Finite Group Databasebeta

← C2×#10615340 #12977879

Subgroups — C2×#10615340 #12977879

Order 1280.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#553C211yesmaximal, characteristic
2C2×#65877C211yesmaximal, characteristic, complemented
3#10615340C2116yesmaximal, direct product factor
4C2×#65352C211yesmaximal, characteristic, complemented
5C2×#65354C211yesmaximal, characteristic, complemented
6C2×#65331C211yesmaximal, characteristic, complemented
7C2×#65330C211yesmaximal, characteristic, complemented
8C2×#65323C211yesmaximal, characteristic, complemented
9C2×#65322C211yesmaximal, characteristic, complemented
10C2×#65300C211yesmaximal, characteristic, complemented
11C2×#65296C211yesmaximal, characteristic, complemented
12C2×#65307C211yesmaximal, characteristic, complemented
13C2×#65285C211yesmaximal, characteristic, complemented
14C2×#65284C211yesmaximal, characteristic, complemented
15C2×#65259C211yesmaximal, characteristic, complemented
16C22×#3939C211yesmaximal, characteristic, complemented
17C5×#553—24no—
18C5×#553C2218yes—
19C2×C5×#126—21no—
20C2×C5×#125C2211yescharacteristic
21C2×C5×#123—21no—
22C2×C5×#121—21no—
23C2×C5×#121C2211yescharacteristic
24C2×C5×#121C2211yescharacteristic
25C2×C4×C5×D4—21no—
26C2×C4×C5×D4C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C5×#117C2211yescharacteristic
29C22×C5×C4⋊C4C2211yescharacteristic
30C2×D4×Dic5—21no—
31C22×#687C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C2×#4070C2211yescharacteristic
35C2×#4070C2211yescharacteristic
36C22×#681C2211yescharacteristic
37C23×#168C2211yescharacteristic
38#65877—24no—
39#65877C2218yescomplemented
40C2×#4036—21no—
41C2×#4024—21no—
42C2×#4024—21no—
43C2×#4015C2211yescharacteristic
44C2×C4×Dic10C2211yescharacteristic
45C2×#3964C2211yescharacteristic
46C2×#3964C2211yescharacteristic
47C2×#3964C2211yescharacteristic
48C2×C22⋊#168C2211yescharacteristic
49C2×C22⋊#168C2211yescharacteristic
50#65354C2218yescomplemented
51#65352C2218yescomplemented
52#65331C2218yescomplemented
53#65330C2218yescomplemented
54#65323C2218yescomplemented
55#65322C2218yescomplemented
56#65307C2218yescomplemented
57#65300C2218yescomplemented
58#65296C2218yescomplemented
59#65285C2218yescomplemented
60#65284C2218yescomplemented
61#65259C2218yescomplemented
62C2×#3942C2211yescharacteristic
63C2×#3942C2211yescharacteristic
64C2×#3942C2211yescharacteristic
65C2×#3940C2211yescharacteristic
66C2×#3940C2211yescharacteristic
67C2×#3940C2211yescharacteristic
68C2×#3939C2211yescharacteristic
69C2×#3939C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71C2×#3939C2211yescharacteristic
72C2×#3939C2211yescharacteristic
73C2×#3939C2211yescharacteristic
74C2×#3939C2218yescomplemented
75C2×C4⋊#168C2211yescharacteristic
76C2×#3935C2211yescharacteristic
77C2×#3346—51nomaximal, Sylow
78C22×C5×D4—21no—
79C22×C5×D4—21no—
80C22×C5×D4D411yescharacteristic
81C22×C5×D4C2311yescharacteristic
82C23×C4×C5—21no—
83C23×C4×C5—21no—
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×Dic5—21no—
87C23×Dic5—21no—
88C22×Dic10—21no—
89C22×Dic10C2311yescharacteristic
90C5×#126—28no—
91C5×#125—22no—
