Subgroups — C₂×C₅×#5724 #14480476

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#239	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#947	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5724	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#896	C₂	1	4	yes	maximal, complemented
8	C₂×C₅×#894	C₂	1	4	yes	maximal, complemented
9	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#536	—	3	1	no	maximal, Hall
12	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#239	—	2	8	no	—
15	C₂×C₅×#239	C₂²	1	8	yes	—
16	C₂×C₅×D₃×Q₈	—	2	8	no	—
17	C₂×C₅×D₃×Q₈	C₂²	1	8	yes	complemented
18	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
20	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
21	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
22	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
23	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
24	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
25	C₃×C₅×C₄⋊Q₈	C₂²	1	8	yes	complemented
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₅×#947	C₂²	1	8	yes	complemented
29	C₅×#944	C₂²	1	8	yes	complemented
30	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
31	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
32	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
33	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
35	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
36	C₅×#896	C₂²	1	32	yes	complemented
37	C₅×#894	C₂²	1	32	yes	complemented
38	C₅×#875	C₂²	1	8	yes	complemented
39	C₅×#872	C₂²	1	8	yes	complemented
40	C₂×#5724	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂²×C₅×#41	—	3	1	no	—
42	C₂³×C₅×Q₈	—	3	1	no	—
43	C₅×#536	—	3	16	no	—
44	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
45	C₂×C₅×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
46	C₂×C₅×#124	—	3	1	no	—
47	C₂×C₅×#124	—	3	1	no	—
48	C₂×C₅×#123	—	3	4	no	—
49	C₂×C₅×C₂²⋊Q₈	—	3	4	no	—
50	C₂×C₅×#117	—	3	1	no	—
51	C₂³×C₅×D₃	C₂³	1	2	yes	—
52	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₅×Q₈	—	2	4	no	—
54	C₂×C₃×C₅×Q₈	—	2	4	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
56	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
62	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
63	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
64	C₅×#239	—	2	32	no	—
65	C₅×D₃×Q₈	—	2	32	no	—
66	C₂×C₅×D₁₂	—	2	8	no	—
67	C₂×C₅×D₁₂	—	2	4	no	—
68	C₂×C₅×D₁₂	C₂³	1	4	yes	—
69	C₂×C₅×D₁₂	C₂³	1	8	yes	—
70	C₂×C₄×C₅×D₃	—	2	8	no	—
71	C₂×C₄×C₅×D₃	—	2	8	no	—
72	C₂×C₄×C₅×D₃	D₄	1	8	yes	—
73	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
74	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
75	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
76	C₂×C₅×Dic₆	—	2	4	no	—
77	C₂×C₅×Dic₆	—	2	8	no	—
78	C₂×C₅×Dic₆	C₂³	1	4	yes	—
79	C₂×C₅×Dic₆	C₂³	1	8	yes	—
80	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	—
81	C₃×C₄²×C₅	C₂³	1	4	yes	—
82	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
83	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
84	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
85	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
86	C₅×Dic₃⋊C₄	C₂³	1	16	yes	—
87	C₄×C₅×Dic₃	C₂³	1	4	yes	—
88	C₂²×#239	C₂×C₅	1	1	yes	characteristic
