Subgroups — C₂×C₃×#65954 #14495182

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×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×#4084	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#4083	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#4083	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4076	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#4075	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65954	C₂	1	16	yes	maximal, direct product factor
11	C₂×C₃×#4044	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#4040	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#4032	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#4030	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#4028	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#4025	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#65954	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂⁴×C₃×D₅	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×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	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
32	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₄×D₅	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×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, complemented
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×#4084	C₂²	1	8	yes	complemented
45	C₃×#4083	C₂²	1	8	yes	complemented
46	C₃×#4083	C₂²	1	8	yes	complemented
47	C₃×#4076	C₂²	1	8	yes	complemented
48	C₃×#4075	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×#685	C₂²	1	1	yes	characteristic
54	C₂×C₃×#685	C₂²	1	1	yes	characteristic
55	C₂×C₃×#685	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₃×#683	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₃×#683	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₃×#683	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
62	C₃×#4044	C₂²	1	8	yes	complemented
63	C₃×#4040	C₂²	1	8	yes	complemented
64	C₃×#4032	C₂²	1	8	yes	complemented
65	C₃×#4030	C₂²	1	8	yes	complemented
66	C₃×#4028	C₂²	1	8	yes	complemented
67	C₃×#4025	C₂²	1	8	yes	complemented
68	C₂×C₃×#560	—	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×#4084	C₂×C₃	1	1	yes	characteristic, complemented
74	C₂×#4083	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×#4083	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×#4076	C₂×C₃	1	1	yes	characteristic, complemented
77	C₂×#4075	C₂×C₃	1	1	yes	characteristic, complemented
78	#65954	C₂×C₃	1	16	yes	direct product factor
79	C₂×#4044	C₂×C₃	1	1	yes	characteristic, complemented
80	C₂×#4040	C₂×C₃	1	1	yes	characteristic, complemented
81	C₂×#4032	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂×#4030	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×#4028	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂×#4025	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	—	4	2	no	—
89	C₂³×C₃×D₅	—	4	2	no	—
90	C₂³×C₃×D₅	—	4	2	no	—
91	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
92	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
93	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
94	C₂³×C₃×D₅	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×C₃×C₂²⋊D₅	—	4	2	no	—
108	C₂×C₃×C₂²⋊D₅	—	4	2	no	—
109	C₂×C₃×C₂²⋊D₅	—	4	2	no	—
110	C₂×C₃×C₂²⋊D₅	—	4	2	no	—
111	C₂×C₃×C₂²⋊D₅	—	4	2	no	—
112	C₂×C₃×C₂²⋊D₅	—	4	2	no	—
113	C₂×C₃×C₂²⋊D₅	—	4	2	no	—
114	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
115	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
116	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
117	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
118	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
119	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	complemented
120	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	complemented
121	C₂²×C₃×Dic₅	—	4	2	no	—
122	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
123	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
124	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
125	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
126	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
127	C₂²×C₃×Dic₅	C₂³	1	4	yes	complemented
