Subgroups — C₃×C₅×#2672 #14275706

Order 1920.

1236 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#399	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#396	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2672	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	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
22	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×#124	—	2	4	no	—
24	C₃×C₅×#123	—	2	4	no	—
25	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
26	C₃×C₅×#121	—	2	4	no	—
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₅×C₄⋊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×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₃×C₄²×C₅	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×C₅×#95	C₂²	1	1	yes	characteristic
55	C₃×C₅×#95	C₂²	1	1	yes	characteristic
56	C₃×#2672	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
57	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic
61	C₅×#399	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#396	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#395	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#388	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
73	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
74	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₅×Q₈	—	2	2	no	—
76	C₂×C₃×C₅×Q₈	—	2	2	no	—
77	C₂×C₃×C₅×Q₈	—	4	1	no	—
78	C₂×C₃×C₅×D₄	—	2	2	no	—
79	C₂×C₃×C₅×D₄	—	2	2	no	—
80	C₂×C₃×C₅×D₄	—	2	2	no	—
81	C₂×C₃×C₅×D₄	—	2	2	no	—
82	C₂×C₃×C₅×D₄	—	2	2	no	—
83	C₂×C₃×C₅×D₄	—	2	2	no	—
84	C₂×C₃×C₅×D₄	—	4	1	no	—
85	C₂×C₃×C₅×D₄	—	4	1	no	—
86	C₂×C₃×C₅×D₄	—	4	1	no	—
87	C₂²×C₃×C₄×C₅	—	2	2	no	—
88	C₂²×C₃×C₄×C₅	—	2	2	no	—
89	C₂²×C₃×C₄×C₅	—	2	2	no	—
90	C₂²×C₃×C₄×C₅	—	2	2	no	—
91	C₂²×C₃×C₄×C₅	—	4	1	no	—
92	C₂²×C₃×C₄×C₅	—	4	1	no	—
93	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
96	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
100	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
101	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
102	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
103	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
104	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
105	C₃×C₅×C₄⋊C₄	—	2	2	no	—
106	C₃×C₅×C₄⋊C₄	—	2	2	no	—
107	C₃×C₅×C₄⋊C₄	—	2	2	no	—
108	C₃×C₅×C₄⋊C₄	—	2	2	no	—
109	C₃×C₅×C₄⋊C₄	—	2	2	no	—
110	C₃×C₅×C₄⋊C₄	—	2	2	no	—
111	C₃×C₅×C₄⋊C₄	—	2	2	no	—
112	C₃×C₅×C₄⋊C₄	—	4	1	no	—
113	C₃×C₅×C₄⋊C₄	—	4	1	no	—
114	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
115	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
116	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
117	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
118	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
119	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
120	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
121	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
122	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
123	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
124	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
125	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	—
126	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	complemented
127	C₃×C₄²×C₅	—	2	2	no	—
128	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
129	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
