Finite Group Databasebeta

← C5×#68199 #14289058

Subgroups — C5×#68199 #14289058

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
2C5×#5015C211yesmaximal, characteristic, complemented
3C5×#4843C211yesmaximal, characteristic, complemented
4C5×#4693C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic, complemented
6C5×#4481C211yesmaximal, characteristic, complemented
7C5×#4459C211yesmaximal, characteristic, complemented
8C5×#1624—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C5×#938—21no—
11C2×C5×#213—21no—
12C5×#930—21no—
13C5×#926—21no—
14C2×C5×D24—21no—
15C2×C5×#204—22no—
16C5×#892—21no—
17C5×#885—22no—
18C5×#874C2211yescharacteristic
19C4×C5×D12C2211yescharacteristic
20C5×#869C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C4×C5×C8C2211yescharacteristic
23C5×#821—21no—
24C5×#809—21no—
25C5×C4⋊(C3⋊C8)C2211yescharacteristic
26#68199C511yesmaximal, characteristic, direct product factor, Hall
27C5×#555—31no—
28C5×#492—31no—
29C5×#459—31no—
30C5×#459—31no—
31C5×#333—31no—
32C5×D4⋊C8—31no—
33C5×D4⋊C8D311yescharacteristic, complemented
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×#67—22no—
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C5×D12—21no—
40C2×C5×D12D411yescharacteristic
41C2×C4×C5×D3—21no—
42C2×C5×Dic6D412yes—
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C5×C22⋊C4—21no—
47C3×C42×C5C2311yescharacteristic
48C5×#217—22no—
49C5×#213—42no—
50C5×(C2×D3)⋊C4—22no—
51C5×(C2×D3)⋊C4—21no—
52C5×C4⋊Dic3—21no—
53C5×C4⋊Dic3—21no—
54C5×C4⋊Dic3D411yescharacteristic
55C4×C5×Dic3—22no—
56C2×C5×C3⋊C8—21no—
57C5×D24—42no—
58C5×#204—44no—
59#5563C2×C511yescharacteristic, complemented
60#5015C2×C511yescharacteristic, complemented
61#4843C2×C511yescharacteristic, complemented
62#4693C2×C511yescharacteristic, complemented
63C3×D4⋊C8C2×C511yescharacteristic, complemented
64#4481C2×C511yescharacteristic, complemented
65#4459C2×C511yescharacteristic, complemented
66C2×C5×SD16—62no—
67C2×C5×D8—61no—
68C2×C5×D8—61no—
69C5×C4⋊Q8—31no—
70C5×#127—31no—
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—61no—
81C5×#102—61no—
82C4×C5×C8C2×D311yescharacteristic
83#1624—31noSylow
84C23×C3×C5—21no—
85C22×C5×D3—21no—
86C22×C5×D3—41no—
87C3×C5×D4—21no—
88C3×C5×D4—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C5×#67—82no—
96C2×C5×Dic3—21no—
97C2×C5×Dic3—22no—
98C5×D12—21no—
99C5×D12—21no—
100C5×D12—42no—
101C5×D12—41no—
102C5×D12—41no—
103C5×D12—41no—
104C5×D12—41no—
105C4×C5×D3—41no—
106C4×C5×D3—41no—
107C5×Dic6—42no—
108C3×C5×C8—22no—
109C3×C5×C8—41no—
110C5×C3⋊C8—41no—
111C3×C4×D4C22×C511yescharacteristic
112#938—21no—
113C2×#213—21no—
114#930—21no—
115#926—21no—
116C2×D24—21no—
117C2×#204—22no—
118#892—21no—
119#885—22no—
120#874C22×C511yescharacteristic
121C4×D12C22×C511yescharacteristic
122#869C22×C511yescharacteristic
123C3×C4⋊C8C22×C511yescharacteristic
124C3×C4×C8C22×C511yescharacteristic
125#821—21no—
126#809—21no—
127C4⋊(C3⋊C8)C22×C511yescharacteristic
128C2×C5×Q8—32no—
129C2×C5×D4—31no—
130C2×C5×D4—62no—
131C2×C5×D4—61no—
132C2×C5×D4—61no—
133C2×C5×D4—61no—
134C2×C5×D4D1211yescharacteristic
135C22×C4×C5—21no—
136C22×C4×C5—61no—
137C5×SD16—124no—
138C5×D8—122no—
139C5×D8—122no—
140C2×C5×C8—21no—
141C2×C5×C8—21no—
142C2×C5×C8—61no—
143C5×C4⋊C4—31no—
144C5×C4⋊C4—61no—
145C5×C4⋊C4—61no—
146C5×C4⋊C4D1211yescharacteristic
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#459—31no—
157#333—31no—
158D4⋊C8—31no—
159D4⋊C8C5×D311yescharacteristic, complemented
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5#12011yescharacteristic
164C2×C5×D3—41no—
165C2×C5×D3—41no—
166C2×C5×D3—41no—
167C2×C5×D3—81no—
168C2×C5×D3—81no—
169C2×C5×D3—81no—
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×D4C5×D411yescharacteristic
179C22×C3×C4—21no—
180C2×#67—22no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12C5×D411yescharacteristic
185C2×C4×D3—21no—
186C2×Dic6C5×D412yes—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C3×C4⋊C4C5×D411yescharacteristic
190C3×C22⋊C4—21no—
191C3×C42C23×C511yescharacteristic
192#217—22no—
193#213—42no—
194(C2×D3)⋊C4—22no—
195(C2×D3)⋊C4—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3C5×D411yescharacteristic
199C4×Dic3—22no—
200C2×C3⋊C8—21no—
201D24—42no—
202#204—44no—
203C23×C5—21no—
204C23×C5—61no—
205C23×C5—121no—
