Finite Group Databasebeta

← C5×#67646 #14278258

Subgroups — C5×#67646 #14278258

Order 1920.

324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#393C211yesmaximal, characteristic
2C5×#4526C211yesmaximal, characteristic
3C5×#4525C211yesmaximal, characteristic
4C5×#1351—31nomaximal, Hall
5C22×C3×C5×Q8C411yescharacteristic, complemented
6C2×C3×C5×C22⋊C4—21no—
7C2×C3×C5×C22⋊C4C2211yescharacteristic
8C2×C5×#217—21no—
9C3×C5×#95—21no—
10C3×C5×#95C411yescharacteristic, complemented
11C5×#830—21no—
12#67646C511yesmaximal, characteristic, direct product factor, Hall
13C5×#393D311yescharacteristic
14C5×#342—31no—
15C5×#323—31no—
16C24×C3×C5D411yescharacteristic
17C2×C3×C5×Q8—42no—
18C2×C3×C5×Q8—41no—
19C22×C3×C4×C5—21no—
20C22×C3×C4×C5—21no—
21C22×C3×C4×C5C2×C411yescharacteristic
22C22×C3×C4×C5D411yescharacteristic
23C22×C5×Dic3—41no—
24C3×C5×C22⋊C4—41no—
25C3×C5×C22⋊C4—42no—
26C5×#217—22no—
27C5×#217—41no—
28C2×C5×C3⋊C8—41no—
29C3×#393C2×C511yescharacteristic
30#4526C2×C511yescharacteristic
31#4525C2×C511yescharacteristic
32C22×C5×Q8Dic311yescharacteristic, complemented
33C2×C5×C22⋊C4—21no—
34C2×C5×C22⋊C4—61no—
35C2×C5×C22⋊C4C2×D311yescharacteristic
36C5×C22⋊C8—61no—
37C5×#95—21no—
38C5×#95Dic311yescharacteristic, complemented
39#1351—31noSylow
40C23×C3×C5—21no—
41C23×C3×C5—21no—
42C23×C3×C5—41no—
43C23×C3×C5—41no—
44C23×C3×C5C22⋊C411yescharacteristic
45C23×C3×C5SD1611yescharacteristic
46C23×C3×C5Q1611yescharacteristic
47C3×C5×Q8—42no—
48C3×C5×Q8—42no—
49C2×C3×C4×C5—22no—
50C2×C3×C4×C5—21no—
51C2×C3×C4×C5—21no—
52C2×C3×C4×C5—41no—
53C2×C3×C4×C5—41no—
54C2×C3×C4×C5—41no—
55C2×C3×C4×C5—41no—
56C2×C3×C4×C5—41no—
57C2×C3×C4×C5—41no—
58C2×C3×C4×C5—41no—
59C2×C5×Dic3—42no—
60C2×C5×Dic3—81no—
61C2×C5×Dic3—81no—
62C5×C3⋊C8—81no—
63C22×C3×Q8C4×C511yescharacteristic, complemented
64C2×C3×C22⋊C4—21no—
65C2×C3×C22⋊C4C22×C511yescharacteristic
66C2×#217—21no—
67C3×#95—21no—
68C3×#95C4×C511yescharacteristic, complemented
69#830—21no—
70C24×C5#6711yescharacteristic
71C2×C5×Q8—42no—
72C2×C5×Q8—41no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5—121no—
76C22×C4×C5C2×Dic311yescharacteristic
77C22×C4×C5#6711yescharacteristic
78C2×C5×C8—121no—
79C5×C22⋊C4—41no—
80C5×C22⋊C4—42no—
81C5×C22⋊C4—62no—
82C5×C22⋊C4—121no—
83#393C5×D311yescharacteristic
84#342—31no—
85#323—31no—
86C22×C3×C5—21no—
87C22×C3×C5—21no—
88C22×C3×C5—21no—
89C22×C3×C5—21no—
90C22×C3×C5—41no—
91C22×C3×C5—41no—
92C22×C3×C5—41no—
93C22×C3×C5—41no—
94C22×C3×C5—81no—
95C22×C3×C5#9911yescharacteristic
96C22×C3×C5#10311yescharacteristic
97C22×C3×C5#10411yescharacteristic
98C3×C4×C5—42no—
99C3×C4×C5—41no—
100C3×C4×C5—41no—
101C3×C4×C5—81no—
102C5×Dic3—82no—
103C24×C3C5×D411yescharacteristic
104C2×C3×Q8—42no—
105C2×C3×Q8—41no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4C2×C4×C511yescharacteristic
109C22×C3×C4C5×D411yescharacteristic
110C22×Dic3—41no—
111C3×C22⋊C4—41no—
112C3×C22⋊C4—42no—
113#217—22no—
114#217—41no—
115C2×C3⋊C8—41no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—41no—
119C23×C5—41no—
120C23×C5#21511yescharacteristic
121C23×C5#21611yescharacteristic
122C23×C5#21711yescharacteristic
123C5×Q8—42no—
124C5×Q8—42no—
125C2×C4×C5—22no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—41no—
129C2×C4×C5—41no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—122no—
136C2×C4×C5—241no—
137C2×C4×C5—241no—
138C5×C8—241no—
139C22×Q8C5×Dic311yescharacteristic, complemented
140C2×C22⋊C4—21no—
141C2×C22⋊C4—61no—
142C2×C22⋊C4C2×C5×D311yescharacteristic
143C22⋊C8—61no—
144#95—21no—
145#95C5×Dic311yescharacteristic, complemented
