Subgroups — C₃×C₅×#2467 #14275501

Order 1920.

1164 conjugacy classes of subgroups.

The subgroup lattice has 876 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	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#392	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#390	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×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2467	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
21	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
22	C₃×C₅×#126	—	2	4	no	—
23	C₃×C₄×C₅×D₄	—	2	4	no	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₄⋊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×C₄²×C₅	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
46	C₃×C₅×#95	C₂²	1	1	yes	characteristic
47	C₃×C₅×#95	C₂²	1	1	yes	characteristic
48	C₃×C₅×#95	C₂²	1	1	yes	characteristic
49	C₃×C₅×#95	C₂²	1	1	yes	characteristic
50	C₃×C₅×#95	C₂²	1	1	yes	characteristic
51	C₃×C₅×#95	C₂²	1	1	yes	characteristic
52	C₃×C₅×#95	C₂²	1	1	yes	characteristic
53	C₃×C₅×#95	C₂²	1	1	yes	characteristic
54	C₃×#2467	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
55	C₂×C₅×#126	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
57	C₅×#399	C₂×C₃	1	1	yes	characteristic, complemented
58	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
59	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
60	C₅×#392	C₂×C₃	1	1	yes	characteristic
61	C₅×#390	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×#387	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
69	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
70	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
71	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
72	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×D₄	—	2	2	no	—
74	C₂×C₃×C₅×D₄	—	2	2	no	—
75	C₂×C₃×C₅×D₄	—	2	2	no	—
76	C₂×C₃×C₅×D₄	—	2	2	no	—
77	C₂×C₃×C₅×D₄	—	2	2	no	—
78	C₂×C₃×C₅×D₄	—	2	2	no	—
79	C₂×C₃×C₅×D₄	—	4	1	no	—
80	C₂×C₃×C₅×D₄	—	4	1	no	—
81	C₂×C₃×C₅×D₄	—	4	1	no	—
82	C₂²×C₃×C₄×C₅	—	2	2	no	—
83	C₂²×C₃×C₄×C₅	—	2	2	no	—
84	C₂²×C₃×C₄×C₅	—	2	2	no	—
85	C₂²×C₃×C₄×C₅	—	2	2	no	—
86	C₂²×C₃×C₄×C₅	—	4	1	no	—
87	C₂²×C₃×C₄×C₅	—	4	1	no	—
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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
100	C₃×C₅×C₄⋊C₄	—	2	2	no	—
101	C₃×C₅×C₄⋊C₄	—	2	2	no	—
102	C₃×C₅×C₄⋊C₄	—	2	2	no	—
103	C₃×C₅×C₄⋊C₄	—	4	1	no	—
104	C₃×C₅×C₄⋊C₄	—	4	1	no	—
105	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	complemented
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×C₄²×C₅	—	2	2	no	—
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	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
124	C₃×#399	C₂×C₅	1	1	yes	characteristic, complemented
125	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
126	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×#392	C₂×C₅	1	1	yes	characteristic
128	C₃×#390	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×#387	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
137	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
138	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
139	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
140	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
141	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
142	C₅×#126	—	2	4	no	—
143	C₄×C₅×D₄	—	2	4	no	—
144	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₅×C₄⋊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×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
166	C₅×#95	C₂²×C₃	1	1	yes	characteristic
167	C₅×#95	C₂²×C₃	1	1	yes	characteristic
168	C₅×#95	C₂²×C₃	1	1	yes	characteristic
