Finite Group Databasebeta

← #14313695

Subgroups — #14313695

Order 1920.

460 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C5×#5675C211yesmaximal, characteristic
2D3×#3968C212yesmaximal, complemented
3#11746363C211yesmaximal, characteristic, complemented
4C3×#64762C211yesmaximal, characteristic, complemented
5#11746016C212yesmaximal, complemented
6#10602665—31nomaximal, Hall
7C2×C5×D3×Q8C2211yescharacteristic
8C2×C5×#237C411yescharacteristic
9C3×C5×#124C2211yescharacteristic
10C5×#944C2211yescharacteristic
11C5×#936C411yescharacteristic
12C5×#883—22no—
13C5×#878—22no—
14C5×#872C411yescharacteristic
15C5×#869C411yescharacteristic
16D3×#681—22no—
17#91120C2212yes—
18C3×#3968C2212yes—
19#90962—22no—
20#69164—51nomaximal, Hall
21C5×#536—31no—
22C2×#3968—32no—
23#64768—32no—
24#64762—31no—
25#64762D311yescharacteristic, complemented
26C2×C3×C5×Q8C2311yescharacteristic
27C2×C3×C5×D4C2×C411yescharacteristic
28C2×C5×#67—21no—
29C22×C5×Dic3—21no—
30C5×D3×Q8—42no—
31C5×#237—42no—
32C2×C4×C5×D3C2×C411yescharacteristic
33C2×C4×C5×D3D412yes—
34C2×C5×Dic6C2×C411yescharacteristic
35C2×C5×Dic6C2×C411yescharacteristic
36C2×C5×Dic6D412yes—
37C3×C5×C22⋊C4—22no—
38C3×C42×C5C2×C411yescharacteristic
39#6710—22no—
40C5×#217—22no—
41C5×(C2×D3)⋊C4—21no—
42C5×C4⋊Dic3—22no—
43C5×Dic3⋊C4—22no—
44C5×Dic3⋊C4—21no—
45C4×C5×Dic3C2×C411yescharacteristic
46C3×#681—22no—
47#6650—42no—
48D3×#168—42no—
49#5675D511yescharacteristic
50D3×#101—52no—
51C3×#355—51no—
52#4542—51no—
53#4478—52no—
54C2×C5×#41—31no—
55C22×C5×Q8—31no—
56C5×C4⋊Q8—31no—
57C5×C4⋊Q8—31no—
58C5×#124—31no—
59C5×#124C2×D311yescharacteristic
60C5×#123—62no—
61C5×C22⋊Q8—62no—
62C5×#117—31no—
63C2×#681—62no—
64#3968—32no—
65#3968—62no—
66#3968C2×D312yes—
67#2133—151noSylow
68C23×C3×C5—21no—
69C22×C5×D3C22⋊C411yescharacteristic
70C3×C5×Q8—41no—
71C3×C5×D4—41no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5C22×C411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75C5×#67—42no—
76C2×C5×Dic3—21no—
77C2×C5×Dic3—21no—
78C2×C5×Dic3—42no—
79C2×C5×Dic3C22⋊C411yescharacteristic
80C2×C5×Dic3C22⋊C412yes—
81C4×C5×D3—22no—
82C4×C5×D3—22no—
83C4×C5×D3—22no—
84C5×Dic6—41no—
85C5×Dic6—42no—
86C5×Dic6—41no—
87C3⋊#168—42no—
88C3×#168—42no—
89C2×D3×Q8C2×D511yescharacteristic
90C2×#237Dic511yescharacteristic
91C3×#124C2×D511yescharacteristic
92#944C2×D511yescharacteristic
93#936Dic511yescharacteristic
94D3×M16—102no—
95#883—22no—
96#878—22no—
97#872Dic511yescharacteristic
