Finite Group Databasebeta

← C2×D5×#834 #14411898

Subgroups — C2×D5×#834 #14411898

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D4×D5C211yesmaximal, characteristic
2C2×D5×#217C212yesmaximal, complemented
3C2×#91118C211yesmaximal, characteristic, complemented
4C2×C5×#834C211yesmaximal, characteristic, complemented
5C2×#90995C212yesmaximal, complemented
6D5×#834C218yesmaximal, direct product factor
7C2×D5×#99—31nomaximal, Hall
8C24×C3×D5C411yescharacteristic, complemented
9C24×C3×D5C2211yescharacteristic
10C22×C3×C5×D4C2211yescharacteristic
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×D20C411yescharacteristic, complemented
19C22×C3×C4×D5C411yescharacteristic, complemented
20C22×D5×Dic3—22no—
21C2×#6719C2212yescomplemented
22C2×C5×#217C2212yescomplemented
23D5×#217—24no—
24D5×#217C2218yescomplemented
25C2×#6665—22no—
26#91118C2214yescomplemented
27C5×#834C2214yescomplemented
28#90995C2218yescomplemented
29C22×#834—51nomaximal, Hall
30C22×D4×D5D311yescharacteristic
31C2×D5×C22⋊C4—32no—
32C2×C5×#99—31no—
33C2×#3966—31no—
34C2×#3938—32no—
35D5×#99—38no—
36C24×C3×C5C2×C411yescharacteristic, complemented
37C24×C3×C5C2311yescharacteristic
38C23×C3×D5—22no—
39C23×C3×D5—21no—
40C23×C3×D5—21no—
41C23×C3×D5—44no—
42C23×C3×D5—44no—
43C23×C3×D5C2×C411yescharacteristic
44C23×C3×D5C2×C411yescharacteristic
45C23×C3×D5C2×C412yes—
46C23×C3×D5C2×C414yescomplemented
47C23×C3×D5C2×C411yescharacteristic, complemented
48C23×C3×D5D412yes—
49C23×C3×D5D412yes—
50C23×C3×D5D414yes—
51C23×C3×D5C2312yes—
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4C2×C412yescomplemented
55C2×C3×C5×D4C2312yes—
56C22×C3×C4×C5C2×C411yescharacteristic, complemented
57C22×Dic15—22no—
58C22×C5×Dic3—22no—
59C2×C3×C22⋊D5—22no—
60C2×C3×C22⋊D5—22no—
61C2×C3×C22⋊D5—22no—
62C2×C3×C22⋊D5—22no—
63C2×C3×C22⋊D5C2×C414yescomplemented
64C2×C3×C22⋊D5C2×C412yescomplemented
65C2×C3×C22⋊D5C2312yes—
66C22×C3×Dic5C2×C411yescharacteristic, complemented
67C3×D4×D5—28no—
68C3×D4×D5—28no—
69C3×D4×D5—28no—
70C3×D4×D5—28no—
71C2×C3×D20—22no—
72C2×C3×D20—22no—
73C2×C3×D20C2×C414yescomplemented
74C2×C3×C4×D5—21no—
75C2×C3×C4×D5—22no—
76C2×C3×C4×D5—21no—
77C2×C3×C4×D5C2×C414yescomplemented
78C2×D5×Dic3—28no—
79C2×D5×Dic3—48no—
80#6719—22no—
81#6719C2314yescomplemented
82C5×#217—22no—
83C5×#217C2314yescomplemented
84#6665—28no—
85C23×C3×D4—51no—
86C22×#217—52no—
87C2×#834—51no—
88C2×#834—52no—
89C2×#834—58no—
90C2×#834D511yescharacteristic, direct product factor
91C24×D5Dic311yescharacteristic, complemented
92C24×D5C2×D311yescharacteristic
