Finite Group Databasebeta

← C2×#10610816 #12964411

Subgroups — C2×#10610816 #12964411

Order 1280.

1882 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65862C211yesmaximal, characteristic
2C2×C5×#424C211yesmaximal, characteristic, complemented
3C2×#65416C211yesmaximal, characteristic, complemented
4C2×#65417C211yesmaximal, characteristic, complemented
5C2×#65400C211yesmaximal, characteristic, complemented
6C2×#65400C211yesmaximal, characteristic, complemented
7C2×#65289C211yesmaximal, characteristic, complemented
8#10610816C2116yesmaximal, direct product factor
9C2×#65128C211yesmaximal, characteristic, complemented
10C2×#65126C211yesmaximal, characteristic, complemented
11C2×#65117C211yesmaximal, characteristic, complemented
12C2×#65120C211yesmaximal, characteristic, complemented
13C2×#65127C211yesmaximal, characteristic, complemented
14C2×#65125C211yesmaximal, characteristic, complemented
15C2×#65129C211yesmaximal, characteristic, complemented
16C2×#65124C211yesmaximal, characteristic, complemented
17C22×C5×M16C2211yescharacteristic
18C23×C5×C8C2211yescharacteristic
19C2×C5×#117C2211yescharacteristic
20C2×C4×C22⋊D5C2211yescharacteristic
21C2×C4×C22⋊D5C2211yescharacteristic
22C22×#676C2211yescharacteristic
23C22×#676C2211yescharacteristic
24C22×#676C2211yescharacteristic
25C22×C8×D5C2211yescharacteristic
26#65862C418yes—
27#65862C2218yes—
28C2×#4044C411yescharacteristic
29C2×#4042C411yescharacteristic
30C2×#4040C411yescharacteristic
31C2×#4035C411yescharacteristic
32C2×#4031C411yescharacteristic
33C2×#4030C411yescharacteristic
34C2×#4029C411yescharacteristic
35C2×#4025C411yescharacteristic
36C2×C4×D20C2211yescharacteristic
37C2×#4018C2211yescharacteristic
38C2×C42×D5C2211yescharacteristic
39C2×C4×Dic10C2211yescharacteristic
40C5×#424C2218yescomplemented
41C2×C5×C4⋊C8C2211yescharacteristic
42C2×C5×C4⋊C8C2211yescharacteristic
43C2×C5×C4⋊C8C2211yescharacteristic
44C2×C5×C4⋊C8C2211yescharacteristic
45C2×C22⋊#168C2211yescharacteristic
46C2×C22⋊#168C2211yescharacteristic
47#65417C2218yescomplemented
48#65416C2218yescomplemented
49#65400C2218yescomplemented
50#65400C2218yescomplemented
51C2×#3952C2211yescharacteristic
52C2×#3952C2211yescharacteristic
53C2×#3952C2211yescharacteristic
54C2×#3952C2211yescharacteristic
55C2×#3947C2211yescharacteristic
56C2×#3947C2211yescharacteristic
57C2×#3947C2211yescharacteristic
58C2×#3946C2211yescharacteristic
59C2×#3946C2211yescharacteristic
60C2×#3946C2211yescharacteristic
61C2×#3946C2211yescharacteristic
62C2×C8×Dic5C2211yescharacteristic
63#65289C2218yescomplemented
64C2×C4⋊#168C2211yescharacteristic
65C2×C4⋊#168C2211yescharacteristic
66C2×#3935C2211yescharacteristic
67C2×C4×#168C2211yescharacteristic
68#65129C2218yescomplemented
69#65128C2218yescomplemented
70#65127C2218yescomplemented
71#65126C2218yescomplemented
72#65125C2218yescomplemented
73#65124C2218yescomplemented
