Finite Group Databasebeta

← C2×#10600214 #12021018

Subgroups — C2×#10600214 #12021018

Order 1280.

2942 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#683C211yesmaximal, characteristic
2C22×C5×#95C211yesmaximal, characteristic
3C22×#3963C211yesmaximal, characteristic
4C22×#3963C211yesmaximal, characteristic
5C22×#3963C211yesmaximal, characteristic
6C22×#3963C211yesmaximal, characteristic
7C22×#3963C211yesmaximal, characteristic
8#10600214C218yesmaximal, direct product factor
9C24×C4×C5C2211yescharacteristic
10C24×C4×C5C2211yescharacteristic
11C24×C4×C5C2211yescharacteristic
12C24×Dic5C2211yescharacteristic
13C24×Dic5C2211yescharacteristic
14C24×Dic5C2211yescharacteristic
15C24×Dic5C2211yescharacteristic
16C22×#683—24no—
17C22×#683—24no—
18C22×#683C418yescomplemented
19C22×#683C2214yes—
20C2×C5×#95—24no—
21C2×C5×#95C2214yes—
22C2×#3963—24no—
23C2×#3963—24no—
24C2×#3963—24no—
25C2×#3963—24no—
26C2×#3963—24no—
27C2×#3963C2214yes—
28C2×#3963C2214yes—
29C2×#3963C2214yes—
30C2×#3963C2214yes—
31C2×#3963C2214yes—
32C2×#1445—51nomaximal, Sylow
33C25×C5C2311yescharacteristic
34C23×C4×C5—22no—
35C23×C4×C5—22no—
36C23×C4×C5—22no—
37C23×C4×C5—22no—
38C23×C4×C5—22no—
39C23×C4×C5—22no—
40C23×C4×C5—22no—
41C23×C4×C5—22no—
42C23×C4×C5—22no—
43C23×C4×C5—22no—
44C23×C4×C5—22no—
45C23×C4×C5—22no—
46C23×C4×C5—22no—
47C23×C4×C5—22no—
48C23×C4×C5—22no—
49C23×C4×C5—22no—
50C23×C4×C5—22no—
51C23×C4×C5—22no—
52C23×C4×C5C2×C414yes—
53C23×C4×C5D414yes—
54C23×C4×C5Q814yes—
55C23×C4×C5C2312yes—
56C23×C4×C5C2312yes—
57C23×C4×C5C2312yes—
58C23×Dic5—22no—
59C23×Dic5—22no—
60C23×Dic5—22no—
61C23×Dic5—22no—
62C23×Dic5—22no—
63C23×Dic5—22no—
64C23×Dic5—22no—
65C23×Dic5—22no—
66C23×Dic5—22no—
67C23×Dic5—22no—
68C23×Dic5—22no—
69C23×Dic5—22no—
70C23×Dic5—22no—
71C23×Dic5—22no—
72C23×Dic5—22no—
73C23×Dic5—22no—
74C23×Dic5—22no—
75C23×Dic5—22no—
76C23×Dic5—22no—
77C23×Dic5—22no—
78C23×Dic5—22no—
79C23×Dic5—22no—
80C23×Dic5C2×C414yes—
81C23×Dic5C2×C414yes—
82C23×Dic5D414yes—
83C23×Dic5D414yes—
84C23×Dic5D414yes—
85C23×Dic5Q814yes—
86C23×Dic5C2312yes—
87C23×Dic5C2312yes—
88C23×Dic5C2312yes—
89C23×Dic5C2312yes—
90C2×#683—232no—
91C2×#683—28no—
92C2×#683—28no—
93C2×#683C2×C4116yescomplemented
94C5×#95—28no—
95#3963—28no—
96#3963—28no—
97#3963—28no—
98#3963—28no—
99#3963—28no—
100C23×C4⋊C4—51no—
101C22×#95—51no—
102C22×#95—51no—
103C22×#95—51no—
104C22×#95—51no—
105C22×#95—51no—
106C22×#95D511yescharacteristic
107#1445—58no—
108C24×C5C22×C412yes—
109C24×C5C2×D412yes—
110C24×C5C2×D412yes—
111C24×C5C2×D412yes—
112C24×C5C2×D412yes—
113C24×C5C2×Q812yes—
114C24×C5C2×Q812yes—
115C24×C5#4112yes—
116C24×C5#4112yes—
117C24×C5#4112yes—
