Finite Group Databasebeta

← C5×#71017 #14289049

Subgroups — C5×#71017 #14289049

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5563C211yesmaximal, characteristic, complemented
2C3×C5×#459C211yesmaximal, characteristic, complemented
3C5×#5076C211yesmaximal, characteristic, complemented
4C5×#5072C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C5×#4483C211yesmaximal, characteristic, complemented
7C5×#4481C211yesmaximal, characteristic, complemented
8C5×#1624—31nomaximal, Hall
9C2×C3×C5×D8—21no—
10C3×C5×#127C2211yescharacteristic
11C3×C4×C5×D4C2211yescharacteristic
12C5×#938—21no—
13C2×C5×#214—22no—
14C2×C5×#213—21no—
15C5×#930—21no—
16C5×#926—21no—
17C5×#892—21no—
18C5×#885—22no—
19C4×C5×D12C2211yescharacteristic
20C5×#869C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×#102—21no—
23C5×#832—21no—
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26#71017C511yesmaximal, characteristic, direct product factor, Hall
27C5×#555—31no—
28C5×#492—31no—
29C5×#459—31no—
30C5×#459D311yescharacteristic, complemented
31C5×#333—31no—
32C5×D4⋊C8—31no—
33C5×D4⋊C8—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4D411yescharacteristic
38C22×C3×C4×C5—21no—
39C2×C5×#67—22no—
40C2×C5×D12D411yescharacteristic
41C2×C4×C5×D3—21no—
42C2×C5×Dic6D412yes—
43C3×C5×D8—42no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C5×C22⋊C4—21no—
47C3×C42×C5C2311yescharacteristic
48C5×#217—22no—
49C5×#214—44no—
50C5×#213—42no—
51C5×(C2×D3)⋊C4—22no—
52C5×(C2×D3)⋊C4—21no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3—21no—
55C5×C4⋊Dic3D411yescharacteristic
56C4×C5×Dic3—22no—
57C2×C5×C3⋊C8—21no—
58C2×C5×C3⋊C8—21no—
59#5563C2×C511yescharacteristic, complemented
60C3×#459C2×C511yescharacteristic, complemented
61#5076C2×C511yescharacteristic, complemented
62#5072C2×C511yescharacteristic, complemented
63D4⋊(C3⋊C8)C2×C511yescharacteristic, complemented
64#4483C2×C511yescharacteristic, complemented
65#4481C2×C511yescharacteristic, complemented
66C2×C5×SD16—62no—
67C2×C5×D8—21no—
68C2×C5×D8—61no—
69C5×C4⋊Q8—31no—
70C5×#127C2×D311yescharacteristic
71C5×#124—62no—
72C5×#121—61no—
73C5×#121—61no—
74C4×C5×D4—31no—
75C4×C5×D4C2×D311yescharacteristic
76C5×#117—61no—
77C5×#117—61no—
78C5×C4⋊C8—31no—
79C5×C4⋊C8C2×D311yescharacteristic
80C5×#102—21no—
81C5×#102—61no—
82C4×C5×C8—31no—
83#1624—31noSylow
84C23×C3×C5—21no—
85C23×C3×C5—41no—
86C22×C5×D3—21no—
87C3×C5×D4—21no—
88C3×C5×D4—21no—
89C3×C5×D4—42no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C5×#67—82no—
101C2×C5×Dic3—21no—
102C2×C5×Dic3—22no—
103C5×D12—21no—
104C5×D12—21no—
105C4×C5×D3—41no—
106C4×C5×D3—41no—
107C5×Dic6—42no—
108C3×C5×C8—41no—
109C5×C3⋊C8—22no—
110C5×C3⋊C8—41no—
111C2×C3×D8—21no—
112C3×#127C22×C511yescharacteristic
113C3×C4×D4C22×C511yescharacteristic
114#938—21no—
115C2×#214—22no—
116C2×#213—21no—
117#930—21no—
118#926—21no—
119#892—21no—
120#885—22no—
121C4×D12C22×C511yescharacteristic
122#869C22×C511yescharacteristic
123C3×C4⋊C8C22×C511yescharacteristic
124C3×#102—21no—
125#832—21no—
126C4⋊(C3⋊C8)C22×C511yescharacteristic
127C4×C3⋊C8C22×C511yescharacteristic
128C2×C5×Q8—32no—
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4—21no—
132C2×C5×D4—31no—
133C2×C5×D4—62no—
134C2×C5×D4#6711yescharacteristic
135C22×C4×C5—21no—
