Finite Group Databasebeta

← #14292470

Subgroups — #14292470

Order 1920.

336 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C3×#65140C211yesmaximal, characteristic, complemented
2#11747081C211yesmaximal, characteristic
3#11747060C211yesmaximal, characteristic
4#11746862C211yesmaximal, characteristic, complemented
5#11746300C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic
7#11745856C211yesmaximal, characteristic, complemented
8#10599205—31nomaximal, Hall
9C5×#874C2211yescharacteristic
10C3×#4015C2211yescharacteristic
11C3×C4×Dic10C2211yescharacteristic
12C2×#6656—21no—
13C2×#6656—21no—
14C2×#6656—21no—
15C3×C5×C4⋊C8C2211yescharacteristic
16C4⋊(C3⋊#168)C2211yescharacteristic
17C4×C3⋊#168C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×#3949—21no—
20C3×#3948—21no—
21#90982—21no—
22#90966—21no—
23#90952—21no—
24#71120—51nomaximal, Hall
25#65365—31no—
26#65364—31no—
27#65140D311yescharacteristic, complemented
28#65120—31no—
29C5×#331—31no—
30#64702—31no—
31#64699—31no—
32C2×C5×D12—21no—
33C2×C5×D12—21no—
34C2×C5×D12—21no—
35C2×C3×Dic10—21no—
36C2×C3×Dic10D411yescharacteristic
37C2×C3×C5×C8—21no—
38C3×C42×C5C2311yescharacteristic
39C2×C3⋊#168—21no—
40C2×C3⋊#168D411yescharacteristic
41C2×C3⋊#168D411yescharacteristic
42C2×C5×C3⋊C8—21no—
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5D411yescharacteristic
46C3×#683—21no—
47C3×C4×Dic5—21no—
48#6656—42no—
49#6656—42no—
50#6656—42no—
51C3×#475—51no—
52#5085—51no—
53#5027—51no—
54#5024—51no—
55#4547—51no—
56#4485D511yescharacteristic
57#4479—51no—
58C5×#127—31no—
59C2×#687—61no—
60C2×#687—61no—
61C2×#687—61no—
62#4015C2×D311yescharacteristic
63C4×Dic10C2×D311yescharacteristic
64C5×C4⋊C8—31no—
65C5×C4⋊C8C2×D311yescharacteristic
66#3964—61no—
67#3949—21no—
68#3948—21no—
69#3947—61no—
70#3946—61no—
71C4⋊#168—31no—
72C4×#168—31no—
73#1686—151noSylow
74C22×C5×D3—41no—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×C3×C4×C5#4111yescharacteristic
78C5×D12—41no—
79C5×D12—41no—
80C5×D12—41no—
81C5×D12—41no—
82C5×D12—81no—
83C2×C3×Dic5—21no—
84C2×C3×Dic5—21no—
85C2×C3×Dic5—41no—
86C3×Dic10—21no—
87C3×Dic10—21no—
88C3×Dic10—41no—
89C3×Dic10—41no—
90C3×C5×C8—41no—
91C3⋊#168—21no—
92C3⋊#168—41no—
93C3⋊#168SD1612yescomplemented
94C5×C3⋊C8—41no—
95C3×C4⋊Q8—51no—
96C3×C4×Q8—51no—
97C2×#215—101no—
98C2×#215—101no—
99C2×#215—101no—
100#874C2×D511yescharacteristic
101C3×#106—101no—
102C3×C4⋊C8C2×D511yescharacteristic
103C3×#103—101no—
104#809—101no—
105C4⋊(C3⋊C8)—51no—
106C4⋊(C3⋊C8)—101no—
107C4⋊(C3⋊C8)C2×D511yescharacteristic
108#803—101no—
109C4×C3⋊C8—51no—
110C2×C5×D4—61no—
111C2×C5×D4—61no—
112C2×C5×D4—61no—
113C2×Dic10—21no—
114C2×Dic10#6711yescharacteristic
115C2×C5×C8—21no—
116C2×C5×C8—61no—
117C42×C5C22×D311yescharacteristic
118#687—122no—
119#687—122no—
120#687—122no—
121C4⋊Dic5—21no—
122C4⋊Dic5—21no—
123C4⋊Dic5#6711yescharacteristic
124#683—21no—
125C4×Dic5—21no—
126C2×#168—31no—
127C2×#168—31no—
128C2×#168—61no—
129#492—151no—
130#475—51no—
131#460—151no—
132#446—151no—
133#335—151no—
134#332—151no—
135#331—31no—
136C22×C3×C5#12111yescharacteristic
137C2×C5×D3—81no—
138C2×C5×D3—81no—
139C2×C5×D3—81no—
140C3×C4×C5—21no—
141C3×C4×C5C2×SD1611yescharacteristic
142C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
143C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
144C3×C4×C5#13711yescharacteristic
145C3×Dic5—41no—
146C3×Dic5—41no—
147C3×Dic5—81no—
148C2×C3×Q8—51no—
149C2×C3×Q8—101no—
150C2×D12—21no—
151C2×D12—21no—
152C2×D12—21no—
153C2×C3×C8—21no—
154C3×C4⋊C4—51no—
155C3×C4⋊C4—101no—
156C3×C4⋊C4—101no—
157C3×C4⋊C4—101no—
158C3×C42—101no—
159C3×C42C22×D511yescharacteristic
160#215—202no—
161#215—202no—
162#215—202no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8—51no—
165C2×C3⋊C8—51no—
