Finite Group Databasebeta

← C2×#10605467 #12269823

Subgroups — C2×#10605467 #12269823

Order 1280.

2334 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#65280C211yesmaximal, characteristic
3C2×#65273C211yesmaximal, characteristic, complemented
4C2×#65279C211yesmaximal, characteristic, complemented
5C2×#65279C211yesmaximal, characteristic, complemented
6C2×#65228C211yesmaximal, characteristic
7C2×#65229C211yesmaximal, characteristic, complemented
8C2×#65229C211yesmaximal, characteristic, complemented
9C2×#65229C211yesmaximal, characteristic, complemented
10C2×#65229C211yesmaximal, characteristic, complemented
11C2×C4×#683C211yesmaximal, characteristic, complemented
12#10605467C2116yesmaximal, direct product factor
13C2×#64949C211yesmaximal, characteristic, complemented
14C2×#64961C211yesmaximal, characteristic
15C2×#64958C211yesmaximal, characteristic, complemented
16C2×#64958C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C42×C5C2211yescharacteristic
21C22×C42×C5C2211yescharacteristic
22C22×C42×C5C2211yescharacteristic
23C22×#685C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C4×C5×C4⋊C4C2218yescomplemented
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53#65280C2218yes—
54#65279C2218yescomplemented
55#65279C2218yescomplemented
56#65273C2218yescomplemented
57#65229C2218yescomplemented
58#65229C2218yescomplemented
59#65229C2218yescomplemented
60#65229C2218yescomplemented
61#65228C2218yes—
62C4×#683C2218yescomplemented
63#64961C2218yes—
64#64958C2218yescomplemented
65#64958C2218yescomplemented
66#64949C2218yescomplemented
67C2×#2593—51nomaximal, Sylow
68C24×D5C2311yescharacteristic
69C24×D5C2311yescharacteristic
70C23×C4×C5C2311yescharacteristic
71C23×C4×C5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×Dic5C2311yescharacteristic
78C23×Dic5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C22×D20—24no—
84C22×D20—42no—
85C22×D20—42no—
86C22×D20C2314yes—
87C2×C5×C4⋊C4—24no—
88C2×C5×C4⋊C4—24no—
89C2×C5×C4⋊C4C2314yes—
90C2×C5×C4⋊C4C2314yes—
91C2×C42×C5—24no—
92C2×C42×C5—42no—
93C2×C42×C5—42no—
94C2×C42×C5C2314yes—
95C2×C42×C5C2314yes—
96C2×C42×C5C2314yes—
97C2×#685—24no—
98C2×#685—24no—
99C2×#685—24no—
100C2×#685—24no—
101C2×#685—24no—
102C2×#685—24no—
103C2×#685—24no—
104C2×#685—24no—
105C2×#685—42no—
106C2×#685—42no—
107C2×#685—42no—
108C2×#685—42no—
109C2×#685C2314yes—
110C2×#685C2314yes—
111C2×#685C2314yes—
112C2×#685C2314yes—
113C2×#685C2314yes—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×C4⋊Dic5—42no—
122C2×C4⋊Dic5C2314yes—
123C2×#683—24no—
124C2×#683—24no—
125C2×#683—42no—
126C2×#683—42no—
127C2×#683C2314yes—
128C2×#683C2314yes—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C2×C4×Dic5—24no—
132C2×C4×Dic5—42no—
