Finite Group Databasebeta

← #14302906

Subgroups — #14302906

Order 1920.

724 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 148 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#11756564C211yesmaximal, characteristic
2C3×#66132C211yesmaximal, characteristic, complemented
3C2×C5×#833C211yesmaximal, characteristic, complemented
4#11748429C212yesmaximal, complemented
5#11745970C212yesmaximal, complemented
6#10600864—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C2×#6817C2211yescharacteristic
9#91842—22no—
10#91829C412yescomplemented
11#91827—22no—
12#91825C412yescomplemented
13#91815C2211yescharacteristic
14C2×C5×#208C2212yes—
15C2×C3×C22⋊Dic5—22no—
16C3×D4×Dic5—24no—
17C3×#4072C2212yes—
18C5×#833—22no—
19#90981—24no—
20#71652—51nomaximal, Hall
21#66139—31no—
22#66132D311yescharacteristic, complemented
23C2×C5×#100—31no—
24#65428—32no—
25#64777—32no—
26C24×C3×C5D412yes—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4—22no—
29C2×C3×C5×D4C2×C412yes—
30C2×C3×C5×D4D412yes—
31C22×C3×C4×C5C2311yescharacteristic
32C2×#1220—21no—
33C2×#1220—24no—
34#6817—22no—
35#6817—22no—
36C2×D60C2×C411yescharacteristic, complemented
37C2×C4×D15—21no—
38C2×Dic30C2×C411yescharacteristic, complemented
39C22×C3×Dic5—24no—
40#6719—24no—
41#6719—21no—
42C4⋊Dic15—21no—
43C4×Dic15C2×C412yescomplemented
44C5×#208—22no—
45C5×#208—22no—
46C2×C5×C3⋊C8—22no—
47C3×C22⋊Dic5—24no—
48C3×C22⋊Dic5—22no—
49C3×C4⋊Dic5—22no—
50C3×C4×Dic5D414yescomplemented
51C3×#518—51no—
52#5805—51no—
53C2×#833D511yescharacteristic, complemented
54#5005—52no—
55#4531—52no—
56C22×C5×D4C2×D311yescharacteristic
57C2×#709—31no—
58C2×C5×M16—32no—
59#4099—62no—
60C2×C22⋊Dic5—22no—
61#4086—32no—
62#4084—62no—
63#4082—32no—
64D4×Dic5—24no—
65#4072—31no—
66#4072C2×D312yes—
67C5×#100—62no—
68#3957—64no—
69#1911—151noSylow
70C23×C3×C5—22no—
71C23×C3×C5—22no—
72C23×C3×C5—82no—
73C23×C3×C5C22⋊C414yes—
74C23×C3×C5C2×D411yescharacteristic
75C22×D15—21no—
76C3×C5×D4—24no—
77C3×C5×D4—24no—
78C2×C3×C4×C5C22×C411yescharacteristic
79C2×C3×C4×C5C2×D412yes—
80C2×C3×C4×C5C2×D411yescharacteristic
81C2×C3×C4×C5#4112yes—
82#1220—41no—
83#1220—41no—
84#1220—84no—
85C2×Dic15—22no—
86C2×Dic15—21no—
87D60—22no—
88C4×D15—42no—
89Dic30—22no—
90C2×C3×Dic5—24no—
91C2×C3×Dic5—84no—
92C5×C3⋊C8—42no—
93C22×C3×D4C2×D511yescharacteristic
94C2×#235—51no—
95C3×C4×D4—104no—
96C3×#117—52no—
97C2×C3×C22⋊C4—102no—
98#953—102no—
99#940—52no—
100#938—102no—
101#936—52no—
102#926—51no—
103C2×#208C2×D512yes—
104#833—22no—
105#805—104no—
106C24×C5#6712yes—
107C2×C5×D4—22no—
108C2×C5×D4—22no—
109C2×C5×D4C4×D312yes—
110C2×C5×D4D1212yes—
111C22×C4×C5C22×D311yescharacteristic
112C2×C22⋊D5—61no—
113C2×C22⋊D5—64no—
114C22×Dic5—24no—
