Subgroups — C₅×#75450 #14320817

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#877	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4976	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4957	C₂	1	1	yes	maximal, characteristic
7	C₅×#4957	C₂	1	1	yes	maximal, characteristic
8	C₅×#4951	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×Dic₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4940	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4669	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4666	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4649	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4647	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2293	—	3	1	no	maximal, Hall
17	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
18	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₂×C₅×#217	C₂²	1	1	yes	characteristic
26	C₂×C₅×#217	C₂²	1	1	yes	characteristic
27	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
33	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
46	C₅×#892	—	2	4	no	—
47	C₅×#67⋊C₄	C₄	1	8	yes	complemented
48	C₅×#877	—	2	4	no	—
49	C₃×C₅×#95	C₂²	1	1	yes	characteristic
50	C₃×C₅×#95	C₂²	1	1	yes	characteristic
51	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
52	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
53	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
54	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
55	#75450	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
56	C₂×C₄×C₅×D₄	—	3	1	no	—
57	C₂×C₅×#117	—	3	1	no	—
58	C₂×C₅×#117	—	3	1	no	—
59	C₅×#390	—	3	1	no	—
60	C₅×#390	—	3	1	no	—
61	C₅×#389	—	3	1	no	—
62	C₅×#389	—	3	1	no	—
63	C₅×#388	—	3	1	no	—
64	C₅×#388	—	3	1	no	—
65	C₅×#388	—	3	1	no	—
66	C₅×#388	D₃	1	1	yes	characteristic, complemented
67	C₄×C₅×C₄⋊C₄	—	3	1	no	—
68	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
69	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
70	C₄³×C₅	—	3	1	no	—
71	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
72	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₅×#67	—	2	2	no	—
80	C₂×C₅×#67	—	2	2	no	—
81	C₂×C₅×#67	C₂×C₄	1	4	yes	—
82	C₂²×C₅×Dic₃	—	2	2	no	—
83	C₂²×C₅×Dic₃	—	2	2	no	—
84	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
85	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
86	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
87	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
88	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
89	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
90	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
91	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
92	C₂×C₄×C₅×D₃	—	2	2	no	—
93	C₂×C₄×C₅×D₃	—	2	2	no	—
94	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
95	C₃×C₅×C₄⋊C₄	—	2	2	no	—
96	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
97	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
98	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
99	C₃×C₄²×C₅	—	2	2	no	—
100	C₅×#217	—	2	2	no	—
101	C₅×#217	—	2	2	no	—
102	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
103	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
104	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
105	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
