Finite Group Databasebeta

← C2×#10608420 #12269374

Subgroups — C2×#10608420 #12269374

Order 1280.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4081C211yesmaximal, characteristic, complemented
2C22×#4025C211yesmaximal, characteristic, complemented
3C2×C5×#392C211yesmaximal, characteristic
4C2×#65511C211yesmaximal, characteristic, complemented
5C2×#65510C211yesmaximal, characteristic, complemented
6C2×#65510C211yesmaximal, characteristic, complemented
7C2×#65510C211yesmaximal, characteristic, complemented
8C2×#65509C211yesmaximal, characteristic, complemented
9C2×#65237C211yesmaximal, characteristic, complemented
10C2×#65234C211yesmaximal, characteristic, complemented
11C2×#65233C211yesmaximal, characteristic, complemented
12C2×#65240C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
14#10608420C2116yesmaximal, direct product factor
15C2×#64950C211yesmaximal, characteristic, complemented
16C2×#64938C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C23×C5×D4C2211yescharacteristic
19C23×C5×D4C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×C22⋊Dic5C2211yescharacteristic
35C2×#4081—28no—
36C2×#4081C2218yescomplemented
37C22×C4⋊Dic5C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C22×C4×Dic5C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C2×#4025—28no—
49C2×#4025C2218yescomplemented
50C5×#392C2218yes—
51C2×C5×#95C2211yescharacteristic
52#65511C2218yescomplemented
53#65510C2218yescomplemented
54#65510C2218yescomplemented
55#65510C2218yescomplemented
56#65509C2218yescomplemented
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#65240C2218yescomplemented
63#65237C2218yescomplemented
64#65234C2218yescomplemented
65#65233C2218yescomplemented
66C22⋊C4×Dic5C2218yescomplemented
67#64950C2218yescomplemented
68#64938C2218yescomplemented
69C2×#2554—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C25×C5C2311yescharacteristic
72C25×C5C2311yescharacteristic
73C22×C5×D4—24no—
74C22×C5×D4—24no—
75C22×C5×D4—24no—
76C22×C5×D4—24no—
77C22×C5×D4—24no—
78C22×C5×D4—42no—
79C22×C5×D4—42no—
80C22×C5×D4—42no—
81C22×C5×D4—42no—
82C22×C5×D4C2314yes—
83C22×C5×D4C2314yes—
84C22×C5×D4C2314yes—
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×Dic5—24no—
90C23×Dic5—24no—
91C23×Dic5—42no—
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2314yes—
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C2×C5×C22⋊C4—24no—
102C2×C5×C22⋊C4—24no—
103C2×C5×C22⋊C4—24no—
104C2×C5×C22⋊C4C2314yes—
105C2×C5×C22⋊C4C2314yes—
106C2×C5×C22⋊C4C2314yes—
107C2×C22⋊Dic5—24no—
108C2×C22⋊Dic5—24no—
109C2×C22⋊Dic5—24no—
110C2×C22⋊Dic5—24no—
111C2×C22⋊Dic5—24no—
112C2×C22⋊Dic5—24no—
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5—24no—
115C2×C22⋊Dic5—42no—
116C2×C22⋊Dic5—42no—
117C2×C22⋊Dic5—42no—
118C2×C22⋊Dic5C2314yes—
119C2×C22⋊Dic5C2314yes—
120C2×C22⋊Dic5C2314yes—
121C2×C22⋊Dic5C2314yes—
122C2×C22⋊Dic5C2314yes—
123C2×C22⋊Dic5C2314yes—
124C2×C22⋊Dic5C2314yes—
