Finite Group Databasebeta

← #12120033

Subgroups — #12120033

Order 1280.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2880C211yesmaximal, characteristic, complemented
2#10615811C211yesmaximal, characteristic
3C22×#3969C211yesmaximal, characteristic, complemented
4C2×#65434C211yesmaximal, characteristic, complemented
5#10610327C211yesmaximal, characteristic, complemented
6#10602810C211yesmaximal, characteristic, complemented
7#10602803C211yesmaximal, characteristic, complemented
8#10602802C211yesmaximal, characteristic, complemented
9#10600804C211yesmaximal, characteristic, complemented
10#10600793C211yesmaximal, characteristic, complemented
11#10600791C211yesmaximal, characteristic, complemented
12#10600789C211yesmaximal, characteristic, complemented
13#10600777C211yesmaximal, characteristic, complemented
14#10600758C211yesmaximal, characteristic, complemented
15#10600699C211yesmaximal, characteristic, complemented
16C22×C5×#41C2211yescharacteristic
17C2×C5×#131C2211yescharacteristic
18C2×C5×#131C2211yescharacteristic
19C2×#4096C2211yescharacteristic
20C2×#4096C2211yescharacteristic
21#66125C2211yescharacteristic
22C22×C4×Dic5C2211yescharacteristic
23C22×#681C2211yescharacteristic
24C2×#4047C2211yescharacteristic, complemented
25C5×#408—21no—
26C5×#408—21no—
27C5×#408C2211yescharacteristic
28C5×#408C2211yescharacteristic
29C5×#407—21no—
30C5×#407C2211yescharacteristic
31C2×C5×C22⋊C8—21no—
32C2×C5×C22⋊C8C2211yescharacteristic
33#65528C411yescharacteristic, complemented
34#65528C411yescharacteristic, complemented
35#65527C411yescharacteristic, complemented
36#65527C411yescharacteristic, complemented
37C2×#3969—24no—
38C2×#3969C2211yescharacteristic
39C2×#3969C2211yescharacteristic
40C2×#3969C2211yescharacteristic
41C2×#3969C2211yescharacteristic
42#65522C2211yescharacteristic
43#65522C2211yescharacteristic
44#65517C411yescharacteristic, complemented
45#65516C411yescharacteristic, complemented
46#65507C411yescharacteristic, complemented
47#65506C411yescharacteristic, complemented
48C2×C22⋊#168C2211yescharacteristic
49#65434—24no—
50C2×#3957C2211yescharacteristic, complemented
51C2×#3957C2211yescharacteristic, complemented
52C2×#3954C2211yescharacteristic, complemented
53C2×#3954C2211yescharacteristic, complemented
54#65399C2211yescharacteristic, complemented
55#65391C2211yescharacteristic, complemented
56#65390C2211yescharacteristic, complemented
57C2×#3947C2211yescharacteristic, complemented
58C2×#3947C2211yescharacteristic, complemented
59#65019—21no—
60#65018—21no—
61#65017—21no—
62#65014—21no—
63#64778C2211yescharacteristic, complemented
64#64778C2211yescharacteristic, complemented
65#64775C2211yescharacteristic, complemented
66#64775C2211yescharacteristic, complemented
67#64770C2211yescharacteristic, complemented
68#64770C2211yescharacteristic, complemented