92C5×#125C2314yes—
93C5×#123—28no—
94C5×#121—28no—
95C5×#121—22no—
96C5×#121—22no—
97C5×#121C2314yes—
98C5×#121C2314yes—
99C4×C5×D4—28no—
100C4×C5×D4—22no—
101C4×C5×D4D414yes—
102C4×C5×D4C2314yes—
103C4×C5×D4C2314yes—
104C5×#117—22no—
105C5×#117C2314yes—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—22no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4D411yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2314yes—
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4D411yescharacteristic
120C2×C5×C22⋊C4D411yescharacteristic
121C2×C42×C5—21no—
122C2×C42×C5C2311yescharacteristic
123C2×C22⋊Dic5—21no—
124C2×C22⋊Dic5—21no—
125D4×Dic5—28no—
126C2×#687—24no—
127C2×#687C2314yes—
128C2×C4⋊Dic5—21no—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5—21no—
131C2×C4⋊Dic5—22no—
132C2×C4⋊Dic5—22no—
133C2×C4⋊Dic5C2314yes—
134C2×C4⋊Dic5C2311yescharacteristic
135C2×C4⋊Dic5C2311yescharacteristic
136C2×C4⋊Dic5C2311yescharacteristic
137C2×C4⋊Dic5C2314yes—
138#4070—22no—
139#4070—22no—
140#4070C2314yes—
141#4070C2314yes—
142C2×#683—21no—
143C2×#683—21no—
144C2×#683—21no—
145C2×C4×Dic5—21no—
146C2×#681—24no—
147C2×#681C2314yes—
148C22×#168—24no—
149C22×#168C2314yes—
150C22×#168C2311yescharacteristic
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C22×#168C2311yescharacteristic
154#4036—28no—
155#4024—28no—
156#4024—28no—
157#4015—22no—
158#4015C2314yes—
159C4×Dic10—22no—
160C4×Dic10C2314yes—
161#3964C2314yes—
162#3964C2314yes—
163#3964C2314yes—
164C22⋊#168C2314yes—
165C22⋊#168C2314yes—
166#3942C2314yes—
167#3942C2314yes—
168#3942C2314yes—
169#3940C2314yes—
170#3940C2314yes—
171#3940C2314yes—
172#3939C2314yes—
173#3939C2314yes—
174#3939C2314yes—
175#3939C2314yes—
176#3939C2314yes—
177#3939C2314yes—
178C4⋊#168C2314yes—
179#3935C2314yes—
180C2×#554—51no—
181C2×#553D511yescharacteristic
182#3346—516no—
183C2×#501—51no—
184C2×#484—51no—
185C2×#481—51no—
186C2×#485—51no—
187C2×#480—51no—
188C2×#479—51no—
189C2×#474—51no—
190C2×#468—51no—
191C2×#465—51no—
192C2×#440—51no—
193C2×#435—51no—
194C2×#428—51no—
195C22×#107—51no—
196C24×C5—21no—
197C24×C5C2×D411yescharacteristic
198C24×C5C2×D411yescharacteristic
199C2×C5×D4—24no—
200C2×C5×D4—24no—
201C2×C5×D4—24no—
202C2×C5×D4—21no—
203C2×C5×D4—22no—
204C2×C5×D4—22no—
205C2×C5×D4—44no—
206C2×C5×D4—82no—
207C2×C5×D4C2×D414yes—
208C2×C5×D4C2412yes—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—24no—
217C22×C4×C5—24no—
218C22×C4×C5—82no—
219C22×C4×C5—82no—
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D412yes—
225C22×C4×C5C2×D412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2411yescharacteristic
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—24no—
234C22×Dic5—24no—
235C22×Dic5—82no—
236C22×Dic5—82no—
237C2×Dic10—22no—
238C2×Dic10—22no—
239C2×Dic10—21no—
240C2×Dic10—24no—
241C2×Dic10—82no—
242C2×Dic10C2412yes—
243C5×C4⋊C4—21no—
244C5×C4⋊C4—21no—
245C5×C4⋊C4—24no—
246C5×C4⋊C4—24no—
247C5×C4⋊C4—24no—
248C5×C4⋊C4—21no—
249C5×C4⋊C4C2×D414yes—
250C5×C4⋊C4C2412yes—
251C5×C4⋊C4C2412yes—
252C5×C4⋊C4C2412yes—
253C5×C22⋊C4—24no—
254C5×C22⋊C4—24no—
255C5×C22⋊C4—24no—