118C24×C5#4112yes—
119C24×C5#4112yes—
120C24×C5#4112yes—
121C24×C5#4112yes—
122C24×C5#4112yes—
123C24×C5C2411yescharacteristic
124C22×C4×C5—28no—
125C22×C4×C5—28no—
126C22×C4×C5—28no—
127C22×C4×C5—28no—
128C22×C4×C5—28no—
129C22×C4×C5—28no—
130C22×C4×C5—28no—
131C22×C4×C5—28no—
132C22×C4×C5—28no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—44no—
152C22×C4×C5—44no—
153C22×C4×C5—44no—
154C22×C4×C5—44no—
155C22×C4×C5—44no—
156C22×C4×C5—44no—
157C22×C4×C5—44no—
158C22×C4×C5—44no—
159C22×C4×C5—44no—
160C22×C4×C5—44no—
161C22×C4×C5—44no—
162C22×C4×C5—44no—
163C22×C4×C5C22×C414yes—
164C22×C4×C5C2×D414yes—
165C22×C4×C5C2×Q814yes—
166C22×Dic5—28no—
167C22×Dic5—28no—
168C22×Dic5—28no—
169C22×Dic5—28no—
170C22×Dic5—28no—
171C22×Dic5—28no—
172C22×Dic5—22no—
173C22×Dic5—22no—
174C22×Dic5—22no—
175C22×Dic5—22no—
176C22×Dic5—28no—
177C22×Dic5—28no—
178C22×Dic5—28no—
179C22×Dic5—28no—
180C22×Dic5—28no—
181C22×Dic5—28no—
182C22×Dic5—28no—
183C22×Dic5—28no—
184C22×Dic5—28no—
185C22×Dic5—22no—
186C22×Dic5—22no—
187C22×Dic5—22no—
188C22×Dic5—22no—
189C22×Dic5—22no—
190C22×Dic5—22no—
191C22×Dic5—22no—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—22no—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—44no—
204C22×Dic5—44no—
205C22×Dic5—44no—
206C22×Dic5—44no—
207C22×Dic5—44no—
208C22×Dic5—44no—
209C22×Dic5—44no—
210C22×Dic5—44no—
211C22×Dic5—44no—
212C22×Dic5—44no—
213C22×Dic5—44no—
214C22×Dic5—44no—
215C22×Dic5C22⋊C4116yes—
216C22×Dic5C22×C414yes—
217C22×Dic5C22×C414yes—
218C22×Dic5C2×D414yes—
219C22×Dic5C2×D414yes—
220C22×Dic5C2×D414yes—
221C22×Dic5C2×Q814yes—
222#683—232no—
223C24×C4—51no—
224C24×C4—51no—
225C24×C4—51no—
226C24×C4—51no—
227C24×C4C2×D511yescharacteristic
228C24×C4C2×D511yescharacteristic
229C24×C4C2×D511yescharacteristic
230C22×C4⋊C4—58no—
231C22×C4⋊C4—54no—
232C22×C4⋊C4—104no—
233C22×C4⋊C4—104no—
234C2×#95—24no—
235C2×#95—54no—
236C2×#95—54no—
237C2×#95—54no—
238C2×#95—54no—
239C2×#95—54no—
240C2×#95—104no—
241C2×#95—104no—
242C2×#95—104no—
243C2×#95—104no—
244C2×#95—104no—
245C2×#95C2×D514yes—
246C23×C5C2×C22⋊C414yes—
247C23×C5#11714yes—
248C23×C5#11714yes—
249C23×C5C4×D414yes—
250C23×C5C4×D414yes—
251C23×C5C4×Q814yes—
252C23×C5C4×Q814yes—
253C23×C5#12114yes—
254C23×C5#12114yes—
255C23×C5C22⋊Q814yes—
256C23×C5C22⋊Q814yes—
257C23×C5C22⋊Q814yes—
258C23×C5C22⋊Q814yes—
259C23×C5C22⋊Q814yes—
260C23×C5C22⋊Q814yes—
261C23×C5#12314yes—
262C23×C5#12314yes—
263C23×C5#12314yes—
264C23×C5#12314yes—
265C23×C5#12314yes—
266C23×C5#12314yes—
267C23×C5#12314yes—
268C23×C5#12314yes—
269C23×C5#12414yes—
270C23×C5#12414yes—
271C23×C5#12514yes—
272C23×C5#12514yes—
273C23×C5#12514yes—
