Subgroups — C₃×C₅×#2648 #14275682

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#396	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#392	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2648	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂³×C₃×C₄×C₅	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×C₂²⋊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×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₄²×C₅	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×#2648	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₅×#400	C₂×C₃	1	1	yes	characteristic, complemented
54	C₅×#397	C₂×C₃	1	1	yes	characteristic, complemented
55	C₅×#397	C₂×C₃	1	1	yes	characteristic, complemented
56	C₅×#396	C₂×C₃	1	1	yes	characteristic, complemented
57	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
58	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
59	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
60	C₅×#392	C₂×C₃	1	1	yes	characteristic
61	C₅×#390	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×#387	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
67	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×D₄	—	2	2	no	—
72	C₂×C₃×C₅×D₄	—	2	2	no	—
73	C₂×C₃×C₅×D₄	—	2	2	no	—
74	C₂×C₃×C₅×D₄	—	4	1	no	—
75	C₂×C₃×C₅×D₄	—	4	1	no	—
76	C₂×C₃×C₅×D₄	—	4	1	no	—
77	C₂×C₃×C₅×D₄	—	4	1	no	—
78	C₂×C₃×C₅×D₄	—	4	1	no	—
79	C₂×C₃×C₅×D₄	—	4	1	no	—
80	C₂²×C₃×C₄×C₅	—	2	2	no	—
81	C₂²×C₃×C₄×C₅	—	4	1	no	—
82	C₂²×C₃×C₄×C₅	—	4	1	no	—
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	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	C₃×C₅×C₄⋊C₄	—	2	2	no	—
96	C₃×C₅×C₄⋊C₄	—	4	1	no	—
97	C₃×C₅×C₄⋊C₄	—	4	1	no	—
98	C₃×C₅×C₄⋊C₄	—	4	1	no	—
99	C₃×C₅×C₄⋊C₄	—	4	1	no	—
100	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
101	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
102	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
103	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
104	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
105	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
106	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
107	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
108	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
109	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
110	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
111	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
112	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
113	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
114	C₃×C₄²×C₅	—	4	1	no	—
115	C₃×C₄²×C₅	—	4	1	no	—
116	C₃×#400	C₂×C₅	1	1	yes	characteristic, complemented
117	C₃×#397	C₂×C₅	1	1	yes	characteristic, complemented
118	C₃×#397	C₂×C₅	1	1	yes	characteristic, complemented
119	C₃×#396	C₂×C₅	1	1	yes	characteristic, complemented
120	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
121	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
122	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
