Subgroups — C₅×#80087 #14424645

Order 1920.

1528 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1009	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#916	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#911	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5608	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5239	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5172	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5156	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5036	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4808	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4776	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×D₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4731	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4727	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3012	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₅×#1009	—	2	4	no	—
19	C₅×#1009	—	2	4	no	—
20	C₂×C₅×#239	C₂²	1	1	yes	characteristic
21	C₂×C₅×#239	C₂²	1	1	yes	characteristic
22	C₂×C₅×#237	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₅×D₃×D₄	—	2	1	no	—
24	C₂×C₅×D₃×D₄	—	2	1	no	—
25	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
26	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₅×#235	—	2	1	no	—
28	C₂×C₅×#235	C₂²	1	1	yes	characteristic
29	C₂²×C₅×D₁₂	—	2	1	no	—
30	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
35	C₅×#939	—	2	1	no	—
36	C₅×#938	—	2	1	no	—
37	C₅×#938	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
41	C₅×#924	C₂²	1	1	yes	characteristic, complemented
42	C₅×#916	—	2	4	no	—
43	C₅×#911	—	2	4	no	—
44	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
48	C₅×#897	C₂²	1	1	yes	characteristic, complemented
49	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₅×#884	—	2	1	no	—
51	C₅×#878	—	2	1	no	—
52	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	C₅×#835	C₂²	1	1	yes	characteristic, complemented
56	C₅×#832	C₂²	1	1	yes	characteristic, complemented
57	C₅×#830	C₂²	1	1	yes	characteristic, complemented
58	C₅×#821	C₂²	1	1	yes	characteristic, complemented
59	C₅×#821	C₂²	1	1	yes	characteristic, complemented
60	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	C₅×#809	C₂²	1	1	yes	characteristic, complemented
63	C₅×#809	C₂²	1	1	yes	characteristic, complemented
64	#80087	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
65	C₂×C₅×H(5,𝔽₂)	—	3	1	no	—
66	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
67	C₂×C₅×#135	—	3	1	no	—
68	C₅×#537	—	3	1	no	—
69	C₅×#452	—	3	1	no	—
70	C₅×#452	—	3	1	no	—
71	C₅×#450	—	3	1	no	—
72	C₅×#450	—	3	1	no	—
73	C₅×#449	—	3	1	no	—
74	C₅×#449	D₃	1	1	yes	characteristic, complemented
75	C₅×#447	—	3	1	no	—
76	C₅×#447	—	3	1	no	—
77	C₅×#417	—	3	1	no	—
78	C₂×C₅×#102	—	3	1	no	—
79	C₅×#408	—	3	1	no	—
80	C₂³×C₅×D₃	—	2	1	no	—
81	C₂³×C₅×D₃	—	2	1	no	—
82	C₂³×C₅×D₃	—	2	1	no	—
83	C₃×C₅×#41	—	2	2	no	—
84	C₃×C₅×#41	—	2	2	no	—
85	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	—	2	1	no	—
88	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄×C₅	—	2	1	no	—
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂×C₅×#67	—	2	1	no	—
93	C₂×C₅×#67	—	2	1	no	—
94	C₂×C₅×#67	—	2	1	no	—
95	C₂×C₅×#67	—	2	1	no	—
96	C₂×C₅×#67	D₄	1	1	yes	characteristic
97	C₂×C₅×#67	D₄	1	1	yes	characteristic
98	C₂²×C₅×Dic₃	—	2	1	no	—
99	C₅×#239	—	2	2	no	—
100	C₅×#239	—	2	2	no	—
101	C₅×#239	—	2	2	no	—
102	C₅×#239	D₄	1	4	yes	complemented
103	C₅×#237	—	2	2	no	—
104	C₅×#237	—	2	2	no	—
105	C₅×D₃×D₄	—	2	8	no	—
106	C₅×D₃×D₄	—	2	8	no	—
107	C₅×D₃×D₄	—	2	2	no	—
108	C₅×D₃×D₄	—	2	2	no	—
109	C₅×D₃×D₄	—	2	2	no	—
110	C₅×D₃×D₄	D₄	1	4	yes	complemented
111	C₅×#235	—	2	8	no	—
112	C₅×#235	—	2	2	no	—
113	C₅×#235	—	2	2	no	—
114	C₂×C₅×D₁₂	—	2	8	no	—
115	C₂×C₅×D₁₂	—	2	1	no	—
116	C₂×C₅×D₁₂	—	2	1	no	—
117	C₂×C₅×D₁₂	—	2	1	no	—
118	C₂×C₅×D₁₂	—	2	2	no	—
119	C₂×C₅×D₁₂	—	2	2	no	—
120	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
121	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
122	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
123	C₂×C₄×C₅×D₃	—	2	1	no	—
124	C₂×C₄×C₅×D₃	—	2	1	no	—
