Subgroups — C₅×#75833 #14326236

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4989	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4955	C₂	1	1	yes	maximal, characteristic
7	C₅×#4951	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4945	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4944	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4668	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4667	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4666	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4664	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2342	—	3	1	no	maximal, Hall
17	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	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, complemented
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, complemented
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×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
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×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
44	C₅×#892	—	2	4	no	—
45	C₅×D₃×C₂²⋊C₄	—	2	4	no	—
46	C₅×D₃×C₂²⋊C₄	C₄	1	8	yes	complemented
47	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
49	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
50	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
51	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
52	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
53	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
54	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
55	#75833	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
56	C₂×C₅×#117	—	3	1	no	—
57	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
58	C₂²×C₅×C₂²⋊C₄	—	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×#385	—	3	1	no	—
64	C₅×#385	—	3	1	no	—
65	C₅×#381	—	3	1	no	—
66	C₅×#380	—	3	1	no	—
67	C₅×#379	—	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	C₂³×C₅×D₃	—	2	2	no	—
73	C₂³×C₅×D₃	—	2	2	no	—
74	C₂³×C₅×D₃	—	2	2	no	—
75	C₂³×C₅×D₃	—	2	2	no	—
76	C₂³×C₅×D₃	—	4	1	no	—
77	C₂³×C₅×D₃	—	4	1	no	—
78	C₂³×C₅×D₃	C₂×C₄	1	4	yes	—
79	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
80	C₂³×C₅×D₃	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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₄×C₅	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	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
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	C₂×C₄×C₅×D₃	—	4	1	no	—
103	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
104	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
105	C₃×C₅×C₄⋊C₄	—	2	2	no	—
106	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
107	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
108	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	complemented
109	C₃×C₄²×C₅	—	4	1	no	—
110	C₅×#217	—	2	2	no	—
111	C₅×#217	—	4	1	no	—
112	C₅×#217	C₂×C₄	1	4	yes	complemented
113	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
114	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
115	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
116	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
117	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
118	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
119	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
120	C₅×(C₂×D₃)⋊C₄	D₄	1	4	yes	—
121	C₅×C₄⋊Dic₃	—	2	2	no	—
122	C₅×Dic₃⋊C₄	—	4	1	no	—
123	C₅×Dic₃⋊C₄	—	4	1	no	—
124	C₄×C₅×Dic₃	—	2	2	no	—
125	C₄×C₅×Dic₃	—	2	2	no	—
126	C₄×C₅×Dic₃	—	4	1	no	—
127	C₂×#892	C₂×C₅	1	1	yes	characteristic, complemented
