Finite Group Databasebeta

← #14292202

Subgroups — #14292202

Order 1920.

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

normal subgroups only

This group has 332 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
1#11750949C211yesmaximal, characteristic
2#11747104C211yesmaximal, characteristic, complemented
3#11746910C211yesmaximal, characteristic
4#11746855C211yesmaximal, characteristic, complemented
5C5×#4479C211yesmaximal, characteristic, complemented
6C3×#64702C211yesmaximal, characteristic, complemented
7#11745854C211yesmaximal, characteristic
8#10599383—31nomaximal, Hall
9C2×#6706—21no—
10#91763C2211yescharacteristic
11C4×Dic30C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C2×#6662—21no—
14C3×C5×C4⋊C8C2211yescharacteristic
15#91105—21no—
16C5×C4⋊(C3⋊C8)C2211yescharacteristic
17C4×C5×C3⋊C8C2211yescharacteristic
18C3×C4⋊#168C2211yescharacteristic
19#90983—21no—
20#90971—21no—
21#90968—21no—
22#90968—21no—
23#90951—21no—
24#68470—51nomaximal, Hall
25#65138—31no—
26#65137—31no—
27#64983—31no—
28C8×Dic10—31no—
29C5×#335—31no—
30#64705—31no—
31#64702D311yescharacteristic, complemented
32C2×D60—21no—
33C2×D60—21no—
34C2×D60—21no—
35C2×Dic30D411yescharacteristic
36C2×C3×Dic10—21no—
37C2×C3×C5×C8—21no—
38C3×C42×C5C2311yescharacteristic
39C4⋊Dic15D411yescharacteristic
40#6712—21no—
41C4×Dic15—21no—
42#6706—42no—
43C2×C5×C3⋊C8—21no—
44C2×C5×C3⋊C8D411yescharacteristic
45C2×C5×C3⋊C8D411yescharacteristic
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5—21no—
48C2×C3×#168—21no—
49#6662—42no—
50#5090—51no—
51#5088—51no—
52#4848—51no—
53#4830—51no—
54C3×#332—51no—
55#4485—51no—
56#4479D511yescharacteristic, complemented
57C2×Dic20—61no—
58C2×#677—61no—
59#4020—31no—
60#4015C2×D311yescharacteristic
61C4×Dic10—31no—
62C5×C4⋊C8—31no—
63C5×C4⋊C8C2×D311yescharacteristic
64C4×C5×C8—31no—
65#3953—61no—
66#3953—61no—
67#3953—61no—
68#3948—61no—
69#3946—61no—
70C8×Dic5—61no—
71C4⋊#168C2×D311yescharacteristic
72#1682—151noSylow
73C22×D15—41no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4111yescharacteristic
77C2×Dic15—21no—
78C2×Dic15—21no—
79D60—41no—
80D60—41no—
81D60—41no—
82D60—41no—
83D60—81no—
84Dic30—21no—
85Dic30D812yes—
86C2×C3×Dic5—41no—
87C3×Dic10—41no—
88C3×Dic10—41no—
89C3×C5×C8—41no—
90C3×#168—41no—
91C5×C3⋊C8—21no—
92C5×C3⋊C8—21no—
93C5×C3⋊C8—41no—
94C3×C4⋊Q8—51no—
95C2×#216—101no—
96C2×#204—101no—
97#874—51no—
98C4×Dic6—51no—
99C3×C4⋊C8—51no—
100C3×C4⋊C8C2×D511yescharacteristic
101#835—101no—
102#821—101no—
103Dic3⋊C8—101no—
104C8×Dic3—101no—
105#809—101no—
106#809—101no—
107C4⋊(C3⋊C8)C2×D511yescharacteristic
108C4×C3⋊C8C2×D511yescharacteristic
109C2×D20—61no—
110C2×D20—61no—
111C2×D20—61no—
112C2×Dic10—21no—
113C2×Dic10—31no—
114C2×C5×C8—21no—
115C2×C5×C8—31no—
116C2×C5×C8—31no—
117C2×C5×C8—61no—
118C42×C5C22×D311yescharacteristic
119C4⋊Dic5—21no—
120C4⋊Dic5—21no—
121C4⋊Dic5—31no—
122#683—61no—
123C4×Dic5—61no—
124C2×#168—21no—
125Dic20—122no—
126#677—122no—
127#486—151no—
128#462—151no—
129#460—151no—
130C8×Q8—151no—
131#335—31no—
132#332—51no—
133#331—151no—
134C22×C3×C5#12111yescharacteristic
135C2×D15—81no—
136C2×D15—81no—
137C2×D15—81no—
138C3×C4×C5—21no—
139C3×C4×C5C2×D811yescharacteristic
140C3×C4×C5#13511yescharacteristic
141C3×C4×C5#13511yescharacteristic
142C3×C4×C5#13711yescharacteristic
143Dic15—22no—
144Dic15—41no—
145C3×Dic5—81no—
146C2×C3×Q8—101no—
147C2×D12—101no—
148C2×D12—101no—
149C2×D12—101no—
150C2×Dic6—51no—
151C2×C3×C8—21no—
152C2×C3×C8—101no—
153C3×C4⋊C4—101no—
154C3×C4⋊C4—101no—
155C3×C42C22×D511yescharacteristic
156#216—202no—
157C4⋊Dic3—51no—
158Dic3⋊C4—101no—
159C4×Dic3—101no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8D2011yescharacteristic
162C2×C3⋊C8D2011yescharacteristic