125	C₂×C₄×C₅×D₃	—	2	1	no	—
126	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
127	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
128	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
129	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
130	C₃×C₅×SD₁₆	—	2	2	no	—
131	C₃×C₅×D₈	—	2	2	no	—
132	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
134	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
136	C₅×#217	—	2	1	no	—
137	C₅×#217	—	2	1	no	—
138	C₅×#216	—	2	2	no	—
139	C₅×#214	—	2	2	no	—
140	C₅×#213	—	2	2	no	—
141	C₅×#213	—	2	2	no	—
142	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
143	C₅×C₄⋊Dic₃	—	2	1	no	—
144	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
145	C₅×Dic₃⋊C₄	—	2	1	no	—
146	C₅×Dic₃⋊C₄	—	2	1	no	—
147	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
148	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
149	C₅×#204	—	2	2	no	—
150	C₅×#204	—	2	2	no	—
151	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
152	C₅×D₃×C₈	—	2	2	no	—
153	C₂×#1009	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂×#916	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×#911	C₂×C₅	1	1	yes	characteristic, complemented
156	#5608	C₂×C₅	1	1	yes	characteristic, complemented
157	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
158	#5239	C₂×C₅	1	1	yes	characteristic, complemented
159	#5172	C₂×C₅	1	1	yes	characteristic, complemented
160	#5156	C₂×C₅	1	1	yes	characteristic, complemented
161	#5036	C₂×C₅	1	1	yes	characteristic, complemented
162	#4808	C₂×C₅	1	1	yes	characteristic, complemented
163	#4803	C₂×C₅	1	1	yes	characteristic, complemented
164	#4776	C₂×C₅	1	1	yes	characteristic, complemented
165	D₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
166	#4731	C₂×C₅	1	1	yes	characteristic, complemented
167	#4727	C₂×C₅	1	1	yes	characteristic, complemented
168	C₅×H(5,𝔽₂)	—	6	4	no	—
169	C₅×H(5,𝔽₂)	—	6	4	no	—
170	C₂×C₅×#41	—	3	1	no	—
171	C₂×C₅×#41	—	3	1	no	—
172	C₂×C₅×#41	—	3	1	no	—
173	C₂×C₅×#41	—	3	1	no	—
174	C₂×C₅×#41	—	6	1	no	—
175	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
176	C₂²×C₅×D₄	—	3	1	no	—
177	C₂²×C₅×D₄	—	3	1	no	—
178	C₂²×C₅×D₄	—	3	1	no	—
179	C₂²×C₅×D₄	—	6	1	no	—
180	C₂²×C₅×D₄	—	6	1	no	—
181	C₂²×C₅×D₄	—	6	1	no	—
182	C₅×AGL(1,ℤ/8)	—	6	4	no	—
183	C₅×#135	—	6	4	no	—
184	C₂×C₅×Q₁₆	—	3	1	no	—
185	C₂×C₅×SD₁₆	—	3	1	no	—
186	C₂×C₅×SD₁₆	—	3	1	no	—
187	C₂×C₅×SD₁₆	—	3	1	no	—
188	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
189	C₂×C₅×D₈	—	3	1	no	—
190	C₂×C₅×D₈	—	3	1	no	—
191	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
192	C₂×C₅×M₁₆	—	3	1	no	—
193	C₂²×C₅×C₈	—	3	1	no	—
194	C₅×C₂²⋊Q₈	—	3	1	no	—
195	C₅×C₂²⋊Q₈	—	3	1	no	—
196	C₅×C₂²⋊Q₈	—	6	1	no	—
197	C₅×#121	—	3	1	no	—
198	C₅×#121	—	6	1	no	—
199	C₅×#121	—	6	1	no	—
200	C₅×#121	—	6	1	no	—
201	C₅×#121	C₂×D₃	1	1	yes	characteristic, complemented
202	C₂×C₅×C₄⋊C₄	—	3	1	no	—
203	C₅×#103	—	3	1	no	—
204	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
205	C₅×#102	—	3	1	no	—
206	C₅×#102	—	3	1	no	—
207	C₅×#102	—	3	1	no	—
208	C₅×#102	—	3	1	no	—
209	C₅×#102	—	3	1	no	—
210	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
211	C₅×C₂²⋊C₈	—	3	1	no	—
212	C₅×C₂²⋊C₈	—	3	1	no	—
213	C₅×C₂²⋊C₈	—	3	1	no	—
214	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
215	#3012	—	3	1	no	Sylow
216	C₂³×C₃×C₅	—	2	1	no	—
217	C₂³×C₃×C₅	—	2	1	no	—
218	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₅×D₃	—	2	1	no	—
220	C₂²×C₅×D₃	—	2	1	no	—
221	C₂²×C₅×D₃	—	2	4	no	—
222	C₂²×C₅×D₃	—	2	4	no	—
223	C₂²×C₅×D₃	—	2	4	no	—
224	C₂²×C₅×D₃	—	8	1	no	—
225	C₂²×C₅×D₃	—	8	1	no	—
226	C₂²×C₅×D₃	—	8	1	no	—
227	C₂²×C₅×D₃	—	8	1	no	—
228	C₂²×C₅×D₃	—	8	1	no	—
229	C₂²×C₅×D₃	—	8	1	no	—
230	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
232	C₃×C₅×Q₈	—	2	1	no	—
233	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
234	C₃×C₅×D₄	—	2	4	no	—
235	C₃×C₅×D₄	—	2	1	no	—
236	C₃×C₅×D₄	—	2	1	no	—
237	C₃×C₅×D₄	—	2	1	no	—
238	C₃×C₅×D₄	—	8	1	no	—
239	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
240	C₂×C₃×C₄×C₅	—	2	4	no	—
241	C₂×C₃×C₄×C₅	—	2	1	no	—
242	C₂×C₃×C₄×C₅	—	2	1	no	—