128	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
129	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
130	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
131	#4989	C₂×C₅	1	1	yes	characteristic, complemented
132	#4955	C₂×C₅	1	1	yes	characteristic
133	#4951	C₂×C₅	1	1	yes	characteristic, complemented
134	#4945	C₂×C₅	1	1	yes	characteristic, complemented
135	#4944	C₂×C₅	1	1	yes	characteristic, complemented
136	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
137	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
138	#4668	C₂×C₅	1	1	yes	characteristic, complemented
139	#4667	C₂×C₅	1	1	yes	characteristic, complemented
140	#4666	C₂×C₅	1	1	yes	characteristic, complemented
141	#4664	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂⁵×C₅	—	3	1	no	—
143	C₂³×C₄×C₅	—	3	1	no	—
144	C₂³×C₄×C₅	—	3	1	no	—
145	C₂³×C₄×C₅	—	3	1	no	—
146	C₂³×C₄×C₅	—	3	1	no	—
147	C₅×#117	—	6	4	no	—
148	C₂×C₅×C₄⋊C₄	—	3	1	no	—
149	C₂×C₅×C₄⋊C₄	—	3	1	no	—
150	C₂×C₅×C₄⋊C₄	—	3	1	no	—
151	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
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	8	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	—	6	4	no	—
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	C₂×D₃	1	1	yes	characteristic, complemented
172	C₅×#95	—	3	1	no	—
173	C₅×#95	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic, complemented
179	C₅×#95	C₂×D₃	1	1	yes	characteristic, complemented
180	#2342	—	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	C₂²×C₄	1	2	yes	—
188	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
195	C₂²×C₅×D₃	—	2	1	no	—
196	C₂²×C₅×D₃	—	2	1	no	—
197	C₂²×C₅×D₃	—	2	8	no	—
198	C₂²×C₅×D₃	—	2	8	no	—
199	C₂²×C₅×D₃	—	4	4	no	—
200	C₂²×C₅×D₃	—	4	4	no	—
201	C₂²×C₅×D₃	—	4	4	no	—
202	C₂²×C₅×D₃	—	4	4	no	—
203	C₂²×C₅×D₃	—	4	4	no	—
204	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
205	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
206	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
207	C₂²×C₅×D₃	#41	1	2	yes	—
208	C₂²×C₅×D₃	#41	1	2	yes	—
209	C₂²×C₅×D₃	#41	1	2	yes	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	1	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	2	1	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	2	1	no	—
224	C₂×C₃×C₄×C₅	—	2	1	no	—
225	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
226	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
227	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
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	—	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	—	2	1	no	—
237	C₂×C₅×Dic₃	—	2	1	no	—
238	C₂×C₅×Dic₃	—	2	1	no	—
239	C₂×C₅×Dic₃	—	2	1	no	—
240	C₂×C₅×Dic₃	—	2	1	no	—
241	C₂×C₅×Dic₃	—	2	1	no	—
242	C₂×C₅×Dic₃	—	2	1	no	—
243	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
244	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
245	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
246	C₄×C₅×D₃	—	2	8	no	—
247	C₄×C₅×D₃	—	4	4	no	—
248	C₄×C₅×D₃	—	4	4	no	—
249	C₄×C₅×D₃	—	4	4	no	—
250	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
251	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
252	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
253	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
254	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
256	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₂×#217	C₂²×C₅	1	1	yes	characteristic
261	C₂×#217	C₂²×C₅	1	1	yes	characteristic
262	C₂×#217	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×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
267	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
