Finite Group Databasebeta

← #12005318

Subgroups — #12005318

Order 1280.

986 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65274C211yesmaximal, characteristic
2C2×C4⋊C4×Dic5C211yesmaximal, characteristic
3C2×C5×#340C211yesmaximal, characteristic
4C2×#64771C211yesmaximal, characteristic
5C2×#64770C211yesmaximal, characteristic
6C2×#64749C211yesmaximal, characteristic
7C2×#64749C211yesmaximal, characteristic
8C23×C5×C8C2211yescharacteristic
9C22×C5×C4⋊C4C2211yescharacteristic
10C22×C5×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic5—21no—
12C22×C4⋊Dic5C2211yescharacteristic
13C22×C4⋊Dic5C2211yescharacteristic
14C22×C4×Dic5—21no—
15C22×C4×Dic5C2211yescharacteristic
16C23×#168C2211yescharacteristic
17C2×#3963—21no—
18C2×#3963—21no—
19#65274—22no—
20#65274C414yescomplemented
21C4⋊C4×Dic5—22no—
22C4⋊C4×Dic5—22no—
23C5×#340C414yescomplemented
24#64771—22no—
25#64770—22no—
26#64749—22no—
27#64749C414yescomplemented
28#10885—51nomaximal, Sylow
29C23×C4×C5—21no—
30C23×C4×C5—21no—
31C23×C4×C5C2311yescharacteristic
32C23×Dic5—21no—
33C23×Dic5—21no—
34C23×Dic5D411yescharacteristic
35C23×Dic5D411yescharacteristic
36C22×C5×C8—21no—
37C22×C5×C8—21no—
38C22×C5×C8—21no—
39C22×C5×C8—21no—
40C22×C5×C8—21no—
41C22×C5×C8—21no—
42C22×C5×C8C2×C412yes—
43C2×C5×C4⋊C4—21no—
44C2×C5×C4⋊C4—21no—
45C2×C5×C4⋊C4—21no—
46C2×C5×C4⋊C4—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4C2×C412yes—
50C2×C5×C4⋊C4C2×C412yes—
51C2×C5×C4⋊C4C2×C412yes—
52C2×C5×C4⋊C4C2×C412yes—
53C2×C5×C4⋊C4D412yes—
54C2×C5×C4⋊C4Q812yes—
55C2×C4⋊Dic5—21no—
56C2×C4⋊Dic5—21no—
57C2×C4⋊Dic5—21no—
58C2×C4⋊Dic5—21no—
59C2×C4⋊Dic5—21no—
60C2×C4⋊Dic5—21no—
61C2×C4⋊Dic5—21no—
62C2×C4⋊Dic5—21no—
63C2×C4⋊Dic5—24no—
64C2×C4⋊Dic5—42no—
65C2×C4⋊Dic5—42no—
66C2×C4⋊Dic5C2×C412yes—
67C2×C4⋊Dic5C2×C412yes—
68C2×C4⋊Dic5D412yes—
69C2×C4⋊Dic5Q812yes—
70C2×C4×Dic5—21no—
71C2×C4×Dic5—21no—
72C2×C4×Dic5—21no—
73C2×C4×Dic5—21no—
74C2×C4×Dic5—24no—
75C2×C4×Dic5—42no—
76C2×C4×Dic5—42no—
77C2×C4×Dic5C2×C412yes—
78C2×C4×Dic5D412yes—
79C22×#168—21no—
80C22×#168—21no—
81C22×#168—21no—
82C22×#168—21no—
83C22×#168—21no—
84C22×#168—21no—
85C22×#168C2×C412yes—
86#3963—24no—
87#3963—24no—
88C2×#389—51no—
89C2×C4×C4⋊C4—51no—
90C2×#340—51no—
91C2×#340—51no—
92C2×#340—51no—
93C2×#340D511yescharacteristic
94C2×#336—51no—
95C24×C5C2×D411yescharacteristic
96C22×C4×C5—22no—
97C22×C4×C5—22no—
98C22×C4×C5—22no—
99C22×C4×C5—22no—
100C22×C4×C5—22no—
101C22×C4×C5—22no—
102C22×C4×C5—41no—
103C22×C4×C5—41no—
104C22×C4×C5—41no—
105C22×C4×C5—41no—
106C22×C4×C5—41no—
107C22×C4×C5—41no—
108C22×C4×C5—41no—
109C22×C4×C5—41no—
110C22×C4×C5C22×C411yescharacteristic
111C22×C4×C5C22×C411yescharacteristic
112C22×C4×C5C22×C411yescharacteristic
