Finite Group Databasebeta

← C2×#10612920 #12975839

Subgroups — C2×#10612920 #12975839

Order 1280.

2578 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66028C211yesmaximal, characteristic, complemented
2C2×D4×D20C211yesmaximal, characteristic
3C2×C5×#478C211yesmaximal, characteristic, complemented
4C2×#65356C211yesmaximal, characteristic, complemented
5C2×#65307C211yesmaximal, characteristic, complemented
6#10612920C2116yesmaximal, direct product factor
7C2×#65171C211yesmaximal, characteristic, complemented
8C2×#65175C211yesmaximal, characteristic, complemented
9C2×#65155C211yesmaximal, characteristic, complemented
10C2×#65153C211yesmaximal, characteristic, complemented
11C2×#65137C211yesmaximal, characteristic, complemented
12C2×#65125C211yesmaximal, characteristic, complemented
13C2×#65065C211yesmaximal, characteristic, complemented
14C2×#65065C211yesmaximal, characteristic, complemented
15C2×#65059C211yesmaximal, characteristic, complemented
16C2×D5×#102C211yesmaximal, characteristic, complemented
17C22×D4×D5C2211yescharacteristic
18C22×D4×D5C2211yescharacteristic
19C23×D20—21no—
20C2×C5×#125C2211yescharacteristic, complemented
21C2×C4×C5×D4C2211yescharacteristic
22C22×#687C2211yescharacteristic
23C2×#4076—21no—
24C22×#677C2211yescharacteristic, complemented
25C22×#677C2211yescharacteristic, complemented
26C22×#676C2211yescharacteristic, complemented
27C22×C8×D5C2211yescharacteristic, complemented
28#66028—24no—
29#66028C2218yescomplemented
30D4×D20—24no—
31D4×D20C2218yes—
32C2×#4044—21no—
33C2×#4043C2211yescharacteristic, complemented
34C2×#4043C2211yescharacteristic, complemented
35C2×#4041C2211yescharacteristic
36C2×#4041C2211yescharacteristic
37C2×#4040—21no—
38C2×#4038—21no—
39C2×#4038C2211yescharacteristic, complemented
40C2×D5×C4⋊C4C2211yescharacteristic, complemented
41C2×#4036—21no—
42C2×#4028—21no—
43C2×#4028—21no—
44C2×#4020C2211yescharacteristic
45C2×C4×D20C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic, complemented
47C5×#478C2218yescomplemented
48C2×C5×#107C2211yescharacteristic, complemented
49C2×C5×#106C2211yescharacteristic, complemented
50C2×C5×C4⋊C8C2211yescharacteristic, complemented
51C2×C5×#102C2211yescharacteristic
52C2×C5×#102C2211yescharacteristic
53C2×#3964C2211yescharacteristic
54C2×#3953C2211yescharacteristic, complemented
55C2×#3953C2211yescharacteristic, complemented
56C2×#3952C2211yescharacteristic, complemented
57C2×#3952C2211yescharacteristic, complemented
58#65356C2218yescomplemented
59#65307C2218yescomplemented
60C2×#3942C2211yescharacteristic, complemented
61C2×#3941C2211yescharacteristic, complemented
62C2×#3941C2211yescharacteristic, complemented
63C2×#3941C2211yescharacteristic, complemented
64C2×#3941C2211yescharacteristic, complemented
65C2×#3939C2211yescharacteristic, complemented
66C2×#3935C2211yescharacteristic, complemented
