Finite Group Databasebeta

← C2×#10615356 #12977873

Subgroups — C2×#10615356 #12977873

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×#554C211yesmaximal, characteristic, complemented
2C2×#65899C211yesmaximal, characteristic
3#10615356C2116yesmaximal, direct product factor
4C2×#65376C211yesmaximal, characteristic, complemented
5C2×#65369C211yesmaximal, characteristic, complemented
6C2×#65338C211yesmaximal, characteristic, complemented
7C2×#65337C211yesmaximal, characteristic, complemented
8C2×#65333C211yesmaximal, characteristic, complemented
9C2×#65334C211yesmaximal, characteristic, complemented
10C2×#65315C211yesmaximal, characteristic, complemented
11C2×#65311C211yesmaximal, characteristic, complemented
12C2×#65300C211yesmaximal, characteristic, complemented
13C2×#65257C211yesmaximal, characteristic, complemented
14C2×#65256C211yesmaximal, characteristic, complemented
15C2×#65253C211yesmaximal, characteristic, complemented
16C22×#3939C211yesmaximal, characteristic, complemented
17C5×#554—24no—
18C5×#554C2218yescomplemented
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×#125—21no—
21C2×C5×C22⋊Q8—21no—
22C2×C5×C22⋊Q8—21no—
23C2×C5×C22⋊Q8C2211yescharacteristic
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×D4—21no—
27C2×C4×C5×D4C2211yescharacteristic
28C22×C5×C4⋊C4C2211yescharacteristic
29C22×C5×C4⋊C4C2211yescharacteristic
30C22×#688C2211yescharacteristic
31C2×#4085—21no—
32C2×#4076C2211yescharacteristic
33C2×#4076C2211yescharacteristic
34C2×#4072C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#681C2211yescharacteristic
37C23×#168C2211yescharacteristic
38#65899—24no—
39#65899C2218yes—
40C2×#4044—21no—
41C2×#4029—21no—
42C2×#4027—21no—
43C2×C4×D20C2211yescharacteristic
44C2×#4016C2211yescharacteristic
45C2×#3967C2211yescharacteristic
46C2×#3967C2211yescharacteristic
47C2×#3967C2211yescharacteristic
48C2×C22⋊#168C2211yescharacteristic
49C2×C22⋊#168C2211yescharacteristic
50#65376C2218yescomplemented
51#65369C2218yescomplemented
52#65338C2218yescomplemented
53#65337C2218yescomplemented
54#65334C2218yescomplemented
55#65333C2218yescomplemented
56#65315C2218yescomplemented
57#65311C2218yescomplemented
58#65300C2218yescomplemented
59#65257C2218yescomplemented
60#65256C2218yescomplemented
61C2×#3941C2211yescharacteristic
62C2×#3941C2211yescharacteristic
63C2×#3941C2211yescharacteristic
64#65253C2218yescomplemented
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×Q8—21no—
79C22×C5×Q8C2311yescharacteristic
80C22×C5×D4D411yescharacteristic
81C23×C4×C5—21no—
82C23×C4×C5—21no—
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C22×C22⋊D5—21no—
86C22×C22⋊D5—21no—
87C23×Dic5—21no—
88C22×D20C2311yescharacteristic
89C22×C4×D5—21no—
90C5×C4⋊Q8—22no—
91C5×C4⋊Q8C2314yes—
92C5×#125—28no—
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8—22no—
95C5×C22⋊Q8—28no—
96C5×C22⋊Q8—28no—
97C5×C22⋊Q8C2314yes—
98C5×C22⋊Q8C2314yes—
99C4×C5×Q8—22no—
100C4×C5×Q8C2314yes—
101C4×C5×D4—28no—
102C4×C5×D4D414yes—
103C4×C5×D4C2314yes—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—22no—
