Subgroups — C₃×C₅×#2480 #14275514

Order 1920.

1328 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#396	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic
14	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic
15	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2480	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
20	C₃×C₅×#126	—	2	4	no	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
54	C₃×#2480	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
55	C₂×C₅×#126	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
57	C₅×#397	C₂×C₃	1	1	yes	characteristic, complemented
58	C₅×#397	C₂×C₃	1	1	yes	characteristic, complemented
59	C₅×#397	C₂×C₃	1	1	yes	characteristic, complemented
60	C₅×#396	C₂×C₃	1	1	yes	characteristic, complemented
61	C₅×#388	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#388	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#388	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#379	C₂×C₃	1	1	yes	characteristic
68	C₅×#379	C₂×C₃	1	1	yes	characteristic
69	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
70	C₂⁴×C₃×C₅	—	2	2	no	—
71	C₂⁴×C₃×C₅	—	2	2	no	—
72	C₂⁴×C₃×C₅	—	2	2	no	—
73	C₂⁴×C₃×C₅	—	2	2	no	—
74	C₂⁴×C₃×C₅	—	2	2	no	—
75	C₂⁴×C₃×C₅	—	4	1	no	—
76	C₂⁴×C₃×C₅	—	4	1	no	—
77	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
78	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
79	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	—	2	2	no	—
81	C₂²×C₃×C₄×C₅	—	2	2	no	—
82	C₂²×C₃×C₄×C₅	—	2	2	no	—
83	C₂²×C₃×C₄×C₅	—	2	2	no	—
84	C₂²×C₃×C₄×C₅	—	4	1	no	—
85	C₂²×C₃×C₄×C₅	—	4	1	no	—
86	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
96	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₃×C₅×C₄⋊C₄	—	2	2	no	—
99	C₃×C₅×C₄⋊C₄	—	2	2	no	—
100	C₃×C₅×C₄⋊C₄	—	2	2	no	—
101	C₃×C₅×C₄⋊C₄	—	4	1	no	—
102	C₃×C₅×C₄⋊C₄	—	4	1	no	—
103	C₃×C₅×C₄⋊C₄	—	4	1	no	—
104	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
105	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
106	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
107	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
108	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
109	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
110	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
111	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
112	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
113	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
114	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
115	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
116	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
117	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
118	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
119	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	—
120	C₃×C₄²×C₅	—	2	2	no	—
121	C₃×C₄²×C₅	—	4	1	no	—
122	C₂×C₃×#126	C₂×C₅	1	1	yes	characteristic, complemented
123	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
124	C₃×#397	C₂×C₅	1	1	yes	characteristic, complemented
125	C₃×#397	C₂×C₅	1	1	yes	characteristic, complemented
126	C₃×#397	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×#396	C₂×C₅	1	1	yes	characteristic, complemented
128	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
129	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#379	C₂×C₅	1	1	yes	characteristic
135	C₃×#379	C₂×C₅	1	1	yes	characteristic
136	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
137	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
138	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
139	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
