Subgroups — C₅×#81856 #14453190

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 904 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×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5717	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5676	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5172	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5171	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5169	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5159	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5156	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5156	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5072	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5057	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4711	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4706	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3264	—	3	1	no	maximal, Hall
17	C₂×C₅×#239	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₅×D₃×D₄	—	2	1	no	—
19	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
28	C₅×#946	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₅×#215	C₂²	1	1	yes	characteristic, complemented
30	C₅×#938	—	2	1	no	—
31	C₅×#938	C₂²	1	1	yes	characteristic
32	C₅×#938	C₂²	1	1	yes	characteristic, complemented
33	C₅×#938	C₂²	1	1	yes	characteristic, complemented
34	C₅×#937	—	2	1	no	—
35	C₅×#937	—	2	1	no	—
36	C₂×C₅×#213	C₂²	1	1	yes	characteristic
37	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
39	C₅×#914	—	2	4	no	—
40	C₅×D₃×D₈	—	2	4	no	—
41	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
42	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
44	C₅×#884	—	2	1	no	—
45	C₅×#883	—	2	1	no	—
46	C₅×#882	—	2	1	no	—
47	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
48	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
49	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
52	C₅×#835	C₂²	1	1	yes	characteristic, complemented
53	C₅×#832	C₂²	1	1	yes	characteristic, complemented
54	C₅×#832	C₂²	1	1	yes	characteristic, complemented
55	C₅×#832	C₂²	1	1	yes	characteristic, complemented
56	C₅×#821	C₂²	1	1	yes	characteristic, complemented
57	C₅×#821	C₂²	1	1	yes	characteristic, complemented
58	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₅×#817	C₂²	1	1	yes	characteristic, complemented
61	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
62	#81856	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
64	C₂²×C₅×D₈	—	3	1	no	—
65	C₅×#546	—	3	1	no	—
66	C₅×D₄²	—	3	1	no	—
67	C₅×#496	D₃	1	1	yes	characteristic, complemented
68	C₅×#469	—	3	1	no	—
69	C₅×#465	—	3	1	no	—
70	C₅×#463	—	3	1	no	—
71	C₅×#459	—	3	1	no	—
72	C₅×#450	—	3	1	no	—
73	C₅×#449	—	3	1	no	—
74	C₅×#447	—	3	1	no	—
75	C₅×#447	—	3	1	no	—
76	C₅×#442	—	3	1	no	—
77	C₅×#435	—	3	1	no	—
78	C₂³×C₅×D₃	—	2	1	no	—
79	C₂³×C₅×D₃	—	2	1	no	—
80	C₂³×C₅×D₃	—	2	1	no	—
81	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×D₄	—	2	1	no	—
83	C₂×C₃×C₅×D₄	—	2	1	no	—
84	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
87	C₂×C₅×#67	—	2	1	no	—
88	C₂×C₅×#67	—	2	1	no	—
89	C₂×C₅×#67	—	2	1	no	—
90	C₂×C₅×#67	—	2	1	no	—
91	C₂×C₅×#67	—	2	1	no	—
92	C₂×C₅×#67	—	2	1	no	—
93	C₅×#239	—	2	2	no	—
94	C₅×#239	—	4	1	no	—
95	C₅×D₃×D₄	—	2	2	no	—
96	C₅×D₃×D₄	—	2	2	no	—
97	C₅×D₃×D₄	—	2	2	no	—
98	C₅×D₃×D₄	—	4	1	no	—
99	C₅×D₃×D₄	—	4	1	no	—
100	C₅×D₃×D₄	—	4	1	no	—
101	C₅×D₃×D₄	—	4	4	no	—
102	C₂×C₅×D₁₂	—	2	1	no	—
103	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
104	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
105	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
106	C₂×C₄×C₅×D₃	—	2	1	no	—
107	C₂×C₄×C₅×D₃	—	2	1	no	—
108	C₂×C₄×C₅×D₃	—	2	1	no	—
109	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