128	C₂×C₃×D₂₀	—	4	2	no	—
129	C₂×C₃×D₂₀	—	4	2	no	—
130	C₂×C₃×D₂₀	C₂³	1	4	yes	—
131	C₂×C₃×D₂₀	C₂³	1	4	yes	—
132	C₂×C₃×C₄×D₅	—	4	2	no	—
133	C₂×C₃×C₄×D₅	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	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
138	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
139	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	complemented
140	C₃×#685	C₂³	1	4	yes	—
141	C₃×#685	C₂³	1	4	yes	—
142	C₃×#685	C₂³	1	4	yes	—
143	C₃×#685	C₂³	1	4	yes	—
144	C₃×#685	C₂³	1	4	yes	—
145	C₃×#685	C₂³	1	4	yes	—
146	C₃×#685	C₂³	1	4	yes	complemented
147	C₃×C₄⋊Dic₅	C₂³	1	4	yes	complemented
148	C₃×C₄⋊Dic₅	C₂³	1	4	yes	complemented
149	C₃×#683	C₂³	1	4	yes	complemented
150	C₃×#683	C₂³	1	4	yes	complemented
151	C₃×#683	C₂³	1	4	yes	complemented
152	C₃×C₄×Dic₅	C₂³	1	4	yes	complemented
153	C₃×#560	—	5	16	no	—
154	C₂×C₃×#127	—	5	1	no	—
155	C₂×C₃×#126	—	5	1	no	—
156	C₂×C₃×#126	—	5	1	no	—
157	C₂×C₃×#123	—	5	1	no	—
158	C₂×C₃×#123	—	5	1	no	—
159	C₂×C₃×#123	—	5	1	no	—
160	C₂×C₃×#121	—	5	1	no	—
161	C₂×C₃×#121	—	5	1	no	—
162	C₂×C₃×#121	—	5	1	no	—
163	C₂×C₃×#121	—	5	1	no	—
164	C₂×C₃×#121	—	5	1	no	—
165	C₂×C₃×#121	D₅	1	1	yes	characteristic, complemented
166	C₂×C₃×#120	—	5	1	no	—
167	C₂×C₃×#120	—	5	1	no	—
168	C₂×C₃×#120	—	5	1	no	—
169	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
170	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
171	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
172	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
175	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
176	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
177	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
178	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
179	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic, complemented
180	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
182	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
183	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
184	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₅×#121	C₂²×C₃	1	8	yes	complemented
186	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
188	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
190	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
191	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
192	#4086	C₂²×C₃	1	8	yes	complemented
193	#4085	C₂²×C₃	1	8	yes	complemented
194	#4085	C₂²×C₃	1	8	yes	complemented
195	#4084	C₂²×C₃	1	8	yes	complemented
196	#4083	C₂²×C₃	1	8	yes	complemented
197	#4083	C₂²×C₃	1	8	yes	complemented
198	#4076	C₂²×C₃	1	8	yes	complemented
199	#4075	C₂²×C₃	1	8	yes	complemented
200	C₂×#685	C₂²×C₃	1	1	yes	characteristic
201	C₂×#685	C₂²×C₃	1	1	yes	characteristic
202	C₂×#685	C₂²×C₃	1	1	yes	characteristic
203	C₂×#685	C₂²×C₃	1	1	yes	characteristic
204	C₂×#685	C₂²×C₃	1	1	yes	characteristic
205	C₂×#685	C₂²×C₃	1	1	yes	characteristic
206	C₂×#685	C₂²×C₃	1	1	yes	characteristic, complemented
207	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
208	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
209	C₂×#683	C₂²×C₃	1	1	yes	characteristic, complemented
210	C₂×#683	C₂²×C₃	1	1	yes	characteristic, complemented
211	C₂×#683	C₂²×C₃	1	1	yes	characteristic, complemented
212	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
213	#4044	C₂²×C₃	1	8	yes	complemented
214	#4040	C₂²×C₃	1	8	yes	complemented
215	#4032	C₂²×C₃	1	8	yes	complemented
216	#4030	C₂²×C₃	1	8	yes	complemented
217	#4028	C₂²×C₃	1	8	yes	complemented
218	#4025	C₂²×C₃	1	8	yes	complemented
219	C₂×#560	—	5	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×C₃×D₅	—	2	2	no	—
234	C₂²×C₃×D₅	—	2	2	no	—
235	C₂²×C₃×D₅	—	2	2	no	—
236	C₂²×C₃×D₅	—	2	2	no	—
237	C₂²×C₃×D₅	—	2	2	no	—
238	C₂²×C₃×D₅	—	2	2	no	—
239	C₂²×C₃×D₅	—	2	2	no	—
240	C₂²×C₃×D₅	—	2	2	no	—
241	C₂²×C₃×D₅	—	2	2	no	—
242	C₂²×C₃×D₅	—	4	4	no	—
243	C₂²×C₃×D₅	—	4	4	no	—
244	C₂²×C₃×D₅	—	4	4	no	—
245	C₂²×C₃×D₅	—	4	16	no	—
246	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
247	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
248	C₂²×C₃×D₅	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	C₃×C₂²⋊D₅	—	4	4	no	—
262	C₃×C₂²⋊D₅	—	4	4	no	—