140	C₅×#126	—	2	4	no	—
141	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
142	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
143	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
144	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
145	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
146	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
147	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
148	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
160	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
161	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
162	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
165	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
174	#2480	C₃×C₅	1	1	yes	characteristic, direct product factor, 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	8	no	—
180	C₂³×C₃×C₅	—	2	1	no	—
181	C₂³×C₃×C₅	—	2	1	no	—
182	C₂³×C₃×C₅	—	2	1	no	—
183	C₂³×C₃×C₅	—	2	1	no	—
184	C₂³×C₃×C₅	—	2	1	no	—
185	C₂³×C₃×C₅	—	2	1	no	—
186	C₂³×C₃×C₅	—	2	1	no	—
187	C₂³×C₃×C₅	—	2	1	no	—
188	C₂³×C₃×C₅	—	2	1	no	—
189	C₂³×C₃×C₅	—	2	1	no	—
190	C₂³×C₃×C₅	—	2	1	no	—
191	C₂³×C₃×C₅	—	2	1	no	—
192	C₂³×C₃×C₅	—	4	4	no	—
193	C₂³×C₃×C₅	—	4	4	no	—
194	C₂³×C₃×C₅	—	4	4	no	—
195	C₂³×C₃×C₅	—	4	4	no	—
196	C₂³×C₃×C₅	—	4	4	no	—
197	C₂³×C₃×C₅	—	4	4	no	—
198	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
199	C₂³×C₃×C₅	#41	1	2	yes	—
200	C₂³×C₃×C₅	#41	1	2	yes	—
201	C₂³×C₃×C₅	#41	1	2	yes	—
202	C₂³×C₃×C₅	#41	1	2	yes	—
203	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	—	2	1	no	—
209	C₂×C₃×C₄×C₅	—	2	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	1	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	2	1	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	2	1	no	—
224	C₂×C₃×C₄×C₅	—	2	1	no	—
225	C₂×C₃×C₄×C₅	—	2	1	no	—
226	C₂×C₃×C₄×C₅	—	2	1	no	—
227	C₂×C₃×C₄×C₅	—	2	1	no	—
228	C₂×C₃×C₄×C₅	—	2	1	no	—
229	C₂×C₃×C₄×C₅	—	2	1	no	—
230	C₂×C₃×C₄×C₅	—	2	1	no	—
231	C₂×C₃×C₄×C₅	—	2	1	no	—
232	C₂×C₃×C₄×C₅	—	2	1	no	—
233	C₂×C₃×C₄×C₅	—	2	1	no	—
234	C₂×C₃×C₄×C₅	—	2	1	no	—
235	C₂×C₃×C₄×C₅	—	2	1	no	—
236	C₂×C₃×C₄×C₅	—	2	1	no	—
237	C₂×C₃×C₄×C₅	—	2	1	no	—
238	C₂×C₃×C₄×C₅	—	4	4	no	—
239	C₂×C₃×C₄×C₅	—	4	4	no	—
240	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
241	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
242	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
243	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
244	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
245	C₃×#126	—	2	4	no	—
246	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
247	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
248	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
249	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
250	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
251	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
252	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
267	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
268	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
269	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
275	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
276	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
277	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
278	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₂⁴×C₅	—	2	2	no	—
280	C₂⁴×C₅	—	2	2	no	—
281	C₂⁴×C₅	—	2	2	no	—
282	C₂⁴×C₅	—	2	2	no	—
283	C₂⁴×C₅	—	2	2	no	—
284	C₂⁴×C₅	—	4	1	no	—
285	C₂⁴×C₅	—	4	1	no	—
286	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
287	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
288	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