67#65175C2218yescomplemented
68#65171C2218yescomplemented
69#65155C2218yescomplemented
70#65153C2218yescomplemented
71#65137C2218yescomplemented
72#65125C2218yescomplemented
73#65065C2218yescomplemented
74#65065C2218yescomplemented
75#65059C2218yescomplemented
76D5×#102C2218yescomplemented
77C2×#3310—51nomaximal, Sylow
78C24×D5—21no—
79C24×D5—21no—
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5—21no—
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C2×D4×D5—24no—
85C2×D4×D5—24no—
86C2×D4×D5—22no—
87C2×D4×D5—22no—
88C2×D4×D5—42no—
89C2×D4×D5—42no—
90C2×D4×D5C2314yes—
91C2×D4×D5C2314yes—
92C22×D20—21no—
93C22×D20—21no—
94C22×D20—21no—
95C22×D20—21no—
96C22×D20—28no—
97C22×D20—48no—
98C22×D20D411yescharacteristic
99C22×D20C2311yescharacteristic
100C22×D20C2311yescharacteristic
101C22×C4×D5—21no—
102C22×C4×D5C2311yescharacteristic
103C22×C4×D5C2311yescharacteristic
104C22×Dic10C2311yescharacteristic
105C22×C5×C8C2311yescharacteristic
106C22×C5×C8C2311yescharacteristic
107C5×#125—22no—
108C5×#125C2314yescomplemented
109C4×C5×D4—22no—
110C4×C5×D4C2314yes—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C22⋊C4—21no—
117C2×C42×C5C2311yescharacteristic
118C2×#687—24no—
119C2×#687C2314yes—
120#4076—28no—
121C2×#685—21no—
122C2×#685—21no—
123C2×#685—21no—
124C2×#685—21no—
125C2×#685—21no—
126C2×#685D411yescharacteristic
127C2×#685D411yescharacteristic
128C2×C4⋊Dic5—21no—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5D411yescharacteristic
131C2×C4⋊Dic5C2311yescharacteristic
132C2×#683—21no—
133C2×#683—21no—
134C2×C4×Dic5—21no—
135C2×C4×Dic5—21no—
136C22×#168C2311yescharacteristic
137C22×#168C2311yescharacteristic
138C2×#677—42no—
139C2×#677—42no—
140C2×#677C2314yescomplemented
141C2×#677C2314yescomplemented
142C2×#676—42no—
143C2×#676C2314yescomplemented
144C2×C8×D5—42no—
145C2×C8×D5C2314yescomplemented
146#4044—28no—
147#4043—22no—
148#4043—22no—
149#4043C2314yescomplemented
150#4043C2314yescomplemented
151#4041—22no—
152#4041—22no—
153#4041C2314yes—
154#4041C2314yes—
155#4040—28no—
156#4038—22no—
157#4038—28no—
158#4038C2314yescomplemented
159D5×C4⋊C4—22no—
160D5×C4⋊C4C2314yescomplemented
161#4036—28no—
162#4028—28no—
163#4028—28no—
164#4020—22no—
165#4020C2314yes—
166C4×D20D414yes—
167C4×D20C2314yes—
168C4×Dic10—22no—
169C4×Dic10C2314yescomplemented
170C5×#107C2314yescomplemented
171C5×#106C2314yescomplemented
172C5×C4⋊C8C2314yescomplemented
173C5×#102C2314yes—
174C5×#102C2314yes—
175#3964C2314yes—
176#3953C2314yescomplemented
177#3953C2314yescomplemented
178#3952C2314yescomplemented
179#3952C2314yescomplemented
180#3942C2314yescomplemented
181#3941C2314yescomplemented
182#3941C2314yescomplemented
183#3941C2314yescomplemented
184#3941C2314yescomplemented
185#3939C2314yescomplemented
186#3935C2314yescomplemented
187C2×#552—51no—
188C2×D42—51no—
189#3310—516no—
190C2×#490—51no—
191C2×#482—51no—
