Finite Group Databasebeta

← #14285430

Subgroups — #14285430

Order 1920.

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

normal subgroups only

This group has 508 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#11750938C211yesmaximal, characteristic, complemented
3#11747015C211yesmaximal, characteristic, complemented
4C5×#4481C211yesmaximal, characteristic, complemented
5C3×#64705C211yesmaximal, characteristic, complemented
6#11745862C211yesmaximal, characteristic, complemented
7#11745852C211yesmaximal, characteristic, complemented
8#10599282—31nomaximal, Hall
9C2×#6766C412yes—
10C2×#6705—21no—
11C42×D15C2211yescharacteristic
12C5×#869C2211yescharacteristic
13C3×#4020C2211yescharacteristic
14#91465—21no—
15#91465—21no—
16#91434—21no—
17#91434—21no—
18#91368C412yes—
19C2×#6651—21no—
20C3×C5×C4⋊C8C2211yescharacteristic
21#91098—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊#168C2211yescharacteristic
25#90983—21no—
26#68389—51nomaximal, Hall
27#66059—31no—
28#65126—31no—
29#65126—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—
50#6705—42no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3—21no—
53C2×C5×C3⋊C8—21no—
54C2×C3×#168—21no—
55#6665—22no—
56#6665—22no—
57#6651—42no—
58#5716—51no—
59#4837—51no—
60#4837—51no—
61C3×#331—51no—
62#4544—51no—
63#4481—51no—
64#4481D511yescharacteristic, complemented
65C2×#713—32no—
66C5×C4⋊Q8—31no—
67#4093—32no—
68C2×#676—61no—
69C2×#676—61no—
70#4041—61no—
71#4041—61no—
72#4039—61no—
73#4039—61no—
74#4020C2×D311yescharacteristic
75C42×D5—31no—
76C5×C4⋊C8—31no—
77C5×C4⋊C8C2×D311yescharacteristic
78#3946—61no—
79#3946—61no—
80C4⋊#168—31no—
81C4⋊#168C2×D311yescharacteristic
82#1560—151noSylow
83C22×D15C22⋊C411yescharacteristic
84C22×C3×D5—22no—
85C2×C3×C4×C5C22×C411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15C22⋊C411yescharacteristic
89C2×Dic15C22⋊C411yescharacteristic
90C2×Dic15C22⋊C411yescharacteristic
91C4×D15—21no—
92C4×D15—21no—
93C4×D15—21no—
94C4×D15—21no—
95C4×D15—22no—
96C2×C5×Dic3—22no—
97C5×Dic6—42no—
98C3×D20—42no—
99C3×D20—41no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103#1202—44no—
104D5×Dic3—44no—
105C3×C5×C8—41no—
106C3⋊#168—41no—
107C3×#168—41no—
108C5×C3⋊C8—41no—
109C2×#237—52no—
110C3×#127—51no—
111#938—101no—
112#938—101no—
113#936—52no—
114D4×Dic3—101no—
115D4×Dic3—101no—
116C2×ΓL(1,𝔽25)—101no—
117C2×ΓL(1,𝔽25)—101no—
118C42×D3—51no—
119#869C2×D511yescharacteristic
120C3×C4⋊C8—51no—
121C3×C4⋊C8C2×D511yescharacteristic
122Dic3⋊C8—101no—
123Dic3⋊C8—101no—
124C4⋊(C3⋊C8)—51no—
125C4⋊(C3⋊C8)C2×D511yescharacteristic
126C2×C5×Q8—32no—
127#713—124no—
128C2×D20—21no—
129C2×D20—21no—
130C2×D20—62no—
131C2×D20C4×D312yes—
132C2×C4×D5—31no—
133C2×C4×D5—31no—
