Subgroups — C₅×#75834 #14327336

Order 1920.

1320 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×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#877	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4978	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4956	C₂	1	1	yes	maximal, characteristic
7	C₅×#4956	C₂	1	1	yes	maximal, characteristic
8	C₅×#4951	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4667	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4666	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4655	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4650	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2352	—	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	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	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×C₃×C₄²×C₅	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×(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×D₃×C₄⋊C₄	—	2	4	no	—
43	C₅×#67⋊C₄	C₄	1	8	yes	complemented
44	C₅×#877	—	2	4	no	—
45	C₃×C₅×#95	C₂²	1	1	yes	characteristic
46	C₃×C₅×#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	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
54	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
55	#75834	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
56	C₂×C₄×C₅×D₄	—	3	1	no	—
57	C₂×C₅×#117	—	3	1	no	—
58	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
59	C₅×#388	—	3	1	no	—
60	C₅×#388	D₃	1	1	yes	characteristic, complemented
61	C₅×#387	—	3	1	no	—
62	C₅×#387	—	3	1	no	—
63	C₅×#386	—	3	1	no	—
64	C₅×#386	—	3	1	no	—
65	C₅×#382	—	3	1	no	—
66	C₅×#380	—	3	1	no	—
67	C₅×#380	—	3	1	no	—
68	C₄×C₅×C₄⋊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	C₂³×C₅×D₃	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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₅×#67	—	2	2	no	—
80	C₂×C₅×#67	—	2	2	no	—
81	C₂×C₅×#67	C₂×C₄	1	4	yes	—
82	C₂²×C₅×Dic₃	—	2	2	no	—
83	C₂²×C₅×Dic₃	—	2	2	no	—
84	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
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	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
91	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
92	C₂×C₄×C₅×D₃	—	2	2	no	—
93	C₂×C₄×C₅×D₃	—	2	2	no	—
94	C₂×C₄×C₅×D₃	—	2	2	no	—
95	C₂×C₄×C₅×D₃	—	2	2	no	—
96	C₂×C₄×C₅×D₃	—	2	2	no	—
97	C₂×C₄×C₅×D₃	—	2	2	no	—
98	C₂×C₄×C₅×D₃	—	4	1	no	—
99	C₂×C₄×C₅×D₃	—	4	1	no	—
100	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
101	C₃×C₅×C₄⋊C₄	—	2	2	no	—
102	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
103	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
104	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	complemented
105	C₃×C₄²×C₅	—	4	1	no	—
106	C₅×#217	—	2	2	no	—
107	C₅×#217	—	4	1	no	—
108	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
109	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
110	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
111	C₅×C₄⋊Dic₃	—	2	2	no	—
112	C₅×Dic₃⋊C₄	—	2	2	no	—
