Finite Group Databasebeta

← C2×#10614577 #12267017

Subgroups — C2×#10614577 #12267017

Order 1280.

3938 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#123C211yesmaximal, characteristic, complemented
2C22×#4085C211yesmaximal, characteristic
3C22×#4075C211yesmaximal, characteristic, complemented
4C22×#4027C211yesmaximal, characteristic, complemented
5C2×#65509C211yesmaximal, characteristic, complemented
6C22×#3963C211yesmaximal, characteristic, complemented
7#10614577C2116yesmaximal, direct product factor
8C2×#65282C211yesmaximal, characteristic, complemented
9C2×#65276C211yesmaximal, characteristic, complemented
10C2×#65269C211yesmaximal, characteristic, complemented
11C2×#65262C211yesmaximal, characteristic, complemented
12C2×#65245C211yesmaximal, characteristic, complemented
13C2×#65237C211yesmaximal, characteristic, complemented
14C2×#65250C211yesmaximal, characteristic, complemented
15C2×#65233C211yesmaximal, characteristic, complemented
16C2×#65239C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C24×Dic5C2211yescharacteristic
22C24×Dic5C2211yescharacteristic
23C23×C4×D5C2211yescharacteristic
24C2×C5×#123—28no—
25C2×C5×#123C2218yescomplemented
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C4⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×C22⋊Dic5C2211yescharacteristic
35C2×#4085—28no—
36C2×#4085C2218yes—
37C2×#4075—28no—
38C2×#4075C2218yescomplemented
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×#685C2211yescharacteristic
42C22×#685C2211yescharacteristic
43C22×C4⋊Dic5C2211yescharacteristic
44C22×C4⋊Dic5C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×#683C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C2×#4027—28no—
51C2×#4027C2218yescomplemented
52#65509C2218yescomplemented
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2218yescomplemented
62#65282C2218yescomplemented
63#65276C2218yescomplemented
64#65269C2218yescomplemented
65#65262C2218yescomplemented
66#65250C2218yescomplemented
67#65245C2218yescomplemented
68#65239C2218yescomplemented
69#65237C2218yescomplemented
70#65233C2218yescomplemented
71C2×#2425—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C25×C5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—24no—
78C22×C5×D4C2314yes—
79C23×C4×C5—24no—
80C23×C4×C5—24no—
81C23×C4×C5—24no—
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2314yes—
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C22×C22⋊D5—24no—
89C22×C22⋊D5—24no—
90C22×C22⋊D5—24no—
91C22×C22⋊D5—24no—
92C22×C22⋊D5—42no—
93C22×C22⋊D5D418yes—
94C22×C22⋊D5C2314yes—
95C22×C22⋊D5C2314yes—
96C23×Dic5—24no—
97C23×Dic5—24no—
98C23×Dic5—24no—
99C23×Dic5—24no—
100C23×Dic5—42no—
101C23×Dic5—42no—
102C23×Dic5C2311yescharacteristic
103C23×Dic5C2311yescharacteristic
104C23×Dic5C2311yescharacteristic
105C23×Dic5C2311yescharacteristic
106C23×Dic5C2314yes—
107C23×Dic5C2314yes—
108C23×Dic5C2311yescharacteristic
109C23×Dic5C2311yescharacteristic
110C23×Dic5C2311yescharacteristic
111C22×C4×D5—24no—
112C22×C4×D5—24no—
113C22×C4×D5—42no—
114C22×C4×D5C2314yes—
115C5×#123—232no—
116C2×C5×C4⋊C4—24no—
117C2×C5×C4⋊C4—24no—
118C2×C5×C4⋊C4C2314yes—
119C2×C5×C4⋊C4C2314yes—
120C2×C5×C22⋊C4—24no—
121C2×C5×C22⋊C4—24no—
122C2×C5×C22⋊C4D418yescomplemented
123C2×C5×C22⋊C4C2314yes—
124C2×C5×C22⋊C4C2314yes—
125C2×C5×C22⋊C4C2314yes—
126C2×C22⋊Dic5—24no—
127C2×C22⋊Dic5—24no—
