Finite Group Databasebeta

← C5×#3568⋊C3 #14511401

Subgroups — C5×#3568⋊C3 #14511401

Order 1920.

386 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 34 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×#5464C211yesmaximal, characteristic, complemented
2C5×#3568C311yesmaximal, characteristic, complemented, Hall
3C5×#126⋊C3—42nomaximal
4C5×#120⋊C3—42nomaximal
5C2×C5×C42⋊C3—41nomaximal
6#3568⋊C3C511yesmaximal, characteristic, direct product factor, Hall
7C5×#563—31no—
8C5×H(3,𝔽4)C2×C311yescharacteristic, complemented
9C5×#556—32no—
10C5×#551—32no—
11C5×#542—32no—
12C5×#538—32no—
13C5×#529—31no—
14C5×C22⋊A4—42no—
15C5×C42⋊C3—41no—
16C5×C42⋊C3—42no—
17#5464C2×C511yescharacteristic, complemented
18C5×C4⋊Q8—32no—
19C5×#126—32no—
20C5×#126—32no—
21C5×#126—32no—
22C5×#126—32no—
23C5×#126A412yescomplemented
24C5×#125—31no—
25C5×#124—32no—
26C5×#124—32no—
27C5×#124—31no—
28C5×#124—32no—
29C5×#123—32no—
30C5×#123—32no—
31C5×#123—32no—
32C5×C22⋊Q8—31no—
33C5×C22⋊Q8—32no—
34C5×C22⋊Q8—32no—
35C5×C22⋊Q8—32no—
36C5×#121—31no—
37C5×#121—32no—
38C5×#120—32no—
39C5×#120A412yescomplemented
40C4×C5×Q8—31no—
41C4×C5×Q8—32no—
42C4×C5×D4—32no—
43C4×C5×D4—31no—
44C4×C5×D4—32no—
45C5×#117—32no—
46C5×#117—32no—
47C2×C5×C22⋊C4—32no—
48C2×C42×C5A411yescharacteristic, complemented
49#3568C3×C511yescharacteristic, complemented, Sylow
50C2×C5×A4—161no—
51#126⋊C3—42no—
52#120⋊C3—42no—
53C2×C42⋊C3—41no—
54C24×C5C2×A412yes—
55C2×C5×Q8—32no—
56C2×C5×Q8—31no—
57C2×C5×D4—31no—
58C2×C5×D4—32no—
59C2×C5×D4—32no—
60C22×C4×C5—32no—
61C22×C4×C5—32no—
62C22×C4×C5—31no—
63C5×C4⋊C4—32no—
64C5×C4⋊C4—32no—
65C5×C4⋊C4—32no—
66C5×C4⋊C4—32no—
67C5×C4⋊C4—31no—
68C5×C4⋊C4—32no—
69C5×C4⋊C4—31no—
70C5×C4⋊C4—32no—
71C5×C22⋊C4—32no—
72C5×C22⋊C4—32no—
73C5×C22⋊C4—32no—
74C5×C22⋊C4—32no—
75C5×C22⋊C4—32no—
76C5×C22⋊C4—32no—
77C5×C22⋊C4—32no—
78C5×C22⋊C4—32no—
79C5×C22⋊C4—32no—
80C42×C5—31no—
81C42×C5—32no—
82C42×C5—32no—
83C42×C5C2×A411yescharacteristic
84C42×C5C2×A412yes—
85#563—31no—
86H(3,𝔽4)C2×C3×C511yescharacteristic, complemented
87#556—32no—
88#551—32no—
89#542—32no—
90#538—32no—
91#529—31no—
92C5×A4—161no—
93C5×A4—324no—
94C22⋊A4—42no—
95C42⋊C3—41no—
96C42⋊C3—42no—
97C23×C5—32no—
98C23×C5—122no—
99C23×C5C22⋊A411yescharacteristic
100C5×Q8—122no—
101C5×Q8—121no—
102C5×D4—122no—
103C5×D4—121no—
104C5×D4—122no—
105C2×C4×C5—31no—
106C2×C4×C5—32no—
107C2×C4×C5—32no—
108C2×C4×C5—31no—
109C2×C4×C5—32no—
110C2×C4×C5—122no—
111C2×C4×C5—121no—
112C2×C4×C5—122no—
113C4⋊Q8—32no—
114#126—32no—
115#126—32no—
116#126—32no—
