Finite Group Databasebeta

← #14316168

Subgroups — #14316168

Order 1920.

512 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×D8×D15C211yesmaximal, characteristic
2C2×#91111C211yesmaximal, characteristic, complemented
3C2×#91084C211yesmaximal, characteristic, complemented
4#11750988C211yesmaximal, characteristic, complemented
5C3×C5×#357C211yesmaximal, characteristic, complemented
6#11746328C211yesmaximal, characteristic, complemented
7#11746312C211yesmaximal, characteristic, complemented
8#10599986—31nomaximal, Hall
9C2×D4×D15—21no—
10C2×C3×C5×D8C2211yescharacteristic
11C2×#6715—21no—
12D8×D15—22no—
13D8×D15—22no—
14C2×Dic60C2211yescharacteristic, complemented
15C2×D120C2211yescharacteristic
16C2×C8×D15C2211yescharacteristic
17#91786—21no—
18C2×C3×C5×C16C2211yescharacteristic, complemented
19C3×C5×#107C2211yescharacteristic, complemented
20#91111—22no—
21C2×C3⋊#672C2211yescharacteristic, complemented
22#91094—21no—
23#91084—22no—
24#69193—51nomaximal, Hall
25C2×D5×D8—31no—
26C2×#3959—31no—
27C2×#3932—31no—
28#65176—31no—
29C5×#357D311yescharacteristic, complemented
30#64727—31no—
31#64711—31no—
32C23×D15—41no—
33C2×C3×C5×D4—21no—
34C2×#1220—41no—
35D4×D15—24no—
36D4×D15—42no—
37C2×D60—21no—
38C2×C4×D15D411yescharacteristic
39C2×Dic30—21no—
40C3×C5×D8—21no—
41C3×C5×D8D412yes—
42C2×C3×C5×C8C2311yescharacteristic
43C3×C5×C4⋊C4—21no—
44#6715—24no—
45#6714—41no—
46C4⋊Dic15—41no—
47C2×C3⋊#168D411yescharacteristic
48Dic60—21no—
49Dic60—21no—
50D120—21no—
51D120D412yes—
52C8×D15—21no—
53C8×D15—21no—
54C3×C5×C16—21no—
55C3⋊#672—21no—
56C2×D3×D8—51no—
57C2×#827—51no—
58C2×#800—51no—
59#4887—51no—
60C3×#357D511yescharacteristic, complemented
61(C2×D3)⋊C16—51no—
62#4491—51no—
63C2×D4×D5—61no—
64C2×C5×D8C2×D311yescharacteristic
65C2×#686—61no—
66D5×D8—62no—
67D5×D8—62no—
68C2×Dic20—31no—
69C2×D40—31no—
70C2×C8×D5—31no—
71#4043—61no—
72C2×C5×C16C2×D311yescharacteristic, complemented
73C5×#107C2×D311yescharacteristic, complemented
74#3959—62no—
75C2×#672—31no—
76#3942—61no—
77#3932—62no—
78#2187—151noSylow
79C23×C3×C5—41no—
80C22×D15—44no—
81C22×D15—41no—
82C22×D15—82no—
83C22×D15—82no—
84C22×D15D811yescharacteristic
85C3×C5×D4—22no—
86C3×C5×D4—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89#1220—44no—
90C2×Dic15—41no—
91C2×Dic15D811yescharacteristic
92D60—22no—
93D60—41no—
94C4×D15—21no—
95C4×D15—21no—
96Dic30—41no—
97Dic30—41no—
98C3×C5×C8C2×D411yescharacteristic
99C3×C5×C8C2×D411yescharacteristic
100C3⋊#168—21no—
101C2×D3×D4—101no—
102C2×C3×D8C2×D511yescharacteristic
103C2×#213—101no—
104D3×D8—102no—
105D3×D8—102no—
106C2×Dic12—51no—
107C2×D24—51no—
108C2×D3×C8—51no—
109#897—101no—
110C2×C3×C16C2×D511yescharacteristic, complemented
111C3×#107C2×D511yescharacteristic, complemented
112#827—102no—
113C2×C3⋊C16—51no—
114#810—101no—
115#800—102no—
116C23×D5—121no—
117C2×C5×D4—21no—
118C2×C22⋊D5—121no—
