Subgroups — C₅×#75458 #14323141

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4987	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4976	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4957	C₂	1	1	yes	maximal, characteristic
6	C₅×#4957	C₂	1	1	yes	maximal, characteristic
7	C₅×#4951	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4943	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4940	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4669	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4664	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4648	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4647	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2319	—	3	1	no	maximal, Hall
17	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
18	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₂×C₅×#217	C₂²	1	1	yes	characteristic
26	C₂×C₅×#217	C₂²	1	1	yes	characteristic
27	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
33	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
42	C₅×#67⋊C₄	C₄	1	8	yes	complemented
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	#75458	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
54	C₂×C₄×C₅×D₄	—	3	1	no	—
55	C₅×#390	—	3	1	no	—
56	C₅×#390	—	3	1	no	—
57	C₅×#389	—	3	1	no	—
58	C₅×#389	—	3	1	no	—
59	C₅×#388	—	3	1	no	—
60	C₅×#388	—	3	1	no	—
61	C₅×#388	—	3	1	no	—
62	C₅×#388	D₃	1	1	yes	characteristic, complemented
63	C₅×#381	—	3	1	no	—
64	C₅×#381	—	3	1	no	—
65	C₅×#380	—	3	1	no	—
66	C₅×#380	—	3	1	no	—
67	C₄×C₅×C₄⋊C₄	—	3	1	no	—
68	C₅×#376	—	3	1	no	—
69	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₅×#67	—	2	2	no	—
78	C₂×C₅×#67	—	2	2	no	—
79	C₂×C₅×#67	C₂×C₄	1	4	yes	—
80	C₂²×C₅×Dic₃	—	4	1	no	—
81	C₂²×C₅×Dic₃	—	4	1	no	—
82	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
83	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
85	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
86	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
87	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
88	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
89	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
90	C₂×C₄×C₅×D₃	—	4	1	no	—
91	C₂×C₄×C₅×D₃	—	4	1	no	—
92	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
93	C₃×C₅×C₄⋊C₄	—	4	1	no	—
94	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
95	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
96	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
97	C₃×C₄²×C₅	—	4	1	no	—
98	C₅×#217	—	4	1	no	—
99	C₅×#217	—	4	1	no	—
100	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
101	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
102	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
103	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
104	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
105	C₅×C₄⋊Dic₃	—	4	1	no	—
106	C₅×Dic₃⋊C₄	—	2	2	no	—
107	C₅×Dic₃⋊C₄	—	2	2	no	—
108	C₅×Dic₃⋊C₄	—	4	1	no	—
109	C₅×Dic₃⋊C₄	—	4	1	no	—
110	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
111	C₄×C₅×Dic₃	—	2	2	no	—
112	C₄×C₅×Dic₃	—	2	2	no	—
113	C₄×C₅×Dic₃	—	4	1	no	—