268	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
269	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
270	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
275	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
276	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
277	#892	—	2	4	no	—
278	D₃×C₂²⋊C₄	—	2	4	no	—
279	D₃×C₂²⋊C₄	C₄×C₅	1	8	yes	complemented
280	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
281	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
282	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
283	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
284	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
286	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
288	C₂⁴×C₅	—	3	1	no	—
289	C₂⁴×C₅	—	3	1	no	—
290	C₂⁴×C₅	—	3	4	no	—
291	C₂⁴×C₅	—	6	2	no	—
292	C₂⁴×C₅	—	6	2	no	—
293	C₂⁴×C₅	—	6	2	no	—
294	C₂⁴×C₅	—	6	2	no	—
295	C₂⁴×C₅	—	12	1	no	—
296	C₂⁴×C₅	—	12	1	no	—
297	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
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	4	no	—
302	C₂²×C₄×C₅	—	3	4	no	—
303	C₂²×C₄×C₅	—	3	1	no	—
304	C₂²×C₄×C₅	—	3	1	no	—
305	C₂²×C₄×C₅	—	3	1	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	—	6	2	no	—
310	C₂²×C₄×C₅	—	6	2	no	—
311	C₂²×C₄×C₅	—	6	2	no	—
312	C₂²×C₄×C₅	—	12	1	no	—
313	C₂²×C₄×C₅	—	12	1	no	—
314	C₂²×C₄×C₅	—	12	1	no	—
315	C₂²×C₄×C₅	—	12	1	no	—
316	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
317	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
318	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
319	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
320	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
321	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
322	C₅×C₄⋊C₄	—	2	2	no	—
323	C₅×C₄⋊C₄	—	6	2	no	—
324	C₅×C₄⋊C₄	—	12	1	no	—
325	C₅×C₄⋊C₄	—	12	1	no	—
326	C₅×C₂²⋊C₄	—	2	2	no	—
327	C₅×C₂²⋊C₄	—	3	4	no	—
328	C₅×C₂²⋊C₄	—	3	4	no	—
329	C₅×C₂²⋊C₄	—	3	4	no	—
330	C₅×C₂²⋊C₄	—	3	4	no	—
331	C₅×C₂²⋊C₄	—	4	1	no	—
332	C₅×C₂²⋊C₄	—	6	2	no	—
333	C₅×C₂²⋊C₄	—	6	2	no	—
334	C₅×C₂²⋊C₄	—	6	2	no	—
335	C₅×C₂²⋊C₄	—	6	2	no	—
336	C₅×C₂²⋊C₄	—	6	2	no	—
337	C₅×C₂²⋊C₄	—	6	2	no	—
338	C₅×C₂²⋊C₄	—	12	1	no	—
339	C₅×C₂²⋊C₄	C₄×D₃	1	4	yes	complemented
340	C₄²×C₅	—	4	1	no	—
341	C₄²×C₅	—	6	2	no	—
342	C₄²×C₅	—	6	2	no	—
343	C₄²×C₅	—	12	1	no	—
344	C₂×#117	—	3	1	no	—
345	C₂²×C₂²⋊C₄	—	3	1	no	—
346	C₂²×C₂²⋊C₄	—	3	1	no	—
347	#388	—	3	1	no	—
348	#388	—	3	1	no	—
349	#388	—	3	1	no	—
350	#388	C₅×D₃	1	1	yes	characteristic, complemented
351	#385	—	3	1	no	—
352	#385	—	3	1	no	—
353	#381	—	3	1	no	—
354	#380	—	3	1	no	—
355	#379	—	3	1	no	—
356	C₄×C₂²⋊C₄	—	3	1	no	—
357	C₄×C₂²⋊C₄	—	3	1	no	—
358	C₄×C₂²⋊C₄	—	3	1	no	—
359	C₂²×C₃×C₅	—	2	2	no	—
360	C₂²×C₃×C₅	—	2	2	no	—
361	C₂²×C₃×C₅	—	2	2	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	C₂³×C₄	1	1	yes	characteristic
367	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
368	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
369	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
370	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
371	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
372	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
373	C₂×C₅×D₃	—	2	2	no	—
374	C₂×C₅×D₃	—	2	2	no	—
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	—	2	2	no	—
379	C₂×C₅×D₃	—	2	2	no	—
380	C₂×C₅×D₃	—	2	2	no	—
381	C₂×C₅×D₃	—	2	2	no	—
382	C₂×C₅×D₃	—	2	2	no	—
383	C₂×C₅×D₃	—	2	2	no	—
384	C₂×C₅×D₃	—	2	2	no	—
385	C₂×C₅×D₃	—	4	16	no	—
386	C₂×C₅×D₃	#117	1	4	yes	complemented
387	C₂×C₅×D₃	C₄×D₄	1	4	yes	—
388	C₃×C₄×C₅	—	2	2	no	—
389	C₃×C₄×C₅	—	2	2	no	—