243	C₂×C₃×C₄×C₅	—	2	1	no	—
244	C₂×C₃×C₄×C₅	—	2	1	no	—
245	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
246	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
247	C₅×#67	—	2	4	no	—
248	C₅×#67	—	2	2	no	—
249	C₅×#67	—	2	2	no	—
250	C₅×#67	—	2	4	no	—
251	C₅×#67	—	4	2	no	—
252	C₅×#67	—	8	1	no	—
253	C₂×C₅×Dic₃	—	2	1	no	—
254	C₂×C₅×Dic₃	—	2	1	no	—
255	C₂×C₅×Dic₃	—	4	2	no	—
256	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
257	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
258	C₅×D₁₂	—	2	4	no	—
259	C₅×D₁₂	—	2	4	no	—
260	C₅×D₁₂	—	2	2	no	—
261	C₅×D₁₂	—	2	4	no	—
262	C₅×D₁₂	—	2	1	no	—
263	C₅×D₁₂	—	2	1	no	—
264	C₅×D₁₂	C₂×D₄	1	2	yes	—
265	C₅×D₁₂	C₂×D₄	1	2	yes	—
266	C₄×C₅×D₃	—	2	4	no	—
267	C₄×C₅×D₃	—	2	1	no	—
268	C₄×C₅×D₃	—	2	1	no	—
269	C₄×C₅×D₃	—	2	4	no	—
270	C₄×C₅×D₃	—	8	1	no	—
271	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
272	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
273	C₅×Dic₆	—	2	2	no	—
274	C₅×Dic₆	—	2	1	no	—
275	C₅×Dic₆	—	2	1	no	—
276	C₃×C₅×C₈	—	2	1	no	—
277	C₃×C₅×C₈	—	2	1	no	—
278	C₅×C₃⋊C₈	—	2	1	no	—
279	C₅×C₃⋊C₈	—	2	1	no	—
280	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
281	#1009	—	2	4	no	—
282	#1009	—	2	4	no	—
283	C₂×#239	C₂²×C₅	1	1	yes	characteristic
284	C₂×#239	C₂²×C₅	1	1	yes	characteristic
285	C₂×#237	C₂²×C₅	1	1	yes	characteristic, complemented
286	C₂×D₃×D₄	—	2	1	no	—
287	C₂×D₃×D₄	—	2	1	no	—
288	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
289	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
290	C₂×#235	—	2	1	no	—
291	C₂×#235	C₂²×C₅	1	1	yes	characteristic
292	C₂²×D₁₂	—	2	1	no	—
293	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
294	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
295	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
296	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
297	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
298	#939	—	2	1	no	—
299	#938	—	2	1	no	—
300	#938	C₂²×C₅	1	1	yes	characteristic, complemented
301	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
302	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
303	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
304	#924	C₂²×C₅	1	1	yes	characteristic, complemented
305	#916	—	2	4	no	—
306	#911	—	2	4	no	—
307	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
308	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
309	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
310	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
311	#897	C₂²×C₅	1	1	yes	characteristic, complemented
312	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
313	#884	—	2	1	no	—
314	#878	—	2	1	no	—
315	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
316	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
317	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
318	#835	C₂²×C₅	1	1	yes	characteristic, complemented
319	#832	C₂²×C₅	1	1	yes	characteristic, complemented
320	#830	C₂²×C₅	1	1	yes	characteristic, complemented
321	#821	C₂²×C₅	1	1	yes	characteristic, complemented
322	#821	C₂²×C₅	1	1	yes	characteristic, complemented
323	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
324	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
325	#809	C₂²×C₅	1	1	yes	characteristic, complemented
326	#809	C₂²×C₅	1	1	yes	characteristic, complemented
327	C₂⁴×C₅	—	6	1	no	—
328	C₂⁴×C₅	—	6	1	no	—
329	C₂⁴×C₅	—	6	1	no	—
330	C₅×#41	—	2	2	no	—
331	C₅×#41	—	2	2	no	—
332	C₅×#41	—	3	4	no	—
333	C₅×#41	—	6	2	no	—
334	C₅×#41	—	6	2	no	—
335	C₅×#41	—	6	8	no	—
336	C₅×#41	—	6	2	no	—
337	C₅×#41	—	6	2	no	—
338	C₅×#41	—	6	2	no	—
339	C₅×#41	—	6	2	no	—
340	C₅×#41	—	6	2	no	—
341	C₂×C₅×Q₈	—	3	1	no	—
342	C₂×C₅×Q₈	—	3	1	no	—
343	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
344	C₂×C₅×D₄	—	2	1	no	—
345	C₂×C₅×D₄	—	2	1	no	—
346	C₂×C₅×D₄	—	3	4	no	—
347	C₂×C₅×D₄	—	3	1	no	—
348	C₂×C₅×D₄	—	3	1	no	—
349	C₂×C₅×D₄	—	3	1	no	—
350	C₂×C₅×D₄	—	3	1	no	—
351	C₂×C₅×D₄	—	3	1	no	—
352	C₂×C₅×D₄	—	6	2	no	—
353	C₂×C₅×D₄	—	6	2	no	—
354	C₂×C₅×D₄	—	6	1	no	—
355	C₂×C₅×D₄	—	6	1	no	—
356	C₂×C₅×D₄	—	6	8	no	—
