Finite Group Databasebeta

← C5×#13316 #11936036

Subgroups — C5×#13316 #11936036

Order 1280.

604 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#509C211yesmaximal, characteristic, complemented
2C5×#3054C211yesmaximal, characteristic, complemented
3C2×C5×#469C211yesmaximal, characteristic, complemented
4C2×C5×#360C211yesmaximal, characteristic, complemented
5C5×#2140C211yesmaximal, characteristic, complemented
6C2×C5×#349C211yesmaximal, characteristic, complemented
7C5×#1386C211yesmaximal, characteristic, complemented
8C2×C5×#135C2211yescharacteristic
9C22×C5×D8C2211yescharacteristic
10C22×C5×M16C2211yescharacteristic
11C5×#525—21no—
12C2×C5×#121—21no—
13C5×#509—22no—
14C5×#509—22no—
15C2×C5×SD32—21no—
16C2×C5×D16—21no—
17C2×C5×M32C2211yescharacteristic
18C2×C5×M32C2211yescharacteristic
19C5×#470—21no—
20C5×#469—22no—
21C5×#469—22no—
22C5×#469—21no—
23C5×#468—22no—
24C5×#427C2211yescharacteristic
25C2×C5×#106C2211yescharacteristic
26C5×#416—21no—
27C2×C5×#102—21no—
28C5×#360—22no—
29C5×#357—22no—
30C5×#349—22no—
31#13316C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41—21no—
33C22×C5×D4—21no—
34C22×C5×D4—41no—
35C23×C4×C5D411yescharacteristic
36C5×#135—21no—
37C5×#135—21no—
38C5×#135—21no—
39C5×#135—21no—
40C2×C5×Q16D411yescharacteristic, complemented
41C2×C5×SD16—21no—
42C2×C5×D8—21no—
43C2×C5×D8—21no—
44C2×C5×D8—21no—
45C2×C5×D8—21no—
46C2×C5×D8—21no—
47C2×C5×D8D411yescharacteristic, complemented
48C2×C5×D8D412yescomplemented
49C2×C5×M16—21no—
50C2×C5×M16—21no—
51C2×C5×M16—21no—
52C2×C5×M16—21no—
53C2×C5×M16—21no—
54C2×C5×M16—21no—
55C22×C5×C8D411yescharacteristic
56C22×C5×C8C2311yescharacteristic
57C5×#123—41no—
58C5×C22⋊Q8—22no—
59C5×#121—22no—
60C5×#121—24no—
61C5×#121—42no—
62C5×#120—41no—
63C4×C5×D4—42no—
64C5×#117—21no—
65C2×C5×C4⋊C4—21no—
66C2×C5×C22⋊C4—41no—
67C5×SD32—24no—
68C5×D16—24no—
69C5×M32—21no—
70C5×M32—21no—
71C5×M32—21no—
72C5×M32D412yescomplemented
73C2×C5×C16—21no—
74C2×C5×C16—21no—
75C5×#107D412yescomplemented
76C5×#106—21no—
77C5×#106—21no—
78C5×#106D412yescomplemented
79C5×#103—22no—
80C5×#102—24no—
81C5×#102—22no—
82C2×#509C2×C511yescharacteristic, complemented
83#3054C2×C511yescharacteristic, complemented
84C2×#469C2×C511yescharacteristic, complemented
85C2×#360C2×C511yescharacteristic, complemented
86#2140C2×C511yescharacteristic, complemented
87C2×#349C2×C511yescharacteristic, complemented
88#1386C2×C511yescharacteristic, complemented
89C24×C5—41no—
90C24×C5D811yescharacteristic
91C5×#41—41no—
92C5×#41—41no—
93C5×#41—41no—
94C5×#41—41no—
95C2×C5×Q8—21no—
96C2×C5×D4—22no—
97C2×C5×D4—21no—
98C2×C5×D4—42no—
99C2×C5×D4—44no—
100C2×C5×D4—41no—
101C2×C5×D4—41no—
102C2×C5×D4—41no—
103C2×C5×D4—41no—
104C2×C5×D4—41no—
105C2×C5×D4—41no—
106C2×C5×D4—84no—
107C22×C4×C5—21no—
108C22×C4×C5—21no—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—21no—
113C22×C4×C5—41no—
114C22×C4×C5—41no—
115C22×C4×C5D811yescharacteristic
116C22×C4×C5C2×D411yescharacteristic
117C5×Q16—21no—
118C5×Q16—21no—
119C5×SD16—41no—
120C5×SD16—41no—
121C5×D8—22no—
122C5×D8—21no—
123C5×D8—22no—
124C5×D8—21no—
125C5×D8—41no—
126C5×D8—41no—
127C5×M16—41no—
128C5×M16—41no—
129C5×M16—41no—
130C5×M16—41no—
131C2×C5×C8—21no—
132C2×C5×C8—21no—
133C2×C5×C8—21no—
134C2×C5×C8C2×D411yescharacteristic
135C2×C5×C8C2×D411yescharacteristic
136C2×C5×C8C2×D411yescharacteristic
