Finite Group Databasebeta

← C2×#10618237 #13006884

Subgroups — C2×#10618237 #13006884

Order 1280.

8814 conjugacy classes of subgroups.

The subgroup lattice has 1480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#535C211yesmaximal, characteristic, complemented
2C2×#66168C211yesmaximal, characteristic, complemented
3C2×#66163C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊D5C211yesmaximal, characteristic, complemented
5C2×D4×C22⋊D5C211yesmaximal, characteristic, complemented
6#10618237C2132yesmaximal, direct product factor
7C2×#66051C211yesmaximal, characteristic, complemented
8C2×#66053C211yesmaximal, characteristic, complemented
9C2×D5×#127C211yesmaximal, characteristic, complemented
10C2×#66052C211yesmaximal, characteristic, complemented
11C2×#66010C211yesmaximal, characteristic, complemented
12C2×#66008C211yesmaximal, characteristic, complemented
13C2×#66015C211yesmaximal, characteristic, complemented
14C2×#66014C211yesmaximal, characteristic, complemented
15C2×#65954C212yesmaximal, complemented
16C2×#65944C212yesmaximal, complemented
17C2×#65939C212yesmaximal, complemented
18C2×#65949C212yesmaximal, complemented
19C2×#65929C212yesmaximal, complemented
20C2×#65924C212yesmaximal, complemented
21C2×#65923C212yesmaximal, complemented
22C2×#65926C212yesmaximal, complemented
23C2×#65869C211yesmaximal, characteristic, complemented
24C2×#65862C211yesmaximal, characteristic, complemented
25C22×C5×#41C2211yescharacteristic, complemented
26C23×C5×D4C2211yescharacteristic, complemented
27C23×C22⋊D5C2212yescomplemented
28C23×C22⋊D5C2212yescomplemented
29C22×#713C2211yescharacteristic, complemented
30C22×#711C2212yescomplemented
31C22×D4×D5C2211yescharacteristic, complemented
32C22×D4×D5C2211yescharacteristic, complemented
33C22×D4×D5C2211yescharacteristic, complemented
34C22×D4×D5C2212yescomplemented
35C22×D4×D5C2212yescomplemented
36C22×D4×D5C2212yescomplemented
37C5×#535C22116yescomplemented
38C2×C5×#127C2211yescharacteristic, complemented
39C2×C5×#127C2211yescharacteristic, complemented
40C2×C5×#124C2211yescharacteristic, complemented
41C2×C5×#124C2211yescharacteristic, complemented
42C2×C5×#121C2212yescomplemented
43C2×C5×#121C2212yescomplemented
44C2×C5×#120C2212yescomplemented
45C2×C5×#120C2212yescomplemented
46C2×C5×#117C2211yescharacteristic, complemented
47C2×#4099C2212yescomplemented
48C2×#4099C2212yescomplemented
49#66168C22116yescomplemented
50#66163C22116yescomplemented
51C2×#4093C2211yescharacteristic, complemented
52C2×#4092C2211yescharacteristic, complemented
53C2×Q8×Dic5C2211yescharacteristic, complemented
54C2×#4086C2211yescharacteristic
55C2×#4086C2211yescharacteristic, complemented
56C2×#4086C2212yescomplemented
57C2×#4086C2211yescharacteristic, complemented
58C2×#4086C2212yescomplemented
59C2×#4086C2212yescomplemented
60C2×#4085C2212yescomplemented
61C2×#4085C2212yescomplemented
62C2×#4085C2212yescomplemented
63C2×#4085C2212yescomplemented
64C2×#4085C2212yescomplemented
65C2×#4085C2212yescomplemented
66C2×#4085C2212yescomplemented
67D4×C22⋊D5C22116yescomplemented
68D4×C22⋊D5C22116yescomplemented
69C2×#4084C2211yescharacteristic
70C2×#4084C2211yescharacteristic, complemented
71C2×#4084C2212yescomplemented
72C2×#4084C2211yescharacteristic, complemented
73C2×#4084C2212yescomplemented
74C2×#4084C2212yescomplemented
75C2×#4083C2212yescomplemented
76C2×#4083C2212yescomplemented
77C2×#4083C2212yescomplemented
78C2×#4083C2212yescomplemented
79C2×#4083C2212yescomplemented
80C2×#4081C2212yescomplemented
81C2×#4081C2212yescomplemented
82C2×D4×Dic5C2211yescharacteristic, complemented
83C2×D4×Dic5C2211yescharacteristic, complemented
84C2×D4×Dic5C2211yescharacteristic, complemented
85C2×#4076C2211yescharacteristic, complemented
86C2×#4076C2211yescharacteristic, complemented
87C2×#4076C2212yescomplemented
88C2×#4075C2212yescomplemented
89C2×C4×C22⋊D5C2211yescharacteristic, complemented
90C2×C4×C22⋊D5C2211yescharacteristic, complemented
91C2×C4×C22⋊D5C2212yescomplemented
92C22×#685C2212yescomplemented
93#66053C22116yescomplemented
94#66052C22116yescomplemented
95#66051C22116yescomplemented
96D5×#127C22116yescomplemented
97#66015C22116yescomplemented
98#66014C22116yescomplemented
99#66010C22116yescomplemented
100#66008C22116yescomplemented
101#65954C22132yescomplemented
102#65949C22132yescomplemented
103#65944C22132yescomplemented
104#65939C22132yescomplemented
105#65929C22132yescomplemented
106#65926C22132yescomplemented
107#65924C22132yescomplemented
108#65923C22132yescomplemented
109#65869C22116yescomplemented
110#65862C22116yescomplemented
111C2×#4044C2211yescharacteristic, complemented
112C2×#4042C2211yescharacteristic, complemented
113C2×#4040C2211yescharacteristic, complemented
114C2×#4040C2212yescomplemented
115C2×#4040C2212yescomplemented
116C2×#4035C2211yescharacteristic, complemented
117C2×#4032C2212yescomplemented
118C2×#4031C2211yescharacteristic, complemented
119C2×#4031C2212yescomplemented
120C2×#4030C2211yescharacteristic
