Finite Group Databasebeta

← #14289520

Subgroups — #14289520

Order 1920.

428 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 90 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#11752660C211yesmaximal, characteristic
2#11750800C211yesmaximal, characteristic, complemented
3#11746916C211yesmaximal, characteristic, complemented
4#11746883C211yesmaximal, characteristic
5C5×#4459C211yesmaximal, characteristic
6C3×#64676C211yesmaximal, characteristic, complemented
7#11745863C211yesmaximal, characteristic, complemented
8#10598995—31nomaximal, Hall
9C2×Dic60—22no—
10#91758C2211yescharacteristic
11#91758C2211yescharacteristic
12C4×C5×D12C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91432—22no—
15D3×C4⋊Dic5—21no—
16Dic5×D12—21no—
17#91388—21no—
18#91369—21no—
19C3×C4×C5×C8C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90990—21no—
23#90985—21no—
24#90971—21no—
25#90967—21no—
26#68246—51nomaximal, Hall
27#65877—31no—
28#65297—31no—
29#65139—31no—
30#64988—31no—
31C5×D4⋊C8—31no—
32#64701—31no—
33#64676D311yescharacteristic, complemented
34C2×Dic30—21no—
35C2×Dic30D412yes—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×D3×Dic5—22no—
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46Dic60—44no—
47C5×(C2×D3)⋊C4—21no—
48C5×C4⋊Dic3D411yescharacteristic
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—21no—
52C3×C4×Dic5—21no—
53C2×C3×#168—21no—
54Dic3⋊Dic5—22no—
55#6669—22no—
56(C2×D3)⋊Dic5—22no—
57#5579—51no—
58#5021—51no—
59#4842—51no—
60#4699—51no—
61C3×Q8⋊C8—51no—
62#4481—51no—
63#4459D511yescharacteristic
64C4×C5×D4—31no—
65D4×Dic5—61no—
66C2×C4⋊Dic5—61no—
67#4070—61no—
68C2×Dic20—62no—
69#4036—61no—
70#4024—62no—
71#4015—31no—
72#4015—31no—
73C4×Dic10C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8C2×D311yescharacteristic
76#3964—61no—
77#3950—61no—
78#3948—61no—
79#3940—61no—
80C4⋊#168C2×D311yescharacteristic
81#1632—151noSylow
82C22×C5×D3—21no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—22no—
87C2×Dic15—41no—
88Dic30—42no—
89Dic30—42no—
90C2×C5×Dic3—21no—
91C5×D12—21no—
92C5×D12Q1612yescomplemented
93C4×C5×D3—41no—
94C4×C5×D3—41no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—21no—
97C3×Dic10—21no—
98C3×Dic10—21no—
99D3×Dic5—82no—
100C3×C5×C8—22no—
101C3×#168—41no—
102C5×C3⋊C8—41no—
103C3×C4×Q8—51no—
104#946—101no—
105C2×Dic12—102no—
106#896—102no—
107D3×C4⋊C4—101no—
108C4×D12—101no—
109C4×D12C2×D511yescharacteristic
110#870—101no—
111#869—51no—
112#869—51no—
113C3×C4⋊C8—51no—
114C3×C4×C8C2×D511yescharacteristic
115#835—101no—
116#821—101no—
117#817—101no—
118#807—101no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C2×C5×D4—31no—
121C22×C4×C5—61no—
122C22×Dic5—62no—
123C2×Dic10—32no—
124C2×Dic10—61no—
125C2×Dic10D1211yescharacteristic
126C2×C5×C8—21no—
127C2×C5×C8—61no—
128C5×C4⋊C4—31no—
129C5×C22⋊C4—61no—
130C42×C5C22×D311yescharacteristic
131C22⋊Dic5—62no—
132C4⋊Dic5—62no—
133C4⋊Dic5—61no—
134C4⋊Dic5—61no—
135C4⋊Dic5—61no—
136C4⋊Dic5—61no—
137C4⋊Dic5D1211yescharacteristic
138#683—21no—
139#683—62no—
140C4×Dic5—21no—
141C2×#168—21no—
142Dic20—124no—
143#554—151no—
144#494—151no—
145#477—151no—
146#476—151no—
147#333—151no—
148Q8⋊C8—51no—
149D4⋊C8—31no—
150C22×C3×C5#12011yescharacteristic
151C2×C5×D3—22no—
152C2×C5×D3—41no—
153C2×C5×D3—41no—
154C3×C4×C5—21no—
155C3×C4×C5C2×Q1611yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×C4×C5#13711yescharacteristic
159Dic15—42no—
160Dic15—81no—
161C3×Dic5—41no—
162C3×Dic5—41no—
163C5×Dic3—41no—
164C2×C3×Q8—51no—
165C2×D12D2011yescharacteristic
166C2×C4×D3—21no—
167C2×C4×D3—102no—
168C2×Dic6—52no—
169C2×Dic6—101no—
170C2×C3×C8—21no—
171C2×C3×C8—101no—
172C3×C4⋊C4—51no—
173C3×C4⋊C4—101no—
174C3×C42—101no—
175C3×C42C22×D511yescharacteristic
176(C2×D3)⋊C4—21no—
177(C2×D3)⋊C4—102no—
178C4⋊Dic3—101no—
179C4⋊Dic3—101no—
180C4⋊Dic3—101no—
181C4⋊Dic3—101no—
182C4⋊Dic3D2011yescharacteristic