256C5×C22⋊C4—24no—
257C5×C22⋊C4C2×D414yes—
258C5×C22⋊C4C2×D414yes—
259C42×C5—24no—
260C42×C5C2×D412yes—
261C42×C5C2412yes—
262C22⋊Dic5—24no—
263C22⋊Dic5—24no—
264#687—28no—
265C4⋊Dic5—21no—
266C4⋊Dic5—21no—
267C4⋊Dic5—21no—
268C4⋊Dic5—24no—
269C4⋊Dic5—24no—
270C4⋊Dic5—24no—
271C4⋊Dic5C2412yes—
272C4⋊Dic5C2412yes—
273C4⋊Dic5C2412yes—
274#683—24no—
275#683—24no—
276#683—24no—
277C4×Dic5—24no—
278#681—28no—
279C2×#168—22no—
280C2×#168—22no—
281C2×#168—22no—
282C2×#168—28no—
283C2×#168#4114yes—
284C2×#168C2412yes—
285C2×#168C2412yes—
286C2×#168C2412yes—
287C2×#168C2412yes—
288C22×SD16—51no—
289C22×M16—51no—
290C23×C8—51no—
291#554—58no—
292#554—104no—
293#553—24no—
294#553C2×D518yes—
295C2×C4⋊Q8—51no—
296C2×#126—21no—
297C2×#125—101no—
298C2×#125C2×D511yescharacteristic
299C2×#123—21no—
300C2×C22⋊Q8—51no—
301C2×C22⋊Q8—51no—
302C2×C22⋊Q8—101no—
303C2×C22⋊Q8—101no—
304C2×#121—21no—
305C2×#121C2×D511yescharacteristic
306C2×#121C2×D511yescharacteristic
307C2×C4×Q8—51no—
308C2×C4×D4—21no—
309C2×C4×D4—101no—
310C2×C4×D4C2×D511yescharacteristic
311C2×C4×D4C2×D511yescharacteristic
312C2×#117C2×D511yescharacteristic
313C22×C4⋊C4—51no—
314C22×C4⋊C4—51no—
315C22×C4⋊C4C2×D511yescharacteristic
316#501—58no—
317#485—58no—
318#484—58no—
319#481—58no—
320#480—58no—
321#479—58no—
322#474—58no—
323#468—58no—
324#465—58no—
325#440—58no—
326#435—58no—
327#428—58no—
328C2×#107—51no—
329C2×#107—51no—
330C2×#107—51no—
331C2×#107—51no—
332C2×#107—58no—
333C2×#107—51no—
334C2×#107—51no—
335C2×#106—51no—
336C2×#106—51no—
337C2×#106—51no—
338C2×C4⋊C8—51no—
339C2×#103—51no—
340C2×#103—51no—
341C2×#103—51no—
342C2×#102—51no—
343C2×#102—51no—
344C2×#102—51no—
345C2×C22⋊C8—51no—
346C2×C22⋊C8—51no—
347C2×#97—51no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—42no—
355C23×C5—42no—
356C23×C5—42no—
357C23×C5#13714yes—
358C23×C5C22×D412yes—
359C23×C5C22×D412yes—
360C23×C5C22×D411yescharacteristic
361C5×D4—28no—
362C5×D4—22no—
363C5×D4—22no—
364C5×D4—48no—
365C5×D4—42no—
366C5×D4—84no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—24no—
372C2×C4×C5—24no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—42no—
381C2×C4×C5—42no—
382C2×C4×C5—42no—
383C2×C4×C5—84no—
384C2×C4×C5—84no—
385C2×C4×C5C22×D412yes—
386C2×C4×C5C22×D412yes—
387C2×C4×C5C22×D412yes—
388C2×C4×C5C22×D412yes—
389C2×C4×C5C22×D411yescharacteristic
390C2×C4×C5C2×#4112yes—
391C2×C4×C52−1+412yes—
392C2×C4×C5C2511yescharacteristic
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—42no—
398C2×Dic5—42no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5—84no—
402C2×Dic5—84no—
403Dic10—22no—
404Dic10—22no—
405Dic10—42no—
406Dic10—84no—
407#168—22no—
408#168—22no—
409#168—22no—
410#168C2×#4114yes—
411C22×Q8—51no—
412C22×Q8—101no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4C22⋊D511yescharacteristic
416C22×D4C22×D511yescharacteristic
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—101no—
420C23×C4—101no—
421C23×C4C22×D511yescharacteristic
422C23×C4C22×D511yescharacteristic
423C2×SD16—54no—
424C2×SD16—104no—
425C2×M16—54no—
426C2×M16—104no—
427C22×C8—51no—
428C22×C8—51no—
429C22×C8—54no—