106	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
107	C₅×C₄⋊Dic₃	—	2	2	no	—
108	C₅×Dic₃⋊C₄	—	2	2	no	—
109	C₅×Dic₃⋊C₄	—	2	2	no	—
110	C₅×Dic₃⋊C₄	—	2	2	no	—
111	C₅×Dic₃⋊C₄	—	2	2	no	—
112	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
113	C₄×C₅×Dic₃	—	2	2	no	—
114	C₄×C₅×Dic₃	—	2	2	no	—
115	C₄×C₅×Dic₃	—	2	2	no	—
116	C₄×C₅×Dic₃	—	2	2	no	—
117	C₄×C₅×Dic₃	—	2	2	no	—
118	C₄×C₅×Dic₃	—	2	2	no	—
119	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
120	C₄×C₅×Dic₃	D₄	1	4	yes	complemented
121	C₂×#892	C₂×C₅	1	1	yes	characteristic, complemented
122	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic
123	C₂×#877	C₂×C₅	1	1	yes	characteristic, complemented
124	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
125	#4976	C₂×C₅	1	1	yes	characteristic, complemented
126	#4957	C₂×C₅	1	1	yes	characteristic
127	#4957	C₂×C₅	1	1	yes	characteristic
128	#4951	C₂×C₅	1	1	yes	characteristic, complemented
129	Dic₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
130	#4940	C₂×C₅	1	1	yes	characteristic, complemented
131	C₄²×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
132	#4669	C₂×C₅	1	1	yes	characteristic, complemented
133	#4666	C₂×C₅	1	1	yes	characteristic, complemented
134	#4649	C₂×C₅	1	1	yes	characteristic, complemented
135	#4647	C₂×C₅	1	1	yes	characteristic, complemented
136	C₂²×C₅×D₄	—	3	1	no	—
137	C₂³×C₄×C₅	—	3	1	no	—
138	C₂³×C₄×C₅	—	3	1	no	—
139	C₄×C₅×D₄	—	3	8	no	—
140	C₅×#117	—	6	4	no	—
141	C₅×#117	—	6	4	no	—
142	C₂×C₅×C₄⋊C₄	—	3	1	no	—
143	C₂×C₅×C₄⋊C₄	—	3	1	no	—
144	C₂×C₅×C₄⋊C₄	—	3	1	no	—
145	C₂×C₅×C₄⋊C₄	—	3	1	no	—
146	C₂×C₅×C₄⋊C₄	—	3	1	no	—
147	C₂×C₅×C₄⋊C₄	—	3	1	no	—
148	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
149	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
150	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
151	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
152	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
153	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
154	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
155	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
156	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
157	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
158	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
159	C₂×C₄²×C₅	—	3	1	no	—
160	C₂×C₄²×C₅	—	3	1	no	—
161	C₂×C₄²×C₅	—	3	1	no	—
162	C₂×C₄²×C₅	—	3	1	no	—
163	C₂×C₄²×C₅	—	3	1	no	—
164	C₂×C₄²×C₅	—	3	1	no	—
165	C₂×C₄²×C₅	—	3	1	no	—
166	C₂×C₄²×C₅	—	3	1	no	—
167	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
168	C₅×#95	—	3	1	no	—
169	C₅×#95	—	3	1	no	—
170	C₅×#95	—	3	1	no	—
171	C₅×#95	—	3	1	no	—
172	C₅×#95	C₂×D₃	1	1	yes	characteristic
173	C₅×#95	C₂×D₃	1	1	yes	characteristic
174	#2293	—	3	1	no	Sylow
175	C₂³×C₃×C₅	—	2	1	no	—
176	C₂³×C₃×C₅	—	2	1	no	—
177	C₂³×C₃×C₅	—	2	1	no	—
178	C₂³×C₃×C₅	—	2	1	no	—
179	C₂³×C₃×C₅	—	2	1	no	—
180	C₂³×C₃×C₅	—	2	1	no	—
181	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
182	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
183	C₂²×C₅×D₃	—	2	1	no	—
184	C₂²×C₅×D₃	—	2	1	no	—
185	C₂²×C₅×D₃	—	2	1	no	—
186	C₂²×C₅×D₃	—	2	1	no	—
187	C₂²×C₅×D₃	—	2	1	no	—
188	C₂²×C₅×D₃	—	2	1	no	—
189	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
190	C₂×C₃×C₄×C₅	—	2	1	no	—
191	C₂×C₃×C₄×C₅	—	2	1	no	—
192	C₂×C₃×C₄×C₅	—	2	1	no	—
