Finite Group Databasebeta

← #13086131

Subgroups — #13086131

Order 1440.

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

normal subgroups only

This group has 334 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
1C2×#67153C211yesmaximal, characteristic, complemented
2C2×#67150C211yesmaximal, characteristic
3#10623829C211yesmaximal, characteristic, complemented
4C5×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
5Dic5×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#6667C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
8#91526—31nomaximal
9#91462—31nomaximal
10C22×C3×D15C2211yescharacteristic
11C22×C3×C5×D3C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17#67153—22no—
18#67150—22no—
19#63915—51nomaximal, Hall
20C2×#1220—31no—
21C2×Dic30—31no—
22C2×#1204—31no—
23C2×#1201—31no—
24C5×#217—31no—
25C5×(C2×D3)⋊C4—31no—
26C3×C22⋊Dic5—31no—
27C3×#685—31no—
28#6667—31no—
29#6667D311yescharacteristic, complemented
30(C2×D3)⋊Dic5D311yescharacteristic, complemented
31#6665—31no—
32Dic3×Dic5—31no—
33Dic3×Dic5—31no—
34Dic3×Dic5—61no—
35C22×C32×C5C2311yescharacteristic
36C2×C3×D15—21no—
37C2×C3×D15—21no—
38C2×C3×D15—21no—
39C2×C3×C5×D3—21no—
40C2×C3×C5×D3—21no—
41C2×C3×C5×D3—21no—
42C3⋊Dic15D412yes—
43C5×C3⋊Dic3—21no—
44C3×Dic15—21no—
45C3×C5×Dic3—21no—
46C32×Dic5—21no—
47#4031—91noHall
48C2×#627—51no—
49C2×#625—51no—
50C4×C3⋊Dic3—51no—
51C3×(C2×D3)⋊C4—51no—
52C3×(C2×D3)⋊C4—51no—
53(C2×D3)⋊Dic3—51no—
54(C2×D3)⋊Dic3D511yescharacteristic, complemented
55C23×C3×C5—31no—
56C22×D15C2×D311yescharacteristic
57C22×C5×D3C2×D311yescharacteristic
58C22×C3×D5—31no—
59C2×C3×C4×C5—31no—
60#1220—62no—
61C2×Dic15—31no—
62C2×Dic15—31no—
63C2×Dic15—61no—
64C2×Dic15C2×D311yescharacteristic
65Dic30—62no—
66C2×C5×Dic3—31no—
67C2×C5×Dic3—31no—
68C2×C5×Dic3—61no—
69C2×C5×Dic3C2×D311yescharacteristic
70C2×C3×Dic5—21no—
71C2×C3×Dic5—31no—
72C2×C3×Dic5C2×D311yescharacteristic
73C2×C3×Dic5C2×D311yescharacteristic
74#1204—62no—
75#1201—62no—
76#885—151no—
77#885—151no—
78C2×C32×C5C2×D411yescharacteristic
79C2×C32×C5#4111yescharacteristic
80C2×C32×C5#4111yescharacteristic
81C3×D15—41no—
82C3×C5×D3—41no—
83C2×C22⋊D5—91no—
84C2×Dic10—91no—
85C5×C22⋊C4—91no—
86C22⋊Dic5—31no—
87#685—31no—
88#685—91no—
89C4×Dic5—91no—
90C22×C3×D3—51no—
91C22×C3×D3C2×D511yescharacteristic
92C2×C32×C4—51no—
93C2×C3⋊Dic3—51no—
94C2×C3⋊Dic3C2×D511yescharacteristic
95C2×C3×Dic3—51no—
96C2×C3×Dic3C2×D511yescharacteristic
97#627—102no—
98#625—102no—
99C22×C3×C5—21no—
100C22×C3×C5—61no—
101C22×C3×C5—61no—
102C22×C3×C5—61no—
103C22×C3×C5C22×D311yescharacteristic
104C22×C3×C5C22×D311yescharacteristic
105C2×D15—21no—
106C2×D15—21no—
107C2×D15—21no—
108C2×C5×D3—21no—
109C2×C5×D3—21no—
110C2×C5×D3—21no—
111C2×C3×D5—61no—
112C2×C3×D5—61no—
113C2×C3×D5—61no—
114C3×C4×C5—61no—
115Dic15—21no—
116Dic15—32no—
117Dic15—32no—
118Dic15—62no—
119C3×Dic5—22no—
120C3×Dic5—21no—
121C3×Dic5—21no—
122C3×Dic5—61no—
123C5×Dic3—21no—
124C5×Dic3—62no—
125C5×Dic3—61no—
126C5×Dic3—61no—
127C2×#67—151no—
128C2×#67—151no—
129C2×Dic6—151no—
130C2×Dic6—151no—
131C3×C22⋊C4—151no—
132C3×C22⋊C4—151no—
133#217—31no—
134#217—151no—
135(C2×D3)⋊C4—31no—
136(C2×D3)⋊C4—51no—
137(C2×D3)⋊C4—51no—
138(C2×D3)⋊C4—151no—
139C4×Dic3—151no—
140C4×Dic3—151no—
141C4×Dic3—301no—
142C32×C5#12411yescharacteristic, complemented, Hall
143C23×C5—31no—
144C22×D5—31no—
145C2×C4×C5—31no—
146C2×C4×C5—91no—
147C22⋊D5—182no—
148C2×Dic5—31no—
149C2×Dic5—91no—
150C2×Dic5D3211yescharacteristic
151Dic10—182no—
152C22×C32C22×D511yescharacteristic
153C2×C3×D3—21no—
154C2×C3×D3—21no—
155C2×C3×D3—21no—
156C2×C3×D3—101no—
157C2×C3×D3—101no—
158C2×C3×D3—101no—
159C32×C4—101no—
160C3⋊Dic3—21no—
161C3⋊Dic3—52no—
