Finite Group Databasebeta

← #11752875

Subgroups — #11752875

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
1C2×#6779C211yesmaximal, characteristic, complemented
2C22×D5×Dic3C211yesmaximal, characteristic, complemented
3#91775C211yesmaximal, characteristic, complemented
4C5×#877C211yesmaximal, characteristic, complemented
5C3×#4028C211yesmaximal, characteristic, complemented
6#91564C211yesmaximal, characteristic, complemented
7#91537C211yesmaximal, characteristic, complemented
8Dic3×D20C212yesmaximal, complemented
9#91422C212yesmaximal, complemented
10#91409C212yesmaximal, complemented
11#91395C212yesmaximal, complemented
12#65858—31nomaximal, Hall
13C23×C3×D5C2211yescharacteristic
14C2×#1220C2211yescharacteristic
15C22×Dic15C2211yescharacteristic
16C22×C5×Dic3C2211yescharacteristic
17C2×C3×C22⋊D5C2211yescharacteristic
18C2×C3×D20C2212yes—
19C2×#1204C2211yescharacteristic, complemented
20C2×#1202C2212yes—
21C2×#1202C2211yescharacteristic, complemented
22C2×#1200C2211yescharacteristic, complemented
23#6779—24no—
24C2×D5×Dic3—24no—
25C2×D5×Dic3C2212yes—
26C2×D5×Dic3C2212yes—
27C2×D5×Dic3C2211yescharacteristic, complemented
28C3×C5×C22⋊C4C2211yescharacteristic
29#6714C2212yescomplemented
30C4⋊Dic15C2212yescomplemented
31C5×#217C2211yescharacteristic
32C5×Dic3⋊C4C2212yescomplemented
33C4×C5×Dic3C2212yescomplemented
34C3×#685C2212yes—
35Dic3⋊Dic5C2212yescomplemented
36#6665C2212yes—
37#6665C2212yescomplemented
38#5586—51nomaximal, Hall
39C2×#709—31no—
40C22×C4×D5—31no—
41C5×#117—31no—
42#4043—32no—
43#4041—32no—
44#4032—31no—
45#4032—31no—
46#4028—31no—
47#4028D311yescharacteristic, complemented
48C4×D20—32no—
49C4×D20—32no—
50C23×C3×C5C2311yescharacteristic
51C22×D15C2311yescharacteristic
52C22×C3×D5—22no—
53C22×C3×D5—24no—
54C22×C3×D5C2311yescharacteristic
55C22×C3×D5C2312yes—
56C2×C3×C4×C5C2312yes—
57#1220—22no—
58C2×Dic15—22no—
59C2×Dic15C2311yescharacteristic
60C2×Dic15C2312yes—
61C2×C5×Dic3D414yescomplemented
62C2×C5×Dic3C2312yes—
63C2×C5×Dic3C2311yescharacteristic
64C2×C5×Dic3C2311yescharacteristic
65C3×C22⋊D5—22no—
66C2×C3×Dic5C2311yescharacteristic
67C3×D20—24no—
68#1204—22no—
69#1202—24no—
70#1202—22no—
71#1200—22no—
72D5×Dic3—24no—
73D5×Dic3—24no—
74D5×Dic3—22no—
75C23×Dic3—51no—
76C2×#237—51no—
77C3×#120—51no—
78#953—51no—
79#939—52no—
80#935—51no—
81D4×Dic3—52no—
82#886—51no—
83#67⋊C4—52no—
84#878—52no—
85#877D511yescharacteristic, complemented
86C23×D5C2×D311yescharacteristic
87C22×C4×C5—31no—
88C2×C22⋊D5—31no—
89C2×C22⋊D5C2×D311yescharacteristic
90C22×Dic5—31no—
91#709—64no—
92C2×D20—31no—
93C2×D20—32no—
94C2×D20C2×D312yes—
95C2×C4×D5—32no—
96C2×C4×D5—32no—
97C2×C4×D5—31no—
98C2×C4×D5—31no—
99C2×C4×D5—64no—
100C2×Dic10—31no—
101C5×C4⋊C4—32no—
102C5×C22⋊C4—31no—
103C5×C22⋊C4C2×D311yescharacteristic
