Subgroups — C₅×D₃×#442 #14416468

Order 1920.

1216 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×D₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×D₃×D₄	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5152	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5014	C₂	1	2	yes	maximal, complemented
6	C₅×#4869	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4785	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×#102	C₂	1	2	yes	maximal, complemented
10	C₅×#4711	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#442	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
14	C₂²×C₄×C₅×D₃	—	2	2	no	—
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
17	C₅×D₄×Dic₃	C₂²	1	2	yes	complemented
18	C₂×C₅×#213	C₂²	1	2	yes	—
19	C₄×C₅×#67	—	2	2	no	—
20	C₅×D₃×D₈	C₄	1	8	yes	complemented
21	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
22	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
24	C₅×#893	C₂²	1	2	yes	complemented
25	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₅×#67⋊C₄	—	2	2	no	—
27	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
28	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
29	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
30	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#102	C₂²	1	2	yes	complemented
32	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
33	C₅×#832	C₂²	1	2	yes	complemented
34	C₅×#821	C₂²	1	2	yes	complemented
35	C₅×#817	C₂²	1	1	yes	characteristic, complemented
36	C₅×#815	C₂²	1	1	yes	characteristic, complemented
37	C₅×#815	C₂²	1	1	yes	characteristic, complemented
38	C₅×#809	C₂²	1	2	yes	complemented
39	C₅×#808	C₂²	1	2	yes	complemented
40	C₅×#803	C₂²	1	1	yes	characteristic, complemented
41	D₃×#442	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂²×C₅×D₈	—	3	1	no	—
43	C₂×C₄×C₅×D₄	—	3	2	no	—
44	C₅×#442	—	3	1	no	—
45	C₅×#442	—	3	2	no	—
46	C₅×#442	—	3	1	no	—
47	C₅×#442	—	3	1	no	—
48	C₅×#442	—	3	2	no	—
49	C₅×#442	D₃	1	1	yes	characteristic, direct product factor
50	C₂×C₅×#106	—	3	1	no	—
51	C₂×C₅×#102	—	3	2	no	—
52	C₂×C₅×#97	—	3	1	no	—
53	C₂³×C₅×D₃	—	2	2	no	—
54	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂×C₅×#67	—	2	2	no	—
57	C₂²×C₅×Dic₃	—	2	2	no	—
58	C₅×D₃×D₄	—	2	4	no	—
59	C₅×D₃×D₄	C₂×C₄	1	8	yes	complemented
60	C₂×C₅×D₁₂	C₂³	1	2	yes	—
61	C₂×C₄×C₅×D₃	—	2	2	no	—
62	C₂×C₄×C₅×D₃	—	2	2	no	—
63	C₂×C₄×C₅×D₃	—	2	2	no	—
64	C₂×C₄×C₅×D₃	—	4	8	no	—
65	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
66	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
67	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
71	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₅×#217	—	2	2	no	—
74	C₅×#213	C₂×C₄	1	8	yes	complemented
75	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