163#204—202no—
164C22×D5—121no—
165C2×C4×C5#23511yescharacteristic
166C2×C4×C5D3×D411yescharacteristic
167C2×C4×C5D3×D411yescharacteristic
168C2×Dic5—41no—
169C2×Dic5—61no—
170C2×Dic5—61no—
171D20—121no—
172D20—121no—
173D20—121no—
174D20—121no—
175D20—241no—
176Dic10—32no—
177Dic10—41no—
178Dic10—41no—
179Dic10—61no—
180C5×C8—41no—
181C5×C8—61no—
182C5×C8—61no—
183C5×C8—121no—
184#168—41no—
185C2×Q16—301no—
186C2×SD16—301no—
187C4⋊Q8—51no—
188#127—151no—
189C4×Q8—151no—
190C4⋊C8—31no—
191C4⋊C8—51no—
192C4⋊C8—301no—
193C4⋊C8D3×D511yescharacteristic
194#103—301no—
195#102—301no—
196#102—301no—
197#102—301no—
198C4×C8—31no—
199C4×C8—301no—
200C2×C3×C5#46411yescharacteristic
201C2×C3×C5#46611yescharacteristic
202C2×C3×C5#47111yescharacteristic
203D15—161no—
204C22×D3—201no—
205C3×Q8—201no—
206C3×Q8—201no—
207C2×C3×C4—201no—
208C2×C3×C4C2×D2011yescharacteristic
209C2×C3×C4D4×D511yescharacteristic
210C2×C3×C4#71311yescharacteristic
211C2×Dic3—101no—
212C2×Dic3—101no—
213D12—201no—
214D12—201no—
215D12—201no—
216D12—201no—
217D12—401no—
218Dic6—52no—
219Dic6—101no—
220C3×C8—41no—
221C3×C8—201no—
222C3⋊C8—21no—
223C3⋊C8—21no—
224C3⋊C8—41no—
225C22×C5#88411yescharacteristic
226C2×D5—241no—
227C2×D5—241no—
228C2×D5—241no—
229C4×C5—21no—
230C4×C5D3×D811yescharacteristic
231C4×C5#91611yescharacteristic
232C4×C5#91611yescharacteristic
233C4×C5#91811yescharacteristic
234Dic5—62no—
235Dic5—81no—
236Dic5—121no—
237C2×Q8—101no—
238C2×Q8—151no—
239C2×D4—301no—
240C2×D4—301no—
241C2×D4—301no—
242Q16—602no—
243SD16—602no—
244C2×C8—21no—
245C2×C8—31no—
246C2×C8—31no—
247C2×C8—61no—
248C2×C8—101no—
249C4⋊C4—101no—
250C4⋊C4—101no—
251C4⋊C4—151no—
252C4⋊C4—301no—
253C42—301no—
254C42C2×D3×D511yescharacteristic
255C3×C5#168211yescharacteristic, complemented, Hall
256C22×C3#404111yescharacteristic
257C2×D3—401no—
258C2×D3—401no—
259C2×D3—401no—
260C3×C4—21no—
261C3×C4—401no—
262C3×C4#405011yescharacteristic
263C3×C4#405511yescharacteristic
264C3×C4D5×D811yescharacteristic
265C3×C4#406511yescharacteristic
266Dic3—102no—
267Dic3—201no—
268C2×C5#475411yescharacteristic
269C2×C5#477511yescharacteristic
270C2×C5#479811yescharacteristic
271D5—481no—
272C23—601no—
273Q8—152no—
274Q8—201no—
275Q8—201no—
276Q8—301no—
277D4—601no—
278D4—601no—
279D4—601no—
280D4—601no—
281D4—1201no—
282C2×C4—201no—
283C2×C4—301no—
284C2×C4—301no—
285C2×C4#677311yescharacteristic
286C2×C4D3×D2011yescharacteristic
287C2×C4#679011yescharacteristic
288C8—41no—
289C8—61no—
290C8—61no—
291C8—121no—
292C8—201no—
293C2×C3#6513411yescharacteristic
294C2×C3#6517211yescharacteristic
295C2×C3#6518711yescharacteristic
296D3—801no—
297C5#6847011yescharacteristic, complemented, Sylow
298C22—1201no—
299C22—1201no—
300C22—1201no—
301C22#9145911yescharacteristic
302C4—21no—
303C4—302no—
304C4—401no—
305C4—601no—
306C4#9126311yescharacteristic
307C4#9127211yescharacteristic
308C4#9148111yescharacteristic
309C4#9152111yescharacteristic
310C3#1059938311yescharacteristic, complemented, Sylow
311C2—2401no—
312C2#1174732911yescharacteristic
313C2#1174787211yescharacteristic
314C2#1174819711yescharacteristic
subgroupG/H
centerC22#91459
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radical#91763C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1682
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
2. #11747104C2semidirect
4. #11746855C2semidirect
5. C5×#4479C2semidirect
6. C3×#64702C2semidirect
31. #64702D3semidirect
56. #4479D5semidirect
255. C3×C5#1682semidirect
297. C5#68470semidirect
310. C3#10599383semidirect

Maximal subgroups

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

subgroupindex
#117509492
#117471042
#117469102
#117468552
C5×#44792
C3×#647022
#117458542
#105993833
#684705