Subgroups — C₃×C₅×#2522 #14275556

Order 1920.

856 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#399	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#396	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#387	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×#385	C₂	1	1	yes	maximal, characteristic
13	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic
14	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₅×#2522	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₄²×C₅	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
40	C₃×C₅×#95	C₂²	1	1	yes	characteristic
41	C₃×C₅×#95	C₂²	1	1	yes	characteristic
42	C₃×C₅×#95	C₂²	1	1	yes	characteristic
43	C₃×C₅×#95	C₂²	1	1	yes	characteristic
44	C₃×C₅×#95	C₂²	1	1	yes	characteristic
45	C₃×C₅×#95	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×#2522	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₅×#399	C₂×C₃	1	1	yes	characteristic
54	C₅×#398	C₂×C₃	1	1	yes	characteristic, complemented
55	C₅×#398	C₂×C₃	1	1	yes	characteristic, complemented
56	C₅×#396	C₂×C₃	1	1	yes	characteristic
57	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
58	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
59	C₅×#388	C₂×C₃	1	1	yes	characteristic
60	C₅×#388	C₂×C₃	1	1	yes	characteristic
61	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#385	C₂×C₃	1	1	yes	characteristic
65	C₅×#380	C₂×C₃	1	1	yes	characteristic
66	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
67	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
68	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	—	2	2	no	—
70	C₂²×C₃×C₄×C₅	—	2	2	no	—
71	C₂²×C₃×C₄×C₅	—	4	1	no	—
72	C₂²×C₃×C₄×C₅	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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₃×C₅×C₄⋊C₄	—	2	2	no	—
87	C₃×C₅×C₄⋊C₄	—	2	2	no	—
88	C₃×C₅×C₄⋊C₄	—	2	2	no	—
89	C₃×C₅×C₄⋊C₄	—	2	2	no	—
90	C₃×C₅×C₄⋊C₄	—	2	2	no	—
91	C₃×C₅×C₄⋊C₄	—	2	2	no	—
92	C₃×C₅×C₄⋊C₄	—	2	2	no	—
93	C₃×C₅×C₄⋊C₄	—	4	1	no	—
94	C₃×C₅×C₄⋊C₄	—	4	1	no	—
95	C₃×C₅×C₄⋊C₄	—	4	1	no	—
96	C₃×C₅×C₄⋊C₄	—	4	1	no	—
97	C₃×C₅×C₄⋊C₄	—	4	1	no	—
98	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
99	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
100	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
101	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
102	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
103	C₃×C₅×C₂²⋊C₄	Q₈	1	4	yes	—
104	C₃×C₄²×C₅	—	2	2	no	—
105	C₃×C₄²×C₅	—	4	1	no	—
106	C₃×C₄²×C₅	—	4	1	no	—
107	C₃×C₄²×C₅	—	4	1	no	—
108	C₃×#399	C₂×C₅	1	1	yes	characteristic
109	C₃×#398	C₂×C₅	1	1	yes	characteristic, complemented
110	C₃×#398	C₂×C₅	1	1	yes	characteristic, complemented
111	C₃×#396	C₂×C₅	1	1	yes	characteristic
112	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
113	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
114	C₃×#388	C₂×C₅	1	1	yes	characteristic
115	C₃×#388	C₂×C₅	1	1	yes	characteristic
116	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
117	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
118	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
119	C₃×#385	C₂×C₅	1	1	yes	characteristic
120	C₃×#380	C₂×C₅	1	1	yes	characteristic
121	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
122	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
123	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
146	C₅×#95	C₂²×C₃	1	1	yes	characteristic
147	C₅×#95	C₂²×C₃	1	1	yes	characteristic
148	C₅×#95	C₂²×C₃	1	1	yes	characteristic
149	C₅×#95	C₂²×C₃	1	1	yes	characteristic