76	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
77	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
78	C₅×Dic₃⋊C₄	—	2	2	no	—
79	C₄×C₅×Dic₃	D₄	1	2	yes	—
80	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
83	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
84	C₅×D₃×C₈	—	2	2	no	—
85	C₅×D₃×C₈	C₂×C₄	1	4	yes	complemented
86	C₂×D₃×D₈	C₂×C₅	1	1	yes	characteristic
87	C₄×D₃×D₄	C₂×C₅	1	2	yes	complemented
88	C₃×#442	C₂×C₅	1	1	yes	characteristic, complemented
89	#5152	C₂×C₅	1	1	yes	characteristic, complemented
90	#5014	C₂×C₅	1	2	yes	complemented
91	#4869	C₂×C₅	1	1	yes	characteristic, complemented
92	D₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
93	#4785	C₂×C₅	1	2	yes	complemented
94	D₃×#102	C₂×C₅	1	2	yes	complemented
95	#4711	C₂×C₅	1	1	yes	characteristic, complemented
96	D₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂²×C₅×D₄	—	3	2	no	—
98	C₂³×C₄×C₅	—	6	2	no	—
99	C₂×C₅×D₈	—	3	2	no	—
100	C₂×C₅×D₈	—	3	8	no	—
101	C₂×C₅×D₈	—	3	1	no	—
102	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
103	C₂²×C₅×C₈	—	3	1	no	—
104	C₂²×C₅×C₈	—	3	1	no	—
105	C₄×C₅×D₄	—	3	2	no	—
106	C₄×C₅×D₄	—	3	2	no	—
107	C₄×C₅×D₄	—	3	2	no	—
108	C₄×C₅×D₄	—	6	2	no	—
109	C₄×C₅×D₄	—	6	2	no	—
110	C₄×C₅×D₄	C₂×D₃	1	2	yes	complemented
111	C₂×C₅×C₄⋊C₄	—	3	2	no	—
112	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
113	C₂×C₄²×C₅	—	3	1	no	—
114	C₅×#106	—	3	1	no	—
115	C₅×#106	—	3	2	no	—
116	C₅×#106	C₂×D₃	1	1	yes	characteristic, complemented
117	C₅×#102	—	3	2	no	—
118	C₅×#102	—	3	2	no	—
119	C₅×#102	—	3	2	no	—
120	C₅×#102	C₂×D₃	1	2	yes	complemented
121	C₅×#97	—	3	1	no	—
122	C₅×#97	—	3	1	no	—
123	C₅×#97	—	3	1	no	—
124	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
125	C₂×#442	—	3	1	no	Sylow
126	C₂³×C₃×C₅	—	2	2	no	—
127	C₂²×C₅×D₃	—	2	2	no	—
128	C₂²×C₅×D₃	—	2	8	no	—
129	C₂²×C₅×D₃	—	4	4	no	—
130	C₂²×C₅×D₃	—	4	4	no	—
131	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
132	C₃×C₅×D₄	—	2	2	no	—
133	C₃×C₅×D₄	C₂²×C₄	1	4	yes	complemented
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	4	4	no	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₅×#67	—	2	8	no	—
139	C₂×C₅×Dic₃	—	2	2	no	—
140	C₂×C₅×Dic₃	—	4	4	no	—
141	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
142	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
143	C₅×D₁₂	—	2	2	no	—
144	C₅×D₁₂	C₂²×C₄	1	4	yes	complemented
145	C₄×C₅×D₃	—	2	4	no	—
146	C₄×C₅×D₃	—	4	4	no	—
147	C₄×C₅×D₃	—	4	4	no	—
148	C₄×C₅×D₃	—	4	4	no	—
149	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
150	C₄×C₅×D₃	#41	1	2	yes	—
151	C₃×C₅×C₈	—	2	1	no	—
152	C₃×C₅×C₈	C₂²×C₄	1	2	yes	complemented
153	C₅×C₃⋊C₈	—	2	1	no	—
154	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	complemented
155	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
156	C₂²×C₄×D₃	—	2	2	no	—
