Finite Group Databasebeta

← #12022686

Subgroups — #12022686

Order 1280.

1810 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic10C211yesmaximal, characteristic
2C2×C4×C5×C4⋊C4C211yesmaximal, characteristic
3C2×#65218C211yesmaximal, characteristic
4C2×#65218C211yesmaximal, characteristic
5C2×#65217C211yesmaximal, characteristic
6#10602361C212yesmaximal
7#10602357C212yesmaximal
8#10602328C211yesmaximal, characteristic
9#10602328C211yesmaximal, characteristic
10#10600207C212yesmaximal
11#10600199C212yesmaximal
12C23×Dic10C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C42×C5C2211yescharacteristic
16C22×C42×C5C2211yescharacteristic
17C22×C42×C5C2211yescharacteristic
18C22×C4⋊Dic5C2211yescharacteristic
19C22×C4⋊Dic5C2211yescharacteristic
20C22×C4⋊Dic5C2211yescharacteristic
21C22×#683C2212yes—
22C22×#683C2212yes—
23C22×C4×Dic5C2212yes—
24C2×C4×Dic10—24no—
25C2×C4×Dic10—24no—
26C2×C4×Dic10—24no—
27C4×C5×C4⋊C4—24no—
28C2×C5×#95C2211yescharacteristic
29C2×C5×#95C2211yescharacteristic
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39#65218—24no—
40#65218C418yescomplemented
41#65217—24no—
42#14017—51nomaximal, Sylow
43C23×C4×C5C2311yescharacteristic
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2311yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C23×Dic5C2312yes—
51C23×Dic5C2312yes—
52C23×Dic5C2312yes—
53C23×Dic5C2312yes—
54C22×Dic10—22no—
55C22×Dic10—22no—
56C22×Dic10—22no—
57C22×Dic10—22no—
58C22×Dic10C2×C414yes—
59C22×Dic10D414yes—
60C22×Dic10Q814yes—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—22no—
63C2×C5×C4⋊C4—22no—
64C2×C5×C4⋊C4—22no—
65C2×C5×C4⋊C4—22no—
66C2×C5×C4⋊C4Q814yescomplemented
67C2×C42×C5—22no—
68C2×C42×C5—22no—
69C2×C42×C5—22no—
70C2×C42×C5—22no—
71C2×C42×C5—22no—
72C2×C42×C5—22no—
73C2×C42×C5—22no—
74C2×C42×C5C2×C414yes—
75C2×C42×C5D414yes—
76C2×C4⋊Dic5—22no—
77C2×C4⋊Dic5—22no—
78C2×C4⋊Dic5—22no—
79C2×C4⋊Dic5—22no—
80C2×C4⋊Dic5—22no—
81C2×C4⋊Dic5—22no—
82C2×C4⋊Dic5—22no—
83C2×C4⋊Dic5C2×C414yes—
84C2×C4⋊Dic5D414yes—
85C2×#683—24no—
86C2×#683—24no—
87C2×#683—24no—
88C2×#683—24no—
89C2×#683—24no—
90C2×#683—42no—
91C2×C4×Dic5—24no—
92C2×C4×Dic5—24no—
93C2×C4×Dic5—24no—
94C4×Dic10—232no—
95C5×#95—22no—
96C5×#95—22no—
97#3963—24no—
98#3963—24no—
99#3963—24no—
100#3963—24no—
101#3963—24no—
102#3963—42no—
103#3963—42no—
104#3963C2×C418yes—
105#3963C2×C418yes—
106C22×C4×Q8—51no—
107C2×#391—51no—
108C2×#391—51no—
109C2×#389—51no—
110C2×C4×C4⋊C4D511yescharacteristic
111#1444—52no—
112#1442—52no—
113#1436—52no—
114#1436—52no—
115C4⋊#95—51no—
116C4⋊#95—51no—
117C24×C5C2411yescharacteristic
118C22×C4×C5—21no—
119C22×C4×C5—21no—
120C22×C4×C5—21no—
121C22×C4×C5—21no—
122C22×C4×C5—21no—
123C22×C4×C5—21no—
124C22×C4×C5—21no—
125C22×C4×C5—21no—
126C22×C4×C5—21no—
127C22×C4×C5—21no—
128C22×C4×C5—21no—
129C22×C4×C5—21no—
130C22×C4×C5—21no—