69#22886—51nomaximal, Sylow
70C2×C5×#41—21no—
71C2×C5×#41—21no—
72C2×C5×#41—22no—
73C2×C5×#41—22no—
74C2×C5×#41—41no—
75C2×C5×#41—41no—
76C2×C5×#41C2×C411yescharacteristic
77C2×C5×#41C2×C411yescharacteristic
78C2×C5×#41C2311yescharacteristic
79C2×C5×#41C2311yescharacteristic
80C22×C5×Q8C2×C411yescharacteristic
81C22×C5×D4—21no—
82C22×C5×D4C2×C411yescharacteristic
83C23×C4×C5—21no—
84C23×C4×C5C2311yescharacteristic
85C23×Dic5—21no—
86C2×#709C2311yescharacteristic
87C5×#131—22no—
88C5×#131—22no—
89C5×#131—41no—
90C5×#131—41no—
91C2×C5×M16—21no—
92C2×C5×M16—21no—
93C2×C5×M16C2311yescharacteristic
94C2×C5×M16C2311yescharacteristic
95C22×C5×C8—21no—
96C22×C5×C8—21no—
97C22×C5×C8C2311yescharacteristic
98C22×C5×C8C2311yescharacteristic
99#4099—21no—
100#4096—22no—
101#4096—22no—
102#4096—41no—
103#4096—41no—
104C2×#689C2×C411yescharacteristic, complemented
105C2×#689C2×C411yescharacteristic, complemented
106C2×#688C2×C411yescharacteristic, complemented
107C2×#688C2×C411yescharacteristic, complemented
108C2×#687C2×C411yescharacteristic, complemented
109C2×#687C2×C411yescharacteristic, complemented
110C2×#686C2×C411yescharacteristic, complemented
111C2×#686C2×C411yescharacteristic, complemented
112#4076C2×C411yescharacteristic
113#4076C2×C411yescharacteristic
114#4075—21no—
115C4×C22⋊D5—21no—
116C4×C22⋊D5—21no—
117#4072C2311yescharacteristic
118#4070C2×C411yescharacteristic
119#4070C2×C411yescharacteristic
120C2×C4×Dic5—22no—
121C2×C4×Dic5—21no—
122C2×C4×Dic5—41no—
123C2×C4×Dic5C2311yescharacteristic
124C2×C4×Dic5C2311yescharacteristic
125C2×#681—21no—
126C2×#681—22no—
127C2×#681—41no—
128C2×#681C2311yescharacteristic
129C2×#681C2311yescharacteristic
130C22×#168—21no—
131C22×#168C2311yescharacteristic
132C22×#168C2311yescharacteristic
133#4047—22no—
134#4047—41no—
135C2×#676—21no—
136C2×C8×D5—21no—
137C5×C22⋊C8—21no—
138C5×C22⋊C8—21no—
139C5×C22⋊C8—21no—
140C5×C22⋊C8—21no—
141C5×C22⋊C8—21no—
142C5×C22⋊C8—21no—
143C5×C22⋊C8D411yescharacteristic
144C5×C22⋊C8D411yescharacteristic
145C5×C22⋊C8D411yescharacteristic
146C5×C22⋊C8D411yescharacteristic
147#3969—22no—
148#3969—22no—
149#3969—22no—
150#3969D414yescomplemented
151#3967C2×C411yescharacteristic, complemented
152#3967C2×C411yescharacteristic, complemented
153#3967C2×C411yescharacteristic, complemented
154#3967C2×C411yescharacteristic, complemented
155#3964C2×C411yescharacteristic, complemented
156#3964C2×C411yescharacteristic, complemented
157#3964C2×C411yescharacteristic, complemented
158#3964C2×C411yescharacteristic, complemented
159C22⋊#168C2×C411yescharacteristic
160C22⋊#168C2×C411yescharacteristic
161C22⋊#168C2×C411yescharacteristic
162C22⋊#168C2×C411yescharacteristic
163#3957—22no—
164#3957—41no—
165#3954—22no—
166#3954—41no—
167#3952—21no—
168#3952—21no—
169#3947—21no—