274C23×C5#12514yes—
275C23×C5#12614yes—
276C23×C5#12614yes—
277C23×C5#12614yes—
278C23×C5#12614yes—
279C23×C5#12714yes—
280C23×C5C4⋊Q814yes—
281C23×C5C23×C411yescharacteristic
282C23×C5C22×D411yescharacteristic
283C23×C5C22×D411yescharacteristic
284C23×C5C22×D411yescharacteristic
285C23×C5C22×D411yescharacteristic
286C23×C5C22×Q811yescharacteristic
287C23×C5C22×Q811yescharacteristic
288C23×C5C2×#4111yescharacteristic
289C23×C5C2×#4111yescharacteristic
290C23×C5C2×#4111yescharacteristic
291C23×C5C2×#4111yescharacteristic
292C23×C5C2×#4111yescharacteristic
293C23×C5C2×#4111yescharacteristic
294C23×C5C2×#4111yescharacteristic
295C23×C5C2×#4111yescharacteristic
296C2×C4×C5—24no—
297C2×C4×C5—24no—
298C2×C4×C5—24no—
299C2×C4×C5—24no—
300C2×C4×C5—24no—
301C2×C4×C5—24no—
302C2×C4×C5—24no—
303C2×C4×C5—24no—
304C2×C4×C5—24no—
305C2×C4×C5—42no—
306C2×C4×C5—42no—
307C2×C4×C5—42no—
308C2×C4×C5—42no—
309C2×C4×C5—42no—
310C2×C4×C5—42no—
311C2×C4×C5—42no—
312C2×C4×C5—42no—
313C2×C4×C5—42no—
314C2×C4×C5—42no—
315C2×C4×C5—42no—
316C2×C4×C5—42no—
317C2×C4×C5—416no—
318C2×C4×C5—416no—
319C2×C4×C5—416no—
320C2×Dic5—24no—
321C2×Dic5—24no—
322C2×Dic5—24no—
323C2×Dic5—24no—
324C2×Dic5—24no—
325C2×Dic5—24no—
326C2×Dic5—232no—
327C2×Dic5—24no—
328C2×Dic5—24no—
329C2×Dic5—24no—
330C2×Dic5—24no—
331C2×Dic5—24no—
332C2×Dic5—24no—
333C2×Dic5—24no—
334C2×Dic5—24no—
335C2×Dic5—24no—
336C2×Dic5—42no—
337C2×Dic5—42no—
338C2×Dic5—42no—
339C2×Dic5—42no—
340C2×Dic5—42no—
341C2×Dic5—42no—
342C2×Dic5—42no—
343C2×Dic5—42no—
344C2×Dic5—42no—
345C2×Dic5—42no—
346C2×Dic5—42no—
347C2×Dic5—42no—
348C2×Dic5—416no—
349C2×Dic5—416no—
350C2×Dic5—416no—
351C2×Dic5C2×C22⋊C418yes—
352C25C22×D511yescharacteristic
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—54no—
372C23×C4—54no—
373C23×C4—54no—
374C23×C4—52no—
375C23×C4—54no—
376C23×C4—54no—
377C23×C4—54no—
378C23×C4—52no—
379C23×C4—52no—
380C23×C4—52no—
381C23×C4—102no—
382C23×C4—102no—
383C23×C4—102no—
384C23×C4—102no—
385C23×C4—102no—
386C23×C4—102no—
387C23×C4—102no—
388C23×C4—102no—
389C23×C4—102no—
390C23×C4—102no—
391C23×C4—102no—
392C23×C4—102no—
393C23×C4—102no—
394C23×C4—102no—
395C23×C4—102no—
396C23×C4—102no—
397C23×C4—102no—
398C23×C4—102no—
399C23×C4—102no—
400C23×C4—102no—
401C23×C4—102no—
402C23×C4—102no—
403C23×C4Dic1014yes—
404C23×C4C4×D514yes—
405C23×C4C22⋊D514yes—
406C23×C4C22×D512yes—
407C23×C4C22×D512yes—
408C23×C4C22×D512yes—
409C2×C4⋊C4—516no—
410C2×C4⋊C4—108no—
411C2×C4⋊C4—108no—
412C2×C4⋊C4—1032no—
413#95—28no—
414#95—108no—
415#95—108no—
416#95—108no—
417#95—108no—
418#95—108no—
419C22×C5#38118yes—
420C22×C5#38718yes—
421C22×C5#38718yes—
422C22×C5#38718yes—
