Finite Group Databasebeta

← C2×#10615263 #12975868

Subgroups — C2×#10615263 #12975868

Order 1280.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#547C211yesmaximal, characteristic, complemented
2C2×#65886C211yesmaximal, characteristic, complemented
3#10615263C2116yesmaximal, direct product factor
4C2×#65380C211yesmaximal, characteristic, complemented
5C2×#65378C211yesmaximal, characteristic, complemented
6C2×#65329C211yesmaximal, characteristic, complemented
7C2×#65326C211yesmaximal, characteristic, complemented
8C2×#65331C211yesmaximal, characteristic, complemented
9C2×#65327C211yesmaximal, characteristic, complemented
10C2×#65305C211yesmaximal, characteristic, complemented
11C2×#65300C211yesmaximal, characteristic, complemented
12C2×#65307C211yesmaximal, characteristic, complemented
13C2×#65259C211yesmaximal, characteristic, complemented
14C22×#3942C211yesmaximal, characteristic, complemented
15C2×#65256C211yesmaximal, characteristic, complemented
16C2×#65255C211yesmaximal, characteristic, complemented
17C22×C5×#41—21no—
18C22×#709C2211yescharacteristic
19C23×Dic10C2211yescharacteristic
20C5×#547—24no—
21C5×#547C2218yescomplemented
22C2×C5×C4⋊Q8C2211yescharacteristic
23C2×C5×#123—21no—
24C2×C5×#123—21no—
25C2×C5×C22⋊Q8—21no—
26C2×C5×#121C2211yescharacteristic
27C2×C5×#121C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C2×C4×C5×D4C2211yescharacteristic
30C22×C5×C4⋊C4C2211yescharacteristic
31C22×C5×C4⋊C4C2211yescharacteristic
32C2×#4085—21no—
33C22×#687C2211yescharacteristic
34C22×#687C2211yescharacteristic
35C22×#686C2211yescharacteristic
36C2×#4076C2211yescharacteristic
37C2×#4070C2211yescharacteristic
38C22×#681C2211yescharacteristic
39C23×#168C2211yescharacteristic
40#65886—24no—
41#65886C2218yescomplemented
42C2×#4042—21no—
43C2×#4031—21no—
44C2×#4027—21no—
45C2×#4021C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic
47C2×#3964C2211yescharacteristic
48C2×C22⋊#168C2211yescharacteristic
49C2×C22⋊#168C2211yescharacteristic
50#65380C2218yescomplemented
51#65378C2218yescomplemented
52#65331C2218yescomplemented
53#65329C2218yescomplemented
54#65327C2218yescomplemented
55#65326C2218yescomplemented
56#65307C2218yescomplemented
57#65305C2218yescomplemented
58#65300C2218yescomplemented
59#65259C2218yescomplemented
60C2×#3942C2211yescharacteristic
61C2×#3942C2211yescharacteristic
62C2×#3942C2211yescharacteristic
63C2×#3942C2211yescharacteristic
64C2×#3942C2211yescharacteristic
65C2×#3942C2211yescharacteristic
66C2×#3942C2218yescomplemented
67#65256C2218yescomplemented
68#65255C2218yescomplemented
69C2×#3941C2211yescharacteristic
70C2×#3941C2211yescharacteristic
71C2×#3941C2211yescharacteristic
72C2×#3939C2211yescharacteristic
73C2×#3939C2211yescharacteristic
74C2×#3939C2211yescharacteristic
75C2×C4⋊#168C2211yescharacteristic
76C2×#3935C2211yescharacteristic
77C2×#3308—51nomaximal, Sylow
78C2×C5×#41—28no—
79C2×C5×#41—48no—
80C22×C5×Q8—21no—
