Finite Group Databasebeta

← C2×#10608523 #12268400

Subgroups — C2×#10608523 #12268400

Order 1280.

3678 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4090C211yesmaximal, characteristic, complemented
2C22×#4093C211yesmaximal, characteristic, complemented
3C22×#4030C211yesmaximal, characteristic
4C22×#4031C211yesmaximal, characteristic, complemented
5C2×C5×#393C211yesmaximal, characteristic, complemented
6C2×#65248C211yesmaximal, characteristic, complemented
7C2×#65246C211yesmaximal, characteristic, complemented
8C2×#65246C211yesmaximal, characteristic, complemented
9C2×#65234C211yesmaximal, characteristic, complemented
10#10608523C2116yesmaximal, direct product factor
11C2×#64962C211yesmaximal, characteristic, complemented
12C2×#64956C211yesmaximal, characteristic, complemented
13C2×#64961C211yesmaximal, characteristic, complemented
14C2×#64958C211yesmaximal, characteristic, complemented
15C2×#64938C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×C5×Q8C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×D20C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×Dic10C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C2×#4093—28no—
29C2×#4093C2218yescomplemented
30C2×#4090—28no—
31C2×#4090C2218yescomplemented
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×C4×Dic5C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C22×C4×Dic5C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C2×#4031—28no—
51C2×#4031C2218yescomplemented
52C2×#4030—28no—
53C2×#4030C2218yes—
54C5×#393C2218yescomplemented
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57C2×C5×#95C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65248C2218yescomplemented
62#65246C2218yescomplemented
63#65246C2218yescomplemented
64#65234C2218yescomplemented
65#64962C2218yescomplemented
66#64961C2218yescomplemented
67#64958C2218yescomplemented
68#64956C2218yescomplemented
69#64955C2218yescomplemented
70#64938C2218yescomplemented
71C2×#2491—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×Q8—24no—
76C22×C5×Q8—24no—
77C22×C5×Q8—42no—
78C22×C5×Q8C2314yes—
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C22×C22⋊D5—24no—
86C22×C22⋊D5—24no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—24no—
89C22×C22⋊D5—24no—
90C22×C22⋊D5—42no—
91C22×C22⋊D5C2314yes—
92C22×C22⋊D5C2314yes—
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C22×D20—24no—
100C22×D20—24no—
101C22×D20—42no—
102C22×D20C2314yes—
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—24no—
106C22×C4×D5C2314yes—
107C22×Dic10—24no—
108C22×Dic10—24no—
109C22×Dic10—42no—
110C22×Dic10C2314yes—
111C2×C5×C22⋊C4—24no—
112C2×C5×C22⋊C4—24no—
113C2×C5×C22⋊C4—42no—
114C2×C5×C22⋊C4C2314yes—
115C2×C5×C22⋊C4C2314yes—
116C2×C5×C22⋊C4C2314yes—
117C2×C22⋊Dic5—24no—
118C2×C22⋊Dic5—24no—
119C2×C22⋊Dic5C2314yes—
120C2×C22⋊Dic5C2314yes—
121#4093—232no—
122#4090—232no—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—42no—
131C2×#685D418yescomplemented
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×#683—24no—
142C2×#683—24no—
143C2×#683—24no—
144C2×#683—24no—
145C2×#683D418yes—
146C2×#683C2314yes—
147C2×#683C2314yes—
148C2×#683C2314yes—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×C4×Dic5—24no—
152C2×C4×Dic5—24no—
153C2×C4×Dic5—24no—
154C2×C4×Dic5—24no—
155C2×C4×Dic5C2314yes—
156C2×C4×Dic5C2314yes—
157C2×C4×Dic5C2314yes—
158C2×C4×Dic5C2314yes—
159#4031—232no—
160#4030—232no—
161C5×#95C2314yes—
162C5×#95C2314yes—
163C5×#95C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×C4⋊Q8—51no—
168C22×#124—51no—
169C22×#124—51no—
170C22×#121—51no—
171#2491—516no—
172C2×#394—51no—
173C2×#394—51no—
174C2×#393—51no—
175C2×#393D511yescharacteristic, complemented
176C2×#390—51no—
177C2×#390—51no—
178C2×#388—51no—
179C2×#388—51no—
180C2×#380—51no—
181C2×C4×C4⋊C4—51no—
