Finite Group Databasebeta

← C2×#10614814 #12268409

Subgroups — C2×#10614814 #12268409

Order 1280.

2574 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#126C211yesmaximal, characteristic
2C22×#4025C211yesmaximal, characteristic
3#10614814C2116yesmaximal, direct product factor
4C2×#65271C211yesmaximal, characteristic, complemented
5C2×#65275C211yesmaximal, characteristic, complemented
6C2×#65261C211yesmaximal, characteristic, complemented
7C2×#65261C211yesmaximal, characteristic, complemented
8C2×#65267C211yesmaximal, characteristic, complemented
9C2×#65265C211yesmaximal, characteristic, complemented
10C2×#65241C211yesmaximal, characteristic
11C2×#65241C211yesmaximal, characteristic
12C2×#65231C211yesmaximal, characteristic
13C2×#65231C211yesmaximal, characteristic
14C2×C22⋊C4×Dic5C211yesmaximal, characteristic
15C2×#65222C211yesmaximal, characteristic, complemented
16C2×C4×#683C211yesmaximal, characteristic, complemented
17C24×Dic5C2211yescharacteristic
18C2×C5×#126—28no—
19C2×C5×#126C2218yes—
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
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×C22⋊Dic5C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×#683C2211yescharacteristic
32C22×#683C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4025—28no—
43C2×#4025C2218yes—
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56#65275C2218yescomplemented
57#65271C2218yescomplemented
58#65267C2218yescomplemented
59#65265C2218yescomplemented
60#65261C2218yescomplemented
61#65261C2218yescomplemented
62#65241C2218yes—
63#65241C2218yes—
64#65231C2218yes—
65#65231C2218yes—
66C22⋊C4×Dic5C2218yes—
67#65222C2218yescomplemented
68C4×#683C2218yescomplemented
69C2×#2496—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×Dic5—24no—
78C23×Dic5—24no—
79C23×Dic5—24no—
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2314yes—
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C5×#126—232no—
90C2×C5×C4⋊C4—24no—
91C2×C5×C4⋊C4—24no—
92C2×C5×C4⋊C4—24no—
93C2×C5×C4⋊C4C2314yes—
94C2×C5×C4⋊C4C2314yes—
95C2×C5×C4⋊C4C2314yes—
96C2×C5×C22⋊C4—24no—
97C2×C5×C22⋊C4—24no—
98C2×C5×C22⋊C4D418yes—
99C2×C5×C22⋊C4C2314yes—
100C2×C5×C22⋊C4C2314yes—
101C2×C5×C22⋊C4C2314yes—
102C2×C42×C5—24no—
103C2×C42×C5C2314yes—
104C2×C22⋊Dic5—24no—
105C2×C22⋊Dic5—24no—
106C2×C22⋊Dic5—24no—
107C2×C22⋊Dic5C2314yes—
108C2×C22⋊Dic5C2314yes—
109C2×C22⋊Dic5C2314yes—
110C2×C4⋊Dic5—24no—
111C2×C4⋊Dic5C2314yes—
112C2×#683—24no—
113C2×#683—24no—
114C2×#683—24no—
115C2×#683—24no—
116C2×#683—24no—
117C2×#683—24no—
118C2×#683—24no—
119C2×#683—24no—
120C2×#683C2314yes—
121C2×#683C2314yes—
122C2×#683C2314yes—
123C2×#683C2314yes—
124C2×#683C2314yes—
