Finite Group Databasebeta

← C5×#13334 #11936054

Subgroups — C5×#13334 #11936054

Order 1280.

568 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3414C211yesmaximal, characteristic, complemented
2C2×C5×#509C211yesmaximal, characteristic, complemented
3C5×#3155C211yesmaximal, characteristic, complemented
4C5×#2145C211yesmaximal, characteristic, complemented
5C5×#2140C211yesmaximal, characteristic, complemented
6C5×#1976C211yesmaximal, characteristic, complemented
7C5×#1378C211yesmaximal, characteristic, complemented
8C2×C5×AGL(1,ℤ/8)—21no—
9C2×C5×#135C2211yescharacteristic
10C2×C5×#135C2211yescharacteristic
11C22×C5×D8C2211yescharacteristic
12C5×#535—21no—
13C5×#510—21no—
14C5×#510—21no—
15C5×#509—22no—
16C5×#509—22no—
17C5×#509—21no—
18C5×#509—21no—
19C5×#508—22no—
20C2×C5×SD32—21no—
21C2×C5×D16—21no—
22C2×C5×M32C2211yescharacteristic
23C2×C5×M32C2211yescharacteristic
24C5×#496—22no—
25C5×#495—21no—
26C5×#493—21no—
27C5×#427C2211yescharacteristic
28C5×#421—21no—
29C5×#410—21no—
30C5×#405C2211yescharacteristic
31C5×#360—22no—
32C5×#357—22no—
33#13334C511yesmaximal, characteristic, direct product factor, Sylow
34C2×C5×#41—21no—
35C2×C5×#41—21no—
36C22×C5×D4—21no—
37C5×AGL(1,ℤ/8)—42no—
38C5×AGL(1,ℤ/8)—42no—
39C5×#135—21no—
40C5×#135—21no—
41C5×#135—21no—
42C5×#135—21no—
43C5×#135—21no—
44C5×#135—21no—
45C5×#135—21no—
46C5×#135—21no—
47C2×C5×Q16D411yescharacteristic
48C2×C5×Q16D411yescharacteristic, complemented
49C2×C5×SD16—22no—
50C2×C5×SD16—21no—
51C2×C5×SD16—21no—
52C2×C5×D8—22no—
53C2×C5×D8—21no—
54C2×C5×D8—21no—
55C2×C5×D8—21no—
56C2×C5×D8—21no—
57C2×C5×D8—21no—
58C2×C5×D8D411yescharacteristic
59C2×C5×D8D412yes—
60C2×C5×D8D411yescharacteristic, complemented
61C2×C5×M16D411yescharacteristic
62C22×C5×C8C2311yescharacteristic
63C5×#127—22no—
64C5×#124—22no—
65C5×#121—42no—
66C5×#120—42no—
67C5×#117—21no—
68C5×#117D411yescharacteristic
69C5×Q32—22no—
70C5×SD32—24no—
71C5×SD32—22no—
72C5×SD32—22no—
73C5×D16—24no—
74C5×D16—22no—
75C5×M32—21no—
76C5×M32—21no—
77C5×M32—21no—
78C5×M32D412yescomplemented
79C2×C5×C16—21no—
80C2×C5×C16D412yescomplemented
81C5×#107—21no—
82C5×#106—21no—
83C5×#104—42no—
84C5×#99—42no—
85C5×#97—21no—
86C4×C5×C8—21no—
87#3414C2×C511yescharacteristic, complemented
88C2×#509C2×C511yescharacteristic, complemented
89#3155C2×C511yescharacteristic, complemented
90#2145C2×C511yescharacteristic, complemented
91#2140C2×C511yescharacteristic, complemented
92#1976C2×C511yescharacteristic, complemented
93#1378C2×C511yescharacteristic, complemented
94C24×C5—41no—
95C5×#41—41no—
96C5×#41—41no—
97C5×#41—41no—
98C5×#41—41no—
99C5×#41—41no—
100C5×#41—41no—
101C5×#41—41no—
102C5×#41—41no—
103C2×C5×Q8—21no—
104C2×C5×Q8—21no—
105C2×C5×D4—22no—
106C2×C5×D4—21no—
107C2×C5×D4—21no—
108C2×C5×D4—44no—
109C2×C5×D4—41no—
110C2×C5×D4—41no—
111C2×C5×D4—41no—
112C2×C5×D4—41no—
113C2×C5×D4—41no—
114C2×C5×D4—41no—
115C2×C5×D4—41no—
116C22×C4×C5—41no—
117C22×C4×C5—41no—
118C22×C4×C5C2×D411yescharacteristic
119C5×Q16—21no—
120C5×Q16—21no—
121C5×Q16—21no—
122C5×Q16—21no—
123C5×SD16—44no—
124C5×SD16—41no—
125C5×SD16—41no—
126C5×SD16—41no—
127C5×SD16—41no—
128C5×D8—22no—
129C5×D8—21no—
130C5×D8—21no—
131C5×D8—21no—
132C5×D8—22no—
133C5×D8—21no—
134C5×D8—44no—
135C5×D8—41no—
136C5×D8—41no—
137C5×M16—21no—
