Subgroups — C₃×C₅×#2671 #14275705

Order 1920.

1364 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#399	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#392	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2671	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	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
24	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
25	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
26	C₃×C₅×#123	—	2	4	no	—
27	C₃×C₅×#121	—	2	4	no	—
28	C₃×C₅×#121	—	2	4	no	—
29	C₃×C₅×#121	—	2	4	no	—
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₅×C₄⋊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×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₅×C₂²⋊C₄	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×C₅×#95	C₂²	1	1	yes	characteristic
55	C₃×C₅×#95	C₂²	1	1	yes	characteristic
56	C₃×#2671	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
57	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
61	C₅×#399	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#398	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#392	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
73	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
74	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
75	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
80	C₂×C₃×C₅×D₄	—	2	2	no	—
81	C₂×C₃×C₅×D₄	—	2	2	no	—
82	C₂×C₃×C₅×D₄	—	2	2	no	—
83	C₂×C₃×C₅×D₄	—	2	2	no	—
84	C₂×C₃×C₅×D₄	—	2	2	no	—
85	C₂×C₃×C₅×D₄	—	4	1	no	—
86	C₂×C₃×C₅×D₄	—	4	1	no	—
87	C₂×C₃×C₅×D₄	—	4	1	no	—
88	C₂×C₃×C₅×D₄	—	4	1	no	—
89	C₂×C₃×C₅×D₄	—	4	1	no	—
90	C₂×C₃×C₅×D₄	—	4	1	no	—
91	C₂×C₃×C₅×D₄	—	4	1	no	—
92	C₂×C₃×C₅×D₄	—	4	1	no	—
93	C₂×C₃×C₅×D₄	D₄	1	4	yes	complemented
94	C₂²×C₃×C₄×C₅	—	2	2	no	—
95	C₂²×C₃×C₄×C₅	—	2	2	no	—
96	C₂²×C₃×C₄×C₅	—	2	2	no	—
97	C₂²×C₃×C₄×C₅	—	2	2	no	—
98	C₂²×C₃×C₄×C₅	—	2	2	no	—
99	C₂²×C₃×C₄×C₅	—	4	1	no	—
100	C₂²×C₃×C₄×C₅	—	4	1	no	—
101	C₂²×C₃×C₄×C₅	—	4	1	no	—
102	C₂²×C₃×C₄×C₅	—	4	1	no	—
103	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
104	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
105	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
106	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
107	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
108	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
109	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
110	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
111	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
112	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
113	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
114	C₃×C₅×C₄⋊C₄	—	2	2	no	—
115	C₃×C₅×C₄⋊C₄	—	2	2	no	—
116	C₃×C₅×C₄⋊C₄	—	2	2	no	—
117	C₃×C₅×C₄⋊C₄	—	2	2	no	—
118	C₃×C₅×C₄⋊C₄	—	2	2	no	—
119	C₃×C₅×C₄⋊C₄	—	4	1	no	—
120	C₃×C₅×C₄⋊C₄	—	4	1	no	—
121	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
122	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
123	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
124	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
125	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
126	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
127	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
128	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
129	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
130	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
131	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
132	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
133	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	complemented
134	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
135	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
136	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
137	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#399	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#398	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