89	C₂²×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×#947	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
93	#5724	C₂×C₅	1	16	yes	direct product factor
94	C₂×#896	C₂×C₅	1	4	yes	complemented
95	C₂×#894	C₂×C₅	1	4	yes	complemented
96	C₂×#875	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂×#872	C₂×C₅	1	1	yes	characteristic, complemented
98	C₂×C₅×#41	—	3	8	no	—
99	C₂×C₅×#41	—	6	8	no	—
100	C₂²×C₅×Q₈	—	3	8	no	—
101	C₂²×C₅×Q₈	—	3	2	no	—
102	C₂²×C₅×Q₈	—	3	1	no	—
103	C₂²×C₅×Q₈	—	6	8	no	—
104	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
105	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
106	C₂²×C₅×D₄	—	3	2	no	—
107	C₂²×C₅×D₄	—	3	1	no	—
108	C₂³×C₄×C₅	—	3	1	no	—
109	C₂³×C₄×C₅	—	3	2	no	—
110	C₂³×C₄×C₅	—	3	2	no	—
111	C₅×C₄⋊Q₈	—	3	8	no	—
112	C₅×C₄⋊Q₈	C₂×D₃	1	8	yes	complemented
113	C₅×#124	—	3	8	no	—
114	C₅×#124	—	3	8	no	—
115	C₅×#123	—	3	32	no	—
116	C₅×C₂²⋊Q₈	—	3	32	no	—
117	C₅×#117	—	3	8	no	—
118	C₂×C₅×C₄⋊C₄	—	3	2	no	—
119	C₂×C₅×C₄⋊C₄	—	3	4	no	—
120	C₂×C₅×C₄⋊C₄	C₂×D₃	1	4	yes	—
121	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
122	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
123	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
124	C₂×C₄²×C₅	—	3	1	no	—
125	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
126	C₂×#536	—	3	1	no	Sylow
127	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
128	C₂²×C₅×D₃	—	2	4	no	—
129	C₂²×C₅×D₃	—	2	4	no	—
130	C₂²×C₅×D₃	—	2	8	no	—
131	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
132	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
133	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
134	C₃×C₅×Q₈	—	2	8	no	—
135	C₃×C₅×Q₈	—	2	8	no	—
136	C₂×C₃×C₄×C₅	—	2	4	no	—
137	C₂×C₃×C₄×C₅	—	2	4	no	—
138	C₂×C₃×C₄×C₅	—	2	4	no	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
140	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
141	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
142	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
143	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
144	C₂×C₅×Dic₃	—	2	4	no	—
145	C₂×C₅×Dic₃	—	2	4	no	—
146	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
147	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
148	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
149	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
150	C₅×D₁₂	—	2	16	no	—
151	C₅×D₁₂	—	2	8	no	—
152	C₄×C₅×D₃	—	2	16	no	—
153	C₄×C₅×D₃	—	2	16	no	—
154	C₄×C₅×D₃	C₂×D₄	1	16	yes	—
155	C₅×Dic₆	—	2	8	no	—
156	C₅×Dic₆	—	2	16	no	—
157	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
158	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
159	C₂×#239	—	2	8	no	—
160	C₂×#239	C₂²×C₅	1	8	yes	—
161	C₂×D₃×Q₈	—	2	8	no	—
162	C₂×D₃×Q₈	C₂²×C₅	1	8	yes	complemented
163	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
164	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
165	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
166	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
167	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
168	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
169	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
170	C₃×C₄⋊Q₈	C₂²×C₅	1	8	yes	complemented
171	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
172	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
