Finite Group Databasebeta

← C5×#68409 #14291448

Subgroups — C5×#68409 #14291448

Order 1920.

376 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
1C5×#5075C211yesmaximal, characteristic, complemented
2C5×#5073C211yesmaximal, characteristic
3C5×#4848C211yesmaximal, characteristic, complemented
4C5×#4830C211yesmaximal, characteristic, complemented
5C3×C5×#331C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic, complemented
7C5×#4479C211yesmaximal, characteristic, complemented
8C5×#1668—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10C2×C5×#214—21no—
11C2×C5×#213—21no—
12C2×C5×#213—21no—
13C2×C5×#204—21no—
14C5×#874C2211yescharacteristic
15C4×C5×Dic6C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17C3×C5×C4⋊C8C2211yescharacteristic
18C5×#832—21no—
19C5×#821—21no—
20C5×Dic3⋊C8—21no—
21C5×C8×Dic3—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24#68409C511yesmaximal, characteristic, direct product factor, Hall
25C5×#493—31no—
26C5×#460—31no—
27C5×#460—31no—
28C5×C8×Q8—31no—
29C5×#335—31no—
30C5×#331—31no—
31C5×#331D311yescharacteristic, complemented
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×Dic6D411yescharacteristic
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42C5×#214—42no—
43C5×#213—42no—
44C5×#213—42no—
45C5×C4⋊Dic3D411yescharacteristic
46C5×Dic3⋊C4—21no—
47C4×C5×Dic3—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8D411yescharacteristic
50C2×C5×C3⋊C8D411yescharacteristic
51C5×#204—42no—
52#5075C2×C511yescharacteristic, complemented
53#5073C2×C511yescharacteristic
54#4848C2×C511yescharacteristic, complemented
55#4830C2×C511yescharacteristic, complemented
56C3×#331C2×C511yescharacteristic, complemented
57#4485C2×C511yescharacteristic, complemented
58#4479C2×C511yescharacteristic, complemented
59C2×C5×SD16—61no—
60C2×C5×SD16—61no—
61C2×C5×D8—61no—
62C2×C5×D8—61no—
63C5×#127—31no—
64C5×#127C2×D311yescharacteristic
65C4×C5×Q8—31no—
66C5×C4⋊C8—31no—
67C5×C4⋊C8—61no—
68C5×C4⋊C8C2×D311yescharacteristic
69C5×C4⋊C8C2×D311yescharacteristic
70C5×#102—61no—
71C5×#102—61no—
72C4×C5×C8—31no—
73C4×C5×C8—61no—
74#1668—31noSylow
75C23×C3×C5—41no—
76C22×C5×D3—41no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—81no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5#4111yescharacteristic
85C2×C5×Dic3—21no—
86C2×C5×Dic3—21no—
87C5×D12—41no—
88C5×D12—41no—
89C5×D12—41no—
90C5×D12—41no—
91C5×D12—81no—
92C5×Dic6—21no—
93C5×Dic6D812yescomplemented
94C3×C5×C8—41no—
95C3×C5×C8—41no—
96C5×C3⋊C8—21no—
97C5×C3⋊C8—41no—
98C5×C3⋊C8SD1612yescomplemented
99C3×#127C22×C511yescharacteristic
100C2×#214—21no—
101C2×#213—21no—
102C2×#213—21no—
103C2×#204—21no—
104#874C22×C511yescharacteristic
105C4×Dic6C22×C511yescharacteristic
106C3×C4⋊C8C22×C511yescharacteristic
107C3×C4⋊C8C22×C511yescharacteristic
108#832—21no—
109#821—21no—
110Dic3⋊C8—21no—
111C8×Dic3—21no—
112C4⋊(C3⋊C8)C22×C511yescharacteristic
113C4×C3⋊C8C22×C511yescharacteristic
114C2×C5×Q8—31no—