130	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
132	C₃×#399	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#396	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#395	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
144	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
145	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
146	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
147	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
148	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
149	C₅×#124	—	2	4	no	—
150	C₅×#123	—	2	4	no	—
151	C₅×C₂²⋊Q₈	—	2	4	no	—
152	C₅×#121	—	2	4	no	—
153	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
160	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
161	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
162	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
167	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
170	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
171	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
175	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
176	C₅×#95	C₂²×C₃	1	1	yes	characteristic
177	C₅×#95	C₂²×C₃	1	1	yes	characteristic
178	C₅×#95	C₂²×C₃	1	1	yes	characteristic
179	C₅×#95	C₂²×C₃	1	1	yes	characteristic
180	C₅×#95	C₂²×C₃	1	1	yes	characteristic
181	C₅×#95	C₂²×C₃	1	1	yes	characteristic
182	#2672	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
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	—	2	1	no	—
188	C₂³×C₃×C₅	—	2	1	no	—
189	C₂³×C₃×C₅	—	2	1	no	—
190	C₂³×C₃×C₅	—	2	1	no	—
191	C₂³×C₃×C₅	—	2	1	no	—
192	C₂³×C₃×C₅	—	2	1	no	—
193	C₂³×C₃×C₅	—	2	1	no	—
194	C₂³×C₃×C₅	—	2	1	no	—
195	C₂³×C₃×C₅	—	2	1	no	—
196	C₂³×C₃×C₅	—	2	1	no	—
197	C₂³×C₃×C₅	—	2	1	no	—
198	C₂³×C₃×C₅	—	2	1	no	—
199	C₂³×C₃×C₅	—	2	1	no	—
200	C₂³×C₃×C₅	—	2	1	no	—
201	C₂³×C₃×C₅	—	2	1	no	—
202	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
203	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
204	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
205	C₃×C₅×Q₈	—	4	4	no	—
206	C₃×C₅×D₄	—	4	4	no	—
207	C₃×C₅×D₄	—	4	4	no	—
208	C₃×C₅×D₄	—	4	4	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	—	2	1	no	—
227	C₂×C₃×C₄×C₅	—	2	1	no	—
228	C₂×C₃×C₄×C₅	—	2	1	no	—
229	C₂×C₃×C₄×C₅	—	2	1	no	—
230	C₂×C₃×C₄×C₅	—	2	1	no	—
231	C₂×C₃×C₄×C₅	—	2	1	no	—
232	C₂×C₃×C₄×C₅	—	2	1	no	—
233	C₂×C₃×C₄×C₅	—	2	1	no	—
234	C₂×C₃×C₄×C₅	—	2	1	no	—
235	C₂×C₃×C₄×C₅	—	2	1	no	—
236	C₂×C₃×C₄×C₅	—	2	1	no	—
237	C₂×C₃×C₄×C₅	—	2	1	no	—
238	C₂×C₃×C₄×C₅	—	2	1	no	—
239	C₂×C₃×C₄×C₅	—	2	1	no	—
240	C₂×C₃×C₄×C₅	—	4	4	no	—
241	C₂×C₃×C₄×C₅	—	4	4	no	—
242	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
243	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
244	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
245	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
246	C₂×C₃×C₄×C₅	#41	1	2	yes	—
247	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
248	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
249	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
250	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
251	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
252	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
253	C₃×#124	—	2	4	no	—
254	C₃×#123	—	2	4	no	—
255	C₃×C₂²⋊Q₈	—	2	4	no	—
256	C₃×#121	—	2	4	no	—
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×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
