Subgroups — C₂×C₅×#5693 #14483397

Order 1920.

2248 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5693	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅×#898	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#898	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#894	C₂	1	1	yes	maximal, characteristic
8	C₂×C₅×#894	C₂	1	1	yes	maximal, characteristic
9	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic
10	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅×#552	—	3	1	no	maximal, Hall
18	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
23	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
24	C₃×C₅×#125	C₂²	1	8	yes	complemented
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
32	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
41	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
42	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
54	C₅×#898	C₂²	1	8	yes	complemented
55	C₅×#898	C₂²	1	8	yes	complemented
56	C₅×#896	C₂²	1	8	yes	complemented
57	C₅×#896	C₂²	1	8	yes	complemented
58	C₅×#894	C₂²	1	8	yes	—
59	C₅×#894	C₂²	1	8	yes	—
60	C₅×#893	C₂²	1	8	yes	—
61	C₅×#892	C₂²	1	8	yes	complemented
62	C₅×D₃×C₄⋊C₄	C₂²	1	8	yes	complemented
63	C₅×#889	C₂²	1	8	yes	complemented
64	C₅×#889	C₂²	1	8	yes	complemented
65	C₅×#887	C₂²	1	8	yes	complemented
66	C₅×#872	C₂²	1	8	yes	complemented
67	C₅×#872	C₂²	1	8	yes	complemented
68	C₂×#5693	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₅×#552	—	3	16	no	—
70	C₂×C₅×#126	—	3	1	no	—
71	C₂×C₅×#126	—	3	1	no	—
72	C₂×C₅×#125	—	3	1	no	—
73	C₂×C₅×#125	—	3	1	no	—
74	C₂×C₅×#125	D₃	1	1	yes	characteristic, complemented
75	C₂×C₅×#123	—	3	1	no	—
76	C₂×C₅×#123	—	3	1	no	—
77	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
78	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
79	C₂×C₄×C₅×Q₈	—	3	1	no	—
80	C₂×C₄×C₅×D₄	—	3	1	no	—
81	C₂×C₅×#117	—	3	1	no	—
82	C₂×C₅×#117	—	3	1	no	—
83	C₂×C₅×#117	—	3	1	no	—
84	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
85	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
86	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
87	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
89	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×C₅×Dic₃	C₂³	1	1	yes	characteristic
95	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
96	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
97	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
98	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
99	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
100	C₂×C₅×D₁₂	—	2	4	no	—
101	C₂×C₅×D₁₂	C₂³	1	4	yes	—
102	C₂×C₄×C₅×D₃	—	2	4	no	—
103	C₂×C₄×C₅×D₃	—	2	4	no	—
104	C₂×C₄×C₅×D₃	—	2	4	no	—
105	C₂×C₄×C₅×D₃	—	2	4	no	—
106	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
107	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
108	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
109	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
110	C₂×C₅×Dic₆	—	2	4	no	—
111	C₂×C₅×Dic₆	C₂³	1	4	yes	—
112	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
113	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
114	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
115	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
116	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
117	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
118	C₃×C₄²×C₅	C₂³	1	4	yes	—
119	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
120	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
121	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
122	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
