Subgroups — C₅×#82099 #14328101

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#953	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×#217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5213	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5210	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₅×#217	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4958	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4957	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4956	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4946	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4945	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4944	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×Dic₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2358	—	3	1	no	maximal, Hall
17	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
20	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
21	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
22	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
23	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
24	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₅×#953	C₄	1	8	yes	complemented
32	C₂×C₅×#217	—	2	4	no	—
33	C₂×C₅×#217	C₂²	1	1	yes	characteristic
34	C₂×C₅×#217	C₂²	1	1	yes	characteristic
35	C₂×C₅×#217	C₂²	1	1	yes	characteristic
36	C₂×C₅×#217	C₂²	1	1	yes	characteristic
37	C₂×C₅×#217	C₂²	1	1	yes	characteristic
38	C₂×C₅×#217	C₂²	1	1	yes	characteristic
39	C₂×C₅×#217	C₂²	1	1	yes	characteristic
40	C₄×C₅×#67	—	2	4	no	—
41	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
50	C₅×#67⋊C₄	—	2	4	no	—
51	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
52	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
53	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
54	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
55	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
56	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
57	#82099	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
58	C₂×C₅×#120	—	3	1	no	—
59	C₂×C₄×C₅×D₄	—	3	1	no	—
60	C₂×C₄×C₅×D₄	—	3	1	no	—
61	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
62	C₂²×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
63	C₅×#390	—	3	1	no	—
64	C₅×#388	—	3	1	no	—
65	C₅×#388	—	3	1	no	—
66	C₅×#386	—	3	1	no	—
67	C₅×#386	—	3	1	no	—
68	C₅×#386	—	3	1	no	—
69	C₅×#385	—	3	1	no	—
70	C₅×#385	—	3	1	no	—
71	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
72	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
73	C₂⁴×C₃×C₅	—	2	2	no	—
74	C₂⁴×C₃×C₅	—	2	2	no	—
75	C₂⁴×C₃×C₅	—	2	2	no	—
76	C₂⁴×C₃×C₅	—	2	2	no	—
77	C₂⁴×C₃×C₅	—	4	1	no	—
78	C₂⁴×C₃×C₅	—	4	1	no	—
79	C₂⁴×C₃×C₅	C₂×C₄	1	4	yes	complemented
80	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
81	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
82	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
83	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	—	2	2	no	—
85	C₂²×C₃×C₄×C₅	—	2	2	no	—
86	C₂²×C₃×C₄×C₅	—	2	2	no	—
87	C₂²×C₃×C₄×C₅	—	2	2	no	—
88	C₂²×C₃×C₄×C₅	—	4	1	no	—
89	C₂²×C₃×C₄×C₅	—	4	1	no	—
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₂×C₅×#67	—	2	2	no	—
95	C₂×C₅×#67	—	2	2	no	—
96	C₂×C₅×#67	—	2	2	no	—
97	C₂×C₅×#67	—	2	2	no	—
98	C₂×C₅×#67	—	4	1	no	—
99	C₂×C₅×#67	—	4	1	no	—
100	C₂×C₅×#67	C₂×C₄	1	4	yes	complemented
101	C₂×C₅×#67	C₂×C₄	1	4	yes	complemented
102	C₂×C₅×#67	C₂×C₄	1	4	yes	complemented
103	C₂²×C₅×Dic₃	—	2	2	no	—
104	C₂²×C₅×Dic₃	—	2	2	no	—
105	C₂²×C₅×Dic₃	—	2	2	no	—
106	C₂²×C₅×Dic₃	—	2	2	no	—
107	C₂²×C₅×Dic₃	—	4	1	no	—
108	C₂²×C₅×Dic₃	—	4	1	no	—
109	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
110	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
111	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
112	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
113	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
114	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
115	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
116	C₂×C₄×C₅×D₃	—	2	2	no	—
117	C₂×C₄×C₅×D₃	—	2	2	no	—
118	C₂×C₄×C₅×D₃	—	4	1	no	—
119	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
120	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
121	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
122	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	complemented
123	C₅×#217	—	2	2	no	—
124	C₅×#217	—	2	2	no	—
125	C₅×#217	—	2	2	no	—
126	C₅×#217	C₂×C₄	1	4	yes	complemented
