Finite Group Databasebeta

← C5×#13318 #11936038

Subgroups — C5×#13318 #11936038

Order 1280.

532 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3414C211yesmaximal, characteristic, complemented
2C5×#3067C211yesmaximal, characteristic, complemented
3C5×#3060C211yesmaximal, characteristic, complemented
4C2×C5×#360C211yesmaximal, characteristic, complemented
5C5×#2143C211yesmaximal, characteristic, complemented
6C5×#2117C211yesmaximal, characteristic, complemented
7C5×#1383C211yesmaximal, characteristic, complemented
8C5×#575—21no—
9C2×C5×#135C2211yescharacteristic
10C2×C5×#135C2211yescharacteristic
11C2×C5×#131C2211yescharacteristic
12C5×#537—21no—
13C5×#510—21no—
14C5×#510—21no—
15C5×#509—21no—
16C5×#509—21no—
17C5×#508—22no—
18C2×C5×M32C2211yescharacteristic
19C2×C5×M32C2211yescharacteristic
20C5×#473—21no—
21C5×#472—21no—
22C5×#471—22no—
23C5×#470—21no—
24C5×#469—21no—
25C5×#465—22no—
26C2×C5×#108C2211yescharacteristic
27C2×C5×#106C2211yescharacteristic
28C5×#417—21no—
29C5×#413—21no—
30C5×#360—22no—
31C5×#359—22no—
32C5×#350—22no—
33#13318C511yesmaximal, characteristic, direct product factor, Sylow
34C2×C5×#41—21no—
35C2×C5×#41—21no—
36C2×C5×#41D411yescharacteristic
37C5×#137—22no—
38C5×#137—41no—
39C5×AGL(1,ℤ/8)—22no—
40C5×AGL(1,ℤ/8)—41no—
41C5×#135—21no—
42C5×#135—21no—
43C5×#135—21no—
44C5×#135—21no—
45C5×#135—21no—
46C5×#135—21no—
47C5×#135—21no—
48C5×#135—21no—
49C5×#135—42no—
50C2×C5×Q16D411yescharacteristic
51C2×C5×Q16D411yescharacteristic, complemented
52C2×C5×SD16—21no—
53C2×C5×SD16—21no—
54C2×C5×D8D411yescharacteristic
55C2×C5×D8D411yescharacteristic, complemented
56C5×#131—21no—
57C5×#131—21no—
58C5×#131—21no—
59C5×#131—21no—
60C2×C5×M16—21no—
61C2×C5×M16—21no—
62C2×C5×M16D411yescharacteristic
63C22×C5×C8—21no—
64C22×C5×C8C2311yescharacteristic
65C5×C22⋊Q8—22no—
66C5×C22⋊Q8—41no—
67C5×#121—22no—
68C5×#121—42no—
69C5×#121—41no—
70C2×C5×C4⋊C4—21no—
71C5×Q32—22no—
72C5×SD32—22no—
73C5×SD32—22no—
74C5×D16—22no—
75C5×M32—21no—
76C5×M32—21no—
77C5×M32—21no—
78C5×M32—21no—
79C2×C5×C16—21no—
80C2×C5×C16D412yescomplemented
81C5×#108—21no—
82C5×#108D412yescomplemented
83C5×#106—21no—
84C5×#106D412yes—
85C5×#103—22no—
86C5×#102—22no—
87C5×#101—22no—
88C5×#100—22no—
89#3414C2×C511yescharacteristic, complemented
90#3067C2×C511yescharacteristic, complemented
91#3060C2×C511yescharacteristic, complemented
92C2×#360C2×C511yescharacteristic, complemented
93#2143C2×C511yescharacteristic, complemented
94#2117C2×C511yescharacteristic, complemented
95#1383C2×C511yescharacteristic, complemented
96C5×#41—21no—
97C5×#41—21no—
98C5×#41—21no—
99C5×#41—21no—
100C5×#41—41no—
101C5×#41—41no—
102C5×#41—41no—
103C5×#41—41no—
104C5×#41—41no—
105C5×#41—41no—
106C5×#41—41no—
107C5×#41—41no—
108C2×C5×Q8—21no—
109C2×C5×Q8—21no—
110C2×C5×Q8D811yescharacteristic
111C2×C5×D4—21no—
112C2×C5×D4—21no—
113C2×C5×D4—21no—
114C2×C5×D4—41no—
115C2×C5×D4—41no—
116C2×C5×D4—42no—
117C2×C5×D4D811yescharacteristic
118C22×C4×C5—21no—
119C22×C4×C5—41no—
120C22×C4×C5—41no—
121C22×C4×C5—41no—
122C22×C4×C5C2×D411yescharacteristic
123C5×Q16—21no—
124C5×Q16—21no—
125C5×Q16—21no—
126C5×Q16—21no—
127C5×Q16—42no—
128C5×SD16—42no—
129C5×SD16—42no—
130C5×SD16—41no—
131C5×SD16—41no—
132C5×SD16—41no—
133C5×SD16—41no—
134C5×D8—21no—
135C5×D8—21no—
136C5×D8—21no—
137C5×D8—21no—
138C5×D8—42no—
139C5×M16—22no—
140C5×M16—21no—
141C5×M16—21no—
142C5×M16—41no—
