Finite Group Databasebeta

← #14413166

Subgroups — #14413166

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#131C211yesmaximal, characteristic
2#41×Dic15C211yesmaximal, characteristic
3C2×#91837C211yesmaximal, characteristic
4#11751220C213yesmaximal, complemented
5#11751219C213yesmaximal, complemented
6#11751203C213yesmaximal, complemented
7C2×#91098C213yesmaximal, complemented
8#10615514—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C3×C5×#131—24no—
11C2×C3×C5×M16C2213yes—
12C22×C3×C5×C8C2213yes—
13#91837—24no—
14Q8×Dic15C411yescharacteristic
15Q8×Dic15C411yescharacteristic
16D4×Dic15C413yes—
17D4×Dic15C413yes—
18#91815C2213yes—
19C2×C4×Dic15C2213yes—
20C2×#6710C2213yes—
21C22×C3⋊#168C2213yes—
22#91098C2211yescharacteristic
23#91098C2213yes—
24#91098C2213yes—
25#91098C2213yes—
26#91098C2216yes—
27#83783—51nomaximal, Hall
28C2×C5×#131D311yescharacteristic
29#41×Dic5—31no—
30C2×#4094—31no—
31#65408—33no—
32#65407—33no—
33#65391—33no—
34C2×#3946—33no—
35C3×C5×#41D414yes—
36C3×C5×#41Q814yes—
37C2×C3×C5×Q8C2×C411yescharacteristic
38C2×C3×C5×D4C2×C413yes—
39C22×C3×C4×C5C2313yes—
40C22×Dic15C2×C413yes—
41C22×Dic15C2×C413yes—
42C3×C5×M16—26no—
43C2×C3×C5×C8—26no—
44C2×C3×C5×C8C2311yescharacteristic
45C2×C3×C5×C8C2313yes—
46#6719C2×C416yes—
47C4⋊Dic15C2×C413yes—
48C4⋊Dic15C2×C413yes—
49C4×Dic15C2×C413yes—
50C4×Dic15C2×C413yes—
51C4×Dic15C2311yescharacteristic
52C4×Dic15C2313yes—
53#6710—26no—
54C2×C3⋊#168—26no—
55C2×C3⋊#168C2311yescharacteristic
56C2×C3⋊#168C2313yes—
57C2×C3×#131D511yescharacteristic
58Dic3×#41—51no—
59C2×#948—51no—
60#5119—53no—
61#5118—53no—
62#5102—53no—
63C2×Dic3⋊C8—53no—
64C2×C5×#41C2×D311yescharacteristic
65C5×#131—24no—
66C2×C5×M16C2×D313yes—
67C22×C5×C8C2×D313yes—
68#4094—64no—
69Q8×Dic5—31no—
70Q8×Dic5—31no—
71D4×Dic5—33no—
72D4×Dic5—33no—
73#4072—33no—
74C2×C4×Dic5—33no—
75C2×#681—33no—
76C22×#168—33no—
77#3946—31no—
78#3946—33no—
79#3946—33no—
80#3946—33no—
81#3946—36no—
82#2906—151noSylow
83C23×C3×C5C22×C413yes—
84C3×C5×Q8C4⋊C414yes—
85C3×C5×D4C4⋊C4112yes—
86C2×C3×C4×C5C22×C413yes—
87C2×C3×C4×C5C2×D416yes—
88C2×C3×C4×C5C2×Q816yes—
89C2×C3×C4×C5C2411yescharacteristic
90C2×Dic15—26no—
91C2×Dic15—43no—
92C2×Dic15C22×C411yescharacteristic
93C2×Dic15C22×C413yes—
94C2×Dic15C22×C413yes—
95C2×Dic15C22×C411yescharacteristic
96C3×C5×C8—21no—
97C3×C5×C8—23no—
98C3⋊#168—21no—
99C3⋊#168—23no—
100C2×C3×#41C2×D511yescharacteristic
101C3×#131—24no—
102C2×C3×M16C2×D513yes—
103C22×C3×C8C2×D513yes—
104#948—104no—
105Q8×Dic3—51no—
106Q8×Dic3—51no—
107D4×Dic3—53no—
108D4×Dic3—53no—
109#926—53no—
