Subgroups — C₂×C₅×#5014 #14416474

Order 1920.

1216 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#213	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#832	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5014	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#808	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#442	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	—	2	1	no	—
12	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₅×D₃	—	2	1	no	—
14	C₃×C₄×C₅×D₄	—	2	2	no	—
15	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×#213	C₄	1	8	yes	complemented
20	C₂×C₅×#213	C₂²	1	4	yes	—
21	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₄×C₅×D₁₂	—	2	2	no	—
26	C₄×C₅×D₁₂	C₂²	1	4	yes	complemented
27	C₅×#832	C₂²	1	4	yes	complemented
28	C₅×#809	C₂²	1	4	yes	complemented
29	C₅×#808	C₂²	1	4	yes	complemented
30	C₅×#803	C₂²	1	4	yes	complemented
31	C₂×#5014	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂²×C₅×D₈	—	3	1	no	—
33	C₂×C₄×C₅×D₄	—	3	1	no	—
34	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic, complemented
35	C₅×#442	—	3	8	no	—
36	C₂×C₅×#106	—	3	1	no	—
37	C₂×C₅×#102	—	3	1	no	—
38	C₂×C₅×#102	—	3	1	no	—
39	C₂×C₅×#97	—	3	1	no	—
40	C₂⁴×C₃×C₅	—	2	1	no	—
41	C₂³×C₅×D₃	—	2	1	no	—
42	C₂×C₃×C₅×D₄	—	2	1	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
45	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	—	2	1	no	—
47	C₂²×C₃×C₄×C₅	—	2	4	no	—
48	C₂²×C₃×C₄×C₅	—	4	4	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₅×Dic₃	—	2	1	no	—
53	C₂×C₅×D₁₂	—	2	1	no	—
54	C₂×C₅×D₁₂	—	2	2	no	—
55	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
56	C₂×C₅×D₁₂	C₂³	1	2	yes	—
57	C₂×C₄×C₅×D₃	—	2	4	no	—
58	C₂×C₄×C₅×D₃	—	4	4	no	—
59	C₃×C₅×C₄⋊C₄	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
62	C₃×C₄²×C₅	D₄	1	2	yes	—
63	C₃×C₄²×C₅	C₂³	1	2	yes	—
64	C₅×#213	C₂×C₄	1	16	yes	complemented
65	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
66	C₅×C₄⋊Dic₃	—	2	1	no	—
67	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
68	C₂×C₅×C₃⋊C₈	—	2	2	no	—
69	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
70	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
71	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
72	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂²×#213	C₂×C₅	1	1	yes	characteristic
74	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#832	C₂×C₅	1	1	yes	characteristic, complemented
76	#5014	C₂×C₅	1	8	yes	direct product factor
77	C₂×#809	C₂×C₅	1	1	yes	characteristic, complemented
78	C₂×#808	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×#803	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂²×C₅×D₄	—	3	1	no	—
81	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
82	C₂³×C₄×C₅	—	2	1	no	—
83	C₂³×C₄×C₅	—	6	1	no	—
84	C₂×C₅×D₈	—	3	8	no	—
85	C₂×C₅×D₈	—	3	4	no	—
86	C₂²×C₅×C₈	—	3	1	no	—
87	C₂²×C₅×C₈	—	3	1	no	—
88	C₄×C₅×D₄	—	2	2	no	—
89	C₄×C₅×D₄	—	3	4	no	—
90	C₄×C₅×D₄	—	6	2	no	—
91	C₄×C₅×D₄	C₂×D₃	1	4	yes	complemented
92	C₂×C₅×C₄⋊C₄	—	3	1	no	—
93	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
94	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
96	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
97	C₅×#106	—	3	4	no	—
98	C₅×#102	—	3	4	no	—
99	C₅×#102	—	3	4	no	—
100	C₅×#97	—	3	4	no	—
101	C₂×#442	—	3	1	no	Sylow
102	C₂³×C₃×C₅	—	2	4	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	—	4	2	no	—
