Finite Group Databasebeta

← C5×#68205 #14289823

Subgroups — C5×#68205 #14289823

Order 1920.

388 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×#5542C211yesmaximal, characteristic
2C5×#5008C211yesmaximal, characteristic
3C5×#4850C211yesmaximal, characteristic, complemented
4C5×#4681C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic
6C5×#4486C211yesmaximal, characteristic, complemented
7C5×#4456C211yesmaximal, characteristic, complemented
8C5×#1638—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C5×#936—21no—
11C5×#926—21no—
12C5×#924—21no—
13C5×#887—21no—
14C5×#879—22no—
15C5×#869C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×C4×C5×C8C2211yescharacteristic
20C5×#832—21no—
21C5×#818—21no—
22C5×#816—21no—
23C5×#816—22no—
24C5×#808—21no—
25C5×C4⋊(C3⋊C8)C2211yescharacteristic
26#68205C511yesmaximal, characteristic, direct product factor, Hall
27C5×#556—31no—
28C5×#487—31no—
29C5×#477—31no—
30C5×#476—31no—
31C5×#332—31no—
32C5×Q8⋊C8—31no—
33C5×D4⋊C8D311yescharacteristic
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×Dic6—21no—
37C2×C5×Dic6—21no—
38C2×C5×Dic6D411yescharacteristic
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44C5×#217—22no—
45C5×#217—22no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×C4⋊Dic3D412yes—
51C5×Dic3⋊C4—22no—
52C5×Dic3⋊C4—21no—
53C4×C5×Dic3—22no—
54C4×C5×Dic3—21no—
55C2×C5×C3⋊C8—21no—
56#5542C2×C511yescharacteristic
57#5008C2×C511yescharacteristic
58#4850C2×C511yescharacteristic, complemented
59#4681C2×C511yescharacteristic, complemented
60C3×D4⋊C8C2×C511yescharacteristic
61#4486C2×C511yescharacteristic, complemented
62#4456C2×C511yescharacteristic, complemented
63C5×C4⋊Q8—31no—
64C5×C4⋊Q8—31no—
65C5×#126—62no—
66C5×#124—61no—
67C5×C22⋊Q8—61no—
68C4×C5×Q8—31no—
69C4×C5×Q8—61no—
70C4×C5×D4C2×D311yescharacteristic
71C5×#117—61no—
72C5×#107—61no—
73C5×#106—61no—
74C5×C4⋊C8—31no—
75C5×C4⋊C8C2×D311yescharacteristic
76C5×#103—62no—
77C5×#103—61no—
78C5×#102—61no—
79C4×C5×C8C2×D311yescharacteristic
80#1638—31noSylow
81C23×C3×C5—21no—
82C3×C5×D4—21no—
83C3×C5×D4—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—22no—
93C2×C5×Dic3—41no—
94C5×Dic6—21no—
95C5×Dic6—21no—
96C5×Dic6—41no—
97C5×Dic6—41no—
98C5×Dic6—42no—
99C3×C5×C8—41no—
100C3×C5×C8—41no—
101C5×C3⋊C8—41no—
102C3×C4×D4C22×C511yescharacteristic
103#936—21no—
104#926—21no—
105#924—21no—
106#887—21no—
107#879—22no—
108#869C22×C511yescharacteristic
109#869C22×C511yescharacteristic
110C4×Dic6C22×C511yescharacteristic
111C3×C4⋊C8C22×C511yescharacteristic
112C3×C4×C8C22×C511yescharacteristic
113#832—21no—
114#818—21no—
115#816—21no—
116#816—22no—
117#808—21no—
118C4⋊(C3⋊C8)C22×C511yescharacteristic
119C2×C5×Q8—31no—
120C2×C5×Q8—61no—
121C2×C5×Q8—61no—
122C2×C5×D4D1211yescharacteristic
123C22×C4×C5—21no—
124C2×C5×C8—21no—
125C2×C5×C8—21no—
126C2×C5×C8—61no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—32no—
129C5×C4⋊C4—62no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4—61no—
133C5×C4⋊C4—61no—
134C5×C4⋊C4D1211yescharacteristic
135C5×C22⋊C4—21no—
136C5×C22⋊C4—62no—
137C5×C22⋊C4—62no—
138C42×C5—62no—
139C42×C5—61no—
140C42×C5C22×D311yescharacteristic
141#556—31no—
142#487—31no—
143#477—31no—
144#476—31no—
145#332—31no—
146Q8⋊C8—31no—
147D4⋊C8C5×D311yescharacteristic
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5—41no—
151C22×C3×C5#12011yescharacteristic
152C3×C4×C5—21no—
153C3×C4×C5—41no—
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13711yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C5×Dic3—41no—
159C5×Dic3—42no—
160C5×Dic3—41no—
161C5×Dic3—81no—
162C2×C3×D4C5×D411yescharacteristic
163C22×C3×C4—21no—
164C2×Dic6—21no—
165C2×Dic6—21no—
166C2×Dic6C5×D411yescharacteristic
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C3×C4⋊C4C5×D411yescharacteristic
170C3×C22⋊C4—21no—
171C3×C42C23×C511yescharacteristic
172#217—22no—
173#217—22no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3C5×D412yes—
178C4⋊Dic3C5×D411yescharacteristic
179Dic3⋊C4—22no—
180Dic3⋊C4—21no—
181C4×Dic3—22no—
182C4×Dic3—21no—
183C2×C3⋊C8—21no—