114	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
115	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic
116	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
117	#4987	C₂×C₅	1	1	yes	characteristic, complemented
118	#4976	C₂×C₅	1	1	yes	characteristic, complemented
119	#4957	C₂×C₅	1	1	yes	characteristic
120	#4957	C₂×C₅	1	1	yes	characteristic
121	#4951	C₂×C₅	1	1	yes	characteristic, complemented
122	#4943	C₂×C₅	1	1	yes	characteristic, complemented
123	#4942	C₂×C₅	1	1	yes	characteristic, complemented
124	#4940	C₂×C₅	1	1	yes	characteristic, complemented
125	C₄×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
126	#4669	C₂×C₅	1	1	yes	characteristic, complemented
127	#4664	C₂×C₅	1	1	yes	characteristic, complemented
128	#4648	C₂×C₅	1	1	yes	characteristic, complemented
129	#4647	C₂×C₅	1	1	yes	characteristic, complemented
130	C₂²×C₅×D₄	—	3	1	no	—
131	C₂³×C₄×C₅	—	3	1	no	—
132	C₂³×C₄×C₅	—	3	1	no	—
133	C₄×C₅×D₄	—	3	8	no	—
134	C₂×C₅×C₄⋊C₄	—	3	1	no	—
135	C₂×C₅×C₄⋊C₄	—	3	1	no	—
136	C₂×C₅×C₄⋊C₄	—	3	1	no	—
137	C₂×C₅×C₄⋊C₄	—	3	1	no	—
138	C₂×C₅×C₄⋊C₄	—	3	1	no	—
139	C₂×C₅×C₄⋊C₄	—	3	1	no	—
140	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
141	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
142	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
143	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
144	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
145	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
146	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
147	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
148	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
149	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
150	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
151	C₂×C₄²×C₅	—	3	1	no	—
152	C₂×C₄²×C₅	—	3	1	no	—
153	C₂×C₄²×C₅	—	3	1	no	—
154	C₂×C₄²×C₅	—	3	1	no	—
155	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
156	C₅×#95	—	3	1	no	—
157	C₅×#95	—	3	1	no	—
158	C₅×#95	—	3	1	no	—
159	C₅×#95	—	3	1	no	—
160	C₅×#95	—	3	1	no	—
161	C₅×#95	—	3	1	no	—
162	C₅×#95	—	3	1	no	—
163	C₅×#95	—	3	1	no	—
164	C₅×#95	C₂×D₃	1	1	yes	characteristic
165	C₅×#95	C₂×D₃	1	1	yes	characteristic
166	#2319	—	3	1	no	Sylow
167	C₂³×C₃×C₅	—	2	1	no	—
168	C₂³×C₃×C₅	—	2	1	no	—
169	C₂³×C₃×C₅	—	2	1	no	—
170	C₂³×C₃×C₅	—	2	1	no	—
171	C₂³×C₃×C₅	—	2	1	no	—
172	C₂³×C₃×C₅	—	2	1	no	—
173	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
174	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
175	C₂²×C₅×D₃	—	2	1	no	—
176	C₂²×C₅×D₃	—	2	1	no	—
177	C₂²×C₅×D₃	—	2	1	no	—
178	C₂²×C₅×D₃	—	2	1	no	—
179	C₂²×C₅×D₃	—	2	1	no	—
180	C₂²×C₅×D₃	—	2	1	no	—
181	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
182	C₂×C₃×C₄×C₅	—	2	1	no	—
183	C₂×C₃×C₄×C₅	—	2	1	no	—
184	C₂×C₃×C₄×C₅	—	2	1	no	—
185	C₂×C₃×C₄×C₅	—	2	1	no	—
186	C₂×C₃×C₄×C₅	—	2	1	no	—
187	C₂×C₃×C₄×C₅	—	2	1	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
190	C₂×C₃×C₄×C₅	—	2	1	no	—
191	C₂×C₃×C₄×C₅	—	2	1	no	—
192	C₂×C₃×C₄×C₅	—	2	1	no	—
193	C₂×C₃×C₄×C₅	—	2	1	no	—
194	C₂×C₃×C₄×C₅	—	2	1	no	—
195	C₂×C₃×C₄×C₅	—	2	1	no	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