263	C₃×C₂²⋊D₅	—	4	4	no	—
264	C₃×C₂²⋊D₅	—	4	4	no	—
265	C₃×C₂²⋊D₅	—	4	4	no	—
266	C₃×C₂²⋊D₅	—	4	4	no	—
267	C₃×C₂²⋊D₅	—	4	4	no	—
268	C₂×C₃×Dic₅	—	2	2	no	—
269	C₂×C₃×Dic₅	—	2	2	no	—
270	C₂×C₃×Dic₅	—	2	2	no	—
271	C₂×C₃×Dic₅	—	2	2	no	—
272	C₂×C₃×Dic₅	—	2	2	no	—
273	C₂×C₃×Dic₅	—	4	4	no	—
274	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
275	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
276	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
277	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
278	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
279	C₃×D₂₀	—	4	4	no	—
280	C₃×D₂₀	—	4	4	no	—
281	C₃×C₄×D₅	—	4	4	no	—
282	C₂⁵×C₃	—	5	1	no	—
283	C₂²×C₃×D₄	—	5	1	no	—
284	C₂²×C₃×D₄	—	5	1	no	—
285	C₂²×C₃×D₄	—	5	1	no	—
286	C₂²×C₃×D₄	—	5	1	no	—
287	C₂²×C₃×D₄	—	5	1	no	—
288	C₂²×C₃×D₄	—	5	1	no	—
289	C₂²×C₃×D₄	—	5	1	no	—
290	C₂²×C₃×D₄	—	5	1	no	—
291	C₂²×C₃×D₄	—	5	1	no	—
292	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
293	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
294	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic, complemented
295	C₂³×C₃×C₄	—	5	1	no	—
296	C₂³×C₃×C₄	—	5	1	no	—
297	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic, complemented
298	C₃×#127	—	5	8	no	—
299	C₃×#126	—	5	8	no	—
300	C₃×#126	—	5	8	no	—
301	C₃×#123	—	5	8	no	—
302	C₃×#123	—	5	8	no	—
303	C₃×#123	—	5	8	no	—
304	C₃×#121	—	5	8	no	—
305	C₃×#121	—	5	8	no	—
306	C₃×#121	—	5	8	no	—
307	C₃×#121	—	5	8	no	—
308	C₃×#121	—	5	8	no	—
309	C₃×#121	C₂×D₅	1	8	yes	complemented
310	C₃×#120	—	5	8	no	—
311	C₃×#120	—	5	8	no	—
312	C₃×#120	—	5	8	no	—
313	C₂×C₃×C₄⋊C₄	—	5	1	no	—
314	C₂×C₃×C₄⋊C₄	—	5	1	no	—
315	C₂×C₃×C₄⋊C₄	—	5	1	no	—
316	C₂×C₃×C₄⋊C₄	—	5	1	no	—
317	C₂×C₃×C₄⋊C₄	—	5	1	no	—
318	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
319	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
320	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
321	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
322	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
323	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
324	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
325	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
326	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
327	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
328	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
329	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
330	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
331	C₂×C₃×C₄²	—	5	1	no	—
332	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
333	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
334	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
335	C₂³×D₅	—	4	2	no	—
336	C₂³×D₅	—	4	2	no	—
337	C₂³×D₅	—	4	2	no	—
338	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
339	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
340	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
341	C₂³×D₅	C₂³×C₃	1	4	yes	—
342	C₂×C₅×D₄	—	4	2	no	—
343	C₂×C₅×D₄	—	4	2	no	—
344	C₂×C₅×D₄	—	4	2	no	—
345	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
346	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
347	C₂×C₅×D₄	C₂³×C₃	1	4	yes	complemented
348	C₂²×C₄×C₅	—	4	2	no	—
349	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
350	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
351	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
352	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
353	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	complemented
354	C₂×C₂²⋊D₅	—	4	2	no	—
355	C₂×C₂²⋊D₅	—	4	2	no	—
356	C₂×C₂²⋊D₅	—	4	2	no	—
357	C₂×C₂²⋊D₅	—	4	2	no	—
358	C₂×C₂²⋊D₅	—	4	2	no	—
359	C₂×C₂²⋊D₅	—	4	2	no	—
360	C₂×C₂²⋊D₅	—	4	2	no	—
361	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
362	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
363	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
364	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
365	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
366	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	complemented
367	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	complemented
