Finite Group Databasebeta

← C2×C5×#1867 #11943607

Subgroups — C2×C5×#1867 #11943607

Order 1280.

1994 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#518C211yesmaximal, characteristic
2C22×C5×#99C211yesmaximal, characteristic
3C2×C5×#386C211yesmaximal, characteristic
4C2×C5×#385C212yesmaximal, complemented
5C5×#1867C218yesmaximal, direct product factor
6C2×C5×#342C212yesmaximal, complemented
7C23×C5×D4C2211yescharacteristic
8C24×C4×C5C2211yescharacteristic
9C5×#518—22no—
10C5×#518—24no—
11C5×#518C2214yes—
12C2×C4×C5×D4—22no—
13C2×C4×C5×D4—22no—
14C2×C5×#117—21no—
15C22×C5×C4⋊C4—22no—
16C22×C5×C22⋊C4—21no—
17C22×C5×C22⋊C4—21no—
18C22×C5×C22⋊C4C2211yescharacteristic
19C22×C5×C22⋊C4C2212yes—
20C22×C5×C22⋊C4C2212yes—
21C2×C5×#99C418yescomplemented
22C2×C5×#99C2214yes—
23C5×#386—22no—
24C5×#386C2214yes—
25C5×#385—24no—
26C5×#385C2218yescomplemented
27C2×C5×#95—22no—
28C2×C5×#95—21no—
29C5×#342C2218yescomplemented
30C2×#1867C511yesmaximal, characteristic, direct product factor, Sylow
31C25×C5D411yescharacteristic
32C25×C5C2311yescharacteristic
33C22×C5×D4—22no—
34C22×C5×D4—22no—
35C22×C5×D4—24no—
36C22×C5×D4C2×C414yes—
37C22×C5×D4D412yes—
38C22×C5×D4Q814yes—
39C22×C5×D4C2312yes—
40C23×C4×C5—21no—
41C23×C4×C5—22no—
42C23×C4×C5—22no—
43C23×C4×C5—21no—
44C23×C4×C5—21no—
45C23×C4×C5—21no—
46C23×C4×C5—22no—
47C23×C4×C5—21no—
48C23×C4×C5—44no—
49C23×C4×C5D411yescharacteristic
50C23×C4×C5D412yes—
51C23×C4×C5D412yes—
52C23×C4×C5C2312yes—
53C4×C5×D4—28no—
54C4×C5×D4—28no—
55C4×C5×D4—28no—
56C4×C5×D4—28no—
57C5×#117—24no—
58C5×#117—24no—
59C2×C5×C4⋊C4—21no—
60C2×C5×C4⋊C4—21no—
61C2×C5×C4⋊C4—28no—
62C2×C5×C4⋊C4—48no—
63C2×C5×C22⋊C4—22no—
64C2×C5×C22⋊C4—24no—
65C2×C5×C22⋊C4—22no—
66C2×C5×C22⋊C4—22no—
67C2×C5×C22⋊C4—24no—
68C2×C5×C22⋊C4—22no—
69C2×C5×C22⋊C4—22no—
70C2×C5×C22⋊C4—22no—
71C2×C5×C22⋊C4—24no—
72C2×C5×C22⋊C4—24no—
73C2×C5×C22⋊C4—21no—
74C2×C5×C22⋊C4—24no—
75C2×C5×C22⋊C4—44no—
76C2×C5×C22⋊C4C2×C418yescomplemented
77C2×C5×C22⋊C4D414yes—
78C2×C5×C22⋊C4C2312yes—
79C2×C5×C22⋊C4C2314yes—
80C2×C5×C22⋊C4C2314yes—
81C2×C42×C5—22no—
82C5×#99C2×C4116yescomplemented
83C5×#95—28no—
84C5×#95—24no—
85C2×#518C2×C511yescharacteristic
86C22×#99C2×C511yescharacteristic
87C2×#386C2×C511yescharacteristic
88C2×#385C2×C512yescomplemented
89#1867C2×C518yesdirect product factor
90C2×#342C2×C512yescomplemented
91C24×C5—21no—
92C24×C5—21no—
93C24×C5—22no—
94C24×C5—42no—
95C24×C5—42no—
96C24×C5—42no—
97C24×C5—42no—
98C24×C5C4⋊C414yescomplemented
99C24×C5C22×C412yes—
100C24×C5C2×D411yescharacteristic
101C24×C5C2×D412yes—
102C24×C5C2×D412yes—
103C24×C5C2×D411yescharacteristic
104C24×C5C2×D412yes—
105C24×C5C2×Q812yes—
106C24×C5#4114yes—
107C24×C5C2411yescharacteristic
108C2×C5×D4—28no—
109C2×C5×D4—28no—
110C2×C5×D4—24no—
111C2×C5×D4—28no—
112C2×C5×D4—28no—
113C2×C5×D4—24no—
114C2×C5×D4—24no—
115C2×C5×D4—24no—
116C2×C5×D4C4⋊C418yescomplemented
117C2×C5×D4C22×C414yes—
118C2×C5×D4C2×Q814yes—
119C22×C4×C5—21no—
120C22×C4×C5—21no—
121C22×C4×C5—22no—
122C22×C4×C5—24no—
123C22×C4×C5—28no—
124C22×C4×C5—28no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—24no—
129C22×C4×C5—24no—