125C2×C22⋊Dic5C2314yes—
126C2×C22⋊Dic5C2314yes—
127C2×C22⋊Dic5C2314yes—
128C2×C22⋊Dic5C2314yes—
129#4081—232no—
130C2×C4⋊Dic5—24no—
131C2×C4⋊Dic5—42no—
132C2×C4⋊Dic5—42no—
133C2×C4⋊Dic5C2314yes—
134C2×C4⋊Dic5C2314yes—
135C2×C4⋊Dic5C2314yes—
136C2×#683—24no—
137C2×#683—24no—
138C2×#683—24no—
139C2×#683D418yescomplemented
140C2×#683C2314yes—
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×C4×Dic5—24no—
145C2×C4×Dic5—24no—
146C2×C4×Dic5—42no—
147C2×C4×Dic5—42no—
148C2×C4×Dic5C2314yes—
149C2×C4×Dic5C2314yes—
150C2×C4×Dic5C2314yes—
151C2×C4×Dic5C2314yes—
152#4025—232no—
153C5×#95C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#126—51no—
160C22×#123—51no—
161#2554—516no—
162C2×#398—51no—
163C2×#396—51no—
164C2×#394—51no—
165C2×#392D511yescharacteristic
166C2×#390—51no—
167C2×#390—51no—
168C2×#390—51no—
169C2×#388—51no—
170C2×#388—51no—
171C2×#388—51no—
172C2×#386—51no—
173C2×C4×C4⋊C4—51no—
174C2×C4×C22⋊C4—51no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5—22no—
182C24×C5—22no—
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×C5—22no—
195C24×C5#4114yes—
196C24×C5C2412yes—
197C24×C5C2412yes—
198C24×C5C2412yes—
199C24×C5C2411yescharacteristic
200C2×C5×D4—28no—
201C2×C5×D4—28no—
202C2×C5×D4—28no—
203C2×C5×D4—28no—
204C2×C5×D4—28no—
205C2×C5×D4—44no—
206C2×C5×D4—44no—
207C2×C5×D4—44no—
208C2×C5×D4—44no—
209C2×C5×D4—416no—
210C2×C5×D4—416no—
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—22no—
220C22×C4×C5—22no—
221C22×C4×C5C2×D414yes—
222C22×C4×C5#4114yes—
223C22×C4×C5#4114yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—28no—
242C22×Dic5—22no—
243C22×Dic5—22no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5—28no—
251C22×Dic5—44no—
252C22×Dic5—416no—
253C22×Dic5C2×D414yes—
254C22×Dic5C2×D414yes—
255C22×Dic5#4114yes—
256C22×Dic5C2412yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C5×C22⋊C4—28no—
265C5×C22⋊C4—28no—
266C5×C22⋊C4—28no—
267C22⋊Dic5—28no—
268C22⋊Dic5—28no—
269C22⋊Dic5—28no—
270C22⋊Dic5—28no—
271C22⋊Dic5—28no—
272C22⋊Dic5—28no—
273C22⋊Dic5—28no—
274C22⋊Dic5—28no—
275C22⋊Dic5—44no—
276C22⋊Dic5—44no—
277C22⋊Dic5—44no—
278C4⋊Dic5—28no—
279C4⋊Dic5—44no—
280C4⋊Dic5—44no—
281#683—28no—
282#683—28no—
283#683—28no—
284#683C2×D4116yescomplemented
285C4×Dic5—28no—
286C4×Dic5—28no—
287C4×Dic5—44no—
288C4×Dic5—44no—
289C23×D4C2×D511yescharacteristic
290C23×D4C2×D511yescharacteristic
291C23×D4C2×D511yescharacteristic
292C24×C4—51no—
293C2×#126—58no—
294C2×#126—108no—
295C2×#123—58no—
296C2×#123—108no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C22⋊C4—51no—
305C22×C22⋊C4—51no—
306C22×C22⋊C4—51no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4—51no—
310C22×C22⋊C4—51no—
311C22×C22⋊C4—51no—
312C22×C22⋊C4—51no—
313C22×C22⋊C4—51no—
314C22×C22⋊C4—51no—
315C22×C22⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42—51no—
320C22×C42—51no—
321C22×C42—51no—
322#398—58no—
323#396—58no—
324#394—58no—
325#392C2×D518yes—
