Finite Group Databasebeta

← C5×#71307 #14289541

Subgroups — C5×#71307 #14289541

Order 1920.

412 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C5×#5722C211yesmaximal, characteristic
2C3×C5×#494C211yesmaximal, characteristic
3C5×#5091C212yesmaximal
4C5×#4546C211yesmaximal, characteristic
5C5×#4456C212yesmaximal
6C5×#1633—31nomaximal, Hall
7C2×C3×C5×Q16—22no—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×C5×C4⋊Q8C2211yescharacteristic
10C5×#944—22no—
11C5×#888—22no—
12C5×#887—22no—
13C4×C5×Dic6C2212yes—
14C3×C4×C5×C8C2211yescharacteristic
15C5×#810—22no—
16C5×#807—22no—
17C5×C4⋊(C3⋊C8)C2212yes—
18#71307C511yesmaximal, characteristic, direct product factor, Hall
19C5×Q82—31no—
20C5×#494D311yescharacteristic
21C5×#477—32no—
22C5×#333—31no—
23C5×Q8⋊C8—32no—
24C2×C3×C5×Q8—21no—
25C2×C3×C5×Q8D412yes—
26C2×C5×Dic6—22no—
27C2×C5×Dic6D412yes—
28C3×C5×Q16—44no—
29C2×C3×C5×C8—21no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4—22no—
32C3×C42×C5C2311yescharacteristic
33C5×C4⋊Dic3D412yes—
34C5×Dic3⋊C4—24no—
35C5×Dic3⋊C4—22no—
36C4×C5×Dic3—22no—
37C4×C5×Dic3—22no—
38C2×C5×C3⋊C8—22no—
39#5722C2×C511yescharacteristic
40C3×#494C2×C511yescharacteristic
41#5091C2×C512yes—
42#4546C2×C511yescharacteristic
43#4456C2×C512yes—
44C2×C5×Q16—22no—
45C5×C4⋊Q8—62no—
46C5×C4⋊Q8—62no—
47C5×C4⋊Q8C2×D311yescharacteristic
48C5×C4⋊Q8C2×D311yescharacteristic
49C4×C5×Q8—32no—
50C4×C5×Q8—62no—
51C5×#107—62no—
52C5×C4⋊C8—32no—
53C5×#103—62no—
54C4×C5×C8C2×D311yescharacteristic
55#1633—31noSylow
56C3×C5×Q8—42no—
57C3×C5×Q8—42no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5—41no—
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×C5×Dic3—22no—
63C2×C5×Dic3—22no—
64C5×Dic6—22no—
65C5×Dic6—82no—
66C5×Dic6Q1614yescomplemented
67C3×C5×C8—22no—
68C5×C3⋊C8—42no—
69C2×C3×Q16—22no—
70C3×C4⋊Q8C22×C511yescharacteristic
71C3×C4⋊Q8C22×C511yescharacteristic
72#944—22no—
73#888—22no—
74#887—22no—
75C4×Dic6C22×C512yes—
76C3×C4×C8C22×C511yescharacteristic
77#810—22no—
78#807—22no—
79C4⋊(C3⋊C8)C22×C512yes—
80C2×C5×Q8—21no—
81C2×C5×Q8—32no—
82C2×C5×Q8—62no—
83C2×C5×Q8#6712yes—
84C5×Q16—44no—
85C2×C5×C8—21no—
86C2×C5×C8—62no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4—22no—
89C5×C4⋊C4—32no—
90C5×C4⋊C4—64no—
91C5×C4⋊C4—62no—
92C42×C5—62no—
93C42×C5—62no—
94C42×C5C22×D311yescharacteristic
95Q82—31no—
96#494C5×D311yescharacteristic
97#477—32no—
98#333—31no—
99Q8⋊C8—32no—
100C22×C3×C5#12011yescharacteristic
101C3×C4×C5—21no—
102C3×C4×C5—42no—
103C3×C4×C5—81no—
104C3×C4×C5C2×Q1612yes—
105C3×C4×C5#13712yes—
106C5×Dic3—24no—
107C5×Dic3—42no—
108C2×C3×Q8—21no—
109C2×C3×Q8C5×D412yes—
110C2×Dic6—22no—
111C2×Dic6C5×D412yes—
112C3×Q16—44no—
113C2×C3×C8—21no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4—22no—
116C3×C42C23×C511yescharacteristic
