Finite Group Databasebeta

← C2×#10608632 #12267551

Subgroups — C2×#10608632 #12267551

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×#4085C211yesmaximal, characteristic
2C22×#4033C211yesmaximal, characteristic, complemented
3C22×#4031C211yesmaximal, characteristic, complemented
4C22×#4024C211yesmaximal, characteristic, complemented
5C2×C5×#394C211yesmaximal, characteristic, complemented
6C2×#65510C211yesmaximal, characteristic, complemented
7C2×#65283C211yesmaximal, characteristic, complemented
8C2×#65248C211yesmaximal, characteristic, complemented
9C2×#65237C211yesmaximal, characteristic, complemented
10C2×#65246C211yesmaximal, characteristic, complemented
11C2×#65246C211yesmaximal, characteristic, complemented
12C2×#65234C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
14#10608632C2116yesmaximal, direct product factor
15C2×#64936C211yesmaximal, characteristic, complemented
16C2×#64959C211yesmaximal, 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
46C22×C4×Dic5C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C22×C4×Dic5C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C2×#4033—28no—
51C2×#4033C2218yescomplemented
52C2×#4031—28no—
53C2×#4031C2218yescomplemented
54C2×#4024—28no—
55C2×#4024C2218yescomplemented
56C5×#394C2218yescomplemented
57C2×C5×#95C2211yescharacteristic
58#65510C2218yescomplemented
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#65283C2218yescomplemented
63#65248C2218yescomplemented
64#65246C2218yescomplemented
65#65246C2218yescomplemented
66#65237C2218yescomplemented
67#65234C2218yescomplemented
68C22⋊C4×Dic5C2218yescomplemented
69#64959C2218yescomplemented
70#64936C2218yescomplemented
71C2×#2426—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C25×C5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—42no—
78C22×C5×D4C2314yes—
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C22×C22⋊D5—24no—
85C22×C22⋊D5—24no—
86C22×C22⋊D5—24no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—24no—
89C22×C22⋊D5—42no—
90C22×C22⋊D5C2314yes—
91C22×C22⋊D5C2314yes—
92C23×Dic5—24no—
93C23×Dic5—24no—
94C23×Dic5—24no—
95C23×Dic5C2314yes—
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
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⋊C4—42no—
113C2×C5×C22⋊C4C2314yes—
114C2×C5×C22⋊C4C2314yes—
115C2×C5×C22⋊C4C2314yes—
116C2×C5×C22⋊C4C2314yes—
117C2×C22⋊Dic5—24no—
118C2×C22⋊Dic5—24no—
119C2×C22⋊Dic5—24no—
120C2×C22⋊Dic5—24no—
121C2×C22⋊Dic5—24no—
122C2×C22⋊Dic5C2314yes—
123C2×C22⋊Dic5C2314yes—
124C2×C22⋊Dic5C2314yes—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127#4085—232no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—24no—
131C2×#685—24no—
132C2×#685—42no—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×C4⋊Dic5—24no—
139C2×C4⋊Dic5—42no—
140C2×C4⋊Dic5C2314yes—
141C2×C4⋊Dic5C2314yes—
142C2×#683—24no—
143C2×#683—24no—
144C2×#683—24no—
145C2×#683—42no—
146C2×#683D418yes—
147C2×#683C2314yes—
148C2×#683C2314yes—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×C4×Dic5—24no—
153C2×C4×Dic5—24no—
154C2×C4×Dic5—24no—
155C2×C4×Dic5—24no—
156C2×C4×Dic5C2314yes—
157C2×C4×Dic5C2314yes—
158C2×C4×Dic5C2314yes—
159C2×C4×Dic5C2314yes—
160#4033—232no—
161#4031—232no—
162#4024—232no—
163C5×#95C2314yes—
164#3963C2314yes—
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×#394D511yescharacteristic, complemented
176C2×#390—51no—
177C2×#390—51no—
178C2×#390—51no—
179C2×#389—51no—
180C2×#388—51no—
181C2×#388—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×C5—22no—
191C24×C5—22no—
192C24×C5—22no—
193C24×C5—22no—
194C24×C5—22no—
195C24×C5—22no—
196C24×C5#4114yes—
197C24×C5C2412yes—
198C24×C5C2412yes—
199C24×C5C2411yescharacteristic
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5—22no—
205C23×D5—22no—
206C23×D5—22no—
207C23×D5C2412yes—
208C2×C5×D4—28no—
209C2×C5×D4—28no—
210C2×C5×D4—44no—
211C2×C5×D4—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×C5C2×D414yes—
226C22×C4×C5C2×D414yes—
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×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5—28no—
256C22×Dic5—28no—
257C22×Dic5—28no—
258C22×Dic5—416no—
259C22×Dic5C2×D414yes—
260C22×Dic5C2×D414yes—
261C22×Dic5C2×D414yes—