430C22×C8—51no—
431C22×C8—51no—
432C22×C8—104no—
433C4⋊Q8—54no—
434C4⋊Q8—102no—
435#126—28no—
436#125—22no—
437#125—108no—
438#125C22×D514yes—
439#123—28no—
440C22⋊Q8—54no—
441C22⋊Q8—54no—
442C22⋊Q8—102no—
443C22⋊Q8—102no—
444C22⋊Q8—108no—
445C22⋊Q8—108no—
446#121—28no—
447#121—22no—
448#121—22no—
449#121C22×D514yes—
450#121C22×D514yes—
451C4×Q8—54no—
452C4×Q8—102no—
453C4×D4—28no—
454C4×D4—22no—
455C4×D4—108no—
456C4×D4C22⋊D514yes—
457C4×D4C22×D514yes—
458C4×D4C22×D514yes—
459#117—22no—
460#117C22×D514yes—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—51no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—51no—
468C2×C4⋊C4—54no—
469C2×C4⋊C4—54no—
470C2×C4⋊C4—101no—
471C2×C4⋊C4—101no—
472C2×C4⋊C4—102no—
473C2×C4⋊C4—102no—
474C2×C4⋊C4—101no—
475C2×C4⋊C4—101no—
476C2×C4⋊C4—101no—
477C2×C4⋊C4—101no—
478C2×C4⋊C4C22⋊D511yescharacteristic
479C2×C4⋊C4C22×D511yescharacteristic
480C2×C4⋊C4C22×D511yescharacteristic
481C2×C4⋊C4C22×D514yes—
482C2×C4⋊C4C22×D511yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—101no—
488C2×C22⋊C4—101no—
489C2×C22⋊C4C22⋊D511yescharacteristic
490C2×C22⋊C4C22⋊D511yescharacteristic
491C2×C42—21no—
492C2×C42—101no—
493C2×C42C22×D511yescharacteristic
494#107—54no—
495#107—54no—
496#107—54no—
497#107—54no—
498#107—54no—
499#107—54no—
500#106—54no—
501#106—54no—
502#106—54no—
503C4⋊C8—54no—
504#103—54no—
505#103—54no—
506#103—54no—
507#102—54no—
508#102—54no—
509#102—54no—
510C22⋊C8—54no—
511C22⋊C8—54no—
512#97—54no—
513C22×C5—28no—
514C22×C5—22no—
515C22×C5—22no—
516C22×C5—22no—
517C22×C5—22no—
518C22×C5—22no—
519C22×C5—44no—
520C22×C5—42no—
521C22×C5—42no—
522C22×C5—42no—
523C22×C5—84no—
524C22×C5#54712yes—
525C22×C5C2×#13714yes—
526C22×C5C2×#13712yes—
527C22×C5#57612yes—
528C22×C5C23×D411yescharacteristic
529C4×C5—22no—
530C4×C5—22no—
531C4×C5—22no—
532C4×C5—22no—
533C4×C5—42no—
534C4×C5—42no—
535C4×C5—42no—
536C4×C5#54712yes—
537C4×C5C22×#4111yescharacteristic
538C4×C5C2×2−1+411yescharacteristic
539Dic5—42no—
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543C24—21no—
544C24C2×C22⋊D511yescharacteristic
545C24C2×C22⋊D511yescharacteristic
546C2×Q8—52no—
547C2×Q8—101no—
548C2×Q8—104no—
549C2×Q8—102no—
550C2×Q8—102no—
551C2×Q8—402no—
552C2×D4—24no—
553C2×D4—24no—
554C2×D4—24no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—44no—
559C2×D4—82no—
560C2×D4C2×C22⋊D514yes—
561C2×D4C23×D512yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4—104no—
578C22×C4—104no—
579C22×C4—402no—
580C22×C4—402no—
581C22×C4C2×C22⋊D512yes—
582C22×C4C2×C22⋊D512yes—
583C22×C4C2×C22⋊D511yescharacteristic
584C22×C4C2×C22⋊D511yescharacteristic
585C22×C4C2×C22⋊D511yescharacteristic
586C22×C4C2×C22⋊D511yescharacteristic
587C22×C4C23×D512yes—
588C22×C4C23×D512yes—
589C22×C4C23×D511yescharacteristic
590SD16—108no—
591M16—108no—
592C2×C8—54no—
593C2×C8—52no—
594C2×C8—52no—
595C2×C8—52no—
596C2×C8—52no—
597C2×C8—108no—
598C2×C8—102no—
599C2×C8—102no—
600C2×C8—102no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—52no—
608C4⋊C4—52no—
609C4⋊C4—52no—
610C4⋊C4—101no—
611C4⋊C4—104no—
612C4⋊C4—104no—
613C4⋊C4—101no—
