Finite Group Databasebeta

← #14316912

Subgroups — #14316912

Order 1920.

496 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 67 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#11756442C211yesmaximal, characteristic, complemented
2C3×C5×#454C211yesmaximal, characteristic, complemented
3#11751346C212yesmaximal, complemented
4#11746363C211yesmaximal, characteristic, complemented
5#11746298C212yesmaximal, complemented
6#10601780—31nomaximal, Hall
7C3×C5×2−1+4C2211yescharacteristic, complemented
8C3×C5×AGL(1,ℤ/8)—21no—
9C3×C5×#124C2211yescharacteristic
10#91838—22no—
11#91836C2212yes—
12#91826—21no—
13#91774—22no—
14#91771—22no—
15#91764—21no—
16C3×C5×#104—21no—
17C3×C5×#101C2211yescharacteristic, complemented
18#91121—22no—
19#91120C2212yescomplemented
20#70987—51nomaximal, Hall
21#66017—31no—
22C5×#454D311yescharacteristic, complemented
23#65534—32no—
24#64762—31no—
25#64697—32no—
26C23×D15—21no—
27C3×C5×#41—22no—
28C3×C5×#41—21no—
29C3×C5×#41—41no—
30C2×C3×C5×Q8—41no—
31C2×C3×C5×Q8C2311yescharacteristic
32C2×C3×C5×D4D411yescharacteristic
33C2×#1220—22no—
34C2×D60—21no—
35C2×D60D412yes—
36C2×Dic30—21no—
37C3×C5×SD16—41no—
38C3×C5×D8—41no—
39C3×C5×M16—21no—
40C3×C5×C22⋊C4—22no—
41C3×C42×C5D411yescharacteristic
42#6719—21no—
43#6717—42no—
44#6715—42no—
45#6714—22no—
46#6714—22no—
47#6714—22no—
48C4×Dic15D412yes—
49#6710—22no—
50#5683—51no—
51C3×#454D511yescharacteristic, complemented
52#5245—52no—
53#4542—51no—
54#4477—52no—
55C5×2−1+4C2×D311yescharacteristic, complemented
56C5×AGL(1,ℤ/8)—21no—
57C5×#124C2×D311yescharacteristic
58#4095—62no—
59#4093—32no—
60#4083—61no—
61#4031—62no—
62#4028—62no—
63#4021—61no—
64C5×#104—21no—
65C5×#101C2×D311yescharacteristic, complemented
66#3969—62no—
67#3968—32no—
68#2202—151noSylow
69C23×C3×C5—21no—
70C22×D15—22no—
71C22×D15—82no—
72C22×D15—81no—
73C3×C5×Q8—22no—
74C3×C5×Q8—21no—
75C3×C5×Q8—41no—
76C3×C5×D4—22no—
77C3×C5×D4—21no—
78C3×C5×D4—41no—
79C3×C5×D4—41no—
80C2×C3×C4×C5—21no—
81C2×C3×C4×C5—42no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5C2×D412yes—
84C2×C3×C4×C5C2×D411yescharacteristic
85#1220—82no—
86C2×Dic15—22no—
87D60—42no—
88D60—81no—
89Dic30—81no—
90C3×C5×C8—41no—
91C3⋊#168—42no—
92C3×2−1+4C2×D511yescharacteristic, complemented
93C3×AGL(1,ℤ/8)—21no—
94C3×#124C2×D511yescharacteristic
95#949—102no—
96#947—52no—
97#937—101no—
98#885—102no—
99#882—102no—
100#875—101no—
101C3×#104—21no—
102C3×#101C2×D511yescharacteristic, complemented
103#837—102no—
104#836—52no—
105C23×D5—61no—
106C5×#41—22no—
107C5×#41—21no—
108C5×#41—41no—
109C2×C5×Q8—41no—
