Finite Group Databasebeta

← C2×#10617947 #13007283

Subgroups — C2×#10617947 #13007283

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×#525C211yesmaximal, characteristic, complemented
2C2×#66168C211yesmaximal, characteristic, complemented
3C2×#66163C211yesmaximal, characteristic, complemented
4C22×#4076C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
6#10617947C2132yesmaximal, direct product factor
7C2×#65991C212yesmaximal, complemented
8C2×#65997C212yesmaximal, complemented
9C2×#65964C211yesmaximal, characteristic, complemented
10C2×#65969C211yesmaximal, characteristic, complemented
11C2×#65958C211yesmaximal, characteristic, complemented
12C2×#65961C211yesmaximal, characteristic, complemented
13C2×#65943C211yesmaximal, characteristic, complemented
14C2×D5×#121C211yesmaximal, characteristic, complemented
15C2×#65952C211yesmaximal, characteristic, complemented
16C2×#65930C211yesmaximal, characteristic, complemented
17C2×#65925C212yesmaximal, complemented
18C2×#65924C212yesmaximal, complemented
19C2×#65888C212yesmaximal, complemented
20C2×#65894C212yesmaximal, complemented
21C2×#65879C212yesmaximal, complemented
22C2×#65874C212yesmaximal, complemented
23C2×#65866C211yesmaximal, characteristic, complemented
24C2×#65864C211yesmaximal, characteristic, complemented
25C22×C5×#41C2211yescharacteristic, complemented
26C24×C4×C5C2211yescharacteristic, complemented
27C23×C22⋊D5C2211yescharacteristic
28C23×C22⋊D5C2212yescomplemented
29C22×#713C2211yescharacteristic, complemented
30C22×#711C2212yescomplemented
31C22×D4×D5C2212yes—
32C22×D4×D5C2211yescharacteristic, complemented
33C22×D4×D5C2212yescomplemented
34C23×D20C2211yescharacteristic, complemented
35C23×C4×D5C2211yescharacteristic, complemented
36C5×#525C22116yescomplemented
37C2×C5×#123C2212yescomplemented
38C2×C5×C22⋊Q8C2211yescharacteristic, complemented
39C2×C5×C22⋊Q8C2211yescharacteristic, complemented
40C2×C5×#121C2211yescharacteristic, complemented
41C2×C5×#121C2211yescharacteristic, complemented
42C2×C5×#120C2212yescomplemented
43C2×C4×C5×D4C2212yescomplemented
44C2×C4×C5×D4C2212yescomplemented
45C2×C5×#117C2211yescharacteristic, complemented
46C22×C22⋊Dic5C2211yescharacteristic, complemented
47#66168C22116yescomplemented
48#66163C22116yescomplemented
49C2×#4093C2211yescharacteristic, complemented
50C2×#4092C2211yescharacteristic, complemented
51C2×Q8×Dic5C2211yescharacteristic, complemented
52C2×#4086C2212yescomplemented
53C2×#4086C2211yescharacteristic, complemented
54C2×#4085C2212yescomplemented
55C2×#4085C2212yescomplemented
56C2×#4085C2212yescomplemented
57C2×#4085C2212yescomplemented
58C2×#4084C2212yescomplemented
59C2×#4084C2211yescharacteristic, complemented
60C2×#4083C2212yescomplemented
61C2×#4083C2212yescomplemented
62C2×D4×Dic5C2211yescharacteristic, complemented
63C2×D4×Dic5C2212yescomplemented
64C2×#4076C2211yescharacteristic
65C2×#4076C2211yescharacteristic, complemented
66C2×#4076C2211yescharacteristic, complemented
67C2×#4076C2211yescharacteristic, complemented
68C2×#4076C2212yescomplemented
69C2×#4076C2212yescomplemented
70C2×#4076C2212yescomplemented
71C2×#4076C22116yescomplemented
72C2×#4075C2212yescomplemented
73C2×C4×C22⋊D5C2211yescharacteristic
74C2×C4×C22⋊D5C2211yescharacteristic
75C2×C4×C22⋊D5C2211yescharacteristic, complemented
76C2×C4×C22⋊D5C2211yescharacteristic, complemented
77C2×C4×C22⋊D5C2211yescharacteristic, complemented
78C2×C4×C22⋊D5C2212yescomplemented
79C2×C4×C22⋊D5C2211yescharacteristic, complemented
80C2×C4×C22⋊D5C2211yescharacteristic, complemented
81C2×C4×C22⋊D5C2211yescharacteristic, complemented
82C2×C4×C22⋊D5C22116yescomplemented
83C22×#685C2212yescomplemented
84C22×#685C2212yescomplemented
85C22×#685C2211yescharacteristic, complemented
86C22×C4⋊Dic5C2211yescharacteristic, complemented
87C22×#683C2211yescharacteristic, complemented
88C22×C4×Dic5C2211yescharacteristic, complemented
89#65997C22132yescomplemented
90#65991C22132yescomplemented
91#65969C22116yescomplemented
92#65964C22116yescomplemented
93#65961C22116yescomplemented
94#65958C22116yescomplemented
95#65952C22116yescomplemented
96#65943C22116yescomplemented
97D5×#121C22116yescomplemented
98#65930C22116yescomplemented
99#65925C22132yescomplemented
100#65924C22132yescomplemented
101#65894C22132yescomplemented
102#65888C22132yescomplemented
103#65879C22132yescomplemented
104#65874C22132yescomplemented
105#65866C22116yescomplemented
106#65864C22116yescomplemented
107C2×#4044C2212yescomplemented
108C2×#4043C2212yescomplemented
109C2×#4041C2211yescharacteristic, complemented
110C2×#4041C2212yescomplemented
111C2×#4041C2211yescharacteristic, complemented
112C2×#4040C2212yescomplemented
113C2×#4040C2212yescomplemented
114C2×#4039C2212yescomplemented
115C2×#4039C2211yescharacteristic, complemented
116C2×#4039C2211yescharacteristic, complemented
117C2×#4038C2211yescharacteristic, complemented