81C22×C5×D4—21no—
82C22×C5×D4—21no—
83C22×C5×D4D411yescharacteristic
84C22×C5×D4C2311yescharacteristic
85C23×C4×C5—21no—
86C23×C4×C5—21no—
87C23×C4×C5—21no—
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C22×C22⋊D5—21no—
91C22×C22⋊D5—21no—
92C23×Dic5—21no—
93C2×#709—22no—
94C2×#709—24no—
95C2×#709—42no—
96C2×#709C2314yes—
97C22×D20C2311yescharacteristic
98C22×C4×D5—21no—
99C22×Dic10—24no—
100C22×Dic10—21no—
101C22×Dic10—22no—
102C22×Dic10—42no—
103C22×Dic10C2311yescharacteristic
104C22×Dic10C2314yes—
105C22×Dic10C2311yescharacteristic
106C5×C4⋊Q8—22no—
107C5×C4⋊Q8C2314yes—
108C5×#123—28no—
109C5×#123—28no—
110C5×C22⋊Q8—28no—
111C5×#121—22no—
112C5×#121—22no—
113C5×#121C2314yes—
114C5×#121C2314yes—
115C4×C5×D4—22no—
116C4×C5×D4D414yes—
117C4×C5×D4C2314yes—
118C4×C5×D4C2314yes—
119C2×C5×C4⋊C4—21no—
120C2×C5×C4⋊C4—21no—
121C2×C5×C4⋊C4—22no—
122C2×C5×C4⋊C4—22no—
123C2×C5×C4⋊C4—21no—
124C2×C5×C4⋊C4D411yescharacteristic
125C2×C5×C4⋊C4C2311yescharacteristic
126C2×C5×C4⋊C4C2311yescharacteristic
127C2×C5×C4⋊C4C2311yescharacteristic
128C2×C5×C4⋊C4C2314yes—
129C2×C5×C4⋊C4C2314yes—
130C2×C5×C22⋊C4—21no—
131C2×C5×C22⋊C4—21no—
132C2×C5×C22⋊C4—21no—
133C2×C5×C22⋊C4D411yescharacteristic
134C2×C5×C22⋊C4D411yescharacteristic
135C2×C42×C5C2311yescharacteristic
136C2×C22⋊Dic5—21no—
137#4085—28no—
138C2×#687—24no—
139C2×#687—42no—
140C2×#687C2314yes—
141C2×#687C2314yes—
142C2×#686—42no—
143C2×#686C2314yes—
144#4076—22no—
145#4076C2314yes—
146C2×#685—21no—
147C2×#685—21no—
148C2×#685—21no—
149C2×C4⋊Dic5C2311yescharacteristic
150#4070—22no—
151#4070C2314yes—
152C2×#683—21no—
153C2×#683—21no—
154C2×C4×Dic5—21no—
155C2×#681—42no—
156C2×#681C2314yes—
157C22×#168—42no—
158C22×#168C2311yescharacteristic
159C22×#168C2311yescharacteristic
160C22×#168C2311yescharacteristic
161C22×#168C2311yescharacteristic
162C22×#168C2314yes—
163#4042—28no—
164#4031—28no—
165#4027—28no—
166#4021—22no—
167#4021C2314yes—
168C4×Dic10—22no—
169C4×Dic10C2314yes—
170#3964C2314yes—
171C22⋊#168C2314yes—
172C22⋊#168C2314yes—
173#3942C2314yes—
174#3942C2314yes—
175#3942C2314yes—
176#3942C2314yes—
177#3942C2314yes—
178#3942C2314yes—
179#3941C2314yes—
180#3941C2314yes—
181#3941C2314yes—
182#3939C2314yes—
183#3939C2314yes—
184#3939C2314yes—
185C4⋊#168C2314yes—
186#3935C2314yes—
187C2×#548—51no—
188C2×#547D511yescharacteristic, complemented
189#3308—516no—
190C2×#489—51no—
191C2×#484—51no—
192C2×#480—51no—
193C2×#477—51no—
194C2×#468—51no—
195C2×#466—51no—
196C2×#463—51no—
197C2×#449—51no—
198C2×#448—51no—
199C2×#440—51no—
200C2×#435—51no—
201C2×#417—51no—
202C22×#103—51no—
203C24×C5—21no—
204C24×C5C2×D411yescharacteristic
205C24×C5C2×D411yescharacteristic
206C23×D5—21no—
207C5×#41—432no—
208C2×C5×Q8—24no—
209C2×C5×Q8—44no—
210C2×C5×D4—24no—
211C2×C5×D4—24no—
212C2×C5×D4—24no—
213C2×C5×D4—21no—
214C2×C5×D4—22no—
215C2×C5×D4—22no—
216C2×C5×D4—44no—
217C2×C5×D4—44no—
218C2×C5×D4C2×D414yes—