193	C₂×C₃×C₄×C₅	—	2	1	no	—
194	C₂×C₃×C₄×C₅	—	2	1	no	—
195	C₂×C₃×C₄×C₅	—	2	1	no	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	—	2	1	no	—
200	C₂×C₃×C₄×C₅	—	2	1	no	—
201	C₂×C₃×C₄×C₅	—	2	1	no	—
202	C₂×C₃×C₄×C₅	—	2	1	no	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
205	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
206	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
207	C₂×C₃×C₄×C₅	#41	1	2	yes	—
208	C₅×#67	—	2	8	no	—
209	C₂×C₅×Dic₃	—	2	1	no	—
210	C₂×C₅×Dic₃	—	2	1	no	—
211	C₂×C₅×Dic₃	—	2	1	no	—
212	C₂×C₅×Dic₃	—	2	1	no	—
213	C₂×C₅×Dic₃	—	2	1	no	—
214	C₂×C₅×Dic₃	—	2	1	no	—
215	C₂×C₅×Dic₃	—	2	8	no	—
216	C₂×C₅×Dic₃	—	2	1	no	—
217	C₂×C₅×Dic₃	—	2	1	no	—
218	C₂×C₅×Dic₃	—	2	1	no	—
219	C₂×C₅×Dic₃	—	2	1	no	—
220	C₂×C₅×Dic₃	—	2	1	no	—
221	C₂×C₅×Dic₃	—	2	1	no	—
222	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
223	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
224	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
225	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
226	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
227	C₂×C₅×Dic₃	#41	1	2	yes	—
228	C₂×C₅×Dic₃	#41	1	2	yes	—
229	C₂×C₅×Dic₃	#41	1	2	yes	—
230	C₂×C₅×Dic₃	#41	1	2	yes	—
231	C₄×C₅×D₃	—	2	8	no	—
232	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
233	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
234	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
240	C₂×#217	C₂²×C₅	1	1	yes	characteristic
241	C₂×#217	C₂²×C₅	1	1	yes	characteristic
242	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
243	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
244	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
245	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
248	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
250	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
251	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
261	#892	—	2	4	no	—
262	#67⋊C₄	C₄×C₅	1	8	yes	complemented
263	#877	—	2	4	no	—
264	C₃×#95	C₂²×C₅	1	1	yes	characteristic
265	C₃×#95	C₂²×C₅	1	1	yes	characteristic
266	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
267	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
268	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
269	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
270	C₂⁴×C₅	—	3	1	no	—
271	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
272	C₂×C₅×D₄	—	3	4	no	—
273	C₂×C₅×D₄	—	6	2	no	—
274	C₂×C₅×D₄	—	6	2	no	—
275	C₂²×C₄×C₅	—	3	1	no	—
276	C₂²×C₄×C₅	—	3	1	no	—
277	C₂²×C₄×C₅	—	3	4	no	—
278	C₂²×C₄×C₅	—	3	1	no	—
279	C₂²×C₄×C₅	—	3	1	no	—
280	C₂²×C₄×C₅	—	3	1	no	—
281	C₂²×C₄×C₅	—	3	4	no	—
282	C₂²×C₄×C₅	—	3	1	no	—
283	C₂²×C₄×C₅	—	3	1	no	—
284	C₂²×C₄×C₅	—	6	2	no	—
285	C₂²×C₄×C₅	—	6	2	no	—
286	C₂²×C₄×C₅	—	6	2	no	—
287	C₂²×C₄×C₅	—	6	2	no	—
288	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
289	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
290	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
291	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
292	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
293	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
294	C₅×C₄⋊C₄	—	2	2	no	—
295	C₅×C₄⋊C₄	—	3	4	no	—
296	C₅×C₄⋊C₄	—	6	2	no	—
297	C₅×C₄⋊C₄	—	6	2	no	—
298	C₅×C₄⋊C₄	—	6	2	no	—
299	C₅×C₄⋊C₄	—	6	2	no	—
