Subgroups — C₃×C₅×#2450 #14275484

Order 1920.

1168 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#396	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#393	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic
10	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic
11	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2450	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	C₂³×C₃×C₄×C₅	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×C₂²⋊Q₈	—	2	4	no	—
24	C₃×C₄×C₅×D₄	—	2	4	no	—
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₄⋊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×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×C₅×#95	C₂²	1	1	yes	characteristic
53	C₃×C₅×#95	C₂²	1	1	yes	characteristic
54	C₃×#2450	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
55	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
57	C₅×#400	C₂×C₃	1	1	yes	characteristic, complemented
58	C₅×#398	C₂×C₃	1	1	yes	characteristic, complemented
59	C₅×#396	C₂×C₃	1	1	yes	characteristic, complemented
60	C₅×#393	C₂×C₃	1	1	yes	characteristic, complemented
61	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#386	C₂×C₃	1	1	yes	characteristic
64	C₅×#386	C₂×C₃	1	1	yes	characteristic
65	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
69	C₂×C₅×#95	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	—	2	2	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	Q₈	1	4	yes	complemented
78	C₂²×C₃×C₄×C₅	—	2	2	no	—
79	C₂²×C₃×C₄×C₅	—	2	2	no	—
80	C₂²×C₃×C₄×C₅	—	2	2	no	—
81	C₂²×C₃×C₄×C₅	—	2	2	no	—
82	C₂²×C₃×C₄×C₅	—	2	2	no	—
83	C₂²×C₃×C₄×C₅	—	2	2	no	—
84	C₂²×C₃×C₄×C₅	—	2	2	no	—
85	C₂²×C₃×C₄×C₅	—	4	1	no	—
86	C₂²×C₃×C₄×C₅	—	4	1	no	—
87	C₂²×C₃×C₄×C₅	—	4	1	no	—
88	C₂²×C₃×C₄×C₅	—	4	1	no	—
89	C₂²×C₃×C₄×C₅	—	4	1	no	—
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	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	C₃×C₅×C₄⋊C₄	—	2	2	no	—
104	C₃×C₅×C₄⋊C₄	—	2	2	no	—
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	—	4	1	no	—
109	C₃×C₅×C₄⋊C₄	—	4	1	no	—
110	C₃×C₅×C₄⋊C₄	—	4	1	no	—
111	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
112	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
113	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
114	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
115	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
116	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
117	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
118	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	—
119	C₃×C₄²×C₅	—	2	2	no	—
120	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
122	C₃×#400	C₂×C₅	1	1	yes	characteristic, complemented
123	C₃×#398	C₂×C₅	1	1	yes	characteristic, complemented
124	C₃×#396	C₂×C₅	1	1	yes	characteristic, complemented
125	C₃×#393	C₂×C₅	1	1	yes	characteristic, complemented
126	C₃×#391	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×#386	C₂×C₅	1	1	yes	characteristic
130	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
134	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
135	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
136	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
137	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
138	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
139	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
140	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
141	C₅×C₂²⋊Q₈	—	2	4	no	—
142	C₄×C₅×D₄	—	2	4	no	—
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×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₅×C₄⋊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×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₄²×C₅	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	C₅×#95	C₂²×C₃	1	1	yes	characteristic
169	C₅×#95	C₂²×C₃	1	1	yes	characteristic
170	C₅×#95	C₂²×C₃	1	1	yes	characteristic
171	C₅×#95	C₂²×C₃	1	1	yes	characteristic
172	#2450	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
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	C₂×D₄	1	2	yes	—
184	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
185	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
186	C₂³×C₃×C₅	#41	1	2	yes	—
187	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