74#65120C2218yescomplemented
75#65117C2218yescomplemented
76C2×#2995—51nomaximal, Sylow
77C23×C4×C5C2311yescharacteristic
78C22×C22⋊D5C2×C411yescharacteristic
79C22×C22⋊D5C2×C411yescharacteristic
80C22×D20C2×C411yescharacteristic
81C22×C4×D5C2×C411yescharacteristic
82C22×C4×D5C2×C411yescharacteristic
83C22×C4×D5C2311yescharacteristic
84C22×C4×D5C2311yescharacteristic
85C22×Dic10C2×C411yescharacteristic
86C2×C5×M16—42no—
87C2×C5×M16C2314yes—
88C22×C5×C8—42no—
89C22×C5×C8C2311yescharacteristic
90C22×C5×C8C2311yescharacteristic
91C22×C5×C8C2311yescharacteristic
92C22×C5×C8C2311yescharacteristic
93C22×C5×C8C2314yes—
94C5×#117C2×C414yes—
95C5×#117C2314yes—
96C2×C5×C4⋊C4C2×C411yescharacteristic
97C2×C5×C4⋊C4C2×C411yescharacteristic
98C2×C5×C22⋊C4C2×C411yescharacteristic
99C2×C5×C22⋊C4C2×C411yescharacteristic
100C2×C42×C5C2311yescharacteristic
101C2×C42×C5C2311yescharacteristic
102C2×C22⋊Dic5C2×C411yescharacteristic
103C2×C22⋊Dic5C2×C411yescharacteristic
104C4×C22⋊D5C2×C414yes—
105C4×C22⋊D5C2×C414yes—
106C4×C22⋊D5C2314yes—
107C4×C22⋊D5C2314yes—
108C2×#685C2×C411yescharacteristic
109C2×#685C2×C411yescharacteristic
110C2×#685C2×C411yescharacteristic
111C2×#685C2×C411yescharacteristic
112C2×#685C2×C411yescharacteristic
113C2×#685C2×C411yescharacteristic
114C2×C4⋊Dic5C2×C411yescharacteristic
115C2×C4⋊Dic5C2×C411yescharacteristic
116C2×#683C2×C411yescharacteristic
117C2×#683C2×C411yescharacteristic
118C2×#683C2×C411yescharacteristic
119C2×#683C2×C411yescharacteristic
120C2×#683C2×C411yescharacteristic
121C2×#683C2×C411yescharacteristic
122C2×C4×Dic5C2×C411yescharacteristic
123C2×C4×Dic5C2×C411yescharacteristic
124C2×C4×Dic5C2311yescharacteristic
125C2×C4×Dic5C2311yescharacteristic
126C22×#168C2311yescharacteristic
127C22×#168C2311yescharacteristic
128C22×#168C2311yescharacteristic
129C22×#168C2311yescharacteristic
130C2×#676—42no—
131C2×#676—42no—
132C2×#676—42no—
133C2×#676C2314yes—
134C2×#676C2314yes—
135C2×#676C2314yes—
136C2×C8×D5—42no—
137C2×C8×D5C2314yes—
138#4044C2×C418yes—
139#4042C2×C418yes—
140#4040C2×C418yes—
141#4035C2×C418yes—
142#4031C2×C418yes—
143#4030C2×C418yes—
144#4029C2×C418yes—
145#4025C2×C418yes—
146C4×D20C2×C414yes—
147C4×D20C2314yes—
148#4018C2×C414yes—
149#4018C2314yes—
150C42×D5C2×C414yes—
151C42×D5C2314yes—
152C4×Dic10C2×C414yes—
153C4×Dic10C2314yes—
154C5×C4⋊C8C2314yes—
155C5×C4⋊C8C2314yes—
156C5×C4⋊C8C2314yes—
157C5×C4⋊C8C2314yes—
158C22⋊#168C2314yes—
159C22⋊#168C2314yes—
160#3952C2314yes—
161#3952C2314yes—
162#3952C2314yes—
163#3952C2314yes—
164#3947C2314yes—
165#3947C2314yes—
166#3947C2314yes—
167#3946C2314yes—
168#3946C2314yes—
169#3946C2314yes—
170#3946C2314yes—
171C8×Dic5C2314yes—
172C4⋊#168C2314yes—
173C4⋊#168C2314yes—
174#3935C2314yes—
175C4×#168C2314yes—
176C2×#529—51no—
177#2995—516no—
178C2×#446—51no—
179C2×#446—51no—
180C2×#436—51no—
181C2×#436—51no—
182C2×#435—51no—
183C2×#435—51no—
184C2×#435—51no—
