Finite Group Databasebeta

← #14291237

Subgroups — #14291237

Order 1920.

368 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 70 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#11752474C211yesmaximal, characteristic
2#11751190C211yesmaximal, characteristic
3C5×#5081C211yesmaximal, characteristic, complemented
4C3×#65371C211yesmaximal, characteristic, complemented
5#11745850C211yesmaximal, characteristic, complemented
6#11745849C211yesmaximal, characteristic, complemented
7#11745848C211yesmaximal, characteristic
8#10602187—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91764C2211yescharacteristic
11C5×#870C2211yescharacteristic
12C3×#4016C2211yescharacteristic
13#91433—21no—
14#91429—21no—
15#91419—21no—
16#91345—21no—
17#91337—21no—
18#91328—21no—
19#91094—21no—
20#91093—21no—
21#91087C2211yescharacteristic
22C5×#808—21no—
23C5×#807—21no—
24C5×#803C2211yescharacteristic
25C3×#3967—21no—
26C3×#3967—21no—
27C3×#3935C2211yescharacteristic
28#71253—51nomaximal, Hall
29#66033—31no—
30C5×#501—31no—
31#65378—31no—
32#65371D311yescharacteristic, complemented
33#64763—31no—
34#64685—31no—
35#64684—31no—
36C2×C3×C5×Q8—21no—
37C2×D60D411yescharacteristic
38C2×Dic30D411yescharacteristic
39C2×#1204—21no—
40C2×#1200—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44#6714—21no—
45#6714—21no—
46C2×C3⋊#168—21no—
47C5×C4⋊Dic3D411yescharacteristic
48C5×C4⋊Dic3D411yescharacteristic
49C5×Dic3⋊C4—21no—
50C5×Dic3⋊C4—21no—
51C2×C5×C3⋊C8—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×C4⋊Dic5D411yescharacteristic
54C3×#683—21no—
55C3×#683—21no—
56C2×C3×#168—21no—
57Dic3⋊Dic5—21no—
58#6668—21no—
59#6667—21no—
60#6667—21no—
61#6667—21no—
62Dic3×Dic5—21no—
63#5699—51no—
64C3×#491—51no—
65#5089—51no—
66#5081D511yescharacteristic, complemented
67#4543—51no—
68#4465—51no—
69#4464—51no—
70C5×C4⋊Q8C2×D311yescharacteristic
71C5×#125—31no—
72#4044—61no—
73#4044—61no—
74#4043—61no—
75#4042—61no—
76#4040—61no—
77#4034—61no—
78#4021—31no—
79#4016C2×D311yescharacteristic
80C5×#107—61no—
81C5×#106—61no—
82C5×#97—31no—
83#3967—21no—
84#3967—21no—
85#3942—61no—
86#3941—61no—
87#3935—31no—
88#3935C2×D311yescharacteristic
89#1664—151noSylow
90C22×D15—21no—
91C3×C5×Q8—42no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—21no—
97D60—41no—
98Dic30—41no—
99C2×C5×Dic3—21no—
100C2×C5×Dic3—21no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—21no—
103#1204—81no—
104#1200—81no—
105C3⋊#168—41no—
106C3×#168—41no—
107C5×C3⋊C8—22no—
108C3×C4⋊Q8C2×D511yescharacteristic
109C3×#125—51no—
110#898—101no—
111#898—101no—
112#897—101no—
113#896—101no—
114#894—101no—
115#888—101no—
116#875—51no—
117#870C2×D511yescharacteristic
118C3×#103—101no—
119C3×#103—101no—
120C3×#97—51no—
121#810—101no—
122#809—101no—
123#808—21no—
124#807—21no—
125#803—51no—
126#803C2×D511yescharacteristic
127C2×C5×Q8—21no—
128C2×D20—31no—
129C2×C4×D5—61no—
130C2×Dic10—31no—
131C2×Dic10—61no—
132C2×C5×C8—61no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—31no—
136C5×C4⋊C4—31no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4—61no—
139C42×C5C22×D311yescharacteristic
140#685—61no—
141#685—61no—
142#685—61no—
143#685—61no—
144#685—61no—
145C4⋊Dic5—61no—
146C4⋊Dic5#6711yescharacteristic
147C4⋊Dic5#6711yescharacteristic
148#683—21no—
149#683—21no—
150#683—61no—
151C4×Dic5—61no—
152C2×#168—21no—
153C2×#168—61no—
154#563—151no—
155#501—31no—
156#491—51no—
157#489—151no—
158#330—151no—
159#330—151no—
160#329—151no—
161C22×C3×C5#12011yescharacteristic
162C2×D15—41no—
163C2×D15—41no—
164C2×D15—41no—
165C3×C4×C5—21no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168C3×C4×C5—81no—
169Dic15—41no—
170C3×Dic5—41no—
171C3×Dic5—41no—
172C5×Dic3—41no—
173C5×Dic3—41no—
174C2×C3×Q8—21no—
175C2×D12—51no—
176C2×C4×D3—101no—
177C2×Dic6—51no—
178C2×Dic6—101no—
179C2×C3×C8—101no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—51no—
