Finite Group Databasebeta

← #12023108

Subgroups — #12023108

Order 1280.

1838 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4034C211yesmaximal, characteristic
2C2×C4×C5×C4⋊C4C211yesmaximal, characteristic
3C2×#65274C211yesmaximal, characteristic
4C2×#65218C212yesmaximal
5#10602356C211yesmaximal, characteristic
6#10602356C211yesmaximal, characteristic
7#10602329C212yesmaximal
8#10602328C211yesmaximal, characteristic
9C4×#3963C211yesmaximal, characteristic
10#10600217C212yesmaximal
11#10600203C212yesmaximal
12C23×Dic10C2212yes—
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C42×C5C2212yes—
16C22×C42×C5C2211yescharacteristic
17C22×C4⋊Dic5C2211yescharacteristic
18C22×C4⋊Dic5C2212yes—
19C22×C4⋊Dic5C2211yescharacteristic
20C22×#683C2212yes—
21C22×C4×Dic5C2211yescharacteristic
22C22×C4×Dic5C2211yescharacteristic
23C2×#4034—24no—
24C2×#4034—24no—
25C2×#4034C418yescomplemented
26C4×C5×C4⋊C4—24no—
27C2×C5×#95C2212yes—
28C2×#3963C2211yescharacteristic
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2211yescharacteristic
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2211yescharacteristic
38C2×#3963C2211yescharacteristic
39#65274—24no—
40#65218—28no—
41#14053—51nomaximal, Sylow
42C23×C4×C5C2311yescharacteristic
43C23×C4×C5C2312yes—
44C23×C4×C5C2312yes—
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×Dic5C2312yes—
48C23×Dic5C2312yes—
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
52C23×Dic5C2311yescharacteristic
53C22×Dic10—24no—
54C22×Dic10—24no—
55C22×Dic10—24no—
56C22×Dic10—24no—
57C22×Dic10—42no—
58C22×Dic10—42no—
59C22×Dic10C2×C418yes—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4C2×C414yes—
63C2×C5×C4⋊C4D414yes—
64C2×C5×C4⋊C4D414yes—
65C2×C5×C4⋊C4Q814yescomplemented
66C2×C42×C5—22no—
67C2×C42×C5—22no—
68C2×C42×C5—24no—
69C2×C42×C5—24no—
70C2×C42×C5—42no—
71C2×C42×C5Q814yescomplemented
72C2×C4⋊Dic5—22no—
73C2×C4⋊Dic5—22no—
74C2×C4⋊Dic5—24no—
75C2×C4⋊Dic5—22no—
76C2×C4⋊Dic5—22no—
77C2×C4⋊Dic5—22no—
78C2×C4⋊Dic5—24no—
79C2×C4⋊Dic5—42no—
80C2×C4⋊Dic5C2×C414yes—
81C2×#683—24no—
82C2×#683—24no—
83C2×#683C2×C418yes—
84C2×C4×Dic5—22no—
85C2×C4×Dic5—22no—
86C2×C4×Dic5—22no—
87C2×C4×Dic5—22no—
88C2×C4×Dic5—22no—
89C2×C4×Dic5C2×C414yes—
90#4034—232no—
91C5×#95—24no—
92#3963—24no—
93#3963—24no—
94#3963—24no—
95#3963—24no—
96#3963—22no—
97#3963—22no—
98#3963—24no—
99#3963—42no—
100#3963—42no—
101#3963D414yes—
102#3963Q814yescomplemented
103C22×C4⋊Q8—51no—
104C2×#391—52no—
105C2×#389—51no—
106C2×C4×C4⋊C4D511yescharacteristic
107#1446—52no—
108#1441—52no—
109#1436—52no—
110C4⋊#95—51no—
