Finite Group Databasebeta

← #13085936

Subgroups — #13085936

Order 1440.

430 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 92 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×#67155C211yesmaximal, characteristic, complemented
2C2×#67149C211yesmaximal, characteristic, complemented
3C2×#67140C211yesmaximal, characteristic
4#10623813C211yesmaximal, characteristic, complemented
5C5×#3722C211yesmaximal, characteristic, complemented
6C3×#6668C211yesmaximal, characteristic, complemented
7C3×Dic3×Dic5C211yesmaximal, characteristic, complemented
8#91406—31nomaximal
9#91405—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#67155—22no—
18#67149—22no—
19#67140C414yescomplemented
20#63894—51nomaximal, Hall
21C2×C4×D15—31no—
22C2×#1203—31no—
23C2×#1203—31no—
24C2×#1203—61no—
25C2×#1200—31no—
26C2×D3×Dic5—31no—
27C2×D3×Dic5—31no—
28#6714—31no—
29C5×(C2×D3)⋊C4—31no—
30C5×(C2×D3)⋊C4—31no—
31C3×#683—31no—
32C3×C4×Dic5—31no—
33#6668D311yescharacteristic, complemented
34#6667—31no—
35Dic3×Dic5D311yescharacteristic, complemented
36C22×C32×C5C2311yescharacteristic
37C2×C3⋊D15—21no—
38C2×C3⋊D15—21no—
39C2×C3⋊D15C2×C412yescomplemented
40C2×C5×C3⋊D3—21no—
41C2×C5×C3⋊D3—21no—
42C2×C5×C3⋊D3C2×C412yescomplemented
43C3×Dic15—21no—
44C3×Dic15D412yescomplemented
45C3×C5×Dic3—21no—
46C3×C5×Dic3—21no—
47C32×Dic5C2×C412yescomplemented
48#4027—91noHall
49C2×C4⋊(C3⋊D3)—51no—
50C2×#624—51no—
51C2×#624—51no—
52C3×C4⋊Dic3—51no—
53C3×C4×Dic3—51no—
54#3722—51no—
55#3722D511yescharacteristic, complemented
56C22×D15—31no—
57C22×D15—31no—
58C22×D15—61no—
59C22×C5×D3—31no—
60C22×C5×D3—31no—
61C22×C5×D3—61no—
62C2×C3×C4×C5—31no—
63C2×C3×C4×C5—31no—
64C2×Dic15C2×D311yescharacteristic
65C2×Dic15C2×D311yescharacteristic
66C4×D15—62no—
67C2×C5×Dic3C2×D311yescharacteristic
68C2×C5×Dic3C2×D311yescharacteristic
69C2×C3×Dic5—21no—
70C2×C3×Dic5—31no—
71C2×C3×Dic5—31no—
72C2×C3×Dic5C2×D311yescharacteristic
73C2×C3×Dic5C2×D311yescharacteristic
74#1203—34no—
75#1203—34no—
76#1203—64no—
77#1200—62no—
78D3×Dic5—62no—
79D3×Dic5—62no—
80#893—151no—
81C4×D12—151no—
82C2×C32×C5C22×C411yescharacteristic
83C2×C32×C5C2×D411yescharacteristic
84C2×C32×C5#4111yescharacteristic
85C3⋊D15—22no—
86C5×C3⋊D3—22no—
87C2×C22⋊D5—91no—
88C22×Dic5—91no—
89C2×C4×D5—91no—
90C5×C22⋊C4—91no—
91#685—91no—
92#683—31no—
93C4×Dic5—31no—
94C22×C3⋊D3—51no—
95C22×C3⋊D3C2×D511yescharacteristic
96C2×C32×C4—51no—
97C4⋊(C3⋊D3)—54no—
98C2×C3×Dic3—51no—
99C2×C3×Dic3—51no—
100C2×C3×Dic3C2×D511yescharacteristic
101C2×C3×Dic3C2×D511yescharacteristic
102#624—102no—
103#624—102no—
104C22×C3×C5—21no—
105C22×C3×C5C22×D311yescharacteristic
106C22×C3×C5C22×D311yescharacteristic
107C2×D15—32no—
108C2×D15—32no—
