Subgroups — C₂×C₃×#65949 #14481080

Order 1920.

2520 conjugacy classes of subgroups.

The subgroup lattice has 928 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×#4086	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4085	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4085	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#4084	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#4081	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4075	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65949	C₂	1	16	yes	maximal, direct product factor
11	C₂×C₃×#4040	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#4035	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#4030	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#4029	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#4027	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#4023	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#65949	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
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	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
26	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
28	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
29	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
30	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
31	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
32	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
33	C₃×C₅×#121	C₂²	1	8	yes	complemented
34	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
41	C₃×#4086	C₂²	1	8	yes	complemented
42	C₃×#4085	C₂²	1	8	yes	complemented
43	C₃×#4085	C₂²	1	8	yes	complemented
44	C₃×#4085	C₂²	1	8	yes	complemented
45	C₃×#4084	C₂²	1	8	yes	complemented
46	C₃×#4081	C₂²	1	8	yes	complemented
47	C₃×#4075	C₂²	1	8	yes	complemented
48	C₃×C₄×C₂²⋊D₅	C₂²	1	8	yes	complemented
49	C₂×C₃×#685	C₂²	1	1	yes	characteristic
50	C₂×C₃×#685	C₂²	1	1	yes	characteristic
51	C₂×C₃×#685	C₂²	1	1	yes	characteristic
52	C₂×C₃×#685	C₂²	1	1	yes	characteristic
53	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
54	C₂×C₃×#683	C₂²	1	1	yes	characteristic
55	C₂×C₃×#683	C₂²	1	1	yes	characteristic
56	C₂×C₃×#683	C₂²	1	1	yes	characteristic
57	C₂×C₃×#683	C₂²	1	1	yes	characteristic
58	C₂×C₃×#683	C₂²	1	1	yes	characteristic
59	C₂×C₃×#683	C₂²	1	1	yes	characteristic
60	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
61	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
62	C₃×#4040	C₂²	1	8	yes	complemented
63	C₃×#4035	C₂²	1	8	yes	complemented
64	C₃×#4030	C₂²	1	8	yes	complemented
65	C₃×#4029	C₂²	1	8	yes	complemented
66	C₃×#4027	C₂²	1	8	yes	complemented
67	C₃×#4023	C₂²	1	8	yes	complemented
68	C₂×C₃×#540	—	5	1	no	maximal, Hall
69	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
70	C₂×#4086	C₂×C₃	1	1	yes	characteristic, complemented
71	C₂×#4085	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂×#4085	C₂×C₃	1	1	yes	characteristic, complemented
73	C₂×#4085	C₂×C₃	1	1	yes	characteristic, complemented
74	C₂×#4084	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×#4081	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×#4075	C₂×C₃	1	1	yes	characteristic, complemented
77	C₂×C₄×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
78	#65949	C₂×C₃	1	16	yes	direct product factor
79	C₂×#4040	C₂×C₃	1	1	yes	characteristic, complemented
80	C₂×#4035	C₂×C₃	1	1	yes	characteristic, complemented
81	C₂×#4030	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂×#4029	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×#4027	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂×#4023	C₂×C₃	1	1	yes	characteristic, complemented
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×C₃×D₅	C₂³	1	1	yes	characteristic
89	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₅×D₄	—	4	2	no	—
91	C₂×C₃×C₅×D₄	—	4	2	no	—
92	C₂×C₃×C₅×D₄	—	4	2	no	—
93	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
94	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
95	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
96	C₂²×C₃×C₄×C₅	—	4	2	no	—
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
100	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