289	C₂²×C₄×C₅	—	2	2	no	—
290	C₂²×C₄×C₅	—	2	2	no	—
291	C₂²×C₄×C₅	—	2	2	no	—
292	C₂²×C₄×C₅	—	2	2	no	—
293	C₂²×C₄×C₅	—	4	1	no	—
294	C₂²×C₄×C₅	—	4	1	no	—
295	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
296	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
297	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
299	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
300	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
301	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
302	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
303	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
304	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
305	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
306	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
307	C₅×C₄⋊C₄	—	2	2	no	—
308	C₅×C₄⋊C₄	—	2	2	no	—
309	C₅×C₄⋊C₄	—	2	2	no	—
310	C₅×C₄⋊C₄	—	4	1	no	—
311	C₅×C₄⋊C₄	—	4	1	no	—
312	C₅×C₄⋊C₄	—	4	1	no	—
313	C₅×C₂²⋊C₄	—	2	2	no	—
314	C₅×C₂²⋊C₄	—	2	2	no	—
315	C₅×C₂²⋊C₄	—	2	2	no	—
316	C₅×C₂²⋊C₄	—	2	2	no	—
317	C₅×C₂²⋊C₄	—	2	2	no	—
318	C₅×C₂²⋊C₄	—	2	2	no	—
319	C₅×C₂²⋊C₄	—	2	2	no	—
320	C₅×C₂²⋊C₄	—	2	2	no	—
321	C₅×C₂²⋊C₄	—	2	2	no	—
322	C₅×C₂²⋊C₄	—	2	2	no	—
323	C₅×C₂²⋊C₄	—	2	2	no	—
324	C₅×C₂²⋊C₄	—	4	1	no	—
325	C₅×C₂²⋊C₄	—	4	1	no	—
326	C₅×C₂²⋊C₄	—	4	1	no	—
327	C₅×C₂²⋊C₄	—	4	1	no	—
328	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	—
329	C₄²×C₅	—	2	2	no	—
330	C₄²×C₅	—	4	1	no	—
331	C₂×#126	C₂×C₃×C₅	1	1	yes	characteristic, complemented
332	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
333	#397	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	#397	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	#397	C₂×C₃×C₅	1	1	yes	characteristic, complemented
336	#396	C₂×C₃×C₅	1	1	yes	characteristic, complemented
337	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
338	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
339	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
340	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
341	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
342	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
343	#379	C₂×C₃×C₅	1	1	yes	characteristic
344	#379	C₂×C₃×C₅	1	1	yes	characteristic
345	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
346	C₂²×C₃×C₅	—	2	2	no	—
347	C₂²×C₃×C₅	—	2	2	no	—
348	C₂²×C₃×C₅	—	2	2	no	—
349	C₂²×C₃×C₅	—	2	2	no	—
350	C₂²×C₃×C₅	—	2	2	no	—
351	C₂²×C₃×C₅	—	2	2	no	—
352	C₂²×C₃×C₅	—	2	2	no	—
353	C₂²×C₃×C₅	—	2	2	no	—
354	C₂²×C₃×C₅	—	2	2	no	—
355	C₂²×C₃×C₅	—	2	2	no	—
356	C₂²×C₃×C₅	—	2	2	no	—
357	C₂²×C₃×C₅	—	2	2	no	—
358	C₂²×C₃×C₅	—	4	16	no	—
359	C₂²×C₃×C₅	—	4	1	no	—
360	C₂²×C₃×C₅	—	4	1	no	—
361	C₂²×C₃×C₅	—	4	1	no	—
362	C₂²×C₃×C₅	—	4	1	no	—
363	C₂²×C₃×C₅	—	4	1	no	—
364	C₂²×C₃×C₅	—	4	1	no	—
365	C₂²×C₃×C₅	—	4	1	no	—
366	C₂²×C₃×C₅	—	4	1	no	—
367	C₂²×C₃×C₅	#126	1	4	yes	complemented
368	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
369	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
370	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
371	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
372	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
373	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
374	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
375	C₃×C₄×C₅	—	2	2	no	—
376	C₃×C₄×C₅	—	2	2	no	—
377	C₃×C₄×C₅	—	4	1	no	—
378	C₃×C₄×C₅	—	4	1	no	—
379	C₃×C₄×C₅	—	4	1	no	—
380	C₃×C₄×C₅	—	4	1	no	—
381	C₃×C₄×C₅	—	4	1	no	—
382	C₃×C₄×C₅	—	4	1	no	—
383	C₃×C₄×C₅	—	4	1	no	—
384	C₃×C₄×C₅	—	4	1	no	—
385	C₃×C₄×C₅	—	4	1	no	—
386	C₃×C₄×C₅	—	4	1	no	—
387	C₂⁴×C₃	—	2	2	no	—
388	C₂⁴×C₃	—	2	2	no	—