267	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
268	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
269	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
273	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
274	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
275	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
276	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
277	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
278	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
279	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
280	C₃×#95	C₂²×C₅	1	1	yes	characteristic
281	C₃×#95	C₂²×C₅	1	1	yes	characteristic
282	C₃×#95	C₂²×C₅	1	1	yes	characteristic
283	C₃×#95	C₂²×C₅	1	1	yes	characteristic
284	C₃×#95	C₂²×C₅	1	1	yes	characteristic
285	C₃×#95	C₂²×C₅	1	1	yes	characteristic
286	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
287	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
288	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₅×Q₈	—	2	2	no	—
290	C₂×C₅×Q₈	—	2	2	no	—
291	C₂×C₅×Q₈	—	4	1	no	—
292	C₂×C₅×D₄	—	2	2	no	—
293	C₂×C₅×D₄	—	2	2	no	—
294	C₂×C₅×D₄	—	2	2	no	—
295	C₂×C₅×D₄	—	2	2	no	—
296	C₂×C₅×D₄	—	2	2	no	—
297	C₂×C₅×D₄	—	2	2	no	—
298	C₂×C₅×D₄	—	4	1	no	—
299	C₂×C₅×D₄	—	4	1	no	—
300	C₂×C₅×D₄	—	4	1	no	—
301	C₂²×C₄×C₅	—	2	2	no	—
302	C₂²×C₄×C₅	—	2	2	no	—
303	C₂²×C₄×C₅	—	2	2	no	—
304	C₂²×C₄×C₅	—	2	2	no	—
305	C₂²×C₄×C₅	—	4	1	no	—
306	C₂²×C₄×C₅	—	4	1	no	—
307	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
308	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
309	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
310	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
311	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
312	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
313	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
314	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
315	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
316	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
317	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
318	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
319	C₅×C₄⋊C₄	—	2	2	no	—
320	C₅×C₄⋊C₄	—	2	2	no	—
321	C₅×C₄⋊C₄	—	2	2	no	—
322	C₅×C₄⋊C₄	—	2	2	no	—
323	C₅×C₄⋊C₄	—	2	2	no	—
324	C₅×C₄⋊C₄	—	2	2	no	—
325	C₅×C₄⋊C₄	—	2	2	no	—
326	C₅×C₄⋊C₄	—	4	1	no	—
327	C₅×C₄⋊C₄	—	4	1	no	—
328	C₅×C₂²⋊C₄	—	2	2	no	—
329	C₅×C₂²⋊C₄	—	2	2	no	—
330	C₅×C₂²⋊C₄	—	2	2	no	—
331	C₅×C₂²⋊C₄	—	2	2	no	—
332	C₅×C₂²⋊C₄	—	2	2	no	—
333	C₅×C₂²⋊C₄	—	2	2	no	—
334	C₅×C₂²⋊C₄	—	2	2	no	—
335	C₅×C₂²⋊C₄	—	4	1	no	—
336	C₅×C₂²⋊C₄	—	4	1	no	—
337	C₅×C₂²⋊C₄	—	4	1	no	—
338	C₅×C₂²⋊C₄	—	4	1	no	—
339	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	—
340	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	complemented
341	C₄²×C₅	—	2	2	no	—
342	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic, complemented
343	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic, complemented
344	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
345	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic
346	#399	C₂×C₃×C₅	1	1	yes	characteristic, complemented
347	#396	C₂×C₃×C₅	1	1	yes	characteristic, complemented
348	#395	C₂×C₃×C₅	1	1	yes	characteristic, complemented
349	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
350	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
351	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
