Subgroups — C₃×C₅×#2703 #14275737

Order 1920.

1224 conjugacy classes of subgroups.

The subgroup lattice has 956 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	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#397	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, complemented
7	C₃×C₅×#392	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#388	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×#386	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2703	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	C₃×C₅×#123	—	2	4	no	—
26	C₃×C₅×#121	—	2	4	no	—
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₅×C₂²⋊C₄	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×#2703	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
55	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
57	C₅×#400	C₂×C₃	1	1	yes	characteristic, complemented
58	C₅×#397	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, complemented
61	C₅×#392	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#392	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#388	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#388	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×#386	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#380	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	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
80	C₂×C₃×C₅×D₄	—	2	2	no	—
81	C₂×C₃×C₅×D₄	—	2	2	no	—
82	C₂×C₃×C₅×D₄	—	4	1	no	—
83	C₂×C₃×C₅×D₄	—	4	1	no	—
84	C₂×C₃×C₅×D₄	—	4	1	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	C₂²×C₃×C₄×C₅	—	2	2	no	—
93	C₂²×C₃×C₄×C₅	—	2	2	no	—
94	C₂²×C₃×C₄×C₅	—	2	2	no	—
95	C₂²×C₃×C₄×C₅	—	4	1	no	—
96	C₂²×C₃×C₄×C₅	—	4	1	no	—
97	C₂²×C₃×C₄×C₅	—	4	1	no	—
98	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
100	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
101	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
102	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	C₃×C₅×C₄⋊C₄	—	2	2	no	—
110	C₃×C₅×C₄⋊C₄	—	2	2	no	—
111	C₃×C₅×C₄⋊C₄	—	2	2	no	—
112	C₃×C₅×C₄⋊C₄	—	4	1	no	—
113	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
114	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
115	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
116	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
117	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
118	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
119	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
120	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
121	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
122	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
123	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
124	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
125	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
126	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	complemented
127	C₃×C₄²×C₅	—	4	1	no	—
128	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
129	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#400	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#397	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#392	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#392	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#392	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
144	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
