Finite Group Databasebeta

← #14281942

Subgroups — #14281942

Order 1920.

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

normal subgroups only

This group has 468 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#11752501C211yesmaximal, characteristic
2D15×C4⋊C8C211yesmaximal, characteristic, complemented
3C4×#6651C211yesmaximal, characteristic, complemented
4C5×#4484C211yesmaximal, characteristic, complemented
5C3×#64703C211yesmaximal, characteristic, complemented
6#11745843C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic, complemented
8#10599027—31nomaximal, Hall
9C2×C8×D15—21no—
10C42×D15C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×C4×D20C2211yescharacteristic
13#91465C411yescharacteristic
14C4×#1202—21no—
15#91384C411yescharacteristic
16#91383C411yescharacteristic
17#91368C411yescharacteristic
18#91366—21no—
19#91357—21no—
20#91354—21no—
21C2×#6651—21no—
22C3×C5×C4⋊C8C2211yescharacteristic
23#91098—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C5×C3⋊C8C2211yescharacteristic
26C3×C4×#168C2211yescharacteristic
27#90954—21no—
28#68170—51nomaximal, Hall
29#65914—31no—
30D5×C4⋊C8—31no—
31C4×#676—31no—
32C5×Q8⋊C8—31no—
33Q8⋊#168—31no—
34#64703D311yescharacteristic, complemented
35#64679—31no—
36C2×C4×D15C2×C411yescharacteristic
37C2×C4×D15D411yescharacteristic
38C2×C4×D15D411yescharacteristic
39C2×C5×Dic6C2×C411yescharacteristic
40C2×C3×D20C2×C411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×#1202—21no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4×Dic15C2×C411yescharacteristic
46C4×Dic15D411yescharacteristic
47C4×Dic15D411yescharacteristic
48C2×C3⋊#168—21no—
49C8×D15—42no—
50C5×C4⋊Dic3C2×C411yescharacteristic
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3—21no—
53C2×C5×C3⋊C8—21no—
54C3×#685—21no—
55C3×C4⋊Dic5C2×C411yescharacteristic
56C2×C3×#168—21no—
57Dic3⋊Dic5—21no—
58#6668—21no—
59#6668—21no—
60#6667—21no—
61#6665—21no—
62#6665—21no—
63#6665—21no—
64#6651—24no—
65#5557—51no—
66D3×C4⋊C8—51no—
67C4×ΓL(1,𝔽25)—51no—
68C3×D4⋊C8—51no—
69D4⋊(C3⋊C8)—51no—
70#4484D511yescharacteristic, complemented
71#4456—51no—
72C4×C5×Q8—31no—
73#4093—31no—
74#4092—31no—
75C2×#676—61no—
76C2×C8×D5—61no—
77#4044—61no—
78#4041—31no—
79#4040—61no—
80#4036—31no—
81C4×D20—61no—
82C4×D20C2×D311yescharacteristic
83#4018—61no—
84C42×D5—31no—
85C5×C4⋊C8C2×D311yescharacteristic
86C4×C5×C8—31no—
87#3947—61no—
88#3946—61no—
89C4⋊#168—31no—
90C4×#168C2×D311yescharacteristic
91#1483—151noSylow
92C22×D15C22⋊C411yescharacteristic
93C22×C3×D5—21no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×Dic15C22⋊C411yescharacteristic
98C2×Dic15C22⋊C411yescharacteristic
99C2×Dic15C22⋊C411yescharacteristic
100C4×D15—22no—
101C4×D15—21no—
102C4×D15—21no—
103C4×D15—21no—
104C4×D15—21no—
105C2×C5×Dic3—21no—
106C2×C5×Dic3—21no—
107C5×Dic6—21no—
108C5×Dic6—21no—
109C2×C3×Dic5—21no—
110C3×D20—21no—
111C3×D20—21no—
112C3×C4×D5—41no—
113C3×C4×D5—41no—
114#1202—42no—
115C3×C5×C8—41no—
116C3⋊#168—41no—
117C3×#168—22no—
118C5×C3⋊C8—22no—
119C3×C4×D4—51no—
120#938—51no—
121#936—51no—
122C4×#67—101no—
123#926—101no—
124C2×ΓL(1,𝔽25)—101no—
125C2×D3×C8—101no—
126#897—51no—
127#890—51no—
128#883—101no—
129#879—101no—
130C42×D3—51no—
