Subgroups — C₅×D₃×#388 #14320432

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 956 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×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4951	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4945	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4944	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4940	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4670	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4669	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×D₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×D₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#388	—	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	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×#217	C₂²	1	1	yes	characteristic
30	C₂×C₅×#217	C₂²	1	1	yes	characteristic
31	C₂×C₅×#217	C₂²	1	1	yes	characteristic
32	C₂×C₅×(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×D₃×C₄⋊C₄	—	2	4	no	—
45	C₅×D₃×C₂²⋊C₄	—	2	4	no	—
46	C₅×D₃×C₂²⋊C₄	—	2	4	no	—
47	C₅×D₃×C₂²⋊C₄	C₄	1	8	yes	complemented
48	C₄²×C₅×D₃	—	2	4	no	—
49	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₅×#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	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
56	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
57	D₃×#388	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
58	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
59	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
60	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
61	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
62	C₂²×C₄²×C₅	—	3	1	no	—
63	C₅×#388	—	3	1	no	—
64	C₅×#388	—	3	1	no	—
65	C₅×#388	—	3	1	no	—
66	C₅×#388	—	3	1	no	—
67	C₅×#388	—	3	1	no	—
68	C₅×#388	—	3	1	no	—
69	C₅×#388	—	3	1	no	—
70	C₅×#388	D₃	1	1	yes	characteristic, direct product factor
71	C₂×C₅×#95	—	3	1	no	—
72	C₂×C₅×#95	—	3	1	no	—
73	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
74	C₂³×C₅×D₃	—	2	2	no	—
75	C₂³×C₅×D₃	—	2	2	no	—
76	C₂³×C₅×D₃	—	2	2	no	—
77	C₂³×C₅×D₃	—	2	2	no	—
78	C₂³×C₅×D₃	—	2	2	no	—
79	C₂³×C₅×D₃	—	2	2	no	—
80	C₂³×C₅×D₃	C₂×C₄	1	4	yes	—
81	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
82	C₂³×C₅×D₃	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×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	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	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
94	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
100	C₂×C₄×C₅×D₃	—	2	2	no	—
101	C₂×C₄×C₅×D₃	—	2	2	no	—
102	C₂×C₄×C₅×D₃	—	2	2	no	—
103	C₂×C₄×C₅×D₃	—	2	2	no	—
104	C₂×C₄×C₅×D₃	—	2	2	no	—
105	C₂×C₄×C₅×D₃	—	2	2	no	—
106	C₂×C₄×C₅×D₃	—	2	2	no	—
107	C₂×C₄×C₅×D₃	—	2	2	no	—
108	C₂×C₄×C₅×D₃	—	2	2	no	—
109	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
110	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
111	C₂×C₄×C₅×D₃	D₄	1	4	yes	—
112	C₂×C₄×C₅×D₃	D₄	1	4	yes	—
113	C₃×C₅×C₄⋊C₄	—	2	2	no	—
114	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
115	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
116	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	complemented
117	C₃×C₄²×C₅	—	2	2	no	—
118	C₅×#217	—	2	2	no	—
119	C₅×#217	—	2	2	no	—
120	C₅×#217	C₂×C₄	1	4	yes	complemented
121	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
122	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
123	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
124	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
125	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
126	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
127	C₅×C₄⋊Dic₃	—	2	2	no	—
128	C₅×Dic₃⋊C₄	—	2	2	no	—
129	C₅×Dic₃⋊C₄	—	2	2	no	—
130	C₄×C₅×Dic₃	—	2	2	no	—
131	C₄×C₅×Dic₃	—	2	2	no	—
132	C₄×C₅×Dic₃	—	2	2	no	—
133	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
134	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
135	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