185C2×#435—51no—
186C2×#433—51no—
187C2×#433—51no—
188C2×#432—51no—
189C2×#424—51no—
190C2×#424D511yescharacteristic, complemented
191C2×#423—51no—
192C24×C5C22×C411yescharacteristic
193C23×D5C22×C411yescharacteristic
194C23×D5C22×C411yescharacteristic
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5C22×C411yescharacteristic
198C22×C4×C5C22×C411yescharacteristic
199C22×C4×C5C22×C411yescharacteristic
200C22×C4×C5C22×C411yescharacteristic
201C22×C4×C5C22×C411yescharacteristic
202C22×C4×C5C22×C412yes—
203C22×C4×C5C2412yes—
204C22×C4×C5C2411yescharacteristic
205C2×C22⋊D5—42no—
206C2×C22⋊D5—42no—
207C2×C22⋊D5C22×C414yes—
208C2×C22⋊D5C22×C414yes—
209C22×Dic5C22×C411yescharacteristic
210C22×Dic5C22×C411yescharacteristic
211C22×Dic5C22×C411yescharacteristic
212C22×Dic5C22×C411yescharacteristic
213C22×Dic5C22×C411yescharacteristic
214C22×Dic5C22×C411yescharacteristic
215C2×D20—42no—
216C2×D20C22×C414yes—
217C2×C4×D5—22no—
218C2×C4×D5—22no—
219C2×C4×D5—22no—
220C2×C4×D5—22no—
221C2×C4×D5—42no—
222C2×C4×D5—42no—
223C2×C4×D5C22×C412yes—
224C2×C4×D5C22×C412yes—
225C2×C4×D5C22×C414yes—
226C2×C4×D5C22×C414yes—
227C2×C4×D5C2412yes—
228C2×C4×D5C2412yes—
229C2×Dic10—42no—
230C2×Dic10C22×C414yes—
231C5×M16—44no—
232C2×C5×C8—22no—
233C2×C5×C8—22no—
234C2×C5×C8—22no—
235C2×C5×C8—22no—
236C2×C5×C8—44no—
237C2×C5×C8C2412yes—
238C2×C5×C8C2412yes—
239C2×C5×C8C2412yes—
240C2×C5×C8C2412yes—
241C5×C4⋊C4C22×C414yes—
242C5×C4⋊C4C22×C414yes—
243C5×C22⋊C4C22×C414yes—
244C5×C22⋊C4C22×C414yes—
245C42×C5C22×C412yes—
246C42×C5C22×C412yes—
247C42×C5C2412yes—
248C42×C5C2412yes—
249C22⋊Dic5C22×C414yes—
250C22⋊Dic5C22×C414yes—
251#685C22×C414yes—
252#685C22×C414yes—
253#685C22×C414yes—
254#685C22×C414yes—
255#685C22×C414yes—
256#685C22×C414yes—
257C4⋊Dic5C22×C414yes—
258C4⋊Dic5C22×C414yes—
259#683C22×C414yes—
260#683C22×C414yes—
261#683C22×C414yes—
262#683C22×C414yes—
263#683C22×C414yes—
264#683C22×C414yes—
265C4×Dic5C22×C412yes—
266C4×Dic5C22×C412yes—
267C4×Dic5C22×C414yes—
268C4×Dic5C22×C414yes—
269C4×Dic5C2412yes—
270C4×Dic5C2412yes—
271C2×#168—22no—
272C2×#168—22no—
273C2×#168—22no—
274C2×#168—22no—
275C2×#168C2412yes—
276C2×#168C2412yes—
277C2×#168C2412yes—
278C2×#168C2412yes—
279#676—44no—
280#676—44no—
281#676—44no—
282C8×D5—44no—
283C22×M16—51no—
284C22×M16—51no—
285C22×M16—51no—
286C22×M16C2×D511yescharacteristic
287C23×C8—51no—
288C23×C8C2×D511yescharacteristic
289#529—58no—
290#529—58no—
291C2×#126—51no—
292C2×#126—51no—
293C2×#125—51no—
294C2×#124—51no—
295C2×#123—51no—
296C2×#123—51no—
297C2×C22⋊Q8—51no—
298C2×#121—51no—
299C2×C4×Q8—51no—
300C2×C4×D4—51no—
301C2×C4×D4—51no—
302C2×C4×D4—51no—
303C2×#117—51no—
304C2×#117C2×D511yescharacteristic
305C22×C42—51no—
306#446—58no—
307#446—58no—
308#436—58no—
309#436—58no—
310#435—58no—
311#435—58no—
312#435—58no—
313#435—58no—
314#433—58no—
315#433—58no—
316#432—58no—
317#424—58no—
318#424C2×D518yescomplemented