199	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
200	C₅×#67	—	2	8	no	—
201	C₂×C₅×Dic₃	—	2	1	no	—
202	C₂×C₅×Dic₃	—	2	1	no	—
203	C₂×C₅×Dic₃	—	2	1	no	—
204	C₂×C₅×Dic₃	—	2	1	no	—
205	C₂×C₅×Dic₃	—	2	1	no	—
206	C₂×C₅×Dic₃	—	2	1	no	—
207	C₂×C₅×Dic₃	—	2	1	no	—
208	C₂×C₅×Dic₃	—	2	1	no	—
209	C₂×C₅×Dic₃	—	2	1	no	—
210	C₂×C₅×Dic₃	—	2	1	no	—
211	C₂×C₅×Dic₃	—	2	1	no	—
212	C₂×C₅×Dic₃	—	2	1	no	—
213	C₂×C₅×Dic₃	—	2	1	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	—	4	4	no	—
218	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
219	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
220	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
221	C₂×C₅×Dic₃	#41	1	2	yes	—
222	C₂×C₅×Dic₃	#41	1	2	yes	—
223	C₄×C₅×D₃	—	4	4	no	—
224	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
225	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
226	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
232	C₂×#217	C₂²×C₅	1	1	yes	characteristic
233	C₂×#217	C₂²×C₅	1	1	yes	characteristic
234	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
235	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
236	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
237	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
238	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
240	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
241	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
242	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
243	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
244	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
249	#67⋊C₄	C₄×C₅	1	8	yes	complemented
250	C₃×#95	C₂²×C₅	1	1	yes	characteristic
251	C₃×#95	C₂²×C₅	1	1	yes	characteristic
252	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
253	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
254	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
255	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
256	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
257	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
258	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
259	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
260	C₂⁴×C₅	—	3	1	no	—
261	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
262	C₂×C₅×D₄	—	3	4	no	—
263	C₂×C₅×D₄	—	6	2	no	—
264	C₂×C₅×D₄	—	6	2	no	—
265	C₂²×C₄×C₅	—	3	1	no	—
266	C₂²×C₄×C₅	—	3	1	no	—
267	C₂²×C₄×C₅	—	3	1	no	—
268	C₂²×C₄×C₅	—	3	4	no	—
269	C₂²×C₄×C₅	—	3	4	no	—
270	C₂²×C₄×C₅	—	3	1	no	—
271	C₂²×C₄×C₅	—	3	1	no	—
272	C₂²×C₄×C₅	—	3	1	no	—
273	C₂²×C₄×C₅	—	3	1	no	—
274	C₂²×C₄×C₅	—	12	1	no	—
275	C₂²×C₄×C₅	—	12	1	no	—
276	C₂²×C₄×C₅	—	12	1	no	—
277	C₂²×C₄×C₅	—	12	1	no	—
278	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
279	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
280	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
281	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
282	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
283	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
284	C₅×C₄⋊C₄	—	3	4	no	—
285	C₅×C₄⋊C₄	—	4	1	no	—
286	C₅×C₄⋊C₄	—	6	2	no	—
287	C₅×C₄⋊C₄	—	6	2	no	—