130C22×C4×C5—24no—
131C22×C4×C5—24no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—44no—
136C22×C4×C5—44no—
137C22×C4×C5—48no—
138C22×C4×C5—44no—
139C22×C4×C5—44no—
140C22×C4×C5—44no—
141C22×C4×C5—42no—
142C22×C4×C5—41no—
143C22×C4×C5—42no—
144C22×C4×C5—41no—
145C22×C4×C5—44no—
146C22×C4×C5—44no—
147C22×C4×C5—42no—
148C22×C4×C5—42no—
149C22×C4×C5—42no—
150C22×C4×C5—82no—
151C22×C4×C5—82no—
152C22×C4×C5C4⋊C414yescomplemented
153C22×C4×C5C2×D412yes—
154C22×C4×C5C2×D414yes—
155C22×C4×C5C2×D414yes—
156C5×C4⋊C4—24no—
157C5×C4⋊C4—24no—
158C5×C4⋊C4—416no—
159C5×C22⋊C4—28no—
160C5×C22⋊C4—28no—
161C5×C22⋊C4—24no—
162C5×C22⋊C4—24no—
163C5×C22⋊C4—24no—
164C5×C22⋊C4—24no—
165C5×C22⋊C4—24no—
166C5×C22⋊C4—24no—
167C5×C22⋊C4—48no—
168C5×C22⋊C4—42no—
169C5×C22⋊C4C22×C418yescomplemented
170C42×C5—28no—
171C23×D4C22×C511yescharacteristic
172C24×C4C22×C511yescharacteristic
173#518—22no—
174#518—24no—
175#518C22×C514yes—
176C2×C4×D4—22no—
177C2×C4×D4—22no—
178C2×#117—21no—
179C22×C4⋊C4—22no—
180C22×C22⋊C4—21no—
181C22×C22⋊C4—21no—
182C22×C22⋊C4C22×C511yescharacteristic
183C22×C22⋊C4C22×C512yes—
184C22×C22⋊C4C22×C512yes—
185C2×#99C4×C518yescomplemented
186C2×#99C22×C514yes—
187#386—22no—
188#386C22×C514yes—
189#385—24no—
190#385C22×C518yescomplemented
191C2×#95—22no—
192C2×#95—21no—
193#342C22×C518yescomplemented
194C23×C5—24no—
195C23×C5—22no—
196C23×C5—24no—
197C23×C5—22no—
198C23×C5—22no—
199C23×C5—24no—
200C23×C5—22no—
201C23×C5—24no—
202C23×C5—42no—
203C23×C5—41no—
204C23×C5—41no—
205C23×C5—44no—
206C23×C5—42no—
207C23×C5—41no—
208C23×C5—44no—
209C23×C5—48no—
210C23×C5—41no—
211C23×C5—42no—
212C23×C5—48no—
213C23×C5—42no—
214C23×C5—42no—
215C23×C5—42no—
216C23×C5—84no—
217C23×C5—81no—
218C23×C5—81no—
219C23×C5C2×C4⋊C412yes—
220C23×C5C2×C4⋊C412yes—
221C23×C5C2×C4⋊C414yescomplemented
222C23×C5C4×D414yes—
223C23×C5C4×D414yes—
224C23×C5#12011yescharacteristic
225C23×C5#12012yes—
226C23×C5#12011yescharacteristic
227C23×C5C22⋊Q814yes—
228C23×C5C22⋊Q814yes—
229C23×C5#12312yes—
230C23×C5#12312yes—
231C23×C5C23×C411yescharacteristic
232C23×C5C22×D411yescharacteristic
233C23×C5C22×D412yes—
234C23×C5C22×Q811yescharacteristic
235C23×C5C2×#4112yes—
236C5×D4—28no—
237C5×D4—28no—
238C5×D4—216no—
239C2×C4×C5—22no—
240C2×C4×C5—22no—
241C2×C4×C5—24no—
242C2×C4×C5—24no—
243C2×C4×C5—24no—
244C2×C4×C5—28no—
245C2×C4×C5—28no—
246C2×C4×C5—24no—
247C2×C4×C5—24no—
248C2×C4×C5—44no—
249C2×C4×C5—416no—
250C2×C4×C5—44no—
251C2×C4×C5—44no—
252C2×C4×C5—42no—
253C2×C4×C5—48no—
254C2×C4×C5—44no—
255C2×C4×C5—42no—
256C2×C4×C5—44no—
257C2×C4×C5—44no—
258C2×C4×C5—44no—
259C2×C4×C5—44no—
260C2×C4×C5—44no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—82no—
265C2×C4×C5—82no—
266C2×C4×C5—84no—
267C2×C4×C5—84no—
268C2×C4×C5—84no—
269C2×C4×C5C2×C4⋊C414yescomplemented
270C25C5×D411yescharacteristic
271C25C23×C511yescharacteristic
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—24no—
275C22×D4C2×C4×C514yes—
276C22×D4C5×D412yes—
277C22×D4C5×Q814yes—
278C22×D4C23×C512yes—
279C23×C4—21no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—21no—
283C23×C4—21no—
284C23×C4—21no—
