Finite Group Databasebeta

← #14317017

Subgroups — #14317017

Order 1920.

448 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C3×#66056C211yesmaximal, characteristic, complemented
2C5×#5095C211yesmaximal, characteristic
3#11749393C212yesmaximal
4#11746369C211yesmaximal, characteristic, complemented
5#11746015C212yesmaximal, complemented
6#10601788—31nomaximal, Hall
7C5×#1007C2211yescharacteristic
8C3×C5×C4⋊Q8C2211yescharacteristic
9C5×#942—21no—
10C3×#4090—21no—
11C3×#4090C2212yes—
12C3×#4034—22no—
13C3×#4033—22no—
14C3×C4×Dic10—21no—
15#91309—22no—
16#91120C2212yes—
17C5×#836C2211yescharacteristic
18C5×#805—21no—
19#90979—22no—
20#71942—51nomaximal, Hall
21#66056D311yescharacteristic, complemented
22C5×#456—31no—
23#65535—32no—
24#64768—31no—
25#64698—32no—
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×Q8C2311yescharacteristic
28C5×#239—41no—
29C5×D3×Q8—41no—
30C5×#235—21no—
31C5×#235—22no—
32C2×C3×Dic10—21no—
33C2×C3×Dic10—21no—
34C2×C3×Dic10D412yes—
35C3×C5×C4⋊C4—22no—
36C3×C42×C5D411yescharacteristic
37#6710—22no—
38C5×#216—41no—
39C5×#215—41no—
40C5×#208—21no—
41C3×C4⋊Dic5—21no—
42C3×#683—22no—
43C3×#683—22no—
44C3×#683—22no—
45C3×C4×Dic5—21no—
46C3×C4×Dic5—22no—
47C3×C4×Dic5D412yes—
48#6661—42no—
49#6656—42no—
50C3×Q82—51no—
51#5095—52no—
52#5095D511yescharacteristic
53#4548—51no—
54#4548—52no—
55C5×2−1+4—31no—
56C5×#137—61no—
57C5×C4⋊Q8C2×D311yescharacteristic
58#4097—62no—
59#4090—21no—
60#4090C2×D312yes—
61#4034—22no—
62#4033—22no—
63C4×Dic10—21no—
64C5×#104—61no—
65C5×#101—31no—
66#3969—62no—
67#3968—32no—
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
75C5×#67—41no—
76C5×D12—22no—
77C5×D12—21no—
78C4×C5×D3—41no—
79C4×C5×D3—42no—
80C5×Dic6—22no—
81C5×Dic6—21no—
82C2×C3×Dic5—22no—
83C2×C3×Dic5—22no—
84C3×Dic10—24no—
85C3×Dic10—42no—
86C3×Dic10—81no—
87C3⋊#168—42no—
88C5×C3⋊C8—41no—
89#1007C2×D511yescharacteristic
90C3×C4⋊Q8—52no—
91C3×C4⋊Q8—102no—
92C3×C4⋊Q8—101no—
93C3×C4⋊Q8C2×D511yescharacteristic
94C3×C4×Q8—102no—
95C3×C4×Q8—101no—
96#942—21no—
97#942—102no—
98#836—52no—
99#836C2×D511yescharacteristic
100#805—21no—
101#805—102no—
102C5×#41—62no—
103C5×#41—61no—
104C5×#41—121no—
105C2×C5×Q8—121no—
106C2×C5×Q8#6711yescharacteristic
107C2×C5×Q8C22×D311yescharacteristic
108C2×Dic10—21no—
109C2×Dic10—21no—
110C2×Dic10#6712yes—
111C5×Q16—121no—
112C5×SD16—121no—
113C5×M16—61no—
114C5×C4⋊C4—22no—
115C42×C5#6711yescharacteristic
116#689—122no—
117#687—122no—
118C4⋊Dic5—21no—
119#683—22no—
120#683—22no—
121#683—22no—
122C4×Dic5—22no—
123C4×Dic5—21no—
124C4×Dic5#6712yes—
125#681—62no—
126Q82—51no—
127#456—31no—
128#456—152no—
129#356—152no—
130#356—151no—
131C22×C3×C5#12011yescharacteristic
132C2×C5×D3—41no—
133C3×C4×C5—22no—
134C3×C4×C5—21no—
135C3×C4×C5—22no—
136C3×C4×C5—41no—
137C3×Dic5—24no—
138C3×Dic5—42no—
139C5×Dic3—41no—
140C2×C3×Q8—52no—
141C2×C3×Q8—101no—
142C2×C3×Q8—101no—
143C2×C3×Q8C22⋊D511yescharacteristic
144C2×C3×Q8C22×D511yescharacteristic
145#239—41no—
146D3×Q8—41no—
147#235—22no—
148#235—21no—
149C3×C4⋊C4—22no—