192C2×#480—51no—
193C2×#478D511yescharacteristic, complemented
194C2×#468—51no—
195C2×#465—51no—
196C2×#460—51no—
197C2×#450—51no—
198C2×#450—51no—
199C2×#440—51no—
200C2×#435—51no—
201C2×#418—51no—
202C22×#102—51no—
203C24×C5—21no—
204C23×D5—21no—
205C23×D5—21no—
206C23×D5—24no—
207C23×D5—24no—
208C23×D5—44no—
209C23×D5—44no—
210C23×D5—44no—
211C23×D5—44no—
212C23×D5—82no—
213C23×D5—82no—
214C23×D5C2×D411yescharacteristic
215C23×D5C2×D411yescharacteristic
216C2×C5×D4—21no—
217C2×C5×D4—22no—
218C2×C5×D4#4114yes—
219C2×C5×D4C2412yes—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—24no—
224C22×C4×C5—44no—
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2411yescharacteristic
228C2×C22⋊D5—24no—
229C2×C22⋊D5—24no—
230C2×C22⋊D5—44no—
231C2×C22⋊D5—44no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5C2×D411yescharacteristic
235C22×Dic5C2×D411yescharacteristic
236D4×D5—28no—
237D4×D5—28no—
238D4×D5—44no—
239D4×D5—44no—
240D4×D5—48no—
241D4×D5—48no—
242C2×D20—24no—
243C2×D20—22no—
244C2×D20—22no—
245C2×D20—22no—
246C2×D20—22no—
247C2×D20—24no—
248C2×D20—24no—
249C2×D20—24no—
250C2×D20—21no—
251C2×D20—21no—
252C2×D20—24no—
253C2×D20—432no—
254C2×D20—44no—
255C2×D20—44no—
256C2×D20—44no—
257C2×D20—82no—
258C2×D20C2×D414yes—
259C2×D20C2412yes—
260C2×D20C2412yes—
261C2×C4×D5—22no—
262C2×C4×D5—22no—
263C2×C4×D5—22no—
264C2×C4×D5—22no—
265C2×C4×D5—24no—
266C2×C4×D5—44no—
267C2×C4×D5C2×D412yes—
268C2×C4×D5C2×D412yes—
269C2×C4×D5C2412yes—
270C2×C4×D5C2412yes—
271C2×Dic10—22no—
272C2×Dic10—22no—
273C2×Dic10—21no—
274C2×Dic10C2412yes—
275C2×C5×C8—22no—
276C2×C5×C8—22no—
277C2×C5×C8C2412yes—
278C2×C5×C8C2412yes—
279C5×C4⋊C4—24no—
280C5×C4⋊C4—24no—
281C5×C4⋊C4—21no—
282C5×C4⋊C4—21no—
283C5×C4⋊C4—21no—
284C5×C4⋊C4C2412yes—
285C5×C4⋊C4C2412yes—
286C5×C4⋊C4C2412yes—
287C5×C22⋊C4—24no—
288C42×C5C2×D412yes—
289C42×C5C2412yes—
290#687—28no—
291#685—24no—
292#685—24no—
293#685—24no—
294#685—24no—
295#685—24no—
296#685C2×D414yes—
297#685C2×D414yes—
298C4⋊Dic5—21no—
299C4⋊Dic5—24no—
300C4⋊Dic5—24no—
301C4⋊Dic5C2×D414yes—
302C4⋊Dic5C2412yes—
303#683—24no—
304#683—24no—
305C4×Dic5—24no—
306C4×Dic5—24no—
307C2×#168—22no—
308C2×#168—22no—
309C2×#168C2412yes—
310C2×#168C2412yes—
311#677—44no—
312#677—44no—
313#676—44no—
314C8×D5—44no—
315C23×D4—51no—
316C23×D4—51no—
317C23×D4—101no—
318C22×SD16—51no—
319C22×SD16—51no—
320C22×SD16—51no—
321C22×M16—51no—
322C23×C8—51no—
323#552—58no—
324#552—104no—
325D42—58no—
326D42—104no—
327C2×#127—51no—
328C2×#126—101no—
329C2×#125—101no—
330C2×#125C2×D511yescharacteristic, complemented
331C2×#123—101no—
332C2×C22⋊Q8—51no—
333C2×C22⋊Q8—51no—
334C2×#121—51no—
335C2×#121—51no—
336C2×#121—101no—
337C2×#120—101no—
338C2×#120—101no—
339C2×C4×Q8—51no—
340C2×C4×D4—51no—
341C2×C4×D4C2×D511yescharacteristic
342C2×#117—51no—
343C2×#117—101no—
344C22×C4⋊C4—51no—
345#490—58no—
346#482—58no—
347#480—58no—