352	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
353	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
354	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
355	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
356	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
357	C₂²×C₃×C₅	—	2	2	no	—
358	C₂²×C₃×C₅	—	2	2	no	—
359	C₂²×C₃×C₅	—	2	2	no	—
360	C₂²×C₃×C₅	—	2	2	no	—
361	C₂²×C₃×C₅	—	2	2	no	—
362	C₂²×C₃×C₅	—	2	2	no	—
363	C₂²×C₃×C₅	—	4	1	no	—
364	C₂²×C₃×C₅	—	4	1	no	—
365	C₂²×C₃×C₅	—	4	1	no	—
366	C₂²×C₃×C₅	—	4	1	no	—
367	C₂²×C₃×C₅	—	4	1	no	—
368	C₂²×C₃×C₅	—	4	1	no	—
369	C₂²×C₃×C₅	—	4	1	no	—
370	C₂²×C₃×C₅	—	4	1	no	—
371	C₂²×C₃×C₅	—	4	1	no	—
372	C₂²×C₃×C₅	—	4	1	no	—
373	C₂²×C₃×C₅	—	4	1	no	—
374	C₂²×C₃×C₅	—	4	1	no	—
375	C₂²×C₃×C₅	—	4	1	no	—
376	C₂²×C₃×C₅	—	4	1	no	—
377	C₂²×C₃×C₅	—	4	1	no	—
378	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
379	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
380	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
381	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
382	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
383	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
384	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
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	C₃×C₄×C₅	—	4	1	no	—
391	C₃×C₄×C₅	—	4	1	no	—
392	C₃×C₄×C₅	—	4	1	no	—
393	C₃×C₄×C₅	—	4	1	no	—
394	C₃×C₄×C₅	—	4	1	no	—
395	C₃×C₄×C₅	—	4	1	no	—
396	C₃×C₄×C₅	—	4	1	no	—
397	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
398	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
399	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
400	C₂×C₃×Q₈	—	2	2	no	—
401	C₂×C₃×Q₈	—	2	2	no	—
402	C₂×C₃×Q₈	—	4	1	no	—
403	C₂×C₃×D₄	—	2	2	no	—
404	C₂×C₃×D₄	—	2	2	no	—
405	C₂×C₃×D₄	—	2	2	no	—
406	C₂×C₃×D₄	—	2	2	no	—
407	C₂×C₃×D₄	—	2	2	no	—
408	C₂×C₃×D₄	—	2	2	no	—
409	C₂×C₃×D₄	—	4	1	no	—
410	C₂×C₃×D₄	—	4	1	no	—
411	C₂×C₃×D₄	—	4	1	no	—
412	C₂²×C₃×C₄	—	2	2	no	—
413	C₂²×C₃×C₄	—	2	2	no	—
414	C₂²×C₃×C₄	—	2	2	no	—
415	C₂²×C₃×C₄	—	2	2	no	—
416	C₂²×C₃×C₄	—	4	1	no	—
417	C₂²×C₃×C₄	—	4	1	no	—
418	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
419	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
420	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
421	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
422	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
423	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
424	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
425	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
426	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
427	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
428	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
430	C₃×C₄⋊C₄	—	2	2	no	—
431	C₃×C₄⋊C₄	—	2	2	no	—
432	C₃×C₄⋊C₄	—	2	2	no	—
433	C₃×C₄⋊C₄	—	2	2	no	—
434	C₃×C₄⋊C₄	—	2	2	no	—
435	C₃×C₄⋊C₄	—	2	2	no	—
436	C₃×C₄⋊C₄	—	2	2	no	—
437	C₃×C₄⋊C₄	—	4	1	no	—
438	C₃×C₄⋊C₄	—	4	1	no	—
439	C₃×C₂²⋊C₄	—	2	2	no	—
440	C₃×C₂²⋊C₄	—	2	2	no	—
441	C₃×C₂²⋊C₄	—	2	2	no	—
442	C₃×C₂²⋊C₄	—	2	2	no	—
443	C₃×C₂²⋊C₄	—	2	2	no	—
444	C₃×C₂²⋊C₄	—	2	2	no	—
445	C₃×C₂²⋊C₄	—	2	2	no	—
446	C₃×C₂²⋊C₄	—	4	1	no	—
447	C₃×C₂²⋊C₄	—	4	1	no	—
448	C₃×C₂²⋊C₄	—	4	1	no	—
449	C₃×C₂²⋊C₄	—	4	1	no	—
450	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	—
451	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	complemented