357	C₂×C₅×D₄	—	6	2	no	—
358	C₂×C₅×D₄	—	6	1	no	—
359	C₂×C₅×D₄	—	6	1	no	—
360	C₂×C₅×D₄	—	6	2	no	—
361	C₂×C₅×D₄	—	6	8	no	—
362	C₂×C₅×D₄	—	6	8	no	—
363	C₂×C₅×D₄	—	6	2	no	—
364	C₂×C₅×D₄	—	6	1	no	—
365	C₂×C₅×D₄	—	6	1	no	—
366	C₂×C₅×D₄	—	6	1	no	—
367	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
368	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
369	C₂²×C₄×C₅	—	2	1	no	—
370	C₂²×C₄×C₅	—	3	1	no	—
371	C₂²×C₄×C₅	—	3	1	no	—
372	C₂²×C₄×C₅	—	6	1	no	—
373	C₂²×C₄×C₅	—	6	1	no	—
374	C₂²×C₄×C₅	—	6	1	no	—
375	C₂²×C₄×C₅	—	6	1	no	—
376	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
377	C₅×Q₁₆	—	6	2	no	—
378	C₅×SD₁₆	—	2	2	no	—
379	C₅×SD₁₆	—	6	2	no	—
380	C₅×SD₁₆	—	6	2	no	—
381	C₅×SD₁₆	—	6	2	no	—
382	C₅×D₈	—	2	2	no	—
383	C₅×D₈	—	6	2	no	—
384	C₅×D₈	—	6	2	no	—
385	C₅×M₁₆	—	6	2	no	—
386	C₂×C₅×C₈	—	3	1	no	—
387	C₂×C₅×C₈	—	3	1	no	—
388	C₂×C₅×C₈	—	6	2	no	—
389	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
390	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
391	C₅×C₄⋊C₄	—	3	1	no	—
392	C₅×C₄⋊C₄	—	6	1	no	—
393	C₅×C₄⋊C₄	—	6	1	no	—
394	C₅×C₄⋊C₄	—	6	1	no	—
395	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
396	C₅×C₂²⋊C₄	—	2	1	no	—
397	C₅×C₂²⋊C₄	—	6	1	no	—
398	C₅×C₂²⋊C₄	—	6	1	no	—
399	C₅×C₂²⋊C₄	—	6	1	no	—
400	C₂×H(5,𝔽₂)	—	3	1	no	—
401	C₂×AGL(1,ℤ/8)	—	3	1	no	—
402	C₂×#135	—	3	1	no	—
403	#537	—	3	1	no	—
404	#452	—	3	1	no	—
405	#452	—	3	1	no	—
406	#450	—	3	1	no	—
407	#450	—	3	1	no	—
408	#449	—	3	1	no	—
409	#449	C₅×D₃	1	1	yes	characteristic, complemented
410	#447	—	3	1	no	—
411	#447	—	3	1	no	—
412	#417	—	3	1	no	—
413	C₂×#102	—	3	1	no	—
414	#408	—	3	1	no	—
415	C₂²×C₃×C₅	—	2	1	no	—
416	C₂²×C₃×C₅	—	2	2	no	—
417	C₂²×C₃×C₅	—	2	1	no	—
418	C₂²×C₃×C₅	—	2	1	no	—
419	C₂²×C₃×C₅	—	4	1	no	—
420	C₂²×C₃×C₅	—	4	1	no	—
421	C₂²×C₃×C₅	—	4	1	no	—
422	C₂²×C₃×C₅	—	4	1	no	—
423	C₂²×C₃×C₅	—	4	1	no	—
424	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₅×D₃	—	2	1	no	—
426	C₂×C₅×D₃	—	2	1	no	—
427	C₂×C₅×D₃	—	2	1	no	—
428	C₂×C₅×D₃	—	2	2	no	—
429	C₂×C₅×D₃	—	2	2	no	—
430	C₂×C₅×D₃	—	2	1	no	—
431	C₂×C₅×D₃	—	2	1	no	—
432	C₂×C₅×D₃	—	4	1	no	—
433	C₂×C₅×D₃	—	4	1	no	—
434	C₂×C₅×D₃	—	4	1	no	—
435	C₂×C₅×D₃	—	4	1	no	—
436	C₂×C₅×D₃	—	8	4	no	—
437	C₂×C₅×D₃	—	8	4	no	—
438	C₂×C₅×D₃	—	8	4	no	—
439	C₂×C₅×D₃	#120	1	2	yes	—
440	C₃×C₄×C₅	—	2	1	no	—
441	C₃×C₄×C₅	—	2	2	no	—
442	C₃×C₄×C₅	—	4	1	no	—
443	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
444	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
445	C₅×Dic₃	—	2	1	no	—
446	C₅×Dic₃	—	4	1	no	—
447	C₅×Dic₃	—	4	1	no	—
448	C₅×Dic₃	#120	1	2	yes	—
449	C₂³×D₃	—	2	1	no	—
450	C₂³×D₃	—	2	1	no	—
451	C₂³×D₃	—	2	1	no	—
452	C₃×#41	—	2	2	no	—
453	C₃×#41	—	2	2	no	—
454	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
455	C₂×C₃×D₄	—	2	1	no	—
456	C₂×C₃×D₄	—	2	1	no	—
457	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
458	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
459	C₂²×C₃×C₄	—	2	1	no	—
460	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
461	C₂×#67	—	2	1	no	—
462	C₂×#67	—	2	1	no	—
463	C₂×#67	—	2	1	no	—
464	C₂×#67	—	2	1	no	—
465	C₂×#67	C₅×D₄	1	1	yes	characteristic
466	C₂×#67	C₅×D₄	1	1	yes	characteristic
467	C₂²×Dic₃	—	2	1	no	—
468	#239	—	2	2	no	—
469	#239	—	2	2	no	—
470	#239	—	2	2	no	—
471	#239	C₅×D₄	1	4	yes	complemented
472	#237	—	2	2	no	—
473	#237	—	2	2	no	—
474	D₃×D₄	—	2	8	no	—
475	D₃×D₄	—	2	8	no	—
476	D₃×D₄	—	2	2	no	—
477	D₃×D₄	—	2	2	no	—
478	D₃×D₄	—	2	2	no	—
479	D₃×D₄	C₅×D₄	1	4	yes	complemented
480	#235	—	2	8	no	—
481	#235	—	2	2	no	—
482	#235	—	2	2	no	—
483	C₂×D₁₂	—	2	8	no	—
484	C₂×D₁₂	—	2	1	no	—
485	C₂×D₁₂	—	2	1	no	—
486	C₂×D₁₂	—	2	1	no	—
487	C₂×D₁₂	—	2	2	no	—
488	C₂×D₁₂	—	2	2	no	—
489	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
490	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
491	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
492	C₂×C₄×D₃	—	2	1	no	—
493	C₂×C₄×D₃	—	2	1	no	—
494	C₂×C₄×D₃	—	2	1	no	—
495	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
496	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
497	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
