Subgroups — C₅×#76305 #14329027

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#939	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#877	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5220	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4976	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4957	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4957	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4956	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4944	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×Dic₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×Dic₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2363	—	3	1	no	maximal, Hall
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
19	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
20	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₂²⋊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×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₂×C₅×#217	C₂²	1	1	yes	characteristic
30	C₂×C₅×#217	C₂²	1	1	yes	characteristic
31	C₂×C₅×#217	C₂²	1	1	yes	characteristic
32	C₂×C₅×#217	C₂²	1	1	yes	characteristic
33	C₅×#939	C₄	1	8	yes	complemented
34	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
47	C₅×#67⋊C₄	—	2	4	no	—
48	C₅×#877	—	2	4	no	—
49	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
50	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
51	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
52	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
53	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
54	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
55	#76305	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
56	C₂×C₅×#121	—	3	1	no	—
57	C₂×C₄×C₅×D₄	—	3	1	no	—
58	C₂×C₅×#117	—	3	1	no	—
59	C₅×#390	—	3	1	no	—
60	C₅×#390	—	3	1	no	—
61	C₅×#390	D₃	1	1	yes	characteristic, complemented
62	C₅×#389	—	3	1	no	—
63	C₅×#388	—	3	1	no	—
64	C₅×#388	—	3	1	no	—
65	C₅×#386	—	3	1	no	—
66	C₅×#386	—	3	1	no	—
67	C₄×C₅×C₄⋊C₄	—	3	1	no	—
68	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
69	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
70	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
71	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
72	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
73	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₅×D₄	—	4	1	no	—
75	C₂×C₃×C₅×D₄	—	4	1	no	—
76	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₅×#67	—	2	2	no	—
83	C₂×C₅×#67	—	2	2	no	—
84	C₂×C₅×#67	—	4	1	no	—
85	C₂×C₅×#67	—	4	1	no	—
86	C₂×C₅×#67	C₂×C₄	1	4	yes	—
87	C₂×C₅×#67	C₂×C₄	1	4	yes	complemented
88	C₂²×C₅×Dic₃	—	2	2	no	—
89	C₂²×C₅×Dic₃	—	2	2	no	—
90	C₂²×C₅×Dic₃	—	2	2	no	—
91	C₂²×C₅×Dic₃	—	2	2	no	—
92	C₂²×C₅×Dic₃	—	4	1	no	—
93	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
94	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
95	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
96	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
97	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
98	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
99	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
100	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
101	C₂×C₄×C₅×D₃	—	2	2	no	—
102	C₂×C₄×C₅×D₃	—	2	2	no	—
103	C₂×C₄×C₅×D₃	—	4	1	no	—
104	C₃×C₅×C₄⋊C₄	—	4	1	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×C₄²×C₅	—	4	1	no	—
110	C₅×#217	—	2	2	no	—
111	C₅×#217	—	2	2	no	—
112	C₅×#217	—	4	1	no	—
113	C₅×#217	C₂×C₄	1	4	yes	complemented
