Finite Group Databasebeta

← #14289850

Subgroups — #14289850

Order 1920.

388 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 86 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#11752491C211yesmaximal, characteristic
2#11750782C211yesmaximal, characteristic, complemented
3#11746916C211yesmaximal, characteristic, complemented
4#11746883C211yesmaximal, characteristic
5C5×#4459C211yesmaximal, characteristic
6C3×#64676C211yesmaximal, characteristic, complemented
7#11745860C211yesmaximal, characteristic, complemented
8#10598998—31nomaximal, Hall
9#91758C2211yescharacteristic
10#91758C2211yescharacteristic
11C4×C5×D12C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13#91373—21no—
14#91369—21no—
15#91342—22no—
16#91338—21no—
17#91333—21no—
18C3×C4×C5×C8C2211yescharacteristic
19#91100—22no—
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90990—21no—
23#90985—21no—
24#90971—21no—
25#90967—21no—
26#68247—51nomaximal, Hall
27#65876—31no—
28#65297—31no—
29#65139—31no—
30#64970—31no—
31C5×D4⋊C8—31no—
32#64706—31no—
33#64676D311yescharacteristic, complemented
34C2×Dic30—21no—
35C2×Dic30—21no—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15—21no—
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C4⋊Dic15D412yes—
45C5×(C2×D3)⋊C4—21no—
46C5×C4⋊Dic3D411yescharacteristic
47C2×C5×C3⋊C8—21no—
48C3×C4⋊Dic5D411yescharacteristic
49C3×#683—21no—
50C3×C4×Dic5—21no—
51C2×C3×#168—21no—
52#6669—22no—
53(C2×D3)⋊Dic5—22no—
54(C2×D3)⋊Dic5—22no—
55Dic3×Dic5—22no—
56#5584—51no—
57#5021—51no—
58#4842—51no—
59#4681—51no—
60C3×Q8⋊C8—51no—
61#4482—51no—
62#4459D511yescharacteristic
63C4×C5×D4—31no—
64#4082—61no—
65#4072—61no—
66#4070—61no—
67#4033—61no—
68#4025—62no—
69#4015—31no—
70#4015—31no—
71C4×Dic10C2×D311yescharacteristic
72C5×C4⋊C8—31no—
73C4×C5×C8C2×D311yescharacteristic
74#3964—61no—
75#3950—61no—
76#3948—62no—
77#3948—61no—
78#3940—61no—
79C4⋊#168C2×D311yescharacteristic
80#1638—151noSylow
81C22×C5×D3—21no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×Dic15—22no—
86C2×Dic15—41no—
87Dic30—41no—
88Dic30—41no—
89Dic30—42no—
90C2×C5×Dic3—21no—
91C5×D12—21no—
92C5×D12—21no—
93C4×C5×D3—41no—
94C4×C5×D3—41no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—21no—
97C3×Dic10—21no—
98C3×Dic10—21no—
99C3×C5×C8—41no—
100C3×#168—41no—
101C5×C3⋊C8—41no—
102C3×C4×Q8—51no—
103#946—101no—
104#898—102no—
105#892—101no—
106#875—101no—
107C4×D12C2×D511yescharacteristic
108#869—51no—
109#869—51no—
110C4×Dic6—101no—
111C3×C4⋊C8—51no—
112C3×C4×C8C2×D511yescharacteristic
113#835—101no—
114#821—101no—
115#817—101no—
116#816—102no—
117#807—101no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C2×C5×D4—31no—
120C22×C4×C5—61no—
121C2×Dic10—61no—
122C2×Dic10—61no—
123C2×Dic10D1211yescharacteristic
124C2×C5×C8—21no—
125C2×C5×C8—61no—
126C5×C4⋊C4—31no—
127C5×C22⋊C4—61no—
128C42×C5C22×D311yescharacteristic
129C22⋊Dic5—62no—
130C22⋊Dic5—62no—
131C4⋊Dic5—32no—
132C4⋊Dic5—61no—
133C4⋊Dic5—61no—
134C4⋊Dic5—61no—
135C4⋊Dic5D1211yescharacteristic
136#683—21no—
137#683—62no—
138C4×Dic5—21no—
139C4×Dic5—62no—
140C2×#168—21no—
141#556—151no—
142#487—151no—
143#477—151no—
144#476—151no—
145#332—151no—
146Q8⋊C8—51no—
147D4⋊C8—31no—
148C22×C3×C5#12011yescharacteristic
149C2×C5×D3—41no—
150C2×C5×D3—41no—
151C2×C5×D3—41no—
152C3×C4×C5—21no—
153C3×C4×C5#13511yescharacteristic
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13711yescharacteristic
156C3×C4×C5#13711yescharacteristic
157Dic15—42no—
158Dic15—81no—
159C3×Dic5—41no—
160C3×Dic5—41no—
161C5×Dic3—41no—
162C2×C3×Q8—51no—
163C2×D12D2011yescharacteristic
164C2×C4×D3—21no—
165C2×Dic6—101no—
166C2×Dic6—101no—
167C2×C3×C8—21no—
168C2×C3×C8—101no—
169C3×C4⋊C4—51no—
170C3×C4⋊C4—101no—
171C3×C42—101no—
172C3×C42C22×D511yescharacteristic
173(C2×D3)⋊C4—21no—
174(C2×D3)⋊C4—102no—
175(C2×D3)⋊C4—102no—
176C4⋊Dic3—52no—
177C4⋊Dic3—101no—
178C4⋊Dic3—101no—
179C4⋊Dic3—101no—