104C42×C5—32no—
105#685—32no—
106#685—32no—
107#685—32no—
108#685C2×D312yes—
109C4⋊Dic5—32no—
110C4⋊Dic5—32no—
111#525—151noSylow
112C22×C3×C5—22no—
113C22×C3×C5C2×D412yes—
114C22×C3×C5C2411yescharacteristic
115C2×D15—21no—
116C2×D15—22no—
117C2×C3×D5—28no—
118C2×C3×D5—22no—
119C2×C3×D5—22no—
120C2×C3×D5—21no—
121C2×C3×D5—22no—
122C2×C3×D5#4114yescomplemented
123C3×C4×C5—22no—
124Dic15—22no—
125Dic15—21no—
126C3×Dic5—21no—
127C5×Dic3—22no—
128C5×Dic3C2×D412yes—
129C5×Dic3C2×D412yes—
130C24×C3—51no—
131C2×C3×D4—51no—
132C2×C3×D4—52no—
133C2×#67—51no—
134C2×#67—52no—
135C2×#67—51no—
136C22×Dic3—51no—
137C22×Dic3—52no—
138C22×Dic3—52no—
139C22×Dic3—51no—
140C22×Dic3—104no—
141C22×Dic3C2×D511yescharacteristic
142#237—104no—
143C2×C4×D3—51no—
144C2×Dic6—51no—
145C3×C22⋊C4—52no—
146C3×C22⋊C4C2×D511yescharacteristic
147#217—52no—
148#217—52no—
149#217C2×D511yescharacteristic
150(C2×D3)⋊C4—52no—
151C4⋊Dic3—52no—
152Dic3⋊C4—52no—
153Dic3⋊C4C2×D512yescomplemented
154C4×Dic3C2×D512yescomplemented
155C23×C5C22×D311yescharacteristic
156C22×D5—22no—
157C22×D5—24no—
158C22×D5—31no—
159C22×D5C22×D311yescharacteristic
160C22×D5C22×D312yes—
161C2×C4×C5—34no—
162C2×C4×C5—31no—
163C2×C4×C5—31no—
164C2×C4×C5—32no—
165C2×C4×C5C22×D312yes—
166C22⋊D5—22no—
167C22⋊D5—62no—
168C2×Dic5—31no—
169C2×Dic5—32no—
170C2×Dic5—62no—
171C2×Dic5C22×D311yescharacteristic
172D20—24no—
173D20—62no—
174D20—64no—
175C4×D5—62no—
176C4×D5—64no—
177C4×D5—64no—
178C4×D5—62no—
179Dic10—62no—
180C2×#41—151no—
181C23×C4—151no—
182#123—151no—
183#123—151no—
184C22⋊Q8—152no—
185#121—152no—
186#120—51no—
187#120—151no—
188C4×D4—152no—
189C4×D4—152no—
190#117—31no—
191C2×C3×C5—22no—
192C2×C3×C5C22×D411yescharacteristic
193C2×C3×C5C2×#4112yes—
194D15—41no—
195C3×D5—24no—
196C3×D5—41no—
197C23×C3—52no—
198C23×C3—51no—
199C23×C3—104no—
200C23×C3—102no—
201C23×C3C22×D511yescharacteristic
202C22×D3—51no—
203C3×D4—104no—
204C3×D4—102no—
205C2×C3×C4—51no—
206C2×C3×C4C22×D512yes—
207#67—104no—
208#67—102no—
209#67—102no—
210C2×Dic3—52no—
211C2×Dic3—51no—
212C2×Dic3—102no—
213C2×Dic3—102no—
214C2×Dic3—104no—
215C2×Dic3—104no—
216C2×Dic3D2014yescomplemented
217C2×Dic3C22×D512yes—
218C2×Dic3C22×D511yescharacteristic
219C2×Dic3C22×D511yescharacteristic
220C4×D3—102no—
221Dic6—102no—
222C22×C5—22no—
223C22×C5D3×D412yes—
224C22×C5C23×D311yescharacteristic
225C2×D5—28no—
226C2×D5—22no—
227C2×D5—22no—
228C2×D5—21no—
229C2×D5—22no—
230C2×D5—61no—
231C2×D5—62no—
232C2×D5#23714yescomplemented
233C4×C5—22no—
234C4×C5—32no—
235C4×C5—32no—
236C4×C5—62no—
237Dic5—21no—
238Dic5—61no—
239Dic5—62no—
240C24—51no—
241#41—304no—
242C2×Q8—151no—
243C2×D4—51no—
244C2×D4—52no—
245C2×D4—152no—
246C2×D4—151no—
247C2×D4—151no—
248C22×C4—31no—
249C22×C4—151no—
250C22×C4—152no—
251C22×C4—151no—
252C22×C4—152no—