105	C₂³×C₃×C₅	—	4	2	no	—
106	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₅×D₃	—	2	4	no	—
108	C₂²×C₅×D₃	—	2	2	no	—
109	C₂²×C₅×D₃	—	4	2	no	—
110	C₂²×C₅×D₃	—	4	2	no	—
111	C₃×C₅×D₄	—	2	4	no	—
112	C₃×C₅×D₄	—	2	2	no	—
113	C₃×C₅×D₄	C₂²×C₄	1	4	yes	complemented
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	4	8	no	—
118	C₂×C₃×C₄×C₅	—	4	2	no	—
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	#41	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
125	C₂×C₅×Dic₃	—	2	2	no	—
126	C₂×C₅×Dic₃	—	4	2	no	—
127	C₅×D₁₂	—	2	4	no	—
128	C₅×D₁₂	—	2	2	no	—
129	C₅×D₁₂	C₂²×C₄	1	4	yes	complemented
130	C₄×C₅×D₃	—	4	8	no	—
131	C₅×C₃⋊C₈	—	2	2	no	—
132	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	complemented
133	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
134	C₂³×C₃×C₄	—	2	1	no	—
135	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
136	C₂²×C₄×D₃	—	2	1	no	—
137	C₃×C₄×D₄	—	2	2	no	—
138	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
139	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
140	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
141	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
142	C₂×#213	C₄×C₅	1	8	yes	complemented
143	C₂×#213	C₂²×C₅	1	4	yes	—
144	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
145	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
146	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
147	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
148	C₄×D₁₂	—	2	2	no	—
149	C₄×D₁₂	C₂²×C₅	1	4	yes	complemented
150	#832	C₂²×C₅	1	4	yes	complemented
151	#809	C₂²×C₅	1	4	yes	complemented
152	#808	C₂²×C₅	1	4	yes	complemented
153	#803	C₂²×C₅	1	4	yes	complemented
154	C₂⁴×C₅	—	2	1	no	—
155	C₂⁴×C₅	—	6	1	no	—
156	C₂×C₅×D₄	—	2	2	no	—
157	C₂×C₅×D₄	—	2	1	no	—
158	C₂×C₅×D₄	—	3	4	no	—
159	C₂×C₅×D₄	—	3	2	no	—
160	C₂×C₅×D₄	—	6	2	no	—
161	C₂×C₅×D₄	—	6	1	no	—
162	C₂×C₅×D₄	C₄×D₃	1	4	yes	complemented
163	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
164	C₂²×C₄×C₅	—	2	1	no	—
165	C₂²×C₄×C₅	—	2	4	no	—
166	C₂²×C₄×C₅	—	4	4	no	—
167	C₂²×C₄×C₅	—	6	1	no	—
168	C₂²×C₄×C₅	—	6	4	no	—
169	C₂²×C₄×C₅	—	12	4	no	—
170	C₂²×C₄×C₅	#67	1	1	yes	characteristic
171	C₂²×C₄×C₅	#67	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
173	C₅×D₈	—	3	16	no	—
174	C₂×C₅×C₈	—	3	4	no	—
175	C₂×C₅×C₈	—	3	2	no	—
176	C₂×C₅×C₈	—	3	2	no	—
177	C₂×C₅×C₈	—	6	2	no	—
178	C₅×C₄⋊C₄	—	2	1	no	—
179	C₅×C₄⋊C₄	—	3	2	no	—
180	C₅×C₄⋊C₄	—	6	1	no	—
181	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
182	C₅×C₂²⋊C₄	—	2	4	no	—
183	C₅×C₂²⋊C₄	—	6	4	no	—
184	C₄²×C₅	#67	1	2	yes	—
185	C₄²×C₅	C₂²×D₃	1	2	yes	—
186	C₂²×D₈	—	3	1	no	—
187	C₂×C₄×D₄	—	3	1	no	—
188	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic, complemented
189	#442	—	3	8	no	—
190	C₂×#106	—	3	1	no	—
191	C₂×#102	—	3	1	no	—
192	C₂×#102	—	3	1	no	—
193	C₂×#97	—	3	1	no	—
194	C₂²×C₃×C₅	—	2	4	no	—
195	C₂²×C₃×C₅	—	4	2	no	—
196	C₂²×C₃×C₅	—	4	2	no	—
197	C₂²×C₃×C₅	—	4	8	no	—
198	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
199	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
200	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
201	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₅×D₃	—	2	4	no	—
203	C₂×C₅×D₃	—	4	2	no	—
204	C₂×C₅×D₃	—	4	2	no	—
205	C₂×C₅×D₃	—	4	8	no	—
206	C₃×C₄×C₅	—	2	2	no	—
207	C₃×C₄×C₅	—	2	2	no	—
208	C₃×C₄×C₅	—	4	2	no	—
