Finite Group Databasebeta

← C5×#85395 #14511133

Subgroups — C5×#85395 #14511133

Order 1920.

420 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 68 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×D4×SL(2,𝔽3)C211yesmaximal, characteristic
2C5×#5420C212yesmaximal, complemented
3C5×#5419C212yesmaximal, complemented
4C4×C5×#226C211yesmaximal, characteristic, complemented
5C5×#5386C211yesmaximal, characteristic, complemented
6C5×#3328—31nomaximal, Hall
7C22×C5×SL(2,𝔽3)C2212yes—
8C2×C5×#226C2211yescharacteristic
9C5×#936—41nomaximal
10C4×C5×SL(2,𝔽3)C2211yescharacteristic
11C5×#859C2212yes—
12C5×#859C2211yescharacteristic
13#85395C511yesmaximal, characteristic, direct product factor, Hall
14C5×#556—31no—
15C5×D4×Q8D311yescharacteristic
16C5×#487—31no—
17C5×#485—32no—
18C5×#475—31no—
19C5×#470—32no—
20C5×#462—31no—
21C5×#451—32no—
22C4×C5×Q16—31no—
23C5×#436—31no—
24C5×#419—32no—
25C2×C3×C5×D4—41no—
26C2×C5×Dic6—41no—
27C2×C5×SL(2,𝔽3)—22no—
28C2×C5×SL(2,𝔽3)C2311yescharacteristic
29C5×#226—21no—
30C5×#217—42no—
31C5×#217—42no—
32C4×C5×Dic3—41no—
33D4×SL(2,𝔽3)C2×C511yescharacteristic
34#5420C2×C512yescomplemented
35#5419C2×C512yescomplemented
36C4×#226C2×C511yescharacteristic, complemented
37#5386C2×C511yescharacteristic, complemented
38C22×C5×Q8C2×D312yes—
39C2×C5×Q16—31no—
40C2×C5×Q16—32no—
41C2×C5×M16—32no—
42C5×C4⋊Q8—31no—
43C5×C4⋊Q8—31no—
44C5×#126—62no—
45C5×#124—61no—
46C5×C22⋊Q8—32no—
47C5×C22⋊Q8—32no—
48C4×C5×Q8—31no—
49C4×C5×Q8—61no—
50C4×C5×Q8C2×D311yescharacteristic
51C4×C5×D4—31no—
52C5×#117—32no—
53C5×#107—31no—
54C5×#106—32no—
55C5×C4⋊C8—31no—
56C5×#103—32no—
57C5×#103—32no—
58C5×#103—31no—
59C5×#103—32no—
60C5×#103—31no—
61C5×#103—32no—
62C5×C22⋊C8—32no—
63C4×C5×C8—31no—
64#3328—31noSylow
65C23×C3×C5—42no—
66C3×C5×D4—82no—
67C2×C3×C4×C5—41no—
68C2×C5×Dic3—41no—
69C2×C5×Dic3—41no—
70C2×C5×Dic3—42no—
71C5×Dic6—82no—
72C5×SL(2,𝔽3)#4111yescharacteristic
73C22×SL(2,𝔽3)C22×C512yes—
74C2×#226C22×C511yescharacteristic
75#936—41no—
76C4×SL(2,𝔽3)C22×C511yescharacteristic
77#859C22×C512yes—
78#859C22×C511yescharacteristic
79C2×C5×Q8—22no—
80C2×C5×Q8—32no—
81C2×C5×Q8—31no—
82C2×C5×Q8—61no—
83C2×C5×Q8—62no—
84C2×C5×Q8C22×D311yescharacteristic
85C2×C5×D4S411yescharacteristic
86C22×C4×C5—32no—
87C5×Q16—61no—
88C5×Q16—61no—
89C5×Q16—122no—
90C5×M16—122no—
91C2×C5×C8—31no—
92C2×C5×C8—32no—
93C2×C5×C8—31no—
94C5×C4⋊C4—31no—
95C5×C4⋊C4—31no—
96C5×C4⋊C4—31no—
97C5×C4⋊C4—32no—
98C5×C4⋊C4—61no—
99C5×C4⋊C4—61no—
100C5×C4⋊C4—62no—
101C5×C4⋊C4—61no—
102C5×C22⋊C4—32no—
103C5×C22⋊C4—62no—
104C5×C22⋊C4—62no—
105C42×C5—31no—
106C42×C5—62no—
107C42×C5—61no—
108#556—31no—
109D4×Q8C5×D311yescharacteristic
110#487—31no—
111#485—32no—
112#475—31no—
113#470—32no—
114#462—31no—
115#451—32no—
116C4×Q16—31no—
117#436—31no—
118#419—32no—
119C22×C3×C5—41no—
120C22×C3×C5—82no—
121C22×C3×C5—82no—
122C22×C3×C5—82no—
123C3×C4×C5—42no—
124C5×Dic3—81no—
125C5×Dic3—82no—
126C5×Dic3—81no—
127C2×C3×D4—41no—
128C2×Dic6—41no—
129C2×SL(2,𝔽3)—22no—
130C2×SL(2,𝔽3)C23×C511yescharacteristic
131#226—21no—
132#217—42no—
133#217—42no—
134C4×Dic3—41no—
135C23×C5C2×S412yes—
136C5×Q8—31no—
137C5×Q8—62no—
138C5×Q8—62no—
139C5×Q8—61no—
140C5×Q8—61no—
141C5×Q8—122no—
142C5×Q8#23711yescharacteristic
143C5×D4—22no—
144C2×C4×C5—31no—
145C2×C4×C5—31no—
146C2×C4×C5—32no—