319#423—58no—
320C2×C4⋊C8—51no—
321C2×C4⋊C8—51no—
322C2×C4⋊C8—51no—
323C2×C4⋊C8—51no—
324C2×C4⋊C8—51no—
325C2×C4⋊C8—51no—
326C2×C4⋊C8C2×D511yescharacteristic
327C2×C4⋊C8C2×D511yescharacteristic
328C2×C4⋊C8C2×D511yescharacteristic
329C2×C4⋊C8C2×D511yescharacteristic
330C2×C22⋊C8—51no—
331C2×C22⋊C8—51no—
332C2×C22⋊C8—51no—
333C2×C22⋊C8—51no—
334C2×C22⋊C8—51no—
335C2×C22⋊C8—51no—
336C2×#97—51no—
337C2×#97—51no—
338C2×#97—51no—
339C2×#97—51no—
340C2×C4×C8—51no—
341C2×C4×C8—51no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5C23×C412yes—
346C23×C5C23×C411yescharacteristic
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5C23×C412yes—
354C22×D5C23×C412yes—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—24no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5C23×C412yes—
364C2×C4×C5C23×C412yes—
365C2×C4×C5C23×C412yes—
366C2×C4×C5C23×C412yes—
367C2×C4×C5C23×C412yes—
368C2×C4×C5C23×C411yescharacteristic
369C2×C4×C5H(5,𝔽2)12yes—
370C2×C4×C52−1+412yes—
371C2×C4×C5C2511yescharacteristic
372C22⋊D5—44no—
373C22⋊D5—44no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5C23×C412yes—
381C2×Dic5C23×C412yes—
382C2×Dic5C23×C412yes—
383C2×Dic5C23×C412yes—
384C2×Dic5C23×C412yes—
385C2×Dic5C23×C412yes—
386D20—44no—
387C4×D5—24no—
388C4×D5—24no—
389C4×D5—22no—
390C4×D5—22no—
391C4×D5—22no—
392C4×D5—22no—
393C4×D5—44no—
394C4×D5—44no—
395Dic10—44no—
396C5×C8—22no—
397C5×C8—22no—
398C5×C8—22no—
399C5×C8—22no—
400#168—22no—
401#168—22no—
402#168—22no—
403#168—22no—
404C22×Q8—51no—
405C22×D4—51no—
406C22×D4—51no—
407C22×D4—51no—
408C23×C4—51no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4C22×D511yescharacteristic
413C2×M16—42no—
414C2×M16—54no—
415C2×M16—54no—
416C2×M16—54no—
417C2×M16—202no—
418C2×M16—202no—
419C2×M16—202no—
420C2×M16C22×D514yes—
421C22×C8—42no—
422C22×C8—51no—
423C22×C8—51no—
424C22×C8—51no—
425C22×C8—51no—
426C22×C8—54no—
427C22×C8—202no—
428C22×C8C22×D511yescharacteristic
429C22×C8C22×D511yescharacteristic
430C22×C8C22×D511yescharacteristic
431C22×C8C22×D511yescharacteristic
432C22×C8C22×D514yes—
433#126—58no—
434#126—58no—
435#125—58no—
436#124—58no—
437#123—58no—
438#123—58no—
439C22⋊Q8—58no—
440#121—58no—
441C4×Q8—54no—
442C4×Q8—54no—
443C4×D4—54no—
444C4×D4—54no—
445C4×D4—54no—
446C4×D4—54no—
447C4×D4—54no—
448C4×D4—54no—
449#117—54no—
450#117—54no—
451#117C4×D514yes—
452#117C22×D514yes—
453C2×C4⋊C4—51no—
454C2×C4⋊C4—51no—
455C2×C4⋊C4—51no—
456C2×C4⋊C4—51no—
457C2×C4⋊C4—51no—
458C2×C4⋊C4—51no—
459C2×C4⋊C4—51no—
460C2×C4⋊C4—51no—
461C2×C4⋊C4C4×D511yescharacteristic
462C2×C4⋊C4C4×D511yescharacteristic
463C2×C22⋊C4—51no—
464C2×C22⋊C4—51no—
465C2×C22⋊C4—51no—
466C2×C22⋊C4—51no—
467C2×C22⋊C4—51no—
468C2×C22⋊C4—51no—
469C2×C22⋊C4—51no—
470C2×C22⋊C4—51no—
471C2×C22⋊C4C4×D511yescharacteristic
472C2×C22⋊C4C4×D511yescharacteristic
473C2×C42—51no—
474C2×C42—51no—
475C2×C42—51no—
476C2×C42—51no—
