Finite Group Databasebeta

← C2×#10617217 #13044661

Subgroups — C2×#10617217 #13044661

Order 1280.

2926 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#704C211yesmaximal, characteristic, complemented
2C22×#4131C211yesmaximal, characteristic, complemented
3C2×#65920C211yesmaximal, characteristic
4C22×C22⋊#170C211yesmaximal, characteristic, complemented
5C2×#65774C211yesmaximal, characteristic, complemented
6C2×#65773C211yesmaximal, characteristic, complemented
7C2×#65773C211yesmaximal, characteristic, complemented
8C2×D4×#170C211yesmaximal, characteristic, complemented
9C2×#65775C211yesmaximal, characteristic, complemented
10#10617217C2116yesmaximal, direct product factor
11C2×#65695C211yesmaximal, characteristic, complemented
12C2×#65694C211yesmaximal, characteristic, complemented
13C2×#65693C211yesmaximal, characteristic, complemented
14C2×#65692C211yesmaximal, characteristic, complemented
15C2×#65696C211yesmaximal, characteristic, complemented
16C2×#65691C211yesmaximal, characteristic, complemented
17C24×Dic5C2211yescharacteristic
18C22×#711C2211yescharacteristic
19C22×#704—28no—
20C22×#704C2211yescharacteristic
21C22×#704C2211yescharacteristic
22C22×#704C2211yescharacteristic
23C22×#704C2211yescharacteristic
24C22×#704C2218yescomplemented
25C22×#704C2211yescharacteristic, complemented
26C23×#170C2211yescharacteristic
27C23×#170C2211yescharacteristic
28C23×#170C2211yescharacteristic
29C23×#170C2211yescharacteristic
30C23×#170C2211yescharacteristic, complemented
31C2×#4131—28no—
32C2×#4131C2218yescomplemented
33C22×#700C2211yescharacteristic, complemented
34C22×D5⋊C8C2211yescharacteristic, complemented
35C2×C5×#120C411yescharacteristic
36C2×#4099C411yescharacteristic
37C2×#4085C411yescharacteristic
38C2×#4085C411yescharacteristic
39C2×#4081C411yescharacteristic
40C2×D4×Dic5C2211yescharacteristic
41C2×D4×Dic5C2211yescharacteristic
42#65920C418yes—
43#65920C2218yes—
44C2×#4032C411yescharacteristic
45C2×#4027C2211yescharacteristic
46C2×#4027C2211yescharacteristic
47C2×#4024C411yescharacteristic
48C2×#4024C411yescharacteristic
49C2×#4023C2211yescharacteristic
50C2×C22⋊#170C2211yescharacteristic
51C2×C22⋊#170C2211yescharacteristic
52C2×C22⋊#170C2211yescharacteristic
53C2×C22⋊#170C2211yescharacteristic
54C2×C22⋊#170C2218yescomplemented
55C2×C22⋊#170C2211yescharacteristic, complemented
56C2×C22⋊#170C2211yescharacteristic, complemented
57#65775C2218yescomplemented
58#65774C2218yescomplemented
59#65773C2218yescomplemented
60#65773C2218yescomplemented
61D4×#170C2218yescomplemented
62C2×#4004C2211yescharacteristic, complemented
