24no—
86C22×C22⋊D5—42no—
87C22×C22⋊D5C2314yes—
88C22×C22⋊D5C2314yes—
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C22×D20—24no—
96C22×D20—24no—
97C22×D20—42no—
98C22×D20C2314yes—
99C22×C4×D5—24no—
100C22×C4×D5—24no—
101C22×C4×D5—24no—
102C22×C4×D5C2314yes—
103C22×Dic10—24no—
104C22×Dic10—24no—
105C22×Dic10D418yescomplemented
106C22×Dic10C2314yes—
107C2×C5×C4⋊C4—24no—
108C2×C5×C4⋊C4C2314yes—
109C2×C5×C22⋊C4—24no—
110C2×C5×C22⋊C4—24no—
111C2×C5×C22⋊C4—24no—
112C2×C5×C22⋊C4C2314yes—
113C2×C5×C22⋊C4C2314yes—
114C2×C5×C22⋊C4C2314yes—
115C2×C42×C5—24no—
116C2×C42×C5C2314yes—
117C2×C22⋊Dic5—24no—
118C2×C22⋊Dic5—42no—
119C2×C22⋊Dic5C2314yes—
120C2×C22⋊Dic5C2314yes—
121C2×#685—24no—
122C2×#685—24no—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—42no—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×C4⋊Dic5—24no—
140C2×C4⋊Dic5—42no—
141C2×C4⋊Dic5C2314yes—
142C2×C4⋊Dic5C2314yes—
143C2×#683—24no—
144C2×#683—24no—
145C2×#683—24no—
146C2×#683—42no—
147C2×#683D418yes—
148C2×#683C2314yes—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×C4×Dic5—24no—
154C2×C4×Dic5—24no—
155C2×C4×Dic5—24no—
156C2×C4×Dic5C2314yes—
157C2×C4×Dic5C2314yes—
158C2×C4×Dic5C2314yes—
159#4042—232no—
160#4031—232no—
161#4030—232no—
162C4×Dic10—232no—
163C5×#95C2314yes—
164C5×#95C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#124—51no—
168C22×C22⋊Q8—51no—
169C22×#121—51no—
170C22×C4×Q8—51no—
171#2426—516no—
172C2×#396—51no—
173C2×#396—51no—
174C2×#394—51no—
175C2×#394—51no—
176C2×#390—51no—
177C2×#390—51no—
178C2×#390—51no—
179C2×#389—51no—
180C2×#388—51no—
181C2×#388D511yescharacteristic, complemented
182C2×C4×C22⋊C4—51no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5—22no—
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×D5—22no—
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5—22no—
205C23×D5#4114yes—
206C23×D5C2412yes—
207C23×D5C2412yes—
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×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5C2×D414yes—
224C22×C4×C5C2×D414yes—
225C22×C4×C5#4114yes—
226C22×C4×C5C2412yes—
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—28no—
236C2×C22⋊D5—28no—
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×Dic5C2×D414yes—
254C22×Dic5C2×D414yes—
255C22×Dic5C2×D414yes—
256C22×Dic5C2×D414yes—
257C22×Dic5#4114yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C2×D20—28no—
265C2×D20—28no—
266C2×D20—44no—
267C2×D20—416no—
268C2×C4×D5—28no—
269C2×C4×D5—28no—
270C2×C4×D5—28no—
271C2×C4×D5—416no—
272C2×Dic10—232no—
273C2×Dic10—28no—
274C2×Dic10—28no—
275C2×Dic10C2×D4116yescomplemented
276C5×C4⋊C4—28no—
277C5×C22⋊C4—28no—
278C5×C22⋊C4—28no—
279C5×C22⋊C4—28no—
280C42×C5—28no—
281C22⋊Dic5—28no—
282C22⋊Dic5—44no—
283#685—28no—
284#685—28no—
285#685—28no—
286#685—28no—
287#685—28no—
288#685—28no—
289#685—28no—
290#685—28no—
291#685—44no—
292C4⋊Dic5—28no—
293C4⋊Dic5—44no—
294#683—28no—
295#683—28no—
296#683—28no—
297#683—44no—
298#683C2×D4116yes—
299C4×Dic5—28no—
300C4×Dic5—28no—
301C4×Dic5—28no—
302C23×Q8—51no—
303C23×D4—51no—
304C23×D4—51no—
305C23×D4—51no—
306C24×C4—51no—
307C2×#124—58no—
308C2×#124—108no—
309C2×C22⋊Q8—58no—
310C2×C22⋊Q8—108no—
311C2×#121—58no—
312C2×#121—108no—
313C2×C4×Q8—58no—
314C2×C4×Q8—108no—
315C22×C4⋊C4—51no—
316C22×C4⋊C4—51no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4C2×D511yescharacteristic
