Subgroups — C₃×C₅×#2516 #14275550

Order 1920.

908 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#399	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#388	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×#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
13	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic, complemented
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, complemented
16	C₅×#2516	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₅	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×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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×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×#2516	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₅×#400	C₂×C₃	1	1	yes	characteristic, complemented
54	C₅×#399	C₂×C₃	1	1	yes	characteristic, complemented
55	C₅×#397	C₂×C₃	1	1	yes	characteristic, complemented
56	C₅×#394	C₂×C₃	1	1	yes	characteristic
57	C₅×#390	C₂×C₃	1	1	yes	characteristic
58	C₅×#388	C₂×C₃	1	1	yes	characteristic, complemented
59	C₅×#388	C₂×C₃	1	1	yes	characteristic, complemented
60	C₅×#388	C₂×C₃	1	1	yes	characteristic, complemented
61	C₅×#388	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×#386	C₂×C₃	1	1	yes	characteristic
65	C₅×#381	C₂×C₃	1	1	yes	characteristic, complemented
66	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
67	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×D₄	—	2	2	no	—
71	C₂×C₃×C₅×D₄	—	2	2	no	—
72	C₂×C₃×C₅×D₄	—	4	1	no	—
73	C₂²×C₃×C₄×C₅	—	2	2	no	—
74	C₂²×C₃×C₄×C₅	—	2	2	no	—
75	C₂²×C₃×C₄×C₅	—	4	1	no	—
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	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	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×C₂²⋊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	—	2	2	no	—
99	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
100	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
101	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
102	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
103	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
104	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
105	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
106	C₃×C₄²×C₅	—	2	2	no	—
107	C₃×C₄²×C₅	—	4	1	no	—
108	C₃×C₄²×C₅	—	4	1	no	—
109	C₃×C₄²×C₅	—	4	1	no	—
110	C₃×#400	C₂×C₅	1	1	yes	characteristic, complemented
111	C₃×#399	C₂×C₅	1	1	yes	characteristic, complemented
112	C₃×#397	C₂×C₅	1	1	yes	characteristic, complemented
113	C₃×#394	C₂×C₅	1	1	yes	characteristic
114	C₃×#390	C₂×C₅	1	1	yes	characteristic
115	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
116	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
117	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
118	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
119	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
120	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
121	C₃×#386	C₂×C₅	1	1	yes	characteristic
122	C₃×#381	C₂×C₅	1	1	yes	characteristic, complemented
123	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
124	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
125	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
126	C₂³×C₄×C₅	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×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₅×C₂²⋊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×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₅×C₂²⋊C₄	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	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₄²×C₅	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	C₅×#95	C₂²×C₃	1	1	yes	characteristic
