Finite Group Databasebeta

← #14292557

Subgroups — #14292557

Order 1920.

332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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#11751193C211yesmaximal, characteristic, complemented
2#11751188C211yesmaximal, characteristic
3#11750947C211yesmaximal, characteristic
4#11750939C211yesmaximal, characteristic
5C3×C5×#332C211yesmaximal, characteristic, complemented
6#11746303C211yesmaximal, characteristic, complemented
7#11746301C211yesmaximal, characteristic, complemented
8#10599242—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C2×#6718—21no—
11C2×#6718—21no—
12C2×#6705—21no—
13C4×D60C2211yescharacteristic
14#91758C2211yescharacteristic
15C3×C5×C4⋊C8C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17#91105—21no—
18#91104—21no—
19#91102—21no—
20#91093—21no—
21#91091—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C4×C3⋊#168C2211yescharacteristic
24#68449—51nomaximal, Hall
25#65381—31no—
26#65376—31no—
27#65135—31no—
28#65127—31no—
29C5×#332D311yescharacteristic, complemented
30#64702—31no—
31#64700—31no—
32C2×C3×C5×Q8—21no—
33C2×D60D411yescharacteristic
34C2×C4×D15—21no—
35C2×Dic30—21no—
36C2×C3×C5×C8—21no—
37C2×C3×C5×C8—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C42×C5C2311yescharacteristic
41#6718—42no—
42#6718—42no—
43#6714—21no—
44C4⋊Dic15—21no—
45C4⋊Dic15—21no—
46C4⋊Dic15D411yescharacteristic
47C2×C3⋊#168—21no—
48C2×C3⋊#168D411yescharacteristic
49C2×C3⋊#168D411yescharacteristic
50#6705—42no—
51#5092—51no—
52#5087—51no—
53#4846—51no—
54#4838—51no—
55C3×#332D511yescharacteristic, complemented
56#4482—51no—
57#4480—51no—
58C5×C4⋊Q8C2×D311yescharacteristic
59C2×#689—61no—
60C2×#689—61no—
61C2×#676—61no—
62C4×D20—31no—
63#4015—31no—
64C5×C4⋊C8C2×D311yescharacteristic
65C5×C4⋊C8C2×D311yescharacteristic
66#3953—61no—
67#3952—61no—
68#3950—61no—
69#3941—61no—
70#3939—61no—
71C4⋊#168—31no—
72C4×#168—31no—
73#1689—151noSylow
74C22×D15—21no—
75C3×C5×Q8—41no—
76C3×C5×Q8—41no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5C2×D411yescharacteristic
80C2×C3×C4×C5#4111yescharacteristic
81C2×Dic15—21no—
82C2×Dic15—41no—
83D60—21no—
84D60—21no—
85C4×D15—41no—
86C4×D15—41no—
87Dic30—41no—
88Dic30—41no—
89C3×C5×C8—41no—
90C3×C5×C8—41no—
91C3⋊#168—21no—
92C3⋊#168—41no—
93C3⋊#168D812yes—
94C3×C4⋊Q8C2×D511yescharacteristic
95C2×#216—101no—
96C2×#216—101no—
97C2×ΓL(1,𝔽25)—101no—
98C4×D12—51no—
99#869—51no—
100C3×C4⋊C8C2×D511yescharacteristic
101C3×C4⋊C8C2×D511yescharacteristic
102#821—101no—
103(C2×D3)⋊C8—101no—
104#818—101no—
105#809—101no—
106#807—101no—
107C4⋊(C3⋊C8)—51no—
108C4×C3⋊C8—51no—
109C2×C5×Q8—21no—
110C2×D20—31no—
111C2×C4×D5—61no—
112C2×Dic10—61no—
113C2×C5×C8—21no—
114C2×C5×C8—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C42×C5C22×D311yescharacteristic
118#689—122no—
119#689—122no—
120#685—61no—
121C4⋊Dic5—31no—
122C4⋊Dic5—61no—
123C4⋊Dic5—61no—
124C2×#168—31no—
125C2×#168—31no—
126C2×#168—61no—
127#676—122no—
128#494—151no—
129#474—151no—
130#474—151no—
131#436—151no—
132#334—151no—
133#332—151no—
134#332D1511yescharacteristic, complemented
135C22×C3×C5#12111yescharacteristic
136C2×D15—41no—
137C2×D15—41no—
138C2×D15—41no—
139C3×C4×C5—21no—
140C3×C4×C5—81no—
141C3×C4×C5C2×D811yescharacteristic
142C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
143C3×C4×C5#13711yescharacteristic
144C3×C4×C5#13711yescharacteristic
145Dic15—41no—
146Dic15—81no—
147C2×C3×Q8—21no—
148C2×D12—51no—
149C2×C4×D3—101no—
150C2×Dic6—101no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C42C22×D511yescharacteristic
156#216—202no—
157#216—202no—
158(C2×D3)⋊C4—101no—
159C4⋊Dic3—51no—
160C4⋊Dic3—101no—
161C4⋊Dic3—101no—
162C2×C3⋊C8—51no—
163C2×C3⋊C8—51no—
164C2×C3⋊C8—101no—
165ΓL(1,𝔽25)—202no—
166C22×D5—61no—
167C5×Q8—41no—
