Finite Group Databasebeta

← Dic10×#41⋊C3 #14514024

Subgroups — Dic10×#41⋊C3 #14514024

Order 1920.

536 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 99 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×#41⋊C3C211yesmaximal, characteristic
2Dic5×#41⋊C3C212yesmaximal
3#65904⋊C3C211yesmaximal, characteristic, complemented
4#65903⋊C3C212yesmaximal, complemented
5SL(2,𝔽3)×Dic10C211yesmaximal, characteristic, complemented
6#41×Dic10C311yesmaximal, characteristic, complemented, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8C3×C4×Dic10—41nomaximal
9C4×C5×SL(2,𝔽3)C2211yescharacteristic
10C4×C5×SL(2,𝔽3)C2211yescharacteristic
11Dic5×SL(2,𝔽3)C2212yes—
12Dic5×SL(2,𝔽3)C2212yes—
13Q8×#41⋊C3—51nomaximal, Hall
14C4×C5×#41C2×C311yescharacteristic
15#41×Dic5C2×C312yes—
16#65904C2×C311yescharacteristic
17#65903C2×C312yes—
18Q8×Dic10C2×C311yescharacteristic
19#65877—31no—
20#65873—32no—
21D4×Dic10—31no—
22#65851—32no—
23#65804—31no—
24C2×C4×Dic10—31no—
25C2×C3×Dic10—41no—
26C5×#41⋊C3Q812yescomplemented
27C2×C5×SL(2,𝔽3)C2311yescharacteristic
28C3×C42×C5—41no—
29C3×C4⋊Dic5—41no—
30C3×#683—42no—
31C3×C4×Dic5—42no—
32Q8×SL(2,𝔽3)—51no—
33#557⋊C3—52no—
34#557⋊C3—51no—
35C4×#41⋊C3—52no—
36C4×#41⋊C3D511yescharacteristic
37C2×C5×#41C22×C311yescharacteristic
38C22×Dic10—31no—
39C4×C5×Q8C22×C311yescharacteristic
40C4×C5×Q8C22×C311yescharacteristic
41C4×C5×D4—31no—
42C4×C5×D4—31no—
43C5×#117—31no—
44C2×C42×C5—31no—
45Q8×Dic5C22×C312yes—
46Q8×Dic5C22×C312yes—
47D4×Dic5—32no—
48D4×Dic5—32no—
49#4072—32no—
50C2×C4⋊Dic5—31no—
51#4070—32no—
52#4070—32no—
53C2×#683—32no—
54C2×C4×Dic5—32no—
55#4036—32no—
56#4036—32no—
57#4034—32no—
58#4034—32no—
59#4024—34no—
60#4024—34no—
61#4016—32no—
62#4015—31no—
63#4015—31no—
64C4×Dic10—32no—
65C4×Dic10—31no—
66C4×Dic10—31no—
67C4×Dic10—31no—
68C4×Dic10—32no—
69C4×Dic10—32no—
70C4×Dic10A411yescharacteristic
71Q8×#41—51noSylow
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—41no—
75C2×C3×Dic5—42no—
76C2×C3×Dic5—42no—
77C3×Dic10—44no—
78C5×SL(2,𝔽3)C2×Q811yescharacteristic, complemented
79C2×#41⋊C3C2×D511yescharacteristic
80C3×C4×Q8—201no—
81C4×SL(2,𝔽3)—52no—
82C4×SL(2,𝔽3)—52no—
83C4×SL(2,𝔽3)C2×D511yescharacteristic
84C4×SL(2,𝔽3)C2×D511yescharacteristic
85C5×#41—32no—
86C5×#41C3×Q812yescomplemented
87C2×C5×Q8C23×C311yescharacteristic
88C2×C5×D4—31no—
89C22×C4×C5—31no—
90C22×C4×C5—31no—
91C22×C4×C5—31no—
92C22×Dic5—32no—
93C22×Dic5—32no—
94C2×Dic10—31no—
95C2×Dic10—32no—
96C2×Dic10—32no—
97C2×Dic10—64no—
98C2×Dic10C2×A411yescharacteristic
