Subgroups — C₂×C₅×#5691 #14479790

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5691	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅×#898	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#897	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×#894	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#893	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#892	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#529	—	3	1	no	maximal, Hall
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
16	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
20	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
21	C₃×C₅×#125	C₂²	1	8	yes	complemented
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
30	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
31	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
33	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
38	C₅×#898	C₂²	1	16	yes	complemented
39	C₅×#897	C₂²	1	8	yes	complemented
40	C₅×#895	C₂²	1	8	yes	—
41	C₅×#894	C₂²	1	16	yes	complemented
42	C₅×#893	C₂²	1	8	yes	complemented
43	C₅×#893	C₂²	1	16	yes	complemented
44	C₅×#892	C₂²	1	16	yes	complemented
45	C₅×#887	C₂²	1	8	yes	complemented
46	C₅×#875	C₂²	1	8	yes	complemented
47	C₄²×C₅×D₃	C₂²	1	8	yes	complemented
48	C₂×#5691	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
49	C₅×#529	—	3	16	no	—
50	C₂×C₅×#126	—	3	2	no	—
51	C₂×C₅×#125	D₃	1	1	yes	characteristic, complemented
52	C₂×C₅×#124	—	3	1	no	—
53	C₂×C₅×#123	—	3	2	no	—
54	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
55	C₂×C₅×#121	—	3	1	no	—
56	C₂×C₄×C₅×Q₈	—	3	1	no	—
57	C₂×C₄×C₅×D₄	—	3	1	no	—
58	C₂×C₄×C₅×D₄	—	3	2	no	—
59	C₂×C₅×#117	—	3	2	no	—
60	C₂²×C₄²×C₅	—	3	1	no	—
61	C₂³×C₅×D₃	C₂³	1	2	yes	—
62	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
69	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
70	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
71	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
72	C₂×C₅×D₁₂	—	2	8	no	—
73	C₂×C₅×D₁₂	—	2	4	no	—
74	C₂×C₅×D₁₂	C₂³	1	4	yes	—
75	C₂×C₅×D₁₂	C₂³	1	8	yes	—
76	C₂×C₄×C₅×D₃	—	2	4	no	—
77	C₂×C₄×C₅×D₃	—	2	4	no	—
78	C₂×C₄×C₅×D₃	—	2	4	no	—
79	C₂×C₄×C₅×D₃	—	2	8	no	—
80	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
81	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
82	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
83	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
84	C₂×C₅×Dic₆	—	2	4	no	—
85	C₂×C₅×Dic₆	C₂³	1	4	yes	—
86	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
87	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
88	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
89	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
90	C₃×C₄²×C₅	C₂³	1	4	yes	—
91	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
92	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
93	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
94	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
95	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
96	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
97	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
98	C₄×C₅×Dic₃	C₂³	1	4	yes	—
99	C₄×C₅×Dic₃	C₂³	1	4	yes	—
100	C₄×C₅×Dic₃	C₂³	1	4	yes	—
