Subgroups — C₃×C₅×#2424 #14275458

Order 1920.

1844 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#396	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#392	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2424	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
26	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
27	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×#121	—	2	4	no	—
29	C₃×C₅×#121	—	2	4	no	—
30	C₃×C₅×#120	—	2	4	no	—
31	C₃×C₅×#120	—	2	4	no	—
32	C₃×C₄×C₅×D₄	—	2	4	no	—
33	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
38	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
56	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
57	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
58	C₃×#2424	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
59	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic, complemented
63	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#396	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#392	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#388	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#385	C₂×C₃	1	1	yes	characteristic, complemented
74	C₂⁴×C₃×C₅	—	2	2	no	—
75	C₂⁴×C₃×C₅	—	2	2	no	—
76	C₂⁴×C₃×C₅	—	2	2	no	—
77	C₂⁴×C₃×C₅	—	2	2	no	—
78	C₂⁴×C₃×C₅	—	2	2	no	—
79	C₂⁴×C₃×C₅	—	4	1	no	—
80	C₂⁴×C₃×C₅	—	4	1	no	—
81	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
82	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
83	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
84	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
85	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×D₄	—	2	2	no	—
87	C₂×C₃×C₅×D₄	—	2	2	no	—
88	C₂×C₃×C₅×D₄	—	2	2	no	—
89	C₂×C₃×C₅×D₄	—	2	2	no	—
90	C₂×C₃×C₅×D₄	—	2	2	no	—
91	C₂×C₃×C₅×D₄	—	2	2	no	—
92	C₂×C₃×C₅×D₄	—	2	2	no	—
93	C₂×C₃×C₅×D₄	—	2	2	no	—
94	C₂×C₃×C₅×D₄	—	2	2	no	—
95	C₂×C₃×C₅×D₄	—	2	2	no	—
96	C₂×C₃×C₅×D₄	—	2	2	no	—
97	C₂×C₃×C₅×D₄	—	2	2	no	—
98	C₂×C₃×C₅×D₄	—	2	2	no	—
99	C₂×C₃×C₅×D₄	—	2	2	no	—
100	C₂×C₃×C₅×D₄	—	2	2	no	—
101	C₂×C₃×C₅×D₄	—	4	1	no	—
102	C₂×C₃×C₅×D₄	—	4	1	no	—
103	C₂×C₃×C₅×D₄	—	4	1	no	—
104	C₂×C₃×C₅×D₄	—	4	1	no	—
105	C₂×C₃×C₅×D₄	—	4	1	no	—
106	C₂×C₃×C₅×D₄	D₄	1	4	yes	complemented
107	C₂²×C₃×C₄×C₅	—	2	2	no	—
108	C₂²×C₃×C₄×C₅	—	2	2	no	—
109	C₂²×C₃×C₄×C₅	—	2	2	no	—
110	C₂²×C₃×C₄×C₅	—	2	2	no	—
111	C₂²×C₃×C₄×C₅	—	2	2	no	—
112	C₂²×C₃×C₄×C₅	—	2	2	no	—
113	C₂²×C₃×C₄×C₅	—	4	1	no	—
114	C₂²×C₃×C₄×C₅	—	4	1	no	—
115	C₂²×C₃×C₄×C₅	—	4	1	no	—
116	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
117	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
118	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
119	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
120	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
121	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
122	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
123	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
124	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
125	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
126	C₃×C₅×C₄⋊C₄	—	2	2	no	—
127	C₃×C₅×C₄⋊C₄	—	2	2	no	—
128	C₃×C₅×C₄⋊C₄	—	2	2	no	—
129	C₃×C₅×C₄⋊C₄	—	4	1	no	—
130	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
131	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
132	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
133	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
134	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
135	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
136	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
137	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
138	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
139	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
140	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
141	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
142	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
143	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	complemented
144	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	complemented
145	C₃×C₄²×C₅	—	2	2	no	—
146	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
147	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic, complemented
149	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic, complemented
150	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
151	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
152	C₃×#396	C₂×C₅	1	1	yes	characteristic, complemented
153	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
154	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
155	C₃×#392	C₂×C₅	1	1	yes	characteristic, complemented
156	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
157	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
158	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
159	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
160	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
161	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
