Finite Group Databasebeta

← C2×#10605312 #12265526

Subgroups — C2×#10605312 #12265526

Order 1280.

4134 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
3C22×C4×D20C211yesmaximal, characteristic, complemented
4C22×#4018C211yesmaximal, characteristic, complemented
5C2×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#65248C211yesmaximal, characteristic, complemented
7C2×#65248C211yesmaximal, characteristic, complemented
8C2×#65249C211yesmaximal, characteristic
9C2×#65237C211yesmaximal, characteristic, complemented
10C2×C4×#683C211yesmaximal, characteristic, complemented
11C2×C4×#685C211yesmaximal, characteristic, complemented
12#10605312C2116yesmaximal, direct product factor
13C2×#64964C211yesmaximal, characteristic, complemented
14C2×#64965C211yesmaximal, characteristic, complemented
15C2×#64946C211yesmaximal, characteristic, complemented
16C2×#64961C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×D20C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C22×C42×C5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C2×C4×C22⋊D5—28no—
30C2×C4×C22⋊D5—28no—
31C2×C4×C22⋊D5C2218yescomplemented
32C2×C4×C22⋊D5C2218yescomplemented
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×C4⋊Dic5C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×C4×Dic5C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C2×C4×D20—28no—
51C2×C4×D20C2218yescomplemented
52C2×#4018—28no—
53C2×#4018C2218yescomplemented
54C4×C5×C22⋊C4C2218yescomplemented
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65249C2218yes—
62#65248C2218yescomplemented
63#65248C2218yescomplemented
64#65237C2218yescomplemented
65C4×#685C2218yescomplemented
66C4×#683C2218yescomplemented
67#64965C2218yescomplemented
68#64964C2218yescomplemented
69#64961C2218yescomplemented
70#64946C2218yescomplemented
71C2×#2392—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C23×C4×C5—24no—
76C23×C4×C5—24no—
77C23×C4×C5—24no—
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2314yes—
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C22×C22⋊D5—24no—
86C22×C22⋊D5—24no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—24no—
89C22×C22⋊D5—24no—
90C22×C22⋊D5—24no—
91C22×C22⋊D5C2314yes—
92C22×C22⋊D5C2314yes—
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C22×D20—24no—
100C22×D20—24no—
101C22×D20—24no—
102C22×D20C2314yes—
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—24no—
106C22×C4×D5—24no—
107C22×C4×D5—24no—
108C22×C4×D5D418yescomplemented
109C22×C4×D5C2314yes—
110C22×C4×D5C2314yes—
111C2×C5×C22⋊C4—24no—
112C2×C5×C22⋊C4—24no—
113C2×C5×C22⋊C4C2314yes—
114C2×C5×C22⋊C4C2314yes—
115C2×C42×C5—24no—
116C2×C42×C5—24no—
117C2×C42×C5C2314yes—
118C2×C42×C5C2314yes—
119C2×C22⋊Dic5—24no—
120C2×C22⋊Dic5—24no—
121C2×C22⋊Dic5C2314yes—
122C2×C22⋊Dic5C2314yes—
123C4×C22⋊D5—232no—
124C4×C22⋊D5—232no—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—24no—
131C2×#685—24no—
132C2×#685—24no—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×C4⋊Dic5—24no—
142C2×C4⋊Dic5C2314yes—
143C2×#683—24no—
144C2×#683—24no—
145C2×#683—24no—
146C2×#683—24no—
147C2×#683—24no—
148C2×#683—24no—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155C2×C4×Dic5—24no—
156C2×C4×Dic5D418yescomplemented