113C22×C4×C5C2×D411yescharacteristic
114C22×C4×C5C2×D411yescharacteristic
115C22×C4×C5C2×D411yescharacteristic
116C22×C4×C5C2×Q811yescharacteristic
117C22×C4×C5C2×Q811yescharacteristic
118C22×C4×C5#4111yescharacteristic
119C22×C4×C5#4111yescharacteristic
120C22×C4×C5#4111yescharacteristic
121C22×C4×C5#4111yescharacteristic
122C22×C4×C5#4111yescharacteristic
123C22×C4×C5#4111yescharacteristic
124C22×Dic5—21no—
125C22×Dic5—21no—
126C22×Dic5—21no—
127C22×Dic5—21no—
128C22×Dic5—22no—
129C22×Dic5—22no—
130C22×Dic5—21no—
131C22×Dic5—22no—
132C22×Dic5—21no—
133C22×Dic5—21no—
134C22×Dic5—21no—
135C22×Dic5—21no—
136C22×Dic5—21no—
137C22×Dic5—22no—
138C22×Dic5—41no—
139C22×Dic5—41no—
140C22×Dic5—41no—
141C22×Dic5—41no—
142C22×Dic5—41no—
143C22×Dic5—41no—
144C22×Dic5—41no—
145C22×Dic5—41no—
146C22×Dic5—41no—
147C22×Dic5—41no—
148C22×Dic5C22⋊C412yes—
149C22×Dic5C22⋊C412yes—
150C22×Dic5SD1612yes—
151C22×Dic5Q1612yes—
152C2×C5×C8—22no—
153C2×C5×C8—22no—
154C2×C5×C8—22no—
155C2×C5×C8—41no—
156C2×C5×C8—41no—
157C2×C5×C8—41no—
158C2×C5×C8—41no—
159C5×C4⋊C4—22no—
160C5×C4⋊C4—22no—
161C5×C4⋊C4—22no—
162C5×C4⋊C4—22no—
163C5×C4⋊C4—22no—
164C5×C4⋊C4—22no—
165C5×C4⋊C4C4214yescomplemented
166C5×C4⋊C4C4⋊C414yescomplemented
167C4⋊Dic5—22no—
168C4⋊Dic5—22no—
169C4⋊Dic5—22no—
170C4⋊Dic5—22no—
171C4⋊Dic5—22no—
172C4⋊Dic5—48no—
173C4⋊Dic5—41no—
174C4⋊Dic5—41no—
175C4⋊Dic5C4⋊C414yescomplemented
176C4×Dic5—22no—
177C4×Dic5—22no—
178C4×Dic5—22no—
179C4×Dic5—22no—
180C4×Dic5—48no—
181C2×#168—22no—
182C2×#168—22no—
183C2×#168—22no—
184C2×#168—41no—
185C2×#168—41no—
186C2×#168—41no—
187C2×#168—41no—
188C23×C8—51no—
189C23×C8C2×D511yescharacteristic
190C22×C4⋊C4—51no—
191C22×C4⋊C4—51no—
192C22×C4⋊C4—101no—
193C22×C4⋊C4C2×D511yescharacteristic
194C22×C4⋊C4C2×D511yescharacteristic
195C22×C42—51no—
196C22×C42—101no—
197#389—54no—
198#389—102no—
199C4×C4⋊C4—102no—
200C4×C4⋊C4—102no—
201C2×#95—101no—
202C2×#95—101no—
203#340—54no—
204#340—102no—
205#340—102no—
206#340Dic514yescomplemented
207#336—102no—
208C23×C5C2×C22⋊C411yescharacteristic
209C23×C5C4×D411yescharacteristic
210C23×C5C4×D411yescharacteristic
211C23×C5#12011yescharacteristic
212C23×C5C22⋊Q811yescharacteristic
213C23×C5C22⋊Q811yescharacteristic
214C23×C5#12311yescharacteristic
215C23×C5C2×SD1611yescharacteristic
216C23×C5C2×Q1611yescharacteristic
217C23×C5#13511yescharacteristic
218C23×C5#13511yescharacteristic
219C23×C5AGL(1,ℤ/8)11yescharacteristic
220C23×C5AGL(1,ℤ/8)11yescharacteristic
221C23×C5AGL(1,ℤ/8)11yescharacteristic
222C23×C5#13711yescharacteristic
223C2×C4×C5—24no—
224C2×C4×C5—24no—
225C2×C4×C5—42no—
226C2×C4×C5—42no—
227C2×C4×C5—42no—
228C2×C4×C5—42no—
229C2×C4×C5—42no—
230C2×C4×C5—42no—
231C2×C4×C5—42no—
232C2×C4×C5—42no—
