Subgroups — C₅×#80404 #14453433

Order 1920.

1092 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#914	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5717	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5576	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5172	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5170	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5074	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5026	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4844	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4836	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4780	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4776	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4775	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4773	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3265	—	3	1	no	maximal, Hall
17	C₂×C₅×#239	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₅×D₃×D₄	—	2	1	no	—
20	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×#127	C₂²	1	1	yes	characteristic
25	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#215	C₂²	1	1	yes	characteristic
27	C₅×#938	—	2	1	no	—
28	C₅×#938	C₂²	1	1	yes	characteristic
29	C₅×#938	C₂²	1	1	yes	characteristic
30	C₅×#937	—	2	1	no	—
31	C₅×#937	—	2	1	no	—
32	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
36	C₅×#914	—	2	4	no	—
37	C₅×D₃×SD₁₆	—	2	4	no	—
38	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
39	C₂×C₅×#204	C₂²	1	1	yes	characteristic
40	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
42	C₅×#897	—	2	1	no	—
43	C₅×#897	C₂²	1	1	yes	characteristic, complemented
44	C₅×#895	—	2	1	no	—
45	C₅×#895	C₂²	1	1	yes	characteristic, complemented
46	C₅×#875	—	2	1	no	—
47	C₅×#875	C₂²	1	1	yes	characteristic, complemented
48	C₄×C₅×D₁₂	—	2	1	no	—
49	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
50	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
51	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
54	C₅×#835	C₂²	1	1	yes	characteristic, complemented
55	C₅×#821	C₂²	1	1	yes	characteristic, complemented
56	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₅×#816	C₂²	1	1	yes	characteristic, complemented
59	C₅×#809	C₂²	1	1	yes	characteristic
60	C₅×#807	C₂²	1	1	yes	characteristic, complemented
61	C₅×#803	C₂²	1	1	yes	characteristic, complemented
62	#80404	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
64	C₂²×C₅×SD₁₆	—	3	1	no	—
65	C₅×#548	—	3	1	no	—
66	C₅×D₄²	—	3	1	no	—
67	C₅×#496	—	3	1	no	—
68	C₅×#468	—	3	1	no	—
69	C₅×#466	—	3	1	no	—
70	C₅×#463	—	3	1	no	—
71	C₅×#460	D₃	1	1	yes	characteristic, complemented
72	C₅×#450	—	3	1	no	—
73	C₅×#449	—	3	1	no	—
74	C₅×#448	—	3	1	no	—
75	C₅×#447	—	3	1	no	—
76	C₅×#440	—	3	1	no	—
77	C₅×#435	—	3	1	no	—
78	C₂³×C₅×D₃	—	2	1	no	—
79	C₂³×C₅×D₃	—	2	1	no	—
80	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×D₄	—	2	1	no	—
82	C₂×C₃×C₅×D₄	—	2	1	no	—
83	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
85	C₂×C₅×#67	—	2	1	no	—
86	C₂×C₅×#67	—	2	1	no	—
87	C₂×C₅×#67	—	2	1	no	—
88	C₂×C₅×#67	—	2	1	no	—
89	C₅×#239	—	2	2	no	—
90	C₅×#239	—	4	1	no	—
91	C₅×D₃×Q₈	—	2	2	no	—
92	C₅×D₃×Q₈	—	4	1	no	—
93	C₅×D₃×D₄	—	2	2	no	—
94	C₅×D₃×D₄	—	2	2	no	—
95	C₅×D₃×D₄	—	4	1	no	—
96	C₅×D₃×D₄	—	4	1	no	—
97	C₅×D₃×D₄	—	4	4	no	—
98	C₂×C₅×D₁₂	—	2	1	no	—
99	C₂×C₅×D₁₂	—	2	1	no	—
100	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
101	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
102	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
103	C₂×C₄×C₅×D₃	—	2	1	no	—
104	C₂×C₄×C₅×D₃	—	2	1	no	—
105	C₂×C₄×C₅×D₃	—	2	1	no	—
106	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
107	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
108	C₂×C₅×Dic₆	—	2	1	no	—
