Subgroups — C₂×C₅×#5774 #14509960

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 832 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×#1004	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#950	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₅×#213	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5774	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#916	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#914	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#911	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×D₃×D₈	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#908	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#907	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#576	—	3	1	no	maximal, Hall
14	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₅×#67	—	2	2	no	—
17	C₅×#1009	—	2	4	no	—
18	C₅×#1009	C₂²	1	8	yes	complemented
19	C₂×C₅×#239	C₂²	1	2	yes	complemented
20	C₅×#1004	—	2	4	no	—
21	C₅×#1004	C₂²	1	8	yes	complemented
22	C₂×C₅×#237	—	2	1	no	—
23	C₂×C₅×#237	C₂²	1	2	yes	complemented
24	C₂×C₅×D₃×D₄	—	2	2	no	—
25	C₂×C₅×D₃×D₄	—	2	1	no	—
26	C₂×C₅×D₃×D₄	C₂²	1	2	yes	complemented
27	C₂×C₅×D₃×D₄	C₂²	1	2	yes	complemented
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	C₂²×C₅×D₁₂	—	2	1	no	—
32	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
34	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
35	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
36	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
37	C₅×#950	C₂²	1	8	yes	complemented
38	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×#215	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₅×#213	C₂²	1	2	yes	complemented
43	C₂×C₅×#213	C₂²	1	2	yes	complemented
44	C₂×C₅×#213	C₂²	1	8	yes	complemented
45	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₅×#916	C₂²	1	16	yes	complemented
47	C₅×#914	C₂²	1	16	yes	complemented
48	C₅×#911	C₂²	1	16	yes	complemented
49	C₅×D₃×D₈	C₂²	1	16	yes	complemented
50	C₅×#908	C₂²	1	8	yes	complemented
51	C₅×#907	C₂²	1	8	yes	complemented
52	C₂×C₅×D₂₄	C₂²	1	2	yes	complemented
53	C₂×C₅×#204	C₂²	1	2	yes	complemented
54	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
55	C₂×C₅×D₃×C₈	C₂²	1	2	yes	complemented
56	C₂×#5774	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
57	C₂×C₅×H(5,𝔽₂)	—	3	1	no	—
58	C₂×C₅×H(5,𝔽₂)	—	3	1	no	—
59	C₅×#576	—	3	16	no	—
60	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
61	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
62	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
63	C₂×C₅×AGL(1,ℤ/8)	D₃	1	1	yes	characteristic, complemented
64	C₂×C₅×#135	—	3	1	no	—
65	C₂×C₅×#135	—	3	2	no	—
66	C₂²×C₅×D₈	—	3	1	no	—
