Finite Group Databasebeta

← #14279157

Subgroups — #14279157

Order 1920.

324 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 99 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×C5×#413C211yesmaximal, characteristic
2#11751341C211yesmaximal, characteristic
3#11751335C211yesmaximal, characteristic
4#10598192—31nomaximal, Hall
5C2×C3×C5×#41C2211yescharacteristic
6C2×C3×C5×M16—21no—
7#91815—21no—
8C2×#6710C411yescharacteristic, complemented
9C22×C3⋊#168C411yescharacteristic, complemented
10C3×C5×#101C412yescomplemented
11C3×C5×#100—21no—
12#91118—21no—
13#91118C412yes—
14#91114—21no—
15#91114—21no—
16#67701—51nomaximal, Hall
17C5×#413D311yescharacteristic
18#65529—31no—
19#65523—31no—
20C3×C5×#41—41no—
21C3×C5×#41—41no—
22C2×C3×C5×Q8C2×C411yescharacteristic
23C2×C3×C5×D4C2×C411yescharacteristic
24C2×C3×C5×D4D411yescharacteristic
25C2×C3×C5×D4Q811yescharacteristic
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×C3×C4×C5D411yescharacteristic
28C22×C3×C4×C5D411yescharacteristic
29C3×C5×M16—22no—
30C3×C5×M16—41no—
31C2×C3×C5×C8—41no—
32#6719—22no—
33C4⋊Dic15—41no—
34C4×Dic15—41no—
35#6710—41no—
36C2×C3⋊#168—21no—
37C2×C3⋊#168—21no—
38C2×C3⋊#168—41no—
39C3×#413D511yescharacteristic
40#5240—51no—
41#5234—51no—
42C2×C5×#41C2×D311yescharacteristic
43C2×C5×M16—21no—
44#4072—61no—
45C2×#681—31no—
46C22×#168—31no—
47C5×#101Dic312yescomplemented
48C5×#100—21no—
49#3966—32no—
50#3966—61no—
51C22⋊#168—61no—
52C22⋊#168—61no—
53#1395—151noSylow
54C23×C3×C5C22⋊C411yescharacteristic
55C23×C3×C5C4⋊C411yescharacteristic
56C23×C3×C5C4⋊C411yescharacteristic
57C3×C5×Q8—41no—
58C3×C5×D4—41no—
59C3×C5×D4—41no—
60C3×C5×D4—41no—
61C2×C3×C4×C5—21no—
62C2×C3×C4×C5—21no—
63C2×C3×C4×C5—21no—
64C2×C3×C4×C5—21no—
65C2×C3×C4×C5—21no—
66C2×C3×C4×C5—21no—
67C2×C3×C4×C5C4211yescharacteristic
68C2×C3×C4×C5C22⋊C411yescharacteristic
69C2×C3×C4×C5C22⋊C411yescharacteristic
70C2×C3×C4×C5C4⋊C411yescharacteristic
71C2×Dic15—42no—
72C3×C5×C8—42no—
73C3⋊#168—41no—
74C3⋊#168—41no—
75C2×C3×#41C2×D511yescharacteristic
76C2×C3×M16—21no—
77#926—101no—
78C2×#208—51no—
79C22×C3⋊C8—51no—
80C3×#101Dic512yescomplemented
81C3×#100—21no—
82#834—52no—
83#834—101no—
84#830—101no—
85#830—101no—
86C5×#41—41no—
87C5×#41—41no—
88C2×C5×Q8C2×Dic311yescharacteristic
89C2×C5×D4Dic611yescharacteristic
90C2×C5×D4C4×D311yescharacteristic
91C2×C5×D4#6711yescharacteristic
92C22×C4×C5C4×D311yescharacteristic
93C22×C4×C5D1211yescharacteristic
94C22×C4×C5#6711yescharacteristic
95C5×M16—22no—
96C5×M16—41no—
97C2×C5×C8—41no—
98C22⋊Dic5—62no—
99C4⋊Dic5—121no—
100C4×Dic5—121no—
101#681—121no—
102C2×#168—61no—
103C2×#168—61no—
104C2×#168—121no—
105#413D1511yescharacteristic
106#410—151no—
107#408—151no—
108C22×C3×C5—21no—
109C22×C3×C5—21no—
110C22×C3×C5—21no—
111C22×C3×C5—41no—
112C22×C3×C5—41no—
113C22×C3×C5—41no—
114C22×C3×C5#9511yescharacteristic
115C3×C4×C5—21no—
116C3×C4×C5—21no—
117C3×C4×C5—21no—
118C3×C4×C5#9911yescharacteristic
119C3×C4×C5#9911yescharacteristic
120Dic15—82no—
121C3×#41—41no—
122C3×#41—41no—
123C2×C3×Q8C2×Dic511yescharacteristic
124C2×C3×D4Dic1011yescharacteristic
125C2×C3×D4C4×D511yescharacteristic
126C2×C3×D4C22⋊D511yescharacteristic
127C22×C3×C4C4×D511yescharacteristic
128C22×C3×C4D2011yescharacteristic
129C22×C3×C4C22⋊D511yescharacteristic
130C3×M16—22no—
131C3×M16—41no—
132C2×C3×C8—41no—
133#217—102no—
134C4⋊Dic3—201no—
135C4×Dic3—201no—
136#208—201no—
137C2×C3⋊C8—101no—
138C2×C3⋊C8—101no—
139C2×C3⋊C8—201no—
140C23×C5Dic3⋊C411yescharacteristic
141C23×C5Dic3⋊C411yescharacteristic
142C23×C5(C2×D3)⋊C411yescharacteristic
