Finite Group Databasebeta

← C5×#82936 #14425658

Subgroups — C5×#82936 #14425658

Order 1920.

1532 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5964C211yesmaximal, characteristic, complemented
2C3×C5×#525C211yesmaximal, characteristic, complemented
3C5×#5791C212yesmaximal, complemented
4C5×#5240C211yesmaximal, characteristic, complemented
5C5×#5053C214yesmaximal, complemented
6C5×#5032C214yesmaximal, complemented
7C5×#5006C212yesmaximal, complemented
8C5×#3025—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C23×C3×C4×C5C2211yescharacteristic, complemented
11C5×#1010—22no—
12C5×#1009—22no—
13C5×D3×#41—24no—
14C5×#1007—21no—
15C5×#1004—21no—
16C5×#1004C2214yes—
17C2×C5×#235—22no—
18C2×C5×#235C2212yes—
19C3×C5×#123C2212yescomplemented
20C3×C5×C22⋊Q8—21no—
21C3×C5×#121—21no—
22C3×C5×#120C2212yescomplemented
23C3×C4×C5×D4—22no—
24C3×C5×#117C2211yescharacteristic, complemented
25C5×#953C2214yescomplemented
26C5×#930—22no—
27C5×#929C2214yescomplemented
28C4×C5×#67—24no—
29C5×#926C2212yescomplemented
30C5×#924—22no—
31C5×#834C2214yescomplemented
32C5×#806C2218yescomplemented
33#82936C511yesmaximal, characteristic, direct product factor, Hall
34C5×#585—31no—
35C5×#525—32no—
36C5×#525D311yescharacteristic, complemented
37C5×#458—34no—
38C5×B(4,𝔽2)—34no—
39C5×#410—31no—
40C5×#410—32no—
41C24×C3×C5C2311yescharacteristic
42C3×C5×#41—22no—
43C3×C5×#41—22no—
44C2×C3×C5×Q8D411yescharacteristic, complemented
45C2×C3×C5×D4—22no—
46C2×C3×C5×D4D411yescharacteristic, complemented
47C2×C3×C5×D4C2312yes—
48C22×C3×C4×C5—22no—
49C22×C3×C4×C5—22no—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5D412yescomplemented
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C2×C5×#67—24no—
56C2×C5×#67—24no—
57C2×C5×#67C2314yes—
58C5×#239—24no—
59C5×D3×Q8—24no—
60C5×#237—24no—
61C5×#237—28no—
62C5×D3×D4—24no—
63C5×D3×D4—28no—
64C5×#235—24no—
65C5×#235—24no—
66C5×#235—22no—
67C5×#235—24no—
68C5×#235—22no—
69C5×#235—22no—
70C5×#235—22no—
71C2×C5×D12—22no—
72C2×C5×D12D412yescomplemented
73C2×C4×C5×D3—24no—
74C2×C4×C5×D3D414yescomplemented
75C2×C5×Dic6—22no—
76C2×C5×Dic6D412yescomplemented
77C3×C5×C4⋊C4—21no—
78C3×C5×C4⋊C4—22no—
79C3×C5×C22⋊C4—22no—
80C3×C5×C22⋊C4—22no—
81C3×C5×C22⋊C4C2312yes—
82C3×C42×C5—21no—
83C5×#217—24no—
84C5×#217C2314yes—
85C5×(C2×D3)⋊C4—24no—
86C5×C4⋊Dic3—22no—
87C5×Dic3⋊C4—24no—
88C4×C5×Dic3—22no—
89#5964C2×C511yescharacteristic, complemented
90C3×#525C2×C511yescharacteristic, complemented
91#5791C2×C512yescomplemented
92#5240C2×C511yescharacteristic, complemented
93#5053C2×C514yescomplemented
94#5032C2×C514yescomplemented
95#5006C2×C512yescomplemented
96C5×2−1+4—62no—
97C5×2−1+4—61no—
98C5×H(5,𝔽2)—34no—
99C5×H(5,𝔽2)—62no—
100C5×H(5,𝔽2)—61no—
101C2×C5×#41—32no—
102C2×C5×#41—64no—
103C2×C5×#41—62no—
104C2×C5×#41C2×D311yescharacteristic
105C23×C4×C5C2×D311yescharacteristic, complemented
106C5×#123—34no—
107C5×#123C2×D312yescomplemented
108C5×C22⋊Q8—21no—
109C5×C22⋊Q8—62no—
110C5×#121—21no—
111C5×#121—62no—
112C5×#120—34no—
113C5×#120C2×D312yescomplemented
114C4×C5×D4—22no—
115C4×C5×D4—64no—
116C5×#117—32no—
117C5×#117C2×D311yescharacteristic, complemented
