Subgroups — C₂×C₅×#5766 #14510121

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1007	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#942	C₂	1	2	yes	maximal, complemented
4	C₅×#5766	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅×#919	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#918	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×D₃×Q₁₆	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#904	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#901	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#578	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₅×#1007	—	2	8	no	—
13	C₅×#1007	C₂²	1	16	yes	complemented
14	C₂×C₅×#239	—	2	2	no	—
15	C₂×C₅×#239	C₂²	1	4	yes	—
16	C₂×C₅×D₃×Q₈	—	2	2	no	—
17	C₂×C₅×D₃×Q₈	C₂²	1	4	yes	—
18	C₂×C₅×#235	—	2	4	no	—
19	C₂×C₅×#235	C₂²	1	1	yes	characteristic
20	C₂×C₅×#235	C₂²	1	2	yes	—
21	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
22	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
23	C₂×C₃×C₅×Q₁₆	C₂²	1	8	yes	complemented
24	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×#216	C₂²	1	4	yes	—
26	C₅×#942	C₂²	1	16	yes	complemented
27	C₂×C₅×#215	C₂²	1	4	yes	—
28	C₂×C₅×#208	C₂²	1	1	yes	characteristic
29	C₅×#919	C₂²	1	16	yes	complemented
30	C₅×#918	C₂²	1	32	yes	complemented
31	C₅×D₃×Q₁₆	C₂²	1	16	yes	complemented
32	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
33	C₅×#904	C₂²	1	8	yes	complemented
34	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
35	C₂×C₅×#204	C₂²	1	2	yes	—
36	C₅×#901	C₂²	1	8	yes	complemented
37	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
38	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
39	C₂×#5766	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂×C₅×2₋¹⁺⁴	—	3	2	no	—
41	C₅×#578	—	3	16	no	—
42	C₂×C₅×#137	—	3	2	no	—
43	C₂×C₅×#137	—	3	4	no	—
44	C₂×C₅×#135	—	3	2	no	—
45	C₂×C₅×#135	—	3	1	no	—
46	C₂²×C₅×Q₁₆	—	3	2	no	—
47	C₂²×C₅×Q₁₆	D₃	1	1	yes	characteristic, complemented
48	C₂×C₅×#131	—	3	1	no	—
49	C₂×C₃×C₅×Q₈	—	2	2	no	—
50	C₂×C₃×C₅×Q₈	—	2	4	no	—
51	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
52	C₂×C₃×C₅×Q₈	C₂³	1	8	yes	—
53	C₂²×C₃×C₄×C₅	—	2	2	no	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₅×#67	—	2	2	no	—
56	C₂×C₅×#67	D₄	1	2	yes	—
57	C₅×#239	—	2	16	no	—
58	C₅×#239	—	2	8	no	—
59	C₅×#239	C₂³	1	16	yes	—
60	C₅×D₃×Q₈	—	2	8	no	—
61	C₅×D₃×Q₈	—	2	16	no	—
62	C₅×D₃×Q₈	C₂³	1	16	yes	—
63	C₅×#235	—	2	4	no	—
64	C₅×#235	—	2	32	no	—
65	C₅×#235	D₄	1	4	yes	—
66	C₅×#235	C₂³	1	4	yes	—
67	C₅×#235	C₂³	1	8	yes	—
68	C₂×C₅×D₁₂	—	2	4	no	—
69	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
70	C₂×C₅×D₁₂	C₂³	1	2	yes	—
