Finite Group Databasebeta

← #14313769

Subgroups — #14313769

Order 1920.

460 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 72 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#11755126C211yesmaximal, characteristic
2#11751917C212yesmaximal
3#11746800C211yesmaximal, characteristic, complemented
4C3×#64929C211yesmaximal, characteristic, complemented
5#11746560C212yesmaximal, complemented
6#10604965—31nomaximal, Hall
7C2×C5×D3×Q8C411yescharacteristic
8C2×#6769C2211yescharacteristic
9#91931—22no—
10#91836C411yescharacteristic
11C3×#4090C2211yescharacteristic
12#91424—22no—
13#91385C2211yescharacteristic
14#91375C411yescharacteristic
15#91371C411yescharacteristic
16#91351—22no—
17#91234C2212yes—
18C3×#4005C2212yes—
19#91174—22no—
20#69173—51nomaximal, Hall
21#66150—31no—
22#65761—32no—
23#64929—31no—
24#64929—32no—
25#64929D311yescharacteristic, complemented
26C2×C3×C5×Q8C2×C411yescharacteristic
27C2×D60C2×C411yescharacteristic
28C5×D3×Q8—42no—
29C2×C4×C5×D3—21no—
30C2×C4×C5×D3C2×C411yescharacteristic
31C2×C5×Dic6—21no—
32C2×C5×Dic6C2×C411yescharacteristic
33C2×C3×Dic10C2311yescharacteristic
34C2×#1203D412yes—
35C2×#1200D412yes—
36#6769—42no—
37#6762—22no—
38C3×#704—22no—
39#6740—42no—
40#6738—42no—
41#6714—22no—
42C4×Dic15C2×C411yescharacteristic
43C3×#683—22no—
44C3×C4×Dic5C2×C411yescharacteristic
45Dic3⋊Dic5—21no—
46#6669—22no—
47#6667—22no—
48(C2×D3)⋊Dic5—21no—
49#5724—51no—
50#4751—52no—
51C3×#356—51no—
52#4548—51no—
53#4478—52no—
54C22×C5×Q8—31no—
55C2×#709—31no—
56D5⋊M16—62no—
57#4093—31no—
58#4093—31no—
59#4092—62no—
60#4090—31no—
61#4090C2×D311yescharacteristic
62#4075—62no—
63#4072—31no—
64#4013—62no—
65#4005—32no—
66#4005C2×D312yes—
67#2135—151noSylow
68C22×D15C22⋊C412yes—
69C22×C5×D3C22⋊C411yescharacteristic
70C3×C5×Q8—41no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5C22×C411yescharacteristic
73C2×Dic15—21no—
74D60—41no—
75C2×C5×Dic3—21no—
76C2×C5×Dic3C22⋊C411yescharacteristic
77C4×C5×D3—22no—
78C4×C5×D3—42no—
79C5×Dic6—42no—
80C5×Dic6—41no—
81C2×C3×Dic5—21no—
82C2×C3×Dic5C2×D412yes—
83C3×Dic10—41no—
84#1203—42no—
85#1200—22no—
86#1200—22no—
87C3⋊#170—42no—
88C3×#170—42no—
89C2×#239—51no—
90C2×D3×Q8AGL(1,𝔽5)11yescharacteristic
91C3×C4⋊Q8—51no—
92#947—51no—
93#944—51no—
94D3×M16—102no—
95#896—102no—
96#894—102no—
97#875—51no—
98#872—51no—
99C3×#101—52no—
100#836—52no—
101#823—102no—
102C2×C5×Q8—31no—
103C2×C5×Q8—61no—
104C2×C5×Q8—122no—
105C2×C5×Q8C4×D311yescharacteristic
106C22×C4×C5—31no—
107C22×C4×C5—61no—
108C2×C22⋊D5—32no—
109#709—122no—
110C2×D20—31no—
111C2×C4×D5—32no—
112C2×Dic10C22×D311yescharacteristic
113#704—22no—
114#704—62no—
115#700—122no—
116D5⋊C8—122no—
117C22⋊Dic5—61no—
118#685—62no—
119#685—62no—
120C4⋊Dic5—61no—
121#683—22no—
122#683—62no—
123C4×Dic5—31no—
124C4×Dic5C4×D311yescharacteristic
125#536—151no—
126#413—152no—
127#356—51no—
128#356—152no—
129#356—151no—
130C22×C3×C5C2×C22⋊C411yescharacteristic
131C2×D15—22no—
132C2×D15—42no—
133C2×C5×D3—21no—
134C2×C5×D3—41no—
135C3×C4×C5—21no—
136C3×C4×C5—41no—
137Dic15—41no—
138C3×Dic5—22no—
139C3×Dic5—41no—
140C5×Dic3—41no—
141C5×Dic3#9912yes—
142C2×C3×Q8—51no—
143C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
144#239—202no—
145D3×Q8—42no—
146C2×D12—52no—
147C2×D12—51no—
148C2×C4×D3—21no—
149C2×C4×D3—52no—
150C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
151C2×Dic6—21no—
152C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
153C3×M16—102no—
154C3×C4⋊C4—102no—
155C3×C42—51no—
156(C2×D3)⋊C4—102no—
157(C2×D3)⋊C4—102no—
158(C2×D3)⋊C4—101no—
159Dic3⋊C4—102no—
160Dic3⋊C4—101no—
