Finite Group Databasebeta

← C2×#10618509 #13007616

Subgroups — C2×#10618509 #13007616

Order 1280.

12982 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4144C212yesmaximal, complemented
2C2×C5×D42C211yesmaximal, characteristic, complemented
3C2×D4×C22⋊D5C212yesmaximal, complemented
4C2×D4×C22⋊D5C212yesmaximal, complemented
5C22×#4086C212yesmaximal, complemented
6#10618509C2132yesmaximal, direct product factor
7C2×D5×#127C211yesmaximal, characteristic, complemented
8C2×#66052C211yesmaximal, characteristic, complemented
9C2×#65943C212yesmaximal, complemented
10C2×#65941C212yesmaximal, complemented
11C2×#65933C212yesmaximal, complemented
12C2×#65930C212yesmaximal, complemented
13C2×#65924C214yesmaximal, complemented
14C2×#65926C214yesmaximal, complemented
15C2×D4×D20C211yesmaximal, characteristic, complemented
16C2×#65882C211yesmaximal, characteristic, complemented
17C2×#65887C211yesmaximal, characteristic, complemented
18C2×C4×#711C211yesmaximal, characteristic, complemented
19C23×C5×D4C2212yescomplemented
20C23×C5×D4C2212yescomplemented
21C23×C22⋊D5C2214yescomplemented
22C23×C22⋊D5C2214yescomplemented
23C23×C22⋊D5C2214yescomplemented
24C2×#4144—232no—
25C2×#4144C22132yescomplemented
26C22×#711C2211yescharacteristic
27C22×#711C2214yescomplemented
28C22×#711C2212yescomplemented
29C22×D4×D5C2212yescomplemented
30C22×D4×D5C2214yescomplemented
31C22×D4×D5C2212yescomplemented
32C22×D4×D5C2212yescomplemented
33C22×D4×D5C2212yescomplemented
34C22×#709C2212yescomplemented
35C22×#709C2212yescomplemented
36C23×D20C2212yescomplemented
37C5×D42C22116yescomplemented
38C2×C5×#127C2211yescharacteristic, complemented
39C2×C5×#121C2212yescomplemented
40C2×C5×#121C2212yescomplemented
41C2×C5×#120C2214yescomplemented
42C2×C4×C5×D4C2211yescharacteristic, complemented
43C2×C4×C5×D4C2211yescharacteristic, complemented
44C2×#4099C2214yescomplemented
45C2×#4086C2212yescomplemented
46C2×#4086C2212yescomplemented
47C2×#4086C2211yescharacteristic, complemented
48C2×#4086C2212yescomplemented
49C2×#4086C2214yescomplemented
50C2×#4086C2214yescomplemented
51C2×#4086C2212yescomplemented
52C2×#4086C2212yescomplemented
53C2×#4086C22132yescomplemented
54C2×#4085C2214yescomplemented
55C2×#4085C2214yescomplemented
56C2×#4085C2214yescomplemented
57D4×C22⋊D5C22132yescomplemented
58D4×C22⋊D5C22132yescomplemented
59C2×#4084C2211yescharacteristic, complemented
60C2×#4084C2212yescomplemented
61C2×#4083C2214yescomplemented
62C2×#4083C2214yescomplemented
63C2×D4×Dic5C2211yescharacteristic, complemented
64C2×D4×Dic5C2212yescomplemented
65C2×#4076C2212yescomplemented
66C2×#4076C2212yescomplemented
67C2×C4×C22⋊D5C2212yescomplemented
68C2×C4×C22⋊D5C2212yescomplemented
69C22×C4×Dic5C2212yescomplemented
70#66052C22116yescomplemented
71D5×#127C22116yescomplemented
72#65943C22132yescomplemented
73#65941C22132yescomplemented
74#65933C22132yescomplemented
75#65930C22132yescomplemented
76#65926C22164yescomplemented
77#65924C22164yescomplemented
78#65887C22116yescomplemented
79D4×D20C22116yescomplemented
80#65882C22116yescomplemented
81C4×#711C22116yescomplemented
82C2×#4041C2211yescharacteristic, complemented
83C2×#4041C2212yescomplemented
84C2×#4039C2212yescomplemented
85C2×#4038C2211yescharacteristic, complemented
86C2×#4034C2211yescharacteristic, complemented
87C2×#4033C2211yescharacteristic, complemented
88C2×#4031C2212yescomplemented
89C2×#4031C2214yescomplemented
90C2×#4030C2214yescomplemented
91C2×#4030C2212yescomplemented
92C2×#4030C2214yescomplemented
93C2×#4028C2214yescomplemented
94C2×#4028C2214yescomplemented
95C2×#4027C2212yescomplemented
96C2×#4027C2214yescomplemented
