Subgroups — C₃×C₅×#2410 #14275444

Order 1920.

2492 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#392	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2410	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
14	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×D₄	—	2	4	no	—
16	C₂²×C₃×C₅×D₄	—	2	8	no	—
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
19	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
20	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
22	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
23	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
24	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	complemented
25	C₃×C₅×#121	—	2	8	no	—
26	C₃×C₅×#120	—	2	4	no	—
27	C₃×C₅×#120	—	2	4	no	—
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
29	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
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	2	yes	complemented
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
36	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
38	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
39	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
40	C₃×C₅×#95	C₂²	1	2	yes	complemented
41	C₃×C₅×#95	C₂²	1	2	yes	complemented
42	C₃×#2410	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₂³×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
45	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#394	C₂×C₃	1	2	yes	complemented
49	C₅×#392	C₂×C₃	1	2	yes	complemented
50	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#386	C₂×C₃	1	2	yes	complemented
52	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×#379	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂⁴×C₃×C₅	—	2	2	no	—
55	C₂⁴×C₃×C₅	—	2	4	no	—
56	C₂⁴×C₃×C₅	—	2	4	no	—
57	C₂⁴×C₃×C₅	—	2	2	no	—
58	C₂⁴×C₃×C₅	—	2	2	no	—
59	C₂⁴×C₃×C₅	—	2	2	no	—
60	C₂⁴×C₃×C₅	—	2	2	no	—
61	C₂⁴×C₃×C₅	—	4	2	no	—
62	C₂⁴×C₃×C₅	—	4	2	no	—
63	C₂⁴×C₃×C₅	D₄	1	4	yes	complemented
64	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
65	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
66	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
67	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
68	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×D₄	—	2	32	no	—
70	C₂×C₃×C₅×D₄	—	2	4	no	—
71	C₂×C₃×C₅×D₄	—	2	4	no	—
72	C₂×C₃×C₅×D₄	—	2	4	no	—
73	C₂×C₃×C₅×D₄	—	2	4	no	—
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	4	no	—
79	C₂×C₃×C₅×D₄	—	2	4	no	—
80	C₂×C₃×C₅×D₄	—	2	2	no	—
81	C₂×C₃×C₅×D₄	—	2	4	no	—
82	C₂×C₃×C₅×D₄	—	2	4	no	—
83	C₂×C₃×C₅×D₄	—	4	2	no	—
84	C₂×C₃×C₅×D₄	—	4	2	no	—
85	C₂×C₃×C₅×D₄	D₄	1	8	yes	complemented
86	C₂²×C₃×C₄×C₅	—	2	2	no	—
87	C₂²×C₃×C₄×C₅	—	2	4	no	—
88	C₂²×C₃×C₄×C₅	—	2	4	no	—
89	C₂²×C₃×C₄×C₅	—	2	4	no	—
90	C₂²×C₃×C₄×C₅	—	4	2	no	—
91	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
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	2	yes	—
96	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
97	C₃×C₅×C₄⋊C₄	—	2	4	no	—
98	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
99	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
100	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
101	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
102	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
103	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
104	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
105	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
106	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
107	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	complemented
108	C₂³×C₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
109	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
110	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
113	C₃×#394	C₂×C₅	1	2	yes	complemented
114	C₃×#392	C₂×C₅	1	2	yes	complemented
