Finite Group Databasebeta

← #11754339

Subgroups — #11754339

Order 960.

660 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 152 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
1C22×C4×C5×D3C211yesmaximal, characteristic, complemented
2C2×#6779C211yesmaximal, characteristic, complemented
3#91818C211yesmaximal, characteristic, complemented
4C3×#4075C211yesmaximal, characteristic, complemented
5#91570C211yesmaximal, characteristic, complemented
6#91568C211yesmaximal, characteristic, complemented
7#91529C211yesmaximal, characteristic, complemented
8#91454C212yesmaximal, complemented
9#91446C212yesmaximal, complemented
10#91441C212yesmaximal, complemented
11#91352C212yesmaximal, complemented
12#66125—31nomaximal, Hall
13C23×C5×D3C2211yescharacteristic
14C22×C3×C4×C5C2211yescharacteristic
15C2×#1220C2211yescharacteristic
16C22×C5×Dic3C2211yescharacteristic
17C2×C4×C5×D3—24no—
18C2×C4×C5×D3C2212yes—
19C2×C4×C5×D3C2212yes—
20C2×C3×C22⋊D5C2211yescharacteristic
21C2×#1204C2211yescharacteristic, complemented
22C2×#1203C2212yes—
23C2×#1202C2211yescharacteristic, complemented
24C2×#1201C2212yes—
25C2×#1200C2211yescharacteristic, complemented
26#6779—24no—
27C2×D5×Dic3C2211yescharacteristic, complemented
28#6719C2211yescharacteristic
29#6714C2212yescomplemented
30#6712C2212yescomplemented
31C3×C22⋊Dic5C2211yescharacteristic
32C3×#685C2212yescomplemented
33C3×#683C2212yescomplemented
34Dic3⋊Dic5C2212yescomplemented
35(C2×D3)⋊Dic5C2212yes—
36(C2×D3)⋊Dic5C2212yes—
37Dic3×Dic5C2212yescomplemented
38#5656—51nomaximal, Hall
39C23×C4×C5—31no—
40C2×#709—31no—
41#4099—31no—
42#4099—31no—
43#4076—32no—
44#4075—31no—
45#4075D311yescharacteristic, complemented
46C4×C22⋊D5—32no—
47C4×C22⋊D5—32no—
48#4072—31no—
49#4070—32no—
50C23×C3×C5C2311yescharacteristic
51C22×D15C2311yescharacteristic
52C22×C5×D3—22no—
53C22×C5×D3—24no—
54C22×C5×D3C2312yes—
55C22×C3×D5C2311yescharacteristic
56C2×C3×C4×C5—22no—
57C2×C3×C4×C5C2312yes—
58#1220—22no—
59C2×Dic15C2312yes—
60C2×Dic15C2311yescharacteristic
61C2×C5×Dic3D414yescomplemented
62C2×C5×Dic3C2311yescharacteristic
63C2×C5×Dic3C2311yescharacteristic
64C4×C5×D3—24no—
65C4×C5×D3—24no—
66C3×C22⋊D5—22no—
67C2×C3×Dic5C2312yes—
68C2×C3×Dic5C2311yescharacteristic
69#1204—22no—
70#1203—24no—
71#1202—22no—
72#1201—24no—
73#1200—22no—
74D5×Dic3—22no—
75C2×#237—51no—
76C22×C4×D3D511yescharacteristic, complemented
77C3×#123—51no—
78#937—51no—
79#929—51no—
80#896—52no—
81#893—52no—
82#884—52no—
83#882—51no—
84#67⋊C4—52no—
85#877—51no—
86C24×C5—31no—
87C22×C4×C5—31no—
88C22×C4×C5—32no—
89C22×C4×C5—32no—
90C22×C4×C5—64no—
91C22×C4×C5C2×D311yescharacteristic
92C2×C22⋊D5—31no—
93C2×C22⋊D5—32no—
94C2×C22⋊D5—32no—
95C2×C22⋊D5C2×D311yescharacteristic
96#709—64no—
97C2×D20—31no—
98C2×C4×D5—31no—
99C2×C4×D5—31no—
100C2×Dic10—31no—
101C22⋊Dic5—31no—