123	C₃×#392	C₂×C₅	1	1	yes	characteristic
124	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
125	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
126	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
128	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
129	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
132	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
133	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
134	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₅×C₂²⋊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×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₄²×C₅	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	#2648	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
167	C₂³×C₃×C₅	—	2	1	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	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	—	2	1	no	—
181	C₂³×C₃×C₅	—	2	1	no	—
182	C₂³×C₃×C₅	—	2	1	no	—
183	C₂³×C₃×C₅	—	2	1	no	—
184	C₂³×C₃×C₅	—	2	1	no	—
185	C₂³×C₃×C₅	—	2	1	no	—
186	C₂³×C₃×C₅	—	2	1	no	—
187	C₂³×C₃×C₅	#41	1	2	yes	—
188	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
189	C₃×C₅×D₄	—	4	4	no	—
190	C₃×C₅×D₄	—	4	4	no	—
191	C₃×C₅×D₄	—	4	4	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	—	2	1	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	2	1	no	—
224	C₂×C₃×C₄×C₅	—	2	1	no	—
225	C₂×C₃×C₄×C₅	—	2	1	no	—
226	C₂×C₃×C₄×C₅	—	4	4	no	—
227	C₂×C₃×C₄×C₅	#41	1	2	yes	—
228	C₂×C₃×C₄×C₅	#41	1	2	yes	—
229	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
230	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
231	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
232	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₃×C₂²⋊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×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₃×C₄²	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	C₂⁴×C₅	C₂³×C₃	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×D₄	—	2	2	no	—
268	C₂×C₅×D₄	—	2	2	no	—
269	C₂×C₅×D₄	—	2	2	no	—
270	C₂×C₅×D₄	—	4	1	no	—
271	C₂×C₅×D₄	—	4	1	no	—
272	C₂×C₅×D₄	—	4	1	no	—
273	C₂×C₅×D₄	—	4	1	no	—
274	C₂×C₅×D₄	—	4	1	no	—
275	C₂×C₅×D₄	—	4	1	no	—
276	C₂²×C₄×C₅	—	2	2	no	—
277	C₂²×C₄×C₅	—	4	1	no	—
278	C₂²×C₄×C₅	—	4	1	no	—
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	1	yes	characteristic
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	C₅×C₄⋊C₄	—	2	2	no	—
292	C₅×C₄⋊C₄	—	4	1	no	—
293	C₅×C₄⋊C₄	—	4	1	no	—
294	C₅×C₄⋊C₄	—	4	1	no	—
295	C₅×C₄⋊C₄	—	4	1	no	—
296	C₅×C₂²⋊C₄	—	2	2	no	—
297	C₅×C₂²⋊C₄	—	2	2	no	—
298	C₅×C₂²⋊C₄	—	2	2	no	—
299	C₅×C₂²⋊C₄	—	2	2	no	—
300	C₅×C₂²⋊C₄	—	4	1	no	—
301	C₅×C₂²⋊C₄	—	4	1	no	—
302	C₅×C₂²⋊C₄	—	4	1	no	—
303	C₅×C₂²⋊C₄	—	4	1	no	—
304	C₅×C₂²⋊C₄	—	4	1	no	—
305	C₅×C₂²⋊C₄	—	4	1	no	—
306	C₅×C₂²⋊C₄	—	4	1	no	—
307	C₅×C₂²⋊C₄	—	4	1	no	—
308	C₅×C₂²⋊C₄	—	4	1	no	—
309	C₅×C₂²⋊C₄	—	4	1	no	—
310	C₄²×C₅	—	4	1	no	—
311	C₄²×C₅	—	4	1	no	—
312	#400	C₂×C₃×C₅	1	1	yes	characteristic, complemented
313	#397	C₂×C₃×C₅	1	1	yes	characteristic, complemented