143C5×M16—41no—
144C5×M16—41no—
145C2×C5×C8—21no—
146C2×C5×C8—41no—
147C2×C5×C8—41no—
148C2×C5×C8—41no—
149C2×C5×C8C2×D411yescharacteristic
150C2×C5×C8C2×D411yescharacteristic
151C2×C5×C8C2×D411yescharacteristic
152C2×C5×C8C2×D411yescharacteristic
153C2×C5×C8C2×D411yescharacteristic
154C2×C5×C8#4111yescharacteristic
155C5×C4⋊C4—22no—
156C5×C4⋊C4—42no—
157C5×C4⋊C4—41no—
158C5×C22⋊C4—42no—
159C5×C22⋊C4—42no—
160C5×C16—22no—
161C5×C16—41no—
162#575—21no—
163C2×#135C22×C511yescharacteristic
164C2×#135C22×C511yescharacteristic
165C2×#131C22×C511yescharacteristic
166#537—21no—
167#510—21no—
168#510—21no—
169#509—21no—
170#509—21no—
171#508—22no—
172C2×M32C22×C511yescharacteristic
173C2×M32C22×C511yescharacteristic
174#473—21no—
175#472—21no—
176#471—22no—
177#470—21no—
178#469—21no—
179#465—22no—
180C2×#108C22×C511yescharacteristic
181C2×#106C22×C511yescharacteristic
182#417—21no—
183#413—21no—
184#360—22no—
185#359—22no—
186#350—22no—
187C23×C5—21no—
188C23×C5—41no—
189C23×C5—41no—
190C23×C5AGL(1,ℤ/8)11yescharacteristic
191C5×Q8—21no—
192C5×Q8—21no—
193C5×Q8—41no—
194C5×Q8—41no—
195C5×Q8—41no—
196C5×Q8—41no—
197C5×D4—21no—
198C5×D4—21no—
199C5×D4—41no—
200C5×D4—41no—
201C5×D4—41no—
202C5×D4—41no—
203C5×D4—41no—
204C5×D4—41no—
205C5×D4—81no—
206C5×D4—81no—
207C5×D4—81no—
208C5×D4—81no—
209C5×D4—162no—
210C2×C4×C5—21no—
211C2×C4×C5—41no—
212C2×C4×C5—41no—
213C2×C4×C5—42no—
214C2×C4×C5—41no—
215C2×C4×C5—41no—
216C2×C4×C5—81no—
217C2×C4×C5—81no—
218C2×C4×C5—81no—
219C2×C4×C5—81no—
220C2×C4×C5—161no—
221C2×C4×C5#12011yescharacteristic
222C2×C4×C5#12011yescharacteristic
223C2×C4×C5#12111yescharacteristic
224C2×C4×C5C2×D811yescharacteristic
225C2×C4×C5#13511yescharacteristic
226C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
227C5×C8—41no—
228C5×C8—42no—
229C5×C8#12011yescharacteristic
230C5×C8#12111yescharacteristic
231C5×C8#12111yescharacteristic
232C5×C8#12711yescharacteristic
233C2×#41—21no—
234C2×#41—21no—
235C2×#41C5×D411yescharacteristic
236#137—22no—
237#137—41no—
238AGL(1,ℤ/8)—22no—
239AGL(1,ℤ/8)—41no—
240#135—21no—
241#135—21no—
242#135—21no—
243#135—21no—
244#135—21no—
245#135—21no—
246#135—21no—
247#135—21no—
248#135—42no—
249C2×Q16C5×D411yescharacteristic
250C2×Q16C5×D411yescharacteristic, complemented
251C2×SD16—21no—
252C2×SD16—21no—
253C2×D8C5×D411yescharacteristic
254C2×D8C5×D411yescharacteristic, complemented
255#131—21no—
256#131—21no—
257#131—21no—
258#131—21no—
259C2×M16—21no—
260C2×M16—21no—
261C2×M16C5×D411yescharacteristic
262C22×C8—21no—
263C22×C8C23×C511yescharacteristic
264C22⋊Q8—22no—
265C22⋊Q8—41no—
266#121—22no—
267#121—42no—
268#121—41no—
269C2×C4⋊C4—21no—
270Q32—22no—
271SD32—22no—
272SD32—22no—
273D16—22no—
274M32—21no—
275M32—21no—
276M32—21no—
277M32—21no—
278C2×C16—21no—
279C2×C16C5×D412yescomplemented
280#108—21no—
281#108C5×D412yescomplemented
282#106—21no—
283#106C5×D412yes—
284#103—22no—
285#102—22no—
286#101—22no—
287#100—22no—
288C22×C5—41no—
289C22×C5—42no—
290C22×C5—41no—
291C22×C5—81no—
292C22×C5—81no—
293C22×C5—81no—
294C22×C5—81no—
295C22×C5—161no—
296C22×C5#44711yescharacteristic
297C22×C5#44911yescharacteristic
298C22×C5#46911yescharacteristic
299C4×C5—41no—
300C4×C5—82no—
301C4×C5—81no—
302C4×C5—81no—
303C4×C5#39211yescharacteristic
304C4×C5#44711yescharacteristic
305C4×C5#44911yescharacteristic
306C4×C5#46611yescharacteristic
307#41—21no—
308#41—21no—
309#41—21no—
310#41—21no—