136	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
137	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
139	#4990	C₂×C₅	1	1	yes	characteristic, complemented
140	#4951	C₂×C₅	1	1	yes	characteristic, complemented
141	#4945	C₂×C₅	1	1	yes	characteristic, complemented
142	#4944	C₂×C₅	1	1	yes	characteristic, complemented
143	#4940	C₂×C₅	1	1	yes	characteristic, complemented
144	#4670	C₂×C₅	1	1	yes	characteristic, complemented
145	#4669	C₂×C₅	1	1	yes	characteristic, complemented
146	D₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
147	D₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂⁵×C₅	—	3	1	no	—
149	C₂³×C₄×C₅	—	3	1	no	—
150	C₂³×C₄×C₅	—	3	1	no	—
151	C₂³×C₄×C₅	—	3	1	no	—
152	C₂³×C₄×C₅	—	3	1	no	—
153	C₂³×C₄×C₅	—	3	1	no	—
154	C₂³×C₄×C₅	—	3	1	no	—
155	C₂×C₅×C₄⋊C₄	—	3	1	no	—
156	C₂×C₅×C₄⋊C₄	—	3	1	no	—
157	C₂×C₅×C₄⋊C₄	—	3	1	no	—
158	C₂×C₅×C₄⋊C₄	—	6	4	no	—
159	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
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	8	no	—
164	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
165	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
166	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
167	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
168	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
169	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
170	C₂×C₅×C₂²⋊C₄	—	6	4	no	—
171	C₂×C₅×C₂²⋊C₄	—	6	4	no	—
172	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
173	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
174	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
175	C₂×C₄²×C₅	—	3	1	no	—
176	C₂×C₄²×C₅	—	3	1	no	—
177	C₂×C₄²×C₅	—	3	1	no	—
178	C₂×C₄²×C₅	—	6	4	no	—
179	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
180	C₅×#95	—	3	1	no	—
181	C₅×#95	—	3	1	no	—
182	C₅×#95	—	3	1	no	—
183	C₅×#95	—	3	1	no	—
184	C₅×#95	—	3	1	no	—
185	C₅×#95	—	3	1	no	—
186	C₅×#95	C₂×D₃	1	1	yes	characteristic, complemented
187	C₅×#95	C₂×D₃	1	1	yes	characteristic, complemented
188	C₂×#388	—	3	1	no	Sylow
189	C₂³×C₃×C₅	—	2	1	no	—
190	C₂³×C₃×C₅	—	2	1	no	—
191	C₂³×C₃×C₅	—	2	1	no	—
192	C₂³×C₃×C₅	—	2	1	no	—
193	C₂³×C₃×C₅	—	2	1	no	—
194	C₂³×C₃×C₅	—	2	1	no	—
195	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
196	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
197	C₂²×C₅×D₃	—	2	1	no	—
198	C₂²×C₅×D₃	—	2	1	no	—
199	C₂²×C₅×D₃	—	2	1	no	—
200	C₂²×C₅×D₃	—	2	1	no	—
201	C₂²×C₅×D₃	—	2	1	no	—
202	C₂²×C₅×D₃	—	2	1	no	—
203	C₂²×C₅×D₃	—	2	8	no	—
204	C₂²×C₅×D₃	—	2	8	no	—
205	C₂²×C₅×D₃	—	2	8	no	—
206	C₂²×C₅×D₃	—	4	4	no	—
207	C₂²×C₅×D₃	—	4	4	no	—
208	C₂²×C₅×D₃	—	4	4	no	—
209	C₂²×C₅×D₃	—	4	4	no	—
210	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
211	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
212	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
213	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
214	C₂²×C₅×D₃	#41	1	2	yes	—
215	C₂²×C₅×D₃	#41	1	2	yes	—
216	C₂²×C₅×D₃	#41	1	2	yes	—
217	C₂²×C₅×D₃	#41	1	2	yes	—
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	—	2	1	no	—
226	C₂×C₃×C₄×C₅	—	2	1	no	—
227	C₂×C₃×C₄×C₅	—	2	1	no	—
228	C₂×C₃×C₄×C₅	—	2	1	no	—
229	C₂×C₃×C₄×C₅	—	2	1	no	—
230	C₂×C₃×C₄×C₅	—	2	1	no	—
231	C₂×C₃×C₄×C₅	—	2	1	no	—
232	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
233	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
234	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
235	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
244	C₂×C₅×Dic₃	—	2	1	no	—
245	C₂×C₅×Dic₃	—	2	1	no	—
246	C₂×C₅×Dic₃	—	2	1	no	—
247	C₂×C₅×Dic₃	—	2	1	no	—
248	C₂×C₅×Dic₃	—	2	1	no	—
249	C₂×C₅×Dic₃	—	2	1	no	—
250	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
251	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
252	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
253	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
254	C₄×C₅×D₃	—	2	8	no	—
255	C₄×C₅×D₃	—	2	8	no	—
256	C₄×C₅×D₃	—	2	8	no	—
257	C₄×C₅×D₃	—	2	8	no	—
