Finite Group Databasebeta

← #14291219

Subgroups — #14291219

Order 1920.

368 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 75 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#11756458C211yesmaximal, characteristic
2C3×C5×#501C211yesmaximal, characteristic, complemented
3#11751190C211yesmaximal, characteristic
4#11751183C211yesmaximal, characteristic, complemented
5#11746364C211yesmaximal, characteristic, complemented
6#11746286C211yesmaximal, characteristic, complemented
7#11746285C211yesmaximal, characteristic
8#10602187—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#125C2211yescharacteristic
11#91787—21no—
12#91787—21no—
13#91786—21no—
14#91785—21no—
15#91783—21no—
16#91777—21no—
17#91764C2211yescharacteristic
18#91759C2211yescharacteristic
19C3×C5×#107—21no—
20C3×C5×#106—21no—
21C3×C5×#97C2211yescharacteristic
22#91119—21no—
23#91119—21no—
24#91094—21no—
25#91093—21no—
26#91087C2211yescharacteristic
27#91087C2211yescharacteristic
28#71394—51nomaximal, Hall
29#66033—31no—
30C5×#501D311yescharacteristic, complemented
31#65378—31no—
32#65371—31no—
33#64763—31no—
34#64685—31no—
35#64684—31no—
36C2×C3×C5×Q8—21no—
37C2×D60D411yescharacteristic
38C2×C4×D15—21no—
39C2×Dic30—21no—
40C2×Dic30D411yescharacteristic
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C42×C5C2311yescharacteristic
49#6714—21no—
50#6714—21no—
51#6714—21no—
52#6714—21no—
53#6714—21no—
54C4⋊Dic15—21no—
55C4⋊Dic15D411yescharacteristic
56C4⋊Dic15D411yescharacteristic
57#6712—21no—
58#6712—21no—
59#6712—21no—
60C4×Dic15—21no—
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63#5699—51no—
64C3×#501D511yescharacteristic, complemented
65#5089—51no—
66#5082—51no—
67#4543—51no—
68#4465—51no—
69#4464—51no—
70C5×C4⋊Q8C2×D311yescharacteristic
71C5×#125C2×D311yescharacteristic
72#4044—61no—
73#4044—61no—
74#4043—61no—
75#4042—61no—
76#4040—61no—
77#4034—61no—
78#4021—31no—
79#4016—31no—
80C5×#107—21no—
81C5×#106—21no—
82C5×#97C2×D311yescharacteristic
83#3967—61no—
84#3967—61no—
85#3942—61no—
86#3941—61no—
87#3935—31no—
88#3935—31no—
89#1664—151noSylow
90C22×D15—21no—
91C3×C5×Q8—42no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×Dic15—21no—
99C2×Dic15—21no—
100C2×Dic15—21no—
101D60—41no—
102C4×D15—81no—
103Dic30—41no—
104Dic30—81no—
105C3×C5×C8—22no—
106C3⋊#168—41no—
107C3⋊#168—41no—
108C3×C4⋊Q8C2×D511yescharacteristic
109C3×#125C2×D511yescharacteristic
110#898—101no—
111#898—101no—
112#897—101no—
113#896—101no—
114#894—101no—
115#888—101no—
116#875—51no—
117#870—51no—
118C3×#107—21no—
119C3×#106—21no—
120C3×#97C2×D511yescharacteristic
121#835—101no—
122#835—101no—
123#810—101no—
124#809—101no—
125#803—51no—
126#803—51no—
127C2×C5×Q8—21no—
128C2×D20—31no—
129C2×C4×D5—61no—
130C2×Dic10—31no—
131C2×Dic10—61no—
132C2×C5×C8—21no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4#6711yescharacteristic
138C5×C4⋊C4#6711yescharacteristic
139C42×C5C22×D311yescharacteristic
140#685—61no—
141#685—61no—
142#685—61no—
143#685—61no—
144#685—61no—
145C4⋊Dic5—31no—
146C4⋊Dic5—31no—
147C4⋊Dic5—61no—
148#683—61no—
149#683—61no—
150#683—61no—
151C4×Dic5—61no—
152C2×#168—61no—
153C2×#168—61no—
154#563—151no—
155#501D1511yescharacteristic, complemented
156#491—151no—
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—41no—
169C3×C4×C5—41no—
170C3×C4×C5—81no—
171Dic15—41no—
172Dic15—41no—
173Dic15—41no—
174C2×C3×Q8—21no—
175C2×D12—51no—
176C2×C4×D3—101no—
177C2×Dic6—51no—
178C2×Dic6—101no—
179C2×C3×C8—21no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4C22⋊D511yescharacteristic
185C3×C4⋊C4C22⋊D511yescharacteristic