97C2×#4023C2212yescomplemented
98C2×#4020C2211yescharacteristic, complemented
99C2×C4×D20C2211yescharacteristic, complemented
100C2×C42×D5C2211yescharacteristic, complemented
101C2×C4×Dic10C2211yescharacteristic, complemented
102C2×#3498—51nomaximal, Sylow
103C25×C5C2314yes—
104C24×D5C2314yes—
105C24×D5C2314yes—
106C22×C5×D4—216no—
107C22×C5×D4—48no—
108C22×C5×D4C2312yes—
109C22×C5×D4C2314yes—
110C22×C5×D4C2311yescharacteristic
111C22×C5×D4C2312yes—
112C22×C5×D4C2314yes—
113C22×C5×D4C2312yes—
114C22×C5×D4C2311yescharacteristic
115C22×C5×D4C23116yescomplemented
116C22×C5×D4C23116yescomplemented
117C23×C4×C5C2312yes—
118C23×C4×C5C2312yes—
119C22×C22⋊D5—232no—
120C22×C22⋊D5—232no—
121C22×C22⋊D5—416no—
122C22×C22⋊D5C2314yes—
123C22×C22⋊D5C2314yes—
124C22×C22⋊D5C2312yes—
125C22×C22⋊D5C2312yes—
126C22×C22⋊D5C2314yes—
127C22×C22⋊D5C2314yes—
128C22×C22⋊D5C2312yes—
129C22×C22⋊D5C2314yes—
130C22×C22⋊D5C2314yes—
131C22×C22⋊D5C2314yes—
132C22×C22⋊D5C2314yes—
133C22×C22⋊D5C2312yes—
134C22×C22⋊D5C23132yescomplemented
135C22×C22⋊D5C23132yescomplemented
136C22×C22⋊D5C23132yescomplemented
137C23×Dic5C2312yes—
138C23×Dic5C2314yes—
139C23×Dic5C2312yes—
140#4144—2256no—
141C2×#711—232no—
142C2×#711—216no—
143C2×#711D4116yescomplemented
144C2×#711C2318yes—
145C2×#711C23116yescomplemented
146C2×#711C23132yescomplemented
147C2×D4×D5—216no—
148C2×D4×D5—232no—
149C2×D4×D5—216no—
150C2×D4×D5—48no—
151C2×D4×D5—48no—
152C2×D4×D5C23116yescomplemented
153C2×D4×D5C23116yescomplemented
154C2×D4×D5C23132yescomplemented
155C2×D4×D5C23116yescomplemented
156C2×D4×D5C23116yescomplemented
157C2×#709—216no—
158C2×#709—216no—
159C2×#709C23116yescomplemented
160C2×#709C23116yescomplemented
161C22×D20—48no—
162C22×D20C2311yescharacteristic
163C22×D20C2312yes—
164C22×D20C2312yes—
165C22×D20C2312yes—
166C22×D20C2312yes—
167C22×D20C2314yes—
168C22×D20C23116yescomplemented
169C22×C4×D5C2311yescharacteristic
170C22×C4×D5C2311yescharacteristic
171C22×C4×D5C2312yes—
172C22×C4×D5C2314yes—
173C22×C4×D5C2311yescharacteristic
174C22×Dic10C2312yes—
175C22×Dic10C2311yescharacteristic
176C5×#127C2318yescomplemented
177C5×#121C23116yescomplemented
178C5×#121C23116yescomplemented
179C5×#120C23132yescomplemented
180C4×C5×D4C2318yescomplemented
181C4×C5×D4C2318yescomplemented
182C2×C5×C4⋊C4C2311yescharacteristic
183C2×C5×C4⋊C4C2311yescharacteristic
184C2×C5×C22⋊C4C2312yes—
185C2×C5×C22⋊C4C2314yes—
186C2×C5×C22⋊C4C2312yes—
187C2×C42×C5C2311yescharacteristic
188#4099C23132yescomplemented
189C2×C22⋊Dic5C2312yes—
190C2×C22⋊Dic5C2312yes—
191C2×C22⋊Dic5C2314yes—
192#4086C23116yescomplemented
193#4086C23116yescomplemented
194#4086C23116yescomplemented
195#4086C23116yescomplemented
196#4086C23116yescomplemented
197#4086C2318yescomplemented
198#4086C23132yescomplemented
199#4086C23132yescomplemented
200#4085C23132yescomplemented
201#4085C23132yescomplemented
202#4085C23132yescomplemented
203#4084C23116yescomplemented
204#4084C2318yescomplemented
205#4083C23132yescomplemented
206#4083C23132yescomplemented
207D4×Dic5C23116yescomplemented
208D4×Dic5C2318yescomplemented
209#4076C23116yescomplemented
210#4076C23116yescomplemented
211C4×C22⋊D5C23116yescomplemented
212C4×C22⋊D5C23116yescomplemented
213C2×#685C2312yes—
214C2×#685C2312yes—
215C2×#685C2314yes—
216C2×#685C2314yes—
217C2×#685C2312yes—
218C2×C4⋊Dic5C2311yescharacteristic
219C2×C4⋊Dic5C2311yescharacteristic
220C2×#683C2312yes—
221C2×#683C2312yes—
222C2×#683C2312yes—
223C2×C4×Dic5C2312yes—
224C2×C4×Dic5C2311yescharacteristic
225C2×C4×Dic5C2311yescharacteristic
226C2×C4×Dic5C2311yescharacteristic
227C2×C4×Dic5C2312yes—
228C2×C4×Dic5C2312yes—
229C2×C4×Dic5C23116yescomplemented
