Finite Group Databasebeta

← #14304794

Subgroups — #14304794

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×C3⋊C8C211yesmaximal, characteristic, complemented
2C2×C3×#3937C211yesmaximal, characteristic
3#11748436C211yesmaximal, characteristic, complemented
4#11748365C211yesmaximal, characteristic
5#11748342C211yesmaximal, characteristic
6#11746344C211yesmaximal, characteristic, complemented
7#11745983C211yesmaximal, characteristic, complemented
8#10600586—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C22×C5×C3⋊C8C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C4×C5×C3⋊C8—22no—
17C3×#3937—22no—
18#90983—22no—
19#90971C412yescomplemented
20#90965C412yescomplemented
21#90955—22no—
22#70371—51nomaximal, Hall
23C2×C4×C5×C8—31no—
24#65402—31no—
25#65399—31no—
26#65391—31no—
27C2×#3937D311yescharacteristic
28#64772—31no—
29#64743—31no—
30C22×C3×C4×C5—21no—
31C22×C3×C4×C5C2311yescharacteristic
32C2×C3×C22⋊D5—21no—
33C3×#709—21no—
34C3×#709—21no—
35C3×#709—21no—
36C3×#709—21no—
37C2×C3×D20C2×C411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×Dic10C2×C411yescharacteristic
40C3×C42×C5—21no—
41C3×C42×C5D412yes—
42#6719—21no—
43C4⋊Dic15C2×C412yes—
44C4×Dic15—21no—
45#6710—21no—
46#6710—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C2×C5×C3⋊C8—21no—
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8C2×C412yes—
53C2×C5×C3⋊C8D412yes—
54C3×#681—21no—
55C3×#681—21no—
56C2×C3×#168—21no—
57C2×C3×#104—51no—
58#5234—51no—
59#5233—51no—
60#5119—51no—
61C2×C4×C3⋊C8D511yescharacteristic, complemented
62#4558—51no—
63#4523—51no—
64C2×#709C2×D311yescharacteristic
65C22×C5×C8—31no—
66C22×C5×C8—31no—
67C2×C42×C5C2×D311yescharacteristic
68#4072—31no—
69C2×#681—31no—
70C2×#681C2×D311yescharacteristic
71C4×C5×C8—62no—
72#3953—32no—
73#3952—62no—
74#3948—32no—
75#3946—62no—
76#3937—22no—
77#1937—151noSylow
78C23×C3×C5#4111yescharacteristic
79C22×C3×D5—21no—
80C2×C3×C4×C5—24no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5#4111yescharacteristic
86C2×C3×C4×C5#4111yescharacteristic
87C2×C3×C4×C5#4111yescharacteristic
88C2×Dic15—22no—
89C3×C22⋊D5—41no—
90C3×C22⋊D5—41no—
91C2×C3×Dic5—21no—
92C3×D20—21no—
93C3×D20—21no—
94C3×C4×D5—41no—
95C3×C4×D5—41no—
96C3×Dic10—21no—
97C3×Dic10—21no—
98C3⋊#168—41no—
99C3×#168—41no—
100C5×C3⋊C8—22no—
101C5×C3⋊C8—22no—
102C2×C3×#41—51no—
103C2×C3×M16—51no—
104C2×C3×C42C2×D511yescharacteristic
105#926—51no—
106C2×#208—51no—
107C22×C3⋊C8C2×D511yescharacteristic
108C22×C3⋊C8C2×D511yescharacteristic
109C3×#104—102no—
110#835—52no—
111#832—52no—
112#830—102no—
113Dic3⋊C8—102no—
114C4×C3⋊C8—22no—
115C22×C4×C5—21no—
116C22×C4×C5C22×D311yescharacteristic
117C2×C22⋊D5—21no—
118#709—21no—
119#709—21no—
120#709—21no—
121#709—21no—
122C2×D20C4×D311yescharacteristic
123C2×C4×D5—21no—