107C2×C5×C4⋊C4—22no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4D411yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C4⋊C4C2314yes—
117C2×C5×C4⋊C4C2314yes—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4D411yescharacteristic
121C2×C5×C22⋊C4D411yescharacteristic
122C2×C42×C5—21no—
123C2×C42×C5C2311yescharacteristic
124C2×C22⋊Dic5—21no—
125C2×#688—24no—
126C2×#688C2314yes—
127#4085—28no—
128#4076—22no—
129#4076—22no—
130#4076C2314yes—
131#4076C2314yes—
132C2×#685—21no—
133C2×#685—21no—
134C2×#685—21no—
135#4072—22no—
136#4072C2314yes—
137C2×C4⋊Dic5—21no—
138C2×C4⋊Dic5—22no—
139C2×C4⋊Dic5C2311yescharacteristic
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142C2×C4⋊Dic5C2314yes—
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#4044—28no—
155#4029—28no—
156#4027—28no—
157C4×D20—22no—
158C4×D20C2314yes—
159#4016—22no—
160#4016C2314yes—
161#3967C2314yes—
162#3967C2314yes—
163#3967C2314yes—
164C22⋊#168C2314yes—
165C22⋊#168C2314yes—
166#3941C2314yes—
167#3941C2314yes—
168#3941C2314yes—
169#3940C2314yes—
170#3940C2314yes—
171#3940C2314yes—
172#3939C2314yes—
173#3939C2314yes—
174#3939C2314yes—
175#3939C2314yes—
176#3939C2314yes—
177#3939C2314yes—
178C4⋊#168C2314yes—
179#3935C2314yes—
180C2×#554D511yescharacteristic, complemented
181C2×#553—51no—
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×C5C2×D411yescharacteristic
197C24×C5C2×D411yescharacteristic
198C23×D5—21no—
199C2×C5×Q8—21no—
200C2×C5×Q8—24no—
201C2×C5×Q8—22no—
202C2×C5×Q8—22no—
203C2×C5×Q8—82no—
204C2×C5×Q8C2412yes—
205C2×C5×D4—24no—
206C2×C5×D4C2×D414yes—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—24no—
216C22×C4×C5—24no—
217C22×C4×C5—82no—
218C22×C4×C5—82no—
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D412yes—
224C22×C4×C5C2×D412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2411yescharacteristic
228C2×C22⋊D5—24no—
229C2×C22⋊D5—24no—
230C2×C22⋊D5—44no—
231C2×C22⋊D5—82no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—21no—
235C22×Dic5—24no—
236C22×Dic5—82no—
237C2×D20—22no—
238C2×D20—22no—
239C2×D20—21no—
240C2×D20C2412yes—
241C2×C4×D5—24no—
242C2×C4×D5—82no—
243C5×C4⋊C4—21no—
244C5×C4⋊C4—24no—
245C5×C4⋊C4—24no—
246C5×C4⋊C4—21no—
247C5×C4⋊C4—21no—
248C5×C4⋊C4—24no—
249C5×C4⋊C4—24no—
250C5×C4⋊C4—24no—
251C5×C4⋊C4—24no—
252C5×C4⋊C4C2×D414yes—
253C5×C4⋊C4C2412yes—
254C5×C4⋊C4C2412yes—
255C5×C4⋊C4C2412yes—
256C5×C22⋊C4—24no—
257C5×C22⋊C4—24no—
258C5×C22⋊C4C2×D414yes—
259C5×C22⋊C4C2×D414yes—
260C42×C5—24no—
261C42×C5C2×D412yes—
262C42×C5C2412yes—
263C22⋊Dic5—24no—
264#688—28no—
265#685—24no—
266#685—24no—
267#685—24no—
268C4⋊Dic5—21no—
269C4⋊Dic5—21no—
270C4⋊Dic5—21no—
271C4⋊Dic5—24no—
272C4⋊Dic5C2412yes—
273C4⋊Dic5C2412yes—
274C4⋊Dic5C2412yes—
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—24no—
292#554C2×D518yescomplemented
293#553—58no—
294#553—104no—
295C2×C4⋊Q8C2×D511yescharacteristic
296C2×#126—101no—
297C2×#125—21no—
298C2×#125—51no—
299C2×#123—101no—
300C2×C22⋊Q8—21no—
301C2×C22⋊Q8—21no—
