Subgroups — C₃×C₅×#2373 #14275407

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#126	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic
10	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
15	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2373	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₃×C₅×#126	C₄	1	8	yes	complemented
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₂²⋊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×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄²×C₅	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	C₂×C₃×C₄²×C₅	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×#2373	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
54	C₂×C₅×#126	C₂×C₃	1	1	yes	characteristic
55	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
56	C₅×#388	C₂×C₃	1	1	yes	characteristic
57	C₅×#388	C₂×C₃	1	1	yes	characteristic
58	C₅×#388	C₂×C₃	1	1	yes	characteristic
59	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
60	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
61	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#385	C₂×C₃	1	1	yes	characteristic
63	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
64	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
65	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
66	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
67	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
68	C₅×#376	C₂×C₃	1	1	yes	characteristic, complemented
69	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	—	2	2	no	—
71	C₂²×C₃×C₄×C₅	—	2	2	no	—
72	C₂²×C₃×C₄×C₅	—	4	1	no	—
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₃×C₅×C₄⋊C₄	—	2	2	no	—
88	C₃×C₅×C₄⋊C₄	—	2	2	no	—
89	C₃×C₅×C₄⋊C₄	—	2	2	no	—
90	C₃×C₅×C₄⋊C₄	—	2	2	no	—
91	C₃×C₅×C₄⋊C₄	—	4	1	no	—
92	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
93	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
94	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
95	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
96	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
97	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
98	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
99	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
100	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
101	C₃×C₄²×C₅	—	2	2	no	—
102	C₃×C₄²×C₅	—	2	2	no	—
103	C₃×C₄²×C₅	—	2	2	no	—
104	C₃×C₄²×C₅	—	2	2	no	—
105	C₃×C₄²×C₅	—	4	1	no	—
106	C₃×C₄²×C₅	—	4	1	no	—
107	C₃×C₄²×C₅	—	4	1	no	—
108	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
109	C₂×C₃×#126	C₂×C₅	1	1	yes	characteristic
110	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
111	C₃×#388	C₂×C₅	1	1	yes	characteristic
112	C₃×#388	C₂×C₅	1	1	yes	characteristic
113	C₃×#388	C₂×C₅	1	1	yes	characteristic
114	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
115	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
116	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
117	C₃×#385	C₂×C₅	1	1	yes	characteristic
118	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
119	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
120	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
121	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
122	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
123	C₃×#376	C₂×C₅	1	1	yes	characteristic, complemented
124	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
125	C₅×#126	C₃×C₄	1	8	yes	complemented
126	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	1	yes	characteristic
140	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
148	C₅×#95	C₂²×C₃	1	1	yes	characteristic
149	C₅×#95	C₂²×C₃	1	1	yes	characteristic
150	C₅×#95	C₂²×C₃	1	1	yes	characteristic
151	C₅×#95	C₂²×C₃	1	1	yes	characteristic
152	C₅×#95	C₂²×C₃	1	1	yes	characteristic
153	C₅×#95	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	#2373	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
161	C₂³×C₃×C₅	—	2	1	no	—
162	C₂³×C₃×C₅	—	2	1	no	—
163	C₂³×C₃×C₅	—	2	1	no	—
