Finite Group Databasebeta

← C5×#10217 #11932937

Subgroups — C5×#10217 #11932937

Order 1280.

430 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3255C211yesmaximal, characteristic
2C5×#3237C212yesmaximal
3C5×#1995C211yesmaximal, characteristic
4C5×#1506C212yesmaximal
5C5×#1307C211yesmaximal, characteristic
6C5×#533C2211yescharacteristic
7C5×#533C2212yes—
8C5×#501—22no—
9C5×#491—22no—
10C5×#485—24no—
11C5×#477—22no—
12C5×#475—22no—
13C5×#475—22no—
14C5×#470—22no—
15C5×#462—22no—
16C5×#432C2212yes—
17C5×#423C2211yescharacteristic
18C5×#376C2211yescharacteristic
19C5×#339—22no—
20C5×#328—24no—
21#10217C511yesmaximal, characteristic, direct product factor, Sylow
22C2×C5×Q16—22no—
23C2×C5×M16D412yes—
24C5×C4⋊Q8D412yes—
25C5×C4⋊Q8D412yes—
26C5×C4⋊Q8D412yes—
27C5×#125—22no—
28C5×#125—21no—
29C5×C22⋊Q8—22no—
30C5×C22⋊Q8—22no—
31C5×C22⋊Q8—22no—
32C4×C5×Q8—22no—
33C4×C5×Q8—22no—
34C4×C5×Q8—22no—
35C5×#117—21no—
36C5×#117—22no—
37C2×C42×C5—21no—
38C2×C42×C5C2311yescharacteristic
39C5×#107—24no—
40C5×#106—22no—
41C5×#106—24no—
42C5×C4⋊C8—22no—
43C5×C4⋊C8—22no—
44C5×#103—24no—
45C5×#103—24no—
46C5×#103—24no—
47C5×C22⋊C8D414yes—
48C5×#97—22no—
49C5×#95—22no—
50#3255C2×C511yescharacteristic
51#3237C2×C512yes—
52#1995C2×C511yescharacteristic
53#1506C2×C512yes—
54#1307C2×C511yescharacteristic
55C2×C5×Q8—22no—
56C2×C5×Q8—22no—
57C2×C5×Q8—22no—
58C22×C4×C5—41no—
59C22×C4×C5C2×D411yescharacteristic
60C22×C4×C5C2×D412yes—
61C5×Q16—82no—
62C5×M16—42no—
63C2×C5×C8—22no—
64C2×C5×C8—24no—
65C5×C4⋊C4—22no—
66C5×C4⋊C4—22no—
67C5×C4⋊C4—22no—
68C5×C4⋊C4—22no—
69C5×C4⋊C4—22no—
70C5×C4⋊C4—22no—
71C5×C4⋊C4—42no—
72C5×C4⋊C4—42no—
73C5×C4⋊C4—42no—
74C5×C22⋊C4—41no—
75C5×C22⋊C4—42no—
76C42×C5—22no—
77C42×C5—41no—
78C42×C5—41no—
79C42×C5—42no—
80C42×C5C2×D412yes—
81C42×C5C2×D411yescharacteristic
82C42×C5#4111yescharacteristic
83#533C22×C511yescharacteristic
84#533C22×C512yes—
85#501—22no—
86#491—22no—
87#485—24no—
88#477—22no—
89#475—22no—
90#475—22no—
91#470—22no—
92#462—22no—
93#432C22×C512yes—
94#423C22×C511yescharacteristic
95#376C22×C511yescharacteristic
96#339—22no—
97#328—24no—
98C23×C5#12711yescharacteristic
99C5×Q8—44no—
100C5×Q8—42no—
101C5×Q8—42no—
102C5×Q8—82no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—42no—
106C2×C4×C5—42no—
107C2×C4×C5—42no—
108C2×C4×C5—42no—
109C2×C4×C5—42no—
110C2×C4×C5—82no—
111C2×C4×C5#12012yes—
112C2×C4×C5#12011yescharacteristic
113C2×C4×C5#12112yes—
114C2×C4×C5#12111yescharacteristic
115C5×C8—44no—
116C5×C8—42no—
117C2×Q16—22no—
118C2×M16C5×D412yes—
119C4⋊Q8C5×D412yes—
120C4⋊Q8C5×D412yes—
121C4⋊Q8C5×D412yes—
122#125—22no—
123#125—21no—
124C22⋊Q8—22no—
125C22⋊Q8—22no—
126C22⋊Q8—22no—
127C4×Q8—22no—
128C4×Q8—22no—
129C4×Q8—22no—
130#117—21no—
131#117—22no—
132C2×C42—21no—
133C2×C42C23×C511yescharacteristic
134#107—24no—
135#106—22no—
136#106—24no—
137C4⋊C8—22no—
138C4⋊C8—22no—
139#103—24no—
140#103—24no—
141#103—24no—
142C22⋊C8C5×D414yes—
143#97—22no—
144#95—22no—
145C22×C5—21no—
146C22×C5—22no—
147C22×C5#39211yescharacteristic
148C4×C5—21no—
149C4×C5—22no—
150C4×C5—22no—
151C4×C5—82no—
152C4×C5—82no—
153C4×C5—82no—
154C4×C5—82no—
155C4×C5#45511yescharacteristic
156C4×C5#45611yescharacteristic
157C2×Q8—22no—
158C2×Q8—22no—
159C2×Q8—22no—
160C22×C4—41no—
161C22×C4C2×C5×D411yescharacteristic
162C22×C4C2×C5×D412yes—
163Q16—82no—
164M16—42no—
165C2×C8—24no—
166C2×C8—22no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C22⋊C4—41no—
177C22⋊C4—42no—
178C42—22no—
179C42—41no—
180C42—41no—
181C42—42no—
182C42C2×C5×D411yescharacteristic
183C42C2×C5×D412yes—
184C42C5×#4111yescharacteristic
185C2×C5—41no—
186C2×C5#200711yescharacteristic
187C2×C5#200912yes—
188C23C5×#12711yescharacteristic
189Q8—44no—
190Q8—42no—
191Q8—42no—
192Q8—82no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—82no—
201C2×C4C5×#12012yes—
202C2×C4C5×#12011yescharacteristic
203C2×C4C5×#12112yes—
204C2×C4C5×#12111yescharacteristic
205C8—44no—
206C8—42no—
207C5#1021711yescharacteristic, direct product factor, Sylow
208C22—21no—
209C22—22no—
210C22C5×#39211yescharacteristic
211C4—21no—
212C4—22no—
213C4—22no—
214C4—82no—
215C4—82no—
216C4—82no—
217C4—82no—
218C4C5×#45511yescharacteristic
219C4C5×#45611yescharacteristic
220C2—41no—
221C2C5×#200711yescharacteristic
222C2C5×#200912yes—
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
21. #10217C5direct (N × H)
207. C5#10217direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#32552
C5×#32372
C5×#19952
C5×#15062
C5×#13072
#102175