145	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
146	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
147	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
148	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
149	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
150	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
151	C₅×#123	—	2	4	no	—
152	C₅×#121	—	2	4	no	—
153	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
160	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
161	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
162	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
167	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₅×C₂²⋊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×C₄²×C₅	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	C₅×#95	C₂²×C₃	1	1	yes	characteristic
175	C₅×#95	C₂²×C₃	1	1	yes	characteristic
176	C₅×#95	C₂²×C₃	1	1	yes	characteristic
177	C₅×#95	C₂²×C₃	1	1	yes	characteristic
178	C₅×#95	C₂²×C₃	1	1	yes	characteristic
179	C₅×#95	C₂²×C₃	1	1	yes	characteristic
180	#2703	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
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	—	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	C₂×D₄	1	2	yes	—
208	C₂³×C₃×C₅	#41	1	2	yes	—
209	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
210	C₃×C₅×D₄	—	4	4	no	—
211	C₃×C₅×D₄	—	4	4	no	—
212	C₃×C₅×D₄	—	4	4	no	—
213	C₃×C₅×D₄	—	4	4	no	—
214	C₃×C₅×D₄	—	4	4	no	—
215	C₃×C₅×D₄	—	4	4	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	2	1	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	2	1	no	—
224	C₂×C₃×C₄×C₅	—	2	1	no	—
225	C₂×C₃×C₄×C₅	—	2	1	no	—
226	C₂×C₃×C₄×C₅	—	2	1	no	—
227	C₂×C₃×C₄×C₅	—	2	1	no	—
228	C₂×C₃×C₄×C₅	—	2	1	no	—
229	C₂×C₃×C₄×C₅	—	2	1	no	—
230	C₂×C₃×C₄×C₅	—	2	1	no	—
231	C₂×C₃×C₄×C₅	—	2	1	no	—
232	C₂×C₃×C₄×C₅	—	2	1	no	—
233	C₂×C₃×C₄×C₅	—	2	1	no	—
234	C₂×C₃×C₄×C₅	—	2	1	no	—
235	C₂×C₃×C₄×C₅	—	2	1	no	—
236	C₂×C₃×C₄×C₅	—	2	1	no	—
237	C₂×C₃×C₄×C₅	—	2	1	no	—
238	C₂×C₃×C₄×C₅	—	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	—	4	4	no	—
247	C₂×C₃×C₄×C₅	—	4	4	no	—
248	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
249	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
250	C₂×C₃×C₄×C₅	#41	1	2	yes	—
251	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
252	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
253	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
254	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
255	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
256	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
257	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
258	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
259	C₃×#123	—	2	4	no	—
260	C₃×#121	—	2	4	no	—
261	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
267	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
268	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
269	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
273	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
274	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
275	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
276	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
277	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
278	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
279	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
