Finite Group Databasebeta

← C5×#13033 #11935753

Subgroups — C5×#13033 #11935753

Order 1280.

498 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#509C211yesmaximal, characteristic
2C5×#2948C211yesmaximal, characteristic, complemented
3C5×#2145C211yesmaximal, characteristic, complemented
4C5×#2140C211yesmaximal, characteristic, complemented
5C5×#1976C211yesmaximal, characteristic, complemented
6C5×#1384C211yesmaximal, characteristic, complemented
7C5×#1378C211yesmaximal, characteristic, complemented
8C2×C5×#135C2211yescharacteristic
9C22×C5×D8C2211yescharacteristic
10C5×#518—21no—
11C5×#509—22no—
12C5×#509—22no—
13C2×C5×SD32C412yescomplemented
14C2×C5×D16C412yescomplemented
15C2×C5×M32C2211yescharacteristic
16C2×C5×M32C2211yescharacteristic
17C5×#442—22no—
18C4×C5×D8—22no—
19C5×#427C2211yescharacteristic
20C5×#427C2211yescharacteristic
21C5×#421—21no—
22C5×#418—21no—
23C5×#410—21no—
24C5×#405C2211yescharacteristic
25C5×#360—22no—
26C5×#357—22no—
27#13033C511yesmaximal, 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, complemented
35C2×C5×SD16—21no—
36C2×C5×D8—21no—
37C2×C5×D8—21no—
38C2×C5×D8—21no—
39C2×C5×D8C2×C412yes—
40C2×C5×D8C2×C411yescharacteristic, complemented
41C2×C5×D8D412yes—
42C2×C5×D8D412yes—
43C2×C5×M16D411yescharacteristic
44C22×C5×C8C2311yescharacteristic
45C4×C5×D4—24no—
46C4×C5×D4—42no—
47C5×#117—21no—
48C5×#117—21no—
49C5×#117D411yescharacteristic
50C2×C5×C22⋊C4—42no—
51C5×SD32—24no—
52C5×D16—24no—
53C5×M32—21no—
54C5×M32—21no—
55C5×M32—21no—
56C5×M32—21no—
57C2×C5×C16—21no—
58C2×C5×C16C2×C412yescomplemented
59C5×#107—21no—
60C5×#107—21no—
61C5×#106—21no—
62C5×#106D412yes—
63C5×#104—42no—
64C5×#102—24no—
65C5×#99—42no—
66C5×#97—21no—
67C4×C5×C8—21no—
68C2×#509C2×C511yescharacteristic
69#2948C2×C511yescharacteristic, complemented
70#2145C2×C511yescharacteristic, complemented
71#2140C2×C511yescharacteristic, complemented
72#1976C2×C511yescharacteristic, complemented
73#1384C2×C511yescharacteristic, complemented
74#1378C2×C511yescharacteristic, complemented
75C24×C5—41no—
76C5×#41—41no—
77C5×#41—41no—
78C5×#41—41no—
79C5×#41—41no—
80C2×C5×Q8—21no—
81C2×C5×D4—22no—
82C2×C5×D4—21no—
83C2×C5×D4—22no—
84C2×C5×D4—22no—
85C2×C5×D4—41no—
86C2×C5×D4—41no—
87C2×C5×D4—41no—
88C2×C5×D4—41no—
89C22×C4×C5—44no—
90C22×C4×C5—41no—
91C22×C4×C5C2×D411yescharacteristic
92C5×Q16—21no—
93C5×Q16—21no—
94C5×SD16—41no—
95C5×SD16—41no—
96C5×D8—21no—
97C5×D8—22no—
98C5×D8—21no—
99C5×D8—22no—
100C5×D8—22no—
101C5×D8C22⋊C414yes—
102C5×M16—21no—
103C5×M16—21no—
104C2×C5×C8—21no—
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—22no—
113C5×C4⋊C4—41no—
114C5×C22⋊C4—44no—
115C5×C22⋊C4—41no—
116C5×C22⋊C4—41no—
117C5×C22⋊C4D812yes—
118C42×C5—21no—
119C42×C5—41no—
120C42×C5—41no—
121C5×C16—22no—
122C5×C16—41no—
123C2×#135C22×C511yescharacteristic
124C22×D8C22×C511yescharacteristic
125#518—21no—
126#509—22no—
127#509—22no—
128C2×SD32C4×C512yescomplemented
129C2×D16C4×C512yescomplemented
130C2×M32C22×C511yescharacteristic
131C2×M32C22×C511yescharacteristic
132#442—22no—
133C4×D8—22no—
134#427C22×C511yescharacteristic
135#427C22×C511yescharacteristic
136#421—21no—
137#418—21no—
138#410—21no—
139#405C22×C511yescharacteristic
140#360—22no—
141#357—22no—
142C23×C5—42no—
143C23×C5—42no—
144C23×C5—42no—
145C23×C5—41no—
146C23×C5—162no—
147C23×C5C2×D811yescharacteristic
148C5×Q8—41no—
149C5×Q8—41no—
150C5×D4—24no—
151C5×D4—41no—
152C5×D4—42no—
153C5×D4—41no—
154C5×D4—42no—
155C5×D4—42no—
156C5×D4—81no—
157C5×D4—81no—
158C2×C4×C5—22no—
159C2×C4×C5—41no—
160C2×C4×C5—42no—
161C2×C4×C5—81no—
162C2×C4×C5—81no—
163C2×C4×C5—81no—
164C2×C4×C5—164no—
165C2×C4×C5C4×D411yescharacteristic
166C2×C4×C5#12011yescharacteristic
167C2×C4×C5#12111yescharacteristic
168C2×C4×C5#13511yescharacteristic
169C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C5×C8—41no—
172C5×C8C2×C22⋊C411yescharacteristic
173C5×C8C4×D411yescharacteristic
174C5×C8#12111yescharacteristic
175C5×C8#12311yescharacteristic
176C2×#41—21no—
177C22×D4—21no—
178#135—21no—
179#135—21no—
180#135—21no—