230#4041C2318yescomplemented
231#4041C23116yescomplemented
232#4039C23116yescomplemented
233#4038C2318yescomplemented
234#4034C2318yescomplemented
235#4033C2318yescomplemented
236#4031C23116yescomplemented
237#4031C23132yescomplemented
238#4030C23116yescomplemented
239#4030C23132yescomplemented
240#4030C23132yescomplemented
241#4028C23132yescomplemented
242#4028C23132yescomplemented
243#4027C23116yescomplemented
244#4027C23132yescomplemented
245#4023C23116yescomplemented
246#4020C2318yescomplemented
247C4×D20C2318yescomplemented
248C42×D5C2318yescomplemented
249C4×Dic10C2318yescomplemented
250C22×H(5,𝔽2)—52no—
251#3498—532no—
252C2×#550—51no—
253C2×#550—52no—
254C2×#550—51no—
255C2×D42—52no—
256C2×D42—52no—
257C2×D42—52no—
258C2×D42—54no—
259C2×D42—51no—
260C2×D42D511yescharacteristic, complemented
261C2×#535—52no—
262C2×#535—54no—
263C2×#532—52no—
264C2×#532—51no—
265C22×#127—52no—
266C22×#127—51no—
267C2×C4×#41—51no—
268C24×C5—216no—
269C24×C5—48no—
270C24×C5—48no—
271C24×C5C2414yes—
272C24×C5C2412yes—
273C24×C5C2412yes—
274C24×C5C24116yes—
275C23×D5—216no—
276C23×D5—216no—
277C23×D5—48no—
278C23×D5—48no—
279C23×D5—48no—
280C23×D5—48no—
281C23×D5C2412yes—
282C23×D5C2414yes—
283C23×D5C2411yescharacteristic
284C23×D5C24116yes—
285C23×D5C24116yes—
286C2×C5×D4—216no—
287C2×C5×D4—264no—
288C2×C5×D4—28no—
289C2×C5×D4—28no—
290C2×C5×D4—24no—
291C2×C5×D4—432no—
292C2×C5×D4—44no—
293C2×C5×D4—48no—
294C2×C5×D4C2×D418yescomplemented
295C2×C5×D4C2414yes—
296C2×C5×D4C24116yes—
297C2×C5×D4C2418yes—
298C2×C5×D4C2418yes—
299C2×C5×D4C2418yes—
300C2×C5×D4C24116yes—
301C2×C5×D4C2414yes—
302C22×C4×C5—28no—
303C22×C4×C5—28no—
304C22×C4×C5C2411yescharacteristic
305C22×C4×C5C2412yes—
306C22×C4×C5C2412yes—
307C22×C4×C5C2418yes—
308C22×C4×C5C2418yes—
309C22×C4×C5C2411yescharacteristic
310C22×C4×C5C2411yescharacteristic
311C2×C22⋊D5—216no—
312C2×C22⋊D5—28no—
313C2×C22⋊D5—2128no—
314C2×C22⋊D5—28no—
315C2×C22⋊D5—216no—
316C2×C22⋊D5—216no—
317C2×C22⋊D5—216no—
318C2×C22⋊D5—2128no—
319C2×C22⋊D5—216no—
320C2×C22⋊D5—28no—
321C2×C22⋊D5—464no—
322C2×C22⋊D5—48no—
323C2×C22⋊D5—48no—
324C2×C22⋊D5—48no—
325C2×C22⋊D5C2×D4116yescomplemented
326C2×C22⋊D5C24116yes—
327C2×C22⋊D5C2418yes—
328C2×C22⋊D5C24116yes—
329C2×C22⋊D5C2418yes—
330C2×C22⋊D5C24116yes—
331C2×C22⋊D5C24116yes—
332C2×C22⋊D5C24116yes—
333C2×C22⋊D5C2418yes—
334C2×C22⋊D5C24116yes—
335C2×C22⋊D5C24116yes—
336C2×C22⋊D5C24116yes—
337C2×C22⋊D5C2418yes—
338C22×Dic5—216no—
339C22×Dic5—28no—
340C22×Dic5C2×D4116yescomplemented
341C22×Dic5C2411yescharacteristic
342C22×Dic5C2412yes—
343C22×Dic5C2412yes—
344C22×Dic5C24116yes—
345C22×Dic5C2418yes—
346C22×Dic5C2411yescharacteristic
347C22×Dic5C2412yes—
348C22×Dic5C2418yes—
349C22×Dic5C2411yescharacteristic
350#711—2128no—
351#711—264no—
352#711C2×D4164yescomplemented
353D4×D5—264no—
354D4×D5—2128no—
355D4×D5—264no—
356D4×D5—432no—
357D4×D5—432no—
358#709—264no—
359#709—264no—
360C2×D20—28no—
361C2×D20—28no—
362C2×D20—24no—
363C2×D20—28no—
364C2×D20—432no—
365C2×D20—48no—
366C2×D20—44no—
367C2×D20C2414yes—
368C2×D20C2418yes—
369C2×D20C2418yes—
370C2×D20C2418yes—
371C2×D20C24116yes—
372C2×D20C2418yes—
373C2×C4×D5—28no—
374C2×C4×D5—24no—
375C2×C4×D5—216no—
376C2×C4×D5—24no—
377C2×C4×D5C2×D418yescomplemented
378C2×C4×D5C2418yes—
379C2×C4×D5C24116yes—
380C2×C4×D5C2414yes—
381C2×C4×D5C2414yes—
382C2×C4×D5C2414yes—
383C2×Dic10—28no—
384C2×Dic10C2×D418yescomplemented
385C2×Dic10C2418yes—
386C2×Dic10C2414yes—
387C5×C4⋊C4C2414yes—
388C5×C4⋊C4C2414yes—
389C5×C22⋊C4C2418yes—
390C5×C22⋊C4C2418yes—
391C5×C22⋊C4C24116yes—
392C42×C5C2414yes—
393C22⋊Dic5C2418yes—
394C22⋊Dic5C2418yes—
