Finite Group Databasebeta

← #14290624

Subgroups — #14290624

Order 1920.

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

normal subgroups only

This group has 400 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
2C3×#65140C211yesmaximal, characteristic, complemented
3#11747070C211yesmaximal, characteristic
4#11746960C211yesmaximal, characteristic, complemented
5#11746307C211yesmaximal, characteristic, complemented
6C5×#4483C211yesmaximal, characteristic
7#11745841C211yesmaximal, characteristic, complemented
8#10599002—31nomaximal, Hall
9#91758C2211yescharacteristic
10C4×C5×D12C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13#91373—21no—
14#91369—21no—
15#91342—22no—
16#91338—21no—
17#91333—21no—
18C2×#6656—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C4×C5×C3⋊C8C2211yescharacteristic
22C3×#3949—21no—
23C3×#3948—21no—
24#90990—22no—
25#90970—21no—
26#71126—51nomaximal, Hall
27#65876—31no—
28#65308—31no—
29#65140D311yescharacteristic, complemented
30#64971—31no—
31C5×D4⋊C8—31no—
32#64706—31no—
33#64676—31no—
34C2×Dic30—21no—
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C3×Dic10—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15—21no—
42C4⋊Dic15D412yes—
43C2×C3⋊#168—21no—
44C5×(C2×D3)⋊C4—21no—
45C5×C4⋊Dic3D411yescharacteristic
46C2×C5×C3⋊C8—21no—
47C3×C4⋊Dic5—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5D411yescharacteristic
50C3×#683—21no—
51C3×C4×Dic5—21no—
52#6669—22no—
53(C2×D3)⋊Dic5—22no—
54(C2×D3)⋊Dic5—22no—
55Dic3×Dic5—22no—
56#6656—42no—
57#5584—51no—
58C3×#475—51no—
59#5083—51no—
60#5078—51no—
61#4535—51no—
62#4486—51no—
63#4483D511yescharacteristic
64C4×C5×D4—31no—
65#4082—61no—
66C2×#687—61no—
67#4072—61no—
68#4070—61no—
69#4033—61no—
70#4025—62no—
71#4015—31no—
72#4015C2×D311yescharacteristic
73C4×Dic10C2×D311yescharacteristic
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8—31no—
76#3950—62no—
77#3949—21no—
78#3948—21no—
79#3942—61no—
80C4⋊#168—31no—
81#1650—151noSylow
82C22×C5×D3—21no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—22no—
87Dic30—41no—
88Dic30—41no—
89C2×C5×Dic3—21no—
90C5×D12—21no—
91C5×D12—21no—
92C4×C5×D3—41no—
93C4×C5×D3—41no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—41no—
97C3×Dic10—21no—
98C3×Dic10—21no—
99C3×Dic10—41no—
100C3×Dic10—41no—
101C3×C5×C8—41no—
102C3⋊#168—41no—
103C5×C3⋊C8—22no—
104C3×C4⋊Q8—51no—
105C3×C4×Q8—51no—
106#946—101no—
107C2×#215—101no—
108#898—102no—
109#892—101no—
110#875—101no—
111C4×D12C2×D511yescharacteristic
112#869—51no—
113C4×Dic6—101no—
114C3×#106—101no—
115C3×C4⋊C8C2×D511yescharacteristic
116C3×#103—101no—
117#835—101no—
118#807—102no—
119C4⋊(C3⋊C8)—51no—
120C4×C3⋊C8C2×D511yescharacteristic
121C2×C5×D4—31no—
122C22×C4×C5—61no—
123C2×Dic10—21no—
124C2×Dic10—61no—
125C2×Dic10#6711yescharacteristic
126C2×C5×C8—21no—
127C2×C5×C8—61no—
128C5×C4⋊C4—31no—
129C5×C22⋊C4—61no—
130C42×C5C22×D311yescharacteristic
131C22⋊Dic5—62no—
132C22⋊Dic5—62no—
133#687—122no—
134C4⋊Dic5—21no—
135C4⋊Dic5—21no—
136C4⋊Dic5—32no—
137C4⋊Dic5—61no—
138C4⋊Dic5#6711yescharacteristic
139#683—21no—
140#683—62no—
141C4×Dic5—21no—
142C4×Dic5—62no—
143C2×#168—61no—
144#556—151no—
145#500—151no—
146#475—51no—
147#461—151no—
148#332—151no—
149Q8⋊C8—151no—
150D4⋊C8—31no—
151C22×C3×C5#12011yescharacteristic
152C2×C5×D3—41no—
153C2×C5×D3—41no—
154C2×C5×D3—41no—
155C3×C4×C5—21no—
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×C4×C5#13711yescharacteristic
160Dic15—42no—
161C3×Dic5—41no—
162C3×Dic5—41no—
163C3×Dic5—81no—
164C5×Dic3—41no—
165C2×C3×Q8—51no—
166C2×C3×Q8—101no—
167C2×D12D2011yescharacteristic
168C2×C4×D3—21no—
169C2×Dic6—101no—
170C2×C3×C8—21no—
171C3×C4⋊C4—51no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C42—101no—
176C3×C42C22×D511yescharacteristic
177#215—202no—
178(C2×D3)⋊C4—21no—
179(C2×D3)⋊C4—102no—
180(C2×D3)⋊C4—102no—
181C4⋊Dic3—52no—
182C4⋊Dic3—101no—
183C4⋊Dic3D2011yescharacteristic
