Subgroups — C₅×#74683 #14330852

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 876 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	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5221	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5213	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5210	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4957	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4944	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4943	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4942	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4669	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4668	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4655	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4652	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2377	—	3	1	no	maximal, Hall
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
20	C₂²×C₅×#67	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×C₂²⋊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×C₅×#217	C₂²	1	1	yes	characteristic
27	C₂×C₅×#217	C₂²	1	1	yes	characteristic
28	C₂×C₅×#217	C₂²	1	1	yes	characteristic
29	C₂×C₅×#217	C₂²	1	1	yes	characteristic
30	C₂×C₅×#217	C₂²	1	1	yes	characteristic
31	C₅×#939	C₄	1	8	yes	complemented
32	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
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×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
37	C₂×C₅×Dic₃⋊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×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
43	C₃×C₅×#95	C₂²	1	1	yes	characteristic
44	C₃×C₅×#95	C₂²	1	1	yes	characteristic
45	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
46	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
47	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
48	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
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	#74683	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
54	C₂×C₅×#121	—	3	1	no	—
55	C₅×#390	—	3	1	no	—
56	C₅×#390	—	3	1	no	—
57	C₅×#388	—	3	1	no	—
58	C₅×#388	—	3	1	no	—
59	C₅×#387	—	3	1	no	—
60	C₅×#387	—	3	1	no	—
61	C₅×#386	—	3	1	no	—
62	C₅×#386	—	3	1	no	—
63	C₅×#386	—	3	1	no	—
64	C₅×#386	D₃	1	1	yes	characteristic, complemented
65	C₅×#385	—	3	1	no	—
66	C₅×#385	—	3	1	no	—
67	C₅×#381	—	3	1	no	—
68	C₅×#380	—	3	1	no	—
69	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
71	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×D₄	—	4	1	no	—
73	C₂×C₃×C₅×D₄	—	4	1	no	—
74	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
75	C₂²×C₃×C₄×C₅	—	4	1	no	—
76	C₂²×C₃×C₄×C₅	—	4	1	no	—
77	C₂²×C₃×C₄×C₅	—	4	1	no	—
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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₅×#67	—	4	1	no	—
84	C₂×C₅×#67	—	4	1	no	—
85	C₂×C₅×#67	—	4	1	no	—
86	C₂×C₅×#67	—	4	1	no	—
87	C₂×C₅×#67	C₂×C₄	1	4	yes	—
88	C₂×C₅×#67	C₂×C₄	1	4	yes	complemented
89	C₂²×C₅×Dic₃	—	4	1	no	—
90	C₂²×C₅×Dic₃	—	4	1	no	—
91	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
92	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
93	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
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	C₂×C₄×C₅×D₃	—	4	1	no	—
100	C₂×C₄×C₅×D₃	—	4	1	no	—
101	C₂×C₄×C₅×D₃	—	4	1	no	—
102	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
