Finite Group Databasebeta

← C2×#10618788 #13007284

Subgroups — C2×#10618788 #13007284

Order 1280.

8774 conjugacy classes of subgroups.

The subgroup lattice has 1472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#553C211yesmaximal, characteristic, complemented
2#10618788C2132yesmaximal, direct product factor
3C2×#66038C212yesmaximal, complemented
4C2×#66043C212yesmaximal, complemented
5C2×#66029C211yesmaximal, characteristic, complemented
6C2×#66025C211yesmaximal, characteristic, complemented
7C2×#65988C212yesmaximal, complemented
8C2×#65997C212yesmaximal, complemented
9C2×#65943C212yesmaximal, complemented
10C2×#65943C211yesmaximal, characteristic, complemented
11C2×#65951C212yesmaximal, complemented
12C2×D5×#121C211yesmaximal, characteristic, complemented
13C2×#65933C211yesmaximal, characteristic, complemented
14C2×#65940C211yesmaximal, characteristic, complemented
15C2×#65884C212yesmaximal, complemented
16C2×#65884C211yesmaximal, characteristic, complemented
17C2×#65888C211yesmaximal, characteristic, complemented
18C2×#65882C211yesmaximal, characteristic, complemented
19C2×#65879C212yesmaximal, complemented
20C2×C4×D4×D5C211yesmaximal, characteristic, complemented
21C2×#65866C211yesmaximal, characteristic, complemented
22C2×#65858C211yesmaximal, characteristic, complemented
23C22×#4041C211yesmaximal, characteristic, complemented
24C2×#65845C211yesmaximal, characteristic, complemented
25C22×#711C2211yescharacteristic, complemented
26C22×D4×D5C2211yescharacteristic
27C22×D4×D5C2212yes—
28C22×D4×D5C2212yescomplemented
29C22×D4×D5C2211yescharacteristic, complemented
30C22×#709C2211yescharacteristic, complemented
31C22×#709C2212yescomplemented
32C23×D20C2211yescharacteristic, complemented
33C23×D20C2212yescomplemented
34C23×C4×D5C2211yescharacteristic, complemented
35C23×C4×D5C2211yescharacteristic, complemented
36C5×#553C22116yescomplemented
37C2×C5×#126C2212yescomplemented
38C2×C5×#125C2211yescharacteristic, complemented
39C2×C5×#123C2212yescomplemented
40C2×C5×#121C2211yescharacteristic, complemented
41C2×C5×#121C2211yescharacteristic, complemented
42C2×C5×#121C2212yescomplemented
43C2×C4×C5×D4C2211yescharacteristic, complemented
44C2×C4×C5×D4C2212yescomplemented
45C2×C4×C5×D4C2211yescharacteristic, complemented
46C2×C5×#117C2211yescharacteristic, complemented
47C22×C5×C4⋊C4C2211yescharacteristic, complemented
48C2×#4086C2212yescomplemented
49C2×#4086C2211yescharacteristic, complemented
50C2×#4085C2212yescomplemented
51C2×#4085C2212yescomplemented
52C2×#4084C2211yescharacteristic, complemented
53C2×#4083C2212yescomplemented
54C2×#4083C2212yescomplemented
55C2×#4083C2212yescomplemented
56C2×D4×Dic5C2211yescharacteristic, complemented
57C2×D4×Dic5C2212yescomplemented
58C2×#4076C2212yescomplemented
59C2×#4076C2211yescharacteristic, complemented
60C2×C4×C22⋊D5C2211yescharacteristic
61C2×C4×C22⋊D5C2212yes—
62C2×C4×C22⋊D5C2212yescomplemented
63C2×C4×C22⋊D5C2211yescharacteristic, complemented
64C22×#685C2212yescomplemented
65C22×#685C2212yescomplemented
66C2×#4070C2211yescharacteristic, complemented
67C2×#4070C2212yescomplemented
68#66043C22132yescomplemented
69#66038C22132yescomplemented
70#66029C22116yescomplemented
71#66025C22116yescomplemented
72#65997C22132yescomplemented
73#65988C22132yescomplemented
74#65951C22132yescomplemented
75#65943C22116yescomplemented
76#65943C22132yescomplemented
77#65940C22116yescomplemented
78D5×#121C22116yescomplemented
79#65933C22116yescomplemented
80#65888C22116yescomplemented
81#65884C22116yescomplemented
82#65884C22132yescomplemented
83#65882C22116yescomplemented
84#65879C22132yescomplemented
85C4×D4×D5C22116yescomplemented
86#65866C22116yescomplemented
87#65858C22116yescomplemented
88C2×#4044C2212yescomplemented
89C2×#4044C2212yescomplemented
90#65845C22116yescomplemented
91C2×#4043C2211yescharacteristic, complemented
92C2×#4043C2211yescharacteristic, complemented
93C2×#4042C2212yescomplemented
94C2×#4041C2211yescharacteristic
95C2×#4041C2211yescharacteristic, complemented
96C2×#4041C2212yescomplemented
97C2×#4041C2211yescharacteristic, complemented
98C2×#4041C2212yescomplemented
99C2×#4041C2211yescharacteristic, complemented
100C2×#4041C2211yescharacteristic, complemented
101C2×#4041C2212yescomplemented
102C2×#4041C22116yescomplemented
103C2×#4040C2212yescomplemented
104C2×#4040C2212yescomplemented
105C2×#4040C2212yescomplemented
106C2×#4039C2211yescharacteristic, complemented
107C2×#4039C2212yescomplemented
108C2×#4039C2211yescharacteristic, complemented
109C2×#4039C2212yescomplemented
110C2×#4038C2212yescomplemented
111C2×#4038C2211yescharacteristic, complemented
112C2×D5×C4⋊C4C2211yescharacteristic, complemented
113C2×D5×C4⋊C4C2211yescharacteristic, complemented
114C2×#4035C2212yescomplemented
115C2×#4034C2211yescharacteristic, complemented
116C2×#4033C2211yescharacteristic, complemented
117C2×#4032C2212yescomplemented
118C2×#4032C2212yescomplemented
119C2×#4031C2212yescomplemented
120C2×#4031C2212yescomplemented