124C2×Dic10C4×D311yescharacteristic
125C2×C5×C8—32no—
126C2×C5×C8—32no—
127C2×C5×C8—61no—
128C2×C5×C8—61no—
129C2×C5×C8—61no—
130C2×C5×C8—61no—
131C42×C5—21no—
132C42×C5#6712yes—
133C22⋊Dic5—61no—
134C4⋊Dic5—32no—
135C4×Dic5—61no—
136#681—21no—
137#681—21no—
138#681—61no—
139#681—61no—
140C2×#168—21no—
141C2×#168—61no—
142#424—151no—
143C2×#104—51no—
144#416—151no—
145#408—151no—
146C2×C4×C8—31no—
147#341—151no—
148#339—151no—
149C22×C3×C5—22no—
150C22×C3×C5C4×D411yescharacteristic
151C22×C3×C5#12311yescharacteristic
152C22×C3×C5#12611yescharacteristic
153C2×C3×D5—41no—
154C2×C3×D5—42no—
155C3×C4×C5—24no—
156C3×C4×C5#11711yescharacteristic
157C3×C4×C5C4×D411yescharacteristic
158C3×C4×C5#12111yescharacteristic
159C3×C4×C5#12411yescharacteristic
160Dic15—42no—
161C3×Dic5—41no—
162C3×#41—101no—
163C3×#41—101no—
164C3×#41—101no—
165C3×#41—101no—
166C2×C3×Q8—51no—
167C2×C3×D4—51no—
168C2×C3×D4—101no—
169C22×C3×C4—21no—
170C22×C3×C4—101no—
171C22×C3×C4C22×D511yescharacteristic
172C3×M16—101no—
173C3×M16—101no—
174C2×C3×C8—101no—
175C3×C42—21no—
176C3×C42C22⋊D512yes—
177#217—101no—
178C4⋊Dic3—52no—
179C4×Dic3—101no—
180#208—101no—
181#208—101no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—101no—
187C2×C3⋊C8C4×D512yes—
188C2×C3⋊C8D2012yes—
189C23×C5#23711yescharacteristic
190C22×D5—21no—
191C2×C4×C5—24no—
192C2×C4×C5—22no—
193C2×C4×C5C2×C4×D311yescharacteristic
194C2×C4×C5#23511yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5#23711yescharacteristic
197C2×C4×C5#23711yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C22⋊D5—41no—
200C22⋊D5—41no—
201C2×Dic5—21no—
202C2×Dic5—62no—
203D20—21no—
204D20—21no—
205C4×D5—41no—
206C4×D5—41no—
207Dic10—21no—
208Dic10—21no—
209C5×C8—62no—
210C5×C8—62no—
211#168—41no—
212#168—121no—
213C2×#41—51no—
214C2×M16—51no—
215C2×M16—151no—
216C22×C8—31no—
217C22×C8—31no—
218#117—151no—
219C2×C42D3×D511yescharacteristic
220C4⋊C8—302no—
221#104—102no—
222#103—152no—
223#102—152no—
224C22⋊C8—302no—
225C4×C8—62no—
226C2×C3×C5—21no—
227C2×C3×C5—21no—
228C2×C3×C5#38811yescharacteristic
229C2×C3×C5#44312yes—
230C3×D5—81no—
231C23×C3—101no—
232C23×C3#70911yescharacteristic
233C3×Q8—101no—
234C3×Q8—101no—
235C3×D4—101no—
236C3×D4—101no—
237C3×D4—201no—
238C3×D4—201no—
239C2×C3×C4—24no—
240C2×C3×C4—22no—
241C2×C3×C4—101no—
242C2×C3×C4—201no—
243C2×C3×C4—201no—
244C2×C3×C4C2×C4×D511yescharacteristic
245C2×C3×C4C2×D2011yescharacteristic
246C2×C3×C4#70911yescharacteristic
247C2×C3×C4#70911yescharacteristic
248C2×C3×C4#70911yescharacteristic
249C2×C3×C4C2×C22⋊D511yescharacteristic
250C2×Dic3—102no—
251C3×C8—201no—
252C3⋊C8—22no—
253C3⋊C8—22no—
254C3⋊C8—201no—
255C22×C5—22no—
256C22×C5#87911yescharacteristic
257C22×C5#67⋊C411yescharacteristic
258C22×C5#93511yescharacteristic
259C2×D5—41no—
