Finite Group Databasebeta

← D5×#396 #10609144

Subgroups — D5×#396 #10609144

Order 640.

908 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 203 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
1C2×D5×C4⋊C4C213yesmaximal, complemented
2C2×D5×C22⋊C4C213yesmaximal
3C5×#396C211yesmaximal, characteristic, complemented
4#65283C213yesmaximal, complemented
5#65237C213yesmaximal, complemented
6#64965C211yesmaximal, characteristic, complemented
7D5×#95C211yesmaximal, characteristic, complemented
8C24×D5C2211yescharacteristic
9C22×C4×D5C2213yes—
10C22×C4×D5C2213yes—
11C2×C5×C4⋊C4C2213yescomplemented
12C2×C5×C22⋊C4C2213yes—
13C2×C22⋊Dic5C2213yes—
14C2×#685C2213yes—
15C2×#685C2213yes—
16C2×C4⋊Dic5C2213yescomplemented
17C2×#683C2213yescomplemented
18C2×#683C2213yescomplemented
19D5×C4⋊C4—212no—
20D5×C22⋊C4—212no—
21C5×#95C2211yescharacteristic, complemented
22#3963C2213yescomplemented
23C2×#396—51nomaximal, Sylow
24C24×C5C2311yescharacteristic
25C23×D5—26no—
26C23×D5—26no—
27C23×D5Q814yes—
28C23×D5C2311yescharacteristic
29C23×D5C2311yescharacteristic
30C22×C4×C5C2313yes—
31C22×C4×C5C2313yes—
32C22×Dic5C2313yes—
33C22×Dic5C2313yes—
34C2×C4×D5—26no—
35C2×C4×D5—26no—
36C2×C4×D5—26no—
37C2×C4×D5—26no—
38C2×C4×D5—26no—
39C2×C4×D5D4112yes—
40C5×C4⋊C4—26no—
41C5×C22⋊C4—26no—
42C22⋊Dic5—26no—
43#685—26no—
44#685—26no—
45C4⋊Dic5—26no—
46#683—26no—
47#683—26no—
48C22×C4⋊C4—53no—
49C22×C22⋊C4—53no—
50#396—53no—
51#396—53no—
52#396—51no—
53#396D511yescharacteristic, direct product factor
54C2×#95—51no—
55C23×C5—23no—
56C23×C5—23no—
57C23×C5C2×Q812yes—
58C23×C5C2411yescharacteristic
59C22×D5—23no—
60C22×D5—23no—
61C22×D5—224no—
62C22×D5—412no—
63C22×D5—44no—
64C22×D5C2×D416yes—
65C22×D5C2×Q812yes—
66C22×D5C2×Q812yes—
67C22×D5#4116yes—
68C2×C4×C5—23no—
69C2×C4×C5—23no—
70C2×C4×C5—23no—
71C2×C4×C5—23no—
72C2×C4×C5—23no—
73C2×C4×C5C2×D416yes—
74C2×Dic5—23no—
75C2×Dic5—23no—
76C2×Dic5—23no—
77C2×Dic5—23no—
78C2×Dic5—23no—
79C2×Dic5C2×D416yes—
80C4×D5—224no—
81C4×D5—412no—
82C25—51no—
83C23×C4—53no—
84C23×C4—53no—
85C2×C4⋊C4—53no—
86C2×C4⋊C4—53no—
87C2×C4⋊C4—53no—
88C2×C4⋊C4—1012no—
89C2×C4⋊C4C2×D513yescomplemented
90C2×C22⋊C4—53no—
91C2×C22⋊C4—53no—
92C2×C22⋊C4—53no—
93C2×C22⋊C4—1012no—
94C2×C22⋊C4C2×D513yes—
95#95—53no—
96#95C2×D511yescharacteristic, complemented
97C22×C5—26no—
98C22×C5—43no—
99C22×C5—41no—
100C22×C5C22×D413yes—
101C22×C5C22×Q811yescharacteristic
102C22×C5C2×#4113yes—
103C2×D5—26no—
104C2×D5—43no—
105C2×D5—41no—
106C2×D5—416no—
107C2×D5#121112yes—
108C2×D5C22⋊Q8112yes—
109C2×D5#12614yes—
110C4×C5—26no—
111C4×C5—43no—
112Dic5—26no—
113Dic5—43no—
114C24—51no—
115C24—54no—
116C24—51no—
117C24—106no—
118C24—106no—
119C24C22×D511yescharacteristic
120C22×C4—53no—
121C22×C4—512no—
122C22×C4—53no—
123C22×C4—106no—
124C22×C4—106no—
125C22×C4—106no—
126C22×C4—106no—
127C22×C4—106no—
128C22×C4C22×D513yes—
129C22×C4C22×D513yes—
130C4⋊C4—26no—
131C4⋊C4—106no—
132C4⋊C4—106no—
133C4⋊C4—106no—
134C22⋊C4—26no—
135C22⋊C4—106no—
136C22⋊C4—106no—
137C22⋊C4—106no—
138C2×C5—42no—
139C2×C5C2×#12113yes—
140C2×C5C2×C22⋊Q813yes—
141C2×C5C2×#12611yescharacteristic
142D5—42no—
143D5#39618yesdirect product factor
144C23—23no—
145C23—23no—
146C23—56no—
147C23—52no—
148C23—56no—
149C23—52no—
150C23—1024no—
151C23—103no—
152C23—103no—
153C23—2012no—
154C23—204no—
155C23Q8×D512yes—
156C23C23×D511yescharacteristic
157C2×C4—23no—
158C2×C4—23no—
159C2×C4—23no—
160C2×C4—23no—
161C2×C4—23no—
162C2×C4—56no—
163C2×C4—1024no—
164C2×C4—103no—
165C2×C4—103no—
166C2×C4—103no—
167C2×C4—103no—
168C2×C4—103no—
169C2×C4—2012no—
170C2×C4D4×D516yes—
171C5C2×#39611yescharacteristic, complemented, Sylow
172C22—26no—
173C22—43no—
174C22—41no—
175C22—512no—
176C22—512no—
177C22—54no—
178C22—106no—
179C22—2016no—
180C22—203no—
181C22—201no—
182C22C2×D4×D513yes—
183C22C2×Q8×D511yescharacteristic
184C22D5×#4113yes—
185C4—26no—
186C4—43no—
187C4—106no—
188C4—203no—
189C2—42no—
190C2—58no—
191C2—202no—
192C2D5×#12113yes—
193C2D5×C22⋊Q813yes—
194C2D5×#12611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#396C2
prime radicalC24×D5C22
hypercenter#396D5
hypocenterC5C2×#396
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×D5×C4⋊C4C2semidirect
3. C5×#396C2semidirect
4. #65283C2semidirect
5. #65237C2semidirect
6. #64965C2semidirect
7. D5×#95C2semidirect
11. C2×C5×C4⋊C4C22semidirect
16. C2×C4⋊Dic5C22semidirect
17. C2×#683C22semidirect
18. C2×#683C22semidirect
21. C5×#95C22semidirect
22. #3963C22semidirect
53. #396D5direct (N × H)
89. C2×C4⋊C4C2×D5semidirect
96. #95C2×D5semidirect
143. D5#396direct (N × H)
171. C5C2×#396semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊C42
C2×D5×C22⋊C42
C5×#3962
#652832
#652372
#649652
D5×#952
C2×#3965