Finite Group Databasebeta

← #11752354

Subgroups — #11752354

Order 960.

244 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 79 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×#6762C211yesmaximal, characteristic, complemented
2C2×#6758C211yesmaximal, characteristic, complemented
3C3×#4027C211yesmaximal, characteristic
4#91241C211yesmaximal, characteristic, complemented
5#91233C211yesmaximal, characteristic, complemented
6#91232C211yesmaximal, characteristic, complemented
7C4×C3⋊#170C211yesmaximal, characteristic, complemented
8#65695—31nomaximal, Hall
9C2×C3×C22⋊D5C411yescharacteristic
10C22×C3×Dic5C2211yescharacteristic
11C2×C3×C4×D5C2211yescharacteristic
12#6762—22no—
13C2×C3⋊#170C2211yescharacteristic
14C2×C3⋊#170C2211yescharacteristic
15C2×C3⋊#170C2211yescharacteristic
16C2×C3⋊#170C2211yescharacteristic
17#6758—22no—
18C3×C5×C22⋊C4C411yescharacteristic
19C3×#685C411yescharacteristic
20C3×#683C411yescharacteristic
21C3×C4×Dic5C2211yescharacteristic
22#5012—51nomaximal, Hall
23C2×#704—31no—
24C2×#700—31no—
25#4027D311yescharacteristic
26C22⋊#170—31no—
27#4004—31no—
28#4003—31no—
29C4×#170—31no—
30C23×C3×C5C2×C411yescharacteristic
31C22×C3×D5C2×C411yescharacteristic
32C2×C3×C4×C5C2×C411yescharacteristic
33C2×C3×C4×C5C2×C411yescharacteristic
34C3×C22⋊D5—22no—
35C2×C3×Dic5—21no—
36C2×C3×Dic5—21no—
37C2×C3×Dic5C2×C411yescharacteristic
38C2×C3×Dic5C2×C411yescharacteristic
39C2×C3×Dic5C2311yescharacteristic
40C3×C4×D5—21no—
41C3×C4×D5—21no—
42C3⋊#170—21no—
43C3⋊#170—21no—
44C3⋊#170—21no—
45C3⋊#170D412yescomplemented
46C3×C4×D4—51no—
47C2×#208—51no—
48C2×#208—51no—
49#830—51no—
50#830—51no—
51C4⋊(C3⋊C8)—51no—
52C4×C3⋊C8—51no—
53C2×C22⋊D5Dic311yescharacteristic
54C22×Dic5C2×D311yescharacteristic
55C2×C4×D5C2×D311yescharacteristic
56#704—62no—
57C2×#170—31no—
58C2×#170—31no—
59C2×#170—31no—
60C2×#170—31no—
61#700—62no—
62C5×C22⋊C4Dic311yescharacteristic
63#685Dic311yescharacteristic
64#683Dic311yescharacteristic
65C4×Dic5C2×D311yescharacteristic
66#436—151noSylow
67C22×C3×C5—21no—
68C22×C3×C5—21no—
69C22×C3×C5—21no—
70C22×C3×C5C22×C411yescharacteristic
71C2×C3×D5—21no—
72C2×C3×D5—21no—
73C2×C3×D5—21no—
74C3×C4×C5—21no—
75C3×C4×C5—21no—
76C3×Dic5—21no—
77C3×Dic5M1612yescomplemented
78C3×Dic5C2×D411yescharacteristic
79C3×Dic5#4111yescharacteristic
80C2×C3×D4—51no—
81C22×C3×C4—51no—
82C22×C3×C4—51no—
83C3×C4⋊C4—51no—
84C3×C22⋊C4—51no—
85C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic
86C3×C42—51no—
87#208—102no—
88#208—102no—
89C2×C3⋊C8—51no—
90C2×C3⋊C8—51no—
91C2×C3⋊C8—51no—
92C2×C3⋊C8—51no—
93C23×C5C2×Dic311yescharacteristic
94C22×D5C2×Dic311yescharacteristic
95C2×C4×C5C2×Dic311yescharacteristic
96C2×C4×C5C2×Dic311yescharacteristic
97C22⋊D5—22no—
98C2×Dic5—21no—
99C2×Dic5—21no—
100C2×Dic5C2×Dic311yescharacteristic
101C2×Dic5C2×Dic311yescharacteristic
102C2×Dic5C22×D311yescharacteristic
103C4×D5—21no—
104C4×D5—21no—
105#170—32no—
106#170—61no—
107#170—61no—
108#170—61no—
109C2×M16—151no—
110C2×M16—151no—
111C4×D4—51no—
112C4⋊C8—151no—
113C22⋊C8—151no—
114C22⋊C8—151no—