136C22×C4×C5—61no—
137C5×SD16—124no—
138C5×D8—42no—
139C5×D8—122no—
140C2×C5×C8—21no—
141C2×C5×C8—61no—
142C2×C5×C8—61no—
143C5×C4⋊C4—31no—
144C5×C4⋊C4—61no—
145C5×C4⋊C4—61no—
146C5×C4⋊C4#6711yescharacteristic
147C5×C22⋊C4—21no—
148C5×C22⋊C4—62no—
149C5×C22⋊C4—62no—
150C5×C22⋊C4—61no—
151C42×C5—62no—
152C42×C5C22×D311yescharacteristic
153#555—31no—
154#492—31no—
155#459—31no—
156#459C5×D311yescharacteristic, complemented
157#333—31no—
158D4⋊C8—31no—
159D4⋊C8—31no—
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5—81no—
164C22×C3×C5—81no—
165C22×C3×C5—81no—
166C22×C3×C5#12011yescharacteristic
167C2×C5×D3—41no—
168C2×C5×D3—41no—
169C2×C5×D3—41no—
170C3×C4×C5—21no—
171C3×C4×C5—41no—
172C3×C4×C5#13511yescharacteristic
173C3×C4×C5#13511yescharacteristic
174C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
175C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
176C5×Dic3—41no—
177C5×Dic3—42no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4C5×D411yescharacteristic
182C22×C3×C4—21no—
183C2×#67—22no—
184C2×D12C5×D411yescharacteristic
185C2×C4×D3—21no—
186C2×Dic6C5×D412yes—
187C3×D8—42no—
188C2×C3×C8—21no—
189C3×C4⋊C4C5×D411yescharacteristic
190C3×C22⋊C4—21no—
191C3×C42C23×C511yescharacteristic
192#217—22no—
193#214—44no—
194#213—42no—
195(C2×D3)⋊C4—22no—
196(C2×D3)⋊C4—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3C5×D411yescharacteristic
200C4×Dic3—22no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C23×C5—21no—
204C23×C5—41no—
205C23×C5—61no—
206C5×Q8—122no—
207C5×D4—21no—
208C5×D4—21no—
209C5×D4—42no—
210C5×D4—41no—
211C5×D4—41no—
212C5×D4—41no—
213C5×D4—41no—
214C5×D4—61no—
215C5×D4—61no—
216C5×D4—242no—
217C2×C4×C5—21no—
218C2×C4×C5—41no—
219C2×C4×C5—41no—
220C2×C4×C5—61no—
221C2×C4×C5—62no—
222C2×C4×C5—121no—
223C2×C4×C5—121no—
224C2×C4×C5D3×D411yescharacteristic
225C2×C4×C5D3×D411yescharacteristic
226C2×C4×C5C2×#6711yescharacteristic
227C5×C8—41no—
228C5×C8—62no—
229C5×C8—121no—
230C2×SD16—62no—
231C2×D8—21no—
232C2×D8—61no—
233C4⋊Q8—31no—
234#127C2×C5×D311yescharacteristic
235#124—62no—
236#121—61no—
237#121—61no—
238C4×D4—31no—
239C4×D4C2×C5×D311yescharacteristic
240#117—61no—
241#117—61no—
242C4⋊C8—31no—
243C4⋊C8C2×C5×D311yescharacteristic
244#102—21no—
245#102—61no—
246C4×C8—31no—
247C2×C3×C5—81no—
248C2×C3×C5—161no—
249C2×C3×C5#44911yescharacteristic
250C2×C3×C5#44911yescharacteristic
251C2×C3×C5#45311yescharacteristic
252C5×D3—81no—
253C23×C3—21no—
254C23×C3—41no—
255C22×D3—21no—
256C3×D4—21no—
257C3×D4—21no—
258C3×D4—42no—
259C3×D4—41no—
260C3×D4—41no—
261C3×D4—41no—
262C3×D4—41no—
263C2×C3×C4—21no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4C2×C5×D411yescharacteristic
267C2×C3×C4C2×C5×D411yescharacteristic
268C2×C3×C4C2×C5×D411yescharacteristic
269#67—82no—
270C2×Dic3—21no—
271C2×Dic3—22no—
272D12—21no—
273D12—21no—
274C4×D3—41no—
275C4×D3—41no—
276Dic6—42no—
277C3×C8—41no—
278C3⋊C8—22no—
279C3⋊C8—41no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5—81no—
284C22×C5—81no—
285C22×C5—81no—
286C22×C5—121no—
287C22×C5—121no—
288C22×C5—121no—
289C22×C5#93711yescharacteristic
290C4×C5—21no—
291C4×C5—41no—
292C4×C5—122no—
293C4×C5—121no—
294C4×C5#91111yescharacteristic
295C4×C5#91211yescharacteristic
296C4×C5#93211yescharacteristic
297C4×C5#95011yescharacteristic