121C2×#4030C2212yescomplemented
122C2×#4030C2212yescomplemented
123C2×#4030C2212yescomplemented
124C2×#4030C2212yescomplemented
125C2×#4030C2212yescomplemented
126C2×#4030C2212yescomplemented
127C2×#4029C2212yescomplemented
128C2×#4028C2212yescomplemented
129C2×#4028C2212yescomplemented
130C2×#4028C2212yescomplemented
131C2×#4027C2211yescharacteristic
132C2×#4027C2211yescharacteristic, complemented
133C2×#4027C2212yescomplemented
134C2×#4027C2212yescomplemented
135C2×D5×C22⋊C4C2211yescharacteristic, complemented
136C2×D5×C22⋊C4C2211yescharacteristic, complemented
137C2×D5×C22⋊C4C2212yescomplemented
138C2×D5×C22⋊C4C2212yescomplemented
139C2×#4021C2212yescomplemented
140C2×#4021C2211yescharacteristic, complemented
141C2×C4×D20C2212yescomplemented
142C2×C4×D20C2212yescomplemented
143C2×C4×D20C2211yescharacteristic, complemented
144C2×C4×D20C2211yescharacteristic, complemented
145C2×#4018C2212yescomplemented
146C2×C42×D5C2211yescharacteristic, complemented
147C2×#3519—51nomaximal, Sylow
148C24×D5C2311yescharacteristic
149C24×D5C2311yescharacteristic
150C24×D5C2312yes—
151C24×D5C2312yes—
152C22×C5×D4C2311yescharacteristic
153C22×C5×D4C2312yes—
154C22×C5×D4C2311yescharacteristic
155C22×C5×D4C2312yes—
156C23×C4×C5C2311yescharacteristic
157C23×C4×C5C2311yescharacteristic
158C23×C4×C5C2312yes—
159C23×C4×C5C2312yes—
160C22×C22⋊D5C2311yescharacteristic
161C22×C22⋊D5C2312yes—
162C22×C22⋊D5C2312yes—
163C22×C22⋊D5C2312yes—
164C22×C22⋊D5C2312yes—
165C22×C22⋊D5C2312yes—
166C22×C22⋊D5C2312yes—
167C22×C22⋊D5C2312yes—
168C22×C22⋊D5C2311yescharacteristic
169C23×Dic5C2311yescharacteristic
170C23×Dic5C2312yes—
171C23×Dic5C2311yescharacteristic
172C2×#711—44no—
173C2×#711C2318yescomplemented
174C2×D4×D5—28no—
175C2×D4×D5—216no—
176C2×D4×D5—44no—
177C2×D4×D5—48no—
178C2×D4×D5C2318yes—
179C2×D4×D5C23116yes—
180C2×D4×D5C2318yescomplemented
181C2×D4×D5C23116yescomplemented
182C2×#709—44no—
183C2×#709—48no—
184C2×#709C2318yescomplemented
185C2×#709C23116yescomplemented
186C22×D20—44no—
187C22×D20—48no—
188C22×D20C2312yes—
189C22×D20C2311yescharacteristic
190C22×D20C2312yes—
191C22×D20C2311yescharacteristic
192C22×D20C2311yescharacteristic
193C22×D20C2312yes—
194C22×D20C2312yes—
195C22×D20C2312yes—
196C22×D20C2312yes—
197C22×D20C2318yescomplemented
198C22×D20C23116yescomplemented
199C22×C4×D5—44no—
200C22×C4×D5—44no—
201C22×C4×D5C2311yescharacteristic
202C22×C4×D5C2311yescharacteristic
203C22×C4×D5C2311yescharacteristic
204C22×C4×D5C2312yes—
205C22×C4×D5C2311yescharacteristic
206C22×C4×D5C2311yescharacteristic
207C22×C4×D5C2311yescharacteristic
208C22×C4×D5C2312yes—
209C22×C4×D5C2311yescharacteristic
210C22×C4×D5C2312yes—
211C22×C4×D5C2311yescharacteristic
212C22×C4×D5C2312yes—
213C22×C4×D5C2311yescharacteristic
214C22×C4×D5C2318yescomplemented
215C22×C4×D5C2318yescomplemented
216C22×Dic10C2311yescharacteristic
217C22×Dic10C2312yes—
218C5×#126C23116yescomplemented
219C5×#125C2318yescomplemented
220C5×#123C23116yescomplemented
221C5×#121C2318yescomplemented
222C5×#121C2318yescomplemented
223C5×#121C23116yescomplemented
224C4×C5×D4C2318yescomplemented
225C4×C5×D4C23116yescomplemented
226C4×C5×D4C2318yescomplemented
227C5×#117C2318yescomplemented
228C2×C5×C4⋊C4C2311yescharacteristic
229C2×C5×C4⋊C4C2311yescharacteristic
230C2×C5×C4⋊C4C2312yes—
231C2×C5×C4⋊C4C2311yescharacteristic
232C2×C5×C4⋊C4C2312yes—
233C2×C5×C4⋊C4C2311yescharacteristic
234C2×C5×C4⋊C4C2312yes—
235C2×C5×C4⋊C4C2318yescomplemented
236C2×C5×C22⋊C4C2311yescharacteristic
237C2×C5×C22⋊C4C2312yes—
238C2×C5×C22⋊C4C2311yescharacteristic
239C2×C5×C22⋊C4C2312yes—
240C2×C5×C22⋊C4C2312yes—
241C2×C5×C22⋊C4C2312yes—
242C2×C42×C5C2311yescharacteristic
243C2×C42×C5C2312yes—
244C2×C22⋊Dic5C2312yes—
245C2×C22⋊Dic5C2311yescharacteristic
246C2×C22⋊Dic5C2311yescharacteristic
247C2×C22⋊Dic5C2312yes—
248#4086C2318yescomplemented
249#4086C23116yescomplemented
250#4085C23116yescomplemented
251#4085C23116yescomplemented
252#4084C2318yescomplemented
253#4083C23116yescomplemented
254#4083C23116yescomplemented
255#4083C23116yescomplemented
256D4×Dic5C2318yescomplemented
257D4×Dic5C23116yescomplemented
258#4076C2318yescomplemented
259#4076C23116yescomplemented
260C4×C22⋊D5C2318yes—
261C4×C22⋊D5C23116yes—
262C4×C22⋊D5C2318yescomplemented
263C4×C22⋊D5C23116yescomplemented
264C2×#685C2312yes—
265C2×#685C2312yes—
266C2×#685C2311yescharacteristic
267C2×#685C2311yescharacteristic
268C2×#685C2312yes—
269C2×#685C2312yes—
270C2×#685C2312yes—
271C2×#685C2312yes—
272C2×#685C2312yes—
273C2×#685C2311yescharacteristic
274C2×#685C2312yes—
275C2×#685C2312yes—
276C2×#685C2312yes—
277C2×#685C2312yes—
278C2×#685C2311yescharacteristic
279C2×#685C2312yes—
280C2×#685C2312yes—
281C2×#685C23116yescomplemented
282C2×#685C23116yescomplemented
283C2×C4⋊Dic5C2312yes—
284C2×C4⋊Dic5C2312yes—
285C2×C4⋊Dic5C2311yescharacteristic
286C2×C4⋊Dic5C2311yescharacteristic
287#4070C2318yescomplemented
288#4070C23116yescomplemented
289C2×#683C2311yescharacteristic