280	C₃×#95	C₂²×C₅	1	1	yes	characteristic
281	C₃×#95	C₂²×C₅	1	1	yes	characteristic
282	C₃×#95	C₂²×C₅	1	1	yes	characteristic
283	C₃×#95	C₂²×C₅	1	1	yes	characteristic
284	C₃×#95	C₂²×C₅	1	1	yes	characteristic
285	C₃×#95	C₂²×C₅	1	1	yes	characteristic
286	C₃×#95	C₂²×C₅	1	1	yes	characteristic
287	C₃×#95	C₂²×C₅	1	1	yes	characteristic
288	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
289	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
290	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
291	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₅×D₄	—	2	2	no	—
293	C₂×C₅×D₄	—	2	2	no	—
294	C₂×C₅×D₄	—	2	2	no	—
295	C₂×C₅×D₄	—	2	2	no	—
296	C₂×C₅×D₄	—	2	2	no	—
297	C₂×C₅×D₄	—	2	2	no	—
298	C₂×C₅×D₄	—	2	2	no	—
299	C₂×C₅×D₄	—	2	2	no	—
300	C₂×C₅×D₄	—	4	1	no	—
301	C₂×C₅×D₄	—	4	1	no	—
302	C₂×C₅×D₄	—	4	1	no	—
303	C₂×C₅×D₄	—	4	1	no	—
304	C₂×C₅×D₄	—	4	1	no	—
305	C₂×C₅×D₄	—	4	1	no	—
306	C₂×C₅×D₄	—	4	1	no	—
307	C₂×C₅×D₄	—	4	1	no	—
308	C₂×C₅×D₄	—	4	1	no	—
309	C₂×C₅×D₄	—	4	1	no	—
310	C₂²×C₄×C₅	—	2	2	no	—
311	C₂²×C₄×C₅	—	2	2	no	—
312	C₂²×C₄×C₅	—	2	2	no	—
313	C₂²×C₄×C₅	—	4	1	no	—
314	C₂²×C₄×C₅	—	4	1	no	—
315	C₂²×C₄×C₅	—	4	1	no	—
316	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
317	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
318	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
319	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
320	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
321	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
322	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
323	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
324	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
325	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
326	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
327	C₅×C₄⋊C₄	—	2	2	no	—
328	C₅×C₄⋊C₄	—	2	2	no	—
329	C₅×C₄⋊C₄	—	2	2	no	—
330	C₅×C₄⋊C₄	—	4	1	no	—
331	C₅×C₂²⋊C₄	—	2	2	no	—
332	C₅×C₂²⋊C₄	—	2	2	no	—
333	C₅×C₂²⋊C₄	—	2	2	no	—
334	C₅×C₂²⋊C₄	—	2	2	no	—
335	C₅×C₂²⋊C₄	—	4	1	no	—
336	C₅×C₂²⋊C₄	—	4	1	no	—
337	C₅×C₂²⋊C₄	—	4	1	no	—
338	C₅×C₂²⋊C₄	—	4	1	no	—
339	C₅×C₂²⋊C₄	—	4	1	no	—
340	C₅×C₂²⋊C₄	—	4	1	no	—
341	C₅×C₂²⋊C₄	—	4	1	no	—
342	C₅×C₂²⋊C₄	—	4	1	no	—
343	C₅×C₂²⋊C₄	—	4	1	no	—
344	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	complemented
345	C₄²×C₅	—	4	1	no	—
346	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic, complemented
347	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
348	#400	C₂×C₃×C₅	1	1	yes	characteristic, complemented
349	#397	C₂×C₃×C₅	1	1	yes	characteristic, complemented
350	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
351	#392	C₂×C₃×C₅	1	1	yes	characteristic, complemented
352	#392	C₂×C₃×C₅	1	1	yes	characteristic, complemented
353	#392	C₂×C₃×C₅	1	1	yes	characteristic, complemented
354	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
355	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
356	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
357	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
358	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
359	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
360	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
361	C₂²×C₃×C₅	—	2	2	no	—
362	C₂²×C₃×C₅	—	2	2	no	—
363	C₂²×C₃×C₅	—	2	2	no	—
364	C₂²×C₃×C₅	—	2	2	no	—
365	C₂²×C₃×C₅	—	2	2	no	—
366	C₂²×C₃×C₅	—	2	2	no	—
367	C₂²×C₃×C₅	—	4	1	no	—