206C5×Q8—122no—
207C5×D4—21no—
208C5×D4—21no—
209C5×D4—61no—
210C5×D4—61no—
211C5×D4—122no—
212C5×D4—121no—
213C5×D4—121no—
214C5×D4—121no—
215C5×D4—121no—
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×C5C2×D1211yescharacteristic
225C2×C4×C5D3×D411yescharacteristic
226C2×C4×C5D3×D411yescharacteristic
227C5×C8—22no—
228C5×C8—41no—
229C5×C8—121no—
230C2×SD16—62no—
231C2×D8—61no—
232C2×D8—61no—
233C4⋊Q8—31no—
234#127—31no—
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—61no—
245#102—61no—
246C4×C8C2×C5×D311yescharacteristic
247C2×C3×C5—81no—
248C2×C3×C5#44911yescharacteristic
249C2×C3×C5#44911yescharacteristic
250C2×C3×C5#45311yescharacteristic
251C5×D3—81no—
252C5×D3—161no—
253C23×C3—21no—
254C22×D3—21no—
255C22×D3—41no—
256C3×D4—21no—
257C3×D4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4C2×C5×D411yescharacteristic
262C2×C3×C4C2×C5×D411yescharacteristic
263C2×C3×C4C2×C5×D411yescharacteristic
264#67—82no—
265C2×Dic3—21no—
266C2×Dic3—22no—
267D12—21no—
268D12—21no—
269D12—42no—
270D12—41no—
271D12—41no—
272D12—41no—
273D12—41no—
274C4×D3—41no—
275C4×D3—41no—
276Dic6—42no—
277C3×C8—22no—
278C3×C8—41no—
279C3⋊C8—41no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5—121no—
284C22×C5—121no—
285C22×C5—121no—
286C22×C5—241no—
287C22×C5—241no—
288C22×C5—241no—
289C22×C5#88211yescharacteristic
290C4×C5—21no—
291C4×C5—41no—
292C4×C5—121no—
293C4×C5—122no—
294C4×C5#90411yescharacteristic
295C4×C5#90811yescharacteristic
296C4×C5#91111yescharacteristic
297C4×C5#91611yescharacteristic
298C2×Q8—32no—
299C2×D4—31no—
300C2×D4—62no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—61no—
304C2×D4C5×D1211yescharacteristic
305C22×C4—21no—
306C22×C4—61no—
307SD16—124no—
308D8—122no—
309D8—122no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—61no—
313C4⋊C4—31no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4C5×D1211yescharacteristic
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×C3C5×#12011yescharacteristic
328C2×D3—41no—
329C2×D3—41no—
330C2×D3—41no—
331C2×D3—81no—
332C2×D3—81no—
333C2×D3—81no—
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—241no—
344C2×C5—481no—
345C2×C5#473411yescharacteristic
346C2×C5#478111yescharacteristic
347C2×C5#482211yescharacteristic
348C23—21no—
349C23—61no—
350C23—121no—
351Q8—122no—
352D4—21no—
353D4—21no—
354D4—61no—
355D4—61no—
356D4—122no—
357D4—121no—
358D4—121no—
359D4—121no—
360D4—121no—
361D4—242no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—61no—
366C2×C4—62no—
367C2×C4—121no—
368C2×C4—121no—
369C2×C4C2×C5×D1211yescharacteristic
370C2×C4C5×D3×D411yescharacteristic
371C2×C4C5×D3×D411yescharacteristic
372C8—22no—
373C8—41no—
374C8—121no—
375C2×C3—81no—
376C2×C3C5×#44911yescharacteristic
377C2×C3C5×#44911yescharacteristic
378C2×C3C5×#45311yescharacteristic
379D3—81no—
380D3—161no—
381C5#6819911yescharacteristic, direct product factor, Sylow
382C22—41no—
383C22—41no—
384C22—41no—
385C22—121no—
386C22—121no—
387C22—121no—
388C22—241no—
389C22—241no—
390C22—241no—
391C22C5×#88211yescharacteristic
392C4—21no—
393C4—41no—
394C4—121no—
395C4—122no—
396C4C5×#90411yescharacteristic
397C4C5×#90811yescharacteristic
398C4C5×#91111yescharacteristic
399C4C5×#91611yescharacteristic
400C3C5×#162411yescharacteristic, complemented, Sylow
401C2—81no—
402C2—241no—
403C2—481no—
404C2C5×#473411yescharacteristic
405C2C5×#478111yescharacteristic
406C2C5×#482211yescharacteristic
subgroupG/H
centerC22×C5#882
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
hypercenterC5×D4⋊C8D3
hypocenterC3C5×#1624
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×D4⋊C8

Complements

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

NH ≅ G/Ntype
1. C5×#5563C2semidirect
2. C5×#5015C2semidirect
3. C5×#4843C2semidirect
4. C5×#4693C2semidirect
5. C3×C5×D4⋊C8C2semidirect
6. C5×#4481C2semidirect
7. C5×#4459C2semidirect
26. #68199C5direct (N × H)
33. C5×D4⋊C8D3semidirect
59. #5563C2×C5semidirect
60. #5015C2×C5semidirect
61. #4843C2×C5semidirect
62. #4693C2×C5semidirect
63. C3×D4⋊C8C2×C5semidirect
64. #4481C2×C5semidirect
65. #4459C2×C5semidirect
159. D4⋊C8C5×D3semidirect
323. C3×C5#1624semidirect
381. C5#68199direct (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
C5×#50152
C5×#48432
C5×#46932
C3×C5×D4⋊C82
C5×#44812
C5×#44592
C5×#16243
#681995