114	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
115	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
116	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
117	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
118	C₅×Dic₃⋊C₄	—	2	2	no	—
119	C₅×Dic₃⋊C₄	—	4	1	no	—
120	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	complemented
121	C₅×Dic₃⋊C₄	D₄	1	4	yes	complemented
122	C₄×C₅×Dic₃	—	2	2	no	—
123	C₄×C₅×Dic₃	—	2	2	no	—
124	C₄×C₅×Dic₃	—	2	2	no	—
125	C₄×C₅×Dic₃	—	2	2	no	—
126	C₄×C₅×Dic₃	—	4	1	no	—
127	C₂×#939	C₂×C₅	1	1	yes	characteristic
128	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
129	C₂×#877	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
131	#5220	C₂×C₅	1	1	yes	characteristic, complemented
132	#4990	C₂×C₅	1	1	yes	characteristic, complemented
133	#4976	C₂×C₅	1	1	yes	characteristic, complemented
134	#4957	C₂×C₅	1	1	yes	characteristic, complemented
135	#4957	C₂×C₅	1	1	yes	characteristic, complemented
136	#4956	C₂×C₅	1	1	yes	characteristic, complemented
137	#4944	C₂×C₅	1	1	yes	characteristic, complemented
138	Dic₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
139	Dic₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
140	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
141	C₄×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂²×C₅×D₄	—	3	1	no	—
143	C₂²×C₅×D₄	—	3	1	no	—
144	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
145	C₂³×C₄×C₅	—	3	1	no	—
146	C₂³×C₄×C₅	—	3	1	no	—
147	C₂³×C₄×C₅	—	3	1	no	—
148	C₅×#121	—	3	8	no	—
149	C₄×C₅×D₄	—	6	4	no	—
150	C₅×#117	—	6	4	no	—
151	C₂×C₅×C₄⋊C₄	—	3	1	no	—
152	C₂×C₅×C₄⋊C₄	—	3	1	no	—
153	C₂×C₅×C₄⋊C₄	—	3	1	no	—
154	C₂×C₅×C₄⋊C₄	—	3	1	no	—
155	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
156	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
157	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
158	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
159	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
160	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
161	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
162	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
163	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
164	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
165	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
166	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
167	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
168	C₂×C₄²×C₅	—	3	1	no	—
169	C₂×C₄²×C₅	—	3	1	no	—
170	C₂×C₄²×C₅	—	3	1	no	—
171	C₂×C₄²×C₅	—	3	1	no	—
172	C₂×C₄²×C₅	—	3	1	no	—
173	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
174	C₅×#95	—	3	1	no	—
175	C₅×#95	—	3	1	no	—
176	C₅×#95	—	3	1	no	—
177	C₅×#95	—	3	1	no	—
178	C₅×#95	—	3	1	no	—
179	C₅×#95	—	3	1	no	—
180	#2363	—	3	1	no	Sylow
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	—	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	C₂²×C₄	1	2	yes	—
194	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
195	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
196	C₂²×C₅×D₃	—	2	1	no	—
197	C₂²×C₅×D₃	—	2	1	no	—
198	C₂²×C₅×D₃	—	2	1	no	—
199	C₂²×C₅×D₃	—	2	1	no	—
200	C₂²×C₅×D₃	—	2	1	no	—
201	C₂²×C₅×D₃	—	2	1	no	—
202	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
203	C₃×C₅×D₄	—	4	4	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	C₂²×C₄	1	2	yes	—
217	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
218	C₂×C₃×C₄×C₅	#41	1	2	yes	—
219	C₅×#67	—	2	8	no	—
220	C₅×#67	—	4	4	no	—
