Finite Group Databasebeta

← C5×#68361 #14283916

Subgroups — C5×#68361 #14283916

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5691C211yesmaximal, characteristic
2C5×#4707C211yesmaximal, characteristic, complemented
3C5×D3×#97C211yesmaximal, characteristic, complemented
4C3×C5×#330C211yesmaximal, characteristic, complemented
5C5×#4543C211yesmaximal, characteristic, complemented
6C5×#4464C211yesmaximal, characteristic, complemented
7C5×#4464C211yesmaximal, characteristic, complemented
8C5×#1524—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10C2×C5×ΓL(1,𝔽25)—21no—
11C2×C5×D3×C8—21no—
12C5×#898—21no—
13C5×#897C411yescharacteristic
14C5×#895C411yescharacteristic
15C5×#894—21no—
16C5×#893—21no—
17C5×#893C411yescharacteristic
18C5×#892—21no—
19C5×#887C411yescharacteristic
20C5×#875C2211yescharacteristic
21C42×C5×D3C2211yescharacteristic
22C3×C5×#97C2211yescharacteristic
23C3×C5×#97C2211yescharacteristic
24C5×#815—21no—
25C5×C8×Dic3—21no—
26C5×#803C2211yescharacteristic
27C5×#803C2211yescharacteristic
28#68361C511yesmaximal, characteristic, direct product factor, Hall
29C5×#529—31no—
30C4×C5×M16—31no—
31C2×C5×#97—31no—
32C5×#330—31no—
33C5×#330D311yescharacteristic, complemented
34C5×#329—31no—
35C5×#329—31no—
36C2×C5×D12—21no—
37C2×C5×D12C2×C411yescharacteristic
38C2×C4×C5×D3—21no—
39C2×C4×C5×D3C2×C411yescharacteristic
40C2×C4×C5×D3D411yescharacteristic
41C2×C4×C5×D3D411yescharacteristic
42C2×C5×Dic6C2×C411yescharacteristic
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4C2×C411yescharacteristic
48C3×C5×C4⋊C4C2×C411yescharacteristic
49C3×C42×C5C2311yescharacteristic
50C5×(C2×D3)⋊C4—21no—
51C5×(C2×D3)⋊C4—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×(C2×D3)⋊C4—21no—
54C5×(C2×D3)⋊C4—21no—
55C5×C4⋊Dic3—21no—
56C5×Dic3⋊C4—21no—
57C4×C5×Dic3—21no—
58C4×C5×Dic3C2×C411yescharacteristic
59C4×C5×Dic3D411yescharacteristic
60C4×C5×Dic3D411yescharacteristic
61C2×C5×C3⋊C8—21no—
62C2×C5×C3⋊C8—21no—
63C5×ΓL(1,𝔽25)—24no—
64C5×D3×C8—24no—
65#5691C2×C511yescharacteristic
66#4707C2×C511yescharacteristic, complemented
67D3×#97C2×C511yescharacteristic, complemented
68C3×#330C2×C511yescharacteristic, complemented
69#4543C2×C511yescharacteristic, complemented
70#4464C2×C511yescharacteristic, complemented
71#4464C2×C511yescharacteristic, complemented
72C2×C5×M16—61no—
73C22×C5×C8—61no—
74C5×#126—61no—
75C5×#125C2×D311yescharacteristic
76C5×#124—31no—
77C5×#123—61no—
78C5×C22⋊Q8—31no—
79C5×#121—31no—
80C4×C5×Q8—31no—
81C4×C5×D4—31no—
82C4×C5×D4—61no—
83C5×#117—61no—
84C2×C42×C5—31no—
85C5×#97—31no—
86C5×#97—31no—
87C5×#97—61no—
88C5×#97C2×D311yescharacteristic
89C5×#97C2×D311yescharacteristic
90C4×C5×C8—61no—
91#1524—31noSylow
92C22×C5×D3—21no—
93C22×C5×D3C22⋊C411yescharacteristic
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C5×Dic3—21no—
100C2×C5×Dic3C22⋊C411yescharacteristic
101C2×C5×Dic3C22⋊C411yescharacteristic
102C2×C5×Dic3C22⋊C411yescharacteristic
103C5×D12—41no—
104C5×D12—42no—
105C4×C5×D3—22no—
106C4×C5×D3—22no—
107C4×C5×D3—41no—
108C4×C5×D3—42no—
109C5×Dic6—41no—
110C3×C5×C8—22no—
111C3×C5×C8—22no—
112C5×C3⋊C8—22no—
113C5×C3⋊C8—22no—
114C3×#125C22×C511yescharacteristic
115C2×ΓL(1,𝔽25)—21no—
116C2×D3×C8—21no—
117#898—21no—
118#897C4×C511yescharacteristic
119#895C4×C511yescharacteristic
120#894—21no—
121#893—21no—
122#893C4×C511yescharacteristic
