Subgroups — C₂×C₅×#5620 #14495181

Order 1920.

2688 conjugacy classes of subgroups.

The subgroup lattice has 984 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×C₅×#940	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#939	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#938	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#937	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#937	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#929	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5620	C₂	1	16	yes	maximal, direct product factor
11	C₂×C₅×#898	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#886	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#882	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#879	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅×#560	—	3	1	no	maximal, Hall
18	C₂⁴×C₅×D₃	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, complemented
22	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
24	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
25	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
26	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
27	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
28	C₂²×C₅×#67	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₅×#67	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
32	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
33	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#121	C₂²	1	8	yes	complemented
35	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₅×#217	C₂²	1	1	yes	characteristic
39	C₂×C₅×#217	C₂²	1	1	yes	characteristic
40	C₂×C₅×#217	C₂²	1	1	yes	characteristic, complemented
41	C₅×#940	C₂²	1	8	yes	complemented
42	C₅×#939	C₂²	1	8	yes	complemented
43	C₅×#939	C₂²	1	8	yes	complemented
44	C₅×#938	C₂²	1	8	yes	complemented
45	C₅×#937	C₂²	1	8	yes	complemented
46	C₅×#937	C₂²	1	8	yes	complemented
47	C₅×#930	C₂²	1	8	yes	complemented
48	C₅×#929	C₂²	1	8	yes	complemented
49	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
51	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
53	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
54	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
55	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
62	C₅×#898	C₂²	1	8	yes	complemented
63	C₅×#894	C₂²	1	8	yes	complemented
64	C₅×#886	C₂²	1	8	yes	complemented
65	C₅×#884	C₂²	1	8	yes	complemented
66	C₅×#882	C₂²	1	8	yes	complemented
67	C₅×#879	C₂²	1	8	yes	complemented
68	C₂×#5620	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₅×#560	—	3	16	no	—
70	C₂×C₅×#127	—	3	1	no	—
71	C₂×C₅×#126	—	3	1	no	—
72	C₂×C₅×#126	—	3	1	no	—
73	C₂×C₅×#123	—	3	1	no	—
74	C₂×C₅×#123	—	3	1	no	—
75	C₂×C₅×#123	—	3	1	no	—
76	C₂×C₅×#121	—	3	1	no	—
77	C₂×C₅×#121	—	3	1	no	—
78	C₂×C₅×#121	—	3	1	no	—
79	C₂×C₅×#121	—	3	1	no	—
80	C₂×C₅×#121	—	3	1	no	—
81	C₂×C₅×#121	D₃	1	1	yes	characteristic, complemented
82	C₂×C₅×#120	—	3	1	no	—
83	C₂×C₅×#120	—	3	1	no	—
84	C₂×C₅×#120	—	3	1	no	—
85	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
86	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
87	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
88	C₂³×C₅×D₃	—	4	2	no	—
89	C₂³×C₅×D₃	—	4	2	no	—
90	C₂³×C₅×D₃	—	4	2	no	—
91	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
92	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
93	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
94	C₂³×C₅×D₃	C₂³	1	4	yes	—
95	C₂×C₃×C₅×D₄	—	4	2	no	—
96	C₂×C₃×C₅×D₄	—	4	2	no	—
97	C₂×C₃×C₅×D₄	—	4	2	no	—
98	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
99	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
100	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
101	C₂²×C₃×C₄×C₅	—	4	2	no	—
102	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
103	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
104	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
105	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
106	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	complemented
107	C₂×C₅×#67	—	4	2	no	—
108	C₂×C₅×#67	—	4	2	no	—
109	C₂×C₅×#67	—	4	2	no	—
110	C₂×C₅×#67	—	4	2	no	—
111	C₂×C₅×#67	—	4	2	no	—
112	C₂×C₅×#67	—	4	2	no	—
113	C₂×C₅×#67	—	4	2	no	—
114	C₂×C₅×#67	C₂³	1	4	yes	—
115	C₂×C₅×#67	C₂³	1	4	yes	—
116	C₂×C₅×#67	C₂³	1	4	yes	—
117	C₂×C₅×#67	C₂³	1	4	yes	—
118	C₂×C₅×#67	C₂³	1	4	yes	—
119	C₂×C₅×#67	C₂³	1	4	yes	complemented
120	C₂×C₅×#67	C₂³	1	4	yes	complemented
121	C₂²×C₅×Dic₃	—	4	2	no	—
122	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
123	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
124	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
125	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
126	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