103	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
104	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
105	C₅×#217	—	4	1	no	—
106	C₅×#217	—	4	1	no	—
107	C₅×#217	—	4	1	no	—
108	C₅×#217	—	4	1	no	—
109	C₅×#217	C₂×C₄	1	4	yes	complemented
110	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
111	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
112	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
113	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
114	C₅×C₄⋊Dic₃	—	4	1	no	—
115	C₅×Dic₃⋊C₄	—	4	1	no	—
116	C₅×Dic₃⋊C₄	—	4	1	no	—
117	C₅×Dic₃⋊C₄	—	4	1	no	—
118	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	complemented
119	C₄×C₅×Dic₃	—	4	1	no	—
120	C₄×C₅×Dic₃	—	4	1	no	—
121	C₂×#939	C₂×C₅	1	1	yes	characteristic
122	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
123	#5221	C₂×C₅	1	1	yes	characteristic, complemented
124	#5213	C₂×C₅	1	1	yes	characteristic, complemented
125	#5210	C₂×C₅	1	1	yes	characteristic, complemented
126	#4957	C₂×C₅	1	1	yes	characteristic, complemented
127	#4956	C₂×C₅	1	1	yes	characteristic, complemented
128	#4956	C₂×C₅	1	1	yes	characteristic, complemented
129	#4944	C₂×C₅	1	1	yes	characteristic, complemented
130	#4943	C₂×C₅	1	1	yes	characteristic, complemented
131	#4942	C₂×C₅	1	1	yes	characteristic, complemented
132	#4669	C₂×C₅	1	1	yes	characteristic, complemented
133	#4668	C₂×C₅	1	1	yes	characteristic, complemented
134	#4655	C₂×C₅	1	1	yes	characteristic, complemented
135	#4652	C₂×C₅	1	1	yes	characteristic, complemented
136	C₂²×C₅×D₄	—	3	1	no	—
137	C₂²×C₅×D₄	—	3	1	no	—
138	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
139	C₂³×C₄×C₅	—	3	1	no	—
140	C₂³×C₄×C₅	—	3	1	no	—
141	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
142	C₅×#121	—	3	8	no	—
143	C₂×C₅×C₄⋊C₄	—	3	1	no	—
144	C₂×C₅×C₄⋊C₄	—	3	1	no	—
145	C₂×C₅×C₄⋊C₄	—	3	1	no	—
146	C₂×C₅×C₄⋊C₄	—	3	1	no	—
147	C₂×C₅×C₄⋊C₄	—	3	1	no	—
148	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
149	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
150	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
151	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
152	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
153	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
154	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
155	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
156	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
157	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
158	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
159	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
160	C₂×C₄²×C₅	—	3	1	no	—
161	C₂×C₄²×C₅	—	3	1	no	—
162	C₅×#95	—	3	1	no	—
163	C₅×#95	—	3	1	no	—
164	C₅×#95	—	3	1	no	—
165	C₅×#95	—	3	1	no	—
166	C₅×#95	—	3	1	no	—
167	C₅×#95	—	3	1	no	—
168	C₅×#95	—	3	1	no	—
169	C₅×#95	—	3	1	no	—
170	C₅×#95	C₂×D₃	1	1	yes	characteristic
171	C₅×#95	C₂×D₃	1	1	yes	characteristic
172	#2377	—	3	1	no	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	—	2	1	no	—
184	C₂³×C₃×C₅	—	2	1	no	—
185	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
186	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
187	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
188	C₂²×C₅×D₃	—	2	1	no	—
189	C₂²×C₅×D₃	—	2	1	no	—
190	C₂²×C₅×D₃	—	2	1	no	—
191	C₂²×C₅×D₃	—	2	1	no	—
192	C₂²×C₅×D₃	—	2	1	no	—
193	C₂²×C₅×D₃	—	2	1	no	—
194	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