110	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
111	C₃×C₅×SD₁₆	—	2	2	no	—
112	C₃×C₅×SD₁₆	—	4	1	no	—
113	C₃×C₅×D₈	—	2	2	no	—
114	C₃×C₅×D₈	—	4	1	no	—
115	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
116	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
117	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
118	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
119	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
120	C₅×#217	—	2	1	no	—
121	C₅×#217	—	2	1	no	—
122	C₅×#217	—	2	1	no	—
123	C₅×#215	—	2	2	no	—
124	C₅×#213	—	2	2	no	—
125	C₅×#213	—	2	2	no	—
126	C₅×#213	—	2	2	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	D₄	1	1	yes	characteristic
133	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
134	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
135	C₅×Dic₃⋊C₄	—	2	1	no	—
136	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
137	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
138	C₅×D₂₄	D₄	1	4	yes	complemented
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×D₈	C₂×C₅	1	1	yes	characteristic, complemented
143	#5717	C₂×C₅	1	1	yes	characteristic, complemented
144	#5676	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#496	C₂×C₅	1	1	yes	characteristic, complemented
146	#5172	C₂×C₅	1	1	yes	characteristic, complemented
147	#5171	C₂×C₅	1	1	yes	characteristic, complemented
148	#5169	C₂×C₅	1	1	yes	characteristic, complemented
149	#5159	C₂×C₅	1	1	yes	characteristic, complemented
150	#5156	C₂×C₅	1	1	yes	characteristic, complemented
151	#5156	C₂×C₅	1	1	yes	characteristic, complemented
152	#5072	C₂×C₅	1	1	yes	characteristic, complemented
153	#5057	C₂×C₅	1	1	yes	characteristic, complemented
154	#4711	C₂×C₅	1	1	yes	characteristic, complemented
155	#4706	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂×C₅×#41	—	3	1	no	—
157	C₂²×C₅×D₄	—	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	C₂×D₃	1	1	yes	characteristic, complemented
164	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
165	C₂×C₅×D₈	—	3	1	no	—
166	C₂×C₅×D₈	—	3	1	no	—
167	C₂×C₅×D₈	—	3	1	no	—
168	C₂×C₅×D₈	—	3	1	no	—
169	C₂×C₅×D₈	—	6	4	no	—
170	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
171	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
172	C₂×C₅×M₁₆	—	3	1	no	—
173	C₂²×C₅×C₈	—	3	1	no	—
174	C₅×#127	C₂×D₃	1	1	yes	characteristic, complemented
175	C₅×#124	C₂×D₃	1	1	yes	characteristic, complemented
176	C₅×#123	—	6	1	no	—
177	C₅×C₂²⋊Q₈	—	3	1	no	—
178	C₅×#121	—	3	1	no	—
179	C₅×#121	—	3	1	no	—
180	C₅×#121	—	3	1	no	—
181	C₅×#121	—	6	1	no	—
182	C₅×#121	—	6	1	no	—
183	C₅×#120	—	6	1	no	—
184	C₅×#120	—	6	1	no	—
185	C₅×#120	—	6	1	no	—
186	C₄×C₅×D₄	—	3	1	no	—
187	C₄×C₅×D₄	—	3	1	no	—
188	C₄×C₅×D₄	—	3	1	no	—
189	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
190	C₅×#106	—	3	1	no	—
191	C₅×C₄⋊C₈	—	3	1	no	—
192	C₅×#103	—	3	1	no	—
193	C₅×#102	—	3	1	no	—
194	C₅×#102	—	3	1	no	—
195	C₅×#102	—	3	1	no	—
196	C₅×#102	—	3	1	no	—
197	C₅×#102	—	3	1	no	—
198	C₅×C₂²⋊C₈	—	3	1	no	—
199	C₅×C₂²⋊C₈	—	3	1	no	—
200	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
201	#3264	—	3	1	no	Sylow
202	C₂³×C₃×C₅	—	2	1	no	—
203	C₂³×C₃×C₅	—	2	1	no	—
204	C₂³×C₃×C₅	—	2	1	no	—
205	C₂²×C₅×D₃	—	2	1	no	—
206	C₂²×C₅×D₃	—	2	1	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	—	4	2	no	—
211	C₂²×C₅×D₃	—	4	2	no	—
212	C₂²×C₅×D₃	—	4	2	no	—
213	C₂²×C₅×D₃	—	8	1	no	—
214	C₂²×C₅×D₃	—	8	1	no	—
215	C₂²×C₅×D₃	—	8	1	no	—
216	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
218	C₃×C₅×Q₈	—	2	1	no	—
219	C₃×C₅×Q₈	—	2	1	no	—
220	C₃×C₅×D₄	—	2	1	no	—
221	C₃×C₅×D₄	—	2	1	no	—
222	C₃×C₅×D₄	—	2	1	no	—
223	C₃×C₅×D₄	—	2	1	no	—
224	C₃×C₅×D₄	—	2	1	no	—
225	C₃×C₅×D₄	—	2	1	no	—
226	C₃×C₅×D₄	—	4	2	no	—
227	C₃×C₅×D₄	—	8	1	no	—
228	C₂×C₃×C₄×C₅	—	2	1	no	—
229	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
