Finite Group Databasebeta

← C5×#71145 #14289583

Subgroups — C5×#71145 #14289583

Order 1920.

436 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5563C211yesmaximal, characteristic
2C3×C5×#476C211yesmaximal, characteristic, complemented
3C5×#5092C211yesmaximal, characteristic, complemented
4C5×#5084C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C5×#4483C211yesmaximal, characteristic, complemented
7C5×#4481C211yesmaximal, characteristic, complemented
8C5×#1634—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×D4C2211yescharacteristic
11C2×C5×#216—22no—
12C5×#938—21no—
13C5×#930—21no—
14C5×#926—21no—
15C5×#892—21no—
16C5×#885—22no—
17C4×C5×D12C2211yescharacteristic
18C5×#869C2211yescharacteristic
19C3×C5×#106—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21C3×C5×#102—21no—
22C5×#809—21no—
23C5×#808—21no—
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26#71145C511yesmaximal, characteristic, direct product factor, Hall
27C5×#555—31no—
28C5×#494—31no—
29C5×#476—31no—
30C5×#476D311yescharacteristic, complemented
31C5×#333—31no—
32C5×D4⋊C8—31no—
33C5×D4⋊C8—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C2×C5×#67—22no—
38C2×C5×D12D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C5×Dic6D412yes—
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C5×C22⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47C5×#217—22no—
48C5×#216—44no—
49C5×(C2×D3)⋊C4—22no—
50C5×(C2×D3)⋊C4—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3—21no—
53C5×C4⋊Dic3D411yescharacteristic
54C4×C5×Dic3—22no—
55C2×C5×C3⋊C8—21no—
56C2×C5×C3⋊C8—21no—
57#5563C2×C511yescharacteristic
58C3×#476C2×C511yescharacteristic, complemented
59#5092C2×C511yescharacteristic, complemented
60#5084C2×C511yescharacteristic, complemented
61D4⋊(C3⋊C8)C2×C511yescharacteristic, complemented
62#4483C2×C511yescharacteristic, complemented
63#4481C2×C511yescharacteristic, complemented
64C2×C5×Q16—62no—
65C5×C4⋊Q8—31no—
66C5×C4⋊Q8C2×D311yescharacteristic
67C5×#124—62no—
68C5×#121—61no—
69C5×#121—61no—
70C4×C5×D4—31no—
71C4×C5×D4C2×D311yescharacteristic
72C5×#117—61no—
73C5×#117—61no—
74C5×#106—21no—
75C5×#106—61no—
76C5×C4⋊C8—31no—
77C5×C4⋊C8C2×D311yescharacteristic
78C5×#102—21no—
79C5×#102—61no—
80C4×C5×C8—31no—
81#1634—31noSylow
82C23×C3×C5—21no—
83C22×C5×D3—21no—
84C3×C5×Q8—42no—
85C3×C5×D4—21no—
86C3×C5×D4—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C5×#67—82no—
95C2×C5×Dic3—21no—
96C2×C5×Dic3—22no—
97C5×D12—21no—
98C5×D12—21no—
99C4×C5×D3—41no—
100C4×C5×D3—41no—
101C5×Dic6—42no—
102C3×C5×C8—41no—
103C5×C3⋊C8—22no—
104C5×C3⋊C8—41no—
105C3×C4⋊Q8C22×C511yescharacteristic
106C3×C4×D4C22×C511yescharacteristic
107C2×#216—22no—
108#938—21no—
109#930—21no—
110#926—21no—
111#892—21no—
112#885—22no—
113C4×D12C22×C511yescharacteristic
114#869C22×C511yescharacteristic
115C3×#106—21no—
116C3×C4⋊C8C22×C511yescharacteristic
117C3×#102—21no—
118#809—21no—
119#808—21no—
120C4⋊(C3⋊C8)C22×C511yescharacteristic
121C4×C3⋊C8C22×C511yescharacteristic
122C2×C5×Q8—21no—