127	C₂²×C₅×Dic₃	C₂³	1	4	yes	complemented
128	C₂×C₅×D₁₂	—	4	2	no	—
129	C₂×C₅×D₁₂	—	4	2	no	—
130	C₂×C₅×D₁₂	C₂³	1	4	yes	—
131	C₂×C₅×D₁₂	C₂³	1	4	yes	—
132	C₂×C₄×C₅×D₃	—	4	2	no	—
133	C₂×C₄×C₅×D₃	C₂³	1	4	yes	complemented
134	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
135	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
137	C₅×#217	C₂³	1	4	yes	—
138	C₅×#217	C₂³	1	4	yes	—
139	C₅×#217	C₂³	1	4	yes	complemented
140	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
141	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
142	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
143	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
144	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
145	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
146	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
147	C₅×C₄⋊Dic₃	C₂³	1	4	yes	complemented
148	C₅×C₄⋊Dic₃	C₂³	1	4	yes	complemented
149	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
150	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
151	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
152	C₄×C₅×Dic₃	C₂³	1	4	yes	complemented
153	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂×#940	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×#939	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂×#939	C₂×C₅	1	1	yes	characteristic, complemented
157	C₂×#938	C₂×C₅	1	1	yes	characteristic, complemented
158	C₂×#937	C₂×C₅	1	1	yes	characteristic, complemented
159	C₂×#937	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂×#930	C₂×C₅	1	1	yes	characteristic, complemented
161	C₂×#929	C₂×C₅	1	1	yes	characteristic, complemented
162	#5620	C₂×C₅	1	16	yes	direct product factor
163	C₂×#898	C₂×C₅	1	1	yes	characteristic, complemented
164	C₂×#894	C₂×C₅	1	1	yes	characteristic, complemented
165	C₂×#886	C₂×C₅	1	1	yes	characteristic, complemented
166	C₂×#884	C₂×C₅	1	1	yes	characteristic, complemented
167	C₂×#882	C₂×C₅	1	1	yes	characteristic, complemented
168	C₂×#879	C₂×C₅	1	1	yes	characteristic, complemented
169	C₂⁵×C₅	—	3	1	no	—
170	C₂²×C₅×D₄	—	3	1	no	—
171	C₂²×C₅×D₄	—	3	1	no	—
172	C₂²×C₅×D₄	—	3	1	no	—
173	C₂²×C₅×D₄	—	3	1	no	—
174	C₂²×C₅×D₄	—	3	1	no	—
175	C₂²×C₅×D₄	—	3	1	no	—
176	C₂²×C₅×D₄	—	3	1	no	—
177	C₂²×C₅×D₄	—	3	1	no	—
178	C₂²×C₅×D₄	—	3	1	no	—
179	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
180	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
181	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
182	C₂³×C₄×C₅	—	3	1	no	—
183	C₂³×C₄×C₅	—	3	1	no	—
184	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
185	C₅×#127	—	3	8	no	—
186	C₅×#126	—	3	8	no	—
187	C₅×#126	—	3	8	no	—
188	C₅×#123	—	3	8	no	—
189	C₅×#123	—	3	8	no	—
190	C₅×#123	—	3	8	no	—
191	C₅×#121	—	3	8	no	—
192	C₅×#121	—	3	8	no	—
193	C₅×#121	—	3	8	no	—
194	C₅×#121	—	3	8	no	—
195	C₅×#121	—	3	8	no	—
196	C₅×#121	C₂×D₃	1	8	yes	complemented
197	C₅×#120	—	3	8	no	—
198	C₅×#120	—	3	8	no	—
199	C₅×#120	—	3	8	no	—
200	C₂×C₅×C₄⋊C₄	—	3	1	no	—
201	C₂×C₅×C₄⋊C₄	—	3	1	no	—
202	C₂×C₅×C₄⋊C₄	—	3	1	no	—
203	C₂×C₅×C₄⋊C₄	—	3	1	no	—
204	C₂×C₅×C₄⋊C₄	—	3	1	no	—
205	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
206	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
207	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
208	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
209	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
210	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
211	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
212	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
213	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
214	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
215	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
216	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
217	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
218	C₂×C₄²×C₅	—	3	1	no	—
219	C₂×#560	—	3	1	no	Sylow
220	C₂³×C₃×C₅	—	2	2	no	—
221	C₂³×C₃×C₅	—	2	2	no	—
222	C₂³×C₃×C₅	—	2	2	no	—
223	C₂³×C₃×C₅	—	2	2	no	—
224	C₂³×C₃×C₅	—	2	2	no	—
225	C₂³×C₃×C₅	—	2	2	no	—
226	C₂³×C₃×C₅	—	2	2	no	—
227	C₂³×C₃×C₅	—	2	2	no	—
228	C₂³×C₃×C₅	—	2	2	no	—
229	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
230	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
231	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
232	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
233	C₂²×C₅×D₃	—	2	2	no	—
234	C₂²×C₅×D₃	—	2	2	no	—
235	C₂²×C₅×D₃	—	2	2	no	—
236	C₂²×C₅×D₃	—	2	2	no	—
237	C₂²×C₅×D₃	—	2	2	no	—
238	C₂²×C₅×D₃	—	2	2	no	—
239	C₂²×C₅×D₃	—	2	2	no	—
240	C₂²×C₅×D₃	—	2	2	no	—
241	C₂²×C₅×D₃	—	2	2	no	—
242	C₂²×C₅×D₃	—	4	4	no	—
243	C₂²×C₅×D₃	—	4	4	no	—
244	C₂²×C₅×D₃	—	4	4	no	—
245	C₂²×C₅×D₃	—	4	16	no	—
