Subgroups — C₂×C₅×#4852 #14416049

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#204	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#810	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic
8	C₅×#4852	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₄×C₅×SD₁₆	—	3	1	no	maximal, Hall
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅×D₃	—	2	1	no	—
12	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
17	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
18	C₂×C₄×C₅×Dic₃	—	2	1	no	—
19	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#204	C₄	1	8	yes	complemented
22	C₂×C₅×#204	C₂²	1	4	yes	—
23	C₅×#893	—	2	2	no	—
24	C₅×#893	C₂²	1	4	yes	—
25	C₅×#887	—	2	2	no	—
26	C₅×#887	C₂²	1	4	yes	complemented
27	C₃×C₅×#106	C₂²	1	4	yes	complemented
28	C₅×C₈×Dic₃	C₂²	1	4	yes	complemented
29	C₅×#810	C₂²	1	4	yes	complemented
30	C₅×#809	C₂²	1	4	yes	—
31	C₂×#4852	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂²×C₅×SD₁₆	—	3	1	no	—
33	C₂×C₄×C₅×Q₈	—	3	1	no	—
34	C₂×C₄×C₅×D₄	—	3	1	no	—
35	C₄×C₅×SD₁₆	—	3	8	no	—
36	C₂×C₅×#106	D₃	1	1	yes	characteristic, complemented
37	C₂×C₅×#103	—	3	1	no	—
38	C₂×C₅×#102	—	3	1	no	—
39	C₂×C₄×C₅×C₈	—	3	1	no	—
40	C₂³×C₅×D₃	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₅×Dic₃	—	2	1	no	—
45	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
47	C₂×C₅×D₁₂	—	2	1	no	—
48	C₂×C₅×D₁₂	—	2	2	no	—
49	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
50	C₂×C₅×D₁₂	C₂³	1	2	yes	—
51	C₂×C₄×C₅×D₃	—	2	4	no	—
52	C₂×C₄×C₅×D₃	—	4	4	no	—
53	C₂×C₅×Dic₆	—	2	1	no	—
54	C₂×C₅×Dic₆	—	2	2	no	—
55	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	complemented
56	C₂×C₅×Dic₆	C₂³	1	2	yes	—
57	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
58	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	—	2	1	no	—
61	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
62	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
63	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
64	C₅×Dic₃⋊C₄	—	2	4	no	—
65	C₄×C₅×Dic₃	—	2	4	no	—
66	C₄×C₅×Dic₃	D₄	1	2	yes	—
67	C₄×C₅×Dic₃	C₂³	1	2	yes	—
68	C₂×C₅×C₃⋊C₈	—	2	2	no	—
69	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
70	C₅×#204	C₂×C₄	1	16	yes	complemented
71	C₂²×#204	C₂×C₅	1	1	yes	characteristic
72	C₂×#893	C₂×C₅	1	1	yes	characteristic
73	C₂×#887	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×C₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×#810	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×#809	C₂×C₅	1	1	yes	characteristic
78	#4852	C₂×C₅	1	8	yes	direct product factor
79	C₂²×C₅×Q₈	—	3	1	no	—
80	C₂²×C₅×D₄	—	3	1	no	—
81	C₂³×C₄×C₅	—	6	1	no	—
82	C₂×C₅×SD₁₆	—	3	8	no	—
83	C₂×C₅×SD₁₆	—	3	4	no	—
84	C₂²×C₅×C₈	—	3	1	no	—
85	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
86	C₄×C₅×Q₈	—	3	4	no	—
87	C₄×C₅×Q₈	—	6	2	no	—
88	C₄×C₅×D₄	—	3	4	no	—
89	C₄×C₅×D₄	—	6	2	no	—
90	C₂×C₅×C₄⋊C₄	—	6	1	no	—
91	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
92	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
93	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
94	C₂×C₄²×C₅	—	3	1	no	—
95	C₂×C₄²×C₅	—	6	1	no	—
96	C₅×#106	C₂×D₃	1	4	yes	complemented
97	C₅×#103	—	3	4	no	—
98	C₅×#102	—	3	4	no	—
99	C₄×C₅×C₈	—	3	4	no	—