188	C₃×C₅×Q₈	—	4	4	no	—
189	C₃×C₅×D₄	—	2	8	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	—	2	1	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	2	1	no	—
224	C₂×C₃×C₄×C₅	—	4	4	no	—
225	C₂×C₃×C₄×C₅	—	4	4	no	—
226	C₂×C₃×C₄×C₅	—	4	4	no	—
227	C₂×C₃×C₄×C₅	—	4	4	no	—
228	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
229	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
230	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
231	C₂×C₃×C₄×C₅	#41	1	2	yes	—
232	C₂×C₃×C₄×C₅	#41	1	2	yes	—
233	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
234	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
235	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
236	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
237	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
238	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
239	C₃×C₂²⋊Q₈	—	2	4	no	—
240	C₃×C₄×D₄	—	2	4	no	—
241	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₃×C₄⋊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×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₃×C₄²	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	C₃×#95	C₂²×C₅	1	1	yes	characteristic
265	C₃×#95	C₂²×C₅	1	1	yes	characteristic
266	C₃×#95	C₂²×C₅	1	1	yes	characteristic
267	C₃×#95	C₂²×C₅	1	1	yes	characteristic
268	C₃×#95	C₂²×C₅	1	1	yes	characteristic
269	C₃×#95	C₂²×C₅	1	1	yes	characteristic
270	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
271	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
272	C₂×C₅×Q₈	—	2	2	no	—
273	C₂×C₅×Q₈	—	2	2	no	—
274	C₂×C₅×Q₈	—	4	1	no	—
275	C₂×C₅×D₄	—	2	2	no	—
276	C₂×C₅×D₄	—	2	2	no	—
277	C₂×C₅×D₄	C₃×Q₈	1	4	yes	complemented
278	C₂²×C₄×C₅	—	2	2	no	—
279	C₂²×C₄×C₅	—	2	2	no	—
280	C₂²×C₄×C₅	—	2	2	no	—
281	C₂²×C₄×C₅	—	2	2	no	—
282	C₂²×C₄×C₅	—	2	2	no	—
283	C₂²×C₄×C₅	—	2	2	no	—
284	C₂²×C₄×C₅	—	2	2	no	—
285	C₂²×C₄×C₅	—	4	1	no	—
286	C₂²×C₄×C₅	—	4	1	no	—
287	C₂²×C₄×C₅	—	4	1	no	—
288	C₂²×C₄×C₅	—	4	1	no	—
289	C₂²×C₄×C₅	—	4	1	no	—
290	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
291	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
292	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
293	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
294	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
295	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
296	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
297	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
299	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
300	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
301	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
302	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
303	C₅×C₄⋊C₄	—	2	2	no	—
304	C₅×C₄⋊C₄	—	2	2	no	—
305	C₅×C₄⋊C₄	—	2	2	no	—
306	C₅×C₄⋊C₄	—	2	2	no	—
307	C₅×C₄⋊C₄	—	2	2	no	—
308	C₅×C₄⋊C₄	—	4	1	no	—
309	C₅×C₄⋊C₄	—	4	1	no	—
310	C₅×C₄⋊C₄	—	4	1	no	—
311	C₅×C₂²⋊C₄	—	2	2	no	—
312	C₅×C₂²⋊C₄	—	2	2	no	—
313	C₅×C₂²⋊C₄	—	2	2	no	—
314	C₅×C₂²⋊C₄	—	2	2	no	—
315	C₅×C₂²⋊C₄	—	4	1	no	—
316	C₅×C₂²⋊C₄	—	4	1	no	—
317	C₅×C₂²⋊C₄	—	4	1	no	—
318	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	—
319	C₄²×C₅	—	2	2	no	—
320	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
321	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic
322	#400	C₂×C₃×C₅	1	1	yes	characteristic, complemented
323	#398	C₂×C₃×C₅	1	1	yes	characteristic, complemented
324	#396	C₂×C₃×C₅	1	1	yes	characteristic, complemented
325	#393	C₂×C₃×C₅	1	1	yes	characteristic, complemented
326	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
327	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
328	#386	C₂×C₃×C₅	1	1	yes	characteristic
329	#386	C₂×C₃×C₅	1	1	yes	characteristic
330	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
331	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
332	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
333	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	C₂×#95	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	C₂²×C₃×C₅	—	2	2	no	—
336	C₂²×C₃×C₅	—	2	2	no	—
337	C₂²×C₃×C₅	—	2	2	no	—
338	C₂²×C₃×C₅	—	2	2	no	—
339	C₂²×C₃×C₅	—	2	2	no	—
340	C₂²×C₃×C₅	—	2	2	no	—
341	C₂²×C₃×C₅	—	2	2	no	—
342	C₂²×C₃×C₅	—	2	2	no	—