258	C₄×C₅×D₃	—	4	4	no	—
259	C₄×C₅×D₃	—	4	4	no	—
260	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
261	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
262	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
263	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
264	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
265	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
266	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
267	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
269	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₂×#217	C₂²×C₅	1	1	yes	characteristic
273	C₂×#217	C₂²×C₅	1	1	yes	characteristic
274	C₂×#217	C₂²×C₅	1	1	yes	characteristic
275	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
276	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
277	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
278	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
279	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
280	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
281	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
282	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
283	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
284	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
286	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
287	D₃×C₄⋊C₄	—	2	4	no	—
288	D₃×C₂²⋊C₄	—	2	4	no	—
289	D₃×C₂²⋊C₄	—	2	4	no	—
290	D₃×C₂²⋊C₄	C₄×C₅	1	8	yes	complemented
291	C₄²×D₃	—	2	4	no	—
292	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
293	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
294	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
295	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
296	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
297	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
298	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
299	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
300	C₂⁴×C₅	—	3	1	no	—
301	C₂⁴×C₅	—	3	4	no	—
302	C₂⁴×C₅	—	3	1	no	—
303	C₂⁴×C₅	—	6	2	no	—
304	C₂⁴×C₅	—	6	2	no	—
305	C₂⁴×C₅	—	6	2	no	—
306	C₂⁴×C₅	—	6	2	no	—
307	C₂⁴×C₅	—	6	2	no	—
308	C₂⁴×C₅	—	6	2	no	—
309	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
310	C₂²×C₄×C₅	—	3	1	no	—
311	C₂²×C₄×C₅	—	3	1	no	—
312	C₂²×C₄×C₅	—	3	1	no	—
313	C₂²×C₄×C₅	—	3	1	no	—
314	C₂²×C₄×C₅	—	3	4	no	—
315	C₂²×C₄×C₅	—	3	4	no	—
316	C₂²×C₄×C₅	—	3	4	no	—
317	C₂²×C₄×C₅	—	3	4	no	—
318	C₂²×C₄×C₅	—	3	1	no	—
319	C₂²×C₄×C₅	—	3	1	no	—
320	C₂²×C₄×C₅	—	6	2	no	—
321	C₂²×C₄×C₅	—	6	2	no	—
322	C₂²×C₄×C₅	—	6	2	no	—
323	C₂²×C₄×C₅	—	6	2	no	—
324	C₂²×C₄×C₅	—	6	2	no	—
325	C₂²×C₄×C₅	—	6	2	no	—
326	C₂²×C₄×C₅	—	6	2	no	—
327	C₂²×C₄×C₅	—	6	2	no	—
328	C₂²×C₄×C₅	—	6	2	no	—
329	C₂²×C₄×C₅	—	6	2	no	—
330	C₂²×C₄×C₅	—	6	2	no	—
331	C₂²×C₄×C₅	—	6	2	no	—
332	C₂²×C₄×C₅	—	6	2	no	—
333	C₂²×C₄×C₅	—	6	2	no	—
334	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
335	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
336	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
337	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
338	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
339	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
340	C₅×C₄⋊C₄	—	2	2	no	—
341	C₅×C₄⋊C₄	—	6	2	no	—
342	C₅×C₄⋊C₄	—	6	2	no	—
343	C₅×C₄⋊C₄	—	6	2	no	—
344	C₅×C₂²⋊C₄	—	2	2	no	—
345	C₅×C₂²⋊C₄	—	2	2	no	—
346	C₅×C₂²⋊C₄	—	3	4	no	—
347	C₅×C₂²⋊C₄	—	3	4	no	—
348	C₅×C₂²⋊C₄	—	3	4	no	—
349	C₅×C₂²⋊C₄	—	6	2	no	—
350	C₅×C₂²⋊C₄	—	6	2	no	—
351	C₅×C₂²⋊C₄	—	6	2	no	—
352	C₅×C₂²⋊C₄	—	6	2	no	—
353	C₅×C₂²⋊C₄	—	6	2	no	—
354	C₅×C₂²⋊C₄	—	6	2	no	—
355	C₅×C₂²⋊C₄	C₄×D₃	1	4	yes	complemented
356	C₄²×C₅	—	2	2	no	—
357	C₄²×C₅	—	6	2	no	—
358	C₄²×C₅	—	6	2	no	—
359	C₄²×C₅	—	6	2	no	—
360	C₂²×C₄⋊C₄	—	3	1	no	—
361	C₂²×C₂²⋊C₄	—	3	1	no	—
362	C₂²×C₂²⋊C₄	—	3	1	no	—
363	C₂²×C₂²⋊C₄	—	3	1	no	—
364	C₂²×C₄²	—	3	1	no	—
365	#388	—	3	1	no	—
366	#388	—	3	1	no	—
367	#388	—	3	1	no	—
368	#388	—	3	1	no	—
369	#388	—	3	1	no	—
370	#388	—	3	1	no	—
371	#388	—	3	1	no	—