101	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
102	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
103	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
104	C₂×C₃×C₂²⋊D₅	—	4	2	no	—
105	C₂×C₃×C₂²⋊D₅	—	4	2	no	—
106	C₂×C₃×C₂²⋊D₅	—	4	2	no	—
107	C₂×C₃×C₂²⋊D₅	—	4	2	no	—
108	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
109	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
110	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
111	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
112	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
113	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
114	C₂²×C₃×Dic₅	—	2	4	no	—
115	C₂²×C₃×Dic₅	—	4	2	no	—
116	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
117	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
118	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
119	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
120	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
121	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
122	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
123	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
124	C₂×C₃×D₂₀	—	4	2	no	—
125	C₂×C₃×D₂₀	C₂³	1	4	yes	—
126	C₂×C₃×C₄×D₅	—	4	2	no	—
127	C₂×C₃×C₄×D₅	—	4	2	no	—
128	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
129	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
130	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
131	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
134	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
135	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
136	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
137	C₃×#685	C₂³	1	4	yes	—
138	C₃×#685	C₂³	1	4	yes	—
139	C₃×#685	C₂³	1	4	yes	—
140	C₃×#685	C₂³	1	4	yes	—
141	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
142	C₃×#683	C₂³	1	4	yes	—
143	C₃×#683	C₂³	1	4	yes	—
144	C₃×#683	C₂³	1	4	yes	—
145	C₃×#683	C₂³	1	4	yes	—
146	C₃×#683	C₂³	1	4	yes	—
147	C₃×#683	C₂³	1	4	yes	—
148	C₃×C₄×Dic₅	C₂³	1	4	yes	—
149	C₃×C₄×Dic₅	C₂³	1	4	yes	—
150	C₃×#540	—	5	16	no	—
151	C₂×C₃×#127	—	5	1	no	—
152	C₂×C₃×#125	—	5	1	no	—
153	C₂×C₃×#123	—	5	1	no	—
154	C₂×C₃×#123	—	5	1	no	—
155	C₂×C₃×#123	—	5	1	no	—
156	C₂×C₃×#123	—	5	1	no	—
157	C₂×C₃×#121	—	5	1	no	—
158	C₂×C₃×#121	—	5	1	no	—
159	C₂×C₃×#121	—	5	1	no	—
160	C₂×C₃×#121	—	5	1	no	—
161	C₂×C₃×#121	—	5	1	no	—
162	C₂×C₃×#121	D₅	1	1	yes	characteristic, complemented
163	C₂×C₃×C₄×D₄	—	5	1	no	—
164	C₂×C₃×C₄×D₄	—	5	1	no	—
165	C₂×C₃×#117	—	5	1	no	—
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
169	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
170	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
171	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
172	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
173	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
174	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
175	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
176	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
177	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
178	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
179	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
180	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
181	C₅×#121	C₂²×C₃	1	8	yes	complemented
182	C₂×C₅×C₄⋊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×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
186	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
187	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
188	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
189	#4086	C₂²×C₃	1	8	yes	complemented
190	#4085	C₂²×C₃	1	8	yes	complemented
191	#4085	C₂²×C₃	1	8	yes	complemented
192	#4085	C₂²×C₃	1	8	yes	complemented
193	#4084	C₂²×C₃	1	8	yes	complemented
194	#4081	C₂²×C₃	1	8	yes	complemented
195	#4075	C₂²×C₃	1	8	yes	complemented
196	C₄×C₂²⋊D₅	C₂²×C₃	1	8	yes	complemented
197	C₂×#685	C₂²×C₃	1	1	yes	characteristic
198	C₂×#685	C₂²×C₃	1	1	yes	characteristic
199	C₂×#685	C₂²×C₃	1	1	yes	characteristic
200	C₂×#685	C₂²×C₃	1	1	yes	characteristic
