Finite Group Databasebeta

← #14318558

Subgroups — #14318558

Order 1920.

248 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 67 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#11751290C211yesmaximal, characteristic
2#11750994C211yesmaximal, characteristic
3C3×C5×#362C211yesmaximal, characteristic, complemented
4#11746386C211yesmaximal, characteristic, complemented
5#11746335C211yesmaximal, characteristic
6#11746334C211yesmaximal, characteristic, complemented
7#11746315C211yesmaximal, characteristic, complemented
8#10600060—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10#91835—21no—
11M16×D15—21no—
12C2×#6705C2211yescharacteristic
13C3×C5×M32C2211yescharacteristic
14C3×C5×#108C2211yescharacteristic
15#91119—21no—
16#91106—21no—
17#91103C2211yescharacteristic
18#91101C2211yescharacteristic
19#91096C2211yescharacteristic
20#69267—51nomaximal, Hall
21#65478—31no—
22#65182—31no—
23C5×#362D311yescharacteristic, complemented
24#64785—31no—
25#64734—31no—
26#64733—31no—
27#64714—31no—
28C2×C3×C5×Q8—21no—
29C2×C4×D15D411yescharacteristic
30C3×C5×Q16—21no—
31C3×C5×Q16—21no—
32C3×C5×M16—21no—
33C2×C3×C5×C8C2311yescharacteristic
34#6714—41no—
35C4⋊Dic15—21no—
36#6712—41no—
37#6710—21no—
38C2×C3⋊#168D411yescharacteristic
39#6705—21no—
40#6705—21no—
41#6705—41no—
42C8×D15—41no—
43C3×C5×C16—21no—
44C3⋊#672—21no—
45#5189—51no—
46#4893—51no—
47C3×#362D511yescharacteristic, complemented
48#4565—51no—
49#4514—51no—
50#4513—51no—
51#4494—51no—
52C2×C5×Q16C2×D311yescharacteristic
53#4092—61no—
54D5×M16—61no—
55C2×#676—31no—
56C5×M32C2×D311yescharacteristic
57C5×#108C2×D311yescharacteristic
58#3967—61no—
59#3954—61no—
60#3951—31no—
61#3949—31no—
62#3944—31no—
63#2239—151noSylow
64C22×D15SD1611yescharacteristic
65C3×C5×Q8—41no—
66C3×C5×Q8—41no—
67C2×C3×C4×C5—41no—
68C2×C3×C4×C5C2×D411yescharacteristic
69C2×Dic15—41no—
70C2×Dic15SD1611yescharacteristic
71C4×D15—21no—
72C4×D15—21no—
73C3×C5×C8—41no—
74C3×C5×C8#4111yescharacteristic
75C3×C5×C8#4111yescharacteristic
76C3⋊#168—21no—
77C3⋊#168—41no—
78C2×C3×Q16C2×D511yescharacteristic
79#946—101no—
80D3×M16—101no—
81C2×ΓL(1,𝔽25)—51no—
82C3×M32C2×D511yescharacteristic
83C3×#108C2×D511yescharacteristic
84#835—101no—
85#822—101no—
86#819—51no—
87#817—51no—
88#812—51no—
89C2×C5×Q8—21no—
90C2×C4×D5—31no—
91C5×Q16—21no—
92C5×Q16—21no—
93C5×M16—21no—
94C2×C5×C8C22×D311yescharacteristic
95#685—121no—
96C4⋊Dic5—61no—
97#683—121no—
98#681—61no—
99C2×#168—31no—
100#676—61no—
101#676—61no—
102#676—121no—
103C8×D5—121no—
104C5×C16—21no—
105#672—61no—
106#470—151no—
107#430—151no—
108#365—151no—
109#365—151no—
110#362—151no—
111#362D1511yescharacteristic, complemented
112#349—151no—
113C22×C3×C5C2×SD1611yescharacteristic
114C2×D15—21no—
115C2×D15—41no—
116C3×C4×C5—81no—
117C3×C4×C5#12311yescharacteristic
118C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
119Dic15—21no—
120Dic15—81no—
121C2×C3×Q8—21no—
122C2×C4×D3—51no—
123C3×Q16—21no—
124C3×Q16—21no—
125C3×M16—21no—
126C2×C3×C8C22×D511yescharacteristic
127(C2×D3)⋊C4—201no—
128C4⋊Dic3—101no—