121C2×#4030C2212yescomplemented
122C2×#4030C2212yescomplemented
123C2×#4030C2212yescomplemented
124C2×#4030C2212yescomplemented
125C2×#4030C2212yescomplemented
126C2×#4029C2211yescharacteristic, complemented
127C2×#4029C2212yescomplemented
128C2×#4029C2212yescomplemented
129C2×#4029C2212yescomplemented
130C2×#4028C2212yescomplemented
131C2×#4028C2212yescomplemented
132C2×#4028C2212yescomplemented
133C2×#4027C2212yescomplemented
134C2×#4027C2212yescomplemented
135C2×D5×C22⋊C4C2212yescomplemented
136C2×#4025C2211yescharacteristic, complemented
137C2×#4025C2212yescomplemented
138C2×#4023C2212yescomplemented
139C2×#4020C2211yescharacteristic, complemented
140C2×C4×D20C2211yescharacteristic, complemented
141C2×C4×D20C2211yescharacteristic, complemented
142C2×C4×D20C2211yescharacteristic, complemented
143C2×#4018C2211yescharacteristic, complemented
144C2×C42×D5C2211yescharacteristic, complemented
145C2×#4016C2211yescharacteristic, complemented
146C2×C4×Dic10C2211yescharacteristic, complemented
147C2×#3543—51nomaximal, Sylow
148C25×C5C2312yes—
149C24×D5C2312yes—
150C24×D5C2312yes—
151C24×D5C2312yes—
152C2×C5×#41—44no—
153C2×C5×#41C2318yescomplemented
154C22×C5×Q8C2311yescharacteristic
155C22×C5×D4—44no—
156C22×C5×D4C2311yescharacteristic
157C22×C5×D4C2311yescharacteristic
158C22×C5×D4C2311yescharacteristic
159C22×C5×D4C2312yes—
160C22×C5×D4C2312yes—
161C22×C5×D4C2312yes—
162C22×C5×D4C2312yes—
163C22×C5×D4C2312yes—
164C22×C5×D4C2312yes—
165C22×C5×D4C2318yescomplemented
166C23×C4×C5C2311yescharacteristic
167C23×C4×C5C2312yes—
168C22×C22⋊D5—48no—
169C22×C22⋊D5—48no—
170C22×C22⋊D5C2312yes—
171C22×C22⋊D5C2312yes—
172C22×C22⋊D5C2311yescharacteristic
173C22×C22⋊D5C2311yescharacteristic
174C22×C22⋊D5C2312yes—
175C22×C22⋊D5C2312yes—
176C22×C22⋊D5C2312yes—
177C22×C22⋊D5C2312yes—
178C22×C22⋊D5C2312yes—
179C22×C22⋊D5C2312yes—
180C22×C22⋊D5C2312yes—
181C22×C22⋊D5C2312yes—
182C22×C22⋊D5C2312yes—
183C22×C22⋊D5C2312yes—
184C22×C22⋊D5C2312yes—
185C22×C22⋊D5C2312yes—
186C22×C22⋊D5C23116yescomplemented
187C22×C22⋊D5C23116yescomplemented
188C23×Dic5C2312yes—
189C23×Dic5C2312yes—
190C23×Dic5C2312yes—
191C2×#713—44no—
192C2×#713C2318yescomplemented
193C2×#711—48no—
194C2×#711C23116yescomplemented
195C2×D4×D5—44no—
196C2×D4×D5—44no—
197C2×D4×D5—44no—
198C2×D4×D5—48no—
199C2×D4×D5—48no—
200C2×D4×D5—48no—
201C2×D4×D5C2318yescomplemented
202C2×D4×D5C2318yescomplemented
203C2×D4×D5C23116yescomplemented
204C2×D4×D5C23116yescomplemented
205C2×D4×D5C2318yescomplemented
206C2×D4×D5C23116yescomplemented
207C22×D20C2311yescharacteristic
208C22×D20C2311yescharacteristic
209C22×D20C2311yescharacteristic
210C22×D20C2312yes—
211C22×D20C2312yes—
212C22×D20C2312yes—
213C22×C4×D5C2311yescharacteristic
214C22×C4×D5C2311yescharacteristic
215C22×C4×D5C2311yescharacteristic
216C22×C4×D5C2311yescharacteristic
217C22×C4×D5C2312yes—
218C22×C4×D5C2312yes—
219C22×C4×D5C2312yes—
220C22×Dic10C2311yescharacteristic
221C5×#127C2318yescomplemented
222C5×#127C2318yescomplemented
223C5×#124C2318yescomplemented
224C5×#124C2318yescomplemented
225C5×#121C23116yescomplemented
226C5×#121C23116yescomplemented
227C5×#120C23116yescomplemented
228C5×#120C23116yescomplemented
229C5×#117C2318yescomplemented
230C2×C5×C4⋊C4C2311yescharacteristic
231C2×C5×C4⋊C4C2311yescharacteristic
232C2×C5×C22⋊C4C2312yes—
233C2×C5×C22⋊C4C2312yes—
234C2×C5×C22⋊C4C2311yescharacteristic
235C2×C5×C22⋊C4C2312yes—
236C2×C5×C22⋊C4C2312yes—
237C2×C5×C22⋊C4C2311yescharacteristic
238C2×C42×C5C2311yescharacteristic
239C2×C42×C5C2311yescharacteristic
240#4099C23116yescomplemented
241#4099C23116yescomplemented
242C2×C22⋊Dic5C2312yes—
243C2×C22⋊Dic5C2311yescharacteristic
244C2×C22⋊Dic5C2312yes—
245C2×C22⋊Dic5C2311yescharacteristic
246C2×C22⋊Dic5C2312yes—
247C2×C22⋊Dic5C2312yes—
248C2×C22⋊Dic5C2312yes—
249C2×C22⋊Dic5C2312yes—
250#4093C2318yescomplemented
251#4092C2318yescomplemented
252Q8×Dic5C2318yescomplemented
253#4086C2318yes—
254#4086C2318yescomplemented
255#4086C23116yescomplemented
256#4086C23116yescomplemented
257#4086C2318yescomplemented
258#4086C23116yescomplemented
259#4085C23116yescomplemented
260#4085C23116yescomplemented
261#4085C23116yescomplemented
262#4085C23116yescomplemented
263#4085C23116yescomplemented
264#4085C23116yescomplemented
265#4085C23116yescomplemented
266#4084C2318yes—
267#4084C2318yescomplemented
268#4084C23116yescomplemented
269#4084C23116yescomplemented
270#4084C2318yescomplemented
271#4084C23116yescomplemented
272#4083C23116yescomplemented
273#4083C23116yescomplemented
274#4083C23116yescomplemented
275#4083C23116yescomplemented
276#4083C23116yescomplemented
277#4081C23116yescomplemented
278#4081C23116yescomplemented
279D4×Dic5C2318yescomplemented
280D4×Dic5C2318yescomplemented
281D4×Dic5C2318yescomplemented
282#4076C2318yescomplemented
283#4076C2318yescomplemented
284#4076C23116yescomplemented
285#4075C23116yescomplemented
286C4×C22⋊D5C2318yescomplemented
287C4×C22⋊D5C2318yescomplemented
288C4×C22⋊D5C23116yescomplemented
289C2×#685C2311yescharacteristic