111C4⋊#95—51no—
112C4⋊#95—51no—
113C4×#95—51no—
114C24×C5C2411yescharacteristic
115C22×C4×C5—21no—
116C22×C4×C5—22no—
117C22×C4×C5—21no—
118C22×C4×C5—22no—
119C22×C4×C5—21no—
120C22×C4×C5—22no—
121C22×C4×C5—22no—
122C22×C4×C5—21no—
123C22×C4×C5—22no—
124C22×C4×C5—22no—
125C22×C4×C5—21no—
126C22×C4×C5—21no—
127C22×C4×C5—22no—
128C22×C4×C5—21no—
129C22×C4×C5—21no—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—21no—
133C22×C4×C5—21no—
134C22×C4×C5—22no—
135C22×C4×C5C22×C414yes—
136C22×C4×C5C22×C412yes—
137C22×C4×C5C2×D414yes—
138C22×C4×C5C2×D412yes—
139C22×C4×C5C2×D412yes—
140C22×C4×C5C2×D414yes—
141C22×C4×C5C2×D412yes—
142C22×C4×C5C2×Q812yes—
143C22×C4×C5C2×Q814yes—
144C22×C4×C5C2×Q812yes—
145C22×C4×C5C2×Q812yes—
146C22×C4×C5C2×Q812yes—
147C22×C4×C5C2×Q812yes—
148C22×C4×C5#4112yes—
149C22×C4×C5#4112yes—
150C22×Dic5—21no—
151C22×Dic5—21no—
152C22×Dic5—21no—
153C22×Dic5—21no—
154C22×Dic5—21no—
155C22×Dic5—21no—
156C22×Dic5—21no—
157C22×Dic5—21no—
158C22×Dic5—22no—
159C22×Dic5—22no—
160C22×Dic5—22no—
161C22×Dic5—21no—
162C22×Dic5—21no—
163C22×Dic5—22no—
164C22×Dic5—21no—
165C22×Dic5—21no—
166C22×Dic5—21no—
167C22×Dic5—21no—
168C22×Dic5—21no—
169C22×Dic5—21no—
170C22×Dic5—22no—
171C22×Dic5—22no—
172C22×Dic5—21no—
173C22×Dic5—21no—
174C22×Dic5—21no—
175C22×Dic5—21no—
176C22×Dic5—22no—
177C22×Dic5—22no—
178C22×Dic5—22no—
179C22×Dic5—22no—
180C22×Dic5—22no—
181C22×Dic5—22no—
182C22×Dic5—22no—
183C22×Dic5C22×C414yes—
184C22×Dic5C22×C412yes—
185C22×Dic5C22×C412yes—
186C22×Dic5C2×D412yes—
187C22×Dic5C2×D412yes—
188C22×Dic5C2×Q812yes—
189C22×Dic5C2×Q812yes—
190C22×Dic5#4112yes—
191C22×Dic5#4112yes—
192C2×Dic10—216no—
193C2×Dic10—216no—
194C2×Dic10—48no—
195C2×Dic10—48no—
196C2×Dic10—48no—
197C2×Dic10—48no—
198C2×Dic10—48no—
199C5×C4⋊C4—28no—
200C5×C4⋊C4C22⋊C4116yes—
201C42×C5—28no—
202C42×C5—48no—
203C4⋊Dic5—28no—
204C4⋊Dic5—48no—
205C4⋊Dic5—44no—
206#683—216no—
207C4×Dic5—28no—
208C4×Dic5—44no—
209C23×Q8—52no—
210C2×C4⋊Q8—58no—
211C2×C4⋊Q8—104no—
212C2×C4⋊Q8—104no—
213C22×C4⋊C4—52no—
214C22×C4⋊C4—51no—
215C22×C4⋊C4—51no—
216C22×C4⋊C4—52no—
217C22×C4⋊C4C2×D511yescharacteristic
218C22×C4⋊C4C2×D511yescharacteristic
219C22×C42—51no—
220C22×C42—51no—
221C22×C42C2×D512yes—
222C22×C42C2×D511yescharacteristic
223#391—108no—
224#389—104no—
225C4×C4⋊C4—24no—
226C2×#95—51no—
227C2×#95—51no—
228C2×#95—51no—
229C2×#95—51no—
230C2×#95—52no—
231C2×#95—52no—
232C2×#95—52no—
233C2×#95—52no—
234C2×#95—52no—
235C2×#95—52no—
236C2×#95—52no—
237C2×#95C2×D512yes—
238C23×C5C23×C411yescharacteristic
239C23×C5C22×D411yescharacteristic