157	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
158	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
159	D₄×Dic₃	C₂²×C₅	1	2	yes	complemented
160	C₂×#213	C₂²×C₅	1	2	yes	—
161	C₄×#67	—	2	2	no	—
162	D₃×D₈	C₄×C₅	1	8	yes	complemented
163	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
164	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
165	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
166	#893	C₂²×C₅	1	2	yes	complemented
167	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
168	#67⋊C₄	—	2	2	no	—
169	D₃×C₂²⋊C₄	—	2	2	no	—
170	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
171	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
172	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
173	C₃×#102	C₂²×C₅	1	2	yes	complemented
174	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
175	#832	C₂²×C₅	1	2	yes	complemented
176	#821	C₂²×C₅	1	2	yes	complemented
177	#817	C₂²×C₅	1	1	yes	characteristic, complemented
178	#815	C₂²×C₅	1	1	yes	characteristic, complemented
179	#815	C₂²×C₅	1	1	yes	characteristic, complemented
180	#809	C₂²×C₅	1	2	yes	complemented
181	#808	C₂²×C₅	1	2	yes	complemented
182	#803	C₂²×C₅	1	1	yes	characteristic, complemented
183	C₂⁴×C₅	—	6	2	no	—
184	C₂×C₅×D₄	—	3	8	no	—
185	C₂×C₅×D₄	—	3	2	no	—
186	C₂×C₅×D₄	—	6	4	no	—
187	C₂×C₅×D₄	—	6	2	no	—
188	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
189	C₂²×C₄×C₅	—	2	2	no	—
190	C₂²×C₄×C₅	—	3	1	no	—
191	C₂²×C₄×C₅	—	3	2	no	—
192	C₂²×C₄×C₅	—	6	2	no	—
193	C₂²×C₄×C₅	—	6	2	no	—
194	C₂²×C₄×C₅	—	6	2	no	—
195	C₂²×C₄×C₅	—	6	2	no	—
196	C₂²×C₄×C₅	—	12	8	no	—
197	C₅×D₈	—	3	8	no	—
198	C₅×D₈	—	3	4	no	—
199	C₅×D₈	C₄×D₃	1	4	yes	complemented
200	C₂×C₅×C₈	—	3	1	no	—
201	C₂×C₅×C₈	—	3	4	no	—
202	C₂×C₅×C₈	—	3	1	no	—
203	C₂×C₅×C₈	—	6	2	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×C₄⋊C₄	—	6	2	no	—
208	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
209	C₅×C₂²⋊C₄	—	2	2	no	—
210	C₅×C₂²⋊C₄	—	6	2	no	—
211	C₅×C₂²⋊C₄	—	6	2	no	—
212	C₅×C₂²⋊C₄	—	6	2	no	—
213	C₄²×C₅	—	3	2	no	—
214	C₄²×C₅	—	3	1	no	—
215	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
216	C₂²×D₈	—	3	1	no	—
217	C₂×C₄×D₄	—	3	2	no	—
218	#442	—	3	1	no	—
219	#442	—	3	2	no	—
220	#442	—	3	1	no	—
221	#442	—	3	2	no	—
222	#442	—	3	1	no	—
223	#442	C₅×D₃	1	1	yes	characteristic, direct product factor
224	C₂×#106	—	3	1	no	—
225	C₂×#102	—	3	2	no	—
226	C₂×#97	—	3	1	no	—
227	C₂²×C₃×C₅	—	2	4	no	—
228	C₂²×C₃×C₅	—	4	2	no	—
229	C₂²×C₃×C₅	—	4	2	no	—
230	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₅×D₃	—	2	4	no	—
232	C₂×C₅×D₃	—	4	2	no	—
233	C₂×C₅×D₃	—	4	2	no	—
234	C₂×C₅×D₃	—	4	16	no	—
235	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
236	C₂×C₅×D₃	AGL(1,ℤ/8)	1	4	yes	—
237	C₃×C₄×C₅	—	2	2	no	—
238	C₃×C₄×C₅	—	4	2	no	—
239	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