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×D5C2×D414yes—
206C23×D5C2412yes—
207C23×D5C2412yes—
208C2×C5×Q8—28no—
209C2×C5×Q8—28no—
210C2×C5×Q8—44no—
211C2×C5×Q8—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—22no—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5—22no—
227C22×C4×C5—22no—
228C22×C4×C5C2×D414yes—
229C22×C4×C5C2×D414yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C2×C22⋊D5—28no—
237C2×C22⋊D5—28no—
238C2×C22⋊D5—28no—
239C2×C22⋊D5—28no—
240C2×C22⋊D5—28no—
241C2×C22⋊D5—44no—
242C2×C22⋊D5—416no—
243C2×C22⋊D5—416no—
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×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5C2×D414yes—
257C22×Dic5C2×D414yes—
258C22×Dic5C2×D414yes—
259C22×Dic5#4114yes—
260C22×Dic5#4114yes—
261C22×Dic5#4114yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C2×D20—28no—
269C2×D20—28no—
270C2×D20—44no—
271C2×D20—416no—
272C2×C4×D5—28no—
273C2×C4×D5—28no—
274C2×C4×D5—28no—
275C2×C4×D5—416no—
276C2×Dic10—28no—
277C2×Dic10—28no—
278C2×Dic10—44no—
279C2×Dic10—416no—
280C5×C22⋊C4—28no—
281C5×C22⋊C4—28no—
282C5×C22⋊C4—44no—
283C22⋊Dic5—28no—
284C22⋊Dic5—28no—
285#685—28no—
286#685—28no—
287#685—28no—
288#685—28no—
289#685—28no—
290#685—28no—
291#685—28no—
292#685—44no—
293#685C2×D4116yescomplemented
294#683—28no—
295#683—28no—
296#683—28no—
297#683—28no—
298#683C2×D4116yes—
299C4×Dic5—28no—
300C4×Dic5—28no—
301C4×Dic5—28no—
302C4×Dic5—28no—
303C23×Q8—51no—
304C23×Q8C2×D511yescharacteristic
305C23×D4—51no—
306C23×D4—51no—
307C23×D4—51no—
308C24×C4—51no—
309C2×C4⋊Q8—58no—
310C2×C4⋊Q8—108no—
311C2×#124—58no—
312C2×#124—58no—
313C2×#124—108no—
314C2×#124—108no—
315C2×#121—58no—
316C2×#121—108no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C22⋊C4—51no—
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⋊C4C2×D511yescharacteristic
334C22×C22⋊C4C2×D511yescharacteristic
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C42—51no—
337C22×C42—51no—
338C22×C42—51no—
339C22×C42—51no—
340#394—58no—
341#394—58no—
342#393—58no—
343#393C2×D518yescomplemented
344#390—58no—
345#390—58no—
346#388—58no—
347#388—58no—
348#380—58no—
349C4×C4⋊C4—58no—
350C4×C22⋊C4—58no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95C2×D511yescharacteristic
355C2×#95C2×D511yescharacteristic
356C2×#95C2×D511yescharacteristic
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—44no—
365C23×C5—44no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5—44no—
371C23×C5C22×D412yes—
372C23×C5C22×D412yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5C2×#4112yes—
376C23×C5H(5,𝔽2)12yes—
377C23×C52−1+412yes—
378C23×C5C2511yescharacteristic
379C22×D5—28no—
380C22×D5—28no—
381C22×D5—28no—
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—22no—
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×D5—44no—
406C22×D5C22×D414yes—
407C5×Q8—416no—
408C2×C4×C5—28no—
409C2×C4×C5—28no—
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—22no—
425C2×C4×C5—22no—
426C2×C4×C5—44no—
427C2×C4×C5—44no—
428C2×C4×C5—44no—
429C2×C4×C5—44no—
430C2×C4×C5C22×D414yes—
431C2×C4×C5C22×D414yes—
432C22⋊D5—416no—
433C22⋊D5—416no—
434C2×Dic5—28no—
435C2×Dic5—28no—
436C2×Dic5—28no—
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—22no—
448C2×Dic5—22no—
449C2×Dic5—44no—
450C2×Dic5—44no—
451C2×Dic5#124116yescomplemented
452C2×Dic5C22×D414yes—
453C2×Dic5C22×D414yes—
454C2×Dic5C22×D414yes—
455C2×Dic5C2×#4114yes—
456C2×Dic5C2×#4114yes—
457C2×Dic5C2×#4114yes—
458D20—416no—
459C4×D5—416no—
460Dic10—416no—
461C25—51no—
462C25—51no—
463C25C22×D511yescharacteristic
464C22×Q8—24no—
465C22×Q8—24no—
466C22×Q8—42no—
467C22×Q8—54no—
468C22×Q8—104no—
469C22×Q8—104no—
470C22×Q8—202no—
471C22×Q8C22×D514yes—
472C22×D4—54no—
473C22×D4—54no—
474C22×D4—54no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4—104no—
