Subgroups — C₂×C₅×#5162 #14425866

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₅×#214	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5162	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#816	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#461	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂³×C₅×Dic₃	—	2	1	no	—
13	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
15	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#217	—	2	1	no	—
18	C₅×#944	—	2	2	no	—
19	C₅×#944	C₂²	1	4	yes	complemented
20	C₅×D₄×Dic₃	—	2	2	no	—
21	C₅×D₄×Dic₃	C₂²	1	4	yes	—
22	C₂×C₅×#214	—	2	4	no	—
23	C₂×C₅×#214	C₂²	1	4	yes	—
24	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
26	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
27	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
28	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₅×#835	C₂²	1	4	yes	complemented
30	C₅×#816	C₂²	1	4	yes	complemented
31	C₅×Dic₃⋊C₈	C₂²	1	4	yes	complemented
32	C₂×#5162	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×SD₁₆	—	3	1	no	—
34	C₂²×C₅×SD₁₆	D₃	1	1	yes	characteristic
35	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
36	C₂×C₄×C₅×D₄	—	3	1	no	—
37	C₅×#461	—	3	8	no	—
38	C₂×C₅×C₄⋊C₈	—	3	1	no	—
39	C₂×C₅×#103	—	3	1	no	—
40	C₂×C₅×#103	—	3	1	no	—
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₂×C₃×C₅×Q₈	—	2	1	no	—
43	C₂×C₃×C₅×Q₈	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	—	2	2	no	—
45	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
46	C₂×C₃×C₅×D₄	—	2	1	no	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	D₄	1	4	yes	—
49	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	—	2	1	no	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₅×Dic₃	—	2	1	no	—
53	C₂²×C₅×Dic₃	—	2	1	no	—
54	C₂²×C₅×Dic₃	—	2	4	no	—
55	C₂²×C₅×Dic₃	—	4	4	no	—
56	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
57	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
58	C₂×C₅×Dic₆	—	2	2	no	—
59	C₂×C₅×Dic₆	—	2	2	no	—
60	C₂×C₅×Dic₆	—	2	1	no	—
61	C₂×C₅×Dic₆	C₂³	1	2	yes	—
62	C₃×C₅×SD₁₆	—	2	8	no	—
63	C₂×C₃×C₅×C₈	—	2	2	no	—
64	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
65	C₅×#217	—	2	4	no	—
66	C₅×#214	—	2	8	no	—
67	C₅×C₄⋊Dic₃	—	2	1	no	—
68	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
69	C₅×Dic₃⋊C₄	—	2	4	no	—
70	C₅×Dic₃⋊C₄	—	2	4	no	—
71	C₄×C₅×Dic₃	D₄	1	2	yes	—
72	C₄×C₅×Dic₃	C₂³	1	2	yes	—
73	C₂×C₅×C₃⋊C₈	—	2	2	no	—
74	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
75	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic
76	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×D₄×Dic₃	C₂×C₅	1	1	yes	characteristic
78	C₂²×#214	C₂×C₅	1	1	yes	characteristic
79	C₂×#835	C₂×C₅	1	1	yes	characteristic, complemented
80	#5162	C₂×C₅	1	8	yes	direct product factor
81	C₂×#816	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂×Dic₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂²×C₅×Q₈	—	3	1	no	—
84	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
86	C₂³×C₄×C₅	—	6	1	no	—
87	C₂×C₅×SD₁₆	—	2	4	no	—
88	C₂×C₅×SD₁₆	—	3	4	no	—
89	C₂×C₅×SD₁₆	—	6	4	no	—
90	C₂×C₅×SD₁₆	C₂×D₃	1	4	yes	—
91	C₂²×C₅×C₈	—	3	1	no	—