159	C₅×#95	C₂²×C₃	1	1	yes	characteristic
160	#2516	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
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	—	2	1	no	—
166	C₂³×C₃×C₅	—	2	1	no	—
167	C₂³×C₃×C₅	—	2	1	no	—
168	C₂³×C₃×C₅	—	2	1	no	—
169	C₂³×C₃×C₅	—	2	1	no	—
170	C₂³×C₃×C₅	—	2	1	no	—
171	C₂³×C₃×C₅	—	2	1	no	—
172	C₂³×C₃×C₅	—	2	1	no	—
173	C₂³×C₃×C₅	—	2	1	no	—
174	C₂³×C₃×C₅	#41	1	2	yes	—
175	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
176	C₃×C₅×D₄	—	4	4	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	—	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	—	4	4	no	—
213	C₂×C₃×C₄×C₅	#41	1	2	yes	—
214	C₂×C₃×C₄×C₅	#41	1	2	yes	—
215	C₂×C₃×C₄×C₅	#41	1	2	yes	—
216	C₂×C₃×C₄×C₅	#41	1	2	yes	—
217	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
218	C₂³×C₃×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×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
224	C₂×C₃×C₄⋊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×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₃×C₄²	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	C₃×#95	C₂²×C₅	1	1	yes	characteristic
246	C₃×#95	C₂²×C₅	1	1	yes	characteristic
247	C₃×#95	C₂²×C₅	1	1	yes	characteristic
248	C₃×#95	C₂²×C₅	1	1	yes	characteristic
249	C₃×#95	C₂²×C₅	1	1	yes	characteristic
250	C₃×#95	C₂²×C₅	1	1	yes	characteristic
251	C₃×#95	C₂²×C₅	1	1	yes	characteristic
252	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
253	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
254	C₂×C₅×D₄	—	2	2	no	—
255	C₂×C₅×D₄	—	2	2	no	—
256	C₂×C₅×D₄	—	4	1	no	—
257	C₂²×C₄×C₅	—	2	2	no	—
258	C₂²×C₄×C₅	—	2	2	no	—
259	C₂²×C₄×C₅	—	4	1	no	—
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	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
264	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
265	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
266	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
267	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
268	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
269	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
270	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
271	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
272	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
273	C₅×C₄⋊C₄	—	2	2	no	—
274	C₅×C₄⋊C₄	—	2	2	no	—
275	C₅×C₄⋊C₄	—	2	2	no	—
276	C₅×C₄⋊C₄	—	2	2	no	—
277	C₅×C₄⋊C₄	—	4	1	no	—
278	C₅×C₄⋊C₄	—	4	1	no	—
279	C₅×C₂²⋊C₄	—	2	2	no	—
280	C₅×C₂²⋊C₄	—	2	2	no	—
281	C₅×C₂²⋊C₄	—	2	2	no	—
282	C₅×C₂²⋊C₄	—	2	2	no	—
283	C₅×C₂²⋊C₄	—	2	2	no	—
284	C₅×C₂²⋊C₄	—	2	2	no	—
285	C₅×C₂²⋊C₄	—	4	1	no	—
286	C₅×C₂²⋊C₄	—	4	1	no	—
287	C₅×C₂²⋊C₄	—	4	1	no	—
288	C₅×C₂²⋊C₄	—	4	1	no	—
289	C₅×C₂²⋊C₄	—	4	1	no	—
290	C₄²×C₅	—	2	2	no	—
291	C₄²×C₅	—	4	1	no	—
292	C₄²×C₅	—	4	1	no	—
293	C₄²×C₅	—	4	1	no	—
294	#400	C₂×C₃×C₅	1	1	yes	characteristic, complemented
295	#399	C₂×C₃×C₅	1	1	yes	characteristic, complemented
296	#397	C₂×C₃×C₅	1	1	yes	characteristic, complemented
297	#394	C₂×C₃×C₅	1	1	yes	characteristic
298	#390	C₂×C₃×C₅	1	1	yes	characteristic
299	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
300	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
301	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
302	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
303	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
