Finite Group Databasebeta

← #14316801

Subgroups — #14316801

Order 1920.

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

normal subgroups only

This group has 540 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
1C5×#5683C211yesmaximal, characteristic, complemented
2C3×#65350C211yesmaximal, characteristic, complemented
3#11749175C212yesmaximal, complemented
4#11746362C211yesmaximal, characteristic, complemented
5#11745997C212yesmaximal, complemented
6#10602743—31nomaximal, Hall
7C3×#4144C2211yescharacteristic
8C3×C5×#124C2211yescharacteristic
9C5×#947—21no—
10C5×#937C2212yes—
11C5×#885—22no—
12C5×#882—22no—
13C5×#875—21no—
14C3×#4088—21no—
15#91568—22no—
16#91118C2212yes—
17C3×#3965C2211yescharacteristic
18C3×#3937—21no—
19#90995—22no—
20#70991—51nomaximal, Hall
21C5×H(3,𝔽4)—31no—
22#65350D311yescharacteristic, complemented
23#65321—32no—
24#64761—31no—
25#64756—32no—
26C23×C5×D3D412yescomplemented
27C2×C3×C5×Q8D411yescharacteristic, complemented
28C2×C3×C5×D4C2311yescharacteristic
29C2×C5×#67—22no—
30C2×C5×D12—21no—
31C2×C5×D12—21no—
32C2×C5×Dic6—21no—
33C2×C3×C22⋊D5—22no—
34C3×#711—41no—
35C3×D4×D5—41no—
36C3×#709—21no—
37C2×#1201—42no—
38C3×C5×C22⋊C4—22no—
39C3×C42×C5D411yescharacteristic, complemented
40#6719—22no—
41C5×#217D412yescomplemented
42C5×(C2×D3)⋊C4—22no—
43C5×(C2×D3)⋊C4—22no—
44C5×(C2×D3)⋊C4—22no—
45C4×C5×Dic3—21no—
46C3×#689—41no—
47C3×#688—41no—
48C3×#681—21no—
49(C2×D3)⋊Dic5—42no—
50#5683D511yescharacteristic, complemented
51C3×#455—51no—
52#5244—52no—
53#4541—51no—
54#4475—52no—
55#4144C2×D311yescharacteristic
56C5×#124—62no—
57C5×#124—61no—
58C5×#124—61no—
59C5×#124C2×D311yescharacteristic
60C5×#120—32no—
61C5×#120—62no—
62#4099—62no—
63#4088—21no—
64#3966—32no—
65#3965C2×D311yescharacteristic
66#3938—62no—
67#3937—21no—
68#2199—151noSylow
69C23×C3×C5C2×D412yes—
70C22×C5×D3—22no—
71C22×C5×D3—42no—
72C22×C5×D3—82no—
73C22×C3×D5—22no—
74C3×C5×Q8—41no—
75C3×C5×D4—41no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×Dic15—42no—
80C5×#67—82no—
81C2×C5×Dic3—22no—
82C5×D12—81no—
83C5×D12—81no—
84C5×Dic6—81no—
85C3×C22⋊D5—42no—
86C3×C22⋊D5—41no—
87C2×C3×Dic5—22no—
88C3×D20—21no—
89C3×C4×D5—41no—
90C3×Dic10—21no—
91#1201—84no—
92C3×#168—41no—
93C3×H(5,𝔽2)—51no—
94C3×#137—101no—
95C3×#124C2×D511yescharacteristic
96#947—21no—
97#937—102no—
98#937C2×D512yes—
99#885—22no—
100#882—22no—
101#875—21no—
102C3×#104—101no—
103C3×#100—51no—
104#834—52no—
105#834—102no—
106C24×C5—32no—
107C2×C5×Q8—61no—
108C2×C5×Q8#6711yescharacteristic, complemented
109C2×C5×D4—61no—
110C2×C5×D4—61no—
111C2×C5×D4—62no—
112C2×C5×D4C22×D311yescharacteristic
113C2×C22⋊D5—22no—
114C2×C22⋊D5—122no—
115#711—41no—
116D4×D5—41no—
