Finite Group Databasebeta

← #14316934

Subgroups — #14316934

Order 1920.

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

normal subgroups only

This group has 432 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#11756431C211yesmaximal, characteristic, complemented
2C3×C5×#454C211yesmaximal, characteristic
3#11751347C212yesmaximal, complemented
4#11746363C211yesmaximal, characteristic, complemented
5#11746299C212yesmaximal, complemented
6#10601782—31nomaximal, Hall
7C3×C5×2−1+4C2211yescharacteristic
8C3×C5×AGL(1,ℤ/8)—21no—
9C3×C5×#124C2211yescharacteristic
10#91840—22no—
11#91833C2212yes—
12#91824—21no—
13#91768—22no—
14#91767—22no—
15#91759—21no—
16C3×C5×#104—21no—
17C3×C5×#101C2211yescharacteristic
18#91121—22no—
19#91120C2212yes—
20#70989—51nomaximal, Hall
21#66006—31no—
22C5×#454D311yescharacteristic
23#65535—32no—
24#64762—31no—
25#64698—32no—
26C3×C5×#41—22no—
27C3×C5×#41—21no—
28C3×C5×#41—41no—
29C2×C3×C5×Q8—41no—
30C2×C3×C5×Q8C2311yescharacteristic
31C2×C3×C5×D4D411yescharacteristic
32C22×Dic15—21no—
33C2×Dic30D412yes—
34C3×C5×SD16—41no—
35C3×C5×D8—41no—
36C3×C5×M16—21no—
37C3×C5×C22⋊C4—22no—
38C3×C42×C5D411yescharacteristic
39#6719—22no—
40#6719—21no—
41#6718—42no—
42#6716—42no—
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45#6712—22no—
46#6712—22no—
47#6712—22no—
48C4×Dic15D412yes—
49#6710—22no—
50#5672—51no—
51C3×#454D511yescharacteristic
52#5246—52no—
53#4542—51no—
54#4478—52no—
55C5×2−1+4C2×D311yescharacteristic
56C5×AGL(1,ℤ/8)—21no—
57C5×#124C2×D311yescharacteristic
58#4097—62no—
59#4090—32no—
60#4081—61no—
61#4025—62no—
62#4024—62no—
63#4016—61no—
64C5×#104—21no—
65C5×#101C2×D311yescharacteristic
66#3969—62no—
67#3968—32no—
68#2203—151noSylow
69C23×C3×C5—21no—
70C3×C5×Q8—22no—
71C3×C5×Q8—21no—
72C3×C5×Q8—41no—
73C3×C5×D4—22no—
74C3×C5×D4—21no—
75C3×C5×D4—41no—
76C3×C5×D4—41no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—42no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5C2×D412yes—
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×Dic15—22no—
83C2×Dic15—22no—
84C2×Dic15—81no—
85Dic30—42no—
86C3×C5×C8—41no—
87C3⋊#168—42no—
88C3×2−1+4C2×D511yescharacteristic
89C3×AGL(1,ℤ/8)—21no—
90C3×#124C2×D511yescharacteristic
91#951—102no—
92#944—52no—
93#935—101no—
94#879—102no—
95#878—102no—
96#870—101no—
97C3×#104—21no—
98C3×#101C2×D511yescharacteristic
99#837—102no—
100#836—52no—
101C5×#41—22no—
102C5×#41—21no—
103C5×#41—41no—
104C2×C5×Q8—41no—
105C2×C5×Q8C22×D311yescharacteristic
106C2×C5×D4#6711yescharacteristic
107C22×Dic5—61no—
108C2×Dic10—32no—
109C5×SD16—41no—
110C5×D8—41no—
111C5×M16—21no—
112C5×C22⋊C4—22no—
113C42×C5#6711yescharacteristic
114C22⋊Dic5—62no—
115C22⋊Dic5—61no—
116#689—122no—
117#687—122no—
118C4⋊Dic5—61no—
119C4⋊Dic5—61no—
120#683—62no—
121#683—62no—
122#683—62no—
123C4×Dic5—32no—
124#681—62no—
125#563—151no—
126#456—152no—
127#454D1511yescharacteristic
128#356—152no—
129#355—151no—
130C22×C3×C5—42no—
131C22×C3×C5—41no—
132C22×C3×C5—41no—
133C22×C3×C5#12011yescharacteristic
134C3×C4×C5—22no—
135C3×C4×C5—21no—
136C3×C4×C5—41no—
137C3×C4×C5—41no—
138Dic15—42no—
139Dic15—42no—
140C3×#41—22no—
141C3×#41—21no—
142C3×#41—41no—
143C2×C3×Q8—41no—
144C2×C3×Q8C22×D511yescharacteristic
145C2×C3×D4C22⋊D511yescharacteristic
146C22×Dic3—101no—
147C2×Dic6—52no—
148C3×SD16—41no—
149C3×D8—41no—
150C3×M16—21no—
151C3×C22⋊C4—22no—
152C3×C42C22⋊D511yescharacteristic