390	C₃×C₄×C₅	—	2	2	no	—
391	C₃×C₄×C₅	—	4	1	no	—
392	C₃×C₄×C₅	—	4	1	no	—
393	C₃×C₄×C₅	—	4	1	no	—
394	C₅×Dic₃	—	2	2	no	—
395	C₅×Dic₃	—	2	2	no	—
396	C₅×Dic₃	—	2	2	no	—
397	C₅×Dic₃	—	4	1	no	—
398	C₅×Dic₃	—	4	1	no	—
399	C₅×Dic₃	—	4	1	no	—
400	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
401	C₂³×D₃	—	2	2	no	—
402	C₂³×D₃	—	2	2	no	—
403	C₂³×D₃	—	2	2	no	—
404	C₂³×D₃	—	2	2	no	—
405	C₂³×D₃	—	4	1	no	—
406	C₂³×D₃	—	4	1	no	—
407	C₂³×D₃	C₂×C₄×C₅	1	4	yes	—
408	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
409	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
410	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
411	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
412	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
413	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
414	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
415	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
416	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
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	C₂×C₄×D₃	—	2	2	no	—
423	C₂×C₄×D₃	—	2	2	no	—
424	C₂×C₄×D₃	—	2	2	no	—
425	C₂×C₄×D₃	—	2	2	no	—
426	C₂×C₄×D₃	—	2	2	no	—
427	C₂×C₄×D₃	—	2	2	no	—
428	C₂×C₄×D₃	—	4	1	no	—
429	C₂×C₄×D₃	—	4	1	no	—
430	C₂×C₄×D₃	—	4	1	no	—
431	C₂×C₄×D₃	—	4	1	no	—
432	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
433	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
434	C₃×C₄⋊C₄	—	2	2	no	—
435	C₃×C₂²⋊C₄	—	2	2	no	—
436	C₃×C₂²⋊C₄	—	4	1	no	—
437	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
438	C₃×C₄²	—	4	1	no	—
439	#217	—	2	2	no	—
440	#217	—	4	1	no	—
441	#217	C₂×C₄×C₅	1	4	yes	complemented
442	(C₂×D₃)⋊C₄	—	2	2	no	—
443	(C₂×D₃)⋊C₄	—	2	2	no	—
444	(C₂×D₃)⋊C₄	—	2	2	no	—
445	(C₂×D₃)⋊C₄	—	2	2	no	—
446	(C₂×D₃)⋊C₄	—	2	2	no	—
447	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
448	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
449	(C₂×D₃)⋊C₄	C₅×D₄	1	4	yes	—
450	C₄⋊Dic₃	—	2	2	no	—
451	Dic₃⋊C₄	—	4	1	no	—
452	Dic₃⋊C₄	—	4	1	no	—
453	C₄×Dic₃	—	2	2	no	—
454	C₄×Dic₃	—	2	2	no	—
455	C₄×Dic₃	—	4	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	—	3	2	no	—
464	C₂³×C₅	—	3	2	no	—
465	C₂³×C₅	—	3	2	no	—
466	C₂³×C₅	—	3	2	no	—
467	C₂³×C₅	—	3	2	no	—
468	C₂³×C₅	—	6	8	no	—
469	C₂³×C₅	—	6	8	no	—
470	C₂³×C₅	—	6	1	no	—
471	C₂³×C₅	—	6	1	no	—
472	C₂³×C₅	—	6	1	no	—
473	C₂³×C₅	—	6	1	no	—
474	C₂³×C₅	—	6	1	no	—
475	C₂³×C₅	—	6	1	no	—
476	C₂³×C₅	—	6	1	no	—
477	C₂³×C₅	—	6	1	no	—
478	C₂³×C₅	—	12	4	no	—
479	C₂³×C₅	—	12	4	no	—
480	C₂³×C₅	—	12	4	no	—
481	C₂³×C₅	—	12	4	no	—
482	C₂³×C₅	—	12	4	no	—
483	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
484	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
485	C₂×C₄×C₅	—	2	1	no	—
486	C₂×C₄×C₅	—	2	1	no	—
487	C₂×C₄×C₅	—	2	1	no	—
488	C₂×C₄×C₅	—	2	1	no	—
489	C₂×C₄×C₅	—	2	1	no	—
490	C₂×C₄×C₅	—	2	1	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	2	1	no	—
493	C₂×C₄×C₅	—	2	1	no	—
494	C₂×C₄×C₅	—	2	1	no	—
495	C₂×C₄×C₅	—	2	1	no	—
496	C₂×C₄×C₅	—	2	1	no	—
497	C₂×C₄×C₅	—	2	1	no	—
498	C₂×C₄×C₅	—	2	1	no	—
499	C₂×C₄×C₅	—	2	1	no	—
500	C₂×C₄×C₅	—	3	2	no	—
501	C₂×C₄×C₅	—	3	2	no	—
502	C₂×C₄×C₅	—	3	2	no	—
503	C₂×C₄×C₅	—	6	8	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	—	6	1	no	—
510	C₂×C₄×C₅	—	6	1	no	—
511	C₂×C₄×C₅	—	6	1	no	—
512	C₂×C₄×C₅	—	6	1	no	—
513	C₂×C₄×C₅	—	6	1	no	—
514	C₂×C₄×C₅	—	6	1	no	—
515	C₂×C₄×C₅	—	6	1	no	—
516	C₂×C₄×C₅	—	6	1	no	—
517	C₂×C₄×C₅	—	6	1	no	—
518	C₂×C₄×C₅	—	6	1	no	—
519	C₂×C₄×C₅	—	12	4	no	—
520	C₂×C₄×C₅	—	12	4	no	—
521	C₂×C₄×C₅	—	12	4	no	—
522	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
523	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
