Finite Group Databasebeta

← #14286497

Subgroups — #14286497

Order 1920.

364 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 101 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#11750939C211yesmaximal, characteristic, complemented
2#11750935C211yesmaximal, characteristic, complemented
3C4×D120C211yesmaximal, characteristic
4C3×C5×#335C211yesmaximal, characteristic, complemented
5#11746304C211yesmaximal, characteristic, complemented
6#11746304C211yesmaximal, characteristic, complemented
7#11746275C211yesmaximal, characteristic, complemented
8#10599352—31nomaximal, Hall
9C2×D120C411yescharacteristic
10C2×#6705—21no—
11C2×C8×D15—21no—
12C4×D60C2211yescharacteristic
13C4×D60C2211yescharacteristic
14C3×C5×C4⋊C8C2211yescharacteristic
15C3×C5×C4⋊C8C2211yescharacteristic
16C3×C4×C5×C8C2211yescharacteristic
17#91105C411yescharacteristic
18#91105C411yescharacteristic
19#91104—21no—
20#91104—21no—
21#91102C411yescharacteristic
22C4×C3⋊#168C2211yescharacteristic
23C4×C3⋊#168C2211yescharacteristic
24#68559—51nomaximal, Hall
25#65127—31no—
26#65123—31no—
27C4×D40—31no—
28C5×#335D311yescharacteristic, complemented
29#64703—31no—
30#64703—31no—
31#64674—31no—
32C2×D60C2×C411yescharacteristic
33C2×D60C2×C411yescharacteristic
34C2×C4×D15—21no—
35C2×C4×D15—21no—
36C2×C3×C5×C8—21no—
37C2×C3×C5×C8—21no—
38C2×C3×C5×C8C2×C411yescharacteristic
39C2×C3×C5×C8C2×C411yescharacteristic
40C3×C42×C5C2311yescharacteristic
41#6714—21no—
42#6714—21no—
43C4⋊Dic15C2×C411yescharacteristic
44C4⋊Dic15C2×C411yescharacteristic
45C2×C3⋊#168—21no—
46C2×C3⋊#168D411yescharacteristic
47C2×C3⋊#168D411yescharacteristic
48D120—22no—
49#6705—42no—
50C8×D15—42no—
51#4838—51no—
52#4834—51no—
53C4×D24—51no—
54C3×#335D511yescharacteristic, complemented
55#4483—51no—
56#4483—51no—
57#4454—51no—
58C2×D40—31no—
59C2×#676—61no—
60C2×C8×D5—61no—
61C4×D20—31no—
62C4×D20—31no—
63C5×C4⋊C8C2×D311yescharacteristic
64C5×C4⋊C8C2×D311yescharacteristic
65C4×C5×C8C2×D311yescharacteristic
66#3953—31no—
67#3953—31no—
68#3952—61no—
69#3952—61no—
70#3950—31no—
71C4×#168—31no—
72C4×#168—31no—
73#1581—151noSylow
74C22×D15—21no—
75C22×D15—21no—
76C2×C3×C4×C5C22×C411yescharacteristic
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5#4111yescharacteristic
79C2×Dic15—21no—
80C2×Dic15—21no—
81D60—21no—
82D60—21no—
83D60—21no—
84D60M1612yescomplemented
85C4×D15—41no—
86C4×D15—41no—
87C4×D15—41no—
88C4×D15—41no—
89C3×C5×C8—21no—
90C3×C5×C8—21no—
91C3×C5×C8—41no—
92C3×C5×C8—41no—
93C3⋊#168—21no—
94C3⋊#168—41no—
95C3⋊#168D812yescomplemented
96C2×D24—51no—
97C2×ΓL(1,𝔽25)—101no—
98C2×D3×C8—101no—
99C4×D12—51no—
100C4×D12—51no—
101C3×C4⋊C8C2×D511yescharacteristic
102C3×C4⋊C8C2×D511yescharacteristic
103C3×C4×C8C2×D511yescharacteristic
104#821—51no—
105#821—51no—
106(C2×D3)⋊C8—101no—