290C2×#683C2312yes—
291C2×#683C2312yes—
292C2×#683C2311yescharacteristic
293C2×#683C2312yes—
294C2×#683C2312yes—
295C2×C4×Dic5C2311yescharacteristic
296C2×C4×Dic5C2311yescharacteristic
297C2×C4×Dic5C2311yescharacteristic
298C2×C4×Dic5C2312yes—
299C2×C4×Dic5C2312yes—
300#4044C23116yescomplemented
301#4044C23116yescomplemented
302#4043C2318yescomplemented
303#4043C2318yescomplemented
304#4042C23116yescomplemented
305#4041C2318yes—
306#4041C2318yescomplemented
307#4041C2318yescomplemented
308#4041C2318yescomplemented
309#4041C23116yescomplemented
310#4041C23116yescomplemented
311#4041C2318yescomplemented
312#4041C23116yescomplemented
313#4040C23116yescomplemented
314#4040C23116yescomplemented
315#4040C23116yescomplemented
316#4039C2318yescomplemented
317#4039C2318yescomplemented
318#4039C23116yescomplemented
319#4039C23116yescomplemented
320#4038C2318yescomplemented
321#4038C23116yescomplemented
322D5×C4⋊C4C2318yescomplemented
323D5×C4⋊C4C2318yescomplemented
324#4035C23116yescomplemented
325#4034C2318yescomplemented
326#4033C2318yescomplemented
327#4032C23116yescomplemented
328#4032C23116yescomplemented
329#4031C23116yescomplemented
330#4031C23116yescomplemented
331#4030C23116yescomplemented
332#4030C23116yescomplemented
333#4030C23116yescomplemented
334#4030C23116yescomplemented
335#4030C23116yescomplemented
336#4030C23116yescomplemented
337#4029C23116yescomplemented
338#4028C23116yescomplemented
339#4028C23116yescomplemented
340#4028C23116yescomplemented
341#4027C2318yes—
342#4027C2318yescomplemented
343#4027C23116yescomplemented
344#4027C23116yescomplemented
345D5×C22⋊C4C2318yescomplemented
346D5×C22⋊C4C2318yescomplemented
347D5×C22⋊C4C23116yescomplemented
348D5×C22⋊C4C23116yescomplemented
349#4021C23116yescomplemented
350#4021C2318yescomplemented
351C4×D20C23116yescomplemented
352C4×D20C23116yescomplemented
353C4×D20C2318yescomplemented
354C4×D20C2318yescomplemented
355#4018C23116yescomplemented
356C42×D5C2318yescomplemented
357#3519—532no—
358C2×#555—51no—
359C2×#554—51no—
360C2×#553—52no—
361C2×#553—51no—
362C2×#553D511yescharacteristic, complemented
363C2×#550—51no—
364C2×#546—52no—
365C2×#546—51no—
366C2×#546—52no—
367C2×#546—51no—
368C2×D42—51no—
369C2×D42—52no—
370C2×#540—52no—
371C2×#538—52no—
372C2×#538—52no—
373C2×#532—51no—
374C2×#529—51no—
375C2×#525—51no—
376C2×#525—51no—
377C22×#121—51no—
378C22×#121—51no—
379C2×#518—52no—
380C22×C4×D4—51no—
381C24×C5C2411yescharacteristic
382C24×C5C2412yes—
383C24×C5C2411yescharacteristic
384C23×D5—24no—
385C23×D5—28no—
386C23×D5—24no—
387C23×D5—24no—
388C23×D5—24no—
389C23×D5—28no—
390C23×D5—42no—
391C23×D5—42no—
392C23×D5—44no—
393C23×D5—44no—
394C23×D5—44no—
395C23×D5—44no—
396C23×D5C2411yescharacteristic
397C23×D5C2412yes—
398C23×D5C2412yes—
399C23×D5C2414yes—
400C23×D5C2414yes—
401C23×D5C2411yescharacteristic
402C23×D5C2411yescharacteristic
403C23×D5C2418yes—
404C23×D5C2418yes—
405C2×C5×D4—24no—
406C2×C5×D4—28no—
407C2×C5×D4—24no—
408C2×C5×D4—44no—
409C2×C5×D4C2414yes—
410C2×C5×D4C2418yes—
411C2×C5×D4C2414yes—
412C2×C5×D4C2418yes—
413C22×C4×C5—24no—
414C22×C4×C5—24no—
415C22×C4×C5—44no—
416C22×C4×C5—44no—
417C22×C4×C5C2411yescharacteristic
418C22×C4×C5C2411yescharacteristic
419C22×C4×C5C2412yes—
420C22×C4×C5C2412yes—
421C22×C4×C5C2411yescharacteristic
422C22×C4×C5C2411yescharacteristic
423C22×C4×C5C2412yes—
424C22×C4×C5C2414yes—
425C22×C4×C5C2414yes—
426C22×C4×C5C2418yes—
427C22×C4×C5C2418yes—
428C22×C4×C5C2411yescharacteristic
429C2×C22⋊D5—28no—
430C2×C22⋊D5—24no—
431C2×C22⋊D5—28no—
432C2×C22⋊D5—44no—
433C2×C22⋊D5—44no—
434C2×C22⋊D5—44no—
435C2×C22⋊D5—44no—
436C2×C22⋊D5—44no—
437C2×C22⋊D5#4118yescomplemented
438C2×C22⋊D5C2418yes—
439C2×C22⋊D5C2414yes—
440C2×C22⋊D5C2418yes—
441C2×C22⋊D5C2418yes—
442C2×C22⋊D5C2418yes—
443C2×C22⋊D5C2418yes—
444C2×C22⋊D5C2418yes—
445C2×C22⋊D5C2418yes—
446C2×C22⋊D5C2414yes—
447C22×Dic5—42no—
448C22×Dic5—42no—
449C22×Dic5—44no—
450C22×Dic5C2411yescharacteristic
451C22×Dic5C2412yes—
452C22×Dic5C2411yescharacteristic
453C22×Dic5C2412yes—
454C22×Dic5C2411yescharacteristic
455C22×Dic5C2411yescharacteristic
456C22×Dic5C2414yes—
457C22×Dic5C2414yes—
458C22×Dic5C2418yes—
459C22×Dic5C2411yescharacteristic
460#711—416no—
461D4×D5—232no—
462D4×D5—264no—
463D4×D5—416no—
464D4×D5—432no—
465#709—416no—
466#709—432no—
467C2×D20—24no—
468C2×D20—28no—
469C2×D20—28no—
470C2×D20—28no—
471C2×D20—24no—
472C2×D20—24no—
473C2×D20—416no—
474C2×D20—432no—
475C2×D20—44no—
476C2×D20—44no—
477C2×D20—44no—
478C2×D20C2418yes—
479C2×D20C2414yes—
480C2×D20C2414yes—
481C2×D20C2418yes—
482C2×D20C2414yes—
483C2×D20C2418yes—
484C2×D20C2418yes—
485C2×D20C2418yes—
486C2×D20C2418yes—
487C2×C4×D5—24no—
488C2×C4×D5—24no—
489C2×C4×D5—24no—
490C2×C4×D5—24no—
491C2×C4×D5—24no—
492C2×C4×D5—28no—
493C2×C4×D5—416no—
494C2×C4×D5—416no—
495C2×C4×D5—42no—
496C2×C4×D5—42no—
497C2×C4×D5—42no—
498C2×C4×D5—42no—
499C2×C4×D5—44no—
500C2×C4×D5—44no—
501C2×C4×D5—44no—
502C2×C4×D5C2414yes—
503C2×C4×D5C2414yes—
504C2×C4×D5C2414yes—