368	C₂²×Dic₅	—	4	2	no	—
369	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
370	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
371	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
372	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
373	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
374	C₂²×Dic₅	C₂³×C₃	1	4	yes	complemented
375	C₂×D₂₀	—	4	2	no	—
376	C₂×D₂₀	—	4	2	no	—
377	C₂×D₂₀	C₂³×C₃	1	4	yes	—
378	C₂×D₂₀	C₂³×C₃	1	4	yes	—
379	C₂×C₄×D₅	—	4	2	no	—
380	C₂×C₄×D₅	C₂³×C₃	1	4	yes	complemented
381	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
382	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
383	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
384	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
385	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
386	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	complemented
387	#685	C₂³×C₃	1	4	yes	—
388	#685	C₂³×C₃	1	4	yes	—
389	#685	C₂³×C₃	1	4	yes	—
390	#685	C₂³×C₃	1	4	yes	—
391	#685	C₂³×C₃	1	4	yes	—
392	#685	C₂³×C₃	1	4	yes	—
393	#685	C₂³×C₃	1	4	yes	complemented
394	C₄⋊Dic₅	C₂³×C₃	1	4	yes	complemented
395	C₄⋊Dic₅	C₂³×C₃	1	4	yes	complemented
396	#683	C₂³×C₃	1	4	yes	complemented
397	#683	C₂³×C₃	1	4	yes	complemented
398	#683	C₂³×C₃	1	4	yes	complemented
399	C₄×Dic₅	C₂³×C₃	1	4	yes	complemented
400	#560	—	5	16	no	—
401	C₂×#127	—	5	1	no	—
402	C₂×#126	—	5	1	no	—
403	C₂×#126	—	5	1	no	—
404	C₂×#123	—	5	1	no	—
405	C₂×#123	—	5	1	no	—
406	C₂×#123	—	5	1	no	—
407	C₂×#121	—	5	1	no	—
408	C₂×#121	—	5	1	no	—
409	C₂×#121	—	5	1	no	—
410	C₂×#121	—	5	1	no	—
411	C₂×#121	—	5	1	no	—
412	C₂×#121	C₃×D₅	1	1	yes	characteristic, complemented
413	C₂×#120	—	5	1	no	—
414	C₂×#120	—	5	1	no	—
415	C₂×#120	—	5	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×C₃×D₅	—	2	2	no	—
433	C₂×C₃×D₅	—	2	2	no	—
434	C₂×C₃×D₅	—	2	2	no	—
435	C₂×C₃×D₅	—	2	2	no	—
436	C₂×C₃×D₅	—	2	2	no	—
437	C₂×C₃×D₅	—	2	2	no	—
438	C₂×C₃×D₅	—	2	2	no	—
439	C₂×C₃×D₅	—	2	2	no	—
440	C₂×C₃×D₅	—	2	2	no	—
441	C₂×C₃×D₅	—	4	16	no	—
442	C₂×C₃×D₅	—	4	4	no	—
443	C₂×C₃×D₅	—	4	4	no	—
444	C₂×C₃×D₅	—	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	C₃×Dic₅	—	2	2	no	—
450	C₃×Dic₅	—	2	2	no	—
451	C₃×Dic₅	—	2	2	no	—
452	C₃×Dic₅	—	2	2	no	—
453	C₃×Dic₅	—	2	2	no	—
454	C₂⁴×C₃	—	5	1	no	—
455	C₂⁴×C₃	—	5	1	no	—
456	C₂⁴×C₃	—	5	1	no	—
457	C₂⁴×C₃	—	5	4	no	—
458	C₂⁴×C₃	—	20	2	no	—
459	C₂⁴×C₃	—	20	2	no	—
460	C₂⁴×C₃	—	20	2	no	—
461	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
462	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
463	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
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	—	5	4	no	—
468	C₂×C₃×D₄	—	5	4	no	—
469	C₂×C₃×D₄	—	5	4	no	—
470	C₂×C₃×D₄	—	5	4	no	—
471	C₂×C₃×D₄	—	5	4	no	—
472	C₂×C₃×D₄	—	5	4	no	—
473	C₂×C₃×D₄	—	5	4	no	—
474	C₂×C₃×D₄	—	5	4	no	—
475	C₂×C₃×D₄	—	5	4	no	—
476	C₂×C₃×D₄	—	20	2	no	—
477	C₂×C₃×D₄	—	20	2	no	—
478	C₂×C₃×D₄	—	20	2	no	—
479	C₂×C₃×D₄	—	20	2	no	—
480	C₂×C₃×D₄	—	20	2	no	—
481	C₂×C₃×D₄	—	20	2	no	—
482	C₂×C₃×D₄	—	20	2	no	—
483	C₂×C₃×D₄	—	20	2	no	—
484	C₂×C₃×D₄	—	20	2	no	—
485	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
486	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
487	C₂×C₃×D₄	C₂²×D₅	1	4	yes	complemented
488	C₂²×C₃×C₄	—	4	2	no	—
489	C₂²×C₃×C₄	—	5	1	no	—
490	C₂²×C₃×C₄	—	5	1	no	—
491	C₂²×C₃×C₄	—	5	1	no	—
492	C₂²×C₃×C₄	—	5	1	no	—
493	C₂²×C₃×C₄	—	5	1	no	—
494	C₂²×C₃×C₄	—	5	4	no	—
495	C₂²×C₃×C₄	—	5	4	no	—
496	C₂²×C₃×C₄	—	20	2	no	—
497	C₂²×C₃×C₄	—	20	2	no	—
498	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
499	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
500	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
501	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
502	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	complemented
503	C₃×C₄⋊C₄	—	5	4	no	—
504	C₃×C₄⋊C₄	—	5	4	no	—
505	C₃×C₄⋊C₄	—	5	4	no	—
506	C₃×C₄⋊C₄	—	5	4	no	—
507	C₃×C₄⋊C₄	—	5	4	no	—
508	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	complemented
509	C₃×C₂²⋊C₄	—	5	4	no	—
510	C₃×C₂²⋊C₄	—	5	4	no	—
511	C₃×C₂²⋊C₄	—	5	4	no	—
512	C₃×C₂²⋊C₄	—	5	4	no	—
513	C₃×C₂²⋊C₄	—	5	4	no	—
514	C₃×C₂²⋊C₄	—	5	4	no	—
515	C₃×C₂²⋊C₄	—	5	4	no	—
