Finite Group Databasebeta

← C5×#71954 #14291142

Subgroups — C5×#71954 #14291142

Order 1920.

392 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 98 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×#562C211yesmaximal, characteristic
2C5×#5069C211yesmaximal, characteristic, complemented
3C5×#5055C212yesmaximal, complemented
4C5×#4543C211yesmaximal, characteristic, complemented
5C5×#4540C212yesmaximal, complemented
6C5×#1662—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C3×C5×#124C2212yes—
9C3×C5×#123—22no—
10C3×C5×C22⋊Q8—22no—
11C3×C5×#121—22no—
12C5×#869C2211yescharacteristic
13C5×#835—22no—
14C5×#832—22no—
15C5×#810—22no—
16C5×#803C2212yes—
17C5×#803C2211yescharacteristic
18#71954C511yesmaximal, characteristic, direct product factor, Hall
19C5×#562D311yescharacteristic
20C5×#491—31no—
21C5×#489—32no—
22C5×#330—31no—
23C5×#329—32no—
24C2×C3×C5×Q8D412yes—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4D412yes—
27C22×C3×C4×C5—22no—
28C2×C5×Dic6—21no—
29C3×C5×C4⋊C4—22no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4D412yes—
32C3×C5×C22⋊C4—22no—
33C3×C5×C22⋊C4—22no—
34C3×C5×C22⋊C4—22no—
35C3×C42×C5C2311yescharacteristic
36C5×C4⋊Dic3—22no—
37C2×C5×C3⋊C8—21no—
38C2×C5×C3⋊C8—22no—
39C3×#562C2×C511yescharacteristic
40#5069C2×C511yescharacteristic, complemented
41#5055C2×C512yescomplemented
42#4543C2×C511yescharacteristic, complemented
43#4540C2×C512yescomplemented
44C5×C4⋊Q8—31no—
45C5×#125C2×D311yescharacteristic
46C5×#124C2×D312yes—
47C5×#123—22no—
48C5×C22⋊Q8—22no—
49C5×#121—22no—
50C5×#103—62no—
51C5×#103—62no—
52C5×#102—62no—
53C5×#97—31no—
54C5×#97—32no—
55#1662—31noSylow
56C23×C3×C5—22no—
57C3×C5×Q8—42no—
58C3×C5×D4—42no—
59C3×C5×D4—82no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5—22no—
62C2×C3×C4×C5—82no—
63C2×C3×C4×C5C2×D412yes—
64C2×C3×C4×C5C2×D411yescharacteristic
65C2×C5×Dic3—41no—
66C5×Dic6—42no—
67C5×C3⋊C8—41no—
68C5×C3⋊C8—42no—
69C3×#125C22×C511yescharacteristic
70C3×#124C22×C512yes—
71C3×#123—22no—
72C3×C22⋊Q8—22no—
73C3×#121—22no—
74#869C22×C511yescharacteristic
75#835—22no—
76#832—22no—
77#810—22no—
78#803C22×C511yescharacteristic
79#803C22×C512yes—
80C2×C5×Q8—61no—
81C2×C5×Q8#6712yes—
82C2×C5×D4—22no—
83C2×C5×D4#6712yes—
84C22×C4×C5—22no—
85C2×C5×C8—62no—
86C2×C5×C8—61no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4—22no—
89C5×C4⋊C4—62no—
90C5×C4⋊C4#6712yes—
91C5×C22⋊C4—22no—
92C5×C22⋊C4—22no—
93C5×C22⋊C4—22no—
94C42×C5C22×D311yescharacteristic
95#562C5×D311yescharacteristic
96#491—31no—
97#489—32no—
98#330—31no—
99#329—32no—
100C22×C3×C5—42no—
101C22×C3×C5—42no—
102C22×C3×C5—42no—
103C22×C3×C5#12011yescharacteristic
104C3×C4×C5—21no—
105C3×C4×C5—22no—
106C3×C4×C5—42no—
107C3×C4×C5—42no—
108C5×Dic3—81no—
109C2×C3×Q8C5×D412yes—
110C2×C3×D4—22no—
111C2×C3×D4C5×D412yes—
112C22×C3×C4—22no—
113C2×Dic6—21no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4C5×D412yes—
117C3×C22⋊C4—22no—
118C3×C22⋊C4—22no—
