Finite Group Databasebeta

← C2×D5⋊#834 #14411893

Subgroups — C2×D5⋊#834 #14411893

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D4×D5C211yesmaximal, characteristic
2C22×#6763C212yesmaximal, complemented
3C2×#91240C212yesmaximal, complemented
4D5⋊#834C218yesmaximal, direct product factor
5C2×#91228C212yesmaximal, complemented
6C2×D5⋊#99—31nomaximal, Hall
7C24×C3×D5C411yescharacteristic, complemented
8C24×C3×D5C2211yescharacteristic
9C23×ΓL(1,𝔽16)—22no—
10C22×C3×C5×D4C411yescharacteristic, complemented
11C22×C3×C22⋊D5C411yescharacteristic, complemented
12C22×C3×C22⋊D5C2211yescharacteristic
13C2×C3×D4×D5—22no—
14C2×C3×D4×D5—22no—
15C2×C3×D4×D5—24no—
16C2×C3×D4×D5C414yescomplemented
17C2×C3×D4×D5C2214yes—
18C22×C3×D20C2211yescharacteristic
19C22×C3×C4×D5C411yescharacteristic, complemented
20C2×#6763—24no—
21C2×#6763—22no—
22C2×#6763C2214yescomplemented
23C2×#6763C2218yescomplemented
24#91240C2218yescomplemented
25#91228C2218yescomplemented
26C22×#834—51nomaximal, Hall
27C22×D4×D5D311yescharacteristic
28C22×C22⋊AGL(1,𝔽5)—32no—
29C2×#4011—32no—
30D5⋊#99—38no—
31C2×#3999—32no—
32C24×C3×C5C2×C411yescharacteristic
33C24×C3×C5C2×C411yescharacteristic, complemented
34C23×C3×D5—22no—
35C23×C3×D5—21no—
36C23×C3×D5—21no—
37C23×C3×D5—44no—
38C23×C3×D5—44no—
39C23×C3×D5C2×C411yescharacteristic
40C23×C3×D5C2×C412yes—
41C23×C3×D5C2×C414yescomplemented
42C23×C3×D5C2×C411yescharacteristic, complemented
43C23×C3×D5D412yes—
44C23×C3×D5D414yes—
45C23×C3×D5D412yes—
46C23×C3×D5C2311yescharacteristic
47C23×C3×D5C2312yes—
48C22×ΓL(1,𝔽16)—24no—
49C22×ΓL(1,𝔽16)—28no—
50C22×ΓL(1,𝔽16)—48no—
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4C2×C414yescomplemented
54C22×C3×C4×C5C2×C411yescharacteristic, complemented
55C2×C3×C22⋊D5—22no—
56C2×C3×C22⋊D5—22no—
57C2×C3×C22⋊D5—22no—
58C2×C3×C22⋊D5—22no—
59C2×C3×C22⋊D5C2×C412yescomplemented
60C2×C3×C22⋊D5C2×C414yescomplemented
61C2×C3×C22⋊D5C2312yes—
62C22×C3×Dic5C2×C411yescharacteristic, complemented
63C3×D4×D5—28no—
64C3×D4×D5—28no—
65C3×D4×D5—28no—
66C3×D4×D5—28no—
67C2×C3×D20—22no—
68C2×C3×D20—22no—
69C2×C3×D20C2×C412yescomplemented
70C2×C3×D20C2312yes—
71C2×C3×C4×D5—21no—
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—21no—
74C2×C3×C4×D5C2×C414yescomplemented
75#6763—24no—
76#6763—28no—
77#6763C2318yescomplemented
78C23×C3×D4—51no—
79C22×#217—52no—
80C2×#834—52no—
81C2×#834—52no—
82C2×#834—58no—
83C24×D5Dic311yescharacteristic, complemented
84C24×D5C2×D311yescharacteristic