516	C₃×C₂²⋊C₄	—	5	4	no	—
517	C₃×C₂²⋊C₄	—	5	4	no	—
518	C₃×C₂²⋊C₄	—	5	4	no	—
519	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
520	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	complemented
521	C₃×C₄²	—	5	4	no	—
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	C₂⁴×C₃	1	2	yes	—
532	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
533	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
534	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
535	C₂²×D₅	—	2	2	no	—
536	C₂²×D₅	—	2	2	no	—
537	C₂²×D₅	—	2	2	no	—
538	C₂²×D₅	—	2	2	no	—
539	C₂²×D₅	—	2	2	no	—
540	C₂²×D₅	—	2	2	no	—
541	C₂²×D₅	—	2	2	no	—
542	C₂²×D₅	—	2	2	no	—
543	C₂²×D₅	—	2	2	no	—
544	C₂²×D₅	—	4	4	no	—
545	C₂²×D₅	—	4	4	no	—
546	C₂²×D₅	—	4	4	no	—
547	C₂²×D₅	—	4	16	no	—
548	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
549	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
550	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
551	C₅×D₄	—	4	4	no	—
552	C₅×D₄	—	4	4	no	—
553	C₅×D₄	—	4	4	no	—
554	C₂×C₄×C₅	—	2	2	no	—
555	C₂×C₄×C₅	—	2	2	no	—
556	C₂×C₄×C₅	—	2	2	no	—
557	C₂×C₄×C₅	—	2	2	no	—
558	C₂×C₄×C₅	—	4	4	no	—
559	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
560	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
561	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
562	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
563	C₂²⋊D₅	—	4	4	no	—
564	C₂²⋊D₅	—	4	4	no	—
565	C₂²⋊D₅	—	4	4	no	—
566	C₂²⋊D₅	—	4	4	no	—
567	C₂²⋊D₅	—	4	4	no	—
568	C₂²⋊D₅	—	4	4	no	—
569	C₂²⋊D₅	—	4	4	no	—
570	C₂×Dic₅	—	2	2	no	—
571	C₂×Dic₅	—	2	2	no	—
572	C₂×Dic₅	—	2	2	no	—
573	C₂×Dic₅	—	2	2	no	—
574	C₂×Dic₅	—	2	2	no	—
575	C₂×Dic₅	—	4	4	no	—
576	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
577	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
578	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
579	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
580	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
581	D₂₀	—	4	4	no	—
582	D₂₀	—	4	4	no	—
583	C₄×D₅	—	4	4	no	—
584	C₂⁵	—	5	1	no	—
585	C₂²×D₄	—	5	1	no	—
586	C₂²×D₄	—	5	1	no	—
587	C₂²×D₄	—	5	1	no	—
588	C₂²×D₄	—	5	1	no	—
589	C₂²×D₄	—	5	1	no	—
590	C₂²×D₄	—	5	1	no	—
591	C₂²×D₄	—	5	1	no	—
592	C₂²×D₄	—	5	1	no	—
593	C₂²×D₄	—	5	1	no	—
594	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
595	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
596	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
597	C₂³×C₄	—	5	1	no	—
598	C₂³×C₄	—	5	1	no	—
599	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
600	#127	—	5	8	no	—
601	#126	—	5	8	no	—
602	#126	—	5	8	no	—
603	#123	—	5	8	no	—
604	#123	—	5	8	no	—
605	#123	—	5	8	no	—
606	#121	—	5	8	no	—
607	#121	—	5	8	no	—
608	#121	—	5	8	no	—
609	#121	—	5	8	no	—
610	#121	—	5	8	no	—
611	#121	C₂×C₃×D₅	1	8	yes	complemented
612	#120	—	5	8	no	—
613	#120	—	5	8	no	—
614	#120	—	5	8	no	—
615	C₂×C₄⋊C₄	—	5	1	no	—
616	C₂×C₄⋊C₄	—	5	1	no	—
617	C₂×C₄⋊C₄	—	5	1	no	—
618	C₂×C₄⋊C₄	—	5	1	no	—
619	C₂×C₄⋊C₄	—	5	1	no	—
620	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
621	C₂×C₂²⋊C₄	—	5	1	no	—
622	C₂×C₂²⋊C₄	—	5	1	no	—
623	C₂×C₂²⋊C₄	—	5	1	no	—
624	C₂×C₂²⋊C₄	—	5	1	no	—
625	C₂×C₂²⋊C₄	—	5	1	no	—
626	C₂×C₂²⋊C₄	—	5	1	no	—
627	C₂×C₂²⋊C₄	—	5	1	no	—
628	C₂×C₂²⋊C₄	—	5	1	no	—
629	C₂×C₂²⋊C₄	—	5	1	no	—
630	C₂×C₂²⋊C₄	—	5	1	no	—
631	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
633	C₂×C₄²	—	5	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	C₃×D₅	—	4	2	no	—
642	C₃×D₅	—	4	2	no	—
643	C₃×D₅	—	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	—	5	2	no	—
654	C₂³×C₃	—	5	2	no	—
655	C₂³×C₃	—	5	2	no	—
656	C₂³×C₃	—	10	2	no	—
657	C₂³×C₃	—	10	2	no	—
658	C₂³×C₃	—	10	2	no	—
659	C₂³×C₃	—	10	2	no	—
660	C₂³×C₃	—	10	2	no	—
661	C₂³×C₃	—	10	2	no	—
662	C₂³×C₃	—	10	2	no	—
663	C₂³×C₃	—	10	2	no	—
664	C₂³×C₃	—	10	2	no	—
665	C₂³×C₃	—	20	4	no	—
666	C₂³×C₃	—	20	4	no	—
667	C₂³×C₃	—	20	4	no	—
668	C₂³×C₃	—	20	16	no	—
669	C₂³×C₃	C₂³×D₅	1	2	yes	—
670	C₂³×C₃	C₂³×D₅	1	2	yes	—
671	C₂³×C₃	C₂³×D₅	1	2	yes	—
672	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
673	C₃×D₄	—	4	4	no	—
674	C₃×D₄	—	4	4	no	—
675	C₃×D₄	—	4	4	no	—
676	C₃×D₄	—	20	4	no	—
677	C₃×D₄	—	20	4	no	—
678	C₃×D₄	—	20	4	no	—