157C2×C4×Dic5C2314yes—
158C2×C4×Dic5C2314yes—
159C4×D20—232no—
160#4018—232no—
161C5×#95C2314yes—
162C5×#95C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×C4×D4—51no—
168C22×C4×D4—51no—
169C22×C4×D4—51no—
170C22×#117—51no—
171#2392—516no—
172C2×#398—51no—
173C2×#397—51no—
174C2×#396—51no—
175C2×#396—51no—
176C2×#394—51no—
177C2×#394—51no—
178C2×#394—51no—
179C2×#392—51no—
180C2×C4×C4⋊C4—51no—
181C2×C4×C22⋊C4—51no—
182C2×C4×C22⋊C4D511yescharacteristic, complemented
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5#4114yes—
190C24×C5C2412yes—
191C24×C5C2411yescharacteristic
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
198C23×D5—22no—
199C23×D5—22no—
200C23×D5—22no—
201C23×D5—22no—
202C23×D5—22no—
203C23×D5—22no—
204C23×D5C2×D414yes—
205C23×D5#4114yes—
206C23×D5C2412yes—
207C23×D5C2412yes—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
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—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—28no—
223C22×C4×C5—28no—
224C22×C4×C5—28no—
225C22×C4×C5—416no—
226C22×C4×C5C2×D414yes—
227C22×C4×C5C2×D414yes—
228C22×C4×C5#4114yes—
229C22×C4×C5#4114yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C2×C22⋊D5—232no—
237C2×C22⋊D5—232no—
238C2×C22⋊D5—28no—
239C2×C22⋊D5—28no—
240C2×C22⋊D5—28no—
241C2×C22⋊D5—28no—
242C2×C22⋊D5—28no—
243C2×C22⋊D5—28no—
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—22no—
254C22×Dic5—22no—
255C22×Dic5—22no—
256C22×Dic5—22no—
257C22×Dic5—22no—
258C22×Dic5C2×D414yes—
259C22×Dic5C2×D414yes—
260C22×Dic5C2×D414yes—
261C22×Dic5#4114yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C22×Dic5C2412yes—
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C2×D20—232no—
269C2×D20—28no—
270C2×D20—28no—
271C2×D20—28no—
272C2×C4×D5—232no—
273C2×C4×D5—28no—
274C2×C4×D5—28no—
275C2×C4×D5—28no—
276C2×C4×D5—28no—
277C2×C4×D5—28no—
278C2×C4×D5—416no—
279C2×C4×D5C2×D4116yescomplemented
280C5×C22⋊C4—28no—
281C5×C22⋊C4—28no—
282C42×C5—28no—
283C42×C5—28no—
284C22⋊Dic5—28no—
285C22⋊Dic5—28no—
286#685—28no—
287#685—28no—
288#685—28no—
289#685—28no—
290#685—28no—
291#685—28no—
292#685—28no—
293#685—28no—
294C4⋊Dic5—28no—
295#683—28no—
296#683—28no—
297#683—28no—
298#683—28no—
299#683—28no—
300#683—28no—
301C4×Dic5—28no—
302C4×Dic5C2×D4116yescomplemented
303C23×D4—51no—
304C23×D4—51no—
305C23×D4—51no—
306C24×C4—51no—
307C24×C4—51no—
308C24×C4C2×D511yescharacteristic
309C2×C4×D4—58no—
310C2×C4×D4—58no—
311C2×C4×D4—58no—
312C2×C4×D4—108no—
313C2×C4×D4—108no—
314C2×C4×D4—108no—
315C2×#117—58no—
316C2×#117—108no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—51no—
323C22×C4⋊C4—51no—
324C22×C22⋊C4—51no—
325C22×C22⋊C4—51no—
326C22×C22⋊C4—51no—
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⋊C4C2×D511yescharacteristic
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C42—51no—
337C22×C42—51no—
338C22×C42C2×D511yescharacteristic
339C22×C42C2×D511yescharacteristic
340#398—58no—
341#397—58no—
342#396—58no—
343#396—58no—
344#394—58no—
345#394—58no—
346#394—58no—
347#392—58no—
348C4×C4⋊C4—58no—
349C4×C22⋊C4—58no—
350C4×C22⋊C4C2×D518yescomplemented
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95C2×D511yescharacteristic
356C2×#95C2×D511yescharacteristic
