Finite Group Databasebeta

← C5×#13247 #11935967

Subgroups — C5×#13247 #11935967

Order 1280.

414 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#509C211yesmaximal, characteristic
2C5×#2155C211yesmaximal, characteristic, complemented
3C5×#2143C211yesmaximal, characteristic, complemented
4C5×#2140C211yesmaximal, characteristic, complemented
5C5×#2110C211yesmaximal, characteristic, complemented
6C5×#1978C211yesmaximal, characteristic, complemented
7C5×#1976C211yesmaximal, characteristic, complemented
8C2×C5×#135C2211yescharacteristic
9C22×C5×D8C2211yescharacteristic
10C5×#509—22no—
11C5×#509—22no—
12C2×C5×SD32C412yescomplemented
13C2×C5×D16C412yescomplemented
14C2×C5×M32C2211yescharacteristic
15C2×C5×M32C2211yescharacteristic
16C2×C5×#108C2211yescharacteristic
17C5×#427C2211yescharacteristic
18C5×#421—21no—
19C5×#418—21no—
20C2×C5×#100—21no—
21C5×#410—21no—
22C5×#405C2211yescharacteristic
23C5×#365—22no—
24C5×#359—22no—
25C5×#357—22no—
26C5×#347—22no—
27#13247C511yesmaximal, characteristic, direct product factor, Sylow
28C2×C5×#41—21no—
29C22×C5×D4—21no—
30C5×#135—21no—
31C5×#135—21no—
32C5×#135—21no—
33C5×#135—21no—
34C2×C5×Q16C2×C411yescharacteristic
35C2×C5×SD16—21no—
36C2×C5×D8—21no—
37C2×C5×D8—21no—
38C2×C5×D8—21no—
39C2×C5×D8—21no—
40C2×C5×D8—21no—
41C2×C5×D8C2×C411yescharacteristic
42C2×C5×D8C2×C412yes—
43C2×C5×M16—21no—
44C2×C5×M16D411yescharacteristic
45C22×C5×C8C2311yescharacteristic
46C5×#117—21no—
47C5×#117D411yescharacteristic
48C5×SD32—24no—
49C5×D16—24no—
50C5×M32—21no—
51C5×M32—21no—
52C5×M32D412yes—
53C5×M32D412yes—
54C2×C5×C16C2×C412yes—
55C2×C5×C16D412yes—
56C5×#108—21no—
57C5×#108—21no—
58C5×#107—21no—
59C5×#106—21no—
60C5×#104—42no—
61C5×#102—42no—
62C5×#100—42no—
63C5×#99—42no—
64C5×#97—21no—
65C4×C5×C8—21no—
66C2×#509C2×C511yescharacteristic
67#2155C2×C511yescharacteristic, complemented
68#2143C2×C511yescharacteristic, complemented
69#2140C2×C511yescharacteristic, complemented
70#2110C2×C511yescharacteristic, complemented
71#1978C2×C511yescharacteristic, complemented
72#1976C2×C511yescharacteristic, complemented
73C24×C5—41no—
74C5×#41—41no—
75C5×#41—41no—
76C5×#41—41no—
77C5×#41—41no—
78C2×C5×Q8—21no—
79C2×C5×D4—22no—
80C2×C5×D4—21no—
81C2×C5×D4—41no—
82C2×C5×D4—41no—
83C2×C5×D4—41no—
84C2×C5×D4—41no—
85C2×C5×D4—41no—
86C2×C5×D4—41no—
87C22×C4×C5—41no—
88C22×C4×C5C2×D411yescharacteristic
89C5×Q16—21no—
90C5×Q16—21no—
91C5×SD16—41no—
92C5×SD16—41no—
93C5×D8—22no—
94C5×D8—21no—
95C5×D8—22no—
96C5×D8—21no—
97C5×D8—41no—
98C5×D8—41no—
99C5×M16—21no—
100C5×M16—21no—
101C5×M16—41no—
102C5×M16—41no—
103C2×C5×C8—21no—
104C2×C5×C8—41no—
105C2×C5×C8C22×C411yescharacteristic
106C2×C5×C8C2×D411yescharacteristic