679	C₃×D₄	—	20	4	no	—
680	C₃×D₄	—	20	4	no	—
681	C₃×D₄	—	20	4	no	—
682	C₃×D₄	—	20	4	no	—
683	C₃×D₄	—	20	4	no	—
684	C₃×D₄	—	20	4	no	—
685	C₂×C₃×C₄	—	2	2	no	—
686	C₂×C₃×C₄	—	2	2	no	—
687	C₂×C₃×C₄	—	2	2	no	—
688	C₂×C₃×C₄	—	2	2	no	—
689	C₂×C₃×C₄	—	4	4	no	—
690	C₂×C₃×C₄	—	5	2	no	—
691	C₂×C₃×C₄	—	5	2	no	—
692	C₂×C₃×C₄	—	5	2	no	—
693	C₂×C₃×C₄	—	5	2	no	—
694	C₂×C₃×C₄	—	5	2	no	—
695	C₂×C₃×C₄	—	10	2	no	—
696	C₂×C₃×C₄	—	10	2	no	—
697	C₂×C₃×C₄	—	10	2	no	—
698	C₂×C₃×C₄	—	10	2	no	—
699	C₂×C₃×C₄	—	10	2	no	—
700	C₂×C₃×C₄	—	20	4	no	—
701	C₂×C₃×C₄	—	20	4	no	—
702	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
703	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
704	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
705	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
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	C₃×H(5,𝔽₂)	1	2	yes	—
719	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
720	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
721	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
722	C₂×D₅	—	2	2	no	—
723	C₂×D₅	—	2	2	no	—
724	C₂×D₅	—	2	2	no	—
725	C₂×D₅	—	2	2	no	—
726	C₂×D₅	—	2	2	no	—
727	C₂×D₅	—	2	2	no	—
728	C₂×D₅	—	2	2	no	—
729	C₂×D₅	—	2	2	no	—
730	C₂×D₅	—	2	2	no	—
731	C₂×D₅	—	4	16	no	—
732	C₂×D₅	—	4	4	no	—
733	C₂×D₅	—	4	4	no	—
734	C₂×D₅	—	4	4	no	—
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	Dic₅	—	2	2	no	—
740	Dic₅	—	2	2	no	—
741	Dic₅	—	2	2	no	—
742	Dic₅	—	2	2	no	—
743	Dic₅	—	2	2	no	—
744	C₂⁴	—	5	1	no	—
745	C₂⁴	—	5	1	no	—
746	C₂⁴	—	5	1	no	—
747	C₂⁴	—	5	4	no	—
748	C₂⁴	—	20	2	no	—
749	C₂⁴	—	20	2	no	—
750	C₂⁴	—	20	2	no	—
751	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
752	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
753	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	5	4	no	—
758	C₂×D₄	—	5	4	no	—
759	C₂×D₄	—	5	4	no	—
760	C₂×D₄	—	5	4	no	—
761	C₂×D₄	—	5	4	no	—
762	C₂×D₄	—	5	4	no	—
763	C₂×D₄	—	5	4	no	—
764	C₂×D₄	—	5	4	no	—
765	C₂×D₄	—	5	4	no	—
766	C₂×D₄	—	20	2	no	—
767	C₂×D₄	—	20	2	no	—
768	C₂×D₄	—	20	2	no	—
769	C₂×D₄	—	20	2	no	—
770	C₂×D₄	—	20	2	no	—
771	C₂×D₄	—	20	2	no	—
772	C₂×D₄	—	20	2	no	—
773	C₂×D₄	—	20	2	no	—
774	C₂×D₄	—	20	2	no	—
775	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
776	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
777	C₂×D₄	C₂²×C₃×D₅	1	4	yes	complemented
778	C₂²×C₄	—	4	2	no	—
779	C₂²×C₄	—	5	1	no	—
780	C₂²×C₄	—	5	1	no	—
781	C₂²×C₄	—	5	1	no	—
782	C₂²×C₄	—	5	1	no	—
783	C₂²×C₄	—	5	1	no	—
784	C₂²×C₄	—	5	4	no	—
785	C₂²×C₄	—	5	4	no	—
786	C₂²×C₄	—	20	2	no	—
787	C₂²×C₄	—	20	2	no	—
788	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
789	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
790	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
791	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
792	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	complemented
793	C₄⋊C₄	—	5	4	no	—
794	C₄⋊C₄	—	5	4	no	—
795	C₄⋊C₄	—	5	4	no	—
796	C₄⋊C₄	—	5	4	no	—
797	C₄⋊C₄	—	5	4	no	—
798	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	complemented
799	C₂²⋊C₄	—	5	4	no	—
800	C₂²⋊C₄	—	5	4	no	—
801	C₂²⋊C₄	—	5	4	no	—
802	C₂²⋊C₄	—	5	4	no	—
803	C₂²⋊C₄	—	5	4	no	—
804	C₂²⋊C₄	—	5	4	no	—
805	C₂²⋊C₄	—	5	4	no	—
806	C₂²⋊C₄	—	5	4	no	—
807	C₂²⋊C₄	—	5	4	no	—
808	C₂²⋊C₄	—	5	4	no	—
809	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
810	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	complemented
811	C₄²	—	5	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	—	10	2	no	—
826	C₂²×C₃	—	10	2	no	—
827	C₂²×C₃	—	10	2	no	—
828	C₂²×C₃	—	10	2	no	—
829	C₂²×C₃	—	10	2	no	—
830	C₂²×C₃	—	10	2	no	—
831	C₂²×C₃	—	10	2	no	—
832	C₂²×C₃	—	10	2	no	—
833	C₂²×C₃	—	10	2	no	—
834	C₂²×C₃	—	20	16	no	—
835	C₂²×C₃	—	20	4	no	—
836	C₂²×C₃	—	20	4	no	—
837	C₂²×C₃	—	20	4	no	—
838	C₂²×C₃	#4144	1	2	yes	—
839	C₂²×C₃	#4144	1	2	yes	—
840	C₂²×C₃	#4149	1	2	yes	—
841	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
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	C₃×C₄	—	10	2	no	—
847	C₃×C₄	—	10	2	no	—
848	C₃×C₄	—	10	2	no	—
849	C₃×C₄	—	10	2	no	—
850	C₃×C₄	—	10	2	no	—
851	C₂×C₅	—	4	2	no	—
852	C₂×C₅	—	4	2	no	—
853	C₂×C₅	—	4	2	no	—
854	C₂×C₅	C₃×#560	1	4	yes	complemented