285C23×C4—22no—
286C23×C4—21no—
287C23×C4—44no—
288C23×C4C5×D411yescharacteristic
289C23×C4C5×D412yes—
290C23×C4C5×D412yes—
291C23×C4C23×C512yes—
292C4×D4—28no—
293C4×D4—28no—
294C4×D4—28no—
295C4×D4—28no—
296#117—24no—
297#117—24no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—48no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4C2×C4×C518yescomplemented
316C2×C22⋊C4C5×D414yes—
317C2×C22⋊C4C23×C512yes—
318C2×C22⋊C4C23×C514yes—
319C2×C22⋊C4C23×C514yes—
320C2×C42—22no—
321#99C2×C4×C5116yescomplemented
322#95—28no—
323#95—24no—
324C22×C5—28no—
325C22×C5—24no—
326C22×C5—24no—
327C22×C5—28no—
328C22×C5—22no—
329C22×C5—21no—
330C22×C5—22no—
331C22×C5—21no—
332C22×C5—22no—
333C22×C5—21no—
334C22×C5—22no—
335C22×C5—21no—
336C22×C5—24no—
337C22×C5—42no—
338C22×C5—44no—
339C22×C5—44no—
340C22×C5—42no—
341C22×C5—41no—
342C22×C5—41no—
343C22×C5—42no—
344C22×C5—44no—
345C22×C5—48no—
346C22×C5—42no—
347C22×C5—42no—
348C22×C5—82no—
349C22×C5—84no—
350C22×C5#38512yes—
351C22×C5#38514yes—
352C22×C5#38512yes—
353C22×C5B(4,𝔽2)12yes—
354C22×C5#45812yes—
355C22×C5C22×C4⋊C411yescharacteristic
356C22×C5C2×C4×D412yes—
357C22×C5C2×#12011yescharacteristic
358C22×C5C2×C22⋊Q812yes—
359C22×C5C2×#12311yescharacteristic
360C4×C5—24no—
361C4×C5—48no—
362C4×C5—44no—
363C4×C5—44no—
364C4×C5—44no—
365C4×C5—82no—
366C24—21no—
367C24—21no—
368C24—22no—
369C24—42no—
370C24—42no—
371C24—42no—
372C24—42no—
373C24C5×C4⋊C414yescomplemented
374C24C22×C4×C512yes—
375C24C2×C5×D411yescharacteristic
376C24C2×C5×D412yes—
377C24C2×C5×D412yes—
378C24C2×C5×D411yescharacteristic
379C24C2×C5×D412yes—
380C24C2×C5×Q812yes—
381C24C5×#4114yes—
382C24C24×C511yescharacteristic
383C2×D4—28no—
384C2×D4—28no—
385C2×D4—24no—
386C2×D4—28no—
387C2×D4—28no—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4C5×C4⋊C418yescomplemented
392C2×D4C22×C4×C514yes—
393C2×D4C2×C5×Q814yes—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—28no—
399C22×C4—28no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—44no—
411C22×C4—44no—
412C22×C4—48no—
413C22×C4—44no—
414C22×C4—44no—
415C22×C4—42no—
416C22×C4—44no—
417C22×C4—41no—
418C22×C4—42no—
419C22×C4—41no—
420C22×C4—44no—
421C22×C4—44no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—82no—
426C22×C4—82no—
427C22×C4C5×C4⋊C414yescomplemented
428C22×C4C2×C5×D412yes—
429C22×C4C2×C5×D414yes—
430C22×C4C2×C5×D414yes—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—416no—
434C22⋊C4—28no—
435C22⋊C4—28no—
436C22⋊C4—24no—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—48no—
443C22⋊C4—42no—
444C22⋊C4C22×C4×C518yescomplemented
445C42—28no—
446C2×C5—22no—
447C2×C5—21no—
448C2×C5—21no—
449C2×C5—22no—
450C2×C5—22no—
451C2×C5—24no—
452C2×C5—44no—
453C2×C5#186714yesdirect product factor
454C2×C5C2×#38511yescharacteristic
455C2×C5C2×B(4,𝔽2)11yescharacteristic
456C2×C5C2×#45811yescharacteristic
457C23—24no—
458C23—22no—
459C23—24no—
460C23—22no—
461C23—24no—
462C23—22no—
463C23—24no—
464C23—22no—
465C23—42no—
466C23—41no—
467C23—41no—
468C23—44no—
469C23—42no—
470C23—41no—
471C23—44no—
472C23—48no—
473C23—41no—
474C23—42no—