323C22×C22⋊C4—51no—
324C22×C22⋊C4—51no—
325C22×C22⋊C4—51no—
326C22×C22⋊C4—51no—
327C22×C22⋊C4—51no—
328C22×C22⋊C4—51no—
329C22×C22⋊C4—51no—
330C22×C22⋊C4—51no—
331C22×C22⋊C4—51no—
332C22×C22⋊C4—51no—
333C22×C22⋊C4—51no—
334C22×C22⋊C4C2×D511yescharacteristic
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C42—51no—
338C22×C42—51no—
339C22×C42—51no—
340C22×C42C2×D511yescharacteristic
341#396—58no—
342#396—58no—
343#394—58no—
344#394—58no—
345#390—58no—
346#390—58no—
347#390—58no—
348#389—58no—
349#388—58no—
350#388C2×D518yescomplemented
351C4×C22⋊C4—58no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95C2×D511yescharacteristic
355C2×#95C2×D511yescharacteristic
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—44no—
364C23×C5—44no—
365C23×C5—44no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5C22×D412yes—
371C23×C5C22×D412yes—
372C23×C5C2×#4112yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5H(5,𝔽2)12yes—
376C23×C52−1+412yes—
377C23×C5C2511yescharacteristic
378C22×D5—28no—
379C22×D5—28no—
380C22×D5—28no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—22no—
391C22×D5—22no—
392C22×D5—22no—
393C22×D5—22no—
394C22×D5—44no—
395C22×D5—44no—
396C22×D5—44no—
397C22×D5—44no—
398C22×D5—44no—
399C22×D5—44no—
400C22×D5—44no—
401C22×D5—44no—
402C22×D5—44no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5C2×#4114yes—
406C2×C4×C5—28no—
407C2×C4×C5—28no—
408C2×C4×C5—28no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—44no—
425C2×C4×C5—44no—
426C2×C4×C5—44no—
427C2×C4×C5C22×D414yes—
428C2×C4×C5C22×D414yes—
429C2×C4×C5C2×#4114yes—
430C22⋊D5—416no—
431C22⋊D5—416no—
432C2×Dic5—28no—
433C2×Dic5—28no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—22no—
441C2×Dic5—22no—
442C2×Dic5—22no—
443C2×Dic5—22no—
444C2×Dic5—22no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—44no—
448C2×Dic5—44no—
449C2×Dic5—44no—
450C2×Dic5#121116yes—
451C2×Dic5C22×D414yes—
452C2×Dic5C22×D414yes—
453C2×Dic5C22×D414yes—
454C2×Dic5C22×D414yes—
455C2×Dic5C2×#4114yes—
456D20—416no—
457C4×D5—416no—
458Dic10—232no—
459C25—51no—
460C25—51no—
461C25C22×D511yescharacteristic
462C22×Q8—58no—
463C22×Q8—54no—
464C22×Q8—104no—
465C22×Q8—104no—
466C22×D4—54no—
467C22×D4—54no—
468C22×D4—54no—
469C22×D4—104no—
470C22×D4—104no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—202no—
477C22×D4—202no—
478C23×C4—51no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—54no—
485C23×C4—104no—
486C23×C4—104no—
487C23×C4—104no—
488C23×C4C22×D511yescharacteristic
489C23×C4C22×D511yescharacteristic
490C23×C4C22×D511yescharacteristic
491C23×C4C22×D511yescharacteristic
492C23×C4C22×D511yescharacteristic
493C23×C4C22×D511yescharacteristic
494#124—1032no—
495C22⋊Q8—1032no—
496#121—1032no—
497C4×Q8—1032no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—58no—
500C2×C4⋊C4—54no—
501C2×C4⋊C4—54no—
502C2×C4⋊C4—54no—
503C2×C4⋊C4—54no—
504C2×C4⋊C4—54no—
505C2×C4⋊C4—54no—
506C2×C4⋊C4—54no—
507C2×C4⋊C4—104no—
508C2×C4⋊C4—104no—
509C2×C4⋊C4—104no—
510C2×C4⋊C4—104no—
511C2×C4⋊C4—202no—
512C2×C4⋊C4—202no—
513C2×C4⋊C4C22×D514yes—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—54no—
518C2×C22⋊C4—54no—
519C2×C22⋊C4—54no—
520C2×C22⋊C4—54no—
521C2×C22⋊C4—54no—
522C2×C22⋊C4—54no—
523C2×C22⋊C4—54no—
524C2×C22⋊C4—54no—
525C2×C22⋊C4—54no—
526C2×C22⋊C4—54no—
527C2×C22⋊C4—54no—
