Subgroups — C₃×C₅×#2488 #14275522

Order 1920.

1092 conjugacy classes of subgroups.

The subgroup lattice has 808 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
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#393	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#391	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×#386	C₂	1	1	yes	maximal, characteristic
11	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic
12	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2488	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
20	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
21	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
22	C₃×C₅×#123	—	2	4	no	—
23	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×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×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₅×C₂²⋊C₄	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×C₅×#95	C₂²	1	1	yes	characteristic
53	C₃×C₅×#95	C₂²	1	1	yes	characteristic
54	C₃×#2488	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
55	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic
56	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
57	C₅×#400	C₂×C₃	1	1	yes	characteristic, complemented
58	C₅×#400	C₂×C₃	1	1	yes	characteristic, complemented
59	C₅×#397	C₂×C₃	1	1	yes	characteristic, complemented
60	C₅×#393	C₂×C₃	1	1	yes	characteristic, complemented
61	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#388	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#388	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#386	C₂×C₃	1	1	yes	characteristic
65	C₅×#386	C₂×C₃	1	1	yes	characteristic
66	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#381	C₂×C₃	1	1	yes	characteristic, complemented
68	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
69	C₂×C₅×#95	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	C₂×C₃×C₅×Q₈	—	2	2	no	—
73	C₂×C₃×C₅×Q₈	—	2	2	no	—
74	C₂×C₃×C₅×Q₈	—	4	1	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	C₂²×C₃×C₄×C₅	—	2	2	no	—
79	C₂²×C₃×C₄×C₅	—	2	2	no	—
80	C₂²×C₃×C₄×C₅	—	2	2	no	—
81	C₂²×C₃×C₄×C₅	—	2	2	no	—
82	C₂²×C₃×C₄×C₅	—	2	2	no	—
83	C₂²×C₃×C₄×C₅	—	2	2	no	—
84	C₂²×C₃×C₄×C₅	—	2	2	no	—
85	C₂²×C₃×C₄×C₅	—	4	1	no	—
86	C₂²×C₃×C₄×C₅	—	4	1	no	—
87	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
96	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
100	C₃×C₅×C₄⋊C₄	—	2	2	no	—
101	C₃×C₅×C₄⋊C₄	—	2	2	no	—
102	C₃×C₅×C₄⋊C₄	—	2	2	no	—
103	C₃×C₅×C₄⋊C₄	—	2	2	no	—
104	C₃×C₅×C₄⋊C₄	—	2	2	no	—
105	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
106	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
107	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
108	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
109	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
110	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
111	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
112	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
113	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	—
114	C₃×C₄²×C₅	—	2	2	no	—
115	C₃×C₄²×C₅	—	4	1	no	—
116	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic
117	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
118	C₃×#400	C₂×C₅	1	1	yes	characteristic, complemented
119	C₃×#400	C₂×C₅	1	1	yes	characteristic, complemented
120	C₃×#397	C₂×C₅	1	1	yes	characteristic, complemented