246	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
247	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
248	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
249	C₃×C₅×D₄	—	4	4	no	—
250	C₃×C₅×D₄	—	4	4	no	—
251	C₃×C₅×D₄	—	4	4	no	—
252	C₂×C₃×C₄×C₅	—	2	2	no	—
253	C₂×C₃×C₄×C₅	—	2	2	no	—
254	C₂×C₃×C₄×C₅	—	2	2	no	—
255	C₂×C₃×C₄×C₅	—	2	2	no	—
256	C₂×C₃×C₄×C₅	—	4	4	no	—
257	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
258	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
259	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
260	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
261	C₅×#67	—	4	4	no	—
262	C₅×#67	—	4	4	no	—
263	C₅×#67	—	4	4	no	—
264	C₅×#67	—	4	4	no	—
265	C₅×#67	—	4	4	no	—
266	C₅×#67	—	4	4	no	—
267	C₅×#67	—	4	4	no	—
268	C₂×C₅×Dic₃	—	2	2	no	—
269	C₂×C₅×Dic₃	—	2	2	no	—
270	C₂×C₅×Dic₃	—	2	2	no	—
271	C₂×C₅×Dic₃	—	2	2	no	—
272	C₂×C₅×Dic₃	—	2	2	no	—
273	C₂×C₅×Dic₃	—	4	4	no	—
274	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
275	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
276	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
277	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
278	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
279	C₅×D₁₂	—	4	4	no	—
280	C₅×D₁₂	—	4	4	no	—
281	C₄×C₅×D₃	—	4	4	no	—
282	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
283	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
284	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
285	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
286	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
288	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
289	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
290	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
291	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
292	C₂²×#67	C₂²×C₅	1	1	yes	characteristic, complemented
293	C₂²×#67	C₂²×C₅	1	1	yes	characteristic, complemented
294	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
295	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
296	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
297	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
298	C₃×#121	C₂²×C₅	1	8	yes	complemented
299	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
300	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
301	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
302	C₂×#217	C₂²×C₅	1	1	yes	characteristic
303	C₂×#217	C₂²×C₅	1	1	yes	characteristic
304	C₂×#217	C₂²×C₅	1	1	yes	characteristic, complemented
305	#940	C₂²×C₅	1	8	yes	complemented
306	#939	C₂²×C₅	1	8	yes	complemented
307	#939	C₂²×C₅	1	8	yes	complemented
308	#938	C₂²×C₅	1	8	yes	complemented
309	#937	C₂²×C₅	1	8	yes	complemented
310	#937	C₂²×C₅	1	8	yes	complemented
311	#930	C₂²×C₅	1	8	yes	complemented
312	#929	C₂²×C₅	1	8	yes	complemented
313	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
314	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
315	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
316	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
317	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
318	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
319	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
320	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
321	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
322	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
323	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
324	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
325	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
326	#898	C₂²×C₅	1	8	yes	complemented
327	#894	C₂²×C₅	1	8	yes	complemented
328	#886	C₂²×C₅	1	8	yes	complemented
329	#884	C₂²×C₅	1	8	yes	complemented
330	#882	C₂²×C₅	1	8	yes	complemented
331	#879	C₂²×C₅	1	8	yes	complemented
332	C₂⁴×C₅	—	3	1	no	—
333	C₂⁴×C₅	—	3	1	no	—
334	C₂⁴×C₅	—	3	1	no	—
335	C₂⁴×C₅	—	3	4	no	—
336	C₂⁴×C₅	—	12	2	no	—
337	C₂⁴×C₅	—	12	2	no	—
338	C₂⁴×C₅	—	12	2	no	—
339	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
340	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
341	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
342	C₂×C₅×D₄	—	3	4	no	—
343	C₂×C₅×D₄	—	3	4	no	—
344	C₂×C₅×D₄	—	3	4	no	—
345	C₂×C₅×D₄	—	3	4	no	—
346	C₂×C₅×D₄	—	3	4	no	—
347	C₂×C₅×D₄	—	3	4	no	—
348	C₂×C₅×D₄	—	3	4	no	—
349	C₂×C₅×D₄	—	3	4	no	—
350	C₂×C₅×D₄	—	3	4	no	—
351	C₂×C₅×D₄	—	4	2	no	—
352	C₂×C₅×D₄	—	4	2	no	—
353	C₂×C₅×D₄	—	4	2	no	—
354	C₂×C₅×D₄	—	12	2	no	—
355	C₂×C₅×D₄	—	12	2	no	—
356	C₂×C₅×D₄	—	12	2	no	—
357	C₂×C₅×D₄	—	12	2	no	—
358	C₂×C₅×D₄	—	12	2	no	—
359	C₂×C₅×D₄	—	12	2	no	—
360	C₂×C₅×D₄	—	12	2	no	—
361	C₂×C₅×D₄	—	12	2	no	—
362	C₂×C₅×D₄	—	12	2	no	—
363	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