110C2×C4×Dic3—53no—
111C2×#208—53no—
112C22×C3⋊C8—53no—
113Dic3⋊C8—51no—
114Dic3⋊C8—53no—
115Dic3⋊C8—53no—
116Dic3⋊C8—53no—
117Dic3⋊C8—56no—
118C5×#41Dic614yes—
119C5×#41#6714yes—
120C2×C5×Q8C4×D311yescharacteristic
121C2×C5×D4C4×D313yes—
122C22×C4×C5C22×D313yes—
123C22×Dic5—33no—
124C22×Dic5—33no—
125C5×M16—26no—
126C2×C5×C8—26no—
127C2×C5×C8C22×D311yescharacteristic
128C2×C5×C8C22×D313yes—
129C22⋊Dic5—36no—
130C4⋊Dic5—33no—
131C4⋊Dic5—33no—
132C4×Dic5—33no—
133C4×Dic5—33no—
134C4×Dic5—31no—
135C4×Dic5—33no—
136#681—66no—
137C2×#168—31no—
138C2×#168—33no—
139C2×#168—66no—
140C2×#131—151no—
141C2×#131D1511yescharacteristic
142C4×#41—151no—
143#424—153no—
144#424—153no—
145#423—153no—
146C2×C4⋊C8—153no—
147C22×C3×C5—23no—
148C22×C3×C5—23no—
149C22×C3×C5C2×C4⋊C416yes—
150C22×C3×C5C23×C411yescharacteristic
151C3×C4×C5C2×C4⋊C416yes—
152C3×C4×C5C22×D411yescharacteristic
153C3×C4×C5C22×Q811yescharacteristic
154Dic15—23no—
155Dic15—21no—
156Dic15—23no—
157Dic15#13112yescomplemented
158C3×#41Dic1014yes—
159C3×#41C22⋊D514yes—
160C2×C3×Q8C4×D511yescharacteristic
161C2×C3×D4C4×D513yes—
162C22×C3×C4C22×D513yes—
163C22×Dic3—53no—
164C22×Dic3—53no—
165C3×M16—26no—
166C2×C3×C8—26no—
167C2×C3×C8C22×D511yescharacteristic
168C2×C3×C8C22×D513yes—
169#217—56no—
170C4⋊Dic3—53no—
171C4⋊Dic3—53no—
172C4×Dic3—53no—
173C4×Dic3—53no—
174C4×Dic3—51no—
175C4×Dic3—53no—
176#208—106no—
177C2×C3⋊C8—51no—
178C2×C3⋊C8—53no—
179C2×C3⋊C8—106no—
180C23×C5C2×C4×D313yes—
181C5×Q8Dic3⋊C414yes—
182C5×D4Dic3⋊C4112yes—
183C2×C4×C5C2×Dic616yes—
184C2×C4×C5C2×C4×D313yes—
185C2×C4×C5C2×#6716yes—
186C2×C4×C5C23×D311yescharacteristic
187C2×Dic5—31no—
188C2×Dic5—31no—
189C2×Dic5—33no—
190C2×Dic5—33no—
191C2×Dic5—66no—
192C2×Dic5—123no—
193C5×C8—21no—
194C5×C8—23no—
195#168—61no—
196#168—63no—
197C2×#41C2×D1511yescharacteristic
198#131—24no—
199#131—304no—
200C2×M16—153no—
201C2×M16C2×D1513yes—
202C22×C8—153no—
203C22×C8C2×D1513yes—
204C4×Q8—151no—
205C4×Q8—151no—
206C4×D4—153no—
207C4×D4—153no—
208#117—153no—
209C2×C42—153no—
210C4⋊C8—151no—
211C4⋊C8—153no—
212C4⋊C8—153no—
213C4⋊C8—153no—
214C4⋊C8—156no—
215C2×C3×C5—26no—
216C2×C3×C5C22×C4⋊C411yescharacteristic
217C2×C3×C5C2×#13111yescharacteristic
218C2×C3×C5#56811yescharacteristic
219C23×C3C2×C4×D513yes—
220C3×Q8#68314yes—
221C3×D4#683112yes—
222C2×C3×C4C2×Dic1016yes—
223C2×C3×C4C2×C4×D513yes—
224C2×C3×C4C2×C22⋊D516yes—
225C2×C3×C4C23×D511yescharacteristic
226C2×Dic3—51no—
227C2×Dic3—51no—
228C2×Dic3—53no—
229C2×Dic3—53no—
230C2×Dic3—106no—
231C2×Dic3—203no—
232C3×C8—21no—
233C3×C8—23no—