288	C₅×C₄⋊C₄	—	12	1	no	—
289	C₅×C₄⋊C₄	—	12	1	no	—
290	C₅×C₄⋊C₄	—	12	1	no	—
291	C₅×C₂²⋊C₄	—	3	4	no	—
292	C₅×C₂²⋊C₄	—	4	1	no	—
293	C₅×C₂²⋊C₄	—	4	1	no	—
294	C₅×C₂²⋊C₄	—	12	1	no	—
295	C₅×C₂²⋊C₄	—	12	1	no	—
296	C₅×C₂²⋊C₄	—	12	1	no	—
297	C₅×C₂²⋊C₄	—	12	1	no	—
298	C₅×C₂²⋊C₄	—	12	1	no	—
299	C₅×C₂²⋊C₄	—	12	1	no	—
300	C₅×C₂²⋊C₄	C₄×D₃	1	4	yes	—
301	C₄²×C₅	—	3	4	no	—
302	C₄²×C₅	—	4	1	no	—
303	C₄²×C₅	—	6	2	no	—
304	C₄²×C₅	—	6	2	no	—
305	C₄²×C₅	—	12	1	no	—
306	C₂×C₄×D₄	—	3	1	no	—
307	#390	—	3	1	no	—
308	#390	—	3	1	no	—
309	#389	—	3	1	no	—
310	#389	—	3	1	no	—
311	#388	—	3	1	no	—
312	#388	—	3	1	no	—
313	#388	—	3	1	no	—
314	#388	C₅×D₃	1	1	yes	characteristic, complemented
315	#381	—	3	1	no	—
316	#381	—	3	1	no	—
317	#380	—	3	1	no	—
318	#380	—	3	1	no	—
319	C₄×C₄⋊C₄	—	3	1	no	—
320	#376	—	3	1	no	—
321	C₂²×C₃×C₅	—	2	2	no	—
322	C₂²×C₃×C₅	—	2	2	no	—
323	C₂²×C₃×C₅	—	2	2	no	—
324	C₂²×C₃×C₅	—	4	1	no	—
325	C₂²×C₃×C₅	—	4	1	no	—
326	C₂²×C₃×C₅	—	4	1	no	—
327	C₂²×C₃×C₅	—	4	1	no	—
328	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
329	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
330	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
331	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
332	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
333	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
335	C₂×C₅×D₃	—	2	2	no	—
336	C₂×C₅×D₃	—	2	2	no	—
337	C₂×C₅×D₃	—	2	2	no	—
338	C₂×C₅×D₃	—	4	1	no	—
339	C₂×C₅×D₃	—	4	1	no	—
340	C₂×C₅×D₃	—	4	1	no	—
341	C₂×C₅×D₃	—	4	1	no	—
342	C₃×C₄×C₅	—	2	2	no	—
343	C₃×C₄×C₅	—	2	2	no	—
344	C₃×C₄×C₅	—	4	1	no	—
345	C₃×C₄×C₅	—	4	1	no	—
346	C₃×C₄×C₅	—	4	1	no	—
347	C₃×C₄×C₅	—	4	1	no	—
348	C₅×Dic₃	—	2	2	no	—
349	C₅×Dic₃	—	2	2	no	—
350	C₅×Dic₃	—	4	1	no	—
351	C₅×Dic₃	—	4	1	no	—
352	C₅×Dic₃	—	4	1	no	—
353	C₅×Dic₃	—	4	1	no	—
354	C₅×Dic₃	#117	1	4	yes	—
355	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
356	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
357	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
358	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
359	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
360	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
361	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
362	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
363	C₂×#67	—	2	2	no	—
364	C₂×#67	—	2	2	no	—
365	C₂×#67	C₂×C₄×C₅	1	4	yes	—
366	C₂²×Dic₃	—	4	1	no	—
367	C₂²×Dic₃	—	4	1	no	—
368	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
369	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
370	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
371	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
372	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
373	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
374	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
375	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₄×D₃	—	4	1	no	—
377	C₂×C₄×D₃	—	4	1	no	—
378	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
379	C₃×C₄⋊C₄	—	4	1	no	—
380	C₃×C₂²⋊C₄	—	4	1	no	—
381	C₃×C₂²⋊C₄	—	4	1	no	—
382	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
