Finite Group Databasebeta

← #14290590

Subgroups — #14290590

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#11752507C211yesmaximal, characteristic
2#11751179C211yesmaximal, characteristic, complemented
3C5×#5094C211yesmaximal, characteristic, complemented
4C3×#65372C211yesmaximal, characteristic
5#11745860C211yesmaximal, characteristic, complemented
6#11745842C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic
8#10601919—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C2×C3×#688—21no—
13C3×C4×D20C2211yescharacteristic
14#91364—21no—
15#91362—22no—
16#91359—21no—
17#91358—21no—
18#91340—21no—
19#91091—22no—
20C4×C3⋊#168C2211yescharacteristic
21C5×#810—21no—
22C5×#808—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×#3967—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71049—51nomaximal, Hall
27#65918—31no—
28C5×#475—31no—
29#65372D311yescharacteristic
30#65367—31no—
31Q8⋊#168—31no—
32#64706—31no—
33#64703—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30—21no—
36C2×C5×Dic6D411yescharacteristic
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15—21no—
43C4⋊Dic15D412yes—
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3D411yescharacteristic
46C5×Dic3⋊C4—21no—
47C4×C5×Dic3—21no—
48C2×C5×C3⋊C8—21no—
49C3×#688—42no—
50C3×#685—21no—
51C3×C4⋊Dic5D411yescharacteristic
52C2×C3×#168—21no—
53#6669—22no—
54#6665—22no—
55#6665—22no—
56Dic3×Dic5—22no—
57#5542—51no—
58C3×#461—51no—
59#5094D511yescharacteristic, complemented
60#5078—51no—
61D4⋊(C3⋊C8)—51no—
62#4484—51no—
63#4482—51no—
64C5×C4⋊Q8C2×D311yescharacteristic
65C4×C5×Q8—31no—
66#4092—61no—
67C2×#688—21no—
68#4044—62no—
69#4038—61no—
70#4021—61no—
71C4×D20C2×D311yescharacteristic
72#4015—31no—
73C4×Dic10—61no—
74C5×#106—61no—
75C5×C4⋊C8—31no—
76C5×#103—61no—
77#3967—21no—
78#3939—62no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168—31no—
81#1650—151noSylow
82C22×C3×D5—21no—
83C3×C5×Q8—41no—
84C3×C5×Q8—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—22no—
90Dic30—41no—
91Dic30—41no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—21no—
94C5×Dic6—21no—
95C5×Dic6—21no—
96C2×C3×Dic5—21no—
97C3×D20—21no—
98C3×D20—21no—
99C3×C4×D5—41no—
100C3×C4×D5—41no—
101C3⋊#168—22no—
102C3×#168—41no—
103C5×C3⋊C8—41no—
104C2×C3×SD16—101no—
105C3×C4⋊Q8C2×D511yescharacteristic
106C3×C4×D4—51no—
107#936—101no—
108#926—101no—
109#924—101no—
110#887—101no—
111#879—102no—
112#869—51no—
113C4×Dic6C2×D511yescharacteristic
114C3×C4⋊C8—51no—
115C3×#103—101no—
116#810—21no—
117#808—21no—
118#807—102no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C4×C3⋊C8—51no—
121C2×C5×Q8—21no—
122C2×C5×Q8—31no—
123C2×D20#6711yescharacteristic
124C2×C4×D5—21no—
125C2×Dic10—61no—
126C2×C5×C8—61no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—31no—
130C5×C4⋊C4—61no—
131C42×C5—61no—
132C42×C5C22×D311yescharacteristic
133#688—42no—
134#685—21no—
135#685—62no—
136#685—62no—
137C4⋊Dic5—32no—
138C4⋊Dic5—61no—
139C4⋊Dic5#6711yescharacteristic
140#683—62no—
141C4×Dic5—62no—
142C2×#168—21no—
143C2×#168—61no—
144#556—151no—
145#500—151no—
146#475—31no—
147#461—51no—
148#332—151no—
149Q8⋊C8—151no—
150D4⋊C8—151no—
151C22×C3×C5#12011yescharacteristic
152C2×C3×D5—41no—
153C2×C3×D5—41no—
154C2×C3×D5—41no—
155C3×C4×C5—21no—
156C3×C4×C5—81no—
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×C4×C5#13711yescharacteristic
161Dic15—42no—
162C3×Dic5—41no—
163C5×Dic3—41no—
164C5×Dic3—41no—
165C2×C3×Q8—21no—
166C2×C3×D4—51no—
167C22×C3×C4—101no—
168C2×Dic6—101no—
169C2×Dic6C22⋊D511yescharacteristic
170C3×SD16—202no—
171C2×C3×C8—101no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—51no—
175C3×C22⋊C4—101no—
176C3×C42C22×D511yescharacteristic
177#217—102no—
178#217—102no—
179C4⋊Dic3—52no—
180C4⋊Dic3—101no—
181C4⋊Dic3C22⋊D511yescharacteristic
182Dic3⋊C4—21no—