127	C₅×#217	C₂×C₄	1	4	yes	complemented
128	C₅×#217	C₂×C₄	1	4	yes	complemented
129	C₅×#217	D₄	1	4	yes	complemented
130	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
131	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
132	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
133	C₅×Dic₃⋊C₄	—	2	2	no	—
134	C₅×Dic₃⋊C₄	—	2	2	no	—
135	C₅×Dic₃⋊C₄	—	4	1	no	—
136	C₄×C₅×Dic₃	—	2	2	no	—
137	C₄×C₅×Dic₃	—	2	2	no	—
138	C₄×C₅×Dic₃	—	4	1	no	—
139	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×#953	C₂×C₅	1	1	yes	characteristic
141	C₂²×#217	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
144	#5213	C₂×C₅	1	1	yes	characteristic, complemented
145	#5210	C₂×C₅	1	1	yes	characteristic, complemented
146	C₄×#217	C₂×C₅	1	1	yes	characteristic, complemented
147	#4958	C₂×C₅	1	1	yes	characteristic, complemented
148	#4957	C₂×C₅	1	1	yes	characteristic, complemented
149	#4956	C₂×C₅	1	1	yes	characteristic, complemented
150	#4946	C₂×C₅	1	1	yes	characteristic, complemented
151	#4945	C₂×C₅	1	1	yes	characteristic, complemented
152	#4944	C₂×C₅	1	1	yes	characteristic, complemented
153	Dic₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic
155	C₂²×C₅×D₄	—	3	1	no	—
156	C₂²×C₅×D₄	—	3	1	no	—
157	C₂²×C₅×D₄	—	3	1	no	—
158	C₂³×C₄×C₅	—	3	1	no	—
159	C₂³×C₄×C₅	—	3	1	no	—
160	C₂³×C₄×C₅	—	3	1	no	—
161	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
162	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
163	C₅×#120	—	3	8	no	—
164	C₄×C₅×D₄	—	6	4	no	—
165	C₄×C₅×D₄	—	6	4	no	—
166	C₂×C₅×C₄⋊C₄	—	3	1	no	—
167	C₂×C₅×C₄⋊C₄	—	3	1	no	—
168	C₂×C₅×C₄⋊C₄	—	3	1	no	—
169	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
170	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
171	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
172	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
173	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
174	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
175	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
176	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
177	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
178	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
179	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
180	C₂×C₅×C₂²⋊C₄	—	6	4	no	—
181	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
182	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
183	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
184	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
185	C₂×C₄²×C₅	—	3	1	no	—
186	C₂×C₄²×C₅	—	3	1	no	—
187	C₂×C₄²×C₅	—	3	1	no	—
188	C₅×#95	—	3	1	no	—
189	C₅×#95	—	3	1	no	—
190	C₅×#95	—	3	1	no	—
191	C₅×#95	—	3	1	no	—
192	C₅×#95	—	3	1	no	—
193	C₅×#95	—	3	1	no	—
194	#2358	—	3	1	no	Sylow
195	C₂³×C₃×C₅	—	2	1	no	—
196	C₂³×C₃×C₅	—	2	1	no	—
197	C₂³×C₃×C₅	—	2	1	no	—
198	C₂³×C₃×C₅	—	2	1	no	—
199	C₂³×C₃×C₅	—	2	1	no	—
200	C₂³×C₃×C₅	—	2	1	no	—
201	C₂³×C₃×C₅	—	2	1	no	—
202	C₂³×C₃×C₅	—	2	1	no	—
203	C₂³×C₃×C₅	—	2	8	no	—
204	C₂³×C₃×C₅	—	2	8	no	—
205	C₂³×C₃×C₅	—	2	1	no	—
206	C₂³×C₃×C₅	—	2	1	no	—
207	C₂³×C₃×C₅	—	2	1	no	—
208	C₂³×C₃×C₅	—	2	1	no	—
209	C₂³×C₃×C₅	—	2	1	no	—
210	C₂³×C₃×C₅	—	2	1	no	—
211	C₂³×C₃×C₅	—	4	4	no	—
212	C₂³×C₃×C₅	—	4	4	no	—
213	C₂³×C₃×C₅	—	4	4	no	—
214	C₂³×C₃×C₅	—	4	4	no	—
215	C₂³×C₃×C₅	—	4	4	no	—
216	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
217	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
218	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
219	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
220	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
221	C₂³×C₃×C₅	#41	1	2	yes	—
222	C₂³×C₃×C₅	#41	1	2	yes	—
223	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
224	C₂²×C₅×D₃	—	2	1	no	—
225	C₂²×C₅×D₃	—	2	1	no	—
226	C₂²×C₅×D₃	—	2	1	no	—
227	C₂²×C₅×D₃	—	2	1	no	—
228	C₂²×C₅×D₃	—	2	1	no	—
229	C₂²×C₅×D₃	—	2	1	no	—
230	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
231	C₂×C₃×C₄×C₅	—	2	1	no	—
232	C₂×C₃×C₄×C₅	—	2	1	no	—
233	C₂×C₃×C₄×C₅	—	2	1	no	—
234	C₂×C₃×C₄×C₅	—	2	1	no	—
235	C₂×C₃×C₄×C₅	—	2	1	no	—
236	C₂×C₃×C₄×C₅	—	2	1	no	—
237	C₂×C₃×C₄×C₅	—	2	1	no	—
238	C₂×C₃×C₄×C₅	—	2	1	no	—
239	C₂×C₃×C₄×C₅	—	2	1	no	—
240	C₂×C₃×C₄×C₅	—	2	1	no	—
241	C₂×C₃×C₄×C₅	—	4	4	no	—
242	C₂×C₃×C₄×C₅	—	4	4	no	—
243	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
244	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
245	C₅×#67	—	2	8	no	—
246	C₅×#67	—	2	8	no	—
247	C₅×#67	—	4	4	no	—
248	C₂×C₅×Dic₃	—	2	1	no	—
249	C₂×C₅×Dic₃	—	2	1	no	—
