Finite Group Databasebeta

← #14284999

Subgroups — #14284999

Order 1920.

432 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 106 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#11752484C211yesmaximal, characteristic
2#11750938C211yesmaximal, characteristic
3#11747000C211yesmaximal, characteristic
4C5×#4481C211yesmaximal, characteristic, complemented
5C3×#64706C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745856C211yesmaximal, characteristic, complemented
8#10599277—31nomaximal, Hall
9C2×#6705—21no—
10C42×D15C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13#91390—21no—
14#91384—21no—
15#91383C412yes—
16#91347—21no—
17#91344C412yes—
18#91331—21no—
19C2×#6648—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21#91098—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊#168C2211yescharacteristic
25#90983—21no—
26#68423—51nomaximal, Hall
27#66062—31no—
28#65126—31no—
29D5×C4⋊C8—31no—
30C5×#333—31no—
31#64766—31no—
32#64706D311yescharacteristic, complemented
33#64702—31no—
34C2×C4×D15C2×C411yescharacteristic
35C2×C4×D15D411yescharacteristic
36C2×C4×D15D411yescharacteristic
37C2×C5×Dic6C2×C412yes—
38C2×C3×Dic10—21no—
39C2×C3×C5×C8—21no—
40C3×C42×C5C2311yescharacteristic
41C4×Dic15C2×C411yescharacteristic
42C4×Dic15D411yescharacteristic
43C4×Dic15D411yescharacteristic
44C2×C3⋊#168—21no—
45#6705—42no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3—21no—
48C2×C5×C3⋊C8—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5C2×C412yes—
51C2×C3×#168—21no—
52Dic3⋊Dic5—22no—
53#6668—22no—
54#6667—22no—
55Dic3×Dic5—22no—
56#6648—42no—
57#5728—51no—
58#4837—51no—
59D3×C4⋊C8—51no—
60C3×#332—51no—
61#4547—51no—
62#4481—51no—
63#4481D511yescharacteristic, complemented
64C5×C4⋊Q8—31no—
65#4092—32no—
66Q8×Dic5—32no—
67C2×#676—61no—
68C2×C8×D5—61no—
69#4043—61no—
70#4038—61no—
71#4036—61no—
72#4033—61no—
73C42×D5—31no—
74#4015C2×D311yescharacteristic
75C5×C4⋊C8—31no—
76C5×C4⋊C8C2×D311yescharacteristic
77#3946—61no—
78#3946—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81#1550—151noSylow
82C22×D15C22⋊C411yescharacteristic
83C2×C3×C4×C5C22×C411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15C22⋊C411yescharacteristic
87C2×Dic15C22⋊C411yescharacteristic
88C2×Dic15C22⋊C411yescharacteristic
89C4×D15—21no—
90C4×D15—21no—
91C4×D15—41no—
92C4×D15SD1612yes—
93C4×D15Q1612yes—
94C2×C5×Dic3—22no—
95C5×Dic6—42no—
96C2×C3×Dic5—22no—
97C3×Dic10—41no—
98C3×Dic10—41no—
99C3×C5×C8—41no—
100C3⋊#168—41no—
101C3×#168—41no—
102C5×C3⋊C8—41no—
103C3×C4⋊Q8—51no—
104#946—101no—
105Q8×Dic3—101no—
106C2×ΓL(1,𝔽25)—101no—
107C2×D3×C8—101no—
108#897—52no—
109#892—101no—
110#890—101no—
111#887—52no—
112C42×D3—51no—
113#869C2×D511yescharacteristic
114C3×C4⋊C8—51no—
115C3×C4⋊C8C2×D511yescharacteristic
116Dic3⋊C8—101no—
117Dic3⋊C8—101no—
118C4⋊(C3⋊C8)—51no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C2×C5×Q8—32no—
121C2×C4×D5—31no—
122C2×C4×D5—31no—
123C2×C4×D5—31no—
124C2×Dic10—21no—
125C2×C5×C8—21no—
126C2×C5×C8—61no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4—61no—
129C42×C5C22×D311yescharacteristic
130#685—62no—
131C4⋊Dic5—21no—
132C4⋊Dic5—62no—
133C4⋊Dic5C4×D312yes—
134#683—62no—
135C4×Dic5—31no—
136C4×Dic5—31no—
137C4×Dic5—31no—
138C4×Dic5—62no—
139C2×#168—21no—
140C2×#168—61no—
141#676—122no—
142C8×D5—122no—
143#533—151no—
144#423—151no—
145C2×C4⋊C8—151no—
146#333—31no—
147#333—151no—
148#332—51no—
149#332—151no—
150C22×C3×C5C2×C22⋊C411yescharacteristic
151C2×D15—21no—
152C2×D15—21no—
153C2×D15#10312yes—
154C3×C4×C5—21no—
155C3×C4×C5C2×SD1611yescharacteristic
156C3×C4×C5C2×Q1611yescharacteristic
157C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
158C3×C4×C5#13711yescharacteristic
159Dic15—21no—
160Dic15—21no—
161Dic15#10312yes—
162C3×Dic5—42no—
163C5×Dic3—42no—
164C2×C3×Q8—101no—
165C2×C4×D3—51no—
166C2×C4×D3—51no—
167C2×C4×D3—51no—
168C2×Dic6C4×D512yes—
169C2×C3×C8—21no—
170C2×C3×C8—101no—
171C3×C4⋊C4—52no—
172C3×C4⋊C4—101no—
173C3×C42C22×D511yescharacteristic
174(C2×D3)⋊C4—102no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3—102no—