153#217—102no—
154#217—101no—
155#216—202no—
156#214—202no—
157C4⋊Dic3—101no—
158C4⋊Dic3—101no—
159Dic3⋊C4—102no—
160Dic3⋊C4—102no—
161Dic3⋊C4—102no—
162C4×Dic3—52no—
163#208—102no—
164C23×C5—21no—
165C5×Q8—22no—
166C5×Q8—21no—
167C5×Q8—41no—
168C5×D4—22no—
169C5×D4—21no—
170C5×D4—41no—
171C5×D4—41no—
172C2×C4×C5—21no—
173C2×C4×C5—42no—
174C2×C4×C5—41no—
175C2×C4×C5D3×D412yes—
176C2×C4×C5C2×#6711yescharacteristic
177C2×Dic5—62no—
178C2×Dic5—62no—
179C2×Dic5—241no—
180Dic10—122no—
181C5×C8—41no—
182#168—122no—
1832−1+4C2×D1511yescharacteristic
184#137—302no—
185AGL(1,ℤ/8)—21no—
186C4⋊Q8—152no—
187#126—302no—
188#125—301no—
189#124C2×D1511yescharacteristic
190#123—301no—
191C22⋊Q8—302no—
192#104—21no—
193#104—302no—
194#101—152no—
195#101C2×D1511yescharacteristic
196C2×C3×C5—21no—
197C2×C3×C5—81no—
198C2×C3×C5—81no—
199C2×C3×C5B(4,𝔽2)11yescharacteristic
200C23×C3—21no—
201C3×Q8—22no—
202C3×Q8—21no—
203C3×Q8—41no—
204C3×D4—22no—
205C3×D4—21no—
206C3×D4—41no—
207C3×D4—41no—
208C2×C3×C4—21no—
209C2×C3×C4—42no—
210C2×C3×C4—41no—
211C2×C3×C4D4×D512yes—
212C2×C3×C4C2×C22⋊D511yescharacteristic
213C2×Dic3—102no—
214C2×Dic3—102no—
215C2×Dic3—401no—
216Dic6—202no—
217C3×C8—41no—
218C3⋊C8—202no—
219C22×C5—42no—
220C22×C5—41no—
221C22×C5—41no—
222C22×C5#93711yescharacteristic
223C4×C5—22no—
224C4×C5—21no—
225C4×C5—41no—
226C4×C5—41no—
227Dic5—122no—
228Dic5—122no—
229#41—22no—
230#41—21no—
231#41—41no—
232C2×Q8—41no—
233C2×Q8—152no—
234C2×Q8C22×D1511yescharacteristic
235C2×D4#122011yescharacteristic
236C22×C4—301no—
237Q16—602no—
238SD16—41no—
239SD16—602no—
240D8—41no—
241M16—21no—
242M16—302no—
243C4⋊C4—301no—
244C4⋊C4—302no—
245C4⋊C4—301no—
246C4⋊C4—302no—
247C4⋊C4—302no—
248C22⋊C4—22no—
249C22⋊C4—302no—
250C22⋊C4—301no—
251C42—152no—
252C42#122011yescharacteristic
253C3×C5#220311yescharacteristic, complemented, Hall
254C22×C3—42no—
255C22×C3—41no—
256C22×C3—41no—
257C22×C3#408311yescharacteristic
258C3×C4—22no—
259C3×C4—21no—
260C3×C4—41no—
261C3×C4—41no—
262Dic3—202no—
263Dic3—202no—
264C2×C5—21no—
265C2×C5—81no—
266C2×C5—81no—
267C2×C5#503211yescharacteristic
268C23—21no—
269Q8—21no—
270Q8—22no—
271Q8—41no—
272Q8—602no—
273D4—21no—
274D4—22no—
275D4—41no—
276D4—41no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—302no—
281C2×C4—302no—
282C2×C4—1201no—
283C2×C4D4×D1512yes—
284C2×C4C2×#122011yescharacteristic
285C8—41no—
286C8—602no—
287C2×C3—21no—
288C2×C3—81no—
289C2×C3—81no—
290C2×C3#6532111yescharacteristic
291C5#7098911yescharacteristic, complemented, Sylow
292C22—42no—
293C22—41no—
294C22—41no—
295C22#9182611yescharacteristic
296C4—21no—
297C4—22no—
298C4—41no—
299C4—41no—
300C4—602no—
301C4—602no—
302C3#1060178211yescharacteristic, complemented, Sylow
303C2—21no—
304C2—81no—
305C2—81no—
306C2#1175113311yescharacteristic
subgroupG/H
centerC2#11751133
commutator, cosocleC2×C3×C5×Q8C23
FrattiniC2×Q8C22×D15
Fitting, prime radicalC3×C5×#454C2
socleC2×C3×C5B(4,𝔽2)
hypercenter#454D15
hypocenterC3×C5#2203
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. #11756431C2semidirect
3. #11751347C2semidirect
4. #11746363C2semidirect
5. #11746299C2semidirect
253. C3×C5#2203semidirect
291. C5#70989semidirect
302. C3#10601782semidirect

Maximal subgroups

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

subgroupindex
#117564312
C3×C5×#4542
#117513472
#117463632
#117462992
#106017823
#709895