290C2×#685C2311yescharacteristic
291C2×#685C2311yescharacteristic
292C2×#685C2312yes—
293C2×#685C2311yescharacteristic
294C2×#685C2312yes—
295C2×#685C2312yes—
296C2×#685C2312yes—
297C2×#685C2312yes—
298C2×#685C2312yes—
299C2×#685C2312yes—
300C2×#685C2311yescharacteristic
301C2×#685C2311yescharacteristic
302C2×#685C23116yescomplemented
303C2×C4⋊Dic5C2311yescharacteristic
304C2×C4⋊Dic5C2311yescharacteristic
305C2×C4⋊Dic5C2311yescharacteristic
306C2×C4⋊Dic5C2311yescharacteristic
307C2×C4⋊Dic5C2312yes—
308C2×#683C2311yescharacteristic
309C2×#683C2311yescharacteristic
310C2×#683C2312yes—
311C2×#683C2312yes—
312C2×#683C2311yescharacteristic
313C2×#683C2311yescharacteristic
314C2×#683C2312yes—
315C2×#683C2311yescharacteristic
316C2×#683C2311yescharacteristic
317C2×C4×Dic5C2311yescharacteristic
318C2×C4×Dic5C2311yescharacteristic
319C2×C4×Dic5C2311yescharacteristic
320C2×C4×Dic5C2311yescharacteristic
321C2×C4×Dic5C2312yes—
322#4044C2318yescomplemented
323#4042C2318yescomplemented
324#4040C2318yescomplemented
325#4040C23116yescomplemented
326#4040C23116yescomplemented
327#4035C2318yescomplemented
328#4032C23116yescomplemented
329#4031C2318yescomplemented
330#4031C23116yescomplemented
331#4030C2318yes—
332#4030C23116yescomplemented
333#4030C23116yescomplemented
334#4030C23116yescomplemented
335#4030C23116yescomplemented
336#4030C23116yescomplemented
337#4029C2318yescomplemented
338#4029C23116yescomplemented
339#4029C23116yescomplemented
340#4029C23116yescomplemented
341#4028C23116yescomplemented
342#4028C23116yescomplemented
343#4028C23116yescomplemented
344#4027C23116yescomplemented
345#4027C23116yescomplemented
346D5×C22⋊C4C23116yescomplemented
347#4025C2318yescomplemented
348#4025C23116yescomplemented
349#4023C23116yescomplemented
350#4020C2318yescomplemented
351C4×D20C2318yescomplemented
352C4×D20C2318yescomplemented
353C4×D20C2318yescomplemented
354#4018C2318yescomplemented
355C42×D5C2318yescomplemented
356#4016C2318yescomplemented
357C4×Dic10C2318yescomplemented
358#3543—532no—
359C2×#560—52no—
360C2×#560—52no—
361C2×#559—51no—
362C2×#550—51no—
363C2×#550—51no—
364C2×#546—51no—
365C2×#546—51no—
366C2×#546—52no—
367C2×D42—51no—
368C2×D42—51no—
369C2×D42—51no—
370C2×D42—52no—
371C2×#540—51no—
372C2×#540—52no—
373C2×#540—51no—
374C2×#535—51no—
375C2×#535—52no—
376C2×#535D511yescharacteristic, complemented
377C2×#534—52no—
378C2×#534—52no—
379C22×#127—51no—
380C2×#529—51no—
381C2×#529—51no—
382C24×C5—44no—
383C24×C5—44no—
384C24×C5—44no—
385C24×C5C2412yes—
386C24×C5C2412yes—
387C24×C5C2411yescharacteristic
388C24×C5C2412yes—
389C24×C5C2418yes—
390C23×D5—28no—
391C23×D5—28no—
392C23×D5—44no—
393C23×D5—44no—
394C23×D5—44no—
395C23×D5—44no—
396C23×D5—44no—
397C23×D5—44no—
398C23×D5—44no—
399C23×D5C2412yes—
400C23×D5C2411yescharacteristic
401C23×D5C2412yes—
402C23×D5C2411yescharacteristic
403C23×D5C2418yes—
404C23×D5C2418yes—
405C23×D5C2418yes—
406C5×#41—416no—
407C2×C5×Q8—24no—
408C2×C5×Q8C2414yes—
409C2×C5×D4—24no—
410C2×C5×D4—24no—
411C2×C5×D4—24no—
412C2×C5×D4—416no—
413C2×C5×D4—44no—
414C2×C5×D4—44no—
415C2×C5×D4—44no—
416C2×C5×D4—44no—
417C2×C5×D4—44no—
418C2×C5×D4—44no—
419C2×C5×D4C2414yes—
420C2×C5×D4C2414yes—
421C2×C5×D4C2414yes—
422C2×C5×D4C2418yes—
423C2×C5×D4C2418yes—
424C2×C5×D4C2418yes—
425C2×C5×D4C2418yes—
426C2×C5×D4C2418yes—
427C2×C5×D4C2418yes—
428C22×C4×C5—24no—
429C22×C4×C5—44no—
430C22×C4×C5C2411yescharacteristic
431C22×C4×C5C2411yescharacteristic
432C22×C4×C5C2411yescharacteristic
433C22×C4×C5C2411yescharacteristic
434C22×C4×C5C2412yes—
435C22×C4×C5C2411yescharacteristic
436C22×C4×C5C2414yes—
437C22×C4×C5C2418yes—
438C22×C4×C5C2411yescharacteristic
439C2×C22⋊D5—28no—
440C2×C22⋊D5—24no—
441C2×C22⋊D5—28no—
442C2×C22⋊D5—28no—
443C2×C22⋊D5—24no—
444C2×C22⋊D5—432no—
445C2×C22⋊D5—44no—
446C2×C22⋊D5—44no—
447C2×C22⋊D5—44no—
448C2×C22⋊D5—44no—
449C2×C22⋊D5—44no—
450C2×C22⋊D5—44no—
451C2×C22⋊D5—44no—
452C2×C22⋊D5—44no—
453C2×C22⋊D5—44no—
454C2×C22⋊D5—44no—
455C2×C22⋊D5—44no—
456C2×C22⋊D5—432no—
457C2×C22⋊D5C2418yes—
458C2×C22⋊D5C2418yes—
459C2×C22⋊D5C2418yes—
460C2×C22⋊D5C2414yes—
461C2×C22⋊D5C2414yes—
462C2×C22⋊D5C2418yes—
463C2×C22⋊D5C2418yes—
464C2×C22⋊D5C2418yes—
465C2×C22⋊D5C2418yes—
466C2×C22⋊D5C2418yes—
467C2×C22⋊D5C2418yes—
468C2×C22⋊D5C2418yes—
469C2×C22⋊D5C2418yes—
470C2×C22⋊D5C2418yes—
471C2×C22⋊D5C2418yes—
472C2×C22⋊D5C2418yes—
473C22×Dic5—28no—
474C22×Dic5—44no—
475C22×Dic5—44no—
476C22×Dic5C2411yescharacteristic
477C22×Dic5C2411yescharacteristic
478C22×Dic5C2412yes—
479C22×Dic5C2412yes—
480C22×Dic5C2411yescharacteristic
481C22×Dic5C2411yescharacteristic
482C22×Dic5C2411yescharacteristic
483C22×Dic5C2418yes—
484C22×Dic5C2418yes—
485C22×Dic5C2418yes—
486C22×Dic5C2411yescharacteristic
487#713—416no—
488#711—432no—
489D4×D5—416no—
490D4×D5—416no—
491D4×D5—416no—
492D4×D5—432no—
493D4×D5—432no—
494D4×D5—432no—
495C2×D20—24no—
496C2×D20—24no—
497C2×D20—24no—
498C2×D20—44no—
499C2×D20—44no—
500C2×D20—44no—
501C2×D20C2414yes—
502C2×D20C2414yes—