219C2×C5×D4C2412yes—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—24no—
228C22×C4×C5—24no—
229C22×C4×C5—24no—
230C22×C4×C5—44no—
231C22×C4×C5—44no—
232C22×C4×C5—44no—
233C22×C4×C5C2×D411yescharacteristic
234C22×C4×C5C2×D411yescharacteristic
235C22×C4×C5C2×D411yescharacteristic
236C22×C4×C5C2×D411yescharacteristic
237C22×C4×C5C2×D412yes—
238C22×C4×C5C2×D412yes—
239C22×C4×C5C2412yes—
240C22×C4×C5C2412yes—
241C22×C4×C5C2411yescharacteristic
242C2×C22⋊D5—24no—
243C2×C22⋊D5—24no—
244C2×C22⋊D5—44no—
245C2×C22⋊D5—44no—
246C22×Dic5—21no—
247C22×Dic5—21no—
248C22×Dic5—21no—
249C22×Dic5—24no—
250C22×Dic5—44no—
251#709—28no—
252#709—44no—
253#709—48no—
254C2×D20—22no—
255C2×D20—22no—
256C2×D20—21no—
257C2×D20C2412yes—
258C2×C4×D5—24no—
259C2×C4×D5—44no—
260C2×Dic10—21no—
261C2×Dic10—22no—
262C2×Dic10—22no—
263C2×Dic10—22no—
264C2×Dic10—28no—
265C2×Dic10—21no—
266C2×Dic10—24no—
267C2×Dic10—44no—
268C2×Dic10—48no—
269C2×Dic10—44no—
270C2×Dic10#4114yescomplemented
271C2×Dic10C2412yes—
272C2×Dic10C2412yes—
273C5×C4⋊C4—21no—
274C5×C4⋊C4—21no—
275C5×C4⋊C4—21no—
276C5×C4⋊C4—24no—
277C5×C4⋊C4—24no—
278C5×C4⋊C4—24no—
279C5×C4⋊C4C2×D414yes—
280C5×C4⋊C4C2412yes—
281C5×C4⋊C4C2412yes—
282C5×C4⋊C4C2412yes—
283C5×C22⋊C4—24no—
284C5×C22⋊C4—24no—
285C5×C22⋊C4—24no—
286C5×C22⋊C4C2×D414yes—
287C5×C22⋊C4C2×D414yes—
288C42×C5C2×D412yes—
289C42×C5C2412yes—
290C22⋊Dic5—24no—
291#687—28no—
292#687—44no—
293#686—44no—
294#685—24no—
295#685—24no—
296#685—24no—
297C4⋊Dic5—21no—
298C4⋊Dic5C2412yes—
299#683—24no—
300#683—24no—
301C4×Dic5—24no—
302#681—44no—
303C2×#168—22no—
304C2×#168—22no—
305C2×#168—22no—
306C2×#168—22no—
307C2×#168—44no—
308C2×#168C2412yes—
309C2×#168C2412yes—
310C2×#168C2412yes—
311C2×#168C2412yes—
312C22×#41—21no—
313C22×#41—51no—
314C23×Q8—51no—
315C22×SD16—51no—
316C22×SD16—51no—
317C22×D8—51no—
318C22×M16—51no—
319C23×C8—51no—
320#548—58no—
321#548—104no—
322#547—24no—
323#547C2×D518yescomplemented
324C2×C4⋊Q8C2×D511yescharacteristic
325C2×#124—51no—
326C2×#124—101no—
327C2×#123—21no—
328C2×#123—21no—
329C2×C22⋊Q8—21no—
330C2×C22⋊Q8—51no—
331C2×C22⋊Q8—101no—
332C2×#121—51no—
333C2×#121—101no—
334C2×#121C2×D511yescharacteristic
335C2×#121C2×D511yescharacteristic
336C2×C4×Q8—51no—
337C2×C4×D4—101no—
338C2×C4×D4C2×D511yescharacteristic
339C2×C4×D4C2×D511yescharacteristic
340C22×C4⋊C4C2×D511yescharacteristic
341C22×C4⋊C4C2×D511yescharacteristic
342#489—58no—
343#484—58no—
344#480—58no—
345#477—58no—
346#468—58no—
347#466—58no—
348#463—58no—
349#449—58no—
350#448—58no—
351#440—58no—
352#435—58no—
353C2×#107—51no—
354C2×#107—51no—
355C2×#107—51no—
356C2×C4⋊C8—51no—
357#417—58no—
358C2×#103—51no—
359C2×#103—51no—
360C2×#103—51no—
361C2×#103—51no—
362C2×#103—51no—
363C2×#103—51no—
364C2×#103—58no—
365C2×#102—51no—
366C2×#102—51no—
367C2×#102—51no—
368C2×#102—51no—
369C2×C22⋊C8—51no—
370C2×C22⋊C8—51no—
371C2×#97—51no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—42no—
