Finite Group Databasebeta

← #14291411

Subgroups — #14291411

Order 1920.

408 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 87 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#11751174C211yesmaximal, characteristic, complemented
2#11751173C211yesmaximal, characteristic, complemented
3#11750944C211yesmaximal, characteristic, complemented
4#11750935C211yesmaximal, characteristic, complemented
5C3×C5×#331C211yesmaximal, characteristic, complemented
6#11746306C211yesmaximal, characteristic, complemented
7#11746300C211yesmaximal, characteristic, complemented
8#10599188—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10C2×#6715—21no—
11C2×#6715—21no—
12C2×#6715—21no—
13C2×D120—21no—
14C2×C8×D15—21no—
15#91763C2211yescharacteristic
16C4×D60C2211yescharacteristic
17C3×C5×C4⋊C8C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19#91116—21no—
20#91105—21no—
21#91104—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4×C3⋊#168C2211yescharacteristic
24#68395—51nomaximal, Hall
25#65362—31no—
26#65361—31no—
27#65132—31no—
28#65123—31no—
29C5×#331D311yescharacteristic, complemented
30#64705—31no—
31#64699—31no—
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×D60D411yescharacteristic
39C2×C4×D15—21no—
40C2×C3×C5×C8—21no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43#6715—42no—
44#6715—42no—
45#6715—42no—
46#6714—21no—
47C4⋊Dic15D411yescharacteristic
48C2×C3⋊#168—21no—
49C2×C3⋊#168D411yescharacteristic
50C2×C3⋊#168D411yescharacteristic
51D120—42no—
52C8×D15—42no—
53#5073—51no—
54#5072—51no—
55#4843—51no—
56#4834—51no—
57C3×#331D511yescharacteristic, complemented
58#4485—51no—
59#4479—51no—
60C5×#127C2×D311yescharacteristic
61C2×#686—61no—
62C2×#686—61no—
63C2×#686—61no—
64C2×D40—61no—
65C2×C8×D5—61no—
66#4020—31no—
67C4×D20—31no—
68C5×C4⋊C8C2×D311yescharacteristic
69C5×C4⋊C8C2×D311yescharacteristic
70#3964—61no—
71#3953—61no—
72#3952—61no—
73C4⋊#168—31no—
74C4×#168—31no—
75#1667—151noSylow
76C23×C3×C5—41no—
77C22×D15—21no—
78C22×D15—41no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—41no—
82C3×C5×D4—41no—
83C3×C5×D4—81no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5#4111yescharacteristic
87C2×Dic15—21no—
88D60—21no—
89D60—41no—
90D60—41no—
91D60—41no—
92D60—41no—
93D60—81no—
94D60D812yescomplemented
95C4×D15—41no—
96C4×D15—41no—
97C3×C5×C8—41no—
98C3×C5×C8—41no—
99C3⋊#168—21no—
100C3⋊#168—41no—
101C3⋊#168D812yescomplemented
102C3×#127C2×D511yescharacteristic
103C2×#213—101no—
104C2×#213—101no—
105C2×#213—101no—
106C2×D24—101no—
107C2×D3×C8—101no—
108#874—51no—
109C4×D12—51no—
110C3×C4⋊C8C2×D511yescharacteristic
111C3×C4⋊C8C2×D511yescharacteristic
112#832—101no—
113#821—101no—
114(C2×D3)⋊C8—101no—
115C4⋊(C3⋊C8)—51no—
116C4×C3⋊C8—51no—
117C2×C5×D4—21no—
118C2×C5×D4—21no—
119C2×C5×D4—21no—
120C2×D20—31no—
121C2×D20—61no—
122C2×D20—61no—
123C2×D20—61no—
124C2×C4×D5—61no—
125C2×C5×C8—21no—
126C2×C5×C8—21no—
127C42×C5C22×D311yescharacteristic
128#686—122no—
129#686—122no—
130#686—122no—
131#685—61no—
132C4⋊Dic5—31no—
133C2×#168—31no—
134C2×#168—31no—
135C2×#168—61no—
136D40—122no—
137C8×D5—122no—
138#493—151no—
139#459—151no—
140#459—151no—
141C8×D4—151no—
142#335—151no—
143#331—151no—
144#331D1511yescharacteristic, complemented
145C22×C3×C5—81no—
146C22×C3×C5—81no—
147C22×C3×C5—81no—
148C22×C3×C5#12111yescharacteristic
149C2×D15—22no—
150C2×D15—41no—
151C2×D15—41no—
152C2×D15—81no—
153C2×D15—81no—
154C2×D15—81no—
155C3×C4×C5—21no—
156C3×C4×C5C2×D811yescharacteristic
157C3×C4×C5C2×D811yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160Dic15—41no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×D12—51no—
165C2×D12—101no—
166C2×D12—101no—
167C2×D12—101no—
168C2×C4×D3—101no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C3×C42C22×D511yescharacteristic
172#213—202no—
173#213—202no—
174#213—202no—
175(C2×D3)⋊C4—101no—
176C4⋊Dic3—51no—
177C2×C3⋊C8—51no—
178C2×C3⋊C8—51no—
179C2×C3⋊C8—101no—
180D24—202no—
181D3×C8—202no—
182C23×C5—41no—
183C22×D5—61no—
184C22×D5—121no—
185C5×D4—41no—
186C5×D4—41no—
187C5×D4—41no—
188C5×D4—41no—
189C5×D4—81no—
190C2×C4×C5#23511yescharacteristic
191C2×C4×C5D3×D411yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×Dic5—61no—