121	C₃×#393	C₂×C₅	1	1	yes	characteristic, complemented
122	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
123	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
124	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
125	C₃×#386	C₂×C₅	1	1	yes	characteristic
126	C₃×#386	C₂×C₅	1	1	yes	characteristic
127	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
128	C₃×#381	C₂×C₅	1	1	yes	characteristic, complemented
129	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
130	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
132	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
133	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
134	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
135	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
136	C₅×#123	—	2	4	no	—
137	C₅×C₂²⋊Q₈	—	2	4	no	—
138	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₄²×C₅	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	C₅×#95	C₂²×C₃	1	1	yes	characteristic
161	C₅×#95	C₂²×C₃	1	1	yes	characteristic
162	C₅×#95	C₂²×C₃	1	1	yes	characteristic
163	C₅×#95	C₂²×C₃	1	1	yes	characteristic
164	C₅×#95	C₂²×C₃	1	1	yes	characteristic
165	C₅×#95	C₂²×C₃	1	1	yes	characteristic
166	C₅×#95	C₂²×C₃	1	1	yes	characteristic
167	C₅×#95	C₂²×C₃	1	1	yes	characteristic
168	#2488	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
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	—	2	1	no	—
175	C₂³×C₃×C₅	—	2	1	no	—
176	C₂³×C₃×C₅	—	2	1	no	—
177	C₂³×C₃×C₅	—	2	1	no	—
178	C₂³×C₃×C₅	—	2	1	no	—
179	C₂³×C₃×C₅	—	2	1	no	—
180	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
181	C₂³×C₃×C₅	#41	1	2	yes	—
182	C₂³×C₃×C₅	#41	1	2	yes	—
183	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
184	C₃×C₅×Q₈	—	4	4	no	—
185	C₃×C₅×D₄	—	4	4	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	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	1	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	4	4	no	—
222	C₂×C₃×C₄×C₅	—	4	4	no	—
223	C₂×C₃×C₄×C₅	—	4	4	no	—
224	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
225	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
226	C₂×C₃×C₄×C₅	#41	1	2	yes	—
227	C₂×C₃×C₄×C₅	#41	1	2	yes	—
228	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
229	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
230	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
231	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
232	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
233	C₃×#123	—	2	4	no	—
234	C₃×C₂²⋊Q₈	—	2	4	no	—
235	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
251	C₃×#95	C₂²×C₅	1	1	yes	characteristic
252	C₃×#95	C₂²×C₅	1	1	yes	characteristic
253	C₃×#95	C₂²×C₅	1	1	yes	characteristic
254	C₃×#95	C₂²×C₅	1	1	yes	characteristic
255	C₃×#95	C₂²×C₅	1	1	yes	characteristic
256	C₃×#95	C₂²×C₅	1	1	yes	characteristic
257	C₃×#95	C₂²×C₅	1	1	yes	characteristic
258	C₃×#95	C₂²×C₅	1	1	yes	characteristic
259	C₃×#95	C₂²×C₅	1	1	yes	characteristic
260	C₃×#95	C₂²×C₅	1	1	yes	characteristic
261	C₃×#95	C₂²×C₅	1	1	yes	characteristic
262	C₃×#95	C₂²×C₅	1	1	yes	characteristic
263	C₃×#95	C₂²×C₅	1	1	yes	characteristic
264	C₃×#95	C₂²×C₅	1	1	yes	characteristic
265	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
266	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
267	C₂×C₅×Q₈	—	2	2	no	—
268	C₂×C₅×Q₈	—	2	2	no	—
269	C₂×C₅×Q₈	—	4	1	no	—
270	C₂×C₅×D₄	—	2	2	no	—
271	C₂×C₅×D₄	—	2	2	no	—
272	C₂×C₅×D₄	—	2	2	no	—
