Finite Group Databasebeta

← #158453

Subgroups — #158453

Order 512.

3632 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#384C211yesmaximal, characteristic, complemented
2C2×#1442C212yesmaximal, complemented
3C2×#1439C212yesmaximal
4C2×#1439C212yesmaximal
5C2×#1439C212yesmaximal
6C2×#1437C211yesmaximal, characteristic
7#7557C212yesmaximal, complemented
8#7557C212yesmaximal, complemented
9#7554C211yesmaximal, characteristic, complemented
10C23×C4⋊C4C2212yes—
11C23×C4⋊C4C2212yes—
12C23×C4⋊C4C2212yes—
13C23×C22⋊C4C2211yescharacteristic
14C23×C22⋊C4C2211yescharacteristic
15C23×C22⋊C4C2211yescharacteristic
16C23×C22⋊C4C2214yes—
17C23×C42C2211yescharacteristic
18C2×#384—24no—
19C2×#384—28no—
20C22×#95C2212yes—
21C22×#95C2212yes—
22C22×#95C2211yescharacteristic
23C22×#95C2211yescharacteristic
24C22×#95C2211yescharacteristic
25C22×#95C2214yes—
26C22×#95C2214yes—
27C22×#95C2212yes—
28C22×#95C2214yes—
29#1442—28no—
30#1439—28no—
31#1439—28no—
32#1439—28no—
33#1437—24no—
34C26C2311yescharacteristic
35C24×C4C2314yes—
36C24×C4C2314yes—
37C24×C4C2311yescharacteristic
38C24×C4C2311yescharacteristic
39C24×C4C2311yescharacteristic
40C24×C4C2311yescharacteristic
41C24×C4C2311yescharacteristic
42C24×C4C2311yescharacteristic
43C22×C4⋊C4—28no—
44C22×C4⋊C4—28no—
45C22×C4⋊C4—24no—
46C22×C4⋊C4—24no—
47C22×C4⋊C4—24no—
48C22×C4⋊C4—24no—
49C22×C4⋊C4—24no—
50C22×C4⋊C4—24no—
51C22×C4⋊C4—24no—
52C22×C4⋊C4—24no—
53C22×C4⋊C4—44no—
54C22×C4⋊C4—44no—
55C22×C4⋊C4—44no—
56C22×C4⋊C4—44no—
57C22×C4⋊C4D418yes—
58C22×C22⋊C4—22no—
59C22×C22⋊C4—22no—
60C22×C22⋊C4—22no—
61C22×C22⋊C4—24no—
62C22×C22⋊C4—24no—
63C22×C22⋊C4—22no—
64C22×C22⋊C4—22no—
65C22×C22⋊C4—24no—
66C22×C22⋊C4—22no—
67C22×C22⋊C4—24no—
68C22×C22⋊C4—24no—
69C22×C22⋊C4—24no—
70C22×C22⋊C4—28no—
71C22×C22⋊C4—28no—
72C22×C22⋊C4—28no—
73C22×C22⋊C4—44no—
74C22×C22⋊C4—44no—
75C22×C22⋊C4—44no—
76C22×C22⋊C4—44no—
77C22×C22⋊C4D414yes—
78C22×C22⋊C4Q814yes—
79C22×C22⋊C4Q814yes—
80C22×C42—24no—
81C22×C42—24no—
82C22×C42—24no—
83C22×C42D414yes—
84#384—232no—
85C2×#95—24no—
86C2×#95—24no—
87C2×#95—22no—
88C2×#95—22no—
89C2×#95—22no—
90C2×#95—28no—
91C2×#95—28no—
92C2×#95—28no—
93C2×#95—24no—
94C2×#95—24no—
95C2×#95—28no—
96C2×#95—28no—
97C2×#95—24no—
98C2×#95—24no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—24no—
102C2×#95—24no—
103C2×#95—24no—
104C2×#95—44no—
105C2×#95—44no—
106C2×#95—44no—
107C2×#95—44no—
108C2×#95D418yes—
109C25—21no—
110C25—22no—
111C25—22no—
112C25—21no—
113C25—21no—
114C25—21no—
115C25—22no—
116C25—22no—
117C25—22no—
118C25—22no—
119C25—22no—
120C25—22no—
121C25—22no—
122C25—22no—
123C25—22no—
124C25—22no—
125C25C2×D412yes—
126C25C2×Q812yes—
127C25C2×Q812yes—
128C25C2411yescharacteristic
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—22no—
132C23×C4—22no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—22no—
138C23×C4—22no—
139C23×C4—22no—
140C23×C4—22no—
141C23×C4—24no—
142C23×C4—24no—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4—22no—