131C22×C4×C5—21no—
132C22×C4×C5—21no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5C22×C412yes—
151C22×C4×C5C22×C412yes—
152C22×C4×C5C22×C412yes—
153C22×C4×C5C2×D412yes—
154C22×C4×C5C2×D412yes—
155C22×C4×C5C2×D412yes—
156C22×C4×C5C2×D412yes—
157C22×C4×C5C2×D412yes—
158C22×C4×C5C2×Q812yes—
159C22×C4×C5C2×Q812yes—
160C22×C4×C5C2×Q812yes—
161C22×C4×C5C2×Q812yes—
162C22×C4×C5#4112yes—
163C22×C4×C5#4112yes—
164C22×C4×C5#4112yes—
165C22×C4×C5#4112yes—
166C22×C4×C5#4112yes—
167C22×Dic5—22no—
168C22×Dic5—22no—
169C22×Dic5—22no—
170C22×Dic5—22no—
171C22×Dic5—22no—
172C22×Dic5—22no—
173C22×Dic5—22no—
174C22×Dic5—22no—
175C22×Dic5—22no—
176C22×Dic5—22no—
177C22×Dic5—22no—
178C22×Dic5—22no—
179C22×Dic5—22no—
180C22×Dic5—22no—
181C22×Dic5—22no—
182C22×Dic5—22no—
183C22×Dic5—22no—
184C22×Dic5—22no—
185C22×Dic5—22no—
186C22×Dic5—22no—
187C22×Dic5—22no—
188C22×Dic5—22no—
189C22×Dic5—22no—
190C22×Dic5C22×C414yes—
191C22×Dic5C22×C414yes—
192C22×Dic5C2×D414yes—
193C22×Dic5C2×D414yes—
194C22×Dic5C2×Q814yes—
195C2×Dic10—28no—
196C2×Dic10—28no—
197C2×Dic10—28no—
198C2×Dic10—28no—
199C2×Dic10—28no—
200C2×Dic10—28no—
201C2×Dic10C4⋊C4116yescomplemented
202C5×C4⋊C4—28no—
203C5×C4⋊C4—28no—
204C42×C5—28no—
205C42×C5—28no—
206C42×C5—44no—
207C4⋊Dic5—28no—
208C4⋊Dic5—28no—
209C4⋊Dic5—44no—
210#683—216no—
211#683—48no—
212C4×Dic5—216no—
213C23×Q8—51no—
214C2×C4×Q8—104no—
215C2×C4×Q8—104no—
216C2×C4×Q8—104no—
217C22×C4⋊C4—51no—
218C22×C4⋊C4—51no—
219C22×C4⋊C4—52no—
220C22×C4⋊C4—51no—
221C22×C4⋊C4—52no—
222C22×C4⋊C4C2×D511yescharacteristic
223C22×C4⋊C4C2×D511yescharacteristic
224C22×C42—52no—
225C22×C42C2×D511yescharacteristic
226C22×C42C2×D511yescharacteristic
227C22×C42C2×D511yescharacteristic
228#391—58no—
229#391—104no—
230#389—104no—
231C4×C4⋊C4—24no—
232C2×#95—52no—
233C2×#95—52no—
234C2×#95—52no—
235C2×#95—52no—
236C2×#95—52no—
237C2×#95—52no—
238C2×#95—52no—
239C2×#95—52no—
240C2×#95—52no—
241C2×#95C2×D511yescharacteristic
242C2×#95C2×D511yescharacteristic
243C23×C5C23×C411yescharacteristic
244C23×C5C22×D411yescharacteristic
245C23×C5C22×D411yescharacteristic
246C23×C5C22×D411yescharacteristic
247C23×C5C22×Q811yescharacteristic
248C23×C5C22×Q811yescharacteristic
249C23×C5C2×#4111yescharacteristic
250C23×C5C2×#4111yescharacteristic
251C23×C5C2×#4111yescharacteristic
252C23×C5C2×#4111yescharacteristic
253C23×C5C2×#4111yescharacteristic
254C23×C5H(5,𝔽2)11yescharacteristic
255C23×C52−1+411yescharacteristic
256C23×C52−1+411yescharacteristic
257C23×C52−1+411yescharacteristic
258C2×C4×C5—22no—
259C2×C4×C5—22no—
260C2×C4×C5—22no—
261C2×C4×C5—22no—
262C2×C4×C5—22no—
263C2×C4×C5—22no—
264C2×C4×C5—22no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—22no—
278C2×C4×C5—22no—
279C2×C4×C5—22no—
280C2×C4×C5—22no—
281C2×C4×C5—22no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5—41no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5—41no—
