Finite Group Databasebeta

← C5×#9979 #11932699

Subgroups — C5×#9979 #11932699

Order 1280.

492 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 102 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×#3189C211yesmaximal, characteristic
2C5×#3095C212yesmaximal
3C5×#1818C211yesmaximal, characteristic
4C5×#1472C212yesmaximal
5C5×#1293C211yesmaximal, characteristic
6C2×C5×C22⋊Q8C2212yes—
7C2×C5×#117C2211yescharacteristic
8C5×#485—24no—
9C5×#484—22no—
10C5×#484—22no—
11C5×#483—22no—
12C5×#467—22no—
13C5×#451—22no—
14C5×#428—22no—
15C5×#419—22no—
16C5×#407C2212yes—
17C2×C5×C22⋊C8C2211yescharacteristic
18C2×C5×C22⋊C8C2211yescharacteristic
19C5×#336—22no—
20C5×#324—24no—
21#9979C511yesmaximal, characteristic, direct product factor, Sylow
22C22×C5×Q8D412yes—
23C23×C4×C5C2311yescharacteristic
24C2×C5×Q16—22no—
25C2×C5×M16—22no—
26C22×C5×C8—21no—
27C22×C5×C8D412yes—
28C5×C22⋊Q8—22no—
29C5×C22⋊Q8—22no—
30C5×C22⋊Q8—22no—
31C5×C22⋊Q8—22no—
32C5×#117—22no—
33C5×#117—22no—
34C2×C5×C4⋊C4—22no—
35C2×C5×C4⋊C4D412yes—
36C2×C5×C4⋊C4D411yescharacteristic
37C2×C5×C4⋊C4D411yescharacteristic
38C2×C5×C22⋊C4—21no—
39C2×C5×C22⋊C4—22no—
40C2×C42×C5—21no—
41C5×#107—24no—
42C5×#107—22no—
43C5×#106—24no—
44C5×#103—24no—
45C5×#103—24no—
46C5×#103—24no—
47C5×C22⋊C8—22no—
48C5×C22⋊C8—22no—
49C5×C22⋊C8—22no—
50C5×C22⋊C8D414yes—
51#3189C2×C511yescharacteristic
52#3095C2×C512yes—
53#1818C2×C511yescharacteristic
54#1472C2×C512yes—
55#1293C2×C511yescharacteristic
56C24×C5#4111yescharacteristic
57C2×C5×Q8—22no—
58C2×C5×Q8—22no—
59C2×C5×Q8—44no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—22no—
63C22×C4×C5—22no—
64C22×C4×C5—42no—
65C22×C4×C5C2×D412yes—
66C22×C4×C5C2×D411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×C4×C5C2×D412yes—
69C5×Q16—82no—
70C5×M16—44no—
71C2×C5×C8—22no—
72C2×C5×C8—24no—
73C2×C5×C8—42no—
74C2×C5×C8—42no—
75C2×C5×C8—41no—
76C5×C4⋊C4—22no—
77C5×C4⋊C4—22no—
78C5×C4⋊C4—22no—
79C5×C4⋊C4—22no—
80C5×C4⋊C4—42no—
81C5×C4⋊C4—42no—
82C5×C22⋊C4—42no—
83C5×C22⋊C4—42no—
84C5×C22⋊C4—42no—
85C42×C5—41no—
86C42×C5—41no—
87C2×C22⋊Q8C22×C512yes—
88C2×#117C22×C511yescharacteristic
89#485—24no—
90#484—22no—
91#484—22no—
92#483—22no—
93#467—22no—
94#451—22no—
95#428—22no—
96#419—22no—
97#407C22×C512yes—
98C2×C22⋊C8C22×C511yescharacteristic
99C2×C22⋊C8C22×C511yescharacteristic
100#336—22no—
101#324—24no—
102C23×C5—22no—
103C23×C5—41no—
104C23×C5—41no—
105C23×C5#12112yes—
106C23×C5#12111yescharacteristic
107C5×Q8—44no—
108C5×Q8—44no—
109C2×C4×C5—22no—
110C2×C4×C5—24no—
111C2×C4×C5—41no—
112C2×C4×C5—42no—
113C2×C4×C5—42no—
114C2×C4×C5—44no—
115C2×C4×C5—41no—
116C2×C4×C5—41no—
117C2×C4×C5—42no—
118C2×C4×C5—42no—