505C2×C4×D5C2414yes—
506C2×C4×D5C2414yes—
507C2×C4×D5C2418yes—
508C2×C4×D5C2414yes—
509C2×C4×D5C2414yes—
510C2×C4×D5C2414yes—
511C2×C4×D5C2414yes—
512C2×C4×D5C2418yes—
513C2×C4×D5C2418yes—
514C2×C4×D5C2418yes—
515C2×Dic10—24no—
516C2×Dic10—44no—
517C2×Dic10C2414yes—
518C2×Dic10C2418yes—
519C5×C4⋊C4C2414yes—
520C5×C4⋊C4C2414yes—
521C5×C4⋊C4C2418yes—
522C5×C4⋊C4C2414yes—
523C5×C4⋊C4C2418yes—
524C5×C4⋊C4C2414yes—
525C5×C4⋊C4C2418yes—
526C5×C22⋊C4C2418yes—
527C5×C22⋊C4C2414yes—
528C5×C22⋊C4C2418yes—
529C5×C22⋊C4C2418yes—
530C5×C22⋊C4C2414yes—
531C5×C22⋊C4C2418yes—
532C42×C5C2418yes—
533C42×C5C2414yes—
534C22⋊Dic5C2418yes—
535C22⋊Dic5C2414yes—
536C22⋊Dic5C2414yes—
537C22⋊Dic5C2418yes—
538#685C2418yes—
539#685C2418yes—
540#685C2414yes—
541#685C2414yes—
542#685C2418yes—
543#685C2418yes—
544#685C2418yes—
545#685C2418yes—
546#685C2418yes—
547#685C2414yes—
548#685C2418yes—
549#685C2418yes—
550#685C2418yes—
551#685C2418yes—
552#685C2414yes—
553#685C2418yes—
554#685C2418yes—
555C4⋊Dic5C2418yes—
556C4⋊Dic5C2418yes—
557C4⋊Dic5C2414yes—
558C4⋊Dic5C2414yes—
559#683C2414yes—
560#683C2418yes—
561#683C2418yes—
562#683C2414yes—
563#683C2418yes—
564#683C2418yes—
565C4×Dic5C2414yes—
566C4×Dic5C2414yes—
567C4×Dic5C2414yes—
568C4×Dic5C2418yes—
569C4×Dic5C2418yes—
570C22×#41—51no—
571C22×#41—51no—
572C22×#41—52no—
573C23×D4—51no—
574C23×D4—52no—
575C23×D4—51no—
576C23×D4—52no—
577C23×D4—51no—
578C23×D4—52no—
579C24×C4—51no—
580C24×C4—51no—
581#555—516no—
582#554—516no—
583#553—532no—
584#553—516no—
585#553C2×D5116yescomplemented
586#550—516no—
587#546—532no—
588#546—532no—
589#546—516no—
590#546—516no—
591D42—516no—
592D42—532no—
593#540—532no—
594#538—532no—
595#538—532no—
596#532—516no—
597C2×C4⋊Q8—51no—
598C2×#127—51no—
599C2×#127—52no—
600#529—516no—
601C2×#126—52no—
602C2×#126—52no—
603C2×#126C2×D512yescomplemented
604C2×#125—52no—
605C2×#125C2×D511yescharacteristic, complemented
606C2×#124—52no—
607C2×#124—52no—
608C2×#124—51no—
609C2×#124—52no—
610#525—516no—
611#525—516no—
612C2×#123—52no—
613C2×#123—52no—
614C2×#123—52no—
615C2×#123—52no—
616C2×#123—52no—
617C2×#123—52no—
618C2×#123C2×D512yescomplemented
619C2×C22⋊Q8—51no—
620C2×C22⋊Q8—52no—
621C2×C22⋊Q8—52no—
622C2×C22⋊Q8—51no—
623C2×C22⋊Q8—51no—
624C2×#121—51no—
625C2×#121—52no—
626C2×#121—52no—
627C2×#121—51no—
628C2×#121—52no—
629C2×#121—516no—
630C2×#121—51no—
631C2×#121—51no—
632C2×#121—52no—
633C2×#121—52no—
634C2×#121—51no—
635C2×#121—51no—
636C2×#121—51no—
637C2×#121—52no—
638C2×#121—516no—
639C2×#121—52no—
640C2×#121—52no—
641C2×#121—52no—
642C2×#121—52no—
643C2×#121—52no—
644C2×#121—52no—
645C2×#121C2×D511yescharacteristic, complemented
646C2×#121C2×D511yescharacteristic, complemented
647C2×#121C2×D512yescomplemented
648C2×#120—52no—
649C2×#120—52no—
650C2×#120—52no—
651C2×#120—52no—
652C2×#120—52no—
653C2×#120—52no—
654#518—532no—
655C2×C4×Q8—51no—
656C2×C4×D4—51no—
657C2×C4×D4—52no—
658C2×C4×D4—51no—
659C2×C4×D4—52no—
660C2×C4×D4—51no—
661C2×C4×D4—52no—
662C2×C4×D4—516no—
663C2×C4×D4—51no—
664C2×C4×D4—52no—
665C2×C4×D4—52no—
666C2×C4×D4—51no—
667C2×C4×D4—51no—
668C2×C4×D4—51no—
669C2×C4×D4—52no—
670C2×C4×D4—52no—
671C2×C4×D4—51no—
672C2×C4×D4—52no—
673C2×C4×D4—52no—
674C2×C4×D4—51no—
675C2×C4×D4C2×D511yescharacteristic, complemented
676C2×C4×D4C2×D512yescomplemented
677C2×C4×D4C2×D511yescharacteristic, complemented
678C2×#117—52no—
679C2×#117—51no—
680C2×#117—52no—
681C2×#117C2×D511yescharacteristic, complemented
682C22×C4⋊C4—51no—
683C22×C4⋊C4—51no—
684C22×C4⋊C4C2×D511yescharacteristic, complemented
685C22×C22⋊C4—52no—
686C22×C22⋊C4—52no—
687C22×C22⋊C4—51no—
688C22×C22⋊C4—51no—
689C22×C22⋊C4—52no—
690C22×C22⋊C4—52no—
691C22×C42—51no—
692C23×C5—22no—
693C23×C5—22no—
694C23×C5—22no—
695C23×C5—24no—
696C23×C5—22no—
697C23×C5—24no—
698C23×C5—24no—
699C23×C5—22no—
700C23×C5C2×#4114yes—
701C23×C5C2512yes—
702C23×C5C2514yes—
703C23×C5C2512yes—
704C23×C5C2511yescharacteristic
705C22×D5—22no—
706C22×D5—22no—
707C22×D5—22no—
708C22×D5—22no—
709C22×D5—24no—
710C22×D5—22no—
711C22×D5—24no—
712C22×D5—28no—
713C22×D5—22no—
714C22×D5—24no—
715C22×D5—24no—
716C22×D5—24no—
717C22×D5—24no—
718C22×D5—22no—
719C22×D5—216no—
720C22×D5—28no—
721C22×D5—28no—
722C22×D5—28no—
723C22×D5—216no—
724C22×D5—44no—
725C22×D5—44no—
726C22×D5—416no—
727C22×D5—48no—
728C22×D5—48no—
729C22×D5—48no—
730C22×D5—48no—
731C22×D5—416no—
732C22×D5—816no—
733C22×D5—816no—
734C22×D5C2×#4114yes—
735C22×D5H(5,𝔽2)14yes—
736C22×D5C2514yes—
737C22×D5C2512yes—
738C22×D5C2514yes—
739C22×D5C2512yes—
740C22×D5C2512yes—
741C5×D4—28no—
742C5×D4—216no—
743C5×D4—28no—
744C5×D4—48no—
745C2×C4×C5—22no—
746C2×C4×C5—24no—
747C2×C4×C5—24no—
748C2×C4×C5—22no—
749C2×C4×C5—22no—
750C2×C4×C5—22no—
751C2×C4×C5—24no—
752C2×C4×C5—28no—
753C2×C4×C5—28no—
754C2×C4×C5—48no—
755C2×C4×C5—48no—
756C2×C4×C5H(5,𝔽2)14yes—
757C2×C4×C5C2514yes—
758C2×C4×C5C2512yes—
759C2×C4×C5C2514yes—
760C2×C4×C5C2512yes—
761C2×C4×C5C2512yes—
762C2×C4×C5C2514yes—
763C2×C4×C5C2512yes—