101	C₄×C₅×Dic₃	C₂³	1	8	yes	—
102	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
103	#5691	C₂×C₅	1	16	yes	direct product factor
104	C₂×#898	C₂×C₅	1	2	yes	complemented
105	C₂×#897	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂×#895	C₂×C₅	1	1	yes	characteristic
107	C₂×#894	C₂×C₅	1	2	yes	complemented
108	C₂×#893	C₂×C₅	1	1	yes	characteristic, complemented
109	C₂×#893	C₂×C₅	1	2	yes	complemented
110	C₂×#892	C₂×C₅	1	2	yes	complemented
111	C₂×#887	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×#875	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂²×C₅×Q₈	—	3	1	no	—
115	C₂²×C₅×D₄	—	3	2	no	—
116	C₂²×C₅×D₄	—	3	1	no	—
117	C₂³×C₄×C₅	—	3	1	no	—
118	C₂³×C₄×C₅	—	3	1	no	—
119	C₂³×C₄×C₅	—	3	1	no	—
120	C₂³×C₄×C₅	—	3	2	no	—
121	C₅×#126	—	3	16	no	—
122	C₅×#125	C₂×D₃	1	8	yes	complemented
123	C₅×#124	—	3	8	no	—
124	C₅×#123	—	3	16	no	—
125	C₅×C₂²⋊Q₈	—	3	8	no	—
126	C₅×#121	—	3	8	no	—
127	C₄×C₅×Q₈	—	3	8	no	—
128	C₄×C₅×D₄	—	3	8	no	—
129	C₄×C₅×D₄	—	3	16	no	—
130	C₅×#117	—	3	16	no	—
131	C₂×C₅×C₄⋊C₄	—	3	2	no	—
132	C₂×C₅×C₄⋊C₄	—	3	2	no	—
133	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
134	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
135	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
136	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
137	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
138	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
139	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
140	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
141	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
142	C₂×C₄²×C₅	—	3	1	no	—
143	C₂×C₄²×C₅	—	3	1	no	—
144	C₂×C₄²×C₅	—	3	1	no	—
145	C₂×C₄²×C₅	—	3	2	no	—
146	C₂×C₄²×C₅	—	3	8	no	—
147	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
148	C₂×#529	—	3	1	no	Sylow
149	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
150	C₂²×C₅×D₃	—	2	2	no	—
151	C₂²×C₅×D₃	—	2	2	no	—
152	C₂²×C₅×D₃	—	2	4	no	—
153	C₂²×C₅×D₃	—	2	4	no	—
154	C₂²×C₅×D₃	—	2	4	no	—
155	C₂²×C₅×D₃	#41	1	4	yes	—
156	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
157	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
158	C₂×C₃×C₄×C₅	—	2	2	no	—
159	C₂×C₃×C₄×C₅	—	2	2	no	—
160	C₂×C₃×C₄×C₅	—	2	4	no	—
161	C₂×C₃×C₄×C₅	—	2	4	no	—
162	C₂×C₃×C₄×C₅	#41	1	4	yes	—
163	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
164	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
165	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
166	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
167	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
168	C₂×C₅×Dic₃	—	2	4	no	—
169	C₂×C₅×Dic₃	—	2	2	no	—
170	C₂×C₅×Dic₃	—	2	2	no	—
171	C₂×C₅×Dic₃	#41	1	4	yes	—
172	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
173	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
174	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
175	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
176	C₅×D₁₂	—	2	16	no	—
177	C₅×D₁₂	—	2	8	no	—
178	C₄×C₅×D₃	—	2	8	no	—
179	C₄×C₅×D₃	—	2	8	no	—
180	C₄×C₅×D₃	—	2	8	no	—
181	C₄×C₅×D₃	—	2	16	no	—
182	C₅×Dic₆	—	2	8	no	—
183	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
184	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