364	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
365	C₂×C₅×D₄	C₂²×D₃	1	4	yes	complemented
366	C₂²×C₄×C₅	—	3	1	no	—
367	C₂²×C₄×C₅	—	3	1	no	—
368	C₂²×C₄×C₅	—	3	1	no	—
369	C₂²×C₄×C₅	—	3	1	no	—
370	C₂²×C₄×C₅	—	3	1	no	—
371	C₂²×C₄×C₅	—	3	4	no	—
372	C₂²×C₄×C₅	—	3	4	no	—
373	C₂²×C₄×C₅	—	4	2	no	—
374	C₂²×C₄×C₅	—	12	2	no	—
375	C₂²×C₄×C₅	—	12	2	no	—
376	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
377	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
378	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
379	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
380	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	complemented
381	C₅×C₄⋊C₄	—	3	4	no	—
382	C₅×C₄⋊C₄	—	3	4	no	—
383	C₅×C₄⋊C₄	—	3	4	no	—
384	C₅×C₄⋊C₄	—	3	4	no	—
385	C₅×C₄⋊C₄	—	3	4	no	—
386	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
387	C₅×C₂²⋊C₄	—	3	4	no	—
388	C₅×C₂²⋊C₄	—	3	4	no	—
389	C₅×C₂²⋊C₄	—	3	4	no	—
390	C₅×C₂²⋊C₄	—	3	4	no	—
391	C₅×C₂²⋊C₄	—	3	4	no	—
392	C₅×C₂²⋊C₄	—	3	4	no	—
393	C₅×C₂²⋊C₄	—	3	4	no	—
394	C₅×C₂²⋊C₄	—	3	4	no	—
395	C₅×C₂²⋊C₄	—	3	4	no	—
396	C₅×C₂²⋊C₄	—	3	4	no	—
397	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
398	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
399	C₄²×C₅	—	3	4	no	—
400	#560	—	3	16	no	—
401	C₂×#127	—	3	1	no	—
402	C₂×#126	—	3	1	no	—
403	C₂×#126	—	3	1	no	—
404	C₂×#123	—	3	1	no	—
405	C₂×#123	—	3	1	no	—
406	C₂×#123	—	3	1	no	—
407	C₂×#121	—	3	1	no	—
408	C₂×#121	—	3	1	no	—
409	C₂×#121	—	3	1	no	—
410	C₂×#121	—	3	1	no	—
411	C₂×#121	—	3	1	no	—
412	C₂×#121	C₅×D₃	1	1	yes	characteristic, complemented
413	C₂×#120	—	3	1	no	—
414	C₂×#120	—	3	1	no	—
415	C₂×#120	—	3	1	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	—	4	4	no	—
426	C₂²×C₃×C₅	—	4	4	no	—
427	C₂²×C₃×C₅	—	4	4	no	—
428	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
429	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
430	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
431	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
432	C₂×C₅×D₃	—	2	2	no	—
433	C₂×C₅×D₃	—	2	2	no	—
434	C₂×C₅×D₃	—	2	2	no	—
435	C₂×C₅×D₃	—	2	2	no	—
436	C₂×C₅×D₃	—	2	2	no	—
437	C₂×C₅×D₃	—	2	2	no	—
438	C₂×C₅×D₃	—	2	2	no	—
439	C₂×C₅×D₃	—	2	2	no	—
440	C₂×C₅×D₃	—	2	2	no	—
441	C₂×C₅×D₃	—	4	16	no	—
442	C₂×C₅×D₃	—	4	4	no	—
443	C₂×C₅×D₃	—	4	4	no	—
444	C₂×C₅×D₃	—	4	4	no	—
445	C₃×C₄×C₅	—	2	2	no	—
446	C₃×C₄×C₅	—	2	2	no	—
447	C₃×C₄×C₅	—	2	2	no	—
448	C₃×C₄×C₅	—	2	2	no	—
449	C₅×Dic₃	—	2	2	no	—
450	C₅×Dic₃	—	2	2	no	—
451	C₅×Dic₃	—	2	2	no	—
452	C₅×Dic₃	—	2	2	no	—
453	C₅×Dic₃	—	2	2	no	—
454	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
455	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
456	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
457	C₂³×D₃	—	4	2	no	—
458	C₂³×D₃	—	4	2	no	—
459	C₂³×D₃	—	4	2	no	—
460	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
461	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
462	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
463	C₂³×D₃	C₂³×C₅	1	4	yes	—
464	C₂×C₃×D₄	—	4	2	no	—
465	C₂×C₃×D₄	—	4	2	no	—
466	C₂×C₃×D₄	—	4	2	no	—
467	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
468	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
469	C₂×C₃×D₄	C₂³×C₅	1	4	yes	complemented
470	C₂²×C₃×C₄	—	4	2	no	—
471	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
472	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
473	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
474	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
475	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	complemented
476	C₂×#67	—	4	2	no	—
477	C₂×#67	—	4	2	no	—
478	C₂×#67	—	4	2	no	—
479	C₂×#67	—	4	2	no	—
480	C₂×#67	—	4	2	no	—
481	C₂×#67	—	4	2	no	—
482	C₂×#67	—	4	2	no	—
483	C₂×#67	C₂³×C₅	1	4	yes	—
484	C₂×#67	C₂³×C₅	1	4	yes	—
485	C₂×#67	C₂³×C₅	1	4	yes	—
486	C₂×#67	C₂³×C₅	1	4	yes	—
487	C₂×#67	C₂³×C₅	1	4	yes	—
488	C₂×#67	C₂³×C₅	1	4	yes	complemented
489	C₂×#67	C₂³×C₅	1	4	yes	complemented
490	C₂²×Dic₃	—	4	2	no	—
491	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
492	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
493	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
494	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
495	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
496	C₂²×Dic₃	C₂³×C₅	1	4	yes	complemented
497	C₂×D₁₂	—	4	2	no	—
498	C₂×D₁₂	—	4	2	no	—
499	C₂×D₁₂	C₂³×C₅	1	4	yes	—
500	C₂×D₁₂	C₂³×C₅	1	4	yes	—
501	C₂×C₄×D₃	—	4	2	no	—
502	C₂×C₄×D₃	C₂³×C₅	1	4	yes	complemented
503	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
504	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
505	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	complemented
506	#217	C₂³×C₅	1	4	yes	—
507	#217	C₂³×C₅	1	4	yes	—