169	C₅×#95	C₂²×C₃	1	1	yes	characteristic
170	C₅×#95	C₂²×C₃	1	1	yes	characteristic
171	C₅×#95	C₂²×C₃	1	1	yes	characteristic
172	C₅×#95	C₂²×C₃	1	1	yes	characteristic
173	C₅×#95	C₂²×C₃	1	1	yes	characteristic
174	#2467	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	1	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	—	2	1	no	—
193	C₂³×C₃×C₅	—	2	1	no	—
194	C₂³×C₃×C₅	#41	1	2	yes	—
195	C₂³×C₃×C₅	#41	1	2	yes	—
196	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
197	C₃×C₅×D₄	—	2	8	no	—
198	C₃×C₅×D₄	—	4	4	no	—
199	C₃×C₅×D₄	—	4	4	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	—	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	—	4	4	no	—
232	C₂×C₃×C₄×C₅	—	4	4	no	—
233	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
234	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
235	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
236	C₂×C₃×C₄×C₅	#41	1	2	yes	—
237	C₂×C₃×C₄×C₅	#41	1	2	yes	—
238	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
239	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
240	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
241	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
242	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
243	C₃×#126	—	2	4	no	—
244	C₃×C₄×D₄	—	2	4	no	—
245	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
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×C₄²	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₃×C₄²	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	C₃×#95	C₂²×C₅	1	1	yes	characteristic
271	C₃×#95	C₂²×C₅	1	1	yes	characteristic
272	C₃×#95	C₂²×C₅	1	1	yes	characteristic
273	C₃×#95	C₂²×C₅	1	1	yes	characteristic
274	C₃×#95	C₂²×C₅	1	1	yes	characteristic
275	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
276	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
277	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
278	C₂×C₅×D₄	—	2	2	no	—
279	C₂×C₅×D₄	—	2	2	no	—
280	C₂×C₅×D₄	—	2	2	no	—
281	C₂×C₅×D₄	—	2	2	no	—
282	C₂×C₅×D₄	—	2	2	no	—
283	C₂×C₅×D₄	—	2	2	no	—
284	C₂×C₅×D₄	—	4	1	no	—
285	C₂×C₅×D₄	—	4	1	no	—
286	C₂×C₅×D₄	—	4	1	no	—
287	C₂²×C₄×C₅	—	2	2	no	—
288	C₂²×C₄×C₅	—	2	2	no	—
289	C₂²×C₄×C₅	—	2	2	no	—
290	C₂²×C₄×C₅	—	2	2	no	—
291	C₂²×C₄×C₅	—	4	1	no	—
292	C₂²×C₄×C₅	—	4	1	no	—
293	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
294	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
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	C₅×C₄⋊C₄	—	2	2	no	—
306	C₅×C₄⋊C₄	—	2	2	no	—
307	C₅×C₄⋊C₄	—	2	2	no	—
308	C₅×C₄⋊C₄	—	4	1	no	—
309	C₅×C₄⋊C₄	—	4	1	no	—
310	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	complemented
311	C₅×C₂²⋊C₄	—	2	2	no	—
312	C₅×C₂²⋊C₄	—	2	2	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	—	4	1	no	—
321	C₅×C₂²⋊C₄	—	4	1	no	—
322	C₅×C₂²⋊C₄	—	4	1	no	—
323	C₅×C₂²⋊C₄	—	4	1	no	—
324	C₄²×C₅	—	2	2	no	—
325	C₄²×C₅	—	2	2	no	—
326	C₄²×C₅	—	4	1	no	—
327	C₂×#126	C₂×C₃×C₅	1	1	yes	characteristic, complemented
328	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
329	#399	C₂×C₃×C₅	1	1	yes	characteristic, complemented
330	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
331	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
332	#392	C₂×C₃×C₅	1	1	yes	characteristic
333	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
336	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
337	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
338	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
339	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
340	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
341	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