230	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
231	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
232	C₅×#67	—	4	2	no	—
233	C₅×#67	—	4	2	no	—
234	C₅×#67	—	4	2	no	—
235	C₅×#67	—	4	2	no	—
236	C₅×#67	—	4	2	no	—
237	C₅×#67	—	8	1	no	—
238	C₂×C₅×Dic₃	—	2	1	no	—
239	C₂×C₅×Dic₃	—	2	1	no	—
240	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
241	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
242	C₅×D₁₂	—	2	2	no	—
243	C₅×D₁₂	—	2	1	no	—
244	C₅×D₁₂	—	2	1	no	—
245	C₅×D₁₂	—	4	2	no	—
246	C₅×D₁₂	C₂×D₄	1	2	yes	—
247	C₅×D₁₂	C₂×D₄	1	2	yes	complemented
248	C₄×C₅×D₃	—	2	1	no	—
249	C₄×C₅×D₃	—	2	1	no	—
250	C₄×C₅×D₃	—	2	1	no	—
251	C₄×C₅×D₃	—	2	1	no	—
252	C₄×C₅×D₃	—	4	2	no	—
253	C₄×C₅×D₃	—	4	2	no	—
254	C₄×C₅×D₃	—	8	1	no	—
255	C₃×C₅×C₈	—	2	1	no	—
256	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
257	C₅×C₃⋊C₈	—	2	1	no	—
258	C₅×C₃⋊C₈	—	2	1	no	—
259	C₂×#239	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₂×D₃×D₄	—	2	1	no	—
261	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
262	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
265	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
266	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
269	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
270	#946	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
272	#938	—	2	1	no	—
273	#938	C₂²×C₅	1	1	yes	characteristic
274	#938	C₂²×C₅	1	1	yes	characteristic, complemented
275	#938	C₂²×C₅	1	1	yes	characteristic, complemented
276	#937	—	2	1	no	—
277	#937	—	2	1	no	—
278	C₂×#213	C₂²×C₅	1	1	yes	characteristic
279	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
280	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
281	#914	—	2	4	no	—
282	D₃×D₈	—	2	4	no	—
283	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
284	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
286	#884	—	2	1	no	—
287	#883	—	2	1	no	—
288	#882	—	2	1	no	—
289	D₃×C₂²⋊C₄	—	2	1	no	—
290	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
291	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
292	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
293	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
294	#835	C₂²×C₅	1	1	yes	characteristic, complemented
295	#832	C₂²×C₅	1	1	yes	characteristic, complemented
296	#832	C₂²×C₅	1	1	yes	characteristic, complemented
297	#832	C₂²×C₅	1	1	yes	characteristic, complemented
298	#821	C₂²×C₅	1	1	yes	characteristic, complemented
299	#821	C₂²×C₅	1	1	yes	characteristic, complemented
300	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
301	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
302	#817	C₂²×C₅	1	1	yes	characteristic, complemented
303	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
304	C₂⁴×C₅	—	6	1	no	—
305	C₂⁴×C₅	—	6	1	no	—
306	C₂⁴×C₅	—	6	1	no	—
307	C₅×#41	—	6	2	no	—
308	C₅×#41	—	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	2	no	—
322	C₂×C₅×D₄	—	6	1	no	—
323	C₂×C₅×D₄	—	6	1	no	—
324	C₂×C₅×D₄	—	6	1	no	—
325	C₂×C₅×D₄	—	12	1	no	—
326	C₂×C₅×D₄	—	12	1	no	—
327	C₂×C₅×D₄	—	12	1	no	—
328	C₂×C₅×D₄	—	12	4	no	—
329	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
330	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
331	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
332	C₂²×C₄×C₅	—	3	1	no	—
333	C₂²×C₄×C₅	—	3	1	no	—
334	C₂²×C₄×C₅	—	6	1	no	—
335	C₂²×C₄×C₅	—	6	1	no	—
336	C₂²×C₄×C₅	—	6	1	no	—
337	C₅×SD₁₆	—	2	2	no	—
338	C₅×SD₁₆	—	4	1	no	—
339	C₅×SD₁₆	—	6	2	no	—
340	C₅×D₈	—	2	2	no	—
341	C₅×D₈	—	3	4	no	—
342	C₅×D₈	—	4	1	no	—
343	C₅×D₈	—	6	2	no	—
344	C₅×D₈	—	6	2	no	—
345	C₅×D₈	—	6	2	no	—
346	C₅×M₁₆	—	6	2	no	—
347	C₂×C₅×C₈	—	3	1	no	—
348	C₂×C₅×C₈	—	3	1	no	—
349	C₂×C₅×C₈	—	6	2	no	—
350	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