185	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
186	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
187	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
188	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
189	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
190	C₃×#125	C₂²×C₅	1	8	yes	complemented
191	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
193	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
194	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
195	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
196	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
197	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
198	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
199	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
200	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
201	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
202	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
203	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
204	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
205	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
206	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
207	#898	C₂²×C₅	1	16	yes	complemented
208	#897	C₂²×C₅	1	8	yes	complemented
209	#895	C₂²×C₅	1	8	yes	—
210	#894	C₂²×C₅	1	16	yes	complemented
211	#893	C₂²×C₅	1	8	yes	complemented
212	#893	C₂²×C₅	1	16	yes	complemented
213	#892	C₂²×C₅	1	16	yes	complemented
214	#887	C₂²×C₅	1	8	yes	complemented
215	#875	C₂²×C₅	1	8	yes	complemented
216	C₄²×D₃	C₂²×C₅	1	8	yes	complemented
217	C₂⁴×C₅	—	3	1	no	—
218	C₂⁴×C₅	—	3	2	no	—
219	C₂×C₅×Q₈	—	3	4	no	—
220	C₂×C₅×Q₈	—	6	4	no	—
221	C₂×C₅×D₄	—	3	8	no	—
222	C₂×C₅×D₄	—	3	4	no	—
223	C₂×C₅×D₄	—	6	8	no	—
224	C₂×C₅×D₄	—	6	4	no	—
225	C₂²×C₄×C₅	—	3	1	no	—
226	C₂²×C₄×C₅	—	3	1	no	—
227	C₂²×C₄×C₅	—	3	1	no	—
228	C₂²×C₄×C₅	—	3	2	no	—
229	C₂²×C₄×C₅	—	3	4	no	—
230	C₂²×C₄×C₅	—	3	4	no	—
231	C₂²×C₄×C₅	—	3	4	no	—
232	C₂²×C₄×C₅	—	3	8	no	—
233	C₂²×C₄×C₅	—	6	4	no	—
234	C₂²×C₄×C₅	—	6	8	no	—
235	C₂²×C₄×C₅	—	6	4	no	—
236	C₂²×C₄×C₅	—	6	4	no	—
237	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
238	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
239	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
240	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
241	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
242	C₅×C₄⋊C₄	—	3	8	no	—
243	C₅×C₄⋊C₄	—	3	8	no	—
244	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
245	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
246	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
247	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
248	C₅×C₂²⋊C₄	—	3	8	no	—
249	C₅×C₂²⋊C₄	—	3	8	no	—
250	C₅×C₂²⋊C₄	—	3	8	no	—
251	C₅×C₂²⋊C₄	—	3	8	no	—
252	C₅×C₂²⋊C₄	—	3	8	no	—
253	C₄²×C₅	—	3	4	no	—
254	C₄²×C₅	—	3	4	no	—
255	C₄²×C₅	—	3	4	no	—
256	C₄²×C₅	—	3	8	no	—
257	C₄²×C₅	C₂²×D₃	1	4	yes	—
258	#529	—	3	16	no	—
259	C₂×#126	—	3	2	no	—
260	C₂×#125	C₅×D₃	1	1	yes	characteristic, complemented
261	C₂×#124	—	3	1	no	—
262	C₂×#123	—	3	2	no	—
263	C₂×C₂²⋊Q₈	—	3	1	no	—
264	C₂×#121	—	3	1	no	—
265	C₂×C₄×Q₈	—	3	1	no	—
266	C₂×C₄×D₄	—	3	2	no	—
267	C₂×C₄×D₄	—	3	1	no	—
268	C₂×#117	—	3	2	no	—