184Dic3⋊C4—102no—
185C4×Dic3—102no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—101no—
188C23×C5—61no—
189C5×D4—61no—
190C5×D4—61no—
191C2×C4×C5—61no—
192C2×C4×C5—121no—
193C2×C4×C5—121no—
194C2×C4×C5D3×D411yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5C2×#6711yescharacteristic
197C2×Dic5—21no—
198C2×Dic5—21no—
199C2×Dic5—41no—
200C2×Dic5—62no—
201Dic10—21no—
202Dic10—21no—
203Dic10—41no—
204Dic10—41no—
205Dic10—121no—
206Dic10—121no—
207C5×C8—41no—
208C5×C8—62no—
209#168—121no—
210C2×SD16—301no—
211C4⋊Q8—51no—
212C4⋊Q8—151no—
213#126—302no—
214#124—301no—
215C22⋊Q8—301no—
216C4×Q8—51no—
217C4×Q8—301no—
218C4×D4—31no—
219#117—301no—
220#107—302no—
221#106—101no—
222C4⋊C8—151no—
223C4⋊C8D3×D511yescharacteristic
224#103—101no—
225#103—301no—
226C4×C8—31no—
227C2×C3×C5#44911yescharacteristic
228C2×C3×C5#45211yescharacteristic
229C2×C3×C5#45611yescharacteristic
230C5×D3—81no—
231C22×D3—21no—
232C3×Q8—101no—
233C3×Q8—101no—
234C3×Q8—201no—
235C3×Q8—201no—
236C2×C3×C4—101no—
237C2×C3×C4—101no—
238C2×C3×C4—201no—
239C2×C3×C4C2×D2011yescharacteristic
240C2×C3×C4D4×D511yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×Dic3—21no—
243C2×Dic3—102no—
244D12—21no—
245D12—21no—
246C4×D3—41no—
247C4×D3—41no—
248Dic6—201no—
249Dic6—201no—
250C3×C8—41no—
251C3⋊C8—22no—
252C3⋊C8—201no—
253C22×C5—121no—
254C22×C5—121no—
255C22×C5—121no—
256C22×C5#93711yescharacteristic
257C4×C5—21no—
258C4×C5—121no—
259C4×C5#91411yescharacteristic
260C4×C5#91611yescharacteristic
261C4×C5#94211yescharacteristic
262C4×C5#95011yescharacteristic
263Dic5—41no—
264Dic5—41no—
265Dic5—81no—
266Dic5—122no—
267C2×Q8—51no—
268C2×Q8—101no—
269C2×Q8—301no—
270C2×D4—31no—
271C22×C4—61no—
272SD16—602no—
273C2×C8—21no—
274C2×C8—61no—
275C2×C8—301no—
276C4⋊C4—31no—
277C4⋊C4—51no—
278C4⋊C4—101no—
279C4⋊C4—101no—
280C4⋊C4—101no—
281C4⋊C4—152no—
282C4⋊C4—302no—
283C4⋊C4—301no—
284C22⋊C4—61no—
285C22⋊C4—302no—
286C22⋊C4—302no—
287C42—101no—
288C42—302no—
289C42C2×D3×D511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3#402811yescharacteristic
292C2×D3—41no—
293C2×D3—41no—
294C2×D3—41no—
295C3×C4—21no—
296C3×C4—201no—
297C3×C4—201no—
298C3×C4—401no—
299C3×C4#405011yescharacteristic
300C3×C4#405411yescharacteristic
301C3×C4#405811yescharacteristic
302C3×C4#406111yescharacteristic
303Dic3—41no—
304Dic3—202no—
305C2×C5—241no—
306C2×C5#504711yescharacteristic
307C2×C5#517211yescharacteristic
308C2×C5#520511yescharacteristic
309C23—61no—
310Q8—101no—
311Q8—101no—
312Q8—201no—
313Q8—201no—
314Q8—601no—
315Q8—601no—
316D4—61no—
317D4—61no—
318C2×C4—61no—
319C2×C4—101no—
320C2×C4—101no—
321C2×C4—121no—
322C2×C4—121no—
323C2×C4—201no—
324C2×C4—302no—
325C2×C4D3×D2011yescharacteristic
326C2×C4#677711yescharacteristic
327C2×C4D5×#6711yescharacteristic
328C8—41no—
329C8—62no—
330C8—601no—
331C2×C3#6502311yescharacteristic
332C2×C3#6507211yescharacteristic
333C2×C3#6511511yescharacteristic
334D3—81no—
335C5#7112611yescharacteristic, complemented, Sylow
336C22—121no—
337C22—121no—
338C22—121no—
339C22#9147411yescharacteristic
340C4—21no—
341C4—121no—
342C4—201no—
343C4—201no—
344C4—401no—
345C4—602no—
346C4#9125311yescharacteristic
347C4#9127211yescharacteristic
348C4#9149011yescharacteristic
349C4#9151311yescharacteristic
350C3#1059900211yescharacteristic, complemented, Sylow
351C2—241no—
352C2#1174751111yescharacteristic
353C2#1174789011yescharacteristic
354C2#1174825211yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1650
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. C3×#65140C2semidirect
4. #11746960C2semidirect
5. #11746307C2semidirect
7. #11745841C2semidirect
29. #65140D3semidirect
290. C3×C5#1650semidirect
335. C5#71126semidirect
350. C3#10599002semidirect

Maximal subgroups

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

subgroupindex
#117524912
C3×#651402
#117470702
#117469602
#117463072
C5×#44832
#117458412
#105990023
#711265