351	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
352	C₅×C₄⋊C₄	—	3	1	no	—
353	C₅×C₄⋊C₄	—	3	1	no	—
354	C₅×C₄⋊C₄	—	3	1	no	—
355	C₅×C₄⋊C₄	—	6	1	no	—
356	C₅×C₂²⋊C₄	—	2	1	no	—
357	C₅×C₂²⋊C₄	—	2	1	no	—
358	C₅×C₂²⋊C₄	—	3	1	no	—
359	C₅×C₂²⋊C₄	—	3	1	no	—
360	C₅×C₂²⋊C₄	—	6	1	no	—
361	C₅×C₂²⋊C₄	—	6	1	no	—
362	C₅×C₂²⋊C₄	—	6	1	no	—
363	C₅×C₂²⋊C₄	—	6	1	no	—
364	C₅×C₂²⋊C₄	—	6	1	no	—
365	C₅×C₂²⋊C₄	—	6	1	no	—
366	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
367	C₂×AGL(1,ℤ/8)	—	3	1	no	—
368	C₂²×D₈	—	3	1	no	—
369	#546	—	3	1	no	—
370	D₄²	—	3	1	no	—
371	#496	C₅×D₃	1	1	yes	characteristic, complemented
372	#469	—	3	1	no	—
373	#465	—	3	1	no	—
374	#463	—	3	1	no	—
375	#459	—	3	1	no	—
376	#450	—	3	1	no	—
377	#449	—	3	1	no	—
378	#447	—	3	1	no	—
379	#447	—	3	1	no	—
380	#442	—	3	1	no	—
381	#435	—	3	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	—	4	1	no	—
386	C₂²×C₃×C₅	—	4	1	no	—
387	C₂²×C₃×C₅	—	4	1	no	—
388	C₂²×C₃×C₅	—	4	1	no	—
389	C₂²×C₃×C₅	—	4	1	no	—
390	C₂²×C₃×C₅	—	4	1	no	—
391	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₅×D₃	—	2	1	no	—
393	C₂×C₅×D₃	—	2	1	no	—
394	C₂×C₅×D₃	—	2	1	no	—
395	C₂×C₅×D₃	—	2	2	no	—
396	C₂×C₅×D₃	—	2	2	no	—
397	C₂×C₅×D₃	—	2	1	no	—
398	C₂×C₅×D₃	—	2	1	no	—
399	C₂×C₅×D₃	—	4	1	no	—
400	C₂×C₅×D₃	—	4	1	no	—
401	C₂×C₅×D₃	—	4	1	no	—
402	C₂×C₅×D₃	—	4	1	no	—
403	C₂×C₅×D₃	—	8	4	no	—
404	C₂×C₅×D₃	—	8	4	no	—
405	C₂×C₅×D₃	—	8	4	no	—
406	C₂×C₅×D₃	AGL(1,ℤ/8)	1	2	yes	complemented
407	C₃×C₄×C₅	—	2	1	no	—
408	C₃×C₄×C₅	—	2	1	no	—
409	C₃×C₄×C₅	—	4	1	no	—
410	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
411	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
412	C₅×Dic₃	—	2	1	no	—
413	C₅×Dic₃	—	2	1	no	—
414	C₅×Dic₃	—	4	1	no	—
415	C₅×Dic₃	—	4	1	no	—
416	C₂³×D₃	—	2	1	no	—
417	C₂³×D₃	—	2	1	no	—
418	C₂³×D₃	—	2	1	no	—
419	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
420	C₂×C₃×D₄	—	2	1	no	—
421	C₂×C₃×D₄	—	2	1	no	—
422	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
423	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
425	C₂×#67	—	2	1	no	—
426	C₂×#67	—	2	1	no	—
427	C₂×#67	—	2	1	no	—
428	C₂×#67	—	2	1	no	—
429	C₂×#67	—	2	1	no	—
430	C₂×#67	—	2	1	no	—
431	#239	—	2	2	no	—
432	#239	—	4	1	no	—
433	D₃×D₄	—	2	2	no	—
434	D₃×D₄	—	2	2	no	—
435	D₃×D₄	—	2	2	no	—
436	D₃×D₄	—	4	1	no	—
437	D₃×D₄	—	4	1	no	—
438	D₃×D₄	—	4	1	no	—
439	D₃×D₄	—	4	4	no	—
440	C₂×D₁₂	—	2	1	no	—
441	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
442	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
443	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
444	C₂×C₄×D₃	—	2	1	no	—
445	C₂×C₄×D₃	—	2	1	no	—
446	C₂×C₄×D₃	—	2	1	no	—
447	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
448	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
449	C₃×SD₁₆	—	2	2	no	—
450	C₃×SD₁₆	—	4	1	no	—
451	C₃×D₈	—	2	2	no	—
452	C₃×D₈	—	4	1	no	—
453	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
454	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
455	C₃×C₂²⋊C₄	—	2	1	no	—
456	C₃×C₂²⋊C₄	—	2	1	no	—
457	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
458	#217	—	2	1	no	—
459	#217	—	2	1	no	—
460	#217	—	2	1	no	—
461	#215	—	2	2	no	—
462	#213	—	2	2	no	—
463	#213	—	2	2	no	—
464	#213	—	2	2	no	—
465	(C₂×D₃)⋊C₄	—	2	1	no	—
466	(C₂×D₃)⋊C₄	—	2	1	no	—
467	(C₂×D₃)⋊C₄	—	2	1	no	—
468	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
469	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
470	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
471	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
472	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
473	Dic₃⋊C₄	—	2	1	no	—
474	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
475	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
476	D₂₄	C₅×D₄	1	4	yes	complemented
477	ΓL(1,𝔽₂₅)	—	2	2	no	—
