Finite Group Databasebeta

← #14315658

Subgroups — #14315658

Order 1920.

292 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 82 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#11748068C211yesmaximal, characteristic, complemented
2#11748066C211yesmaximal, characteristic, complemented
3#11747542C211yesmaximal, characteristic
4#11746331C211yesmaximal, characteristic, complemented
5C5×Dic3×C16C211yesmaximal, characteristic, complemented
6C3×#64730C211yesmaximal, characteristic, complemented
7#11745947C211yesmaximal, characteristic, complemented
8#10599860—31nomaximal, Hall
9#91793C2211yescharacteristic
10C3×#4050C2211yescharacteristic
11#91291—21no—
12#91283—21no—
13C2×C3×C5×C16C2211yescharacteristic
14#91103C2211yescharacteristic
15C5×C8×Dic3C2211yescharacteristic
16C2×C5×C3⋊C16C2211yescharacteristic
17C3×#3951C2211yescharacteristic
18#90980—21no—
19#90977—21no—
20#90947C411yescharacteristic, complemented
21#90943C411yescharacteristic, complemented
22#90942C411yescharacteristic, complemented
23#90938C411yescharacteristic, complemented
24#69238—51nomaximal, Hall
25#65193—31no—
26#64989—31no—
27#64989—31no—
28C4×C5×C16—31no—
29#64730—31no—
30#64730D311yescharacteristic, complemented
31#64726—31no—
32#6817—21no—
33C3×#709—21no—
34C2×C3×C5×C8C2311yescharacteristic
35#6710—21no—
36Dic60C2×C411yescharacteristic
37D120C2×C411yescharacteristic
38#6706—21no—
39C4×C5×Dic3D411yescharacteristic
40C2×C5×C3⋊C8D411yescharacteristic
41C3×#681—21no—
42C3×Dic20C2×C411yescharacteristic
43C3×D40C2×C411yescharacteristic
44C3×#677—21no—
45#6651—41no—
46#6649—41no—
47#6648—41no—
48D5×C3⋊C8—41no—
49C3×C5×C16—21no—
50C5×C3⋊C16C2×C411yescharacteristic
51C5×C3⋊C16C2×C411yescharacteristic
52#5196—51no—
53#5194—51no—
54#4895—51no—
55C3×#359—51no—
56#4510—51no—
57Dic3×C16D511yescharacteristic, complemented
58#4493—51no—
59#4050—31no—
60#4050C2×D311yescharacteristic
61#4047—61no—
62#4047—61no—
63C2×C5×C16—31no—
64C2×C5×C16C2×D311yescharacteristic
65C4×C5×C8—31no—
66#3951—31no—
67#3951C2×D311yescharacteristic
68#3937—61no—
69#3937—61no—
70Dic40—31no—
71#3932—31no—
72#3932—31no—
73D80—31no—
74#2178—151noSylow
75C2×C3×C4×C5C2×D411yescharacteristic
76#1220—41no—
77D60—21no—
78C4×D15—41no—
79Dic30—21no—
80C2×C5×Dic3—21no—
81C3×C22⋊D5—41no—
82C3×D20—21no—
83C3×C4×D5—41no—
84C3×Dic10—21no—
85C3×C5×C8C22×C411yescharacteristic
86C3×C5×C8#4111yescharacteristic
87C3⋊#168—41no—
88C3×#168—41no—
89C5×C3⋊C8D811yescharacteristic
90C5×C3⋊C8D811yescharacteristic
91C3×#135—51no—
92#948—101no—
93#907—101no—
94#904—51no—
95C2×C3×C16C2×D511yescharacteristic
96C3×#108—51no—
97#837—101no—
98#829—51no—
99#828—51no—
100#827—51no—
101#826—51no—
102#825—101no—
103#819—51no—
104C8×Dic3C2×D511yescharacteristic
105C2×C3⋊C16C2×D511yescharacteristic
106#709—21no—
107#709—61no—
108C2×C5×C8—31no—
109C2×C5×C8C22×D311yescharacteristic
110C42×C5—31no—
111#681—21no—
112#681—61no—
113Dic20—31no—
114Dic20C4×D311yescharacteristic
115D40—31no—
116D40C4×D311yescharacteristic
117#677—21no—
118#677—61no—
119#676—121no—
120#676—121no—
121C8×D5—121no—
122C8×D5—121no—
123C5×C16—21no—
124C5×C16—31no—
125C5×C16—31no—
126#508—151no—
127#443—151no—
128#443—151no—
129#368—151no—
130#359—51no—
131#359—151no—
132C4×C16—31no—
133C22×C3×C5#13511yescharacteristic
134C2×D15—41no—
135C2×C3×D5—41no—
136C3×C4×C5C4×D411yescharacteristic
137C3×C4×C5C2×D811yescharacteristic
138Dic15—41no—
139C3×Dic5—41no—
140C5×Dic3—22no—
141C3×#41—101no—
142#235—101no—
143C3×Q16—51no—
144C3×SD16—101no—
145C3×D8—51no—
146C3×M16—101no—
147C2×C3×C8C22×D511yescharacteristic