115C2×C5×D4—21no—
116C2×C5×D4—21no—
117C2×C5×D4—21no—
118C2×C5×D4—61no—
119C2×C5×D4—61no—
120C2×C5×D4—61no—
121C5×SD16—122no—
122C5×SD16—122no—
123C5×D8—122no—
124C5×D8—122no—
125C2×C5×C8—21no—
126C2×C5×C8—21no—
127C2×C5×C8—31no—
128C2×C5×C8—31no—
129C2×C5×C8—61no—
130C5×C4⋊C4—31no—
131C5×C4⋊C4—61no—
132C42×C5—61no—
133C42×C5C22×D311yescharacteristic
134#493—31no—
135#460—31no—
136#460—31no—
137C8×Q8—31no—
138#335—31no—
139#331—31no—
140#331C5×D311yescharacteristic, complemented
141C22×C3×C5—81no—
142C22×C3×C5—81no—
143C22×C3×C5—81no—
144C22×C3×C5#12111yescharacteristic
145C2×C5×D3—81no—
146C2×C5×D3—81no—
147C2×C5×D3—81no—
148C3×C4×C5—21no—
149C3×C4×C5C2×D811yescharacteristic
150C3×C4×C5C2×SD1611yescharacteristic
151C3×C4×C5#13511yescharacteristic
152C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
153C5×Dic3—22no—
154C5×Dic3—41no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×D12—21no—
159C2×D12—21no—
160C2×D12—21no—
161C2×Dic6C5×D411yescharacteristic
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C3×C42C23×C511yescharacteristic
165#214—42no—
166#213—42no—
167#213—42no—
168C4⋊Dic3C5×D411yescharacteristic
169Dic3⋊C4—21no—
170C4×Dic3—21no—
171C2×C3⋊C8—21no—
172C2×C3⋊C8C5×D411yescharacteristic
173C2×C3⋊C8C5×D411yescharacteristic
174#204—42no—
175C23×C5—41no—
176C23×C5—121no—
177C5×Q8—32no—
178C5×Q8—61no—
179C5×D4—41no—
180C5×D4—41no—
181C5×D4—41no—
182C5×D4—41no—
183C5×D4—81no—
184C5×D4—121no—
185C5×D4—121no—
186C5×D4—121no—
187C5×D4—121no—
188C5×D4—241no—
189C2×C4×C5—61no—
190C2×C4×C5—61no—
191C2×C4×C5#23511yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5D3×D411yescharacteristic
194C5×C8—32no—
195C5×C8—41no—
196C5×C8—41no—
197C5×C8—61no—
198C5×C8—121no—
199C2×SD16—61no—
200C2×SD16—61no—
201C2×D8—61no—
202C2×D8—61no—
203#127—31no—
204#127C2×C5×D311yescharacteristic
205C4×Q8—31no—
206C4⋊C8—31no—
207C4⋊C8—61no—
208C4⋊C8C2×C5×D311yescharacteristic
209C4⋊C8C2×C5×D311yescharacteristic
210#102—61no—
211#102—61no—
212C4×C8—31no—
213C4×C8—61no—
214C2×C3×C5—161no—
215C2×C3×C5#46011yescharacteristic
216C2×C3×C5#46611yescharacteristic
217C2×C3×C5#47211yescharacteristic
218C5×D3—161no—
219C23×C3—41no—
220C22×D3—41no—
221C3×D4—41no—
222C3×D4—41no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4—81no—
226C2×C3×C4C2×C5×D411yescharacteristic
227C2×C3×C4C2×C5×D411yescharacteristic
228C2×C3×C4C5×#4111yescharacteristic
229C2×Dic3—21no—
230C2×Dic3—21no—
231D12—41no—
232D12—41no—
233D12—41no—
234D12—41no—
235D12—81no—
236Dic6—21no—
237Dic6C5×D812yescomplemented
238C3×C8—41no—
239C3×C8—41no—
240C3⋊C8—21no—
241C3⋊C8—41no—
242C3⋊C8C5×SD1612yescomplemented
243C22×C5—81no—
244C22×C5—81no—
245C22×C5—81no—
246C22×C5—241no—
247C22×C5—241no—
248C22×C5—241no—
249C22×C5#88411yescharacteristic
250C4×C5—21no—
251C4×C5—62no—
252C4×C5—121no—
253C4×C5D3×D811yescharacteristic
254C4×C5#91111yescharacteristic
255C4×C5D3×SD1611yescharacteristic
256C4×C5#91611yescharacteristic
