Finite Group Databasebeta

← #10605915

Subgroups — #10605915

Order 640.

548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#4039C211yesmaximal, characteristic
2C2×#4036C211yesmaximal, characteristic, complemented
3C5×#382C211yesmaximal, characteristic, complemented
4#65277C211yesmaximal, characteristic
5#65265C211yesmaximal, characteristic, complemented
6#65228C211yesmaximal, characteristic
7C4×#683C211yesmaximal, characteristic, complemented
8#64965C214yesmaximal, complemented
9#64957C214yesmaximal, complemented
10C22×D20C2211yescharacteristic
11C22×C4×D5C2212yes—
12C2×C5×C4⋊C4C2211yescharacteristic
13C2×C5×C4⋊C4C2211yescharacteristic
14C2×C42×C5C2211yescharacteristic
15C2×#685C2212yes—
16C2×#685C2214yes—
17C2×#685C2214yes—
18C2×C4⋊Dic5C2212yes—
19C2×C4⋊Dic5C2211yescharacteristic
20C2×#683C2212yes—
21C2×#683C2212yes—
22C2×#683C2214yes—
23C2×C4×Dic5C2211yescharacteristic
24C2×C4×Dic5C2211yescharacteristic
25#4039—24no—
26#4036—24no—
27C5×#95C2214yes—
28#3963C2212yes—
29#2566—51nomaximal, Sylow
30C23×D5C2312yes—
31C22×C4×C5C2312yes—
32C22×C4×C5C2312yes—
33C22×C4×C5C2312yes—
34C22×C4×C5C2311yescharacteristic
35C22×Dic5C2312yes—
36C22×Dic5C2311yescharacteristic
37C22×Dic5C2311yescharacteristic
38C22×Dic5C2312yes—
39C2×D20—22no—
40C2×D20—22no—
41C2×D20Q814yes—
42C2×C4×D5—24no—
43C2×C4×D5—44no—
44C5×C4⋊C4—22no—
45C5×C4⋊C4—22no—
46C42×C5—22no—
47#685—24no—
48#685—28no—
49#685—44no—
50C4⋊Dic5—22no—
51C4⋊Dic5—24no—
52#683—24no—
53#683—24no—
54#683—44no—
55C4×Dic5—22no—
56C4×Dic5D414yes—
57C2×#125—51no—
58C2×C4×D4—51no—
59#396—54no—
60#390—51no—
61#390—51no—
62#385—54no—
63#384—51no—
64#382D511yescharacteristic, complemented
65C4×C4⋊C4—51no—
66C23×C5C2411yescharacteristic
67C22×D5—22no—
68C22×D5—24no—
69C22×D5—22no—
70C22×D5—24no—
71C22×D5C2×Q814yes—
72C2×C4×C5—22no—
73C2×C4×C5—22no—
74C2×C4×C5—22no—
75C2×C4×C5—24no—
76C2×C4×C5—22no—
77C2×C4×C5—24no—
78C2×C4×C5—22no—
79C2×C4×C5C2×D412yes—
80C2×C4×C5C2×Q812yes—
81C2×C4×C5#4112yes—
82C2×Dic5—22no—
83C2×Dic5—22no—
84C2×Dic5—22no—
85C2×Dic5—22no—
86C2×Dic5—22no—
87C2×Dic5—24no—
88C2×Dic5C2×D412yes—
89C2×Dic5C2×D412yes—
90C2×Dic5#4114yes—
91D20—28no—
92C4×D5—48no—
93C22×D4—51no—
94C23×C4—52no—
95#125—104no—
96C4×D4—104no—
97C2×C4⋊C4—51no—
98C2×C4⋊C4—52no—
99C2×C4⋊C4—52no—
100C2×C4⋊C4—52no—
101C2×C4⋊C4—54no—
102C2×C4⋊C4C2×D511yescharacteristic
103C2×C4⋊C4C2×D511yescharacteristic
104C2×C22⋊C4—52no—
105C2×C22⋊C4—54no—
106C2×C22⋊C4—54no—
107C2×C42—51no—
108C2×C42—51no—
109C2×C42C2×D511yescharacteristic
110#95—52no—
111#95C2×D514yes—
112C22×C5C22×D411yescharacteristic
113C22×C5C22×Q811yescharacteristic
114C22×C5C2×#4111yescharacteristic
115C22×C5C2×#4112yes—
116C22×C5H(5,𝔽2)12yes—
117C2×D5—24no—
118C2×D5—28no—
119C2×D5—42no—
120C2×D5—42no—
121C2×D5—44no—
122C4×C5—42no—
123C4×C5—42no—
124C4×C5—42no—
125C4×C5C22⋊Q814yes—
126Dic5—22no—
127Dic5—22no—
128Dic5—24no—
129Dic5—42no—
130C24—52no—
131C2×D4—54no—
132C2×D4—102no—
133C2×D4—102no—
134C22×C4—51no—
135C22×C4—52no—
136C22×C4—51no—
137C22×C4—52no—
138C22×C4—104no—
139C22×C4—204no—
140C22×C4C22×D512yes—
141C22×C4C22×D512yes—
142C22×C4C22×D512yes—
143C22×C4C22×D511yescharacteristic
144C4⋊C4—22no—
145C4⋊C4—22no—
146C4⋊C4—104no—
147C4⋊C4—104no—
148C4⋊C4—104no—
149C4⋊C4—102no—
150C4⋊C4—204no—
151C22⋊C4—104no—
152C22⋊C4—108no—
153C22⋊C4—204no—
154C42—22no—
155C42—54no—
156C42—102no—
157C2×C5C2×C22⋊Q811yescharacteristic
158C2×C5#53211yescharacteristic
159C2×C5#53511yescharacteristic
160C2×C5#55312yes—
161C2×C5#55412yes—
162D5—44no—
163C23—54no—
164C23—102no—
165C23—102no—
166C23—104no—
167C23—104no—
168C23C23×D511yescharacteristic
169D4—108no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—52no—
178C2×C4—52no—
179C2×C4—54no—
180C2×C4—102no—
181C2×C4—102no—
182C2×C4—102no—
183C2×C4—102no—
184C2×C4—102no—
185C2×C4—104no—
186C2×C4—208no—
187C2×C4#70912yes—
188C2×C4D4×D512yes—
189C2×C4Q8×D512yes—
190C5#256611yescharacteristic, complemented, Sylow
191C22—104no—
192C22—108no—
193C22—204no—
194C22—202no—
195C22—202no—
196C22C2×#70911yescharacteristic
197C22C2×D4×D511yescharacteristic
198C22C2×Q8×D511yescharacteristic
199C22D5×#4112yes—
200C22#414912yes—
201C4—42no—
202C4—42no—
203C4—42no—
204C4—104no—
205C4—102no—
206C4—102no—
207C4—202no—
208C4#404214yes—
209C2—204no—
210C2C2×#404211yescharacteristic
211C2#6586412yes—
212C2#6600211yescharacteristic
213C2#6600811yescharacteristic
214C2#6602412yes—
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#382C2
prime radicalC22×D20C22
hypercenter#382D5
hypocenterC5#2566
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×#4036C2semidirect
3. C5×#382C2semidirect
5. #65265C2semidirect
7. C4×#683C2semidirect
8. #64965C2semidirect
9. #64957C2semidirect
64. #382D5semidirect
190. C5#2566semidirect

Maximal subgroups

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

subgroupindex
C2×#40392
C2×#40362
C5×#3822
#652772
#652652
#652282
C4×#6832
#649652
#649572
#25665