143	C₃×#392	C₂×C₅	1	1	yes	characteristic, complemented
144	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
146	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
147	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
148	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
149	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
150	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
151	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
152	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
153	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
154	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
155	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
156	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
157	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
158	C₅×#123	—	2	4	no	—
159	C₅×#121	—	2	4	no	—
160	C₅×#121	—	2	4	no	—
161	C₅×#121	—	2	4	no	—
162	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
167	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
170	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
171	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
175	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
177	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
178	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
179	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
180	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
181	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
182	C₅×#95	C₂²×C₃	1	1	yes	characteristic
183	C₅×#95	C₂²×C₃	1	1	yes	characteristic
184	C₅×#95	C₂²×C₃	1	1	yes	characteristic
185	C₅×#95	C₂²×C₃	1	1	yes	characteristic
186	C₅×#95	C₂²×C₃	1	1	yes	characteristic
187	C₅×#95	C₂²×C₃	1	1	yes	characteristic
188	#2671	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
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	—	2	1	no	—
195	C₂³×C₃×C₅	—	2	1	no	—
196	C₂³×C₃×C₅	—	2	1	no	—
197	C₂³×C₃×C₅	—	2	1	no	—
198	C₂³×C₃×C₅	—	2	1	no	—
199	C₂³×C₃×C₅	—	2	1	no	—
200	C₂³×C₃×C₅	—	2	1	no	—
201	C₂³×C₃×C₅	—	2	1	no	—
202	C₂³×C₃×C₅	—	2	1	no	—
203	C₂³×C₃×C₅	—	2	1	no	—
204	C₂³×C₃×C₅	—	2	1	no	—
205	C₂³×C₃×C₅	—	2	1	no	—
206	C₂³×C₃×C₅	—	2	1	no	—
207	C₂³×C₃×C₅	—	2	1	no	—
208	C₂³×C₃×C₅	—	2	1	no	—
209	C₂³×C₃×C₅	—	2	1	no	—
210	C₂³×C₃×C₅	—	2	1	no	—
211	C₂³×C₃×C₅	—	2	1	no	—
212	C₂³×C₃×C₅	—	2	1	no	—
213	C₂³×C₃×C₅	—	2	1	no	—
214	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
215	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
216	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
217	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
218	C₃×C₅×D₄	—	4	4	no	—
219	C₃×C₅×D₄	—	4	4	no	—
220	C₃×C₅×D₄	—	4	4	no	—
221	C₃×C₅×D₄	—	4	4	no	—
222	C₃×C₅×D₄	—	4	4	no	—
223	C₃×C₅×D₄	—	4	4	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	—	2	1	no	—
239	C₂×C₃×C₄×C₅	—	2	1	no	—
240	C₂×C₃×C₄×C₅	—	2	1	no	—
241	C₂×C₃×C₄×C₅	—	2	1	no	—
242	C₂×C₃×C₄×C₅	—	2	1	no	—
243	C₂×C₃×C₄×C₅	—	2	1	no	—
244	C₂×C₃×C₄×C₅	—	2	1	no	—
245	C₂×C₃×C₄×C₅	—	2	1	no	—
246	C₂×C₃×C₄×C₅	—	2	1	no	—
247	C₂×C₃×C₄×C₅	—	2	1	no	—
248	C₂×C₃×C₄×C₅	—	2	1	no	—
249	C₂×C₃×C₄×C₅	—	2	1	no	—
250	C₂×C₃×C₄×C₅	—	2	1	no	—
251	C₂×C₃×C₄×C₅	—	2	1	no	—
252	C₂×C₃×C₄×C₅	—	2	1	no	—
253	C₂×C₃×C₄×C₅	—	4	4	no	—
254	C₂×C₃×C₄×C₅	—	4	4	no	—
255	C₂×C₃×C₄×C₅	—	4	4	no	—
256	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
257	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
258	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
259	C₂×C₃×C₄×C₅	#41	1	2	yes	—
260	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
261	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
262	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
263	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
264	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
