Subgroups — C₂×C₅×#5170 #14423289

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#938	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₅×#214	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5170	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#816	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#448	—	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	C₂²×C₅×#67	—	2	1	no	—
13	C₂×C₅×D₃×Q₈	—	2	4	no	—
14	C₂×C₅×D₃×Q₈	—	2	2	no	—
15	C₂×C₅×D₃×Q₈	—	2	4	no	—
16	C₂×C₅×D₃×Q₈	C₂²	1	4	yes	complemented
17	C₂²×C₄×C₅×D₃	—	2	1	no	—
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₅×Dic₆	—	2	1	no	—
20	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
22	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	complemented
23	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×#217	—	2	1	no	—
25	C₅×#938	—	2	2	no	—
26	C₅×#938	C₂²	1	4	yes	—
27	C₂×C₅×#214	—	2	4	no	—
28	C₂×C₅×#214	C₂²	1	4	yes	complemented
29	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
30	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₅×#835	C₂²	1	4	yes	complemented
32	C₅×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
33	C₅×#816	C₂²	1	4	yes	complemented
34	C₂×#5170	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂³×C₅×Q₈	—	3	1	no	—
36	C₂²×C₅×SD₁₆	—	3	1	no	—
37	C₂²×C₅×SD₁₆	D₃	1	1	yes	characteristic, complemented
38	C₂×C₅×#121	—	3	1	no	—
39	C₅×#448	—	3	8	no	—
40	C₂×C₅×#103	—	3	1	no	—
41	C₂×C₅×#103	—	3	1	no	—
42	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
43	C₂⁴×C₃×C₅	—	2	1	no	—
44	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
45	C₂×C₃×C₅×Q₈	—	2	2	no	—
46	C₂×C₃×C₅×Q₈	—	2	1	no	—
47	C₂×C₃×C₅×Q₈	D₄	1	4	yes	complemented
48	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
49	C₂×C₃×C₅×D₄	—	2	2	no	—
50	C₂×C₃×C₅×D₄	—	2	2	no	—
51	C₂×C₃×C₅×D₄	—	2	1	no	—
52	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	—	2	1	no	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₅×#67	—	2	4	no	—
56	C₂×C₅×#67	—	4	4	no	—
57	C₂²×C₅×Dic₃	—	2	1	no	—
58	C₂²×C₅×Dic₃	—	2	1	no	—
59	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
60	C₅×D₃×Q₈	—	2	16	no	—
61	C₅×D₃×Q₈	—	2	8	no	—
62	C₅×D₃×Q₈	—	2	8	no	—
63	C₂×C₄×C₅×D₃	—	2	8	no	—
64	C₂×C₄×C₅×D₃	—	2	4	no	—
65	C₂×C₄×C₅×D₃	—	2	2	no	—
66	C₂×C₄×C₅×D₃	—	2	2	no	—
67	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
68	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
69	C₂×C₅×Dic₆	—	2	8	no	—
70	C₂×C₅×Dic₆	—	2	1	no	—
71	C₂×C₅×Dic₆	—	2	2	no	—
72	C₂×C₅×Dic₆	—	2	4	no	—
73	C₂×C₅×Dic₆	D₄	1	4	yes	complemented
74	C₂×C₅×Dic₆	C₂³	1	2	yes	—
75	C₃×C₅×SD₁₆	—	2	8	no	—
76	C₂×C₃×C₅×C₈	—	2	2	no	—
77	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
78	C₅×#217	—	2	4	no	—