67	C₂²×C₅×D₈	—	3	2	no	—
68	C₂×C₅×#131	—	3	1	no	—
69	C₂⁴×C₃×C₅	—	2	1	no	—
70	C₂³×C₅×D₃	—	2	1	no	—
71	C₂³×C₅×D₃	—	2	2	no	—
72	C₂³×C₅×D₃	—	2	2	no	—
73	C₃×C₅×#41	—	2	2	no	—
74	C₃×C₅×#41	C₂³	1	4	yes	complemented
75	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
76	C₂×C₃×C₅×D₄	—	2	1	no	—
77	C₂×C₃×C₅×D₄	—	2	1	no	—
78	C₂×C₃×C₅×D₄	—	2	2	no	—
79	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
80	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
82	C₂²×C₃×C₄×C₅	—	2	1	no	—
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂×C₅×#67	—	2	1	no	—
85	C₂×C₅×#67	—	2	2	no	—
86	C₂×C₅×#67	—	2	16	no	—
87	C₂×C₅×#67	—	2	2	no	—
88	C₂×C₅×#67	—	2	2	no	—
89	C₂×C₅×#67	D₄	1	2	yes	—
90	C₂²×C₅×Dic₃	—	2	2	no	—
91	C₅×#239	—	2	4	no	—
92	C₅×#239	C₂³	1	8	yes	complemented
93	C₅×#237	—	2	4	no	—
94	C₅×#237	—	2	8	no	—
95	C₅×#237	C₂³	1	8	yes	complemented
96	C₅×D₃×D₄	—	2	16	no	—
97	C₅×D₃×D₄	—	2	8	no	—
98	C₅×D₃×D₄	—	2	4	no	—
99	C₅×D₃×D₄	—	2	4	no	—
100	C₅×D₃×D₄	C₂³	1	8	yes	complemented
101	C₅×D₃×D₄	C₂³	1	8	yes	complemented
102	C₅×#235	—	2	2	no	—
103	C₅×#235	—	2	8	no	—
104	C₅×#235	D₄	1	4	yes	—
105	C₅×#235	C₂³	1	4	yes	—
106	C₅×#235	C₂³	1	4	yes	complemented
107	C₂×C₅×D₁₂	—	2	2	no	—
108	C₂×C₅×D₁₂	—	2	1	no	—
109	C₂×C₅×D₁₂	—	2	2	no	—
110	C₂×C₅×D₁₂	—	2	8	no	—
111	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
112	C₂×C₅×D₁₂	C₂³	1	2	yes	—
113	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
114	C₂×C₅×D₁₂	C₂³	1	4	yes	complemented
115	C₂×C₄×C₅×D₃	—	2	1	no	—
116	C₂×C₄×C₅×D₃	—	2	2	no	—
117	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
118	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
119	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
120	C₃×C₅×SD₁₆	C₂³	1	8	yes	complemented
121	C₃×C₅×D₈	C₂³	1	8	yes	complemented
122	C₃×C₅×M₁₆	C₂³	1	4	yes	complemented
123	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
124	C₅×#216	C₂³	1	4	yes	complemented
125	C₅×#215	C₂³	1	4	yes	complemented
126	C₅×#214	C₂³	1	4	yes	complemented
127	C₅×#213	C₂³	1	4	yes	complemented
128	C₅×#213	C₂³	1	8	yes	complemented
129	C₅×#213	C₂³	1	8	yes	complemented
130	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
131	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
132	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	complemented
133	C₅×D₂₄	C₂³	1	8	yes	complemented
134	C₅×#204	C₂³	1	8	yes	complemented
135	C₅×ΓL(1,𝔽₂₅)	C₂³	1	8	yes	complemented
136	C₅×D₃×C₈	C₂³	1	8	yes	complemented
137	C₂×#1009	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂×#1004	C₂×C₅	1	1	yes	characteristic, complemented
139	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×#950	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂²×#213	C₂×C₅	1	1	yes	characteristic, complemented