195	C₃×C₅×D₄	—	4	4	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	—	4	4	no	—
211	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
212	C₅×#67	—	4	4	no	—
213	C₅×#67	—	4	4	no	—
214	C₂×C₅×Dic₃	—	2	1	no	—
215	C₂×C₅×Dic₃	—	2	1	no	—
216	C₂×C₅×Dic₃	—	2	1	no	—
217	C₂×C₅×Dic₃	—	2	1	no	—
218	C₂×C₅×Dic₃	—	2	1	no	—
219	C₂×C₅×Dic₃	—	2	1	no	—
220	C₂×C₅×Dic₃	—	2	1	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	1	no	—
230	C₂×C₅×Dic₃	—	2	1	no	—
231	C₂×C₅×Dic₃	—	2	1	no	—
232	C₂×C₅×Dic₃	—	4	4	no	—
233	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
234	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
235	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
236	C₄×C₅×D₃	—	4	4	no	—
237	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
238	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
239	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
240	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
241	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
242	C₂²×C₄×D₃	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×#217	C₂²×C₅	1	1	yes	characteristic
247	C₂×#217	C₂²×C₅	1	1	yes	characteristic
248	C₂×#217	C₂²×C₅	1	1	yes	characteristic
249	C₂×#217	C₂²×C₅	1	1	yes	characteristic
250	C₂×#217	C₂²×C₅	1	1	yes	characteristic
251	#939	C₄×C₅	1	8	yes	complemented
252	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
253	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
254	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
255	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
257	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
258	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
259	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
260	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₄×Dic₃	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	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
271	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
272	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
273	C₂⁴×C₅	—	3	1	no	—
274	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
275	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
276	C₂×C₅×D₄	—	3	4	no	—
277	C₂×C₅×D₄	—	3	4	no	—
278	C₂×C₅×D₄	—	4	1	no	—
279	C₂×C₅×D₄	—	4	1	no	—
280	C₂×C₅×D₄	—	12	1	no	—
281	C₂×C₅×D₄	—	12	1	no	—
282	C₂×C₅×D₄	—	12	1	no	—
283	C₂×C₅×D₄	—	12	1	no	—
284	C₂×C₅×D₄	C₄×D₃	1	4	yes	complemented
285	C₂²×C₄×C₅	—	3	1	no	—
286	C₂²×C₄×C₅	—	3	1	no	—
287	C₂²×C₄×C₅	—	3	1	no	—
288	C₂²×C₄×C₅	—	3	4	no	—
289	C₂²×C₄×C₅	—	3	1	no	—
290	C₂²×C₄×C₅	—	3	1	no	—
291	C₂²×C₄×C₅	—	3	1	no	—
292	C₂²×C₄×C₅	—	3	1	no	—
293	C₂²×C₄×C₅	—	4	1	no	—
294	C₂²×C₄×C₅	—	4	1	no	—
295	C₂²×C₄×C₅	—	4	1	no	—
296	C₂²×C₄×C₅	—	12	1	no	—
297	C₂²×C₄×C₅	—	12	1	no	—
298	C₂²×C₄×C₅	—	12	1	no	—
299	C₂²×C₄×C₅	—	12	1	no	—
300	C₂²×C₄×C₅	—	12	1	no	—
301	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
302	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
303	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
304	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
305	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
306	C₅×C₄⋊C₄	—	3	4	no	—
307	C₅×C₄⋊C₄	—	12	1	no	—
308	C₅×C₄⋊C₄	—	12	1	no	—
309	C₅×C₄⋊C₄	—	12	1	no	—
310	C₅×C₄⋊C₄	—	12	1	no	—
311	C₅×C₂²⋊C₄	—	3	4	no	—
312	C₅×C₂²⋊C₄	—	3	4	no	—
313	C₅×C₂²⋊C₄	—	4	1	no	—
314	C₅×C₂²⋊C₄	—	4	1	no	—
315	C₅×C₂²⋊C₄	—	4	1	no	—