368	C₂²×C₃×C₅	—	4	1	no	—
369	C₂²×C₃×C₅	—	4	1	no	—
370	C₂²×C₃×C₅	—	4	1	no	—
371	C₂²×C₃×C₅	—	4	1	no	—
372	C₂²×C₃×C₅	—	4	1	no	—
373	C₂²×C₃×C₅	—	4	1	no	—
374	C₂²×C₃×C₅	—	4	1	no	—
375	C₂²×C₃×C₅	—	4	1	no	—
376	C₂²×C₃×C₅	—	4	1	no	—
377	C₂²×C₃×C₅	—	4	1	no	—
378	C₂²×C₃×C₅	—	4	1	no	—
379	C₂²×C₃×C₅	—	4	1	no	—
380	C₂²×C₃×C₅	—	4	1	no	—
381	C₂²×C₃×C₅	—	4	1	no	—
382	C₂²×C₃×C₅	—	4	1	no	—
383	C₂²×C₃×C₅	—	4	1	no	—
384	C₂²×C₃×C₅	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
390	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
391	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
392	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
393	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
394	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
395	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
396	C₃×C₄×C₅	—	2	2	no	—
397	C₃×C₄×C₅	—	2	2	no	—
398	C₃×C₄×C₅	—	2	2	no	—
399	C₃×C₄×C₅	—	4	1	no	—
400	C₃×C₄×C₅	—	4	1	no	—
401	C₃×C₄×C₅	—	4	1	no	—
402	C₃×C₄×C₅	—	4	1	no	—
403	C₃×C₄×C₅	—	4	1	no	—
404	C₃×C₄×C₅	—	4	1	no	—
405	C₃×C₄×C₅	—	4	1	no	—
406	C₃×C₄×C₅	—	4	1	no	—
407	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
408	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
409	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
410	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
411	C₂×C₃×D₄	—	2	2	no	—
412	C₂×C₃×D₄	—	2	2	no	—
413	C₂×C₃×D₄	—	2	2	no	—
414	C₂×C₃×D₄	—	2	2	no	—
415	C₂×C₃×D₄	—	2	2	no	—
416	C₂×C₃×D₄	—	2	2	no	—
417	C₂×C₃×D₄	—	2	2	no	—
418	C₂×C₃×D₄	—	2	2	no	—
419	C₂×C₃×D₄	—	4	1	no	—
420	C₂×C₃×D₄	—	4	1	no	—
421	C₂×C₃×D₄	—	4	1	no	—
422	C₂×C₃×D₄	—	4	1	no	—
423	C₂×C₃×D₄	—	4	1	no	—
424	C₂×C₃×D₄	—	4	1	no	—
425	C₂×C₃×D₄	—	4	1	no	—
426	C₂×C₃×D₄	—	4	1	no	—
427	C₂×C₃×D₄	—	4	1	no	—
428	C₂×C₃×D₄	—	4	1	no	—
429	C₂²×C₃×C₄	—	2	2	no	—
430	C₂²×C₃×C₄	—	2	2	no	—
431	C₂²×C₃×C₄	—	2	2	no	—
432	C₂²×C₃×C₄	—	4	1	no	—
433	C₂²×C₃×C₄	—	4	1	no	—
434	C₂²×C₃×C₄	—	4	1	no	—
435	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
436	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
437	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
438	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
439	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
440	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
441	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
442	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
443	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
444	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
445	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
446	C₃×C₄⋊C₄	—	2	2	no	—
447	C₃×C₄⋊C₄	—	2	2	no	—
448	C₃×C₄⋊C₄	—	2	2	no	—
449	C₃×C₄⋊C₄	—	4	1	no	—
450	C₃×C₂²⋊C₄	—	2	2	no	—
451	C₃×C₂²⋊C₄	—	2	2	no	—
452	C₃×C₂²⋊C₄	—	2	2	no	—
453	C₃×C₂²⋊C₄	—	2	2	no	—
454	C₃×C₂²⋊C₄	—	4	1	no	—
455	C₃×C₂²⋊C₄	—	4	1	no	—
456	C₃×C₂²⋊C₄	—	4	1	no	—
457	C₃×C₂²⋊C₄	—	4	1	no	—
458	C₃×C₂²⋊C₄	—	4	1	no	—
459	C₃×C₂²⋊C₄	—	4	1	no	—
460	C₃×C₂²⋊C₄	—	4	1	no	—
461	C₃×C₂²⋊C₄	—	4	1	no	—
462	C₃×C₂²⋊C₄	—	4	1	no	—
463	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	complemented
464	C₃×C₄²	—	4	1	no	—
465	C₂³×C₅	—	2	1	no	—
466	C₂³×C₅	—	2	1	no	—
467	C₂³×C₅	—	2	1	no	—
468	C₂³×C₅	—	2	1	no	—
469	C₂³×C₅	—	2	1	no	—
470	C₂³×C₅	—	2	1	no	—
471	C₂³×C₅	—	2	1	no	—
472	C₂³×C₅	—	2	1	no	—
473	C₂³×C₅	—	2	1	no	—
474	C₂³×C₅	—	2	1	no	—
475	C₂³×C₅	—	2	1	no	—
476	C₂³×C₅	—	2	1	no	—
477	C₂³×C₅	—	2	1	no	—
478	C₂³×C₅	—	2	1	no	—
