Finite Group Databasebeta

← #10617754⋊C3 #14514028

Subgroups — #10617754⋊C3 #14514028

Order 1920.

534 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 79 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#66168⋊C3C212yesmaximal, complemented
3#65904⋊C3C211yesmaximal, characteristic, complemented
4C4⋊(C5⋊(#41⋊C3))C211yesmaximal, characteristic, complemented
5#65908⋊C3C212yesmaximal, complemented
6#10617754C311yesmaximal, characteristic, complemented, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8C2×C5⋊(#41⋊C3)C2212yes—
9C3×#4016—41nomaximal
10C4×C5×SL(2,𝔽3)C2211yescharacteristic
11C4×C5×SL(2,𝔽3)C2211yescharacteristic
12Dic5×SL(2,𝔽3)C2212yes—
13#3517⋊C3—51nomaximal, Hall
14C4×C5×#41C2×C311yescharacteristic
15#66168C2×C312yes—
16#65911C2×C311yescharacteristic
17#65908C2×C312yes—
18#65904C2×C311yescharacteristic
19#65896—32no—
20#65887—31no—
21#65885—31no—
22#65864—32no—
23#65813—31no—
24#65811—31no—
25C5×#41⋊C3—21no—
26C2×C5×SL(2,𝔽3)C2311yescharacteristic
27C5⋊(#41⋊C3)—22no—
28C3×C42×C5—41no—
29C3×C4⋊Dic5—41no—
30C3×C4⋊Dic5—41no—
31C3×#683—42no—
32C3×#683—42no—
33#557⋊C3—51no—
34C4⋊(#41⋊C3)—52no—
35C4⋊(#41⋊C3)—51no—
36#520⋊C3—52no—
37C4×#41⋊C3D511yescharacteristic, complemented
38C2×C5×#41C22×C311yescharacteristic
39C2×#713C22×C312yes—
40C2×#709—32no—
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#4086—32no—
49#4084—32no—
50#4076—32no—
51#4076—32no—
52#4076—31no—
53#4075—32no—
54C4×C22⋊D5—32no—
55#4070—31no—
56#4041—32no—
57#4039—32no—
58D5×C4⋊C4—32no—
59#4036—32no—
60#4030—34no—
61#4029—34no—
62#4022—32no—
63#4021—31no—
64#4020—31no—
65C4×D20—32no—
66C4×D20—32no—
67C4×D20—31no—
68#4018—32no—
69#4016A411yescharacteristic
70#4015—31no—
71C4×Dic10—31no—
72#3517—51noSylow
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5—41no—
76C2×C3×Dic5—42no—
77C2×C3×Dic5—42no—
78C5×SL(2,𝔽3)#4111yescharacteristic, complemented
79C2×#41⋊C3—52no—
80C2×#41⋊C3C2×D511yescharacteristic
81C3×#125—201no—
82C4×SL(2,𝔽3)—52no—
83C4×SL(2,𝔽3)C2×D511yescharacteristic
84C4×SL(2,𝔽3)C2×D511yescharacteristic
85C5×#41—21no—
86C5×#41—61no—
87C2×C5×Q8C23×C311yescharacteristic
88C2×C5×D4—31no—
89C22×C4×C5—31no—
90C22×C4×C5—31no—
91C22×C4×C5—31no—
92C2×C22⋊D5—34no—
93C2×C22⋊D5—32no—
94#713—22no—
95#713—62no—
96#709—124no—
97C2×D20—32no—
98C2×D20—31no—
99C2×D20—32no—
100C2×C4×D5—32no—
101C2×C4×D5—34no—
102C2×Dic10—31no—
103C5×C4⋊C4—31no—
104C5×C4⋊C4—31no—
105C5×C22⋊C4—32no—
106C42×C5—31no—
107C42×C5—31no—