79	C₅×#214	—	2	8	no	—
80	C₅×C₄⋊Dic₃	—	2	1	no	—
81	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
82	C₂×C₅×C₃⋊C₈	—	2	2	no	—
83	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
84	C₂²×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂×#938	C₂×C₅	1	1	yes	characteristic
87	C₂²×#214	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×#835	C₂×C₅	1	1	yes	characteristic, complemented
89	#5170	C₂×C₅	1	8	yes	direct product factor
90	C₂×(C₂×D₃)⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×#816	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂²×C₅×Q₈	—	3	4	no	—
93	C₂²×C₅×Q₈	—	3	1	no	—
94	C₂²×C₅×Q₈	—	6	1	no	—
95	C₂²×C₅×Q₈	—	6	2	no	—
96	C₂²×C₅×Q₈	—	6	4	no	—
97	C₂²×C₅×Q₈	—	6	4	no	—
98	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
99	C₂²×C₅×D₄	—	6	1	no	—
100	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
101	C₂³×C₄×C₅	—	3	1	no	—
102	C₂³×C₄×C₅	—	6	1	no	—
103	C₂×C₅×SD₁₆	—	2	4	no	—
104	C₂×C₅×SD₁₆	—	3	4	no	—
105	C₂×C₅×SD₁₆	—	6	4	no	—
106	C₂×C₅×SD₁₆	C₂×D₃	1	4	yes	complemented
107	C₂²×C₅×C₈	—	3	1	no	—
108	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
109	C₅×#121	—	3	4	no	—
110	C₅×#121	—	6	2	no	—
111	C₂×C₅×C₄⋊C₄	—	3	1	no	—
112	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
113	C₅×#103	—	3	4	no	—
114	C₅×#103	—	3	4	no	—
115	C₅×C₂²⋊C₈	—	3	4	no	—
116	C₂×#448	—	3	1	no	Sylow
117	C₂³×C₃×C₅	—	2	2	no	—
118	C₂³×C₃×C₅	—	4	2	no	—
119	C₂³×C₃×C₅	—	4	2	no	—
120	C₂³×C₃×C₅	—	4	2	no	—
121	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₅×D₃	—	2	2	no	—
123	C₂²×C₅×D₃	—	2	2	no	—
124	C₂²×C₅×D₃	SD₁₆	1	4	yes	complemented
125	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
126	C₃×C₅×Q₈	—	2	4	no	—
127	C₃×C₅×Q₈	—	2	2	no	—
128	C₃×C₅×Q₈	C₂×D₄	1	4	yes	complemented
129	C₃×C₅×D₄	—	2	2	no	—
130	C₃×C₅×D₄	—	2	2	no	—
131	C₃×C₅×D₄	—	4	2	no	—
132	C₂×C₃×C₄×C₅	—	2	4	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₅×#67	—	4	8	no	—
139	C₂×C₅×Dic₃	—	2	2	no	—
140	C₂×C₅×Dic₃	—	2	4	no	—
141	C₂×C₅×Dic₃	—	2	2	no	—
142	C₂×C₅×Dic₃	—	2	2	no	—
143	C₂×C₅×Dic₃	—	4	2	no	—
144	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
145	C₄×C₅×D₃	—	2	16	no	—
146	C₄×C₅×D₃	—	2	4	no	—
147	C₄×C₅×D₃	—	2	2	no	—
148	C₄×C₅×D₃	—	2	2	no	—
149	C₅×Dic₆	—	2	16	no	—
150	C₅×Dic₆	—	2	4	no	—
151	C₅×Dic₆	—	2	2	no	—
152	C₅×Dic₆	C₂×D₄	1	4	yes	complemented
153	C₃×C₅×C₈	—	2	2	no	—
154	C₅×C₃⋊C₈	—	2	2	no	—
155	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
156	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
157	C₂²×#67	—	2	1	no	—
158	C₂×D₃×Q₈	—	2	4	no	—
159	C₂×D₃×Q₈	—	2	2	no	—
160	C₂×D₃×Q₈	—	2	4	no	—
161	C₂×D₃×Q₈	C₂²×C₅	1	4	yes	complemented
162	C₂²×C₄×D₃	—	2	1	no	—
163	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
164	C₂²×Dic₆	—	2	1	no	—