304	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
305	#386	C₂×C₃×C₅	1	1	yes	characteristic
306	#381	C₂×C₃×C₅	1	1	yes	characteristic, complemented
307	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
308	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
309	C₂²×C₃×C₅	—	2	2	no	—
310	C₂²×C₃×C₅	—	2	2	no	—
311	C₂²×C₃×C₅	—	2	2	no	—
312	C₂²×C₃×C₅	—	4	1	no	—
313	C₂²×C₃×C₅	—	4	1	no	—
314	C₂²×C₃×C₅	—	4	1	no	—
315	C₂²×C₃×C₅	—	4	1	no	—
316	C₂²×C₃×C₅	—	4	1	no	—
317	C₂²×C₃×C₅	—	4	1	no	—
318	C₂²×C₃×C₅	—	4	1	no	—
319	C₂²×C₃×C₅	—	4	1	no	—
320	C₂²×C₃×C₅	—	4	1	no	—
321	C₂²×C₃×C₅	—	4	1	no	—
322	C₂²×C₃×C₅	—	4	1	no	—
323	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
324	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
325	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
326	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
327	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
328	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
329	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
330	C₃×C₄×C₅	—	2	2	no	—
331	C₃×C₄×C₅	—	2	2	no	—
332	C₃×C₄×C₅	—	2	2	no	—
333	C₃×C₄×C₅	—	2	2	no	—
334	C₃×C₄×C₅	—	4	1	no	—
335	C₃×C₄×C₅	—	4	1	no	—
336	C₃×C₄×C₅	—	4	1	no	—
337	C₃×C₄×C₅	—	4	1	no	—
338	C₃×C₄×C₅	—	4	1	no	—
339	C₃×C₄×C₅	—	4	1	no	—
340	C₃×C₄×C₅	—	4	1	no	—
341	C₃×C₄×C₅	—	4	1	no	—
342	C₃×C₄×C₅	—	4	1	no	—
343	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
344	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
345	C₂×C₃×D₄	—	2	2	no	—
346	C₂×C₃×D₄	—	2	2	no	—
347	C₂×C₃×D₄	—	4	1	no	—
348	C₂²×C₃×C₄	—	2	2	no	—
349	C₂²×C₃×C₄	—	2	2	no	—
350	C₂²×C₃×C₄	—	4	1	no	—
351	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
352	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
353	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
354	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
355	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
356	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
357	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
358	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
359	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
360	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
361	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
362	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
363	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
364	C₃×C₄⋊C₄	—	2	2	no	—
365	C₃×C₄⋊C₄	—	2	2	no	—
366	C₃×C₄⋊C₄	—	2	2	no	—
367	C₃×C₄⋊C₄	—	2	2	no	—
368	C₃×C₄⋊C₄	—	4	1	no	—
369	C₃×C₄⋊C₄	—	4	1	no	—
370	C₃×C₂²⋊C₄	—	2	2	no	—
371	C₃×C₂²⋊C₄	—	2	2	no	—
372	C₃×C₂²⋊C₄	—	2	2	no	—
373	C₃×C₂²⋊C₄	—	2	2	no	—
374	C₃×C₂²⋊C₄	—	2	2	no	—
375	C₃×C₂²⋊C₄	—	2	2	no	—
376	C₃×C₂²⋊C₄	—	4	1	no	—
377	C₃×C₂²⋊C₄	—	4	1	no	—
378	C₃×C₂²⋊C₄	—	4	1	no	—
379	C₃×C₂²⋊C₄	—	4	1	no	—
380	C₃×C₂²⋊C₄	—	4	1	no	—
381	C₃×C₄²	—	2	2	no	—
382	C₃×C₄²	—	4	1	no	—
383	C₃×C₄²	—	4	1	no	—
384	C₃×C₄²	—	4	1	no	—
385	C₂³×C₅	—	2	1	no	—
386	C₂³×C₅	—	2	1	no	—
387	C₂³×C₅	—	2	1	no	—
388	C₂³×C₅	—	2	1	no	—
389	C₂³×C₅	—	2	1	no	—
390	C₂³×C₅	—	2	1	no	—
391	C₂³×C₅	—	2	1	no	—
392	C₂³×C₅	—	2	1	no	—
393	C₂³×C₅	—	2	1	no	—
394	C₂³×C₅	—	2	1	no	—
395	C₂³×C₅	—	2	1	no	—
396	C₂³×C₅	—	2	1	no	—
397	C₂³×C₅	—	2	1	no	—
398	C₂³×C₅	C₃×#41	1	2	yes	—
399	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
400	C₅×D₄	—	4	4	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	—	2	1	no	—
413	C₂×C₄×C₅	—	2	1	no	—
414	C₂×C₄×C₅	—	2	1	no	—
415	C₂×C₄×C₅	—	2	1	no	—
416	C₂×C₄×C₅	—	2	1	no	—
417	C₂×C₄×C₅	—	2	1	no	—
418	C₂×C₄×C₅	—	2	1	no	—
