Finite Group Databasebeta

← C5×#13250 #11935970

Subgroups — C5×#13250 #11935970

Order 1280.

408 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#510C211yesmaximal, characteristic
2C2×C5×#365C211yesmaximal, characteristic, complemented
3C2×C5×#362C211yesmaximal, characteristic, complemented
4C2×C5×#360C211yesmaximal, characteristic
5C2×C5×#347C211yesmaximal, characteristic, complemented
6C5×#1975C211yesmaximal, characteristic
7C5×#1971C211yesmaximal, characteristic, complemented
8C2×C5×#135C2211yescharacteristic
9C22×C5×Q16C2211yescharacteristic
10C5×#510—22no—
11C5×#510—22no—
12C2×C5×Q32C412yescomplemented
13C2×C5×SD32C412yescomplemented
14C2×C5×M32C2211yescharacteristic
15C2×C5×M32C2211yescharacteristic
16C2×C5×#108C2211yescharacteristic
17C2×C5×#106C2211yescharacteristic
18C2×C5×#104—21no—
19C2×C5×#103—21no—
20C5×#408—21no—
21C2×C5×#97C2211yescharacteristic
22C5×#391—21no—
23C5×#365—22no—
24C5×#362—22no—
25C5×#360—22no—
26C5×#347—22no—
27#13250C511yesmaximal, characteristic, direct product factor, Sylow
28C2×C5×#41—21no—
29C22×C5×Q8—21no—
30C5×#135—21no—
31C5×#135—21no—
32C5×#135—21no—
33C5×#135—21no—
34C2×C5×Q16—21no—
35C2×C5×Q16—21no—
36C2×C5×Q16—21no—
37C2×C5×Q16—21no—
38C2×C5×Q16—21no—
39C2×C5×Q16C2×C412yes—
40C2×C5×Q16C2×C411yescharacteristic
41C2×C5×SD16—21no—
42C2×C5×D8C2×C411yescharacteristic
43C2×C5×M16—21no—
44C22×C5×C8D411yescharacteristic
45C22×C5×C8C2311yescharacteristic
46C2×C5×C4⋊C4—21no—
47C2×C42×C5D411yescharacteristic
48C5×Q32—24no—
49C5×SD32—24no—
50C5×M32—21no—
51C5×M32D412yes—
52C5×M32D412yes—
53C5×M32D412yes—
54C2×C5×C16—21no—
55C2×C5×C16C2×C412yes—
56C5×#108—21no—
57C5×#108—21no—
58C5×#106—21no—
59C5×#106—21no—
60C5×#104—42no—
61C5×#103—42no—
62C5×C22⋊C8—42no—
63C5×#97—21no—
64C5×#97—21no—
65C5×#95—42no—
66C2×#510C2×C511yescharacteristic
67C2×#365C2×C511yescharacteristic, complemented
68C2×#362C2×C511yescharacteristic, complemented
69C2×#360C2×C511yescharacteristic
70C2×#347C2×C511yescharacteristic, complemented
71#1975C2×C511yescharacteristic
72#1971C2×C511yescharacteristic, complemented
73C5×#41—41no—
74C5×#41—41no—
75C5×#41—41no—
76C5×#41—41no—
77C2×C5×Q8—21no—
78C2×C5×Q8—22no—
79C2×C5×Q8—41no—
80C2×C5×Q8—41no—
81C2×C5×Q8—41no—
82C2×C5×Q8—41no—
83C2×C5×Q8—41no—
84C2×C5×D4—21no—
85C2×C5×D4—41no—
86C22×C4×C5—21no—
87C22×C4×C5—41no—
88C22×C4×C5—41no—
89C22×C4×C5—41no—
90C22×C4×C5C2×D411yescharacteristic
91C5×Q16—22no—
92C5×Q16—21no—
93C5×Q16—22no—
94C5×Q16—21no—
95C5×Q16—41no—
96C5×Q16—41no—
97C5×SD16—41no—
98C5×SD16—41no—
99C5×D8—21no—
100C5×D8—21no—
101C5×M16—41no—
102C5×M16—41no—
103C2×C5×C8—21no—
104C2×C5×C8—21no—
105C2×C5×C8—21no—
106C2×C5×C8—41no—
107C2×C5×C8C22×C411yescharacteristic
108C2×C5×C8C2×D411yescharacteristic
109C2×C5×C8C2×D411yescharacteristic
110C2×C5×C8C2×D411yescharacteristic
111C2×C5×C8#4111yescharacteristic
112C2×C5×C8#4111yescharacteristic
113C5×C4⋊C4—41no—
114C5×C4⋊C4—41no—
115C42×C5—21no—
116C42×C5—21no—
117C5×C16—22no—
118C5×C16C22⋊C414yes—
119C2×#135C22×C511yescharacteristic
120C22×Q16C22×C511yescharacteristic
121#510—22no—
122#510—22no—
123C2×Q32C4×C512yescomplemented
124C2×SD32C4×C512yescomplemented
125C2×M32C22×C511yescharacteristic
126C2×M32C22×C511yescharacteristic
127C2×#108C22×C511yescharacteristic
128C2×#106C22×C511yescharacteristic
129C2×#104—21no—
130C2×#103—21no—
131#408—21no—
132C2×#97C22×C511yescharacteristic
133#391—21no—
134#365—22no—
135#362—22no—
136#360—22no—
137#347—22no—
138C23×C5—41no—
139C23×C5AGL(1,ℤ/8)11yescharacteristic
140C5×Q8—41no—
141C5×Q8—42no—
142C5×Q8—42no—
143C5×Q8—41no—
144C5×Q8—81no—
145C5×Q8—81no—
146C5×D4—41no—
147C5×D4—41no—
148C5×D4—81no—
149C5×D4—81no—
150C2×C4×C5—42no—
151C2×C4×C5—41no—
152C2×C4×C5—42no—
153C2×C4×C5—41no—
154C2×C4×C5—81no—
155C2×C4×C5—81no—
156C2×C4×C5—81no—
157C2×C4×C5—81no—
158C2×C4×C5—82no—
159C2×C4×C5—81no—
160C2×C4×C5C4×D411yescharacteristic