201	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
202	C₂×#683	C₂²×C₃	1	1	yes	characteristic
203	C₂×#683	C₂²×C₃	1	1	yes	characteristic
204	C₂×#683	C₂²×C₃	1	1	yes	characteristic
205	C₂×#683	C₂²×C₃	1	1	yes	characteristic
206	C₂×#683	C₂²×C₃	1	1	yes	characteristic
207	C₂×#683	C₂²×C₃	1	1	yes	characteristic
208	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
209	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
210	#4040	C₂²×C₃	1	8	yes	complemented
211	#4035	C₂²×C₃	1	8	yes	complemented
212	#4030	C₂²×C₃	1	8	yes	complemented
213	#4029	C₂²×C₃	1	8	yes	complemented
214	#4027	C₂²×C₃	1	8	yes	complemented
215	#4023	C₂²×C₃	1	8	yes	complemented
216	C₂×#540	—	5	1	no	Sylow
217	C₂³×C₃×C₅	—	2	2	no	—
218	C₂³×C₃×C₅	—	2	2	no	—
219	C₂³×C₃×C₅	—	2	2	no	—
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	C₂⁴	1	2	yes	—
227	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
228	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
229	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
230	C₂²×C₃×D₅	—	2	2	no	—
231	C₂²×C₃×D₅	—	2	2	no	—
232	C₂²×C₃×D₅	—	2	2	no	—
233	C₂²×C₃×D₅	—	2	2	no	—
234	C₂²×C₃×D₅	—	2	2	no	—
235	C₂²×C₃×D₅	—	2	2	no	—
236	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
237	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
238	C₃×C₅×D₄	—	4	4	no	—
239	C₃×C₅×D₄	—	4	4	no	—
240	C₃×C₅×D₄	—	4	4	no	—
241	C₂×C₃×C₄×C₅	—	2	2	no	—
242	C₂×C₃×C₄×C₅	—	2	2	no	—
243	C₂×C₃×C₄×C₅	—	2	2	no	—
244	C₂×C₃×C₄×C₅	—	2	2	no	—
245	C₂×C₃×C₄×C₅	—	4	4	no	—
246	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
247	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
248	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
249	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
250	C₃×C₂²⋊D₅	—	2	8	no	—
251	C₃×C₂²⋊D₅	—	2	8	no	—
252	C₃×C₂²⋊D₅	—	4	4	no	—
253	C₃×C₂²⋊D₅	—	4	4	no	—
254	C₃×C₂²⋊D₅	—	4	4	no	—
255	C₃×C₂²⋊D₅	—	4	4	no	—
256	C₂×C₃×Dic₅	—	2	2	no	—
257	C₂×C₃×Dic₅	—	2	2	no	—
258	C₂×C₃×Dic₅	—	2	2	no	—
259	C₂×C₃×Dic₅	—	2	2	no	—
260	C₂×C₃×Dic₅	—	2	2	no	—
261	C₂×C₃×Dic₅	—	2	8	no	—
262	C₂×C₃×Dic₅	—	4	4	no	—
263	C₂×C₃×Dic₅	#41	1	4	yes	—
264	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
265	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
266	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
267	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
268	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
269	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
270	C₃×D₂₀	—	4	4	no	—
271	C₃×C₄×D₅	—	4	4	no	—
272	C₃×C₄×D₅	—	4	4	no	—
273	C₂²×C₃×D₄	—	5	1	no	—
274	C₂²×C₃×D₄	—	5	1	no	—
275	C₂²×C₃×D₄	—	5	1	no	—
276	C₂²×C₃×D₄	—	5	1	no	—
277	C₂²×C₃×D₄	—	5	1	no	—
278	C₂²×C₃×D₄	—	5	1	no	—
279	C₂²×C₃×D₄	—	5	1	no	—
280	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
281	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
282	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
283	C₂³×C₃×C₄	—	5	1	no	—
284	C₂³×C₃×C₄	—	5	1	no	—
285	C₂³×C₃×C₄	—	5	1	no	—
286	C₂³×C₃×C₄	—	5	1	no	—
287	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
288	C₃×#127	—	5	8	no	—
289	C₃×#125	—	5	8	no	—
290	C₃×#123	—	5	8	no	—
291	C₃×#123	—	5	8	no	—
292	C₃×#123	—	5	8	no	—
293	C₃×#123	—	5	8	no	—
294	C₃×#121	—	5	8	no	—
295	C₃×#121	—	5	8	no	—
296	C₃×#121	—	5	8	no	—
297	C₃×#121	—	5	8	no	—
298	C₃×#121	—	5	8	no	—
299	C₃×#121	C₂×D₅	1	8	yes	complemented
300	C₃×C₄×D₄	—	5	8	no	—
301	C₃×C₄×D₄	—	5	8	no	—
302	C₃×#117	—	5	8	no	—
303	C₂×C₃×C₄⋊C₄	—	5	1	no	—
304	C₂×C₃×C₄⋊C₄	—	5	1	no	—
305	C₂×C₃×C₄⋊C₄	—	5	1	no	—
306	C₂×C₃×C₄⋊C₄	—	5	1	no	—
307	C₂×C₃×C₄⋊C₄	—	5	1	no	—
308	C₂×C₃×C₄⋊C₄	—	5	1	no	—
309	C₂×C₃×C₄⋊C₄	—	5	1	no	—
310	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
311	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
312	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
313	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
314	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
315	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
316	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
317	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
318	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
319	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