162	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
163	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
164	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
165	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
166	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
167	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
168	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
170	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
171	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₅×#121	—	2	4	no	—
173	C₅×#121	—	2	4	no	—
174	C₅×#120	—	2	4	no	—
175	C₅×#120	—	2	4	no	—
176	C₄×C₅×D₄	—	2	4	no	—
177	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
178	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
180	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
182	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
183	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
184	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
185	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
186	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
187	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
188	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
189	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
190	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
191	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
192	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
194	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
195	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
196	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
198	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
199	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
200	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
201	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
202	#2424	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
203	C₂³×C₃×C₅	—	2	1	no	—
204	C₂³×C₃×C₅	—	2	1	no	—
205	C₂³×C₃×C₅	—	2	1	no	—
206	C₂³×C₃×C₅	—	2	1	no	—
207	C₂³×C₃×C₅	—	2	8	no	—
208	C₂³×C₃×C₅	—	2	1	no	—
209	C₂³×C₃×C₅	—	2	1	no	—
210	C₂³×C₃×C₅	—	2	1	no	—
211	C₂³×C₃×C₅	—	2	1	no	—
212	C₂³×C₃×C₅	—	2	1	no	—
213	C₂³×C₃×C₅	—	2	1	no	—
214	C₂³×C₃×C₅	—	2	1	no	—
215	C₂³×C₃×C₅	—	2	1	no	—
216	C₂³×C₃×C₅	—	2	1	no	—
217	C₂³×C₃×C₅	—	2	1	no	—
218	C₂³×C₃×C₅	—	2	1	no	—
219	C₂³×C₃×C₅	—	2	1	no	—
220	C₂³×C₃×C₅	—	2	1	no	—
221	C₂³×C₃×C₅	—	2	1	no	—
222	C₂³×C₃×C₅	—	2	1	no	—
223	C₂³×C₃×C₅	—	2	1	no	—
224	C₂³×C₃×C₅	—	2	1	no	—
225	C₂³×C₃×C₅	—	2	1	no	—
226	C₂³×C₃×C₅	—	2	1	no	—
227	C₂³×C₃×C₅	—	2	1	no	—
228	C₂³×C₃×C₅	—	2	1	no	—
229	C₂³×C₃×C₅	—	2	1	no	—
230	C₂³×C₃×C₅	—	2	1	no	—
231	C₂³×C₃×C₅	—	2	1	no	—
232	C₂³×C₃×C₅	—	2	1	no	—
233	C₂³×C₃×C₅	—	4	4	no	—
234	C₂³×C₃×C₅	—	4	4	no	—
235	C₂³×C₃×C₅	—	4	4	no	—
236	C₂³×C₃×C₅	—	4	4	no	—
237	C₂³×C₃×C₅	—	4	4	no	—
238	C₂³×C₃×C₅	—	4	4	no	—
239	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
240	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
241	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
242	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
243	C₂³×C₃×C₅	#41	1	2	yes	—
244	C₂³×C₃×C₅	#41	1	2	yes	—
245	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
246	C₃×C₅×D₄	—	2	8	no	—
247	C₃×C₅×D₄	—	4	4	no	—
248	C₃×C₅×D₄	—	4	4	no	—
249	C₃×C₅×D₄	—	4	4	no	—
250	C₃×C₅×D₄	—	4	4	no	—
251	C₃×C₅×D₄	—	4	4	no	—
252	C₃×C₅×D₄	—	4	4	no	—
253	C₂×C₃×C₄×C₅	—	2	1	no	—
254	C₂×C₃×C₄×C₅	—	2	1	no	—
255	C₂×C₃×C₄×C₅	—	2	1	no	—
256	C₂×C₃×C₄×C₅	—	2	1	no	—
257	C₂×C₃×C₄×C₅	—	2	1	no	—
258	C₂×C₃×C₄×C₅	—	2	1	no	—
259	C₂×C₃×C₄×C₅	—	2	1	no	—
260	C₂×C₃×C₄×C₅	—	2	1	no	—
261	C₂×C₃×C₄×C₅	—	2	1	no	—
262	C₂×C₃×C₄×C₅	—	2	1	no	—
263	C₂×C₃×C₄×C₅	—	2	1	no	—
264	C₂×C₃×C₄×C₅	—	2	1	no	—
265	C₂×C₃×C₄×C₅	—	2	1	no	—
266	C₂×C₃×C₄×C₅	—	2	1	no	—
267	C₂×C₃×C₄×C₅	—	2	1	no	—
268	C₂×C₃×C₄×C₅	—	2	1	no	—
269	C₂×C₃×C₄×C₅	—	2	1	no	—
270	C₂×C₃×C₄×C₅	—	2	1	no	—
271	C₂×C₃×C₄×C₅	—	2	1	no	—
272	C₂×C₃×C₄×C₅	—	2	1	no	—
273	C₂×C₃×C₄×C₅	—	2	1	no	—
274	C₂×C₃×C₄×C₅	—	2	1	no	—
275	C₂×C₃×C₄×C₅	—	2	1	no	—
276	C₂×C₃×C₄×C₅	—	2	1	no	—
277	C₂×C₃×C₄×C₅	—	2	1	no	—
278	C₂×C₃×C₄×C₅	—	4	4	no	—
279	C₂×C₃×C₄×C₅	—	4	4	no	—
280	C₂×C₃×C₄×C₅	—	4	4	no	—
281	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
282	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
283	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
284	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
285	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
286	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
287	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
288	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
289	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
290	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
291	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
292	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
293	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
294	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
295	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