170#3947—22no—
171#3947—41no—
172#3946—21no—
173#3946—21no—
174C8×Dic5—21no—
175#3002—51no—
176C2×#444—51no—
177#2933—51no—
178C22×#104—51no—
179#2880D511yescharacteristic, complemented
180#1975—51no—
181#1938—51no—
182#1929—51no—
183#1896—51no—
184#1876—51no—
185#1876—51no—
186#1866—51no—
187#1855—51no—
188#1765—51no—
189#1749—51no—
190C24×C5—21no—
191C24×C5#4111yescharacteristic
192C5×#41—21no—
193C5×#41—21no—
194C5×#41—22no—
195C5×#41—22no—
196C5×#41—21no—
197C5×#41—21no—
198C5×#41—21no—
199C5×#41—21no—
200C5×#41—42no—
201C5×#41—42no—
202C5×#41—41no—
203C5×#41—41no—
204C5×#41—42no—
205C5×#41—42no—
206C5×#41C2×D412yes—
207C5×#41#4112yes—
208C2×C5×Q8—21no—
209C2×C5×Q8—22no—
210C2×C5×Q8—41no—
211C2×C5×Q8C22×C411yescharacteristic
212C2×C5×Q8C22×C411yescharacteristic
213C2×C5×D4—21no—
214C2×C5×D4—22no—
215C2×C5×D4—21no—
216C2×C5×D4—21no—
217C2×C5×D4—21no—
218C2×C5×D4—21no—
219C2×C5×D4—41no—
220C2×C5×D4—42no—
221C2×C5×D4—42no—
222C2×C5×D4C22×C411yescharacteristic
223C2×C5×D4C22×C411yescharacteristic
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—21no—
228C22×C4×C5—21no—
229C22×C4×C5—21no—
230C22×C4×C5—21no—
231C22×C4×C5—21no—
232C22×C4×C5—21no—
233C22×C4×C5—42no—
234C22×C4×C5—42no—
235C22×C4×C5C22×C411yescharacteristic
236C22×C4×C5C22×C411yescharacteristic
237C22×C4×C5C2×D411yescharacteristic
238C22×C4×C5C2×D411yescharacteristic
239C22×C4×C5#4111yescharacteristic
240C22×C4×C5C2411yescharacteristic
241C2×C22⋊D5—21no—
242C2×C22⋊D5—21no—
243C2×C22⋊D5—21no—
244C22×Dic5—21no—
245C22×Dic5—21no—
246C22×Dic5—42no—
247C22×Dic5—42no—
248C22×Dic5—42no—
249#709—21no—
250#709—21no—
251#709—21no—
252#709—21no—
253C2×D20C22×C411yescharacteristic
254C2×C4×D5—21no—
255C2×Dic10C22×C411yescharacteristic
256C5×M16—21no—
257C5×M16—21no—
258C5×M16—21no—
259C5×M16—21no—
260C5×M16—42no—
261C5×M16—42no—
262C2×C5×C8—21no—
263C2×C5×C8—21no—
264C2×C5×C8—21no—
265C2×C5×C8—21no—
266C2×C5×C8—21no—
267C2×C5×C8—21no—
268C2×C5×C8—42no—
269C2×C5×C8—42no—
270C2×C5×C8C2×D411yescharacteristic
271C2×C5×C8C2×D411yescharacteristic
272C2×C5×C8C2×D411yescharacteristic
273C2×C5×C8C2×D411yescharacteristic
274C22⋊Dic5—21no—
275C22⋊Dic5—21no—
276C22⋊Dic5—21no—
277#689—22no—
278#689—41no—
279#688—22no—
280#688—41no—
281#687—22no—
282#687—41no—
283#686—22no—
284#686—41no—
285#685—21no—
286#685—21no—
287C4⋊Dic5C22×C411yescharacteristic
288C4⋊Dic5C22×C411yescharacteristic
289#683—21no—
290#683—21no—
291C4×Dic5—21no—
292C4×Dic5—21no—
293C4×Dic5—21no—
294C4×Dic5—21no—
295C4×Dic5—42no—
296C4×Dic5C2×D412yes—
297#681—21no—
298#681—21no—
299#681—21no—
300#681—42no—
301#681C2×D412yes—
302C2×#168—21no—
303C2×#168—21no—
304C2×#168—21no—
305C2×#168—21no—
306C2×#168—21no—
307C2×#168—21no—
308C2×#168—42no—
309C2×#168C22×C411yescharacteristic
310C2×#168C22×C411yescharacteristic
311C2×#168C22×C411yescharacteristic