119D4×D5—64no—
120D4×D5—122no—
121C2×D20—61no—
122C2×C4×D5—31no—
123C2×Dic10—61no—
124C5×D8—21no—
125C5×D8D1212yes—
126C2×C5×C8C22×D311yescharacteristic
127C5×C4⋊C4—21no—
128#686—64no—
129#685—121no—
130C4⋊Dic5—121no—
131C2×#168—31no—
132Dic20—61no—
133Dic20—61no—
134D40—32no—
135D40—61no—
136C8×D5—61no—
137C8×D5—61no—
138C5×C16—21no—
139#672—61no—
140C22×D8—151no—
141C2×SD32—151no—
142C2×SD32—151no—
143#467—151no—
144#357—151no—
145#357D1511yescharacteristic, complemented
146C22⋊C16—151no—
147C22×C3×C5—42no—
148C22×C3×C5—81no—
149C22×C3×C5—81no—
150C22×C3×C5C2×D811yescharacteristic
151C2×D15—21no—
152C2×D15—21no—
153C2×D15—42no—
154C2×D15—88no—
155C2×D15—81no—
156C2×D15—81no—
157C2×D15SD3212yescomplemented
158C3×C4×C5—81no—
159C3×C4×C5#12011yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161Dic15—21no—
162Dic15—81no—
163C23×D3—201no—
164C2×C3×D4—21no—
165C2×#67—201no—
166D3×D4—104no—
167D3×D4—202no—
168C2×D12—101no—
169C2×C4×D3—51no—
170C2×Dic6—101no—
171C3×D8—21no—
172C3×D8D2012yes—
173C2×C3×C8C22×D511yescharacteristic
174C3×C4⋊C4—21no—
175#213—104no—
176(C2×D3)⋊C4—201no—
177C4⋊Dic3—201no—
178C2×C3⋊C8—51no—
179Dic12—101no—
180Dic12—101no—
181D24—52no—
182D24—101no—
183D3×C8—101no—
184D3×C8—101no—
185C3×C16—21no—
186C3⋊C16—101no—
187C23×C5—41no—
188C22×D5—31no—
189C22×D5—124no—
190C22×D5—121no—
191C22×D5—242no—
192C22×D5—242no—
193C5×D4—22no—
194C5×D4—41no—
195C2×C4×C5—41no—
196C2×C4×C5D3×D411yescharacteristic
197C22⋊D5—124no—
198C2×Dic5—31no—
199C2×Dic5—121no—
200D20—62no—
201D20—121no—
202C4×D5—61no—
203C4×D5—61no—
204Dic10—121no—
205Dic10—121no—
206C5×C8C2×D1211yescharacteristic
207C5×C8D3×D411yescharacteristic
208#168—61no—
209C22×D4—301no—
210C2×Q16—151no—
211C2×D8—151no—
212C2×D8—301no—
213C2×D8—302no—
214C2×D8—302no—
215C2×D8C2×D1511yescharacteristic
216C22×C8—151no—
217C22⋊Q8—301no—
218SD32—302no—
219SD32—302no—
220C2×C16—151no—
221C2×C16C2×D1511yescharacteristic, complemented
222#107C2×D1511yescharacteristic, complemented
223#103—301no—
224C2×C3×C5—82no—
225C2×C3×C5#44711yescharacteristic
226C2×C3×C5C2×SD3211yescharacteristic
227C2×C3×C5#50911yescharacteristic
228D15—22no—
229D15—82no—
230C23×C3—41no—
231C22×D3—51no—
232C22×D3—204no—
233C22×D3—201no—
234C22×D3—402no—
235C22×D3—402no—
236C3×D4—22no—
237C3×D4—41no—
238C2×C3×C4—41no—
239C2×C3×C4D4×D511yescharacteristic
240#67—204no—
241C2×Dic3—51no—
242C2×Dic3—201no—
243D12—102no—
244D12—201no—
245C4×D3—101no—
246C4×D3—101no—
247Dic6—201no—
248Dic6—201no—
249C3×C8C2×D2011yescharacteristic
250C3×C8D4×D511yescharacteristic
251C3⋊C8—101no—
252C22×C5—42no—
253C22×C5—81no—
254C22×C5—81no—
255C22×C5D3×D811yescharacteristic
256C2×D5—32no—
257C2×D5—61no—
258C2×D5—61no—
259C2×D5—122no—
260C2×D5—248no—
261C2×D5—241no—
262C2×D5—241no—
263C4×C5—81no—
264C4×C5#88211yescharacteristic
265C4×C5#91411yescharacteristic
266Dic5—61no—
267Dic5—241no—
268C24—601no—