383	C₃×C₄²	—	4	1	no	—
384	#217	—	4	1	no	—
385	#217	—	4	1	no	—
386	(C₂×D₃)⋊C₄	—	4	1	no	—
387	(C₂×D₃)⋊C₄	—	4	1	no	—
388	(C₂×D₃)⋊C₄	—	4	1	no	—
389	(C₂×D₃)⋊C₄	—	4	1	no	—
390	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
391	C₄⋊Dic₃	—	4	1	no	—
392	Dic₃⋊C₄	—	2	2	no	—
393	Dic₃⋊C₄	—	2	2	no	—
394	Dic₃⋊C₄	—	4	1	no	—
395	Dic₃⋊C₄	—	4	1	no	—
396	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
397	C₄×Dic₃	—	2	2	no	—
398	C₄×Dic₃	—	2	2	no	—
399	C₄×Dic₃	—	4	1	no	—
400	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
401	C₂³×C₅	—	2	1	no	—
402	C₂³×C₅	—	2	1	no	—
403	C₂³×C₅	—	2	1	no	—
404	C₂³×C₅	—	2	1	no	—
405	C₂³×C₅	—	2	1	no	—
406	C₂³×C₅	—	2	1	no	—
407	C₂³×C₅	—	3	2	no	—
408	C₂³×C₅	—	6	1	no	—
409	C₂³×C₅	—	6	1	no	—
410	C₂³×C₅	—	6	1	no	—
411	C₂³×C₅	—	6	1	no	—
412	C₂³×C₅	—	6	1	no	—
413	C₂³×C₅	—	6	1	no	—
414	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
415	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
416	C₅×D₄	—	6	8	no	—
417	C₂×C₄×C₅	—	2	1	no	—
418	C₂×C₄×C₅	—	2	1	no	—
419	C₂×C₄×C₅	—	2	1	no	—
420	C₂×C₄×C₅	—	2	1	no	—
421	C₂×C₄×C₅	—	2	1	no	—
422	C₂×C₄×C₅	—	2	1	no	—
423	C₂×C₄×C₅	—	2	1	no	—
424	C₂×C₄×C₅	—	2	1	no	—
425	C₂×C₄×C₅	—	2	1	no	—
426	C₂×C₄×C₅	—	2	1	no	—
427	C₂×C₄×C₅	—	2	1	no	—
428	C₂×C₄×C₅	—	2	1	no	—
429	C₂×C₄×C₅	—	2	1	no	—
430	C₂×C₄×C₅	—	2	1	no	—
431	C₂×C₄×C₅	—	2	1	no	—
432	C₂×C₄×C₅	—	2	1	no	—
433	C₂×C₄×C₅	—	3	2	no	—
434	C₂×C₄×C₅	—	3	2	no	—
435	C₂×C₄×C₅	—	3	2	no	—
436	C₂×C₄×C₅	—	3	2	no	—
437	C₂×C₄×C₅	—	3	2	no	—
438	C₂×C₄×C₅	—	6	1	no	—
439	C₂×C₄×C₅	—	6	1	no	—
440	C₂×C₄×C₅	—	6	1	no	—
441	C₂×C₄×C₅	—	6	1	no	—
442	C₂×C₄×C₅	—	6	1	no	—
443	C₂×C₄×C₅	—	6	1	no	—
444	C₂×C₄×C₅	—	6	1	no	—
445	C₂×C₄×C₅	—	6	1	no	—
446	C₂×C₄×C₅	—	6	1	no	—
447	C₂×C₄×C₅	—	6	1	no	—
448	C₂×C₄×C₅	—	6	1	no	—
449	C₂×C₄×C₅	—	6	1	no	—
450	C₂×C₄×C₅	—	6	1	no	—
451	C₂×C₄×C₅	—	6	1	no	—
452	C₂×C₄×C₅	—	6	1	no	—
453	C₂×C₄×C₅	—	6	1	no	—
454	C₂×C₄×C₅	—	12	4	no	—
455	C₂×C₄×C₅	—	12	4	no	—
456	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
457	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
458	C₂²×D₄	—	3	1	no	—
459	C₂³×C₄	—	3	1	no	—
460	C₂³×C₄	—	3	1	no	—
461	C₄×D₄	—	3	8	no	—
462	C₂×C₄⋊C₄	—	3	1	no	—
463	C₂×C₄⋊C₄	—	3	1	no	—
464	C₂×C₄⋊C₄	—	3	1	no	—
465	C₂×C₄⋊C₄	—	3	1	no	—
466	C₂×C₄⋊C₄	—	3	1	no	—
467	C₂×C₄⋊C₄	—	3	1	no	—
468	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	—	3	1	no	—
470	C₂×C₂²⋊C₄	—	3	1	no	—
471	C₂×C₂²⋊C₄	—	3	1	no	—
472	C₂×C₂²⋊C₄	—	3	1	no	—
473	C₂×C₂²⋊C₄	—	3	1	no	—
474	C₂×C₂²⋊C₄	—	3	1	no	—
475	C₂×C₂²⋊C₄	—	3	1	no	—
476	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
479	C₂×C₄²	—	3	1	no	—
480	C₂×C₄²	—	3	1	no	—
481	C₂×C₄²	—	3	1	no	—
482	C₂×C₄²	—	3	1	no	—
483	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
484	#95	—	3	1	no	—
485	#95	—	3	1	no	—
486	#95	—	3	1	no	—
487	#95	—	3	1	no	—
488	#95	—	3	1	no	—
489	#95	—	3	1	no	—
490	#95	—	3	1	no	—
491	#95	—	3	1	no	—
492	#95	C₂×C₅×D₃	1	1	yes	characteristic
493	#95	C₂×C₅×D₃	1	1	yes	characteristic
494	C₂×C₃×C₅	—	4	2	no	—
495	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
496	C₂×C₃×C₅	#518	1	1	yes	characteristic
497	C₂×C₃×C₅	#520	1	1	yes	characteristic
498	C₂×C₃×C₅	#540	1	1	yes	characteristic