113	C₅×Dic₃⋊C₄	—	2	2	no	—
114	C₅×Dic₃⋊C₄	—	2	2	no	—
115	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	complemented
116	C₅×Dic₃⋊C₄	D₄	1	4	yes	complemented
117	C₄×C₅×Dic₃	—	2	2	no	—
118	C₄×C₅×Dic₃	—	2	2	no	—
119	C₄×C₅×Dic₃	—	4	1	no	—
120	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
121	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
122	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic
123	C₂×#877	C₂×C₅	1	1	yes	characteristic, complemented
124	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
125	#4978	C₂×C₅	1	1	yes	characteristic, complemented
126	#4956	C₂×C₅	1	1	yes	characteristic
127	#4956	C₂×C₅	1	1	yes	characteristic
128	#4951	C₂×C₅	1	1	yes	characteristic, complemented
129	#4942	C₂×C₅	1	1	yes	characteristic, complemented
130	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
131	C₄×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
132	#4667	C₂×C₅	1	1	yes	characteristic, complemented
133	#4666	C₂×C₅	1	1	yes	characteristic, complemented
134	#4655	C₂×C₅	1	1	yes	characteristic, complemented
135	#4650	C₂×C₅	1	1	yes	characteristic, complemented
136	C₂²×C₅×D₄	—	3	1	no	—
137	C₂³×C₄×C₅	—	3	1	no	—
138	C₂³×C₄×C₅	—	3	1	no	—
139	C₂³×C₄×C₅	—	3	1	no	—
140	C₂³×C₄×C₅	—	3	1	no	—
141	C₄×C₅×D₄	—	3	8	no	—
142	C₅×#117	—	6	4	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×C₄⋊C₄	—	3	1	no	—
149	C₂×C₅×C₄⋊C₄	—	6	4	no	—
150	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic
157	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
158	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
159	C₂×C₄²×C₅	—	3	1	no	—
160	C₂×C₄²×C₅	—	3	1	no	—
161	C₂×C₄²×C₅	—	3	1	no	—
162	C₂×C₄²×C₅	—	3	1	no	—
163	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
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	—	3	1	no	—
171	C₅×#95	—	3	1	no	—
172	C₅×#95	C₂×D₃	1	1	yes	characteristic
173	C₅×#95	C₂×D₃	1	1	yes	characteristic
174	#2352	—	3	1	no	Sylow
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	C₂²×C₄	1	2	yes	—
182	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
183	C₂²×C₅×D₃	—	2	1	no	—
184	C₂²×C₅×D₃	—	2	1	no	—
185	C₂²×C₅×D₃	—	2	1	no	—
186	C₂²×C₅×D₃	—	2	1	no	—
187	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
188	C₂²×C₅×D₃	#41	1	2	yes	—
189	C₂²×C₅×D₃	#41	1	2	yes	—
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	C₂²×C₄	1	2	yes	—
206	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
207	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
208	C₅×#67	—	2	8	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	8	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	C₂²×C₄	1	2	yes	—
226	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
227	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
228	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
229	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
230	C₂×C₅×Dic₃	#41	1	2	yes	—
231	C₄×C₅×D₃	—	2	8	no	—
232	C₄×C₅×D₃	—	4	4	no	—
233	C₄×C₅×D₃	—	4	4	no	—
234	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
