Finite Group Databasebeta

← #14291483

Subgroups — #14291483

Order 1920.

344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 99 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×C5×#494C211yesmaximal, characteristic, complemented
2#11751188C212yesmaximal
3C8×D60C211yesmaximal, characteristic
4#11746368C212yesmaximal, complemented
5#11746279C211yesmaximal, characteristic, complemented
6#10602098—31nomaximal, Hall
7C2×C3×C5×Q16—21no—
8C2×C3×C5×Q16—21no—
9C3×C5×C4⋊Q8C2212yes—
10C2×C8×D15—21no—
11C4×D60C2211yescharacteristic
12C3×C4×C5×C8C2211yescharacteristic
13#91104—21no—
14#91093—22no—
15#91091—22no—
16C4⋊(C3⋊#168)C2212yes—
17C4⋊(C3⋊#168)C2211yescharacteristic
18#71305—51nomaximal, Hall
19C5×#494D311yescharacteristic, complemented
20#65376—32no—
21C8×D20—31no—
22#64767—32no—
23#64678—31no—
24C2×C3×C5×Q8—22no—
25C2×D60D411yescharacteristic
26C2×C4×D15—21no—
27C3×C5×Q16—42no—
28C3×C5×Q16—42no—
29C2×C3×C5×C8D411yescharacteristic
30C2×C3×C5×C8D411yescharacteristic
31C3×C5×C4⋊C4—22no—
32C3×C5×C4⋊C4—22no—
33C3×C42×C5C2311yescharacteristic
34#6714—21no—
35C4⋊Dic15D411yescharacteristic
36C2×C3⋊#168—21no—
37C2×C3⋊#168—22no—
38C8×D15—42no—
39C3×#494D511yescharacteristic, complemented
40#5087—52no—
41C8×D12—51no—
42#4547—52no—
43#4458—51no—
44C2×C5×Q16—21no—
45C2×C5×Q16—21no—
46C5×C4⋊Q8C2×D312yes—
47C2×C8×D5—61no—
48C4×D20—31no—
49C4×C5×C8C2×D311yescharacteristic
50#3952—61no—
51#3941—62no—
52#3939—62no—
53C4⋊#168—32no—
54C4⋊#168—31no—
55#1669—151noSylow
56C22×D15—21no—
57C3×C5×Q8—42no—
58C3×C5×Q8—42no—
59C2×C3×C4×C5—42no—
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×C3×C4×C5C2×D411yescharacteristic
62C2×C3×C4×C5#4111yescharacteristic
63C2×Dic15—21no—
64D60—21no—
65D60Q1612yescomplemented
66C4×D15—41no—
67C4×D15—41no—
68C3×C5×C8—21no—
69C3×C5×C8D812yes—
70C3⋊#168—41no—
71C3⋊#168—42no—
72C2×C3×Q16—21no—
73C2×C3×Q16—21no—
74C3×C4⋊Q8C2×D512yes—
75C2×D3×C8—101no—
76C4×D12—51no—
77C3×C4×C8C2×D511yescharacteristic
78(C2×D3)⋊C8—101no—
79#809—102no—
80#807—102no—
81C4⋊(C3⋊C8)—51no—
82C4⋊(C3⋊C8)—52no—
83C2×C5×Q8—22no—
84C2×D20—31no—
85C2×C4×D5—61no—
86C5×Q16—42no—
87C5×Q16—42no—
88C2×C5×C8#6711yescharacteristic
89C2×C5×C8#6711yescharacteristic
90C5×C4⋊C4—22no—
91C5×C4⋊C4—22no—
92C42×C5C22×D311yescharacteristic
93#685—61no—
94C4⋊Dic5—31no—
95C2×#168—62no—
96C2×#168—61no—
97C8×D5—122no—
98#494D1511yescharacteristic, complemented
99#474—152no—
100C8×D4—151no—
101#335—151no—
102#332—152no—
103C22×C3×C5#12111yescharacteristic
104C2×D15—22no—
105C2×D15—41no—
106C2×D15—41no—
107C3×C4×C5—21no—
108C3×C4×C5—82no—
109C3×C4×C5C2×D811yescharacteristic
110C3×C4×C5C2×Q1611yescharacteristic
111C3×C4×C5#13511yescharacteristic
112C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
113Dic15—41no—
114C2×C3×Q8—22no—
115C2×D12—51no—
116C2×C4×D3—101no—
117C3×Q16—42no—
118C3×Q16—42no—
119C2×C3×C8C22⋊D511yescharacteristic
120C2×C3×C8C22⋊D511yescharacteristic
121C3×C4⋊C4—22no—
122C3×C4⋊C4—22no—
123C3×C42C22×D511yescharacteristic
124(C2×D3)⋊C4—101no—
125C4⋊Dic3—51no—
126C2×C3⋊C8—102no—
127C2×C3⋊C8—101no—
128D3×C8—202no—
129C22×D5—61no—
130C5×Q8—42no—
131C5×Q8—42no—
132C2×C4×C5—42no—
133C2×C4×C5D3×D411yescharacteristic
134C2×C4×C5#23711yescharacteristic
135C2×C4×C5C2×#6711yescharacteristic