265	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
266	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
267	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
268	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
269	C₃×#123	—	2	4	no	—
270	C₃×#121	—	2	4	no	—
271	C₃×#121	—	2	4	no	—
272	C₃×#121	—	2	4	no	—
273	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
274	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
275	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
276	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
277	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
278	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
279	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
280	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
281	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
282	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
283	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
284	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
285	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
286	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
287	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
288	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
289	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
290	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
291	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
292	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
293	C₃×#95	C₂²×C₅	1	1	yes	characteristic
294	C₃×#95	C₂²×C₅	1	1	yes	characteristic
295	C₃×#95	C₂²×C₅	1	1	yes	characteristic
296	C₃×#95	C₂²×C₅	1	1	yes	characteristic
297	C₃×#95	C₂²×C₅	1	1	yes	characteristic
298	C₃×#95	C₂²×C₅	1	1	yes	characteristic
299	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
300	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
301	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
302	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
303	C₂×C₅×D₄	—	2	2	no	—
304	C₂×C₅×D₄	—	2	2	no	—
305	C₂×C₅×D₄	—	2	2	no	—
306	C₂×C₅×D₄	—	2	2	no	—
307	C₂×C₅×D₄	—	2	2	no	—
308	C₂×C₅×D₄	—	2	2	no	—
309	C₂×C₅×D₄	—	2	2	no	—
310	C₂×C₅×D₄	—	2	2	no	—
311	C₂×C₅×D₄	—	2	2	no	—
312	C₂×C₅×D₄	—	4	1	no	—
313	C₂×C₅×D₄	—	4	1	no	—
314	C₂×C₅×D₄	—	4	1	no	—
315	C₂×C₅×D₄	—	4	1	no	—
316	C₂×C₅×D₄	—	4	1	no	—
317	C₂×C₅×D₄	—	4	1	no	—
318	C₂×C₅×D₄	—	4	1	no	—
319	C₂×C₅×D₄	—	4	1	no	—
320	C₂×C₅×D₄	C₃×D₄	1	4	yes	complemented
321	C₂²×C₄×C₅	—	2	2	no	—
322	C₂²×C₄×C₅	—	2	2	no	—
323	C₂²×C₄×C₅	—	2	2	no	—
324	C₂²×C₄×C₅	—	2	2	no	—
325	C₂²×C₄×C₅	—	2	2	no	—
326	C₂²×C₄×C₅	—	4	1	no	—
327	C₂²×C₄×C₅	—	4	1	no	—
328	C₂²×C₄×C₅	—	4	1	no	—
329	C₂²×C₄×C₅	—	4	1	no	—
330	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
331	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
332	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
333	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
334	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
335	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
336	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
337	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
338	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
339	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
340	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
341	C₅×C₄⋊C₄	—	2	2	no	—
342	C₅×C₄⋊C₄	—	2	2	no	—
343	C₅×C₄⋊C₄	—	2	2	no	—
344	C₅×C₄⋊C₄	—	2	2	no	—
345	C₅×C₄⋊C₄	—	2	2	no	—
346	C₅×C₄⋊C₄	—	4	1	no	—
347	C₅×C₄⋊C₄	—	4	1	no	—
348	C₅×C₂²⋊C₄	—	2	2	no	—
349	C₅×C₂²⋊C₄	—	2	2	no	—
350	C₅×C₂²⋊C₄	—	2	2	no	—
351	C₅×C₂²⋊C₄	—	2	2	no	—
352	C₅×C₂²⋊C₄	—	2	2	no	—
353	C₅×C₂²⋊C₄	—	2	2	no	—
354	C₅×C₂²⋊C₄	—	2	2	no	—
355	C₅×C₂²⋊C₄	—	2	2	no	—
356	C₅×C₂²⋊C₄	—	4	1	no	—
357	C₅×C₂²⋊C₄	—	4	1	no	—
358	C₅×C₂²⋊C₄	—	4	1	no	—
359	C₅×C₂²⋊C₄	—	4	1	no	—
360	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	complemented
