Finite Group Databasebeta

← C5×#71928 #14289586

Subgroups — C5×#71928 #14289586

Order 1920.

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

normal subgroups only

This group has 436 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
1C3×C5×#555C211yesmaximal, characteristic
2C5×#5092C211yesmaximal, characteristic, complemented
3C5×#5008C212yesmaximal, complemented
4C5×#4546C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C212yesmaximal, complemented
6C5×#1634—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C3×C5×#124—22no—
9C3×C5×#121—22no—
10C3×C4×C5×D4C2212yes—
11C3×C5×#117—22no—
12C2×C5×#216—22no—
13C5×#869C2211yescharacteristic
14C5×#832—22no—
15C5×#808—22no—
16C5×C4⋊(C3⋊C8)C2212yes—
17C4×C5×C3⋊C8C2211yescharacteristic
18#71928C511yesmaximal, characteristic, direct product factor, Hall
19C5×#555D311yescharacteristic
20C5×#494—31no—
21C5×#476—32no—
22C5×#333—31no—
23C5×D4⋊C8—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⋊C4D412yes—
31C3×C5×C22⋊C4—24no—
32C3×C5×C22⋊C4—22no—
33C3×C42×C5—22no—
34C3×C42×C5C2311yescharacteristic
35C5×#216—44no—
36C5×C4⋊Dic3—22no—
37C2×C5×C3⋊C8—21no—
38C2×C5×C3⋊C8—22no—
39C3×#555C2×C511yescharacteristic
40#5092C2×C511yescharacteristic, complemented
41#5008C2×C512yescomplemented
42#4546C2×C511yescharacteristic, complemented
43D4⋊(C3⋊C8)C2×C512yescomplemented
44C2×C5×Q16—62no—
45C5×C4⋊Q8—31no—
46C5×C4⋊Q8C2×D311yescharacteristic
47C5×#124—22no—
48C5×#121—22no—
49C4×C5×D4C2×D312yes—
50C5×#117—22no—
51C5×#106—62no—
52C5×C4⋊C8—32no—
53C5×#102—62no—
54C4×C5×C8—31no—
55#1634—31noSylow
56C23×C3×C5—22no—
57C3×C5×Q8—42no—
58C3×C5×D4—22no—
59C3×C5×D4—22no—
60C3×C5×D4—82no—
61C2×C3×C4×C5—22no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—42no—
64C2×C3×C4×C5—42no—
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×C3×C4×C5C2×D412yes—
67C2×C5×Dic3—41no—
68C5×Dic6—42no—
69C5×C3⋊C8—22no—
70C5×C3⋊C8—42no—
71C3×C4⋊Q8C22×C511yescharacteristic
72C3×#124—22no—
73C3×#121—22no—
74C3×C4×D4C22×C512yes—
75C3×#117—22no—
76C2×#216—22no—
77#869C22×C511yescharacteristic
78#832—22no—
79#808—22no—
80C4⋊(C3⋊C8)C22×C512yes—
81C4×C3⋊C8C22×C511yescharacteristic
82C2×C5×Q8—61no—
83C2×C5×Q8#6712yes—
84C2×C5×D4—22no—
85C2×C5×D4#6712yes—
86C22×C4×C5—22no—
87C5×Q16—124no—
88C2×C5×C8—61no—
89C2×C5×C8—62no—
90C5×C4⋊C4—22no—
91C5×C4⋊C4—62no—
92C5×C4⋊C4#6712yes—
93C5×C22⋊C4—24no—
94C5×C22⋊C4—22no—
95C42×C5—22no—
96C42×C5C22×D311yescharacteristic
97#555C5×D311yescharacteristic
98#494—31no—
99#476—32no—
100#333—31no—
101D4⋊C8—32no—
102C22×C3×C5—42no—
103C22×C3×C5—42no—
104C22×C3×C5—42no—
105C22×C3×C5#12011yescharacteristic
106C3×C4×C5—21no—
107C3×C4×C5—42no—
108C3×C4×C5—42no—
109C3×C4×C5#13512yes—
110C3×C4×C5#13712yes—
111C5×Dic3—81no—
112C2×C3×Q8C5×D412yes—
113C2×C3×D4—22no—
114C2×C3×D4C5×D412yes—
115C22×C3×C4—22no—
116C2×Dic6—21no—
117C3×C4⋊C4—22no—
118C3×C4⋊C4C5×D412yes—
119C3×C22⋊C4—24no—
120C3×C22⋊C4—22no—
121C3×C42—22no—
122C3×C42C23×C511yescharacteristic
123#216—44no—
124C4⋊Dic3—22no—
125C2×C3⋊C8—21no—