240C23×C5C22×D411yescharacteristic
241C23×C5C22×D411yescharacteristic
242C23×C5C22×Q811yescharacteristic
243C23×C5C22×Q811yescharacteristic
244C23×C5C22×Q811yescharacteristic
245C23×C5C2×#4111yescharacteristic
246C23×C5C2×#4111yescharacteristic
247C23×C5C2×#4111yescharacteristic
248C23×C5C2×#4111yescharacteristic
249C23×C5H(5,𝔽2)11yescharacteristic
250C23×C5H(5,𝔽2)11yescharacteristic
251C23×C52−1+411yescharacteristic
252C23×C52−1+411yescharacteristic
253C2×C4×C5—24no—
254C2×C4×C5—24no—
255C2×C4×C5—22no—
256C2×C4×C5—22no—
257C2×C4×C5—24no—
258C2×C4×C5—22no—
259C2×C4×C5—24no—
260C2×C4×C5—24no—
261C2×C4×C5—24no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—22no—
265C2×C4×C5—22no—
266C2×C4×C5—24no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—24no—
270C2×C4×C5—24no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—42no—
274C2×C4×C5—41no—
275C2×C4×C5—41no—
276C2×C4×C5—42no—
277C2×C4×C5—41no—
278C2×C4×C5—41no—
279C2×C4×C5C2×C22⋊C418yes—
280C2×C4×C5C2×C22⋊C414yes—
281C2×C4×C5C4×Q814yes—
282C2×C4×C5C4×Q814yes—
283C2×C4×C5C22⋊Q814yes—
284C2×C4×C5C22⋊Q814yes—
285C2×C4×C5#12414yes—
286C2×C4×C5C4⋊Q814yes—
287C2×C4×C5C4⋊Q814yescomplemented
288C2×Dic5—22no—
289C2×Dic5—22no—
290C2×Dic5—22no—
291C2×Dic5—22no—
292C2×Dic5—22no—
293C2×Dic5—22no—
294C2×Dic5—22no—
295C2×Dic5—22no—
296C2×Dic5—22no—
297C2×Dic5—22no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—24no—
301C2×Dic5—24no—
302C2×Dic5—24no—
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—22no—
306C2×Dic5—22no—
307C2×Dic5—22no—
308C2×Dic5—22no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—42no—
314C2×Dic5—42no—
315C2×Dic5—42no—
316C2×Dic5—42no—
317C2×Dic5—41no—
318C2×Dic5—41no—
319C2×Dic5—41no—
320C2×Dic5—41no—
321C2×Dic5—42no—
322C2×Dic5—42no—
323C2×Dic5—42no—
324C2×Dic5—42no—
325C2×Dic5—42no—
326C2×Dic5—42no—
327C2×Dic5—42no—
328C2×Dic5C4×D414yes—
329C2×Dic5C4×Q814yes—
330Dic10—432no—
331C22×Q8—58no—
332C22×Q8—104no—
333C22×Q8—104no—
334C22×Q8—104no—
335C22×Q8—104no—
336C22×Q8—202no—
337C22×Q8—202no—
338C23×C4—51no—
339C23×C4—51no—
340C23×C4—52no—
341C23×C4—51no—
342C23×C4—51no—
343C23×C4—52no—
344C23×C4C22×D512yes—
345C23×C4C22×D511yescharacteristic
346C23×C4C22×D511yescharacteristic
347C23×C4C22×D512yes—
348C23×C4C22×D511yescharacteristic
349C4⋊Q8—1032no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—58no—
353C2×C4⋊C4—54no—
354C2×C4⋊C4—104no—
355C2×C4⋊C4—102no—
356C2×C4⋊C4—104no—
357C2×C4⋊C4—102no—
358C2×C4⋊C4—104no—
359C2×C4⋊C4—104no—
360C2×C4⋊C4—102no—
361C2×C4⋊C4—102no—
362C2×C4⋊C4—102no—
363C2×C4⋊C4—202no—
364C2×C4⋊C4Dic1014yescomplemented