379C23×C5—42no—
380C23×C5—42no—
381C23×C5AGL(1,ℤ/8)14yes—
382C23×C5C22×D412yes—
383C23×C5C22×D412yes—
384C23×C5C22×D411yescharacteristic
385C22×D5—22no—
386C22×D5—42no—
387C22×D5—42no—
388C22×D5—42no—
389C5×Q8—48no—
390C5×D4—28no—
391C5×D4—22no—
392C5×D4—22no—
393C5×D4—48no—
394C5×D4—48no—
395C5×D4—42no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—24no—
401C2×C4×C5—24no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—48no—
410C2×C4×C5—48no—
411C2×C4×C5—42no—
412C2×C4×C5—42no—
413C2×C4×C5—42no—
414C2×C4×C5—48no—
415C2×C4×C5C22×D412yes—
416C2×C4×C5C22×D412yes—
417C2×C4×C5C22×D412yes—
418C2×C4×C5C22×D412yes—
419C2×C4×C5C22×D411yescharacteristic
420C2×C4×C5C2×#4112yes—
421C2×C4×C5H(5,𝔽2)12yes—
422C2×C4×C5C2511yescharacteristic
423C22⋊D5—48no—
424C22⋊D5—48no—
425C2×Dic5—24no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—48no—
430C2×Dic5—42no—
431C2×Dic5—42no—
432D20—22no—
433D20—22no—
434D20—42no—
435C4×D5—48no—
436Dic10—24no—
437Dic10—22no—
438Dic10—22no—
439Dic10—22no—
440Dic10—48no—
441Dic10—42no—
442Dic10C2×#4114yescomplemented
443#168—22no—
444#168—22no—
445#168—22no—
446#168—22no—
447C2×#41—28no—
448C2×#41—48no—
449C2×#41—54no—
450C2×#41—104no—
451C2×#41—102no—
452C2×#41—202no—
453C22×Q8—21no—
454C22×Q8—51no—
455C22×Q8—51no—
456C22×Q8—54no—
457C22×Q8—104no—
458C22×Q8—101no—
459C22×Q8—102no—
460C22×Q8—202no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—51no—
464C22×D4—101no—
465C22×D4—101no—
466C22×D4C22⋊D511yescharacteristic
467C22×D4C22×D511yescharacteristic
468C23×C4—21no—
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—101no—
472C23×C4—101no—
473C23×C4C22×D511yescharacteristic
474C23×C4C22×D511yescharacteristic
475C2×SD16—54no—
476C2×SD16—54no—
477C2×SD16—104no—
478C2×SD16—202no—
479C2×D8—54no—
480C2×D8—202no—
481C2×M16—54no—
482C2×M16—202no—
483C22×C8—51no—
484C22×C8—51no—
485C22×C8—51no—
486C22×C8—51no—
487C22×C8—54no—
488C22×C8—202no—
489C4⋊Q8—22no—
490C4⋊Q8C22×D514yes—
491#124—54no—
492#124—108no—
493#124—102no—
494#123—28no—
495#123—28no—
496C22⋊Q8—28no—
497C22⋊Q8—54no—
498C22⋊Q8—102no—
499C22⋊Q8—108no—
500#121—22no—
501#121—22no—
502#121—54no—
503#121—108no—
504#121—102no—
505#121C22×D514yes—
506#121C22×D514yes—
507C4×Q8—54no—
508C4×Q8—102no—
509C4×D4—22no—
510C4×D4—108no—
511C4×D4C22⋊D514yes—
512C4×D4C22×D514yes—
513C4×D4C22×D514yes—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—51no—
520C2×C4⋊C4—101no—
521C2×C4⋊C4—101no—
522C2×C4⋊C4C22⋊D511yescharacteristic
523C2×C4⋊C4C22×D511yescharacteristic
524C2×C4⋊C4C22×D511yescharacteristic
525C2×C4⋊C4C22×D511yescharacteristic
526C2×C4⋊C4C22×D514yes—
527C2×C4⋊C4C22×D514yes—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—101no—
532C2×C22⋊C4—101no—
533C2×C22⋊C4—101no—
534C2×C22⋊C4—101no—
535C2×C22⋊C4C22⋊D511yescharacteristic
536C2×C22⋊C4C22⋊D511yescharacteristic
537C2×C42—101no—
538C2×C42C22×D511yescharacteristic
539#107—54no—
540#107—54no—