119C3×C22⋊C4—22no—
120C3×C42C23×C511yescharacteristic
121C4⋊Dic3—22no—
122C2×C3⋊C8—21no—
123C2×C3⋊C8—22no—
124C23×C5—22no—
125C5×Q8—42no—
126C5×Q8—122no—
127C5×D4—42no—
128C5×D4—82no—
129C2×C4×C5—22no—
130C2×C4×C5—22no—
131C2×C4×C5—82no—
132C2×C4×C5—121no—
133C2×C4×C5C2×#6711yescharacteristic
134C2×C4×C5C2×#6712yes—
135C5×C8—122no—
136C5×C8—121no—
137C4⋊Q8—31no—
138#125C2×C5×D311yescharacteristic
139#124C2×C5×D312yes—
140#123—22no—
141C22⋊Q8—22no—
142#121—22no—
143#103—62no—
144#103—62no—
145#102—62no—
146#97—31no—
147#97—32no—
148C2×C3×C5—82no—
149C2×C3×C5#45411yescharacteristic
150C2×C3×C5#45512yes—
151C23×C3—22no—
152C3×Q8—42no—
153C3×D4—42no—
154C3×D4—82no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—82no—
158C2×C3×C4C2×C5×D412yes—
159C2×C3×C4C2×C5×D411yescharacteristic
160C2×Dic3—41no—
161Dic6—42no—
162C3⋊C8—41no—
163C3⋊C8—42no—
164C22×C5—42no—
165C22×C5—42no—
166C22×C5—42no—
167C22×C5#95311yescharacteristic
168C4×C5—22no—
169C4×C5—21no—
170C4×C5—42no—
171C4×C5—42no—
172C4×C5—241no—
173C2×Q8—61no—
174C2×Q8C5×#6712yes—
175C2×D4—22no—
176C2×D4C5×#6712yes—
177C22×C4—22no—
178C2×C8—62no—
179C2×C8—61no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—62no—
183C4⋊C4C5×#6712yes—
184C22⋊C4—22no—
185C22⋊C4—22no—
186C22⋊C4—22no—
187C42C22×C5×D311yescharacteristic
188C3×C5#166211yescharacteristic, complemented, Hall
189C22×C3—42no—
190C22×C3—42no—
191C22×C3—42no—
192C22×C3C5×#12011yescharacteristic
193C3×C4—21no—
194C3×C4—22no—
195C3×C4—42no—
196C3×C4—42no—
197Dic3—81no—
198C2×C5—82no—
199C2×C5#524212yes—
200C2×C5#524511yescharacteristic
201C23—22no—
202Q8—42no—
203Q8—122no—
204D4—42no—
205D4—82no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—82no—
209C2×C4—121no—
210C2×C4C2×C5×#6711yescharacteristic
211C2×C4C2×C5×#6712yes—
212C8—122no—
213C8—121no—
214C2×C3—82no—
215C2×C3C5×#45411yescharacteristic
216C2×C3C5×#45512yes—
217C5#7195411yescharacteristic, direct product factor, Sylow
218C22—42no—
219C22—42no—
220C22—42no—
221C22C5×#95311yescharacteristic
222C4—22no—
223C4—21no—
224C4—42no—
225C4—42no—
226C4—241no—
227C3C5×#166211yescharacteristic, complemented, Sylow
228C2—82no—
229C2C5×#524212yes—
230C2C5×#524511yescharacteristic
subgroupG/H
centerC22×C5#953
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
Fitting, prime radicalC3×C5×#562C2
socleC22×C3×C5#120
hypercenterC5×#562D3
hypocenterC3C5×#1662
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#562

Complements

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

NH ≅ G/Ntype
2. C5×#5069C2semidirect
3. C5×#5055C2semidirect
4. C5×#4543C2semidirect
5. C5×#4540C2semidirect
18. #71954C5direct (N × H)
40. #5069C2×C5semidirect
41. #5055C2×C5semidirect
42. #4543C2×C5semidirect
43. #4540C2×C5semidirect
188. C3×C5#1662semidirect
217. C5#71954direct (N × H)
227. C3C5×#1662semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5622
C5×#50692
C5×#50552
C5×#45432
C5×#45402
C5×#16623
#719545