71	C₂×C₄×C₅×D₃	—	2	4	no	—
72	C₂×C₄×C₅×D₃	—	2	2	no	—
73	C₂×C₄×C₅×D₃	—	2	4	no	—
74	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
75	C₂×C₅×Dic₆	—	2	4	no	—
76	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
77	C₂×C₅×Dic₆	C₂³	1	2	yes	—
78	C₃×C₅×Q₁₆	C₂³	1	8	yes	—
79	C₃×C₅×Q₁₆	C₂³	1	8	yes	—
80	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
83	C₅×#216	C₂³	1	16	yes	—
84	C₅×#215	C₂³	1	16	yes	—
85	C₅×#208	C₂³	1	4	yes	—
86	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
87	C₅×Dic₁₂	C₂³	1	4	yes	—
88	C₅×D₂₄	C₂³	1	4	yes	—
89	C₅×#204	C₂³	1	8	yes	—
90	C₅×ΓL(1,𝔽₂₅)	C₂³	1	8	yes	—
91	C₅×D₃×C₈	C₂³	1	8	yes	—
92	C₂×#1007	C₂×C₅	1	2	yes	complemented
93	C₂²×C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#942	C₂×C₅	1	2	yes	complemented
95	#5766	C₂×C₅	1	16	yes	direct product factor
96	C₂×#919	C₂×C₅	1	2	yes	complemented
97	C₂×#918	C₂×C₅	1	4	yes	complemented
98	C₂×D₃×Q₁₆	C₂×C₅	1	2	yes	complemented
99	C₂×#904	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂×#901	C₂×C₅	1	1	yes	characteristic, complemented
101	C₅×2₋¹⁺⁴	—	3	16	no	—
102	C₅×2₋¹⁺⁴	—	6	8	no	—
103	C₂×C₅×#41	—	3	1	no	—
104	C₂×C₅×#41	—	3	4	no	—
105	C₂×C₅×#41	—	3	2	no	—
106	C₂×C₅×#41	—	6	4	no	—
107	C₂×C₅×#41	—	6	2	no	—
108	C₂²×C₅×Q₈	—	3	4	no	—
109	C₂²×C₅×Q₈	—	6	2	no	—
110	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	—
111	C₅×#137	—	3	16	no	—
112	C₅×#137	—	3	32	no	—
113	C₅×#135	—	3	16	no	—
114	C₅×#135	—	3	8	no	—
115	C₂×C₅×Q₁₆	—	3	4	no	—
116	C₂×C₅×Q₁₆	—	3	16	no	—
117	C₂×C₅×Q₁₆	—	3	1	no	—
118	C₂×C₅×Q₁₆	C₂×D₃	1	2	yes	—
119	C₂×C₅×Q₁₆	C₂×D₃	1	2	yes	—
120	C₂×C₅×Q₁₆	C₂×D₃	1	8	yes	complemented
121	C₂×C₅×SD₁₆	—	3	4	no	—
122	C₂×C₅×SD₁₆	—	3	2	no	—
123	C₂×C₅×D₈	—	3	1	no	—
124	C₅×#131	—	3	8	no	—
125	C₂×C₅×M₁₆	—	3	1	no	—
126	C₂×C₅×M₁₆	—	3	2	no	—
127	C₂²×C₅×C₈	—	3	2	no	—
128	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
129	C₂×#578	—	3	1	no	Sylow
130	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₅×D₃	—	2	2	no	—
132	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
133	C₃×C₅×Q₈	—	2	4	no	—
134	C₃×C₅×Q₈	—	2	8	no	—
135	C₃×C₅×Q₈	C₂⁴	1	8	yes	—
136	C₂×C₃×C₄×C₅	—	2	4	no	—
137	C₂×C₃×C₄×C₅	—	2	8	no	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
142	C₅×#67	—	2	8	no	—
143	C₅×#67	C₂×D₄	1	8	yes	—
144	C₂×C₅×Dic₃	—	2	2	no	—
145	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
146	C₅×D₁₂	—	2	16	no	—
147	C₅×D₁₂	—	2	2	no	—
148	C₅×D₁₂	C₂×D₄	1	4	yes	—
149	C₅×D₁₂	C₂⁴	1	4	yes	—
150	C₄×C₅×D₃	—	2	16	no	—
151	C₄×C₅×D₃	—	2	8	no	—
152	C₄×C₅×D₃	—	2	16	no	—
153	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
154	C₄×C₅×D₃	C₂⁴	1	4	yes	—
155	C₅×Dic₆	—	2	2	no	—
156	C₅×Dic₆	—	2	16	no	—