250	C₂×C₅×Dic₃	—	2	1	no	—
251	C₂×C₅×Dic₃	—	2	1	no	—
252	C₂×C₅×Dic₃	—	2	1	no	—
253	C₂×C₅×Dic₃	—	2	1	no	—
254	C₂×C₅×Dic₃	—	2	1	no	—
255	C₂×C₅×Dic₃	—	2	1	no	—
256	C₂×C₅×Dic₃	—	2	1	no	—
257	C₂×C₅×Dic₃	—	2	1	no	—
258	C₂×C₅×Dic₃	—	2	1	no	—
259	C₂×C₅×Dic₃	—	2	1	no	—
260	C₂×C₅×Dic₃	—	2	1	no	—
261	C₂×C₅×Dic₃	—	2	1	no	—
262	C₂×C₅×Dic₃	—	2	1	no	—
263	C₂×C₅×Dic₃	—	2	1	no	—
264	C₂×C₅×Dic₃	—	4	4	no	—
265	C₂×C₅×Dic₃	—	4	4	no	—
266	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
267	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
268	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
269	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
270	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
271	C₄×C₅×D₃	—	4	4	no	—
272	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
273	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
274	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
275	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
276	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
277	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
278	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
279	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
280	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
281	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
282	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
283	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
284	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
285	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
286	#953	C₄×C₅	1	8	yes	complemented
287	C₂×#217	—	2	4	no	—
288	C₂×#217	C₂²×C₅	1	1	yes	characteristic
289	C₂×#217	C₂²×C₅	1	1	yes	characteristic
290	C₂×#217	C₂²×C₅	1	1	yes	characteristic
291	C₂×#217	C₂²×C₅	1	1	yes	characteristic
292	C₂×#217	C₂²×C₅	1	1	yes	characteristic
293	C₂×#217	C₂²×C₅	1	1	yes	characteristic
294	C₂×#217	C₂²×C₅	1	1	yes	characteristic
295	C₄×#67	—	2	4	no	—
296	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
297	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
298	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
299	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
300	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
301	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
302	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
303	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
304	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
305	#67⋊C₄	—	2	4	no	—
306	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
307	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
308	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
309	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
310	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
311	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
312	C₂⁴×C₅	—	2	2	no	—
313	C₂⁴×C₅	—	2	2	no	—
314	C₂⁴×C₅	—	2	2	no	—
315	C₂⁴×C₅	—	2	2	no	—
316	C₂⁴×C₅	—	3	1	no	—
317	C₂⁴×C₅	—	4	1	no	—
318	C₂⁴×C₅	—	4	1	no	—
319	C₂⁴×C₅	C₄×D₃	1	4	yes	complemented
320	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
321	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
322	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
323	C₂×C₅×D₄	—	3	4	no	—
324	C₂×C₅×D₄	—	3	4	no	—
325	C₂×C₅×D₄	—	3	4	no	—
326	C₂×C₅×D₄	—	6	2	no	—
327	C₂×C₅×D₄	—	6	2	no	—
328	C₂×C₅×D₄	—	6	2	no	—
329	C₂×C₅×D₄	—	6	2	no	—
330	C₂×C₅×D₄	—	12	1	no	—
331	C₂×C₅×D₄	—	12	1	no	—
332	C₂²×C₄×C₅	—	2	2	no	—
333	C₂²×C₄×C₅	—	2	2	no	—
334	C₂²×C₄×C₅	—	2	2	no	—
335	C₂²×C₄×C₅	—	2	2	no	—
336	C₂²×C₄×C₅	—	3	1	no	—
337	C₂²×C₄×C₅	—	3	1	no	—
338	C₂²×C₄×C₅	—	3	1	no	—
339	C₂²×C₄×C₅	—	3	1	no	—
340	C₂²×C₄×C₅	—	3	1	no	—
341	C₂²×C₄×C₅	—	3	1	no	—
342	C₂²×C₄×C₅	—	3	1	no	—
343	C₂²×C₄×C₅	—	4	1	no	—
344	C₂²×C₄×C₅	—	4	1	no	—
345	C₂²×C₄×C₅	—	6	2	no	—
346	C₂²×C₄×C₅	—	6	2	no	—
347	C₂²×C₄×C₅	—	6	2	no	—
348	C₂²×C₄×C₅	—	6	2	no	—
349	C₂²×C₄×C₅	—	6	2	no	—
350	C₂²×C₄×C₅	—	6	2	no	—
351	C₂²×C₄×C₅	—	12	1	no	—
352	C₂²×C₄×C₅	—	12	1	no	—
353	C₂²×C₄×C₅	—	12	1	no	—
354	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
355	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
356	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
357	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
358	C₅×C₄⋊C₄	—	6	2	no	—
359	C₅×C₄⋊C₄	—	6	2	no	—
360	C₅×C₄⋊C₄	—	12	1	no	—
361	C₅×C₂²⋊C₄	—	2	2	no	—
362	C₅×C₂²⋊C₄	—	2	2	no	—
363	C₅×C₂²⋊C₄	—	2	2	no	—
364	C₅×C₂²⋊C₄	—	3	4	no	—
365	C₅×C₂²⋊C₄	—	3	4	no	—