314	#397	C₂×C₃×C₅	1	1	yes	characteristic, complemented
315	#396	C₂×C₃×C₅	1	1	yes	characteristic, complemented
316	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
317	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
318	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
319	#392	C₂×C₃×C₅	1	1	yes	characteristic
320	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
321	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
322	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
323	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
324	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
325	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
326	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
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	—	4	1	no	—
331	C₂²×C₃×C₅	—	4	1	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	—	4	1	no	—
340	C₂²×C₃×C₅	—	4	1	no	—
341	C₂²×C₃×C₅	—	4	1	no	—
342	C₂²×C₃×C₅	—	4	1	no	—
343	C₂²×C₃×C₅	—	4	1	no	—
344	C₂²×C₃×C₅	—	4	1	no	—
345	C₂²×C₃×C₅	—	4	1	no	—
346	C₂²×C₃×C₅	—	4	1	no	—
347	C₂²×C₃×C₅	—	4	1	no	—
348	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
349	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
350	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
351	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
353	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
355	C₃×C₄×C₅	—	2	2	no	—
356	C₃×C₄×C₅	—	2	2	no	—
357	C₃×C₄×C₅	—	4	1	no	—
358	C₃×C₄×C₅	—	4	1	no	—
359	C₃×C₄×C₅	—	4	1	no	—
360	C₃×C₄×C₅	—	4	1	no	—
361	C₃×C₄×C₅	—	4	1	no	—
362	C₃×C₄×C₅	—	4	1	no	—
363	C₃×C₄×C₅	—	4	1	no	—
364	C₃×C₄×C₅	—	4	1	no	—
365	C₃×C₄×C₅	—	4	1	no	—
366	C₃×C₄×C₅	—	4	1	no	—
367	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
368	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
369	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
370	C₂×C₃×D₄	—	2	2	no	—
371	C₂×C₃×D₄	—	2	2	no	—
372	C₂×C₃×D₄	—	2	2	no	—
373	C₂×C₃×D₄	—	4	1	no	—
374	C₂×C₃×D₄	—	4	1	no	—
375	C₂×C₃×D₄	—	4	1	no	—
376	C₂×C₃×D₄	—	4	1	no	—
377	C₂×C₃×D₄	—	4	1	no	—
378	C₂×C₃×D₄	—	4	1	no	—
379	C₂²×C₃×C₄	—	2	2	no	—
380	C₂²×C₃×C₄	—	4	1	no	—
381	C₂²×C₃×C₄	—	4	1	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	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	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
391	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
392	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
393	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
394	C₃×C₄⋊C₄	—	2	2	no	—
395	C₃×C₄⋊C₄	—	4	1	no	—
396	C₃×C₄⋊C₄	—	4	1	no	—
397	C₃×C₄⋊C₄	—	4	1	no	—
398	C₃×C₄⋊C₄	—	4	1	no	—
399	C₃×C₂²⋊C₄	—	2	2	no	—
400	C₃×C₂²⋊C₄	—	2	2	no	—
401	C₃×C₂²⋊C₄	—	2	2	no	—
402	C₃×C₂²⋊C₄	—	2	2	no	—
403	C₃×C₂²⋊C₄	—	4	1	no	—
404	C₃×C₂²⋊C₄	—	4	1	no	—
405	C₃×C₂²⋊C₄	—	4	1	no	—
406	C₃×C₂²⋊C₄	—	4	1	no	—
407	C₃×C₂²⋊C₄	—	4	1	no	—
408	C₃×C₂²⋊C₄	—	4	1	no	—
409	C₃×C₂²⋊C₄	—	4	1	no	—
410	C₃×C₂²⋊C₄	—	4	1	no	—
411	C₃×C₂²⋊C₄	—	4	1	no	—
412	C₃×C₂²⋊C₄	—	4	1	no	—
413	C₃×C₄²	—	4	1	no	—
414	C₃×C₄²	—	4	1	no	—
415	C₂³×C₅	—	2	1	no	—