342	C₂²×C₃×C₅	—	2	2	no	—
343	C₂²×C₃×C₅	—	2	2	no	—
344	C₂²×C₃×C₅	—	2	2	no	—
345	C₂²×C₃×C₅	—	2	2	no	—
346	C₂²×C₃×C₅	—	2	2	no	—
347	C₂²×C₃×C₅	—	2	2	no	—
348	C₂²×C₃×C₅	—	4	1	no	—
349	C₂²×C₃×C₅	—	4	1	no	—
350	C₂²×C₃×C₅	—	4	1	no	—
351	C₂²×C₃×C₅	—	4	1	no	—
352	C₂²×C₃×C₅	—	4	1	no	—
353	C₂²×C₃×C₅	—	4	1	no	—
354	C₂²×C₃×C₅	—	4	1	no	—
355	C₂²×C₃×C₅	—	4	1	no	—
356	C₂²×C₃×C₅	—	4	1	no	—
357	C₂²×C₃×C₅	—	4	1	no	—
358	C₂²×C₃×C₅	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
364	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
365	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
366	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
367	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
368	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
369	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
370	C₃×C₄×C₅	—	2	2	no	—
371	C₃×C₄×C₅	—	2	2	no	—
372	C₃×C₄×C₅	—	2	2	no	—
373	C₃×C₄×C₅	—	2	2	no	—
374	C₃×C₄×C₅	—	2	2	no	—
375	C₃×C₄×C₅	—	4	1	no	—
376	C₃×C₄×C₅	—	4	1	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	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
383	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
384	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₃×D₄	—	2	2	no	—
386	C₂×C₃×D₄	—	2	2	no	—
387	C₂×C₃×D₄	—	2	2	no	—
388	C₂×C₃×D₄	—	2	2	no	—
389	C₂×C₃×D₄	—	2	2	no	—
390	C₂×C₃×D₄	—	2	2	no	—
391	C₂×C₃×D₄	—	4	1	no	—
392	C₂×C₃×D₄	—	4	1	no	—
393	C₂×C₃×D₄	—	4	1	no	—
394	C₂²×C₃×C₄	—	2	2	no	—
395	C₂²×C₃×C₄	—	2	2	no	—
396	C₂²×C₃×C₄	—	2	2	no	—
397	C₂²×C₃×C₄	—	2	2	no	—
398	C₂²×C₃×C₄	—	4	1	no	—
399	C₂²×C₃×C₄	—	4	1	no	—
400	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
401	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
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	C₃×C₄⋊C₄	—	2	2	no	—
413	C₃×C₄⋊C₄	—	2	2	no	—
414	C₃×C₄⋊C₄	—	2	2	no	—
415	C₃×C₄⋊C₄	—	4	1	no	—
416	C₃×C₄⋊C₄	—	4	1	no	—
417	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	complemented
418	C₃×C₂²⋊C₄	—	2	2	no	—
419	C₃×C₂²⋊C₄	—	2	2	no	—
420	C₃×C₂²⋊C₄	—	2	2	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	—	4	1	no	—
428	C₃×C₂²⋊C₄	—	4	1	no	—
429	C₃×C₂²⋊C₄	—	4	1	no	—
430	C₃×C₂²⋊C₄	—	4	1	no	—
431	C₃×C₄²	—	2	2	no	—
432	C₃×C₄²	—	2	2	no	—
433	C₃×C₄²	—	4	1	no	—
434	C₂³×C₅	—	2	1	no	—
435	C₂³×C₅	—	2	1	no	—
436	C₂³×C₅	—	2	1	no	—
437	C₂³×C₅	—	2	1	no	—
438	C₂³×C₅	—	2	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	1	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	C₃×#41	1	2	yes	—
454	C₂³×C₅	C₃×#41	1	2	yes	—
455	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
456	C₅×D₄	—	2	8	no	—
457	C₅×D₄	—	4	4	no	—
458	C₅×D₄	—	4	4	no	—
459	C₂×C₄×C₅	—	2	1	no	—
460	C₂×C₄×C₅	—	2	1	no	—
461	C₂×C₄×C₅	—	2	1	no	—
462	C₂×C₄×C₅	—	2	1	no	—
463	C₂×C₄×C₅	—	2	1	no	—
464	C₂×C₄×C₅	—	2	1	no	—
465	C₂×C₄×C₅	—	2	1	no	—
466	C₂×C₄×C₅	—	2	1	no	—
467	C₂×C₄×C₅	—	2	1	no	—
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	—	4	4	no	—
491	C₂×C₄×C₅	—	4	4	no	—
492	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
493	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
494	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
495	C₂×C₄×C₅	C₃×#41	1	2	yes	—
496	C₂×C₄×C₅	C₃×#41	1	2	yes	—
497	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
498	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
499	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
500	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
501	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
502	#126	—	2	4	no	—
503	C₄×D₄	—	2	4	no	—
504	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
510	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