477C2×C42—54no—
478C2×C42—54no—
479C2×C42C22×D511yescharacteristic
480C2×C42C22×D511yescharacteristic
481C4⋊C8—54no—
482C4⋊C8—54no—
483C4⋊C8—54no—
484C4⋊C8—54no—
485C4⋊C8—54no—
486C4⋊C8—54no—
487C4⋊C8C22×D514yes—
488C4⋊C8C22×D514yes—
489C4⋊C8C22×D514yes—
490C4⋊C8C22×D514yes—
491C22⋊C8—54no—
492C22⋊C8—54no—
493C22⋊C8—54no—
494C22⋊C8—54no—
495C22⋊C8—54no—
496C22⋊C8—54no—
497#97—54no—
498#97—54no—
499#97—54no—
500#97—54no—
501C4×C8—54no—
502C4×C8—54no—
503C22×C5—22no—
504C22×C5—22no—
505C22×C5—22no—
506C22×C5—44no—
507C22×C5#52012yes—
508C22×C5#56812yes—
509C22×C5#56812yes—
510C22×C5C24×C411yescharacteristic
511C2×D5—22no—
512C2×D5—22no—
513C2×D5—22no—
514C2×D5—22no—
515C2×D5—22no—
516C2×D5—22no—
517C2×D5—44no—
518C2×D5—44no—
519C4×C5—22no—
520C4×C5—22no—
521C4×C5—22no—
522C4×C5—22no—
523C4×C5—22no—
524C4×C5#52012yes—
525C4×C5C2×H(5,𝔽2)11yescharacteristic
526C4×C5C2×2−1+411yescharacteristic
527Dic5—22no—
528Dic5—22no—
529Dic5—22no—
530Dic5—22no—
531Dic5—22no—
532Dic5—22no—
533C24—51no—
534C24—51no—
535C24C2×C4×D511yescharacteristic
536C2×Q8—54no—
537C2×Q8—202no—
538C2×D4—54no—
539C2×D4—54no—
540C2×D4—54no—
541C2×D4—202no—
542C2×D4—202no—
543C2×D4—202no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—51no—
547C22×C4—51no—
548C22×C4—51no—
549C22×C4—51no—
550C22×C4—51no—
551C22×C4—51no—
552C22×C4—52no—
553C22×C4—52no—
554C22×C4—52no—
555C22×C4—52no—
556C22×C4—54no—
557C22×C4—54no—
558C22×C4—102no—
559C22×C4—102no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—202no—
563C22×C4—202no—
564C22×C4C2×C4×D511yescharacteristic
565C22×C4C2×C4×D511yescharacteristic
566C22×C4C2×C4×D511yescharacteristic
567C22×C4C2×C4×D511yescharacteristic
568C22×C4C2×C4×D511yescharacteristic
569C22×C4C2×C4×D512yes—
570C22×C4C23×D512yes—
571C22×C4C23×D511yescharacteristic
572M16—44no—
573M16—204no—
574M16—204no—
575M16—204no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—44no—
581C2×C8—52no—
582C2×C8—52no—
583C2×C8—52no—
584C2×C8—52no—
585C2×C8—102no—
586C2×C8—102no—
587C2×C8—102no—
588C2×C8—102no—
589C2×C8—204no—
590C2×C8C23×D512yes—
591C2×C8C23×D512yes—
592C2×C8C23×D512yes—
593C2×C8C23×D512yes—
594C4⋊C4—54no—
595C4⋊C4—54no—
596C4⋊C4—54no—
597C4⋊C4—54no—
598C4⋊C4—54no—
599C4⋊C4—54no—
600C4⋊C4—54no—
601C4⋊C4—54no—
602C4⋊C4C2×C4×D514yes—
603C4⋊C4C2×C4×D514yes—
604C22⋊C4—54no—
605C22⋊C4—54no—
606C22⋊C4—54no—
607C22⋊C4—54no—
608C22⋊C4—54no—
609C22⋊C4—54no—
610C22⋊C4—54no—
611C22⋊C4—54no—
612C22⋊C4C2×C4×D514yes—
613C22⋊C4C2×C4×D514yes—
614C42—52no—
615C42—54no—
616C42—54no—
617C42—52no—
618C42—52no—
619C42—52no—
620C42C2×C4×D512yes—
621C42C2×C4×D512yes—
622C42C23×D512yes—
623C42C23×D512yes—
624C2×C5—42no—
625C2×C5#299514yescomplemented
626C2×C5C2×#52011yescharacteristic
627C2×C5C2×#56811yescharacteristic
628C2×C5C2×#56811yescharacteristic
629D5—42no—
630D5—42no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—52no—
635C23—52no—
636C23—102no—