475C23—48no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—81no—
480C23—81no—
481C23—84no—
482C23C2×C5×C4⋊C412yes—
483C23C2×C5×C4⋊C412yes—
484C23C2×C5×C4⋊C414yescomplemented
485C23C4×C5×D414yes—
486C23C4×C5×D414yes—
487C23C5×#12011yescharacteristic
488C23C5×#12012yes—
489C23C5×#12011yescharacteristic
490C23C5×C22⋊Q814yes—
491C23C5×C22⋊Q814yes—
492C23C5×#12312yes—
493C23C5×#12312yes—
494C23C23×C4×C511yescharacteristic
495C23C22×C5×D411yescharacteristic
496C23C22×C5×D412yes—
497C23C22×C5×Q811yescharacteristic
498C23C2×C5×#4112yes—
499D4—216no—
500D4—28no—
501D4—28no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—28no—
508C2×C4—28no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—44no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—48no—
515C2×C4—44no—
516C2×C4—44no—
517C2×C4—416no—
518C2×C4—44no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—84no—
530C2×C4—84no—
531C2×C4—84no—
532C2×C4C2×C5×C4⋊C414yescomplemented
533C5C2×#186711yescharacteristic, direct product factor, Sylow
534C22—22no—
535C22—21no—
536C22—22no—
537C22—21no—
538C22—22no—
539C22—21no—
540C22—22no—
541C22—21no—
542C22—28no—
543C22—24no—
544C22—24no—
545C22—28no—
546C22—24no—
547C22—42no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—41no—
552C22—41no—
553C22—42no—
554C22—44no—
555C22—42no—
556C22—42no—
557C22—48no—
558C22—82no—
559C22—84no—
560C22C5×#38512yes—
561C22C5×#38514yes—
562C22C5×#38512yes—
563C22C5×B(4,𝔽2)12yes—
564C22C5×#45812yes—
565C22C22×C5×C4⋊C411yescharacteristic
566C22C2×C4×C5×D412yes—
567C22C2×C5×#12011yescharacteristic
568C22C2×C5×C22⋊Q812yes—
569C22C2×C5×#12311yescharacteristic
570C4—24no—
571C4—48no—
572C4—44no—
573C4—44no—
574C4—44no—
575C4—82no—
576C2—22no—
577C2—21no—
578C2—21no—
579C2—22no—
580C2—24no—
581C2—22no—
582C2—44no—
583C2C5×#186714yesdirect product factor
584C2C2×C5×#38511yescharacteristic
585C2C2×C5×B(4,𝔽2)11yescharacteristic
586C2C2×C5×#45811yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutatorC23C23×C4×C5
Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C25×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C5×#385C2semidirect
5. C5×#1867C2direct (N × H)
6. C2×C5×#342C2semidirect
21. C2×C5×#99C4semidirect
26. C5×#385C22semidirect
29. C5×#342C22semidirect
30. C2×#1867C5direct (N × H)
76. C2×C5×C22⋊C4C2×C4semidirect
82. C5×#99C2×C4semidirect
88. C2×#385C2×C5semidirect
89. #1867C2×C5direct (N × H)
90. C2×#342C2×C5semidirect
98. C24×C5C4⋊C4semidirect
116. C2×C5×D4C4⋊C4semidirect
152. C22×C4×C5C4⋊C4semidirect
169. C5×C22⋊C4C22×C4semidirect
185. C2×#99C4×C5semidirect
190. #385C22×C5semidirect
193. #342C22×C5semidirect
221. C23×C5C2×C4⋊C4semidirect
269. C2×C4×C5C2×C4⋊C4semidirect
315. C2×C22⋊C4C2×C4×C5semidirect
321. #99C2×C4×C5semidirect
373. C24C5×C4⋊C4semidirect
391. C2×D4C5×C4⋊C4semidirect
427. C22×C4C5×C4⋊C4semidirect
444. C22⋊C4C22×C4×C5semidirect
453. C2×C5#1867direct (N × H)
484. C23C2×C5×C4⋊C4semidirect
532. C2×C4C2×C5×C4⋊C4semidirect
533. C5C2×#1867direct (N × H)
583. C2C5×#1867direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5182
C22×C5×#992
C2×C5×#3862
C2×C5×#3852
C5×#18672
C2×C5×#3422
C2×#18675