Finite Group Databasebeta

← #13086107

Subgroups — #13086107

Order 1440.

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

normal subgroups only

This group has 366 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×#67149C211yesmaximal, characteristic, complemented
2C2×#67140C211yesmaximal, characteristic
3#10623830C211yesmaximal, characteristic, complemented
4#10623813C211yesmaximal, characteristic, complemented
5C5×#3722C211yesmaximal, characteristic, complemented
6C3×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
7C3×#6669C211yesmaximal, characteristic, complemented
8#91438—31nomaximal
9#91355—31nomaximal
10C22×C3⋊D15C2211yescharacteristic
11C22×C5×C3⋊D3C2211yescharacteristic
12C2×C3×Dic15C2211yescharacteristic
13C2×C3×Dic15C2211yescharacteristic
14C2×C3×C5×Dic3C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17#67149—22no—
18#67140—22no—
19#63897—51nomaximal, Hall
20C2×C4×D15—31no—
21C2×#1203—31no—
22C2×#1203—31no—
23C2×#1203—61no—
24C2×#1200—31no—
25#6714—31no—
26C5×(C2×D3)⋊C4—31no—
27C5×(C2×D3)⋊C4—31no—
28C3×C4⋊Dic5—31no—
29C3×#683—31no—
30Dic3⋊Dic5D311yescharacteristic, complemented
31#6669D311yescharacteristic, complemented
32#6667—31no—
33(C2×D3)⋊Dic5—31no—
34(C2×D3)⋊Dic5—31no—
35C22×C32×C5C2311yescharacteristic
36C2×C3⋊D15—21no—
37C2×C3⋊D15—21no—
38C2×C3⋊D15D412yes—
39C2×C5×C3⋊D3—21no—
40C2×C5×C3⋊D3—21no—
41C2×C5×C3⋊D3—21no—
42C3×Dic15—21no—
43C3×Dic15—21no—
44C3×C5×Dic3—21no—
45C3×C5×Dic3—21no—
46C32×Dic5—21no—
47#4029—91noHall
48C2×C4⋊(C3⋊D3)—51no—
49C2×#624—51no—
50C3×Dic3⋊C4—51no—
51C3×Dic3⋊C4—51no—
52#3722—51no—
53#3722—51no—
54#3722D511yescharacteristic, complemented
55C22×D15—31no—
56C22×D15—31no—
57C22×D15—61no—
58C22×C5×D3—31no—
59C22×C5×D3—31no—
60C22×C5×D3—61no—
61C2×C3×C4×C5—31no—
62C2×C3×C4×C5—31no—
63C2×Dic15C2×D311yescharacteristic
64C2×Dic15C2×D311yescharacteristic
65C4×D15—62no—
66C2×C5×Dic3C2×D311yescharacteristic
67C2×C5×Dic3C2×D311yescharacteristic
68C2×C3×Dic5—21no—
69C2×C3×Dic5—31no—
70C2×C3×Dic5—31no—
71C2×C3×Dic5C2×D311yescharacteristic
72C2×C3×Dic5C2×D311yescharacteristic
73#1203—62no—
74#1203—62no—
75#1203—64no—
76#1200—62no—
77#894—151no—
78#894—151no—
79C2×C32×C5C2×D411yescharacteristic
80C2×C32×C5#4111yescharacteristic
81C2×C32×C5#4111yescharacteristic
82C3⋊D15—22no—
83C5×C3⋊D3—41no—
84C2×C22⋊D5—91no—
85C2×C4×D5—91no—
86C5×C22⋊C4—91no—
87C22⋊Dic5—91no—
88#685—91no—
89C4⋊Dic5—31no—
90#683—31no—
91C22×C3⋊D3—51no—
92C22×C3⋊D3C2×D511yescharacteristic
93C2×C32×C4—51no—
94C4⋊(C3⋊D3)—102no—
95C2×C3×Dic3—51no—
96C2×C3×Dic3—51no—
97C2×C3×Dic3C2×D511yescharacteristic
