Finite Group Databasebeta

← #14289575

Subgroups — #14289575

Order 1920.

412 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 92 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#11752473C211yesmaximal, characteristic
2#11750951C211yesmaximal, characteristic
3#11747096C211yesmaximal, characteristic
4#11746916C211yesmaximal, characteristic
5C5×#4481C211yesmaximal, characteristic
6C3×#64704C211yesmaximal, characteristic
7#11745845C211yesmaximal, characteristic
8#10599298—31nomaximal, Hall
9#91758C2211yescharacteristic
10C4×Dic30C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13#91470—21no—
14#91468—21no—
15#91333—21no—
16#91331—21no—
17#91329—22no—
18C2×#6663—22no—
19C3×C5×C4⋊C8C2211yescharacteristic
20#91102—21no—
21#91100—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24#90990—21no—
25#90971—21no—
26#68267—51nomaximal, Hall
27#66056—31no—
28#65381—31no—
29#65139—31no—
30#65139—31no—
31C5×#333—31no—
32#64704—31no—
33#64704D311yescharacteristic
34C2×Dic30—21no—
35C2×Dic30D411yescharacteristic
36C2×C5×Dic6D412yes—
37C2×C3×Dic10D411yescharacteristic
38C2×#1204—22no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15—21no—
42C4⋊Dic15—21no—
43C4⋊Dic15D411yescharacteristic
44#6712—21no—
45C4×Dic15—21no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3—21no—
48C2×C5×C3⋊C8—21no—
49C3×C4⋊Dic5D411yescharacteristic
50C3×#683—21no—
51C3×C4×Dic5—21no—
52C2×C3×#168—21no—
53#6669—22no—
54#6668—22no—
55Dic3×Dic5—22no—
56#6663—44no—
57Q8×Dic6—51no—
58#5021—51no—
59#4850—51no—
60#4699—51no—
61C3×Q8⋊C8—51no—
62#4481D511yescharacteristic
63#4456—51no—
64C5×C4⋊Q8—31no—
65#4090—62no—
66C2×#689—62no—
67#4034—61no—
68#4034—61no—
69#4033—61no—
70#4033—61no—
71#4015—31no—
72C4×Dic10—31no—
73C4×Dic10C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C5×C4⋊C8C2×D311yescharacteristic
76#3950—61no—
77#3950—61no—
78#3948—61no—
79#3948—61no—
80C4×#168C2×D311yescharacteristic
81#1633—151noSylow
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×Dic15—21no—
86C2×Dic15—21no—
87C2×Dic15—41no—
88Dic30—21no—
89Dic30—42no—
90Dic30Q1612yescomplemented
91C2×C5×Dic3—22no—
92C5×Dic6—42no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C3×Dic10—21no—
96C3×Dic10Q1612yescomplemented
97#1204—82no—
98C3×C5×C8—41no—
99C3×#168—22no—
100C5×C3⋊C8—41no—
101C3×C4×Q8—51no—
102Q8×Dic3—101no—
103C2×Dic12—102no—
104#888—101no—
105#888—102no—
106#869—51no—
107#869—101no—
108#869C2×D511yescharacteristic
109C4×Dic6—51no—
110C4×Dic6—101no—
111C3×C4⋊C8C2×D511yescharacteristic
112C3×C4×C8—51no—
113#835—101no—
114#818—101no—
115#816—101no—
116#807—101no—
117C4⋊(C3⋊C8)C2×D511yescharacteristic
118C2×C5×Q8—32no—
119C2×Dic10—31no—
120C2×Dic10—61no—
121C2×Dic10—62no—
122C2×Dic10D1211yescharacteristic
123C2×C5×C8—21no—
124C2×C5×C8—61no—
125C5×C4⋊C4—61no—
126C5×C4⋊C4—61no—
127C42×C5C22×D311yescharacteristic
128#689—124no—
129C4⋊Dic5—31no—
130C4⋊Dic5—61no—
131C4⋊Dic5—61no—
132C4⋊Dic5D1211yescharacteristic
133#683—21no—
134#683—62no—
135#683—62no—
136#683—61no—
137C4×Dic5—21no—
138C4×Dic5—62no—
139C4×Dic5—61no—
140C2×#168—21no—
141Q82—151no—
142#494—151no—
143#477—151no—
144#477—151no—
145#333—31no—
146Q8⋊C8—51no—
147Q8⋊C8—151no—
148C22×C3×C5#12011yescharacteristic
149C3×C4×C5—21no—
150C3×C4×C5C2×Q1611yescharacteristic
151C3×C4×C5C2×Q1611yescharacteristic
152C3×C4×C5#13711yescharacteristic
153C3×C4×C5#13711yescharacteristic
154Dic15—22no—
155Dic15—41no—
156Dic15—81no—
157C3×Dic5—22no—
158C3×Dic5—41no—
159C5×Dic3—42no—
160C2×C3×Q8—51no—
161C2×Dic6—51no—
162C2×Dic6—101no—
163C2×Dic6—102no—
164C2×Dic6D2012yes—
165C2×C3×C8—21no—
166C2×C3×C8—101no—
167C3×C4⋊C4—51no—
168C3×C4⋊C4—101no—
169C3×C42—101no—
170C3×C42C22×D511yescharacteristic
171C4⋊Dic3—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—51no—
174C4⋊Dic3—102no—