235	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
236	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
237	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
238	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
244	C₂×#217	C₂²×C₅	1	1	yes	characteristic
245	C₂×#217	C₂²×C₅	1	1	yes	characteristic
246	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
247	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
248	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
250	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
251	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
253	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
254	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
259	D₃×C₄⋊C₄	—	2	4	no	—
260	#67⋊C₄	C₄×C₅	1	8	yes	complemented
261	#877	—	2	4	no	—
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	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
271	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
272	C₂⁴×C₅	—	3	1	no	—
273	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
274	C₂×C₅×D₄	—	3	4	no	—
275	C₂×C₅×D₄	—	6	2	no	—
276	C₂×C₅×D₄	—	6	2	no	—
277	C₂²×C₄×C₅	—	3	1	no	—
278	C₂²×C₄×C₅	—	3	4	no	—
279	C₂²×C₄×C₅	—	3	1	no	—
280	C₂²×C₄×C₅	—	3	1	no	—
281	C₂²×C₄×C₅	—	3	1	no	—
282	C₂²×C₄×C₅	—	3	4	no	—
283	C₂²×C₄×C₅	—	3	1	no	—
284	C₂²×C₄×C₅	—	3	1	no	—
285	C₂²×C₄×C₅	—	3	1	no	—
286	C₂²×C₄×C₅	—	6	2	no	—
287	C₂²×C₄×C₅	—	6	2	no	—
288	C₂²×C₄×C₅	—	6	2	no	—
289	C₂²×C₄×C₅	—	6	2	no	—
290	C₂²×C₄×C₅	—	6	2	no	—
291	C₂²×C₄×C₅	—	6	2	no	—
292	C₂²×C₄×C₅	—	6	2	no	—
293	C₂²×C₄×C₅	—	6	2	no	—
294	C₂²×C₄×C₅	—	12	1	no	—
295	C₂²×C₄×C₅	—	12	1	no	—
296	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
297	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
299	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
300	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
301	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
302	C₅×C₄⋊C₄	—	2	2	no	—
303	C₅×C₄⋊C₄	—	3	4	no	—
304	C₅×C₄⋊C₄	—	3	4	no	—
305	C₅×C₄⋊C₄	—	6	2	no	—
306	C₅×C₄⋊C₄	—	6	2	no	—
307	C₅×C₄⋊C₄	—	6	2	no	—
308	C₅×C₄⋊C₄	—	6	2	no	—
309	C₅×C₂²⋊C₄	—	2	2	no	—
310	C₅×C₂²⋊C₄	—	3	4	no	—
311	C₅×C₂²⋊C₄	—	4	1	no	—
312	C₅×C₂²⋊C₄	—	6	2	no	—
313	C₅×C₂²⋊C₄	—	6	2	no	—
314	C₅×C₂²⋊C₄	—	6	2	no	—
315	C₅×C₂²⋊C₄	—	12	1	no	—
316	C₅×C₂²⋊C₄	C₄×D₃	1	4	yes	complemented
317	C₄²×C₅	—	3	4	no	—
318	C₄²×C₅	—	4	1	no	—
319	C₄²×C₅	—	6	2	no	—
320	C₄²×C₅	—	6	2	no	—
321	C₄²×C₅	—	12	1	no	—
322	C₂×C₄×D₄	—	3	1	no	—
323	C₂×#117	—	3	1	no	—
324	C₂²×C₄⋊C₄	—	3	1	no	—
325	#388	—	3	1	no	—
326	#388	C₅×D₃	1	1	yes	characteristic, complemented
327	#387	—	3	1	no	—
328	#387	—	3	1	no	—
329	#386	—	3	1	no	—
330	#386	—	3	1	no	—
331	#382	—	3	1	no	—
332	#380	—	3	1	no	—
333	#380	—	3	1	no	—
334	C₄×C₄⋊C₄	—	3	1	no	—
335	C₄×C₂²⋊C₄	—	3	1	no	—
336	C₄×C₂²⋊C₄	—	3	1	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	—	4	1	no	—
341	C₂²×C₃×C₅	—	4	1	no	—
342	C₂²×C₃×C₅	—	4	1	no	—
343	C₂²×C₃×C₅	—	4	1	no	—