361	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic, complemented
362	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
363	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
364	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
365	#399	C₂×C₃×C₅	1	1	yes	characteristic, complemented
366	#398	C₂×C₃×C₅	1	1	yes	characteristic, complemented
367	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
368	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
369	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
370	#392	C₂×C₃×C₅	1	1	yes	characteristic, complemented
371	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
372	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
373	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
374	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
375	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
376	C₂²×C₃×C₅	—	2	2	no	—
377	C₂²×C₃×C₅	—	2	2	no	—
378	C₂²×C₃×C₅	—	2	2	no	—
379	C₂²×C₃×C₅	—	2	2	no	—
380	C₂²×C₃×C₅	—	2	2	no	—
381	C₂²×C₃×C₅	—	2	2	no	—
382	C₂²×C₃×C₅	—	2	2	no	—
383	C₂²×C₃×C₅	—	2	2	no	—
384	C₂²×C₃×C₅	—	2	2	no	—
385	C₂²×C₃×C₅	—	4	1	no	—
386	C₂²×C₃×C₅	—	4	1	no	—
387	C₂²×C₃×C₅	—	4	1	no	—
388	C₂²×C₃×C₅	—	4	1	no	—
389	C₂²×C₃×C₅	—	4	1	no	—
390	C₂²×C₃×C₅	—	4	1	no	—
391	C₂²×C₃×C₅	—	4	1	no	—
392	C₂²×C₃×C₅	—	4	1	no	—
393	C₂²×C₃×C₅	—	4	1	no	—
394	C₂²×C₃×C₅	—	4	1	no	—
395	C₂²×C₃×C₅	—	4	1	no	—
396	C₂²×C₃×C₅	—	4	1	no	—
397	C₂²×C₃×C₅	—	4	1	no	—
398	C₂²×C₃×C₅	—	4	1	no	—
399	C₂²×C₃×C₅	—	4	1	no	—
400	C₂²×C₃×C₅	—	4	1	no	—
401	C₂²×C₃×C₅	—	4	1	no	—
402	C₂²×C₃×C₅	—	4	1	no	—
403	C₂²×C₃×C₅	—	4	1	no	—
404	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
405	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
406	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
407	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
408	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
409	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
410	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
411	C₃×C₄×C₅	—	2	2	no	—
412	C₃×C₄×C₅	—	2	2	no	—
413	C₃×C₄×C₅	—	2	2	no	—
414	C₃×C₄×C₅	—	2	2	no	—
415	C₃×C₄×C₅	—	4	1	no	—
416	C₃×C₄×C₅	—	4	1	no	—
417	C₃×C₄×C₅	—	4	1	no	—
418	C₃×C₄×C₅	—	4	1	no	—
419	C₃×C₄×C₅	—	4	1	no	—
420	C₃×C₄×C₅	—	4	1	no	—
421	C₃×C₄×C₅	—	4	1	no	—
422	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
423	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
424	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
425	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
426	C₂×C₃×D₄	—	2	2	no	—
427	C₂×C₃×D₄	—	2	2	no	—
428	C₂×C₃×D₄	—	2	2	no	—
429	C₂×C₃×D₄	—	2	2	no	—
430	C₂×C₃×D₄	—	2	2	no	—
431	C₂×C₃×D₄	—	2	2	no	—
432	C₂×C₃×D₄	—	2	2	no	—
433	C₂×C₃×D₄	—	2	2	no	—
434	C₂×C₃×D₄	—	2	2	no	—
435	C₂×C₃×D₄	—	4	1	no	—
436	C₂×C₃×D₄	—	4	1	no	—
437	C₂×C₃×D₄	—	4	1	no	—
438	C₂×C₃×D₄	—	4	1	no	—
439	C₂×C₃×D₄	—	4	1	no	—
440	C₂×C₃×D₄	—	4	1	no	—
441	C₂×C₃×D₄	—	4	1	no	—
442	C₂×C₃×D₄	—	4	1	no	—
443	C₂×C₃×D₄	C₅×D₄	1	4	yes	complemented
444	C₂²×C₃×C₄	—	2	2	no	—
445	C₂²×C₃×C₄	—	2	2	no	—
446	C₂²×C₃×C₄	—	2	2	no	—
447	C₂²×C₃×C₄	—	2	2	no	—
448	C₂²×C₃×C₄	—	2	2	no	—
449	C₂²×C₃×C₄	—	4	1	no	—
450	C₂²×C₃×C₄	—	4	1	no	—
451	C₂²×C₃×C₄	—	4	1	no	—
452	C₂²×C₃×C₄	—	4	1	no	—
453	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
454	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
455	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
456	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
457	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
458	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
459	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
460	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
461	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
462	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
463	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
464	C₃×C₄⋊C₄	—	2	2	no	—
