Subgroups — C₄×D₅×D₂₄ #14416005

Order 1920.

1232 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×D₂₄	C₂	1	1	yes	maximal, characteristic
2	C₄×D₅×D₁₂	C₂	1	2	yes	maximal, complemented
3	C₄×D₁₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	D₅×#821	C₂	1	2	yes	maximal, complemented
7	#11747766	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
9	#11747745	C₂	1	2	yes	maximal, complemented
10	D₅×#818	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#6654	C₂	1	2	yes	maximal, complemented
12	C₄×D₅×D₈	—	3	1	no	maximal, Hall
13	C₂×D₅×D₁₂	C₂²	1	2	yes	—
14	C₂×C₄×D₃×D₅	—	2	2	no	—
15	C₂×D₁₂₀	C₂²	1	1	yes	characteristic
16	C₄×D₆₀	C₂²	1	2	yes	complemented
17	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
18	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
19	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
21	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
22	D₅×(C₂×D₃)⋊C₄	—	2	2	no	—
23	C₄×#1203	—	2	2	no	—
24	#91418	C₂²	1	2	yes	complemented
25	Dic₅×D₁₂	C₂²	1	2	yes	complemented
26	D₅×C₄⋊Dic₃	C₂²	1	2	yes	—
27	#91405	—	2	2	no	—
28	C₂×#6654	C₂²	1	2	yes	—
29	D₅×D₂₄	C₄	1	8	yes	direct product factor
30	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
31	#91105	C₂²	1	2	yes	complemented
32	#91102	C₂²	1	1	yes	characteristic, complemented
33	C₅×#821	C₂²	1	2	yes	complemented
34	C₅×#818	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
38	#90988	C₂²	1	2	yes	complemented
39	#90969	C₂²	1	2	yes	complemented
40	#90967	C₂²	1	2	yes	complemented
41	C₂×C₄×D₂₄	—	5	1	no	maximal, Hall
42	C₂×D₅×D₈	—	3	1	no	—
43	C₄×D₄×D₅	—	3	2	no	—
44	C₄×C₅×D₈	—	3	1	no	—
45	D₈×Dic₅	—	3	1	no	—
46	C₄×#686	—	3	2	no	—
47	D₅×#107	—	3	1	no	—
48	#65161	—	3	1	no	—
49	D₅×#102	—	3	2	no	—
50	#65045	—	3	2	no	—
51	C₄×D₄₀	—	3	1	no	—
52	C₄×C₈×D₅	D₃	1	1	yes	characteristic, complemented
53	C₂²×D₃×D₅	—	2	2	no	—
54	C₂×D₆₀	C₂³	1	2	yes	—
55	C₂×C₄×D₁₅	—	2	2	no	—
56	C₂×C₅×D₁₂	C₂³	1	2	yes	—
57	C₂×C₄×C₅×D₃	—	2	2	no	—
58	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
60	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
61	C₂×#1203	—	2	2	no	—
62	C₂×#1200	—	2	2	no	—
63	C₂×D₃×Dic₅	—	2	2	no	—
64	C₂×D₅×Dic₃	—	2	2	no	—
65	D₅×D₁₂	—	2	4	no	—
66	D₅×D₁₂	C₂×C₄	1	8	yes	complemented
67	C₄×D₃×D₅	—	4	8	no	—
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	#6714	—	2	2	no	—
72	C₄⋊Dic₁₅	C₂³	1	2	yes	—
73	D₁₂₀	C₂×C₄	1	4	yes	complemented
74	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
75	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
76	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
