Finite Group Databasebeta

← C4×C5×#356 #11935350

Subgroups — C4×C5×#356 #11935350

Order 1280.

500 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 166 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
1C4×C5×C4⋊Q8C211yesmaximal, characteristic
2C2×C5×#356C212yesmaximal
3C4×C5×#101C212yesmaximal
4C5×#1394C212yesmaximal
5C2×C5×C4⋊Q8C2211yescharacteristic
6C2×C4×C5×Q8C411yescharacteristic
7C2×C4×C5×Q8C2211yescharacteristic
8C2×C5×#101C2214yes—
9C4×C5×M16—22no—
10C5×#391C411yescharacteristic
11C5×#391C2211yescharacteristic
12C5×#389—22no—
13C5×#384C411yescharacteristic
14C4×C5×C4⋊C4—22no—
15C43×C5C411yescharacteristic
16C5×#356C418yesdirect product factor
17C5×#343—22no—
18C4×#356C511yesmaximal, characteristic, direct product factor, Sylow
19C22×C5×Q8C2×C411yescharacteristic
20C22×C5×Q8C2311yescharacteristic
21C2×C5×M16—24no—
22C5×C4⋊Q8—22no—
23C5×C4⋊Q8C2×C414yes—
24C4×C5×Q8—41no—
25C4×C5×Q8—41no—
26C4×C5×Q8—41no—
27C4×C5×Q8—41no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—22no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4C2×C411yescharacteristic
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C5×C4⋊C4D412yes—
34C2×C42×C5—21no—
35C2×C42×C5—21no—
36C2×C42×C5—21no—
37C2×C42×C5C2×C411yescharacteristic
38C2×C42×C5C2×C411yescharacteristic
39C2×C42×C5C2×C411yescharacteristic
40C2×C42×C5D412yes—
41C5×#101—24no—
42C5×#101C2×C418yes—
43C5×#97—42no—
44C4×C5×C8—42no—
45C5×#95—22no—
46C5×#95—22no—
47C4×C4⋊Q8C2×C511yescharacteristic
48C2×#356C2×C512yes—
49C4×#101C2×C512yes—
50#1394C2×C512yes—
51C2×C5×Q8—21no—
52C2×C5×Q8—41no—
53C2×C5×Q8—41no—
54C2×C5×Q8—41no—
55C2×C5×Q8—41no—
56C2×C5×Q8C4212yes—
57C2×C5×Q8C22×C412yes—
58C2×C5×Q8#4112yes—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22⋊C412yes—
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22×C411yescharacteristic
67C22×C4×C5C2×D412yes—
68C5×M16—28no—
69C5×M16—44no—
70C2×C5×C8—44no—
71C5×C4⋊C4—28no—
72C5×C4⋊C4—41no—
73C5×C4⋊C4—42no—
74C5×C4⋊C4—41no—
75C5×C4⋊C4—44no—
76C5×C4⋊C4—42no—
77C42×C5—24no—
78C42×C5—21no—
79C42×C5—22no—
80C42×C5—21no—
81C42×C5—22no—
82C42×C5—21no—
83C42×C5—41no—
84C42×C5—42no—
85C42×C5—41no—
86C42×C5—41no—
87C42×C5C4212yes—
88C2×C4⋊Q8C22×C511yescharacteristic
89C2×C4×Q8C4×C511yescharacteristic
90C2×C4×Q8C22×C511yescharacteristic
91C2×#101C22×C514yes—
92C4×M16—22no—
93#391C4×C511yescharacteristic
94#391C22×C511yescharacteristic
95#389—22no—
96#384C4×C511yescharacteristic
97C4×C4⋊C4—22no—
98C43C4×C511yescharacteristic
99#356C4×C518yesdirect product factor
100#343—22no—
101C23×C5C2×C22⋊C411yescharacteristic
102C5×Q8—42no—
103C5×Q8—42no—
104C5×Q8—42no—
105C5×Q8—42no—
106C2×C4×C5—22no—
107C2×C4×C5—22no—
108C2×C4×C5—22no—
109C2×C4×C5—21no—
110C2×C4×C5—22no—
111C2×C4×C5—21no—
112C2×C4×C5—22no—
113C2×C4×C5—22no—
114C2×C4×C5—22no—
115C2×C4×C5—22no—
116C2×C4×C5—21no—
117C2×C4×C5—22no—
118C2×C4×C5—41no—
119C2×C4×C5—41no—
120C2×C4×C5—41no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—42no—
124C2×C4×C5—42no—
125C2×C4×C5—41no—
126C2×C4×C5#9911yescharacteristic
