Finite Group Databasebeta

← C5×#13144 #11935864

Subgroups — C5×#13144 #11935864

Order 1280.

334 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#361C211yesmaximal, characteristic
2C2×C5×#357C211yesmaximal, characteristic
3C5×#2108C211yesmaximal, characteristic, complemented
4C5×#1978C211yesmaximal, characteristic
5C5×#1952C211yesmaximal, characteristic, complemented
6C5×#1387C211yesmaximal, characteristic, complemented
7C5×#1381C211yesmaximal, characteristic, complemented
8C22×C5×D8C2211yescharacteristic
9C2×C5×M32C2211yescharacteristic
10C22×C5×C16C2211yescharacteristic
11C2×C5×#108C2211yescharacteristic
12C2×C5×#108C2211yescharacteristic
13C5×#428—21no—
14C2×C5×#107C2211yescharacteristic
15C5×#418—21no—
16C2×C5×#100—21no—
17C5×#405C2211yescharacteristic
18C5×#361C414yescomplemented
19C5×#357—21no—
20C5×#357—21no—
21C5×#346—21no—
22C4×C5×C16—21no—
23C5×#343—21no—
24#13144C511yesmaximal, characteristic, direct product factor, Sylow
25C22×C5×D4—21no—
26C2×C5×D8—21no—
27C2×C5×D8—21no—
28C2×C5×D8—21no—
29C2×C5×D8—21no—
30C2×C5×D8—21no—
31C2×C5×D8C2×C412yes—
32C2×C5×M16—21no—
33C2×C5×M16—21no—
34C2×C5×M16D411yescharacteristic
35C22×C5×C8C2311yescharacteristic
36C5×#117D411yescharacteristic
37C2×C5×C4⋊C4—21no—
38C5×M32—21no—
39C5×M32C2×C412yes—
40C2×C5×C16—21no—
41C2×C5×C16—21no—
42C2×C5×C16—21no—
43C2×C5×C16D411yescharacteristic
44C2×C5×C16D411yescharacteristic
45C5×#108—21no—
46C5×#108—21no—
47C5×#108—21no—
48C5×#108C2×C412yes—
49C5×#107—21no—
50C5×#107—21no—
51C5×#107—41no—
52C5×#106—41no—
53C5×#102—41no—
54C5×#102—41no—
55C5×#100—42no—
56C5×#97—21no—
57C4×C5×C8—21no—
58C2×#361C2×C511yescharacteristic
59C2×#357C2×C511yescharacteristic
60#2108C2×C511yescharacteristic, complemented
61#1978C2×C511yescharacteristic
62#1952C2×C511yescharacteristic, complemented
63#1387C2×C511yescharacteristic, complemented
64#1381C2×C511yescharacteristic, complemented
65C24×C5—41no—
66C2×C5×D4—22no—
67C2×C5×D4—41no—
68C2×C5×D4—41no—
69C2×C5×D4—41no—
70C2×C5×D4—41no—
71C2×C5×D4—41no—
72C22×C4×C5—41no—
73C22×C4×C5C2×D411yescharacteristic
74C5×D8—22no—
75C5×D8—22no—
76C5×D8—41no—
77C5×D8—41no—
78C5×M16—21no—
79C5×M16—22no—
80C5×M16—41no—
81C5×M16—41no—
82C5×M16—41no—
83C5×M16SD1612yes—
84C2×C5×C8—21no—
85C2×C5×C8—41no—
86C2×C5×C8—41no—
87C2×C5×C8C22×C411yescharacteristic
88C2×C5×C8C2×D411yescharacteristic
89C2×C5×C8#4111yescharacteristic
90C2×C5×C8#4111yescharacteristic
91C2×C5×C8#4111yescharacteristic
92C2×C5×C8#4111yescharacteristic
93C5×C4⋊C4—41no—
94C5×C4⋊C4—41no—
95C5×C4⋊C4D811yescharacteristic
96C5×C4⋊C4D811yescharacteristic
97C5×C22⋊C4—21no—
98C42×C5—21no—
99C5×C16—22no—
100C5×C16—21no—
101C5×C16—21no—
102C22×D8C22×C511yescharacteristic
103C2×M32C22×C511yescharacteristic
104C22×C16C22×C511yescharacteristic
105C2×#108C22×C511yescharacteristic
106C2×#108C22×C511yescharacteristic
107#428—21no—
108C2×#107C22×C511yescharacteristic
109#418—21no—
110C2×#100—21no—
111#405C22×C511yescharacteristic
112#361C4×C514yescomplemented
113#357—21no—
114#357—21no—
115#346—21no—
116C4×C16—21no—
117#343—21no—
118C23×C5—42no—
119C23×C5—81no—
120C23×C5—81no—
121C23×C5—161no—
122C23×C5—161no—
123C23×C5#13511yescharacteristic
124C5×D4—42no—
125C5×D4—42no—
126C5×D4—81no—
127C5×D4—81no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—81no—
131C2×C4×C5—161no—
132C2×C4×C5C4×D411yescharacteristic
133C2×C4×C5#12111yescharacteristic
134C2×C4×C5#12411yescharacteristic
135C2×C4×C5C2×D811yescharacteristic
136C2×C4×C5C2×SD1611yescharacteristic
137C2×C4×C5#13511yescharacteristic
138C5×C8—22no—
139C5×C8—42no—
140C5×C8—81no—
141C5×C8#11711yescharacteristic
142C5×C8C4×D411yescharacteristic
143C5×C8#12311yescharacteristic
144C5×C8#12611yescharacteristic