326#390—58no—
327#390—58no—
328#390—58no—
329#388—58no—
330#388—58no—
331#388—58no—
332#386—58no—
333C4×C4⋊C4—58no—
334C4×C22⋊C4—58no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95C2×D511yescharacteristic
341C23×C5—28no—
342C23×C5—28no—
343C23×C5—28no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—44no—
365C23×C5—44no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5—44no—
371C23×C5—44no—
372C23×C5—44no—
373C23×C5—44no—
374C23×C5—44no—
375C23×C5—44no—
376C23×C5—44no—
377C23×C5—44no—
378C23×C5—44no—
379C23×C5—44no—
380C23×C5—44no—
381C23×C5—44no—
382C23×C5C22×D412yes—
383C23×C5C2×#4114yes—
384C23×C5C2×#4112yes—
385C23×C5C2×#4112yes—
386C23×C5C2×#4112yes—
387C23×C5C2×#4112yes—
388C23×C5H(5,𝔽2)12yes—
389C23×C5H(5,𝔽2)12yes—
390C23×C5C2511yescharacteristic
391C5×D4—416no—
392C5×D4—416no—
393C5×D4—416no—
394C2×C4×C5—28no—
395C2×C4×C5—28no—
396C2×C4×C5—28no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—44no—
407C2×C4×C5C22×D414yes—
408C2×C4×C5C2×#4114yes—
409C2×C4×C5C2×#4114yes—
410C2×Dic5—28no—
411C2×Dic5—28no—
412C2×Dic5—28no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
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—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—22no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—416no—
435C2×Dic5—44no—
436C2×Dic5—44no—
437C2×Dic5—44no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5C22×D414yes—
441C2×Dic5C22×D414yes—
442C2×Dic5C2×#4114yes—
443C25C22×D511yescharacteristic
444C25C22×D511yescharacteristic
445C25C22×D511yescharacteristic
446C22×D4—24no—
447C22×D4—24no—
448C22×D4—24no—
449C22×D4—24no—
450C22×D4—24no—
451C22×D4—42no—
452C22×D4—42no—
453C22×D4—42no—
454C22×D4—42no—
455C22×D4C22×D514yes—
456C22×D4C22×D514yes—
457C22×D4C22×D514yes—
458C23×C4—51no—
459C23×C4—51no—
460C23×C4—51no—
461C23×C4—51no—
462C23×C4—51no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—54no—
467C23×C4—104no—
468C23×C4—104no—
469C23×C4—202no—
470C23×C4C22×D511yescharacteristic
471C23×C4C22×D511yescharacteristic
472C23×C4C22×D511yescharacteristic
473C23×C4C22×D511yescharacteristic
474#126—1032no—
475#123—1032no—
476C2×C4⋊C4—58no—
477C2×C4⋊C4—54no—
478C2×C4⋊C4—54no—
479C2×C4⋊C4—54no—
480C2×C4⋊C4—54no—
481C2×C4⋊C4—54no—
482C2×C4⋊C4—54no—
483C2×C4⋊C4—54no—
484C2×C4⋊C4—104no—
485C2×C4⋊C4—104no—
486C2×C4⋊C4—104no—
487C2×C4⋊C4—104no—
488C2×C4⋊C4—202no—
489C2×C4⋊C4—202no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—54no—
494C2×C22⋊C4—54no—
495C2×C22⋊C4—54no—
496C2×C22⋊C4—54no—
497C2×C22⋊C4—54no—
498C2×C22⋊C4—54no—
499C2×C22⋊C4—54no—
500C2×C22⋊C4—54no—
501C2×C22⋊C4—54no—
502C2×C22⋊C4—54no—
503C2×C22⋊C4—54no—
504C2×C22⋊C4—104no—
505C2×C22⋊C4—104no—
506C2×C22⋊C4—104no—
507C2×C22⋊C4—104no—
508C2×C22⋊C4—104no—
509C2×C22⋊C4—104no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—202no—
513C2×C22⋊C4—202no—
514C2×C22⋊C4—202no—
515C2×C22⋊C4C22×D514yes—
516C2×C22⋊C4C22×D514yes—
517C2×C22⋊C4C22×D514yes—