372	#388	C₅×D₃	1	1	yes	characteristic, direct product factor
373	C₂×#95	—	3	1	no	—
374	C₂×#95	—	3	1	no	—
375	C₂²×C₃×C₅	—	2	2	no	—
376	C₂²×C₃×C₅	—	2	2	no	—
377	C₂²×C₃×C₅	—	2	2	no	—
378	C₂²×C₃×C₅	—	4	1	no	—
379	C₂²×C₃×C₅	—	4	1	no	—
380	C₂²×C₃×C₅	—	4	1	no	—
381	C₂²×C₃×C₅	—	4	1	no	—
382	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
383	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
384	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
385	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
386	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
387	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
388	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
389	C₂×C₅×D₃	—	2	2	no	—
390	C₂×C₅×D₃	—	2	2	no	—
391	C₂×C₅×D₃	—	2	2	no	—
392	C₂×C₅×D₃	—	4	1	no	—
393	C₂×C₅×D₃	—	4	1	no	—
394	C₂×C₅×D₃	—	4	1	no	—
395	C₂×C₅×D₃	—	4	1	no	—
396	C₂×C₅×D₃	—	4	16	no	—
397	C₂×C₅×D₃	#117	1	4	yes	—
398	C₂×C₅×D₃	C₄×D₄	1	4	yes	—
399	C₂×C₅×D₃	C₄×D₄	1	4	yes	—
400	C₂×C₅×D₃	#121	1	4	yes	—
401	C₂×C₅×D₃	#123	1	4	yes	—
402	C₂×C₅×D₃	#124	1	4	yes	—
403	C₂×C₅×D₃	#126	1	4	yes	—
404	C₃×C₄×C₅	—	2	2	no	—
405	C₃×C₄×C₅	—	2	2	no	—
406	C₃×C₄×C₅	—	2	2	no	—
407	C₃×C₄×C₅	—	2	2	no	—
408	C₃×C₄×C₅	—	4	1	no	—
409	C₃×C₄×C₅	—	4	1	no	—
410	C₅×Dic₃	—	2	2	no	—
411	C₅×Dic₃	—	2	2	no	—
412	C₅×Dic₃	—	2	2	no	—
413	C₅×Dic₃	—	2	2	no	—
414	C₅×Dic₃	—	4	1	no	—
415	C₅×Dic₃	—	4	1	no	—
416	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
417	C₂³×D₃	—	2	2	no	—
418	C₂³×D₃	—	2	2	no	—
419	C₂³×D₃	—	2	2	no	—
420	C₂³×D₃	—	2	2	no	—
421	C₂³×D₃	—	2	2	no	—
422	C₂³×D₃	—	2	2	no	—
423	C₂³×D₃	C₂×C₄×C₅	1	4	yes	—
424	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
425	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
426	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
427	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
428	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
430	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
431	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
432	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
433	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
434	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
435	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
436	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
437	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
438	C₂×C₄×D₃	—	2	2	no	—
439	C₂×C₄×D₃	—	2	2	no	—
440	C₂×C₄×D₃	—	2	2	no	—
441	C₂×C₄×D₃	—	2	2	no	—
442	C₂×C₄×D₃	—	2	2	no	—
443	C₂×C₄×D₃	—	2	2	no	—
444	C₂×C₄×D₃	—	2	2	no	—
445	C₂×C₄×D₃	—	2	2	no	—
446	C₂×C₄×D₃	—	2	2	no	—
447	C₂×C₄×D₃	—	2	2	no	—
448	C₂×C₄×D₃	—	2	2	no	—
449	C₂×C₄×D₃	—	2	2	no	—
450	C₂×C₄×D₃	—	2	2	no	—
451	C₂×C₄×D₃	—	2	2	no	—
452	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
453	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
454	C₂×C₄×D₃	C₅×D₄	1	4	yes	—
455	C₂×C₄×D₃	C₅×D₄	1	4	yes	—
456	C₃×C₄⋊C₄	—	2	2	no	—
457	C₃×C₂²⋊C₄	—	2	2	no	—
458	C₃×C₂²⋊C₄	—	2	2	no	—
459	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
460	C₃×C₄²	—	2	2	no	—
461	#217	—	2	2	no	—
462	#217	—	2	2	no	—
463	#217	C₂×C₄×C₅	1	4	yes	complemented
464	(C₂×D₃)⋊C₄	—	2	2	no	—
465	(C₂×D₃)⋊C₄	—	2	2	no	—
466	(C₂×D₃)⋊C₄	—	2	2	no	—
467	(C₂×D₃)⋊C₄	—	2	2	no	—
468	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
469	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
470	C₄⋊Dic₃	—	2	2	no	—
471	Dic₃⋊C₄	—	2	2	no	—
472	Dic₃⋊C₄	—	2	2	no	—
473	C₄×Dic₃	—	2	2	no	—
474	C₄×Dic₃	—	2	2	no	—
475	C₄×Dic₃	—	2	2	no	—
476	C₂³×C₅	—	2	1	no	—
477	C₂³×C₅	—	2	1	no	—
478	C₂³×C₅	—	2	1	no	—
479	C₂³×C₅	—	2	1	no	—
480	C₂³×C₅	—	2	1	no	—
481	C₂³×C₅	—	2	1	no	—
482	C₂³×C₅	—	3	2	no	—
483	C₂³×C₅	—	3	2	no	—
484	C₂³×C₅	—	3	2	no	—
485	C₂³×C₅	—	3	2	no	—
486	C₂³×C₅	—	3	2	no	—
487	C₂³×C₅	—	3	2	no	—
488	C₂³×C₅	—	3	2	no	—
489	C₂³×C₅	—	3	2	no	—
490	C₂³×C₅	—	6	8	no	—
491	C₂³×C₅	—	6	8	no	—
492	C₂³×C₅	—	6	8	no	—
493	C₂³×C₅	—	6	1	no	—
494	C₂³×C₅	—	6	1	no	—
495	C₂³×C₅	—	6	1	no	—
