Finite Group Databasebeta

← #14313669

Subgroups — #14313669

Order 1920.

460 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 81 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#11756434C211yesmaximal, characteristic
2D15×#101C212yesmaximal, complemented
3C3×C5×#355C211yesmaximal, characteristic, complemented
4#11746363C211yesmaximal, characteristic, complemented
5#11746299C212yesmaximal, complemented
6#10599957—31nomaximal, Hall
7C2×Q8×D15C2211yescharacteristic
8C2×#6819C411yescharacteristic
9C3×C5×#124C2211yescharacteristic
10#91833C2211yescharacteristic
11#91825C411yescharacteristic
12M16×D15—22no—
13#91772—22no—
14#91767—22no—
15#91761C411yescharacteristic
16#91758C411yescharacteristic
17C3×C5×#101C2212yes—
18#91120C2212yes—
19#91108—22no—
20#69164—51nomaximal, Hall
21#66009—31no—
22D5×#101—32no—
23C5×#355D311yescharacteristic, complemented
24#64762—31no—
25#64698—32no—
26C2×C3×C5×Q8C2311yescharacteristic
27C2×C3×C5×D4C2×C411yescharacteristic
28C2×#1220—21no—
29C22×Dic15—21no—
30Q8×D15—42no—
31#6819—42no—
32C2×C4×D15C2×C411yescharacteristic
33C2×C4×D15D412yes—
34C2×Dic30C2×C411yescharacteristic
35C2×Dic30C2×C411yescharacteristic
36C2×Dic30D412yes—
37C3×C5×M16—22no—
38C3×C5×C22⋊C4—22no—
39C3×C42×C5C2×C411yescharacteristic
40#6719—22no—
41#6714—21no—
42C4⋊Dic15—22no—
43#6712—22no—
44#6712—21no—
45C4×Dic15C2×C411yescharacteristic
46#6710—22no—
47#6705—42no—
48C8×D15—42no—
49#5675—51no—
50D3×#101—52no—
51C3×#355D511yescharacteristic, complemented
52#4542—51no—
53#4478—52no—
54C2×Q8×D5—31no—
55C2×#711—31no—
56C5×#124C2×D311yescharacteristic
57#4090—31no—
58#4082—31no—
59D5×M16—62no—
60#4029—62no—
61#4024—62no—
62#4018—31no—
63#4015—31no—
64C5×#101C2×D312yes—
65#3968—32no—
66#3956—62no—
67#2133—151noSylow
68C23×C3×C5—21no—
69C22×D15C22⋊C411yescharacteristic
70C3×C5×Q8—41no—
71C3×C5×D4—41no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5C22×C411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75#1220—42no—
76C2×Dic15—21no—
77C2×Dic15—21no—
78C2×Dic15—42no—
79C2×Dic15C22⋊C411yescharacteristic
80C2×Dic15C22⋊C412yes—
81C4×D15—22no—
82C4×D15—22no—
83C4×D15—22no—
84Dic30—41no—
85Dic30—42no—
86Dic30—41no—
87C3×C5×C8—42no—
88C3⋊#168—42no—
89C2×D3×Q8—51no—
90C2×#237—51no—
91C3×#124C2×D511yescharacteristic
92#944—51no—
93#936—51no—
94D3×M16—102no—
95#883—102no—
96#878—102no—
97#872—51no—
98#869—51no—
99C3×#101C2×D512yes—
100#836—52no—
101#824—102no—
102C2×C5×Q8C22×D311yescharacteristic
103C2×C5×D4C4×D311yescharacteristic
104C2×C22⋊D5—61no—
105C22×Dic5—61no—
106Q8×D5—122no—
107#711—122no—
108C2×C4×D5—31no—
109C2×C4×D5—32no—
110C2×Dic10—31no—
111C2×Dic10—32no—
112C2×Dic10—31no—
113C5×M16—22no—
114C5×C22⋊C4—22no—
115C42×C5C4×D311yescharacteristic
116C22⋊Dic5—62no—
117#685—61no—
118C4⋊Dic5—62no—
119#683—61no—
120#683—62no—
121C4×Dic5—31no—
122#681—62no—
123#676—122no—
124C8×D5—122no—
125#536—151no—
126C2×#101—152no—
127#356—152no—
128#355—151no—
129#355D1511yescharacteristic, complemented
130C22×C3×C5—42no—
131C22×C3×C5—41no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C2×D15—41no—
134C2×D15#9912yes—
135C3×C4×C5—22no—
136C3×C4×C5—21no—
137C3×C4×C5—41no—
138Dic15—21no—
139Dic15—22no—
140Dic15—41no—
141Dic15—41no—
142C2×C3×Q8C22×D511yescharacteristic
143C2×C3×D4C4×D511yescharacteristic
144C2×#67—101no—
145C22×Dic3—101no—
146D3×Q8—202no—
147#237—202no—
148C2×C4×D3—51no—
149C2×C4×D3—52no—
150C2×Dic6—51no—
151C2×Dic6—52no—
152C2×Dic6—51no—
153C3×M16—22no—
154C3×C22⋊C4—22no—
155C3×C42C4×D511yescharacteristic
156#217—102no—
157(C2×D3)⋊C4—101no—
158C4⋊Dic3—102no—