348#478C2×D518yescomplemented
349#468—58no—
350#465—58no—
351#460—58no—
352#450—58no—
353#450—58no—
354#440—58no—
355#435—58no—
356C2×#107—51no—
357C2×#107C2×D511yescharacteristic, complemented
358C2×#106C2×D511yescharacteristic, complemented
359C2×C4⋊C8C2×D511yescharacteristic, complemented
360#418—58no—
361C2×#103—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×#102—51no—
366C2×#102—51no—
367C2×#102—51no—
368C2×#102—51no—
369C2×#102—58no—
370C2×#102C2×D511yescharacteristic
371C2×#102C2×D511yescharacteristic
372C2×C22⋊C8—51no—
373C2×C22⋊C8—51no—
374C2×#97—51no—
375C23×C5—24no—
376C23×C5—22no—
377C23×C5—42no—
378C23×C5—42no—
379C23×C5C22×D411yescharacteristic
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—48no—
388C22×D5—48no—
389C22×D5—48no—
390C22×D5—42no—
391C22×D5—42no—
392C22×D5—42no—
393C22×D5—42no—
394C22×D5—42no—
395C22×D5—42no—
396C22×D5—48no—
397C22×D5—84no—
398C22×D5—84no—
399C22×D5—816no—
400C22×D5—816no—
401C22×D5AGL(1,ℤ/8)14yes—
402C22×D5C22×D412yes—
403C22×D5C22×D412yes—
404C5×D4—24no—
405C5×D4—22no—
406C5×D4C2×#4114yes—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—48no—
413C2×C4×C5—42no—
414C2×C4×C5—42no—
415C2×C4×C5—42no—
416C2×C4×C5C22×D412yes—
417C2×C4×C5C22×D412yes—
418C2×C4×C5C22×D411yescharacteristic
419C2×C4×C5C2×#4112yes—
420C2×C4×C5H(5,𝔽2)12yes—
421C2×C4×C5C2511yescharacteristic
422C22⋊D5—48no—
423C22⋊D5—48no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—42no—
429C2×Dic5—42no—
430C2×Dic5C22×D412yes—
431C2×Dic5C22×D412yes—
432D20—28no—
433D20—22no—
434D20—22no—
435D20—22no—
436D20—22no—
437D20—48no—
438D20—48no—
439D20—48no—
440D20—42no—
441D20—42no—
442D20—84no—
443C4×D5—24no—
444C4×D5—24no—
445C4×D5—22no—
446C4×D5—22no—
447C4×D5—22no—
448C4×D5—22no—
449C4×D5—48no—
450Dic10—22no—
451Dic10—22no—
452Dic10—42no—
453C5×C8—22no—
454C5×C8—22no—
455#168—22no—
456#168—22no—
457C25—101no—
458C25—101no—
459C22×Q8—51no—
460C22×D4—54no—
461C22×D4—54no—
462C22×D4—51no—
463C22×D4—51no—
464C22×D4—51no—
465C22×D4—108no—
466C22×D4—101no—
467C22×D4—101no—
468C22×D4—102no—
469C22×D4—102no—
470C22×D4—101no—
471C22×D4—101no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—101no—
475C22×D4—101no—
476C22×D4—208no—
477C22×D4—202no—
478C22×D4—202no—
479C22×D4C22×D511yescharacteristic
480C23×C4—21no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—101no—
484C2×SD16—54no—
485C2×SD16—54no—
486C2×SD16—54no—
487C2×SD16—104no—
488C2×SD16—202no—
489C2×SD16—202no—
490C2×M16—54no—
491C2×M16—202no—
492C22×C8—51no—
493C22×C8—51no—
494C22×C8—54no—
495C22×C8—202no—
496C22×C8C22×D511yescharacteristic
497C22×C8C22×D511yescharacteristic
498#127—54no—
499#127—102no—
500#126—108no—
501#125—22no—
502#125—108no—
503#125C22×D514yescomplemented
504#123—108no—
505C22⋊Q8—54no—
506C22⋊Q8—54no—
507C22⋊Q8—102no—
508C22⋊Q8—102no—
509#121—54no—
510#121—54no—
511#121—102no—
512#121—102no—