165	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₃×SD₁₆	—	2	4	no	—
167	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	complemented
168	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
169	C₂×#217	—	2	1	no	—
170	#938	—	2	2	no	—
171	#938	C₂²×C₅	1	4	yes	—
172	C₂×#214	—	2	4	no	—
173	C₂×#214	C₂²×C₅	1	4	yes	complemented
174	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
175	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
176	#835	C₂²×C₅	1	4	yes	complemented
177	(C₂×D₃)⋊C₈	C₂²×C₅	1	4	yes	complemented
178	#816	C₂²×C₅	1	4	yes	complemented
179	C₂⁴×C₅	—	2	1	no	—
180	C₂⁴×C₅	—	3	1	no	—
181	C₂×C₅×Q₈	—	2	2	no	—
182	C₂×C₅×Q₈	—	2	1	no	—
183	C₂×C₅×Q₈	—	3	4	no	—
184	C₂×C₅×Q₈	—	3	2	no	—
185	C₂×C₅×Q₈	—	6	4	no	—
186	C₂×C₅×Q₈	—	6	8	no	—
187	C₂×C₅×Q₈	—	6	8	no	—
188	C₂×C₅×Q₈	—	6	16	no	—
189	C₂×C₅×Q₈	—	6	8	no	—
190	C₂×C₅×Q₈	—	6	1	no	—
191	C₂×C₅×Q₈	—	6	2	no	—
192	C₂×C₅×Q₈	#67	1	4	yes	complemented
193	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
194	C₂×C₅×D₄	—	2	2	no	—
195	C₂×C₅×D₄	—	2	1	no	—
196	C₂×C₅×D₄	—	2	2	no	—
197	C₂×C₅×D₄	—	6	4	no	—
198	C₂×C₅×D₄	—	12	4	no	—
199	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
200	C₂²×C₄×C₅	—	2	1	no	—
201	C₂²×C₄×C₅	—	3	1	no	—
202	C₂²×C₄×C₅	—	3	2	no	—
203	C₂²×C₄×C₅	—	3	2	no	—
204	C₂²×C₄×C₅	—	6	4	no	—
205	C₂²×C₄×C₅	—	6	8	no	—
206	C₂²×C₄×C₅	—	6	1	no	—
207	C₂²×C₄×C₅	—	6	2	no	—
208	C₂²×C₄×C₅	—	6	2	no	—
209	C₂²×C₄×C₅	—	6	1	no	—
210	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
211	C₅×SD₁₆	—	2	8	no	—
212	C₅×SD₁₆	—	6	8	no	—
213	C₂×C₅×C₈	—	2	2	no	—
214	C₂×C₅×C₈	—	3	2	no	—
215	C₂×C₅×C₈	—	6	2	no	—
216	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
217	C₅×C₄⋊C₄	—	3	2	no	—
218	C₅×C₄⋊C₄	—	6	1	no	—
219	C₅×C₂²⋊C₄	—	6	4	no	—
220	C₂³×Q₈	—	3	1	no	—
221	C₂²×SD₁₆	—	3	1	no	—
222	C₂²×SD₁₆	C₅×D₃	1	1	yes	characteristic, complemented
223	C₂×#121	—	3	1	no	—
224	#448	—	3	8	no	—
225	C₂×#103	—	3	1	no	—
226	C₂×#103	—	3	1	no	—
227	C₂×C₂²⋊C₈	—	3	1	no	—
228	C₂²×C₃×C₅	—	4	2	no	—
229	C₂²×C₃×C₅	—	4	2	no	—
230	C₂²×C₃×C₅	—	4	2	no	—
231	C₂²×C₃×C₅	—	8	4	no	—
232	C₂²×C₃×C₅	#120	1	2	yes	—
233	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
234	C₂²×C₃×C₅	#137	1	2	yes	—
235	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₅×D₃	—	2	2	no	—
237	C₂×C₅×D₃	—	2	2	no	—
238	C₂×C₅×D₃	—	2	8	no	—
239	C₂×C₅×D₃	C₂×SD₁₆	1	4	yes	complemented
240	C₃×C₄×C₅	—	2	4	no	—
241	C₃×C₄×C₅	#120	1	2	yes	—
242	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
243	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
244	C₅×Dic₃	—	2	2	no	—
245	C₅×Dic₃	—	2	4	no	—
246	C₅×Dic₃	—	4	2	no	—
247	C₂⁴×C₃	—	2	1	no	—
248	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
249	C₂×C₃×Q₈	—	2	2	no	—