508	#217	C₂³×C₅	1	4	yes	complemented
509	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
510	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
511	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
512	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
513	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
514	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
515	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	complemented
516	C₄⋊Dic₃	C₂³×C₅	1	4	yes	complemented
517	C₄⋊Dic₃	C₂³×C₅	1	4	yes	complemented
518	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
519	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
520	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
521	C₄×Dic₃	C₂³×C₅	1	4	yes	complemented
522	C₂³×C₅	—	2	2	no	—
523	C₂³×C₅	—	2	2	no	—
524	C₂³×C₅	—	2	2	no	—
525	C₂³×C₅	—	2	2	no	—
526	C₂³×C₅	—	2	2	no	—
527	C₂³×C₅	—	2	2	no	—
528	C₂³×C₅	—	2	2	no	—
529	C₂³×C₅	—	2	2	no	—
530	C₂³×C₅	—	2	2	no	—
531	C₂³×C₅	—	3	2	no	—
532	C₂³×C₅	—	3	2	no	—
533	C₂³×C₅	—	3	2	no	—
534	C₂³×C₅	—	6	2	no	—
535	C₂³×C₅	—	6	2	no	—
536	C₂³×C₅	—	6	2	no	—
537	C₂³×C₅	—	6	2	no	—
538	C₂³×C₅	—	6	2	no	—
539	C₂³×C₅	—	6	2	no	—
540	C₂³×C₅	—	6	2	no	—
541	C₂³×C₅	—	6	2	no	—
542	C₂³×C₅	—	6	2	no	—
543	C₂³×C₅	—	12	4	no	—
544	C₂³×C₅	—	12	4	no	—
545	C₂³×C₅	—	12	4	no	—
546	C₂³×C₅	—	12	16	no	—
547	C₂³×C₅	C₂³×D₃	1	2	yes	—
548	C₂³×C₅	C₂³×D₃	1	2	yes	—
549	C₂³×C₅	C₂³×D₃	1	2	yes	—
550	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
551	C₅×D₄	—	4	4	no	—
552	C₅×D₄	—	4	4	no	—
553	C₅×D₄	—	4	4	no	—
554	C₅×D₄	—	12	4	no	—
555	C₅×D₄	—	12	4	no	—
556	C₅×D₄	—	12	4	no	—
557	C₅×D₄	—	12	4	no	—
558	C₅×D₄	—	12	4	no	—
559	C₅×D₄	—	12	4	no	—
560	C₅×D₄	—	12	4	no	—
561	C₅×D₄	—	12	4	no	—
562	C₅×D₄	—	12	4	no	—
563	C₂×C₄×C₅	—	2	2	no	—
564	C₂×C₄×C₅	—	2	2	no	—
565	C₂×C₄×C₅	—	2	2	no	—
566	C₂×C₄×C₅	—	2	2	no	—
567	C₂×C₄×C₅	—	3	2	no	—
568	C₂×C₄×C₅	—	3	2	no	—
569	C₂×C₄×C₅	—	3	2	no	—
570	C₂×C₄×C₅	—	3	2	no	—
571	C₂×C₄×C₅	—	3	2	no	—
572	C₂×C₄×C₅	—	4	4	no	—
573	C₂×C₄×C₅	—	6	2	no	—
574	C₂×C₄×C₅	—	6	2	no	—
575	C₂×C₄×C₅	—	6	2	no	—
576	C₂×C₄×C₅	—	6	2	no	—
577	C₂×C₄×C₅	—	6	2	no	—
578	C₂×C₄×C₅	—	12	4	no	—
579	C₂×C₄×C₅	—	12	4	no	—
580	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
581	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
582	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
583	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
584	C₂⁵	—	3	1	no	—
585	C₂²×D₄	—	3	1	no	—
586	C₂²×D₄	—	3	1	no	—
587	C₂²×D₄	—	3	1	no	—
588	C₂²×D₄	—	3	1	no	—
589	C₂²×D₄	—	3	1	no	—
590	C₂²×D₄	—	3	1	no	—
591	C₂²×D₄	—	3	1	no	—
592	C₂²×D₄	—	3	1	no	—
593	C₂²×D₄	—	3	1	no	—
594	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
595	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
596	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
597	C₂³×C₄	—	3	1	no	—
598	C₂³×C₄	—	3	1	no	—
599	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
600	#127	—	3	8	no	—
601	#126	—	3	8	no	—
602	#126	—	3	8	no	—
603	#123	—	3	8	no	—
604	#123	—	3	8	no	—
605	#123	—	3	8	no	—
606	#121	—	3	8	no	—
607	#121	—	3	8	no	—
608	#121	—	3	8	no	—
609	#121	—	3	8	no	—
610	#121	—	3	8	no	—
611	#121	C₂×C₅×D₃	1	8	yes	complemented
612	#120	—	3	8	no	—
613	#120	—	3	8	no	—
614	#120	—	3	8	no	—
615	C₂×C₄⋊C₄	—	3	1	no	—
616	C₂×C₄⋊C₄	—	3	1	no	—
617	C₂×C₄⋊C₄	—	3	1	no	—
618	C₂×C₄⋊C₄	—	3	1	no	—
619	C₂×C₄⋊C₄	—	3	1	no	—
620	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
621	C₂×C₂²⋊C₄	—	3	1	no	—
622	C₂×C₂²⋊C₄	—	3	1	no	—
623	C₂×C₂²⋊C₄	—	3	1	no	—
624	C₂×C₂²⋊C₄	—	3	1	no	—
625	C₂×C₂²⋊C₄	—	3	1	no	—
626	C₂×C₂²⋊C₄	—	3	1	no	—
627	C₂×C₂²⋊C₄	—	3	1	no	—
628	C₂×C₂²⋊C₄	—	3	1	no	—
629	C₂×C₂²⋊C₄	—	3	1	no	—
630	C₂×C₂²⋊C₄	—	3	1	no	—
631	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
633	C₂×C₄²	—	3	1	no	—
634	C₂×C₃×C₅	—	4	2	no	—
635	C₂×C₃×C₅	—	4	2	no	—
636	C₂×C₃×C₅	—	4	2	no	—
637	C₂×C₃×C₅	#560	1	4	yes	complemented
638	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
639	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
640	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
641	C₅×D₃	—	4	2	no	—
642	C₅×D₃	—	4	2	no	—
643	C₅×D₃	—	4	2	no	—
644	C₂³×C₃	—	2	2	no	—
645	C₂³×C₃	—	2	2	no	—
646	C₂³×C₃	—	2	2	no	—
647	C₂³×C₃	—	2	2	no	—
648	C₂³×C₃	—	2	2	no	—
649	C₂³×C₃	—	2	2	no	—
650	C₂³×C₃	—	2	2	no	—
651	C₂³×C₃	—	2	2	no	—
652	C₂³×C₃	—	2	2	no	—
653	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
654	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
655	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
656	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
657	C₂²×D₃	—	2	2	no	—
658	C₂²×D₃	—	2	2	no	—
659	C₂²×D₃	—	2	2	no	—
660	C₂²×D₃	—	2	2	no	—
661	C₂²×D₃	—	2	2	no	—
662	C₂²×D₃	—	2	2	no	—
663	C₂²×D₃	—	2	2	no	—
664	C₂²×D₃	—	2	2	no	—
665	C₂²×D₃	—	2	2	no	—
666	C₂²×D₃	—	4	4	no	—