499	C₂×C₃×C₅	#540	1	1	yes	characteristic
500	C₂×C₃×C₅	#542	1	1	yes	characteristic
501	C₂×C₃×C₅	#542	1	1	yes	characteristic
502	C₅×D₃	—	4	2	no	—
503	C₂³×C₃	—	2	1	no	—
504	C₂³×C₃	—	2	1	no	—
505	C₂³×C₃	—	2	1	no	—
506	C₂³×C₃	—	2	1	no	—
507	C₂³×C₃	—	2	1	no	—
508	C₂³×C₃	—	2	1	no	—
509	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
510	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
511	C₂²×D₃	—	2	1	no	—
512	C₂²×D₃	—	2	1	no	—
513	C₂²×D₃	—	2	1	no	—
514	C₂²×D₃	—	2	1	no	—
515	C₂²×D₃	—	2	1	no	—
516	C₂²×D₃	—	2	1	no	—
517	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
518	C₂×C₃×C₄	—	2	1	no	—
519	C₂×C₃×C₄	—	2	1	no	—
520	C₂×C₃×C₄	—	2	1	no	—
521	C₂×C₃×C₄	—	2	1	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	2	1	no	—
524	C₂×C₃×C₄	—	2	1	no	—
525	C₂×C₃×C₄	—	2	1	no	—
526	C₂×C₃×C₄	—	2	1	no	—
527	C₂×C₃×C₄	—	2	1	no	—
528	C₂×C₃×C₄	—	2	1	no	—
529	C₂×C₃×C₄	—	2	1	no	—
530	C₂×C₃×C₄	—	2	1	no	—
531	C₂×C₃×C₄	—	2	1	no	—
532	C₂×C₃×C₄	—	2	1	no	—
533	C₂×C₃×C₄	—	2	1	no	—
534	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
535	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
536	#67	—	2	8	no	—
537	C₂×Dic₃	—	2	1	no	—
538	C₂×Dic₃	—	2	1	no	—
539	C₂×Dic₃	—	2	1	no	—
540	C₂×Dic₃	—	2	1	no	—
541	C₂×Dic₃	—	2	1	no	—
542	C₂×Dic₃	—	2	1	no	—
543	C₂×Dic₃	—	2	1	no	—
544	C₂×Dic₃	—	2	1	no	—
545	C₂×Dic₃	—	2	1	no	—
546	C₂×Dic₃	—	2	1	no	—
547	C₂×Dic₃	—	2	1	no	—
548	C₂×Dic₃	—	2	1	no	—
549	C₂×Dic₃	—	2	1	no	—
550	C₂×Dic₃	—	2	1	no	—
551	C₂×Dic₃	—	2	1	no	—
552	C₂×Dic₃	—	2	1	no	—
553	C₂×Dic₃	—	4	4	no	—
554	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
555	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
556	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
557	C₂×Dic₃	C₅×#41	1	2	yes	—
558	C₂×Dic₃	C₅×#41	1	2	yes	—
559	C₄×D₃	—	4	4	no	—
560	C₂²×C₅	—	2	2	no	—
561	C₂²×C₅	—	2	2	no	—
562	C₂²×C₅	—	2	2	no	—
563	C₂²×C₅	—	4	1	no	—
564	C₂²×C₅	—	4	1	no	—
565	C₂²×C₅	—	4	1	no	—
566	C₂²×C₅	—	4	1	no	—
567	C₂²×C₅	—	6	2	no	—
568	C₂²×C₅	—	6	2	no	—
569	C₂²×C₅	—	6	2	no	—
570	C₂²×C₅	—	12	1	no	—
571	C₂²×C₅	—	12	1	no	—
572	C₂²×C₅	—	12	1	no	—
573	C₂²×C₅	—	12	1	no	—
574	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
575	C₂²×C₅	#1004	1	1	yes	characteristic
576	C₂²×C₅	#1004	1	1	yes	characteristic
577	C₂²×C₅	D₃×#41	1	1	yes	characteristic
578	C₂²×C₅	D₃×#41	1	1	yes	characteristic
579	C₂²×C₅	#1009	1	1	yes	characteristic
580	C₂²×C₅	#1010	1	1	yes	characteristic
581	C₄×C₅	—	2	2	no	—
582	C₄×C₅	—	2	2	no	—
583	C₄×C₅	—	3	4	no	—
584	C₄×C₅	—	4	1	no	—
585	C₄×C₅	—	4	1	no	—
586	C₄×C₅	—	4	1	no	—
587	C₄×C₅	—	4	1	no	—
588	C₄×C₅	—	6	2	no	—
589	C₄×C₅	—	6	2	no	—
590	C₄×C₅	—	12	1	no	—
591	C₄×C₅	—	12	1	no	—
592	C₄×C₅	—	12	1	no	—
593	C₄×C₅	—	12	1	no	—
594	C₂⁴	—	3	1	no	—
595	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
596	C₂×D₄	—	3	4	no	—
597	C₂×D₄	—	6	2	no	—
598	C₂×D₄	—	6	2	no	—
599	C₂²×C₄	—	3	1	no	—
600	C₂²×C₄	—	3	1	no	—
601	C₂²×C₄	—	3	1	no	—
602	C₂²×C₄	—	3	4	no	—
603	C₂²×C₄	—	3	4	no	—
604	C₂²×C₄	—	3	1	no	—
605	C₂²×C₄	—	3	1	no	—
606	C₂²×C₄	—	3	1	no	—
607	C₂²×C₄	—	3	1	no	—
608	C₂²×C₄	—	12	1	no	—
609	C₂²×C₄	—	12	1	no	—
610	C₂²×C₄	—	12	1	no	—