123C2×C5×Q8—32no—
124C2×C5×D4—31no—
125C2×C5×D4—62no—
126C2×C5×D4#6711yescharacteristic
127C22×C4×C5—21no—
128C22×C4×C5—61no—
129C5×Q16—124no—
130C2×C5×C8—21no—
131C2×C5×C8—61no—
132C2×C5×C8—61no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—31no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4#6711yescharacteristic
139C5×C22⋊C4—21no—
140C5×C22⋊C4—62no—
141C5×C22⋊C4—62no—
142C5×C22⋊C4—61no—
143C42×C5—62no—
144C42×C5C22×D311yescharacteristic
145#555—31no—
146#494—31no—
147#476—31no—
148#476C5×D311yescharacteristic, complemented
149#333—31no—
150D4⋊C8—31no—
151D4⋊C8—31no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5#12011yescharacteristic
156C2×C5×D3—41no—
157C2×C5×D3—41no—
158C2×C5×D3—41no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5—81no—
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5#13511yescharacteristic
164C3×C4×C5#13711yescharacteristic
165C3×C4×C5#13711yescharacteristic
166C5×Dic3—41no—
167C5×Dic3—42no—
168C2×C3×Q8—21no—
169C2×C3×D4C5×D411yescharacteristic
170C22×C3×C4—21no—
171C2×#67—22no—
172C2×D12C5×D411yescharacteristic
173C2×C4×D3—21no—
174C2×Dic6C5×D412yes—
175C2×C3×C8—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4C5×D411yescharacteristic
179C3×C22⋊C4—21no—
180C3×C42C23×C511yescharacteristic
181#217—22no—
182#216—44no—
183(C2×D3)⋊C4—22no—
184(C2×D3)⋊C4—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3C5×D411yescharacteristic
188C4×Dic3—22no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C23×C5—21no—
192C23×C5—61no—
193C5×Q8—42no—
194C5×Q8—122no—
195C5×D4—21no—
196C5×D4—21no—
197C5×D4—61no—
198C5×D4—61no—
199C5×D4—242no—
200C2×C4×C5—21no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5—61no—
205C2×C4×C5—62no—
206C2×C4×C5—121no—
207C2×C4×C5—121no—
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5C2×#6711yescharacteristic
211C5×C8—41no—
212C5×C8—62no—
213C5×C8—121no—
214C2×Q16—62no—
215C4⋊Q8—31no—
216C4⋊Q8C2×C5×D311yescharacteristic
217#124—62no—
218#121—61no—
219#121—61no—
220C4×D4—31no—
221C4×D4C2×C5×D311yescharacteristic
222#117—61no—
223#117—61no—
224#106—21no—
225#106—61no—
226C4⋊C8—31no—
227C4⋊C8C2×C5×D311yescharacteristic
228#102—21no—
229#102—61no—
230C4×C8—31no—
231C2×C3×C5—81no—
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45211yescharacteristic
234C2×C3×C5#45311yescharacteristic
235C5×D3—81no—
236C23×C3—21no—
237C22×D3—21no—
238C3×Q8—42no—
239C3×D4—21no—
240C3×D4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4C2×C5×D411yescharacteristic
246C2×C3×C4C2×C5×D411yescharacteristic
247C2×C3×C4C2×C5×D411yescharacteristic
248#67—82no—
249C2×Dic3—21no—
250C2×Dic3—22no—
251D12—21no—
252D12—21no—
253C4×D3—41no—
254C4×D3—41no—
255Dic6—42no—
256C3×C8—41no—
257C3⋊C8—22no—
258C3⋊C8—41no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5—121no—
263C22×C5—121no—
264C22×C5—121no—
265C22×C5#93711yescharacteristic
266C4×C5—21no—
267C4×C5—41no—
268C4×C5—81no—
269C4×C5—122no—
270C4×C5—121no—
271C4×C5#91511yescharacteristic
272C4×C5#91611yescharacteristic
