Finite Group Databasebeta

← C5×#10227 #11932947

Subgroups — C5×#10227 #11932947

Order 1280.

466 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3229C212yesmaximal
2C5×#3162C211yesmaximal, characteristic
3C5×#1960C211yesmaximal, characteristic
4C5×#1518C212yesmaximal
5C5×#1281C211yesmaximal, characteristic
6C5×#533C2212yes—
7C2×C5×C4⋊Q8C2211yescharacteristic
8C5×#501—22no—
9C5×#501—22no—
10C5×#498—22no—
11C5×#487—22no—
12C5×#483—24no—
13C5×#475—24no—
14C5×#431C2212yes—
15C5×#427—22no—
16C2×C5×#103—22no—
17C2×C5×#97C2211yescharacteristic
18C5×#382C2211yescharacteristic
19C5×#328—24no—
20#10227C511yesmaximal, characteristic, direct product factor, Sylow
21C22×C5×Q8—21no—
22C22×C5×C8D412yes—
23C5×C4⋊Q8—22no—
24C5×C4⋊Q8—21no—
25C5×C4⋊Q8D412yes—
26C5×C4⋊Q8D412yes—
27C5×C4⋊Q8D412yes—
28C5×#125—22no—
29C5×C22⋊Q8—22no—
30C5×C22⋊Q8—22no—
31C4×C5×Q8—22no—
32C4×C5×Q8—22no—
33C5×#117—22no—
34C2×C5×C4⋊C4—22no—
35C2×C5×C4⋊C4—21no—
36C2×C42×C5C2311yescharacteristic
37C5×#107—24no—
38C5×#106—22no—
39C5×#106—22no—
40C5×#106—28no—
41C5×C4⋊C8—22no—
42C5×#103—28no—
43C5×#103—44no—
44C5×C22⋊C8D414yes—
45C5×#97—22no—
46C4×C5×C8—22no—
47C5×#95—22no—
48#3229C2×C512yes—
49#3162C2×C511yescharacteristic
50#1960C2×C511yescharacteristic
51#1518C2×C512yes—
52#1281C2×C511yescharacteristic
53C2×C5×Q8—22no—
54C2×C5×Q8—22no—
55C2×C5×Q8—22no—
56C2×C5×Q8—41no—
57C2×C5×Q8—42no—
58C2×C5×Q8—42no—
59C22×C4×C5—41no—
60C22×C4×C5—41no—
61C22×C4×C5C2×D412yes—
62C22×C4×C5C2×D411yescharacteristic
63C2×C5×C8—22no—
64C2×C5×C8—22no—
65C2×C5×C8—24no—
66C2×C5×C8SD1614yes—
67C5×C4⋊C4—24no—
68C5×C4⋊C4—22no—
69C5×C4⋊C4—22no—
70C5×C4⋊C4—22no—
71C5×C4⋊C4—22no—
72C5×C4⋊C4—42no—
73C5×C4⋊C4—42no—
74C5×C4⋊C4—42no—
75C5×C4⋊C4—42no—
76C5×C22⋊C4—42no—
77C42×C5—42no—
78C42×C5C2×D411yescharacteristic
79C42×C5C2×D412yes—
80C42×C5#4111yescharacteristic
81#533C22×C512yes—
82C2×C4⋊Q8C22×C511yescharacteristic
83#501—22no—
84#501—22no—
85#498—22no—
86#487—22no—
87#483—24no—
88#475—24no—
89#431C22×C512yes—
90#427—22no—
91C2×#103—22no—
92C2×#97C22×C511yescharacteristic
93#382C22×C511yescharacteristic
94#328—24no—
95C23×C5#12711yescharacteristic
96C5×Q8—44no—
97C5×Q8—44no—
98C5×Q8—82no—
99C5×Q8—82no—
100C2×C4×C5—42no—
101C2×C4×C5—42no—
102C2×C4×C5—42no—
103C2×C4×C5—42no—
104C2×C4×C5—81no—
105C2×C4×C5—81no—
106C2×C4×C5—82no—
107C2×C4×C5—81no—
108C2×C4×C5#12012yes—
109C2×C4×C5#12011yescharacteristic
110C2×C4×C5#12112yes—
111C2×C4×C5#12111yescharacteristic
112C2×C4×C5C2×SD1612yes—
113C2×C4×C5#13712yes—
114C5×C8—24no—
115C5×C8—44no—
116C22×Q8—21no—
117C22×C8C5×D412yes—
118C4⋊Q8—22no—
119C4⋊Q8—21no—
120C4⋊Q8C5×D412yes—
121C4⋊Q8C5×D412yes—
122C4⋊Q8C5×D412yes—
123#125—22no—
124C22⋊Q8—22no—
125C22⋊Q8—22no—
126C4×Q8—22no—
127C4×Q8—22no—
128#117—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—21no—
131C2×C42C23×C511yescharacteristic
132#107—24no—
133#106—22no—
134#106—22no—
135#106—28no—
136C4⋊C8—22no—
137#103—28no—
138#103—44no—
139C22⋊C8C5×D414yes—
140#97—22no—
141C4×C8—22no—
142#95—22no—
143C22×C5—22no—
144C22×C5#39211yescharacteristic
145C22×C5#49211yescharacteristic
146C22×C5#49711yescharacteristic
147C4×C5—22no—
148C4×C5—22no—
149C4×C5—82no—
150C4×C5—82no—
151C4×C5—82no—
152C4×C5—161no—
153C4×C5#44812yes—
154C4×C5#46112yes—
155C2×Q8—22no—
156C2×Q8—22no—
157C2×Q8—22no—
158C2×Q8—41no—
159C2×Q8—42no—
160C2×Q8—42no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4C2×C5×D412yes—
164C22×C4C2×C5×D411yescharacteristic
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—24no—
168C2×C8C5×SD1614yes—
169C4⋊C4—24no—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—42no—
178C22⋊C4—42no—
179C42—42no—
180C42C2×C5×D412yes—
181C42C2×C5×D411yescharacteristic
182C42C5×#4111yescharacteristic
183C2×C5—21no—
184C2×C5—21no—
185C2×C5#200912yes—
186C2×C5#201311yescharacteristic
187C23C5×#12711yescharacteristic
188Q8—44no—
189Q8—44no—
190Q8—82no—
191Q8—82no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—82no—
199C2×C4—81no—
200C2×C4C5×#12012yes—
201C2×C4C5×#12011yescharacteristic
202C2×C4C5×#12112yes—
203C2×C4C5×#12111yescharacteristic
204C2×C4C2×C5×SD1612yes—
205C2×C4C5×#13712yes—
206C8—24no—
207C8—44no—
208C5#1022711yescharacteristic, direct product factor, Sylow
209C22—22no—
210C22C5×#39211yescharacteristic
211C22C5×#49211yescharacteristic
212C22C5×#49711yescharacteristic
213C4—22no—
214C4—22no—
215C4—82no—
216C4—82no—
217C4—82no—
218C4—161no—
219C4C5×#44812yes—
220C4C5×#46112yes—
221C2—21no—
222C2—21no—
223C2C5×#200912yes—
224C2C5×#201311yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC23×C5#127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
20. #10227C5direct (N × H)
208. C5#10227direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32292
C5×#31622
C5×#19602
C5×#15182
C5×#12812
#102275