209	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
210	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
212	C₅×Dic₃	—	4	2	no	—
213	C₂⁴×C₃	—	2	1	no	—
214	C₂³×D₃	—	2	1	no	—
215	C₂×C₃×D₄	—	2	1	no	—
216	C₂×C₃×D₄	—	2	2	no	—
217	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
218	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
219	C₂²×C₃×C₄	—	2	1	no	—
220	C₂²×C₃×C₄	—	2	4	no	—
221	C₂²×C₃×C₄	—	4	4	no	—
222	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂²×Dic₃	—	2	1	no	—
226	C₂×D₁₂	—	2	1	no	—
227	C₂×D₁₂	—	2	2	no	—
228	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
229	C₂×D₁₂	C₂³×C₅	1	2	yes	—
230	C₂×C₄×D₃	—	2	4	no	—
231	C₂×C₄×D₃	—	4	4	no	—
232	C₃×C₄⋊C₄	—	2	1	no	—
233	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
234	C₃×C₂²⋊C₄	—	2	4	no	—
235	C₃×C₄²	C₅×D₄	1	2	yes	—
236	C₃×C₄²	C₂³×C₅	1	2	yes	—
237	#213	C₂×C₄×C₅	1	16	yes	complemented
238	(C₂×D₃)⋊C₄	—	2	4	no	—
239	C₄⋊Dic₃	—	2	1	no	—
240	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
241	C₂×C₃⋊C₈	—	2	2	no	—
242	C₂×C₃⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
243	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
244	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
245	C₂³×C₅	—	2	4	no	—
246	C₂³×C₅	—	2	2	no	—
247	C₂³×C₅	—	4	2	no	—
248	C₂³×C₅	—	4	2	no	—
249	C₂³×C₅	—	6	4	no	—
250	C₂³×C₅	—	6	2	no	—
251	C₂³×C₅	—	12	2	no	—
252	C₂³×C₅	—	12	2	no	—
253	C₂³×C₅	C₂×#67	1	1	yes	characteristic
254	C₅×D₄	—	2	4	no	—
255	C₅×D₄	—	2	2	no	—
256	C₅×D₄	—	3	4	no	—
257	C₅×D₄	—	6	4	no	—
258	C₅×D₄	—	6	2	no	—
259	C₅×D₄	C₂×C₄×D₃	1	4	yes	complemented
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	4	8	no	—
264	C₂×C₄×C₅	—	4	2	no	—
265	C₂×C₄×C₅	—	6	2	no	—
266	C₂×C₄×C₅	—	12	8	no	—
267	C₂×C₄×C₅	—	12	2	no	—
268	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
269	C₂×C₄×C₅	#235	1	2	yes	—
270	C₂×C₄×C₅	C₂×#67	1	2	yes	—
271	C₂×C₄×C₅	C₂×#67	1	2	yes	—
272	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
274	C₅×C₈	—	3	4	no	—
275	C₅×C₈	—	6	2	no	—
276	C₂²×D₄	—	3	1	no	—
277	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	—	6	1	no	—
280	C₂×D₈	—	3	8	no	—
281	C₂×D₈	—	3	4	no	—
282	C₂²×C₈	—	3	1	no	—
283	C₂²×C₈	—	3	1	no	—
284	C₄×D₄	—	2	2	no	—
285	C₄×D₄	—	3	4	no	—
286	C₄×D₄	—	6	2	no	—
287	C₄×D₄	C₂×C₅×D₃	1	4	yes	complemented
288	C₂×C₄⋊C₄	—	3	1	no	—
289	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	6	1	no	—
292	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
293	#106	—	3	4	no	—
294	#102	—	3	4	no	—
295	#102	—	3	4	no	—
296	#97	—	3	4	no	—
297	C₂×C₃×C₅	—	4	4	no	—
298	C₂×C₃×C₅	#442	1	4	yes	complemented
299	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
300	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
301	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
302	C₅×D₃	—	4	4	no	—
303	C₂³×C₃	—	2	4	no	—
304	C₂³×C₃	—	2	2	no	—
305	C₂³×C₃	—	4	2	no	—
306	C₂³×C₃	—	4	2	no	—
307	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
308	C₂²×D₃	—	2	4	no	—
309	C₂²×D₃	—	2	2	no	—
310	C₂²×D₃	—	4	2	no	—
311	C₂²×D₃	—	4	2	no	—
312	C₃×D₄	—	2	4	no	—
313	C₃×D₄	—	2	2	no	—
314	C₃×D₄	C₂²×C₄×C₅	1	4	yes	complemented
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	4	8	no	—
319	C₂×C₃×C₄	—	4	2	no	—
320	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
321	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
322	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
