Finite Group Databasebeta

← #14315786

Subgroups — #14315786

Order 1920.

284 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 76 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#11748073C211yesmaximal, characteristic
2#11747884C211yesmaximal, characteristic, complemented
3#11747552C211yesmaximal, characteristic
4#11746333C211yesmaximal, characteristic, complemented
5C5×#4518C211yesmaximal, characteristic
6C3×#64737C211yesmaximal, characteristic, complemented
7#11745936C211yesmaximal, characteristic, complemented
8#10600041—31nomaximal, Hall
9C5×#904C2211yescharacteristic
10C2×C3×Dic20C2211yescharacteristic
11#91331—21no—
12#91288—21no—
13C3×C5×M32C2211yescharacteristic
14#91099C2211yescharacteristic
15#91096C2211yescharacteristic
16C5×#817C2211yescharacteristic
17C3×#3951C2211yescharacteristic
18#90978—21no—
19#90970—21no—
20#90946C412yescomplemented
21#90941C412yescomplemented
22#69264—51nomaximal, Hall
23#65486—31no—
24#65484—31no—
25#65142—31no—
26C5×#360—31no—
27#64737D311yescharacteristic, complemented
28#64732—31no—
29#64707—31no—
30C5×#235—21no—
31C2×C3×Dic10—21no—
32C2×C3×C5×C8C2311yescharacteristic
33C4×Dic15D411yescharacteristic
34C2×C3⋊#168D411yescharacteristic
35C5×C4⋊Dic3—21no—
36C5×Dic12C2×C411yescharacteristic
37C5×D24C2×C411yescharacteristic
38C5×#204—21no—
39C3×#681—21no—
40C3×Dic20—21no—
41C3×Dic20C2×C412yes—
42#6668—41no—
43Dic3×Dic5—41no—
44#6650—41no—
45D3×#168—41no—
46C3×C5×C16—21no—
47C3⋊#672C2×C412yes—
48#5184—51no—
49#5179—51no—
50#4894—51no—
51C3×#362—51no—
52#4518D511yescharacteristic
53#4512—51no—
54#4494—51no—
55C5×#135—31no—
56#4094—61no—
57C2×Dic20C2×D311yescharacteristic
58#4033—61no—
59C5×M32C2×D311yescharacteristic
60C5×#106—31no—
61#3969—61no—
62#3961—32no—
63#3959—32no—
64#3951C2×D311yescharacteristic
65#3947—31no—
66#3944—31no—
67#3942—61no—
68#2180—151noSylow
69C2×C3×C4×C5C2×D411yescharacteristic
70C2×Dic15—21no—
71C5×#67—41no—
72C2×C5×Dic3—41no—
73C5×D12—21no—
74C4×C5×D3—41no—
75C5×Dic6—21no—
76C2×C3×Dic5—41no—
77C3×Dic10—22no—
78C3×Dic10—41no—
79C3×C5×C8C22×C411yescharacteristic
80C3×C5×C8#4111yescharacteristic
81C3⋊#168—21no—
82C3×#168—41no—
83C2×C3×Q16—51no—
84Q8×Dic3—101no—
85#907—101no—
86#904C2×D511yescharacteristic
87C3×M32C2×D511yescharacteristic
88C3×#108—51no—
89#835—101no—
90#829—52no—
91#828—52no—
92#825—101no—
93#817C2×D511yescharacteristic
94#815—51no—
95#812—51no—
96C5×#41—61no—
97C2×Dic10—21no—
98C5×Q16—31no—
99C5×SD16—61no—
100C5×D8—31no—
101C2×C5×C8C22×D311yescharacteristic
102C5×C4⋊C4—61no—
103#683—121no—
104C4×Dic5—31no—
105C4×Dic5—121no—
106#681—21no—
107#681—121no—
108C2×#168—31no—
109C2×#168—121no—
110Dic20—21no—
111Dic20C4×D312yes—
112C5×C16—21no—
113#672—32no—
114#510—151no—
115#444—151no—
116#441—151no—
117#365—151no—
118#362—51no—
119#360—31no—
120#347—151no—
121C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
122C2×C5×D3—41no—
123C3×C4×C5C4×D411yescharacteristic
124C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
125Dic15—41no—
126C3×Dic5—42no—
127C5×Dic3—41no—
128C5×Dic3—81no—
129C2×C3×Q8—101no—
130#235—21no—
131C3×Q16—52no—
132C3×Q16—101no—
133C3×M16—101no—
134C2×C3×C8C22×D511yescharacteristic