541#107—54no—
542C4⋊C8—54no—
543#103—54no—
544#103—54no—
545#103—54no—
546#103—54no—
547#103—54no—
548#103—54no—
549#102—54no—
550#102—54no—
551#102—54no—
552#102—54no—
553C22⋊C8—54no—
554C22⋊C8—54no—
555#97—54no—
556C22×C5—22no—
557C22×C5—28no—
558C22×C5—22no—
559C22×C5—22no—
560C22×C5—22no—
561C22×C5—22no—
562C22×C5—44no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5—84no—
567C22×C5#54612yes—
568C22×C5C2×AGL(1,ℤ/8)14yes—
569C22×C5C2×AGL(1,ℤ/8)12yes—
570C22×C5#57812yes—
571C22×C5C23×D411yescharacteristic
572C2×D5—42no—
573C2×D5—42no—
574C2×D5—42no—
575C2×D5—84no—
576C4×C5—22no—
577C4×C5—22no—
578C4×C5—22no—
579C4×C5—22no—
580C4×C5—42no—
581C4×C5—42no—
582C4×C5—42no—
583C4×C5#54612yes—
584C4×C5C22×#4111yescharacteristic
585C4×C5C2×H(5,𝔽2)11yescharacteristic
586Dic5—24no—
587Dic5—42no—
588Dic5—42no—
589C24—21no—
590C24—101no—
591C24C2×C22⋊D511yescharacteristic
592C24C2×C22⋊D511yescharacteristic
593#41—432no—
594#41—108no—
595#41—204no—
596#41—208no—
597C2×Q8—24no—
598C2×Q8—44no—
599C2×Q8—54no—
600C2×Q8—52no—
601C2×Q8—52no—
602C2×Q8—108no—
603C2×Q8—102no—
604C2×Q8—101no—
605C2×Q8—104no—
606C2×Q8—101no—
607C2×Q8—102no—
608C2×Q8—102no—
609C2×Q8—204no—
610C2×Q8—204no—
611C2×Q8—208no—
612C2×D4—24no—
613C2×D4—24no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—44no—
619C2×D4—44no—
620C2×D4—52no—
621C2×D4—104no—
622C2×D4—104no—
623C2×D4—102no—
624C2×D4—102no—
625C2×D4—101no—
626C2×D4—204no—
627C2×D4—204no—
628C2×D4C2×C22⋊D514yes—
629C2×D4C23×D512yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—101no—
644C22×C4—104no—
645C22×C4—101no—
646C22×C4—101no—
647C22×C4—104no—
648C22×C4—204no—
649C22×C4—204no—
650C22×C4C2×C22⋊D512yes—
651C22×C4C2×C22⋊D512yes—
652C22×C4C2×C22⋊D511yescharacteristic
653C22×C4C2×C22⋊D511yescharacteristic
654C22×C4C2×C22⋊D511yescharacteristic
655C22×C4C2×C22⋊D511yescharacteristic
656C22×C4C23×D512yes—
657C22×C4C23×D512yes—
658C22×C4C23×D511yescharacteristic
659SD16—108no—
660SD16—204no—
661D8—204no—
662M16—204no—
663C2×C8—52no—
664C2×C8—52no—
665C2×C8—52no—
666C2×C8—52no—
667C2×C8—102no—
668C2×C8—102no—
669C2×C8—102no—
670C2×C8—102no—
671C2×C8—204no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—24no—
678C4⋊C4—52no—
679C4⋊C4—101no—
680C4⋊C4—104no—
681C4⋊C4—104no—
682C4⋊C4C2×C22⋊D514yes—
683C4⋊C4C23×D512yes—
684C4⋊C4C23×D512yes—
685C4⋊C4C23×D512yes—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—104no—
690C22⋊C4—104no—
691C22⋊C4—104no—
692C22⋊C4—104no—
693C22⋊C4C2×C22⋊D514yes—
694C22⋊C4C2×C22⋊D514yes—
695C42—104no—
696C42C2×C22⋊D512yes—
697C42C23×D512yes—
698C2×C5—24no—
699C2×C5—42no—
700C2×C5—82no—
701C2×C5#330814yescomplemented
702C2×C5C2×#54611yescharacteristic
703C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
704C2×C5C2×#57811yescharacteristic
705D5—82no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—102no—
716C23—202no—
717C23—202no—
718C23—202no—
719C23#407814yes—
720C23C22×C22⋊D512yes—