118C2×#4038C2212yescomplemented
119C2×D5×C4⋊C4C2211yescharacteristic, complemented
120C2×#4036C2211yescharacteristic, complemented
121C2×#4035C2212yescomplemented
122C2×#4034C2211yescharacteristic, complemented
123C2×#4032C2212yescomplemented
124C2×#4032C2212yescomplemented
125C2×#4031C2212yescomplemented
126C2×#4031C2212yescomplemented
127C2×#4030C2212yescomplemented
128C2×#4030C2212yescomplemented
129C2×#4030C2212yescomplemented
130C2×#4030C2212yescomplemented
131C2×#4029C2212yescomplemented
132C2×#4028C2212yescomplemented
133C2×#4028C2212yescomplemented
134C2×#4028C2212yescomplemented
135C2×#4027C2212yes—
136C2×#4027C2212yescomplemented
137C2×#4027C2212yescomplemented
138C2×#4027C2212yescomplemented
139C2×D5×C22⋊C4C2212yescomplemented
140C2×D5×C22⋊C4C2212yescomplemented
141C2×#4025C2212yescomplemented
142C2×#4024C2212yescomplemented
143C2×#4022C2212yescomplemented
144C2×#4021C2212yescomplemented
145C2×C4×D20C2212yescomplemented
146C2×#4018C2212yescomplemented
147C2×#3519—51nomaximal, Sylow
148C25×C5C2311yescharacteristic
149C24×D5C2311yescharacteristic
150C24×D5C2312yes—
151C24×D5C2312yes—
152C2×C5×#41—44no—
153C2×C5×#41C2318yescomplemented
154C22×C5×Q8C2311yescharacteristic
155C22×C5×D4C2312yes—
156C22×C5×D4C2311yescharacteristic
157C22×C5×D4C2312yes—
158C22×C5×D4C2312yes—
159C23×C4×C5—44no—
160C23×C4×C5C2311yescharacteristic
161C23×C4×C5C2311yescharacteristic
162C23×C4×C5C2311yescharacteristic
163C23×C4×C5C2311yescharacteristic
164C23×C4×C5C2311yescharacteristic
165C23×C4×C5C2312yes—
166C23×C4×C5C2311yescharacteristic
167C23×C4×C5C2318yescomplemented
168C22×C22⋊D5—28no—
169C22×C22⋊D5—48no—
170C22×C22⋊D5C2312yes—
171C22×C22⋊D5C2312yes—
172C22×C22⋊D5C2312yes—
173C22×C22⋊D5C2311yescharacteristic
174C22×C22⋊D5C2311yescharacteristic
175C22×C22⋊D5C2311yescharacteristic
176C22×C22⋊D5C2318yes—
177C22×C22⋊D5C2312yes—
178C22×C22⋊D5C2312yes—
179C22×C22⋊D5C2312yes—
180C22×C22⋊D5C2312yes—
181C22×C22⋊D5C2312yes—
182C22×C22⋊D5C2311yescharacteristic
183C22×C22⋊D5C23116yescomplemented
184C23×Dic5C2311yescharacteristic
185C23×Dic5C2311yescharacteristic
186C23×Dic5C2312yes—
187C23×Dic5C2311yescharacteristic
188C23×Dic5C2312yes—
189C2×#713—44no—
190C2×#713C2318yescomplemented
191C2×#711—48no—
192C2×#711C23116yescomplemented
193C2×D4×D5—216no—
194C2×D4×D5—44no—
195C2×D4×D5—48no—
196C2×D4×D5C23116yes—
197C2×D4×D5C23116yescomplemented
198C2×D4×D5C2318yescomplemented
199C22×D20—44no—
200C22×D20C2312yes—
201C22×D20C2311yescharacteristic
202C22×D20C2311yescharacteristic
203C22×D20C2312yes—
204C22×D20C2312yes—
205C22×D20C2312yes—
206C22×D20C2318yescomplemented
207C22×C4×D5—44no—
208C22×C4×D5C2312yes—
209C22×C4×D5C2311yescharacteristic
210C22×C4×D5C2311yescharacteristic
211C22×C4×D5C2312yes—
212C22×C4×D5C2312yes—
213C22×C4×D5C2311yescharacteristic
214C22×C4×D5C2312yes—
215C22×C4×D5C2311yescharacteristic
216C22×C4×D5C2318yescomplemented
217C22×Dic10C2312yes—
218C5×#123C23116yescomplemented
219C5×C22⋊Q8C2318yescomplemented
220C5×C22⋊Q8C2318yescomplemented
221C5×#121C2318yescomplemented
222C5×#121C2318yescomplemented
223C5×#120C23116yescomplemented
224C4×C5×D4C23116yescomplemented
225C4×C5×D4C23116yescomplemented
226C5×#117C2318yescomplemented
227C2×C5×C4⋊C4C2311yescharacteristic
228C2×C5×C4⋊C4C2312yes—
229C2×C5×C4⋊C4C2311yescharacteristic
230C2×C5×C4⋊C4C2312yes—
231C2×C5×C22⋊C4C2312yes—
232C2×C5×C22⋊C4C2312yes—
233C2×C5×C22⋊C4C2312yes—
234C2×C5×C22⋊C4C2312yes—
235C2×C5×C22⋊C4C2312yes—
236C2×C42×C5C2312yes—
237C2×C22⋊Dic5C2311yescharacteristic
238C2×C22⋊Dic5C2312yes—
239C2×C22⋊Dic5C2312yes—
240C2×C22⋊Dic5C2311yescharacteristic
241C2×C22⋊Dic5C2311yescharacteristic
242C2×C22⋊Dic5C2311yescharacteristic
243C2×C22⋊Dic5C2318yescomplemented
244#4093C2318yescomplemented
245#4092C2318yescomplemented
246Q8×Dic5C2318yescomplemented
247#4086C23116yescomplemented
248#4086C2318yescomplemented
249#4085C23116yescomplemented
250#4085C23116yescomplemented
251#4085C23116yescomplemented
252#4085C23116yescomplemented
253#4084C23116yescomplemented
254#4084C2318yescomplemented
255#4083C23116yescomplemented
256#4083C23116yescomplemented
257D4×Dic5C23116yescomplemented
258D4×Dic5C2318yescomplemented
259#4076C2318yes—
260#4076C2318yescomplemented
261#4076C2318yescomplemented
262#4076C23116yescomplemented
263#4076C2318yescomplemented
264#4076C23116yescomplemented
265#4076C23116yescomplemented
266#4075C23116yescomplemented
267C4×C22⋊D5C2318yes—
268C4×C22⋊D5C2318yes—
269C4×C22⋊D5C2318yescomplemented
270C4×C22⋊D5C2318yescomplemented
271C4×C22⋊D5C2318yescomplemented
272C4×C22⋊D5C2318yescomplemented
273C4×C22⋊D5C2318yescomplemented
274C4×C22⋊D5C2318yescomplemented
275C4×C22⋊D5C23116yescomplemented
276C2×#685C2312yes—
277C2×#685C2312yes—
278C2×#685C2311yescharacteristic
279C2×#685C2312yes—
280C2×#685C2311yescharacteristic
281C2×#685C2312yes—
282C2×#685C2312yes—
283C2×#685C2312yes—
284C2×#685C2312yes—
