Finite Group Databasebeta

← #14317018

Subgroups — #14317018

Order 1920.

448 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 64 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#11756481C211yesmaximal, characteristic, complemented
2C5×#5095C211yesmaximal, characteristic
3#11749394C212yesmaximal
4C3×#64768C211yesmaximal, characteristic, complemented
5#11746017C212yesmaximal, complemented
6#10601788—31nomaximal, Hall
7C5×#1007C2211yescharacteristic
8C3×C5×C4⋊Q8C2211yescharacteristic
9#91833—21no—
10#91833C2212yes—
11#91777—22no—
12#91776—22no—
13C4×Dic30—21no—
14C5×#942—21no—
15#91322—22no—
16C5×#836C2211yescharacteristic
17C5×#805—21no—
18C3×#3968C2212yes—
19#90978—22no—
20#69169—51nomaximal, Hall
21#66056—31no—
22C5×#456—31no—
23#65535—32no—
24#64768D311yescharacteristic, complemented
25#64698—32no—
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×Q8C2311yescharacteristic
28C2×Dic30—21no—
29C2×Dic30—21no—
30C2×Dic30D412yes—
31C5×#239—41no—
32C5×D3×Q8—41no—
33C5×#235—21no—
34C5×#235—22no—
35C3×C5×C4⋊C4—22no—
36C3×C42×C5D411yescharacteristic
37C4⋊Dic15—21no—
38#6712—22no—
39#6712—22no—
40#6712—22no—
41C4×Dic15—22no—
42C4×Dic15—21no—
43C4×Dic15D412yes—
44C5×#216—41no—
45C5×#215—41no—
46C5×#208—21no—
47C3×#681—22no—
48#6663—42no—
49#6659—42no—
50#5722—51no—
51#5095D511yescharacteristic
52#4752—52no—
53C3×#356—51no—
54#4478—52no—
55C5×2−1+4—31no—
56C5×#137—61no—
57C5×C4⋊Q8C2×D311yescharacteristic
58#4097—62no—
59#4090—32no—
60#4090—61no—
61#4034—62no—
62#4033—62no—
63C4×Dic10—61no—
64C5×#104—61no—
65C5×#101—31no—
66#3969—62no—
67#3968C2×D312yes—
68#2205—151noSylow
69C3×C5×Q8—41no—
70C3×C5×Q8—41no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5C2×D412yes—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×Dic15—22no—
76C2×Dic15—22no—
77Dic30—24no—
78Dic30—42no—
79Dic30—81no—
80C5×#67—41no—
81C5×D12—22no—
82C5×D12—21no—
83C4×C5×D3—41no—
84C4×C5×D3—42no—
85C5×Dic6—22no—
86C5×Dic6—21no—
87C3×#168—42no—
88C5×C3⋊C8—41no—
89#1007C2×D511yescharacteristic
90C3×C4⋊Q8C2×D511yescharacteristic
91#944—52no—
92#944—101no—
93#942—21no—
94#909—102no—
95#888—102no—
96#887—102no—
97C4×Dic6—101no—
98C3×#101—52no—
99#836C2×D511yescharacteristic
100#825—102no—
101#805—21no—
102C5×#41—61no—
103C5×#41—62no—
104C5×#41—121no—
105C2×C5×Q8—121no—
106C2×C5×Q8D1211yescharacteristic
107C2×C5×Q8C22×D311yescharacteristic
108C2×Dic10—32no—
109C2×Dic10—61no—
110C2×Dic10—61no—
111C5×Q16—121no—
112C5×SD16—121no—
113C5×M16—61no—
114C5×C4⋊C4—22no—
115C42×C5D1211yescharacteristic
116#689—122no—
117#687—122no—
118C4⋊Dic5—61no—
119#683—62no—
120#683—62no—
121#683—62no—
122C4×Dic5—32no—
123C4×Dic5—62no—
124C4×Dic5—61no—
125#681—22no—
126Q82—151no—
127#456—31no—
128#456—152no—
129#356—51no—
130#356—152no—
131C22×C3×C5#12011yescharacteristic
132C2×C5×D3—41no—
133C3×C4×C5—22no—
134C3×C4×C5—21no—
135C3×C4×C5—22no—
136C3×C4×C5—41no—
137Dic15—24no—
138Dic15—42no—
139C5×Dic3—41no—
140C2×C3×Q8C22⋊D511yescharacteristic
141C2×C3×Q8C22×D511yescharacteristic
142#239—41no—
143D3×Q8—41no—
144#235—22no—
145#235—21no—
146C2×Dic6—52no—
147C2×Dic6—101no—
148C2×Dic6—101no—
149C3×M16—102no—
150C3×C4⋊C4—22no—
151C3×C42C22⋊D511yescharacteristic
152#216—41no—
153#215—41no—
154C4⋊Dic3—101no—
155Dic3⋊C4—102no—
156Dic3⋊C4—102no—