109	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
110	C₃×C₅×SD₁₆	—	2	2	no	—
111	C₃×C₅×SD₁₆	—	2	2	no	—
112	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
113	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
114	C₃×C₅×C₄⋊C₄	—	2	1	no	—
115	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₃×C₄²×C₅	—	2	1	no	—
117	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
118	C₅×#217	—	2	1	no	—
119	C₅×#217	—	2	1	no	—
120	C₅×#215	D₄	1	4	yes	complemented
121	C₅×#214	—	2	2	no	—
122	C₅×#214	—	4	1	no	—
123	C₅×#213	—	2	2	no	—
124	C₅×#213	—	4	1	no	—
125	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
126	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
127	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
128	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
129	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
130	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
131	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
132	C₅×C₄⋊Dic₃	—	2	1	no	—
133	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
134	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
135	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
136	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
137	C₅×D₂₄	—	2	2	no	—
138	C₅×#204	—	2	2	no	—
139	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
140	C₅×D₃×C₈	—	2	2	no	—
141	C₂×#914	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×D₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
143	#5717	C₂×C₅	1	1	yes	characteristic, complemented
144	#5576	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#460	C₂×C₅	1	1	yes	characteristic, complemented
146	#5172	C₂×C₅	1	1	yes	characteristic, complemented
147	#5170	C₂×C₅	1	1	yes	characteristic, complemented
148	#5074	C₂×C₅	1	1	yes	characteristic, complemented
149	#5026	C₂×C₅	1	1	yes	characteristic, complemented
150	#4844	C₂×C₅	1	1	yes	characteristic, complemented
151	#4836	C₂×C₅	1	1	yes	characteristic, complemented
152	#4780	C₂×C₅	1	1	yes	characteristic, complemented
153	#4776	C₂×C₅	1	1	yes	characteristic, complemented
154	#4775	C₂×C₅	1	1	yes	characteristic, complemented
155	#4773	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂×C₅×#41	—	3	1	no	—
157	C₂²×C₅×Q₈	—	3	1	no	—
158	C₂²×C₅×D₄	—	3	1	no	—
159	C₂²×C₅×D₄	—	3	1	no	—
160	C₂²×C₅×D₄	—	6	1	no	—
161	C₅×AGL(1,ℤ/8)	—	6	4	no	—
162	C₂×C₅×SD₁₆	—	3	1	no	—
163	C₂×C₅×SD₁₆	—	3	1	no	—
164	C₂×C₅×SD₁₆	—	3	1	no	—
165	C₂×C₅×SD₁₆	—	3	1	no	—
166	C₂×C₅×SD₁₆	—	6	4	no	—
167	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
168	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
169	C₂×C₅×D₈	—	3	1	no	—
170	C₂×C₅×D₈	—	3	1	no	—
171	C₂×C₅×D₈	—	3	1	no	—
172	C₂×C₅×M₁₆	—	3	1	no	—
173	C₂²×C₅×C₈	—	3	1	no	—
174	C₅×#127	C₂×D₃	1	1	yes	characteristic
175	C₅×#124	—	3	1	no	—
176	C₅×#124	—	6	1	no	—
177	C₅×C₂²⋊Q₈	—	3	1	no	—
178	C₅×C₂²⋊Q₈	—	6	1	no	—
179	C₅×#121	—	3	1	no	—
180	C₅×#121	—	3	1	no	—
181	C₅×#121	—	3	1	no	—
182	C₅×#121	—	6	1	no	—
183	C₅×#121	—	6	1	no	—
184	C₅×#120	—	6	1	no	—
185	C₅×#120	—	6	1	no	—
186	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
187	C₄×C₅×D₄	—	3	1	no	—
188	C₄×C₅×D₄	—	3	1	no	—
189	C₄×C₅×D₄	—	6	1	no	—
190	C₅×#107	—	3	1	no	—
191	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
192	C₅×#103	—	3	1	no	—
193	C₅×#103	—	3	1	no	—
194	C₅×#102	—	3	1	no	—
195	C₅×#102	—	3	1	no	—
196	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
197	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
198	C₅×C₂²⋊C₈	—	3	1	no	—
199	C₅×C₂²⋊C₈	—	3	1	no	—
200	C₅×#97	—	3	1	no	—
201	#3265	—	3	1	no	Sylow
202	C₂³×C₃×C₅	—	2	1	no	—
203	C₂³×C₃×C₅	—	2	1	no	—
204	C₂²×C₅×D₃	—	2	1	no	—
205	C₂²×C₅×D₃	—	2	1	no	—
206	C₂²×C₅×D₃	—	4	2	no	—
207	C₂²×C₅×D₃	—	4	2	no	—
208	C₂²×C₅×D₃	—	4	2	no	—