110C2×C5×Q8C22×D311yescharacteristic
111C2×C5×D4#6711yescharacteristic
112C2×C22⋊D5—62no—
113C2×D20—32no—
114C2×D20—61no—
115C2×Dic10—61no—
116C5×SD16—41no—
117C5×D8—41no—
118C5×M16—21no—
119C5×C22⋊C4—22no—
120C42×C5#6711yescharacteristic
121C22⋊Dic5—61no—
122#688—122no—
123#686—122no—
124#685—62no—
125#685—62no—
126#685—62no—
127C4×Dic5—32no—
128#681—62no—
129H(3,𝔽4)—151no—
130#454—152no—
131#454D1511yescharacteristic, complemented
132#355—151no—
133#355—152no—
134C22×C3×C5—42no—
135C22×C3×C5—41no—
136C22×C3×C5—41no—
137C22×C3×C5#12011yescharacteristic
138C2×D15—42no—
139C2×D15—42no—
140C2×D15—42no—
141C2×D15—84no—
142C3×C4×C5—22no—
143C3×C4×C5—21no—
144C3×C4×C5—41no—
145C3×C4×C5—41no—
146Dic15—42no—
147C23×D3—101no—
148C3×#41—22no—
149C3×#41—21no—
150C3×#41—41no—
151C2×C3×Q8—41no—
152C2×C3×Q8C22×D511yescharacteristic
153C2×C3×D4C22⋊D511yescharacteristic
154C2×#67—102no—
155C2×D12—52no—
156C2×D12—101no—
157C2×Dic6—101no—
158C3×SD16—41no—
159C3×D8—41no—
160C3×M16—21no—
161C3×C22⋊C4—22no—
162C3×C42C22⋊D511yescharacteristic
163#217—101no—
164#215—202no—
165#213—202no—
166(C2×D3)⋊C4—102no—
167(C2×D3)⋊C4—102no—
168(C2×D3)⋊C4—102no—
169C4×Dic3—52no—
170#208—102no—
171C23×C5—21no—
172C22×D5—62no—
173C22×D5—242no—
174C22×D5—241no—
175C5×Q8—22no—
176C5×Q8—21no—
177C5×Q8—41no—
178C5×D4—22no—
179C5×D4—21no—
180C5×D4—41no—
181C5×D4—41no—
182C2×C4×C5—21no—
183C2×C4×C5—42no—
184C2×C4×C5—41no—
185C2×C4×C5D3×D412yes—
186C2×C4×C5C2×#6711yescharacteristic
187C22⋊D5—242no—
188C2×Dic5—62no—
189D20—122no—
190D20—241no—
191Dic10—241no—
192C5×C8—41no—
193#168—122no—
1942−1+4C2×D1511yescharacteristic, complemented
195AGL(1,ℤ/8)—21no—
196AGL(1,ℤ/8)—302no—
197#124—152no—
198#124—302no—
199#124—301no—
200#124C2×D1511yescharacteristic
201#120—302no—
202#120—301no—
203#104—21no—
204#104—302no—
205#101—152no—
206#101C2×D1511yescharacteristic, complemented
207C2×C3×C5—21no—
208C2×C3×C5—81no—
209C2×C3×C5—81no—
210C2×C3×C5B(4,𝔽2)11yescharacteristic
211D15—82no—
212C23×C3—21no—
213C22×D3—102no—
214C22×D3—402no—
215C22×D3—401no—
216C3×Q8—22no—
217C3×Q8—21no—
218C3×Q8—41no—
219C3×D4—22no—
220C3×D4—21no—
221C3×D4—41no—
222C3×D4—41no—
223C2×C3×C4—21no—
224C2×C3×C4—42no—
225C2×C3×C4—41no—
226C2×C3×C4D4×D512yes—
227C2×C3×C4C2×C22⋊D511yescharacteristic
228#67—402no—
229C2×Dic3—102no—
230D12—202no—
231D12—401no—
232Dic6—401no—
233C3×C8—41no—
234C3⋊C8—202no—
235C22×C5—42no—
236C22×C5—41no—
237C22×C5—41no—
238C22×C5#93711yescharacteristic
239C2×D5—122no—
240C2×D5—122no—
241C2×D5—122no—
242C2×D5—244no—
243C4×C5—22no—
244C4×C5—21no—
245C4×C5—41no—