496	C₂³×C₅	—	6	1	no	—
497	C₂³×C₅	—	6	1	no	—
498	C₂³×C₅	—	6	1	no	—
499	C₂³×C₅	—	12	4	no	—
500	C₂³×C₅	—	12	4	no	—
501	C₂³×C₅	—	12	4	no	—
502	C₂³×C₅	—	12	4	no	—
503	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
504	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
505	C₂×C₄×C₅	—	2	1	no	—
506	C₂×C₄×C₅	—	2	1	no	—
507	C₂×C₄×C₅	—	2	1	no	—
508	C₂×C₄×C₅	—	2	1	no	—
509	C₂×C₄×C₅	—	2	1	no	—
510	C₂×C₄×C₅	—	2	1	no	—
511	C₂×C₄×C₅	—	2	1	no	—
512	C₂×C₄×C₅	—	2	1	no	—
513	C₂×C₄×C₅	—	2	1	no	—
514	C₂×C₄×C₅	—	2	1	no	—
515	C₂×C₄×C₅	—	2	1	no	—
516	C₂×C₄×C₅	—	2	1	no	—
517	C₂×C₄×C₅	—	2	1	no	—
518	C₂×C₄×C₅	—	2	1	no	—
519	C₂×C₄×C₅	—	3	2	no	—
520	C₂×C₄×C₅	—	3	2	no	—
521	C₂×C₄×C₅	—	3	2	no	—
522	C₂×C₄×C₅	—	3	2	no	—
523	C₂×C₄×C₅	—	6	8	no	—
524	C₂×C₄×C₅	—	6	8	no	—
525	C₂×C₄×C₅	—	6	8	no	—
526	C₂×C₄×C₅	—	6	8	no	—
527	C₂×C₄×C₅	—	6	1	no	—
528	C₂×C₄×C₅	—	6	1	no	—
529	C₂×C₄×C₅	—	6	1	no	—
530	C₂×C₄×C₅	—	6	1	no	—
531	C₂×C₄×C₅	—	6	1	no	—
532	C₂×C₄×C₅	—	6	1	no	—
533	C₂×C₄×C₅	—	6	1	no	—
534	C₂×C₄×C₅	—	6	1	no	—
535	C₂×C₄×C₅	—	6	1	no	—
536	C₂×C₄×C₅	—	6	1	no	—
537	C₂×C₄×C₅	—	6	1	no	—
538	C₂×C₄×C₅	—	6	1	no	—
539	C₂×C₄×C₅	—	6	1	no	—
540	C₂×C₄×C₅	—	6	1	no	—
541	C₂×C₄×C₅	—	12	4	no	—
542	C₂×C₄×C₅	—	12	4	no	—
543	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
544	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
545	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
546	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
547	C₂⁵	—	3	1	no	—
548	C₂³×C₄	—	3	1	no	—
549	C₂³×C₄	—	3	1	no	—
550	C₂³×C₄	—	3	1	no	—
551	C₂³×C₄	—	3	1	no	—
552	C₂³×C₄	—	3	1	no	—
553	C₂³×C₄	—	3	1	no	—
554	C₂×C₄⋊C₄	—	3	1	no	—
555	C₂×C₄⋊C₄	—	3	1	no	—
556	C₂×C₄⋊C₄	—	3	1	no	—
557	C₂×C₄⋊C₄	—	6	4	no	—
558	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
559	C₂×C₂²⋊C₄	—	3	1	no	—
560	C₂×C₂²⋊C₄	—	3	1	no	—
561	C₂×C₂²⋊C₄	—	3	1	no	—
562	C₂×C₂²⋊C₄	—	3	8	no	—
563	C₂×C₂²⋊C₄	—	3	1	no	—
564	C₂×C₂²⋊C₄	—	3	1	no	—
565	C₂×C₂²⋊C₄	—	3	1	no	—
566	C₂×C₂²⋊C₄	—	3	1	no	—
567	C₂×C₂²⋊C₄	—	3	1	no	—
568	C₂×C₂²⋊C₄	—	3	1	no	—
569	C₂×C₂²⋊C₄	—	6	4	no	—
570	C₂×C₂²⋊C₄	—	6	4	no	—
571	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
572	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
573	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
574	C₂×C₄²	—	3	1	no	—
575	C₂×C₄²	—	3	1	no	—
576	C₂×C₄²	—	3	1	no	—
577	C₂×C₄²	—	6	4	no	—
578	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
579	#95	—	3	1	no	—
580	#95	—	3	1	no	—
581	#95	—	3	1	no	—
582	#95	—	3	1	no	—
583	#95	—	3	1	no	—
584	#95	—	3	1	no	—
585	#95	C₂×C₅×D₃	1	1	yes	characteristic, complemented
586	#95	C₂×C₅×D₃	1	1	yes	characteristic, complemented
587	C₂×C₃×C₅	—	4	2	no	—
588	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
589	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
590	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
591	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
592	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
593	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
594	C₂×C₃×C₅	C₂×#126	1	1	yes	characteristic
595	C₅×D₃	—	4	2	no	—
596	C₅×D₃	#388	1	8	yes	direct product factor
597	C₂³×C₃	—	2	1	no	—
598	C₂³×C₃	—	2	1	no	—
599	C₂³×C₃	—	2	1	no	—
600	C₂³×C₃	—	2	1	no	—
601	C₂³×C₃	—	2	1	no	—
602	C₂³×C₃	—	2	1	no	—
603	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
604	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
605	C₂²×D₃	—	2	1	no	—
606	C₂²×D₃	—	2	1	no	—
607	C₂²×D₃	—	2	1	no	—
608	C₂²×D₃	—	2	1	no	—
609	C₂²×D₃	—	2	1	no	—
610	C₂²×D₃	—	2	1	no	—
611	C₂²×D₃	—	2	8	no	—
612	C₂²×D₃	—	2	8	no	—
613	C₂²×D₃	—	2	8	no	—
614	C₂²×D₃	—	4	4	no	—
615	C₂²×D₃	—	4	4	no	—
616	C₂²×D₃	—	4	4	no	—
617	C₂²×D₃	—	4	4	no	—
618	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
619	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
620	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
621	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
622	C₂²×D₃	C₅×#41	1	2	yes	—
623	C₂²×D₃	C₅×#41	1	2	yes	—
624	C₂²×D₃	C₅×#41	1	2	yes	—