150	C₅×#95	C₂²×C₃	1	1	yes	characteristic
151	C₅×#95	C₂²×C₃	1	1	yes	characteristic
152	C₅×#95	C₂²×C₃	1	1	yes	characteristic
153	C₅×#95	C₂²×C₃	1	1	yes	characteristic
154	C₅×#95	C₂²×C₃	1	1	yes	characteristic
155	C₅×#95	C₂²×C₃	1	1	yes	characteristic
156	C₅×#95	C₂²×C₃	1	1	yes	characteristic
157	C₅×#95	C₂²×C₃	1	1	yes	characteristic
158	#2522	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
159	C₂³×C₃×C₅	—	2	1	no	—
160	C₂³×C₃×C₅	—	2	1	no	—
161	C₂³×C₃×C₅	—	2	1	no	—
162	C₂³×C₃×C₅	—	2	1	no	—
163	C₂³×C₃×C₅	—	2	1	no	—
164	C₂³×C₃×C₅	—	2	1	no	—
165	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
166	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
167	C₂×C₃×C₄×C₅	—	2	1	no	—
168	C₂×C₃×C₄×C₅	—	2	1	no	—
169	C₂×C₃×C₄×C₅	—	2	1	no	—
170	C₂×C₃×C₄×C₅	—	2	1	no	—
171	C₂×C₃×C₄×C₅	—	2	1	no	—
172	C₂×C₃×C₄×C₅	—	2	1	no	—
173	C₂×C₃×C₄×C₅	—	2	1	no	—
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	—	2	1	no	—
176	C₂×C₃×C₄×C₅	—	2	1	no	—
177	C₂×C₃×C₄×C₅	—	2	1	no	—
178	C₂×C₃×C₄×C₅	—	2	1	no	—
179	C₂×C₃×C₄×C₅	—	2	1	no	—
180	C₂×C₃×C₄×C₅	—	2	1	no	—
181	C₂×C₃×C₄×C₅	—	2	1	no	—
182	C₂×C₃×C₄×C₅	—	2	1	no	—
183	C₂×C₃×C₄×C₅	—	2	1	no	—
184	C₂×C₃×C₄×C₅	—	2	1	no	—
185	C₂×C₃×C₄×C₅	—	2	1	no	—
186	C₂×C₃×C₄×C₅	—	2	1	no	—
187	C₂×C₃×C₄×C₅	—	2	1	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
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	—	4	4	no	—
204	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
205	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
206	C₂×C₃×C₄×C₅	#41	1	2	yes	—
207	C₂×C₃×C₄×C₅	#41	1	2	yes	—
208	C₂×C₃×C₄×C₅	#41	1	2	yes	—
209	C₂×C₃×C₄×C₅	#41	1	2	yes	—
210	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
212	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
214	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
215	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
222	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
224	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
233	C₃×#95	C₂²×C₅	1	1	yes	characteristic
234	C₃×#95	C₂²×C₅	1	1	yes	characteristic
235	C₃×#95	C₂²×C₅	1	1	yes	characteristic
236	C₃×#95	C₂²×C₅	1	1	yes	characteristic
237	C₃×#95	C₂²×C₅	1	1	yes	characteristic
238	C₃×#95	C₂²×C₅	1	1	yes	characteristic
239	C₃×#95	C₂²×C₅	1	1	yes	characteristic
240	C₃×#95	C₂²×C₅	1	1	yes	characteristic
241	C₃×#95	C₂²×C₅	1	1	yes	characteristic
242	C₃×#95	C₂²×C₅	1	1	yes	characteristic
243	C₃×#95	C₂²×C₅	1	1	yes	characteristic
244	C₃×#95	C₂²×C₅	1	1	yes	characteristic
245	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
246	C₂²×C₄×C₅	—	2	2	no	—
247	C₂²×C₄×C₅	—	2	2	no	—
248	C₂²×C₄×C₅	—	4	1	no	—
249	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
250	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
251	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
252	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
253	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
254	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
255	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
256	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
257	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
258	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
259	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
260	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
261	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
262	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
263	C₅×C₄⋊C₄	—	2	2	no	—
264	C₅×C₄⋊C₄	—	2	2	no	—
265	C₅×C₄⋊C₄	—	2	2	no	—
