Finite Group Databasebeta

← #14290603

Subgroups — #14290603

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#11752508C211yesmaximal, characteristic
2C5×#4682C211yesmaximal, characteristic, complemented
3#11747059C211yesmaximal, characteristic
4#11746946C211yesmaximal, characteristic, complemented
5#11746277C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic
7#11745857C211yesmaximal, characteristic, complemented
8#10602163—31nomaximal, Hall
9C4×Dic30C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×C4×D20C2211yescharacteristic
13#91368—21no—
14#91361—22no—
15#91360—21no—
16#91358—21no—
17#91344—21no—
18C2×#6655—21no—
19C3×C4×C5×C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×#818—22no—
22C3×C4⋊#168C2211yescharacteristic
23#90985—21no—
24#90975—21no—
25#90972—21no—
26#68209—51nomaximal, Hall
27#66066—31no—
28C5×#500—31no—
29#65383—31no—
30#65372—31no—
31#64767—31no—
32#64679D311yescharacteristic
33#64676—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×Dic6—21no—
36C2×C5×Dic6—21no—
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C4⋊Dic15D411yescharacteristic
42#6712—21no—
43C4×Dic15—21no—
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3D412yes—
49C3×#685—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C2×C3×#168—21no—
52Dic3⋊Dic5—22no—
53#6665—22no—
54#6665—22no—
55Dic3×Dic5—22no—
56#6655—42no—
57#5542—51no—
58#5019—51no—
59#4851—51no—
60#4682D511yescharacteristic, complemented
61C3×D4⋊C8—51no—
62#4486—51no—
63#4456—51no—
64C5×C4⋊Q8—31no—
65C5×C4⋊Q8—31no—
66#4093—61no—
67Q8×Dic5—61no—
68C2×#688—61no—
69#4044—62no—
70#4043—61no—
71#4038—61no—
72C4×D20C2×D311yescharacteristic
73C4×Dic10—31no—
74C5×#107—62no—
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3942—61no—
78#3940—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81#1650—151noSylow
82C22×C3×D5—21no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—21no—
87C2×Dic15—21no—
88Dic30—21no—
89Dic30—21no—
90C2×C5×Dic3—22no—
91C2×C5×Dic3—41no—
92C5×Dic6—41no—
93C5×Dic6—41no—
94C5×Dic6—41no—
95C5×Dic6—41no—
96C2×C3×Dic5—21no—
97C3×D20—21no—
98C3×D20—21no—
99C3×C4×D5—41no—
100C3×C4×D5—41no—
101C3×C5×C8—22no—
102C3⋊#168—41no—
103C3×#168—41no—
104C3×C4×D4—51no—
105#936—101no—
106C2×#214—101no—
107#926—101no—
108#924—101no—
109#887—101no—
110#879—102no—
111#869C2×D511yescharacteristic
112#869C2×D511yescharacteristic
113C4×Dic6—51no—
114C3×C4⋊C8—51no—
115C3×C4×C8C2×D511yescharacteristic
116#818—22no—
117#817—101no—
118#816—101no—
119#810—101no—
120C4⋊(C3⋊C8)—51no—
121C2×C5×Q8—61no—
122C2×C5×Q8—61no—
123C2×D20D1211yescharacteristic
124C2×C4×D5—21no—
125C2×Dic10—31no—
126C2×C5×C8—21no—
127C5×C4⋊C4—32no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4—61no—
131C42×C5C22×D311yescharacteristic
132#688—122no—
133#685—21no—
134#685—62no—
135#685—62no—
136C4⋊Dic5—31no—
137C4⋊Dic5—62no—
138C4⋊Dic5D1211yescharacteristic
139#683—61no—
140C4×Dic5—62no—
141C4×Dic5—61no—
142C2×#168—21no—
143C2×#168—61no—
144#556—151no—
145#500—31no—
146#475—151no—
147#461—151no—
148#332—151no—
149Q8⋊C8—151no—
150D4⋊C8—51no—
151C22×C3×C5#12011yescharacteristic
152C2×C3×D5—41no—
153C2×C3×D5—41no—
154C2×C3×D5—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—41no—
161Dic15—41no—
162C3×Dic5—41no—
163C5×Dic3—42no—
164C5×Dic3—81no—
165C2×C3×D4—51no—
166C22×C3×C4—101no—
167C2×Dic6—21no—
168C2×Dic6—21no—
169C2×Dic6—51no—
170C2×C3×C8—21no—
171C2×C3×C8—101no—
172C3×C4⋊C4—51no—
173C3×C22⋊C4—101no—
174C3×C42C22×D511yescharacteristic
175#217—102no—
176#217—102no—
177#214—202no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—21no—
181C4⋊Dic3—51no—
182C4⋊Dic3C22⋊D512yes—
183Dic3⋊C4—102no—
184Dic3⋊C4—101no—
185C4×Dic3—102no—
186C4×Dic3—101no—
187C2×C3⋊C8—101no—
188C22×D5—21no—
189C5×Q8—121no—
190C5×Q8—121no—