240	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₅×Dic₃	—	2	2	no	—
242	C₅×Dic₃	—	4	2	no	—
243	C₅×Dic₃	C₄×D₄	1	2	yes	—
244	C₂³×D₃	—	2	2	no	—
245	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
246	C₂²×C₃×C₄	—	2	2	no	—
247	C₂×#67	—	2	2	no	—
248	C₂²×Dic₃	—	2	2	no	—
249	D₃×D₄	—	2	4	no	—
250	D₃×D₄	C₂×C₄×C₅	1	8	yes	complemented
251	C₂×D₁₂	C₂³×C₅	1	2	yes	—
252	C₂×C₄×D₃	—	2	2	no	—
253	C₂×C₄×D₃	—	2	2	no	—
254	C₂×C₄×D₃	—	2	2	no	—
255	C₂×C₄×D₃	—	4	8	no	—
256	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
257	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
258	C₃×D₈	C₂×C₄×C₅	1	4	yes	complemented
259	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
260	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
261	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
262	C₃×C₂²⋊C₄	—	2	2	no	—
263	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
264	#217	—	2	2	no	—
265	#213	C₂×C₄×C₅	1	8	yes	complemented
266	(C₂×D₃)⋊C₄	—	2	2	no	—
267	(C₂×D₃)⋊C₄	—	2	2	no	—
268	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
269	Dic₃⋊C₄	—	2	2	no	—
270	C₄×Dic₃	C₅×D₄	1	2	yes	—
271	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
273	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
274	D₂₄	C₂×C₄×C₅	1	4	yes	complemented
275	D₃×C₈	—	2	2	no	—
276	D₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
277	C₂³×C₅	—	2	2	no	—
278	C₂³×C₅	—	3	1	no	—
279	C₂³×C₅	—	6	8	no	—
280	C₂³×C₅	—	6	2	no	—
281	C₂³×C₅	—	12	4	no	—
282	C₂³×C₅	—	12	4	no	—
283	C₅×D₄	—	2	2	no	—
284	C₅×D₄	—	3	4	no	—
285	C₅×D₄	—	6	8	no	—
286	C₅×D₄	—	6	2	no	—
287	C₅×D₄	C₂×C₄×D₃	1	4	yes	complemented
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	3	1	no	—
290	C₂×C₄×C₅	—	3	2	no	—
291	C₂×C₄×C₅	—	3	2	no	—
292	C₂×C₄×C₅	—	3	2	no	—
293	C₂×C₄×C₅	—	4	4	no	—
294	C₂×C₄×C₅	—	6	4	no	—
295	C₂×C₄×C₅	—	6	2	no	—
296	C₂×C₄×C₅	—	12	4	no	—
297	C₂×C₄×C₅	—	12	4	no	—
298	C₂×C₄×C₅	—	12	4	no	—
299	C₂×C₄×C₅	—	12	4	no	—
300	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
301	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
302	C₅×C₈	—	2	1	no	—
303	C₅×C₈	—	3	2	no	—
304	C₅×C₈	—	6	1	no	—
305	C₅×C₈	C₂×C₄×D₃	1	2	yes	complemented
306	C₂²×D₄	—	3	2	no	—
307	C₂³×C₄	—	6	2	no	—
308	C₂×D₈	—	3	2	no	—
309	C₂×D₈	—	3	8	no	—
310	C₂×D₈	—	3	1	no	—
311	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
312	C₂²×C₈	—	3	1	no	—
313	C₂²×C₈	—	3	1	no	—
314	C₄×D₄	—	3	2	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	6	2	no	—
318	C₄×D₄	—	6	2	no	—
319	C₄×D₄	C₂×C₅×D₃	1	2	yes	complemented
320	C₂×C₄⋊C₄	—	3	2	no	—
321	C₂×C₂²⋊C₄	—	6	2	no	—
322	C₂×C₄²	—	3	1	no	—
323	#106	—	3	1	no	—
324	#106	—	3	2	no	—
325	#106	C₂×C₅×D₃	1	1	yes	characteristic, complemented
326	#102	—	3	2	no	—
327	#102	—	3	2	no	—
328	#102	—	3	2	no	—
329	#102	C₂×C₅×D₃	1	2	yes	complemented
