Finite Group Databasebeta

← #14317310

Subgroups — #14317310

Order 1920.

308 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 81 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×#495C211yesmaximal, characteristic, complemented
2#11751280C211yesmaximal, characteristic, complemented
3#11751248C211yesmaximal, characteristic
4#11750801C211yesmaximal, characteristic, complemented
5#11746386C211yesmaximal, characteristic, complemented
6#11746384C211yesmaximal, characteristic, complemented
7#11746284C211yesmaximal, characteristic, complemented
8#10602118—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10C2×C3×C5×SD16—21no—
11C2×C3×C5×D8C2211yescharacteristic
12C3×C5×#124—21no—
13#91793C2211yescharacteristic
14#91790—21no—
15C3×C4×C5×C8C2211yescharacteristic
16#91113—21no—
17#91112—21no—
18#91111—21no—
19#91110—21no—
20#91103C2211yescharacteristic
21#91096C2211yescharacteristic
22#91096C2211yescharacteristic
23#91089—21no—
24#71325—51nomaximal, Hall
25C5×#495D311yescharacteristic, complemented
26#65468—31no—
27#65436—31no—
28#64989—31no—
29#64785—31no—
30#64783—31no—
31#64683—31no—
32C2×C3×C5×Q8—21no—
33C2×C3×C5×D4—21no—
34#6817—21no—
35C3×C5×Q16—21no—
36C3×C5×Q16—21no—
37C3×C5×SD16—41no—
38C3×C5×SD16—41no—
39C3×C5×D8—21no—
40C3×C5×D8—21no—
41C2×C3×C5×C8D411yescharacteristic
42C2×C3×C5×C8C2311yescharacteristic
43C3×C5×C22⋊C4—42no—
44C3×C42×C5D411yescharacteristic
45#6710—21no—
46Dic60D411yescharacteristic
47D120D411yescharacteristic
48#6706—21no—
49#6705—41no—
50C8×D15—41no—
51C3⋊#672—21no—
52C3⋊#672—21no—
53C3×#495D511yescharacteristic, complemented
54#5179—51no—
55#5147—51no—
56#4700—51no—
57#4565—51no—
58#4563—51no—
59#4463—51no—
60C2×C5×Q16C2×D311yescharacteristic
61C2×C5×SD16—21no—
62C2×C5×D8C2×D311yescharacteristic
63C5×#124—21no—
64#4050—31no—
65#4047—61no—
66C4×C5×C8C2×D311yescharacteristic
67#3961—61no—
68#3960—61no—
69#3959—61no—
70#3958—61no—
71#3951—31no—
72#3944—31no—
73#3944—31no—
74#3937—61no—
75#2212—151noSylow
76C23×C3×C5—41no—
77C3×C5×Q8—41no—
78C3×C5×Q8—41no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C2×C3×C4×C5—21no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C2×D411yescharacteristic
84#1220—41no—
85D60—21no—
86C4×D15—41no—
87Dic30—21no—
88C3×C5×C8D811yescharacteristic
89C3×C5×C8D811yescharacteristic
90C3×C5×C8C2×D411yescharacteristic
91C3×C5×C8#4111yescharacteristic
92C3⋊#168—41no—
93C2×C3×Q16C2×D511yescharacteristic
94C2×C3×SD16—21no—
95C2×C3×D8C2×D511yescharacteristic
96C3×#124—21no—
97#904—51no—
98#901—101no—
99C3×C4×C8C2×D511yescharacteristic
100#829—101no—
101#828—101no—
102#827—101no—
103#826—101no—
104#819—51no—
105#812—51no—
106#812—51no—
107#805—101no—
108C2×C5×Q8—21no—
109C2×C5×D4—21no—
110#709—61no—
111C5×Q16—21no—
112C5×Q16—21no—
113C5×SD16—41no—
114C5×SD16—41no—
115C5×D8—21no—
116C5×D8—21no—
117C2×C5×C8#6711yescharacteristic
118C2×C5×C8C22×D311yescharacteristic
119C5×C22⋊C4—42no—
120C42×C5#6711yescharacteristic
121#681—61no—
122Dic20—31no—
123D40—31no—
124#677—61no—
125#676—121no—
126C8×D5—121no—
127#672—61no—
128#672—61no—
129#510—151no—
130#509—151no—
131#495D1511yescharacteristic, complemented
132#443—151no—
133#364—151no—
134#362—151no—
135#361—151no—
136C22×C3×C5—82no—
137C22×C3×C5—81no—
138C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
139C2×D15—41no—
140C3×C4×C5—41no—
141C3×C4×C5—81no—
142C3×C4×C5#12111yescharacteristic
143C3×C4×C5C2×D811yescharacteristic
144Dic15—41no—
145C2×C3×Q8—21no—
146C2×C3×D4—21no—
147#235—101no—
148C3×Q16—21no—
149C3×Q16—21no—
150C3×SD16—41no—
151C3×SD16—41no—
152C3×D8—21no—
153C3×D8—21no—
154C2×C3×C8C22⋊D511yescharacteristic