128C2×C22⋊Dic5—24no—
129C2×C22⋊Dic5—42no—
130C2×C22⋊Dic5C2314yes—
131C2×C22⋊Dic5C2314yes—
132C2×C22⋊Dic5C2314yes—
133C2×C22⋊Dic5C2314yes—
134#4085—232no—
135#4075—232no—
136C2×#685—24no—
137C2×#685—24no—
138C2×#685—24no—
139C2×#685—24no—
140C2×#685C2314yes—
141C2×#685C2314yes—
142C2×#685C2314yes—
143C2×#685C2314yes—
144C2×C4⋊Dic5—24no—
145C2×C4⋊Dic5—42no—
146C2×C4⋊Dic5C2314yes—
147C2×C4⋊Dic5C2314yes—
148C2×#683—24no—
149C2×#683—24no—
150C2×#683—24no—
151C2×#683—24no—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×#683C2314yes—
156C2×C4×Dic5—24no—
157C2×C4×Dic5C2314yes—
158#4027—232no—
159#3963C2314yes—
160#3963C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#123—51no—
168C22×#123D511yescharacteristic, complemented
169C22×#121—51no—
170C22×C4×D4—51no—
171#2425—516no—
172C2×#398—51no—
173C2×#397—51no—
174C2×#396—51no—
175C2×#394—51no—
176C2×#389—51no—
177C2×#388—51no—
178C2×#386—51no—
179C2×#386—51no—
180C2×#385—51no—
181C2×#380—51no—
182C22×#95—51no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5—22no—
190C24×C5—22no—
191C24×C5—22no—
192C24×C5—22no—
193C24×C5—22no—
194C24×C5C2×D414yes—
195C24×C5C2×D414yes—
196C24×C5#4114yes—
197C24×C5C2412yes—
198C24×C5C2412yes—
199C24×C5C2411yescharacteristic
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5—22no—
205C23×D5—22no—
206C23×D5C2×D414yes—
207C23×D5C2412yes—
208C2×C5×D4—28no—
209C2×C5×D4—28no—
210C2×C5×D4—28no—
211C2×C5×D4—416no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—28no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—28no—
223C22×C4×C5—22no—
224C22×C4×C5—28no—
225C22×C4×C5—22no—
226C22×C4×C5—22no—
227C22×C4×C5—22no—
228C22×C4×C5—416no—
229C22×C4×C5C2×D414yes—
230C22×C4×C5C2×D414yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C2×C22⋊D5—232no—
237C2×C22⋊D5—28no—
238C2×C22⋊D5—28no—
239C2×C22⋊D5—28no—
240C2×C22⋊D5—28no—
241C2×C22⋊D5—44no—
242C2×C22⋊D5—416no—
243C2×C22⋊D5C2×D4116yes—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—28no—
254C22×Dic5—22no—
255C22×Dic5—28no—
256C22×Dic5—22no—
257C22×Dic5—22no—
258C22×Dic5—22no—
259C22×Dic5—22no—
260C22×Dic5—22no—
261C22×Dic5—22no—
262C22×Dic5—22no—
263C22×Dic5—22no—
264C22×Dic5—28no—
265C22×Dic5—28no—
266C22×Dic5—44no—
267C22×Dic5—44no—
268C22×Dic5—416no—
269C22×Dic5—416no—
270C22×Dic5C2×D414yes—
271C22×Dic5#4114yes—
272C22×Dic5#4114yes—
273C22×Dic5C2412yes—
274C22×Dic5C2412yes—
275C22×Dic5C2412yes—
276C22×Dic5C2412yes—
277C22×Dic5C2412yes—
278C22×Dic5C2412yes—
279C22×Dic5C2412yes—
280C2×C4×D5—28no—
281C2×C4×D5—28no—
282C2×C4×D5—44no—
283C2×C4×D5—416no—
284C5×C4⋊C4—28no—
285C5×C4⋊C4—28no—
286C5×C22⋊C4—28no—
287C5×C22⋊C4—28no—
288C5×C22⋊C4C2×D4116yescomplemented
289C22⋊Dic5—28no—
290C22⋊Dic5—28no—
291C22⋊Dic5—28no—
292C22⋊Dic5—44no—
293#685—28no—
294#685—28no—
295#685—28no—
296#685—28no—
297C4⋊Dic5—28no—
298C4⋊Dic5—44no—
299#683—28no—
300#683—28no—
301#683—28no—
302#683—28no—
303C4×Dic5—28no—
304C23×D4—51no—
305C23×D4—51no—
306C23×D4C2×D511yescharacteristic
307C24×C4—51no—
308C24×C4—51no—
309C24×C4—51no—
310C24×C4C2×D511yescharacteristic
311C2×#123—28no—
312C2×#123—58no—
313C2×#123—108no—
314C2×#123C2×D518yescomplemented
315C2×#121—58no—
316C2×#121—108no—
317C2×C4×D4—58no—
318C2×C4×D4—108no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—51no—
323C22×C4⋊C4—51no—
324C22×C4⋊C4—51no—
325C22×C4⋊C4C2×D511yescharacteristic