311#41—41no—
312#41—41no—
313#41—41no—
314#41—41no—
315#41—41no—
316#41—41no—
317#41—41no—
318#41—41no—
319C2×Q8—21no—
320C2×Q8—21no—
321C2×Q8C5×D811yescharacteristic
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—42no—
328C2×D4C5×D811yescharacteristic
329C22×C4—21no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4C2×C5×D411yescharacteristic
334Q16—21no—
335Q16—21no—
336Q16—21no—
337Q16—21no—
338Q16—42no—
339SD16—42no—
340SD16—42no—
341SD16—41no—
342SD16—41no—
343SD16—41no—
344SD16—41no—
345D8—21no—
346D8—21no—
347D8—21no—
348D8—21no—
349D8—42no—
350M16—21no—
351M16—22no—
352M16—21no—
353M16—41no—
354M16—41no—
355M16—41no—
356C2×C8—21no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8C2×C5×D411yescharacteristic
361C2×C8C2×C5×D411yescharacteristic
362C2×C8C2×C5×D411yescharacteristic
363C2×C8C2×C5×D411yescharacteristic
364C2×C8C2×C5×D411yescharacteristic
365C2×C8C5×#4111yescharacteristic
366C4⋊C4—22no—
367C4⋊C4—42no—
368C4⋊C4—41no—
369C22⋊C4—42no—
370C22⋊C4—42no—
371C16—22no—
372C16—41no—
373C2×C5—21no—
374C2×C5—21no—
375C2×C5—21no—
376C2×C5—81no—
377C2×C5—161no—
378C2×C5—161no—
379C2×C5#199911yescharacteristic
380C23—21no—
381C23—41no—
382C23—41no—
383C23C5×AGL(1,ℤ/8)11yescharacteristic
384Q8—21no—
385Q8—21no—
386Q8—41no—
387Q8—41no—
388Q8—41no—
389Q8—41no—
390D4—21no—
391D4—21no—
392D4—41no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—41no—
397D4—41no—
398D4—81no—
399D4—81no—
400D4—81no—
401D4—81no—
402D4—162no—
403C2×C4—21no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—161no—
414C2×C4C5×#12011yescharacteristic
415C2×C4C5×#12011yescharacteristic
416C2×C4C5×#12111yescharacteristic
417C2×C4C2×C5×D811yescharacteristic
418C2×C4C5×#13511yescharacteristic
419C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
420C8—41no—
421C8—42no—
422C8C5×#12011yescharacteristic
423C8C5×#12111yescharacteristic
424C8C5×#12111yescharacteristic
425C8C5×#12711yescharacteristic
426C5#1331811yescharacteristic, direct product factor, Sylow
427C22—41no—
428C22—42no—
429C22—41no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—161no—
435C22C5×#44711yescharacteristic
436C22C5×#44911yescharacteristic
437C22C5×#46911yescharacteristic
438C4—41no—
439C4—82no—
440C4—81no—
441C4—81no—
442C4C5×#39211yescharacteristic
443C4C5×#44711yescharacteristic
444C4C5×#44911yescharacteristic
445C4C5×#46611yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—81no—
450C2—161no—
451C2—161no—
452C2C5×#199911yescharacteristic
subgroupG/H
center, socleC2×C5#1999
commutator, Frattini, cosocleC22×C8C23×C5
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C2×C5×#131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3414C2semidirect
2. C5×#3067C2semidirect
3. C5×#3060C2semidirect
4. C2×C5×#360C2semidirect
5. C5×#2143C2semidirect
6. C5×#2117C2semidirect
7. C5×#1383C2semidirect
33. #13318C5direct (N × H)
51. C2×C5×Q16D4semidirect
55. C2×C5×D8D4semidirect
80. C2×C5×C16D4semidirect
82. C5×#108D4semidirect
89. #3414C2×C5semidirect
90. #3067C2×C5semidirect
91. #3060C2×C5semidirect
92. C2×#360C2×C5semidirect
93. #2143C2×C5semidirect
94. #2117C2×C5semidirect
95. #1383C2×C5semidirect
250. C2×Q16C5×D4semidirect
254. C2×D8C5×D4semidirect
279. C2×C16C5×D4semidirect
281. #108C5×D4semidirect
426. C5#13318direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34142
C5×#30672
C5×#30602
C2×C5×#3602
C5×#21432
C5×#21172
C5×#13832
#133185