Finite Group Databasebeta

← #13086101

Subgroups — #13086101

Order 1440.

366 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 74 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×C5×#626C211yesmaximal, characteristic
2C2×C3⋊D3×Dic5C211yesmaximal, characteristic, complemented
3#10623830C211yesmaximal, characteristic, complemented
4#10623814C211yesmaximal, characteristic, complemented
5(C2×D3)⋊Dic15C211yesmaximal, characteristic, complemented
6C3×#6669C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
8#91555—31nomaximal
9#91423—31nomaximal
10C22×C5×C3⋊D3C2211yescharacteristic
11C22×C3×C5×D3C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C3×Dic15C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17C5×#626—22no—
18C3⋊D3×Dic5—22no—
19#63853—51nomaximal, Hall
20C2×C5×#67—31no—
21C2×C5×D12—31no—
22C2×D3×Dic5—31no—
23C2×D3×Dic5—31no—
24C2×D3×Dic5—61no—
25#6719—31no—
26#6712—31no—
27C3×C22⋊Dic5—31no—
28C3×#683—31no—
29#6669D311yescharacteristic, complemented
30#6668—31no—
31(C2×D3)⋊Dic5—31no—
32(C2×D3)⋊Dic5—31no—
33(C2×D3)⋊Dic5—31no—
34(C2×D3)⋊Dic5D311yescharacteristic, complemented
35C22×C32×C5C2311yescharacteristic
36C2×C5×C3⋊D3—21no—
37C2×C5×C3⋊D3—21no—
38C2×C5×C3⋊D3D412yes—
39C2×C3×C5×D3—21no—
40C2×C3×C5×D3—21no—
41C2×C3×C5×D3—21no—
42C3⋊Dic15—21no—
43C3×Dic15—21no—
44C3×Dic15—21no—
45C3×C5×Dic3—21no—
46C32×Dic5—21no—
47#4081—91noHall
48C2×C4×C3⋊D3—51no—
49C2×#626D511yescharacteristic
50C3×(C2×D3)⋊C4—51no—
51C3×Dic3⋊C4—51no—
52Dic3⋊Dic3—51no—
53#3722—51no—
54(C2×D3)⋊Dic3—51no—
55C23×C3×C5—31no—
56C22×C5×D3—31no—
57C22×C5×D3—31no—
58C22×C5×D3—61no—
59C22×C5×D3C2×D311yescharacteristic
60C2×C3×C4×C5—31no—
61C2×Dic15—31no—
62C2×Dic15—31no—
63C2×Dic15—61no—
64C2×Dic15C2×D311yescharacteristic
65C2×Dic15C2×D311yescharacteristic
66C5×#67—62no—
67C2×C5×Dic3C2×D311yescharacteristic
68C5×D12—62no—
69C2×C3×Dic5—21no—
70C2×C3×Dic5—31no—
71C2×C3×Dic5—31no—
72C2×C3×Dic5C2×D311yescharacteristic
73C2×C3×Dic5C2×D311yescharacteristic
74D3×Dic5—62no—
75D3×Dic5—62no—
76D3×Dic5—64no—
77#894—151no—
78#883—151no—
79C2×C32×C5C2×D411yescharacteristic
80C2×C32×C5#4111yescharacteristic
81C2×C32×C5#4111yescharacteristic
82C5×C3⋊D3—22no—
83C3×C5×D3—41no—
84C2×C5×D4—91no—
85C22×Dic5—91no—
86C22⋊Dic5—31no—
87C22⋊Dic5—91no—
88C22⋊Dic5—91no—
89#683—31no—
90#683—91no—
91C22×C3⋊D3C2×D511yescharacteristic
92C22×C3×D3C2×D511yescharacteristic
93C2×C32×C4—51no—
94C2×C3⋊Dic3—51no—
95C4×C3⋊D3—102no—
96C2×C3×Dic3—51no—
97C2×C3×Dic3—51no—
98C2×C3×Dic3C2×D511yescharacteristic