115	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
116	C₃×#386	C₂×C₅	1	2	yes	complemented
117	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
118	C₃×#379	C₂×C₅	1	1	yes	characteristic, complemented
119	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
120	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
121	C₂²×C₅×D₄	—	2	4	no	—
122	C₂²×C₅×D₄	—	2	8	no	—
123	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
124	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
125	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
126	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
128	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
130	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	complemented
131	C₅×#121	—	2	8	no	—
132	C₅×#120	—	2	4	no	—
133	C₅×#120	—	2	4	no	—
134	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
135	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
136	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
140	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
141	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
142	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
143	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
144	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
145	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
146	C₅×#95	C₂²×C₃	1	2	yes	complemented
147	C₅×#95	C₂²×C₃	1	2	yes	complemented
148	#2410	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
149	C₂³×C₃×C₅	—	2	1	no	—
150	C₂³×C₃×C₅	—	2	2	no	—
151	C₂³×C₃×C₅	—	2	1	no	—
152	C₂³×C₃×C₅	—	2	2	no	—
153	C₂³×C₃×C₅	—	2	2	no	—
154	C₂³×C₃×C₅	—	2	8	no	—
155	C₂³×C₃×C₅	—	2	8	no	—
156	C₂³×C₃×C₅	—	2	8	no	—
157	C₂³×C₃×C₅	—	2	1	no	—
158	C₂³×C₃×C₅	—	2	2	no	—
159	C₂³×C₃×C₅	—	2	2	no	—
160	C₂³×C₃×C₅	—	2	2	no	—
161	C₂³×C₃×C₅	—	2	2	no	—
162	C₂³×C₃×C₅	—	2	1	no	—
163	C₂³×C₃×C₅	—	2	2	no	—
164	C₂³×C₃×C₅	—	2	2	no	—
165	C₂³×C₃×C₅	—	2	2	no	—
166	C₂³×C₃×C₅	—	2	2	no	—
167	C₂³×C₃×C₅	—	2	2	no	—
168	C₂³×C₃×C₅	—	2	1	no	—
169	C₂³×C₃×C₅	—	2	1	no	—
170	C₂³×C₃×C₅	—	2	1	no	—
171	C₂³×C₃×C₅	—	2	2	no	—
172	C₂³×C₃×C₅	—	4	4	no	—
173	C₂³×C₃×C₅	—	4	8	no	—
174	C₂³×C₃×C₅	—	4	8	no	—
175	C₂³×C₃×C₅	—	4	8	no	—
176	C₂³×C₃×C₅	—	4	8	no	—
177	C₂³×C₃×C₅	—	4	4	no	—
178	C₂³×C₃×C₅	—	4	4	no	—
179	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
180	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
181	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
182	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
183	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
184	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
185	C₂³×C₃×C₅	#41	1	2	yes	—
186	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
187	C₃×C₅×D₄	—	2	16	no	—
188	C₃×C₅×D₄	—	2	16	no	—
189	C₃×C₅×D₄	—	4	8	no	—
190	C₃×C₅×D₄	—	4	4	no	—
191	C₃×C₅×D₄	—	4	4	no	—
192	C₃×C₅×D₄	—	4	4	no	—
193	C₂×C₃×C₄×C₅	—	2	8	no	—
194	C₂×C₃×C₄×C₅	—	2	2	no	—
195	C₂×C₃×C₄×C₅	—	2	2	no	—
196	C₂×C₃×C₄×C₅	—	2	2	no	—
197	C₂×C₃×C₄×C₅	—	2	2	no	—
198	C₂×C₃×C₄×C₅	—	2	2	no	—
199	C₂×C₃×C₄×C₅	—	2	2	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	2	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	2	no	—
207	C₂×C₃×C₄×C₅	—	2	2	no	—
208	C₂×C₃×C₄×C₅	—	4	8	no	—
209	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
210	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	complemented
211	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
212	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
213	C₂²×C₃×D₄	—	2	4	no	—
214	C₂²×C₃×D₄	—	2	8	no	—
215	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
216	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
217	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
218	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
219	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
220	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