320	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
321	C₂×C₃×C₄²	—	5	1	no	—
322	C₂×C₃×C₄²	—	5	1	no	—
323	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
324	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
325	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
326	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
327	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
328	C₂×C₅×D₄	—	4	2	no	—
329	C₂×C₅×D₄	—	4	2	no	—
330	C₂×C₅×D₄	—	4	2	no	—
331	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
332	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
333	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
334	C₂²×C₄×C₅	—	4	2	no	—
335	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
336	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
337	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
338	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
339	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
340	C₂×C₂²⋊D₅	—	2	4	no	—
341	C₂×C₂²⋊D₅	—	2	4	no	—
342	C₂×C₂²⋊D₅	—	4	2	no	—
343	C₂×C₂²⋊D₅	—	4	2	no	—
344	C₂×C₂²⋊D₅	—	4	2	no	—
345	C₂×C₂²⋊D₅	—	4	2	no	—
346	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
347	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
348	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
349	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
350	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
351	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
352	C₂²×Dic₅	—	2	4	no	—
353	C₂²×Dic₅	—	4	2	no	—
354	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
355	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
356	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
357	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
358	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
359	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
360	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
361	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
362	C₂×D₂₀	—	4	2	no	—
363	C₂×D₂₀	C₂³×C₃	1	4	yes	—
364	C₂×C₄×D₅	—	4	2	no	—
365	C₂×C₄×D₅	—	4	2	no	—
366	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
367	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
368	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
369	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
370	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
371	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
372	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
373	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
374	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
375	#685	C₂³×C₃	1	4	yes	—
376	#685	C₂³×C₃	1	4	yes	—
377	#685	C₂³×C₃	1	4	yes	—
378	#685	C₂³×C₃	1	4	yes	—
379	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
380	#683	C₂³×C₃	1	4	yes	—
381	#683	C₂³×C₃	1	4	yes	—
382	#683	C₂³×C₃	1	4	yes	—
383	#683	C₂³×C₃	1	4	yes	—
384	#683	C₂³×C₃	1	4	yes	—
385	#683	C₂³×C₃	1	4	yes	—
386	C₄×Dic₅	C₂³×C₃	1	4	yes	—
387	C₄×Dic₅	C₂³×C₃	1	4	yes	—
388	#540	—	5	16	no	—
389	C₂×#127	—	5	1	no	—
390	C₂×#125	—	5	1	no	—
391	C₂×#123	—	5	1	no	—
392	C₂×#123	—	5	1	no	—
393	C₂×#123	—	5	1	no	—
394	C₂×#123	—	5	1	no	—
395	C₂×#121	—	5	1	no	—
396	C₂×#121	—	5	1	no	—
397	C₂×#121	—	5	1	no	—
398	C₂×#121	—	5	1	no	—
399	C₂×#121	—	5	1	no	—
400	C₂×#121	C₃×D₅	1	1	yes	characteristic, complemented
401	C₂×C₄×D₄	—	5	1	no	—
402	C₂×C₄×D₄	—	5	1	no	—
403	C₂×#117	—	5	1	no	—
404	C₂²×C₃×C₅	—	2	2	no	—
405	C₂²×C₃×C₅	—	2	2	no	—
406	C₂²×C₃×C₅	—	2	2	no	—
407	C₂²×C₃×C₅	—	2	2	no	—
408	C₂²×C₃×C₅	—	2	2	no	—
409	C₂²×C₃×C₅	—	2	2	no	—
410	C₂²×C₃×C₅	—	2	2	no	—
411	C₂²×C₃×C₅	—	2	2	no	—
412	C₂²×C₃×C₅	—	2	2	no	—
413	C₂²×C₃×C₅	—	4	4	no	—
414	C₂²×C₃×C₅	—	4	4	no	—
415	C₂²×C₃×C₅	—	4	4	no	—
416	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
417	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
418	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
419	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
420	C₂×C₃×D₅	—	2	2	no	—
421	C₂×C₃×D₅	—	2	2	no	—
422	C₂×C₃×D₅	—	2	2	no	—
423	C₂×C₃×D₅	—	2	2	no	—
424	C₂×C₃×D₅	—	2	2	no	—
425	C₂×C₃×D₅	—	2	2	no	—
426	C₂×C₃×D₅	—	4	4	no	—
427	C₂×C₃×D₅	—	4	4	no	—