93C22×C5×D4C2×D311yescharacteristic
94C22×C22⋊D5Dic311yescharacteristic, complemented
95C22×C22⋊D5C2×D311yescharacteristic
96C2×D4×D5—22no—
97C2×D4×D5—24no—
98C2×D4×D5—22no—
99C2×D4×D5Dic314yescomplemented
100C2×D4×D5C2×D314yes—
101C22×D20Dic311yescharacteristic, complemented
102C22×C4×D5—62no—
103C22×C4×D5Dic311yescharacteristic, complemented
104C2×C5×C22⋊C4—32no—
105C2×C22⋊Dic5—32no—
106C2×#685—62no—
107D5×C22⋊C4—38no—
108D5×C22⋊C4—64no—
109C5×#99—34no—
110#3966—34no—
111#3938—38no—
112C22×#99—151noSylow
113C23×C3×C5—21no—
114C23×C3×C5—21no—
115C23×C3×C5—42no—
116C23×C3×C5—42no—
117C23×C3×C5C22×C411yescharacteristic
118C23×C3×C5C22×C411yescharacteristic
119C23×C3×C5C22×C412yescomplemented
120C23×C3×C5C2×D412yes—
121C23×C3×C5C2×D412yes—
122C23×C3×C5C2411yescharacteristic
123C22×C3×D5—28no—
124C22×C3×D5—24no—
125C22×C3×D5—21no—
126C22×C3×D5—21no—
127C22×C3×D5—24no—
128C22×C3×D5—24no—
129C22×C3×D5—44no—
130C22×C3×D5—48no—
131C22×C3×D5—44no—
132C22×C3×D5—42no—
133C22×C3×D5—44no—
134C22×C3×D5—44no—
135C22×C3×D5—48no—
136C22×C3×D5—48no—
137C22×C3×D5—44no—
138C22×C3×D5—42no—
139C22×C3×D5C22⋊C411yescharacteristic
140C22×C3×D5C22⋊C412yes—
141C22×C3×D5C22⋊C412yes—
142C22×C3×D5C22⋊C414yes—
143C22×C3×D5C22⋊C412yes—
144C22×C3×D5C22⋊C414yes—
145C22×C3×D5C22⋊C411yescharacteristic
146C22×C3×D5C22×C412yes—
147C22×C3×D5C22×C412yes—
148C22×C3×D5C22×C412yescomplemented
149C22×C3×D5C2×D414yes—
150C22×C3×D5C2×D414yes—
151C3×C5×D4—24no—
152C3×C5×D4—24no—
153C2×C3×C4×C5—21no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5C22×C412yescomplemented
156C2×Dic15—24no—
157C2×Dic15—44no—
158C2×C5×Dic3—24no—
159C2×C5×Dic3—44no—
160C3×C22⋊D5—24no—
161C3×C22⋊D5—24no—
162C3×C22⋊D5—28no—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—21no—
165C2×C3×Dic5C22×C412yescomplemented
166C3×D20—28no—
167C3×C4×D5—24no—
168C3×C4×D5—24no—
169D5×Dic3—416no—
170C25×C3—51no—
171C25×C3—51no—
172C22×C3×D4—51no—
173C22×C3×D4—51no—
174C22×C3×D4—54no—
175C22×C3×D4—54no—
176C22×C3×D4—51no—
177C22×C3×D4—102no—
178C22×C3×D4—102no—
179C22×C3×D4—104no—
180C22×C3×D4C2×D511yescharacteristic
181C23×C3×C4—51no—
182C23×Dic3—102no—
183C2×#217—52no—
184C2×#217—58no—
185C2×#217—104no—
186C2×#217—102no—
187C2×#217C2×D512yescomplemented
188#834—54no—
189#834—58no—
190#834C2×D514yesdirect product factor
191C24×C5C2×Dic311yescharacteristic, complemented
192C24×C5C22×D311yescharacteristic
193C23×D5—22no—
194C23×D5—21no—
195C23×D5—21no—
196C23×D5—44no—
197C23×D5—44no—
198C23×D5C2×Dic311yescharacteristic
199C23×D5C2×Dic311yescharacteristic
200C23×D5C2×Dic312yes—