365C2×C4⋊C4C4×D514yes—
366C2×C4⋊C4D2014yes—
367C2×C4⋊C4C22⋊D514yes—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—42no—
373C2×C42—54no—
374C2×C42—102no—
375C2×C42—102no—
376C2×C42—102no—
377C2×C42—102no—
378C2×C42—102no—
379C2×C42Dic1014yescomplemented
380#95—24no—
381#95—54no—
382#95—54no—
383#95—102no—
384#95—104no—
385#95—102no—
386#95—104no—
387#95—104no—
388#95—104no—
389#95—104no—
390#95—202no—
391#95—202no—
392C22×C5C22×C22⋊C411yescharacteristic
393C22×C5C2×C4×D411yescharacteristic
394C22×C5C2×C4×Q811yescharacteristic
395C22×C5C2×C4×Q811yescharacteristic
396C22×C5C2×C4×Q811yescharacteristic
397C22×C5#51811yescharacteristic
398C22×C5#51911yescharacteristic
399C22×C5C2×C22⋊Q811yescharacteristic
400C22×C5C2×C22⋊Q811yescharacteristic
401C22×C5C2×#12411yescharacteristic
402C22×C5C2×C4⋊Q811yescharacteristic
403C22×C5C2×C4⋊Q811yescharacteristic
404C22×C5#53211yescharacteristic
405C22×C5#53311yescharacteristic
406C22×C5#53311yescharacteristic
407C22×C5#54211yescharacteristic
408C22×C5#54211yescharacteristic
409C22×C5#54411yescharacteristic
410C22×C5#54411yescharacteristic
411C22×C5D4211yescharacteristic
412C22×C5D4211yescharacteristic
413C22×C5#54611yescharacteristic
414C22×C5#54611yescharacteristic
415C22×C5#54711yescharacteristic
416C22×C5#54811yescharacteristic
417C22×C5#54811yescharacteristic
418C22×C5D4×Q811yescharacteristic
419C22×C5D4×Q811yescharacteristic
420C22×C5D4×Q811yescharacteristic
421C22×C5#55411yescharacteristic
422C22×C5#55411yescharacteristic
423C22×C5#55511yescharacteristic
424C22×C5#55611yescharacteristic
425C22×C5#55711yescharacteristic
426C22×C5Q8211yescharacteristic
427C4×C5—28no—
428C4×C5—24no—
429C4×C5—42no—
430C4×C5—44no—
431C4×C5#39118yescomplemented
432Dic5—24no—
433Dic5—24no—
434Dic5—44no—
435Dic5—42no—
436Dic5—42no—
437Dic5—82no—
438C24C23×D511yescharacteristic
439C2×Q8—1016no—
440C2×Q8—1016no—
441C2×Q8—208no—
442C2×Q8—208no—
443C2×Q8—208no—
444C2×Q8—208no—
445C2×Q8—208no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—52no—
467C22×C4—52no—
468C22×C4—52no—
469C22×C4—52no—
470C22×C4—52no—
471C22×C4—52no—
472C22×C4—54no—
473C22×C4—52no—
474C22×C4—52no—
475C22×C4—101no—
476C22×C4—101no—
477C22×C4—101no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4—101no—
481C22×C4—101no—
482C22×C4—101no—
483C22×C4—101no—
484C22×C4—101no—
485C22×C4—102no—
486C22×C4—101no—
487C22×C4—101no—
488C22×C4—101no—
489C22×C4—101no—
490C22×C4—102no—
491C22×C4—101no—
492C22×C4—102no—
493C22×C4—101no—
494C22×C4—101no—
495C22×C4—101no—
496C22×C4—102no—
497C22×C4—102no—
498C22×C4—101no—
499C22×C4—101no—