142	#5774	C₂×C₅	1	16	yes	direct product factor
143	C₂×#916	C₂×C₅	1	2	yes	complemented
144	C₂×#914	C₂×C₅	1	2	yes	complemented
145	C₂×#911	C₂×C₅	1	2	yes	complemented
146	C₂×D₃×D₈	C₂×C₅	1	2	yes	complemented
147	C₂×#908	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂×#907	C₂×C₅	1	1	yes	characteristic, complemented
149	C₅×H(5,𝔽₂)	—	3	8	no	—
150	C₅×H(5,𝔽₂)	—	3	8	no	—
151	C₅×H(5,𝔽₂)	—	6	4	no	—
152	C₅×H(5,𝔽₂)	—	6	4	no	—
153	C₂×C₅×#41	—	3	1	no	—
154	C₂×C₅×#41	—	3	2	no	—
155	C₂×C₅×#41	—	3	2	no	—
156	C₂×C₅×#41	—	3	1	no	—
157	C₂×C₅×#41	—	6	1	no	—
158	C₂×C₅×#41	—	6	1	no	—
159	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic, complemented
160	C₂²×C₅×D₄	—	3	2	no	—
161	C₂²×C₅×D₄	—	3	2	no	—
162	C₂²×C₅×D₄	—	3	1	no	—
163	C₂²×C₅×D₄	—	6	1	no	—
164	C₂²×C₅×D₄	—	6	2	no	—
165	C₂²×C₅×D₄	—	6	1	no	—
166	C₂²×C₅×D₄	—	6	2	no	—
167	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
168	C₅×AGL(1,ℤ/8)	—	3	16	no	—
169	C₅×AGL(1,ℤ/8)	—	3	16	no	—
170	C₅×AGL(1,ℤ/8)	—	3	8	no	—
171	C₅×AGL(1,ℤ/8)	C₂×D₃	1	8	yes	complemented
172	C₅×#135	—	3	8	no	—
173	C₅×#135	—	3	16	no	—
174	C₂×C₅×Q₁₆	—	3	1	no	—
175	C₂×C₅×SD₁₆	—	3	1	no	—
176	C₂×C₅×SD₁₆	—	3	1	no	—
177	C₂×C₅×SD₁₆	—	3	2	no	—
178	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	complemented
179	C₂×C₅×D₈	—	3	2	no	—
180	C₂×C₅×D₈	—	3	1	no	—
181	C₂×C₅×D₈	—	3	2	no	—
182	C₂×C₅×D₈	—	3	8	no	—
183	C₂×C₅×D₈	—	3	16	no	—
184	C₂×C₅×D₈	—	3	2	no	—
185	C₂×C₅×D₈	C₂×D₃	1	2	yes	complemented
186	C₅×#131	—	3	8	no	—
187	C₂×C₅×M₁₆	—	3	2	no	—
188	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
189	C₂²×C₅×C₈	—	3	1	no	—
190	C₂²×C₅×C₈	—	3	2	no	—
191	C₂×#576	—	3	1	no	Sylow
192	C₂³×C₃×C₅	—	2	2	no	—
193	C₂³×C₃×C₅	—	2	1	no	—
194	C₂³×C₃×C₅	—	2	4	no	—
195	C₂³×C₃×C₅	—	8	2	no	—
196	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₅×D₃	—	2	2	no	—
198	C₂²×C₅×D₃	—	2	1	no	—
199	C₂²×C₅×D₃	—	2	4	no	—
200	C₂²×C₅×D₃	—	2	8	no	—
201	C₂²×C₅×D₃	—	2	8	no	—
202	C₂²×C₅×D₃	—	8	4	no	—
203	C₂²×C₅×D₃	—	8	4	no	—
204	C₂²×C₅×D₃	—	8	2	no	—
205	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
206	C₃×C₅×Q₈	—	2	1	no	—
207	C₃×C₅×Q₈	C₂⁴	1	2	yes	—
208	C₃×C₅×D₄	—	2	4	no	—
209	C₃×C₅×D₄	—	2	1	no	—
210	C₃×C₅×D₄	—	2	2	no	—
211	C₃×C₅×D₄	—	2	4	no	—
212	C₃×C₅×D₄	C₂⁴	1	4	yes	—
213	C₃×C₅×D₄	C₂⁴	1	2	yes	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	2	4	no	—
216	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
217	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
218	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
219	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
220	C₅×#67	—	2	4	no	—
221	C₅×#67	—	2	8	no	—
222	C₅×#67	—	2	8	no	—
223	C₅×#67	—	2	8	no	—
224	C₅×#67	C₂×D₄	1	8	yes	—
