Finite Group Databasebeta

← #14308922

Subgroups — #14308922

Order 1920.

564 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 120 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
2C5×#4988C211yesmaximal, characteristic
3#11748386C212yesmaximal
4#11746351C211yesmaximal, characteristic, complemented
5#11745974C212yesmaximal, complemented
6#10600436—31nomaximal, Hall
7C22×C5×D12C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2211yescharacteristic
9C2×#6710C2212yes—
10C2×C5×(C2×D3)⋊C4—22no—
11C2×C4×C5×Dic3C2211yescharacteristic
12C3×#4072C2212yes—
13C3×#4070—22no—
14C3×#4036—22no—
15C3×#4034—22no—
16#90966—22no—
17#90966—22no—
18#71903—51nomaximal, Hall
19#65834D311yescharacteristic, complemented
20C5×#390—31no—
21#65504—32no—
22#64750—31no—
23#64743—32no—
24C23×C5×D3—21no—
25C22×C3×C4×C5D412yes—
26C22×C3×C4×C5C2311yescharacteristic
27C22×C5×Dic3—21no—
28C2×C5×D12—22no—
29C2×C5×D12—22no—
30C2×C5×D12—21no—
31C2×C5×D12Q812yescomplemented
32C2×C3×Dic10—22no—
33C3×C5×C4⋊C4—22no—
34#6710—22no—
35#6710—22no—
36C2×C3⋊#168—22no—
37C5×(C2×D3)⋊C4—44no—
38C4×C5×Dic3—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#4988D511yescharacteristic
48#4532—52no—
49#4530—51no—
50C22×C5×D4—31no—
51C2×C5×C4⋊C4C2×D311yescharacteristic
52C2×C5×C22⋊C4—62no—
53C2×C42×C5—31no—
54#4072C2×D312yes—
55#4070—22no—
56C2×#681—32no—
57#4036—22no—
58#4034—22no—
59#3964—62no—
60#3964—62no—
61#2027—151noSylow
62C23×C3×C5C2×D411yescharacteristic
63C22×C5×D3—22no—
64C22×C5×D3—42no—
65C22×C5×D3—42no—
66C22×C5×D3—41no—
67C22×C5×D3—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×C5×Dic3—22no—
75C2×C5×Dic3—41no—
76C2×C5×Dic3—41no—
77C5×D12—24no—
78C5×D12—42no—
79C2×C3×Dic5—22no—
80C2×C3×Dic5—22no—
81C3×Dic10—82no—
82C3⋊#168—42no—
83C22×D12C2×D511yescharacteristic
84C3×C4⋊Q8—102no—
85C3×#125—102no—
86C3×C22⋊Q8—102no—
87C3×#117—52no—
88C2×C3×C4⋊C4C2×D511yescharacteristic
89C2×(C2×D3)⋊C4—22no—
90C2×C4×Dic3C2×D511yescharacteristic
91C2×#208—52no—
92#809—102no—
93#809—102no—
94C24×C5—61no—
95C2×C5×D4—32no—
96C2×C5×D4—62no—
97C2×C5×D4—61no—
98C2×C5×D4—62no—
99C22×C4×C5—61no—
100C22×C4×C5#6712yes—
101C22×C4×C5C22×D311yescharacteristic
102C2×Dic10—22no—
103C5×C4⋊C4—22no—
104C5×C22⋊C4—124no—
105C42×C5—62no—
106C22⋊Dic5—22no—
107C4⋊Dic5—22no—
108C4⋊Dic5#6712yes—
109C4⋊Dic5#6712yes—
110#683—24no—
111C4×Dic5—22no—
112#681—62no—
113#681—62no—
114C2×#168—62no—
115#544—51no—
116#418—152no—
117#390—31no—
118#343—151no—
119#339—152no—
120C22×C3×C5—21no—
121C22×C3×C5—21no—
122C22×C3×C5#12011yescharacteristic
123C22×C3×C5C22⋊Q811yescharacteristic
124C22×C3×C5#12411yescharacteristic
125C2×C5×D3—44no—
126C2×C5×D3—42no—
127C2×C5×D3—82no—
128C2×C5×D3—81no—
129C2×C5×D3—81no—
130C3×C4×C5—42no—
131C3×C4×C5C22⋊Q812yes—
132C3×C4×C5#12412yes—
133C3×Dic5—42no—
134C3×Dic5—42no—
135C5×Dic3—42no—
136C23×D3—21no—
137C2×C3×Q8—102no—
138C22×C3×C4C22⋊D512yes—
139C22×C3×C4C22×D511yescharacteristic
140C22×Dic3—21no—
141C2×D12—22no—
142C2×D12—22no—
143C2×D12—21no—
144C2×D12Dic1012yescomplemented
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—44no—
153C4×Dic3—22no—
154#208—102no—
155#208—102no—
156C2×C3⋊C8—102no—
157C23×C5—62no—
158C23×C5—122no—
159C23×C5—122no—
160C23×C5—121no—
161C23×C5—121no—
162C23×C5C2×#6711yescharacteristic
163C5×D4—64no—
164C5×D4—122no—
165C2×C4×C5—22no—
166C2×C4×C5—42no—
167C2×C4×C5—62no—
168C2×C4×C5—121no—
169C2×C4×C5—121no—
170C2×C4×C5D3×Q811yescharacteristic
171C2×C4×C5#23912yes—
172C2×C4×C5#23911yescharacteristic