63C2×#4004C2211yescharacteristic, complemented
64C2×#4003C2211yescharacteristic, complemented
65C2×#4003C2211yescharacteristic, complemented
66C2×#4002C2211yescharacteristic, complemented
67C2×#4002C2211yescharacteristic, complemented
68C2×C4⋊#170C2211yescharacteristic, complemented
69C2×C4⋊#170C2211yescharacteristic, complemented
70C2×C4×#170C2211yescharacteristic, complemented
71C2×C4×#170C2211yescharacteristic, complemented
72#65696C2218yescomplemented
73#65695C2218yescomplemented
74#65694C2218yescomplemented
75#65693C2218yescomplemented
76#65692C2218yescomplemented
77#65691C2218yescomplemented
78C2×#2933—51nomaximal, Sylow
79C25×C5C2×C411yescharacteristic
80C22×C5×D4C2×C411yescharacteristic
81C22×C5×D4C2×C411yescharacteristic
82C22×C5×D4C2×C411yescharacteristic
83C22×C22⋊D5C2×C411yescharacteristic
84C22×C22⋊D5C2×C411yescharacteristic
85C22×C22⋊D5C2×C411yescharacteristic
86C22×C22⋊D5C2×C411yescharacteristic
87C23×Dic5—24no—
88C23×Dic5—24no—
89C23×Dic5C2×C411yescharacteristic
90C23×Dic5C2×C411yescharacteristic
91C23×Dic5C2×C411yescharacteristic
92C23×Dic5C2×C414yes—
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2314yes—
97C23×Dic5C2311yescharacteristic
98C2×#711—24no—
99C2×#711—24no—
100C2×#711C2×C414yes—
101C2×#711C2314yes—
102C22×C4×D5C2311yescharacteristic
103C22×Dic10C2×C411yescharacteristic
104C2×#704—24no—
105C2×#704—232no—
106C2×#704—24no—
107C2×#704—24no—
108C2×#704—24no—
109C2×#704D418yescomplemented
110C2×#704C2314yes—
111C2×#704C2314yes—
112C2×#704C2314yes—
113C2×#704C2314yes—
114C2×#704C2314yescomplemented
115C22×#170—24no—
116C22×#170—24no—
117C22×#170—24no—
118C22×#170—24no—
119C22×#170—24no—
120C22×#170C2311yescharacteristic
121C22×#170C2311yescharacteristic
122C22×#170C2311yescharacteristic
123C22×#170C2311yescharacteristic
124C22×#170C2314yes—
125C22×#170C2314yes—
126C22×#170C2311yescharacteristic
127C22×#170C2311yescharacteristic
128C22×#170C2314yes—
129C22×#170C2314yes—
130C22×#170C2311yescharacteristic
131C22×#170C2311yescharacteristic
132C22×#170C2314yescomplemented
133#4131—232no—
134C2×#700—24no—
135C2×#700C2314yescomplemented
136C2×D5⋊C8—24no—
137C2×D5⋊C8C2314yescomplemented
138C5×#120C2×C418yes—
139C2×C5×C22⋊C4C2×C411yescharacteristic
140C2×C5×C22⋊C4C2×C411yescharacteristic
141C2×C5×C22⋊C4C2×C411yescharacteristic
142#4099C2×C418yes—
143C2×C22⋊Dic5C2×C411yescharacteristic
144C2×C22⋊Dic5C2×C411yescharacteristic
145C2×C22⋊Dic5C2×C411yescharacteristic
146C2×C22⋊Dic5C2×C411yescharacteristic
147C2×C22⋊Dic5C2×C411yescharacteristic
148#4085C2×C418yes—
149#4085C2×C418yes—
150#4081C2×C418yes—
151D4×Dic5C2×C414yes—
152D4×Dic5C2×C414yes—