115C4×C8—151no—
116C2×C3×C5—41no—
117C2×C3×C5C4×D411yescharacteristic
118C2×C3×C5C2×M1611yescharacteristic
119C2×C3×C5#13111yescharacteristic
120C3×D5—41no—
121C23×C3—51no—
122C23×C3C2×AGL(1,𝔽5)11yescharacteristic
123C3×D4—102no—
124C2×C3×C4—51no—
125C2×C3×C4—51no—
126C2×C3×C4—51no—
127C2×C3×C4—101no—
128C2×C3×C4—101no—
129C2×C3×C4—101no—
130C2×C3×C4—101no—
131C2×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
132C2×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
133C3⋊C8—52no—
134C3⋊C8—101no—
135C3⋊C8—101no—
136C3⋊C8—101no—
137C22×C5—21no—
138C22×C5—21no—
139C22×C5—21no—
140C22×C5C22×Dic311yescharacteristic
141C2×D5—21no—
142C2×D5—21no—
143C2×D5—21no—
144C4×C5—21no—
145C4×C5—21no—
146Dic5—21no—
147Dic5#20812yescomplemented
148Dic5D3×D411yescharacteristic
149Dic5#23711yescharacteristic
150C2×D4—51no—
151C22×C4—51no—
152C22×C4—51no—
153M16—302no—
154M16—302no—
155C2×C8—151no—
156C2×C8—151no—
157C2×C8—151no—
158C2×C8—151no—
159C4⋊C4—51no—
160C22⋊C4—51no—
161C22⋊C4ΓL(1,𝔽16)11yescharacteristic
162C42—51no—
163C3×C5#43611yescharacteristic, complemented, Hall
164C22×C3—21no—
165C22×C3—21no—
166C22×C3—21no—
167C22×C3—101no—
168C22×C3—101no—
169C22×C3—101no—
170C22×C3C22×AGL(1,𝔽5)11yescharacteristic
171C3×C4—21no—
172C3×C4—21no—
173C3×C4—52no—
174C3×C4—51no—
175C3×C4—51no—
176C3×C4—101no—
177C2×C5—41no—
178C2×C5C2×#20811yescharacteristic
179C2×C5D4×Dic311yescharacteristic
180C2×C5#94811yescharacteristic
181D5—41no—
182C23—51no—
183C23C2×ΓL(1,𝔽16)11yescharacteristic
184D4—102no—
185C2×C4—51no—
186C2×C4—51no—
187C2×C4—51no—
188C2×C4—101no—
189C2×C4—101no—
190C2×C4—101no—
191C2×C4—101no—
192C2×C4C2×ΓL(1,𝔽16)11yescharacteristic
193C2×C4C2×ΓL(1,𝔽16)11yescharacteristic
194C8—152no—
195C8—301no—
196C8—301no—
197C8—301no—
198C2×C3—41no—
199C2×C3—201no—
200C2×C3D5⋊M1611yescharacteristic
201C2×C3#413111yescharacteristic
202C2×C3D4×AGL(1,𝔽5)11yescharacteristic
203C5#501211yescharacteristic, complemented, Sylow
204C22—21no—
205C22—21no—
206C22—21no—
207C22—101no—
208C22—101no—
209C22—101no—
210C22C22×ΓL(1,𝔽16)11yescharacteristic
211C4—21no—
212C4—21no—
213C4—52no—
214C4—51no—
215C4—51no—
216C4—101no—
217C3#6569511yescharacteristic, complemented, Sylow
218C2—41no—
219C2—201no—
220C2D5⋊#20811yescharacteristic
221C2#9199011yescharacteristic
222C2D4×ΓL(1,𝔽16)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×ΓL(1,𝔽16)
commutator, socleC22×C3×C5C22×C4
FittingC3×C5×C22⋊C4C4
prime radicalC2×C3×C22⋊D5C4
cosocleC2×C3×Dic5C23
hypercenterC22⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#436
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×#6762C2semidirect
2. C2×#6758C2semidirect
4. #91241C2semidirect
5. #91233C2semidirect
6. #91232C2semidirect
7. C4×C3⋊#170C2semidirect
45. C3⋊#170D4semidirect
77. C3×Dic5M16semidirect
147. Dic5#208semidirect
163. C3×C5#436semidirect
203. C5#5012semidirect
217. C3#65695semidirect

Maximal subgroups

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

subgroupindex
C2×#67622
C2×#67582
C3×#40272
#912412
#912332
#912322
C4×C3⋊#1702
#656953
#50125