285C2×#685C2312yes—
286C2×#685C2312yes—
287C2×#685C2312yes—
288C2×#685C2312yes—
289C2×#685C2312yes—
290C2×#685C2311yescharacteristic
291C2×#685C2311yescharacteristic
292C2×#685C2318yescomplemented
293C2×#685C23116yescomplemented
294C2×#685C23116yescomplemented
295C2×C4⋊Dic5C2312yes—
296C2×C4⋊Dic5C2312yes—
297C2×C4⋊Dic5C2312yes—
298C2×C4⋊Dic5C2311yescharacteristic
299C2×C4⋊Dic5C2311yescharacteristic
300C2×C4⋊Dic5C2318yescomplemented
301C2×#683C2311yescharacteristic
302C2×#683C2312yes—
303C2×#683C2311yescharacteristic
304C2×#683C2312yes—
305C2×#683C2312yes—
306C2×#683C2312yes—
307C2×#683C2311yescharacteristic
308C2×#683C2311yescharacteristic
309C2×#683C2318yescomplemented
310C2×C4×Dic5C2312yes—
311C2×C4×Dic5C2312yes—
312C2×C4×Dic5C2311yescharacteristic
313C2×C4×Dic5C2311yescharacteristic
314C2×C4×Dic5C2311yescharacteristic
315C2×C4×Dic5C2311yescharacteristic
316C2×C4×Dic5C2318yescomplemented
317#4044C23116yescomplemented
318#4043C23116yescomplemented
319#4041C2318yescomplemented
320#4041C2318yescomplemented
321#4041C23116yescomplemented
322#4040C23116yescomplemented
323#4040C23116yescomplemented
324#4039C2318yescomplemented
325#4039C2318yescomplemented
326#4039C23116yescomplemented
327#4038C2318yescomplemented
328#4038C23116yescomplemented
329D5×C4⋊C4C2318yescomplemented
330#4036C2318yescomplemented
331#4035C23116yescomplemented
332#4034C2318yescomplemented
333#4032C23116yescomplemented
334#4032C23116yescomplemented
335#4031C23116yescomplemented
336#4031C23116yescomplemented
337#4030C23116yescomplemented
338#4030C23116yescomplemented
339#4030C23116yescomplemented
340#4030C23116yescomplemented
341#4029C23116yescomplemented
342#4028C23116yescomplemented
343#4028C23116yescomplemented
344#4028C23116yescomplemented
345#4027C23116yes—
346#4027C23116yescomplemented
347#4027C23116yescomplemented
348#4027C23116yescomplemented
349D5×C22⋊C4C23116yescomplemented
350D5×C22⋊C4C23116yescomplemented
351#4025C23116yescomplemented
352#4024C23116yescomplemented
353#4022C23116yescomplemented
354#4021C23116yescomplemented
355C4×D20C23116yescomplemented
356#4018C23116yescomplemented
357#3519—532no—
358C2×#555—51no—
359C2×#554—51no—
360C2×#553—51no—
361C2×#553—52no—
362C2×#553—51no—
363C2×#550—51no—
364C2×#546—51no—
365C2×#546—51no—
366C2×#546—52no—
367C2×#546—52no—
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×#525D511yescharacteristic, complemented
377C22×#121—51no—
378C22×#121—51no—
379C2×#518—52no—
380C22×C4×D4—51no—
381C24×C5—24no—
382C24×C5—24no—
383C24×C5—42no—
384C24×C5C2412yes—
385C24×C5C2411yescharacteristic
386C24×C5C2414yes—
387C24×C5C2411yescharacteristic
388C24×C5C2411yescharacteristic
389C23×D5—24no—
390C23×D5—28no—
391C23×D5—24no—
392C23×D5—28no—
393C23×D5—42no—
394C23×D5—44no—
395C23×D5—44no—
396C23×D5—44no—
397C23×D5—44no—
398C23×D5C2412yes—
399C23×D5C2411yescharacteristic
400C23×D5C2412yes—
401C23×D5C2414yes—
402C23×D5C2411yescharacteristic
403C23×D5C2418yes—
404C23×D5C2418yes—
405C5×#41—416no—
406C2×C5×Q8—24no—
407C2×C5×Q8C2414yes—
408C2×C5×D4—28no—
409C2×C5×D4—28no—
410C2×C5×D4—24no—
411C2×C5×D4—44no—
412C2×C5×D4C2418yes—
413C2×C5×D4C2418yes—
414C2×C5×D4C2414yes—
415C2×C5×D4C2418yes—
416C22×C4×C5—24no—
417C22×C4×C5—24no—
418C22×C4×C5—24no—
419C22×C4×C5—416no—
420C22×C4×C5—42no—
421C22×C4×C5—42no—
422C22×C4×C5—42no—
423C22×C4×C5—44no—
424C22×C4×C5C2411yescharacteristic
425C22×C4×C5C2412yes—
426C22×C4×C5C2412yes—
427C22×C4×C5C2411yescharacteristic
428C22×C4×C5C2412yes—
429C22×C4×C5C2411yescharacteristic
430C22×C4×C5C2414yes—
431C22×C4×C5C2414yes—
432C22×C4×C5C2414yes—
433C22×C4×C5C2414yes—
434C22×C4×C5C2414yes—
435C22×C4×C5C2418yes—
436C22×C4×C5C2414yes—
437C22×C4×C5C2411yescharacteristic
438C2×C22⋊D5—24no—
439C2×C22⋊D5—28no—
440C2×C22⋊D5—28no—
441C2×C22⋊D5—24no—
442C2×C22⋊D5—232no—
443C2×C22⋊D5—28no—
444C2×C22⋊D5—24no—
445C2×C22⋊D5—44no—
446C2×C22⋊D5—44no—
447C2×C22⋊D5—44no—
448C2×C22⋊D5—44no—
449C2×C22⋊D5—44no—
450C2×C22⋊D5—432no—
451C2×C22⋊D5#4118yescomplemented
452C2×C22⋊D5C2418yes—
453C2×C22⋊D5C2418yes—
454C2×C22⋊D5C2418yes—
455C2×C22⋊D5C2414yes—
456C2×C22⋊D5C2414yes—
457C2×C22⋊D5C2414yes—
458C2×C22⋊D5C2418yes—
459C2×C22⋊D5C2418yes—
460C2×C22⋊D5C2418yes—
461C2×C22⋊D5C2418yes—
462C2×C22⋊D5C2418yes—
463C2×C22⋊D5C2414yes—
464C22×Dic5—24no—
465C22×Dic5—24no—
466C22×Dic5—42no—
467C22×Dic5—44no—
468C22×Dic5—44no—
469C22×Dic5C2411yescharacteristic
470C22×Dic5C2411yescharacteristic
471C22×Dic5C2411yescharacteristic
472C22×Dic5C2411yescharacteristic
473C22×Dic5C2411yescharacteristic
474C22×Dic5C2412yes—
475C22×Dic5C2412yes—
476C22×Dic5C2414yes—
477C22×Dic5C2414yes—
478C22×Dic5C2414yes—
479C22×Dic5C2418yes—
480C22×Dic5C2418yes—
481C22×Dic5C2411yescharacteristic
482#713—416no—
483#711—432no—
484D4×D5—264no—
485D4×D5—416no—
486D4×D5—432no—
487C2×D20—28no—
488C2×D20—24no—
489C2×D20—24no—
490C2×D20—416no—
491C2×D20—44no—
492C2×D20—44no—
493C2×D20—44no—