102C22⋊Dic5—32no—
103C22⋊Dic5—32no—
104C22⋊Dic5C2×D311yescharacteristic
105#685—32no—
106#685C2×D312yescomplemented
107C4⋊Dic5—32no—
108#683—32no—
109#683C2×D312yescomplemented
110C4×Dic5—32no—
111#525—151noSylow
112C22×C3×C5—22no—
113C22×C3×C5C2×D412yes—
114C22×C3×C5C2411yescharacteristic
115C2×D15—21no—
116C2×D15—22no—
117C2×C5×D3—28no—
118C2×C5×D3—22no—
119C2×C5×D3—22no—
120C2×C5×D3#4114yescomplemented
121C2×C3×D5—21no—
122C2×C3×D5—22no—
123C3×C4×C5—22no—
124Dic15—21no—
125Dic15—22no—
126C3×Dic5—21no—
127C3×Dic5—22no—
128C5×Dic3C2×D412yes—
129C5×Dic3C2×D412yes—
130C23×D3C2×D511yescharacteristic
131C2×C3×D4—51no—
132C22×C3×C4C2×D511yescharacteristic
133C2×#67—51no—
134C2×#67—52no—
135C2×#67—51no—
136C22×Dic3—51no—
137C22×Dic3C2×D511yescharacteristic
138#237—104no—
139C2×D12—52no—
140C2×C4×D3—24no—
141C2×C4×D3—51no—
142C2×C4×D3C2×D512yes—
143C2×C4×D3C2×D512yes—
144C2×Dic6—51no—
145C3×C4⋊C4—52no—
146C3×C22⋊C4—51no—
147C3×C22⋊C4—52no—
148#217—51no—
149(C2×D3)⋊C4—52no—
150(C2×D3)⋊C4—52no—
151(C2×D3)⋊C4—52no—
152Dic3⋊C4—52no—
153Dic3⋊C4—52no—
154C4×Dic3—52no—
155C23×C5—32no—
156C23×C5—64no—
157C23×C5—62no—
158C23×C5C22×D311yescharacteristic
159C22×D5—31no—
160C22×D5C22×D311yescharacteristic
161C2×C4×C5—22no—
162C2×C4×C5—34no—
163C2×C4×C5—31no—
164C2×C4×C5—31no—
165C2×C4×C5—64no—
166C2×C4×C5—64no—
167C2×C4×C5C22×D312yes—
168C22⋊D5—22no—
169C22⋊D5—64no—
170C22⋊D5—64no—
171C22⋊D5—62no—
172C2×Dic5—32no—
173C2×Dic5—31no—
174C2×Dic5C22×D312yes—
175C2×Dic5C22×D311yescharacteristic
176D20—62no—
177C4×D5—62no—
178C4×D5—62no—
179Dic10—62no—
180C2×#41—151no—
181C23×C4—31no—
182#123—51no—
183#123—151no—
184C22⋊Q8—152no—
185#121—152no—
186#120—151no—
187#120—151no—
188C4×D4—152no—
189C4×D4—152no—
190#117—151no—
191C2×C3×C5—22no—
192C2×C3×C5C22×D411yescharacteristic
193C2×C3×C5C2×#4112yes—
194D15—41no—
195C3×D5—41no—
196C5×D3—24no—
197C23×C3—51no—
198C23×C3C22×D511yescharacteristic
199C22×D3—22no—
200C22×D3—24no—
201C22×D3—51no—
202C22×D3C22×D512yes—
203C3×D4—102no—
204C2×C3×C4—22no—
205C2×C3×C4—52no—
206C2×C3×C4—51no—
207C2×C3×C4C22×D512yes—
208#67—102no—
209#67—104no—
210#67—102no—
211C2×Dic3—52no—
212C2×Dic3—51no—
213C2×Dic3—102no—
214C2×Dic3C22⋊D514yescomplemented
215C2×Dic3C22×D511yescharacteristic
216C2×Dic3C22×D511yescharacteristic
217D12—104no—
218C4×D3—24no—
219C4×D3—24no—
220C4×D3—102no—
221Dic6—102no—
222C22×C5—22no—
223C22×C5—34no—
224C22×C5—68no—
225C22×C5—62no—
226C22×C5—62no—
227C22×C5D3×D412yes—
228C22×C5C23×D311yescharacteristic
229C2×D5—21no—
230C2×D5—22no—
231C2×D5—61no—
232C2×D5—62no—
233C4×C5—22no—
234C4×C5—32no—
235C4×C5—32no—
236Dic5—21no—
237Dic5—22no—
238Dic5—61no—
239Dic5—62no—
240C24—31no—
241#41—304no—
242C2×Q8—151no—
243C2×D4—51no—
244C2×D4—151no—
245C2×D4—152no—
246C2×D4—152no—
247C2×D4—151no—
248C22×C4—31no—
249C22×C4—32no—
