Subgroups — C₃×C₅×#2723 #14275757

Order 1920.

996 conjugacy classes of subgroups.

The subgroup lattice has 800 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, complemented
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#395	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#393	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
10	C₃×C₅×#389	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
14	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2723	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
20	C₃×C₅×#126	—	2	4	no	—
21	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
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×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×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×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
44	C₃×C₅×#95	C₂²	1	1	yes	characteristic
45	C₃×C₅×#95	C₂²	1	1	yes	characteristic
46	C₃×C₅×#95	C₂²	1	1	yes	characteristic
47	C₃×C₅×#95	C₂²	1	1	yes	characteristic
48	C₃×C₅×#95	C₂²	1	1	yes	characteristic
49	C₃×C₅×#95	C₂²	1	1	yes	characteristic
50	C₃×C₅×#95	C₂²	1	1	yes	characteristic
51	C₃×C₅×#95	C₂²	1	1	yes	characteristic
52	C₃×C₅×#95	C₂²	1	1	yes	characteristic
53	C₃×C₅×#95	C₂²	1	1	yes	characteristic
54	C₃×#2723	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
55	C₂×C₅×#126	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
57	C₅×#399	C₂×C₃	1	1	yes	characteristic, complemented
58	C₅×#397	C₂×C₃	1	1	yes	characteristic, complemented
59	C₅×#397	C₂×C₃	1	1	yes	characteristic, complemented
60	C₅×#395	C₂×C₃	1	1	yes	characteristic, complemented
61	C₅×#394	C₂×C₃	1	1	yes	characteristic
62	C₅×#393	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#390	C₂×C₃	1	1	yes	characteristic
64	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#388	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#386	C₂×C₃	1	1	yes	characteristic
68	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
70	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
71	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×Q₈	—	2	2	no	—
73	C₂×C₃×C₅×Q₈	—	4	1	no	—
74	C₂×C₃×C₅×Q₈	—	4	1	no	—
75	C₂×C₃×C₅×D₄	—	2	2	no	—
76	C₂×C₃×C₅×D₄	—	2	2	no	—
77	C₂×C₃×C₅×D₄	—	4	1	no	—
78	C₂²×C₃×C₄×C₅	—	2	2	no	—
79	C₂²×C₃×C₄×C₅	—	4	1	no	—
80	C₂²×C₃×C₄×C₅	—	4	1	no	—
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	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	C₃×C₅×C₄⋊C₄	—	2	2	no	—
95	C₃×C₅×C₄⋊C₄	—	2	2	no	—
96	C₃×C₅×C₄⋊C₄	—	2	2	no	—
97	C₃×C₅×C₄⋊C₄	—	2	2	no	—
98	C₃×C₅×C₄⋊C₄	—	2	2	no	—
99	C₃×C₅×C₄⋊C₄	—	4	1	no	—
100	C₃×C₅×C₄⋊C₄	—	4	1	no	—
101	C₃×C₅×C₄⋊C₄	—	4	1	no	—
102	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	complemented
103	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
104	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
105	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
106	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
107	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
108	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
109	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
110	C₃×C₅×C₂²⋊C₄	—	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	—	2	2	no	—
115	C₃×C₄²×C₅	—	2	2	no	—
116	C₂×C₃×#126	C₂×C₅	1	1	yes	characteristic, complemented
117	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