117#709—21no—
118C5×C22⋊C4—22no—
119C5×C22⋊C4—32no—
120C5×C22⋊C4—62no—
121C5×C22⋊C4—62no—
122C5×C22⋊C4—62no—
123C42×C5—61no—
124C42×C5#6711yescharacteristic, complemented
125C22⋊Dic5—62no—
126C22⋊Dic5—122no—
127#689—41no—
128#688—41no—
129#681—21no—
130H(3,𝔽4)—31no—
131B(4,𝔽2)—152no—
132#455—51no—
133#354—151no—
134AΣL(1,𝔽16)—152no—
135C22×C3×C5—22no—
136C22×C3×C5—42no—
137C22×C3×C5#12011yescharacteristic
138C2×C5×D3—42no—
139C2×C5×D3—42no—
140C2×C5×D3—44no—
141C2×C5×D3—42no—
142C2×C5×D3—82no—
143C2×C3×D5—41no—
144C2×C3×D5—82no—
145C3×C4×C5—21no—
146C3×C4×C5—41no—
147C3×C4×C5—41no—
148Dic15—82no—
149C3×Dic5—41no—
150C5×Dic3—42no—
151C23×D3C22⋊D512yescomplemented
152C3×#41—101no—
153C3×#41—201no—
154C2×C3×Q8C22⋊D511yescharacteristic, complemented
155C2×C3×D4—102no—
156C2×C3×D4—201no—
157C2×C3×D4C22×D511yescharacteristic
158C2×#67—22no—
159C2×#67—202no—
160C2×D12—21no—
161C2×D12—21no—
162C2×Dic6—21no—
163C3×Q16—201no—
164C3×SD16—201no—
165C3×M16—101no—
166C3×C22⋊C4—22no—
167C3×C42C22⋊D511yescharacteristic, complemented
168#217—102no—
169#217C22⋊D512yescomplemented
170(C2×D3)⋊C4—22no—
171(C2×D3)⋊C4—22no—
172(C2×D3)⋊C4—22no—
173(C2×D3)⋊C4—202no—
174C4×Dic3—21no—
175C23×C5—62no—
176C23×C5—122no—
177C23×C5—242no—
178C23×C5D3×D412yes—
179C22×D5—22no—
180C5×Q8—41no—
181C5×Q8—241no—
182C5×D4—41no—
183C5×D4—241no—
184C5×D4—241no—
185C5×D4—242no—
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—62no—
189C2×C4×C5C2×#6711yescharacteristic
190C22⋊D5—42no—
191C22⋊D5—41no—
192C22⋊D5—244no—
193C2×Dic5—22no—
194C2×Dic5—122no—
195D20—21no—
196C4×D5—41no—
197Dic10—21no—
198#168—41no—
199H(5,𝔽2)—51no—
200#137—101no—
201#124—62no—
202#124—61no—
203#124—61no—
204#124D3×D511yescharacteristic
205#120—32no—
206#120—62no—
207#120—302no—
208#104—101no—
209#100—51no—
210#99—152no—
211#99—302no—
212C2×C3×C5—21no—
213C2×C3×C5—42no—
214C2×C3×C5B(4,𝔽2)11yescharacteristic
215C3×D5—81no—
216C5×D3—82no—
217C23×C3—102no—
218C23×C3C2×C22⋊D512yes—
219C22×D3—22no—
220C22×D3—42no—
221C22×D3—82no—
222C3×Q8—41no—
223C3×Q8—101no—
224C3×D4—41no—
225C3×D4—101no—
226C3×D4—202no—
227C3×D4—201no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—102no—
231C2×C3×C4—201no—
232C2×C3×C4C2×C22⋊D511yescharacteristic
233#67—82no—
234#67—404no—
235C2×Dic3—22no—
236C2×Dic3—202no—
237D12—81no—
238D12—81no—
239Dic6—81no—
240C3×C8—201no—
241C22×C5—22no—
242C22×C5—42no—
243C22×C5—122no—
244C22×C5—122no—
245C22×C5—124no—
246C22×C5—122no—
247C22×C5—242no—
248C22×C5#93711yescharacteristic
249C2×D5—41no—
250C2×D5—82no—
251C4×C5—21no—
252C4×C5—41no—
253C4×C5—41no—
254C4×C5—122no—
255Dic5—41no—
256Dic5—242no—
257C24—32no—
258#41—101no—
259#41—201no—
260C2×Q8—61no—
