Finite Group Databasebeta

← #14318506

Subgroups — #14318506

Order 1920.

264 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 72 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#11750981C211yesmaximal, characteristic
2#11747958C211yesmaximal, characteristic
3C5×#4490C211yesmaximal, characteristic, complemented
4C3×#64712C211yesmaximal, characteristic, complemented
5#11745939C211yesmaximal, characteristic, complemented
6#11745898C211yesmaximal, characteristic, complemented
7#11745881C211yesmaximal, characteristic
8#10600135—31nomaximal, Hall
9C2×C8×D15C2211yescharacteristic
10#91781—21no—
11C2×C3×Dic20C2211yescharacteristic
12#91390—21no—
13C3×C5×#107C2211yescharacteristic
14#91102C2211yescharacteristic
15#91092—21no—
16C5×#818C2211yescharacteristic
17C2×C5×C3⋊C16C2211yescharacteristic
18C2×C3×#672C2211yescharacteristic
19#90970—21no—
20#69214—51nomaximal, Hall
21#65176—31no—
22#65169—31no—
23C5×#367—31no—
24#64727—31no—
25#64723—31no—
26#64712D311yescharacteristic, complemented
27#64709—31no—
28C2×C4×D15D411yescharacteristic
29C2×C3×Dic10—21no—
30C2×C3×C5×C8C2311yescharacteristic
31C3×C5×C4⋊C4—21no—
32#6714—41no—
33C4⋊Dic15—21no—
34C4×Dic15—41no—
35C2×C3⋊#168D411yescharacteristic
36C8×D15—21no—
37C8×D15—21no—
38C5×C4⋊Dic3—21no—
39C3×Dic20—21no—
40C3×Dic20—21no—
41Dic3⋊Dic5—41no—
42#6667—41no—
43C3×#672—21no—
44C5×C3⋊C16—21no—
45#5188—51no—
46#4880—51no—
47C3×#358—51no—
48#4564—51no—
49(C2×D3)⋊C16—51no—
50#4504—51no—
51#4490D511yescharacteristic, complemented
52C2×Dic20C2×D311yescharacteristic
53C2×C8×D5—31no—
54#4043—61no—
55#4038—61no—
56C2×C5×C16—31no—
57C5×#107—31no—
58C5×#107C2×D311yescharacteristic
59#3950—31no—
60C2×#672C2×D311yescharacteristic
61#3942—61no—
62#3940—61no—
63#2237—151noSylow
64C22×D15D811yescharacteristic
65C2×C3×C4×C5—41no—
66C2×C3×C4×C5C2×D411yescharacteristic
67C2×Dic15—41no—
68C2×Dic15D811yescharacteristic
69C4×D15—21no—
70C4×D15—21no—
71C2×C5×Dic3—41no—
72C2×C3×Dic5—41no—
73C3×Dic10—41no—
74C3×Dic10—41no—
75C3×C5×C8#4111yescharacteristic
76C3×C5×C8#4111yescharacteristic
77C3⋊#168—21no—
78C2×C3×Q16—51no—
79#946—101no—
80C2×D3×C8—51no—
81#892—101no—
82C2×C3×C16—51no—
83C3×#107C2×D511yescharacteristic
84#835—101no—
85#818—51no—
86#818C2×D511yescharacteristic
87C2×C3⋊C16C2×D511yescharacteristic
88#808—101no—
89C2×C4×D5—31no—
90C2×Dic10—21no—
91C2×C5×C8C22×D311yescharacteristic
92C5×C4⋊C4—21no—
93C5×C4⋊C4—61no—
94#685—121no—
95#685—121no—
96C4⋊Dic5—61no—
97C4⋊Dic5—121no—
98C4×Dic5—121no—
99C2×#168—31no—
100Dic20—21no—
101Dic20—21no—
102C8×D5—61no—
103C8×D5—61no—
104C5×C16—61no—
105#672—21no—
106#467—151no—
107#427—151no—
108#367—31no—
109#366—151no—
110#358—51no—
111#358—151no—
112C22⋊C16—151no—
113C22×C3×C5C2×D811yescharacteristic
114C2×D15—21no—
115C2×D15—21no—
116C2×D15—21no—
117C3×C4×C5—81no—
118C3×C4×C5#12311yescharacteristic
119C3×C4×C5#13711yescharacteristic
120Dic15—21no—
121Dic15—81no—
122C3×Dic5—81no—
123C5×Dic3—81no—
124C2×C3×Q8—101no—
125C2×C4×D3—51no—
126C3×Q16—101no—
127C3×Q16—101no—
128C2×C3×C8C22×D511yescharacteristic
129C3×C4⋊C4—21no—
130(C2×D3)⋊C4—201no—
131(C2×D3)⋊C4—201no—
132C4⋊Dic3—21no—
133C4⋊Dic3—101no—
134Dic3⋊C4—201no—
135C4×Dic3—201no—
136C2×C3⋊C8—51no—
137D3×C8—101no—
138D3×C8—101no—