107(C2×D3)⋊C8—101no—
108#818—51no—
109C4×C3⋊C8—51no—
110C4×C3⋊C8—51no—
111C2×D20—31no—
112C2×D20—31no—
113C2×C4×D5—61no—
114C2×C4×D5—61no—
115C2×C5×C8—21no—
116C2×C5×C8—21no—
117C2×C5×C8C4×D311yescharacteristic
118C2×C5×C8C4×D311yescharacteristic
119C42×C5C22×D311yescharacteristic
120#685—61no—
121#685—61no—
122C4⋊Dic5—31no—
123C4⋊Dic5—31no—
124C2×#168—31no—
125C2×#168—31no—
126C2×#168—61no—
127D40—62no—
128#676—122no—
129C8×D5—122no—
130C4×D8—151no—
131#436—151no—
132C8×D4—151no—
133#335D1511yescharacteristic, complemented
134D4⋊C8—151no—
135D4⋊C8—151no—
136#322—151no—
137C22×C3×C5C4×D411yescharacteristic
138C2×D15—22no—
139C2×D15—41no—
140C2×D15—41no—
141C2×D15—41no—
142C2×D15—41no—
143C2×D15—41no—
144C3×C4×C5—21no—
145C3×C4×C5C2×M1611yescharacteristic
146C3×C4×C5#13111yescharacteristic
147C3×C4×C5C2×D811yescharacteristic
148C3×C4×C5#13511yescharacteristic
149Dic15—41no—
150Dic15—41no—
151C2×D12—51no—
152C2×D12—51no—
153C2×C4×D3—101no—
154C2×C4×D3—101no—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8C4×D511yescharacteristic
158C2×C3×C8C4×D511yescharacteristic
159C3×C42C22×D511yescharacteristic
160(C2×D3)⋊C4—101no—
161(C2×D3)⋊C4—101no—
162C4⋊Dic3—51no—
163C4⋊Dic3—51no—
164C2×C3⋊C8—51no—
165C2×C3⋊C8—51no—
166C2×C3⋊C8—101no—
167D24—102no—
168ΓL(1,𝔽25)—202no—
169D3×C8—202no—
170C22×D5—61no—
171C22×D5—61no—
172C2×C4×C5C2×C4×D311yescharacteristic
173C2×C4×C5D3×D411yescharacteristic
174C2×C4×C5#23911yescharacteristic
175C2×Dic5—61no—
176C2×Dic5—61no—
177D20—32no—
178D20—61no—
179D20—61no—
180D20—61no—
181C4×D5—121no—
182C4×D5—121no—
183C4×D5—121no—
184C4×D5—121no—
185C5×C8—21no—
186C5×C8—21no—
187C5×C8—41no—
188C5×C8—41no—
189#168—32no—
190#168—61no—
191#168—121no—
192C2×D8—151no—
193C2×M16—301no—
194C22×C8—301no—
195C4×D4—151no—
196C4×D4—151no—
197#107—151no—
198C4⋊C8C2×D1511yescharacteristic
199C4⋊C8C2×D1511yescharacteristic
200#102—151no—
201#102—151no—
202C22⋊C8—301no—
203C22⋊C8—301no—
204C4×C8—151no—
205C4×C8—151no—
206C4×C8C2×D1511yescharacteristic
207C2×C3×C5#43511yescharacteristic
208C2×C3×C5C4×D811yescharacteristic
209C2×C3×C5#44411yescharacteristic
210D15—42no—
211D15—81no—
212C22×D3—101no—
213C22×D3—101no—
214C2×C3×C4C2×C4×D511yescharacteristic
215C2×C3×C4D4×D511yescharacteristic
216C2×C3×C4#71311yescharacteristic
217C2×Dic3—101no—
218C2×Dic3—101no—
219D12—52no—
220D12—101no—
221D12—101no—
222D12—101no—
223C4×D3—201no—
224C4×D3—201no—
225C4×D3—201no—
226C4×D3—201no—
227C3×C8—21no—
228C3×C8—21no—
229C3×C8—41no—
230C3×C8—41no—
231C3⋊C8—52no—
232C3⋊C8—101no—
233C3⋊C8—201no—
234C22×C5#89311yescharacteristic
235C2×D5—62no—
236C2×D5—121no—
237C2×D5—121no—
238C2×D5—121no—
239C2×D5—121no—
240C2×D5—121no—
241C4×C5—21no—
242C4×C5#90111yescharacteristic
243C4×C5D3×M1611yescharacteristic