296C2×C4×C5—41no—
297C2×C4×C5—41no—
298C2×C4×C5C2×C4⋊C414yes—
299C2×C4×C5C4×D414yes—
300C2×C4×C5C4×D414yes—
301C2×C4×C5C4×Q814yescomplemented
302C2×C4×C5#12014yes—
303C2×C4×C5C22⋊Q814yes—
304C2×C4×C5C22⋊Q814yes—
305C2×C4×C5C22⋊Q814yes—
306C2×C4×C5#12314yes—
307C2×Dic5—24no—
308C2×Dic5—24no—
309C2×Dic5—24no—
310C2×Dic5—24no—
311C2×Dic5—24no—
312C2×Dic5—24no—
313C2×Dic5—24no—
314C2×Dic5—24no—
315C2×Dic5—24no—
316C2×Dic5—24no—
317C2×Dic5—24no—
318C2×Dic5—24no—
319C2×Dic5—42no—
320C2×Dic5—42no—
321C2×Dic5—42no—
322C2×Dic5—42no—
323C2×Dic5—42no—
324C2×Dic5—42no—
325C2×Dic5—42no—
326C2×Dic5—42no—
327C2×Dic5—42no—
328C2×Dic5—42no—
329C2×Dic5—42no—
330C2×Dic5—42no—
331C2×Dic5—42no—
332C2×Dic5—42no—
333C2×Dic5—42no—
334C2×Dic5C2×C4⋊C418yes—
335Dic10—232no—
336C22×Q8—54no—
337C22×Q8—54no—
338C22×Q8—54no—
339C22×Q8—102no—
340C22×Q8—102no—
341C22×Q8—102no—
342C22×Q8—102no—
343C23×C4—52no—
344C23×C4—52no—
345C23×C4—52no—
346C23×C4—52no—
347C23×C4C22×D511yescharacteristic
348C23×C4C22×D511yescharacteristic
349C23×C4C22×D511yescharacteristic
350C23×C4C22×D511yescharacteristic
351C23×C4C22×D511yescharacteristic
352C23×C4C22×D511yescharacteristic
353C23×C4C22×D511yescharacteristic
354C4×Q8—1032no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—54no—
361C2×C4⋊C4—54no—
362C2×C4⋊C4—104no—
363C2×C4⋊C4—104no—
364C2×C4⋊C4—102no—
365C2×C4⋊C4—102no—
366C2×C4⋊C4—102no—
367C2×C4⋊C4—104no—
368C2×C4⋊C4—102no—
369C2×C4⋊C4—104no—
370C2×C4⋊C4—104no—
371C2×C4⋊C4—102no—
372C2×C4⋊C4—102no—
373C2×C4⋊C4—102no—
374C2×C4⋊C4—202no—
375C2×C4⋊C4Dic1014yescomplemented
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—104no—
384C2×C42—104no—
385C2×C42—104no—
386C2×C42C4×D514yes—
387C2×C42C22⋊D514yes—
388#95—22no—
389#95—22no—
390#95—58no—
391#95—58no—
392#95—104no—
393#95—104no—
394#95—104no—
395#95—104no—
396#95—104no—
397#95—202no—
398#95—202no—
399C22×C5C22×C4⋊C411yescharacteristic
400C22×C5C2×C4×D411yescharacteristic
401C22×C5C2×C4×D411yescharacteristic
402C22×C5C2×C4×Q811yescharacteristic
403C22×C5C4×#4111yescharacteristic
404C22×C5#51911yescharacteristic
405C22×C5#52011yescharacteristic
406C22×C5C2×#12011yescharacteristic
407C22×C5C2×C22⋊Q811yescharacteristic
408C22×C5C2×C22⋊Q811yescharacteristic
409C22×C5C2×C22⋊Q811yescharacteristic
410C22×C5C2×#12311yescharacteristic
411C22×C5#52511yescharacteristic
412C22×C5#52911yescharacteristic
413C22×C5#53311yescharacteristic
414C22×C5#53611yescharacteristic
415C22×C5#53711yescharacteristic
416C22×C5#54111yescharacteristic
417C22×C5#54211yescharacteristic
418C22×C5#54611yescharacteristic
419C22×C5#54711yescharacteristic
420C22×C5#54811yescharacteristic
421C22×C5#54811yescharacteristic
422C22×C5#54811yescharacteristic
423C22×C5D4×Q811yescharacteristic
424C22×C5D4×Q811yescharacteristic
425C22×C5#55011yescharacteristic