423C22×C5#38718yes—
424C22×C5#39018yes—
425C22×C5#39118yes—
426C22×C5#39718yes—
427C22×C5#39718yes—
428C22×C5#39818yes—
429C22×C5#39818yes—
430C22×C5#39918yes—
431C22×C5#39918yes—
432C22×C5#40018yes—
433C22×C5#40018yes—
434C22×C5C22×C22⋊C411yescharacteristic
435C22×C5C2×#11711yescharacteristic
436C22×C5C2×#11711yescharacteristic
437C22×C5C2×C4×D411yescharacteristic
438C22×C5C2×C4×D411yescharacteristic
439C22×C5C2×C4×Q811yescharacteristic
440C22×C5C2×C4×Q811yescharacteristic
441C22×C5C2×#12111yescharacteristic
442C22×C5C2×#12111yescharacteristic
443C22×C5C2×C22⋊Q811yescharacteristic
444C22×C5C2×C22⋊Q811yescharacteristic
445C22×C5C2×C22⋊Q811yescharacteristic
446C22×C5C2×C22⋊Q811yescharacteristic
447C22×C5C2×C22⋊Q811yescharacteristic
448C22×C5C2×C22⋊Q811yescharacteristic
449C22×C5C2×#12311yescharacteristic
450C22×C5C2×#12311yescharacteristic
451C22×C5C2×#12311yescharacteristic
452C22×C5C2×#12311yescharacteristic
453C22×C5C2×#12311yescharacteristic
454C22×C5C2×#12311yescharacteristic
455C22×C5C2×#12311yescharacteristic
456C22×C5C2×#12311yescharacteristic
457C22×C5C2×#12411yescharacteristic
458C22×C5C2×#12411yescharacteristic
459C22×C5C2×#12511yescharacteristic
460C22×C5C2×#12511yescharacteristic
461C22×C5C2×#12511yescharacteristic
462C22×C5C2×#12511yescharacteristic
463C22×C5C2×#12611yescharacteristic
464C22×C5C2×#12611yescharacteristic
465C22×C5C2×#12611yescharacteristic
466C22×C5C2×#12611yescharacteristic
467C22×C5C2×#12711yescharacteristic
468C22×C5C2×C4⋊Q811yescharacteristic
469C4×C5—44no—
470C4×C5—44no—
471C4×C5—44no—
472Dic5—28no—
473Dic5—44no—
474Dic5—44no—
475Dic5—44no—
476C24C2×Dic1012yes—
477C24C2×C4×D512yes—
478C24#70912yes—
479C24#70912yes—
480C24#70912yes—
481C24#70912yes—
482C24D4×D512yes—
483C24D4×D512yes—
484C24D4×D512yes—
485C24#71112yes—
486C24#71112yes—
487C24#71112yes—
488C24Q8×D512yes—
489C24#71312yes—
490C24C2×C22⋊D512yes—
491C24C23×D511yescharacteristic
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—54no—
532C22×C4—54no—
533C22×C4—54no—
534C22×C4—516no—
535C22×C4—54no—
536C22×C4—54no—
537C22×C4—54no—
538C22×C4—102no—
539C22×C4—102no—
540C22×C4—102no—
541C22×C4—102no—
542C22×C4—108no—
543C22×C4—108no—
544C22×C4—108no—
545C22×C4—108no—
546C22×C4—108no—
547C22×C4—108no—
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—102no—
559C22×C4—102no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—102no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—108no—
567C22×C4—108no—
568C22×C4—108no—
569C22×C4—108no—
570C22×C4—108no—
571C22×C4—108no—
572C22×C4—108no—
573C22×C4—108no—
574C22×C4—108no—
575C22×C4—204no—
576C22×C4—204no—
577C22×C4—204no—
578C22×C4—204no—