614C4⋊C4—101no—
615C4⋊C4—104no—
616C4⋊C4—104no—
617C4⋊C4—104no—
618C4⋊C4—104no—
619C4⋊C4C2×C22⋊D514yes—
620C4⋊C4C23×D512yes—
621C4⋊C4C23×D512yes—
622C4⋊C4C23×D512yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—104no—
628C22⋊C4—104no—
629C22⋊C4C2×C22⋊D514yes—
630C22⋊C4C2×C22⋊D514yes—
631C42—24no—
632C42—104no—
633C42C2×C22⋊D512yes—
634C42C23×D512yes—
635C2×C5—24no—
636C2×C5—42no—
637C2×C5—82no—
638C2×C5#334614yescomplemented
639C2×C5C2×#54711yescharacteristic
640C2×C5C22×#13711yescharacteristic
641C2×C5C2×#57611yescharacteristic
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23#409714yes—
652C23C22×C22⋊D512yes—
653C23C22×C22⋊D512yes—
654C23C22×C22⋊D511yescharacteristic
655Q8—102no—
656Q8—102no—
657Q8—202no—
658Q8—404no—
659D4—28no—
660D4—22no—
661D4—22no—
662D4—48no—
663D4—42no—
664D4—84no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—84no—
682C2×C4—84no—
683C2×C4—102no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—202no—
688C2×C4—202no—
689C2×C4—202no—
690C2×C4—202no—
691C2×C4—404no—
692C2×C4—404no—
693C2×C4D5×#4112yes—
694C2×C4#415012yes—
695C2×C4C22×C22⋊D512yes—
696C2×C4C22×C22⋊D512yes—
697C2×C4C22×C22⋊D512yes—
698C2×C4C22×C22⋊D512yes—
699C2×C4C22×C22⋊D511yescharacteristic
700C2×C4C24×D511yescharacteristic
701C8—54no—
702C8—102no—
703C8—102no—
704C8—102no—
705C5C2×#334611yescharacteristic, complemented, Sylow
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22C2×#409714yes—
718C22C2×#409712yes—
719C22#6615812yes—
720C22#6616912yes—
721C22C23×C22⋊D511yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—202no—
730C4—202no—
731C4—202no—
732C4—202no—
733C4#6615812yes—
734C4C2×D5×#4111yescharacteristic
735C4C2×#415011yescharacteristic
736C2—24no—
737C2—42no—
738C2—82no—
739C2#1061534014yesdirect product factor
740C2C22×#409711yescharacteristic
741C2C2×#6615811yescharacteristic
742C2C2×#6616911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
Fitting, prime radicalC2×C5×#553C2
socleC23×C5C22×D4
hypercenterC2×#553D5
hypocenterC5C2×#3346
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
2. C2×#65877C2semidirect
3. #10615340C2direct (N × H)
4. C2×#65352C2semidirect
5. C2×#65354C2semidirect
6. C2×#65331C2semidirect
7. C2×#65330C2semidirect
8. C2×#65323C2semidirect
9. C2×#65322C2semidirect
10. C2×#65300C2semidirect
11. C2×#65296C2semidirect
12. C2×#65307C2semidirect
13. C2×#65285C2semidirect
14. C2×#65284C2semidirect
15. C2×#65259C2semidirect
16. C22×#3939C2semidirect
39. #65877C22semidirect
50. #65354C22semidirect
51. #65352C22semidirect
52. #65331C22semidirect
53. #65330C22semidirect
54. #65323C22semidirect
55. #65322C22semidirect
56. #65307C22semidirect
57. #65300C22semidirect
58. #65296C22semidirect
59. #65285C22semidirect
60. #65284C22semidirect
61. #65259C22semidirect
74. C2×#3939C22semidirect
638. C2×C5#3346semidirect
705. C5C2×#3346semidirect
739. C2#10615340direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5532
C2×#658772
#106153402
C2×#653522
C2×#653542
C2×#653312
C2×#653302
C2×#653232
C2×#653222
C2×#653002
C2×#652962
C2×#653072
C2×#652852
C2×#652842
C2×#652592
C22×#39392
C2×#33465