Finite Group Databasebeta

← #14285053

Subgroups — #14285053

Order 1920.

504 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 100 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#11752556C211yesmaximal, characteristic
2#11750936C211yesmaximal, characteristic, complemented
3#11747000C211yesmaximal, characteristic, complemented
4C5×#4481C211yesmaximal, characteristic, complemented
5C3×#64705C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745852C211yesmaximal, characteristic, complemented
8#10599278—31nomaximal, Hall
9C2×#6766C412yes—
10C42×D15C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4020C2211yescharacteristic
13#91465—21no—
14#91465—21no—
15#91434—21no—
16#91434—21no—
17#91368C412yes—
18C2×#6648—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20#91104—21no—
21#91099—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊#168C2211yescharacteristic
25#90983—21no—
26#68385—51nomaximal, Hall
27#66059—31no—
28#65124—31no—
29D5×C4⋊C8—31no—
30C5×#333—31no—
31#64766—31no—
32#64705—31no—
33#64705D311yescharacteristic, complemented
34C2×C4×D15C2×C411yescharacteristic
35C2×C4×D15D411yescharacteristic
36C2×C4×D15D411yescharacteristic
37C2×C5×Dic6C2×C412yes—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20C2×C412yes—
41C2×#1202—22no—
42C2×D5×Dic3—22no—
43#6766—44no—
44C2×C3×C5×C8—21no—
45C3×C42×C5C2311yescharacteristic
46C4×Dic15C2×C411yescharacteristic
47C4×Dic15D411yescharacteristic
48C4×Dic15D411yescharacteristic
49C2×C3⋊#168—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3—21no—
52C2×C5×C3⋊C8—21no—
53C2×C3×#168—21no—
54#6665—22no—
55#6665—22no—
56#6648—42no—
57#5716—51no—
58#4835—51no—
59D3×C4⋊C8—51no—
60C3×#331—51no—
61#4544—51no—
62#4481—51no—
63#4481D511yescharacteristic, complemented
64C2×#713—32no—
65C5×C4⋊Q8—31no—
66#4093—32no—
67C2×C8×D5—61no—
68#4041—61no—
69#4041—61no—
70#4039—61no—
71#4039—61no—
72#4020C2×D311yescharacteristic
73C42×D5—31no—
74C5×C4⋊C8—31no—
75C5×C4⋊C8C2×D311yescharacteristic
76#3952—61no—
77#3947—61no—
78#3946—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81#1551—151noSylow
82C22×D15C22⋊C411yescharacteristic
83C22×C3×D5—22no—
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15C22⋊C411yescharacteristic
88C2×Dic15C22⋊C411yescharacteristic
89C2×Dic15C22⋊C411yescharacteristic
90C4×D15—22no—
91C4×D15—21no—
92C4×D15—21no—
93C4×D15—21no—
94C4×D15—21no—
95C2×C5×Dic3—22no—
96C5×Dic6—42no—
97C3×D20—42no—
98C3×D20—41no—
99C3×D20—41no—
100C3×D20—41no—
101C3×D20—41no—
102#1202—44no—
103D5×Dic3—44no—
104C3×C5×C8—41no—
105C3⋊#168—41no—
106C3×#168—41no—
107C5×C3⋊C8—41no—
108C2×#237—52no—
109C3×#127—51no—
110#938—101no—
111#938—101no—
112#936—52no—
113D4×Dic3—101no—
114D4×Dic3—101no—
115C2×D3×C8—101no—
116C42×D3—51no—
117#869C2×D511yescharacteristic
118C3×C4⋊C8—51no—
119C3×C4⋊C8C2×D511yescharacteristic
120(C2×D3)⋊C8—101no—
121#815—101no—
122Dic3⋊C8—101no—