300	C₅×C₄⋊C₄	—	6	2	no	—
301	C₅×C₂²⋊C₄	—	2	2	no	—
302	C₅×C₂²⋊C₄	—	2	2	no	—
303	C₅×C₂²⋊C₄	—	3	4	no	—
304	C₅×C₂²⋊C₄	—	6	2	no	—
305	C₅×C₂²⋊C₄	—	6	2	no	—
306	C₅×C₂²⋊C₄	—	6	2	no	—
307	C₅×C₂²⋊C₄	—	6	2	no	—
308	C₅×C₂²⋊C₄	—	6	2	no	—
309	C₅×C₂²⋊C₄	—	6	2	no	—
310	C₅×C₂²⋊C₄	C₄×D₃	1	4	yes	—
311	C₄²×C₅	—	2	2	no	—
312	C₄²×C₅	—	3	4	no	—
313	C₄²×C₅	—	3	4	no	—
314	C₄²×C₅	—	6	2	no	—
315	C₄²×C₅	—	6	2	no	—
316	C₄²×C₅	—	6	2	no	—
317	C₄²×C₅	—	6	2	no	—
318	C₄²×C₅	—	6	2	no	—
319	C₄²×C₅	—	6	2	no	—
320	C₂×C₄×D₄	—	3	1	no	—
321	C₂×#117	—	3	1	no	—
322	C₂×#117	—	3	1	no	—
323	#390	—	3	1	no	—
324	#390	—	3	1	no	—
325	#389	—	3	1	no	—
326	#389	—	3	1	no	—
327	#388	—	3	1	no	—
328	#388	—	3	1	no	—
329	#388	—	3	1	no	—
330	#388	C₅×D₃	1	1	yes	characteristic, complemented
331	C₄×C₄⋊C₄	—	3	1	no	—
332	C₄×C₂²⋊C₄	—	3	1	no	—
333	C₄×C₂²⋊C₄	—	3	1	no	—
334	C₄³	—	3	1	no	—
335	C₂²×C₃×C₅	—	2	2	no	—
336	C₂²×C₃×C₅	—	2	2	no	—
337	C₂²×C₃×C₅	—	2	2	no	—
338	C₂²×C₃×C₅	—	4	1	no	—
339	C₂²×C₃×C₅	—	4	1	no	—
340	C₂²×C₃×C₅	—	4	1	no	—
341	C₂²×C₃×C₅	—	4	1	no	—
342	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
343	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
344	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
345	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
346	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
347	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
348	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
349	C₂×C₅×D₃	—	2	2	no	—
350	C₂×C₅×D₃	—	2	2	no	—
351	C₂×C₅×D₃	—	2	2	no	—
352	C₂×C₅×D₃	—	4	1	no	—
353	C₂×C₅×D₃	—	4	1	no	—
354	C₂×C₅×D₃	—	4	1	no	—
355	C₂×C₅×D₃	—	4	1	no	—
356	C₃×C₄×C₅	—	2	2	no	—
357	C₃×C₄×C₅	—	2	2	no	—
358	C₃×C₄×C₅	—	2	2	no	—
359	C₃×C₄×C₅	—	2	2	no	—
360	C₃×C₄×C₅	—	4	1	no	—
361	C₃×C₄×C₅	—	4	1	no	—
362	C₅×Dic₃	—	2	2	no	—
363	C₅×Dic₃	—	2	2	no	—
364	C₅×Dic₃	—	2	2	no	—
365	C₅×Dic₃	—	4	1	no	—
366	C₅×Dic₃	—	4	1	no	—
367	C₅×Dic₃	#117	1	4	yes	complemented
368	C₅×Dic₃	C₄×D₄	1	4	yes	—
369	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
370	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
371	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
372	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
373	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
374	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
375	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
376	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
377	C₂×#67	—	2	2	no	—
378	C₂×#67	—	2	2	no	—
379	C₂×#67	C₂×C₄×C₅	1	4	yes	—
380	C₂²×Dic₃	—	2	2	no	—
381	C₂²×Dic₃	—	2	2	no	—
382	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
383	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
384	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
385	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
386	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
387	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
388	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
389	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₄×D₃	—	2	2	no	—
391	C₂×C₄×D₃	—	2	2	no	—
392	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
393	C₃×C₄⋊C₄	—	2	2	no	—
394	C₃×C₂²⋊C₄	—	2	2	no	—
395	C₃×C₂²⋊C₄	—	2	2	no	—
396	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
397	C₃×C₄²	—	2	2	no	—
398	#217	—	2	2	no	—
399	#217	—	2	2	no	—
