Finite Group Databasebeta

← #10617733⋊C3 #14514038

Subgroups — #10617733⋊C3 #14514038

Order 1920.

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

normal subgroups only

This group has 530 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#66165⋊C3C212yesmaximal, complemented
3#65906⋊C3C212yesmaximal, complemented
4SL(2,𝔽3)×D20C211yesmaximal, characteristic, complemented
5SL(2,𝔽3)×Dic10C211yesmaximal, characteristic, complemented
6#10617733C311yesmaximal, characteristic, complemented, Hall
7C2×C5×#41⋊C3C2211yescharacteristic
8C2×D5×SL(2,𝔽3)C2212yes—
9C3×#4021—41nomaximal
10C4×C5×SL(2,𝔽3)C2211yescharacteristic
11C4×C5×SL(2,𝔽3)C2211yescharacteristic
12Dic5×SL(2,𝔽3)C2212yes—
13#3518⋊C3—51nomaximal, Hall
14C4×C5×#41C2×C311yescharacteristic, complemented
15#66165C2×C312yescomplemented
16Q8×D20C2×C311yescharacteristic
17#65906C2×C312yescomplemented
18Q8×Dic10C2×C311yescharacteristic, complemented
19#65897—31no—
20#65895—32no—
21#65876—31no—
22#65867—32no—
23#65813—31no—
24#65804—31no—
25C2×C3×D20—41no—
26C2×C3×Dic10—41no—
27C5×#41⋊C3—21no—
28C2×C5×SL(2,𝔽3)C2311yescharacteristic
29D5×SL(2,𝔽3)—22no—
30C3×C42×C5—41no—
31C3×#685—42no—
32C3×#685—42no—
33Q8×SL(2,𝔽3)—51no—
34D4×SL(2,𝔽3)—51no—
35#548⋊C3—52no—
36#519⋊C3—52no—
37C4×#41⋊C3D511yescharacteristic, complemented
38C2×C5×#41C22×C311yescharacteristic
39C2×Q8×D5C22×C312yes—
40C4×C5×Q8C22×C311yescharacteristic
41C4×C5×Q8C22×C311yescharacteristic
42C4×C5×D4—31no—
43C4×C5×D4—31no—
44C5×#117—31no—
45C2×C42×C5—31no—
46Q8×Dic5C22×C312yes—
47#4084—32no—
48#4082—32no—
49#4076—31no—
50#4075—32no—
51C4×C22⋊D5—32no—
52#4072—32no—
53#4070—32no—
54#4070—31no—
55#4070—32no—
56#4043—32no—
57#4038—32no—
58#4034—32no—
59#4033—32no—
60#4031—34no—
61#4025—34no—
62#4022—32no—
63#4021A411yescharacteristic
64C4×D20—31no—
65#4018—32no—
66#4016—31no—
67#4015—31no—
68#4015—31no—
69C4×Dic10—32no—
70C4×Dic10—31no—
71C4×Dic10—32no—
72#3518—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—82no—
79C3×Dic10—82no—
80C5×SL(2,𝔽3)#4111yescharacteristic
81C2×#41⋊C3C2×D511yescharacteristic
82C22×SL(2,𝔽3)—52no—
83C3×#124—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—
97C2×D20C2×A411yescharacteristic
98C2×C4×D5—32no—
99C2×Dic10—32no—
100C2×Dic10—32no—
101C2×Dic10C2×A411yescharacteristic
102C5×C4⋊C4—31no—
103C5×C4⋊C4—31no—
104C5×C22⋊C4—32no—
105C42×C5—31no—
106C42×C5—31no—
107C42×C5—31no—
108C42×C5C2×A411yescharacteristic
109C22⋊Dic5—34no—
110C22⋊Dic5—32no—
111#685—32no—
112#685—32no—
113#685C2×A412yes—
114#685C2×A412yes—
115C4⋊Dic5—32no—
116C4⋊Dic5—31no—
117C4⋊Dic5—31no—
118C4⋊Dic5—32no—
119#683—32no—
120#683—32no—
121#683—32no—
122#683—32no—
123C4×Dic5—34no—
124C4×Dic5—32no—
125Q82—51no—
126#556—152no—
127#556—151no—
128#555—151no—
129D4×Q8—51no—
130#548—52no—
131#542—152no—
132#533—151no—
133#529—151no—
134#519—52no—
135C4×#41C3×D511yescharacteristic, complemented
136C22×C3×C5—41no—
137C2×C3×D5—82no—
138C2×C3×D5—82no—
139C2×C3×D5—82no—
140C3×C4×C5—42no—
141C3×C4×C5—81no—
142C3×C4×C5—81no—
143C3×Dic5—82no—
144C2×C3×Q8—201no—
145C2×C3×D4—201no—
146#41⋊C3—21no—
147C2×SL(2,𝔽3)—102no—
148C2×SL(2,𝔽3)C22×D511yescharacteristic
149C3×C22⋊C4—202no—
150C3×C22⋊C4—202no—
151C3×C42—41no—
152C23×C5—31no—
153C22×D5C22×A412yes—
154C5×Q8—31no—
155C5×Q8C3×#4111yescharacteristic
156C5×D4—61no—
157C5×D4—61no—
158C2×C4×C5—31no—
159C2×C4×C5—31no—
160C2×C4×C5—31no—
161C2×C4×C5—61no—
162C2×C4×C5—61no—
163C2×C4×C5—62no—
164C2×C4×C5—121no—
165C2×C4×C5C22×A411yescharacteristic
166C2×C4×C5C22×A411yescharacteristic
167C2×C4×C5C22×A411yescharacteristic
168C22⋊D5—122no—
169C2×Dic5—32no—
170C2×Dic5—32no—