98#869Dic511yescharacteristic
99C3×#101—52no—
100#836—52no—
101#824—102no—
102C5×#41—122no—
103C2×C5×Q8—31no—
104C2×C5×Q8—32no—
105C2×C5×Q8—31no—
106C2×C5×Q8—122no—
107C2×C5×Q8C22×D311yescharacteristic
108C2×C5×D4—61no—
109C2×C5×D4C4×D311yescharacteristic
110C22×C4×C5—31no—
111C22×C4×C5—32no—
112C22×C4×C5—61no—
113C5×C4⋊C4—61no—
114C5×C4⋊C4—62no—
115C5×C4⋊C4—62no—
116C5×C22⋊C4—22no—
117C5×C22⋊C4—61no—
118C5×C22⋊C4—62no—
119C42×C5—31no—
120C42×C5C4×D311yescharacteristic
121#681—22no—
122#681—62no—
123#681—122no—
124C2×#168—122no—
125#536—31no—
126C2×#101—152no—
127#356—152no—
128#355—51no—
129#355—151no—
130C22×C3×C5—42no—
131C22×C3×C5—41no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C2×C5×D3—41no—
134C2×C5×D3#9912yes—
135C3×C4×C5—22no—
136C3×C4×C5—21no—
137C3×C4×C5—41no—
138C5×Dic3—21no—
139C5×Dic3—22no—
140C5×Dic3—41no—
141C5×Dic3—41no—
142C2×C3×Q8C22×D511yescharacteristic
143C2×C3×D4C2×Dic511yescharacteristic
144C2×#67—21no—
145C22×Dic3—21no—
146D3×Q8—42no—
147#237—42no—
148C2×C4×D3C2×Dic511yescharacteristic
149C2×C4×D3C22⋊D512yes—
150C2×Dic6C2×Dic511yescharacteristic
151C2×Dic6C2×Dic511yescharacteristic
152C2×Dic6C22⋊D512yes—
153C3×M16—102no—
154C3×C22⋊C4—22no—
155C3×C42C2×Dic511yescharacteristic
156#217—22no—
157(C2×D3)⋊C4—21no—
158C4⋊Dic3—22no—
159Dic3⋊C4—22no—
160Dic3⋊C4—21no—
161C4×Dic3C2×Dic511yescharacteristic
162#208—102no—
163ΓL(1,𝔽25)—202no—
164D3×C8—202no—
165C23×C5—21no—
166C23×C5—31no—
167C5×Q8—41no—
168C5×Q8—122no—
169C5×Q8—121no—
170C5×Q8—121no—
171C5×D4—41no—
172C5×D4—122no—
173C2×C4×C5—21no—
174C2×C4×C5—32no—
175C2×C4×C5—31no—
176C2×C4×C5—62no—
177C2×C4×C5—62no—
178C2×C4×C5—62no—
179C2×C4×C5—61no—
180C2×C4×C5—61no—
181C2×C4×C5—122no—
182C2×C4×C5C2×C4×D311yescharacteristic
183C2×C4×C5D3×D412yes—
184#168—42no—
185#168—122no—
186C2×#41—31no—
187C22×Q8—31no—
188C2×M16—302no—
189C4⋊Q8—31no—
190C4⋊Q8—31no—
191#124—31no—
192#124D3×D511yescharacteristic
193#123—62no—
194C22⋊Q8—62no—
195#117—31no—
196#101—52no—
197#101—152no—
198#101—302no—
199C2×C3×C5—21no—
200C2×C3×C5—81no—
201C2×C3×C5C2×#9911yescharacteristic
202C5×D3—22no—
203C23×C3—21no—
204C22×D3C22⋊Dic511yescharacteristic
205C3×Q8—41no—
206C3×D4—41no—
207C2×C3×C4—21no—
208C2×C3×C4C22×Dic511yescharacteristic
209C2×C3×C4C2×C22⋊D512yes—
210#67—42no—
211C2×Dic3—21no—
212C2×Dic3—21no—
213C2×Dic3—42no—
214C2×Dic3C22⋊Dic511yescharacteristic
215C2×Dic3C22⋊Dic512yes—
216C4×D3—22no—
217C4×D3—22no—
218C4×D3—22no—