164	C₂³×C₃×C₅	—	2	1	no	—
165	C₂³×C₃×C₅	—	2	1	no	—
166	C₂³×C₃×C₅	—	2	1	no	—
167	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
168	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
169	C₂×C₃×C₄×C₅	—	2	1	no	—
170	C₂×C₃×C₄×C₅	—	2	1	no	—
171	C₂×C₃×C₄×C₅	—	2	1	no	—
172	C₂×C₃×C₄×C₅	—	2	1	no	—
173	C₂×C₃×C₄×C₅	—	2	1	no	—
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	—	2	1	no	—
176	C₂×C₃×C₄×C₅	—	2	1	no	—
177	C₂×C₃×C₄×C₅	—	2	1	no	—
178	C₂×C₃×C₄×C₅	—	2	1	no	—
179	C₂×C₃×C₄×C₅	—	2	1	no	—
180	C₂×C₃×C₄×C₅	—	2	1	no	—
181	C₂×C₃×C₄×C₅	—	2	1	no	—
182	C₂×C₃×C₄×C₅	—	2	1	no	—
183	C₂×C₃×C₄×C₅	—	2	1	no	—
184	C₂×C₃×C₄×C₅	—	2	1	no	—
185	C₂×C₃×C₄×C₅	—	2	1	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	—	4	4	no	—
202	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
203	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
204	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
205	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
206	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
207	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
208	C₂×C₃×C₄×C₅	#41	1	2	yes	—
209	C₂×C₃×C₄×C₅	#41	1	2	yes	—
210	C₂×C₃×C₄×C₅	#41	1	2	yes	—
211	C₂×C₃×C₄×C₅	#41	1	2	yes	—
212	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
213	C₃×#126	C₄×C₅	1	8	yes	complemented
214	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
215	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
222	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
224	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
236	C₃×#95	C₂²×C₅	1	1	yes	characteristic
237	C₃×#95	C₂²×C₅	1	1	yes	characteristic
238	C₃×#95	C₂²×C₅	1	1	yes	characteristic
239	C₃×#95	C₂²×C₅	1	1	yes	characteristic
240	C₃×#95	C₂²×C₅	1	1	yes	characteristic
241	C₃×#95	C₂²×C₅	1	1	yes	characteristic
242	C₃×#95	C₂²×C₅	1	1	yes	characteristic
243	C₃×#95	C₂²×C₅	1	1	yes	characteristic
244	C₃×#95	C₂²×C₅	1	1	yes	characteristic
245	C₃×#95	C₂²×C₅	1	1	yes	characteristic
246	C₃×#95	C₂²×C₅	1	1	yes	characteristic
247	C₃×#95	C₂²×C₅	1	1	yes	characteristic
248	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
249	C₂²×C₄×C₅	—	2	2	no	—
250	C₂²×C₄×C₅	—	2	2	no	—
251	C₂²×C₄×C₅	—	4	1	no	—
252	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
253	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
254	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
255	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
256	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
257	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
258	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
259	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
260	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
261	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
262	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
263	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
264	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
265	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
266	C₅×C₄⋊C₄	—	2	2	no	—
267	C₅×C₄⋊C₄	—	2	2	no	—
268	C₅×C₄⋊C₄	—	2	2	no	—
269	C₅×C₄⋊C₄	—	2	2	no	—
270	C₅×C₄⋊C₄	—	4	1	no	—
271	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
272	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
273	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
274	C₅×C₂²⋊C₄	—	2	2	no	—
275	C₅×C₂²⋊C₄	—	2	2	no	—
276	C₅×C₂²⋊C₄	—	4	1	no	—
277	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
278	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
279	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
280	C₄²×C₅	—	2	2	no	—
281	C₄²×C₅	—	2	2	no	—
282	C₄²×C₅	—	2	2	no	—
283	C₄²×C₅	—	2	2	no	—
284	C₄²×C₅	—	4	1	no	—
285	C₄²×C₅	—	4	1	no	—
286	C₄²×C₅	—	4	1	no	—
287	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
288	C₂×#126	C₂×C₃×C₅	1	1	yes	characteristic
289	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
290	#388	C₂×C₃×C₅	1	1	yes	characteristic
291	#388	C₂×C₃×C₅	1	1	yes	characteristic
292	#388	C₂×C₃×C₅	1	1	yes	characteristic
