Finite Group Databasebeta

← #14289963

Subgroups — #14289963

Order 1920.

424 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C5×#5713C211yesmaximal, characteristic
2C3×#65359C211yesmaximal, characteristic
3#11747099C211yesmaximal, characteristic, complemented
4#11746927C211yesmaximal, characteristic, complemented
5#11746365C211yesmaximal, characteristic
6#11745843C211yesmaximal, characteristic, complemented
7#11745843C211yesmaximal, characteristic, complemented
8#10602738—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10C5×#936—21no—
11C5×#936—21no—
12C5×#935—22no—
13C5×D4×Dic3—21no—
14C5×D4×Dic3—21no—
15C4×C5×Dic6C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6661—21no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C3×#3964—22no—
22C3×C4×#168C2211yescharacteristic
23#90986—21no—
24#90972—21no—
25#90970—21no—
26#71206—51nomaximal, Hall
27C5×#559—31no—
28#65359D311yescharacteristic
29#65320—31no—
30#65309—31no—
31#64764—31no—
32Q8⋊#168—31no—
33Q8⋊#168—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4D412yes—
37C22×C5×Dic3—22no—
38C2×C5×Dic6D411yescharacteristic
39C2×C5×Dic6D411yescharacteristic
40C2×C3×Dic10—21no—
41C3×C42×C5C2311yescharacteristic
42C2×C3⋊#168—21no—
43C2×C3⋊#168—21no—
44C5×#217—22no—
45C5×#217—22no—
46C5×#217—22no—
47C5×C4⋊Dic3D411yescharacteristic
48C5×C4⋊Dic3D411yescharacteristic
49C5×Dic3⋊C4—21no—
50C5×Dic3⋊C4—21no—
51C4×C5×Dic3—21no—
52C4×C5×Dic3—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C2×C3×#168—21no—
56#6661—42no—
57#5713D511yescharacteristic
58C3×#486—51no—
59#5094—51no—
60#5090—51no—
61#4544—51no—
62#4456—51no—
63#4456—51no—
64C5×#127C2×D311yescharacteristic
65C5×#124—61no—
66C5×#124—61no—
67C5×#123—62no—
68C4×C5×Q8—31no—
69C4×C5×Q8—31no—
70C4×C5×D4—61no—
71C4×C5×D4—61no—
72C2×#689—61no—
73#4015C2×D311yescharacteristic
74#3967—61no—
75#3964—22no—
76#3942—61no—
77#3940—61no—
78C4⋊#168—31no—
79C4⋊#168—31no—
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×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—21no—
94C2×C5×Dic3—21no—
95C2×C5×Dic3—82no—
96C5×Dic6—21no—
97C5×Dic6—21no—
98C5×Dic6—21no—
99C5×Dic6—21no—
100C2×C3×Dic5—41no—
101C3×Dic10—41no—
102C3×Dic10—41no—
103C3⋊#168—41no—
104C3⋊#168—41no—
105C3×#168—41no—
106C3×C4⋊Q8—51no—
107C3×#127C2×D511yescharacteristic
108C2×#216—101no—
109#936—21no—
110#936—21no—
111#935—22no—
112D4×Dic3—21no—
113D4×Dic3—21no—
114C4×Dic6C2×D511yescharacteristic
115C4×Dic6C2×D511yescharacteristic
116C3×#102—102no—
117C3×C4×C8—51no—
118#835—101no—
119#810—101no—
120#808—101no—
121C4⋊(C3⋊C8)—51no—
122C4⋊(C3⋊C8)—51no—
123C2×C5×Q8—31no—
124C2×C5×Q8—31no—
125C2×C5×D4—21no—
126C2×C5×D4—21no—
127C2×C5×D4#6712yes—
128C22×C4×C5—62no—
129C2×Dic10—21no—
130C5×C4⋊C4—31no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—61no—
133C5×C4⋊C4—61no—
134C5×C22⋊C4—62no—
135C5×C22⋊C4—62no—
136C5×C22⋊C4—62no—
137C42×C5—61no—
138C42×C5—61no—
139C42×C5C22×D311yescharacteristic
140#689—122no—
141C4⋊Dic5—21no—
142C4⋊Dic5—21no—
143C2×#168—21no—
144C2×#168—61no—
145C2×#168—61no—
146#559—31no—
147#486—51no—
148#475—151no—
149#462—151no—
150#331—151no—
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
162C3×Dic5—81no—
163C5×Dic3—41no—
164C5×Dic3—41no—
165C5×Dic3—41no—
166C5×Dic3—41no—
167C2×C3×Q8—101no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4C22⋊D512yes—
171C22×Dic3—22no—
172C2×Dic6C22⋊D511yescharacteristic
173C2×Dic6C22⋊D511yescharacteristic
174C2×C3×C8—101no—
175C3×C4⋊C4—101no—
176C3×C4⋊C4—101no—
177C3×C42C22×D511yescharacteristic
178#217—22no—
179#217—22no—
180#217—22no—
181#216—202no—
182C4⋊Dic3C22⋊D511yescharacteristic
183C4⋊Dic3C22⋊D511yescharacteristic
184Dic3⋊C4—21no—
185Dic3⋊C4—21no—
186C4×Dic3—21no—
187C4×Dic3—21no—
188C2×C3⋊C8—101no—
189C2×C3⋊C8—101no—
190C23×C5—22no—
191C5×Q8—61no—
192C5×Q8—61no—
193C5×Q8—61no—