153D4×Dic5C2314yes—
154D4×Dic5C2314yes—
155C2×#685C2×C411yescharacteristic
156C2×#685C2×C411yescharacteristic
157C2×C4⋊Dic5C2×C411yescharacteristic
158C2×C4⋊Dic5C2×C411yescharacteristic
159C2×#683C2×C411yescharacteristic
160C2×#683C2×C411yescharacteristic
161C2×#683C2×C411yescharacteristic
162C2×#683C2×C411yescharacteristic
163C2×C4×Dic5C2311yescharacteristic
164C2×C4×Dic5C2311yescharacteristic
165#4032C2×C418yes—
166#4027C2×C414yes—
167#4027C2×C414yes—
168#4027C2314yes—
169#4027C2314yes—
170#4024C2×C418yes—
171#4024C2×C418yes—
172#4023C2×C414yes—
173#4023C2314yes—
174C22⋊#170C2314yes—
175C22⋊#170C2314yes—
176C22⋊#170C2314yes—
177C22⋊#170C2314yes—
178C22⋊#170C2314yescomplemented
179C22⋊#170C2314yescomplemented
180#4004C2314yescomplemented
181#4004C2314yescomplemented
182#4003C2314yescomplemented
183#4003C2314yescomplemented
184#4002C2314yescomplemented
185#4002C2314yescomplemented
186C4⋊#170C2314yescomplemented
187C4⋊#170C2314yescomplemented
188C4×#170C2314yescomplemented
189C4×#170C2314yescomplemented
190C22×#131—51no—
191C23×M16—51no—
192C2×#525—51no—
193#2933—516no—
194C2×#436—51no—
195C2×#436—51no—
196C2×#435—51no—
197C2×#435—51no—
198C2×#435—51no—
199C2×#435—51no—
200C2×C8×D4—51no—
201C2×C8×D4—51no—
202C2×#424—51no—
203C2×#408—51no—
204C22×C22⋊C8—51no—
205C2×#405—51no—
206C24×C5—24no—
207C24×C5—24no—
208C24×C5—42no—
209C24×C5C22×C411yescharacteristic
210C24×C5C22×C411yescharacteristic
211C24×C5C22×C414yes—
212C24×C5C22×C411yescharacteristic
213C24×C5C22×C411yescharacteristic
214C23×D5C22×C411yescharacteristic
215C2×C5×D4—24no—
216C2×C5×D4—24no—
217C2×C5×D4—42no—
218C2×C5×D4C22×C414yes—
219C2×C5×D4C22×C414yes—
220C2×C5×D4C22×C414yes—
221C22×C4×C5C22×C411yescharacteristic
222C22×C4×C5C22×C411yescharacteristic
223C22×C4×C5C22×C411yescharacteristic
224C2×C22⋊D5—24no—
225C2×C22⋊D5—24no—
226C2×C22⋊D5—24no—
227C2×C22⋊D5—42no—
228C2×C22⋊D5C22×C414yes—
229C2×C22⋊D5C22×C414yes—
230C2×C22⋊D5C22×C414yes—
231C2×C22⋊D5C22×C414yes—
232C22×Dic5—24no—
233C22×Dic5—24no—
234C22×Dic5—24no—
235C22×Dic5—216no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—28no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—28no—
244C22×Dic5C22×C411yescharacteristic
245C22×Dic5C22×C411yescharacteristic
246C22×Dic5C22×C411yescharacteristic
247C22×Dic5C22×C411yescharacteristic
248C22×Dic5C22×C411yescharacteristic
249C22×Dic5C22×C412yes—
250C22×Dic5C22×C414yes—
251C22×Dic5C22×C414yes—
252C22×Dic5C22×C412yes—
253C22×Dic5C22×C412yes—
254C22×Dic5C22×C414yes—
255C22×Dic5C22×C411yescharacteristic
256C22×Dic5C22×C412yes—
257C22×Dic5C2×D414yes—