426C22×C5#55611yescharacteristic
427C22×C5#55611yescharacteristic
428C22×C5#55711yescharacteristic
429C22×C5#55711yescharacteristic
430C22×C5#55711yescharacteristic
431C22×C5#55711yescharacteristic
432C22×C5Q8211yescharacteristic
433C22×C5#55911yescharacteristic
434C4×C5—24no—
435C4×C5—24no—
436C4×C5—42no—
437C4×C5—42no—
438C4×C5—42no—
439C4×C5—42no—
440C4×C5#38518yes—
441Dic5—28no—
442Dic5—44no—
443Dic5—44no—
444Dic5—82no—
445C24C23×D511yescharacteristic
446C2×Q8—516no—
447C2×Q8—108no—
448C2×Q8—108no—
449C2×Q8—108no—
450C2×Q8—108no—
451C2×Q8—108no—
452C2×Q8—108no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—54no—
486C22×C4—54no—
487C22×C4—54no—
488C22×C4—54no—
489C22×C4—54no—
490C22×C4—102no—
491C22×C4—102no—
492C22×C4—102no—
493C22×C4—102no—
494C22×C4—102no—
495C22×C4—102no—
496C22×C4—102no—
497C22×C4—102no—
498C22×C4—102no—
499C22×C4—102no—
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×C4—102no—
509C22×C4—102no—
510C22×C4—102no—
511C22×C4—102no—
512C22×C4—102no—
513C22×C4C2×Dic1012yes—
514C22×C4C2×Dic1012yes—
515C22×C4C2×Dic1012yes—
516C22×C4C2×C4×D512yes—
517C22×C4C2×C4×D512yes—
518C22×C4C2×C4×D512yes—
519C22×C4#70912yes—
520C22×C4#70912yes—
521C22×C4#70912yes—
522C22×C4#70912yes—
523C22×C4D4×D512yes—
524C22×C4D4×D512yes—
525C22×C4Q8×D512yes—
526C22×C4#71312yes—
527C22×C4C2×C22⋊D512yes—
528C22×C4C2×C22⋊D512yes—
529C22×C4C2×C22⋊D512yes—
530C4⋊C4—28no—
531C4⋊C4—28no—
532C4⋊C4—1016no—
533C4⋊C4—108no—
534C4⋊C4—108no—
535C4⋊C4—208no—
536C4⋊C4—204no—
537C42—28no—
538C42—28no—
539C42—44no—
540C42—1016no—
541C2×C5C2×#38511yescharacteristic
542C2×C5C4×C22⋊Q811yescharacteristic
543C2×C5#232311yescharacteristic
544C2×C5Q8×C4⋊C411yescharacteristic
545C2×C5#235111yescharacteristic
546C2×C5#236511yescharacteristic
547C2×C5#236711yescharacteristic
548C2×C5#240711yescharacteristic
549C2×C5#240911yescharacteristic
550C2×C5#244611yescharacteristic
551C2×C5#244811yescharacteristic
552C2×C5#245111yescharacteristic
553C2×C5#245311yescharacteristic
554C2×C5#258111yescharacteristic
555C2×C5#258211yescharacteristic
556C23C22×Dic1011yescharacteristic
557C23C22×C4×D511yescharacteristic
558C23C2×#70911yescharacteristic
559C23C2×#70911yescharacteristic
560C23C2×#70911yescharacteristic
561C23C2×#70911yescharacteristic
562C23C2×D4×D511yescharacteristic
563C23C2×D4×D511yescharacteristic
564C23C2×Q8×D511yescharacteristic
565C23C2×#71311yescharacteristic
566C23#414911yescharacteristic
567C23#415011yescharacteristic
568C23#415011yescharacteristic
569C23#415011yescharacteristic
570C23C22×C22⋊D511yescharacteristic
571Q8—1032no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—58no—
613C2×C4—104no—
614C2×C4—104no—
615C2×C4—104no—
616C2×C4—104no—
617C2×C4—104no—
618C2×C4—104no—
619C2×C4—104no—
620C2×C4—104no—
621C2×C4—104no—
622C2×C4—104no—
623C2×C4—104no—
624C2×C4—104no—