134C2×C4×D5—31no—
135C2×C4×D5—62no—
136C2×C5×C8—21no—
137C2×C5×C8—61no—
138C5×C4⋊C4—61no—
139C5×C4⋊C4—61no—
140C42×C5C22×D311yescharacteristic
141#685—62no—
142#685—62no—
143C4×Dic5—31no—
144C4×Dic5—31no—
145C4×Dic5—31no—
146C2×#168—21no—
147C2×#168—61no—
148#676—122no—
149#676—122no—
150#532—151no—
151#423—151no—
152#423—151no—
153#333—31no—
154#333—151no—
155#331—51no—
156#331—151no—
157C22×C3×C5C2×C22⋊C411yescharacteristic
158C2×D15—21no—
159C2×D15—21no—
160C2×D15—21no—
161C2×C3×D5—42no—
162C2×C3×D5—42no—
163C2×C3×D5—42no—
164C3×C4×C5—21no—
165C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5#13711yescharacteristic
168C3×C4×C5#13711yescharacteristic
169Dic15—21no—
170Dic15—21no—
171Dic15#10012yes—
172C5×Dic3—42no—
173C2×C3×D4—52no—
174C2×C3×D4—101no—
175C2×C3×D4—101no—
176C2×#67—102no—
177C22×Dic3—102no—
178#237—204no—
179C2×C4×D3—51no—
180C2×C4×D3—51no—
181C2×C4×D3—51no—
182C2×Dic6C4×D512yes—
183C2×C3×C8—21no—
184C2×C3×C8—101no—
185C3×C42C22×D511yescharacteristic
186#217—102no—
187#217—102no—
188C4⋊Dic3—21no—
189C4⋊Dic3—21no—
190C4×Dic3—51no—
191C4×Dic3—51no—
192C4×Dic3—51no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—101no—
195ΓL(1,𝔽25)—202no—
196ΓL(1,𝔽25)—202no—
197C22×D5—22no—
198C22×D5—31no—
199C5×Q8—122no—
200C2×C4×C5—62no—
201C2×C4×C5C2×C4×D311yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×Dic5—31no—
205C2×Dic5—31no—
206C2×Dic5—31no—
207D20—42no—
208D20—41no—
209D20—41no—
210D20—41no—
211D20—41no—
212D20—124no—
213C4×D5—62no—
214C4×D5—61no—
215C4×D5—61no—
216C4×D5—61no—
217C4×D5—61no—
218C4×D5—124no—
219C5×C8—41no—
220C5×C8—121no—
221#168—41no—
222#168—121no—
223C2×#41—152no—
224C2×M16—301no—
225C2×M16—301no—
226C4⋊Q8—31no—
227#127—51no—
228#124—152no—
229#121—301no—
230#121—301no—
231C4×D4—301no—
232C4×D4—301no—
233C2×C42—151no—
234C4⋊C8—31no—
235C4⋊C8—51no—
236C4⋊C8—151no—
237C4⋊C8—301no—
238C4⋊C8—301no—
239C4⋊C8D3×D511yescharacteristic
240C2×C3×C5C2×#10011yescharacteristic
241C2×C3×C5#41711yescharacteristic
242C2×C3×C5#41711yescharacteristic
243D15—41no—
244C3×D5—82no—
245C23×C3—102no—
246C22×D3—51no—
247C3×D4—202no—
248C3×D4—201no—
249C3×D4—201no—
250C3×D4—201no—
251C3×D4—201no—
252C2×C3×C4C2×C4×D511yescharacteristic
253C2×C3×C4D4×D511yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255#67—204no—
256C2×Dic3—22no—
257C2×Dic3—51no—
258C2×Dic3—51no—
259C2×Dic3—51no—
260C2×Dic3—204no—
261C4×D3—102no—
262C4×D3—101no—
263C4×D3—101no—
264C4×D3—101no—
265C4×D3—101no—
266Dic6—42no—
267C3×C8—41no—
268C3×C8—201no—
269C3⋊C8—41no—
270C3⋊C8—201no—
271C22×C5D3×C22⋊C411yescharacteristic
272C2×D5—42no—
273C2×D5—42no—
274C2×D5—42no—
275C2×D5—61no—
276C2×D5—61no—
277C2×D5—61no—
278C4×C5—21no—
279C4×C5—122no—
280C4×C5#91111yescharacteristic