258C22×Dic5#4114yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2411yescharacteristic
263C22×Dic5C2412yes—
264#711—216no—
265#711—28no—
266#711—28no—
267C2×C4×D5—22no—
268C2×C4×D5—22no—
269C2×C4×D5C22×C412yes—
270C2×C4×D5C2412yes—
271C2×Dic10—24no—
272C2×Dic10C22×C414yes—
273#704—28no—
274#704—28no—
275#704—28no—
276#704—28no—
277#704C2×D4116yescomplemented
278C2×#170—22no—
279C2×#170—22no—
280C2×#170—28no—
281C2×#170—22no—
282C2×#170—22no—
283C2×#170—22no—
284C2×#170—22no—
285C2×#170—28no—
286C2×#170—28no—
287C2×#170—28no—
288C2×#170—28no—
289C2×#170C2×D414yes—
290C2×#170C2×D414yes—
291C2×#170C2412yes—
292C2×#170C2412yes—
293C2×#170C2412yes—
294C2×#170C2412yes—
295C2×#170C2412yes—
296C2×#170C2412yes—
297C2×#170C2412yes—
298C2×#170C2412yes—
299#700—28no—
300D5⋊C8—28no—
301C5×C22⋊C4C22×C414yes—
302C5×C22⋊C4C22×C414yes—
303C5×C22⋊C4C22×C414yes—
304C22⋊Dic5C22×C414yes—
305C22⋊Dic5C22×C414yes—
306C22⋊Dic5C22×C414yes—
307C22⋊Dic5C22×C414yes—
308C22⋊Dic5C22×C414yes—
309#685C22×C414yes—
310#685C22×C414yes—
311C4⋊Dic5C22×C414yes—
312C4⋊Dic5C22×C414yes—
313#683C22×C414yes—
314#683C22×C414yes—
315#683C22×C414yes—
316#683C22×C414yes—
317C4×Dic5C22×C412yes—
318C4×Dic5C22×C412yes—
319C4×Dic5C2412yes—
320C4×Dic5C2412yes—
321C22×#41—51no—
322C24×C4—51no—
323C2×#131—58no—
324C2×#131—108no—
325C22×M16—51no—
326C22×M16—51no—
327C22×M16—51no—
328C22×M16—51no—
329C22×M16—51no—
330C22×M16—51no—
331C22×M16—58no—
332C22×M16—108no—
333C23×C8—51no—
334C23×C8—51no—
335C23×C8—51no—
336C23×C8—51no—
337C23×C8—51no—
338C23×C8—51no—
339#525—58no—
340#525—58no—
341C2×#123—51no—
342C2×#123—51no—
343C2×C22⋊Q8—51no—
344C2×C22⋊Q8—51no—
345C2×#121—51no—
346C2×#121—51no—
347C2×#120—51no—
348C2×#120AGL(1,𝔽5)11yescharacteristic
349C2×C4×D4—51no—
350C2×C4×D4—51no—
351C2×C4×D4—51no—
352C2×C4×D4—51no—
353C2×#117—51no—
354#436—58no—
355#436—58no—
356#435—58no—
357#435—58no—
358#435—58no—
359#435—58no—
360C8×D4—58no—
361C8×D4—58no—
362#424—58no—
363C2×C4⋊C8—51no—
364C2×C4⋊C8—51no—
365C2×C4⋊C8—51no—
366C2×C4⋊C8—51no—
367#408—58no—
368C2×C22⋊C8—51no—
369C2×C22⋊C8—51no—
370C2×C22⋊C8—51no—
371C2×C22⋊C8—51no—
372C2×C22⋊C8—58no—
373C2×C22⋊C8—51no—
374C2×C22⋊C8—51no—
375C2×C22⋊C8—51no—
376C2×C22⋊C8—51no—
377#405—58no—
378C2×#97—51no—
379C2×#97—51no—
380C2×C4×C8—51no—
381C2×C4×C8—51no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5—22no—
386C23×C5—28no—
387C23×C5—22no—
388C23×C5—22no—
389C23×C5—22no—
390C23×C5—22no—
391C23×C5—28no—
392C23×C5—22no—
393C23×C5—22no—
394C23×C5—44no—
395C23×C5—416no—
396C23×C5C4×D414yes—
397C23×C5#13114yescomplemented
398C23×C5C23×C412yes—
399C23×C5C23×C412yes—
400C23×C5C23×C412yes—