99#626—22no—
100C22×C3×C5—21no—
101C22×C3×C5—61no—
102C22×C3×C5—61no—
103C22×C3×C5—61no—
104C22×C3×C5C22×D311yescharacteristic
105C22×C3×C5C22×D311yescharacteristic
106C2×C5×D3—21no—
107C2×C5×D3—21no—
108C2×C5×D3—21no—
109C2×C5×D3—32no—
110C2×C5×D3—32no—
111C2×C5×D3—62no—
112C2×C5×D3—62no—
113C2×C5×D3—62no—
114C2×C5×D3—61no—
115C2×C5×D3—61no—
116C2×C5×D3—61no—
117C2×C5×D3—61no—
118C3×C4×C5—61no—
119Dic15—21no—
120Dic15—21no—
121Dic15—62no—
122Dic15—61no—
123Dic15—61no—
124C3×Dic5—22no—
125C3×Dic5—21no—
126C3×Dic5—21no—
127C3×Dic5—61no—
128C3×Dic5—61no—
129C5×Dic3—21no—
130C2×#67—31no—
131C2×D12—31no—
132C2×C4×D3—151no—
133C2×C4×D3—151no—
134C2×C4×D3—301no—
135C3×C4⋊C4—151no—
136C3×C22⋊C4—151no—
137#217—151no—
138(C2×D3)⋊C4—51no—
139(C2×D3)⋊C4—151no—
140(C2×D3)⋊C4—151no—
141(C2×D3)⋊C4—151no—
142C4⋊Dic3—151no—
143Dic3⋊C4—51no—
144Dic3⋊C4—151no—
145C32×C5#12311yescharacteristic, complemented, Hall
146C23×C5—31no—
147C23×C5—91no—
148C5×D4—182no—
149C2×C4×C5—31no—
150C2×Dic5—31no—
151C2×Dic5—31no—
152C2×Dic5—91no—
153C2×Dic5—182no—
154C2×Dic5D3211yescharacteristic
155C22×C32C22×D511yescharacteristic
156C2×C3⋊D3—21no—
157C2×C3⋊D3—21no—
158C2×C3⋊D3C22⋊D512yes—
159C2×C3×D3—21no—
160C2×C3×D3—21no—
161C2×C3×D3—21no—
162C32×C4—101no—
163C3⋊Dic3—101no—
164C3×Dic3—21no—
165C3×Dic3—101no—
166C3×Dic3—101no—
167#123—451noSylow
168C2×C3×C5—21no—
169C2×C3×C5—21no—
170C2×C3×C5—21no—
171C2×C3×C5—121no—
172C2×C3×C5#23511yescharacteristic
173C2×C3×C5#23511yescharacteristic
174C2×C3×C5D3×D411yescharacteristic
175C2×C3×C5D3×D411yescharacteristic
176C2×C3×C5#23711yescharacteristic
177C2×C3×C5#23911yescharacteristic
178C5×D3—41no—
179C5×D3—64no—
180C5×D3—62no—
181C5×D3—62no—
182C23×C3—31no—
183C22×D3—31no—
184C22×D3—31no—
185C22×D3—61no—
186C22×D3D3×D511yescharacteristic
187C2×C3×C4—31no—
188C2×C3×C4—51no—
189C2×C3×C4—51no—
190C2×C3×C4—101no—
191C2×C3×C4—151no—
192C2×C3×C4—151no—
193#67—62no—
194C2×Dic3—51no—
195C2×Dic3—51no—
196C2×Dic3—151no—
197C2×Dic3—151no—
198C2×Dic3—301no—
199C2×Dic3D3×D511yescharacteristic
200D12—62no—
201C4×D3—302no—
202C4×D3—302no—
203C4×D3—304no—
204C22×C5—61no—
205C22×C5—61no—
206C22×C5—61no—
207C22×C5—92no—
208C22×C5—181no—
209C22×C5—181no—
210C22×C5C2×D3211yescharacteristic
211C4×C5—61no—
212Dic5—21no—
213Dic5—61no—
214Dic5—61no—
215Dic5—181no—
216C2×C32#71111yescharacteristic
217C2×C32#71111yescharacteristic
218C2×C32C2×C22⋊D511yescharacteristic
219C3⋊D3—22no—
220C3×D3—41no—
221C2×D4—91no—
222C22×C4—451no—
223C4⋊C4—151no—