524	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
525	C₂⁵	—	3	1	no	—
526	C₂³×C₄	—	3	1	no	—
527	C₂³×C₄	—	3	1	no	—
528	C₂³×C₄	—	3	1	no	—
529	C₂³×C₄	—	3	1	no	—
530	#117	—	6	4	no	—
531	C₂×C₄⋊C₄	—	3	1	no	—
532	C₂×C₄⋊C₄	—	3	1	no	—
533	C₂×C₄⋊C₄	—	3	1	no	—
534	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
535	C₂×C₂²⋊C₄	—	3	1	no	—
536	C₂×C₂²⋊C₄	—	3	1	no	—
537	C₂×C₂²⋊C₄	—	3	1	no	—
538	C₂×C₂²⋊C₄	—	3	1	no	—
539	C₂×C₂²⋊C₄	—	3	8	no	—
540	C₂×C₂²⋊C₄	—	3	1	no	—
541	C₂×C₂²⋊C₄	—	3	1	no	—
542	C₂×C₂²⋊C₄	—	3	1	no	—
543	C₂×C₂²⋊C₄	—	3	1	no	—
544	C₂×C₂²⋊C₄	—	3	1	no	—
545	C₂×C₂²⋊C₄	—	3	1	no	—
546	C₂×C₂²⋊C₄	—	3	1	no	—
547	C₂×C₂²⋊C₄	—	6	4	no	—
548	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
551	C₂×C₄²	—	3	1	no	—
552	C₂×C₄²	—	3	1	no	—
553	C₂×C₄²	—	3	1	no	—
554	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
555	#95	—	3	1	no	—
556	#95	—	3	1	no	—
557	#95	—	3	1	no	—
558	#95	—	3	1	no	—
559	#95	—	3	1	no	—
560	#95	—	3	1	no	—
561	#95	C₂×C₅×D₃	1	1	yes	characteristic, complemented
562	#95	C₂×C₅×D₃	1	1	yes	characteristic, complemented
563	C₂×C₃×C₅	—	4	2	no	—
564	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
565	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
566	C₂×C₃×C₅	#518	1	1	yes	characteristic
567	C₂×C₃×C₅	#546	1	1	yes	characteristic
568	C₂×C₃×C₅	#546	1	1	yes	characteristic
569	C₂×C₃×C₅	#551	1	1	yes	characteristic
570	C₂×C₃×C₅	#551	1	1	yes	characteristic
571	C₅×D₃	—	2	4	no	—
572	C₅×D₃	—	2	4	no	—
573	C₂³×C₃	—	2	1	no	—
574	C₂³×C₃	—	2	1	no	—
575	C₂³×C₃	—	2	1	no	—
576	C₂³×C₃	—	2	1	no	—
577	C₂³×C₃	—	2	1	no	—
578	C₂³×C₃	—	2	1	no	—
579	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
580	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
581	C₂²×D₃	—	2	1	no	—
582	C₂²×D₃	—	2	1	no	—
583	C₂²×D₃	—	2	1	no	—
584	C₂²×D₃	—	2	1	no	—
585	C₂²×D₃	—	2	1	no	—
586	C₂²×D₃	—	2	1	no	—
587	C₂²×D₃	—	2	1	no	—
588	C₂²×D₃	—	2	1	no	—
589	C₂²×D₃	—	2	8	no	—
590	C₂²×D₃	—	2	8	no	—
591	C₂²×D₃	—	4	4	no	—
592	C₂²×D₃	—	4	4	no	—
593	C₂²×D₃	—	4	4	no	—
594	C₂²×D₃	—	4	4	no	—
595	C₂²×D₃	—	4	4	no	—
596	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
597	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
598	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
599	C₂²×D₃	C₅×#41	1	2	yes	—
600	C₂²×D₃	C₅×#41	1	2	yes	—
601	C₂²×D₃	C₅×#41	1	2	yes	—
602	C₂×C₃×C₄	—	2	1	no	—
603	C₂×C₃×C₄	—	2	1	no	—
604	C₂×C₃×C₄	—	2	1	no	—
605	C₂×C₃×C₄	—	2	1	no	—
606	C₂×C₃×C₄	—	2	1	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	1	no	—
609	C₂×C₃×C₄	—	2	1	no	—
610	C₂×C₃×C₄	—	2	1	no	—
611	C₂×C₃×C₄	—	2	1	no	—
612	C₂×C₃×C₄	—	2	1	no	—
613	C₂×C₃×C₄	—	2	1	no	—
614	C₂×C₃×C₄	—	2	1	no	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	2	1	no	—
617	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
618	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
619	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
620	C₂×Dic₃	—	2	1	no	—
621	C₂×Dic₃	—	2	1	no	—
622	C₂×Dic₃	—	2	1	no	—
623	C₂×Dic₃	—	2	1	no	—
624	C₂×Dic₃	—	2	1	no	—
625	C₂×Dic₃	—	2	1	no	—
626	C₂×Dic₃	—	2	1	no	—
627	C₂×Dic₃	—	2	1	no	—
628	C₂×Dic₃	—	2	1	no	—
629	C₂×Dic₃	—	2	1	no	—
630	C₂×Dic₃	—	2	1	no	—
631	C₂×Dic₃	—	2	1	no	—
632	C₂×Dic₃	—	2	1	no	—
633	C₂×Dic₃	—	2	1	no	—
634	C₂×Dic₃	—	2	1	no	—
635	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
636	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
637	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
638	C₄×D₃	—	2	8	no	—
639	C₄×D₃	—	4	4	no	—
640	C₄×D₃	—	4	4	no	—
641	C₄×D₃	—	4	4	no	—
642	C₂²×C₅	—	2	2	no	—
643	C₂²×C₅	—	2	2	no	—
644	C₂²×C₅	—	2	2	no	—
645	C₂²×C₅	—	3	4	no	—
