Finite Group Databasebeta

← #14289962

Subgroups — #14289962

Order 1920.

424 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 88 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#11756472C211yesmaximal, characteristic
2C5×#5070C211yesmaximal, characteristic
3#11747105C211yesmaximal, characteristic, complemented
4#11746946C211yesmaximal, characteristic, complemented
5C3×#64764C211yesmaximal, characteristic
6#11745844C211yesmaximal, characteristic, complemented
7#11745844C211yesmaximal, characteristic, complemented
8#10601999—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10#91825—21no—
11#91825—21no—
12#91824—22no—
13D4×Dic15—21no—
14D4×Dic15—21no—
15C4×Dic30C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C2×#6663—21no—
19C5×#832—22no—
20C4×C5×C3⋊C8C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23#90985—21no—
24#90975—21no—
25#90973—21no—
26#68406—51nomaximal, Hall
27#66047—31no—
28C5×#486—31no—
29#65383—31no—
30#65379—31no—
31#64764D311yescharacteristic
32#64676—31no—
33#64676—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4D412yes—
37C22×Dic15—22no—
38C2×Dic30D411yescharacteristic
39C2×Dic30D411yescharacteristic
40C2×C5×Dic6—21no—
41C3×C42×C5C2311yescharacteristic
42#6719—22no—
43#6719—22no—
44#6719—22no—
45C4⋊Dic15D411yescharacteristic
46C4⋊Dic15D411yescharacteristic
47#6712—21no—
48#6712—21no—
49C4×Dic15—21no—
50C4×Dic15—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3—21no—
53C2×C5×C3⋊C8—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#6663—42no—
57#5713—51no—
58#5070D511yescharacteristic
59#4851—51no—
60#4849—51no—
61C3×#331—51no—
62#4484—51no—
63#4484—51no—
64C5×C4⋊Q8—31no—
65C5×#127C2×D311yescharacteristic
66C2×#689—61no—
67#4082—61no—
68#4082—61no—
69#4081—62no—
70D4×Dic5—61no—
71D4×Dic5—61no—
72C4×Dic10—31no—
73C4×Dic10—31no—
74C5×#102—62no—
75C4×C5×C8—31no—
76#3967—61no—
77#3942—61no—
78#3940—61no—
79C4⋊#168C2×D311yescharacteristic
80C4⋊#168C2×D311yescharacteristic
81#1640—151noSylow
82C23×C3×C5—22no—
83C3×C5×D4—42no—
84C3×C5×D4—41no—
85C3×C5×D4—41no—
86C3×C5×D4—41no—
87C3×C5×D4—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92C2×Dic15—21no—
93C2×Dic15—21no—
94C2×Dic15—21no—
95C2×Dic15—82no—
96Dic30—21no—
97Dic30—21no—
98Dic30—21no—
99Dic30—21no—
100C2×C5×Dic3—41no—
101C5×Dic6—41no—
102C5×Dic6—41no—
103C3×#168—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C3×#127C2×D511yescharacteristic
107#936—101no—
108#936—101no—
109#935—102no—
110D4×Dic3—101no—
111D4×Dic3—101no—
112C2×Dic12—101no—
113#869C2×D511yescharacteristic
114C4×Dic6—51no—
115C4×Dic6—51no—
116C3×C4⋊C8—51no—
117C3×C4⋊C8—51no—
118#832—22no—
119#817—101no—
120#816—101no—
121#816—101no—
122C4×C3⋊C8C2×D511yescharacteristic
123C2×C5×Q8—61no—
124C2×C5×D4—21no—
125C2×C5×D4—21no—
126C2×C5×D4D1212yes—
127C22×Dic5—62no—
128C2×Dic10—31no—
129C2×Dic10—31no—
130C2×C5×C8—61no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4—61no—
133C42×C5C22×D311yescharacteristic
134C22⋊Dic5—62no—
135C22⋊Dic5—62no—
136C22⋊Dic5—62no—
137#689—122no—
138C4⋊Dic5—31no—
139C4⋊Dic5—31no—
140#683—61no—
141#683—61no—
142C4×Dic5—61no—
143C4×Dic5—61no—
144C2×#168—21no—
145C2×#168—21no—
146#559—151no—
147#486—31no—
148#475—151no—
149#462—151no—
150#331—51no—
151Q8⋊C8—151no—
152Q8⋊C8—151no—
153C22×C3×C5—42no—
154C22×C3×C5—42no—
155C22×C3×C5—42no—
156C22×C3×C5#12011yescharacteristic
157C3×C4×C5—21no—
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13511yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C3×C4×C5#13711yescharacteristic
162Dic15—41no—
163Dic15—41no—
164Dic15—41no—
165Dic15—41no—
166C5×Dic3—81no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4C22⋊D512yes—
170C22×Dic3—102no—
171C2×Dic6—21no—
172C2×Dic6—51no—
173C2×Dic6—51no—
174C2×C3×C8—101no—
175C2×C3×C8—101no—
176C3×C42C22×D511yescharacteristic
177#217—102no—
178#217—102no—
179#217—102no—
180C4⋊Dic3—21no—
181C4⋊Dic3—21no—
182C4⋊Dic3—51no—
183C4⋊Dic3—51no—
184Dic3⋊C4—101no—
185Dic3⋊C4—101no—
186C4×Dic3—101no—
187C4×Dic3—101no—