221	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
222	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	complemented
223	C₃×#121	—	2	8	no	—
224	C₃×#120	—	2	4	no	—
225	C₃×#120	—	2	4	no	—
226	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
227	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
228	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
232	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
233	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
234	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
235	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
236	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
237	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
238	C₃×#95	C₂²×C₅	1	2	yes	complemented
239	C₃×#95	C₂²×C₅	1	2	yes	complemented
240	C₂⁴×C₅	—	2	2	no	—
241	C₂⁴×C₅	—	2	4	no	—
242	C₂⁴×C₅	—	2	4	no	—
243	C₂⁴×C₅	—	2	2	no	—
244	C₂⁴×C₅	—	2	2	no	—
245	C₂⁴×C₅	—	2	2	no	—
246	C₂⁴×C₅	—	2	2	no	—
247	C₂⁴×C₅	—	4	2	no	—
248	C₂⁴×C₅	—	4	2	no	—
249	C₂⁴×C₅	C₃×D₄	1	4	yes	complemented
250	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
251	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
252	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
253	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
254	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
255	C₂×C₅×D₄	—	2	32	no	—
256	C₂×C₅×D₄	—	2	4	no	—
257	C₂×C₅×D₄	—	2	4	no	—
258	C₂×C₅×D₄	—	2	4	no	—
259	C₂×C₅×D₄	—	2	4	no	—
260	C₂×C₅×D₄	—	2	2	no	—
261	C₂×C₅×D₄	—	2	2	no	—
262	C₂×C₅×D₄	—	2	2	no	—
263	C₂×C₅×D₄	—	2	2	no	—
264	C₂×C₅×D₄	—	2	4	no	—
265	C₂×C₅×D₄	—	2	4	no	—
266	C₂×C₅×D₄	—	2	2	no	—
267	C₂×C₅×D₄	—	2	4	no	—
268	C₂×C₅×D₄	—	2	4	no	—
269	C₂×C₅×D₄	—	4	2	no	—
270	C₂×C₅×D₄	—	4	2	no	—
271	C₂×C₅×D₄	C₃×D₄	1	8	yes	complemented
272	C₂²×C₄×C₅	—	2	2	no	—
273	C₂²×C₄×C₅	—	2	4	no	—
274	C₂²×C₄×C₅	—	2	4	no	—
275	C₂²×C₄×C₅	—	2	4	no	—
276	C₂²×C₄×C₅	—	4	2	no	—
277	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
278	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
279	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
280	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
281	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
282	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
283	C₅×C₄⋊C₄	—	2	4	no	—
284	C₅×C₂²⋊C₄	—	2	2	no	—
285	C₅×C₂²⋊C₄	—	2	2	no	—
286	C₅×C₂²⋊C₄	—	2	2	no	—
287	C₅×C₂²⋊C₄	—	2	2	no	—
288	C₅×C₂²⋊C₄	—	2	4	no	—
289	C₅×C₂²⋊C₄	—	2	4	no	—
290	C₅×C₂²⋊C₄	—	2	4	no	—
291	C₅×C₂²⋊C₄	—	2	4	no	—
292	C₅×C₂²⋊C₄	—	4	2	no	—
293	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	complemented
294	C₂³×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
295	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
296	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic, complemented
297	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic, complemented
298	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
299	#394	C₂×C₃×C₅	1	2	yes	complemented
300	#392	C₂×C₃×C₅	1	2	yes	complemented
301	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
302	#386	C₂×C₃×C₅	1	2	yes	complemented
303	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
304	#379	C₂×C₃×C₅	1	1	yes	characteristic, complemented
305	C₂²×C₃×C₅	—	2	2	no	—
306	C₂²×C₃×C₅	—	2	2	no	—
307	C₂²×C₃×C₅	—	2	2	no	—
308	C₂²×C₃×C₅	—	2	2	no	—
309	C₂²×C₃×C₅	—	2	4	no	—
310	C₂²×C₃×C₅	—	2	4	no	—
311	C₂²×C₃×C₅	—	2	4	no	—
312	C₂²×C₃×C₅	—	2	4	no	—
313	C₂²×C₃×C₅	—	2	2	no	—
314	C₂²×C₃×C₅	—	2	4	no	—
315	C₂²×C₃×C₅	—	2	2	no	—
316	C₂²×C₃×C₅	—	2	2	no	—
317	C₂²×C₃×C₅	—	2	4	no	—
318	C₂²×C₃×C₅	—	2	4	no	—
319	C₂²×C₃×C₅	—	4	16	no	—
320	C₂²×C₃×C₅	—	4	16	no	—
321	C₂²×C₃×C₅	—	4	2	no	—
322	C₂²×C₃×C₅	—	4	2	no	—
323	C₂²×C₃×C₅	—	4	2	no	—
324	C₂²×C₃×C₅	—	4	2	no	—
325	C₂²×C₃×C₅	—	4	2	no	—
326	C₂²×C₃×C₅	—	4	2	no	—
327	C₂²×C₃×C₅	—	4	1	no	—
328	C₂²×C₃×C₅	—	4	1	no	—