157	C₅×Dic₆	C₂×D₄	1	4	yes	—
158	C₅×Dic₆	C₂⁴	1	4	yes	—
159	C₃×C₅×C₈	C₂⁴	1	2	yes	—
160	C₃×C₅×C₈	C₂⁴	1	2	yes	—
161	C₅×C₃⋊C₈	C₂⁴	1	4	yes	—
162	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
163	#1007	—	2	8	no	—
164	#1007	C₂²×C₅	1	16	yes	complemented
165	C₂×#239	—	2	2	no	—
166	C₂×#239	C₂²×C₅	1	4	yes	—
167	C₂×D₃×Q₈	—	2	2	no	—
168	C₂×D₃×Q₈	C₂²×C₅	1	4	yes	—
169	C₂×#235	—	2	4	no	—
170	C₂×#235	C₂²×C₅	1	1	yes	characteristic
171	C₂×#235	C₂²×C₅	1	2	yes	—
172	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
173	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
174	C₂×C₃×Q₁₆	C₂²×C₅	1	8	yes	complemented
175	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
176	C₂×#216	C₂²×C₅	1	4	yes	—
177	#942	C₂²×C₅	1	16	yes	complemented
178	C₂×#215	C₂²×C₅	1	4	yes	—
179	C₂×#208	C₂²×C₅	1	1	yes	characteristic
180	#919	C₂²×C₅	1	16	yes	complemented
181	#918	C₂²×C₅	1	32	yes	complemented
182	D₃×Q₁₆	C₂²×C₅	1	16	yes	complemented
183	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
184	#904	C₂²×C₅	1	8	yes	complemented
185	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
186	C₂×#204	C₂²×C₅	1	2	yes	—
187	#901	C₂²×C₅	1	8	yes	complemented
188	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
189	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
190	C₅×#41	—	3	4	no	—
191	C₅×#41	—	3	4	no	—
192	C₅×#41	—	3	16	no	—
193	C₅×#41	—	3	8	no	—
194	C₅×#41	—	6	32	no	—
195	C₅×#41	—	6	8	no	—
196	C₅×#41	—	6	16	no	—
197	C₅×#41	—	6	4	no	—
198	C₂×C₅×Q₈	—	2	2	no	—
199	C₂×C₅×Q₈	—	2	4	no	—
200	C₂×C₅×Q₈	—	3	1	no	—
201	C₂×C₅×Q₈	—	3	16	no	—
202	C₂×C₅×Q₈	—	3	2	no	—
203	C₂×C₅×Q₈	—	6	4	no	—
204	C₂×C₅×Q₈	—	6	8	no	—
205	C₂×C₅×Q₈	—	6	16	no	—
206	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
207	C₂×C₅×Q₈	C₂²×D₃	1	8	yes	—
208	C₂×C₅×D₄	—	3	2	no	—
209	C₂×C₅×D₄	—	3	1	no	—
210	C₂×C₅×D₄	—	3	2	no	—
211	C₂×C₅×D₄	—	6	4	no	—
212	C₂×C₅×D₄	—	6	2	no	—
213	C₂²×C₄×C₅	—	2	2	no	—
214	C₂²×C₄×C₅	—	3	2	no	—
215	C₂²×C₄×C₅	—	6	4	no	—
216	C₂²×C₄×C₅	—	6	4	no	—
217	C₂²×C₄×C₅	—	6	2	no	—
218	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₅×Q₁₆	—	3	16	no	—
220	C₅×Q₁₆	—	3	4	no	—
221	C₅×Q₁₆	C₂²×D₃	1	8	yes	—
222	C₅×Q₁₆	C₂²×D₃	1	8	yes	—
223	C₅×SD₁₆	—	3	16	no	—
224	C₅×SD₁₆	—	3	8	no	—
225	C₅×D₈	—	3	4	no	—
226	C₅×M₁₆	—	3	4	no	—
227	C₅×M₁₆	—	3	8	no	—
228	C₂×C₅×C₈	—	3	2	no	—
229	C₂×C₅×C₈	—	3	8	no	—
230	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
231	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
232	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
233	C₂×2₋¹⁺⁴	—	3	2	no	—
234	#578	—	3	16	no	—
235	C₂×#137	—	3	2	no	—
236	C₂×#137	—	3	4	no	—
237	C₂×#135	—	3	2	no	—
238	C₂×#135	—	3	1	no	—
239	C₂²×Q₁₆	—	3	2	no	—