262C22×Dic5C2×D414yes—
263C22×Dic5#4114yes—
264C22×Dic5#4114yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C22×Dic5C2412yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
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—
280C5×C22⋊C4—44no—
281C22⋊Dic5—28no—
282C22⋊Dic5—28no—
283C22⋊Dic5—28no—
284C22⋊Dic5—28no—
285C22⋊Dic5—28no—
286#685—28no—
287#685—28no—
288#685—28no—
289#685—28no—
290#685—44no—
291C4⋊Dic5—28no—
292C4⋊Dic5—44no—
293#683—28no—
294#683—28no—
295#683—28no—
296#683—44no—
297#683C2×D4116yes—
298C4×Dic5—28no—
299C4×Dic5—28no—
300C4×Dic5—28no—
301C4×Dic5—28no—
302C23×Q8—51no—
303C23×D4—51no—
304C23×D4—51no—
305C23×D4C2×D511yescharacteristic
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⋊C4C2×D511yescharacteristic
334C22×C22⋊C4C2×D511yescharacteristic
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C42—51no—
338C22×C42—51no—
339C22×C42—51no—
340C22×C42—51no—
341#396—58no—
342#396—58no—
343#394—58no—
344#394C2×D518yescomplemented
345#390—58no—
346#390—58no—
347#390—58no—
348#389—58no—
349#388—58no—
350#388—58no—
351C4×C22⋊C4—58no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95C2×D511yescharacteristic
356C23×C5—28no—
357C23×C5—28no—
358C23×C5—28no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—44no—
373C23×C5—44no—
374C23×C5—44no—
375C23×C5—44no—
376C23×C5—44no—
377C23×C5—44no—
378C23×C5—44no—
379C23×C5—44no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5—44no—
383C23×C5C22×D412yes—
384C23×C5C22×D412yes—
385C23×C5C2×#4114yes—
386C23×C5C2×#4112yes—
387C23×C5C2×#4112yes—
388C23×C5C2×#4112yes—
389C23×C5H(5,𝔽2)12yes—
390C23×C52−1+412yes—
391C23×C5C2511yescharacteristic
392C22×D5—22no—
393C22×D5—22no—
394C22×D5—22no—
395C22×D5—22no—
396C22×D5—22no—
397C22×D5—22no—
398C22×D5—22no—
399C22×D5—44no—
400C22×D5—44no—
401C22×D5—44no—
402C22×D5—44no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5—44no—
406C5×D4—416no—
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—44no—
423C2×C4×C5—44no—
424C2×C4×C5—44no—
425C2×C4×C5C22×D414yes—
426C2×C4×C5C22×D414yes—
427C22⋊D5—416no—
428C22⋊D5—416no—
429C2×Dic5—28no—
430C2×Dic5—28no—
431C2×Dic5—28no—
432C2×Dic5—22no—
433C2×Dic5—22no—
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—416no—
451C2×Dic5#121116yes—
452C2×Dic5C22×D414yes—
453C2×Dic5C22×D414yes—
454C2×Dic5C22×D414yes—
455C2×Dic5C22×D414yes—
456C2×Dic5C2×#4114yes—
457C2×Dic5C2×#4114yes—
458Dic10—232no—
459C25—51no—
460C25C22×D511yescharacteristic
461C25C22×D511yescharacteristic
462C22×Q8—58no—
463C22×Q8—54no—
464C22×Q8—104no—
465C22×Q8—104no—
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—42no—
469C22×D4—54no—
470C22×D4—54no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—202no—
477C22×D4C22×D514yes—
478C23×C4—51no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—54no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—104no—
487C23×C4—104no—
488C23×C4—104no—
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—42no—
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⋊C4C22×D514yes—
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—
554C22×C5—24no—
555C22×C5—24no—
556C22×C5—24no—
557C22×C5—42no—
558C22×C5—416no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—88no—
570C22×C5C2×#12114yes—
571C22×C5#52914yes—
572C22×C5#54214yes—
573C22×C5#54614yes—
574C22×C5#54814yes—
575C22×C5#54814yes—
576C22×C5#55014yes—
577C22×C5C23×D411yescharacteristic
578C22×C5C23×D411yescharacteristic
579C22×C5C22×#4111yescharacteristic
580C22×C5C22×#4111yescharacteristic
581C22×C5C22×#4111yescharacteristic
582C22×C5C2×H(5,𝔽2)11yescharacteristic
583C22×C5C2×2−1+411yescharacteristic
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—42no—
595C4×C5—42no—
596C4×C5—42no—
597Dic5—24no—
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—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—52no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24#71114yes—
626C24C23×D512yes—
627C24C23×D512yes—
628C24C23×D511yescharacteristic
629C2×Q8—516no—
630C2×Q8—108no—
631C2×Q8—1032no—
632C2×Q8—108no—
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—44no—
636C2×D4—416no—
637C2×D4—108no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—108no—