293	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
294	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
295	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
296	#385	C₂×C₃×C₅	1	1	yes	characteristic
297	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
298	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
299	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
300	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
301	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
302	#376	C₂×C₃×C₅	1	1	yes	characteristic, complemented
303	C₂²×C₃×C₅	—	2	2	no	—
304	C₂²×C₃×C₅	—	2	2	no	—
305	C₂²×C₃×C₅	—	2	2	no	—
306	C₂²×C₃×C₅	—	4	1	no	—
307	C₂²×C₃×C₅	—	4	1	no	—
308	C₂²×C₃×C₅	—	4	1	no	—
309	C₂²×C₃×C₅	—	4	1	no	—
310	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
311	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
312	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
313	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
314	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
315	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
316	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
317	C₃×C₄×C₅	—	2	2	no	—
318	C₃×C₄×C₅	—	2	2	no	—
319	C₃×C₄×C₅	—	2	2	no	—
320	C₃×C₄×C₅	—	2	2	no	—
321	C₃×C₄×C₅	—	2	2	no	—
322	C₃×C₄×C₅	—	2	2	no	—
323	C₃×C₄×C₅	—	2	2	no	—
324	C₃×C₄×C₅	—	2	2	no	—
325	C₃×C₄×C₅	—	2	2	no	—
326	C₃×C₄×C₅	—	2	2	no	—
327	C₃×C₄×C₅	—	4	1	no	—
328	C₃×C₄×C₅	—	4	1	no	—
329	C₃×C₄×C₅	—	4	1	no	—
330	C₃×C₄×C₅	—	4	1	no	—
331	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
332	C₂²×C₃×C₄	—	2	2	no	—
333	C₂²×C₃×C₄	—	2	2	no	—
334	C₂²×C₃×C₄	—	4	1	no	—
335	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
336	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
337	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
338	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
339	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
340	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
341	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
342	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
343	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
344	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
345	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
346	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
347	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
348	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
349	C₃×C₄⋊C₄	—	2	2	no	—
350	C₃×C₄⋊C₄	—	2	2	no	—
351	C₃×C₄⋊C₄	—	2	2	no	—
352	C₃×C₄⋊C₄	—	2	2	no	—
353	C₃×C₄⋊C₄	—	4	1	no	—
354	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
355	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
356	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
357	C₃×C₂²⋊C₄	—	2	2	no	—
358	C₃×C₂²⋊C₄	—	2	2	no	—
359	C₃×C₂²⋊C₄	—	4	1	no	—
360	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
361	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
362	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
363	C₃×C₄²	—	2	2	no	—
364	C₃×C₄²	—	2	2	no	—
365	C₃×C₄²	—	2	2	no	—
366	C₃×C₄²	—	2	2	no	—
367	C₃×C₄²	—	4	1	no	—
368	C₃×C₄²	—	4	1	no	—
369	C₃×C₄²	—	4	1	no	—
370	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
371	C₂³×C₅	—	2	1	no	—
372	C₂³×C₅	—	2	1	no	—
373	C₂³×C₅	—	2	1	no	—
374	C₂³×C₅	—	2	1	no	—
375	C₂³×C₅	—	2	1	no	—
376	C₂³×C₅	—	2	1	no	—
377	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
378	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
379	C₂×C₄×C₅	—	2	1	no	—
380	C₂×C₄×C₅	—	2	1	no	—
381	C₂×C₄×C₅	—	2	1	no	—
382	C₂×C₄×C₅	—	2	1	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	—	2	1	no	—
387	C₂×C₄×C₅	—	2	1	no	—
388	C₂×C₄×C₅	—	2	1	no	—
389	C₂×C₄×C₅	—	2	1	no	—
390	C₂×C₄×C₅	—	2	1	no	—
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	2	1	no	—
394	C₂×C₄×C₅	—	2	1	no	—
395	C₂×C₄×C₅	—	2	1	no	—
396	C₂×C₄×C₅	—	2	1	no	—
397	C₂×C₄×C₅	—	2	1	no	—
398	C₂×C₄×C₅	—	2	1	no	—
399	C₂×C₄×C₅	—	2	1	no	—
400	C₂×C₄×C₅	—	2	1	no	—
