Finite Group Databasebeta

← C5×#73077 #14510801

Subgroups — C5×#73077 #14510801

Order 1920.

326 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 52 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
1C2×C5×#984C211yesmaximal, characteristic
2C5×#520⋊C3C211yesmaximal, characteristic
3C2×C5×GU(2,𝔽3)C211yesmaximal, characteristic
4C5×#1882—31nomaximal, Hall
5C2×C5×#41⋊C3C2211yescharacteristic
6C5×#984—21no—
7C5×#984C412yescomplemented
8C2×C5×#226—21no—
9C4×C5×SL(2,𝔽3)—21no—
10C5×GU(2,𝔽3)—21no—
11C5×#810—41nomaximal
12#73077C511yesmaximal, characteristic, direct product factor, Hall
13C2×C5×#137—31no—
14C5×#520D311yescharacteristic
15C2×C5×#104—31no—
16C5×#419—31no—
17C5×#391—31no—
18C5×#343—31no—
19C5×#339—31no—
20C2×C5×Dic6—41no—
21C5×#41⋊C3C2×C411yescharacteristic
22C5×#41⋊C3D411yescharacteristic
23C2×C5×SL(2,𝔽3)D411yescharacteristic
24C5×#226—22no—
25C3×C5×C4⋊C4—41no—
26C2×C5×C3⋊C8—41no—
27C2×#984C2×C511yescharacteristic
28#520⋊C3C2×C511yescharacteristic
29C2×GU(2,𝔽3)C2×C511yescharacteristic
30C2×C5×#41C2×D311yescharacteristic
31C22×C5×Q8—31no—
32C5×#137—32no—
33C5×#137—32no—
34C5×#137—61no—
35C5×#137—61no—
36C2×C5×Q16—61no—
37C2×C5×SD16—61no—
38C2×C5×M16—31no—
39C2×C5×M16—31no—
40C4×C5×Q8—21no—
41C4×C5×D4—61no—
42C5×#117—31no—
43C2×C5×C4⋊C4—31no—
44C2×C42×C5—31no—
45C5×#104—61no—
46C5×#104—61no—
47C5×#103—61no—
48C5×#103—61no—
49C5×#95—62no—
50#1882—31noSylow
51C2×C3×C4×C5—41no—
52C2×C3×C4×C5—81no—
53C2×C5×Dic3—81no—
54C5×Dic6—42no—
55C5×Dic6—81no—
56C5×SL(2,𝔽3)C22⋊C411yescharacteristic
57C5×C3⋊C8—81no—
58C2×#41⋊C3C22×C511yescharacteristic
59#984—21no—
60#984C4×C512yescomplemented
61C2×#226—21no—
62C4×SL(2,𝔽3)—21no—
63GU(2,𝔽3)—21no—
64#810—41no—
65C5×#41—31no—
66C5×#41—31no—
67C5×#41C4×D311yescharacteristic
68C5×#41D1211yescharacteristic
69C2×C5×Q8—32no—
70C2×C5×Q8—61no—
71C2×C5×Q8—61no—
72C2×C5×Q8—61no—
73C2×C5×Q8—61no—
74C2×C5×Q8—61no—
75C2×C5×Q8#6711yescharacteristic
76C2×C5×D4—31no—
77C22×C4×C5—31no—
78C22×C4×C5—32no—
79C22×C4×C5—61no—
80C22×C4×C5—61no—
81C5×Q16—62no—
82C5×Q16—62no—
83C5×SD16—62no—
84C5×SD16—62no—
85C5×M16—32no—
86C5×M16—61no—
87C5×M16—61no—
88C5×M16—61no—
89C2×C5×C8—61no—
90C2×C5×C8—61no—
91C5×C4⋊C4—31no—
92C5×C4⋊C4—61no—
93C5×C4⋊C4S411yescharacteristic
94C5×C22⋊C4—61no—
95C42×C5—61no—
96C42×C5—61no—
97C42×C5—61no—
98C2×#137—31no—
99#520C5×D311yescharacteristic
100C2×#104—31no—
101#419—31no—
102#391—31no—
103#343—31no—
104#339—31no—
105C22×C3×C5—41no—
106C3×C4×C5—41no—
107C3×C4×C5—41no—
108C3×C4×C5—161no—
109C5×Dic3—82no—
110C2×Dic6—41no—
111#41⋊C3C2×C4×C511yescharacteristic
112#41⋊C3C5×D411yescharacteristic
113C2×SL(2,𝔽3)C5×D411yescharacteristic
114#226—22no—
115C3×C4⋊C4—41no—
116C2×C3⋊C8—41no—
117C23×C5—31no—
118C5×Q8—31no—
119C5×Q8—62no—
120C5×Q8—62no—
121C5×Q8—121no—
122C5×Q8—121no—
123C5×Q8(C2×D3)⋊C411yescharacteristic
124C5×D4—31no—
125C5×D4—31no—
126C5×D4—61no—
127C2×C4×C5—21no—
128C2×C4×C5—31no—
129C2×C4×C5—31no—
130C2×C4×C5—31no—
131C2×C4×C5—31no—
132C2×C4×C5—31no—
133C2×C4×C5—62no—
134C2×C4×C5—62no—
135C2×C4×C5—61no—
136C2×C4×C5—121no—
137C2×C4×C5—121no—
138C2×C4×C5—121no—
139C2×C4×C5—121no—
140C2×C4×C5—122no—