326C22×C4⋊C4C2×D511yescharacteristic
327C22×C22⋊C4—51no—
328C22×C22⋊C4—51no—
329C22×C22⋊C4—51no—
330C22×C22⋊C4—51no—
331C22×C22⋊C4—51no—
332C22×C22⋊C4—51no—
333C22×C22⋊C4—51no—
334C22×C22⋊C4—51no—
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C22⋊C4C2×D511yescharacteristic
338C22×C42—51no—
339#398—58no—
340#397—58no—
341#396—58no—
342#394—58no—
343#389—58no—
344#388—58no—
345#386—58no—
346#386—58no—
347#385—58no—
348#380—58no—
349C2×#95—51no—
350C2×#95—51no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—58no—
355C2×#95—51no—
356C2×#95—51no—
357C2×#95—51no—
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—28no—
361C23×C5—28no—
362C23×C5—28no—
363C23×C5—28no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5—22no—
372C23×C5—22no—
373C23×C5—22no—
374C23×C5—22no—
375C23×C5—44no—
376C23×C5—44no—
377C23×C5—44no—
378C23×C5—44no—
379C23×C5—44no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5#121116yes—
383C23×C5C22×D414yes—
384C23×C5C22×D412yes—
385C23×C5C22×D414yes—
386C23×C5C22×D412yes—
387C23×C5C2×#4114yes—
388C23×C5C2×#4112yes—
389C23×C5C2×#4112yes—
390C23×C5C2×#4112yes—
391C23×C5H(5,𝔽2)12yes—
392C23×C52−1+412yes—
393C23×C5C2511yescharacteristic
394C22×D5—28no—
395C22×D5—28no—
396C22×D5—28no—
397C22×D5—22no—
398C22×D5—22no—
399C22×D5—22no—
400C22×D5—22no—
401C22×D5—22no—
402C22×D5—22no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5—44no—
406C22×D5—44no—
407C22×D5C22×D414yes—
408C5×D4—416no—
409C2×C4×C5—28no—
410C2×C4×C5—28no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—416no—
425C2×C4×C5—44no—
426C2×C4×C5—44no—
427C2×C4×C5—44no—
428C2×C4×C5C22×D414yes—
429C2×C4×C5C22×D414yes—
430C22⋊D5—232no—
431C22⋊D5—416no—
432C2×Dic5—28no—
433C2×Dic5—28no—
434C2×Dic5—28no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—22no—
441C2×Dic5—22no—
442C2×Dic5—22no—
443C2×Dic5—22no—
444C2×Dic5—22no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—22no—
448C2×Dic5—22no—
449C2×Dic5—22no—
450C2×Dic5—22no—
451C2×Dic5—22no—
452C2×Dic5—22no—
453C2×Dic5—416no—
454C2×Dic5—416no—
455C2×Dic5—44no—
456C2×Dic5—44no—
457C2×Dic5—44no—
458C2×Dic5—44no—
459C2×Dic5C22×D414yes—
460C2×Dic5C2×#4114yes—
461C2×Dic5C2×#4114yes—
462C4×D5—416no—
463C25—51no—
464C25C22×D511yescharacteristic
465C25C22×D511yescharacteristic
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—24no—
469C22×D4—58no—
470C22×D4—54no—
471C22×D4—54no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—202no—
477C22×D4C22×D514yes—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—51no—
488C23×C4—54no—
489C23×C4—54no—
490C23×C4—54no—
491C23×C4—104no—
492C23×C4—104no—
493C23×C4—104no—
494C23×C4—104no—
495C23×C4—104no—
496C23×C4—104no—
497C23×C4—202no—
498C23×C4—202no—
499C23×C4—202no—
500C23×C4C22×D514yes—
501C23×C4C22×D511yescharacteristic
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506#123—232no—
507#123—1032no—
508#121—1032no—
509C4×D4—1032no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—54no—
513C2×C4⋊C4—54no—
514C2×C4⋊C4—54no—
515C2×C4⋊C4—54no—
516C2×C4⋊C4—54no—
517C2×C4⋊C4—54no—
518C2×C4⋊C4—104no—
519C2×C4⋊C4—104no—
520C2×C4⋊C4—104no—
521C2×C4⋊C4—104no—
522C2×C4⋊C4—104no—
523C2×C4⋊C4—202no—
524C2×C4⋊C4C22×D514yes—
525C2×C4⋊C4C22×D514yes—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—54no—
529C2×C22⋊C4—54no—
530C2×C22⋊C4—54no—
531C2×C22⋊C4—54no—
532C2×C22⋊C4—54no—
533C2×C22⋊C4—54no—