343	C₂²×C₃×C₅	—	2	2	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	C₂²⋊Q₈	1	4	yes	—
349	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
350	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
351	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
352	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
353	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
354	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
355	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
356	C₃×C₄×C₅	—	2	2	no	—
357	C₃×C₄×C₅	—	2	2	no	—
358	C₃×C₄×C₅	—	2	2	no	—
359	C₃×C₄×C₅	—	2	2	no	—
360	C₃×C₄×C₅	—	2	2	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	C₃×C₄×C₅	—	4	1	no	—
368	C₃×C₄×C₅	—	4	1	no	—
369	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
370	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
371	C₂×C₃×Q₈	—	2	2	no	—
372	C₂×C₃×Q₈	—	2	2	no	—
373	C₂×C₃×Q₈	—	4	1	no	—
374	C₂×C₃×D₄	—	2	2	no	—
375	C₂×C₃×D₄	—	2	2	no	—
376	C₂×C₃×D₄	C₅×Q₈	1	4	yes	complemented
377	C₂²×C₃×C₄	—	2	2	no	—
378	C₂²×C₃×C₄	—	2	2	no	—
379	C₂²×C₃×C₄	—	2	2	no	—
380	C₂²×C₃×C₄	—	2	2	no	—
381	C₂²×C₃×C₄	—	2	2	no	—
382	C₂²×C₃×C₄	—	2	2	no	—
383	C₂²×C₃×C₄	—	2	2	no	—
384	C₂²×C₃×C₄	—	4	1	no	—
385	C₂²×C₃×C₄	—	4	1	no	—
386	C₂²×C₃×C₄	—	4	1	no	—
387	C₂²×C₃×C₄	—	4	1	no	—
388	C₂²×C₃×C₄	—	4	1	no	—
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	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
395	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
396	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
397	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
398	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
399	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
400	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
401	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
402	C₃×C₄⋊C₄	—	2	2	no	—
403	C₃×C₄⋊C₄	—	2	2	no	—
404	C₃×C₄⋊C₄	—	2	2	no	—
405	C₃×C₄⋊C₄	—	2	2	no	—
406	C₃×C₄⋊C₄	—	2	2	no	—
407	C₃×C₄⋊C₄	—	4	1	no	—
408	C₃×C₄⋊C₄	—	4	1	no	—
409	C₃×C₄⋊C₄	—	4	1	no	—
410	C₃×C₂²⋊C₄	—	2	2	no	—
411	C₃×C₂²⋊C₄	—	2	2	no	—
412	C₃×C₂²⋊C₄	—	2	2	no	—
413	C₃×C₂²⋊C₄	—	2	2	no	—
414	C₃×C₂²⋊C₄	—	4	1	no	—
415	C₃×C₂²⋊C₄	—	4	1	no	—
416	C₃×C₂²⋊C₄	—	4	1	no	—
417	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	—
418	C₃×C₄²	—	2	2	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	C₂×C₃×D₄	1	2	yes	—
430	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
431	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
432	C₂³×C₅	C₃×#41	1	2	yes	—
433	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
434	C₅×Q₈	—	4	4	no	—
435	C₅×D₄	—	2	8	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	—	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	—	4	4	no	—
471	C₂×C₄×C₅	—	4	4	no	—
472	C₂×C₄×C₅	—	4	4	no	—
473	C₂×C₄×C₅	—	4	4	no	—
474	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
475	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
476	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
477	C₂×C₄×C₅	C₃×#41	1	2	yes	—
478	C₂×C₄×C₅	C₃×#41	1	2	yes	—
479	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
480	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
481	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
482	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
483	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
484	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
485	C₂²⋊Q₈	—	2	4	no	—
486	C₄×D₄	—	2	4	no	—
487	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
494	C₂×C₄⋊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×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
503	C₂×C₄²	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	#95	C₂²×C₃×C₅	1	1	yes	characteristic
513	#95	C₂²×C₃×C₅	1	1	yes	characteristic
514	#95	C₂²×C₃×C₅	1	1	yes	characteristic
515	#95	C₂²×C₃×C₅	1	1	yes	characteristic
516	C₂×C₃×C₅	—	2	4	no	—
517	C₂×C₃×C₅	—	4	2	no	—
518	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
519	C₂×C₃×C₅	#529	1	1	yes	characteristic
520	C₂×C₃×C₅	#538	1	1	yes	characteristic
521	C₂×C₃×C₅	#546	1	1	yes	characteristic
522	C₂×C₃×C₅	#546	1	1	yes	characteristic
523	C₂×C₃×C₅	#554	1	1	yes	characteristic
524	C₂×C₃×C₅	#554	1	1	yes	characteristic