400	(C₂×D₃)⋊C₄	—	2	2	no	—
401	(C₂×D₃)⋊C₄	—	2	2	no	—
402	(C₂×D₃)⋊C₄	—	2	2	no	—
403	(C₂×D₃)⋊C₄	—	2	2	no	—
404	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
405	C₄⋊Dic₃	—	2	2	no	—
406	Dic₃⋊C₄	—	2	2	no	—
407	Dic₃⋊C₄	—	2	2	no	—
408	Dic₃⋊C₄	—	2	2	no	—
409	Dic₃⋊C₄	—	2	2	no	—
410	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
411	C₄×Dic₃	—	2	2	no	—
412	C₄×Dic₃	—	2	2	no	—
413	C₄×Dic₃	—	2	2	no	—
414	C₄×Dic₃	—	2	2	no	—
415	C₄×Dic₃	—	2	2	no	—
416	C₄×Dic₃	—	2	2	no	—
417	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
418	C₄×Dic₃	C₅×D₄	1	4	yes	complemented
419	C₂³×C₅	—	2	1	no	—
420	C₂³×C₅	—	2	1	no	—
421	C₂³×C₅	—	2	1	no	—
422	C₂³×C₅	—	2	1	no	—
423	C₂³×C₅	—	2	1	no	—
424	C₂³×C₅	—	2	1	no	—
425	C₂³×C₅	—	3	2	no	—
426	C₂³×C₅	—	6	1	no	—
427	C₂³×C₅	—	6	1	no	—
428	C₂³×C₅	—	6	1	no	—
429	C₂³×C₅	—	6	1	no	—
430	C₂³×C₅	—	6	1	no	—
431	C₂³×C₅	—	6	1	no	—
432	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
433	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
434	C₅×D₄	—	6	8	no	—
435	C₂×C₄×C₅	—	2	1	no	—
436	C₂×C₄×C₅	—	2	1	no	—
437	C₂×C₄×C₅	—	2	1	no	—
438	C₂×C₄×C₅	—	2	1	no	—
439	C₂×C₄×C₅	—	2	1	no	—
440	C₂×C₄×C₅	—	2	1	no	—
441	C₂×C₄×C₅	—	2	1	no	—
442	C₂×C₄×C₅	—	2	1	no	—
443	C₂×C₄×C₅	—	2	1	no	—
444	C₂×C₄×C₅	—	2	1	no	—
445	C₂×C₄×C₅	—	2	1	no	—
446	C₂×C₄×C₅	—	2	1	no	—
447	C₂×C₄×C₅	—	2	1	no	—
448	C₂×C₄×C₅	—	2	1	no	—
449	C₂×C₄×C₅	—	3	2	no	—
450	C₂×C₄×C₅	—	3	2	no	—
451	C₂×C₄×C₅	—	3	2	no	—
452	C₂×C₄×C₅	—	3	2	no	—
453	C₂×C₄×C₅	—	3	2	no	—
454	C₂×C₄×C₅	—	3	2	no	—
455	C₂×C₄×C₅	—	3	2	no	—
456	C₂×C₄×C₅	—	3	2	no	—
457	C₂×C₄×C₅	—	3	2	no	—
458	C₂×C₄×C₅	—	6	8	no	—
459	C₂×C₄×C₅	—	6	8	no	—
460	C₂×C₄×C₅	—	6	1	no	—
461	C₂×C₄×C₅	—	6	1	no	—
462	C₂×C₄×C₅	—	6	1	no	—
463	C₂×C₄×C₅	—	6	1	no	—
464	C₂×C₄×C₅	—	6	1	no	—
465	C₂×C₄×C₅	—	6	1	no	—
466	C₂×C₄×C₅	—	6	1	no	—
467	C₂×C₄×C₅	—	6	1	no	—
468	C₂×C₄×C₅	—	6	1	no	—
469	C₂×C₄×C₅	—	6	1	no	—
470	C₂×C₄×C₅	—	6	1	no	—
471	C₂×C₄×C₅	—	6	1	no	—
472	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
473	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
474	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
475	C₂×C₄×C₅	#237	1	2	yes	—
476	C₂²×D₄	—	3	1	no	—
477	C₂³×C₄	—	3	1	no	—
478	C₂³×C₄	—	3	1	no	—
479	C₄×D₄	—	3	8	no	—
480	#117	—	6	4	no	—
481	#117	—	6	4	no	—
482	C₂×C₄⋊C₄	—	3	1	no	—
483	C₂×C₄⋊C₄	—	3	1	no	—
484	C₂×C₄⋊C₄	—	3	1	no	—
485	C₂×C₄⋊C₄	—	3	1	no	—
486	C₂×C₄⋊C₄	—	3	1	no	—
487	C₂×C₄⋊C₄	—	3	1	no	—
488	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	—	3	1	no	—
490	C₂×C₂²⋊C₄	—	3	1	no	—
491	C₂×C₂²⋊C₄	—	3	1	no	—
492	C₂×C₂²⋊C₄	—	3	1	no	—
493	C₂×C₂²⋊C₄	—	3	1	no	—
494	C₂×C₂²⋊C₄	—	3	1	no	—
495	C₂×C₂²⋊C₄	—	3	1	no	—
496	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
499	C₂×C₄²	—	3	1	no	—
500	C₂×C₄²	—	3	1	no	—
501	C₂×C₄²	—	3	1	no	—
502	C₂×C₄²	—	3	1	no	—
503	C₂×C₄²	—	3	1	no	—
504	C₂×C₄²	—	3	1	no	—
505	C₂×C₄²	—	3	1	no	—
506	C₂×C₄²	—	3	1	no	—
507	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
508	#95	—	3	1	no	—
509	#95	—	3	1	no	—
510	#95	—	3	1	no	—
511	#95	—	3	1	no	—
512	#95	C₂×C₅×D₃	1	1	yes	characteristic
513	#95	C₂×C₅×D₃	1	1	yes	characteristic
514	C₂×C₃×C₅	—	4	2	no	—
515	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
516	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
517	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
518	C₂×C₃×C₅	#529	1	1	yes	characteristic