92	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
93	C₅×C₄⋊Q₈	—	3	4	no	—
94	C₅×C₄⋊Q₈	—	6	2	no	—
95	C₄×C₅×D₄	—	3	4	no	—
96	C₄×C₅×D₄	—	6	2	no	—
97	C₂×C₅×C₄⋊C₄	—	3	1	no	—
98	C₂×C₅×C₄⋊C₄	—	6	1	no	—
99	C₂×C₅×C₄⋊C₄	—	6	1	no	—
100	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
101	C₂×C₄²×C₅	—	3	1	no	—
102	C₅×C₄⋊C₈	—	3	4	no	—
103	C₅×#103	—	3	4	no	—
104	C₅×#103	—	3	4	no	—
105	C₂×#461	—	3	1	no	Sylow
106	C₂³×C₃×C₅	—	2	4	no	—
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	—	4	2	no	—
109	C₂³×C₃×C₅	—	4	2	no	—
110	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
111	C₃×C₅×Q₈	—	2	2	no	—
112	C₃×C₅×Q₈	—	2	2	no	—
113	C₃×C₅×Q₈	—	4	2	no	—
114	C₃×C₅×D₄	—	2	4	no	—
115	C₃×C₅×D₄	—	2	2	no	—
116	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	4	2	no	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂×C₃×C₄×C₅	#41	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
123	C₂×C₅×Dic₃	—	2	2	no	—
124	C₂×C₅×Dic₃	—	2	2	no	—
125	C₂×C₅×Dic₃	—	2	2	no	—
126	C₂×C₅×Dic₃	—	4	2	no	—
127	C₂×C₅×Dic₃	—	4	2	no	—
128	C₂×C₅×Dic₃	—	4	8	no	—
129	C₂×C₅×Dic₃	SD₁₆	1	4	yes	complemented
130	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
131	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
132	C₅×Dic₆	—	2	2	no	—
133	C₅×Dic₆	—	2	2	no	—
134	C₅×Dic₆	—	4	2	no	—
135	C₃×C₅×C₈	—	2	2	no	—
136	C₅×C₃⋊C₈	—	2	2	no	—
137	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
138	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
139	C₂³×Dic₃	—	2	1	no	—
140	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₃×SD₁₆	—	2	4	no	—
142	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
143	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
144	C₂×#217	—	2	1	no	—
145	#944	—	2	2	no	—
146	#944	C₂²×C₅	1	4	yes	complemented
147	D₄×Dic₃	—	2	2	no	—
148	D₄×Dic₃	C₂²×C₅	1	4	yes	—
149	C₂×#214	—	2	4	no	—
150	C₂×#214	C₂²×C₅	1	4	yes	—
151	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
152	C₂×Dic₃⋊C₄	—	2	1	no	—
153	C₂×Dic₃⋊C₄	—	2	1	no	—
154	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
155	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
156	#835	C₂²×C₅	1	4	yes	complemented
157	#816	C₂²×C₅	1	4	yes	complemented
158	Dic₃⋊C₈	C₂²×C₅	1	4	yes	complemented
159	C₂⁴×C₅	—	2	1	no	—
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	2	no	—
162	C₂×C₅×Q₈	—	2	2	no	—
163	C₂×C₅×Q₈	—	3	2	no	—
164	C₂×C₅×Q₈	—	6	1	no	—
165	C₂×C₅×Q₈	—	6	2	no	—
166	C₂×C₅×Q₈	—	6	2	no	—
167	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	—	2	2	no	—
170	C₂×C₅×D₄	#67	1	4	yes	—
171	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	3	1	no	—
174	C₂²×C₄×C₅	—	3	1	no	—
175	C₂²×C₄×C₅	—	6	4	no	—
176	C₂²×C₄×C₅	—	6	1	no	—
177	C₂²×C₄×C₅	—	6	1	no	—
178	C₂²×C₄×C₅	—	12	4	no	—
179	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₅×SD₁₆	—	2	8	no	—
181	C₅×SD₁₆	—	6	8	no	—
182	C₂×C₅×C₈	—	2	2	no	—
183	C₂×C₅×C₈	—	3	2	no	—
184	C₂×C₅×C₈	—	6	2	no	—
185	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
186	C₅×C₄⋊C₄	—	3	2	no	—
187	C₅×C₄⋊C₄	—	6	4	no	—
188	C₅×C₄⋊C₄	—	6	4	no	—
189	C₅×C₄⋊C₄	—	6	1	no	—
190	C₅×C₂²⋊C₄	—	6	4	no	—
191	C₄²×C₅	—	3	2	no	—
192	C₄²×C₅	—	3	2	no	—
