Finite Group Databasebeta

← #14290599

Subgroups — #14290599

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
1C5×#5542C211yesmaximal, characteristic
2C3×#65308C211yesmaximal, characteristic
3#11746962C211yesmaximal, characteristic, complemented
4#11746927C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic
6#11745858C211yesmaximal, characteristic, complemented
7#11745842C211yesmaximal, characteristic, complemented
8#10602726—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C5×#936—21no—
11C5×#926—21no—
12C5×#924—21no—
13C5×#887—21no—
14C5×#879—22no—
15C5×#869C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C2×C3×#687—21no—
18C3×#4015C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C3×#3942—21no—
22C3×C4⋊#168C2211yescharacteristic
23#90989—22no—
24#90986—21no—
25#90972—21no—
26#71049—51nomaximal, Hall
27C5×#556—31no—
28#65367—31no—
29#65309—31no—
30#65308D311yescharacteristic
31#64767—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×Dic6—21no—
37C2×C5×Dic6D411yescharacteristic
38C2×C3×Dic10—21no—
39C3×C5×C4⋊C4D411yescharacteristic
40C3×C5×C22⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42C2×C3⋊#168—21no—
43C2×C3⋊#168—21no—
44C5×#217—22no—
45C5×#217—22no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3D411yescharacteristic
48C5×C4⋊Dic3D412yes—
49C5×Dic3⋊C4—22no—
50C5×Dic3⋊C4—21no—
51C4×C5×Dic3—22no—
52C4×C5×Dic3—21no—
53C3×#687—42no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5—21no—
56C2×C3×#168—21no—
57#5542D511yescharacteristic
58C3×#461—51no—
59#5094—51no—
60#5078—51no—
61D4⋊(C3⋊C8)—51no—
62#4484—51no—
63#4482—51no—
64C5×C4⋊Q8—31no—
65C5×#126—62no—
66C5×#124—61no—
67C5×C22⋊Q8—61no—
68C4×C5×Q8—31no—
69C4×C5×Q8—61no—
70C4×C5×D4C2×D311yescharacteristic
71C5×#117—61no—
72C2×#687—21no—
73#4015C2×D311yescharacteristic
74#3967—61no—
75#3942—21no—
76#3940—61no—
77#3939—62no—
78C4⋊#168—31no—
79C4⋊#168C2×D311yescharacteristic
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×C5×Dic3—21no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—22no—
94C5×Dic6—21no—
95C5×Dic6—21no—
96C5×Dic6—41no—
97C5×Dic6—41no—
98C2×C3×Dic5—41no—
99C3×Dic10—41no—
100C3×Dic10—41no—
101C3⋊#168—22no—
102C3⋊#168—41no—
103C3×#168—41no—
104C2×C3×SD16—101no—
105C3×C4⋊Q8—51no—
106C3×C4×D4C2×D511yescharacteristic
107#936—21no—
108#926—21no—
109#924—21no—
110#887—21no—
111#879—22no—
112#869C2×D511yescharacteristic
113C4×Dic6C2×D511yescharacteristic
114C3×C4⋊C8—51no—
115C3×#103—101no—
116#810—101no—
117#808—101no—
118#807—102no—
119C4⋊(C3⋊C8)—51no—
120C4×C3⋊C8—51no—
121C2×C5×Q8—31no—
122C2×C5×Q8—61no—
123C2×C5×D4#6711yescharacteristic
124C22×C4×C5—21no—
125C2×Dic10—21no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—32no—
128C5×C4⋊C4—62no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4#6711yescharacteristic
132C5×C22⋊C4—21no—
133C5×C22⋊C4—62no—
134C5×C22⋊C4—62no—
135C42×C5—62no—
136C42×C5—61no—
137C42×C5C22×D311yescharacteristic
138#687—42no—
139C4⋊Dic5—21no—
140C4⋊Dic5—21no—
141C2×#168—21no—
142C2×#168—61no—
143C2×#168—61no—
144#556—31no—
145#500—151no—
146#475—151no—
147#461—51no—
148#332—151no—
149Q8⋊C8—151no—
150D4⋊C8—151no—
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
161C3×Dic5—81no—
162C5×Dic3—42no—
163C5×Dic3—41no—
164C5×Dic3—41no—
165C2×C3×Q8—101no—
166C2×C3×D4C22⋊D511yescharacteristic
167C22×C3×C4—21no—
168C2×Dic6—21no—
169C2×Dic6C22⋊D511yescharacteristic
170C3×SD16—202no—
171C2×C3×C8—101no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4C22⋊D511yescharacteristic
175C3×C22⋊C4—21no—
176C3×C42C22×D511yescharacteristic
177#217—22no—
178#217—22no—
179C4⋊Dic3—21no—
180C4⋊Dic3C22⋊D512yes—
181C4⋊Dic3C22⋊D511yescharacteristic
182Dic3⋊C4—22no—
183Dic3⋊C4—21no—
184C4×Dic3—22no—
185C4×Dic3—21no—
186C2×C3⋊C8—101no—
187C2×C3⋊C8—101no—
188C23×C5—21no—