452	C₃×C₄²	—	2	2	no	—
453	C₂³×C₅	—	2	1	no	—
454	C₂³×C₅	—	2	1	no	—
455	C₂³×C₅	—	2	1	no	—
456	C₂³×C₅	—	2	1	no	—
457	C₂³×C₅	—	2	1	no	—
458	C₂³×C₅	—	2	1	no	—
459	C₂³×C₅	—	2	1	no	—
460	C₂³×C₅	—	2	1	no	—
461	C₂³×C₅	—	2	1	no	—
462	C₂³×C₅	—	2	1	no	—
463	C₂³×C₅	—	2	1	no	—
464	C₂³×C₅	—	2	1	no	—
465	C₂³×C₅	—	2	1	no	—
466	C₂³×C₅	—	2	1	no	—
467	C₂³×C₅	—	2	1	no	—
468	C₂³×C₅	—	2	1	no	—
469	C₂³×C₅	—	2	1	no	—
470	C₂³×C₅	—	2	1	no	—
471	C₂³×C₅	—	2	1	no	—
472	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
473	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
474	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
475	C₅×Q₈	—	4	4	no	—
476	C₅×D₄	—	4	4	no	—
477	C₅×D₄	—	4	4	no	—
478	C₅×D₄	—	4	4	no	—
479	C₂×C₄×C₅	—	2	1	no	—
480	C₂×C₄×C₅	—	2	1	no	—
481	C₂×C₄×C₅	—	2	1	no	—
482	C₂×C₄×C₅	—	2	1	no	—
483	C₂×C₄×C₅	—	2	1	no	—
484	C₂×C₄×C₅	—	2	1	no	—
485	C₂×C₄×C₅	—	2	1	no	—
486	C₂×C₄×C₅	—	2	1	no	—
487	C₂×C₄×C₅	—	2	1	no	—
488	C₂×C₄×C₅	—	2	1	no	—
489	C₂×C₄×C₅	—	2	1	no	—
490	C₂×C₄×C₅	—	2	1	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	2	1	no	—
493	C₂×C₄×C₅	—	2	1	no	—
494	C₂×C₄×C₅	—	2	1	no	—
495	C₂×C₄×C₅	—	2	1	no	—
496	C₂×C₄×C₅	—	2	1	no	—
497	C₂×C₄×C₅	—	2	1	no	—
498	C₂×C₄×C₅	—	2	1	no	—
499	C₂×C₄×C₅	—	2	1	no	—
500	C₂×C₄×C₅	—	2	1	no	—
501	C₂×C₄×C₅	—	2	1	no	—
502	C₂×C₄×C₅	—	2	1	no	—
503	C₂×C₄×C₅	—	2	1	no	—
504	C₂×C₄×C₅	—	2	1	no	—
505	C₂×C₄×C₅	—	2	1	no	—
506	C₂×C₄×C₅	—	2	1	no	—
507	C₂×C₄×C₅	—	2	1	no	—
508	C₂×C₄×C₅	—	2	1	no	—
509	C₂×C₄×C₅	—	2	1	no	—
510	C₂×C₄×C₅	—	4	4	no	—
511	C₂×C₄×C₅	—	4	4	no	—
512	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
513	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
514	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
515	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
516	C₂×C₄×C₅	C₃×#41	1	2	yes	—
517	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
518	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
519	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
520	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
521	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
522	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
523	#124	—	2	4	no	—
524	#123	—	2	4	no	—
525	C₂²⋊Q₈	—	2	4	no	—
526	#121	—	2	4	no	—
527	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
549	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
550	#95	C₂²×C₃×C₅	1	1	yes	characteristic
551	#95	C₂²×C₃×C₅	1	1	yes	characteristic
552	#95	C₂²×C₃×C₅	1	1	yes	characteristic
553	#95	C₂²×C₃×C₅	1	1	yes	characteristic
554	#95	C₂²×C₃×C₅	1	1	yes	characteristic
555	#95	C₂²×C₃×C₅	1	1	yes	characteristic
556	C₂×C₃×C₅	—	4	2	no	—
557	C₂×C₃×C₅	—	4	2	no	—
558	C₂×C₃×C₅	—	8	1	no	—
559	C₂×C₃×C₅	#536	1	1	yes	characteristic
560	C₂×C₃×C₅	#537	1	1	yes	characteristic
561	C₂×C₃×C₅	#542	1	1	yes	characteristic
562	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
563	C₂×C₃×C₅	#546	1	1	yes	characteristic
564	C₂×C₃×C₅	#547	1	1	yes	characteristic
565	C₂×C₃×C₅	#562	1	1	yes	characteristic
566	C₂³×C₃	—	2	1	no	—
567	C₂³×C₃	—	2	1	no	—
568	C₂³×C₃	—	2	1	no	—
569	C₂³×C₃	—	2	1	no	—
570	C₂³×C₃	—	2	1	no	—
571	C₂³×C₃	—	2	1	no	—
572	C₂³×C₃	—	2	1	no	—
573	C₂³×C₃	—	2	1	no	—
574	C₂³×C₃	—	2	1	no	—
575	C₂³×C₃	—	2	1	no	—
576	C₂³×C₃	—	2	1	no	—
577	C₂³×C₃	—	2	1	no	—
578	C₂³×C₃	—	2	1	no	—
579	C₂³×C₃	—	2	1	no	—
580	C₂³×C₃	—	2	1	no	—
581	C₂³×C₃	—	2	1	no	—
582	C₂³×C₃	—	2	1	no	—
583	C₂³×C₃	—	2	1	no	—
584	C₂³×C₃	—	2	1	no	—