357C23×C5—28no—
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5C22×D412yes—
371C23×C5C22×D412yes—
372C23×C5C2×#4114yes—
373C23×C5C2×#4112yes—
374C23×C5C2×#4112yes—
375C23×C5C2×#4112yes—
376C23×C5C2×#4112yes—
377C23×C5C2×#4112yes—
378C23×C5C2511yescharacteristic
379C22×D5—28no—
380C22×D5—28no—
381C22×D5—28no—
382C22×D5—28no—
383C22×D5—28no—
384C22×D5—28no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—22no—
391C22×D5—22no—
392C22×D5—22no—
393C22×D5—22no—
394C22×D5—22no—
395C22×D5—22no—
396C22×D5—22no—
397C22×D5—44no—
398C22×D5—44no—
399C22×D5—44no—
400C22×D5—44no—
401C22×D5—44no—
402C22×D5—44no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5C22×D414yes—
406C22×D5C2×#4114yes—
407C2×C4×C5—28no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
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—44no—
423C2×C4×C5—44no—
424C2×C4×C5—44no—
425C2×C4×C5—44no—
426C2×C4×C5—416no—
427C2×C4×C5#121116yes—
428C2×C4×C5C22×D414yes—
429C2×C4×C5C22×D414yes—
430C2×C4×C5C2×#4114yes—
431C2×C4×C5C2×#4114yes—
432C22⋊D5—232no—
433C22⋊D5—232no—
434C2×Dic5—28no—
435C2×Dic5—28no—
436C2×Dic5—28no—
437C2×Dic5—28no—
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—44no—
453C2×Dic5—44no—
454C2×Dic5C22×D414yes—
455C2×Dic5C22×D414yes—
456C2×Dic5C22×D414yes—
457C2×Dic5C2×#4114yes—
458D20—232no—
459C4×D5—232no—
460C4×D5—416no—
461C25—51no—
462C25—51no—
463C25C22×D511yescharacteristic
464C22×D4—54no—
465C22×D4—54no—
466C22×D4—54no—
467C22×D4—104no—
468C22×D4—104no—
469C22×D4—104no—
470C22×D4—104no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C23×C4—24no—
477C23×C4—24no—
478C23×C4—24no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—58no—
484C23×C4—54no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—54no—
488C23×C4—104no—
489C23×C4—104no—
490C23×C4—104no—
491C23×C4—104no—
492C23×C4—104no—
493C23×C4C22×D511yescharacteristic
494C23×C4C22×D511yescharacteristic
495C23×C4C22×D511yescharacteristic
496C23×C4C22×D511yescharacteristic
497C23×C4C22×D514yes—
498C23×C4C22×D511yescharacteristic
499C23×C4C22×D511yescharacteristic
500C4×D4—1032no—
501C4×D4—1032no—
502C4×D4—1032no—
503#117—1032no—
504C2×C4⋊C4—54no—
505C2×C4⋊C4—54no—
506C2×C4⋊C4—54no—
507C2×C4⋊C4—54no—
508C2×C4⋊C4—54no—
509C2×C4⋊C4—54no—
510C2×C4⋊C4—54no—
511C2×C4⋊C4—104no—
512C2×C4⋊C4—104no—
513C2×C4⋊C4—104no—
514C2×C4⋊C4—104no—
515C2×C4⋊C4—104no—
516C2×C4⋊C4—104no—
517C2×C4⋊C4—104no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—54no—
521C2×C22⋊C4—54no—
522C2×C22⋊C4—54no—
523C2×C22⋊C4—54no—
524C2×C22⋊C4—54no—
525C2×C22⋊C4—54no—
526C2×C22⋊C4—54no—
527C2×C22⋊C4—54no—
528C2×C22⋊C4—54no—
529C2×C22⋊C4—54no—
530C2×C22⋊C4—104no—
531C2×C22⋊C4—104no—
532C2×C22⋊C4—104no—
533C2×C22⋊C4—104no—
534C2×C22⋊C4—104no—
535C2×C22⋊C4—104no—
536C2×C22⋊C4—104no—
537C2×C22⋊C4—104no—
538C2×C22⋊C4—104no—
539C2×C22⋊C4—104no—
540C2×C22⋊C4C22×D514yes—
541C2×C22⋊C4C22×D514yes—
542C2×C42—24no—
543C2×C42—24no—
544C2×C42—58no—
545C2×C42—54no—
546C2×C42—54no—
547C2×C42—104no—
548C2×C42C22×D514yes—
549C2×C42C22×D514yes—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95C22×D514yes—
555#95C22×D514yes—
556C22×C5—24no—
557C22×C5—24no—
558C22×C5—24no—