171C2×Dic5C22×A412yes—
172D20—22no—
173C4×D5—62no—
174C4×D5—62no—
175Dic10—22no—
176Dic10—62no—
177Dic10—62no—
178Dic10—122no—
179C2×#41C2×C3×D511yescharacteristic
180C22×Q8—52no—
181C4⋊Q8—151no—
182C4⋊Q8—151no—
183C4⋊Q8—152no—
184#126—152no—
185#126—154no—
186#125—151no—
187#124—51no—
188#124—154no—
189#124—152no—
190#123—152no—
191C22⋊Q8—151no—
192C22⋊Q8—152no—
193C22⋊Q8—152no—
194C22⋊Q8—152no—
195#121—151no—
196#121—152no—
197C4×Q8—52no—
198C4×Q8—151no—
199C4×Q8—152no—
200C4×Q8—152no—
201C4×Q8—152no—
202C4×Q8C2×C3×D511yescharacteristic
203C4×Q8C2×C3×D511yescharacteristic
204C4×D4—31no—
205C4×D4—31no—
206C4×D4—151no—
207C4×D4—152no—
208#117—31no—
209#117—152no—
210#117—152no—
211#117—152no—
212C2×C42—31no—
213C2×C3×C5—41no—
214C2×C3×C5—41no—
215C2×C3×C5—41no—
216C3×D5—162no—
217C23×C3—202no—
218C3×Q8—402no—
219C3×D4—402no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—202no—
224SL(2,𝔽3)#70911yescharacteristic
225C22×C5—61no—
226C22×C5—61no—
227C22×C5—61no—
228C22×C5C23×A411yescharacteristic
229C2×D5—22no—
230C2×D5—22no—
231C2×D5—22no—
232C4×C5—21no—
233C4×C5—21no—
234C4×C5—31no—
235C4×C5—31no—
236C4×C5—61no—
237C4×C5—61no—
238C4×C52−1+4⋊C312yes—
239Dic5—22no—
240Dic5—62no—
241Dic5—62no—
242#41—21no—
243#41—61no—
244C2×Q8—51no—
245C2×Q8—102no—
246C2×Q8—152no—
247C2×Q8—152no—
248C2×Q8—302no—
249C2×Q8C22×C3×D511yescharacteristic
250C2×D4—31no—
251C2×D4—51no—
252C2×D4—152no—
253C22×C4—31no—
254C22×C4—31no—
255C22×C4—31no—
256C22×C4—152no—
257C4⋊C4—31no—
258C4⋊C4—31no—
259C4⋊C4—152no—
260C4⋊C4—152no—
261C4⋊C4—152no—
262C4⋊C4—152no—
263C4⋊C4—151no—
264C4⋊C4—151no—
265C4⋊C4—152no—
266C4⋊C4—152no—
267C22⋊C4—32no—
268C22⋊C4—52no—
269C22⋊C4—52no—
270C22⋊C4—152no—
271C22⋊C4—152no—
272C22⋊C4—152no—
273C22⋊C4—154no—
274C42—31no—
275C42—31no—
276C42—31no—
277C42—152no—
278C42—154no—
279C42D5×A411yescharacteristic
280C3×C5—41noHall
281C22×C3—41no—
282C22×C3—402no—
283C22×C3—402no—
284C22×C3—402no—
285C3×C4—42no—
286C3×C4—81no—
287C3×C4—81no—
288C3×C4—402no—
289C2×C5—121no—
290C2×C5A4×#4111yescharacteristic
291C2×C5C2×2−1+4⋊C311yescharacteristic
292C2×C5#594511yescharacteristic
293D5—42no—
294C23—31no—
295C23—52no—
296Q8—31no—
297Q8—102no—
298Q8—302no—
299Q8—302no—
300Q8—602no—
301Q8C3×#70911yescharacteristic
302D4—61no—
303D4—61no—
304D4—102no—
305D4—602no—
306C2×C4—31no—
307C2×C4—31no—
308C2×C4—31no—
309C2×C4—52no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—62no—
313C2×C4—121no—
314C2×C4—152no—
315C2×C4—152no—
316C2×C4—302no—
317C2×C4—302no—
318C2×C4C2×D5×A411yescharacteristic
319C2×C4C2×D5×A411yescharacteristic
320C2×C4C2×D5×A411yescharacteristic
321C2×C3—41no—
322C2×C3—41no—
323C2×C3—41no—
324C2×C3—802no—
325C5#3518⋊C311yescharacteristic, complemented, Sylow
326C22—61no—
327C22—61no—
328C22—61no—
329C22—102no—
330C22—102no—
331C22—102no—
332C22C22×D5×A411yescharacteristic
333C4—21no—
334C4—21no—
335C4—31no—
336C4—31no—
337C4—61no—
338C4—61no—
339C4—102no—
340C4—302no—
341C4—302no—
342C4#4150⋊C312yes—
343C3—41noSylow
344C2—121no—
345C2—202no—
346C2A4×#70911yescharacteristic
347C2C2×#4150⋊C311yescharacteristic
348C2#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. #66165⋊C3C2semidirect
3. #65906⋊C3C2semidirect
4. SL(2,𝔽3)×D20C2semidirect
5. SL(2,𝔽3)×Dic10C2semidirect
6. #10617733C3semidirect
14. C4×C5×#41C2×C3semidirect
15. #66165C2×C3semidirect
17. #65906C2×C3semidirect
18. Q8×Dic10C2×C3semidirect
37. C4×#41⋊C3D5semidirect
135. C4×#41C3×D5semidirect
325. C5#3518⋊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
#65906⋊C32
SL(2,𝔽3)×D202
SL(2,𝔽3)×Dic102
#106177333
C3×#40214
#3518⋊C35