Finite Group Databasebeta

← C2×#10617218 #13045026

Subgroups — C2×#10617218 #13045026

Order 1280.

2306 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65920C211yesmaximal, characteristic
2C2×#65798C211yesmaximal, characteristic, complemented
3C22×C22⋊#170C211yesmaximal, characteristic, complemented
4C2×#65774C211yesmaximal, characteristic, complemented
5C2×#65773C211yesmaximal, characteristic, complemented
6C2×#65773C211yesmaximal, characteristic, complemented
7C2×D4×#170C211yesmaximal, characteristic, complemented
8C2×#65776C211yesmaximal, characteristic, complemented
9C2×#65775C211yesmaximal, characteristic, complemented
10#10617218C2116yesmaximal, direct product factor
11C2×#65695C211yesmaximal, characteristic, complemented
12C2×#65694C211yesmaximal, characteristic, complemented
13C2×#65693C211yesmaximal, characteristic, complemented
14C2×#65692C211yesmaximal, characteristic, complemented
15C2×#65697C211yesmaximal, characteristic, complemented
16C2×#65697C211yesmaximal, characteristic, complemented
17C24×Dic5C2211yescharacteristic
18C22×#711C2211yescharacteristic
19C22×#704C2211yescharacteristic
20C22×#704C2211yescharacteristic
21C22×#704C2211yescharacteristic, complemented
22C23×#170C2211yescharacteristic
23C23×#170C2211yescharacteristic
24C23×#170C2211yescharacteristic, complemented
25C22×#700C2211yescharacteristic, complemented
26C22×D5⋊C8C2211yescharacteristic, complemented
27C2×C5×#120C411yescharacteristic
28C2×#4099C411yescharacteristic
29C2×#4085C411yescharacteristic
30C2×#4085C411yescharacteristic
31C2×#4081C411yescharacteristic
32C2×D4×Dic5C2211yescharacteristic
33C2×D4×Dic5C2211yescharacteristic
34#65920C418yes—
35#65920C2218yes—
36C2×#4032C411yescharacteristic
37C2×#4027C2211yescharacteristic
38C2×#4027C2211yescharacteristic
39C2×#4024C411yescharacteristic
40C2×#4024C411yescharacteristic
41C2×#4023C2211yescharacteristic
42#65798C2218yescomplemented
43C2×C22⋊#170C2211yescharacteristic
44C2×C22⋊#170C2211yescharacteristic
45C2×C22⋊#170C2211yescharacteristic
46C2×C22⋊#170C2211yescharacteristic
47C2×C22⋊#170C2211yescharacteristic
48C2×C22⋊#170C2211yescharacteristic
49C2×C22⋊#170C2211yescharacteristic
50C2×C22⋊#170C2211yescharacteristic
51C2×C22⋊#170C2218yescomplemented
52C2×C22⋊#170C2211yescharacteristic, complemented
53C2×C22⋊#170C2211yescharacteristic, complemented
54#65776C2218yescomplemented
55#65775C2218yescomplemented
56#65774C2218yescomplemented
57#65773C2218yescomplemented
58#65773C2218yescomplemented
59D4×#170C2218yescomplemented
60C2×#4004C2211yescharacteristic, complemented
61C2×#4004C2211yescharacteristic, complemented
62C2×#4003C2211yescharacteristic, complemented
63C2×#4003C2211yescharacteristic, complemented
64C2×#4002C2211yescharacteristic, complemented
65C2×#4002C2211yescharacteristic, complemented
