Finite Group Databasebeta

← #10614301⋊C3 #14512239

Subgroups — #10614301⋊C3 #14512239

Order 1920.

382 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 57 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×#4150⋊C3C211yesmaximal, characteristic
2C5×#520⋊C3C211yesmaximal, characteristic, complemented
3C2×#4094⋊C3C211yesmaximal, characteristic, complemented
4#10614301C311yesmaximal, characteristic, complemented, Hall
5C2×C5×#41⋊C3C2211yescharacteristic
6#4150⋊C3—21no—
7#4150⋊C3C412yescomplemented
8C2×D5×SL(2,𝔽3)—21no—
9C4×C5×SL(2,𝔽3)—21no—
10#4094⋊C3—21no—
11C3×#3941—41nomaximal
12#2898⋊C3—51nomaximal, Hall
13C2×#4150C2×C311yescharacteristic
14C5×#520C2×C311yescharacteristic, complemented
15C2×#4094C2×C311yescharacteristic, complemented
16#65293—31no—
17#65291—31no—
18C2×#3942—31no—
19#65255—31no—
20C2×C3×D20—41no—
21C5×#41⋊C3C2×C411yescharacteristic
22C5×#41⋊C3D411yescharacteristic
23C2×C5×SL(2,𝔽3)D411yescharacteristic
24D5×SL(2,𝔽3)—22no—
25C3×C5×C4⋊C4—41no—
26C2×C3×#168—41no—
27C2×2−1+4⋊C3—51no—
28C2×#131⋊C3—51no—
29#520⋊C3D511yescharacteristic, complemented
30C2×C5×#41C22×C311yescharacteristic
31#4150—21no—
32#4150—32no—
33#4150—61no—
34#4150C3×C412yescomplemented
35C2×Q8×D5—21no—
36C2×#711—61no—
37C2×#709—31no—
38C22×Dic10—31no—
39C4×C5×Q8—21no—
40C4×C5×D4—61no—
41C5×#117—31no—
42C2×C5×C4⋊C4—31no—
43#4094—21no—
44#4094—61no—
45C2×#681—31no—
46C22×#168—31no—
47#3942—32no—
48#3942—31no—
49#3942—31no—
50#3941—31no—
51#3941A411yescharacteristic
52#2898—51noSylow
53C22×C3×D5—81no—
54C2×C3×C4×C5—41no—
55C2×C3×C4×C5—81no—
56C3×D20—42no—
57C3×D20—81no—
58C5×SL(2,𝔽3)C22⋊C411yescharacteristic
59C3×#168—81no—
602−1+4⋊C3—52no—
612−1+4⋊C3—101no—
62C2×#41⋊C3C2×D511yescharacteristic
63C22×SL(2,𝔽3)—101no—
64#131⋊C3—101no—
65C4×SL(2,𝔽3)—21no—
66C3×#102—201no—
67C5×#41—31no—
68C5×#41—31no—
69C5×#41C2×C3×C411yescharacteristic
70C5×#41C3×D411yescharacteristic
71C2×C5×Q8C3×D411yescharacteristic
72C2×C5×D4—31no—
73C22×C4×C5—31no—
74C22×C4×C5—61no—
75C2×C22⋊D5—61no—
76C22×Dic5—61no—
77Q8×D5—22no—
78Q8×D5—62no—
79#711—64no—
80#711—62no—
81#711—62no—
82#709—32no—
83#709—32no—
84#709—61no—
85#709—61no—
86C2×D20C2×A411yescharacteristic
87C2×C4×D5—61no—
88C2×Dic10—32no—
89C2×Dic10—31no—
90C2×Dic10—32no—
91C2×Dic10—61no—
92C2×Dic10—61no—
93C2×Dic10—61no—
94C5×C4⋊C4—31no—
95C5×C4⋊C4—61no—
96C5×C4⋊C4C2×A411yescharacteristic
97C5×C22⋊C4—61no—
98C42×C5—61no—
99#681—61no—
100#681—61no—
101C2×#168—31no—
102C2×#168—61no—
103C2×#168—61no—
104C2×#168C2×A411yescharacteristic
105C2×2−1+4—51no—
106C2×#131—51no—
107#520C3×D511yescharacteristic, complemented
108#419—151no—
109#417—151no—
110#416—151no—
111C2×#103—151no—
112C22×C3×C5—41no—
113C2×C3×D5—82no—
114C2×C3×D5—161no—
115C2×C3×D5—161no—
116C3×C4×C5—41no—
117C3×C4×C5—41no—
118C3×C4×C5—161no—
119C2×C3×D4—201no—
120#41⋊C3C4×D511yescharacteristic
121#41⋊C3D2011yescharacteristic
122C2×SL(2,𝔽3)—102no—
123C2×SL(2,𝔽3)C22⋊D511yescharacteristic
124C2×C3×C8—201no—
125C3×C4⋊C4—41no—
126C23×C5—31no—
127C22×D5—21no—
128C5×Q8—31no—
129C5×Q8C3×C22⋊C411yescharacteristic
130C5×D4—31no—
131C5×D4—31no—
132C5×D4—32no—
133C2×C4×C5—21no—
134C2×C4×C5—31no—
135C2×C4×C5—31no—
136C2×C4×C5—31no—
137C2×C4×C5—31no—
138C2×C4×C5—31no—
139C2×C4×C5—61no—
140C2×C4×C5—241no—
141C2×C4×C5C22×A411yescharacteristic
142C22⋊D5—62no—
143C22⋊D5—62no—
144C2×Dic5—62no—
145C2×Dic5—61no—
146C2×Dic5—62no—
147D20—21no—
148D20C4×A412yes—
149C4×D5—62no—
150C4×D5—62no—
151Dic10—32no—
152Dic10—62no—
153Dic10—61no—
154Dic10—62no—
