Finite Group Databasebeta

← #14302886

Subgroups — #14302886

Order 1920.

724 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 159 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×C5×#518C211yesmaximal, characteristic, complemented
2#11756564C211yesmaximal, characteristic
3C2×#91117C211yesmaximal, characteristic, complemented
4#11751106C212yesmaximal, complemented
5#11746352C212yesmaximal, complemented
6#10602445—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C2×#6817C2211yescharacteristic
9C3×C4×C5×D4—24no—
10C3×C5×#117C2212yes—
11C2×C3×C5×C22⋊C4—22no—
12#91842—22no—
13#91829C412yescomplemented
14#91827—22no—
15#91825C412yescomplemented
16#91815C2211yescharacteristic
17C2×#6710C2212yes—
18#91117—22no—
19#91089—24no—
20#71652—51nomaximal, Hall
21C5×#518D311yescharacteristic, complemented
22#66139—31no—
23C2×#3965—31no—
24#65294—32no—
25#64751—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×C5—24no—
32C22×C3×C4×C5C2311yescharacteristic
33C2×#1220—21no—
34C2×#1220—24no—
35#6817—22no—
36#6817—22no—
37C2×D60C2×C411yescharacteristic, complemented
38C2×C4×D15—21no—
39C2×Dic30C2×C411yescharacteristic, complemented
40C3×C5×C4⋊C4—22no—
41C3×C5×C22⋊C4—24no—
42C3×C5×C22⋊C4—22no—
43C3×C42×C5D414yescomplemented
44#6719—24no—
45#6719—21no—
46C4⋊Dic15—21no—
47C4×Dic15C2×C412yescomplemented
48#6710—22no—
49#6710—22no—
50C2×C3⋊#168—22no—
51C3×#518D511yescharacteristic, complemented
52#5805—51no—
53C2×#833—51no—
54#5005—52no—
55#4531—52no—
56C22×C5×D4C2×D311yescharacteristic
57C2×#709—31no—
58C4×C5×D4—24no—
59C5×#117C2×D312yes—
60C2×C5×C22⋊C4—22no—
61#4099—62no—
62#4086—32no—
63#4084—62no—
64#4082—32no—
65#4072—31no—
66C2×#681—32no—
67#3965—62no—
68#3937—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×C5—24no—
79C2×C3×C4×C5—84no—
80C2×C3×C4×C5C22×C411yescharacteristic
81C2×C3×C4×C5C2×D412yes—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5#4112yes—
84#1220—41no—
85#1220—41no—
86#1220—84no—
87C2×Dic15—22no—
88C2×Dic15—21no—
89D60—22no—
90C4×D15—42no—
91Dic30—22no—
92C3⋊#168—42no—
93C22×C3×D4C2×D511yescharacteristic
94C2×#235—51no—
95C3×C4×D4—24no—
96C3×#117C2×D512yes—
97C2×C3×C22⋊C4—22no—
98#953—102no—
99#940—52no—
100#938—102no—
101#936—52no—
102#926—51no—
103C2×#208—52no—
104#833—102no—
105#805—104no—
106C24×C5#6712yes—
107C2×C5×D4—22no—
108C2×C5×D4—22no—
109C2×C5×D4C4×D312yes—
110C2×C5×D4D1212yes—
111C22×C4×C5—24no—
112C22×C4×C5C22×D311yescharacteristic
113C2×C22⋊D5—61no—
114C2×C22⋊D5—64no—
115#709—62no—
116#709—62no—
117C2×D20—31no—
118C2×C4×D5—61no—
119C2×Dic10—31no—
120C5×C4⋊C4—22no—
121C5×C22⋊C4—24no—
122C5×C22⋊C4—22no—
123C42×C5#6714yescomplemented
124C22⋊Dic5—64no—
125C22⋊Dic5—61no—
126C4⋊Dic5—61no—
127C4×Dic5—32no—
128#681—62no—
129#681—62no—
130C2×#168—62no—
131#535—151no—
132#518D1511yescharacteristic, complemented
133#421—152no—
134C2×#100—151no—
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×C5—44no—
147C3×C4×C5C4×D412yes—
148C3×C4×C5#12112yes—
149Dic15—42no—
150Dic15—41no—
151C24×C3C22⋊D512yes—
152C2×C3×D4—22no—
153C2×C3×D4—22no—
154C2×C3×D4C4×D512yes—
155C2×C3×D4D2012yes—
156C22×C3×C4—24no—
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—22no—
166C3×C22⋊C4—24no—
167C3×C22⋊C4—22no—
168C3×C42C22⋊D514yescomplemented
169#217—104no—
170#217—101no—
171C4⋊Dic3—101no—
172C4×Dic3—52no—
173#208—102no—
174#208—102no—
175C2×C3⋊C8—102no—
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×C5—24no—
185C2×C4×C5—84no—
186C2×C4×C5C2×C4×D311yescharacteristic
187C2×C4×C5C2×D1211yescharacteristic