85C23×AGL(1,𝔽5)—62no—
86C22×C5×D4Dic311yescharacteristic, complemented
87C22×C22⋊D5Dic311yescharacteristic, complemented
88C22×C22⋊D5C2×D311yescharacteristic
89C2×D4×D5—22no—
90C2×D4×D5—22no—
91C2×D4×D5—24no—
92C2×D4×D5Dic314yescomplemented
93C2×D4×D5C2×D314yes—
94C22×D20C2×D311yescharacteristic
95C22×C4×D5Dic311yescharacteristic, complemented
96C2×C22⋊AGL(1,𝔽5)—34no—
97C2×C22⋊AGL(1,𝔽5)—38no—
98C2×C22⋊AGL(1,𝔽5)—64no—
99C2×C22⋊AGL(1,𝔽5)—62no—
100#4011—38no—
101#3999—38no—
102C22×#99—151noSylow
103C23×C3×C5—21no—
104C23×C3×C5—21no—
105C23×C3×C5—42no—
106C23×C3×C5—42no—
107C23×C3×C5C22⋊C412yes—
108C23×C3×C5C22⋊C412yes—
109C23×C3×C5C22×C411yescharacteristic
110C23×C3×C5C22×C412yes—
111C23×C3×C5C22×C412yescomplemented
112C22×C3×D5—28no—
113C22×C3×D5—24no—
114C22×C3×D5—21no—
115C22×C3×D5—21no—
116C22×C3×D5—24no—
117C22×C3×D5—24no—
118C22×C3×D5—44no—
119C22×C3×D5—48no—
120C22×C3×D5—44no—
121C22×C3×D5—44no—
122C22×C3×D5—42no—
123C22×C3×D5—44no—
124C22×C3×D5—48no—
125C22×C3×D5—48no—
126C22×C3×D5—44no—
127C22×C3×D5—42no—
128C22×C3×D5C22⋊C411yescharacteristic
129C22×C3×D5C22⋊C412yes—
130C22×C3×D5C22⋊C414yes—
131C22×C3×D5C22⋊C414yes—
132C22×C3×D5C22⋊C411yescharacteristic
133C22×C3×D5C22×C412yes—
134C22×C3×D5C22×C411yescharacteristic
135C22×C3×D5C22×C412yescomplemented
136C22×C3×D5C2×D412yes—
137C22×C3×D5C2×D414yes—
138C22×C3×D5C2×D412yes—
139C22×C3×D5C2×D414yes—
140C22×C3×D5C2411yescharacteristic
141C2×ΓL(1,𝔽16)—28no—
142C2×ΓL(1,𝔽16)—48no—
143C2×ΓL(1,𝔽16)—416no—
144C3×C5×D4—28no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5C22×C412yescomplemented
148C3×C22⋊D5—28no—
149C3×C22⋊D5—24no—
150C3×C22⋊D5—24no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5C22×C412yescomplemented
154C3×D20—24no—
155C3×D20—24no—
156C3×C4×D5—24no—
157C3×C4×D5—24no—
158C25×C3—51no—
159C25×C3—51no—
160C22×C3×D4—51no—
161C22×C3×D4—51no—
162C22×C3×D4—54no—
163C22×C3×D4—54no—
164C22×C3×D4—51no—
165C22×C3×D4—102no—
166C22×C3×D4—102no—
167C22×C3×D4—104no—
168C22×C3×D4AGL(1,𝔽5)11yescharacteristic, complemented
169C23×C3×C4—51no—
170C23×Dic3—102no—
171C2×#217—54no—
172C2×#217—58no—
173C2×#217—104no—
174C2×#217—102no—
175#834—58no—
176#834—58no—
177C24×C5C2×Dic311yescharacteristic
178C24×C5C2×Dic311yescharacteristic, complemented
179C23×D5—22no—
180C23×D5—21no—
181C23×D5—21no—
182C23×D5—44no—
183C23×D5—44no—
184C23×D5C2×Dic311yescharacteristic
185C23×D5C2×Dic312yes—
186C23×D5C2×Dic314yescomplemented
187C23×D5C2×Dic311yescharacteristic, complemented
188C23×D5#6712yes—