161C4×Dic3—51no—
162#208—102no—
163ΓL(1,𝔽25)—202no—
164D3×C8—202no—
165C23×C5—31no—
166C22×D5—32no—
167C5×Q8—41no—
168C5×Q8—121no—
169C5×Q8—122no—
170C2×C4×C5—21no—
171C2×C4×C5—31no—
172C2×C4×C5—62no—
173C2×C4×C5—61no—
174C2×C4×C5—122no—
175C2×C4×C5C2×C4×D311yescharacteristic
176C22⋊D5—122no—
177C2×Dic5—21no—
178C2×Dic5—61no—
179C2×Dic5D3×D412yes—
180D20—121no—
181C4×D5—62no—
182C4×D5—62no—
183Dic10—41no—
184#170—42no—
185#170—122no—
186C2×#41—151no—
187C22×Q8—31no—
188C2×M16—302no—
189C4⋊Q8—51no—
190C4⋊Q8—151no—
191#124—151no—
192#124—151no—
193#123—302no—
194C22⋊Q8—302no—
195#117—151no—
196#101—52no—
197#101—152no—
198#100—302no—
199C2×C3×C5—21no—
200C2×C3×C5C2×#9911yescharacteristic
201D15—42no—
202C5×D3—41no—
203C22×D3—52no—
204C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
205C3×Q8—41no—
206C3×Q8—201no—
207C2×C3×C4—21no—
208C2×C3×C4—52no—
209C2×C3×C4—101no—
210C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
211C2×Dic3—21no—
212C2×Dic3—101no—
213C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
214D12—201no—
215D12—202no—
216C4×D3—22no—
217C4×D3—42no—
218C4×D3—102no—
219C4×D3—102no—
220Dic6—42no—
221Dic6—41no—
222C3×C8—202no—
223C3⋊C8—202no—
224C22×C5—61no—
225C22×C5—121no—
226C22×C5D3×C22⋊C411yescharacteristic
227C2×D5—62no—
228C2×D5—122no—
229C4×C5—21no—
230C4×C5—32no—
231C4×C5—41no—
232C4×C5—121no—
233Dic5—22no—
234Dic5—41no—
235Dic5—121no—
236#41—602no—
237C2×Q8—31no—
238C2×Q8—51no—
239C2×Q8—61no—
240C2×Q8—122no—
241C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
242C2×D4—152no—
243C2×D4—151no—
244C22×C4—31no—
245C22×C4—61no—
246C22×C4—152no—
247M16—102no—
248M16—302no—
249M16—602no—
250C2×C8—602no—
251C4⋊C4—102no—
252C4⋊C4—301no—
253C4⋊C4—302no—
254C22⋊C4—302no—
255C22⋊C4—302no—
256C22⋊C4—301no—
257C42—51no—
258C42—151no—
259C3×C5#213511yescharacteristic, complemented, Hall
260C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
261C2×D3—21no—
262C2×D3—41no—
263C2×D3—102no—
264C2×D3—202no—
265C3×C4—21no—
266C3×C4—41no—
267C3×C4—102no—
268C3×C4—201no—
269Dic3—41no—
270Dic3—201no—
271Dic3#401112yes—
272C2×C5—21no—
273C2×C5—121no—
274C2×C5D3×#9911yescharacteristic
275D5—122no—
276C23—31no—
277C23—152no—
278Q8—41no—
279Q8—121no—
280Q8—122no—
281Q8—201no—
282D4—601no—
283D4—602no—
284C2×C4—21no—
285C2×C4—31no—
286C2×C4—52no—
287C2×C4—62no—
288C2×C4—61no—
289C2×C4—101no—
290C2×C4—122no—
291C2×C4—302no—
292C2×C4—302no—
293C2×C4—301no—
294C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
295C8—202no—
296C8—602no—
297C2×C3—21no—
298C2×C3C2×#401111yescharacteristic
299D3—41no—
300D3—202no—
301C5#6917311yescharacteristic, complemented, Sylow
302C22—61no—
303C22—121no—
304C22—302no—
305C22—602no—
306C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
307C4—21no—
308C4—32no—
309C4—41no—
310C4—102no—
311C4—121no—
312C4—201no—
313C4—601no—
314C3#1060496511yescharacteristic, complemented, Sylow
315C2—21no—
316C2—121no—
317C2—602no—
318C2D3×#401111yescharacteristic
subgroupG/H
centerC2D3×#4011
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×Q8C2×C4
socleC2×C3×C5C2×#99
prime radicalC2×#6769C22
cosocleC2×C3×Dic10C23
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#2135
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
3. #11746800C2semidirect
4. C3×#64929C2semidirect
5. #11746560C2semidirect
25. #64929D3semidirect
259. C3×C5#2135semidirect
301. C5#69173semidirect
314. C3#10604965semidirect

Maximal subgroups

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

subgroupindex
#117551262
#117519172
#117468002
C3×#649292
#117465602
#106049653
#691735