118	C₃×#399	C₂×C₅	1	1	yes	characteristic, complemented
119	C₃×#397	C₂×C₅	1	1	yes	characteristic, complemented
120	C₃×#397	C₂×C₅	1	1	yes	characteristic, complemented
121	C₃×#395	C₂×C₅	1	1	yes	characteristic, complemented
122	C₃×#394	C₂×C₅	1	1	yes	characteristic
123	C₃×#393	C₂×C₅	1	1	yes	characteristic, complemented
124	C₃×#390	C₂×C₅	1	1	yes	characteristic
125	C₃×#389	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
129	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
132	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
133	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
134	C₅×#126	—	2	4	no	—
135	C₅×C₂²⋊Q₈	—	2	4	no	—
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×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₅×C₄⋊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×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
158	C₅×#95	C₂²×C₃	1	1	yes	characteristic
159	C₅×#95	C₂²×C₃	1	1	yes	characteristic
160	C₅×#95	C₂²×C₃	1	1	yes	characteristic
161	C₅×#95	C₂²×C₃	1	1	yes	characteristic
162	C₅×#95	C₂²×C₃	1	1	yes	characteristic
163	C₅×#95	C₂²×C₃	1	1	yes	characteristic
164	C₅×#95	C₂²×C₃	1	1	yes	characteristic
165	C₅×#95	C₂²×C₃	1	1	yes	characteristic
166	C₅×#95	C₂²×C₃	1	1	yes	characteristic
167	C₅×#95	C₂²×C₃	1	1	yes	characteristic
168	#2723	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
169	C₂³×C₃×C₅	—	2	1	no	—
170	C₂³×C₃×C₅	—	2	1	no	—
171	C₂³×C₃×C₅	—	2	1	no	—
172	C₂³×C₃×C₅	—	2	1	no	—
173	C₂³×C₃×C₅	—	2	1	no	—
174	C₂³×C₃×C₅	—	2	1	no	—
175	C₂³×C₃×C₅	—	2	1	no	—
176	C₂³×C₃×C₅	—	2	1	no	—
177	C₂³×C₃×C₅	—	2	1	no	—
178	C₂³×C₃×C₅	—	2	1	no	—
179	C₂³×C₃×C₅	—	2	1	no	—
180	C₂³×C₃×C₅	—	2	1	no	—
181	C₂³×C₃×C₅	—	2	1	no	—
182	C₂³×C₃×C₅	#41	1	2	yes	—
183	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
184	C₃×C₅×Q₈	—	4	4	no	—
185	C₃×C₅×D₄	—	4	4	no	—
186	C₂×C₃×C₄×C₅	—	2	1	no	—
187	C₂×C₃×C₄×C₅	—	2	1	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
190	C₂×C₃×C₄×C₅	—	2	1	no	—
191	C₂×C₃×C₄×C₅	—	2	1	no	—
192	C₂×C₃×C₄×C₅	—	2	1	no	—
193	C₂×C₃×C₄×C₅	—	2	1	no	—
194	C₂×C₃×C₄×C₅	—	2	1	no	—
195	C₂×C₃×C₄×C₅	—	2	1	no	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	—	2	1	no	—
200	C₂×C₃×C₄×C₅	—	2	1	no	—
201	C₂×C₃×C₄×C₅	—	2	1	no	—
202	C₂×C₃×C₄×C₅	—	2	1	no	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	—	2	1	no	—
209	C₂×C₃×C₄×C₅	—	2	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	1	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	4	4	no	—
222	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
223	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
224	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
225	C₂×C₃×C₄×C₅	#41	1	2	yes	—
226	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
227	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
228	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
229	C₃×#126	—	2	4	no	—
230	C₃×C₂²⋊Q₈	—	2	4	no	—
231	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₃×C₄⋊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×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
253	C₃×#95	C₂²×C₅	1	1	yes	characteristic
254	C₃×#95	C₂²×C₅	1	1	yes	characteristic
255	C₃×#95	C₂²×C₅	1	1	yes	characteristic
256	C₃×#95	C₂²×C₅	1	1	yes	characteristic
257	C₃×#95	C₂²×C₅	1	1	yes	characteristic
258	C₃×#95	C₂²×C₅	1	1	yes	characteristic
259	C₃×#95	C₂²×C₅	1	1	yes	characteristic
260	C₃×#95	C₂²×C₅	1	1	yes	characteristic