246C4×C5—41no—
247Dic5—122no—
248C24—301no—
249#41—22no—
250#41—21no—
251#41—41no—
252C2×Q8—41no—
253C2×Q8—301no—
254C2×Q8C22×D1511yescharacteristic
255C2×D4—152no—
256C2×D4—301no—
257C2×D4—302no—
258C2×D4#122011yescharacteristic
259SD16—41no—
260SD16—602no—
261D8—41no—
262D8—602no—
263M16—21no—
264M16—302no—
265C22⋊C4—22no—
266C22⋊C4—302no—
267C22⋊C4—301no—
268C22⋊C4—302no—
269C22⋊C4—302no—
270C42—152no—
271C42#122011yescharacteristic
272C3×C5#220211yescharacteristic, complemented, Hall
273C22×C3—42no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3#408311yescharacteristic
277C2×D3—202no—
278C2×D3—202no—
279C2×D3—202no—
280C2×D3—404no—
281C3×C4—22no—
282C3×C4—21no—
283C3×C4—41no—
284C3×C4—41no—
285Dic3—202no—
286C2×C5—21no—
287C2×C5—81no—
288C2×C5—81no—
289C2×C5#503211yescharacteristic
290D5—242no—
291C23—21no—
292C23—302no—
293C23—1202no—
294C23—1201no—
295Q8—21no—
296Q8—22no—
297Q8—41no—
298Q8—1201no—
299D4—21no—
300D4—22no—
301D4—41no—
302D4—41no—
303D4—602no—
304D4—1201no—
305D4—1202no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—302no—
310C2×C4D4×D1512yes—
311C2×C4C2×#122011yescharacteristic
312C8—41no—
313C8—602no—
314C2×C3—21no—
315C2×C3—81no—
316C2×C3—81no—
317C2×C3#6532111yescharacteristic
318D3—402no—
319C5#7098711yescharacteristic, complemented, Sylow
320C22—42no—
321C22—41no—
322C22—41no—
323C22—602no—
324C22—602no—
325C22—602no—
326C22—1204no—
327C22#9182611yescharacteristic
328C4—21no—
329C4—22no—
330C4—41no—
331C4—41no—
332C4—602no—
333C3#1060178011yescharacteristic, complemented, Sylow
334C2—21no—
335C2—81no—
336C2—81no—
337C2—1202no—
338C2#1175113311yescharacteristic
subgroupG/H
centerC2#11751133
commutator, cosocleC2×C3×C5×Q8C23
FrattiniC2×Q8C22×D15
FittingC3×C5×#454C2
socleC2×C3×C5B(4,𝔽2)
hypercenter#454D15
hypocenterC3×C5#2202
LCSG ▷ C2×C3×C5×Q8 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #11756442C2semidirect
2. C3×C5×#454C2semidirect
3. #11751346C2semidirect
4. #11746363C2semidirect
5. #11746298C2semidirect
7. C3×C5×2−1+4C22semidirect
17. C3×C5×#101C22semidirect
19. #91120C22semidirect
22. C5×#454D3semidirect
51. C3×#454D5semidirect
55. C5×2−1+4C2×D3semidirect
65. C5×#101C2×D3semidirect
92. C3×2−1+4C2×D5semidirect
102. C3×#101C2×D5semidirect
131. #454D15semidirect
194. 2−1+4C2×D15semidirect
206. #101C2×D15semidirect
272. C3×C5#2202semidirect
319. C5#70987semidirect
333. C3#10601780semidirect

Maximal subgroups

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

subgroupindex
#117564422
C3×C5×#4542
#117513462
#117463632
#117462982
#106017803
#709875