Finite Group Databasebeta

← #14292104

Subgroups — #14292104

Order 1920.

364 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 103 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×C5×C8×D4C211yesmaximal, characteristic, complemented
2#11751120C211yesmaximal, characteristic, complemented
3#11751116C211yesmaximal, characteristic
4#11750795C211yesmaximal, characteristic, complemented
5#11746307C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic, complemented
7#11746279C211yesmaximal, characteristic, complemented
8#10601642—31nomaximal, Hall
9C22×C3×C5×C8—21no—
10C3×C4×C5×D4C2211yescharacteristic
11C2×#6716—21no—
12C2×#6715—21no—
13#91763C2211yescharacteristic
14#91758C2211yescharacteristic
15C3×C5×C4⋊C8C2211yescharacteristic
16C3×C5×C22⋊C8—21no—
17C3×C4×C5×C8C2211yescharacteristic
18#91105—21no—
19#91105—21no—
20#91094—21no—
21#91093—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4⋊(C3⋊#168)C2211yescharacteristic
24#70849—51nomaximal, Hall
25C5×C8×D4D311yescharacteristic, complemented
26#65308—31no—
27#65304—31no—
28#64983—31no—
29#64706—31no—
30#64705—31no—
31#64678—31no—
32C2×C3×C5×D4D411yescharacteristic
33C22×C3×C4×C5—21no—
34C2×D60—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×Dic30—21no—
38C2×C3×C5×C8—21no—
39C2×C3×C5×C8—42no—
40C2×C3×C5×C8D411yescharacteristic
41C2×C3×C5×C8D411yescharacteristic
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C42×C5C2311yescharacteristic
45#6716—42no—
46#6715—42no—
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49C2×C3⋊#168—21no—
50C2×C3⋊#168—21no—
51C3×C8×D4D511yescharacteristic, complemented
52#5019—51no—
53#5015—51no—
54#4694—51no—
55#4486—51no—
56#4485—51no—
57#4458—51no—
58C22×C5×C8—21no—
59C4×C5×D4C2×D311yescharacteristic
60C2×#687—61no—
61C2×#686—61no—
62#4020—31no—
63#4015—31no—
64C5×C4⋊C8C2×D311yescharacteristic
65C5×C22⋊C8—21no—
66C4×C5×C8C2×D311yescharacteristic
67#3953—61no—
68#3953—61no—
69#3942—61no—
70#3941—61no—
71C4⋊#168—31no—
72C4⋊#168—31no—
73#1681—151noSylow
74C23×C3×C5—21no—
75C22×D15—41no—
76C3×C5×D4—21no—
77C3×C5×D4D812yes—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5#4111yescharacteristic
84C2×Dic15—41no—
85D60—41no—
86D60—41no—
87D60—41no—
88D60—41no—
89D60—81no—
90Dic30—41no—
91Dic30—41no—
92C3×C5×C8—21no—
93C3×C5×C8—21no—
94C3×C5×C8—41no—
95C3⋊#168—41no—
96C3⋊#168—41no—
97C22×C3×C8—21no—
98C3×C4×D4C2×D511yescharacteristic
99C2×#214—101no—
100C2×#213—101no—
101#874—51no—
102#869—51no—
103C3×C4⋊C8C2×D511yescharacteristic
104C3×C22⋊C8—21no—
105C3×C4×C8C2×D511yescharacteristic
106#821—101no—
107#821—101no—
108#810—101no—
109#809—101no—
110C4⋊(C3⋊C8)—51no—
111C4⋊(C3⋊C8)—51no—
112C2×C5×D4D1211yescharacteristic
113C22×C4×C5—21no—
114C2×D20—61no—
115C2×D20—61no—
116C2×D20—61no—
117C2×Dic10—61no—
118C2×C5×C8—21no—
119C2×C5×C8—42no—
120C2×C5×C8#6711yescharacteristic
121C2×C5×C8#6711yescharacteristic
122C5×C4⋊C4D1211yescharacteristic
123C5×C22⋊C4—21no—
124C42×C5C22×D311yescharacteristic
125#687—122no—
126#686—122no—
127C4⋊Dic5—61no—
128C4⋊Dic5—61no—
129C2×#168—61no—
130C2×#168—61no—
131#486—151no—
132#461—151no—
133#459—151no—
134C8×D4D1511yescharacteristic, complemented
135#335—151no—
136#332—151no—
137#331—151no—
138C22×C3×C5—22no—
139C22×C3×C5—41no—
140C22×C3×C5—41no—
141C22×C3×C5#12111yescharacteristic
142C2×D15—81no—
143C2×D15—81no—
144C2×D15—81no—
145C3×C4×C5—21no—
146C3×C4×C5—41no—
147C3×C4×C5C2×D811yescharacteristic
148C3×C4×C5#13511yescharacteristic
149C3×C4×C5#13511yescharacteristic
150C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
151Dic15—81no—
152C2×C3×D4D2011yescharacteristic
153C22×C3×C4—21no—
154C2×D12—101no—
155C2×D12—101no—
156C2×D12—101no—
157C2×Dic6—101no—
158C2×C3×C8—21no—
159C2×C3×C8—42no—
160C2×C3×C8C22⋊D511yescharacteristic
161C2×C3×C8C22⋊D511yescharacteristic
162C3×C4⋊C4D2011yescharacteristic
163C3×C22⋊C4—21no—
164C3×C42C22×D511yescharacteristic
165#214—202no—
166#213—202no—
167C4⋊Dic3—101no—
168C4⋊Dic3—101no—
169C2×C3⋊C8—101no—
170C2×C3⋊C8—101no—
171C23×C5—21no—
172C22×D5—121no—
173C5×D4—21no—
174C5×D4D2412yes—