175C4⋊Dic3—101no—
176C4⋊Dic3—101no—
177Dic3⋊C4—102no—
178Dic3⋊C4—101no—
179C4×Dic3—102no—
180C4×Dic3—101no—
181C2×C3⋊C8—21no—
182Dic12—204no—
183C5×Q8—122no—
184C2×C4×C5—62no—
185C2×C4×C5C2×D1211yescharacteristic
186C2×C4×C5D3×D411yescharacteristic
187C2×C4×C5D3×D411yescharacteristic
188C2×Dic5—21no—
189C2×Dic5—21no—
190C2×Dic5—61no—
191C2×Dic5—61no—
192C2×Dic5—121no—
193Dic10—21no—
194Dic10—32no—
195Dic10—61no—
196Dic10—122no—
197Dic10—242no—
198Dic10Dic1212yescomplemented
199C5×C8—41no—
200C5×C8—121no—
201#168—22no—
202C2×Q16—302no—
203C4⋊Q8—31no—
204C4⋊Q8—151no—
205C4⋊Q8—301no—
206C4⋊Q8—301no—
207C4⋊Q8—302no—
208C4×Q8—51no—
209C4×Q8—151no—
210C4×Q8—301no—
211C4×Q8—301no—
212#107—301no—
213#107—301no—
214C4⋊C8—31no—
215C4⋊C8D3×D511yescharacteristic
216#103—301no—
217#103—301no—
218C4×C8—51no—
219C2×C3×C5#45111yescharacteristic
220C2×C3×C5#45111yescharacteristic
221C2×C3×C5#45311yescharacteristic
222C3×Q8—52no—
223C3×Q8—101no—
224C2×C3×C4—101no—
225C2×C3×C4—101no—
226C2×C3×C4C2×D2011yescharacteristic
227C2×C3×C4D4×D511yescharacteristic
228C2×C3×C4D4×D511yescharacteristic
229C2×Dic3—22no—
230C2×Dic3—101no—
231C2×Dic3—101no—
232C2×Dic3—201no—
233Dic6—42no—
234Dic6—52no—
235Dic6—101no—
236Dic6—202no—
237Dic6—402no—
238C3×C8—41no—
239C3×C8—102no—
240C3⋊C8—41no—
241C22×C5#88211yescharacteristic
242C4×C5—21no—
243C4×C5—122no—
244C4×C5C2×Dic1211yescharacteristic
245C4×C5#90911yescharacteristic
246C4×C5#91511yescharacteristic
247C4×C5D3×Q1611yescharacteristic
248Dic5—22no—
249Dic5—41no—
250Dic5—62no—
251Dic5—121no—
252Dic5—241no—
253C2×Q8—32no—
254C2×Q8—51no—
255C2×Q8—151no—
256C2×Q8—302no—
257C2×Q8—301no—
258Q16—604no—
259C2×C8—21no—
260C2×C8—61no—
261C2×C8—101no—
262C4⋊C4—51no—
263C4⋊C4—61no—
264C4⋊C4—61no—
265C4⋊C4—101no—
266C4⋊C4—151no—
267C4⋊C4—302no—
268C4⋊C4—302no—
269C4⋊C4—301no—
270C4⋊C4—301no—
271C4⋊C4—301no—
272C42—101no—
273C42—302no—
274C42—301no—
275C42C2×D3×D511yescharacteristic
276C3×C5#163311yescharacteristic, complemented, Hall
277C22×C3#402811yescharacteristic
278C3×C4—21no—
279C3×C4—102no—
280C3×C4—201no—
281C3×C4#406111yescharacteristic
282C3×C4#406111yescharacteristic
283C3×C4D5×Q1611yescharacteristic
284C3×C4D5×Q1611yescharacteristic
285Dic3—42no—
286Dic3—102no—
287Dic3—201no—
288Dic3—401no—
289C2×C5#473911yescharacteristic
290C2×C5#480911yescharacteristic
291C2×C5#482211yescharacteristic
292Q8—52no—
293Q8—101no—
294Q8—122no—
295Q8—152no—
296Q8—301no—
297Q8—602no—
298Q8—1202no—
299C2×C4—62no—
300C2×C4—101no—
301C2×C4—101no—
302C2×C4—301no—
303C2×C4—301no—
304C2×C4—601no—
305C2×C4D5×D1211yescharacteristic
306C2×C4D3×D2011yescharacteristic
307C2×C4#679011yescharacteristic
308C8—41no—
309C8—102no—
310C8—121no—
311C2×C3#6503611yescharacteristic
312C2×C3#6509711yescharacteristic
313C2×C3#6509711yescharacteristic
314C5#6826711yescharacteristic, complemented, Sylow
315C22#9147611yescharacteristic
316C4—21no—
317C4—102no—
318C4—122no—
319C4—201no—
320C4—302no—
321C4—601no—
322C4—1201no—
323C4D5×Dic1211yescharacteristic
324C4#9126011yescharacteristic
325C4#9148811yescharacteristic
326C4#9151111yescharacteristic
327C3#1059929811yescharacteristic, complemented, Sylow
328C2#1174749611yescharacteristic
329C2#1174813011yescharacteristic
330C2#1174824911yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socle, prime radicalC22×C3×C5#120
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1633
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
90. Dic30Q16semidirect
96. C3×Dic10Q16semidirect
198. Dic10Dic12semidirect
276. C3×C5#1633semidirect
314. C5#68267semidirect
327. C3#10599298semidirect

Maximal subgroups

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

subgroupindex
#117524732
#117509512
#117470962
#117469162
C5×#44812
C3×#647042
#117458452
#105992983
#682675