478	D₃×C₈	—	2	2	no	—
479	C₂³×C₅	—	2	1	no	—
480	C₂³×C₅	—	2	1	no	—
481	C₂³×C₅	—	2	1	no	—
482	C₂³×C₅	—	3	1	no	—
483	C₂³×C₅	—	3	1	no	—
484	C₂³×C₅	—	6	1	no	—
485	C₂³×C₅	—	6	1	no	—
486	C₂³×C₅	—	12	2	no	—
487	C₂³×C₅	—	12	2	no	—
488	C₂³×C₅	—	12	2	no	—
489	C₂³×C₅	—	12	2	no	—
490	C₂³×C₅	—	12	2	no	—
491	C₂³×C₅	—	12	2	no	—
492	C₂³×C₅	—	24	1	no	—
493	C₂³×C₅	—	24	1	no	—
494	C₂³×C₅	—	24	1	no	—
495	C₅×Q₈	—	2	1	no	—
496	C₅×Q₈	—	2	1	no	—
497	C₅×D₄	—	2	1	no	—
498	C₅×D₄	—	2	1	no	—
499	C₅×D₄	—	2	1	no	—
500	C₅×D₄	—	2	1	no	—
501	C₅×D₄	—	2	1	no	—
502	C₅×D₄	—	2	1	no	—
503	C₅×D₄	—	3	2	no	—
504	C₅×D₄	—	3	2	no	—
505	C₅×D₄	—	4	2	no	—
506	C₅×D₄	—	6	2	no	—
507	C₅×D₄	—	6	1	no	—
508	C₅×D₄	—	6	1	no	—
509	C₅×D₄	—	8	1	no	—
510	C₅×D₄	—	12	2	no	—
511	C₅×D₄	—	12	2	no	—
512	C₅×D₄	—	12	2	no	—
513	C₅×D₄	—	12	2	no	—
514	C₅×D₄	—	12	2	no	—
515	C₅×D₄	—	12	2	no	—
516	C₅×D₄	—	24	1	no	—
517	C₂×C₄×C₅	—	2	1	no	—
518	C₂×C₄×C₅	—	3	1	no	—
519	C₂×C₄×C₅	—	3	1	no	—
520	C₂×C₄×C₅	—	6	1	no	—
521	C₂×C₄×C₅	—	6	1	no	—
522	C₂×C₄×C₅	—	6	1	no	—
523	C₂×C₄×C₅	—	6	1	no	—
524	C₂×C₄×C₅	—	6	1	no	—
525	C₂×C₄×C₅	—	6	1	no	—
526	C₂×C₄×C₅	—	12	2	no	—
527	C₂×C₄×C₅	—	12	2	no	—
528	C₂×C₄×C₅	—	24	1	no	—
529	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
530	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
531	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
532	C₅×C₈	—	2	1	no	—
533	C₅×C₈	—	6	1	no	—
534	C₅×C₈	—	6	1	no	—
535	C₅×C₈	D₃×D₄	1	2	yes	complemented
536	C₂×#41	—	3	1	no	—
537	C₂²×D₄	—	3	1	no	—
538	C₂²×D₄	—	3	1	no	—
539	C₂²×D₄	—	3	1	no	—
540	C₂²×D₄	—	6	1	no	—
541	AGL(1,ℤ/8)	—	6	4	no	—
542	C₂×SD₁₆	—	3	1	no	—
543	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
544	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
545	C₂×D₈	—	3	1	no	—
546	C₂×D₈	—	3	1	no	—
547	C₂×D₈	—	3	1	no	—
548	C₂×D₈	—	3	1	no	—
549	C₂×D₈	—	6	4	no	—
550	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
551	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
552	C₂×M₁₆	—	3	1	no	—
553	C₂²×C₈	—	3	1	no	—
554	#127	C₂×C₅×D₃	1	1	yes	characteristic, complemented
555	#124	C₂×C₅×D₃	1	1	yes	characteristic, complemented
556	#123	—	6	1	no	—
557	C₂²⋊Q₈	—	3	1	no	—
558	#121	—	3	1	no	—
559	#121	—	3	1	no	—
560	#121	—	3	1	no	—
561	#121	—	6	1	no	—
562	#121	—	6	1	no	—
563	#120	—	6	1	no	—
564	#120	—	6	1	no	—
565	#120	—	6	1	no	—
566	C₄×D₄	—	3	1	no	—
567	C₄×D₄	—	3	1	no	—
568	C₄×D₄	—	3	1	no	—
569	C₂×C₂²⋊C₄	—	6	1	no	—
570	#106	—	3	1	no	—
571	C₄⋊C₈	—	3	1	no	—
572	#103	—	3	1	no	—
573	#102	—	3	1	no	—
574	#102	—	3	1	no	—
575	#102	—	3	1	no	—
576	#102	—	3	1	no	—
577	#102	—	3	1	no	—
578	C₂²⋊C₈	—	3	1	no	—
579	C₂²⋊C₈	—	3	1	no	—
580	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
581	C₂×C₃×C₅	—	8	1	no	—
582	C₂×C₃×C₅	—	8	1	no	—
583	C₂×C₃×C₅	—	8	1	no	—
584	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
585	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
586	C₂×C₃×C₅	#576	1	1	yes	characteristic
587	C₅×D₃	—	2	2	no	—
588	C₅×D₃	—	4	1	no	—
589	C₅×D₃	—	4	2	no	—
590	C₅×D₃	—	4	2	no	—
591	C₂³×C₃	—	2	1	no	—
592	C₂³×C₃	—	2	1	no	—
593	C₂³×C₃	—	2	1	no	—
594	C₂²×D₃	—	2	1	no	—
595	C₂²×D₃	—	2	1	no	—
596	C₂²×D₃	—	4	2	no	—
597	C₂²×D₃	—	4	2	no	—
598	C₂²×D₃	—	4	2	no	—
599	C₂²×D₃	—	4	2	no	—
600	C₂²×D₃	—	4	2	no	—
601	C₂²×D₃	—	4	2	no	—
602	C₂²×D₃	—	8	1	no	—
603	C₂²×D₃	—	8	1	no	—
604	C₂²×D₃	—	8	1	no	—
605	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
606	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
607	C₃×Q₈	—	2	1	no	—
608	C₃×Q₈	—	2	1	no	—
609	C₃×D₄	—	2	1	no	—
610	C₃×D₄	—	2	1	no	—
611	C₃×D₄	—	2	1	no	—
612	C₃×D₄	—	2	1	no	—
613	C₃×D₄	—	2	1	no	—
614	C₃×D₄	—	2	1	no	—
615	C₃×D₄	—	4	2	no	—
616	C₃×D₄	—	8	1	no	—
617	C₂×C₃×C₄	—	2	1	no	—
618	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
619	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