667	C₂²×D₃	—	4	4	no	—
668	C₂²×D₃	—	4	4	no	—
669	C₂²×D₃	—	4	16	no	—
670	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
671	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
672	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
673	C₃×D₄	—	4	4	no	—
674	C₃×D₄	—	4	4	no	—
675	C₃×D₄	—	4	4	no	—
676	C₂×C₃×C₄	—	2	2	no	—
677	C₂×C₃×C₄	—	2	2	no	—
678	C₂×C₃×C₄	—	2	2	no	—
679	C₂×C₃×C₄	—	2	2	no	—
680	C₂×C₃×C₄	—	4	4	no	—
681	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
682	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
683	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
684	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
685	#67	—	4	4	no	—
686	#67	—	4	4	no	—
687	#67	—	4	4	no	—
688	#67	—	4	4	no	—
689	#67	—	4	4	no	—
690	#67	—	4	4	no	—
691	#67	—	4	4	no	—
692	C₂×Dic₃	—	2	2	no	—
693	C₂×Dic₃	—	2	2	no	—
694	C₂×Dic₃	—	2	2	no	—
695	C₂×Dic₃	—	2	2	no	—
696	C₂×Dic₃	—	2	2	no	—
697	C₂×Dic₃	—	4	4	no	—
698	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
699	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
700	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
701	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
702	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
703	D₁₂	—	4	4	no	—
704	D₁₂	—	4	4	no	—
705	C₄×D₃	—	4	4	no	—
706	C₂²×C₅	—	2	2	no	—
707	C₂²×C₅	—	2	2	no	—
708	C₂²×C₅	—	2	2	no	—
709	C₂²×C₅	—	2	2	no	—
710	C₂²×C₅	—	2	2	no	—
711	C₂²×C₅	—	2	2	no	—
712	C₂²×C₅	—	2	2	no	—
713	C₂²×C₅	—	2	2	no	—
714	C₂²×C₅	—	2	2	no	—
715	C₂²×C₅	—	4	4	no	—
716	C₂²×C₅	—	4	4	no	—
717	C₂²×C₅	—	4	4	no	—
718	C₂²×C₅	—	6	2	no	—
719	C₂²×C₅	—	6	2	no	—
720	C₂²×C₅	—	6	2	no	—
721	C₂²×C₅	—	6	2	no	—
722	C₂²×C₅	—	6	2	no	—
723	C₂²×C₅	—	6	2	no	—
724	C₂²×C₅	—	6	2	no	—
725	C₂²×C₅	—	6	2	no	—
726	C₂²×C₅	—	6	2	no	—
727	C₂²×C₅	—	12	16	no	—
728	C₂²×C₅	—	12	4	no	—
729	C₂²×C₅	—	12	4	no	—
730	C₂²×C₅	—	12	4	no	—
731	C₂²×C₅	#1004	1	2	yes	—
732	C₂²×C₅	#1004	1	2	yes	—
733	C₂²×C₅	#1009	1	2	yes	—
734	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
735	C₄×C₅	—	2	2	no	—
736	C₄×C₅	—	2	2	no	—
737	C₄×C₅	—	2	2	no	—
738	C₄×C₅	—	2	2	no	—
739	C₄×C₅	—	6	2	no	—
740	C₄×C₅	—	6	2	no	—
741	C₄×C₅	—	6	2	no	—
742	C₄×C₅	—	6	2	no	—
743	C₄×C₅	—	6	2	no	—
744	C₂⁴	—	3	1	no	—
745	C₂⁴	—	3	1	no	—
746	C₂⁴	—	3	1	no	—
747	C₂⁴	—	3	4	no	—
748	C₂⁴	—	12	2	no	—
749	C₂⁴	—	12	2	no	—
750	C₂⁴	—	12	2	no	—
751	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
752	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
753	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
754	C₂×D₄	—	3	4	no	—
755	C₂×D₄	—	3	4	no	—
756	C₂×D₄	—	3	4	no	—
757	C₂×D₄	—	3	4	no	—
758	C₂×D₄	—	3	4	no	—
759	C₂×D₄	—	3	4	no	—
760	C₂×D₄	—	3	4	no	—
761	C₂×D₄	—	3	4	no	—
762	C₂×D₄	—	3	4	no	—
763	C₂×D₄	—	4	2	no	—
764	C₂×D₄	—	4	2	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂×D₄	—	12	2	no	—
767	C₂×D₄	—	12	2	no	—
768	C₂×D₄	—	12	2	no	—
769	C₂×D₄	—	12	2	no	—
770	C₂×D₄	—	12	2	no	—
771	C₂×D₄	—	12	2	no	—
772	C₂×D₄	—	12	2	no	—
773	C₂×D₄	—	12	2	no	—
774	C₂×D₄	—	12	2	no	—
775	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
776	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
777	C₂×D₄	C₂²×C₅×D₃	1	4	yes	complemented
778	C₂²×C₄	—	3	1	no	—
779	C₂²×C₄	—	3	1	no	—
780	C₂²×C₄	—	3	1	no	—
781	C₂²×C₄	—	3	1	no	—
782	C₂²×C₄	—	3	1	no	—
783	C₂²×C₄	—	3	4	no	—
784	C₂²×C₄	—	3	4	no	—
785	C₂²×C₄	—	4	2	no	—
786	C₂²×C₄	—	12	2	no	—
787	C₂²×C₄	—	12	2	no	—
788	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
789	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
790	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
791	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
792	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	complemented
793	C₄⋊C₄	—	3	4	no	—
794	C₄⋊C₄	—	3	4	no	—
795	C₄⋊C₄	—	3	4	no	—
796	C₄⋊C₄	—	3	4	no	—
797	C₄⋊C₄	—	3	4	no	—
798	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
799	C₂²⋊C₄	—	3	4	no	—
800	C₂²⋊C₄	—	3	4	no	—
801	C₂²⋊C₄	—	3	4	no	—
802	C₂²⋊C₄	—	3	4	no	—
803	C₂²⋊C₄	—	3	4	no	—
804	C₂²⋊C₄	—	3	4	no	—
805	C₂²⋊C₄	—	3	4	no	—
806	C₂²⋊C₄	—	3	4	no	—
807	C₂²⋊C₄	—	3	4	no	—
808	C₂²⋊C₄	—	3	4	no	—
809	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
810	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
811	C₄²	—	3	4	no	—
812	C₃×C₅	C₂×#560	1	1	yes	characteristic, complemented, Hall
813	C₂²×C₃	—	2	2	no	—
814	C₂²×C₃	—	2	2	no	—
815	C₂²×C₃	—	2	2	no	—
816	C₂²×C₃	—	2	2	no	—
817	C₂²×C₃	—	2	2	no	—
818	C₂²×C₃	—	2	2	no	—
819	C₂²×C₃	—	2	2	no	—
820	C₂²×C₃	—	2	2	no	—
821	C₂²×C₃	—	2	2	no	—
822	C₂²×C₃	—	4	4	no	—
823	C₂²×C₃	—	4	4	no	—
824	C₂²×C₃	—	4	4	no	—
825	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
826	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
827	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