123	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
124	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
125	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
126	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
127	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
128	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
129	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
130	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
131	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
132	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
133	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
134	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
135	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
136	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
137	C₄×C₅×Dic₃	C₂³	1	4	yes	—
138	C₄×C₅×Dic₃	C₂³	1	4	yes	—
139	C₄×C₅×Dic₃	C₂³	1	4	yes	—
140	C₄×C₅×Dic₃	C₂³	1	4	yes	—
141	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
142	#5693	C₂×C₅	1	16	yes	direct product factor
143	C₂×#898	C₂×C₅	1	1	yes	characteristic, complemented
144	C₂×#898	C₂×C₅	1	1	yes	characteristic, complemented
145	C₂×#896	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂×#896	C₂×C₅	1	1	yes	characteristic, complemented
147	C₂×#894	C₂×C₅	1	1	yes	characteristic
148	C₂×#894	C₂×C₅	1	1	yes	characteristic
149	C₂×#893	C₂×C₅	1	1	yes	characteristic
150	C₂×#892	C₂×C₅	1	1	yes	characteristic, complemented
151	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂×#889	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂×#889	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂×#887	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×#872	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂×#872	C₂×C₅	1	1	yes	characteristic, complemented
157	C₂²×C₅×Q₈	—	3	1	no	—
158	C₂²×C₅×D₄	—	3	1	no	—
159	C₂³×C₄×C₅	—	3	1	no	—
160	C₂³×C₄×C₅	—	3	1	no	—
161	C₂³×C₄×C₅	—	3	1	no	—
162	C₂³×C₄×C₅	—	3	1	no	—
163	C₅×#126	—	3	8	no	—
164	C₅×#126	—	3	8	no	—
165	C₅×#125	—	3	8	no	—
166	C₅×#125	—	3	8	no	—
167	C₅×#125	C₂×D₃	1	8	yes	complemented
168	C₅×#123	—	3	8	no	—
169	C₅×#123	—	3	8	no	—
170	C₅×C₂²⋊Q₈	—	3	8	no	—
171	C₅×C₂²⋊Q₈	—	3	8	no	—
172	C₄×C₅×Q₈	—	3	8	no	—
173	C₄×C₅×D₄	—	3	8	no	—
174	C₅×#117	—	3	8	no	—
175	C₅×#117	—	3	8	no	—
176	C₅×#117	—	3	8	no	—
177	C₂×C₅×C₄⋊C₄	—	3	1	no	—
178	C₂×C₅×C₄⋊C₄	—	3	1	no	—
179	C₂×C₅×C₄⋊C₄	—	3	1	no	—
180	C₂×C₅×C₄⋊C₄	—	3	1	no	—
181	C₂×C₅×C₄⋊C₄	—	3	1	no	—
182	C₂×C₅×C₄⋊C₄	—	3	1	no	—
183	C₂×C₅×C₄⋊C₄	—	3	1	no	—
184	C₂×C₅×C₄⋊C₄	—	3	1	no	—
185	C₂×C₅×C₄⋊C₄	—	3	1	no	—
186	C₂×C₅×C₄⋊C₄	—	3	1	no	—
187	C₂×C₅×C₄⋊C₄	—	3	8	no	—
188	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
189	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
190	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
191	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
192	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
193	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
194	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
195	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
196	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
197	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
198	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
199	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
200	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
201	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
202	C₂×C₄²×C₅	—	3	1	no	—
203	C₂×C₄²×C₅	—	3	1	no	—
204	C₂×C₄²×C₅	—	3	1	no	—
205	C₂×C₄²×C₅	—	3	1	no	—
206	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