201C23×D5C2×Dic314yescomplemented
202C23×D5C2×Dic311yescharacteristic, complemented
203C23×D5#6712yes—
204C23×D5#6714yes—
205C23×D5#6712yes—
206C23×D5C22×D312yes—
207C2×C5×D4—22no—
208C2×C5×D4—22no—
209C2×C5×D4C2×Dic312yescomplemented
210C2×C5×D4C22×D312yes—
211C22×C4×C5—62no—
212C22×C4×C5C2×Dic311yescharacteristic, complemented
213C2×C22⋊D5—22no—
214C2×C22⋊D5—22no—
215C2×C22⋊D5—22no—
216C2×C22⋊D5—22no—
217C2×C22⋊D5C2×Dic314yescomplemented
218C2×C22⋊D5C2×Dic312yescomplemented
219C2×C22⋊D5C22×D312yes—
220C22×Dic5—62no—
221C22×Dic5C2×Dic311yescharacteristic, complemented
222D4×D5—28no—
223D4×D5—28no—
224D4×D5—28no—
225D4×D5—28no—
226C2×D20—22no—
227C2×D20—22no—
228C2×D20C2×Dic314yescomplemented
229C2×C4×D5—22no—
230C2×C4×D5—21no—
231C2×C4×D5—21no—
232C2×C4×D5—68no—
233C2×C4×D5—128no—
234C2×C4×D5C2×Dic314yescomplemented
235C5×C22⋊C4—34no—
236C5×C22⋊C4—62no—
237C22⋊Dic5—34no—
238C22⋊Dic5—62no—
239#685—68no—
240C23×D4—51no—
241C22×C22⋊C4—152no—
242C2×#99—31no—
243C2×#99—158no—
244C2×#99—152no—
245C2×#99—151no—
246C22×C3×C5—24no—
247C22×C3×C5—22no—
248C22×C3×C5—22no—
249C22×C3×C5—41no—
250C22×C3×C5—42no—
251C22×C3×C5—41no—
252C22×C3×C5—42no—
253C22×C3×C5—42no—
254C22×C3×C5—42no—
255C22×C3×C5C2×C22⋊C411yescharacteristic
256C22×C3×C5C2×C22⋊C412yes—
257C22×C3×C5C2×C22⋊C411yescharacteristic
258C22×C3×C5C23×C411yescharacteristic
259C22×C3×C5C22×D412yes—
260C2×C3×D5—22no—
261C2×C3×D5—24no—
262C2×C3×D5—28no—
263C2×C3×D5—24no—
264C2×C3×D5—24no—
265C2×C3×D5—28no—
266C2×C3×D5—22no—
267C2×C3×D5—44no—
268C2×C3×D5—42no—
269C2×C3×D5—42no—
270C2×C3×D5—44no—
271C2×C3×D5—48no—
272C2×C3×D5—42no—
273C2×C3×D5—42no—
274C2×C3×D5—48no—
275C2×C3×D5—42no—
276C2×C3×D5#9914yescomplemented
277C2×C3×D5C2×C22⋊C412yes—
278C2×C3×D5C2×C22⋊C414yes—
279C2×C3×D5C2×C22⋊C412yes—
280C3×C4×C5—22no—
281Dic15—44no—
282C3×Dic5—22no—
283C5×Dic3—44no—
284C24×C3—51no—
285C24×C3—52no—
286C24×C3—52no—
287C24×C3—51no—
288C24×C3—54no—
289C24×C3—52no—
290C24×C3—52no—
291C24×C3—51no—
292C24×C3—54no—
293C24×C3—101no—
294C24×C3—102no—
295C24×C3—101no—
296C24×C3—204no—
297C24×C3—204no—
298C24×C3C4×D511yescharacteristic, complemented
299C24×C3C22×D511yescharacteristic
300C2×C3×D4—22no—
301C2×C3×D4—22no—
302C2×C3×D4—52no—
303C2×C3×D4—54no—
304C2×C3×D4—52no—
305C2×C3×D4—54no—
306C2×C3×D4—102no—
307C2×C3×D4—102no—
308C2×C3×D4—108no—
309C2×C3×D4—108no—
310C2×C3×D4—108no—
311C2×C3×D4—108no—
312C2×C3×D4—102no—
313C2×C3×D4—102no—
314C2×C3×D4—102no—
315C2×C3×D4—102no—
316C2×C3×D4C4×D512yescomplemented
317C2×C3×D4C22×D512yes—
318C22×C3×C4—51no—
319C22×C3×C4—54no—
