Finite Group Databasebeta

← #14291180

Subgroups — #14291180

Order 1920.

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

normal subgroups only

This group has 344 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#11756445C211yesmaximal, characteristic
2C3×C5×#501C211yesmaximal, characteristic
3#11751183C211yesmaximal, characteristic
4#11751182C211yesmaximal, characteristic
5#11746364C211yesmaximal, characteristic
6#11746286C211yesmaximal, characteristic
7#11746286C211yesmaximal, characteristic
8#10602186—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#125C2211yescharacteristic
11#91779—21no—
12#91779—21no—
13#91778—21no—
14#91778—21no—
15#91778—21no—
16#91778—21no—
17#91759C2211yescharacteristic
18#91759C2211yescharacteristic
19C3×C5×#107—21no—
20C3×C5×#106—21no—
21C3×C5×#97C2211yescharacteristic
22#91119—21no—
23#91119—21no—
24#91092—21no—
25#91091—21no—
26#91087C2211yescharacteristic
27#91087C2211yescharacteristic
28#71393—51nomaximal, Hall
29C5⋊#564—31no—
30C5×#501D311yescharacteristic
31#65371—31no—
32#65369—31no—
33#64763—31no—
34#64685—31no—
35#64685—31no—
36C2×C3×C5×Q8—21no—
37C2×C3×C5×C8—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15—21no—
46C4⋊Dic15—21no—
47C4⋊Dic15D411yescharacteristic
48C4⋊Dic15D411yescharacteristic
49C4⋊Dic15D411yescharacteristic
50C4⋊Dic15D411yescharacteristic
51#6712—21no—
52#6712—21no—
53#6712—21no—
54#6712—21no—
55#6712—21no—
56#6712—21no—
57#6712—21no—
58#6712—21no—
59C4×Dic15—21no—
60C4×Dic15—21no—
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63C3⋊#564—51no—
64C3×#501D511yescharacteristic
65#5082—51no—
66#5081—51no—
67#4543—51no—
68#4465—51no—
69#4465—51no—
70C5×C4⋊Q8C2×D311yescharacteristic
71C5×#125C2×D311yescharacteristic
72#4036—61no—
73#4036—61no—
74#4035—61no—
75#4035—61no—
76#4035—61no—
77#4035—61no—
78#4016—31no—
79#4016—31no—
80C5×#107—21no—
81C5×#106—21no—
82C5×#97C2×D311yescharacteristic
83#3967—61no—
84#3967—61no—
85#3940—61no—
86#3939—61no—
87#3935—31no—
88#3935—31no—
89#1663—151noSylow
90C3×C5×Q8—42no—
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×Dic15—21no—
98C2×Dic15—21no—
99C2×Dic15—21no—
100C2×Dic15—21no—
101C3×C5×C8—22no—
102C3⋊#168—22no—
103C3⋊#168—41no—
104C3×C4⋊Q8C2×D511yescharacteristic
105C3×#125C2×D511yescharacteristic
106#890—101no—
107#890—101no—
108#889—101no—
109#889—101no—
110#889—101no—
111#889—101no—
112#870—51no—
113#870—51no—
114C3×#107—21no—
115C3×#106—21no—
116C3×#97C2×D511yescharacteristic
117#835—101no—
118#835—101no—
119#808—101no—
120#807—101no—
121#803—51no—
122#803—51no—
123C2×C5×Q8—21no—
124C2×C5×C8—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4#6711yescharacteristic
130C5×C4⋊C4#6711yescharacteristic
131C42×C5C22×D311yescharacteristic
132C4⋊Dic5—31no—
133C4⋊Dic5—31no—
134C4⋊Dic5—31no—
135C4⋊Dic5—31no—
136C4⋊Dic5—61no—
137C4⋊Dic5—61no—
138#683—61no—
139#683—61no—
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—61no—
149C2×#168—61no—
150#564—151no—
151#501—151no—
152#501D1511yescharacteristic
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—41no—
162C3×C4×C5—41no—
163C3×C4×C5—81no—
164Dic15—41no—
165Dic15—41no—
166Dic15—41no—
167Dic15—41no—
168C2×C3×Q8—21no—
169C2×C3×C8—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4C22⋊D511yescharacteristic