123#892—21no—
124#887C4×C511yescharacteristic
125#875C22×C511yescharacteristic
126C42×D3C22×C511yescharacteristic
127C3×#97C22×C511yescharacteristic
128C3×#97C22×C511yescharacteristic
129#815—21no—
130C8×Dic3—21no—
131#803C22×C511yescharacteristic
132#803C22×C511yescharacteristic
133C2×C5×Q8—31no—
134C2×C5×D4—31no—
135C2×C5×D4—61no—
136C22×C4×C5—31no—
137C22×C4×C5—31no—
138C22×C4×C5—31no—
139C22×C4×C5—61no—
140C5×M16—64no—
141C2×C5×C8—21no—
142C2×C5×C8—21no—
143C2×C5×C8—64no—
144C2×C5×C8—61no—
145C2×C5×C8—61no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—21no—
148C5×C4⋊C4—61no—
149C5×C4⋊C4—61no—
150C5×C4⋊C4C4×D311yescharacteristic
151C5×C4⋊C4C4×D311yescharacteristic
152C5×C22⋊C4—61no—
153C5×C22⋊C4—61no—
154C5×C22⋊C4—61no—
155C5×C22⋊C4—61no—
156C5×C22⋊C4—61no—
157C42×C5—31no—
158C42×C5—31no—
159C42×C5—31no—
160C42×C5—61no—
161C42×C5C22×D311yescharacteristic
162#529—31no—
163C4×M16—31no—
164C2×#97—31no—
165#330—31no—
166#330C5×D311yescharacteristic, complemented
167#329—31no—
168#329—31no—
169C22×C3×C5C2×C22⋊C411yescharacteristic
170C2×C5×D3—21no—
171C2×C5×D3—21no—
172C2×C5×D3—41no—
173C2×C5×D3—41no—
174C2×C5×D3—41no—
175C2×C5×D3#10412yes—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—21no—
179C3×C4×C5—41no—
180C3×C4×C5—41no—
181C5×Dic3—21no—
182C5×Dic3—21no—
183C5×Dic3—41no—
184C5×Dic3#10412yes—
185C2×D12—21no—
186C2×D12C2×C4×C511yescharacteristic
187C2×C4×D3—21no—
188C2×C4×D3C2×C4×C511yescharacteristic
189C2×C4×D3C5×D411yescharacteristic
190C2×C4×D3C5×D411yescharacteristic
191C2×Dic6C2×C4×C511yescharacteristic
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4C2×C4×C511yescharacteristic
197C3×C4⋊C4C2×C4×C511yescharacteristic
198C3×C42C23×C511yescharacteristic
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201(C2×D3)⋊C4—21no—
202(C2×D3)⋊C4—21no—
203(C2×D3)⋊C4—21no—
204C4⋊Dic3—21no—
205Dic3⋊C4—21no—
206C4×Dic3—21no—
207C4×Dic3C2×C4×C511yescharacteristic
208C4×Dic3C5×D411yescharacteristic
209C4×Dic3C5×D411yescharacteristic
210C2×C3⋊C8—21no—
211C2×C3⋊C8—21no—
212ΓL(1,𝔽25)—24no—
213D3×C8—24no—
214C23×C5—31no—
215C23×C5—61no—
216C5×Q8—121no—
217C5×D4—121no—
218C5×D4—122no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5—31no—
222C2×C4×C5—31no—
223C2×C4×C5—31no—
224C2×C4×C5—62no—
225C2×C4×C5—62no—
226C2×C4×C5—61no—
227C2×C4×C5—121no—
228C2×C4×C5—122no—
229C2×C4×C5C2×C4×D311yescharacteristic
230C2×C4×C5D3×D411yescharacteristic
231C2×C4×C5D3×D411yescharacteristic
232C5×C8—22no—
233C5×C8—22no—
234C5×C8—62no—
235C5×C8—62no—
236C2×M16—61no—
237C22×C8—61no—
238#126—61no—
239#125C2×C5×D311yescharacteristic
240#124—31no—
241#123—61no—
242C22⋊Q8—31no—
243#121—31no—
244C4×Q8—31no—
245C4×D4—31no—
246C4×D4—61no—
247#117—61no—
248C2×C42—31no—
249#97—31no—
250#97—31no—
251#97—61no—
252#97C2×C5×D311yescharacteristic
253#97C2×C5×D311yescharacteristic
254C4×C8—61no—
255C2×C3×C5#41311yescharacteristic
256C2×C3×C5C2×#10411yescharacteristic
257C2×C3×C5C2×#10411yescharacteristic
258C5×D3—22no—
259C5×D3—81no—
260C22×D3—21no—
261C22×D3C5×C22⋊C411yescharacteristic
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4C22×C4×C511yescharacteristic
265C2×C3×C4C2×C5×D411yescharacteristic
266C2×C3×C4C2×C5×D411yescharacteristic
267C2×Dic3—21no—
268C2×Dic3C5×C22⋊C411yescharacteristic
269C2×Dic3C5×C22⋊C411yescharacteristic
270C2×Dic3C5×C22⋊C411yescharacteristic
271D12—41no—
272D12—42no—