479	C₂³×C₅	—	2	1	no	—
480	C₂³×C₅	—	2	1	no	—
481	C₂³×C₅	—	2	1	no	—
482	C₂³×C₅	—	2	1	no	—
483	C₂³×C₅	—	2	1	no	—
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	C₂×C₃×D₄	1	2	yes	—
492	C₂³×C₅	C₃×#41	1	2	yes	—
493	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
494	C₅×D₄	—	4	4	no	—
495	C₅×D₄	—	4	4	no	—
496	C₅×D₄	—	4	4	no	—
497	C₅×D₄	—	4	4	no	—
498	C₅×D₄	—	4	4	no	—
499	C₅×D₄	—	4	4	no	—
500	C₂×C₄×C₅	—	2	1	no	—
501	C₂×C₄×C₅	—	2	1	no	—
502	C₂×C₄×C₅	—	2	1	no	—
503	C₂×C₄×C₅	—	2	1	no	—
504	C₂×C₄×C₅	—	2	1	no	—
505	C₂×C₄×C₅	—	2	1	no	—
506	C₂×C₄×C₅	—	2	1	no	—
507	C₂×C₄×C₅	—	2	1	no	—
508	C₂×C₄×C₅	—	2	1	no	—
509	C₂×C₄×C₅	—	2	1	no	—
510	C₂×C₄×C₅	—	2	1	no	—
511	C₂×C₄×C₅	—	2	1	no	—
512	C₂×C₄×C₅	—	2	1	no	—
513	C₂×C₄×C₅	—	2	1	no	—
514	C₂×C₄×C₅	—	2	1	no	—
515	C₂×C₄×C₅	—	2	1	no	—
516	C₂×C₄×C₅	—	2	1	no	—
517	C₂×C₄×C₅	—	2	1	no	—
518	C₂×C₄×C₅	—	2	1	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	—	4	4	no	—
531	C₂×C₄×C₅	—	4	4	no	—
532	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
533	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
534	C₂×C₄×C₅	C₃×#41	1	2	yes	—
535	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
536	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
537	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
538	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
539	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
540	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
541	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
542	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
543	#123	—	2	4	no	—
544	#121	—	2	4	no	—
545	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
555	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
556	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
557	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
558	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
559	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
560	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
561	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
563	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
564	#95	C₂²×C₃×C₅	1	1	yes	characteristic
565	#95	C₂²×C₃×C₅	1	1	yes	characteristic
566	#95	C₂²×C₃×C₅	1	1	yes	characteristic
567	#95	C₂²×C₃×C₅	1	1	yes	characteristic
568	#95	C₂²×C₃×C₅	1	1	yes	characteristic
569	#95	C₂²×C₃×C₅	1	1	yes	characteristic
570	#95	C₂²×C₃×C₅	1	1	yes	characteristic
571	#95	C₂²×C₃×C₅	1	1	yes	characteristic
572	C₂×C₃×C₅	—	4	2	no	—
573	C₂×C₃×C₅	—	4	2	no	—
574	C₂×C₃×C₅	—	8	1	no	—
575	C₂×C₃×C₅	—	8	1	no	—
576	C₂×C₃×C₅	#535	1	1	yes	characteristic
577	C₂×C₃×C₅	#538	1	1	yes	characteristic
578	C₂×C₃×C₅	#540	1	1	yes	characteristic
579	C₂×C₃×C₅	#546	1	1	yes	characteristic
580	C₂×C₃×C₅	#546	1	1	yes	characteristic
581	C₂×C₃×C₅	#553	1	1	yes	characteristic
582	C₂×C₃×C₅	#560	1	1	yes	characteristic
583	C₂³×C₃	—	2	1	no	—
584	C₂³×C₃	—	2	1	no	—
585	C₂³×C₃	—	2	1	no	—
586	C₂³×C₃	—	2	1	no	—
587	C₂³×C₃	—	2	1	no	—
588	C₂³×C₃	—	2	1	no	—
589	C₂³×C₃	—	2	1	no	—
590	C₂³×C₃	—	2	1	no	—
591	C₂³×C₃	—	2	1	no	—
592	C₂³×C₃	—	2	1	no	—
593	C₂³×C₃	—	2	1	no	—
594	C₂³×C₃	—	2	1	no	—
595	C₂³×C₃	—	2	1	no	—
596	C₂³×C₃	—	2	1	no	—
597	C₂³×C₃	—	2	1	no	—
598	C₂³×C₃	—	2	1	no	—
599	C₂³×C₃	—	2	1	no	—
600	C₂³×C₃	—	2	1	no	—
601	C₂³×C₃	—	2	1	no	—
602	C₂³×C₃	—	2	1	no	—
603	C₂³×C₃	—	2	1	no	—
604	C₂³×C₃	—	2	1	no	—
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	C₂×C₅×D₄	1	2	yes	—
