Finite Group Databasebeta

← #14292113

Subgroups — #14292113

Order 1920.

364 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 85 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#11751189C211yesmaximal, characteristic, complemented
2#11751184C211yesmaximal, characteristic, complemented
3#11750944C211yesmaximal, characteristic
4#11750935C211yesmaximal, characteristic, complemented
5C3×C5×#332C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic, complemented
7#11746300C211yesmaximal, characteristic, complemented
8#10599239—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C2×#6717—21no—
11C2×D120—21no—
12C2×C8×D15—21no—
13#91763C2211yescharacteristic
14C4×D60C2211yescharacteristic
15C3×C5×C4⋊C8C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17#91119—21no—
18#91105—21no—
19#91104—21no—
20#91093—21no—
21#91093—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4×C3⋊#168C2211yescharacteristic
24#68446—51nomaximal, Hall
25#65377—31no—
26#65372—31no—
27#65132—31no—
28#65123—31no—
29C5×#332D311yescharacteristic, complemented
30#64705—31no—
31#64699—31no—
32C2×C3×C5×Q8—21no—
33C2×D60—21no—
34C2×D60—21no—
35C2×D60—21no—
36C2×D60D411yescharacteristic
37C2×C4×D15—21no—
38C2×C3×C5×C8—21no—
39C2×C3×C5×C8—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43#6717—42no—
44#6714—21no—
45C4⋊Dic15D411yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168D411yescharacteristic
48C2×C3⋊#168D411yescharacteristic
49D120—42no—
50C8×D15—42no—
51#5088—51no—
52#5083—51no—
53#4843—51no—
54#4834—51no—
55C3×#332D511yescharacteristic, complemented
56#4485—51no—
57#4479—51no—
58C5×C4⋊Q8C2×D311yescharacteristic
59C2×#688—61no—
60C2×D40—61no—
61C2×C8×D5—61no—
62#4020—31no—
63C4×D20—31no—
64C5×C4⋊C8C2×D311yescharacteristic
65C5×C4⋊C8C2×D311yescharacteristic
66#3967—61no—
67#3953—61no—
68#3952—61no—
69#3941—61no—
70#3941—61no—
71C4⋊#168—31no—
72C4×#168—31no—
73#1681—151noSylow
74C22×D15—21no—
75C22×D15—41no—
76C3×C5×Q8—41no—
77C3×C5×Q8—41no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5C2×D411yescharacteristic
80C2×C3×C4×C5C2×D411yescharacteristic
81C2×C3×C4×C5#4111yescharacteristic
82C2×Dic15—21no—
83D60—21no—
84D60—41no—
85D60—41no—
86D60—41no—
87D60—41no—
88D60—81no—
89D60D812yes—
90C4×D15—41no—
91C4×D15—41no—
92C3×C5×C8—41no—
93C3×C5×C8—41no—
94C3⋊#168—21no—
95C3⋊#168—21no—
96C3⋊#168—41no—
97C3×C4⋊Q8C2×D511yescharacteristic
98C2×#215—101no—
99C2×D24—101no—
100C2×D3×C8—101no—
101#874—51no—
102C4×D12—51no—
103C3×C4⋊C8C2×D511yescharacteristic
104C3×C4⋊C8C2×D511yescharacteristic
105#835—101no—
106#821—101no—
107(C2×D3)⋊C8—101no—
108#809—101no—
109#809—101no—
110C4⋊(C3⋊C8)—51no—
111C4×C3⋊C8—51no—
112C2×C5×Q8—21no—
113C2×D20—31no—
114C2×D20—61no—
115C2×D20—61no—
116C2×D20—61no—
117C2×C4×D5—61no—
118C2×C5×C8—21no—
119C2×C5×C8—21no—
120C5×C4⋊C4—21no—
121C5×C4⋊C4—21no—
122C42×C5C22×D311yescharacteristic
123#688—122no—
124#685—61no—
125C4⋊Dic5—31no—
126C2×#168—31no—
127C2×#168—31no—
128C2×#168—61no—
129D40—122no—
130C8×D5—122no—
131#486—151no—
132#461—151no—
133#459—151no—
134C8×D4—151no—
135#335—151no—
136#332D1511yescharacteristic, complemented
137#331—151no—
138C22×C3×C5#12111yescharacteristic
139C2×D15—22no—
140C2×D15—41no—
141C2×D15—41no—
142C2×D15—81no—
143C2×D15—81no—
144C2×D15—81no—
145C3×C4×C5—21no—
146C3×C4×C5—81no—
147C3×C4×C5C2×D811yescharacteristic
148C3×C4×C5#13511yescharacteristic
149C3×C4×C5#13511yescharacteristic
150C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
151Dic15—41no—
152C2×C3×Q8—21no—
153C2×D12—51no—
154C2×D12—101no—
155C2×D12—101no—
156C2×D12—101no—
157C2×C4×D3—101no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C42C22×D511yescharacteristic
163#215—202no—
164(C2×D3)⋊C4—101no—
165C4⋊Dic3—51no—
166C2×C3⋊C8—51no—
167C2×C3⋊C8—51no—
168C2×C3⋊C8—101no—
169D24—202no—
170D3×C8—202no—
171C22×D5—61no—
172C22×D5—121no—
173C5×Q8—41no—
174C5×Q8—41no—
175C2×C4×C5—41no—
176C2×C4×C5#23511yescharacteristic
177C2×C4×C5D3×D411yescharacteristic