344	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
345	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
346	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
347	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
348	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
349	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
350	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
351	C₂×C₅×D₃	—	2	2	no	—
352	C₂×C₅×D₃	—	2	2	no	—
353	C₂×C₅×D₃	—	2	2	no	—
354	C₂×C₅×D₃	—	2	2	no	—
355	C₂×C₅×D₃	—	2	2	no	—
356	C₂×C₅×D₃	—	2	2	no	—
357	C₂×C₅×D₃	#117	1	4	yes	complemented
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	C₅×Dic₃	—	2	2	no	—
365	C₅×Dic₃	—	2	2	no	—
366	C₅×Dic₃	—	2	2	no	—
367	C₅×Dic₃	—	4	1	no	—
368	C₅×Dic₃	—	4	1	no	—
369	C₅×Dic₃	—	4	1	no	—
370	C₅×Dic₃	C₄×D₄	1	4	yes	—
371	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
372	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
373	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
374	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
375	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
376	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
377	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
378	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
379	C₂×#67	—	2	2	no	—
380	C₂×#67	—	2	2	no	—
381	C₂×#67	C₂×C₄×C₅	1	4	yes	—
382	C₂²×Dic₃	—	2	2	no	—
383	C₂²×Dic₃	—	2	2	no	—
384	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
385	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
386	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
387	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
388	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
389	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
390	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
391	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
392	C₂×C₄×D₃	—	2	2	no	—
393	C₂×C₄×D₃	—	2	2	no	—
394	C₂×C₄×D₃	—	2	2	no	—
395	C₂×C₄×D₃	—	2	2	no	—
396	C₂×C₄×D₃	—	2	2	no	—
397	C₂×C₄×D₃	—	2	2	no	—
398	C₂×C₄×D₃	—	4	1	no	—
399	C₂×C₄×D₃	—	4	1	no	—
400	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
401	C₃×C₄⋊C₄	—	2	2	no	—
402	C₃×C₂²⋊C₄	—	2	2	no	—
403	C₃×C₂²⋊C₄	—	4	1	no	—
404	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
405	C₃×C₄²	—	4	1	no	—
406	#217	—	2	2	no	—
407	#217	—	4	1	no	—
408	(C₂×D₃)⋊C₄	—	2	2	no	—
409	(C₂×D₃)⋊C₄	—	2	2	no	—
410	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
411	C₄⋊Dic₃	—	2	2	no	—
412	Dic₃⋊C₄	—	2	2	no	—
413	Dic₃⋊C₄	—	2	2	no	—
414	Dic₃⋊C₄	—	2	2	no	—
415	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
416	Dic₃⋊C₄	C₅×D₄	1	4	yes	complemented
417	C₄×Dic₃	—	2	2	no	—
418	C₄×Dic₃	—	2	2	no	—
419	C₄×Dic₃	—	4	1	no	—
420	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
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	—	3	2	no	—
428	C₂³×C₅	—	3	2	no	—
429	C₂³×C₅	—	3	2	no	—
430	C₂³×C₅	—	6	1	no	—
431	C₂³×C₅	—	6	1	no	—
432	C₂³×C₅	—	6	1	no	—
433	C₂³×C₅	—	6	1	no	—
434	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