519	C₂×C₃×C₅	#529	1	1	yes	characteristic
520	C₂×C₃×C₅	#532	1	1	yes	characteristic
521	C₂×C₃×C₅	#532	1	1	yes	characteristic
522	C₅×D₃	—	4	2	no	—
523	C₂³×C₃	—	2	1	no	—
524	C₂³×C₃	—	2	1	no	—
525	C₂³×C₃	—	2	1	no	—
526	C₂³×C₃	—	2	1	no	—
527	C₂³×C₃	—	2	1	no	—
528	C₂³×C₃	—	2	1	no	—
529	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
530	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
531	C₂²×D₃	—	2	1	no	—
532	C₂²×D₃	—	2	1	no	—
533	C₂²×D₃	—	2	1	no	—
534	C₂²×D₃	—	2	1	no	—
535	C₂²×D₃	—	2	1	no	—
536	C₂²×D₃	—	2	1	no	—
537	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
538	C₂×C₃×C₄	—	2	1	no	—
539	C₂×C₃×C₄	—	2	1	no	—
540	C₂×C₃×C₄	—	2	1	no	—
541	C₂×C₃×C₄	—	2	1	no	—
542	C₂×C₃×C₄	—	2	1	no	—
543	C₂×C₃×C₄	—	2	1	no	—
544	C₂×C₃×C₄	—	2	1	no	—
545	C₂×C₃×C₄	—	2	1	no	—
546	C₂×C₃×C₄	—	2	1	no	—
547	C₂×C₃×C₄	—	2	1	no	—
548	C₂×C₃×C₄	—	2	1	no	—
549	C₂×C₃×C₄	—	2	1	no	—
550	C₂×C₃×C₄	—	2	1	no	—
551	C₂×C₃×C₄	—	2	1	no	—
552	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
553	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
554	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
555	C₂×C₃×C₄	C₅×#41	1	2	yes	—
556	#67	—	2	8	no	—
557	C₂×Dic₃	—	2	1	no	—
558	C₂×Dic₃	—	2	1	no	—
559	C₂×Dic₃	—	2	1	no	—
560	C₂×Dic₃	—	2	1	no	—
561	C₂×Dic₃	—	2	1	no	—
562	C₂×Dic₃	—	2	1	no	—
563	C₂×Dic₃	—	2	8	no	—
564	C₂×Dic₃	—	2	1	no	—
565	C₂×Dic₃	—	2	1	no	—
566	C₂×Dic₃	—	2	1	no	—
567	C₂×Dic₃	—	2	1	no	—
568	C₂×Dic₃	—	2	1	no	—
569	C₂×Dic₃	—	2	1	no	—
570	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
571	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
572	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
573	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
574	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
575	C₂×Dic₃	C₅×#41	1	2	yes	—
576	C₂×Dic₃	C₅×#41	1	2	yes	—
577	C₂×Dic₃	C₅×#41	1	2	yes	—
578	C₂×Dic₃	C₅×#41	1	2	yes	—
579	C₄×D₃	—	2	8	no	—
580	C₂²×C₅	—	2	2	no	—
581	C₂²×C₅	—	2	2	no	—
582	C₂²×C₅	—	2	2	no	—
583	C₂²×C₅	—	4	1	no	—
584	C₂²×C₅	—	4	1	no	—
585	C₂²×C₅	—	4	1	no	—
586	C₂²×C₅	—	4	1	no	—
587	C₂²×C₅	—	6	2	no	—
588	C₂²×C₅	—	6	2	no	—
589	C₂²×C₅	—	6	2	no	—
590	C₂²×C₅	—	12	1	no	—
591	C₂²×C₅	—	12	1	no	—
592	C₂²×C₅	—	12	1	no	—
593	C₂²×C₅	—	12	1	no	—
594	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
595	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
596	C₂²×C₅	C₂×#237	1	1	yes	characteristic
597	C₂²×C₅	D₃×#41	1	1	yes	characteristic
598	C₂²×C₅	D₃×#41	1	1	yes	characteristic
599	C₂²×C₅	D₃×#41	1	1	yes	characteristic
600	C₂²×C₅	D₃×#41	1	1	yes	characteristic
601	C₄×C₅	—	2	2	no	—
602	C₄×C₅	—	2	2	no	—
603	C₄×C₅	—	2	2	no	—
604	C₄×C₅	—	2	2	no	—
605	C₄×C₅	—	3	4	no	—
606	C₄×C₅	—	3	4	no	—
607	C₄×C₅	—	4	1	no	—
608	C₄×C₅	—	4	1	no	—
609	C₄×C₅	—	6	2	no	—
610	C₄×C₅	—	6	2	no	—
611	C₄×C₅	—	6	2	no	—
612	C₄×C₅	—	12	1	no	—
613	C₄×C₅	—	12	1	no	—
614	C₂⁴	—	3	1	no	—
615	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
616	C₂×D₄	—	3	4	no	—
617	C₂×D₄	—	6	2	no	—
618	C₂×D₄	—	6	2	no	—
619	C₂²×C₄	—	3	1	no	—
620	C₂²×C₄	—	3	1	no	—
621	C₂²×C₄	—	3	4	no	—
622	C₂²×C₄	—	3	1	no	—
623	C₂²×C₄	—	3	1	no	—
624	C₂²×C₄	—	3	1	no	—
625	C₂²×C₄	—	3	4	no	—
626	C₂²×C₄	—	3	1	no	—
627	C₂²×C₄	—	3	1	no	—
628	C₂²×C₄	—	6	2	no	—
629	C₂²×C₄	—	6	2	no	—
630	C₂²×C₄	—	6	2	no	—
631	C₂²×C₄	—	6	2	no	—