559C22×C5—416no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5C2×#12114yes—
565C22×C5#52514yes—
566C22×C5#52514yes—
567C22×C5#52514yes—
568C22×C5#52914yes—
569C22×C5#52914yes—
570C22×C5#53214yes—
571C22×C5C23×D411yescharacteristic
572C22×C5C23×D411yescharacteristic
573C22×C5C22×#4111yescharacteristic
574C22×C5C22×#4111yescharacteristic
575C22×C5C22×#4111yescharacteristic
576C22×C5C22×#4111yescharacteristic
577C22×C5C22×#4111yescharacteristic
578C2×D5—24no—
579C2×D5—24no—
580C2×D5—24no—
581C2×D5—24no—
582C2×D5—24no—
583C2×D5—24no—
584C2×D5—416no—
585C2×D5—416no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—42no—
594C4×C5—24no—
595C4×C5—42no—
596C4×C5—42no—
597C4×C5—42no—
598C4×C5—42no—
599C4×C5C2×#12118yes—
600Dic5—24no—
601Dic5—24no—
602Dic5—24no—
603Dic5—24no—
604Dic5—42no—
605Dic5—42no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—54no—
613C24—54no—
614C24—52no—
615C24—52no—
616C24—102no—
617C24—102no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24#70914yes—
629C24C23×D512yes—
630C24C23×D511yescharacteristic
631C2×D4—108no—
632C2×D4—108no—
633C2×D4—1032no—
634C2×D4—108no—
635C2×D4—108no—
636C2×D4—108no—
637C2×D4—108no—
638C2×D4—1032no—
639C2×D4—1032no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—108no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—28no—
658C22×C4—28no—
659C22×C4—28no—
660C22×C4—416no—
661C22×C4—54no—
662C22×C4—54no—
663C22×C4—54no—
664C22×C4—54no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—516no—
670C22×C4—52no—
671C22×C4—52no—
672C22×C4—102no—
673C22×C4—102no—
674C22×C4—102no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—108no—
681C22×C4—108no—
682C22×C4—1032no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—108no—
690C22×C4—108no—
691C22×C4—108no—
692C22×C4—2016no—
693C22×C4#70914yes—
694C22×C4#70914yes—
695C22×C4D4×D514yes—
696C22×C4D4×D514yes—
697C22×C4C23×D512yes—
698C22×C4C23×D512yes—
699C22×C4C23×D512yes—
700C22×C4C23×D512yes—
701C22×C4C23×D512yes—
702C22×C4C23×D512yes—
703C4⋊C4—108no—
704C4⋊C4—108no—
705C4⋊C4—108no—
706C4⋊C4—108no—
707C4⋊C4—108no—
708C4⋊C4—108no—
709C4⋊C4—108no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—108no—
713C22⋊C4—108no—
714C22⋊C4—108no—
715C22⋊C4—108no—
716C22⋊C4—108no—
717C22⋊C4—108no—
718C22⋊C4—108no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C42—28no—
723C42—28no—
724C42—516no—
725C42—108no—
726C2×C5—44no—
727C2×C5#239218yescomplemented
728C2×C5C22×#12111yescharacteristic
729C2×C5C2×#52511yescharacteristic
730C2×C5C2×#52511yescharacteristic
731C2×C5C2×#52511yescharacteristic
732C2×C5C2×#52911yescharacteristic
733C2×C5C2×#52911yescharacteristic
734C2×C5C2×#53211yescharacteristic
735D5—44no—
736D5—44no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—54no—
751C23—54no—
752C23—108no—
753C23—108no—
754C23—108no—
755C23—108no—
756C23—108no—
757C23—108no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—102no—
765C23—102no—
766C23—102no—
767C23—102no—
768C23—102no—
769C23—102no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23C2×#70914yes—
779C23C2×#70912yes—
780C23C2×#70912yes—
781C23C2×#70912yes—
782C23C2×D4×D512yes—
783C23C2×D4×D512yes—
784C23D5×#4112yes—
785C23D5×#4112yes—
786C23C24×D511yescharacteristic
787D4—1032no—
788D4—1032no—