147C2×C4×C5—62no—
148C2×C4×C5—62no—
149C2×C4×C5—61no—
150C2×C4×C5—62no—
151C2×C4×C5—61no—
152C2×C4×C5C2×S411yescharacteristic
153C5×C8—61no—
154C5×C8—62no—
155C5×C8—61no—
156C22×Q8C2×C5×D312yes—
157C2×Q16—31no—
158C2×Q16—32no—
159C2×M16—32no—
160C4⋊Q8—31no—
161C4⋊Q8—31no—
162#126—62no—
163#124—61no—
164C22⋊Q8—32no—
165C22⋊Q8—32no—
166C4×Q8—31no—
167C4×Q8—61no—
168C4×Q8C2×C5×D311yescharacteristic
169C4×D4—31no—
170#117—32no—
171#107—31no—
172#106—32no—
173C4⋊C8—31no—
174#103—32no—
175#103—32no—
176#103—31no—
177#103—32no—
178#103—31no—
179#103—32no—
180C22⋊C8—32no—
181C4×C8—31no—
182C2×C3×C5—41no—
183C2×C3×C5—41no—
184C2×C3×C5—41no—
185C2×C3×C5—162no—
186C23×C3—42no—
187C3×D4—82no—
188C2×C3×C4—41no—
189C2×Dic3—41no—
190C2×Dic3—42no—
191C2×Dic3—41no—
192Dic6—82no—
193SL(2,𝔽3)C5×#4111yescharacteristic
194C22×C5—22no—
195C22×C5—22no—
196C22×C5—22no—
197C22×C5C22×S411yescharacteristic
198C4×C5—31no—
199C4×C5—31no—
200C4×C5—62no—
201C4×C5—61no—
202C4×C5—121no—
203C4×C5—122no—
204C4×C5—121no—
205C4×C5#98312yes—
206C2×Q8—22no—
207C2×Q8—32no—
208C2×Q8—31no—
209C2×Q8—61no—
210C2×Q8—62no—
211C2×Q8C22×C5×D311yescharacteristic
212C2×D4C5×S411yescharacteristic
213C22×C4—32no—
214Q16—61no—
215Q16—61no—
216Q16—122no—
217M16—122no—
218C2×C8—31no—
219C2×C8—31no—
220C2×C8—32no—
221C4⋊C4—31no—
222C4⋊C4—31no—
223C4⋊C4—32no—
224C4⋊C4—31no—
225C4⋊C4—61no—
226C4⋊C4—61no—
227C4⋊C4—62no—
228C4⋊C4—61no—
229C22⋊C4—32no—
230C22⋊C4—62no—
231C22⋊C4—62no—
232C42—31no—
233C42—62no—
234C42—61no—
235C3×C5—41noHall
236C22×C3—41no—
237C22×C3—82no—
238C22×C3—82no—
239C22×C3—82no—
240C3×C4—42no—
241Dic3—82no—
242Dic3—81no—
243Dic3—81no—
244C2×C5—42no—
245C2×C5#591411yescharacteristic
246C2×C5C2×#98311yescharacteristic
247C2×C5#592711yescharacteristic
248C23C2×C5×S412yes—
249Q8—31no—
250Q8—62no—
251Q8—62no—
252Q8—61no—
253Q8—61no—
254Q8—122no—
255Q8C5×#23711yescharacteristic
256D4—22no—
257C2×C4—31no—
258C2×C4—31no—
259C2×C4—32no—
260C2×C4—62no—
261C2×C4—62no—
262C2×C4—61no—
263C2×C4—62no—
264C2×C4—61no—
265C2×C4C2×C5×S411yescharacteristic
266C8—61no—
267C8—62no—
268C8—61no—
269C2×C3—41no—
270C2×C3—41no—
271C2×C3—41no—
272C2×C3—162no—
273C5#8539511yescharacteristic, direct product factor, Sylow
274C22—22no—
275C22—22no—
276C22—22no—
277C22C22×C5×S411yescharacteristic
278C4—31no—
279C4—31no—
280C4—62no—
281C4—61no—
282C4—121no—
283C4—122no—
284C4—121no—
285C4C5×#98312yes—
286C3—41noSylow
287C2—42no—
288C2C5×#591411yescharacteristic
289C2C2×C5×#98311yescharacteristic
290C2C5×#592711yescharacteristic
subgroupG/H
center, socleC22×C5C22×S4
commutator, cosocleC2×SL(2,𝔽3)C23×C5
FrattiniC22C22×C5×S4
FittingC5×D4×Q8D3
prime radicalC5×D4×SL(2,𝔽3)C2
hypercenterC2×C5×D4S4
hypocenterSL(2,𝔽3)C5×#41
LCSG ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3)
UCSC1 ◁ C22×C5 ◁ C2×C5×D4

Complements

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

NH ≅ G/Ntype
2. C5×#5420C2semidirect
3. C5×#5419C2semidirect
4. C4×C5×#226C2semidirect
5. C5×#5386C2semidirect
13. #85395C5direct (N × H)
34. #5420C2×C5semidirect
35. #5419C2×C5semidirect
36. C4×#226C2×C5semidirect
37. #5386C2×C5semidirect
273. C5#85395direct (N × H)

Maximal subgroups

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

subgroupindex
C5×D4×SL(2,𝔽3)2
C5×#54202
C5×#54192
C4×C5×#2262
C5×#53862
C5×#33283
C5×#9364
#853955