Finite Group Databasebeta

← C5×#9996 #11932716

Subgroups — C5×#9996 #11932716

Order 1280.

686 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3100C211yesmaximal, characteristic, complemented
2C5×#3036C211yesmaximal, characteristic, complemented
3C5×#2535C211yesmaximal, characteristic, complemented
4C5×#1517C211yesmaximal, characteristic, complemented
5C5×#1486C211yesmaximal, characteristic, complemented
6C5×#1478C211yesmaximal, characteristic, complemented
7C5×#1286C211yesmaximal, characteristic, complemented
8C2×C5×AGL(1,ℤ/8)—21no—
9C5×#532C2211yescharacteristic
10C2×C5×#121—21no—
11C2×C4×C5×D4C2211yescharacteristic
12C2×C4×C5×D4C2211yescharacteristic
13C5×#480—21no—
14C5×#474—21no—
15C5×#463—22no—
16C5×#461—21no—
17C5×#459—21no—
18C5×#459—21no—
19C5×#447—21no—
20C4×C5×D8—22no—
21C5×#431C2211yescharacteristic
22C5×#431C2211yescharacteristic
23C5×#423C2211yescharacteristic
24C5×#417—21no—
25C5×#397—21no—
26C5×#392—21no—
27C5×#386—22no—
28C5×#382C2211yescharacteristic
29C5×#380—21no—
30C5×#327—22no—
31C5×D4⋊C8—22no—
32C5×D4⋊C8—22no—
33#9996C511yesmaximal, characteristic, direct product factor, Sylow
34C2×C5×#41—21no—
35C22×C5×D4—22no—
36C22×C5×D4D411yescharacteristic
37C22×C5×D4D411yescharacteristic
38C23×C4×C5—21no—
39C23×C4×C5—21no—
40C5×AGL(1,ℤ/8)—42no—
41C5×AGL(1,ℤ/8)—42no—
42C2×C5×SD16—22no—
43C2×C5×D8—22no—
44C2×C5×D8—22no—
45C2×C5×M16—21no—
46C5×C4⋊Q8D411yescharacteristic, complemented
47C5×#127D411yescharacteristic, complemented
48C5×#124—21no—
49C5×#121—21no—
50C5×#121—21no—
51C5×#121—42no—
52C5×#121—42no—
53C4×C5×D4—21no—
54C4×C5×D4—21no—
55C4×C5×D4—21no—
56C4×C5×D4—21no—
57C4×C5×D4—21no—
58C4×C5×D4—21no—
59C4×C5×D4—21no—
60C4×C5×D4—21no—
61C4×C5×D4—21no—
62C4×C5×D4—21no—
63C2×C5×C4⋊C4—21no—
64C2×C5×C4⋊C4D411yescharacteristic
65C2×C5×C4⋊C4D411yescharacteristic
66C2×C5×C22⋊C4—22no—
67C2×C5×C22⋊C4—21no—
68C2×C5×C22⋊C4—21no—
69C2×C5×C22⋊C4—22no—
70C2×C42×C5C2311yescharacteristic
71C5×#107—22no—
72C5×C4⋊C8—21no—
73C5×C4⋊C8—21no—
74C5×C4⋊C8—21no—
75C5×C4⋊C8D412yescomplemented
76C5×#103—22no—
77C5×#102—22no—
78C5×#102—22no—
79C5×#102—22no—
80C5×C22⋊C8—21no—
81C5×C22⋊C8—21no—
82C4×C5×C8—21no—
83C4×C5×C8D412yescomplemented
84C5×#95—22no—
85C5×#95—21no—
86C5×#95D412yes—
87#3100C2×C511yescharacteristic, complemented
88#3036C2×C511yescharacteristic, complemented
89#2535C2×C511yescharacteristic, complemented
90#1517C2×C511yescharacteristic, complemented
91#1486C2×C511yescharacteristic, complemented
92#1478C2×C511yescharacteristic, complemented
93#1286C2×C511yescharacteristic, complemented
94C24×C5—21no—
95C24×C5—21no—
96C5×#41—41no—
97C5×#41—41no—
98C5×#41—41no—
99C5×#41—41no—
100C2×C5×Q8—21no—
101C2×C5×D4—21no—
102C2×C5×D4—21no—
103C2×C5×D4—21no—
104C2×C5×D4—21no—
105C2×C5×D4—21no—
106C2×C5×D4—21no—
107C2×C5×D4—21no—
108C2×C5×D4—21no—
109C2×C5×D4—21no—
110C2×C5×D4—21no—
111C2×C5×D4—42no—
112C2×C5×D4—44no—
113C2×C5×D4—44no—
114C2×C5×D4—41no—
115C2×C5×D4—82no—
116C2×C5×D4D812yescomplemented
117C22×C4×C5—21no—
118C22×C4×C5—21no—
119C22×C4×C5—22no—
120C22×C4×C5—41no—
121C22×C4×C5—41no—
122C22×C4×C5—41no—
123C22×C4×C5—41no—
124C22×C4×C5—41no—
125C22×C4×C5—41no—
126C22×C4×C5—41no—
127C22×C4×C5—41no—
128C22×C4×C5—41no—
129C22×C4×C5—82no—
130C22×C4×C5C2×D411yescharacteristic
131C22×C4×C5C2×D411yescharacteristic
132C22×C4×C5C2×D411yescharacteristic
133C5×SD16—44no—
134C5×D8—44no—
135C5×D8—44no—
136C5×M16—41no—
137C5×M16—41no—
138C2×C5×C8—22no—
139C2×C5×C8—22no—
140C2×C5×C8—41no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—41no—
148C5×C4⋊C4—41no—
149C5×C22⋊C4—44no—