146C2×C3×C5—21no—
147C2×C3×C5—21no—
148C2×C3×C5—41no—
149C2×C3×C5—41no—
150C2×C3×C5#32811yescharacteristic
151C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
152C2×C3×C5#35411yescharacteristic
153C23×C3—21no—
154C23×C3—21no—
155C23×C3—41no—
156C23×C3—41no—
157C23×C3C5×C22⋊C411yescharacteristic
158C23×C3C5×SD1611yescharacteristic
159C23×C3C5×Q1611yescharacteristic
160C3×Q8—42no—
161C3×Q8—42no—
162C2×C3×C4—22no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—41no—
166C2×C3×C4—41no—
167C2×C3×C4—41no—
168C2×C3×C4—41no—
169C2×C3×C4—41no—
170C2×C3×C4—41no—
171C2×C3×C4—41no—
172C2×Dic3—42no—
173C2×Dic3—81no—
174C2×Dic3—81no—
175C3⋊C8—81no—
176C22×C5—21no—
177C22×C5—21no—
178C22×C5—21no—
179C22×C5—21no—
180C22×C5—41no—
181C22×C5—41no—
182C22×C5—41no—
183C22×C5—41no—
184C22×C5—81no—
185C22×C5#83411yescharacteristic
186C22×C5#83511yescharacteristic
187C22×C5#83711yescharacteristic
188C4×C5—42no—
189C4×C5—41no—
190C4×C5—41no—
191C4×C5—81no—
192C4×C5—242no—
193C24C5×#6711yescharacteristic
194C2×Q8—42no—
195C2×Q8—41no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—121no—
199C22×C4C2×C5×Dic311yescharacteristic
200C22×C4C5×#6711yescharacteristic
201C2×C8—121no—
202C22⋊C4—41no—
203C22⋊C4—42no—
204C22⋊C4—62no—
205C22⋊C4—121no—
206C3×C5#135111yescharacteristic, complemented, Hall
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—41no—
212C22×C3—41no—
213C22×C3—41no—
214C22×C3—41no—
215C22×C3—81no—
216C22×C3C5×#9911yescharacteristic
217C22×C3C5×#10311yescharacteristic
218C22×C3C5×#10411yescharacteristic
219C3×C4—42no—
220C3×C4—41no—
221C3×C4—41no—
222C3×C4—81no—
223Dic3—82no—
224C2×C5—21no—
225C2×C5—21no—
226C2×C5—41no—
227C2×C5—41no—
228C2×C5#453611yescharacteristic
229C2×C5#453811yescharacteristic
230C2×C5#454111yescharacteristic
231C23—21no—
232C23—21no—
233C23—41no—
234C23—41no—
235C23C5×#21511yescharacteristic
236C23C5×#21611yescharacteristic
237C23C5×#21711yescharacteristic
238Q8—42no—
239Q8—42no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—122no—
251C2×C4—241no—
252C2×C4—241no—
253C8—241no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—41no—
257C2×C3—41no—
258C2×C3C5×#32811yescharacteristic
259C2×C3C5×AΣL(1,𝔽16)11yescharacteristic
260C2×C3C5×#35411yescharacteristic
261C5#6764611yescharacteristic, direct product factor, Sylow
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—41no—
269C22—41no—
270C22—81no—
271C22C5×#83411yescharacteristic
272C22C5×#83511yescharacteristic
273C22C5×#83711yescharacteristic
274C4—42no—
275C4—41no—
276C4—41no—
277C4—81no—
278C4—242no—
279C3C5×#135111yescharacteristic, complemented, Sylow
280C2—21no—
281C2—21no—
282C2—41no—
283C2—41no—
284C2C5×#453611yescharacteristic
285C2C5×#453811yescharacteristic
286C2C5×#454111yescharacteristic
subgroupG/H
centerC22×C5#834
commutatorC22×C3×C4C2×C4×C5
FrattiniC2×C22⋊C4C2×C5×D3
FittingC3×C5×#393C2
socleC22×C3×C5#99
prime radicalC24×C3×C5D4
cosocleC2×C3×C22⋊C4C22×C5
hypercenterC5×#393D3
hypocenterC3C5×#1351
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C23×C5 ◁ C2×C5×C22⋊C4 ◁ C5×#393

Complements

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

NH ≅ G/Ntype
5. C22×C3×C5×Q8C4semidirect
10. C3×C5×#95C4semidirect
12. #67646C5direct (N × H)
32. C22×C5×Q8Dic3semidirect
38. C5×#95Dic3semidirect
63. C22×C3×Q8C4×C5semidirect
68. C3×#95C4×C5semidirect
139. C22×Q8C5×Dic3semidirect
145. #95C5×Dic3semidirect
206. C3×C5#1351semidirect
261. C5#67646direct (N × H)
279. C3C5×#1351semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#3932
C5×#45262
C5×#45252
C5×#13513
#676465