503C2×D20C2414yes—
504C2×D20C2418yes—
505C2×D20C2418yes—
506C2×D20C2418yes—
507C2×C4×D5—24no—
508C2×C4×D5—24no—
509C2×C4×D5—24no—
510C2×C4×D5—24no—
511C2×C4×D5—44no—
512C2×C4×D5—44no—
513C2×C4×D5—44no—
514C2×C4×D5C2414yes—
515C2×C4×D5C2414yes—
516C2×C4×D5C2414yes—
517C2×C4×D5C2414yes—
518C2×C4×D5C2418yes—
519C2×C4×D5C2418yes—
520C2×C4×D5C2418yes—
521C2×Dic10—24no—
522C2×Dic10C2414yes—
523C5×C4⋊C4C2414yes—
524C5×C4⋊C4C2414yes—
525C5×C22⋊C4C2414yes—
526C5×C22⋊C4C2414yes—
527C5×C22⋊C4C2418yes—
528C5×C22⋊C4C2418yes—
529C5×C22⋊C4C2418yes—
530C5×C22⋊C4C2418yes—
531C42×C5C2414yes—
532C42×C5C2414yes—
533C22⋊Dic5C2414yes—
534C22⋊Dic5C2414yes—
535C22⋊Dic5C2418yes—
536C22⋊Dic5C2418yes—
537C22⋊Dic5C2418yes—
538C22⋊Dic5C2418yes—
539C22⋊Dic5C2418yes—
540C22⋊Dic5C2418yes—
541#685C2414yes—
542#685C2414yes—
543#685C2414yes—
544#685C2418yes—
545#685C2414yes—
546#685C2418yes—
547#685C2418yes—
548#685C2418yes—
549#685C2418yes—
550#685C2418yes—
551#685C2418yes—
552#685C2414yes—
553#685C2414yes—
554C4⋊Dic5C2414yes—
555C4⋊Dic5C2414yes—
556C4⋊Dic5C2414yes—
557C4⋊Dic5C2414yes—
558C4⋊Dic5C2418yes—
559#683C2414yes—
560#683C2414yes—
561#683C2418yes—
562#683C2418yes—
563#683C2414yes—
564#683C2414yes—
565#683C2418yes—
566#683C2414yes—
567#683C2414yes—
568C4×Dic5C2414yes—
569C4×Dic5C2414yes—
570C4×Dic5C2414yes—
571C4×Dic5C2414yes—
572C4×Dic5C2418yes—
573C22×#41—51no—
574C22×#41—52no—
575C22×#41C2×D511yescharacteristic, complemented
576C23×D4—52no—
577C23×D4—52no—
578C23×D4—52no—
579C23×D4—52no—
580C23×D4—51no—
581C23×D4—51no—
582C23×D4—52no—
583C23×D4—51no—
584C23×D4C2×D511yescharacteristic, complemented
585#560—532no—
586#560—532no—
587#559—516no—
588#550—516no—
589#550—516no—
590#546—516no—
591#546—516no—
592#546—532no—
593D42—516no—
594D42—516no—
595D42—516no—
596D42—532no—
597#540—516no—
598#540—532no—
599#540—516no—
600#535—516no—
601#535—532no—
602#535C2×D5116yescomplemented
603#534—532no—
604#534—532no—
605C2×#127—51no—
606C2×#127—52no—
607C2×#127—51no—
608C2×#127—52no—
609C2×#127—52no—
610C2×#127—51no—
611C2×#127—516no—
612C2×#127—51no—
613C2×#127C2×D511yescharacteristic, complemented
614C2×#127C2×D511yescharacteristic, complemented
615#529—516no—
616#529—516no—
617C2×#126—51no—
618C2×#126—52no—
619C2×#126—51no—
620C2×#125—51no—
621C2×#125—51no—
622C2×#124—51no—
623C2×#124—51no—
624C2×#124—52no—
625C2×#124C2×D511yescharacteristic, complemented
626C2×#124C2×D511yescharacteristic, complemented
627C2×#123—52no—
628C2×#123—52no—
629C2×#123—52no—
630C2×#123—51no—
631C2×#123—52no—
632C2×#123—52no—
633C2×#123—52no—
634C2×#123—51no—
635C2×#123—52no—
636C2×#123—52no—
637C2×#123—52no—
638C2×C22⋊Q8—51no—
639C2×C22⋊Q8—51no—
640C2×#121—51no—
641C2×#121—52no—
642C2×#121—52no—
643C2×#121—51no—
644C2×#121—51no—
645C2×#121—52no—
646C2×#121—52no—
647C2×#121—52no—
648C2×#121—52no—
649C2×#121—52no—
650C2×#121—52no—
651C2×#121—52no—
652C2×#121—52no—
653C2×#121—52no—
654C2×#121—51no—
655C2×#121—51no—
656C2×#121—51no—
657C2×#121—52no—
658C2×#121—52no—
659C2×#121—52no—
660C2×#121—52no—
661C2×#121—52no—
662C2×#121C2×D512yescomplemented
663C2×#121C2×D512yescomplemented
664C2×#120—52no—
665C2×#120—52no—
666C2×#120—52no—
667C2×#120—52no—
668C2×#120—52no—
669C2×#120—52no—
670C2×#120—52no—
671C2×#120—52no—
672C2×#120—52no—
673C2×#120—52no—
674C2×#120C2×D512yescomplemented
675C2×#120C2×D512yescomplemented
676C2×C4×Q8—51no—
677C2×C4×Q8—51no—
678C2×C4×D4—51no—
679C2×C4×D4—51no—
680C2×C4×D4—51no—
681C2×C4×D4—51no—
682C2×C4×D4—51no—
683C2×C4×D4—52no—
684C2×C4×D4—52no—
685C2×C4×D4—52no—
686C2×C4×D4—51no—
687C2×C4×D4—51no—
688C2×C4×D4—51no—
689C2×#117—52no—
690C2×#117—51no—
691C2×#117C2×D511yescharacteristic, complemented
692C22×C22⋊C4—52no—
693C22×C22⋊C4—52no—
694C22×C42—51no—
695C23×C5—24no—
696C23×C5—24no—
697C23×C5—24no—
698C23×C5—22no—
699C23×C5—22no—
700C23×C5—24no—
701C23×C5—24no—
702C23×C5—24no—
703C23×C5—24no—
704C23×C5—24no—
705C23×C5—24no—
706C23×C5—22no—
707C23×C5—48no—
708C23×C5—48no—
709C23×C5—48no—
710C23×C5—816no—
711C23×C5C2514yes—
712C23×C5C2514yes—
713C23×C5C2512yes—
714C23×C5C2514yes—
715C23×C5C2511yescharacteristic
716C22×D5—22no—
717C22×D5—22no—
718C22×D5—22no—
719C22×D5—24no—
720C22×D5—24no—
721C22×D5—24no—
722C22×D5—24no—
723C22×D5—22no—
724C22×D5—24no—
725C22×D5—24no—
726C22×D5—22no—
727C22×D5—216no—
728C22×D5—216no—
729C22×D5—48no—
730C22×D5—48no—
731C22×D5—48no—
732C22×D5—48no—
733C22×D5—48no—
734C22×D5—48no—
735C22×D5—48no—
736C22×D5—816no—
737C22×D5—816no—
738C22×D5—816no—
739C22×D5H(5,𝔽2)14yes—
740C22×D5C2512yes—
741C22×D5C2514yes—
742C22×D5C2514yes—
743C22×D5C2512yes—
744C5×Q8—28no—
745C5×D4—28no—
746C5×D4—28no—
747C5×D4—28no—
748C5×D4—48no—
749C5×D4—48no—
750C5×D4—48no—
751C5×D4—48no—
752C5×D4—48no—
753C5×D4—48no—
754C2×C4×C5—22no—
755C2×C4×C5—22no—
756C2×C4×C5—22no—
757C2×C4×C5—22no—
758C2×C4×C5—24no—
759C2×C4×C5—22no—
760C2×C4×C5—28no—
761C2×C4×C5—48no—
762C2×C4×C5H(5,𝔽2)14yes—
763C2×C4×C5C2512yes—
764C2×C4×C5C2512yes—
765C2×C4×C5C2514yes—
766C2×C4×C5C2512yes—
767C2×C4×C5C2512yes—