209	C₂²×C₅×D₃	—	4	2	no	—
210	C₂²×C₅×D₃	—	8	1	no	—
211	C₂²×C₅×D₃	—	8	1	no	—
212	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
214	C₃×C₅×Q₈	—	2	1	no	—
215	C₃×C₅×Q₈	C₂×D₄	1	2	yes	complemented
216	C₃×C₅×D₄	—	2	1	no	—
217	C₃×C₅×D₄	—	2	1	no	—
218	C₃×C₅×D₄	—	2	1	no	—
219	C₃×C₅×D₄	—	2	1	no	—
220	C₃×C₅×D₄	—	4	2	no	—
221	C₃×C₅×D₄	—	8	1	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	2	1	no	—
224	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
225	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
226	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
227	C₅×#67	—	4	2	no	—
228	C₅×#67	—	4	2	no	—
229	C₅×#67	—	4	2	no	—
230	C₅×#67	—	4	2	no	—
231	C₂×C₅×Dic₃	—	2	1	no	—
232	C₂×C₅×Dic₃	—	2	1	no	—
233	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
234	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
235	C₅×D₁₂	—	2	2	no	—
236	C₅×D₁₂	—	2	1	no	—
237	C₅×D₁₂	—	2	1	no	—
238	C₅×D₁₂	—	2	1	no	—
239	C₅×D₁₂	—	4	2	no	—
240	C₅×D₁₂	—	4	2	no	—
241	C₅×D₁₂	C₂×D₄	1	2	yes	—
242	C₄×C₅×D₃	—	2	1	no	—
243	C₄×C₅×D₃	—	2	1	no	—
244	C₄×C₅×D₃	—	2	1	no	—
245	C₄×C₅×D₃	—	2	1	no	—
246	C₄×C₅×D₃	—	4	2	no	—
247	C₄×C₅×D₃	—	4	2	no	—
248	C₄×C₅×D₃	—	4	2	no	—
249	C₅×Dic₆	—	2	1	no	—
250	C₅×Dic₆	—	2	1	no	—
251	C₅×Dic₆	—	4	2	no	—
252	C₃×C₅×C₈	—	2	1	no	—
253	C₃×C₅×C₈	—	2	1	no	—
254	C₅×C₃⋊C₈	—	2	1	no	—
255	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	complemented
256	C₂×#239	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
258	C₂×D₃×D₄	—	2	1	no	—
259	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
260	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₃×#127	C₂²×C₅	1	1	yes	characteristic
264	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
265	C₂×#215	C₂²×C₅	1	1	yes	characteristic
266	#938	—	2	1	no	—
267	#938	C₂²×C₅	1	1	yes	characteristic
268	#938	C₂²×C₅	1	1	yes	characteristic
269	#937	—	2	1	no	—
270	#937	—	2	1	no	—
271	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
275	#914	—	2	4	no	—
276	D₃×SD₁₆	—	2	4	no	—
277	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
278	C₂×#204	C₂²×C₅	1	1	yes	characteristic
279	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
280	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
281	#897	—	2	1	no	—
282	#897	C₂²×C₅	1	1	yes	characteristic, complemented
283	#895	—	2	1	no	—
284	#895	C₂²×C₅	1	1	yes	characteristic, complemented
285	#875	—	2	1	no	—
286	#875	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₄×D₁₂	—	2	1	no	—
288	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
289	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
290	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
291	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
292	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
293	#835	C₂²×C₅	1	1	yes	characteristic, complemented
294	#821	C₂²×C₅	1	1	yes	characteristic, complemented
295	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
296	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
297	#816	C₂²×C₅	1	1	yes	characteristic, complemented
298	#809	C₂²×C₅	1	1	yes	characteristic
299	#807	C₂²×C₅	1	1	yes	characteristic, complemented
300	#803	C₂²×C₅	1	1	yes	characteristic, complemented
301	C₂⁴×C₅	—	6	1	no	—
302	C₂⁴×C₅	—	6	1	no	—
303	C₅×#41	—	6	2	no	—
304	C₅×#41	—	12	1	no	—
305	C₂×C₅×Q₈	—	3	1	no	—
306	C₂×C₅×Q₈	—	6	1	no	—
307	C₂×C₅×Q₈	—	6	2	no	—
308	C₂×C₅×Q₈	—	12	1	no	—
309	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
310	C₂×C₅×D₄	—	2	1	no	—
311	C₂×C₅×D₄	—	2	1	no	—
312	C₂×C₅×D₄	—	3	1	no	—
313	C₂×C₅×D₄	—	3	1	no	—
314	C₂×C₅×D₄	—	3	1	no	—
315	C₂×C₅×D₄	—	6	1	no	—
316	C₂×C₅×D₄	—	6	1	no	—
317	C₂×C₅×D₄	—	6	1	no	—
318	C₂×C₅×D₄	—	6	1	no	—
319	C₂×C₅×D₄	—	6	2	no	—
320	C₂×C₅×D₄	—	6	2	no	—
321	C₂×C₅×D₄	—	6	1	no	—
322	C₂×C₅×D₄	—	6	1	no	—
323	C₂×C₅×D₄	—	12	1	no	—
