Finite Group Databasebeta

← #10617745⋊C3 #14514035

Subgroups — #10617745⋊C3 #14514035

Order 1920.

588 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 91 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, complemented
2#66165⋊C3C212yesmaximal, complemented
3SL(2,𝔽3)×D20C211yesmaximal, characteristic, complemented
4C4×D5×SL(2,𝔽3)C212yesmaximal, complemented
5#65904⋊C3C211yesmaximal, characteristic, complemented
6#10617745C311yesmaximal, characteristic, complemented, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8C2×D5×SL(2,𝔽3)C2212yes—
9C3×C4×D20—41nomaximal
10C4×C5×SL(2,𝔽3)C2211yescharacteristic
11C4×C5×SL(2,𝔽3)C2211yescharacteristic
12Dic5×SL(2,𝔽3)C2212yes—
13#3482⋊C3—51nomaximal, Hall
14C4×C5×#41C2×C311yescharacteristic, complemented
15#66165C2×C312yescomplemented
16Q8×D20C2×C311yescharacteristic
17C4×Q8×D5C2×C312yescomplemented
18#65904C2×C311yescharacteristic, complemented
19#65891—32no—
20#65885—31no—
21#65876—31no—
22#65863—32no—
23C4×#709—31no—
24#65804—31no—
25C2×C3×D20—41no—
26C2×C3×C4×D5—42no—
27C5×#41⋊C3—21no—
28C2×C5×SL(2,𝔽3)C2311yescharacteristic
29D5×SL(2,𝔽3)—22no—
30C3×C42×C5—41no—
31C3×#685—42no—
32C3×C4⋊Dic5—41no—
33#557⋊C3—51no—
34D4×SL(2,𝔽3)—51no—
35#548⋊C3—52no—
36C4×#41⋊C3D511yescharacteristic, complemented
37C2×C4×SL(2,𝔽3)—52no—
38C2×C5×#41C22×C311yescharacteristic
39C2×Q8×D5C22×C312yes—
40C2×#709—31no—
41C4×C5×Q8C22×C311yescharacteristic
42C4×C5×Q8C22×C311yescharacteristic
43C4×C5×D4—31no—
44C4×C5×D4—31no—
45C5×#117—31no—
46C2×C42×C5—31no—
47Q8×Dic5C22×C312yes—
48#4084—32no—
49#4082—32no—
50C4×C22⋊D5—32no—
51C4×C22⋊D5—32no—
52#4072—32no—
53#4072—31no—
54#4070—32no—
55#4070—32no—
56#4043—32no—
57D5×C4⋊C4—32no—
58#4036—32no—
59#4033—32no—
60#4029—34no—
61#4025—34no—
62C4×D20—31no—
63C4×D20A411yescharacteristic
64#4018—32no—
65C42×D5—32no—
66#4016—32no—
67#4015—31no—
68#4015—31no—
69C4×Dic10—31no—
70C4×Dic10—31no—
71C4×Dic10—32no—
72#3482—51noSylow
73C22×C3×D5—42no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5—41no—
77C2×C3×Dic5—42no—
78C3×D20—44no—
79C3×C4×D5—84no—
80C5×SL(2,𝔽3)#4111yescharacteristic, complemented
81C2×#41⋊C3C2×D511yescharacteristic
82C22×SL(2,𝔽3)—52no—
83C3×C4×D4—201no—
84C4×SL(2,𝔽3)—52no—
85C4×SL(2,𝔽3)C2×D511yescharacteristic
86C4×SL(2,𝔽3)C2×D511yescharacteristic
87C5×#41—21no—
88C5×#41—61no—
89C2×C5×Q8C23×C311yescharacteristic
90C2×C5×D4—31no—
91C22×C4×C5—31no—
92C22×C4×C5—31no—
93C22×C4×C5—31no—
94C2×C22⋊D5—32no—
95Q8×D5—22no—
96Q8×D5—62no—
97#709—64no—
98C2×D20C2×A411yescharacteristic
99C2×C4×D5—32no—
100C2×C4×D5—32no—
101C2×C4×D5C2×A412yes—
102C2×Dic10—31no—
103C2×Dic10—32no—
104C5×C4⋊C4—31no—
105C5×C4⋊C4—31no—
106C5×C22⋊C4—32no—