768C2×C4×C5C2512yes—
769C2×C4×C5C2512yes—
770C22⋊D5—216no—
771C22⋊D5—28no—
772C22⋊D5—216no—
773C22⋊D5—216no—
774C22⋊D5—28no—
775C22⋊D5—48no—
776C22⋊D5—48no—
777C22⋊D5—48no—
778C22⋊D5—48no—
779C22⋊D5—48no—
780C22⋊D5—48no—
781C22⋊D5—48no—
782C22⋊D5—48no—
783C22⋊D5—48no—
784C22⋊D5—48no—
785C22⋊D5—48no—
786C2×Dic5—22no—
787C2×Dic5—22no—
788C2×Dic5—22no—
789C2×Dic5—22no—
790C2×Dic5—24no—
791C2×Dic5—24no—
792C2×Dic5—22no—
793C2×Dic5—216no—
794C2×Dic5—48no—
795C2×Dic5—48no—
796C2×Dic5H(5,𝔽2)14yes—
797C2×Dic5C2512yes—
798C2×Dic5C2512yes—
799C2×Dic5C2512yes—
800C2×Dic5C2514yes—
801C2×Dic5C2512yes—
802C2×Dic5C2514yes—
803C2×Dic5C2512yes—
804C2×Dic5C2512yes—
805D20—28no—
806D20—28no—
807D20—28no—
808D20—48no—
809D20—48no—
810D20—48no—
811C4×D5—28no—
812C4×D5—28no—
813C4×D5—28no—
814C4×D5—28no—
815C4×D5—48no—
816C4×D5—48no—
817C4×D5—48no—
818Dic10—28no—
819C25—52no—
820C25—52no—
821C25—52no—
822C25C22×D512yes—
823C2×#41—44no—
824C2×#41—58no—
825C2×#41—516no—
826C2×#41—208no—
827C2×#41—204no—
828C2×#41C22×D518yescomplemented
829C22×Q8—51no—
830C22×Q8C22×D511yescharacteristic
831C22×D4—44no—
832C22×D4—52no—
833C22×D4—51no—
834C22×D4—52no—
835C22×D4—51no—
836C22×D4—52no—
837C22×D4—52no—
838C22×D4—52no—
839C22×D4—52no—
840C22×D4—52no—
841C22×D4—52no—
842C22×D4—52no—
843C22×D4—52no—
844C22×D4—52no—
845C22×D4—52no—
846C22×D4—52no—
847C22×D4—52no—
848C22×D4—516no—
849C22×D4—516no—
850C22×D4—516no—
851C22×D4—516no—
852C22×D4—58no—
853C22×D4—58no—
854C22×D4—516no—
855C22×D4—58no—
856C22×D4—51no—
857C22×D4—51no—
858C22×D4—51no—
859C22×D4—52no—
860C22×D4—52no—
861C22×D4—52no—
862C22×D4—204no—
863C22×D4—204no—
864C22×D4—204no—
865C22×D4—208no—
866C22×D4—208no—
867C22×D4—208no—
868C22×D4—208no—
869C22×D4—208no—
870C22×D4C22×D511yescharacteristic
871C22×D4C22×D511yescharacteristic
872C22×D4C22×D511yescharacteristic
873C22×D4C22×D512yes—
874C22×D4C22×D512yes—
875C22×D4C22×D512yes—
876C22×D4C22×D512yes—
877C22×D4C22×D512yes—
878C22×D4C22×D512yes—
879C22×D4C22×D518yescomplemented
880C23×C4—52no—
881C23×C4—52no—
882C23×C4—52no—
883C23×C4—51no—
884C23×C4—51no—
885C23×C4—51no—
886C23×C4—51no—
887C23×C4—52no—
888C23×C4—52no—
889C23×C4—52no—
890C23×C4C22×D511yescharacteristic
891C23×C4C22×D512yes—
892#127—516no—
893#127—58no—
894#127—58no—
895#127—516no—
896#127—516no—
897#127—58no—
898#127—58no—
899#127C22×D518yescomplemented
900#127C22×D518yescomplemented
901#126—58no—
902#126—516no—
903#126—58no—
904#125—58no—
905#125—58no—
906#124—58no—
907#124—58no—
908#124—516no—
909#124C22×D518yescomplemented
910#124C22×D518yescomplemented
911#123—516no—
912#123—516no—
913#123—516no—
914#123—58no—
915#123—516no—
916#123—516no—
917#123—516no—
918#123—58no—
919#123—516no—
920#123—516no—
921#123—516no—
922C22⋊Q8—58no—
923C22⋊Q8—58no—
924#121—58no—
925#121—516no—
926#121—516no—
927#121—516no—
928#121—516no—
929#121—516no—
930#121—58no—
931#121—516no—
932#121—58no—
933#121—516no—
934#121—516no—
935#121—516no—
936#121—516no—
937#121—516no—
938#121—58no—
939#121—58no—
940#121—58no—
941#121—516no—
942#121—516no—
943#121—516no—
944#121—516no—
945#121—516no—
946#121C22×D5116yescomplemented
947#121C22×D5116yescomplemented
948#120—516no—
949#120—516no—
950#120—516no—
951#120—516no—
952#120—516no—
953#120—516no—
954#120—516no—
955#120—516no—
956#120—516no—
957#120—516no—
958#120C22×D5116yescomplemented
959#120C22×D5116yescomplemented
960C4×Q8—58no—
961C4×Q8—58no—
962C4×D4—58no—
963C4×D4—58no—
964C4×D4—58no—
965C4×D4—58no—
966C4×D4—58no—
967C4×D4—516no—
968C4×D4—516no—
969C4×D4—516no—
970C4×D4—58no—
971C4×D4—58no—
972C4×D4—58no—
973#117—516no—
974#117—58no—
975#117C22×D518yescomplemented
976C2×C4⋊C4—52no—
977C2×C4⋊C4—51no—
978C2×C4⋊C4—52no—
979C2×C4⋊C4—51no—
980C2×C4⋊C4—51no—
981C2×C4⋊C4—51no—
982C2×C4⋊C4—51no—
983C2×C4⋊C4—51no—
984C2×C4⋊C4—51no—
985C2×C4⋊C4—52no—
986C2×C4⋊C4—51no—
987C2×C4⋊C4—51no—
988C2×C4⋊C4—52no—
989C2×C4⋊C4—51no—
990C2×C4⋊C4C22×D511yescharacteristic
991C2×C4⋊C4C22×D511yescharacteristic
992C2×C22⋊C4—52no—
993C2×C22⋊C4—52no—
994C2×C22⋊C4—52no—
995C2×C22⋊C4—51no—
996C2×C22⋊C4—51no—
997C2×C22⋊C4—52no—
998C2×C22⋊C4—52no—
999C2×C22⋊C4—52no—
1000C2×C22⋊C4—51no—
1001C2×C22⋊C4—52no—
1002C2×C22⋊C4—51no—
1003C2×C22⋊C4—52no—
1004C2×C22⋊C4—52no—
1005C2×C22⋊C4—516no—
1006C2×C22⋊C4—51no—
1007C2×C22⋊C4—51no—
1008C2×C22⋊C4—51no—
1009C2×C22⋊C4—51no—
1010C2×C22⋊C4—52no—
1011C2×C22⋊C4—52no—
1012C2×C22⋊C4—52no—
1013C2×C22⋊C4—52no—
1014C2×C22⋊C4—516no—
1015C2×C22⋊C4C22×D512yes—
1016C2×C22⋊C4C22×D512yes—
1017C2×C22⋊C4C22×D511yescharacteristic
1018C2×C22⋊C4C22×D511yescharacteristic
1019C2×C22⋊C4C22×D512yes—
1020C2×C22⋊C4C22×D512yes—
1021C2×C42—51no—
1022C2×C42—52no—
1023C2×C42—51no—
1024C2×C42—51no—
1025C2×C42—51no—
1026C2×C42—58no—
1027C2×C42C22×D511yescharacteristic
1028C2×C42C22×D511yescharacteristic
1029C22×C5—24no—
1030C22×C5—24no—
1031C22×C5—24no—
1032C22×C5—22no—
1033C22×C5—22no—
1034C22×C5—24no—
1035C22×C5—24no—
1036C22×C5—24no—
1037C22×C5—24no—
1038C22×C5—24no—
1039C22×C5—24no—
1040C22×C5—22no—
1041C22×C5—48no—
