Finite Group Databasebeta

← #14291205

Subgroups — #14291205

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
2C5×#4703C211yesmaximal, characteristic
3#11746970C211yesmaximal, characteristic
4#11746957C211yesmaximal, characteristic
5#11746286C211yesmaximal, characteristic
6C3×#64685C211yesmaximal, characteristic
7#11745850C211yesmaximal, characteristic
8#10602045—31nomaximal, Hall
9#91759C2211yescharacteristic
10C5×#870C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4016C2211yescharacteristic
13#91346—21no—
14#91343—21no—
15#91339—21no—
16#91336—21no—
17#91335—21no—
18#91334—21no—
19C3×C5×#97C2211yescharacteristic
20#91087C2211yescharacteristic
21C5×#816—21no—
22C5×#816—21no—
23C3×#3935C2211yescharacteristic
24#90989—21no—
25#90988—21no—
26#90986—21no—
27#90985—21no—
28#68376—51nomaximal, Hall
29C5⋊#564—31no—
30C5×#491—31no—
31#65369—31no—
32#65369—31no—
33#64763—31no—
34#64685—31no—
35#64685D311yescharacteristic
36C2×C5×Dic6—21no—
37C2×C3×C5×C8—21no—
38C3×C42×C5C2311yescharacteristic
39C4⋊Dic15D411yescharacteristic
40C4⋊Dic15D411yescharacteristic
41#6712—21no—
42#6712—21no—
43C2×C3⋊#168—21no—
44C5×C4⋊Dic3—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3D411yescharacteristic
47C5×C4⋊Dic3D411yescharacteristic
48C5×Dic3⋊C4—21no—
49C5×Dic3⋊C4—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—
64#5064—51no—
65#4703D511yescharacteristic
66#4702—51no—
67C3×#330—51no—
68#4465—51no—
69#4465—51no—
70C5×C4⋊Q8—31no—
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×#103—61no—
81C5×#103—61no—
82C5×#97C2×D311yescharacteristic
83#3940—61no—
84#3940—61no—
85#3939—61no—
86#3939—61no—
87#3935—31no—
88#3935C2×D311yescharacteristic
89#1663—151noSylow
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×Dic15—21no—
94C2×Dic15—21no—
95C2×C5×Dic3—21no—
96C2×C5×Dic3—21no—
97C2×C5×Dic3—41no—
98C5×Dic6—42no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C3×C5×C8—41no—
102C3⋊#168—22no—
103C3×#168—22no—
104C3×#125—51no—
105#890—101no—
106#890—101no—
107#889—101no—
108#889—101no—
109#889—101no—
110#889—101no—
111#870—51no—
112#870C2×D511yescharacteristic
113#869C2×D511yescharacteristic
114C3×#97—51no—
115C3×#97C2×D511yescharacteristic
116#818—101no—
117#817—101no—
118#816—21no—
119#816—21no—
120#808—101no—
121#807—101no—
122#803—51no—
123C2×C5×Q8—61no—
124C2×C5×C8—21no—
125C5×C4⋊C4—31no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4—61no—
131C42×C5C22×D311yescharacteristic
132C4⋊Dic5—31no—
133C4⋊Dic5—31no—
134C4⋊Dic5—61no—
135C4⋊Dic5—61no—
136C4⋊Dic5D1211yescharacteristic
137C4⋊Dic5D1211yescharacteristic
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—151no—
152#501—151no—
153#491—31no—
154#330—51no—
155#330—151no—
156#330—151no—
157C22×C3×C5#12011yescharacteristic
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161Dic15—41no—
162Dic15—41no—
163C3×Dic5—41no—
164C3×Dic5—41no—
165C5×Dic3—41no—
166C5×Dic3—41no—
167C5×Dic3—81no—
168C2×Dic6—21no—
169C2×C3×C8—21no—
170C2×C3×C8—101no—
171C3×C4⋊C4—51no—
172C3×C4⋊C4—51no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C42C22×D511yescharacteristic