632	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
633	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
634	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
635	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
636	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
637	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	3	4	no	—
640	C₄⋊C₄	—	6	2	no	—
641	C₄⋊C₄	—	6	2	no	—
642	C₄⋊C₄	—	6	2	no	—
643	C₄⋊C₄	—	6	2	no	—
644	C₄⋊C₄	—	6	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	3	4	no	—
648	C₂²⋊C₄	—	6	2	no	—
649	C₂²⋊C₄	—	6	2	no	—
650	C₂²⋊C₄	—	6	2	no	—
651	C₂²⋊C₄	—	6	2	no	—
652	C₂²⋊C₄	—	6	2	no	—
653	C₂²⋊C₄	—	6	2	no	—
654	C₂²⋊C₄	C₄×C₅×D₃	1	4	yes	—
655	C₄²	—	2	2	no	—
656	C₄²	—	3	4	no	—
657	C₄²	—	3	4	no	—
658	C₄²	—	6	2	no	—
659	C₄²	—	6	2	no	—
660	C₄²	—	6	2	no	—
661	C₄²	—	6	2	no	—
662	C₄²	—	6	2	no	—
663	C₄²	—	6	2	no	—
664	C₃×C₅	#2293	1	1	yes	characteristic, complemented, Hall
665	C₂²×C₃	—	2	2	no	—
666	C₂²×C₃	—	2	2	no	—
667	C₂²×C₃	—	2	2	no	—
668	C₂²×C₃	—	4	1	no	—
669	C₂²×C₃	—	4	1	no	—
670	C₂²×C₃	—	4	1	no	—
671	C₂²×C₃	—	4	1	no	—
672	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
673	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
674	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
675	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
676	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
677	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
678	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
679	C₂×D₃	—	2	2	no	—
680	C₂×D₃	—	2	2	no	—
681	C₂×D₃	—	2	2	no	—
682	C₂×D₃	—	4	1	no	—
683	C₂×D₃	—	4	1	no	—
684	C₂×D₃	—	4	1	no	—
685	C₂×D₃	—	4	1	no	—
686	C₃×C₄	—	2	2	no	—
687	C₃×C₄	—	2	2	no	—
688	C₃×C₄	—	2	2	no	—
689	C₃×C₄	—	2	2	no	—
690	C₃×C₄	—	4	1	no	—
691	C₃×C₄	—	4	1	no	—
692	Dic₃	—	2	2	no	—
693	Dic₃	—	2	2	no	—
694	Dic₃	—	2	2	no	—
695	Dic₃	—	4	1	no	—
696	Dic₃	—	4	1	no	—
697	Dic₃	C₅×#117	1	4	yes	complemented
698	Dic₃	C₄×C₅×D₄	1	4	yes	—
699	C₂×C₅	—	4	2	no	—
700	C₂×C₅	—	12	2	no	—
701	C₂×C₅	D₃×#117	1	1	yes	characteristic
702	C₂×C₅	C₄×#237	1	1	yes	characteristic
703	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
704	C₂×C₅	#5596	1	1	yes	characteristic
705	C₂×C₅	#5649	1	1	yes	characteristic
706	C₂×C₅	#5668	1	1	yes	characteristic
707	C₂×C₅	#5706	1	1	yes	characteristic
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	3	2	no	—
715	C₂³	—	6	1	no	—
716	C₂³	—	6	1	no	—
717	C₂³	—	6	1	no	—
718	C₂³	—	6	1	no	—
719	C₂³	—	6	1	no	—
720	C₂³	—	6	1	no	—
721	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
722	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
723	D₄	—	6	8	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	3	2	no	—
739	C₂×C₄	—	3	2	no	—
740	C₂×C₄	—	3	2	no	—
741	C₂×C₄	—	3	2	no	—
742	C₂×C₄	—	3	2	no	—
743	C₂×C₄	—	3	2	no	—
744	C₂×C₄	—	3	2	no	—
745	C₂×C₄	—	3	2	no	—
746	C₂×C₄	—	3	2	no	—
747	C₂×C₄	—	6	8	no	—
748	C₂×C₄	—	6	8	no	—
749	C₂×C₄	—	6	1	no	—
750	C₂×C₄	—	6	1	no	—
751	C₂×C₄	—	6	1	no	—
752	C₂×C₄	—	6	1	no	—
753	C₂×C₄	—	6	1	no	—
754	C₂×C₄	—	6	1	no	—
755	C₂×C₄	—	6	1	no	—
756	C₂×C₄	—	6	1	no	—
757	C₂×C₄	—	6	1	no	—
758	C₂×C₄	—	6	1	no	—
759	C₂×C₄	—	6	1	no	—
760	C₂×C₄	—	6	1	no	—
761	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
762	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
763	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
764	C₂×C₄	C₅×#237	1	2	yes	—