191C5×Q8—121no—
192C5×Q8—121no—
193C2×C4×C5—62no—
194C2×C4×C5—121no—
195C2×C4×C5C2×D1211yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×Dic5—21no—
199C2×Dic5—61no—
200C2×Dic5—61no—
201D20—21no—
202D20—21no—
203C4×D5—41no—
204C4×D5—41no—
205Dic10—61no—
206Dic10—61no—
207C5×C8—22no—
208#168—41no—
209#168—121no—
210C2×SD16—301no—
211C4⋊Q8—31no—
212C4⋊Q8—31no—
213#126—302no—
214#124—301no—
215C22⋊Q8—301no—
216C4×Q8—151no—
217C4×Q8—301no—
218C4×D4—51no—
219#117—301no—
220#107—62no—
221#106—301no—
222C4⋊C8—51no—
223C4⋊C8—151no—
224#103—301no—
225#103—301no—
226C4×C8D3×D511yescharacteristic
227C2×C3×C5#44911yescharacteristic
228C2×C3×C5#45211yescharacteristic
229C2×C3×C5#45611yescharacteristic
230C3×D5—81no—
231C23×C3—101no—
232C3×D4—101no—
233C3×D4—101no—
234C2×C3×C4—101no—
235C2×C3×C4—201no—
236C2×C3×C4—201no—
237C2×C3×C4D4×D511yescharacteristic
238C2×C3×C4D4×D511yescharacteristic
239C2×C3×C4C2×C22⋊D511yescharacteristic
240C2×Dic3—22no—
241C2×Dic3—41no—
242C2×Dic3—101no—
243C2×Dic3—101no—
244Dic6—41no—
245Dic6—41no—
246Dic6—41no—
247Dic6—41no—
248Dic6—101no—
249Dic6—101no—
250C3×C8—22no—
251C3×C8—201no—
252C3⋊C8—201no—
253C22×C5#88211yescharacteristic
254C2×D5—41no—
255C2×D5—41no—
256C2×D5—41no—
257C4×C5—21no—
258C4×C5—122no—
259C4×C5—241no—
260C4×C5#90411yescharacteristic
261C4×C5#90811yescharacteristic
262C4×C5#91211yescharacteristic
263C4×C5#91511yescharacteristic
264Dic5—41no—
265Dic5—121no—
266Dic5—121no—
267C2×Q8—61no—
268C2×Q8—61no—
269C2×Q8—151no—
270C2×D4—51no—
271C22×C4—101no—
272SD16—602no—
273C2×C8—21no—
274C2×C8—101no—
275C2×C8—301no—
276C4⋊C4—32no—
277C4⋊C4—51no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4—151no—
282C4⋊C4—302no—
283C4⋊C4—301no—
284C22⋊C4—101no—
285C22⋊C4—302no—
286C22⋊C4—302no—
287C42—302no—
288C42—301no—
289C42C2×D3×D511yescharacteristic
290C3×C5#165011yescharacteristic, complemented, Hall
291C22×C3—201no—
292C22×C3—201no—
293C22×C3—201no—
294C22×C3#408311yescharacteristic
295C3×C4—21no—
296C3×C4—201no—
297C3×C4#405711yescharacteristic
298C3×C4#405811yescharacteristic
299C3×C4#406411yescharacteristic
300C3×C4#406511yescharacteristic
301Dic3—42no—
302Dic3—81no—
303Dic3—201no—
304Dic3—201no—
305C2×C5#473411yescharacteristic
306C2×C5#478311yescharacteristic
307C2×C5#482611yescharacteristic
308D5—81no—
309C23—101no—
310Q8—121no—
311Q8—121no—
312Q8—121no—
313Q8—121no—
314Q8—301no—
315Q8—301no—
316D4—101no—
317D4—101no—
318C2×C4—62no—
319C2×C4—101no—
320C2×C4—121no—
321C2×C4—201no—
322C2×C4—201no—
323C2×C4—301no—
324C2×C4—301no—
325C2×C4D5×D1211yescharacteristic
326C2×C4#677711yescharacteristic
327C2×C4D3×C22⋊D511yescharacteristic
328C8—22no—
329C8—201no—
330C8—601no—
331C2×C3—401no—
332C2×C3#6538411yescharacteristic
333C2×C3#6544711yescharacteristic
334C2×C3#6547611yescharacteristic
335C5#6820911yescharacteristic, complemented, Sylow
336C22—201no—
337C22—201no—
338C22—201no—
339C22#9147511yescharacteristic
340C4—21no—
341C4—122no—
342C4—201no—
343C4—241no—
344C4—601no—
345C4—601no—
346C4#9125011yescharacteristic
347C4#9127011yescharacteristic
348C4#9127711yescharacteristic
349C4#9127811yescharacteristic
350C3#1060216311yescharacteristic, complemented, Sylow
351C2—401no—
352C2#1174712211yescharacteristic
353C2#1174815411yescharacteristic
354C2#1174815611yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
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. C5×#4682C2semidirect
4. #11746946C2semidirect
5. #11746277C2semidirect
7. #11745857C2semidirect
60. #4682D5semidirect
290. C3×C5#1650semidirect
335. C5#68209semidirect
350. C3#10602163semidirect

Maximal subgroups

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

subgroupindex
#117525082
C5×#46822
#117470592
#117469462
#117462772
C3×#646792
#117458572
#106021633
#682095