100	C₂×C₄×SD₁₆	—	3	1	no	Sylow
101	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₅×D₃	—	2	4	no	—
103	C₂²×C₅×D₃	—	2	2	no	—
104	C₂²×C₅×D₃	—	4	2	no	—
105	C₂²×C₅×D₃	—	4	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	4	2	no	—
109	C₂×C₃×C₄×C₅	—	4	2	no	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	#41	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
114	C₂×C₅×Dic₃	—	2	4	no	—
115	C₂×C₅×Dic₃	—	2	2	no	—
116	C₂×C₅×Dic₃	—	2	2	no	—
117	C₂×C₅×Dic₃	SD₁₆	1	4	yes	complemented
118	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
119	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
120	C₅×D₁₂	—	2	4	no	—
121	C₅×D₁₂	—	2	2	no	—
122	C₅×D₁₂	C₂²×C₄	1	4	yes	—
123	C₄×C₅×D₃	—	4	8	no	—
124	C₅×Dic₆	—	2	4	no	—
125	C₅×Dic₆	—	2	2	no	—
126	C₅×Dic₆	C₂²×C₄	1	4	yes	complemented
127	C₃×C₅×C₈	C₂²×C₄	1	4	yes	complemented
128	C₅×C₃⋊C₈	—	2	2	no	—
129	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₄×D₃	—	2	1	no	—
131	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
132	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
135	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
136	C₂×Dic₃⋊C₄	—	2	1	no	—
137	C₂×C₄×Dic₃	—	2	1	no	—
138	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
139	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
140	C₂×#204	C₄×C₅	1	8	yes	complemented
141	C₂×#204	C₂²×C₅	1	4	yes	—
142	#893	—	2	2	no	—
143	#893	C₂²×C₅	1	4	yes	—
144	#887	—	2	2	no	—
145	#887	C₂²×C₅	1	4	yes	complemented
146	C₃×#106	C₂²×C₅	1	4	yes	complemented
147	C₈×Dic₃	C₂²×C₅	1	4	yes	complemented
148	#810	C₂²×C₅	1	4	yes	complemented
149	#809	C₂²×C₅	1	4	yes	—
150	C₂⁴×C₅	—	6	1	no	—
151	C₂×C₅×Q₈	—	3	4	no	—
152	C₂×C₅×Q₈	—	3	2	no	—
153	C₂×C₅×Q₈	—	6	1	no	—
154	C₂×C₅×Q₈	—	6	2	no	—
155	C₂×C₅×D₄	—	3	4	no	—
156	C₂×C₅×D₄	—	3	2	no	—
157	C₂×C₅×D₄	—	6	1	no	—
158	C₂×C₅×D₄	—	6	2	no	—
159	C₂²×C₄×C₅	—	2	1	no	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	3	1	no	—
162	C₂²×C₄×C₅	—	3	1	no	—
163	C₂²×C₄×C₅	—	6	4	no	—
164	C₂²×C₄×C₅	—	6	1	no	—
165	C₂²×C₄×C₅	—	12	4	no	—
166	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
167	C₅×SD₁₆	—	3	16	no	—
168	C₂×C₅×C₈	—	3	2	no	—
169	C₂×C₅×C₈	—	6	2	no	—
170	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
171	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
172	C₅×C₄⋊C₄	—	2	1	no	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	—	6	4	no	—
175	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
176	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
177	C₅×C₂²⋊C₄	—	6	4	no	—
178	C₄²×C₅	—	3	2	no	—
179	C₄²×C₅	—	3	2	no	—
180	C₄²×C₅	—	6	4	no	—
181	C₂²×SD₁₆	—	3	1	no	—
182	C₂×C₄×Q₈	—	3	1	no	—
183	C₂×C₄×D₄	—	3	1	no	—
184	C₄×SD₁₆	—	3	8	no	—
185	C₂×#106	C₅×D₃	1	1	yes	characteristic, complemented
186	C₂×#103	—	3	1	no	—
187	C₂×#102	—	3	1	no	—
188	C₂×C₄×C₈	—	3	1	no	—
189	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
190	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
191	C₂²×C₃×C₅	#135	1	2	yes	—
192	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₅×D₃	—	2	4	no	—
194	C₂×C₅×D₃	—	4	2	no	—
195	C₂×C₅×D₃	—	4	2	no	—
196	C₂×C₅×D₃	—	4	8	no	—
197	C₃×C₄×C₅	—	4	2	no	—
198	C₃×C₄×C₅	—	4	2	no	—
199	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