518C2×C42—54no—
519C2×C42—54no—
520C2×C42—54no—
521C2×C42—54no—
522C2×C42—104no—
523C2×C42—104no—
524C2×C42—202no—
525C2×C42—202no—
526#95—54no—
527#95—54no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95C22×D514yes—
532C22×C5—24no—
533C22×C5—24no—
534C22×C5—24no—
535C22×C5—42no—
536C22×C5—42no—
537C22×C5—42no—
538C22×C5—42no—
539C22×C5—416no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—42no—
552C22×C5—42no—
553C22×C5—42no—
554C22×C5—88no—
555C22×C5—88no—
556C22×C5#52914yes—
557C22×C5#53214yes—
558C22×C5#53814yes—
559C22×C5#54614yes—
560C22×C5#55014yes—
561C22×C5#55114yes—
562C22×C5#55314yes—
563C22×C5C23×D411yescharacteristic
564C22×C5C22×#4111yescharacteristic
565C22×C5C22×#4111yescharacteristic
566C22×C5C22×#4111yescharacteristic
567C22×C5C22×#4111yescharacteristic
568C22×C5C2×H(5,𝔽2)11yescharacteristic
569C22×C5C2×H(5,𝔽2)11yescharacteristic
570C4×C5—24no—
571C4×C5—24no—
572C4×C5—24no—
573C4×C5—42no—
574Dic5—24no—
575Dic5—24no—
576Dic5—24no—
577Dic5—42no—
578Dic5—42no—
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24#71114yes—
603C24C23×D512yes—
604C24C23×D512yes—
605C24C23×D512yes—
606C24C23×D511yescharacteristic
607C2×D4—28no—
608C2×D4—28no—
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—416no—
617C2×D4—416no—
618C2×D4—416no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—54no—
629C22×C4—54no—
630C22×C4—54no—
631C22×C4—52no—
632C22×C4—52no—
633C22×C4—52no—
634C22×C4—52no—
635C22×C4—52no—
636C22×C4—52no—
637C22×C4—52no—
638C22×C4—52no—
639C22×C4—108no—
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—102no—
650C22×C4—102no—
651C22×C4—108no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—102no—
659C22×C4—102no—
660C22×C4—102no—
661C22×C4—102no—
662C22×C4—204no—
663C22×C4—2016no—
664C22×C4D4×D514yes—
665C22×C4#71114yes—
666C22×C4#71114yes—
667C22×C4C23×D512yes—
668C22×C4C23×D512yes—
669C22×C4C23×D512yes—
670C22×C4C23×D512yes—
671C4⋊C4—516no—
672C4⋊C4—108no—
673C4⋊C4—108no—
674C4⋊C4—108no—
675C4⋊C4—108no—
676C4⋊C4—204no—
677C4⋊C4—204no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—108no—
682C22⋊C4—108no—
683C22⋊C4—108no—
684C22⋊C4—108no—
685C22⋊C4—108no—
686C22⋊C4—108no—
687C22⋊C4—108no—
688C22⋊C4—108no—
689C22⋊C4—204no—
690C22⋊C4—204no—
691C22⋊C4—204no—
692C42—108no—
693C42—108no—
694C42—204no—
695C42—204no—
696C2×C5—44no—
697C2×C5—82no—
698C2×C5—82no—
699C2×C5#255418yescomplemented
700C2×C5C2×#52911yescharacteristic
701C2×C5C2×#53211yescharacteristic
702C2×C5C2×#53811yescharacteristic
703C2×C5C2×#54611yescharacteristic
704C2×C5C2×#55011yescharacteristic
705C2×C5C2×#55111yescharacteristic
706C2×C5C2×#55311yescharacteristic
707C23—28no—
708C23—28no—
709C23—28no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23C2×D4×D512yes—
749C23C2×#71114yes—
750C23C2×#71112yes—
751C23C2×#71112yes—
752C23C2×#71112yes—
753C23#414412yes—
754C23#414412yes—
755C23D5×#4112yes—
756C23C24×D511yescharacteristic