401C23×C5C23×C412yes—
402C23×C5C23×C411yescharacteristic
403C22×D5—22no—
404C22×D5—22no—
405C22×D5—22no—
406C22×D5C23×C412yes—
407C5×D4—28no—
408C5×D4—28no—
409C5×D4—44no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5C23×C412yes—
414C2×C4×C5C23×C412yes—
415C2×C4×C5C23×C412yes—
416C22⋊D5—28no—
417C22⋊D5—28no—
418C22⋊D5—28no—
419C22⋊D5—44no—
420C2×Dic5—22no—
421C2×Dic5—28no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—24no—
427C2×Dic5—28no—
428C2×Dic5—28no—
429C2×Dic5—24no—
430C2×Dic5—24no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5C4×D414yes—
438C2×Dic5C4×D418yes—
439C2×Dic5C23×C412yes—
440C2×Dic5C23×C412yes—
441C2×Dic5C23×C412yes—
442C2×Dic5C23×C412yes—
443C2×Dic5C23×C412yes—
444C2×Dic5C23×C411yescharacteristic
445C2×Dic5C23×C412yes—
446C2×Dic5C22×D412yes—
447C2×Dic5C22×D414yes—
448C2×Dic5C2×#4112yes—
449C2×Dic5C2×#4114yes—
450C2×Dic5C2511yescharacteristic
451C4×D5—24no—
452C4×D5—22no—
453C4×D5—22no—
454Dic10—28no—
455#170—22no—
456#170—22no—
457#170—22no—
458#170—22no—
459#170—22no—
460#170—22no—
461#170C22×D414yes—
462#170C22×D414yes—
463C25C2×AGL(1,𝔽5)11yescharacteristic
464C2×#41—54no—
465C2×#41—54no—
466C2×#41—104no—
467C2×#41—104no—
468C22×Q8—51no—
469C22×D4—51no—
470C22×D4—51no—
471C22×D4—51no—
472C22×D4—51no—
473C22×D4C2×AGL(1,𝔽5)11yescharacteristic
474C22×D4C2×AGL(1,𝔽5)11yescharacteristic
475C22×D4C2×AGL(1,𝔽5)11yescharacteristic
476C23×C4—51no—
477C23×C4—51no—
478C23×C4—51no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—54no—
484C23×C4—54no—
485C23×C4—51no—
486C23×C4—104no—
487C23×C4—104no—
488#131—1032no—
489C2×M16—58no—
490C2×M16—54no—
491C2×M16—54no—
492C2×M16—54no—
493C2×M16—54no—
494C2×M16—54no—
495C2×M16—54no—
496C2×M16—104no—
497C2×M16—104no—
498C2×M16—104no—
499C2×M16—104no—
500C2×M16—1032no—
501C2×M16—104no—
502C22×C8—51no—
503C22×C8—51no—
504C22×C8—54no—
505C22×C8—51no—
506C22×C8—51no—
507C22×C8—51no—
508C22×C8—51no—
509C22×C8—54no—
510C22×C8—54no—
511C22×C8—54no—
512C22×C8—51no—
513C22×C8—51no—
514C22×C8—54no—
515C22×C8—54no—
516C22×C8—104no—
517C22×C8—104no—
518C22×C8—104no—
519C22×C8—104no—
520C22×C8—104no—
521C22×C8—104no—
522#123—58no—
523#123—58no—
524C22⋊Q8—58no—
525C22⋊Q8—58no—
526#121—58no—
527#121—58no—
528#120—58no—
529#120C2×AGL(1,𝔽5)18yes—
530C4×D4—54no—
531C4×D4—54no—
532C4×D4—54no—
533C4×D4—54no—
534C4×D4—54no—
535C4×D4—54no—
536C4×D4—54no—
537C4×D4—54no—
538#117—54no—
539#117—54no—
540C2×C4⋊C4—51no—
541C2×C4⋊C4—51no—
542C2×C4⋊C4—51no—
543C2×C4⋊C4—51no—
544C2×C4⋊C4—51no—
545C2×C4⋊C4—51no—
546C2×C22⋊C4—51no—
547C2×C22⋊C4—51no—
548C2×C22⋊C4—51no—
549C2×C22⋊C4—51no—
550C2×C22⋊C4—51no—