150C3×C4⋊C4—102no—
151C3×C4⋊C4—101no—
152C3×C4⋊C4—102no—
153C3×C4⋊C4—102no—
154C3×C42—52no—
155C3×C42—102no—
156C3×C42—101no—
157C3×C42C22⋊D511yescharacteristic
158#216—41no—
159#216—202no—
160#215—41no—
161#215—202no—
162#208—21no—
163#208—102no—
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×#6711yescharacteristic
176C2×C4×C5C2×#6712yes—
177C2×Dic5—22no—
178C2×Dic5—22no—
179Dic10—24no—
180Dic10—42no—
181Dic10—81no—
182C5×C8—121no—
183#168—122no—
1842−1+4—31no—
185#137—61no—
186#137—302no—
187C4⋊Q8—52no—
188C4⋊Q8—102no—
189C4⋊Q8—101no—
190C4⋊Q8D3×D511yescharacteristic
191C4×Q8—102no—
192C4×Q8—101no—
193#104—61no—
194#104—302no—
195#101—31no—
196#101—152no—
197C2×C3×C5—21no—
198C2×C3×C5B(4,𝔽2)11yescharacteristic
199C5×D3—81no—
200C3×Q8—41no—
201C3×Q8—41no—
202C3×Q8—104no—
203C3×Q8—202no—
204C3×Q8—401no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—102no—
208C2×C3×C4—102no—
209C2×C3×C4D4×D512yes—
210C2×C3×C4C2×C22⋊D511yescharacteristic
211#67—41no—
212D12—21no—
213D12—22no—
214C4×D3—41no—
215C4×D3—42no—
216Dic6—21no—
217Dic6—22no—
218C3⋊C8—41no—
219C3⋊C8—202no—
220C22×C5—121no—
221C22×C5#95311yescharacteristic
222C4×C5—22no—
223C4×C5—22no—
224C4×C5—21no—
225C4×C5—41no—
226C4×C5—121no—
227Dic5—24no—
228Dic5—42no—
229#41—61no—
230#41—62no—
231#41—121no—
232C2×Q8—52no—
233C2×Q8—101no—
234C2×Q8—101no—
235C2×Q8—121no—
236C2×Q8#120111yescharacteristic
237C2×Q8C2×D3×D511yescharacteristic
238Q16—121no—
239Q16—602no—
240SD16—121no—
241SD16—602no—
242M16—61no—
243M16—302no—
244C4⋊C4—22no—
245C4⋊C4—102no—
246C4⋊C4—101no—
247C4⋊C4—102no—
248C4⋊C4—102no—
249C42—52no—
250C42—102no—
251C42—101no—
252C42#120111yescharacteristic
253C3×C5#220511yescharacteristic, complemented, Hall
254C22×C3#408311yescharacteristic
255C2×D3—41no—
256C3×C4—22no—
257C3×C4—21no—
258C3×C4—22no—
259C3×C4—41no—
260C3×C4—104no—
261C3×C4—202no—
262Dic3—41no—
263C2×C5—21no—
264C2×C5—241no—
265C2×C5#524411yescharacteristic
266Q8—41no—
267Q8—41no—
268Q8—61no—
269Q8—62no—
270Q8—104no—
271Q8—202no—
272Q8—401no—
273D4—61no—
274D4—62no—
275D4—121no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—102no—
279C2×C4—102no—
280C2×C4—121no—
281C2×C4—122no—
282C2×C4C2×#120111yescharacteristic
283C2×C4D5×#6712yes—
284C8—121no—
285C8—602no—
286C2×C3—21no—
287C2×C3#6532111yescharacteristic
288D3—81no—
289C5#7194211yescharacteristic, complemented, Sylow
290C22—121no—
291C22#9156311yescharacteristic
292C4—22no—
293C4—21no—
294C4—22no—
295C4—41no—
296C4—104no—
297C4—121no—
298C4—202no—
299C3#1060178811yescharacteristic, complemented, Sylow
300C2—21no—
301C2—241no—
302C2#1174917511yescharacteristic
subgroupG/H
centerC2#11749175
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. C3×#66056C2semidirect
4. #11746369C2semidirect
5. #11746015C2semidirect
21. #66056D3semidirect
253. C3×C5#2205semidirect
289. C5#71942semidirect
299. C3#10601788semidirect

Maximal subgroups

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

subgroupindex
C3×#660562
C5×#50952
#117493932
#117463692
#117460152
#106017883
#719425