125C2×#683C2314yes—
126C2×#683C2314yes—
127C2×#683C2314yes—
128C2×C4×Dic5—24no—
129C2×C4×Dic5—24no—
130C2×C4×Dic5—24no—
131C2×C4×Dic5C2314yes—
132C2×C4×Dic5C2314yes—
133C2×C4×Dic5C2314yes—
134#4025—232no—
135#3963C2314yes—
136#3963C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147C22×#126—51no—
148C22×#126D511yescharacteristic
149#2496—516no—
150C2×#400—51no—
151C2×#400—51no—
152C2×#397—51no—
153C2×#397—51no—
154C2×#389—51no—
155C2×#389—51no—
156C2×#387—51no—
157C2×#387—51no—
158C2×#384—51no—
159C2×#380—51no—
160C2×#380—51no—
161C2×C4×C4⋊C4—51no—
162C2×C4×C22⋊C4—51no—
163C24×C5—22no—
164C24×C5—22no—
165C24×C5—22no—
166C24×C5—22no—
167C24×C5—22no—
168C24×C5—22no—
169C24×C5C2×D414yes—
170C24×C5C2412yes—
171C24×C5C2411yescharacteristic
172C22×C4×C5—22no—
173C22×C4×C5—22no—
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—22no—
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5C2×D414yes—
189C22×C4×C5C2×D414yes—
190C22×C4×C5C2412yes—
191C22×C4×C5C2412yes—
192C22×C4×C5C2412yes—
193C22×C4×C5C2412yes—
194C22×C4×C5C2412yes—
195C22×C4×C5C2412yes—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5—22no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—22no—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—28no—
217C22×Dic5—28no—
218C22×Dic5—28no—
219C22×Dic5—416no—
220C22×Dic5#4114yes—
221C22×Dic5#4114yes—
222C22×Dic5#4114yes—
223C22×Dic5#4114yes—
224C22×Dic5C2412yes—
225C22×Dic5C2412yes—
226C22×Dic5C2412yes—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C22×Dic5C2412yes—
231C22×Dic5C2412yes—
232C5×C4⋊C4—28no—
233C5×C4⋊C4—28no—
234C5×C4⋊C4—28no—
235C5×C22⋊C4—28no—
236C5×C22⋊C4—28no—
237C5×C22⋊C4C2×D4116yes—
238C42×C5—28no—
239C22⋊Dic5—28no—
240C22⋊Dic5—28no—
241C22⋊Dic5—28no—
242C4⋊Dic5—28no—
243#683—28no—
244#683—28no—
245#683—28no—
246#683—28no—
247#683—28no—
248#683—28no—
249#683—28no—
250#683—28no—
251C4×Dic5—28no—
252C4×Dic5—28no—
253C4×Dic5—28no—
254C24×C4—51no—
255C2×#126—28no—
256C2×#126—58no—
257C2×#126—108no—
258C2×#126C2×D518yes—
259C22×C4⋊C4—51no—
260C22×C4⋊C4—51no—
261C22×C4⋊C4—51no—
262C22×C4⋊C4—51no—
263C22×C4⋊C4—51no—
264C22×C4⋊C4—51no—
265C22×C4⋊C4—51no—
266C22×C4⋊C4—51no—
267C22×C4⋊C4—51no—
268C22×C4⋊C4C2×D511yescharacteristic
269C22×C4⋊C4C2×D511yescharacteristic
270C22×C4⋊C4C2×D511yescharacteristic
271C22×C22⋊C4—51no—
272C22×C22⋊C4—51no—
273C22×C22⋊C4—51no—
274C22×C22⋊C4C2×D511yescharacteristic
275C22×C22⋊C4C2×D511yescharacteristic
276C22×C22⋊C4C2×D511yescharacteristic
277C22×C42—51no—
278C22×C42—51no—
279C22×C42—51no—
280C22×C42C2×D511yescharacteristic
281#400—58no—
282#400—58no—
283#397—58no—
284#397—58no—
285#389—58no—
286#389—58no—
287#387—58no—
288#387—58no—
289#384—58no—
