Finite Group Databasebeta

← #11754741

Subgroups — #11754741

Order 960.

432 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 128 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
1#91827C211yesmaximal, characteristic
2C5×#936C211yesmaximal, characteristic, complemented
3C3×D4×Dic5C211yesmaximal, characteristic, complemented
4#91574C212yesmaximal, complemented
5#91546C212yesmaximal, complemented
6#91531C212yesmaximal, complemented
7#91526C212yesmaximal, complemented
8#91469C211yesmaximal, characteristic, complemented
9#91386C211yesmaximal, characteristic, complemented
10#91383C211yesmaximal, characteristic, complemented
11Dic5×Dic6C211yesmaximal, characteristic, complemented
12#66016—31nomaximal, Hall
13C2×C3×C5×D4C2211yescharacteristic
14C2×#1220C2212yes—
15C2×C4×D15C2211yescharacteristic
16C2×C5×Dic6C2211yescharacteristic
17C22×C3×Dic5C2212yes—
18C2×#1204C2212yes—
19#6719C2212yes—
20C4⋊Dic15C2211yescharacteristic
21C5×#217C2212yes—
22C5×#217C2212yes—
23C4×C5×Dic3C2211yescharacteristic
24C3×C22⋊Dic5C2212yes—
25C3×C4⋊Dic5C2211yescharacteristic
26C3×C4×Dic5C2211yescharacteristic
27Dic3⋊Dic5C2212yes—
28Dic3⋊Dic5C2212yes—
29#6669C2211yescharacteristic
30#6669C2211yescharacteristic
31#6668C2212yes—
32#6667C2211yescharacteristic
33#6667C2212yes—
34#6667C2211yescharacteristic
35Dic3×Dic5C2212yes—
36#5561—51nomaximal, Hall
37C5×#124—31no—
38#4092—31no—
39Q8×Dic5—31no—
40#4084—31no—
41D4×Dic5D311yescharacteristic, complemented
42#4032—32no—
43#4031—32no—
44#4025—32no—
45#4024—32no—
46#4018—31no—
47#4015—31no—
48C23×C3×C5C2312yes—
49C22×D15C2311yescharacteristic
50C3×C5×D4—22no—
51C2×C3×C4×C5C2311yescharacteristic
52#1220—42no—
53C2×Dic15C2312yes—
54C2×Dic15C2311yescharacteristic
55C4×D15—22no—
56C2×C5×Dic3C2312yes—
57C2×C5×Dic3C2311yescharacteristic
58C2×C5×Dic3C2311yescharacteristic
59C5×Dic6—22no—
60C2×C3×Dic5—42no—
61C2×C3×Dic5C2311yescharacteristic
62C2×C3×Dic5C2312yes—
63C2×C3×Dic5C2311yescharacteristic
64#1204—42no—
65C3×C4×D4—51no—
66#938—51no—
67#936D511yescharacteristic, complemented
68#929—52no—
69#924—52no—
70#897—51no—
71#888—51no—
72#885—52no—
73#879—52no—
74#872—51no—
75C4×Dic6—51no—
76C2×C5×Q8—31no—
77C2×C5×D4C2×D311yescharacteristic
78C2×C22⋊D5—32no—
79C22×Dic5C2×D312yes—
80C2×C4×D5—31no—
81C2×Dic10—32no—
82C5×C22⋊C4—32no—
83C5×C22⋊C4—32no—
84C42×C5—31no—
85C22⋊Dic5—32no—
86C22⋊Dic5C2×D312yes—
87#685—31no—
88#685—31no—
89#685—32no—
90C4⋊Dic5—31no—
91C4⋊Dic5—32no—
92C4⋊Dic5—32no—
93C4⋊Dic5C2×D311yescharacteristic
94#683—32no—
95#683—31no—
96#683—31no—
97C4×Dic5—32no—
98C4×Dic5C2×D311yescharacteristic
99#542—151noSylow
100C22×C3×C5—22no—
101C22×C3×C5—22no—
102C22×C3×C5—22no—
103C22×C3×C5C2411yescharacteristic
104C2×D15—21no—
105C2×D15—21no—
106C2×D15—21no—
107C3×C4×C5#4112yes—
108Dic15—21no—
109Dic15—22no—
110C3×Dic5—22no—
111C3×Dic5—21no—
112C3×Dic5—21no—
113C5×Dic3—22no—
114C5×Dic3—21no—
115C5×Dic3—21no—
116C2×C3×D4C2×D511yescharacteristic
117C22×C3×C4—52no—
118C2×#67—52no—
119C2×C4×D3—51no—
120C2×Dic6—52no—
121C2×Dic6C2×D511yescharacteristic
122C3×C4⋊C4—51no—
123C3×C22⋊C4—52no—
124C3×C42—51no—
125#217—52no—
126#217C2×D512yes—
127#217C2×D512yes—
128(C2×D3)⋊C4—51no—
129(C2×D3)⋊C4—51no—
130(C2×D3)⋊C4—52no—
131C4⋊Dic3—51no—
132C4⋊Dic3—52no—
133Dic3⋊C4—51no—
134Dic3⋊C4—51no—
135Dic3⋊C4—52no—
136Dic3⋊C4—52no—
137C4×Dic3—52no—
138C4×Dic3C2×D511yescharacteristic
139C23×C5C22×D312yes—
140C22×D5—31no—
141C5×Q8—62no—
142C5×D4—22no—
143C2×C4×C5—32no—
144C2×C4×C5—31no—
145C2×C4×C5—31no—
146C2×C4×C5C22×D311yescharacteristic
