Finite Group Databasebeta

← #14292551

Subgroups — #14292551

Order 1920.

332 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 97 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
3#11750789C211yesmaximal, characteristic
4#11746368C212yesmaximal, complemented
5#11746278C211yesmaximal, characteristic, complemented
6#10602099—31nomaximal, Hall
7C2×C3×C5×Q16—21no—
8C2×C3×C5×Q16—21no—
9C3×C5×C4⋊Q8C2212yes—
10C2×#6705—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#71306—51nomaximal, Hall
19C5×#494D311yescharacteristic, complemented
20#65376—32no—
21#64977—31no—
22#64767—32no—
23#64677—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—
38#6705—42no—
39C3×#494D511yescharacteristic, complemented
40#5087—52no—
41#4688—51no—
42#4547—52no—
43#4457—51no—
44C2×C5×Q16—21no—
45C2×C5×Q16—21no—
46C5×C4⋊Q8C2×D312yes—
47C2×#676—61no—
48C4×D20—31no—
49C4×C5×C8C2×D311yescharacteristic
50#3952—61no—
51#3941—62no—
52#3939—62no—
53C4⋊#168—32no—
54C4⋊#168—31no—
55#1689—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—22no—
65C4×D15—41no—
66C4×D15—41no—
67C3×C5×C8—21no—
68C3×C5×C8D812yes—
69C3⋊#168—41no—
70C3⋊#168—42no—
71C2×C3×Q16—21no—
72C2×C3×Q16—21no—
73C3×C4⋊Q8C2×D512yes—
74C2×ΓL(1,𝔽25)—101no—
75C4×D12—51no—
76C3×C4×C8C2×D511yescharacteristic
77(C2×D3)⋊C8—101no—
78#809—102no—
79#807—102no—
80C4⋊(C3⋊C8)—51no—
81C4⋊(C3⋊C8)—52no—
82C2×C5×Q8—22no—
83C2×D20—31no—
84C2×C4×D5—61no—
85C5×Q16—42no—
86C5×Q16—42no—
87C2×C5×C8#6711yescharacteristic
88C2×C5×C8#6711yescharacteristic
89C5×C4⋊C4—22no—
90C5×C4⋊C4—22no—
91C42×C5C22×D311yescharacteristic
92#685—61no—
93C4⋊Dic5—31no—
94C2×#168—62no—
95C2×#168—61no—
96#676—122no—
97#494D1511yescharacteristic, complemented
98#474—152no—
99#436—151no—
100#334—151no—
101#332—152no—
102C22×C3×C5#12111yescharacteristic
103C2×D15—41no—
104C2×D15—41no—
105C2×D15—41no—
106C3×C4×C5—21no—
107C3×C4×C5—82no—
108C3×C4×C5C2×D811yescharacteristic
109C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
110C3×C4×C5#13712yes—
111Dic15—41no—
112C2×C3×Q8—22no—
113C2×D12—51no—
114C2×C4×D3—101no—
115C3×Q16—42no—
116C3×Q16—42no—
117C2×C3×C8C22⋊D511yescharacteristic
118C2×C3×C8C22⋊D511yescharacteristic
119C3×C4⋊C4—22no—
120C3×C4⋊C4—22no—
121C3×C42C22×D511yescharacteristic
122(C2×D3)⋊C4—101no—
123C4⋊Dic3—51no—
124C2×C3⋊C8—102no—
125C2×C3⋊C8—101no—
126ΓL(1,𝔽25)—202no—
127C22×D5—61no—
128C5×Q8—42no—
129C5×Q8—42no—
130C2×C4×C5—42no—
131C2×C4×C5D3×D411yescharacteristic
132C2×C4×C5#23711yescharacteristic
133C2×C4×C5C2×#6711yescharacteristic
134C2×Dic5—61no—
135D20—62no—
136C4×D5—121no—
137C4×D5—121no—
138C5×C8—21no—
139C5×C8#21312yes—
140#168—122no—
141#168—121no—
142C2×Q16—21no—
143C2×Q16—21no—
144C2×M16—301no—
145C4⋊Q8C2×D1512yes—
146C4×D4—151no—
147#107—302no—
148C4⋊C8—151no—
149C4⋊C8—152no—
150#102—302no—
151C22⋊C8—301no—
152C4×C8C2×D1511yescharacteristic
153C2×C3×C5#45911yescharacteristic
154C2×C3×C5#47011yescharacteristic
155C2×C3×C5#47311yescharacteristic
156D15—81no—
157C22×D3—101no—
158C3×Q8—42no—
159C3×Q8—42no—
160C2×C3×C4—42no—
161C2×C3×C4D4×D511yescharacteristic
162C2×C3×C4#71111yescharacteristic
163C2×C3×C4C2×C22⋊D511yescharacteristic
164C2×Dic3—101no—
165D12—102no—
166C4×D3—201no—
167C4×D3—201no—
168C3×C8—21no—
169C3×C8#68612yes—
170C3⋊C8—202no—
171C3⋊C8—201no—
172C22×C5#93811yescharacteristic
173C2×D5—121no—
174C2×D5—121no—
175C2×D5—121no—
176C4×C5—21no—
177C4×C5—82no—
178C4×C5#91812yes—
179C4×C5C2×#21311yescharacteristic
180C4×C5#93211yescharacteristic
181Dic5—121no—
182C2×Q8—22no—
183C2×D4—151no—
184C22×C4—301no—
185Q16—42no—
186Q16—42no—
187M16—602no—
188C2×C8—302no—
189C2×C8—301no—
190C2×C8#122011yescharacteristic
191C2×C8#122011yescharacteristic
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—151no—
195C22⋊C4—301no—
196C42C22×D1511yescharacteristic
197C3×C5#168911yescharacteristic, complemented, Hall
198C22×C3#408411yescharacteristic
199C2×D3—201no—
200C2×D3—201no—
201C2×D3—201no—
202C3×C4—21no—
203C3×C4—82no—
204C3×C4#406412yes—
205C3×C4C2×#68611yescharacteristic
206C3×C4#407811yescharacteristic
207Dic3—201no—
208C2×C5#507211yescharacteristic
209C2×C5#518911yescharacteristic
210C2×C5#519211yescharacteristic
211D5—241no—
212C23—301no—
213Q8—42no—
214Q8—42no—
215D4—302no—
216C2×C4—42no—
217C2×C4—301no—
218C2×C4—601no—
219C2×C4—601no—
220C2×C4D4×D1511yescharacteristic
221C2×C4#681911yescharacteristic
222C2×C4C2×#122011yescharacteristic
223C8—21no—
224C8—602no—
225C8—601no—
226C8#671512yes—
227C2×C3#6536111yescharacteristic
228C2×C3#6547811yescharacteristic
229C2×C3#6548111yescharacteristic
230D3—401no—
231C5#7130611yescharacteristic, complemented, Sylow
232C22—601no—
233C22—601no—
234C22—601no—
235C22#9182711yescharacteristic
236C4—21no—
237C4—82no—
238C4—601no—
239C4#9180712yes—
240C4C2×#671511yescharacteristic
241C4#9182111yescharacteristic
242C3#1060209911yescharacteristic, complemented, Sylow
243C2—1201no—
244C2#1175117311yescharacteristic
245C2#1175129011yescharacteristic
246C2#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#1689
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. #11746278C2semidirect
19. C5×#494D3semidirect
39. C3×#494D5semidirect
97. #494D15semidirect
197. C3×C5#1689semidirect
231. C5#71306semidirect
242. C3#10602099semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4942
#117511882
#117507892
#117463682
#117462782
#106020993
#713065