Finite Group Databasebeta

← #14318511

Subgroups — #14318511

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#11747958C211yesmaximal, characteristic
2#11747690C211yesmaximal, characteristic
3#11746328C211yesmaximal, characteristic
4C5×#4504C211yesmaximal, characteristic, complemented
5C3×#64723C211yesmaximal, characteristic, complemented
6#11745943C211yesmaximal, characteristic, complemented
7#11745897C211yesmaximal, characteristic, complemented
8#10600125—31nomaximal, Hall
9C2×C8×D15C2211yescharacteristic
10C2×C3×Dic20C2211yescharacteristic
11#91390—21no—
12#91347—21no—
13C2×C3×C5×C16C2211yescharacteristic
14C2×C3⋊#672C2211yescharacteristic
15C5×#818C2211yescharacteristic
16C5×#818C2211yescharacteristic
17C3×#3950C2211yescharacteristic
18#90986—21no—
19#90970—21no—
20#69214—51nomaximal, Hall
21#65176—31no—
22#65169—31no—
23C5×#366—31no—
24#64727—31no—
25#64723D311yescharacteristic, complemented
26#64712—31no—
27#64710—31no—
28C2×C4×D15D411yescharacteristic
29C2×C3×Dic10—21no—
30C2×C3×C5×C8C2311yescharacteristic
31C2×C3⋊#168D411yescharacteristic
32C8×D15—21no—
33C8×D15—21no—
34C5×C4⋊Dic3—21no—
35C5×C4⋊Dic3—21no—
36C3×C4⋊Dic5—21no—
37C3×Dic20—21no—
38C3×Dic20—21no—
39Dic3⋊Dic5—41no—
40#6667—41no—
41#6667—41no—
42Dic3×Dic5—41no—
43C3×C5×C16—21no—
44C3⋊#672—21no—
45#5188—51no—
46#4880—51no—
47C3×#358—51no—
48#4564—51no—
49(C2×D3)⋊C16—51no—
50#4504D511yescharacteristic, complemented
51#4490—51no—
52C2×Dic20C2×D311yescharacteristic
53C2×C8×D5—31no—
54#4043—61no—
55#4038—61no—
56C2×C5×C16C2×D311yescharacteristic
57C5×#107—31no—
58C5×#107—31no—
59#3950C2×D311yescharacteristic
60C2×#672—31no—
61#3942—61no—
62#3940—61no—
63#2237—151noSylow
64C22×D15D811yescharacteristic
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×Dic15D811yescharacteristic
67C4×D15—21no—
68C4×D15—21no—
69C2×C5×Dic3—41no—
70C2×C5×Dic3—41no—
71C2×C3×Dic5—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×C16C2×D511yescharacteristic
83C3×#107—51no—
84#835—101no—
85#818C2×D511yescharacteristic
86#818C2×D511yescharacteristic
87C2×C3⋊C16—51no—
88#808—101no—
89C2×C4×D5—31no—
90C2×Dic10—21no—
91C2×C5×C8C22×D311yescharacteristic
92C5×C4⋊C4—61no—
93C5×C4⋊C4—61no—
94#685—121no—
95#685—121no—
96C4⋊Dic5—21no—
97C4⋊Dic5—121no—
98C4×Dic5—121no—
99C2×#168—31no—
100Dic20—21no—
101Dic20—21no—
102C8×D5—61no—
103C8×D5—61no—
104C5×C16—21no—
105#672—61no—
106#467—151no—
107#427—151no—
108#367—151no—
109#366—31no—
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#12311yescharacteristic
118C3×C4×C5#13711yescharacteristic
119Dic15—21no—
120C3×Dic5—81no—
121C3×Dic5—81no—
122C5×Dic3—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—101no—
130(C2×D3)⋊C4—201no—
131(C2×D3)⋊C4—201no—
132C4⋊Dic3—21no—
133C4⋊Dic3—21no—
134Dic3⋊C4—201no—
135C4×Dic3—201no—
136C2×C3⋊C8—51no—
137D3×C8—101no—
138D3×C8—101no—
139C3×C16—21no—
140C3⋊C16—101no—
141C22×D5—31no—
142C2×C4×C5—121no—
143C2×C4×C5—121no—
144C2×C4×C5D3×D411yescharacteristic
145C2×Dic5—31no—
146C2×Dic5—41no—
147C2×Dic5—41no—
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—151no—
160C2×C16D3×D511yescharacteristic
161#107—31no—
162#107—31no—
163#107—51no—
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—201no—
174C2×C3×C4—201no—
175C2×C3×C4D4×D511yescharacteristic
176C2×Dic3—41no—
177C2×Dic3—41no—
178C2×Dic3—51no—
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—241no—
189C4×C5—241no—
190C4×C5#88311yescharacteristic
191C4×C5#91511yescharacteristic
192Dic5—61no—
193Dic5—81no—
194Dic5—81no—
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—61no—
204C4⋊C4—61no—
205C4⋊C4—101no—
206C4⋊C4—601no—
207C22⋊C4—601no—
208C22⋊C4—601no—
209C42—601no—
210C16—21no—
211C16—301no—
212C3×C5#223711yescharacteristic, complemented, Hall
213C22×C3D5×D811yescharacteristic
214C2×D3—101no—
215C2×D3—101no—
216C2×D3—101no—
217C3×C4—401no—
218C3×C4—401no—
219C3×C4#404011yescharacteristic
220C3×C4#406411yescharacteristic
221Dic3—81no—
222Dic3—81no—
223Dic3—101no—
224C2×C5#477411yescharacteristic
225C2×C5#491511yescharacteristic
226C2×C5#491911yescharacteristic
227D5—121no—
228C23—151no—
229Q8—201no—
230Q8—201no—
231C2×C4—121no—
232C2×C4—121no—
233C2×C4—151no—
234C2×C4—201no—
235C2×C4—201no—
236C2×C4—301no—
237C2×C4—301no—
238C2×C4#677711yescharacteristic
239C8—301no—
240C8#677311yescharacteristic
241C8#677911yescharacteristic
242C2×C3#6517111yescharacteristic
243C2×C3#6520111yescharacteristic
244C2×C3#6520711yescharacteristic
245D3—201no—
246C5#6921411yescharacteristic, complemented, Sylow
247C22—301no—
248C22—301no—
249C22—301no—
250C22#9125611yescharacteristic
251C4—241no—
252C4—241no—
253C4—301no—
254C4—401no—
255C4—401no—
256C4#9127811yescharacteristic
257C4#9135611yescharacteristic
258C3#1060012511yescharacteristic, complemented, Sylow
259C2—601no—
260C2#1174684111yescharacteristic
261C2#1174684211yescharacteristic
262C2#1174757111yescharacteristic
subgroupG/H
centerC22#91256
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×C16C22
socleC22×C3×C5C2×D8
prime radicalC22×D15D8
hypercenterC2×C16D3×D5
hypocenterC3×C5#2237
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
4. C5×#4504C2semidirect
5. C3×#64723C2semidirect
6. #11745943C2semidirect
7. #11745897C2semidirect
25. #64723D3semidirect
50. #4504D5semidirect
212. C3×C5#2237semidirect
246. C5#69214semidirect
258. C3#10600125semidirect

Maximal subgroups

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

subgroupindex
#117479582
#117476902
#117463282
C5×#45042
C3×#647232
#117459432
#117458972
#106001253
#692145