534C2×C22⋊C4—54no—
535C2×C22⋊C4—54no—
536C2×C22⋊C4—104no—
537C2×C22⋊C4—104no—
538C2×C22⋊C4—104no—
539C2×C22⋊C4—104no—
540C2×C22⋊C4—104no—
541C2×C22⋊C4—104no—
542C2×C22⋊C4—104no—
543C2×C22⋊C4—202no—
544C2×C22⋊C4C22⋊D518yescomplemented
545C2×C22⋊C4C22×D514yes—
546C2×C22⋊C4C22×D514yes—
547C2×C22⋊C4C22×D514yes—
548C2×C42—54no—
549C2×C42—104no—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95—54no—
555#95—54no—
556#95—54no—
557#95—54no—
558C22×C5—24no—
559C22×C5—232no—
560C22×C5—24no—
561C22×C5—24no—
562C22×C5—24no—
563C22×C5—24no—
564C22×C5—24no—
565C22×C5—42no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5—88no—
573C22×C5C2×#12118yes—
574C22×C5C2×#12114yes—
575C22×C5#52914yes—
576C22×C5#53914yes—
577C22×C5#54614yes—
578C22×C5#54614yes—
579C22×C5#54714yes—
580C22×C5#54714yes—
581C22×C5C23×D411yescharacteristic
582C22×C5C23×D411yescharacteristic
583C22×C5C22×#4111yescharacteristic
584C22×C5C22×#4111yescharacteristic
585C22×C5C22×#4111yescharacteristic
586C22×C5C2×H(5,𝔽2)11yescharacteristic
587C22×C5C2×2−1+411yescharacteristic
588C2×D5—24no—
589C2×D5—24no—
590C2×D5—24no—
591C2×D5—42no—
592C2×D5—416no—
593C2×D5—42no—
594C2×D5—42no—
595C2×D5—42no—
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—42no—
599C4×C5—42no—
600C4×C5—42no—
601Dic5—24no—
602Dic5—24no—
603Dic5—24no—
604Dic5—42no—
605Dic5—42no—
606Dic5—42no—
607Dic5—42no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—54no—
620C24—52no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24D4×D514yes—
628C24#71114yes—
629C24C2×C22⋊D514yes—
630C24C23×D512yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C2×D4—28no—
634C2×D4—28no—
635C2×D4—28no—
636C2×D4—416no—
637C2×D4—516no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—1032no—
642C2×D4—108no—
643C2×D4—204no—
644C2×D4—2016no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—28no—
653C22×C4—28no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—28no—
661C22×C4—416no—
662C22×C4—54no—
663C22×C4—54no—
664C22×C4—54no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—52no—
671C22×C4—52no—
672C22×C4—108no—
673C22×C4—108no—
674C22×C4—108no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—108no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—102no—
690C22×C4—102no—
691C22×C4—102no—
692C22×C4—102no—
693C22×C4—102no—
694C22×C4—108no—
695C22×C4—108no—
696C22×C4—204no—
697C22×C4—2016no—
698C22×C4—204no—
699C22×C4—204no—
700C22×C4—2016no—
701C22×C4—2016no—
702C22×C4C2×C22⋊D514yes—
703C22×C4C2×C22⋊D514yes—
704C22×C4C23×D512yes—
705C22×C4C23×D512yes—
706C22×C4C23×D512yes—
707C22×C4C23×D512yes—
708C22×C4C23×D512yes—
709C4⋊C4—28no—
710C4⋊C4—28no—
711C4⋊C4—108no—
712C4⋊C4—108no—
713C4⋊C4—108no—
714C4⋊C4—108no—
715C4⋊C4—108no—
716C4⋊C4—204no—
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C22⋊C4—108no—
724C22⋊C4—108no—
725C22⋊C4—108no—
726C22⋊C4—204no—
727C22⋊C4C2×C22⋊D5116yescomplemented
728C42—108no—
729C2×C5—28no—
730C2×C5—82no—
731C2×C5#242518yescomplemented
732C2×C5C22×#12111yescharacteristic
733C2×C5C2×#52911yescharacteristic
734C2×C5C2×#53911yescharacteristic
735C2×C5C2×#54611yescharacteristic
736C2×C5C2×#54611yescharacteristic
737C2×C5C2×#54711yescharacteristic
738C2×C5C2×#54711yescharacteristic
739D5—44no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—54no—
765C23—108no—
766C23—108no—
767C23—108no—
768C23—102no—
769C23—102no—
770C23—102no—