207	C₂×#552	—	3	1	no	Sylow
208	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
209	C₂²×C₅×D₃	—	2	2	no	—
210	C₂²×C₅×D₃	—	2	2	no	—
211	C₂²×C₅×D₃	—	2	2	no	—
212	C₂²×C₅×D₃	—	2	2	no	—
213	C₂²×C₅×D₃	—	2	2	no	—
214	C₂²×C₅×D₃	#41	1	4	yes	—
215	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
216	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
217	C₂×C₃×C₄×C₅	—	2	2	no	—
218	C₂×C₃×C₄×C₅	—	2	2	no	—
219	C₂×C₃×C₄×C₅	—	2	2	no	—
220	C₂×C₃×C₄×C₅	—	2	2	no	—
221	C₂×C₃×C₄×C₅	—	2	2	no	—
222	C₂×C₃×C₄×C₅	—	2	2	no	—
223	C₂×C₃×C₄×C₅	—	2	2	no	—
224	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
225	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
226	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
227	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
228	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
229	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
230	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
231	C₂×C₅×Dic₃	—	2	2	no	—
232	C₂×C₅×Dic₃	—	2	2	no	—
233	C₂×C₅×Dic₃	—	2	2	no	—
234	C₂×C₅×Dic₃	—	2	2	no	—
235	C₂×C₅×Dic₃	—	2	2	no	—
236	C₂×C₅×Dic₃	#41	1	4	yes	—
237	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
238	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
239	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
240	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
241	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
242	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
243	C₅×D₁₂	—	2	8	no	—
244	C₄×C₅×D₃	—	2	8	no	—
245	C₄×C₅×D₃	—	2	8	no	—
246	C₄×C₅×D₃	—	2	8	no	—
247	C₄×C₅×D₃	—	2	8	no	—
248	C₅×Dic₆	—	2	8	no	—
249	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
250	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
251	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
252	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
253	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
254	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
255	C₃×#125	C₂²×C₅	1	8	yes	complemented
256	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
263	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
264	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
265	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
266	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
267	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
268	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
269	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
270	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
273	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
274	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
275	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
276	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
277	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
278	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
279	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
280	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
281	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
282	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
283	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
284	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
285	#898	C₂²×C₅	1	8	yes	complemented
286	#898	C₂²×C₅	1	8	yes	complemented
287	#896	C₂²×C₅	1	8	yes	complemented
288	#896	C₂²×C₅	1	8	yes	complemented
289	#894	C₂²×C₅	1	8	yes	—
290	#894	C₂²×C₅	1	8	yes	—
291	#893	C₂²×C₅	1	8	yes	—
292	#892	C₂²×C₅	1	8	yes	complemented
293	D₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