261	C₃×#95	C₂²×C₅	1	1	yes	characteristic
262	C₃×#95	C₂²×C₅	1	1	yes	characteristic
263	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
264	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₅×Q₈	—	2	2	no	—
266	C₂×C₅×Q₈	—	4	1	no	—
267	C₂×C₅×Q₈	—	4	1	no	—
268	C₂×C₅×D₄	—	2	2	no	—
269	C₂×C₅×D₄	—	2	2	no	—
270	C₂×C₅×D₄	—	4	1	no	—
271	C₂²×C₄×C₅	—	2	2	no	—
272	C₂²×C₄×C₅	—	4	1	no	—
273	C₂²×C₄×C₅	—	4	1	no	—
274	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
275	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
276	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
277	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
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	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	C₅×C₄⋊C₄	—	2	2	no	—
288	C₅×C₄⋊C₄	—	2	2	no	—
289	C₅×C₄⋊C₄	—	2	2	no	—
290	C₅×C₄⋊C₄	—	2	2	no	—
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	C₃×D₄	1	4	yes	complemented
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	—	2	2	no	—
301	C₅×C₂²⋊C₄	—	2	2	no	—
302	C₅×C₂²⋊C₄	—	2	2	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	C₄²×C₅	—	2	2	no	—
308	C₄²×C₅	—	2	2	no	—
309	C₂×#126	C₂×C₃×C₅	1	1	yes	characteristic, complemented
310	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
311	#399	C₂×C₃×C₅	1	1	yes	characteristic, complemented
312	#397	C₂×C₃×C₅	1	1	yes	characteristic, complemented
313	#397	C₂×C₃×C₅	1	1	yes	characteristic, complemented
314	#395	C₂×C₃×C₅	1	1	yes	characteristic, complemented
315	#394	C₂×C₃×C₅	1	1	yes	characteristic
316	#393	C₂×C₃×C₅	1	1	yes	characteristic, complemented
317	#390	C₂×C₃×C₅	1	1	yes	characteristic
318	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
319	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
320	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
321	#386	C₂×C₃×C₅	1	1	yes	characteristic
322	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
323	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
324	C₂²×C₃×C₅	—	2	2	no	—
325	C₂²×C₃×C₅	—	2	2	no	—
326	C₂²×C₃×C₅	—	2	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	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	C₂²×D₄	1	1	yes	characteristic
339	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
340	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
341	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
342	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
343	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
344	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
345	C₃×C₄×C₅	—	2	2	no	—
346	C₃×C₄×C₅	—	2	2	no	—
347	C₃×C₄×C₅	—	2	2	no	—
348	C₃×C₄×C₅	—	2	2	no	—
349	C₃×C₄×C₅	—	4	1	no	—
350	C₃×C₄×C₅	—	4	1	no	—
351	C₃×C₄×C₅	—	4	1	no	—
352	C₃×C₄×C₅	—	4	1	no	—
353	C₃×C₄×C₅	—	4	1	no	—
354	C₃×C₄×C₅	—	4	1	no	—
355	C₃×C₄×C₅	—	4	1	no	—
356	C₃×C₄×C₅	—	4	1	no	—
357	C₃×C₄×C₅	—	4	1	no	—
358	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
359	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
360	C₂×C₃×Q₈	—	2	2	no	—
361	C₂×C₃×Q₈	—	4	1	no	—
362	C₂×C₃×Q₈	—	4	1	no	—
363	C₂×C₃×D₄	—	2	2	no	—
364	C₂×C₃×D₄	—	2	2	no	—
365	C₂×C₃×D₄	—	4	1	no	—
366	C₂²×C₃×C₄	—	2	2	no	—
367	C₂²×C₃×C₄	—	4	1	no	—
368	C₂²×C₃×C₄	—	4	1	no	—
369	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
370	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
371	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