329	C₂²×C₃×C₅	—	4	1	no	—
330	C₂²×C₃×C₅	—	4	2	no	—
331	C₂²×C₃×C₅	—	4	2	no	—
332	C₂²×C₃×C₅	#120	1	4	yes	complemented
333	C₂²×C₃×C₅	#121	1	4	yes	complemented
334	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
335	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
336	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
337	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
338	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
339	C₃×C₄×C₅	—	2	4	no	—
340	C₃×C₄×C₅	—	2	4	no	—
341	C₃×C₄×C₅	—	4	1	no	—
342	C₃×C₄×C₅	—	4	1	no	—
343	C₃×C₄×C₅	—	4	1	no	—
344	C₃×C₄×C₅	—	4	2	no	—
345	C₂⁴×C₃	—	2	2	no	—
346	C₂⁴×C₃	—	2	4	no	—
347	C₂⁴×C₃	—	2	4	no	—
348	C₂⁴×C₃	—	2	2	no	—
349	C₂⁴×C₃	—	2	2	no	—
350	C₂⁴×C₃	—	2	2	no	—
351	C₂⁴×C₃	—	2	2	no	—
352	C₂⁴×C₃	—	4	2	no	—
353	C₂⁴×C₃	—	4	2	no	—
354	C₂⁴×C₃	C₅×D₄	1	4	yes	complemented
355	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
356	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
357	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
358	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
359	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
360	C₂×C₃×D₄	—	2	32	no	—
361	C₂×C₃×D₄	—	2	4	no	—
362	C₂×C₃×D₄	—	2	4	no	—
363	C₂×C₃×D₄	—	2	4	no	—
364	C₂×C₃×D₄	—	2	4	no	—
365	C₂×C₃×D₄	—	2	2	no	—
366	C₂×C₃×D₄	—	2	2	no	—
367	C₂×C₃×D₄	—	2	2	no	—
368	C₂×C₃×D₄	—	2	2	no	—
369	C₂×C₃×D₄	—	2	4	no	—
370	C₂×C₃×D₄	—	2	4	no	—
371	C₂×C₃×D₄	—	2	2	no	—
372	C₂×C₃×D₄	—	2	4	no	—
373	C₂×C₃×D₄	—	2	4	no	—
374	C₂×C₃×D₄	—	4	2	no	—
375	C₂×C₃×D₄	—	4	2	no	—
376	C₂×C₃×D₄	C₅×D₄	1	8	yes	complemented
377	C₂²×C₃×C₄	—	2	2	no	—
378	C₂²×C₃×C₄	—	2	4	no	—
379	C₂²×C₃×C₄	—	2	4	no	—
380	C₂²×C₃×C₄	—	2	4	no	—
381	C₂²×C₃×C₄	—	4	2	no	—
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	2	yes	—
385	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
386	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
387	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
388	C₃×C₄⋊C₄	—	2	4	no	—
389	C₃×C₂²⋊C₄	—	2	2	no	—
390	C₃×C₂²⋊C₄	—	2	2	no	—
391	C₃×C₂²⋊C₄	—	2	2	no	—
392	C₃×C₂²⋊C₄	—	2	2	no	—
393	C₃×C₂²⋊C₄	—	2	4	no	—
394	C₃×C₂²⋊C₄	—	2	4	no	—
395	C₃×C₂²⋊C₄	—	2	4	no	—
396	C₃×C₂²⋊C₄	—	2	4	no	—
397	C₃×C₂²⋊C₄	—	4	2	no	—
398	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	complemented
399	C₂³×C₅	—	2	1	no	—
400	C₂³×C₅	—	2	2	no	—
401	C₂³×C₅	—	2	1	no	—
402	C₂³×C₅	—	2	2	no	—
403	C₂³×C₅	—	2	2	no	—
404	C₂³×C₅	—	2	8	no	—
405	C₂³×C₅	—	2	8	no	—
406	C₂³×C₅	—	2	8	no	—
407	C₂³×C₅	—	2	1	no	—
408	C₂³×C₅	—	2	2	no	—
409	C₂³×C₅	—	2	2	no	—
410	C₂³×C₅	—	2	2	no	—
411	C₂³×C₅	—	2	2	no	—
412	C₂³×C₅	—	2	1	no	—
413	C₂³×C₅	—	2	2	no	—
414	C₂³×C₅	—	2	2	no	—
415	C₂³×C₅	—	2	2	no	—
416	C₂³×C₅	—	2	2	no	—
417	C₂³×C₅	—	2	2	no	—
418	C₂³×C₅	—	2	1	no	—
419	C₂³×C₅	—	2	1	no	—
420	C₂³×C₅	—	2	1	no	—
421	C₂³×C₅	—	2	2	no	—
422	C₂³×C₅	—	4	4	no	—
423	C₂³×C₅	—	4	8	no	—
424	C₂³×C₅	—	4	8	no	—
425	C₂³×C₅	—	4	8	no	—
426	C₂³×C₅	—	4	8	no	—
427	C₂³×C₅	—	4	4	no	—
428	C₂³×C₅	—	4	4	no	—
429	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
430	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
431	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
432	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
433	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
434	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
435	C₂³×C₅	C₃×#41	1	2	yes	—
436	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
437	C₅×D₄	—	2	16	no	—
438	C₅×D₄	—	2	16	no	—
439	C₅×D₄	—	4	8	no	—
440	C₅×D₄	—	4	4	no	—
441	C₅×D₄	—	4	4	no	—
442	C₅×D₄	—	4	4	no	—
443	C₂×C₄×C₅	—	2	8	no	—
444	C₂×C₄×C₅	—	2	2	no	—
445	C₂×C₄×C₅	—	2	2	no	—
446	C₂×C₄×C₅	—	2	2	no	—
447	C₂×C₄×C₅	—	2	2	no	—
448	C₂×C₄×C₅	—	2	2	no	—
449	C₂×C₄×C₅	—	2	2	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	2	no	—
455	C₂×C₄×C₅	—	2	1	no	—
456	C₂×C₄×C₅	—	2	2	no	—
457	C₂×C₄×C₅	—	2	2	no	—
458	C₂×C₄×C₅	—	4	8	no	—