240	C₂²×Q₁₆	C₅×D₃	1	1	yes	characteristic, complemented
241	C₂×#131	—	3	1	no	—
242	C₂²×C₃×C₅	—	2	2	no	—
243	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
244	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₅×D₃	—	2	4	no	—
246	C₂×C₅×D₃	—	2	4	no	—
247	C₂×C₅×D₃	—	4	4	no	—
248	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
249	C₃×C₄×C₅	—	2	8	no	—
250	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
252	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
253	C₅×Dic₃	—	2	4	no	—
254	C₅×Dic₃	C₂²×D₄	1	4	yes	—
255	C₂×C₃×Q₈	—	2	2	no	—
256	C₂×C₃×Q₈	—	2	4	no	—
257	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
258	C₂×C₃×Q₈	C₂³×C₅	1	8	yes	—
259	C₂²×C₃×C₄	—	2	2	no	—
260	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
261	C₂×#67	—	2	2	no	—
262	C₂×#67	C₅×D₄	1	2	yes	—
263	#239	—	2	16	no	—
264	#239	—	2	8	no	—
265	#239	C₂³×C₅	1	16	yes	—
266	D₃×Q₈	—	2	8	no	—
267	D₃×Q₈	—	2	16	no	—
268	D₃×Q₈	C₂³×C₅	1	16	yes	—
269	#235	—	2	4	no	—
270	#235	—	2	32	no	—
271	#235	C₅×D₄	1	4	yes	—
272	#235	C₂³×C₅	1	4	yes	—
273	#235	C₂³×C₅	1	8	yes	—
274	C₂×D₁₂	—	2	4	no	—
275	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
276	C₂×D₁₂	C₂³×C₅	1	2	yes	—
277	C₂×C₄×D₃	—	2	4	no	—
278	C₂×C₄×D₃	—	2	2	no	—
279	C₂×C₄×D₃	—	2	4	no	—
280	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
281	C₂×Dic₆	—	2	4	no	—
282	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
283	C₂×Dic₆	C₂³×C₅	1	2	yes	—
284	C₃×Q₁₆	C₂³×C₅	1	8	yes	—
285	C₃×Q₁₆	C₂³×C₅	1	8	yes	—
286	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
287	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
288	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
289	#216	C₂³×C₅	1	16	yes	—
290	#215	C₂³×C₅	1	16	yes	—
291	#208	C₂³×C₅	1	4	yes	—
292	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
293	Dic₁₂	C₂³×C₅	1	4	yes	—
294	D₂₄	C₂³×C₅	1	4	yes	—
295	#204	C₂³×C₅	1	8	yes	—
296	ΓL(1,𝔽₂₅)	C₂³×C₅	1	8	yes	—
297	D₃×C₈	C₂³×C₅	1	8	yes	—
298	C₂³×C₅	—	3	2	no	—
299	C₂³×C₅	—	6	2	no	—
300	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
301	C₅×Q₈	—	2	4	no	—
302	C₅×Q₈	—	2	8	no	—
303	C₅×Q₈	—	3	4	no	—
304	C₅×Q₈	—	3	4	no	—
305	C₅×Q₈	—	6	16	no	—
306	C₅×Q₈	—	6	2	no	—
307	C₅×Q₈	C₂³×D₃	1	8	yes	—
308	C₅×D₄	—	3	8	no	—
309	C₅×D₄	—	3	4	no	—
310	C₅×D₄	—	3	4	no	—
311	C₅×D₄	—	6	16	no	—
312	C₅×D₄	—	6	8	no	—
313	C₅×D₄	—	6	2	no	—
314	C₂×C₄×C₅	—	2	8	no	—
315	C₂×C₄×C₅	—	2	4	no	—
316	C₂×C₄×C₅	—	3	2	no	—
317	C₂×C₄×C₅	—	3	4	no	—
318	C₂×C₄×C₅	—	3	4	no	—
319	C₂×C₄×C₅	—	6	16	no	—
320	C₂×C₄×C₅	—	6	16	no	—
321	C₂×C₄×C₅	—	6	2	no	—
322	C₂×C₄×C₅	—	6	8	no	—
323	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