225	C₂×C₅×Dic₃	—	2	1	no	—
226	C₂×C₅×Dic₃	—	2	8	no	—
227	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
228	C₅×D₁₂	—	2	8	no	—
229	C₅×D₁₂	—	2	4	no	—
230	C₅×D₁₂	—	2	2	no	—
231	C₅×D₁₂	—	2	1	no	—
232	C₅×D₁₂	C₂×D₄	1	4	yes	—
233	C₅×D₁₂	C₂⁴	1	4	yes	—
234	C₅×D₁₂	C₂⁴	1	2	yes	—
235	C₄×C₅×D₃	—	2	4	no	—
236	C₄×C₅×D₃	—	2	8	no	—
237	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
238	C₄×C₅×D₃	C₂⁴	1	4	yes	—
239	C₅×Dic₆	—	2	1	no	—
240	C₅×Dic₆	C₂×D₄	1	4	yes	—
241	C₅×Dic₆	C₂⁴	1	2	yes	—
242	C₃×C₅×C₈	C₂⁴	1	4	yes	—
243	C₅×C₃⋊C₈	C₂⁴	1	2	yes	—
244	C₅×C₃⋊C₈	C₂⁴	1	2	yes	—
245	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
246	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
247	C₂²×#67	—	2	2	no	—
248	#1009	—	2	4	no	—
249	#1009	C₂²×C₅	1	8	yes	complemented
250	C₂×#239	C₂²×C₅	1	2	yes	complemented
251	#1004	—	2	4	no	—
252	#1004	C₂²×C₅	1	8	yes	complemented
253	C₂×#237	—	2	1	no	—
254	C₂×#237	C₂²×C₅	1	2	yes	complemented
255	C₂×D₃×D₄	—	2	2	no	—
256	C₂×D₃×D₄	—	2	1	no	—
257	C₂×D₃×D₄	C₂²×C₅	1	2	yes	complemented
258	C₂×D₃×D₄	C₂²×C₅	1	2	yes	complemented
259	C₂×#235	—	2	1	no	—
260	C₂×#235	C₂²×C₅	1	1	yes	characteristic
261	C₂×#235	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₂²×D₁₂	—	2	1	no	—
263	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₃×AGL(1,ℤ/8)	C₂²×C₅	1	8	yes	complemented
265	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
266	C₂×C₃×D₈	C₂²×C₅	1	2	yes	complemented
267	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
268	#950	C₂²×C₅	1	8	yes	complemented
269	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₂×#213	C₂²×C₅	1	2	yes	complemented
274	C₂×#213	C₂²×C₅	1	2	yes	complemented
275	C₂×#213	C₂²×C₅	1	8	yes	complemented
276	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
277	#916	C₂²×C₅	1	16	yes	complemented
278	#914	C₂²×C₅	1	16	yes	complemented
279	#911	C₂²×C₅	1	16	yes	complemented
280	D₃×D₈	C₂²×C₅	1	16	yes	complemented
281	#908	C₂²×C₅	1	8	yes	complemented
282	#907	C₂²×C₅	1	8	yes	complemented
283	C₂×D₂₄	C₂²×C₅	1	2	yes	complemented
284	C₂×#204	C₂²×C₅	1	2	yes	complemented
285	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	complemented
286	C₂×D₃×C₈	C₂²×C₅	1	2	yes	complemented
287	C₂⁴×C₅	—	2	1	no	—
288	C₂⁴×C₅	—	6	2	no	—
289	C₂⁴×C₅	—	6	2	no	—
290	C₂⁴×C₅	—	6	1	no	—
291	C₅×#41	—	2	2	no	—
292	C₅×#41	—	3	4	no	—
293	C₅×#41	—	3	4	no	—
294	C₅×#41	—	3	8	no	—
295	C₅×#41	—	3	8	no	—
296	C₅×#41	—	3	4	no	—
297	C₅×#41	—	6	8	no	—
298	C₅×#41	—	6	4	no	—
299	C₅×#41	—	6	4	no	—
300	C₅×#41	—	6	8	no	—
301	C₅×#41	—	6	2	no	—
302	C₅×#41	C₂²×D₃	1	4	yes	complemented
303	C₂×C₅×Q₈	—	3	1	no	—
304	C₂×C₅×Q₈	—	3	1	no	—
305	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
306	C₂×C₅×D₄	—	2	1	no	—