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3—51no—
179C4⋊Dic3—51no—
180C4⋊Dic3—101no—
181C4⋊Dic3—101no—
182C4⋊Dic3C22⋊D511yescharacteristic
183C4⋊Dic3C22⋊D511yescharacteristic
184Dic3⋊C4—21no—
185Dic3⋊C4—21no—
186Dic3⋊C4—101no—
187Dic3⋊C4—101no—
188Dic3⋊C4—101no—
189Dic3⋊C4—101no—
190Dic3⋊C4—101no—
191Dic3⋊C4—101no—
192C4×Dic3—101no—
193C4×Dic3—101no—
194C2×C3⋊C8—101no—
195C5×Q8—122no—
196C2×C4×C5—61no—
197C2×C4×C5—61no—
198C2×C4×C5—121no—
199C2×C4×C5C2×D1211yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×Dic5—21no—
203C2×Dic5—21no—
204C2×Dic5—61no—
205C2×Dic5—61no—
206C5×C8—41no—
207#168—22no—
208#168—62no—
209C4⋊Q8—31no—
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—301no—
220#107—301no—
221#106—301no—
222#106—301no—
223#103—61no—
224#103—61no—
225#97—51no—
226#97—151no—
227#97D3×D511yescharacteristic
228C2×C3×C5#45411yescharacteristic
229C2×C3×C5#45611yescharacteristic
230C2×C3×C5#45611yescharacteristic
231C2×C3×C4—101no—
232C2×C3×C4—101no—
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4D4×D511yescharacteristic
235C2×C3×C4C2×C22⋊D511yescharacteristic
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3—41no—
239C2×Dic3—101no—
240C2×Dic3—101no—
241Dic6—42no—
242C3×C8—41no—
243C3×C8—102no—
244C3⋊C8—102no—
245C22×C5#88211yescharacteristic
246C4×C5—21no—
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—121no—
250C4×C5—121no—
251C4×C5—241no—
252Dic5—41no—
253Dic5—41no—
254Dic5—121no—
255Dic5—121no—
256C2×Q8—61no—
257C2×C8—21no—
258C2×C8—101no—
259C2×C8—301no—
260C4⋊C4—31no—
261C4⋊C4—31no—
262C4⋊C4—51no—
263C4⋊C4—51no—
264C4⋊C4—61no—
265C4⋊C4—61no—
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—201no—
289C3×C4—201no—
290Dic3—41no—
291Dic3—41no—
292Dic3—81no—
293Dic3—201no—
294Dic3—201no—
295C2×C5#475211yescharacteristic
296C2×C5#482611yescharacteristic
297C2×C5#482711yescharacteristic
298Q8—122no—
299C2×C4—61no—
300C2×C4—61no—
301C2×C4—101no—
302C2×C4—101no—
303C2×C4—121no—
304C2×C4—301no—
305C2×C4—301no—
306C2×C4D5×D1211yescharacteristic
307C2×C4#677711yescharacteristic
308C2×C4D3×C22⋊D511yescharacteristic
309C8—41no—
310C8—102no—
311C8—302no—
312C2×C3#6535111yescharacteristic
313C2×C3#6549411yescharacteristic
314C2×C3#6549411yescharacteristic
315C5#6837611yescharacteristic, complemented, Sylow
316C22#9147511yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—121no—
321C4—121no—
322C4—201no—
323C4—201no—
324C4—241no—
325C4—601no—
326C4—601no—
327C3#1060204511yescharacteristic, complemented, Sylow
328C2#1174712311yescharacteristic
329C2#1174825711yescharacteristic
330C2#1174825811yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#97C22
socle, prime radicalC22×C3×C5#120
hypercenter#97D3×D5
hypocenterC3×C5#1663
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
283. C3×C5#1663semidirect
315. C5#68376semidirect
327. C3#10602045semidirect

Maximal subgroups

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

subgroupindex
#117524882
C5×#47032
#117469702
#117469572
#117462862
C3×#646852
#117458502
#106020453
#683765