200	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
201	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
202	C₅×Dic₃	—	2	4	no	—
203	C₅×Dic₃	—	2	2	no	—
204	C₅×Dic₃	C₂×SD₁₆	1	4	yes	complemented
205	C₂³×D₃	—	2	1	no	—
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	—	2	1	no	—
208	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
209	C₂²×Dic₃	—	2	1	no	—
210	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
211	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
212	C₂×D₁₂	—	2	1	no	—
213	C₂×D₁₂	—	2	2	no	—
214	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
215	C₂×D₁₂	C₂³×C₅	1	2	yes	—
216	C₂×C₄×D₃	—	2	4	no	—
217	C₂×C₄×D₃	—	4	4	no	—
218	C₂×Dic₆	—	2	1	no	—
219	C₂×Dic₆	—	2	2	no	—
220	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	complemented
221	C₂×Dic₆	C₂³×C₅	1	2	yes	—
222	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
223	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
224	C₃×C₄⋊C₄	—	2	1	no	—
225	C₃×C₄⋊C₄	—	2	1	no	—
226	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
227	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
228	(C₂×D₃)⋊C₄	—	2	4	no	—
229	Dic₃⋊C₄	—	2	4	no	—
230	C₄×Dic₃	—	2	4	no	—
231	C₄×Dic₃	C₅×D₄	1	2	yes	—
232	C₄×Dic₃	C₂³×C₅	1	2	yes	—
233	C₂×C₃⋊C₈	—	2	2	no	—
234	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
235	#204	C₂×C₄×C₅	1	16	yes	complemented
236	C₂³×C₅	—	6	4	no	—
237	C₂³×C₅	—	6	2	no	—
238	C₂³×C₅	—	12	2	no	—
239	C₂³×C₅	—	12	2	no	—
240	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
241	C₅×Q₈	—	3	4	no	—
242	C₅×Q₈	—	6	4	no	—
243	C₅×Q₈	—	6	2	no	—
244	C₅×D₄	—	3	4	no	—
245	C₅×D₄	—	6	4	no	—
246	C₅×D₄	—	6	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	3	4	no	—
250	C₂×C₄×C₅	—	3	2	no	—
251	C₂×C₄×C₅	—	3	2	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	—	6	4	no	—
255	C₂×C₄×C₅	—	6	2	no	—
256	C₂×C₄×C₅	—	6	2	no	—
257	C₂×C₄×C₅	—	12	8	no	—
258	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
259	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
260	C₂×C₄×C₅	#239	1	2	yes	—
261	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
262	C₅×C₈	—	6	2	no	—
263	C₅×C₈	C₂×C₄×D₃	1	4	yes	complemented
264	C₂²×Q₈	—	3	1	no	—
265	C₂²×D₄	—	3	1	no	—
266	C₂³×C₄	—	6	1	no	—
267	C₂×SD₁₆	—	3	8	no	—
268	C₂×SD₁₆	—	3	4	no	—
269	C₂²×C₈	—	3	1	no	—
270	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
271	C₄×Q₈	—	3	4	no	—
272	C₄×Q₈	—	6	2	no	—
273	C₄×D₄	—	3	4	no	—
274	C₄×D₄	—	6	2	no	—
275	C₂×C₄⋊C₄	—	6	1	no	—
276	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	—	6	1	no	—
279	C₂×C₄²	—	3	1	no	—
280	C₂×C₄²	—	6	1	no	—
281	#106	C₂×C₅×D₃	1	4	yes	complemented
282	#103	—	3	4	no	—
283	#102	—	3	4	no	—
284	C₄×C₈	—	3	4	no	—
285	C₂×C₃×C₅	C₄×SD₁₆	1	4	yes	complemented
286	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
287	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
289	C₅×D₃	—	4	4	no	—
290	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
291	C₂²×D₃	—	2	4	no	—
292	C₂²×D₃	—	2	2	no	—
293	C₂²×D₃	—	4	2	no	—
294	C₂²×D₃	—	4	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	4	2	no	—
298	C₂×C₃×C₄	—	4	2	no	—
299	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
300	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₅×#41	1	2	yes	—