250	C₂×C₃×Q₈	—	2	1	no	—
251	C₂×C₃×Q₈	C₅×D₄	1	4	yes	complemented
252	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
253	C₂×C₃×D₄	—	2	2	no	—
254	C₂×C₃×D₄	—	2	2	no	—
255	C₂×C₃×D₄	—	2	1	no	—
256	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
257	C₂²×C₃×C₄	—	2	1	no	—
258	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
259	C₂×#67	—	2	4	no	—
260	C₂×#67	—	4	4	no	—
261	C₂²×Dic₃	—	2	1	no	—
262	C₂²×Dic₃	—	2	1	no	—
263	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
264	D₃×Q₈	—	2	16	no	—
265	D₃×Q₈	—	2	8	no	—
266	D₃×Q₈	—	2	8	no	—
267	C₂×C₄×D₃	—	2	8	no	—
268	C₂×C₄×D₃	—	2	4	no	—
269	C₂×C₄×D₃	—	2	2	no	—
270	C₂×C₄×D₃	—	2	2	no	—
271	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
272	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
273	C₂×Dic₆	—	2	8	no	—
274	C₂×Dic₆	—	2	1	no	—
275	C₂×Dic₆	—	2	2	no	—
276	C₂×Dic₆	—	2	4	no	—
277	C₂×Dic₆	C₅×D₄	1	4	yes	complemented
278	C₂×Dic₆	C₂³×C₅	1	2	yes	—
279	C₃×SD₁₆	—	2	8	no	—
280	C₂×C₃×C₈	—	2	2	no	—
281	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
282	#217	—	2	4	no	—
283	#214	—	2	8	no	—
284	C₄⋊Dic₃	—	2	1	no	—
285	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
286	C₂×C₃⋊C₈	—	2	2	no	—
287	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
288	C₂³×C₅	—	2	2	no	—
289	C₂³×C₅	—	3	4	no	—
290	C₂³×C₅	—	3	2	no	—
291	C₂³×C₅	—	4	2	no	—
292	C₂³×C₅	—	4	2	no	—
293	C₂³×C₅	—	4	2	no	—
294	C₂³×C₅	—	6	2	no	—
295	C₂³×C₅	—	6	2	no	—
296	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
297	C₅×Q₈	—	2	4	no	—
298	C₅×Q₈	—	2	2	no	—
299	C₅×Q₈	—	3	4	no	—
300	C₅×Q₈	—	6	16	no	—
301	C₅×Q₈	—	6	4	no	—
302	C₅×Q₈	—	6	2	no	—
303	C₅×Q₈	C₂×#67	1	4	yes	complemented
304	C₅×D₄	—	2	2	no	—
305	C₅×D₄	—	2	2	no	—
306	C₅×D₄	—	4	2	no	—
307	C₅×D₄	—	12	8	no	—
308	C₂×C₄×C₅	—	2	4	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	3	2	no	—
311	C₂×C₄×C₅	—	6	16	no	—
312	C₂×C₄×C₅	—	6	2	no	—
313	C₂×C₄×C₅	—	6	4	no	—
314	C₂×C₄×C₅	—	6	2	no	—
315	C₂×C₄×C₅	—	6	4	no	—
316	C₂×C₄×C₅	—	6	2	no	—
317	C₂×C₄×C₅	—	6	2	no	—
318	C₂×C₄×C₅	—	6	2	no	—
319	C₂×C₄×C₅	—	12	2	no	—
320	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
321	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
322	C₂×C₄×C₅	C₂×#67	1	2	yes	—
323	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
324	C₅×C₈	—	2	2	no	—
325	C₅×C₈	—	6	2	no	—
326	C₂²×Q₈	—	3	4	no	—
327	C₂²×Q₈	—	3	1	no	—
328	C₂²×Q₈	—	6	1	no	—
329	C₂²×Q₈	—	6	2	no	—
330	C₂²×Q₈	—	6	4	no	—
331	C₂²×Q₈	—	6	4	no	—
332	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
333	C₂²×D₄	—	6	1	no	—
334	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
335	C₂³×C₄	—	3	1	no	—
336	C₂³×C₄	—	6	1	no	—
337	C₂×SD₁₆	—	2	4	no	—
338	C₂×SD₁₆	—	3	4	no	—
339	C₂×SD₁₆	—	6	4	no	—
340	C₂×SD₁₆	C₂×C₅×D₃	1	4	yes	complemented