324	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
326	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
327	C₅×C₈	—	3	4	no	—
328	C₅×C₈	C₂³×D₃	1	2	yes	—
329	C₅×C₈	C₂³×D₃	1	2	yes	—
330	2₋¹⁺⁴	—	3	16	no	—
331	2₋¹⁺⁴	—	6	8	no	—
332	C₂×#41	—	3	1	no	—
333	C₂×#41	—	3	4	no	—
334	C₂×#41	—	3	2	no	—
335	C₂×#41	—	6	4	no	—
336	C₂×#41	—	6	2	no	—
337	C₂²×Q₈	—	3	4	no	—
338	C₂²×Q₈	—	6	2	no	—
339	C₂²×Q₈	C₂×C₅×D₃	1	2	yes	—
340	#137	—	3	16	no	—
341	#137	—	3	32	no	—
342	#135	—	3	16	no	—
343	#135	—	3	8	no	—
344	C₂×Q₁₆	—	3	4	no	—
345	C₂×Q₁₆	—	3	16	no	—
346	C₂×Q₁₆	—	3	1	no	—
347	C₂×Q₁₆	C₂×C₅×D₃	1	2	yes	—
348	C₂×Q₁₆	C₂×C₅×D₃	1	2	yes	—
349	C₂×Q₁₆	C₂×C₅×D₃	1	8	yes	complemented
350	C₂×SD₁₆	—	3	4	no	—
351	C₂×SD₁₆	—	3	2	no	—
352	C₂×D₈	—	3	1	no	—
353	#131	—	3	8	no	—
354	C₂×M₁₆	—	3	1	no	—
355	C₂×M₁₆	—	3	2	no	—
356	C₂²×C₈	—	3	2	no	—
357	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
358	C₂×C₃×C₅	—	2	2	no	—
359	C₂×C₃×C₅	#578	1	2	yes	complemented
360	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
361	C₅×D₃	—	2	4	no	—
362	C₅×D₃	—	4	4	no	—
363	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
364	C₂²×D₃	—	2	2	no	—
365	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
366	C₃×Q₈	—	2	4	no	—
367	C₃×Q₈	—	2	8	no	—
368	C₃×Q₈	C₂⁴×C₅	1	8	yes	—
369	C₂×C₃×C₄	—	2	4	no	—
370	C₂×C₃×C₄	—	2	8	no	—
371	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
373	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
375	#67	—	2	8	no	—
376	#67	C₂×C₅×D₄	1	8	yes	—
377	C₂×Dic₃	—	2	2	no	—
378	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
379	D₁₂	—	2	16	no	—
380	D₁₂	—	2	2	no	—
381	D₁₂	C₂×C₅×D₄	1	4	yes	—
382	D₁₂	C₂⁴×C₅	1	4	yes	—
383	C₄×D₃	—	2	16	no	—
384	C₄×D₃	—	2	8	no	—
385	C₄×D₃	—	2	16	no	—
386	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
387	C₄×D₃	C₂⁴×C₅	1	4	yes	—
388	Dic₆	—	2	2	no	—
389	Dic₆	—	2	16	no	—
390	Dic₆	C₂×C₅×D₄	1	4	yes	—
391	Dic₆	C₂⁴×C₅	1	4	yes	—
392	C₃×C₈	C₂⁴×C₅	1	2	yes	—
393	C₃×C₈	C₂⁴×C₅	1	2	yes	—
394	C₃⋊C₈	C₂⁴×C₅	1	4	yes	—
395	C₂²×C₅	—	2	2	no	—
396	C₂²×C₅	—	3	4	no	—
397	C₂²×C₅	—	6	4	no	—
398	C₂²×C₅	—	6	4	no	—
399	C₂²×C₅	—	12	4	no	—
400	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
401	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
402	C₄×C₅	—	2	8	no	—
403	C₄×C₅	—	3	4	no	—
404	C₄×C₅	—	6	4	no	—
405	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
406	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
407	C₄×C₅	C₂⁴×D₃	1	1	yes	characteristic
408	#41	—	3	4	no	—
409	#41	—	3	4	no	—
410	#41	—	3	16	no	—
411	#41	—	3	8	no	—
412	#41	—	6	32	no	—
413	#41	—	6	8	no	—
414	#41	—	6	16	no	—
415	#41	—	6	4	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	3	1	no	—