193	C₂²×SD₁₆	—	3	1	no	—
194	C₂²×SD₁₆	C₅×D₃	1	1	yes	characteristic
195	C₂×C₄⋊Q₈	—	3	1	no	—
196	C₂×C₄×D₄	—	3	1	no	—
197	#461	—	3	8	no	—
198	C₂×C₄⋊C₈	—	3	1	no	—
199	C₂×#103	—	3	1	no	—
200	C₂×#103	—	3	1	no	—
201	C₂²×C₃×C₅	—	2	4	no	—
202	C₂²×C₃×C₅	—	4	2	no	—
203	C₂²×C₃×C₅	—	4	2	no	—
204	C₂²×C₃×C₅	—	4	8	no	—
205	C₂²×C₃×C₅	#121	1	2	yes	—
206	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
207	C₂²×C₃×C₅	#137	1	2	yes	—
208	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₃×C₄×C₅	—	4	2	no	—
210	C₃×C₄×C₅	#121	1	2	yes	—
211	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
212	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
213	C₅×Dic₃	—	2	2	no	—
214	C₅×Dic₃	—	4	2	no	—
215	C₅×Dic₃	—	4	2	no	—
216	C₅×Dic₃	C₂×SD₁₆	1	4	yes	complemented
217	C₂⁴×C₃	—	2	1	no	—
218	C₂×C₃×Q₈	—	2	1	no	—
219	C₂×C₃×Q₈	—	2	2	no	—
220	C₂×C₃×Q₈	—	2	2	no	—
221	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
222	C₂×C₃×D₄	—	2	1	no	—
223	C₂×C₃×D₄	—	2	2	no	—
224	C₂×C₃×D₄	C₅×D₄	1	4	yes	—
225	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
226	C₂²×C₃×C₄	—	2	1	no	—
227	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
228	C₂²×Dic₃	—	2	1	no	—
229	C₂²×Dic₃	—	2	1	no	—
230	C₂²×Dic₃	—	2	4	no	—
231	C₂²×Dic₃	—	4	4	no	—
232	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
233	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
234	C₂×Dic₆	—	2	2	no	—
235	C₂×Dic₆	—	2	2	no	—
236	C₂×Dic₆	—	2	1	no	—
237	C₂×Dic₆	C₂³×C₅	1	2	yes	—
238	C₃×SD₁₆	—	2	8	no	—
239	C₂×C₃×C₈	—	2	2	no	—
240	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
241	#217	—	2	4	no	—
242	#214	—	2	8	no	—
243	C₄⋊Dic₃	—	2	1	no	—
244	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
245	Dic₃⋊C₄	—	2	4	no	—
246	Dic₃⋊C₄	—	2	4	no	—
247	C₄×Dic₃	C₅×D₄	1	2	yes	—
248	C₄×Dic₃	C₂³×C₅	1	2	yes	—
249	C₂×C₃⋊C₈	—	2	2	no	—
250	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
251	C₂³×C₅	—	2	4	no	—
252	C₂³×C₅	—	2	2	no	—
253	C₂³×C₅	—	4	2	no	—
254	C₂³×C₅	—	4	2	no	—
255	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
256	C₅×Q₈	—	2	2	no	—
257	C₅×Q₈	—	2	2	no	—
258	C₅×Q₈	—	4	2	no	—
259	C₅×Q₈	—	6	2	no	—
260	C₅×Q₈	—	6	2	no	—
261	C₅×Q₈	—	12	2	no	—
262	C₅×D₄	—	2	4	no	—
263	C₅×D₄	—	2	2	no	—
264	C₅×D₄	C₂×#67	1	4	yes	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	3	4	no	—
267	C₂×C₄×C₅	—	3	2	no	—
268	C₂×C₄×C₅	—	3	2	no	—
269	C₂×C₄×C₅	—	4	2	no	—
270	C₂×C₄×C₅	—	6	2	no	—
271	C₂×C₄×C₅	—	6	2	no	—
272	C₂×C₄×C₅	—	6	2	no	—
273	C₂×C₄×C₅	—	12	8	no	—
274	C₂×C₄×C₅	—	12	2	no	—
275	C₂×C₄×C₅	—	12	2	no	—
276	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
277	C₂×C₄×C₅	#237	1	2	yes	—
278	C₂×C₄×C₅	C₂×#67	1	2	yes	—
279	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
280	C₅×C₈	—	2	2	no	—
281	C₅×C₈	—	6	2	no	—
282	C₂²×Q₈	—	3	1	no	—
283	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
284	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
285	C₂³×C₄	—	6	1	no	—
286	C₂×SD₁₆	—	2	4	no	—
287	C₂×SD₁₆	—	3	4	no	—
288	C₂×SD₁₆	—	6	4	no	—
289	C₂×SD₁₆	C₂×C₅×D₃	1	4	yes	—
290	C₂²×C₈	—	3	1	no	—
291	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
292	C₄⋊Q₈	—	3	4	no	—
293	C₄⋊Q₈	—	6	2	no	—
294	C₄×D₄	—	3	4	no	—