129Dic3⋊C4—201no—
130#208—101no—
131C2×C3⋊C8—51no—
132ΓL(1,𝔽25)—101no—
133ΓL(1,𝔽25)—101no—
134ΓL(1,𝔽25)—201no—
135D3×C8—201no—
136C3×C16—21no—
137C3⋊C16—101no—
138C22×D5—31no—
139C5×Q8—41no—
140C5×Q8—41no—
141C2×C4×C5—41no—
142C2×C4×C5D3×D411yescharacteristic
143C2×Dic5—31no—
144C2×Dic5—121no—
145C4×D5—61no—
146C4×D5—61no—
147C5×C8—41no—
148C5×C8#23511yescharacteristic
149C5×C8#23711yescharacteristic
150#168—61no—
151#168—121no—
152C2×Q16C2×D1511yescharacteristic
153C2×M16—151no—
154C2×M16—301no—
155C22⋊Q8—301no—
156M32—151no—
157M32C2×D1511yescharacteristic
158#108—151no—
159#108—301no—
160#108C2×D1511yescharacteristic
161#106—151no—
162#103—301no—
163C2×C3×C5—21no—
164C2×C3×C5#48111yescharacteristic
165D15—41no—
166C22×D3—51no—
167C3×Q8—41no—
168C3×Q8—41no—
169C2×C3×C4—41no—
170C2×C3×C4D4×D511yescharacteristic
171C2×Dic3—51no—
172C2×Dic3—201no—
173C4×D3—101no—
174C4×D3—101no—
175C3×C8—41no—
176C3×C8#70911yescharacteristic
177C3×C8#71111yescharacteristic
178C3⋊C8—101no—
179C3⋊C8—201no—
180C22×C5D3×SD1611yescharacteristic
181C2×D5—61no—
182C2×D5—121no—
183C4×C5—81no—
184C4×C5#88311yescharacteristic
185C4×C5#91111yescharacteristic
186Dic5—61no—
187Dic5—241no—
188C2×Q8—21no—
189C22×C4—151no—
190Q16—21no—
191Q16—21no—
192M16—21no—
193M16—301no—
194M16—301no—
195M16—301no—
196M16—601no—
197C2×C8—151no—
198C2×C8—601no—
199C2×C8C22×D1511yescharacteristic
200C4⋊C4—301no—
201C4⋊C4—601no—
202C22⋊C4—601no—
203C16—21no—
204C16—301no—
205C3×C5#223911yescharacteristic, complemented, Hall
206C22×C3D5×SD1611yescharacteristic
207C2×D3—101no—
208C2×D3—201no—
209C3×C4—81no—
210C3×C4#402911yescharacteristic
211C3×C4#405711yescharacteristic
212Dic3—101no—
213Dic3—401no—
214C2×C5—21no—
215C2×C5#477711yescharacteristic
216D5—121no—
217C23—151no—
218Q8—41no—
219Q8—41no—
220C2×C4—41no—
221C2×C4—151no—
222C2×C4—301no—
223C2×C4—301no—
224C2×C4—601no—
225C2×C4D4×D1511yescharacteristic
226C8—41no—
227C8—301no—
228C8—601no—
229C8#681711yescharacteristic
230C8#681911yescharacteristic
231C2×C3—21no—
232C2×C3#6506611yescharacteristic
233D3—201no—
234C5#6926711yescharacteristic, complemented, Sylow
235C22—301no—
236C22—601no—
237C22SD16×D1511yescharacteristic
238C4—81no—
239C4—301no—
240C4—1201no—
241C4#9177211yescharacteristic
242C4#9180011yescharacteristic
243C3#1060006011yescharacteristic, complemented, Sylow
244C2—21no—
245C2—601no—
246C2#1175087811yescharacteristic
subgroupG/H
centerC2#11750878
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#362C2
socleC2×C3×C5#481
prime radicalC22×D15SD16
hypercenter#362D15
hypocenterC3×C5#2239
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
3. C3×C5×#362C2semidirect
4. #11746386C2semidirect
6. #11746334C2semidirect
7. #11746315C2semidirect
23. C5×#362D3semidirect
47. C3×#362D5semidirect
111. #362D15semidirect
205. C3×C5#2239semidirect
234. C5#69267semidirect
243. C3#10600060semidirect

Maximal subgroups

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

subgroupindex
#117512902
#117509942
C3×C5×#3622
#117463862
#117463352
#117463342
#117463152
#106000603
#692675