273	C₂²×C₄×C₅	—	2	2	no	—
274	C₂²×C₄×C₅	—	2	2	no	—
275	C₂²×C₄×C₅	—	2	2	no	—
276	C₂²×C₄×C₅	—	2	2	no	—
277	C₂²×C₄×C₅	—	2	2	no	—
278	C₂²×C₄×C₅	—	2	2	no	—
279	C₂²×C₄×C₅	—	2	2	no	—
280	C₂²×C₄×C₅	—	4	1	no	—
281	C₂²×C₄×C₅	—	4	1	no	—
282	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
283	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
284	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
285	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
286	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
287	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
288	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
289	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
290	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
291	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
292	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
293	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
294	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
295	C₅×C₄⋊C₄	—	2	2	no	—
296	C₅×C₄⋊C₄	—	2	2	no	—
297	C₅×C₄⋊C₄	—	2	2	no	—
298	C₅×C₄⋊C₄	—	2	2	no	—
299	C₅×C₄⋊C₄	—	2	2	no	—
300	C₅×C₂²⋊C₄	—	2	2	no	—
301	C₅×C₂²⋊C₄	—	2	2	no	—
302	C₅×C₂²⋊C₄	—	2	2	no	—
303	C₅×C₂²⋊C₄	—	2	2	no	—
304	C₅×C₂²⋊C₄	—	2	2	no	—
305	C₅×C₂²⋊C₄	—	2	2	no	—
306	C₅×C₂²⋊C₄	—	4	1	no	—
307	C₅×C₂²⋊C₄	—	4	1	no	—
308	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	—
309	C₄²×C₅	—	2	2	no	—
310	C₄²×C₅	—	4	1	no	—
311	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic
312	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
313	#400	C₂×C₃×C₅	1	1	yes	characteristic, complemented
314	#400	C₂×C₃×C₅	1	1	yes	characteristic, complemented
315	#397	C₂×C₃×C₅	1	1	yes	characteristic, complemented
316	#393	C₂×C₃×C₅	1	1	yes	characteristic, complemented
317	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
318	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
319	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
320	#386	C₂×C₃×C₅	1	1	yes	characteristic
321	#386	C₂×C₃×C₅	1	1	yes	characteristic
322	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
323	#381	C₂×C₃×C₅	1	1	yes	characteristic, complemented
324	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
325	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic, complemented
326	C₂²×C₃×C₅	—	2	2	no	—
327	C₂²×C₃×C₅	—	2	2	no	—
328	C₂²×C₃×C₅	—	2	2	no	—
329	C₂²×C₃×C₅	—	2	2	no	—
330	C₂²×C₃×C₅	—	2	2	no	—
331	C₂²×C₃×C₅	—	2	2	no	—
332	C₂²×C₃×C₅	—	4	1	no	—
333	C₂²×C₃×C₅	—	4	1	no	—
334	C₂²×C₃×C₅	—	4	1	no	—
335	C₂²×C₃×C₅	—	4	1	no	—
336	C₂²×C₃×C₅	—	4	1	no	—
337	C₂²×C₃×C₅	—	4	1	no	—
338	C₂²×C₃×C₅	—	4	1	no	—
339	C₂²×C₃×C₅	#124	1	4	yes	—
340	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
341	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
342	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
343	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
344	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
345	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
346	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
347	C₃×C₄×C₅	—	2	2	no	—
348	C₃×C₄×C₅	—	2	2	no	—
349	C₃×C₄×C₅	—	2	2	no	—
350	C₃×C₄×C₅	—	2	2	no	—
351	C₃×C₄×C₅	—	4	1	no	—
352	C₃×C₄×C₅	—	4	1	no	—
353	C₃×C₄×C₅	—	4	1	no	—
354	C₃×C₄×C₅	—	4	1	no	—
355	C₃×C₄×C₅	—	4	1	no	—
356	C₃×C₄×C₅	—	4	1	no	—
357	C₃×C₄×C₅	—	4	1	no	—
358	C₃×C₄×C₅	—	4	1	no	—
359	C₃×C₄×C₅	—	4	1	no	—
360	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