157Dic3⋊C4—102no—
158C4×Dic3—52no—
159C4×Dic3—102no—
160C4×Dic3—101no—
161#208—21no—
162Dic12—202no—
163#204—202no—
164C5×Q8—41no—
165C5×Q8—41no—
166C5×Q8—62no—
167C5×Q8—61no—
168C5×D4—62no—
169C5×D4—61no—
170C5×D4—121no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—122no—
174C2×C4×C5—121no—
175C2×C4×C5C2×D1211yescharacteristic
176C2×C4×C5D3×D412yes—
177C2×Dic5—62no—
178C2×Dic5—62no—
179Dic10—64no—
180Dic10—122no—
181Dic10—241no—
182C5×C8—121no—
183#168—42no—
1842−1+4—31no—
185#137—61no—
186#137—302no—
187C4⋊Q8—152no—
188C4⋊Q8—302no—
189C4⋊Q8—301no—
190C4⋊Q8D3×D511yescharacteristic
191C4×Q8—302no—
192C4×Q8—301no—
193#104—61no—
194#104—302no—
195#101—31no—
196#101—52no—
197C2×C3×C5—21no—
198C2×C3×C5B(4,𝔽2)11yescharacteristic
199C5×D3—81no—
200C3×Q8—41no—
201C3×Q8—41no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4D4×D512yes—
205C2×C3×C4C2×C22⋊D511yescharacteristic
206#67—41no—
207C2×Dic3—102no—
208C2×Dic3—102no—
209D12—22no—
210D12—21no—
211C4×D3—41no—
212C4×D3—42no—
213Dic6—22no—
214Dic6—21no—
215Dic6—104no—
216Dic6—202no—
217Dic6—401no—
218C3×C8—202no—
219C3⋊C8—41no—
220C22×C5—121no—
221C22×C5#88211yescharacteristic
222C4×C5—22no—
223C4×C5—22no—
224C4×C5—21no—
225C4×C5—41no—
226C4×C5—121no—
227Dic5—64no—
228Dic5—122no—
229#41—61no—
230#41—62no—
231#41—121no—
232C2×Q8—121no—
233C2×Q8—152no—
234C2×Q8—301no—
235C2×Q8—301no—
236C2×Q8#120311yescharacteristic
237C2×Q8C2×D3×D511yescharacteristic
238Q16—121no—
239Q16—602no—
240SD16—121no—
241SD16—602no—
242M16—61no—
243M16—102no—
244C4⋊C4—22no—
245C4⋊C4—302no—
246C4⋊C4—301no—
247C4⋊C4—302no—
248C4⋊C4—302no—
249C42—152no—
250C42—302no—
251C42—301no—
252C42#120311yescharacteristic
253C3×C5#220511yescharacteristic, complemented, Hall
254C22×C3#408311yescharacteristic
255C2×D3—41no—
256C3×C4—22no—
257C3×C4—21no—
258C3×C4—22no—
259C3×C4—41no—
260Dic3—41no—
261Dic3—104no—
262Dic3—202no—
263C2×C5—21no—
264C2×C5—241no—
265C2×C5#474111yescharacteristic
266Q8—41no—
267Q8—41no—
268Q8—61no—
269Q8—62no—
270Q8—304no—
271Q8—602no—
272Q8—1201no—
273D4—61no—
274D4—62no—
275D4—121no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—121no—
279C2×C4—122no—
280C2×C4—302no—
281C2×C4—302no—
282C2×C4C2×#120311yescharacteristic
283C2×C4#679012yes—
284C8—121no—
285C8—202no—
286C2×C3—21no—
287C2×C3#6532111yescharacteristic
288D3—81no—
289C5#6916911yescharacteristic, complemented, Sylow
290C22—121no—
291C22#9157311yescharacteristic
292C4—22no—
293C4—21no—
294C4—22no—
295C4—41no—
296C4—121no—
297C4—304no—
298C4—602no—
299C3#1060178811yescharacteristic, complemented, Sylow
300C2—21no—
301C2—241no—
302C2#1174918011yescharacteristic
subgroupG/H
centerC2#11749180
commutator, cosocleC2×C3×C5×Q8C23
FrattiniC2×Q8C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC2×C3×C5B(4,𝔽2)
prime radicalC5×#1007C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#2205
LCSG ▷ C2×C3×C5×Q8 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #11756481C2semidirect
4. C3×#64768C2semidirect
5. #11746017C2semidirect
24. #64768D3semidirect
253. C3×C5#2205semidirect
289. C5#69169semidirect
299. C3#10601788semidirect

Maximal subgroups

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

subgroupindex
#117564812
C5×#50952
#117493942
C3×#647682
#117460172
#106017883
#691695