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—51no—
193C4⋊Dic3—51no—
194C4⋊Dic3—101no—
195Dic3⋊C4—101no—
196Dic3⋊C4—101no—
197Dic3⋊C4—101no—
198C4×Dic3—101no—
199C2×C3⋊C8—101no—
200C2×C3⋊C8—101no—
201C22×D5—61no—
202C5×Q8—42no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5—41no—
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C2×C4×C5C2×#6711yescharacteristic
209C2×Dic5—61no—
210C2×Dic5—61no—
211C2×Dic5—61no—
212D20—121no—
213C4×D5—241no—
214Dic10—121no—
215Dic10—241no—
216C5×C8—22no—
217#168—121no—
218#168—121no—
219C4⋊Q8—301no—
220C4⋊Q8C2×D1511yescharacteristic
221#126—301no—
222#126—301no—
223#125—151no—
224#125C2×D1511yescharacteristic
225#124—151no—
226#123—301no—
227C22⋊Q8—301no—
228C22⋊Q8—301no—
229#107—21no—
230#106—21no—
231#103—301no—
232#103—301no—
233#103—301no—
234#102—301no—
235#97—151no—
236#97—151no—
237#97C2×D1511yescharacteristic
238C2×C3×C5#45411yescharacteristic
239C2×C3×C5#45511yescharacteristic
240C2×C3×C5#45611yescharacteristic
241D15—81no—
242C22×D3—101no—
243C3×Q8—42no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—41no—
247C2×C3×C4D4×D511yescharacteristic
248C2×C3×C4D4×D511yescharacteristic
249C2×C3×C4C2×C22⋊D511yescharacteristic
250C2×Dic3—101no—
251C2×Dic3—101no—
252C2×Dic3—101no—
253D12—201no—
254C4×D3—401no—
255Dic6—201no—
256Dic6—401no—
257C3×C8—22no—
258C3⋊C8—201no—
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—41no—
268C4×C5—41no—
269C4×C5—81no—
270Dic5—121no—
271Dic5—121no—
272Dic5—121no—
273C2×Q8—21no—
274C2×Q8—151no—
275C2×Q8—301no—
276C2×D4—151no—
277C22×C4—301no—
278C2×C8—21no—
279C2×C8—301no—
280C2×C8—301no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—151no—
286C4⋊C4—151no—
287C4⋊C4—301no—
288C4⋊C4—301no—
289C4⋊C4—301no—
290C4⋊C4—301no—
291C4⋊C4#122011yescharacteristic
292C4⋊C4#122011yescharacteristic
293C22⋊C4—301no—
294C22⋊C4—301no—
295C22⋊C4—301no—
296C22⋊C4—301no—
297C22⋊C4—301no—
298C42—301no—
299C42C22×D1511yescharacteristic
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—41no—
309C3×C4—41no—
310C3×C4—81no—
311Dic3—201no—
312Dic3—201no—
313Dic3—201no—
314C2×C5#509511yescharacteristic
315C2×C5#520111yescharacteristic
316C2×C5#520211yescharacteristic
317D5—241no—
318C23—301no—
319Q8—42no—
320Q8—601no—
321Q8—1201no—
322D4—601no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—301no—
327C2×C4—301no—
328C2×C4—301no—
329C2×C4—1201no—
330C2×C4D4×D1511yescharacteristic
331C2×C4D4×D1511yescharacteristic
332C2×C4C2×#122011yescharacteristic
333C8—22no—
334C8—601no—
335C8—601no—
336C2×C3#6538411yescharacteristic
337C2×C3#6549011yescharacteristic
338C2×C3#6549111yescharacteristic
339D3—401no—
340C5#7139411yescharacteristic, complemented, Sylow
341C22—601no—
342C22—601no—
343C22—601no—
344C22#9182611yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—81no—
351C4—601no—
352C4—601no—
353C4—601no—
354C3#1060218711yescharacteristic, complemented, Sylow
355C2—1201no—
356C2#1175119611yescharacteristic
357C2#1175130211yescharacteristic
358C2#1175130311yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#501C2
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenter#501D15
hypocenterC3×C5#1664
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. C3×C5×#501C2semidirect
4. #11751183C2semidirect
5. #11746364C2semidirect
6. #11746286C2semidirect
30. C5×#501D3semidirect
64. C3×#501D5semidirect
155. #501D15semidirect
300. C3×C5#1664semidirect
340. C5#71394semidirect
354. C3#10602187semidirect

Maximal subgroups

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

subgroupindex
#117564582
C3×C5×#5012
#117511902
#117511832
#117463642
#117462862
#117462852
#106021873
#713945