312C2×#168C22×C411yescharacteristic
313#676—42no—
314C8×D5—42no—
315C22×#41C2×D511yescharacteristic
316C2×#135—51no—
317C2×#135—51no—
318C2×#131—51no—
319C2×#131C2×D511yescharacteristic
320C2×#131C2×D511yescharacteristic
321C22×M16—51no—
322#525—51no—
323C22×C42—51no—
324#452—51no—
325#452—51no—
326#451—51no—
327#450—51no—
328#449—51no—
329#449—51no—
330#448—51no—
331#447—51no—
332#444—104no—
333#436—101no—
334#435—101no—
335#435—101no—
336C8×D4—101no—
337C2×#108—51no—
338C2×#108—51no—
339#424—51no—
340C2×#104—51no—
341C2×#104—51no—
342C2×#104—51no—
343C2×#104—51no—
344C2×#104—51no—
345C2×#104—51no—
346C2×#104—104no—
347#416—51no—
348#416—51no—
349#408—21no—
350#408—21no—
351#408—51no—
352#408C2×D511yescharacteristic
353#408C2×D511yescharacteristic
354#407—21no—
355#407C2×D511yescharacteristic
356C2×C22⋊C8—21no—
357C2×C22⋊C8—51no—
358C2×C22⋊C8C2×D511yescharacteristic
359#405—51no—
360C2×#97—51no—
361C2×#97—51no—
362#341—51no—
363#341—51no—
364#339—51no—
365#339—51no—
366#336—51no—
367#336—51no—
368C23×C5—21no—
369C23×C5—21no—
370C23×C5—21no—
371C23×C5—22no—
372C23×C5—21no—
373C23×C5—41no—
374C23×C5—42no—
375C23×C5—42no—
376C23×C5—81no—
377C23×C5C4×D411yescharacteristic
378C23×C5C4×D411yescharacteristic
379C23×C5C2×#4111yescharacteristic
380C22×D5—21no—
381C5×Q8—21no—
382C5×Q8—21no—
383C5×Q8—21no—
384C5×Q8—42no—
385C5×Q8C4×D412yes—
386C5×D4—22no—
387C5×D4—22no—
388C5×D4—21no—
389C5×D4—21no—
390C5×D4—21no—
391C5×D4—42no—
392C5×D4—42no—
393C5×D4—42no—
394C5×D4—41no—
395C5×D4—41no—
396C5×D4C4×D412yes—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5—21no—
400C2×C4×C5—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—21no—
409C2×C4×C5—21no—
410C2×C4×C5—21no—
411C2×C4×C5—42no—
412C2×C4×C5—42no—
413C2×C4×C5—42no—
414C2×C4×C5—41no—
415C2×C4×C5—41no—
416C2×C4×C5C4×D411yescharacteristic
417C2×C4×C5C4×D411yescharacteristic
418C2×C4×C5C23×C411yescharacteristic
419C2×C4×C5C22×D411yescharacteristic
420C2×C4×C5C22×D411yescharacteristic
421C2×C4×C5C2×#4111yescharacteristic
422C2×C4×C5H(5,𝔽2)11yescharacteristic
423C2×C4×C5H(5,𝔽2)11yescharacteristic
424C22⋊D5—41no—
425C22⋊D5—41no—
426C22⋊D5—42no—
427C22⋊D5—81no—
428C2×Dic5—22no—
429C2×Dic5—21no—
430C2×Dic5—21no—
431C2×Dic5—21no—
432C2×Dic5—22no—
433C2×Dic5—41no—
434C2×Dic5—41no—
435C2×Dic5—41no—
436C2×Dic5—48no—
437C2×Dic5—41no—
438D20—21no—
439D20—21no—
440C4×D5—41no—
441C4×D5—41no—
442Dic10—21no—
443Dic10—21no—
444C5×C8—21no—
445C5×C8—21no—
446C5×C8—21no—
447C5×C8—21no—
448C5×C8—41no—
449C5×C8—41no—
450#168—21no—
451#168—21no—
452#168—21no—
453#168—21no—
454#168—22no—
455#168—41no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—22no—
459C2×#41—22no—
460C2×#41—41no—
461C2×#41—41no—
462C2×#41—51no—
463C2×#41C4×D511yescharacteristic
464C2×#41C4×D511yescharacteristic
465C2×#41C22×D511yescharacteristic