266	C₅×C₄⋊C₄	—	2	2	no	—
267	C₅×C₄⋊C₄	—	2	2	no	—
268	C₅×C₄⋊C₄	—	2	2	no	—
269	C₅×C₄⋊C₄	—	2	2	no	—
270	C₅×C₄⋊C₄	—	4	1	no	—
271	C₅×C₄⋊C₄	—	4	1	no	—
272	C₅×C₄⋊C₄	—	4	1	no	—
273	C₅×C₄⋊C₄	—	4	1	no	—
274	C₅×C₄⋊C₄	—	4	1	no	—
275	C₅×C₂²⋊C₄	—	2	2	no	—
276	C₅×C₂²⋊C₄	—	2	2	no	—
277	C₅×C₂²⋊C₄	—	4	1	no	—
278	C₅×C₂²⋊C₄	—	4	1	no	—
279	C₅×C₂²⋊C₄	—	4	1	no	—
280	C₅×C₂²⋊C₄	C₃×Q₈	1	4	yes	—
281	C₄²×C₅	—	2	2	no	—
282	C₄²×C₅	—	4	1	no	—
283	C₄²×C₅	—	4	1	no	—
284	C₄²×C₅	—	4	1	no	—
285	#399	C₂×C₃×C₅	1	1	yes	characteristic
286	#398	C₂×C₃×C₅	1	1	yes	characteristic, complemented
287	#398	C₂×C₃×C₅	1	1	yes	characteristic, complemented
288	#396	C₂×C₃×C₅	1	1	yes	characteristic
289	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
290	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
291	#388	C₂×C₃×C₅	1	1	yes	characteristic
292	#388	C₂×C₃×C₅	1	1	yes	characteristic
293	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
294	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
295	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
296	#385	C₂×C₃×C₅	1	1	yes	characteristic
297	#380	C₂×C₃×C₅	1	1	yes	characteristic
298	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
299	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
300	C₂²×C₃×C₅	—	2	2	no	—
301	C₂²×C₃×C₅	—	2	2	no	—
302	C₂²×C₃×C₅	—	2	2	no	—
303	C₂²×C₃×C₅	—	4	1	no	—
304	C₂²×C₃×C₅	—	4	1	no	—
305	C₂²×C₃×C₅	—	4	1	no	—
306	C₂²×C₃×C₅	—	4	1	no	—
307	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
308	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
309	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
310	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
311	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
312	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
313	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
314	C₃×C₄×C₅	—	2	2	no	—
315	C₃×C₄×C₅	—	2	2	no	—
316	C₃×C₄×C₅	—	2	2	no	—
317	C₃×C₄×C₅	—	2	2	no	—
318	C₃×C₄×C₅	—	2	2	no	—
319	C₃×C₄×C₅	—	2	2	no	—
320	C₃×C₄×C₅	—	4	1	no	—
321	C₃×C₄×C₅	—	4	1	no	—
322	C₃×C₄×C₅	—	4	1	no	—
323	C₃×C₄×C₅	—	4	1	no	—
324	C₃×C₄×C₅	—	4	1	no	—
325	C₃×C₄×C₅	—	4	1	no	—
326	C₃×C₄×C₅	—	4	1	no	—
327	C₃×C₄×C₅	—	4	1	no	—
328	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
329	C₂²×C₃×C₄	—	2	2	no	—
330	C₂²×C₃×C₄	—	2	2	no	—
331	C₂²×C₃×C₄	—	4	1	no	—
332	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
333	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
334	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
335	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
336	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
337	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
338	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
339	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
340	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
341	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
342	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
343	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
344	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
345	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
346	C₃×C₄⋊C₄	—	2	2	no	—
347	C₃×C₄⋊C₄	—	2	2	no	—
348	C₃×C₄⋊C₄	—	2	2	no	—
349	C₃×C₄⋊C₄	—	2	2	no	—
350	C₃×C₄⋊C₄	—	2	2	no	—
351	C₃×C₄⋊C₄	—	2	2	no	—
352	C₃×C₄⋊C₄	—	2	2	no	—
353	C₃×C₄⋊C₄	—	4	1	no	—
354	C₃×C₄⋊C₄	—	4	1	no	—
355	C₃×C₄⋊C₄	—	4	1	no	—
356	C₃×C₄⋊C₄	—	4	1	no	—
357	C₃×C₄⋊C₄	—	4	1	no	—
358	C₃×C₂²⋊C₄	—	2	2	no	—
359	C₃×C₂²⋊C₄	—	2	2	no	—
360	C₃×C₂²⋊C₄	—	4	1	no	—