173	#947	C₂²×C₅	1	8	yes	complemented
174	#944	C₂²×C₅	1	8	yes	complemented
175	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
176	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
177	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
178	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
179	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
180	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
181	#896	C₂²×C₅	1	32	yes	complemented
182	#894	C₂²×C₅	1	32	yes	complemented
183	#875	C₂²×C₅	1	8	yes	complemented
184	#872	C₂²×C₅	1	8	yes	complemented
185	C₂⁴×C₅	—	3	1	no	—
186	C₂⁴×C₅	—	3	2	no	—
187	C₅×#41	—	6	32	no	—
188	C₂×C₅×Q₈	—	2	4	no	—
189	C₂×C₅×Q₈	—	2	4	no	—
190	C₂×C₅×Q₈	—	3	8	no	—
191	C₂×C₅×Q₈	—	3	4	no	—
192	C₂×C₅×Q₈	—	6	8	no	—
193	C₂×C₅×Q₈	—	6	32	no	—
194	C₂×C₅×Q₈	—	6	4	no	—
195	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
196	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
197	C₂×C₅×D₄	—	3	8	no	—
198	C₂×C₅×D₄	—	3	4	no	—
199	C₂×C₅×D₄	—	6	8	no	—
200	C₂×C₅×D₄	—	6	4	no	—
201	C₂²×C₄×C₅	—	3	1	no	—
202	C₂²×C₄×C₅	—	3	8	no	—
203	C₂²×C₄×C₅	—	3	4	no	—
204	C₂²×C₄×C₅	—	3	2	no	—
205	C₂²×C₄×C₅	—	3	2	no	—
206	C₂²×C₄×C₅	—	3	8	no	—
207	C₂²×C₄×C₅	—	3	8	no	—
208	C₂²×C₄×C₅	—	6	8	no	—
209	C₂²×C₄×C₅	—	6	8	no	—
210	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
211	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
212	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
213	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
214	C₅×C₄⋊C₄	—	3	8	no	—
215	C₅×C₄⋊C₄	—	3	16	no	—
216	C₅×C₄⋊C₄	C₂²×D₃	1	16	yes	—
217	C₅×C₂²⋊C₄	—	3	8	no	—
218	C₅×C₂²⋊C₄	—	3	16	no	—
219	C₅×C₂²⋊C₄	—	3	16	no	—
220	C₄²×C₅	—	3	4	no	—
221	C₄²×C₅	C₂²×D₃	1	4	yes	—
222	C₂²×#41	—	3	1	no	—
223	C₂³×Q₈	—	3	1	no	—
224	#536	—	3	16	no	—
225	C₂×C₄⋊Q₈	—	3	1	no	—
226	C₂×C₄⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
227	C₂×#124	—	3	1	no	—
228	C₂×#124	—	3	1	no	—
229	C₂×#123	—	3	4	no	—
230	C₂×C₂²⋊Q₈	—	3	4	no	—
231	C₂×#117	—	3	1	no	—
232	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
233	C₂²×C₃×C₅	2₋¹⁺⁴	1	4	yes	—
234	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
235	C₂×C₅×D₃	—	2	8	no	—
236	C₂×C₅×D₃	—	2	4	no	—
237	C₂×C₅×D₃	—	2	4	no	—
238	C₂×C₅×D₃	—	2	8	no	—
239	C₂×C₅×D₃	—	4	8	no	—
240	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
241	C₃×C₄×C₅	—	2	4	no	—
242	C₃×C₄×C₅	—	2	4	no	—
243	C₃×C₄×C₅	—	2	4	no	—
244	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
245	C₅×Dic₃	—	2	4	no	—
246	C₅×Dic₃	—	2	4	no	—
247	C₅×Dic₃	C₂²×D₄	1	4	yes	—
248	C₂³×D₃	C₂³×C₅	1	2	yes	—
249	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
250	C₂×C₃×Q₈	—	2	4	no	—
251	C₂×C₃×Q₈	—	2	4	no	—
252	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
253	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
254	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
255	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
256	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
257	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
258	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
259	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
260	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
261	#239	—	2	32	no	—
262	D₃×Q₈	—	2	32	no	—
263	C₂×D₁₂	—	2	8	no	—