610	C₂³×C₃	C₅×#41	1	2	yes	—
611	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
612	C₃×D₄	—	4	4	no	—
613	C₃×D₄	—	4	4	no	—
614	C₃×D₄	—	4	4	no	—
615	C₃×D₄	—	4	4	no	—
616	C₃×D₄	—	4	4	no	—
617	C₃×D₄	—	4	4	no	—
618	C₂×C₃×C₄	—	2	1	no	—
619	C₂×C₃×C₄	—	2	1	no	—
620	C₂×C₃×C₄	—	2	1	no	—
621	C₂×C₃×C₄	—	2	1	no	—
622	C₂×C₃×C₄	—	2	1	no	—
623	C₂×C₃×C₄	—	2	1	no	—
624	C₂×C₃×C₄	—	2	1	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	—	2	1	no	—
631	C₂×C₃×C₄	—	2	1	no	—
632	C₂×C₃×C₄	—	2	1	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	2	1	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	1	no	—
637	C₂×C₃×C₄	—	2	1	no	—
638	C₂×C₃×C₄	—	2	1	no	—
639	C₂×C₃×C₄	—	2	1	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	—	4	4	no	—
649	C₂×C₃×C₄	—	4	4	no	—
650	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
651	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
652	C₂×C₃×C₄	C₅×#41	1	2	yes	—
653	C₂²×C₅	—	2	2	no	—
654	C₂²×C₅	—	2	2	no	—
655	C₂²×C₅	—	2	2	no	—
656	C₂²×C₅	—	2	2	no	—
657	C₂²×C₅	—	2	2	no	—
658	C₂²×C₅	—	2	2	no	—
659	C₂²×C₅	—	4	1	no	—
660	C₂²×C₅	—	4	1	no	—
661	C₂²×C₅	—	4	1	no	—
662	C₂²×C₅	—	4	1	no	—
663	C₂²×C₅	—	4	1	no	—
664	C₂²×C₅	—	4	1	no	—
665	C₂²×C₅	—	4	1	no	—
666	C₂²×C₅	—	4	1	no	—
667	C₂²×C₅	—	4	1	no	—
668	C₂²×C₅	—	4	1	no	—
669	C₂²×C₅	—	4	1	no	—
670	C₂²×C₅	—	4	1	no	—
671	C₂²×C₅	—	4	1	no	—
672	C₂²×C₅	—	4	1	no	—
673	C₂²×C₅	—	4	1	no	—
674	C₂²×C₅	—	4	1	no	—
675	C₂²×C₅	—	4	1	no	—
676	C₂²×C₅	—	4	1	no	—
677	C₂²×C₅	—	4	1	no	—
678	C₂²×C₅	—	4	1	no	—
679	C₂²×C₅	—	4	1	no	—
680	C₂²×C₅	—	4	1	no	—
681	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
682	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
683	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
684	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
685	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
686	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
687	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
688	C₄×C₅	—	2	2	no	—
689	C₄×C₅	—	2	2	no	—
690	C₄×C₅	—	2	2	no	—
691	C₄×C₅	—	4	1	no	—
692	C₄×C₅	—	4	1	no	—
693	C₄×C₅	—	4	1	no	—
694	C₄×C₅	—	4	1	no	—
695	C₄×C₅	—	4	1	no	—
696	C₄×C₅	—	4	1	no	—
697	C₄×C₅	—	4	1	no	—
698	C₄×C₅	—	4	1	no	—
699	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
700	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
701	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
702	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	4	1	no	—
712	C₂×D₄	—	4	1	no	—
713	C₂×D₄	—	4	1	no	—
714	C₂×D₄	—	4	1	no	—
715	C₂×D₄	—	4	1	no	—
716	C₂×D₄	—	4	1	no	—
717	C₂×D₄	—	4	1	no	—
718	C₂×D₄	—	4	1	no	—
719	C₂×D₄	—	4	1	no	—
720	C₂×D₄	—	4	1	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	4	1	no	—
725	C₂²×C₄	—	4	1	no	—
726	C₂²×C₄	—	4	1	no	—
727	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
728	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
729	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
730	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
731	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
732	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
733	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
734	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
735	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
736	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