189C23×D5#6714yes—
190C23×D5#6712yes—
191C23×D5C22×D311yescharacteristic
192C23×D5C22×D312yes—
193C22×AGL(1,𝔽5)—64no—
194C22×AGL(1,𝔽5)—68no—
195C22×AGL(1,𝔽5)—128no—
196C2×C5×D4—22no—
197C2×C5×D4—22no—
198C2×C5×D4C2×Dic314yescomplemented
199C22×C4×C5C2×Dic311yescharacteristic, complemented
200C2×C22⋊D5—22no—
201C2×C22⋊D5—22no—
202C2×C22⋊D5—22no—
203C2×C22⋊D5—22no—
204C2×C22⋊D5C2×Dic312yescomplemented
205C2×C22⋊D5C2×Dic314yescomplemented
206C2×C22⋊D5C22×D312yes—
207C22×Dic5C2×Dic311yescharacteristic, complemented
208D4×D5—28no—
209D4×D5—28no—
210D4×D5—28no—
211D4×D5—28no—
212C2×D20—22no—
213C2×D20—22no—
214C2×D20C2×Dic312yescomplemented
215C2×D20C22×D312yes—
216C2×C4×D5—22no—
217C2×C4×D5—21no—
218C2×C4×D5—21no—
219C2×C4×D5C2×Dic314yescomplemented
220C22⋊AGL(1,𝔽5)—38no—
221C22⋊AGL(1,𝔽5)—64no—
222C22⋊AGL(1,𝔽5)—68no—
223C23×D4—51no—
224C22×C22⋊C4—152no—
225C2×#99—152no—
226C2×#99—152no—
227C2×#99—158no—
228C22×C3×C5—22no—
229C22×C3×C5—24no—
230C22×C3×C5—22no—
231C22×C3×C5—42no—
232C22×C3×C5—42no—
233C22×C3×C5—42no—
234C22×C3×C5—42no—
235C22×C3×C5—42no—
236C22×C3×C5C2×C22⋊C411yescharacteristic
237C22×C3×C5C2×C22⋊C414yes—
238C22×C3×C5C2×C22⋊C411yescharacteristic
239C22×C3×C5C23×C411yescharacteristic
240C2×C3×D5—24no—
241C2×C3×D5—22no—
242C2×C3×D5—28no—
243C2×C3×D5—24no—
244C2×C3×D5—24no—
245C2×C3×D5—28no—
246C2×C3×D5—22no—
247C2×C3×D5—44no—
248C2×C3×D5—41no—
249C2×C3×D5—44no—
250C2×C3×D5—42no—
251C2×C3×D5—41no—
252C2×C3×D5—48no—
253C2×C3×D5—42no—
254C2×C3×D5—42no—
255C2×C3×D5—48no—
256C2×C3×D5—42no—
257C2×C3×D5#9914yescomplemented
258C2×C3×D5C2×C22⋊C412yes—
259C2×C3×D5C2×C22⋊C412yes—
260C2×C3×D5C2×C22⋊C412yes—
261C2×C3×D5C22×D412yes—
262ΓL(1,𝔽16)—48no—
263C3×C4×C5—22no—
264C3×Dic5—22no—
265C24×C3—52no—
266C24×C3—51no—
267C24×C3—54no—
268C24×C3—52no—
269C24×C3—52no—
270C24×C3—51no—
271C24×C3—52no—
272C24×C3—51no—
273C24×C3—54no—
274C24×C3—101no—
275C24×C3—102no—
276C24×C3—101no—
277C24×C3—204no—
278C24×C3—204no—
279C24×C3C2×AGL(1,𝔽5)11yescharacteristic
280C24×C3C2×AGL(1,𝔽5)11yescharacteristic, complemented
281C2×C3×D4—22no—
282C2×C3×D4—22no—
283C2×C3×D4—54no—
284C2×C3×D4—52no—
285C2×C3×D4—52no—
286C2×C3×D4—52no—
287C2×C3×D4—52no—
288C2×C3×D4—102no—
289C2×C3×D4—102no—
290C2×C3×D4—108no—
291C2×C3×D4—108no—
292C2×C3×D4—108no—
293C2×C3×D4—108no—
294C2×C3×D4—102no—
295C2×C3×D4—102no—
296C2×C3×D4—102no—
297C2×C3×D4—102no—
298C2×C3×D4C2×AGL(1,𝔽5)14yescomplemented
299C22×C3×C4—51no—
300C22×C3×C4—54no—
301C22×C3×C4—101no—