307	C₂×C₅×D₄	—	2	1	no	—
308	C₂×C₅×D₄	—	2	2	no	—
309	C₂×C₅×D₄	—	3	2	no	—
310	C₂×C₅×D₄	—	3	8	no	—
311	C₂×C₅×D₄	—	3	8	no	—
312	C₂×C₅×D₄	—	3	1	no	—
313	C₂×C₅×D₄	—	3	2	no	—
314	C₂×C₅×D₄	—	3	1	no	—
315	C₂×C₅×D₄	—	3	4	no	—
316	C₂×C₅×D₄	—	6	8	no	—
317	C₂×C₅×D₄	—	6	2	no	—
318	C₂×C₅×D₄	—	6	4	no	—
319	C₂×C₅×D₄	—	6	4	no	—
320	C₂×C₅×D₄	—	6	2	no	—
321	C₂×C₅×D₄	—	6	2	no	—
322	C₂×C₅×D₄	—	6	16	no	—
323	C₂×C₅×D₄	—	6	8	no	—
324	C₂×C₅×D₄	—	6	16	no	—
325	C₂×C₅×D₄	—	6	2	no	—
326	C₂×C₅×D₄	—	6	1	no	—
327	C₂×C₅×D₄	—	6	1	no	—
328	C₂×C₅×D₄	—	6	2	no	—
329	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
330	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
331	C₂×C₅×D₄	C₂²×D₃	1	4	yes	complemented
332	C₂²×C₄×C₅	—	2	1	no	—
333	C₂²×C₄×C₅	—	3	2	no	—
334	C₂²×C₄×C₅	—	6	2	no	—
335	C₂²×C₄×C₅	—	6	2	no	—
336	C₂²×C₄×C₅	—	6	1	no	—
337	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
338	C₅×Q₁₆	—	3	4	no	—
339	C₅×SD₁₆	—	3	4	no	—
340	C₅×SD₁₆	—	3	4	no	—
341	C₅×SD₁₆	—	3	8	no	—
342	C₅×SD₁₆	C₂²×D₃	1	8	yes	complemented
343	C₅×D₈	—	3	8	no	—
344	C₅×D₈	—	3	4	no	—
345	C₅×D₈	—	3	8	no	—
346	C₅×D₈	—	3	8	no	—
347	C₅×D₈	C₂²×D₃	1	8	yes	complemented
348	C₅×M₁₆	—	3	8	no	—
349	C₅×M₁₆	C₂²×D₃	1	4	yes	complemented
350	C₂×C₅×C₈	—	3	1	no	—
351	C₂×C₅×C₈	—	3	1	no	—
352	C₂×C₅×C₈	—	3	4	no	—
353	C₂×C₅×C₈	—	3	8	no	—
354	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
355	C₂×H(5,𝔽₂)	—	3	1	no	—
356	C₂×H(5,𝔽₂)	—	3	1	no	—
357	#576	—	3	16	no	—
358	C₂×AGL(1,ℤ/8)	—	3	2	no	—
359	C₂×AGL(1,ℤ/8)	—	3	2	no	—
360	C₂×AGL(1,ℤ/8)	—	3	1	no	—
361	C₂×AGL(1,ℤ/8)	C₅×D₃	1	1	yes	characteristic, complemented
362	C₂×#135	—	3	1	no	—
363	C₂×#135	—	3	2	no	—
364	C₂²×D₈	—	3	1	no	—
365	C₂²×D₈	—	3	2	no	—
366	C₂×#131	—	3	1	no	—
367	C₂²×C₃×C₅	—	2	2	no	—
368	C₂²×C₃×C₅	—	2	4	no	—
369	C₂²×C₃×C₅	—	2	2	no	—
370	C₂²×C₃×C₅	—	4	2	no	—
371	C₂²×C₃×C₅	—	4	4	no	—
372	C₂²×C₃×C₅	—	8	4	no	—
373	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
374	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₅×D₃	—	2	4	no	—
376	C₂×C₅×D₃	—	2	4	no	—
377	C₂×C₅×D₃	—	2	2	no	—
378	C₂×C₅×D₃	—	4	4	no	—
379	C₂×C₅×D₃	—	4	2	no	—
380	C₂×C₅×D₃	—	8	8	no	—
381	C₂×C₅×D₃	—	8	8	no	—
382	C₂×C₅×D₃	—	8	4	no	—
383	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
384	C₃×C₄×C₅	—	2	2	no	—
385	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
386	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
387	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
388	C₅×Dic₃	—	2	2	no	—
389	C₅×Dic₃	C₂²×D₄	1	4	yes	—
390	C₂⁴×C₃	—	2	1	no	—
391	C₂³×D₃	—	2	1	no	—
392	C₂³×D₃	—	2	2	no	—
393	C₂³×D₃	—	2	2	no	—
394	C₃×#41	—	2	2	no	—
395	C₃×#41	C₂³×C₅	1	4	yes	complemented
396	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
397	C₂×C₃×D₄	—	2	1	no	—