625	C₂²×D₃	C₅×#41	1	2	yes	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	—	2	1	no	—
631	C₂×C₃×C₄	—	2	1	no	—
632	C₂×C₃×C₄	—	2	1	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	2	1	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	1	no	—
637	C₂×C₃×C₄	—	2	1	no	—
638	C₂×C₃×C₄	—	2	1	no	—
639	C₂×C₃×C₄	—	2	1	no	—
640	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
641	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
642	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
643	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
644	C₂×Dic₃	—	2	1	no	—
645	C₂×Dic₃	—	2	1	no	—
646	C₂×Dic₃	—	2	1	no	—
647	C₂×Dic₃	—	2	1	no	—
648	C₂×Dic₃	—	2	1	no	—
649	C₂×Dic₃	—	2	1	no	—
650	C₂×Dic₃	—	2	1	no	—
651	C₂×Dic₃	—	2	1	no	—
652	C₂×Dic₃	—	2	1	no	—
653	C₂×Dic₃	—	2	1	no	—
654	C₂×Dic₃	—	2	1	no	—
655	C₂×Dic₃	—	2	1	no	—
656	C₂×Dic₃	—	2	1	no	—
657	C₂×Dic₃	—	2	1	no	—
658	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
659	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
660	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
661	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
662	C₄×D₃	—	2	8	no	—
663	C₄×D₃	—	2	8	no	—
664	C₄×D₃	—	2	8	no	—
665	C₄×D₃	—	2	8	no	—
666	C₄×D₃	—	4	4	no	—
667	C₄×D₃	—	4	4	no	—
668	C₂²×C₅	—	2	2	no	—
669	C₂²×C₅	—	2	2	no	—
670	C₂²×C₅	—	2	2	no	—
671	C₂²×C₅	—	3	4	no	—
672	C₂²×C₅	—	3	4	no	—
673	C₂²×C₅	—	3	4	no	—
674	C₂²×C₅	—	3	4	no	—
675	C₂²×C₅	—	3	4	no	—
676	C₂²×C₅	—	3	4	no	—
677	C₂²×C₅	—	3	4	no	—
678	C₂²×C₅	—	4	1	no	—
679	C₂²×C₅	—	4	1	no	—
680	C₂²×C₅	—	4	1	no	—
681	C₂²×C₅	—	4	1	no	—
682	C₂²×C₅	—	6	2	no	—
683	C₂²×C₅	—	6	2	no	—
684	C₂²×C₅	—	6	2	no	—
685	C₂²×C₅	—	12	16	no	—
686	C₂²×C₅	—	12	1	no	—
687	C₂²×C₅	—	12	1	no	—
688	C₂²×C₅	—	12	1	no	—
689	C₂²×C₅	—	12	1	no	—
690	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
691	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
692	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
693	C₂²×C₅	D₃×#41	1	1	yes	characteristic
694	C₂²×C₅	D₃×#41	1	1	yes	characteristic
695	C₂²×C₅	D₃×#41	1	1	yes	characteristic
696	C₂²×C₅	D₃×#41	1	1	yes	characteristic
697	C₄×C₅	—	2	2	no	—
698	C₄×C₅	—	2	2	no	—
699	C₄×C₅	—	2	2	no	—
700	C₄×C₅	—	2	2	no	—
701	C₄×C₅	—	4	1	no	—
702	C₄×C₅	—	4	1	no	—
703	C₄×C₅	—	6	2	no	—
704	C₄×C₅	—	6	2	no	—
705	C₄×C₅	—	6	2	no	—
706	C₄×C₅	—	6	2	no	—
707	C₄×C₅	—	12	1	no	—
708	C₄×C₅	—	12	1	no	—
709	C₂⁴	—	3	1	no	—
710	C₂⁴	—	3	4	no	—
711	C₂⁴	—	3	1	no	—
712	C₂⁴	—	6	2	no	—
713	C₂⁴	—	6	2	no	—
714	C₂⁴	—	6	2	no	—
715	C₂⁴	—	6	2	no	—
716	C₂⁴	—	6	2	no	—
717	C₂⁴	—	6	2	no	—
718	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
719	C₂²×C₄	—	3	1	no	—
720	C₂²×C₄	—	3	1	no	—
721	C₂²×C₄	—	3	1	no	—
722	C₂²×C₄	—	3	1	no	—
723	C₂²×C₄	—	3	4	no	—
724	C₂²×C₄	—	3	4	no	—
725	C₂²×C₄	—	3	4	no	—
726	C₂²×C₄	—	3	4	no	—
727	C₂²×C₄	—	3	1	no	—
728	C₂²×C₄	—	3	1	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	—	6	2	no	—
734	C₂²×C₄	—	6	2	no	—
735	C₂²×C₄	—	6	2	no	—
736	C₂²×C₄	—	6	2	no	—
737	C₂²×C₄	—	6	2	no	—
738	C₂²×C₄	—	6	2	no	—
739	C₂²×C₄	—	6	2	no	—
740	C₂²×C₄	—	6	2	no	—
741	C₂²×C₄	—	6	2	no	—
742	C₂²×C₄	—	6	2	no	—
743	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
744	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
745	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
746	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
747	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
748	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	6	2	no	—
751	C₄⋊C₄	—	6	2	no	—
752	C₄⋊C₄	—	6	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	3	4	no	—
756	C₂²⋊C₄	—	3	4	no	—
757	C₂²⋊C₄	—	3	4	no	—
758	C₂²⋊C₄	—	6	2	no	—
759	C₂²⋊C₄	—	6	2	no	—
760	C₂²⋊C₄	—	6	2	no	—
761	C₂²⋊C₄	—	6	2	no	—
762	C₂²⋊C₄	—	6	2	no	—
763	C₂²⋊C₄	—	6	2	no	—
764	C₂²⋊C₄	C₄×C₅×D₃	1	4	yes	complemented
765	C₄²	—	2	2	no	—
766	C₄²	—	6	2	no	—
767	C₄²	—	6	2	no	—
768	C₄²	—	6	2	no	—
769	C₃×C₅	C₂×#388	1	1	yes	characteristic, complemented, Hall
770	C₂²×C₃	—	2	2	no	—
771	C₂²×C₃	—	2	2	no	—