296	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
297	C₃×#121	—	2	4	no	—
298	C₃×#121	—	2	4	no	—
299	C₃×#120	—	2	4	no	—
300	C₃×#120	—	2	4	no	—
301	C₃×C₄×D₄	—	2	4	no	—
302	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
303	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
304	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
305	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
306	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
307	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
308	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
309	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
310	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
311	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
312	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
313	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
314	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
315	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
316	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
317	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
318	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
319	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
320	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
321	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
322	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
323	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
324	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
325	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
326	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
327	C₂⁴×C₅	—	2	2	no	—
328	C₂⁴×C₅	—	2	2	no	—
329	C₂⁴×C₅	—	2	2	no	—
330	C₂⁴×C₅	—	2	2	no	—
331	C₂⁴×C₅	—	2	2	no	—
332	C₂⁴×C₅	—	4	1	no	—
333	C₂⁴×C₅	—	4	1	no	—
334	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
335	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
336	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
337	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
338	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
339	C₂×C₅×D₄	—	2	2	no	—
340	C₂×C₅×D₄	—	2	2	no	—
341	C₂×C₅×D₄	—	2	2	no	—
342	C₂×C₅×D₄	—	2	2	no	—
343	C₂×C₅×D₄	—	2	2	no	—
344	C₂×C₅×D₄	—	2	2	no	—
345	C₂×C₅×D₄	—	2	2	no	—
346	C₂×C₅×D₄	—	2	2	no	—
347	C₂×C₅×D₄	—	2	2	no	—
348	C₂×C₅×D₄	—	2	2	no	—
349	C₂×C₅×D₄	—	2	2	no	—
350	C₂×C₅×D₄	—	2	2	no	—
351	C₂×C₅×D₄	—	2	2	no	—
352	C₂×C₅×D₄	—	2	2	no	—
353	C₂×C₅×D₄	—	2	2	no	—
354	C₂×C₅×D₄	—	4	1	no	—
355	C₂×C₅×D₄	—	4	1	no	—
356	C₂×C₅×D₄	—	4	1	no	—
357	C₂×C₅×D₄	—	4	1	no	—
358	C₂×C₅×D₄	—	4	1	no	—
359	C₂×C₅×D₄	C₃×D₄	1	4	yes	complemented
360	C₂²×C₄×C₅	—	2	2	no	—
361	C₂²×C₄×C₅	—	2	2	no	—
362	C₂²×C₄×C₅	—	2	2	no	—
363	C₂²×C₄×C₅	—	2	2	no	—
364	C₂²×C₄×C₅	—	2	2	no	—
365	C₂²×C₄×C₅	—	2	2	no	—
366	C₂²×C₄×C₅	—	4	1	no	—
367	C₂²×C₄×C₅	—	4	1	no	—
368	C₂²×C₄×C₅	—	4	1	no	—
369	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
370	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
371	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
372	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
373	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
374	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
375	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
376	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
377	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
378	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
379	C₅×C₄⋊C₄	—	2	2	no	—
380	C₅×C₄⋊C₄	—	2	2	no	—
381	C₅×C₄⋊C₄	—	2	2	no	—
382	C₅×C₄⋊C₄	—	4	1	no	—
383	C₅×C₂²⋊C₄	—	2	2	no	—
384	C₅×C₂²⋊C₄	—	2	2	no	—
385	C₅×C₂²⋊C₄	—	2	2	no	—
386	C₅×C₂²⋊C₄	—	2	2	no	—
387	C₅×C₂²⋊C₄	—	2	2	no	—
388	C₅×C₂²⋊C₄	—	2	2	no	—
389	C₅×C₂²⋊C₄	—	2	2	no	—
390	C₅×C₂²⋊C₄	—	2	2	no	—
391	C₅×C₂²⋊C₄	—	2	2	no	—
392	C₅×C₂²⋊C₄	—	2	2	no	—
393	C₅×C₂²⋊C₄	—	2	2	no	—
394	C₅×C₂²⋊C₄	—	2	2	no	—
395	C₅×C₂²⋊C₄	—	4	1	no	—
396	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	complemented
397	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	complemented
398	C₄²×C₅	—	2	2	no	—
399	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
400	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
401	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic, complemented
402	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic, complemented
403	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
404	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
405	#396	C₂×C₃×C₅	1	1	yes	characteristic, complemented
406	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
407	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
408	#392	C₂×C₃×C₅	1	1	yes	characteristic, complemented
409	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
410	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
411	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
412	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
413	#385	C₂×C₃×C₅	1	1	yes	characteristic, complemented
414	C₂²×C₃×C₅	—	2	2	no	—
415	C₂²×C₃×C₅	—	2	2	no	—
416	C₂²×C₃×C₅	—	2	2	no	—
417	C₂²×C₃×C₅	—	2	2	no	—
