Finite Group Databasebeta

← #14291267

Subgroups — #14291267

Order 1920.

368 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 76 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×#5672C211yesmaximal, characteristic
2C3×#65344C211yesmaximal, characteristic
3#11746969C211yesmaximal, characteristic, complemented
4#11746925C211yesmaximal, characteristic, complemented
5#11746361C211yesmaximal, characteristic
6#11745850C211yesmaximal, characteristic, complemented
7#11745850C211yesmaximal, characteristic, complemented
8#10602750—31nomaximal, Hall
9C3×C5×#124C2211yescharacteristic
10C5×#944—21no—
11C5×#935—21no—
12C5×#879—21no—
13C5×#879—21no—
14C5×#878—21no—
15C5×#878—21no—
16C5×#870C2211yescharacteristic
17C5×#870C2211yescharacteristic
18C3×#4015C2211yescharacteristic
19#91087C2211yescharacteristic
20#91087C2211yescharacteristic
21C3×#3967—21no—
22C3×#3964—21no—
23C3×#3935C2211yescharacteristic
24#90989—21no—
25#90986—21no—
26#90970—21no—
27#90970—21no—
28#71247—51nomaximal, Hall
29C5×#563—31no—
30#65358—31no—
31#65354—31no—
32#65344D311yescharacteristic
33#64763—31no—
34#64763—31no—
35#64760—31no—
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4D411yescharacteristic
38C22×C5×Dic3—21no—
39C2×C5×Dic6—21no—
40C2×C3×Dic10—21no—
41C3×C5×C22⋊C4—21no—
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44C2×C3⋊#168—21no—
45C2×C3⋊#168—21no—
46C5×#217—21no—
47C5×#217—21no—
48C5×#217—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×C4⋊Dic3D411yescharacteristic
51C5×C4⋊Dic3D411yescharacteristic
52C5×C4⋊Dic3D411yescharacteristic
53C5×Dic3⋊C4—21no—
54C5×Dic3⋊C4—21no—
55C5×Dic3⋊C4—21no—
56C5×Dic3⋊C4—21no—
57C5×Dic3⋊C4—21no—
58C5×Dic3⋊C4—21no—
59C4×C5×Dic3—21no—
60C3×C4⋊Dic5—21no—
61C3×C4⋊Dic5—21no—
62C2×C3×#168—21no—
63#5672D511yescharacteristic
64C3×#489—51no—
65#5082—51no—
66#5081—51no—
67#4540—51no—
68#4465—51no—
69#4465—51no—
70C5×C4⋊Q8—61no—
71C5×#126—61no—
72C5×#126—61no—
73C5×#125—31no—
74C5×#125—31no—
75C5×#124C2×D311yescharacteristic
76C5×#123—61no—
77C5×C22⋊Q8—61no—
78C5×C22⋊Q8—61no—
79#4015C2×D311yescharacteristic
80#3967—21no—
81#3964—21no—
82#3942—61no—
83#3942—61no—
84#3940—61no—
85#3939—61no—
86#3935—31no—
87#3935—31no—
88#3935C2×D311yescharacteristic
89#1664—151noSylow
90C23×C3×C5—21no—
91C3×C5×Q8—41no—
92C3×C5×D4—41no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C5×Dic3—21no—
98C2×C5×Dic3—21no—
99C2×C5×Dic3—21no—
100C2×C5×Dic3—21no—
101C2×C5×Dic3—81no—
102C5×Dic6—81no—
103C2×C3×Dic5—41no—
104C3×Dic10—42no—
105C3⋊#168—22no—
106C3⋊#168—41no—
107C3×#168—41no—
108C3×C4⋊Q8—51no—
109C3×#124C2×D511yescharacteristic
110#944—21no—
111#935—21no—
112#879—21no—
113#879—21no—
114#878—21no—
115#878—21no—
116#870C2×D511yescharacteristic
117#870C2×D511yescharacteristic
118C3×#103—101no—
119C3×#102—101no—
120C3×#97—51no—
121#835—101no—
122#835—101no—
123#808—101no—
124#807—101no—
125#803—51no—
126#803—51no—
127C2×C5×Q8—61no—
128C2×C5×Q8#6711yescharacteristic
129C2×C5×D4#6711yescharacteristic
130C22×C4×C5—61no—
131C2×Dic10—21no—
132C5×C4⋊C4—31no—
133C5×C4⋊C4—31no—
134C5×C4⋊C4—31no—
135C5×C4⋊C4—31no—
136C5×C4⋊C4—61no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4—61no—
139C5×C4⋊C4—61no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4—61no—
142C5×C22⋊C4—21no—
143C5×C22⋊C4—21no—
144C5×C22⋊C4—61no—
145C5×C22⋊C4—61no—
146C5×C22⋊C4—61no—
147C42×C5—61no—
148C42×C5C22×D311yescharacteristic
149C4⋊Dic5—21no—
150C4⋊Dic5—21no—
151C2×#168—21no—
152C2×#168—61no—
153C2×#168—61no—
154#563—31no—
155#501—151no—
156#491—151no—
157#489—51no—
158#330—151no—
159#330—151no—
160#329—151no—
161C22×C3×C5—41no—
162C22×C3×C5—41no—
163C22×C3×C5—41no—
164C22×C3×C5#12011yescharacteristic
165C3×C4×C5—21no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168C3×C4×C5—41no—
169C3×Dic5—81no—
170C5×Dic3—41no—
171C5×Dic3—41no—
172C5×Dic3—41no—
173C5×Dic3—41no—
174C2×C3×Q8—101no—
175C2×C3×Q8C22⋊D511yescharacteristic
176C2×C3×D4C22⋊D511yescharacteristic
177C22×Dic3—21no—
178C2×Dic6—21no—