302C2×C22⋊Q8C2×D511yescharacteristic
303C2×C22⋊Q8C2×D511yescharacteristic
304C2×#121—51no—
305C2×#121—51no—
306C2×#121—101no—
307C2×C4×Q8C2×D511yescharacteristic
308C2×C4×D4—21no—
309C2×C4×D4—51no—
310C2×C4×D4—101no—
311C2×C4×D4C2×D511yescharacteristic
312C2×#117—51no—
313C22×C4⋊C4—51no—
314C22×C4⋊C4C2×D511yescharacteristic
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#13714yes—
354C23×C5C22×D412yes—
355C23×C5C22×D412yes—
356C23×C5C22×D411yescharacteristic
357C22×D5—22no—
358C22×D5—42no—
359C22×D5—42no—
360C22×D5—42no—
361C5×Q8—22no—
362C5×Q8—22no—
363C5×Q8—42no—
364C5×Q8—84no—
365C5×D4—28no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—24no—
371C2×C4×C5—24no—
372C2×C4×C5—22no—
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—42no—
384C2×C4×C5—84no—
385C2×C4×C5—84no—
386C2×C4×C5C22×D412yes—
387C2×C4×C5C22×D412yes—
388C2×C4×C5C22×D412yes—
389C2×C4×C5C22×D412yes—
390C2×C4×C5C22×D411yescharacteristic
391C2×C4×C5C2×#4112yes—
392C2×C4×C52−1+412yes—
393C2×C4×C5C2511yescharacteristic
394C22⋊D5—48no—
395C22⋊D5—84no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5—42no—
402C2×Dic5—84no—
403D20—22no—
404D20—22no—
405D20—42no—
406C4×D5—84no—
407#168—22no—
408#168—22no—
409#168—22no—
410#168C2×#4114yes—
411C22×Q8—21no—
412C22×Q8C22×D511yescharacteristic
413C22×D4—51no—
414C22×D4—101no—
415C22×D4—101no—
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—22no—
434C4⋊Q8C22×D514yes—
435#126—108no—
436#125—28no—
437#125—54no—
438#125—102no—
439#123—108no—
440C22⋊Q8—22no—
441C22⋊Q8—22no—
442C22⋊Q8—28no—
443C22⋊Q8—28no—
444C22⋊Q8C22×D514yes—
445C22⋊Q8C22×D514yes—
446#121—54no—
447#121—54no—
448#121—108no—
449#121—102no—
450#121—102no—
451C4×Q8—22no—
452C4×Q8C22×D514yes—
453C4×D4—28no—
454C4×D4—54no—
455C4×D4—108no—
456C4×D4—102no—
457C4×D4C22⋊D514yes—
458C4×D4C22×D514yes—
459#117—54no—
460#117—102no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—51no—
470C2×C4⋊C4—51no—
471C2×C4⋊C4—54no—
472C2×C4⋊C4—51no—
473C2×C4⋊C4—101no—
474C2×C4⋊C4—102no—
475C2×C4⋊C4—101no—
476C2×C4⋊C4—101no—
477C2×C4⋊C4C22⋊D511yescharacteristic
478C2×C4⋊C4C22×D511yescharacteristic
479C2×C4⋊C4C22×D511yescharacteristic
480C2×C4⋊C4C22×D511yescharacteristic
481C2×C4⋊C4C22×D514yes—
482C2×C4⋊C4C22×D514yes—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—101no—
486C2×C22⋊C4—101no—
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#54712yes—
521C22×C5C2×#13714yes—
522C22×C5C2×#13712yes—
523C22×C5#57612yes—
524C22×C5C23×D411yescharacteristic
525C2×D5—42no—
526C2×D5—42no—
527C2×D5—42no—
528C2×D5—84no—
529C4×C5—22no—
530C4×C5—22no—
531C4×C5—22no—
532C4×C5—22no—
533C4×C5—42no—
534C4×C5—42no—
535C4×C5—42no—
536C4×C5—42no—
537C4×C5#54712yes—
538C4×C5C22×#4111yescharacteristic
539C4×C5C2×2−1+411yescharacteristic
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543C24—101no—
544C24C2×C22⋊D511yescharacteristic
545C24C2×C22⋊D511yescharacteristic
546C2×Q8—21no—
547C2×Q8—24no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—82no—
551C2×Q8C23×D512yes—
552C2×D4—24no—
553C2×D4—52no—