135C4⋊Dic3—21no—
136C4⋊Dic3—201no—
137C4×Dic3—51no—
138C4×Dic3—201no—
139C2×C3⋊C8—51no—
140Dic12C4×D511yescharacteristic
141D24C4×D511yescharacteristic
142#204—21no—
143ΓL(1,𝔽25)—201no—
144D3×C8—201no—
145C3×C16—21no—
146C3⋊C16—52no—
147C5×Q8—61no—
148C5×D4—61no—
149C5×D4—121no—
150C2×C4×C5—121no—
151C2×C4×C5—121no—
152C2×C4×C5D3×D411yescharacteristic
153C2×Dic5—41no—
154C2×Dic5—61no—
155Dic10—22no—
156Dic10—41no—
157C5×C8C2×C4×D311yescharacteristic
158C5×C8#23711yescharacteristic
159#168—41no—
160#168—61no—
161#135—31no—
162C2×Q16—51no—
163#131—301no—
164C4×Q8—301no—
165Q32—152no—
166SD32—152no—
167M32—151no—
168M32D3×D511yescharacteristic
169#108—51no—
170#106—31no—
171#104—301no—
172#103—301no—
173#97—151no—
174C2×C3×C5—21no—
175C2×C3×C5#44211yescharacteristic
176C5×D3—81no—
177C3×Q8—102no—
178C3×Q8—201no—
179C2×C3×C4—201no—
180C2×C3×C4D4×D511yescharacteristic
181#67—41no—
182C2×Dic3—41no—
183C2×Dic3—101no—
184D12—21no—
185C4×D3—41no—
186Dic6—21no—
187C3×C8—201no—
188C3×C8C2×C4×D511yescharacteristic
189C3×C8#71111yescharacteristic
190C3⋊C8—101no—
191C22×C5—121no—
192C22×C5#91411yescharacteristic
193C4×C5—121no—
194C4×C5—241no—
195C4×C5#67⋊C411yescharacteristic
196C4×C5#91111yescharacteristic
197Dic5—42no—
198Dic5—121no—
199#41—61no—
200C2×Q8—101no—
201Q16—31no—
202Q16—52no—
203Q16—101no—
204SD16—61no—
205D8—31no—
206M16—101no—
207M16—601no—
208C2×C8—151no—
209C2×C8—601no—
210C2×C8C2×D3×D511yescharacteristic
211C4⋊C4—61no—
212C4⋊C4—601no—
213C42—151no—
214C42—601no—
215C16—21no—
216C16—152no—
217C3×C5#218011yescharacteristic, complemented, Hall
218C22×C3#405711yescharacteristic
219C2×D3—41no—
220C3×C4—202no—
221C3×C4#402711yescharacteristic
222C3×C4#406011yescharacteristic
223Dic3—41no—
224Dic3—81no—
225Dic3—201no—
226C2×C5—21no—
227C2×C5—241no—
228C2×C5#478511yescharacteristic
229Q8—61no—
230Q8—102no—
231Q8—201no—
232D4—61no—
233D4—121no—
234C2×C4—121no—
235C2×C4—121no—
236C2×C4—201no—
237C2×C4—301no—
238C2×C4#677711yescharacteristic
239C8—201no—
240C8—301no—
241C8C4×D3×D511yescharacteristic
242C8#678011yescharacteristic
243C2×C3—21no—
244C2×C3#6507411yescharacteristic
245D3—81no—
246C5#6926411yescharacteristic, complemented, Sylow
247C22—121no—
248C22#9125711yescharacteristic
249C4—121no—
250C4—202no—
251C4—241no—
252C4—601no—
253C4#9125811yescharacteristic
254C4#9144211yescharacteristic
255C3#1060004111yescharacteristic, complemented, Sylow
256C2—21no—
257C2—241no—
258C2#1174773411yescharacteristic
subgroupG/H
centerC2#11747734
commutatorC3×C5×C8C22×C4
FrattiniC2×C8C2×D3×D5
FittingC3×C5×M32C22
socleC2×C3×C5#442
prime radicalC5×#904C22
cosocleC2×C3×C5×C8C23
hypercenterM32D3×D5
hypocenterC3×C5#2180
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
2. #11747884C2semidirect
4. #11746333C2semidirect
6. C3×#64737C2semidirect
7. #11745936C2semidirect
20. #90946C4semidirect
21. #90941C4semidirect
27. #64737D3semidirect
217. C3×C5#2180semidirect
246. C5#69264semidirect
255. C3#10600041semidirect

Maximal subgroups

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

subgroupindex
#117480732
#117478842
#117475522
#117463332
C5×#45182
C3×#647372
#117459362
#106000413
#692645