389	C₂⁴×C₃	—	2	2	no	—
390	C₂⁴×C₃	—	2	2	no	—
391	C₂⁴×C₃	—	2	2	no	—
392	C₂⁴×C₃	—	4	1	no	—
393	C₂⁴×C₃	—	4	1	no	—
394	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
395	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
396	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
397	C₂²×C₃×C₄	—	2	2	no	—
398	C₂²×C₃×C₄	—	2	2	no	—
399	C₂²×C₃×C₄	—	2	2	no	—
400	C₂²×C₃×C₄	—	2	2	no	—
401	C₂²×C₃×C₄	—	4	1	no	—
402	C₂²×C₃×C₄	—	4	1	no	—
403	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
404	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
405	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
406	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
407	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
408	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
409	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
410	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
411	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
412	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
413	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
414	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
415	C₃×C₄⋊C₄	—	2	2	no	—
416	C₃×C₄⋊C₄	—	2	2	no	—
417	C₃×C₄⋊C₄	—	2	2	no	—
418	C₃×C₄⋊C₄	—	4	1	no	—
419	C₃×C₄⋊C₄	—	4	1	no	—
420	C₃×C₄⋊C₄	—	4	1	no	—
421	C₃×C₂²⋊C₄	—	2	2	no	—
422	C₃×C₂²⋊C₄	—	2	2	no	—
423	C₃×C₂²⋊C₄	—	2	2	no	—
424	C₃×C₂²⋊C₄	—	2	2	no	—
425	C₃×C₂²⋊C₄	—	2	2	no	—
426	C₃×C₂²⋊C₄	—	2	2	no	—
427	C₃×C₂²⋊C₄	—	2	2	no	—
428	C₃×C₂²⋊C₄	—	2	2	no	—
429	C₃×C₂²⋊C₄	—	2	2	no	—
430	C₃×C₂²⋊C₄	—	2	2	no	—
431	C₃×C₂²⋊C₄	—	2	2	no	—
432	C₃×C₂²⋊C₄	—	4	1	no	—
433	C₃×C₂²⋊C₄	—	4	1	no	—
434	C₃×C₂²⋊C₄	—	4	1	no	—
435	C₃×C₂²⋊C₄	—	4	1	no	—
436	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	—
437	C₃×C₄²	—	2	2	no	—
438	C₃×C₄²	—	4	1	no	—
439	C₂³×C₅	—	2	1	no	—
440	C₂³×C₅	—	2	1	no	—
441	C₂³×C₅	—	2	1	no	—
442	C₂³×C₅	—	2	1	no	—
443	C₂³×C₅	—	2	8	no	—
444	C₂³×C₅	—	2	1	no	—
445	C₂³×C₅	—	2	1	no	—
446	C₂³×C₅	—	2	1	no	—
447	C₂³×C₅	—	2	1	no	—
448	C₂³×C₅	—	2	1	no	—
449	C₂³×C₅	—	2	1	no	—
450	C₂³×C₅	—	2	1	no	—
451	C₂³×C₅	—	2	1	no	—
452	C₂³×C₅	—	2	1	no	—
453	C₂³×C₅	—	2	1	no	—
454	C₂³×C₅	—	2	1	no	—
455	C₂³×C₅	—	2	1	no	—
456	C₂³×C₅	—	4	4	no	—
457	C₂³×C₅	—	4	4	no	—
458	C₂³×C₅	—	4	4	no	—
459	C₂³×C₅	—	4	4	no	—
460	C₂³×C₅	—	4	4	no	—
461	C₂³×C₅	—	4	4	no	—
462	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
463	C₂³×C₅	C₃×#41	1	2	yes	—
464	C₂³×C₅	C₃×#41	1	2	yes	—
465	C₂³×C₅	C₃×#41	1	2	yes	—
466	C₂³×C₅	C₃×#41	1	2	yes	—
467	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
468	C₂×C₄×C₅	—	2	1	no	—
469	C₂×C₄×C₅	—	2	1	no	—
470	C₂×C₄×C₅	—	2	1	no	—
471	C₂×C₄×C₅	—	2	1	no	—
472	C₂×C₄×C₅	—	2	1	no	—
473	C₂×C₄×C₅	—	2	1	no	—
474	C₂×C₄×C₅	—	2	1	no	—
475	C₂×C₄×C₅	—	2	1	no	—
476	C₂×C₄×C₅	—	2	1	no	—
477	C₂×C₄×C₅	—	2	1	no	—
478	C₂×C₄×C₅	—	2	1	no	—
479	C₂×C₄×C₅	—	2	1	no	—
480	C₂×C₄×C₅	—	2	1	no	—
481	C₂×C₄×C₅	—	2	1	no	—
482	C₂×C₄×C₅	—	2	1	no	—
483	C₂×C₄×C₅	—	2	1	no	—
484	C₂×C₄×C₅	—	2	1	no	—
485	C₂×C₄×C₅	—	2	1	no	—
486	C₂×C₄×C₅	—	2	1	no	—
487	C₂×C₄×C₅	—	2	1	no	—
488	C₂×C₄×C₅	—	2	1	no	—
489	C₂×C₄×C₅	—	2	1	no	—
490	C₂×C₄×C₅	—	2	1	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	2	1	no	—
493	C₂×C₄×C₅	—	2	1	no	—
494	C₂×C₄×C₅	—	2	1	no	—
495	C₂×C₄×C₅	—	2	1	no	—
496	C₂×C₄×C₅	—	2	1	no	—
497	C₂×C₄×C₅	—	2	1	no	—
498	C₂×C₄×C₅	—	2	1	no	—
499	C₂×C₄×C₅	—	2	1	no	—
500	C₂×C₄×C₅	—	2	1	no	—
501	C₂×C₄×C₅	—	2	1	no	—
502	C₂×C₄×C₅	—	4	4	no	—
503	C₂×C₄×C₅	—	4	4	no	—
504	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
505	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
506	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
507	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