554C2×D4—104no—
555C2×D4—104no—
556C2×D4—102no—
557C2×D4—102no—
558C2×D4—101no—
559C2×D4—204no—
560C2×D4—402no—
561C2×D4C2×C22⋊D514yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—82no—
573C22×C4—82no—
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—24no—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—52no—
611C4⋊C4—52no—
612C4⋊C4—52no—
613C4⋊C4—101no—
614C4⋊C4—101no—
615C4⋊C4—104no—
616C4⋊C4—101no—
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—104no—
626C22⋊C4—104no—
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#334614yescomplemented
638C2×C5C2×#54711yescharacteristic
639C2×C5C22×#13711yescharacteristic
640C2×C5C2×#57611yescharacteristic
641D5—82no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—102no—
648C23—202no—
649C23—202no—
650C23—202no—
651C23#408814yes—
652C23C22×C22⋊D512yes—
653C23C22×C22⋊D512yes—
654C23C22×C22⋊D511yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—42no—
658Q8—84no—
659D4—28no—
660D4—102no—
661D4—102no—
662D4—208no—
663D4—202no—
664D4—404no—
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—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—84no—
684C2×C4—84no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
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—202no—
714C22—202no—
715C22—202no—
716C22—404no—
717C22C2×#408814yes—
718C22C2×#408812yes—
719C22#6615812yes—
720C22#6616912yes—
721C22C23×C22⋊D511yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—202no—
731C4—202no—
732C4—202no—
733C4#6615812yes—
734C4C2×D5×#4111yescharacteristic
735C4C2×#415011yescharacteristic
736C2—24no—
737C2—42no—
738C2—402no—
739C2#1061535614yesdirect product factor
740C2C22×#408811yescharacteristic
741C2C2×#6615811yescharacteristic
742C2C2×#6616911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#554C2
socleC23×C5C22×D4
prime radicalC2×#65899C2
hypercenterC2×#554D5
hypocenterC5C2×#3346
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×C5×#554C2semidirect
3. #10615356C2direct (N × H)
4. C2×#65376C2semidirect
5. C2×#65369C2semidirect
6. C2×#65338C2semidirect
7. C2×#65337C2semidirect
8. C2×#65333C2semidirect
9. C2×#65334C2semidirect
10. C2×#65315C2semidirect
11. C2×#65311C2semidirect
12. C2×#65300C2semidirect
13. C2×#65257C2semidirect
14. C2×#65256C2semidirect
15. C2×#65253C2semidirect
16. C22×#3939C2semidirect
18. C5×#554C22semidirect
50. #65376C22semidirect
51. #65369C22semidirect
52. #65338C22semidirect
53. #65337C22semidirect
54. #65334C22semidirect
55. #65333C22semidirect
56. #65315C22semidirect
57. #65311C22semidirect
58. #65300C22semidirect
59. #65257C22semidirect
60. #65256C22semidirect
64. #65253C22semidirect
74. C2×#3939C22semidirect
180. C2×#554D5semidirect
292. #554C2×D5semidirect
637. C2×C5#3346semidirect
705. C5C2×#3346semidirect
739. C2#10615356direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5542
C2×#658992
#106153562
C2×#653762
C2×#653692
C2×#653382
C2×#653372
C2×#653332
C2×#653342
C2×#653152
C2×#653112
C2×#653002
C2×#652572
C2×#652562
C2×#652532
C22×#39392
C2×#33465