133C2×C4×Dic5C2314yes—
134C2×C4×Dic5C2314yes—
135C5×#95C2314yes—
136C5×#95C2314yes—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#2593—516no—
146C2×#400—51no—
147C2×#398—51no—
148C2×#394—51no—
149C2×#394—51no—
150C2×#390—51no—
151C2×#388—51no—
152C2×#388—51no—
153C2×#388—51no—
154C2×#388—51no—
155C2×#388—51no—
156C2×#388—51no—
157C2×#388—51no—
158C2×#388—51no—
159C2×C4×C4⋊C4—51no—
160C2×C4×C4⋊C4D511yescharacteristic, complemented
161C24×C5C2411yescharacteristic
162C23×D5—22no—
163C23×D5—22no—
164C23×D5—22no—
165C23×D5—22no—
166C23×D5—22no—
167C23×D5—22no—
168C23×D5—22no—
169C23×D5—22no—
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5—22no—
175C23×D5—22no—
176C23×D5C2412yes—
177C23×D5C2412yes—
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×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5#4114yes—
196C22×C4×C5#4114yes—
197C22×C4×C5#4114yes—
198C22×C4×C5#4114yes—
199C22×C4×C5C2412yes—
200C22×C4×C5C2412yes—
201C22×C4×C5C2412yes—
202C22×C4×C5C2412yes—
203C22×C4×C5C2412yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
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—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5—22no—
220C22×Dic5—22no—
221C22×Dic5—22no—
222C22×Dic5—22no—
223C22×Dic5#4114yes—
224C22×Dic5C2412yes—
225C22×Dic5C2412yes—
226C22×Dic5C2412yes—
227C22×Dic5C2412yes—
228C22×Dic5C2412yes—
229C22×Dic5C2412yes—
230C2×D20—28no—
231C2×D20—44no—
232C2×D20—44no—
233C2×D20—416no—
234C5×C4⋊C4—28no—
235C5×C4⋊C4—28no—
236C42×C5—28no—
237C42×C5—44no—
238C42×C5—44no—
239#685—28no—
240#685—28no—
241#685—28no—
242#685—28no—
243#685—28no—
244#685—28no—
245#685—28no—
246#685—28no—
247#685—44no—
248#685—44no—
249#685—44no—
250#685—44no—
251C4⋊Dic5—44no—
252#683—28no—
253#683—28no—
254#683—44no—
255#683—44no—
256C4×Dic5—28no—
257C4×Dic5—44no—
258C23×D4—51no—
259C22×C4⋊C4—51no—
260C22×C4⋊C4—51no—
261C22×C4⋊C4—51no—
262C22×C4⋊C4—51no—
263C22×C4⋊C4—51no—
264C22×C4⋊C4C2×D511yescharacteristic
265C22×C4⋊C4C2×D511yescharacteristic
266C22×C22⋊C4—51no—
267C22×C22⋊C4—51no—
268C22×C22⋊C4—51no—
269C22×C22⋊C4—51no—
270C22×C22⋊C4—51no—
271C22×C22⋊C4—51no—
272C22×C22⋊C4—51no—
273C22×C22⋊C4—51no—
274C22×C22⋊C4—51no—
275C22×C22⋊C4—51no—
276C22×C22⋊C4—51no—
277C22×C22⋊C4—51no—
278C22×C42—51no—
279C22×C42—51no—
280C22×C42C2×D511yescharacteristic
281C22×C42C2×D511yescharacteristic
282C22×C42C2×D511yescharacteristic
283#400—58no—
284#398—58no—
285#394—58no—
286#394—58no—
287#390—58no—
288#388—58no—
289#388—58no—
290#388—58no—
291#388—58no—
292#388—58no—
293#388—58no—
294#388—58no—
295#388—58no—
296C4×C4⋊C4—58no—
297C4×C4⋊C4C2×D518yescomplemented
298C2×#95—51no—
299C2×#95—51no—
300C2×#95—51no—
301C2×#95—51no—
302C2×#95—51no—
303C2×#95—51no—
304C2×#95—51no—
305C2×#95—51no—
