Subgroups — C₅×#80041 #14424414

Order 1920.

1464 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1007	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#914	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5607	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#448	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5227	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5172	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5170	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5037	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4810	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4806	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4804	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4802	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4734	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4727	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3010	—	3	1	no	maximal, Hall
17	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₅×#1007	—	2	4	no	—
19	C₅×#1007	—	2	4	no	—
20	C₂×C₅×#239	—	2	1	no	—
21	C₂×C₅×#239	C₂²	1	1	yes	characteristic
22	C₂×C₅×#239	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₅×D₃×Q₈	—	2	1	no	—
24	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₅×#235	—	2	1	no	—
28	C₂×C₅×#235	—	2	1	no	—
29	C₂×C₅×#235	C₂²	1	1	yes	characteristic
30	C₂×C₅×#235	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
33	C₃×C₅×#121	C₂²	1	1	yes	characteristic
34	C₂×C₅×#215	C₂²	1	1	yes	characteristic
35	C₂×C₅×#215	C₂²	1	1	yes	characteristic
36	C₅×#940	—	2	1	no	—
37	C₅×#938	C₂²	1	1	yes	characteristic
38	C₅×#937	—	2	1	no	—
39	C₂×C₅×#214	C₂²	1	1	yes	characteristic
40	C₂×C₅×#213	C₂²	1	1	yes	characteristic
41	C₅×#930	C₂²	1	1	yes	characteristic
42	C₅×#914	—	2	4	no	—
43	C₅×D₃×SD₁₆	—	2	4	no	—
44	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
45	C₂×C₅×#204	C₂²	1	1	yes	characteristic
46	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
47	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
48	C₅×#895	C₂²	1	1	yes	characteristic
49	C₅×#892	C₂²	1	1	yes	characteristic
50	C₅×#885	—	2	1	no	—
51	C₅×#882	—	2	1	no	—
52	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#103	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×#835	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×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₅×#816	C₂²	1	1	yes	characteristic, complemented
62	C₅×#810	C₂²	1	1	yes	characteristic, complemented
63	C₅×#809	C₂²	1	1	yes	characteristic, complemented
64	#80041	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
65	C₂×C₅×2₋¹⁺⁴	—	3	1	no	—
66	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
67	C₂²×C₅×SD₁₆	—	3	1	no	—
68	C₅×#535	—	3	1	no	—
69	C₅×#449	—	3	1	no	—
70	C₅×#449	—	3	1	no	—
71	C₅×#449	—	3	1	no	—
72	C₅×#449	—	3	1	no	—
73	C₅×#448	—	3	1	no	—
74	C₅×#448	—	3	1	no	—
75	C₅×#448	—	3	1	no	—
76	C₅×#448	D₃	1	1	yes	characteristic, complemented
77	C₅×#419	—	3	1	no	—
78	C₅×#416	—	3	1	no	—
79	C₅×#408	—	3	1	no	—
80	C₂³×C₅×D₃	—	2	1	no	—
81	C₂×C₃×C₅×Q₈	—	2	2	no	—
82	C₂×C₃×C₅×Q₈	—	2	2	no	—
83	C₂×C₃×C₅×Q₈	—	2	1	no	—
84	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	—	2	1	no	—
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₅×#67	—	2	1	no	—
91	C₂×C₅×#67	—	2	1	no	—
92	C₂×C₅×#67	—	2	1	no	—
93	C₂×C₅×#67	—	2	1	no	—
94	C₂×C₅×#67	D₄	1	1	yes	characteristic
95	C₂×C₅×#67	D₄	1	1	yes	characteristic
96	C₅×#239	—	2	8	no	—
97	C₅×#239	—	2	2	no	—
98	C₅×#239	—	2	2	no	—
99	C₅×#239	—	2	2	no	—
100	C₅×#239	D₄	1	4	yes	complemented
101	C₅×D₃×Q₈	—	2	8	no	—
102	C₅×D₃×Q₈	—	2	2	no	—
103	C₅×D₃×Q₈	—	2	2	no	—
104	C₅×D₃×Q₈	—	2	2	no	—
105	C₅×D₃×Q₈	D₄	1	4	yes	complemented
106	C₅×D₃×D₄	—	2	2	no	—
107	C₅×D₃×D₄	—	2	2	no	—
108	C₅×#235	—	2	8	no	—
109	C₅×#235	—	2	8	no	—
110	C₅×#235	—	2	2	no	—
111	C₅×#235	—	2	2	no	—