183C3×C4⋊C4—51no—
184C3×C4⋊C4—101no—
185C3×C4⋊C4—101no—
186C3×C42C22×D511yescharacteristic
187(C2×D3)⋊C4—101no—
188(C2×D3)⋊C4—101no—
189(C2×D3)⋊C4—101no—
190(C2×D3)⋊C4—101no—
191(C2×D3)⋊C4—101no—
192C4⋊Dic3—101no—
193C4⋊Dic3C22⋊D511yescharacteristic
194C4⋊Dic3C22⋊D511yescharacteristic
195Dic3⋊C4—21no—
196Dic3⋊C4—21no—
197Dic3⋊C4—101no—
198C4×Dic3—101no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—101no—
201C22×D5—61no—
202C5×Q8—42no—
203C2×C4×C5—41no—
204C2×C4×C5—61no—
205C2×C4×C5—61no—
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5C2×#6711yescharacteristic
209C2×Dic5—21no—
210C2×Dic5—21no—
211C2×Dic5—61no—
212D20—121no—
213C4×D5—241no—
214Dic10—121no—
215Dic10—241no—
216C5×C8—62no—
217#168—41no—
218#168—121no—
219C4⋊Q8—301no—
220C4⋊Q8D3×D511yescharacteristic
221#126—301no—
222#126—301no—
223#125—31no—
224#125—51no—
225#124—151no—
226#123—301no—
227C22⋊Q8—301no—
228C22⋊Q8—301no—
229#107—61no—
230#106—61no—
231#103—101no—
232#103—101no—
233#103—301no—
234#102—301no—
235#97—31no—
236#97—51no—
237#97—151no—
238C2×C3×C5#45411yescharacteristic
239C2×C3×C5#45511yescharacteristic
240C2×C3×C5#45611yescharacteristic
241D15—81no—
242C22×D3—101no—
243C3×Q8—42no—
244C2×C3×C4—41no—
245C2×C3×C4—101no—
246C2×C3×C4—101no—
247C2×C3×C4D4×D511yescharacteristic
248C2×C3×C4D4×D511yescharacteristic
249C2×C3×C4C2×C22⋊D511yescharacteristic
250C2×Dic3—21no—
251C2×Dic3—21no—
252C2×Dic3—101no—
253D12—201no—
254C4×D3—401no—
255Dic6—201no—
256Dic6—401no—
257C3×C8—201no—
258C3⋊C8—22no—
259C3⋊C8—201no—
260C22×C5#93711yescharacteristic
261C2×D5—121no—
262C2×D5—121no—
263C2×D5—121no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—81no—
268C4×C5—121no—
269C4×C5—121no—
270Dic5—41no—
271Dic5—41no—
272Dic5—121no—
273C2×Q8—21no—
274C2×Q8—151no—
275C2×Q8—301no—
276C2×D4—151no—
277C22×C4—301no—
278C2×C8—61no—
279C2×C8—101no—
280C2×C8—301no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—51no—
286C4⋊C4—51no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—101no—
290C4⋊C4—101no—
291C4⋊C4—301no—
292C4⋊C4—301no—
293C22⋊C4—301no—
294C22⋊C4—301no—
295C22⋊C4—301no—
296C22⋊C4—301no—
297C22⋊C4—301no—
298C42—301no—
299C42C2×D3×D511yescharacteristic
300C3×C5#166411yescharacteristic, complemented, Hall
301C22×C3#408311yescharacteristic
302C2×D3—201no—
303C2×D3—201no—
304C2×D3—201no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—81no—
309C3×C4—201no—
310C3×C4—201no—
311Dic3—41no—
312Dic3—41no—
313Dic3—201no—
314C2×C5#506211yescharacteristic
315C2×C5#520211yescharacteristic
316C2×C5#520511yescharacteristic
317D5—241no—
318C23—301no—
319Q8—42no—
320Q8—601no—
321Q8—1201no—
322D4—601no—
323C2×C4—41no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—301no—
329C2×C4—1201no—
330C2×C4D5×#6711yescharacteristic
331C2×C4D3×C22⋊D511yescharacteristic
332C2×C4#679011yescharacteristic
333C8—62no—
334C8—201no—
335C8—601no—
336C2×C3#6538411yescharacteristic
337C2×C3#6549011yescharacteristic
338C2×C3#6549111yescharacteristic
339D3—401no—
340C5#7125311yescharacteristic, complemented, Sylow
341C22—601no—
342C22—601no—
343C22—601no—
344C22#9157711yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—81no—
349C4—121no—
350C4—121no—
351C4—201no—
352C4—201no—
353C4—601no—
354C3#1060218711yescharacteristic, complemented, Sylow
355C2—1201no—
356C2#1174916811yescharacteristic
357C2#1174941011yescharacteristic
358C2#1174941311yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1664
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. C5×#5081C2semidirect
4. C3×#65371C2semidirect
5. #11745850C2semidirect
6. #11745849C2semidirect
32. #65371D3semidirect
66. #5081D5semidirect
300. C3×C5#1664semidirect
340. C5#71253semidirect
354. C3#10602187semidirect

Maximal subgroups

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

subgroupindex
#117524742
#117511902
C5×#50812
C3×#653712
#117458502
#117458492
#117458482
#106021873
#712535