77	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
78	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
79	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×#168	C₂³	1	1	yes	characteristic
81	C₂×C₃×#168	C₂³	1	1	yes	characteristic
82	C₃×C₈×D₅	—	2	2	no	—
83	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
84	#6668	—	2	2	no	—
85	#6667	—	2	2	no	—
86	(C₂×D₃)⋊Dic₅	—	2	2	no	—
87	#6654	C₂×C₄	1	8	yes	complemented
88	C₂²×D₂₄	—	5	1	no	—
89	C₂×C₄×D₁₂	—	5	2	no	—
90	C₂×C₃×C₄×C₈	—	5	1	no	—
91	C₂×#821	—	5	2	no	—
92	C₂×#818	—	5	1	no	—
93	C₄×D₂₄	—	5	1	no	—
94	C₄×D₂₄	—	5	2	no	—
95	C₄×D₂₄	—	5	1	no	—
96	C₄×D₂₄	—	5	2	no	—
97	C₄×D₂₄	—	5	1	no	—
98	C₄×D₂₄	D₅	1	1	yes	characteristic, direct product factor
99	C₂×D₄×D₅	—	3	2	no	—
100	C₂²×C₄×D₅	—	6	2	no	—
101	C₂×C₅×D₈	—	3	1	no	—
102	C₄×C₅×D₄	—	3	2	no	—
103	D₄×Dic₅	—	3	2	no	—
104	C₂×#686	—	3	2	no	—
105	C₄×C₂²⋊D₅	—	6	2	no	—
106	D₅×D₈	—	3	8	no	—
107	C₂×D₄₀	—	3	1	no	—
108	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
109	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
110	#4039	—	3	2	no	—
111	D₅×C₄⋊C₄	—	3	2	no	—
112	#4027	—	6	2	no	—
113	D₅×C₂²⋊C₄	—	6	2	no	—
114	C₄×D₂₀	—	3	2	no	—
115	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
116	C₅×#107	—	3	1	no	—
117	C₅×#102	—	3	2	no	—
118	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
119	#3964	—	3	2	no	—
120	#3953	—	3	2	no	—
121	#3950	—	3	1	no	—
122	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic, complemented
123	C₈×Dic₅	C₂×D₃	1	1	yes	characteristic, complemented
124	#3941	—	3	2	no	—
125	#3939	—	3	2	no	—
126	C₄×#168	C₂×D₃	1	1	yes	characteristic, complemented
127	C₂×C₄×D₈	—	15	1	no	Sylow
128	C₂²×D₁₅	—	2	2	no	—
129	C₂²×C₅×D₃	—	2	2	no	—
130	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
131	C₂×D₃×D₅	—	2	8	no	—
132	C₂×D₃×D₅	—	4	4	no	—
133	C₂×D₃×D₅	—	4	4	no	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₂×Dic₁₅	—	2	2	no	—
138	D₆₀	—	2	2	no	—
139	D₆₀	C₂²×C₄	1	4	yes	complemented
140	C₄×D₁₅	—	4	4	no	—
141	C₂×C₅×Dic₃	—	2	2	no	—
142	C₅×D₁₂	—	2	2	no	—
143	C₅×D₁₂	C₂²×C₄	1	4	yes	complemented
144	C₄×C₅×D₃	—	4	4	no	—
145	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
148	C₃×C₄×D₅	—	2	2	no	—
149	C₃×C₄×D₅	D₈	1	4	yes	complemented
150	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
151	C₃×C₄×D₅	#41	1	2	yes	—
152	#1203	—	2	8	no	—
153	#1200	—	4	4	no	—
154	D₃×Dic₅	—	4	4	no	—
155	D₅×Dic₃	—	4	4	no	—
156	C₃×C₅×C₈	—	2	1	no	—
157	C₃×C₅×C₈	C₂²×C₄	1	2	yes	complemented
158	C₃×#168	—	2	1	no	—
159	C₃×#168	C₂²×C₄	1	2	yes	complemented
160	C₂²×D₁₂	—	5	2	no	—
161	C₂²×C₄×D₃	—	10	2	no	—
162	C₂²×C₃×C₈	—	5	1	no	—