141C2×C4×C5C2×S411yescharacteristic
142C5×C8—62no—
143C5×C8—121no—
144C2×#41C2×C5×D311yescharacteristic
145C22×Q8—31no—
146#137—32no—
147#137—32no—
148#137—61no—
149#137—61no—
150C2×Q16—61no—
151C2×SD16—61no—
152C2×M16—31no—
153C2×M16—31no—
154C4×Q8—21no—
155C4×D4—61no—
156#117—31no—
157C2×C4⋊C4—31no—
158C2×C42—31no—
159#104—61no—
160#104—61no—
161#103—61no—
162#103—61no—
163#95—62no—
164C2×C3×C5—41no—
165C2×C3×C5—41no—
166C2×C3×C5—41no—
167C2×C3×C4—41no—
168C2×C3×C4—81no—
169C2×Dic3—81no—
170Dic6—42no—
171Dic6—81no—
172SL(2,𝔽3)C5×C22⋊C411yescharacteristic
173C3⋊C8—81no—
174C22×C5—31no—
175C22×C5—31no—
176C22×C5—61no—
177C22×C5—61no—
178C22×C5GL(2,ℤ/4)11yescharacteristic
179C4×C5—31no—
180C4×C5—31no—
181C4×C5—41no—
182C4×C5—122no—
183C4×C5—122no—
184C4×C5—121no—
185C4×C5C4×S411yescharacteristic
186C4×C5C4⋊S411yescharacteristic
187#41—31no—
188#41—31no—
189#41C4×C5×D311yescharacteristic
190#41C5×D1211yescharacteristic
191C2×Q8—32no—
192C2×Q8—61no—
193C2×Q8—61no—
194C2×Q8—61no—
195C2×Q8—61no—
196C2×Q8—61no—
197C2×Q8C5×#6711yescharacteristic
198C2×D4—31no—
199C22×C4—31no—
200C22×C4—32no—
201C22×C4—61no—
202C22×C4—61no—
203Q16—62no—
204Q16—62no—
205SD16—62no—
206SD16—62no—
207M16—32no—
208M16—61no—
209M16—61no—
210M16—61no—
211C2×C8—61no—
212C2×C8—61no—
213C4⋊C4—31no—
214C4⋊C4—61no—
215C4⋊C4C5×S411yescharacteristic
216C22⋊C4—61no—
217C42—61no—
218C42—61no—
219C42—61no—
220C3×C5—41noHall
221C22×C3—41no—
222C3×C4—41no—
223C3×C4—41no—
224C3×C4—161no—
225Dic3—82no—
226C2×C5—61no—
227C2×C5—61no—
228C2×C5(C2×S4)⋊C411yescharacteristic
229C2×C5#542811yescharacteristic
230C2×C5#543011yescharacteristic
231C23—31no—
232Q8—31no—
233Q8—62no—
234Q8—62no—
235Q8—121no—
236Q8—121no—
237Q8C5×(C2×D3)⋊C411yescharacteristic
238D4—31no—
239D4—31no—
240D4—61no—
241C2×C4—21no—
242C2×C4—31no—
243C2×C4—31no—
244C2×C4—31no—
245C2×C4—31no—
246C2×C4—31no—
247C2×C4—62no—
248C2×C4—62no—
249C2×C4—61no—
250C2×C4—121no—
251C2×C4—121no—
252C2×C4—121no—
253C2×C4—121no—
254C2×C4—122no—
255C2×C4C2×C5×S411yescharacteristic
256C8—62no—
257C8—121no—
258C2×C3—41no—
259C2×C3—41no—
260C2×C3—41no—
261C5#7307711yescharacteristic, direct product factor, Sylow
262C22—31no—
263C22—31no—
264C22—61no—
265C22—61no—
266C22C5×GL(2,ℤ/4)11yescharacteristic
267C4—31no—
268C4—31no—
269C4—41no—
270C4—122no—
271C4—122no—
272C4—121no—
273C4C4×C5×S411yescharacteristic
274C4C5×C4⋊S411yescharacteristic
275C3—41noSylow
276C2—61no—
277C2—61no—
278C2C5×(C2×S4)⋊C411yescharacteristic
279C2C5×#542811yescharacteristic
280C2C5×#543011yescharacteristic
subgroupG/H
center, socleC22×C5GL(2,ℤ/4)
commutator#41⋊C3C2×C4×C5
FrattiniC2×C4C2×C5×S4
FittingC5×#520D3
prime radicalC2×C5×#41⋊C3C22
cosocleC2×#41⋊C3C22×C5
hypercenterC5×C4⋊C4S4
hypocenterSL(2,𝔽3)C5×C22⋊C4
LCSG ▷ #41⋊C3 ▷ SL(2,𝔽3)
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C5×C4⋊C4

Complements

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

NH ≅ G/Ntype
7. C5×#984C4semidirect
12. #73077C5direct (N × H)
60. #984C4×C5semidirect
261. C5#73077direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#9842
C5×#520⋊C32
C2×C5×GU(2,𝔽3)2
C5×#18823
C5×#8104
#730775