66C2×C4⋊#170C2211yescharacteristic, complemented
67C2×C4⋊#170C2211yescharacteristic, complemented
68C2×C4×#170C2211yescharacteristic, complemented
69C2×C4×#170C2211yescharacteristic, complemented
70#65697C2218yescomplemented
71#65697C2218yescomplemented
72#65695C2218yescomplemented
73#65694C2218yescomplemented
74#65693C2218yescomplemented
75#65692C2218yescomplemented
76C2×#2976—51nomaximal, Sylow
77C25×C5C2×C411yescharacteristic
78C22×C5×D4C2×C411yescharacteristic
79C22×C5×D4C2×C411yescharacteristic
80C22×C5×D4C2×C411yescharacteristic
81C22×C22⋊D5C2×C411yescharacteristic
82C22×C22⋊D5C2×C411yescharacteristic
83C22×C22⋊D5C2×C411yescharacteristic
84C22×C22⋊D5C2×C411yescharacteristic
85C23×Dic5—42no—
86C23×Dic5—42no—
87C23×Dic5C2×C411yescharacteristic
88C23×Dic5C2×C411yescharacteristic
89C23×Dic5C2×C411yescharacteristic
90C23×Dic5C2×C414yes—
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2314yes—
96C2×#711—42no—
97C2×#711—42no—
98C2×#711C2×C414yes—
99C2×#711C2314yes—
100C22×C4×D5C2311yescharacteristic
101C22×Dic10C2×C411yescharacteristic
102C2×#704—42no—
103C2×#704—42no—
104C2×#704—42no—
105C2×#704C2314yes—
106C2×#704C2314yes—
107C2×#704C2314yescomplemented
108C22×#170—42no—
109C22×#170—42no—
110C22×#170—42no—
111C22×#170C2311yescharacteristic
112C22×#170C2311yescharacteristic
113C22×#170C2311yescharacteristic
114C22×#170C2311yescharacteristic
115C22×#170C2311yescharacteristic
116C22×#170C2311yescharacteristic
117C22×#170C2311yescharacteristic
118C22×#170C2311yescharacteristic
119C22×#170C2314yes—
120C22×#170C2314yes—
121C22×#170C2314yescomplemented
122C2×#700—42no—
123C2×#700C2314yescomplemented
124C2×D5⋊C8—42no—
125C2×D5⋊C8C2314yescomplemented
126C5×#120C2×C418yes—
127C2×C5×C22⋊C4C2×C411yescharacteristic
128C2×C5×C22⋊C4C2×C411yescharacteristic
129C2×C5×C22⋊C4C2×C411yescharacteristic
130#4099C2×C418yes—
131C2×C22⋊Dic5C2×C411yescharacteristic
132C2×C22⋊Dic5C2×C411yescharacteristic
133C2×C22⋊Dic5C2×C411yescharacteristic
134C2×C22⋊Dic5C2×C411yescharacteristic
135C2×C22⋊Dic5C2×C411yescharacteristic
136#4085C2×C418yes—
137#4085C2×C418yes—
138#4081C2×C418yes—
139D4×Dic5C2×C414yes—
140D4×Dic5C2×C414yes—
141D4×Dic5C2314yes—
142D4×Dic5C2314yes—
143C2×#685C2×C411yescharacteristic
144C2×#685C2×C411yescharacteristic
145C2×C4⋊Dic5C2×C411yescharacteristic
146C2×C4⋊Dic5C2×C411yescharacteristic
147C2×#683C2×C411yescharacteristic
148C2×#683C2×C411yescharacteristic
149C2×#683C2×C411yescharacteristic
150C2×#683C2×C411yescharacteristic
151C2×C4×Dic5C2311yescharacteristic
152C2×C4×Dic5C2311yescharacteristic
153#4032C2×C418yes—
154#4027C2×C414yes—
155#4027C2×C414yes—
156#4027C2314yes—
157#4027C2314yes—
158#4024C2×C418yes—
159#4024C2×C418yes—
160#4023C2×C414yes—
161#4023C2314yes—
162C22⋊#170C2314yes—
163C22⋊#170C2314yes—
164C22⋊#170C2314yes—
165C22⋊#170C2314yes—
166C22⋊#170C2314yes—
167C22⋊#170C2314yes—