361	C₃×C₂²⋊C₄	—	4	1	no	—
362	C₃×C₂²⋊C₄	—	4	1	no	—
363	C₃×C₂²⋊C₄	C₅×Q₈	1	4	yes	—
364	C₃×C₄²	—	2	2	no	—
365	C₃×C₄²	—	4	1	no	—
366	C₃×C₄²	—	4	1	no	—
367	C₃×C₄²	—	4	1	no	—
368	C₂³×C₅	—	2	1	no	—
369	C₂³×C₅	—	2	1	no	—
370	C₂³×C₅	—	2	1	no	—
371	C₂³×C₅	—	2	1	no	—
372	C₂³×C₅	—	2	1	no	—
373	C₂³×C₅	—	2	1	no	—
374	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
375	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
376	C₂×C₄×C₅	—	2	1	no	—
377	C₂×C₄×C₅	—	2	1	no	—
378	C₂×C₄×C₅	—	2	1	no	—
379	C₂×C₄×C₅	—	2	1	no	—
380	C₂×C₄×C₅	—	2	1	no	—
381	C₂×C₄×C₅	—	2	1	no	—
382	C₂×C₄×C₅	—	2	1	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	—	2	1	no	—
387	C₂×C₄×C₅	—	2	1	no	—
388	C₂×C₄×C₅	—	2	1	no	—
389	C₂×C₄×C₅	—	2	1	no	—
390	C₂×C₄×C₅	—	2	1	no	—
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	2	1	no	—
394	C₂×C₄×C₅	—	2	1	no	—
395	C₂×C₄×C₅	—	2	1	no	—
396	C₂×C₄×C₅	—	2	1	no	—
397	C₂×C₄×C₅	—	2	1	no	—
398	C₂×C₄×C₅	—	2	1	no	—
399	C₂×C₄×C₅	—	2	1	no	—
400	C₂×C₄×C₅	—	2	1	no	—
401	C₂×C₄×C₅	—	2	1	no	—
402	C₂×C₄×C₅	—	2	1	no	—
403	C₂×C₄×C₅	—	2	1	no	—
404	C₂×C₄×C₅	—	2	1	no	—
405	C₂×C₄×C₅	—	2	1	no	—
406	C₂×C₄×C₅	—	2	1	no	—
407	C₂×C₄×C₅	—	2	1	no	—
408	C₂×C₄×C₅	—	2	1	no	—
409	C₂×C₄×C₅	—	2	1	no	—
410	C₂×C₄×C₅	—	2	1	no	—
411	C₂×C₄×C₅	—	2	1	no	—
412	C₂×C₄×C₅	—	4	4	no	—
413	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
414	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
415	C₂×C₄×C₅	C₃×#41	1	2	yes	—
416	C₂×C₄×C₅	C₃×#41	1	2	yes	—
417	C₂×C₄×C₅	C₃×#41	1	2	yes	—
418	C₂×C₄×C₅	C₃×#41	1	2	yes	—
419	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
434	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
435	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
438	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
439	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
440	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
441	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
442	#95	C₂²×C₃×C₅	1	1	yes	characteristic
443	#95	C₂²×C₃×C₅	1	1	yes	characteristic
444	#95	C₂²×C₃×C₅	1	1	yes	characteristic
445	#95	C₂²×C₃×C₅	1	1	yes	characteristic
446	#95	C₂²×C₃×C₅	1	1	yes	characteristic
447	#95	C₂²×C₃×C₅	1	1	yes	characteristic
448	#95	C₂²×C₃×C₅	1	1	yes	characteristic
449	#95	C₂²×C₃×C₅	1	1	yes	characteristic
450	#95	C₂²×C₃×C₅	1	1	yes	characteristic
451	#95	C₂²×C₃×C₅	1	1	yes	characteristic
452	#95	C₂²×C₃×C₅	1	1	yes	characteristic
453	#95	C₂²×C₃×C₅	1	1	yes	characteristic
454	C₂×C₃×C₅	—	4	2	no	—
455	C₂×C₃×C₅	#529	1	1	yes	characteristic
456	C₂×C₃×C₅	#533	1	1	yes	characteristic
457	C₂×C₃×C₅	#540	1	1	yes	characteristic
458	C₂×C₃×C₅	#551	1	1	yes	characteristic
459	C₂×C₃×C₅	#553	1	1	yes	characteristic
460	C₂×C₃×C₅	#554	1	1	yes	characteristic
461	C₂×C₃×C₅	#554	1	1	yes	characteristic
462	C₂³×C₃	—	2	1	no	—
463	C₂³×C₃	—	2	1	no	—
464	C₂³×C₃	—	2	1	no	—
465	C₂³×C₃	—	2	1	no	—
466	C₂³×C₃	—	2	1	no	—
467	C₂³×C₃	—	2	1	no	—
468	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
469	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
470	C₂×C₃×C₄	—	2	1	no	—
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	2	1	no	—
473	C₂×C₃×C₄	—	2	1	no	—
474	C₂×C₃×C₄	—	2	1	no	—
475	C₂×C₃×C₄	—	2	1	no	—
476	C₂×C₃×C₄	—	2	1	no	—
477	C₂×C₃×C₄	—	2	1	no	—
478	C₂×C₃×C₄	—	2	1	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	1	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	1	no	—
488	C₂×C₃×C₄	—	2	1	no	—
489	C₂×C₃×C₄	—	2	1	no	—
490	C₂×C₃×C₄	—	2	1	no	—
491	C₂×C₃×C₄	—	2	1	no	—
492	C₂×C₃×C₄	—	2	1	no	—