513#121—108no—
514#120—108no—
515#120—108no—
516C4×Q8—54no—
517C4×Q8—102no—
518C4×D4—22no—
519C4×D4—54no—
520C4×D4—54no—
521C4×D4C22×D514yes—
522#117—54no—
523#117—108no—
524#117—102no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—51no—
528C2×C4⋊C4—51no—
529C2×C4⋊C4—54no—
530C2×C4⋊C4—102no—
531C2×C4⋊C4—101no—
532C2×C4⋊C4—101no—
533C2×C4⋊C4—101no—
534C2×C4⋊C4—101no—
535C2×C4⋊C4C22×D511yescharacteristic
536C2×C4⋊C4C22×D511yescharacteristic
537C2×C4⋊C4C22×D511yescharacteristic
538C2×C22⋊C4—21no—
539C2×C22⋊C4—51no—
540C2×C22⋊C4—51no—
541C2×C22⋊C4—101no—
542C2×C22⋊C4—101no—
543C2×C22⋊C4—101no—
544C2×C22⋊C4—101no—
545C2×C22⋊C4—101no—
546C2×C42—101no—
547C2×C42—101no—
548C2×C42C22×D511yescharacteristic
549#107—54no—
550#107C22×D514yescomplemented
551#106C22×D514yescomplemented
552C4⋊C8C22×D514yescomplemented
553#103—54no—
554#102—54no—
555#102—54no—
556#102—54no—
557#102—54no—
558#102—54no—
559#102—54no—
560#102—54no—
561#102C22×D514yes—
562#102C22×D514yes—
563C22⋊C8—54no—
564C22⋊C8—54no—
565#97—54no—
566C22×C5—24no—
567C22×C5—48no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5#54612yes—
571C22×C5C2×AGL(1,ℤ/8)12yes—
572C22×C5#57712yes—
573C22×C5C23×D411yescharacteristic
574C2×D5—22no—
575C2×D5—28no—
576C2×D5—22no—
577C2×D5—22no—
578C2×D5—22no—
579C2×D5—22no—
580C2×D5—44no—
581C2×D5—42no—
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—42no—
586C2×D5—42no—
587C2×D5—816no—
588C2×D5—816no—
589C2×D5—84no—
590C2×D5—84no—
591C2×D5C2×AGL(1,ℤ/8)14yes—
592C4×C5—22no—
593C4×C5—22no—
594C4×C5—42no—
595C4×C5—42no—
596C4×C5—42no—
597C4×C5#54612yes—
598C4×C5C22×#4111yescharacteristic
599C4×C5C2×H(5,𝔽2)11yescharacteristic
600Dic5—22no—
601Dic5—22no—
602Dic5—42no—
603Dic5—42no—
604C24—21no—
605C24—51no—
606C24—51no—
607C24—104no—
608C24—104no—
609C24—101no—
610C24—101no—
611C24—204no—
612C24—204no—
613C24—204no—
614C24—204no—
615C24—402no—
616C24—402no—
617C2×Q8—52no—
618C2×Q8—101no—
619C2×Q8—102no—
620C2×Q8—102no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—54no—
624C2×D4—52no—
625C2×D4—52no—
626C2×D4—104no—
627C2×D4—104no—
628C2×D4—104no—
629C2×D4—104no—
630C2×D4—104no—
631C2×D4—108no—
632C2×D4—108no—
633C2×D4—104no—
634C2×D4—101no—
635C2×D4—101no—
636C2×D4—104no—
637C2×D4—102no—
638C2×D4—102no—
639C2×D4—102no—
640C2×D4—102no—
641C2×D4—204no—
642C2×D4—2032no—
643C2×D4—204no—
644C2×D4—204no—
645C2×D4—204no—
646C2×D4—204no—
647C2×D4—208no—
648C2×D4—208no—
649C2×D4—204no—
650C2×D4—204no—
651C2×D4—402no—
652C2×D4#71314yes—
653C2×D4C23×D512yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—24no—
658C22×C4—44no—
659C22×C4—51no—
660C22×C4—51no—
661C22×C4—52no—
662C22×C4—52no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—104no—
666C22×C4—102no—
667C22×C4—102no—
668C22×C4—102no—
669C22×C4—102no—
670C22×C4—101no—
671C22×C4—101no—
672C22×C4—204no—
673C22×C4D4×D511yescharacteristic
674C22×C4D4×D511yescharacteristic