109C2×D15—62no—
110C2×D15—61no—
111C2×D15—61no—
112C2×D15—61no—
113C2×D15—61no—
114C2×D15—121no—
115C2×D15—121no—
116C2×C5×D3—32no—
117C2×C5×D3—32no—
118C2×C5×D3—62no—
119C2×C5×D3—61no—
120C2×C5×D3—61no—
121C2×C5×D3—61no—
122C2×C5×D3—61no—
123C2×C5×D3—121no—
124C2×C5×D3—121no—
125C3×C4×C5—61no—
126C3×C4×C5—61no—
127Dic15—21no—
128Dic15D1212yescomplemented
129C3×Dic5—22no—
130C3×Dic5—32no—
131C3×Dic5—61no—
132C3×Dic5C4×D312yescomplemented
133C3×Dic5C4×D312yescomplemented
134C5×Dic3—21no—
135C5×Dic3—21no—
136C2×D12—151no—
137C2×D12—151no—
138C2×D12—301no—
139C2×C4×D3—151no—
140C2×C4×D3—151no—
141C2×C4×D3—151no—
142C2×C4×D3—151no—
143C3×C4⋊C4—151no—
144C3×C42—151no—
145(C2×D3)⋊C4—31no—
146(C2×D3)⋊C4—31no—
147(C2×D3)⋊C4—151no—
148(C2×D3)⋊C4—151no—
149C4⋊Dic3—51no—
150C4×Dic3—51no—
151C32×C5C4×D411yescharacteristic, complemented, Hall
152C23×C5—91no—
153C22×D5—91no—
154C2×C4×C5—31no—
155C2×C4×C5—31no—
156C22⋊D5—94no—
157C2×Dic5—31no—
158C2×Dic5—31no—
159C2×Dic5—182no—
160C2×Dic5D3211yescharacteristic
161C4×D5—182no—
162C22×C32C22×D511yescharacteristic
163C2×C3⋊D3—21no—
164C2×C3⋊D3—21no—
165C2×C3⋊D3—52no—
166C2×C3⋊D3—101no—
167C2×C3⋊D3—101no—
168C2×C3⋊D3C4×D512yescomplemented
169C32×C4—52no—
170C3×Dic3—21no—
171C3×Dic3—21no—
172C3×Dic3—52no—
173C3×Dic3—101no—
174C4×D4—451noSylow
175C2×C3×C5—21no—
176C2×C3×C5—21no—
177C2×C3×C5—21no—
178C2×C3×C5C2×C4×D311yescharacteristic
179C2×C3×C5C2×C4×D311yescharacteristic
180C2×C3×C5C2×D1211yescharacteristic
181C2×C3×C5#23511yescharacteristic
182C2×C3×C5D3×D411yescharacteristic
183C2×C3×C5#23911yescharacteristic
184D15—62no—
185D15—62no—
186D15—122no—
187C5×D3—62no—
188C5×D3—62no—
189C5×D3—122no—
190C22×D3—31no—
191C22×D3—31no—
192C22×D3—61no—
193C22×D3—151no—
194C22×D3—151no—
195C22×D3—301no—
196C2×C3×C4—31no—
197C2×C3×C4—31no—
198C2×C3×C4—51no—
199C2×C3×C4—51no—
200C2×C3×C4—101no—
201C2×C3×C4—151no—
202C2×C3×C4—151no—
203C2×Dic3—51no—
204C2×Dic3—51no—
205C2×Dic3D3×D511yescharacteristic
206C2×Dic3D3×D511yescharacteristic
207D12—154no—
208D12—154no—
209D12—304no—
210C4×D3—302no—
211C4×D3—302no—
212C4×D3—302no—
213C4×D3—302no—
214C22×C5—92no—
215C22×C5—181no—
216C22×C5—181no—
217C22×C5C2×D3211yescharacteristic
218C2×D5—92no—
219C2×D5—181no—
220C2×D5—181no—
221C4×C5—61no—
222C4×C5—61no—
223Dic5—32no—
224Dic5—61no—
225Dic5#62412yescomplemented
226C2×C32C2×C4×D511yescharacteristic
227C2×C32D4×D511yescharacteristic
228C2×C32#71111yescharacteristic
229C3⋊D3—22no—
230C3⋊D3—102no—
231C2×D4—451no—
232C22×C4—451no—
233C22×C4—451no—
234C4⋊C4—151no—
235C22⋊C4—91no—
236C22⋊C4—451no—
237C42—151no—
238C3×C5—21no—
239C3×C5C4×D1211yescharacteristic, complemented
240C3×C5#89311yescharacteristic, complemented
241C22×C3—21no—