181#135—21no—
182C2×Q16C2×C4×C511yescharacteristic, complemented
183C2×SD16—21no—
184C2×D8—21no—
185C2×D8—21no—
186C2×D8—21no—
187C2×D8C2×C4×C512yes—
188C2×D8C2×C4×C511yescharacteristic, complemented
189C2×D8C5×D412yes—
190C2×D8C5×D412yes—
191C2×M16C5×D411yescharacteristic
192C22×C8C23×C511yescharacteristic
193C4×D4—24no—
194C4×D4—42no—
195#117—21no—
196#117—21no—
197#117C5×D411yescharacteristic
198C2×C22⋊C4—42no—
199SD32—24no—
200D16—24no—
201M32—21no—
202M32—21no—
203M32—21no—
204M32—21no—
205C2×C16—21no—
206C2×C16C2×C4×C512yescomplemented
207#107—21no—
208#107—21no—
209#106—21no—
210#106C5×D412yes—
211#104—42no—
212#102—24no—
213#99—42no—
214#97—21no—
215C4×C8—21no—
216C22×C5—41no—
217C22×C5—44no—
218C22×C5—84no—
219C22×C5—81no—
220C22×C5—162no—
221C22×C5—162no—
222C22×C5—161no—
223C22×C5C4×D811yescharacteristic
224C22×C5#44711yescharacteristic
225C22×C5#45911yescharacteristic
226C4×C5—42no—
227C4×C5—82no—
228C4×C5—81no—
229C4×C5—161no—
230C4×C5#38611yescharacteristic
231C4×C5#44211yescharacteristic
232C4×C5#44911yescharacteristic
233C4×C5#46311yescharacteristic
234C24—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238#41—41no—
239C2×Q8—21no—
240C2×D4—22no—
241C2×D4—21no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C22×C4—44no—
249C22×C4—41no—
250C22×C4C2×C5×D411yescharacteristic
251Q16—21no—
252Q16—21no—
253SD16—41no—
254SD16—41no—
255D8—21no—
256D8—22no—
257D8—21no—
258D8—22no—
259D8—22no—
260D8C5×C22⋊C414yes—
261M16—21no—
262M16—21no—
263C2×C8—21no—
264C2×C8C22×C4×C511yescharacteristic
265C2×C8C2×C5×D411yescharacteristic
266C2×C8C2×C5×D411yescharacteristic
267C2×C8C2×C5×D411yescharacteristic
268C2×C8C5×#4111yescharacteristic
269C2×C8C5×#4111yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C22⋊C4—44no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4C5×D812yes—
277C42—21no—
278C42—41no—
279C42—41no—
280C16—22no—
281C16—41no—
282C2×C5—21no—
283C2×C5—21no—
284C2×C5—21no—
285C2×C5—84no—
286C2×C5—161no—
287C2×C5#187911yescharacteristic
288C23—42no—
289C23—42no—
290C23—42no—
291C23—41no—
292C23—162no—
293C23C2×C5×D811yescharacteristic
294Q8—41no—
295Q8—41no—
296D4—24no—
297D4—41no—
298D4—42no—
299D4—41no—
300D4—42no—
301D4—42no—
302D4—81no—
303D4—81no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—164no—
311C2×C4C4×C5×D411yescharacteristic
312C2×C4C5×#12011yescharacteristic
313C2×C4C5×#12111yescharacteristic
314C2×C4C5×#13511yescharacteristic
315C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
316C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
317C8—41no—
318C8C2×C5×C22⋊C411yescharacteristic
319C8C4×C5×D411yescharacteristic
320C8C5×#12111yescharacteristic
321C8C5×#12311yescharacteristic
322C5#1303311yescharacteristic, direct product factor, Sylow
323C22—41no—
324C22—44no—
325C22—84no—
326C22—81no—
327C22—162no—
328C22—162no—
329C22—161no—
330C22C4×C5×D811yescharacteristic
331C22C5×#44711yescharacteristic
332C22C5×#45911yescharacteristic
333C4—42no—
334C4—82no—
335C4—81no—
336C4—161no—
337C4C5×#38611yescharacteristic
338C4C5×#44211yescharacteristic
339C4C5×#44911yescharacteristic
340C4C5×#46311yescharacteristic
341C2—21no—
342C2—21no—
343C2—21no—
344C2—84no—
345C2—161no—
346C2C5×#187911yescharacteristic
subgroupG/H
center, socleC2×C5#1879
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×#2948C2semidirect
3. C5×#2145C2semidirect
4. C5×#2140C2semidirect
5. C5×#1976C2semidirect
6. C5×#1384C2semidirect
7. C5×#1378C2semidirect
13. C2×C5×SD32C4semidirect
14. C2×C5×D16C4semidirect
27. #13033C5direct (N × H)
34. C2×C5×Q16C2×C4semidirect
40. C2×C5×D8C2×C4semidirect
58. C2×C5×C16C2×C4semidirect
69. #2948C2×C5semidirect
70. #2145C2×C5semidirect
71. #2140C2×C5semidirect
72. #1976C2×C5semidirect
73. #1384C2×C5semidirect
74. #1378C2×C5semidirect
128. C2×SD32C4×C5semidirect
129. C2×D16C4×C5semidirect
182. C2×Q16C2×C4×C5semidirect
188. C2×D8C2×C4×C5semidirect
206. C2×C16C2×C4×C5semidirect
322. C5#13033direct (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×#29482
C5×#21452
C5×#21402
C5×#19762
C5×#13842
C5×#13782
#130335