136C2×Dic5—61no—
137D20—32no—
138D20—61no—
139C4×D5—121no—
140C4×D5—121no—
141C5×C8—21no—
142C5×C8#21312yes—
143#168—122no—
144#168—121no—
145C2×Q16—21no—
146C2×Q16—21no—
147C22×C8—301no—
148C4⋊Q8C2×D1512yes—
149C4×D4—151no—
150#107—302no—
151C4⋊C8—151no—
152C4⋊C8—152no—
153#102—302no—
154C22⋊C8—301no—
155C4×C8C2×D1511yescharacteristic
156C2×C3×C5#45911yescharacteristic
157C2×C3×C5#46711yescharacteristic
158C2×C3×C5#47311yescharacteristic
159D15—42no—
160C22×D3—101no—
161C3×Q8—42no—
162C3×Q8—42no—
163C2×C3×C4—42no—
164C2×C3×C4D4×D511yescharacteristic
165C2×C3×C4#71111yescharacteristic
166C2×C3×C4C2×C22⋊D511yescharacteristic
167C2×Dic3—101no—
168D12—52no—
169D12—101no—
170C4×D3—201no—
171C4×D3—201no—
172C3×C8—21no—
173C3×C8#68612yes—
174C3⋊C8—202no—
175C3⋊C8—201no—
176C22×C5#93811yescharacteristic
177C2×D5—62no—
178C2×D5—121no—
179C2×D5—121no—
180C4×C5—21no—
181C4×C5—82no—
182C4×C5D3×Q1611yescharacteristic
183C4×C5#91911yescharacteristic
184C4×C5C2×#21311yescharacteristic
185C4×C5#93211yescharacteristic
186Dic5—121no—
187C2×Q8—22no—
188C2×D4—151no—
189C22×C4—301no—
190Q16—42no—
191Q16—42no—
192C2×C8—302no—
193C2×C8—301no—
194C2×C8—602no—
195C2×C8#122011yescharacteristic
196C2×C8#122011yescharacteristic
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—151no—
200C22⋊C4—301no—
201C42C22×D1511yescharacteristic
202C3×C5#166911yescharacteristic, complemented, Hall
203C22×C3#408411yescharacteristic
204C2×D3—102no—
205C2×D3—201no—
206C2×D3—201no—
207C3×C4—21no—
208C3×C4—82no—
209C3×C4D5×Q1611yescharacteristic
210C3×C4#406511yescharacteristic
211C3×C4C2×#68611yescharacteristic
212C3×C4#407811yescharacteristic
213Dic3—201no—
214C2×C5#507211yescharacteristic
215C2×C5#518811yescharacteristic
216C2×C5#519211yescharacteristic
217D5—122no—
218C23—301no—
219Q8—42no—
220Q8—42no—
221D4—152no—
222D4—301no—
223C2×C4—42no—
224C2×C4—301no—
225C2×C4—601no—
226C2×C4—601no—
227C2×C4D4×D1511yescharacteristic
228C2×C4#681911yescharacteristic
229C2×C4C2×#122011yescharacteristic
230C8—21no—
231C8—602no—
232C8—601no—
233C8#671512yes—
234C2×C3#6536111yescharacteristic
235C2×C3#6547711yescharacteristic
236C2×C3#6548111yescharacteristic
237D3—202no—
238C5#7130511yescharacteristic, complemented, Sylow
239C22—302no—
240C22—601no—
241C22—601no—
242C22#9182711yescharacteristic
243C4—21no—
244C4—82no—
245C4—601no—
246C4Q16×D1511yescharacteristic
247C4#9180811yescharacteristic
248C4C2×#671511yescharacteristic
249C4#9182111yescharacteristic
250C3#1060209811yescharacteristic, complemented, Sylow
251C2—602no—
252C2#1175117311yescharacteristic
253C2#1175128911yescharacteristic
254C2#1175129311yescharacteristic
subgroupG/H
centerC22#91827
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#494C2
socleC22×C3×C5#121
prime radicalC2×D60D4
hypercenter#494D15
hypocenterC3×C5#1669
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. C3×C5×#494C2semidirect
4. #11746368C2semidirect
5. #11746279C2semidirect
19. C5×#494D3semidirect
39. C3×#494D5semidirect
65. D60Q16semidirect
98. #494D15semidirect
202. C3×C5#1669semidirect
238. C5#71305semidirect
250. C3#10602098semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4942
#117511882
C8×D602
#117463682
#117462792
#106020983
#713055