418	C₂²×C₃×C₅	—	2	2	no	—
419	C₂²×C₃×C₅	—	2	2	no	—
420	C₂²×C₃×C₅	—	2	2	no	—
421	C₂²×C₃×C₅	—	2	2	no	—
422	C₂²×C₃×C₅	—	2	2	no	—
423	C₂²×C₃×C₅	—	2	2	no	—
424	C₂²×C₃×C₅	—	2	2	no	—
425	C₂²×C₃×C₅	—	2	2	no	—
426	C₂²×C₃×C₅	—	2	2	no	—
427	C₂²×C₃×C₅	—	2	2	no	—
428	C₂²×C₃×C₅	—	2	2	no	—
429	C₂²×C₃×C₅	—	4	16	no	—
430	C₂²×C₃×C₅	—	4	1	no	—
431	C₂²×C₃×C₅	—	4	1	no	—
432	C₂²×C₃×C₅	—	4	1	no	—
433	C₂²×C₃×C₅	—	4	1	no	—
434	C₂²×C₃×C₅	—	4	1	no	—
435	C₂²×C₃×C₅	—	4	1	no	—
436	C₂²×C₃×C₅	—	4	1	no	—
437	C₂²×C₃×C₅	—	4	1	no	—
438	C₂²×C₃×C₅	—	4	1	no	—
439	C₂²×C₃×C₅	—	4	1	no	—
440	C₂²×C₃×C₅	—	4	1	no	—
441	C₂²×C₃×C₅	—	4	1	no	—
442	C₂²×C₃×C₅	—	4	1	no	—
443	C₂²×C₃×C₅	—	4	1	no	—
444	C₂²×C₃×C₅	—	4	1	no	—
445	C₂²×C₃×C₅	—	4	1	no	—
446	C₂²×C₃×C₅	—	4	1	no	—
447	C₂²×C₃×C₅	—	4	1	no	—
448	C₂²×C₃×C₅	—	4	1	no	—
449	C₂²×C₃×C₅	#121	1	4	yes	complemented
450	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
451	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
452	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
453	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
454	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
455	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
456	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
457	C₃×C₄×C₅	—	2	2	no	—
458	C₃×C₄×C₅	—	2	2	no	—
459	C₃×C₄×C₅	—	2	2	no	—
460	C₃×C₄×C₅	—	2	2	no	—
461	C₃×C₄×C₅	—	2	2	no	—
462	C₃×C₄×C₅	—	4	1	no	—
463	C₃×C₄×C₅	—	4	1	no	—
464	C₃×C₄×C₅	—	4	1	no	—
465	C₃×C₄×C₅	—	4	1	no	—
466	C₃×C₄×C₅	—	4	1	no	—
467	C₂⁴×C₃	—	2	2	no	—
468	C₂⁴×C₃	—	2	2	no	—
469	C₂⁴×C₃	—	2	2	no	—
470	C₂⁴×C₃	—	2	2	no	—
471	C₂⁴×C₃	—	2	2	no	—
472	C₂⁴×C₃	—	4	1	no	—
473	C₂⁴×C₃	—	4	1	no	—
474	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
475	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
476	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
477	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
478	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
479	C₂×C₃×D₄	—	2	2	no	—
480	C₂×C₃×D₄	—	2	2	no	—
481	C₂×C₃×D₄	—	2	2	no	—
482	C₂×C₃×D₄	—	2	2	no	—
483	C₂×C₃×D₄	—	2	2	no	—
484	C₂×C₃×D₄	—	2	2	no	—
485	C₂×C₃×D₄	—	2	2	no	—
486	C₂×C₃×D₄	—	2	2	no	—
487	C₂×C₃×D₄	—	2	2	no	—
488	C₂×C₃×D₄	—	2	2	no	—
489	C₂×C₃×D₄	—	2	2	no	—
490	C₂×C₃×D₄	—	2	2	no	—
491	C₂×C₃×D₄	—	2	2	no	—
492	C₂×C₃×D₄	—	2	2	no	—
493	C₂×C₃×D₄	—	2	2	no	—
494	C₂×C₃×D₄	—	4	1	no	—
495	C₂×C₃×D₄	—	4	1	no	—
496	C₂×C₃×D₄	—	4	1	no	—
497	C₂×C₃×D₄	—	4	1	no	—
498	C₂×C₃×D₄	—	4	1	no	—
499	C₂×C₃×D₄	C₅×D₄	1	4	yes	complemented
500	C₂²×C₃×C₄	—	2	2	no	—
501	C₂²×C₃×C₄	—	2	2	no	—
502	C₂²×C₃×C₄	—	2	2	no	—
503	C₂²×C₃×C₄	—	2	2	no	—
504	C₂²×C₃×C₄	—	2	2	no	—
505	C₂²×C₃×C₄	—	2	2	no	—
506	C₂²×C₃×C₄	—	4	1	no	—
507	C₂²×C₃×C₄	—	4	1	no	—
508	C₂²×C₃×C₄	—	4	1	no	—
509	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
510	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
511	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
512	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
513	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
514	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
515	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
516	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
517	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
518	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
519	C₃×C₄⋊C₄	—	2	2	no	—
520	C₃×C₄⋊C₄	—	2	2	no	—
521	C₃×C₄⋊C₄	—	2	2	no	—
522	C₃×C₄⋊C₄	—	4	1	no	—
523	C₃×C₂²⋊C₄	—	2	2	no	—
524	C₃×C₂²⋊C₄	—	2	2	no	—
525	C₃×C₂²⋊C₄	—	2	2	no	—
526	C₃×C₂²⋊C₄	—	2	2	no	—
527	C₃×C₂²⋊C₄	—	2	2	no	—
528	C₃×C₂²⋊C₄	—	2	2	no	—
529	C₃×C₂²⋊C₄	—	2	2	no	—
530	C₃×C₂²⋊C₄	—	2	2	no	—
531	C₃×C₂²⋊C₄	—	2	2	no	—
532	C₃×C₂²⋊C₄	—	2	2	no	—
533	C₃×C₂²⋊C₄	—	2	2	no	—
534	C₃×C₂²⋊C₄	—	2	2	no	—
535	C₃×C₂²⋊C₄	—	4	1	no	—
536	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	complemented
537	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	complemented
538	C₃×C₄²	—	2	2	no	—
539	C₂³×C₅	—	2	1	no	—
540	C₂³×C₅	—	2	1	no	—
541	C₂³×C₅	—	2	1	no	—
542	C₂³×C₅	—	2	1	no	—
543	C₂³×C₅	—	2	8	no	—
544	C₂³×C₅	—	2	1	no	—
545	C₂³×C₅	—	2	1	no	—
546	C₂³×C₅	—	2	1	no	—
547	C₂³×C₅	—	2	1	no	—
548	C₂³×C₅	—	2	1	no	—
549	C₂³×C₅	—	2	1	no	—
550	C₂³×C₅	—	2	1	no	—
551	C₂³×C₅	—	2	1	no	—
552	C₂³×C₅	—	2	1	no	—
553	C₂³×C₅	—	2	1	no	—
554	C₂³×C₅	—	2	1	no	—
555	C₂³×C₅	—	2	1	no	—
556	C₂³×C₅	—	2	1	no	—
557	C₂³×C₅	—	2	1	no	—
558	C₂³×C₅	—	2	1	no	—
559	C₂³×C₅	—	2	1	no	—
560	C₂³×C₅	—	2	1	no	—
561	C₂³×C₅	—	2	1	no	—
562	C₂³×C₅	—	2	1	no	—
563	C₂³×C₅	—	2	1	no	—
564	C₂³×C₅	—	2	1	no	—
565	C₂³×C₅	—	2	1	no	—
566	C₂³×C₅	—	2	1	no	—
567	C₂³×C₅	—	2	1	no	—
568	C₂³×C₅	—	2	1	no	—
569	C₂³×C₅	—	4	4	no	—
570	C₂³×C₅	—	4	4	no	—
571	C₂³×C₅	—	4	4	no	—
572	C₂³×C₅	—	4	4	no	—
573	C₂³×C₅	—	4	4	no	—
574	C₂³×C₅	—	4	4	no	—
575	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
576	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
577	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
578	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
579	C₂³×C₅	C₃×#41	1	2	yes	—
580	C₂³×C₅	C₃×#41	1	2	yes	—
581	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