855	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
856	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
857	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
858	D₅	—	4	2	no	—
859	D₅	—	4	2	no	—
860	D₅	—	4	2	no	—
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	—	5	2	no	—
871	C₂³	—	5	2	no	—
872	C₂³	—	5	2	no	—
873	C₂³	—	10	2	no	—
874	C₂³	—	10	2	no	—
875	C₂³	—	10	2	no	—
876	C₂³	—	10	2	no	—
877	C₂³	—	10	2	no	—
878	C₂³	—	10	2	no	—
879	C₂³	—	10	2	no	—
880	C₂³	—	10	2	no	—
881	C₂³	—	10	2	no	—
882	C₂³	—	20	4	no	—
883	C₂³	—	20	4	no	—
884	C₂³	—	20	4	no	—
885	C₂³	—	20	16	no	—
886	C₂³	C₂³×C₃×D₅	1	2	yes	—
887	C₂³	C₂³×C₃×D₅	1	2	yes	—
888	C₂³	C₂³×C₃×D₅	1	2	yes	—
889	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
890	D₄	—	4	4	no	—
891	D₄	—	4	4	no	—
892	D₄	—	4	4	no	—
893	D₄	—	20	4	no	—
894	D₄	—	20	4	no	—
895	D₄	—	20	4	no	—
896	D₄	—	20	4	no	—
897	D₄	—	20	4	no	—
898	D₄	—	20	4	no	—
899	D₄	—	20	4	no	—
900	D₄	—	20	4	no	—
901	D₄	—	20	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	—	4	4	no	—
907	C₂×C₄	—	5	2	no	—
908	C₂×C₄	—	5	2	no	—
909	C₂×C₄	—	5	2	no	—
910	C₂×C₄	—	5	2	no	—
911	C₂×C₄	—	5	2	no	—
912	C₂×C₄	—	10	2	no	—
913	C₂×C₄	—	10	2	no	—
914	C₂×C₄	—	10	2	no	—
915	C₂×C₄	—	10	2	no	—
916	C₂×C₄	—	10	2	no	—
917	C₂×C₄	—	20	4	no	—
918	C₂×C₄	—	20	4	no	—
919	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
920	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
921	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
922	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
923	C₂×C₃	—	4	2	no	—
924	C₂×C₃	—	4	2	no	—
925	C₂×C₃	—	4	2	no	—
926	C₂×C₃	—	20	2	no	—
927	C₂×C₃	—	20	2	no	—
928	C₂×C₃	—	20	2	no	—
929	C₂×C₃	#65954	1	4	yes	direct product factor
930	C₂×C₃	C₂×#4144	1	1	yes	characteristic
931	C₂×C₃	C₂×#4144	1	1	yes	characteristic
932	C₂×C₃	C₂×#4149	1	1	yes	characteristic
933	C₅	C₂×C₃×#560	1	1	yes	characteristic, complemented, 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	—	10	2	no	—
947	C₂²	—	10	2	no	—
948	C₂²	—	10	2	no	—
949	C₂²	—	10	2	no	—
950	C₂²	—	10	2	no	—
951	C₂²	—	10	2	no	—
952	C₂²	—	10	2	no	—
953	C₂²	—	10	2	no	—
954	C₂²	—	10	2	no	—
955	C₂²	—	20	16	no	—
956	C₂²	—	20	4	no	—
957	C₂²	—	20	4	no	—
958	C₂²	—	20	4	no	—
959	C₂²	C₃×#4144	1	2	yes	—
960	C₂²	C₃×#4144	1	2	yes	—
961	C₂²	C₃×#4149	1	2	yes	—
962	C₂²	C₂⁴×C₃×D₅	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	—	10	2	no	—
968	C₄	—	10	2	no	—
969	C₄	—	10	2	no	—
970	C₄	—	10	2	no	—
971	C₄	—	10	2	no	—
972	C₃	C₂×#65954	1	1	yes	characteristic, direct product factor, Sylow
973	C₂	—	4	2	no	—
974	C₂	—	4	2	no	—
975	C₂	—	4	2	no	—
976	C₂	—	20	2	no	—
977	C₂	—	20	2	no	—
978	C₂	—	20	2	no	—
979	C₂	C₃×#65954	1	4	yes	direct product factor
980	C₂	C₂×C₃×#4144	1	1	yes	characteristic
981	C₂	C₂×C₃×#4144	1	1	yes	characteristic
982	C₂	C₂×C₃×#4149	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×#560
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×#4084	C₂	semidirect
6. C₂×C₃×#4083	C₂	semidirect
7. C₂×C₃×#4083	C₂	semidirect
8. C₂×C₃×#4076	C₂	semidirect
9. C₂×C₃×#4075	C₂	semidirect
10. C₃×#65954	C₂	direct (N × H)
11. C₂×C₃×#4044	C₂	semidirect
12. C₂×C₃×#4040	C₂	semidirect
13. C₂×C₃×#4032	C₂	semidirect
14. C₂×C₃×#4030	C₂	semidirect
15. C₂×C₃×#4028	C₂	semidirect
16. C₂×C₃×#4025	C₂	semidirect
17. C₂×#65954	C₃	direct (N × H)
21. C₂²×C₃×C₅×D₄	C₂²	semidirect
22. C₂³×C₃×C₄×C₅	C₂²	semidirect
28. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
29. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
30. C₂³×C₃×Dic₅	C₂²	semidirect
33. C₂²×C₃×C₄×D₅	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×C₃×C₂²⋊Dic₅	C₂²	semidirect
41. C₃×#4086	C₂²	semidirect
42. C₃×#4085	C₂²	semidirect
43. C₃×#4085	C₂²	semidirect
44. C₃×#4084	C₂²	semidirect
45. C₃×#4083	C₂²	semidirect
46. C₃×#4083	C₂²	semidirect
47. C₃×#4076	C₂²	semidirect
48. C₃×#4075	C₂²	semidirect
55. C₂×C₃×#685	C₂²	semidirect
56. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
57. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
58. C₂×C₃×#683	C₂²	semidirect
59. C₂×C₃×#683	C₂²	semidirect
60. C₂×C₃×#683	C₂²	semidirect
61. C₂×C₃×C₄×Dic₅	C₂²	semidirect
62. C₃×#4044	C₂²	semidirect
63. C₃×#4040	C₂²	semidirect