620	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
621	#67	—	4	2	no	—
622	#67	—	4	2	no	—
623	#67	—	4	2	no	—
624	#67	—	4	2	no	—
625	#67	—	4	2	no	—
626	#67	—	8	1	no	—
627	C₂×Dic₃	—	2	1	no	—
628	C₂×Dic₃	—	2	1	no	—
629	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
630	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
631	D₁₂	—	2	2	no	—
632	D₁₂	—	2	1	no	—
633	D₁₂	—	2	1	no	—
634	D₁₂	—	4	2	no	—
635	D₁₂	C₂×C₅×D₄	1	2	yes	—
636	D₁₂	C₂×C₅×D₄	1	2	yes	complemented
637	C₄×D₃	—	2	1	no	—
638	C₄×D₃	—	2	1	no	—
639	C₄×D₃	—	2	1	no	—
640	C₄×D₃	—	2	1	no	—
641	C₄×D₃	—	4	2	no	—
642	C₄×D₃	—	4	2	no	—
643	C₄×D₃	—	8	1	no	—
644	C₃×C₈	—	2	1	no	—
645	C₃×C₈	C₂×C₅×D₄	1	2	yes	complemented
646	C₃⋊C₈	—	2	1	no	—
647	C₃⋊C₈	—	2	1	no	—
648	C₂²×C₅	—	3	2	no	—
649	C₂²×C₅	—	4	1	no	—
650	C₂²×C₅	—	4	1	no	—
651	C₂²×C₅	—	4	1	no	—
652	C₂²×C₅	—	4	1	no	—
653	C₂²×C₅	—	4	1	no	—
654	C₂²×C₅	—	4	1	no	—
655	C₂²×C₅	—	4	1	no	—
656	C₂²×C₅	—	4	1	no	—
657	C₂²×C₅	—	4	1	no	—
658	C₂²×C₅	—	6	1	no	—
659	C₂²×C₅	—	6	1	no	—
660	C₂²×C₅	—	6	1	no	—
661	C₂²×C₅	—	6	2	no	—
662	C₂²×C₅	—	6	2	no	—
663	C₂²×C₅	—	6	1	no	—
664	C₂²×C₅	—	6	1	no	—
665	C₂²×C₅	—	12	1	no	—
666	C₂²×C₅	—	12	1	no	—
667	C₂²×C₅	—	12	1	no	—
668	C₂²×C₅	—	12	1	no	—
669	C₂²×C₅	—	24	4	no	—
670	C₂²×C₅	—	24	4	no	—
671	C₂²×C₅	—	24	4	no	—
672	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
673	C₄×C₅	—	2	1	no	—
674	C₄×C₅	—	2	1	no	—
675	C₄×C₅	—	4	1	no	—
676	C₄×C₅	—	6	1	no	—
677	C₄×C₅	—	6	1	no	—
678	C₄×C₅	—	12	1	no	—
679	C₄×C₅	—	12	1	no	—
680	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
681	C₄×C₅	#1004	1	1	yes	characteristic
682	C₂⁴	—	6	1	no	—
683	C₂⁴	—	6	1	no	—
684	C₂⁴	—	6	1	no	—
685	#41	—	6	2	no	—
686	#41	—	12	1	no	—
687	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	3	1	no	—
691	C₂×D₄	—	3	1	no	—
692	C₂×D₄	—	3	1	no	—
693	C₂×D₄	—	6	1	no	—
694	C₂×D₄	—	6	1	no	—
695	C₂×D₄	—	6	1	no	—
696	C₂×D₄	—	6	1	no	—
697	C₂×D₄	—	6	2	no	—
698	C₂×D₄	—	6	2	no	—
699	C₂×D₄	—	6	2	no	—
700	C₂×D₄	—	6	1	no	—
701	C₂×D₄	—	6	1	no	—
702	C₂×D₄	—	6	1	no	—
703	C₂×D₄	—	12	1	no	—
704	C₂×D₄	—	12	1	no	—
705	C₂×D₄	—	12	1	no	—
706	C₂×D₄	—	12	4	no	—
707	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
708	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
709	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
710	C₂²×C₄	—	3	1	no	—
711	C₂²×C₄	—	3	1	no	—
712	C₂²×C₄	—	6	1	no	—
713	C₂²×C₄	—	6	1	no	—
714	C₂²×C₄	—	6	1	no	—
715	SD₁₆	—	2	2	no	—
716	SD₁₆	—	4	1	no	—
717	SD₁₆	—	6	2	no	—
718	D₈	—	2	2	no	—
719	D₈	—	3	4	no	—
720	D₈	—	4	1	no	—
721	D₈	—	6	2	no	—
722	D₈	—	6	2	no	—
723	D₈	—	6	2	no	—
724	M₁₆	—	6	2	no	—
725	C₂×C₈	—	3	1	no	—
726	C₂×C₈	—	3	1	no	—
727	C₂×C₈	—	6	2	no	—
728	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
729	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
730	C₄⋊C₄	—	3	1	no	—
731	C₄⋊C₄	—	3	1	no	—
732	C₄⋊C₄	—	3	1	no	—
733	C₄⋊C₄	—	6	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	3	1	no	—
737	C₂²⋊C₄	—	3	1	no	—
738	C₂²⋊C₄	—	6	1	no	—
739	C₂²⋊C₄	—	6	1	no	—
740	C₂²⋊C₄	—	6	1	no	—
741	C₂²⋊C₄	—	6	1	no	—
742	C₂²⋊C₄	—	6	1	no	—
743	C₂²⋊C₄	—	6	1	no	—
744	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
745	C₃×C₅	#3264	1	1	yes	characteristic, complemented, Hall
746	C₂²×C₃	—	4	1	no	—
747	C₂²×C₃	—	4	1	no	—
748	C₂²×C₃	—	4	1	no	—
749	C₂²×C₃	—	4	1	no	—
750	C₂²×C₃	—	4	1	no	—
751	C₂²×C₃	—	4	1	no	—
752	C₂²×C₃	—	4	1	no	—
753	C₂²×C₃	—	4	1	no	—
754	C₂²×C₃	—	4	1	no	—
755	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
756	C₂×D₃	—	2	1	no	—
757	C₂×D₃	—	2	1	no	—
758	C₂×D₃	—	2	1	no	—
759	C₂×D₃	—	2	2	no	—
760	C₂×D₃	—	2	2	no	—
761	C₂×D₃	—	2	1	no	—
762	C₂×D₃	—	2	1	no	—
763	C₂×D₃	—	4	1	no	—
764	C₂×D₃	—	4	1	no	—
765	C₂×D₃	—	4	1	no	—
766	C₂×D₃	—	4	1	no	—
767	C₂×D₃	—	8	4	no	—
768	C₂×D₃	—	8	4	no	—
769	C₂×D₃	—	8	4	no	—