302	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
303	C₂×Dic₃	—	2	4	no	—
304	C₂×Dic₃	—	2	2	no	—
305	C₂×Dic₃	—	2	2	no	—
306	C₂×Dic₃	C₅×SD₁₆	1	4	yes	complemented
307	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
308	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
309	D₁₂	—	2	4	no	—
310	D₁₂	—	2	2	no	—
311	D₁₂	C₂²×C₄×C₅	1	4	yes	—
312	C₄×D₃	—	4	8	no	—
313	Dic₆	—	2	4	no	—
314	Dic₆	—	2	2	no	—
315	Dic₆	C₂²×C₄×C₅	1	4	yes	complemented
316	C₃×C₈	C₂²×C₄×C₅	1	4	yes	complemented
317	C₃⋊C₈	—	2	2	no	—
318	C₂²×C₅	—	6	4	no	—
319	C₂²×C₅	—	12	2	no	—
320	C₂²×C₅	—	12	2	no	—
321	C₂²×C₅	—	12	8	no	—
322	C₂²×C₅	#893	1	2	yes	—
323	C₂²×C₅	D₃×SD₁₆	1	2	yes	—
324	C₂²×C₅	#916	1	2	yes	—
325	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
326	C₄×C₅	—	3	4	no	—
327	C₄×C₅	—	4	2	no	—
328	C₄×C₅	—	4	2	no	—
329	C₄×C₅	—	6	4	no	—
330	C₄×C₅	—	6	2	no	—
331	C₄×C₅	#893	1	2	yes	—
332	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
333	C₄×C₅	C₂×#239	1	1	yes	characteristic
334	C₂⁴	—	6	1	no	—
335	C₂×Q₈	—	3	4	no	—
336	C₂×Q₈	—	3	2	no	—
337	C₂×Q₈	—	6	1	no	—
338	C₂×Q₈	—	6	2	no	—
339	C₂×D₄	—	3	4	no	—
340	C₂×D₄	—	3	2	no	—
341	C₂×D₄	—	6	1	no	—
342	C₂×D₄	—	6	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	3	1	no	—
346	C₂²×C₄	—	3	1	no	—
347	C₂²×C₄	—	6	4	no	—
348	C₂²×C₄	—	6	1	no	—
349	C₂²×C₄	—	12	4	no	—
350	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
351	SD₁₆	—	3	16	no	—
352	C₂×C₈	—	3	2	no	—
353	C₂×C₈	—	6	2	no	—
354	C₂×C₈	C₄×C₅×D₃	1	4	yes	complemented
355	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	6	4	no	—
359	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
360	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
361	C₂²⋊C₄	—	6	4	no	—
362	C₄²	—	3	2	no	—
363	C₄²	—	3	2	no	—
364	C₄²	—	6	4	no	—
365	C₃×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
367	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
368	C₂²×C₃	C₅×#135	1	2	yes	—
369	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
370	C₂×D₃	—	2	4	no	—
371	C₂×D₃	—	4	8	no	—
372	C₂×D₃	—	4	2	no	—
373	C₂×D₃	—	4	2	no	—
374	C₃×C₄	—	4	2	no	—
375	C₃×C₄	—	4	2	no	—
376	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
377	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
378	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
379	Dic₃	—	2	4	no	—
380	Dic₃	—	2	2	no	—
381	Dic₃	C₂×C₅×SD₁₆	1	4	yes	complemented
382	C₂×C₅	—	12	4	no	—
383	C₂×C₅	#4852	1	4	yes	direct product factor
384	C₂×C₅	C₂×#893	1	1	yes	characteristic
385	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
386	C₂×C₅	C₂×#916	1	1	yes	characteristic
387	C₂³	—	6	4	no	—
388	C₂³	—	6	2	no	—
389	C₂³	—	12	2	no	—
390	C₂³	—	12	2	no	—
391	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
392	Q₈	—	3	4	no	—
393	Q₈	—	6	4	no	—
394	Q₈	—	6	2	no	—
395	D₄	—	3	4	no	—
396	D₄	—	6	4	no	—
397	D₄	—	6	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	3	4	no	—
401	C₂×C₄	—	3	2	no	—
402	C₂×C₄	—	3	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	6	4	no	—
406	C₂×C₄	—	6	2	no	—
407	C₂×C₄	—	6	2	no	—
408	C₂×C₄	—	12	8	no	—
409	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
410	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
411	C₂×C₄	C₅×#239	1	2	yes	—
412	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