112	C₅×#235	—	2	2	no	—
113	C₅×#235	—	2	2	no	—
114	C₂×C₅×D₁₂	—	2	1	no	—
115	C₂×C₅×D₁₂	—	2	1	no	—
116	C₂×C₅×D₁₂	—	2	1	no	—
117	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
118	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
119	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
120	C₂×C₄×C₅×D₃	—	2	1	no	—
121	C₂×C₄×C₅×D₃	—	2	1	no	—
122	C₂×C₄×C₅×D₃	—	2	1	no	—
123	C₂×C₄×C₅×D₃	—	2	1	no	—
124	C₂×C₄×C₅×D₃	—	2	1	no	—
125	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
126	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
127	C₂×C₅×Dic₆	—	2	1	no	—
128	C₂×C₅×Dic₆	—	2	1	no	—
129	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
130	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
131	C₃×C₅×SD₁₆	—	2	2	no	—
132	C₃×C₅×SD₁₆	—	2	2	no	—
133	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
134	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
135	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
137	C₅×#217	—	2	1	no	—
138	C₅×#215	—	2	2	no	—
139	C₅×#215	—	2	2	no	—
140	C₅×#214	—	2	2	no	—
141	C₅×#213	—	2	2	no	—
142	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
143	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
144	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
145	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
146	C₄×C₅×Dic₃	—	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×D₂₄	—	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×#1007	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂×#914	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×D₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
156	#5607	C₂×C₅	1	1	yes	characteristic, complemented
157	C₃×#448	C₂×C₅	1	1	yes	characteristic, complemented
158	#5227	C₂×C₅	1	1	yes	characteristic, complemented
159	#5172	C₂×C₅	1	1	yes	characteristic, complemented
160	#5170	C₂×C₅	1	1	yes	characteristic, complemented
161	#5037	C₂×C₅	1	1	yes	characteristic, complemented
162	#4810	C₂×C₅	1	1	yes	characteristic, complemented
163	#4806	C₂×C₅	1	1	yes	characteristic, complemented
164	#4804	C₂×C₅	1	1	yes	characteristic, complemented
165	#4802	C₂×C₅	1	1	yes	characteristic, complemented
166	#4734	C₂×C₅	1	1	yes	characteristic, complemented
167	#4727	C₂×C₅	1	1	yes	characteristic, complemented
168	C₅×2₋¹⁺⁴	—	6	4	no	—
169	C₅×2₋¹⁺⁴	—	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	—	6	1	no	—
176	C₂×C₅×#41	—	6	1	no	—
177	C₂²×C₅×Q₈	—	3	1	no	—
178	C₂²×C₅×Q₈	—	3	1	no	—
179	C₂²×C₅×Q₈	—	6	1	no	—
180	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
181	C₂²×C₅×D₄	—	3	1	no	—
182	C₅×AGL(1,ℤ/8)	—	6	4	no	—
183	C₂×C₅×SD₁₆	—	3	1	no	—
184	C₂×C₅×SD₁₆	—	3	1	no	—
185	C₂×C₅×SD₁₆	—	3	1	no	—
186	C₂×C₅×SD₁₆	—	3	1	no	—
187	C₂×C₅×SD₁₆	—	6	4	no	—
188	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
189	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
190	C₂×C₅×D₈	—	3	1	no	—
191	C₂×C₅×D₈	—	3	1	no	—
192	C₂×C₅×M₁₆	—	3	1	no	—
193	C₂²×C₅×C₈	—	3	1	no	—
194	C₅×#127	—	6	1	no	—
195	C₅×#124	—	6	1	no	—
196	C₅×#121	—	3	1	no	—
197	C₅×#121	—	3	1	no	—
198	C₅×#121	—	3	1	no	—
199	C₅×#121	C₂×D₃	1	1	yes	characteristic
200	C₅×#120	—	6	1	no	—
201	C₅×#120	—	6	1	no	—
202	C₅×#117	—	3	1	no	—
203	C₅×#103	—	3	1	no	—
204	C₅×#103	—	3	1	no	—
205	C₅×#103	—	3	1	no	—
206	C₅×#103	—	3	1	no	—
207	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
208	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
209	C₅×#102	—	3	1	no	—
210	C₅×#102	—	3	1	no	—
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	#3010	—	3	1	no	Sylow
216	C₂³×C₃×C₅	—	2	1	no	—
217	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₅×D₃	—	2	1	no	—
219	C₂²×C₅×D₃	—	2	1	no	—
220	C₂²×C₅×D₃	—	4	2	no	—
221	C₂²×C₅×D₃	—	8	1	no	—
222	C₂²×C₅×D₃	—	8	1	no	—
223	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
225	C₃×C₅×Q₈	—	2	4	no	—
226	C₃×C₅×Q₈	—	2	1	no	—