168C22⋊#170C2314yes—
169C22⋊#170C2314yes—
170C22⋊#170C2314yescomplemented
171C22⋊#170C2314yescomplemented
172#4004C2314yescomplemented
173#4004C2314yescomplemented
174#4003C2314yescomplemented
175#4003C2314yescomplemented
176#4002C2314yescomplemented
177#4002C2314yescomplemented
178C4⋊#170C2314yescomplemented
179C4⋊#170C2314yescomplemented
180C4×#170C2314yescomplemented
181C4×#170C2314yescomplemented
182C2×#525—51no—
183#2976—516no—
184C2×#436—51no—
185C2×#436—51no—
186C2×#435—51no—
187C2×#435—51no—
188C2×#435—51no—
189C2×#435—51no—
190C2×C8×D4—51no—
191C2×C8×D4—51no—
192C2×#433—51no—
193C2×#433—51no—
194C2×#408—51no—
195C2×#408—51no—
196C2×#407—51no—
197C22×C22⋊C8—51no—
198C24×C5—24no—
199C24×C5—42no—
200C24×C5—42no—
201C24×C5C22×C411yescharacteristic
202C24×C5C22×C411yescharacteristic
203C24×C5C22×C411yescharacteristic
204C24×C5C22×C411yescharacteristic
205C24×C5C22×C414yes—
206C23×D5C22×C411yescharacteristic
207C2×C5×D4—24no—
208C2×C5×D4—42no—
209C2×C5×D4—42no—
210C2×C5×D4C22×C414yes—
211C2×C5×D4C22×C414yes—
212C2×C5×D4C22×C414yes—
213C22×C4×C5C22×C411yescharacteristic
214C22×C4×C5C22×C411yescharacteristic
215C22×C4×C5C22×C411yescharacteristic
216C2×C22⋊D5—24no—
217C2×C22⋊D5—42no—
218C2×C22⋊D5—42no—
219C2×C22⋊D5—42no—
220C2×C22⋊D5C22×C414yes—
221C2×C22⋊D5C22×C414yes—
222C2×C22⋊D5C22×C414yes—
223C2×C22⋊D5C22×C414yes—
224C22×Dic5—22no—
225C22×Dic5—22no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—48no—
233C22×Dic5—44no—
234C22×Dic5—44no—
235C22×Dic5—42no—
236C22×Dic5—42no—
237C22×Dic5—42no—
238C22×Dic5C22×C411yescharacteristic
239C22×Dic5C22×C411yescharacteristic
240C22×Dic5C22×C411yescharacteristic
241C22×Dic5C22×C411yescharacteristic
242C22×Dic5C22×C411yescharacteristic
243C22×Dic5C22×C411yescharacteristic
244C22×Dic5C22×C412yes—
245C22×Dic5C22×C412yes—
246C22×Dic5C22×C412yes—
247C22×Dic5C22×C412yes—
248C22×Dic5C22×C414yes—
249C22×Dic5C22×C414yes—
250C22×Dic5C22×C414yes—
251C22×Dic5C2412yes—
252C22×Dic5C2412yes—
253C22×Dic5C2412yes—
254C22×Dic5C2412yes—
255C22×Dic5C2411yescharacteristic
256#711—48no—
257#711—44no—
258#711—44no—
259C2×C4×D5—22no—
260C2×C4×D5—22no—
261C2×C4×D5C22×C412yes—
262C2×C4×D5C2412yes—
263C2×Dic10—42no—
264C2×Dic10C22×C414yes—
265#704—44no—
266#704—44no—
267#704—44no—
268C2×#170—22no—
269C2×#170—22no—
270C2×#170—22no—
271C2×#170—22no—
272C2×#170—22no—
273C2×#170—22no—
274C2×#170—22no—
275C2×#170—22no—
276C2×#170—44no—
277C2×#170—44no—
278C2×#170—44no—
279C2×#170C2412yes—
280C2×#170C2412yes—
281C2×#170C2412yes—
282C2×#170C2412yes—
283C2×#170C2412yes—
284C2×#170C2412yes—
285C2×#170C2412yes—
286C2×#170C2412yes—
287#700—44no—
288D5⋊C8—44no—
289C5×C22⋊C4C22×C414yes—
290C5×C22⋊C4C22×C414yes—
291C5×C22⋊C4C22×C414yes—
292C22⋊Dic5C22×C414yes—
293C22⋊Dic5C22×C414yes—
294C22⋊Dic5C22×C414yes—
295C22⋊Dic5C22×C414yes—