98C2×C3×Dic3C2×D511yescharacteristic
99#624—102no—
100C22×C3×C5—21no—
101C22×C3×C5C22×D311yescharacteristic
102C22×C3×C5C22×D311yescharacteristic
103C2×D15—32no—
104C2×D15—32no—
105C2×D15—62no—
106C2×D15—61no—
107C2×D15—61no—
108C2×D15—61no—
109C2×D15—61no—
110C2×D15—121no—
111C2×D15—121no—
112C2×C5×D3—62no—
113C2×C5×D3—61no—
114C2×C5×D3—61no—
115C2×C5×D3—61no—
116C2×C5×D3—61no—
117C2×C5×D3—61no—
118C2×C5×D3—61no—
119C2×C5×D3—121no—
120C2×C5×D3—121no—
121C3×C4×C5—61no—
122C3×C4×C5—61no—
123Dic15—21no—
124Dic15—21no—
125C3×Dic5—22no—
126C3×Dic5—21no—
127C3×Dic5—21no—
128C3×Dic5—61no—
129C3×Dic5—61no—
130C5×Dic3—21no—
131C5×Dic3—21no—
132C2×D12—151no—
133C2×D12—151no—
134C2×D12—301no—
135C2×C4×D3—151no—
136C2×C4×D3—151no—
137C3×C4⋊C4—151no—
138C3×C4⋊C4—151no—
139(C2×D3)⋊C4—31no—
140(C2×D3)⋊C4—31no—
141(C2×D3)⋊C4—151no—
142(C2×D3)⋊C4—151no—
143(C2×D3)⋊C4—151no—
144(C2×D3)⋊C4—151no—
145Dic3⋊C4—51no—
146Dic3⋊C4—51no—
147C32×C5#12311yescharacteristic, complemented, Hall
148C23×C5—91no—
149C22×D5—91no—
150C2×C4×C5—31no—
151C2×C4×C5—31no—
152C22⋊D5—182no—
153C2×Dic5—31no—
154C2×Dic5—31no—
155C2×Dic5D3211yescharacteristic
156C4×D5—182no—
157C22×C32C22×D511yescharacteristic
158C2×C3⋊D3—21no—
159C2×C3⋊D3—21no—
160C2×C3⋊D3—21no—
161C2×C3⋊D3—52no—
162C2×C3⋊D3—101no—
163C2×C3⋊D3—101no—
164C32×C4—101no—
165C3×Dic3—21no—
166C3×Dic3—21no—
167C3×Dic3—101no—
168C3×Dic3—101no—
169#123—451noSylow
170C2×C3×C5—21no—
171C2×C3×C5—21no—
172C2×C3×C5—21no—
173C2×C3×C5#23511yescharacteristic
174C2×C3×C5#23511yescharacteristic
175C2×C3×C5D3×D411yescharacteristic
176C2×C3×C5D3×D411yescharacteristic
177C2×C3×C5#23911yescharacteristic
178C2×C3×C5#23911yescharacteristic
179D15—62no—
180D15—62no—
181D15—122no—
182C5×D3—122no—
183C5×D3—121no—
184C5×D3—121no—
185C22×D3—31no—
186C22×D3—31no—
187C22×D3—61no—
188C22×D3—151no—
189C22×D3—151no—
190C22×D3—301no—
191C2×C3×C4—31no—
192C2×C3×C4—31no—
193C2×C3×C4—51no—
194C2×C3×C4—51no—
195C2×C3×C4—101no—
196C2×C3×C4—151no—
197C2×C3×C4—151no—
198C2×Dic3—51no—
199C2×Dic3—51no—
200C2×Dic3D3×D511yescharacteristic
201C2×Dic3D3×D511yescharacteristic
202D12—302no—
203D12—302no—
204D12—304no—
205C4×D3—302no—
206C4×D3—302no—
207C22×C5—181no—
208C22×C5—181no—
209C22×C5—181no—
210C22×C5C2×D3211yescharacteristic
211C2×D5—92no—
212C2×D5—181no—
213C2×D5—181no—
214C4×C5—61no—
215C4×C5—61no—
216Dic5—21no—
217Dic5—61no—
218Dic5—61no—
219C2×C32#70911yescharacteristic
220C2×C32D4×D511yescharacteristic
221C2×C32#71111yescharacteristic
222C3⋊D3—41no—
223C3⋊D3—102no—
224C2×D4—451no—
225C22×C4—451no—
226C4⋊C4—151no—