126C2×C3⋊C8—22no—
127C23×C5—22no—
128C5×Q8—42no—
129C5×Q8—122no—
130C5×D4—22no—
131C5×D4—22no—
132C5×D4—82no—
133C2×C4×C5—22no—
134C2×C4×C5—22no—
135C2×C4×C5—42no—
136C2×C4×C5—42no—
137C2×C4×C5—121no—
138C2×C4×C5C2×#6711yescharacteristic
139C2×C4×C5C2×#6712yes—
140C5×C8—62no—
141C5×C8—122no—
142C2×Q16—62no—
143C4⋊Q8—31no—
144C4⋊Q8C2×C5×D311yescharacteristic
145#124—22no—
146#121—22no—
147C4×D4C2×C5×D312yes—
148#117—22no—
149#106—62no—
150C4⋊C8—32no—
151#102—62no—
152C4×C8—31no—
153C2×C3×C5—82no—
154C2×C3×C5#45212yes—
155C2×C3×C5#45311yescharacteristic
156C23×C3—22no—
157C3×Q8—42no—
158C3×D4—22no—
159C3×D4—22no—
160C3×D4—82no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—42no—
164C2×C3×C4—42no—
165C2×C3×C4C2×C5×D411yescharacteristic
166C2×C3×C4C2×C5×D412yes—
167C2×Dic3—41no—
168Dic6—42no—
169C3⋊C8—22no—
170C3⋊C8—42no—
171C22×C5—42no—
172C22×C5—42no—
173C22×C5—42no—
174C22×C5#95311yescharacteristic
175C4×C5—21no—
176C4×C5—42no—
177C4×C5—42no—
178C4×C5—241no—
179C4×C5#95012yes—
180C4×C5#95112yes—
181C2×Q8—61no—
182C2×Q8C5×#6712yes—
183C2×D4—22no—
184C2×D4C5×#6712yes—
185C22×C4—22no—
186Q16—124no—
187C2×C8—61no—
188C2×C8—62no—
189C4⋊C4—22no—
190C4⋊C4—62no—
191C4⋊C4C5×#6712yes—
192C22⋊C4—24no—
193C22⋊C4—22no—
194C42—22no—
195C42C22×C5×D311yescharacteristic
196C3×C5#163411yescharacteristic, complemented, Hall
197C22×C3—42no—
198C22×C3—42no—
199C22×C3—42no—
200C22×C3C5×#12011yescharacteristic
201C3×C4—21no—
202C3×C4—42no—
203C3×C4—42no—
204C3×C4C5×#13512yes—
205C3×C4C5×#13712yes—
206Dic3—81no—
207C2×C5—82no—
208C2×C5#523912yes—
209C2×C5#524111yescharacteristic
210C23—22no—
211Q8—42no—
212Q8—122no—
213D4—22no—
214D4—22no—
215D4—82no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—121no—
221C2×C4C2×C5×#6711yescharacteristic
222C2×C4C2×C5×#6712yes—
223C8—62no—
224C8—122no—
225C2×C3—82no—
226C2×C3C5×#45212yes—
227C2×C3C5×#45311yescharacteristic
228C5#7192811yescharacteristic, direct product factor, Sylow
229C22—42no—
230C22—42no—
231C22—42no—
232C22C5×#95311yescharacteristic
233C4—21no—
234C4—42no—
235C4—42no—
236C4—241no—
237C4C5×#95012yes—
238C4C5×#95112yes—
239C3C5×#163411yescharacteristic, complemented, Sylow
240C2—82no—
241C2C5×#523912yes—
242C2C5×#524111yescharacteristic
subgroupG/H
centerC22×C5#953
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
Fitting, prime radicalC3×C5×#555C2
socleC22×C3×C5#120
hypercenterC5×#555D3
hypocenterC3C5×#1634
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#555

Complements

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

NH ≅ G/Ntype
2. C5×#5092C2semidirect
3. C5×#5008C2semidirect
4. C5×#4546C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
18. #71928C5direct (N × H)
40. #5092C2×C5semidirect
41. #5008C2×C5semidirect
42. #4546C2×C5semidirect
43. D4⋊(C3⋊C8)C2×C5semidirect
196. C3×C5#1634semidirect
228. C5#71928direct (N × H)
239. C3C5×#1634semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5552
C5×#50922
C5×#50082
C5×#45462
C5×D4⋊(C3⋊C8)2
C5×#16343
#719285