295	C₄×D₄	—	6	2	no	—
296	C₂×C₄⋊C₄	—	3	1	no	—
297	C₂×C₄⋊C₄	—	6	1	no	—
298	C₂×C₄⋊C₄	—	6	1	no	—
299	C₂×C₂²⋊C₄	—	6	1	no	—
300	C₂×C₄²	—	3	1	no	—
301	C₄⋊C₈	—	3	4	no	—
302	#103	—	3	4	no	—
303	#103	—	3	4	no	—
304	C₂×C₃×C₅	—	4	4	no	—
305	C₂×C₃×C₅	#461	1	4	yes	complemented
306	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
307	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
308	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
309	C₂³×C₃	—	2	4	no	—
310	C₂³×C₃	—	2	2	no	—
311	C₂³×C₃	—	4	2	no	—
312	C₂³×C₃	—	4	2	no	—
313	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
314	C₃×Q₈	—	2	2	no	—
315	C₃×Q₈	—	2	2	no	—
316	C₃×Q₈	—	4	2	no	—
317	C₃×D₄	—	2	4	no	—
318	C₃×D₄	—	2	2	no	—
319	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	4	2	no	—
322	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
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	—	2	2	no	—
328	C₂×Dic₃	—	2	2	no	—
329	C₂×Dic₃	—	4	2	no	—
330	C₂×Dic₃	—	4	2	no	—
331	C₂×Dic₃	—	4	8	no	—
332	C₂×Dic₃	C₅×SD₁₆	1	4	yes	complemented
333	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
334	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
335	Dic₆	—	2	2	no	—
336	Dic₆	—	2	2	no	—
337	Dic₆	—	4	2	no	—
338	C₃×C₈	—	2	2	no	—
339	C₃⋊C₈	—	2	2	no	—
340	C₂²×C₅	—	2	4	no	—
341	C₂²×C₅	—	4	8	no	—
342	C₂²×C₅	—	4	2	no	—
343	C₂²×C₅	—	4	2	no	—
344	C₂²×C₅	D₃×SD₁₆	1	2	yes	—
345	C₂²×C₅	#915	1	2	yes	—
346	C₂²×C₅	#939	1	2	yes	—
347	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
348	C₄×C₅	—	3	4	no	—
349	C₄×C₅	—	4	2	no	—
350	C₄×C₅	—	6	2	no	—
351	C₄×C₅	—	12	2	no	—
352	C₄×C₅	—	12	2	no	—
353	C₄×C₅	#939	1	2	yes	—
354	C₄×C₅	C₂×#237	1	1	yes	characteristic
355	C₄×C₅	C₂²×#67	1	1	yes	characteristic
356	C₂⁴	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	3	2	no	—
361	C₂×Q₈	—	6	1	no	—
362	C₂×Q₈	—	6	2	no	—
363	C₂×Q₈	—	6	2	no	—
364	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	C₅×#67	1	4	yes	—
368	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	3	1	no	—
371	C₂²×C₄	—	3	1	no	—
372	C₂²×C₄	—	6	4	no	—
373	C₂²×C₄	—	6	1	no	—
374	C₂²×C₄	—	6	1	no	—
375	C₂²×C₄	—	12	4	no	—
376	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
377	SD₁₆	—	2	8	no	—
378	SD₁₆	—	6	8	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	3	2	no	—
381	C₂×C₈	—	6	2	no	—
382	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
383	C₄⋊C₄	—	3	2	no	—
384	C₄⋊C₄	—	6	4	no	—
385	C₄⋊C₄	—	6	4	no	—
386	C₄⋊C₄	—	6	1	no	—
387	C₂²⋊C₄	—	6	4	no	—
388	C₄²	—	3	2	no	—
389	C₄²	—	3	2	no	—
390	C₃×C₅	C₂×#461	1	1	yes	characteristic, complemented, Hall
391	C₂²×C₃	—	2	4	no	—
392	C₂²×C₃	—	4	8	no	—
393	C₂²×C₃	—	4	2	no	—
394	C₂²×C₃	—	4	2	no	—
395	C₂²×C₃	C₅×#121	1	2	yes	—
396	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
397	C₂²×C₃	C₅×#137	1	2	yes	—
398	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
399	C₃×C₄	—	4	2	no	—
400	C₃×C₄	C₅×#121	1	2	yes	—
401	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
402	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
403	Dic₃	—	2	2	no	—
404	Dic₃	—	4	2	no	—
405	Dic₃	—	4	2	no	—
406	Dic₃	C₂×C₅×SD₁₆	1	4	yes	complemented
407	C₂×C₅	—	4	4	no	—