493	C₂×C₃×C₄	—	2	1	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	1	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	1	no	—
501	C₂×C₃×C₄	—	2	1	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	2	1	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	4	4	no	—
507	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
508	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
509	C₂×C₃×C₄	C₅×#41	1	2	yes	—
510	C₂×C₃×C₄	C₅×#41	1	2	yes	—
511	C₂×C₃×C₄	C₅×#41	1	2	yes	—
512	C₂×C₃×C₄	C₅×#41	1	2	yes	—
513	C₂²×C₅	—	2	2	no	—
514	C₂²×C₅	—	2	2	no	—
515	C₂²×C₅	—	2	2	no	—
516	C₂²×C₅	—	4	1	no	—
517	C₂²×C₅	—	4	1	no	—
518	C₂²×C₅	—	4	1	no	—
519	C₂²×C₅	—	4	1	no	—
520	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
521	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
522	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
523	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
524	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
525	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
527	C₄×C₅	—	2	2	no	—
528	C₄×C₅	—	2	2	no	—
529	C₄×C₅	—	2	2	no	—
530	C₄×C₅	—	2	2	no	—
531	C₄×C₅	—	2	2	no	—
532	C₄×C₅	—	2	2	no	—
533	C₄×C₅	—	4	1	no	—
534	C₄×C₅	—	4	1	no	—
535	C₄×C₅	—	4	1	no	—
536	C₄×C₅	—	4	1	no	—
537	C₄×C₅	—	4	1	no	—
538	C₄×C₅	—	4	1	no	—
539	C₄×C₅	—	4	1	no	—
540	C₄×C₅	—	4	1	no	—
541	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	4	1	no	—
545	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
546	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
547	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
548	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
549	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
550	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
551	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
552	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
553	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
554	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
555	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
556	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
557	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
558	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	4	1	no	—
567	C₄⋊C₄	—	4	1	no	—
568	C₄⋊C₄	—	4	1	no	—
569	C₄⋊C₄	—	4	1	no	—
570	C₄⋊C₄	—	4	1	no	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	4	1	no	—
574	C₂²⋊C₄	—	4	1	no	—
575	C₂²⋊C₄	—	4	1	no	—
576	C₂²⋊C₄	C₃×C₅×Q₈	1	4	yes	—
577	C₄²	—	2	2	no	—
578	C₄²	—	4	1	no	—
579	C₄²	—	4	1	no	—
580	C₄²	—	4	1	no	—
581	C₃×C₅	#2522	1	1	yes	characteristic, direct product factor, Hall
582	C₂²×C₃	—	2	2	no	—
583	C₂²×C₃	—	2	2	no	—
584	C₂²×C₃	—	2	2	no	—
585	C₂²×C₃	—	4	1	no	—
586	C₂²×C₃	—	4	1	no	—
587	C₂²×C₃	—	4	1	no	—
588	C₂²×C₃	—	4	1	no	—
589	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
590	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
591	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
592	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
593	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
594	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
595	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
596	C₃×C₄	—	2	2	no	—
597	C₃×C₄	—	2	2	no	—
598	C₃×C₄	—	2	2	no	—
599	C₃×C₄	—	2	2	no	—
600	C₃×C₄	—	2	2	no	—
601	C₃×C₄	—	2	2	no	—
602	C₃×C₄	—	4	1	no	—
603	C₃×C₄	—	4	1	no	—
604	C₃×C₄	—	4	1	no	—
605	C₃×C₄	—	4	1	no	—
606	C₃×C₄	—	4	1	no	—
607	C₃×C₄	—	4	1	no	—
608	C₃×C₄	—	4	1	no	—
609	C₃×C₄	—	4	1	no	—
610	C₂×C₅	—	4	2	no	—
611	C₂×C₅	C₃×#529	1	1	yes	characteristic
