Finite Group Databasebeta

← C5×#68247 #14289826

Subgroups — C5×#68247 #14289826

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×#5584C211yesmaximal, characteristic
2C5×#5021C211yesmaximal, characteristic, complemented
3C5×#4842C211yesmaximal, characteristic
4C5×#4681C211yesmaximal, characteristic, complemented
5C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
6C5×#4482C211yesmaximal, characteristic, complemented
7C5×#4459C211yesmaximal, characteristic
8C5×#1638—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C5×#946—21no—
11C5×#898—22no—
12C5×#892—21no—
13C5×#875—21no—
14C4×C5×D12C2211yescharacteristic
15C5×#869C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C4×C5×Dic6—21no—
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×C4×C5×C8C2211yescharacteristic
20C5×#835—21no—
21C5×#821—21no—
22C5×#817—21no—
23C5×#816—22no—
24C5×#807—21no—
25C5×C4⋊(C3⋊C8)C2211yescharacteristic
26#68247C511yesmaximal, characteristic, direct product factor, Hall
27C5×#556—31no—
28C5×#487—31no—
29C5×#477—31no—
30C5×#476—31no—
31C5×#332—31no—
32C5×Q8⋊C8D311yescharacteristic, complemented
33C5×D4⋊C8—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C5×Dic6—21no—
38C2×C5×Dic6—21no—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45C5×(C2×D3)⋊C4—22no—
46C5×(C2×D3)⋊C4—22no—
47C5×(C2×D3)⋊C4—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C5×C4⋊Dic3D412yes—
53C5×Dic3⋊C4—22no—
54C4×C5×Dic3—22no—
55C2×C5×C3⋊C8—21no—
56#5584C2×C511yescharacteristic
57#5021C2×C511yescharacteristic, complemented
58#4842C2×C511yescharacteristic
59#4681C2×C511yescharacteristic, complemented
60C3×Q8⋊C8C2×C511yescharacteristic, complemented
61#4482C2×C511yescharacteristic, complemented
62#4459C2×C511yescharacteristic
63C5×C4⋊Q8—31no—
64C5×C4⋊Q8—31no—
65C5×#126—62no—
66C5×#124—61no—
67C5×C22⋊Q8—61no—
68C4×C5×Q8—61no—
69C4×C5×Q8C2×D311yescharacteristic
70C4×C5×D4—31no—
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
81C22×C5×D3—21no—
82C3×C5×Q8—21no—
83C3×C5×Q8—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C5×Dic3—21no—
90C2×C5×Dic3—22no—
91C2×C5×Dic3—41no—
92C5×D12—21no—
93C5×D12—21no—
94C4×C5×D3—41no—
95C4×C5×D3—41no—
96C5×Dic6—41no—
97C5×Dic6—41no—
98C5×Dic6—42no—
99C3×C5×C8—41no—
100C3×C5×C8—41no—
101C5×C3⋊C8—41no—
102C3×C4×Q8C22×C511yescharacteristic
103#946—21no—
104#898—22no—
105#892—21no—
106#875—21no—
107C4×D12C22×C511yescharacteristic
108#869C22×C511yescharacteristic
109#869C22×C511yescharacteristic
110C4×Dic6—21no—
111C3×C4⋊C8C22×C511yescharacteristic
112C3×C4×C8C22×C511yescharacteristic
113#835—21no—
114#821—21no—
115#817—21no—
116#816—22no—
117#807—21no—
118C4⋊(C3⋊C8)C22×C511yescharacteristic
119C2×C5×Q8—61no—
120C2×C5×Q8—61no—
121C2×C5×Q8D1211yescharacteristic
122C2×C5×D4—31no—
123C22×C4×C5—61no—
124C2×C5×C8—21no—
125C2×C5×C8—21no—
126C2×C5×C8—61no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4—32no—
130C5×C4⋊C4—62no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4—61no—
133C5×C4⋊C4—61no—
134C5×C4⋊C4D1211yescharacteristic
135C5×C22⋊C4—62no—
136C5×C22⋊C4—62no—
137C5×C22⋊C4—61no—
138C42×C5—21no—
139C42×C5—62no—
140C42×C5C22×D311yescharacteristic
141#556—31no—
142#487—31no—
143#477—31no—
144#476—31no—
145#332—31no—
146Q8⋊C8C5×D311yescharacteristic, complemented
147D4⋊C8—31no—
148C22×C3×C5#12011yescharacteristic
149C2×C5×D3—41no—
150C2×C5×D3—41no—
151C2×C5×D3—41no—
152C3×C4×C5—21no—
153C3×C4×C5—41no—
154C3×C4×C5—41no—
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C5×Dic3—42no—
160C5×Dic3—41no—
161C5×Dic3—81no—
162C2×C3×Q8C5×D411yescharacteristic
163C2×D12C5×D411yescharacteristic
164C2×C4×D3—21no—
165C2×Dic6—21no—
166C2×Dic6—21no—
167C2×C3×C8—21no—
168C2×C3×C8—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4C5×D411yescharacteristic
171C3×C42—21no—
172C3×C42C23×C511yescharacteristic
173(C2×D3)⋊C4—22no—
174(C2×D3)⋊C4—22no—