316	C₅×C₂²⋊C₄	—	12	1	no	—
317	C₅×C₂²⋊C₄	—	12	1	no	—
318	C₅×C₂²⋊C₄	—	12	1	no	—
319	C₅×C₂²⋊C₄	—	12	1	no	—
320	C₅×C₂²⋊C₄	—	12	1	no	—
321	C₅×C₂²⋊C₄	—	12	1	no	—
322	C₅×C₂²⋊C₄	—	12	1	no	—
323	C₄²×C₅	—	12	1	no	—
324	C₄²×C₅	—	12	1	no	—
325	C₂×#121	—	3	1	no	—
326	#390	—	3	1	no	—
327	#390	—	3	1	no	—
328	#388	—	3	1	no	—
329	#388	—	3	1	no	—
330	#387	—	3	1	no	—
331	#387	—	3	1	no	—
332	#386	—	3	1	no	—
333	#386	—	3	1	no	—
334	#386	—	3	1	no	—
335	#386	C₅×D₃	1	1	yes	characteristic, complemented
336	#385	—	3	1	no	—
337	#385	—	3	1	no	—
338	#381	—	3	1	no	—
339	#380	—	3	1	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	—	2	2	no	—
345	C₂²×C₃×C₅	—	2	2	no	—
346	C₂²×C₃×C₅	—	4	1	no	—
347	C₂²×C₃×C₅	—	4	1	no	—
348	C₂²×C₃×C₅	—	4	1	no	—
349	C₂²×C₃×C₅	—	4	1	no	—
350	C₂²×C₃×C₅	—	4	1	no	—
351	C₂²×C₃×C₅	—	4	1	no	—
352	C₂²×C₃×C₅	—	4	1	no	—
353	C₂²×C₃×C₅	—	4	1	no	—
354	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
355	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
356	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
357	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
358	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
359	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
360	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
361	C₂×C₅×D₃	—	2	2	no	—
362	C₂×C₅×D₃	—	2	2	no	—
363	C₂×C₅×D₃	—	2	2	no	—
364	C₂×C₅×D₃	—	4	1	no	—
365	C₂×C₅×D₃	—	4	1	no	—
366	C₂×C₅×D₃	—	4	1	no	—
367	C₂×C₅×D₃	—	4	1	no	—
368	C₃×C₄×C₅	—	2	2	no	—
369	C₃×C₄×C₅	—	4	1	no	—
370	C₃×C₄×C₅	—	4	1	no	—
371	C₃×C₄×C₅	—	4	1	no	—
372	C₃×C₄×C₅	—	4	1	no	—
373	C₅×Dic₃	—	2	2	no	—
374	C₅×Dic₃	—	2	2	no	—
375	C₅×Dic₃	—	2	2	no	—
376	C₅×Dic₃	—	4	1	no	—
377	C₅×Dic₃	—	4	1	no	—
378	C₅×Dic₃	—	4	1	no	—
379	C₅×Dic₃	—	4	1	no	—
380	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
381	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
382	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
383	C₂×C₃×D₄	—	4	1	no	—
384	C₂×C₃×D₄	—	4	1	no	—
385	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
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	C₂×#67	—	4	1	no	—
395	C₂×#67	—	4	1	no	—
396	C₂×#67	—	4	1	no	—
397	C₂×#67	—	4	1	no	—
398	C₂×#67	C₂×C₄×C₅	1	4	yes	—
399	C₂×#67	C₂×C₄×C₅	1	4	yes	complemented
400	C₂²×Dic₃	—	4	1	no	—
401	C₂²×Dic₃	—	4	1	no	—
402	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
403	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
404	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
405	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
406	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
407	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
408	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
409	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₄×D₃	—	4	1	no	—
411	C₂×C₄×D₃	—	4	1	no	—
412	C₂×C₄×D₃	—	4	1	no	—
413	C₃×C₂²⋊C₄	—	4	1	no	—
414	C₃×C₂²⋊C₄	—	4	1	no	—
415	C₃×C₂²⋊C₄	—	4	1	no	—
416	#217	—	4	1	no	—
417	#217	—	4	1	no	—
418	#217	—	4	1	no	—
419	#217	—	4	1	no	—
420	#217	C₂×C₄×C₅	1	4	yes	complemented
421	(C₂×D₃)⋊C₄	—	4	1	no	—
422	(C₂×D₃)⋊C₄	—	4	1	no	—
423	(C₂×D₃)⋊C₄	—	4	1	no	—
424	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
425	C₄⋊Dic₃	—	4	1	no	—
426	Dic₃⋊C₄	—	4	1	no	—
427	Dic₃⋊C₄	—	4	1	no	—
428	Dic₃⋊C₄	—	4	1	no	—
429	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
430	C₄×Dic₃	—	4	1	no	—
431	C₄×Dic₃	—	4	1	no	—
432	C₂³×C₅	—	2	1	no	—