320C22×C3×C4—101no—
321C22×C3×C4—102no—
322C22×C3×C4—101no—
323C22×C3×C4C4×D511yescharacteristic, complemented
324C22×Dic3—22no—
325C22×Dic3—108no—
326C22×Dic3—102no—
327C22×Dic3—208no—
328#217—22no—
329#217—54no—
330#217—108no—
331#217—102no—
332#217C22×D514yescomplemented
333C23×C5—21no—
334C23×C5—21no—
335C23×C5—42no—
336C23×C5—42no—
337C23×C5C22×Dic311yescharacteristic
338C23×C5C22×Dic311yescharacteristic
339C23×C5C22×Dic312yescomplemented
340C23×C5C2×#6712yes—
341C23×C5C2×#6712yes—
342C23×C5C23×D311yescharacteristic
343C22×D5—28no—
344C22×D5—24no—
345C22×D5—21no—
346C22×D5—21no—
347C22×D5—24no—
348C22×D5—24no—
349C22×D5—44no—
350C22×D5—48no—
351C22×D5—44no—
352C22×D5—42no—
353C22×D5—44no—
354C22×D5—44no—
355C22×D5—48no—
356C22×D5—48no—
357C22×D5—44no—
358C22×D5—42no—
359C22×D5#21712yes—
360C22×D5#21711yescharacteristic
361C22×D5#21712yes—
362C22×D5#21714yes—
363C22×D5#21712yes—
364C22×D5#21714yes—
365C22×D5#21711yescharacteristic
366C22×D5C22×Dic312yes—
367C22×D5C22×Dic312yes—
368C22×D5C22×Dic312yescomplemented
369C22×D5C2×#6714yes—
370C22×D5C2×#6714yes—
371C5×D4—24no—
372C5×D4—24no—
373C2×C4×C5—21no—
374C2×C4×C5—21no—
375C2×C4×C5—64no—
376C2×C4×C5—124no—
377C2×C4×C5C22×Dic312yescomplemented
378C22⋊D5—24no—
379C22⋊D5—24no—
380C22⋊D5—28no—
381C2×Dic5—21no—
382C2×Dic5—21no—
383C2×Dic5—64no—
384C2×Dic5—124no—
385C2×Dic5C22×Dic312yescomplemented
386D20—28no—
387C4×D5—24no—
388C4×D5—24no—
389C4×D5—1216no—
390C25—51no—
391C25—51no—
392C22×D4—51no—
393C22×D4—51no—
394C22×D4—54no—
395C22×D4—54no—
396C22×D4—51no—
397C22×D4—102no—
398C22×D4—104no—
399C22×D4—102no—
400C22×D4D3×D511yescharacteristic
401C23×C4—51no—
402C23×C4—302no—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—158no—
405C2×C22⋊C4—152no—
406C2×C22⋊C4—304no—
407C2×C22⋊C4—302no—
408#99—34no—
409#99—158no—
410#99—154no—
411C2×C3×C5—22no—
412C2×C3×C5—21no—
413C2×C3×C5—21no—
414C2×C3×C5—22no—
415C2×C3×C5—42no—
416C2×C3×C5C2×#9912yescomplemented
417C2×C3×C5C22×C22⋊C411yescharacteristic
418C3×D5—22no—
419C3×D5—24no—
420C3×D5—42no—
421C3×D5C2×#9914yescomplemented
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—42no—
425C23×C3—42no—
426C23×C3—51no—
427C23×C3—52no—
428C23×C3—54no—
429C23×C3—52no—
430C23×C3—51no—
431C23×C3—54no—
432C23×C3—52no—
433C23×C3—52no—
434C23×C3—54no—
435C23×C3—54no—
436C23×C3—52no—
437C23×C3—52no—
438C23×C3—108no—
439C23×C3—104no—
440C23×C3—104no—
441C23×C3—104no—
442C23×C3—101no—
443C23×C3—101no—
444C23×C3—204no—
445C23×C3—202no—
446C23×C3—202no—
447C23×C3—204no—
448C23×C3—204no—
449C23×C3—208no—
450C23×C3—204no—