227	C₃×C₅×Q₈	—	2	1	no	—
228	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
229	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
230	C₃×C₅×D₄	—	2	1	no	—
231	C₃×C₅×D₄	—	2	1	no	—
232	C₃×C₅×D₄	—	8	1	no	—
233	C₂×C₃×C₄×C₅	—	2	4	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	C₂×D₄	1	1	yes	characteristic
240	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
241	C₅×#67	—	2	4	no	—
242	C₅×#67	—	2	2	no	—
243	C₅×#67	—	2	2	no	—
244	C₅×#67	—	4	2	no	—
245	C₅×#67	—	8	1	no	—
246	C₅×#67	—	8	1	no	—
247	C₂×C₅×Dic₃	—	2	1	no	—
248	C₂×C₅×Dic₃	—	2	1	no	—
249	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
250	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
251	C₅×D₁₂	—	2	4	no	—
252	C₅×D₁₂	—	2	4	no	—
253	C₅×D₁₂	—	2	2	no	—
254	C₅×D₁₂	—	2	1	no	—
255	C₅×D₁₂	—	2	1	no	—
256	C₅×D₁₂	—	2	1	no	—
257	C₅×D₁₂	—	8	1	no	—
258	C₅×D₁₂	C₂×D₄	1	2	yes	—
259	C₄×C₅×D₃	—	2	4	no	—
260	C₄×C₅×D₃	—	2	4	no	—
261	C₄×C₅×D₃	—	2	4	no	—
262	C₄×C₅×D₃	—	2	4	no	—
263	C₄×C₅×D₃	—	2	1	no	—
264	C₄×C₅×D₃	—	2	1	no	—
265	C₄×C₅×D₃	—	2	4	no	—
266	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
267	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
268	C₅×Dic₆	—	2	4	no	—
269	C₅×Dic₆	—	2	1	no	—
270	C₅×Dic₆	—	2	4	no	—
271	C₅×Dic₆	—	2	2	no	—
272	C₅×Dic₆	C₂×D₄	1	2	yes	—
273	C₃×C₅×C₈	—	2	1	no	—
274	C₃×C₅×C₈	—	2	1	no	—
275	C₅×C₃⋊C₈	—	2	1	no	—
276	C₅×C₃⋊C₈	—	2	1	no	—
277	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
278	#1007	—	2	4	no	—
279	#1007	—	2	4	no	—
280	C₂×#239	—	2	1	no	—
281	C₂×#239	C₂²×C₅	1	1	yes	characteristic
282	C₂×#239	C₂²×C₅	1	1	yes	characteristic, complemented
283	C₂×D₃×Q₈	—	2	1	no	—
284	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
285	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
286	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
287	C₂×#235	—	2	1	no	—
288	C₂×#235	—	2	1	no	—
289	C₂×#235	C₂²×C₅	1	1	yes	characteristic
290	C₂×#235	C₂²×C₅	1	1	yes	characteristic, complemented
291	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
292	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
293	C₃×#121	C₂²×C₅	1	1	yes	characteristic
294	C₂×#215	C₂²×C₅	1	1	yes	characteristic
295	C₂×#215	C₂²×C₅	1	1	yes	characteristic
296	#940	—	2	1	no	—
297	#938	C₂²×C₅	1	1	yes	characteristic
298	#937	—	2	1	no	—
299	C₂×#214	C₂²×C₅	1	1	yes	characteristic
300	C₂×#213	C₂²×C₅	1	1	yes	characteristic
301	#930	C₂²×C₅	1	1	yes	characteristic
302	#914	—	2	4	no	—
303	D₃×SD₁₆	—	2	4	no	—
304	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
305	C₂×#204	C₂²×C₅	1	1	yes	characteristic
306	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
307	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
308	#895	C₂²×C₅	1	1	yes	characteristic
309	#892	C₂²×C₅	1	1	yes	characteristic
310	#885	—	2	1	no	—
311	#882	—	2	1	no	—
312	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
313	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
314	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
315	#835	C₂²×C₅	1	1	yes	characteristic, complemented
316	#835	C₂²×C₅	1	1	yes	characteristic, complemented
317	#830	C₂²×C₅	1	1	yes	characteristic, complemented
318	#821	C₂²×C₅	1	1	yes	characteristic, complemented
319	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
320	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
321	#816	C₂²×C₅	1	1	yes	characteristic, complemented
322	#810	C₂²×C₅	1	1	yes	characteristic, complemented
323	#809	C₂²×C₅	1	1	yes	characteristic, complemented
324	C₂⁴×C₅	—	6	1	no	—
325	C₅×#41	—	3	4	no	—
326	C₅×#41	—	6	2	no	—
327	C₅×#41	—	6	2	no	—
328	C₅×#41	—	6	2	no	—
329	C₅×#41	—	6	2	no	—
330	C₅×#41	—	6	8	no	—
331	C₅×#41	—	6	8	no	—
332	C₅×#41	—	6	2	no	—
333	C₅×#41	—	6	2	no	—
334	C₅×#41	—	6	8	no	—
335	C₅×#41	—	6	2	no	—
336	C₂×C₅×Q₈	—	2	2	no	—
337	C₂×C₅×Q₈	—	2	2	no	—
338	C₂×C₅×Q₈	—	2	1	no	—