459	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
460	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	complemented
461	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
462	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
463	C₂²×D₄	—	2	4	no	—
464	C₂²×D₄	—	2	8	no	—
465	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
466	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
467	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
468	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
469	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	complemented
470	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
471	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
472	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	complemented
473	#121	—	2	8	no	—
474	#120	—	2	4	no	—
475	#120	—	2	4	no	—
476	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
477	C₂×C₂²⋊C₄	—	2	4	no	—
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	2	yes	complemented
482	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
483	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
484	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
485	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
486	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
487	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
488	#95	C₂²×C₃×C₅	1	2	yes	complemented
489	#95	C₂²×C₃×C₅	1	2	yes	complemented
490	C₂×C₃×C₅	—	2	4	no	—
491	C₂×C₃×C₅	—	2	4	no	—
492	C₂×C₃×C₅	—	4	2	no	—
493	C₂×C₃×C₅	—	4	4	no	—
494	C₂×C₃×C₅	—	8	1	no	—
495	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
496	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
497	C₂×C₃×C₅	#534	1	1	yes	characteristic
498	C₂×C₃×C₅	D₄²	1	2	yes	—
499	C₂×C₃×C₅	#546	1	2	yes	—
500	C₂³×C₃	—	2	1	no	—
501	C₂³×C₃	—	2	2	no	—
502	C₂³×C₃	—	2	1	no	—
503	C₂³×C₃	—	2	2	no	—
504	C₂³×C₃	—	2	2	no	—
505	C₂³×C₃	—	2	8	no	—
506	C₂³×C₃	—	2	8	no	—
507	C₂³×C₃	—	2	8	no	—
508	C₂³×C₃	—	2	1	no	—
509	C₂³×C₃	—	2	2	no	—
510	C₂³×C₃	—	2	2	no	—
511	C₂³×C₃	—	2	2	no	—
512	C₂³×C₃	—	2	2	no	—
513	C₂³×C₃	—	2	1	no	—
514	C₂³×C₃	—	2	2	no	—
515	C₂³×C₃	—	2	2	no	—
516	C₂³×C₃	—	2	2	no	—
517	C₂³×C₃	—	2	2	no	—
518	C₂³×C₃	—	2	2	no	—
519	C₂³×C₃	—	2	1	no	—
520	C₂³×C₃	—	2	1	no	—
521	C₂³×C₃	—	2	1	no	—
522	C₂³×C₃	—	2	2	no	—
523	C₂³×C₃	—	4	4	no	—
524	C₂³×C₃	—	4	8	no	—
525	C₂³×C₃	—	4	8	no	—
526	C₂³×C₃	—	4	8	no	—
527	C₂³×C₃	—	4	8	no	—
528	C₂³×C₃	—	4	4	no	—
529	C₂³×C₃	—	4	4	no	—
530	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
531	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
532	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
533	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
534	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
535	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
536	C₂³×C₃	C₅×#41	1	2	yes	—
537	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
538	C₃×D₄	—	2	16	no	—
539	C₃×D₄	—	2	16	no	—
540	C₃×D₄	—	4	8	no	—
541	C₃×D₄	—	4	4	no	—
542	C₃×D₄	—	4	4	no	—
543	C₃×D₄	—	4	4	no	—
544	C₂×C₃×C₄	—	2	8	no	—
545	C₂×C₃×C₄	—	2	2	no	—
546	C₂×C₃×C₄	—	2	2	no	—
547	C₂×C₃×C₄	—	2	2	no	—
548	C₂×C₃×C₄	—	2	2	no	—
549	C₂×C₃×C₄	—	2	2	no	—
550	C₂×C₃×C₄	—	2	2	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	2	no	—
556	C₂×C₃×C₄	—	2	1	no	—
557	C₂×C₃×C₄	—	2	2	no	—
558	C₂×C₃×C₄	—	2	2	no	—
559	C₂×C₃×C₄	—	4	8	no	—
560	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
561	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	complemented
562	C₂²×C₅	—	2	2	no	—
563	C₂²×C₅	—	2	2	no	—
564	C₂²×C₅	—	2	2	no	—
565	C₂²×C₅	—	2	2	no	—
566	C₂²×C₅	—	2	4	no	—
567	C₂²×C₅	—	2	4	no	—
568	C₂²×C₅	—	2	4	no	—
569	C₂²×C₅	—	2	4	no	—
570	C₂²×C₅	—	2	2	no	—
571	C₂²×C₅	—	2	4	no	—
572	C₂²×C₅	—	2	2	no	—
573	C₂²×C₅	—	2	2	no	—
574	C₂²×C₅	—	2	4	no	—
575	C₂²×C₅	—	2	4	no	—
576	C₂²×C₅	—	4	16	no	—
577	C₂²×C₅	—	4	16	no	—
578	C₂²×C₅	—	4	2	no	—