137C2×C5×C8C2×D411yescharacteristic
138C2×C5×C8C2×D411yescharacteristic
139C2×C5×C8#4111yescharacteristic
140C5×C4⋊C4—22no—
141C5×C4⋊C4—22no—
142C5×C4⋊C4—42no—
143C5×C4⋊C4—41no—
144C5×C22⋊C4—44no—
145C5×C22⋊C4—42no—
146C5×C22⋊C4—42no—
147C5×C22⋊C4—41no—
148C42×C5—41no—
149C5×C16—22no—
150C5×C16—41no—
151C2×#135C22×C511yescharacteristic
152C22×D8C22×C511yescharacteristic
153C22×M16C22×C511yescharacteristic
154#525—21no—
155C2×#121—21no—
156#509—22no—
157#509—22no—
158C2×SD32—21no—
159C2×D16—21no—
160C2×M32C22×C511yescharacteristic
161C2×M32C22×C511yescharacteristic
162#470—21no—
163#469—22no—
164#469—21no—
165#469—22no—
166#468—22no—
167#427C22×C511yescharacteristic
168C2×#106C22×C511yescharacteristic
169#416—21no—
170C2×#102—21no—
171#360—22no—
172#357—22no—
173#349—22no—
174C23×C5—21no—
175C23×C5—21no—
176C23×C5—21no—
177C23×C5—42no—
178C23×C5—42no—
179C23×C5—41no—
180C23×C5—82no—
181C23×C5—82no—
182C23×C5—81no—
183C23×C5—81no—
184C23×C5C2×D811yescharacteristic
185C5×Q8—41no—
186C5×Q8—41no—
187C5×D4—42no—
188C5×D4—41no—
189C5×D4—42no—
190C5×D4—41no—
191C5×D4—84no—
192C5×D4—88no—
193C5×D4—81no—
194C5×D4—81no—
195C5×D4—81no—
196C5×D4—81no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—41no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5—42no—
205C2×C4×C5—42no—
206C2×C4×C5—41no—
207C2×C4×C5—82no—
208C2×C4×C5—81no—
209C2×C4×C5—81no—
210C2×C4×C5#12011yescharacteristic
211C2×C4×C5#12011yescharacteristic
212C2×C4×C5#12111yescharacteristic
213C2×C4×C5#13511yescharacteristic
214C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
215C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
216C5×C8—41no—
217C5×C8#12011yescharacteristic
218C5×C8#12111yescharacteristic
219C5×C8#12111yescharacteristic
220C5×C8#12711yescharacteristic
221C2×#41—21no—
222C22×D4—21no—
223C22×D4—41no—
224C23×C4C5×D411yescharacteristic
225#135—21no—
226#135—21no—
227#135—21no—
228#135—21no—
229C2×Q16C5×D411yescharacteristic, complemented
230C2×SD16—21no—
231C2×D8—21no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8—21no—
236C2×D8C5×D412yescomplemented
237C2×D8C5×D411yescharacteristic, complemented
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16—21no—
244C22×C8C5×D411yescharacteristic
245C22×C8C23×C511yescharacteristic
246#123—41no—
247C22⋊Q8—22no—
248#121—24no—
249#121—22no—
250#121—42no—
251#120—41no—
252C4×D4—42no—
253#117—21no—
254C2×C4⋊C4—21no—
255C2×C22⋊C4—41no—
256SD32—24no—
257D16—24no—
258M32—21no—
259M32—21no—
260M32—21no—
261M32C5×D412yescomplemented
262C2×C16—21no—
263C2×C16—21no—
264#107C5×D412yescomplemented
265#106—21no—
266#106—21no—
267#106C5×D412yescomplemented
268#103—22no—
269#102—24no—
270#102—22no—
271C22×C5—22no—
272C22×C5—42no—
273C22×C5—42no—
274C22×C5—41no—
275C22×C5—81no—
276C22×C5—82no—
277C22×C5—82no—
278C22×C5—82no—
279C22×C5—81no—
280C22×C5—82no—
281C22×C5—162no—
282C22×C5—162no—
283C22×C5#44711yescharacteristic
284C22×C5#44711yescharacteristic
285C22×C5#46611yescharacteristic
286C4×C5—41no—
287C4×C5—82no—
288C4×C5—82no—
289C4×C5—81no—
290C4×C5#39211yescharacteristic
291C4×C5#44911yescharacteristic
292C4×C5#44911yescharacteristic
293C4×C5#46911yescharacteristic
294C24—41no—
295C24C5×D811yescharacteristic
296#41—41no—
297#41—41no—
298#41—41no—
299#41—41no—
300C2×Q8—21no—
301C2×D4—22no—
302C2×D4—21no—
303C2×D4—42no—