294	#889	C₂²×C₅	1	8	yes	complemented
295	#889	C₂²×C₅	1	8	yes	complemented
296	#887	C₂²×C₅	1	8	yes	complemented
297	#872	C₂²×C₅	1	8	yes	complemented
298	#872	C₂²×C₅	1	8	yes	complemented
299	C₂⁴×C₅	—	3	1	no	—
300	C₂⁴×C₅	—	3	1	no	—
301	C₂×C₅×Q₈	—	3	4	no	—
302	C₂×C₅×Q₈	—	6	4	no	—
303	C₂×C₅×D₄	—	3	4	no	—
304	C₂×C₅×D₄	—	6	4	no	—
305	C₂²×C₄×C₅	—	3	1	no	—
306	C₂²×C₄×C₅	—	3	1	no	—
307	C₂²×C₄×C₅	—	3	1	no	—
308	C₂²×C₄×C₅	—	3	1	no	—
309	C₂²×C₄×C₅	—	3	1	no	—
310	C₂²×C₄×C₅	—	3	1	no	—
311	C₂²×C₄×C₅	—	3	4	no	—
312	C₂²×C₄×C₅	—	3	4	no	—
313	C₂²×C₄×C₅	—	3	4	no	—
314	C₂²×C₄×C₅	—	3	4	no	—
315	C₂²×C₄×C₅	—	6	4	no	—
316	C₂²×C₄×C₅	—	6	4	no	—
317	C₂²×C₄×C₅	—	6	4	no	—
318	C₂²×C₄×C₅	—	6	4	no	—
319	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
320	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
321	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
322	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
323	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
324	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
325	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
326	C₅×C₄⋊C₄	—	3	4	no	—
327	C₅×C₄⋊C₄	—	3	4	no	—
328	C₅×C₄⋊C₄	—	3	4	no	—
329	C₅×C₄⋊C₄	—	3	4	no	—
330	C₅×C₄⋊C₄	—	3	4	no	—
331	C₅×C₄⋊C₄	—	3	4	no	—
332	C₅×C₄⋊C₄	—	3	4	no	—
333	C₅×C₄⋊C₄	—	3	4	no	—
334	C₅×C₄⋊C₄	—	3	4	no	—
335	C₅×C₄⋊C₄	—	3	4	no	—
336	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
337	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
338	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
339	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
340	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
341	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
342	C₅×C₂²⋊C₄	—	3	4	no	—
343	C₅×C₂²⋊C₄	—	3	4	no	—
344	C₅×C₂²⋊C₄	—	3	4	no	—
345	C₅×C₂²⋊C₄	—	3	4	no	—
346	C₅×C₂²⋊C₄	—	3	4	no	—
347	C₅×C₂²⋊C₄	—	3	4	no	—
348	C₅×C₂²⋊C₄	—	3	4	no	—
349	C₅×C₂²⋊C₄	—	3	4	no	—
350	C₄²×C₅	—	3	4	no	—
351	C₄²×C₅	—	3	4	no	—
352	C₄²×C₅	—	3	4	no	—
353	C₄²×C₅	—	3	4	no	—
354	C₄²×C₅	C₂²×D₃	1	4	yes	—
355	#552	—	3	16	no	—
356	C₂×#126	—	3	1	no	—
357	C₂×#126	—	3	1	no	—
358	C₂×#125	—	3	1	no	—
359	C₂×#125	—	3	1	no	—
360	C₂×#125	C₅×D₃	1	1	yes	characteristic, complemented
361	C₂×#123	—	3	1	no	—
362	C₂×#123	—	3	1	no	—
363	C₂×C₂²⋊Q₈	—	3	1	no	—
364	C₂×C₂²⋊Q₈	—	3	1	no	—
365	C₂×C₄×Q₈	—	3	1	no	—
366	C₂×C₄×D₄	—	3	1	no	—
367	C₂×#117	—	3	1	no	—
368	C₂×#117	—	3	1	no	—
369	C₂×#117	—	3	1	no	—
370	C₂²×C₄⋊C₄	—	3	1	no	—
371	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
372	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
373	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
374	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
375	C₂×C₅×D₃	—	2	8	no	—
376	C₂×C₅×D₃	—	2	2	no	—
377	C₂×C₅×D₃	—	2	2	no	—
378	C₂×C₅×D₃	—	2	2	no	—
379	C₂×C₅×D₃	—	2	2	no	—
380	C₂×C₅×D₃	—	2	2	no	—
381	C₂×C₅×D₃	—	4	4	no	—
382	C₂×C₅×D₃	C₂×#41	1	4	yes	—
383	C₃×C₄×C₅	—	2	2	no	—
384	C₃×C₄×C₅	—	2	2	no	—
385	C₃×C₄×C₅	—	2	2	no	—
386	C₃×C₄×C₅	—	2	2	no	—
387	C₃×C₄×C₅	—	2	2	no	—
388	C₃×C₄×C₅	—	2	2	no	—
389	C₃×C₄×C₅	—	2	2	no	—
390	C₅×Dic₃	—	2	2	no	—
391	C₅×Dic₃	—	2	2	no	—
392	C₅×Dic₃	—	2	2	no	—
393	C₅×Dic₃	—	2	2	no	—
394	C₅×Dic₃	—	2	2	no	—
395	C₅×Dic₃	C₂×#41	1	4	yes	—
396	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
397	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
398	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
399	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
400	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
401	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
403	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