625C2×C4—202no—
626C2×C4—202no—
627C2×C4—202no—
628C2×C4—202no—
629C2×C4—202no—
630C2×C4—202no—
631C2×C4—202no—
632C2×C4—202no—
633C2×C4—202no—
634C2×C4—202no—
635C2×C4—202no—
636C2×C4—202no—
637C2×C4—202no—
638C2×C4—202no—
639C2×C4—202no—
640C2×C4C4×Dic1014yescomplemented
641C2×C4D5×C4⋊C414yes—
642C2×C4#403914yes—
643C2×C4#404014yes—
644C2×C4#404214yes—
645C2×C4#407014yes—
646C2×C4C4×C22⋊D514yes—
647C2×C4#408314yes—
648C2×C4#409214yes—
649C5#1401711yescharacteristic, complemented, Sylow
650C22C2×C4×Dic1011yescharacteristic
651C22#6580411yescharacteristic
652C22C4×#70911yescharacteristic
653C22#6581311yescharacteristic
654C22C2×D5×C4⋊C411yescharacteristic
655C22C2×#403911yescharacteristic
656C22C2×#404011yescharacteristic
657C22C2×#404211yescharacteristic
658C22#6585011yescharacteristic
659C22#6585211yescharacteristic
660C22#6585711yescharacteristic
661C22#6586811yescharacteristic
662C22D4×Dic1011yescharacteristic
663C22D4×Dic1011yescharacteristic
664C22#6588411yescharacteristic
665C22#6588511yescharacteristic
666C22#6588611yescharacteristic
667C22#6588611yescharacteristic
668C22#6588611yescharacteristic
669C22#6588711yescharacteristic
670C22Q8×Dic1011yescharacteristic
671C22#6590111yescharacteristic
672C22#6590111yescharacteristic
673C22#6590111yescharacteristic
674C22#6590411yescharacteristic
675C22#6591811yescharacteristic
676C22#6591811yescharacteristic
677C22#6591911yescharacteristic
678C22C2×#407011yescharacteristic
679C22C2×C4×C22⋊D511yescharacteristic
680C22#6612511yescharacteristic
681C22C2×#408311yescharacteristic
682C22C2×#409211yescharacteristic
683C22#6615911yescharacteristic
684C22#6616711yescharacteristic
685C4—24no—
686C4—24no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—108no—
692C4—204no—
693C4—204no—
694C4—402no—
695C4#6527818yes—
696C2C4⋊C4×Dic1011yescharacteristic
697C2#1060536811yescharacteristic
698C2#1060538211yescharacteristic
699C2#1060538611yescharacteristic
700C2#1060540311yescharacteristic
701C2#1060540411yescharacteristic
702C2#1060540511yescharacteristic
703C2#1060540711yescharacteristic
704C2C4×#407011yescharacteristic
705C2C2×#6527811yescharacteristic
706C2#1061396611yescharacteristic
707C2#1061408011yescharacteristic
708C2#1061413311yescharacteristic
709C2#1061421111yescharacteristic
710C2#1061421311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C4×C5×C4⋊C4C2
socle, prime radical, cosocleC24×C5C24
hypercenterC2×C4×C4⋊C4D5
hypocenterC5#14017
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
40. #65218C4semidirect
66. C2×C5×C4⋊C4Q8semidirect
201. C2×Dic10C4⋊C4semidirect
301. C2×C4×C5C4×Q8semidirect
375. C2×C4⋊C4Dic10semidirect
640. C2×C4C4×Dic10semidirect
649. C5#14017semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic102
C2×C4×C5×C4⋊C42
C2×#652182
C2×#652172
#106023612
#106023572
#106023282
#106002072
#106001992
#140175