341	C₂²×C₈	—	3	1	no	—
342	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
343	#121	—	3	4	no	—
344	#121	—	6	2	no	—
345	C₂×C₄⋊C₄	—	3	1	no	—
346	C₂×C₂²⋊C₄	—	6	1	no	—
347	#103	—	3	4	no	—
348	#103	—	3	4	no	—
349	C₂²⋊C₈	—	3	4	no	—
350	C₂×C₃×C₅	—	8	2	no	—
351	C₂×C₃×C₅	#448	1	4	yes	complemented
352	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
353	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
354	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
355	C₅×D₃	—	2	4	no	—
356	C₂³×C₃	—	2	2	no	—
357	C₂³×C₃	—	4	2	no	—
358	C₂³×C₃	—	4	2	no	—
359	C₂³×C₃	—	4	2	no	—
360	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
361	C₂²×D₃	—	2	2	no	—
362	C₂²×D₃	—	2	2	no	—
363	C₂²×D₃	C₅×SD₁₆	1	4	yes	complemented
364	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
365	C₃×Q₈	—	2	4	no	—
366	C₃×Q₈	—	2	2	no	—
367	C₃×Q₈	C₂×C₅×D₄	1	4	yes	complemented
368	C₃×D₄	—	2	2	no	—
369	C₃×D₄	—	2	2	no	—
370	C₃×D₄	—	4	2	no	—
371	C₂×C₃×C₄	—	2	4	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
375	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
376	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
377	#67	—	4	8	no	—
378	C₂×Dic₃	—	2	2	no	—
379	C₂×Dic₃	—	2	4	no	—
380	C₂×Dic₃	—	2	2	no	—
381	C₂×Dic₃	—	2	2	no	—
382	C₂×Dic₃	—	4	2	no	—
383	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
384	C₄×D₃	—	2	16	no	—
385	C₄×D₃	—	2	4	no	—
386	C₄×D₃	—	2	2	no	—
387	C₄×D₃	—	2	2	no	—
388	Dic₆	—	2	16	no	—
389	Dic₆	—	2	4	no	—
390	Dic₆	—	2	2	no	—
391	Dic₆	C₂×C₅×D₄	1	4	yes	complemented
392	C₃×C₈	—	2	2	no	—
393	C₃⋊C₈	—	2	2	no	—
394	C₂²×C₅	—	3	4	no	—
395	C₂²×C₅	—	4	2	no	—
396	C₂²×C₅	—	4	2	no	—
397	C₂²×C₅	—	4	2	no	—
398	C₂²×C₅	—	6	8	no	—
399	C₂²×C₅	—	6	2	no	—
400	C₂²×C₅	—	6	2	no	—
401	C₂²×C₅	—	8	4	no	—
402	C₂²×C₅	D₃×SD₁₆	1	2	yes	—
403	C₂²×C₅	#915	1	2	yes	—
404	C₂²×C₅	#937	1	2	yes	—
405	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
406	C₄×C₅	—	2	4	no	—
407	C₄×C₅	—	6	2	no	—
408	C₄×C₅	—	6	4	no	—
409	C₄×C₅	—	12	2	no	—
410	C₄×C₅	#937	1	2	yes	—
411	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
412	C₄×C₅	C₂²×#67	1	1	yes	characteristic
413	C₂⁴	—	2	1	no	—
414	C₂⁴	—	3	1	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	3	4	no	—
418	C₂×Q₈	—	3	2	no	—
419	C₂×Q₈	—	6	4	no	—
420	C₂×Q₈	—	6	8	no	—
421	C₂×Q₈	—	6	8	no	—
422	C₂×Q₈	—	6	16	no	—
423	C₂×Q₈	—	6	8	no	—
424	C₂×Q₈	—	6	1	no	—
425	C₂×Q₈	—	6	2	no	—
426	C₂×Q₈	C₅×#67	1	4	yes	complemented
427	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	6	4	no	—
432	C₂×D₄	—	12	4	no	—
433	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	2	no	—
437	C₂²×C₄	—	3	2	no	—
438	C₂²×C₄	—	6	4	no	—
439	C₂²×C₄	—	6	8	no	—
440	C₂²×C₄	—	6	1	no	—
441	C₂²×C₄	—	6	2	no	—
442	C₂²×C₄	—	6	2	no	—