183Dic3⋊C4—102no—
184C4×Dic3—21no—
185C4×Dic3—102no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—101no—
188C22×D5—21no—
189C5×Q8—41no—
190C5×Q8—41no—
191C5×Q8—61no—
192C5×Q8—61no—
193C2×C4×C5—41no—
194C2×C4×C5—61no—
195C2×C4×C5—61no—
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5C2×#6711yescharacteristic
199C2×Dic5—21no—
200C2×Dic5—62no—
201D20—21no—
202D20—21no—
203C4×D5—41no—
204C4×D5—41no—
205Dic10—121no—
206Dic10—121no—
207C5×C8—121no—
208#168—41no—
209#168—62no—
210C2×SD16—101no—
211C4⋊Q8—151no—
212C4⋊Q8D3×D511yescharacteristic
213#126—302no—
214#124—301no—
215C22⋊Q8—301no—
216C4×Q8—31no—
217C4×Q8—301no—
218C4×D4—51no—
219#117—301no—
220#107—302no—
221#106—61no—
222C4⋊C8—31no—
223C4⋊C8—51no—
224#103—61no—
225#103—101no—
226C4×C8—151no—
227C2×C3×C5#44911yescharacteristic
228C2×C3×C5#45211yescharacteristic
229C2×C3×C5#45611yescharacteristic
230C3×D5—81no—
231C23×C3—101no—
232C3×Q8—41no—
233C3×Q8—41no—
234C3×D4—101no—
235C3×D4—101no—
236C2×C3×C4—41no—
237C2×C3×C4—101no—
238C2×C3×C4—201no—
239C2×C3×C4—201no—
240C2×C3×C4D4×D511yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4C2×C22⋊D511yescharacteristic
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—102no—
246Dic6—21no—
247Dic6—21no—
248Dic6—201no—
249Dic6—201no—
250C3×C8—201no—
251C3⋊C8—41no—
252C3⋊C8—102no—
253C22×C5#93711yescharacteristic
254C2×D5—41no—
255C2×D5—41no—
256C2×D5—41no—
257C4×C5—21no—
258C4×C5—81no—
259C4×C5—121no—
260C4×C5—121no—
261C4×C5#91511yescharacteristic
262C4×C5#91611yescharacteristic
263C4×C5#93211yescharacteristic
264C4×C5#95011yescharacteristic
265Dic5—41no—
266Dic5—122no—
267C2×Q8—21no—
268C2×Q8—31no—
269C2×Q8—301no—
270C2×D4—51no—
271C22×C4—101no—
272SD16—202no—
273C2×C8—61no—
274C2×C8—101no—
275C2×C8—301no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—31no—
279C4⋊C4—51no—
280C4⋊C4—61no—
281C4⋊C4—152no—
282C4⋊C4—302no—
283C4⋊C4—301no—
284C22⋊C4—101no—
285C22⋊C4—302no—
286C22⋊C4—302no—
287C42—61no—
288C42—302no—
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—81no—
297C3×C4—201no—
298C3×C4#406011yescharacteristic
299C3×C4#406211yescharacteristic
300C3×C4#408811yescharacteristic
301C3×C4#409611yescharacteristic
302Dic3—41no—
303Dic3—41no—
304Dic3—202no—
305C2×C5#503711yescharacteristic
306C2×C5#517311yescharacteristic
307C2×C5#520511yescharacteristic
308D5—81no—
309C23—101no—
310Q8—41no—
311Q8—41no—
312Q8—61no—
313Q8—61no—
314Q8—601no—
315Q8—601no—
316D4—101no—
317D4—101no—
318C2×C4—41no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4—101no—
322C2×C4—201no—
323C2×C4—201no—
324C2×C4—302no—
325C2×C4D5×#6711yescharacteristic
326C2×C4D3×C22⋊D511yescharacteristic
327C2×C4#679011yescharacteristic
328C8—121no—
329C8—201no—
330C8—302no—
331C2×C3—401no—
332C2×C3#6533611yescharacteristic
333C2×C3#6546111yescharacteristic
334C2×C3#6549411yescharacteristic
335C5#7104911yescharacteristic, complemented, Sylow
336C22—201no—
337C22—201no—
338C22—201no—
339C22#9157711yescharacteristic
340C4—21no—
341C4—81no—
342C4—121no—
343C4—121no—
344C4—201no—
345C4—602no—
346C4#9149111yescharacteristic
347C4#9149211yescharacteristic
348C4#9151711yescharacteristic
349C4#9151811yescharacteristic
350C3#1060191911yescharacteristic, complemented, Sylow
351C2—401no—
352C2#1174916011yescharacteristic
353C2#1174940311yescharacteristic
354C2#1174941211yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1650
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11751179C2semidirect
3. C5×#5094C2semidirect
5. #11745860C2semidirect
6. #11745842C2semidirect
59. #5094D5semidirect
290. C3×C5#1650semidirect
335. C5#71049semidirect
350. C3#10601919semidirect

Maximal subgroups

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

subgroupindex
#117525072
#117511792
C5×#50942
C3×#653722
#117458602
#117458422
#117458342
#106019193
#710495