115#709—62no—
116#709—62no—
117C2×D20—31no—
118C2×C4×D5—61no—
119C2×Dic10—31no—
120C5×M16—62no—
121C5×M16—62no—
122C2×C5×C8—62no—
123C22⋊Dic5—24no—
124C22⋊Dic5—22no—
125C22⋊Dic5—64no—
126C22⋊Dic5—61no—
127C4⋊Dic5—22no—
128C4⋊Dic5—61no—
129C4×Dic5—32no—
130C4×Dic5#6714yescomplemented
131#535—151no—
132#518—51no—
133#421—152no—
134C2×#100—31no—
135H(3,ℤ/4)—152no—
136C22×C3×C5—24no—
137C22×C3×C5—41no—
138C22×C3×C5—44no—
139C22×C3×C5—44no—
140C22×C3×C5—82no—
141C22×C3×C5C2×C22⋊C411yescharacteristic
142C22×C3×C5#12011yescharacteristic
143C22×C3×C5#12311yescharacteristic
144C2×D15—42no—
145C2×D15—41no—
146C3×C4×C5C4×D412yes—
147C3×C4×C5#12112yes—
148Dic15—42no—
149Dic15—41no—
150C3×Dic5—44no—
151C24×C3D2012yes—
152C2×C3×D4—22no—
153C2×C3×D4—22no—
154C2×C3×D4C4×D512yes—
155C2×C3×D4C22⋊D512yes—
156C22×C3×C4—104no—
157C22×C3×C4C22×D511yescharacteristic
158C2×#67—101no—
159C2×#67—104no—
160#235—102no—
161#235—102no—
162C2×D12—51no—
163C2×C4×D3—101no—
164C2×Dic6—51no—
165C3×C4⋊C4—102no—
166C3×C22⋊C4—104no—
167C3×C22⋊C4—102no—
168C3×C42—54no—
169#217—104no—
170#217—101no—
171C4⋊Dic3—101no—
172C4×Dic3—52no—
173#208—22no—
174#208—22no—
175C2×C3⋊C8—22no—
176C23×C5—22no—
177C23×C5—22no—
178C23×C5—82no—
179C23×C5(C2×D3)⋊C414yes—
180C23×C5C2×#6711yescharacteristic
181C22×D5—61no—
182C5×D4—24no—
183C5×D4—24no—
184C2×C4×C5C2×C4×D311yescharacteristic
185C2×C4×C5C2×D1211yescharacteristic
186C2×C4×C5#23512yes—
187C2×C4×C5C2×#6712yes—
188C22⋊D5—121no—
189C22⋊D5—121no—
190C22⋊D5—244no—
191C2×Dic5—24no—
192C2×Dic5—62no—
193C2×Dic5—61no—
194C2×Dic5—84no—
195D20—62no—
196C4×D5—122no—
197Dic10—62no—
198C5×C8—122no—
199C2×#41—151no—
200C22×D4D3×D511yescharacteristic
201C2×M16—32no—
202#127—152no—
203#124—152no—
204#121—302no—
205#120—302no—
206C4×D4—104no—
207#117—52no—
208#117—151no—
209C2×C22⋊C4—102no—
210#104—304no—
211#100—62no—
212C2×C3×C5—21no—
213C2×C3×C5—21no—
214C2×C3×C5—21no—
215C2×C3×C5—44no—
216C2×C3×C5#38611yescharacteristic
217D15—81no—
218C23×C3—22no—
219C23×C3—22no—
220C23×C3—82no—
221C23×C3#68514yes—
222C23×C3C2×D2011yescharacteristic
223C22×D3—101no—
224C3×D4—24no—
225C3×D4—24no—
226C2×C3×C4—104no—
227C2×C3×C4—404no—
228C2×C3×C4C2×C4×D511yescharacteristic
229C2×C3×C4D4×D512yes—
230C2×C3×C4#71112yes—
231C2×C3×C4C2×C22⋊D511yescharacteristic
232#67—201no—
233#67—201no—
234#67—404no—
235C2×Dic3—102no—
236C2×Dic3—101no—
237D12—102no—
238C4×D3—202no—
239Dic6—102no—
240C3⋊C8—42no—
241C22×C5—24no—
242C22×C5—41no—
243C22×C5—44no—
244C22×C5—44no—
245C22×C5—82no—
246C22×C5C2×(C2×D3)⋊C411yescharacteristic
247C22×C5#92911yescharacteristic
248C22×C5#95311yescharacteristic
249C2×D5—122no—
250C2×D5—121no—
251C4×C5C4×#6712yes—
252C4×C5#93012yes—
253Dic5—44no—
254Dic5—122no—