224C4⋊C4—451no—
225C22⋊C4—151no—
226C22⋊C4—451no—
227C22⋊C4—451no—
228C3×C5—21no—
229C3×C5#88311yescharacteristic, complemented
230C3×C5#89411yescharacteristic, complemented
231C22×C3—21no—
232C22×C3—61no—
233C22×C3—61no—
234C22×C3—61no—
235C22×C3C2×D3×D511yescharacteristic
236C22×C3C2×D3×D511yescharacteristic
237C2×D3—21no—
238C2×D3—21no—
239C2×D3—21no—
240C2×D3—32no—
241C2×D3—32no—
242C2×D3—62no—
243C2×D3—62no—
244C2×D3—62no—
245C2×D3—61no—
246C2×D3—61no—
247C2×D3—61no—
248C2×D3—61no—
249C3×C4—61no—
250C3×C4—102no—
251C3×C4—101no—
252C3×C4—101no—
253C3×C4—301no—
254C3×C4—301no—
255Dic3—21no—
256Dic3—101no—
257Dic3—101no—
258Dic3—302no—
259Dic3—301no—
260Dic3—301no—
261C2×C5—121no—
262C2×C5—182no—
263C2×C5#379611yescharacteristic
264C2×C5#379811yescharacteristic
265C2×C5#381111yescharacteristic
266C32#408111yescharacteristic, complemented, Sylow
267C23—31no—
268C23—91no—
269D4—182no—
270C2×C4—31no—
271C2×C4—51no—
272C2×C4—151no—
273C2×C4—151no—
274C2×C4—451no—
275C2×C4—902no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—121no—
280C2×C3#676811yescharacteristic
281C2×C3#677211yescharacteristic
282C2×C3#678011yescharacteristic
283C2×C3#678211yescharacteristic
284C2×C3D3×C22⋊D511yescharacteristic
285C2×C3D3×C22⋊D511yescharacteristic
286D3—41no—
287D3—64no—
288D3—62no—
289D3—62no—
290C5#6385311yescharacteristic, complemented, Sylow
291C22—61no—
292C22—61no—
293C22—61no—
294C22—92no—
295C22—181no—
296C22—181no—
297C22D32×D511yescharacteristic
298C4—61no—
299C4—101no—
300C4—301no—
301C4—301no—
302C4—901no—
303C3—21no—
304C3#9142311yescharacteristic, complemented
305C3#9155511yescharacteristic, complemented
306C2—121no—
307C2—182no—
308C2#1062402911yescharacteristic
309C2#1062404911yescharacteristic
310C2#1062405611yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutator, Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×C5×#626C2
hypocenterC32×C5#123
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C2×C3⋊D3×Dic5C2semidirect
3. #10623830C2semidirect
4. #10623814C2semidirect
5. (C2×D3)⋊Dic15C2semidirect
6. C3×#6669C2semidirect
7. C3×(C2×D3)⋊Dic5C2semidirect
29. #6669D3semidirect
34. (C2×D3)⋊Dic5D3semidirect
145. C32×C5#123semidirect
229. C3×C5#883semidirect
230. C3×C5#894semidirect
266. C32#4081semidirect
290. C5#63853semidirect
304. C3#91423semidirect
305. C3#91555semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#6262
C2×C3⋊D3×Dic52
#106238302
#106238142
(C2×D3)⋊Dic152
C3×#66692
C3×(C2×D3)⋊Dic52
#915553
#914233
#638535