250C22×C4—32no—
251C22×C4—64no—
252C22×C4—151no—
253C22×C4—151no—
254C22×C4D3×D511yescharacteristic
255C4⋊C4—52no—
256C4⋊C4—152no—
257C4⋊C4—152no—
258C22⋊C4—51no—
259C22⋊C4—52no—
260C22⋊C4—152no—
261C22⋊C4—152no—
262C22⋊C4—151no—
263C22⋊C4—152no—
264C42—152no—
265C3×C5#52511yescharacteristic, complemented, Hall
266C22×C3—22no—
267C22×C3—102no—
268C22×C3—101no—
269C22×C3C2×C22⋊D512yes—
270C22×C3C23×D511yescharacteristic
271C2×D3—28no—
272C2×D3—22no—
273C2×D3—22no—
274C2×D3—102no—
275C2×D3—101no—
276C2×D3#70914yescomplemented
277C3×C4—22no—
278C3×C4—102no—
279C3×C4—101no—
280Dic3—102no—
281Dic3—101no—
282Dic3C2×C22⋊D512yes—
283Dic3C2×C22⋊D512yes—
284C2×C5—22no—
285C2×C5—64no—
286C2×C5C2×D3×D411yescharacteristic
287C2×C5D3×#4112yes—
288D5—41no—
289D5—121no—
290C23—32no—
291C23—51no—
292C23—64no—
293C23—62no—
294C23—151no—
295C23C2×D3×D511yescharacteristic
296Q8—302no—
297D4—102no—
298D4—302no—
299D4—304no—
300D4—304no—
301D4—302no—
302C2×C4—22no—
303C2×C4—34no—
304C2×C4—31no—
305C2×C4—31no—
306C2×C4—52no—
307C2×C4—51no—
308C2×C4—64no—
309C2×C4—64no—
310C2×C4—152no—
311C2×C4—151no—
312C2×C4—302no—
313C2×C4—302no—
314C2×C4C2×D3×D512yes—
315C2×C3—22no—
316C2×C3—201no—
317C2×C3C2×#70912yes—
318C2×C3C22×C22⋊D511yescharacteristic
319D3—24no—
320D3—201no—
321C5#565611yescharacteristic, complemented, Sylow
322C22—22no—
323C22—34no—
324C22—68no—
325C22—62no—
326C22—62no—
327C22—102no—
328C22—101no—
329C22—302no—
330C22—301no—
331C22D3×C22⋊D512yes—
332C22C22×D3×D511yescharacteristic
333C4—22no—
334C4—32no—
335C4—32no—
336C4—102no—
337C4—101no—
338C4—302no—
339C4—301no—
340C3#6612511yescharacteristic, complemented, Sylow
341C2—22no—
342C2—64no—
343C2—201no—
344C2—601no—
345C2D3×#70912yes—
346C2C2×D3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC22×C3×C4×C5C22
hypercenterC22×C4D3×D5
hypocenterC3×C5#525
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×D3C2semidirect
2. C2×#6779C2semidirect
3. #91818C2semidirect
4. C3×#4075C2semidirect
5. #91570C2semidirect
6. #91568C2semidirect
7. #91529C2semidirect
8. #91454C2semidirect
9. #91446C2semidirect
10. #91441C2semidirect
11. #91352C2semidirect
21. C2×#1204C22semidirect
23. C2×#1202C22semidirect
25. C2×#1200C22semidirect
27. C2×D5×Dic3C22semidirect
29. #6714C22semidirect
30. #6712C22semidirect
32. C3×#685C22semidirect
33. C3×#683C22semidirect
34. Dic3⋊Dic5C22semidirect
37. Dic3×Dic5C22semidirect
45. #4075D3semidirect
61. C2×C5×Dic3D4semidirect
76. C22×C4×D3D5semidirect
106. #685C2×D3semidirect
109. #683C2×D3semidirect
120. C2×C5×D3#41semidirect
214. C2×Dic3C22⋊D5semidirect
265. C3×C5#525semidirect
276. C2×D3#709semidirect
321. C5#5656semidirect
340. C3#66125semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C5×D32
C2×#67792
#918182
C3×#40752
#915702
#915682
#915292
#914542
#914462
#914412
#913522
#661253
#56565