494C2×D20C2414yes—
495C2×D20C2414yes—
496C2×D20C2418yes—
497C2×D20C2418yes—
498C2×D20C2418yes—
499C2×D20C2418yes—
500C2×C4×D5—24no—
501C2×C4×D5—24no—
502C2×C4×D5—28no—
503C2×C4×D5—416no—
504C2×C4×D5—42no—
505C2×C4×D5—42no—
506C2×C4×D5—44no—
507C2×C4×D5—44no—
508C2×C4×D5—44no—
509C2×C4×D5C2414yes—
510C2×C4×D5C2414yes—
511C2×C4×D5C2418yes—
512C2×C4×D5C2414yes—
513C2×C4×D5C2414yes—
514C2×C4×D5C2418yes—
515C2×C4×D5C2418yes—
516C2×C4×D5C2418yes—
517C2×Dic10—44no—
518C2×Dic10C2418yes—
519C5×C4⋊C4C2414yes—
520C5×C4⋊C4C2414yes—
521C5×C4⋊C4C2418yes—
522C5×C4⋊C4C2418yes—
523C5×C22⋊C4C2418yes—
524C5×C22⋊C4C2418yes—
525C5×C22⋊C4C2418yes—
526C5×C22⋊C4C2418yes—
527C5×C22⋊C4C2418yes—
528C42×C5C2418yes—
529C22⋊Dic5C2414yes—
530C22⋊Dic5C2414yes—
531C22⋊Dic5C2414yes—
532C22⋊Dic5C2414yes—
533C22⋊Dic5C2418yes—
534C22⋊Dic5C2418yes—
535#685C2418yes—
536#685C2418yes—
537#685C2414yes—
538#685C2418yes—
539#685C2414yes—
540#685C2418yes—
541#685C2418yes—
542#685C2418yes—
543#685C2418yes—
544#685C2418yes—
545#685C2418yes—
546#685C2418yes—
547#685C2418yes—
548#685C2418yes—
549#685C2414yes—
550#685C2414yes—
551C4⋊Dic5C2418yes—
552C4⋊Dic5C2418yes—
553C4⋊Dic5C2418yes—
554C4⋊Dic5C2414yes—
555C4⋊Dic5C2414yes—
556#683C2414yes—
557#683C2418yes—
558#683C2414yes—
559#683C2418yes—
560#683C2418yes—
561#683C2418yes—
562#683C2414yes—
563#683C2414yes—
564C4×Dic5C2418yes—
565C4×Dic5C2418yes—
566C4×Dic5C2414yes—
567C4×Dic5C2414yes—
568C4×Dic5C2414yes—
569C4×Dic5C2414yes—
570C22×#41—51no—
571C22×#41—52no—
572C22×#41C2×D511yescharacteristic, complemented
573C23×D4—51no—
574C23×D4—52no—
575C23×D4—52no—
576C23×D4—51no—
577C23×D4—52no—
578C23×D4—51no—
579C24×C4—51no—
580C24×C4C2×D511yescharacteristic, complemented
581#555—516no—
582#554—516no—
583#553—516no—
584#553—532no—
585#553—516no—
586#550—516no—
587#546—516no—
588#546—516no—
589#546—532no—
590#546—532no—
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×#126—52no—
604C2×#125—52no—
605C2×#125—51no—
606C2×#124—51no—
607C2×#124—52no—
608C2×#124—52no—
609C2×#124—52no—
610#525—516no—
611#525C2×D5116yescomplemented
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⋊Q8C2×D511yescharacteristic, complemented
623C2×C22⋊Q8C2×D511yescharacteristic, complemented
624C2×#121—51no—
625C2×#121—52no—
626C2×#121—52no—
627C2×#121—52no—
628C2×#121—52no—
629C2×#121—52no—
630C2×#121—51no—
631C2×#121—51no—
632C2×#121—52no—
633C2×#121—52no—
634C2×#121—51no—
635C2×#121—51no—
636C2×#121—52no—
637C2×#121—516no—
638C2×#121—516no—
639C2×#121—51no—
640C2×#121—51no—
641C2×#121—52no—
642C2×#121—52no—
643C2×#121—52no—
644C2×#121—52no—
645C2×#121—52no—
646C2×#121C2×D511yescharacteristic, complemented
647C2×#121C2×D511yescharacteristic, complemented
648C2×#120—52no—
649C2×#120—52no—
650C2×#120—52no—
651C2×#120—52no—
652C2×#120—52no—
653C2×#120C2×D512yescomplemented
654#518—532no—
655C2×C4×Q8—51no—
656C2×C4×D4—52no—
657C2×C4×D4—51no—
658C2×C4×D4—51no—
659C2×C4×D4—51no—
660C2×C4×D4—51no—
661C2×C4×D4—51no—
662C2×C4×D4—51no—
663C2×C4×D4—51no—
664C2×C4×D4—51no—
665C2×C4×D4—51no—
666C2×C4×D4—52no—
667C2×C4×D4—516no—
668C2×C4×D4—52no—
669C2×C4×D4—51no—
670C2×C4×D4—51no—
671C2×C4×D4—52no—
672C2×C4×D4—52no—
673C2×C4×D4—52no—
674C2×C4×D4—52no—
675C2×C4×D4—52no—
676C2×C4×D4C2×D512yescomplemented
677C2×C4×D4C2×D512yescomplemented
678C2×#117—52no—
679C2×#117—51no—
680C2×#117—52no—
681C2×#117C2×D511yescharacteristic, complemented
682C22×C4⋊C4—51no—
683C22×C4⋊C4—51no—
684C22×C4⋊C4—51no—
685C22×C22⋊C4—51no—
686C22×C22⋊C4—51no—
687C22×C22⋊C4—52no—
688C22×C22⋊C4—52no—
689C22×C22⋊C4—52no—
690C22×C22⋊C4—52no—
691C22×C42—51no—
692C23×C5—22no—
693C23×C5—22no—
694C23×C5—22no—
695C23×C5—22no—
696C23×C5—28no—
697C23×C5—22no—
698C23×C5—24no—
699C23×C5—24no—
700C23×C5—28no—
701C23×C5—22no—
702C23×C5—24no—
703C23×C5—22no—
704C23×C5—44no—
705C23×C5—416no—
706C23×C5C2×#4114yes—
707C23×C5H(5,𝔽2)14yes—
708C23×C5C2514yes—
709C23×C5C2512yes—
710C23×C5C2512yes—
711C23×C5C2512yes—
712C23×C5C2511yescharacteristic
713C22×D5—22no—
714C22×D5—22no—
715C22×D5—24no—
716C22×D5—24no—
717C22×D5—22no—
718C22×D5—22no—
719C22×D5—24no—
720C22×D5—24no—
721C22×D5—24no—
722C22×D5—22no—
723C22×D5—24no—
724C22×D5—28no—
725C22×D5—216no—
726C22×D5—28no—
727C22×D5—216no—
728C22×D5—44no—
729C22×D5—48no—
730C22×D5—48no—
731C22×D5—48no—
732C22×D5—48no—
733C22×D5—416no—
734C22×D5—816no—
735C22×D5—816no—
736C22×D5C2×#4114yes—
737C22×D5C2514yes—
738C22×D5C2514yes—
739C22×D5C2512yes—
740C22×D5C2512yes—
741C5×Q8—28no—
742C5×D4—216no—
743C5×D4—216no—
744C5×D4—28no—
745C5×D4—48no—
746C2×C4×C5—24no—
747C2×C4×C5—24no—
748C2×C4×C5—22no—
749C2×C4×C5—24no—
750C2×C4×C5—22no—
751C2×C4×C5—22no—
752C2×C4×C5—28no—
753C2×C4×C5—28no—
754C2×C4×C5—28no—
755C2×C4×C5—44no—
756C2×C4×C5—44no—
757C2×C4×C5—44no—
758C2×C4×C5—48no—
759C2×C4×C5H(5,𝔽2)14yes—
760C2×C4×C5C2512yes—
761C2×C4×C5C2514yes—
762C2×C4×C5C2514yes—
763C2×C4×C5C2512yes—
764C2×C4×C5C2512yes—