99C5×C4⋊C4—31no—
100C5×C4⋊C4—31no—
101C5×C22⋊C4—32no—
102C42×C5—31no—
103C42×C5—31no—
104C42×C5—31no—
105C42×C5C2×A411yescharacteristic
106C22⋊Dic5—34no—
107C4⋊Dic5—32no—
108C4⋊Dic5—31no—
109C4⋊Dic5—32no—
110C4⋊Dic5—32no—
111C4⋊Dic5—32no—
112C4⋊Dic5C2×A411yescharacteristic
113#683—34no—
114#683—32no—
115#683—32no—
116#683—32no—
117#683C2×A412yes—
118C4×Dic5—32no—
119C4×Dic5—32no—
120C4×Dic5—32no—
121C4×Dic5C2×A412yes—
122Q82—51no—
123#557—52no—
124#557—51no—
125#554—152no—
126#554—151no—
127D4×Q8—151no—
128#533—151no—
129#533—152no—
130C4×#41—52no—
131C4×#41C3×D511yescharacteristic
132C2×C4×Q8—151no—
133C22×C3×C5—41no—
134C3×C4×C5—42no—
135C3×C4×C5—42no—
136C3×C4×C5—81no—
137C3×Dic5—44no—
138C3×Dic5—82no—
139C2×C3×Q8—201no—
140#41⋊C3Dic1012yesdirect product factor
141C2×SL(2,𝔽3)C22×D511yescharacteristic
142C3×C4⋊C4—202no—
143C3×C4⋊C4—201no—
144C3×C42—41no—
145C3×C42—202no—
146C23×C5—31no—
147C5×Q8—31no—
148C5×Q8C2×C3×Q811yescharacteristic
149C5×D4—32no—
150C5×D4—32no—
151C2×C4×C5—31no—
152C2×C4×C5—32no—
153C2×C4×C5—32no—
154C2×C4×C5—31no—
155C2×C4×C5—31no—
156C2×C4×C5—62no—
157C2×C4×C5—121no—
158C2×C4×C5C22×A411yescharacteristic
159C2×C4×C5C22×A411yescharacteristic
160C2×C4×C5C22×A411yescharacteristic
161C2×Dic5—32no—
162C2×Dic5—32no—
163C2×Dic5—64no—
164C2×Dic5—122no—
165C2×Dic5C22×A412yes—
166C2×Dic5C22×A412yes—
167Dic10—62no—
168Dic10—64no—
169Dic10—122no—
170Dic10#41⋊C314yesdirect product factor
171C2×#41C2×C3×D511yescharacteristic
172C22×Q8—151no—
173C4⋊Q8—151no—
174C4⋊Q8—151no—
175C4⋊Q8—152no—
176C4⋊Q8—152no—
177#125—152no—
178#125—152no—
179#125—152no—
180C22⋊Q8—154no—
181C22⋊Q8—154no—
182C22⋊Q8—152no—
183C22⋊Q8—152no—
184C4×Q8—51no—
185C4×Q8—52no—
186C4×Q8—52no—
187C4×Q8—152no—
188C4×Q8—152no—
189C4×Q8—151no—
190C4×Q8—151no—
191C4×Q8—152no—
192C4×Q8—151no—
193C4×Q8C2×C3×D511yescharacteristic
194C4×Q8C2×C3×D511yescharacteristic
195C4×D4—31no—
196C4×D4—31no—
197C4×D4—152no—
198C4×D4—152no—
199#117—31no—
200#117—152no—
201C2×C4⋊C4—152no—
202C2×C4⋊C4—151no—
203C2×C42—31no—
204C2×C42—152no—
205C2×C3×C5—41no—
206C2×C3×C5—41no—
207C2×C3×C5—41no—
208C3×Q8—204no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—202no—
213C2×C3×C4—202no—
214SL(2,𝔽3)C2×Dic1011yescharacteristic, complemented
215C22×C5—32no—
216C22×C5—61no—
217C22×C5—61no—
218C22×C5C23×A411yescharacteristic
219C4×C5—21no—
220C4×C5—31no—
221C4×C5—31no—
222C4×C5—61no—
223C4×C5—61no—
224C4×C5Q8×A412yes—
225C4×C5C2×#41⋊C312yes—
226Dic5—22no—
227Dic5—62no—
228Dic5—62no—
229Dic5C2×#41⋊C314yes—