163	C₂²×C₃×C₈	—	5	1	no	—
164	C₂×C₃×C₄²	—	5	1	no	—
165	C₂×(C₂×D₃)⋊C₄	—	10	2	no	—
166	C₂×C₄⋊Dic₃	—	5	2	no	—
167	C₂×D₂₄	—	5	2	no	—
168	C₂×D₂₄	—	5	1	no	—
169	C₂×D₂₄	—	5	8	no	—
170	C₂×D₂₄	C₂×D₅	1	1	yes	characteristic
171	C₄×D₁₂	—	5	2	no	—
172	C₄×D₁₂	—	5	2	no	—
173	C₄×D₁₂	—	5	2	no	—
174	C₄×D₁₂	—	10	2	no	—
175	C₄×D₁₂	—	10	2	no	—
176	C₄×D₁₂	C₂×D₅	1	2	yes	complemented
177	C₃×C₄×C₈	—	5	1	no	—
178	C₃×C₄×C₈	—	5	1	no	—
179	C₃×C₄×C₈	—	5	1	no	—
180	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
181	#821	—	5	2	no	—
182	#821	—	5	2	no	—
183	#821	—	5	2	no	—
184	#821	C₂×D₅	1	2	yes	complemented
185	#818	—	5	1	no	—
186	#818	—	5	2	no	—
187	#818	C₂×D₅	1	1	yes	characteristic, complemented
188	C₂³×D₅	—	6	2	no	—
189	C₂×C₅×D₄	—	3	2	no	—
190	C₂²×C₄×C₅	—	6	2	no	—
191	C₂×C₂²⋊D₅	—	6	2	no	—
192	C₂²×Dic₅	—	6	2	no	—
193	D₄×D₅	—	3	8	no	—
194	D₄×D₅	—	6	4	no	—
195	C₂×D₂₀	—	3	2	no	—
196	C₂×C₄×D₅	—	6	2	no	—
197	C₂×C₄×D₅	—	6	2	no	—
198	C₂×C₄×D₅	—	6	2	no	—
199	C₂×C₄×D₅	—	12	8	no	—
200	C₂×C₄×D₅	D₁₂	1	1	yes	characteristic
201	C₂×C₄×D₅	D₁₂	1	1	yes	characteristic
202	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
203	C₅×D₈	—	3	4	no	—
204	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
205	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
206	C₅×C₄⋊C₄	—	3	2	no	—
207	C₅×C₂²⋊C₄	—	6	2	no	—
208	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
209	C₂²⋊Dic₅	—	6	2	no	—
210	#686	—	3	8	no	—
211	#685	—	6	2	no	—
212	#685	—	6	2	no	—
213	C₄⋊Dic₅	—	3	2	no	—
214	#683	—	6	2	no	—
215	C₄×Dic₅	D₁₂	1	1	yes	characteristic
216	C₄×Dic₅	D₁₂	1	1	yes	characteristic
217	C₄×Dic₅	C₂²×D₃	1	1	yes	characteristic
218	C₂×#168	C₂²×D₃	1	1	yes	characteristic
219	C₂×#168	C₂²×D₃	1	1	yes	characteristic
220	D₄₀	—	3	4	no	—
221	C₈×D₅	—	2	2	no	—
222	C₈×D₅	C₄×D₃	1	4	yes	complemented
223	C₂²×D₈	—	15	1	no	—
224	C₂×C₄×D₄	—	15	2	no	—
225	C₄×D₈	—	3	1	no	—
226	C₄×D₈	—	15	2	no	—
227	C₄×D₈	—	15	1	no	—
228	C₄×D₈	—	15	2	no	—
229	C₄×D₈	—	15	1	no	—
230	C₄×D₈	—	15	1	no	—
231	C₂×#107	—	15	1	no	—
232	C₂×#102	—	15	2	no	—
233	C₂×C₄×C₈	—	5	1	no	—
234	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
235	C₂×D₁₅	—	2	4	no	—
236	C₂×D₁₅	—	4	2	no	—
237	C₂×D₁₅	—	4	2	no	—
238	C₂×C₅×D₃	—	2	4	no	—
239	C₂×C₅×D₃	—	4	2	no	—
240	C₂×C₅×D₃	—	4	2	no	—
241	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
242	C₂×C₃×D₅	C₂×D₈	1	2	yes	—
243	C₂×C₃×D₅	#135	1	2	yes	—
244	D₃×D₅	—	4	16	no	—
245	C₃×C₄×C₅	—	2	1	no	—
246	C₃×C₄×C₅	C₂×D₈	1	2	yes	complemented
247	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
248	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