227C4⋊C4—151no—
228C22⋊C4—91no—
229C22⋊C4—451no—
230C22⋊C4—451no—
231C3×C5—21no—
232C3×C5#89411yescharacteristic, complemented
233C3×C5#89411yescharacteristic, complemented
234C22×C3—21no—
235C22×C3C2×D3×D511yescharacteristic
236C22×C3C2×D3×D511yescharacteristic
237C2×D3—62no—
238C2×D3—61no—
239C2×D3—61no—
240C2×D3—61no—
241C2×D3—61no—
242C2×D3—61no—
243C2×D3—61no—
244C2×D3—121no—
245C2×D3—121no—
246C2×D3—152no—
247C2×D3—152no—
248C2×D3—302no—
249C2×D3—301no—
250C2×D3—301no—
251C2×D3—301no—
252C2×D3—301no—
253C2×D3—601no—
254C2×D3—601no—
255C3×C4—61no—
256C3×C4—61no—
257C3×C4—102no—
258C3×C4—101no—
259C3×C4—101no—
260C3×C4—301no—
261C3×C4—301no—
262Dic3—21no—
263Dic3—21no—
264Dic3—101no—
265Dic3—101no—
266C2×C5—361no—
267C2×C5#379911yescharacteristic
268C2×C5#379911yescharacteristic
269C2×C5#381111yescharacteristic
270D5—182no—
271C32#402911yescharacteristic, complemented, Sylow
272C23—91no—
273C23—451no—
274D4—902no—
275C2×C4—31no—
276C2×C4—31no—
277C2×C4—51no—
278C2×C4—151no—
279C2×C4—151no—
280C2×C4—902no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3#676811yescharacteristic
285C2×C3#676911yescharacteristic
286C2×C3#677111yescharacteristic
287C2×C3#677711yescharacteristic
288C2×C3#678211yescharacteristic
289C2×C3#679011yescharacteristic
290D3—122no—
291D3—121no—
292D3—121no—
293D3—302no—
294D3—302no—
295D3—602no—
296C5#6389711yescharacteristic, complemented, Sylow
297C22—181no—
298C22—181no—
299C22—181no—
300C22—452no—
301C22—901no—
302C22—901no—
303C22D32×D511yescharacteristic
304C4—61no—
305C4—61no—
306C4—101no—
307C4—301no—
308C4—301no—
309C3—21no—
310C3#9135511yescharacteristic, complemented
311C3#9143811yescharacteristic, complemented
312C2—361no—
313C2—902no—
314C2#1062403011yescharacteristic
315C2#1062405111yescharacteristic
316C2#1062405411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutator, Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×#67140C2
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
1. C2×#67149C2semidirect
3. #10623830C2semidirect
4. #10623813C2semidirect
5. C5×#3722C2semidirect
6. C3×Dic3⋊Dic5C2semidirect
7. C3×#6669C2semidirect
30. Dic3⋊Dic5D3semidirect
31. #6669D3semidirect
54. #3722D5semidirect
147. C32×C5#123semidirect
232. C3×C5#894semidirect
233. C3×C5#894semidirect
271. C32#4029semidirect
296. C5#63897semidirect
310. C3#91355semidirect
311. C3#91438semidirect

Maximal subgroups

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

subgroupindex
C2×#671492
C2×#671402
#106238302
#106238132
C5×#37222
C3×Dic3⋊Dic52
C3×#66692
#914383
#913553
#638975