401	C₂×C₄×C₅	—	2	1	no	—
402	C₂×C₄×C₅	—	2	1	no	—
403	C₂×C₄×C₅	—	2	1	no	—
404	C₂×C₄×C₅	—	2	1	no	—
405	C₂×C₄×C₅	—	2	1	no	—
406	C₂×C₄×C₅	—	2	1	no	—
407	C₂×C₄×C₅	—	2	1	no	—
408	C₂×C₄×C₅	—	2	1	no	—
409	C₂×C₄×C₅	—	2	1	no	—
410	C₂×C₄×C₅	—	2	1	no	—
411	C₂×C₄×C₅	—	4	4	no	—
412	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
413	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
414	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
415	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
416	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
417	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
418	C₂×C₄×C₅	C₃×#41	1	2	yes	—
419	C₂×C₄×C₅	C₃×#41	1	2	yes	—
420	C₂×C₄×C₅	C₃×#41	1	2	yes	—
421	C₂×C₄×C₅	C₃×#41	1	2	yes	—
422	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
423	#126	C₃×C₄×C₅	1	8	yes	complemented
424	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
434	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
435	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
438	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
439	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
440	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
441	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
442	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
443	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
444	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
445	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
446	#95	C₂²×C₃×C₅	1	1	yes	characteristic
447	#95	C₂²×C₃×C₅	1	1	yes	characteristic
448	#95	C₂²×C₃×C₅	1	1	yes	characteristic
449	#95	C₂²×C₃×C₅	1	1	yes	characteristic
450	#95	C₂²×C₃×C₅	1	1	yes	characteristic
451	#95	C₂²×C₃×C₅	1	1	yes	characteristic
452	#95	C₂²×C₃×C₅	1	1	yes	characteristic
453	#95	C₂²×C₃×C₅	1	1	yes	characteristic
454	#95	C₂²×C₃×C₅	1	1	yes	characteristic
455	#95	C₂²×C₃×C₅	1	1	yes	characteristic
456	#95	C₂²×C₃×C₅	1	1	yes	characteristic
457	#95	C₂²×C₃×C₅	1	1	yes	characteristic
458	C₂×C₃×C₅	—	4	2	no	—
459	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
460	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
461	C₂×C₃×C₅	#520	1	1	yes	characteristic
462	C₂×C₃×C₅	#551	1	1	yes	characteristic
463	C₂×C₃×C₅	#552	1	1	yes	characteristic
464	C₂×C₃×C₅	#553	1	1	yes	characteristic
465	C₂×C₃×C₅	#556	1	1	yes	characteristic
466	C₂³×C₃	—	2	1	no	—
467	C₂³×C₃	—	2	1	no	—
468	C₂³×C₃	—	2	1	no	—
469	C₂³×C₃	—	2	1	no	—
470	C₂³×C₃	—	2	1	no	—
471	C₂³×C₃	—	2	1	no	—
472	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
473	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
474	C₂×C₃×C₄	—	2	1	no	—
475	C₂×C₃×C₄	—	2	1	no	—
476	C₂×C₃×C₄	—	2	1	no	—
477	C₂×C₃×C₄	—	2	1	no	—
478	C₂×C₃×C₄	—	2	1	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	1	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	1	no	—
488	C₂×C₃×C₄	—	2	1	no	—
489	C₂×C₃×C₄	—	2	1	no	—
490	C₂×C₃×C₄	—	2	1	no	—
491	C₂×C₃×C₄	—	2	1	no	—
492	C₂×C₃×C₄	—	2	1	no	—
493	C₂×C₃×C₄	—	2	1	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	1	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	1	no	—
501	C₂×C₃×C₄	—	2	1	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	2	1	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	4	4	no	—
507	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
508	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
509	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
510	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
511	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
512	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
513	C₂×C₃×C₄	C₅×#41	1	2	yes	—
514	C₂×C₃×C₄	C₅×#41	1	2	yes	—
515	C₂×C₃×C₄	C₅×#41	1	2	yes	—
516	C₂×C₃×C₄	C₅×#41	1	2	yes	—
517	C₂²×C₅	—	2	2	no	—
518	C₂²×C₅	—	2	2	no	—
519	C₂²×C₅	—	2	2	no	—
520	C₂²×C₅	—	4	1	no	—
521	C₂²×C₅	—	4	1	no	—
522	C₂²×C₅	—	4	1	no	—
523	C₂²×C₅	—	4	1	no	—
524	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
525	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