324	C₂×C₅×D₄	—	12	1	no	—
325	C₂×C₅×D₄	—	12	4	no	—
326	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
327	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
328	C₂²×C₄×C₅	—	3	1	no	—
329	C₂²×C₄×C₅	—	3	1	no	—
330	C₂²×C₄×C₅	—	6	1	no	—
331	C₂²×C₄×C₅	—	6	1	no	—
332	C₂²×C₄×C₅	—	6	1	no	—
333	C₅×SD₁₆	—	2	2	no	—
334	C₅×SD₁₆	—	2	2	no	—
335	C₅×SD₁₆	—	3	4	no	—
336	C₅×SD₁₆	—	6	2	no	—
337	C₅×SD₁₆	—	6	2	no	—
338	C₅×SD₁₆	—	12	1	no	—
339	C₅×D₈	—	6	2	no	—
340	C₅×D₈	—	6	2	no	—
341	C₅×D₈	—	12	1	no	—
342	C₅×M₁₆	—	6	2	no	—
343	C₂×C₅×C₈	—	3	1	no	—
344	C₂×C₅×C₈	—	3	1	no	—
345	C₂×C₅×C₈	—	6	2	no	—
346	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
347	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
348	C₅×C₄⋊C₄	—	2	1	no	—
349	C₅×C₄⋊C₄	—	3	1	no	—
350	C₅×C₄⋊C₄	—	3	1	no	—
351	C₅×C₄⋊C₄	—	6	1	no	—
352	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
353	C₅×C₂²⋊C₄	—	3	1	no	—
354	C₅×C₂²⋊C₄	—	3	1	no	—
355	C₅×C₂²⋊C₄	—	6	1	no	—
356	C₅×C₂²⋊C₄	—	6	1	no	—
357	C₅×C₂²⋊C₄	—	6	1	no	—
358	C₅×C₂²⋊C₄	—	6	1	no	—
359	C₅×C₂²⋊C₄	—	6	1	no	—
360	C₅×C₂²⋊C₄	—	6	1	no	—
361	C₅×C₂²⋊C₄	—	6	1	no	—
362	C₄²×C₅	—	2	1	no	—
363	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
364	C₂×AGL(1,ℤ/8)	—	3	1	no	—
365	C₂²×SD₁₆	—	3	1	no	—
366	#548	—	3	1	no	—
367	D₄²	—	3	1	no	—
368	#496	—	3	1	no	—
369	#468	—	3	1	no	—
370	#466	—	3	1	no	—
371	#463	—	3	1	no	—
372	#460	C₅×D₃	1	1	yes	characteristic, complemented
373	#450	—	3	1	no	—
374	#449	—	3	1	no	—
375	#448	—	3	1	no	—
376	#447	—	3	1	no	—
377	#440	—	3	1	no	—
378	#435	—	3	1	no	—
379	C₂²×C₃×C₅	—	4	1	no	—
380	C₂²×C₃×C₅	—	4	1	no	—
381	C₂²×C₃×C₅	—	4	1	no	—
382	C₂²×C₃×C₅	—	4	1	no	—
383	C₂²×C₃×C₅	—	4	1	no	—
384	C₂²×C₃×C₅	—	4	1	no	—
385	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₅×D₃	—	2	1	no	—
387	C₂×C₅×D₃	—	2	1	no	—
388	C₂×C₅×D₃	—	2	1	no	—
389	C₂×C₅×D₃	—	2	2	no	—
390	C₂×C₅×D₃	—	2	1	no	—
391	C₂×C₅×D₃	—	2	1	no	—
392	C₂×C₅×D₃	—	4	1	no	—
393	C₂×C₅×D₃	—	4	1	no	—
394	C₂×C₅×D₃	—	4	1	no	—
395	C₂×C₅×D₃	—	4	1	no	—
396	C₂×C₅×D₃	—	4	1	no	—
397	C₂×C₅×D₃	—	8	4	no	—
398	C₂×C₅×D₃	—	8	4	no	—
399	C₂×C₅×D₃	AGL(1,ℤ/8)	1	2	yes	complemented
400	C₃×C₄×C₅	—	2	2	no	—
401	C₃×C₄×C₅	—	2	1	no	—
402	C₃×C₄×C₅	—	2	1	no	—
403	C₃×C₄×C₅	—	4	1	no	—
404	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
405	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
406	C₅×Dic₃	—	2	1	no	—
407	C₅×Dic₃	—	2	1	no	—
408	C₅×Dic₃	—	4	1	no	—
409	C₅×Dic₃	—	4	1	no	—
410	C₂³×D₃	—	2	1	no	—
411	C₂³×D₃	—	2	1	no	—
412	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
413	C₂×C₃×D₄	—	2	1	no	—
414	C₂×C₃×D₄	—	2	1	no	—
415	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
416	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
417	C₂×#67	—	2	1	no	—
418	C₂×#67	—	2	1	no	—
419	C₂×#67	—	2	1	no	—
420	C₂×#67	—	2	1	no	—
421	#239	—	2	2	no	—
422	#239	—	4	1	no	—
423	D₃×Q₈	—	2	2	no	—
424	D₃×Q₈	—	4	1	no	—
425	D₃×D₄	—	2	2	no	—
426	D₃×D₄	—	2	2	no	—
427	D₃×D₄	—	4	1	no	—
428	D₃×D₄	—	4	1	no	—
429	D₃×D₄	—	4	4	no	—
430	C₂×D₁₂	—	2	1	no	—
431	C₂×D₁₂	—	2	1	no	—
432	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
433	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
434	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
435	C₂×C₄×D₃	—	2	1	no	—
436	C₂×C₄×D₃	—	2	1	no	—
437	C₂×C₄×D₃	—	2	1	no	—
438	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
439	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
440	C₂×Dic₆	—	2	1	no	—
441	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
442	C₃×SD₁₆	—	2	2	no	—
443	C₃×SD₁₆	—	2	2	no	—
444	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
445	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
446	C₃×C₄⋊C₄	—	2	1	no	—
447	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
448	C₃×C₄²	—	2	1	no	—