249	Dic₁₅	—	4	2	no	—
250	C₃×Dic₅	—	2	1	no	—
251	C₃×Dic₅	C₄×D₄	1	2	yes	—
252	C₃×Dic₅	C₂×D₈	1	2	yes	complemented
253	C₅×Dic₃	—	4	2	no	—
254	C₂³×D₃	—	10	2	no	—
255	C₂²×C₃×C₄	—	5	1	no	—
256	C₂²×C₃×C₄	—	5	1	no	—
257	C₂²×C₃×C₄	—	5	1	no	—
258	C₂²×Dic₃	—	10	2	no	—
259	C₂×D₁₂	—	5	2	no	—
260	C₂×D₁₂	—	5	8	no	—
261	C₂×D₁₂	—	10	4	no	—
262	C₂×D₁₂	—	10	2	no	—
263	C₂×D₁₂	C₂²×D₅	1	2	yes	—
264	C₂×C₄×D₃	—	2	2	no	—
265	C₂×C₄×D₃	—	10	2	no	—
266	C₂×C₄×D₃	—	10	2	no	—
267	C₂×C₄×D₃	—	10	2	no	—
268	C₂×C₄×D₃	—	20	8	no	—
269	C₂×C₃×C₈	—	5	1	no	—
270	C₂×C₃×C₈	—	5	4	no	—
271	C₂×C₃×C₈	—	5	1	no	—
272	C₂×C₃×C₈	—	10	2	no	—
273	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
274	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
275	C₃×C₄²	—	5	1	no	—
276	C₃×C₄²	—	5	1	no	—
277	C₃×C₄²	—	5	1	no	—
278	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
279	(C₂×D₃)⋊C₄	—	2	2	no	—
280	(C₂×D₃)⋊C₄	—	10	2	no	—
281	(C₂×D₃)⋊C₄	—	10	2	no	—
282	(C₂×D₃)⋊C₄	—	10	2	no	—
283	C₄⋊Dic₃	—	5	2	no	—
284	C₄⋊Dic₃	—	10	2	no	—
285	C₄⋊Dic₃	C₂²×D₅	1	2	yes	—
286	D₂₄	—	5	8	no	—
287	D₂₄	—	5	4	no	—
288	D₂₄	C₄×D₅	1	4	yes	direct product factor
289	C₂³×C₅	—	6	2	no	—
290	C₂²×D₅	—	6	2	no	—
291	C₂²×D₅	—	6	8	no	—
292	C₂²×D₅	—	12	4	no	—
293	C₂²×D₅	—	12	4	no	—
294	C₂²×D₅	C₂×D₁₂	1	1	yes	characteristic
295	C₅×D₄	—	3	4	no	—
296	C₅×D₄	—	6	2	no	—
297	C₂×C₄×C₅	—	6	2	no	—
298	C₂×C₄×C₅	—	12	4	no	—
299	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
301	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
302	C₂²⋊D₅	—	6	8	no	—
303	C₂×Dic₅	—	6	2	no	—
304	C₂×Dic₅	—	12	4	no	—
305	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
306	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
307	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
308	D₂₀	—	3	4	no	—
309	D₂₀	—	6	2	no	—
310	C₄×D₅	—	2	2	no	—
311	C₄×D₅	—	12	4	no	—
312	C₄×D₅	—	12	4	no	—
313	C₄×D₅	—	12	4	no	—
314	C₄×D₅	D₂₄	1	4	yes	direct product factor
315	C₄×D₅	C₂×C₄×D₃	1	2	yes	—
316	C₄×D₅	#235	1	2	yes	—
317	C₅×C₈	—	2	1	no	—
318	C₅×C₈	C₂×C₄×D₃	1	2	yes	complemented
319	#168	—	2	1	no	—
320	#168	C₂×C₄×D₃	1	2	yes	complemented
321	C₂²×D₄	—	15	2	no	—
322	C₂³×C₄	—	30	2	no	—
323	C₂×D₈	—	3	1	no	—
324	C₂×D₈	—	15	8	no	—
325	C₂×D₈	—	15	2	no	—
326	C₂×D₈	—	15	1	no	—
327	C₂²×C₈	—	5	1	no	—
328	C₂²×C₈	—	5	1	no	—
329	C₄×D₄	—	3	2	no	—
330	C₄×D₄	—	15	2	no	—
331	C₄×D₄	—	15	2	no	—
332	C₄×D₄	—	15	2	no	—
333	C₄×D₄	—	30	2	no	—
334	C₄×D₄	—	30	2	no	—
335	C₂×C₄⋊C₄	—	15	2	no	—
336	C₂×C₂²⋊C₄	—	30	2	no	—
337	C₂×C₄²	—	5	1	no	—
338	#107	—	3	1	no	—
339	#107	—	15	2	no	—
340	#107	—	15	1	no	—
341	#102	—	3	2	no	—
342	#102	—	15	2	no	—