765C2×C4×C5C2514yes—
766C2×C4×C5C2512yes—
767C22⋊D5—28no—
768C22⋊D5—216no—
769C22⋊D5—216no—
770C22⋊D5—28no—
771C22⋊D5—216no—
772C22⋊D5—28no—
773C22⋊D5—48no—
774C22⋊D5—48no—
775C22⋊D5—48no—
776C22⋊D5—48no—
777C22⋊D5—48no—
778C22⋊D5C2×#41116yescomplemented
779C2×Dic5—22no—
780C2×Dic5—22no—
781C2×Dic5—24no—
782C2×Dic5—22no—
783C2×Dic5—22no—
784C2×Dic5—22no—
785C2×Dic5—24no—
786C2×Dic5—28no—
787C2×Dic5—28no—
788C2×Dic5—44no—
789C2×Dic5—48no—
790C2×Dic5—48no—
791C2×Dic5C2×#4114yes—
792C2×Dic5C2512yes—
793C2×Dic5C2512yes—
794C2×Dic5C2512yes—
795C2×Dic5C2512yes—
796C2×Dic5C2514yes—
797C2×Dic5C2514yes—
798C2×Dic5C2512yes—
799C2×Dic5C2512yes—
800D20—216no—
801D20—28no—
802D20—28no—
803D20—48no—
804D20—48no—
805D20—48no—
806C4×D5—28no—
807C4×D5—28no—
808C4×D5—216no—
809C4×D5—44no—
810C4×D5—44no—
811C4×D5—48no—
812C4×D5—48no—
813C4×D5—48no—
814Dic10—48no—
815C25—51no—
816C25—52no—
817C25—52no—
818C25C22×D511yescharacteristic
819C2×#41—44no—
820C2×#41—58no—
821C2×#41—516no—
822C2×#41—208no—
823C2×#41—204no—
824C2×#41C22×D518yescomplemented
825C22×Q8—52no—
826C22×Q8C22×D511yescharacteristic
827C22×D4—51no—
828C22×D4—51no—
829C22×D4—51no—
830C22×D4—52no—
831C22×D4—51no—
832C22×D4—58no—
833C22×D4—52no—
834C22×D4—52no—
835C22×D4—52no—
836C22×D4—52no—
837C22×D4—52no—
838C22×D4—52no—
839C22×D4—52no—
840C22×D4—516no—
841C22×D4—516no—
842C22×D4—58no—
843C22×D4—516no—
844C22×D4—52no—
845C22×D4—51no—
846C22×D4—51no—
847C22×D4—52no—
848C22×D4—52no—
849C22×D4—52no—
850C22×D4—58no—
851C22×D4—1016no—
852C22×D4—108no—
853C22×D4—204no—
854C22×D4—204no—
855C22×D4—208no—
856C22×D4—208no—
857C22×D4C22×D512yes—
858C22×D4C22×D511yescharacteristic
859C22×D4C22×D512yes—
860C22×D4C22×D512yes—
861C23×C4—44no—
862C23×C4—51no—
863C23×C4—51no—
864C23×C4—51no—
865C23×C4—52no—
866C23×C4—52no—
867C23×C4—51no—
868C23×C4—52no—
869C23×C4—51no—
870C23×C4—51no—
871C23×C4—52no—
872C23×C4—52no—
873C23×C4—52no—
874C23×C4—51no—
875C23×C4—58no—
876C23×C4—204no—
877C23×C4C22×D511yescharacteristic
878C23×C4C22×D511yescharacteristic
879C23×C4C22×D511yescharacteristic
880C23×C4C22×D511yescharacteristic
881C23×C4C22×D511yescharacteristic
882C23×C4C22×D512yes—
883C23×C4C22×D511yescharacteristic
884C23×C4C22×D518yescomplemented
885C4⋊Q8—58no—
886#127—58no—
887#127—516no—
888#126—516no—
889#126—516no—
890#126—516no—
891#125—58no—
892#125—516no—
893#124—58no—
894#124—516no—
895#124—516no—
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—516no—
907C22⋊Q8C22×D518yescomplemented
908C22⋊Q8C22×D518yescomplemented
909#121—516no—
910#121—58no—
911#121—516no—
912#121—516no—
913#121—516no—
914#121—516no—
915#121—58no—
916#121—58no—
917#121—516no—
918#121—516no—
919#121—58no—
920#121—58no—
921#121—516no—
922#121—58no—
923#121—58no—
924#121—516no—
925#121—516no—
926#121—516no—
927#121—516no—
928#121—516no—
929#121C22×D518yescomplemented
930#121C22×D518yescomplemented
931#120—516no—
932#120—516no—
933#120—516no—
934#120—516no—
935#120—516no—
936#120C22×D5116yescomplemented
937C4×Q8—58no—
938C4×D4—516no—
939C4×D4—58no—
940C4×D4—58no—
941C4×D4—58no—
942C4×D4—58no—
943C4×D4—58no—
944C4×D4—58no—
945C4×D4—58no—
946C4×D4—58no—
947C4×D4—58no—
948C4×D4—516no—
949C4×D4—516no—
950C4×D4—58no—
951C4×D4—58no—
952C4×D4—516no—
953C4×D4—516no—
954C4×D4—516no—
955C4×D4—516no—
956C4×D4—516no—
957C4×D4C22×D5116yescomplemented
958C4×D4C22×D5116yescomplemented
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—51no—
968C2×C4⋊C4—51no—
969C2×C4⋊C4—58no—
970C2×C4⋊C4—52no—
971C2×C4⋊C4—52no—
972C2×C4⋊C4—58no—
973C2×C4⋊C4—52no—
974C2×C4⋊C4—52no—
975C2×C4⋊C4—52no—
976C2×C4⋊C4—52no—
977C2×C4⋊C4—52no—
978C2×C4⋊C4—58no—
979C2×C4⋊C4C22×D511yescharacteristic
980C2×C4⋊C4C22×D511yescharacteristic
981C2×C4⋊C4C22×D512yes—
982C2×C4⋊C4C22×D512yes—
983C2×C22⋊C4—51no—
984C2×C22⋊C4—51no—
985C2×C22⋊C4—52no—
986C2×C22⋊C4—51no—
987C2×C22⋊C4—51no—
988C2×C22⋊C4—58no—
989C2×C22⋊C4—52no—
990C2×C22⋊C4—51no—
991C2×C22⋊C4—52no—
992C2×C22⋊C4—52no—
993C2×C22⋊C4—52no—
994C2×C22⋊C4—52no—
995C2×C22⋊C4—51no—
996C2×C22⋊C4—52no—
997C2×C22⋊C4—52no—
998C2×C22⋊C4—51no—
999C2×C22⋊C4—52no—
1000C2×C22⋊C4—51no—
1001C2×C22⋊C4—58no—
1002C2×C22⋊C4—516no—
1003C2×C22⋊C4—516no—
1004C2×C22⋊C4—52no—
1005C2×C22⋊C4—52no—
1006C2×C22⋊C4—52no—
1007C2×C22⋊C4—52no—
1008C2×C22⋊C4—52no—
1009C2×C22⋊C4—516no—
1010C2×C22⋊C4—516no—
1011C2×C22⋊C4C22×D512yes—
1012C2×C22⋊C4C22×D512yes—
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—51no—
1022C2×C42—58no—
1023C2×C42C22×D512yes—
1024C22×C5—22no—
1025C22×C5—22no—
1026C22×C5—22no—
1027C22×C5—22no—
1028C22×C5—28no—
1029C22×C5—28no—
1030C22×C5—22no—
1031C22×C5—24no—
1032C22×C5—24no—
1033C22×C5—22no—
1034C22×C5—24no—
1035C22×C5—22no—
1036C22×C5—416no—
1037C22×C5—48no—
1038C22×C5—44no—
1039C22×C5C22×#4114yes—
1040C22×C5C22×#4112yes—
1041C22×C5C2×H(5,𝔽2)12yes—
1042C22×C5C2×H(5,𝔽2)14yes—
1043C22×C5C2×H(5,𝔽2)12yes—
1044C22×C5C2611yescharacteristic