302C22×C3×C4—102no—
303C22×C3×C4—101no—
304C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
305C22×Dic3—108no—
306C22×Dic3—104no—
307C22×Dic3—208no—
308#217—58no—
309#217—108no—
310#217—104no—
311C23×C5—21no—
312C23×C5—21no—
313C23×C5—42no—
314C23×C5—42no—
315C23×C5#21712yes—
316C23×C5#21712yes—
317C23×C5C22×Dic311yescharacteristic
318C23×C5C22×Dic312yes—
319C23×C5C22×Dic312yescomplemented
320C22×D5—28no—
321C22×D5—24no—
322C22×D5—21no—
323C22×D5—21no—
324C22×D5—24no—
325C22×D5—24no—
326C22×D5—44no—
327C22×D5—48no—
328C22×D5—44no—
329C22×D5—44no—
330C22×D5—42no—
331C22×D5—44no—
332C22×D5—48no—
333C22×D5—48no—
334C22×D5—44no—
335C22×D5—42no—
336C22×D5#21712yes—
337C22×D5#21711yescharacteristic
338C22×D5#21714yes—
339C22×D5#21714yes—
340C22×D5#21711yescharacteristic
341C22×D5C22×Dic312yes—
342C22×D5C22×Dic311yescharacteristic
343C22×D5C22×Dic312yescomplemented
344C22×D5C2×#6712yes—
345C22×D5C2×#6714yes—
346C22×D5C2×#6712yes—
347C22×D5C2×#6714yes—
348C22×D5C23×D311yescharacteristic
349C2×AGL(1,𝔽5)—68no—
350C2×AGL(1,𝔽5)—128no—
351C2×AGL(1,𝔽5)—1216no—
352C5×D4—28no—
353C2×C4×C5—21no—
354C2×C4×C5—21no—
355C2×C4×C5C22×Dic312yescomplemented
356C22⋊D5—28no—
357C22⋊D5—24no—
358C22⋊D5—24no—
359C2×Dic5—21no—
360C2×Dic5—21no—
361C2×Dic5C22×Dic312yescomplemented
362D20—24no—
363D20—24no—
364C4×D5—24no—
365C4×D5—24no—
366C25—51no—
367C25—51no—
368C22×D4—51no—
369C22×D4—51no—
370C22×D4—54no—
371C22×D4—54no—
372C22×D4—51no—
373C22×D4—102no—
374C22×D4—104no—
375C22×D4—102no—
376C22×D4ΓL(1,𝔽16)11yescharacteristic, complemented
377C23×C4—51no—
378C23×C4—302no—
379C2×C22⋊C4—154no—
380C2×C22⋊C4—158no—
381C2×C22⋊C4—304no—
382C2×C22⋊C4—302no—
383#99—158no—
384#99—158no—
385C2×C3×C5—21no—
386C2×C3×C5—21no—
387C2×C3×C5—24no—
388C2×C3×C5—42no—
389C2×C3×C5C2×#9912yescomplemented
390C2×C3×C5C22×C22⋊C411yescharacteristic
391C3×D5—22no—
392C3×D5—22no—
393C3×D5—22no—
394C3×D5—42no—
395C3×D5C2×#9914yescomplemented
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—51no—
401C23×C3—52no—
402C23×C3—51no—
403C23×C3—54no—
404C23×C3—54no—
405C23×C3—52no—
406C23×C3—52no—
407C23×C3—54no—
408C23×C3—54no—
409C23×C3—52no—
410C23×C3—51no—
411C23×C3—51no—
412C23×C3—52no—
413C23×C3—108no—
414C23×C3—104no—
415C23×C3—104no—
416C23×C3—104no—
417C23×C3—101no—
418C23×C3—101no—
419C23×C3—202no—
420C23×C3—204no—
421C23×C3—202no—
422C23×C3—204no—
423C23×C3—208no—
424C23×C3—204no—
425C23×C3—204no—
426C23×C3—208no—
427C23×C3—208no—
428C23×C3—204no—
429C23×C3C22⋊AGL(1,𝔽5)12yes—