178C2×C4×C5D3×D411yescharacteristic
179C2×Dic5—61no—
180D20—32no—
181D20—61no—
182D20—121no—
183D20—121no—
184D20—121no—
185D20—121no—
186D20—241no—
187C4×D5—121no—
188C4×D5—121no—
189C5×C8—41no—
190C5×C8—41no—
191#168—61no—
192#168—61no—
193#168—121no—
194C2×SD16—301no—
195C2×D8—301no—
196C22×C8—301no—
197C4⋊Q8C2×D1511yescharacteristic
198#127—151no—
199C4×D4—151no—
200C4⋊C8—151no—
201C4⋊C8C2×D1511yescharacteristic
202C4⋊C8C2×D1511yescharacteristic
203#103—301no—
204#102—301no—
205#102—301no—
206#102—301no—
207C22⋊C8—301no—
208C4×C8—151no—
209C2×C3×C5#46311yescharacteristic
210C2×C3×C5#46611yescharacteristic
211C2×C3×C5#47111yescharacteristic
212D15—42no—
213D15—161no—
214C22×D3—101no—
215C22×D3—201no—
216C3×Q8—41no—
217C3×Q8—41no—
218C2×C3×C4—41no—
219C2×C3×C4#70911yescharacteristic
220C2×C3×C4D4×D511yescharacteristic
221C2×C3×C4D4×D511yescharacteristic
222C2×Dic3—101no—
223D12—52no—
224D12—101no—
225D12—201no—
226D12—201no—
227D12—201no—
228D12—201no—
229D12—401no—
230C4×D3—201no—
231C4×D3—201no—
232C3×C8—41no—
233C3×C8—41no—
234C3⋊C8—101no—
235C3⋊C8—101no—
236C3⋊C8—201no—
237C22×C5#88411yescharacteristic
238C2×D5—62no—
239C2×D5—121no—
240C2×D5—121no—
241C2×D5—241no—
242C2×D5—241no—
243C2×D5—241no—
244C4×C5—21no—
245C4×C5—81no—
246C4×C5D3×D811yescharacteristic
247C4×C5#91411yescharacteristic
248C4×C5#91611yescharacteristic
249C4×C5#91911yescharacteristic
250Dic5—121no—
251C2×Q8—21no—
252C2×D4—151no—
253C2×D4—301no—
254C2×D4—301no—
255C2×D4—301no—
256C22×C4—301no—
257SD16—602no—
258D8—602no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—151no—
262C2×C8—151no—
263C2×C8—301no—
264C2×C8—602no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—151no—
268C22⋊C4—301no—
269C42C22×D1511yescharacteristic
270C3×C5#168111yescharacteristic, complemented, Hall
271C22×C3#403011yescharacteristic
272C2×D3—102no—
273C2×D3—201no—
274C2×D3—201no—
275C2×D3—401no—
276C2×D3—401no—
277C2×D3—401no—
278C3×C4—21no—
279C3×C4—81no—
280C3×C4D5×D811yescharacteristic
281C3×C4#406011yescharacteristic
282C3×C4#406211yescharacteristic
283C3×C4#406511yescharacteristic
284Dic3—201no—
285C2×C5#475411yescharacteristic
286C2×C5#477511yescharacteristic
287C2×C5#481911yescharacteristic
288D5—122no—
289D5—481no—
290C23—301no—
291C23—601no—
292Q8—41no—
293Q8—41no—
294D4—152no—
295D4—301no—
296D4—601no—
297D4—601no—
298D4—601no—
299D4—601no—
300D4—1201no—
301C2×C4—41no—
302C2×C4—301no—
303C2×C4—601no—
304C2×C4—601no—
305C2×C4#681711yescharacteristic
306C2×C4D4×D1511yescharacteristic
307C2×C4D4×D1511yescharacteristic
308C8—41no—
309C8—41no—
310C8—301no—
311C8—301no—
312C8—601no—
313C2×C3#6504311yescharacteristic
314C2×C3#6506411yescharacteristic
315C2×C3#6510811yescharacteristic
316D3—202no—
317D3—801no—
318C5#6844611yescharacteristic, complemented, Sylow
319C22—302no—
320C22—601no—
321C22—601no—
322C22—1201no—
323C22—1201no—
324C22—1201no—
325C22#9177311yescharacteristic
326C4—21no—
327C4—81no—
328C4—601no—
329C4D8×D1511yescharacteristic
330C4#9180311yescharacteristic
331C4#9180511yescharacteristic
332C4#9180811yescharacteristic
333C3#1059923911yescharacteristic, complemented, Sylow
334C2—602no—
335C2—2401no—
336C2#1175085511yescharacteristic
337C2#1175087611yescharacteristic
338C2#1175092011yescharacteristic
subgroupG/H
centerC22#91773
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#332C2
socleC22×C3×C5#121
prime radical#11750944C2
hypercenter#332D15
hypocenterC3×C5#1681
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #11751189C2semidirect
2. #11751184C2semidirect
4. #11750935C2semidirect
5. C3×C5×#332C2semidirect
6. #11746306C2semidirect
7. #11746300C2semidirect
29. C5×#332D3semidirect
55. C3×#332D5semidirect
136. #332D15semidirect
270. C3×C5#1681semidirect
318. C5#68446semidirect
333. C3#10599239semidirect

Maximal subgroups

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

subgroupindex
#117511892
#117511842
#117509442
#117509352
C3×C5×#3322
#117463062
#117463002
#105992393
#684465