188C2×C4×C5#23512yes—
189C2×C4×C5C2×#6712yes—
190C22⋊D5—121no—
191C22⋊D5—121no—
192C22⋊D5—244no—
193C2×Dic5—62no—
194C2×Dic5—61no—
195D20—62no—
196C4×D5—122no—
197Dic10—62no—
198#168—122no—
199C2×#41—151no—
200C22×D4C2×D1511yescharacteristic
201C2×M16—152no—
202#127—152no—
203#124—152no—
204#121—302no—
205#120—302no—
206C4×D4—24no—
207#117—151no—
208#117C2×D1512yes—
209C2×C22⋊C4—22no—
210#104—304no—
211#100—302no—
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×C22⋊D511yescharacteristic
223C22×D3—101no—
224C3×D4—24no—
225C3×D4—24no—
226C2×C3×C4—24no—
227C2×C3×C4—84no—
228C2×C3×C4C2×C4×D511yescharacteristic
229C2×C3×C4C2×D2011yescharacteristic
230C2×C3×C4#70912yes—
231C2×C3×C4C2×C22⋊D512yes—
232#67—201no—
233#67—201no—
234#67—404no—
235C2×Dic3—102no—
236C2×Dic3—101no—
237D12—102no—
238C4×D3—202no—
239Dic6—102no—
240C3⋊C8—202no—
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×C5—44no—
252C4×C5C4×#6712yes—
253C4×C5#93012yes—
254Dic5—122no—
255Dic5—121no—
256C24#122012yes—
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×D4C4×D1512yes—
266C2×D4D6012yes—
267C22×C4—24no—
268C22×C4—301no—
269C22×C4C22×D1511yescharacteristic
270M16—302no—
271M16—302no—
272C2×C8—302no—
273C4⋊C4—22no—
274C4⋊C4—301no—
275C22⋊C4—24no—
276C22⋊C4—22no—
277C22⋊C4—304no—
278C22⋊C4—301no—
279C42—152no—
280C42#122014yescomplemented
281C3×C5#191111yescharacteristic, complemented, Hall
282C22×C3—24no—
283C22×C3—41no—
284C22×C3—44no—
285C22×C3—44no—
286C22×C3—82no—
287C22×C3C2×#68511yescharacteristic
288C22×C3#407511yescharacteristic
289C22×C3#409911yescharacteristic
290C2×D3—202no—
291C2×D3—201no—
292C3×C4—44no—
293C3×C4C4×C22⋊D512yes—
294C3×C4#407612yes—
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#671414yes—
308C23C2×#122011yescharacteristic
309Q8—302no—
310D4—24no—
311D4—24no—
312D4—302no—
313D4—601no—
314D4—601no—
315D4—1204no—
316C2×C4—24no—
317C2×C4—84no—
318C2×C4—302no—
319C2×C4—301no—
320C2×C4—602no—
321C2×C4C2×C4×D1511yescharacteristic
322C2×C4C2×D6011yescharacteristic
323C2×C4#681712yes—
324C2×C4C2×#122012yes—
325C8—602no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—44no—
330C2×C3#6550211yescharacteristic
331D3—401no—
332C5#7165211yescharacteristic, complemented, Sylow
333C22—24no—
334C22—41no—
335C22—44no—
336C22—44no—
337C22—82no—
338C22—602no—
339C22—601no—
340C22C2×#671411yescharacteristic
341C22#9181811yescharacteristic
342C22#9184211yescharacteristic
343C4—44no—
344C4—602no—
345C4—601no—
346C4C4×#122012yes—
347C4#9181912yes—
348C3#1060244511yescharacteristic, complemented, Sylow
349C2—21no—
350C2—21no—
351C2—21no—
352C2—44no—
353C2—1201no—
354C2#1175131411yescharacteristic
subgroupG/H
centerC2#11751314
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#518C2
socleC2×C3×C5#386
prime radical#11756564C2
cosocleC22×C3×C4×C5C23
hypercenter#518D15
hypocenterC3×C5#1911
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
1. C3×C5×#518C2semidirect
3. C2×#91117C2semidirect
4. #11751106C2semidirect
5. #11746352C2semidirect
13. #91829C4semidirect
15. #91825C4semidirect
21. C5×#518D3semidirect
37. C2×D60C2×C4semidirect
39. C2×Dic30C2×C4semidirect
43. C3×C42×C5D4semidirect
47. C4×Dic15C2×C4semidirect
51. C3×#518D5semidirect
123. C42×C5#67semidirect
132. #518D15semidirect
168. C3×C42C22⋊D5semidirect
280. C42#1220semidirect
281. C3×C5#1911semidirect
332. C5#71652semidirect
348. C3#10602445semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5182
#117565642
C2×#911172
#117511062
#117463522
#106024453
#716525