637C23—102no—
638C23—102no—
639C23—102no—
640C23—102no—
641C23—102no—
642C23C22×C4×D512yes—
643C23C22×C4×D511yescharacteristic
644Q8—204no—
645D4—204no—
646D4—204no—
647D4—204no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—52no—
657C2×C4—52no—
658C2×C4—52no—
659C2×C4—52no—
660C2×C4—52no—
661C2×C4—52no—
662C2×C4—102no—
663C2×C4—102no—
664C2×C4—102no—
665C2×C4—102no—
666C2×C4—102no—
667C2×C4—102no—
668C2×C4—104no—
669C2×C4—104no—
670C2×C4—102no—
671C2×C4—102no—
672C2×C4—102no—
673C2×C4—102no—
674C2×C4—204no—
675C2×C4—204no—
676C2×C4C22×C4×D512yes—
677C2×C4C22×C4×D512yes—
678C2×C4C22×C4×D512yes—
679C2×C4C22×C4×D512yes—
680C2×C4C22×C4×D512yes—
681C2×C4C22×C4×D511yescharacteristic
682C2×C4#414412yes—
683C2×C4#414712yes—
684C2×C4C24×D511yescharacteristic
685C8—22no—
686C8—22no—
687C8—22no—
688C8—22no—
689C8—102no—
690C8—102no—
691C8—102no—
692C8—102no—
693C5C2×#299511yescharacteristic, complemented, Sylow
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—102no—
699C22—102no—
700C22—102no—
701C22—102no—
702C22—102no—
703C22—102no—
704C22—204no—
705C22—204no—
706C22#6583812yes—
707C22#6608412yes—
708C22#6608412yes—
709C22C23×C4×D511yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—102no—
716C4—102no—
717C4—102no—
718C4—102no—
719C4—102no—
720C4—102no—
721C4#6583812yes—
722C4C2×#414411yescharacteristic
723C4C2×#414711yescharacteristic
724C2—42no—
725C2—202no—
726C2—202no—
727C2#1061081614yesdirect product factor
728C2C2×#6583811yescharacteristic
729C2C2×#6608411yescharacteristic
730C2C2×#6608411yescharacteristic
subgroupG/H
centerC22×C4C23×D5
commutatorC22×C5C24×C4
FrattiniC2×C4C24×D5
FittingC2×C5×#424C2
socleC23×C5C23×C4
prime radicalC2×#4030C4
cosocleC2×C4×C5C25
hypercenterC2×#424D5
hypocenterC5C2×#2995
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. C2×C5×#424C2semidirect
3. C2×#65416C2semidirect
4. C2×#65417C2semidirect
5. C2×#65400C2semidirect
6. C2×#65400C2semidirect
7. C2×#65289C2semidirect
8. #10610816C2direct (N × H)
9. C2×#65128C2semidirect
10. C2×#65126C2semidirect
11. C2×#65117C2semidirect
12. C2×#65120C2semidirect
13. C2×#65127C2semidirect
14. C2×#65125C2semidirect
15. C2×#65129C2semidirect
16. C2×#65124C2semidirect
40. C5×#424C22semidirect
47. #65417C22semidirect
48. #65416C22semidirect
49. #65400C22semidirect
50. #65400C22semidirect
63. #65289C22semidirect
68. #65129C22semidirect
69. #65128C22semidirect
70. #65127C22semidirect
71. #65126C22semidirect
72. #65125C22semidirect
73. #65124C22semidirect
74. #65120C22semidirect
75. #65117C22semidirect
190. C2×#424D5semidirect
318. #424C2×D5semidirect
625. C2×C5#2995semidirect
693. C5C2×#2995semidirect
727. C2#10610816direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658622
C2×C5×#4242
C2×#654162
C2×#654172
C2×#654002
C2×#652892
#106108162
C2×#651282
C2×#651262
C2×#651172
C2×#651202
C2×#651272
C2×#651252
C2×#651292
C2×#651242
C2×#29955