269	C₂²×C₄²	—	3	1	no	—
270	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
271	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
272	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
273	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
274	C₂×C₅×D₃	—	2	8	no	—
275	C₂×C₅×D₃	—	2	2	no	—
276	C₂×C₅×D₃	—	2	2	no	—
277	C₂×C₅×D₃	—	2	4	no	—
278	C₂×C₅×D₃	—	2	4	no	—
279	C₂×C₅×D₃	—	2	4	no	—
280	C₂×C₅×D₃	—	4	8	no	—
281	C₂×C₅×D₃	C₂×#41	1	4	yes	—
282	C₃×C₄×C₅	—	2	2	no	—
283	C₃×C₄×C₅	—	2	2	no	—
284	C₃×C₄×C₅	—	2	4	no	—
285	C₃×C₄×C₅	—	2	4	no	—
286	C₃×C₄×C₅	C₂×#41	1	4	yes	—
287	C₅×Dic₃	—	2	4	no	—
288	C₅×Dic₃	—	2	2	no	—
289	C₅×Dic₃	—	2	2	no	—
290	C₅×Dic₃	C₂×#41	1	4	yes	—
291	C₂³×D₃	C₂³×C₅	1	2	yes	—
292	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
293	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
294	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
295	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
296	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
297	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
298	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
299	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
300	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
301	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
302	C₂×D₁₂	—	2	8	no	—
303	C₂×D₁₂	—	2	4	no	—
304	C₂×D₁₂	C₂³×C₅	1	4	yes	—
305	C₂×D₁₂	C₂³×C₅	1	8	yes	—
306	C₂×C₄×D₃	—	2	4	no	—
307	C₂×C₄×D₃	—	2	4	no	—
308	C₂×C₄×D₃	—	2	4	no	—
309	C₂×C₄×D₃	—	2	8	no	—
310	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
311	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
312	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
313	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
314	C₂×Dic₆	—	2	4	no	—
315	C₂×Dic₆	C₂³×C₅	1	4	yes	—
316	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
317	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
318	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
319	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
320	C₃×C₄²	C₂³×C₅	1	4	yes	—
321	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
322	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
323	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
324	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
325	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
326	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
327	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
328	C₄×Dic₃	C₂³×C₅	1	4	yes	—
329	C₄×Dic₃	C₂³×C₅	1	4	yes	—
330	C₄×Dic₃	C₂³×C₅	1	4	yes	—
331	C₄×Dic₃	C₂³×C₅	1	8	yes	—
332	C₂³×C₅	—	3	4	no	—
333	C₂³×C₅	—	3	2	no	—
334	C₂³×C₅	—	3	4	no	—
335	C₂³×C₅	—	6	2	no	—
336	C₂³×C₅	—	6	2	no	—
337	C₂³×C₅	—	6	4	no	—
338	C₂³×C₅	—	6	4	no	—
339	C₂³×C₅	—	6	4	no	—
340	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
341	C₅×Q₈	—	6	8	no	—
342	C₅×D₄	—	6	16	no	—
343	C₅×D₄	—	6	8	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	2	4	no	—
346	C₂×C₄×C₅	—	2	2	no	—
347	C₂×C₄×C₅	—	2	4	no	—
348	C₂×C₄×C₅	—	3	4	no	—
349	C₂×C₄×C₅	—	3	2	no	—
350	C₂×C₄×C₅	—	3	2	no	—
351	C₂×C₄×C₅	—	3	2	no	—
352	C₂×C₄×C₅	—	3	4	no	—
353	C₂×C₄×C₅	—	6	8	no	—
354	C₂×C₄×C₅	—	6	16	no	—
355	C₂×C₄×C₅	—	6	8	no	—