162C3×Dic3—21no—
163C3×Dic3—101no—
164#124—451noSylow
165C2×C3×C5—21no—
166C2×C3×C5—21no—
167C2×C3×C5—21no—
168C2×C3×C5—121no—
169C2×C3×C5#23511yescharacteristic
170C2×C3×C5#23511yescharacteristic
171C2×C3×C5D3×D411yescharacteristic
172C2×C3×C5D3×D411yescharacteristic
173C2×C3×C5#23711yescharacteristic
174C2×C3×C5#23711yescharacteristic
175D15—41no—
176C3×D5—121no—
177C5×D3—41no—
178C23×C3—31no—
179C23×C3—151no—
180C22×D3—51no—
181C22×D3D3×D511yescharacteristic
182C2×C3×C4—31no—
183C2×C3×C4—51no—
184C2×C3×C4—51no—
185C2×C3×C4—101no—
186C2×C3×C4—151no—
187#67—302no—
188#67—302no—
189C2×Dic3—31no—
190C2×Dic3—31no—
191C2×Dic3—51no—
192C2×Dic3—61no—
193C2×Dic3—151no—
194C2×Dic3—151no—
195C2×Dic3—301no—
196C2×Dic3D3×D511yescharacteristic
197Dic6—302no—
198Dic6—302no—
199C22×C5—61no—
200C22×C5—61no—
201C22×C5—61no—
202C22×C5C2×D3211yescharacteristic
203C2×D5—61no—
204C2×D5—61no—
205C2×D5—61no—
206C4×C5—61no—
207C4×C5—181no—
208Dic5—21no—
209Dic5—61no—
210Dic5—92no—
211C2×C32#70911yescharacteristic
212C2×C32D4×D511yescharacteristic
213C2×C32#71111yescharacteristic
214C3×D3—41no—
215C3×D3—201no—
216C2×Q8—451no—
217C2×D4—451no—
218C22⋊C4—91no—
219C22⋊C4—151no—
220C22⋊C4—151no—
221C22⋊C4—451no—
222C42—451no—
223C3×C5—21no—
224C3×C5#88511yescharacteristic, complemented
225C3×C5#88511yescharacteristic, complemented
226C22×C3—21no—
227C22×C3—61no—
228C22×C3—61no—
229C22×C3—61no—
230C22×C3—301no—
231C22×C3—301no—
232C22×C3—301no—
233C22×C3C2×D3×D511yescharacteristic
234C22×C3C2×D3×D511yescharacteristic
235C2×D3—21no—
236C2×D3—21no—
237C2×D3—21no—
238C2×D3—101no—
239C2×D3—101no—
240C2×D3—101no—
241C3×C4—61no—
242C3×C4—102no—
243C3×C4—101no—
244C3×C4—101no—
245C3×C4—301no—
246Dic3—21no—
247Dic3—62no—
248Dic3—61no—
249Dic3—61no—
250Dic3—101no—
251Dic3—152no—
252Dic3—152no—
253Dic3—302no—
254C2×C5—121no—
255C2×C5#379811yescharacteristic
256C2×C5#380211yescharacteristic
257C2×C5#380511yescharacteristic
258D5—121no—
259C32#403111yescharacteristic, complemented, Sylow
260C23—31no—
261C23—151no—
262Q8—902no—
263D4—902no—
264C2×C4—31no—
265C2×C4—51no—
266C2×C4—91no—
267C2×C4—151no—
268C2×C4—451no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—121no—
273C2×C3—601no—
274C2×C3#676511yescharacteristic
275C2×C3#677211yescharacteristic
276C2×C3#677911yescharacteristic
277C2×C3#678211yescharacteristic
278C2×C3#679011yescharacteristic
279C2×C3#679011yescharacteristic
280D3—41no—
281D3—201no—
282C5#6391511yescharacteristic, complemented, Sylow
283C22—61no—
284C22—61no—
285C22—61no—
286C22—301no—
287C22—301no—
288C22—301no—
289C22D32×D511yescharacteristic
290C4—61no—
291C4—101no—
292C4—181no—
293C4—301no—
294C4—452no—
295C3—21no—
296C3#9146211yescharacteristic, complemented
297C3#9152611yescharacteristic, complemented
298C2—121no—
299C2—601no—
300C2#1062403511yescharacteristic
301C2#1062404511yescharacteristic
302C2#1062404911yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutator, Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×#67150C2
hypocenterC32×C5#124
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#67153C2semidirect
3. #10623829C2semidirect
4. C5×(C2×D3)⋊Dic3C2semidirect
5. Dic5×C3⋊Dic3C2semidirect
6. C3×#6667C2semidirect
7. C3×(C2×D3)⋊Dic5C2semidirect
29. #6667D3semidirect
30. (C2×D3)⋊Dic5D3semidirect
54. (C2×D3)⋊Dic3D5semidirect
142. C32×C5#124semidirect
224. C3×C5#885semidirect
225. C3×C5#885semidirect
259. C32#4031semidirect
282. C5#63915semidirect
296. C3#91462semidirect
297. C3#91526semidirect

Maximal subgroups

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

subgroupindex
C2×#671532
C2×#671502
#106238292
C5×(C2×D3)⋊Dic32
Dic5×C3⋊Dic32
C3×#66672
C3×(C2×D3)⋊Dic52
#915263
#914623
#639155