433	C₂³×C₅	—	2	1	no	—
434	C₂³×C₅	—	2	1	no	—
435	C₂³×C₅	—	2	1	no	—
436	C₂³×C₅	—	2	1	no	—
437	C₂³×C₅	—	2	1	no	—
438	C₂³×C₅	—	2	1	no	—
439	C₂³×C₅	—	2	1	no	—
440	C₂³×C₅	—	2	1	no	—
441	C₂³×C₅	—	2	1	no	—
442	C₂³×C₅	—	2	1	no	—
443	C₂³×C₅	—	2	1	no	—
444	C₂³×C₅	—	3	2	no	—
445	C₂³×C₅	—	6	1	no	—
446	C₂³×C₅	—	6	1	no	—
447	C₂³×C₅	—	6	1	no	—
448	C₂³×C₅	—	6	1	no	—
449	C₂³×C₅	—	6	1	no	—
450	C₂³×C₅	—	6	1	no	—
451	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
452	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
453	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
454	C₅×D₄	—	4	4	no	—
455	C₅×D₄	—	12	4	no	—
456	C₅×D₄	—	12	4	no	—
457	C₂×C₄×C₅	—	2	1	no	—
458	C₂×C₄×C₅	—	2	1	no	—
459	C₂×C₄×C₅	—	2	1	no	—
460	C₂×C₄×C₅	—	2	1	no	—
461	C₂×C₄×C₅	—	2	1	no	—
462	C₂×C₄×C₅	—	2	1	no	—
463	C₂×C₄×C₅	—	2	1	no	—
464	C₂×C₄×C₅	—	2	1	no	—
465	C₂×C₄×C₅	—	2	1	no	—
466	C₂×C₄×C₅	—	2	1	no	—
467	C₂×C₄×C₅	—	2	1	no	—
468	C₂×C₄×C₅	—	2	1	no	—
469	C₂×C₄×C₅	—	2	1	no	—
470	C₂×C₄×C₅	—	2	1	no	—
471	C₂×C₄×C₅	—	3	2	no	—
472	C₂×C₄×C₅	—	3	2	no	—
473	C₂×C₄×C₅	—	3	2	no	—
474	C₂×C₄×C₅	—	4	4	no	—
475	C₂×C₄×C₅	—	6	1	no	—
476	C₂×C₄×C₅	—	6	1	no	—
477	C₂×C₄×C₅	—	6	1	no	—
478	C₂×C₄×C₅	—	6	1	no	—
479	C₂×C₄×C₅	—	6	1	no	—
480	C₂×C₄×C₅	—	6	1	no	—
481	C₂×C₄×C₅	—	6	1	no	—
482	C₂×C₄×C₅	—	6	1	no	—
483	C₂×C₄×C₅	—	6	1	no	—
484	C₂×C₄×C₅	—	6	1	no	—
485	C₂×C₄×C₅	—	6	1	no	—
486	C₂×C₄×C₅	—	6	1	no	—
487	C₂×C₄×C₅	—	6	1	no	—
488	C₂×C₄×C₅	—	6	1	no	—
489	C₂×C₄×C₅	—	6	1	no	—
490	C₂×C₄×C₅	—	6	1	no	—
491	C₂×C₄×C₅	—	6	1	no	—
492	C₂×C₄×C₅	—	6	1	no	—
493	C₂×C₄×C₅	—	12	4	no	—
494	C₂×C₄×C₅	—	12	4	no	—
495	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
496	C₂²×D₄	—	3	1	no	—
497	C₂²×D₄	—	3	1	no	—
498	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
499	C₂³×C₄	—	3	1	no	—
500	C₂³×C₄	—	3	1	no	—
501	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
502	#121	—	3	8	no	—
503	C₂×C₄⋊C₄	—	3	1	no	—
504	C₂×C₄⋊C₄	—	3	1	no	—
505	C₂×C₄⋊C₄	—	3	1	no	—
506	C₂×C₄⋊C₄	—	3	1	no	—
507	C₂×C₄⋊C₄	—	3	1	no	—
508	C₂×C₂²⋊C₄	—	3	1	no	—
509	C₂×C₂²⋊C₄	—	3	1	no	—
510	C₂×C₂²⋊C₄	—	3	1	no	—
511	C₂×C₂²⋊C₄	—	3	1	no	—
512	C₂×C₂²⋊C₄	—	3	1	no	—
513	C₂×C₂²⋊C₄	—	3	1	no	—
514	C₂×C₂²⋊C₄	—	3	1	no	—
515	C₂×C₂²⋊C₄	—	3	1	no	—
516	C₂×C₂²⋊C₄	—	3	1	no	—
517	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
520	C₂×C₄²	—	3	1	no	—
521	C₂×C₄²	—	3	1	no	—
522	#95	—	3	1	no	—
523	#95	—	3	1	no	—
524	#95	—	3	1	no	—
525	#95	—	3	1	no	—
526	#95	—	3	1	no	—
527	#95	—	3	1	no	—
528	#95	—	3	1	no	—
529	#95	—	3	1	no	—
530	#95	C₂×C₅×D₃	1	1	yes	characteristic
531	#95	C₂×C₅×D₃	1	1	yes	characteristic
532	C₂×C₃×C₅	—	4	2	no	—
533	C₂×C₃×C₅	—	4	2	no	—
534	C₂×C₃×C₅	#518	1	1	yes	characteristic
535	C₂×C₃×C₅	#518	1	1	yes	characteristic
536	C₂×C₃×C₅	#520	1	1	yes	characteristic
537	C₂×C₃×C₅	#560	1	1	yes	characteristic
538	C₂×C₃×C₅	#560	1	1	yes	characteristic
539	C₂×C₃×C₅	#562	1	1	yes	characteristic
540	C₂×C₃×C₅	#562	1	1	yes	characteristic
541	C₅×D₃	—	4	2	no	—
542	C₂³×C₃	—	2	1	no	—
543	C₂³×C₃	—	2	1	no	—
544	C₂³×C₃	—	2	1	no	—
545	C₂³×C₃	—	2	1	no	—
546	C₂³×C₃	—	2	1	no	—
547	C₂³×C₃	—	2	1	no	—
548	C₂³×C₃	—	2	1	no	—
549	C₂³×C₃	—	2	1	no	—
550	C₂³×C₃	—	2	1	no	—
551	C₂³×C₃	—	2	1	no	—
552	C₂³×C₃	—	2	1	no	—
553	C₂³×C₃	—	2	1	no	—
554	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
555	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
556	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
557	C₂²×D₃	—	2	1	no	—