161C2×C4×C5#12111yescharacteristic
162C2×C4×C5#12711yescharacteristic
163C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
166C5×C8—41no—
167C5×C8—81no—
168C5×C8C2×C22⋊C411yescharacteristic
169C5×C8C4×D411yescharacteristic
170C5×C8#12111yescharacteristic
171C5×C8#12411yescharacteristic
172C2×#41—21no—
173C22×Q8—21no—
174#135—21no—
175#135—21no—
176#135—21no—
177#135—21no—
178C2×Q16—21no—
179C2×Q16—21no—
180C2×Q16—21no—
181C2×Q16—21no—
182C2×Q16—21no—
183C2×Q16C2×C4×C512yes—
184C2×Q16C2×C4×C511yescharacteristic
185C2×SD16—21no—
186C2×D8C2×C4×C511yescharacteristic
187C2×M16—21no—
188C22×C8C5×D411yescharacteristic
189C22×C8C23×C511yescharacteristic
190C2×C4⋊C4—21no—
191C2×C42C5×D411yescharacteristic
192Q32—24no—
193SD32—24no—
194M32—21no—
195M32C5×D412yes—
196M32C5×D412yes—
197M32C5×D412yes—
198C2×C16—21no—
199C2×C16C2×C4×C512yes—
200#108—21no—
201#108—21no—
202#106—21no—
203#106—21no—
204#104—42no—
205#103—42no—
206C22⋊C8—42no—
207#97—21no—
208#97—21no—
209#95—42no—
210C22×C5—22no—
211C22×C5—82no—
212C22×C5—81no—
213C22×C5#44211yescharacteristic
214C22×C5#46911yescharacteristic
215C22×C5#49611yescharacteristic
216C4×C5—81no—
217C4×C5—81no—
218C4×C5—82no—
219C4×C5—161no—
220C4×C5#39011yescharacteristic
221C4×C5#44211yescharacteristic
222C4×C5#46911yescharacteristic
223C4×C5#49611yescharacteristic
224#41—41no—
225#41—41no—
226#41—41no—
227#41—41no—
228C2×Q8—21no—
229C2×Q8—22no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×D4—21no—
236C2×D4—41no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4C2×C5×D411yescharacteristic
242Q16—22no—
243Q16—21no—
244Q16—22no—
245Q16—21no—
246Q16—41no—
247Q16—41no—
248SD16—41no—
249SD16—41no—
250D8—21no—
251D8—21no—
252M16—41no—
253M16—41no—
254C2×C8—21no—
255C2×C8—21no—
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—41no—
265C4⋊C4—41no—
266C42—21no—
267C42—21no—
268C16—22no—
269C16C5×C22⋊C414yes—
270C2×C5—21no—
271C2×C5—21no—
272C2×C5—161no—
273C2×C5#197211yescharacteristic
274C2×C5#218012yes—
275C23—41no—
276C23C5×AGL(1,ℤ/8)11yescharacteristic
277Q8—41no—
278Q8—42no—
279Q8—42no—
280Q8—41no—
281Q8—81no—
282Q8—81no—
283D4—41no—
284D4—41no—
285D4—81no—
286D4—81no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—82no—
296C2×C4—81no—
297C2×C4C4×C5×D411yescharacteristic
298C2×C4C5×#12111yescharacteristic
299C2×C4C5×#12711yescharacteristic
300C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
301C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
302C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
303C8—41no—
304C8—81no—
305C8C2×C5×C22⋊C411yescharacteristic
306C8C4×C5×D411yescharacteristic
307C8C5×#12111yescharacteristic
308C8C5×#12411yescharacteristic
309C5#1325011yescharacteristic, direct product factor, Sylow
310C22—22no—
311C22—82no—
312C22—81no—
313C22C5×#44211yescharacteristic
314C22C5×#46911yescharacteristic
315C22C5×#49611yescharacteristic
316C4—81no—
317C4—81no—
318C4—82no—
319C4—161no—
320C4C5×#39011yescharacteristic
321C4C5×#44211yescharacteristic
322C4C5×#46911yescharacteristic
323C4C5×#49611yescharacteristic
324C2—21no—
325C2—21no—
326C2—161no—
327C2C5×#197211yescharacteristic
328C2C5×#218012yes—
subgroupG/H
center, socleC22×C5#442
commutatorC2×C8C22×C4×C5
Frattini, cosocleC22×C8C23×C5
prime radicalC2×C5×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×#97 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#365C2semidirect
3. C2×C5×#362C2semidirect
5. C2×C5×#347C2semidirect
7. C5×#1971C2semidirect
12. C2×C5×Q32C4semidirect
13. C2×C5×SD32C4semidirect
27. #13250C5direct (N × H)
67. C2×#365C2×C5semidirect
68. C2×#362C2×C5semidirect
70. C2×#347C2×C5semidirect
72. #1971C2×C5semidirect
123. C2×Q32C4×C5semidirect
124. C2×SD32C4×C5semidirect
309. C5#13250direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5102
C2×C5×#3652
C2×C5×#3622
C2×C5×#3602
C2×C5×#3472
C5×#19752
C5×#19712
#132505