194D20—32no—
195D20—61no—
196D20—121no—
197D20—121no—
198D20—121no—
199D20—121no—
200D20—241no—
201C4×D5—121no—
202C4×D5—121no—
203C5×C8—41no—
204C5×C8—41no—
205#168—32no—
206#168—61no—
207#168—121no—
208C2×D8—301no—
209C2×D8—301no—
210C2×D8—301no—
211C2×D8—301no—
212C22×C8—301no—
213#127—151no—
214#127C2×D1511yescharacteristic
215C4×D4—151no—
216C4⋊C8—151no—
217C4⋊C8C2×D1511yescharacteristic
218C4⋊C8C2×D1511yescharacteristic
219#102—301no—
220#102—301no—
221C22⋊C8—301no—
222C4×C8—151no—
223C2×C3×C5—161no—
224C2×C3×C5#45911yescharacteristic
225C2×C3×C5#46611yescharacteristic
226C2×C3×C5#47211yescharacteristic
227D15—42no—
228D15—161no—
229C23×C3—41no—
230C22×D3—101no—
231C22×D3—201no—
232C3×D4—41no—
233C3×D4—41no—
234C3×D4—41no—
235C3×D4—41no—
236C3×D4—81no—
237C2×C3×C4#70911yescharacteristic
238C2×C3×C4D4×D511yescharacteristic
239C2×C3×C4D4×D511yescharacteristic
240C2×Dic3—101no—
241D12—52no—
242D12—101no—
243D12—201no—
244D12—201no—
245D12—201no—
246D12—201no—
247D12—401no—
248C4×D3—201no—
249C4×D3—201no—
250C3×C8—41no—
251C3×C8—41no—
252C3⋊C8—52no—
253C3⋊C8—101no—
254C3⋊C8—201no—
255C22×C5—81no—
256C22×C5—81no—
257C22×C5—81no—
258C22×C5#88411yescharacteristic
259C2×D5—62no—
260C2×D5—121no—
261C2×D5—121no—
262C2×D5—241no—
263C2×D5—241no—
264C2×D5—241no—
265C4×C5—21no—
266C4×C5D3×D811yescharacteristic
267C4×C5D3×D811yescharacteristic
268C4×C5#91411yescharacteristic
269C4×C5#91611yescharacteristic
270Dic5—121no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—151no—
275C2×D4—301no—
276C2×D4—301no—
277C2×D4—301no—
278C22×C4—301no—
279D8—602no—
280D8—602no—
281D8—602no—
282D8—602no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—151no—
286C2×C8—151no—
287C2×C8—301no—
288C2×C8—602no—
289C4⋊C4—151no—
290C22⋊C4—301no—
291C42C22×D1511yescharacteristic
292C3×C5#166711yescharacteristic, complemented, Hall
293C22×C3—81no—
294C22×C3—81no—
295C22×C3—81no—
296C22×C3#403011yescharacteristic
297C2×D3—102no—
298C2×D3—201no—
299C2×D3—201no—
300C2×D3—401no—
301C2×D3—401no—
302C2×D3—401no—
303C3×C4—21no—
304C3×C4D5×D811yescharacteristic
305C3×C4D5×D811yescharacteristic
306C3×C4#406011yescharacteristic
307C3×C4#406211yescharacteristic
308Dic3—201no—
309C2×C5—161no—
310C2×C5#474911yescharacteristic
311C2×C5#477511yescharacteristic
312C2×C5#478611yescharacteristic
313D5—122no—
314D5—481no—
315C23—41no—
316C23—301no—
317C23—601no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—81no—
323D4—152no—
324D4—301no—
325D4—601no—
326D4—601no—
327D4—601no—
328D4—601no—
329D4—1201no—
330C2×C4—301no—
331C2×C4—601no—
332C2×C4—601no—
333C2×C4#681711yescharacteristic
334C2×C4D4×D1511yescharacteristic
335C2×C4D4×D1511yescharacteristic
336C8—41no—
337C8—41no—
338C8—152no—
339C8—301no—
340C8—601no—
341C2×C3—161no—
342C2×C3#6503811yescharacteristic
343C2×C3#6506411yescharacteristic
344C2×C3#6507511yescharacteristic
345D3—202no—
346D3—801no—
347C5#6839511yescharacteristic, complemented, Sylow
348C22—81no—
349C22—81no—
350C22—81no—
351C22—302no—
352C22—601no—
353C22—601no—
354C22—1201no—
355C22—1201no—
356C22—1201no—
357C22#9177311yescharacteristic
358C4—21no—
359C4—601no—
360C4D8×D1511yescharacteristic
361C4D8×D1511yescharacteristic
362C4#9180311yescharacteristic
363C4#9180511yescharacteristic
364C3#1059918811yescharacteristic, complemented, Sylow
365C2—161no—
366C2—602no—
367C2—2401no—
368C2#1175085011yescharacteristic
369C2#1175087611yescharacteristic
370C2#1175088711yescharacteristic
subgroupG/H
centerC22#91773
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#331C2
socleC22×C3×C5#121
hypercenter#331D15
hypocenterC3×C5#1667
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #11751174C2semidirect
2. #11751173C2semidirect
3. #11750944C2semidirect
4. #11750935C2semidirect
5. C3×C5×#331C2semidirect
6. #11746306C2semidirect
7. #11746300C2semidirect
29. C5×#331D3semidirect
57. C3×#331D5semidirect
94. D60D8semidirect
101. C3⋊#168D8semidirect
144. #331D15semidirect
292. C3×C5#1667semidirect
347. C5#68395semidirect
364. C3#10599188semidirect

Maximal subgroups

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

subgroupindex
#117511742
#117511732
#117509442
#117509352
C3×C5×#3312
#117463062
#117463002
#105991883
#683955