173C2×C4×C5C2×#6712yes—
174C2×Dic5—22no—
175C2×Dic5—22no—
176Dic10—82no—
177#168—122no—
178C22×D4—31no—
179C2×M16—152no—
180C4⋊Q8—102no—
181#125—102no—
182C22⋊Q8—102no—
183#117—52no—
184C2×C4⋊C4D3×D511yescharacteristic
185C2×C22⋊C4—62no—
186C2×C42—31no—
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
194C5×D3—82no—
195C23×C3C2×C22⋊D511yescharacteristic
196C22×D3—22no—
197C22×D3—42no—
198C22×D3—42no—
199C22×D3—41no—
200C22×D3—41no—
201C3×Q8—402no—
202C2×C3×C4—22no—
203C2×C3×C4—42no—
204C2×C3×C4—102no—
205C2×C3×C4—102no—
206C2×C3×C4C2×Dic1011yescharacteristic
207C2×C3×C4#70911yescharacteristic
208C2×C3×C4D4×D512yes—
209C2×C3×C4#71112yes—
210C2×Dic3—22no—
211C2×Dic3—41no—
212C2×Dic3—41no—
213D12—24no—
214D12—42no—
215C3⋊C8—202no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5—124no—
219C22×C5—122no—
220C22×C5—242no—
221C22×C5—241no—
222C22×C5—241no—
223C22×C5#94611yescharacteristic
224C22×C5#94711yescharacteristic
225C22×C5#95311yescharacteristic
226C4×C5—42no—
227C4×C5—122no—
228C4×C5#94612yes—
229C4×C5#94712yes—
230Dic5—42no—
231Dic5—42no—
232C24—61no—
233C2×Q8—102no—
234C2×D4—32no—
235C2×D4—62no—
236C2×D4—61no—
237C2×D4—62no—
238C22×C4—61no—
239C22×C4#120112yes—
240C22×C4C2×D3×D511yescharacteristic
241M16—302no—
242M16—302no—
243C2×C8—302no—
244C4⋊C4—22no—
245C4⋊C4—52no—
246C4⋊C4—52no—
247C4⋊C4—102no—
248C4⋊C4—104no—
249C22⋊C4—102no—
250C22⋊C4—124no—
251C42—62no—
252C42—102no—
253C3×C5#202711yescharacteristic, complemented, Hall
254C22×C3—21no—
255C22×C3—21no—
256C22×C3#407011yescharacteristic
257C22×C3#408211yescharacteristic
258C22×C3#408311yescharacteristic
259C2×D3—44no—
260C2×D3—42no—
261C2×D3—82no—
262C2×D3—81no—
263C2×D3—81no—
264C3×C4—42no—
265C3×C4—202no—
266C3×C4—202no—
267C3×C4#402412yes—
268C3×C4#403112yes—
269Dic3—42no—
270C2×C5—21no—
271C2×C5—21no—
272C2×C5—242no—
273C2×C5#523111yescharacteristic
274C2×C5#524111yescharacteristic
275C2×C5#524511yescharacteristic
276C23—62no—
277C23—122no—
278C23—122no—
279C23—121no—
280C23—121no—
281C23C2×#120111yescharacteristic
282Q8—402no—
283D4—64no—
284D4—122no—
285C2×C4—22no—
286C2×C4—42no—
287C2×C4—62no—
288C2×C4—102no—
289C2×C4—102no—
290C2×C4—121no—
291C2×C4—121no—
292C2×C4D3×Dic1011yescharacteristic
293C2×C4#676812yes—
294C2×C4#676911yescharacteristic
295C2×C4D5×#6712yes—
296C8—602no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3#6523611yescharacteristic
300C2×C3#6535111yescharacteristic
301C2×C3#6536611yescharacteristic
302D3—82no—
303C5#7190311yescharacteristic, complemented, Sylow
304C22—21no—
305C22—21no—
306C22—124no—
307C22—122no—
308C22—242no—
309C22—241no—
310C22—241no—
311C22#9136911yescharacteristic
312C22#9137011yescharacteristic
313C22#9156311yescharacteristic
314C4—42no—
315C4—122no—
316C4—202no—
317C4—202no—
318C4#9132612yes—
319C4#9141012yes—
320C3#1060043611yescharacteristic, complemented, Sylow
321C2—21no—
322C2—21no—
323C2—242no—
324C2#1174874611yescharacteristic
325C2#1174913711yescharacteristic
326C2#1174938311yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radicalC22×C5×D12C22
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. #11746351C2semidirect
5. #11745974C2semidirect
19. #65834D3semidirect
31. C2×C5×D12Q8semidirect
144. C2×D12Dic10semidirect
253. C3×C5#2027semidirect
303. C5#71903semidirect
320. C3#10600436semidirect

Maximal subgroups

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

subgroupindex
C3×#658342
C5×#49882
#117483862
#117463512
#117459742
#106004363
#719035