330	#97	—	3	1	no	—
331	#97	—	3	1	no	—
332	#97	—	3	1	no	—
333	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
334	C₂×C₃×C₅	—	4	4	no	—
335	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
336	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
337	C₅×D₃	—	4	4	no	—
338	C₅×D₃	#442	1	4	yes	direct product factor
339	C₂³×C₃	—	2	2	no	—
340	C₂²×D₃	—	2	2	no	—
341	C₂²×D₃	—	2	8	no	—
342	C₂²×D₃	—	4	4	no	—
343	C₂²×D₃	—	4	4	no	—
344	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
345	C₃×D₄	—	2	2	no	—
346	C₃×D₄	C₂²×C₄×C₅	1	4	yes	complemented
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	4	4	no	—
349	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
350	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
351	#67	—	2	8	no	—
352	C₂×Dic₃	—	2	2	no	—
353	C₂×Dic₃	—	4	4	no	—
354	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
355	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
356	D₁₂	—	2	2	no	—
357	D₁₂	C₂²×C₄×C₅	1	4	yes	complemented
358	C₄×D₃	—	2	4	no	—
359	C₄×D₃	—	4	4	no	—
360	C₄×D₃	—	4	4	no	—
361	C₄×D₃	—	4	4	no	—
362	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
363	C₄×D₃	C₅×#41	1	2	yes	—
364	C₃×C₈	—	2	1	no	—
365	C₃×C₈	C₂²×C₄×C₅	1	2	yes	complemented
366	C₃⋊C₈	—	2	1	no	—
367	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	complemented
368	C₂²×C₅	—	2	4	no	—
369	C₂²×C₅	—	3	4	no	—
370	C₂²×C₅	—	3	2	no	—
371	C₂²×C₅	—	4	2	no	—
372	C₂²×C₅	—	4	2	no	—
373	C₂²×C₅	—	6	4	no	—
374	C₂²×C₅	—	12	16	no	—
375	C₂²×C₅	—	12	2	no	—
376	C₂²×C₅	—	12	2	no	—
377	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
378	C₄×C₅	—	2	2	no	—
379	C₄×C₅	—	3	2	no	—
380	C₄×C₅	—	4	2	no	—
381	C₄×C₅	—	6	2	no	—
382	C₄×C₅	—	12	2	no	—
383	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
384	C₄×C₅	D₃×#41	1	1	yes	characteristic
385	C₂⁴	—	6	2	no	—
386	C₂×D₄	—	3	8	no	—
387	C₂×D₄	—	3	2	no	—
388	C₂×D₄	—	6	4	no	—
389	C₂×D₄	—	6	2	no	—
390	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	3	1	no	—
393	C₂²×C₄	—	3	2	no	—
394	C₂²×C₄	—	6	2	no	—
395	C₂²×C₄	—	6	2	no	—
396	C₂²×C₄	—	6	2	no	—
397	C₂²×C₄	—	6	2	no	—
398	C₂²×C₄	—	12	8	no	—
399	D₈	—	3	8	no	—
400	D₈	—	3	4	no	—
401	D₈	C₄×C₅×D₃	1	4	yes	complemented
402	C₂×C₈	—	3	1	no	—
403	C₂×C₈	—	3	4	no	—
404	C₂×C₈	—	3	1	no	—
405	C₂×C₈	—	6	2	no	—
406	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
407	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
408	C₄⋊C₄	—	3	2	no	—
409	C₄⋊C₄	—	6	2	no	—
410	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	6	2	no	—
413	C₂²⋊C₄	—	6	2	no	—
414	C₂²⋊C₄	—	6	2	no	—
415	C₄²	—	3	2	no	—
416	C₄²	—	3	1	no	—
417	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
418	C₃×C₅	C₂×#442	1	1	yes	characteristic, complemented, Hall
419	C₂²×C₃	—	2	4	no	—
420	C₂²×C₃	—	4	2	no	—
421	C₂²×C₃	—	4	2	no	—