585	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
586	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
587	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
588	C₃×Q₈	—	4	4	no	—
589	C₃×D₄	—	4	4	no	—
590	C₃×D₄	—	4	4	no	—
591	C₃×D₄	—	4	4	no	—
592	C₂×C₃×C₄	—	2	1	no	—
593	C₂×C₃×C₄	—	2	1	no	—
594	C₂×C₃×C₄	—	2	1	no	—
595	C₂×C₃×C₄	—	2	1	no	—
596	C₂×C₃×C₄	—	2	1	no	—
597	C₂×C₃×C₄	—	2	1	no	—
598	C₂×C₃×C₄	—	2	1	no	—
599	C₂×C₃×C₄	—	2	1	no	—
600	C₂×C₃×C₄	—	2	1	no	—
601	C₂×C₃×C₄	—	2	1	no	—
602	C₂×C₃×C₄	—	2	1	no	—
603	C₂×C₃×C₄	—	2	1	no	—
604	C₂×C₃×C₄	—	2	1	no	—
605	C₂×C₃×C₄	—	2	1	no	—
606	C₂×C₃×C₄	—	2	1	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	1	no	—
609	C₂×C₃×C₄	—	2	1	no	—
610	C₂×C₃×C₄	—	2	1	no	—
611	C₂×C₃×C₄	—	2	1	no	—
612	C₂×C₃×C₄	—	2	1	no	—
613	C₂×C₃×C₄	—	2	1	no	—
614	C₂×C₃×C₄	—	2	1	no	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	2	1	no	—
617	C₂×C₃×C₄	—	2	1	no	—
618	C₂×C₃×C₄	—	2	1	no	—
619	C₂×C₃×C₄	—	2	1	no	—
620	C₂×C₃×C₄	—	2	1	no	—
621	C₂×C₃×C₄	—	2	1	no	—
622	C₂×C₃×C₄	—	2	1	no	—
623	C₂×C₃×C₄	—	4	4	no	—
624	C₂×C₃×C₄	—	4	4	no	—
625	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
626	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
627	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
628	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
629	C₂×C₃×C₄	C₅×#41	1	2	yes	—
630	C₂²×C₅	—	2	2	no	—
631	C₂²×C₅	—	2	2	no	—
632	C₂²×C₅	—	2	2	no	—
633	C₂²×C₅	—	2	2	no	—
634	C₂²×C₅	—	2	2	no	—
635	C₂²×C₅	—	2	2	no	—
636	C₂²×C₅	—	4	1	no	—
637	C₂²×C₅	—	4	1	no	—
638	C₂²×C₅	—	4	1	no	—
639	C₂²×C₅	—	4	1	no	—
640	C₂²×C₅	—	4	1	no	—
641	C₂²×C₅	—	4	1	no	—
642	C₂²×C₅	—	4	1	no	—
643	C₂²×C₅	—	4	1	no	—
644	C₂²×C₅	—	4	1	no	—
645	C₂²×C₅	—	4	1	no	—
646	C₂²×C₅	—	4	1	no	—
647	C₂²×C₅	—	4	1	no	—
648	C₂²×C₅	—	4	1	no	—
649	C₂²×C₅	—	4	1	no	—
650	C₂²×C₅	—	4	1	no	—
651	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
652	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
653	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
654	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
655	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
657	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
658	C₄×C₅	—	2	2	no	—
659	C₄×C₅	—	2	2	no	—
660	C₄×C₅	—	2	2	no	—
661	C₄×C₅	—	2	2	no	—
662	C₄×C₅	—	2	2	no	—
663	C₄×C₅	—	4	1	no	—
664	C₄×C₅	—	4	1	no	—
665	C₄×C₅	—	4	1	no	—
666	C₄×C₅	—	4	1	no	—
667	C₄×C₅	—	4	1	no	—
668	C₄×C₅	—	4	1	no	—
669	C₄×C₅	—	4	1	no	—
670	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
671	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
672	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	4	1	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	4	1	no	—
683	C₂×D₄	—	4	1	no	—
684	C₂×D₄	—	4	1	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	4	1	no	—
690	C₂²×C₄	—	4	1	no	—
691	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
692	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
693	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
694	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
695	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
696	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
697	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
698	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
699	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
700	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