512	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
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×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
524	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
525	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
526	#95	C₂²×C₃×C₅	1	1	yes	characteristic
527	#95	C₂²×C₃×C₅	1	1	yes	characteristic
528	#95	C₂²×C₃×C₅	1	1	yes	characteristic
529	#95	C₂²×C₃×C₅	1	1	yes	characteristic
530	#95	C₂²×C₃×C₅	1	1	yes	characteristic
531	#95	C₂²×C₃×C₅	1	1	yes	characteristic
532	#95	C₂²×C₃×C₅	1	1	yes	characteristic
533	#95	C₂²×C₃×C₅	1	1	yes	characteristic
534	C₂×C₃×C₅	—	4	2	no	—
535	C₂×C₃×C₅	—	4	2	no	—
536	C₂×C₃×C₅	—	8	1	no	—
537	C₂×C₃×C₅	#525	1	1	yes	characteristic
538	C₂×C₃×C₅	#529	1	1	yes	characteristic
539	C₂×C₃×C₅	#538	1	1	yes	characteristic
540	C₂×C₃×C₅	#546	1	1	yes	characteristic
541	C₂×C₃×C₅	#550	1	1	yes	characteristic
542	C₂×C₃×C₅	#551	1	1	yes	characteristic
543	C₂×C₃×C₅	#553	1	1	yes	characteristic
544	C₂³×C₃	—	2	1	no	—
545	C₂³×C₃	—	2	1	no	—
546	C₂³×C₃	—	2	1	no	—
547	C₂³×C₃	—	2	1	no	—
548	C₂³×C₃	—	2	1	no	—
549	C₂³×C₃	—	2	1	no	—
550	C₂³×C₃	—	2	1	no	—
551	C₂³×C₃	—	2	1	no	—
552	C₂³×C₃	—	2	1	no	—
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	1	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	C₅×#41	1	2	yes	—
564	C₂³×C₃	C₅×#41	1	2	yes	—
565	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
566	C₃×D₄	—	2	8	no	—
567	C₃×D₄	—	4	4	no	—
568	C₃×D₄	—	4	4	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	2	1	no	—
572	C₂×C₃×C₄	—	2	1	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	2	1	no	—
575	C₂×C₃×C₄	—	2	1	no	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	2	1	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	2	1	no	—
581	C₂×C₃×C₄	—	2	1	no	—
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	—	4	4	no	—
601	C₂×C₃×C₄	—	4	4	no	—
602	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
603	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
604	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
605	C₂×C₃×C₄	C₅×#41	1	2	yes	—
606	C₂×C₃×C₄	C₅×#41	1	2	yes	—
607	C₂²×C₅	—	2	2	no	—
608	C₂²×C₅	—	2	2	no	—
609	C₂²×C₅	—	2	2	no	—
610	C₂²×C₅	—	2	2	no	—
611	C₂²×C₅	—	2	2	no	—
612	C₂²×C₅	—	2	2	no	—
613	C₂²×C₅	—	4	1	no	—
614	C₂²×C₅	—	4	1	no	—
615	C₂²×C₅	—	4	1	no	—
616	C₂²×C₅	—	4	1	no	—
617	C₂²×C₅	—	4	1	no	—
618	C₂²×C₅	—	4	1	no	—
619	C₂²×C₅	—	4	1	no	—
620	C₂²×C₅	—	4	1	no	—
621	C₂²×C₅	—	4	1	no	—
622	C₂²×C₅	—	4	1	no	—
623	C₂²×C₅	—	4	1	no	—
624	C₂²×C₅	—	4	1	no	—
625	C₂²×C₅	—	4	1	no	—
626	C₂²×C₅	—	4	1	no	—
627	C₂²×C₅	—	4	1	no	—
628	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
629	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
630	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
631	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
632	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
633	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
634	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
635	C₄×C₅	—	2	2	no	—
636	C₄×C₅	—	2	2	no	—
637	C₄×C₅	—	2	2	no	—
638	C₄×C₅	—	2	2	no	—
639	C₄×C₅	—	2	2	no	—
640	C₄×C₅	—	4	1	no	—
641	C₄×C₅	—	4	1	no	—
642	C₄×C₅	—	4	1	no	—
643	C₄×C₅	—	4	1	no	—
644	C₄×C₅	—	4	1	no	—
645	C₄×C₅	—	4	1	no	—
646	C₄×C₅	—	4	1	no	—
647	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
648	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
649	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
650	C₂×D₄	—	2	2	no	—
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	2	2	no	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	4	1	no	—
657	C₂×D₄	—	4	1	no	—