221	C₂×C₅×Dic₃	—	2	1	no	—
222	C₂×C₅×Dic₃	—	2	1	no	—
223	C₂×C₅×Dic₃	—	2	1	no	—
224	C₂×C₅×Dic₃	—	2	1	no	—
225	C₂×C₅×Dic₃	—	2	1	no	—
226	C₂×C₅×Dic₃	—	2	1	no	—
227	C₂×C₅×Dic₃	—	2	1	no	—
228	C₂×C₅×Dic₃	—	2	1	no	—
229	C₂×C₅×Dic₃	—	2	8	no	—
230	C₂×C₅×Dic₃	—	2	1	no	—
231	C₂×C₅×Dic₃	—	2	1	no	—
232	C₂×C₅×Dic₃	—	2	1	no	—
233	C₂×C₅×Dic₃	—	2	1	no	—
234	C₂×C₅×Dic₃	—	2	1	no	—
235	C₂×C₅×Dic₃	—	2	1	no	—
236	C₂×C₅×Dic₃	—	4	4	no	—
237	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
238	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
239	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
240	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
241	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
242	C₂×C₅×Dic₃	#41	1	2	yes	—
243	C₂×C₅×Dic₃	#41	1	2	yes	—
244	C₄×C₅×D₃	—	4	4	no	—
245	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
246	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
247	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
248	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
249	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
250	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₃×C₄⋊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×C₄²	C₂²×C₅	1	1	yes	characteristic
257	C₂×#217	C₂²×C₅	1	1	yes	characteristic
258	C₂×#217	C₂²×C₅	1	1	yes	characteristic
259	C₂×#217	C₂²×C₅	1	1	yes	characteristic
260	C₂×#217	C₂²×C₅	1	1	yes	characteristic
261	#939	C₄×C₅	1	8	yes	complemented
262	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
263	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
264	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
265	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
266	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
267	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
268	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
269	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
273	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
274	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
275	#67⋊C₄	—	2	4	no	—
276	#877	—	2	4	no	—
277	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
278	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
279	C₃⋊#95	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	C₂⁴×C₅	—	3	1	no	—
284	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
285	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
286	C₂×C₅×D₄	—	3	4	no	—
287	C₂×C₅×D₄	—	3	4	no	—
288	C₂×C₅×D₄	—	4	1	no	—
289	C₂×C₅×D₄	—	4	1	no	—
290	C₂×C₅×D₄	—	6	2	no	—
291	C₂×C₅×D₄	—	6	2	no	—
292	C₂×C₅×D₄	—	12	1	no	—
293	C₂×C₅×D₄	—	12	1	no	—
294	C₂×C₅×D₄	C₄×D₃	1	4	yes	complemented
295	C₂²×C₄×C₅	—	3	1	no	—
296	C₂²×C₄×C₅	—	3	4	no	—
297	C₂²×C₄×C₅	—	3	1	no	—
298	C₂²×C₄×C₅	—	3	1	no	—
299	C₂²×C₄×C₅	—	3	1	no	—
300	C₂²×C₄×C₅	—	3	1	no	—
301	C₂²×C₄×C₅	—	3	1	no	—
302	C₂²×C₄×C₅	—	3	1	no	—
303	C₂²×C₄×C₅	—	6	2	no	—
304	C₂²×C₄×C₅	—	6	2	no	—
305	C₂²×C₄×C₅	—	6	2	no	—
306	C₂²×C₄×C₅	—	6	2	no	—
307	C₂²×C₄×C₅	—	6	2	no	—
308	C₂²×C₄×C₅	—	6	2	no	—
309	C₂²×C₄×C₅	—	12	1	no	—
310	C₂²×C₄×C₅	—	12	1	no	—
311	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
312	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
313	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
314	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
315	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
316	C₅×C₄⋊C₄	—	3	4	no	—
317	C₅×C₄⋊C₄	—	3	4	no	—
318	C₅×C₄⋊C₄	—	4	1	no	—
319	C₅×C₄⋊C₄	—	6	2	no	—
320	C₅×C₄⋊C₄	—	12	1	no	—
321	C₅×C₂²⋊C₄	—	2	2	no	—