528C2×C22⋊C4—104no—
529C2×C22⋊C4—104no—
530C2×C22⋊C4—104no—
531C2×C22⋊C4—104no—
532C2×C22⋊C4—104no—
533C2×C22⋊C4—104no—
534C2×C22⋊C4—104no—
535C2×C22⋊C4—104no—
536C2×C22⋊C4—104no—
537C2×C22⋊C4—202no—
538C2×C22⋊C4—202no—
539C2×C22⋊C4C22×D514yes—
540C2×C22⋊C4C22×D514yes—
541C2×C22⋊C4C22×D514yes—
542C2×C42—24no—
543C2×C42—54no—
544C2×C42—54no—
545C2×C42—54no—
546C2×C42—104no—
547C2×C42—104no—
548C2×C42—104no—
549C2×C42C22×D514yes—
550#95—54no—
551#95—54no—
552#95C22×D514yes—
553#95C22×D514yes—
554C22×C5—42no—
555C22×C5—42no—
556C22×C5—42no—
557C22×C5—42no—
558C22×C5—42no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—88no—
562C22×C5C2×#12114yes—
563C22×C5#52914yes—
564C22×C5#54214yes—
565C22×C5#54614yes—
566C22×C5#54814yes—
567C22×C5#54814yes—
568C22×C5#55014yes—
569C22×C5C23×D411yescharacteristic
570C22×C5C23×D411yescharacteristic
571C22×C5C22×#4111yescharacteristic
572C22×C5C22×#4111yescharacteristic
573C22×C5C22×#4111yescharacteristic
574C22×C5C2×H(5,𝔽2)11yescharacteristic
575C22×C5C2×2−1+411yescharacteristic
576C2×D5—24no—
577C2×D5—24no—
578C2×D5—24no—
579C2×D5—42no—
580C2×D5—416no—
581C2×D5—42no—
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—42no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—88no—
592C4×C5—24no—
593C4×C5—24no—
594C4×C5—24no—
595C4×C5—42no—
596C4×C5—42no—
597C4×C5—42no—
598Dic5—24no—
599Dic5—24no—
600Dic5—42no—
601Dic5—42no—
602Dic5—42no—
603Dic5C2×#12118yes—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—54no—
612C24—52no—
613C24—52no—
614C24—102no—
615C24—102no—
616C24—102no—
617C24—102no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24C23×D512yes—
628C24C23×D511yescharacteristic
629C2×Q8—516no—
630C2×Q8—108no—
631C2×Q8—1032no—
632C2×Q8—108no—
633C2×D4—108no—
634C2×D4—108no—
635C2×D4—108no—
636C2×D4—108no—
637C2×D4—108no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—204no—
641C2×D4—2016no—
642C2×D4—2016no—
643C2×D4—204no—
644C2×D4—2016no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—54no—
661C22×C4—54no—
662C22×C4—54no—
663C22×C4—52no—
664C22×C4—54no—
665C22×C4—54no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—52no—
671C22×C4—108no—
672C22×C4—108no—
673C22×C4—108no—
674C22×C4—102no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—2016no—
688C22×C4#70914yes—
689C22×C4D4×D514yes—
690C22×C4D4×D514yes—
691C22×C4C23×D512yes—
692C22×C4C23×D512yes—
693C22×C4C23×D512yes—
694C22×C4C23×D512yes—
695C22×C4C23×D512yes—
696C22×C4C23×D512yes—
697C4⋊C4—28no—
698C4⋊C4—516no—
699C4⋊C4—108no—
700C4⋊C4—108no—
701C4⋊C4—108no—
702C4⋊C4—108no—
703C4⋊C4—204no—
704C4⋊C4—204no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—108no—
709C22⋊C4—108no—
710C22⋊C4—108no—
711C22⋊C4—108no—
712C22⋊C4—108no—
713C22⋊C4—108no—
714C22⋊C4—108no—
715C22⋊C4—108no—
716C22⋊C4—108no—
717C22⋊C4—204no—
718C22⋊C4—204no—
719C42—28no—
720C42—108no—
721C42—108no—
722C42—108no—
723C2×C5—82no—
724C2×C5#242618yescomplemented
725C2×C5C22×#12111yescharacteristic
726C2×C5C2×#52911yescharacteristic
727C2×C5C2×#54211yescharacteristic
728C2×C5C2×#54611yescharacteristic
729C2×C5C2×#54811yescharacteristic
730C2×C5C2×#54811yescharacteristic
731C2×C5C2×#55011yescharacteristic
732D5—44no—
733D5—82no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—54no—
749C23—108no—
750C23—108no—
751C23—108no—
752C23—102no—
753C23—102no—
754C23—102no—