178Dic3⋊C4—102no—
179C4×Dic3—51no—
180C4×Dic3—51no—
181C4×Dic3—51no—
182C4×Dic3—102no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—101no—
185ΓL(1,𝔽25)—202no—
186D3×C8—202no—
187C22×D5—31no—
188C5×Q8—122no—
189C2×C4×C5—62no—
190C2×C4×C5C2×C4×D311yescharacteristic
191C2×C4×C5D3×D411yescharacteristic
192C2×C4×C5D3×D411yescharacteristic
193C2×Dic5—22no—
194C2×Dic5—31no—
195C2×Dic5—31no—
196C2×Dic5—31no—
197C4×D5—32no—
198C4×D5—32no—
199C4×D5—61no—
200C4×D5—61no—
201C4×D5—121no—
202Dic10—41no—
203Dic10—41no—
204C5×C8—41no—
205C5×C8—121no—
206#168—41no—
207#168—121no—
208C2×M16—301no—
209C22×C8—301no—
210C4⋊Q8—31no—
211C4⋊Q8—51no—
212#125—301no—
213C22⋊Q8—152no—
214C22⋊Q8—301no—
215C4×Q8—152no—
216C4×Q8—301no—
217#117—301no—
218C2×C42—151no—
219C4⋊C8—31no—
220C4⋊C8—51no—
221C4⋊C8—151no—
222C4⋊C8—301no—
223C4⋊C8—301no—
224C4⋊C8D3×D511yescharacteristic
225C2×C3×C5#41311yescharacteristic
226C2×C3×C5C2×#10311yescharacteristic
227C2×C3×C5#41711yescharacteristic
228D15—22no—
229C22×D3—51no—
230C3×Q8—201no—
231C3×Q8—201no—
232C2×C3×C4—102no—
233C2×C3×C4C2×C4×D511yescharacteristic
234C2×C3×C4D4×D511yescharacteristic
235C2×C3×C4D4×D511yescharacteristic
236C2×Dic3—22no—
237C2×Dic3—51no—
238C2×Dic3—51no—
239C2×Dic3—51no—
240C4×D3—52no—
241C4×D3—52no—
242C4×D3—101no—
243C4×D3—101no—
244C4×D3—201no—
245Dic6—42no—
246C3×C8—41no—
247C3×C8—201no—
248C3⋊C8—41no—
249C3⋊C8—201no—
250C22×C5D3×C22⋊C411yescharacteristic
251C2×D5—32no—
252C2×D5—61no—
253C2×D5—61no—
254C4×C5—21no—
255C4×C5—122no—
256C4×C5#91111yescharacteristic
257C4×C5D3×SD1611yescharacteristic
258C4×C5#91511yescharacteristic
259C4×C5D3×Q1611yescharacteristic
260Dic5—32no—
261Dic5—42no—
262Dic5—61no—
263Dic5—61no—
264C2×Q8—32no—
265C2×Q8—101no—
266C22×C4—151no—
267C22×C4—151no—
268C22×C4—151no—
269M16—602no—
270C2×C8—21no—
271C2×C8—61no—
272C2×C8—101no—
273C2×C8—301no—
274C2×C8—602no—
275C4⋊C4—52no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—101no—
279C4⋊C4—302no—
280C4⋊C4—302no—
281C22⋊C4—302no—
282C42—151no—
283C42—151no—
284C42—151no—
285C42—302no—
286C42C2×D3×D511yescharacteristic
287C3×C5#155011yescharacteristic, complemented, Hall
288C22×C3D5×C22⋊C411yescharacteristic
289C2×D3—52no—
290C2×D3—101no—
291C2×D3—101no—
292C3×C4—21no—
293C3×C4—202no—
294C3×C4D5×SD1611yescharacteristic
295C3×C4#406011yescharacteristic
296C3×C4D5×Q1611yescharacteristic
297C3×C4#406411yescharacteristic
298Dic3—42no—
299Dic3—52no—
300Dic3—101no—
301Dic3—101no—
302C2×C5#475111yescharacteristic
303C2×C5#477111yescharacteristic
304C2×C5D3×#10311yescharacteristic
305D5—62no—
306C23—151no—
307Q8—122no—
308Q8—201no—
309Q8—201no—
310C2×C4—62no—
311C2×C4—102no—
312C2×C4—151no—
313C2×C4—152no—
314C2×C4—152no—
315C2×C4—151no—
316C2×C4—151no—
317C2×C4—301no—
318C2×C4—301no—
319C2×C4—601no—
320C2×C4C4×D3×D511yescharacteristic
321C2×C4#677711yescharacteristic
322C2×C4#679011yescharacteristic
323C8—41no—
324C8—121no—
325C8—201no—
326C8—601no—
327C2×C3#6503411yescharacteristic
328C2×C3D5×#10311yescharacteristic
329C2×C3#6509211yescharacteristic
330D3—102no—
331C5#6842311yescharacteristic, complemented, Sylow
332C22—152no—
333C22—301no—
334C22—301no—
335C22#9147311yescharacteristic
336C4—21no—
337C4—122no—
338C4—152no—
339C4—202no—
340C4—301no—
341C4—301no—
342C4#9125811yescharacteristic
343C4#9127811yescharacteristic
344C4#9148711yescharacteristic
345C4#9151111yescharacteristic
346C3#1059927711yescharacteristic, complemented, Sylow
347C2—302no—
348C2#1174749011yescharacteristic
349C2#1174814211yescharacteristic
350C2#1174823911yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1550
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C5×#4481C2semidirect
5. C3×#64706C2semidirect
6. #11745862C2semidirect
7. #11745856C2semidirect
32. #64706D3semidirect
63. #4481D5semidirect
287. C3×C5#1550semidirect
331. C5#68423semidirect
346. C3#10599277semidirect

Maximal subgroups

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

subgroupindex
#117524842
#117509382
#117470002
C5×#44812
C3×#647062
#117458622
#117458562
#105992773
#684235