343	#102	—	15	2	no	—
344	#102	—	15	2	no	—
345	C₄×C₈	—	5	1	no	—
346	C₄×C₈	—	5	1	no	—
347	C₄×C₈	—	5	1	no	—
348	C₄×C₈	D₃×D₅	1	1	yes	characteristic, complemented
349	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
350	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
351	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
352	D₁₅	—	4	4	no	—
353	C₃×D₅	C₄×D₈	1	4	yes	complemented
354	C₅×D₃	—	4	4	no	—
355	C₂³×C₃	—	5	1	no	—
356	C₂²×D₃	—	2	2	no	—
357	C₂²×D₃	—	10	8	no	—
358	C₂²×D₃	—	10	2	no	—
359	C₂²×D₃	—	20	4	no	—
360	C₂²×D₃	—	20	4	no	—
361	C₂×C₃×C₄	—	5	1	no	—
362	C₂×C₃×C₄	—	5	1	no	—
363	C₂×C₃×C₄	—	5	2	no	—
364	C₂×C₃×C₄	—	5	2	no	—
365	C₂×C₃×C₄	—	5	4	no	—
366	C₂×C₃×C₄	—	5	1	no	—
367	C₂×C₃×C₄	—	10	2	no	—
368	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
369	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
371	C₂×Dic₃	—	2	2	no	—
372	C₂×Dic₃	—	10	2	no	—
373	C₂×Dic₃	—	20	4	no	—
374	D₁₂	—	2	2	no	—
375	D₁₂	—	5	4	no	—
376	D₁₂	—	10	8	no	—
377	D₁₂	—	10	2	no	—
378	D₁₂	C₂×C₄×D₅	1	4	yes	complemented
379	C₄×D₃	—	4	4	no	—
380	C₄×D₃	—	20	4	no	—
381	C₄×D₃	—	20	4	no	—
382	C₄×D₃	—	20	4	no	—
383	C₃×C₈	—	2	1	no	—
384	C₃×C₈	—	5	2	no	—
385	C₃×C₈	—	10	1	no	—
386	C₃×C₈	C₂×C₄×D₅	1	2	yes	complemented
387	C₂²×C₅	—	6	4	no	—
388	C₂²×C₅	—	12	2	no	—
389	C₂²×C₅	—	12	2	no	—
390	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
391	C₂×D₅	—	6	4	no	—
392	C₂×D₅	—	12	2	no	—
393	C₂×D₅	—	12	2	no	—
394	C₂×D₅	—	12	16	no	—
395	C₂×D₅	C₄×D₁₂	1	2	yes	—
396	C₂×D₅	C₂×D₂₄	1	2	yes	—
397	C₂×D₅	#904	1	2	yes	—
398	C₄×C₅	—	2	1	no	—
399	C₄×C₅	—	12	2	no	—
400	C₄×C₅	C₂×D₂₄	1	2	yes	complemented
401	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
402	C₄×C₅	C₂×#235	1	1	yes	characteristic
403	Dic₅	—	2	1	no	—
404	Dic₅	—	12	2	no	—
405	Dic₅	C₄×D₁₂	1	2	yes	—
406	Dic₅	C₂×D₂₄	1	2	yes	complemented
407	C₂⁴	—	30	2	no	—
408	C₂×D₄	—	3	2	no	—
409	C₂×D₄	—	15	8	no	—
410	C₂×D₄	—	15	2	no	—
411	C₂×D₄	—	30	4	no	—
412	C₂×D₄	—	30	2	no	—
413	C₂²×C₄	—	5	1	no	—
414	C₂²×C₄	—	5	1	no	—
415	C₂²×C₄	—	5	1	no	—
416	C₂²×C₄	—	6	2	no	—
417	C₂²×C₄	—	30	2	no	—
418	C₂²×C₄	—	30	2	no	—
419	C₂²×C₄	—	30	2	no	—
420	C₂²×C₄	—	30	2	no	—
421	C₂²×C₄	—	60	8	no	—
422	D₈	—	3	4	no	—
423	D₈	—	15	8	no	—
424	D₈	—	15	4	no	—
425	C₂×C₈	—	5	1	no	—
426	C₂×C₈	—	5	4	no	—
427	C₂×C₈	—	5	1	no	—
428	C₂×C₈	—	10	2	no	—
429	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
430	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
431	C₄⋊C₄	—	3	2	no	—
432	C₄⋊C₄	—	15	2	no	—
433	C₄⋊C₄	—	30	2	no	—
434	C₂²⋊C₄	—	6	2	no	—
435	C₂²⋊C₄	—	30	2	no	—
436	C₂²⋊C₄	—	30	2	no	—
437	C₂²⋊C₄	—	30	2	no	—