466C2×#41C22×D511yescharacteristic
467C22×Q8C4×D511yescharacteristic
468C22×D4—21no—
469C22×D4C4×D511yescharacteristic
470C23×C4—21no—
471C23×C4—101no—
472C23×C4C22×D511yescharacteristic
473#135—102no—
474#135—102no—
475#135—201no—
476#135—201no—
477C2×Q16—51no—
478C2×Q16—51no—
479C2×SD16—51no—
480C2×SD16—51no—
481C2×SD16—51no—
482C2×SD16—51no—
483C2×D8—51no—
484C2×D8—51no—
485#131—22no—
486#131—22no—
487#131—41no—
488#131—41no—
489#131—102no—
490#131—201no—
491C2×M16—21no—
492C2×M16—21no—
493C2×M16—51no—
494C2×M16—51no—
495C2×M16—101no—
496C2×M16—101no—
497C2×M16—102no—
498C2×M16—201no—
499C2×M16C22×D511yescharacteristic
500C2×M16C22×D511yescharacteristic
501C22×C8—21no—
502C22×C8—21no—
503C22×C8—51no—
504C22×C8—51no—
505C22×C8—101no—
506C22×C8—101no—
507C22×C8C22×D511yescharacteristic
508C22×C8C22×D511yescharacteristic
509#123—101no—
510C22⋊Q8—51no—
511C22⋊Q8—51no—
512#121—51no—
513#121—51no—
514#120—101no—
515C4×D4—101no—
516C4×D4—101no—
517#117—51no—
518C2×C42—51no—
519C2×C42—51no—
520C2×C42—102no—
521C2×C42—101no—
522C2×C42—201no—
523#108—102no—
524#108—201no—
525C4⋊C8—101no—
526C4⋊C8—101no—
527#104—54no—
528#104—102no—
529#104—102no—
530#104—102no—
531#104—102no—
532#104—201no—
533#103—51no—
534#103—51no—
535#103—51no—
536#103—51no—
537#102—51no—
538#102—51no—
539#102—51no—
540#102—51no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544C22⋊C8—21no—
545C22⋊C8—21no—
546C22⋊C8—21no—
547C22⋊C8—51no—
548C22⋊C8—51no—
549C22⋊C8—51no—
550C22⋊C8—51no—
551C22⋊C8—101no—
552C22⋊C8—101no—
553C22⋊C8C22⋊D511yescharacteristic
554C22⋊C8C22⋊D511yescharacteristic
555C22⋊C8C22⋊D511yescharacteristic
556C22⋊C8C22⋊D511yescharacteristic
557#97—102no—
558#97—101no—
559#97—201no—
560C4×C8—101no—
561C22×C5—21no—
562C22×C5—21no—
563C22×C5—21no—
564C22×C5—21no—
565C22×C5—21no—
566C22×C5—22no—
567C22×C5—21no—
568C22×C5—21no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—41no—
572C22×C5—41no—
573C22×C5—41no—
574C22×C5—41no—
575C22×C5—41no—
576C22×C5—84no—
577C22×C5#44412yescomplemented
578C22×C5C2×C4×D411yescharacteristic
579C22×C5#54611yescharacteristic
580C22×C5#55111yescharacteristic
581C2×D5—41no—
582C2×D5—41no—
583C2×D5—41no—
584C4×C5—21no—
585C4×C5—21no—
586C4×C5—22no—
587C4×C5—41no—
588C4×C5C2×C4×D411yescharacteristic
589C4×C5#51811yescharacteristic
590C4×C5D4211yescharacteristic
591C4×C5#54611yescharacteristic
592Dic5—42no—
593Dic5—42no—
594Dic5—41no—
595Dic5—41no—
596Dic5—41no—
597C24—21no—
598C24#70911yescharacteristic
599#41—21no—
600#41—21no—
601#41—22no—
602#41—22no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—21no—
607#41—42no—
608#41—42no—
609#41—41no—
610#41—41no—
611#41—42no—
612#41—42no—
613#41—101no—
614#41—101no—
615#41—101no—
616#41—101no—
617#41D4×D512yes—
618#41#71112yes—
619C2×Q8—21no—
620C2×Q8—22no—
621C2×Q8—41no—
622C2×Q8—51no—