119C2×C4×C5—42no—
120C2×C4×C5—82no—
121C2×C4×C5#12012yes—
122C2×C4×C5#12011yescharacteristic
123C2×C4×C5#12711yescharacteristic
124C5×C8—44no—
125C5×C8—42no—
126C5×C8—81no—
127C22×Q8C5×D412yes—
128C23×C4C23×C511yescharacteristic
129C2×Q16—22no—
130C2×M16—22no—
131C22×C8—21no—
132C22×C8C5×D412yes—
133C22⋊Q8—22no—
134C22⋊Q8—22no—
135C22⋊Q8—22no—
136C22⋊Q8—22no—
137#117—22no—
138#117—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4C5×D411yescharacteristic
141C2×C4⋊C4C5×D411yescharacteristic
142C2×C4⋊C4C5×D412yes—
143C2×C22⋊C4—21no—
144C2×C22⋊C4—22no—
145C2×C42—21no—
146#107—24no—
147#107—22no—
148#106—24no—
149#103—24no—
150#103—24no—
151#103—24no—
152C22⋊C8—22no—
153C22⋊C8—22no—
154C22⋊C8—22no—
155C22⋊C8C5×D414yes—
156C22×C5—21no—
157C22×C5—21no—
158C22×C5—22no—
159C22×C5—22no—
160C22×C5—22no—
161C22×C5—82no—
162C22×C5#39211yescharacteristic
163C22×C5#47312yes—
164C4×C5—22no—
165C4×C5—21no—
166C4×C5—81no—
167C4×C5—82no—
168C4×C5—81no—
169C4×C5—82no—
170C4×C5#45812yes—
171C24C5×#4111yescharacteristic
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—44no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—42no—
180C22×C4C2×C5×D412yes—
181C22×C4C2×C5×D411yescharacteristic
182C22×C4C2×C5×D411yescharacteristic
183C22×C4C2×C5×D412yes—
184Q16—82no—
185M16—44no—
186C2×C8—22no—
187C2×C8—24no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—41no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C22⋊C4—42no—
198C22⋊C4—42no—
199C22⋊C4—42no—
200C42—41no—
201C42—41no—
202C2×C5—22no—
203C2×C5—42no—
204C2×C5#201711yescharacteristic
205C2×C5#202011yescharacteristic
206C2×C5#202211yescharacteristic
207C23—22no—
208C23—41no—
209C23—41no—
210C23C5×#12112yes—
211C23C5×#12111yescharacteristic
212Q8—44no—
213Q8—44no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—44no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—82no—
226C2×C4C5×#12012yes—
227C2×C4C5×#12011yescharacteristic
228C2×C4C5×#12711yescharacteristic
229C8—44no—
230C8—42no—
231C8—81no—
232C5#997911yescharacteristic, direct product factor, Sylow
233C22—21no—
234C22—21no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—82no—
239C22C5×#39211yescharacteristic
240C22C5×#47312yes—
241C4—22no—
242C4—21no—
243C4—81no—
244C4—82no—
245C4—81no—
246C4—82no—
247C4C5×#45812yes—
248C2—22no—
249C2—42no—
250C2C5×#201711yescharacteristic
251C2C5×#202011yescharacteristic
252C2C5×#202211yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5#41
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
21. #9979C5direct (N × H)
232. C5#9979direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31892
C5×#30952
C5×#18182
C5×#14722
C5×#12932
#99795