233C2×C4×C5—42no—
234C2×C4×C5—42no—
235C2×C4×C5—42no—
236C2×C4×C5—42no—
237C2×C4×C5C2×C4211yescharacteristic
238C2×C4×C5C2×C4⋊C411yescharacteristic
239C2×C4×C5C2×C4⋊C411yescharacteristic
240C2×C4×C5#11711yescharacteristic
241C2×C4×C5#11711yescharacteristic
242C2×C4×C5#11711yescharacteristic
243C2×C4×C5C4×D411yescharacteristic
244C2×C4×C5C4×D411yescharacteristic
245C2×C4×C5C4×D411yescharacteristic
246C2×C4×C5C4×D411yescharacteristic
247C2×C4×C5C4×D411yescharacteristic
248C2×C4×C5C4×D411yescharacteristic
249C2×C4×C5C4×Q811yescharacteristic
250C2×C4×C5C4×Q811yescharacteristic
251C2×C4×C5C4×Q811yescharacteristic
252C2×C4×C5C4×Q811yescharacteristic
253C2×C4×C5#12111yescharacteristic
254C2×C4×C5#12111yescharacteristic
255C2×C4×C5C22⋊Q811yescharacteristic
256C2×C4×C5C22⋊Q811yescharacteristic
257C2×C4×C5#12311yescharacteristic
258C2×C4×C5#12311yescharacteristic
259C2×C4×C5#12411yescharacteristic
260C2×C4×C5#12511yescharacteristic
261C2×C4×C5#12511yescharacteristic
262C2×C4×C5#12611yescharacteristic
263C2×C4×C5#12611yescharacteristic
264C2×C4×C5C4⋊Q811yescharacteristic
265C2×Dic5—22no—
266C2×Dic5—22no—
267C2×Dic5—22no—
268C2×Dic5—22no—
269C2×Dic5—22no—
270C2×Dic5—22no—
271C2×Dic5—24no—
272C2×Dic5—22no—
273C2×Dic5—22no—
274C2×Dic5—22no—
275C2×Dic5—42no—
276C2×Dic5—42no—
277C2×Dic5—41no—
278C2×Dic5—41no—
279C2×Dic5—42no—
280C2×Dic5—42no—
281C2×Dic5—42no—
282C2×Dic5—42no—
283C2×Dic5—41no—
284C2×Dic5—41no—
285C2×Dic5—42no—
286C2×Dic5—42no—
287C2×Dic5—42no—
288C2×Dic5—81no—
289C2×Dic5—81no—
290C2×Dic5—81no—
291C2×Dic5—81no—
292C2×Dic5#10314yes—
293C5×C8—42no—
294#168—42no—
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—51no—
298C23×C4—51no—
299C23×C4—101no—
300C23×C4—101no—
301C23×C4C22×D511yescharacteristic
302C22×C8—21no—
303C22×C8—21no—
304C22×C8—21no—
305C22×C8—21no—
306C22×C8—21no—
307C22×C8—21no—
308C22×C8—52no—
309C22×C8—101no—
310C22×C8—101no—
311C22×C8—101no—
312C22×C8—101no—
313C22×C8—101no—
314C22×C8—101no—
315C22×C8C2×Dic512yes—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—52no—
323C2×C4⋊C4—52no—
324C2×C4⋊C4—52no—
325C2×C4⋊C4—52no—
326C2×C4⋊C4—101no—
327C2×C4⋊C4—101no—
328C2×C4⋊C4—101no—
329C2×C4⋊C4—101no—
330C2×C4⋊C4—101no—
331C2×C4⋊C4—101no—
332C2×C4⋊C4—101no—
333C2×C4⋊C4—104no—
334C2×C4⋊C4—101no—
335C2×C4⋊C4—202no—
336C2×C4⋊C4—202no—
337C2×C4⋊C4Dic1012yes—
338C2×C4⋊C4C4×D512yes—
339C2×C4⋊C4C4×D512yes—
340C2×C4⋊C4D2012yes—
341C2×C4⋊C4C2×Dic512yes—
342C2×C4⋊C4C2×Dic512yes—
343C2×C42—52no—
344C2×C42—52no—
345C2×C42—101no—
346C2×C42—101no—
347C2×C42—101no—
348C2×C42—101no—
349C2×C42—104no—
350C2×C42—202no—
351C2×C42—202no—
352#95—104no—
353#95—104no—
354C22×C5C4×C22⋊C411yescharacteristic
355C22×C5#38511yescharacteristic
356C22×C5#38511yescharacteristic