260C2×D5—42no—
261C4×C5—24no—
262C4×C5#87711yescharacteristic
263C4×C5#88511yescharacteristic
264C4×C5C4×#6711yescharacteristic
265C4×C5#93811yescharacteristic
266Dic5—41no—
267Dic5—122no—
268#41—101no—
269#41—101no—
270#41—101no—
271#41—101no—
272C2×Q8—51no—
273C2×D4—51no—
274C2×D4—101no—
275C22×C4—21no—
276C22×C4—101no—
277C22×C4C2×D3×D511yescharacteristic
278M16—101no—
279M16—101no—
280M16—301no—
281M16—301no—
282C2×C8—32no—
283C2×C8—32no—
284C2×C8—61no—
285C2×C8—61no—
286C2×C8—61no—
287C2×C8—61no—
288C2×C8—101no—
289C2×C8—301no—
290C4⋊C4—152no—
291C22⋊C4—301no—
292C42—21no—
293C42—301no—
294C42#120112yes—
295C3×C5#193711yescharacteristic, complemented, Hall
296C22×C3—22no—
297C22×C3—201no—
298C22×C3—202no—
299C22×C3C4×D2011yescharacteristic
300C22×C3#402211yescharacteristic
301C22×C3#407511yescharacteristic
302C3×C4—24no—
303C3×C4—201no—
304C3×C4#401811yescharacteristic
305C3×C4#402111yescharacteristic
306C3×C4C4×C22⋊D511yescharacteristic
307C3×C4#407611yescharacteristic
308Dic3—202no—
309C2×C5—21no—
310C2×C5—21no—
311C2×C5#482412yes—
312C2×C5#494411yescharacteristic
313D5—81no—
314C23—101no—
315C23#677911yescharacteristic
316Q8—101no—
317Q8—101no—
318D4—101no—
319D4—101no—
320D4—201no—
321D4—201no—
322C2×C4—24no—
323C2×C4—22no—
324C2×C4—101no—
325C2×C4—201no—
326C2×C4—201no—
327C2×C4—302no—
328C2×C4#676511yescharacteristic
329C2×C4#677111yescharacteristic
330C2×C4C4×D3×D511yescharacteristic
331C2×C4D3×D2011yescharacteristic
332C2×C4#677911yescharacteristic
333C2×C4C2×#120111yescharacteristic
334C8—62no—
335C8—62no—
336C8—201no—
337C8—601no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—401no—
341C2×C3#6498912yes—
342C2×C3#6522911yescharacteristic
343C5#7037111yescharacteristic, complemented, Sylow
344C22—22no—
345C22—201no—
346C22—202no—
347C22#9136311yescharacteristic
348C22#9139511yescharacteristic
349C22#9153611yescharacteristic
350C4—24no—
351C4—201no—
352C4—602no—
353C4#9135311yescharacteristic
354C4#9139311yescharacteristic
355C4C4×#120111yescharacteristic
356C4#9145611yescharacteristic
357C3#1060058611yescharacteristic, complemented, Sylow
358C2—21no—
359C2—21no—
360C2—401no—
361C2#1174701612yes—
362C2#1174870511yescharacteristic
subgroupG/H
centerC2×C4D3×D20
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C4×D4
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1937
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×C3⋊C8C2semidirect
3. #11748436C2semidirect
6. #11746344C2semidirect
7. #11745983C2semidirect
19. #90971C4semidirect
20. #90965C4semidirect
61. C2×C4×C3⋊C8D5semidirect
295. C3×C5#1937semidirect
343. C5#70371semidirect
357. C3#10600586semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×C3⋊C82
C2×C3×#39372
#117484362
#117483652
#117483422
#117463442
#117459832
#106005863
#703715