500C22×C4—102no—
501C22×C4—102no—
502C22×C4—102no—
503C22×C4—102no—
504C22×C4—102no—
505C22×C4—102no—
506C22×C4—102no—
507C22×C4—102no—
508C22×C4C2×Dic1012yes—
509C22×C4C2×Dic1014yes—
510C22×C4C2×Dic1012yes—
511C22×C4C2×Dic1012yes—
512C22×C4C2×Dic1012yes—
513C22×C4C2×C4×D514yes—
514C22×C4C2×C4×D512yes—
515C22×C4C2×D2014yes—
516C22×C4C2×D2012yes—
517C22×C4#70912yes—
518C22×C4#70912yes—
519C22×C4D4×D512yes—
520C22×C4Q8×D512yes—
521C22×C4C2×C22⋊D514yes—
522C22×C4C2×C22⋊D512yes—
523C4⋊C4—28no—
524C4⋊C4—1016no—
525C4⋊C4—108no—
526C4⋊C4—208no—
527C4⋊C4—204no—
528C4⋊C4#685116yes—
529C42—28no—
530C42—48no—
531C42—108no—
532C42—204no—
533C2×C5C2×#39111yescharacteristic
534C2×C5C4×C4⋊Q811yescharacteristic
535C2×C5#233111yescharacteristic
536C2×C5D4×C22⋊C411yescharacteristic
537C2×C5Q8×C22⋊C411yescharacteristic
538C2×C5#236511yescharacteristic
539C2×C5#236911yescharacteristic
540C2×C5#243911yescharacteristic
541C2×C5#244011yescharacteristic
542C2×C5#245111yescharacteristic
543C2×C5#245211yescharacteristic
544C2×C5#249111yescharacteristic
545C2×C5#249211yescharacteristic
546C2×C5#255011yescharacteristic
547C2×C5#255111yescharacteristic
548C23C22×Dic1011yescharacteristic
549C23C22×Dic1011yescharacteristic
550C23C22×C4×D511yescharacteristic
551C23C22×D2011yescharacteristic
552C23C2×#70911yescharacteristic
553C23C2×#70911yescharacteristic
554C23C2×D4×D511yescharacteristic
555C23#414411yescharacteristic
556C23C2×Q8×D511yescharacteristic
557C23#414711yescharacteristic
558C23D5×#4111yescharacteristic
559C23D5×#4111yescharacteristic
560C23#414911yescharacteristic
561C23#415011yescharacteristic
562C23C22×C22⋊D511yescharacteristic
563Q8—2032no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—54no—
591C2×C4—54no—
592C2×C4—102no—
593C2×C4—102no—
594C2×C4—102no—
595C2×C4—102no—
596C2×C4—102no—
597C2×C4—102no—
598C2×C4—102no—
599C2×C4—102no—
600C2×C4—102no—
601C2×C4—102no—
602C2×C4—102no—
603C2×C4—102no—
604C2×C4—102no—
605C2×C4—102no—
606C2×C4—104no—
607C2×C4—104no—
608C2×C4—104no—
609C2×C4—102no—
610C2×C4—102no—
611C2×C4—102no—
612C2×C4—102no—
613C2×C4—201no—
614C2×C4—201no—
615C2×C4—201no—
616C2×C4—201no—
617C2×C4—202no—
618C2×C4—202no—
619C2×C4—202no—
620C2×C4—201no—
621C2×C4—201no—
622C2×C4—202no—
623C2×C4—201no—
624C2×C4—201no—
625C2×C4—202no—
626C2×C4—202no—
627C2×C4—202no—
628C2×C4—202no—
629C2×C4—202no—
630C2×C4—202no—
631C2×C4—202no—
632C2×C4C4×Dic1014yes—
633C2×C4C4×Dic1014yes—
634C2×C4#401514yes—
635C2×C4#402114yes—
636C2×C4#403414yescomplemented
637C2×C4#407014yes—
638C2×C4#407014yes—
639C2×C4C2×#68518yes—
640C2×C4C2×#68514yes—