123C4⋊(C3⋊C8)—51no—
124C4⋊(C3⋊C8)C2×D511yescharacteristic
125C2×C5×Q8—32no—
126#713—124no—
127C2×D20—21no—
128C2×D20—21no—
129C2×D20—62no—
130C2×D20C4×D312yes—
131C2×C4×D5—31no—
132C2×C4×D5—31no—
133C2×C4×D5—31no—
134C2×C4×D5—62no—
135C2×C5×C8—21no—
136C2×C5×C8—61no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4—61no—
139C42×C5C22×D311yescharacteristic
140#685—62no—
141#685—62no—
142C4×Dic5—31no—
143C4×Dic5—31no—
144C4×Dic5—31no—
145C2×#168—21no—
146C2×#168—61no—
147C8×D5—122no—
148#532—151no—
149#432—151no—
150C2×C4⋊C8—151no—
151#333—31no—
152#333—151no—
153#331—51no—
154#331—151no—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C2×D15—21no—
157C2×D15—21no—
158C2×D15#10012yes—
159C2×C3×D5—42no—
160C2×C3×D5—42no—
161C2×C3×D5—42no—
162C3×C4×C5—21no—
163C3×C4×C5#13511yescharacteristic
164C3×C4×C5#13511yescharacteristic
165C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
166C3×C4×C5#13711yescharacteristic
167Dic15—21no—
168Dic15—21no—
169Dic15—21no—
170C5×Dic3—42no—
171C2×C3×D4—52no—
172C2×C3×D4—101no—
173C2×C3×D4—101no—
174C2×#67—102no—
175C22×Dic3—102no—
176#237—204no—
177C2×C4×D3—51no—
178C2×C4×D3—51no—
179C2×C4×D3—51no—
180C2×Dic6C4×D512yes—
181C2×C3×C8—21no—
182C2×C3×C8—101no—
183C3×C42C22×D511yescharacteristic
184#217—102no—
185#217—102no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C4×Dic3—51no—
189C4×Dic3—51no—
190C4×Dic3—51no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—101no—
193D3×C8—202no—
194C22×D5—22no—
195C22×D5—31no—
196C5×Q8—122no—
197C2×C4×C5—62no—
198C2×C4×C5C2×C4×D311yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×Dic5—31no—
202C2×Dic5—31no—
203C2×Dic5—31no—
204D20—42no—
205D20—41no—
206D20—41no—
207D20—41no—
208D20—41no—
209D20—124no—
210C4×D5—62no—
211C4×D5—61no—
212C4×D5—61no—
213C4×D5—61no—
214C4×D5—61no—
215C4×D5—124no—
216C5×C8—41no—
217C5×C8—121no—
218#168—41no—
219#168—121no—
220C2×#41—152no—
221C22×C8—301no—
222C4⋊Q8—31no—
223#127—51no—
224#124—152no—
225#121—301no—
226#121—301no—
227C4×D4—301no—
228C4×D4—301no—
229C2×C42—151no—
230C4⋊C8—31no—
231C4⋊C8—51no—
232C4⋊C8—151no—
233C4⋊C8—301no—
234C4⋊C8D3×D511yescharacteristic
235C22⋊C8—301no—
236#97—301no—
237C2×C3×C5C2×#10011yescharacteristic
238C2×C3×C5#41611yescharacteristic
239C2×C3×C5#41711yescharacteristic
240D15—22no—
241C3×D5—82no—
242C23×C3—102no—
243C22×D3—51no—
244C3×D4—202no—
245C3×D4—201no—
246C3×D4—201no—
247C3×D4—201no—
248C3×D4—201no—
249C2×C3×C4C2×C4×D511yescharacteristic
250C2×C3×C4D4×D511yescharacteristic
251C2×C3×C4D4×D511yescharacteristic
252#67—204no—
253C2×Dic3—22no—
254C2×Dic3—51no—
255C2×Dic3—51no—
256C2×Dic3—51no—
257C2×Dic3—204no—
258C4×D3—102no—
259C4×D3—101no—
260C4×D3—101no—
261C4×D3—101no—
262C4×D3—101no—
263Dic6—42no—
264C3×C8—41no—
265C3×C8—201no—
266C3⋊C8—41no—
267C3⋊C8—201no—
268C22×C5D3×C22⋊C411yescharacteristic
269C2×D5—32no—
270C2×D5—42no—
271C2×D5—42no—
