Finite Group Databasebeta

← C2×#10624045 #13089028

Subgroups — C2×#10624045 #13089028

Order 1440.

710 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 156 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×#67154C211yesmaximal, characteristic, complemented
2C2×#67153C211yesmaximal, characteristic, complemented
3C2×#67150C211yesmaximal, characteristic, complemented
4C2×C5×D3×Dic3C211yesmaximal, characteristic, complemented
5C2×D5×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C2×C3×#1202C211yesmaximal, characteristic, complemented
7C2×C3×#1201C211yesmaximal, characteristic, complemented
8#10624045C218yesmaximal, direct product factor
9C2×#6779—31nomaximal
10C2×#6765—31nomaximal
11C22×C3×D15C2211yescharacteristic
12C22×C3×C5×D3C2211yescharacteristic
13C22×C32×D5C2211yescharacteristic
14C2×C3⋊Dic15C2211yescharacteristic
15C2×C5×C3⋊Dic3C2211yescharacteristic
16C2×C3×Dic15C2211yescharacteristic
17C2×C3×C5×Dic3C2211yescharacteristic
18#67154C2214yescomplemented
19#67153C2214yescomplemented
20#67150C2214yescomplemented
21C5×D3×Dic3C2214yescomplemented
22D5×C3⋊Dic3C2214yescomplemented
23C3×#1202C2214yescomplemented
24C3×#1201C2214yescomplemented
25C2×#3805—51nomaximal, Hall
26C2×#1220—31no—
27C2×Dic30—31no—
28C22×C5×Dic3—31no—
29C2×C4×C5×D3—31no—
30C2×C3×C22⋊D5—31no—
31C2×C3×D20—31no—
32C2×#1204—31no—
33C2×#1202D311yescharacteristic, complemented
34C2×#1201—31no—
35C2×#1201D311yescharacteristic, complemented
36C2×#1200—31no—
37#6779—38no—
38C2×D5×Dic3—31no—
39C2×D5×Dic3—31no—
40C2×D5×Dic3—31no—
41C2×D5×Dic3—61no—
42#6765—38no—
43C22×C32×C5C2311yescharacteristic
44C2×C3×D15—22no—
45C2×C3×D15C2312yes—
46C2×C3×C5×D3—22no—
47C2×C3×C5×D3C2312yes—
48C2×C32×D5—22no—
49C2×C32×D5C2312yes—
50C3⋊Dic15C2312yes—
51C5×C3⋊Dic3C2312yes—
52C3×Dic15C2312yes—
53C3×C5×Dic3C2312yes—
54C2×#709—91noHall
55C22×C3⋊Dic3—51no—
56C2×C3×#67—51no—
57C2×C3×#67—51no—
58C2×#627—51no—
59C2×#625—51no—
60#3805—58no—
61C2×D3×Dic3—51no—
62C2×D3×Dic3D511yescharacteristic, complemented
63C23×C3×C5—31no—
64C22×D15C2×D311yescharacteristic
65C22×C5×D3C2×D311yescharacteristic
66C22×C3×D5—21no—
67C22×C3×D5—31no—
68C22×C3×D5C2×D311yescharacteristic
69C22×C3×D5C2×D311yescharacteristic
70C2×C3×C4×C5—31no—
71#1220—34no—
72C2×Dic15—31no—
73C2×Dic15—31no—
74C2×Dic15—61no—
75C2×Dic15C2×D311yescharacteristic
76Dic30—34no—
77C2×C5×Dic3—31no—
78C2×C5×Dic3—31no—
79C2×C5×Dic3—34no—
80C2×C5×Dic3—61no—
81C2×C5×Dic3C2×D311yescharacteristic
82C4×C5×D3—34no—
83C3×C22⋊D5—34no—
84C2×C3×Dic5—31no—
85C3×D20—34no—
86#1204—34no—
87#1202C2×D314yescomplemented
88#1201—34no—
89#1201C2×D314yescomplemented
90#1200—34no—
91D5×Dic3—34no—
92D5×Dic3—34no—
93D5×Dic3—34no—
94D5×Dic3—64no—
95C2×#237—151no—
96C2×#237—151no—
97C2×C32×C5#4112yescomplemented
98C2×C32×C5C2411yescharacteristic
99C3×D15—22no—
100C3×C5×D3—22no—
101C32×D5—22no—
102C22×C4×C5—91no—
103C2×C22⋊D5—31no—
104C2×C22⋊D5—91no—
105#709—98no—
106C2×D20—31no—
107C2×C4×D5—91no—
108C2×C4×D5—91no—
109C2×Dic10—91no—
110C23×C32—51no—