419	C₂×C₄×C₅	—	2	1	no	—
420	C₂×C₄×C₅	—	2	1	no	—
421	C₂×C₄×C₅	—	2	1	no	—
422	C₂×C₄×C₅	—	2	1	no	—
423	C₂×C₄×C₅	—	2	1	no	—
424	C₂×C₄×C₅	—	2	1	no	—
425	C₂×C₄×C₅	—	2	1	no	—
426	C₂×C₄×C₅	—	2	1	no	—
427	C₂×C₄×C₅	—	2	1	no	—
428	C₂×C₄×C₅	—	2	1	no	—
429	C₂×C₄×C₅	—	2	1	no	—
430	C₂×C₄×C₅	—	2	1	no	—
431	C₂×C₄×C₅	—	2	1	no	—
432	C₂×C₄×C₅	—	2	1	no	—
433	C₂×C₄×C₅	—	2	1	no	—
434	C₂×C₄×C₅	—	2	1	no	—
435	C₂×C₄×C₅	—	2	1	no	—
436	C₂×C₄×C₅	—	4	4	no	—
437	C₂×C₄×C₅	C₃×#41	1	2	yes	—
438	C₂×C₄×C₅	C₃×#41	1	2	yes	—
439	C₂×C₄×C₅	C₃×#41	1	2	yes	—
440	C₂×C₄×C₅	C₃×#41	1	2	yes	—
441	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
442	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
454	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
457	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
460	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
461	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
462	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
463	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
464	#95	C₂²×C₃×C₅	1	1	yes	characteristic
465	#95	C₂²×C₃×C₅	1	1	yes	characteristic
466	#95	C₂²×C₃×C₅	1	1	yes	characteristic
467	#95	C₂²×C₃×C₅	1	1	yes	characteristic
468	#95	C₂²×C₃×C₅	1	1	yes	characteristic
469	#95	C₂²×C₃×C₅	1	1	yes	characteristic
470	#95	C₂²×C₃×C₅	1	1	yes	characteristic
471	#95	C₂²×C₃×C₅	1	1	yes	characteristic
472	#95	C₂²×C₃×C₅	1	1	yes	characteristic
473	#95	C₂²×C₃×C₅	1	1	yes	characteristic
474	#95	C₂²×C₃×C₅	1	1	yes	characteristic
475	#95	C₂²×C₃×C₅	1	1	yes	characteristic
476	C₂×C₃×C₅	—	4	2	no	—
477	C₂×C₃×C₅	—	8	1	no	—
478	C₂×C₃×C₅	#529	1	1	yes	characteristic
479	C₂×C₃×C₅	#529	1	1	yes	characteristic
480	C₂×C₃×C₅	#540	1	1	yes	characteristic
481	C₂×C₃×C₅	#551	1	1	yes	characteristic
482	C₂×C₃×C₅	#551	1	1	yes	characteristic
483	C₂×C₃×C₅	#553	1	1	yes	characteristic
484	C₂×C₃×C₅	#559	1	1	yes	characteristic
485	C₂³×C₃	—	2	1	no	—
486	C₂³×C₃	—	2	1	no	—
487	C₂³×C₃	—	2	1	no	—
488	C₂³×C₃	—	2	1	no	—
489	C₂³×C₃	—	2	1	no	—
490	C₂³×C₃	—	2	1	no	—
491	C₂³×C₃	—	2	1	no	—
492	C₂³×C₃	—	2	1	no	—
493	C₂³×C₃	—	2	1	no	—
494	C₂³×C₃	—	2	1	no	—
495	C₂³×C₃	—	2	1	no	—
496	C₂³×C₃	—	2	1	no	—
497	C₂³×C₃	—	2	1	no	—
498	C₂³×C₃	C₅×#41	1	2	yes	—
499	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
500	C₃×D₄	—	4	4	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	—	2	1	no	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	—	2	1	no	—
512	C₂×C₃×C₄	—	2	1	no	—
513	C₂×C₃×C₄	—	2	1	no	—
514	C₂×C₃×C₄	—	2	1	no	—
515	C₂×C₃×C₄	—	2	1	no	—
516	C₂×C₃×C₄	—	2	1	no	—
517	C₂×C₃×C₄	—	2	1	no	—
518	C₂×C₃×C₄	—	2	1	no	—
519	C₂×C₃×C₄	—	2	1	no	—
520	C₂×C₃×C₄	—	2	1	no	—
521	C₂×C₃×C₄	—	2	1	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	2	1	no	—
524	C₂×C₃×C₄	—	2	1	no	—
525	C₂×C₃×C₄	—	2	1	no	—
526	C₂×C₃×C₄	—	2	1	no	—
527	C₂×C₃×C₄	—	2	1	no	—
528	C₂×C₃×C₄	—	2	1	no	—
529	C₂×C₃×C₄	—	2	1	no	—
530	C₂×C₃×C₄	—	2	1	no	—
531	C₂×C₃×C₄	—	2	1	no	—
532	C₂×C₃×C₄	—	2	1	no	—
533	C₂×C₃×C₄	—	2	1	no	—
534	C₂×C₃×C₄	—	2	1	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	—	4	4	no	—
537	C₂×C₃×C₄	C₅×#41	1	2	yes	—
538	C₂×C₃×C₄	C₅×#41	1	2	yes	—
539	C₂×C₃×C₄	C₅×#41	1	2	yes	—
540	C₂×C₃×C₄	C₅×#41	1	2	yes	—
541	C₂²×C₅	—	2	2	no	—
542	C₂²×C₅	—	2	2	no	—
543	C₂²×C₅	—	2	2	no	—
544	C₂²×C₅	—	4	1	no	—
545	C₂²×C₅	—	4	1	no	—
546	C₂²×C₅	—	4	1	no	—
547	C₂²×C₅	—	4	1	no	—
548	C₂²×C₅	—	4	1	no	—
549	C₂²×C₅	—	4	1	no	—
550	C₂²×C₅	—	4	1	no	—
551	C₂²×C₅	—	4	1	no	—
552	C₂²×C₅	—	4	1	no	—
553	C₂²×C₅	—	4	1	no	—
554	C₂²×C₅	—	4	1	no	—
555	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