146C23×C4—21no—
147C23×C4—22no—
148C23×C4—24no—
149C23×C4—24no—
150C23×C4—24no—
151C23×C4—24no—
152C23×C4—24no—
153C23×C4—22no—
154C23×C4—22no—
155C23×C4—21no—
156C23×C4—22no—
157C23×C4—21no—
158C23×C4—22no—
159C23×C4—21no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—24no—
163C23×C4—24no—
164C23×C4—24no—
165C23×C4—24no—
166C23×C4—24no—
167C23×C4—24no—
168C23×C4—22no—
169C23×C4—24no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—24no—
174C23×C4—24no—
175C23×C4—24no—
176C23×C4—24no—
177C23×C4—24no—
178C23×C4—24no—
179C23×C4—24no—
180C23×C4—24no—
181C23×C4—24no—
182C23×C4—24no—
183C23×C4—24no—
184C23×C4—24no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
190C23×C4—24no—
191C23×C4—24no—
192C23×C4—22no—
193C23×C4C2×D418yes—
194C23×C4C2×D418yes—
195C23×C4C2×D412yes—
196C23×C4C2×D412yes—
197C23×C4C2×D414yes—
198C23×C4C2×D412yes—
199C23×C4C2×D412yes—
200C23×C4C2×D414yes—
201C23×C4C2×D412yes—
202C23×C4C2×Q812yes—
203C23×C4C2×Q812yes—
204C23×C4C2×Q812yes—
205C23×C4C2×Q812yes—
206C23×C4#4112yes—
207C23×C4#4112yes—
208C23×C4#4114yes—
209C23×C4#4114yes—
210C23×C4#4112yes—
211C23×C4#4114yes—
212C23×C4#4114yes—
213C2×C4⋊C4—216no—
214C2×C4⋊C4—216no—
215C2×C4⋊C4—216no—
216C2×C4⋊C4—416no—
217C2×C4⋊C4—416no—
218C2×C4⋊C4—416no—
219C2×C4⋊C4—416no—
220C2×C4⋊C4—416no—
221C2×C4⋊C4—416no—
222C2×C4⋊C4—48no—
223C2×C4⋊C4—48no—
224C2×C4⋊C4—48no—
225C2×C4⋊C4—48no—
226C2×C4⋊C4—48no—
227C2×C4⋊C4—48no—
228C2×C22⋊C4—28no—
229C2×C22⋊C4—28no—
230C2×C22⋊C4—216no—
231C2×C22⋊C4—28no—
232C2×C22⋊C4—216no—
233C2×C22⋊C4—216no—
234C2×C22⋊C4—416no—
235C2×C22⋊C4—416no—
236C2×C22⋊C4—416no—
237C2×C22⋊C4—416no—
238C2×C22⋊C4—416no—
239C2×C22⋊C4—416no—
240C2×C22⋊C4—416no—
241C2×C22⋊C4—44no—
242C2×C22⋊C4—44no—
243C2×C22⋊C4—48no—
244C2×C22⋊C4—44no—
245C2×C22⋊C4—44no—
246C2×C22⋊C4—48no—
247C2×C22⋊C4—44no—
248C2×C22⋊C4—48no—
249C2×C22⋊C4—44no—
250C2×C42—232no—
251C2×C42—28no—
252C2×C42—28no—
253C2×C42—28no—
254#95—216no—
255#95—416no—
256#95—416no—
257#95—416no—
258#95—48no—
259#95—44no—
260#95—48no—
261#95—44no—
262#95—44no—
263C24—22no—
264C24—22no—
265C24—22no—
266C24—24no—
267C24—24no—
268C24—24no—
269C24—22no—
270C24—22no—
271C24—22no—
272C24—24no—
273C24—24no—
274C24—24no—
275C24—24no—
276C24—24no—
277C24—24no—
278C24—24no—
279C24—24no—
280C24—24no—
281C24—24no—
282C24—24no—
283C24—24no—
284C24—24no—
285C24—24no—
286C24—24no—
287C24—41no—
288C24—41no—
289C24—42no—
290C24—41no—
291C24—44no—
292C24—41no—
293C24—41no—
294C24—42no—
295C24—42no—
296C24—41no—
297C24—44no—
298C24—44no—
299C24—44no—
300C24—41no—
301C24—41no—
302C24—41no—
303C24—41no—
304C24—41no—
305C24—41no—
306C24—44no—
307C24—44no—
308C24—42no—
309C24—42no—
310C24—42no—
311C24—44no—
312C24—44no—
313C24—44no—
314C24—42no—
315C24—42no—
316C24—44no—
317C24—42no—
318C24—44no—
319C24—42no—
320C24—42no—
321C24—44no—
322C24—44no—
323C24—44no—
324C24—42no—
325C24—42no—
326C24—42no—
327C24—42no—
328C24—42no—
329C24—42no—
330C24—42no—