428	C₃×C₄×C₅	—	2	2	no	—
429	C₃×C₄×C₅	—	2	2	no	—
430	C₃×C₄×C₅	—	2	2	no	—
431	C₃×C₄×C₅	—	2	2	no	—
432	C₃×Dic₅	—	2	2	no	—
433	C₃×Dic₅	—	2	2	no	—
434	C₃×Dic₅	—	2	2	no	—
435	C₃×Dic₅	—	2	2	no	—
436	C₃×Dic₅	—	2	2	no	—
437	C₃×Dic₅	C₂×#41	1	4	yes	—
438	C₂⁴×C₃	—	5	1	no	—
439	C₂⁴×C₃	—	5	1	no	—
440	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
441	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
442	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
443	C₂×C₃×D₄	—	4	2	no	—
444	C₂×C₃×D₄	—	4	2	no	—
445	C₂×C₃×D₄	—	4	2	no	—
446	C₂×C₃×D₄	—	5	4	no	—
447	C₂×C₃×D₄	—	5	4	no	—
448	C₂×C₃×D₄	—	5	4	no	—
449	C₂×C₃×D₄	—	5	4	no	—
450	C₂×C₃×D₄	—	5	4	no	—
451	C₂×C₃×D₄	—	5	4	no	—
452	C₂×C₃×D₄	—	5	4	no	—
453	C₂×C₃×D₄	—	10	4	no	—
454	C₂×C₃×D₄	—	10	4	no	—
455	C₂×C₃×D₄	—	20	2	no	—
456	C₂×C₃×D₄	—	20	2	no	—
457	C₂×C₃×D₄	—	20	2	no	—
458	C₂×C₃×D₄	—	20	2	no	—
459	C₂×C₃×D₄	—	20	2	no	—
460	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
461	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
462	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
463	C₂²×C₃×C₄	—	4	2	no	—
464	C₂²×C₃×C₄	—	5	1	no	—
465	C₂²×C₃×C₄	—	5	4	no	—
466	C₂²×C₃×C₄	—	5	1	no	—
467	C₂²×C₃×C₄	—	5	1	no	—
468	C₂²×C₃×C₄	—	5	1	no	—
469	C₂²×C₃×C₄	—	5	1	no	—
470	C₂²×C₃×C₄	—	5	1	no	—
471	C₂²×C₃×C₄	—	5	4	no	—
472	C₂²×C₃×C₄	—	5	4	no	—
473	C₂²×C₃×C₄	—	5	4	no	—
474	C₂²×C₃×C₄	—	10	4	no	—
475	C₂²×C₃×C₄	—	20	2	no	—
476	C₂²×C₃×C₄	—	20	2	no	—
477	C₂²×C₃×C₄	—	20	2	no	—
478	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
479	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
480	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
481	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
482	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
483	C₃×C₄⋊C₄	—	5	4	no	—
484	C₃×C₄⋊C₄	—	5	4	no	—
485	C₃×C₄⋊C₄	—	5	4	no	—
486	C₃×C₄⋊C₄	—	5	4	no	—
487	C₃×C₄⋊C₄	—	5	4	no	—
488	C₃×C₄⋊C₄	—	5	4	no	—
489	C₃×C₄⋊C₄	—	5	4	no	—
490	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
491	C₃×C₂²⋊C₄	—	5	4	no	—
492	C₃×C₂²⋊C₄	—	5	4	no	—
493	C₃×C₂²⋊C₄	—	5	4	no	—
494	C₃×C₂²⋊C₄	—	5	4	no	—
495	C₃×C₂²⋊C₄	—	5	4	no	—
496	C₃×C₂²⋊C₄	—	5	4	no	—
497	C₃×C₂²⋊C₄	—	5	4	no	—
498	C₃×C₂²⋊C₄	—	5	4	no	—
499	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
500	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
501	C₃×C₄²	—	5	4	no	—
502	C₃×C₄²	—	5	4	no	—
503	C₂³×C₅	—	2	2	no	—
504	C₂³×C₅	—	2	2	no	—
505	C₂³×C₅	—	2	2	no	—
506	C₂³×C₅	—	2	2	no	—
507	C₂³×C₅	—	2	2	no	—
508	C₂³×C₅	—	2	2	no	—
509	C₂³×C₅	—	2	2	no	—
510	C₂³×C₅	—	2	2	no	—
511	C₂³×C₅	—	2	2	no	—
512	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
513	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
514	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
515	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
516	C₂²×D₅	—	2	2	no	—
517	C₂²×D₅	—	2	2	no	—
518	C₂²×D₅	—	2	2	no	—
519	C₂²×D₅	—	2	2	no	—
520	C₂²×D₅	—	2	2	no	—
521	C₂²×D₅	—	2	2	no	—
522	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
523	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
524	C₅×D₄	—	4	4	no	—
525	C₅×D₄	—	4	4	no	—
526	C₅×D₄	—	4	4	no	—
527	C₂×C₄×C₅	—	2	2	no	—
528	C₂×C₄×C₅	—	2	2	no	—
529	C₂×C₄×C₅	—	2	2	no	—
530	C₂×C₄×C₅	—	2	2	no	—
531	C₂×C₄×C₅	—	4	4	no	—
532	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
533	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
534	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
535	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
536	C₂²⋊D₅	—	2	8	no	—
537	C₂²⋊D₅	—	2	8	no	—
538	C₂²⋊D₅	—	4	4	no	—
539	C₂²⋊D₅	—	4	4	no	—
540	C₂²⋊D₅	—	4	4	no	—
541	C₂²⋊D₅	—	4	4	no	—
542	C₂×Dic₅	—	2	2	no	—
543	C₂×Dic₅	—	2	2	no	—
544	C₂×Dic₅	—	2	2	no	—
545	C₂×Dic₅	—	2	2	no	—
546	C₂×Dic₅	—	2	2	no	—
547	C₂×Dic₅	—	2	8	no	—
548	C₂×Dic₅	—	4	4	no	—
549	C₂×Dic₅	C₃×#41	1	4	yes	—
550	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
551	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
552	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
553	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
554	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
555	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
556	D₂₀	—	4	4	no	—