508	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
509	#126	—	2	4	no	—
510	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
511	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
512	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
513	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
514	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
515	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
516	C₂×C₂²⋊C₄	—	2	4	no	—
517	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
533	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
534	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
535	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
536	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
537	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
538	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
539	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
540	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
541	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
542	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
543	C₂×C₃×C₅	—	2	4	no	—
544	C₂×C₃×C₅	—	4	2	no	—
545	C₂×C₃×C₅	—	4	2	no	—
546	C₂×C₃×C₅	#525	1	1	yes	characteristic
547	C₂×C₃×C₅	C₂×#126	1	1	yes	characteristic
548	C₂×C₃×C₅	#538	1	1	yes	characteristic
549	C₂×C₃×C₅	#546	1	1	yes	characteristic
550	C₂×C₃×C₅	#546	1	1	yes	characteristic
551	C₂×C₃×C₅	#551	1	1	yes	characteristic
552	C₂×C₃×C₅	#551	1	1	yes	characteristic
553	C₂³×C₃	—	2	1	no	—
554	C₂³×C₃	—	2	1	no	—
555	C₂³×C₃	—	2	1	no	—
556	C₂³×C₃	—	2	1	no	—
557	C₂³×C₃	—	2	8	no	—
558	C₂³×C₃	—	2	1	no	—
559	C₂³×C₃	—	2	1	no	—
560	C₂³×C₃	—	2	1	no	—
561	C₂³×C₃	—	2	1	no	—
562	C₂³×C₃	—	2	1	no	—
563	C₂³×C₃	—	2	1	no	—
564	C₂³×C₃	—	2	1	no	—
565	C₂³×C₃	—	2	1	no	—
566	C₂³×C₃	—	2	1	no	—
567	C₂³×C₃	—	2	1	no	—
568	C₂³×C₃	—	2	1	no	—
569	C₂³×C₃	—	2	1	no	—
570	C₂³×C₃	—	4	4	no	—
571	C₂³×C₃	—	4	4	no	—
572	C₂³×C₃	—	4	4	no	—
573	C₂³×C₃	—	4	4	no	—
574	C₂³×C₃	—	4	4	no	—
575	C₂³×C₃	—	4	4	no	—
576	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
577	C₂³×C₃	C₅×#41	1	2	yes	—
578	C₂³×C₃	C₅×#41	1	2	yes	—
579	C₂³×C₃	C₅×#41	1	2	yes	—
580	C₂³×C₃	C₅×#41	1	2	yes	—
581	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
582	C₂×C₃×C₄	—	2	1	no	—
583	C₂×C₃×C₄	—	2	1	no	—
584	C₂×C₃×C₄	—	2	1	no	—
585	C₂×C₃×C₄	—	2	1	no	—
586	C₂×C₃×C₄	—	2	1	no	—
587	C₂×C₃×C₄	—	2	1	no	—
588	C₂×C₃×C₄	—	2	1	no	—
589	C₂×C₃×C₄	—	2	1	no	—
590	C₂×C₃×C₄	—	2	1	no	—
591	C₂×C₃×C₄	—	2	1	no	—
592	C₂×C₃×C₄	—	2	1	no	—
593	C₂×C₃×C₄	—	2	1	no	—
594	C₂×C₃×C₄	—	2	1	no	—
595	C₂×C₃×C₄	—	2	1	no	—
596	C₂×C₃×C₄	—	2	1	no	—
597	C₂×C₃×C₄	—	2	1	no	—
598	C₂×C₃×C₄	—	2	1	no	—
599	C₂×C₃×C₄	—	2	1	no	—
600	C₂×C₃×C₄	—	2	1	no	—
601	C₂×C₃×C₄	—	2	1	no	—
602	C₂×C₃×C₄	—	2	1	no	—
603	C₂×C₃×C₄	—	2	1	no	—
604	C₂×C₃×C₄	—	2	1	no	—
605	C₂×C₃×C₄	—	2	1	no	—
606	C₂×C₃×C₄	—	2	1	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	1	no	—
609	C₂×C₃×C₄	—	2	1	no	—
610	C₂×C₃×C₄	—	2	1	no	—
611	C₂×C₃×C₄	—	2	1	no	—
612	C₂×C₃×C₄	—	2	1	no	—
613	C₂×C₃×C₄	—	2	1	no	—
614	C₂×C₃×C₄	—	2	1	no	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	4	4	no	—
617	C₂×C₃×C₄	—	4	4	no	—
618	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
619	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
620	C₂²×C₅	—	2	2	no	—
621	C₂²×C₅	—	2	2	no	—
622	C₂²×C₅	—	2	2	no	—
623	C₂²×C₅	—	2	2	no	—
624	C₂²×C₅	—	2	2	no	—
625	C₂²×C₅	—	2	2	no	—
626	C₂²×C₅	—	2	2	no	—
627	C₂²×C₅	—	2	2	no	—
628	C₂²×C₅	—	2	2	no	—
629	C₂²×C₅	—	2	2	no	—
630	C₂²×C₅	—	2	2	no	—
631	C₂²×C₅	—	2	2	no	—
632	C₂²×C₅	—	4	16	no	—
633	C₂²×C₅	—	4	1	no	—
634	C₂²×C₅	—	4	1	no	—
635	C₂²×C₅	—	4	1	no	—
636	C₂²×C₅	—	4	1	no	—