331C24—44no—
332C24—44no—
333C24C4⋊Q814yes—
334C24C22×D411yescharacteristic
335C24C22×D412yes—
336C24C22×D411yescharacteristic
337C24C22×D412yes—
338C24C22×Q811yescharacteristic
339C24C22×Q811yescharacteristic
340C24C2×#4111yescharacteristic
341C24C2×#4112yes—
342C24C2×#4111yescharacteristic
343C24C2×#4112yes—
344C24C2×#4111yescharacteristic
345C24C2×#4112yes—
346C24C2×#4112yes—
347C24H(5,𝔽2)12yes—
348C24H(5,𝔽2)12yes—
349C24H(5,𝔽2)12yes—
350C24H(5,𝔽2)12yes—
351C242−1+412yes—
352C242−1+412yes—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—28no—
360C22×C4—28no—
361C22×C4—28no—
362C22×C4—28no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—28no—
370C22×C4—28no—
371C22×C4—24no—
372C22×C4—28no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—28no—
376C22×C4—24no—
377C22×C4—28no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—28no—
381C22×C4—28no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—28no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—28no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—28no—
396C22×C4—24no—
397C22×C4—28no—
398C22×C4—28no—
399C22×C4—28no—
400C22×C4—28no—
401C22×C4—24no—
402C22×C4—28no—
403C22×C4—28no—
404C22×C4—28no—
405C22×C4—28no—
406C22×C4—28no—
407C22×C4—28no—
408C22×C4—24no—
409C22×C4—28no—
410C22×C4—28no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—41no—
416C22×C4—44no—
417C22×C4—44no—
418C22×C4—41no—
419C22×C4—42no—
420C22×C4—41no—
421C22×C4—44no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—44no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—42no—
429C22×C4—41no—
430C22×C4—42no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—44no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4—44no—
440C22×C4—44no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4—44no—
444C22×C4—44no—
445C22×C4—44no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—44no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—44no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4—44no—
475C22×C4—44no—
476C22×C4—44no—
477C22×C4—44no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—42no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4—44no—
486C22×C4—44no—
487C22×C4—42no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—42no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4#12014yes—
511C22×C4#12114yes—
512C22×C4C22⋊Q818yes—
513C22×C4C22⋊Q814yes—
514C22×C4C22⋊Q814yes—
515C22×C4C22⋊Q818yes—
516C22×C4#12318yes—
517C22×C4#12314yes—
518C22×C4#12318yes—
519C22×C4#12314yes—
520C22×C4#12418yes—
521C22×C4#12414yes—
522C22×C4#12414yes—
523C22×C4#12618yes—
524C22×C4#12714yes—
525C4⋊C4—432no—
526C4⋊C4—432no—
527C4⋊C4—432no—
528C22⋊C4—464no—
529C22⋊C4—416no—
530C22⋊C4—416no—
531C22⋊C4—416no—
532C42—232no—
533C23—24no—
534C23—28no—
535C23—28no—
536C23—28no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—48no—
541C23—48no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—48no—
551C23—44no—
552C23—48no—
553C23—44no—