150C5×C22⋊C4—41no—
151C5×C22⋊C4—41no—
152C5×C22⋊C4—41no—
153C5×C22⋊C4—41no—
154C5×C22⋊C4—41no—
155C5×C22⋊C4—41no—
156C5×C22⋊C4—82no—
157C42×C5C2×D411yescharacteristic
158C42×C5C2×D411yescharacteristic
159C42×C5C2×D411yescharacteristic
160C42×C5#4111yescharacteristic
161C2×AGL(1,ℤ/8)—21no—
162#532C22×C511yescharacteristic
163C2×#121—21no—
164C2×C4×D4C22×C511yescharacteristic
165C2×C4×D4C22×C511yescharacteristic
166#480—21no—
167#474—21no—
168#463—22no—
169#461—21no—
170#459—21no—
171#459—21no—
172#447—21no—
173C4×D8—22no—
174#431C22×C511yescharacteristic
175#431C22×C511yescharacteristic
176#423C22×C511yescharacteristic
177#417—21no—
178#397—21no—
179#392—21no—
180#386—22no—
181#382C22×C511yescharacteristic
182#380—21no—
183#327—22no—
184D4⋊C8—22no—
185D4⋊C8—22no—
186C23×C5—22no—
187C23×C5—22no—
188C23×C5—41no—
189C23×C5—42no—
190C23×C5—42no—
191C23×C5—41no—
192C23×C5—41no—
193C23×C5—41no—
194C23×C5—41no—
195C23×C5—41no—
196C23×C5—41no—
197C23×C5—41no—
198C23×C5—41no—
199C23×C5#12011yescharacteristic
200C5×Q8—41no—
201C5×Q8—41no—
202C5×D4—22no—
203C5×D4—22no—
204C5×D4—22no—
205C5×D4—22no—
206C5×D4—41no—
207C5×D4—41no—
208C5×D4—42no—
209C5×D4—41no—
210C5×D4—41no—
211C5×D4—41no—
212C5×D4—41no—
213C5×D4—81no—
214C5×D4—88no—
215C5×D4—81no—
216C5×D4—81no—
217C2×C4×C5—41no—
218C2×C4×C5—41no—
219C2×C4×C5—42no—
220C2×C4×C5—42no—
221C2×C4×C5—42no—
222C2×C4×C5—41no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5—42no—
227C2×C4×C5—41no—
228C2×C4×C5—82no—
229C2×C4×C5—82no—
230C2×C4×C5—81no—
231C2×C4×C5—81no—
232C2×C4×C5—81no—
233C2×C4×C5—81no—
234C2×C4×C5—81no—
235C2×C4×C5—81no—
236C2×C4×C5#12011yescharacteristic
237C2×C4×C5#12011yescharacteristic
238C2×C4×C5#12111yescharacteristic
239C2×C4×C5#12111yescharacteristic
240C2×C4×C5#12111yescharacteristic
241C2×C4×C5#12711yescharacteristic
242C2×C4×C5C2×D811yescharacteristic
243C2×C4×C5#13511yescharacteristic
244C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
245C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
246C5×C8—42no—
247C5×C8—42no—
248C5×C8—81no—
249C2×#41—21no—
250C22×D4—22no—
251C22×D4C5×D411yescharacteristic
252C22×D4C5×D411yescharacteristic
253C23×C4—21no—
254C23×C4—21no—
255AGL(1,ℤ/8)—42no—
256AGL(1,ℤ/8)—42no—
257C2×SD16—22no—
258C2×D8—22no—
259C2×D8—22no—
260C2×M16—21no—
261C4⋊Q8C5×D411yescharacteristic, complemented
262#127C5×D411yescharacteristic, complemented
263#124—21no—
264#121—21no—
265#121—21no—
266#121—42no—
267#121—42no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—21no—
271C4×D4—21no—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4C5×D411yescharacteristic
280C2×C4⋊C4C5×D411yescharacteristic
281C2×C22⋊C4—22no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—22no—
285C2×C42C23×C511yescharacteristic
286#107—22no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8C5×D412yescomplemented
291#103—22no—
292#102—22no—
293#102—22no—
294#102—22no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C4×C8—21no—
298C4×C8C5×D412yescomplemented
299#95—22no—
300#95—21no—
301#95C5×D412yes—
302C22×C5—21no—
303C22×C5—21no—
304C22×C5—42no—
305C22×C5—44no—
306C22×C5—42no—
307C22×C5—42no—
308C22×C5—42no—
309C22×C5—81no—
310C22×C5—82no—
311C22×C5—81no—
312C22×C5—81no—
313C22×C5—81no—
314C22×C5—81no—
315C22×C5—81no—
316C22×C5—81no—
317C22×C5—81no—
318C22×C5—81no—
319C22×C5#39211yescharacteristic
320C22×C5#44711yescharacteristic
321C22×C5#44911yescharacteristic
322C4×C5—21no—
323C4×C5—21no—
324C4×C5—21no—
325C4×C5—21no—
326C4×C5—82no—
327C4×C5—81no—
328C4×C5—81no—
329C4×C5—81no—
330C4×C5#44711yescharacteristic