107C2×C5×C8C2×D411yescharacteristic
108C2×C5×C8C2×D411yescharacteristic
109C2×C5×C8#4111yescharacteristic
110C2×C5×C8#4111yescharacteristic
111C5×C4⋊C4—21no—
112C5×C4⋊C4—41no—
113C5×C22⋊C4—21no—
114C5×C22⋊C4—41no—
115C42×C5—21no—
116C42×C5—41no—
117C5×C16—22no—
118C5×C16C22⋊C414yes—
119C2×#135C22×C511yescharacteristic
120C22×D8C22×C511yescharacteristic
121#509—22no—
122#509—22no—
123C2×SD32C4×C512yescomplemented
124C2×D16C4×C512yescomplemented
125C2×M32C22×C511yescharacteristic
126C2×M32C22×C511yescharacteristic
127C2×#108C22×C511yescharacteristic
128#427C22×C511yescharacteristic
129#421—21no—
130#418—21no—
131C2×#100—21no—
132#410—21no—
133#405C22×C511yescharacteristic
134#365—22no—
135#359—22no—
136#357—22no—
137#347—22no—
138C23×C5—41no—
139C23×C5—42no—
140C23×C5—81no—
141C23×C5—81no—
142C23×C5—162no—
143C23×C5AGL(1,ℤ/8)11yescharacteristic
144C5×Q8—41no—
145C5×Q8—41no—
146C5×D4—42no—
147C5×D4—41no—
148C5×D4—42no—
149C5×D4—41no—
150C5×D4—81no—
151C5×D4—81no—
152C5×D4—81no—
153C5×D4—81no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—81no—
157C2×C4×C5—81no—
158C2×C4×C5—81no—
159C2×C4×C5C4×D411yescharacteristic
160C2×C4×C5#12111yescharacteristic
161C2×C4×C5#12711yescharacteristic
162C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
165C5×C8—41no—
166C5×C8—81no—
167C5×C8C2×C22⋊C411yescharacteristic
168C5×C8C4×D411yescharacteristic
169C5×C8#12111yescharacteristic
170C5×C8#12411yescharacteristic
171C2×#41—21no—
172C22×D4—21no—
173#135—21no—
174#135—21no—
175#135—21no—
176#135—21no—
177C2×Q16C2×C4×C511yescharacteristic
178C2×SD16—21no—
179C2×D8—21no—
180C2×D8—21no—
181C2×D8—21no—
182C2×D8—21no—
183C2×D8—21no—
184C2×D8C2×C4×C512yes—
185C2×D8C2×C4×C511yescharacteristic
186C2×M16—21no—
187C2×M16C5×D411yescharacteristic
188C22×C8C23×C511yescharacteristic
189#117—21no—
190#117C5×D411yescharacteristic
191SD32—24no—
192D16—24no—
193M32—21no—
194M32—21no—
195M32C5×D412yes—
196M32C5×D412yes—
197C2×C16C2×C4×C512yes—
198C2×C16C5×D412yes—
199#108—21no—
200#108—21no—
201#107—21no—
202#106—21no—
203#104—42no—
204#102—42no—
205#100—42no—
206#99—42no—
207#97—21no—
208C4×C8—21no—
209C22×C5—41no—
210C22×C5—81no—
211C22×C5—82no—
212C22×C5—161no—
213C22×C5—162no—
214C22×C5—162no—
215C22×C5—162no—
216C22×C5#44211yescharacteristic
217C22×C5#46911yescharacteristic
218C22×C5#49611yescharacteristic
219C4×C5—81no—
220C4×C5—81no—
221C4×C5—161no—
222C4×C5#39011yescharacteristic
223C4×C5#44211yescharacteristic
224C4×C5#46911yescharacteristic
225C4×C5#49611yescharacteristic
226C24—41no—
227#41—41no—
228#41—41no—
229#41—41no—
230#41—41no—
231C2×Q8—21no—
232C2×D4—22no—
233C2×D4—21no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C22×C4—41no—