623C2×Q8C2×C4×D511yescharacteristic
624C2×Q8C2×C4×D511yescharacteristic
625C2×D4—21no—
626C2×D4—22no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—41no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—51no—
635C2×D4—101no—
636C2×D4—101no—
637C2×D4—101no—
638C2×D4C2×C4×D511yescharacteristic
639C2×D4C2×C4×D511yescharacteristic
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—101no—
652C22×C4—101no—
653C22×C4—101no—
654C22×C4—202no—
655C22×C4—202no—
656C22×C4—202no—
657C22×C4C2×C4×D511yescharacteristic
658C22×C4C2×C4×D511yescharacteristic
659C22×C4#70911yescharacteristic
660C22×C4C2×C22⋊D511yescharacteristic
661C22×C4C2×C22⋊D511yescharacteristic
662C22×C4C23×D511yescharacteristic
663Q16—102no—
664Q16—201no—
665SD16—102no—
666SD16—102no—
667SD16—201no—
668SD16—201no—
669D8—102no—
670D8—201no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—42no—
676M16—42no—
677M16—52no—
678M16—101no—
679M16—101no—
680M16—101no—
681M16—202no—
682M16—202no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8—51no—
692C2×C8—51no—
693C2×C8—51no—
694C2×C8—51no—
695C2×C8—101no—
696C2×C8—101no—
697C2×C8—101no—
698C2×C8—101no—
699C2×C8—101no—
700C2×C8—101no—
701C2×C8—202no—
702C2×C8—202no—
703C2×C8C2×C22⋊D511yescharacteristic
704C2×C8C2×C22⋊D511yescharacteristic
705C2×C8C2×C22⋊D511yescharacteristic
706C2×C8C2×C22⋊D511yescharacteristic
707C4⋊C4—51no—
708C4⋊C4—51no—
709C4⋊C4—101no—
710C4⋊C4—101no—
711C22⋊C4—101no—
712C22⋊C4—101no—
713C22⋊C4—101no—
714C22⋊C4—101no—
715C22⋊C4—101no—
716C42—52no—
717C42—101no—
718C42—101no—
719C42—101no—
720C42—101no—
721C42—202no—
722C2×C5—21no—
723C2×C5—22no—
724C2×C5—21no—
725C2×C5—41no—
726C2×C5—42no—
727C2×C5—81no—
728C2×C5#235811yescharacteristic
729C2×C5C2×#44411yescharacteristic
730C2×C5#295611yescharacteristic
731D5—81no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—21no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—81no—
741C23—101no—
742C23C4×C22⋊D511yescharacteristic
743C23C4×C22⋊D511yescharacteristic
744C23C2×#70911yescharacteristic
745Q8—21no—
746Q8—21no—
747Q8—21no—
748Q8—42no—
749Q8—101no—
750Q8—101no—
751Q8#402712yes—
752D4—22no—
753D4—22no—
754D4—21no—
755D4—21no—
756D4—21no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—41no—
761D4—41no—
762D4—101no—
763D4—101no—
764D4—201no—
765D4—201no—
766D4—202no—
767D4—401no—
768D4#402712yes—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—101no—
791C2×C4—101no—
792C2×C4—101no—
793C2×C4—201no—
794C2×C4—201no—
795C2×C4—201no—
796C2×C4—208no—
797C2×C4—201no—
798C2×C4—201no—
799C2×C4—201no—
800C2×C4C4×C22⋊D511yescharacteristic
801C2×C4C4×C22⋊D511yescharacteristic
802C2×C4C22×C4×D511yescharacteristic
803C2×C4C2×D4×D511yescharacteristic
804C2×C4C2×#71111yescharacteristic
805C2×C4#414411yescharacteristic
806C2×C4#414411yescharacteristic