298C2×Q8—32no—
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—31no—
303C2×D4—62no—
304C2×D4C5×#6711yescharacteristic
305C22×C4—21no—
306C22×C4—61no—
307SD16—124no—
308D8—42no—
309D8—122no—
310C2×C8—21no—
311C2×C8—61no—
312C2×C8—61no—
313C4⋊C4—31no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4C5×#6711yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—62no—
319C22⋊C4—62no—
320C22⋊C4—61no—
321C42—62no—
322C42C22×C5×D311yescharacteristic
323C3×C5#162411yescharacteristic, complemented, Hall
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—81no—
328C22×C3—81no—
329C22×C3—81no—
330C22×C3C5×#12011yescharacteristic
331C2×D3—41no—
332C2×D3—41no—
333C2×D3—41no—
334C3×C4—21no—
335C3×C4—41no—
336C3×C4C5×#13511yescharacteristic
337C3×C4C5×#13511yescharacteristic
338C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
339C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
340Dic3—41no—
341Dic3—42no—
342C2×C5—81no—
343C2×C5—161no—
344C2×C5—241no—
345C2×C5#503711yescharacteristic
346C2×C5#515811yescharacteristic
347C2×C5#519811yescharacteristic
348C23—21no—
349C23—41no—
350C23—61no—
351Q8—122no—
352D4—21no—
353D4—21no—
354D4—42no—
355D4—41no—
356D4—41no—
357D4—41no—
358D4—41no—
359D4—61no—
360D4—61no—
361D4—242no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—61no—
366C2×C4—62no—
367C2×C4—121no—
368C2×C4—121no—
369C2×C4C5×D3×D411yescharacteristic
370C2×C4C5×D3×D411yescharacteristic
371C2×C4C2×C5×#6711yescharacteristic
372C8—41no—
373C8—62no—
374C8—121no—
375C2×C3—81no—
376C2×C3—161no—
377C2×C3C5×#44911yescharacteristic
378C2×C3C5×#44911yescharacteristic
379C2×C3C5×#45311yescharacteristic
380D3—81no—
381C5#7101711yescharacteristic, direct product factor, Sylow
382C22—41no—
383C22—41no—
384C22—41no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—121no—
389C22—121no—
390C22—121no—
391C22C5×#93711yescharacteristic
392C4—21no—
393C4—41no—
394C4—122no—
395C4—121no—
396C4C5×#91111yescharacteristic
397C4C5×#91211yescharacteristic
398C4C5×#93211yescharacteristic
399C4C5×#95011yescharacteristic
400C3C5×#162411yescharacteristic, complemented, Sylow
401C2—81no—
402C2—161no—
403C2—241no—
404C2C5×#503711yescharacteristic
405C2C5×#515811yescharacteristic
406C2C5×#519811yescharacteristic
subgroupG/H
centerC22×C5#937
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#459C2
socleC22×C3×C5#120
hypercenterC5×#459D3
hypocenterC3C5×#1624
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#459

Complements

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

NH ≅ G/Ntype
1. C5×#5563C2semidirect
2. C3×C5×#459C2semidirect
3. C5×#5076C2semidirect
4. C5×#5072C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. C5×#4483C2semidirect
7. C5×#4481C2semidirect
26. #71017C5direct (N × H)
30. C5×#459D3semidirect
59. #5563C2×C5semidirect
60. C3×#459C2×C5semidirect
61. #5076C2×C5semidirect
62. #5072C2×C5semidirect
63. D4⋊(C3⋊C8)C2×C5semidirect
64. #4483C2×C5semidirect
65. #4481C2×C5semidirect
156. #459C5×D3semidirect
323. C3×C5#1624semidirect
381. C5#71017direct (N × H)
400. C3C5×#1624semidirect

Maximal subgroups

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

subgroupindex
C5×#55632
C3×C5×#4592
C5×#50762
C5×#50722
C5×D4⋊(C3⋊C8)2
C5×#44832
C5×#44812
C5×#16243
#710175