168C5×Q8—41no—
169C2×C4×C5—41no—
170C2×C4×C5#23511yescharacteristic
171C2×C4×C5D3×D411yescharacteristic
172C2×C4×C5D3×D411yescharacteristic
173C2×Dic5—61no—
174C2×Dic5—121no—
175D20—61no—
176D20—61no—
177C4×D5—121no—
178C4×D5—121no—
179Dic10—121no—
180Dic10—121no—
181C5×C8—41no—
182C5×C8—41no—
183#168—32no—
184#168—61no—
185#168—121no—
186C2×Q16—301no—
187C2×Q16—301no—
188C2×M16—301no—
189C4⋊Q8—151no—
190C4⋊Q8C2×D1511yescharacteristic
191C4×D4—151no—
192#107—301no—
193#107—301no—
194C4⋊C8—151no—
195C4⋊C8C2×D1511yescharacteristic
196C4⋊C8C2×D1511yescharacteristic
197#102—301no—
198#102—301no—
199C22⋊C8—301no—
200C4×C8—151no—
201C2×C3×C5#45911yescharacteristic
202C2×C3×C5#47011yescharacteristic
203C2×C3×C5#47311yescharacteristic
204D15—81no—
205C22×D3—101no—
206C3×Q8—41no—
207C3×Q8—41no—
208C2×C3×C4—41no—
209C2×C3×C4#70911yescharacteristic
210C2×C3×C4D4×D511yescharacteristic
211C2×C3×C4D4×D511yescharacteristic
212C2×Dic3—101no—
213C2×Dic3—201no—
214D12—101no—
215D12—101no—
216C4×D3—201no—
217C4×D3—201no—
218Dic6—201no—
219Dic6—201no—
220C3×C8—41no—
221C3×C8—41no—
222C3⋊C8—52no—
223C3⋊C8—101no—
224C3⋊C8—201no—
225C22×C5#88411yescharacteristic
226C2×D5—121no—
227C2×D5—121no—
228C2×D5—121no—
229C4×C5—21no—
230C4×C5—81no—
231C4×C5D3×D811yescharacteristic
232C4×C5#91411yescharacteristic
233C4×C5#91511yescharacteristic
234C4×C5#91811yescharacteristic
235Dic5—121no—
236Dic5—241no—
237C2×Q8—21no—
238C2×Q8—301no—
239C2×D4—151no—
240C22×C4—301no—
241Q16—602no—
242Q16—602no—
243M16—602no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—151no—
247C2×C8—151no—
248C2×C8—301no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—151no—
252C4⋊C4—301no—
253C4⋊C4—301no—
254C22⋊C4—301no—
255C42C22×D1511yescharacteristic
256C3×C5#168911yescharacteristic, complemented, Hall
257C22×C3#403011yescharacteristic
258C2×D3—201no—
259C2×D3—201no—
260C2×D3—201no—
261C3×C4—21no—
262C3×C4—81no—
263C3×C4D5×D811yescharacteristic
264C3×C4#406011yescharacteristic
265C3×C4#406111yescharacteristic
266C3×C4#406411yescharacteristic
267Dic3—201no—
268Dic3—401no—
269C2×C5#475511yescharacteristic
270C2×C5#478611yescharacteristic
271C2×C5#481611yescharacteristic
272D5—241no—
273C23—301no—
274Q8—41no—
275Q8—41no—
276Q8—601no—
277Q8—601no—
278D4—301no—
279D4—301no—
280C2×C4—41no—
281C2×C4—301no—
282C2×C4—601no—
283C2×C4—601no—
284C2×C4—601no—
285C2×C4#681711yescharacteristic
286C2×C4D4×D1511yescharacteristic
287C2×C4D4×D1511yescharacteristic
288C8—41no—
289C8—41no—
290C8—152no—
291C8—301no—
292C8—601no—
293C2×C3#6504411yescharacteristic
294C2×C3#6507511yescharacteristic
295C2×C3#6510511yescharacteristic
296D3—401no—
297C5#6844911yescharacteristic, complemented, Sylow
298C22—601no—
299C22—601no—
300C22—601no—
301C22#9177311yescharacteristic
302C4—21no—
303C4—81no—
304C4—601no—
305C4—1201no—
306C4D8×D1511yescharacteristic
307C4#9180311yescharacteristic
308C4#9180411yescharacteristic
309C4#9180711yescharacteristic
310C3#1059924211yescharacteristic, complemented, Sylow
311C2—1201no—
312C2#1175085611yescharacteristic
313C2#1175088711yescharacteristic
314C2#1175091711yescharacteristic
subgroupG/H
centerC22#91773
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#332C2
socleC22×C3×C5#121
prime radicalC2×D60D4
hypercenter#332D15
hypocenterC3×C5#1689
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #11751193C2semidirect
5. C3×C5×#332C2semidirect
6. #11746303C2semidirect
7. #11746301C2semidirect
29. C5×#332D3semidirect
55. C3×#332D5semidirect
134. #332D15semidirect
256. C3×C5#1689semidirect
297. C5#68449semidirect
310. C3#10599242semidirect

Maximal subgroups

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

subgroupindex
#117511932
#117511882
#117509472
#117509392
C3×C5×#3322
#117463032
#117463012
#105992423
#684495