281C4×C5#91111yescharacteristic
282C4×C5#91511yescharacteristic
283C4×C5#91511yescharacteristic
284Dic5—32no—
285Dic5—61no—
286Dic5—61no—
287#41—604no—
288C2×Q8—32no—
289C2×D4—52no—
290C2×D4—101no—
291C2×D4—101no—
292C2×D4—302no—
293C22×C4—151no—
294C22×C4—151no—
295C22×C4—151no—
296C22×C4—302no—
297M16—602no—
298M16—602no—
299C2×C8—21no—
300C2×C8—61no—
301C2×C8—101no—
302C2×C8—301no—
303C4⋊C4—61no—
304C4⋊C4—61no—
305C22⋊C4—302no—
306C22⋊C4—302no—
307C42—151no—
308C42—151no—
309C42—151no—
310C42C2×D3×D511yescharacteristic
311C3×C5#156011yescharacteristic, complemented, Hall
312C22×C3—202no—
313C22×C3—202no—
314C22×C3—202no—
315C22×C3D5×C22⋊C411yescharacteristic
316C2×D3—101no—
317C2×D3—101no—
318C2×D3—101no—
319C3×C4—21no—
320C3×C4#406011yescharacteristic
321C3×C4#406011yescharacteristic
322C3×C4#406411yescharacteristic
323C3×C4#406411yescharacteristic
324Dic3—42no—
325Dic3—52no—
326Dic3—101no—
327Dic3—101no—
328C2×C5D3×#10011yescharacteristic
329C2×C5#477111yescharacteristic
330C2×C5#477111yescharacteristic
331D5—82no—
332D5—121no—
333C23—102no—
334C23—151no—
335Q8—122no—
336D4—202no—
337D4—201no—
338D4—201no—
339D4—201no—
340D4—201no—
341D4—604no—
342C2×C4—62no—
343C2×C4—151no—
344C2×C4—151no—
345C2×C4—151no—
346C2×C4—302no—
347C2×C4—301no—
348C2×C4—301no—
349C2×C4—301no—
350C2×C4—301no—
351C2×C4—604no—
352C2×C4C4×D3×D511yescharacteristic
353C2×C4#677711yescharacteristic
354C2×C4#679011yescharacteristic
355C8—41no—
356C8—121no—
357C8—201no—
358C8—601no—
359C2×C3—402no—
360C2×C3D5×#10011yescharacteristic
361C2×C3#6509211yescharacteristic
362C2×C3#6509211yescharacteristic
363D3—201no—
364C5#6838911yescharacteristic, complemented, Sylow
365C22—202no—
366C22—202no—
367C22—202no—
368C22—301no—
369C22—301no—
370C22—301no—
371C22#9147311yescharacteristic
372C4—21no—
373C4—122no—
374C4—152no—
375C4—301no—
376C4—301no—
377C4#9125811yescharacteristic
378C4#9127811yescharacteristic
379C4#9149811yescharacteristic
380C4#9152211yescharacteristic
381C3#1059928211yescharacteristic, complemented, Sylow
382C2—402no—
383C2—601no—
384C2#1174750711yescharacteristic
385C2#1174814211yescharacteristic
386C2#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#1560
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. #11750938C2semidirect
3. #11747015C2semidirect
4. C5×#4481C2semidirect
5. C3×#64705C2semidirect
6. #11745862C2semidirect
7. #11745852C2semidirect
33. #64705D3semidirect
64. #4481D5semidirect
311. C3×C5#1560semidirect
364. C5#68389semidirect
381. C3#10599282semidirect

Maximal subgroups

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

subgroupindex
#117525562
#117509382
#117470152
C5×#44812
C3×#647052
#117458622
#117458522
#105992823
#683895