422	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
423	C₂×D₃	—	2	4	no	—
424	C₂×D₃	—	4	2	no	—
425	C₂×D₃	—	4	2	no	—
426	C₂×D₃	—	4	16	no	—
427	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
428	C₂×D₃	C₅×AGL(1,ℤ/8)	1	4	yes	—
429	C₃×C₄	—	2	2	no	—
430	C₃×C₄	—	4	2	no	—
431	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
432	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
433	Dic₃	—	2	2	no	—
434	Dic₃	—	4	2	no	—
435	Dic₃	C₄×C₅×D₄	1	2	yes	—
436	C₂×C₅	—	3	4	no	—
437	C₂×C₅	—	4	4	no	—
438	C₂×C₅	—	12	4	no	—
439	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
440	C₂×C₅	D₃×AGL(1,ℤ/8)	1	2	yes	—
441	C₂³	—	2	2	no	—
442	C₂³	—	3	1	no	—
443	C₂³	—	6	8	no	—
444	C₂³	—	6	2	no	—
445	C₂³	—	12	4	no	—
446	C₂³	—	12	4	no	—
447	D₄	—	2	2	no	—
448	D₄	—	3	4	no	—
449	D₄	—	6	8	no	—
450	D₄	—	6	2	no	—
451	D₄	C₂×C₄×C₅×D₃	1	4	yes	complemented
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	3	1	no	—
454	C₂×C₄	—	3	2	no	—
455	C₂×C₄	—	3	2	no	—
456	C₂×C₄	—	3	2	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	6	4	no	—
459	C₂×C₄	—	6	2	no	—
460	C₂×C₄	—	12	4	no	—
461	C₂×C₄	—	12	4	no	—
462	C₂×C₄	—	12	4	no	—
463	C₂×C₄	—	12	4	no	—
464	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
465	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
466	C₈	—	2	1	no	—
467	C₈	—	3	2	no	—
468	C₈	—	6	1	no	—
469	C₈	C₂×C₄×C₅×D₃	1	2	yes	complemented
470	C₂×C₃	—	4	4	no	—
471	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
472	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
473	D₃	—	4	4	no	—
474	D₃	C₅×#442	1	4	yes	direct product factor
475	C₅	D₃×#442	1	1	yes	characteristic, direct product factor, Sylow
476	C₂²	—	2	4	no	—
477	C₂²	—	3	4	no	—
478	C₂²	—	3	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	6	4	no	—
482	C₂²	—	12	16	no	—
483	C₂²	—	12	2	no	—
484	C₂²	—	12	2	no	—
485	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	3	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	6	2	no	—
490	C₄	—	12	2	no	—
491	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
492	C₄	C₅×D₃×#41	1	1	yes	characteristic
493	C₃	C₂×C₅×#442	1	1	yes	characteristic, complemented, Sylow
494	C₂	—	3	4	no	—
495	C₂	—	4	4	no	—
496	C₂	—	12	4	no	—
497	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
498	C₂	C₅×D₃×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#442	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₃×D₈	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#442	D₃
hypocenter	C₃	C₂×C₅×#442
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#442

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×D₃×D₄	C₂	semidirect
3. C₃×C₅×#442	C₂	semidirect
4. C₅×#5152	C₂	semidirect
5. C₅×#5014	C₂	semidirect
6. C₅×#4869	C₂	semidirect
7. C₅×D₃×#106	C₂	semidirect
8. C₅×#4785	C₂	semidirect
9. C₅×D₃×#102	C₂	semidirect
10. C₅×#4711	C₂	semidirect
