Finite Group Databasebeta

← C5×#9590 #11932310

Subgroups — C5×#9590 #11932310

Order 1280.

364 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#1980C211yesmaximal, characteristic
2C5×#1950C211yesmaximal, characteristic, complemented
3C5×#1540C211yesmaximal, characteristic
4C5×#1492C211yesmaximal, characteristic
5C5×C8×M16C211yesmaximal, characteristic, complemented
6C5×#1303C211yesmaximal, characteristic, complemented
7C5×#1279C211yesmaximal, characteristic, complemented
8C5×#532C2211yescharacteristic
9C5×#431C2211yescharacteristic
10C2×C5×#108—21no—
11C5×#423C2211yescharacteristic
12C2×C5×C4⋊C8C2211yescharacteristic
13C2×C5×#104—21no—
14C2×C5×#104—21no—
15C4×C5×M16C2211yescharacteristic
16C2×C4×C5×C8C2211yescharacteristic
17C4×C5×C4⋊C4C2211yescharacteristic
18C5×#341—21no—
19C5×#332C411yescharacteristic, complemented
20C5×#332C411yescharacteristic, complemented
21C5×#331C411yescharacteristic, complemented
22C5×#331C411yescharacteristic, complemented
23C5×D4⋊C8—21no—
24C5×D4⋊C8—21no—
25C5×#322—21no—
26C5×C82—21no—
27#9590C511yesmaximal, characteristic, direct product factor, Sylow
28C2×C5×#41—21no—
29C2×C5×M16—21no—
30C2×C5×M16D411yescharacteristic
31C2×C5×M16D411yescharacteristic
32C22×C5×C8—21no—
33C22×C5×C8—21no—
34C5×C4⋊Q8C2×C411yescharacteristic
35C5×#127C2×C411yescharacteristic
36C5×#124—21no—
37C5×#121—21no—
38C5×#121—21no—
39C4×C5×D4—21no—
40C4×C5×D4—21no—
41C2×C5×C4⋊C4—21no—
42C2×C42×C5—21no—
43C2×C42×C5C2311yescharacteristic
44C5×#108—42no—
45C5×C4⋊C8—21no—
46C5×C4⋊C8—21no—
47C5×C4⋊C8—21no—
48C5×C4⋊C8C2×C411yescharacteristic
49C5×C4⋊C8C2×C411yescharacteristic
50C5×C4⋊C8C2×C411yescharacteristic
51C5×C4⋊C8C2×C411yescharacteristic
52C5×#104—42no—
53C5×#104—42no—
54C5×C22⋊C8—21no—
55C5×#97—21no—
56C4×C5×C8—21no—
57C4×C5×C8—21no—
58C4×C5×C8—21no—
59C4×C5×C8D411yescharacteristic
60C4×C5×C8D411yescharacteristic
61C5×#95—21no—
62#1980C2×C511yescharacteristic
63#1950C2×C511yescharacteristic, complemented
64#1540C2×C511yescharacteristic
65#1492C2×C511yescharacteristic
66C8×M16C2×C511yescharacteristic, complemented
67#1303C2×C511yescharacteristic, complemented
68#1279C2×C511yescharacteristic, complemented
69C5×#41—41no—
70C5×#41—41no—
71C5×#41—41no—
72C5×#41—41no—
73C2×C5×Q8—21no—
74C2×C5×D4—21no—
75C2×C5×D4—21no—
76C2×C5×D4—21no—
77C2×C5×D4—41no—
78C22×C4×C5—41no—
79C22×C4×C5—41no—
80C22×C4×C5C2×D411yescharacteristic
81C22×C4×C5#4111yescharacteristic
82C22×C4×C5#4111yescharacteristic
83C5×M16—21no—
84C5×M16—21no—
85C5×M16—41no—
86C5×M16—41no—
87C5×M16D812yes—
88C5×M16SD1612yes—
89C2×C5×C8—21no—
90C2×C5×C8—21no—
91C2×C5×C8—21no—
92C2×C5×C8—21no—
93C2×C5×C8—21no—
94C2×C5×C8—21no—
95C2×C5×C8—21no—
96C2×C5×C8—21no—
97C2×C5×C8—42no—
98C2×C5×C8—41no—
99C2×C5×C8—41no—
100C2×C5×C8—41no—
101C5×C4⋊C4—22no—
102C5×C4⋊C4—21no—
103C5×C4⋊C4—21no—
104C5×C4⋊C4—41no—