438	C₄²	—	5	1	no	—
439	C₄²	—	5	1	no	—
440	C₄²	—	5	1	no	—
441	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
442	C₃×C₅	C₂×C₄×D₈	1	1	yes	characteristic, complemented, Hall
443	C₂²×C₃	—	5	2	no	—
444	C₂²×C₃	—	5	2	no	—
445	C₂²×C₃	—	5	2	no	—
446	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
447	C₂×D₃	—	2	4	no	—
448	C₂×D₃	—	4	2	no	—
449	C₂×D₃	—	4	2	no	—
450	C₂×D₃	—	10	4	no	—
451	C₂×D₃	—	20	16	no	—
452	C₂×D₃	—	20	2	no	—
453	C₂×D₃	—	20	2	no	—
454	C₃×C₄	—	2	1	no	—
455	C₃×C₄	—	5	2	no	—
456	C₃×C₄	—	5	2	no	—
457	C₃×C₄	—	10	1	no	—
458	C₃×C₄	D₅×D₈	1	2	yes	complemented
459	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
460	C₃×C₄	D₅×#41	1	1	yes	characteristic
461	Dic₃	—	4	2	no	—
462	Dic₃	—	20	2	no	—
463	C₂×C₅	—	12	4	no	—
464	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
465	C₂×C₅	C₂²×D₂₄	1	1	yes	characteristic
466	C₂×C₅	C₂×#904	1	1	yes	characteristic
467	D₅	—	12	4	no	—
468	D₅	C₄×D₂₄	1	4	yes	direct product factor
469	C₂³	—	5	1	no	—
470	C₂³	—	6	2	no	—
471	C₂³	—	30	8	no	—
472	C₂³	—	30	2	no	—
473	C₂³	—	60	4	no	—
474	C₂³	—	60	4	no	—
475	D₄	—	3	4	no	—
476	D₄	—	6	2	no	—
477	D₄	—	15	4	no	—
478	D₄	—	30	8	no	—
479	D₄	—	30	2	no	—
480	C₂×C₄	—	5	1	no	—
481	C₂×C₄	—	5	1	no	—
482	C₂×C₄	—	5	2	no	—
483	C₂×C₄	—	5	2	no	—
484	C₂×C₄	—	5	4	no	—
485	C₂×C₄	—	5	1	no	—
486	C₂×C₄	—	6	2	no	—
487	C₂×C₄	—	10	2	no	—
488	C₂×C₄	—	12	4	no	—
489	C₂×C₄	—	30	2	no	—
490	C₂×C₄	—	60	4	no	—
491	C₂×C₄	—	60	4	no	—
492	C₂×C₄	—	60	4	no	—
493	C₂×C₄	—	60	4	no	—
494	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
495	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
497	C₈	—	2	1	no	—
498	C₈	—	5	2	no	—
499	C₈	—	10	1	no	—
500	C₈	C₄×D₃×D₅	1	2	yes	complemented
501	C₂×C₃	—	5	4	no	—
502	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
503	C₂×C₃	C₂×D₅×D₈	1	1	yes	characteristic
504	C₂×C₃	D₅×#135	1	1	yes	characteristic
505	D₃	—	4	4	no	—
506	D₃	—	20	4	no	—
507	C₅	C₂×C₄×D₂₄	1	1	yes	characteristic, complemented, Sylow
508	C₂²	—	5	2	no	—
509	C₂²	—	5	2	no	—
510	C₂²	—	5	2	no	—
511	C₂²	—	6	4	no	—
512	C₂²	—	12	2	no	—
513	C₂²	—	12	2	no	—
514	C₂²	—	30	4	no	—
515	C₂²	—	60	16	no	—
516	C₂²	—	60	2	no	—
517	C₂²	—	60	2	no	—
518	C₂²	C₂×D₅×D₁₂	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	5	2	no	—
521	C₄	—	5	2	no	—
522	C₄	—	10	1	no	—
523	C₄	—	12	2	no	—
524	C₄	—	60	2	no	—
525	C₄	D₅×D₂₄	1	2	yes	direct product factor
526	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
527	C₄	D₅×#235	1	1	yes	characteristic
528	C₃	C₄×D₅×D₈	1	1	yes	characteristic, complemented, Sylow
529	C₂	—	5	4	no	—
530	C₂	—	12	4	no	—
531	C₂	—	60	4	no	—
