Finite Group Databasebeta

← #14289568

Subgroups — #14289568

Order 1920.

412 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C5×Q8×Dic6C211yesmaximal, characteristic
2#11751122C211yesmaximal, characteristic
3#11747096C211yesmaximal, characteristic
4#11746961C211yesmaximal, characteristic
5C3×Q8⋊#168C211yesmaximal, characteristic
6#11745862C211yesmaximal, characteristic
7#11745843C211yesmaximal, characteristic
8#10602733—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C5×Q8×Dic3—21no—
12C5×#888—22no—
13C5×#888—21no—
14C5×#869—21no—
15C5×#869C2211yescharacteristic
16C4×C5×Dic6—21no—
17C4×C5×Dic6C2211yescharacteristic
18C2×#6663—22no—
19#91119—21no—
20#91091—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24#90988—21no—
25#90973—21no—
26#68267—51nomaximal, Hall
27C5×Q82—31no—
28#65381—31no—
29#65310—31no—
30#65310—31no—
31#64766—31no—
32Q8⋊#168—31no—
33Q8⋊#168D311yescharacteristic
34C2×C3×C5×Q8D411yescharacteristic
35C2×Dic30—21no—
36C2×C5×Dic6—22no—
37C2×C5×Dic6D411yescharacteristic
38C2×C5×Dic6D412yes—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C42×C5—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C2×C3⋊#168—21no—
46C5×C4⋊Dic3—22no—
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×Dic3⋊C4—22no—
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3—22no—
53C4×C5×Dic3—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#6663—44no—
57Q8×Dic6D511yescharacteristic
58#5021—51no—
59#4850—51no—
60#4699—51no—
61C3×Q8⋊C8—51no—
62#4481—51no—
63#4456—51no—
64C5×C4⋊Q8—31no—
65C5×C4⋊Q8—61no—
66C5×C4⋊Q8—62no—
67C5×C4⋊Q8—61no—
68C4×C5×Q8—31no—
69C4×C5×Q8—61no—
70C4×C5×Q8—61no—
71C4×C5×Q8C2×D311yescharacteristic
72C2×#689—62no—
73#4015—31no—
74#3967—61no—
75#3967—61no—
76#3939—61no—
77#3939—61no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168C2×D311yescharacteristic
81#1633—151noSylow
82C3×C5×Q8—21no—
83C3×C5×Q8Q1612yescomplemented
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—41no—
90Dic30—42no—
91C2×C5×Dic3—21no—
92C2×C5×Dic3—22no—
93C2×C5×Dic3—21no—
94C5×Dic6—21no—
95C5×Dic6—42no—
96C5×Dic6—82no—
97C5×Dic6Q1612yescomplemented
98C3⋊#168—41no—
99C3×#168—22no—
100C3×#168—41no—
101C3×C4×Q8C2×D511yescharacteristic
102Q8×Dic3—21no—
103C2×Dic12—102no—
104#888—22no—
105#888—21no—
106#869—21no—
107#869—51no—
108#869C2×D511yescharacteristic
109C4×Dic6—21no—
110C4×Dic6C2×D511yescharacteristic
111C3×C4⋊C8—51no—
112C3×C4×C8—51no—
113#835—101no—
114#818—101no—
115#816—101no—
116#807—101no—
117C4⋊(C3⋊C8)—51no—
118C2×C5×Q8—31no—
119C2×C5×Q8—32no—
120C2×C5×Q8—62no—
121C2×C5×Q8D1211yescharacteristic
122C2×Dic10—61no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—31no—
125C5×C4⋊C4—62no—
126C5×C4⋊C4—62no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4D1211yescharacteristic
131C42×C5—21no—
132C42×C5—62no—
133C42×C5—61no—
134C42×C5C22×D311yescharacteristic
135#689—124no—
136C4⋊Dic5—61no—
137C4⋊Dic5—61no—
138C2×#168—21no—
139C2×#168—21no—
140C2×#168—61no—
141Q82—31no—
142#494—151no—
143#477—151no—
144#477—151no—
145#333—151no—
146Q8⋊C8—51no—
147Q8⋊C8—151no—
148C22×C3×C5#12011yescharacteristic
149C3×C4×C5—22no—
150C3×C4×C5—21no—
151C3×C4×C5—41no—
152C3×C4×C5C2×Q1611yescharacteristic
153C3×C4×C5C2×Q1611yescharacteristic
154C3×C4×C5#13711yescharacteristic
155C3×C4×C5#13711yescharacteristic
156Dic15—81no—
157C5×Dic3—22no—
158C5×Dic3—42no—
159C5×Dic3—41no—
160C2×C3×Q8C22⋊D511yescharacteristic
161C2×Dic6—22no—
162C2×Dic6—101no—
163C2×Dic6C22⋊D511yescharacteristic
164C2×Dic6C22⋊D512yes—
165C2×C3×C8—101no—
166C2×C3×C8—101no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4C22⋊D511yescharacteristic
169C3×C42—21no—
170C3×C42C22×D511yescharacteristic
171C4⋊Dic3—22no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3—101no—
175C4⋊Dic3—101no—
176C4⋊Dic3C22⋊D511yescharacteristic
177Dic3⋊C4—22no—
178Dic3⋊C4—21no—