701	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
702	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	4	1	no	—
711	C₄⋊C₄	—	4	1	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	—	2	2	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	4	1	no	—
720	C₂²⋊C₄	—	4	1	no	—
721	C₂²⋊C₄	—	4	1	no	—
722	C₂²⋊C₄	—	4	1	no	—
723	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	—
724	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
725	C₄²	—	2	2	no	—
726	C₃×C₅	#2672	1	1	yes	characteristic, direct product factor, Hall
727	C₂²×C₃	—	2	2	no	—
728	C₂²×C₃	—	2	2	no	—
729	C₂²×C₃	—	2	2	no	—
730	C₂²×C₃	—	2	2	no	—
731	C₂²×C₃	—	2	2	no	—
732	C₂²×C₃	—	2	2	no	—
733	C₂²×C₃	—	4	1	no	—
734	C₂²×C₃	—	4	1	no	—
735	C₂²×C₃	—	4	1	no	—
736	C₂²×C₃	—	4	1	no	—
737	C₂²×C₃	—	4	1	no	—
738	C₂²×C₃	—	4	1	no	—
739	C₂²×C₃	—	4	1	no	—
740	C₂²×C₃	—	4	1	no	—
741	C₂²×C₃	—	4	1	no	—
742	C₂²×C₃	—	4	1	no	—
743	C₂²×C₃	—	4	1	no	—
744	C₂²×C₃	—	4	1	no	—
745	C₂²×C₃	—	4	1	no	—
746	C₂²×C₃	—	4	1	no	—
747	C₂²×C₃	—	4	1	no	—
748	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
749	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
750	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
751	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
752	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
753	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
754	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
755	C₃×C₄	—	2	2	no	—
756	C₃×C₄	—	2	2	no	—
757	C₃×C₄	—	2	2	no	—
758	C₃×C₄	—	2	2	no	—
759	C₃×C₄	—	2	2	no	—
760	C₃×C₄	—	4	1	no	—
761	C₃×C₄	—	4	1	no	—
762	C₃×C₄	—	4	1	no	—
763	C₃×C₄	—	4	1	no	—
764	C₃×C₄	—	4	1	no	—
765	C₃×C₄	—	4	1	no	—
766	C₃×C₄	—	4	1	no	—
767	C₂×C₅	—	4	2	no	—
768	C₂×C₅	—	4	2	no	—
769	C₂×C₅	—	8	1	no	—
770	C₂×C₅	C₃×#536	1	1	yes	characteristic
771	C₂×C₅	C₃×#537	1	1	yes	characteristic
772	C₂×C₅	C₃×#542	1	1	yes	characteristic
773	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
774	C₂×C₅	C₃×#546	1	1	yes	characteristic
775	C₂×C₅	C₃×#547	1	1	yes	characteristic
776	C₂×C₅	C₃×#562	1	1	yes	characteristic
777	C₂³	—	2	1	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	1	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
797	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
798	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
799	Q₈	—	4	4	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	4	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
837	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
838	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
839	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
840	C₂×C₄	C₃×C₅×#41	1	2	yes	—
841	C₂×C₃	—	4	2	no	—
842	C₂×C₃	—	4	2	no	—
843	C₂×C₃	—	8	1	no	—
844	C₂×C₃	C₅×#536	1	1	yes	characteristic
845	C₂×C₃	C₅×#537	1	1	yes	characteristic
846	C₂×C₃	C₅×#542	1	1	yes	characteristic
847	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
848	C₂×C₃	C₅×#546	1	1	yes	characteristic
849	C₂×C₃	C₅×#547	1	1	yes	characteristic
850	C₂×C₃	C₅×#562	1	1	yes	characteristic
851	C₅	C₃×#2672	1	1	yes	characteristic, direct product factor, Sylow
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	1	no	—
873	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
874	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
875	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
876	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