138C5×M16D812yes—
139C2×C5×C8—21no—
140C2×C5×C8C2×D411yescharacteristic
141C2×C5×C8C2×D411yescharacteristic
142C2×C5×C8C2×D411yescharacteristic
143C2×C5×C8C2×D411yescharacteristic
144C2×C5×C8C2×D411yescharacteristic
145C2×C5×C8#4111yescharacteristic
146C5×C4⋊C4—21no—
147C5×C4⋊C4—41no—
148C5×C22⋊C4—44no—
149C5×C22⋊C4—41no—
150C5×C22⋊C4D812yes—
151C42×C5—21no—
152C42×C5—41no—
153C5×C16—22no—
154C5×C16—22no—
155C2×AGL(1,ℤ/8)—21no—
156C2×#135C22×C511yescharacteristic
157C2×#135C22×C511yescharacteristic
158C22×D8C22×C511yescharacteristic
159#535—21no—
160#510—21no—
161#510—21no—
162#509—22no—
163#509—21no—
164#509—21no—
165#509—22no—
166#508—22no—
167C2×SD32—21no—
168C2×D16—21no—
169C2×M32C22×C511yescharacteristic
170C2×M32C22×C511yescharacteristic
171#496—22no—
172#495—21no—
173#493—21no—
174#427C22×C511yescharacteristic
175#421—21no—
176#410—21no—
177#405C22×C511yescharacteristic
178#360—22no—
179#357—22no—
180C23×C5—42no—
181C23×C5—41no—
182C23×C5—41no—
183C23×C5—81no—
184C23×C5—81no—
185C23×C5—162no—
186C23×C5C2×D811yescharacteristic
187C5×Q8—41no—
188C5×Q8—41no—
189C5×Q8—41no—
190C5×Q8—41no—
191C5×D4—42no—
192C5×D4—41no—
193C5×D4—41no—
194C5×D4—41no—
195C5×D4—42no—
196C5×D4—41no—
197C5×D4—81no—
198C5×D4—81no—
199C5×D4—81no—
200C5×D4—81no—
201C5×D4—81no—
202C5×D4—81no—
203C5×D4—164no—
204C2×C4×C5—22no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—81no—
208C2×C4×C5—81no—
209C2×C4×C5—81no—
210C2×C4×C5—81no—
211C2×C4×C5—81no—
212C2×C4×C5#12011yescharacteristic
213C2×C4×C5#12111yescharacteristic
214C2×C4×C5#12711yescharacteristic
215C2×C4×C5C2×D811yescharacteristic
216C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
217C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
218C5×C8—22no—
219C5×C8#12011yescharacteristic
220C5×C8#12011yescharacteristic
221C5×C8#12111yescharacteristic
222C5×C8#12111yescharacteristic
223C2×#41—21no—
224C2×#41—21no—
225C22×D4—21no—
226AGL(1,ℤ/8)—42no—
227AGL(1,ℤ/8)—42no—
228#135—21no—
229#135—21no—
230#135—21no—
231#135—21no—
232#135—21no—
233#135—21no—
234#135—21no—
235#135—21no—
236C2×Q16C5×D411yescharacteristic
237C2×Q16C5×D411yescharacteristic, complemented
238C2×SD16—22no—
239C2×SD16—21no—
240C2×SD16—21no—
241C2×D8—22no—
242C2×D8—21no—
243C2×D8—21no—
244C2×D8—21no—
245C2×D8—21no—
246C2×D8—21no—
247C2×D8C5×D412yes—
248C2×D8C5×D411yescharacteristic
249C2×D8C5×D411yescharacteristic, complemented
250C2×M16C5×D411yescharacteristic
251C22×C8C23×C511yescharacteristic
252#127—22no—
253#124—22no—
254#121—42no—
255#120—42no—
256#117—21no—
257#117C5×D411yescharacteristic
258Q32—22no—
259SD32—24no—
260SD32—22no—
261SD32—22no—
262D16—24no—
263D16—22no—
264M32—21no—
265M32—21no—
266M32—21no—
267M32C5×D412yescomplemented
268C2×C16—21no—
269C2×C16C5×D412yescomplemented
270#107—21no—
271#106—21no—
272#104—42no—
273#99—42no—
274#97—21no—
275C4×C8—21no—
276C22×C5—41no—
277C22×C5—82no—
278C22×C5—84no—
279C22×C5—81no—
280C22×C5—81no—
281C22×C5—82no—
282C22×C5—161no—
283C22×C5—162no—
284C22×C5—162no—
285C22×C5#44711yescharacteristic
286C22×C5#45911yescharacteristic
287C22×C5#49311yescharacteristic
288C4×C5—42no—
289C4×C5—81no—
290C4×C5—81no—
291C4×C5—161no—
292C4×C5#39211yescharacteristic
293C4×C5#44711yescharacteristic
294C4×C5#45911yescharacteristic
295C4×C5#49611yescharacteristic