658	C₂×D₄	—	4	1	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	4	1	no	—
664	C₂²×C₄	—	4	1	no	—
665	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
666	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
667	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
668	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
669	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
670	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
671	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
672	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
673	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
674	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
675	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
676	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	4	1	no	—
681	C₄⋊C₄	—	4	1	no	—
682	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	4	1	no	—
693	C₂²⋊C₄	—	4	1	no	—
694	C₂²⋊C₄	—	4	1	no	—
695	C₂²⋊C₄	—	4	1	no	—
696	C₄²	—	2	2	no	—
697	C₄²	—	2	2	no	—
698	C₄²	—	4	1	no	—
699	C₃×C₅	#2467	1	1	yes	characteristic, direct product factor, Hall
700	C₂²×C₃	—	2	2	no	—
701	C₂²×C₃	—	2	2	no	—
702	C₂²×C₃	—	2	2	no	—
703	C₂²×C₃	—	2	2	no	—
704	C₂²×C₃	—	2	2	no	—
705	C₂²×C₃	—	2	2	no	—
706	C₂²×C₃	—	4	1	no	—
707	C₂²×C₃	—	4	1	no	—
708	C₂²×C₃	—	4	1	no	—
709	C₂²×C₃	—	4	1	no	—
710	C₂²×C₃	—	4	1	no	—
711	C₂²×C₃	—	4	1	no	—
712	C₂²×C₃	—	4	1	no	—
713	C₂²×C₃	—	4	1	no	—
714	C₂²×C₃	—	4	1	no	—
715	C₂²×C₃	—	4	1	no	—
716	C₂²×C₃	—	4	1	no	—
717	C₂²×C₃	—	4	1	no	—
718	C₂²×C₃	—	4	1	no	—
719	C₂²×C₃	—	4	1	no	—
720	C₂²×C₃	—	4	1	no	—
721	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
722	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
723	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
724	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
725	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
726	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
727	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
728	C₃×C₄	—	2	2	no	—
729	C₃×C₄	—	2	2	no	—
730	C₃×C₄	—	2	2	no	—
731	C₃×C₄	—	2	2	no	—
732	C₃×C₄	—	2	2	no	—
733	C₃×C₄	—	4	1	no	—
734	C₃×C₄	—	4	1	no	—
735	C₃×C₄	—	4	1	no	—
736	C₃×C₄	—	4	1	no	—
737	C₃×C₄	—	4	1	no	—
738	C₃×C₄	—	4	1	no	—
739	C₃×C₄	—	4	1	no	—
740	C₂×C₅	—	4	2	no	—
741	C₂×C₅	—	4	2	no	—
742	C₂×C₅	—	8	1	no	—
743	C₂×C₅	C₃×#525	1	1	yes	characteristic
744	C₂×C₅	C₃×#529	1	1	yes	characteristic
745	C₂×C₅	C₃×#538	1	1	yes	characteristic
746	C₂×C₅	C₃×#546	1	1	yes	characteristic
747	C₂×C₅	C₃×#550	1	1	yes	characteristic
748	C₂×C₅	C₃×#551	1	1	yes	characteristic
749	C₂×C₅	C₃×#553	1	1	yes	characteristic
750	C₂³	—	2	1	no	—
751	C₂³	—	2	1	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	1	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	2	1	no	—
769	C₂³	C₃×C₅×#41	1	2	yes	—
770	C₂³	C₃×C₅×#41	1	2	yes	—
771	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
772	D₄	—	2	8	no	—
773	D₄	—	4	4	no	—
774	D₄	—	4	4	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
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	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
809	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
810	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
811	C₂×C₄	C₃×C₅×#41	1	2	yes	—
812	C₂×C₄	C₃×C₅×#41	1	2	yes	—
813	C₂×C₃	—	4	2	no	—
814	C₂×C₃	—	4	2	no	—
815	C₂×C₃	—	8	1	no	—
816	C₂×C₃	C₅×#525	1	1	yes	characteristic
817	C₂×C₃	C₅×#529	1	1	yes	characteristic
818	C₂×C₃	C₅×#538	1	1	yes	characteristic
819	C₂×C₃	C₅×#546	1	1	yes	characteristic
820	C₂×C₃	C₅×#550	1	1	yes	characteristic
821	C₂×C₃	C₅×#551	1	1	yes	characteristic
822	C₂×C₃	C₅×#553	1	1	yes	characteristic