1045C2×D5—22no—
1046C2×D5—22no—
1047C2×D5—28no—
1048C2×D5—24no—
1049C2×D5—24no—
1050C2×D5—22no—
1051C2×D5—22no—
1052C2×D5—24no—
1053C2×D5—24no—
1054C2×D5—24no—
1055C2×D5—22no—
1056C2×D5—24no—
1057C2×D5—416no—
1058C2×D5—44no—
1059C2×D5—48no—
1060C2×D5—48no—
1061C2×D5—816no—
1062C2×D5—816no—
1063C2×D5C22×#4114yes—
1064C4×C5—24no—
1065C4×C5—24no—
1066C4×C5—22no—
1067C4×C5—24no—
1068C4×C5—22no—
1069C4×C5—22no—
1070C4×C5C2×H(5,𝔽2)14yes—
1071Dic5—22no—
1072Dic5—22no—
1073Dic5—24no—
1074Dic5—22no—
1075Dic5—22no—
1076Dic5—22no—
1077Dic5—24no—
1078Dic5C22×#4114yes—
1079C24—24no—
1080C24—24no—
1081C24—42no—
1082C24—51no—
1083C24—52no—
1084C24—51no—
1085C24—52no—
1086C24—54no—
1087C24—58no—
1088C24—58no—
1089C24—104no—
1090C24—108no—
1091C24—104no—
1092C24—108no—
1093C24—202no—
1094C24—204no—
1095C24—204no—
1096C24—204no—
1097C24—204no—
1098C24C23×D512yes—
1099C24C23×D511yescharacteristic
1100C24C23×D514yes—
1101C24C23×D511yescharacteristic
1102C24C23×D511yescharacteristic
1103#41—416no—
1104#41—2032no—
1105#41—2016no—
1106C2×Q8—24no—
1107C2×Q8—58no—
1108C2×Q8—204no—
1109C2×Q8C23×D514yes—
1110C2×D4—28no—
1111C2×D4—28no—
1112C2×D4—24no—
1113C2×D4—44no—
1114C2×D4—58no—
1115C2×D4—54no—
1116C2×D4—54no—
1117C2×D4—54no—
1118C2×D4—58no—
1119C2×D4—54no—
1120C2×D4—58no—
1121C2×D4—58no—
1122C2×D4—58no—
1123C2×D4—58no—
1124C2×D4—58no—
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—108no—
1134C2×D4—108no—
1135C2×D4—104no—
1136C2×D4—1064no—
1137C2×D4—1032no—
1138C2×D4—104no—
1139C2×D4—104no—
1140C2×D4—108no—
1141C2×D4—108no—
1142C2×D4—104no—
1143C2×D4—104no—
1144C2×D4—2016no—
1145C2×D4—204no—
1146C2×D4—204no—
1147C2×D4—204no—
1148C2×D4—2016no—
1149C2×D4—204no—
1150C2×D4—204no—
1151C2×D4—204no—
1152C2×D4—204no—
1153C2×D4—204no—
1154C2×D4—2032no—
1155C2×D4—2032no—
1156C2×D4C23×D518yes—
1157C2×D4C23×D514yes—
1158C2×D4C23×D518yes—
1159C2×D4C23×D518yes—
1160C22×C4—24no—
1161C22×C4—24no—
1162C22×C4—24no—
1163C22×C4—416no—
1164C22×C4—42no—
1165C22×C4—42no—
1166C22×C4—42no—
1167C22×C4—44no—
1168C22×C4—51no—
1169C22×C4—54no—
1170C22×C4—54no—
1171C22×C4—51no—
1172C22×C4—51no—
1173C22×C4—51no—
1174C22×C4—51no—
1175C22×C4—52no—
1176C22×C4—52no—
1177C22×C4—51no—
1178C22×C4—54no—
1179C22×C4—58no—
1180C22×C4—58no—
1181C22×C4—54no—
1182C22×C4—58no—
1183C22×C4—54no—
1184C22×C4—54no—
1185C22×C4—58no—
1186C22×C4—58no—
1187C22×C4—58no—
1188C22×C4—54no—
1189C22×C4—108no—
1190C22×C4—104no—
1191C22×C4—104no—
1192C22×C4—104no—
1193C22×C4—104no—
1194C22×C4—2016no—
1195C22×C4—202no—
1196C22×C4—202no—
1197C22×C4—204no—
1198C22×C4—204no—
1199C22×C4—204no—
1200C22×C4—202no—
1201C22×C4—204no—
1202C22×C4—204no—
1203C22×C4C23×D514yes—
1204C22×C4C23×D514yes—
1205C22×C4C23×D514yes—
1206C22×C4C23×D511yescharacteristic
1207C22×C4C23×D512yes—
1208C22×C4C23×D512yes—
1209C22×C4C23×D511yescharacteristic
1210C22×C4C23×D512yes—
1211C22×C4C23×D511yescharacteristic
1212C22×C4C23×D514yes—
1213C22×C4C23×D514yes—
1214C22×C4C23×D518yes—
1215C22×C4C23×D514yes—
1216C22×C4C23×D511yescharacteristic
1217C4⋊C4—54no—
1218C4⋊C4—54no—
1219C4⋊C4—54no—
1220C4⋊C4—54no—
1221C4⋊C4—54no—
1222C4⋊C4—54no—
1223C4⋊C4—58no—
1224C4⋊C4—58no—
1225C4⋊C4—58no—
1226C4⋊C4—58no—
1227C4⋊C4—58no—
1228C4⋊C4—58no—
1229C4⋊C4—58no—
1230C4⋊C4C23×D514yes—
1231C4⋊C4C23×D514yes—
1232C4⋊C4C23×D518yes—
1233C4⋊C4C23×D518yes—
1234C22⋊C4—54no—
1235C22⋊C4—54no—
1236C22⋊C4—58no—
1237C22⋊C4—54no—
1238C22⋊C4—54no—
1239C22⋊C4—58no—
1240C22⋊C4—54no—
1241C22⋊C4—58no—
1242C22⋊C4—58no—
1243C22⋊C4—58no—
1244C22⋊C4—58no—
1245C22⋊C4—54no—
1246C22⋊C4—58no—
1247C22⋊C4—58no—
1248C22⋊C4—54no—
1249C22⋊C4—58no—
1250C22⋊C4—54no—
1251C22⋊C4—58no—
1252C22⋊C4—58no—
1253C22⋊C4—58no—
1254C22⋊C4—58no—
1255C22⋊C4—58no—
1256C22⋊C4C23×D518yes—
1257C22⋊C4C23×D518yes—
1258C22⋊C4C23×D518yes—
1259C22⋊C4C23×D518yes—
1260C22⋊C4C23×D518yes—
1261C42—54no—
1262C42—54no—
1263C42—54no—
1264C42—54no—
1265C42—58no—
1266C42—58no—
1267C42C23×D518yes—
1268C2×C5—24no—
1269C2×C5—24no—
1270C2×C5—44no—
1271C2×C5—42no—
1272C2×C5#351914yescomplemented
1273C2×C5C23×#4111yescharacteristic
1274C2×C5C22×H(5,𝔽2)11yescharacteristic
1275C2×C5C22×H(5,𝔽2)11yescharacteristic
1276D5—24no—
1277D5—42no—
1278D5—44no—
1279D5—44no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—24no—
1286C23—24no—
1287C23—28no—
1288C23—22no—
1289C23—24no—
1290C23—28no—
1291C23—22no—
1292C23—44no—
1293C23—416no—
1294C23—54no—
1295C23—52no—
1296C23—54no—
1297C23—52no—
1298C23—54no—
1299C23—108no—
1300C23—1016no—
1301C23—102no—
1302C23—102no—
1303C23—102no—
1304C23—104no—
1305C23—104no—
1306C23—104no—
1307C23—102no—
1308C23—104no—
1309C23—104no—
1310C23—104no—
1311C23—108no—
1312C23—102no—
1313C23—1016no—
1314C23—204no—
1315C23—208no—
1316C23—208no—
1317C23—208no—
1318C23—208no—
1319C23—2016no—
1320C23—4016no—
1321C23—4016no—
1322C23D5×#4114yes—
1323C23#414914yes—
1324C23C24×D514yes—
1325C23C24×D512yes—
1326C23C24×D512yes—
1327C23C24×D512yes—