159Dic3⋊C4—101no—
160Dic3⋊C4—102no—
161C4×Dic3—51no—
162#208—102no—
163ΓL(1,𝔽25)—202no—
164D3×C8—202no—
165C23×C5—21no—
166C22×D5—31no—
167C5×Q8—41no—
168C5×D4—41no—
169C2×C4×C5—21no—
170C2×C4×C5C2×C4×D311yescharacteristic
171C2×C4×C5D3×D412yes—
172C22⋊D5—122no—
173C2×Dic5—31no—
174C2×Dic5—32no—
175C2×Dic5—61no—
176C2×Dic5—61no—
177C2×Dic5—122no—
178C4×D5—62no—
179C4×D5—62no—
180C4×D5—62no—
181Dic10—121no—
182Dic10—122no—
183Dic10—121no—
184C5×C8—42no—
185#168—122no—
186C2×#41—151no—
187C22×Q8—151no—
188C2×M16—302no—
189C4⋊Q8—151no—
190C4⋊Q8—151no—
191#124—151no—
192#124C2×D1511yescharacteristic
193#123—302no—
194C22⋊Q8—302no—
195#117—151no—
196#101—152no—
197#101—302no—
198#101C2×D1512yes—
199C2×C3×C5—21no—
200C2×C3×C5—81no—
201C2×C3×C5C2×#9911yescharacteristic
202D15—22no—
203C23×C3—21no—
204C22×D3—51no—
205C3×Q8—41no—
206C3×D4—41no—
207C2×C3×C4—21no—
208C2×C3×C4C2×C4×D511yescharacteristic
209C2×C3×C4D4×D512yes—
210#67—202no—
211C2×Dic3—51no—
212C2×Dic3—52no—
213C2×Dic3—101no—
214C2×Dic3—101no—
215C2×Dic3—202no—
216C4×D3—102no—
217C4×D3—102no—
218C4×D3—102no—
219Dic6—201no—
220Dic6—202no—
221Dic6—201no—
222C3×C8—42no—
223C3⋊C8—202no—
224C22×C5—42no—
225C22×C5—41no—
226C22×C5D3×C22⋊C411yescharacteristic
227C2×D5—32no—
228C2×D5—121no—
229C4×C5—22no—
230C4×C5—21no—
231C4×C5—41no—
232Dic5—62no—
233Dic5—61no—
234Dic5—121no—
235Dic5—121no—
236#41—602no—
237C2×Q8—151no—
238C2×Q8—152no—
239C2×Q8—151no—
240C2×Q8—602no—
241C2×Q8C22×D1511yescharacteristic
242C2×D4—301no—
243C2×D4C4×D1511yescharacteristic
244C22×C4—151no—
245C22×C4—152no—
246C22×C4—301no—
247M16—22no—
248M16—302no—
249M16—602no—
250C2×C8—602no—
251C4⋊C4—301no—
252C4⋊C4—302no—
253C4⋊C4—302no—
254C22⋊C4—22no—
255C22⋊C4—301no—
256C22⋊C4—302no—
257C42—151no—
258C42C4×D1511yescharacteristic
259C3×C5#213311yescharacteristic, complemented, Hall
260C22×C3—42no—
261C22×C3—41no—
262C22×C3D5×C22⋊C411yescharacteristic
263C2×D3—52no—
264C2×D3—201no—
265C3×C4—22no—
266C3×C4—21no—
267C3×C4—41no—
268Dic3—102no—
269Dic3—101no—
270Dic3—201no—
271Dic3—201no—
272C2×C5—21no—
273C2×C5—81no—
274C2×C5D3×#9911yescharacteristic
275D5—62no—
276C23—21no—
277C23—151no—
278Q8—41no—
279Q8—602no—
280Q8—601no—
281Q8—601no—
282D4—41no—
283D4—602no—
284C2×C4—21no—
285C2×C4—152no—
286C2×C4—151no—
287C2×C4—302no—
288C2×C4—302no—
289C2×C4—302no—
290C2×C4—301no—
291C2×C4—301no—
292C2×C4—602no—
293C2×C4C2×C4×D1511yescharacteristic
294C2×C4D4×D1512yes—
295C8—42no—
296C8—602no—
297C2×C3—21no—
298C2×C3—81no—
299C2×C3D5×#9911yescharacteristic
300D3—102no—
301C5#6916411yescharacteristic, complemented, Sylow
302C22—42no—
303C22—41no—
304C22—152no—
305C22—601no—
306C22C22⋊C4×D1511yescharacteristic
307C4—22no—
308C4—21no—
309C4—41no—
310C4—301no—
311C4—302no—
312C4—601no—
313C4—601no—
314C3#1059995711yescharacteristic, complemented, Sylow
315C2—21no—
316C2—81no—
317C2—302no—
318C2D15×#9911yescharacteristic
subgroupG/H
centerC2D15×#99
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×Q8C22×D15
FittingC3×C5×#355C2
socleC2×C3×C5C2×#99
prime radicalC2×#6819C4
cosocleC2×C3×C5×Q8C23
hypercenter#355D15
hypocenterC3×C5#2133
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. D15×#101C2semidirect
3. C3×C5×#355C2semidirect
4. #11746363C2semidirect
5. #11746299C2semidirect
23. C5×#355D3semidirect
51. C3×#355D5semidirect
129. #355D15semidirect
259. C3×C5#2133semidirect
301. C5#69164semidirect
314. C3#10599957semidirect

Maximal subgroups

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

subgroupindex
#117564342
D15×#1012
C3×C5×#3552
#117463632
#117462992
#105999573
#691645