556	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
557	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
558	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
559	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
560	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
562	C₄×C₅	—	2	2	no	—
563	C₄×C₅	—	2	2	no	—
564	C₄×C₅	—	2	2	no	—
565	C₄×C₅	—	2	2	no	—
566	C₄×C₅	—	4	1	no	—
567	C₄×C₅	—	4	1	no	—
568	C₄×C₅	—	4	1	no	—
569	C₄×C₅	—	4	1	no	—
570	C₄×C₅	—	4	1	no	—
571	C₄×C₅	—	4	1	no	—
572	C₄×C₅	—	4	1	no	—
573	C₄×C₅	—	4	1	no	—
574	C₄×C₅	—	4	1	no	—
575	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
576	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	4	1	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	4	1	no	—
583	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
584	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
585	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
586	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
587	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
588	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
589	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
590	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
591	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
592	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
593	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
594	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
595	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	4	1	no	—
601	C₄⋊C₄	—	4	1	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	4	1	no	—
609	C₂²⋊C₄	—	4	1	no	—
610	C₂²⋊C₄	—	4	1	no	—
611	C₂²⋊C₄	—	4	1	no	—
612	C₂²⋊C₄	—	4	1	no	—
613	C₄²	—	2	2	no	—
614	C₄²	—	4	1	no	—
615	C₄²	—	4	1	no	—
616	C₄²	—	4	1	no	—
617	C₃×C₅	#2516	1	1	yes	characteristic, direct product factor, Hall
618	C₂²×C₃	—	2	2	no	—
619	C₂²×C₃	—	2	2	no	—
620	C₂²×C₃	—	2	2	no	—
621	C₂²×C₃	—	4	1	no	—
622	C₂²×C₃	—	4	1	no	—
623	C₂²×C₃	—	4	1	no	—
624	C₂²×C₃	—	4	1	no	—
625	C₂²×C₃	—	4	1	no	—
626	C₂²×C₃	—	4	1	no	—
627	C₂²×C₃	—	4	1	no	—
628	C₂²×C₃	—	4	1	no	—
629	C₂²×C₃	—	4	1	no	—
630	C₂²×C₃	—	4	1	no	—
631	C₂²×C₃	—	4	1	no	—
632	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
633	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
634	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
635	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
636	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
637	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
638	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
639	C₃×C₄	—	2	2	no	—
640	C₃×C₄	—	2	2	no	—
641	C₃×C₄	—	2	2	no	—
642	C₃×C₄	—	2	2	no	—
643	C₃×C₄	—	4	1	no	—
644	C₃×C₄	—	4	1	no	—
645	C₃×C₄	—	4	1	no	—
646	C₃×C₄	—	4	1	no	—
647	C₃×C₄	—	4	1	no	—
648	C₃×C₄	—	4	1	no	—
649	C₃×C₄	—	4	1	no	—
650	C₃×C₄	—	4	1	no	—
651	C₃×C₄	—	4	1	no	—
652	C₂×C₅	—	4	2	no	—
653	C₂×C₅	—	8	1	no	—
654	C₂×C₅	C₃×#529	1	1	yes	characteristic
655	C₂×C₅	C₃×#529	1	1	yes	characteristic
656	C₂×C₅	C₃×#540	1	1	yes	characteristic
657	C₂×C₅	C₃×#551	1	1	yes	characteristic
658	C₂×C₅	C₃×#551	1	1	yes	characteristic
659	C₂×C₅	C₃×#553	1	1	yes	characteristic
660	C₂×C₅	C₃×#559	1	1	yes	characteristic
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	C₃×C₅×#41	1	2	yes	—
675	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
676	D₄	—	4	4	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	C₃×C₅×#41	1	2	yes	—
714	C₂×C₄	C₃×C₅×#41	1	2	yes	—
715	C₂×C₄	C₃×C₅×#41	1	2	yes	—
716	C₂×C₄	C₃×C₅×#41	1	2	yes	—
717	C₂×C₃	—	4	2	no	—