451C23×C3—208no—
452C23×C3—208no—
453C23×C3—204no—
454C23×C3C2×C4×D511yescharacteristic
455C23×C3C2×C4×D511yescharacteristic
456C23×C3C2×C4×D512yescomplemented
457C23×C3D4×D512yes—
458C23×C3D4×D512yes—
459C23×C3C23×D511yescharacteristic
460C3×D4—24no—
461C3×D4—24no—
462C3×D4—108no—
463C3×D4—108no—
464C3×D4—104no—
465C3×D4—104no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—52no—
469C2×C3×C4—104no—
470C2×C3×C4—104no—
471C2×C3×C4—101no—
472C2×C3×C4—101no—
473C2×C3×C4C2×C4×D512yescomplemented
474C2×Dic3—24no—
475C2×Dic3—44no—
476C2×Dic3—104no—
477C2×Dic3—2016no—
478C2×Dic3—204no—
479C22×C5—24no—
480C22×C5—22no—
481C22×C5—22no—
482C22×C5—41no—
483C22×C5—42no—
484C22×C5—41no—
485C22×C5—42no—
486C22×C5—42no—
487C22×C5—42no—
488C22×C5C2×#21711yescharacteristic
489C22×C5C2×#21712yes—
490C22×C5C2×#21711yescharacteristic
491C22×C5C23×Dic311yescharacteristic
492C22×C5C22×#6712yes—
493C2×D5—22no—
494C2×D5—24no—
495C2×D5—28no—
496C2×D5—24no—
497C2×D5—24no—
498C2×D5—28no—
499C2×D5—22no—
500C2×D5—44no—
501C2×D5—42no—
502C2×D5—42no—
503C2×D5—44no—
504C2×D5—48no—
505C2×D5—42no—
506C2×D5—42no—
507C2×D5—48no—
508C2×D5—42no—
509C2×D5#83414yesdirect product factor
510C2×D5C2×#21712yes—
511C2×D5C2×#21714yes—
512C2×D5C2×#21712yes—
513C4×C5—22no—
514C4×C5—124no—
515Dic5—22no—
516Dic5—124no—
517C24—51no—
518C24—52no—
519C24—52no—
520C24—51no—
521C24—54no—
522C24—52no—
523C24—52no—
524C24—51no—
525C24—54no—
526C24—102no—
527C24—101no—
528C24—101no—
529C24—204no—
530C24—204no—
531C24D5×Dic311yescharacteristic, complemented
532C24C2×D3×D511yescharacteristic
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—52no—
536C2×D4—54no—
537C2×D4—52no—
538C2×D4—54no—
539C2×D4—102no—
540C2×D4—102no—
541C2×D4—108no—
542C2×D4—108no—
543C2×D4—108no—
544C2×D4—108no—
545C2×D4—102no—
546C2×D4—102no—
547C2×D4—102no—
548C2×D4—102no—
549C2×D4D5×Dic312yescomplemented
550C2×D4C2×D3×D512yes—
551C22×C4—51no—
552C22×C4—54no—
553C22×C4—62no—
554C22×C4—102no—
555C22×C4—101no—
556C22×C4—101no—
557C22×C4—308no—
558C22×C4—302no—
559C22×C4—608no—
560C22×C4D5×Dic311yescharacteristic, complemented
561C22⋊C4—34no—
562C22⋊C4—62no—
563C22⋊C4—154no—
564C22⋊C4—308no—
565C22⋊C4—302no—
566C3×C5C22×#9911yescharacteristic, complemented, Hall
567C22×C3—24no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—41no—
571C22×C3—42no—
572C22×C3—41no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—54no—
577C22×C3—52no—
578C22×C3—52no—
579C22×C3—54no—
580C22×C3—108no—
581C22×C3—108no—
582C22×C3—104no—
583C22×C3—104no—
584C22×C3—104no—
585C22×C3—102no—
