Finite Group Databasebeta

← #14291192

Subgroups — #14291192

Order 1920.

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

normal subgroups only

This group has 344 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#11752488C211yesmaximal, characteristic
2#11751183C211yesmaximal, characteristic
3C5×#5081C211yesmaximal, characteristic
4C3×#65369C211yesmaximal, characteristic
5#11745851C211yesmaximal, characteristic
6#11745850C211yesmaximal, characteristic
7#11745849C211yesmaximal, characteristic
8#10602186—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91759C2211yescharacteristic
11C5×#870C2211yescharacteristic
12C3×#4016C2211yescharacteristic
13#91346—21no—
14#91343—21no—
15#91339—21no—
16#91336—21no—
17#91335—21no—
18#91334—21no—
19#91119—21no—
20#91119—21no—
21#91087C2211yescharacteristic
22C5×#808—21no—
23C5×#807—21no—
24C5×#803C2211yescharacteristic
25C3×#3940—21no—
26C3×#3939—21no—
27C3×#3935C2211yescharacteristic
28#71393—51nomaximal, Hall
29C5⋊#564—31no—
30C5×#501—31no—
31#65371—31no—
32#65369D311yescharacteristic
33#64763—31no—
34#64685—31no—
35#64685—31no—
36C2×C3×C5×Q8—21no—
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—21no—
39C3×C42×C5C2311yescharacteristic
40C4⋊Dic15D411yescharacteristic
41C4⋊Dic15D411yescharacteristic
42#6712—21no—
43#6712—21no—
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3D411yescharacteristic
46C5×C4⋊Dic3D411yescharacteristic
47C5×Dic3⋊C4—21no—
48C5×Dic3⋊C4—21no—
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×C4⋊Dic5D411yescharacteristic
52C3×#683—21no—
53C3×#683—21no—
54C2×C3×#168—21no—
55Dic3⋊Dic5—21no—
56Dic3⋊Dic5—21no—
57#6669—21no—
58#6669—21no—
59#6668—21no—
60#6668—21no—
61Dic3×Dic5—21no—
62Dic3×Dic5—21no—
63C3⋊#564—51no—
64C3×#501—51no—
65#5082—51no—
66#5081D511yescharacteristic
67#4543—51no—
68#4465—51no—
69#4465—51no—
70C5×C4⋊Q8C2×D311yescharacteristic
71C5×#125—31no—
72#4036—61no—
73#4036—61no—
74#4035—61no—
75#4035—61no—
76#4035—61no—
77#4035—61no—
78#4016—31no—
79#4016C2×D311yescharacteristic
80C5×#107—61no—
81C5×#106—61no—
82C5×#97—31no—
83#3967—61no—
84#3967—61no—
85#3940—21no—
86#3939—21no—
87#3935—31no—
88#3935C2×D311yescharacteristic
89#1663—151noSylow
90C3×C5×Q8—42no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×Dic15—21no—
96C2×Dic15—21no—
97C2×C5×Dic3—21no—
98C2×C5×Dic3—21no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C3⋊#168—41no—
102C3×#168—22no—
103C5×C3⋊C8—22no—
104C3×C4⋊Q8C2×D511yescharacteristic
105C3×#125—51no—
106#890—101no—
107#890—101no—
108#889—101no—
109#889—101no—
110#889—101no—
111#889—101no—
112#870—51no—
113#870C2×D511yescharacteristic
114C3×#107—101no—
115C3×#106—101no—
116C3×#97—51no—
117#835—101no—
118#835—101no—
119#808—21no—
120#807—21no—
121#803—51no—
122#803C2×D511yescharacteristic
123C2×C5×Q8—21no—
124C2×C5×C8—61no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—31no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4—61no—
131C42×C5C22×D311yescharacteristic
132C4⋊Dic5—31no—
133C4⋊Dic5—31no—
134C4⋊Dic5—61no—
135C4⋊Dic5—61no—
136C4⋊Dic5#6711yescharacteristic
137C4⋊Dic5#6711yescharacteristic
138#683—21no—
139#683—21no—
140#683—61no—
141#683—61no—
142#683—61no—
143#683—61no—
144#683—61no—
145#683—61no—
146C4×Dic5—61no—
147C4×Dic5—61no—
148C2×#168—21no—
149C2×#168—61no—
150#564—151no—
151#501—31no—
152#501—51no—
153#491—151no—
154#330—151no—
155#330—151no—
156#330—151no—
157C22×C3×C5#12011yescharacteristic
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—81no—
162Dic15—41no—
163Dic15—41no—
164C3×Dic5—41no—
165C3×Dic5—41no—
166C5×Dic3—41no—
167C5×Dic3—41no—
168C2×C3×Q8—21no—
169C2×C3×C8—101no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—51no—