241C22×C4C2×C5×D411yescharacteristic
242Q16—21no—
243Q16—21no—
244SD16—41no—
245SD16—41no—
246D8—21no—
247D8—22no—
248D8—22no—
249D8—21no—
250D8—41no—
251D8—41no—
252M16—21no—
253M16—21no—
254M16—41no—
255M16—41no—
256C2×C8—21no—
257C2×C8—41no—
258C2×C8C22×C4×C511yescharacteristic
259C2×C8C2×C5×D411yescharacteristic
260C2×C8C2×C5×D411yescharacteristic
261C2×C8C2×C5×D411yescharacteristic
262C2×C8C5×#4111yescharacteristic
263C2×C8C5×#4111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—41no—
266C22⋊C4—21no—
267C22⋊C4—41no—
268C42—21no—
269C42—41no—
270C16—22no—
271C16C5×C22⋊C414yes—
272C2×C5—21no—
273C2×C5—21no—
274C2×C5—21no—
275C2×C5—161no—
276C2×C5—162no—
277C2×C5#197211yescharacteristic
278C23—41no—
279C23—42no—
280C23—81no—
281C23—81no—
282C23—162no—
283C23C5×AGL(1,ℤ/8)11yescharacteristic
284Q8—41no—
285Q8—41no—
286D4—42no—
287D4—41no—
288D4—42no—
289D4—41no—
290D4—81no—
291D4—81no—
292D4—81no—
293D4—81no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4C4×C5×D411yescharacteristic
300C2×C4C5×#12111yescharacteristic
301C2×C4C5×#12711yescharacteristic
302C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
303C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
304C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
305C8—41no—
306C8—81no—
307C8C2×C5×C22⋊C411yescharacteristic
308C8C4×C5×D411yescharacteristic
309C8C5×#12111yescharacteristic
310C8C5×#12411yescharacteristic
311C5#1324711yescharacteristic, direct product factor, Sylow
312C22—41no—
313C22—81no—
314C22—82no—
315C22—162no—
316C22—161no—
317C22—162no—
318C22—162no—
319C22C5×#44211yescharacteristic
320C22C5×#46911yescharacteristic
321C22C5×#49611yescharacteristic
322C4—81no—
323C4—81no—
324C4—161no—
325C4C5×#39011yescharacteristic
326C4C5×#44211yescharacteristic
327C4C5×#46911yescharacteristic
328C4C5×#49611yescharacteristic
329C2—21no—
330C2—21no—
331C2—21no—
332C2—162no—
333C2—161no—
334C2C5×#197211yescharacteristic
subgroupG/H
center, socleC2×C5#1972
commutatorC2×C8C22×C4×C5
Frattini, cosocleC22×C8C23×C5
prime radicalC2×C5×#509C2
LCSG ▷ C2×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
2. C5×#2155C2semidirect
3. C5×#2143C2semidirect
4. C5×#2140C2semidirect
5. C5×#2110C2semidirect
6. C5×#1978C2semidirect
7. C5×#1976C2semidirect
12. C2×C5×SD32C4semidirect
13. C2×C5×D16C4semidirect
27. #13247C5direct (N × H)
67. #2155C2×C5semidirect
68. #2143C2×C5semidirect
69. #2140C2×C5semidirect
70. #2110C2×C5semidirect
71. #1978C2×C5semidirect
72. #1976C2×C5semidirect
123. C2×SD32C4×C5semidirect
124. C2×D16C4×C5semidirect
311. C5#13247direct (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×#21552
C5×#21432
C5×#21402
C5×#21102
C5×#19782
C5×#19762
#132475