430C23×C3C22⋊AGL(1,𝔽5)12yes—
431C23×C3C22×AGL(1,𝔽5)11yescharacteristic
432C23×C3C22×AGL(1,𝔽5)12yes—
433C23×C3C22×AGL(1,𝔽5)12yescomplemented
434C3×D4—28no—
435C3×D4—104no—
436C3×D4—104no—
437C3×D4—104no—
438C3×D4—104no—
439C3×D4—108no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—52no—
443C2×C3×C4—104no—
444C2×C3×C4—104no—
445C2×C3×C4—101no—
446C2×C3×C4—101no—
447C2×C3×C4C22×AGL(1,𝔽5)12yescomplemented
448C2×Dic3—108no—
449C2×Dic3—2016no—
450C2×Dic3—208no—
451C22×C5—22no—
452C22×C5—24no—
453C22×C5—22no—
454C22×C5—42no—
455C22×C5—42no—
456C22×C5—42no—
457C22×C5—42no—
458C22×C5—42no—
459C22×C5C2×#21711yescharacteristic
460C22×C5C2×#21714yes—
461C22×C5C2×#21711yescharacteristic
462C22×C5C23×Dic311yescharacteristic
463C2×D5—24no—
464C2×D5—22no—
465C2×D5—28no—
466C2×D5—24no—
467C2×D5—24no—
468C2×D5—28no—
469C2×D5—22no—
470C2×D5—44no—
471C2×D5—41no—
472C2×D5—44no—
473C2×D5—42no—
474C2×D5—41no—
475C2×D5—48no—
476C2×D5—42no—
477C2×D5—42no—
478C2×D5—48no—
479C2×D5—42no—
480C2×D5#83414yescomplemented
481C2×D5C2×#21712yes—
482C2×D5C2×#21712yes—
483C2×D5C2×#21712yes—
484C2×D5C22×#6712yes—
485AGL(1,𝔽5)—128no—
486C4×C5—22no—
487Dic5—22no—
488C24—52no—
489C24—51no—
490C24—54no—
491C24—52no—
492C24—52no—
493C24—51no—
494C24—52no—
495C24—51no—
496C24—54no—
497C24—102no—
498C24—101no—
499C24—101no—
500C24—204no—
501C24—204no—
502C24C2×ΓL(1,𝔽16)11yescharacteristic
503C24C2×ΓL(1,𝔽16)11yescharacteristic, complemented
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—54no—
507C2×D4—52no—
508C2×D4—52no—
509C2×D4—52no—
510C2×D4—52no—
511C2×D4—102no—
512C2×D4—102no—
513C2×D4—108no—
514C2×D4—108no—
515C2×D4—108no—
516C2×D4—108no—
517C2×D4—102no—
518C2×D4—102no—
519C2×D4—102no—
520C2×D4—102no—
521C2×D4C2×ΓL(1,𝔽16)14yescomplemented
522C22×C4—51no—
523C22×C4—54no—
524C22×C4—102no—
525C22×C4—101no—
526C22×C4—101no—
527C22×C4—308no—
528C22×C4—304no—
529C22×C4—608no—
530C22×C4C2×ΓL(1,𝔽16)11yescharacteristic, complemented
531C22⋊C4—158no—
532C22⋊C4—308no—
533C22⋊C4—304no—
534C3×C5C22×#9911yescharacteristic, complemented, Hall
535C22×C3—22no—
536C22×C3—24no—
537C22×C3—22no—
538C22×C3—42no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—42no—
543C22×C3—52no—
544C22×C3—54no—
545C22×C3—52no—
546C22×C3—52no—
547C22×C3—52no—
548C22×C3—108no—
549C22×C3—108no—
550C22×C3—104no—
551C22×C3—104no—
552C22×C3—104no—
553C22×C3—102no—
554C22×C3—102no—
555C22×C3—202no—
556C22×C3—201no—
557C22×C3—201no—
558C22×C3—204no—
559C22×C3—204no—
560C22×C3—202no—