323	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
324	C₂×C₃×C₄	C₅×#41	1	2	yes	—
325	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
326	C₂×Dic₃	—	2	2	no	—
327	C₂×Dic₃	—	4	2	no	—
328	D₁₂	—	2	4	no	—
329	D₁₂	—	2	2	no	—
330	D₁₂	C₂²×C₄×C₅	1	4	yes	complemented
331	C₄×D₃	—	4	8	no	—
332	C₃⋊C₈	—	2	2	no	—
333	C₃⋊C₈	C₂²×C₄×C₅	1	4	yes	complemented
334	C₂²×C₅	—	2	4	no	—
335	C₂²×C₅	—	4	8	no	—
336	C₂²×C₅	—	4	2	no	—
337	C₂²×C₅	—	4	2	no	—
338	C₂²×C₅	—	6	4	no	—
339	C₂²×C₅	—	12	8	no	—
340	C₂²×C₅	—	12	2	no	—
341	C₂²×C₅	—	12	2	no	—
342	C₂²×C₅	C₄×#67	1	2	yes	—
343	C₂²×C₅	#932	1	2	yes	—
344	C₂²×C₅	#949	1	2	yes	—
345	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
346	C₄×C₅	—	2	2	no	—
347	C₄×C₅	—	2	2	no	—
348	C₄×C₅	—	4	2	no	—
349	C₄×C₅	—	12	2	no	—
350	C₄×C₅	C₄×#67	1	2	yes	—
351	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
352	C₄×C₅	C₂×#235	1	1	yes	characteristic
353	C₂⁴	—	2	1	no	—
354	C₂⁴	—	6	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	3	4	no	—
358	C₂×D₄	—	3	2	no	—
359	C₂×D₄	—	6	2	no	—
360	C₂×D₄	—	6	1	no	—
361	C₂×D₄	C₄×C₅×D₃	1	4	yes	complemented
362	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	6	1	no	—
367	C₂²×C₄	—	6	4	no	—
368	C₂²×C₄	—	12	4	no	—
369	C₂²×C₄	C₅×#67	1	1	yes	characteristic
370	C₂²×C₄	C₅×#67	1	1	yes	characteristic
371	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
372	D₈	—	3	16	no	—
373	C₂×C₈	—	3	4	no	—
374	C₂×C₈	—	3	2	no	—
375	C₂×C₈	—	3	2	no	—
376	C₂×C₈	—	6	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	3	2	no	—
379	C₄⋊C₄	—	6	1	no	—
380	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	6	4	no	—
383	C₄²	C₅×#67	1	2	yes	—
384	C₄²	C₂²×C₅×D₃	1	2	yes	—
385	C₃×C₅	C₂×#442	1	1	yes	characteristic, complemented, Hall
386	C₂²×C₃	—	2	4	no	—
387	C₂²×C₃	—	4	8	no	—
388	C₂²×C₃	—	4	2	no	—
389	C₂²×C₃	—	4	2	no	—
390	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
391	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
392	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
393	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
394	C₂×D₃	—	2	4	no	—
395	C₂×D₃	—	4	8	no	—
396	C₂×D₃	—	4	2	no	—
397	C₂×D₃	—	4	2	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	4	2	no	—
401	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
402	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
403	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
404	Dic₃	—	4	2	no	—
405	C₂×C₅	—	4	4	no	—
406	C₂×C₅	—	12	4	no	—
407	C₂×C₅	#5014	1	4	yes	direct product factor
408	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
409	C₂×C₅	C₂×#932	1	1	yes	characteristic
410	C₂×C₅	C₂×#949	1	1	yes	characteristic
411	C₂³	—	2	4	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	6	4	no	—
416	C₂³	—	6	2	no	—
417	C₂³	—	12	2	no	—
418	C₂³	—	12	2	no	—
419	C₂³	C₂×C₅×#67	1	1	yes	characteristic
420	D₄	—	2	4	no	—
421	D₄	—	2	2	no	—
422	D₄	—	3	4	no	—
423	D₄	—	6	4	no	—
424	D₄	—	6	2	no	—
425	D₄	C₂×C₄×C₅×D₃	1	4	yes	complemented
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	6	2	no	—
432	C₂×C₄	—	12	8	no	—
433	C₂×C₄	—	12	2	no	—
434	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
435	C₂×C₄	C₅×#235	1	2	yes	—
436	C₂×C₄	C₂×C₅×#67	1	2	yes	—
437	C₂×C₄	C₂×C₅×#67	1	2	yes	—
438	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
439	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
440	C₈	—	3	4	no	—
441	C₈	—	6	2	no	—