1042C22×C5—48no—
1043C22×C5—48no—
1044C22×C5—44no—
1045C22×C5—816no—
1046C22×C5C2×H(5,𝔽2)12yes—
1047C22×C5C2×H(5,𝔽2)12yes—
1048C22×C5C2×H(5,𝔽2)12yes—
1049C22×C5C2611yescharacteristic
1050C2×D5—22no—
1051C2×D5—22no—
1052C2×D5—28no—
1053C2×D5—22no—
1054C2×D5—24no—
1055C2×D5—24no—
1056C2×D5—24no—
1057C2×D5—24no—
1058C2×D5—22no—
1059C2×D5—24no—
1060C2×D5—24no—
1061C2×D5—22no—
1062C2×D5—48no—
1063C2×D5—44no—
1064C2×D5—48no—
1065C2×D5—816no—
1066C2×D5—816no—
1067C2×D5—816no—
1068C2×D5C2×H(5,𝔽2)14yes—
1069C4×C5—22no—
1070C4×C5—22no—
1071C4×C5—22no—
1072C4×C5—22no—
1073C4×C5—24no—
1074C4×C5—22no—
1075C4×C5C2×H(5,𝔽2)14yes—
1076Dic5—22no—
1077Dic5—22no—
1078Dic5—22no—
1079Dic5—22no—
1080Dic5—24no—
1081Dic5—24no—
1082Dic5—22no—
1083Dic5C2×H(5,𝔽2)14yes—
1084C24—44no—
1085C24—44no—
1086C24—44no—
1087C24—51no—
1088C24—51no—
1089C24—52no—
1090C24—52no—
1091C24—58no—
1092C24—58no—
1093C24—58no—
1094C24—108no—
1095C24—108no—
1096C24—204no—
1097C24—204no—
1098C24—204no—
1099C24—204no—
1100C24—204no—
1101C24—204no—
1102C24—204no—
1103C24C23×D512yes—
1104C24C23×D512yes—
1105C24C23×D511yescharacteristic
1106C24C23×D512yes—
1107C24C23×D518yes—
1108#41—416no—
1109#41—2032no—
1110#41—2016no—
1111C2×Q8—24no—
1112C2×Q8—54no—
1113C2×Q8—104no—
1114C2×Q8C23×D514yes—
1115C2×D4—24no—
1116C2×D4—24no—
1117C2×D4—24no—
1118C2×D4—416no—
1119C2×D4—44no—
1120C2×D4—44no—
1121C2×D4—44no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C2×D4—44no—
1125C2×D4—58no—
1126C2×D4—54no—
1127C2×D4—58no—
1128C2×D4—54no—
1129C2×D4—58no—
1130C2×D4—58no—
1131C2×D4—58no—
1132C2×D4—58no—
1133C2×D4—58no—
1134C2×D4—58no—
1135C2×D4—58no—
1136C2×D4—58no—
1137C2×D4—58no—
1138C2×D4—58no—
1139C2×D4—58no—
1140C2×D4—58no—
1141C2×D4—54no—
1142C2×D4—54no—
1143C2×D4—54no—
1144C2×D4—58no—
1145C2×D4—58no—
1146C2×D4—58no—
1147C2×D4—104no—
1148C2×D4—108no—
1149C2×D4—104no—
1150C2×D4—108no—
1151C2×D4—108no—
1152C2×D4—104no—
1153C2×D4—104no—
1154C2×D4—104no—
1155C2×D4—204no—
1156C2×D4—204no—
1157C2×D4—204no—
1158C2×D4—2016no—
1159C2×D4—2016no—
1160C2×D4—2016no—
1161C2×D4—2032no—
1162C2×D4—2032no—
1163C2×D4—2032no—
1164C2×D4—204no—
1165C2×D4—204no—
1166C2×D4—204no—
1167C2×D4—204no—
1168C2×D4—204no—
1169C2×D4—204no—
1170C2×D4—204no—
1171C2×D4—204no—
1172C2×D4—204no—
1173C2×D4—204no—
1174C2×D4—204no—
1175C2×D4—2032no—
1176C2×D4—2032no—
1177C2×D4C23×D514yes—
1178C2×D4C23×D514yes—
1179C2×D4C23×D514yes—
1180C2×D4C23×D518yes—
1181C2×D4C23×D518yes—
1182C2×D4C23×D518yes—
1183C2×D4C23×D518yes—
1184C2×D4C23×D518yes—
1185C2×D4C23×D518yes—
1186C22×C4—24no—
1187C22×C4—44no—
1188C22×C4—51no—
1189C22×C4—58no—
1190C22×C4—51no—
1191C22×C4—51no—
1192C22×C4—51no—
1193C22×C4—52no—
1194C22×C4—51no—
1195C22×C4—51no—
1196C22×C4—52no—
1197C22×C4—58no—
1198C22×C4—58no—
1199C22×C4—54no—
1200C22×C4—54no—
1201C22×C4—54no—
1202C22×C4—54no—
1203C22×C4—58no—
1204C22×C4—58no—
1205C22×C4—58no—
1206C22×C4—104no—
1207C22×C4—104no—
1208C22×C4—108no—
1209C22×C4—104no—
1210C22×C4—104no—
1211C22×C4—204no—
1212C22×C4—204no—
1213C22×C4—204no—
1214C22×C4—204no—
1215C22×C4—204no—
1216C22×C4C23×D514yes—
1217C22×C4C23×D511yescharacteristic
1218C22×C4C23×D511yescharacteristic
1219C22×C4C23×D512yes—
1220C22×C4C23×D511yescharacteristic
1221C22×C4C23×D511yescharacteristic
1222C22×C4C23×D511yescharacteristic
1223C22×C4C23×D518yes—
1224C22×C4C23×D511yescharacteristic
1225C4⋊C4—58no—
1226C4⋊C4—54no—
1227C4⋊C4—58no—
1228C4⋊C4—54no—
1229C4⋊C4—54no—
1230C4⋊C4—54no—
1231C4⋊C4—54no—
1232C4⋊C4—54no—
1233C4⋊C4—54no—
1234C4⋊C4—58no—
1235C4⋊C4—54no—
1236C4⋊C4—54no—
1237C4⋊C4—58no—
1238C4⋊C4—54no—
1239C4⋊C4C23×D514yes—
1240C4⋊C4C23×D514yes—
1241C22⋊C4—58no—
1242C22⋊C4—58no—
1243C22⋊C4—58no—
1244C22⋊C4—54no—
1245C22⋊C4—54no—
1246C22⋊C4—58no—
1247C22⋊C4—58no—
1248C22⋊C4—58no—
1249C22⋊C4—54no—
1250C22⋊C4—58no—
1251C22⋊C4—54no—
1252C22⋊C4—58no—
1253C22⋊C4—58no—
1254C22⋊C4—54no—
1255C22⋊C4—54no—
1256C22⋊C4—54no—
1257C22⋊C4—54no—
1258C22⋊C4—58no—
1259C22⋊C4—58no—
1260C22⋊C4—58no—
1261C22⋊C4—58no—
1262C22⋊C4C23×D518yes—
1263C22⋊C4C23×D518yes—
1264C22⋊C4C23×D514yes—
1265C22⋊C4C23×D514yes—
1266C22⋊C4C23×D518yes—
1267C22⋊C4C23×D518yes—
1268C42—54no—
1269C42—54no—
1270C42—54no—
1271C42—58no—
1272C42—54no—
1273C42C23×D514yes—
1274C42C23×D514yes—
1275C2×C5—44no—
1276C2×C5—44no—
1277C2×C5—44no—
1278C2×C5—42no—
1279C2×C5#354314yescomplemented
1280C2×C5C22×H(5,𝔽2)11yescharacteristic
1281C2×C5C22×H(5,𝔽2)11yescharacteristic
1282C2×C5C22×H(5,𝔽2)11yescharacteristic
1283D5—24no—
1284D5—44no—
1285D5—42no—
1286D5—44no—
1287C23—22no—
1288C23—24no—
1289C23—24no—
1290C23—24no—
1291C23—24no—
1292C23—24no—
1293C23—24no—
1294C23—24no—
1295C23—24no—
1296C23—24no—
1297C23—22no—
1298C23—22no—
1299C23—48no—
1300C23—48no—
1301C23—48no—
1302C23—54no—
1303C23—52no—
1304C23—52no—
1305C23—54no—
1306C23—54no—
1307C23—816no—
1308C23—1016no—
1309C23—1016no—
1310C23—102no—
1311C23—102no—
1312C23—102no—
1313C23—104no—
1314C23—104no—
1315C23—104no—
1316C23—104no—
1317C23—104no—
1318C23—102no—
1319C23—102no—
1320C23—104no—
1321C23—208no—