582	C₅×D₄	—	2	8	no	—
583	C₅×D₄	—	4	4	no	—
584	C₅×D₄	—	4	4	no	—
585	C₅×D₄	—	4	4	no	—
586	C₅×D₄	—	4	4	no	—
587	C₅×D₄	—	4	4	no	—
588	C₅×D₄	—	4	4	no	—
589	C₂×C₄×C₅	—	2	1	no	—
590	C₂×C₄×C₅	—	2	1	no	—
591	C₂×C₄×C₅	—	2	1	no	—
592	C₂×C₄×C₅	—	2	1	no	—
593	C₂×C₄×C₅	—	2	1	no	—
594	C₂×C₄×C₅	—	2	1	no	—
595	C₂×C₄×C₅	—	2	1	no	—
596	C₂×C₄×C₅	—	2	1	no	—
597	C₂×C₄×C₅	—	2	1	no	—
598	C₂×C₄×C₅	—	2	1	no	—
599	C₂×C₄×C₅	—	2	1	no	—
600	C₂×C₄×C₅	—	2	1	no	—
601	C₂×C₄×C₅	—	2	1	no	—
602	C₂×C₄×C₅	—	2	1	no	—
603	C₂×C₄×C₅	—	2	1	no	—
604	C₂×C₄×C₅	—	2	1	no	—
605	C₂×C₄×C₅	—	2	1	no	—
606	C₂×C₄×C₅	—	2	1	no	—
607	C₂×C₄×C₅	—	2	1	no	—
608	C₂×C₄×C₅	—	2	1	no	—
609	C₂×C₄×C₅	—	2	1	no	—
610	C₂×C₄×C₅	—	2	1	no	—
611	C₂×C₄×C₅	—	2	1	no	—
612	C₂×C₄×C₅	—	2	1	no	—
613	C₂×C₄×C₅	—	2	1	no	—
614	C₂×C₄×C₅	—	4	4	no	—
615	C₂×C₄×C₅	—	4	4	no	—
616	C₂×C₄×C₅	—	4	4	no	—
617	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
618	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
619	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
620	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
621	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
622	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
623	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
624	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
625	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
626	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
627	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
628	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
629	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
630	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
631	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
632	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
633	#121	—	2	4	no	—
634	#121	—	2	4	no	—
635	#120	—	2	4	no	—
636	#120	—	2	4	no	—
637	C₄×D₄	—	2	4	no	—
638	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
639	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
640	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
641	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
642	C₂×C₂²⋊C₄	—	2	4	no	—
643	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
644	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
651	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
653	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
654	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
655	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
656	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
657	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
658	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
659	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
660	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
661	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
662	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
663	C₂×C₃×C₅	—	2	4	no	—
664	C₂×C₃×C₅	—	4	2	no	—
665	C₂×C₃×C₅	—	4	2	no	—
666	C₂×C₃×C₅	—	4	2	no	—
667	C₂×C₃×C₅	—	8	1	no	—
668	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
669	C₂×C₃×C₅	#525	1	1	yes	characteristic
670	C₂×C₃×C₅	#538	1	1	yes	characteristic
671	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
672	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
673	C₂×C₃×C₅	#546	1	1	yes	characteristic
674	C₂×C₃×C₅	#546	1	1	yes	characteristic
675	C₂³×C₃	—	2	1	no	—
676	C₂³×C₃	—	2	1	no	—
677	C₂³×C₃	—	2	1	no	—
678	C₂³×C₃	—	2	1	no	—
679	C₂³×C₃	—	2	8	no	—
680	C₂³×C₃	—	2	1	no	—
681	C₂³×C₃	—	2	1	no	—
682	C₂³×C₃	—	2	1	no	—
683	C₂³×C₃	—	2	1	no	—
684	C₂³×C₃	—	2	1	no	—
685	C₂³×C₃	—	2	1	no	—
686	C₂³×C₃	—	2	1	no	—
687	C₂³×C₃	—	2	1	no	—
688	C₂³×C₃	—	2	1	no	—
689	C₂³×C₃	—	2	1	no	—
690	C₂³×C₃	—	2	1	no	—
691	C₂³×C₃	—	2	1	no	—
692	C₂³×C₃	—	2	1	no	—
693	C₂³×C₃	—	2	1	no	—
694	C₂³×C₃	—	2	1	no	—
695	C₂³×C₃	—	2	1	no	—
696	C₂³×C₃	—	2	1	no	—
697	C₂³×C₃	—	2	1	no	—
698	C₂³×C₃	—	2	1	no	—
699	C₂³×C₃	—	2	1	no	—
700	C₂³×C₃	—	2	1	no	—
701	C₂³×C₃	—	2	1	no	—
702	C₂³×C₃	—	2	1	no	—
703	C₂³×C₃	—	2	1	no	—
704	C₂³×C₃	—	2	1	no	—
705	C₂³×C₃	—	4	4	no	—
706	C₂³×C₃	—	4	4	no	—
707	C₂³×C₃	—	4	4	no	—
708	C₂³×C₃	—	4	4	no	—
709	C₂³×C₃	—	4	4	no	—
710	C₂³×C₃	—	4	4	no	—
711	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
712	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
713	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
714	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
715	C₂³×C₃	C₅×#41	1	2	yes	—
716	C₂³×C₃	C₅×#41	1	2	yes	—
717	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
718	C₃×D₄	—	2	8	no	—
719	C₃×D₄	—	4	4	no	—
720	C₃×D₄	—	4	4	no	—
721	C₃×D₄	—	4	4	no	—
722	C₃×D₄	—	4	4	no	—
723	C₃×D₄	—	4	4	no	—
724	C₃×D₄	—	4	4	no	—
725	C₂×C₃×C₄	—	2	1	no	—
726	C₂×C₃×C₄	—	2	1	no	—
727	C₂×C₃×C₄	—	2	1	no	—
728	C₂×C₃×C₄	—	2	1	no	—
729	C₂×C₃×C₄	—	2	1	no	—
730	C₂×C₃×C₄	—	2	1	no	—
731	C₂×C₃×C₄	—	2	1	no	—
732	C₂×C₃×C₄	—	2	1	no	—
733	C₂×C₃×C₄	—	2	1	no	—
734	C₂×C₃×C₄	—	2	1	no	—
735	C₂×C₃×C₄	—	2	1	no	—
736	C₂×C₃×C₄	—	2	1	no	—
737	C₂×C₃×C₄	—	2	1	no	—
738	C₂×C₃×C₄	—	2	1	no	—