498	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
499	C₃×SD₁₆	—	2	2	no	—
500	C₃×D₈	—	2	2	no	—
501	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
502	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
503	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
504	C₃×C₂²⋊C₄	—	2	1	no	—
505	#217	—	2	1	no	—
506	#217	—	2	1	no	—
507	#216	—	2	2	no	—
508	#214	—	2	2	no	—
509	#213	—	2	2	no	—
510	#213	—	2	2	no	—
511	(C₂×D₃)⋊C₄	—	2	1	no	—
512	C₄⋊Dic₃	—	2	1	no	—
513	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
514	Dic₃⋊C₄	—	2	1	no	—
515	Dic₃⋊C₄	—	2	1	no	—
516	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
517	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
518	#204	—	2	2	no	—
519	#204	—	2	2	no	—
520	ΓL(1,𝔽₂₅)	—	2	2	no	—
521	D₃×C₈	—	2	2	no	—
522	C₂³×C₅	—	2	1	no	—
523	C₂³×C₅	—	2	1	no	—
524	C₂³×C₅	—	3	1	no	—
525	C₂³×C₅	—	3	1	no	—
526	C₂³×C₅	—	6	4	no	—
527	C₂³×C₅	—	6	4	no	—
528	C₂³×C₅	—	6	4	no	—
529	C₂³×C₅	—	6	1	no	—
530	C₂³×C₅	—	6	1	no	—
531	C₂³×C₅	—	24	1	no	—
532	C₂³×C₅	—	24	1	no	—
533	C₂³×C₅	—	24	1	no	—
534	C₂³×C₅	—	24	1	no	—
535	C₂³×C₅	—	24	1	no	—
536	C₂³×C₅	—	24	1	no	—
537	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
538	C₅×Q₈	—	2	1	no	—
539	C₅×Q₈	—	6	2	no	—
540	C₅×Q₈	—	6	1	no	—
541	C₅×Q₈	—	6	1	no	—
542	C₅×Q₈	D₃×D₄	1	2	yes	—
543	C₅×D₄	—	2	4	no	—
544	C₅×D₄	—	2	1	no	—
545	C₅×D₄	—	2	1	no	—
546	C₅×D₄	—	2	1	no	—
547	C₅×D₄	—	3	2	no	—
548	C₅×D₄	—	3	2	no	—
549	C₅×D₄	—	6	2	no	—
550	C₅×D₄	—	6	4	no	—
551	C₅×D₄	—	6	4	no	—
552	C₅×D₄	—	6	4	no	—
553	C₅×D₄	—	6	2	no	—
554	C₅×D₄	—	6	4	no	—
555	C₅×D₄	—	6	2	no	—
556	C₅×D₄	—	6	4	no	—
557	C₅×D₄	—	6	1	no	—
558	C₅×D₄	—	6	1	no	—
559	C₅×D₄	—	8	1	no	—
560	C₅×D₄	—	12	2	no	—
561	C₅×D₄	—	24	1	no	—
562	C₅×D₄	D₃×D₄	1	2	yes	—
563	C₂×C₄×C₅	—	2	4	no	—
564	C₂×C₄×C₅	—	2	1	no	—
565	C₂×C₄×C₅	—	2	1	no	—
566	C₂×C₄×C₅	—	2	1	no	—
567	C₂×C₄×C₅	—	2	1	no	—
568	C₂×C₄×C₅	—	3	1	no	—
569	C₂×C₄×C₅	—	3	2	no	—
570	C₂×C₄×C₅	—	3	2	no	—
571	C₂×C₄×C₅	—	3	1	no	—
572	C₂×C₄×C₅	—	6	4	no	—
573	C₂×C₄×C₅	—	6	4	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	2	no	—
579	C₂×C₄×C₅	—	24	1	no	—
580	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
581	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
582	C₅×C₈	—	2	1	no	—
583	C₅×C₈	—	2	1	no	—
584	C₅×C₈	—	6	1	no	—
585	C₅×C₈	—	6	1	no	—
586	H(5,𝔽₂)	—	6	4	no	—
587	H(5,𝔽₂)	—	6	4	no	—
588	C₂×#41	—	3	1	no	—
589	C₂×#41	—	3	1	no	—
590	C₂×#41	—	3	1	no	—
591	C₂×#41	—	3	1	no	—
592	C₂×#41	—	6	1	no	—
593	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
594	C₂²×D₄	—	3	1	no	—
595	C₂²×D₄	—	3	1	no	—
596	C₂²×D₄	—	3	1	no	—
597	C₂²×D₄	—	6	1	no	—
598	C₂²×D₄	—	6	1	no	—
599	C₂²×D₄	—	6	1	no	—
600	AGL(1,ℤ/8)	—	6	4	no	—
601	#135	—	6	4	no	—
602	C₂×Q₁₆	—	3	1	no	—
603	C₂×SD₁₆	—	3	1	no	—
604	C₂×SD₁₆	—	3	1	no	—
605	C₂×SD₁₆	—	3	1	no	—
606	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
607	C₂×D₈	—	3	1	no	—
608	C₂×D₈	—	3	1	no	—
609	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
610	C₂×M₁₆	—	3	1	no	—
611	C₂²×C₈	—	3	1	no	—
612	C₂²⋊Q₈	—	3	1	no	—
613	C₂²⋊Q₈	—	3	1	no	—
614	C₂²⋊Q₈	—	6	1	no	—
615	#121	—	3	1	no	—
616	#121	—	6	1	no	—
617	#121	—	6	1	no	—
618	#121	—	6	1	no	—
619	#121	C₂×C₅×D₃	1	1	yes	characteristic, complemented
620	C₂×C₄⋊C₄	—	3	1	no	—
621	#103	—	3	1	no	—
622	#103	C₂×C₅×D₃	1	1	yes	characteristic, complemented
623	#102	—	3	1	no	—
624	#102	—	3	1	no	—
625	#102	—	3	1	no	—
626	#102	—	3	1	no	—
627	#102	—	3	1	no	—
628	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
629	C₂²⋊C₈	—	3	1	no	—
630	C₂²⋊C₈	—	3	1	no	—
631	C₂²⋊C₈	—	3	1	no	—
632	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
633	C₂×C₃×C₅	—	4	1	no	—
634	C₂×C₃×C₅	—	4	2	no	—
635	C₂×C₃×C₅	—	8	1	no	—
636	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
637	C₂×C₃×C₅	#576	1	1	yes	characteristic
638	C₂×C₃×C₅	#577	1	1	yes	characteristic
639	C₅×D₃	—	2	2	no	—
640	C₅×D₃	—	4	1	no	—
641	C₅×D₃	—	4	2	no	—
642	C₅×D₃	—	4	2	no	—
643	C₂³×C₃	—	2	1	no	—
644	C₂³×C₃	—	2	1	no	—
645	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
646	C₂²×D₃	—	2	1	no	—
647	C₂²×D₃	—	2	1	no	—
648	C₂²×D₃	—	2	4	no	—
649	C₂²×D₃	—	2	4	no	—
650	C₂²×D₃	—	2	4	no	—