145C22×D4—21no—
146C2×D8—21no—
147C2×D8—21no—
148C2×D8—21no—
149C2×D8—21no—
150C2×D8—21no—
151C2×D8C2×C4×C512yes—
152C2×M16—21no—
153C2×M16—21no—
154C2×M16C5×D411yescharacteristic
155C22×C8C23×C511yescharacteristic
156#117C5×D411yescharacteristic
157C2×C4⋊C4—21no—
158M32—21no—
159M32C2×C4×C512yes—
160C2×C16—21no—
161C2×C16—21no—
162C2×C16—21no—
163C2×C16C5×D411yescharacteristic
164C2×C16C5×D411yescharacteristic
165#108—21no—
166#108—21no—
167#108—21no—
168#108C2×C4×C512yes—
169#107—21no—
170#107—21no—
171#107—41no—
172#106—41no—
173#102—41no—
174#102—41no—
175#100—42no—
176#97—21no—
177C4×C8—21no—
178C22×C5—21no—
179C22×C5—21no—
180C22×C5—82no—
181C22×C5—162no—
182C22×C5—162no—
183C22×C5—161no—
184C22×C5—161no—
185C22×C5C4×SD1611yescharacteristic
186C22×C5#46611yescharacteristic
187C22×C5#48811yescharacteristic
188C4×C5—41no—
189C4×C5—41no—
190C4×C5—161no—
191C4×C5#38811yescharacteristic
192C4×C5C4×D811yescharacteristic
193C4×C5#46511yescharacteristic
194C4×C5#48611yescharacteristic
195C24—41no—
196C2×D4—22no—
197C2×D4—41no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4—41no—
202C22×C4—41no—
203C22×C4C2×C5×D411yescharacteristic
204D8—22no—
205D8—22no—
206D8—41no—
207D8—41no—
208M16—21no—
209M16—22no—
210M16—41no—
211M16—41no—
212M16—41no—
213M16C5×SD1612yes—
214C2×C8—21no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8C22×C4×C511yescharacteristic
218C2×C8C2×C5×D411yescharacteristic
219C2×C8C5×#4111yescharacteristic
220C2×C8C5×#4111yescharacteristic
221C2×C8C5×#4111yescharacteristic
222C2×C8C5×#4111yescharacteristic
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4C5×D811yescharacteristic
226C4⋊C4C5×D811yescharacteristic
227C22⋊C4—21no—
228C42—21no—
229C16—22no—
230C16—21no—
231C16—21no—
232C2×C5—21no—
233C2×C5—21no—
234C2×C5—162no—
235C2×C5#193411yescharacteristic
236C2×C5#222111yescharacteristic
237C2×C5#222311yescharacteristic
238C23—42no—
239C23—81no—
240C23—81no—
241C23—161no—
242C23—161no—
243C23C5×#13511yescharacteristic
244D4—42no—
245D4—42no—
246D4—81no—
247D4—81no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—81no—
251C2×C4—161no—
252C2×C4C4×C5×D411yescharacteristic
253C2×C4C5×#12111yescharacteristic
254C2×C4C5×#12411yescharacteristic
255C2×C4C2×C5×D811yescharacteristic
256C2×C4C2×C5×SD1611yescharacteristic
257C2×C4C5×#13511yescharacteristic
258C8—22no—
259C8—42no—
260C8—81no—
261C8C5×#11711yescharacteristic
262C8C4×C5×D411yescharacteristic
263C8C5×#12311yescharacteristic
264C8C5×#12611yescharacteristic
265C5#1314411yescharacteristic, direct product factor, Sylow
266C22—21no—
267C22—21no—
268C22—82no—
269C22—162no—
270C22—162no—
271C22—161no—
272C22—161no—
273C22C4×C5×SD1611yescharacteristic
274C22C5×#46611yescharacteristic
275C22C5×#48811yescharacteristic
276C4—41no—
277C4—41no—
278C4—161no—
279C4C5×#38811yescharacteristic
280C4C4×C5×D811yescharacteristic
281C4C5×#46511yescharacteristic
282C4C5×#48611yescharacteristic
283C2—21no—
284C2—21no—
285C2—162no—
286C2C5×#193411yescharacteristic
287C2C5×#222111yescharacteristic
288C2C5×#222311yescharacteristic
subgroupG/H
center, socleC22×C5#466
commutatorC2×C8C22×C4×C5
Frattini, cosocleC22×C8C23×C5
prime radicalC22×C5×D8C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#405 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#2108C2semidirect
5. C5×#1952C2semidirect
6. C5×#1387C2semidirect
7. C5×#1381C2semidirect
18. C5×#361C4semidirect
24. #13144C5direct (N × H)
60. #2108C2×C5semidirect
62. #1952C2×C5semidirect
63. #1387C2×C5semidirect
64. #1381C2×C5semidirect
112. #361C4×C5semidirect
265. C5#13144direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3612
C2×C5×#3572
C5×#21082
C5×#19782
C5×#19522
C5×#13872
C5×#13812
#131445