Finite Group Databasebeta

← #14279106

Subgroups — #14279106

Order 1920.

316 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 96 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#11751338C211yesmaximal, characteristic
2C5×#5234C211yesmaximal, characteristic
3C3×#65526C211yesmaximal, characteristic
4#10598184—31nomaximal, Hall
5C2×C3×C5×#41C2211yescharacteristic
6C2×#6710—21no—
7C2×C5×#208C411yescharacteristic
8C22×C5×C3⋊C8C411yescharacteristic
9C2×C3×#681—21no—
10#91120—21no—
11#91117C412yes—
12C5×#830—21no—
13C5×#830—21no—
14C3×#3968—21no—
15C3×#3965C412yes—
16#67700—51nomaximal, Hall
17C5×#408—31no—
18#65526—31no—
19#65526D311yescharacteristic
20C3×C5×#41—41no—
21C3×C5×#41—41no—
22C2×C3×C5×Q8D411yescharacteristic
23C2×C3×C5×D4C2×C411yescharacteristic
24C2×C3×C5×D4C2×C411yescharacteristic
25C2×C3×C5×D4Q811yescharacteristic
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×C3×C4×C5D411yescharacteristic
28C22×C3×C4×C5D411yescharacteristic
29#6710—22no—
30#6710—41no—
31C2×C3⋊#168—41no—
32C5×#208—41no—
33C2×C5×C3⋊C8—21no—
34C2×C5×C3⋊C8—21no—
35C2×C5×C3⋊C8—41no—
36C3×#681—22no—
37C3×#681—41no—
38C2×C3×#168—41no—
39C3×#413—51no—
40#5237—51no—
41#5234D511yescharacteristic
42C2×C5×#41C2×D311yescharacteristic
43C2×C5×M16—31no—
44C22×C5×C8—31no—
45C2×#681—21no—
46C2×#681—61no—
47C5×C22⋊C8—61no—
48C5×C22⋊C8—61no—
49#3968—21no—
50#3968—61no—
51#3965—32no—
52#3965Dic312yes—
53#1392—151noSylow
54C23×C3×C5C4211yescharacteristic
55C23×C3×C5C4⋊C411yescharacteristic
56C23×C3×C5C4⋊C411yescharacteristic
57C3×C5×Q8—41no—
58C3×C5×D4—41no—
59C3×C5×D4—41no—
60C3×C5×D4—41no—
61C2×C3×C4×C5—21no—
62C2×C3×C4×C5—21no—
63C2×C3×C4×C5—21no—
64C2×C3×C4×C5—21no—
65C2×C3×C4×C5—21no—
66C2×C3×C4×C5—21no—
67C2×C3×C4×C5C22⋊C411yescharacteristic
68C2×C3×C4×C5C22⋊C411yescharacteristic
69C2×C3×C4×C5C22⋊C411yescharacteristic
70C2×C3×C4×C5C4⋊C411yescharacteristic
71C3⋊#168—42no—
72C3×#168—42no—
73C5×C3⋊C8—41no—
74C5×C3⋊C8—41no—
75C2×C3×#41C2×D511yescharacteristic
76C2×C3×M16—101no—
77C2×#208—101no—
78C2×#208Dic511yescharacteristic
79C22×C3⋊C8Dic511yescharacteristic
80C3×#101—101no—
81C3×#100—52no—
82#836—101no—
83#833—52no—
84#830—21no—
85#830—21no—
86C5×#41—41no—
87C5×#41—41no—
88C2×C5×Q8#6711yescharacteristic
89C2×C5×D4Dic611yescharacteristic
90C2×C5×D4C4×D311yescharacteristic
91C2×C5×D4C2×Dic311yescharacteristic
92C22×C4×C5C4×D311yescharacteristic
93C22×C4×C5D1211yescharacteristic
94C22×C4×C5#6711yescharacteristic
95C5×M16—121no—
96C2×C5×C8—61no—
97C2×C5×C8—61no—
98C2×C5×C8—121no—
99#681—22no—
100#681—41no—
101#681—62no—
102#681—121no—
103C2×#168—41no—
104C2×#168—121no—
105#413—51no—
106#413—151no—
107#408—31no—
108C22×C3×C5—21no—
109C22×C3×C5—21no—
110C22×C3×C5—21no—
111C22×C3×C5—41no—
112C22×C3×C5—41no—
113C22×C3×C5—41no—
114C22×C3×C5#9511yescharacteristic
115C3×C4×C5—21no—
116C3×C4×C5—21no—
117C3×C4×C5—21no—
118C3×C4×C5#9911yescharacteristic
119C3×C4×C5#9911yescharacteristic
120C3×#41—41no—
121C3×#41—41no—
122C2×C3×Q8D2011yescharacteristic
123C2×C3×D4Dic1011yescharacteristic
124C2×C3×D4C4×D511yescharacteristic
125C2×C3×D4C4×D511yescharacteristic
126C22×C3×C4C2×Dic511yescharacteristic
127C22×C3×C4C22⋊D511yescharacteristic
128C22×C3×C4C22⋊D511yescharacteristic
129C3×M16—102no—
130C3×M16—201no—
131C2×C3×C8—201no—
132#208—41no—
133#208—102no—
134#208—201no—
135C2×C3⋊C8—21no—
136C2×C3⋊C8—21no—
137C2×C3⋊C8—41no—
138C2×C3⋊C8—201no—
139C23×C5C4×Dic311yescharacteristic
140C23×C5Dic3⋊C411yescharacteristic