339	C₂×C₅×Q₈	—	3	1	no	—
340	C₂×C₅×Q₈	—	3	4	no	—
341	C₂×C₅×Q₈	—	3	1	no	—
342	C₂×C₅×Q₈	—	6	1	no	—
343	C₂×C₅×Q₈	—	6	1	no	—
344	C₂×C₅×Q₈	—	6	2	no	—
345	C₂×C₅×Q₈	—	6	2	no	—
346	C₂×C₅×Q₈	—	6	8	no	—
347	C₂×C₅×Q₈	—	6	2	no	—
348	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
349	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
350	C₂×C₅×D₄	—	2	1	no	—
351	C₂×C₅×D₄	—	3	1	no	—
352	C₂×C₅×D₄	—	3	1	no	—
353	C₂×C₅×D₄	—	3	1	no	—
354	C₂×C₅×D₄	—	3	1	no	—
355	C₂×C₅×D₄	—	3	1	no	—
356	C₂×C₅×D₄	—	6	1	no	—
357	C₂×C₅×D₄	—	6	1	no	—
358	C₂×C₅×D₄	—	6	1	no	—
359	C₂×C₅×D₄	—	6	2	no	—
360	C₂×C₅×D₄	—	6	2	no	—
361	C₂×C₅×D₄	—	6	1	no	—
362	C₂×C₅×D₄	—	6	1	no	—
363	C₂×C₅×D₄	—	6	1	no	—
364	C₂×C₅×D₄	—	6	1	no	—
365	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
366	C₂²×C₄×C₅	—	2	1	no	—
367	C₂²×C₄×C₅	—	3	1	no	—
368	C₂²×C₄×C₅	—	3	1	no	—
369	C₂²×C₄×C₅	—	6	1	no	—
370	C₂²×C₄×C₅	—	6	1	no	—
371	C₂²×C₄×C₅	—	6	1	no	—
372	C₂²×C₄×C₅	—	6	1	no	—
373	C₂²×C₄×C₅	—	6	1	no	—
374	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
375	C₅×SD₁₆	—	2	2	no	—
376	C₅×SD₁₆	—	2	2	no	—
377	C₅×SD₁₆	—	6	2	no	—
378	C₅×SD₁₆	—	6	2	no	—
379	C₅×SD₁₆	—	6	2	no	—
380	C₅×SD₁₆	—	6	2	no	—
381	C₅×D₈	—	6	2	no	—
382	C₅×D₈	—	6	2	no	—
383	C₅×M₁₆	—	6	2	no	—
384	C₂×C₅×C₈	—	3	1	no	—
385	C₂×C₅×C₈	—	3	1	no	—
386	C₂×C₅×C₈	—	6	2	no	—
387	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
388	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
389	C₅×C₄⋊C₄	—	3	1	no	—
390	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
391	C₅×C₂²⋊C₄	—	2	1	no	—
392	C₅×C₂²⋊C₄	—	6	1	no	—
393	C₅×C₂²⋊C₄	—	6	1	no	—
394	C₅×C₂²⋊C₄	—	6	1	no	—
395	C₅×C₂²⋊C₄	—	6	1	no	—
396	C₄²×C₅	—	6	1	no	—
397	C₂×2₋¹⁺⁴	—	3	1	no	—
398	C₂×AGL(1,ℤ/8)	—	3	1	no	—
399	C₂²×SD₁₆	—	3	1	no	—
400	#535	—	3	1	no	—
401	#449	—	3	1	no	—
402	#449	—	3	1	no	—
403	#449	—	3	1	no	—
404	#449	—	3	1	no	—
405	#448	—	3	1	no	—
406	#448	—	3	1	no	—
407	#448	—	3	1	no	—
408	#448	C₅×D₃	1	1	yes	characteristic, complemented
409	#419	—	3	1	no	—
410	#416	—	3	1	no	—
411	#408	—	3	1	no	—
412	C₂²×C₃×C₅	—	2	1	no	—
413	C₂²×C₃×C₅	—	2	1	no	—
414	C₂²×C₃×C₅	—	2	1	no	—
415	C₂²×C₃×C₅	—	4	1	no	—
416	C₂²×C₃×C₅	—	4	1	no	—
417	C₂²×C₃×C₅	—	4	1	no	—
418	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₅×D₃	—	2	1	no	—
420	C₂×C₅×D₃	—	2	1	no	—
421	C₂×C₅×D₃	—	2	1	no	—
422	C₂×C₅×D₃	—	2	2	no	—
423	C₂×C₅×D₃	—	2	1	no	—
424	C₂×C₅×D₃	—	2	1	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	C₂×C₅×D₃	—	4	1	no	—
430	C₂×C₅×D₃	—	8	4	no	—
431	C₂×C₅×D₃	#120	1	2	yes	—
432	C₃×C₄×C₅	—	2	2	no	—
433	C₃×C₄×C₅	—	2	2	no	—
434	C₃×C₄×C₅	—	2	1	no	—
435	C₃×C₄×C₅	—	4	1	no	—
436	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
437	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
438	C₅×Dic₃	—	2	1	no	—
439	C₅×Dic₃	—	2	2	no	—
440	C₅×Dic₃	—	4	1	no	—
441	C₅×Dic₃	#120	1	2	yes	—
442	C₂³×D₃	—	2	1	no	—
443	C₂×C₃×Q₈	—	2	2	no	—
444	C₂×C₃×Q₈	—	2	2	no	—
445	C₂×C₃×Q₈	—	2	1	no	—
446	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
447	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
448	C₂×C₃×D₄	—	2	1	no	—
449	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
450	C₂²×C₃×C₄	—	2	1	no	—
451	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
452	C₂×#67	—	2	1	no	—
453	C₂×#67	—	2	1	no	—
454	C₂×#67	—	2	1	no	—
455	C₂×#67	—	2	1	no	—
456	C₂×#67	C₅×D₄	1	1	yes	characteristic
457	C₂×#67	C₅×D₄	1	1	yes	characteristic
458	#239	—	2	8	no	—
459	#239	—	2	2	no	—
460	#239	—	2	2	no	—
461	#239	—	2	2	no	—
462	#239	C₅×D₄	1	4	yes	complemented
463	D₃×Q₈	—	2	8	no	—
464	D₃×Q₈	—	2	2	no	—
465	D₃×Q₈	—	2	2	no	—
466	D₃×Q₈	—	2	2	no	—
467	D₃×Q₈	C₅×D₄	1	4	yes	complemented
468	D₃×D₄	—	2	2	no	—
469	D₃×D₄	—	2	2	no	—
470	#235	—	2	8	no	—
471	#235	—	2	8	no	—
472	#235	—	2	2	no	—
473	#235	—	2	2	no	—
474	#235	—	2	2	no	—
475	#235	—	2	2	no	—
476	C₂×D₁₂	—	2	1	no	—
477	C₂×D₁₂	—	2	1	no	—