637	C₂²×C₅	—	4	1	no	—
638	C₂²×C₅	—	4	1	no	—
639	C₂²×C₅	—	4	1	no	—
640	C₂²×C₅	—	4	1	no	—
641	C₂²×C₅	C₃×#126	1	4	yes	complemented
642	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
643	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
644	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
645	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
646	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
647	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
648	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
649	C₄×C₅	—	2	2	no	—
650	C₄×C₅	—	2	2	no	—
651	C₄×C₅	—	4	1	no	—
652	C₄×C₅	—	4	1	no	—
653	C₄×C₅	—	4	1	no	—
654	C₄×C₅	—	4	1	no	—
655	C₄×C₅	—	4	1	no	—
656	C₄×C₅	—	4	1	no	—
657	C₄×C₅	—	4	1	no	—
658	C₄×C₅	—	4	1	no	—
659	C₄×C₅	—	4	1	no	—
660	C₄×C₅	—	4	1	no	—
661	C₂⁴	—	2	2	no	—
662	C₂⁴	—	2	2	no	—
663	C₂⁴	—	2	2	no	—
664	C₂⁴	—	2	2	no	—
665	C₂⁴	—	2	2	no	—
666	C₂⁴	—	4	1	no	—
667	C₂⁴	—	4	1	no	—
668	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
669	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
670	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	4	1	no	—
676	C₂²×C₄	—	4	1	no	—
677	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
678	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
679	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
680	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
681	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
682	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
683	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
684	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
685	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
686	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
687	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
688	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	4	1	no	—
693	C₄⋊C₄	—	4	1	no	—
694	C₄⋊C₄	—	4	1	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	4	1	no	—
707	C₂²⋊C₄	—	4	1	no	—
708	C₂²⋊C₄	—	4	1	no	—
709	C₂²⋊C₄	—	4	1	no	—
710	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	—
711	C₄²	—	2	2	no	—
712	C₄²	—	4	1	no	—
713	C₃×C₅	#2480	1	1	yes	characteristic, direct product factor, Hall
714	C₂²×C₃	—	2	2	no	—
715	C₂²×C₃	—	2	2	no	—
716	C₂²×C₃	—	2	2	no	—
717	C₂²×C₃	—	2	2	no	—
718	C₂²×C₃	—	2	2	no	—
719	C₂²×C₃	—	2	2	no	—
720	C₂²×C₃	—	2	2	no	—
721	C₂²×C₃	—	2	2	no	—
722	C₂²×C₃	—	2	2	no	—
723	C₂²×C₃	—	2	2	no	—
724	C₂²×C₃	—	2	2	no	—
725	C₂²×C₃	—	2	2	no	—
726	C₂²×C₃	—	4	16	no	—
727	C₂²×C₃	—	4	1	no	—
728	C₂²×C₃	—	4	1	no	—
729	C₂²×C₃	—	4	1	no	—
730	C₂²×C₃	—	4	1	no	—
731	C₂²×C₃	—	4	1	no	—
732	C₂²×C₃	—	4	1	no	—
733	C₂²×C₃	—	4	1	no	—
734	C₂²×C₃	—	4	1	no	—
735	C₂²×C₃	C₅×#126	1	4	yes	complemented
736	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
737	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
738	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
739	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
740	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
741	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
742	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
743	C₃×C₄	—	2	2	no	—
744	C₃×C₄	—	2	2	no	—
745	C₃×C₄	—	4	1	no	—
746	C₃×C₄	—	4	1	no	—
747	C₃×C₄	—	4	1	no	—
748	C₃×C₄	—	4	1	no	—
749	C₃×C₄	—	4	1	no	—
750	C₃×C₄	—	4	1	no	—
751	C₃×C₄	—	4	1	no	—
752	C₃×C₄	—	4	1	no	—
753	C₃×C₄	—	4	1	no	—
754	C₃×C₄	—	4	1	no	—
755	C₂×C₅	—	2	4	no	—
756	C₂×C₅	—	4	2	no	—
757	C₂×C₅	—	4	2	no	—
758	C₂×C₅	C₃×#525	1	1	yes	characteristic
759	C₂×C₅	C₂×C₃×#126	1	1	yes	characteristic
760	C₂×C₅	C₃×#538	1	1	yes	characteristic
761	C₂×C₅	C₃×#546	1	1	yes	characteristic
762	C₂×C₅	C₃×#546	1	1	yes	characteristic