478C22×D4—104no—
479C22×D4—104no—
480C22×D4—104no—
481C22×D4—104no—
482C22×D4—202no—
483C22×D4—202no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—51no—
488C23×C4—51no—
489C23×C4—51no—
490C23×C4—54no—
491C23×C4—104no—
492C23×C4—104no—
493C23×C4—104no—
494C23×C4C22×D511yescharacteristic
495C23×C4C22×D511yescharacteristic
496C23×C4C22×D511yescharacteristic
497C23×C4C22×D511yescharacteristic
498C23×C4C22×D511yescharacteristic
499C23×C4C22×D511yescharacteristic
500C4⋊Q8—1032no—
501#124—1032no—
502#124—1032no—
503#121—1032no—
504C2×C4⋊C4—58no—
505C2×C4⋊C4—54no—
506C2×C4⋊C4—54no—
507C2×C4⋊C4—54no—
508C2×C4⋊C4—54no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—104no—
511C2×C4⋊C4—104no—
512C2×C4⋊C4—104no—
513C2×C4⋊C4—104no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—58no—
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—54no—
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—104no—
538C2×C22⋊C4—202no—
539C2×C22⋊C4C22×D514yes—
540C2×C22⋊C4C22×D514yes—
541C2×C22⋊C4C22×D514yes—
542C2×C42—54no—
543C2×C42—54no—
544C2×C42—54no—
545C2×C42—54no—
546C2×C42—104no—
547C2×C42—104no—
548C2×C42—104no—
549C2×C42—104no—
550#95—54no—
551#95—54no—
552#95—54no—
553#95C22×D514yes—
554#95C22×D514yes—
555#95C22×D514yes—
556C22×C5—42no—
557C22×C5—42no—
558C22×C5—42no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—88no—
564C22×C5C2×#12414yes—
565C22×C5#53214yes—
566C22×C5#54214yes—
567C22×C5D4214yes—
568C22×C5#54714yes—
569C22×C5#54814yes—
570C22×C5#55514yes—
571C22×C5C23×D411yescharacteristic
572C22×C5C23×D411yescharacteristic
573C22×C5C22×#4111yescharacteristic
574C22×C5C22×#4111yescharacteristic
575C22×C5C22×#4111yescharacteristic
576C22×C5C2×H(5,𝔽2)11yescharacteristic
577C22×C5C2×2−1+411yescharacteristic
578C2×D5—24no—
579C2×D5—24no—
580C2×D5—24no—
581C2×D5—42no—
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—416no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—88no—
594C4×C5—24no—
595C4×C5—24no—
596C4×C5—42no—
597C4×C5—42no—
598C4×C5—42no—
599C4×C5—42no—
600Dic5—24no—
601Dic5—24no—
602Dic5—24no—
603Dic5—42no—
604Dic5—42no—
605Dic5C2×#12418yescomplemented
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—54no—
614C24—52no—
615C24—52no—
616C24—102no—
617C24—102no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24—102no—
629C24C23×D512yes—
630C24C23×D511yescharacteristic
631C2×Q8—28no—
632C2×Q8—28no—
633C2×Q8—44no—
634C2×Q8—416no—
635C2×Q8—108no—
636C2×Q8—108no—
637C2×Q8—204no—
638C2×Q8—2016no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—108no—
643C2×D4—108no—
644C2×D4—108no—
645C2×D4—108no—
646C2×D4—204no—
647C2×D4—2016no—
648C2×D4—2016no—
649C2×D4—204no—
650C2×D4—2016no—
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—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—54no—
668C22×C4—54no—
669C22×C4—54no—
670C22×C4—52no—
671C22×C4—54no—
672C22×C4—54no—
673C22×C4—54no—
674C22×C4—52no—
675C22×C4—52no—
676C22×C4—52no—
677C22×C4—52no—
678C22×C4—52no—
679C22×C4—108no—
680C22×C4—108no—
681C22×C4—108no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—102no—
690C22×C4—102no—
691C22×C4—102no—
692C22×C4—102no—
693C22×C4—102no—
694C22×C4—2016no—
695C22×C4D4×D514yes—
696C22×C4D4×D514yes—
697C22×C4C23×D512yes—
698C22×C4C23×D512yes—
699C22×C4C23×D512yes—
700C22×C4C23×D512yes—
701C22×C4C23×D512yes—
702C22×C4C23×D512yes—
703C4⋊C4—516no—
704C4⋊C4—108no—
705C4⋊C4—108no—
706C4⋊C4—108no—
707C4⋊C4—108no—
708C22⋊C4—28no—
709C22⋊C4—28no—
710C22⋊C4—44no—
711C22⋊C4—516no—
712C22⋊C4—108no—
713C22⋊C4—108no—
714C22⋊C4—108no—
715C22⋊C4—108no—
716C22⋊C4—108no—
717C22⋊C4—108no—
718C22⋊C4—108no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—204no—
722C42—108no—
723C42—108no—
724C42—108no—
725C42—108no—
726C2×C5—82no—
727C2×C5#249118yescomplemented