764C2×C4×C5C2512yes—
765C22⋊D5—216no—
766C22⋊D5—28no—
767C22⋊D5—216no—
768C22⋊D5—48no—
769C22⋊D5—48no—
770C22⋊D5—48no—
771C22⋊D5—48no—
772C22⋊D5—48no—
773C22⋊D5C2×#41116yescomplemented
774C2×Dic5—24no—
775C2×Dic5—22no—
776C2×Dic5—24no—
777C2×Dic5—22no—
778C2×Dic5—22no—
779C2×Dic5—22no—
780C2×Dic5—44no—
781C2×Dic5—44no—
782C2×Dic5—48no—
783C2×Dic5C2×#4114yes—
784C2×Dic5C2512yes—
785C2×Dic5C2512yes—
786C2×Dic5C2512yes—
787C2×Dic5C2514yes—
788C2×Dic5C2514yes—
789C2×Dic5C2512yes—
790C2×Dic5C2512yes—
791D20—28no—
792D20—216no—
793D20—216no—
794D20—216no—
795D20—28no—
796D20—28no—
797D20—48no—
798D20—48no—
799D20—48no—
800C4×D5—28no—
801C4×D5—28no—
802C4×D5—28no—
803C4×D5—28no—
804C4×D5—28no—
805C4×D5—216no—
806C4×D5—44no—
807C4×D5—44no—
808C4×D5—44no—
809C4×D5—44no—
810C4×D5—48no—
811C4×D5—48no—
812C4×D5—48no—
813Dic10—28no—
814Dic10—48no—
815C25—51no—
816C25—51no—
817C25—52no—
818C25—52no—
819C2×#41—58no—
820C2×#41—58no—
821C2×#41—516no—
822C2×#41—204no—
823C2×#41—208no—
824C2×#41—204no—
825C22×Q8—51no—
826C22×Q8—52no—
827C22×D4—51no—
828C22×D4—51no—
829C22×D4—52no—
830C22×D4—52no—
831C22×D4—52no—
832C22×D4—52no—
833C22×D4—52no—
834C22×D4—52no—
835C22×D4—52no—
836C22×D4—58no—
837C22×D4—516no—
838C22×D4—58no—
839C22×D4—516no—
840C22×D4—51no—
841C22×D4—52no—
842C22×D4—52no—
843C22×D4—52no—
844C22×D4—51no—
845C22×D4—51no—
846C22×D4—52no—
847C22×D4—52no—
848C22×D4—52no—
849C22×D4—58no—
850C22×D4—516no—
851C22×D4—108no—
852C22×D4—1016no—
853C22×D4—204no—
854C22×D4—208no—
855C22×D4—204no—
856C22×D4—208no—
857C22×D4C22×D511yescharacteristic
858C22×D4C22×D512yes—
859C22×D4C22×D511yescharacteristic
860C22×D4C22×D512yes—
861C23×C4—51no—
862C23×C4—52no—
863C23×C4—51no—
864C23×C4—51no—
865C23×C4—51no—
866C23×C4—51no—
867C23×C4—52no—
868C23×C4—51no—
869C23×C4—51no—
870C23×C4—51no—
871C23×C4—51no—
872C23×C4—51no—
873C23×C4—52no—
874C23×C4—52no—
875C23×C4—52no—
876C23×C4—51no—
877C23×C4—58no—
878C23×C4—58no—
879C23×C4—204no—
880C23×C4—204no—
881C23×C4C22×D511yescharacteristic
882C23×C4C22×D511yescharacteristic
883C23×C4C22×D512yes—
884C23×C4C22×D512yes—
885C4⋊Q8—58no—
886#127—58no—
887#127—516no—
888#126—516no—
889#126—516no—
890#126C22×D5116yescomplemented
891#125—516no—
892#125C22×D518yescomplemented
893#124—516no—
894#124—516no—
895#124—58no—
896#124—516no—
897#123—516no—
898#123—516no—
899#123—516no—
900#123—516no—
901#123—516no—
902#123—516no—
903#123C22×D5116yescomplemented
904C22⋊Q8—58no—
905C22⋊Q8—516no—
906C22⋊Q8—58no—
907C22⋊Q8—58no—
908C22⋊Q8—516no—
909#121—58no—
910#121—516no—
911#121—516no—
912#121—58no—
913#121—516no—
914#121—58no—
915#121—58no—
916#121—516no—
917#121—516no—
918#121—58no—
919#121—58no—
920#121—58no—
921#121—516no—
922#121—516no—
923#121—516no—
924#121—516no—
925#121—516no—
926#121—516no—
927#121—516no—
928#121C22×D518yescomplemented
929#121C22×D518yescomplemented
930#121C22×D5116yescomplemented
931#120—516no—
932#120—516no—
933#120—516no—
934#120—516no—
935#120—516no—
936#120—516no—
937C4×Q8—58no—
938C4×D4—58no—
939C4×D4—516no—
940C4×D4—58no—
941C4×D4—58no—
942C4×D4—516no—
943C4×D4—516no—
944C4×D4—58no—
945C4×D4—516no—
946C4×D4—516no—
947C4×D4—58no—
948C4×D4—58no—
949C4×D4—58no—
950C4×D4—516no—
951C4×D4—516no—
952C4×D4—58no—
953C4×D4—516no—
954C4×D4—516no—
955C4×D4—58no—
956C4×D4C22×D518yescomplemented
957C4×D4C22×D5116yescomplemented
958C4×D4C22×D518yescomplemented
959#117—516no—
960#117—58no—
961#117—516no—
962#117C22×D518yescomplemented
963C2×C4⋊C4—51no—
964C2×C4⋊C4—51no—
965C2×C4⋊C4—51no—
966C2×C4⋊C4—51no—
967C2×C4⋊C4—52no—
968C2×C4⋊C4—52no—
969C2×C4⋊C4—52no—
970C2×C4⋊C4—52no—
971C2×C4⋊C4—52no—
972C2×C4⋊C4—52no—
973C2×C4⋊C4—58no—
974C2×C4⋊C4—58no—
975C2×C4⋊C4C22×D511yescharacteristic
976C2×C4⋊C4C22×D511yescharacteristic
977C2×C4⋊C4C22×D511yescharacteristic
978C2×C4⋊C4C22×D512yes—
979C2×C4⋊C4C22×D511yescharacteristic
980C2×C4⋊C4C22×D512yes—
981C2×C4⋊C4C22×D512yes—
982C2×C4⋊C4C22×D518yescomplemented
983C2×C22⋊C4—51no—
984C2×C22⋊C4—52no—
985C2×C22⋊C4—52no—
986C2×C22⋊C4—51no—
987C2×C22⋊C4—51no—
988C2×C22⋊C4—52no—
989C2×C22⋊C4—52no—
990C2×C22⋊C4—52no—
991C2×C22⋊C4—52no—
992C2×C22⋊C4—51no—
993C2×C22⋊C4—52no—
994C2×C22⋊C4—52no—
995C2×C22⋊C4—51no—
996C2×C22⋊C4—52no—
997C2×C22⋊C4—51no—
998C2×C22⋊C4—516no—
999C2×C22⋊C4—516no—
1000C2×C22⋊C4—52no—
1001C2×C22⋊C4—52no—
1002C2×C22⋊C4—52no—
1003C2×C22⋊C4—52no—
1004C2×C22⋊C4—52no—
1005C2×C22⋊C4—52no—
1006C2×C22⋊C4—58no—
1007C2×C22⋊C4—58no—
1008C2×C22⋊C4—516no—
1009C2×C22⋊C4—516no—
1010C2×C22⋊C4C22×D511yescharacteristic
1011C2×C22⋊C4C22×D512yes—
1012C2×C22⋊C4C22×D511yescharacteristic
1013C2×C22⋊C4C22×D512yes—
1014C2×C22⋊C4C22×D512yes—
1015C2×C22⋊C4C22×D512yes—
1016C2×C42—51no—
1017C2×C42—52no—
1018C2×C42—52no—
1019C2×C42—51no—
1020C2×C42—51no—
1021C2×C42—58no—
1022C2×C42C22×D512yes—
1023C2×C42C22×D511yescharacteristic
1024C22×C5—22no—
1025C22×C5—22no—
1026C22×C5—28no—
1027C22×C5—22no—
1028C22×C5—24no—
1029C22×C5—22no—
1030C22×C5—24no—
1031C22×C5—24no—
1032C22×C5—22no—
1033C22×C5—44no—
1034C22×C5—48no—