443	C₂²×C₄	—	6	1	no	—
444	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
445	SD₁₆	—	2	8	no	—
446	SD₁₆	—	6	8	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	3	2	no	—
449	C₂×C₈	—	6	2	no	—
450	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
451	C₄⋊C₄	—	3	2	no	—
452	C₄⋊C₄	—	6	1	no	—
453	C₂²⋊C₄	—	6	4	no	—
454	C₃×C₅	C₂×#448	1	1	yes	characteristic, complemented, Hall
455	C₂²×C₃	—	4	2	no	—
456	C₂²×C₃	—	4	2	no	—
457	C₂²×C₃	—	4	2	no	—
458	C₂²×C₃	—	8	4	no	—
459	C₂²×C₃	C₅×#120	1	2	yes	—
460	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
461	C₂²×C₃	C₅×#137	1	2	yes	—
462	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
463	C₂×D₃	—	2	8	no	—
464	C₂×D₃	—	2	2	no	—
465	C₂×D₃	—	2	2	no	—
466	C₂×D₃	C₂×C₅×SD₁₆	1	4	yes	complemented
467	C₃×C₄	—	2	4	no	—
468	C₃×C₄	C₅×#120	1	2	yes	—
469	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
470	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
471	Dic₃	—	2	2	no	—
472	Dic₃	—	2	4	no	—
473	Dic₃	—	4	2	no	—
474	C₂×C₅	—	6	4	no	—
475	C₂×C₅	—	8	2	no	—
476	C₂×C₅	#5170	1	4	yes	direct product factor
477	C₂×C₅	C₂×D₃×SD₁₆	1	1	yes	characteristic
478	C₂×C₅	C₂×#915	1	1	yes	characteristic
479	C₂×C₅	C₂×#937	1	1	yes	characteristic
480	C₂³	—	2	2	no	—
481	C₂³	—	3	4	no	—
482	C₂³	—	3	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	6	2	no	—
487	C₂³	—	6	2	no	—
488	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
489	Q₈	—	2	4	no	—
490	Q₈	—	2	2	no	—
491	Q₈	—	3	4	no	—
492	Q₈	—	6	16	no	—
493	Q₈	—	6	4	no	—
494	Q₈	—	6	2	no	—
495	Q₈	C₂×C₅×#67	1	4	yes	complemented
496	D₄	—	2	2	no	—
497	D₄	—	2	2	no	—
498	D₄	—	4	2	no	—
499	D₄	—	12	8	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	3	2	no	—
503	C₂×C₄	—	6	16	no	—
504	C₂×C₄	—	6	2	no	—
505	C₂×C₄	—	6	4	no	—
506	C₂×C₄	—	6	2	no	—
507	C₂×C₄	—	6	4	no	—
508	C₂×C₄	—	6	2	no	—
509	C₂×C₄	—	6	2	no	—
510	C₂×C₄	—	6	2	no	—
511	C₂×C₄	—	12	2	no	—
512	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
513	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
514	C₂×C₄	C₂×C₅×#67	1	2	yes	—
515	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
516	C₈	—	2	2	no	—
517	C₈	—	6	2	no	—
518	C₂×C₃	—	8	2	no	—
519	C₂×C₃	C₅×#448	1	4	yes	complemented
520	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
521	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
522	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
523	D₃	—	2	4	no	—
524	C₅	C₂×#5170	1	1	yes	characteristic, direct product factor, Sylow
525	C₂²	—	3	4	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	6	8	no	—
530	C₂²	—	6	2	no	—
531	C₂²	—	6	2	no	—
532	C₂²	—	8	4	no	—
533	C₂²	C₅×D₃×SD₁₆	1	2	yes	—
534	C₂²	C₅×#915	1	2	yes	—
535	C₂²	C₅×#937	1	2	yes	—
536	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