395C22⋊Dic5C24116yes—
396#685C2418yes—
397#685C2418yes—
398#685C24116yes—
399#685C24116yes—
400#685C2418yes—
401C4⋊Dic5C2414yes—
402C4⋊Dic5C2414yes—
403#683C2418yes—
404#683C2418yes—
405#683C2418yes—
406C4×Dic5C2418yes—
407C4×Dic5C2414yes—
408C4×Dic5C2414yes—
409C4×Dic5C2414yes—
410C4×Dic5C2418yes—
411C4×Dic5C2418yes—
412C2×H(5,𝔽2)—532no—
413C2×H(5,𝔽2)—1032no—
414C22×#41—51no—
415C22×#41—54no—
416C22×#41—52no—
417C22×#41—52no—
418C22×#41—52no—
419C23×D4—54no—
420C23×D4—54no—
421C23×D4—54no—
422C23×D4—52no—
423C23×D4—54no—
424C23×D4—52no—
425C23×D4—52no—
426C23×D4—52no—
427C23×D4—52no—
428C23×D4C2×D512yescomplemented
429C23×D4C2×D512yescomplemented
430#550—516no—
431#550—532no—
432#550—516no—
433D42—532no—
434D42—532no—
435D42—532no—
436D42—564no—
437D42—516no—
438D42C2×D5116yescomplemented
439#535—532no—
440#535—564no—
441#532—532no—
442#532—516no—
443C2×C4⋊Q8—51no—
444C2×#127—52no—
445C2×#127—51no—
446C2×#127—54no—
447C2×#127—52no—
448C2×#127—54no—
449C2×#127—52no—
450C2×#127—52no—
451C2×#127—52no—
452C2×#127—532no—
453C2×#127—516no—
454C2×#127—51no—
455C2×#127C2×D511yescharacteristic, complemented
456C2×#124—54no—
457C2×#124—52no—
458C2×#121—51no—
459C2×#121—52no—
460C2×#121—54no—
461C2×#121—54no—
462C2×#121—54no—
463C2×#121—52no—
464C2×#121—52no—
465C2×#121—51no—
466C2×#121—52no—
467C2×#121—52no—
468C2×#121—54no—
469C2×#121—54no—
470C2×#121C2×D512yescomplemented
471C2×#121C2×D512yescomplemented
472C2×#120—54no—
473C2×#120—54no—
474C2×#120—54no—
475C2×#120—54no—
476C2×#120—54no—
477C2×#120C2×D514yescomplemented
478C4×#41—516no—
479C2×C4×Q8—51no—
480C2×C4×Q8—51no—
481C2×C4×D4—51no—
482C2×C4×D4—52no—
483C2×C4×D4—52no—
484C2×C4×D4—52no—
485C2×C4×D4—52no—
486C2×C4×D4—52no—
487C2×C4×D4—54no—
488C2×C4×D4—51no—
489C2×C4×D4C2×D511yescharacteristic, complemented
490C2×C4×D4C2×D511yescharacteristic, complemented
491C2×#117—51no—
492C2×#117—52no—
493C22×C42—52no—
494C22×C42—51no—
495C23×C5—24no—
496C23×C5—24no—
497C23×C5—28no—
498C23×C5—24no—
499C23×C5—24no—
500C23×C5—28no—
501C23×C5—28no—
502C23×C5—24no—
503C23×C5—232no—
504C23×C5—416no—
505C23×C5—416no—
506C23×C5—832no—
507C23×C5C22×D418yes—
508C23×C5C2518yes—
509C23×C5C2514yes—
510C23×C5C2514yes—
511C23×C5C2511yescharacteristic
512C22×D5—22no—
513C22×D5—22no—
514C22×D5—24no—
515C22×D5—28no—
516C22×D5—24no—
517C22×D5—28no—
518C22×D5—28no—
519C22×D5—24no—
520C22×D5—232no—
521C22×D5—232no—
522C22×D5—416no—
523C22×D5—416no—
524C22×D5—416no—
525C22×D5—416no—
526C22×D5—832no—
527C22×D5—832no—
528C22×D5C22×D414yes—
529C22×D5C2514yes—
530C22×D5C2518yes—
531C22×D5C2512yes—
532C5×D4—232no—
533C5×D4—216no—
534C5×D4—216no—
535C5×D4—28no—
536C5×D4—48no—
537C5×D4—416no—
538C5×D4C22×D4116yescomplemented
539C2×C4×C5—24no—
540C2×C4×C5—22no—
541C2×C4×C5—24no—
542C2×C4×C5—216no—
543C2×C4×C5—216no—
544C2×C4×C5C22×D414yes—
545C2×C4×C5H(5,𝔽2)14yescomplemented
546C2×C4×C5C2514yes—
547C2×C4×C5C2512yes—
548C2×C4×C5C2514yes—
549C2×C4×C5C2512yes—
550C2×C4×C5C2512yes—
551C22⋊D5—232no—
552C22⋊D5—216no—
553C22⋊D5—216no—
554C22⋊D5—232no—
555C22⋊D5—232no—
556C22⋊D5—232no—
557C22⋊D5—232no—
558C22⋊D5—216no—
559C22⋊D5—416no—
560C22⋊D5—416no—
561C22⋊D5—416no—
562C22⋊D5C22×D4132yescomplemented
563C2×Dic5—24no—
564C2×Dic5—22no—
565C2×Dic5—24no—
566C2×Dic5—232no—
567C2×Dic5—216no—
568C2×Dic5C22×D414yes—
569C2×Dic5C22×D418yes—
570C2×Dic5C22×D4132yescomplemented
571C2×Dic5H(5,𝔽2)14yescomplemented
572C2×Dic5C2512yes—
573C2×Dic5C2514yes—
574C2×Dic5C2514yes—
575C2×Dic5C2512yes—
576C2×Dic5C2514yes—
577C2×Dic5C2512yes—
578D20—216no—
579D20—216no—
580D20—28no—
581D20—216no—
582D20—416no—
583D20—48no—
584C4×D5—216no—
585C4×D5—28no—
586C4×D5—232no—