372	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
373	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
374	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
375	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
376	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
377	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
378	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
379	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
380	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
381	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
382	C₃×C₄⋊C₄	—	2	2	no	—
383	C₃×C₄⋊C₄	—	2	2	no	—
384	C₃×C₄⋊C₄	—	2	2	no	—
385	C₃×C₄⋊C₄	—	2	2	no	—
386	C₃×C₄⋊C₄	—	2	2	no	—
387	C₃×C₄⋊C₄	—	4	1	no	—
388	C₃×C₄⋊C₄	—	4	1	no	—
389	C₃×C₄⋊C₄	—	4	1	no	—
390	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	complemented
391	C₃×C₂²⋊C₄	—	2	2	no	—
392	C₃×C₂²⋊C₄	—	2	2	no	—
393	C₃×C₂²⋊C₄	—	2	2	no	—
394	C₃×C₂²⋊C₄	—	2	2	no	—
395	C₃×C₂²⋊C₄	—	2	2	no	—
396	C₃×C₂²⋊C₄	—	2	2	no	—
397	C₃×C₂²⋊C₄	—	2	2	no	—
398	C₃×C₂²⋊C₄	—	4	1	no	—
399	C₃×C₂²⋊C₄	—	4	1	no	—
400	C₃×C₂²⋊C₄	—	4	1	no	—
401	C₃×C₂²⋊C₄	—	4	1	no	—
402	C₃×C₄²	—	2	2	no	—
403	C₃×C₄²	—	2	2	no	—
404	C₂³×C₅	—	2	1	no	—
405	C₂³×C₅	—	2	1	no	—
406	C₂³×C₅	—	2	1	no	—
407	C₂³×C₅	—	2	1	no	—
408	C₂³×C₅	—	2	1	no	—
409	C₂³×C₅	—	2	1	no	—
410	C₂³×C₅	—	2	1	no	—
411	C₂³×C₅	—	2	1	no	—
412	C₂³×C₅	—	2	1	no	—
413	C₂³×C₅	—	2	1	no	—
414	C₂³×C₅	—	2	1	no	—
415	C₂³×C₅	—	2	1	no	—
416	C₂³×C₅	—	2	1	no	—
417	C₂³×C₅	C₃×#41	1	2	yes	—
418	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
419	C₅×Q₈	—	4	4	no	—
420	C₅×D₄	—	4	4	no	—
421	C₂×C₄×C₅	—	2	1	no	—
422	C₂×C₄×C₅	—	2	1	no	—
423	C₂×C₄×C₅	—	2	1	no	—
424	C₂×C₄×C₅	—	2	1	no	—
425	C₂×C₄×C₅	—	2	1	no	—
426	C₂×C₄×C₅	—	2	1	no	—
427	C₂×C₄×C₅	—	2	1	no	—
428	C₂×C₄×C₅	—	2	1	no	—
429	C₂×C₄×C₅	—	2	1	no	—
430	C₂×C₄×C₅	—	2	1	no	—
431	C₂×C₄×C₅	—	2	1	no	—
432	C₂×C₄×C₅	—	2	1	no	—
433	C₂×C₄×C₅	—	2	1	no	—
434	C₂×C₄×C₅	—	2	1	no	—
435	C₂×C₄×C₅	—	2	1	no	—
436	C₂×C₄×C₅	—	2	1	no	—
437	C₂×C₄×C₅	—	2	1	no	—
438	C₂×C₄×C₅	—	2	1	no	—
439	C₂×C₄×C₅	—	2	1	no	—
440	C₂×C₄×C₅	—	2	1	no	—
441	C₂×C₄×C₅	—	2	1	no	—
442	C₂×C₄×C₅	—	2	1	no	—
443	C₂×C₄×C₅	—	2	1	no	—
444	C₂×C₄×C₅	—	2	1	no	—
445	C₂×C₄×C₅	—	2	1	no	—
446	C₂×C₄×C₅	—	2	1	no	—
447	C₂×C₄×C₅	—	2	1	no	—
448	C₂×C₄×C₅	—	2	1	no	—
449	C₂×C₄×C₅	—	2	1	no	—
450	C₂×C₄×C₅	—	2	1	no	—
451	C₂×C₄×C₅	—	2	1	no	—
452	C₂×C₄×C₅	—	2	1	no	—
453	C₂×C₄×C₅	—	2	1	no	—
454	C₂×C₄×C₅	—	2	1	no	—
455	C₂×C₄×C₅	—	2	1	no	—
456	C₂×C₄×C₅	—	4	4	no	—
457	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
458	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
459	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
460	C₂×C₄×C₅	C₃×#41	1	2	yes	—
461	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
462	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
463	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
464	#126	—	2	4	no	—
465	C₂²⋊Q₈	—	2	4	no	—
466	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
472	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
475	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
481	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
486	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
487	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
488	#95	C₂²×C₃×C₅	1	1	yes	characteristic
489	#95	C₂²×C₃×C₅	1	1	yes	characteristic