131C4×Dic6C2×D511yescharacteristic
132C3×C4⋊C8C2×D511yescharacteristic
133C3×C4×C8—51no—
134#815—101no—
135Dic3⋊C8—101no—
136C4⋊(C3⋊C8)—51no—
137C4×C3⋊C8C2×D511yescharacteristic
138C2×C5×Q8—31no—
139C2×D20—61no—
140C2×D20C4×D311yescharacteristic
141C2×C4×D5—21no—
142C2×C4×D5—31no—
143C2×C4×D5—31no—
144C2×C4×D5—31no—
145C2×C5×C8—21no—
146C2×C5×C8—61no—
147C5×C4⋊C4—31no—
148C5×C4⋊C4—61no—
149C42×C5—61no—
150C42×C5C22×D311yescharacteristic
151#685—21no—
152#685—61no—
153#685—61no—
154#685—61no—
155#685—61no—
156C4⋊Dic5—61no—
157C4⋊Dic5C4×D311yescharacteristic
158#683—61no—
159#683—61no—
160C4×Dic5—31no—
161C4×Dic5—31no—
162C4×Dic5—31no—
163C2×#168—21no—
164C2×#168—61no—
165#676—64no—
166C8×D5—122no—
167#529—151no—
168C2×C4⋊C8—151no—
169C4×M16—151no—
170Q8⋊C8—31no—
171Q8⋊C8—151no—
172D4⋊C8—51no—
173D4⋊C8—151no—
174C22×C3×C5C2×C22⋊C411yescharacteristic
175C2×D15—21no—
176C2×D15—21no—
177C2×D15#10412yes—
178C2×C3×D5—41no—
179C2×C3×D5—41no—
180C2×C3×D5—41no—
181C3×C4×C5—21no—
182C3×C4×C5#13111yescharacteristic
183C3×C4×C5#13111yescharacteristic
184C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C3×C4×C5#13711yescharacteristic
186Dic15—21no—
187Dic15—21no—
188Dic15—21no—
189C3×Dic5—41no—
190C5×Dic3—41no—
191C5×Dic3—41no—
192C2×C3×D4—51no—
193C22×C3×C4—101no—
194C2×#67—101no—
195C2×C4×D3—51no—
196C2×C4×D3—51no—
197C2×C4×D3—51no—
198C2×Dic6C4×D511yescharacteristic
199C2×C3×C8—21no—
200C2×C3×C8—101no—
201C3×C4⋊C4—51no—
202C3×C22⋊C4—101no—
203C3×C42C22×D511yescharacteristic
204#217—101no—
205#217—101no—
206#217—101no—
207(C2×D3)⋊C4—101no—
208C4⋊Dic3—101no—
209C4⋊Dic3—101no—
210C4⋊Dic3C4×D511yescharacteristic
211Dic3⋊C4—21no—
212Dic3⋊C4—101no—
213C4×Dic3—21no—
214C4×Dic3—51no—
215C4×Dic3—51no—
216C4×Dic3—51no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—101no—
219ΓL(1,𝔽25)—104no—
220D3×C8—202no—
221C22×D5—21no—
222C22×D5—31no—
223C5×Q8—61no—
224C5×Q8—61no—
225C2×C4×C5—61no—
226C2×C4×C5—61no—
227C2×C4×C5C2×C4×D311yescharacteristic
228C2×C4×C5D3×D411yescharacteristic
229C2×C4×C5D3×D411yescharacteristic
230C2×Dic5—21no—
231C2×Dic5—31no—
232C2×Dic5—31no—
233C2×Dic5—31no—
234D20—21no—
235D20—21no—
236D20—122no—
237C4×D5—41no—
238C4×D5—41no—
239C4×D5—62no—
240C4×D5—61no—
241C4×D5—61no—
242C4×D5—61no—
243C4×D5—61no—
244C5×C8—41no—
245C5×C8—62no—
246#168—22no—
247#168—121no—
248C2×M16—301no—
249C22×C8—301no—
250#126—301no—
251#125—151no—
252#124—151no—
253#123—301no—
254C22⋊Q8—151no—
255#121—151no—
256C4×Q8—31no—
257C4×D4—51no—
258C4×D4—301no—
259#117—301no—
260C2×C42—151no—
261C4⋊C8—151no—
262C4⋊C8—301no—
263C4⋊C8D3×D511yescharacteristic
264#97—301no—
265C4×C8—31no—
266C4×C8—51no—
267C2×C3×C5#40811yescharacteristic
268C2×C3×C5#41711yescharacteristic
269C2×C3×C5C2×#10411yescharacteristic
270D15—22no—
271C3×D5—81no—
272C23×C3—101no—
273C22×D3—51no—
274C3×D4—101no—
275C3×D4—101no—
276C2×C3×C4—101no—
277C2×C3×C4—201no—
278C2×C3×C4—201no—
279C2×C3×C4C2×C4×D511yescharacteristic
280C2×C3×C4D4×D511yescharacteristic
281C2×C3×C4D4×D511yescharacteristic
282#67—202no—
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—51no—
286C2×Dic3—51no—
287C2×Dic3—51no—
288C4×D3—102no—
289C4×D3—101no—
290C4×D3—101no—
291C4×D3—101no—
292C4×D3—101no—
293Dic6—21no—
294Dic6—21no—