823	C₅	C₃×#2467	1	1	yes	characteristic, direct product factor, Sylow
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
846	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
847	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
848	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
849	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
850	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
851	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
852	C₄	—	2	2	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	2	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	1	no	—
864	C₃	C₅×#2467	1	1	yes	characteristic, direct product factor, Sylow
865	C₂	—	4	2	no	—
866	C₂	—	4	2	no	—
867	C₂	—	8	1	no	—
868	C₂	C₃×C₅×#525	1	1	yes	characteristic
869	C₂	C₃×C₅×#529	1	1	yes	characteristic
870	C₂	C₃×C₅×#538	1	1	yes	characteristic
871	C₂	C₃×C₅×#546	1	1	yes	characteristic
872	C₂	C₃×C₅×#550	1	1	yes	characteristic
873	C₂	C₃×C₅×#551	1	1	yes	characteristic
874	C₂	C₃×C₅×#553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#392	C₂
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
2. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₃×C₅×#399	C₂	semidirect
4. C₃×C₅×#394	C₂	semidirect
5. C₃×C₅×#394	C₂	semidirect
7. C₃×C₅×#390	C₂	semidirect
8. C₃×C₅×#388	C₂	semidirect
9. C₃×C₅×#388	C₂	semidirect
10. C₃×C₅×#387	C₂	semidirect
11. C₃×C₅×#387	C₂	semidirect
12. C₃×C₅×#386	C₂	semidirect
13. C₃×C₅×#386	C₂	semidirect
14. C₃×C₅×#380	C₂	semidirect
15. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
16. C₅×#2467	C₃	direct (N × H)
54. C₃×#2467	C₅	direct (N × H)
55. C₂×C₅×#126	C₂×C₃	semidirect
56. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
57. C₅×#399	C₂×C₃	semidirect
58. C₅×#394	C₂×C₃	semidirect
59. C₅×#394	C₂×C₃	semidirect
61. C₅×#390	C₂×C₃	semidirect
62. C₅×#388	C₂×C₃	semidirect
63. C₅×#388	C₂×C₃	semidirect
64. C₅×#387	C₂×C₃	semidirect
65. C₅×#387	C₂×C₃	semidirect
66. C₅×#386	C₂×C₃	semidirect
67. C₅×#386	C₂×C₃	semidirect
68. C₅×#380	C₂×C₃	semidirect
69. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
105. C₃×C₅×C₄⋊C₄	D₄	semidirect
122. C₂×C₃×#126	C₂×C₅	semidirect
123. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
124. C₃×#399	C₂×C₅	semidirect
125. C₃×#394	C₂×C₅	semidirect
126. C₃×#394	C₂×C₅	semidirect
128. C₃×#390	C₂×C₅	semidirect
129. C₃×#388	C₂×C₅	semidirect
130. C₃×#388	C₂×C₅	semidirect
131. C₃×#387	C₂×C₅	semidirect
132. C₃×#387	C₂×C₅	semidirect
133. C₃×#386	C₂×C₅	semidirect
134. C₃×#386	C₂×C₅	semidirect
135. C₃×#380	C₂×C₅	semidirect
136. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
174. #2467	C₃×C₅	direct (N × H)
310. C₅×C₄⋊C₄	C₃×D₄	semidirect
327. C₂×#126	C₂×C₃×C₅	semidirect
328. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
329. #399	C₂×C₃×C₅	semidirect
330. #394	C₂×C₃×C₅	semidirect
331. #394	C₂×C₃×C₅	semidirect
333. #390	C₂×C₃×C₅	semidirect
334. #388	C₂×C₃×C₅	semidirect
335. #388	C₂×C₃×C₅	semidirect
336. #387	C₂×C₃×C₅	semidirect
337. #387	C₂×C₃×C₅	semidirect
338. #386	C₂×C₃×C₅	semidirect
339. #386	C₂×C₃×C₅	semidirect
340. #380	C₂×C₃×C₅	semidirect
341. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
417. C₃×C₄⋊C₄	C₅×D₄	semidirect
682. C₄⋊C₄	C₃×C₅×D₄	semidirect
699. C₃×C₅	#2467	direct (N × H)
823. C₅	C₃×#2467	direct (N × H)
864. C₃	C₅×#2467	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
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#399	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#386	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2467	3
C₃×#2467	5

Subgroups — C3×C5×#2467 #14275501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2467 #14275501