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	C₂×C₅×D₄	1	2	yes	—
536	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
537	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
538	C₂³×C₃	C₅×#41	1	2	yes	—
539	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
540	C₃×Q₈	—	4	4	no	—
541	C₃×D₄	—	2	8	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	—	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	—	4	4	no	—
577	C₂×C₃×C₄	—	4	4	no	—
578	C₂×C₃×C₄	—	4	4	no	—
579	C₂×C₃×C₄	—	4	4	no	—
580	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
581	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
582	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
583	C₂×C₃×C₄	C₅×#41	1	2	yes	—
584	C₂×C₃×C₄	C₅×#41	1	2	yes	—
585	C₂²×C₅	—	2	2	no	—
586	C₂²×C₅	—	2	2	no	—
587	C₂²×C₅	—	2	2	no	—
588	C₂²×C₅	—	2	2	no	—
589	C₂²×C₅	—	2	2	no	—
590	C₂²×C₅	—	2	2	no	—
591	C₂²×C₅	—	2	2	no	—
592	C₂²×C₅	—	2	2	no	—
593	C₂²×C₅	—	2	2	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	C₃×C₂²⋊Q₈	1	4	yes	—
599	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
600	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
601	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
602	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
603	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
604	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
605	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
606	C₄×C₅	—	2	2	no	—
607	C₄×C₅	—	2	2	no	—
608	C₄×C₅	—	2	2	no	—
609	C₄×C₅	—	2	2	no	—
610	C₄×C₅	—	2	2	no	—
611	C₄×C₅	—	4	1	no	—
612	C₄×C₅	—	4	1	no	—
613	C₄×C₅	—	4	1	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	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
620	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
621	C₂×Q₈	—	2	2	no	—
622	C₂×Q₈	—	2	2	no	—
623	C₂×Q₈	—	4	1	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	C₃×C₅×Q₈	1	4	yes	complemented
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	4	1	no	—
635	C₂²×C₄	—	4	1	no	—
636	C₂²×C₄	—	4	1	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	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	2	no	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	4	1	no	—
658	C₄⋊C₄	—	4	1	no	—
659	C₄⋊C₄	—	4	1	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	4	1	no	—
665	C₂²⋊C₄	—	4	1	no	—
666	C₂²⋊C₄	—	4	1	no	—
667	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	—
668	C₄²	—	2	2	no	—
669	C₃×C₅	#2450	1	1	yes	characteristic, direct product factor, Hall
670	C₂²×C₃	—	2	2	no	—
671	C₂²×C₃	—	2	2	no	—
672	C₂²×C₃	—	2	2	no	—
673	C₂²×C₃	—	2	2	no	—
674	C₂²×C₃	—	2	2	no	—
675	C₂²×C₃	—	2	2	no	—
676	C₂²×C₃	—	2	2	no	—
677	C₂²×C₃	—	2	2	no	—
678	C₂²×C₃	—	2	2	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	C₅×C₂²⋊Q₈	1	4	yes	—
684	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
685	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
686	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
687	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
688	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
689	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
690	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
691	C₃×C₄	—	2	2	no	—
692	C₃×C₄	—	2	2	no	—
693	C₃×C₄	—	2	2	no	—
694	C₃×C₄	—	2	2	no	—
695	C₃×C₄	—	2	2	no	—
696	C₃×C₄	—	4	1	no	—
697	C₃×C₄	—	4	1	no	—
698	C₃×C₄	—	4	1	no	—
699	C₃×C₄	—	4	1	no	—
700	C₃×C₄	—	4	1	no	—
701	C₃×C₄	—	4	1	no	—
702	C₃×C₄	—	4	1	no	—
703	C₃×C₄	—	4	1	no	—
704	C₂×C₅	—	2	4	no	—
705	C₂×C₅	—	4	2	no	—
706	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
707	C₂×C₅	C₃×#529	1	1	yes	characteristic
708	C₂×C₅	C₃×#538	1	1	yes	characteristic
709	C₂×C₅	C₃×#546	1	1	yes	characteristic
710	C₂×C₅	C₃×#546	1	1	yes	characteristic
711	C₂×C₅	C₃×#554	1	1	yes	characteristic
712	C₂×C₅	C₃×#554	1	1	yes	characteristic
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
724	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
725	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
726	C₂³	C₃×C₅×#41	1	2	yes	—
727	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
728	Q₈	—	4	4	no	—
729	D₄	—	2	8	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	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	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	—	4	4	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	4	4	no	—