579	C₂²×C₅	—	4	2	no	—
580	C₂²×C₅	—	4	2	no	—
581	C₂²×C₅	—	4	2	no	—
582	C₂²×C₅	—	4	2	no	—
583	C₂²×C₅	—	4	2	no	—
584	C₂²×C₅	—	4	1	no	—
585	C₂²×C₅	—	4	1	no	—
586	C₂²×C₅	—	4	1	no	—
587	C₂²×C₅	—	4	2	no	—
588	C₂²×C₅	—	4	2	no	—
589	C₂²×C₅	C₃×#120	1	4	yes	complemented
590	C₂²×C₅	C₃×#121	1	4	yes	complemented
591	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
592	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
593	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
594	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
595	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
596	C₄×C₅	—	2	4	no	—
597	C₄×C₅	—	2	4	no	—
598	C₄×C₅	—	4	1	no	—
599	C₄×C₅	—	4	1	no	—
600	C₄×C₅	—	4	1	no	—
601	C₄×C₅	—	4	2	no	—
602	C₂⁴	—	2	2	no	—
603	C₂⁴	—	2	4	no	—
604	C₂⁴	—	2	4	no	—
605	C₂⁴	—	2	2	no	—
606	C₂⁴	—	2	2	no	—
607	C₂⁴	—	2	2	no	—
608	C₂⁴	—	2	2	no	—
609	C₂⁴	—	4	2	no	—
610	C₂⁴	—	4	2	no	—
611	C₂⁴	C₃×C₅×D₄	1	4	yes	complemented
612	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
613	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
614	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
615	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
616	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
617	C₂×D₄	—	2	32	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	4	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	4	2	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	C₃×C₅×D₄	1	8	yes	complemented
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	4	2	no	—
639	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
640	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
641	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
642	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
643	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
644	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
645	C₄⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
656	C₃×C₅	#2410	1	1	yes	characteristic, direct product factor, Hall
657	C₂²×C₃	—	2	2	no	—
658	C₂²×C₃	—	2	2	no	—
659	C₂²×C₃	—	2	2	no	—
660	C₂²×C₃	—	2	2	no	—
661	C₂²×C₃	—	2	4	no	—
662	C₂²×C₃	—	2	4	no	—
663	C₂²×C₃	—	2	4	no	—
664	C₂²×C₃	—	2	4	no	—
665	C₂²×C₃	—	2	2	no	—
666	C₂²×C₃	—	2	4	no	—
667	C₂²×C₃	—	2	2	no	—
668	C₂²×C₃	—	2	2	no	—
669	C₂²×C₃	—	2	4	no	—
670	C₂²×C₃	—	2	4	no	—
671	C₂²×C₃	—	4	16	no	—
672	C₂²×C₃	—	4	16	no	—
673	C₂²×C₃	—	4	2	no	—
674	C₂²×C₃	—	4	2	no	—
675	C₂²×C₃	—	4	2	no	—
676	C₂²×C₃	—	4	2	no	—
677	C₂²×C₃	—	4	2	no	—
678	C₂²×C₃	—	4	2	no	—
679	C₂²×C₃	—	4	1	no	—
680	C₂²×C₃	—	4	1	no	—
681	C₂²×C₃	—	4	1	no	—
682	C₂²×C₃	—	4	2	no	—
683	C₂²×C₃	—	4	2	no	—
684	C₂²×C₃	C₅×#120	1	4	yes	complemented
685	C₂²×C₃	C₅×#121	1	4	yes	complemented
686	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
687	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
688	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
689	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
690	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
691	C₃×C₄	—	2	4	no	—
692	C₃×C₄	—	2	4	no	—
693	C₃×C₄	—	4	1	no	—
694	C₃×C₄	—	4	1	no	—
695	C₃×C₄	—	4	1	no	—
696	C₃×C₄	—	4	2	no	—
697	C₂×C₅	—	2	4	no	—
698	C₂×C₅	—	2	4	no	—
699	C₂×C₅	—	4	2	no	—
700	C₂×C₅	—	4	4	no	—
701	C₂×C₅	—	8	1	no	—
702	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
703	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
704	C₂×C₅	C₃×#534	1	1	yes	characteristic
705	C₂×C₅	C₃×D₄²	1	2	yes	—
706	C₂×C₅	C₃×#546	1	2	yes	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	8	no	—
713	C₂³	—	2	8	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	8	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	4	4	no	—
731	C₂³	—	4	8	no	—
732	C₂³	—	4	8	no	—
733	C₂³	—	4	8	no	—
734	C₂³	—	4	8	no	—
735	C₂³	—	4	4	no	—
736	C₂³	—	4	4	no	—
737	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
738	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