449	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
450	#217	—	2	1	no	—
451	#217	—	2	1	no	—
452	#215	C₅×D₄	1	4	yes	complemented
453	#214	—	2	2	no	—
454	#214	—	4	1	no	—
455	#213	—	2	2	no	—
456	#213	—	4	1	no	—
457	(C₂×D₃)⋊C₄	—	2	1	no	—
458	(C₂×D₃)⋊C₄	—	2	1	no	—
459	(C₂×D₃)⋊C₄	—	2	1	no	—
460	(C₂×D₃)⋊C₄	—	2	1	no	—
461	(C₂×D₃)⋊C₄	—	2	1	no	—
462	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
463	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
464	C₄⋊Dic₃	—	2	1	no	—
465	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
466	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
467	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
468	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
469	D₂₄	—	2	2	no	—
470	#204	—	2	2	no	—
471	ΓL(1,𝔽₂₅)	—	2	2	no	—
472	D₃×C₈	—	2	2	no	—
473	C₂³×C₅	—	2	1	no	—
474	C₂³×C₅	—	2	1	no	—
475	C₂³×C₅	—	3	1	no	—
476	C₂³×C₅	—	3	1	no	—
477	C₂³×C₅	—	6	1	no	—
478	C₂³×C₅	—	6	1	no	—
479	C₂³×C₅	—	12	2	no	—
480	C₂³×C₅	—	12	2	no	—
481	C₂³×C₅	—	12	2	no	—
482	C₂³×C₅	—	12	2	no	—
483	C₂³×C₅	—	24	1	no	—
484	C₂³×C₅	—	24	1	no	—
485	C₅×Q₈	—	2	1	no	—
486	C₅×Q₈	—	6	1	no	—
487	C₅×Q₈	—	6	1	no	—
488	C₅×Q₈	—	12	2	no	—
489	C₅×Q₈	D₃×D₄	1	2	yes	complemented
490	C₅×D₄	—	2	1	no	—
491	C₅×D₄	—	2	1	no	—
492	C₅×D₄	—	2	1	no	—
493	C₅×D₄	—	2	1	no	—
494	C₅×D₄	—	3	2	no	—
495	C₅×D₄	—	4	2	no	—
496	C₅×D₄	—	6	2	no	—
497	C₅×D₄	—	6	1	no	—
498	C₅×D₄	—	6	1	no	—
499	C₅×D₄	—	6	1	no	—
500	C₅×D₄	—	8	1	no	—
501	C₅×D₄	—	12	2	no	—
502	C₅×D₄	—	12	2	no	—
503	C₅×D₄	—	12	2	no	—
504	C₅×D₄	—	12	2	no	—
505	C₅×D₄	—	12	2	no	—
506	C₅×D₄	—	12	2	no	—
507	C₂×C₄×C₅	—	2	1	no	—
508	C₂×C₄×C₅	—	2	1	no	—
509	C₂×C₄×C₅	—	3	1	no	—
510	C₂×C₄×C₅	—	3	1	no	—
511	C₂×C₄×C₅	—	6	1	no	—
512	C₂×C₄×C₅	—	6	1	no	—
513	C₂×C₄×C₅	—	6	1	no	—
514	C₂×C₄×C₅	—	6	1	no	—
515	C₂×C₄×C₅	—	6	1	no	—
516	C₂×C₄×C₅	—	6	1	no	—
517	C₂×C₄×C₅	—	12	2	no	—
518	C₂×C₄×C₅	—	12	2	no	—
519	C₂×C₄×C₅	—	12	2	no	—
520	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
521	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
522	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
523	C₅×C₈	—	2	1	no	—
524	C₅×C₈	—	2	1	no	—
525	C₅×C₈	—	3	2	no	—
526	C₅×C₈	—	6	1	no	—
527	C₂×#41	—	3	1	no	—
528	C₂²×Q₈	—	3	1	no	—
529	C₂²×D₄	—	3	1	no	—
530	C₂²×D₄	—	3	1	no	—
531	C₂²×D₄	—	6	1	no	—
532	AGL(1,ℤ/8)	—	6	4	no	—
533	C₂×SD₁₆	—	3	1	no	—
534	C₂×SD₁₆	—	3	1	no	—
535	C₂×SD₁₆	—	3	1	no	—
536	C₂×SD₁₆	—	3	1	no	—
537	C₂×SD₁₆	—	6	4	no	—
538	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
539	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
540	C₂×D₈	—	3	1	no	—
541	C₂×D₈	—	3	1	no	—
542	C₂×D₈	—	3	1	no	—
543	C₂×M₁₆	—	3	1	no	—
544	C₂²×C₈	—	3	1	no	—
545	#127	C₂×C₅×D₃	1	1	yes	characteristic
546	#124	—	3	1	no	—
547	#124	—	6	1	no	—
548	C₂²⋊Q₈	—	3	1	no	—
549	C₂²⋊Q₈	—	6	1	no	—
550	#121	—	3	1	no	—
551	#121	—	3	1	no	—
552	#121	—	3	1	no	—
553	#121	—	6	1	no	—
554	#121	—	6	1	no	—
555	#120	—	6	1	no	—
556	#120	—	6	1	no	—
557	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
558	C₄×D₄	—	3	1	no	—
559	C₄×D₄	—	3	1	no	—
560	C₄×D₄	—	6	1	no	—
561	#107	—	3	1	no	—
562	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
563	#103	—	3	1	no	—
564	#103	—	3	1	no	—
565	#102	—	3	1	no	—
566	#102	—	3	1	no	—
567	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
568	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
569	C₂²⋊C₈	—	3	1	no	—
570	C₂²⋊C₈	—	3	1	no	—
571	#97	—	3	1	no	—
572	C₂×C₃×C₅	—	8	1	no	—
573	C₂×C₃×C₅	—	8	1	no	—
574	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
575	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
576	C₂×C₃×C₅	#577	1	1	yes	characteristic
577	C₅×D₃	—	2	2	no	—
578	C₅×D₃	—	4	1	no	—
579	C₅×D₃	—	4	2	no	—
580	C₅×D₃	—	8	1	no	—
581	C₂³×C₃	—	2	1	no	—
582	C₂³×C₃	—	2	1	no	—
583	C₂²×D₃	—	2	1	no	—