554C23—44no—
555C23—44no—
556C23—48no—
557C23—48no—
558C23—48no—
559C23—48no—
560C23—48no—
561C23—48no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—44no—
567C23—44no—
568C23—44no—
569C23—44no—
570C23—44no—
571C23—48no—
572C23—48no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—81no—
577C23—81no—
578C23—84no—
579C23—81no—
580C23—81no—
581C23—81no—
582C23—81no—
583C23—81no—
584C23—81no—
585C23—81no—
586C23—81no—
587C23—84no—
588C23—81no—
589C23—81no—
590C23—84no—
591C23—84no—
592C23—84no—
593C23—84no—
594C23—84no—
595C23—84no—
596C23—81no—
597C23—81no—
598C23—81no—
599C23—81no—
600C23—84no—
601C23—84no—
602C23—84no—
603C23—84no—
604C23C2×#12011yescharacteristic
605C23C2×#12111yescharacteristic
606C23C2×C22⋊Q811yescharacteristic
607C23C2×C22⋊Q811yescharacteristic
608C23C2×C22⋊Q812yes—
609C23C2×C22⋊Q812yes—
610C23C2×#12311yescharacteristic
611C23C2×#12311yescharacteristic
612C23C2×#12312yes—
613C23C2×#12312yes—
614C23#52514yes—
615C23C2×#12411yescharacteristic
616C23C2×#12411yescharacteristic
617C23C2×#12412yes—
618C23C2×#12612yes—
619C23C2×#12711yescharacteristic
620C23C2×C4⋊Q811yescharacteristic
621C23#53214yes—
622C23#53211yescharacteristic
623C23#53311yescharacteristic
624C23#53311yescharacteristic
625C23#53414yes—
626C23#53511yescharacteristic
627C23#53511yescharacteristic
628C23#53511yescharacteristic
629C23#53511yescharacteristic
630C23#53514yes—
631C23#53512yes—
632C23#53611yescharacteristic
633C23#53611yescharacteristic
634C23#53914yes—
635C23#53914yes—
636C23#54012yes—
637C23#54212yes—
638C23#54212yes—
639C23#54214yes—
640C23#54214yes—
641C23#54412yes—
642C23#54412yes—
643C23D4212yes—
644C23D4212yes—
645C23D4214yes—
646C23#54612yes—
647C23#54712yes—
648C23#54712yes—
649C23#54712yes—
650C23#54714yes—
651C23#54812yes—
652C23#54814yes—
653C23D4×Q812yes—
654C23D4×Q812yes—
655C23#55012yes—
656C23#55212yes—
657C23#55314yes—
658C23#55314yes—
659C23#55314yes—
660C23#55312yes—
661C23#55312yes—
662C23#55312yes—
663C23#55412yes—
664C23#55412yes—
665C23#55412yes—
666C23#55412yes—
667C23#55412yes—
668C23#55412yes—
669C23#55512yes—
670C23#55512yes—
671C23#55512yes—
672C23#55612yes—
673C23#56014yes—
674C23#56314yes—
675C2×C4—216no—
676C2×C4—216no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—216no—
688C2×C4—216no—
689C2×C4—216no—
690C2×C4—216no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—48no—
703C2×C4—48no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—48no—
708C2×C4—48no—
709C2×C4—48no—
710C2×C4—48no—
711C2×C4—48no—
712C2×C4—48no—
713C2×C4—48no—
714C2×C4—48no—
715C2×C4—48no—
716C2×C4—48no—
717C2×C4—48no—
718C2×C4—48no—
719C2×C4—48no—
720C2×C4—48no—
721C2×C4—48no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—84no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—84no—
734C2×C4—81no—
735C2×C4—84no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4—84no—
755C2×C4—84no—
756C2×C4#39318yes—
757C2×C4#39718yes—
758C2×C4#39918yes—
759C22—44no—