118C5×#99—34no—
119C5×#99—38no—
120#3025—31noSylow
121C23×C3×C5—22no—
122C23×C3×C5—21no—
123C23×C3×C5—42no—
124C23×C3×C5C2×D412yes—
125C23×C3×C5C2411yescharacteristic
126C22×C5×D3—24no—
127C22×C5×D3C2×D414yes—
128C3×C5×Q8—22no—
129C3×C5×D4—24no—
130C3×C5×D4—22no—
131C3×C5×D4—44no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—41no—
138C2×C3×C4×C5—42no—
139C2×C3×C4×C5—41no—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2×D411yescharacteristic
144C2×C3×C4×C5C2×D411yescharacteristic
145C5×#67—28no—
146C5×#67—24no—
147C5×#67—24no—
148C5×#67—48no—
149C2×C5×Dic3—24no—
150C2×C5×Dic3—24no—
151C2×C5×Dic3C2×D414yes—
152C5×D12—24no—
153C5×D12—22no—
154C5×D12—22no—
155C4×C5×D3—28no—
156C4×C5×D3—24no—
157C4×C5×D3—24no—
158C5×Dic6—24no—
159C5×Dic6—22no—
160C5×Dic6—22no—
161C2×C3×#41C22×C511yescharacteristic
162C23×C3×C4C22×C511yescharacteristic, complemented
163#1010—22no—
164#1009—22no—
165D3×#41—24no—
166#1007—21no—
167#1004—21no—
168#1004C22×C514yes—
169C2×#235—22no—
170C2×#235C22×C512yes—
171C3×#123C22×C512yescomplemented
172C3×C22⋊Q8—21no—
173C3×#121—21no—
174C3×#120C22×C512yescomplemented
175C3×C4×D4—22no—
176C3×#117C22×C511yescharacteristic, complemented
177#953C22×C514yescomplemented
178#930—22no—
179#929C22×C514yescomplemented
180C4×#67—24no—
181#926C22×C512yescomplemented
182#924—22no—
183#834C22×C514yescomplemented
184#806C22×C518yescomplemented
185C24×C5C22×D311yescharacteristic
186C5×#41—22no—
187C5×#41—22no—
188C5×#41—64no—
189C5×#41—64no—
190C5×#41—68no—
191C5×#41—64no—
192C5×#41—64no—
193C5×#41—62no—
194C5×#41—62no—
195C5×#41—62no—
196C5×#41—62no—
197C5×#41—64no—
198C2×C5×Q8—32no—
199C2×C5×Q8—62no—
200C2×C5×Q8—64no—
201C2×C5×Q8#6711yescharacteristic, complemented
202C2×C5×D4—22no—
203C2×C5×D4—34no—
204C2×C5×D4—32no—
205C2×C5×D4—62no—
206C2×C5×D4—68no—
207C2×C5×D4—64no—
208C2×C5×D4—64no—
209C2×C5×D4—64no—
210C2×C5×D4#6711yescharacteristic, complemented
211C2×C5×D4C22×D312yes—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—34no—
217C22×C4×C5—64no—
218C22×C4×C5#6712yescomplemented
219C22×C4×C5C22×D311yescharacteristic
220C22×C4×C5C22×D311yescharacteristic
221C5×C4⋊C4—21no—
222C5×C4⋊C4—22no—
223C5×C4⋊C4—64no—
224C5×C4⋊C4—62no—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—22no—
227C5×C22⋊C4—34no—
228C5×C22⋊C4—64no—
229C5×C22⋊C4—64no—
230C5×C22⋊C4C22×D312yes—
231C42×C5—21no—
232C42×C5—62no—
233#585—31no—
234#525—32no—
235#525C5×D311yescharacteristic, complemented
236#458—34no—
237B(4,𝔽2)—34no—
238#410—31no—
239#410—32no—
240C22×C3×C5—24no—
241C22×C3×C5—22no—
242C22×C3×C5—22no—
243C22×C3×C5—41no—
244C22×C3×C5—42no—
245C22×C3×C5—42no—
246C22×C3×C5—41no—
247C22×C3×C5—41no—
248C22×C3×C5C22×D412yes—
249C22×C3×C5C22×D411yescharacteristic
250C2×C5×D3—24no—
251C2×C5×D3—44no—
252C2×C5×D3—84no—
253C3×C4×C5—22no—
254C3×C4×C5—42no—
255C3×C4×C5—41no—
256C3×C4×C5#12011yescharacteristic
257C3×C4×C5#12012yes—
258C3×C4×C5#12011yescharacteristic
259C5×Dic3—24no—
260C5×Dic3—44no—
261C24×C3C23×C511yescharacteristic
262C3×#41—22no—
263C3×#41—22no—
264C2×C3×Q8C5×D411yescharacteristic, complemented
265C2×C3×D4—22no—