264	C₂×D₁₂	—	2	4	no	—
265	C₂×D₁₂	C₂³×C₅	1	4	yes	—
266	C₂×D₁₂	C₂³×C₅	1	8	yes	—
267	C₂×C₄×D₃	—	2	8	no	—
268	C₂×C₄×D₃	—	2	8	no	—
269	C₂×C₄×D₃	C₅×D₄	1	8	yes	—
270	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
271	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
272	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
273	C₂×Dic₆	—	2	4	no	—
274	C₂×Dic₆	—	2	8	no	—
275	C₂×Dic₆	C₂³×C₅	1	4	yes	—
276	C₂×Dic₆	C₂³×C₅	1	8	yes	—
277	C₃×C₄⋊C₄	C₂³×C₅	1	16	yes	—
278	C₃×C₄²	C₂³×C₅	1	4	yes	—
279	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
280	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
281	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
282	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
283	Dic₃⋊C₄	C₂³×C₅	1	16	yes	—
284	C₄×Dic₃	C₂³×C₅	1	4	yes	—
285	C₂³×C₅	—	3	4	no	—
286	C₂³×C₅	—	3	2	no	—
287	C₂³×C₅	—	3	4	no	—
288	C₂³×C₅	—	6	4	no	—
289	C₂³×C₅	—	6	4	no	—
290	C₂³×C₅	—	6	8	no	—
291	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
292	C₅×Q₈	—	2	8	no	—
293	C₅×Q₈	—	2	8	no	—
294	C₅×Q₈	—	6	16	no	—
295	C₅×Q₈	—	6	8	no	—
296	C₅×D₄	—	6	16	no	—
297	C₅×D₄	—	6	8	no	—
298	C₂×C₄×C₅	—	2	4	no	—
299	C₂×C₄×C₅	—	2	4	no	—
300	C₂×C₄×C₅	—	2	4	no	—
301	C₂×C₄×C₅	—	3	4	no	—
302	C₂×C₄×C₅	—	3	2	no	—
303	C₂×C₄×C₅	—	3	16	no	—
304	C₂×C₄×C₅	—	3	4	no	—
305	C₂×C₄×C₅	—	3	4	no	—
306	C₂×C₄×C₅	—	6	16	no	—
307	C₂×C₄×C₅	—	6	16	no	—
308	C₂×C₄×C₅	—	6	4	no	—
309	C₂×C₄×C₅	—	6	4	no	—
310	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
311	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
312	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
313	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
314	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
315	C₂×#41	—	3	8	no	—
316	C₂×#41	—	6	8	no	—
317	C₂²×Q₈	—	3	8	no	—
318	C₂²×Q₈	—	3	2	no	—
319	C₂²×Q₈	—	3	1	no	—
320	C₂²×Q₈	—	6	8	no	—
321	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
322	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
323	C₂²×D₄	—	3	2	no	—
324	C₂²×D₄	—	3	1	no	—
325	C₂³×C₄	—	3	1	no	—
326	C₂³×C₄	—	3	2	no	—
327	C₂³×C₄	—	3	2	no	—
328	C₄⋊Q₈	—	3	8	no	—
329	C₄⋊Q₈	C₂×C₅×D₃	1	8	yes	complemented
330	#124	—	3	8	no	—
331	#124	—	3	8	no	—
332	#123	—	3	32	no	—
333	C₂²⋊Q₈	—	3	32	no	—
334	#117	—	3	8	no	—
335	C₂×C₄⋊C₄	—	3	2	no	—
336	C₂×C₄⋊C₄	—	3	4	no	—
337	C₂×C₄⋊C₄	C₂×C₅×D₃	1	4	yes	—
338	C₂×C₂²⋊C₄	—	3	2	no	—
339	C₂×C₂²⋊C₄	—	3	4	no	—
340	C₂×C₂²⋊C₄	—	3	4	no	—
341	C₂×C₄²	—	3	1	no	—
342	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
343	C₂×C₃×C₅	#536	1	4	yes	complemented
344	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
345	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
346	C₅×D₃	—	2	4	no	—
347	C₅×D₃	—	4	4	no	—
348	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
349	C₂²×D₃	—	2	4	no	—
350	C₂²×D₃	—	2	4	no	—
351	C₂²×D₃	—	2	8	no	—
352	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
353	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
354	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
355	C₃×Q₈	—	2	8	no	—
356	C₃×Q₈	—	2	8	no	—
357	C₂×C₃×C₄	—	2	4	no	—
358	C₂×C₃×C₄	—	2	4	no	—
359	C₂×C₃×C₄	—	2	4	no	—
360	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
361	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
362	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