322	C₅×C₂²⋊C₄	—	2	2	no	—
323	C₅×C₂²⋊C₄	—	2	2	no	—
324	C₅×C₂²⋊C₄	—	2	2	no	—
325	C₅×C₂²⋊C₄	—	3	4	no	—
326	C₅×C₂²⋊C₄	—	3	4	no	—
327	C₅×C₂²⋊C₄	—	6	2	no	—
328	C₅×C₂²⋊C₄	—	6	2	no	—
329	C₅×C₂²⋊C₄	—	6	2	no	—
330	C₅×C₂²⋊C₄	—	6	2	no	—
331	C₅×C₂²⋊C₄	—	12	1	no	—
332	C₅×C₂²⋊C₄	—	12	1	no	—
333	C₄²×C₅	—	4	1	no	—
334	C₄²×C₅	—	6	2	no	—
335	C₄²×C₅	—	6	2	no	—
336	C₄²×C₅	—	6	2	no	—
337	C₄²×C₅	—	6	2	no	—
338	C₄²×C₅	—	12	1	no	—
339	C₂×#121	—	3	1	no	—
340	C₂×C₄×D₄	—	3	1	no	—
341	C₂×#117	—	3	1	no	—
342	#390	—	3	1	no	—
343	#390	—	3	1	no	—
344	#390	C₅×D₃	1	1	yes	characteristic, complemented
345	#389	—	3	1	no	—
346	#388	—	3	1	no	—
347	#388	—	3	1	no	—
348	#386	—	3	1	no	—
349	#386	—	3	1	no	—
350	C₄×C₄⋊C₄	—	3	1	no	—
351	C₄×C₂²⋊C₄	—	3	1	no	—
352	C₄×C₂²⋊C₄	—	3	1	no	—
353	C₄×C₂²⋊C₄	—	3	1	no	—
354	C₂²×C₃×C₅	—	2	2	no	—
355	C₂²×C₃×C₅	—	2	2	no	—
356	C₂²×C₃×C₅	—	2	2	no	—
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	—	4	1	no	—
361	C₂²×C₃×C₅	—	4	1	no	—
362	C₂²×C₃×C₅	—	4	1	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	C₂³×C₄	1	1	yes	characteristic
369	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
370	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
371	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
372	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
373	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
374	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
375	C₂×C₅×D₃	—	2	2	no	—
376	C₂×C₅×D₃	—	2	2	no	—
377	C₂×C₅×D₃	—	2	2	no	—
378	C₂×C₅×D₃	—	4	1	no	—
379	C₂×C₅×D₃	—	4	1	no	—
380	C₂×C₅×D₃	—	4	1	no	—
381	C₂×C₅×D₃	—	4	1	no	—
382	C₃×C₄×C₅	—	2	2	no	—
383	C₃×C₄×C₅	—	2	2	no	—
384	C₃×C₄×C₅	—	2	2	no	—
385	C₃×C₄×C₅	—	4	1	no	—
386	C₃×C₄×C₅	—	4	1	no	—
387	C₅×Dic₃	—	2	2	no	—
388	C₅×Dic₃	—	2	2	no	—
389	C₅×Dic₃	—	2	2	no	—
390	C₅×Dic₃	—	2	2	no	—
391	C₅×Dic₃	—	4	1	no	—
392	C₅×Dic₃	—	4	1	no	—
393	C₅×Dic₃	C₄×D₄	1	4	yes	—
394	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
395	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
396	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
397	C₂×C₃×D₄	—	4	1	no	—
398	C₂×C₃×D₄	—	4	1	no	—
399	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
400	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
401	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
403	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
404	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
405	C₂×#67	—	2	2	no	—
406	C₂×#67	—	2	2	no	—
407	C₂×#67	—	4	1	no	—
408	C₂×#67	—	4	1	no	—
409	C₂×#67	C₂×C₄×C₅	1	4	yes	—
410	C₂×#67	C₂×C₄×C₅	1	4	yes	complemented
411	C₂²×Dic₃	—	2	2	no	—
412	C₂²×Dic₃	—	2	2	no	—
413	C₂²×Dic₃	—	2	2	no	—
414	C₂²×Dic₃	—	2	2	no	—
415	C₂²×Dic₃	—	4	1	no	—
416	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
417	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
418	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
419	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
420	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
421	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
422	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
423	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₄×D₃	—	2	2	no	—
425	C₂×C₄×D₃	—	2	2	no	—
426	C₂×C₄×D₃	—	4	1	no	—
427	C₃×C₄⋊C₄	—	4	1	no	—
428	C₃×C₂²⋊C₄	—	2	2	no	—
429	C₃×C₂²⋊C₄	—	2	2	no	—
430	C₃×C₂²⋊C₄	—	2	2	no	—
431	C₃×C₂²⋊C₄	—	2	2	no	—
432	C₃×C₄²	—	4	1	no	—
433	#217	—	2	2	no	—
434	#217	—	2	2	no	—
435	#217	—	4	1	no	—
436	#217	C₂×C₄×C₅	1	4	yes	complemented
437	(C₂×D₃)⋊C₄	—	2	2	no	—
438	(C₂×D₃)⋊C₄	—	2	2	no	—