107C42×C5—31no—
108C42×C5—31no—
109C42×C5—31no—
110C42×C5C2×A411yescharacteristic
111C22⋊Dic5—34no—
112C22⋊Dic5—32no—
113#685—32no—
114#685C2×A412yes—
115C4⋊Dic5—32no—
116C4⋊Dic5—32no—
117C4⋊Dic5—31no—
118C4⋊Dic5—32no—
119C4⋊Dic5C2×A411yescharacteristic
120#683—34no—
121#683—32no—
122#683—32no—
123C4×Dic5—32no—
124C4×Dic5—32no—
125C4×Dic5—32no—
126#557—51no—
127#556—151no—
128#552—152no—
129D4×Q8—51no—
130#548—52no—
131#547—151no—
132#533—151no—
133#529—152no—
134C4×#41—151no—
135C4×#41C3×D511yescharacteristic, complemented
136C2×C4×Q8—52no—
137C22×C3×C5—41no—
138C2×C3×D5—44no—
139C2×C3×D5—82no—
140C2×C3×D5—82no—
141C3×C4×C5—42no—
142C3×C4×C5—42no—
143C3×C4×C5—81no—
144C3×Dic5—82no—
145C2×C3×D4—201no—
146C22×C3×C4—202no—
147#41⋊C3—21no—
148C2×SL(2,𝔽3)—102no—
149C2×SL(2,𝔽3)C22×D511yescharacteristic
150C3×C4⋊C4—201no—
151C3×C22⋊C4—202no—
152C3×C42—41no—
153C23×C5—31no—
154C22×D5C22×A412yes—
155C5×Q8—31no—
156C5×Q8C3×#4111yescharacteristic
157C5×D4—61no—
158C5×D4—61no—
159C2×C4×C5—31no—
160C2×C4×C5—31no—
161C2×C4×C5—31no—
162C2×C4×C5—61no—
163C2×C4×C5—61no—
164C2×C4×C5—62no—
165C2×C4×C5—62no—
166C2×C4×C5C22×A411yescharacteristic
167C2×C4×C5C22×A411yescharacteristic
168C2×C4×C5C22×A411yescharacteristic
169C22⋊D5—64no—
170C2×Dic5—32no—
171C2×Dic5—32no—
172C2×Dic5C22×A412yes—
173D20#41⋊C314yescomplemented
174C4×D5—24no—
175C4×D5—62no—
176C4×D5—62no—
177C4×D5—64no—
178Dic10—62no—
179Dic10—62no—
180Dic10—62no—
181C2×#41—151no—
182C2×#41C2×C3×D511yescharacteristic
183C22×Q8—52no—
184C4⋊Q8—151no—
185C4⋊Q8—151no—
186#126—154no—
187#125—152no—
188#125—152no—
189#124—152no—
190#123—154no—
191C22⋊Q8—152no—
192C22⋊Q8—152no—
193C22⋊Q8—152no—
194#121—152no—
195C4×Q8—52no—
196C4×Q8—151no—
197C4×Q8—152no—
198C4×Q8—151no—
199C4×Q8—152no—
200C4×Q8C2×C3×D511yescharacteristic
201C4×Q8C2×C3×D511yescharacteristic
202C4×D4—31no—
203C4×D4—31no—
204C4×D4—51no—
205C4×D4—151no—
206C4×D4—152no—
207C4×D4—152no—
208#117—31no—
209#117—152no—
210#117—151no—
211#117—152no—
212C2×C4⋊C4—152no—
213C2×C42—31no—
214C2×C42—152no—
215C2×C3×C5—41no—
216C2×C3×C5—41no—
217C2×C3×C5—41no—
218C3×D5—84no—
219C23×C3—202no—
220C3×D4—204no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4—202no—
225C2×C3×C4—404no—
226SL(2,𝔽3)#70911yescharacteristic, complemented
227C22×C5—61no—
228C22×C5—61no—
229C22×C5—61no—
230C22×C5C23×A411yescharacteristic
231C2×D5—22no—
232C2×D5—22no—
233C2×D5C2×#41⋊C314yes—
234C4×C5—21no—
235C4×C5—31no—
236C4×C5—31no—
237C4×C5—61no—
238C4×C5—61no—
239C4×C5C2×#41⋊C312yes—
240C4×C52−1+4⋊C312yes—
241Dic5—22no—
242Dic5—62no—
243Dic5—62no—
244#41—21no—
245#41—61no—
246#41—304no—
247C2×Q8—102no—
248C2×Q8—152no—