127C2×C4×C5#9911yescharacteristic
128C2×C4×C5C2×C4211yescharacteristic
129C2×C4×C5#11711yescharacteristic
130C2×C4×C5C4×D414yes—
131C5×C8—48no—
132C22×Q8C2×C4×C511yescharacteristic
133C22×Q8C23×C511yescharacteristic
134C2×M16—24no—
135C4⋊Q8—22no—
136C4⋊Q8C2×C4×C514yes—
137C4×Q8—41no—
138C4×Q8—41no—
139C4×Q8—41no—
140C4×Q8—41no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4C2×C4×C511yescharacteristic
145C2×C4⋊C4C2×C4×C511yescharacteristic
146C2×C4⋊C4C5×D412yes—
147C2×C42—21no—
148C2×C42—21no—
149C2×C42—21no—
150C2×C42C2×C4×C511yescharacteristic
151C2×C42C2×C4×C511yescharacteristic
152C2×C42C2×C4×C511yescharacteristic
153C2×C42C5×D412yes—
154#101—24no—
155#101C2×C4×C518yes—
156#97—42no—
157C4×C8—42no—
158#95—22no—
159#95—22no—
160C22×C5—21no—
161C22×C5—21no—
162C22×C5C4×C22⋊C411yescharacteristic
163C22×C5C2×#9911yescharacteristic
164C22×C5#41011yescharacteristic
165C4×C5—24no—
166C4×C5—21no—
167C4×C5—24no—
168C4×C5—21no—
169C4×C5—21no—
170C4×C5—42no—
171C4×C5—41no—
172C4×C5—42no—
173C4×C5—42no—
174C4×C5—81no—
175C4×C5#35612yesdirect product factor
176C2×Q8—21no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8C42×C512yes—
182C2×Q8C22×C4×C512yes—
183C2×Q8C5×#4112yes—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4C5×C22⋊C411yescharacteristic
189C22×C4C5×C22⋊C412yes—
190C22×C4C5×C22⋊C411yescharacteristic
191C22×C4C22×C4×C511yescharacteristic
192C22×C4C2×C5×D412yes—
193M16—28no—
194M16—44no—
195C2×C8—44no—
196C4⋊C4—28no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—44no—
202C42—24no—
203C42—21no—
204C42—22no—
205C42—22no—
206C42—21no—
207C42—21no—
208C42—41no—
209C42—42no—
210C42—41no—
211C42—41no—
212C42C42×C512yes—
213C2×C5—21no—
214C2×C5—21no—
215C2×C5C4×#9911yescharacteristic
216C2×C5C2×#35611yescharacteristic
217C2×C5#213211yescharacteristic
218C23C2×C5×C22⋊C411yescharacteristic
219Q8—42no—
220Q8—42no—
221Q8—42no—
222Q8—42no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4C5×#9911yescharacteristic
244C2×C4C5×#9911yescharacteristic
245C2×C4C2×C42×C511yescharacteristic
246C2×C4C5×#11711yescharacteristic
247C2×C4C4×C5×D414yes—
248C8—48no—
249C5C4×#35611yescharacteristic, direct product factor, Sylow
250C22—21no—
251C22—21no—
252C22C4×C5×C22⋊C411yescharacteristic
253C22C2×C5×#9911yescharacteristic
254C22C5×#41011yescharacteristic
255C4—24no—
256C4—21no—
257C4—24no—
258C4—21no—
259C4—21no—
260C4—42no—
261C4—41no—
262C4—42no—
263C4—42no—
264C4—81no—
265C4C5×#35612yesdirect product factor
266C2—21no—
267C2—21no—
268C2C4×C5×#9911yescharacteristic
269C2C2×C5×#35611yescharacteristic
270C2C5×#213211yescharacteristic
subgroupG/H
centerC2×C4×C5#99
commutatorC2×C4C2×C42×C5
Frattini, cosocleC22×Q8C23×C5
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
16. C5×#356C4direct (N × H)
18. C4×#356C5direct (N × H)
99. #356C4×C5direct (N × H)
175. C4×C5#356direct (N × H)
249. C5C4×#356direct (N × H)
265. C4C5×#356direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C5×C4⋊Q82
C2×C5×#3562
C4×C5×#1012
C5×#13942
C4×#3565