296C22⋊Dic5C22×C414yes—
297#685C22×C414yes—
298#685C22×C414yes—
299C4⋊Dic5C22×C414yes—
300C4⋊Dic5C22×C414yes—
301#683C22×C414yes—
302#683C22×C414yes—
303#683C22×C414yes—
304#683C22×C414yes—
305C4×Dic5C22×C412yes—
306C4×Dic5C22×C412yes—
307C4×Dic5C2412yes—
308C4×Dic5C2412yes—
309C22×#41—51no—
310C24×C4—51no—
311C22×M16—51no—
312C22×M16—51no—
313C22×M16—51no—
314C22×M16—51no—
315C23×C8—51no—
316C23×C8—51no—
317C23×C8—51no—
318C23×C8—51no—
319#525—58no—
320#525—58no—
321C2×#123—51no—
322C2×#123—51no—
323C2×C22⋊Q8—51no—
324C2×C22⋊Q8—51no—
325C2×#121—51no—
326C2×#121—51no—
327C2×#120—51no—
328C2×#120AGL(1,𝔽5)11yescharacteristic
329C2×C4×D4—51no—
330C2×C4×D4—51no—
331C2×C4×D4—51no—
332C2×C4×D4—51no—
333C2×#117—51no—
334#436—58no—
335#436—58no—
336#435—58no—
337#435—58no—
338#435—58no—
339#435—58no—
340C8×D4—58no—
341C8×D4—58no—
342#433—58no—
343#433—58no—
344C2×C4⋊C8—51no—
345C2×C4⋊C8—51no—
346C2×C4⋊C8—51no—
347C2×C4⋊C8—51no—
348#408—58no—
349#408—58no—
350#407—58no—
351C2×C22⋊C8—51no—
352C2×C22⋊C8—51no—
353C2×C22⋊C8—51no—
354C2×C22⋊C8—51no—
355C2×C22⋊C8—51no—
356C2×C22⋊C8—51no—
357C2×C22⋊C8—51no—
358C2×C22⋊C8—51no—
359C2×C22⋊C8—58no—
360C2×C22⋊C8—51no—
361C2×C22⋊C8—51no—
362C2×C22⋊C8—51no—
363C2×C22⋊C8—51no—
364C2×#97—51no—
365C2×#97—51no—
366C2×C4×C8—51no—
367C2×C4×C8—51no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—28no—
375C23×C5—22no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—22no—
379C23×C5—22no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5—416no—
383C23×C5#13114yes—
384C23×C5C23×C412yes—
385C23×C5C23×C412yes—
386C23×C5C23×C412yes—
387C23×C5C23×C412yes—
388C23×C5C23×C411yescharacteristic
389C22×D5—22no—
390C22×D5—22no—
391C22×D5—22no—
392C22×D5C23×C412yes—
393C5×D4—28no—
394C5×D4—44no—
395C5×D4—44no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5C23×C412yes—
400C2×C4×C5C23×C412yes—
401C2×C4×C5C23×C412yes—
402C22⋊D5—28no—
403C22⋊D5—44no—
404C22⋊D5—44no—
405C22⋊D5—44no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—24no—
413C2×Dic5—24no—
414C2×Dic5—24no—
415C2×Dic5—24no—
416C2×Dic5—22no—
417C2×Dic5—22no—
418C2×Dic5—22no—
419C2×Dic5—22no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—44no—
425C2×Dic5—44no—
426C2×Dic5—44no—
427C2×Dic5C23×C412yes—
428C2×Dic5C23×C412yes—
429C2×Dic5C23×C412yes—
430C2×Dic5C23×C412yes—
431C2×Dic5C23×C412yes—
432C2×Dic5C23×C412yes—
433C2×Dic5C23×C411yescharacteristic
434C2×Dic5H(5,𝔽2)12yes—
435C2×Dic5H(5,𝔽2)12yes—
436C2×Dic5C2511yescharacteristic
437C4×D5—24no—
438C4×D5—22no—
439C4×D5—22no—
440Dic10—44no—
441#170—22no—
442#170—22no—
443#170—22no—
444#170—22no—
445#170—22no—
446#170—22no—
447#170—22no—
448#170—22no—
449C25C2×AGL(1,𝔽5)11yescharacteristic
450C2×#41—54no—
451C2×#41—54no—
452C2×#41—202no—
453C2×#41—202no—
454C22×Q8—51no—
455C22×D4—51no—
456C22×D4—51no—
457C22×D4—51no—
458C22×D4—51no—