439	(C₂×D₃)⋊C₄	—	4	1	no	—
440	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
441	Dic₃⋊C₄	—	2	2	no	—
442	Dic₃⋊C₄	—	4	1	no	—
443	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
444	Dic₃⋊C₄	C₅×D₄	1	4	yes	complemented
445	C₄×Dic₃	—	2	2	no	—
446	C₄×Dic₃	—	2	2	no	—
447	C₄×Dic₃	—	2	2	no	—
448	C₄×Dic₃	—	2	2	no	—
449	C₄×Dic₃	—	4	1	no	—
450	C₂³×C₅	—	2	1	no	—
451	C₂³×C₅	—	2	1	no	—
452	C₂³×C₅	—	2	1	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	—	3	2	no	—
463	C₂³×C₅	—	6	1	no	—
464	C₂³×C₅	—	6	1	no	—
465	C₂³×C₅	—	6	1	no	—
466	C₂³×C₅	—	6	1	no	—
467	C₂³×C₅	—	6	1	no	—
468	C₂³×C₅	—	6	1	no	—
469	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
470	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
471	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
472	C₅×D₄	—	4	4	no	—
473	C₅×D₄	—	6	8	no	—
474	C₅×D₄	—	12	4	no	—
475	C₂×C₄×C₅	—	2	1	no	—
476	C₂×C₄×C₅	—	2	1	no	—
477	C₂×C₄×C₅	—	2	1	no	—
478	C₂×C₄×C₅	—	2	1	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	—	3	2	no	—
488	C₂×C₄×C₅	—	3	2	no	—
489	C₂×C₄×C₅	—	3	2	no	—
490	C₂×C₄×C₅	—	3	2	no	—
491	C₂×C₄×C₅	—	3	2	no	—
492	C₂×C₄×C₅	—	3	2	no	—
493	C₂×C₄×C₅	—	3	2	no	—
494	C₂×C₄×C₅	—	6	8	no	—
495	C₂×C₄×C₅	—	6	1	no	—
496	C₂×C₄×C₅	—	6	1	no	—
497	C₂×C₄×C₅	—	6	1	no	—
498	C₂×C₄×C₅	—	6	1	no	—
499	C₂×C₄×C₅	—	6	1	no	—
500	C₂×C₄×C₅	—	6	1	no	—
501	C₂×C₄×C₅	—	6	1	no	—
502	C₂×C₄×C₅	—	6	1	no	—
503	C₂×C₄×C₅	—	6	1	no	—
504	C₂×C₄×C₅	—	6	1	no	—
505	C₂×C₄×C₅	—	6	1	no	—
506	C₂×C₄×C₅	—	6	1	no	—
507	C₂×C₄×C₅	—	6	1	no	—
508	C₂×C₄×C₅	—	6	1	no	—
509	C₂×C₄×C₅	—	12	4	no	—
510	C₂×C₄×C₅	—	12	4	no	—
511	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
512	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
513	C₂×C₄×C₅	#237	1	2	yes	—
514	C₂²×D₄	—	3	1	no	—
515	C₂²×D₄	—	3	1	no	—
516	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
517	C₂³×C₄	—	3	1	no	—
518	C₂³×C₄	—	3	1	no	—
519	C₂³×C₄	—	3	1	no	—
520	#121	—	3	8	no	—
521	C₄×D₄	—	6	4	no	—
522	#117	—	6	4	no	—
523	C₂×C₄⋊C₄	—	3	1	no	—
524	C₂×C₄⋊C₄	—	3	1	no	—
525	C₂×C₄⋊C₄	—	3	1	no	—
526	C₂×C₄⋊C₄	—	3	1	no	—
527	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	—	3	1	no	—
529	C₂×C₂²⋊C₄	—	3	1	no	—
530	C₂×C₂²⋊C₄	—	3	1	no	—
531	C₂×C₂²⋊C₄	—	3	1	no	—
532	C₂×C₂²⋊C₄	—	3	1	no	—
533	C₂×C₂²⋊C₄	—	3	1	no	—
534	C₂×C₂²⋊C₄	—	3	1	no	—
535	C₂×C₂²⋊C₄	—	3	1	no	—
536	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
540	C₂×C₄²	—	3	1	no	—
541	C₂×C₄²	—	3	1	no	—
542	C₂×C₄²	—	3	1	no	—
543	C₂×C₄²	—	3	1	no	—
544	C₂×C₄²	—	3	1	no	—
545	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
546	#95	—	3	1	no	—
547	#95	—	3	1	no	—
548	#95	—	3	1	no	—
549	#95	—	3	1	no	—
550	#95	—	3	1	no	—
551	#95	—	3	1	no	—
552	C₂×C₃×C₅	—	4	2	no	—
553	C₂×C₃×C₅	—	4	2	no	—
554	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
555	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
556	C₂×C₃×C₅	#518	1	1	yes	characteristic
557	C₂×C₃×C₅	#546	1	1	yes	characteristic
558	C₂×C₃×C₅	#550	1	1	yes	characteristic
559	C₂×C₃×C₅	#553	1	1	yes	characteristic
560	C₂×C₃×C₅	#555	1	1	yes	characteristic
561	C₅×D₃	—	4	2	no	—
562	C₂³×C₃	—	2	1	no	—
563	C₂³×C₃	—	2	1	no	—
564	C₂³×C₃	—	2	1	no	—
565	C₂³×C₃	—	2	1	no	—
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	C₂²×C₄×C₅	1	2	yes	—
575	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
576	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
577	C₂²×D₃	—	2	1	no	—
578	C₂²×D₃	—	2	1	no	—
579	C₂²×D₃	—	2	1	no	—
580	C₂²×D₃	—	2	1	no	—
581	C₂²×D₃	—	2	1	no	—
582	C₂²×D₃	—	2	1	no	—
583	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
