Finite Group Databasebeta

← #13086119

Subgroups — #13086119

Order 1440.

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

normal subgroups only

This group has 338 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×#67153C211yesmaximal, characteristic, complemented
2C2×C3×#1201C211yesmaximal, characteristic
3#10623828C211yesmaximal, characteristic, complemented
4(C2×D3)⋊Dic15C211yesmaximal, characteristic, complemented
5C5×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
6#10623770C211yesmaximal, characteristic, complemented
7C3×#6665C211yesmaximal, characteristic, complemented
8#91534—31nomaximal
9#91462—31nomaximal
10C22×C3×C5×D3C2211yescharacteristic
11C22×C32×D5C2211yescharacteristic
12C2×C3⋊Dic15C2211yescharacteristic
13C2×C5×C3⋊Dic3C2211yescharacteristic
14C2×C3×Dic15C2211yescharacteristic
15C2×C3×Dic15C2211yescharacteristic
16C2×C3×C5×Dic3C2211yescharacteristic
17#67153—22no—
18C3×#1201—22no—
19#63959—51nomaximal, Hall
20C2×Dic30—31no—
21C2×C3×C22⋊D5—31no—
22C2×#1204—31no—
23C2×#1201D311yescharacteristic
24#6719—31no—
25C5×#217—31no—
26C5×(C2×D3)⋊C4—31no—
27C3×#685—31no—
28(C2×D3)⋊Dic5—31no—
29#6665—31no—
30#6665—31no—
31#6665—61no—
32#6665D311yescharacteristic, complemented
33Dic3×Dic5—31no—
34Dic3×Dic5—31no—
35C22×C32×C5C2311yescharacteristic
36C2×C3×C5×D3—21no—
37C2×C3×C5×D3—21no—
38C2×C3×C5×D3—21no—
39C2×C32×D5—21no—
40C2×C32×D5—21no—
41C2×C32×D5—21no—
42C3⋊Dic15—21no—
43C5×C3⋊Dic3—21no—
44C3×Dic15—21no—
45C3×Dic15D412yes—
46C3×C5×Dic3—21no—
47#4031—91noHall
48C2×C3×#67—51no—
49C2×#627—51no—
50#3757—51no—
51C3×#217—51no—
52(C2×D3)⋊Dic3—51no—
53(C2×D3)⋊Dic3D511yescharacteristic, complemented
54Dic32—51no—
55C23×C3×C5—31no—
56C22×C5×D3C2×D311yescharacteristic
57C22×C3×D5—21no—
58C22×C3×D5C2×D311yescharacteristic
59C22×C3×D5C2×D311yescharacteristic
60C2×C3×C4×C5—31no—
61C2×Dic15—31no—
62C2×Dic15—31no—
63C2×Dic15—61no—
64C2×Dic15C2×D311yescharacteristic
65C2×Dic15C2×D311yescharacteristic
66Dic30—62no—
67C2×C5×Dic3—31no—
68C2×C5×Dic3—31no—
69C2×C5×Dic3—61no—
70C2×C5×Dic3C2×D311yescharacteristic
71C3×C22⋊D5—62no—
72C2×C3×Dic5—31no—
73C2×C3×Dic5—31no—
74#1204—62no—
75#1201—22no—
76#936—151no—
77#885—151no—
78C2×C32×C5C2×D411yescharacteristic
79C2×C32×C5#4111yescharacteristic
80C2×C32×C5#4111yescharacteristic
81C3×C5×D3—41no—
82C32×D5—41no—
83C2×C22⋊D5—31no—
84C2×Dic10—91no—
85C5×C22⋊C4—91no—
86C22⋊Dic5—91no—
87#685—31no—
88#685—91no—
89C4×Dic5—91no—
90C23×C32—51no—
91C22×C3×D3C2×D511yescharacteristic
92C2×C3⋊Dic3—51no—
93C2×C3⋊Dic3C2×D511yescharacteristic
94C3×#67—102no—
95C2×C3×Dic3—51no—
96C2×C3×Dic3—51no—
97C2×C3×Dic3C2×D511yescharacteristic
98#627—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×C5×D3—21no—
106C2×C5×D3—21no—
107C2×C5×D3—21no—
108C2×C3×D5—22no—
109C2×C3×D5—21no—
110C2×C3×D5—21no—
111C2×C3×D5—21no—
112C2×C3×D5—21no—
113C2×C3×D5—21no—
114C2×C3×D5—21no—
115C2×C3×D5—41no—
116C2×C3×D5—41no—
117C3×C4×C5—61no—
118Dic15—21no—
119Dic15—61no—
120Dic15—61no—
121Dic15—121no—
122Dic15#6712yes—
123C3×Dic5—32no—
124C3×Dic5—61no—
125C5×Dic3—21no—
126C5×Dic3—61no—
127C5×Dic3—61no—
128C5×Dic3—121no—
129C2×C3×D4—151no—
130C2×#67—51no—
131C2×Dic6—151no—
132C2×Dic6—151no—
133C3×C22⋊C4—151no—
134#217—31no—
135#217—51no—
136#217—151no—
137#217—151no—
138#217—151no—
139#217—301no—
140(C2×D3)⋊C4—31no—
141(C2×D3)⋊C4—151no—
142C4×Dic3—151no—
143C4×Dic3—151no—
144C32×C5#12411yescharacteristic, complemented, Hall
145C23×C5—31no—
146C22×D5D3211yescharacteristic
147C2×C4×C5—31no—
148C2×C4×C5—91no—
149C22⋊D5—62no—
150C2×Dic5—31no—
151C2×Dic5—31no—
152C2×Dic5—91no—
153Dic10—182no—
154C22×C32—101no—
155C22×C32—101no—
156C22×C32—101no—
157C22×C32C22×D511yescharacteristic
158C2×C3×D3—21no—
159C2×C3×D3—21no—
160C2×C3×D3—21no—
161C3⋊Dic3—21no—