273C4×C5#94211yescharacteristic
274C4×C5#95011yescharacteristic
275C2×Q8—21no—
276C2×Q8—32no—
277C2×D4—31no—
278C2×D4—62no—
279C2×D4C5×#6711yescharacteristic
280C22×C4—21no—
281C22×C4—61no—
282Q16—124no—
283C2×C8—21no—
284C2×C8—61no—
285C2×C8—61no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—31no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4C5×#6711yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—61no—
296C42—62no—
297C42C22×C5×D311yescharacteristic
298C3×C5#163411yescharacteristic, complemented, Hall
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3C5×#12011yescharacteristic
303C2×D3—41no—
304C2×D3—41no—
305C2×D3—41no—
306C3×C4—21no—
307C3×C4—41no—
308C3×C4—81no—
309C3×C4C5×#13511yescharacteristic
310C3×C4C5×#13511yescharacteristic
311C3×C4C5×#13711yescharacteristic
312C3×C4C5×#13711yescharacteristic
313Dic3—41no—
314Dic3—42no—
315C2×C5—81no—
316C2×C5—241no—
317C2×C5#504711yescharacteristic
318C2×C5#517311yescharacteristic
319C2×C5#519811yescharacteristic
320C23—21no—
321C23—61no—
322Q8—42no—
323Q8—122no—
324D4—21no—
325D4—21no—
326D4—61no—
327D4—61no—
328D4—242no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—61no—
334C2×C4—62no—
335C2×C4—121no—
336C2×C4—121no—
337C2×C4C5×D3×D411yescharacteristic
338C2×C4C5×D3×D411yescharacteristic
339C2×C4C2×C5×#6711yescharacteristic
340C8—41no—
341C8—62no—
342C8—121no—
343C2×C3—81no—
344C2×C3C5×#45211yescharacteristic
345C2×C3C5×#45211yescharacteristic
346C2×C3C5×#45311yescharacteristic
347D3—81no—
348C5#7114511yescharacteristic, direct product factor, Sylow
349C22—41no—
350C22—41no—
351C22—41no—
352C22—121no—
353C22—121no—
354C22—121no—
355C22C5×#93711yescharacteristic
356C4—21no—
357C4—41no—
358C4—81no—
359C4—122no—
360C4—121no—
361C4C5×#91511yescharacteristic
362C4C5×#91611yescharacteristic
363C4C5×#94211yescharacteristic
364C4C5×#95011yescharacteristic
365C3C5×#163411yescharacteristic, complemented, Sylow
366C2—81no—
367C2—241no—
368C2C5×#504711yescharacteristic
369C2C5×#517311yescharacteristic
370C2C5×#519811yescharacteristic
subgroupG/H
centerC22×C5#937
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#476C2
socleC22×C3×C5#120
prime radicalC5×#5563C2
hypercenterC5×#476D3
hypocenterC3C5×#1634
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#476

Complements

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

NH ≅ G/Ntype
2. C3×C5×#476C2semidirect
3. C5×#5092C2semidirect
4. C5×#5084C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
6. C5×#4483C2semidirect
7. C5×#4481C2semidirect
26. #71145C5direct (N × H)
30. C5×#476D3semidirect
58. C3×#476C2×C5semidirect
59. #5092C2×C5semidirect
60. #5084C2×C5semidirect
61. D4⋊(C3⋊C8)C2×C5semidirect
62. #4483C2×C5semidirect
63. #4481C2×C5semidirect
148. #476C5×D3semidirect
298. C3×C5#1634semidirect
348. C5#71145direct (N × H)
365. C3C5×#1634semidirect

Maximal subgroups

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

subgroupindex
C5×#55632
C3×C5×#4762
C5×#50922
C5×#50842
C5×D4⋊(C3⋊C8)2
C5×#44832
C5×#44812
C5×#16343
#711455