465	C₃×C₄⋊C₄	—	2	2	no	—
466	C₃×C₄⋊C₄	—	2	2	no	—
467	C₃×C₄⋊C₄	—	2	2	no	—
468	C₃×C₄⋊C₄	—	2	2	no	—
469	C₃×C₄⋊C₄	—	4	1	no	—
470	C₃×C₄⋊C₄	—	4	1	no	—
471	C₃×C₂²⋊C₄	—	2	2	no	—
472	C₃×C₂²⋊C₄	—	2	2	no	—
473	C₃×C₂²⋊C₄	—	2	2	no	—
474	C₃×C₂²⋊C₄	—	2	2	no	—
475	C₃×C₂²⋊C₄	—	2	2	no	—
476	C₃×C₂²⋊C₄	—	2	2	no	—
477	C₃×C₂²⋊C₄	—	2	2	no	—
478	C₃×C₂²⋊C₄	—	2	2	no	—
479	C₃×C₂²⋊C₄	—	4	1	no	—
480	C₃×C₂²⋊C₄	—	4	1	no	—
481	C₃×C₂²⋊C₄	—	4	1	no	—
482	C₃×C₂²⋊C₄	—	4	1	no	—
483	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	complemented
484	C₂³×C₅	—	2	1	no	—
485	C₂³×C₅	—	2	1	no	—
486	C₂³×C₅	—	2	1	no	—
487	C₂³×C₅	—	2	1	no	—
488	C₂³×C₅	—	2	1	no	—
489	C₂³×C₅	—	2	1	no	—
490	C₂³×C₅	—	2	1	no	—
491	C₂³×C₅	—	2	1	no	—
492	C₂³×C₅	—	2	1	no	—
493	C₂³×C₅	—	2	1	no	—
494	C₂³×C₅	—	2	1	no	—
495	C₂³×C₅	—	2	1	no	—
496	C₂³×C₅	—	2	1	no	—
497	C₂³×C₅	—	2	1	no	—
498	C₂³×C₅	—	2	1	no	—
499	C₂³×C₅	—	2	1	no	—
500	C₂³×C₅	—	2	1	no	—
501	C₂³×C₅	—	2	1	no	—
502	C₂³×C₅	—	2	1	no	—
503	C₂³×C₅	—	2	1	no	—
504	C₂³×C₅	—	2	1	no	—
505	C₂³×C₅	—	2	1	no	—
506	C₂³×C₅	—	2	1	no	—
507	C₂³×C₅	—	2	1	no	—
508	C₂³×C₅	—	2	1	no	—
509	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
510	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
511	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
512	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
513	C₅×D₄	—	4	4	no	—
514	C₅×D₄	—	4	4	no	—
515	C₅×D₄	—	4	4	no	—
516	C₅×D₄	—	4	4	no	—
517	C₅×D₄	—	4	4	no	—
518	C₅×D₄	—	4	4	no	—
519	C₂×C₄×C₅	—	2	1	no	—
520	C₂×C₄×C₅	—	2	1	no	—
521	C₂×C₄×C₅	—	2	1	no	—
522	C₂×C₄×C₅	—	2	1	no	—
523	C₂×C₄×C₅	—	2	1	no	—
524	C₂×C₄×C₅	—	2	1	no	—
525	C₂×C₄×C₅	—	2	1	no	—
526	C₂×C₄×C₅	—	2	1	no	—
527	C₂×C₄×C₅	—	2	1	no	—
528	C₂×C₄×C₅	—	2	1	no	—
529	C₂×C₄×C₅	—	2	1	no	—
530	C₂×C₄×C₅	—	2	1	no	—
531	C₂×C₄×C₅	—	2	1	no	—
532	C₂×C₄×C₅	—	2	1	no	—
533	C₂×C₄×C₅	—	2	1	no	—
534	C₂×C₄×C₅	—	2	1	no	—
535	C₂×C₄×C₅	—	2	1	no	—
536	C₂×C₄×C₅	—	2	1	no	—
537	C₂×C₄×C₅	—	2	1	no	—
538	C₂×C₄×C₅	—	2	1	no	—
539	C₂×C₄×C₅	—	2	1	no	—
540	C₂×C₄×C₅	—	2	1	no	—
541	C₂×C₄×C₅	—	2	1	no	—
542	C₂×C₄×C₅	—	2	1	no	—
543	C₂×C₄×C₅	—	2	1	no	—
544	C₂×C₄×C₅	—	2	1	no	—
545	C₂×C₄×C₅	—	2	1	no	—
546	C₂×C₄×C₅	—	2	1	no	—
547	C₂×C₄×C₅	—	2	1	no	—
548	C₂×C₄×C₅	—	4	4	no	—
549	C₂×C₄×C₅	—	4	4	no	—
550	C₂×C₄×C₅	—	4	4	no	—
551	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
552	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
553	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
554	C₂×C₄×C₅	C₃×#41	1	2	yes	—
555	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
556	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
557	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
558	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
559	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
560	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
561	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
562	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
563	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
564	#123	—	2	4	no	—
565	#121	—	2	4	no	—
566	#121	—	2	4	no	—
567	#121	—	2	4	no	—
568	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
575	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
576	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
577	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
578	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
585	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
586	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
587	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
588	#95	C₂²×C₃×C₅	1	1	yes	characteristic
589	#95	C₂²×C₃×C₅	1	1	yes	characteristic
590	#95	C₂²×C₃×C₅	1	1	yes	characteristic
591	#95	C₂²×C₃×C₅	1	1	yes	characteristic
592	#95	C₂²×C₃×C₅	1	1	yes	characteristic
593	#95	C₂²×C₃×C₅	1	1	yes	characteristic
594	C₂×C₃×C₅	—	4	2	no	—
595	C₂×C₃×C₅	—	4	2	no	—
596	C₂×C₃×C₅	—	4	2	no	—
597	C₂×C₃×C₅	—	8	1	no	—