184C23×C5—21no—
185C5×Q8—61no—
186C5×Q8—61no—
187C5×Q8—122no—
188C5×Q8—121no—
189C5×Q8—121no—
190C5×D4—21no—
191C5×D4—21no—
192C2×C4×C5—21no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5—61no—
196C2×C4×C5—62no—
197C2×C4×C5—61no—
198C2×C4×C5—121no—
199C2×C4×C5C2×D1211yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C5×C8—41no—
203C5×C8—41no—
204C5×C8—121no—
205C4⋊Q8—31no—
206C4⋊Q8—31no—
207#126—62no—
208#124—61no—
209C22⋊Q8—61no—
210C4×Q8—31no—
211C4×Q8—61no—
212C4×D4C2×C5×D311yescharacteristic
213#117—61no—
214#107—61no—
215#106—61no—
216C4⋊C8—31no—
217C4⋊C8C2×C5×D311yescharacteristic
218#103—62no—
219#103—61no—
220#102—61no—
221C4×C8C2×C5×D311yescharacteristic
222C2×C3×C5—81no—
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45211yescharacteristic
225C2×C3×C5#45411yescharacteristic
226C23×C3—21no—
227C3×D4—21no—
228C3×D4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—41no—
231C2×C3×C4—41no—
232C2×C3×C4C2×C5×D411yescharacteristic
233C2×C3×C4C2×C5×D411yescharacteristic
234C2×C3×C4C2×C5×D411yescharacteristic
235C2×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3—22no—
238C2×Dic3—41no—
239Dic6—21no—
240Dic6—21no—
241Dic6—41no—
242Dic6—41no—
243Dic6—42no—
244C3×C8—41no—
245C3×C8—41no—
246C3⋊C8—41no—
247C22×C5—41no—
248C22×C5—41no—
249C22×C5—41no—
250C22×C5#88211yescharacteristic
251C4×C5—21no—
252C4×C5—41no—
253C4×C5—122no—
254C4×C5—121no—
255C4×C5—121no—
256C4×C5—241no—
257C4×C5#90411yescharacteristic
258C4×C5#90911yescharacteristic
259C4×C5#91211yescharacteristic
260C4×C5#91511yescharacteristic
261C2×Q8—31no—
262C2×Q8—61no—
263C2×Q8—61no—
264C2×D4C5×D1211yescharacteristic
265C22×C4—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—61no—
269C4⋊C4—32no—
270C4⋊C4—31no—
271C4⋊C4—62no—
272C4⋊C4—61no—
273C4⋊C4—61no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4C5×D1211yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—62no—
279C22⋊C4—62no—
280C42—62no—
281C42—61no—
282C42C22×C5×D311yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3—41no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3C5×#12011yescharacteristic
288C3×C4—21no—
289C3×C4—41no—
290C3×C4C5×#13511yescharacteristic
291C3×C4C5×#13511yescharacteristic
292C3×C4C5×#13711yescharacteristic
293C3×C4C5×#13711yescharacteristic
294Dic3—41no—
295Dic3—42no—
296Dic3—41no—
297Dic3—81no—
298C2×C5—81no—
299C2×C5#473311yescharacteristic
300C2×C5#478311yescharacteristic
301C2×C5#482711yescharacteristic
302C23—21no—
303Q8—61no—
304Q8—61no—
305Q8—122no—
306Q8—121no—
307Q8—121no—
308D4—21no—
309D4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—61no—
314C2×C4—62no—
315C2×C4—61no—
316C2×C4—121no—
317C2×C4C2×C5×D1211yescharacteristic
318C2×C4C5×D3×D411yescharacteristic
319C2×C4C5×D3×D411yescharacteristic
320C8—41no—
321C8—41no—
322C8—121no—
323C2×C3—81no—
324C2×C3C5×#45211yescharacteristic
325C2×C3C5×#45211yescharacteristic
326C2×C3C5×#45411yescharacteristic
327C5#6820511yescharacteristic, direct product factor, Sylow
328C22—41no—
329C22—41no—
330C22—41no—
331C22C5×#88211yescharacteristic
332C4—21no—
333C4—41no—
334C4—122no—
335C4—121no—
336C4—121no—
337C4—241no—
338C4C5×#90411yescharacteristic
339C4C5×#90911yescharacteristic
340C4C5×#91211yescharacteristic
341C4C5×#91511yescharacteristic
342C3C5×#163811yescharacteristic, complemented, Sylow
343C2—81no—
344C2C5×#473311yescharacteristic
345C2C5×#478311yescharacteristic
346C2C5×#482711yescharacteristic
subgroupG/H
centerC22×C5#882
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC5×D4⋊C8D3
hypocenterC3C5×#1638
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
3. C5×#4850C2semidirect
4. C5×#4681C2semidirect
6. C5×#4486C2semidirect
7. C5×#4456C2semidirect
26. #68205C5direct (N × H)
58. #4850C2×C5semidirect
59. #4681C2×C5semidirect
61. #4486C2×C5semidirect
62. #4456C2×C5semidirect
283. C3×C5#1638semidirect
327. C5#68205direct (N × H)
342. C3C5×#1638semidirect

Maximal subgroups

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

subgroupindex
C5×#55422
C5×#50082
C5×#48502
C5×#46812
C3×C5×D4⋊C82
C5×#44862
C5×#44562
C5×#16383
#682055