584	C₂²×D₃	—	2	1	no	—
585	C₂²×D₃	—	4	2	no	—
586	C₂²×D₃	—	4	2	no	—
587	C₂²×D₃	—	4	2	no	—
588	C₂²×D₃	—	4	2	no	—
589	C₂²×D₃	—	8	1	no	—
590	C₂²×D₃	—	8	1	no	—
591	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
592	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
593	C₃×Q₈	—	2	1	no	—
594	C₃×Q₈	C₂×C₅×D₄	1	2	yes	complemented
595	C₃×D₄	—	2	1	no	—
596	C₃×D₄	—	2	1	no	—
597	C₃×D₄	—	2	1	no	—
598	C₃×D₄	—	2	1	no	—
599	C₃×D₄	—	4	2	no	—
600	C₃×D₄	—	8	1	no	—
601	C₂×C₃×C₄	—	2	1	no	—
602	C₂×C₃×C₄	—	2	1	no	—
603	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
604	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
605	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
606	#67	—	4	2	no	—
607	#67	—	4	2	no	—
608	#67	—	4	2	no	—
609	#67	—	4	2	no	—
610	C₂×Dic₃	—	2	1	no	—
611	C₂×Dic₃	—	2	1	no	—
612	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
613	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
614	D₁₂	—	2	2	no	—
615	D₁₂	—	2	1	no	—
616	D₁₂	—	2	1	no	—
617	D₁₂	—	2	1	no	—
618	D₁₂	—	4	2	no	—
619	D₁₂	—	4	2	no	—
620	D₁₂	C₂×C₅×D₄	1	2	yes	—
621	C₄×D₃	—	2	1	no	—
622	C₄×D₃	—	2	1	no	—
623	C₄×D₃	—	2	1	no	—
624	C₄×D₃	—	2	1	no	—
625	C₄×D₃	—	4	2	no	—
626	C₄×D₃	—	4	2	no	—
627	C₄×D₃	—	4	2	no	—
628	Dic₆	—	2	1	no	—
629	Dic₆	—	2	1	no	—
630	Dic₆	—	4	2	no	—
631	C₃×C₈	—	2	1	no	—
632	C₃×C₈	—	2	1	no	—
633	C₃⋊C₈	—	2	1	no	—
634	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	complemented
635	C₂²×C₅	—	3	2	no	—
636	C₂²×C₅	—	4	1	no	—
637	C₂²×C₅	—	4	1	no	—
638	C₂²×C₅	—	4	1	no	—
639	C₂²×C₅	—	4	1	no	—
640	C₂²×C₅	—	4	1	no	—
641	C₂²×C₅	—	4	1	no	—
642	C₂²×C₅	—	6	1	no	—
643	C₂²×C₅	—	6	1	no	—
644	C₂²×C₅	—	6	1	no	—
645	C₂²×C₅	—	6	1	no	—
646	C₂²×C₅	—	6	1	no	—
647	C₂²×C₅	—	6	2	no	—
648	C₂²×C₅	—	12	1	no	—
649	C₂²×C₅	—	12	1	no	—
650	C₂²×C₅	—	12	1	no	—
651	C₂²×C₅	—	12	1	no	—
652	C₂²×C₅	—	12	1	no	—
653	C₂²×C₅	—	24	4	no	—
654	C₂²×C₅	—	24	4	no	—
655	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
656	C₄×C₅	—	2	1	no	—
657	C₄×C₅	—	2	1	no	—
658	C₄×C₅	—	2	2	no	—
659	C₄×C₅	—	4	1	no	—
660	C₄×C₅	—	6	1	no	—
661	C₄×C₅	—	6	1	no	—
662	C₄×C₅	—	12	1	no	—
663	C₄×C₅	—	12	1	no	—
664	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
665	C₄×C₅	#1009	1	1	yes	characteristic
666	C₂⁴	—	6	1	no	—
667	C₂⁴	—	6	1	no	—
668	#41	—	6	2	no	—
669	#41	—	12	1	no	—
670	C₂×Q₈	—	3	1	no	—
671	C₂×Q₈	—	6	1	no	—
672	C₂×Q₈	—	6	2	no	—
673	C₂×Q₈	—	12	1	no	—
674	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	3	1	no	—
678	C₂×D₄	—	3	1	no	—
679	C₂×D₄	—	3	1	no	—
680	C₂×D₄	—	6	1	no	—
681	C₂×D₄	—	6	1	no	—
682	C₂×D₄	—	6	1	no	—
683	C₂×D₄	—	6	1	no	—
684	C₂×D₄	—	6	2	no	—
685	C₂×D₄	—	6	2	no	—
686	C₂×D₄	—	6	1	no	—
687	C₂×D₄	—	6	1	no	—
688	C₂×D₄	—	12	1	no	—
689	C₂×D₄	—	12	1	no	—
690	C₂×D₄	—	12	4	no	—
691	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
692	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
693	C₂²×C₄	—	3	1	no	—
694	C₂²×C₄	—	3	1	no	—
695	C₂²×C₄	—	6	1	no	—
696	C₂²×C₄	—	6	1	no	—
697	C₂²×C₄	—	6	1	no	—
698	SD₁₆	—	2	2	no	—
699	SD₁₆	—	2	2	no	—
700	SD₁₆	—	3	4	no	—
701	SD₁₆	—	6	2	no	—
702	SD₁₆	—	6	2	no	—
703	SD₁₆	—	12	1	no	—
704	D₈	—	6	2	no	—
705	D₈	—	6	2	no	—
706	D₈	—	12	1	no	—
707	M₁₆	—	6	2	no	—
708	C₂×C₈	—	3	1	no	—
709	C₂×C₈	—	3	1	no	—
710	C₂×C₈	—	6	2	no	—
711	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
712	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	3	1	no	—
715	C₄⋊C₄	—	3	1	no	—
716	C₄⋊C₄	—	6	1	no	—
717	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
718	C₂²⋊C₄	—	3	1	no	—
719	C₂²⋊C₄	—	3	1	no	—
720	C₂²⋊C₄	—	6	1	no	—
721	C₂²⋊C₄	—	6	1	no	—
722	C₂²⋊C₄	—	6	1	no	—
723	C₂²⋊C₄	—	6	1	no	—
724	C₂²⋊C₄	—	6	1	no	—
725	C₂²⋊C₄	—	6	1	no	—
726	C₂²⋊C₄	—	6	1	no	—
727	C₄²	—	2	1	no	—
728	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
729	C₃×C₅	#3265	1	1	yes	characteristic, complemented, Hall