404	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
405	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
406	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
407	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
408	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
409	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
410	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
411	C₂×D₁₂	—	2	4	no	—
412	C₂×D₁₂	C₂³×C₅	1	4	yes	—
413	C₂×C₄×D₃	—	2	4	no	—
414	C₂×C₄×D₃	—	2	4	no	—
415	C₂×C₄×D₃	—	2	4	no	—
416	C₂×C₄×D₃	—	2	4	no	—
417	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
418	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
419	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
420	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
421	C₂×Dic₆	—	2	4	no	—
422	C₂×Dic₆	C₂³×C₅	1	4	yes	—
423	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
424	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
425	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
426	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
427	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
428	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
429	C₃×C₄²	C₂³×C₅	1	4	yes	—
430	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
431	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
432	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
433	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
434	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
435	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
436	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
437	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
438	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
439	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
440	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
441	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
442	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
443	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
444	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
445	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
446	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
447	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
448	C₄×Dic₃	C₂³×C₅	1	4	yes	—
449	C₄×Dic₃	C₂³×C₅	1	4	yes	—
450	C₄×Dic₃	C₂³×C₅	1	4	yes	—
451	C₄×Dic₃	C₂³×C₅	1	4	yes	—
452	C₂³×C₅	—	3	4	no	—
453	C₂³×C₅	—	3	2	no	—
454	C₂³×C₅	—	3	2	no	—
455	C₂³×C₅	—	6	2	no	—
456	C₂³×C₅	—	6	2	no	—
457	C₂³×C₅	—	6	2	no	—
458	C₂³×C₅	—	6	2	no	—
459	C₂³×C₅	—	6	2	no	—
460	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
461	C₅×Q₈	—	6	8	no	—
462	C₅×D₄	—	6	8	no	—
463	C₂×C₄×C₅	—	2	2	no	—
464	C₂×C₄×C₅	—	2	2	no	—
465	C₂×C₄×C₅	—	2	2	no	—
466	C₂×C₄×C₅	—	2	2	no	—
467	C₂×C₄×C₅	—	2	2	no	—
468	C₂×C₄×C₅	—	2	2	no	—
469	C₂×C₄×C₅	—	2	2	no	—
470	C₂×C₄×C₅	—	3	4	no	—
471	C₂×C₄×C₅	—	3	2	no	—
472	C₂×C₄×C₅	—	3	2	no	—
473	C₂×C₄×C₅	—	3	2	no	—
474	C₂×C₄×C₅	—	3	2	no	—
475	C₂×C₄×C₅	—	3	2	no	—
476	C₂×C₄×C₅	—	3	2	no	—
477	C₂×C₄×C₅	—	6	8	no	—
478	C₂×C₄×C₅	—	6	8	no	—
479	C₂×C₄×C₅	—	6	8	no	—
480	C₂×C₄×C₅	—	6	8	no	—
481	C₂×C₄×C₅	—	6	2	no	—
482	C₂×C₄×C₅	—	6	2	no	—
483	C₂×C₄×C₅	—	6	2	no	—
484	C₂×C₄×C₅	—	6	2	no	—
485	C₂×C₄×C₅	—	6	2	no	—
486	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
487	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
488	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
489	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
490	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
491	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