561C22×C3—202no—
562C22×C3—208no—
563C22×C3—208no—
564C22×C3—202no—
565C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
566C22×C3C2×C22⋊AGL(1,𝔽5)14yes—
567C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
568C22×C3C23×AGL(1,𝔽5)11yescharacteristic
569C3×C4—22no—
570C3×C4—102no—
571Dic3—208no—
572C2×C5—21no—
573C2×C5—21no—
574C2×C5—24no—
575C2×C5—42no—
576C2×C5C2×#83412yescomplemented
577C2×C5C22×#21711yescharacteristic
578D5—22no—
579D5—22no—
580D5—22no—
581D5—42no—
582D5C2×#83414yescomplemented
583C23—21no—
584C23—21no—
585C23—42no—
586C23—42no—
587C23—51no—
588C23—52no—
589C23—54no—
590C23—54no—
591C23—51no—
592C23—52no—
593C23—52no—
594C23—54no—
595C23—52no—
596C23—54no—
597C23—51no—
598C23—51no—
599C23—52no—
600C23—108no—
601C23—104no—
602C23—104no—
603C23—104no—
604C23—101no—
605C23—101no—
606C23—202no—
607C23—204no—
608C23—202no—
609C23—204no—
610C23—208no—
611C23—204no—
612C23—204no—
613C23—208no—
614C23—208no—
615C23—204no—
616C23#676312yes—
617C23#676312yes—
618C23C22×ΓL(1,𝔽16)11yescharacteristic
619C23C22×ΓL(1,𝔽16)12yes—
620C23C22×ΓL(1,𝔽16)12yescomplemented
621D4—28no—
622D4—104no—
623D4—104no—
624D4—104no—
625D4—104no—
626D4—108no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—52no—
630C2×C4—104no—
631C2×C4—104no—
632C2×C4—101no—
633C2×C4—101no—
634C2×C4—308no—
635C2×C4—6016no—
636C2×C4—608no—
637C2×C4C22×ΓL(1,𝔽16)12yescomplemented
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—24no—
641C2×C3—42no—
642C2×C3—54no—
643C2×C3—102no—
644C2×C3—102no—
645C2×C3—102no—
646C2×C3—202no—
647C2×C3D5⋊#9912yescomplemented
648C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
649C5C22×#83411yescharacteristic, complemented, Sylow
650C22—22no—
651C22—24no—
652C22—22no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—52no—
659C22—54no—
660C22—52no—
661C22—52no—
662C22—52no—
663C22—108no—
664C22—104no—
665C22—104no—
666C22—108no—
667C22—104no—
668C22—102no—
669C22—102no—
670C22—202no—
671C22—201no—
672C22—201no—
673C22—204no—
674C22—204no—
675C22—202no—
676C22—202no—
677C22—208no—
678C22—208no—
679C22—202no—
680C22C2×#676311yescharacteristic
681C22C2×#676314yes—
682C22C2×#676311yescharacteristic
683C22C23×ΓL(1,𝔽16)11yescharacteristic
684C4—22no—
685C4—102no—
686C4—608no—
687C3C2×D5⋊#9911yescharacteristic, complemented, Sylow
688C2—21no—
689C2—21no—
690C2—24no—
691C2—42no—
692C2—54no—
693C2—102no—
694C2—102no—
695C2—102no—
696C2—202no—
697C2D5⋊#83412yesdirect product factor