147C22⋊D5—122no—
148C2×Dic5—32no—
149C2×Dic5—31no—
150C2×Dic5—42no—
151C2×Dic5C22×D311yescharacteristic
152C2×Dic5C22×D311yescharacteristic
153C2×Dic5C22×D312yes—
154C4×D5—62no—
155Dic10—122no—
156C4⋊Q8—151no—
157#126—152no—
158#124—31no—
159#124—152no—
160#123—152no—
161C22⋊Q8—152no—
162C22⋊Q8—151no—
163#121—151no—
164C4×Q8—151no—
165C4×D4—51no—
166#117—151no—
167C2×C3×C5—42no—
168C2×C3×C5C2×#4111yescharacteristic
169C2×C3×C5H(5,𝔽2)11yescharacteristic
170C2×C3×C52−1+411yescharacteristic
171D15—41no—
172C23×C3C22×D512yes—
173C22×D3—51no—
174C3×D4—22no—
175C2×C3×C4—51no—
176C2×C3×C4—51no—
177C2×C3×C4—52no—
178C2×C3×C4—202no—
179C2×C3×C4C22×D511yescharacteristic
180#67—202no—
181C2×Dic3—52no—
182C2×Dic3—51no—
183C2×Dic3C22×D512yes—
184C2×Dic3C22×D511yescharacteristic
185C2×Dic3C22×D511yescharacteristic
186C4×D3—102no—
187Dic6—22no—
188Dic6—202no—
189C22×C5—22no—
190C22×C5—22no—
191C22×C5—22no—
192C22×C5C23×D311yescharacteristic
193C2×D5—61no—
194C2×D5—61no—
195C2×D5—61no—
196C4×C5—62no—
197C4×C5—61no—
198C4×C5—61no—
199C4×C5#23512yes—
200Dic5—22no—
201Dic5—21no—
202Dic5—21no—
203Dic5—61no—
204Dic5—62no—
205C2×Q8—31no—
206C2×Q8—152no—
207C2×D4—152no—
208C2×D4D3×D511yescharacteristic
209C22×C4—52no—
210C22×C4—151no—
211C4⋊C4—51no—
212C4⋊C4—151no—
213C4⋊C4—151no—
214C4⋊C4—152no—
215C4⋊C4—152no—
216C4⋊C4—152no—
217C4⋊C4—151no—
218C22⋊C4—32no—
219C22⋊C4—32no—
220C22⋊C4—52no—
221C22⋊C4—151no—
222C22⋊C4—151no—
223C22⋊C4—152no—
224C22⋊C4—152no—
225C42—31no—
226C42—51no—
227C42—152no—
228C3×C5#54211yescharacteristic, complemented, Hall
229C22×C3—22no—
230C22×C3—22no—
231C22×C3—22no—
232C22×C3C23×D511yescharacteristic
233C2×D3—101no—
234C2×D3—101no—
235C2×D3—101no—
236C3×C4—102no—
237C3×C4—101no—
238C3×C4—101no—
239C3×C4#71112yes—
240Dic3—22no—
241Dic3—21no—
242Dic3—21no—
243Dic3—101no—
244Dic3—102no—
245C2×C5—42no—
246C2×C5C2×#23511yescharacteristic
247C2×C5#100411yescharacteristic
248C2×C5#101011yescharacteristic
249D5—121no—
250C23—151no—
251C23C2×D3×D512yes—
252Q8—62no—
253Q8—602no—
254D4—22no—
255D4—602no—
256C2×C4—31no—
257C2×C4—31no—
258C2×C4—32no—
259C2×C4—51no—
260C2×C4—51no—
261C2×C4—52no—
262C2×C4—152no—
263C2×C4—151no—
264C2×C4—202no—
265C2×C4—302no—
266C2×C4C2×D3×D511yescharacteristic
267C2×C3—42no—
268C2×C3C2×#71111yescharacteristic
269C2×C3#414911yescharacteristic
270C2×C3#415011yescharacteristic
271D3—201no—
272C5#556111yescharacteristic, complemented, Sylow
273C22—22no—
274C22—22no—
275C22—22no—
276C22—301no—
277C22—301no—
278C22—301no—
279C22C22×D3×D511yescharacteristic
280C4—61no—
281C4—61no—
282C4—62no—
283C4—101no—
284C4—101no—
285C4—102no—
286C4—302no—
287C4—301no—
288C4#678212yes—
289C3#6601611yescharacteristic, complemented, Sylow
290C2—42no—
291C2—601no—
292C2#9202011yescharacteristic
293C2#9202611yescharacteristic
294C2C2×#678211yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
prime radical#91827C2
hypercenterC2×D4D3×D5
hypocenterC3×C5#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C5×#936C2semidirect
3. C3×D4×Dic5C2semidirect
4. #91574C2semidirect
5. #91546C2semidirect
6. #91531C2semidirect
7. #91526C2semidirect
8. #91469C2semidirect
9. #91386C2semidirect
10. #91383C2semidirect
11. Dic5×Dic6C2semidirect
41. D4×Dic5D3semidirect
67. #936D5semidirect
228. C3×C5#542semidirect
272. C5#5561semidirect
289. C3#66016semidirect

Maximal subgroups

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

subgroupindex
#918272
C5×#9362
C3×D4×Dic52
#915742
#915462
#915312
#915262
#914692
#913862
#913832
Dic5×Dic62
#660163
#55615