737	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	4	1	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	4	1	no	—
747	C₂²⋊C₄	—	4	1	no	—
748	C₂²⋊C₄	—	4	1	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	—	4	1	no	—
754	C₂²⋊C₄	—	4	1	no	—
755	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
756	C₄²	—	4	1	no	—
757	C₃×C₅	#2703	1	1	yes	characteristic, direct product factor, Hall
758	C₂²×C₃	—	2	2	no	—
759	C₂²×C₃	—	2	2	no	—
760	C₂²×C₃	—	2	2	no	—
761	C₂²×C₃	—	2	2	no	—
762	C₂²×C₃	—	2	2	no	—
763	C₂²×C₃	—	2	2	no	—
764	C₂²×C₃	—	4	1	no	—
765	C₂²×C₃	—	4	1	no	—
766	C₂²×C₃	—	4	1	no	—
767	C₂²×C₃	—	4	1	no	—
768	C₂²×C₃	—	4	1	no	—
769	C₂²×C₃	—	4	1	no	—
770	C₂²×C₃	—	4	1	no	—
771	C₂²×C₃	—	4	1	no	—
772	C₂²×C₃	—	4	1	no	—
773	C₂²×C₃	—	4	1	no	—
774	C₂²×C₃	—	4	1	no	—
775	C₂²×C₃	—	4	1	no	—
776	C₂²×C₃	—	4	1	no	—
777	C₂²×C₃	—	4	1	no	—
778	C₂²×C₃	—	4	1	no	—
779	C₂²×C₃	—	4	1	no	—
780	C₂²×C₃	—	4	1	no	—
781	C₂²×C₃	—	4	1	no	—
782	C₂²×C₃	—	4	1	no	—
783	C₂²×C₃	—	4	1	no	—
784	C₂²×C₃	—	4	1	no	—
785	C₂²×C₃	—	4	1	no	—
786	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
787	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
788	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
789	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
790	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
791	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
792	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
793	C₃×C₄	—	2	2	no	—
794	C₃×C₄	—	2	2	no	—
795	C₃×C₄	—	2	2	no	—
796	C₃×C₄	—	4	1	no	—
797	C₃×C₄	—	4	1	no	—
798	C₃×C₄	—	4	1	no	—
799	C₃×C₄	—	4	1	no	—
800	C₃×C₄	—	4	1	no	—
801	C₃×C₄	—	4	1	no	—
802	C₃×C₄	—	4	1	no	—
803	C₃×C₄	—	4	1	no	—
804	C₂×C₅	—	4	2	no	—
805	C₂×C₅	—	4	2	no	—
806	C₂×C₅	—	8	1	no	—
807	C₂×C₅	—	8	1	no	—
808	C₂×C₅	C₃×#535	1	1	yes	characteristic
809	C₂×C₅	C₃×#538	1	1	yes	characteristic
810	C₂×C₅	C₃×#540	1	1	yes	characteristic
811	C₂×C₅	C₃×#546	1	1	yes	characteristic
812	C₂×C₅	C₃×#546	1	1	yes	characteristic
813	C₂×C₅	C₃×#553	1	1	yes	characteristic
814	C₂×C₅	C₃×#560	1	1	yes	characteristic
815	C₂³	—	2	1	no	—
816	C₂³	—	2	1	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	1	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	1	no	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
842	C₂³	C₃×C₅×#41	1	2	yes	—
843	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
844	D₄	—	4	4	no	—
845	D₄	—	4	4	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	4	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	4	no	—
882	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
883	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
884	C₂×C₄	C₃×C₅×#41	1	2	yes	—
885	C₂×C₃	—	4	2	no	—
886	C₂×C₃	—	4	2	no	—
887	C₂×C₃	—	8	1	no	—
888	C₂×C₃	—	8	1	no	—
889	C₂×C₃	C₅×#535	1	1	yes	characteristic
890	C₂×C₃	C₅×#538	1	1	yes	characteristic
891	C₂×C₃	C₅×#540	1	1	yes	characteristic
892	C₂×C₃	C₅×#546	1	1	yes	characteristic
893	C₂×C₃	C₅×#546	1	1	yes	characteristic
894	C₂×C₃	C₅×#553	1	1	yes	characteristic
895	C₂×C₃	C₅×#560	1	1	yes	characteristic
896	C₅	C₃×#2703	1	1	yes	characteristic, direct product factor, Sylow
897	C₂²	—	2	2	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	2	2	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	1	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	4	1	no	—
909	C₂²	—	4	1	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	1	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	1	no	—
925	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