675C22×C4C23×D511yescharacteristic
676SD16—108no—
677SD16—204no—
678SD16—204no—
679M16—204no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—52no—
683C2×C8—52no—
684C2×C8—102no—
685C2×C8—102no—
686C2×C8—204no—
687C2×C8C23×D512yes—
688C2×C8C23×D512yes—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—54no—
695C4⋊C4—52no—
696C4⋊C4—104no—
697C4⋊C4—104no—
698C4⋊C4—104no—
699C4⋊C4—101no—
700C4⋊C4—104no—
701C4⋊C4C23×D512yes—
702C4⋊C4C23×D512yes—
703C4⋊C4C23×D512yes—
704C22⋊C4—24no—
705C22⋊C4—54no—
706C22⋊C4—54no—
707C22⋊C4—104no—
708C22⋊C4—104no—
709C22⋊C4—104no—
710C22⋊C4—104no—
711C22⋊C4—104no—
712C42—104no—
713C42—104no—
714C42D4×D512yes—
715C42C23×D512yes—
716C2×C5—44no—
717C2×C5#331014yescomplemented
718C2×C5C2×#54611yescharacteristic
719C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
720C2×C5C2×#57711yescharacteristic
721D5—24no—
722D5—42no—
723D5—82no—
724D5—82no—
725C23—24no—
726C23—22no—
727C23—42no—
728C23—42no—
729C23—54no—
730C23—52no—
731C23—52no—
732C23—102no—
733C23—102no—
734C23—102no—
735C23—102no—
736C23—102no—
737C23—102no—
738C23—102no—
739C23—208no—
740C23—208no—
741C23—208no—
742C23—208no—
743C23—202no—
744C23—202no—
745C23—202no—
746C23—202no—
747C23—202no—
748C23—202no—
749C23—404no—
750C23—404no—
751C23—4016no—
752C23—4016no—
753C23C2×D4×D511yescharacteristic
754Q8—102no—
755Q8—102no—
756Q8—202no—
757D4—24no—
758D4—22no—
759D4—108no—
760D4—102no—
761D4—102no—
762D4—102no—
763D4—102no—
764D4—208no—
765D4—208no—
766D4—208no—
767D4—208no—
768D4—208no—
769D4—202no—
770D4—202no—
771D4—404no—
772D4C2×#71314yes—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—48no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—52no—
783C2×C4—52no—
784C2×C4—102no—
785C2×C4—102no—
786C2×C4—104no—
787C2×C4—104no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—102no—
791C2×C4—102no—
792C2×C4—102no—
793C2×C4—102no—
794C2×C4—208no—
795C2×C4—202no—
796C2×C4—202no—
797C2×C4C2×D4×D512yes—
798C2×C4C2×D4×D512yes—
799C2×C4C2×D4×D511yescharacteristic
800C2×C4C2×#71312yes—
801C2×C4#414912yes—
802C2×C4C24×D511yescharacteristic
803C8—22no—
804C8—22no—
805C8—102no—
806C8—102no—
807C5C2×#331011yescharacteristic, complemented, Sylow
808C22—24no—
809C22—48no—
810C22—42no—
811C22—42no—
812C22—54no—
813C22—102no—
814C22—108no—
815C22—102no—
816C22—102no—
817C22—102no—
818C22—102no—
819C22—204no—
820C22—202no—
821C22—202no—
822C22—202no—
823C22—202no—
824C22—202no—
825C22—202no—
826C22—4016no—
827C22—4016no—
828C22—404no—
829C22—404no—
830C22#6596412yes—
831C22#6610412yes—
832C22D5×AGL(1,ℤ/8)12yes—
833C22C22×D4×D511yescharacteristic
834C4—22no—
835C4—22no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—102no—
840C4—102no—
841C4—202no—
842C4—202no—
843C4#6596412yes—
844C4C22×#71311yescharacteristic
845C4C2×#414911yescharacteristic
846C2—44no—
847C2—104no—
848C2—202no—
849C2—402no—