532	C₂	C₄×D₅×D₁₂	1	1	yes	characteristic
533	C₂	C₂×D₅×D₂₄	1	1	yes	characteristic
534	C₂	D₅×#904	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₅×D₁₂
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₄×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×D₅×D₂₄	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×C₄×D₈
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₄×D₅×D₁₂	C₂	semidirect
3. C₄×D₁₂₀	C₂	semidirect
4. C₄×C₅×D₂₄	C₂	semidirect
5. C₃×C₄×C₈×D₅	C₂	semidirect
6. D₅×#821	C₂	semidirect
7. #11747766	C₂	semidirect
8. Dic₅×D₂₄	C₂	semidirect
9. #11747745	C₂	semidirect
10. D₅×#818	C₂	semidirect
11. C₄×#6654	C₂	semidirect
16. C₄×D₆₀	C₂²	semidirect
18. C₄×C₅×D₁₂	C₂²	semidirect
24. #91418	C₂²	semidirect
25. Dic₅×D₁₂	C₂²	semidirect
29. D₅×D₂₄	C₄	direct (N × H)
30. C₃×C₄×C₅×C₈	C₂²	semidirect
31. #91105	C₂²	semidirect
32. #91102	C₂²	semidirect
33. C₅×#821	C₂²	semidirect
34. C₅×#818	C₂²	semidirect
35. C₃×C₈×Dic₅	C₂²	semidirect
36. C₃×C₈×Dic₅	C₂²	semidirect
37. C₃×C₄×#168	C₂²	semidirect
38. #90988	C₂²	semidirect
39. #90969	C₂²	semidirect
40. #90967	C₂²	semidirect
52. C₄×C₈×D₅	D₃	semidirect
66. D₅×D₁₂	C₂×C₄	semidirect
73. D₁₂₀	C₂×C₄	semidirect
76. C₅×D₂₄	C₂×C₄	semidirect
83. C₃×C₈×D₅	C₂×C₄	semidirect
87. #6654	C₂×C₄	semidirect
98. C₄×D₂₄	D₅	direct (N × H)
118. C₄×C₅×C₈	C₂×D₃	semidirect
122. C₈×Dic₅	C₂×D₃	semidirect
123. C₈×Dic₅	C₂×D₃	semidirect
126. C₄×#168	C₂×D₃	semidirect
139. D₆₀	C₂²×C₄	semidirect
143. C₅×D₁₂	C₂²×C₄	semidirect
149. C₃×C₄×D₅	D₈	semidirect
157. C₃×C₅×C₈	C₂²×C₄	semidirect
159. C₃×#168	C₂²×C₄	semidirect
176. C₄×D₁₂	C₂×D₅	semidirect
180. C₃×C₄×C₈	C₂×D₅	semidirect
184. #821	C₂×D₅	semidirect
187. #818	C₂×D₅	semidirect
222. C₈×D₅	C₄×D₃	semidirect
246. C₃×C₄×C₅	C₂×D₈	semidirect
252. C₃×Dic₅	C₂×D₈	semidirect
288. D₂₄	C₄×D₅	direct (N × H)
314. C₄×D₅	D₂₄	direct (N × H)
318. C₅×C₈	C₂×C₄×D₃	semidirect
320. #168	C₂×C₄×D₃	semidirect
348. C₄×C₈	D₃×D₅	semidirect
353. C₃×D₅	C₄×D₈	semidirect
378. D₁₂	C₂×C₄×D₅	semidirect
386. C₃×C₈	C₂×C₄×D₅	semidirect
400. C₄×C₅	C₂×D₂₄	semidirect
406. Dic₅	C₂×D₂₄	semidirect
442. C₃×C₅	C₂×C₄×D₈	semidirect
458. C₃×C₄	D₅×D₈	semidirect
468. D₅	C₄×D₂₄	direct (N × H)
500. C₈	C₄×D₃×D₅	semidirect
507. C₅	C₂×C₄×D₂₄	semidirect
525. C₄	D₅×D₂₄	direct (N × H)
528. C₃	C₄×D₅×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅×D₂₄	2
C₄×D₅×D₁₂	2
C₄×D₁₂₀	2
C₄×C₅×D₂₄	2
C₃×C₄×C₈×D₅	2
D₅×#821	2
#11747766	2
Dic₅×D₂₄	2
#11747745	2
D₅×#818	2
C₄×#6654	2
C₄×D₅×D₈	3
C₂×C₄×D₂₄	5

Subgroups — C4×D5×D24 #14416005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₅×D₂₄ #14416005