926	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
927	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
928	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
929	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
930	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
931	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
932	C₄	—	2	2	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	—	4	1	no	—
936	C₄	—	4	1	no	—
937	C₄	—	4	1	no	—
938	C₄	—	4	1	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	1	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	1	no	—
943	C₃	C₅×#2703	1	1	yes	characteristic, direct product factor, Sylow
944	C₂	—	4	2	no	—
945	C₂	—	4	2	no	—
946	C₂	—	8	1	no	—
947	C₂	—	8	1	no	—
948	C₂	C₃×C₅×#535	1	1	yes	characteristic
949	C₂	C₃×C₅×#538	1	1	yes	characteristic
950	C₂	C₃×C₅×#540	1	1	yes	characteristic
951	C₂	C₃×C₅×#546	1	1	yes	characteristic
952	C₂	C₃×C₅×#546	1	1	yes	characteristic
953	C₂	C₃×C₅×#553	1	1	yes	characteristic
954	C₂	C₃×C₅×#560	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. C₃×C₅×#400	C₂	semidirect
4. C₃×C₅×#397	C₂	semidirect
5. C₃×C₅×#394	C₂	semidirect
6. C₃×C₅×#392	C₂	semidirect
7. C₃×C₅×#392	C₂	semidirect
8. C₃×C₅×#392	C₂	semidirect
9. C₃×C₅×#390	C₂	semidirect
10. C₃×C₅×#388	C₂	semidirect
11. C₃×C₅×#388	C₂	semidirect
12. C₃×C₅×#386	C₂	semidirect
13. C₃×C₅×#386	C₂	semidirect
14. C₃×C₅×#386	C₂	semidirect
15. C₃×C₅×#380	C₂	semidirect
16. C₅×#2703	C₃	direct (N × H)
54. C₃×#2703	C₅	direct (N × H)
55. C₂×C₅×#123	C₂×C₃	semidirect
56. C₂×C₅×#121	C₂×C₃	semidirect
57. C₅×#400	C₂×C₃	semidirect
58. C₅×#397	C₂×C₃	semidirect
59. C₅×#394	C₂×C₃	semidirect
60. C₅×#392	C₂×C₃	semidirect
61. C₅×#392	C₂×C₃	semidirect
62. C₅×#392	C₂×C₃	semidirect
63. C₅×#390	C₂×C₃	semidirect
64. C₅×#388	C₂×C₃	semidirect
65. C₅×#388	C₂×C₃	semidirect
66. C₅×#386	C₂×C₃	semidirect
67. C₅×#386	C₂×C₃	semidirect
68. C₅×#386	C₂×C₃	semidirect
69. C₅×#380	C₂×C₃	semidirect
126. C₃×C₅×C₂²⋊C₄	D₄	semidirect
128. C₂×C₃×#123	C₂×C₅	semidirect
129. C₂×C₃×#121	C₂×C₅	semidirect
130. C₃×#400	C₂×C₅	semidirect
131. C₃×#397	C₂×C₅	semidirect
132. C₃×#394	C₂×C₅	semidirect
133. C₃×#392	C₂×C₅	semidirect
134. C₃×#392	C₂×C₅	semidirect
135. C₃×#392	C₂×C₅	semidirect
136. C₃×#390	C₂×C₅	semidirect
137. C₃×#388	C₂×C₅	semidirect
138. C₃×#388	C₂×C₅	semidirect
139. C₃×#386	C₂×C₅	semidirect
140. C₃×#386	C₂×C₅	semidirect
141. C₃×#386	C₂×C₅	semidirect
142. C₃×#380	C₂×C₅	semidirect
180. #2703	C₃×C₅	direct (N × H)
344. C₅×C₂²⋊C₄	C₃×D₄	semidirect
346. C₂×#123	C₂×C₃×C₅	semidirect
347. C₂×#121	C₂×C₃×C₅	semidirect
348. #400	C₂×C₃×C₅	semidirect
349. #397	C₂×C₃×C₅	semidirect
350. #394	C₂×C₃×C₅	semidirect
351. #392	C₂×C₃×C₅	semidirect
352. #392	C₂×C₃×C₅	semidirect
353. #392	C₂×C₃×C₅	semidirect
354. #390	C₂×C₃×C₅	semidirect
355. #388	C₂×C₃×C₅	semidirect
356. #388	C₂×C₃×C₅	semidirect
357. #386	C₂×C₃×C₅	semidirect
358. #386	C₂×C₃×C₅	semidirect
359. #386	C₂×C₃×C₅	semidirect
360. #380	C₂×C₃×C₅	semidirect
463. C₃×C₂²⋊C₄	C₅×D₄	semidirect
755. C₂²⋊C₄	C₃×C₅×D₄	semidirect
757. C₃×C₅	#2703	direct (N × H)
896. C₅	C₃×#2703	direct (N × H)
943. C₃	C₅×#2703	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×#400	2
C₃×C₅×#397	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#380	2
C₅×#2703	3
C₃×#2703	5

Subgroups — C3×C5×#2703 #14275737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2703 #14275737