Finite Group Databasebeta

← #14292101

Subgroups — #14292101

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#11751173C211yesmaximal, characteristic
2#11751171C211yesmaximal, characteristic, complemented
3#11750942C211yesmaximal, characteristic, complemented
4#11750935C211yesmaximal, characteristic, complemented
5C3×C5×#331C211yesmaximal, characteristic, complemented
6#11746307C211yesmaximal, characteristic, complemented
7#11746300C211yesmaximal, characteristic, complemented
8#10599190—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10C2×#6715—21no—
11C2×#6706—21no—
12C2×C8×D15—21no—
13C4×D60C2211yescharacteristic
14#91758C2211yescharacteristic
15C3×C5×C4⋊C8C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17#91116—21no—
18#91116—21no—
19#91116—21no—
20#91104—21no—
21#91100—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4×C3⋊#168C2211yescharacteristic
24#68397—51nomaximal, Hall
25#65361—31no—
26#65359—31no—
27#65130—31no—
28#65123—31no—
29C5×#331D311yescharacteristic, complemented
30#64706—31no—
31#64699—31no—
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×Dic30—21no—
38C2×C3×C5×C8—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41#6715—42no—
42#6714—21no—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15D411yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168D411yescharacteristic
48C2×C3⋊#168D411yescharacteristic
49#6706—42no—
50C8×D15—42no—
51#5072—51no—
52#5070—51no—
53#4841—51no—
54#4834—51no—
55C3×#331D511yescharacteristic, complemented
56#4486—51no—
57#4479—51no—
58C5×#127C2×D311yescharacteristic
59C2×#686—61no—
60C2×#677—61no—
61C2×C8×D5—61no—
62C4×D20—31no—
63#4015—31no—
64C5×C4⋊C8C2×D311yescharacteristic
65C5×C4⋊C8C2×D311yescharacteristic
66#3964—61no—
67#3964—61no—
68#3964—61no—
69#3952—61no—
70#3948—61no—
71C4⋊#168—31no—
72C4×#168—31no—
73#1681—151noSylow
74C23×C3×C5—41no—
75C22×D15—21no—
76C3×C5×D4—41no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C3×C5×D4—81no—
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5#4111yescharacteristic
84C2×Dic15—21no—
85C2×Dic15—41no—
86D60—21no—
87D60D812yes—
88C4×D15—41no—
89C4×D15—41no—
90Dic30—41no—
91Dic30—41no—
92C3×C5×C8—41no—
93C3×C5×C8—41no—
94C3⋊#168—21no—
95C3⋊#168—21no—
96C3⋊#168—41no—
97C3×#127C2×D511yescharacteristic
98C2×#213—101no—
99C2×#204—101no—
100C2×D3×C8—101no—
101C4×D12—51no—
102#869—51no—
103C3×C4⋊C8C2×D511yescharacteristic
104C3×C4⋊C8C2×D511yescharacteristic
105#832—101no—
106#832—101no—
107#832—101no—
108(C2×D3)⋊C8—101no—
109#816—101no—
110C4⋊(C3⋊C8)—51no—
111C4×C3⋊C8—51no—
112C2×C5×D4—21no—
113C2×C5×D4—21no—
114C2×C5×D4—21no—
115C2×D20—31no—
116C2×C4×D5—61no—
117C2×Dic10—61no—
118C2×C5×C8—21no—
119C2×C5×C8—21no—
120C42×C5C22×D311yescharacteristic
121#686—122no—
122#685—61no—
123C4⋊Dic5—31no—
124C4⋊Dic5—61no—
125C4⋊Dic5—61no—
126C2×#168—31no—
127C2×#168—31no—
128C2×#168—61no—
129#677—122no—
130C8×D5—122no—
131#486—151no—
132#461—151no—
133#459—151no—
134C8×D4—151no—
135#335—151no—
136#332—151no—
137#331D1511yescharacteristic, complemented
138C22×C3×C5—81no—
139C22×C3×C5—81no—
140C22×C3×C5—81no—
141C22×C3×C5#12111yescharacteristic
142C2×D15—22no—
143C2×D15—41no—
144C2×D15—41no—
145C3×C4×C5—21no—
146C3×C4×C5C2×D811yescharacteristic
147C3×C4×C5#13511yescharacteristic
148C3×C4×C5#13511yescharacteristic
149C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
150Dic15—41no—
151Dic15—81no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×D12—51no—
156C2×C4×D3—101no—
157C2×Dic6—101no—
158C2×C3×C8—21no—
159C2×C3×C8—21no—
160C3×C42C22×D511yescharacteristic
161#213—202no—
162(C2×D3)⋊C4—101no—
163C4⋊Dic3—51no—
164C4⋊Dic3—101no—
165C4⋊Dic3—101no—
166C2×C3⋊C8—51no—
167C2×C3⋊C8—51no—