363	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
364	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
365	C₂×Dic₃	—	2	4	no	—
366	C₂×Dic₃	—	2	4	no	—
367	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
368	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
369	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
370	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
371	D₁₂	—	2	16	no	—
372	D₁₂	—	2	8	no	—
373	C₄×D₃	—	2	16	no	—
374	C₄×D₃	—	2	16	no	—
375	C₄×D₃	C₂×C₅×D₄	1	16	yes	—
376	Dic₆	—	2	8	no	—
377	Dic₆	—	2	16	no	—
378	C₂²×C₅	—	3	4	no	—
379	C₂²×C₅	—	6	4	no	—
380	C₂²×C₅	—	6	8	no	—
381	C₂²×C₅	—	6	4	no	—
382	C₂²×C₅	—	6	8	no	—
383	C₂²×C₅	—	12	8	no	—
384	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
385	C₂²×C₅	#1007	1	4	yes	—
386	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
387	C₄×C₅	—	2	4	no	—
388	C₄×C₅	—	2	4	no	—
389	C₄×C₅	—	2	4	no	—
390	C₄×C₅	—	3	4	no	—
391	C₄×C₅	—	6	4	no	—
392	C₄×C₅	—	6	4	no	—
393	C₄×C₅	C₂×D₃×D₄	1	4	yes	—
394	C₂⁴	—	3	1	no	—
395	C₂⁴	—	3	2	no	—
396	#41	—	6	32	no	—
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	2	4	no	—
399	C₂×Q₈	—	3	8	no	—
400	C₂×Q₈	—	3	4	no	—
401	C₂×Q₈	—	6	8	no	—
402	C₂×Q₈	—	6	32	no	—
403	C₂×Q₈	—	6	4	no	—
404	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
405	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
406	C₂×D₄	—	3	8	no	—
407	C₂×D₄	—	3	4	no	—
408	C₂×D₄	—	6	8	no	—
409	C₂×D₄	—	6	4	no	—
410	C₂²×C₄	—	3	1	no	—
411	C₂²×C₄	—	3	8	no	—
412	C₂²×C₄	—	3	4	no	—
413	C₂²×C₄	—	3	2	no	—
414	C₂²×C₄	—	3	2	no	—
415	C₂²×C₄	—	3	8	no	—
416	C₂²×C₄	—	3	8	no	—
417	C₂²×C₄	—	6	8	no	—
418	C₂²×C₄	—	6	8	no	—
419	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
420	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
421	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
422	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
423	C₄⋊C₄	—	3	8	no	—
424	C₄⋊C₄	—	3	16	no	—
425	C₄⋊C₄	C₂²×C₅×D₃	1	16	yes	—
426	C₂²⋊C₄	—	3	8	no	—
427	C₂²⋊C₄	—	3	16	no	—
428	C₂²⋊C₄	—	3	16	no	—
429	C₄²	—	3	4	no	—
430	C₄²	C₂²×C₅×D₃	1	4	yes	—
431	C₃×C₅	C₂×#536	1	1	yes	characteristic, complemented, Hall
432	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
433	C₂²×C₃	C₅×2₋¹⁺⁴	1	4	yes	—
434	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
435	C₂×D₃	—	2	8	no	—
436	C₂×D₃	—	2	4	no	—
437	C₂×D₃	—	2	4	no	—
438	C₂×D₃	—	2	8	no	—
439	C₂×D₃	—	4	8	no	—
440	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
441	C₃×C₄	—	2	4	no	—
442	C₃×C₄	—	2	4	no	—
443	C₃×C₄	—	2	4	no	—
444	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
445	Dic₃	—	2	4	no	—
446	Dic₃	—	2	4	no	—
447	Dic₃	C₂²×C₅×D₄	1	4	yes	—
448	C₂×C₅	—	6	4	no	—
449	C₂×C₅	—	12	4	no	—
450	C₂×C₅	#5724	1	4	yes	direct product factor
451	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
452	C₂×C₅	C₂×#1007	1	2	yes	—
453	C₂³	—	3	4	no	—
454	C₂³	—	3	2	no	—
455	C₂³	—	3	4	no	—
456	C₂³	—	6	4	no	—
457	C₂³	—	6	4	no	—
458	C₂³	—	6	8	no	—
459	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
460	Q₈	—	2	8	no	—
461	Q₈	—	2	8	no	—
462	Q₈	—	6	16	no	—
463	Q₈	—	6	8	no	—
464	D₄	—	6	16	no	—
465	D₄	—	6	8	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	3	4	no	—
470	C₂×C₄	—	3	2	no	—
471	C₂×C₄	—	3	16	no	—
472	C₂×C₄	—	3	4	no	—
473	C₂×C₄	—	3	4	no	—
474	C₂×C₄	—	6	16	no	—