366	C₅×C₂²⋊C₄	—	3	4	no	—
367	C₅×C₂²⋊C₄	—	3	4	no	—
368	C₅×C₂²⋊C₄	—	6	2	no	—
369	C₅×C₂²⋊C₄	—	6	2	no	—
370	C₅×C₂²⋊C₄	—	6	2	no	—
371	C₅×C₂²⋊C₄	—	6	2	no	—
372	C₅×C₂²⋊C₄	—	6	2	no	—
373	C₅×C₂²⋊C₄	—	12	1	no	—
374	C₅×C₂²⋊C₄	#67	1	4	yes	complemented
375	C₄²×C₅	—	6	2	no	—
376	C₄²×C₅	—	6	2	no	—
377	C₄²×C₅	—	12	1	no	—
378	C₂×#120	—	3	1	no	—
379	C₂×C₄×D₄	—	3	1	no	—
380	C₂×C₄×D₄	—	3	1	no	—
381	C₂²×C₂²⋊C₄	—	3	1	no	—
382	C₂²×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
383	#390	—	3	1	no	—
384	#388	—	3	1	no	—
385	#388	—	3	1	no	—
386	#386	—	3	1	no	—
387	#386	—	3	1	no	—
388	#386	—	3	1	no	—
389	#385	—	3	1	no	—
390	#385	—	3	1	no	—
391	C₄×C₂²⋊C₄	—	3	1	no	—
392	C₄×C₂²⋊C₄	—	3	1	no	—
393	C₂²×C₃×C₅	—	2	2	no	—
394	C₂²×C₃×C₅	—	2	2	no	—
395	C₂²×C₃×C₅	—	2	2	no	—
396	C₂²×C₃×C₅	—	2	2	no	—
397	C₂²×C₃×C₅	—	2	2	no	—
398	C₂²×C₃×C₅	—	2	2	no	—
399	C₂²×C₃×C₅	—	2	2	no	—
400	C₂²×C₃×C₅	—	2	2	no	—
401	C₂²×C₃×C₅	—	2	2	no	—
402	C₂²×C₃×C₅	—	2	2	no	—
403	C₂²×C₃×C₅	—	2	2	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	—	4	16	no	—
409	C₂²×C₃×C₅	—	4	1	no	—
410	C₂²×C₃×C₅	—	4	1	no	—
411	C₂²×C₃×C₅	—	4	1	no	—
412	C₂²×C₃×C₅	—	4	1	no	—
413	C₂²×C₃×C₅	C₄×D₄	1	4	yes	complemented
414	C₂²×C₃×C₅	C₄×D₄	1	4	yes	complemented
415	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
416	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
417	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
418	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
419	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
420	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
421	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
422	C₂×C₅×D₃	—	2	2	no	—
423	C₂×C₅×D₃	—	2	2	no	—
424	C₂×C₅×D₃	—	2	2	no	—
425	C₂×C₅×D₃	—	4	1	no	—
426	C₂×C₅×D₃	—	4	1	no	—
427	C₂×C₅×D₃	—	4	1	no	—
428	C₂×C₅×D₃	—	4	1	no	—
429	C₃×C₄×C₅	—	2	2	no	—
430	C₃×C₄×C₅	—	2	2	no	—
431	C₃×C₄×C₅	—	4	1	no	—
432	C₃×C₄×C₅	—	4	1	no	—
433	C₅×Dic₃	—	2	2	no	—
434	C₅×Dic₃	—	2	2	no	—
435	C₅×Dic₃	—	2	2	no	—
436	C₅×Dic₃	—	2	2	no	—
437	C₅×Dic₃	—	2	2	no	—
438	C₅×Dic₃	—	4	1	no	—
439	C₅×Dic₃	—	4	1	no	—
440	C₂⁴×C₃	—	2	2	no	—
441	C₂⁴×C₃	—	2	2	no	—
442	C₂⁴×C₃	—	2	2	no	—
443	C₂⁴×C₃	—	2	2	no	—
444	C₂⁴×C₃	—	4	1	no	—
445	C₂⁴×C₃	—	4	1	no	—
446	C₂⁴×C₃	C₂×C₄×C₅	1	4	yes	complemented
447	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
448	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
449	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
450	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
451	C₂²×C₃×C₄	—	2	2	no	—
452	C₂²×C₃×C₄	—	2	2	no	—
453	C₂²×C₃×C₄	—	2	2	no	—
454	C₂²×C₃×C₄	—	2	2	no	—
455	C₂²×C₃×C₄	—	4	1	no	—
456	C₂²×C₃×C₄	—	4	1	no	—
457	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
458	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
459	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
460	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
461	C₂×#67	—	2	2	no	—
462	C₂×#67	—	2	2	no	—
463	C₂×#67	—	2	2	no	—
464	C₂×#67	—	2	2	no	—
465	C₂×#67	—	4	1	no	—
466	C₂×#67	—	4	1	no	—
467	C₂×#67	C₂×C₄×C₅	1	4	yes	complemented
468	C₂×#67	C₂×C₄×C₅	1	4	yes	complemented
469	C₂×#67	C₂×C₄×C₅	1	4	yes	complemented
470	C₂²×Dic₃	—	2	2	no	—
471	C₂²×Dic₃	—	2	2	no	—
472	C₂²×Dic₃	—	2	2	no	—
473	C₂²×Dic₃	—	2	2	no	—
474	C₂²×Dic₃	—	4	1	no	—
475	C₂²×Dic₃	—	4	1	no	—
476	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
477	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
478	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
479	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
480	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
481	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
482	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
483	C₂×C₄×D₃	—	2	2	no	—
484	C₂×C₄×D₃	—	2	2	no	—
485	C₂×C₄×D₃	—	4	1	no	—
486	C₃×C₂²⋊C₄	—	2	2	no	—
487	C₃×C₂²⋊C₄	—	2	2	no	—
488	C₃×C₂²⋊C₄	—	2	2	no	—
489	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	complemented
490	#217	—	2	2	no	—
491	#217	—	2	2	no	—
492	#217	—	2	2	no	—
493	#217	C₂×C₄×C₅	1	4	yes	complemented
494	#217	C₂×C₄×C₅	1	4	yes	complemented
495	#217	C₂×C₄×C₅	1	4	yes	complemented
496	#217	C₅×D₄	1	4	yes	complemented
497	(C₂×D₃)⋊C₄	—	2	2	no	—
498	(C₂×D₃)⋊C₄	—	2	2	no	—
499	(C₂×D₃)⋊C₄	—	4	1	no	—
500	Dic₃⋊C₄	—	2	2	no	—
501	Dic₃⋊C₄	—	2	2	no	—
502	Dic₃⋊C₄	—	4	1	no	—
503	C₄×Dic₃	—	2	2	no	—
504	C₄×Dic₃	—	2	2	no	—
505	C₄×Dic₃	—	4	1	no	—
506	C₂³×C₅	—	2	1	no	—
507	C₂³×C₅	—	2	1	no	—
508	C₂³×C₅	—	2	1	no	—
509	C₂³×C₅	—	2	1	no	—
510	C₂³×C₅	—	2	1	no	—
511	C₂³×C₅	—	2	1	no	—