739	C₂×C₃×C₄	—	2	1	no	—
740	C₂×C₃×C₄	—	2	1	no	—
741	C₂×C₃×C₄	—	2	1	no	—
742	C₂×C₃×C₄	—	2	1	no	—
743	C₂×C₃×C₄	—	2	1	no	—
744	C₂×C₃×C₄	—	2	1	no	—
745	C₂×C₃×C₄	—	2	1	no	—
746	C₂×C₃×C₄	—	2	1	no	—
747	C₂×C₃×C₄	—	2	1	no	—
748	C₂×C₃×C₄	—	2	1	no	—
749	C₂×C₃×C₄	—	2	1	no	—
750	C₂×C₃×C₄	—	4	4	no	—
751	C₂×C₃×C₄	—	4	4	no	—
752	C₂×C₃×C₄	—	4	4	no	—
753	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
754	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
755	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
756	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
757	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
758	C₂²×C₅	—	2	2	no	—
759	C₂²×C₅	—	2	2	no	—
760	C₂²×C₅	—	2	2	no	—
761	C₂²×C₅	—	2	2	no	—
762	C₂²×C₅	—	2	2	no	—
763	C₂²×C₅	—	2	2	no	—
764	C₂²×C₅	—	2	2	no	—
765	C₂²×C₅	—	2	2	no	—
766	C₂²×C₅	—	2	2	no	—
767	C₂²×C₅	—	2	2	no	—
768	C₂²×C₅	—	2	2	no	—
769	C₂²×C₅	—	2	2	no	—
770	C₂²×C₅	—	2	2	no	—
771	C₂²×C₅	—	2	2	no	—
772	C₂²×C₅	—	2	2	no	—
773	C₂²×C₅	—	4	16	no	—
774	C₂²×C₅	—	4	1	no	—
775	C₂²×C₅	—	4	1	no	—
776	C₂²×C₅	—	4	1	no	—
777	C₂²×C₅	—	4	1	no	—
778	C₂²×C₅	—	4	1	no	—
779	C₂²×C₅	—	4	1	no	—
780	C₂²×C₅	—	4	1	no	—
781	C₂²×C₅	—	4	1	no	—
782	C₂²×C₅	—	4	1	no	—
783	C₂²×C₅	—	4	1	no	—
784	C₂²×C₅	—	4	1	no	—
785	C₂²×C₅	—	4	1	no	—
786	C₂²×C₅	—	4	1	no	—
787	C₂²×C₅	—	4	1	no	—
788	C₂²×C₅	—	4	1	no	—
789	C₂²×C₅	—	4	1	no	—
790	C₂²×C₅	—	4	1	no	—
791	C₂²×C₅	—	4	1	no	—
792	C₂²×C₅	—	4	1	no	—
793	C₂²×C₅	C₃×#121	1	4	yes	complemented
794	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
795	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
796	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
797	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
798	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
799	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
800	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
801	C₄×C₅	—	2	2	no	—
802	C₄×C₅	—	2	2	no	—
803	C₄×C₅	—	2	2	no	—
804	C₄×C₅	—	2	2	no	—
805	C₄×C₅	—	2	2	no	—
806	C₄×C₅	—	4	1	no	—
807	C₄×C₅	—	4	1	no	—
808	C₄×C₅	—	4	1	no	—
809	C₄×C₅	—	4	1	no	—
810	C₄×C₅	—	4	1	no	—
811	C₂⁴	—	2	2	no	—
812	C₂⁴	—	2	2	no	—
813	C₂⁴	—	2	2	no	—
814	C₂⁴	—	2	2	no	—
815	C₂⁴	—	2	2	no	—
816	C₂⁴	—	4	1	no	—
817	C₂⁴	—	4	1	no	—
818	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
819	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
820	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
821	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
822	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	2	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	4	1	no	—
839	C₂×D₄	—	4	1	no	—
840	C₂×D₄	—	4	1	no	—
841	C₂×D₄	—	4	1	no	—
842	C₂×D₄	—	4	1	no	—
843	C₂×D₄	C₃×C₅×D₄	1	4	yes	complemented
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	4	1	no	—
851	C₂²×C₄	—	4	1	no	—
852	C₂²×C₄	—	4	1	no	—
853	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
854	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
855	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
856	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
857	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
858	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
859	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
860	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
861	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
862	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	4	1	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	4	1	no	—
880	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
881	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
882	C₄²	—	2	2	no	—
883	C₃×C₅	#2424	1	1	yes	characteristic, direct product factor, Hall
884	C₂²×C₃	—	2	2	no	—
885	C₂²×C₃	—	2	2	no	—
886	C₂²×C₃	—	2	2	no	—
887	C₂²×C₃	—	2	2	no	—
888	C₂²×C₃	—	2	2	no	—
889	C₂²×C₃	—	2	2	no	—
890	C₂²×C₃	—	2	2	no	—
891	C₂²×C₃	—	2	2	no	—
892	C₂²×C₃	—	2	2	no	—
893	C₂²×C₃	—	2	2	no	—
894	C₂²×C₃	—	2	2	no	—
895	C₂²×C₃	—	2	2	no	—
896	C₂²×C₃	—	2	2	no	—
897	C₂²×C₃	—	2	2	no	—
898	C₂²×C₃	—	2	2	no	—
899	C₂²×C₃	—	4	16	no	—
900	C₂²×C₃	—	4	1	no	—
901	C₂²×C₃	—	4	1	no	—
902	C₂²×C₃	—	4	1	no	—
903	C₂²×C₃	—	4	1	no	—
904	C₂²×C₃	—	4	1	no	—
905	C₂²×C₃	—	4	1	no	—
906	C₂²×C₃	—	4	1	no	—
907	C₂²×C₃	—	4	1	no	—
908	C₂²×C₃	—	4	1	no	—
909	C₂²×C₃	—	4	1	no	—
910	C₂²×C₃	—	4	1	no	—
911	C₂²×C₃	—	4	1	no	—
912	C₂²×C₃	—	4	1	no	—
913	C₂²×C₃	—	4	1	no	—
914	C₂²×C₃	—	4	1	no	—
915	C₂²×C₃	—	4	1	no	—
916	C₂²×C₃	—	4	1	no	—
917	C₂²×C₃	—	4	1	no	—
918	C₂²×C₃	—	4	1	no	—
919	C₂²×C₃	C₅×#121	1	4	yes	complemented
920	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
921	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
922	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
923	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
924	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
925	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
926	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
927	C₃×C₄	—	2	2	no	—
928	C₃×C₄	—	2	2	no	—
929	C₃×C₄	—	2	2	no	—
930	C₃×C₄	—	2	2	no	—
931	C₃×C₄	—	2	2	no	—