651	C₂²×D₃	—	8	1	no	—
652	C₂²×D₃	—	8	1	no	—
653	C₂²×D₃	—	8	1	no	—
654	C₂²×D₃	—	8	1	no	—
655	C₂²×D₃	—	8	1	no	—
656	C₂²×D₃	—	8	1	no	—
657	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
658	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
659	C₃×Q₈	—	2	1	no	—
660	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
661	C₃×D₄	—	2	4	no	—
662	C₃×D₄	—	2	1	no	—
663	C₃×D₄	—	2	1	no	—
664	C₃×D₄	—	2	1	no	—
665	C₃×D₄	—	8	1	no	—
666	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
667	C₂×C₃×C₄	—	2	4	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	1	no	—
670	C₂×C₃×C₄	—	2	1	no	—
671	C₂×C₃×C₄	—	2	1	no	—
672	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
673	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
674	#67	—	2	4	no	—
675	#67	—	2	2	no	—
676	#67	—	2	2	no	—
677	#67	—	2	4	no	—
678	#67	—	4	2	no	—
679	#67	—	8	1	no	—
680	C₂×Dic₃	—	2	1	no	—
681	C₂×Dic₃	—	2	1	no	—
682	C₂×Dic₃	—	4	2	no	—
683	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
684	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
685	D₁₂	—	2	4	no	—
686	D₁₂	—	2	4	no	—
687	D₁₂	—	2	2	no	—
688	D₁₂	—	2	4	no	—
689	D₁₂	—	2	1	no	—
690	D₁₂	—	2	1	no	—
691	D₁₂	C₂×C₅×D₄	1	2	yes	—
692	D₁₂	C₂×C₅×D₄	1	2	yes	—
693	C₄×D₃	—	2	4	no	—
694	C₄×D₃	—	2	1	no	—
695	C₄×D₃	—	2	1	no	—
696	C₄×D₃	—	2	4	no	—
697	C₄×D₃	—	8	1	no	—
698	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
699	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
700	Dic₆	—	2	2	no	—
701	Dic₆	—	2	1	no	—
702	Dic₆	—	2	1	no	—
703	C₃×C₈	—	2	1	no	—
704	C₃×C₈	—	2	1	no	—
705	C₃⋊C₈	—	2	1	no	—
706	C₃⋊C₈	—	2	1	no	—
707	C₂²×C₅	—	2	1	no	—
708	C₂²×C₅	—	2	1	no	—
709	C₂²×C₅	—	2	1	no	—
710	C₂²×C₅	—	2	2	no	—
711	C₂²×C₅	—	3	2	no	—
712	C₂²×C₅	—	4	1	no	—
713	C₂²×C₅	—	4	1	no	—
714	C₂²×C₅	—	4	1	no	—
715	C₂²×C₅	—	4	1	no	—
716	C₂²×C₅	—	4	1	no	—
717	C₂²×C₅	—	6	1	no	—
718	C₂²×C₅	—	6	1	no	—
719	C₂²×C₅	—	6	1	no	—
720	C₂²×C₅	—	6	1	no	—
721	C₂²×C₅	—	6	2	no	—
722	C₂²×C₅	—	6	2	no	—
723	C₂²×C₅	—	6	1	no	—
724	C₂²×C₅	—	12	1	no	—
725	C₂²×C₅	—	12	1	no	—
726	C₂²×C₅	—	12	1	no	—
727	C₂²×C₅	—	12	1	no	—
728	C₂²×C₅	—	24	4	no	—
729	C₂²×C₅	—	24	4	no	—
730	C₂²×C₅	—	24	4	no	—
731	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
732	C₄×C₅	—	2	1	no	—
733	C₄×C₅	—	2	2	no	—
734	C₄×C₅	—	3	2	no	—
735	C₄×C₅	—	4	1	no	—
736	C₄×C₅	—	6	1	no	—
737	C₄×C₅	—	12	1	no	—
738	C₄×C₅	—	12	1	no	—
739	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
740	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
741	C₂⁴	—	6	1	no	—
742	C₂⁴	—	6	1	no	—
743	C₂⁴	—	6	1	no	—
744	#41	—	2	2	no	—
745	#41	—	2	2	no	—
746	#41	—	3	4	no	—
747	#41	—	6	2	no	—
748	#41	—	6	2	no	—
749	#41	—	6	8	no	—
750	#41	—	6	2	no	—
751	#41	—	6	2	no	—
752	#41	—	6	2	no	—
753	#41	—	6	2	no	—
754	#41	—	6	2	no	—
755	C₂×Q₈	—	3	1	no	—
756	C₂×Q₈	—	3	1	no	—
757	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
758	C₂×D₄	—	2	1	no	—
759	C₂×D₄	—	2	1	no	—
760	C₂×D₄	—	3	4	no	—
761	C₂×D₄	—	3	1	no	—
762	C₂×D₄	—	3	1	no	—
763	C₂×D₄	—	3	1	no	—
764	C₂×D₄	—	3	1	no	—
765	C₂×D₄	—	3	1	no	—
766	C₂×D₄	—	6	2	no	—
767	C₂×D₄	—	6	2	no	—
768	C₂×D₄	—	6	1	no	—
769	C₂×D₄	—	6	1	no	—
770	C₂×D₄	—	6	8	no	—
771	C₂×D₄	—	6	2	no	—
772	C₂×D₄	—	6	1	no	—
773	C₂×D₄	—	6	1	no	—
774	C₂×D₄	—	6	2	no	—
775	C₂×D₄	—	6	8	no	—
776	C₂×D₄	—	6	8	no	—
777	C₂×D₄	—	6	2	no	—
778	C₂×D₄	—	6	1	no	—
779	C₂×D₄	—	6	1	no	—
780	C₂×D₄	—	6	1	no	—
781	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
782	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
783	C₂²×C₄	—	2	1	no	—
784	C₂²×C₄	—	3	1	no	—
785	C₂²×C₄	—	3	1	no	—
786	C₂²×C₄	—	6	1	no	—
787	C₂²×C₄	—	6	1	no	—
788	C₂²×C₄	—	6	1	no	—
789	C₂²×C₄	—	6	1	no	—
790	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
791	Q₁₆	—	6	2	no	—
792	SD₁₆	—	2	2	no	—
793	SD₁₆	—	6	2	no	—
794	SD₁₆	—	6	2	no	—
795	SD₁₆	—	6	2	no	—
796	D₈	—	2	2	no	—
797	D₈	—	6	2	no	—
798	D₈	—	6	2	no	—
799	M₁₆	—	6	2	no	—
800	C₂×C₈	—	3	1	no	—
801	C₂×C₈	—	3	1	no	—
802	C₂×C₈	—	6	2	no	—
803	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
804	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
805	C₄⋊C₄	—	3	1	no	—
806	C₄⋊C₄	—	6	1	no	—
807	C₄⋊C₄	—	6	1	no	—