64. C₃×#4032	C₂²	semidirect
65. C₃×#4030	C₂²	semidirect
66. C₃×#4028	C₂²	semidirect
67. C₃×#4025	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×#4084	C₂×C₃	semidirect
74. C₂×#4083	C₂×C₃	semidirect
75. C₂×#4083	C₂×C₃	semidirect
76. C₂×#4076	C₂×C₃	semidirect
77. C₂×#4075	C₂×C₃	semidirect
78. #65954	C₂×C₃	direct (N × H)
79. C₂×#4044	C₂×C₃	semidirect
80. C₂×#4040	C₂×C₃	semidirect
81. C₂×#4032	C₂×C₃	semidirect
82. C₂×#4030	C₂×C₃	semidirect
83. C₂×#4028	C₂×C₃	semidirect
84. C₂×#4025	C₂×C₃	semidirect
100. C₂×C₃×C₅×D₄	C₂³	semidirect
106. C₂²×C₃×C₄×C₅	C₂³	semidirect
119. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
120. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
127. C₂²×C₃×Dic₅	C₂³	semidirect
133. C₂×C₃×C₄×D₅	C₂³	semidirect
134. C₃×C₅×C₄⋊C₄	C₂³	semidirect
136. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
139. C₃×C₂²⋊Dic₅	C₂³	semidirect
146. C₃×#685	C₂³	semidirect
147. C₃×C₄⋊Dic₅	C₂³	semidirect
148. C₃×C₄⋊Dic₅	C₂³	semidirect
149. C₃×#683	C₂³	semidirect
150. C₃×#683	C₂³	semidirect
151. C₃×#683	C₂³	semidirect
152. C₃×C₄×Dic₅	C₂³	semidirect
165. C₂×C₃×#121	D₅	semidirect
172. C₂²×C₅×D₄	C₂²×C₃	semidirect
173. C₂³×C₄×C₅	C₂²×C₃	semidirect
179. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
180. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
181. C₂³×Dic₅	C₂²×C₃	semidirect
184. C₂²×C₄×D₅	C₂²×C₃	semidirect
185. C₅×#121	C₂²×C₃	semidirect
186. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
188. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
191. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
192. #4086	C₂²×C₃	semidirect
193. #4085	C₂²×C₃	semidirect
194. #4085	C₂²×C₃	semidirect
195. #4084	C₂²×C₃	semidirect
196. #4083	C₂²×C₃	semidirect
197. #4083	C₂²×C₃	semidirect
198. #4076	C₂²×C₃	semidirect
199. #4075	C₂²×C₃	semidirect
206. C₂×#685	C₂²×C₃	semidirect
207. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
208. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
209. C₂×#683	C₂²×C₃	semidirect
210. C₂×#683	C₂²×C₃	semidirect
211. C₂×#683	C₂²×C₃	semidirect
212. C₂×C₄×Dic₅	C₂²×C₃	semidirect
213. #4044	C₂²×C₃	semidirect
214. #4040	C₂²×C₃	semidirect
215. #4032	C₂²×C₃	semidirect
216. #4030	C₂²×C₃	semidirect
217. #4028	C₂²×C₃	semidirect
218. #4025	C₂²×C₃	semidirect
294. C₂²×C₃×D₄	C₂×D₅	semidirect
297. C₂³×C₃×C₄	C₂×D₅	semidirect
309. C₃×#121	C₂×D₅	semidirect
318. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
330. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
347. C₂×C₅×D₄	C₂³×C₃	semidirect
353. C₂²×C₄×C₅	C₂³×C₃	semidirect
366. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
367. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
374. C₂²×Dic₅	C₂³×C₃	semidirect
380. C₂×C₄×D₅	C₂³×C₃	semidirect
381. C₅×C₄⋊C₄	C₂³×C₃	semidirect
383. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
386. C₂²⋊Dic₅	C₂³×C₃	semidirect
393. #685	C₂³×C₃	semidirect
394. C₄⋊Dic₅	C₂³×C₃	semidirect
395. C₄⋊Dic₅	C₂³×C₃	semidirect
396. #683	C₂³×C₃	semidirect
397. #683	C₂³×C₃	semidirect
398. #683	C₂³×C₃	semidirect
399. C₄×Dic₅	C₂³×C₃	semidirect
412. C₂×#121	C₃×D₅	semidirect
487. C₂×C₃×D₄	C₂²×D₅	semidirect
502. C₂²×C₃×C₄	C₂²×D₅	semidirect
508. C₃×C₄⋊C₄	C₂²×D₅	semidirect
520. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
596. C₂²×D₄	C₂×C₃×D₅	semidirect
599. C₂³×C₄	C₂×C₃×D₅	semidirect
611. #121	C₂×C₃×D₅	semidirect
620. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
632. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
637. C₂×C₃×C₅	#560	semidirect
777. C₂×D₄	C₂²×C₃×D₅	semidirect
792. C₂²×C₄	C₂²×C₃×D₅	semidirect
798. C₄⋊C₄	C₂²×C₃×D₅	semidirect
810. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
812. C₃×C₅	C₂×#560	semidirect
854. C₂×C₅	C₃×#560	semidirect
929. C₂×C₃	#65954	direct (N × H)
933. C₅	C₂×C₃×#560	semidirect
972. C₃	C₂×#65954	direct (N × H)
979. C₂	C₃×#65954	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×#4083	2
C₂×C₃×#4076	2
C₂×C₃×#4075	2
C₃×#65954	2
C₂×C₃×#4044	2
C₂×C₃×#4040	2
C₂×C₃×#4032	2
C₂×C₃×#4030	2
C₂×C₃×#4028	2
C₂×C₃×#4025	2
C₂×#65954	3
C₂×C₃×#560	5

Subgroups — C2×C3×#65954 #14495182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65954 #14495182