Finite Group Databasebeta

← #14290602

Subgroups — #14290602

Order 1920.

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

normal subgroups only

This group has 400 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
1C3×#65876C211yesmaximal, characteristic
2#11751120C211yesmaximal, characteristic
3#11746960C211yesmaximal, characteristic, complemented
4#11746943C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic
6#11745855C211yesmaximal, characteristic, complemented
7#11745841C211yesmaximal, characteristic, complemented
8#10599002—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C2×#6716—21no—
11#91758C2211yescharacteristic
12C3×#4082—21no—
13C3×#4072—21no—
14C3×#4070—21no—
15C3×#4033—21no—
16C3×#4025—22no—
17C3×#4015C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19#91094—21no—
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C4×C5×C3⋊C8C2211yescharacteristic
23#90990—22no—
24#90987—21no—
25#90971—21no—
26#71933—51nomaximal, Hall
27#65876D311yescharacteristic
28#65308—31no—
29#65140—31no—
30#64971—31no—
31C5×D4⋊C8—31no—
32#64706—31no—
33#64676—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×Dic30—21no—
37C2×C3×Dic10—21no—
38C2×C3×Dic10D411yescharacteristic
39C3×C5×C4⋊C4D411yescharacteristic
40C3×C5×C22⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42#6716—42no—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C2×C3⋊#168—21no—
46C2×C5×C3⋊C8—21no—
47C2×C5×C3⋊C8—21no—
48C3×C22⋊Dic5—22no—
49C3×C22⋊Dic5—22no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5D411yescharacteristic
52C3×C4⋊Dic5D412yes—
53C3×#683—22no—
54C3×#683—21no—
55C3×C4×Dic5—22no—
56C3×C4×Dic5—21no—
57C3×#556—51no—
58#5078—51no—
59#5020—51no—
60#5019—51no—
61#4547—51no—
62#4535—51no—
63D4⋊(C3⋊C8)D511yescharacteristic
64C4×C5×D4C2×D311yescharacteristic
65#4082—21no—
66C2×#687—61no—
67#4072—21no—
68#4070—21no—
69#4033—21no—
70#4025—22no—
71#4015—31no—
72#4015C2×D311yescharacteristic
73C4×Dic10C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8—31no—
76#3950—62no—
77#3949—61no—
78#3948—61no—
79#3942—61no—
80C4⋊#168—31no—
81#1650—151noSylow
82C23×C3×C5—21no—
83C3×C5×D4—21no—
84C3×C5×D4—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—41no—
92Dic30—41no—
93Dic30—41no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—22no—
97C3×Dic10—21no—
98C3×Dic10—21no—
99C3×Dic10—41no—
100C3×Dic10—41no—
101C3⋊#168—41no—
102C5×C3⋊C8—22no—
103C5×C3⋊C8—41no—
104C3×C4⋊Q8—51no—
105C3×#126—102no—
106C3×#124—101no—
107C3×C22⋊Q8—101no—
108C3×C4×Q8—51no—
109C3×C4×Q8—101no—
110C3×C4×D4C2×D511yescharacteristic
111C3×#117—101no—
112C2×#214—101no—
113#869—51no—
114#835—101no—
115#810—101no—
116#808—101no—
117#807—102no—
118C4⋊(C3⋊C8)—51no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C4×C3⋊C8C2×D511yescharacteristic
121C2×C5×D4#6711yescharacteristic
122C22×C4×C5—21no—
123C2×Dic10—21no—
124C2×Dic10—61no—
125C2×Dic10#6711yescharacteristic
126C2×C5×C8—61no—
127C2×C5×C8—61no—
128C5×C4⋊C4#6711yescharacteristic
129C5×C22⋊C4—21no—
130C42×C5C22×D311yescharacteristic
131C22⋊Dic5—22no—
132C22⋊Dic5—22no—
133#687—122no—
134C4⋊Dic5—21no—
135C4⋊Dic5—61no—
136C4⋊Dic5—61no—
137C4⋊Dic5#6711yescharacteristic
138C4⋊Dic5#6712yes—
139#683—22no—
140#683—21no—
141C4×Dic5—22no—
142C4×Dic5—21no—
143C2×#168—61no—
144#556—51no—
145#500—151no—
146#475—151no—
147#461—151no—
148#332—151no—
149Q8⋊C8—151no—
150D4⋊C8—31no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5#12011yescharacteristic
155C3×C4×C5—21no—
156C3×C4×C5—41no—
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×C4×C5#13711yescharacteristic
161Dic15—81no—
162C3×Dic5—42no—
163C3×Dic5—41no—
164C3×Dic5—41no—
165C2×C3×Q8—51no—
166C2×C3×Q8—101no—
167C2×C3×D4D2011yescharacteristic
168C22×C3×C4—21no—
169C2×Dic6—101no—
170C3×C4⋊C4—52no—
171C3×C4⋊C4—51no—
172C3×C4⋊C4—102no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4D2011yescharacteristic
176C3×C22⋊C4—21no—
177C3×C22⋊C4—102no—
178C3×C22⋊C4—102no—
179C3×C42—102no—
180C3×C42—101no—