551C2×C22⋊C4—51no—
552C2×C22⋊C4—51no—
553C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
554C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
555C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
556C2×C42—51no—
557C2×C42—51no—
558C4⋊C8—54no—
559C4⋊C8—54no—
560C4⋊C8—54no—
561C4⋊C8—54no—
562C22⋊C8—54no—
563C22⋊C8—54no—
564C22⋊C8—54no—
565C22⋊C8—54no—
566C22⋊C8—54no—
567C22⋊C8—54no—
568C22⋊C8—54no—
569C22⋊C8—54no—
570#97—54no—
571#97—54no—
572C4×C8—54no—
573C4×C8—54no—
574C22×C5—22no—
575C22×C5—28no—
576C22×C5—28no—
577C22×C5—22no—
578C22×C5—22no—
579C22×C5—22no—
580C22×C5—22no—
581C22×C5—22no—
582C22×C5—22no—
583C22×C5—22no—
584C22×C5—22no—
585C22×C5—22no—
586C22×C5—416no—
587C22×C5—44no—
588C22×C5—44no—
589C22×C5C2×C4×D414yes—
590C22×C5C2×C4×D412yes—
591C22×C5C2×#13112yes—
592C22×C5C2×#13114yescomplemented
593C22×C5#56812yes—
594C22×C5C24×C411yescharacteristic
595C2×D5—22no—
596C2×D5—22no—
597C2×D5—22no—
598C2×D5—44no—
599C4×C5—22no—
600C4×C5—22no—
601C4×C5—22no—
602Dic5—22no—
603Dic5—22no—
604Dic5—22no—
605Dic5—22no—
606Dic5—22no—
607Dic5C2×C4×D414yes—
608Dic5C2×C4×D412yes—
609Dic5C23×D411yescharacteristic
610Dic5C22×#4111yescharacteristic
611C24—24no—
612C24—24no—
613C24—42no—
614C24—51no—
615C24C22×AGL(1,𝔽5)11yescharacteristic
616C24C22×AGL(1,𝔽5)11yescharacteristic
617C24C22×AGL(1,𝔽5)14yes—
618C24C22×AGL(1,𝔽5)11yescharacteristic
619C24C22×AGL(1,𝔽5)11yescharacteristic
620#41—108no—
621#41—108no—
622#41—1016no—
623C2×Q8—54no—
624C2×Q8—104no—
625C2×D4—24no—
626C2×D4—24no—
627C2×D4—42no—
628C2×D4—54no—
629C2×D4—54no—
630C2×D4—54no—
631C2×D4—54no—
632C2×D4—104no—
633C2×D4—104no—
634C2×D4—104no—
635C2×D4—202no—
636C2×D4C22×AGL(1,𝔽5)14yes—
637C2×D4C22×AGL(1,𝔽5)14yes—
638C2×D4C22×AGL(1,𝔽5)14yes—
639C22×C4—54no—
640C22×C4—54no—
641C22×C4—52no—
642C22×C4—52no—
643C22×C4—51no—
644C22×C4—51no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—52no—
650C22×C4—52no—
651C22×C4—54no—
652C22×C4—54no—
653C22×C4—54no—
654C22×C4—51no—
655C22×C4—51no—
656C22×C4—51no—
657C22×C4—51no—
658C22×C4—51no—
659C22×C4—52no—
660C22×C4—52no—
661C22×C4—102no—
662C22×C4—102no—
663C22×C4—102no—
664C22×C4—102no—
665C22×C4—102no—
666C22×C4—108no—
667C22×C4—102no—
668C22×C4—102no—
669C22×C4—108no—
670C22×C4—104no—
671C22×C4—104no—
672C22×C4—1016no—
673C22×C4—102no—
674C22×C4—104no—
675C22×C4C22×AGL(1,𝔽5)11yescharacteristic
676C22×C4C22×AGL(1,𝔽5)11yescharacteristic
677C22×C4C22×AGL(1,𝔽5)11yescharacteristic
678M16—516no—
679M16—108no—
680M16—108no—
681M16—108no—
682M16—108no—
683M16—108no—
684C2×C8—52no—
685C2×C8—52no—
686C2×C8—54no—
687C2×C8—54no—
688C2×C8—52no—
689C2×C8—52no—