168C2×C3⋊C8—101no—
169#204—202no—
170D3×C8—202no—
171C23×C5—41no—
172C22×D5—61no—
173C5×D4—41no—
174C5×D4—41no—
175C5×D4—41no—
176C5×D4—41no—
177C5×D4—81no—
178C2×C4×C5#23511yescharacteristic
179C2×C4×C5D3×D411yescharacteristic
180C2×C4×C5D3×D411yescharacteristic
181C2×Dic5—61no—
182C2×Dic5—121no—
183D20—32no—
184D20—61no—
185C4×D5—121no—
186C4×D5—121no—
187Dic10—121no—
188Dic10—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⋊Q8—151no—
198#127C2×D1511yescharacteristic
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—161no—
210C2×C3×C5#46311yescharacteristic
211C2×C3×C5#46611yescharacteristic
212C2×C3×C5#47111yescharacteristic
213D15—42no—
214C23×C3—41no—
215C22×D3—101no—
216C3×D4—41no—
217C3×D4—41no—
218C3×D4—41no—
219C3×D4—41no—
220C3×D4—81no—
221C2×C3×C4#70911yescharacteristic
222C2×C3×C4D4×D511yescharacteristic
223C2×C3×C4D4×D511yescharacteristic
224C2×Dic3—101no—
225C2×Dic3—201no—
226D12—52no—
227D12—101no—
228C4×D3—201no—
229C4×D3—201no—
230Dic6—201no—
231Dic6—201no—
232C3×C8—41no—
233C3×C8—41no—
234C3⋊C8—101no—
235C3⋊C8—101no—
236C3⋊C8—201no—
237C22×C5—81no—
238C22×C5—81no—
239C22×C5—81no—
240C22×C5#88411yescharacteristic
241C2×D5—62no—
242C2×D5—121no—
243C2×D5—121no—
244C4×C5—21no—
245C4×C5D3×D811yescharacteristic
246C4×C5#91111yescharacteristic
247C4×C5#91611yescharacteristic
248C4×C5#91611yescharacteristic
249Dic5—121no—
250Dic5—241no—
251C2×Q8—301no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—151no—
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—151no—
266C4⋊C4—301no—
267C4⋊C4—301no—
268C22⋊C4—301no—
269C42C22×D1511yescharacteristic
270C3×C5#168111yescharacteristic, complemented, Hall
271C22×C3—81no—
272C22×C3—81no—
273C22×C3—81no—
274C22×C3#403011yescharacteristic
275C2×D3—102no—
276C2×D3—201no—
277C2×D3—201no—
278C3×C4—21no—
279C3×C4D5×D811yescharacteristic
280C3×C4#405711yescharacteristic
281C3×C4#406211yescharacteristic
282C3×C4#406211yescharacteristic
283Dic3—201no—
284Dic3—401no—
285C2×C5—161no—
286C2×C5#474811yescharacteristic
287C2×C5#477511yescharacteristic
288C2×C5#478711yescharacteristic
289D5—122no—
290C23—41no—
291C23—301no—
292Q8—601no—
293Q8—601no—
294D4—41no—
295D4—41no—
296D4—41no—
297D4—41no—
298D4—81no—
299D4—152no—
300D4—301no—
301C2×C4—301no—
302C2×C4—601no—
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—161no—
314C2×C3#6503711yescharacteristic
315C2×C3#6506411yescharacteristic
316C2×C3#6507611yescharacteristic
317D3—202no—
318C5#6839711yescharacteristic, complemented, Sylow
319C22—81no—
320C22—81no—
321C22—81no—
322C22—302no—
323C22—601no—
324C22—601no—
325C22#9177311yescharacteristic
326C4—21no—
327C4—601no—
328C4—1201no—
329C4D8×D1511yescharacteristic
330C4#9180011yescharacteristic
331C4#9180511yescharacteristic
332C4#9180511yescharacteristic
333C3#1059919011yescharacteristic, complemented, Sylow
334C2—161no—
335C2—602no—
336C2#1175084911yescharacteristic
337C2#1175087611yescharacteristic
338C2#1175088811yescharacteristic
subgroupG/H
centerC22#91773
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#331C2
socleC22×C3×C5#121
prime radical#11751173C2
hypercenter#331D15
hypocenterC3×C5#1681
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
2. #11751171C2semidirect
3. #11750942C2semidirect
4. #11750935C2semidirect
5. C3×C5×#331C2semidirect
6. #11746307C2semidirect
7. #11746300C2semidirect
29. C5×#331D3semidirect
55. C3×#331D5semidirect
137. #331D15semidirect
270. C3×C5#1681semidirect
318. C5#68397semidirect
333. C3#10599190semidirect

Maximal subgroups

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

subgroupindex
#117511732
#117511712
#117509422
#117509352
C3×C5×#3312
#117463072
#117463002
#105991903
#683975