290#380—58no—
291#380—58no—
292C4×C4⋊C4—58no—
293C4×C22⋊C4—58no—
294C2×#95—51no—
295C2×#95—51no—
296C2×#95—51no—
297C2×#95—51no—
298C2×#95—51no—
299C2×#95—51no—
300C2×#95—51no—
301C2×#95—51no—
302C2×#95—51no—
303C2×#95—51no—
304C2×#95—51no—
305C2×#95—51no—
306C23×C5—28no—
307C23×C5—28no—
308C23×C5—28no—
309C23×C5—22no—
310C23×C5—22no—
311C23×C5—22no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—22no—
315C23×C5—44no—
316C23×C5—44no—
317C23×C5—44no—
318C23×C5—44no—
319C23×C5C22×D414yes—
320C23×C5C22×D412yes—
321C23×C5C2×#4112yes—
322C23×C5C2×#4112yes—
323C23×C5C2×#4112yes—
324C23×C5C2×#4112yes—
325C23×C52−1+412yes—
326C23×C52−1+412yes—
327C23×C5C2511yescharacteristic
328C2×C4×C5—28no—
329C2×C4×C5—28no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—44no—
347C2×C4×C5—44no—
348C2×C4×C5—44no—
349C2×C4×C5—44no—
350C2×C4×C5C22×D414yes—
351C2×C4×C5C22×D414yes—
352C2×Dic5—28no—
353C2×Dic5—22no—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—22no—
363C2×Dic5—22no—
364C2×Dic5—22no—
365C2×Dic5—22no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—44no—
374C2×Dic5—44no—
375C2×Dic5—44no—
376C2×Dic5—44no—
377C2×Dic5—44no—
378C2×Dic5—44no—
379C2×Dic5—416no—
380C2×Dic5#126116yescomplemented
381C2×Dic5C2×#4114yes—
382C2×Dic5C2×#4114yes—
383C2×Dic5C2×#4114yes—
384C2×Dic5C2×#4114yes—
385C25C22×D511yescharacteristic
386C23×C4—51no—
387C23×C4—51no—
388C23×C4—54no—
389C23×C4—51no—
390C23×C4—51no—
391C23×C4—51no—
392C23×C4—51no—
393C23×C4—51no—
394C23×C4—51no—
395C23×C4—104no—
396C23×C4—104no—
397C23×C4—104no—
398C23×C4C22×D511yescharacteristic
399C23×C4C22×D511yescharacteristic
400C23×C4C22×D511yescharacteristic
401C23×C4C22×D511yescharacteristic
402C23×C4C22×D511yescharacteristic
403C23×C4C22×D511yescharacteristic
404#126—232no—
405#126—1032no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—54no—
410C2×C4⋊C4—54no—
411C2×C4⋊C4—54no—
412C2×C4⋊C4—54no—
413C2×C4⋊C4—54no—
414C2×C4⋊C4—54no—
415C2×C4⋊C4—54no—
416C2×C4⋊C4—54no—
417C2×C4⋊C4—54no—
418C2×C4⋊C4—104no—
419C2×C4⋊C4—104no—
420C2×C4⋊C4—104no—
421C2×C4⋊C4—104no—
422C2×C4⋊C4—104no—
423C2×C4⋊C4—104no—
424C2×C4⋊C4—104no—
425C2×C4⋊C4—104no—
426C2×C4⋊C4—104no—
427C2×C4⋊C4C22×D514yes—
428C2×C4⋊C4C22×D514yes—
429C2×C4⋊C4C22×D514yes—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—54no—
433C2×C22⋊C4—54no—
434C2×C22⋊C4—54no—
435C2×C22⋊C4—104no—
436C2×C22⋊C4—104no—
437C2×C22⋊C4—104no—
438C2×C22⋊C4C22⋊D518yes—
439C2×C22⋊C4C22×D514yes—
440C2×C22⋊C4C22×D514yes—
441C2×C22⋊C4C22×D514yes—
442C2×C42—24no—
443C2×C42—54no—
444C2×C42—54no—
445C2×C42—54no—
446C2×C42—104no—
447C2×C42—104no—
448C2×C42—104no—
449C2×C42C22×D514yes—
450#95—54no—
451#95—54no—
452#95—54no—