108C42×C5—31no—
109C42×C5C2×A411yescharacteristic
110C22⋊Dic5—32no—
111#685—32no—
112#685—32no—
113#685—32no—
114#685—32no—
115C4⋊Dic5—32no—
116C4⋊Dic5—32no—
117C4⋊Dic5C2×A411yescharacteristic
118C4⋊Dic5C2×A411yescharacteristic
119#683—32no—
120#683—32no—
121#683C2×A412yes—
122#683C2×A412yes—
123C4×Dic5—32no—
124#557—51no—
125#553—152no—
126#550—52no—
127#550—51no—
128#550—151no—
129#547—151no—
130#540—152no—
131#532—151no—
132#529—151no—
133#520—52no—
134C4×#41C3×D511yescharacteristic
135C22×C3×C5—41no—
136C3×C4×C5—42no—
137C3×C4×C5—81no—
138C3×C4×C5—81no—
139C3×Dic5—82no—
140C3×Dic5—82no—
141#41⋊C3—21no—
142#41⋊C3—102no—
143C2×SL(2,𝔽3)C22×D511yescharacteristic
144C3×C4⋊C4—202no—
145C3×C4⋊C4—202no—
146C3×C4⋊C4—201no—
147C3×C4⋊C4—201no—
148C3×C42—41no—
149C23×C5—31no—
150C22×D5—32no—
151C5×Q8—31no—
152C5×Q8C3×#4111yescharacteristic
153C5×D4—61no—
154C5×D4—61no—
155C2×C4×C5—31no—
156C2×C4×C5—31no—
157C2×C4×C5—31no—
158C2×C4×C5—61no—
159C2×C4×C5—61no—
160C2×C4×C5—62no—
161C2×C4×C5—121no—
162C2×C4×C5C22×A411yescharacteristic
163C2×C4×C5C22×A411yescharacteristic
164C2×C4×C5C22×A411yescharacteristic
165C22⋊D5—122no—
166C22⋊D5—124no—
167C2×Dic5—32no—
168C2×Dic5C22×A412yes—
169C2×Dic5C22×A412yes—
170D20—62no—
171D20—62no—
172D20—62no—
173D20—122no—
174C4×D5—62no—
175C4×D5—62no—
176C4×D5—124no—
177Dic10—62no—
178C2×#41—52no—
179C2×#41—152no—
180C2×#41C2×C3×D511yescharacteristic
181C4⋊Q8—151no—
182#127—151no—
183#127—152no—
184#126—152no—
185#125—51no—
186#125—152no—
187#124—151no—
188#123—154no—
189#123—152no—
190C22⋊Q8—151no—
191#121—154no—
192#121—151no—
193#121—152no—
194#121—152no—
195#121—152no—
196#121—152no—
197C4×Q8—52no—
198C4×Q8—151no—
199C4×Q8C2×C3×D511yescharacteristic
200C4×Q8C2×C3×D511yescharacteristic
201C4×D4—31no—
202C4×D4—31no—
203C4×D4—151no—
204C4×D4—152no—
205C4×D4—152no—
206C4×D4—152no—
207C4×D4—152no—
208#117—31no—
209#117—152no—
210C2×C4⋊C4—152no—
211C2×C42—31no—
212C2×C3×C5—41no—
213C2×C3×C5—41no—
214C2×C3×C5—41no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—202no—
219C2×C3×C4—202no—
220SL(2,𝔽3)#70911yescharacteristic, complemented
221C22×C5—61no—
222C22×C5—61no—
223C22×C5—61no—
224C22×C5C23×A411yescharacteristic
225C2×D5—62no—
226C2×D5—62no—
227C2×D5—62no—
228C4×C5—21no—
229C4×C5—21no—
230C4×C5—31no—
231C4×C5—31no—
232C4×C5—61no—
233C4×C5—61no—
234C4×C5#99412yes—
235Dic5—22no—
236Dic5—22no—
237Dic5—62no—
238#41—21no—
239#41—61no—
240#41—102no—
241#41—302no—