1322C23—208no—
1323C23—208no—
1324C23—208no—
1325C23—208no—
1326C23—208no—
1327C23—208no—
1328C23—4016no—
1329C23—4016no—
1330C23—4016no—
1331C23C24×D514yes—
1332C23C24×D514yes—
1333C23C24×D512yes—
1334C23C24×D514yes—
1335C23C24×D511yescharacteristic
1336Q8—28no—
1337Q8—108no—
1338D4—28no—
1339D4—28no—
1340D4—28no—
1341D4—48no—
1342D4—48no—
1343D4—48no—
1344D4—48no—
1345D4—48no—
1346D4—48no—
1347D4—108no—
1348D4—1016no—
1349D4—108no—
1350D4—1016no—
1351D4—1016no—
1352D4—108no—
1353D4—108no—
1354D4—108no—
1355D4—208no—
1356D4—208no—
1357D4—208no—
1358D4—208no—
1359D4—208no—
1360D4—208no—
1361D4—208no—
1362D4—208no—
1363D4—208no—
1364D4—208no—
1365D4—208no—
1366D4—208no—
1367D4—208no—
1368D4—208no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—28no—
1376C2×C4—48no—
1377C2×C4—54no—
1378C2×C4—52no—
1379C2×C4—52no—
1380C2×C4—52no—
1381C2×C4—52no—
1382C2×C4—54no—
1383C2×C4—52no—
1384C2×C4—52no—
1385C2×C4—54no—
1386C2×C4—108no—
1387C2×C4—108no—
1388C2×C4—1016no—
1389C2×C4—102no—
1390C2×C4—102no—
1391C2×C4—104no—
1392C2×C4—102no—
1393C2×C4—104no—
1394C2×C4—102no—
1395C2×C4—102no—
1396C2×C4—108no—
1397C2×C4—108no—
1398C2×C4—208no—
1399C2×C4—208no—
1400C2×C4—208no—
1401C2×C4—208no—
1402C2×C4—208no—
1403C2×C4#414414yes—
1404C2×C4C24×D512yes—
1405C2×C4C24×D512yes—
1406C2×C4C24×D514yes—
1407C2×C4C24×D512yes—
1408C2×C4C24×D512yes—
1409C2×C4C24×D512yes—
1410C2×C4C24×D512yes—
1411C5C2×#354311yescharacteristic, complemented, Sylow
1412C22—22no—
1413C22—24no—
1414C22—24no—
1415C22—24no—
1416C22—24no—
1417C22—24no—
1418C22—24no—
1419C22—24no—
1420C22—24no—
1421C22—24no—
1422C22—22no—
1423C22—22no—
1424C22—44no—
1425C22—48no—
1426C22—48no—
1427C22—48no—
1428C22—54no—
1429C22—816no—
1430C22—102no—
1431C22—102no—
1432C22—108no—
1433C22—102no—
1434C22—104no—
1435C22—104no—
1436C22—104no—
1437C22—104no—
1438C22—104no—
1439C22—102no—
1440C22—102no—
1441C22—104no—
1442C22—204no—
1443C22—208no—
1444C22—208no—
1445C22—4016no—
1446C22—4016no—
1447C22—4016no—
1448C22C2×#414412yes—
1449C22D5×H(5,𝔽2)12yes—
1450C22D5×H(5,𝔽2)12yes—
1451C22C25×D511yescharacteristic
1452C4—22no—
1453C4—24no—
1454C4—22no—
1455C4—22no—
1456C4—22no—
1457C4—22no—
1458C4—54no—
1459C4—102no—
1460C4—102no—
1461C4—104no—
1462C4—102no—
1463C4—104no—
1464C4—102no—
1465C4—102no—
1466C4C2×#414414yes—
1467C2—42no—
1468C2—44no—
1469C2—44no—
1470C2—44no—
1471C2—104no—
1472C2—202no—
1473C2—204no—
1474C2—204no—
1475C2#1061823714yesdirect product factor
1476C2C22×#414411yescharacteristic
1477C2C2×D5×H(5,𝔽2)11yescharacteristic
1478C2C2×D5×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#535C2
socleC23×C5C25
hypercenterC2×#535D5
hypocenterC5C2×#3543
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×C5×#535C2semidirect
2. C2×#66168C2semidirect
3. C2×#66163C2semidirect
4. C2×D4×C22⋊D5C2semidirect
5. C2×D4×C22⋊D5C2semidirect
6. #10618237C2direct (N × H)
7. C2×#66051C2semidirect
8. C2×#66053C2semidirect
9. C2×D5×#127C2semidirect
10. C2×#66052C2semidirect
11. C2×#66010C2semidirect
12. C2×#66008C2semidirect
13. C2×#66015C2semidirect
14. C2×#66014C2semidirect
15. C2×#65954C2semidirect
16. C2×#65944C2semidirect
17. C2×#65939C2semidirect
18. C2×#65949C2semidirect
19. C2×#65929C2semidirect
20. C2×#65924C2semidirect
21. C2×#65923C2semidirect
22. C2×#65926C2semidirect
23. C2×#65869C2semidirect
24. C2×#65862C2semidirect
25. C22×C5×#41C22semidirect
26. C23×C5×D4C22semidirect
27. C23×C22⋊D5C22semidirect
28. C23×C22⋊D5C22semidirect
29. C22×#713C22semidirect
30. C22×#711C22semidirect
31. C22×D4×D5C22semidirect
32. C22×D4×D5C22semidirect
33. C22×D4×D5C22semidirect
34. C22×D4×D5C22semidirect
35. C22×D4×D5C22semidirect
36. C22×D4×D5C22semidirect
37. C5×#535C22semidirect
38. C2×C5×#127C22semidirect
39. C2×C5×#127C22semidirect
40. C2×C5×#124C22semidirect
41. C2×C5×#124C22semidirect
42. C2×C5×#121C22semidirect
43. C2×C5×#121C22semidirect
44. C2×C5×#120C22semidirect
45. C2×C5×#120C22semidirect
46. C2×C5×#117C22semidirect
47. C2×#4099C22semidirect
48. C2×#4099C22semidirect
49. #66168C22semidirect
50. #66163C22semidirect
51. C2×#4093C22semidirect
52. C2×#4092C22semidirect
53. C2×Q8×Dic5C22semidirect
55. C2×#4086C22semidirect
56. C2×#4086C22semidirect
57. C2×#4086C22semidirect
58. C2×#4086C22semidirect
59. C2×#4086C22semidirect
60. C2×#4085C22semidirect
61. C2×#4085C22semidirect
62. C2×#4085C22semidirect
63. C2×#4085C22semidirect
64. C2×#4085C22semidirect
65. C2×#4085C22semidirect
66. C2×#4085C22semidirect
67. D4×C22⋊D5C22semidirect
68. D4×C22⋊D5C22semidirect
70. C2×#4084C22semidirect
71. C2×#4084C22semidirect
72. C2×#4084C22semidirect
73. C2×#4084C22semidirect
74. C2×#4084C22semidirect
75. C2×#4083C22semidirect
76. C2×#4083C22semidirect
77. C2×#4083C22semidirect
78. C2×#4083C22semidirect
79. C2×#4083C22semidirect
80. C2×#4081C22semidirect
81. C2×#4081C22semidirect
82. C2×D4×Dic5C22semidirect
83. C2×D4×Dic5C22semidirect
84. C2×D4×Dic5C22semidirect
85. C2×#4076C22semidirect
86. C2×#4076C22semidirect
87. C2×#4076C22semidirect
88. C2×#4075C22semidirect