598	C₂×C₃×C₅	#534	1	1	yes	characteristic
599	C₂×C₃×C₅	#537	1	1	yes	characteristic
600	C₂×C₃×C₅	#540	1	1	yes	characteristic
601	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
602	C₂×C₃×C₅	#546	1	1	yes	characteristic
603	C₂×C₃×C₅	#547	1	1	yes	characteristic
604	C₂×C₃×C₅	#562	1	1	yes	characteristic
605	C₂³×C₃	—	2	1	no	—
606	C₂³×C₃	—	2	1	no	—
607	C₂³×C₃	—	2	1	no	—
608	C₂³×C₃	—	2	1	no	—
609	C₂³×C₃	—	2	1	no	—
610	C₂³×C₃	—	2	1	no	—
611	C₂³×C₃	—	2	1	no	—
612	C₂³×C₃	—	2	1	no	—
613	C₂³×C₃	—	2	1	no	—
614	C₂³×C₃	—	2	1	no	—
615	C₂³×C₃	—	2	1	no	—
616	C₂³×C₃	—	2	1	no	—
617	C₂³×C₃	—	2	1	no	—
618	C₂³×C₃	—	2	1	no	—
619	C₂³×C₃	—	2	1	no	—
620	C₂³×C₃	—	2	1	no	—
621	C₂³×C₃	—	2	1	no	—
622	C₂³×C₃	—	2	1	no	—
623	C₂³×C₃	—	2	1	no	—
624	C₂³×C₃	—	2	1	no	—
625	C₂³×C₃	—	2	1	no	—
626	C₂³×C₃	—	2	1	no	—
627	C₂³×C₃	—	2	1	no	—
628	C₂³×C₃	—	2	1	no	—
629	C₂³×C₃	—	2	1	no	—
630	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
631	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
632	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
633	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
634	C₃×D₄	—	4	4	no	—
635	C₃×D₄	—	4	4	no	—
636	C₃×D₄	—	4	4	no	—
637	C₃×D₄	—	4	4	no	—
638	C₃×D₄	—	4	4	no	—
639	C₃×D₄	—	4	4	no	—
640	C₂×C₃×C₄	—	2	1	no	—
641	C₂×C₃×C₄	—	2	1	no	—
642	C₂×C₃×C₄	—	2	1	no	—
643	C₂×C₃×C₄	—	2	1	no	—
644	C₂×C₃×C₄	—	2	1	no	—
645	C₂×C₃×C₄	—	2	1	no	—
646	C₂×C₃×C₄	—	2	1	no	—
647	C₂×C₃×C₄	—	2	1	no	—
648	C₂×C₃×C₄	—	2	1	no	—
649	C₂×C₃×C₄	—	2	1	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	—	2	1	no	—
653	C₂×C₃×C₄	—	2	1	no	—
654	C₂×C₃×C₄	—	2	1	no	—
655	C₂×C₃×C₄	—	2	1	no	—
656	C₂×C₃×C₄	—	2	1	no	—
657	C₂×C₃×C₄	—	2	1	no	—
658	C₂×C₃×C₄	—	2	1	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	—	2	1	no	—
661	C₂×C₃×C₄	—	2	1	no	—
662	C₂×C₃×C₄	—	2	1	no	—
663	C₂×C₃×C₄	—	2	1	no	—
664	C₂×C₃×C₄	—	2	1	no	—
665	C₂×C₃×C₄	—	2	1	no	—
666	C₂×C₃×C₄	—	2	1	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	4	4	no	—
670	C₂×C₃×C₄	—	4	4	no	—
671	C₂×C₃×C₄	—	4	4	no	—
672	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
673	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
674	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
675	C₂×C₃×C₄	C₅×#41	1	2	yes	—
676	C₂²×C₅	—	2	2	no	—
677	C₂²×C₅	—	2	2	no	—
678	C₂²×C₅	—	2	2	no	—
679	C₂²×C₅	—	2	2	no	—
680	C₂²×C₅	—	2	2	no	—
681	C₂²×C₅	—	2	2	no	—
682	C₂²×C₅	—	2	2	no	—
683	C₂²×C₅	—	2	2	no	—
684	C₂²×C₅	—	2	2	no	—
685	C₂²×C₅	—	4	1	no	—
686	C₂²×C₅	—	4	1	no	—
687	C₂²×C₅	—	4	1	no	—
688	C₂²×C₅	—	4	1	no	—
689	C₂²×C₅	—	4	1	no	—
690	C₂²×C₅	—	4	1	no	—
691	C₂²×C₅	—	4	1	no	—
692	C₂²×C₅	—	4	1	no	—
693	C₂²×C₅	—	4	1	no	—
694	C₂²×C₅	—	4	1	no	—
695	C₂²×C₅	—	4	1	no	—
696	C₂²×C₅	—	4	1	no	—
697	C₂²×C₅	—	4	1	no	—
698	C₂²×C₅	—	4	1	no	—
699	C₂²×C₅	—	4	1	no	—
700	C₂²×C₅	—	4	1	no	—
701	C₂²×C₅	—	4	1	no	—
702	C₂²×C₅	—	4	1	no	—
703	C₂²×C₅	—	4	1	no	—
704	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
705	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
706	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
707	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
708	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
709	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
710	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
711	C₄×C₅	—	2	2	no	—
712	C₄×C₅	—	2	2	no	—
713	C₄×C₅	—	2	2	no	—
714	C₄×C₅	—	2	2	no	—
715	C₄×C₅	—	4	1	no	—
716	C₄×C₅	—	4	1	no	—
717	C₄×C₅	—	4	1	no	—
718	C₄×C₅	—	4	1	no	—
719	C₄×C₅	—	4	1	no	—
720	C₄×C₅	—	4	1	no	—
721	C₄×C₅	—	4	1	no	—
722	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
723	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
724	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
725	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	4	1	no	—
736	C₂×D₄	—	4	1	no	—
737	C₂×D₄	—	4	1	no	—
738	C₂×D₄	—	4	1	no	—
739	C₂×D₄	—	4	1	no	—
740	C₂×D₄	—	4	1	no	—
741	C₂×D₄	—	4	1	no	—
742	C₂×D₄	—	4	1	no	—