435	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
436	C₅×D₄	—	6	8	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	—	3	2	no	—
453	C₂×C₄×C₅	—	3	2	no	—
454	C₂×C₄×C₅	—	3	2	no	—
455	C₂×C₄×C₅	—	3	2	no	—
456	C₂×C₄×C₅	—	3	2	no	—
457	C₂×C₄×C₅	—	3	2	no	—
458	C₂×C₄×C₅	—	6	8	no	—
459	C₂×C₄×C₅	—	6	8	no	—
460	C₂×C₄×C₅	—	6	1	no	—
461	C₂×C₄×C₅	—	6	1	no	—
462	C₂×C₄×C₅	—	6	1	no	—
463	C₂×C₄×C₅	—	6	1	no	—
464	C₂×C₄×C₅	—	6	1	no	—
465	C₂×C₄×C₅	—	6	1	no	—
466	C₂×C₄×C₅	—	6	1	no	—
467	C₂×C₄×C₅	—	6	1	no	—
468	C₂×C₄×C₅	—	6	1	no	—
469	C₂×C₄×C₅	—	6	1	no	—
470	C₂×C₄×C₅	—	6	1	no	—
471	C₂×C₄×C₅	—	6	1	no	—
472	C₂×C₄×C₅	—	6	1	no	—
473	C₂×C₄×C₅	—	6	1	no	—
474	C₂×C₄×C₅	—	6	1	no	—
475	C₂×C₄×C₅	—	12	4	no	—
476	C₂×C₄×C₅	—	12	4	no	—
477	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
478	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
479	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
480	C₂²×D₄	—	3	1	no	—
481	C₂³×C₄	—	3	1	no	—
482	C₂³×C₄	—	3	1	no	—
483	C₂³×C₄	—	3	1	no	—
484	C₂³×C₄	—	3	1	no	—
485	C₄×D₄	—	3	8	no	—
486	#117	—	6	4	no	—
487	C₂×C₄⋊C₄	—	3	1	no	—
488	C₂×C₄⋊C₄	—	3	1	no	—
489	C₂×C₄⋊C₄	—	3	1	no	—
490	C₂×C₄⋊C₄	—	3	1	no	—
491	C₂×C₄⋊C₄	—	3	1	no	—
492	C₂×C₄⋊C₄	—	3	1	no	—
493	C₂×C₄⋊C₄	—	6	4	no	—
494	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
495	C₂×C₂²⋊C₄	—	3	1	no	—
496	C₂×C₂²⋊C₄	—	3	1	no	—
497	C₂×C₂²⋊C₄	—	3	1	no	—
498	C₂×C₂²⋊C₄	—	3	1	no	—
499	C₂×C₂²⋊C₄	—	3	1	no	—
500	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
503	C₂×C₄²	—	3	1	no	—
504	C₂×C₄²	—	3	1	no	—
505	C₂×C₄²	—	3	1	no	—
506	C₂×C₄²	—	3	1	no	—
507	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
508	#95	—	3	1	no	—
509	#95	—	3	1	no	—
510	#95	—	3	1	no	—
511	#95	—	3	1	no	—
512	#95	—	3	1	no	—
513	#95	—	3	1	no	—
514	#95	—	3	1	no	—
515	#95	—	3	1	no	—
516	#95	C₂×C₅×D₃	1	1	yes	characteristic
517	#95	C₂×C₅×D₃	1	1	yes	characteristic
518	C₂×C₃×C₅	—	4	2	no	—
519	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
520	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
521	C₂×C₃×C₅	#520	1	1	yes	characteristic
522	C₂×C₃×C₅	#546	1	1	yes	characteristic
523	C₂×C₃×C₅	#548	1	1	yes	characteristic
524	C₂×C₃×C₅	#552	1	1	yes	characteristic
525	C₂×C₃×C₅	#553	1	1	yes	characteristic
526	C₅×D₃	—	2	4	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	C₂²×C₄×C₅	1	2	yes	—
534	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
535	C₂²×D₃	—	2	1	no	—
536	C₂²×D₃	—	2	1	no	—
537	C₂²×D₃	—	2	1	no	—
538	C₂²×D₃	—	2	1	no	—
539	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
540	C₂²×D₃	C₅×#41	1	2	yes	—
541	C₂²×D₃	C₅×#41	1	2	yes	—
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	C₂²×C₄×C₅	1	2	yes	—
558	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
559	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
560	#67	—	2	8	no	—
561	C₂×Dic₃	—	2	1	no	—
562	C₂×Dic₃	—	2	1	no	—
563	C₂×Dic₃	—	2	1	no	—
564	C₂×Dic₃	—	2	1	no	—
565	C₂×Dic₃	—	2	1	no	—
566	C₂×Dic₃	—	2	1	no	—
567	C₂×Dic₃	—	2	8	no	—
568	C₂×Dic₃	—	2	1	no	—