155#168—21no—
156#168—61no—
1572−1+4—52no—
1582−1+4—101no—
1592−1+4—152no—
1602−1+4—301no—
161C2×#41—151no—
162C2×#41—301no—
163C2×#41C2×C3×D511yescharacteristic
164C22×Q8—101no—
165C22×Q8—151no—
166#131—101no—
167#131—301no—
168C2×M16—151no—
169C22×C8—151no—
170C4×Q8—21no—
171C4×D4—61no—
172#117—31no—
173C2×C4⋊C4—31no—
174#103—151no—
175#103—152no—
176#103—151no—
177#102—51no—
178#102—151no—
179C2×C3×C5—41no—
180C2×C3×C5—41no—
181C2×C3×C5—41no—
182C3×D5—162no—
183C23×C3—401no—
184C3×D4—202no—
185C3×D4—401no—
186C2×C3×C4—41no—
187C2×C3×C4—81no—
188SL(2,𝔽3)#68511yescharacteristic
189C3×C8—401no—
190C22×C5—31no—
191C22×C5—31no—
192C22×C5—61no—
193C22×C5—61no—
194C22×C5D4×A411yescharacteristic
195C2×D5—22no—
196C2×D5—41no—
197C2×D5—41no—
198C4×C5—31no—
199C4×C5—31no—
200C4×C5—41no—
201C4×C5—121no—
202C4×C5C2×C4×A411yescharacteristic
203C4×C5D4×A411yescharacteristic
204Dic5—62no—
205#41—31no—
206#41—31no—
207#41—152no—
208#41—152no—
209#41—301no—
210#41—301no—
211#41—304no—
212#41—302no—
213#41—302no—
214#41C3×C4×D511yescharacteristic
215#41C3×D2011yescharacteristic
216C2×Q8—102no—
217C2×Q8—152no—
218C2×Q8—152no—
219C2×Q8—151no—
220C2×Q8—301no—
221C2×Q8—301no—
222C2×Q8—301no—
223C2×Q8—302no—
224C2×Q8C3×C22⋊D511yescharacteristic
225C2×D4—31no—
226C2×D4—51no—
227C2×D4—301no—
228C22×C4—31no—
229C22×C4—61no—
230C22×C4—301no—
231C22×C4—301no—
232M16—301no—
233M16—301no—
234C2×C8—51no—
235C2×C8—151no—
236C2×C8—301no—
237C2×C8—301no—
238C4⋊C4—31no—
239C4⋊C4—61no—
240C4⋊C4D5×A411yescharacteristic
241C22⋊C4—61no—
242C42—61no—
243C3×C5—41noHall
244C22×C3—41no—
245C22×C3—402no—
246C22×C3—801no—
247C22×C3—801no—
248C3×C4—41no—
249C3×C4—41no—
250C3×C4—161no—
251C2×C5—61no—
252C2×C5—61no—
253C2×C5A4×C22⋊C411yescharacteristic
254C2×C5#577⋊C311yescharacteristic
255C2×C5#578⋊C311yescharacteristic
256D5—42no—
257C23—31no—
258C23—101no—
259Q8—31no—
260Q8—152no—
261Q8—302no—
262Q8—302no—
263Q8—301no—
264Q8C3×#68511yescharacteristic
265D4—31no—
266D4—31no—
267D4—32no—
268D4—52no—
269D4—101no—
270D4—302no—
271D4—302no—
272C2×C4—21no—
273C2×C4—31no—
274C2×C4—31no—
275C2×C4—31no—
276C2×C4—31no—
277C2×C4—31no—
278C2×C4—61no—
279C2×C4—241no—
280C2×C4—302no—
281C2×C4—302no—
282C2×C4—302no—
283C2×C4—301no—
284C2×C4—302no—
285C2×C4C2×D5×A411yescharacteristic
286C8—101no—
287C8—301no—
288C2×C3—41no—
289C2×C3—41no—
290C2×C3—41no—
291C2×C3—802no—
292C5#2898⋊C311yescharacteristic, complemented, Sylow
293C22—31no—
294C22—31no—
295C22—61no—
296C22—61no—
297C22—102no—
298C22—201no—
299C22—201no—
300C22A4×C22⋊D511yescharacteristic
301C4—31no—
302C4—31no—
303C4—41no—
304C4—121no—
305C4—302no—
306C4C4×D5×A411yescharacteristic
307C4A4×D2011yescharacteristic
308C3—41noSylow
309C2—61no—
310C2—61no—
311C2—202no—
312C2A4×#68511yescharacteristic
313C2#66170⋊C311yescharacteristic
314C2#66172⋊C311yescharacteristic
subgroupG/H
centerC22A4×C22⋊D5
commutatorC5×#41C2×C3×C4
FrattiniC2×C4C2×D5×A4
FittingC5×#520C2×C3
socleC22×C5D4×A4
prime radicalC2×#4150⋊C3C2
cosocleC2×C5×#41C22×C3
hypercenterC4⋊C4D5×A4
hypocenterC5×Q8C3×C22⋊C4
LCSG ▷ C5×#41 ▷ C5×Q8
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#520⋊C3C2semidirect
3. C2×#4094⋊C3C2semidirect
4. #10614301C3semidirect
7. #4150⋊C3C4semidirect
14. C5×#520C2×C3semidirect
15. C2×#4094C2×C3semidirect
29. #520⋊C3D5semidirect
34. #4150C3×C4semidirect
107. #520C3×D5semidirect
292. C5#2898⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#4150⋊C32
C5×#520⋊C32
C2×#4094⋊C32
#106143013
C3×#39414
#2898⋊C35