148C4×Dic3D2011yescharacteristic
149#208—101no—
150#208—201no—
151C2×C3⋊C8—201no—
152C2×C3⋊C8D2011yescharacteristic
153Dic12—51no—
154D24—51no—
155#204—101no—
156ΓL(1,𝔽25)—201no—
157D3×C8—201no—
158C3×C16—21no—
159C3⋊C16C4×D511yescharacteristic
160C3⋊C16C4×D511yescharacteristic
161C2×C4×C5—61no—
162C2×C4×C5D3×D411yescharacteristic
163C22⋊D5—41no—
164C22⋊D5—121no—
165D20—21no—
166D20—61no—
167C4×D5—41no—
168C4×D5—121no—
169Dic10—21no—
170Dic10—61no—
171C5×C8—31no—
172C5×C8—31no—
173C5×C8C2×C4×D311yescharacteristic
174C5×C8#23711yescharacteristic
175#168—41no—
176#168—121no—
177#135—51no—
178#135—151no—
179#131—301no—
180#131—301no—
181Q32—151no—
182SD32—151no—
183SD32—151no—
184D16—151no—
185C2×C16—31no—
186C2×C16D3×D511yescharacteristic
187#108—51no—
188#108—151no—
189#104—301no—
190#104—301no—
191C4×C8—31no—
192C2×C3×C5—21no—
193C2×C3×C5C4×D811yescharacteristic
194D15—81no—
195C3×D5—81no—
196C3×Q8—101no—
197C3×D4—101no—
198C3×D4—201no—
199C2×C3×C4—201no—
200C2×C3×C4C2×D2011yescharacteristic
201#67—201no—
202C2×Dic3—21no—
203D12—101no—
204C4×D3—201no—
205Dic6—101no—
206C3×C8—201no—
207C3×C8C2×C4×D511yescharacteristic
208C3×C8#70911yescharacteristic
209C3⋊C8—201no—
210C3⋊C8D4011yescharacteristic
211C3⋊C8D4011yescharacteristic
212C22×C5#91611yescharacteristic
213C2×D5—41no—
214C2×D5—121no—
215C4×C5—62no—
216C4×C5#67⋊C411yescharacteristic
217C4×C5D3×D811yescharacteristic
218Dic5—41no—
219Dic5—121no—
220#41—101no—
221#41—301no—
222Q16—51no—
223Q16—151no—
224SD16—101no—
225SD16—301no—
226D8—51no—
227D8—151no—
228M16—101no—
229M16—301no—
230M16—601no—
231M16—601no—
232C2×C8—31no—
233C2×C8—601no—
234C2×C8—601no—
235C2×C8C2×D3×D511yescharacteristic
236C42—31no—
237C16—21no—
238C16—31no—
239C16—31no—
240C3×C5#217811yescharacteristic, complemented, Hall
241C22×C3—201no—
242C22×C3#405011yescharacteristic
243C2×D3—201no—
244C3×C4—201no—
245C3×C4C4×D2011yescharacteristic
246C3×C4C2×D4011yescharacteristic
247Dic3—22no—
248Dic3—201no—
249C2×C5—21no—
250C2×C5#475611yescharacteristic
251D5—81no—
252D5—241no—
253Q8—101no—
254Q8—301no—
255D4—101no—
256D4—201no—
257D4—301no—
258D4—601no—
259C2×C4—61no—
260C2×C4—201no—
261C2×C4—601no—
262C2×C4D3×D2011yescharacteristic
263C8—31no—
264C8—31no—
265C8—201no—
266C8—601no—
267C8C4×D3×D511yescharacteristic
268C8#677911yescharacteristic
269C2×C3—21no—
270C2×C3—401no—
271C2×C3C4×D4011yescharacteristic
272D3—401no—
273C5#6923811yescharacteristic, complemented, Sylow
274C22—201no—
275C22—601no—
276C22#9127211yescharacteristic
277C4—62no—
278C4—201no—
279C4—601no—
280C4D3×D4011yescharacteristic
281C4#9139511yescharacteristic
282C3#1059986011yescharacteristic, complemented, Sylow
283C2—21no—
284C2—401no—
285C2—1201no—
286C2#1174774011yescharacteristic
subgroupG/H
centerC4D3×D40
commutatorC3×C5×C8C22×C4
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×C16C22
socleC2×C3×C5C4×D8
prime radical#11747542C2
cosocleC2×C3×C5×C8C23
hypercenterC2×C16D3×D5
hypocenterC3×C5#2178
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. #11748068C2semidirect
2. #11748066C2semidirect
4. #11746331C2semidirect
5. C5×Dic3×C16C2semidirect
6. C3×#64730C2semidirect
7. #11745947C2semidirect
20. #90947C4semidirect
21. #90943C4semidirect
22. #90942C4semidirect
23. #90938C4semidirect
30. #64730D3semidirect
57. Dic3×C16D5semidirect
240. C3×C5#2178semidirect
273. C5#69238semidirect
282. C3#10599860semidirect

Maximal subgroups

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

subgroupindex
#117480682
#117480662
#117475422
#117463312
C5×Dic3×C162
C3×#647302
#117459472
#105998603
#692385