361	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₃×Q₈	—	2	2	no	—
363	C₂×C₃×Q₈	—	2	2	no	—
364	C₂×C₃×Q₈	—	4	1	no	—
365	C₂×C₃×D₄	—	2	2	no	—
366	C₂×C₃×D₄	—	2	2	no	—
367	C₂×C₃×D₄	—	2	2	no	—
368	C₂²×C₃×C₄	—	2	2	no	—
369	C₂²×C₃×C₄	—	2	2	no	—
370	C₂²×C₃×C₄	—	2	2	no	—
371	C₂²×C₃×C₄	—	2	2	no	—
372	C₂²×C₃×C₄	—	2	2	no	—
373	C₂²×C₃×C₄	—	2	2	no	—
374	C₂²×C₃×C₄	—	2	2	no	—
375	C₂²×C₃×C₄	—	4	1	no	—
376	C₂²×C₃×C₄	—	4	1	no	—
377	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
378	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
379	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
380	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
381	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
382	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
383	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
384	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
385	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
386	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
390	C₃×C₄⋊C₄	—	2	2	no	—
391	C₃×C₄⋊C₄	—	2	2	no	—
392	C₃×C₄⋊C₄	—	2	2	no	—
393	C₃×C₄⋊C₄	—	2	2	no	—
394	C₃×C₄⋊C₄	—	2	2	no	—
395	C₃×C₂²⋊C₄	—	2	2	no	—
396	C₃×C₂²⋊C₄	—	2	2	no	—
397	C₃×C₂²⋊C₄	—	2	2	no	—
398	C₃×C₂²⋊C₄	—	2	2	no	—
399	C₃×C₂²⋊C₄	—	2	2	no	—
400	C₃×C₂²⋊C₄	—	2	2	no	—
401	C₃×C₂²⋊C₄	—	4	1	no	—
402	C₃×C₂²⋊C₄	—	4	1	no	—
403	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	—
404	C₃×C₄²	—	2	2	no	—
405	C₃×C₄²	—	4	1	no	—
406	C₂³×C₅	—	2	1	no	—
407	C₂³×C₅	—	2	1	no	—
408	C₂³×C₅	—	2	1	no	—
409	C₂³×C₅	—	2	1	no	—
410	C₂³×C₅	—	2	1	no	—
411	C₂³×C₅	—	2	1	no	—
412	C₂³×C₅	—	2	1	no	—
413	C₂³×C₅	—	2	1	no	—
414	C₂³×C₅	—	2	1	no	—
415	C₂³×C₅	—	2	1	no	—
416	C₂³×C₅	—	2	1	no	—
417	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
418	C₂³×C₅	C₃×#41	1	2	yes	—
419	C₂³×C₅	C₃×#41	1	2	yes	—
420	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
421	C₅×Q₈	—	4	4	no	—
422	C₅×D₄	—	4	4	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	—	2	1	no	—
437	C₂×C₄×C₅	—	2	1	no	—
438	C₂×C₄×C₅	—	2	1	no	—
439	C₂×C₄×C₅	—	2	1	no	—
440	C₂×C₄×C₅	—	2	1	no	—
441	C₂×C₄×C₅	—	2	1	no	—
442	C₂×C₄×C₅	—	2	1	no	—
443	C₂×C₄×C₅	—	2	1	no	—
444	C₂×C₄×C₅	—	2	1	no	—
445	C₂×C₄×C₅	—	2	1	no	—
446	C₂×C₄×C₅	—	2	1	no	—
447	C₂×C₄×C₅	—	2	1	no	—
448	C₂×C₄×C₅	—	2	1	no	—
449	C₂×C₄×C₅	—	2	1	no	—
450	C₂×C₄×C₅	—	2	1	no	—
451	C₂×C₄×C₅	—	2	1	no	—
452	C₂×C₄×C₅	—	2	1	no	—
453	C₂×C₄×C₅	—	2	1	no	—
454	C₂×C₄×C₅	—	2	1	no	—
455	C₂×C₄×C₅	—	2	1	no	—
456	C₂×C₄×C₅	—	2	1	no	—
457	C₂×C₄×C₅	—	2	1	no	—
458	C₂×C₄×C₅	—	4	4	no	—
459	C₂×C₄×C₅	—	4	4	no	—
460	C₂×C₄×C₅	—	4	4	no	—
461	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
462	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
463	C₂×C₄×C₅	C₃×#41	1	2	yes	—
464	C₂×C₄×C₅	C₃×#41	1	2	yes	—
465	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
466	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
467	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
468	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
469	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
470	#123	—	2	4	no	—
471	C₂²⋊Q₈	—	2	4	no	—
472	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
481	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
486	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
487	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
488	#95	C₂²×C₃×C₅	1	1	yes	characteristic
489	#95	C₂²×C₃×C₅	1	1	yes	characteristic