272C2×D5—42no—
273C2×D5—61no—
274C2×D5—61no—
275C4×C5—21no—
276C4×C5—122no—
277C4×C5#91111yescharacteristic
278C4×C5#91211yescharacteristic
279C4×C5#91511yescharacteristic
280C4×C5#91611yescharacteristic
281Dic5—61no—
282Dic5—61no—
283Dic5—61no—
284#41—604no—
285C2×Q8—32no—
286C2×D4—52no—
287C2×D4—101no—
288C2×D4—101no—
289C2×D4—302no—
290C22×C4—151no—
291C22×C4—151no—
292C22×C4—151no—
293C22×C4—302no—
294C2×C8—21no—
295C2×C8—61no—
296C2×C8—101no—
297C2×C8—301no—
298C2×C8—602no—
299C4⋊C4—61no—
300C4⋊C4—61no—
301C22⋊C4—302no—
302C22⋊C4—302no—
303C42—151no—
304C42—151no—
305C42—151no—
306C42C2×D3×D511yescharacteristic
307C3×C5#155111yescharacteristic, complemented, Hall
308C22×C3—202no—
309C22×C3—202no—
310C22×C3—202no—
311C22×C3D5×C22⋊C411yescharacteristic
312C2×D3—52no—
313C2×D3—101no—
314C2×D3—101no—
315C3×C4—21no—
316C3×C4#406011yescharacteristic
317C3×C4#406211yescharacteristic
318C3×C4#406411yescharacteristic
319C3×C4#406511yescharacteristic
320Dic3—42no—
321Dic3—101no—
322Dic3—101no—
323Dic3—101no—
324C2×C5D3×#10011yescharacteristic
325C2×C5#477111yescharacteristic
326C2×C5#477211yescharacteristic
327D5—62no—
328D5—82no—
329C23—102no—
330C23—151no—
331Q8—122no—
332D4—202no—
333D4—201no—
334D4—201no—
335D4—201no—
336D4—201no—
337D4—604no—
338C2×C4—62no—
339C2×C4—151no—
340C2×C4—151no—
341C2×C4—151no—
342C2×C4—302no—
343C2×C4—301no—
344C2×C4—301no—
345C2×C4—301no—
346C2×C4—301no—
347C2×C4—604no—
348C2×C4C4×D3×D511yescharacteristic
349C2×C4#677711yescharacteristic
350C2×C4#679011yescharacteristic
351C8—41no—
352C8—121no—
353C8—201no—
354C8—601no—
355C2×C3—402no—
356C2×C3D5×#10011yescharacteristic
357C2×C3#6509211yescharacteristic
358C2×C3#6509311yescharacteristic
359D3—102no—
360C5#6838511yescharacteristic, complemented, Sylow
361C22—152no—
362C22—202no—
363C22—202no—
364C22—202no—
365C22—301no—
366C22—301no—
367C22#9147311yescharacteristic
368C4—21no—
369C4—122no—
370C4—301no—
371C4—301no—
372C4—301no—
373C4#9125811yescharacteristic
374C4#9127811yescharacteristic
375C4#9149711yescharacteristic
376C4#9152111yescharacteristic
377C3#1059927811yescharacteristic, complemented, Sylow
378C2—302no—
379C2—402no—
380C2#1174750611yescharacteristic
381C2#1174814211yescharacteristic
382C2#1174822411yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11752556C2
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1551
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
2. #11750936C2semidirect
3. #11747000C2semidirect
4. C5×#4481C2semidirect
5. C3×#64705C2semidirect
6. #11745862C2semidirect
7. #11745852C2semidirect
33. #64705D3semidirect
63. #4481D5semidirect
307. C3×C5#1551semidirect
360. C5#68385semidirect
377. C3#10599278semidirect

Maximal subgroups

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

subgroupindex
#117525562
#117509362
#117470002
C5×#44812
C3×#647052
#117458622
#117458522
#105992783
#683855