755C23—102no—
756C23—102no—
757C23—102no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—102no—
765C23—204no—
766C23—204no—
767C23—204no—
768C23—204no—
769C23—204no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23C2×#70912yes—
777C23C2×D4×D512yes—
778C23C2×D4×D512yes—
779C23D5×#4112yes—
780C23D5×#4112yes—
781C23#414912yes—
782C23#415012yes—
783C23C24×D511yescharacteristic
784Q8—1032no—
785D4—2016no—
786D4—2016no—
787D4—2016no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—28no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—516no—
810C2×C4—54no—
811C2×C4—54no—
812C2×C4—54no—
813C2×C4—54no—
814C2×C4—54no—
815C2×C4—108no—
816C2×C4—108no—
817C2×C4—102no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—2016no—
831C2×C4—204no—
832C2×C4—204no—
833C2×C4—204no—
834C2×C4C2×#70914yes—
835C2×C4C2×D4×D514yes—
836C2×C4C2×D4×D514yes—
837C5C2×#242611yescharacteristic, complemented, Sylow
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—88no—
846C22—104no—
847C22—104no—
848C22—104no—
849C22—202no—
850C22—202no—
851C22—2016no—
852C22—202no—
853C22—202no—
854C22—202no—
855C22—202no—
856C22—202no—
857C22—202no—
858C22—202no—
859C22—202no—
860C22—202no—
861C22—408no—
862C22#6586214yes—
863C22#6588614yes—
864C22#6588714yes—
865C22D5×#12114yes—
866C22#6598814yes—
867C22#6601114yes—
868C22#6604414yes—
869C22C22×#70911yescharacteristic
870C22C22×D4×D511yescharacteristic
871C22C22×D4×D511yescharacteristic
872C22C2×D5×#4111yescharacteristic
873C22C2×D5×#4111yescharacteristic
874C22C2×#414911yescharacteristic
875C22C2×#415011yescharacteristic
876C4—24no—
877C4—24no—
878C4—24no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—58no—
883C4—104no—
884C4—104no—
885C4—202no—
886C4—202no—
887C4—202no—
888C2—82no—
889C2—204no—
890C2—402no—
891C2#1060723018yesdirect product factor
892C2C2×#6586211yescharacteristic
893C2C2×#6588611yescharacteristic
894C2C2×#6588711yescharacteristic
895C2C2×D5×#12111yescharacteristic
896C2C2×#6598811yescharacteristic
897C2C2×#6601111yescharacteristic
898C2C2×#6604411yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC22×#4030C2
hypercenterC2×#388D5
hypocenterC5C2×#2426
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#4042C2semidirect
3. C22×#4031C2semidirect
4. C22×C4×Dic10C2semidirect
5. C2×C5×#388C2semidirect
6. C2×#65283C2semidirect
7. C2×#65237C2semidirect
8. C2×#65250C2semidirect
9. C2×#65246C2semidirect
10. C2×#65246C2semidirect
11. C2×#65228C2semidirect
12. #10607230C2direct (N × H)
13. C2×#64961C2semidirect
14. C2×#64936C2semidirect
15. C2×#64958C2semidirect
16. C2×#64955C2semidirect
49. C2×#4042C22semidirect
51. C2×#4031C22semidirect
55. C2×C4×Dic10C22semidirect
56. C5×#388C22semidirect
61. #65283C22semidirect
62. #65250C22semidirect
63. #65246C22semidirect
64. #65246C22semidirect
65. #65237C22semidirect
66. #65228C22semidirect
67. #64961C22semidirect
68. #64958C22semidirect
69. #64955C22semidirect
70. #64936C22semidirect
105. C22×Dic10D4semidirect
181. C2×#388D5semidirect
275. C2×Dic10C2×D4semidirect
350. #388C2×D5semidirect
724. C2×C5#2426semidirect
837. C5C2×#2426semidirect
891. C2#10607230direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40422
C22×#40302
C22×#40312
C22×C4×Dic102
C2×C5×#3882
C2×#652832
C2×#652372
C2×#652502
C2×#652462
C2×#652282
#106072302
C2×#649612
C2×#649362
C2×#649582
C2×#649552
C2×#24265