768	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
769	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
770	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
771	C₂×C₄	C₃×C₅×#41	1	2	yes	—
772	C₂×C₄	C₃×C₅×#41	1	2	yes	—
773	C₂×C₃	—	2	4	no	—
774	C₂×C₃	—	4	2	no	—
775	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
776	C₂×C₃	C₅×#529	1	1	yes	characteristic
777	C₂×C₃	C₅×#538	1	1	yes	characteristic
778	C₂×C₃	C₅×#546	1	1	yes	characteristic
779	C₂×C₃	C₅×#546	1	1	yes	characteristic
780	C₂×C₃	C₅×#554	1	1	yes	characteristic
781	C₂×C₃	C₅×#554	1	1	yes	characteristic
782	C₅	C₃×#2450	1	1	yes	characteristic, direct product factor, Sylow
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	2	2	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	1	no	—
796	C₂²	C₃×C₅×C₂²⋊Q₈	1	4	yes	—
797	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
798	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
799	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
800	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
801	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
802	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
803	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
804	C₄	—	2	2	no	—
805	C₄	—	2	2	no	—
806	C₄	—	2	2	no	—
807	C₄	—	2	2	no	—
808	C₄	—	2	2	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	1	no	—
812	C₄	—	4	1	no	—
813	C₄	—	4	1	no	—
814	C₄	—	4	1	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	1	no	—
817	C₃	C₅×#2450	1	1	yes	characteristic, direct product factor, Sylow
818	C₂	—	2	4	no	—
819	C₂	—	4	2	no	—
820	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
821	C₂	C₃×C₅×#529	1	1	yes	characteristic
822	C₂	C₃×C₅×#538	1	1	yes	characteristic
823	C₂	C₃×C₅×#546	1	1	yes	characteristic
824	C₂	C₃×C₅×#546	1	1	yes	characteristic
825	C₂	C₃×C₅×#554	1	1	yes	characteristic
826	C₂	C₃×C₅×#554	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×C₂²⋊Q₈	C₂	semidirect
3. C₃×C₅×#400	C₂	semidirect
4. C₃×C₅×#398	C₂	semidirect
5. C₃×C₅×#396	C₂	semidirect
6. C₃×C₅×#393	C₂	semidirect
7. C₃×C₅×#391	C₂	semidirect
8. C₃×C₅×#387	C₂	semidirect
11. C₃×C₅×#385	C₂	semidirect
12. C₃×C₅×#385	C₂	semidirect
13. C₃×C₅×#385	C₂	semidirect
14. C₃×C₅×#380	C₂	semidirect
15. C₂×C₃×C₅×#95	C₂	semidirect
16. C₅×#2450	C₃	direct (N × H)
54. C₃×#2450	C₅	direct (N × H)
55. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
57. C₅×#400	C₂×C₃	semidirect
58. C₅×#398	C₂×C₃	semidirect
59. C₅×#396	C₂×C₃	semidirect
60. C₅×#393	C₂×C₃	semidirect
61. C₅×#391	C₂×C₃	semidirect
62. C₅×#387	C₂×C₃	semidirect
65. C₅×#385	C₂×C₃	semidirect
66. C₅×#385	C₂×C₃	semidirect
67. C₅×#385	C₂×C₃	semidirect
68. C₅×#380	C₂×C₃	semidirect
69. C₂×C₅×#95	C₂×C₃	semidirect
77. C₂×C₃×C₅×D₄	Q₈	semidirect
120. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
122. C₃×#400	C₂×C₅	semidirect
123. C₃×#398	C₂×C₅	semidirect
124. C₃×#396	C₂×C₅	semidirect
125. C₃×#393	C₂×C₅	semidirect
126. C₃×#391	C₂×C₅	semidirect
127. C₃×#387	C₂×C₅	semidirect
130. C₃×#385	C₂×C₅	semidirect
131. C₃×#385	C₂×C₅	semidirect
132. C₃×#385	C₂×C₅	semidirect
133. C₃×#380	C₂×C₅	semidirect
134. C₂×C₃×#95	C₂×C₅	semidirect
172. #2450	C₃×C₅	direct (N × H)
277. C₂×C₅×D₄	C₃×Q₈	semidirect
320. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
322. #400	C₂×C₃×C₅	semidirect
323. #398	C₂×C₃×C₅	semidirect
324. #396	C₂×C₃×C₅	semidirect
325. #393	C₂×C₃×C₅	semidirect
326. #391	C₂×C₃×C₅	semidirect
327. #387	C₂×C₃×C₅	semidirect
330. #385	C₂×C₃×C₅	semidirect
331. #385	C₂×C₃×C₅	semidirect
332. #385	C₂×C₃×C₅	semidirect
333. #380	C₂×C₃×C₅	semidirect
334. C₂×#95	C₂×C₃×C₅	semidirect
376. C₂×C₃×D₄	C₅×Q₈	semidirect
626. C₂×D₄	C₃×C₅×Q₈	semidirect
669. C₃×C₅	#2450	direct (N × H)
782. C₅	C₃×#2450	direct (N × H)
817. C₃	C₅×#2450	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×C₂²⋊Q₈	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#400	2
C₃×C₅×#398	2
C₃×C₅×#396	2
C₃×C₅×#393	2
C₃×C₅×#391	2
C₃×C₅×#387	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#380	2
C₂×C₃×C₅×#95	2
C₅×#2450	3
C₃×#2450	5

Subgroups — C3×C5×#2450 #14275484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2450 #14275484