331C4×C5#44911yescharacteristic
332C4×C5#46611yescharacteristic
333C4×C5#46911yescharacteristic
334C24—21no—
335C24—21no—
336#41—41no—
337#41—41no—
338#41—41no—
339#41—41no—
340C2×Q8—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—42no—
352C2×D4—44no—
353C2×D4—44no—
354C2×D4—41no—
355C2×D4—82no—
356C2×D4C5×D812yescomplemented
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—82no—
370C22×C4C2×C5×D411yescharacteristic
371C22×C4C2×C5×D411yescharacteristic
372C22×C4C2×C5×D411yescharacteristic
373SD16—44no—
374D8—44no—
375D8—44no—
376M16—41no—
377M16—41no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—41no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C22⋊C4—44no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—82no—
397C42C2×C5×D411yescharacteristic
398C42C2×C5×D411yescharacteristic
399C42C2×C5×D411yescharacteristic
400C42C5×#4111yescharacteristic
401C2×C5—21no—
402C2×C5—21no—
403C2×C5—82no—
404C2×C5—82no—
405C2×C5—161no—
406C2×C5#199911yescharacteristic
407C2×C5#200811yescharacteristic
408C2×C5#201011yescharacteristic
409C23—22no—
410C23—22no—
411C23—41no—
412C23—42no—
413C23—42no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23C5×#12011yescharacteristic
423Q8—41no—
424Q8—41no—
425D4—22no—
426D4—22no—
427D4—22no—
428D4—22no—
429D4—41no—
430D4—41no—
431D4—42no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—81no—
437D4—88no—
438D4—81no—
439D4—81no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—82no—
452C2×C4—82no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4C5×#12011yescharacteristic
460C2×C4C5×#12011yescharacteristic
461C2×C4C5×#12111yescharacteristic
462C2×C4C5×#12111yescharacteristic
463C2×C4C5×#12111yescharacteristic
464C2×C4C5×#12711yescharacteristic
465C2×C4C2×C5×D811yescharacteristic
466C2×C4C5×#13511yescharacteristic
467C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
468C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
469C8—42no—
470C8—42no—
471C8—81no—
472C5#999611yescharacteristic, direct product factor, Sylow
473C22—21no—
474C22—21no—
475C22—42no—
476C22—44no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—81no—
481C22—82no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22C5×#39211yescharacteristic
491C22C5×#44711yescharacteristic
492C22C5×#44911yescharacteristic
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—82no—
498C4—81no—
499C4—81no—
500C4—81no—
501C4C5×#44711yescharacteristic
502C4C5×#44911yescharacteristic
503C4C5×#46611yescharacteristic
504C4C5×#46911yescharacteristic
505C2—21no—
506C2—21no—
507C2—82no—
508C2—82no—
509C2—161no—
510C2C5×#199911yescharacteristic
511C2C5×#200811yescharacteristic
512C2C5×#201011yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC2×C42C23×C5
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3100C2semidirect
2. C5×#3036C2semidirect
3. C5×#2535C2semidirect
4. C5×#1517C2semidirect
5. C5×#1486C2semidirect
6. C5×#1478C2semidirect
7. C5×#1286C2semidirect
33. #9996C5direct (N × H)
46. C5×C4⋊Q8D4semidirect
47. C5×#127D4semidirect
75. C5×C4⋊C8D4semidirect
83. C4×C5×C8D4semidirect
87. #3100C2×C5semidirect
88. #3036C2×C5semidirect
89. #2535C2×C5semidirect
90. #1517C2×C5semidirect
91. #1486C2×C5semidirect
92. #1478C2×C5semidirect
93. #1286C2×C5semidirect
116. C2×C5×D4D8semidirect
261. C4⋊Q8C5×D4semidirect
262. #127C5×D4semidirect
290. C4⋊C8C5×D4semidirect
298. C4×C8C5×D4semidirect
356. C2×D4C5×D8semidirect
472. C5#9996direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31002
C5×#30362
C5×#25352
C5×#15172
C5×#14862
C5×#14782
C5×#12862
#99965