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—54no—
659C22×C4—54no—
660C22×C4—54no—
661C22×C4—52no—
662C22×C4—54no—
663C22×C4—54no—
664C22×C4—54no—
665C22×C4—52no—
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—102no—
688C22×C4—102no—
689C22×C4—2016no—
690C22×C4D4×D514yes—
691C22×C4D4×D514yes—
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—44no—
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—108no—
718C22⋊C4—204no—
719C42—108no—
720C42—108no—
721C42—108no—
722C42—108no—
723C2×C5—44no—
724C2×C5—82no—
725C2×C5#242618yescomplemented
726C2×C5C22×#12111yescharacteristic
727C2×C5C2×#52911yescharacteristic
728C2×C5C2×#54211yescharacteristic
729C2×C5C2×#54611yescharacteristic
730C2×C5C2×#54811yescharacteristic
731C2×C5C2×#54811yescharacteristic
732C2×C5C2×#55011yescharacteristic
733D5—82no—
734C23—28no—
735C23—28no—
736C23—28no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
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—
775C23C2×D4×D512yes—
776C23C2×D4×D512yes—
777C23C2×#71114yes—
778C23C2×#71112yes—
779C23#414412yes—
780C23D5×#4112yes—
781C23D5×#4112yes—
782C23#415012yes—
783C23C24×D511yescharacteristic
784Q8—1032no—
785D4—416no—
786D4—2016no—
787D4—2016no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—22no—
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—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—516no—
807C2×C4—54no—
808C2×C4—54no—
809C2×C4—54no—
810C2×C4—54no—
811C2×C4—54no—
812C2×C4—54no—
813C2×C4—108no—
814C2×C4—108no—
815C2×C4—108no—
816C2×C4—102no—
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—102no—
831C2×C4—2016no—
832C2×C4—204no—
833C2×C4—204no—
834C2×C4—204no—
835C2×C4C2×D4×D514yes—
836C2×C4C2×D4×D514yes—
837C5C2×#242611yescharacteristic, complemented, Sylow
838C22—24no—
839C22—24no—
840C22—24no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—416no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—88no—
854C22—202no—
855C22—202no—
856C22—202no—
857C22—202no—
858C22—202no—
859C22—202no—
860C22—202no—
861C22—408no—
862C22#6592514yes—
863C22#6593214yes—
864C22#6593314yes—
865C22D5×#12114yes—
866C22#6598314yes—
867C22#6599614yes—
868C22#6601114yes—
869C22C22×D4×D511yescharacteristic
870C22C22×D4×D511yescharacteristic
871C22C22×#71111yescharacteristic
872C22C2×#414411yescharacteristic
873C22C2×D5×#4111yescharacteristic
874C22C2×D5×#4111yescharacteristic
875C22C2×#415011yescharacteristic
876C4—24no—
877C4—24no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—58no—
882C4—104no—
883C4—104no—
884C4—104no—
885C4—202no—
886C4—202no—
887C4—202no—
888C2—44no—
889C2—82no—
890C2—402no—
891C2#1060863218yesdirect product factor
892C2C2×#6592511yescharacteristic
893C2C2×#6593211yescharacteristic
894C2C2×#6593311yescharacteristic
895C2C2×D5×#12111yescharacteristic
896C2C2×#6598311yescharacteristic
897C2C2×#6599611yescharacteristic
898C2C2×#6601111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#394C2
socleC24×C5C24
prime radicalC22×#4085C2
hypercenterC2×#394D5
hypocenterC5C2×#2426
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C22×#4033C2semidirect
3. C22×#4031C2semidirect
4. C22×#4024C2semidirect
5. C2×C5×#394C2semidirect
6. C2×#65510C2semidirect
7. C2×#65283C2semidirect
8. C2×#65248C2semidirect
9. C2×#65237C2semidirect
10. C2×#65246C2semidirect
11. C2×#65246C2semidirect
12. C2×#65234C2semidirect
13. C2×C22⋊C4×Dic5C2semidirect
14. #10608632C2direct (N × H)
15. C2×#64936C2semidirect
16. C2×#64959C2semidirect
51. C2×#4033C22semidirect
53. C2×#4031C22semidirect
55. C2×#4024C22semidirect
56. C5×#394C22semidirect
58. #65510C22semidirect
62. #65283C22semidirect
63. #65248C22semidirect
64. #65246C22semidirect
65. #65246C22semidirect
66. #65237C22semidirect
67. #65234C22semidirect
68. C22⋊C4×Dic5C22semidirect
69. #64959C22semidirect
70. #64936C22semidirect
105. C22×Dic10D4semidirect
175. C2×#394D5semidirect
275. C2×Dic10C2×D4semidirect
344. #394C2×D5semidirect
725. C2×C5#2426semidirect
837. C5C2×#2426semidirect
891. C2#10608632direct (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×#40332
C22×#40312
C22×#40242
C2×C5×#3942
C2×#655102
C2×#652832
C2×#652482
C2×#652372
C2×#652462
C2×#652342
C2×C22⋊C4×Dic52
#106086322
C2×#649362
C2×#649592
C2×#24265