512	C₂³×C₅	—	2	1	no	—
513	C₂³×C₅	—	2	1	no	—
514	C₂³×C₅	—	2	8	no	—
515	C₂³×C₅	—	2	8	no	—
516	C₂³×C₅	—	2	1	no	—
517	C₂³×C₅	—	2	1	no	—
518	C₂³×C₅	—	2	1	no	—
519	C₂³×C₅	—	2	1	no	—
520	C₂³×C₅	—	2	1	no	—
521	C₂³×C₅	—	2	1	no	—
522	C₂³×C₅	—	3	2	no	—
523	C₂³×C₅	—	4	4	no	—
524	C₂³×C₅	—	4	4	no	—
525	C₂³×C₅	—	4	4	no	—
526	C₂³×C₅	—	4	4	no	—
527	C₂³×C₅	—	4	4	no	—
528	C₂³×C₅	—	6	1	no	—
529	C₂³×C₅	—	6	1	no	—
530	C₂³×C₅	—	6	1	no	—
531	C₂³×C₅	—	6	1	no	—
532	C₂³×C₅	—	6	1	no	—
533	C₂³×C₅	—	6	1	no	—
534	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
535	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
536	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
537	C₂³×C₅	#235	1	2	yes	—
538	C₂³×C₅	D₃×D₄	1	2	yes	—
539	C₂³×C₅	#237	1	2	yes	—
540	C₂³×C₅	C₂×#67	1	2	yes	—
541	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
542	C₅×D₄	—	6	8	no	—
543	C₅×D₄	—	6	8	no	—
544	C₅×D₄	—	12	4	no	—
545	C₂×C₄×C₅	—	2	1	no	—
546	C₂×C₄×C₅	—	2	1	no	—
547	C₂×C₄×C₅	—	2	1	no	—
548	C₂×C₄×C₅	—	2	1	no	—
549	C₂×C₄×C₅	—	2	1	no	—
550	C₂×C₄×C₅	—	2	1	no	—
551	C₂×C₄×C₅	—	2	1	no	—
552	C₂×C₄×C₅	—	2	1	no	—
553	C₂×C₄×C₅	—	2	1	no	—
554	C₂×C₄×C₅	—	2	1	no	—
555	C₂×C₄×C₅	—	3	2	no	—
556	C₂×C₄×C₅	—	3	2	no	—
557	C₂×C₄×C₅	—	3	2	no	—
558	C₂×C₄×C₅	—	3	2	no	—
559	C₂×C₄×C₅	—	3	2	no	—
560	C₂×C₄×C₅	—	4	4	no	—
561	C₂×C₄×C₅	—	4	4	no	—
562	C₂×C₄×C₅	—	6	1	no	—
563	C₂×C₄×C₅	—	6	1	no	—
564	C₂×C₄×C₅	—	6	1	no	—
565	C₂×C₄×C₅	—	6	1	no	—
566	C₂×C₄×C₅	—	6	1	no	—
567	C₂×C₄×C₅	—	6	1	no	—
568	C₂×C₄×C₅	—	6	1	no	—
569	C₂×C₄×C₅	—	6	1	no	—
570	C₂×C₄×C₅	—	6	1	no	—
571	C₂×C₄×C₅	—	6	1	no	—
572	C₂×C₄×C₅	—	6	1	no	—
573	C₂×C₄×C₅	—	6	1	no	—
574	C₂×C₄×C₅	—	6	1	no	—
575	C₂×C₄×C₅	—	6	1	no	—
576	C₂×C₄×C₅	—	6	1	no	—
577	C₂×C₄×C₅	—	6	1	no	—
578	C₂×C₄×C₅	—	12	4	no	—
579	C₂×C₄×C₅	—	12	4	no	—
580	C₂×C₄×C₅	—	12	4	no	—
581	C₂×C₄×C₅	C₂×#67	1	2	yes	—
582	C₂×C₄×C₅	C₂×#67	1	2	yes	—
583	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic
584	C₂²×D₄	—	3	1	no	—
585	C₂²×D₄	—	3	1	no	—
586	C₂²×D₄	—	3	1	no	—
587	C₂³×C₄	—	3	1	no	—
588	C₂³×C₄	—	3	1	no	—
589	C₂³×C₄	—	3	1	no	—
590	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
591	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
592	#120	—	3	8	no	—
593	C₄×D₄	—	6	4	no	—
594	C₄×D₄	—	6	4	no	—
595	C₂×C₄⋊C₄	—	3	1	no	—
596	C₂×C₄⋊C₄	—	3	1	no	—
597	C₂×C₄⋊C₄	—	3	1	no	—
598	C₂×C₂²⋊C₄	—	2	4	no	—
599	C₂×C₂²⋊C₄	—	3	1	no	—
600	C₂×C₂²⋊C₄	—	3	1	no	—
601	C₂×C₂²⋊C₄	—	3	1	no	—
602	C₂×C₂²⋊C₄	—	3	1	no	—
603	C₂×C₂²⋊C₄	—	3	1	no	—
604	C₂×C₂²⋊C₄	—	3	1	no	—
605	C₂×C₂²⋊C₄	—	3	1	no	—
606	C₂×C₂²⋊C₄	—	3	1	no	—
607	C₂×C₂²⋊C₄	—	3	1	no	—
608	C₂×C₂²⋊C₄	—	3	1	no	—
609	C₂×C₂²⋊C₄	—	6	4	no	—
610	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
614	C₂×C₄²	—	3	1	no	—
615	C₂×C₄²	—	3	1	no	—
616	C₂×C₄²	—	3	1	no	—
617	#95	—	3	1	no	—
618	#95	—	3	1	no	—
619	#95	—	3	1	no	—
620	#95	—	3	1	no	—
621	#95	—	3	1	no	—
622	#95	—	3	1	no	—
623	C₂×C₃×C₅	—	2	4	no	—
624	C₂×C₃×C₅	—	2	4	no	—
625	C₂×C₃×C₅	—	4	2	no	—
626	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
627	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
628	C₂×C₃×C₅	#518	1	1	yes	characteristic
629	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
630	C₂×C₃×C₅	#546	1	1	yes	characteristic
631	C₂×C₃×C₅	#546	1	1	yes	characteristic
632	C₂×C₃×C₅	#551	1	1	yes	characteristic
633	C₅×D₃	—	4	2	no	—
634	C₂³×C₃	—	2	1	no	—
635	C₂³×C₃	—	2	1	no	—
636	C₂³×C₃	—	2	1	no	—
637	C₂³×C₃	—	2	1	no	—
638	C₂³×C₃	—	2	1	no	—
639	C₂³×C₃	—	2	1	no	—
640	C₂³×C₃	—	2	1	no	—
641	C₂³×C₃	—	2	1	no	—
642	C₂³×C₃	—	2	8	no	—
643	C₂³×C₃	—	2	8	no	—
644	C₂³×C₃	—	2	1	no	—
645	C₂³×C₃	—	2	1	no	—
646	C₂³×C₃	—	2	1	no	—
647	C₂³×C₃	—	2	1	no	—
648	C₂³×C₃	—	2	1	no	—
649	C₂³×C₃	—	2	1	no	—
650	C₂³×C₃	—	4	4	no	—
651	C₂³×C₃	—	4	4	no	—
652	C₂³×C₃	—	4	4	no	—
653	C₂³×C₃	—	4	4	no	—
654	C₂³×C₃	—	4	4	no	—
655	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
656	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
657	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
658	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
659	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
660	C₂³×C₃	C₅×#41	1	2	yes	—
661	C₂³×C₃	C₅×#41	1	2	yes	—
662	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
663	C₂²×D₃	—	2	1	no	—
664	C₂²×D₃	—	2	1	no	—
665	C₂²×D₃	—	2	1	no	—
666	C₂²×D₃	—	2	1	no	—
667	C₂²×D₃	—	2	1	no	—
668	C₂²×D₃	—	2	1	no	—
669	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
670	C₂×C₃×C₄	—	2	1	no	—
671	C₂×C₃×C₄	—	2	1	no	—
672	C₂×C₃×C₄	—	2	1	no	—
673	C₂×C₃×C₄	—	2	1	no	—