771C23—102no—
772C23—102no—
773C23—102no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23#4084116yes—
779C23C2×D4×D514yes—
780C23C2×D4×D512yes—
781C23C2×#71114yes—
782C23C2×#71112yes—
783C23D5×#4112yes—
784C23D5×#4112yes—
785C23#414912yes—
786C23#415012yes—
787C23C22×C22⋊D514yes—
788C23C22×C22⋊D512yes—
789C23C24×D511yescharacteristic
790D4—416no—
791D4—1032no—
792D4—2016no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—416no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—54no—
813C2×C4—54no—
814C2×C4—54no—
815C2×C4—108no—
816C2×C4—108no—
817C2×C4—108no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—102no—
834C2×C4—102no—
835C2×C4—102no—
836C2×C4—2016no—
837C2×C4—2016no—
838C2×C4—2016no—
839C2×C4—204no—
840C2×C4—204no—
841C2×C4—204no—
842C2×C4—204no—
843C2×C4C22×C22⋊D514yes—
844C2×C4C22×C22⋊D514yes—
845C5C2×#242511yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—232no—
851C22—24no—
852C22—24no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—88no—
861C22—104no—
862C22—104no—
863C22—104no—
864C22—202no—
865C22—202no—
866C22—202no—
867C22—202no—
868C22—2016no—
869C22#6598314yes—
870C22#6598814yes—
871C22#6598914yes—
872C22#6599914yes—
873C22C2×#408418yes—
874C22C2×#408414yes—
875C22#6615814yes—
876C22#6616314yes—
877C22C22×D4×D511yescharacteristic
878C22C22×#71111yescharacteristic
879C22C2×D5×#4111yescharacteristic
880C22C2×D5×#4111yescharacteristic
881C22C2×#414911yescharacteristic
882C22C2×#415011yescharacteristic
883C22C23×C22⋊D511yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—104no—
890C4—104no—
891C4—104no—
892C4—202no—
893C4—202no—
894C4—202no—
895C4—202no—
896C2—28no—
897C2—82no—
898C2—204no—
899C2#1061457718yesdirect product factor
900C2C2×#6598311yescharacteristic
901C2C2×#6599911yescharacteristic
902C2C2×#6598811yescharacteristic
903C2C2×#6598911yescharacteristic
904C2C22×#408411yescharacteristic
905C2C2×#6615811yescharacteristic
906C2C2×#6616311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#123C2
socleC24×C5C24
prime radicalC22×#4085C2
hypercenterC22×#123D5
hypocenterC5C2×#2425
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C5×#123C2semidirect
3. C22×#4075C2semidirect
4. C22×#4027C2semidirect
5. C2×#65509C2semidirect
6. C22×#3963C2semidirect
7. #10614577C2direct (N × H)
8. C2×#65282C2semidirect
9. C2×#65276C2semidirect
10. C2×#65269C2semidirect
11. C2×#65262C2semidirect
12. C2×#65245C2semidirect
13. C2×#65237C2semidirect
14. C2×#65250C2semidirect
15. C2×#65233C2semidirect
16. C2×#65239C2semidirect
25. C2×C5×#123C22semidirect
38. C2×#4075C22semidirect
51. C2×#4027C22semidirect
52. #65509C22semidirect
61. C2×#3963C22semidirect
62. #65282C22semidirect
63. #65276C22semidirect
64. #65269C22semidirect
65. #65262C22semidirect
66. #65250C22semidirect
67. #65245C22semidirect
68. #65239C22semidirect
69. #65237C22semidirect
70. #65233C22semidirect
122. C2×C5×C22⋊C4D4semidirect
168. C22×#123D5semidirect
288. C5×C22⋊C4C2×D4semidirect
314. C2×#123C2×D5semidirect
544. C2×C22⋊C4C22⋊D5semidirect
727. C22⋊C4C2×C22⋊D5semidirect
731. C2×C5#2425semidirect
845. C5C2×#2425semidirect
899. C2#10614577direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1232
C22×#40852
C22×#40752
C22×#40272
C2×#655092
C22×#39632
#106145772
C2×#652822
C2×#652762
C2×#652692
C2×#652622
C2×#652452
C2×#652372
C2×#652502
C2×#652332
C2×#652392
C2×#24255