179C4×Dic3—22no—
180C4×Dic3—21no—
181C2×C3⋊C8—101no—
182Dic12—204no—
183C5×Q8—21no—
184C5×Q8—32no—
185C5×Q8—61no—
186C5×Q8—122no—
187C5×Q8—242no—
188C5×Q8Dic1212yescomplemented
189C2×C4×C5—21no—
190C2×C4×C5—21no—
191C2×C4×C5—61no—
192C2×C4×C5—61no—
193C2×C4×C5—62no—
194C2×C4×C5C2×D1211yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×Dic5—121no—
198Dic10—122no—
199#168—22no—
200#168—41no—
201#168—121no—
202C2×Q16—302no—
203C4⋊Q8—31no—
204C4⋊Q8—61no—
205C4⋊Q8—62no—
206C4⋊Q8—61no—
207C4⋊Q8—151no—
208C4×Q8—31no—
209C4×Q8—61no—
210C4×Q8—61no—
211C4×Q8D3×D511yescharacteristic
212#107—301no—
213#107—301no—
214C4⋊C8—51no—
215C4⋊C8—151no—
216#103—301no—
217#103—301no—
218C4×C8—51no—
219C2×C3×C5#45111yescharacteristic
220C2×C3×C5#45111yescharacteristic
221C2×C3×C5#45311yescharacteristic
222C3×Q8—21no—
223C3×Q8#68912yescomplemented
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4C2×C22⋊D511yescharacteristic
227C2×C3×C4C2×C22⋊D511yescharacteristic
228C2×C3×C4C2×C22⋊D511yescharacteristic
229C2×Dic3—21no—
230C2×Dic3—22no—
231C2×Dic3—21no—
232C2×Dic3—201no—
233Dic6—21no—
234Dic6—42no—
235Dic6—82no—
236Dic6—202no—
237Dic6#68912yescomplemented
238C3×C8—102no—
239C3×C8—201no—
240C3⋊C8—201no—
241C22×C5#88211yescharacteristic
242C4×C5—22no—
243C4×C5—21no—
244C4×C5—41no—
245C4×C5—62no—
246C4×C5—122no—
247C4×C5—121no—
248C4×C5C2×Dic1211yescharacteristic
249C4×C5#90911yescharacteristic
250C4×C5#91511yescharacteristic
251C4×C5D3×Q1611yescharacteristic
252Dic5—241no—
253C2×Q8—31no—
254C2×Q8—32no—
255C2×Q8—62no—
256C2×Q8—301no—
257C2×Q8#120311yescharacteristic
258Q16—604no—
259C2×C8—101no—
260C2×C8—101no—
261C2×C8—301no—
262C4⋊C4—21no—
263C4⋊C4—31no—
264C4⋊C4—62no—
265C4⋊C4—62no—
266C4⋊C4—61no—
267C4⋊C4—61no—
268C4⋊C4—61no—
269C4⋊C4—301no—
270C4⋊C4—301no—
271C4⋊C4#120311yescharacteristic
272C42—21no—
273C42—62no—
274C42—61no—
275C42C2×D3×D511yescharacteristic
276C3×C5#163311yescharacteristic, complemented, Hall
277C22×C3#409911yescharacteristic
278C3×C4—22no—
279C3×C4—21no—
280C3×C4—41no—
281C3×C4#408811yescharacteristic
282C3×C4#408811yescharacteristic
283C3×C4C2×#68911yescharacteristic
284C3×C4C2×#68911yescharacteristic
285Dic3—22no—
286Dic3—42no—
287Dic3—41no—
288Dic3—401no—
289C2×C5#473911yescharacteristic
290C2×C5#480911yescharacteristic
291C2×C5#482211yescharacteristic
292Q8—21no—
293Q8—32no—
294Q8—61no—
295Q8—122no—
296Q8—242no—
297Q8—602no—
298Q8#666312yescomplemented
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—61no—
302C2×C4—61no—
303C2×C4—62no—
304C2×C4—601no—
305C2×C4C2×#120311yescharacteristic
306C2×C4D3×C22⋊D511yescharacteristic
307C2×C4D3×C22⋊D511yescharacteristic
308C8—102no—
309C8—201no—
310C8—601no—
311C2×C3#6551711yescharacteristic
312C2×C3#6551711yescharacteristic
313C2×C3#6553011yescharacteristic
314C5#6826711yescharacteristic, complemented, Sylow
315C22#9157011yescharacteristic
316C4—21no—
317C4—22no—
318C4—41no—
319C4—62no—
320C4—122no—
321C4—121no—
322C4—1201no—
323C4C2×#666311yescharacteristic
324C4#9132111yescharacteristic
325C4D3×#68911yescharacteristic
326C4#9151811yescharacteristic
327C3#1060273311yescharacteristic, complemented, Sylow
328C2#1174856111yescharacteristic
329C2#1174930211yescharacteristic
330C2#1174942011yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socle, prime radicalC22×C3×C5#120
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1633
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
83. C3×C5×Q8Q16semidirect
97. C5×Dic6Q16semidirect
188. C5×Q8Dic12semidirect
223. C3×Q8#689semidirect
237. Dic6#689semidirect
276. C3×C5#1633semidirect
298. Q8#6663semidirect
314. C5#68267semidirect
327. C3#10602733semidirect

Maximal subgroups

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

subgroupindex
C5×Q8×Dic62
#117511222
#117470962
#117469612
C3×Q8⋊#1682
#117458622
#117458432
#106027333
#682675