584	C₃×D₄	—	4	4	no	—
585	C₂×C₃×C₄	—	2	1	no	—
586	C₂×C₃×C₄	—	2	1	no	—
587	C₂×C₃×C₄	—	2	1	no	—
588	C₂×C₃×C₄	—	2	1	no	—
589	C₂×C₃×C₄	—	2	1	no	—
590	C₂×C₃×C₄	—	2	1	no	—
591	C₂×C₃×C₄	—	2	1	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	C₂²×C₄×C₅	1	2	yes	—
598	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
599	C₂×C₃×C₄	C₅×#41	1	2	yes	—
600	#67	—	2	8	no	—
601	#67	—	4	4	no	—
602	C₂×Dic₃	—	2	1	no	—
603	C₂×Dic₃	—	2	1	no	—
604	C₂×Dic₃	—	2	1	no	—
605	C₂×Dic₃	—	2	1	no	—
606	C₂×Dic₃	—	2	1	no	—
607	C₂×Dic₃	—	2	1	no	—
608	C₂×Dic₃	—	2	1	no	—
609	C₂×Dic₃	—	2	1	no	—
610	C₂×Dic₃	—	2	8	no	—
611	C₂×Dic₃	—	2	1	no	—
612	C₂×Dic₃	—	2	1	no	—
613	C₂×Dic₃	—	2	1	no	—
614	C₂×Dic₃	—	2	1	no	—
615	C₂×Dic₃	—	2	1	no	—
616	C₂×Dic₃	—	2	1	no	—
617	C₂×Dic₃	—	4	4	no	—
618	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
619	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
620	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
621	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
622	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
623	C₂×Dic₃	C₅×#41	1	2	yes	—
624	C₂×Dic₃	C₅×#41	1	2	yes	—
625	C₄×D₃	—	4	4	no	—
626	C₂²×C₅	—	2	2	no	—
627	C₂²×C₅	—	2	2	no	—
628	C₂²×C₅	—	2	2	no	—
629	C₂²×C₅	—	2	2	no	—
630	C₂²×C₅	—	2	2	no	—
631	C₂²×C₅	—	2	2	no	—
632	C₂²×C₅	—	4	1	no	—
633	C₂²×C₅	—	4	1	no	—
634	C₂²×C₅	—	4	1	no	—
635	C₂²×C₅	—	4	1	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	—	6	2	no	—
641	C₂²×C₅	—	6	2	no	—
642	C₂²×C₅	—	6	2	no	—
643	C₂²×C₅	—	12	1	no	—
644	C₂²×C₅	—	12	1	no	—
645	C₂²×C₅	—	12	1	no	—
646	C₂²×C₅	—	12	1	no	—
647	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
648	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
649	C₂²×C₅	C₂×#237	1	1	yes	characteristic
650	C₂²×C₅	#1004	1	1	yes	characteristic
651	C₂²×C₅	#1004	1	1	yes	characteristic
652	C₂²×C₅	D₃×#41	1	1	yes	characteristic
653	C₂²×C₅	D₃×#41	1	1	yes	characteristic
654	C₄×C₅	—	2	2	no	—
655	C₄×C₅	—	2	2	no	—
656	C₄×C₅	—	2	2	no	—
657	C₄×C₅	—	3	4	no	—
658	C₄×C₅	—	4	1	no	—
659	C₄×C₅	—	4	1	no	—
660	C₄×C₅	—	6	2	no	—
661	C₄×C₅	—	6	2	no	—
662	C₄×C₅	—	6	2	no	—
663	C₄×C₅	—	6	2	no	—
664	C₄×C₅	—	12	1	no	—
665	C₄×C₅	—	12	1	no	—
666	C₂⁴	—	3	1	no	—
667	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
668	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
669	C₂×D₄	—	3	4	no	—
670	C₂×D₄	—	3	4	no	—
671	C₂×D₄	—	4	1	no	—
672	C₂×D₄	—	4	1	no	—
673	C₂×D₄	—	6	2	no	—
674	C₂×D₄	—	6	2	no	—
675	C₂×D₄	—	12	1	no	—
676	C₂×D₄	—	12	1	no	—
677	C₂×D₄	C₄×C₅×D₃	1	4	yes	complemented
678	C₂²×C₄	—	3	1	no	—
679	C₂²×C₄	—	3	4	no	—
680	C₂²×C₄	—	3	1	no	—
681	C₂²×C₄	—	3	1	no	—
682	C₂²×C₄	—	3	1	no	—
683	C₂²×C₄	—	3	1	no	—
684	C₂²×C₄	—	3	1	no	—
685	C₂²×C₄	—	3	1	no	—
686	C₂²×C₄	—	6	2	no	—
687	C₂²×C₄	—	6	2	no	—
688	C₂²×C₄	—	6	2	no	—
689	C₂²×C₄	—	6	2	no	—
690	C₂²×C₄	—	6	2	no	—
691	C₂²×C₄	—	6	2	no	—
692	C₂²×C₄	—	12	1	no	—
693	C₂²×C₄	—	12	1	no	—
694	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
695	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
696	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
697	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
698	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
699	C₄⋊C₄	—	3	4	no	—
700	C₄⋊C₄	—	3	4	no	—
701	C₄⋊C₄	—	4	1	no	—
702	C₄⋊C₄	—	6	2	no	—
703	C₄⋊C₄	—	12	1	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₂²⋊C₄	—	3	4	no	—
709	C₂²⋊C₄	—	3	4	no	—
710	C₂²⋊C₄	—	6	2	no	—
711	C₂²⋊C₄	—	6	2	no	—
712	C₂²⋊C₄	—	6	2	no	—
713	C₂²⋊C₄	—	6	2	no	—
714	C₂²⋊C₄	—	12	1	no	—
715	C₂²⋊C₄	—	12	1	no	—