175C2×C4×C5—21no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5C2×D1211yescharacteristic
179C2×C4×C5#23511yescharacteristic
180C2×C4×C5C2×#6711yescharacteristic
181C2×Dic5—121no—
182D20—121no—
183D20—121no—
184D20—121no—
185D20—121no—
186D20—241no—
187Dic10—121no—
188Dic10—121no—
189C5×C8—21no—
190C5×C8—21no—
191C5×C8—41no—
192#168—121no—
193#168—121no—
194C2×SD16—301no—
195C2×D8—301no—
196C22×C8—21no—
197C4⋊Q8—151no—
198#127—151no—
199C4×D4C2×D1511yescharacteristic
200C4⋊C8—151no—
201C4⋊C8—151no—
202C4⋊C8C2×D1511yescharacteristic
203#103—301no—
204#102—301no—
205#102—301no—
206#102—301no—
207C22⋊C8—21no—
208C4×C8C2×D1511yescharacteristic
209C2×C3×C5—42no—
210C2×C3×C5#46311yescharacteristic
211C2×C3×C5#46611yescharacteristic
212C2×C3×C5#47111yescharacteristic
213D15—161no—
214C23×C3—21no—
215C22×D3—201no—
216C3×D4—21no—
217C3×D4D4012yes—
218C2×C3×C4—21no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4C2×D2011yescharacteristic
222C2×C3×C4#70911yescharacteristic
223C2×C3×C4C2×C22⋊D511yescharacteristic
224C2×Dic3—201no—
225D12—201no—
226D12—201no—
227D12—201no—
228D12—201no—
229D12—401no—
230Dic6—201no—
231Dic6—201no—
232C3×C8—21no—
233C3×C8—21no—
234C3×C8—41no—
235C3⋊C8—201no—
236C3⋊C8—201no—
237C22×C5—22no—
238C22×C5—41no—
239C22×C5—41no—
240C22×C5#93011yescharacteristic
241C2×D5—241no—
242C2×D5—241no—
243C2×D5—241no—
244C4×C5—21no—
245C4×C5—41no—
246C4×C5C2×D2411yescharacteristic
247C4×C5#90411yescharacteristic
248C4×C5#93211yescharacteristic
249C4×C5#95011yescharacteristic
250Dic5—241no—
251C2×Q8—301no—
252C2×D4—301no—
253C2×D4—301no—
254C2×D4—301no—
255C2×D4D6011yescharacteristic
256C22×C4—21no—
257SD16—602no—
258D8—602no—
259C2×C8—21no—
260C2×C8—42no—
261C2×C8—301no—
262C2×C8—301no—
263C2×C8#122011yescharacteristic
264C2×C8#122011yescharacteristic
265C4⋊C4—301no—
266C4⋊C4—301no—
267C4⋊C4D6011yescharacteristic
268C22⋊C4—21no—
269C42C22×D1511yescharacteristic
270C3×C5#168111yescharacteristic, complemented, Hall
271C22×C3—22no—
272C22×C3—41no—
273C22×C3—41no—
274C22×C3#407611yescharacteristic
275C2×D3—401no—
276C2×D3—401no—
277C2×D3—401no—
278C3×C4—21no—
279C3×C4—41no—
280C3×C4C2×D4011yescharacteristic
281C3×C4#405011yescharacteristic
282C3×C4#407811yescharacteristic
283C3×C4#409611yescharacteristic
284Dic3—401no—
285C2×C5—42no—
286C2×C5#501611yescharacteristic
287C2×C5#511511yescharacteristic
288C2×C5#514111yescharacteristic
289D5—481no—
290C23—21no—
291C23—601no—
292Q8—601no—
293Q8—601no—
294D4—21no—
295D4—601no—
296D4—601no—
297D4—601no—
298D4—601no—
299D4—1201no—
300D4D12012yes—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—601no—
305C2×C4C2×D6011yescharacteristic
306C2×C4#681711yescharacteristic
307C2×C4C2×#122011yescharacteristic
308C8—21no—
309C8—21no—
310C8—41no—
311C8—601no—
312C8—601no—
313C2×C3—42no—
314C2×C3#6530511yescharacteristic
315C2×C3#6540411yescharacteristic
316C2×C3#6543011yescharacteristic
317D3—801no—
318C5#7084911yescharacteristic, complemented, Sylow
319C22—22no—
320C22—41no—
321C22—41no—
322C22—1201no—
323C22—1201no—
324C22—1201no—
325C22#9181911yescharacteristic
326C4—21no—
327C4—41no—
328C4—1201no—
329C4C2×D12011yescharacteristic
330C4#9179311yescharacteristic
331C4#9182111yescharacteristic
332C4#9183911yescharacteristic
333C3#1060164211yescharacteristic, complemented, Sylow
334C2—42no—
335C2—2401no—
336C2#1175111711yescharacteristic
337C2#1175121611yescharacteristic
338C2#1175124211yescharacteristic
subgroupG/H
centerC22#91819
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×C8×D4C2
socleC22×C3×C5#121
prime radical#11751116C2
hypercenterC8×D4D15
hypocenterC3×C5#1681
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C3×C5×C8×D4C2semidirect
2. #11751120C2semidirect
4. #11750795C2semidirect
5. #11746307C2semidirect
6. #11746306C2semidirect
7. #11746279C2semidirect
25. C5×C8×D4D3semidirect
51. C3×C8×D4D5semidirect
134. C8×D4D15semidirect
270. C3×C5#1681semidirect
318. C5#70849semidirect
333. C3#10601642semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C8×D42
#117511202
#117511162
#117507952
#117463072
#117463062
#117462792
#106016423
#708495