249C2×Q8—151no—
250C2×Q8—302no—
251C2×Q8C22×C3×D511yescharacteristic
252C2×D4—31no—
253C2×D4—51no—
254C2×D4—152no—
255C22×C4—31no—
256C22×C4—31no—
257C22×C4—31no—
258C22×C4—52no—
259C22×C4—152no—
260C22×C4—152no—
261C4⋊C4—31no—
262C4⋊C4—31no—
263C4⋊C4—51no—
264C4⋊C4—152no—
265C4⋊C4—152no—
266C4⋊C4—154no—
267C4⋊C4—152no—
268C4⋊C4—152no—
269C4⋊C4—151no—
270C4⋊C4—152no—
271C22⋊C4—32no—
272C22⋊C4—52no—
273C22⋊C4—152no—
274C22⋊C4—152no—
275C22⋊C4—154no—
276C42—31no—
277C42—31no—
278C42—31no—
279C42—152no—
280C42—152no—
281C42—152no—
282C42D5×A411yescharacteristic
283C3×C5—41noHall
284C22×C3—41no—
285C22×C3—204no—
286C22×C3—402no—
287C22×C3—402no—
288C3×C4—42no—
289C3×C4—42no—
290C3×C4—81no—
291C3×C4—402no—
292C2×C5—121no—
293C2×C5C22×#41⋊C311yescharacteristic
294C2×C5A4×#4111yescharacteristic
295C2×C5C2×2−1+4⋊C311yescharacteristic
296D5—24no—
297C23—31no—
298C23—52no—
299Q8—31no—
300Q8—302no—
301Q8—302no—
302Q8—302no—
303Q8C3×#70911yescharacteristic
304D4—54no—
305D4—61no—
306D4—61no—
307D4—304no—
308C2×C4—31no—
309C2×C4—31no—
310C2×C4—31no—
311C2×C4—52no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—62no—
315C2×C4—62no—
316C2×C4—104no—
317C2×C4—152no—
318C2×C4—152no—
319C2×C4—302no—
320C2×C4—302no—
321C2×C4—304no—
322C2×C4C2×D5×A411yescharacteristic
323C2×C4C2×D5×A411yescharacteristic
324C2×C4C2×D5×A411yescharacteristic
325C2×C3—41no—
326C2×C3—41no—
327C2×C3—41no—
328C2×C3—404no—
329C5#3482⋊C311yescharacteristic, complemented, Sylow
330C22—54no—
331C22—61no—
332C22—61no—
333C22—61no—
334C22—102no—
335C22—102no—
336C22C22×D5×A411yescharacteristic
337C4—21no—
338C4—31no—
339C4—31no—
340C4—61no—
341C4—61no—
342C4—102no—
343C4—302no—
344C4—302no—
345C4D5×#41⋊C312yes—
346C4#4150⋊C312yes—
347C3—41noSylow
348C2—104no—
349C2—121no—
350C2A4×#70911yescharacteristic
351C2C2×D5×#41⋊C311yescharacteristic
352C2C2×#4150⋊C311yescharacteristic
subgroupG/H
centerC2×C4C2×D5×A4
commutator, cosocleC2×C5×Q8C23×C3
FrattiniC22C22×D5×A4
FittingC4×C5×#41C2×C3
socleC22×C5C23×A4
hypercenterC42D5×A4
hypocenterC5×Q8C3×#41
LCSG ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×C5×#41⋊C3C2semidirect
2. #66165⋊C3C2semidirect
3. SL(2,𝔽3)×D20C2semidirect
4. C4×D5×SL(2,𝔽3)C2semidirect
5. #65904⋊C3C2semidirect
6. #10617745C3semidirect
14. C4×C5×#41C2×C3semidirect
15. #66165C2×C3semidirect
17. C4×Q8×D5C2×C3semidirect
18. #65904C2×C3semidirect
36. C4×#41⋊C3D5semidirect
80. C5×SL(2,𝔽3)#41semidirect
135. C4×#41C3×D5semidirect
173. D20#41⋊C3semidirect
226. SL(2,𝔽3)#709semidirect
329. C5#3482⋊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
#66165⋊C32
SL(2,𝔽3)×D202
C4×D5×SL(2,𝔽3)2
#65904⋊C32
#106177453
C3×C4×D204
#3482⋊C35