1035C22×C5C22×#4114yes—
1036C22×C5C22×#4112yes—
1037C22×C5C2×H(5,𝔽2)12yes—
1038C22×C5C2×H(5,𝔽2)12yes—
1039C22×C5C2611yescharacteristic
1040C2×D5—22no—
1041C2×D5—22no—
1042C2×D5—22no—
1043C2×D5—22no—
1044C2×D5—28no—
1045C2×D5—28no—
1046C2×D5—24no—
1047C2×D5—22no—
1048C2×D5—24no—
1049C2×D5—22no—
1050C2×D5—24no—
1051C2×D5—24no—
1052C2×D5—24no—
1053C2×D5—24no—
1054C2×D5—22no—
1055C2×D5—416no—
1056C2×D5—416no—
1057C2×D5—44no—
1058C2×D5—48no—
1059C2×D5—48no—
1060C2×D5—816no—
1061C2×D5—816no—
1062C2×D5C22×#4114yes—
1063C2×D5C2×H(5,𝔽2)14yes—
1064C4×C5—22no—
1065C4×C5—24no—
1066C4×C5—24no—
1067C4×C5—22no—
1068C4×C5—22no—
1069C4×C5—22no—
1070C4×C5—24no—
1071C4×C5C2×H(5,𝔽2)14yes—
1072Dic5—24no—
1073Dic5—22no—
1074Dic5—24no—
1075Dic5—22no—
1076Dic5—22no—
1077Dic5—22no—
1078Dic5C22×#4114yes—
1079C24—51no—
1080C24—51no—
1081C24—52no—
1082C24—51no—
1083C24—52no—
1084C24—54no—
1085C24—54no—
1086C24—58no—
1087C24—58no—
1088C24—104no—
1089C24—104no—
1090C24—104no—
1091C24—108no—
1092C24—104no—
1093C24—108no—
1094C24—202no—
1095C24—202no—
1096C24—204no—
1097C24—204no—
1098C24—204no—
1099C24—204no—
1100C24C23×D511yescharacteristic
1101C24C23×D512yes—
1102C24C23×D511yescharacteristic
1103#41—2016no—
1104#41—2032no—
1105#41—2016no—
1106C2×Q8—54no—
1107C2×Q8—58no—
1108C2×Q8—104no—
1109C2×Q8—204no—
1110C2×D4—24no—
1111C2×D4—28no—
1112C2×D4—24no—
1113C2×D4—44no—
1114C2×D4—58no—
1115C2×D4—54no—
1116C2×D4—54no—
1117C2×D4—58no—
1118C2×D4—58no—
1119C2×D4—58no—
1120C2×D4—58no—
1121C2×D4—58no—
1122C2×D4—58no—
1123C2×D4—58no—
1124C2×D4—54no—
1125C2×D4—58no—
1126C2×D4—58no—
1127C2×D4—58no—
1128C2×D4—54no—
1129C2×D4—54no—
1130C2×D4—58no—
1131C2×D4—58no—
1132C2×D4—58no—
1133C2×D4—104no—
1134C2×D4—108no—
1135C2×D4—108no—
1136C2×D4—108no—
1137C2×D4—104no—
1138C2×D4—108no—
1139C2×D4—1032no—
1140C2×D4—1064no—
1141C2×D4—108no—
1142C2×D4—104no—
1143C2×D4—104no—
1144C2×D4—2016no—
1145C2×D4—204no—
1146C2×D4—204no—
1147C2×D4—204no—
1148C2×D4—2032no—
1149C2×D4—2016no—
1150C2×D4—204no—
1151C2×D4—204no—
1152C2×D4—204no—
1153C2×D4—204no—
1154C2×D4—204no—
1155C2×D4—2032no—
1156C2×D4C23×D514yes—
1157C2×D4C23×D518yes—
1158C2×D4C23×D514yes—
1159C2×D4C23×D518yes—
1160C22×C4—24no—
1161C22×C4—24no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—51no—
1165C22×C4—51no—
1166C22×C4—51no—
1167C22×C4—51no—
1168C22×C4—52no—
1169C22×C4—52no—
1170C22×C4—51no—
1171C22×C4—54no—
1172C22×C4—58no—
1173C22×C4—54no—
1174C22×C4—54no—
1175C22×C4—54no—
1176C22×C4—54no—
1177C22×C4—54no—
1178C22×C4—58no—
1179C22×C4—54no—
1180C22×C4—54no—
1181C22×C4—54no—
1182C22×C4—54no—
1183C22×C4—58no—
1184C22×C4—58no—
1185C22×C4—58no—
1186C22×C4—54no—
1187C22×C4—104no—
1188C22×C4—108no—
1189C22×C4—104no—
1190C22×C4—104no—
1191C22×C4—104no—
1192C22×C4—104no—
1193C22×C4—2016no—
1194C22×C4—2016no—
1195C22×C4—202no—
1196C22×C4—202no—
1197C22×C4—202no—
1198C22×C4—202no—
1199C22×C4—204no—
1200C22×C4—204no—
1201C22×C4—204no—
1202C22×C4—202no—
1203C22×C4—202no—
1204C22×C4—204no—
1205C22×C4C23×D514yes—
1206C22×C4C23×D514yes—
1207C22×C4C23×D512yes—
1208C22×C4C23×D511yescharacteristic
1209C22×C4C23×D511yescharacteristic
1210C22×C4C23×D512yes—
1211C22×C4C23×D511yescharacteristic
1212C22×C4C23×D512yes—
1213C22×C4C23×D511yescharacteristic
1214C22×C4C23×D518yes—
1215C22×C4C23×D518yes—
1216C22×C4C23×D511yescharacteristic
1217C4⋊C4—54no—
1218C4⋊C4—54no—
1219C4⋊C4—54no—
1220C4⋊C4—54no—
1221C4⋊C4—58no—
1222C4⋊C4—58no—
1223C4⋊C4—58no—
1224C4⋊C4—58no—
1225C4⋊C4—58no—
1226C4⋊C4—58no—
1227C4⋊C4C23×D514yes—
1228C4⋊C4C23×D514yes—
1229C4⋊C4C23×D514yes—
1230C4⋊C4C23×D518yes—
1231C4⋊C4C23×D514yes—
1232C4⋊C4C23×D518yes—
1233C4⋊C4C23×D518yes—
1234C22⋊C4—54no—
1235C22⋊C4—58no—
1236C22⋊C4—58no—
1237C22⋊C4—54no—
1238C22⋊C4—54no—
1239C22⋊C4—58no—
1240C22⋊C4—58no—
1241C22⋊C4—58no—
1242C22⋊C4—58no—
1243C22⋊C4—54no—
1244C22⋊C4—58no—
1245C22⋊C4—58no—
1246C22⋊C4—54no—
1247C22⋊C4—58no—
1248C22⋊C4—54no—
1249C22⋊C4—58no—
1250C22⋊C4—58no—
1251C22⋊C4—58no—
1252C22⋊C4—58no—
1253C22⋊C4—58no—
1254C22⋊C4—58no—
1255C22⋊C4C23×D514yes—
1256C22⋊C4C23×D518yes—
1257C22⋊C4C23×D514yes—
1258C22⋊C4C23×D518yes—
1259C22⋊C4C23×D518yes—
1260C22⋊C4C23×D518yes—
1261C42—54no—
1262C42—54no—
1263C42—54no—
1264C42—58no—
1265C42—58no—
1266C42C23×D514yes—
1267C42C23×D518yes—
1268C2×C5—24no—
1269C2×C5—42no—
1270C2×C5—44no—
1271C2×C5#351914yescomplemented
1272C2×C5C23×#4111yescharacteristic
1273C2×C5C22×H(5,𝔽2)11yescharacteristic
1274C2×C5C22×H(5,𝔽2)11yescharacteristic
1275D5—24no—
1276D5—24no—
1277D5—42no—
1278D5—44no—
1279D5—44no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23—24no—
1284C23—22no—
1285C23—24no—
1286C23—24no—
1287C23—22no—
1288C23—54no—
1289C23—54no—
1290C23—52no—
1291C23—52no—
1292C23—54no—
1293C23—52no—
1294C23—54no—
1295C23—108no—
1296C23—108no—
1297C23—108no—
1298C23—1016no—
1299C23—102no—
1300C23—102no—
1301C23—102no—
1302C23—102no—
1303C23—104no—
1304C23—108no—
1305C23—102no—
1306C23—104no—
1307C23—102no—
1308C23—104no—
1309C23—104no—
1310C23—104no—
1311C23—104no—
1312C23—102no—