111C22×C3×D3—51no—
112C22×C3×D3C2×D511yescharacteristic
113C2×C3⋊Dic3—51no—
114C2×C3⋊Dic3—54no—
115C2×C3⋊Dic3C2×D511yescharacteristic
116C3×#67—54no—
117C3×#67—54no—
118C2×C3×Dic3—51no—
119C2×C3×Dic3C2×D511yescharacteristic
120#627—54no—
121#625—54no—
122D3×Dic3—54no—
123D3×Dic3C2×D514yescomplemented
124C22×C3×C5—21no—
125C22×C3×C5—32no—
126C22×C3×C5—62no—
127C22×C3×C5C22×D311yescharacteristic
128C22×C3×C5C22×D311yescharacteristic
129C2×D15—22no—
130C2×D15C22×D312yes—
131C2×C5×D3—22no—
132C2×C5×D3C22×D312yes—
133C2×C3×D5—24no—
134C2×C3×D5—22no—
135C2×C3×D5—22no—
136C2×C3×D5—22no—
137C2×C3×D5—32no—
138C2×C3×D5—62no—
139C2×C3×D5C22×D312yes—
140C2×C3×D5C22×D312yes—
141C3×C4×C5—32no—
142Dic15—32no—
143Dic15—32no—
144Dic15—62no—
145Dic15C22×D312yes—
146C3×Dic5—32no—
147C5×Dic3—32no—
148C5×Dic3—32no—
149C5×Dic3—62no—
150C5×Dic3C22×D312yes—
151C2×C3×D4—151no—
152C2×C3×D4—151no—
153C2×#67—51no—
154C2×#67—51no—
155C2×#67—151no—
156C2×#67—151no—
157C22×Dic3—31no—
158C22×Dic3—151no—
159C22×Dic3—151no—
160C22×Dic3—151no—
161C22×Dic3—301no—
162#237—158no—
163#237—158no—
164C2×C4×D3—31no—
165C2×C4×D3—151no—
166C2×Dic6—151no—
167C2×Dic6—151no—
168C32×C5C2×#4111yescharacteristic, complemented, Hall
169C23×C5—31no—
170C22×D5—31no—
171C22×D5D3211yescharacteristic
172C2×C4×C5—31no—
173C2×C4×C5—94no—
174C2×C4×C5—91no—
175C22⋊D5—34no—
176C22⋊D5—94no—
177C2×Dic5—31no—
178C2×Dic5—91no—
179D20—34no—
180C4×D5—94no—
181C4×D5—94no—
182Dic10—94no—
183C22×C32—52no—
184C22×C32—102no—
185C22×C32C22×D511yescharacteristic
186C2×C3×D3—22no—
187C2×C3×D3—52no—
188C2×C3×D3—102no—
189C2×C3×D3C22×D512yes—
190C3⋊Dic3—52no—
191C3⋊Dic3C22×D512yes—
192C3×Dic3—52no—
193C3×Dic3C22×D512yes—
194C2×#41—451noSylow
195C2×C3×C5—21no—
196C2×C3×C5—22no—
197C2×C3×C5—62no—
198C2×C3×C5#23712yescomplemented
199C2×C3×C5#23712yescomplemented
200C2×C3×C5C23×D311yescharacteristic
201C2×C3×C5C23×D311yescharacteristic
202D15—22no—
203C3×D5—24no—
204C3×D5—22no—
205C3×D5—22no—
206C3×D5—62no—
207C5×D3—22no—
208C23×C3—31no—
209C23×C3—51no—
210C23×C3—51no—
211C23×C3—101no—
212C23×C3—151no—
213C22×D3—51no—
214C22×D3D3×D511yescharacteristic
215C3×D4—154no—
216C3×D4—154no—
217C2×C3×C4—31no—
218C2×C3×C4—151no—
219#67—54no—
220#67—54no—
221#67—154no—
222#67—154no—
223C2×Dic3—31no—
224C2×Dic3—31no—
225C2×Dic3—34no—
226C2×Dic3—51no—
227C2×Dic3—61no—
228C2×Dic3—154no—
229C2×Dic3—154no—
230C2×Dic3—154no—
231C2×Dic3—151no—
232C2×Dic3—151no—
233C2×Dic3—304no—
234C2×Dic3—301no—
235C2×Dic3D3×D511yescharacteristic
236C4×D3—34no—
237C4×D3—154no—
238Dic6—154no—
239Dic6—154no—
240C22×C5—32no—
241C22×C5—62no—
242C22×C5C2×D3211yescharacteristic
243C2×D5—22no—
244C2×D5—32no—
245C2×D5—62no—
246C2×D5C2×D3212yes—
247C4×C5—32no—
248C4×C5—92no—
249Dic5—32no—
250Dic5—92no—
251C2×C32—102no—
252C2×C32#70912yescomplemented
253C2×C32C23×D511yescharacteristic
254C3×D3—22no—
255C3×D3—102no—
256#41—458no—
257C2×Q8—451no—
258C2×D4—151no—
259C2×D4—151no—
260C2×D4—451no—
261C22×C4—91no—
262C22×C4—451no—
263C22×C4—451no—