490	#95	C₂²×C₃×C₅	1	1	yes	characteristic
491	#95	C₂²×C₃×C₅	1	1	yes	characteristic
492	#95	C₂²×C₃×C₅	1	1	yes	characteristic
493	#95	C₂²×C₃×C₅	1	1	yes	characteristic
494	#95	C₂²×C₃×C₅	1	1	yes	characteristic
495	#95	C₂²×C₃×C₅	1	1	yes	characteristic
496	#95	C₂²×C₃×C₅	1	1	yes	characteristic
497	#95	C₂²×C₃×C₅	1	1	yes	characteristic
498	#95	C₂²×C₃×C₅	1	1	yes	characteristic
499	#95	C₂²×C₃×C₅	1	1	yes	characteristic
500	#95	C₂²×C₃×C₅	1	1	yes	characteristic
501	#95	C₂²×C₃×C₅	1	1	yes	characteristic
502	C₂×C₃×C₅	—	2	4	no	—
503	C₂×C₃×C₅	—	8	1	no	—
504	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
505	C₂×C₃×C₅	#529	1	1	yes	characteristic
506	C₂×C₃×C₅	#539	1	1	yes	characteristic
507	C₂×C₃×C₅	#546	1	1	yes	characteristic
508	C₂×C₃×C₅	#547	1	1	yes	characteristic
509	C₂×C₃×C₅	#551	1	1	yes	characteristic
510	C₂×C₃×C₅	#552	1	1	yes	characteristic
511	C₂³×C₃	—	2	1	no	—
512	C₂³×C₃	—	2	1	no	—
513	C₂³×C₃	—	2	1	no	—
514	C₂³×C₃	—	2	1	no	—
515	C₂³×C₃	—	2	1	no	—
516	C₂³×C₃	—	2	1	no	—
517	C₂³×C₃	—	2	1	no	—
518	C₂³×C₃	—	2	1	no	—
519	C₂³×C₃	—	2	1	no	—
520	C₂³×C₃	—	2	1	no	—
521	C₂³×C₃	—	2	1	no	—
522	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
523	C₂³×C₃	C₅×#41	1	2	yes	—
524	C₂³×C₃	C₅×#41	1	2	yes	—
525	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
526	C₃×Q₈	—	4	4	no	—
527	C₃×D₄	—	4	4	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	—	2	1	no	—
537	C₂×C₃×C₄	—	2	1	no	—
538	C₂×C₃×C₄	—	2	1	no	—
539	C₂×C₃×C₄	—	2	1	no	—
540	C₂×C₃×C₄	—	2	1	no	—
541	C₂×C₃×C₄	—	2	1	no	—
542	C₂×C₃×C₄	—	2	1	no	—
543	C₂×C₃×C₄	—	2	1	no	—
544	C₂×C₃×C₄	—	2	1	no	—
545	C₂×C₃×C₄	—	2	1	no	—
546	C₂×C₃×C₄	—	2	1	no	—
547	C₂×C₃×C₄	—	2	1	no	—
548	C₂×C₃×C₄	—	2	1	no	—
549	C₂×C₃×C₄	—	2	1	no	—
550	C₂×C₃×C₄	—	2	1	no	—
551	C₂×C₃×C₄	—	2	1	no	—
552	C₂×C₃×C₄	—	2	1	no	—
553	C₂×C₃×C₄	—	2	1	no	—
554	C₂×C₃×C₄	—	2	1	no	—
555	C₂×C₃×C₄	—	2	1	no	—
556	C₂×C₃×C₄	—	2	1	no	—
557	C₂×C₃×C₄	—	2	1	no	—
558	C₂×C₃×C₄	—	2	1	no	—
559	C₂×C₃×C₄	—	2	1	no	—
560	C₂×C₃×C₄	—	2	1	no	—
561	C₂×C₃×C₄	—	2	1	no	—
562	C₂×C₃×C₄	—	2	1	no	—
563	C₂×C₃×C₄	—	4	4	no	—
564	C₂×C₃×C₄	—	4	4	no	—
565	C₂×C₃×C₄	—	4	4	no	—
566	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
567	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
568	C₂×C₃×C₄	C₅×#41	1	2	yes	—
569	C₂×C₃×C₄	C₅×#41	1	2	yes	—
570	C₂²×C₅	—	2	2	no	—
571	C₂²×C₅	—	2	2	no	—
572	C₂²×C₅	—	2	2	no	—
573	C₂²×C₅	—	2	2	no	—
574	C₂²×C₅	—	2	2	no	—
575	C₂²×C₅	—	2	2	no	—
576	C₂²×C₅	—	4	1	no	—
577	C₂²×C₅	—	4	1	no	—
578	C₂²×C₅	—	4	1	no	—
579	C₂²×C₅	—	4	1	no	—
580	C₂²×C₅	—	4	1	no	—
581	C₂²×C₅	—	4	1	no	—
582	C₂²×C₅	—	4	1	no	—
583	C₂²×C₅	C₃×#124	1	4	yes	—
584	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
585	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
586	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
587	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
588	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
589	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
590	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
591	C₄×C₅	—	2	2	no	—
592	C₄×C₅	—	2	2	no	—
593	C₄×C₅	—	2	2	no	—
594	C₄×C₅	—	2	2	no	—
595	C₄×C₅	—	4	1	no	—
596	C₄×C₅	—	4	1	no	—
597	C₄×C₅	—	4	1	no	—
598	C₄×C₅	—	4	1	no	—
599	C₄×C₅	—	4	1	no	—
600	C₄×C₅	—	4	1	no	—
601	C₄×C₅	—	4	1	no	—
602	C₄×C₅	—	4	1	no	—
603	C₄×C₅	—	4	1	no	—
604	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
605	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