459C22×D4C2×AGL(1,𝔽5)11yescharacteristic
460C22×D4C2×AGL(1,𝔽5)11yescharacteristic
461C22×D4C2×AGL(1,𝔽5)11yescharacteristic
462C23×C4—51no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—54no—
470C23×C4—54no—
471C23×C4—51no—
472C23×C4—202no—
473C23×C4—202no—
474C2×M16—54no—
475C2×M16—54no—
476C2×M16—54no—
477C2×M16—54no—
478C2×M16—202no—
479C2×M16—202no—
480C2×M16—202no—
481C2×M16—202no—
482C22×C8—51no—
483C22×C8—51no—
484C22×C8—51no—
485C22×C8—51no—
486C22×C8—51no—
487C22×C8—51no—
488C22×C8—51no—
489C22×C8—51no—
490C22×C8—54no—
491C22×C8—54no—
492C22×C8—54no—
493C22×C8—54no—
494C22×C8—202no—
495C22×C8—202no—
496C22×C8—202no—
497C22×C8—202no—
498#123—58no—
499#123—58no—
500C22⋊Q8—58no—
501C22⋊Q8—58no—
502#121—58no—
503#121—58no—
504#120—58no—
505#120C2×AGL(1,𝔽5)18yes—
506C4×D4—54no—
507C4×D4—54no—
508C4×D4—54no—
509C4×D4—54no—
510C4×D4—54no—
511C4×D4—54no—
512C4×D4—54no—
513C4×D4—54no—
514#117—54no—
515#117—54no—
516C2×C4⋊C4—51no—
517C2×C4⋊C4—51no—
518C2×C4⋊C4—51no—
519C2×C4⋊C4—51no—
520C2×C4⋊C4—51no—
521C2×C4⋊C4—51no—
522C2×C22⋊C4—51no—
523C2×C22⋊C4—51no—
524C2×C22⋊C4—51no—
525C2×C22⋊C4—51no—
526C2×C22⋊C4—51no—
527C2×C22⋊C4—51no—
528C2×C22⋊C4—51no—
529C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
530C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
531C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
532C2×C42—51no—
533C2×C42—51no—
534C4⋊C8—54no—
535C4⋊C8—54no—
536C4⋊C8—54no—
537C4⋊C8—54no—
538C22⋊C8—54no—
539C22⋊C8—54no—
540C22⋊C8—54no—
541C22⋊C8—54no—
542C22⋊C8—54no—
543C22⋊C8—54no—
544C22⋊C8—54no—
545C22⋊C8—54no—
546C22⋊C8—54no—
547C22⋊C8—54no—
548C22⋊C8—54no—
549C22⋊C8—54no—
550#97—54no—
551#97—54no—
552C4×C8—54no—
553C4×C8—54no—
554C22×C5—22no—
555C22×C5—28no—
556C22×C5—22no—
557C22×C5—22no—
558C22×C5—22no—
559C22×C5—22no—
560C22×C5—22no—
561C22×C5—22no—
562C22×C5—22no—
563C22×C5—22no—
564C22×C5—22no—
565C22×C5—22no—
566C22×C5—416no—
567C22×C5—44no—
568C22×C5—44no—
569C22×C5—44no—
570C22×C5#51812yes—
571C22×C5C2×#13114yes—
572C22×C5C2×#13112yes—
573C22×C5#56812yes—
574C22×C5C24×C411yescharacteristic
575C2×D5—22no—
576C2×D5—22no—
577C2×D5—22no—
578C2×D5—44no—
579C4×C5—22no—
580C4×C5—22no—
581C4×C5—22no—
582Dic5—22no—
583Dic5—22no—
584Dic5—22no—
585Dic5—22no—
586Dic5—22no—
587Dic5—22no—
588Dic5#51812yes—
589Dic5C2×H(5,𝔽2)11yescharacteristic
590Dic5C2×H(5,𝔽2)11yescharacteristic
591C24—24no—
592C24—42no—
593C24—42no—
594C24—51no—
595C24C22×AGL(1,𝔽5)11yescharacteristic
596C24C22×AGL(1,𝔽5)11yescharacteristic
597C24C22×AGL(1,𝔽5)11yescharacteristic
598C24C22×AGL(1,𝔽5)11yescharacteristic
599C24C22×AGL(1,𝔽5)14yes—
600#41—204no—
601#41—204no—
602#41—208no—
603C2×Q8—54no—
604C2×Q8—202no—
605C2×D4—24no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—54no—
609C2×D4—54no—
610C2×D4—54no—
611C2×D4—54no—
612C2×D4—104no—
613C2×D4—202no—