557	C₄×D₅	—	4	4	no	—
558	C₄×D₅	—	4	4	no	—
559	C₂²×D₄	—	5	1	no	—
560	C₂²×D₄	—	5	1	no	—
561	C₂²×D₄	—	5	1	no	—
562	C₂²×D₄	—	5	1	no	—
563	C₂²×D₄	—	5	1	no	—
564	C₂²×D₄	—	5	1	no	—
565	C₂²×D₄	—	5	1	no	—
566	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
567	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
568	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
569	C₂³×C₄	—	5	1	no	—
570	C₂³×C₄	—	5	1	no	—
571	C₂³×C₄	—	5	1	no	—
572	C₂³×C₄	—	5	1	no	—
573	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
574	#127	—	5	8	no	—
575	#125	—	5	8	no	—
576	#123	—	5	8	no	—
577	#123	—	5	8	no	—
578	#123	—	5	8	no	—
579	#123	—	5	8	no	—
580	#121	—	5	8	no	—
581	#121	—	5	8	no	—
582	#121	—	5	8	no	—
583	#121	—	5	8	no	—
584	#121	—	5	8	no	—
585	#121	C₂×C₃×D₅	1	8	yes	complemented
586	C₄×D₄	—	5	8	no	—
587	C₄×D₄	—	5	8	no	—
588	#117	—	5	8	no	—
589	C₂×C₄⋊C₄	—	5	1	no	—
590	C₂×C₄⋊C₄	—	5	1	no	—
591	C₂×C₄⋊C₄	—	5	1	no	—
592	C₂×C₄⋊C₄	—	5	1	no	—
593	C₂×C₄⋊C₄	—	5	1	no	—
594	C₂×C₄⋊C₄	—	5	1	no	—
595	C₂×C₄⋊C₄	—	5	1	no	—
596	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	—	5	1	no	—
598	C₂×C₂²⋊C₄	—	5	1	no	—
599	C₂×C₂²⋊C₄	—	5	1	no	—
600	C₂×C₂²⋊C₄	—	5	1	no	—
601	C₂×C₂²⋊C₄	—	5	1	no	—
602	C₂×C₂²⋊C₄	—	5	1	no	—
603	C₂×C₂²⋊C₄	—	5	1	no	—
604	C₂×C₂²⋊C₄	—	5	1	no	—
605	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
607	C₂×C₄²	—	5	1	no	—
608	C₂×C₄²	—	5	1	no	—
609	C₂×C₃×C₅	—	4	2	no	—
610	C₂×C₃×C₅	—	4	2	no	—
611	C₂×C₃×C₅	—	4	2	no	—
612	C₂×C₃×C₅	#540	1	4	yes	complemented
613	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
614	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
616	C₃×D₅	—	4	2	no	—
617	C₃×D₅	—	4	2	no	—
618	C₂³×C₃	—	2	2	no	—
619	C₂³×C₃	—	2	2	no	—
620	C₂³×C₃	—	2	2	no	—
621	C₂³×C₃	—	2	2	no	—
622	C₂³×C₃	—	2	2	no	—
623	C₂³×C₃	—	2	2	no	—
624	C₂³×C₃	—	2	2	no	—
625	C₂³×C₃	—	2	2	no	—
626	C₂³×C₃	—	2	2	no	—
627	C₂³×C₃	—	5	2	no	—
628	C₂³×C₃	—	5	2	no	—
629	C₂³×C₃	—	10	2	no	—
630	C₂³×C₃	—	10	2	no	—
631	C₂³×C₃	—	10	2	no	—
632	C₂³×C₃	—	10	2	no	—
633	C₂³×C₃	—	10	2	no	—
634	C₂³×C₃	—	10	2	no	—
635	C₂³×C₃	C₂³×D₅	1	2	yes	—
636	C₂³×C₃	C₂³×D₅	1	2	yes	—
637	C₂³×C₃	C₂³×D₅	1	2	yes	—
638	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
639	C₃×D₄	—	4	4	no	—
640	C₃×D₄	—	4	4	no	—
641	C₃×D₄	—	4	4	no	—
642	C₃×D₄	—	10	8	no	—
643	C₃×D₄	—	10	8	no	—
644	C₃×D₄	—	20	4	no	—
645	C₃×D₄	—	20	4	no	—
646	C₃×D₄	—	20	4	no	—
647	C₃×D₄	—	20	4	no	—
648	C₃×D₄	—	20	4	no	—
649	C₂×C₃×C₄	—	2	2	no	—
650	C₂×C₃×C₄	—	2	2	no	—
651	C₂×C₃×C₄	—	2	2	no	—
652	C₂×C₃×C₄	—	2	2	no	—
653	C₂×C₃×C₄	—	4	4	no	—
654	C₂×C₃×C₄	—	5	4	no	—
655	C₂×C₃×C₄	—	5	2	no	—
656	C₂×C₃×C₄	—	5	2	no	—
657	C₂×C₃×C₄	—	5	2	no	—
658	C₂×C₃×C₄	—	5	2	no	—
659	C₂×C₃×C₄	—	5	2	no	—
660	C₂×C₃×C₄	—	5	2	no	—
661	C₂×C₃×C₄	—	10	8	no	—
662	C₂×C₃×C₄	—	10	2	no	—
663	C₂×C₃×C₄	—	10	2	no	—
664	C₂×C₃×C₄	—	10	2	no	—
665	C₂×C₃×C₄	—	10	2	no	—
666	C₂×C₃×C₄	—	10	2	no	—
667	C₂×C₃×C₄	—	20	4	no	—
668	C₂×C₃×C₄	—	20	4	no	—
669	C₂×C₃×C₄	—	20	4	no	—
670	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
671	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
672	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
673	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
674	C₂²×C₅	—	2	2	no	—
675	C₂²×C₅	—	2	2	no	—
676	C₂²×C₅	—	2	2	no	—
677	C₂²×C₅	—	2	2	no	—
678	C₂²×C₅	—	2	2	no	—
679	C₂²×C₅	—	2	2	no	—
680	C₂²×C₅	—	2	2	no	—
681	C₂²×C₅	—	2	2	no	—
682	C₂²×C₅	—	2	2	no	—
683	C₂²×C₅	—	4	4	no	—
684	C₂²×C₅	—	4	4	no	—
685	C₂²×C₅	—	4	4	no	—
686	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
687	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
688	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
689	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
690	C₂×D₅	—	2	2	no	—
691	C₂×D₅	—	2	2	no	—
692	C₂×D₅	—	2	2	no	—
693	C₂×D₅	—	2	2	no	—
694	C₂×D₅	—	2	2	no	—
695	C₂×D₅	—	2	2	no	—
696	C₂×D₅	—	4	4	no	—
697	C₂×D₅	—	4	4	no	—
698	C₄×C₅	—	2	2	no	—
699	C₄×C₅	—	2	2	no	—
700	C₄×C₅	—	2	2	no	—
701	C₄×C₅	—	2	2	no	—
702	Dic₅	—	2	2	no	—
703	Dic₅	—	2	2	no	—
704	Dic₅	—	2	2	no	—
705	Dic₅	—	2	2	no	—
706	Dic₅	—	2	2	no	—
707	Dic₅	C₂×C₃×#41	1	4	yes	—
708	C₂⁴	—	5	1	no	—
709	C₂⁴	—	5	1	no	—
710	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