181C3×C42C22×D511yescharacteristic
182#214—202no—
183C4⋊Dic3—101no—
184C4⋊Dic3—101no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—101no—
188C23×C5—21no—
189C5×D4—21no—
190C5×D4—21no—
191C2×C4×C5—21no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5C2×#6711yescharacteristic
195C2×C4×C5C2×#6711yescharacteristic
196C2×C4×C5C2×#6711yescharacteristic
197C2×Dic5—21no—
198C2×Dic5—21no—
199C2×Dic5—22no—
200C2×Dic5—121no—
201Dic10—21no—
202Dic10—21no—
203Dic10—41no—
204Dic10—41no—
205Dic10—121no—
206Dic10—121no—
207C5×C8—62no—
208C5×C8—121no—
209#168—121no—
210C2×SD16—301no—
211C4⋊Q8—51no—
212C4⋊Q8—151no—
213#126—102no—
214#124—101no—
215C22⋊Q8—101no—
216C4×Q8—51no—
217C4×Q8—101no—
218C4×D4D3×D511yescharacteristic
219#117—101no—
220#107—302no—
221#106—301no—
222C4⋊C8—31no—
223C4⋊C8—151no—
224#103—301no—
225#103—301no—
226C4×C8—31no—
227C2×C3×C5—81no—
228C2×C3×C5#44911yescharacteristic
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45611yescharacteristic
231C23×C3—21no—
232C3×Q8—101no—
233C3×Q8—101no—
234C3×Q8—201no—
235C3×Q8—201no—
236C3×D4—21no—
237C3×D4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—101no—
242C2×C3×C4—102no—
243C2×C3×C4—101no—
244C2×C3×C4C2×D2011yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×Dic3—201no—
248Dic6—201no—
249Dic6—201no—
250C3⋊C8—22no—
251C3⋊C8—41no—
252C3⋊C8—201no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5—41no—
256C22×C5#95311yescharacteristic
257C4×C5—21no—
258C4×C5—41no—
259C4×C5#94911yescharacteristic
260C4×C5#95011yescharacteristic
261C4×C5#95011yescharacteristic
262C4×C5#95111yescharacteristic
263Dic5—42no—
264Dic5—41no—
265Dic5—41no—
266Dic5—241no—
267C2×Q8—51no—
268C2×Q8—101no—
269C2×Q8—301no—
270C2×D4#120211yescharacteristic
271C22×C4—21no—
272SD16—602no—
273C2×C8—61no—
274C2×C8—61no—
275C2×C8—301no—
276C4⋊C4—51no—
277C4⋊C4—52no—
278C4⋊C4—102no—
279C4⋊C4—101no—
280C4⋊C4—101no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C4⋊C4#120211yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—102no—
286C22⋊C4—102no—
287C42—102no—
288C42—101no—
289C42C2×D3×D511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3—41no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3#402811yescharacteristic
295C3×C4—21no—
296C3×C4—41no—
297C3×C4—201no—
298C3×C4—201no—
299C3×C4—202no—
300C3×C4#405011yescharacteristic
301C3×C4#405411yescharacteristic
302C3×C4#405811yescharacteristic
303C3×C4#406111yescharacteristic
304Dic3—401no—
305C2×C5—81no—
306C2×C5#523811yescharacteristic
307C2×C5#523911yescharacteristic
308C2×C5#524611yescharacteristic
309C23—21no—
310Q8—101no—
311Q8—101no—
312Q8—201no—
313Q8—201no—
314Q8—601no—
315Q8—601no—
316D4—21no—
317D4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—101no—
322C2×C4—102no—
323C2×C4—101no—
324C2×C4—601no—
325C2×C4C2×#120211yescharacteristic
326C2×C4D5×#6711yescharacteristic
327C2×C4D5×#6711yescharacteristic
328C8—62no—
329C8—121no—
330C8—601no—
331C2×C3—81no—
332C2×C3#6502311yescharacteristic
333C2×C3#6507211yescharacteristic
334C2×C3#6511511yescharacteristic
335C5#7193311yescharacteristic, complemented, Sylow
336C22—41no—
337C22—41no—
338C22—41no—
339C22#9156411yescharacteristic
340C4—21no—
341C4—41no—
342C4—201no—
343C4—202no—
344C4—201no—
345C4—1201no—
346C4#9130111yescharacteristic
347C4#9131111yescharacteristic
348C4#9148411yescharacteristic
349C4#9149011yescharacteristic
350C3#1059900211yescharacteristic, complemented, Sylow
351C2—81no—
352C2#1174851311yescharacteristic
353C2#1174904911yescharacteristic
354C2#1174946411yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#1650
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #11746960C2semidirect
4. #11746943C2semidirect
6. #11745855C2semidirect
7. #11745841C2semidirect
290. C3×C5#1650semidirect
335. C5#71933semidirect
350. C3#10599002semidirect

Maximal subgroups

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

subgroupindex
C3×#658762
#117511202
#117469602
#117469432
C5×D4⋊(C3⋊C8)2
#117458552
#117458412
#105990023
#719335