261C2×Q8#120111yescharacteristic, complemented
262C2×D4—61no—
263C2×D4—61no—
264C2×D4—62no—
265C2×D4—102no—
266C2×D4—201no—
267C2×D4—602no—
268C2×D4C2×D3×D511yescharacteristic
269Q16—201no—
270SD16—201no—
271M16—101no—
272C22⋊C4—22no—
273C22⋊C4—32no—
274C22⋊C4—62no—
275C22⋊C4—62no—
276C22⋊C4—62no—
277C22⋊C4—302no—
278C22⋊C4—602no—
279C42—61no—
280C42#120111yescharacteristic, complemented
281C3×C5#219911yescharacteristic, complemented, Hall
282C22×C3—22no—
283C22×C3—42no—
284C22×C3—201no—
285C22×C3—402no—
286C22×C3#409911yescharacteristic
287C2×D3—42no—
288C2×D3—42no—
289C2×D3—44no—
290C2×D3—42no—
291C2×D3—82no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—41no—
295C3×C4—201no—
296Dic3—42no—
297Dic3—402no—
298C2×C5—21no—
299C2×C5—42no—
300C2×C5—242no—
301C2×C5#503211yescharacteristic
302D5—81no—
303C23—62no—
304C23—102no—
305C23—122no—
306C23—242no—
307C23D3×C22⋊D512yes—
308Q8—41no—
309Q8—101no—
310Q8—241no—
311D4—41no—
312D4—101no—
313D4—202no—
314D4—201no—
315D4—241no—
316D4—241no—
317D4—242no—
318D4—1204no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—62no—
322C2×C4—102no—
323C2×C4—201no—
324C2×C4—602no—
325C2×C4C2×#120111yescharacteristic
326C8—201no—
327C2×C3—21no—
328C2×C3—42no—
329C2×C3—401no—
330C2×C3#6553311yescharacteristic
331D3—82no—
332C5#7099111yescharacteristic, complemented, Sylow
333C22—22no—
334C22—42no—
335C22—122no—
336C22—122no—
337C22—124no—
338C22—122no—
339C22—201no—
340C22—242no—
341C22—402no—
342C22#9156811yescharacteristic
343C4—21no—
344C4—41no—
345C4—41no—
346C4—122no—
347C4—201no—
348C4—1202no—
349C3#1060274311yescharacteristic, complemented, Sylow
350C2—21no—
351C2—42no—
352C2—242no—
353C2—401no—
354C2#1174917711yescharacteristic
subgroupG/H
centerC2#11749177
commutator, cosocleC2×C3×C5×D4C23
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#124C22
socleC2×C3×C5B(4,𝔽2)
hypercenter#124D3×D5
hypocenterC3×C5#2199
LCSG ▷ C2×C3×C5×D4 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C5×#5683C2semidirect
2. C3×#65350C2semidirect
3. #11749175C2semidirect
4. #11746362C2semidirect
5. #11745997C2semidirect
22. #65350D3semidirect
26. C23×C5×D3D4semidirect
27. C2×C3×C5×Q8D4semidirect
39. C3×C42×C5D4semidirect
41. C5×#217D4semidirect
50. #5683D5semidirect
108. C2×C5×Q8#67semidirect
124. C42×C5#67semidirect
151. C23×D3C22⋊D5semidirect
154. C2×C3×Q8C22⋊D5semidirect
167. C3×C42C22⋊D5semidirect
169. #217C22⋊D5semidirect
261. C2×Q8#1201semidirect
280. C42#1201semidirect
281. C3×C5#2199semidirect
332. C5#70991semidirect
349. C3#10602743semidirect

Maximal subgroups

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

subgroupindex
C5×#56832
C3×#653502
#117491752
#117463622
#117459972
#106027433
#709915