674	C₂×C₃×C₄	—	2	1	no	—
675	C₂×C₃×C₄	—	2	1	no	—
676	C₂×C₃×C₄	—	2	1	no	—
677	C₂×C₃×C₄	—	2	1	no	—
678	C₂×C₃×C₄	—	2	1	no	—
679	C₂×C₃×C₄	—	2	1	no	—
680	C₂×C₃×C₄	—	4	4	no	—
681	C₂×C₃×C₄	—	4	4	no	—
682	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
683	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
684	#67	—	2	8	no	—
685	#67	—	2	8	no	—
686	#67	—	4	4	no	—
687	C₂×Dic₃	—	2	1	no	—
688	C₂×Dic₃	—	2	1	no	—
689	C₂×Dic₃	—	2	1	no	—
690	C₂×Dic₃	—	2	1	no	—
691	C₂×Dic₃	—	2	1	no	—
692	C₂×Dic₃	—	2	1	no	—
693	C₂×Dic₃	—	2	1	no	—
694	C₂×Dic₃	—	2	1	no	—
695	C₂×Dic₃	—	2	1	no	—
696	C₂×Dic₃	—	2	1	no	—
697	C₂×Dic₃	—	2	1	no	—
698	C₂×Dic₃	—	2	1	no	—
699	C₂×Dic₃	—	2	1	no	—
700	C₂×Dic₃	—	2	1	no	—
701	C₂×Dic₃	—	2	1	no	—
702	C₂×Dic₃	—	2	1	no	—
703	C₂×Dic₃	—	4	4	no	—
704	C₂×Dic₃	—	4	4	no	—
705	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
706	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
707	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
708	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
709	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
710	C₄×D₃	—	4	4	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	—	2	2	no	—
716	C₂²×C₅	—	2	2	no	—
717	C₂²×C₅	—	2	2	no	—
718	C₂²×C₅	—	2	2	no	—
719	C₂²×C₅	—	2	2	no	—
720	C₂²×C₅	—	2	2	no	—
721	C₂²×C₅	—	2	2	no	—
722	C₂²×C₅	—	2	2	no	—
723	C₂²×C₅	—	2	2	no	—
724	C₂²×C₅	—	2	2	no	—
725	C₂²×C₅	—	2	2	no	—
726	C₂²×C₅	—	4	16	no	—
727	C₂²×C₅	—	4	1	no	—
728	C₂²×C₅	—	4	1	no	—
729	C₂²×C₅	—	4	1	no	—
730	C₂²×C₅	—	4	1	no	—
731	C₂²×C₅	—	6	2	no	—
732	C₂²×C₅	—	6	2	no	—
733	C₂²×C₅	—	6	2	no	—
734	C₂²×C₅	—	12	1	no	—
735	C₂²×C₅	—	12	1	no	—
736	C₂²×C₅	—	12	1	no	—
737	C₂²×C₅	—	12	1	no	—
738	C₂²×C₅	#67⋊C₄	1	4	yes	complemented
739	C₂²×C₅	C₄×#67	1	4	yes	complemented
740	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
741	C₂²×C₅	C₂×#235	1	1	yes	characteristic
742	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
743	C₂²×C₅	C₂×#237	1	1	yes	characteristic
744	C₂²×C₅	#1004	1	1	yes	characteristic
745	C₂²×C₅	#1004	1	1	yes	characteristic
746	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
747	C₄×C₅	—	2	2	no	—
748	C₄×C₅	—	2	2	no	—
749	C₄×C₅	—	4	1	no	—
750	C₄×C₅	—	4	1	no	—
751	C₄×C₅	—	6	2	no	—
752	C₄×C₅	—	6	2	no	—
753	C₄×C₅	—	6	2	no	—
754	C₄×C₅	—	6	2	no	—
755	C₄×C₅	—	6	2	no	—
756	C₄×C₅	—	12	1	no	—
757	C₄×C₅	—	12	1	no	—
758	C₂⁴	—	2	2	no	—
759	C₂⁴	—	2	2	no	—
760	C₂⁴	—	2	2	no	—
761	C₂⁴	—	2	2	no	—
762	C₂⁴	—	3	1	no	—
763	C₂⁴	—	4	1	no	—
764	C₂⁴	—	4	1	no	—
765	C₂⁴	C₄×C₅×D₃	1	4	yes	complemented
766	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
767	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
768	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
769	C₂×D₄	—	3	4	no	—
770	C₂×D₄	—	3	4	no	—
771	C₂×D₄	—	3	4	no	—
772	C₂×D₄	—	6	2	no	—
773	C₂×D₄	—	6	2	no	—
774	C₂×D₄	—	6	2	no	—
775	C₂×D₄	—	6	2	no	—
776	C₂×D₄	—	12	1	no	—
777	C₂×D₄	—	12	1	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	3	1	no	—
783	C₂²×C₄	—	3	1	no	—
784	C₂²×C₄	—	3	1	no	—
785	C₂²×C₄	—	3	1	no	—
786	C₂²×C₄	—	3	1	no	—
787	C₂²×C₄	—	3	1	no	—
788	C₂²×C₄	—	3	1	no	—
789	C₂²×C₄	—	4	1	no	—
790	C₂²×C₄	—	4	1	no	—
791	C₂²×C₄	—	6	2	no	—
792	C₂²×C₄	—	6	2	no	—
793	C₂²×C₄	—	6	2	no	—
794	C₂²×C₄	—	6	2	no	—
795	C₂²×C₄	—	6	2	no	—
796	C₂²×C₄	—	6	2	no	—
797	C₂²×C₄	—	12	1	no	—
798	C₂²×C₄	—	12	1	no	—
799	C₂²×C₄	—	12	1	no	—
800	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
801	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
802	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
803	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
804	C₄⋊C₄	—	6	2	no	—
805	C₄⋊C₄	—	6	2	no	—
806	C₄⋊C₄	—	12	1	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	3	4	no	—
811	C₂²⋊C₄	—	3	4	no	—
812	C₂²⋊C₄	—	3	4	no	—
813	C₂²⋊C₄	—	3	4	no	—
814	C₂²⋊C₄	—	6	2	no	—
815	C₂²⋊C₄	—	6	2	no	—
816	C₂²⋊C₄	—	6	2	no	—
817	C₂²⋊C₄	—	6	2	no	—
818	C₂²⋊C₄	—	6	2	no	—
819	C₂²⋊C₄	—	12	1	no	—
820	C₂²⋊C₄	C₅×#67	1	4	yes	complemented
821	C₄²	—	6	2	no	—
822	C₄²	—	6	2	no	—
823	C₄²	—	12	1	no	—
824	C₃×C₅	#2358	1	1	yes	characteristic, complemented, Hall
825	C₂²×C₃	—	2	2	no	—
826	C₂²×C₃	—	2	2	no	—
827	C₂²×C₃	—	2	2	no	—
828	C₂²×C₃	—	2	2	no	—
829	C₂²×C₃	—	2	2	no	—
830	C₂²×C₃	—	2	2	no	—
831	C₂²×C₃	—	2	2	no	—
832	C₂²×C₃	—	2	2	no	—
833	C₂²×C₃	—	2	2	no	—
834	C₂²×C₃	—	2	2	no	—
835	C₂²×C₃	—	2	2	no	—
836	C₂²×C₃	—	2	2	no	—
837	C₂²×C₃	—	2	2	no	—
838	C₂²×C₃	—	2	2	no	—
839	C₂²×C₃	—	2	2	no	—
840	C₂²×C₃	—	4	16	no	—
841	C₂²×C₃	—	4	1	no	—
842	C₂²×C₃	—	4	1	no	—
843	C₂²×C₃	—	4	1	no	—