416	C₂³×C₅	—	2	1	no	—
417	C₂³×C₅	—	2	1	no	—
418	C₂³×C₅	—	2	1	no	—
419	C₂³×C₅	—	2	1	no	—
420	C₂³×C₅	—	2	1	no	—
421	C₂³×C₅	—	2	1	no	—
422	C₂³×C₅	—	2	1	no	—
423	C₂³×C₅	—	2	1	no	—
424	C₂³×C₅	—	2	1	no	—
425	C₂³×C₅	—	2	1	no	—
426	C₂³×C₅	—	2	1	no	—
427	C₂³×C₅	—	2	1	no	—
428	C₂³×C₅	—	2	1	no	—
429	C₂³×C₅	—	2	1	no	—
430	C₂³×C₅	—	2	1	no	—
431	C₂³×C₅	—	2	1	no	—
432	C₂³×C₅	—	2	1	no	—
433	C₂³×C₅	—	2	1	no	—
434	C₂³×C₅	—	2	1	no	—
435	C₂³×C₅	C₃×#41	1	2	yes	—
436	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
437	C₅×D₄	—	4	4	no	—
438	C₅×D₄	—	4	4	no	—
439	C₅×D₄	—	4	4	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	—	2	1	no	—
459	C₂×C₄×C₅	—	2	1	no	—
460	C₂×C₄×C₅	—	2	1	no	—
461	C₂×C₄×C₅	—	2	1	no	—
462	C₂×C₄×C₅	—	2	1	no	—
463	C₂×C₄×C₅	—	2	1	no	—
464	C₂×C₄×C₅	—	2	1	no	—
465	C₂×C₄×C₅	—	2	1	no	—
466	C₂×C₄×C₅	—	2	1	no	—
467	C₂×C₄×C₅	—	2	1	no	—
468	C₂×C₄×C₅	—	2	1	no	—
469	C₂×C₄×C₅	—	2	1	no	—
470	C₂×C₄×C₅	—	2	1	no	—
471	C₂×C₄×C₅	—	2	1	no	—
472	C₂×C₄×C₅	—	2	1	no	—
473	C₂×C₄×C₅	—	2	1	no	—
474	C₂×C₄×C₅	—	4	4	no	—
475	C₂×C₄×C₅	C₃×#41	1	2	yes	—
476	C₂×C₄×C₅	C₃×#41	1	2	yes	—
477	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
478	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
479	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
480	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
487	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
488	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
494	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
495	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
499	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
500	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
501	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
502	#95	C₂²×C₃×C₅	1	1	yes	characteristic
503	#95	C₂²×C₃×C₅	1	1	yes	characteristic
504	#95	C₂²×C₃×C₅	1	1	yes	characteristic
505	#95	C₂²×C₃×C₅	1	1	yes	characteristic
506	#95	C₂²×C₃×C₅	1	1	yes	characteristic
507	#95	C₂²×C₃×C₅	1	1	yes	characteristic
508	#95	C₂²×C₃×C₅	1	1	yes	characteristic
509	#95	C₂²×C₃×C₅	1	1	yes	characteristic
510	#95	C₂²×C₃×C₅	1	1	yes	characteristic
511	#95	C₂²×C₃×C₅	1	1	yes	characteristic
512	C₂×C₃×C₅	—	4	2	no	—
513	C₂×C₃×C₅	—	8	1	no	—
514	C₂×C₃×C₅	—	8	1	no	—
515	C₂×C₃×C₅	#529	1	1	yes	characteristic
516	C₂×C₃×C₅	#538	1	1	yes	characteristic
517	C₂×C₃×C₅	#538	1	1	yes	characteristic
518	C₂×C₃×C₅	#538	1	1	yes	characteristic
519	C₂×C₃×C₅	#538	1	1	yes	characteristic
520	C₂×C₃×C₅	#540	1	1	yes	characteristic
521	C₂×C₃×C₅	#540	1	1	yes	characteristic
522	C₂³×C₃	—	2	1	no	—
523	C₂³×C₃	—	2	1	no	—
524	C₂³×C₃	—	2	1	no	—
525	C₂³×C₃	—	2	1	no	—
526	C₂³×C₃	—	2	1	no	—
527	C₂³×C₃	—	2	1	no	—
528	C₂³×C₃	—	2	1	no	—
529	C₂³×C₃	—	2	1	no	—
530	C₂³×C₃	—	2	1	no	—
531	C₂³×C₃	—	2	1	no	—
532	C₂³×C₃	—	2	1	no	—
533	C₂³×C₃	—	2	1	no	—
534	C₂³×C₃	—	2	1	no	—
535	C₂³×C₃	—	2	1	no	—
536	C₂³×C₃	—	2	1	no	—
537	C₂³×C₃	—	2	1	no	—
538	C₂³×C₃	—	2	1	no	—
539	C₂³×C₃	—	2	1	no	—
540	C₂³×C₃	—	2	1	no	—
541	C₂³×C₃	—	2	1	no	—
542	C₂³×C₃	C₅×#41	1	2	yes	—