690C2×C8—52no—
691C2×C8—52no—
692C2×C8—52no—
693C2×C8—52no—
694C2×C8—108no—
695C2×C8—108no—
696C2×C8—108no—
697C2×C8—108no—
698C2×C8—102no—
699C2×C8—102no—
700C2×C8—102no—
701C2×C8—102no—
702C2×C8—108no—
703C2×C8—102no—
704C2×C8—102no—
705C2×C8—108no—
706C4⋊C4—54no—
707C4⋊C4—54no—
708C4⋊C4—54no—
709C4⋊C4—54no—
710C4⋊C4—54no—
711C4⋊C4—54no—
712C22⋊C4—54no—
713C22⋊C4—54no—
714C22⋊C4—54no—
715C22⋊C4—54no—
716C22⋊C4—54no—
717C22⋊C4—54no—
718C22⋊C4—54no—
719C22⋊C4C22×AGL(1,𝔽5)14yes—
720C22⋊C4C22×AGL(1,𝔽5)14yes—
721C22⋊C4C22×AGL(1,𝔽5)14yes—
722C42—52no—
723C42—52no—
724C42—52no—
725C42—52no—
726C2×C5—24no—
727C2×C5—24no—
728C2×C5—42no—
729C2×C5—42no—
730C2×C5#293314yescomplemented
731C2×C5C22×C4×D411yescharacteristic
732C2×C5C22×#13111yescharacteristic
733C2×C5C2×#56811yescharacteristic
734D5—42no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—28no—
742C23—22no—
743C23—22no—
744C23—28no—
745C23—22no—
746C23—22no—
747C23—44no—
748C23—416no—
749C23—52no—
750C23—102no—
751C23—102no—
752C23—102no—
753C23#413114yescomplemented
754C23D4×AGL(1,𝔽5)14yes—
755C23C23×AGL(1,𝔽5)12yes—
756C23C23×AGL(1,𝔽5)12yes—
757C23C23×AGL(1,𝔽5)12yes—
758C23C23×AGL(1,𝔽5)12yes—
759C23C23×AGL(1,𝔽5)11yescharacteristic
760Q8—108no—
761D4—28no—
762D4—28no—
763D4—44no—
764D4—108no—
765D4—108no—
766D4—108no—
767D4—204no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—52no—
772C2×C4—54no—
773C2×C4—52no—
774C2×C4—54no—
775C2×C4—54no—
776C2×C4—58no—
777C2×C4—51no—
778C2×C4—51no—
779C2×C4—52no—
780C2×C4—52no—
781C2×C4—52no—
782C2×C4—52no—
783C2×C4—52no—
784C2×C4—52no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—104no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—102no—
791C2×C4—102no—
792C2×C4—102no—
793C2×C4—104no—
794C2×C4—104no—
795C2×C4—108no—
796C2×C4—108no—
797C2×C4—102no—
798C2×C4—104no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—108no—
802C2×C4—102no—
803C2×C4—102no—
804C2×C4—102no—
805C2×C4C23×AGL(1,𝔽5)12yes—
806C2×C4C23×AGL(1,𝔽5)12yes—
807C2×C4C23×AGL(1,𝔽5)12yes—
808C8—54no—
809C8—54no—
810C8—102no—
811C8—102no—
812C8—102no—
813C8—102no—
814C8—102no—
815C8—102no—
816C5C2×#293311yescharacteristic, complemented, Sylow
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—28no—
822C22—28no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—416no—
830C22—44no—
831C22—44no—
832C22—102no—
833C22—102no—
834C22—102no—
835C22—204no—
836C22C2×#413112yes—
837C22C2×#413114yescomplemented
838C22#6625612yes—
839C22C2×D4×AGL(1,𝔽5)14yes—
840C22C2×D4×AGL(1,𝔽5)12yes—
841C22C24×AGL(1,𝔽5)11yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—51no—
846C4—51no—