760C22—44no—
761C22—416no—
762C22—44no—
763C22—88no—
764C22—82no—
765C22—88no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—88no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22C2×#39311yescharacteristic
779C22C2×#39711yescharacteristic
780C22C2×#39911yescharacteristic
781C22#240811yescharacteristic
782C22#240911yescharacteristic
783C22#242212yes—
784C22#242214yes—
785C22#242312yes—
786C22#243311yescharacteristic
787C22#243611yescharacteristic
788C22#243912yes—
789C22#244012yes—
790C22#244012yes—
791C22#244112yes—
792C22#244314yes—
793C22#244314yes—
794C22#244914yes—
795C22#245214yes—
796C22#248114yes—
797C22#248611yescharacteristic
798C22#248711yescharacteristic
799C22#248711yescharacteristic
800C22#248711yescharacteristic
801C22#249112yes—
802C22#249114yes—
803C22#249212yes—
804C22#249712yes—
805C22#249712yes—
806C22#250012yes—
807C22#250014yes—
808C22#250111yescharacteristic
809C22#250212yes—
810C22#250411yescharacteristic
811C22#250411yescharacteristic
812C22#250411yescharacteristic
813C22#251214yes—
814C22#254111yescharacteristic
815C22#254211yescharacteristic
816C22#254711yescharacteristic
817C22#256311yescharacteristic
818C22#256311yescharacteristic
819C22#256311yescharacteristic
820C22#256614yes—
821C22#257914yes—
822C22#259114yes—
823C22#261311yescharacteristic
824C22#261911yescharacteristic
825C22#262311yescharacteristic
826C22#262311yescharacteristic
827C22#262811yescharacteristic
828C22#262811yescharacteristic
829C22#264011yescharacteristic
830C22#264011yescharacteristic
831C22#265711yescharacteristic
832C22#266914yes—
833C22#267314yes—
834C22#271814yes—
835C22#271814yes—
836C22#272014yes—
837C22#272914yes—
838C22#273114yes—
839C22#279014yes—
840C22#279014yes—
841C22#279314yes—
842C22#279514yes—
843C22#279514yes—
844C22#281811yescharacteristic
845C22#282111yescharacteristic
846C22#284911yescharacteristic
847C22#285711yescharacteristic
848C22#285811yescharacteristic
849C4—28no—
850C4—28no—
851C4—28no—
852C4—88no—
853C4—82no—
854C4—82no—
855C4—88no—
856C4—82no—
857C2—84no—
858C2#1477611yescharacteristic
859C2#1477711yescharacteristic
860C2#1509111yescharacteristic
861C2#1512511yescharacteristic
862C2#1513511yescharacteristic
863C2#1513611yescharacteristic
864C2#1514411yescharacteristic
865C2#1519511yescharacteristic
866C2#1524411yescharacteristic
867C2#1539214yes—
868C2#1539614yes—
869C2#1564314yes—
870C2#1577114yes—
871C2#1650211yescharacteristic
872C2#1660211yescharacteristic
873C2#1706011yescharacteristic
874C2#1706411yescharacteristic
875C2#1706611yescharacteristic
876C2#1706611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC25C24
prime radicalC26C23
LCSG ▷ C25 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#384C2semidirect
2. C2×#1442C2semidirect
7. #7557C2semidirect
8. #7557C2semidirect
9. #7554C2semidirect

Maximal subgroups

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

subgroupindex
C22×#3842
C2×#14422
C2×#14392
C2×#14372
#75572
#75542