253C22×C4—151no—
254C22×C4—304no—
255C4⋊C4—32no—
256C4⋊C4—152no—
257C4⋊C4—152no—
258C22⋊C4—31no—
259C22⋊C4—52no—
260C22⋊C4—152no—
261C22⋊C4—152no—
262C22⋊C4—152no—
263C22⋊C4D3×D511yescharacteristic
264C42—32no—
265C3×C5#52511yescharacteristic, complemented, Hall
266C22×C3—22no—
267C22×C3—54no—
268C22×C3—108no—
269C22×C3—102no—
270C22×C3—102no—
271C22×C3—101no—
272C22×C3—102no—
273C22×C3C2×D2012yes—
274C22×C3C23×D511yescharacteristic
275C2×D3—101no—
276C2×D3—102no—
277C3×C4—22no—
278C3×C4—101no—
279Dic3—22no—
280Dic3—101no—
281Dic3—102no—
282Dic3C2×D2012yes—
283Dic3C2×D2012yes—
284C2×C5—22no—
285C2×C5C2×D3×D411yescharacteristic
286C2×C5C2×#23712yes—
287D5—24no—
288D5—41no—
289D5—121no—
290C23—52no—
291C23—51no—
292C23—104no—
293C23—102no—
294C23—151no—
295C23C2×D3×D511yescharacteristic
296Q8—302no—
297D4—104no—
298D4—102no—
299D4—302no—
300D4—304no—
301D4—302no—
302C2×C4—34no—
303C2×C4—31no—
304C2×C4—31no—
305C2×C4—32no—
306C2×C4—51no—
307C2×C4—152no—
308C2×C4—151no—
309C2×C4—302no—
310C2×C4—304no—
311C2×C4—304no—
312C2×C4—302no—
313C2×C4—302no—
314C2×C4C2×D3×D512yes—
315C2×C3—22no—
316C2×C3—104no—
317C2×C3—201no—
318C2×C3C22×D2011yescharacteristic
319C2×C3D5×#4112yes—
320D3—201no—
321C5#558611yescharacteristic, complemented, Sylow
322C22—22no—
323C22—54no—
324C22—108no—
325C22—102no—
326C22—102no—
327C22—101no—
328C22—102no—
329C22—301no—
330C22—302no—
331C22D3×D2012yes—
332C22C22×D3×D511yescharacteristic
333C4—22no—
334C4—32no—
335C4—32no—
336C4—62no—
337C4—101no—
338C4—302no—
339C4—301no—
340C3#6585811yescharacteristic, complemented, Sylow
341C2—22no—
342C2—104no—
343C2—201no—
344C2—601no—
345C2C2×D3×D2011yescharacteristic
346C2D5×#23712yes—
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
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. C2×#6779C2semidirect
2. C22×D5×Dic3C2semidirect
3. #91775C2semidirect
4. C5×#877C2semidirect
5. C3×#4028C2semidirect
6. #91564C2semidirect
7. #91537C2semidirect
8. Dic3×D20C2semidirect
9. #91422C2semidirect
10. #91409C2semidirect
11. #91395C2semidirect
19. C2×#1204C22semidirect
21. C2×#1202C22semidirect
22. C2×#1200C22semidirect
27. C2×D5×Dic3C22semidirect
29. #6714C22semidirect
30. C4⋊Dic15C22semidirect
32. C5×Dic3⋊C4C22semidirect
33. C4×C5×Dic3C22semidirect
35. Dic3⋊Dic5C22semidirect
37. #6665C22semidirect
47. #4028D3semidirect
61. C2×C5×Dic3D4semidirect
85. #877D5semidirect
122. C2×C3×D5#41semidirect
153. Dic3⋊C4C2×D5semidirect
154. C4×Dic3C2×D5semidirect
216. C2×Dic3D20semidirect
232. C2×D5#237semidirect
265. C3×C5#525semidirect
321. C5#5586semidirect
340. C3#65858semidirect

Maximal subgroups

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

subgroupindex
C2×#67792
C22×D5×Dic32
#917752
C5×#8772
C3×#40282
#915642
#915372
Dic3×D202
#914222
#914092
#913952
#658583
#55865