1313C23—1016no—
1314C23—204no—
1315C23—204no—
1316C23—208no—
1317C23—208no—
1318C23—208no—
1319C23—208no—
1320C23—2016no—
1321C23—2016no—
1322C23—4016no—
1323C23—4016no—
1324C23D5×#4114yes—
1325C23C24×D512yes—
1326C23C24×D514yes—
1327C23C24×D512yes—
1328C23C24×D511yescharacteristic
1329Q8—108no—
1330Q8—208no—
1331D4—28no—
1332D4—216no—
1333D4—28no—
1334D4—48no—
1335D4—516no—
1336D4—108no—
1337D4—1016no—
1338D4—1016no—
1339D4—1016no—
1340D4—108no—
1341D4—1016no—
1342D4—1016no—
1343D4—108no—
1344D4—108no—
1345D4—208no—
1346D4—208no—
1347D4—208no—
1348D4—208no—
1349D4—208no—
1350D4—208no—
1351D4—208no—
1352D4—208no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—24no—
1360C2×C4—28no—
1361C2×C4—28no—
1362C2×C4—48no—
1363C2×C4—48no—
1364C2×C4—54no—
1365C2×C4—52no—
1366C2×C4—52no—
1367C2×C4—52no—
1368C2×C4—52no—
1369C2×C4—54no—
1370C2×C4—54no—
1371C2×C4—52no—
1372C2×C4—108no—
1373C2×C4—1016no—
1374C2×C4—108no—
1375C2×C4—102no—
1376C2×C4—102no—
1377C2×C4—102no—
1378C2×C4—104no—
1379C2×C4—102no—
1380C2×C4—104no—
1381C2×C4—108no—
1382C2×C4—108no—
1383C2×C4—108no—
1384C2×C4—204no—
1385C2×C4—204no—
1386C2×C4—204no—
1387C2×C4—204no—
1388C2×C4—208no—
1389C2×C4—208no—
1390C2×C4—208no—
1391C2×C4—204no—
1392C2×C4—204no—
1393C2×C4—208no—
1394C2×C4#414914yes—
1395C2×C4C24×D512yes—
1396C2×C4C24×D514yes—
1397C2×C4C24×D512yes—
1398C2×C4C24×D514yes—
1399C2×C4C24×D512yes—
1400C2×C4C24×D514yes—
1401C2×C4C24×D512yes—
1402C2×C4C24×D512yes—
1403C5C2×#351911yescharacteristic, complemented, Sylow
1404C22—22no—
1405C22—22no—
1406C22—28no—
1407C22—22no—
1408C22—24no—
1409C22—22no—
1410C22—24no—
1411C22—24no—
1412C22—22no—
1413C22—44no—
1414C22—48no—
1415C22—54no—
1416C22—54no—
1417C22—102no—
1418C22—102no—
1419C22—102no—
1420C22—102no—
1421C22—108no—
1422C22—108no—
1423C22—104no—
1424C22—102no—
1425C22—104no—
1426C22—102no—
1427C22—104no—
1428C22—104no—
1429C22—104no—
1430C22—104no—
1431C22—102no—
1432C22—2016no—
1433C22—2016no—
1434C22—204no—
1435C22—208no—
1436C22—208no—
1437C22—4016no—
1438C22—4016no—
1439C22C2×D5×#4114yes—
1440C22C2×D5×#4112yes—
1441C22C2×#414912yes—
1442C22D5×H(5,𝔽2)12yes—
1443C22C25×D511yescharacteristic
1444C4—22no—
1445C4—24no—
1446C4—22no—
1447C4—22no—
1448C4—22no—
1449C4—24no—
1450C4—24no—
1451C4—54no—
1452C4—102no—
1453C4—102no—
1454C4—102no—
1455C4—104no—
1456C4—102no—
1457C4—104no—
1458C4C2×#414914yes—
1459C2—24no—
1460C2—42no—
1461C2—44no—
1462C2—104no—
1463C2—104no—
1464C2—202no—
1465C2—204no—
1466C2—204no—
1467C2#1061878814yesdirect product factor
1468C2C22×D5×#4111yescharacteristic
1469C2C22×#414911yescharacteristic
1470C2C2×D5×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#553C2
socleC23×C5C25
hypercenterC2×#553D5
hypocenterC5C2×#3519
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×C5×#553C2semidirect
2. #10618788C2direct (N × H)
3. C2×#66038C2semidirect
4. C2×#66043C2semidirect
5. C2×#66029C2semidirect
6. C2×#66025C2semidirect
7. C2×#65988C2semidirect
8. C2×#65997C2semidirect
9. C2×#65943C2semidirect
10. C2×#65943C2semidirect
11. C2×#65951C2semidirect
12. C2×D5×#121C2semidirect
13. C2×#65933C2semidirect
14. C2×#65940C2semidirect
15. C2×#65884C2semidirect
16. C2×#65884C2semidirect
17. C2×#65888C2semidirect
18. C2×#65882C2semidirect
19. C2×#65879C2semidirect
20. C2×C4×D4×D5C2semidirect
21. C2×#65866C2semidirect
22. C2×#65858C2semidirect
23. C22×#4041C2semidirect
24. C2×#65845C2semidirect
25. C22×#711C22semidirect
28. C22×D4×D5C22semidirect
29. C22×D4×D5C22semidirect
30. C22×#709C22semidirect
31. C22×#709C22semidirect
32. C23×D20C22semidirect
33. C23×D20C22semidirect
34. C23×C4×D5C22semidirect
35. C23×C4×D5C22semidirect
36. C5×#553C22semidirect
37. C2×C5×#126C22semidirect
38. C2×C5×#125C22semidirect
39. C2×C5×#123C22semidirect
40. C2×C5×#121C22semidirect
41. C2×C5×#121C22semidirect
42. C2×C5×#121C22semidirect
43. C2×C4×C5×D4C22semidirect
44. C2×C4×C5×D4C22semidirect
45. C2×C4×C5×D4C22semidirect
46. C2×C5×#117C22semidirect
47. C22×C5×C4⋊C4C22semidirect
48. C2×#4086C22semidirect
49. C2×#4086C22semidirect
50. C2×#4085C22semidirect
51. C2×#4085C22semidirect
52. C2×#4084C22semidirect
53. C2×#4083C22semidirect
54. C2×#4083C22semidirect
55. C2×#4083C22semidirect
56. C2×D4×Dic5C22semidirect
57. C2×D4×Dic5C22semidirect
58. C2×#4076C22semidirect
59. C2×#4076C22semidirect
62. C2×C4×C22⋊D5C22semidirect
63. C2×C4×C22⋊D5C22semidirect
64. C22×#685C22semidirect
65. C22×#685C22semidirect
66. C2×#4070C22semidirect
67. C2×#4070C22semidirect
68. #66043C22semidirect
69. #66038C22semidirect
70. #66029C22semidirect
71. #66025C22semidirect
72. #65997C22semidirect
73. #65988C22semidirect
74. #65951C22semidirect
75. #65943C22semidirect
76. #65943C22semidirect
77. #65940C22semidirect
78. D5×#121C22semidirect
79. #65933C22semidirect
80. #65888C22semidirect
81. #65884C22semidirect
82. #65884C22semidirect
83. #65882C22semidirect
84. #65879C22semidirect
85. C4×D4×D5C22semidirect
86. #65866C22semidirect
87. #65858C22semidirect
88. C2×#4044C22semidirect