269C2×Q8—301no—
270C2×D4—21no—
271C2×D4—304no—
272C2×D4—301no—
273C2×D4—601no—
274C2×D4—602no—
275C22×C4—151no—
276Q16—301no—
277Q16—301no—
278D8—21no—
279D8—152no—
280D8—304no—
281D8—301no—
282D8D6012yes—
283C2×C8—151no—
284C2×C8—301no—
285C2×C8—301no—
286C2×C8C22×D1511yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—601no—
289C22⋊C4—601no—
290C16—21no—
291C16—301no—
292C3×C5#218711yescharacteristic, complemented, Hall
293C22×C3—42no—
294C22×C3—81no—
295C22×C3—81no—
296C22×C3D5×D811yescharacteristic
297C2×D3—52no—
298C2×D3—101no—
299C2×D3—101no—
300C2×D3—202no—
301C2×D3—408no—
302C2×D3—401no—
303C2×D3—401no—
304C3×C4—81no—
305C3×C4#402811yescharacteristic
306C3×C4#406011yescharacteristic
307Dic3—101no—
308Dic3—401no—
309C2×C5—82no—
310C2×C5#477311yescharacteristic
311C2×C5#491111yescharacteristic
312C2×C5D3×SD3211yescharacteristic
313D5—62no—
314D5—242no—
315C23—41no—
316C23—151no—
317C23—604no—
318C23—601no—
319C23—1202no—
320C23—1202no—
321Q8—601no—
322Q8—601no—
323D4—22no—
324D4—41no—
325D4—302no—
326D4—604no—
327D4—601no—
328C2×C4—41no—
329C2×C4—151no—
330C2×C4—301no—
331C2×C4—301no—
332C2×C4—601no—
333C2×C4D4×D1511yescharacteristic
334C8—301no—
335C8C2×D6011yescharacteristic
336C8D4×D1511yescharacteristic
337C2×C3—82no—
338C2×C3#6506211yescharacteristic
339C2×C3#6520011yescharacteristic
340C2×C3D5×SD3211yescharacteristic
341D3—102no—
342D3—402no—
343C5#6919311yescharacteristic, complemented, Sylow
344C22—42no—
345C22—81no—
346C22—81no—
347C22—152no—
348C22—301no—
349C22—301no—
350C22—602no—
351C22—1208no—
352C22—1201no—
353C22—1201no—
354C22D8×D1511yescharacteristic
355C4—81no—
356C4—301no—
357C4—1201no—
358C4#9177111yescharacteristic
359C4#9180311yescharacteristic
360C3#1059998611yescharacteristic, complemented, Sylow
361C2—82no—
362C2—302no—
363C2—1202no—
364C2#1175087411yescharacteristic
365C2#1175101211yescharacteristic
366C2D15×SD3211yescharacteristic
subgroupG/H
centerC22D8×D15
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#357C2
socleC22×C3×C5C2×D8
prime radicalC2×D8×D15C2
hypercenter#357D15
hypocenterC3×C5#2187
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. C2×#91111C2semidirect
3. C2×#91084C2semidirect
4. #11750988C2semidirect
5. C3×C5×#357C2semidirect
6. #11746328C2semidirect
7. #11746312C2semidirect
14. C2×Dic60C22semidirect
18. C2×C3×C5×C16C22semidirect
19. C3×C5×#107C22semidirect
21. C2×C3⋊#672C22semidirect
29. C5×#357D3semidirect
60. C3×#357D5semidirect
72. C2×C5×C16C2×D3semidirect
73. C5×#107C2×D3semidirect
110. C2×C3×C16C2×D5semidirect
111. C3×#107C2×D5semidirect
145. #357D15semidirect
157. C2×D15SD32semidirect
221. C2×C16C2×D15semidirect
222. #107C2×D15semidirect
292. C3×C5#2187semidirect
343. C5#69193semidirect
360. C3#10599986semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D152
C2×#911112
C2×#910842
#117509882
C3×C5×#3572
#117463282
#117463122
#105999863
#691935