606	C₂×Q₈	—	2	2	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	4	1	no	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	4	1	no	—
620	C₂²×C₄	—	4	1	no	—
621	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
622	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
623	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
624	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
625	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
626	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
627	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
628	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
629	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
630	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
631	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
632	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
633	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	4	1	no	—
646	C₂²⋊C₄	—	4	1	no	—
647	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	—
648	C₄²	—	2	2	no	—
649	C₄²	—	4	1	no	—
650	C₃×C₅	#2488	1	1	yes	characteristic, direct product factor, Hall
651	C₂²×C₃	—	2	2	no	—
652	C₂²×C₃	—	2	2	no	—
653	C₂²×C₃	—	2	2	no	—
654	C₂²×C₃	—	2	2	no	—
655	C₂²×C₃	—	2	2	no	—
656	C₂²×C₃	—	2	2	no	—
657	C₂²×C₃	—	4	1	no	—
658	C₂²×C₃	—	4	1	no	—
659	C₂²×C₃	—	4	1	no	—
660	C₂²×C₃	—	4	1	no	—
661	C₂²×C₃	—	4	1	no	—
662	C₂²×C₃	—	4	1	no	—
663	C₂²×C₃	—	4	1	no	—
664	C₂²×C₃	C₅×#124	1	4	yes	—
665	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
666	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
667	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
668	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
669	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
670	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
671	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
672	C₃×C₄	—	2	2	no	—
673	C₃×C₄	—	2	2	no	—
674	C₃×C₄	—	2	2	no	—
675	C₃×C₄	—	2	2	no	—
676	C₃×C₄	—	4	1	no	—
677	C₃×C₄	—	4	1	no	—
678	C₃×C₄	—	4	1	no	—
679	C₃×C₄	—	4	1	no	—
680	C₃×C₄	—	4	1	no	—
681	C₃×C₄	—	4	1	no	—
682	C₃×C₄	—	4	1	no	—
683	C₃×C₄	—	4	1	no	—
684	C₃×C₄	—	4	1	no	—
685	C₂×C₅	—	2	4	no	—
686	C₂×C₅	—	8	1	no	—
687	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
688	C₂×C₅	C₃×#529	1	1	yes	characteristic
689	C₂×C₅	C₃×#539	1	1	yes	characteristic
690	C₂×C₅	C₃×#546	1	1	yes	characteristic
691	C₂×C₅	C₃×#547	1	1	yes	characteristic
692	C₂×C₅	C₃×#551	1	1	yes	characteristic
693	C₂×C₅	C₃×#552	1	1	yes	characteristic
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
706	C₂³	C₃×C₅×#41	1	2	yes	—
707	C₂³	C₃×C₅×#41	1	2	yes	—
708	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
709	Q₈	—	4	4	no	—
710	D₄	—	4	4	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	4	4	no	—
747	C₂×C₄	—	4	4	no	—
748	C₂×C₄	—	4	4	no	—
749	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
750	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
751	C₂×C₄	C₃×C₅×#41	1	2	yes	—
752	C₂×C₄	C₃×C₅×#41	1	2	yes	—
753	C₂×C₃	—	2	4	no	—
754	C₂×C₃	—	8	1	no	—
755	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
756	C₂×C₃	C₅×#529	1	1	yes	characteristic
757	C₂×C₃	C₅×#539	1	1	yes	characteristic
758	C₂×C₃	C₅×#546	1	1	yes	characteristic
759	C₂×C₃	C₅×#547	1	1	yes	characteristic
760	C₂×C₃	C₅×#551	1	1	yes	characteristic
761	C₂×C₃	C₅×#552	1	1	yes	characteristic
762	C₅	C₃×#2488	1	1	yes	characteristic, direct product factor, Sylow