1328C23C24×D511yescharacteristic
1329Q8—28no—
1330Q8—208no—
1331D4—216no—
1332D4—216no—
1333D4—28no—
1334D4—48no—
1335D4—516no—
1336D4—1016no—
1337D4—1016no—
1338D4—108no—
1339D4—108no—
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—22no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—28no—
1360C2×C4—28no—
1361C2×C4—28no—
1362C2×C4—44no—
1363C2×C4—44no—
1364C2×C4—44no—
1365C2×C4—48no—
1366C2×C4—54no—
1367C2×C4—52no—
1368C2×C4—52no—
1369C2×C4—52no—
1370C2×C4—52no—
1371C2×C4—52no—
1372C2×C4—54no—
1373C2×C4—54no—
1374C2×C4—52no—
1375C2×C4—1016no—
1376C2×C4—108no—
1377C2×C4—102no—
1378C2×C4—102no—
1379C2×C4—102no—
1380C2×C4—102no—
1381C2×C4—102no—
1382C2×C4—108no—
1383C2×C4—104no—
1384C2×C4—104no—
1385C2×C4—108no—
1386C2×C4—108no—
1387C2×C4—204no—
1388C2×C4—204no—
1389C2×C4—208no—
1390C2×C4—208no—
1391C2×C4—208no—
1392C2×C4—204no—
1393C2×C4—208no—
1394C2×C4—208no—
1395C2×C4#414414yes—
1396C2×C4C24×D512yes—
1397C2×C4C24×D514yes—
1398C2×C4C24×D514yes—
1399C2×C4C24×D512yes—
1400C2×C4C24×D514yes—
1401C2×C4C24×D512yes—
1402C2×C4C24×D512yes—
1403C5C2×#351911yescharacteristic, complemented, Sylow
1404C22—22no—
1405C22—22no—
1406C22—22no—
1407C22—22no—
1408C22—28no—
1409C22—28no—
1410C22—22no—
1411C22—24no—
1412C22—24no—
1413C22—22no—
1414C22—24no—
1415C22—22no—
1416C22—416no—
1417C22—44no—
1418C22—48no—
1419C22—54no—
1420C22—102no—
1421C22—102no—
1422C22—108no—
1423C22—102no—
1424C22—104no—
1425C22—104no—
1426C22—104no—
1427C22—102no—
1428C22—104no—
1429C22—104no—
1430C22—104no—
1431C22—102no—
1432C22—2016no—
1433C22—204no—
1434C22—208no—
1435C22—208no—
1436C22—4016no—
1437C22—4016no—
1438C22C2×#414412yes—
1439C22C2×D5×#4114yes—
1440C22C2×D5×#4112yes—
1441C22C2×#414914yes—
1442C22C2×#414912yes—
1443C22C25×D511yescharacteristic
1444C4—22no—
1445C4—22no—
1446C4—22no—
1447C4—24no—
1448C4—24no—
1449C4—24no—
1450C4—54no—
1451C4—102no—
1452C4—102no—
1453C4—102no—
1454C4—102no—
1455C4—102no—
1456C4—104no—
1457C4—104no—
1458C4C2×#414414yes—
1459C2—24no—
1460C2—24no—
1461C2—42no—
1462C2—44no—
1463C2—104no—
1464C2—202no—
1465C2—204no—
1466C2—204no—
1467C2#1061794714yesdirect product factor
1468C2C22×#414411yescharacteristic
1469C2C22×D5×#4111yescharacteristic
1470C2C22×#414911yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#525C2
socleC23×C5C25
hypercenterC2×#525D5
hypocenterC5C2×#3519
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×C5×#525C2semidirect
2. C2×#66168C2semidirect
3. C2×#66163C2semidirect
4. C22×#4076C2semidirect
5. C22×C4×C22⋊D5C2semidirect
6. #10617947C2direct (N × H)
7. C2×#65991C2semidirect
8. C2×#65997C2semidirect
9. C2×#65964C2semidirect
10. C2×#65969C2semidirect
11. C2×#65958C2semidirect
12. C2×#65961C2semidirect
13. C2×#65943C2semidirect
14. C2×D5×#121C2semidirect
15. C2×#65952C2semidirect
16. C2×#65930C2semidirect
17. C2×#65925C2semidirect
18. C2×#65924C2semidirect
19. C2×#65888C2semidirect
20. C2×#65894C2semidirect
21. C2×#65879C2semidirect
22. C2×#65874C2semidirect
23. C2×#65866C2semidirect
24. C2×#65864C2semidirect
25. C22×C5×#41C22semidirect
26. C24×C4×C5C22semidirect
28. C23×C22⋊D5C22semidirect
29. C22×#713C22semidirect
30. C22×#711C22semidirect
32. C22×D4×D5C22semidirect
33. C22×D4×D5C22semidirect
34. C23×D20C22semidirect
35. C23×C4×D5C22semidirect
36. C5×#525C22semidirect
37. C2×C5×#123C22semidirect
38. C2×C5×C22⋊Q8C22semidirect
39. C2×C5×C22⋊Q8C22semidirect
40. C2×C5×#121C22semidirect
41. C2×C5×#121C22semidirect
42. C2×C5×#120C22semidirect
43. C2×C4×C5×D4C22semidirect
44. C2×C4×C5×D4C22semidirect
45. C2×C5×#117C22semidirect
46. C22×C22⋊Dic5C22semidirect
47. #66168C22semidirect
48. #66163C22semidirect
49. C2×#4093C22semidirect
50. C2×#4092C22semidirect
51. C2×Q8×Dic5C22semidirect
52. C2×#4086C22semidirect
53. C2×#4086C22semidirect
54. C2×#4085C22semidirect
55. C2×#4085C22semidirect
56. C2×#4085C22semidirect
57. C2×#4085C22semidirect
58. C2×#4084C22semidirect
59. C2×#4084C22semidirect
60. C2×#4083C22semidirect
61. C2×#4083C22semidirect
62. C2×D4×Dic5C22semidirect
63. C2×D4×Dic5C22semidirect
65. C2×#4076C22semidirect
66. C2×#4076C22semidirect
67. C2×#4076C22semidirect
68. C2×#4076C22semidirect
69. C2×#4076C22semidirect
70. C2×#4076C22semidirect
71. C2×#4076C22semidirect
72. C2×#4075C22semidirect
75. C2×C4×C22⋊D5C22semidirect
76. C2×C4×C22⋊D5C22semidirect
77. C2×C4×C22⋊D5C22semidirect
78. C2×C4×C22⋊D5C22semidirect
79. C2×C4×C22⋊D5C22semidirect
80. C2×C4×C22⋊D5C22semidirect
81. C2×C4×C22⋊D5C22semidirect
82. C2×C4×C22⋊D5C22semidirect
83. C22×#685C22semidirect
84. C22×#685C22semidirect
85. C22×#685C22semidirect
86. C22×C4⋊Dic5C22semidirect
87. C22×#683C22semidirect
88. C22×C4×Dic5C22semidirect
89. #65997C22semidirect
90. #65991C22semidirect
91. #65969C22semidirect
92. #65964C22semidirect
93. #65961C22semidirect
94. #65958C22semidirect
95. #65952C22semidirect
96. #65943C22semidirect
97. D5×#121C22semidirect