579C22×C4—204no—
580C22×C4—204no—
581C22×C4—204no—
582C22×C4—204no—
583C22×C4—204no—
584C22×C4—204no—
585C22×C4—204no—
586C22×C4—204no—
587C22×C4C2×Dic1014yes—
588C22×C4C2×C4×D514yes—
589C22×C4C2×C22⋊D514yes—
590C4⋊C4—1032no—
591C2×C5#1445116yescomplemented
592C2×C5C2×#38111yescharacteristic
593C2×C5C2×#38711yescharacteristic
594C2×C5C2×#38711yescharacteristic
595C2×C5C2×#38711yescharacteristic
596C2×C5C2×#38711yescharacteristic
597C2×C5C2×#39011yescharacteristic
598C2×C5C2×#39111yescharacteristic
599C2×C5C2×#39711yescharacteristic
600C2×C5C2×#39711yescharacteristic
601C2×C5C2×#39811yescharacteristic
602C2×C5C2×#39811yescharacteristic
603C2×C5C2×#39911yescharacteristic
604C2×C5C2×#39911yescharacteristic
605C2×C5C2×#40011yescharacteristic
606C2×C5C2×#40011yescharacteristic
607C23C4×Dic1014yes—
608C23#401614yes—
609C23#401814yes—
610C23#402214yes—
611C23#402414yes—
612C23#402414yes—
613C23#402514yes—
614C23#402514yes—
615C23D5×C22⋊C414yes—
616C23#402714yes—
617C23#402914yes—
618C23#402914yes—
619C23#402914yes—
620C23#403014yes—
621C23#403114yes—
622C23#403114yes—
623C23#403314yes—
624C23#403414yes—
625C23#403514yes—
626C23#403514yes—
627C23#403614yes—
628C23#403814yes—
629C23#404014yes—
630C23#404014yes—
631C23#404014yes—
632C23#404214yes—
633C23#404214yes—
634C23#404414yes—
635C23#407014yes—
636C23C4×C22⋊D514yes—
637C23#407514yes—
638C23#408114yes—
639C23#408514yes—
640C23#408614yes—
641C23#409214yes—
642C23C22×Dic1011yescharacteristic
643C23C22×C4×D511yescharacteristic
644C23C2×#70911yescharacteristic
645C23C2×#70911yescharacteristic
646C23C2×#70911yescharacteristic
647C23C2×#70911yescharacteristic
648C23C2×D4×D511yescharacteristic
649C23C2×D4×D511yescharacteristic
650C23C2×D4×D511yescharacteristic
651C23C2×#71111yescharacteristic
652C23C2×#71111yescharacteristic
653C23C2×#71111yescharacteristic
654C23C2×Q8×D511yescharacteristic
655C23C2×#71311yescharacteristic
656C23C22×C22⋊D511yescharacteristic
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—416no—
679C2×C4—416no—
680C2×C4—416no—
681C2×C4—58no—
682C2×C4—104no—
683C2×C4—104no—
684C2×C4—104no—
685C2×C4—104no—
686C2×C4—104no—
687C2×C4—104no—
688C2×C4—1032no—
689C2×C4—104no—
690C2×C4—104no—
691C2×C4—104no—
692C2×C4—104no—
693C2×C4—104no—
694C2×C4—104no—
695C2×C4—104no—
696C2×C4—104no—
697C2×C4—104no—
698C2×C4—2016no—
699C2×C4—202no—
700C2×C4—202no—
701C2×C4—202no—
702C2×C4—202no—
703C2×C4—202no—
704C2×C4—202no—
705C2×C4—202no—
706C2×C4—202no—
707C2×C4—202no—
708C2×C4—202no—
709C2×C4—202no—
710C2×C4—202no—
711C2×C4—2016no—
712C2×C4—2016no—
713C5C2×#144511yescharacteristic, complemented, Sylow
714C22#6493518yes—
715C22#6494118yes—