739	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
740	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
741	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
742	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
743	C₂³	C₃×C₅×#41	1	2	yes	—
744	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
745	D₄	—	2	16	no	—
746	D₄	—	2	16	no	—
747	D₄	—	4	8	no	—
748	D₄	—	4	4	no	—
749	D₄	—	4	4	no	—
750	D₄	—	4	4	no	—
751	C₂×C₄	—	2	8	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	4	8	no	—
767	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
768	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	complemented
769	C₂×C₃	—	2	4	no	—
770	C₂×C₃	—	2	4	no	—
771	C₂×C₃	—	4	2	no	—
772	C₂×C₃	—	4	4	no	—
773	C₂×C₃	—	8	1	no	—
774	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
775	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
776	C₂×C₃	C₅×#534	1	1	yes	characteristic
777	C₂×C₃	C₅×D₄²	1	2	yes	—
778	C₂×C₃	C₅×#546	1	2	yes	—
779	C₅	C₃×#2410	1	1	yes	characteristic, direct product factor, Sylow
780	C₂²	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	2	4	no	—
786	C₂²	—	2	4	no	—
787	C₂²	—	2	4	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	4	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	2	4	no	—
794	C₂²	—	4	16	no	—
795	C₂²	—	4	16	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	C₃×C₅×#120	1	4	yes	complemented
808	C₂²	C₃×C₅×#121	1	4	yes	complemented
809	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
810	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
811	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
812	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
813	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
814	C₄	—	2	4	no	—
815	C₄	—	2	4	no	—
816	C₄	—	4	1	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	2	no	—
820	C₃	C₅×#2410	1	1	yes	characteristic, direct product factor, Sylow
821	C₂	—	2	4	no	—
822	C₂	—	2	4	no	—
823	C₂	—	4	2	no	—
824	C₂	—	4	4	no	—
825	C₂	—	8	1	no	—
826	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic
827	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
828	C₂	C₃×C₅×#534	1	1	yes	characteristic
829	C₂	C₃×C₅×D₄²	1	2	yes	—
830	C₂	C₃×C₅×#546	1	2	yes	—

	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. C₂³×C₃×C₅×D₄	C₂	semidirect
2. C₂×C₃×C₅×#121	C₂	semidirect
3. C₂×C₃×C₅×#120	C₂	semidirect
4. C₂×C₃×C₅×#120	C₂	semidirect
5. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
6. C₃×C₅×#394	C₂	semidirect
7. C₃×C₅×#392	C₂	semidirect
8. C₃×C₅×#386	C₂	semidirect
9. C₃×C₅×#386	C₂	semidirect
10. C₃×C₅×#385	C₂	semidirect
11. C₃×C₅×#379	C₂	semidirect
12. C₅×#2410	C₃	direct (N × H)
20. C₂²×C₃×C₅×D₄	C₂²	semidirect
21. C₂²×C₃×C₅×D₄	C₂²	semidirect
22. C₂²×C₃×C₅×D₄	C₂²	semidirect
24. C₂³×C₃×C₄×C₅	C₂²	semidirect
28. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
33. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
34. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
35. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
36. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
37. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
38. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
39. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
40. C₃×C₅×#95	C₂²	semidirect
41. C₃×C₅×#95	C₂²	semidirect
42. C₃×#2410	C₅	direct (N × H)
43. C₂³×C₅×D₄	C₂×C₃	semidirect
44. C₂×C₅×#121	C₂×C₃	semidirect
45. C₂×C₅×#120	C₂×C₃	semidirect
46. C₂×C₅×#120	C₂×C₃	semidirect
47. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
48. C₅×#394	C₂×C₃	semidirect
49. C₅×#392	C₂×C₃	semidirect
50. C₅×#386	C₂×C₃	semidirect
51. C₅×#386	C₂×C₃	semidirect
52. C₅×#385	C₂×C₃	semidirect
53. C₅×#379	C₂×C₃	semidirect
63. C₂⁴×C₃×C₅	D₄	semidirect
85. C₂×C₃×C₅×D₄	D₄	semidirect
107. C₃×C₅×C₂²⋊C₄	D₄	semidirect
108. C₂³×C₃×D₄	C₂×C₅	semidirect