789D4—1032no—
790C2×C4—28no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
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—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—416no—
810C2×C4—54no—
811C2×C4—54no—
812C2×C4—54no—
813C2×C4—54no—
814C2×C4—108no—
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—1032no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—204no—
834C2×C4—204no—
835C2×C4—2016no—
836C2×C4#4030116yes—
837C2×C4C2×#70914yes—
838C2×C4C2×#70914yes—
839C2×C4C2×D4×D514yes—
840C2×C4C2×D4×D514yes—
841C5C2×#239211yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—416no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—104no—
851C22—104no—
852C22—104no—
853C22—104no—
854C22—104no—
855C22—104no—
856C22—2016no—
857C22—2016no—
858C22—202no—
859C22—202no—
860C22—202no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—202no—
866C22#6581314yes—
867C22C2×#403014yes—
868C22#6586214yes—
869C22#6588114yes—
870C22#6588114yes—
871C22#6588114yes—
872C22#6588214yes—
873C22C22×#70911yescharacteristic
874C22C22×#70911yescharacteristic
875C22C22×#70911yescharacteristic
876C22C22×D4×D511yescharacteristic
877C22C22×D4×D511yescharacteristic
878C22C2×D5×#4111yescharacteristic
879C22C2×D5×#4111yescharacteristic
880C4—24no—
881C4—42no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—104no—
886C4—104no—
887C4—104no—
888C4—104no—
889C4—202no—
890C4—202no—
891C4C2×#403018yes—
892C2—44no—
893C2—204no—
894C2—204no—
895C2#1060531218yesdirect product factor
896C2C2×#6581311yescharacteristic
897C2C22×#403011yescharacteristic
898C2C2×#6586211yescharacteristic
899C2C2×#6588111yescharacteristic
900C2C2×#6588111yescharacteristic
901C2C2×#6588111yescharacteristic
902C2C2×#6588211yescharacteristic
subgroupG/H
centerC23×C4C22×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C4×C5×C22⋊C4C2
socleC24×C5C24
prime radicalC2×#65249C2
hypercenterC2×C4×C22⋊C4D5
hypocenterC5C2×#2392
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊D5C2semidirect
2. C22×C4×C22⋊D5C2semidirect
3. C22×C4×D20C2semidirect
4. C22×#4018C2semidirect
5. C2×C4×C5×C22⋊C4C2semidirect
6. C2×#65248C2semidirect
7. C2×#65248C2semidirect
9. C2×#65237C2semidirect
10. C2×C4×#683C2semidirect
11. C2×C4×#685C2semidirect
12. #10605312C2direct (N × H)
13. C2×#64964C2semidirect
14. C2×#64965C2semidirect
15. C2×#64946C2semidirect
16. C2×#64961C2semidirect
31. C2×C4×C22⋊D5C22semidirect
32. C2×C4×C22⋊D5C22semidirect
51. C2×C4×D20C22semidirect
53. C2×#4018C22semidirect
54. C4×C5×C22⋊C4C22semidirect
62. #65248C22semidirect
63. #65248C22semidirect
64. #65237C22semidirect
65. C4×#685C22semidirect
66. C4×#683C22semidirect
67. #64965C22semidirect
68. #64964C22semidirect
69. #64961C22semidirect
70. #64946C22semidirect
108. C22×C4×D5D4semidirect
156. C2×C4×Dic5D4semidirect
182. C2×C4×C22⋊C4D5semidirect
279. C2×C4×D5C2×D4semidirect
302. C4×Dic5C2×D4semidirect
350. C4×C22⋊C4C2×D5semidirect
727. C2×C5#2392semidirect
841. C5C2×#2392semidirect
895. C2#10605312direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D52
C22×C4×D202
C22×#40182
C2×C4×C5×C22⋊C42
C2×#652482
C2×#652492
C2×#652372
C2×C4×#6832
C2×C4×#6852
#106053122
C2×#649642
C2×#649652
C2×#649462
C2×#649612
C2×#23925