478	C₂×D₁₂	—	2	1	no	—
479	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
480	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
481	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
482	C₂×C₄×D₃	—	2	1	no	—
483	C₂×C₄×D₃	—	2	1	no	—
484	C₂×C₄×D₃	—	2	1	no	—
485	C₂×C₄×D₃	—	2	1	no	—
486	C₂×C₄×D₃	—	2	1	no	—
487	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
488	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
489	C₂×Dic₆	—	2	1	no	—
490	C₂×Dic₆	—	2	1	no	—
491	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
492	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
493	C₃×SD₁₆	—	2	2	no	—
494	C₃×SD₁₆	—	2	2	no	—
495	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
496	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
497	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
498	C₃×C₂²⋊C₄	—	2	1	no	—
499	#217	—	2	1	no	—
500	#215	—	2	2	no	—
501	#215	—	2	2	no	—
502	#214	—	2	2	no	—
503	#213	—	2	2	no	—
504	(C₂×D₃)⋊C₄	—	2	1	no	—
505	(C₂×D₃)⋊C₄	—	2	1	no	—
506	(C₂×D₃)⋊C₄	—	2	1	no	—
507	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
508	C₄×Dic₃	—	2	1	no	—
509	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
510	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
511	D₂₄	—	2	2	no	—
512	#204	—	2	2	no	—
513	ΓL(1,𝔽₂₅)	—	2	2	no	—
514	D₃×C₈	—	2	2	no	—
515	C₂³×C₅	—	2	1	no	—
516	C₂³×C₅	—	3	1	no	—
517	C₂³×C₅	—	3	1	no	—
518	C₂³×C₅	—	6	1	no	—
519	C₂³×C₅	—	6	1	no	—
520	C₂³×C₅	—	12	2	no	—
521	C₂³×C₅	—	24	1	no	—
522	C₂³×C₅	—	24	1	no	—
523	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
524	C₅×Q₈	—	2	4	no	—
525	C₅×Q₈	—	2	1	no	—
526	C₅×Q₈	—	2	1	no	—
527	C₅×Q₈	—	3	2	no	—
528	C₅×Q₈	—	6	4	no	—
529	C₅×Q₈	—	6	2	no	—
530	C₅×Q₈	—	6	4	no	—
531	C₅×Q₈	—	6	1	no	—
532	C₅×Q₈	D₃×D₄	1	2	yes	—
533	C₅×Q₈	D₃×D₄	1	2	yes	—
534	C₅×D₄	—	2	1	no	—
535	C₅×D₄	—	2	1	no	—
536	C₅×D₄	—	3	2	no	—
537	C₅×D₄	—	6	2	no	—
538	C₅×D₄	—	6	4	no	—
539	C₅×D₄	—	6	4	no	—
540	C₅×D₄	—	6	2	no	—
541	C₅×D₄	—	6	2	no	—
542	C₅×D₄	—	6	4	no	—
543	C₅×D₄	—	6	1	no	—
544	C₅×D₄	—	6	1	no	—
545	C₅×D₄	—	6	1	no	—
546	C₅×D₄	—	8	1	no	—
547	C₅×D₄	—	12	2	no	—
548	C₅×D₄	—	24	1	no	—
549	C₅×D₄	—	24	1	no	—
550	C₅×D₄	—	24	1	no	—
551	C₂×C₄×C₅	—	2	4	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	—	2	1	no	—
556	C₂×C₄×C₅	—	2	1	no	—
557	C₂×C₄×C₅	—	3	1	no	—
558	C₂×C₄×C₅	—	3	2	no	—
559	C₂×C₄×C₅	—	3	2	no	—
560	C₂×C₄×C₅	—	3	1	no	—
561	C₂×C₄×C₅	—	6	4	no	—
562	C₂×C₄×C₅	—	6	4	no	—
563	C₂×C₄×C₅	—	6	4	no	—
564	C₂×C₄×C₅	—	6	4	no	—
565	C₂×C₄×C₅	—	6	4	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	D₃×D₄	1	1	yes	characteristic
571	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
572	C₅×C₈	—	2	1	no	—
573	C₅×C₈	—	2	1	no	—
574	C₅×C₈	—	6	1	no	—
575	C₅×C₈	—	6	1	no	—
576	2₋¹⁺⁴	—	6	4	no	—
577	2₋¹⁺⁴	—	6	4	no	—
578	C₂×#41	—	3	1	no	—
579	C₂×#41	—	3	1	no	—
580	C₂×#41	—	3	1	no	—
581	C₂×#41	—	3	1	no	—
582	C₂×#41	—	6	1	no	—
583	C₂×#41	—	6	1	no	—
584	C₂×#41	—	6	1	no	—
585	C₂²×Q₈	—	3	1	no	—
586	C₂²×Q₈	—	3	1	no	—
587	C₂²×Q₈	—	6	1	no	—
588	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
589	C₂²×D₄	—	3	1	no	—
590	AGL(1,ℤ/8)	—	6	4	no	—
591	C₂×SD₁₆	—	3	1	no	—
592	C₂×SD₁₆	—	3	1	no	—
593	C₂×SD₁₆	—	3	1	no	—
594	C₂×SD₁₆	—	3	1	no	—
595	C₂×SD₁₆	—	6	4	no	—
596	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
597	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
598	C₂×D₈	—	3	1	no	—
599	C₂×D₈	—	3	1	no	—
600	C₂×M₁₆	—	3	1	no	—
601	C₂²×C₈	—	3	1	no	—
602	#127	—	6	1	no	—
603	#124	—	6	1	no	—
604	#121	—	3	1	no	—
605	#121	—	3	1	no	—
606	#121	—	3	1	no	—
607	#121	C₂×C₅×D₃	1	1	yes	characteristic
608	#120	—	6	1	no	—
609	#120	—	6	1	no	—
610	#117	—	3	1	no	—
611	#103	—	3	1	no	—
612	#103	—	3	1	no	—
613	#103	—	3	1	no	—
614	#103	—	3	1	no	—
615	#103	C₂×C₅×D₃	1	1	yes	characteristic, complemented
616	#103	C₂×C₅×D₃	1	1	yes	characteristic, complemented