844	C₂²×C₃	—	4	1	no	—
845	C₂²×C₃	C₄×C₅×D₄	1	4	yes	complemented
846	C₂²×C₃	C₄×C₅×D₄	1	4	yes	complemented
847	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
848	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
849	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
850	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
851	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
852	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
853	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
854	C₂×D₃	—	2	2	no	—
855	C₂×D₃	—	2	2	no	—
856	C₂×D₃	—	2	2	no	—
857	C₂×D₃	—	4	1	no	—
858	C₂×D₃	—	4	1	no	—
859	C₂×D₃	—	4	1	no	—
860	C₂×D₃	—	4	1	no	—
861	C₃×C₄	—	2	2	no	—
862	C₃×C₄	—	2	2	no	—
863	C₃×C₄	—	4	1	no	—
864	C₃×C₄	—	4	1	no	—
865	Dic₃	—	2	2	no	—
866	Dic₃	—	2	2	no	—
867	Dic₃	—	2	2	no	—
868	Dic₃	—	2	2	no	—
869	Dic₃	—	2	2	no	—
870	Dic₃	—	4	1	no	—
871	Dic₃	—	4	1	no	—
872	C₂×C₅	—	2	4	no	—
873	C₂×C₅	—	2	4	no	—
874	C₂×C₅	—	4	2	no	—
875	C₂×C₅	—	12	2	no	—
876	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
877	C₂×C₅	#5486	1	1	yes	characteristic
878	C₂×C₅	#5490	1	1	yes	characteristic
879	C₂×C₅	#5495	1	1	yes	characteristic
880	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
881	C₂×C₅	D₄×#67	1	1	yes	characteristic
882	C₂×C₅	#5806	1	1	yes	characteristic
883	C₂³	—	2	1	no	—
884	C₂³	—	2	1	no	—
885	C₂³	—	2	1	no	—
886	C₂³	—	2	1	no	—
887	C₂³	—	2	1	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	1	no	—
890	C₂³	—	2	1	no	—
891	C₂³	—	2	8	no	—
892	C₂³	—	2	8	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	3	2	no	—
900	C₂³	—	4	4	no	—
901	C₂³	—	4	4	no	—
902	C₂³	—	4	4	no	—
903	C₂³	—	4	4	no	—
904	C₂³	—	4	4	no	—
905	C₂³	—	6	1	no	—
906	C₂³	—	6	1	no	—
907	C₂³	—	6	1	no	—
908	C₂³	—	6	1	no	—
909	C₂³	—	6	1	no	—
910	C₂³	—	6	1	no	—
911	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
912	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
913	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
914	C₂³	C₅×#235	1	2	yes	—
915	C₂³	C₅×D₃×D₄	1	2	yes	—
916	C₂³	C₅×#237	1	2	yes	—
917	C₂³	C₂×C₅×#67	1	2	yes	—
918	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
919	D₄	—	6	8	no	—
920	D₄	—	6	8	no	—
921	D₄	—	12	4	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	3	2	no	—
933	C₂×C₄	—	3	2	no	—
934	C₂×C₄	—	3	2	no	—
935	C₂×C₄	—	3	2	no	—
936	C₂×C₄	—	3	2	no	—
937	C₂×C₄	—	4	4	no	—
938	C₂×C₄	—	4	4	no	—
939	C₂×C₄	—	6	1	no	—
940	C₂×C₄	—	6	1	no	—
941	C₂×C₄	—	6	1	no	—
942	C₂×C₄	—	6	1	no	—
943	C₂×C₄	—	6	1	no	—
944	C₂×C₄	—	6	1	no	—
945	C₂×C₄	—	6	1	no	—
946	C₂×C₄	—	6	1	no	—
947	C₂×C₄	—	6	1	no	—
948	C₂×C₄	—	6	1	no	—
949	C₂×C₄	—	6	1	no	—
950	C₂×C₄	—	6	1	no	—
951	C₂×C₄	—	6	1	no	—
952	C₂×C₄	—	6	1	no	—
953	C₂×C₄	—	6	1	no	—
954	C₂×C₄	—	6	1	no	—
955	C₂×C₄	—	12	4	no	—
956	C₂×C₄	—	12	4	no	—
957	C₂×C₄	—	12	4	no	—
958	C₂×C₄	C₂×C₅×#67	1	2	yes	—
959	C₂×C₄	C₂×C₅×#67	1	2	yes	—
960	C₂×C₃	—	2	4	no	—
961	C₂×C₃	—	2	4	no	—
962	C₂×C₃	—	4	2	no	—
963	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
964	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
965	C₂×C₃	C₅×#518	1	1	yes	characteristic
966	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
967	C₂×C₃	C₅×#546	1	1	yes	characteristic
968	C₂×C₃	C₅×#546	1	1	yes	characteristic
969	C₂×C₃	C₅×#551	1	1	yes	characteristic
970	D₃	—	4	2	no	—
971	C₅	#82099	1	1	yes	characteristic, direct product factor, Sylow
972	C₂²	—	2	2	no	—
973	C₂²	—	2	2	no	—
974	C₂²	—	2	2	no	—
975	C₂²	—	2	2	no	—
976	C₂²	—	2	2	no	—
977	C₂²	—	2	2	no	—
978	C₂²	—	2	2	no	—
979	C₂²	—	2	2	no	—
980	C₂²	—	2	2	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	4	16	no	—
988	C₂²	—	4	1	no	—
989	C₂²	—	4	1	no	—
990	C₂²	—	4	1	no	—
991	C₂²	—	4	1	no	—
992	C₂²	—	6	2	no	—
993	C₂²	—	6	2	no	—
994	C₂²	—	6	2	no	—
995	C₂²	—	12	1	no	—
996	C₂²	—	12	1	no	—
997	C₂²	—	12	1	no	—
998	C₂²	—	12	1	no	—
999	C₂²	C₅×#67⋊C₄	1	4	yes	complemented
1000	C₂²	C₄×C₅×#67	1	4	yes	complemented
1001	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
1002	C₂²	C₂×C₅×#235	1	1	yes	characteristic
1003	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
1004	C₂²	C₂×C₅×#237	1	1	yes	characteristic
1005	C₂²	C₅×#1004	1	1	yes	characteristic
1006	C₂²	C₅×#1004	1	1	yes	characteristic
1007	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
1008	C₄	—	2	2	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	4	1	no	—
1011	C₄	—	4	1	no	—
1012	C₄	—	6	2	no	—
1013	C₄	—	6	2	no	—
1014	C₄	—	6	2	no	—
1015	C₄	—	6	2	no	—
1016	C₄	—	6	2	no	—
1017	C₄	—	12	1	no	—
1018	C₄	—	12	1	no	—