716C22#6494418yes—
717C22#6494618yes—
718C22#6494718yes—
719C22#6494918yes—
720C22#6495318yes—
721C22#6496418yes—
722C22#6522218yes—
723C22#6523818yes—
724C22#6524118yes—
725C22#6524618yes—
726C22#6526718yes—
727C22#6527318yes—
728C22#6528118yes—
729C22C2×C4×Dic1011yescharacteristic
730C22C2×#401611yescharacteristic
731C22C2×#401811yescharacteristic
732C22C2×#402211yescharacteristic
733C22C2×#402411yescharacteristic
734C22C2×#402411yescharacteristic
735C22C2×#402511yescharacteristic
736C22C2×#402511yescharacteristic
737C22C2×D5×C22⋊C411yescharacteristic
738C22C2×#402711yescharacteristic
739C22C2×#402911yescharacteristic
740C22C2×#402911yescharacteristic
741C22C2×#402911yescharacteristic
742C22C2×#403011yescharacteristic
743C22C2×#403111yescharacteristic
744C22C2×#403111yescharacteristic
745C22C2×#403311yescharacteristic
746C22C2×#403411yescharacteristic
747C22C2×#403511yescharacteristic
748C22C2×#403511yescharacteristic
749C22C2×#403611yescharacteristic
750C22C2×#403811yescharacteristic
751C22C2×#404011yescharacteristic
752C22C2×#404011yescharacteristic
753C22C2×#404011yescharacteristic
754C22C2×#404211yescharacteristic
755C22C2×#404211yescharacteristic
756C22C2×#404411yescharacteristic
757C22C2×#407011yescharacteristic
758C22C2×C4×C22⋊D511yescharacteristic
759C22C2×#407511yescharacteristic
760C22C2×#408111yescharacteristic
761C22C2×#408511yescharacteristic
762C22C2×#408611yescharacteristic
763C22C2×#409211yescharacteristic
764C4—44no—
765C4—44no—
766C4—44no—
767C4—108no—
768C4—204no—
769C4—204no—
770C4—204no—
771C2#10600214116yesdirect product factor
772C2C2×#6494111yescharacteristic
773C2C2×#6494411yescharacteristic
774C2C2×#6493511yescharacteristic
775C2C2×#6494611yescharacteristic
776C2C2×#6494711yescharacteristic
777C2C2×#6494911yescharacteristic
778C2C2×#6495311yescharacteristic
779C2C2×#6496411yescharacteristic
780C2C2×#6522211yescharacteristic
781C2C2×#6524611yescharacteristic
782C2C2×#6524111yescharacteristic
783C2C2×#6523811yescharacteristic
784C2C2×#6526711yescharacteristic
785C2C2×#6527311yescharacteristic
786C2C2×#6528111yescharacteristic
subgroupG/H
centerC25C22×D5
commutatorC23×C5C23×C4
FrattiniC24C23×D5
FittingC22×C5×#95C2
socle, prime radicalC25×C5C23
cosocleC24×C5C24
hypercenterC22×#95D5
hypocenterC5C2×#1445
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C25 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
8. #10600214C2direct (N × H)
18. C22×#683C4semidirect
93. C2×#683C2×C4semidirect
591. C2×C5#1445semidirect
713. C5C2×#1445semidirect
771. C2#10600214direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6832
C22×C5×#952
C22×#39632
#106002142
C2×#14455