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	C₃×C₅×#124	1	4	yes	—
777	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
778	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
779	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
780	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
781	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
782	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
783	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
784	C₄	—	2	2	no	—
785	C₄	—	2	2	no	—
786	C₄	—	2	2	no	—
787	C₄	—	2	2	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	1	no	—
790	C₄	—	4	1	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	1	no	—
795	C₄	—	4	1	no	—
796	C₄	—	4	1	no	—
797	C₃	C₅×#2488	1	1	yes	characteristic, direct product factor, Sylow
798	C₂	—	2	4	no	—
799	C₂	—	8	1	no	—
800	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
801	C₂	C₃×C₅×#529	1	1	yes	characteristic
802	C₂	C₃×C₅×#539	1	1	yes	characteristic
803	C₂	C₃×C₅×#546	1	1	yes	characteristic
804	C₂	C₃×C₅×#547	1	1	yes	characteristic
805	C₂	C₃×C₅×#551	1	1	yes	characteristic
806	C₂	C₃×C₅×#552	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
2. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
3. C₃×C₅×#400	C₂	semidirect
4. C₃×C₅×#400	C₂	semidirect
5. C₃×C₅×#397	C₂	semidirect
6. C₃×C₅×#393	C₂	semidirect
7. C₃×C₅×#391	C₂	semidirect
8. C₃×C₅×#388	C₂	semidirect
9. C₃×C₅×#388	C₂	semidirect
12. C₃×C₅×#382	C₂	semidirect
13. C₃×C₅×#381	C₂	semidirect
14. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
15. C₂×C₃×C₅×#95	C₂	semidirect
16. C₅×#2488	C₃	direct (N × H)
54. C₃×#2488	C₅	direct (N × H)
56. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
57. C₅×#400	C₂×C₃	semidirect
58. C₅×#400	C₂×C₃	semidirect
59. C₅×#397	C₂×C₃	semidirect
60. C₅×#393	C₂×C₃	semidirect
61. C₅×#391	C₂×C₃	semidirect
62. C₅×#388	C₂×C₃	semidirect
63. C₅×#388	C₂×C₃	semidirect
66. C₅×#382	C₂×C₃	semidirect
67. C₅×#381	C₂×C₃	semidirect
68. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
69. C₂×C₅×#95	C₂×C₃	semidirect
117. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
118. C₃×#400	C₂×C₅	semidirect
119. C₃×#400	C₂×C₅	semidirect
120. C₃×#397	C₂×C₅	semidirect
121. C₃×#393	C₂×C₅	semidirect
122. C₃×#391	C₂×C₅	semidirect
123. C₃×#388	C₂×C₅	semidirect
124. C₃×#388	C₂×C₅	semidirect
127. C₃×#382	C₂×C₅	semidirect
128. C₃×#381	C₂×C₅	semidirect
129. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
130. C₂×C₃×#95	C₂×C₅	semidirect
168. #2488	C₃×C₅	direct (N × H)
312. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
313. #400	C₂×C₃×C₅	semidirect
314. #400	C₂×C₃×C₅	semidirect
315. #397	C₂×C₃×C₅	semidirect
316. #393	C₂×C₃×C₅	semidirect
317. #391	C₂×C₃×C₅	semidirect
318. #388	C₂×C₃×C₅	semidirect
319. #388	C₂×C₃×C₅	semidirect
322. #382	C₂×C₃×C₅	semidirect
323. #381	C₂×C₃×C₅	semidirect
324. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
325. C₂×#95	C₂×C₃×C₅	semidirect
650. C₃×C₅	#2488	direct (N × H)
762. C₅	C₃×#2488	direct (N × H)
797. C₃	C₅×#2488	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×C₂²⋊Q₈	2
C₃×C₅×#400	2
C₃×C₅×#397	2
C₃×C₅×#393	2
C₃×C₅×#391	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#382	2
C₃×C₅×#381	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₂×C₃×C₅×#95	2
C₅×#2488	3
C₃×#2488	5

Subgroups — C3×C5×#2488 #14275522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2488 #14275522