180C4⋊Dic3D2011yescharacteristic
181Dic3⋊C4—102no—
182C4×Dic3—102no—
183C2×C3⋊C8—21no—
184C23×C5—61no—
185C5×D4—61no—
186C5×D4—61no—
187C2×C4×C5—61no—
188C2×C4×C5—121no—
189C2×C4×C5—121no—
190C2×C4×C5C2×D1211yescharacteristic
191C2×C4×C5D3×D411yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×Dic5—21no—
194C2×Dic5—21no—
195C2×Dic5—62no—
196C2×Dic5—121no—
197Dic10—21no—
198Dic10—21no—
199Dic10—121no—
200Dic10—121no—
201Dic10—122no—
202C5×C8—41no—
203C5×C8—121no—
204#168—41no—
205C4⋊Q8—151no—
206C4⋊Q8—151no—
207#126—302no—
208#124—301no—
209C22⋊Q8—301no—
210C4×Q8—51no—
211C4×Q8—301no—
212C4×D4—31no—
213#117—301no—
214#107—301no—
215#106—301no—
216C4⋊C8—31no—
217C4⋊C8—51no—
218#103—302no—
219#103—301no—
220#102—301no—
221C4×C8D3×D511yescharacteristic
222C2×C3×C5#45211yescharacteristic
223C2×C3×C5#45211yescharacteristic
224C2×C3×C5#45411yescharacteristic
225C5×D3—81no—
226C22×D3—21no—
227C3×Q8—101no—
228C3×Q8—101no—
229C2×C3×C4—101no—
230C2×C3×C4—101no—
231C2×C3×C4C2×D2011yescharacteristic
232C2×C3×C4D4×D511yescharacteristic
233C2×C3×C4D4×D511yescharacteristic
234C2×Dic3—21no—
235C2×Dic3—102no—
236C2×Dic3—201no—
237D12—21no—
238D12—21no—
239C4×D3—41no—
240C4×D3—41no—
241Dic6—201no—
242Dic6—201no—
243Dic6—202no—
244C3×C8—41no—
245C3×C8—201no—
246C3⋊C8—41no—
247C22×C5—121no—
248C22×C5—121no—
249C22×C5—121no—
250C22×C5#88211yescharacteristic
251C4×C5—21no—
252C4×C5—121no—
253C4×C5#90411yescharacteristic
254C4×C5#90911yescharacteristic
255C4×C5#91611yescharacteristic
256C4×C5#91811yescharacteristic
257Dic5—41no—
258Dic5—41no—
259Dic5—122no—
260Dic5—241no—
261C2×Q8—51no—
262C2×Q8—301no—
263C2×Q8—301no—
264C2×D4—31no—
265C22×C4—61no—
266C2×C8—21no—
267C2×C8—61no—
268C2×C8—101no—
269C4⋊C4—31no—
270C4⋊C4—51no—
271C4⋊C4—101no—
272C4⋊C4—152no—
273C4⋊C4—302no—
274C4⋊C4—301no—
275C4⋊C4—301no—
276C4⋊C4—301no—
277C22⋊C4—61no—
278C22⋊C4—302no—
279C22⋊C4—302no—
280C42—101no—
281C42—302no—
282C42C2×D3×D511yescharacteristic
283C3×C5#163811yescharacteristic, complemented, Hall
284C22×C3#402811yescharacteristic
285C2×D3—41no—
286C2×D3—41no—
287C2×D3—41no—
288C3×C4—21no—
289C3×C4—201no—
290C3×C4—201no—
291C3×C4#405011yescharacteristic
292C3×C4#405511yescharacteristic
293C3×C4#405811yescharacteristic
294C3×C4#406111yescharacteristic
295Dic3—41no—
296Dic3—202no—
297Dic3—401no—
298C2×C5—241no—
299C2×C5#473311yescharacteristic
300C2×C5#480811yescharacteristic
301C2×C5#482711yescharacteristic
302C23—61no—
303Q8—101no—
304Q8—101no—
305Q8—602no—
306Q8—601no—
307Q8—601no—
308D4—61no—
309D4—61no—
310C2×C4—61no—
311C2×C4—101no—
312C2×C4—101no—
313C2×C4—121no—
314C2×C4—121no—
315C2×C4—302no—
316C2×C4—601no—
317C2×C4D5×D1211yescharacteristic
318C2×C4D3×D2011yescharacteristic
319C2×C4#679011yescharacteristic
320C8—41no—
321C8—121no—
322C8—201no—
323C2×C3#6502211yescharacteristic
324C2×C3#6507211yescharacteristic
325C2×C3#6511611yescharacteristic
326D3—81no—
327C5#6824711yescharacteristic, complemented, Sylow
328C22—121no—
329C22—121no—
330C22—121no—
331C22#9147611yescharacteristic
332C4—21no—
333C4—121no—
334C4—201no—
335C4—201no—
336C4—602no—
337C4—1201no—
338C4#9126011yescharacteristic
339C4#9126311yescharacteristic
340C4#9127011yescharacteristic
341C4#9127211yescharacteristic
342C3#1059899811yescharacteristic, complemented, Sylow
343C2—241no—
344C2#1174712511yescharacteristic
345C2#1174816411yescharacteristic
346C2#1174816611yescharacteristic
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#1638
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. #11750782C2semidirect
3. #11746916C2semidirect
6. C3×#64676C2semidirect
7. #11745860C2semidirect
33. #64676D3semidirect
283. C3×C5#1638semidirect
327. C5#68247semidirect
342. C3#10598998semidirect

Maximal subgroups

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

subgroupindex
#117524912
#117507822
#117469162
#117468832
C5×#44592
C3×#646762
#117458602
#105989983
#682475