646	C₂²×C₅	—	3	4	no	—
647	C₂²×C₅	—	4	1	no	—
648	C₂²×C₅	—	4	1	no	—
649	C₂²×C₅	—	4	1	no	—
650	C₂²×C₅	—	4	1	no	—
651	C₂²×C₅	—	6	2	no	—
652	C₂²×C₅	—	6	2	no	—
653	C₂²×C₅	—	6	2	no	—
654	C₂²×C₅	—	6	2	no	—
655	C₂²×C₅	—	6	2	no	—
656	C₂²×C₅	—	6	2	no	—
657	C₂²×C₅	—	6	2	no	—
658	C₂²×C₅	—	6	2	no	—
659	C₂²×C₅	—	6	2	no	—
660	C₂²×C₅	—	6	2	no	—
661	C₂²×C₅	—	6	2	no	—
662	C₂²×C₅	—	6	2	no	—
663	C₂²×C₅	—	12	16	no	—
664	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
665	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
666	C₂²×C₅	#1004	1	1	yes	characteristic
667	C₂²×C₅	D₃×#41	1	1	yes	characteristic
668	C₂²×C₅	D₃×#41	1	1	yes	characteristic
669	C₂²×C₅	D₃×#41	1	1	yes	characteristic
670	C₂²×C₅	#1009	1	1	yes	characteristic
671	C₄×C₅	—	2	2	no	—
672	C₄×C₅	—	2	2	no	—
673	C₄×C₅	—	2	2	no	—
674	C₄×C₅	—	4	1	no	—
675	C₄×C₅	—	4	1	no	—
676	C₄×C₅	—	4	1	no	—
677	C₄×C₅	—	6	2	no	—
678	C₄×C₅	—	6	2	no	—
679	C₄×C₅	—	6	2	no	—
680	C₄×C₅	—	12	1	no	—
681	C₄×C₅	—	12	1	no	—
682	C₄×C₅	—	12	1	no	—
683	C₂⁴	—	3	1	no	—
684	C₂⁴	—	3	1	no	—
685	C₂⁴	—	3	4	no	—
686	C₂⁴	—	6	2	no	—
687	C₂⁴	—	6	2	no	—
688	C₂⁴	—	6	2	no	—
689	C₂⁴	—	6	2	no	—
690	C₂⁴	—	12	1	no	—
691	C₂⁴	—	12	1	no	—
692	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
693	C₂²×C₄	—	3	1	no	—
694	C₂²×C₄	—	3	1	no	—
695	C₂²×C₄	—	3	1	no	—
696	C₂²×C₄	—	3	4	no	—
697	C₂²×C₄	—	3	4	no	—
698	C₂²×C₄	—	3	1	no	—
699	C₂²×C₄	—	3	1	no	—
700	C₂²×C₄	—	3	1	no	—
701	C₂²×C₄	—	6	2	no	—
702	C₂²×C₄	—	6	2	no	—
703	C₂²×C₄	—	6	2	no	—
704	C₂²×C₄	—	6	2	no	—
705	C₂²×C₄	—	6	2	no	—
706	C₂²×C₄	—	6	2	no	—
707	C₂²×C₄	—	12	1	no	—
708	C₂²×C₄	—	12	1	no	—
709	C₂²×C₄	—	12	1	no	—
710	C₂²×C₄	—	12	1	no	—
711	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
712	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
713	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
714	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
715	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
716	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	6	2	no	—
719	C₄⋊C₄	—	12	1	no	—
720	C₄⋊C₄	—	12	1	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	3	4	no	—
723	C₂²⋊C₄	—	3	4	no	—
724	C₂²⋊C₄	—	3	4	no	—
725	C₂²⋊C₄	—	3	4	no	—
726	C₂²⋊C₄	—	4	1	no	—
727	C₂²⋊C₄	—	6	2	no	—
728	C₂²⋊C₄	—	6	2	no	—
729	C₂²⋊C₄	—	6	2	no	—
730	C₂²⋊C₄	—	6	2	no	—
731	C₂²⋊C₄	—	6	2	no	—
732	C₂²⋊C₄	—	6	2	no	—
733	C₂²⋊C₄	—	12	1	no	—
734	C₂²⋊C₄	C₄×C₅×D₃	1	4	yes	complemented
735	C₄²	—	4	1	no	—
736	C₄²	—	6	2	no	—
737	C₄²	—	6	2	no	—
738	C₄²	—	12	1	no	—
739	C₃×C₅	#2342	1	1	yes	characteristic, complemented, Hall
740	C₂²×C₃	—	2	2	no	—
741	C₂²×C₃	—	2	2	no	—
742	C₂²×C₃	—	2	2	no	—
743	C₂²×C₃	—	4	1	no	—
744	C₂²×C₃	—	4	1	no	—
745	C₂²×C₃	—	4	1	no	—
746	C₂²×C₃	—	4	1	no	—
747	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
748	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
749	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
750	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
751	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
752	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
753	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
754	C₂×D₃	—	2	2	no	—
755	C₂×D₃	—	2	2	no	—
756	C₂×D₃	—	2	2	no	—
757	C₂×D₃	—	2	2	no	—
758	C₂×D₃	—	2	2	no	—
759	C₂×D₃	—	2	2	no	—
760	C₂×D₃	—	2	2	no	—
761	C₂×D₃	—	2	2	no	—
762	C₂×D₃	—	2	2	no	—
763	C₂×D₃	—	2	2	no	—
764	C₂×D₃	—	2	2	no	—
765	C₂×D₃	—	2	2	no	—
766	C₂×D₃	—	4	16	no	—
767	C₂×D₃	C₅×#117	1	4	yes	complemented
768	C₂×D₃	C₄×C₅×D₄	1	4	yes	—
769	C₃×C₄	—	2	2	no	—
770	C₃×C₄	—	2	2	no	—
771	C₃×C₄	—	2	2	no	—
772	C₃×C₄	—	4	1	no	—
773	C₃×C₄	—	4	1	no	—
774	C₃×C₄	—	4	1	no	—
775	Dic₃	—	2	2	no	—
776	Dic₃	—	2	2	no	—