770	C₂×D₃	C₅×AGL(1,ℤ/8)	1	2	yes	complemented
771	C₃×C₄	—	2	1	no	—
772	C₃×C₄	—	2	1	no	—
773	C₃×C₄	—	4	1	no	—
774	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
775	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
776	Dic₃	—	2	1	no	—
777	Dic₃	—	2	1	no	—
778	Dic₃	—	4	1	no	—
779	Dic₃	—	4	1	no	—
780	C₂×C₅	—	6	2	no	—
781	C₂×C₅	—	8	1	no	—
782	C₂×C₅	—	8	1	no	—
783	C₂×C₅	—	8	1	no	—
784	C₂×C₅	—	12	1	no	—
785	C₂×C₅	—	12	2	no	—
786	C₂×C₅	—	12	2	no	—
787	C₂×C₅	#5717	1	1	yes	characteristic
788	C₂×C₅	D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
789	C₂×C₅	#5774	1	1	yes	characteristic
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	3	1	no	—
794	C₂³	—	3	1	no	—
795	C₂³	—	6	1	no	—
796	C₂³	—	6	1	no	—
797	C₂³	—	12	2	no	—
798	C₂³	—	12	2	no	—
799	C₂³	—	12	2	no	—
800	C₂³	—	12	2	no	—
801	C₂³	—	12	2	no	—
802	C₂³	—	12	2	no	—
803	C₂³	—	24	1	no	—
804	C₂³	—	24	1	no	—
805	C₂³	—	24	1	no	—
806	Q₈	—	2	1	no	—
807	Q₈	—	2	1	no	—
808	D₄	—	2	1	no	—
809	D₄	—	2	1	no	—
810	D₄	—	2	1	no	—
811	D₄	—	2	1	no	—
812	D₄	—	2	1	no	—
813	D₄	—	2	1	no	—
814	D₄	—	3	2	no	—
815	D₄	—	3	2	no	—
816	D₄	—	4	2	no	—
817	D₄	—	6	2	no	—
818	D₄	—	6	1	no	—
819	D₄	—	6	1	no	—
820	D₄	—	8	1	no	—
821	D₄	—	12	2	no	—
822	D₄	—	12	2	no	—
823	D₄	—	12	2	no	—
824	D₄	—	12	2	no	—
825	D₄	—	12	2	no	—
826	D₄	—	12	2	no	—
827	D₄	—	24	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	3	1	no	—
830	C₂×C₄	—	3	1	no	—
831	C₂×C₄	—	6	1	no	—
832	C₂×C₄	—	6	1	no	—
833	C₂×C₄	—	6	1	no	—
834	C₂×C₄	—	6	1	no	—
835	C₂×C₄	—	6	1	no	—
836	C₂×C₄	—	6	1	no	—
837	C₂×C₄	—	12	2	no	—
838	C₂×C₄	—	12	2	no	—
839	C₂×C₄	—	24	1	no	—
840	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
841	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
842	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
843	C₈	—	2	1	no	—
844	C₈	—	6	1	no	—
845	C₈	—	6	1	no	—
846	C₈	C₅×D₃×D₄	1	2	yes	complemented
847	C₂×C₃	—	8	1	no	—
848	C₂×C₃	—	8	1	no	—
849	C₂×C₃	—	8	1	no	—
850	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
851	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
852	C₂×C₃	C₅×#576	1	1	yes	characteristic
853	D₃	—	2	2	no	—
854	D₃	—	4	1	no	—
855	D₃	—	4	2	no	—
856	D₃	—	4	2	no	—
857	C₅	#81856	1	1	yes	characteristic, direct product factor, Sylow
858	C₂²	—	3	2	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	6	1	no	—
869	C₂²	—	6	1	no	—
870	C₂²	—	6	1	no	—
871	C₂²	—	6	2	no	—
872	C₂²	—	6	2	no	—
873	C₂²	—	6	1	no	—
874	C₂²	—	6	1	no	—
875	C₂²	—	12	1	no	—
876	C₂²	—	12	1	no	—
877	C₂²	—	12	1	no	—
878	C₂²	—	12	1	no	—
879	C₂²	—	24	4	no	—
880	C₂²	—	24	4	no	—
881	C₂²	—	24	4	no	—
882	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
885	C₄	—	4	1	no	—
886	C₄	—	6	1	no	—
887	C₄	—	6	1	no	—
888	C₄	—	12	1	no	—
889	C₄	—	12	1	no	—
890	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
891	C₄	C₅×#1004	1	1	yes	characteristic
892	C₃	C₅×#3264	1	1	yes	characteristic, complemented, Sylow
893	C₂	—	6	2	no	—
894	C₂	—	8	1	no	—
895	C₂	—	8	1	no	—
896	C₂	—	8	1	no	—
897	C₂	—	12	1	no	—
898	C₂	—	12	2	no	—
899	C₂	—	12	2	no	—
900	C₂	C₅×#5717	1	1	yes	characteristic
901	C₂	C₅×D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
902	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×#496	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#496	D₃
hypocenter	C₃	C₅×#3264
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#496

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×D₈	C₂	semidirect
3. C₅×#5717	C₂	semidirect
4. C₅×#5676	C₂	semidirect
5. C₃×C₅×#496	C₂	semidirect
6. C₅×#5172	C₂	semidirect
7. C₅×#5171	C₂	semidirect
8. C₅×#5169	C₂	semidirect
9. C₅×#5159	C₂	semidirect
10. C₅×#5156	C₂	semidirect
11. C₅×#5156	C₂	semidirect
12. C₅×#5072	C₂	semidirect
13. C₅×#5057	C₂	semidirect
14. C₅×#4711	C₂	semidirect
15. C₅×#4706	C₂	semidirect
17. C₂×C₅×#239	C₂²	semidirect