117#126—32no—
118#126C5×A412yescomplemented
119#125—31no—
120#124—32no—
121#124—32no—
122#124—31no—
123#124—32no—
124#123—32no—
125#123—32no—
126#123—32no—
127C22⋊Q8—31no—
128C22⋊Q8—32no—
129C22⋊Q8—32no—
130C22⋊Q8—32no—
131#121—31no—
132#121—32no—
133#120—32no—
134#120C5×A412yescomplemented
135C4×Q8—31no—
136C4×Q8—32no—
137C4×D4—32no—
138C4×D4—31no—
139C4×D4—32no—
140#117—32no—
141#117—32no—
142C2×C22⋊C4—32no—
143C2×C42C5×A411yescharacteristic, complemented
144C2×C3×C5—641no—
145C2×A4—161no—
146C22×C5—61no—
147C22×C5—62no—
148C22×C5—62no—
149C22×C5—62no—
150C22×C5—84no—
151C22×C5C2×C22⋊A411yescharacteristic
152C4×C5—61no—
153C4×C5—62no—
154C4×C5—62no—
155C4×C5—61no—
156C4×C5—62no—
157C24C2×C5×A412yes—
158C2×Q8—32no—
159C2×Q8—31no—
160C2×D4—31no—
161C2×D4—32no—
162C2×D4—32no—
163C22×C4—32no—
164C22×C4—32no—
165C22×C4—31no—
166C4⋊C4—32no—
167C4⋊C4—32no—
168C4⋊C4—32no—
169C4⋊C4—32no—
170C4⋊C4—31no—
171C4⋊C4—32no—
172C4⋊C4—31no—
173C4⋊C4—32no—
174C22⋊C4—32no—
175C22⋊C4—32no—
176C22⋊C4—32no—
177C22⋊C4—32no—
178C22⋊C4—32no—
179C22⋊C4—32no—
180C22⋊C4—32no—
181C22⋊C4—32no—
182C22⋊C4—32no—
183C42—31no—
184C42—32no—
185C42—32no—
186C42C2×C5×A411yescharacteristic
187C42C2×C5×A412yes—
188C3×C5—641noHall
189A4—161no—
190A4—324no—
191C2×C5—31no—
192C2×C5—41no—
193C2×C5—122no—
194C23—32no—
195C23—122no—
196C23C5×C22⋊A411yescharacteristic
197Q8—122no—
198Q8—121no—
199D4—122no—
200D4—121no—
201D4—122no—
202C2×C4—31no—
203C2×C4—32no—
204C2×C4—32no—
205C2×C4—31no—
206C2×C4—32no—
207C2×C4—122no—
208C2×C4—121no—
209C2×C4—122no—
210C2×C3—641no—
211C5#3568⋊C311yescharacteristic, direct product factor, Sylow
212C22—61no—
213C22—62no—
214C22—62no—
215C22—62no—
216C22—84no—
217C22C2×C5×C22⋊A411yescharacteristic
218C4—61no—
219C4—62no—
220C4—62no—
221C4—61no—
222C4—62no—
223C3—641noSylow
224C2—31no—
225C2—41no—
226C2—122no—
subgroupG/H
center, hypercenterC5#3568⋊C3
commutator, cosocle, hypocenterH(3,𝔽4)C2×C3×C5
FrattiniC22C2×C5×C22⋊A4
FittingC5×#3568C3
socleC22×C5C2×C22⋊A4
LCSG ▷ H(3,𝔽4)
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×#5464C2semidirect
2. C5×#3568C3semidirect
6. #3568⋊C3C5direct (N × H)
8. C5×H(3,𝔽4)C2×C3semidirect
17. #5464C2×C5semidirect
23. C5×#126A4semidirect
39. C5×#120A4semidirect
48. C2×C42×C5A4semidirect
49. #3568C3×C5semidirect
86. H(3,𝔽4)C2×C3×C5semidirect
118. #126C5×A4semidirect
134. #120C5×A4semidirect
143. C2×C42C5×A4semidirect
211. C5#3568⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#54642
C5×#35683
C5×#126⋊C34
C5×#120⋊C34
C2×C5×C42⋊C34
#3568⋊C35