828	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
829	C₂×D₃	—	2	2	no	—
830	C₂×D₃	—	2	2	no	—
831	C₂×D₃	—	2	2	no	—
832	C₂×D₃	—	2	2	no	—
833	C₂×D₃	—	2	2	no	—
834	C₂×D₃	—	2	2	no	—
835	C₂×D₃	—	2	2	no	—
836	C₂×D₃	—	2	2	no	—
837	C₂×D₃	—	2	2	no	—
838	C₂×D₃	—	4	16	no	—
839	C₂×D₃	—	4	4	no	—
840	C₂×D₃	—	4	4	no	—
841	C₂×D₃	—	4	4	no	—
842	C₃×C₄	—	2	2	no	—
843	C₃×C₄	—	2	2	no	—
844	C₃×C₄	—	2	2	no	—
845	C₃×C₄	—	2	2	no	—
846	Dic₃	—	2	2	no	—
847	Dic₃	—	2	2	no	—
848	Dic₃	—	2	2	no	—
849	Dic₃	—	2	2	no	—
850	Dic₃	—	2	2	no	—
851	C₂×C₅	—	4	2	no	—
852	C₂×C₅	—	4	2	no	—
853	C₂×C₅	—	4	2	no	—
854	C₂×C₅	—	12	2	no	—
855	C₂×C₅	—	12	2	no	—
856	C₂×C₅	—	12	2	no	—
857	C₂×C₅	#5620	1	4	yes	direct product factor
858	C₂×C₅	C₂×#1004	1	1	yes	characteristic
859	C₂×C₅	C₂×#1004	1	1	yes	characteristic
860	C₂×C₅	C₂×#1009	1	1	yes	characteristic
861	C₂³	—	2	2	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	3	2	no	—
871	C₂³	—	3	2	no	—
872	C₂³	—	3	2	no	—
873	C₂³	—	6	2	no	—
874	C₂³	—	6	2	no	—
875	C₂³	—	6	2	no	—
876	C₂³	—	6	2	no	—
877	C₂³	—	6	2	no	—
878	C₂³	—	6	2	no	—
879	C₂³	—	6	2	no	—
880	C₂³	—	6	2	no	—
881	C₂³	—	6	2	no	—
882	C₂³	—	12	4	no	—
883	C₂³	—	12	4	no	—
884	C₂³	—	12	4	no	—
885	C₂³	—	12	16	no	—
886	C₂³	C₂³×C₅×D₃	1	2	yes	—
887	C₂³	C₂³×C₅×D₃	1	2	yes	—
888	C₂³	C₂³×C₅×D₃	1	2	yes	—
889	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
890	D₄	—	4	4	no	—
891	D₄	—	4	4	no	—
892	D₄	—	4	4	no	—
893	D₄	—	12	4	no	—
894	D₄	—	12	4	no	—
895	D₄	—	12	4	no	—
896	D₄	—	12	4	no	—
897	D₄	—	12	4	no	—
898	D₄	—	12	4	no	—
899	D₄	—	12	4	no	—
900	D₄	—	12	4	no	—
901	D₄	—	12	4	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	3	2	no	—
907	C₂×C₄	—	3	2	no	—
908	C₂×C₄	—	3	2	no	—
909	C₂×C₄	—	3	2	no	—
910	C₂×C₄	—	3	2	no	—
911	C₂×C₄	—	4	4	no	—
912	C₂×C₄	—	6	2	no	—
913	C₂×C₄	—	6	2	no	—
914	C₂×C₄	—	6	2	no	—
915	C₂×C₄	—	6	2	no	—
916	C₂×C₄	—	6	2	no	—
917	C₂×C₄	—	12	4	no	—
918	C₂×C₄	—	12	4	no	—
919	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
920	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
921	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
922	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
923	C₂×C₃	—	4	2	no	—
924	C₂×C₃	—	4	2	no	—
925	C₂×C₃	—	4	2	no	—
926	C₂×C₃	C₅×#560	1	4	yes	complemented
927	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
928	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
929	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
930	D₃	—	4	2	no	—
931	D₃	—	4	2	no	—
932	D₃	—	4	2	no	—
933	C₅	C₂×#5620	1	1	yes	characteristic, direct product factor, Sylow
934	C₂²	—	2	2	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	4	4	no	—
944	C₂²	—	4	4	no	—
945	C₂²	—	4	4	no	—
946	C₂²	—	6	2	no	—
947	C₂²	—	6	2	no	—
948	C₂²	—	6	2	no	—
949	C₂²	—	6	2	no	—
950	C₂²	—	6	2	no	—
951	C₂²	—	6	2	no	—
952	C₂²	—	6	2	no	—
953	C₂²	—	6	2	no	—
954	C₂²	—	6	2	no	—
955	C₂²	—	12	16	no	—
956	C₂²	—	12	4	no	—
957	C₂²	—	12	4	no	—
958	C₂²	—	12	4	no	—
959	C₂²	C₅×#1004	1	2	yes	—
960	C₂²	C₅×#1004	1	2	yes	—
961	C₂²	C₅×#1009	1	2	yes	—
962	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	2	no	—
967	C₄	—	6	2	no	—
968	C₄	—	6	2	no	—
969	C₄	—	6	2	no	—
970	C₄	—	6	2	no	—
971	C₄	—	6	2	no	—
972	C₃	C₂×C₅×#560	1	1	yes	characteristic, complemented, Sylow
973	C₂	—	4	2	no	—
974	C₂	—	4	2	no	—
975	C₂	—	4	2	no	—
976	C₂	—	12	2	no	—
977	C₂	—	12	2	no	—
978	C₂	—	12	2	no	—
979	C₂	C₅×#5620	1	4	yes	direct product factor
980	C₂	C₂×C₅×#1004	1	1	yes	characteristic
981	C₂	C₂×C₅×#1004	1	1	yes	characteristic
982	C₂	C₂×C₅×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#121	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#121	D₃
hypocenter	C₃	C₂×C₅×#560
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#121

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×C₅×#940	C₂	semidirect
3. C₂×C₅×#939	C₂	semidirect
4. C₂×C₅×#939	C₂	semidirect
5. C₂×C₅×#938	C₂	semidirect
6. C₂×C₅×#937	C₂	semidirect
7. C₂×C₅×#937	C₂	semidirect
8. C₂×C₅×#930	C₂	semidirect
9. C₂×C₅×#929	C₂	semidirect
10. C₅×#5620	C₂	direct (N × H)
11. C₂×C₅×#898	C₂	semidirect
12. C₂×C₅×#894	C₂	semidirect
13. C₂×C₅×#886	C₂	semidirect
14. C₂×C₅×#884	C₂	semidirect
15. C₂×C₅×#882	C₂	semidirect
16. C₂×C₅×#879	C₂	semidirect
21. C₂²×C₃×C₅×D₄	C₂²	semidirect
22. C₂³×C₃×C₄×C₅	C₂²	semidirect
28. C₂²×C₅×#67	C₂²	semidirect
29. C₂²×C₅×#67	C₂²	semidirect
30. C₂³×C₅×Dic₃	C₂²	semidirect
33. C₂²×C₄×C₅×D₃	C₂²	semidirect
34. C₃×C₅×#121	C₂²	semidirect
35. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
37. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
40. C₂×C₅×#217	C₂²	semidirect
41. C₅×#940	C₂²	semidirect
42. C₅×#939	C₂²	semidirect
43. C₅×#939	C₂²	semidirect
44. C₅×#938	C₂²	semidirect
45. C₅×#937	C₂²	semidirect
46. C₅×#937	C₂²	semidirect
47. C₅×#930	C₂²	semidirect