490	#95	C₂²×C₃×C₅	1	1	yes	characteristic
491	#95	C₂²×C₃×C₅	1	1	yes	characteristic
492	#95	C₂²×C₃×C₅	1	1	yes	characteristic
493	#95	C₂²×C₃×C₅	1	1	yes	characteristic
494	#95	C₂²×C₃×C₅	1	1	yes	characteristic
495	#95	C₂²×C₃×C₅	1	1	yes	characteristic
496	#95	C₂²×C₃×C₅	1	1	yes	characteristic
497	#95	C₂²×C₃×C₅	1	1	yes	characteristic
498	C₂×C₃×C₅	—	4	2	no	—
499	C₂×C₃×C₅	—	8	1	no	—
500	C₂×C₃×C₅	#535	1	1	yes	characteristic
501	C₂×C₃×C₅	#539	1	1	yes	characteristic
502	C₂×C₃×C₅	#542	1	1	yes	characteristic
503	C₂×C₃×C₅	#547	1	1	yes	characteristic
504	C₂×C₃×C₅	#548	1	1	yes	characteristic
505	C₂×C₃×C₅	#551	1	1	yes	characteristic
506	C₂×C₃×C₅	#563	1	1	yes	characteristic
507	C₂³×C₃	—	2	1	no	—
508	C₂³×C₃	—	2	1	no	—
509	C₂³×C₃	—	2	1	no	—
510	C₂³×C₃	—	2	1	no	—
511	C₂³×C₃	—	2	1	no	—
512	C₂³×C₃	—	2	1	no	—
513	C₂³×C₃	—	2	1	no	—
514	C₂³×C₃	—	2	1	no	—
515	C₂³×C₃	—	2	1	no	—
516	C₂³×C₃	—	2	1	no	—
517	C₂³×C₃	—	2	1	no	—
518	C₂³×C₃	—	2	1	no	—
519	C₂³×C₃	—	2	1	no	—
520	C₂³×C₃	C₅×#41	1	2	yes	—
521	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
522	C₃×Q₈	—	4	4	no	—
523	C₃×D₄	—	4	4	no	—
524	C₂×C₃×C₄	—	2	1	no	—
525	C₂×C₃×C₄	—	2	1	no	—
526	C₂×C₃×C₄	—	2	1	no	—
527	C₂×C₃×C₄	—	2	1	no	—
528	C₂×C₃×C₄	—	2	1	no	—
529	C₂×C₃×C₄	—	2	1	no	—
530	C₂×C₃×C₄	—	2	1	no	—
531	C₂×C₃×C₄	—	2	1	no	—
532	C₂×C₃×C₄	—	2	1	no	—
533	C₂×C₃×C₄	—	2	1	no	—
534	C₂×C₃×C₄	—	2	1	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	—	2	1	no	—
537	C₂×C₃×C₄	—	2	1	no	—
538	C₂×C₃×C₄	—	2	1	no	—
539	C₂×C₃×C₄	—	2	1	no	—
540	C₂×C₃×C₄	—	2	1	no	—
541	C₂×C₃×C₄	—	2	1	no	—
542	C₂×C₃×C₄	—	2	1	no	—
543	C₂×C₃×C₄	—	2	1	no	—
544	C₂×C₃×C₄	—	2	1	no	—
545	C₂×C₃×C₄	—	2	1	no	—
546	C₂×C₃×C₄	—	2	1	no	—
547	C₂×C₃×C₄	—	2	1	no	—
548	C₂×C₃×C₄	—	2	1	no	—
549	C₂×C₃×C₄	—	2	1	no	—
550	C₂×C₃×C₄	—	2	1	no	—
551	C₂×C₃×C₄	—	2	1	no	—
552	C₂×C₃×C₄	—	2	1	no	—
553	C₂×C₃×C₄	—	2	1	no	—
554	C₂×C₃×C₄	—	2	1	no	—
555	C₂×C₃×C₄	—	2	1	no	—
556	C₂×C₃×C₄	—	2	1	no	—
557	C₂×C₃×C₄	—	2	1	no	—
558	C₂×C₃×C₄	—	2	1	no	—
559	C₂×C₃×C₄	—	4	4	no	—
560	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
561	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
562	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
563	C₂×C₃×C₄	C₅×#41	1	2	yes	—
564	C₂²×C₅	—	2	2	no	—
565	C₂²×C₅	—	2	2	no	—
566	C₂²×C₅	—	2	2	no	—
567	C₂²×C₅	—	4	1	no	—
568	C₂²×C₅	—	4	1	no	—
569	C₂²×C₅	—	4	1	no	—
570	C₂²×C₅	—	4	1	no	—
571	C₂²×C₅	—	4	1	no	—
572	C₂²×C₅	—	4	1	no	—
573	C₂²×C₅	—	4	1	no	—
574	C₂²×C₅	—	4	1	no	—
575	C₂²×C₅	—	4	1	no	—
576	C₂²×C₅	—	4	1	no	—
577	C₂²×C₅	—	4	1	no	—
578	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
579	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
580	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
581	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
582	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
583	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
584	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
585	C₄×C₅	—	2	2	no	—
586	C₄×C₅	—	2	2	no	—
587	C₄×C₅	—	2	2	no	—
588	C₄×C₅	—	2	2	no	—
589	C₄×C₅	—	4	1	no	—
590	C₄×C₅	—	4	1	no	—
591	C₄×C₅	—	4	1	no	—
592	C₄×C₅	—	4	1	no	—
593	C₄×C₅	—	4	1	no	—
594	C₄×C₅	—	4	1	no	—
595	C₄×C₅	—	4	1	no	—
596	C₄×C₅	—	4	1	no	—
597	C₄×C₅	—	4	1	no	—
598	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
599	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
600	C₂×Q₈	—	2	2	no	—