611	C₂²×C₄	—	12	1	no	—
612	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
613	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
614	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
615	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
616	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
617	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
618	C₄⋊C₄	—	3	4	no	—
619	C₄⋊C₄	—	4	1	no	—
620	C₄⋊C₄	—	6	2	no	—
621	C₄⋊C₄	—	6	2	no	—
622	C₄⋊C₄	—	12	1	no	—
623	C₄⋊C₄	—	12	1	no	—
624	C₄⋊C₄	—	12	1	no	—
625	C₂²⋊C₄	—	3	4	no	—
626	C₂²⋊C₄	—	4	1	no	—
627	C₂²⋊C₄	—	4	1	no	—
628	C₂²⋊C₄	—	12	1	no	—
629	C₂²⋊C₄	—	12	1	no	—
630	C₂²⋊C₄	—	12	1	no	—
631	C₂²⋊C₄	—	12	1	no	—
632	C₂²⋊C₄	—	12	1	no	—
633	C₂²⋊C₄	—	12	1	no	—
634	C₂²⋊C₄	C₄×C₅×D₃	1	4	yes	—
635	C₄²	—	3	4	no	—
636	C₄²	—	4	1	no	—
637	C₄²	—	6	2	no	—
638	C₄²	—	6	2	no	—
639	C₄²	—	12	1	no	—
640	C₃×C₅	#2319	1	1	yes	characteristic, complemented, Hall
641	C₂²×C₃	—	2	2	no	—
642	C₂²×C₃	—	2	2	no	—
643	C₂²×C₃	—	2	2	no	—
644	C₂²×C₃	—	4	1	no	—
645	C₂²×C₃	—	4	1	no	—
646	C₂²×C₃	—	4	1	no	—
647	C₂²×C₃	—	4	1	no	—
648	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
649	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
650	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
651	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
652	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
653	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
654	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
655	C₂×D₃	—	2	2	no	—
656	C₂×D₃	—	2	2	no	—
657	C₂×D₃	—	2	2	no	—
658	C₂×D₃	—	4	1	no	—
659	C₂×D₃	—	4	1	no	—
660	C₂×D₃	—	4	1	no	—
661	C₂×D₃	—	4	1	no	—
662	C₃×C₄	—	2	2	no	—
663	C₃×C₄	—	2	2	no	—
664	C₃×C₄	—	4	1	no	—
665	C₃×C₄	—	4	1	no	—
666	C₃×C₄	—	4	1	no	—
667	C₃×C₄	—	4	1	no	—
668	Dic₃	—	2	2	no	—
669	Dic₃	—	2	2	no	—
670	Dic₃	—	4	1	no	—
671	Dic₃	—	4	1	no	—
672	Dic₃	—	4	1	no	—
673	Dic₃	—	4	1	no	—
674	Dic₃	C₅×#117	1	4	yes	—
675	C₂×C₅	—	4	2	no	—
676	C₂×C₅	—	12	2	no	—
677	C₂×C₅	D₃×#117	1	1	yes	characteristic
678	C₂×C₅	#5545	1	1	yes	characteristic
679	C₂×C₅	#5546	1	1	yes	characteristic
680	C₂×C₅	#5615	1	1	yes	characteristic
681	C₂×C₅	#5663	1	1	yes	characteristic
682	C₂×C₅	#5669	1	1	yes	characteristic
683	C₂×C₅	#5710	1	1	yes	characteristic
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	3	2	no	—
691	C₂³	—	6	1	no	—
692	C₂³	—	6	1	no	—
693	C₂³	—	6	1	no	—
694	C₂³	—	6	1	no	—
695	C₂³	—	6	1	no	—
696	C₂³	—	6	1	no	—
697	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
698	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
699	D₄	—	6	8	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	3	2	no	—
717	C₂×C₄	—	3	2	no	—
718	C₂×C₄	—	3	2	no	—
719	C₂×C₄	—	3	2	no	—
720	C₂×C₄	—	3	2	no	—
721	C₂×C₄	—	6	1	no	—
722	C₂×C₄	—	6	1	no	—
723	C₂×C₄	—	6	1	no	—
724	C₂×C₄	—	6	1	no	—
725	C₂×C₄	—	6	1	no	—
726	C₂×C₄	—	6	1	no	—
727	C₂×C₄	—	6	1	no	—
728	C₂×C₄	—	6	1	no	—
729	C₂×C₄	—	6	1	no	—
730	C₂×C₄	—	6	1	no	—
731	C₂×C₄	—	6	1	no	—
732	C₂×C₄	—	6	1	no	—
733	C₂×C₄	—	6	1	no	—
734	C₂×C₄	—	6	1	no	—
735	C₂×C₄	—	6	1	no	—
736	C₂×C₄	—	6	1	no	—
737	C₂×C₄	—	12	4	no	—
738	C₂×C₄	—	12	4	no	—
739	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