48. C₅×#929	C₂²	semidirect
55. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
56. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
57. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
58. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
59. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
60. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
61. C₂×C₄×C₅×Dic₃	C₂²	semidirect
62. C₅×#898	C₂²	semidirect
63. C₅×#894	C₂²	semidirect
64. C₅×#886	C₂²	semidirect
65. C₅×#884	C₂²	semidirect
66. C₅×#882	C₂²	semidirect
67. C₅×#879	C₂²	semidirect
68. C₂×#5620	C₅	direct (N × H)
81. C₂×C₅×#121	D₃	semidirect
100. C₂×C₃×C₅×D₄	C₂³	semidirect
106. C₂²×C₃×C₄×C₅	C₂³	semidirect
119. C₂×C₅×#67	C₂³	semidirect
120. C₂×C₅×#67	C₂³	semidirect
127. C₂²×C₅×Dic₃	C₂³	semidirect
133. C₂×C₄×C₅×D₃	C₂³	semidirect
134. C₃×C₅×C₄⋊C₄	C₂³	semidirect
136. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
139. C₅×#217	C₂³	semidirect
146. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
147. C₅×C₄⋊Dic₃	C₂³	semidirect
148. C₅×C₄⋊Dic₃	C₂³	semidirect
149. C₅×Dic₃⋊C₄	C₂³	semidirect
150. C₅×Dic₃⋊C₄	C₂³	semidirect
151. C₅×Dic₃⋊C₄	C₂³	semidirect
152. C₄×C₅×Dic₃	C₂³	semidirect
153. C₂×C₃×#121	C₂×C₅	semidirect
154. C₂×#940	C₂×C₅	semidirect
155. C₂×#939	C₂×C₅	semidirect
156. C₂×#939	C₂×C₅	semidirect
157. C₂×#938	C₂×C₅	semidirect
158. C₂×#937	C₂×C₅	semidirect
159. C₂×#937	C₂×C₅	semidirect
160. C₂×#930	C₂×C₅	semidirect
161. C₂×#929	C₂×C₅	semidirect
162. #5620	C₂×C₅	direct (N × H)
163. C₂×#898	C₂×C₅	semidirect
164. C₂×#894	C₂×C₅	semidirect
165. C₂×#886	C₂×C₅	semidirect
166. C₂×#884	C₂×C₅	semidirect
167. C₂×#882	C₂×C₅	semidirect
168. C₂×#879	C₂×C₅	semidirect
181. C₂²×C₅×D₄	C₂×D₃	semidirect
184. C₂³×C₄×C₅	C₂×D₃	semidirect
196. C₅×#121	C₂×D₃	semidirect
205. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
217. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
285. C₂²×C₃×D₄	C₂²×C₅	semidirect
286. C₂³×C₃×C₄	C₂²×C₅	semidirect
292. C₂²×#67	C₂²×C₅	semidirect
293. C₂²×#67	C₂²×C₅	semidirect
294. C₂³×Dic₃	C₂²×C₅	semidirect
297. C₂²×C₄×D₃	C₂²×C₅	semidirect
298. C₃×#121	C₂²×C₅	semidirect
299. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
301. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
304. C₂×#217	C₂²×C₅	semidirect
305. #940	C₂²×C₅	semidirect
306. #939	C₂²×C₅	semidirect
307. #939	C₂²×C₅	semidirect
308. #938	C₂²×C₅	semidirect
309. #937	C₂²×C₅	semidirect
310. #937	C₂²×C₅	semidirect
311. #930	C₂²×C₅	semidirect
312. #929	C₂²×C₅	semidirect
319. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
320. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
321. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
322. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
323. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
324. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
325. C₂×C₄×Dic₃	C₂²×C₅	semidirect
326. #898	C₂²×C₅	semidirect
327. #894	C₂²×C₅	semidirect
328. #886	C₂²×C₅	semidirect
329. #884	C₂²×C₅	semidirect
330. #882	C₂²×C₅	semidirect
331. #879	C₂²×C₅	semidirect
365. C₂×C₅×D₄	C₂²×D₃	semidirect
380. C₂²×C₄×C₅	C₂²×D₃	semidirect
386. C₅×C₄⋊C₄	C₂²×D₃	semidirect
398. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
412. C₂×#121	C₅×D₃	semidirect
469. C₂×C₃×D₄	C₂³×C₅	semidirect
475. C₂²×C₃×C₄	C₂³×C₅	semidirect
488. C₂×#67	C₂³×C₅	semidirect
489. C₂×#67	C₂³×C₅	semidirect
496. C₂²×Dic₃	C₂³×C₅	semidirect
502. C₂×C₄×D₃	C₂³×C₅	semidirect
503. C₃×C₄⋊C₄	C₂³×C₅	semidirect
505. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
508. #217	C₂³×C₅	semidirect
515. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
516. C₄⋊Dic₃	C₂³×C₅	semidirect
517. C₄⋊Dic₃	C₂³×C₅	semidirect
518. Dic₃⋊C₄	C₂³×C₅	semidirect
519. Dic₃⋊C₄	C₂³×C₅	semidirect
520. Dic₃⋊C₄	C₂³×C₅	semidirect
521. C₄×Dic₃	C₂³×C₅	semidirect
596. C₂²×D₄	C₂×C₅×D₃	semidirect
599. C₂³×C₄	C₂×C₅×D₃	semidirect
611. #121	C₂×C₅×D₃	semidirect
620. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
632. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
637. C₂×C₃×C₅	#560	semidirect
777. C₂×D₄	C₂²×C₅×D₃	semidirect
792. C₂²×C₄	C₂²×C₅×D₃	semidirect
798. C₄⋊C₄	C₂²×C₅×D₃	semidirect
810. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
812. C₃×C₅	C₂×#560	semidirect
857. C₂×C₅	#5620	direct (N × H)
926. C₂×C₃	C₅×#560	semidirect
933. C₅	C₂×#5620	direct (N × H)
972. C₃	C₂×C₅×#560	semidirect
979. C₂	C₅×#5620	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×C₅×#940	2
C₂×C₅×#939	2
C₂×C₅×#938	2
C₂×C₅×#937	2
C₂×C₅×#930	2
C₂×C₅×#929	2
C₅×#5620	2
C₂×C₅×#898	2
C₂×C₅×#894	2
C₂×C₅×#886	2
C₂×C₅×#884	2
C₂×C₅×#882	2
C₂×C₅×#879	2
C₂×C₅×#560	3
C₂×#5620	5

Subgroups — C2×C5×#5620 #14495181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5620 #14495181