586C22×C3—102no—
587C22×C3—204no—
588C22×C3—202no—
589C22×C3—202no—
590C22×C3—204no—
591C22×C3—202no—
592C22×C3—202no—
593C22×C3—208no—
594C22×C3—208no—
595C22×C3—202no—
596C22×C3D5×C22⋊C411yescharacteristic
597C22×C3D5×C22⋊C412yes—
598C22×C3D5×C22⋊C411yescharacteristic
599C22×C3C22×C4×D511yescharacteristic
600C22×C3C2×D4×D512yes—
601C3×C4—22no—
602C3×C4—102no—
603Dic3—44no—
604Dic3—204no—
605C2×C5—22no—
606C2×C5—21no—
607C2×C5—21no—
608C2×C5—22no—
609C2×C5—42no—
610C2×C5C2×#83412yescomplemented
611C2×C5C22×#21711yescharacteristic
612D5—22no—
613D5—24no—
614D5—42no—
615D5C2×#83414yesdirect product factor
616C23—21no—
617C23—21no—
618C23—42no—
619C23—42no—
620C23—51no—
621C23—52no—
622C23—54no—
623C23—52no—
624C23—54no—
625C23—51no—
626C23—52no—
627C23—52no—
628C23—54no—
629C23—54no—
630C23—52no—
631C23—52no—
632C23—108no—
633C23—104no—
634C23—104no—
635C23—104no—
636C23—101no—
637C23—101no—
638C23—204no—
639C23—202no—
640C23—202no—
641C23—204no—
642C23—204no—
643C23—208no—
644C23—204no—
645C23—208no—
646C23—208no—
647C23—204no—
648C23C2×D5×Dic311yescharacteristic
649C23C2×D5×Dic311yescharacteristic
650C23C2×D5×Dic312yescomplemented
651C23D5×#6712yes—
652C23D5×#6712yes—
653C23C22×D3×D511yescharacteristic
654D4—24no—
655D4—24no—
656D4—108no—
657D4—108no—
658D4—104no—
659D4—104no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—52no—
663C2×C4—64no—
664C2×C4—104no—
665C2×C4—104no—
666C2×C4—101no—
667C2×C4—101no—
668C2×C4—124no—
669C2×C4—304no—
670C2×C4—6016no—
671C2×C4—604no—
672C2×C4C2×D5×Dic312yescomplemented
673C2×C3—22no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—22no—
677C2×C3—42no—
678C2×C3—54no—
679C2×C3—102no—
680C2×C3—104no—
681C2×C3—202no—
682C2×C3D5×#9912yescomplemented
683C2×C3C2×D5×C22⋊C411yescharacteristic
684C5C22×#83411yescharacteristic, complemented, Sylow
685C22—24no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—42no—
690C22—41no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—54no—
695C22—52no—
696C22—52no—
697C22—54no—
698C22—108no—
699C22—104no—
700C22—104no—
701C22—108no—
702C22—102no—
703C22—104no—
704C22—102no—
705C22—204no—
706C22—202no—
707C22—202no—
708C22—204no—
709C22—202no—
710C22—202no—
711C22—208no—
712C22—208no—
713C22—202no—
714C22D5×#21711yescharacteristic
715C22D5×#21712yes—
716C22D5×#21711yescharacteristic
717C22C22×D5×Dic311yescharacteristic
718C22C2×D5×#6712yes—
719C4—22no—
720C4—102no—
721C4—124no—
722C4—604no—
723C3C2×D5×#9911yescharacteristic, complemented, Sylow
724C2—22no—
725C2—21no—
726C2—21no—
727C2—22no—
728C2—42no—