587C4×D5—28no—
588C4×D5C22×D4116yescomplemented
589Dic10—216no—
590Dic10C22×D4116yescomplemented
591C25—54no—
592C25—54no—
593C25C22×D514yes—
594H(5,𝔽2)—10256no—
595C2×#41—516no—
596C2×#41—58no—
597C2×#41—532no—
598C2×#41—516no—
599C2×#41—516no—
600C2×#41—516no—
601C2×#41—1016no—
602C2×#41—1016no—
603C2×#41—1032no—
604C2×#41—1016no—
605C22×Q8—51no—
606C22×Q8—52no—
607C22×D4—216no—
608C22×D4—48no—
609C22×D4—52no—
610C22×D4—54no—
611C22×D4—52no—
612C22×D4—52no—
613C22×D4—54no—
614C22×D4—54no—
615C22×D4—54no—
616C22×D4—54no—
617C22×D4—52no—
618C22×D4—532no—
619C22×D4—532no—
620C22×D4—54no—
621C22×D4—54no—
622C22×D4—54no—
623C22×D4—532no—
624C22×D4—516no—
625C22×D4—532no—
626C22×D4—516no—
627C22×D4—516no—
628C22×D4—516no—
629C22×D4—52no—
630C22×D4—51no—
631C22×D4—52no—
632C22×D4—52no—
633C22×D4—54no—
634C22×D4—52no—
635C22×D4—516no—
636C22×D4—1016no—
637C22×D4—1032no—
638C22×D4—1032no—
639C22×D4—1032no—
640C22×D4—1016no—
641C22×D4—208no—
642C22×D4—208no—
643C22×D4—208no—
644C22×D4—2016no—
645C22×D4C22×D512yes—
646C22×D4C22×D511yescharacteristic
647C22×D4C22×D514yes—
648C22×D4C22×D512yes—
649C22×D4C22×D514yes—
650C22×D4C22×D512yes—
651C22×D4C22×D511yescharacteristic
652C22×D4C22×D5116yescomplemented
653C22×D4C22×D5116yescomplemented
654C23×C4—52no—
655C23×C4—51no—
656C23×C4—52no—
657C23×C4—54no—
658C23×C4—51no—
659C23×C4—51no—
660C23×C4—54no—
661C23×C4—52no—
662C23×C4C22×D512yes—
663C23×C4C22×D512yes—
664C4⋊Q8—58no—
665#127—516no—
666#127—58no—
667#127—532no—
668#127—516no—
669#127—532no—
670#127—516no—
671#127—516no—
672#127—516no—
673#127—58no—
674#127C22×D518yescomplemented
675#124—532no—
676#124—516no—
677#121—58no—
678#121—532no—
679#121—516no—
680#121—532no—
681#121—532no—
682#121—516no—
683#121—516no—
684#121—58no—
685#121—516no—
686#121—516no—
687#121—532no—
688#121—532no—
689#121C22×D5116yescomplemented
690#121C22×D5116yescomplemented
691#120—532no—
692#120—532no—
693#120—532no—
694#120—532no—
695#120—532no—
696#120C22×D5132yescomplemented
697C4×Q8—58no—
698C4×Q8—58no—
699C4×D4—58no—
700C4×D4—516no—
701C4×D4—516no—
702C4×D4—516no—
703C4×D4—516no—
704C4×D4—516no—
705C4×D4—532no—
706C4×D4—58no—
707C4×D4C22×D518yescomplemented
708C4×D4C22×D518yescomplemented
709#117—58no—
710#117—516no—
711C2×C4⋊C4—52no—
712C2×C4⋊C4—52no—
713C2×C4⋊C4—51no—
714C2×C4⋊C4—52no—
715C2×C4⋊C4—51no—
716C2×C4⋊C4C22×D511yescharacteristic
717C2×C4⋊C4C22×D511yescharacteristic
718C2×C22⋊C4—52no—
719C2×C22⋊C4—54no—
720C2×C22⋊C4—52no—
721C2×C22⋊C4—52no—
722C2×C22⋊C4—52no—
723C2×C22⋊C4—54no—
724C2×C22⋊C4—54no—
725C2×C22⋊C4—52no—
726C2×C22⋊C4C22×D512yes—
727C2×C22⋊C4C22×D514yes—
728C2×C22⋊C4C22×D512yes—
729C2×C42—52no—
730C2×C42—51no—
731C2×C42—52no—
732C2×C42—51no—
733C2×C42—52no—
734C2×C42—516no—
735C2×C42—51no—
736C2×C42—58no—
737C2×C42C22×D511yescharacteristic
738C22×C5—24no—
739C22×C5—24no—
740C22×C5—216no—
741C22×C5—28no—
742C22×C5—24no—
743C22×C5—24no—
744C22×C5—28no—
745C22×C5—28no—
746C22×C5—24no—
747C22×C5—416no—
748C22×C5—48no—
749C22×C5—832no—
750C22×C5C23×D418yes—
751C22×C5C23×D412yes—
752C22×C5C2×H(5,𝔽2)12yes—
753C22×C5C2×H(5,𝔽2)12yes—
754C22×C5C2611yescharacteristic
755C2×D5—22no—
756C2×D5—22no—
757C2×D5—28no—
758C2×D5—24no—
759C2×D5—28no—
760C2×D5—24no—
761C2×D5—28no—
762C2×D5—28no—
763C2×D5—24no—
764C2×D5—48no—
765C2×D5—416no—
766C2×D5—832no—
767C2×D5—832no—
768C2×D5C23×D414yes—
769C4×C5—24no—
770C4×C5—22no—
771C4×C5—24no—
772C4×C5C23×D414yes—
773C4×C5C2×H(5,𝔽2)14yescomplemented
774Dic5—24no—
775Dic5—22no—
776Dic5—24no—
777Dic5C23×D414yes—
778Dic5C23×D418yes—
779Dic5C2×H(5,𝔽2)14yescomplemented
780C24—216no—
781C24—48no—
782C24—48no—
783C24—51no—
784C24—54no—