543	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
544	C₃×D₄	—	4	4	no	—
545	C₃×D₄	—	4	4	no	—
546	C₃×D₄	—	4	4	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	—	2	1	no	—
564	C₂×C₃×C₄	—	2	1	no	—
565	C₂×C₃×C₄	—	2	1	no	—
566	C₂×C₃×C₄	—	2	1	no	—
567	C₂×C₃×C₄	—	2	1	no	—
568	C₂×C₃×C₄	—	2	1	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	2	1	no	—
572	C₂×C₃×C₄	—	2	1	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	2	1	no	—
575	C₂×C₃×C₄	—	2	1	no	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	2	1	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	2	1	no	—
581	C₂×C₃×C₄	—	4	4	no	—
582	C₂×C₃×C₄	C₅×#41	1	2	yes	—
583	C₂×C₃×C₄	C₅×#41	1	2	yes	—
584	C₂²×C₅	—	2	2	no	—
585	C₂²×C₅	—	2	2	no	—
586	C₂²×C₅	—	2	2	no	—
587	C₂²×C₅	—	4	1	no	—
588	C₂²×C₅	—	4	1	no	—
589	C₂²×C₅	—	4	1	no	—
590	C₂²×C₅	—	4	1	no	—
591	C₂²×C₅	—	4	1	no	—
592	C₂²×C₅	—	4	1	no	—
593	C₂²×C₅	—	4	1	no	—
594	C₂²×C₅	—	4	1	no	—
595	C₂²×C₅	—	4	1	no	—
596	C₂²×C₅	—	4	1	no	—
597	C₂²×C₅	—	4	1	no	—
598	C₂²×C₅	—	4	1	no	—
599	C₂²×C₅	—	4	1	no	—
600	C₂²×C₅	—	4	1	no	—
601	C₂²×C₅	—	4	1	no	—
602	C₂²×C₅	—	4	1	no	—
603	C₂²×C₅	—	4	1	no	—
604	C₂²×C₅	—	4	1	no	—
605	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
606	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
607	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
608	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
609	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
610	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
611	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
612	C₄×C₅	—	2	2	no	—
613	C₄×C₅	—	2	2	no	—
614	C₄×C₅	—	4	1	no	—
615	C₄×C₅	—	4	1	no	—
616	C₄×C₅	—	4	1	no	—
617	C₄×C₅	—	4	1	no	—
618	C₄×C₅	—	4	1	no	—
619	C₄×C₅	—	4	1	no	—
620	C₄×C₅	—	4	1	no	—
621	C₄×C₅	—	4	1	no	—
622	C₄×C₅	—	4	1	no	—
623	C₄×C₅	—	4	1	no	—
624	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
625	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
626	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	—	4	1	no	—
631	C₂×D₄	—	4	1	no	—
632	C₂×D₄	—	4	1	no	—
633	C₂×D₄	—	4	1	no	—
634	C₂×D₄	—	4	1	no	—
635	C₂×D₄	—	4	1	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	4	1	no	—
638	C₂²×C₄	—	4	1	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	1	yes	characteristic
642	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
643	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
644	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
645	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
646	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
647	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
648	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
649	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
650	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	4	1	no	—
653	C₄⋊C₄	—	4	1	no	—
654	C₄⋊C₄	—	4	1	no	—
655	C₄⋊C₄	—	4	1	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	4	1	no	—
661	C₂²⋊C₄	—	4	1	no	—
662	C₂²⋊C₄	—	4	1	no	—
663	C₂²⋊C₄	—	4	1	no	—
664	C₂²⋊C₄	—	4	1	no	—