772	C₂²×C₃	—	2	2	no	—
773	C₂²×C₃	—	4	1	no	—
774	C₂²×C₃	—	4	1	no	—
775	C₂²×C₃	—	4	1	no	—
776	C₂²×C₃	—	4	1	no	—
777	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
778	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
779	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
780	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
781	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
782	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
783	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
784	C₂×D₃	—	2	2	no	—
785	C₂×D₃	—	2	2	no	—
786	C₂×D₃	—	2	2	no	—
787	C₂×D₃	—	4	1	no	—
788	C₂×D₃	—	4	1	no	—
789	C₂×D₃	—	4	1	no	—
790	C₂×D₃	—	4	1	no	—
791	C₂×D₃	—	4	16	no	—
792	C₂×D₃	C₅×#117	1	4	yes	—
793	C₂×D₃	C₄×C₅×D₄	1	4	yes	—
794	C₂×D₃	C₄×C₅×D₄	1	4	yes	—
795	C₂×D₃	C₅×#121	1	4	yes	—
796	C₂×D₃	C₅×#123	1	4	yes	—
797	C₂×D₃	C₅×#124	1	4	yes	—
798	C₂×D₃	C₅×#126	1	4	yes	—
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	—	2	2	no	—
801	C₃×C₄	—	2	2	no	—
802	C₃×C₄	—	2	2	no	—
803	C₃×C₄	—	4	1	no	—
804	C₃×C₄	—	4	1	no	—
805	Dic₃	—	2	2	no	—
806	Dic₃	—	2	2	no	—
807	Dic₃	—	2	2	no	—
808	Dic₃	—	2	2	no	—
809	Dic₃	—	4	1	no	—
810	Dic₃	—	4	1	no	—
811	C₂×C₅	—	3	8	no	—
812	C₂×C₅	—	4	2	no	—
813	C₂×C₅	—	12	2	no	—
814	C₂×C₅	D₃×#117	1	1	yes	characteristic
815	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
816	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
817	C₂×C₅	D₃×#121	1	1	yes	characteristic
818	C₂×C₅	D₃×#123	1	1	yes	characteristic
819	C₂×C₅	D₃×#124	1	1	yes	characteristic
820	C₂×C₅	D₃×#126	1	1	yes	characteristic
821	C₂³	—	2	1	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	3	2	no	—
828	C₂³	—	3	2	no	—
829	C₂³	—	3	2	no	—
830	C₂³	—	3	2	no	—
831	C₂³	—	3	2	no	—
832	C₂³	—	3	2	no	—
833	C₂³	—	3	2	no	—
834	C₂³	—	3	2	no	—
835	C₂³	—	6	8	no	—
836	C₂³	—	6	8	no	—
837	C₂³	—	6	8	no	—
838	C₂³	—	6	1	no	—
839	C₂³	—	6	1	no	—
840	C₂³	—	6	1	no	—
841	C₂³	—	6	1	no	—
842	C₂³	—	6	1	no	—
843	C₂³	—	6	1	no	—
844	C₂³	—	12	4	no	—
845	C₂³	—	12	4	no	—
846	C₂³	—	12	4	no	—
847	C₂³	—	12	4	no	—
848	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
849	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	3	2	no	—
865	C₂×C₄	—	3	2	no	—
866	C₂×C₄	—	3	2	no	—
867	C₂×C₄	—	3	2	no	—
868	C₂×C₄	—	6	8	no	—
869	C₂×C₄	—	6	8	no	—
870	C₂×C₄	—	6	8	no	—
871	C₂×C₄	—	6	8	no	—
872	C₂×C₄	—	6	1	no	—
873	C₂×C₄	—	6	1	no	—
874	C₂×C₄	—	6	1	no	—
875	C₂×C₄	—	6	1	no	—
876	C₂×C₄	—	6	1	no	—
877	C₂×C₄	—	6	1	no	—
878	C₂×C₄	—	6	1	no	—
879	C₂×C₄	—	6	1	no	—
880	C₂×C₄	—	6	1	no	—
881	C₂×C₄	—	6	1	no	—
882	C₂×C₄	—	6	1	no	—
883	C₂×C₄	—	6	1	no	—
884	C₂×C₄	—	6	1	no	—
885	C₂×C₄	—	6	1	no	—
886	C₂×C₄	—	12	4	no	—
887	C₂×C₄	—	12	4	no	—
888	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
889	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
890	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
891	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
892	C₂×C₃	—	4	2	no	—
893	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
894	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
895	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
896	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
897	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
898	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
899	C₂×C₃	C₂×C₅×#126	1	1	yes	characteristic
900	D₃	—	4	2	no	—
901	D₃	C₅×#388	1	8	yes	direct product factor
902	C₅	D₃×#388	1	1	yes	characteristic, direct product factor, Sylow
903	C₂²	—	2	2	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	2	2	no	—
906	C₂²	—	3	4	no	—
907	C₂²	—	3	4	no	—
908	C₂²	—	3	4	no	—
909	C₂²	—	3	4	no	—
910	C₂²	—	3	4	no	—
911	C₂²	—	3	4	no	—
912	C₂²	—	3	4	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	6	2	no	—
918	C₂²	—	6	2	no	—
919	C₂²	—	6	2	no	—
920	C₂²	—	12	16	no	—
921	C₂²	—	12	1	no	—
922	C₂²	—	12	1	no	—
923	C₂²	—	12	1	no	—
924	C₂²	—	12	1	no	—
925	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
926	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