785C24—52no—
786C24—516no—
787C24—516no—
788C24—1016no—
789C24—1016no—
790C24—208no—
791C24—208no—
792C24—208no—
793C24—208no—
794C24C23×D514yes—
795C24C23×D512yes—
796C24C23×D512yes—
797C24C23×D5116yes—
798#41—564no—
799#41—1064no—
800#41—1064no—
801#41—10128no—
802#41—1064no—
803C2×Q8—58no—
804C2×Q8—54no—
805C2×Q8—58no—
806C2×Q8—108no—
807C2×D4—216no—
808C2×D4—264no—
809C2×D4—28no—
810C2×D4—24no—
811C2×D4—28no—
812C2×D4—432no—
813C2×D4—48no—
814C2×D4—44no—
815C2×D4—516no—
816C2×D4—58no—
817C2×D4—516no—
818C2×D4—58no—
819C2×D4—58no—
820C2×D4—516no—
821C2×D4—516no—
822C2×D4—516no—
823C2×D4—516no—
824C2×D4—58no—
825C2×D4—516no—
826C2×D4—516no—
827C2×D4—516no—
828C2×D4—58no—
829C2×D4—54no—
830C2×D4—58no—
831C2×D4—58no—
832C2×D4—516no—
833C2×D4—58no—
834C2×D4—108no—
835C2×D4—1064no—
836C2×D4—108no—
837C2×D4—1016no—
838C2×D4—1016no—
839C2×D4—1016no—
840C2×D4—10128no—
841C2×D4—1016no—
842C2×D4—108no—
843C2×D4—10128no—
844C2×D4—10128no—
845C2×D4—108no—
846C2×D4—1016no—
847C2×D4—1064no—
848C2×D4—108no—
849C2×D4—104no—
850C2×D4—108no—
851C2×D4—2032no—
852C2×D4—208no—
853C2×D4—204no—
854C2×D4—2032no—
855C2×D4—2032no—
856C2×D4—2064no—
857C2×D4—208no—
858C2×D4—208no—
859C2×D4—208no—
860C2×D4D4×D518yescomplemented
861C2×D4C23×D518yes—
862C2×D4C23×D514yes—
863C2×D4C23×D5116yes—
864C2×D4C23×D518yes—
865C2×D4C23×D5116yes—
866C2×D4C23×D518yes—
867C2×D4C23×D514yes—
868C22×C4—28no—
869C22×C4—28no—
870C22×C4—516no—
871C22×C4—58no—
872C22×C4—51no—
873C22×C4—51no—
874C22×C4—52no—
875C22×C4—58no—
876C22×C4—54no—
877C22×C4—58no—
878C22×C4—516no—
879C22×C4—51no—
880C22×C4—52no—
881C22×C4—52no—
882C22×C4—54no—
883C22×C4—54no—
884C22×C4—516no—
885C22×C4—58no—
886C22×C4—1016no—
887C22×C4—104no—
888C22×C4—1016no—
889C22×C4—108no—
890C22×C4—108no—
891C22×C4—104no—
892C22×C4C23×D518yes—
893C22×C4C23×D518yes—
894C22×C4C23×D512yes—
895C22×C4C23×D511yescharacteristic
896C22×C4C23×D512yes—
897C22×C4C23×D511yescharacteristic
898C22×C4C23×D511yescharacteristic
899C4⋊C4—58no—
900C4⋊C4—58no—
901C4⋊C4—54no—
902C4⋊C4—58no—
903C4⋊C4—54no—
904C4⋊C4C23×D514yes—
905C4⋊C4C23×D514yes—
906C22⋊C4—58no—
907C22⋊C4—516no—
908C22⋊C4—58no—
909C22⋊C4—58no—
910C22⋊C4—58no—
911C22⋊C4—516no—
912C22⋊C4—516no—
913C22⋊C4—58no—
914C22⋊C4C23×D518yes—
915C22⋊C4C23×D5116yes—
916C22⋊C4C23×D518yes—
917C42—54no—
918C42—58no—
919C42—54no—
920C42—58no—
921C42—54no—
922C42—58no—
923C42C23×D514yes—
924C2×C5—28no—
925C2×C5—48no—
926C2×C5—44no—
927C2×C5#349814yescomplemented
928C2×C5C24×D411yescharacteristic
929C2×C5C22×H(5,𝔽2)11yescharacteristic
930C2×C5C22×H(5,𝔽2)11yescharacteristic
931D5—24no—
932D5—44no—
933D5—48no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—28no—
938C23—24no—
939C23—28no—
940C23—28no—
941C23—24no—
942C23—232no—
943C23—416no—
944C23—416no—
945C23—54no—
946C23—52no—
947C23—58no—
948C23—54no—
949C23—832no—
950C23—1032no—
951C23—102no—
952C23—102no—
953C23—108no—
954C23—104no—
955C23—104no—
956C23—108no—
957C23—108no—
958C23—104no—
959C23—1032no—
960C23—2016no—
961C23—2016no—
962C23—2016no—
963C23—2016no—
964C23—4032no—
965C23—4032no—
966C23C2×D4×D518yes—
967C23C24×D518yes—
968C23C24×D514yes—
969C23C24×D514yes—
970C23C24×D511yescharacteristic
971Q8—516no—
972Q8—1016no—
973D4—232no—
974D4—216no—
975D4—28no—
976D4—216no—
977D4—416no—
978D4—48no—
979D4—532no—
980D4—1016no—
981D4—1016no—
982D4—1032no—
983D4—1032no—
984D4—1032no—
985D4—1032no—
986D4—1016no—
987D4—1016no—
988D4—1032no—
989D4—1016no—
990D4—108no—
991D4—1016no—
992D4—2016no—
993D4—208no—
994D4—2016no—
995D4—2016no—
996D4—2016no—
997D4C2×D4×D5116yescomplemented
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—216no—