665	C₂²⋊C₄	—	4	1	no	—
666	C₂²⋊C₄	—	4	1	no	—
667	C₂²⋊C₄	—	4	1	no	—
668	C₂²⋊C₄	—	4	1	no	—
669	C₂²⋊C₄	—	4	1	no	—
670	C₄²	—	4	1	no	—
671	C₄²	—	4	1	no	—
672	C₃×C₅	#2648	1	1	yes	characteristic, direct product factor, Hall
673	C₂²×C₃	—	2	2	no	—
674	C₂²×C₃	—	2	2	no	—
675	C₂²×C₃	—	2	2	no	—
676	C₂²×C₃	—	4	1	no	—
677	C₂²×C₃	—	4	1	no	—
678	C₂²×C₃	—	4	1	no	—
679	C₂²×C₃	—	4	1	no	—
680	C₂²×C₃	—	4	1	no	—
681	C₂²×C₃	—	4	1	no	—
682	C₂²×C₃	—	4	1	no	—
683	C₂²×C₃	—	4	1	no	—
684	C₂²×C₃	—	4	1	no	—
685	C₂²×C₃	—	4	1	no	—
686	C₂²×C₃	—	4	1	no	—
687	C₂²×C₃	—	4	1	no	—
688	C₂²×C₃	—	4	1	no	—
689	C₂²×C₃	—	4	1	no	—
690	C₂²×C₃	—	4	1	no	—
691	C₂²×C₃	—	4	1	no	—
692	C₂²×C₃	—	4	1	no	—
693	C₂²×C₃	—	4	1	no	—
694	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
695	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
696	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
697	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
698	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
699	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
700	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
701	C₃×C₄	—	2	2	no	—
702	C₃×C₄	—	2	2	no	—
703	C₃×C₄	—	4	1	no	—
704	C₃×C₄	—	4	1	no	—
705	C₃×C₄	—	4	1	no	—
706	C₃×C₄	—	4	1	no	—
707	C₃×C₄	—	4	1	no	—
708	C₃×C₄	—	4	1	no	—
709	C₃×C₄	—	4	1	no	—
710	C₃×C₄	—	4	1	no	—
711	C₃×C₄	—	4	1	no	—
712	C₃×C₄	—	4	1	no	—
713	C₂×C₅	—	4	2	no	—
714	C₂×C₅	—	8	1	no	—
715	C₂×C₅	—	8	1	no	—
716	C₂×C₅	C₃×#529	1	1	yes	characteristic
717	C₂×C₅	C₃×#538	1	1	yes	characteristic
718	C₂×C₅	C₃×#538	1	1	yes	characteristic
719	C₂×C₅	C₃×#538	1	1	yes	characteristic
720	C₂×C₅	C₃×#538	1	1	yes	characteristic
721	C₂×C₅	C₃×#540	1	1	yes	characteristic
722	C₂×C₅	C₃×#540	1	1	yes	characteristic
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	2	1	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	1	no	—
741	C₂³	—	2	1	no	—
742	C₂³	—	2	1	no	—
743	C₂³	C₃×C₅×#41	1	2	yes	—
744	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
745	D₄	—	4	4	no	—
746	D₄	—	4	4	no	—
747	D₄	—	4	4	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	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	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	4	4	no	—
783	C₂×C₄	C₃×C₅×#41	1	2	yes	—
784	C₂×C₄	C₃×C₅×#41	1	2	yes	—
785	C₂×C₃	—	4	2	no	—
786	C₂×C₃	—	8	1	no	—
787	C₂×C₃	—	8	1	no	—
788	C₂×C₃	C₅×#529	1	1	yes	characteristic
789	C₂×C₃	C₅×#538	1	1	yes	characteristic
790	C₂×C₃	C₅×#538	1	1	yes	characteristic
791	C₂×C₃	C₅×#538	1	1	yes	characteristic
792	C₂×C₃	C₅×#538	1	1	yes	characteristic
793	C₂×C₃	C₅×#540	1	1	yes	characteristic
794	C₂×C₃	C₅×#540	1	1	yes	characteristic
795	C₅	C₃×#2648	1	1	yes	characteristic, direct product factor, Sylow
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
818	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
819	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
820	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
821	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
822	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