729C2—54no—
730C2—102no—
731C2—104no—
732C2—202no—
733C2D5×#83412yesdirect product factor
734C2C2×D5×#21711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D4×D5C2
cosocleC23×C3×C5C24
hypercenterC22×D4D3×D5
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. C2×D5×#217C2semidirect
3. C2×#91118C2semidirect
4. C2×C5×#834C2semidirect
5. C2×#90995C2semidirect
6. D5×#834C2direct (N × H)
8. C24×C3×D5C4semidirect
11. C22×C3×C22⋊D5C4semidirect
16. C2×C3×D4×D5C4semidirect
18. C22×C3×D20C4semidirect
19. C22×C3×C4×D5C4semidirect
21. C2×#6719C22semidirect
22. C2×C5×#217C22semidirect
24. D5×#217C22semidirect
26. #91118C22semidirect
27. C5×#834C22semidirect
28. #90995C22semidirect
36. C24×C3×C5C2×C4semidirect
46. C23×C3×D5C2×C4semidirect
47. C23×C3×D5C2×C4semidirect
54. C2×C3×C5×D4C2×C4semidirect
56. C22×C3×C4×C5C2×C4semidirect
63. C2×C3×C22⋊D5C2×C4semidirect
64. C2×C3×C22⋊D5C2×C4semidirect
66. C22×C3×Dic5C2×C4semidirect
73. C2×C3×D20C2×C4semidirect
77. C2×C3×C4×D5C2×C4semidirect
81. #6719C23semidirect
83. C5×#217C23semidirect
90. C2×#834D5direct (N × H)
91. C24×D5Dic3semidirect
94. C22×C22⋊D5Dic3semidirect
99. C2×D4×D5Dic3semidirect
101. C22×D20Dic3semidirect
103. C22×C4×D5Dic3semidirect
119. C23×C3×C5C22×C4semidirect
148. C22×C3×D5C22×C4semidirect
155. C2×C3×C4×C5C22×C4semidirect
165. C2×C3×Dic5C22×C4semidirect
187. C2×#217C2×D5semidirect
190. #834C2×D5direct (N × H)
191. C24×C5C2×Dic3semidirect
201. C23×D5C2×Dic3semidirect
202. C23×D5C2×Dic3semidirect
209. C2×C5×D4C2×Dic3semidirect
212. C22×C4×C5C2×Dic3semidirect
217. C2×C22⋊D5C2×Dic3semidirect
218. C2×C22⋊D5C2×Dic3semidirect
221. C22×Dic5C2×Dic3semidirect
228. C2×D20C2×Dic3semidirect
234. C2×C4×D5C2×Dic3semidirect
276. C2×C3×D5#99semidirect
298. C24×C3C4×D5semidirect
316. C2×C3×D4C4×D5semidirect
323. C22×C3×C4C4×D5semidirect
332. #217C22×D5semidirect
339. C23×C5C22×Dic3semidirect
368. C22×D5C22×Dic3semidirect
377. C2×C4×C5C22×Dic3semidirect
385. C2×Dic5C22×Dic3semidirect
416. C2×C3×C5C2×#99semidirect
421. C3×D5C2×#99semidirect
456. C23×C3C2×C4×D5semidirect
473. C2×C3×C4C2×C4×D5semidirect
509. C2×D5#834direct (N × H)
531. C24D5×Dic3semidirect
549. C2×D4D5×Dic3semidirect
560. C22×C4D5×Dic3semidirect
566. C3×C5C22×#99semidirect
610. C2×C5C2×#834semidirect
615. D5C2×#834direct (N × H)
650. C23C2×D5×Dic3semidirect
672. C2×C4C2×D5×Dic3semidirect
682. C2×C3D5×#99semidirect
684. C5C22×#834semidirect
723. C3C2×D5×#99semidirect
733. 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
C2×D5×#2172
C2×#911182
C2×C5×#8342
C2×#909952
D5×#8342
C2×D5×#993
C22×#8345