850C2—402no—
851C2#1061292014yesdirect product factor
852C2C2×#6596411yescharacteristic
853C2C2×#6610411yescharacteristic
854C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#478C2
socleC23×C5C22×D4
prime radicalC2×D4×D20C2
hypercenterC2×#478D5
hypocenterC5C2×#3310
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#66028C2semidirect
3. C2×C5×#478C2semidirect
4. C2×#65356C2semidirect
5. C2×#65307C2semidirect
6. #10612920C2direct (N × H)
7. C2×#65171C2semidirect
8. C2×#65175C2semidirect
9. C2×#65155C2semidirect
10. C2×#65153C2semidirect
11. C2×#65137C2semidirect
12. C2×#65125C2semidirect
13. C2×#65065C2semidirect
14. C2×#65065C2semidirect
15. C2×#65059C2semidirect
16. C2×D5×#102C2semidirect
20. C2×C5×#125C22semidirect
24. C22×#677C22semidirect
25. C22×#677C22semidirect
26. C22×#676C22semidirect
27. C22×C8×D5C22semidirect
29. #66028C22semidirect
33. C2×#4043C22semidirect
34. C2×#4043C22semidirect
39. C2×#4038C22semidirect
40. C2×D5×C4⋊C4C22semidirect
46. C2×C4×Dic10C22semidirect
47. C5×#478C22semidirect
48. C2×C5×#107C22semidirect
49. C2×C5×#106C22semidirect
50. C2×C5×C4⋊C8C22semidirect
54. C2×#3953C22semidirect
55. C2×#3953C22semidirect
56. C2×#3952C22semidirect
57. C2×#3952C22semidirect
58. #65356C22semidirect
59. #65307C22semidirect
60. C2×#3942C22semidirect
61. C2×#3941C22semidirect
62. C2×#3941C22semidirect
63. C2×#3941C22semidirect
64. C2×#3941C22semidirect
65. C2×#3939C22semidirect
66. C2×#3935C22semidirect
67. #65175C22semidirect
68. #65171C22semidirect
69. #65155C22semidirect
70. #65153C22semidirect
71. #65137C22semidirect
72. #65125C22semidirect
73. #65065C22semidirect
74. #65065C22semidirect
75. #65059C22semidirect
76. D5×#102C22semidirect
108. C5×#125C23semidirect
140. C2×#677C23semidirect
141. C2×#677C23semidirect
143. C2×#676C23semidirect
145. C2×C8×D5C23semidirect
149. #4043C23semidirect
150. #4043C23semidirect
158. #4038C23semidirect
160. D5×C4⋊C4C23semidirect
169. C4×Dic10C23semidirect
170. C5×#107C23semidirect
171. C5×#106C23semidirect
172. C5×C4⋊C8C23semidirect
176. #3953C23semidirect
177. #3953C23semidirect
178. #3952C23semidirect
179. #3952C23semidirect
180. #3942C23semidirect
181. #3941C23semidirect
182. #3941C23semidirect
183. #3941C23semidirect
184. #3941C23semidirect
185. #3939C23semidirect
186. #3935C23semidirect
193. C2×#478D5semidirect
330. C2×#125C2×D5semidirect
348. #478C2×D5semidirect
357. C2×#107C2×D5semidirect
358. C2×#106C2×D5semidirect
359. C2×C4⋊C8C2×D5semidirect
503. #125C22×D5semidirect
550. #107C22×D5semidirect
551. #106C22×D5semidirect
552. C4⋊C8C22×D5semidirect
717. C2×C5#3310semidirect
807. C5C2×#3310semidirect
851. C2#10612920direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660282
C2×D4×D202
C2×C5×#4782
C2×#653562
C2×#653072
#106129202
C2×#651712
C2×#651752
C2×#651552
C2×#651532
C2×#651372
C2×#651252
C2×#650652
C2×#650592
C2×D5×#1022
C2×#33105