194C5×Q8—61no—
195C5×D4—42no—
196C5×D4—41no—
197C5×D4—41no—
198C5×D4—41no—
199C5×D4—41no—
200C2×C4×C5—61no—
201C2×C4×C5—61no—
202C2×C4×C5—61no—
203C2×C4×C5—61no—
204C2×C4×C5—242no—
205C2×C4×C5D3×D411yescharacteristic
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5C2×#6711yescharacteristic
208C2×Dic5—41no—
209Dic10—41no—
210Dic10—41no—
211#168—41no—
212#168—121no—
213#168—121no—
214C2×Q16—301no—
215C4⋊Q8—51no—
216#127D3×D511yescharacteristic
217#124—61no—
218#124—61no—
219#123—62no—
220C4×Q8—31no—
221C4×Q8—31no—
222C4×D4—61no—
223C4×D4—61no—
224#106—301no—
225C4⋊C8—151no—
226C4⋊C8—151no—
227#103—301no—
228#103—301no—
229#102—102no—
230C4×C8—51no—
231C2×C3×C5—82no—
232C2×C3×C5#44911yescharacteristic
233C2×C3×C5#45211yescharacteristic
234C2×C3×C5#45511yescharacteristic
235C23×C3—22no—
236C3×Q8—201no—
237C3×Q8—201no—
238C3×D4—42no—
239C3×D4—41no—
240C3×D4—41no—
241C3×D4—41no—
242C3×D4—41no—
243C2×C3×C4—201no—
244C2×C3×C4C2×C22⋊D511yescharacteristic
245C2×C3×C4C2×C22⋊D511yescharacteristic
246C2×C3×C4C2×C22⋊D511yescharacteristic
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—82no—
252Dic6—21no—
253Dic6—21no—
254Dic6—21no—
255Dic6—21no—
256C3×C8—201no—
257C3⋊C8—201no—
258C3⋊C8—201no—
259C22×C5—42no—
260C22×C5—42no—
261C22×C5—42no—
262C22×C5#93711yescharacteristic
263C4×C5—21no—
264C4×C5—121no—
265C4×C5—121no—
266C4×C5—121no—
267C4×C5—121no—
268C4×C5#91111yescharacteristic
269C4×C5#91211yescharacteristic
270C4×C5#91511yescharacteristic
271C4×C5#91611yescharacteristic
272Dic5—81no—
273C2×Q8—31no—
274C2×Q8—31no—
275C2×Q8—101no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4#120112yes—
279C22×C4—62no—
280Q16—602no—
281C2×C8—101no—
282C2×C8—301no—
283C2×C8—301no—
284C4⋊C4—31no—
285C4⋊C4—31no—
286C4⋊C4—61no—
287C4⋊C4—61no—
288C4⋊C4—101no—
289C4⋊C4—101no—
290C22⋊C4—62no—
291C22⋊C4—62no—
292C22⋊C4—62no—
293C42—61no—
294C42—61no—
295C42C2×D3×D511yescharacteristic
296C3×C5#164011yescharacteristic, complemented, Hall
297C22×C3—42no—
298C22×C3—42no—
299C22×C3—42no—
300C22×C3#409911yescharacteristic
301C3×C4—21no—
302C3×C4—401no—
303C3×C4#409511yescharacteristic
304C3×C4#409611yescharacteristic
305C3×C4#409611yescharacteristic
306C3×C4#409711yescharacteristic
307Dic3—41no—
308Dic3—41no—
309Dic3—41no—
310Dic3—41no—
311C2×C5—82no—
312C2×C5#506111yescharacteristic
313C2×C5#515811yescharacteristic
314C2×C5#517311yescharacteristic
315C23—22no—
316Q8—61no—
317Q8—61no—
318Q8—61no—
319Q8—61no—
320Q8—201no—
321Q8—201no—
322D4—42no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—41no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—61no—
331C2×C4—201no—
332C2×C4—242no—
333C2×C4C2×#120111yescharacteristic
334C2×C4D3×C22⋊D511yescharacteristic
335C2×C4D3×C22⋊D511yescharacteristic
336C8—201no—
337C8—601no—
338C8—601no—
339C2×C3—82no—
340C2×C3#6552711yescharacteristic
341C2×C3#6552811yescharacteristic
342C2×C3#6553111yescharacteristic
343C5#7120611yescharacteristic, complemented, Sylow
344C22—42no—
345C22—42no—
346C22—42no—
347C22#9156811yescharacteristic
348C4—21no—
349C4—121no—
350C4—121no—
351C4—121no—
352C4—121no—
353C4—401no—
354C4#9148011yescharacteristic
355C4#9148611yescharacteristic
356C4#9149311yescharacteristic
357C4#9149511yescharacteristic
358C3#1060273811yescharacteristic, complemented, Sylow
359C2—82no—
360C2#1174903511yescharacteristic
361C2#1174905911yescharacteristic
362C2#1174914711yescharacteristic
subgroupG/H
centerC22#91568
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. #11747099C2semidirect
4. #11746927C2semidirect
6. #11745843C2semidirect
7. #11745843C2semidirect
296. C3×C5#1640semidirect
343. C5#71206semidirect
358. C3#10602738semidirect

Maximal subgroups

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

subgroupindex
C5×#57132
C3×#653592
#117470992
#117469272
#117463652
#117458432
#106027383
#712065