617	#102	—	3	1	no	—
618	#102	—	3	1	no	—
619	C₂²⋊C₈	—	3	1	no	—
620	C₂²⋊C₈	—	3	1	no	—
621	C₂²⋊C₈	—	3	1	no	—
622	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
623	C₂×C₃×C₅	—	4	1	no	—
624	C₂×C₃×C₅	—	8	1	no	—
625	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
626	C₂×C₃×C₅	#577	1	1	yes	characteristic
627	C₂×C₃×C₅	#577	1	1	yes	characteristic
628	C₅×D₃	—	2	2	no	—
629	C₅×D₃	—	4	1	no	—
630	C₅×D₃	—	4	2	no	—
631	C₅×D₃	—	8	1	no	—
632	C₂³×C₃	—	2	1	no	—
633	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
634	C₂²×D₃	—	2	1	no	—
635	C₂²×D₃	—	2	1	no	—
636	C₂²×D₃	—	4	2	no	—
637	C₂²×D₃	—	8	1	no	—
638	C₂²×D₃	—	8	1	no	—
639	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
640	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
641	C₃×Q₈	—	2	4	no	—
642	C₃×Q₈	—	2	1	no	—
643	C₃×Q₈	—	2	1	no	—
644	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
645	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
646	C₃×D₄	—	2	1	no	—
647	C₃×D₄	—	2	1	no	—
648	C₃×D₄	—	8	1	no	—
649	C₂×C₃×C₄	—	2	4	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	—	2	1	no	—
653	C₂×C₃×C₄	—	2	1	no	—
654	C₂×C₃×C₄	—	2	1	no	—
655	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
656	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
657	#67	—	2	4	no	—
658	#67	—	2	2	no	—
659	#67	—	2	2	no	—
660	#67	—	4	2	no	—
661	#67	—	8	1	no	—
662	#67	—	8	1	no	—
663	C₂×Dic₃	—	2	1	no	—
664	C₂×Dic₃	—	2	1	no	—
665	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
666	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
667	D₁₂	—	2	4	no	—
668	D₁₂	—	2	4	no	—
669	D₁₂	—	2	2	no	—
670	D₁₂	—	2	1	no	—
671	D₁₂	—	2	1	no	—
672	D₁₂	—	2	1	no	—
673	D₁₂	—	8	1	no	—
674	D₁₂	C₂×C₅×D₄	1	2	yes	—
675	C₄×D₃	—	2	4	no	—
676	C₄×D₃	—	2	4	no	—
677	C₄×D₃	—	2	4	no	—
678	C₄×D₃	—	2	4	no	—
679	C₄×D₃	—	2	1	no	—
680	C₄×D₃	—	2	1	no	—
681	C₄×D₃	—	2	4	no	—
682	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
683	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
684	Dic₆	—	2	4	no	—
685	Dic₆	—	2	1	no	—
686	Dic₆	—	2	4	no	—
687	Dic₆	—	2	2	no	—
688	Dic₆	C₂×C₅×D₄	1	2	yes	—
689	C₃×C₈	—	2	1	no	—
690	C₃×C₈	—	2	1	no	—
691	C₃⋊C₈	—	2	1	no	—
692	C₃⋊C₈	—	2	1	no	—
693	C₂²×C₅	—	2	1	no	—
694	C₂²×C₅	—	2	1	no	—
695	C₂²×C₅	—	2	1	no	—
696	C₂²×C₅	—	3	2	no	—
697	C₂²×C₅	—	4	1	no	—
698	C₂²×C₅	—	4	1	no	—
699	C₂²×C₅	—	4	1	no	—
700	C₂²×C₅	—	6	1	no	—
701	C₂²×C₅	—	6	1	no	—
702	C₂²×C₅	—	6	1	no	—
703	C₂²×C₅	—	6	1	no	—
704	C₂²×C₅	—	6	2	no	—
705	C₂²×C₅	—	6	1	no	—
706	C₂²×C₅	—	12	1	no	—
707	C₂²×C₅	—	12	1	no	—
708	C₂²×C₅	—	12	1	no	—
709	C₂²×C₅	—	12	1	no	—
710	C₂²×C₅	—	12	1	no	—
711	C₂²×C₅	—	24	4	no	—
712	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
713	C₄×C₅	—	2	2	no	—
714	C₄×C₅	—	2	2	no	—
715	C₄×C₅	—	2	1	no	—
716	C₄×C₅	—	3	2	no	—
717	C₄×C₅	—	4	1	no	—
718	C₄×C₅	—	6	1	no	—
719	C₄×C₅	—	6	2	no	—
720	C₄×C₅	—	12	1	no	—
721	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
722	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
723	C₂⁴	—	6	1	no	—
724	#41	—	3	4	no	—
725	#41	—	6	2	no	—
726	#41	—	6	2	no	—
727	#41	—	6	2	no	—
728	#41	—	6	2	no	—
729	#41	—	6	8	no	—
730	#41	—	6	8	no	—
731	#41	—	6	2	no	—
732	#41	—	6	2	no	—
733	#41	—	6	8	no	—
734	#41	—	6	2	no	—
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	2	1	no	—
738	C₂×Q₈	—	3	1	no	—
739	C₂×Q₈	—	3	4	no	—
740	C₂×Q₈	—	3	1	no	—
741	C₂×Q₈	—	6	1	no	—
742	C₂×Q₈	—	6	1	no	—
743	C₂×Q₈	—	6	2	no	—
744	C₂×Q₈	—	6	2	no	—
745	C₂×Q₈	—	6	8	no	—
746	C₂×Q₈	—	6	2	no	—
747	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
748	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
749	C₂×D₄	—	2	1	no	—
750	C₂×D₄	—	3	1	no	—
751	C₂×D₄	—	3	1	no	—
752	C₂×D₄	—	3	1	no	—
753	C₂×D₄	—	3	1	no	—
754	C₂×D₄	—	3	1	no	—
755	C₂×D₄	—	6	1	no	—
756	C₂×D₄	—	6	1	no	—
757	C₂×D₄	—	6	1	no	—
758	C₂×D₄	—	6	2	no	—
759	C₂×D₄	—	6	2	no	—
760	C₂×D₄	—	6	1	no	—