777	Dic₃	—	2	2	no	—
778	Dic₃	—	4	1	no	—
779	Dic₃	—	4	1	no	—
780	Dic₃	—	4	1	no	—
781	C₂×C₅	—	4	2	no	—
782	C₂×C₅	—	6	4	no	—
783	C₂×C₅	—	6	4	no	—
784	C₂×C₅	D₃×#117	1	1	yes	characteristic
785	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
786	C₂×C₅	#5545	1	1	yes	characteristic
787	C₂×C₅	#5610	1	1	yes	characteristic
788	C₂×C₅	#5659	1	1	yes	characteristic
789	C₂×C₅	#5676	1	1	yes	characteristic
790	C₂×C₅	#5705	1	1	yes	characteristic
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	1	no	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	3	2	no	—
798	C₂³	—	3	2	no	—
799	C₂³	—	3	2	no	—
800	C₂³	—	3	2	no	—
801	C₂³	—	3	2	no	—
802	C₂³	—	3	2	no	—
803	C₂³	—	6	8	no	—
804	C₂³	—	6	8	no	—
805	C₂³	—	6	1	no	—
806	C₂³	—	6	1	no	—
807	C₂³	—	6	1	no	—
808	C₂³	—	6	1	no	—
809	C₂³	—	6	1	no	—
810	C₂³	—	6	1	no	—
811	C₂³	—	6	1	no	—
812	C₂³	—	6	1	no	—
813	C₂³	—	12	4	no	—
814	C₂³	—	12	4	no	—
815	C₂³	—	12	4	no	—
816	C₂³	—	12	4	no	—
817	C₂³	—	12	4	no	—
818	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
819	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	3	2	no	—
836	C₂×C₄	—	3	2	no	—
837	C₂×C₄	—	3	2	no	—
838	C₂×C₄	—	6	8	no	—
839	C₂×C₄	—	6	1	no	—
840	C₂×C₄	—	6	1	no	—
841	C₂×C₄	—	6	1	no	—
842	C₂×C₄	—	6	1	no	—
843	C₂×C₄	—	6	1	no	—
844	C₂×C₄	—	6	1	no	—
845	C₂×C₄	—	6	1	no	—
846	C₂×C₄	—	6	1	no	—
847	C₂×C₄	—	6	1	no	—
848	C₂×C₄	—	6	1	no	—
849	C₂×C₄	—	6	1	no	—
850	C₂×C₄	—	6	1	no	—
851	C₂×C₄	—	6	1	no	—
852	C₂×C₄	—	6	1	no	—
853	C₂×C₄	—	6	1	no	—
854	C₂×C₄	—	12	4	no	—
855	C₂×C₄	—	12	4	no	—
856	C₂×C₄	—	12	4	no	—
857	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
858	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
859	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
860	C₂×C₃	—	4	2	no	—
861	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
862	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
863	C₂×C₃	C₅×#518	1	1	yes	characteristic
864	C₂×C₃	C₅×#546	1	1	yes	characteristic
865	C₂×C₃	C₅×#546	1	1	yes	characteristic
866	C₂×C₃	C₅×#551	1	1	yes	characteristic
867	C₂×C₃	C₅×#551	1	1	yes	characteristic
868	D₃	—	2	4	no	—
869	D₃	—	2	4	no	—
870	C₅	#75833	1	1	yes	characteristic, direct product factor, Sylow
871	C₂²	—	2	2	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	3	4	no	—
875	C₂²	—	3	4	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	6	2	no	—
881	C₂²	—	6	2	no	—
882	C₂²	—	6	2	no	—
883	C₂²	—	6	2	no	—
884	C₂²	—	6	2	no	—
885	C₂²	—	6	2	no	—
886	C₂²	—	6	2	no	—
887	C₂²	—	6	2	no	—
888	C₂²	—	6	2	no	—
889	C₂²	—	6	2	no	—
890	C₂²	—	6	2	no	—
891	C₂²	—	6	2	no	—
892	C₂²	—	12	16	no	—
893	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
894	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
895	C₂²	C₅×#1004	1	1	yes	characteristic
896	C₂²	C₅×D₃×#41	1	1	yes	characteristic
897	C₂²	C₅×D₃×#41	1	1	yes	characteristic
898	C₂²	C₅×D₃×#41	1	1	yes	characteristic
899	C₂²	C₅×#1009	1	1	yes	characteristic
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	2	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	1	no	—
906	C₄	—	6	2	no	—
907	C₄	—	6	2	no	—
908	C₄	—	6	2	no	—
909	C₄	—	12	1	no	—
910	C₄	—	12	1	no	—
911	C₄	—	12	1	no	—
912	C₃	C₅×#2342	1	1	yes	characteristic, complemented, Sylow
913	C₂	—	4	2	no	—
914	C₂	—	6	4	no	—
915	C₂	—	6	4	no	—
916	C₂	C₅×D₃×#117	1	1	yes	characteristic
917	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
918	C₂	C₅×#5545	1	1	yes	characteristic
919	C₂	C₅×#5610	1	1	yes	characteristic
920	C₂	C₅×#5659	1	1	yes	characteristic
921	C₂	C₅×#5676	1	1	yes	characteristic
922	C₂	C₅×#5705	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	C₂⁴×C₅×D₃	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#388	D₃