266C2×C3×D4C5×D411yescharacteristic, complemented
267C2×C3×D4C23×C512yes—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4C5×D412yescomplemented
273C22×C3×C4C23×C511yescharacteristic
274C22×C3×C4C23×C511yescharacteristic
275C2×#67—24no—
276C2×#67—24no—
277C2×#67C23×C514yes—
278#239—24no—
279D3×Q8—24no—
280#237—24no—
281#237—28no—
282D3×D4—24no—
283D3×D4—28no—
284#235—24no—
285#235—24no—
286#235—22no—
287#235—24no—
288#235—22no—
289#235—22no—
290#235—22no—
291C2×D12—22no—
292C2×D12C5×D412yescomplemented
293C2×C4×D3—24no—
294C2×C4×D3C5×D414yescomplemented
295C2×Dic6—22no—
296C2×Dic6C5×D412yescomplemented
297C3×C4⋊C4—21no—
298C3×C4⋊C4—22no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4C23×C512yes—
302C3×C42—21no—
303#217—24no—
304#217C23×C514yes—
305(C2×D3)⋊C4—24no—
306C4⋊Dic3—22no—
307Dic3⋊C4—24no—
308C4×Dic3—22no—
309C23×C5—22no—
310C23×C5—21no—
311C23×C5—34no—
312C23×C5—42no—
313C23×C5—64no—
314C23×C5C2×#6712yes—
315C23×C5C23×D311yescharacteristic
316C5×Q8—22no—
317C5×Q8—64no—
318C5×Q8—62no—
319C5×Q8—62no—
320C5×D4—24no—
321C5×D4—22no—
322C5×D4—44no—
323C5×D4—64no—
324C5×D4—68no—
325C5×D4—64no—
326C5×D4—64no—
327C5×D4—62no—
328C5×D4—62no—
329C5×D4—128no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—21no—
335C2×C4×C5—34no—
336C2×C4×C5—41no—
337C2×C4×C5—42no—
338C2×C4×C5—41no—
339C2×C4×C5—68no—
340C2×C4×C5—64no—
341C2×C4×C5—64no—
342C2×C4×C5—64no—
343C2×C4×C5—64no—
344C2×C4×C5D3×D412yes—
345C2×C4×C5D3×D412yes—
346C2×C4×C5C2×#6712yes—
347C2×C4×C5C2×#6711yescharacteristic
348C2×C4×C5C2×#6711yescharacteristic
3492−1+4—62no—
3502−1+4—61no—
351H(5,𝔽2)—34no—
352H(5,𝔽2)—62no—
353H(5,𝔽2)—61no—
354C2×#41—32no—
355C2×#41—64no—
356C2×#41—62no—
357C2×#41C2×C5×D311yescharacteristic
358C23×C4C2×C5×D311yescharacteristic, complemented
359#123—34no—
360#123C2×C5×D312yescomplemented
361C22⋊Q8—21no—
362C22⋊Q8—62no—
363#121—21no—
364#121—62no—
365#120—34no—
366#120C2×C5×D312yescomplemented
367C4×D4—22no—
368C4×D4—64no—
369#117—32no—
370#117C2×C5×D311yescharacteristic, complemented
371#99—34no—
372#99—38no—
373C2×C3×C5—22no—
374C2×C3×C5—21no—
375C2×C3×C5—42no—
376C2×C3×C5—42no—
377C2×C3×C5C2×#12011yescharacteristic
378C5×D3—44no—
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—42no—
382C23×C3C2×C5×D412yes—
383C23×C3C24×C511yescharacteristic
384C22×D3—24no—
385C22×D3C2×C5×D414yes—
386C3×Q8—22no—
387C3×D4—24no—
388C3×D4—22no—
389C3×D4—44no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—41no—
396C2×C3×C4—42no—
397C2×C3×C4—41no—
398C2×C3×C4C2×C5×D412yes—
399C2×C3×C4C2×C5×D412yes—
400C2×C3×C4C2×C5×D412yes—
401C2×C3×C4C2×C5×D411yescharacteristic
402C2×C3×C4C2×C5×D411yescharacteristic
403#67—28no—
404#67—24no—
405#67—24no—
406#67—48no—
407C2×Dic3—24no—
408C2×Dic3—24no—
409C2×Dic3C2×C5×D414yes—
410D12—24no—
411D12—22no—
412D12—22no—
413C4×D3—28no—
414C4×D3—24no—
415C4×D3—24no—
416Dic6—24no—
417Dic6—22no—
418Dic6—22no—
419C22×C5—22no—
420C22×C5—24no—
421C22×C5—22no—
422C22×C5—41no—
423C22×C5—42no—
424C22×C5—41no—
425C22×C5—42no—
426C22×C5—41no—
427C22×C5—64no—
428C22×C5—124no—
429C22×C5—244no—
430C22×C5C2×D3×D412yes—
431C22×C5C22×#6711yescharacteristic