718	C₂×C₃	—	8	1	no	—
719	C₂×C₃	C₅×#529	1	1	yes	characteristic
720	C₂×C₃	C₅×#529	1	1	yes	characteristic
721	C₂×C₃	C₅×#540	1	1	yes	characteristic
722	C₂×C₃	C₅×#551	1	1	yes	characteristic
723	C₂×C₃	C₅×#551	1	1	yes	characteristic
724	C₂×C₃	C₅×#553	1	1	yes	characteristic
725	C₂×C₃	C₅×#559	1	1	yes	characteristic
726	C₅	C₃×#2516	1	1	yes	characteristic, direct product factor, Sylow
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	1	no	—
741	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
742	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
743	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
744	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
745	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
746	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
747	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	1	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	1	no	—
761	C₃	C₅×#2516	1	1	yes	characteristic, direct product factor, Sylow
762	C₂	—	4	2	no	—
763	C₂	—	8	1	no	—
764	C₂	C₃×C₅×#529	1	1	yes	characteristic
765	C₂	C₃×C₅×#529	1	1	yes	characteristic
766	C₂	C₃×C₅×#540	1	1	yes	characteristic
767	C₂	C₃×C₅×#551	1	1	yes	characteristic
768	C₂	C₃×C₅×#551	1	1	yes	characteristic
769	C₂	C₃×C₅×#553	1	1	yes	characteristic
770	C₂	C₃×C₅×#559	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	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. C₃×C₅×#400	C₂	semidirect
2. C₃×C₅×#399	C₂	semidirect
3. C₃×C₅×#397	C₂	semidirect
6. C₃×C₅×#388	C₂	semidirect
7. C₃×C₅×#388	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
13. C₃×C₅×#381	C₂	semidirect
14. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
15. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
16. C₅×#2516	C₃	direct (N × H)
52. C₃×#2516	C₅	direct (N × H)
53. C₅×#400	C₂×C₃	semidirect
54. C₅×#399	C₂×C₃	semidirect
55. C₅×#397	C₂×C₃	semidirect
58. C₅×#388	C₂×C₃	semidirect
59. C₅×#388	C₂×C₃	semidirect
60. C₅×#388	C₂×C₃	semidirect
61. C₅×#388	C₂×C₃	semidirect
62. C₅×#387	C₂×C₃	semidirect
63. C₅×#387	C₂×C₃	semidirect
65. C₅×#381	C₂×C₃	semidirect
66. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
67. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
110. C₃×#400	C₂×C₅	semidirect
111. C₃×#399	C₂×C₅	semidirect
112. C₃×#397	C₂×C₅	semidirect
115. C₃×#388	C₂×C₅	semidirect
116. C₃×#388	C₂×C₅	semidirect
117. C₃×#388	C₂×C₅	semidirect
118. C₃×#388	C₂×C₅	semidirect
119. C₃×#387	C₂×C₅	semidirect
120. C₃×#387	C₂×C₅	semidirect
122. C₃×#381	C₂×C₅	semidirect
123. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
124. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
160. #2516	C₃×C₅	direct (N × H)
294. #400	C₂×C₃×C₅	semidirect
295. #399	C₂×C₃×C₅	semidirect
296. #397	C₂×C₃×C₅	semidirect
299. #388	C₂×C₃×C₅	semidirect
300. #388	C₂×C₃×C₅	semidirect
301. #388	C₂×C₃×C₅	semidirect
302. #388	C₂×C₃×C₅	semidirect
303. #387	C₂×C₃×C₅	semidirect
304. #387	C₂×C₃×C₅	semidirect
306. #381	C₂×C₃×C₅	semidirect
307. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
308. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
617. C₃×C₅	#2516	direct (N × H)
726. C₅	C₃×#2516	direct (N × H)
761. C₃	C₅×#2516	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×#400	2
C₃×C₅×#399	2
C₃×C₅×#397	2
C₃×C₅×#394	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#386	2
C₃×C₅×#381	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2516	3
C₃×#2516	5

Subgroups — C3×C5×#2516 #14275550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2516 #14275550