175(C2×D3)⋊C4—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3C5×D412yes—
180C4⋊Dic3C5×D411yescharacteristic
181Dic3⋊C4—22no—
182C4×Dic3—22no—
183C2×C3⋊C8—21no—
184C23×C5—61no—
185C5×Q8—21no—
186C5×Q8—21no—
187C5×Q8—122no—
188C5×Q8—121no—
189C5×Q8—121no—
190C5×D4—61no—
191C5×D4—61no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—61no—
195C2×C4×C5—62no—
196C2×C4×C5—121no—
197C2×C4×C5—121no—
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—61no—
211C4×Q8C2×C5×D311yescharacteristic
212C4×D4—31no—
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#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225C5×D3—81no—
226C22×D3—21no—
227C3×Q8—21no—
228C3×Q8—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4C2×C5×D411yescharacteristic
232C2×C3×C4C2×C5×D411yescharacteristic
233C2×C3×C4C2×C5×D411yescharacteristic
234C2×Dic3—21no—
235C2×Dic3—22no—
236C2×Dic3—41no—
237D12—21no—
238D12—21no—
239C4×D3—41no—
240C4×D3—41no—
241Dic6—41no—
242Dic6—41no—
243Dic6—42no—
244C3×C8—41no—
245C3×C8—41no—
246C3⋊C8—41no—
247C22×C5—121no—
248C22×C5—121no—
249C22×C5—121no—
250C22×C5#88211yescharacteristic
251C4×C5—21no—
252C4×C5—41no—
253C4×C5—41no—
254C4×C5—121no—
255C4×C5—122no—
256C4×C5—241no—
257C4×C5#90411yescharacteristic
258C4×C5#90911yescharacteristic
259C4×C5#91611yescharacteristic
260C4×C5#91811yescharacteristic
261C2×Q8—61no—
262C2×Q8—61no—
263C2×Q8C5×D1211yescharacteristic
264C2×D4—31no—
265C22×C4—61no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—61no—
269C4⋊C4—21no—
270C4⋊C4—32no—
271C4⋊C4—31no—
272C4⋊C4—62no—
273C4⋊C4—61no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4C5×D1211yescharacteristic
277C22⋊C4—62no—
278C22⋊C4—62no—
279C22⋊C4—61no—
280C42—21no—
281C42—62no—
282C42C22×C5×D311yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3C5×#12011yescharacteristic
285C2×D3—41no—
286C2×D3—41no—
287C2×D3—41no—
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—41no—
291C3×C4C5×#13511yescharacteristic
292C3×C4C5×#13511yescharacteristic
293C3×C4C5×#13711yescharacteristic
294C3×C4C5×#13711yescharacteristic
295Dic3—42no—
296Dic3—41no—
297Dic3—81no—
298C2×C5—241no—
299C2×C5#473311yescharacteristic
300C2×C5#480811yescharacteristic
301C2×C5#482711yescharacteristic
302C23—61no—
303Q8—21no—
304Q8—21no—
305Q8—122no—
306Q8—121no—
307Q8—121no—
308D4—61no—
309D4—61no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—61no—
313C2×C4—62no—
314C2×C4—121no—
315C2×C4—121no—
316C2×C4—121no—
317C2×C4C2×C5×D1211yescharacteristic
318C2×C4C5×D3×D411yescharacteristic
319C2×C4C5×D3×D411yescharacteristic
320C8—41no—
321C8—41no—
322C8—121no—
323C2×C3C5×#45211yescharacteristic
324C2×C3C5×#45211yescharacteristic
325C2×C3C5×#45411yescharacteristic
326D3—81no—
327C5#6824711yescharacteristic, direct product factor, Sylow
328C22—121no—
329C22—121no—
330C22—121no—
331C22C5×#88211yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—121no—
336C4—122no—
337C4—241no—
338C4C5×#90411yescharacteristic
339C4C5×#90911yescharacteristic
340C4C5×#91611yescharacteristic
341C4C5×#91811yescharacteristic
342C3C5×#163811yescharacteristic, complemented, Sylow
343C2—241no—
344C2C5×#473311yescharacteristic
345C2C5×#480811yescharacteristic
346C2C5×#482711yescharacteristic
subgroupG/H
centerC22×C5#882
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
hypercenterC5×Q8⋊C8D3
hypocenterC3C5×#1638
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C5×#5021C2semidirect
4. C5×#4681C2semidirect
5. C3×C5×Q8⋊C8C2semidirect
6. C5×#4482C2semidirect
26. #68247C5direct (N × H)
32. C5×Q8⋊C8D3semidirect
57. #5021C2×C5semidirect
59. #4681C2×C5semidirect
60. C3×Q8⋊C8C2×C5semidirect
61. #4482C2×C5semidirect
146. Q8⋊C8C5×D3semidirect
283. C3×C5#1638semidirect
327. C5#68247direct (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×#55842
C5×#50212
C5×#48422
C5×#46812
C3×C5×Q8⋊C82
C5×#44822
C5×#44592
C5×#16383
#682475