419	C₂×Q₈	—	3	16	no	—
420	C₂×Q₈	—	3	2	no	—
421	C₂×Q₈	—	6	4	no	—
422	C₂×Q₈	—	6	8	no	—
423	C₂×Q₈	—	6	16	no	—
424	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
425	C₂×Q₈	C₂²×C₅×D₃	1	8	yes	—
426	C₂×D₄	—	3	2	no	—
427	C₂×D₄	—	3	1	no	—
428	C₂×D₄	—	3	2	no	—
429	C₂×D₄	—	6	4	no	—
430	C₂×D₄	—	6	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	3	2	no	—
433	C₂²×C₄	—	6	4	no	—
434	C₂²×C₄	—	6	4	no	—
435	C₂²×C₄	—	6	2	no	—
436	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
437	Q₁₆	—	3	16	no	—
438	Q₁₆	—	3	4	no	—
439	Q₁₆	C₂²×C₅×D₃	1	8	yes	—
440	Q₁₆	C₂²×C₅×D₃	1	8	yes	—
441	SD₁₆	—	3	16	no	—
442	SD₁₆	—	3	8	no	—
443	D₈	—	3	4	no	—
444	M₁₆	—	3	4	no	—
445	M₁₆	—	3	8	no	—
446	C₂×C₈	—	3	2	no	—
447	C₂×C₈	—	3	8	no	—
448	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
449	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
450	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
451	C₃×C₅	C₂×#578	1	1	yes	characteristic, complemented, Hall
452	C₂²×C₃	—	2	2	no	—
453	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
454	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
455	C₂×D₃	—	2	4	no	—
456	C₂×D₃	—	2	4	no	—
457	C₂×D₃	—	4	4	no	—
458	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
459	C₃×C₄	—	2	8	no	—
460	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
461	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
462	C₃×C₄	C₂⁵×C₅	1	1	yes	characteristic
463	Dic₃	—	2	4	no	—
464	Dic₃	C₂²×C₅×D₄	1	4	yes	—
465	C₂×C₅	—	2	2	no	—
466	C₂×C₅	—	6	4	no	—
467	C₂×C₅	—	12	4	no	—
468	C₂×C₅	#5766	1	2	yes	direct product factor
469	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
470	C₂³	—	3	2	no	—
471	C₂³	—	6	2	no	—
472	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
473	Q₈	—	2	4	no	—
474	Q₈	—	2	8	no	—
475	Q₈	—	3	4	no	—
476	Q₈	—	3	4	no	—
477	Q₈	—	6	16	no	—
478	Q₈	—	6	2	no	—
479	Q₈	C₂³×C₅×D₃	1	8	yes	—
480	D₄	—	3	8	no	—
481	D₄	—	3	4	no	—
482	D₄	—	3	4	no	—
483	D₄	—	6	16	no	—
484	D₄	—	6	8	no	—
485	D₄	—	6	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	3	2	no	—
489	C₂×C₄	—	3	4	no	—
490	C₂×C₄	—	3	4	no	—
491	C₂×C₄	—	6	16	no	—
492	C₂×C₄	—	6	16	no	—
493	C₂×C₄	—	6	2	no	—
494	C₂×C₄	—	6	8	no	—
495	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
496	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
497	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
498	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
499	C₈	—	3	4	no	—
500	C₈	C₂³×C₅×D₃	1	2	yes	—
501	C₈	C₂³×C₅×D₃	1	2	yes	—
502	C₂×C₃	—	2	2	no	—
503	C₂×C₃	C₅×#578	1	2	yes	complemented
504	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
505	D₃	—	2	4	no	—
506	D₃	—	4	4	no	—
