Finite Group Databasebeta

← #14308924

Subgroups — #14308924

Order 1920.

564 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 118 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×#65834C211yesmaximal, characteristic, complemented
2#11751089C211yesmaximal, characteristic
3#11748392C212yesmaximal
4C5×#4530C211yesmaximal, characteristic, complemented
5#11745973C212yesmaximal, complemented
6#10599788—31nomaximal, Hall
7C22×D60C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×#6714—22no—
10C2×C4×Dic15C2211yescharacteristic
11C2×C5×#208C2212yes—
12C3×#4072C2212yes—
13C3×#4070—22no—
14C3×#4036—22no—
15C3×#4034—22no—
16#90968—22no—
17#90968—22no—
18#71903—51nomaximal, Hall
19#65834D311yescharacteristic, complemented
20#65420—32no—
21#65277—31no—
22C5×#343—31no—
23#64775—32no—
24C23×D15—21no—
25C22×C3×C4×C5D412yes—
26C22×C3×C4×C5C2311yescharacteristic
27C22×Dic15—21no—
28C2×D60—22no—
29C2×D60—22no—
30C2×D60—21no—
31C2×D60Q812yescomplemented
32C2×C3×Dic10—22no—
33C3×C5×C4⋊C4—22no—
34#6714—44no—
35C4×Dic15—22no—
36C5×#208—22no—
37C5×#208—22no—
38C2×C5×C3⋊C8—22no—
39C3×C22⋊Dic5—22no—
40C3×C4⋊Dic5—22no—
41C3×C4⋊Dic5D412yes—
42C3×C4⋊Dic5D412yes—
43C3×#683—24no—
44C3×C4×Dic5—22no—
45C3×#544—51no—
46#5001—52no—
47#4988—51no—
48#4532—52no—
49#4530D511yescharacteristic, complemented
50C22×D20—31no—
51C2×C5×M16—32no—
52C2×C5×C4⋊C4C2×D311yescharacteristic
53C2×#685—62no—
54#4072C2×D312yes—
55#4070—22no—
56C2×C4×Dic5—31no—
57#4036—22no—
58#4034—22no—
59#3953—62no—
60#3953—62no—
61#2027—151noSylow
62C23×C3×C5C2×D411yescharacteristic
63C22×D15—22no—
64C22×D15—42no—
65C22×D15—42no—
66C22×D15—41no—
67C22×D15—41no—
68C2×C3×C4×C5—22no—
69C2×C3×C4×C5—42no—
70C2×C3×C4×C5C2×D412yes—
71C2×C3×C4×C5C2×Q811yescharacteristic
72C2×C3×C4×C5#4112yes—
73C2×C3×C4×C5#4111yescharacteristic
74C2×Dic15—22no—
75C2×Dic15—41no—
76C2×Dic15—41no—
77D60—24no—
78D60—42no—
79C2×C3×Dic5—22no—
80C2×C3×Dic5—22no—
81C3×Dic10—82no—
82C5×C3⋊C8—42no—
83C22×D12—51no—
84C3×C4⋊Q8—102no—
85C3×#125—102no—
86C3×C22⋊Q8—102no—
87C3×#117—52no—
88C2×C3×C4⋊C4C2×D511yescharacteristic
89C2×(C2×D3)⋊C4—102no—
90C2×C4×Dic3—51no—
91C2×#208C2×D512yes—
92#809—102no—
93#809—102no—
94C23×D5—61no—
95C22×C4×C5#6712yes—
96C22×C4×C5C22×D311yescharacteristic
97C22×Dic5—61no—
98C2×D20—32no—
99C2×D20—62no—
100C2×D20—62no—
101C2×D20—61no—
102C2×Dic10—22no—
103C5×M16—62no—
104C5×M16—62no—
105C2×C5×C8—62no—
106C5×C4⋊C4—22no—
107C22⋊Dic5—22no—
108#685—124no—
109C4⋊Dic5—22no—
110C4⋊Dic5#6712yes—
111C4⋊Dic5#6712yes—
112#683—24no—
113C4×Dic5—22no—
114C4×Dic5—62no—
115#544—51no—
116#418—152no—
117#390—151no—
118#343—31no—
119#339—152no—
120C22×C3×C5—21no—
121C22×C3×C5—21no—
122C22×C3×C5#12011yescharacteristic
123C22×C3×C5C22⋊Q811yescharacteristic
124C22×C3×C5#12411yescharacteristic
125C2×D15—44no—
126C2×D15—42no—
127C2×D15—82no—
128C2×D15—81no—
129C2×D15—81no—
130C3×C4×C5—42no—
131C3×C4×C5C22⋊Q812yes—
132C3×C4×C5#12412yes—
133Dic15—42no—
134C3×Dic5—42no—
135C3×Dic5—42no—
136C23×D3—101no—
137C2×C3×Q8—102no—
138C22×C3×C4D2012yes—
139C22×C3×C4C22×D511yescharacteristic
140C22×Dic3—101no—
141C2×D12—52no—
142C2×D12—102no—
143C2×D12—102no—
144C2×D12—101no—
145C3×C4⋊C4—22no—
146C3×C4⋊C4—52no—
147C3×C4⋊C4—52no—
148C3×C4⋊C4—104no—
149C3×C4⋊C4—102no—
150C3×C22⋊C4—102no—
151C3×C42—102no—
152(C2×D3)⋊C4—204no—
153C4×Dic3—102no—
154#208—22no—
155#208—22no—
156C2×C3⋊C8—22no—
157C23×C5C2×#6711yescharacteristic
158C22×D5—62no—
159C22×D5—122no—
160C22×D5—122no—
161C22×D5—121no—
162C22×D5—121no—
163C2×C4×C5—22no—
164C2×C4×C5—42no—
165C2×C4×C5D3×Q811yescharacteristic
166C2×C4×C5#23911yescharacteristic
167C2×C4×C5#23912yes—
168C2×C4×C5C2×#6712yes—
169C2×Dic5—22no—
170C2×Dic5—22no—