711	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
712	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
713	C₂×D₄	—	4	2	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	5	4	no	—
717	C₂×D₄	—	5	4	no	—
718	C₂×D₄	—	5	4	no	—
719	C₂×D₄	—	5	4	no	—
720	C₂×D₄	—	5	4	no	—
721	C₂×D₄	—	5	4	no	—
722	C₂×D₄	—	5	4	no	—
723	C₂×D₄	—	10	4	no	—
724	C₂×D₄	—	10	4	no	—
725	C₂×D₄	—	20	2	no	—
726	C₂×D₄	—	20	2	no	—
727	C₂×D₄	—	20	2	no	—
728	C₂×D₄	—	20	2	no	—
729	C₂×D₄	—	20	2	no	—
730	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
731	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
732	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	—	5	1	no	—
735	C₂²×C₄	—	5	1	no	—
736	C₂²×C₄	—	5	1	no	—
737	C₂²×C₄	—	5	1	no	—
738	C₂²×C₄	—	5	1	no	—
739	C₂²×C₄	—	5	1	no	—
740	C₂²×C₄	—	5	4	no	—
741	C₂²×C₄	—	5	4	no	—
742	C₂²×C₄	—	5	4	no	—
743	C₂²×C₄	—	5	4	no	—
744	C₂²×C₄	—	10	4	no	—
745	C₂²×C₄	—	20	2	no	—
746	C₂²×C₄	—	20	2	no	—
747	C₂²×C₄	—	20	2	no	—
748	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
749	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
750	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
751	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
752	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
753	C₄⋊C₄	—	5	4	no	—
754	C₄⋊C₄	—	5	4	no	—
755	C₄⋊C₄	—	5	4	no	—
756	C₄⋊C₄	—	5	4	no	—
757	C₄⋊C₄	—	5	4	no	—
758	C₄⋊C₄	—	5	4	no	—
759	C₄⋊C₄	—	5	4	no	—
760	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
761	C₂²⋊C₄	—	5	4	no	—
762	C₂²⋊C₄	—	5	4	no	—
763	C₂²⋊C₄	—	5	4	no	—
764	C₂²⋊C₄	—	5	4	no	—
765	C₂²⋊C₄	—	5	4	no	—
766	C₂²⋊C₄	—	5	4	no	—
767	C₂²⋊C₄	—	5	4	no	—
768	C₂²⋊C₄	—	5	4	no	—
769	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
770	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
771	C₄²	—	5	4	no	—
772	C₄²	—	5	4	no	—
773	C₃×C₅	C₂×#540	1	1	yes	characteristic, complemented, Hall
774	C₂²×C₃	—	2	2	no	—
775	C₂²×C₃	—	2	2	no	—
776	C₂²×C₃	—	2	2	no	—
777	C₂²×C₃	—	2	2	no	—
778	C₂²×C₃	—	2	2	no	—
779	C₂²×C₃	—	2	2	no	—
780	C₂²×C₃	—	2	2	no	—
781	C₂²×C₃	—	2	2	no	—
782	C₂²×C₃	—	2	2	no	—
783	C₂²×C₃	—	4	4	no	—
784	C₂²×C₃	—	4	4	no	—
785	C₂²×C₃	—	4	4	no	—
786	C₂²×C₃	—	10	2	no	—
787	C₂²×C₃	—	10	2	no	—
788	C₂²×C₃	—	10	2	no	—
789	C₂²×C₃	—	10	2	no	—
790	C₂²×C₃	—	10	2	no	—
791	C₂²×C₃	—	10	2	no	—
792	C₂²×C₃	—	20	4	no	—
793	C₂²×C₃	—	20	4	no	—
794	C₂²×C₃	#4144	1	2	yes	—
795	C₂²×C₃	#4144	1	2	yes	—
796	C₂²×C₃	D₅×#41	1	2	yes	—
797	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
798	C₃×C₄	—	2	2	no	—
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	—	2	2	no	—
801	C₃×C₄	—	2	2	no	—
802	C₃×C₄	—	5	4	no	—
803	C₃×C₄	—	10	2	no	—
804	C₃×C₄	—	10	2	no	—
805	C₃×C₄	—	10	2	no	—
806	C₃×C₄	—	10	2	no	—
807	C₃×C₄	—	10	2	no	—
808	C₂×C₅	—	4	2	no	—
809	C₂×C₅	—	4	2	no	—
810	C₂×C₅	—	4	2	no	—
811	C₂×C₅	C₃×#540	1	4	yes	complemented
812	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
813	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
814	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
815	D₅	—	4	2	no	—
816	D₅	—	4	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	5	2	no	—
827	C₂³	—	5	2	no	—
828	C₂³	—	10	2	no	—
829	C₂³	—	10	2	no	—
830	C₂³	—	10	2	no	—
831	C₂³	—	10	2	no	—
832	C₂³	—	10	2	no	—
833	C₂³	—	10	2	no	—
834	C₂³	C₂³×C₃×D₅	1	2	yes	—
835	C₂³	C₂³×C₃×D₅	1	2	yes	—
836	C₂³	C₂³×C₃×D₅	1	2	yes	—
837	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
838	D₄	—	4	4	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	4	no	—
841	D₄	—	10	8	no	—
842	D₄	—	10	8	no	—
843	D₄	—	20	4	no	—
844	D₄	—	20	4	no	—
845	D₄	—	20	4	no	—
846	D₄	—	20	4	no	—
847	D₄	—	20	4	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	5	4	no	—
854	C₂×C₄	—	5	2	no	—
855	C₂×C₄	—	5	2	no	—
856	C₂×C₄	—	5	2	no	—
857	C₂×C₄	—	5	2	no	—
858	C₂×C₄	—	5	2	no	—
859	C₂×C₄	—	5	2	no	—
860	C₂×C₄	—	10	8	no	—
861	C₂×C₄	—	10	2	no	—
862	C₂×C₄	—	10	2	no	—
863	C₂×C₄	—	10	2	no	—
864	C₂×C₄	—	10	2	no	—
865	C₂×C₄	—	10	2	no	—
866	C₂×C₄	—	20	4	no	—
867	C₂×C₄	—	20	4	no	—
868	C₂×C₄	—	20	4	no	—
869	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
870	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
871	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
872	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