641C5#1405311yescharacteristic, complemented, Sylow
642C22C2×C4×Dic1011yescharacteristic
643C22C2×C4×Dic1011yescharacteristic
644C22C2×#401511yescharacteristic
645C22C2×#402111yescharacteristic
646C22C2×#403411yescharacteristic
647C22#6583411yescharacteristic
648C22#6584111yescharacteristic
649C22#6584511yescharacteristic
650C22#6585111yescharacteristic
651C22#6585311yescharacteristic
652C22#6586611yescharacteristic
653C22#6586711yescharacteristic
654C22D4×Dic1011yescharacteristic
655C22#6587311yescharacteristic
656C22C4×D4×D511yescharacteristic
657C22#6587911yescharacteristic
658C22#6588211yescharacteristic
659C22D4×D2011yescharacteristic
660C22#6588811yescharacteristic
661C22#6589511yescharacteristic
662C22Q8×Dic1011yescharacteristic
663C22#6590311yescharacteristic
664C22C4×Q8×D511yescharacteristic
665C22#6590611yescharacteristic
666C22Q8×D2011yescharacteristic
667C22#6591011yescharacteristic
668C22#6591211yescharacteristic
669C22#6591611yescharacteristic
670C22C2×#407011yescharacteristic
671C22C2×#407011yescharacteristic
672C22C22×#68511yescharacteristic
673C22D4×C22⋊D511yescharacteristic
674C22Q8×C22⋊D511yescharacteristic
675C22#6616311yescharacteristic
676C22#6616511yescharacteristic
677C4—28no—
678C4—24no—
679C4—44no—
680C4—42no—
681C4—104no—
682C4—104no—
683C4—204no—
684C4—202no—
685C4—202no—
686C4—402no—
687C4#6521818yescomplemented
688C2C4×#403411yescharacteristic
689C2#1060535811yescharacteristic
690C2#1060538311yescharacteristic
691C2#1060538811yescharacteristic
692C2#1060544511yescharacteristic
693C2#1060544611yescharacteristic
694C2#1060551911yescharacteristic
695C2#1060552011yescharacteristic
696C2C2×#6521811yescharacteristic
697C2#1061390211yescharacteristic
698C2#1061397911yescharacteristic
699C2#1061409311yescharacteristic
700C2D4×#68511yescharacteristic
701C2#1061420111yescharacteristic
702C2Q8×#68511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C4×C5×C4⋊C4C2
socle, prime radical, cosocleC24×C5C24
hypercenterC2×C4×C4⋊C4D5
hypocenterC5#14053
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
25. C2×#4034C4semidirect
65. C2×C5×C4⋊C4Q8semidirect
71. C2×C42×C5Q8semidirect
102. #3963Q8semidirect
287. C2×C4×C5C4⋊Q8semidirect
364. C2×C4⋊C4Dic10semidirect
379. C2×C42Dic10semidirect
431. C4×C5#391semidirect
636. C2×C4#4034semidirect
641. C5#14053semidirect
687. C4#65218semidirect

Maximal subgroups

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

subgroupindex
C22×#40342
C2×C4×C5×C4⋊C42
C2×#652742
C2×#652182
#106023562
#106023292
#106023282
C4×#39632
#106002172
#106002032
#140535