601	C₂×Q₈	—	4	1	no	—
602	C₂×Q₈	—	4	1	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	4	1	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	4	1	no	—
608	C₂²×C₄	—	4	1	no	—
609	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
610	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
611	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
612	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
613	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
614	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
615	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
616	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
617	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
618	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
619	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
620	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
621	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	4	1	no	—
628	C₄⋊C₄	—	4	1	no	—
629	C₄⋊C₄	—	4	1	no	—
630	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	4	1	no	—
639	C₂²⋊C₄	—	4	1	no	—
640	C₂²⋊C₄	—	4	1	no	—
641	C₂²⋊C₄	—	4	1	no	—
642	C₄²	—	2	2	no	—
643	C₄²	—	2	2	no	—
644	C₃×C₅	#2723	1	1	yes	characteristic, direct product factor, Hall
645	C₂²×C₃	—	2	2	no	—
646	C₂²×C₃	—	2	2	no	—
647	C₂²×C₃	—	2	2	no	—
648	C₂²×C₃	—	4	1	no	—
649	C₂²×C₃	—	4	1	no	—
650	C₂²×C₃	—	4	1	no	—
651	C₂²×C₃	—	4	1	no	—
652	C₂²×C₃	—	4	1	no	—
653	C₂²×C₃	—	4	1	no	—
654	C₂²×C₃	—	4	1	no	—
655	C₂²×C₃	—	4	1	no	—
656	C₂²×C₃	—	4	1	no	—
657	C₂²×C₃	—	4	1	no	—
658	C₂²×C₃	—	4	1	no	—
659	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
660	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
661	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
662	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
663	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
664	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
665	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
666	C₃×C₄	—	2	2	no	—
667	C₃×C₄	—	2	2	no	—
668	C₃×C₄	—	2	2	no	—
669	C₃×C₄	—	2	2	no	—
670	C₃×C₄	—	4	1	no	—
671	C₃×C₄	—	4	1	no	—
672	C₃×C₄	—	4	1	no	—
673	C₃×C₄	—	4	1	no	—
674	C₃×C₄	—	4	1	no	—
675	C₃×C₄	—	4	1	no	—
676	C₃×C₄	—	4	1	no	—
677	C₃×C₄	—	4	1	no	—
678	C₃×C₄	—	4	1	no	—
679	C₂×C₅	—	4	2	no	—
680	C₂×C₅	—	8	1	no	—
681	C₂×C₅	C₃×#535	1	1	yes	characteristic
682	C₂×C₅	C₃×#539	1	1	yes	characteristic
683	C₂×C₅	C₃×#542	1	1	yes	characteristic
684	C₂×C₅	C₃×#547	1	1	yes	characteristic
685	C₂×C₅	C₃×#548	1	1	yes	characteristic
686	C₂×C₅	C₃×#551	1	1	yes	characteristic
687	C₂×C₅	C₃×#563	1	1	yes	characteristic
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	C₃×C₅×#41	1	2	yes	—
702	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
703	Q₈	—	4	4	no	—
704	D₄	—	4	4	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	4	4	no	—
741	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
742	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
743	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
744	C₂×C₄	C₃×C₅×#41	1	2	yes	—
745	C₂×C₃	—	4	2	no	—
746	C₂×C₃	—	8	1	no	—
747	C₂×C₃	C₅×#535	1	1	yes	characteristic
748	C₂×C₃	C₅×#539	1	1	yes	characteristic
749	C₂×C₃	C₅×#542	1	1	yes	characteristic
750	C₂×C₃	C₅×#547	1	1	yes	characteristic
751	C₂×C₃	C₅×#548	1	1	yes	characteristic
752	C₂×C₃	C₅×#551	1	1	yes	characteristic
753	C₂×C₃	C₅×#563	1	1	yes	characteristic
