Finite Group Databasebeta

← C5×#9985 #11932705

Subgroups — C5×#9985 #11932705

Order 1280.

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

normal subgroups only

This group has 502 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×#3095C212yesmaximal
2C5×#2817C211yesmaximal, characteristic
3C5×#1820C211yesmaximal, characteristic
4C5×#1511C212yesmaximal
5C5×#1306C211yesmaximal, characteristic
6C2×C5×C22⋊Q8C2212yes—
7C2×C5×#117C2211yescharacteristic
8C5×#485—24no—
9C5×#484—22no—
10C5×#483—22no—
11C5×#428—22no—
12C5×#419—22no—
13C5×#407C2212yes—
14C5×#400—22no—
15C5×#397—22no—
16C5×#395—22no—
17C5×#381C2211yescharacteristic
18C5×#381C2211yescharacteristic
19C5×#342—22no—
20C5×#328—24no—
21#9985C511yesmaximal, characteristic, direct product factor, Sylow
22C22×C5×Q8D412yes—
23C23×C4×C5C2311yescharacteristic
24C2×C5×M16—22no—
25C5×C22⋊Q8—22no—
26C5×C22⋊Q8—22no—
27C5×C22⋊Q8—22no—
28C5×C22⋊Q8—22no—
29C5×#117—22no—
30C5×#117—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4—22no—
33C2×C5×C4⋊C4D412yes—
34C2×C5×C4⋊C4D412yes—
35C2×C5×C22⋊C4—22no—
36C2×C5×C22⋊C4—21no—
37C2×C5×C22⋊C4—21no—
38C2×C5×C22⋊C4D412yes—
39C2×C42×C5—21no—
40C5×#107—24no—
41C5×#106—24no—
42C5×#103—24no—
43C5×#103—24no—
44C5×C22⋊C8—22no—
45C5×C22⋊C8D414yes—
46C5×#95—24no—
47C5×#95—22no—
48C5×#95—22no—
49C5×#95—22no—
50#3095C2×C512yes—
51#2817C2×C511yescharacteristic
52#1820C2×C511yescharacteristic
53#1511C2×C512yes—
54#1306C2×C511yescharacteristic
55C24×C5C2×D411yescharacteristic
56C2×C5×Q8—22no—
57C2×C5×Q8—22no—
58C2×C5×Q8—44no—
59C22×C4×C5—22no—
60C22×C4×C5—22no—
61C22×C4×C5—22no—
62C22×C4×C5—22no—
63C22×C4×C5—42no—
64C22×C4×C5—41no—
65C22×C4×C5C2×D412yes—
66C22×C4×C5C2×D411yescharacteristic
67C22×C4×C5C2×D412yes—
68C22×C4×C5#4111yescharacteristic
69C5×M16—44no—
70C2×C5×C8—24no—
71C5×C4⋊C4—22no—
72C5×C4⋊C4—22no—
73C5×C4⋊C4—22no—
74C5×C4⋊C4—22no—
75C5×C4⋊C4—42no—
76C5×C4⋊C4—42no—
77C5×C4⋊C4—82no—
78C5×C22⋊C4—41no—
79C5×C22⋊C4—42no—
80C5×C22⋊C4—41no—
81C5×C22⋊C4—42no—
82C5×C22⋊C4—42no—
83C5×C22⋊C4—42no—
84C42×C5—42no—
85C2×C22⋊Q8C22×C512yes—
86C2×#117C22×C511yescharacteristic
87#485—24no—
88#484—22no—
89#483—22no—
90#428—22no—
91#419—22no—
92#407C22×C512yes—
93#400—22no—
94#397—22no—
95#395—22no—
96#381C22×C511yescharacteristic
97#381C22×C511yescharacteristic
98#342—22no—
99#328—24no—
100C23×C5—22no—
101C23×C5—42no—
102C23×C5#12011yescharacteristic
103C23×C5#12111yescharacteristic
104C23×C5#12711yescharacteristic
105C5×Q8—44no—
106C5×Q8—82no—
107C2×C4×C5—24no—
108C2×C4×C5—41no—
109C2×C4×C5—42no—
110C2×C4×C5—41no—