357C22×C5#38611yescharacteristic
358C22×C5#38711yescharacteristic
359C22×C5#38711yescharacteristic
360C22×C5#39111yescharacteristic
361C22×C5C2×#10311yescharacteristic
362C22×C5#41611yescharacteristic
363C22×C5#41711yescharacteristic
364C22×C5#41811yescharacteristic
365C22×C5C4×SD1611yescharacteristic
366C22×C5C4×SD1611yescharacteristic
367C22×C5C4×Q1611yescharacteristic
368C22×C5C4×Q1611yescharacteristic
369C22×C5#44011yescharacteristic
370C22×C5#44011yescharacteristic
371C22×C5#44211yescharacteristic
372C22×C5#44211yescharacteristic
373C22×C5#44911yescharacteristic
374C22×C5#44911yescharacteristic
375C22×C5#45011yescharacteristic
376C22×C5#45111yescharacteristic
377C22×C5#47611yescharacteristic
378C22×C5#47611yescharacteristic
379C22×C5#47711yescharacteristic
380C22×C5#47711yescharacteristic
381C22×C5#47811yescharacteristic
382C22×C5#47811yescharacteristic
383C22×C5#47911yescharacteristic
384C22×C5#47911yescharacteristic
385C22×C5#48211yescharacteristic
386C22×C5#48211yescharacteristic
387C22×C5#48311yescharacteristic
388C22×C5#48411yescharacteristic
389C4×C5—44no—
390C4×C5—44no—
391C4×C5C4×C4⋊C411yescharacteristic
392C4×C5C4×C4⋊C411yescharacteristic
393C4×C5#38711yescharacteristic
394C4×C5#38711yescharacteristic
395C4×C5#38811yescharacteristic
396C4×C5#38811yescharacteristic
397C4×C5#38911yescharacteristic
398C4×C5#38911yescharacteristic
399Dic5—24no—
400Dic5—44no—
401Dic5—42no—
402Dic5—82no—
403C24D4×D511yescharacteristic
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—52no—
419C22×C4—52no—
420C22×C4—52no—
421C22×C4—52no—
422C22×C4—101no—
423C22×C4—101no—
424C22×C4—101no—
425C22×C4—101no—
426C22×C4—102no—
427C22×C4—101no—
428C22×C4—102no—
429C22×C4—101no—
430C22×C4—102no—
431C22×C4—101no—
432C22×C4—101no—
433C22×C4—101no—
434C22×C4—101no—
435C22×C4—102no—
436C22×C4—201no—
437C22×C4—201no—
438C22×C4—201no—
439C22×C4—201no—
440C22×C4—201no—
441C22×C4—201no—
442C22×C4—201no—
443C22×C4—201no—
444C22×C4—201no—
445C22×C4—201no—
446C22×C4C2×Dic1011yescharacteristic
447C22×C4C2×C4×D511yescharacteristic
448C22×C4C2×C4×D511yescharacteristic
449C22×C4C2×D2011yescharacteristic
450C22×C4#70911yescharacteristic
451C22×C4#70911yescharacteristic
452C22×C4D4×D511yescharacteristic
453C22×C4D4×D511yescharacteristic
454C22×C4#71111yescharacteristic
455C22×C4#71111yescharacteristic
456C22×C4#71111yescharacteristic
457C22×C4Q8×D511yescharacteristic
458C22×C4#71311yescharacteristic
459C22×C4C22×Dic511yescharacteristic
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—41no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—102no—
468C2×C8—102no—
469C2×C8—102no—
470C2×C8—201no—
471C2×C8—201no—
472C2×C8—201no—
473C2×C8—201no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—54no—