295C3×C8—41no—
296C3×C8—102no—
297C3⋊C8—22no—
298C3⋊C8—201no—
299C22×C5D3×C22⋊C411yescharacteristic
300C2×D5—32no—
301C2×D5—41no—
302C2×D5—41no—
303C2×D5—41no—
304C2×D5—61no—
305C2×D5—61no—
306C4×C5—21no—
307C4×C5—121no—
308C4×C5—121no—
309C4×C5#90111yescharacteristic
310C4×C5#90711yescharacteristic
311C4×C5#91111yescharacteristic
312C4×C5#91511yescharacteristic
313Dic5—41no—
314Dic5—61no—
315Dic5—61no—
316Dic5—61no—
317C2×Q8—31no—
318C2×D4—51no—
319C2×D4—301no—
320C22×C4—101no—
321C22×C4—151no—
322C22×C4—151no—
323C22×C4—151no—
324M16—304no—
325C2×C8—21no—
326C2×C8—61no—
327C2×C8—101no—
328C2×C8—301no—
329C2×C8—602no—
330C4⋊C4—31no—
331C4⋊C4—51no—
332C4⋊C4—61no—
333C4⋊C4—301no—
334C4⋊C4—301no—
335C4⋊C4—301no—
336C22⋊C4—101no—
337C22⋊C4—301no—
338C22⋊C4—301no—
339C22⋊C4—301no—
340C22⋊C4—301no—
341C42—61no—
342C42—151no—
343C42—151no—
344C42—151no—
345C42C2×D3×D511yescharacteristic
346C3×C5#148311yescharacteristic, complemented, Hall
347C22×C3—201no—
348C22×C3—201no—
349C22×C3—201no—
350C22×C3D5×C22⋊C411yescharacteristic
351C2×D3—52no—
352C2×D3—101no—
353C2×D3—101no—
354C3×C4—21no—
355C3×C4—201no—
356C3×C4#404711yescharacteristic
357C3×C4#405311yescharacteristic
358C3×C4#406011yescharacteristic
359C3×C4#406411yescharacteristic
360Dic3—41no—
361Dic3—41no—
362Dic3—101no—
363Dic3—101no—
364Dic3—101no—
365C2×C5#472711yescharacteristic
366C2×C5#477111yescharacteristic
367C2×C5D3×#10411yescharacteristic
368D5—62no—
369D5—81no—
370C23—101no—
371C23—151no—
372Q8—61no—
373Q8—61no—
374D4—101no—
375D4—101no—
376D4—602no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—101no—
380C2×C4—151no—
381C2×C4—151no—
382C2×C4—151no—
383C2×C4—201no—
384C2×C4—201no—
385C2×C4—302no—
386C2×C4—301no—
387C2×C4—301no—
388C2×C4—301no—
389C2×C4—301no—
390C2×C4C4×D3×D511yescharacteristic
391C2×C4#677711yescharacteristic
392C2×C4#679011yescharacteristic
393C8—41no—
394C8—62no—
395C8—102no—
396C8—601no—
397C2×C3—401no—
398C2×C3#6501611yescharacteristic
399C2×C3#6509211yescharacteristic
400C2×C3D5×#10411yescharacteristic
401D3—102no—
402C5#6817011yescharacteristic, complemented, Sylow
403C22—152no—
404C22—201no—
405C22—201no—
406C22—201no—
407C22—301no—
408C22—301no—
409C22#9147311yescharacteristic
410C4—21no—
411C4—121no—
412C4—121no—
413C4—201no—
414C4—301no—
415C4—301no—
416C4—301no—
417C4#9126511yescharacteristic
418C4#9126811yescharacteristic
419C4#9149811yescharacteristic
420C4#9152211yescharacteristic
421C3#1059902711yescharacteristic, complemented, Sylow
422C2—302no—
423C2—401no—
424C2#1174750711yescharacteristic
425C2#1174814311yescharacteristic
426C2#1174823611yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91465C4
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1483
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. D15×C4⋊C8C2semidirect
3. C4×#6651C2semidirect
4. C5×#4484C2semidirect
5. C3×#64703C2semidirect
6. #11745843C2semidirect
7. #11745835C2semidirect
34. #64703D3semidirect
70. #4484D5semidirect
346. C3×C5#1483semidirect
402. C5#68170semidirect
421. C3#10599027semidirect

Maximal subgroups

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

subgroupindex
#117525012
D15×C4⋊C82
C4×#66512
C5×#44842
C3×#647032
#117458432
#117458352
#105990273
#681705