537	C₄	—	2	4	no	—
538	C₄	—	6	2	no	—
539	C₄	—	6	4	no	—
540	C₄	—	12	2	no	—
541	C₄	C₅×#937	1	2	yes	—
542	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
543	C₄	C₂²×C₅×#67	1	1	yes	characteristic
544	C₃	C₂×C₅×#448	1	1	yes	characteristic, complemented, Sylow
545	C₂	—	6	4	no	—
546	C₂	—	8	2	no	—
547	C₂	C₅×#5170	1	4	yes	direct product factor
548	C₂	C₂×C₅×D₃×SD₁₆	1	1	yes	characteristic
549	C₂	C₂×C₅×#915	1	1	yes	characteristic
550	C₂	C₂×C₅×#937	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	C₂×C₅×#938	C₂
hypercenter	C₂²×C₅×SD₁₆	D₃
hypocenter	C₃	C₂×C₅×#448
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
1. C₂²×C₅×D₃×Q₈	C₂	semidirect
2. C₂²×C₃×C₅×SD₁₆	C₂	semidirect
4. C₂²×C₅×#214	C₂	semidirect
5. C₂×C₅×#835	C₂	semidirect
6. C₅×#5170	C₂	direct (N × H)
7. C₂×C₅×(C₂×D₃)⋊C₈	C₂	semidirect
8. C₂×C₅×#816	C₂	semidirect
16. C₂×C₅×D₃×Q₈	C₂²	semidirect
22. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
28. C₂×C₅×#214	C₂²	semidirect
31. C₅×#835	C₂²	semidirect
32. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
33. C₅×#816	C₂²	semidirect
34. C₂×#5170	C₅	direct (N × H)
37. C₂²×C₅×SD₁₆	D₃	semidirect
47. C₂×C₃×C₅×Q₈	D₄	semidirect
73. C₂×C₅×Dic₆	D₄	semidirect
84. C₂²×D₃×Q₈	C₂×C₅	semidirect
85. C₂²×C₃×SD₁₆	C₂×C₅	semidirect
87. C₂²×#214	C₂×C₅	semidirect
88. C₂×#835	C₂×C₅	semidirect
89. #5170	C₂×C₅	direct (N × H)
90. C₂×(C₂×D₃)⋊C₈	C₂×C₅	semidirect
91. C₂×#816	C₂×C₅	semidirect
106. C₂×C₅×SD₁₆	C₂×D₃	semidirect
124. C₂²×C₅×D₃	SD₁₆	semidirect
128. C₃×C₅×Q₈	C₂×D₄	semidirect
152. C₅×Dic₆	C₂×D₄	semidirect
161. C₂×D₃×Q₈	C₂²×C₅	semidirect
167. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
173. C₂×#214	C₂²×C₅	semidirect
176. #835	C₂²×C₅	semidirect
177. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
178. #816	C₂²×C₅	semidirect
192. C₂×C₅×Q₈	#67	semidirect
222. C₂²×SD₁₆	C₅×D₃	semidirect
239. C₂×C₅×D₃	C₂×SD₁₆	semidirect
251. C₂×C₃×Q₈	C₅×D₄	semidirect
277. C₂×Dic₆	C₅×D₄	semidirect
303. C₅×Q₈	C₂×#67	semidirect
340. C₂×SD₁₆	C₂×C₅×D₃	semidirect
351. C₂×C₃×C₅	#448	semidirect
363. C₂²×D₃	C₅×SD₁₆	semidirect
367. C₃×Q₈	C₂×C₅×D₄	semidirect
391. Dic₆	C₂×C₅×D₄	semidirect
426. C₂×Q₈	C₅×#67	semidirect
454. C₃×C₅	C₂×#448	semidirect
466. C₂×D₃	C₂×C₅×SD₁₆	semidirect
476. C₂×C₅	#5170	direct (N × H)
495. Q₈	C₂×C₅×#67	semidirect
519. C₂×C₃	C₅×#448	semidirect
524. C₅	C₂×#5170	direct (N × H)
544. C₃	C₂×C₅×#448	semidirect
547. C₂	C₅×#5170	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×D₃×Q₈	2
C₂²×C₃×C₅×SD₁₆	2
C₂×C₅×#938	2
C₂²×C₅×#214	2
C₂×C₅×#835	2
C₅×#5170	2
C₂×C₅×(C₂×D₃)⋊C₈	2
C₂×C₅×#816	2
C₂×C₅×#448	3
C₂×#5170	5

Subgroups — C2×C5×#5170 #14423289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5170 #14423289