481C4⋊C4—102no—
482C4⋊C4—102no—
483C4⋊C4—102no—
484C4⋊C4—102no—
485C4⋊C4—102no—
486C4⋊C4—208no—
487C4⋊C4—201no—
488C4⋊C4—201no—
489C4⋊C4C4×Dic514yescomplemented
490C4⋊C4C4⋊Dic514yescomplemented
491C42—102no—
492C42—102no—
493C42—102no—
494C42—102no—
495C42—208no—
496C2×C5#143611yescharacteristic
497C2×C5C4×#10311yescharacteristic
498C2×C5#176211yescharacteristic
499C2×C5#186311yescharacteristic
500C2×C5#186311yescharacteristic
501C2×C5#186411yescharacteristic
502C2×C5#186411yescharacteristic
503C2×C5#187211yescharacteristic
504C2×C5#187511yescharacteristic
505C2×C5#192011yescharacteristic
506C2×C5#192011yescharacteristic
507C2×C5#192111yescharacteristic
508C2×C5#192111yescharacteristic
509C2×C5#198711yescharacteristic
510C2×C5#198911yescharacteristic
511C23#402411yescharacteristic
512C23D5×C22⋊C411yescharacteristic
513C23#402711yescharacteristic
514C23#402811yescharacteristic
515C23#404011yescharacteristic
516C23#404211yescharacteristic
517C23#405711yescharacteristic
518C23#405711yescharacteristic
519C23D5×SD1611yescharacteristic
520C23#406011yescharacteristic
521C23#406111yescharacteristic
522C23#406211yescharacteristic
523C23D5×Q1611yescharacteristic
524C23#406511yescharacteristic
525C23D4×Dic511yescharacteristic
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—54no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—102no—
545C2×C4—102no—
546C2×C4—102no—
547C2×C4—102no—
548C2×C4—102no—
549C2×C4—102no—
550C2×C4—104no—
551C2×C4—202no—
552C2×C4—201no—
553C2×C4—202no—
554C2×C4—202no—
555C2×C4—201no—
556C2×C4—202no—
557C2×C4—201no—
558C2×C4—202no—
559C2×C4—201no—
560C2×C4—202no—
561C2×C4—202no—
562C2×C4—202no—
563C2×C4—202no—
564C2×C4—401no—
565C2×C4—401no—
566C2×C4—401no—
567C2×C4—401no—
568C2×C4C4×Dic1011yescharacteristic
569C2×C4C4×Dic1011yescharacteristic
570C2×C4C4×D2011yescharacteristic
571C2×C4C4×D2011yescharacteristic
572C2×C4#402311yescharacteristic
573C2×C4#402411yescharacteristic
574C2×C4#402511yescharacteristic
575C2×C4#402711yescharacteristic
576C2×C4#402911yescharacteristic
577C2×C4#403011yescharacteristic
578C2×C4#403111yescharacteristic
579C2×C4#403211yescharacteristic
580C2×C4#403311yescharacteristic
581C2×C4#403411yescharacteristic
582C2×C4#403511yescharacteristic
583C2×C4#403611yescharacteristic
584C2×C4D5×C4⋊C411yescharacteristic
585C2×C4#403811yescharacteristic
586C2×C4#403911yescharacteristic
587C2×C4#404111yescharacteristic
588C2×C4#404311yescharacteristic
589C2×C4#404411yescharacteristic
590C2×C4C2×C4×Dic511yescharacteristic
591C2×C4C2×C4⋊Dic511yescharacteristic
592C2×C4#407211yescharacteristic
593C2×C4D4×Dic511yescharacteristic
594C2×C4D4×Dic511yescharacteristic
595C2×C4Q8×Dic511yescharacteristic
596C8—42no—