526	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
527	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
528	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
529	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
530	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
531	C₄×C₅	—	2	2	no	—
532	C₄×C₅	—	2	2	no	—
533	C₄×C₅	—	2	2	no	—
534	C₄×C₅	—	2	2	no	—
535	C₄×C₅	—	2	2	no	—
536	C₄×C₅	—	2	2	no	—
537	C₄×C₅	—	2	2	no	—
538	C₄×C₅	—	2	2	no	—
539	C₄×C₅	—	2	2	no	—
540	C₄×C₅	—	2	2	no	—
541	C₄×C₅	—	4	1	no	—
542	C₄×C₅	—	4	1	no	—
543	C₄×C₅	—	4	1	no	—
544	C₄×C₅	—	4	1	no	—
545	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	4	1	no	—
549	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
550	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
551	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
552	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
553	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
554	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
555	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
556	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
557	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
558	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
559	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
560	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
561	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
562	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	4	1	no	—
568	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
569	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
570	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	4	1	no	—
574	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
575	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
576	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
577	C₄²	—	2	2	no	—
578	C₄²	—	2	2	no	—
579	C₄²	—	2	2	no	—
580	C₄²	—	2	2	no	—
581	C₄²	—	4	1	no	—
582	C₄²	—	4	1	no	—
583	C₄²	—	4	1	no	—
584	C₄²	C₂×C₃×C₄×C₅	1	4	yes	complemented
585	C₃×C₅	#2373	1	1	yes	characteristic, direct product factor, Hall
586	C₂²×C₃	—	2	2	no	—
587	C₂²×C₃	—	2	2	no	—
588	C₂²×C₃	—	2	2	no	—
589	C₂²×C₃	—	4	1	no	—
590	C₂²×C₃	—	4	1	no	—
591	C₂²×C₃	—	4	1	no	—
592	C₂²×C₃	—	4	1	no	—
593	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
594	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
595	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
596	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
597	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
598	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
599	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
600	C₃×C₄	—	2	2	no	—
601	C₃×C₄	—	2	2	no	—
602	C₃×C₄	—	2	2	no	—
603	C₃×C₄	—	2	2	no	—
604	C₃×C₄	—	2	2	no	—
605	C₃×C₄	—	2	2	no	—
606	C₃×C₄	—	2	2	no	—
607	C₃×C₄	—	2	2	no	—
608	C₃×C₄	—	2	2	no	—
609	C₃×C₄	—	2	2	no	—
610	C₃×C₄	—	4	1	no	—
611	C₃×C₄	—	4	1	no	—
612	C₃×C₄	—	4	1	no	—
613	C₃×C₄	—	4	1	no	—
614	C₂×C₅	—	4	2	no	—
615	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
616	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
617	C₂×C₅	C₃×#520	1	1	yes	characteristic
618	C₂×C₅	C₃×#551	1	1	yes	characteristic
619	C₂×C₅	C₃×#552	1	1	yes	characteristic
620	C₂×C₅	C₃×#553	1	1	yes	characteristic
621	C₂×C₅	C₃×#556	1	1	yes	characteristic
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
629	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
664	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
665	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
666	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
667	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
668	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
669	C₂×C₄	C₃×C₅×#41	1	2	yes	—
670	C₂×C₄	C₃×C₅×#41	1	2	yes	—
671	C₂×C₄	C₃×C₅×#41	1	2	yes	—
672	C₂×C₄	C₃×C₅×#41	1	2	yes	—
673	C₂×C₃	—	4	2	no	—
674	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
675	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