89. C2×C4×C22⋊D5C22semidirect
90. C2×C4×C22⋊D5C22semidirect
91. C2×C4×C22⋊D5C22semidirect
92. C22×#685C22semidirect
93. #66053C22semidirect
94. #66052C22semidirect
95. #66051C22semidirect
96. D5×#127C22semidirect
97. #66015C22semidirect
98. #66014C22semidirect
99. #66010C22semidirect
100. #66008C22semidirect
101. #65954C22semidirect
102. #65949C22semidirect
103. #65944C22semidirect
104. #65939C22semidirect
105. #65929C22semidirect
106. #65926C22semidirect
107. #65924C22semidirect
108. #65923C22semidirect
109. #65869C22semidirect
110. #65862C22semidirect
111. C2×#4044C22semidirect
112. C2×#4042C22semidirect
113. C2×#4040C22semidirect
114. C2×#4040C22semidirect
115. C2×#4040C22semidirect
116. C2×#4035C22semidirect
117. C2×#4032C22semidirect
118. C2×#4031C22semidirect
119. C2×#4031C22semidirect
121. C2×#4030C22semidirect
122. C2×#4030C22semidirect
123. C2×#4030C22semidirect
124. C2×#4030C22semidirect
125. C2×#4030C22semidirect
126. C2×#4029C22semidirect
127. C2×#4029C22semidirect
128. C2×#4029C22semidirect
129. C2×#4029C22semidirect
130. C2×#4028C22semidirect
131. C2×#4028C22semidirect
132. C2×#4028C22semidirect
133. C2×#4027C22semidirect
134. C2×#4027C22semidirect
135. C2×D5×C22⋊C4C22semidirect
136. C2×#4025C22semidirect
137. C2×#4025C22semidirect
138. C2×#4023C22semidirect
139. C2×#4020C22semidirect
140. C2×C4×D20C22semidirect
141. C2×C4×D20C22semidirect
142. C2×C4×D20C22semidirect
143. C2×#4018C22semidirect
144. C2×C42×D5C22semidirect
145. C2×#4016C22semidirect
146. C2×C4×Dic10C22semidirect
153. C2×C5×#41C23semidirect
165. C22×C5×D4C23semidirect
186. C22×C22⋊D5C23semidirect
187. C22×C22⋊D5C23semidirect
192. C2×#713C23semidirect
194. C2×#711C23semidirect
201. C2×D4×D5C23semidirect
202. C2×D4×D5C23semidirect
203. C2×D4×D5C23semidirect
204. C2×D4×D5C23semidirect
205. C2×D4×D5C23semidirect
206. C2×D4×D5C23semidirect
221. C5×#127C23semidirect
222. C5×#127C23semidirect
223. C5×#124C23semidirect
224. C5×#124C23semidirect
225. C5×#121C23semidirect
226. C5×#121C23semidirect
227. C5×#120C23semidirect
228. C5×#120C23semidirect
229. C5×#117C23semidirect
240. #4099C23semidirect
241. #4099C23semidirect
250. #4093C23semidirect
251. #4092C23semidirect
252. Q8×Dic5C23semidirect
254. #4086C23semidirect
255. #4086C23semidirect
256. #4086C23semidirect
257. #4086C23semidirect
258. #4086C23semidirect
259. #4085C23semidirect
260. #4085C23semidirect
261. #4085C23semidirect
262. #4085C23semidirect
263. #4085C23semidirect
264. #4085C23semidirect
265. #4085C23semidirect
267. #4084C23semidirect
268. #4084C23semidirect
269. #4084C23semidirect
270. #4084C23semidirect
271. #4084C23semidirect
272. #4083C23semidirect
273. #4083C23semidirect
274. #4083C23semidirect
275. #4083C23semidirect
276. #4083C23semidirect
277. #4081C23semidirect
278. #4081C23semidirect
279. D4×Dic5C23semidirect
280. D4×Dic5C23semidirect
281. D4×Dic5C23semidirect
282. #4076C23semidirect
283. #4076C23semidirect
284. #4076C23semidirect
285. #4075C23semidirect
286. C4×C22⋊D5C23semidirect
287. C4×C22⋊D5C23semidirect
288. C4×C22⋊D5C23semidirect
302. C2×#685C23semidirect
322. #4044C23semidirect
323. #4042C23semidirect
324. #4040C23semidirect
325. #4040C23semidirect
326. #4040C23semidirect
327. #4035C23semidirect
328. #4032C23semidirect
329. #4031C23semidirect
330. #4031C23semidirect
332. #4030C23semidirect
333. #4030C23semidirect
334. #4030C23semidirect
335. #4030C23semidirect
336. #4030C23semidirect
337. #4029C23semidirect
338. #4029C23semidirect
339. #4029C23semidirect
340. #4029C23semidirect
341. #4028C23semidirect
342. #4028C23semidirect
343. #4028C23semidirect
344. #4027C23semidirect
345. #4027C23semidirect
346. D5×C22⋊C4C23semidirect
347. #4025C23semidirect
348. #4025C23semidirect
349. #4023C23semidirect
350. #4020C23semidirect
351. C4×D20C23semidirect
352. C4×D20C23semidirect
353. C4×D20C23semidirect
354. #4018C23semidirect
355. C42×D5C23semidirect
356. #4016C23semidirect
357. C4×Dic10C23semidirect
376. C2×#535D5semidirect
575. C22×#41C2×D5semidirect
584. C23×D4C2×D5semidirect
602. #535C2×D5semidirect
613. C2×#127C2×D5semidirect
614. C2×#127C2×D5semidirect
625. C2×#124C2×D5semidirect
626. C2×#124C2×D5semidirect
662. C2×#121C2×D5semidirect
663. C2×#121C2×D5semidirect
674. C2×#120C2×D5semidirect
675. C2×#120C2×D5semidirect
691. C2×#117C2×D5semidirect
828. C2×#41C22×D5semidirect
879. C22×D4C22×D5semidirect
899. #127C22×D5semidirect
900. #127C22×D5semidirect
909. #124C22×D5semidirect
910. #124C22×D5semidirect
946. #121C22×D5semidirect
947. #121C22×D5semidirect
958. #120C22×D5semidirect
959. #120C22×D5semidirect
975. #117C22×D5semidirect
1279. C2×C5#3543semidirect
1411. C5C2×#3543semidirect
1475. C2#10618237direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5352
C2×#661682
C2×#661632
C2×D4×C22⋊D52
#106182372
C2×#660512
C2×#660532
C2×D5×#1272
C2×#660522
C2×#660102
C2×#660082
C2×#660152
C2×#660142
C2×#659542
C2×#659442
C2×#659392
C2×#659492
C2×#659292
C2×#659242
C2×#659232
C2×#659262
C2×#658692
C2×#658622
C2×#35435