219Dic6—41no—
220Dic6—42no—
221Dic6—41no—
222C3×C8—202no—
223C3⋊C8—202no—
224C22×C5—32no—
225C22×C5—42no—
226C22×C5—41no—
227C22×C5—121no—
228C22×C5D3×C22⋊C411yescharacteristic
229C4×C5—22no—
230C4×C5—21no—
231C4×C5—41no—
232C4×C5—61no—
233C4×C5—62no—
234C4×C5—121no—
235C4×C5—121no—
236#41—122no—
237C2×Q8—31no—
238C2×Q8—32no—
239C2×Q8—31no—
240C2×Q8—122no—
241C2×Q8C2×D3×D511yescharacteristic
242C2×D4—61no—
243C2×D4D3×Dic511yescharacteristic
244C22×C4—31no—
245C22×C4—32no—
246C22×C4—61no—
247M16—102no—
248M16—302no—
249M16—602no—
250C2×C8—602no—
251C4⋊C4—61no—
252C4⋊C4—62no—
253C4⋊C4—62no—
254C22⋊C4—22no—
255C22⋊C4—61no—
256C22⋊C4—62no—
257C42—31no—
258C42D3×Dic511yescharacteristic
259C3×C5#213311yescharacteristic, complemented, Hall
260C22×C3—42no—
261C22×C3—41no—
262C22×C3C2×C22⋊Dic511yescharacteristic
263C2×D3—41no—
264C2×D3#396612yes—
265C3×C4—22no—
266C3×C4—21no—
267C3×C4—41no—
268Dic3—21no—
269Dic3—22no—
270Dic3—41no—
271Dic3—41no—
272C2×C5—21no—
273C2×C5—62no—
274C2×C5—81no—
275C2×C5D3×#9911yescharacteristic
276C23—21no—
277C23—31no—
278Q8—41no—
279Q8—122no—
280Q8—121no—
281Q8—121no—
282D4—41no—
283D4—122no—
284C2×C4—21no—
285C2×C4—32no—
286C2×C4—31no—
287C2×C4—62no—
288C2×C4—62no—
289C2×C4—62no—
290C2×C4—61no—
291C2×C4—61no—
292C2×C4—122no—
293C2×C4C2×D3×Dic511yescharacteristic
294C2×C4D3×C22⋊D512yes—
295C8—202no—
296C8—602no—
297C2×C3—21no—
298C2×C3—81no—
299C2×C3C2×#396611yescharacteristic
300D3—22no—
301C5#6916411yescharacteristic, complemented, Sylow
302C22—32no—
303C22—42no—
304C22—41no—
305C22—121no—
306C22D3×C22⋊Dic511yescharacteristic
307C4—22no—
308C4—21no—
309C4—41no—
310C4—61no—
311C4—62no—
312C4—121no—
313C4—121no—
314C3#1060266511yescharacteristic, complemented, Sylow
315C2—21no—
316C2—62no—
317C2—81no—
318C2D3×#396611yescharacteristic
subgroupG/H
centerC2D3×#3966
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×Q8C2×D3×D5
FittingC3×C5×#124C22
socleC2×C3×C5C2×#99
prime radicalC2×C5×#237C4
cosocleC2×C3×C5×Q8C23
hypercenter#124D3×D5
hypocenterC3×C5#2133
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
2. D3×#3968C2semidirect
3. #11746363C2semidirect
4. C3×#64762C2semidirect
5. #11746016C2semidirect
25. #64762D3semidirect
259. C3×C5#2133semidirect
301. C5#69164semidirect
314. C3#10602665semidirect

Maximal subgroups

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

subgroupindex
C5×#56752
D3×#39682
#117463632
C3×#647622
#117460162
#106026653
#691645