173C3×C4⋊C4—51no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4—101no—
176C3×C42C22×D511yescharacteristic
177C4⋊Dic3—51no—
178C4⋊Dic3—51no—
179C4⋊Dic3—101no—
180C4⋊Dic3—101no—
181C4⋊Dic3C22⋊D511yescharacteristic
182C4⋊Dic3C22⋊D511yescharacteristic
183Dic3⋊C4—21no—
184Dic3⋊C4—21no—
185Dic3⋊C4—101no—
186Dic3⋊C4—101no—
187Dic3⋊C4—101no—
188Dic3⋊C4—101no—
189Dic3⋊C4—101no—
190Dic3⋊C4—101no—
191C4×Dic3—101no—
192C4×Dic3—101no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—101no—
195C5×Q8—42no—
196C2×C4×C5—41no—
197C2×C4×C5—61no—
198C2×C4×C5—61no—
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5C2×#6711yescharacteristic
202C2×Dic5—21no—
203C2×Dic5—21no—
204C2×Dic5—61no—
205C2×Dic5—61no—
206C5×C8—62no—
207#168—22no—
208#168—121no—
209C4⋊Q8D3×D511yescharacteristic
210#125—31no—
211#125—51no—
212#125—151no—
213#125—301no—
214#125—301no—
215#125—301no—
216#125—301no—
217#125—301no—
218#125—301no—
219#107—61no—
220#107—101no—
221#106—61no—
222#106—101no—
223#103—301no—
224#103—301no—
225#97—31no—
226#97—51no—
227#97—151no—
228C2×C3×C5#45411yescharacteristic
229C2×C3×C5#45611yescharacteristic
230C2×C3×C5#45611yescharacteristic
231C3×Q8—42no—
232C2×C3×C4—41no—
233C2×C3×C4—101no—
234C2×C3×C4—101no—
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4C2×C22⋊D511yescharacteristic
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—101no—
241C2×Dic3—101no—
242C3×C8—102no—
243C3⋊C8—22no—
244C3⋊C8—201no—
245C22×C5#93711yescharacteristic
246C4×C5—21no—
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—81no—
250C4×C5—121no—
251C4×C5—121no—
252Dic5—41no—
253Dic5—41no—
254Dic5—121no—
255Dic5—121no—
256C2×Q8—21no—
257C2×C8—61no—
258C2×C8—101no—
259C2×C8—301no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—31no—
263C4⋊C4—31no—
264C4⋊C4—51no—
265C4⋊C4—51no—
266C4⋊C4—61no—
267C4⋊C4—61no—
268C4⋊C4—101no—
269C4⋊C4—101no—
270C4⋊C4—151no—
271C4⋊C4—151no—
272C4⋊C4—301no—
273C4⋊C4—301no—
274C4⋊C4—301no—
275C4⋊C4—301no—
276C4⋊C4—301no—
277C4⋊C4—301no—
278C4⋊C4—301no—
279C4⋊C4—301no—
280C42—301no—
281C42—301no—
282C42C2×D3×D511yescharacteristic
283C3×C5#166311yescharacteristic, complemented, Hall
284C22×C3#408311yescharacteristic
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—81no—
289C3×C4—201no—
290C3×C4—201no—
291Dic3—41no—
292Dic3—41no—
293Dic3—201no—
294Dic3—201no—
295C2×C5#509511yescharacteristic
296C2×C5#520111yescharacteristic
297C2×C5#520511yescharacteristic
298Q8—42no—
299C2×C4—41no—
300C2×C4—61no—
301C2×C4—61no—
302C2×C4—101no—
303C2×C4—101no—
304C2×C4—301no—
305C2×C4—301no—
306C2×C4D5×#6711yescharacteristic
307C2×C4D3×C22⋊D511yescharacteristic
308C2×C4#679011yescharacteristic
309C8—62no—
310C8—102no—
311C8—601no—
312C2×C3#6538411yescharacteristic
313C2×C3#6549011yescharacteristic
314C2×C3#6549411yescharacteristic
315C5#7139311yescharacteristic, complemented, Sylow
316C22#9157711yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—81no—
321C4—121no—
322C4—121no—
323C4—201no—
324C4—201no—
325C4—601no—
326C4—601no—
327C3#1060218611yescharacteristic, complemented, Sylow
328C2#1174916611yescharacteristic
329C2#1174941311yescharacteristic
330C2#1174941411yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socle, prime radicalC22×C3×C5#120
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1663
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
283. C3×C5#1663semidirect
315. C5#71393semidirect
327. C3#10602186semidirect

Maximal subgroups

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

subgroupindex
#117524882
#117511832
C5×#50812
C3×#653692
#117458512
#117458502
#117458492
#106021863
#713935