89. C2×#4044C22semidirect
90. #65845C22semidirect
91. C2×#4043C22semidirect
92. C2×#4043C22semidirect
93. C2×#4042C22semidirect
95. C2×#4041C22semidirect
96. C2×#4041C22semidirect
97. C2×#4041C22semidirect
98. C2×#4041C22semidirect
99. C2×#4041C22semidirect
100. C2×#4041C22semidirect
101. C2×#4041C22semidirect
102. C2×#4041C22semidirect
103. C2×#4040C22semidirect
104. C2×#4040C22semidirect
105. C2×#4040C22semidirect
106. C2×#4039C22semidirect
107. C2×#4039C22semidirect
108. C2×#4039C22semidirect
109. C2×#4039C22semidirect
110. C2×#4038C22semidirect
111. C2×#4038C22semidirect
112. C2×D5×C4⋊C4C22semidirect
113. C2×D5×C4⋊C4C22semidirect
114. C2×#4035C22semidirect
115. C2×#4034C22semidirect
116. C2×#4033C22semidirect
117. C2×#4032C22semidirect
118. C2×#4032C22semidirect
119. C2×#4031C22semidirect
120. C2×#4031C22semidirect
121. C2×#4030C22semidirect
122. C2×#4030C22semidirect
123. C2×#4030C22semidirect
124. C2×#4030C22semidirect
125. C2×#4030C22semidirect
126. C2×#4030C22semidirect
127. C2×#4029C22semidirect
128. C2×#4028C22semidirect
129. C2×#4028C22semidirect
130. C2×#4028C22semidirect
132. C2×#4027C22semidirect
133. C2×#4027C22semidirect
134. C2×#4027C22semidirect
135. C2×D5×C22⋊C4C22semidirect
136. C2×D5×C22⋊C4C22semidirect
137. C2×D5×C22⋊C4C22semidirect
138. C2×D5×C22⋊C4C22semidirect
139. C2×#4021C22semidirect
140. C2×#4021C22semidirect
141. C2×C4×D20C22semidirect
142. C2×C4×D20C22semidirect
143. C2×C4×D20C22semidirect
144. C2×C4×D20C22semidirect
145. C2×#4018C22semidirect
146. C2×C42×D5C22semidirect
173. C2×#711C23semidirect
180. C2×D4×D5C23semidirect
181. C2×D4×D5C23semidirect
184. C2×#709C23semidirect
185. C2×#709C23semidirect
197. C22×D20C23semidirect
198. C22×D20C23semidirect
214. C22×C4×D5C23semidirect
215. C22×C4×D5C23semidirect
218. C5×#126C23semidirect
219. C5×#125C23semidirect
220. C5×#123C23semidirect
221. C5×#121C23semidirect
222. C5×#121C23semidirect
223. C5×#121C23semidirect
224. C4×C5×D4C23semidirect
225. C4×C5×D4C23semidirect
226. C4×C5×D4C23semidirect
227. C5×#117C23semidirect
235. C2×C5×C4⋊C4C23semidirect
248. #4086C23semidirect
249. #4086C23semidirect
250. #4085C23semidirect
251. #4085C23semidirect
252. #4084C23semidirect
253. #4083C23semidirect
254. #4083C23semidirect
255. #4083C23semidirect
256. D4×Dic5C23semidirect
257. D4×Dic5C23semidirect
258. #4076C23semidirect
259. #4076C23semidirect
262. C4×C22⋊D5C23semidirect
263. C4×C22⋊D5C23semidirect
281. C2×#685C23semidirect
282. C2×#685C23semidirect
287. #4070C23semidirect
288. #4070C23semidirect
300. #4044C23semidirect
301. #4044C23semidirect
302. #4043C23semidirect
303. #4043C23semidirect
304. #4042C23semidirect
306. #4041C23semidirect
307. #4041C23semidirect
308. #4041C23semidirect
309. #4041C23semidirect
310. #4041C23semidirect
311. #4041C23semidirect
312. #4041C23semidirect
313. #4040C23semidirect
314. #4040C23semidirect
315. #4040C23semidirect
316. #4039C23semidirect
317. #4039C23semidirect
318. #4039C23semidirect
319. #4039C23semidirect
320. #4038C23semidirect
321. #4038C23semidirect
322. D5×C4⋊C4C23semidirect
323. D5×C4⋊C4C23semidirect
324. #4035C23semidirect
325. #4034C23semidirect
326. #4033C23semidirect
327. #4032C23semidirect
328. #4032C23semidirect
329. #4031C23semidirect
330. #4031C23semidirect
331. #4030C23semidirect
332. #4030C23semidirect
333. #4030C23semidirect
334. #4030C23semidirect
335. #4030C23semidirect
336. #4030C23semidirect
337. #4029C23semidirect
338. #4028C23semidirect
339. #4028C23semidirect
340. #4028C23semidirect
342. #4027C23semidirect
343. #4027C23semidirect
344. #4027C23semidirect
345. D5×C22⋊C4C23semidirect
346. D5×C22⋊C4C23semidirect
347. D5×C22⋊C4C23semidirect
348. D5×C22⋊C4C23semidirect
349. #4021C23semidirect
350. #4021C23semidirect
351. C4×D20C23semidirect
352. C4×D20C23semidirect
353. C4×D20C23semidirect
354. C4×D20C23semidirect
355. #4018C23semidirect
356. C42×D5C23semidirect
362. C2×#553D5semidirect
437. C2×C22⋊D5#41semidirect
585. #553C2×D5semidirect
603. C2×#126C2×D5semidirect
605. C2×#125C2×D5semidirect
618. C2×#123C2×D5semidirect
645. C2×#121C2×D5semidirect
646. C2×#121C2×D5semidirect
647. C2×#121C2×D5semidirect
675. C2×C4×D4C2×D5semidirect
676. C2×C4×D4C2×D5semidirect
677. C2×C4×D4C2×D5semidirect
681. C2×#117C2×D5semidirect
684. C22×C4⋊C4C2×D5semidirect
773. C22⋊D5C2×#41semidirect
890. #126C22×D5semidirect
892. #125C22×D5semidirect
903. #123C22×D5semidirect
928. #121C22×D5semidirect
929. #121C22×D5semidirect
930. #121C22×D5semidirect
956. C4×D4C22×D5semidirect
957. C4×D4C22×D5semidirect
958. C4×D4C22×D5semidirect
962. #117C22×D5semidirect
982. C2×C4⋊C4C22×D5semidirect
1271. C2×C5#3519semidirect
1403. C5C2×#3519semidirect
1467. C2#10618788direct (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
#106187882
C2×#660382
C2×#660432
C2×#660292
C2×#660252
C2×#659882
C2×#659972
C2×#659432
C2×#659512
C2×D5×#1212
C2×#659332
C2×#659402
C2×#658842
C2×#658882
C2×#658822
C2×#658792
C2×C4×D4×D52
C2×#658662
C2×#658582
C22×#40412
C2×#658452
C2×#35195