111C2×C4×C5—44no—
112C2×C4×C5—44no—
113C2×C4×C5—42no—
114C2×C4×C5—42no—
115C2×C4×C5—42no—
116C2×C4×C5—42no—
117C2×C4×C5—44no—
118C2×C4×C5—82no—
119C2×C4×C5—81no—
120C2×C4×C5—82no—
121C2×C4×C5#12012yes—
122C2×C4×C5#12112yes—
123C5×C8—44no—
124C22×Q8C5×D412yes—
125C23×C4C23×C511yescharacteristic
126C2×M16—22no—
127C22⋊Q8—22no—
128C22⋊Q8—22no—
129C22⋊Q8—22no—
130C22⋊Q8—22no—
131#117—22no—
132#117—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4C5×D412yes—
136C2×C4⋊C4C5×D412yes—
137C2×C22⋊C4—21no—
138C2×C22⋊C4—22no—
139C2×C22⋊C4—21no—
140C2×C22⋊C4C5×D412yes—
141C2×C42—21no—
142#107—24no—
143#106—24no—
144#103—24no—
145#103—24no—
146C22⋊C8—22no—
147C22⋊C8C5×D414yes—
148#95—24no—
149#95—22no—
150#95—22no—
151#95—22no—
152C22×C5—22no—
153C22×C5—22no—
154C22×C5—22no—
155C22×C5—21no—
156C22×C5—21no—
157C22×C5—82no—
158C22×C5#39211yescharacteristic
159C22×C5#45812yes—
160C4×C5—22no—
161C4×C5—22no—
162C4×C5—82no—
163C4×C5—82no—
164C4×C5—82no—
165C4×C5—82no—
166C4×C5—161no—
167C24C2×C5×D411yescharacteristic
168C2×Q8—22no—
169C2×Q8—22no—
170C2×Q8—44no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—42no—
176C22×C4—41no—
177C22×C4C2×C5×D412yes—
178C22×C4C2×C5×D411yescharacteristic
179C22×C4C2×C5×D412yes—
180C22×C4C5×#4111yescharacteristic
181M16—44no—
182C2×C8—24no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—82no—
190C22⋊C4—41no—
191C22⋊C4—42no—
192C22⋊C4—41no—
193C22⋊C4—42no—
194C22⋊C4—42no—
195C22⋊C4—42no—
196C42—42no—
197C2×C5—22no—
198C2×C5—41no—
199C2×C5—41no—
200C2×C5#200912yes—
201C2×C5#202211yescharacteristic
202C23—22no—
203C23—42no—
204C23C5×#12011yescharacteristic
205C23C5×#12111yescharacteristic
206C23C5×#12711yescharacteristic
207Q8—44no—
208Q8—82no—
209C2×C4—24no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—44no—
214C2×C4—44no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—44no—
220C2×C4—82no—
221C2×C4—81no—
222C2×C4—82no—
223C2×C4C5×#12012yes—
224C2×C4C5×#12112yes—
225C8—44no—
226C5#998511yescharacteristic, direct product factor, Sylow
227C22—22no—
228C22—21no—
229C22—21no—
230C22—22no—
231C22—22no—
232C22—82no—
233C22C5×#39211yescharacteristic
234C22C5×#45812yes—
235C4—22no—
236C4—22no—
237C4—82no—
238C4—82no—
239C4—82no—
240C4—82no—
241C4—161no—
242C2—22no—
243C2—41no—
244C2—41no—
245C2C5×#200912yes—
246C2C5×#202211yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C2×D4
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. #9985C5direct (N × H)
226. C5#9985direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30952
C5×#28172
C5×#18202
C5×#15112
C5×#13062
#99855