264C3×C5—21no—
265C3×C5C2×#23711yescharacteristic, complemented
266C3×C5C2×#23711yescharacteristic, complemented
267C22×C3—21no—
268C22×C3—32no—
269C22×C3—52no—
270C22×C3—52no—
271C22×C3—62no—
272C22×C3—102no—
273C22×C3—104no—
274C22×C3—102no—
275C22×C3—102no—
276C22×C3—152no—
277C22×C3—302no—
278C22×C3C2×D3×D511yescharacteristic
279C22×C3C2×D3×D511yescharacteristic
280C2×D3—22no—
281C2×D3—52no—
282C2×D3—102no—
283C2×D3C2×D3×D512yes—
284C3×C4—32no—
285C3×C4—152no—
286Dic3—32no—
287Dic3—32no—
288Dic3—52no—
289Dic3—62no—
290Dic3—152no—
291Dic3—152no—
292Dic3—302no—
293Dic3C2×D3×D512yes—
294C2×C5—62no—
295C2×C5#380512yescomplemented
296C2×C5C22×D3211yescharacteristic
297D5—22no—
298D5—62no—
299C32C2×#70911yescharacteristic, complemented, Sylow
300C23—31no—
301C23—51no—
302C23—151no—
303Q8—454no—
304D4—154no—
305D4—154no—
306D4—454no—
307C2×C4—31no—
308C2×C4—94no—
309C2×C4—91no—
310C2×C4—151no—
311C2×C4—454no—
312C2×C4—454no—
313C2×C4—451no—
314C2×C3—22no—
315C2×C3—21no—
316C2×C3—62no—
317C2×C3—104no—
318C2×C3—102no—
319C2×C3—102no—
320C2×C3—302no—
321C2×C3#676512yescomplemented
322C2×C3#677912yescomplemented
323C2×C3C22×D3×D511yescharacteristic
324C2×C3C22×D3×D511yescharacteristic
325D3—22no—
326D3—102no—
327C5C2×#380511yescharacteristic, complemented, Sylow
328C22—32no—
329C22—52no—
330C22—62no—
331C22—102no—
332C22—152no—
333C22—302no—
334C22D32×D511yescharacteristic
335C4—32no—
336C4—92no—
337C4—152no—
338C4—452no—
339C3—21no—
340C3C2×#676511yescharacteristic, complemented
341C3C2×#677911yescharacteristic, complemented
342C2—62no—
343C2—102no—
344C2—302no—
345C2#1062404512yesdirect product factor
346C2C2×D32×D511yescharacteristic
subgroupG/H
center, hypercenterC22D32×D5
commutator, cosocleC2×C32×C5C24
FrattiniC2C2×D32×D5
Fitting, socleC22×C32×C5C23
hypocenterC32×C5C2×#41
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#67154C2semidirect
2. C2×#67153C2semidirect
3. C2×#67150C2semidirect
4. C2×C5×D3×Dic3C2semidirect
5. C2×D5×C3⋊Dic3C2semidirect
6. C2×C3×#1202C2semidirect
7. C2×C3×#1201C2semidirect
8. #10624045C2direct (N × H)
18. #67154C22semidirect
19. #67153C22semidirect
20. #67150C22semidirect
21. C5×D3×Dic3C22semidirect
22. D5×C3⋊Dic3C22semidirect
23. C3×#1202C22semidirect
24. C3×#1201C22semidirect
33. C2×#1202D3semidirect
35. C2×#1201D3semidirect
62. C2×D3×Dic3D5semidirect
87. #1202C2×D3semidirect
89. #1201C2×D3semidirect
97. C2×C32×C5#41semidirect
123. D3×Dic3C2×D5semidirect
168. C32×C5C2×#41semidirect
198. C2×C3×C5#237semidirect
199. C2×C3×C5#237semidirect
252. C2×C32#709semidirect
265. C3×C5C2×#237semidirect
266. C3×C5C2×#237semidirect
295. C2×C5#3805semidirect
299. C32C2×#709semidirect
321. C2×C3#6765semidirect
322. C2×C3#6779semidirect
327. C5C2×#3805semidirect
340. C3C2×#6765semidirect
341. C3C2×#6779semidirect
345. C2#10624045direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#671542
C2×#671532
C2×#671502
C2×C5×D3×Dic32
C2×D5×C3⋊Dic32
C2×C3×#12022
C2×C3×#12012
#106240452
C2×#67793
C2×#67653
C2×#38055