569	C₂×Dic₃	—	2	1	no	—
570	C₂×Dic₃	—	2	1	no	—
571	C₂×Dic₃	—	2	1	no	—
572	C₂×Dic₃	—	2	1	no	—
573	C₂×Dic₃	—	2	1	no	—
574	C₂×Dic₃	—	2	1	no	—
575	C₂×Dic₃	—	2	1	no	—
576	C₂×Dic₃	—	2	1	no	—
577	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
578	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
579	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
580	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
581	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
582	C₂×Dic₃	C₅×#41	1	2	yes	—
583	C₄×D₃	—	2	8	no	—
584	C₄×D₃	—	4	4	no	—
585	C₄×D₃	—	4	4	no	—
586	C₂²×C₅	—	2	2	no	—
587	C₂²×C₅	—	2	2	no	—
588	C₂²×C₅	—	2	2	no	—
589	C₂²×C₅	—	3	4	no	—
590	C₂²×C₅	—	4	1	no	—
591	C₂²×C₅	—	4	1	no	—
592	C₂²×C₅	—	4	1	no	—
593	C₂²×C₅	—	4	1	no	—
594	C₂²×C₅	—	6	2	no	—
595	C₂²×C₅	—	6	2	no	—
596	C₂²×C₅	—	6	2	no	—
597	C₂²×C₅	—	6	2	no	—
598	C₂²×C₅	—	6	2	no	—
599	C₂²×C₅	—	6	2	no	—
600	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
601	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
602	C₂²×C₅	#1004	1	1	yes	characteristic
603	C₂²×C₅	D₃×#41	1	1	yes	characteristic
604	C₂²×C₅	D₃×#41	1	1	yes	characteristic
605	C₂²×C₅	D₃×#41	1	1	yes	characteristic
606	C₂²×C₅	#1010	1	1	yes	characteristic
607	C₄×C₅	—	2	2	no	—
608	C₄×C₅	—	2	2	no	—
609	C₄×C₅	—	2	2	no	—
610	C₄×C₅	—	3	4	no	—
611	C₄×C₅	—	4	1	no	—
612	C₄×C₅	—	4	1	no	—
613	C₄×C₅	—	4	1	no	—
614	C₄×C₅	—	6	2	no	—
615	C₄×C₅	—	6	2	no	—
616	C₄×C₅	—	6	2	no	—
617	C₄×C₅	—	12	1	no	—
618	C₄×C₅	—	12	1	no	—
619	C₄×C₅	—	12	1	no	—
620	C₂⁴	—	3	1	no	—
621	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
622	C₂×D₄	—	3	4	no	—
623	C₂×D₄	—	6	2	no	—
624	C₂×D₄	—	6	2	no	—
625	C₂²×C₄	—	3	1	no	—
626	C₂²×C₄	—	3	4	no	—
627	C₂²×C₄	—	3	1	no	—
628	C₂²×C₄	—	3	1	no	—
629	C₂²×C₄	—	3	1	no	—
630	C₂²×C₄	—	3	4	no	—
631	C₂²×C₄	—	3	1	no	—
632	C₂²×C₄	—	3	1	no	—
633	C₂²×C₄	—	3	1	no	—
634	C₂²×C₄	—	6	2	no	—
635	C₂²×C₄	—	6	2	no	—
636	C₂²×C₄	—	6	2	no	—
637	C₂²×C₄	—	6	2	no	—
638	C₂²×C₄	—	6	2	no	—
639	C₂²×C₄	—	6	2	no	—
640	C₂²×C₄	—	6	2	no	—
641	C₂²×C₄	—	6	2	no	—
642	C₂²×C₄	—	12	1	no	—
643	C₂²×C₄	—	12	1	no	—
644	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
645	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
646	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
647	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
648	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
649	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	3	4	no	—
652	C₄⋊C₄	—	3	4	no	—
653	C₄⋊C₄	—	6	2	no	—
654	C₄⋊C₄	—	6	2	no	—
655	C₄⋊C₄	—	6	2	no	—
656	C₄⋊C₄	—	6	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	3	4	no	—
659	C₂²⋊C₄	—	4	1	no	—
660	C₂²⋊C₄	—	6	2	no	—
661	C₂²⋊C₄	—	6	2	no	—
662	C₂²⋊C₄	—	6	2	no	—
663	C₂²⋊C₄	—	12	1	no	—
664	C₂²⋊C₄	C₄×C₅×D₃	1	4	yes	complemented
665	C₄²	—	3	4	no	—
666	C₄²	—	4	1	no	—
667	C₄²	—	6	2	no	—
668	C₄²	—	6	2	no	—
669	C₄²	—	12	1	no	—
670	C₃×C₅	#2352	1	1	yes	characteristic, complemented, Hall
671	C₂²×C₃	—	2	2	no	—
672	C₂²×C₃	—	2	2	no	—
673	C₂²×C₃	—	2	2	no	—