823	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
824	C₄	—	2	2	no	—
825	C₄	—	2	2	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	1	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	1	no	—
836	C₃	C₅×#2648	1	1	yes	characteristic, direct product factor, Sylow
837	C₂	—	4	2	no	—
838	C₂	—	8	1	no	—
839	C₂	—	8	1	no	—
840	C₂	C₃×C₅×#529	1	1	yes	characteristic
841	C₂	C₃×C₅×#538	1	1	yes	characteristic
842	C₂	C₃×C₅×#538	1	1	yes	characteristic
843	C₂	C₃×C₅×#538	1	1	yes	characteristic
844	C₂	C₃×C₅×#538	1	1	yes	characteristic
845	C₂	C₃×C₅×#540	1	1	yes	characteristic
846	C₂	C₃×C₅×#540	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#392	C₂
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. C₃×C₅×#400	C₂	semidirect
2. C₃×C₅×#397	C₂	semidirect
3. C₃×C₅×#397	C₂	semidirect
4. C₃×C₅×#396	C₂	semidirect
5. C₃×C₅×#394	C₂	semidirect
6. C₃×C₅×#394	C₂	semidirect
7. C₃×C₅×#394	C₂	semidirect
9. C₃×C₅×#390	C₂	semidirect
10. C₃×C₅×#388	C₂	semidirect
11. C₃×C₅×#388	C₂	semidirect
12. C₃×C₅×#387	C₂	semidirect
13. C₃×C₅×#386	C₂	semidirect
14. C₃×C₅×#386	C₂	semidirect
15. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
16. C₅×#2648	C₃	direct (N × H)
52. C₃×#2648	C₅	direct (N × H)
53. C₅×#400	C₂×C₃	semidirect
54. C₅×#397	C₂×C₃	semidirect
55. C₅×#397	C₂×C₃	semidirect
56. C₅×#396	C₂×C₃	semidirect
57. C₅×#394	C₂×C₃	semidirect
58. C₅×#394	C₂×C₃	semidirect
59. C₅×#394	C₂×C₃	semidirect
61. C₅×#390	C₂×C₃	semidirect
62. C₅×#388	C₂×C₃	semidirect
63. C₅×#388	C₂×C₃	semidirect
64. C₅×#387	C₂×C₃	semidirect
65. C₅×#386	C₂×C₃	semidirect
66. C₅×#386	C₂×C₃	semidirect
67. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
116. C₃×#400	C₂×C₅	semidirect
117. C₃×#397	C₂×C₅	semidirect
118. C₃×#397	C₂×C₅	semidirect
119. C₃×#396	C₂×C₅	semidirect
120. C₃×#394	C₂×C₅	semidirect
121. C₃×#394	C₂×C₅	semidirect
122. C₃×#394	C₂×C₅	semidirect
124. C₃×#390	C₂×C₅	semidirect
125. C₃×#388	C₂×C₅	semidirect
126. C₃×#388	C₂×C₅	semidirect
127. C₃×#387	C₂×C₅	semidirect
128. C₃×#386	C₂×C₅	semidirect
129. C₃×#386	C₂×C₅	semidirect
130. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
166. #2648	C₃×C₅	direct (N × H)
312. #400	C₂×C₃×C₅	semidirect
313. #397	C₂×C₃×C₅	semidirect
314. #397	C₂×C₃×C₅	semidirect
315. #396	C₂×C₃×C₅	semidirect
316. #394	C₂×C₃×C₅	semidirect
317. #394	C₂×C₃×C₅	semidirect
318. #394	C₂×C₃×C₅	semidirect
320. #390	C₂×C₃×C₅	semidirect
321. #388	C₂×C₃×C₅	semidirect
322. #388	C₂×C₃×C₅	semidirect
323. #387	C₂×C₃×C₅	semidirect
324. #386	C₂×C₃×C₅	semidirect
325. #386	C₂×C₃×C₅	semidirect
326. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
672. C₃×C₅	#2648	direct (N × H)
795. C₅	C₃×#2648	direct (N × H)
836. C₃	C₅×#2648	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#400	2
C₃×C₅×#397	2
C₃×C₅×#396	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#386	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2648	3
C₃×#2648	5

Subgroups — C3×C5×#2648 #14275682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2648 #14275682