558	C₂²×D₃	—	2	1	no	—
559	C₂²×D₃	—	2	1	no	—
560	C₂²×D₃	—	2	1	no	—
561	C₂²×D₃	—	2	1	no	—
562	C₂²×D₃	—	2	1	no	—
563	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
564	C₃×D₄	—	4	4	no	—
565	C₂×C₃×C₄	—	2	1	no	—
566	C₂×C₃×C₄	—	2	1	no	—
567	C₂×C₃×C₄	—	2	1	no	—
568	C₂×C₃×C₄	—	2	1	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	2	1	no	—
572	C₂×C₃×C₄	—	2	1	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	2	1	no	—
575	C₂×C₃×C₄	—	2	1	no	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	2	1	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	4	4	no	—
580	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
581	#67	—	4	4	no	—
582	#67	—	4	4	no	—
583	C₂×Dic₃	—	2	1	no	—
584	C₂×Dic₃	—	2	1	no	—
585	C₂×Dic₃	—	2	1	no	—
586	C₂×Dic₃	—	2	1	no	—
587	C₂×Dic₃	—	2	1	no	—
588	C₂×Dic₃	—	2	1	no	—
589	C₂×Dic₃	—	2	1	no	—
590	C₂×Dic₃	—	2	1	no	—
591	C₂×Dic₃	—	2	1	no	—
592	C₂×Dic₃	—	2	1	no	—
593	C₂×Dic₃	—	2	1	no	—
594	C₂×Dic₃	—	2	1	no	—
595	C₂×Dic₃	—	2	1	no	—
596	C₂×Dic₃	—	2	1	no	—
597	C₂×Dic₃	—	2	1	no	—
598	C₂×Dic₃	—	2	1	no	—
599	C₂×Dic₃	—	2	1	no	—
600	C₂×Dic₃	—	2	1	no	—
601	C₂×Dic₃	—	4	4	no	—
602	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
603	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
604	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
605	C₄×D₃	—	4	4	no	—
606	C₂²×C₅	—	2	2	no	—
607	C₂²×C₅	—	2	2	no	—
608	C₂²×C₅	—	2	2	no	—
609	C₂²×C₅	—	2	2	no	—
610	C₂²×C₅	—	2	2	no	—
611	C₂²×C₅	—	2	2	no	—
612	C₂²×C₅	—	4	1	no	—
613	C₂²×C₅	—	4	1	no	—
614	C₂²×C₅	—	4	1	no	—
615	C₂²×C₅	—	4	1	no	—
616	C₂²×C₅	—	4	1	no	—
617	C₂²×C₅	—	4	1	no	—
618	C₂²×C₅	—	4	1	no	—
619	C₂²×C₅	—	4	1	no	—
620	C₂²×C₅	—	6	2	no	—
621	C₂²×C₅	—	6	2	no	—
622	C₂²×C₅	—	6	2	no	—
623	C₂²×C₅	—	12	1	no	—
624	C₂²×C₅	—	12	1	no	—
625	C₂²×C₅	—	12	1	no	—
626	C₂²×C₅	—	12	1	no	—
627	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
628	C₂²×C₅	#1004	1	1	yes	characteristic
629	C₂²×C₅	#1004	1	1	yes	characteristic
630	C₂²×C₅	#1004	1	1	yes	characteristic
631	C₂²×C₅	#1004	1	1	yes	characteristic
632	C₂²×C₅	#1009	1	1	yes	characteristic
633	C₂²×C₅	#1010	1	1	yes	characteristic
634	C₄×C₅	—	2	2	no	—
635	C₄×C₅	—	4	1	no	—
636	C₄×C₅	—	4	1	no	—
637	C₄×C₅	—	4	1	no	—
638	C₄×C₅	—	4	1	no	—
639	C₄×C₅	—	6	2	no	—
640	C₄×C₅	—	6	2	no	—
641	C₄×C₅	—	6	2	no	—
642	C₄×C₅	—	12	1	no	—
643	C₄×C₅	—	12	1	no	—
644	C₄×C₅	—	12	1	no	—
645	C₄×C₅	—	12	1	no	—
646	C₂⁴	—	3	1	no	—
647	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
648	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
649	C₂×D₄	—	3	4	no	—
650	C₂×D₄	—	3	4	no	—
651	C₂×D₄	—	4	1	no	—
652	C₂×D₄	—	4	1	no	—
653	C₂×D₄	—	12	1	no	—
654	C₂×D₄	—	12	1	no	—
655	C₂×D₄	—	12	1	no	—
656	C₂×D₄	—	12	1	no	—
657	C₂×D₄	C₄×C₅×D₃	1	4	yes	complemented
658	C₂²×C₄	—	3	1	no	—
659	C₂²×C₄	—	3	1	no	—
660	C₂²×C₄	—	3	1	no	—
661	C₂²×C₄	—	3	4	no	—
662	C₂²×C₄	—	3	1	no	—
663	C₂²×C₄	—	3	1	no	—
664	C₂²×C₄	—	3	1	no	—
665	C₂²×C₄	—	3	1	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	—	4	1	no	—
668	C₂²×C₄	—	4	1	no	—
669	C₂²×C₄	—	12	1	no	—
670	C₂²×C₄	—	12	1	no	—
671	C₂²×C₄	—	12	1	no	—
672	C₂²×C₄	—	12	1	no	—
673	C₂²×C₄	—	12	1	no	—
674	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
675	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
676	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
677	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
678	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