757D4—416no—
758D4—416no—
759D4—416no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—44no—
773C2×C4—54no—
774C2×C4—54no—
775C2×C4—54no—
776C2×C4—108no—
777C2×C4—108no—
778C2×C4—108no—
779C2×C4—102no—
780C2×C4—102no—
781C2×C4—102no—
782C2×C4—102no—
783C2×C4—102no—
784C2×C4—102no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—102no—
791C2×C4—102no—
792C2×C4—102no—
793C2×C4—102no—
794C2×C4—102no—
795C2×C4—102no—
796C2×C4—102no—
797C2×C4—102no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—2016no—
801C2×C4—204no—
802C2×C4—204no—
803C2×C4—204no—
804C2×C4—204no—
805C2×C4—204no—
806C2×C4C2×D4×D514yes—
807C2×C4C2×#71114yes—
808C2×C4C2×#71114yes—
809C5C2×#255411yescharacteristic, complemented, Sylow
810C22—24no—
811C22—24no—
812C22—24no—
813C22—416no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—88no—
833C22—88no—
834C22#6592114yes—
835C22#6592514yes—
836C22#6592714yes—
837C22#6593314yes—
838C22#6593414yes—
839C22#6594814yes—
840C22#6605014yes—
841C22C22×D4×D511yescharacteristic
842C22C22×#71111yescharacteristic
843C22C22×#71111yescharacteristic
844C22C22×#71111yescharacteristic
845C22C2×#414411yescharacteristic
846C22C2×#414411yescharacteristic
847C22C2×D5×#4111yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—104no—
853C4—104no—
854C4—104no—
855C4—202no—
856C4—202no—
857C4—202no—
858C4—202no—
859C4—202no—
860C2—44no—
861C2—82no—
862C2—82no—
863C2#1060842018yesdirect product factor
864C2C2×#6592711yescharacteristic
865C2C2×#6592111yescharacteristic
866C2C2×#6592511yescharacteristic
867C2C2×#6593411yescharacteristic
868C2C2×#6593311yescharacteristic
869C2C2×#6594811yescharacteristic
870C2C2×#6605011yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
Fitting, prime radicalC2×C5×#392C2
socleC24×C5C24
hypercenterC2×#392D5
hypocenterC5C2×#2554
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#4081C2semidirect
2. C22×#4025C2semidirect
4. C2×#65511C2semidirect
5. C2×#65510C2semidirect
6. C2×#65510C2semidirect
7. C2×#65510C2semidirect
8. C2×#65509C2semidirect
9. C2×#65237C2semidirect
10. C2×#65234C2semidirect
11. C2×#65233C2semidirect
12. C2×#65240C2semidirect
13. C2×C22⋊C4×Dic5C2semidirect
14. #10608420C2direct (N × H)
15. C2×#64950C2semidirect
16. C2×#64938C2semidirect
36. C2×#4081C22semidirect
49. C2×#4025C22semidirect
52. #65511C22semidirect
53. #65510C22semidirect
54. #65510C22semidirect
55. #65510C22semidirect
56. #65509C22semidirect
62. #65240C22semidirect
63. #65237C22semidirect
64. #65234C22semidirect
65. #65233C22semidirect
66. C22⋊C4×Dic5C22semidirect
67. #64950C22semidirect
68. #64938C22semidirect
139. C2×#683D4semidirect
284. #683C2×D4semidirect
699. C2×C5#2554semidirect
809. C5C2×#2554semidirect
863. C2#10608420direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40812
C22×#40252
C2×C5×#3922
C2×#655112
C2×#655102
C2×#655092
C2×#652372
C2×#652342
C2×#652332
C2×#652402
C2×C22⋊C4×Dic52
#106084202
C2×#649502
C2×#649382
C2×#25545