11. C₅×D₃×#97	C₂	semidirect
16. C₃×C₄×C₅×D₄	C₂²	semidirect
17. C₅×D₄×Dic₃	C₂²	semidirect
20. C₅×D₃×D₈	C₄	semidirect
24. C₅×#893	C₂²	semidirect
28. C₄×C₅×D₁₂	C₂²	semidirect
30. C₃×C₅×#106	C₂²	semidirect
31. C₃×C₅×#102	C₂²	semidirect
32. C₃×C₅×#97	C₂²	semidirect
33. C₅×#832	C₂²	semidirect
34. C₅×#821	C₂²	semidirect
35. C₅×#817	C₂²	semidirect
36. C₅×#815	C₂²	semidirect
37. C₅×#815	C₂²	semidirect
38. C₅×#809	C₂²	semidirect
39. C₅×#808	C₂²	semidirect
40. C₅×#803	C₂²	semidirect
41. D₃×#442	C₅	direct (N × H)
49. C₅×#442	D₃	direct (N × H)
59. C₅×D₃×D₄	C₂×C₄	semidirect
67. C₃×C₅×D₈	C₂×C₄	semidirect
74. C₅×#213	C₂×C₄	semidirect
83. C₅×D₂₄	C₂×C₄	semidirect
85. C₅×D₃×C₈	C₂×C₄	semidirect
87. C₄×D₃×D₄	C₂×C₅	semidirect
88. C₃×#442	C₂×C₅	semidirect
89. #5152	C₂×C₅	semidirect
90. #5014	C₂×C₅	semidirect
91. #4869	C₂×C₅	semidirect
92. D₃×#106	C₂×C₅	semidirect
93. #4785	C₂×C₅	semidirect
94. D₃×#102	C₂×C₅	semidirect
95. #4711	C₂×C₅	semidirect
96. D₃×#97	C₂×C₅	semidirect
110. C₄×C₅×D₄	C₂×D₃	semidirect
116. C₅×#106	C₂×D₃	semidirect
120. C₅×#102	C₂×D₃	semidirect
124. C₅×#97	C₂×D₃	semidirect
133. C₃×C₅×D₄	C₂²×C₄	semidirect
144. C₅×D₁₂	C₂²×C₄	semidirect
152. C₃×C₅×C₈	C₂²×C₄	semidirect
154. C₅×C₃⋊C₈	C₂²×C₄	semidirect
158. C₃×C₄×D₄	C₂²×C₅	semidirect
159. D₄×Dic₃	C₂²×C₅	semidirect
162. D₃×D₈	C₄×C₅	semidirect
166. #893	C₂²×C₅	semidirect
170. C₄×D₁₂	C₂²×C₅	semidirect
172. C₃×#106	C₂²×C₅	semidirect
173. C₃×#102	C₂²×C₅	semidirect
174. C₃×#97	C₂²×C₅	semidirect
175. #832	C₂²×C₅	semidirect
176. #821	C₂²×C₅	semidirect
177. #817	C₂²×C₅	semidirect
178. #815	C₂²×C₅	semidirect
179. #815	C₂²×C₅	semidirect
180. #809	C₂²×C₅	semidirect
181. #808	C₂²×C₅	semidirect
182. #803	C₂²×C₅	semidirect
199. C₅×D₈	C₄×D₃	semidirect
223. #442	C₅×D₃	direct (N × H)
250. D₃×D₄	C₂×C₄×C₅	semidirect
258. C₃×D₈	C₂×C₄×C₅	semidirect
265. #213	C₂×C₄×C₅	semidirect
274. D₂₄	C₂×C₄×C₅	semidirect
276. D₃×C₈	C₂×C₄×C₅	semidirect
287. C₅×D₄	C₂×C₄×D₃	semidirect
305. C₅×C₈	C₂×C₄×D₃	semidirect
319. C₄×D₄	C₂×C₅×D₃	semidirect
325. #106	C₂×C₅×D₃	semidirect
329. #102	C₂×C₅×D₃	semidirect
333. #97	C₂×C₅×D₃	semidirect
338. C₅×D₃	#442	direct (N × H)
346. C₃×D₄	C₂²×C₄×C₅	semidirect
357. D₁₂	C₂²×C₄×C₅	semidirect
365. C₃×C₈	C₂²×C₄×C₅	semidirect
367. C₃⋊C₈	C₂²×C₄×C₅	semidirect
401. D₈	C₄×C₅×D₃	semidirect
418. C₃×C₅	C₂×#442	semidirect
451. D₄	C₂×C₄×C₅×D₃	semidirect
469. C₈	C₂×C₄×C₅×D₃	semidirect
474. D₃	C₅×#442	direct (N × H)
475. C₅	D₃×#442	direct (N × H)
493. C₃	C₂×C₅×#442	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×D₈	2
C₄×C₅×D₃×D₄	2
C₃×C₅×#442	2
C₅×#5152	2
C₅×#5014	2
C₅×#4869	2
C₅×D₃×#106	2
C₅×#4785	2
C₅×D₃×#102	2
C₅×#4711	2
C₅×D₃×#97	2
C₂×C₅×#442	3
D₃×#442	5

Subgroups — C5×D3×#442 #14416468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#442 #14416468