408	C₂×C₅	#5162	1	4	yes	direct product factor
409	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
410	C₂×C₅	C₂×#915	1	1	yes	characteristic
411	C₂×C₅	C₂×#939	1	1	yes	characteristic
412	C₂³	—	2	4	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	6	2	no	—
421	Q₈	—	6	2	no	—
422	Q₈	—	12	2	no	—
423	D₄	—	2	4	no	—
424	D₄	—	2	2	no	—
425	D₄	C₂×C₅×#67	1	4	yes	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	3	4	no	—
428	C₂×C₄	—	3	2	no	—
429	C₂×C₄	—	3	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	6	2	no	—
432	C₂×C₄	—	6	2	no	—
433	C₂×C₄	—	6	2	no	—
434	C₂×C₄	—	12	8	no	—
435	C₂×C₄	—	12	2	no	—
436	C₂×C₄	—	12	2	no	—
437	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
438	C₂×C₄	C₅×#237	1	2	yes	—
439	C₂×C₄	C₂×C₅×#67	1	2	yes	—
440	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
441	C₈	—	2	2	no	—
442	C₈	—	6	2	no	—
443	C₂×C₃	—	4	4	no	—
444	C₂×C₃	C₅×#461	1	4	yes	complemented
445	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
446	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
447	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
448	C₅	C₂×#5162	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	C₅×D₃×SD₁₆	1	2	yes	—
454	C₂²	C₅×#915	1	2	yes	—
455	C₂²	C₅×#939	1	2	yes	—
456	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
457	C₄	—	3	4	no	—
458	C₄	—	4	2	no	—
459	C₄	—	6	2	no	—
460	C₄	—	12	2	no	—
461	C₄	—	12	2	no	—
462	C₄	C₅×#939	1	2	yes	—
463	C₄	C₂×C₅×#237	1	1	yes	characteristic
464	C₄	C₂²×C₅×#67	1	1	yes	characteristic
465	C₃	C₂×C₅×#461	1	1	yes	characteristic, complemented, Sylow
466	C₂	—	4	4	no	—
467	C₂	C₅×#5162	1	4	yes	direct product factor
468	C₂	C₂×C₅×D₃×SD₁₆	1	1	yes	characteristic
469	C₂	C₂×C₅×#915	1	1	yes	characteristic
470	C₂	C₂×C₅×#939	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×SD₁₆	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
hypercenter	C₂²×C₅×SD₁₆	D₃
hypocenter	C₃	C₂×C₅×#461
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#944	C₂	semidirect
5. C₂×C₅×#835	C₂	semidirect
6. C₅×#5162	C₂	direct (N × H)
7. C₂×C₅×#816	C₂	semidirect
8. C₂×C₅×Dic₃⋊C₈	C₂	semidirect
19. C₅×#944	C₂²	semidirect
29. C₅×#835	C₂²	semidirect
30. C₅×#816	C₂²	semidirect
31. C₅×Dic₃⋊C₈	C₂²	semidirect
32. C₂×#5162	C₅	direct (N × H)
76. C₂×#944	C₂×C₅	semidirect
79. C₂×#835	C₂×C₅	semidirect
80. #5162	C₂×C₅	direct (N × H)
81. C₂×#816	C₂×C₅	semidirect
82. C₂×Dic₃⋊C₈	C₂×C₅	semidirect
129. C₂×C₅×Dic₃	SD₁₆	semidirect
146. #944	C₂²×C₅	semidirect
156. #835	C₂²×C₅	semidirect
157. #816	C₂²×C₅	semidirect
158. Dic₃⋊C₈	C₂²×C₅	semidirect
216. C₅×Dic₃	C₂×SD₁₆	semidirect
305. C₂×C₃×C₅	#461	semidirect
332. C₂×Dic₃	C₅×SD₁₆	semidirect
390. C₃×C₅	C₂×#461	semidirect
406. Dic₃	C₂×C₅×SD₁₆	semidirect
408. C₂×C₅	#5162	direct (N × H)
444. C₂×C₃	C₅×#461	semidirect
448. C₅	C₂×#5162	direct (N × H)
465. C₃	C₂×C₅×#461	semidirect
467. C₂	C₅×#5162	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×C₃×C₅×SD₁₆	2
C₂×C₅×#944	2
C₂×C₅×D₄×Dic₃	2
C₂²×C₅×#214	2
C₂×C₅×#835	2
C₅×#5162	2
C₂×C₅×#816	2
C₂×C₅×Dic₃⋊C₈	2
C₂×C₅×#461	3
C₂×#5162	5

Subgroups — C2×C5×#5162 #14425866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5162 #14425866