453#95—54no—
454#95—54no—
455#95—54no—
456#95—54no—
457#95—54no—
458#95—54no—
459#95—54no—
460#95—54no—
461#95—54no—
462C22×C5—24no—
463C22×C5—24no—
464C22×C5—24no—
465C22×C5—42no—
466C22×C5—42no—
467C22×C5—42no—
468C22×C5—42no—
469C22×C5—416no—
470C22×C5C2×#12614yes—
471C22×C5#53214yes—
472C22×C5#54114yes—
473C22×C5#54714yes—
474C22×C5#54714yes—
475C22×C5#55214yes—
476C22×C5#55614yes—
477C22×C5C23×D411yescharacteristic
478C22×C5C22×#4111yescharacteristic
479C22×C5C22×#4111yescharacteristic
480C22×C5C22×#4111yescharacteristic
481C22×C5C22×#4111yescharacteristic
482C22×C5C2×2−1+411yescharacteristic
483C22×C5C2×2−1+411yescharacteristic
484C4×C5—24no—
485C4×C5—24no—
486C4×C5—42no—
487C4×C5—42no—
488C4×C5—42no—
489C4×C5—42no—
490Dic5—24no—
491Dic5—42no—
492Dic5—42no—
493Dic5—42no—
494Dic5—42no—
495Dic5—42no—
496Dic5—42no—
497Dic5C2×#12618yescomplemented
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24C2×C22⋊D514yes—
505C24C23×D512yes—
506C24C23×D511yescharacteristic
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—54no—
524C22×C4—54no—
525C22×C4—54no—
526C22×C4—52no—
527C22×C4—54no—
528C22×C4—52no—
529C22×C4—52no—
530C22×C4—52no—
531C22×C4—52no—
532C22×C4—52no—
533C22×C4—52no—
534C22×C4—52no—
535C22×C4—108no—
536C22×C4—108no—
537C22×C4—108no—
538C22×C4—102no—
539C22×C4—102no—
540C22×C4—102no—
541C22×C4—102no—
542C22×C4—102no—
543C22×C4—102no—
544C22×C4—102no—
545C22×C4—102no—
546C22×C4—102no—
547C22×C4—102no—
548C22×C4—102no—
549C22×C4—102no—
550C22×C4—102no—
551C22×C4—102no—
552C22×C4—102no—
553C22×C4—102no—
554C22×C4—102no—
555C22×C4—102no—
556C22×C4—102no—
557C22×C4—102no—
558C22×C4—2016no—
559C22×C4C2×C22⋊D514yes—
560C22×C4C2×C22⋊D514yes—
561C22×C4C23×D512yes—
562C22×C4C23×D512yes—
563C22×C4C23×D512yes—
564C22×C4C23×D512yes—
565C22×C4C23×D512yes—
566C22×C4C23×D512yes—
567C4⋊C4—28no—
568C4⋊C4—28no—
569C4⋊C4—28no—
570C4⋊C4—108no—
571C4⋊C4—108no—
572C4⋊C4—108no—
573C4⋊C4—108no—
574C4⋊C4—108no—
575C4⋊C4—108no—
576C4⋊C4—108no—
577C4⋊C4—108no—
578C4⋊C4—108no—
579C22⋊C4—28no—
580C22⋊C4—28no—
581C22⋊C4—108no—
582C22⋊C4—108no—
583C22⋊C4—108no—
584C22⋊C4C2×C22⋊D5116yes—
585C42—28no—
586C42—108no—
587C42—108no—
588C42—108no—
589C2×C5—44no—
590C2×C5#249618yescomplemented
591C2×C5C22×#12611yescharacteristic
592C2×C5C2×#53211yescharacteristic
593C2×C5C2×#54111yescharacteristic
594C2×C5C2×#54711yescharacteristic
595C2×C5C2×#54711yescharacteristic
596C2×C5C2×#55211yescharacteristic
597C2×C5C2×#55611yescharacteristic
598C23—28no—
599C23—28no—
600C23—28no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23D5×#4112yes—
612C23D5×#4112yes—
613C23D5×#4112yes—
614C23D5×#4112yes—
615C23#415012yes—
616C23#415012yes—