105C5×C22⋊C4—41no—
106C5×C22⋊C4—41no—
107C42×C5—41no—
108C42×C5—41no—
109C42×C5C22×C411yescharacteristic
110C42×C5C2×D411yescharacteristic
111C42×C5#4111yescharacteristic
112C42×C5#4111yescharacteristic
113#532C22×C511yescharacteristic
114#431C22×C511yescharacteristic
115C2×#108—21no—
116#423C22×C511yescharacteristic
117C2×C4⋊C8C22×C511yescharacteristic
118C2×#104—21no—
119C2×#104—21no—
120C4×M16C22×C511yescharacteristic
121C2×C4×C8C22×C511yescharacteristic
122C4×C4⋊C4C22×C511yescharacteristic
123#341—21no—
124#332C4×C511yescharacteristic, complemented
125#332C4×C511yescharacteristic, complemented
126#331C4×C511yescharacteristic, complemented
127#331C4×C511yescharacteristic, complemented
128D4⋊C8—21no—
129D4⋊C8—21no—
130#322—21no—
131C82—21no—
132C23×C5—41no—
133C23×C5#12411yescharacteristic
134C5×Q8—41no—
135C5×Q8—41no—
136C5×D4—41no—
137C5×D4—41no—
138C5×D4—41no—
139C5×D4—41no—
140C5×D4—81no—
141C5×D4—81no—
142C5×D4—81no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—41no—
146C2×C4×C5—42no—
147C2×C4×C5—41no—
148C2×C4×C5—81no—
149C2×C4×C5—81no—
150C2×C4×C5—81no—
151C2×C4×C5—81no—
152C2×C4×C5#11711yescharacteristic
153C2×C4×C5C4×D411yescharacteristic
154C2×C4×C5C4×D411yescharacteristic
155C2×C4×C5#12111yescharacteristic
156C2×C4×C5#12311yescharacteristic
157C2×C4×C5#12611yescharacteristic
158C2×C4×C5C2×D811yescharacteristic
159C2×C4×C5C2×SD1611yescharacteristic
160C2×C4×C5#13511yescharacteristic
161C2×C4×C5#13511yescharacteristic
162C5×C8—22no—
163C5×C8—22no—
164C5×C8—22no—
165C5×C8—41no—
166C5×C8—41no—
167C5×C8—41no—
168C5×C8—41no—
169C5×C8—41no—
170C5×C8—81no—
171C2×#41—21no—
172C2×M16—21no—
173C2×M16C5×D411yescharacteristic
174C2×M16C5×D411yescharacteristic
175C22×C8—21no—
176C22×C8—21no—
177C4⋊Q8C2×C4×C511yescharacteristic
178#127C2×C4×C511yescharacteristic
179#124—21no—
180#121—21no—
181#121—21no—
182C4×D4—21no—
183C4×D4—21no—
184C2×C4⋊C4—21no—
185C2×C42—21no—
186C2×C42C23×C511yescharacteristic
187#108—42no—
188C4⋊C8—21no—
189C4⋊C8—21no—
190C4⋊C8—21no—
191C4⋊C8C2×C4×C511yescharacteristic
192C4⋊C8C2×C4×C511yescharacteristic
193C4⋊C8C2×C4×C511yescharacteristic
194C4⋊C8C2×C4×C511yescharacteristic
195#104—42no—
196#104—42no—
197C22⋊C8—21no—
198#97—21no—
199C4×C8—21no—
200C4×C8—21no—
201C4×C8—21no—
202C4×C8C5×D411yescharacteristic
203C4×C8C5×D411yescharacteristic
204#95—21no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5—81no—
208C22×C5—81no—
209C22×C5—81no—
210C22×C5#38811yescharacteristic
211C22×C5#48611yescharacteristic
212C22×C5#48811yescharacteristic
213C4×C5—21no—
214C4×C5—21no—
215C4×C5—21no—
216C4×C5—82no—
217C4×C5—81no—
218C4×C5C4×D811yescharacteristic
219C4×C5C4×SD1611yescharacteristic
220C4×C5#44311yescharacteristic
221C4×C5#44411yescharacteristic
222C4×C5#46511yescharacteristic
223C4×C5#46611yescharacteristic
224#41—41no—
225#41—41no—
226#41—41no—