1002C2×C4—216no—
1003C2×C4—54no—
1004C2×C4—58no—
1005C2×C4—532no—
1006C2×C4—54no—
1007C2×C4—52no—
1008C2×C4—52no—
1009C2×C4—54no—
1010C2×C4—516no—
1011C2×C4—52no—
1012C2×C4—54no—
1013C2×C4—54no—
1014C2×C4—1032no—
1015C2×C4—108no—
1016C2×C4—1032no—
1017C2×C4—1016no—
1018C2×C4—104no—
1019C2×C4—102no—
1020C2×C4—104no—
1021C2×C4—1016no—
1022C2×C4—108no—
1023C2×C4C2×D4×D514yes—
1024C2×C4#414414yescomplemented
1025C2×C4C24×D514yes—
1026C2×C4C24×D512yes—
1027C2×C4C24×D514yes—
1028C2×C4C24×D512yes—
1029C2×C4C24×D512yes—
1030C5C2×#349811yescharacteristic, complemented, Sylow
1031C22—24no—
1032C22—24no—
1033C22—216no—
1034C22—24no—
1035C22—28no—
1036C22—24no—
1037C22—28no—
1038C22—28no—
1039C22—24no—
1040C22—48no—
1041C22—416no—
1042C22—54no—
1043C22—832no—
1044C22—102no—
1045C22—102no—
1046C22—108no—
1047C22—108no—
1048C22—104no—
1049C22—104no—
1050C22—108no—
1051C22—108no—
1052C22—104no—
1053C22—208no—
1054C22—2016no—
1055C22—4032no—
1056C22—4032no—
1057C22C22×D4×D518yes—
1058C22C22×D4×D512yes—
1059C22C2×#414412yes—
1060C22D5×H(5,𝔽2)12yes—
1061C22C25×D511yescharacteristic
1062C4—24no—
1063C4—24no—
1064C4—22no—
1065C4—54no—
1066C4—58no—
1067C4—54no—
1068C4—104no—
1069C4—102no—
1070C4—104no—
1071C4C22×D4×D514yes—
1072C4C2×#414414yescomplemented
1073C2—28no—
1074C2—44no—
1075C2—48no—
1076C2—104no—
1077C2—204no—
1078C2—208no—
1079C2#1061850914yesdirect product factor
1080C2C23×D4×D511yescharacteristic
1081C2C22×#414411yescharacteristic
1082C2C2×D5×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×D42C2
socleC23×C5C25
hypercenterC2×D42D5
hypocenterC5C2×#3498
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C22×#4144C2semidirect
2. C2×C5×D42C2semidirect
3. C2×D4×C22⋊D5C2semidirect
4. C2×D4×C22⋊D5C2semidirect
5. C22×#4086C2semidirect
6. #10618509C2direct (N × H)
7. C2×D5×#127C2semidirect
8. C2×#66052C2semidirect
9. C2×#65943C2semidirect
10. C2×#65941C2semidirect
11. C2×#65933C2semidirect
12. C2×#65930C2semidirect
13. C2×#65924C2semidirect
14. C2×#65926C2semidirect
15. C2×D4×D20C2semidirect
16. C2×#65882C2semidirect
17. C2×#65887C2semidirect
18. C2×C4×#711C2semidirect
19. C23×C5×D4C22semidirect
20. C23×C5×D4C22semidirect
21. C23×C22⋊D5C22semidirect
22. C23×C22⋊D5C22semidirect
23. C23×C22⋊D5C22semidirect
25. C2×#4144C22semidirect
27. C22×#711C22semidirect
28. C22×#711C22semidirect
29. C22×D4×D5C22semidirect
30. C22×D4×D5C22semidirect
31. C22×D4×D5C22semidirect
32. C22×D4×D5C22semidirect
33. C22×D4×D5C22semidirect
34. C22×#709C22semidirect
35. C22×#709C22semidirect
36. C23×D20C22semidirect
37. C5×D42C22semidirect
38. C2×C5×#127C22semidirect
39. C2×C5×#121C22semidirect
40. C2×C5×#121C22semidirect
41. C2×C5×#120C22semidirect
42. C2×C4×C5×D4C22semidirect
43. C2×C4×C5×D4C22semidirect
44. C2×#4099C22semidirect
45. C2×#4086C22semidirect
46. C2×#4086C22semidirect
47. C2×#4086C22semidirect
48. C2×#4086C22semidirect
49. C2×#4086C22semidirect
50. C2×#4086C22semidirect
51. C2×#4086C22semidirect
52. C2×#4086C22semidirect
53. C2×#4086C22semidirect
54. C2×#4085C22semidirect
55. C2×#4085C22semidirect
56. C2×#4085C22semidirect
57. D4×C22⋊D5C22semidirect
58. D4×C22⋊D5C22semidirect
59. C2×#4084C22semidirect
60. C2×#4084C22semidirect
61. C2×#4083C22semidirect
62. C2×#4083C22semidirect
63. C2×D4×Dic5C22semidirect
64. C2×D4×Dic5C22semidirect
65. C2×#4076C22semidirect
66. C2×#4076C22semidirect
67. C2×C4×C22⋊D5C22semidirect
68. C2×C4×C22⋊D5C22semidirect
69. C22×C4×Dic5C22semidirect
70. #66052C22semidirect
71. D5×#127C22semidirect
72. #65943C22semidirect
73. #65941C22semidirect
74. #65933C22semidirect
75. #65930C22semidirect
76. #65926C22semidirect
77. #65924C22semidirect