306C2×#95C2×D511yescharacteristic
307C2×#95C2×D511yescharacteristic
308C23×C5C2×#4112yes—
309C23×C5C2×#4112yes—
310C23×C5C2×#4112yes—
311C23×C5C2×#4112yes—
312C23×C5C2×#4112yes—
313C23×C5H(5,𝔽2)12yes—
314C23×C5H(5,𝔽2)12yes—
315C23×C5C2511yescharacteristic
316C22×D5—22no—
317C22×D5—22no—
318C22×D5—22no—
319C22×D5—22no—
320C22×D5—22no—
321C22×D5—22no—
322C22×D5—22no—
323C22×D5—22no—
324C22×D5—22no—
325C22×D5—22no—
326C22×D5—22no—
327C22×D5—22no—
328C22×D5—22no—
329C22×D5—22no—
330C22×D5—44no—
331C22×D5—44no—
332C22×D5—44no—
333C22×D5—44no—
334C22×D5—44no—
335C22×D5—44no—
336C22×D5—44no—
337C22×D5—44no—
338C22×D5—44no—
339C22×D5—44no—
340C22×D5—44no—
341C22×D5—44no—
342C22×D5—44no—
343C22×D5—44no—
344C2×C4×C5—28no—
345C2×C4×C5—28no—
346C2×C4×C5—28no—
347C2×C4×C5—28no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—44no—
366C2×C4×C5—44no—
367C2×C4×C5—44no—
368C2×C4×C5C2×#4114yes—
369C2×C4×C5C2×#4114yes—
370C2×C4×C5C2×#4114yes—
371C2×C4×C5C2×#4114yes—
372C2×Dic5—28no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5—22no—
382C2×Dic5—22no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—44no—
391C2×Dic5—44no—
392C2×Dic5—44no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5C2×#4114yes—
396D20—416no—
397C25—51no—
398C25—51no—
399C22×D4—54no—
400C22×D4—104no—
401C22×D4—202no—
402C22×D4—202no—
403C23×C4—51no—
404C23×C4—51no—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4C22×D511yescharacteristic
410C23×C4C22×D511yescharacteristic
411C23×C4C22×D511yescharacteristic
412C23×C4C22×D511yescharacteristic
413C23×C4C22×D511yescharacteristic
414C23×C4C22×D511yescharacteristic
415C23×C4C22×D511yescharacteristic
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—54no—
419C2×C4⋊C4—54no—
420C2×C4⋊C4—54no—
421C2×C4⋊C4—54no—
422C2×C4⋊C4—54no—
423C2×C4⋊C4—104no—
424C2×C4⋊C4—104no—
425C2×C4⋊C4—202no—
426C2×C4⋊C4—202no—
427C2×C4⋊C4—202no—
428C2×C4⋊C4C22×D514yes—
429C2×C4⋊C4C22×D514yes—
430C2×C22⋊C4—54no—
431C2×C22⋊C4—54no—
432C2×C22⋊C4—54no—
433C2×C22⋊C4—54no—
434C2×C22⋊C4—54no—
435C2×C22⋊C4—54no—
436C2×C22⋊C4—54no—
437C2×C22⋊C4—54no—
438C2×C22⋊C4—54no—
439C2×C22⋊C4—54no—
440C2×C22⋊C4—54no—
441C2×C22⋊C4—54no—
442C2×C22⋊C4—104no—
443C2×C22⋊C4—104no—
444C2×C22⋊C4—104no—
445C2×C22⋊C4—104no—
446C2×C22⋊C4—104no—
447C2×C22⋊C4—104no—
448C2×C22⋊C4—104no—
449C2×C22⋊C4—104no—
450C2×C22⋊C4—202no—
451C2×C22⋊C4—202no—
452C2×C22⋊C4—202no—
453C2×C22⋊C4—202no—
454C2×C42—24no—
455C2×C42—42no—
456C2×C42—42no—
457C2×C42—54no—
458C2×C42—54no—
459C2×C42—104no—
460C2×C42—202no—
461C2×C42C22×D514yes—
462C2×C42C22×D514yes—
463C2×C42C22×D514yes—
464#95—54no—
465#95—54no—
466#95—54no—
467#95—54no—
468#95—54no—
469#95—54no—
470#95—54no—
471#95—54no—
472#95C22×D514yes—
473#95C22×D514yes—