932	C₃×C₄	—	4	1	no	—
933	C₃×C₄	—	4	1	no	—
934	C₃×C₄	—	4	1	no	—
935	C₃×C₄	—	4	1	no	—
936	C₃×C₄	—	4	1	no	—
937	C₂×C₅	—	2	4	no	—
938	C₂×C₅	—	4	2	no	—
939	C₂×C₅	—	4	2	no	—
940	C₂×C₅	—	4	2	no	—
941	C₂×C₅	—	8	1	no	—
942	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
943	C₂×C₅	C₃×#525	1	1	yes	characteristic
944	C₂×C₅	C₃×#538	1	1	yes	characteristic
945	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
946	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
947	C₂×C₅	C₃×#546	1	1	yes	characteristic
948	C₂×C₅	C₃×#546	1	1	yes	characteristic
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	8	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	1	no	—
957	C₂³	—	2	1	no	—
958	C₂³	—	2	1	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	2	1	no	—
963	C₂³	—	2	1	no	—
964	C₂³	—	2	1	no	—
965	C₂³	—	2	1	no	—
966	C₂³	—	2	1	no	—
967	C₂³	—	2	1	no	—
968	C₂³	—	2	1	no	—
969	C₂³	—	2	1	no	—
970	C₂³	—	2	1	no	—
971	C₂³	—	2	1	no	—
972	C₂³	—	2	1	no	—
973	C₂³	—	2	1	no	—
974	C₂³	—	2	1	no	—
975	C₂³	—	2	1	no	—
976	C₂³	—	2	1	no	—
977	C₂³	—	2	1	no	—
978	C₂³	—	2	1	no	—
979	C₂³	—	4	4	no	—
980	C₂³	—	4	4	no	—
981	C₂³	—	4	4	no	—
982	C₂³	—	4	4	no	—
983	C₂³	—	4	4	no	—
984	C₂³	—	4	4	no	—
985	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
986	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
987	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
988	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
989	C₂³	C₃×C₅×#41	1	2	yes	—
990	C₂³	C₃×C₅×#41	1	2	yes	—
991	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
992	D₄	—	2	8	no	—
993	D₄	—	4	4	no	—
994	D₄	—	4	4	no	—
995	D₄	—	4	4	no	—
996	D₄	—	4	4	no	—
997	D₄	—	4	4	no	—
998	D₄	—	4	4	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	4	4	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	4	4	no	—
1027	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
1028	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
1029	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
1030	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
1031	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
1032	C₂×C₃	—	2	4	no	—
1033	C₂×C₃	—	4	2	no	—
1034	C₂×C₃	—	4	2	no	—
1035	C₂×C₃	—	4	2	no	—
1036	C₂×C₃	—	8	1	no	—
1037	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
1038	C₂×C₃	C₅×#525	1	1	yes	characteristic
1039	C₂×C₃	C₅×#538	1	1	yes	characteristic
1040	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
1041	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
1042	C₂×C₃	C₅×#546	1	1	yes	characteristic
1043	C₂×C₃	C₅×#546	1	1	yes	characteristic
1044	C₅	C₃×#2424	1	1	yes	characteristic, direct product factor, Sylow
1045	C₂²	—	2	2	no	—
1046	C₂²	—	2	2	no	—
1047	C₂²	—	2	2	no	—
1048	C₂²	—	2	2	no	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	4	16	no	—
1061	C₂²	—	4	1	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	1	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	1	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	C₃×C₅×#121	1	4	yes	complemented
1081	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
1082	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
1083	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
1084	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
1085	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
1086	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1087	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1088	C₄	—	2	2	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₃	C₅×#2424	1	1	yes	characteristic, direct product factor, Sylow
1099	C₂	—	2	4	no	—
1100	C₂	—	4	2	no	—
1101	C₂	—	4	2	no	—
1102	C₂	—	4	2	no	—
1103	C₂	—	8	1	no	—
1104	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
1105	C₂	C₃×C₅×#525	1	1	yes	characteristic
1106	C₂	C₃×C₅×#538	1	1	yes	characteristic
1107	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
1108	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
1109	C₂	C₃×C₅×#546	1	1	yes	characteristic
1110	C₂	C₃×C₅×#546	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#121	C₂	semidirect
2. C₂×C₃×C₅×#121	C₂	semidirect
3. C₂×C₃×C₅×#120	C₂	semidirect
4. C₂×C₃×C₅×#120	C₂	semidirect
5. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
6. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
7. C₃×C₅×#396	C₂	semidirect
8. C₃×C₅×#394	C₂	semidirect
9. C₃×C₅×#394	C₂	semidirect
10. C₃×C₅×#392	C₂	semidirect
11. C₃×C₅×#390	C₂	semidirect
12. C₃×C₅×#388	C₂	semidirect
13. C₃×C₅×#386	C₂	semidirect
14. C₃×C₅×#386	C₂	semidirect
15. C₃×C₅×#385	C₂	semidirect
16. C₅×#2424	C₃	direct (N × H)
24. C₂²×C₃×C₅×D₄	C₂²	semidirect
27. C₂³×C₃×C₄×C₅	C₂²	semidirect
33. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
34. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
35. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
36. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
48. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
49. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
50. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
51. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
52. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
53. C₂×C₃×C₄²×C₅	C₂²	semidirect
54. C₃×C₅×#95	C₂²	semidirect
55. C₃×C₅×#95	C₂²	semidirect
56. C₃×C₅×#95	C₂²	semidirect
57. C₃×C₅×#95	C₂²	semidirect
58. C₃×#2424	C₅	direct (N × H)
59. C₂×C₅×#121	C₂×C₃	semidirect
60. C₂×C₅×#121	C₂×C₃	semidirect
61. C₂×C₅×#120	C₂×C₃	semidirect
62. C₂×C₅×#120	C₂×C₃	semidirect
63. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
64. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
65. C₅×#396	C₂×C₃	semidirect
66. C₅×#394	C₂×C₃	semidirect
67. C₅×#394	C₂×C₃	semidirect
68. C₅×#392	C₂×C₃	semidirect
69. C₅×#390	C₂×C₃	semidirect
70. C₅×#388	C₂×C₃	semidirect
71. C₅×#386	C₂×C₃	semidirect
72. C₅×#386	C₂×C₃	semidirect
73. C₅×#385	C₂×C₃	semidirect
106. C₂×C₃×C₅×D₄	D₄	semidirect
143. C₃×C₅×C₂²⋊C₄	D₄	semidirect
144. C₃×C₅×C₂²⋊C₄	D₄	semidirect
146. C₂×C₃×#121	C₂×C₅	semidirect
147. C₂×C₃×#121	C₂×C₅	semidirect
148. C₂×C₃×#120	C₂×C₅	semidirect
149. C₂×C₃×#120	C₂×C₅	semidirect
150. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
151. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
152. C₃×#396	C₂×C₅	semidirect
153. C₃×#394	C₂×C₅	semidirect
154. C₃×#394	C₂×C₅	semidirect
155. C₃×#392	C₂×C₅	semidirect
156. C₃×#390	C₂×C₅	semidirect
157. C₃×#388	C₂×C₅	semidirect
158. C₃×#386	C₂×C₅	semidirect
159. C₃×#386	C₂×C₅	semidirect
160. C₃×#385	C₂×C₅	semidirect
168. C₂²×C₅×D₄	C₂²×C₃	semidirect
171. C₂³×C₄×C₅	C₂²×C₃	semidirect
177. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
178. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
179. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
180. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
192. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
193. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
194. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
195. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
196. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
197. C₂×C₄²×C₅	C₂²×C₃	semidirect
198. C₅×#95	C₂²×C₃	semidirect
199. C₅×#95	C₂²×C₃	semidirect
200. C₅×#95	C₂²×C₃	semidirect
201. C₅×#95	C₂²×C₃	semidirect
202. #2424	C₃×C₅	direct (N × H)
293. C₂²×C₃×D₄	C₂²×C₅	semidirect
296. C₂³×C₃×C₄	C₂²×C₅	semidirect
302. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
303. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
304. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
305. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
317. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
318. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
319. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
320. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
321. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
322. C₂×C₃×C₄²	C₂²×C₅	semidirect
323. C₃×#95	C₂²×C₅	semidirect
324. C₃×#95	C₂²×C₅	semidirect
325. C₃×#95	C₂²×C₅	semidirect
326. C₃×#95	C₂²×C₅	semidirect
359. C₂×C₅×D₄	C₃×D₄	semidirect
396. C₅×C₂²⋊C₄	C₃×D₄	semidirect
397. C₅×C₂²⋊C₄	C₃×D₄	semidirect
399. C₂×#121	C₂×C₃×C₅	semidirect
400. C₂×#121	C₂×C₃×C₅	semidirect
401. C₂×#120	C₂×C₃×C₅	semidirect
402. C₂×#120	C₂×C₃×C₅	semidirect
403. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
404. C₂²×C₂²⋊C₄	C₂×C₃×C₅	semidirect
405. #396	C₂×C₃×C₅	semidirect
406. #394	C₂×C₃×C₅	semidirect
407. #394	C₂×C₃×C₅	semidirect
408. #392	C₂×C₃×C₅	semidirect
409. #390	C₂×C₃×C₅	semidirect
410. #388	C₂×C₃×C₅	semidirect
411. #386	C₂×C₃×C₅	semidirect
412. #386	C₂×C₃×C₅	semidirect
413. #385	C₂×C₃×C₅	semidirect
449. C₂²×C₃×C₅	#121	semidirect
499. C₂×C₃×D₄	C₅×D₄	semidirect
536. C₃×C₂²⋊C₄	C₅×D₄	semidirect
537. C₃×C₂²⋊C₄	C₅×D₄	semidirect
629. C₂²×D₄	C₂²×C₃×C₅	semidirect
632. C₂³×C₄	C₂²×C₃×C₅	semidirect
638. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
639. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
640. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
641. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
653. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
654. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
655. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
656. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
657. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
658. C₂×C₄²	C₂²×C₃×C₅	semidirect
659. #95	C₂²×C₃×C₅	semidirect
660. #95	C₂²×C₃×C₅	semidirect
661. #95	C₂²×C₃×C₅	semidirect
662. #95	C₂²×C₃×C₅	semidirect
793. C₂²×C₅	C₃×#121	semidirect
843. C₂×D₄	C₃×C₅×D₄	semidirect
880. C₂²⋊C₄	C₃×C₅×D₄	semidirect
881. C₂²⋊C₄	C₃×C₅×D₄	semidirect
883. C₃×C₅	#2424	direct (N × H)
919. C₂²×C₃	C₅×#121	semidirect
1044. C₅	C₃×#2424	direct (N × H)
1080. C₂²	C₃×C₅×#121	semidirect
1098. C₃	C₅×#2424	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#121	2
C₂×C₃×C₅×#120	2
C₂×C₃×C₄×C₅×D₄	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#396	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₅×#2424	3
C₃×#2424	5

Subgroups — C3×C5×#2424 #14275458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2424 #14275458