244C4×C5D3×D811yescharacteristic
245C4×C5#91911yescharacteristic
246Dic5—121no—
247Dic5—121no—
248C2×D4—151no—
249C2×D4—151no—
250C22×C4—301no—
251C22×C4—301no—
252D8—302no—
253M16—602no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—151no—
257C2×C8—151no—
258C2×C8—301no—
259C2×C8—602no—
260C2×C8C4×D1511yescharacteristic
261C2×C8C4×D1511yescharacteristic
262C4⋊C4—151no—
263C4⋊C4—151no—
264C22⋊C4—301no—
265C22⋊C4—301no—
266C42C22×D1511yescharacteristic
267C3×C5#158111yescharacteristic, complemented, Hall
268C22×C3#403911yescharacteristic
269C2×D3—102no—
270C2×D3—201no—
271C2×D3—201no—
272C2×D3—201no—
273C2×D3—201no—
274C2×D3—201no—
275C3×C4—21no—
276C3×C4#404711yescharacteristic
277C3×C4D5×M1611yescharacteristic
278C3×C4D5×D811yescharacteristic
279C3×C4#406511yescharacteristic
280Dic3—201no—
281Dic3—201no—
282C2×C5#483611yescharacteristic
283C2×C5#487211yescharacteristic
284C2×C5#489411yescharacteristic
285D5—122no—
286D5—241no—
287C23—301no—
288C23—301no—
289D4—152no—
290D4—301no—
291D4—301no—
292D4—301no—
293C2×C4—301no—
294C2×C4—301no—
295C2×C4—601no—
296C2×C4—601no—
297C2×C4—601no—
298C2×C4—601no—
299C2×C4C2×C4×D1511yescharacteristic
300C2×C4D4×D1511yescharacteristic
301C2×C4#682111yescharacteristic
302C8—21no—
303C8—21no—
304C8—41no—
305C8—41no—
306C8—152no—
307C8—301no—
308C8—601no—
309C2×C3#6512511yescharacteristic
310C2×C3#6516111yescharacteristic
311C2×C3#6518311yescharacteristic
312D3—202no—
313D3—401no—
314C5#6855911yescharacteristic, complemented, Sylow
315C22—302no—
316C22—601no—
317C22—601no—
318C22—601no—
319C22—601no—
320C22—601no—
321C22#9178211yescharacteristic
322C4—21no—
323C4—601no—
324C4—601no—
325C4#9179011yescharacteristic
326C4M16×D1511yescharacteristic
327C4D8×D1511yescharacteristic
328C4#9180811yescharacteristic
329C3#1059935211yescharacteristic, complemented, Sylow
330C2—602no—
331C2—1201no—
332C2#1175093711yescharacteristic
333C2#1175097311yescharacteristic
334C2#1175099511yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#335C2
socleC22×C3×C5C4×D4
prime radicalC2×D120C4
cosocleC3×C42×C5C23
hypercenter#335D15
hypocenterC3×C5#1581
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ #335

Complements

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

NH ≅ G/Ntype
1. #11750939C2semidirect
2. #11750935C2semidirect
4. C3×C5×#335C2semidirect
5. #11746304C2semidirect
6. #11746304C2semidirect
7. #11746275C2semidirect
28. C5×#335D3semidirect
54. C3×#335D5semidirect
84. D60M16semidirect
95. C3⋊#168D8semidirect
133. #335D15semidirect
267. C3×C5#1581semidirect
314. C5#68559semidirect
329. C3#10599352semidirect

Maximal subgroups

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

subgroupindex
#117509392
#117509352
C4×D1202
C3×C5×#3352
#117463042
#117462752
#105993523
#685595