740	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
741	C₂×C₃	—	4	2	no	—
742	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
743	C₂×C₃	C₅×#518	1	1	yes	characteristic
744	C₂×C₃	C₅×#520	1	1	yes	characteristic
745	C₂×C₃	C₅×#540	1	1	yes	characteristic
746	C₂×C₃	C₅×#540	1	1	yes	characteristic
747	C₂×C₃	C₅×#542	1	1	yes	characteristic
748	C₂×C₃	C₅×#542	1	1	yes	characteristic
749	D₃	—	4	2	no	—
750	C₅	#75458	1	1	yes	characteristic, direct product factor, Sylow
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	6	2	no	—
759	C₂²	—	6	2	no	—
760	C₂²	—	6	2	no	—
761	C₂²	—	12	1	no	—
762	C₂²	—	12	1	no	—
763	C₂²	—	12	1	no	—
764	C₂²	—	12	1	no	—
765	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
766	C₂²	C₅×#1004	1	1	yes	characteristic
767	C₂²	C₅×#1004	1	1	yes	characteristic
768	C₂²	C₅×D₃×#41	1	1	yes	characteristic
769	C₂²	C₅×D₃×#41	1	1	yes	characteristic
770	C₂²	C₅×#1009	1	1	yes	characteristic
771	C₂²	C₅×#1010	1	1	yes	characteristic
772	C₄	—	2	2	no	—
773	C₄	—	2	2	no	—
774	C₄	—	3	4	no	—
775	C₄	—	4	1	no	—
776	C₄	—	4	1	no	—
777	C₄	—	4	1	no	—
778	C₄	—	4	1	no	—
779	C₄	—	6	2	no	—
780	C₄	—	6	2	no	—
781	C₄	—	12	1	no	—
782	C₄	—	12	1	no	—
783	C₄	—	12	1	no	—
784	C₄	—	12	1	no	—
785	C₃	C₅×#2319	1	1	yes	characteristic, complemented, Sylow
786	C₂	—	4	2	no	—
787	C₂	—	12	2	no	—
788	C₂	C₅×D₃×#117	1	1	yes	characteristic
789	C₂	C₅×#5545	1	1	yes	characteristic
790	C₂	C₅×#5546	1	1	yes	characteristic
791	C₂	C₅×#5615	1	1	yes	characteristic
792	C₂	C₅×#5663	1	1	yes	characteristic
793	C₂	C₅×#5669	1	1	yes	characteristic
794	C₂	C₅×#5710	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×#388	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#67	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#388	D₃
hypocenter	C₃	C₅×#2319
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#388

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#388	C₂	semidirect
3. C₅×#4987	C₂	semidirect
4. C₅×#4976	C₂	semidirect
7. C₅×#4951	C₂	semidirect
8. C₅×#4943	C₂	semidirect
9. C₅×#4942	C₂	semidirect
10. C₅×#4940	C₂	semidirect
11. C₄×C₅×Dic₃⋊C₄	C₂	semidirect
12. C₅×#4669	C₂	semidirect
13. C₅×#4664	C₂	semidirect
14. C₅×#4648	C₂	semidirect
15. C₅×#4647	C₂	semidirect
42. C₅×#67⋊C₄	C₄	semidirect
53. #75458	C₅	direct (N × H)
62. C₅×#388	D₃	semidirect
116. C₃×#388	C₂×C₅	semidirect
117. #4987	C₂×C₅	semidirect
118. #4976	C₂×C₅	semidirect
121. #4951	C₂×C₅	semidirect
122. #4943	C₂×C₅	semidirect
123. #4942	C₂×C₅	semidirect
124. #4940	C₂×C₅	semidirect
125. C₄×Dic₃⋊C₄	C₂×C₅	semidirect
126. #4669	C₂×C₅	semidirect
127. #4664	C₂×C₅	semidirect
128. #4648	C₂×C₅	semidirect
129. #4647	C₂×C₅	semidirect
249. #67⋊C₄	C₄×C₅	semidirect
314. #388	C₅×D₃	semidirect
640. C₃×C₅	#2319	semidirect
750. C₅	#75458	direct (N × H)
785. C₃	C₅×#2319	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#67⋊C₄	2
C₃×C₅×#388	2
C₅×#4987	2
C₅×#4976	2
C₅×#4957	2
C₅×#4951	2
C₅×#4943	2
C₅×#4942	2
C₅×#4940	2
C₄×C₅×Dic₃⋊C₄	2
C₅×#4669	2
C₅×#4664	2
C₅×#4648	2
C₅×#4647	2
C₅×#2319	3
#75458	5

Subgroups — C5×#75458 #14323141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#75458 #14323141