716	C₄²	—	4	1	no	—
717	C₄²	—	6	2	no	—
718	C₄²	—	6	2	no	—
719	C₄²	—	6	2	no	—
720	C₄²	—	6	2	no	—
721	C₄²	—	12	1	no	—
722	C₃×C₅	#2363	1	1	yes	characteristic, complemented, Hall
723	C₂²×C₃	—	2	2	no	—
724	C₂²×C₃	—	2	2	no	—
725	C₂²×C₃	—	2	2	no	—
726	C₂²×C₃	—	2	2	no	—
727	C₂²×C₃	—	2	2	no	—
728	C₂²×C₃	—	2	2	no	—
729	C₂²×C₃	—	4	1	no	—
730	C₂²×C₃	—	4	1	no	—
731	C₂²×C₃	—	4	1	no	—
732	C₂²×C₃	—	4	1	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	C₂³×C₄×C₅	1	1	yes	characteristic
738	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
739	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
740	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
741	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
742	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
743	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
744	C₂×D₃	—	2	2	no	—
745	C₂×D₃	—	2	2	no	—
746	C₂×D₃	—	2	2	no	—
747	C₂×D₃	—	4	1	no	—
748	C₂×D₃	—	4	1	no	—
749	C₂×D₃	—	4	1	no	—
750	C₂×D₃	—	4	1	no	—
751	C₃×C₄	—	2	2	no	—
752	C₃×C₄	—	2	2	no	—
753	C₃×C₄	—	2	2	no	—
754	C₃×C₄	—	4	1	no	—
755	C₃×C₄	—	4	1	no	—
756	Dic₃	—	2	2	no	—
757	Dic₃	—	2	2	no	—
758	Dic₃	—	2	2	no	—
759	Dic₃	—	2	2	no	—
760	Dic₃	—	4	1	no	—
761	Dic₃	—	4	1	no	—
762	Dic₃	C₄×C₅×D₄	1	4	yes	—
763	C₂×C₅	—	4	2	no	—
764	C₂×C₅	—	4	2	no	—
765	C₂×C₅	—	12	2	no	—
766	C₂×C₅	#5486	1	1	yes	characteristic
767	C₂×C₅	C₄×#237	1	1	yes	characteristic
768	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
769	C₂×C₅	#5601	1	1	yes	characteristic
770	C₂×C₅	#5610	1	1	yes	characteristic
771	C₂×C₅	#5670	1	1	yes	characteristic
772	C₂×C₅	#5718	1	1	yes	characteristic
773	C₂³	—	2	1	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	1	no	—
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	—	3	2	no	—
786	C₂³	—	6	1	no	—
787	C₂³	—	6	1	no	—
788	C₂³	—	6	1	no	—
789	C₂³	—	6	1	no	—
790	C₂³	—	6	1	no	—
791	C₂³	—	6	1	no	—
792	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
793	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
794	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
795	D₄	—	4	4	no	—
796	D₄	—	6	8	no	—
797	D₄	—	12	4	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	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	—	3	2	no	—
811	C₂×C₄	—	3	2	no	—
812	C₂×C₄	—	3	2	no	—
813	C₂×C₄	—	3	2	no	—
814	C₂×C₄	—	3	2	no	—
815	C₂×C₄	—	3	2	no	—
816	C₂×C₄	—	3	2	no	—
817	C₂×C₄	—	6	8	no	—
818	C₂×C₄	—	6	1	no	—
819	C₂×C₄	—	6	1	no	—
820	C₂×C₄	—	6	1	no	—
821	C₂×C₄	—	6	1	no	—
822	C₂×C₄	—	6	1	no	—
823	C₂×C₄	—	6	1	no	—
824	C₂×C₄	—	6	1	no	—
825	C₂×C₄	—	6	1	no	—
826	C₂×C₄	—	6	1	no	—
827	C₂×C₄	—	6	1	no	—
828	C₂×C₄	—	6	1	no	—
829	C₂×C₄	—	6	1	no	—
830	C₂×C₄	—	6	1	no	—
831	C₂×C₄	—	6	1	no	—
832	C₂×C₄	—	12	4	no	—
833	C₂×C₄	—	12	4	no	—
834	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
835	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
836	C₂×C₄	C₅×#237	1	2	yes	—
837	C₂×C₃	—	4	2	no	—
838	C₂×C₃	—	4	2	no	—
839	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
840	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
841	C₂×C₃	C₅×#518	1	1	yes	characteristic
842	C₂×C₃	C₅×#546	1	1	yes	characteristic
843	C₂×C₃	C₅×#550	1	1	yes	characteristic
844	C₂×C₃	C₅×#553	1	1	yes	characteristic
845	C₂×C₃	C₅×#555	1	1	yes	characteristic
846	D₃	—	4	2	no	—
847	C₅	#76305	1	1	yes	characteristic, direct product factor, Sylow
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	4	1	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	6	2	no	—
863	C₂²	—	6	2	no	—
864	C₂²	—	6	2	no	—
865	C₂²	—	12	1	no	—