255Dic5—121no—
256C24#120212yes—
257#41—302no—
258#41—302no—
259C2×Q8—151no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—151no—
263C2×D4—301no—
264C2×D4—304no—
265C2×D4#120012yes—
266C2×D4#120312yes—
267C22×C4—104no—
268C22×C4—301no—
269C22×C4C2×D3×D511yescharacteristic
270M16—62no—
271M16—62no—
272C2×C8—62no—
273C4⋊C4—102no—
274C4⋊C4—301no—
275C22⋊C4—104no—
276C22⋊C4—102no—
277C22⋊C4—304no—
278C22⋊C4—301no—
279C42—54no—
280C42—152no—
281C3×C5#191111yescharacteristic, complemented, Hall
282C22×C3—24no—
283C22×C3—41no—
284C22×C3—44no—
285C22×C3—44no—
286C22×C3—82no—
287C22×C3#402811yescharacteristic
288C22×C3#403211yescharacteristic
289C22×C3C2×#68511yescharacteristic
290C2×D3—202no—
291C2×D3—201no—
292C3×C4—204no—
293C3×C4#402712yes—
294C3×C4#408512yes—
295Dic3—202no—
296Dic3—201no—
297C2×C5—21no—
298C2×C5—21no—
299C2×C5—21no—
300C2×C5—44no—
301C2×C5#521311yescharacteristic
302D5—241no—
303C23—22no—
304C23—22no—
305C23—82no—
306C23—301no—
307C23#666714yes—
308C23C2×#120211yescharacteristic
309Q8—302no—
310D4—24no—
311D4—24no—
312D4—302no—
313D4—601no—
314D4—601no—
315D4—1204no—
316C2×C4—104no—
317C2×C4—302no—
318C2×C4—301no—
319C2×C4—404no—
320C2×C4—602no—
321C2×C4#678212yes—
322C2×C4C2×#120011yescharacteristic
323C2×C4C2×#120311yescharacteristic
324C2×C4D5×#6712yes—
325C8—122no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—44no—
330C2×C3#6524711yescharacteristic
331D3—401no—
332C5#7165211yescharacteristic, complemented, Sylow
333C22—24no—
334C22—41no—
335C22—44no—
336C22—44no—
337C22—82no—
338C22—602no—
339C22—601no—
340C22C2×#666711yescharacteristic
341C22#9154611yescharacteristic
342C22#9156411yescharacteristic
343C4—204no—
344C4—602no—
345C4—601no—
346C4#9155212yes—
347C4#9156612yes—
348C3#1060086411yescharacteristic, complemented, Sylow
349C2—21no—
350C2—21no—
351C2—21no—
352C2—44no—
353C2—1201no—
354C2#1174949411yescharacteristic
subgroupG/H
centerC2#11749494
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×D4C22
socleC2×C3×C5#386
prime radical#11756564C2
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1911
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C3×#66132C2semidirect
3. C2×C5×#833C2semidirect
4. #11748429C2semidirect
5. #11745970C2semidirect
10. #91829C4semidirect
12. #91825C4semidirect
22. #66132D3semidirect
36. C2×D60C2×C4semidirect
38. C2×Dic30C2×C4semidirect
43. C4×Dic15C2×C4semidirect
50. C3×C4×Dic5D4semidirect
53. C2×#833D5semidirect
130. C4×Dic5#67semidirect
281. C3×C5#1911semidirect
332. C5#71652semidirect
348. C3#10600864semidirect

Maximal subgroups

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

subgroupindex
#117565642
C3×#661322
C2×C5×#8332
#117484292
#117459702
#106008643
#716525