356	C₂×C₄×C₅	—	6	2	no	—
357	C₂×C₄×C₅	—	6	4	no	—
358	C₂×C₄×C₅	—	6	2	no	—
359	C₂×C₄×C₅	—	6	8	no	—
360	C₂×C₄×C₅	#239	1	4	yes	—
361	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
362	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
363	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
364	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
365	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
366	C₂²×Q₈	—	3	1	no	—
367	C₂²×D₄	—	3	2	no	—
368	C₂²×D₄	—	3	1	no	—
369	C₂³×C₄	—	3	2	no	—
370	C₂³×C₄	—	3	1	no	—
371	C₂³×C₄	—	3	1	no	—
372	C₂³×C₄	—	3	1	no	—
373	#126	—	3	16	no	—
374	#125	C₂×C₅×D₃	1	8	yes	complemented
375	#124	—	3	8	no	—
376	#123	—	3	16	no	—
377	C₂²⋊Q₈	—	3	8	no	—
378	#121	—	3	8	no	—
379	C₄×Q₈	—	3	8	no	—
380	C₄×D₄	—	3	8	no	—
381	C₄×D₄	—	3	16	no	—
382	#117	—	3	16	no	—
383	C₂×C₄⋊C₄	—	3	2	no	—
384	C₂×C₄⋊C₄	—	3	2	no	—
385	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
386	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
388	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	3	2	no	—
390	C₂×C₂²⋊C₄	—	3	2	no	—
391	C₂×C₂²⋊C₄	—	3	2	no	—
392	C₂×C₂²⋊C₄	—	3	2	no	—
393	C₂×C₂²⋊C₄	—	3	2	no	—
394	C₂×C₄²	—	3	1	no	—
395	C₂×C₄²	—	3	2	no	—
396	C₂×C₄²	—	3	1	no	—
397	C₂×C₄²	—	3	1	no	—
398	C₂×C₄²	—	3	8	no	—
399	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
400	C₂×C₃×C₅	#529	1	4	yes	complemented
401	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
402	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
403	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
404	C₅×D₃	—	2	4	no	—
405	C₅×D₃	—	4	4	no	—
406	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
407	C₂²×D₃	—	2	2	no	—
408	C₂²×D₃	—	2	2	no	—
409	C₂²×D₃	—	2	4	no	—
410	C₂²×D₃	—	2	4	no	—
411	C₂²×D₃	—	2	4	no	—
412	C₂²×D₃	C₅×#41	1	4	yes	—
413	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
414	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
415	C₂×C₃×C₄	—	2	2	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	—	2	4	no	—
418	C₂×C₃×C₄	—	2	4	no	—
419	C₂×C₃×C₄	C₅×#41	1	4	yes	—
420	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
421	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
422	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
423	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
424	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
425	C₂×Dic₃	—	2	4	no	—
426	C₂×Dic₃	—	2	2	no	—
427	C₂×Dic₃	—	2	2	no	—
428	C₂×Dic₃	C₅×#41	1	4	yes	—
429	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
430	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
431	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
432	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
433	D₁₂	—	2	16	no	—
434	D₁₂	—	2	8	no	—
435	C₄×D₃	—	2	8	no	—
436	C₄×D₃	—	2	8	no	—
437	C₄×D₃	—	2	8	no	—
438	C₄×D₃	—	2	16	no	—
439	Dic₆	—	2	8	no	—
440	C₂²×C₅	—	3	4	no	—
441	C₂²×C₅	—	6	8	no	—
442	C₂²×C₅	—	6	2	no	—
443	C₂²×C₅	—	6	2	no	—
444	C₂²×C₅	—	6	4	no	—
445	C₂²×C₅	—	6	4	no	—
446	C₂²×C₅	—	6	4	no	—
447	C₂²×C₅	—	12	8	no	—
448	C₂²×C₅	C₂×#239	1	2	yes	—
449	C₂²×C₅	D₃×#41	1	2	yes	—
450	C₂²×C₅	D₃×#41	1	2	yes	—
451	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
452	C₄×C₅	—	2	2	no	—
453	C₄×C₅	—	2	4	no	—
454	C₄×C₅	—	2	2	no	—