413	C₈	—	6	2	no	—
414	C₈	C₂×C₄×C₅×D₃	1	4	yes	complemented
415	C₂×C₃	C₄×C₅×SD₁₆	1	4	yes	complemented
416	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
417	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
418	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
419	D₃	—	4	4	no	—
420	C₅	C₂×#4852	1	1	yes	characteristic, direct product factor, Sylow
421	C₂²	—	6	4	no	—
422	C₂²	—	12	2	no	—
423	C₂²	—	12	2	no	—
424	C₂²	—	12	8	no	—
425	C₂²	C₅×#893	1	2	yes	—
426	C₂²	C₅×D₃×SD₁₆	1	2	yes	—
427	C₂²	C₅×#916	1	2	yes	—
428	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
429	C₄	—	3	4	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	6	4	no	—
433	C₄	—	6	2	no	—
434	C₄	C₅×#893	1	2	yes	—
435	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
436	C₄	C₂×C₅×#239	1	1	yes	characteristic
437	C₃	C₂×C₄×C₅×SD₁₆	1	1	yes	characteristic, complemented, Sylow
438	C₂	—	12	4	no	—
439	C₂	C₅×#4852	1	4	yes	direct product factor
440	C₂	C₂×C₅×#893	1	1	yes	characteristic
441	C₂	C₂×C₅×D₃×SD₁₆	1	1	yes	characteristic
442	C₂	C₂×C₅×#916	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#106	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#106	D₃
hypocenter	C₃	C₂×C₄×C₅×SD₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#106

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×#887	C₂	semidirect
4. C₂×C₃×C₅×#106	C₂	semidirect
5. C₂×C₅×C₈×Dic₃	C₂	semidirect
6. C₂×C₅×#810	C₂	semidirect
8. C₅×#4852	C₂	direct (N × H)
21. C₂×C₅×#204	C₄	semidirect
26. C₅×#887	C₂²	semidirect
27. C₃×C₅×#106	C₂²	semidirect
28. C₅×C₈×Dic₃	C₂²	semidirect
29. C₅×#810	C₂²	semidirect
31. C₂×#4852	C₅	direct (N × H)
36. C₂×C₅×#106	D₃	semidirect
55. C₂×C₅×Dic₆	C₂×C₄	semidirect
57. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
70. C₅×#204	C₂×C₄	semidirect
73. C₂×#887	C₂×C₅	semidirect
74. C₂×C₃×#106	C₂×C₅	semidirect
75. C₂×C₈×Dic₃	C₂×C₅	semidirect
76. C₂×#810	C₂×C₅	semidirect
78. #4852	C₂×C₅	direct (N × H)
96. C₅×#106	C₂×D₃	semidirect
117. C₂×C₅×Dic₃	SD₁₆	semidirect
126. C₅×Dic₆	C₂²×C₄	semidirect
127. C₃×C₅×C₈	C₂²×C₄	semidirect
140. C₂×#204	C₄×C₅	semidirect
145. #887	C₂²×C₅	semidirect
146. C₃×#106	C₂²×C₅	semidirect
147. C₈×Dic₃	C₂²×C₅	semidirect
148. #810	C₂²×C₅	semidirect
170. C₂×C₅×C₈	C₄×D₃	semidirect
185. C₂×#106	C₅×D₃	semidirect
204. C₅×Dic₃	C₂×SD₁₆	semidirect
220. C₂×Dic₆	C₂×C₄×C₅	semidirect
222. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
235. #204	C₂×C₄×C₅	semidirect
263. C₅×C₈	C₂×C₄×D₃	semidirect
281. #106	C₂×C₅×D₃	semidirect
285. C₂×C₃×C₅	C₄×SD₁₆	semidirect
306. C₂×Dic₃	C₅×SD₁₆	semidirect
315. Dic₆	C₂²×C₄×C₅	semidirect
316. C₃×C₈	C₂²×C₄×C₅	semidirect
354. C₂×C₈	C₄×C₅×D₃	semidirect
365. C₃×C₅	C₂×C₄×SD₁₆	semidirect
381. Dic₃	C₂×C₅×SD₁₆	semidirect
383. C₂×C₅	#4852	direct (N × H)
414. C₈	C₂×C₄×C₅×D₃	semidirect
415. C₂×C₃	C₄×C₅×SD₁₆	semidirect
420. C₅	C₂×#4852	direct (N × H)
437. C₃	C₂×C₄×C₅×SD₁₆	semidirect
439. C₂	C₅×#4852	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#204	2
C₂×C₅×#893	2
C₂×C₅×#887	2
C₂×C₃×C₅×#106	2
C₂×C₅×C₈×Dic₃	2
C₂×C₅×#810	2
C₂×C₅×#809	2
C₅×#4852	2
C₂×C₄×C₅×SD₁₆	3
C₂×#4852	5

Subgroups — C2×C5×#4852 #14416049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4852 #14416049