474C22×C5#52914yes—
475C22×C5#52914yes—
476C22×C5#53814yes—
477C22×C5#55314yes—
478C22×C5#55314yes—
479C22×C5#55514yes—
480C22×C5#55914yes—
481C22×C5C22×#4111yescharacteristic
482C22×C5C22×#4111yescharacteristic
483C22×C5C22×#4111yescharacteristic
484C22×C5C22×#4111yescharacteristic
485C22×C5C22×#4111yescharacteristic
486C22×C5C2×H(5,𝔽2)11yescharacteristic
487C22×C5C2×H(5,𝔽2)11yescharacteristic
488C2×D5—42no—
489C2×D5—42no—
490C2×D5—42no—
491C2×D5—42no—
492C2×D5—42no—
493C2×D5—42no—
494C2×D5—42no—
495C2×D5—42no—
496C2×D5—42no—
497C2×D5—42no—
498C2×D5—42no—
499C2×D5—42no—
500C2×D5—42no—
501C2×D5—42no—
502C2×D5—88no—
503C2×D5—88no—
504C4×C5—24no—
505C4×C5—24no—
506C4×C5—24no—
507C4×C5—24no—
508C4×C5—42no—
509C4×C5—42no—
510C4×C5—42no—
511Dic5—24no—
512Dic5—42no—
513Dic5—42no—
514Dic5—42no—
515Dic5—42no—
516Dic5—42no—
517C24—52no—
518C24—52no—
519C24—102no—
520C24—102no—
521C24—102no—
522C24—102no—
523C24—102no—
524C24—102no—
525C24—102no—
526C24—102no—
527C24—102no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24C23×D511yescharacteristic
534C2×D4—108no—
535C2×D4—204no—
536C2×D4—204no—
537C2×D4—2016no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—54no—
556C22×C4—52no—
557C22×C4—52no—
558C22×C4—52no—
559C22×C4—52no—
560C22×C4—52no—
561C22×C4—52no—
562C22×C4—102no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—102no—
579C22×C4#70914yes—
580C22×C4#70914yes—
581C22×C4#70914yes—
582C22×C4#71314yes—
583C22×C4C23×D512yes—
584C22×C4C23×D512yes—
585C22×C4C23×D512yes—
586C22×C4C23×D512yes—
587C22×C4C23×D512yes—
588C22×C4C23×D512yes—
589C22×C4C23×D512yes—
590C4⋊C4—28no—
591C4⋊C4—28no—
592C4⋊C4—108no—
593C4⋊C4—108no—
594C4⋊C4—204no—
595C4⋊C4—204no—
596C4⋊C4—204no—
597C22⋊C4—108no—
598C22⋊C4—108no—
599C22⋊C4—108no—
600C22⋊C4—108no—
601C22⋊C4—108no—
602C22⋊C4—108no—
603C22⋊C4—108no—
604C22⋊C4—108no—
605C22⋊C4—204no—
606C22⋊C4—204no—
607C22⋊C4—204no—
608C22⋊C4—204no—
609C42—28no—
610C42—44no—
611C42—44no—
612C42—108no—
613C42—204no—
614C2×C5#259318yescomplemented
615C2×C5C2×#52911yescharacteristic
616C2×C5C2×#52911yescharacteristic
617C2×C5C2×#53811yescharacteristic
618C2×C5C2×#55311yescharacteristic
619C2×C5C2×#55311yescharacteristic
620C2×C5C2×#55511yescharacteristic
621C2×C5C2×#55911yescharacteristic
622D5—82no—
623D5—82no—
624C23—102no—
625C23—102no—
626C23—102no—
627C23—102no—
628C23—102no—
629C23—102no—
630C23—102no—
631C23—102no—
632C23—102no—
633C23—102no—
634C23—102no—
635C23—102no—
636C23—102no—
637C23—102no—
638C23—204no—
639C23—204no—
640C23—204no—
641C23—204no—
642C23—204no—
643C23—204no—
644C23—204no—
645C23—204no—
646C23—204no—
647C23—204no—
648C23—204no—
649C23—204no—
650C23—204no—
651C23—204no—
652C23C2×#70912yes—
653C23C2×#70912yes—
654C23C2×#70912yes—