183Dic3⋊C4—102no—
184Dic3⋊C4—102no—
185C2×C3⋊C8—21no—
186Dic12—204no—
187C23×C5—61no—
188C5×D4—32no—
189C5×D4—61no—
190C2×C4×C5—61no—
191C2×C4×C5—121no—
192C2×C4×C5—121no—
193C2×C4×C5C2×D1211yescharacteristic
194C2×C4×C5D3×D411yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×Dic5—21no—
197C2×Dic5—21no—
198C2×Dic5—62no—
199C2×Dic5—121no—
200C2×Dic5—242no—
201Dic10—21no—
202Dic10—21no—
203Dic10—122no—
204Dic10—122no—
205C5×C8—22no—
206C5×C8—121no—
207#168—41no—
208C2×Q16—302no—
209C4⋊Q8—151no—
210C4⋊Q8—151no—
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8—51no—
215C4×D4—31no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—301no—
219#106—301no—
220C4⋊C8—31no—
221C4⋊C8—51no—
222#103—301no—
223#102—301no—
224C4×C8D3×D511yescharacteristic
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228C5×D3—42no—
229C22×D3—21no—
230C3×Q8—101no—
231C3×Q8—101no—
232C2×C3×C4—101no—
233C2×C3×C4—101no—
234C2×C3×C4C2×D2011yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×Dic3—21no—
238C2×Dic3—102no—
239C2×Dic3—201no—
240D12—21no—
241D12Dic2012yescomplemented
242C4×D3—41no—
243C4×D3—41no—
244C4×D3—402no—
245Dic6—202no—
246Dic6—202no—
247C3×C8—22no—
248C3×C8—201no—
249C3⋊C8—41no—
250C22×C5—62no—
251C22×C5—121no—
252C22×C5—121no—
253C22×C5#88211yescharacteristic
254C4×C5—21no—
255C4×C5—121no—
256C4×C5#90411yescharacteristic
257C4×C5#90911yescharacteristic
258C4×C5#91511yescharacteristic
259C4×C5D3×Q1611yescharacteristic
260Dic5—41no—
261Dic5—41no—
262Dic5—122no—
263Dic5—241no—
264C2×Q8—51no—
265C2×Q8—152no—
266C2×Q8—301no—
267C2×D4—31no—
268C22×C4—61no—
269C22×C4—302no—
270Q16—604no—
271C2×C8—21no—
272C2×C8—61no—
273C2×C8—101no—
274C4⋊C4—31no—
275C4⋊C4—51no—
276C4⋊C4—101no—
277C4⋊C4—302no—
278C4⋊C4—302no—
279C4⋊C4—301no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C22⋊C4—61no—
284C22⋊C4—302no—
285C42—101no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3#402811yescharacteristic
289C2×D3—22no—
290C2×D3—41no—
291C2×D3—41no—
292C3×C4—21no—
293C3×C4—201no—
294C3×C4—201no—
295C3×C4C2×Dic2011yescharacteristic
296C3×C4#405511yescharacteristic
297C3×C4#405811yescharacteristic
298C3×C4#406111yescharacteristic
299Dic3—41no—
300Dic3—202no—
301Dic3—401no—
302C2×C5—122no—
303C2×C5#473311yescharacteristic
304C2×C5#480911yescharacteristic
305C2×C5#482211yescharacteristic
306C23—61no—
307Q8—101no—
308Q8—101no—
309Q8—602no—
310Q8—602no—
311D4—32no—
312D4—61no—
313C2×C4—61no—
314C2×C4—101no—
315C2×C4—101no—
316C2×C4—121no—
317C2×C4—121no—
318C2×C4—302no—
319C2×C4—601no—
320C2×C4—1202no—
321C2×C4D5×D1211yescharacteristic
322C2×C4D3×D2011yescharacteristic
323C2×C4#679011yescharacteristic
324C8—22no—
325C8—121no—
326C8—201no—
327C2×C3#6502811yescharacteristic
328C2×C3#6507211yescharacteristic
329C2×C3#6511111yescharacteristic
330D3—42no—
331C5#6824611yescharacteristic, complemented, Sylow
332C22—62no—
333C22—121no—
334C22—121no—
335C22#9147611yescharacteristic
336C4—21no—
337C4—121no—
338C4—201no—
339C4—201no—
340C4—602no—
341C4—1201no—
342C4#9126011yescharacteristic
343C4D3×Dic2011yescharacteristic
344C4#9127011yescharacteristic
345C4#9127411yescharacteristic
346C3#1059899511yescharacteristic, complemented, Sylow
347C2—122no—
348C2#1174711811yescharacteristic
349C2#1174813311yescharacteristic
350C2#1174816411yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
hypercenterC4×C8D3×D5
hypocenterC3×C5#1632
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
2. #11750800C2semidirect
3. #11746916C2semidirect
6. C3×#64676C2semidirect
7. #11745863C2semidirect
33. #64676D3semidirect
92. C5×D12Q16semidirect
241. D12Dic20semidirect
287. C3×C5#1632semidirect
331. C5#68246semidirect
346. C3#10598995semidirect

Maximal subgroups

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

subgroupindex
#117526602
#117508002
#117469162
#117468832
C5×#44592
C3×#646762
#117458632
#105989953
#682465