117C4⋊Dic3C5×D412yes—
118Dic3⋊C4—24no—
119Dic3⋊C4—22no—
120C4×Dic3—22no—
121C4×Dic3—22no—
122C2×C3⋊C8—22no—
123C5×Q8—34no—
124C5×Q8—42no—
125C5×Q8—42no—
126C5×Q8—62no—
127C5×Q8—242no—
128C2×C4×C5—22no—
129C2×C4×C5—41no—
130C2×C4×C5—62no—
131C2×C4×C5—62no—
132C2×C4×C5D3×D412yes—
133C2×C4×C5C2×#6711yescharacteristic
134C5×C8—22no—
135C5×C8—122no—
136C2×Q16—22no—
137C4⋊Q8—62no—
138C4⋊Q8—62no—
139C4⋊Q8C2×C5×D311yescharacteristic
140C4⋊Q8C2×C5×D311yescharacteristic
141C4×Q8—32no—
142C4×Q8—62no—
143#107—62no—
144C4⋊C8—32no—
145#103—62no—
146C4×C8C2×C5×D311yescharacteristic
147C2×C3×C5#45112yes—
148C2×C3×C5#45311yescharacteristic
149C3×Q8—42no—
150C3×Q8—42no—
151C2×C3×C4—22no—
152C2×C3×C4—41no—
153C2×C3×C4C2×C5×D412yes—
154C2×C3×C4C2×C5×D411yescharacteristic
155C2×Dic3—22no—
156C2×Dic3—22no—
157Dic6—22no—
158Dic6—82no—
159Dic6C5×Q1614yescomplemented
160C3×C8—22no—
161C3⋊C8—42no—
162C22×C5#93711yescharacteristic
163C4×C5—21no—
164C4×C5—42no—
165C4×C5—64no—
166C4×C5—81no—
167C4×C5—122no—
168C4×C5D3×Q1612yes—
169C4×C5#91812yes—
170C2×Q8—21no—
171C2×Q8—32no—
172C2×Q8—62no—
173C2×Q8C5×#6712yes—
174Q16—44no—
175C2×C8—21no—
176C2×C8—62no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—32no—
180C4⋊C4—64no—
181C4⋊C4—62no—
182C42—62no—
183C42—62no—
184C42C22×C5×D311yescharacteristic
185C3×C5#163311yescharacteristic, complemented, Hall
186C22×C3C5×#12011yescharacteristic
187C3×C4—21no—
188C3×C4—42no—
189C3×C4—81no—
190C3×C4C2×C5×Q1612yes—
191C3×C4C5×#13712yes—
192Dic3—24no—
193Dic3—42no—
194C2×C5#507711yescharacteristic
195C2×C5#518612yes—
196Q8—34no—
197Q8—42no—
198Q8—42no—
199Q8—62no—
200Q8—242no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—62no—
204C2×C4—62no—
205C2×C4C5×D3×D412yes—
206C2×C4C2×C5×#6711yescharacteristic
207C8—22no—
208C8—122no—
209C2×C3C5×#45112yes—
210C2×C3C5×#45311yescharacteristic
211C5#7130711yescharacteristic, direct product factor, Sylow
212C22C5×#93711yescharacteristic
213C4—21no—
214C4—42no—
215C4—64no—
216C4—81no—
217C4—122no—
218C4C5×D3×Q1612yes—
219C4C5×#91812yes—
220C3C5×#163311yescharacteristic, complemented, Sylow
221C2C5×#507711yescharacteristic
222C2C5×#518612yes—
subgroupG/H
centerC22×C5#937
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#494C2
socle, prime radicalC22×C3×C5#120
hypercenterC5×#494D3
hypocenterC3C5×#1633
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#494

Complements

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

NH ≅ G/Ntype
18. #71307C5direct (N × H)
66. C5×Dic6Q16semidirect
159. Dic6C5×Q16semidirect
185. C3×C5#1633semidirect
211. C5#71307direct (N × H)
220. C3C5×#1633semidirect

Maximal subgroups

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

subgroupindex
C5×#57222
C3×C5×#4942
C5×#50912
C5×#45462
C5×#44562
C5×#16333
#713075