78. #65887C22semidirect
79. D4×D20C22semidirect
80. #65882C22semidirect
81. C4×#711C22semidirect
82. C2×#4041C22semidirect
83. C2×#4041C22semidirect
84. C2×#4039C22semidirect
85. C2×#4038C22semidirect
86. C2×#4034C22semidirect
87. C2×#4033C22semidirect
88. C2×#4031C22semidirect
89. C2×#4031C22semidirect
90. C2×#4030C22semidirect
91. C2×#4030C22semidirect
92. C2×#4030C22semidirect
93. C2×#4028C22semidirect
94. C2×#4028C22semidirect
95. C2×#4027C22semidirect
96. C2×#4027C22semidirect
97. C2×#4023C22semidirect
98. C2×#4020C22semidirect
99. C2×C4×D20C22semidirect
100. C2×C42×D5C22semidirect
101. C2×C4×Dic10C22semidirect
115. C22×C5×D4C23semidirect
116. C22×C5×D4C23semidirect
134. C22×C22⋊D5C23semidirect
135. C22×C22⋊D5C23semidirect
136. C22×C22⋊D5C23semidirect
143. C2×#711D4semidirect
145. C2×#711C23semidirect
146. C2×#711C23semidirect
152. C2×D4×D5C23semidirect
153. C2×D4×D5C23semidirect
154. C2×D4×D5C23semidirect
155. C2×D4×D5C23semidirect
156. C2×D4×D5C23semidirect
159. C2×#709C23semidirect
160. C2×#709C23semidirect
168. C22×D20C23semidirect
176. C5×#127C23semidirect
177. C5×#121C23semidirect
178. C5×#121C23semidirect
179. C5×#120C23semidirect
180. C4×C5×D4C23semidirect
181. C4×C5×D4C23semidirect
188. #4099C23semidirect
192. #4086C23semidirect
193. #4086C23semidirect
194. #4086C23semidirect
195. #4086C23semidirect
196. #4086C23semidirect
197. #4086C23semidirect
198. #4086C23semidirect
199. #4086C23semidirect
200. #4085C23semidirect
201. #4085C23semidirect
202. #4085C23semidirect
203. #4084C23semidirect
204. #4084C23semidirect
205. #4083C23semidirect
206. #4083C23semidirect
207. D4×Dic5C23semidirect
208. D4×Dic5C23semidirect
209. #4076C23semidirect
210. #4076C23semidirect
211. C4×C22⋊D5C23semidirect
212. C4×C22⋊D5C23semidirect
229. C2×C4×Dic5C23semidirect
230. #4041C23semidirect
231. #4041C23semidirect
232. #4039C23semidirect
233. #4038C23semidirect
234. #4034C23semidirect
235. #4033C23semidirect
236. #4031C23semidirect
237. #4031C23semidirect
238. #4030C23semidirect
239. #4030C23semidirect
240. #4030C23semidirect
241. #4028C23semidirect
242. #4028C23semidirect
243. #4027C23semidirect
244. #4027C23semidirect
245. #4023C23semidirect
246. #4020C23semidirect
247. C4×D20C23semidirect
248. C42×D5C23semidirect
249. C4×Dic10C23semidirect
260. C2×D42D5semidirect
294. C2×C5×D4C2×D4semidirect
325. C2×C22⋊D5C2×D4semidirect
340. C22×Dic5C2×D4semidirect
352. #711C2×D4semidirect
377. C2×C4×D5C2×D4semidirect
384. C2×Dic10C2×D4semidirect
428. C23×D4C2×D5semidirect
429. C23×D4C2×D5semidirect
438. D42C2×D5semidirect
455. C2×#127C2×D5semidirect
470. C2×#121C2×D5semidirect
471. C2×#121C2×D5semidirect
477. C2×#120C2×D5semidirect
489. C2×C4×D4C2×D5semidirect
490. C2×C4×D4C2×D5semidirect
538. C5×D4C22×D4semidirect
545. C2×C4×C5H(5,𝔽2)semidirect
562. C22⋊D5C22×D4semidirect
570. C2×Dic5C22×D4semidirect
571. C2×Dic5H(5,𝔽2)semidirect
588. C4×D5C22×D4semidirect
590. Dic10C22×D4semidirect
652. C22×D4C22×D5semidirect
653. C22×D4C22×D5semidirect
674. #127C22×D5semidirect
689. #121C22×D5semidirect
690. #121C22×D5semidirect
696. #120C22×D5semidirect
707. C4×D4C22×D5semidirect
708. C4×D4C22×D5semidirect
773. C4×C5C2×H(5,𝔽2)semidirect
779. Dic5C2×H(5,𝔽2)semidirect
860. C2×D4D4×D5semidirect
927. C2×C5#3498semidirect
997. D4C2×D4×D5semidirect
1024. C2×C4#4144semidirect
1030. C5C2×#3498semidirect
1072. C4C2×#4144semidirect
1079. C2#10618509direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41442
C2×C5×D422
C2×D4×C22⋊D52
C22×#40862
#106185092
C2×D5×#1272
C2×#660522
C2×#659432
C2×#659412
C2×#659332
C2×#659302
C2×#659242
C2×#659262
C2×D4×D202
C2×#658822
C2×#658872
C2×C4×#7112
C2×#34985