304C2×D4—44no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—84no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C5×D811yescharacteristic
321C22×C4C2×C5×D411yescharacteristic
322Q16—21no—
323Q16—21no—
324SD16—41no—
325SD16—41no—
326D8—21no—
327D8—22no—
328D8—22no—
329D8—21no—
330D8—41no—
331D8—41no—
332M16—41no—
333M16—41no—
334M16—41no—
335M16—41no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8C2×C5×D411yescharacteristic
340C2×C8C2×C5×D411yescharacteristic
341C2×C8C2×C5×D411yescharacteristic
342C2×C8C2×C5×D411yescharacteristic
343C2×C8C2×C5×D411yescharacteristic
344C2×C8C5×#4111yescharacteristic
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—42no—
348C4⋊C4—41no—
349C22⋊C4—44no—
350C22⋊C4—42no—
351C22⋊C4—42no—
352C22⋊C4—41no—
353C42—41no—
354C16—22no—
355C16—41no—
356C2×C5—21no—
357C2×C5—21no—
358C2×C5—81no—
359C2×C5—161no—
360C2×C5—162no—
361C2×C5#199911yescharacteristic
362C2×C5#219012yes—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—42no—
367C23—41no—
368C23—42no—
369C23—82no—
370C23—82no—
371C23—81no—
372C23—81no—
373C23C2×C5×D811yescharacteristic
374Q8—41no—
375Q8—41no—
376D4—42no—
377D4—41no—
378D4—42no—
379D4—41no—
380D4—88no—
381D4—84no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—81no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—82no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4C5×#12011yescharacteristic
400C2×C4C5×#12011yescharacteristic
401C2×C4C5×#12111yescharacteristic
402C2×C4C5×#13511yescharacteristic
403C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
404C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
405C8—41no—
406C8C5×#12011yescharacteristic
407C8C5×#12111yescharacteristic
408C8C5×#12111yescharacteristic
409C8C5×#12711yescharacteristic
410C5#1331611yescharacteristic, direct product factor, Sylow
411C22—22no—
412C22—42no—
413C22—42no—
414C22—41no—
415C22—81no—
416C22—82no—
417C22—82no—
418C22—82no—
419C22—81no—
420C22—82no—
421C22—162no—
422C22—162no—
423C22C5×#44711yescharacteristic
424C22C5×#44711yescharacteristic
425C22C5×#46611yescharacteristic
426C4—41no—
427C4—82no—
428C4—82no—
429C4—81no—
430C4C5×#39211yescharacteristic
431C4C5×#44911yescharacteristic
432C4C5×#44911yescharacteristic
433C4C5×#46911yescharacteristic
434C2—21no—
435C2—21no—
436C2—81no—
437C2—162no—
438C2—161no—
439C2C5×#199911yescharacteristic
440C2C5×#219012yes—
subgroupG/H
center, socleC22×C5#447
commutator, Frattini, cosocleC22×C8C23×C5
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C22×C5×M16 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#509C2semidirect
2. C5×#3054C2semidirect
3. C2×C5×#469C2semidirect
4. C2×C5×#360C2semidirect
5. C5×#2140C2semidirect
6. C2×C5×#349C2semidirect
7. C5×#1386C2semidirect
31. #13316C5direct (N × H)
40. C2×C5×Q16D4semidirect
47. C2×C5×D8D4semidirect
48. C2×C5×D8D4semidirect
72. C5×M32D4semidirect
75. C5×#107D4semidirect
78. C5×#106D4semidirect
82. C2×#509C2×C5semidirect
83. #3054C2×C5semidirect
84. C2×#469C2×C5semidirect
85. C2×#360C2×C5semidirect
86. #2140C2×C5semidirect
87. C2×#349C2×C5semidirect
88. #1386C2×C5semidirect
229. C2×Q16C5×D4semidirect
236. C2×D8C5×D4semidirect
237. C2×D8C5×D4semidirect
261. M32C5×D4semidirect
264. #107C5×D4semidirect
267. #106C5×D4semidirect
410. C5#13316direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5092
C5×#30542
C2×C5×#4692
C2×C5×#3602
C5×#21402
C2×C5×#3492
C5×#13862
#133165