179C2×C3×C8—101no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4—101no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C42C22×D511yescharacteristic
185#217—21no—
186#217—21no—
187#217—21no—
188C4⋊Dic3C22⋊D511yescharacteristic
189C4⋊Dic3C22⋊D511yescharacteristic
190C4⋊Dic3C22⋊D511yescharacteristic
191C4⋊Dic3C22⋊D511yescharacteristic
192Dic3⋊C4—21no—
193Dic3⋊C4—21no—
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197Dic3⋊C4—21no—
198C4×Dic3—21no—
199C2×C3⋊C8—101no—
200C2×C3⋊C8—101no—
201C23×C5—21no—
202C5×Q8—41no—
203C5×Q8—241no—
204C5×D4—41no—
205C2×C4×C5—21no—
206C2×C4×C5—61no—
207C2×C4×C5—61no—
208C2×C4×C5—61no—
209C2×C4×C5—61no—
210C2×C4×C5—241no—
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C2×C4×C5C2×#6711yescharacteristic
214C2×Dic5—41no—
215Dic10—42no—
216#168—41no—
217#168—62no—
218#168—121no—
219C4⋊Q8—51no—
220C4⋊Q8—61no—
221#126—61no—
222#126—61no—
223#125—31no—
224#125—31no—
225#124D3×D511yescharacteristic
226#123—61no—
227C22⋊Q8—61no—
228C22⋊Q8—61no—
229#107—301no—
230#106—301no—
231#103—101no—
232#103—301no—
233#103—301no—
234#102—101no—
235#97—51no—
236#97—151no—
237#97—151no—
238C2×C3×C5—81no—
239C2×C3×C5#45411yescharacteristic
240C2×C3×C5#45511yescharacteristic
241C2×C3×C5#45611yescharacteristic
242C23×C3—21no—
243C3×Q8—41no—
244C3×Q8—202no—
245C3×D4—41no—
246C2×C3×C4—21no—
247C2×C3×C4—201no—
248C2×C3×C4C2×C22⋊D511yescharacteristic
249C2×C3×C4C2×C22⋊D511yescharacteristic
250C2×C3×C4C2×C22⋊D511yescharacteristic
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—81no—
256Dic6—81no—
257C3×C8—201no—
258C3⋊C8—102no—
259C3⋊C8—201no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5—41no—
263C22×C5#93711yescharacteristic
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—41no—
268C4×C5—121no—
269C4×C5—121no—
270C4×C5—121no—
271C4×C5—121no—
272Dic5—81no—
273C2×Q8—61no—
274C2×Q8—101no—
275C2×Q8#120111yescharacteristic
276C2×D4#120111yescharacteristic
277C22×C4—61no—
278C2×C8—101no—
279C2×C8—301no—
280C2×C8—301no—
281C4⋊C4—31no—
282C4⋊C4—31no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—61no—
286C4⋊C4—61no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4—101no—
292C4⋊C4—101no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—61no—
296C22⋊C4—61no—
297C22⋊C4—61no—
298C42—61no—
299C42C2×D3×D511yescharacteristic
300C3×C5#166411yescharacteristic, complemented, Hall
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3#409911yescharacteristic
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4—401no—
310Dic3—41no—
311Dic3—41no—
312Dic3—41no—
313Dic3—41no—
314C2×C5—81no—
315C2×C5#506111yescharacteristic
316C2×C5#520111yescharacteristic
317C2×C5#520511yescharacteristic
318C23—21no—
319Q8—41no—
320Q8—202no—
321Q8—241no—
322D4—41no—
323C2×C4—21no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—201no—
329C2×C4—241no—
330C2×C4C2×#120111yescharacteristic
331C2×C4D3×C22⋊D511yescharacteristic
332C2×C4D3×C22⋊D511yescharacteristic
333C8—201no—
334C8—302no—
335C8—601no—
336C2×C3—81no—
337C2×C3#6553111yescharacteristic
338C2×C3#6553411yescharacteristic
339C2×C3#6553511yescharacteristic
340C5#7124711yescharacteristic, complemented, Sylow
341C22—41no—
342C22—41no—
343C22—41no—
344C22#9156811yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—121no—
350C4—121no—
351C4—121no—
352C4—121no—
353C4—401no—
354C3#1060275011yescharacteristic, complemented, Sylow
355C2—81no—
356C2#1174914711yescharacteristic
357C2#1174945811yescharacteristic
358C2#1174946511yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenter#124D3×D5
hypocenterC3×C5#1664
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
3. #11746969C2semidirect
4. #11746925C2semidirect
6. #11745850C2semidirect
7. #11745850C2semidirect
300. C3×C5#1664semidirect
340. C5#71247semidirect
354. C3#10602750semidirect

Maximal subgroups

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

subgroupindex
C5×#56722
C3×#653442
#117469692
#117469252
#117463612
#117458502
#106027503
#712475