763	C₂×C₅	C₃×#551	1	1	yes	characteristic
764	C₂×C₅	C₃×#551	1	1	yes	characteristic
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	2	8	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	4	4	no	—
783	C₂³	—	4	4	no	—
784	C₂³	—	4	4	no	—
785	C₂³	—	4	4	no	—
786	C₂³	—	4	4	no	—
787	C₂³	—	4	4	no	—
788	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
789	C₂³	C₃×C₅×#41	1	2	yes	—
790	C₂³	C₃×C₅×#41	1	2	yes	—
791	C₂³	C₃×C₅×#41	1	2	yes	—
792	C₂³	C₃×C₅×#41	1	2	yes	—
793	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	4	4	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
831	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
832	C₂×C₃	—	2	4	no	—
833	C₂×C₃	—	4	2	no	—
834	C₂×C₃	—	4	2	no	—
835	C₂×C₃	C₅×#525	1	1	yes	characteristic
836	C₂×C₃	C₂×C₅×#126	1	1	yes	characteristic
837	C₂×C₃	C₅×#538	1	1	yes	characteristic
838	C₂×C₃	C₅×#546	1	1	yes	characteristic
839	C₂×C₃	C₅×#546	1	1	yes	characteristic
840	C₂×C₃	C₅×#551	1	1	yes	characteristic
841	C₂×C₃	C₅×#551	1	1	yes	characteristic
842	C₅	C₃×#2480	1	1	yes	characteristic, direct product factor, Sylow
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	2	2	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	4	16	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	C₃×C₅×#126	1	4	yes	complemented
865	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
866	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
867	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
868	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
869	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
870	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
871	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
872	C₄	—	2	2	no	—
873	C₄	—	2	2	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	1	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	1	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	1	no	—
884	C₃	C₅×#2480	1	1	yes	characteristic, direct product factor, Sylow
885	C₂	—	2	4	no	—
886	C₂	—	4	2	no	—
887	C₂	—	4	2	no	—
888	C₂	C₃×C₅×#525	1	1	yes	characteristic
889	C₂	C₂×C₃×C₅×#126	1	1	yes	characteristic
890	C₂	C₃×C₅×#538	1	1	yes	characteristic
891	C₂	C₃×C₅×#546	1	1	yes	characteristic
892	C₂	C₃×C₅×#546	1	1	yes	characteristic
893	C₂	C₃×C₅×#551	1	1	yes	characteristic
894	C₂	C₃×C₅×#551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁵×C₃×C₅	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#126	C₂	semidirect
3. C₃×C₅×#397	C₂	semidirect
4. C₃×C₅×#397	C₂	semidirect
5. C₃×C₅×#397	C₂	semidirect
6. C₃×C₅×#396	C₂	semidirect
7. C₃×C₅×#388	C₂	semidirect
8. C₃×C₅×#388	C₂	semidirect
9. C₃×C₅×#388	C₂	semidirect
10. C₃×C₅×#385	C₂	semidirect
11. C₃×C₅×#385	C₂	semidirect
12. C₃×C₅×#380	C₂	semidirect
15. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
16. C₅×#2480	C₃	direct (N × H)
21. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
22. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
23. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
24. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
25. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
26. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
44. C₂×C₃×C₄²×C₅	C₂²	semidirect
45. C₂×C₃×C₄²×C₅	C₂²	semidirect
46. C₃×C₅×#95	C₂²	semidirect
47. C₃×C₅×#95	C₂²	semidirect
48. C₃×C₅×#95	C₂²	semidirect
49. C₃×C₅×#95	C₂²	semidirect
50. C₃×C₅×#95	C₂²	semidirect
51. C₃×C₅×#95	C₂²	semidirect
52. C₃×C₅×#95	C₂²	semidirect
53. C₃×C₅×#95	C₂²	semidirect
54. C₃×#2480	C₅	direct (N × H)
55. C₂×C₅×#126	C₂×C₃	semidirect
57. C₅×#397	C₂×C₃	semidirect
58. C₅×#397	C₂×C₃	semidirect
59. C₅×#397	C₂×C₃	semidirect
60. C₅×#396	C₂×C₃	semidirect