492	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
493	C₂²×Q₈	—	3	1	no	—
494	C₂²×D₄	—	3	1	no	—
495	C₂³×C₄	—	3	1	no	—
496	C₂³×C₄	—	3	1	no	—
497	C₂³×C₄	—	3	1	no	—
498	C₂³×C₄	—	3	1	no	—
499	#126	—	3	8	no	—
500	#126	—	3	8	no	—
501	#125	—	3	8	no	—
502	#125	—	3	8	no	—
503	#125	C₂×C₅×D₃	1	8	yes	complemented
504	#123	—	3	8	no	—
505	#123	—	3	8	no	—
506	C₂²⋊Q₈	—	3	8	no	—
507	C₂²⋊Q₈	—	3	8	no	—
508	C₄×Q₈	—	3	8	no	—
509	C₄×D₄	—	3	8	no	—
510	#117	—	3	8	no	—
511	#117	—	3	8	no	—
512	#117	—	3	8	no	—
513	C₂×C₄⋊C₄	—	3	1	no	—
514	C₂×C₄⋊C₄	—	3	1	no	—
515	C₂×C₄⋊C₄	—	3	1	no	—
516	C₂×C₄⋊C₄	—	3	1	no	—
517	C₂×C₄⋊C₄	—	3	1	no	—
518	C₂×C₄⋊C₄	—	3	1	no	—
519	C₂×C₄⋊C₄	—	3	1	no	—
520	C₂×C₄⋊C₄	—	3	1	no	—
521	C₂×C₄⋊C₄	—	3	1	no	—
522	C₂×C₄⋊C₄	—	3	1	no	—
523	C₂×C₄⋊C₄	—	3	8	no	—
524	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	—	3	1	no	—
531	C₂×C₂²⋊C₄	—	3	1	no	—
532	C₂×C₂²⋊C₄	—	3	1	no	—
533	C₂×C₂²⋊C₄	—	3	1	no	—
534	C₂×C₂²⋊C₄	—	3	1	no	—
535	C₂×C₂²⋊C₄	—	3	1	no	—
536	C₂×C₂²⋊C₄	—	3	1	no	—
537	C₂×C₂²⋊C₄	—	3	1	no	—
538	C₂×C₄²	—	3	1	no	—
539	C₂×C₄²	—	3	1	no	—
540	C₂×C₄²	—	3	1	no	—
541	C₂×C₄²	—	3	1	no	—
542	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
543	C₂×C₃×C₅	#552	1	4	yes	complemented
544	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
545	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
546	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
547	C₅×D₃	—	2	4	no	—
548	C₅×D₃	—	4	2	no	—
549	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
550	C₂²×D₃	—	2	2	no	—
551	C₂²×D₃	—	2	2	no	—
552	C₂²×D₃	—	2	2	no	—
553	C₂²×D₃	—	2	2	no	—
554	C₂²×D₃	—	2	2	no	—
555	C₂²×D₃	C₅×#41	1	4	yes	—
556	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
557	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
558	C₂×C₃×C₄	—	2	2	no	—
559	C₂×C₃×C₄	—	2	2	no	—
560	C₂×C₃×C₄	—	2	2	no	—
561	C₂×C₃×C₄	—	2	2	no	—
562	C₂×C₃×C₄	—	2	2	no	—
563	C₂×C₃×C₄	—	2	2	no	—
564	C₂×C₃×C₄	—	2	2	no	—
565	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
566	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
567	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
568	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
569	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
570	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
571	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
572	C₂×Dic₃	—	2	2	no	—
573	C₂×Dic₃	—	2	2	no	—
574	C₂×Dic₃	—	2	2	no	—
575	C₂×Dic₃	—	2	2	no	—
576	C₂×Dic₃	—	2	2	no	—
577	C₂×Dic₃	C₅×#41	1	4	yes	—
578	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
579	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
580	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
581	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
582	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
583	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
584	D₁₂	—	2	8	no	—
585	C₄×D₃	—	2	8	no	—
586	C₄×D₃	—	2	8	no	—
587	C₄×D₃	—	2	8	no	—
588	C₄×D₃	—	2	8	no	—
589	Dic₆	—	2	8	no	—
590	C₂²×C₅	—	3	4	no	—
591	C₂²×C₅	—	6	8	no	—
592	C₂²×C₅	—	6	2	no	—
593	C₂²×C₅	—	6	2	no	—
594	C₂²×C₅	—	6	2	no	—
595	C₂²×C₅	—	6	2	no	—
596	C₂²×C₅	—	6	2	no	—
597	C₂²×C₅	—	12	4	no	—
598	C₂²×C₅	#1007	1	2	yes	—
599	C₂²×C₅	D₃×#41	1	2	yes	—
600	C₂²×C₅	D₃×#41	1	2	yes	—
601	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
602	C₄×C₅	—	2	2	no	—
603	C₄×C₅	—	2	2	no	—
604	C₄×C₅	—	2	2	no	—
605	C₄×C₅	—	2	2	no	—
606	C₄×C₅	—	2	2	no	—
607	C₄×C₅	—	2	2	no	—
608	C₄×C₅	—	2	2	no	—
609	C₄×C₅	—	3	4	no	—
610	C₄×C₅	—	6	2	no	—
611	C₄×C₅	—	6	2	no	—
612	C₄×C₅	—	6	2	no	—
613	C₄×C₅	—	6	2	no	—
614	C₄×C₅	—	6	2	no	—
615	C₂⁴	—	3	1	no	—
616	C₂⁴	—	3	1	no	—
617	C₂×Q₈	—	3	4	no	—