728C2×C5C22×#12411yescharacteristic
729C2×C5C2×#53211yescharacteristic
730C2×C5C2×#54211yescharacteristic
731C2×C5C2×D4211yescharacteristic
732C2×C5C2×#54711yescharacteristic
733C2×C5C2×#54811yescharacteristic
734C2×C5C2×#55511yescharacteristic
735D5—44no—
736D5—82no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—54no—
752C23—108no—
753C23—108no—
754C23—108no—
755C23—102no—
756C23—102no—
757C23—102no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—102no—
765C23—102no—
766C23—102no—
767C23—102no—
768C23—204no—
769C23—204no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23—204no—
779C23C2×D4×D512yes—
780C23C2×D4×D512yes—
781C23#414412yes—
782C23#414712yes—
783C23D5×#4112yes—
784C23D5×#4112yes—
785C23D5×#4112yes—
786C23C24×D511yescharacteristic
787Q8—416no—
788Q8—2016no—
789D4—2016no—
790D4—2016no—
791D4—2016no—
792C2×C4—28no—
793C2×C4—28no—
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—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—516no—
815C2×C4—54no—
816C2×C4—54no—
817C2×C4—54no—
818C2×C4—54no—
819C2×C4—54no—
820C2×C4—54no—
821C2×C4—108no—
822C2×C4—108no—
823C2×C4—108no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—102no—
834C2×C4—102no—
835C2×C4—102no—
836C2×C4—2016no—
837C2×C4—204no—
838C2×C4—204no—
839C2×C4C2×D4×D514yes—
840C2×C4C2×D4×D514yes—
841C5C2×#249111yescharacteristic, complemented, Sylow
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—88no—
850C22—104no—
851C22—104no—
852C22—104no—
853C22—202no—
854C22—202no—
855C22—202no—
856C22—202no—
857C22—2016no—
858C22—202no—
859C22—202no—
860C22—202no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—408no—
866C22#6592414yes—
867C22#6596514yes—
868C22#6596714yes—
869C22#6597414yes—
870C22#6600214yes—
871C22#6600414yes—
872C22D5×#12414yes—
873C22C22×D4×D511yescharacteristic
874C22C22×D4×D511yescharacteristic
875C22C2×#414411yescharacteristic
876C22C2×#414711yescharacteristic
877C22C2×D5×#4111yescharacteristic
878C22C2×D5×#4111yescharacteristic
879C22C2×D5×#4111yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—58no—
887C4—104no—
888C4—104no—
889C4—104no—
890C4—202no—
891C4—202no—
892C2—82no—
893C2—204no—
894C2—402no—
895C2#1060852318yesdirect product factor
896C2C2×#6592411yescharacteristic
897C2C2×#6597411yescharacteristic
898C2C2×#6596511yescharacteristic
899C2C2×#6596711yescharacteristic
900C2C2×#6600211yescharacteristic
901C2C2×#6600411yescharacteristic
902C2C2×D5×#12411yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#393C2
socleC24×C5C24
prime radicalC22×#4030C2
hypercenterC2×#393D5
hypocenterC5C2×#2491
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×#4090C2semidirect
2. C22×#4093C2semidirect
4. C22×#4031C2semidirect
5. C2×C5×#393C2semidirect
6. C2×#65248C2semidirect
7. C2×#65246C2semidirect
8. C2×#65246C2semidirect
9. C2×#65234C2semidirect
10. #10608523C2direct (N × H)
11. C2×#64962C2semidirect
12. C2×#64956C2semidirect
13. C2×#64961C2semidirect
14. C2×#64958C2semidirect
15. C2×#64938C2semidirect
16. C2×#64955C2semidirect
29. C2×#4093C22semidirect
31. C2×#4090C22semidirect
51. C2×#4031C22semidirect
54. C5×#393C22semidirect
61. #65248C22semidirect
62. #65246C22semidirect
63. #65246C22semidirect
64. #65234C22semidirect
65. #64962C22semidirect
66. #64961C22semidirect
67. #64958C22semidirect
68. #64956C22semidirect
69. #64955C22semidirect
70. #64938C22semidirect
131. C2×#685D4semidirect
175. C2×#393D5semidirect
293. #685C2×D4semidirect
343. #393C2×D5semidirect
451. C2×Dic5#124semidirect
605. Dic5C2×#124semidirect
727. C2×C5#2491semidirect
841. C5C2×#2491semidirect
895. C2#10608523direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40902
C22×#40932
C22×#40302
C22×#40312
C2×C5×#3932
C2×#652482
C2×#652462
C2×#652342
#106085232
C2×#649622
C2×#649562
C2×#649612
C2×#649582
C2×#649382
C2×#649552
C2×#24915