614C2×D4—202no—
615C2×D4—202no—
616C2×D4C22×AGL(1,𝔽5)14yes—
617C2×D4C22×AGL(1,𝔽5)14yes—
618C2×D4C22×AGL(1,𝔽5)14yes—
619C22×C4—51no—
620C22×C4—52no—
621C22×C4—52no—
622C22×C4—52no—
623C22×C4—52no—
624C22×C4—52no—
625C22×C4—52no—
626C22×C4—52no—
627C22×C4—52no—
628C22×C4—51no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—51no—
633C22×C4—51no—
634C22×C4—54no—
635C22×C4—54no—
636C22×C4—54no—
637C22×C4—52no—
638C22×C4—52no—
639C22×C4—102no—
640C22×C4—102no—
641C22×C4—102no—
642C22×C4—102no—
643C22×C4—102no—
644C22×C4—102no—
645C22×C4—102no—
646C22×C4—102no—
647C22×C4—102no—
648C22×C4—102no—
649C22×C4—204no—
650C22×C4—204no—
651C22×C4—208no—
652C22×C4—202no—
653C22×C4—202no—
654C22×C4—202no—
655C22×C4C22×AGL(1,𝔽5)11yescharacteristic
656C22×C4C22×AGL(1,𝔽5)11yescharacteristic
657C22×C4C22×AGL(1,𝔽5)11yescharacteristic
658M16—204no—
659M16—204no—
660M16—204no—
661M16—204no—
662C2×C8—52no—
663C2×C8—52no—
664C2×C8—52no—
665C2×C8—52no—
666C2×C8—52no—
667C2×C8—52no—
668C2×C8—52no—
669C2×C8—52no—
670C2×C8—102no—
671C2×C8—102no—
672C2×C8—102no—
673C2×C8—102no—
674C2×C8—102no—
675C2×C8—102no—
676C2×C8—102no—
677C2×C8—102no—
678C2×C8—204no—
679C2×C8—204no—
680C2×C8—204no—
681C2×C8—204no—
682C4⋊C4—54no—
683C4⋊C4—54no—
684C4⋊C4—54no—
685C4⋊C4—54no—
686C4⋊C4—54no—
687C4⋊C4—54no—
688C22⋊C4—54no—
689C22⋊C4—54no—
690C22⋊C4—54no—
691C22⋊C4—54no—
692C22⋊C4—54no—
693C22⋊C4—54no—
694C22⋊C4—54no—
695C22⋊C4C22×AGL(1,𝔽5)14yes—
696C22⋊C4C22×AGL(1,𝔽5)14yes—
697C22⋊C4C22×AGL(1,𝔽5)14yes—
698C42—52no—
699C42—52no—
700C42—52no—
701C42—52no—
702C2×C5—24no—
703C2×C5—42no—
704C2×C5—42no—
705C2×C5—42no—
706C2×C5#297614yescomplemented
707C2×C5C2×#51811yescharacteristic
708C2×C5C22×#13111yescharacteristic
709C2×C5C2×#56811yescharacteristic
710D5—42no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—28no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—44no—
724C23—44no—
725C23—416no—
726C23—52no—
727C23—102no—
728C23—102no—
729C23—102no—
730C23#413114yes—
731C23C23×AGL(1,𝔽5)12yes—
732C23C23×AGL(1,𝔽5)12yes—
733C23C23×AGL(1,𝔽5)12yes—
734C23C23×AGL(1,𝔽5)12yes—
735C23C23×AGL(1,𝔽5)11yescharacteristic
736Q8—204no—
737D4—28no—
738D4—44no—
739D4—44no—
740D4—108no—
741D4—204no—
742D4—204no—
743D4—204no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—52no—
748C2×C4—52no—
749C2×C4—51no—
750C2×C4—51no—
751C2×C4—52no—
752C2×C4—52no—
753C2×C4—52no—
754C2×C4—52no—
755C2×C4—52no—
756C2×C4—52no—
757C2×C4—102no—
758C2×C4—102no—
759C2×C4—104no—
760C2×C4—102no—
761C2×C4—102no—
762C2×C4—102no—
763C2×C4—102no—
764C2×C4—102no—
765C2×C4—102no—
766C2×C4—102no—
767C2×C4—102no—
768C2×C4—104no—
769C2×C4—104no—
770C2×C4—104no—
771C2×C4—104no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—102no—
778C2×C4—204no—
779C2×C4—204no—
780C2×C4—204no—
781C2×C4C23×AGL(1,𝔽5)12yes—
782C2×C4C23×AGL(1,𝔽5)12yes—