242C22×C3C2×D3×D511yescharacteristic
243C22×C3C2×D3×D511yescharacteristic
244C2×D3—32no—
245C2×D3—32no—
246C2×D3—62no—
247C2×D3—61no—
248C2×D3—61no—
249C2×D3—61no—
250C2×D3—61no—
251C2×D3—121no—
252C2×D3—121no—
253C2×D3—152no—
254C2×D3—152no—
255C2×D3—302no—
256C2×D3—301no—
257C2×D3—301no—
258C2×D3—301no—
259C2×D3—301no—
260C2×D3—601no—
261C2×D3—601no—
262C3×C4—52no—
263C3×C4—52no—
264C3×C4—61no—
265C3×C4—61no—
266C3×C4—102no—
267C3×C4—152no—
268C3×C4—301no—
269Dic3—21no—
270Dic3—21no—
271Dic3—52no—
272Dic3—101no—
273C2×C5—182no—
274C2×C5#379911yescharacteristic
275C2×C5D3×D1211yescharacteristic
276C2×C5C2×#62411yescharacteristic
277D5—182no—
278C32#402711yescharacteristic, complemented, Sylow
279C23—91no—
280C23—451no—
281D4—454no—
282C2×C4—31no—
283C2×C4—31no—
284C2×C4—51no—
285C2×C4—151no—
286C2×C4—151no—
287C2×C4—902no—
288C2×C4—902no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3#676811yescharacteristic
293C2×C3C4×D3×D511yescharacteristic
294C2×C3C4×D3×D511yescharacteristic
295C2×C3D5×D1211yescharacteristic
296C2×C3#678211yescharacteristic
297C2×C3#679011yescharacteristic
298D3—62no—
299D3—62no—
300D3—122no—
301D3—302no—
302D3—302no—
303D3—602no—
304C5#6389411yescharacteristic, complemented, Sylow
305C22—92no—
306C22—181no—
307C22—181no—
308C22—452no—
309C22—901no—
310C22—901no—
311C22D32×D511yescharacteristic
312C4—52no—
313C4—61no—
314C4—61no—
315C4—152no—
316C4—301no—
317C3—21no—
318C3#9140511yescharacteristic, complemented
319C3#9140611yescharacteristic, complemented
320C2—182no—
321C2—902no—
322C2D5×#62411yescharacteristic
323C2#1062403311yescharacteristic
324C2#1062405111yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutatorC2×C32×C5C22×C4
Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×#67140C2
hypocenterC32×C5C4×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#67155C2semidirect
2. C2×#67149C2semidirect
4. #10623813C2semidirect
5. C5×#3722C2semidirect
6. C3×#6668C2semidirect
7. C3×Dic3×Dic5C2semidirect
19. #67140C4semidirect
33. #6668D3semidirect
35. Dic3×Dic5D3semidirect
39. C2×C3⋊D15C2×C4semidirect
42. C2×C5×C3⋊D3C2×C4semidirect
44. C3×Dic15D4semidirect
47. C32×Dic5C2×C4semidirect
55. #3722D5semidirect
128. Dic15D12semidirect
132. C3×Dic5C4×D3semidirect
133. C3×Dic5C4×D3semidirect
151. C32×C5C4×D4semidirect
168. C2×C3⋊D3C4×D5semidirect
225. Dic5#624semidirect
239. C3×C5C4×D12semidirect
240. C3×C5#893semidirect
278. C32#4027semidirect
304. C5#63894semidirect
318. C3#91405semidirect
319. C3#91406semidirect

Maximal subgroups

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

subgroupindex
C2×#671552
C2×#671492
C2×#671402
#106238132
C5×#37222
C3×#66682
C3×Dic3×Dic52
#914063
#914053
#638945