655C23#414412yes—
656C23C2×#71312yes—
657C23D5×#4112yes—
658C23#414912yes—
659C23C24×D511yescharacteristic
660D4—2016no—
661C2×C4—28no—
662C2×C4—28no—
663C2×C4—28no—
664C2×C4—28no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—54no—
686C2×C4—108no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—204no—
705C2×C4—204no—
706C2×C4—204no—
707C2×C4—204no—
708C2×C4—204no—
709C2×C4C2×#70914yes—
710C2×C4C2×#70914yes—
711C2×C4C2×#70914yes—
712C2×C4C2×#71314yes—
713C5C2×#259311yescharacteristic, complemented, Sylow
714C22—202no—
715C22—202no—
716C22—202no—
717C22—202no—
718C22—202no—
719C22—202no—
720C22—202no—
721C22—202no—
722C22—202no—
723C22—202no—
724C22—202no—
725C22—202no—
726C22—202no—
727C22—202no—
728C22—408no—
729C22—408no—
730C22#6581314yes—
731C22#6584814yes—
732C22#6586614yes—
733C22#6587414yes—
734C22#6589414yes—
735C22#6591414yes—
736C22#6591914yes—
737C22C22×#70911yescharacteristic
738C22C22×#70911yescharacteristic
739C22C22×#70911yescharacteristic
740C22C2×#414411yescharacteristic
741C22C22×#71311yescharacteristic
742C22C2×D5×#4111yescharacteristic
743C22C2×#414911yescharacteristic
744C4—24no—
745C4—24no—
746C4—24no—
747C4—24no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—104no—
752C4—202no—
753C4—202no—
754C4—202no—
755C4—202no—
756C4—202no—
757C2—402no—
758C2—402no—
759C2#1060546718yesdirect product factor
760C2C2×#6581311yescharacteristic
761C2C2×#6584811yescharacteristic
762C2C2×#6586611yescharacteristic
763C2C2×#6587411yescharacteristic
764C2C2×#6589411yescharacteristic
765C2C2×#6591911yescharacteristic
766C2C2×#6591411yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C4×C5×C4⋊C4C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×C4×C4⋊C4D5
hypocenterC5C2×#2593
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×C4⋊C4C2semidirect
3. C2×#65273C2semidirect
4. C2×#65279C2semidirect
5. C2×#65279C2semidirect
7. C2×#65229C2semidirect
8. C2×#65229C2semidirect
9. C2×#65229C2semidirect
10. C2×#65229C2semidirect
11. C2×C4×#683C2semidirect
12. #10605467C2direct (N × H)
13. C2×#64949C2semidirect
15. C2×#64958C2semidirect
16. C2×#64958C2semidirect
42. C4×C5×C4⋊C4C22semidirect
54. #65279C22semidirect
55. #65279C22semidirect
56. #65273C22semidirect
57. #65229C22semidirect
58. #65229C22semidirect
59. #65229C22semidirect
60. #65229C22semidirect
62. C4×#683C22semidirect
64. #64958C22semidirect
65. #64958C22semidirect
66. #64949C22semidirect
160. C2×C4×C4⋊C4D5semidirect
297. C4×C4⋊C4C2×D5semidirect
614. C2×C5#2593semidirect
713. C5C2×#2593semidirect
759. C2#10605467direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C5×C4⋊C42
C2×#652802
C2×#652732
C2×#652792
C2×#652282
C2×#652292
C2×C4×#6832
#106054672
C2×#649492
C2×#649612
C2×#649582
C2×#25935