730	C₂²×C₃	—	4	1	no	—
731	C₂²×C₃	—	4	1	no	—
732	C₂²×C₃	—	4	1	no	—
733	C₂²×C₃	—	4	1	no	—
734	C₂²×C₃	—	4	1	no	—
735	C₂²×C₃	—	4	1	no	—
736	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
737	C₂×D₃	—	2	1	no	—
738	C₂×D₃	—	2	1	no	—
739	C₂×D₃	—	2	1	no	—
740	C₂×D₃	—	2	2	no	—
741	C₂×D₃	—	2	1	no	—
742	C₂×D₃	—	2	1	no	—
743	C₂×D₃	—	4	1	no	—
744	C₂×D₃	—	4	1	no	—
745	C₂×D₃	—	4	1	no	—
746	C₂×D₃	—	4	1	no	—
747	C₂×D₃	—	4	1	no	—
748	C₂×D₃	—	8	4	no	—
749	C₂×D₃	—	8	4	no	—
750	C₂×D₃	C₅×AGL(1,ℤ/8)	1	2	yes	complemented
751	C₃×C₄	—	2	2	no	—
752	C₃×C₄	—	2	1	no	—
753	C₃×C₄	—	2	1	no	—
754	C₃×C₄	—	4	1	no	—
755	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
756	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
757	Dic₃	—	2	1	no	—
758	Dic₃	—	2	1	no	—
759	Dic₃	—	4	1	no	—
760	Dic₃	—	4	1	no	—
761	C₂×C₅	—	6	2	no	—
762	C₂×C₅	—	8	1	no	—
763	C₂×C₅	—	8	1	no	—
764	C₂×C₅	—	12	1	no	—
765	C₂×C₅	—	12	2	no	—
766	C₂×C₅	—	24	1	no	—
767	C₂×C₅	#5609	1	1	yes	characteristic
768	C₂×C₅	#5762	1	1	yes	characteristic
769	C₂×C₅	D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	3	1	no	—
773	C₂³	—	3	1	no	—
774	C₂³	—	6	1	no	—
775	C₂³	—	6	1	no	—
776	C₂³	—	12	2	no	—
777	C₂³	—	12	2	no	—
778	C₂³	—	12	2	no	—
779	C₂³	—	12	2	no	—
780	C₂³	—	24	1	no	—
781	C₂³	—	24	1	no	—
782	Q₈	—	2	1	no	—
783	Q₈	—	6	1	no	—
784	Q₈	—	6	1	no	—
785	Q₈	—	12	2	no	—
786	Q₈	C₅×D₃×D₄	1	2	yes	complemented
787	D₄	—	2	1	no	—
788	D₄	—	2	1	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	1	no	—
791	D₄	—	3	2	no	—
792	D₄	—	4	2	no	—
793	D₄	—	6	2	no	—
794	D₄	—	6	1	no	—
795	D₄	—	6	1	no	—
796	D₄	—	6	1	no	—
797	D₄	—	8	1	no	—
798	D₄	—	12	2	no	—
799	D₄	—	12	2	no	—
800	D₄	—	12	2	no	—
801	D₄	—	12	2	no	—
802	D₄	—	12	2	no	—
803	D₄	—	12	2	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	3	1	no	—
807	C₂×C₄	—	3	1	no	—
808	C₂×C₄	—	6	1	no	—
809	C₂×C₄	—	6	1	no	—
810	C₂×C₄	—	6	1	no	—
811	C₂×C₄	—	6	1	no	—
812	C₂×C₄	—	6	1	no	—
813	C₂×C₄	—	6	1	no	—
814	C₂×C₄	—	12	2	no	—
815	C₂×C₄	—	12	2	no	—
816	C₂×C₄	—	12	2	no	—
817	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
818	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
819	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
820	C₈	—	2	1	no	—
821	C₈	—	2	1	no	—
822	C₈	—	3	2	no	—
823	C₈	—	6	1	no	—
824	C₂×C₃	—	8	1	no	—
825	C₂×C₃	—	8	1	no	—
826	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
827	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
828	C₂×C₃	C₅×#577	1	1	yes	characteristic
829	D₃	—	2	2	no	—
830	D₃	—	4	1	no	—
831	D₃	—	4	2	no	—
832	D₃	—	8	1	no	—
833	C₅	#80404	1	1	yes	characteristic, direct product factor, Sylow
834	C₂²	—	3	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	6	1	no	—
842	C₂²	—	6	1	no	—
843	C₂²	—	6	1	no	—
844	C₂²	—	6	1	no	—
845	C₂²	—	6	1	no	—
846	C₂²	—	6	2	no	—
847	C₂²	—	12	1	no	—
848	C₂²	—	12	1	no	—
849	C₂²	—	12	1	no	—
850	C₂²	—	12	1	no	—
851	C₂²	—	12	1	no	—
852	C₂²	—	24	4	no	—
853	C₂²	—	24	4	no	—
854	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	2	no	—
858	C₄	—	4	1	no	—
859	C₄	—	6	1	no	—
860	C₄	—	6	1	no	—
861	C₄	—	12	1	no	—
862	C₄	—	12	1	no	—
863	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
864	C₄	C₅×#1009	1	1	yes	characteristic
865	C₃	C₅×#3265	1	1	yes	characteristic, complemented, Sylow
866	C₂	—	6	2	no	—
867	C₂	—	8	1	no	—
868	C₂	—	8	1	no	—
869	C₂	—	12	1	no	—
870	C₂	—	12	2	no	—
871	C₂	—	24	1	no	—
872	C₂	C₅×#5609	1	1	yes	characteristic
873	C₂	C₅×#5762	1	1	yes	characteristic
874	C₂	C₅×D₃×AGL(1,ℤ/8)	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×#460	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#460	D₃
hypocenter	C₃	C₅×#3265
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#460

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#914	C₂	semidirect