507	C₅	C₂×#5766	1	1	yes	characteristic, direct product factor, Sylow
508	C₂²	—	2	2	no	—
509	C₂²	—	3	4	no	—
510	C₂²	—	6	4	no	—
511	C₂²	—	6	4	no	—
512	C₂²	—	12	4	no	—
513	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
514	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
515	C₄	—	2	8	no	—
516	C₄	—	3	4	no	—
517	C₄	—	6	4	no	—
518	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
519	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
520	C₄	C₂⁴×C₅×D₃	1	1	yes	characteristic
521	C₃	C₂×C₅×#578	1	1	yes	characteristic, complemented, Sylow
522	C₂	—	2	2	no	—
523	C₂	—	6	4	no	—
524	C₂	—	12	4	no	—
525	C₂	C₅×#5766	1	2	yes	direct product factor
526	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁵×C₅
Frattini	C₄	C₂⁴×C₅×D₃
Fitting	C₂²×C₃×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂²×C₅×Q₁₆	D₃
hypocenter	C₃	C₂×C₅×#578
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#1007	C₂	semidirect
2. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
3. C₂×C₅×#942	C₂	semidirect
4. C₅×#5766	C₂	direct (N × H)
5. C₂×C₅×#919	C₂	semidirect
6. C₂×C₅×#918	C₂	semidirect
7. C₂×C₅×D₃×Q₁₆	C₂	semidirect
8. C₂×C₅×#904	C₂	semidirect
9. C₂×C₅×#901	C₂	semidirect
13. C₅×#1007	C₂²	semidirect
23. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
26. C₅×#942	C₂²	semidirect
29. C₅×#919	C₂²	semidirect
30. C₅×#918	C₂²	semidirect
31. C₅×D₃×Q₁₆	C₂²	semidirect
33. C₅×#904	C₂²	semidirect
36. C₅×#901	C₂²	semidirect
39. C₂×#5766	C₅	direct (N × H)
47. C₂²×C₅×Q₁₆	D₃	semidirect
92. C₂×#1007	C₂×C₅	semidirect
93. C₂²×C₃×Q₁₆	C₂×C₅	semidirect
94. C₂×#942	C₂×C₅	semidirect
95. #5766	C₂×C₅	direct (N × H)
96. C₂×#919	C₂×C₅	semidirect
97. C₂×#918	C₂×C₅	semidirect
98. C₂×D₃×Q₁₆	C₂×C₅	semidirect
99. C₂×#904	C₂×C₅	semidirect
100. C₂×#901	C₂×C₅	semidirect
120. C₂×C₅×Q₁₆	C₂×D₃	semidirect
164. #1007	C₂²×C₅	semidirect
174. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
177. #942	C₂²×C₅	semidirect
180. #919	C₂²×C₅	semidirect
181. #918	C₂²×C₅	semidirect
182. D₃×Q₁₆	C₂²×C₅	semidirect
184. #904	C₂²×C₅	semidirect
187. #901	C₂²×C₅	semidirect
240. C₂²×Q₁₆	C₅×D₃	semidirect
349. C₂×Q₁₆	C₂×C₅×D₃	semidirect
359. C₂×C₃×C₅	#578	semidirect
451. C₃×C₅	C₂×#578	semidirect
468. C₂×C₅	#5766	direct (N × H)
503. C₂×C₃	C₅×#578	semidirect
507. C₅	C₂×#5766	direct (N × H)
521. C₃	C₂×C₅×#578	semidirect
525. C₂	C₅×#5766	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×C₅×#1007	2
C₂²×C₃×C₅×Q₁₆	2
C₂×C₅×#942	2
C₅×#5766	2
C₂×C₅×#919	2
C₂×C₅×#918	2
C₂×C₅×D₃×Q₁₆	2
C₂×C₅×#904	2
C₂×C₅×#901	2
C₂×C₅×#578	3
C₂×#5766	5

Subgroups — C2×C5×#5766 #14510121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5766 #14510121