171C2×Dic5—62no—
172C2×Dic5—121no—
173C2×Dic5—121no—
174D20—64no—
175D20—122no—
176Dic10—82no—
177C5×C8—122no—
178C22×D4—151no—
179C2×M16—32no—
180C4⋊Q8—102no—
181#125—102no—
182C22⋊Q8—102no—
183#117—52no—
184C2×C4⋊C4D3×D511yescharacteristic
185C2×C22⋊C4—302no—
186C2×C42—151no—
187#102—302no—
188#102—302no—
189C2×C3×C5—21no—
190C2×C3×C5—21no—
191C2×C3×C5#39311yescharacteristic
192C2×C3×C5#45311yescharacteristic
193C2×C3×C5#45411yescharacteristic
194D15—82no—
195C23×C3C2×D2011yescharacteristic
196C22×D3—102no—
197C22×D3—202no—
198C22×D3—202no—
199C22×D3—201no—
200C22×D3—201no—
201C3×Q8—402no—
202C2×C3×C4—22no—
203C2×C3×C4—42no—
204C2×C3×C4—102no—
205C2×C3×C4—102no—
206C2×C3×C4#70912yes—
207C2×C3×C4D4×D512yes—
208C2×C3×C4#71111yescharacteristic
209C2×C3×C4Q8×D511yescharacteristic
210C2×Dic3—102no—
211C2×Dic3—201no—
212C2×Dic3—201no—
213D12—104no—
214D12—202no—
215C3⋊C8—42no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5#94611yescharacteristic
219C22×C5#94711yescharacteristic
220C22×C5#95311yescharacteristic
221C2×D5—124no—
222C2×D5—122no—
223C2×D5—242no—
224C2×D5—241no—
225C2×D5—241no—
226C4×C5—42no—
227C4×C5#94612yes—
228C4×C5#94712yes—
229Dic5—42no—
230Dic5—42no—
231Dic5—122no—
232C24—301no—
233C2×Q8—102no—
234C2×D4—152no—
235C2×D4—301no—
236C2×D4—302no—
237C2×D4—302no—
238C22×C4—301no—
239C22×C4#120212yes—
240C22×C4C2×D3×D511yescharacteristic
241M16—62no—
242M16—62no—
243C2×C8—62no—
244C4⋊C4—22no—
245C4⋊C4—52no—
246C4⋊C4—52no—
247C4⋊C4—102no—
248C4⋊C4—104no—
249C22⋊C4—102no—
250C22⋊C4—604no—
251C42—102no—
252C42—302no—
253C3×C5#202711yescharacteristic, complemented, Hall
254C22×C3—21no—
255C22×C3—21no—
256C22×C3#402111yescharacteristic
257C22×C3#402811yescharacteristic
258C22×C3#404311yescharacteristic
259C2×D3—204no—
260C2×D3—202no—
261C2×D3—402no—
262C2×D3—401no—
263C2×D3—401no—
264C3×C4—42no—
265C3×C4—202no—
266C3×C4—202no—
267C3×C4#403112yes—
268C3×C4#404212yes—
269Dic3—202no—
270C2×C5—21no—
271C2×C5—21no—
272C2×C5#523111yescharacteristic
273C2×C5#524111yescharacteristic
274C2×C5#524511yescharacteristic
275D5—242no—
276C23—302no—
277C23—602no—
278C23—602no—
279C23—601no—
280C23—601no—
281C23C2×#120211yescharacteristic
282Q8—402no—
283D4—304no—
284D4—602no—
285C2×C4—22no—
286C2×C4—42no—
287C2×C4—102no—
288C2×C4—102no—
289C2×C4—302no—
290C2×C4—601no—
291C2×C4—601no—
292C2×C4#676811yescharacteristic
293C2×C4#676912yes—
294C2×C4D15⋊Q811yescharacteristic
295C2×C4D5×#6712yes—
296C8—122no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3#6496211yescharacteristic
300C2×C3#6503611yescharacteristic
301C2×C3#6504211yescharacteristic
302D3—402no—
303C5#7190311yescharacteristic, complemented, Sylow
304C22—21no—
305C22—21no—
306C22—604no—
307C22—602no—
308C22—1202no—
309C22—1201no—
310C22—1201no—
311C22#9137411yescharacteristic
312C22#9139011yescharacteristic
313C22#9156411yescharacteristic
314C4—42no—
315C4—202no—
316C4—202no—
317C4—602no—
318C4#9132612yes—
319C4#9141112yes—
320C3#1059978811yescharacteristic, complemented, Sylow
321C2—21no—
322C2—21no—
323C2—1202no—
324C2#1174875311yescharacteristic
325C2#1174913811yescharacteristic
326C2#1174938411yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC22×D60C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2027
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#65834C2semidirect
4. C5×#4530C2semidirect
5. #11745973C2semidirect
19. #65834D3semidirect
31. C2×D60Q8semidirect
49. #4530D5semidirect
253. C3×C5#2027semidirect
303. C5#71903semidirect
320. C3#10599788semidirect

Maximal subgroups

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

subgroupindex
C3×#658342
#117510892
#117483922
C5×#45302
#117459732
#105997883
#719035