761	C₂×D₄	—	6	1	no	—
762	C₂×D₄	—	6	1	no	—
763	C₂×D₄	—	6	1	no	—
764	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
765	C₂²×C₄	—	2	1	no	—
766	C₂²×C₄	—	3	1	no	—
767	C₂²×C₄	—	3	1	no	—
768	C₂²×C₄	—	6	1	no	—
769	C₂²×C₄	—	6	1	no	—
770	C₂²×C₄	—	6	1	no	—
771	C₂²×C₄	—	6	1	no	—
772	C₂²×C₄	—	6	1	no	—
773	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
774	SD₁₆	—	2	2	no	—
775	SD₁₆	—	2	2	no	—
776	SD₁₆	—	6	2	no	—
777	SD₁₆	—	6	2	no	—
778	SD₁₆	—	6	2	no	—
779	SD₁₆	—	6	2	no	—
780	D₈	—	6	2	no	—
781	D₈	—	6	2	no	—
782	M₁₆	—	6	2	no	—
783	C₂×C₈	—	3	1	no	—
784	C₂×C₈	—	3	1	no	—
785	C₂×C₈	—	6	2	no	—
786	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
787	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
788	C₄⋊C₄	—	3	1	no	—
789	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	6	1	no	—
792	C₂²⋊C₄	—	6	1	no	—
793	C₂²⋊C₄	—	6	1	no	—
794	C₂²⋊C₄	—	6	1	no	—
795	C₄²	—	6	1	no	—
796	C₃×C₅	#3010	1	1	yes	characteristic, complemented, Hall
797	C₂²×C₃	—	2	1	no	—
798	C₂²×C₃	—	2	1	no	—
799	C₂²×C₃	—	2	1	no	—
800	C₂²×C₃	—	4	1	no	—
801	C₂²×C₃	—	4	1	no	—
802	C₂²×C₃	—	4	1	no	—
803	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
804	C₂×D₃	—	2	1	no	—
805	C₂×D₃	—	2	1	no	—
806	C₂×D₃	—	2	1	no	—
807	C₂×D₃	—	2	2	no	—
808	C₂×D₃	—	2	1	no	—
809	C₂×D₃	—	2	1	no	—
810	C₂×D₃	—	4	1	no	—
811	C₂×D₃	—	4	1	no	—
812	C₂×D₃	—	4	1	no	—
813	C₂×D₃	—	4	1	no	—
814	C₂×D₃	—	4	1	no	—
815	C₂×D₃	—	8	4	no	—
816	C₂×D₃	C₅×#120	1	2	yes	—
817	C₃×C₄	—	2	2	no	—
818	C₃×C₄	—	2	2	no	—
819	C₃×C₄	—	2	1	no	—
820	C₃×C₄	—	4	1	no	—
821	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
822	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
823	Dic₃	—	2	1	no	—
824	Dic₃	—	2	2	no	—
825	Dic₃	—	4	1	no	—
826	Dic₃	C₅×#120	1	2	yes	—
827	C₂×C₅	—	4	1	no	—
828	C₂×C₅	—	6	2	no	—
829	C₂×C₅	—	8	1	no	—
830	C₂×C₅	—	12	1	no	—
831	C₂×C₅	—	12	2	no	—
832	C₂×C₅	—	24	1	no	—
833	C₂×C₅	D₃×#120	1	1	yes	characteristic
834	C₂×C₅	#5762	1	1	yes	characteristic
835	C₂×C₅	#5778	1	1	yes	characteristic
836	C₂³	—	2	1	no	—
837	C₂³	—	3	1	no	—
838	C₂³	—	3	1	no	—
839	C₂³	—	6	1	no	—
840	C₂³	—	6	1	no	—
841	C₂³	—	12	2	no	—
842	C₂³	—	24	1	no	—
843	C₂³	—	24	1	no	—
844	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
845	Q₈	—	2	4	no	—
846	Q₈	—	2	1	no	—
847	Q₈	—	2	1	no	—
848	Q₈	—	3	2	no	—
849	Q₈	—	6	4	no	—
850	Q₈	—	6	2	no	—
851	Q₈	—	6	4	no	—
852	Q₈	—	6	1	no	—
853	Q₈	C₅×D₃×D₄	1	2	yes	—
854	Q₈	C₅×D₃×D₄	1	2	yes	—
855	D₄	—	2	1	no	—
856	D₄	—	2	1	no	—
857	D₄	—	3	2	no	—
858	D₄	—	6	2	no	—
859	D₄	—	6	4	no	—
860	D₄	—	6	4	no	—
861	D₄	—	6	2	no	—
862	D₄	—	6	2	no	—
863	D₄	—	6	4	no	—
864	D₄	—	6	1	no	—
865	D₄	—	6	1	no	—
866	D₄	—	6	1	no	—
867	D₄	—	8	1	no	—
868	D₄	—	12	2	no	—
869	D₄	—	24	1	no	—
870	D₄	—	24	1	no	—
871	D₄	—	24	1	no	—
872	C₂×C₄	—	2	4	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	3	1	no	—
879	C₂×C₄	—	3	2	no	—
880	C₂×C₄	—	3	2	no	—
881	C₂×C₄	—	3	1	no	—
882	C₂×C₄	—	6	4	no	—
883	C₂×C₄	—	6	4	no	—
884	C₂×C₄	—	6	4	no	—
885	C₂×C₄	—	6	4	no	—
886	C₂×C₄	—	6	4	no	—
887	C₂×C₄	—	6	1	no	—
888	C₂×C₄	—	6	1	no	—
889	C₂×C₄	—	6	1	no	—
890	C₂×C₄	—	6	1	no	—
891	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
892	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
893	C₈	—	2	1	no	—
894	C₈	—	2	1	no	—
895	C₈	—	6	1	no	—
896	C₈	—	6	1	no	—
897	C₂×C₃	—	4	1	no	—
898	C₂×C₃	—	8	1	no	—
899	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
900	C₂×C₃	C₅×#577	1	1	yes	characteristic
901	C₂×C₃	C₅×#577	1	1	yes	characteristic
902	D₃	—	2	2	no	—
903	D₃	—	4	1	no	—
904	D₃	—	4	2	no	—
905	D₃	—	8	1	no	—
906	C₅	#80041	1	1	yes	characteristic, direct product factor, Sylow
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	3	2	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	6	1	no	—
915	C₂²	—	6	1	no	—
916	C₂²	—	6	1	no	—
917	C₂²	—	6	1	no	—
918	C₂²	—	6	2	no	—
919	C₂²	—	6	1	no	—
920	C₂²	—	12	1	no	—