296C24—41no—
297#41—41no—
298#41—41no—
299#41—41no—
300#41—41no—
301#41—41no—
302#41—41no—
303#41—41no—
304#41—41no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—44no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C2×C5×D411yescharacteristic
321Q16—21no—
322Q16—21no—
323Q16—21no—
324Q16—21no—
325SD16—44no—
326SD16—41no—
327SD16—41no—
328SD16—41no—
329SD16—41no—
330D8—21no—
331D8—22no—
332D8—21no—
333D8—21no—
334D8—22no—
335D8—21no—
336D8—44no—
337D8—41no—
338D8—41no—
339M16—21no—
340M16C5×D812yes—
341C2×C8—21no—
342C2×C8C2×C5×D411yescharacteristic
343C2×C8C2×C5×D411yescharacteristic
344C2×C8C2×C5×D411yescharacteristic
345C2×C8C2×C5×D411yescharacteristic
346C2×C8C2×C5×D411yescharacteristic
347C2×C8C5×#4111yescharacteristic
348C4⋊C4—21no—
349C4⋊C4—41no—
350C22⋊C4—44no—
351C22⋊C4—41no—
352C22⋊C4C5×D812yes—
353C42—21no—
354C42—41no—
355C16—22no—
356C16—22no—
357C2×C5—21no—
358C2×C5—21no—
359C2×C5—21no—
360C2×C5—161no—
361C2×C5—162no—
362C2×C5—161no—
363C2×C5#201111yescharacteristic
364C23—42no—
365C23—41no—
366C23—41no—
367C23—81no—
368C23—81no—
369C23—162no—
370C23C2×C5×D811yescharacteristic
371Q8—41no—
372Q8—41no—
373Q8—41no—
374Q8—41no—
375D4—42no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—42no—
380D4—41no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387D4—164no—
388C2×C4—22no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4C5×#12011yescharacteristic
397C2×C4C5×#12111yescharacteristic
398C2×C4C5×#12711yescharacteristic
399C2×C4C2×C5×D811yescharacteristic
400C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
401C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
402C8—22no—
403C8C5×#12011yescharacteristic
404C8C5×#12011yescharacteristic
405C8C5×#12111yescharacteristic
406C8C5×#12111yescharacteristic
407C5#1333411yescharacteristic, direct product factor, Sylow
408C22—41no—
409C22—82no—
410C22—84no—
411C22—81no—
412C22—81no—
413C22—82no—
414C22—161no—
415C22—162no—
416C22—162no—
417C22C5×#44711yescharacteristic
418C22C5×#45911yescharacteristic
419C22C5×#49311yescharacteristic
420C4—42no—
421C4—81no—
422C4—81no—
423C4—161no—
424C4C5×#39211yescharacteristic
425C4C5×#44711yescharacteristic
426C4C5×#45911yescharacteristic
427C4C5×#49611yescharacteristic
428C2—21no—
429C2—21no—
430C2—21no—
431C2—162no—
432C2—161no—
433C2—161no—
434C2C5×#201111yescharacteristic
subgroupG/H
center, socleC2×C5#2011
commutator, Frattini, cosocleC22×C8C23×C5
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C5×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3414C2semidirect
2. C2×C5×#509C2semidirect
3. C5×#3155C2semidirect
4. C5×#2145C2semidirect
5. C5×#2140C2semidirect
6. C5×#1976C2semidirect
7. C5×#1378C2semidirect
33. #13334C5direct (N × H)
48. C2×C5×Q16D4semidirect
60. C2×C5×D8D4semidirect
78. C5×M32D4semidirect
80. C2×C5×C16D4semidirect
87. #3414C2×C5semidirect
88. C2×#509C2×C5semidirect
89. #3155C2×C5semidirect
90. #2145C2×C5semidirect
91. #2140C2×C5semidirect
92. #1976C2×C5semidirect
93. #1378C2×C5semidirect
237. C2×Q16C5×D4semidirect
249. C2×D8C5×D4semidirect
267. M32C5×D4semidirect
269. C2×C16C5×D4semidirect
407. C5#13334direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34142
C2×C5×#5092
C5×#31552
C5×#21452
C5×#21402
C5×#19762
C5×#13782
#133345