175C3×C4⋊C4C22⋊D511yescharacteristic
176C3×C42C22×D511yescharacteristic
177C4⋊Dic3—51no—
178C4⋊Dic3—51no—
179C4⋊Dic3—51no—
180C4⋊Dic3—51no—
181C4⋊Dic3—101no—
182C4⋊Dic3—101no—
183Dic3⋊C4—101no—
184Dic3⋊C4—101no—
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—101no—
194C2×C3⋊C8—101no—
195C5×Q8—42no—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—41no—
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5C2×#6711yescharacteristic
202C2×Dic5—61no—
203C2×Dic5—61no—
204C2×Dic5—61no—
205C2×Dic5—61no—
206C5×C8—22no—
207#168—62no—
208#168—121no—
209C4⋊Q8C2×D1511yescharacteristic
210#125—151no—
211#125—151no—
212#125—301no—
213#125—301no—
214#125—301no—
215#125—301no—
216#125—301no—
217#125—301no—
218#125C2×D1511yescharacteristic
219#107—21no—
220#107—301no—
221#106—21no—
222#106—301no—
223#103—301no—
224#103—301no—
225#97—151no—
226#97—151no—
227#97C2×D1511yescharacteristic
228C2×C3×C5#45411yescharacteristic
229C2×C3×C5#45611yescharacteristic
230C2×C3×C5#45611yescharacteristic
231C3×Q8—42no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—41no—
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4C2×C22⋊D511yescharacteristic
238C2×Dic3—101no—
239C2×Dic3—101no—
240C2×Dic3—101no—
241C2×Dic3—101no—
242C3×C8—22no—
243C3⋊C8—102no—
244C3⋊C8—201no—
245C22×C5#93711yescharacteristic
246C4×C5—21no—
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—41no—
250C4×C5—41no—
251C4×C5—81no—
252Dic5—121no—
253Dic5—121no—
254Dic5—121no—
255Dic5—121no—
256C2×Q8—21no—
257C2×C8—21no—
258C2×C8—301no—
259C2×C8—301no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—151no—
265C4⋊C4—151no—
266C4⋊C4—151no—
267C4⋊C4—151no—
268C4⋊C4—301no—
269C4⋊C4—301no—
270C4⋊C4—301no—
271C4⋊C4—301no—
272C4⋊C4—301no—
273C4⋊C4—301no—
274C4⋊C4—301no—
275C4⋊C4—301no—
276C4⋊C4—301no—
277C4⋊C4—301no—
278C4⋊C4#122011yescharacteristic
279C4⋊C4#122011yescharacteristic
280C42—301no—
281C42—301no—
282C42C22×D1511yescharacteristic
283C3×C5#166311yescharacteristic, complemented, Hall
284C22×C3#408311yescharacteristic
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—41no—
289C3×C4—41no—
290C3×C4—81no—
291Dic3—201no—
292Dic3—201no—
293Dic3—201no—
294Dic3—201no—
295C2×C5#509511yescharacteristic
296C2×C5#520111yescharacteristic
297C2×C5#520511yescharacteristic
298Q8—42no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—301no—
303C2×C4—301no—
304C2×C4—301no—
305C2×C4—301no—
306C2×C4D4×D1511yescharacteristic
307C2×C4D4×D1511yescharacteristic
308C2×C4C2×#122011yescharacteristic
309C8—22no—
310C8—302no—
311C8—601no—
312C2×C3#6538411yescharacteristic
313C2×C3#6549011yescharacteristic
314C2×C3#6549411yescharacteristic
315C5#7139311yescharacteristic, complemented, Sylow
316C22#9182611yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—81no—
323C4—601no—
324C4—601no—
325C4—601no—
326C4—601no—
327C3#1060218611yescharacteristic, complemented, Sylow
328C2#1175119611yescharacteristic
329C2#1175130211yescharacteristic
330C2#1175130611yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#501C2
socle, prime radicalC22×C3×C5#120
hypercenter#501D15
hypocenterC3×C5#1663
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
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
#117564452
C3×C5×#5012
#117511832
#117511822
#117463642
#117462862
#106021863
#713935