618	C₂×Q₈	—	6	4	no	—
619	C₂×D₄	—	3	4	no	—
620	C₂×D₄	—	6	4	no	—
621	C₂²×C₄	—	3	1	no	—
622	C₂²×C₄	—	3	1	no	—
623	C₂²×C₄	—	3	1	no	—
624	C₂²×C₄	—	3	1	no	—
625	C₂²×C₄	—	3	1	no	—
626	C₂²×C₄	—	3	1	no	—
627	C₂²×C₄	—	3	4	no	—
628	C₂²×C₄	—	3	4	no	—
629	C₂²×C₄	—	3	4	no	—
630	C₂²×C₄	—	3	4	no	—
631	C₂²×C₄	—	6	4	no	—
632	C₂²×C₄	—	6	4	no	—
633	C₂²×C₄	—	6	4	no	—
634	C₂²×C₄	—	6	4	no	—
635	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
636	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
637	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
638	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
639	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
640	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
641	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
642	C₄⋊C₄	—	3	4	no	—
643	C₄⋊C₄	—	3	4	no	—
644	C₄⋊C₄	—	3	4	no	—
645	C₄⋊C₄	—	3	4	no	—
646	C₄⋊C₄	—	3	4	no	—
647	C₄⋊C₄	—	3	4	no	—
648	C₄⋊C₄	—	3	4	no	—
649	C₄⋊C₄	—	3	4	no	—
650	C₄⋊C₄	—	3	4	no	—
651	C₄⋊C₄	—	3	4	no	—
652	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
653	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
654	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
655	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
656	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
657	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
658	C₂²⋊C₄	—	3	4	no	—
659	C₂²⋊C₄	—	3	4	no	—
660	C₂²⋊C₄	—	3	4	no	—
661	C₂²⋊C₄	—	3	4	no	—
662	C₂²⋊C₄	—	3	4	no	—
663	C₂²⋊C₄	—	3	4	no	—
664	C₂²⋊C₄	—	3	4	no	—
665	C₂²⋊C₄	—	3	4	no	—
666	C₄²	—	3	4	no	—
667	C₄²	—	3	4	no	—
668	C₄²	—	3	4	no	—
669	C₄²	—	3	4	no	—
670	C₄²	C₂²×C₅×D₃	1	4	yes	—
671	C₃×C₅	C₂×#552	1	1	yes	characteristic, complemented, Hall
672	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
673	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
674	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
675	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
676	C₂×D₃	—	2	8	no	—
677	C₂×D₃	—	2	2	no	—
678	C₂×D₃	—	2	2	no	—
679	C₂×D₃	—	2	2	no	—
680	C₂×D₃	—	2	2	no	—
681	C₂×D₃	—	2	2	no	—
682	C₂×D₃	—	4	4	no	—
683	C₂×D₃	C₂×C₅×#41	1	4	yes	—
684	C₃×C₄	—	2	2	no	—
685	C₃×C₄	—	2	2	no	—
686	C₃×C₄	—	2	2	no	—
687	C₃×C₄	—	2	2	no	—
688	C₃×C₄	—	2	2	no	—
689	C₃×C₄	—	2	2	no	—
690	C₃×C₄	—	2	2	no	—
691	Dic₃	—	2	2	no	—
692	Dic₃	—	2	2	no	—
693	Dic₃	—	2	2	no	—
694	Dic₃	—	2	2	no	—
695	Dic₃	—	2	2	no	—
696	Dic₃	C₂×C₅×#41	1	4	yes	—
697	C₂×C₅	—	6	4	no	—
698	C₂×C₅	—	12	2	no	—
699	C₂×C₅	#5693	1	4	yes	direct product factor
700	C₂×C₅	C₂×#1007	1	1	yes	characteristic
701	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
702	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
703	C₂³	—	3	4	no	—
704	C₂³	—	3	2	no	—
705	C₂³	—	3	2	no	—
706	C₂³	—	6	2	no	—
707	C₂³	—	6	2	no	—
708	C₂³	—	6	2	no	—
709	C₂³	—	6	2	no	—
710	C₂³	—	6	2	no	—
711	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
712	Q₈	—	6	8	no	—
713	D₄	—	6	8	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	3	4	no	—
722	C₂×C₄	—	3	2	no	—
723	C₂×C₄	—	3	2	no	—
724	C₂×C₄	—	3	2	no	—
725	C₂×C₄	—	3	2	no	—
726	C₂×C₄	—	3	2	no	—
727	C₂×C₄	—	3	2	no	—
728	C₂×C₄	—	6	8	no	—
729	C₂×C₄	—	6	8	no	—
730	C₂×C₄	—	6	8	no	—
731	C₂×C₄	—	6	8	no	—
732	C₂×C₄	—	6	2	no	—
733	C₂×C₄	—	6	2	no	—
734	C₂×C₄	—	6	2	no	—
735	C₂×C₄	—	6	2	no	—
736	C₂×C₄	—	6	2	no	—
737	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
738	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
739	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
740	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
741	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
742	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