143C5×Q8—41no—
144C5×D4—41no—
145C5×D4—41no—
146C5×D4—41no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5C4×Dic311yescharacteristic
154C2×C4×C5C4⋊Dic311yescharacteristic
155C2×C4×C5(C2×D3)⋊C411yescharacteristic
156C2×C4×C5#21711yescharacteristic
157C2×Dic5—122no—
158C5×C8—42no—
159#168—121no—
160#168—121no—
161C2×#41C2×D1511yescharacteristic
162C2×M16—21no—
163C2×M16—151no—
164C22×C8—151no—
165#117—301no—
166#101Dic1512yescomplemented
167#100—21no—
168#99—152no—
169#99—301no—
170C22⋊C8—301no—
171C22⋊C8—301no—
172C2×C3×C5—21no—
173C2×C3×C5—41no—
174C2×C3×C5—41no—
175C2×C3×C5—41no—
176C2×C3×C5#34211yescharacteristic
177C23×C3#68311yescharacteristic
178C23×C3#68311yescharacteristic
179C23×C3#68511yescharacteristic
180C3×Q8—41no—
181C3×D4—41no—
182C3×D4—41no—
183C3×D4—41no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4C4×Dic511yescharacteristic
191C2×C3×C4C4⋊Dic511yescharacteristic
192C2×C3×C4#68511yescharacteristic
193C2×C3×C4C22⋊Dic511yescharacteristic
194C2×Dic3—202no—
195C3×C8—42no—
196C3⋊C8—201no—
197C3⋊C8—201no—
198C22×C5—21no—
199C22×C5—21no—
200C22×C5—21no—
201C22×C5—41no—
202C22×C5—41no—
203C22×C5—41no—
204C22×C5C3⋊#9511yescharacteristic
205C4×C5—21no—
206C4×C5—21no—
207C4×C5—21no—
208C4×C5#80611yescharacteristic
209C4×C5#80611yescharacteristic
210Dic5—242no—
211#41—41no—
212#41—41no—
213C2×Q8C2×Dic1511yescharacteristic
214C2×D4Dic3011yescharacteristic
215C2×D4C4×D1511yescharacteristic
216C2×D4#122011yescharacteristic
217C22×C4C4×D1511yescharacteristic
218C22×C4D6011yescharacteristic
219C22×C4#122011yescharacteristic
220M16—22no—
221M16—41no—
222M16—601no—
223C2×C8—41no—
224C2×C8—301no—
225C2×C8—301no—
226C2×C8—601no—
227C4⋊C4—601no—
228C22⋊C4—302no—
229C42—601no—
230C3×C5#139511yescharacteristic, complemented, Hall
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—41no—
235C22×C3—41no—
236C22×C3—41no—
237C22×C3#396311yescharacteristic
238C3×C4—21no—
239C3×C4—21no—
240C3×C4—21no—
241C3×C4#393811yescharacteristic
242C3×C4#393811yescharacteristic
243Dic3—402no—
244C2×C5—21no—
245C2×C5—41no—
246C2×C5—41no—
247C2×C5—41no—
248C2×C5#452711yescharacteristic
249C23#671211yescharacteristic
250C23#671211yescharacteristic
251C23#671411yescharacteristic
252Q8—41no—
253D4—41no—
254D4—41no—
255D4—41no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—602no—
263C2×C4C4×Dic1511yescharacteristic
264C2×C4C4⋊Dic1511yescharacteristic
265C2×C4#671411yescharacteristic
266C2×C4#671911yescharacteristic
267C8—42no—
268C8—601no—
269C8—601no—
270C2×C3—21no—
271C2×C3—41no—
272C2×C3—41no—
273C2×C3—41no—
274C2×C3#6474711yescharacteristic
275C5#6770111yescharacteristic, complemented, Sylow
276C22—21no—
277C22—21no—
278C22—21no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22#9111511yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—1202no—
287C4#9109011yescharacteristic
288C4#9109011yescharacteristic
289C3#1059819211yescharacteristic, complemented, Sylow
290C2—21no—
291C2—41no—
292C2—41no—
293C2—41no—
294C2#1174634811yescharacteristic
subgroupG/H
centerC4#91090
commutatorC2×C3×C4×C5C42
FrattiniC2×#41C2×D15
FittingC3×C5×#413C2
socleC2×C3×C5#342
prime radical, cosocleC2×C3×C5×#41C22
hypercenter#413D15
hypocenterC3×C5#1395
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
8. C2×#6710C4semidirect
9. C22×C3⋊#168C4semidirect
10. C3×C5×#101C4semidirect
47. C5×#101Dic3semidirect
80. C3×#101Dic5semidirect
166. #101Dic15semidirect
230. C3×C5#1395semidirect
275. C5#67701semidirect
289. C3#10598192semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4132
#117513412
#117513352
#105981923
#677015