98. #65930C22semidirect
99. #65925C22semidirect
100. #65924C22semidirect
101. #65894C22semidirect
102. #65888C22semidirect
103. #65879C22semidirect
104. #65874C22semidirect
105. #65866C22semidirect
106. #65864C22semidirect
107. C2×#4044C22semidirect
108. C2×#4043C22semidirect
109. C2×#4041C22semidirect
110. C2×#4041C22semidirect
111. C2×#4041C22semidirect
112. C2×#4040C22semidirect
113. C2×#4040C22semidirect
114. C2×#4039C22semidirect
115. C2×#4039C22semidirect
116. C2×#4039C22semidirect
117. C2×#4038C22semidirect
118. C2×#4038C22semidirect
119. C2×D5×C4⋊C4C22semidirect
120. C2×#4036C22semidirect
121. C2×#4035C22semidirect
122. C2×#4034C22semidirect
123. C2×#4032C22semidirect
124. C2×#4032C22semidirect
125. C2×#4031C22semidirect
126. C2×#4031C22semidirect
127. C2×#4030C22semidirect
128. C2×#4030C22semidirect
129. C2×#4030C22semidirect
130. C2×#4030C22semidirect
131. C2×#4029C22semidirect
132. C2×#4028C22semidirect
133. C2×#4028C22semidirect
134. C2×#4028C22semidirect
136. C2×#4027C22semidirect
137. C2×#4027C22semidirect
138. C2×#4027C22semidirect
139. C2×D5×C22⋊C4C22semidirect
140. C2×D5×C22⋊C4C22semidirect
141. C2×#4025C22semidirect
142. C2×#4024C22semidirect
143. C2×#4022C22semidirect
144. C2×#4021C22semidirect
145. C2×C4×D20C22semidirect
146. C2×#4018C22semidirect
153. C2×C5×#41C23semidirect
167. C23×C4×C5C23semidirect
183. C22×C22⋊D5C23semidirect
190. C2×#713C23semidirect
192. C2×#711C23semidirect
197. C2×D4×D5C23semidirect
198. C2×D4×D5C23semidirect
206. C22×D20C23semidirect
216. C22×C4×D5C23semidirect
218. C5×#123C23semidirect
219. C5×C22⋊Q8C23semidirect
220. C5×C22⋊Q8C23semidirect
221. C5×#121C23semidirect
222. C5×#121C23semidirect
223. C5×#120C23semidirect
224. C4×C5×D4C23semidirect
225. C4×C5×D4C23semidirect
226. C5×#117C23semidirect
243. C2×C22⋊Dic5C23semidirect
244. #4093C23semidirect
245. #4092C23semidirect
246. Q8×Dic5C23semidirect
247. #4086C23semidirect
248. #4086C23semidirect
249. #4085C23semidirect
250. #4085C23semidirect
251. #4085C23semidirect
252. #4085C23semidirect
253. #4084C23semidirect
254. #4084C23semidirect
255. #4083C23semidirect
256. #4083C23semidirect
257. D4×Dic5C23semidirect
258. D4×Dic5C23semidirect
260. #4076C23semidirect
261. #4076C23semidirect
262. #4076C23semidirect
263. #4076C23semidirect
264. #4076C23semidirect
265. #4076C23semidirect
266. #4075C23semidirect
269. C4×C22⋊D5C23semidirect
270. C4×C22⋊D5C23semidirect
271. C4×C22⋊D5C23semidirect
272. C4×C22⋊D5C23semidirect
273. C4×C22⋊D5C23semidirect
274. C4×C22⋊D5C23semidirect
275. C4×C22⋊D5C23semidirect
292. C2×#685C23semidirect
293. C2×#685C23semidirect
294. C2×#685C23semidirect
300. C2×C4⋊Dic5C23semidirect
309. C2×#683C23semidirect
316. C2×C4×Dic5C23semidirect
317. #4044C23semidirect
318. #4043C23semidirect
319. #4041C23semidirect
320. #4041C23semidirect
321. #4041C23semidirect
322. #4040C23semidirect
323. #4040C23semidirect
324. #4039C23semidirect
325. #4039C23semidirect
326. #4039C23semidirect
327. #4038C23semidirect
328. #4038C23semidirect
329. D5×C4⋊C4C23semidirect
330. #4036C23semidirect
331. #4035C23semidirect
332. #4034C23semidirect
333. #4032C23semidirect
334. #4032C23semidirect
335. #4031C23semidirect
336. #4031C23semidirect
337. #4030C23semidirect
338. #4030C23semidirect
339. #4030C23semidirect
340. #4030C23semidirect
341. #4029C23semidirect
342. #4028C23semidirect
343. #4028C23semidirect
344. #4028C23semidirect
346. #4027C23semidirect
347. #4027C23semidirect
348. #4027C23semidirect
349. D5×C22⋊C4C23semidirect
350. D5×C22⋊C4C23semidirect
351. #4025C23semidirect
352. #4024C23semidirect
353. #4022C23semidirect
354. #4021C23semidirect
355. C4×D20C23semidirect
356. #4018C23semidirect
376. C2×#525D5semidirect
451. C2×C22⋊D5#41semidirect
572. C22×#41C2×D5semidirect
580. C24×C4C2×D5semidirect
611. #525C2×D5semidirect
618. C2×#123C2×D5semidirect
622. C2×C22⋊Q8C2×D5semidirect
623. C2×C22⋊Q8C2×D5semidirect
646. C2×#121C2×D5semidirect
647. C2×#121C2×D5semidirect
653. C2×#120C2×D5semidirect
676. C2×C4×D4C2×D5semidirect
677. C2×C4×D4C2×D5semidirect
681. C2×#117C2×D5semidirect
778. C22⋊D5C2×#41semidirect
824. C2×#41C22×D5semidirect
884. C23×C4C22×D5semidirect
903. #123C22×D5semidirect
907. C22⋊Q8C22×D5semidirect
908. C22⋊Q8C22×D5semidirect
929. #121C22×D5semidirect
930. #121C22×D5semidirect
936. #120C22×D5semidirect
957. C4×D4C22×D5semidirect
958. C4×D4C22×D5semidirect
962. #117C22×D5semidirect
1272. C2×C5#3519semidirect
1403. C5C2×#3519semidirect
1467. C2#10617947direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5252
C2×#661682
C2×#661632
C22×#40762
C22×C4×C22⋊D52
#106179472
C2×#659912
C2×#659972
C2×#659642
C2×#659692
C2×#659582
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C2×#659432
C2×D5×#1212
C2×#659522
C2×#659302
C2×#659252
C2×#659242
C2×#658882
C2×#658942
C2×#658792
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C2×#658662
C2×#658642
C2×#35195