866	C₂²	—	12	1	no	—
867	C₂²	—	12	1	no	—
868	C₂²	—	12	1	no	—
869	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
870	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
871	C₂²	C₂×C₅×#237	1	1	yes	characteristic
872	C₂²	C₅×#1004	1	1	yes	characteristic
873	C₂²	C₅×#1004	1	1	yes	characteristic
874	C₂²	C₅×D₃×#41	1	1	yes	characteristic
875	C₂²	C₅×D₃×#41	1	1	yes	characteristic
876	C₄	—	2	2	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	2	no	—
879	C₄	—	3	4	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	1	no	—
882	C₄	—	6	2	no	—
883	C₄	—	6	2	no	—
884	C₄	—	6	2	no	—
885	C₄	—	6	2	no	—
886	C₄	—	12	1	no	—
887	C₄	—	12	1	no	—
888	C₃	C₅×#2363	1	1	yes	characteristic, complemented, Sylow
889	C₂	—	4	2	no	—
890	C₂	—	4	2	no	—
891	C₂	—	12	2	no	—
892	C₂	C₅×#5486	1	1	yes	characteristic
893	C₂	C₄×C₅×#237	1	1	yes	characteristic
894	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
895	C₂	C₅×#5601	1	1	yes	characteristic
896	C₂	C₅×#5610	1	1	yes	characteristic
897	C₂	C₅×#5670	1	1	yes	characteristic
898	C₂	C₅×#5718	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#390	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#939	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#390	D₃
hypocenter	C₃	C₅×#2363
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#390

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#67⋊C₄	C₂	semidirect
3. C₂×C₅×#877	C₂	semidirect
4. C₃×C₅×#390	C₂	semidirect
5. C₅×#5220	C₂	semidirect
6. C₅×#4990	C₂	semidirect
7. C₅×#4976	C₂	semidirect
8. C₅×#4957	C₂	semidirect
9. C₅×#4957	C₂	semidirect
10. C₅×#4956	C₂	semidirect
11. C₅×#4944	C₂	semidirect
12. C₅×Dic₃×C₂²⋊C₄	C₂	semidirect
13. C₅×Dic₃×C₂²⋊C₄	C₂	semidirect
14. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
15. C₄×C₅×Dic₃⋊C₄	C₂	semidirect
33. C₅×#939	C₄	semidirect
55. #76305	C₅	direct (N × H)
61. C₅×#390	D₃	semidirect
76. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
87. C₂×C₅×#67	C₂×C₄	semidirect
93. C₂²×C₅×Dic₃	C₂×C₄	semidirect
113. C₅×#217	C₂×C₄	semidirect
117. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
120. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
121. C₅×Dic₃⋊C₄	D₄	semidirect
128. C₂×#67⋊C₄	C₂×C₅	semidirect
129. C₂×#877	C₂×C₅	semidirect
130. C₃×#390	C₂×C₅	semidirect
131. #5220	C₂×C₅	semidirect
132. #4990	C₂×C₅	semidirect
133. #4976	C₂×C₅	semidirect
134. #4957	C₂×C₅	semidirect
135. #4957	C₂×C₅	semidirect
136. #4956	C₂×C₅	semidirect
137. #4944	C₂×C₅	semidirect
138. Dic₃×C₂²⋊C₄	C₂×C₅	semidirect
139. Dic₃×C₂²⋊C₄	C₂×C₅	semidirect
140. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
141. C₄×Dic₃⋊C₄	C₂×C₅	semidirect
261. #939	C₄×C₅	semidirect
294. C₂×C₅×D₄	C₄×D₃	semidirect
344. #390	C₅×D₃	semidirect
399. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
410. C₂×#67	C₂×C₄×C₅	semidirect
416. C₂²×Dic₃	C₂×C₄×C₅	semidirect
436. #217	C₂×C₄×C₅	semidirect
440. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
443. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
444. Dic₃⋊C₄	C₅×D₄	semidirect
677. C₂×D₄	C₄×C₅×D₃	semidirect
722. C₃×C₅	#2363	semidirect
847. C₅	#76305	direct (N × H)
888. C₃	C₅×#2363	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#939	2
C₂×C₅×#67⋊C₄	2
C₂×C₅×#877	2
C₃×C₅×#390	2
C₅×#5220	2
C₅×#4990	2
C₅×#4976	2
C₅×#4957	2
C₅×#4956	2
C₅×#4944	2
C₅×Dic₃×C₂²⋊C₄	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₄×C₅×Dic₃⋊C₄	2
C₅×#2363	3
#76305	5

Subgroups — C5×#76305 #14329027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#76305 #14329027