230#41—32no—
231#41C3×Dic1012yescomplemented
232C2×Q8—51no—
233C2×Q8—152no—
234C2×Q8—152no—
235C2×Q8—151no—
236C2×Q8—304no—
237C2×Q8C22×C3×D511yescharacteristic
238C2×D4—31no—
239C22×C4—31no—
240C22×C4—31no—
241C22×C4—31no—
242C22×C4—152no—
243C22×C4—152no—
244C4⋊C4—31no—
245C4⋊C4—31no—
246C4⋊C4—52no—
247C4⋊C4—51no—
248C4⋊C4—152no—
249C4⋊C4—152no—
250C4⋊C4—152no—
251C4⋊C4—152no—
252C4⋊C4—152no—
253C4⋊C4—154no—
254C4⋊C4—152no—
255C4⋊C4—152no—
256C4⋊C4—151no—
257C22⋊C4—32no—
258C22⋊C4—154no—
259C42—31no—
260C42—31no—
261C42—31no—
262C42—52no—
263C42—152no—
264C42—152no—
265C42—152no—
266C42D5×A411yescharacteristic
267C3×C5—41noHall
268C22×C3—41no—
269C3×C4—42no—
270C3×C4—42no—
271C3×C4—81no—
272C3×C4—204no—
273C3×C4—402no—
274C2×C5—62no—
275C2×C5C2×Q8×A411yescharacteristic
276C2×C5C22×#41⋊C311yescharacteristic
277C2×C5#594511yescharacteristic
278C23—31no—
279Q8—31no—
280Q8—54no—
281Q8—304no—
282Q8—302no—
283Q8—602no—
284Q8C2×C3×Dic1011yescharacteristic
285D4—32no—
286D4—32no—
287C2×C4—31no—
288C2×C4—32no—
289C2×C4—32no—
290C2×C4—31no—
291C2×C4—31no—
292C2×C4—52no—
293C2×C4—52no—
294C2×C4—62no—
295C2×C4—121no—
296C2×C4—152no—
297C2×C4—152no—
298C2×C4—304no—
299C2×C4—602no—
300C2×C4C2×D5×A411yescharacteristic
301C2×C4C2×D5×A411yescharacteristic
302C2×C4C2×D5×A411yescharacteristic
303C2×C3—41no—
304C2×C3—41no—
305C2×C3—41no—
306C5Q8×#41⋊C311yescharacteristic, complemented, Sylow
307C22—32no—
308C22—61no—
309C22—61no—
310C22C22×D5×A411yescharacteristic
311C4—21no—
312C4—31no—
313C4—31no—
314C4—54no—
315C4—61no—
316C4—61no—
317C4—102no—
318C4—302no—
319C4—302no—
320C4A4×Dic1012yes—
321C4D5×#41⋊C312yes—
322C3—41noSylow
323C2—62no—
324C2C2×A4×Dic1011yescharacteristic
325C2C2×D5×#41⋊C311yescharacteristic
326C2#66283⋊C311yescharacteristic
subgroupG/H
centerC2×C4C2×D5×A4
commutator, cosocleC2×C5×Q8C23×C3
FrattiniC22C22×D5×A4
FittingC4×C5×#41C2×C3
socleC22×C5C23×A4
prime radicalC2×C5×#41⋊C3C22
hypercenterC42D5×A4
hypocenterC5×Q8C2×C3×Q8
LCSG ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #65904⋊C3C2semidirect
4. #65903⋊C3C2semidirect
5. SL(2,𝔽3)×Dic10C2semidirect
6. #41×Dic10C3semidirect
26. C5×#41⋊C3Q8semidirect
78. C5×SL(2,𝔽3)C2×Q8semidirect
86. C5×#41C3×Q8semidirect
140. #41⋊C3Dic10direct (N × H)
170. Dic10#41⋊C3direct (N × H)
214. SL(2,𝔽3)C2×Dic10semidirect
231. #41C3×Dic10semidirect
306. C5Q8×#41⋊C3semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#41⋊C32
Dic5×#41⋊C32
#65904⋊C32
#65903⋊C32
SL(2,𝔽3)×Dic102
#41×Dic103
C3×C4×Dic104
Q8×#41⋊C35