188C2×C3⋊C8—21no—
189Dic12—202no—
190C23×C5—22no—
191C5×Q8—121no—
192C5×Q8—121no—
193C5×D4—42no—
194C5×D4—41no—
195C5×D4—41no—
196C5×D4—41no—
197C5×D4—41no—
198C2×C4×C5—121no—
199C2×C4×C5C2×D1211yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×Dic5—61no—
203C2×Dic5—61no—
204C2×Dic5—61no—
205C2×Dic5—61no—
206C2×Dic5—242no—
207Dic10—61no—
208Dic10—61no—
209Dic10—61no—
210Dic10—61no—
211C5×C8—121no—
212#168—41no—
213#168—41no—
214C2×Q16—301no—
215C4⋊Q8—31no—
216#127D3×D511yescharacteristic
217#124—301no—
218#124—301no—
219#123—302no—
220C4×Q8—151no—
221C4×Q8—151no—
222C4×D4—301no—
223C4×D4—301no—
224#106—301no—
225C4⋊C8—51no—
226C4⋊C8—51no—
227#103—301no—
228#103—301no—
229#102—62no—
230C4×C8—31no—
231C2×C3×C5—82no—
232C2×C3×C5#44911yescharacteristic
233C2×C3×C5#45211yescharacteristic
234C2×C3×C5#45511yescharacteristic
235C23×C3—22no—
236C3×D4—42no—
237C3×D4—41no—
238C3×D4—41no—
239C3×D4—41no—
240C3×D4—41no—
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4C2×C22⋊D511yescharacteristic
244C2×Dic3—41no—
245C2×Dic3—101no—
246C2×Dic3—101no—
247C2×Dic3—101no—
248C2×Dic3—101no—
249C2×Dic3—402no—
250Dic6—41no—
251Dic6—41no—
252Dic6—101no—
253Dic6—101no—
254Dic6—101no—
255Dic6—101no—
256C3×C8—201no—
257C3×C8—201no—
258C3⋊C8—41no—
259C22×C5—42no—
260C22×C5—42no—
261C22×C5—42no—
262C22×C5#88211yescharacteristic
263C4×C5—21no—
264C4×C5—241no—
265C4×C5#91111yescharacteristic
266C4×C5#91211yescharacteristic
267C4×C5#91511yescharacteristic
268C4×C5#91611yescharacteristic
269Dic5—121no—
270Dic5—121no—
271Dic5—121no—
272Dic5—121no—
273C2×Q8—61no—
274C2×Q8—151no—
275C2×Q8—151no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4#120312yes—
279C22×C4—302no—
280Q16—602no—
281C2×C8—61no—
282C2×C8—101no—
283C2×C8—101no—
284C4⋊C4—61no—
285C4⋊C4—61no—
286C4⋊C4—151no—
287C4⋊C4—151no—
288C4⋊C4—301no—
289C4⋊C4—301no—
290C22⋊C4—302no—
291C22⋊C4—302no—
292C22⋊C4—302no—
293C42—301no—
294C42—301no—
295C42C2×D3×D511yescharacteristic
296C3×C5#164011yescharacteristic, complemented, Hall
297C22×C3—42no—
298C22×C3—42no—
299C22×C3—42no—
300C22×C3#408311yescharacteristic
301C3×C4—21no—
302C3×C4#405711yescharacteristic
303C3×C4#405811yescharacteristic
304C3×C4#406111yescharacteristic
305C3×C4#406211yescharacteristic
306Dic3—81no—
307Dic3—201no—
308Dic3—201no—
309Dic3—201no—
310Dic3—201no—
311C2×C5—82no—
312C2×C5#474611yescharacteristic
313C2×C5#478111yescharacteristic
314C2×C5#478311yescharacteristic
315C23—22no—
316Q8—121no—
317Q8—121no—
318Q8—301no—
319Q8—301no—
320Q8—301no—
321Q8—301no—
322D4—42no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—41no—
327C2×C4—121no—
328C2×C4—301no—
329C2×C4—301no—
330C2×C4—301no—
331C2×C4—301no—
332C2×C4—1202no—
333C2×C4C2×#120311yescharacteristic
334C2×C4#679011yescharacteristic
335C2×C4#679011yescharacteristic
336C8—121no—
337C8—201no—
338C8—201no—
339C2×C3—82no—
340C2×C3#6535011yescharacteristic
341C2×C3#6544711yescharacteristic
342C2×C3#6546211yescharacteristic
343C5#6840611yescharacteristic, complemented, Sylow
344C22—42no—
345C22—42no—
346C22—42no—
347C22#9157311yescharacteristic
348C4—21no—
349C4—241no—
350C4—601no—
351C4—601no—
352C4—601no—
353C4—601no—
354C4#9148211yescharacteristic
355C4#9148811yescharacteristic
356C4#9149711yescharacteristic
357C4#9149911yescharacteristic
358C3#1060199911yescharacteristic, complemented, Sylow
359C2—82no—
360C2#1174904311yescharacteristic
361C2#1174906111yescharacteristic
362C2#1174915011yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
Fitting, prime radicalC3×C5×#127C22
socleC22×C3×C5#120
hypercenter#127D3×D5
hypocenterC3×C5#1640
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
3. #11747105C2semidirect
4. #11746946C2semidirect
6. #11745844C2semidirect
7. #11745844C2semidirect
296. C3×C5#1640semidirect
343. C5#68406semidirect
358. C3#10601999semidirect

Maximal subgroups

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

subgroupindex
#117564722
C5×#50702
#117471052
#117469462
C3×#647642
#117458442
#106019993
#684065