807C2×C4C22×C22⋊D511yescharacteristic
808C8—21no—
809C8—21no—
810C8—21no—
811C8—21no—
812C8—41no—
813C8—41no—
814C8—101no—
815C8—101no—
816C8—101no—
817C8—101no—
818C8—102no—
819C8—201no—
820C5#2288611yescharacteristic, complemented, Sylow
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—84no—
837C22—201no—
838C22—201no—
839C22—201no—
840C22#6543412yescomplemented
841C22#6582411yescharacteristic
842C22#6582911yescharacteristic
843C22C2×C4×C22⋊D511yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—41no—
848C4—202no—
849C4—202no—
850C4—201no—
851C4—201no—
852C4—201no—
853C4C2×#402711yescharacteristic
854C4#6582011yescharacteristic
855C4D4×C22⋊D511yescharacteristic
856C4#6614011yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—401no—
864C2#1061383011yescharacteristic
865C2C2×#6543411yescharacteristic
866C2#1061554211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#2880C2
socleC22×C5C2×C4×D4
prime radical#10615811C2
cosocleC22×C4×C5C24
hypercenter#2880D5
hypocenterC5#22886
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
1. C5×#2880C2semidirect
3. C22×#3969C2semidirect
4. C2×#65434C2semidirect
5. #10610327C2semidirect
6. #10602810C2semidirect
7. #10602803C2semidirect
8. #10602802C2semidirect
9. #10600804C2semidirect
10. #10600793C2semidirect
11. #10600791C2semidirect
12. #10600789C2semidirect
13. #10600777C2semidirect
14. #10600758C2semidirect
15. #10600699C2semidirect
24. C2×#4047C22semidirect
33. #65528C4semidirect
34. #65528C4semidirect
35. #65527C4semidirect
36. #65527C4semidirect
44. #65517C4semidirect
45. #65516C4semidirect
46. #65507C4semidirect
47. #65506C4semidirect
50. C2×#3957C22semidirect
51. C2×#3957C22semidirect
52. C2×#3954C22semidirect
53. C2×#3954C22semidirect
54. #65399C22semidirect
55. #65391C22semidirect
56. #65390C22semidirect
57. C2×#3947C22semidirect
58. C2×#3947C22semidirect
63. #64778C22semidirect
64. #64778C22semidirect
65. #64775C22semidirect
66. #64775C22semidirect
67. #64770C22semidirect
68. #64770C22semidirect
104. C2×#689C2×C4semidirect
105. C2×#689C2×C4semidirect
106. C2×#688C2×C4semidirect
107. C2×#688C2×C4semidirect
108. C2×#687C2×C4semidirect
109. C2×#687C2×C4semidirect
110. C2×#686C2×C4semidirect
111. C2×#686C2×C4semidirect
150. #3969D4semidirect
151. #3967C2×C4semidirect
152. #3967C2×C4semidirect
153. #3967C2×C4semidirect
154. #3967C2×C4semidirect
155. #3964C2×C4semidirect
156. #3964C2×C4semidirect
157. #3964C2×C4semidirect
158. #3964C2×C4semidirect
179. #2880D5semidirect
577. C22×C5#444semidirect
820. C5#22886semidirect
840. C22#65434semidirect

Maximal subgroups

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

subgroupindex
C5×#28802
#106158112
C22×#39692
C2×#654342
#106103272
#106028102
#106028032
#106028022
#106008042
#106007932
#106007912
#106007892
#106007772
#106007582
#106006992
#228865