617C23C22×C22⋊D514yes—
618C23C22×C22⋊D512yes—
619C23C24×D511yescharacteristic
620C2×C4—28no—
621C2×C4—28no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—54no—
643C2×C4—54no—
644C2×C4—54no—
645C2×C4—516no—
646C2×C4—54no—
647C2×C4—102no—
648C2×C4—102no—
649C2×C4—108no—
650C2×C4—102no—
651C2×C4—102no—
652C2×C4—102no—
653C2×C4—102no—
654C2×C4—102no—
655C2×C4—102no—
656C2×C4—102no—
657C2×C4—102no—
658C2×C4—102no—
659C2×C4—102no—
660C2×C4—102no—
661C2×C4—102no—
662C2×C4—102no—
663C2×C4—102no—
664C2×C4—102no—
665C2×C4—102no—
666C2×C4—102no—
667C2×C4—102no—
668C2×C4—2016no—
669C2×C4—204no—
670C2×C4—204no—
671C2×C4—204no—
672C2×C4—204no—
673C2×C4—204no—
674C2×C4—204no—
675C2×C4C22×C22⋊D514yes—
676C2×C4C22×C22⋊D514yes—
677C5C2×#249611yescharacteristic, complemented, Sylow
678C22—24no—
679C22—24no—
680C22—24no—
681C22—416no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22#6603514yes—
687C22#6603614yes—
688C22D5×#12614yes—
689C22#6604214yes—
690C22#6615814yes—
691C22#6615814yes—
692C22#6616614yes—
693C22C2×D5×#4111yescharacteristic
694C22C2×D5×#4111yescharacteristic
695C22C2×D5×#4111yescharacteristic
696C22C2×D5×#4111yescharacteristic
697C22C2×#415011yescharacteristic
698C22C2×#415011yescharacteristic
699C22C23×C22⋊D511yescharacteristic
700C4—24no—
701C4—24no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—58no—
707C4—104no—
708C4—202no—
709C4—202no—
710C4—202no—
711C4—202no—
712C4—202no—
713C4—202no—
714C2—44no—
715C2#1061481418yesdirect product factor
716C2C2×#6603511yescharacteristic
717C2C2×#6603611yescharacteristic
718C2C2×D5×#12611yescharacteristic
719C2C2×#6604211yescharacteristic
720C2C2×#6616611yescharacteristic
721C2C2×#6615811yescharacteristic
722C2C2×#6615811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#126C2
socleC24×C5C24
prime radicalC25×C5C23
hypercenterC22×#126D5
hypocenterC5C2×#2496
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
3. #10614814C2direct (N × H)
4. C2×#65271C2semidirect
5. C2×#65275C2semidirect
6. C2×#65261C2semidirect
7. C2×#65261C2semidirect
8. C2×#65267C2semidirect
9. C2×#65265C2semidirect
15. C2×#65222C2semidirect
16. C2×C4×#683C2semidirect
56. #65275C22semidirect
57. #65271C22semidirect
58. #65267C22semidirect
59. #65265C22semidirect
60. #65261C22semidirect
61. #65261C22semidirect
67. #65222C22semidirect
68. C4×#683C22semidirect
380. C2×Dic5#126semidirect
497. Dic5C2×#126semidirect
590. C2×C5#2496semidirect
677. C5C2×#2496semidirect
715. C2#10614814direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1262
C22×#40252
#106148142
C2×#652712
C2×#652752
C2×#652612
C2×#652672
C2×#652652
C2×#652412
C2×#652312
C2×C22⋊C4×Dic52
C2×#652222
C2×C4×#6832
C2×#24965