273C4×D3—22no—
274C4×D3—22no—
275C4×D3—41no—
276C4×D3—42no—
277Dic6—41no—
278C3×C8—22no—
279C3×C8—22no—
280C3⋊C8—22no—
281C3⋊C8—22no—
282C22×C5—32no—
283C22×C5—61no—
284C22×C5—61no—
285C22×C5—121no—
286C22×C5—121no—
287C22×C5—121no—
288C22×C5D3×C22⋊C411yescharacteristic
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—21no—
292C4×C5—32no—
293C4×C5—41no—
294C4×C5—41no—
295C4×C5—61no—
296C4×C5—61no—
297C4×C5—121no—
298C2×Q8—31no—
299C2×D4—31no—
300C2×D4—61no—
301C22×C4—31no—
302C22×C4—31no—
303C22×C4—31no—
304C22×C4—61no—
305M16—64no—
306C2×C8—21no—
307C2×C8—21no—
308C2×C8—64no—
309C2×C8—61no—
310C2×C8—61no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C4⋊C4C4×C5×D311yescharacteristic
316C4⋊C4C4×C5×D311yescharacteristic
317C22⋊C4—61no—
318C22⋊C4—61no—
319C22⋊C4—61no—
320C22⋊C4—61no—
321C22⋊C4—61no—
322C42—31no—
323C42—31no—
324C42—31no—
325C42—61no—
326C42C22×C5×D311yescharacteristic
327C3×C5#152411yescharacteristic, complemented, Hall
328C22×C3C2×C5×C22⋊C411yescharacteristic
329C2×D3—21no—
330C2×D3—21no—
331C2×D3—41no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3C5×#10412yes—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—41no—
339C3×C4—41no—
340Dic3—21no—
341Dic3—21no—
342Dic3—41no—
343Dic3C5×#10412yes—
344C2×C5—62no—
345C2×C5—241no—
346C2×C5#475111yescharacteristic
347C2×C5D3×#10411yescharacteristic
348C2×C5D3×#10411yescharacteristic
349C23—31no—
350C23—61no—
351Q8—121no—
352D4—121no—
353D4—122no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—31no—
357C2×C4—31no—
358C2×C4—31no—
359C2×C4—62no—
360C2×C4—62no—
361C2×C4—61no—
362C2×C4—121no—
363C2×C4—122no—
364C2×C4C2×C4×C5×D311yescharacteristic
365C2×C4C5×D3×D411yescharacteristic
366C2×C4C5×D3×D411yescharacteristic
367C8—22no—
368C8—22no—
369C8—62no—
370C8—62no—
371C2×C3C5×#41311yescharacteristic
372C2×C3C2×C5×#10411yescharacteristic
373C2×C3C2×C5×#10411yescharacteristic
374D3—22no—
375D3—81no—
376C5#6836111yescharacteristic, direct product factor, Sylow
377C22—32no—
378C22—61no—
379C22—61no—
380C22—121no—
381C22—121no—
382C22—121no—
383C22C5×D3×C22⋊C411yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—32no—
388C4—41no—
389C4—41no—
390C4—61no—
391C4—61no—
392C4—121no—
393C3C5×#152411yescharacteristic, complemented, Sylow
394C2—62no—
395C2—241no—
396C2C5×#475111yescharacteristic
397C2C5×D3×#10411yescharacteristic
398C2C5×D3×#10411yescharacteristic
subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#330C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#895C4
cosocleC3×C42C23×C5
hypercenterC5×#330D3
hypocenterC3C5×#1524
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#330

Complements

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

NH ≅ G/Ntype
2. C5×#4707C2semidirect
3. C5×D3×#97C2semidirect
4. C3×C5×#330C2semidirect
5. C5×#4543C2semidirect
6. C5×#4464C2semidirect
7. C5×#4464C2semidirect
28. #68361C5direct (N × H)
33. C5×#330D3semidirect
66. #4707C2×C5semidirect
67. D3×#97C2×C5semidirect
68. C3×#330C2×C5semidirect
69. #4543C2×C5semidirect
70. #4464C2×C5semidirect
71. #4464C2×C5semidirect
166. #330C5×D3semidirect
327. C3×C5#1524semidirect
376. C5#68361direct (N × H)
393. C3C5×#1524semidirect

Maximal subgroups

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

subgroupindex
C5×#56912
C5×#47072
C5×D3×#972
C3×C5×#3302
C5×#45432
C5×#44642
C5×#15243
#683615