109. C₂×C₃×#121	C₂×C₅	semidirect
110. C₂×C₃×#120	C₂×C₅	semidirect
111. C₂×C₃×#120	C₂×C₅	semidirect
112. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
113. C₃×#394	C₂×C₅	semidirect
114. C₃×#392	C₂×C₅	semidirect
115. C₃×#386	C₂×C₅	semidirect
116. C₃×#386	C₂×C₅	semidirect
117. C₃×#385	C₂×C₅	semidirect
118. C₃×#379	C₂×C₅	semidirect
126. C₂²×C₅×D₄	C₂²×C₃	semidirect
127. C₂²×C₅×D₄	C₂²×C₃	semidirect
128. C₂²×C₅×D₄	C₂²×C₃	semidirect
130. C₂³×C₄×C₅	C₂²×C₃	semidirect
134. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
139. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
140. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
141. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
142. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
143. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
144. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
145. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
146. C₅×#95	C₂²×C₃	semidirect
147. C₅×#95	C₂²×C₃	semidirect
148. #2410	C₃×C₅	direct (N × H)
210. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
218. C₂²×C₃×D₄	C₂²×C₅	semidirect
219. C₂²×C₃×D₄	C₂²×C₅	semidirect
220. C₂²×C₃×D₄	C₂²×C₅	semidirect
222. C₂³×C₃×C₄	C₂²×C₅	semidirect
226. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
231. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
232. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
233. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
234. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
235. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
236. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
237. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
238. C₃×#95	C₂²×C₅	semidirect
239. C₃×#95	C₂²×C₅	semidirect
249. C₂⁴×C₅	C₃×D₄	semidirect
271. C₂×C₅×D₄	C₃×D₄	semidirect
293. C₅×C₂²⋊C₄	C₃×D₄	semidirect
294. C₂³×D₄	C₂×C₃×C₅	semidirect
295. C₂×#121	C₂×C₃×C₅	semidirect
296. C₂×#120	C₂×C₃×C₅	semidirect
297. C₂×#120	C₂×C₃×C₅	semidirect
298. C₂²×C₂²⋊C₄	C₂×C₃×C₅	semidirect
299. #394	C₂×C₃×C₅	semidirect
300. #392	C₂×C₃×C₅	semidirect
301. #386	C₂×C₃×C₅	semidirect
302. #386	C₂×C₃×C₅	semidirect
303. #385	C₂×C₃×C₅	semidirect
304. #379	C₂×C₃×C₅	semidirect
332. C₂²×C₃×C₅	#120	semidirect
333. C₂²×C₃×C₅	#121	semidirect
354. C₂⁴×C₃	C₅×D₄	semidirect
376. C₂×C₃×D₄	C₅×D₄	semidirect
398. C₃×C₂²⋊C₄	C₅×D₄	semidirect
460. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
468. C₂²×D₄	C₂²×C₃×C₅	semidirect
469. C₂²×D₄	C₂²×C₃×C₅	semidirect
470. C₂²×D₄	C₂²×C₃×C₅	semidirect
472. C₂³×C₄	C₂²×C₃×C₅	semidirect
476. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
481. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
482. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
483. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
484. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
485. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
486. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
487. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
488. #95	C₂²×C₃×C₅	semidirect
489. #95	C₂²×C₃×C₅	semidirect
561. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
589. C₂²×C₅	C₃×#120	semidirect
590. C₂²×C₅	C₃×#121	semidirect
611. C₂⁴	C₃×C₅×D₄	semidirect
633. C₂×D₄	C₃×C₅×D₄	semidirect
655. C₂²⋊C₄	C₃×C₅×D₄	semidirect
656. C₃×C₅	#2410	direct (N × H)
684. C₂²×C₃	C₅×#120	semidirect
685. C₂²×C₃	C₅×#121	semidirect
768. C₂×C₄	C₂×C₃×C₅×D₄	semidirect
779. C₅	C₃×#2410	direct (N × H)
807. C₂²	C₃×C₅×#120	semidirect
808. C₂²	C₃×C₅×#121	semidirect
820. C₃	C₅×#2410	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×D₄	2
C₂×C₃×C₅×#121	2
C₂×C₃×C₅×#120	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#379	2
C₅×#2410	3
C₃×#2410	5

Subgroups — C3×C5×#2410 #14275444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2410 #14275444