20. C₂×C₅×D₃×D₄	C₂²	semidirect
21. C₂×C₅×D₃×D₄	C₂²	semidirect
22. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
23. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
24. C₂×C₃×C₅×D₈	C₂²	semidirect
25. C₂×C₃×C₅×D₈	C₂²	semidirect
26. C₃×C₅×#127	C₂²	semidirect
27. C₃×C₅×#124	C₂²	semidirect
28. C₅×#946	C₂²	semidirect
29. C₂×C₅×#215	C₂²	semidirect
32. C₅×#938	C₂²	semidirect
33. C₅×#938	C₂²	semidirect
37. C₂×C₅×#213	C₂²	semidirect
38. C₂×C₅×#213	C₂²	semidirect
42. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
43. C₂×C₅×D₃×C₈	C₂²	semidirect
49. C₄×C₅×D₁₂	C₂²	semidirect
50. C₄×C₅×D₁₂	C₂²	semidirect
51. C₃×C₅×#97	C₂²	semidirect
52. C₅×#835	C₂²	semidirect
53. C₅×#832	C₂²	semidirect
54. C₅×#832	C₂²	semidirect
55. C₅×#832	C₂²	semidirect
56. C₅×#821	C₂²	semidirect
57. C₅×#821	C₂²	semidirect
58. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
59. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
60. C₅×#817	C₂²	semidirect
61. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
62. #81856	C₅	direct (N × H)
67. C₅×#496	D₃	semidirect
138. C₅×D₂₄	D₄	semidirect
141. C₂×#914	C₂×C₅	semidirect
142. C₂×D₃×D₈	C₂×C₅	semidirect
143. #5717	C₂×C₅	semidirect
144. #5676	C₂×C₅	semidirect
145. C₃×#496	C₂×C₅	semidirect
146. #5172	C₂×C₅	semidirect
147. #5171	C₂×C₅	semidirect
148. #5169	C₂×C₅	semidirect
149. #5159	C₂×C₅	semidirect
150. #5156	C₂×C₅	semidirect
151. #5156	C₂×C₅	semidirect
152. #5072	C₂×C₅	semidirect
153. #5057	C₂×C₅	semidirect
154. #4711	C₂×C₅	semidirect
155. #4706	C₂×C₅	semidirect
163. C₂×C₅×SD₁₆	C₂×D₃	semidirect
164. C₂×C₅×SD₁₆	C₂×D₃	semidirect
170. C₂×C₅×D₈	C₂×D₃	semidirect
171. C₂×C₅×D₈	C₂×D₃	semidirect
174. C₅×#127	C₂×D₃	semidirect
175. C₅×#124	C₂×D₃	semidirect
200. C₅×#97	C₂×D₃	semidirect
247. C₅×D₁₂	C₂×D₄	semidirect
256. C₃×C₅×C₈	C₂×D₄	semidirect
259. C₂×#239	C₂²×C₅	semidirect
262. C₂×D₃×D₄	C₂²×C₅	semidirect
263. C₂×D₃×D₄	C₂²×C₅	semidirect
264. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
265. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
266. C₂×C₃×D₈	C₂²×C₅	semidirect
267. C₂×C₃×D₈	C₂²×C₅	semidirect
268. C₃×#127	C₂²×C₅	semidirect
269. C₃×#124	C₂²×C₅	semidirect
270. #946	C₂²×C₅	semidirect
271. C₂×#215	C₂²×C₅	semidirect
274. #938	C₂²×C₅	semidirect
275. #938	C₂²×C₅	semidirect
279. C₂×#213	C₂²×C₅	semidirect
280. C₂×#213	C₂²×C₅	semidirect
284. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
285. C₂×D₃×C₈	C₂²×C₅	semidirect
291. C₄×D₁₂	C₂²×C₅	semidirect
292. C₄×D₁₂	C₂²×C₅	semidirect
293. C₃×#97	C₂²×C₅	semidirect
294. #835	C₂²×C₅	semidirect
295. #832	C₂²×C₅	semidirect
296. #832	C₂²×C₅	semidirect
297. #832	C₂²×C₅	semidirect
298. #821	C₂²×C₅	semidirect
299. #821	C₂²×C₅	semidirect
300. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
301. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
302. #817	C₂²×C₅	semidirect
303. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
371. #496	C₅×D₃	semidirect
406. C₂×C₅×D₃	AGL(1,ℤ/8)	semidirect
476. D₂₄	C₅×D₄	semidirect
535. C₅×C₈	D₃×D₄	semidirect
543. C₂×SD₁₆	C₂×C₅×D₃	semidirect
544. C₂×SD₁₆	C₂×C₅×D₃	semidirect
550. C₂×D₈	C₂×C₅×D₃	semidirect
551. C₂×D₈	C₂×C₅×D₃	semidirect
554. #127	C₂×C₅×D₃	semidirect
555. #124	C₂×C₅×D₃	semidirect
580. #97	C₂×C₅×D₃	semidirect
636. D₁₂	C₂×C₅×D₄	semidirect
645. C₃×C₈	C₂×C₅×D₄	semidirect
745. C₃×C₅	#3264	semidirect
770. C₂×D₃	C₅×AGL(1,ℤ/8)	semidirect
846. C₈	C₅×D₃×D₄	semidirect
857. C₅	#81856	direct (N × H)
892. C₃	C₅×#3264	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×D₈	2
C₅×#5717	2
C₅×#5676	2
C₃×C₅×#496	2
C₅×#5172	2
C₅×#5171	2
C₅×#5169	2
C₅×#5159	2
C₅×#5156	2
C₅×#5072	2
C₅×#5057	2
C₅×#4711	2
C₅×#4706	2
C₅×#3264	3
#81856	5

Subgroups — C5×#81856 #14453190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81856 #14453190