808	C₄⋊C₄	—	6	1	no	—
809	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
810	C₂²⋊C₄	—	2	1	no	—
811	C₂²⋊C₄	—	6	1	no	—
812	C₂²⋊C₄	—	6	1	no	—
813	C₂²⋊C₄	—	6	1	no	—
814	C₃×C₅	#3012	1	1	yes	characteristic, complemented, Hall
815	C₂²×C₃	—	2	1	no	—
816	C₂²×C₃	—	2	2	no	—
817	C₂²×C₃	—	2	1	no	—
818	C₂²×C₃	—	2	1	no	—
819	C₂²×C₃	—	4	1	no	—
820	C₂²×C₃	—	4	1	no	—
821	C₂²×C₃	—	4	1	no	—
822	C₂²×C₃	—	4	1	no	—
823	C₂²×C₃	—	4	1	no	—
824	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
825	C₂×D₃	—	2	1	no	—
826	C₂×D₃	—	2	1	no	—
827	C₂×D₃	—	2	1	no	—
828	C₂×D₃	—	2	2	no	—
829	C₂×D₃	—	2	2	no	—
830	C₂×D₃	—	2	1	no	—
831	C₂×D₃	—	2	1	no	—
832	C₂×D₃	—	4	1	no	—
833	C₂×D₃	—	4	1	no	—
834	C₂×D₃	—	4	1	no	—
835	C₂×D₃	—	4	1	no	—
836	C₂×D₃	—	8	4	no	—
837	C₂×D₃	—	8	4	no	—
838	C₂×D₃	—	8	4	no	—
839	C₂×D₃	C₅×#120	1	2	yes	—
840	C₃×C₄	—	2	1	no	—
841	C₃×C₄	—	2	2	no	—
842	C₃×C₄	—	4	1	no	—
843	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
844	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
845	Dic₃	—	2	1	no	—
846	Dic₃	—	4	1	no	—
847	Dic₃	—	4	1	no	—
848	Dic₃	C₅×#120	1	2	yes	—
849	C₂×C₅	—	4	1	no	—
850	C₂×C₅	—	4	2	no	—
851	C₂×C₅	—	6	2	no	—
852	C₂×C₅	—	8	1	no	—
853	C₂×C₅	—	12	1	no	—
854	C₂×C₅	—	12	2	no	—
855	C₂×C₅	—	12	2	no	—
856	C₂×C₅	D₃×#120	1	1	yes	characteristic
857	C₂×C₅	#5770	1	1	yes	characteristic
858	C₂×C₅	#5774	1	1	yes	characteristic
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	3	1	no	—
862	C₂³	—	3	1	no	—
863	C₂³	—	6	4	no	—
864	C₂³	—	6	4	no	—
865	C₂³	—	6	4	no	—
866	C₂³	—	6	1	no	—
867	C₂³	—	6	1	no	—
868	C₂³	—	24	1	no	—
869	C₂³	—	24	1	no	—
870	C₂³	—	24	1	no	—
871	C₂³	—	24	1	no	—
872	C₂³	—	24	1	no	—
873	C₂³	—	24	1	no	—
874	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
875	Q₈	—	2	1	no	—
876	Q₈	—	6	2	no	—
877	Q₈	—	6	1	no	—
878	Q₈	—	6	1	no	—
879	Q₈	C₅×D₃×D₄	1	2	yes	—
880	D₄	—	2	4	no	—
881	D₄	—	2	1	no	—
882	D₄	—	2	1	no	—
883	D₄	—	2	1	no	—
884	D₄	—	3	2	no	—
885	D₄	—	3	2	no	—
886	D₄	—	6	2	no	—
887	D₄	—	6	4	no	—
888	D₄	—	6	4	no	—
889	D₄	—	6	4	no	—
890	D₄	—	6	2	no	—
891	D₄	—	6	4	no	—
892	D₄	—	6	2	no	—
893	D₄	—	6	4	no	—
894	D₄	—	6	1	no	—
895	D₄	—	6	1	no	—
896	D₄	—	8	1	no	—
897	D₄	—	12	2	no	—
898	D₄	—	24	1	no	—
899	D₄	C₅×D₃×D₄	1	2	yes	—
900	C₂×C₄	—	2	4	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	3	1	no	—
906	C₂×C₄	—	3	2	no	—
907	C₂×C₄	—	3	2	no	—
908	C₂×C₄	—	3	1	no	—
909	C₂×C₄	—	6	4	no	—
910	C₂×C₄	—	6	4	no	—
911	C₂×C₄	—	6	1	no	—
912	C₂×C₄	—	6	1	no	—
913	C₂×C₄	—	6	1	no	—
914	C₂×C₄	—	6	1	no	—
915	C₂×C₄	—	12	2	no	—
916	C₂×C₄	—	24	1	no	—
917	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
918	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
919	C₈	—	2	1	no	—
920	C₈	—	2	1	no	—
921	C₈	—	6	1	no	—
922	C₈	—	6	1	no	—
923	C₂×C₃	—	4	1	no	—
924	C₂×C₃	—	4	2	no	—
925	C₂×C₃	—	8	1	no	—
926	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
927	C₂×C₃	C₅×#576	1	1	yes	characteristic
928	C₂×C₃	C₅×#577	1	1	yes	characteristic
929	D₃	—	2	2	no	—
930	D₃	—	4	1	no	—
931	D₃	—	4	2	no	—
932	D₃	—	4	2	no	—
933	C₅	#80087	1	1	yes	characteristic, direct product factor, Sylow
934	C₂²	—	2	1	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	1	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	3	2	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	6	1	no	—
945	C₂²	—	6	1	no	—
946	C₂²	—	6	1	no	—
947	C₂²	—	6	1	no	—
948	C₂²	—	6	2	no	—
949	C₂²	—	6	2	no	—
950	C₂²	—	6	1	no	—
951	C₂²	—	12	1	no	—
952	C₂²	—	12	1	no	—
953	C₂²	—	12	1	no	—
954	C₂²	—	12	1	no	—
955	C₂²	—	24	4	no	—
956	C₂²	—	24	4	no	—
957	C₂²	—	24	4	no	—
958	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
959	C₄	—	2	1	no	—
960	C₄	—	2	2	no	—
961	C₄	—	3	2	no	—
962	C₄	—	4	1	no	—
963	C₄	—	6	1	no	—
964	C₄	—	12	1	no	—
965	C₄	—	12	1	no	—
966	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
967	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
968	C₃	C₅×#3012	1	1	yes	characteristic, complemented, Sylow
969	C₂	—	4	1	no	—
970	C₂	—	4	2	no	—
971	C₂	—	6	2	no	—
972	C₂	—	8	1	no	—
973	C₂	—	12	1	no	—
974	C₂	—	12	2	no	—
975	C₂	—	12	2	no	—
976	C₂	C₅×D₃×#120	1	1	yes	characteristic
977	C₂	C₅×#5770	1	1	yes	characteristic