141C23×C5C4⋊Dic311yescharacteristic
142C5×Q8—41no—
143C5×D4—41no—
144C5×D4—41no—
145C5×D4—41no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5Dic3⋊C411yescharacteristic
153C2×C4×C5(C2×D3)⋊C411yescharacteristic
154C2×C4×C5(C2×D3)⋊C411yescharacteristic
155C2×C4×C5#21711yescharacteristic
156C5×C8—121no—
157C5×C8—121no—
158#168—42no—
159#168—122no—
160C2×#41D3×D511yescharacteristic
161C2×M16—31no—
162C2×M16—101no—
163C2×M16—301no—
164C22×C8—31no—
165#101—101no—
166#101—301no—
167#100—52no—
168#100—152no—
169C22⋊C8—61no—
170C22⋊C8—61no—
171C2×C3×C5—21no—
172C2×C3×C5—41no—
173C2×C3×C5—41no—
174C2×C3×C5—41no—
175C2×C3×C5#34211yescharacteristic
176C23×C3C4×Dic511yescharacteristic
177C23×C3#68311yescharacteristic
178C23×C3#68311yescharacteristic
179C3×Q8—41no—
180C3×D4—41no—
181C3×D4—41no—
182C3×D4—41no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4C4⋊Dic511yescharacteristic
190C2×C3×C4#68511yescharacteristic
191C2×C3×C4#68511yescharacteristic
192C2×C3×C4C22⋊Dic511yescharacteristic
193C3×C8—202no—
194C3⋊C8—41no—
195C3⋊C8—41no—
196C3⋊C8—202no—
197C22×C5—21no—
198C22×C5—21no—
199C22×C5—21no—
200C22×C5—41no—
201C22×C5—41no—
202C22×C5—41no—
203C22×C5C3⋊#9511yescharacteristic
204C4×C5—21no—
205C4×C5—21no—
206C4×C5—21no—
207C4×C5#80611yescharacteristic
208C4×C5#80611yescharacteristic
209#41—41no—
210#41—41no—
211C2×Q8#120211yescharacteristic
212C2×D4D5×Dic311yescharacteristic
213C2×D4#120011yescharacteristic
214C2×D4#120411yescharacteristic
215C22×C4D3×Dic511yescharacteristic
216C22×C4#120111yescharacteristic
217C22×C4#120311yescharacteristic
218M16—102no—
219M16—121no—
220M16—201no—
221M16—302no—
222M16—601no—
223C2×C8—61no—
224C2×C8—61no—
225C2×C8—121no—
226C2×C8—201no—
227C2×C8—601no—
228C3×C5#139211yescharacteristic, complemented, Hall
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—41no—
233C22×C3—41no—
234C22×C3—41no—
235C22×C3#396311yescharacteristic
236C3×C4—21no—
237C3×C4—21no—
238C3×C4—21no—
239C3×C4#396611yescharacteristic
240C3×C4#396611yescharacteristic
241C2×C5—21no—
242C2×C5—41no—
243C2×C5—41no—
244C2×C5—41no—
245C2×C5#452711yescharacteristic
246C23Dic3×Dic511yescharacteristic
247C23#666811yescharacteristic
248C23#666911yescharacteristic
249Q8—41no—
250D4—41no—
251D4—41no—
252D4—41no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4#666511yescharacteristic
260C2×C4(C2×D3)⋊Dic511yescharacteristic
261C2×C4#666711yescharacteristic
262C2×C4Dic3⋊Dic511yescharacteristic
263C8—121no—
264C8—121no—
265C8—202no—
266C8—602no—
267C2×C3—21no—
268C2×C3—41no—
269C2×C3—41no—
270C2×C3—41no—
271C2×C3#6474611yescharacteristic
272C5#6770011yescharacteristic, complemented, Sylow
273C22—21no—
274C22—21no—
275C22—21no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22#9099411yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4#9099611yescharacteristic
284C4#9099611yescharacteristic
285C3#1059818411yescharacteristic, complemented, Sylow
286C2—21no—
287C2—41no—
288C2—41no—
289C2—41no—
290C2#1174601811yescharacteristic
subgroupG/H
centerC4#90996
commutatorC23×C3×C5C42
Frattini, hypercenterC2×#41D3×D5
Fitting, prime radical, cosocleC2×C3×C5×#41C22
socleC2×C3×C5#342
hypocenterC3×C5#1392
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
228. C3×C5#1392semidirect
272. C5#67700semidirect
285. C3#10598184semidirect

Maximal subgroups

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

subgroupindex
#117513382
C5×#52342
C3×#655262
#105981843
#677005