743	C₂×D₄	C₃×C₅×D₄	1	4	yes	complemented
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	4	1	no	—
750	C₂²×C₄	—	4	1	no	—
751	C₂²×C₄	—	4	1	no	—
752	C₂²×C₄	—	4	1	no	—
753	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
754	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
755	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
756	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
757	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
758	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
759	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
760	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
761	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
762	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
763	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	4	1	no	—
770	C₄⋊C₄	—	4	1	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	4	1	no	—
780	C₂²⋊C₄	—	4	1	no	—
781	C₂²⋊C₄	—	4	1	no	—
782	C₂²⋊C₄	—	4	1	no	—
783	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
784	C₃×C₅	#2671	1	1	yes	characteristic, direct product factor, Hall
785	C₂²×C₃	—	2	2	no	—
786	C₂²×C₃	—	2	2	no	—
787	C₂²×C₃	—	2	2	no	—
788	C₂²×C₃	—	2	2	no	—
789	C₂²×C₃	—	2	2	no	—
790	C₂²×C₃	—	2	2	no	—
791	C₂²×C₃	—	2	2	no	—
792	C₂²×C₃	—	2	2	no	—
793	C₂²×C₃	—	2	2	no	—
794	C₂²×C₃	—	4	1	no	—
795	C₂²×C₃	—	4	1	no	—
796	C₂²×C₃	—	4	1	no	—
797	C₂²×C₃	—	4	1	no	—
798	C₂²×C₃	—	4	1	no	—
799	C₂²×C₃	—	4	1	no	—
800	C₂²×C₃	—	4	1	no	—
801	C₂²×C₃	—	4	1	no	—
802	C₂²×C₃	—	4	1	no	—
803	C₂²×C₃	—	4	1	no	—
804	C₂²×C₃	—	4	1	no	—
805	C₂²×C₃	—	4	1	no	—
806	C₂²×C₃	—	4	1	no	—
807	C₂²×C₃	—	4	1	no	—
808	C₂²×C₃	—	4	1	no	—
809	C₂²×C₃	—	4	1	no	—
810	C₂²×C₃	—	4	1	no	—
811	C₂²×C₃	—	4	1	no	—
812	C₂²×C₃	—	4	1	no	—
813	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
814	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
815	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
816	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
817	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
818	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
819	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
820	C₃×C₄	—	2	2	no	—
821	C₃×C₄	—	2	2	no	—
822	C₃×C₄	—	2	2	no	—
823	C₃×C₄	—	2	2	no	—
824	C₃×C₄	—	4	1	no	—
825	C₃×C₄	—	4	1	no	—
826	C₃×C₄	—	4	1	no	—
827	C₃×C₄	—	4	1	no	—
828	C₃×C₄	—	4	1	no	—
829	C₃×C₄	—	4	1	no	—
830	C₃×C₄	—	4	1	no	—
831	C₂×C₅	—	4	2	no	—
832	C₂×C₅	—	4	2	no	—
833	C₂×C₅	—	4	2	no	—
834	C₂×C₅	—	8	1	no	—
835	C₂×C₅	C₃×#534	1	1	yes	characteristic
836	C₂×C₅	C₃×#537	1	1	yes	characteristic
837	C₂×C₅	C₃×#540	1	1	yes	characteristic
838	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
839	C₂×C₅	C₃×#546	1	1	yes	characteristic
840	C₂×C₅	C₃×#547	1	1	yes	characteristic
841	C₂×C₅	C₃×#562	1	1	yes	characteristic
842	C₂³	—	2	1	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	1	no	—
867	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
868	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
869	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
870	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
871	D₄	—	4	4	no	—
872	D₄	—	4	4	no	—
873	D₄	—	4	4	no	—
874	D₄	—	4	4	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	4	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	4	4	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
910	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
911	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
912	C₂×C₄	C₃×C₅×#41	1	2	yes	—
913	C₂×C₃	—	4	2	no	—
914	C₂×C₃	—	4	2	no	—
915	C₂×C₃	—	4	2	no	—
916	C₂×C₃	—	8	1	no	—
917	C₂×C₃	C₅×#534	1	1	yes	characteristic
918	C₂×C₃	C₅×#537	1	1	yes	characteristic
919	C₂×C₃	C₅×#540	1	1	yes	characteristic
920	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
921	C₂×C₃	C₅×#546	1	1	yes	characteristic
922	C₂×C₃	C₅×#547	1	1	yes	characteristic
923	C₂×C₃	C₅×#562	1	1	yes	characteristic