877	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
878	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
879	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
880	C₄	—	2	2	no	—
881	C₄	—	2	2	no	—
882	C₄	—	2	2	no	—
883	C₄	—	2	2	no	—
884	C₄	—	2	2	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	1	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	1	no	—
891	C₄	—	4	1	no	—
892	C₃	C₅×#2672	1	1	yes	characteristic, direct product factor, Sylow
893	C₂	—	4	2	no	—
894	C₂	—	4	2	no	—
895	C₂	—	8	1	no	—
896	C₂	C₃×C₅×#536	1	1	yes	characteristic
897	C₂	C₃×C₅×#537	1	1	yes	characteristic
898	C₂	C₃×C₅×#542	1	1	yes	characteristic
899	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
900	C₂	C₃×C₅×#546	1	1	yes	characteristic
901	C₂	C₃×C₅×#547	1	1	yes	characteristic
902	C₂	C₃×C₅×#562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#121	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. C₂×C₃×C₅×#124	C₂	semidirect
2. C₂×C₃×C₅×#123	C₂	semidirect
3. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
5. C₃×C₅×#399	C₂	semidirect
6. C₃×C₅×#396	C₂	semidirect
7. C₃×C₅×#395	C₂	semidirect
8. C₃×C₅×#394	C₂	semidirect
9. C₃×C₅×#394	C₂	semidirect
10. C₃×C₅×#394	C₂	semidirect
11. C₃×C₅×#389	C₂	semidirect
12. C₃×C₅×#388	C₂	semidirect
13. C₃×C₅×#386	C₂	semidirect
14. C₃×C₅×#385	C₂	semidirect
15. C₃×C₅×#380	C₂	semidirect
16. C₅×#2672	C₃	direct (N × H)
56. C₃×#2672	C₅	direct (N × H)
57. C₂×C₅×#124	C₂×C₃	semidirect
58. C₂×C₅×#123	C₂×C₃	semidirect
59. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
61. C₅×#399	C₂×C₃	semidirect
62. C₅×#396	C₂×C₃	semidirect
63. C₅×#395	C₂×C₃	semidirect
64. C₅×#394	C₂×C₃	semidirect
65. C₅×#394	C₂×C₃	semidirect
66. C₅×#394	C₂×C₃	semidirect
67. C₅×#389	C₂×C₃	semidirect
68. C₅×#388	C₂×C₃	semidirect
69. C₅×#386	C₂×C₃	semidirect
70. C₅×#385	C₂×C₃	semidirect
71. C₅×#380	C₂×C₃	semidirect
126. C₃×C₅×C₂²⋊C₄	D₄	semidirect
128. C₂×C₃×#124	C₂×C₅	semidirect
129. C₂×C₃×#123	C₂×C₅	semidirect
130. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
132. C₃×#399	C₂×C₅	semidirect
133. C₃×#396	C₂×C₅	semidirect
134. C₃×#395	C₂×C₅	semidirect
135. C₃×#394	C₂×C₅	semidirect
136. C₃×#394	C₂×C₅	semidirect
137. C₃×#394	C₂×C₅	semidirect
138. C₃×#389	C₂×C₅	semidirect
139. C₃×#388	C₂×C₅	semidirect
140. C₃×#386	C₂×C₅	semidirect
141. C₃×#385	C₂×C₅	semidirect
142. C₃×#380	C₂×C₅	semidirect
182. #2672	C₃×C₅	direct (N × H)
340. C₅×C₂²⋊C₄	C₃×D₄	semidirect
342. C₂×#124	C₂×C₃×C₅	semidirect
343. C₂×#123	C₂×C₃×C₅	semidirect
344. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
346. #399	C₂×C₃×C₅	semidirect
347. #396	C₂×C₃×C₅	semidirect
348. #395	C₂×C₃×C₅	semidirect
349. #394	C₂×C₃×C₅	semidirect
350. #394	C₂×C₃×C₅	semidirect
351. #394	C₂×C₃×C₅	semidirect
352. #389	C₂×C₃×C₅	semidirect
353. #388	C₂×C₃×C₅	semidirect
354. #386	C₂×C₃×C₅	semidirect
355. #385	C₂×C₃×C₅	semidirect
356. #380	C₂×C₃×C₅	semidirect
451. C₃×C₂²⋊C₄	C₅×D₄	semidirect
724. C₂²⋊C₄	C₃×C₅×D₄	semidirect
726. C₃×C₅	#2672	direct (N × H)
851. C₅	C₃×#2672	direct (N × H)
892. C₃	C₅×#2672	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×#124	2
C₂×C₃×C₅×#123	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂×C₃×C₅×#121	2
C₃×C₅×#399	2
C₃×C₅×#396	2
C₃×C₅×#395	2
C₃×C₅×#394	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#380	2
C₅×#2672	3
C₃×#2672	5

Subgroups — C3×C5×#2672 #14275706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2672 #14275706