455	C₄×C₅	—	2	4	no	—
456	C₄×C₅	—	3	4	no	—
457	C₄×C₅	—	6	2	no	—
458	C₄×C₅	—	6	4	no	—
459	C₄×C₅	—	6	2	no	—
460	C₄×C₅	C₂×#239	1	4	yes	—
461	C₂⁴	—	3	1	no	—
462	C₂⁴	—	3	2	no	—
463	C₂×Q₈	—	3	4	no	—
464	C₂×Q₈	—	6	4	no	—
465	C₂×D₄	—	3	8	no	—
466	C₂×D₄	—	3	4	no	—
467	C₂×D₄	—	6	8	no	—
468	C₂×D₄	—	6	4	no	—
469	C₂²×C₄	—	3	1	no	—
470	C₂²×C₄	—	3	1	no	—
471	C₂²×C₄	—	3	1	no	—
472	C₂²×C₄	—	3	2	no	—
473	C₂²×C₄	—	3	4	no	—
474	C₂²×C₄	—	3	4	no	—
475	C₂²×C₄	—	3	4	no	—
476	C₂²×C₄	—	3	8	no	—
477	C₂²×C₄	—	6	4	no	—
478	C₂²×C₄	—	6	8	no	—
479	C₂²×C₄	—	6	4	no	—
480	C₂²×C₄	—	6	4	no	—
481	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
482	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
483	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
484	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
485	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
486	C₄⋊C₄	—	3	8	no	—
487	C₄⋊C₄	—	3	8	no	—
488	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
489	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
490	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
491	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
492	C₂²⋊C₄	—	3	8	no	—
493	C₂²⋊C₄	—	3	8	no	—
494	C₂²⋊C₄	—	3	8	no	—
495	C₂²⋊C₄	—	3	8	no	—
496	C₂²⋊C₄	—	3	8	no	—
497	C₄²	—	3	4	no	—
498	C₄²	—	3	4	no	—
499	C₄²	—	3	4	no	—
500	C₄²	—	3	8	no	—
501	C₄²	C₂²×C₅×D₃	1	4	yes	—
502	C₃×C₅	C₂×#529	1	1	yes	characteristic, complemented, Hall
503	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
504	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
505	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
506	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
507	C₂×D₃	—	2	8	no	—
508	C₂×D₃	—	2	2	no	—
509	C₂×D₃	—	2	2	no	—
510	C₂×D₃	—	2	4	no	—
511	C₂×D₃	—	2	4	no	—
512	C₂×D₃	—	2	4	no	—
513	C₂×D₃	—	4	8	no	—
514	C₂×D₃	C₂×C₅×#41	1	4	yes	—
515	C₃×C₄	—	2	2	no	—
516	C₃×C₄	—	2	2	no	—
517	C₃×C₄	—	2	4	no	—
518	C₃×C₄	—	2	4	no	—
519	C₃×C₄	C₂×C₅×#41	1	4	yes	—
520	Dic₃	—	2	4	no	—
521	Dic₃	—	2	2	no	—
522	Dic₃	—	2	2	no	—
523	Dic₃	C₂×C₅×#41	1	4	yes	—
524	C₂×C₅	—	6	4	no	—
525	C₂×C₅	—	12	4	no	—
526	C₂×C₅	#5691	1	4	yes	direct product factor
527	C₂×C₅	C₂²×#239	1	1	yes	characteristic
528	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
529	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
530	C₂³	—	3	4	no	—
531	C₂³	—	3	2	no	—
532	C₂³	—	3	4	no	—
533	C₂³	—	6	2	no	—
534	C₂³	—	6	2	no	—
535	C₂³	—	6	4	no	—
536	C₂³	—	6	4	no	—
537	C₂³	—	6	4	no	—
538	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
539	Q₈	—	6	8	no	—
540	D₄	—	6	16	no	—
541	D₄	—	6	8	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	3	4	no	—
547	C₂×C₄	—	3	2	no	—
548	C₂×C₄	—	3	2	no	—
549	C₂×C₄	—	3	2	no	—
550	C₂×C₄	—	3	4	no	—
551	C₂×C₄	—	6	8	no	—
552	C₂×C₄	—	6	16	no	—
553	C₂×C₄	—	6	8	no	—
554	C₂×C₄	—	6	2	no	—
555	C₂×C₄	—	6	4	no	—
556	C₂×C₄	—	6	2	no	—
557	C₂×C₄	—	6	8	no	—
558	C₂×C₄	C₅×#239	1	4	yes	—
559	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
560	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
561	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
562	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
563	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
564	C₂×C₃	C₅×#529	1	4	yes	complemented