679	C₄⋊C₄	—	3	4	no	—
680	C₄⋊C₄	—	12	1	no	—
681	C₄⋊C₄	—	12	1	no	—
682	C₄⋊C₄	—	12	1	no	—
683	C₄⋊C₄	—	12	1	no	—
684	C₂²⋊C₄	—	3	4	no	—
685	C₂²⋊C₄	—	3	4	no	—
686	C₂²⋊C₄	—	4	1	no	—
687	C₂²⋊C₄	—	4	1	no	—
688	C₂²⋊C₄	—	4	1	no	—
689	C₂²⋊C₄	—	12	1	no	—
690	C₂²⋊C₄	—	12	1	no	—
691	C₂²⋊C₄	—	12	1	no	—
692	C₂²⋊C₄	—	12	1	no	—
693	C₂²⋊C₄	—	12	1	no	—
694	C₂²⋊C₄	—	12	1	no	—
695	C₂²⋊C₄	—	12	1	no	—
696	C₄²	—	12	1	no	—
697	C₄²	—	12	1	no	—
698	C₃×C₅	#2377	1	1	yes	characteristic, complemented, Hall
699	C₂²×C₃	—	2	2	no	—
700	C₂²×C₃	—	2	2	no	—
701	C₂²×C₃	—	2	2	no	—
702	C₂²×C₃	—	2	2	no	—
703	C₂²×C₃	—	2	2	no	—
704	C₂²×C₃	—	2	2	no	—
705	C₂²×C₃	—	4	1	no	—
706	C₂²×C₃	—	4	1	no	—
707	C₂²×C₃	—	4	1	no	—
708	C₂²×C₃	—	4	1	no	—
709	C₂²×C₃	—	4	1	no	—
710	C₂²×C₃	—	4	1	no	—
711	C₂²×C₃	—	4	1	no	—
712	C₂²×C₃	—	4	1	no	—
713	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
714	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
715	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
716	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
717	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
718	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
719	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
720	C₂×D₃	—	2	2	no	—
721	C₂×D₃	—	2	2	no	—
722	C₂×D₃	—	2	2	no	—
723	C₂×D₃	—	4	1	no	—
724	C₂×D₃	—	4	1	no	—
725	C₂×D₃	—	4	1	no	—
726	C₂×D₃	—	4	1	no	—
727	C₃×C₄	—	2	2	no	—
728	C₃×C₄	—	4	1	no	—
729	C₃×C₄	—	4	1	no	—
730	C₃×C₄	—	4	1	no	—
731	C₃×C₄	—	4	1	no	—
732	Dic₃	—	2	2	no	—
733	Dic₃	—	2	2	no	—
734	Dic₃	—	2	2	no	—
735	Dic₃	—	4	1	no	—
736	Dic₃	—	4	1	no	—
737	Dic₃	—	4	1	no	—
738	Dic₃	—	4	1	no	—
739	C₂×C₅	—	4	2	no	—
740	C₂×C₅	—	4	2	no	—
741	C₂×C₅	—	12	2	no	—
742	C₂×C₅	#5486	1	1	yes	characteristic
743	C₂×C₅	#5545	1	1	yes	characteristic
744	C₂×C₅	#5546	1	1	yes	characteristic
745	C₂×C₅	#5595	1	1	yes	characteristic
746	C₂×C₅	#5620	1	1	yes	characteristic
747	C₂×C₅	#5621	1	1	yes	characteristic
748	C₂×C₅	#5667	1	1	yes	characteristic
749	C₂³	—	2	1	no	—
750	C₂³	—	2	1	no	—
751	C₂³	—	2	1	no	—
752	C₂³	—	2	1	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	3	2	no	—
762	C₂³	—	6	1	no	—
763	C₂³	—	6	1	no	—
764	C₂³	—	6	1	no	—
765	C₂³	—	6	1	no	—
766	C₂³	—	6	1	no	—
767	C₂³	—	6	1	no	—
768	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
769	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
770	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
771	D₄	—	4	4	no	—
772	D₄	—	12	4	no	—
773	D₄	—	12	4	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	3	2	no	—
789	C₂×C₄	—	3	2	no	—
790	C₂×C₄	—	3	2	no	—
791	C₂×C₄	—	4	4	no	—
792	C₂×C₄	—	6	1	no	—
793	C₂×C₄	—	6	1	no	—
794	C₂×C₄	—	6	1	no	—
795	C₂×C₄	—	6	1	no	—
796	C₂×C₄	—	6	1	no	—
797	C₂×C₄	—	6	1	no	—
798	C₂×C₄	—	6	1	no	—
799	C₂×C₄	—	6	1	no	—
800	C₂×C₄	—	6	1	no	—
801	C₂×C₄	—	6	1	no	—
802	C₂×C₄	—	6	1	no	—
803	C₂×C₄	—	6	1	no	—
804	C₂×C₄	—	6	1	no	—
805	C₂×C₄	—	6	1	no	—
806	C₂×C₄	—	6	1	no	—
807	C₂×C₄	—	6	1	no	—
808	C₂×C₄	—	6	1	no	—
809	C₂×C₄	—	6	1	no	—
810	C₂×C₄	—	12	4	no	—
811	C₂×C₄	—	12	4	no	—
812	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
813	C₂×C₃	—	4	2	no	—
814	C₂×C₃	—	4	2	no	—
815	C₂×C₃	C₅×#518	1	1	yes	characteristic
816	C₂×C₃	C₅×#518	1	1	yes	characteristic
817	C₂×C₃	C₅×#520	1	1	yes	characteristic
818	C₂×C₃	C₅×#560	1	1	yes	characteristic
819	C₂×C₃	C₅×#560	1	1	yes	characteristic
820	C₂×C₃	C₅×#562	1	1	yes	characteristic
821	C₂×C₃	C₅×#562	1	1	yes	characteristic