873	C₂×C₃	—	4	2	no	—
874	C₂×C₃	—	4	2	no	—
875	C₂×C₃	—	4	2	no	—
876	C₂×C₃	—	20	2	no	—
877	C₂×C₃	—	20	2	no	—
878	C₂×C₃	#65949	1	4	yes	direct product factor
879	C₂×C₃	C₂×#4144	1	1	yes	characteristic
880	C₂×C₃	C₂×#4144	1	1	yes	characteristic
881	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
882	C₅	C₂×C₃×#540	1	1	yes	characteristic, complemented, Sylow
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	4	4	no	—
893	C₂²	—	4	4	no	—
894	C₂²	—	4	4	no	—
895	C₂²	—	10	2	no	—
896	C₂²	—	10	2	no	—
897	C₂²	—	10	2	no	—
898	C₂²	—	10	2	no	—
899	C₂²	—	10	2	no	—
900	C₂²	—	10	2	no	—
901	C₂²	—	20	4	no	—
902	C₂²	—	20	4	no	—
903	C₂²	C₃×#4144	1	2	yes	—
904	C₂²	C₃×#4144	1	2	yes	—
905	C₂²	C₃×D₅×#41	1	2	yes	—
906	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
907	C₄	—	2	2	no	—
908	C₄	—	2	2	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	2	no	—
911	C₄	—	5	4	no	—
912	C₄	—	10	2	no	—
913	C₄	—	10	2	no	—
914	C₄	—	10	2	no	—
915	C₄	—	10	2	no	—
916	C₄	—	10	2	no	—
917	C₃	C₂×#65949	1	1	yes	characteristic, direct product factor, Sylow
918	C₂	—	4	2	no	—
919	C₂	—	4	2	no	—
920	C₂	—	4	2	no	—
921	C₂	—	20	2	no	—
922	C₂	—	20	2	no	—
923	C₂	C₃×#65949	1	4	yes	direct product factor
924	C₂	C₂×C₃×#4144	1	1	yes	characteristic
925	C₂	C₂×C₃×#4144	1	1	yes	characteristic
926	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#121	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#121	D₅
hypocenter	C₅	C₂×C₃×#540
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#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×C₃×#4086	C₂	semidirect
3. C₂×C₃×#4085	C₂	semidirect
4. C₂×C₃×#4085	C₂	semidirect
5. C₂×C₃×#4085	C₂	semidirect
6. C₂×C₃×#4084	C₂	semidirect
7. C₂×C₃×#4081	C₂	semidirect
8. C₂×C₃×#4075	C₂	semidirect
9. C₂×C₃×C₄×C₂²⋊D₅	C₂	semidirect
10. C₃×#65949	C₂	direct (N × H)
11. C₂×C₃×#4040	C₂	semidirect
12. C₂×C₃×#4035	C₂	semidirect
13. C₂×C₃×#4030	C₂	semidirect
14. C₂×C₃×#4029	C₂	semidirect
15. C₂×C₃×#4027	C₂	semidirect
16. C₂×C₃×#4023	C₂	semidirect
17. C₂×#65949	C₃	direct (N × H)
33. C₃×C₅×#121	C₂²	semidirect
41. C₃×#4086	C₂²	semidirect
42. C₃×#4085	C₂²	semidirect
43. C₃×#4085	C₂²	semidirect
44. C₃×#4085	C₂²	semidirect
45. C₃×#4084	C₂²	semidirect
46. C₃×#4081	C₂²	semidirect
47. C₃×#4075	C₂²	semidirect
48. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
62. C₃×#4040	C₂²	semidirect
63. C₃×#4035	C₂²	semidirect
64. C₃×#4030	C₂²	semidirect
65. C₃×#4029	C₂²	semidirect
66. C₃×#4027	C₂²	semidirect
67. C₃×#4023	C₂²	semidirect
69. C₂×C₅×#121	C₂×C₃	semidirect
70. C₂×#4086	C₂×C₃	semidirect
71. C₂×#4085	C₂×C₃	semidirect
72. C₂×#4085	C₂×C₃	semidirect
73. C₂×#4085	C₂×C₃	semidirect
74. C₂×#4084	C₂×C₃	semidirect
75. C₂×#4081	C₂×C₃	semidirect
76. C₂×#4075	C₂×C₃	semidirect
77. C₂×C₄×C₂²⋊D₅	C₂×C₃	semidirect
78. #65949	C₂×C₃	direct (N × H)
79. C₂×#4040	C₂×C₃	semidirect
80. C₂×#4035	C₂×C₃	semidirect
81. C₂×#4030	C₂×C₃	semidirect
82. C₂×#4029	C₂×C₃	semidirect
83. C₂×#4027	C₂×C₃	semidirect
84. C₂×#4023	C₂×C₃	semidirect
162. C₂×C₃×#121	D₅	semidirect
181. C₅×#121	C₂²×C₃	semidirect
189. #4086	C₂²×C₃	semidirect
190. #4085	C₂²×C₃	semidirect
191. #4085	C₂²×C₃	semidirect
192. #4085	C₂²×C₃	semidirect
193. #4084	C₂²×C₃	semidirect
194. #4081	C₂²×C₃	semidirect
195. #4075	C₂²×C₃	semidirect
196. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
210. #4040	C₂²×C₃	semidirect
211. #4035	C₂²×C₃	semidirect
212. #4030	C₂²×C₃	semidirect
213. #4029	C₂²×C₃	semidirect
214. #4027	C₂²×C₃	semidirect
215. #4023	C₂²×C₃	semidirect
299. C₃×#121	C₂×D₅	semidirect
400. C₂×#121	C₃×D₅	semidirect
585. #121	C₂×C₃×D₅	semidirect
612. C₂×C₃×C₅	#540	semidirect
773. C₃×C₅	C₂×#540	semidirect
811. C₂×C₅	C₃×#540	semidirect
878. C₂×C₃	#65949	direct (N × H)
882. C₅	C₂×C₃×#540	semidirect
917. C₃	C₂×#65949	direct (N × H)
923. C₂	C₃×#65949	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×#4086	2
C₂×C₃×#4085	2
C₂×C₃×#4084	2
C₂×C₃×#4081	2
C₂×C₃×#4075	2
C₂×C₃×C₄×C₂²⋊D₅	2
C₃×#65949	2
C₂×C₃×#4040	2
C₂×C₃×#4035	2
C₂×C₃×#4030	2
C₂×C₃×#4029	2
C₂×C₃×#4027	2
C₂×C₃×#4023	2
C₂×#65949	3
C₂×C₃×#540	5

Subgroups — C2×C3×#65949 #14481080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65949 #14481080