674	C₂²×C₃	—	4	1	no	—
675	C₂²×C₃	—	4	1	no	—
676	C₂²×C₃	—	4	1	no	—
677	C₂²×C₃	—	4	1	no	—
678	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
679	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
680	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
681	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
682	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
683	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
684	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
685	C₂×D₃	—	2	2	no	—
686	C₂×D₃	—	2	2	no	—
687	C₂×D₃	—	2	2	no	—
688	C₂×D₃	—	2	2	no	—
689	C₂×D₃	—	2	2	no	—
690	C₂×D₃	—	2	2	no	—
691	C₂×D₃	C₅×#117	1	4	yes	complemented
692	C₃×C₄	—	2	2	no	—
693	C₃×C₄	—	2	2	no	—
694	C₃×C₄	—	2	2	no	—
695	C₃×C₄	—	4	1	no	—
696	C₃×C₄	—	4	1	no	—
697	C₃×C₄	—	4	1	no	—
698	Dic₃	—	2	2	no	—
699	Dic₃	—	2	2	no	—
700	Dic₃	—	2	2	no	—
701	Dic₃	—	4	1	no	—
702	Dic₃	—	4	1	no	—
703	Dic₃	—	4	1	no	—
704	Dic₃	C₄×C₅×D₄	1	4	yes	—
705	C₂×C₅	—	4	2	no	—
706	C₂×C₅	—	6	4	no	—
707	C₂×C₅	D₃×#117	1	1	yes	characteristic
708	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
709	C₂×C₅	#5546	1	1	yes	characteristic
710	C₂×C₅	#5610	1	1	yes	characteristic
711	C₂×C₅	#5661	1	1	yes	characteristic
712	C₂×C₅	#5677	1	1	yes	characteristic
713	C₂×C₅	#5708	1	1	yes	characteristic
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	—	3	2	no	—
721	C₂³	—	3	2	no	—
722	C₂³	—	3	2	no	—
723	C₂³	—	6	1	no	—
724	C₂³	—	6	1	no	—
725	C₂³	—	6	1	no	—
726	C₂³	—	6	1	no	—
727	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
728	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
729	D₄	—	6	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	—	3	2	no	—
746	C₂×C₄	—	3	2	no	—
747	C₂×C₄	—	3	2	no	—
748	C₂×C₄	—	3	2	no	—
749	C₂×C₄	—	3	2	no	—
750	C₂×C₄	—	3	2	no	—
751	C₂×C₄	—	6	8	no	—
752	C₂×C₄	—	6	8	no	—
753	C₂×C₄	—	6	1	no	—
754	C₂×C₄	—	6	1	no	—
755	C₂×C₄	—	6	1	no	—
756	C₂×C₄	—	6	1	no	—
757	C₂×C₄	—	6	1	no	—
758	C₂×C₄	—	6	1	no	—
759	C₂×C₄	—	6	1	no	—
760	C₂×C₄	—	6	1	no	—
761	C₂×C₄	—	6	1	no	—
762	C₂×C₄	—	6	1	no	—
763	C₂×C₄	—	6	1	no	—
764	C₂×C₄	—	6	1	no	—
765	C₂×C₄	—	6	1	no	—
766	C₂×C₄	—	6	1	no	—
767	C₂×C₄	—	6	1	no	—
768	C₂×C₄	—	12	4	no	—
769	C₂×C₄	—	12	4	no	—
770	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
771	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
772	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
773	C₂×C₃	—	4	2	no	—
774	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
775	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
776	C₂×C₃	C₅×#520	1	1	yes	characteristic
777	C₂×C₃	C₅×#546	1	1	yes	characteristic
778	C₂×C₃	C₅×#548	1	1	yes	characteristic
779	C₂×C₃	C₅×#552	1	1	yes	characteristic
780	C₂×C₃	C₅×#553	1	1	yes	characteristic
781	D₃	—	2	4	no	—
782	C₅	#75834	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	—	3	4	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	6	2	no	—
792	C₂²	—	6	2	no	—
793	C₂²	—	6	2	no	—
794	C₂²	—	6	2	no	—
795	C₂²	—	6	2	no	—
796	C₂²	—	6	2	no	—