721C23C22×C22⋊D512yes—
722C23C22×C22⋊D511yescharacteristic
723Q8—48no—
724Q8—54no—
725Q8—104no—
726Q8—102no—
727Q8—102no—
728Q8—102no—
729Q8—208no—
730Q8—202no—
731D4—28no—
732D4—22no—
733D4—22no—
734D4—48no—
735D4—48no—
736D4—42no—
737D4—102no—
738D4—102no—
739D4—208no—
740D4—208no—
741D4—202no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—48no—
756C2×C4—48no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—48no—
761C2×C4—104no—
762C2×C4—102no—
763C2×C4—102no—
764C2×C4—102no—
765C2×C4—208no—
766C2×C4—208no—
767C2×C4—202no—
768C2×C4—202no—
769C2×C4D5×#4112yes—
770C2×C4#414912yes—
771C2×C4C22×C22⋊D512yes—
772C2×C4C22×C22⋊D512yes—
773C2×C4C22×C22⋊D512yes—
774C2×C4C22×C22⋊D512yes—
775C2×C4C22×C22⋊D511yescharacteristic
776C2×C4C24×D511yescharacteristic
777C8—102no—
778C8—102no—
779C8—102no—
780C8—102no—
781C5C2×#330811yescharacteristic, complemented, Sylow
782C22—22no—
783C22—22no—
784C22—28no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—44no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—84no—
793C22—202no—
794C22—202no—
795C22—202no—
796C22—404no—
797C22C2×#407814yes—
798C22C2×#407812yes—
799C22#6616312yes—
800C22#6617212yes—
801C22C23×C22⋊D511yescharacteristic
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—104no—
810C4—202no—
811C4—202no—
812C4#6616312yes—
813C4C2×D5×#4111yescharacteristic
814C4C2×#414911yescharacteristic
815C2—24no—
816C2—42no—
817C2—82no—
818C2—402no—
819C2#1061526314yesdirect product factor
820C2C22×#407811yescharacteristic
821C2C2×#6616311yescharacteristic
822C2C2×#6617211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#547C2
socleC23×C5C22×D4
hypercenterC2×#547D5
hypocenterC5C2×#3308
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×C5×#547C2semidirect
2. C2×#65886C2semidirect
3. #10615263C2direct (N × H)
4. C2×#65380C2semidirect
5. C2×#65378C2semidirect
6. C2×#65329C2semidirect
7. C2×#65326C2semidirect
8. C2×#65331C2semidirect
9. C2×#65327C2semidirect
10. C2×#65305C2semidirect
11. C2×#65300C2semidirect
12. C2×#65307C2semidirect
13. C2×#65259C2semidirect
14. C22×#3942C2semidirect
15. C2×#65256C2semidirect
16. C2×#65255C2semidirect
21. C5×#547C22semidirect
41. #65886C22semidirect
50. #65380C22semidirect
51. #65378C22semidirect
52. #65331C22semidirect
53. #65329C22semidirect
54. #65327C22semidirect
55. #65326C22semidirect
56. #65307C22semidirect
57. #65305C22semidirect
58. #65300C22semidirect
59. #65259C22semidirect
66. C2×#3942C22semidirect
67. #65256C22semidirect
68. #65255C22semidirect
188. C2×#547D5semidirect
270. C2×Dic10#41semidirect
323. #547C2×D5semidirect
442. Dic10C2×#41semidirect
701. C2×C5#3308semidirect
781. C5C2×#3308semidirect
819. C2#10615263direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5472
C2×#658862
#106152632
C2×#653802
C2×#653782
C2×#653292
C2×#653262
C2×#653312
C2×#653272
C2×#653052
C2×#653002
C2×#653072
C2×#652592
C22×#39422
C2×#652562
C2×#652552
C2×#33085