565	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
566	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
567	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
568	D₃	—	2	4	no	—
569	D₃	—	4	4	no	—
570	C₅	C₂×#5691	1	1	yes	characteristic, direct product factor, Sylow
571	C₂²	—	3	4	no	—
572	C₂²	—	6	8	no	—
573	C₂²	—	6	2	no	—
574	C₂²	—	6	2	no	—
575	C₂²	—	6	4	no	—
576	C₂²	—	6	4	no	—
577	C₂²	—	6	4	no	—
578	C₂²	—	12	8	no	—
579	C₂²	C₂×C₅×#239	1	2	yes	—
580	C₂²	C₅×D₃×#41	1	2	yes	—
581	C₂²	C₅×D₃×#41	1	2	yes	—
582	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	4	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	4	no	—
587	C₄	—	3	4	no	—
588	C₄	—	6	2	no	—
589	C₄	—	6	4	no	—
590	C₄	—	6	2	no	—
591	C₄	C₂×C₅×#239	1	4	yes	—
592	C₃	C₂×C₅×#529	1	1	yes	characteristic, complemented, Sylow
593	C₂	—	6	4	no	—
594	C₂	—	12	4	no	—
595	C₂	C₅×#5691	1	4	yes	direct product factor
596	C₂	C₂²×C₅×#239	1	1	yes	characteristic
597	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
598	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#125	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#895	C₂
hypercenter	C₂×C₅×#125	D₃
hypocenter	C₃	C₂×C₅×#529
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#125

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#125	C₂	semidirect
2. C₅×#5691	C₂	direct (N × H)
3. C₂×C₅×#898	C₂	semidirect
4. C₂×C₅×#897	C₂	semidirect
6. C₂×C₅×#894	C₂	semidirect
7. C₂×C₅×#893	C₂	semidirect
8. C₂×C₅×#893	C₂	semidirect
9. C₂×C₅×#892	C₂	semidirect
10. C₂×C₅×#887	C₂	semidirect
11. C₂×C₅×#875	C₂	semidirect
12. C₂×C₄²×C₅×D₃	C₂	semidirect
21. C₃×C₅×#125	C₂²	semidirect
38. C₅×#898	C₂²	semidirect
39. C₅×#897	C₂²	semidirect
41. C₅×#894	C₂²	semidirect
42. C₅×#893	C₂²	semidirect
43. C₅×#893	C₂²	semidirect
44. C₅×#892	C₂²	semidirect
45. C₅×#887	C₂²	semidirect
46. C₅×#875	C₂²	semidirect
47. C₄²×C₅×D₃	C₂²	semidirect
48. C₂×#5691	C₅	direct (N × H)
51. C₂×C₅×#125	D₃	semidirect
102. C₂×C₃×#125	C₂×C₅	semidirect
103. #5691	C₂×C₅	direct (N × H)
104. C₂×#898	C₂×C₅	semidirect
105. C₂×#897	C₂×C₅	semidirect
107. C₂×#894	C₂×C₅	semidirect
108. C₂×#893	C₂×C₅	semidirect
109. C₂×#893	C₂×C₅	semidirect
110. C₂×#892	C₂×C₅	semidirect
111. C₂×#887	C₂×C₅	semidirect
112. C₂×#875	C₂×C₅	semidirect
113. C₂×C₄²×D₃	C₂×C₅	semidirect
122. C₅×#125	C₂×D₃	semidirect
190. C₃×#125	C₂²×C₅	semidirect
207. #898	C₂²×C₅	semidirect
208. #897	C₂²×C₅	semidirect
210. #894	C₂²×C₅	semidirect
211. #893	C₂²×C₅	semidirect
212. #893	C₂²×C₅	semidirect
213. #892	C₂²×C₅	semidirect
214. #887	C₂²×C₅	semidirect
215. #875	C₂²×C₅	semidirect
216. C₄²×D₃	C₂²×C₅	semidirect
260. C₂×#125	C₅×D₃	semidirect
374. #125	C₂×C₅×D₃	semidirect
400. C₂×C₃×C₅	#529	semidirect
502. C₃×C₅	C₂×#529	semidirect
526. C₂×C₅	#5691	direct (N × H)
564. C₂×C₃	C₅×#529	semidirect
570. C₅	C₂×#5691	direct (N × H)
592. C₃	C₂×C₅×#529	semidirect
595. C₂	C₅×#5691	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×C₃×C₅×#125	2
C₅×#5691	2
C₂×C₅×#898	2
C₂×C₅×#897	2
C₂×C₅×#895	2
C₂×C₅×#894	2
C₂×C₅×#893	2
C₂×C₅×#892	2
C₂×C₅×#887	2
C₂×C₅×#875	2
C₂×C₄²×C₅×D₃	2
C₂×C₅×#529	3
C₂×#5691	5

Subgroups — C2×C5×#5691 #14479790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5691 #14479790