754	C₅	C₃×#2723	1	1	yes	characteristic, direct product factor, Sylow
755	C₂²	—	2	2	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	—	4	1	no	—
768	C₂²	—	4	1	no	—
769	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
770	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
771	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
772	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
773	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
774	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
775	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	1	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	1	no	—
785	C₄	—	4	1	no	—
786	C₄	—	4	1	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	1	no	—
789	C₃	C₅×#2723	1	1	yes	characteristic, direct product factor, Sylow
790	C₂	—	4	2	no	—
791	C₂	—	8	1	no	—
792	C₂	C₃×C₅×#535	1	1	yes	characteristic
793	C₂	C₃×C₅×#539	1	1	yes	characteristic
794	C₂	C₃×C₅×#542	1	1	yes	characteristic
795	C₂	C₃×C₅×#547	1	1	yes	characteristic
796	C₂	C₃×C₅×#548	1	1	yes	characteristic
797	C₂	C₃×C₅×#551	1	1	yes	characteristic
798	C₂	C₃×C₅×#563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#126	C₂	semidirect
2. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
3. C₃×C₅×#399	C₂	semidirect
4. C₃×C₅×#397	C₂	semidirect
5. C₃×C₅×#397	C₂	semidirect
6. C₃×C₅×#395	C₂	semidirect
8. C₃×C₅×#393	C₂	semidirect
10. C₃×C₅×#389	C₂	semidirect
11. C₃×C₅×#388	C₂	semidirect
12. C₃×C₅×#387	C₂	semidirect
14. C₃×C₅×#385	C₂	semidirect
15. C₃×C₅×#382	C₂	semidirect
16. C₅×#2723	C₃	direct (N × H)
54. C₃×#2723	C₅	direct (N × H)
55. C₂×C₅×#126	C₂×C₃	semidirect
56. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
57. C₅×#399	C₂×C₃	semidirect
58. C₅×#397	C₂×C₃	semidirect
59. C₅×#397	C₂×C₃	semidirect
60. C₅×#395	C₂×C₃	semidirect
62. C₅×#393	C₂×C₃	semidirect
64. C₅×#389	C₂×C₃	semidirect
65. C₅×#388	C₂×C₃	semidirect
66. C₅×#387	C₂×C₃	semidirect
68. C₅×#385	C₂×C₃	semidirect
69. C₅×#382	C₂×C₃	semidirect
102. C₃×C₅×C₄⋊C₄	D₄	semidirect
116. C₂×C₃×#126	C₂×C₅	semidirect
117. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
118. C₃×#399	C₂×C₅	semidirect
119. C₃×#397	C₂×C₅	semidirect
120. C₃×#397	C₂×C₅	semidirect
121. C₃×#395	C₂×C₅	semidirect
123. C₃×#393	C₂×C₅	semidirect
125. C₃×#389	C₂×C₅	semidirect
126. C₃×#388	C₂×C₅	semidirect
127. C₃×#387	C₂×C₅	semidirect
129. C₃×#385	C₂×C₅	semidirect
130. C₃×#382	C₂×C₅	semidirect
168. #2723	C₃×C₅	direct (N × H)
295. C₅×C₄⋊C₄	C₃×D₄	semidirect
309. C₂×#126	C₂×C₃×C₅	semidirect
310. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
311. #399	C₂×C₃×C₅	semidirect
312. #397	C₂×C₃×C₅	semidirect
313. #397	C₂×C₃×C₅	semidirect
314. #395	C₂×C₃×C₅	semidirect
316. #393	C₂×C₃×C₅	semidirect
318. #389	C₂×C₃×C₅	semidirect
319. #388	C₂×C₃×C₅	semidirect
320. #387	C₂×C₃×C₅	semidirect
322. #385	C₂×C₃×C₅	semidirect
323. #382	C₂×C₃×C₅	semidirect
390. C₃×C₄⋊C₄	C₅×D₄	semidirect
630. C₄⋊C₄	C₃×C₅×D₄	semidirect
644. C₃×C₅	#2723	direct (N × H)
754. C₅	C₃×#2723	direct (N × H)
789. C₃	C₅×#2723	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
C₂×C₃×C₅×C₂²⋊Q₈	2
C₃×C₅×#399	2
C₃×C₅×#397	2
C₃×C₅×#395	2
C₃×C₅×#394	2
C₃×C₅×#393	2
C₃×C₅×#390	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#382	2
C₅×#2723	3
C₃×#2723	5

Subgroups — C3×C5×#2723 #14275757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2723 #14275757