1019	C₃	C₅×#2358	1	1	yes	characteristic, complemented, Sylow
1020	C₂	—	2	4	no	—
1021	C₂	—	2	4	no	—
1022	C₂	—	4	2	no	—
1023	C₂	—	12	2	no	—
1024	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic
1025	C₂	C₅×#5486	1	1	yes	characteristic
1026	C₂	C₅×#5490	1	1	yes	characteristic
1027	C₂	C₅×#5495	1	1	yes	characteristic
1028	C₂	C₂×C₄×C₅×#67	1	1	yes	characteristic
1029	C₂	C₅×D₄×#67	1	1	yes	characteristic
1030	C₂	C₅×#5806	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×C₂²⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#953	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₂²×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₅×#2358
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₅×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
3. C₂²×C₅×#217	C₂	semidirect
4. C₂×C₄×C₅×#67	C₂	semidirect
5. C₂×C₅×#67⋊C₄	C₂	semidirect
6. C₅×#5213	C₂	semidirect
7. C₅×#5210	C₂	semidirect
8. C₄×C₅×#217	C₂	semidirect
9. C₅×#4958	C₂	semidirect
10. C₅×#4957	C₂	semidirect
11. C₅×#4956	C₂	semidirect
12. C₅×#4946	C₂	semidirect
13. C₅×#4945	C₂	semidirect
14. C₅×#4944	C₂	semidirect
15. C₅×Dic₃×C₂²⋊C₄	C₂	semidirect
25. C₂²×C₄×C₅×D₃	C₂²	semidirect
31. C₅×#953	C₄	semidirect
41. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
42. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
43. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
44. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
45. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
46. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
47. C₂×C₄×C₅×Dic₃	C₂²	semidirect
48. C₂×C₄×C₅×Dic₃	C₂²	semidirect
49. C₂×C₄×C₅×Dic₃	C₂²	semidirect
51. C₅×C₃⋊#95	C₂²	semidirect
52. C₅×C₃⋊#95	C₂²	semidirect
53. C₅×C₃⋊#95	C₂²	semidirect
54. C₅×C₃⋊#95	C₂²	semidirect
55. C₅×C₃⋊#95	C₂²	semidirect
56. C₅×C₃⋊#95	C₂²	semidirect
57. #82099	C₅	direct (N × H)
62. C₂²×C₅×C₂²⋊C₄	D₃	semidirect
79. C₂⁴×C₃×C₅	C₂×C₄	semidirect
100. C₂×C₅×#67	C₂×C₄	semidirect
101. C₂×C₅×#67	C₂×C₄	semidirect
102. C₂×C₅×#67	C₂×C₄	semidirect
122. C₃×C₅×C₂²⋊C₄	D₄	semidirect
126. C₅×#217	C₂×C₄	semidirect
127. C₅×#217	C₂×C₄	semidirect
128. C₅×#217	C₂×C₄	semidirect
129. C₅×#217	D₄	semidirect
139. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
141. C₂²×#217	C₂×C₅	semidirect
142. C₂×C₄×#67	C₂×C₅	semidirect
143. C₂×#67⋊C₄	C₂×C₅	semidirect
144. #5213	C₂×C₅	semidirect
145. #5210	C₂×C₅	semidirect
146. C₄×#217	C₂×C₅	semidirect
147. #4958	C₂×C₅	semidirect
148. #4957	C₂×C₅	semidirect
149. #4956	C₂×C₅	semidirect
150. #4946	C₂×C₅	semidirect
151. #4945	C₂×C₅	semidirect
152. #4944	C₂×C₅	semidirect
153. Dic₃×C₂²⋊C₄	C₂×C₅	semidirect
280. C₂²×C₄×D₃	C₂²×C₅	semidirect
286. #953	C₄×C₅	semidirect
296. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
297. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
298. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
299. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
300. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
301. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
302. C₂×C₄×Dic₃	C₂²×C₅	semidirect
303. C₂×C₄×Dic₃	C₂²×C₅	semidirect
304. C₂×C₄×Dic₃	C₂²×C₅	semidirect
306. C₃⋊#95	C₂²×C₅	semidirect
307. C₃⋊#95	C₂²×C₅	semidirect
308. C₃⋊#95	C₂²×C₅	semidirect
309. C₃⋊#95	C₂²×C₅	semidirect
310. C₃⋊#95	C₂²×C₅	semidirect
311. C₃⋊#95	C₂²×C₅	semidirect
319. C₂⁴×C₅	C₄×D₃	semidirect
374. C₅×C₂²⋊C₄	#67	semidirect
382. C₂²×C₂²⋊C₄	C₅×D₃	semidirect
413. C₂²×C₃×C₅	C₄×D₄	semidirect
414. C₂²×C₃×C₅	C₄×D₄	semidirect
446. C₂⁴×C₃	C₂×C₄×C₅	semidirect
467. C₂×#67	C₂×C₄×C₅	semidirect
468. C₂×#67	C₂×C₄×C₅	semidirect
469. C₂×#67	C₂×C₄×C₅	semidirect
489. C₃×C₂²⋊C₄	C₅×D₄	semidirect
493. #217	C₂×C₄×C₅	semidirect
494. #217	C₂×C₄×C₅	semidirect
495. #217	C₂×C₄×C₅	semidirect
496. #217	C₅×D₄	semidirect
738. C₂²×C₅	#67⋊C₄	semidirect
739. C₂²×C₅	C₄×#67	semidirect
765. C₂⁴	C₄×C₅×D₃	semidirect
820. C₂²⋊C₄	C₅×#67	semidirect
824. C₃×C₅	#2358	semidirect
845. C₂²×C₃	C₄×C₅×D₄	semidirect
846. C₂²×C₃	C₄×C₅×D₄	semidirect
971. C₅	#82099	direct (N × H)
999. C₂²	C₅×#67⋊C₄	semidirect
1000. C₂²	C₄×C₅×#67	semidirect
1019. C₃	C₅×#2358	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×C₂²⋊C₄	2
C₂×C₅×#953	2
C₂²×C₅×#217	2
C₂×C₄×C₅×#67	2
C₂×C₅×#67⋊C₄	2
C₅×#5213	2
C₅×#5210	2
C₄×C₅×#217	2
C₅×#4958	2
C₅×#4957	2
C₅×#4956	2
C₅×#4946	2
C₅×#4945	2
C₅×#4944	2
C₅×Dic₃×C₂²⋊C₄	2
C₅×#2358	3
#82099	5

Subgroups — C5×#82099 #14328101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82099 #14328101