676	C₂×C₃	C₅×#520	1	1	yes	characteristic
677	C₂×C₃	C₅×#551	1	1	yes	characteristic
678	C₂×C₃	C₅×#552	1	1	yes	characteristic
679	C₂×C₃	C₅×#553	1	1	yes	characteristic
680	C₂×C₃	C₅×#556	1	1	yes	characteristic
681	C₅	C₃×#2373	1	1	yes	characteristic, direct product factor, Sylow
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
690	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
691	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
692	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
693	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
694	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
695	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
696	C₄	—	2	2	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	2	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	2	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₃	C₅×#2373	1	1	yes	characteristic, direct product factor, Sylow
711	C₂	—	4	2	no	—
712	C₂	C₃×C₄×C₅×#41	1	1	yes	characteristic
713	C₂	C₃×C₄×C₅×#41	1	1	yes	characteristic
714	C₂	C₃×C₅×#520	1	1	yes	characteristic
715	C₂	C₃×C₅×#551	1	1	yes	characteristic
716	C₂	C₃×C₅×#552	1	1	yes	characteristic
717	C₂	C₃×C₅×#553	1	1	yes	characteristic
718	C₂	C₃×C₅×#556	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#389	C₂	semidirect
6. C₃×C₅×#387	C₂	semidirect
7. C₃×C₅×#387	C₂	semidirect
8. C₃×C₅×#387	C₂	semidirect
10. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
11. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
12. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
15. C₃×C₅×#376	C₂	semidirect
16. C₅×#2373	C₃	direct (N × H)
18. C₃×C₅×#126	C₄	semidirect
53. C₃×#2373	C₅	direct (N × H)
55. C₅×#389	C₂×C₃	semidirect
59. C₅×#387	C₂×C₃	semidirect
60. C₅×#387	C₂×C₃	semidirect
61. C₅×#387	C₂×C₃	semidirect
63. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
64. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
65. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
68. C₅×#376	C₂×C₃	semidirect
92. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
93. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
94. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
108. C₃×C₄²×C₅	C₂×C₄	semidirect
110. C₃×#389	C₂×C₅	semidirect
114. C₃×#387	C₂×C₅	semidirect
115. C₃×#387	C₂×C₅	semidirect
116. C₃×#387	C₂×C₅	semidirect
118. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
119. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
120. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
123. C₃×#376	C₂×C₅	semidirect
125. C₅×#126	C₃×C₄	semidirect
160. #2373	C₃×C₅	direct (N × H)
213. C₃×#126	C₄×C₅	semidirect
271. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
272. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
273. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
287. C₄²×C₅	C₂×C₃×C₄	semidirect
289. #389	C₂×C₃×C₅	semidirect
293. #387	C₂×C₃×C₅	semidirect
294. #387	C₂×C₃×C₅	semidirect
295. #387	C₂×C₃×C₅	semidirect
297. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
298. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
299. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
302. #376	C₂×C₃×C₅	semidirect
354. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
355. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
356. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
370. C₃×C₄²	C₂×C₄×C₅	semidirect
423. #126	C₃×C₄×C₅	semidirect
568. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
569. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
570. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
584. C₄²	C₂×C₃×C₄×C₅	semidirect
585. C₃×C₅	#2373	direct (N × H)
681. C₅	C₃×#2373	direct (N × H)
710. C₃	C₅×#2373	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×#126	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#385	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₃×C₅×#376	2
C₅×#2373	3
C₃×#2373	5

Subgroups — C3×C5×#2373 #14275407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2373 #14275407