765	C₂×C₃	—	4	2	no	—
766	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
767	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
768	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
769	C₂×C₃	C₅×#529	1	1	yes	characteristic
770	C₂×C₃	C₅×#529	1	1	yes	characteristic
771	C₂×C₃	C₅×#532	1	1	yes	characteristic
772	C₂×C₃	C₅×#532	1	1	yes	characteristic
773	D₃	—	4	2	no	—
774	C₅	#75450	1	1	yes	characteristic, direct product factor, Sylow
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	6	2	no	—
783	C₂²	—	6	2	no	—
784	C₂²	—	6	2	no	—
785	C₂²	—	12	1	no	—
786	C₂²	—	12	1	no	—
787	C₂²	—	12	1	no	—
788	C₂²	—	12	1	no	—
789	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
790	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
791	C₂²	C₂×C₅×#237	1	1	yes	characteristic
792	C₂²	C₅×D₃×#41	1	1	yes	characteristic
793	C₂²	C₅×D₃×#41	1	1	yes	characteristic
794	C₂²	C₅×D₃×#41	1	1	yes	characteristic
795	C₂²	C₅×D₃×#41	1	1	yes	characteristic
796	C₄	—	2	2	no	—
797	C₄	—	2	2	no	—
798	C₄	—	2	2	no	—
799	C₄	—	2	2	no	—
800	C₄	—	3	4	no	—
801	C₄	—	3	4	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	1	no	—
804	C₄	—	6	2	no	—
805	C₄	—	6	2	no	—
806	C₄	—	6	2	no	—
807	C₄	—	12	1	no	—
808	C₄	—	12	1	no	—
809	C₃	C₅×#2293	1	1	yes	characteristic, complemented, Sylow
810	C₂	—	4	2	no	—
811	C₂	—	12	2	no	—
812	C₂	C₅×D₃×#117	1	1	yes	characteristic
813	C₂	C₄×C₅×#237	1	1	yes	characteristic
814	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
815	C₂	C₅×#5596	1	1	yes	characteristic
816	C₂	C₅×#5649	1	1	yes	characteristic
817	C₂	C₅×#5668	1	1	yes	characteristic
818	C₂	C₅×#5706	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#388	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#67	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#388	D₃
hypocenter	C₃	C₅×#2293
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#388

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#892	C₂	semidirect
3. C₂×C₅×#877	C₂	semidirect
4. C₃×C₅×#388	C₂	semidirect
5. C₅×#4976	C₂	semidirect
8. C₅×#4951	C₂	semidirect
9. C₅×Dic₃×C₂²⋊C₄	C₂	semidirect
10. C₅×#4940	C₂	semidirect
11. C₄²×C₅×Dic₃	C₂	semidirect
12. C₅×#4669	C₂	semidirect
13. C₅×#4666	C₂	semidirect
14. C₅×#4649	C₂	semidirect
15. C₅×#4647	C₂	semidirect
47. C₅×#67⋊C₄	C₄	semidirect
55. #75450	C₅	direct (N × H)
66. C₅×#388	D₃	semidirect
120. C₄×C₅×Dic₃	D₄	semidirect
121. C₂×#892	C₂×C₅	semidirect
123. C₂×#877	C₂×C₅	semidirect
124. C₃×#388	C₂×C₅	semidirect
125. #4976	C₂×C₅	semidirect
128. #4951	C₂×C₅	semidirect
129. Dic₃×C₂²⋊C₄	C₂×C₅	semidirect
130. #4940	C₂×C₅	semidirect
131. C₄²×Dic₃	C₂×C₅	semidirect
132. #4669	C₂×C₅	semidirect
133. #4666	C₂×C₅	semidirect
134. #4649	C₂×C₅	semidirect
135. #4647	C₂×C₅	semidirect
262. #67⋊C₄	C₄×C₅	semidirect
330. #388	C₅×D₃	semidirect
367. C₅×Dic₃	#117	semidirect
418. C₄×Dic₃	C₅×D₄	semidirect
664. C₃×C₅	#2293	semidirect
697. Dic₃	C₅×#117	semidirect
774. C₅	#75450	direct (N × H)
809. C₃	C₅×#2293	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#892	2
C₂×C₅×#67⋊C₄	2
C₂×C₅×#877	2
C₃×C₅×#388	2
C₅×#4976	2
C₅×#4957	2
C₅×#4951	2
C₅×Dic₃×C₂²⋊C₄	2
C₅×#4940	2
C₄²×C₅×Dic₃	2
C₅×#4669	2
C₅×#4666	2
C₅×#4649	2
C₅×#4647	2
C₅×#2293	3
#75450	5

Subgroups — C5×#75450 #14320817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#75450 #14320817