hypocenter	C₃	C₅×#2342
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×#892	C₂	semidirect
4. C₃×C₅×#388	C₂	semidirect
5. C₅×#4989	C₂	semidirect
7. C₅×#4951	C₂	semidirect
8. C₅×#4945	C₂	semidirect
9. C₅×#4944	C₂	semidirect
10. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
11. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
12. C₅×#4668	C₂	semidirect
13. C₅×#4667	C₂	semidirect
14. C₅×#4666	C₂	semidirect
15. C₅×#4664	C₂	semidirect
22. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
26. C₂×C₃×C₄²×C₅	C₂²	semidirect
38. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
39. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
40. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
41. C₂×C₄×C₅×Dic₃	C₂²	semidirect
42. C₂×C₄×C₅×Dic₃	C₂²	semidirect
43. C₂×C₄×C₅×Dic₃	C₂²	semidirect
46. C₅×D₃×C₂²⋊C₄	C₄	semidirect
47. C₃×C₅×#95	C₂²	semidirect
48. C₃×C₅×#95	C₂²	semidirect
49. C₅×C₃⋊#95	C₂²	semidirect
50. C₅×C₃⋊#95	C₂²	semidirect
51. C₅×C₃⋊#95	C₂²	semidirect
52. C₅×C₃⋊#95	C₂²	semidirect
53. C₅×C₃⋊#95	C₂²	semidirect
54. C₅×C₃⋊#95	C₂²	semidirect
55. #75833	C₅	direct (N × H)
62. C₅×#388	D₃	semidirect
103. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
104. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
108. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
112. C₅×#217	C₂×C₄	semidirect
127. C₂×#892	C₂×C₅	semidirect
130. C₃×#388	C₂×C₅	semidirect
131. #4989	C₂×C₅	semidirect
133. #4951	C₂×C₅	semidirect
134. #4945	C₂×C₅	semidirect
135. #4944	C₂×C₅	semidirect
136. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
137. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
138. #4668	C₂×C₅	semidirect
139. #4667	C₂×C₅	semidirect
140. #4666	C₂×C₅	semidirect
141. #4664	C₂×C₅	semidirect
151. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
171. C₂×C₄²×C₅	C₂×D₃	semidirect
178. C₅×#95	C₂×D₃	semidirect
179. C₅×#95	C₂×D₃	semidirect
255. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
259. C₂×C₃×C₄²	C₂²×C₅	semidirect
271. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
272. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
273. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
274. C₂×C₄×Dic₃	C₂²×C₅	semidirect
275. C₂×C₄×Dic₃	C₂²×C₅	semidirect
276. C₂×C₄×Dic₃	C₂²×C₅	semidirect
279. D₃×C₂²⋊C₄	C₄×C₅	semidirect
280. C₃×#95	C₂²×C₅	semidirect
281. C₃×#95	C₂²×C₅	semidirect
282. C₃⋊#95	C₂²×C₅	semidirect
283. C₃⋊#95	C₂²×C₅	semidirect
284. C₃⋊#95	C₂²×C₅	semidirect
285. C₃⋊#95	C₂²×C₅	semidirect
286. C₃⋊#95	C₂²×C₅	semidirect
287. C₃⋊#95	C₂²×C₅	semidirect
339. C₅×C₂²⋊C₄	C₄×D₃	semidirect
350. #388	C₅×D₃	semidirect
386. C₂×C₅×D₃	#117	semidirect
432. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
433. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
437. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
441. #217	C₂×C₄×C₅	semidirect
534. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
554. C₂×C₄²	C₂×C₅×D₃	semidirect
561. #95	C₂×C₅×D₃	semidirect
562. #95	C₂×C₅×D₃	semidirect
734. C₂²⋊C₄	C₄×C₅×D₃	semidirect
739. C₃×C₅	#2342	semidirect
767. C₂×D₃	C₅×#117	semidirect
870. C₅	#75833	direct (N × H)
912. C₃	C₅×#2342	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#892	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₃×C₅×#388	2
C₅×#4989	2
C₅×#4955	2
C₅×#4951	2
C₅×#4945	2
C₅×#4944	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₅×#4668	2
C₅×#4667	2
C₅×#4666	2
C₅×#4664	2
C₅×#2342	3
#75833	5

Subgroups — C5×#75833 #14326236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#75833 #14326236