61. C₅×#388	C₂×C₃	semidirect
62. C₅×#388	C₂×C₃	semidirect
63. C₅×#388	C₂×C₃	semidirect
64. C₅×#385	C₂×C₃	semidirect
65. C₅×#385	C₂×C₃	semidirect
66. C₅×#380	C₂×C₃	semidirect
69. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
122. C₂×C₃×#126	C₂×C₅	semidirect
124. C₃×#397	C₂×C₅	semidirect
125. C₃×#397	C₂×C₅	semidirect
126. C₃×#397	C₂×C₅	semidirect
127. C₃×#396	C₂×C₅	semidirect
128. C₃×#388	C₂×C₅	semidirect
129. C₃×#388	C₂×C₅	semidirect
130. C₃×#388	C₂×C₅	semidirect
131. C₃×#385	C₂×C₅	semidirect
132. C₃×#385	C₂×C₅	semidirect
133. C₃×#380	C₂×C₅	semidirect
136. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
141. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
142. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
143. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
144. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
145. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
146. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
164. C₂×C₄²×C₅	C₂²×C₃	semidirect
165. C₂×C₄²×C₅	C₂²×C₃	semidirect
166. C₅×#95	C₂²×C₃	semidirect
167. C₅×#95	C₂²×C₃	semidirect
168. C₅×#95	C₂²×C₃	semidirect
169. C₅×#95	C₂²×C₃	semidirect
170. C₅×#95	C₂²×C₃	semidirect
171. C₅×#95	C₂²×C₃	semidirect
172. C₅×#95	C₂²×C₃	semidirect
173. C₅×#95	C₂²×C₃	semidirect
174. #2480	C₃×C₅	direct (N × H)
246. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
247. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
248. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
249. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
250. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
251. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
269. C₂×C₃×C₄²	C₂²×C₅	semidirect
270. C₂×C₃×C₄²	C₂²×C₅	semidirect
271. C₃×#95	C₂²×C₅	semidirect
272. C₃×#95	C₂²×C₅	semidirect
273. C₃×#95	C₂²×C₅	semidirect
274. C₃×#95	C₂²×C₅	semidirect
275. C₃×#95	C₂²×C₅	semidirect
276. C₃×#95	C₂²×C₅	semidirect
277. C₃×#95	C₂²×C₅	semidirect
278. C₃×#95	C₂²×C₅	semidirect
331. C₂×#126	C₂×C₃×C₅	semidirect
333. #397	C₂×C₃×C₅	semidirect
334. #397	C₂×C₃×C₅	semidirect
335. #397	C₂×C₃×C₅	semidirect
336. #396	C₂×C₃×C₅	semidirect
337. #388	C₂×C₃×C₅	semidirect
338. #388	C₂×C₃×C₅	semidirect
339. #388	C₂×C₃×C₅	semidirect
340. #385	C₂×C₃×C₅	semidirect
341. #385	C₂×C₃×C₅	semidirect
342. #380	C₂×C₃×C₅	semidirect
345. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
367. C₂²×C₃×C₅	#126	semidirect
510. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
511. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
512. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
513. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
514. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
515. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
533. C₂×C₄²	C₂²×C₃×C₅	semidirect
534. C₂×C₄²	C₂²×C₃×C₅	semidirect
535. #95	C₂²×C₃×C₅	semidirect
536. #95	C₂²×C₃×C₅	semidirect
537. #95	C₂²×C₃×C₅	semidirect
538. #95	C₂²×C₃×C₅	semidirect
539. #95	C₂²×C₃×C₅	semidirect
540. #95	C₂²×C₃×C₅	semidirect
541. #95	C₂²×C₃×C₅	semidirect
542. #95	C₂²×C₃×C₅	semidirect
641. C₂²×C₅	C₃×#126	semidirect
713. C₃×C₅	#2480	direct (N × H)
735. C₂²×C₃	C₅×#126	semidirect
842. C₅	C₃×#2480	direct (N × H)
864. C₂²	C₃×C₅×#126	semidirect
884. C₃	C₅×#2480	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×#126	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#397	2
C₃×C₅×#396	2
C₃×C₅×#388	2
C₃×C₅×#385	2
C₃×C₅×#380	2
C₃×C₅×#379	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2480	3
C₃×#2480	5

Subgroups — C3×C5×#2480 #14275514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2480 #14275514