743	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
744	C₂×C₃	C₅×#552	1	4	yes	complemented
745	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
746	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
747	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
748	D₃	—	2	4	no	—
749	D₃	—	4	2	no	—
750	C₅	C₂×#5693	1	1	yes	characteristic, direct product factor, Sylow
751	C₂²	—	3	4	no	—
752	C₂²	—	6	8	no	—
753	C₂²	—	6	2	no	—
754	C₂²	—	6	2	no	—
755	C₂²	—	6	2	no	—
756	C₂²	—	6	2	no	—
757	C₂²	—	6	2	no	—
758	C₂²	—	12	4	no	—
759	C₂²	C₅×#1007	1	2	yes	—
760	C₂²	C₅×D₃×#41	1	2	yes	—
761	C₂²	C₅×D₃×#41	1	2	yes	—
762	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	2	no	—
769	C₄	—	2	2	no	—
770	C₄	—	3	4	no	—
771	C₄	—	6	2	no	—
772	C₄	—	6	2	no	—
773	C₄	—	6	2	no	—
774	C₄	—	6	2	no	—
775	C₄	—	6	2	no	—
776	C₃	C₂×C₅×#552	1	1	yes	characteristic, complemented, Sylow
777	C₂	—	6	4	no	—
778	C₂	—	12	2	no	—
779	C₂	C₅×#5693	1	4	yes	direct product factor
780	C₂	C₂×C₅×#1007	1	1	yes	characteristic
781	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
782	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#125	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₁₂	C₂²
hypercenter	C₂×C₅×#125	D₃
hypocenter	C₃	C₂×C₅×#552
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#125

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×C₅×#125	C₂	semidirect
2. C₅×#5693	C₂	direct (N × H)
3. C₂×C₅×#898	C₂	semidirect
4. C₂×C₅×#898	C₂	semidirect
5. C₂×C₅×#896	C₂	semidirect
6. C₂×C₅×#896	C₂	semidirect
10. C₂×C₅×#892	C₂	semidirect
11. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
12. C₂×C₅×#889	C₂	semidirect
13. C₂×C₅×#889	C₂	semidirect
14. C₂×C₅×#887	C₂	semidirect
15. C₂×C₅×#872	C₂	semidirect
16. C₂×C₅×#872	C₂	semidirect
24. C₃×C₅×#125	C₂²	semidirect
54. C₅×#898	C₂²	semidirect
55. C₅×#898	C₂²	semidirect
56. C₅×#896	C₂²	semidirect
57. C₅×#896	C₂²	semidirect
61. C₅×#892	C₂²	semidirect
62. C₅×D₃×C₄⋊C₄	C₂²	semidirect
63. C₅×#889	C₂²	semidirect
64. C₅×#889	C₂²	semidirect
65. C₅×#887	C₂²	semidirect
66. C₅×#872	C₂²	semidirect
67. C₅×#872	C₂²	semidirect
68. C₂×#5693	C₅	direct (N × H)
74. C₂×C₅×#125	D₃	semidirect
141. C₂×C₃×#125	C₂×C₅	semidirect
142. #5693	C₂×C₅	direct (N × H)
143. C₂×#898	C₂×C₅	semidirect
144. C₂×#898	C₂×C₅	semidirect
145. C₂×#896	C₂×C₅	semidirect
146. C₂×#896	C₂×C₅	semidirect
150. C₂×#892	C₂×C₅	semidirect
151. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
152. C₂×#889	C₂×C₅	semidirect
153. C₂×#889	C₂×C₅	semidirect
154. C₂×#887	C₂×C₅	semidirect
155. C₂×#872	C₂×C₅	semidirect
156. C₂×#872	C₂×C₅	semidirect
167. C₅×#125	C₂×D₃	semidirect
255. C₃×#125	C₂²×C₅	semidirect
285. #898	C₂²×C₅	semidirect
286. #898	C₂²×C₅	semidirect
287. #896	C₂²×C₅	semidirect
288. #896	C₂²×C₅	semidirect
292. #892	C₂²×C₅	semidirect
293. D₃×C₄⋊C₄	C₂²×C₅	semidirect
294. #889	C₂²×C₅	semidirect
295. #889	C₂²×C₅	semidirect
296. #887	C₂²×C₅	semidirect
297. #872	C₂²×C₅	semidirect
298. #872	C₂²×C₅	semidirect
360. C₂×#125	C₅×D₃	semidirect
503. #125	C₂×C₅×D₃	semidirect
543. C₂×C₃×C₅	#552	semidirect
671. C₃×C₅	C₂×#552	semidirect
699. C₂×C₅	#5693	direct (N × H)
744. C₂×C₃	C₅×#552	semidirect
750. C₅	C₂×#5693	direct (N × H)
776. C₃	C₂×C₅×#552	semidirect
779. C₂	C₅×#5693	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×#125	2
C₅×#5693	2
C₂×C₅×#898	2
C₂×C₅×#896	2
C₂×C₅×#894	2
C₂×C₅×#893	2
C₂×C₅×#892	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#889	2
C₂×C₅×#887	2
C₂×C₅×#872	2
C₂×C₅×#552	3
C₂×#5693	5

Subgroups — C2×C5×#5693 #14483397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5693 #14483397