242#41—604no—
243C2×Q8—151no—
244C2×Q8C22×C3×D511yescharacteristic
245C2×D4—31no—
246C2×D4—152no—
247C2×D4—152no—
248C2×D4—152no—
249C2×D4—154no—
250C2×D4—151no—
251C22×C4—31no—
252C22×C4—31no—
253C22×C4—31no—
254C22×C4—152no—
255C22×C4—154no—
256C4⋊C4—31no—
257C4⋊C4—31no—
258C4⋊C4—52no—
259C4⋊C4—51no—
260C4⋊C4—52no—
261C4⋊C4—51no—
262C4⋊C4—152no—
263C4⋊C4—152no—
264C4⋊C4—152no—
265C4⋊C4—152no—
266C22⋊C4—32no—
267C22⋊C4—152no—
268C22⋊C4—152no—
269C22⋊C4—152no—
270C22⋊C4—152no—
271C22⋊C4—152no—
272C42—31no—
273C42—31no—
274C42—31no—
275C42—152no—
276C42D5×A411yescharacteristic
277C3×C5—41noHall
278C22×C3—41no—
279C3×C4—42no—
280C3×C4—81no—
281C3×C4—81no—
282C3×C4—402no—
283C3×C4—402no—
284C2×C5—121no—
285C2×C5A4×#4111yescharacteristic
286C2×C5C2×#99411yescharacteristic
287C2×C5#594511yescharacteristic
288D5—122no—
289C23—31no—
290C23—152no—
291Q8—31no—
292Q8—302no—
293Q8C3×#70911yescharacteristic
294D4—61no—
295D4—61no—
296D4—302no—
297D4—302no—
298D4—302no—
299D4—602no—
300D4—602no—
301D4—604no—
302C2×C4—31no—
303C2×C4—31no—
304C2×C4—31no—
305C2×C4—52no—
306C2×C4—52no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—62no—
310C2×C4—121no—
311C2×C4—152no—
312C2×C4—302no—
313C2×C4—302no—
314C2×C4—604no—
315C2×C4C2×D5×A411yescharacteristic
316C2×C4C2×D5×A411yescharacteristic
317C2×C4C2×D5×A411yescharacteristic
318C2×C3—41no—
319C2×C3—41no—
320C2×C3—41no—
321C5#3517⋊C311yescharacteristic, complemented, Sylow
322C22—61no—
323C22—61no—
324C22—61no—
325C22—302no—
326C22—302no—
327C22—302no—
328C22C22×D5×A411yescharacteristic
329C4—21no—
330C4—21no—
331C4—31no—
332C4—31no—
333C4—61no—
334C4—61no—
335C4—102no—
336C4—102no—
337C4—302no—
338C4C5⋊#99412yes—
339C3—41noSylow
340C2—121no—
341C2—602no—
342C2A4×#70911yescharacteristic
343C2C2×C5⋊#99411yescharacteristic
344C2#66283⋊C311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutator, cosocleC2×C5×Q8C23×C3
FittingC4×C5×#41C2×C3
socleC22×C5C23×A4
hypercenterC42D5×A4
hypocenterC5×Q8C3×#41
LCSG ▷ C2×C5×Q8 ▷ C5×Q8
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C4×C5×#41⋊C3C2semidirect
2. #66168⋊C3C2semidirect
3. #65904⋊C3C2semidirect
4. C4⋊(C5⋊(#41⋊C3))C2semidirect
5. #65908⋊C3C2semidirect
6. #10617754C3semidirect
37. C4×#41⋊C3D5semidirect
78. C5×SL(2,𝔽3)#41semidirect
220. SL(2,𝔽3)#709semidirect
321. C5#3517⋊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
#66168⋊C32
#65904⋊C32
C4⋊(C5⋊(#41⋊C3))2
#65908⋊C32
#106177543
C3×#40164
#3517⋊C35