612	C₂×C₅	C₃×#533	1	1	yes	characteristic
613	C₂×C₅	C₃×#540	1	1	yes	characteristic
614	C₂×C₅	C₃×#551	1	1	yes	characteristic
615	C₂×C₅	C₃×#553	1	1	yes	characteristic
616	C₂×C₅	C₃×#554	1	1	yes	characteristic
617	C₂×C₅	C₃×#554	1	1	yes	characteristic
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
625	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
664	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
665	C₂×C₄	C₃×C₅×#41	1	2	yes	—
666	C₂×C₄	C₃×C₅×#41	1	2	yes	—
667	C₂×C₄	C₃×C₅×#41	1	2	yes	—
668	C₂×C₄	C₃×C₅×#41	1	2	yes	—
669	C₂×C₃	—	4	2	no	—
670	C₂×C₃	C₅×#529	1	1	yes	characteristic
671	C₂×C₃	C₅×#533	1	1	yes	characteristic
672	C₂×C₃	C₅×#540	1	1	yes	characteristic
673	C₂×C₃	C₅×#551	1	1	yes	characteristic
674	C₂×C₃	C₅×#553	1	1	yes	characteristic
675	C₂×C₃	C₅×#554	1	1	yes	characteristic
676	C₂×C₃	C₅×#554	1	1	yes	characteristic
677	C₅	C₃×#2522	1	1	yes	characteristic, direct product factor, Sylow
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
686	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
687	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
688	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
689	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
690	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
691	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	2	no	—
696	C₄	—	2	2	no	—
697	C₄	—	2	2	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	1	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	1	no	—
706	C₃	C₅×#2522	1	1	yes	characteristic, direct product factor, Sylow
707	C₂	—	4	2	no	—
708	C₂	C₃×C₅×#529	1	1	yes	characteristic
709	C₂	C₃×C₅×#533	1	1	yes	characteristic
710	C₂	C₃×C₅×#540	1	1	yes	characteristic
711	C₂	C₃×C₅×#551	1	1	yes	characteristic
712	C₂	C₃×C₅×#553	1	1	yes	characteristic
713	C₂	C₃×C₅×#554	1	1	yes	characteristic
714	C₂	C₃×C₅×#554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
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
2. C₃×C₅×#398	C₂	semidirect
3. C₃×C₅×#398	C₂	semidirect
5. C₃×C₅×#389	C₂	semidirect
6. C₃×C₅×#389	C₂	semidirect
9. C₃×C₅×#387	C₂	semidirect
10. C₃×C₅×#387	C₂	semidirect
11. C₃×C₅×#387	C₂	semidirect
14. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
16. C₅×#2522	C₃	direct (N × H)
52. C₃×#2522	C₅	direct (N × H)
54. C₅×#398	C₂×C₃	semidirect
55. C₅×#398	C₂×C₃	semidirect
57. C₅×#389	C₂×C₃	semidirect
58. C₅×#389	C₂×C₃	semidirect
61. C₅×#387	C₂×C₃	semidirect
62. C₅×#387	C₂×C₃	semidirect
63. C₅×#387	C₂×C₃	semidirect
66. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
109. C₃×#398	C₂×C₅	semidirect
110. C₃×#398	C₂×C₅	semidirect
112. C₃×#389	C₂×C₅	semidirect
113. C₃×#389	C₂×C₅	semidirect
116. C₃×#387	C₂×C₅	semidirect
117. C₃×#387	C₂×C₅	semidirect
118. C₃×#387	C₂×C₅	semidirect
121. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
158. #2522	C₃×C₅	direct (N × H)
286. #398	C₂×C₃×C₅	semidirect
287. #398	C₂×C₃×C₅	semidirect
289. #389	C₂×C₃×C₅	semidirect
290. #389	C₂×C₃×C₅	semidirect
293. #387	C₂×C₃×C₅	semidirect
294. #387	C₂×C₃×C₅	semidirect
295. #387	C₂×C₃×C₅	semidirect
298. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
581. C₃×C₅	#2522	direct (N × H)
677. C₅	C₃×#2522	direct (N × H)
706. C₃	C₅×#2522	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#399	2
C₃×C₅×#398	2
C₃×C₅×#396	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#385	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2522	3
C₃×#2522	5

Subgroups — C3×C5×#2522 #14275556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2522 #14275556