2. C₂×C₅×D₃×SD₁₆	C₂	semidirect
3. C₅×#5717	C₂	semidirect
4. C₅×#5576	C₂	semidirect
5. C₃×C₅×#460	C₂	semidirect
6. C₅×#5172	C₂	semidirect
7. C₅×#5170	C₂	semidirect
8. C₅×#5074	C₂	semidirect
9. C₅×#5026	C₂	semidirect
10. C₅×#4844	C₂	semidirect
11. C₅×#4836	C₂	semidirect
12. C₅×#4780	C₂	semidirect
13. C₅×#4776	C₂	semidirect
14. C₅×#4775	C₂	semidirect
15. C₅×#4773	C₂	semidirect
17. C₂×C₅×#239	C₂²	semidirect
18. C₂×C₅×D₃×Q₈	C₂²	semidirect
22. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
23. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
25. C₃×C₄×C₅×Q₈	C₂²	semidirect
32. C₂×C₅×#214	C₂²	semidirect
33. C₂×C₅×#214	C₂²	semidirect
34. C₂×C₅×#213	C₂²	semidirect
35. C₂×C₅×#213	C₂²	semidirect
40. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
41. C₂×C₅×D₃×C₈	C₂²	semidirect
43. C₅×#897	C₂²	semidirect
45. C₅×#895	C₂²	semidirect
47. C₅×#875	C₂²	semidirect
51. C₃×C₅×C₄⋊C₈	C₂²	semidirect
52. C₃×C₅×#102	C₂²	semidirect
53. C₃×C₅×#102	C₂²	semidirect
54. C₅×#835	C₂²	semidirect
55. C₅×#821	C₂²	semidirect
56. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
57. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
58. C₅×#816	C₂²	semidirect
60. C₅×#807	C₂²	semidirect
61. C₅×#803	C₂²	semidirect
62. #80404	C₅	direct (N × H)
71. C₅×#460	D₃	semidirect
120. C₅×#215	D₄	semidirect
141. C₂×#914	C₂×C₅	semidirect
142. C₂×D₃×SD₁₆	C₂×C₅	semidirect
143. #5717	C₂×C₅	semidirect
144. #5576	C₂×C₅	semidirect
145. C₃×#460	C₂×C₅	semidirect
146. #5172	C₂×C₅	semidirect
147. #5170	C₂×C₅	semidirect
148. #5074	C₂×C₅	semidirect
149. #5026	C₂×C₅	semidirect
150. #4844	C₂×C₅	semidirect
151. #4836	C₂×C₅	semidirect
152. #4780	C₂×C₅	semidirect
153. #4776	C₂×C₅	semidirect
154. #4775	C₂×C₅	semidirect
155. #4773	C₂×C₅	semidirect
167. C₂×C₅×SD₁₆	C₂×D₃	semidirect
168. C₂×C₅×SD₁₆	C₂×D₃	semidirect
186. C₄×C₅×Q₈	C₂×D₃	semidirect
191. C₅×C₄⋊C₈	C₂×D₃	semidirect
196. C₅×#102	C₂×D₃	semidirect
197. C₅×#102	C₂×D₃	semidirect
215. C₃×C₅×Q₈	C₂×D₄	semidirect
255. C₅×C₃⋊C₈	C₂×D₄	semidirect
256. C₂×#239	C₂²×C₅	semidirect
257. C₂×D₃×Q₈	C₂²×C₅	semidirect
261. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
262. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
264. C₃×C₄×Q₈	C₂²×C₅	semidirect
271. C₂×#214	C₂²×C₅	semidirect
272. C₂×#214	C₂²×C₅	semidirect
273. C₂×#213	C₂²×C₅	semidirect
274. C₂×#213	C₂²×C₅	semidirect
279. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
280. C₂×D₃×C₈	C₂²×C₅	semidirect
282. #897	C₂²×C₅	semidirect
284. #895	C₂²×C₅	semidirect
286. #875	C₂²×C₅	semidirect
290. C₃×C₄⋊C₈	C₂²×C₅	semidirect
291. C₃×#102	C₂²×C₅	semidirect
292. C₃×#102	C₂²×C₅	semidirect
293. #835	C₂²×C₅	semidirect
294. #821	C₂²×C₅	semidirect
295. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
296. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
297. #816	C₂²×C₅	semidirect
299. #807	C₂²×C₅	semidirect
300. #803	C₂²×C₅	semidirect
372. #460	C₅×D₃	semidirect
399. C₂×C₅×D₃	AGL(1,ℤ/8)	semidirect
452. #215	C₅×D₄	semidirect
489. C₅×Q₈	D₃×D₄	semidirect
538. C₂×SD₁₆	C₂×C₅×D₃	semidirect
539. C₂×SD₁₆	C₂×C₅×D₃	semidirect
557. C₄×Q₈	C₂×C₅×D₃	semidirect
562. C₄⋊C₈	C₂×C₅×D₃	semidirect
567. #102	C₂×C₅×D₃	semidirect
568. #102	C₂×C₅×D₃	semidirect
594. C₃×Q₈	C₂×C₅×D₄	semidirect
634. C₃⋊C₈	C₂×C₅×D₄	semidirect
729. C₃×C₅	#3265	semidirect
750. C₂×D₃	C₅×AGL(1,ℤ/8)	semidirect
786. Q₈	C₅×D₃×D₄	semidirect
833. C₅	#80404	direct (N × H)
865. C₃	C₅×#3265	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#914	2
C₂×C₅×D₃×SD₁₆	2
C₅×#5717	2
C₅×#5576	2
C₃×C₅×#460	2
C₅×#5172	2
C₅×#5170	2
C₅×#5074	2
C₅×#5026	2
C₅×#4844	2
C₅×#4836	2
C₅×#4780	2
C₅×#4776	2
C₅×#4775	2
C₅×#4773	2
C₅×#3265	3
#80404	5

Subgroups — C5×#80404 #14453433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80404 #14453433