257C2×Q8—31no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—61no—
262C2×D4—61no—
263C2×D4—61no—
264SD16—122no—
265SD16—122no—
266D8—122no—
267D8—122no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—31no—
271C2×C8—31no—
272C2×C8—61no—
273C4⋊C4—31no—
274C4⋊C4—61no—
275C42—61no—
276C42C22×C5×D311yescharacteristic
277C3×C5#166811yescharacteristic, complemented, Hall
278C22×C3—81no—
279C22×C3—81no—
280C22×C3—81no—
281C22×C3C5×#12111yescharacteristic
282C2×D3—81no—
283C2×D3—81no—
284C2×D3—81no—
285C3×C4—21no—
286C3×C4C2×C5×D811yescharacteristic
287C3×C4C2×C5×SD1611yescharacteristic
288C3×C4C5×#13511yescharacteristic
289C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
290Dic3—22no—
291Dic3—41no—
292C2×C5—161no—
293C2×C5—481no—
294C2×C5#474911yescharacteristic
295C2×C5#476211yescharacteristic
296C2×C5#477511yescharacteristic
297C23—41no—
298C23—121no—
299Q8—32no—
300Q8—61no—
301D4—41no—
302D4—41no—
303D4—41no—
304D4—41no—
305D4—81no—
306D4—121no—
307D4—121no—
308D4—121no—
309D4—121no—
310D4—241no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4C5×#23511yescharacteristic
314C2×C4C5×D3×D411yescharacteristic
315C2×C4C5×D3×D411yescharacteristic
316C8—32no—
317C8—41no—
318C8—41no—
319C8—61no—
320C8—121no—
321C2×C3—161no—
322C2×C3C5×#46011yescharacteristic
323C2×C3C5×#46611yescharacteristic
324C2×C3C5×#47211yescharacteristic
325D3—161no—
326C5#6840911yescharacteristic, direct product factor, Sylow
327C22—81no—
328C22—81no—
329C22—81no—
330C22—241no—
331C22—241no—
332C22—241no—
333C22C5×#88411yescharacteristic
334C4—21no—
335C4—62no—
336C4—121no—
337C4C5×D3×D811yescharacteristic
338C4C5×#91111yescharacteristic
339C4C5×D3×SD1611yescharacteristic
340C4C5×#91611yescharacteristic
341C3C5×#166811yescharacteristic, complemented, Sylow
342C2—161no—
343C2—481no—
344C2C5×#474911yescharacteristic
345C2C5×#476211yescharacteristic
346C2C5×#477511yescharacteristic
subgroupG/H
centerC22×C5#884
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#331C2
socleC22×C3×C5#121
prime radicalC5×#5073C2
hypercenterC5×#331D3
hypocenterC3C5×#1668
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#331

Complements

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

NH ≅ G/Ntype
1. C5×#5075C2semidirect
3. C5×#4848C2semidirect
4. C5×#4830C2semidirect
5. C3×C5×#331C2semidirect
6. C5×#4485C2semidirect
7. C5×#4479C2semidirect
24. #68409C5direct (N × H)
31. C5×#331D3semidirect
52. #5075C2×C5semidirect
54. #4848C2×C5semidirect
55. #4830C2×C5semidirect
56. C3×#331C2×C5semidirect
57. #4485C2×C5semidirect
58. #4479C2×C5semidirect
93. C5×Dic6D8semidirect
98. C5×C3⋊C8SD16semidirect
140. #331C5×D3semidirect
237. Dic6C5×D8semidirect
242. C3⋊C8C5×SD16semidirect
277. C3×C5#1668semidirect
326. C5#68409direct (N × H)
341. C3C5×#1668semidirect

Maximal subgroups

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

subgroupindex
C5×#50752
C5×#50732
C5×#48482
C5×#48302
C3×C5×#3312
C5×#44852
C5×#44792
C5×#16683
#684095