924	C₅	C₃×#2671	1	1	yes	characteristic, direct product factor, Sylow
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	1	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	1	no	—
950	C₂²	—	4	1	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	1	no	—
953	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
954	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
955	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
956	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
957	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
958	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
959	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	2	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	1	no	—
969	C₄	—	4	1	no	—
970	C₄	—	4	1	no	—
971	C₃	C₅×#2671	1	1	yes	characteristic, direct product factor, Sylow
972	C₂	—	4	2	no	—
973	C₂	—	4	2	no	—
974	C₂	—	4	2	no	—
975	C₂	—	8	1	no	—
976	C₂	C₃×C₅×#534	1	1	yes	characteristic
977	C₂	C₃×C₅×#537	1	1	yes	characteristic
978	C₂	C₃×C₅×#540	1	1	yes	characteristic
979	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
980	C₂	C₃×C₅×#546	1	1	yes	characteristic
981	C₂	C₃×C₅×#547	1	1	yes	characteristic
982	C₂	C₃×C₅×#562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
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×#123	C₂	semidirect
2. C₂×C₃×C₅×#121	C₂	semidirect
3. C₂×C₃×C₅×#121	C₂	semidirect
4. C₂×C₃×C₅×#121	C₂	semidirect
5. C₃×C₅×#399	C₂	semidirect
6. C₃×C₅×#398	C₂	semidirect
7. C₃×C₅×#394	C₂	semidirect
8. C₃×C₅×#394	C₂	semidirect
9. C₃×C₅×#394	C₂	semidirect
10. C₃×C₅×#392	C₂	semidirect
11. C₃×C₅×#386	C₂	semidirect
12. C₃×C₅×#386	C₂	semidirect
13. C₃×C₅×#385	C₂	semidirect
14. C₃×C₅×#385	C₂	semidirect
15. C₃×C₅×#380	C₂	semidirect
16. C₅×#2671	C₃	direct (N × H)
56. C₃×#2671	C₅	direct (N × H)
57. C₂×C₅×#123	C₂×C₃	semidirect
58. C₂×C₅×#121	C₂×C₃	semidirect
59. C₂×C₅×#121	C₂×C₃	semidirect
60. C₂×C₅×#121	C₂×C₃	semidirect
61. C₅×#399	C₂×C₃	semidirect
62. C₅×#398	C₂×C₃	semidirect
63. C₅×#394	C₂×C₃	semidirect
64. C₅×#394	C₂×C₃	semidirect
65. C₅×#394	C₂×C₃	semidirect
66. C₅×#392	C₂×C₃	semidirect
67. C₅×#386	C₂×C₃	semidirect
68. C₅×#386	C₂×C₃	semidirect
69. C₅×#385	C₂×C₃	semidirect
70. C₅×#385	C₂×C₃	semidirect
71. C₅×#380	C₂×C₃	semidirect
93. C₂×C₃×C₅×D₄	D₄	semidirect
133. C₃×C₅×C₂²⋊C₄	D₄	semidirect
134. C₂×C₃×#123	C₂×C₅	semidirect
135. C₂×C₃×#121	C₂×C₅	semidirect
136. C₂×C₃×#121	C₂×C₅	semidirect
137. C₂×C₃×#121	C₂×C₅	semidirect
138. C₃×#399	C₂×C₅	semidirect
139. C₃×#398	C₂×C₅	semidirect
140. C₃×#394	C₂×C₅	semidirect
141. C₃×#394	C₂×C₅	semidirect
142. C₃×#394	C₂×C₅	semidirect
143. C₃×#392	C₂×C₅	semidirect
144. C₃×#386	C₂×C₅	semidirect
145. C₃×#386	C₂×C₅	semidirect
146. C₃×#385	C₂×C₅	semidirect
147. C₃×#385	C₂×C₅	semidirect
148. C₃×#380	C₂×C₅	semidirect
188. #2671	C₃×C₅	direct (N × H)
320. C₂×C₅×D₄	C₃×D₄	semidirect
360. C₅×C₂²⋊C₄	C₃×D₄	semidirect
361. C₂×#123	C₂×C₃×C₅	semidirect
362. C₂×#121	C₂×C₃×C₅	semidirect
363. C₂×#121	C₂×C₃×C₅	semidirect
364. C₂×#121	C₂×C₃×C₅	semidirect
365. #399	C₂×C₃×C₅	semidirect
366. #398	C₂×C₃×C₅	semidirect
367. #394	C₂×C₃×C₅	semidirect
368. #394	C₂×C₃×C₅	semidirect
369. #394	C₂×C₃×C₅	semidirect
370. #392	C₂×C₃×C₅	semidirect
371. #386	C₂×C₃×C₅	semidirect
372. #386	C₂×C₃×C₅	semidirect
373. #385	C₂×C₃×C₅	semidirect
374. #385	C₂×C₃×C₅	semidirect
375. #380	C₂×C₃×C₅	semidirect
443. C₂×C₃×D₄	C₅×D₄	semidirect
483. C₃×C₂²⋊C₄	C₅×D₄	semidirect
743. C₂×D₄	C₃×C₅×D₄	semidirect
783. C₂²⋊C₄	C₃×C₅×D₄	semidirect
784. C₃×C₅	#2671	direct (N × H)
924. C₅	C₃×#2671	direct (N × H)
971. C₃	C₅×#2671	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×#123	2
C₂×C₃×C₅×#121	2
C₃×C₅×#399	2
C₃×C₅×#398	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#380	2
C₅×#2671	3
C₃×#2671	5

Subgroups — C3×C5×#2671 #14275705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2671 #14275705