797	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
798	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
799	C₂²	C₅×#1004	1	1	yes	characteristic
800	C₂²	C₅×D₃×#41	1	1	yes	characteristic
801	C₂²	C₅×D₃×#41	1	1	yes	characteristic
802	C₂²	C₅×D₃×#41	1	1	yes	characteristic
803	C₂²	C₅×#1010	1	1	yes	characteristic
804	C₄	—	2	2	no	—
805	C₄	—	2	2	no	—
806	C₄	—	2	2	no	—
807	C₄	—	3	4	no	—
808	C₄	—	4	1	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	6	2	no	—
812	C₄	—	6	2	no	—
813	C₄	—	6	2	no	—
814	C₄	—	12	1	no	—
815	C₄	—	12	1	no	—
816	C₄	—	12	1	no	—
817	C₃	C₅×#2352	1	1	yes	characteristic, complemented, Sylow
818	C₂	—	4	2	no	—
819	C₂	—	6	4	no	—
820	C₂	C₅×D₃×#117	1	1	yes	characteristic
821	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
822	C₂	C₅×#5546	1	1	yes	characteristic
823	C₂	C₅×#5610	1	1	yes	characteristic
824	C₂	C₅×#5661	1	1	yes	characteristic
825	C₂	C₅×#5677	1	1	yes	characteristic
826	C₂	C₅×#5708	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×#2352
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
1. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
3. C₂×C₅×#877	C₂	semidirect
4. C₃×C₅×#388	C₂	semidirect
5. C₅×#4978	C₂	semidirect
8. C₅×#4951	C₂	semidirect
9. C₅×#4942	C₂	semidirect
10. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
11. C₄×C₅×Dic₃⋊C₄	C₂	semidirect
12. C₅×#4667	C₂	semidirect
13. C₅×#4666	C₂	semidirect
14. C₅×#4655	C₂	semidirect
15. C₅×#4650	C₂	semidirect
43. C₅×#67⋊C₄	C₄	semidirect
55. #75834	C₅	direct (N × H)
60. C₅×#388	D₃	semidirect
84. C₂²×C₅×Dic₃	C₂×C₄	semidirect
104. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
115. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
116. C₅×Dic₃⋊C₄	D₄	semidirect
120. C₄×C₅×Dic₃	C₂×C₄	semidirect
121. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
123. C₂×#877	C₂×C₅	semidirect
124. C₃×#388	C₂×C₅	semidirect
125. #4978	C₂×C₅	semidirect
128. #4951	C₂×C₅	semidirect
129. #4942	C₂×C₅	semidirect
130. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
131. C₄×Dic₃⋊C₄	C₂×C₅	semidirect
132. #4667	C₂×C₅	semidirect
133. #4666	C₂×C₅	semidirect
134. #4655	C₂×C₅	semidirect
135. #4650	C₂×C₅	semidirect
260. #67⋊C₄	C₄×C₅	semidirect
316. C₅×C₂²⋊C₄	C₄×D₃	semidirect
326. #388	C₅×D₃	semidirect
357. C₂×C₅×D₃	#117	semidirect
384. C₂²×Dic₃	C₂×C₄×C₅	semidirect
404. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
415. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
416. Dic₃⋊C₄	C₅×D₄	semidirect
420. C₄×Dic₃	C₂×C₄×C₅	semidirect
664. C₂²⋊C₄	C₄×C₅×D₃	semidirect
670. C₃×C₅	#2352	semidirect
691. C₂×D₃	C₅×#117	semidirect
782. C₅	#75834	direct (N × H)
817. C₃	C₅×#2352	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#67⋊C₄	2
C₂×C₅×#877	2
C₃×C₅×#388	2
C₅×#4978	2
C₅×#4956	2
C₅×#4951	2
C₅×#4942	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₄×C₅×Dic₃⋊C₄	2
C₅×#4667	2
C₅×#4666	2
C₅×#4655	2
C₅×#4650	2
C₅×#2352	3
#75834	5

Subgroups — C5×#75834 #14327336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#75834 #14327336