162C3⋊Dic3—101no—
163C3×Dic3—21no—
164C3×Dic3—52no—
165C3×Dic3—101no—
166#124—451noSylow
167C2×C3×C5—21no—
168C2×C3×C5—21no—
169C2×C3×C5—21no—
170C2×C3×C5—121no—
171C2×C3×C5#23511yescharacteristic
172C2×C3×C5D3×D411yescharacteristic
173C2×C3×C5#23711yescharacteristic
174C2×C3×C5#23711yescharacteristic
175C2×C3×C5#23711yescharacteristic
176C2×C3×C5C2×#6711yescharacteristic
177C3×D5—42no—
178C3×D5—41no—
179C3×D5—41no—
180C5×D3—41no—
181C23×C3—31no—
182C23×C3—51no—
183C23×C3—51no—
184C23×C3—101no—
185C22×D3D3×D511yescharacteristic
186C3×D4—302no—
187C2×C3×C4—31no—
188C2×C3×C4—151no—
189C2×C3×C4—151no—
190#67—102no—
191C2×Dic3—31no—
192C2×Dic3—31no—
193C2×Dic3—51no—
194C2×Dic3—51no—
195C2×Dic3—61no—
196C2×Dic3—151no—
197C2×Dic3—151no—
198C2×Dic3—301no—
199C2×Dic3D3×D511yescharacteristic
200Dic6—302no—
201Dic6—302no—
202C22×C5—61no—
203C22×C5—61no—
204C22×C5—61no—
205C22×C5C2×D3211yescharacteristic
206C2×D5—21no—
207C2×D5—21no—
208C2×D5—21no—
209C4×C5—61no—
210C4×C5—181no—
211Dic5—32no—
212Dic5—61no—
213Dic5—181no—
214C2×C32—201no—
215C2×C32#70911yescharacteristic
216C2×C32D4×D511yescharacteristic
217C2×C32#71111yescharacteristic
218C3×D3—41no—
219C2×Q8—451no—
220C2×D4—151no—
221C22⋊C4—91no—
222C22⋊C4—151no—
223C22⋊C4—451no—
224C22⋊C4—451no—
225C42—451no—
226C3×C5—21no—
227C3×C5#88511yescharacteristic, complemented
228C3×C5#93611yescharacteristic, complemented
229C22×C3—21no—
230C22×C3—61no—
231C22×C3—61no—
232C22×C3—61no—
233C22×C3—102no—
234C22×C3—101no—
235C22×C3—101no—
236C22×C3—101no—
237C22×C3—101no—
238C22×C3—101no—
239C22×C3—101no—
240C22×C3—201no—
241C22×C3—201no—
242C22×C3C2×D3×D511yescharacteristic
243C22×C3C2×D3×D511yescharacteristic
244C2×D3—21no—
245C2×D3—21no—
246C2×D3—21no—
247C3×C4—61no—
248C3×C4—152no—
249C3×C4—301no—
250Dic3—21no—
251Dic3—52no—
252Dic3—61no—
253Dic3—61no—
254Dic3—101no—
255Dic3—121no—
256Dic3—301no—
257Dic3—301no—
258Dic3—601no—
259C2×C5—121no—
260C2×C5#380411yescharacteristic
261C2×C5#380511yescharacteristic
262C2×C5D3×#6711yescharacteristic
263D5—41no—
264C32#403111yescharacteristic, complemented, Sylow
265C23—31no—
266C23—51no—
267Q8—902no—
268D4—302no—
269C2×C4—31no—
270C2×C4—91no—
271C2×C4—151no—
272C2×C4—151no—
273C2×C4—451no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—121no—
278C2×C3—202no—
279C2×C3—201no—
280C2×C3—201no—
281C2×C3#676511yescharacteristic
282C2×C3#677211yescharacteristic
283C2×C3#677911yescharacteristic
284C2×C3#678011yescharacteristic
285C2×C3D5×#6711yescharacteristic
286C2×C3#679011yescharacteristic
287D3—41no—
288C5#6395911yescharacteristic, complemented, Sylow
289C22—61no—
290C22—61no—
291C22—61no—
292C22—101no—
293C22—101no—
294C22—101no—
295C22D32×D511yescharacteristic
296C4—61no—
297C4—152no—
298C4—181no—
299C4—301no—
300C4—901no—
301C3—21no—
302C3#9146211yescharacteristic, complemented
303C3#9153411yescharacteristic, complemented
304C2—121no—
305C2—201no—
306C2#1062402711yescharacteristic
307C2#1062404311yescharacteristic
308C2#1062404511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC22D32×D5
commutator, Fitting, socle, cosocleC22×C32×C5C23
prime radicalC2×C3×#1201C2
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. #10623828C2semidirect
4. (C2×D3)⋊Dic15C2semidirect
5. C5×(C2×D3)⋊Dic3C2semidirect
6. #10623770C2semidirect
7. C3×#6665C2semidirect
32. #6665D3semidirect
53. (C2×D3)⋊Dic3D5semidirect
144. C32×C5#124semidirect
227. C3×C5#885semidirect
228. C3×C5#936semidirect
264. C32#4031semidirect
288. C5#63959semidirect
302. C3#91462semidirect
303. C3#91534semidirect

Maximal subgroups

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

subgroupindex
C2×#671532
C2×C3×#12012
#106238282
(C2×D3)⋊Dic152
C5×(C2×D3)⋊Dic32
#106237702
C3×#66652
#915343
#914623
#639595