822	D₃	—	4	2	no	—
823	C₅	#74683	1	1	yes	characteristic, direct product factor, Sylow
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	6	2	no	—
839	C₂²	—	6	2	no	—
840	C₂²	—	6	2	no	—
841	C₂²	—	12	1	no	—
842	C₂²	—	12	1	no	—
843	C₂²	—	12	1	no	—
844	C₂²	—	12	1	no	—
845	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
846	C₂²	C₅×#1004	1	1	yes	characteristic
847	C₂²	C₅×#1004	1	1	yes	characteristic
848	C₂²	C₅×#1004	1	1	yes	characteristic
849	C₂²	C₅×#1004	1	1	yes	characteristic
850	C₂²	C₅×#1009	1	1	yes	characteristic
851	C₂²	C₅×#1010	1	1	yes	characteristic
852	C₄	—	2	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	1	no	—
857	C₄	—	6	2	no	—
858	C₄	—	6	2	no	—
859	C₄	—	6	2	no	—
860	C₄	—	12	1	no	—
861	C₄	—	12	1	no	—
862	C₄	—	12	1	no	—
863	C₄	—	12	1	no	—
864	C₃	C₅×#2377	1	1	yes	characteristic, complemented, Sylow
865	C₂	—	4	2	no	—
866	C₂	—	4	2	no	—
867	C₂	—	12	2	no	—
868	C₂	C₅×#5486	1	1	yes	characteristic
869	C₂	C₅×#5545	1	1	yes	characteristic
870	C₂	C₅×#5546	1	1	yes	characteristic
871	C₂	C₅×#5595	1	1	yes	characteristic
872	C₂	C₅×#5620	1	1	yes	characteristic
873	C₂	C₅×#5621	1	1	yes	characteristic
874	C₂	C₅×#5667	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×#386	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#939	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#386	D₃
hypocenter	C₃	C₅×#2377
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#386

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#386	C₂	semidirect
3. C₅×#5221	C₂	semidirect
4. C₅×#5213	C₂	semidirect
5. C₅×#5210	C₂	semidirect
6. C₅×#4957	C₂	semidirect
7. C₅×#4956	C₂	semidirect
8. C₅×#4956	C₂	semidirect
9. C₅×#4944	C₂	semidirect
10. C₅×#4943	C₂	semidirect
11. C₅×#4942	C₂	semidirect
12. C₅×#4669	C₂	semidirect
13. C₅×#4668	C₂	semidirect
14. C₅×#4655	C₂	semidirect
15. C₅×#4652	C₂	semidirect
31. C₅×#939	C₄	semidirect
53. #74683	C₅	direct (N × H)
64. C₅×#386	D₃	semidirect
74. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
88. C₂×C₅×#67	C₂×C₄	semidirect
91. C₂²×C₅×Dic₃	C₂×C₄	semidirect
109. C₅×#217	C₂×C₄	semidirect
113. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
118. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
122. C₃×#386	C₂×C₅	semidirect
123. #5221	C₂×C₅	semidirect
124. #5213	C₂×C₅	semidirect
125. #5210	C₂×C₅	semidirect
126. #4957	C₂×C₅	semidirect
127. #4956	C₂×C₅	semidirect
128. #4956	C₂×C₅	semidirect
129. #4944	C₂×C₅	semidirect
130. #4943	C₂×C₅	semidirect
131. #4942	C₂×C₅	semidirect
132. #4669	C₂×C₅	semidirect
133. #4668	C₂×C₅	semidirect
134. #4655	C₂×C₅	semidirect
135. #4652	C₂×C₅	semidirect
251. #939	C₄×C₅	semidirect
284. C₂×C₅×D₄	C₄×D₃	semidirect
335. #386	C₅×D₃	semidirect
385. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
399. C₂×#67	C₂×C₄×C₅	semidirect
402. C₂²×Dic₃	C₂×C₄×C₅	semidirect
420. #217	C₂×C₄×C₅	semidirect
424. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
429. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
657. C₂×D₄	C₄×C₅×D₃	semidirect
698. C₃×C₅	#2377	semidirect
823. C₅	#74683	direct (N × H)
864. C₃	C₅×#2377	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
C₃×C₅×#386	2
C₅×#5221	2
C₅×#5213	2
C₅×#5210	2
C₅×#4957	2
C₅×#4956	2
C₅×#4944	2
C₅×#4943	2
C₅×#4942	2
C₅×#4669	2
C₅×#4668	2
C₅×#4655	2
C₅×#4652	2
C₅×#2377	3
#74683	5

Subgroups — C5×#74683 #14330852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#74683 #14330852