234C3⋊C8—101no—
235C3⋊C8—103no—
236C22×C5—23no—
237C22×C5—23no—
238C22×C5C2×Dic3⋊C416yes—
239C22×C5C22×C4×D311yescharacteristic
240C4×C5C2×Dic3⋊C416yes—
241C4×C5C22×Dic611yescharacteristic
242C4×C5C22×#6711yescharacteristic
243Dic5—32no—
244Dic5—63no—
245Dic5—63no—
246Dic5—61no—
247#41Dic3014yes—
248#41#122014yes—
249C2×Q8C4×D1511yescharacteristic
250C2×D4C4×D1513yes—
251C22×C4—153no—
252C22×C4—153no—
253C22×C4C22×D1513yes—
254M16—26no—
255M16—306no—
256C2×C8—26no—
257C2×C8—151no—
258C2×C8—153no—
259C2×C8—306no—
260C2×C8C22×D1511yescharacteristic
261C2×C8C22×D1513yes—
262C4⋊C4—153no—
263C4⋊C4—153no—
264C22⋊C4—156no—
265C42—153no—
266C42—153no—
267C42—151no—
268C42—153no—
269C3×C5#290611yescharacteristic, complemented, Hall
270C22×C3—23no—
271C22×C3—23no—
272C22×C3C2×#68316yes—
273C22×C3C22×C4×D511yescharacteristic
274C3×C4C2×#68316yes—
275C3×C4C22×Dic1011yescharacteristic
276C3×C4C22×C22⋊D511yescharacteristic
277Dic3—52no—
278Dic3—103no—
279Dic3—103no—
280Dic3—101no—
281C2×C5—26no—
282C2×C5D3×#13111yescharacteristic
283C2×C5#575011yescharacteristic
284C2×C5C22×Dic3⋊C411yescharacteristic
285C23C2×C4×D1513yes—
286Q8#671214yes—
287D4#6712112yes—
288C2×C4—151no—
289C2×C4—151no—
290C2×C4—153no—
291C2×C4—153no—
292C2×C4—306no—
293C2×C4—603no—
294C2×C4C2×Dic3016yes—
295C2×C4C2×C4×D1513yes—
296C2×C4C2×#122016yes—
297C2×C4C23×D1511yescharacteristic
298C8—21no—
299C8—23no—
300C8—301no—
301C8—303no—
302C2×C3—26no—
303C2×C3D5×#13111yescharacteristic
304C2×C3#6608411yescharacteristic
305C2×C3C22×#68311yescharacteristic
306C5#8378311yescharacteristic, complemented, Sylow
307C22—23no—
308C22—23no—
309C22C2×#671216yes—
310C22C22×C4×D1511yescharacteristic
311C4—152no—
312C4—303no—
313C4—301no—
314C4—303no—
315C4C2×#671216yes—
316C4C22×Dic3011yescharacteristic
317C4C22×#122011yescharacteristic
318C3#1061551411yescharacteristic, complemented, Sylow
319C2—26no—
320C2D15×#13111yescharacteristic
321C2#1175650911yescharacteristic
322C2C22×#671211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D15
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×#131C2
prime radicalC2×C3×C5×#41C22
cosocleC2×C3×C4×C5C24
hypercenterC2×#131D15
hypocenterC3×C5#2906
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
4. #11751220C2semidirect
5. #11751219C2semidirect
6. #11751203C2semidirect
7. C2×#91098C2semidirect
157. Dic15#131semidirect
269. C3×C5#2906semidirect
306. C5#83783semidirect
318. C3#10615514semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1312
#41×Dic152
C2×#918372
#117512202
#117512192
#117512032
C2×#910982
#106155143
#837835