847C4—52no—
848C4—54no—
849C4—102no—
850C4—102no—
851C4—102no—
852C4—102no—
853C4—102no—
854C2—24no—
855C2—24no—
856C2—42no—
857C2—42no—
858C2—202no—
859C2#1061721714yesdirect product factor
860C2C22×#413111yescharacteristic
861C2C2×#6625611yescharacteristic
862C2C22×D4×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC23C23×AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC2×C5×#120C4
socleC23×C5C23×C4
prime radicalC2×#65920C2
cosocleC2×Dic5C25
hypercenterC2×#120AGL(1,𝔽5)
hypocenterC5C2×#2933
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C23×#704C2semidirect
2. C22×#4131C2semidirect
4. C22×C22⋊#170C2semidirect
5. C2×#65774C2semidirect
6. C2×#65773C2semidirect
7. C2×#65773C2semidirect
8. C2×D4×#170C2semidirect
9. C2×#65775C2semidirect
10. #10617217C2direct (N × H)
11. C2×#65695C2semidirect
12. C2×#65694C2semidirect
13. C2×#65693C2semidirect
14. C2×#65692C2semidirect
15. C2×#65696C2semidirect
16. C2×#65691C2semidirect
24. C22×#704C22semidirect
25. C22×#704C22semidirect
30. C23×#170C22semidirect
32. C2×#4131C22semidirect
33. C22×#700C22semidirect
34. C22×D5⋊C8C22semidirect
54. C2×C22⋊#170C22semidirect
55. C2×C22⋊#170C22semidirect
56. C2×C22⋊#170C22semidirect
57. #65775C22semidirect
58. #65774C22semidirect
59. #65773C22semidirect
60. #65773C22semidirect
61. D4×#170C22semidirect
62. C2×#4004C22semidirect
63. C2×#4004C22semidirect
64. C2×#4003C22semidirect
65. C2×#4003C22semidirect
66. C2×#4002C22semidirect
67. C2×#4002C22semidirect
68. C2×C4⋊#170C22semidirect
69. C2×C4⋊#170C22semidirect
70. C2×C4×#170C22semidirect
71. C2×C4×#170C22semidirect
72. #65696C22semidirect
73. #65695C22semidirect
74. #65694C22semidirect
75. #65693C22semidirect
76. #65692C22semidirect
77. #65691C22semidirect
109. C2×#704D4semidirect
114. C2×#704C23semidirect
132. C22×#170C23semidirect
135. C2×#700C23semidirect
137. C2×D5⋊C8C23semidirect
178. C22⋊#170C23semidirect
179. C22⋊#170C23semidirect
180. #4004C23semidirect
181. #4004C23semidirect
182. #4003C23semidirect
183. #4003C23semidirect
184. #4002C23semidirect
185. #4002C23semidirect
186. C4⋊#170C23semidirect
187. C4⋊#170C23semidirect
188. C4×#170C23semidirect
189. C4×#170C23semidirect
277. #704C2×D4semidirect
397. C23×C5#131semidirect
592. C22×C5C2×#131semidirect
730. C2×C5#2933semidirect
753. C23#4131semidirect
816. C5C2×#2933semidirect
837. C22C2×#4131semidirect
859. C2#10617217direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#7042
C22×#41312
C2×#659202
C22×C22⋊#1702
C2×#657742
C2×#657732
C2×D4×#1702
C2×#657752
#106172172
C2×#656952
C2×#656942
C2×#656932
C2×#656922
C2×#656962
C2×#656912
C2×#29335