475	C₂×C₄	—	6	16	no	—
476	C₂×C₄	—	6	4	no	—
477	C₂×C₄	—	6	4	no	—
478	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
479	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
480	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
481	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
482	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
483	C₂×C₃	C₅×#536	1	4	yes	complemented
484	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
485	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
486	D₃	—	2	4	no	—
487	D₃	—	4	4	no	—
488	C₅	C₂×#5724	1	1	yes	characteristic, direct product factor, Sylow
489	C₂²	—	3	4	no	—
490	C₂²	—	6	4	no	—
491	C₂²	—	6	8	no	—
492	C₂²	—	6	4	no	—
493	C₂²	—	6	8	no	—
494	C₂²	—	12	8	no	—
495	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
496	C₂²	C₅×#1007	1	4	yes	—
497	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
498	C₄	—	2	4	no	—
499	C₄	—	2	4	no	—
500	C₄	—	2	4	no	—
501	C₄	—	3	4	no	—
502	C₄	—	6	4	no	—
503	C₄	—	6	4	no	—
504	C₄	C₂×C₅×D₃×D₄	1	4	yes	—
505	C₃	C₂×C₅×#536	1	1	yes	characteristic, complemented, Sylow
506	C₂	—	6	4	no	—
507	C₂	—	12	4	no	—
508	C₂	C₅×#5724	1	4	yes	direct product factor
509	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
510	C₂	C₂×C₅×#1007	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×C₄⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#239	C₂
hypercenter	C₂×C₅×C₄⋊Q₈	D₃
hypocenter	C₃	C₂×C₅×#536
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×D₃×Q₈	C₂	semidirect
3. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
4. C₂×C₅×#947	C₂	semidirect
5. C₂×C₅×#944	C₂	semidirect
6. C₅×#5724	C₂	direct (N × H)
7. C₂×C₅×#896	C₂	semidirect
8. C₂×C₅×#894	C₂	semidirect
9. C₂×C₅×#875	C₂	semidirect
10. C₂×C₅×#872	C₂	semidirect
17. C₂×C₅×D₃×Q₈	C₂²	semidirect
25. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
28. C₅×#947	C₂²	semidirect
29. C₅×#944	C₂²	semidirect
36. C₅×#896	C₂²	semidirect
37. C₅×#894	C₂²	semidirect
38. C₅×#875	C₂²	semidirect
39. C₅×#872	C₂²	semidirect
40. C₂×#5724	C₅	direct (N × H)
45. C₂×C₅×C₄⋊Q₈	D₃	semidirect
89. C₂²×D₃×Q₈	C₂×C₅	semidirect
90. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
91. C₂×#947	C₂×C₅	semidirect
92. C₂×#944	C₂×C₅	semidirect
93. #5724	C₂×C₅	direct (N × H)
94. C₂×#896	C₂×C₅	semidirect
95. C₂×#894	C₂×C₅	semidirect
96. C₂×#875	C₂×C₅	semidirect
97. C₂×#872	C₂×C₅	semidirect
112. C₅×C₄⋊Q₈	C₂×D₃	semidirect
162. C₂×D₃×Q₈	C₂²×C₅	semidirect
170. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
173. #947	C₂²×C₅	semidirect
174. #944	C₂²×C₅	semidirect
181. #896	C₂²×C₅	semidirect
182. #894	C₂²×C₅	semidirect
183. #875	C₂²×C₅	semidirect
184. #872	C₂²×C₅	semidirect
226. C₂×C₄⋊Q₈	C₅×D₃	semidirect
329. C₄⋊Q₈	C₂×C₅×D₃	semidirect
343. C₂×C₃×C₅	#536	semidirect
431. C₃×C₅	C₂×#536	semidirect
450. C₂×C₅	#5724	direct (N × H)
483. C₂×C₃	C₅×#536	semidirect
488. C₅	C₂×#5724	direct (N × H)
505. C₃	C₂×C₅×#536	semidirect
508. C₂	C₅×#5724	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×#239	2
C₂²×C₅×D₃×Q₈	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₂×C₅×#947	2
C₂×C₅×#944	2
C₅×#5724	2
C₂×C₅×#896	2
C₂×C₅×#894	2
C₂×C₅×#875	2
C₂×C₅×#872	2
C₂×C₅×#536	3
C₂×#5724	5

Subgroups — C2×C5×#5724 #14480476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5724 #14480476