597C8—202no—
598C5#1088511yescharacteristic, complemented, Sylow
599C22#6493511yescharacteristic
600C22#6494411yescharacteristic
601C22#6495411yescharacteristic
602C22#6495711yescharacteristic
603C22#6504611yescharacteristic
604C22#6505011yescharacteristic
605C22#6505211yescharacteristic
606C22#6505911yescharacteristic
607C22#6506011yescharacteristic
608C22#6506511yescharacteristic
609C22#6507011yescharacteristic
610C22#6507411yescharacteristic
611C22#6507711yescharacteristic
612C22#6507911yescharacteristic
613C22#6508311yescharacteristic
614C22#6508511yescharacteristic
615C22D5×#10311yescharacteristic
616C22#6509311yescharacteristic
617C22#6509711yescharacteristic
618C22#6510011yescharacteristic
619C22#6514611yescharacteristic
620C22#6515111yescharacteristic
621C22#6515511yescharacteristic
622C22#6515911yescharacteristic
623C22#6516411yescharacteristic
624C22#6517311yescharacteristic
625C22#6517411yescharacteristic
626C22#6518011yescharacteristic
627C22C22⋊C4×Dic511yescharacteristic
628C22#6523911yescharacteristic
629C22#6527011yescharacteristic
630C22#6544111yescharacteristic
631C22SD16×Dic511yescharacteristic
632C22#6545311yescharacteristic
633C22Q16×Dic511yescharacteristic
634C4—44no—
635C4—44no—
636C4—104no—
637C4—204no—
638C4—202no—
639C4—402no—
640C4#6493611yescharacteristic
641C4#6494211yescharacteristic
642C4#6494311yescharacteristic
643C4#6495911yescharacteristic
644C4C4×C4⋊Dic511yescharacteristic
645C4#6524011yescharacteristic
646C4C4⋊C4×Dic511yescharacteristic
647C4#6527411yescharacteristic
648C2#1059959211yescharacteristic
649C2#1059959411yescharacteristic
650C2#1059961211yescharacteristic
651C2#1059961411yescharacteristic
652C2#1059967111yescharacteristic
653C2#1059967411yescharacteristic
654C2#1059968811yescharacteristic
655C2#1059969911yescharacteristic
656C2#1060020011yescharacteristic
657C2#1060094511yescharacteristic
658C2#1060096311yescharacteristic
659C2Dic5×#10311yescharacteristic
660C2#1060102911yescharacteristic
661C2#1060135111yescharacteristic
662C2#1060140311yescharacteristic
subgroupG/H
centerC24D4×D5
commutatorC2×C4×C5C2×C42
FrattiniC23×C4C22×D5
FittingC2×C5×#340C2
socle, prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenterC2×#340D5
hypocenterC5#10885
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
20. #65274C4semidirect
23. C5×#340C4semidirect
27. #64749C4semidirect
165. C5×C4⋊C4C42semidirect
166. C5×C4⋊C4C4⋊C4semidirect
175. C4⋊Dic5C4⋊C4semidirect
206. #340Dic5semidirect
489. C4⋊C4C4×Dic5semidirect
490. C4⋊C4C4⋊Dic5semidirect
598. C5#10885semidirect

Maximal subgroups

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

subgroupindex
C2×#652742
C2×C4⋊C4×Dic52
C2×C5×#3402
C2×#647712
C2×#647702
C2×#647492
#108855