166C2×C3⋊C8—101no—
167C23×C5—121no—
168C5×D4—121no—
169C5×D4—121no—
170C5×D4—121no—
171C5×D4—121no—
172C5×D4—241no—
173C2×C4×C5D3×D411yescharacteristic
174C2×C4×C5#23711yescharacteristic
175C2×C4×C5C2×#6711yescharacteristic
176C2×Dic5—21no—
177C2×Dic5—21no—
178C2×Dic5—41no—
179Dic10—21no—
180Dic10—21no—
181Dic10—41no—
182Dic10—41no—
183C5×C8—41no—
184C5×C8—121no—
185#168—32no—
186#168—61no—
187#168—121no—
188C2×SD16—301no—
189C2×SD16—301no—
190C2×SD16—301no—
191C4⋊Q8—51no—
192#127—31no—
193C4×Q8—51no—
194#106—101no—
195C4⋊C8—31no—
196C4⋊C8—151no—
197C4⋊C8—301no—
198C4⋊C8D3×D511yescharacteristic
199#103—101no—
200#102—301no—
201#97—301no—
202C4×C8—151no—
203C2×C3×C5#46011yescharacteristic
204C2×C3×C5#46811yescharacteristic
205C2×C3×C5#47111yescharacteristic
206C5×D3—161no—
207C22×D3—41no—
208C3×Q8—101no—
209C3×Q8—101no—
210C3×Q8—201no—
211C3×Q8—201no—
212C2×C3×C4—101no—
213C2×C3×C4—101no—
214C2×C3×C4—201no—
215C2×C3×C4#70911yescharacteristic
216C2×C3×C4D4×D511yescharacteristic
217C2×C3×C4D4×D511yescharacteristic
218D12—41no—
219D12—41no—
220D12—41no—
221D12—41no—
222D12—81no—
223C3×C8—41no—
224C3⋊C8—41no—
225C3⋊C8—52no—
226C3⋊C8—101no—
227C3⋊C8—201no—
228C22×C5—241no—
229C22×C5—241no—
230C22×C5—241no—
231C22×C5#93911yescharacteristic
232C4×C5—21no—
233C4×C5D3×SD1611yescharacteristic
234C4×C5#91411yescharacteristic
235C4×C5#94211yescharacteristic
236C4×C5#94911yescharacteristic
237Dic5—41no—
238Dic5—41no—
239Dic5—81no—
240C2×Q8—51no—
241C2×Q8—101no—
242C2×D4—61no—
243C2×D4—61no—
244C2×D4—61no—
245SD16—602no—
246SD16—602no—
247SD16—602no—
248C2×C8—21no—
249C2×C8—61no—
250C2×C8—151no—
251C2×C8—151no—
252C2×C8—301no—
253C4⋊C4—51no—
254C4⋊C4—101no—
255C4⋊C4—101no—
256C4⋊C4—101no—
257C42—101no—
258C42C2×D3×D511yescharacteristic
259C3×C5#168611yescharacteristic, complemented, Hall
260C22×C3#403011yescharacteristic
261C2×D3—81no—
262C2×D3—81no—
263C2×D3—81no—
264C3×C4—21no—
265C3×C4—201no—
266C3×C4—201no—
267C3×C4—401no—
268C3×C4#405711yescharacteristic
269C3×C4#405711yescharacteristic
270C3×C4D5×SD1611yescharacteristic
271C3×C4#406111yescharacteristic
272C2×C5—481no—
273C2×C5#504911yescharacteristic
274C2×C5#516311yescharacteristic
275C2×C5#520311yescharacteristic
276C23—121no—
277Q8—101no—
278Q8—101no—
279Q8—201no—
280Q8—201no—
281D4—121no—
282D4—121no—
283D4—121no—
284D4—121no—
285D4—241no—
286C2×C4—101no—
287C2×C4—101no—
288C2×C4—201no—
289C2×C4#676511yescharacteristic
290C2×C4#677711yescharacteristic
291C2×C4D5×#6711yescharacteristic
292C8—41no—
293C8—121no—
294C8—152no—
295C8—301no—
296C8—601no—
297C2×C3#6503711yescharacteristic
298C2×C3#6505111yescharacteristic
299C2×C3#6506911yescharacteristic
300D3—161no—
301C5#7112011yescharacteristic, complemented, Sylow
302C22—241no—
303C22—241no—
304C22—241no—
305C22#9140811yescharacteristic
306C4—21no—
307C4—201no—
308C4—201no—
309C4—401no—
310C4#9125511yescharacteristic
311C4#9125711yescharacteristic
312C4#9147811yescharacteristic
313C4#9151311yescharacteristic
314C3#1059920511yescharacteristic, complemented, Sylow
315C2—481no—
316C2#1174731111yescharacteristic
317C2#1174799311yescharacteristic
318C2#1174817811yescharacteristic
subgroupG/H
centerC22#91408
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radicalC5×#874C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1686
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C3×#65140C2semidirect
4. #11746862C2semidirect
5. #11746300C2semidirect
7. #11745856C2semidirect
27. #65140D3semidirect
93. C3⋊#168SD16semidirect
259. C3×C5#1686semidirect
301. C5#71120semidirect
314. C3#10599205semidirect

Maximal subgroups

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

subgroupindex
C3×#651402
#117470812
#117470602
#117468622
#117463002
C5×#44852
#117458562
#105992053
#711205