189C5×Q8—61no—
190C5×Q8—61no—
191C5×Q8—121no—
192C5×Q8—121no—
193C5×D4—21no—
194C5×D4—21no—
195C2×C4×C5—21no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—61no—
199C2×C4×C5—62no—
200C2×C4×C5—61no—
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204C2×Dic5—41no—
205Dic10—41no—
206Dic10—41no—
207#168—41no—
208#168—62no—
209#168—121no—
210C2×SD16—101no—
211C4⋊Q8—31no—
212C4⋊Q8—51no—
213#126—62no—
214#124—61no—
215C22⋊Q8—61no—
216C4×Q8—31no—
217C4×Q8—61no—
218C4×D4D3×D511yescharacteristic
219#117—61no—
220#107—302no—
221#106—301no—
222C4⋊C8—51no—
223C4⋊C8—151no—
224#103—101no—
225#103—301no—
226C4×C8—151no—
227C2×C3×C5—81no—
228C2×C3×C5#44911yescharacteristic
229C2×C3×C5#45211yescharacteristic
230C2×C3×C5#45611yescharacteristic
231C23×C3—21no—
232C3×Q8—201no—
233C3×Q8—201no—
234C3×D4—21no—
235C3×D4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—201no—
240C2×C3×C4C2×C22⋊D511yescharacteristic
241C2×C3×C4C2×C22⋊D511yescharacteristic
242C2×C3×C4C2×C22⋊D511yescharacteristic
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—22no—
246Dic6—21no—
247Dic6—21no—
248Dic6—41no—
249Dic6—41no—
250C3×C8—201no—
251C3⋊C8—102no—
252C3⋊C8—201no—
253C22×C5—41no—
254C22×C5—41no—
255C22×C5—41no—
256C22×C5#93711yescharacteristic
257C4×C5—21no—
258C4×C5—41no—
259C4×C5—121no—
260C4×C5—121no—
261C4×C5—122no—
262C4×C5#91511yescharacteristic
263C4×C5#91611yescharacteristic
264C4×C5#93211yescharacteristic
265C4×C5#95011yescharacteristic
266Dic5—81no—
267C2×Q8—31no—
268C2×Q8—61no—
269C2×Q8—101no—
270C2×D4#120111yescharacteristic
271C22×C4—21no—
272SD16—202no—
273C2×C8—101no—
274C2×C8—301no—
275C2×C8—301no—
276C4⋊C4—31no—
277C4⋊C4—32no—
278C4⋊C4—62no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4—101no—
282C4⋊C4—101no—
283C4⋊C4#120111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—62no—
286C22⋊C4—62no—
287C42—62no—
288C42—61no—
289C42C2×D3×D511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3—41no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3#409911yescharacteristic
295C3×C4—21no—
296C3×C4—41no—
297C3×C4—401no—
298C3×C4#409511yescharacteristic
299C3×C4#409611yescharacteristic
300C3×C4#409611yescharacteristic
301C3×C4#409711yescharacteristic
302Dic3—42no—
303Dic3—41no—
304Dic3—41no—
305C2×C5—81no—
306C2×C5#503711yescharacteristic
307C2×C5#517311yescharacteristic
308C2×C5#520511yescharacteristic
309C23—21no—
310Q8—61no—
311Q8—61no—
312Q8—121no—
313Q8—121no—
314Q8—201no—
315Q8—201no—
316D4—21no—
317D4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—61no—
322C2×C4—62no—
323C2×C4—61no—
324C2×C4—201no—
325C2×C4C2×#120111yescharacteristic
326C2×C4D3×C22⋊D511yescharacteristic
327C2×C4D3×C22⋊D511yescharacteristic
328C8—201no—
329C8—302no—
330C8—601no—
331C2×C3—81no—
332C2×C3#6552711yescharacteristic
333C2×C3#6552811yescharacteristic
334C2×C3#6553511yescharacteristic
335C5#7104911yescharacteristic, complemented, Sylow
336C22—41no—
337C22—41no—
338C22—41no—
339C22#9156811yescharacteristic
340C4—21no—
341C4—41no—
342C4—121no—
343C4—122no—
344C4—121no—
345C4—401no—
346C4#9129711yescharacteristic
347C4#9129811yescharacteristic
348C4#9148611yescharacteristic
349C4#9149511yescharacteristic
350C3#1060272611yescharacteristic, complemented, Sylow
351C2—81no—
352C2#1174851711yescharacteristic
353C2#1174905911yescharacteristic
354C2#1174946511yescharacteristic
subgroupG/H
centerC22#91568
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. #11746962C2semidirect
4. #11746927C2semidirect
6. #11745858C2semidirect
7. #11745842C2semidirect
290. C3×C5#1650semidirect
335. C5#71049semidirect
350. C3#10602726semidirect

Maximal subgroups

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

subgroupindex
C5×#55422
C3×#653082
#117469622
#117469272
D4⋊(C3⋊#168)2
#117458582
#117458422
#106027263
#710495