927	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
928	C₂²	C₅×D₃×#41	1	1	yes	characteristic
929	C₂²	C₅×D₃×#41	1	1	yes	characteristic
930	C₂²	C₅×D₃×#41	1	1	yes	characteristic
931	C₂²	C₅×D₃×#41	1	1	yes	characteristic
932	C₄	—	2	2	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	4	1	no	—
937	C₄	—	4	1	no	—
938	C₄	—	6	2	no	—
939	C₄	—	6	2	no	—
940	C₄	—	6	2	no	—
941	C₄	—	6	2	no	—
942	C₄	—	12	1	no	—
943	C₄	—	12	1	no	—
944	C₃	C₂×C₅×#388	1	1	yes	characteristic, complemented, Sylow
945	C₂	—	3	8	no	—
946	C₂	—	4	2	no	—
947	C₂	—	12	2	no	—
948	C₂	C₅×D₃×#117	1	1	yes	characteristic
949	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
950	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
951	C₂	C₅×D₃×#121	1	1	yes	characteristic
952	C₂	C₅×D₃×#123	1	1	yes	characteristic
953	C₂	C₅×D₃×#124	1	1	yes	characteristic
954	C₂	C₅×D₃×#126	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	C₂×C₅×#388
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
5. C₂×C₄²×C₅×D₃	C₂	semidirect
6. C₃×C₅×#388	C₂	semidirect
7. C₅×#4990	C₂	semidirect
8. C₅×#4951	C₂	semidirect
9. C₅×#4945	C₂	semidirect
10. C₅×#4944	C₂	semidirect
11. C₅×#4940	C₂	semidirect
12. C₅×#4670	C₂	semidirect
13. C₅×#4669	C₂	semidirect
14. C₅×D₃×#95	C₂	semidirect
15. C₅×D₃×#95	C₂	semidirect
24. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
28. 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
47. C₅×D₃×C₂²⋊C₄	C₄	semidirect
49. C₃×C₅×#95	C₂²	semidirect
50. C₃×C₅×#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. C₅×C₃⋊#95	C₂²	semidirect
56. C₅×C₃⋊#95	C₂²	semidirect
57. D₃×#388	C₅	direct (N × H)
70. C₅×#388	D₃	direct (N × H)
116. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
120. C₅×#217	C₂×C₄	semidirect
125. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
126. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
133. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
137. C₂×C₄²×D₃	C₂×C₅	semidirect
138. C₃×#388	C₂×C₅	semidirect
139. #4990	C₂×C₅	semidirect
140. #4951	C₂×C₅	semidirect
141. #4945	C₂×C₅	semidirect
142. #4944	C₂×C₅	semidirect
143. #4940	C₂×C₅	semidirect
144. #4670	C₂×C₅	semidirect
145. #4669	C₂×C₅	semidirect
146. D₃×#95	C₂×C₅	semidirect
147. D₃×#95	C₂×C₅	semidirect
159. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
179. C₂×C₄²×C₅	C₂×D₃	semidirect
186. C₅×#95	C₂×D₃	semidirect
187. C₅×#95	C₂×D₃	semidirect
267. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
271. C₂×C₃×C₄²	C₂²×C₅	semidirect
281. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
282. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
283. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
284. C₂×C₄×Dic₃	C₂²×C₅	semidirect
285. C₂×C₄×Dic₃	C₂²×C₅	semidirect
286. C₂×C₄×Dic₃	C₂²×C₅	semidirect
290. D₃×C₂²⋊C₄	C₄×C₅	semidirect
292. C₃×#95	C₂²×C₅	semidirect
293. C₃×#95	C₂²×C₅	semidirect
294. C₃⋊#95	C₂²×C₅	semidirect
295. C₃⋊#95	C₂²×C₅	semidirect
296. C₃⋊#95	C₂²×C₅	semidirect
297. C₃⋊#95	C₂²×C₅	semidirect
298. C₃⋊#95	C₂²×C₅	semidirect
299. C₃⋊#95	C₂²×C₅	semidirect
355. C₅×C₂²⋊C₄	C₄×D₃	semidirect
372. #388	C₅×D₃	direct (N × H)
459. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
463. #217	C₂×C₄×C₅	semidirect
468. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
469. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
558. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
578. C₂×C₄²	C₂×C₅×D₃	semidirect
585. #95	C₂×C₅×D₃	semidirect
586. #95	C₂×C₅×D₃	semidirect
596. C₅×D₃	#388	direct (N × H)
764. C₂²⋊C₄	C₄×C₅×D₃	semidirect
769. C₃×C₅	C₂×#388	semidirect
901. D₃	C₅×#388	direct (N × H)
902. C₅	D₃×#388	direct (N × H)
944. C₃	C₂×C₅×#388	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×D₃×C₂²⋊C₄	2
C₂×C₄²×C₅×D₃	2
C₃×C₅×#388	2
C₅×#4990	2
C₅×#4951	2
C₅×#4945	2
C₅×#4944	2
C₅×#4940	2
C₅×#4670	2
C₅×#4669	2
C₅×D₃×#95	2
C₂×C₅×#388	3
D₃×#388	5

Subgroups — C5×D3×#388 #14320432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#388 #14320432