783C2×C4C23×AGL(1,𝔽5)12yes—
784C8—102no—
785C8—102no—
786C8—102no—
787C8—102no—
788C8—102no—
789C8—102no—
790C8—102no—
791C8—102no—
792C5C2×#297611yescharacteristic, complemented, Sylow
793C22—22no—
794C22—22no—
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—416no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—102no—
810C22—102no—
811C22—102no—
812C22—204no—
813C22C2×#413114yes—
814C22C2×#413112yes—
815C22#6625612yes—
816C22#6625812yes—
817C22C24×AGL(1,𝔽5)11yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—51no—
822C4—51no—
823C4—52no—
824C4—102no—
825C4—102no—
826C4—102no—
827C4—102no—
828C4—102no—
829C4—102no—
830C2—24no—
831C2—42no—
832C2—42no—
833C2—42no—
834C2—202no—
835C2#1061721814yesdirect product factor
836C2C22×#413111yescharacteristic
837C2C2×#6625611yescharacteristic
838C2C2×#6625811yescharacteristic
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×#2976
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
2. C2×#65798C2semidirect
3. C22×C22⋊#170C2semidirect
4. C2×#65774C2semidirect
5. C2×#65773C2semidirect
6. C2×#65773C2semidirect
7. C2×D4×#170C2semidirect
8. C2×#65776C2semidirect
9. C2×#65775C2semidirect
10. #10617218C2direct (N × H)
11. C2×#65695C2semidirect
12. C2×#65694C2semidirect
13. C2×#65693C2semidirect
14. C2×#65692C2semidirect
15. C2×#65697C2semidirect
16. C2×#65697C2semidirect
21. C22×#704C22semidirect
24. C23×#170C22semidirect
25. C22×#700C22semidirect
26. C22×D5⋊C8C22semidirect
42. #65798C22semidirect
51. C2×C22⋊#170C22semidirect
52. C2×C22⋊#170C22semidirect
53. C2×C22⋊#170C22semidirect
54. #65776C22semidirect
55. #65775C22semidirect
56. #65774C22semidirect
57. #65773C22semidirect
58. #65773C22semidirect
59. D4×#170C22semidirect
60. C2×#4004C22semidirect
61. C2×#4004C22semidirect
62. C2×#4003C22semidirect
63. C2×#4003C22semidirect
64. C2×#4002C22semidirect
65. C2×#4002C22semidirect
66. C2×C4⋊#170C22semidirect
67. C2×C4⋊#170C22semidirect
68. C2×C4×#170C22semidirect
69. C2×C4×#170C22semidirect
70. #65697C22semidirect
71. #65697C22semidirect
72. #65695C22semidirect
73. #65694C22semidirect
74. #65693C22semidirect
75. #65692C22semidirect
107. C2×#704C23semidirect
121. C22×#170C23semidirect
123. C2×#700C23semidirect
125. C2×D5⋊C8C23semidirect
170. C22⋊#170C23semidirect
171. C22⋊#170C23semidirect
172. #4004C23semidirect
173. #4004C23semidirect
174. #4003C23semidirect
175. #4003C23semidirect
176. #4002C23semidirect
177. #4002C23semidirect
178. C4⋊#170C23semidirect
179. C4⋊#170C23semidirect
180. C4×#170C23semidirect
181. C4×#170C23semidirect
706. C2×C5#2976semidirect
792. C5C2×#2976semidirect
835. C2#10617218direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659202
C2×#657982
C22×C22⋊#1702
C2×#657742
C2×#657732
C2×D4×#1702
C2×#657762
C2×#657752
#106172182
C2×#656952
C2×#656942
C2×#656932
C2×#656922
C2×#656972
C2×#29765