139C3×C16—101no—
140C3⋊C16—21no—
141C22×D5—31no—
142C2×C4×C5—41no—
143C2×C4×C5—121no—
144C2×C4×C5D3×D411yescharacteristic
145C2×Dic5—31no—
146C2×Dic5—41no—
147C2×Dic5—121no—
148C4×D5—61no—
149C4×D5—61no—
150Dic10—41no—
151Dic10—41no—
152C5×C8#23511yescharacteristic
153C5×C8#23711yescharacteristic
154#168—61no—
155C2×Q16—51no—
156C22×C8—151no—
157C22⋊Q8—301no—
158#117—301no—
159C2×C16—31no—
160C2×C16—51no—
161#107—31no—
162#107—151no—
163#107D3×D511yescharacteristic
164#106—301no—
165#103—301no—
166C2×C3×C5#48011yescharacteristic
167C2×C3×C5#50811yescharacteristic
168C2×C3×C5#51011yescharacteristic
169D15—41no—
170C22×D3—51no—
171C3×Q8—201no—
172C3×Q8—201no—
173C2×C3×C4—41no—
174C2×C3×C4—201no—
175C2×C3×C4D4×D511yescharacteristic
176C2×Dic3—41no—
177C2×Dic3—51no—
178C2×Dic3—201no—
179C4×D3—101no—
180C4×D3—101no—
181C3×C8#70911yescharacteristic
182C3×C8#71311yescharacteristic
183C3⋊C8—101no—
184C22×C5D3×D811yescharacteristic
185C2×D5—61no—
186C2×D5—61no—
187C2×D5—61no—
188C4×C5—81no—
189C4×C5—241no—
190C4×C5#88311yescharacteristic
191C4×C5#91511yescharacteristic
192Dic5—61no—
193Dic5—81no—
194Dic5—241no—
195C2×Q8—101no—
196C22×C4—151no—
197Q16—101no—
198Q16—101no—
199C2×C8—151no—
200C2×C8—301no—
201C2×C8—301no—
202C2×C8C2×D3×D511yescharacteristic
203C4⋊C4—21no—
204C4⋊C4—61no—
205C4⋊C4—301no—
206C4⋊C4—601no—
207C22⋊C4—601no—
208C22⋊C4—601no—
209C42—601no—
210C16—61no—
211C16—101no—
212C3×C5#223711yescharacteristic, complemented, Hall
213C22×C3D5×D811yescharacteristic
214C2×D3—101no—
215C2×D3—101no—
216C2×D3—101no—
217C3×C4—81no—
218C3×C4—401no—
219C3×C4#404011yescharacteristic
220C3×C4#406411yescharacteristic
221Dic3—81no—
222Dic3—101no—
223Dic3—401no—
224C2×C5#477411yescharacteristic
225C2×C5#491511yescharacteristic
226C2×C5#491911yescharacteristic
227D5—121no—
228C23—151no—
229Q8—201no—
230Q8—201no—
231C2×C4—41no—
232C2×C4—121no—
233C2×C4—151no—
234C2×C4—201no—
235C2×C4—301no—
236C2×C4—301no—
237C2×C4—601no—
238C2×C4#679011yescharacteristic
239C8—301no—
240C8#676611yescharacteristic
241C8#677111yescharacteristic
242C2×C3#6517111yescharacteristic
243C2×C3#6520411yescharacteristic
244C2×C3#6520511yescharacteristic
245D3—201no—
246C5#6921411yescharacteristic, complemented, Sylow
247C22—301no—
248C22—301no—
249C22—301no—
250C22#9148111yescharacteristic
251C4—81no—
252C4—241no—
253C4—301no—
254C4—401no—
255C4—1201no—
256C4#9135411yescharacteristic
257C4#9152211yescharacteristic
258C3#1060013511yescharacteristic, complemented, Sylow
259C2—601no—
260C2#1174733011yescharacteristic
261C2#1174827511yescharacteristic
262C2#1174831011yescharacteristic
subgroupG/H
centerC22#91481
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
prime radicalC22×D15D8
hypercenter#107D3×D5
hypocenterC3×C5#2237
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
3. C5×#4490C2semidirect
4. C3×#64712C2semidirect
5. #11745939C2semidirect
6. #11745898C2semidirect
26. #64712D3semidirect
51. #4490D5semidirect
212. C3×C5#2237semidirect
246. C5#69214semidirect
258. C3#10600135semidirect

Maximal subgroups

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

subgroupindex
#117509812
#117479582
C5×#44902
C3×#647122
#117459392
#117458982
#117458812
#106001353
#692145