978	C₂	C₅×#5774	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#449	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#449	D₃
hypocenter	C₃	C₅×#3012
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#449

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#1009	C₂	semidirect
2. C₂×C₅×#916	C₂	semidirect
3. C₂×C₅×#911	C₂	semidirect
4. C₅×#5608	C₂	semidirect
5. C₃×C₅×#449	C₂	semidirect
6. C₅×#5239	C₂	semidirect
7. C₅×#5172	C₂	semidirect
8. C₅×#5156	C₂	semidirect
9. C₅×#5036	C₂	semidirect
10. C₅×#4808	C₂	semidirect
11. C₅×#4803	C₂	semidirect
12. C₅×#4776	C₂	semidirect
13. C₅×D₃×#102	C₂	semidirect
14. C₅×#4731	C₂	semidirect
15. C₅×#4727	C₂	semidirect
22. C₂×C₅×#237	C₂²	semidirect
31. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
32. C₂×C₃×C₅×D₈	C₂²	semidirect
33. C₃×C₅×#121	C₂²	semidirect
34. C₂×C₅×#216	C₂²	semidirect
37. C₅×#938	C₂²	semidirect
38. C₂×C₅×#214	C₂²	semidirect
39. C₂×C₅×#213	C₂²	semidirect
40. C₂×C₅×#213	C₂²	semidirect
41. C₅×#924	C₂²	semidirect
44. C₂×C₅×#204	C₂²	semidirect
45. C₂×C₅×#204	C₂²	semidirect
46. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
47. C₂×C₅×D₃×C₈	C₂²	semidirect
48. C₅×#897	C₂²	semidirect
49. C₅×D₃×C₄⋊C₄	C₂²	semidirect
52. C₃×C₅×#103	C₂²	semidirect
53. C₃×C₅×#102	C₂²	semidirect
54. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
55. C₅×#835	C₂²	semidirect
56. C₅×#832	C₂²	semidirect
57. C₅×#830	C₂²	semidirect
58. C₅×#821	C₂²	semidirect
59. C₅×#821	C₂²	semidirect
60. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
61. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
62. C₅×#809	C₂²	semidirect
63. C₅×#809	C₂²	semidirect
64. #80087	C₅	direct (N × H)
74. C₅×#449	D₃	semidirect
102. C₅×#239	D₄	semidirect
110. C₅×D₃×D₄	D₄	semidirect
153. C₂×#1009	C₂×C₅	semidirect
154. C₂×#916	C₂×C₅	semidirect
155. C₂×#911	C₂×C₅	semidirect
156. #5608	C₂×C₅	semidirect
157. C₃×#449	C₂×C₅	semidirect
158. #5239	C₂×C₅	semidirect
159. #5172	C₂×C₅	semidirect
160. #5156	C₂×C₅	semidirect
161. #5036	C₂×C₅	semidirect
162. #4808	C₂×C₅	semidirect
163. #4803	C₂×C₅	semidirect
164. #4776	C₂×C₅	semidirect
165. D₃×#102	C₂×C₅	semidirect
166. #4731	C₂×C₅	semidirect
167. #4727	C₂×C₅	semidirect
188. C₂×C₅×SD₁₆	C₂×D₃	semidirect
191. C₂×C₅×D₈	C₂×D₃	semidirect
201. C₅×#121	C₂×D₃	semidirect
204. C₅×#103	C₂×D₃	semidirect
210. C₅×#102	C₂×D₃	semidirect
214. C₅×C₂²⋊C₈	C₂×D₃	semidirect
285. C₂×#237	C₂²×C₅	semidirect
294. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
295. C₂×C₃×D₈	C₂²×C₅	semidirect
296. C₃×#121	C₂²×C₅	semidirect
297. C₂×#216	C₂²×C₅	semidirect
300. #938	C₂²×C₅	semidirect
301. C₂×#214	C₂²×C₅	semidirect
302. C₂×#213	C₂²×C₅	semidirect
303. C₂×#213	C₂²×C₅	semidirect
304. #924	C₂²×C₅	semidirect
307. C₂×#204	C₂²×C₅	semidirect
308. C₂×#204	C₂²×C₅	semidirect
309. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
310. C₂×D₃×C₈	C₂²×C₅	semidirect
311. #897	C₂²×C₅	semidirect
312. D₃×C₄⋊C₄	C₂²×C₅	semidirect
315. C₃×#103	C₂²×C₅	semidirect
316. C₃×#102	C₂²×C₅	semidirect
317. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
318. #835	C₂²×C₅	semidirect
319. #832	C₂²×C₅	semidirect
320. #830	C₂²×C₅	semidirect
321. #821	C₂²×C₅	semidirect
322. #821	C₂²×C₅	semidirect
323. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
324. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
325. #809	C₂²×C₅	semidirect
326. #809	C₂²×C₅	semidirect
409. #449	C₅×D₃	semidirect
471. #239	C₅×D₄	semidirect
479. D₃×D₄	C₅×D₄	semidirect
606. C₂×SD₁₆	C₂×C₅×D₃	semidirect
609. C₂×D₈	C₂×C₅×D₃	semidirect
619. #121	C₂×C₅×D₃	semidirect
622. #103	C₂×C₅×D₃	semidirect
628. #102	C₂×C₅×D₃	semidirect
632. C₂²⋊C₈	C₂×C₅×D₃	semidirect
814. C₃×C₅	#3012	semidirect
933. C₅	#80087	direct (N × H)
968. C₃	C₅×#3012	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#1009	2
C₂×C₅×#916	2
C₂×C₅×#911	2
C₅×#5608	2
C₃×C₅×#449	2
C₅×#5239	2
C₅×#5172	2
C₅×#5156	2
C₅×#5036	2
C₅×#4808	2
C₅×#4803	2
C₅×#4776	2
C₅×D₃×#102	2
C₅×#4731	2
C₅×#4727	2
C₅×#3012	3
#80087	5

Subgroups — C5×#80087 #14424645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80087 #14424645