432C4×C5—22no—
433C4×C5—42no—
434C4×C5—41no—
435C4×C5—64no—
436C4×C5—124no—
437C4×C5#93711yescharacteristic
438C4×C5#93712yes—
439C4×C5#93711yescharacteristic
440C24C22×C5×D311yescharacteristic
441#41—22no—
442#41—22no—
443#41—64no—
444#41—64no—
445#41—68no—
446#41—64no—
447#41—64no—
448#41—62no—
449#41—62no—
450#41—62no—
451#41—62no—
452#41—64no—
453C2×Q8—32no—
454C2×Q8—62no—
455C2×Q8—64no—
456C2×Q8C5×#6711yescharacteristic, complemented
457C2×D4—22no—
458C2×D4—34no—
459C2×D4—32no—
460C2×D4—62no—
461C2×D4—68no—
462C2×D4—64no—
463C2×D4—64no—
464C2×D4—64no—
465C2×D4C5×#6711yescharacteristic, complemented
466C2×D4C22×C5×D312yes—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—34no—
472C22×C4—64no—
473C22×C4C5×#6712yescomplemented
474C22×C4C22×C5×D311yescharacteristic
475C22×C4C22×C5×D311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—22no—
478C4⋊C4—64no—
479C4⋊C4—62no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—34no—
483C22⋊C4—64no—
484C22⋊C4—64no—
485C22⋊C4C22×C5×D312yes—
486C42—21no—
487C42—62no—
488C3×C5#302511yescharacteristic, complemented, Hall
489C22×C3—24no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—41no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3C22×C5×D412yes—
498C22×C3C22×C5×D411yescharacteristic
499C2×D3—24no—
500C2×D3—44no—
501C2×D3—84no—
502C3×C4—22no—
503C3×C4—42no—
504C3×C4—41no—
505C3×C4C5×#12011yescharacteristic
506C3×C4C5×#12012yes—
507C3×C4C5×#12011yescharacteristic
508Dic3—24no—
509Dic3—44no—
510C2×C5—21no—
511C2×C5—22no—
512C2×C5—42no—
513C2×C5—42no—
514C2×C5—124no—
515C2×C5C2×#93711yescharacteristic
516C23—22no—
517C23—21no—
518C23—34no—
519C23—42no—
520C23—64no—
521C23C2×C5×#6712yes—
522C23C23×C5×D311yescharacteristic
523Q8—22no—
524Q8—64no—
525Q8—62no—
526Q8—62no—
527D4—24no—
528D4—22no—
529D4—44no—
530D4—64no—
531D4—68no—
532D4—64no—
533D4—64no—
534D4—62no—
535D4—62no—
536D4—128no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—34no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—68no—
547C2×C4—64no—
548C2×C4—64no—
549C2×C4—64no—
550C2×C4—64no—
551C2×C4C5×D3×D412yes—
552C2×C4C5×D3×D412yes—
553C2×C4C2×C5×#6712yes—
554C2×C4C2×C5×#6711yescharacteristic
555C2×C4C2×C5×#6711yescharacteristic
556C2×C3—22no—
557C2×C3—21no—
558C2×C3—42no—
559C2×C3—42no—
560C2×C3C2×C5×#12011yescharacteristic
561D3—44no—
562C5#8293611yescharacteristic, direct product factor, Sylow
563C22—22no—
564C22—24no—
565C22—22no—
566C22—41no—
567C22—42no—
568C22—41no—
569C22—42no—
570C22—41no—
571C22—64no—
572C22—124no—
573C22—244no—
574C22C2×C5×D3×D412yes—
575C22C22×C5×#6711yescharacteristic
576C4—22no—
577C4—42no—
578C4—41no—
579C4—64no—
580C4—124no—
581C4C5×#93711yescharacteristic
582C4C5×#93711yescharacteristic
583C4C5×#93712yes—
584C3C5×#302511yescharacteristic, complemented, Sylow
585C2—21no—
586C2—22no—
587C2—42no—
588C2—42no—
589C2—124no—
590C2C2×C5×#93711yescharacteristic
subgroupG/H
centerC4×C5#937
commutator, cosocleC23×C3C24×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#525C2
socleC2×C3×C5C2×#120
hypercenterC5×#525D3
hypocenterC3C5×#3025
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C5×#525