155C2×C3×C8C22×D511yescharacteristic
156C3×C22⋊C4—42no—
157C3×C42C22⋊D511yescharacteristic
158#208—101no—
159Dic12—51no—
160D24—51no—
161#204—101no—
162ΓL(1,𝔽25)—201no—
163D3×C8—201no—
164C3⋊C16—101no—
165C3⋊C16—101no—
166C23×C5—41no—
167C5×Q8—41no—
168C5×Q8—41no—
169C5×D4—41no—
170C5×D4—41no—
171C2×C4×C5—21no—
172C2×C4×C5—41no—
173C2×C4×C5C2×#6711yescharacteristic
174C22⋊D5—121no—
175D20—61no—
176C4×D5—121no—
177Dic10—61no—
178C5×C8#21311yescharacteristic
179C5×C8#21311yescharacteristic
180C5×C8D3×D411yescharacteristic
181C5×C8#23711yescharacteristic
182#168—121no—
183#135—151no—
184C2×Q16C2×D1511yescharacteristic
185C2×SD16—21no—
186C2×D8C2×D1511yescharacteristic
187#131—301no—
188#124—21no—
189Q32—301no—
190SD32—301no—
191SD32—301no—
192D16—301no—
193M32—151no—
194M32—151no—
195#108—151no—
196#104—301no—
197C4×C8C2×D1511yescharacteristic
198C2×C3×C5—21no—
199C2×C3×C5—161no—
200C2×C3×C5#45911yescharacteristic
201D15—81no—
202C23×C3—41no—
203C3×Q8—41no—
204C3×Q8—41no—
205C3×D4—41no—
206C3×D4—41no—
207C2×C3×C4—21no—
208C2×C3×C4—41no—
209C2×C3×C4C2×C22⋊D511yescharacteristic
210#67—201no—
211D12—101no—
212C4×D3—201no—
213Dic6—101no—
214C3×C8#68611yescharacteristic
215C3×C8#68611yescharacteristic
216C3×C8D4×D511yescharacteristic
217C3×C8#71111yescharacteristic
218C3⋊C8—201no—
219C22×C5—82no—
220C22×C5—81no—
221C22×C5#93211yescharacteristic
222C2×D5—121no—
223C4×C5—41no—
224C4×C5—81no—
225C4×C5C2×#21311yescharacteristic
226C4×C5#93811yescharacteristic
227Dic5—121no—
228#41—301no—
229C2×Q8—21no—
230C2×D4—21no—
231Q16—21no—
232Q16—21no—
233Q16—151no—
234SD16—41no—
235SD16—41no—
236SD16—301no—
237D8—21no—
238D8—21no—
239D8—151no—
240M16—301no—
241M16—601no—
242C2×C8—601no—
243C2×C8#122011yescharacteristic
244C2×C8C22×D1511yescharacteristic
245C22⋊C4—42no—
246C42#122011yescharacteristic
247C16—301no—
248C16—301no—
249C3×C5#221211yescharacteristic, complemented, Hall
250C22×C3—82no—
251C22×C3—81no—
252C22×C3#407811yescharacteristic
253C2×D3—201no—
254C3×C4—41no—
255C3×C4—81no—
256C3×C4C2×#68611yescharacteristic
257C3×C4#408411yescharacteristic
258Dic3—201no—
259C2×C5—21no—
260C2×C5—161no—
261C2×C5#507211yescharacteristic
262D5—241no—
263C23—41no—
264Q8—41no—
265Q8—41no—
266Q8—301no—
267D4—41no—
268D4—41no—
269D4—301no—
270D4—601no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—601no—
274C2×C4C2×#122011yescharacteristic
275C8—601no—
276C8#671511yescharacteristic
277C8#671511yescharacteristic
278C8D4×D1511yescharacteristic
279C8#681911yescharacteristic
280C2×C3—21no—
281C2×C3—161no—
282C2×C3#6536111yescharacteristic
283D3—401no—
284C5#7132511yescharacteristic, complemented, Sylow
285C22—82no—
286C22—81no—
287C22—601no—
288C22#9182111yescharacteristic
289C4—41no—
290C4—81no—
291C4—601no—
292C4C2×#671511yescharacteristic
293C4#9182711yescharacteristic
294C3#1060211811yescharacteristic, complemented, Sylow
295C2—21no—
296C2—161no—
297C2—1201no—
298C2#1175117311yescharacteristic
subgroupG/H
centerC2#11751173
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#495C2
socleC2×C3×C5#459
prime radical#11751248C2
hypercenter#495D15
hypocenterC3×C5#2212
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C3×C5×#495C2semidirect
2. #11751280C2semidirect
4. #11750801C2semidirect
5. #11746386C2semidirect
6. #11746384C2semidirect
7. #11746284C2semidirect
25. C5×#495D3semidirect
53. C3×#495D5semidirect
131. #495D15semidirect
249. C3×C5#2212semidirect
284. C5#71325semidirect
294. C3#10602118semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4952
#117512802
#117512482
#117508012
#117463862
#117463842
#117462842
#106021183
#713255