442	C₂×C₃	—	4	4	no	—
443	C₂×C₃	C₅×#442	1	4	yes	complemented
444	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
445	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
446	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
447	D₃	—	4	4	no	—
448	C₅	C₂×#5014	1	1	yes	characteristic, direct product factor, Sylow
449	C₂²	—	2	4	no	—
450	C₂²	—	4	8	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	6	4	no	—
454	C₂²	—	12	8	no	—
455	C₂²	—	12	2	no	—
456	C₂²	—	12	2	no	—
457	C₂²	C₄×C₅×#67	1	2	yes	—
458	C₂²	C₅×#932	1	2	yes	—
459	C₂²	C₅×#949	1	2	yes	—
460	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	4	2	no	—
464	C₄	—	12	2	no	—
465	C₄	C₄×C₅×#67	1	2	yes	—
466	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
467	C₄	C₂×C₅×#235	1	1	yes	characteristic
468	C₃	C₂×C₅×#442	1	1	yes	characteristic, complemented, Sylow
469	C₂	—	4	4	no	—
470	C₂	—	12	4	no	—
471	C₂	C₅×#5014	1	4	yes	direct product factor
472	C₂	C₂×C₄×C₅×#67	1	1	yes	characteristic
473	C₂	C₂×C₅×#932	1	1	yes	characteristic
474	C₂	C₂×C₅×#949	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×#213	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#442
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₂×C₄×C₅×D₁₂	C₂	semidirect
4. C₂×C₅×#832	C₂	semidirect
5. C₅×#5014	C₂	direct (N × H)
6. C₂×C₅×#809	C₂	semidirect
7. C₂×C₅×#808	C₂	semidirect
8. C₂×C₅×#803	C₂	semidirect
15. C₃×C₄×C₅×D₄	C₂²	semidirect
19. C₂×C₅×#213	C₄	semidirect
26. C₄×C₅×D₁₂	C₂²	semidirect
27. C₅×#832	C₂²	semidirect
28. C₅×#809	C₂²	semidirect
29. C₅×#808	C₂²	semidirect
30. C₅×#803	C₂²	semidirect
31. C₂×#5014	C₅	direct (N × H)
34. C₂×C₄×C₅×D₄	D₃	semidirect
44. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
55. C₂×C₅×D₁₂	C₂×C₄	semidirect
64. C₅×#213	C₂×C₄	semidirect
69. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
72. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
74. C₂×C₄×D₁₂	C₂×C₅	semidirect
75. C₂×#832	C₂×C₅	semidirect
76. #5014	C₂×C₅	direct (N × H)
77. C₂×#809	C₂×C₅	semidirect
78. C₂×#808	C₂×C₅	semidirect
79. C₂×#803	C₂×C₅	semidirect
91. C₄×C₅×D₄	C₂×D₃	semidirect
113. C₃×C₅×D₄	C₂²×C₄	semidirect
129. C₅×D₁₂	C₂²×C₄	semidirect
132. C₅×C₃⋊C₈	C₂²×C₄	semidirect
138. C₃×C₄×D₄	C₂²×C₅	semidirect
142. C₂×#213	C₄×C₅	semidirect
149. C₄×D₁₂	C₂²×C₅	semidirect
150. #832	C₂²×C₅	semidirect
151. #809	C₂²×C₅	semidirect
152. #808	C₂²×C₅	semidirect
153. #803	C₂²×C₅	semidirect
162. C₂×C₅×D₄	C₄×D₃	semidirect
188. C₂×C₄×D₄	C₅×D₃	semidirect
217. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
228. C₂×D₁₂	C₂×C₄×C₅	semidirect
237. #213	C₂×C₄×C₅	semidirect
242. C₂×C₃⋊C₈	C₂×C₄×C₅	semidirect
259. C₅×D₄	C₂×C₄×D₃	semidirect
287. C₄×D₄	C₂×C₅×D₃	semidirect
298. C₂×C₃×C₅	#442	semidirect
314. C₃×D₄	C₂²×C₄×C₅	semidirect
330. D₁₂	C₂²×C₄×C₅	semidirect
333. C₃⋊C₈	C₂²×C₄×C₅	semidirect
361. C₂×D₄	C₄×C₅×D₃	semidirect
385. C₃×C₅	C₂×#442	semidirect
407. C₂×C₅	#5014	direct (N × H)
425. D₄	C₂×C₄×C₅×D₃	semidirect
443. C₂×C₃	C₅×#442	semidirect
448. C₅	C₂×#5014	direct (N × H)
468. C₃	C₂×C₅×#442	semidirect
471. C₂	C₅×#5014	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅×D₄	2
C₂²×C₅×#213	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×#832	2
C₅×#5014	2
C₂×C₅×#809	2
C₂×C₅×#808	2
C₂×C₅×#803	2
C₂×C₅×#442	3
C₂×#5014	5

Subgroups — C2×C5×#5014 #14416474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5014 #14416474