Complements

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

NH ≅ G/Ntype
1. C5×#5964C2semidirect
2. C3×C5×#525C2semidirect
3. C5×#5791C2semidirect
4. C5×#5240C2semidirect
5. C5×#5053C2semidirect
6. C5×#5032C2semidirect
7. C5×#5006C2semidirect
10. C23×C3×C4×C5C22semidirect
19. C3×C5×#123C22semidirect
22. C3×C5×#120C22semidirect
24. C3×C5×#117C22semidirect
25. C5×#953C22semidirect
27. C5×#929C22semidirect
29. C5×#926C22semidirect
31. C5×#834C22semidirect
32. C5×#806C22semidirect
33. #82936C5direct (N × H)
36. C5×#525D3semidirect
44. C2×C3×C5×Q8D4semidirect
46. C2×C3×C5×D4D4semidirect
52. C22×C3×C4×C5D4semidirect
72. C2×C5×D12D4semidirect
74. C2×C4×C5×D3D4semidirect
76. C2×C5×Dic6D4semidirect
89. #5964C2×C5semidirect
90. C3×#525C2×C5semidirect
91. #5791C2×C5semidirect
92. #5240C2×C5semidirect
93. #5053C2×C5semidirect
94. #5032C2×C5semidirect
95. #5006C2×C5semidirect
105. C23×C4×C5C2×D3semidirect
107. C5×#123C2×D3semidirect
113. C5×#120C2×D3semidirect
117. C5×#117C2×D3semidirect
162. C23×C3×C4C22×C5semidirect
171. C3×#123C22×C5semidirect
174. C3×#120C22×C5semidirect
176. C3×#117C22×C5semidirect
177. #953C22×C5semidirect
179. #929C22×C5semidirect
181. #926C22×C5semidirect
183. #834C22×C5semidirect
184. #806C22×C5semidirect
201. C2×C5×Q8#67semidirect
210. C2×C5×D4#67semidirect
218. C22×C4×C5#67semidirect
235. #525C5×D3semidirect
264. C2×C3×Q8C5×D4semidirect
266. C2×C3×D4C5×D4semidirect
272. C22×C3×C4C5×D4semidirect
292. C2×D12C5×D4semidirect
294. C2×C4×D3C5×D4semidirect
296. C2×Dic6C5×D4semidirect
358. C23×C4C2×C5×D3semidirect
360. #123C2×C5×D3semidirect
366. #120C2×C5×D3semidirect
370. #117C2×C5×D3semidirect
456. C2×Q8C5×#67semidirect
465. C2×D4C5×#67semidirect
473. C22×C4C5×#67semidirect
488. C3×C5#3025semidirect
562. C5#82936direct (N × H)
584. C3C5×#3025semidirect

Maximal subgroups

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

subgroupindex
C5×#59642
C3×C5×#5252
C5×#57912
C5×#52402
C5×#50532
C5×#50322
C5×#50062
C5×#30253
#829365