698C2C22×#676311yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC22×C3×C5C23×C4
FrattiniC22C23×ΓL(1,𝔽16)
FittingC22×C3×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D4×D5C2
cosocleC22×C3×D5C24
hypercenterC22×D4ΓL(1,𝔽16)
hypocenterC3×C5C22×#99
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×#6763C2semidirect
3. C2×#91240C2semidirect
4. D5⋊#834C2direct (N × H)
5. C2×#91228C2semidirect
7. C24×C3×D5C4semidirect
10. C22×C3×C5×D4C4semidirect
11. C22×C3×C22⋊D5C4semidirect
16. C2×C3×D4×D5C4semidirect
19. C22×C3×C4×D5C4semidirect
22. C2×#6763C22semidirect
23. C2×#6763C22semidirect
24. #91240C22semidirect
25. #91228C22semidirect
33. C24×C3×C5C2×C4semidirect
41. C23×C3×D5C2×C4semidirect
42. C23×C3×D5C2×C4semidirect
53. C2×C3×C5×D4C2×C4semidirect
54. C22×C3×C4×C5C2×C4semidirect
59. C2×C3×C22⋊D5C2×C4semidirect
60. C2×C3×C22⋊D5C2×C4semidirect
62. C22×C3×Dic5C2×C4semidirect
69. C2×C3×D20C2×C4semidirect
74. C2×C3×C4×D5C2×C4semidirect
77. #6763C23semidirect
83. C24×D5Dic3semidirect
86. C22×C5×D4Dic3semidirect
87. C22×C22⋊D5Dic3semidirect
92. C2×D4×D5Dic3semidirect
95. C22×C4×D5Dic3semidirect
111. C23×C3×C5C22×C4semidirect
135. C22×C3×D5C22×C4semidirect
147. C2×C3×C4×C5C22×C4semidirect
153. C2×C3×Dic5C22×C4semidirect
168. C22×C3×D4AGL(1,𝔽5)semidirect
178. C24×C5C2×Dic3semidirect
186. C23×D5C2×Dic3semidirect
187. C23×D5C2×Dic3semidirect
198. C2×C5×D4C2×Dic3semidirect
199. C22×C4×C5C2×Dic3semidirect
204. C2×C22⋊D5C2×Dic3semidirect
205. C2×C22⋊D5C2×Dic3semidirect
207. C22×Dic5C2×Dic3semidirect
214. C2×D20C2×Dic3semidirect
219. C2×C4×D5C2×Dic3semidirect
257. C2×C3×D5#99semidirect
280. C24×C3C2×AGL(1,𝔽5)semidirect
298. C2×C3×D4C2×AGL(1,𝔽5)semidirect
304. C22×C3×C4C2×AGL(1,𝔽5)semidirect
319. C23×C5C22×Dic3semidirect
343. C22×D5C22×Dic3semidirect
355. C2×C4×C5C22×Dic3semidirect
361. C2×Dic5C22×Dic3semidirect
376. C22×D4ΓL(1,𝔽16)semidirect
389. C2×C3×C5C2×#99semidirect
395. C3×D5C2×#99semidirect
433. C23×C3C22×AGL(1,𝔽5)semidirect
447. C2×C3×C4C22×AGL(1,𝔽5)semidirect
480. C2×D5#834semidirect
503. C24C2×ΓL(1,𝔽16)semidirect
521. C2×D4C2×ΓL(1,𝔽16)semidirect
530. C22×C4C2×ΓL(1,𝔽16)semidirect
534. C3×C5C22×#99semidirect
576. C2×C5C2×#834semidirect
582. D5C2×#834semidirect
620. C23C22×ΓL(1,𝔽16)semidirect
637. C2×C4C22×ΓL(1,𝔽16)semidirect
647. C2×C3D5⋊#99semidirect
649. C5C22×#834semidirect
687. C3C2×D5⋊#99semidirect
697. C2D5⋊#834direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D4×D52
C22×#67632
C2×#912402
D5⋊#8342
C2×#912282
C2×D5⋊#993
C22×#8345