921	C₂²	—	12	1	no	—
922	C₂²	—	12	1	no	—
923	C₂²	—	12	1	no	—
924	C₂²	—	12	1	no	—
925	C₂²	—	24	4	no	—
926	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
927	C₄	—	2	2	no	—
928	C₄	—	2	2	no	—
929	C₄	—	2	1	no	—
930	C₄	—	3	2	no	—
931	C₄	—	4	1	no	—
932	C₄	—	6	1	no	—
933	C₄	—	6	2	no	—
934	C₄	—	12	1	no	—
935	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
936	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
937	C₃	C₅×#3010	1	1	yes	characteristic, complemented, Sylow
938	C₂	—	4	1	no	—
939	C₂	—	6	2	no	—
940	C₂	—	8	1	no	—
941	C₂	—	12	1	no	—
942	C₂	—	12	2	no	—
943	C₂	—	24	1	no	—
944	C₂	C₅×D₃×#120	1	1	yes	characteristic
945	C₂	C₅×#5762	1	1	yes	characteristic
946	C₂	C₅×#5778	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×#448	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#448	D₃
hypocenter	C₃	C₅×#3010
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#448

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#1007	C₂	semidirect
2. C₂×C₅×#914	C₂	semidirect
3. C₂×C₅×D₃×SD₁₆	C₂	semidirect
4. C₅×#5607	C₂	semidirect
5. C₃×C₅×#448	C₂	semidirect
6. C₅×#5227	C₂	semidirect
7. C₅×#5172	C₂	semidirect
8. C₅×#5170	C₂	semidirect
9. C₅×#5037	C₂	semidirect
10. C₅×#4810	C₂	semidirect
11. C₅×#4806	C₂	semidirect
12. C₅×#4804	C₂	semidirect
13. C₅×#4802	C₂	semidirect
14. C₅×#4734	C₂	semidirect
15. C₅×#4727	C₂	semidirect
17. C₂²×C₃×C₅×Q₈	C₂²	semidirect
22. C₂×C₅×#239	C₂²	semidirect
25. C₂×C₅×D₃×Q₈	C₂²	semidirect
30. C₂×C₅×#235	C₂²	semidirect
52. C₃×C₅×#103	C₂²	semidirect
53. C₃×C₅×#103	C₂²	semidirect
54. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
55. C₅×#835	C₂²	semidirect
56. C₅×#835	C₂²	semidirect
57. C₅×#830	C₂²	semidirect
58. C₅×#821	C₂²	semidirect
59. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
60. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
61. C₅×#816	C₂²	semidirect
62. C₅×#810	C₂²	semidirect
63. C₅×#809	C₂²	semidirect
64. #80041	C₅	direct (N × H)
76. C₅×#448	D₃	semidirect
100. C₅×#239	D₄	semidirect
105. C₅×D₃×Q₈	D₄	semidirect
153. C₂×#1007	C₂×C₅	semidirect
154. C₂×#914	C₂×C₅	semidirect
155. C₂×D₃×SD₁₆	C₂×C₅	semidirect
156. #5607	C₂×C₅	semidirect
157. C₃×#448	C₂×C₅	semidirect
158. #5227	C₂×C₅	semidirect
159. #5172	C₂×C₅	semidirect
160. #5170	C₂×C₅	semidirect
161. #5037	C₂×C₅	semidirect
162. #4810	C₂×C₅	semidirect
163. #4806	C₂×C₅	semidirect
164. #4804	C₂×C₅	semidirect
165. #4802	C₂×C₅	semidirect
166. #4734	C₂×C₅	semidirect
167. #4727	C₂×C₅	semidirect
180. C₂²×C₅×Q₈	C₂×D₃	semidirect
207. C₅×#103	C₂×D₃	semidirect
208. C₅×#103	C₂×D₃	semidirect
214. C₅×C₂²⋊C₈	C₂×D₃	semidirect
277. C₂²×C₃×Q₈	C₂²×C₅	semidirect
282. C₂×#239	C₂²×C₅	semidirect
285. C₂×D₃×Q₈	C₂²×C₅	semidirect
290. C₂×#235	C₂²×C₅	semidirect
312. C₃×#103	C₂²×C₅	semidirect
313. C₃×#103	C₂²×C₅	semidirect
314. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
315. #835	C₂²×C₅	semidirect
316. #835	C₂²×C₅	semidirect
317. #830	C₂²×C₅	semidirect
318. #821	C₂²×C₅	semidirect
319. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
320. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
321. #816	C₂²×C₅	semidirect
322. #810	C₂²×C₅	semidirect
323. #809	C₂²×C₅	semidirect
408. #448	C₅×D₃	semidirect
462. #239	C₅×D₄	semidirect
467. D₃×Q₈	C₅×D₄	semidirect
588. C₂²×Q₈	C₂×C₅×D₃	semidirect
615. #103	C₂×C₅×D₃	semidirect
616. #103	C₂×C₅×D₃	semidirect
622. C₂²⋊C₈	C₂×C₅×D₃	semidirect
796. C₃×C₅	#3010	semidirect
906. C₅	#80041	direct (N × H)
937. C₃	C₅×#3010	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#1007	2
C₂×C₅×#914	2
C₂×C₅×D₃×SD₁₆	2
C₅×#5607	2
C₃×C₅×#448	2
C₅×#5227	2
C₅×#5172	2
C₅×#5170	2
C₅×#5037	2
C₅×#4810	2
C₅×#4806	2
C₅×#4804	2
C₅×#4802	2
C₅×#4734	2
C₅×#4727	2
C₅×#3010	3
#80041	5

Subgroups — C5×#80041 #14424414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80041 #14424414