227#41—41no—
228C2×Q8—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4—21no—
232C2×D4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4C2×C5×D411yescharacteristic
236C22×C4C5×#4111yescharacteristic
237C22×C4C5×#4111yescharacteristic
238M16—21no—
239M16—21no—
240M16—41no—
241M16—41no—
242M16C5×D812yes—
243M16C5×SD1612yes—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—42no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C4⋊C4—22no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C42—41no—
263C42—41no—
264C42C22×C4×C511yescharacteristic
265C42C2×C5×D411yescharacteristic
266C42C5×#4111yescharacteristic
267C42C5×#4111yescharacteristic
268C2×C5—21no—
269C2×C5—21no—
270C2×C5—161no—
271C2×C5#192911yescharacteristic
272C2×C5#193211yescharacteristic
273C2×C5#193411yescharacteristic
274C23—41no—
275C23C5×#12411yescharacteristic
276Q8—41no—
277Q8—41no—
278D4—41no—
279D4—41no—
280D4—41no—
281D4—41no—
282D4—81no—
283D4—81no—
284D4—81no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4C5×#11711yescharacteristic
295C2×C4C4×C5×D411yescharacteristic
296C2×C4C4×C5×D411yescharacteristic
297C2×C4C5×#12111yescharacteristic
298C2×C4C5×#12311yescharacteristic
299C2×C4C5×#12611yescharacteristic
300C2×C4C2×C5×D811yescharacteristic
301C2×C4C2×C5×SD1611yescharacteristic
302C2×C4C5×#13511yescharacteristic
303C2×C4C5×#13511yescharacteristic
304C8—22no—
305C8—22no—
306C8—22no—
307C8—41no—
308C8—41no—
309C8—41no—
310C8—41no—
311C8—41no—
312C8—81no—
313C5#959011yescharacteristic, direct product factor, Sylow
314C22—21no—
315C22—21no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22C5×#38811yescharacteristic
320C22C5×#48611yescharacteristic
321C22C5×#48811yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—82no—
326C4—81no—
327C4C4×C5×D811yescharacteristic
328C4C4×C5×SD1611yescharacteristic
329C4C5×#44311yescharacteristic
330C4C5×#44411yescharacteristic
331C4C5×#46511yescharacteristic
332C4C5×#46611yescharacteristic
333C2—21no—
334C2—21no—
335C2—161no—
336C2C5×#192911yescharacteristic
337C2C5×#193211yescharacteristic
338C2C5×#193411yescharacteristic
subgroupG/H
centerC2×C4×C5#121
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
socleC22×C5#388
prime radicalC5×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1950C2semidirect
5. C5×C8×M16C2semidirect
6. C5×#1303C2semidirect
7. C5×#1279C2semidirect
19. C5×#332C4semidirect
20. C5×#332C4semidirect
21. C5×#331C4semidirect
22. C5×#331C4semidirect
27. #9590C5direct (N × H)
63. #1950C2×C5semidirect
66. C8×M16C2×C5semidirect
67. #1303C2×C5semidirect
68. #1279C2×C5semidirect
124. #332C4×C5semidirect
125. #332C4×C5semidirect
126. #331C4×C5semidirect
127. #331C4×C5semidirect
313. C5#9590direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#19802
C5×#19502
C5×#15402
C5×#14922
C5×C8×M162
C5×#13032
C5×#12792
#95905