398	C₂×C₃×D₄	—	2	1	no	—
399	C₂×C₃×D₄	—	2	2	no	—
400	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
401	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
402	C₂×C₃×D₄	C₂³×C₅	1	4	yes	complemented
403	C₂²×C₃×C₄	—	2	1	no	—
404	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
405	C₂×#67	—	2	1	no	—
406	C₂×#67	—	2	2	no	—
407	C₂×#67	—	2	16	no	—
408	C₂×#67	—	2	2	no	—
409	C₂×#67	—	2	2	no	—
410	C₂×#67	C₅×D₄	1	2	yes	—
411	C₂²×Dic₃	—	2	2	no	—
412	#239	—	2	4	no	—
413	#239	C₂³×C₅	1	8	yes	complemented
414	#237	—	2	4	no	—
415	#237	—	2	8	no	—
416	#237	C₂³×C₅	1	8	yes	complemented
417	D₃×D₄	—	2	16	no	—
418	D₃×D₄	—	2	8	no	—
419	D₃×D₄	—	2	4	no	—
420	D₃×D₄	—	2	4	no	—
421	D₃×D₄	C₂³×C₅	1	8	yes	complemented
422	D₃×D₄	C₂³×C₅	1	8	yes	complemented
423	#235	—	2	2	no	—
424	#235	—	2	8	no	—
425	#235	C₅×D₄	1	4	yes	—
426	#235	C₂³×C₅	1	4	yes	—
427	#235	C₂³×C₅	1	4	yes	complemented
428	C₂×D₁₂	—	2	2	no	—
429	C₂×D₁₂	—	2	1	no	—
430	C₂×D₁₂	—	2	2	no	—
431	C₂×D₁₂	—	2	8	no	—
432	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
433	C₂×D₁₂	C₂³×C₅	1	2	yes	—
434	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
435	C₂×D₁₂	C₂³×C₅	1	4	yes	complemented
436	C₂×C₄×D₃	—	2	1	no	—
437	C₂×C₄×D₃	—	2	2	no	—
438	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
439	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
440	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
441	C₃×SD₁₆	C₂³×C₅	1	8	yes	complemented
442	C₃×D₈	C₂³×C₅	1	8	yes	complemented
443	C₃×M₁₆	C₂³×C₅	1	4	yes	complemented
444	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
445	#216	C₂³×C₅	1	4	yes	complemented
446	#215	C₂³×C₅	1	4	yes	complemented
447	#214	C₂³×C₅	1	4	yes	complemented
448	#213	C₂³×C₅	1	4	yes	complemented
449	#213	C₂³×C₅	1	8	yes	complemented
450	#213	C₂³×C₅	1	8	yes	complemented
451	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
452	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
453	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	complemented
454	D₂₄	C₂³×C₅	1	8	yes	complemented
455	#204	C₂³×C₅	1	8	yes	complemented
456	ΓL(1,𝔽₂₅)	C₂³×C₅	1	8	yes	complemented
457	D₃×C₈	C₂³×C₅	1	8	yes	complemented
458	C₂³×C₅	—	2	1	no	—
459	C₂³×C₅	—	2	2	no	—
460	C₂³×C₅	—	2	4	no	—
461	C₂³×C₅	—	3	2	no	—
462	C₂³×C₅	—	6	8	no	—
463	C₂³×C₅	—	6	8	no	—
464	C₂³×C₅	—	6	2	no	—
465	C₂³×C₅	—	6	1	no	—
466	C₂³×C₅	—	6	4	no	—
467	C₂³×C₅	—	8	2	no	—
468	C₂³×C₅	—	24	2	no	—
469	C₂³×C₅	—	24	4	no	—
470	C₂³×C₅	—	24	4	no	—
471	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
472	C₅×Q₈	—	2	1	no	—
473	C₅×Q₈	—	3	4	no	—
474	C₅×Q₈	—	3	2	no	—
475	C₅×Q₈	—	6	1	no	—
476	C₅×Q₈	C₂³×D₃	1	2	yes	—
477	C₅×D₄	—	2	4	no	—
478	C₅×D₄	—	2	2	no	—
479	C₅×D₄	—	2	4	no	—
480	C₅×D₄	—	2	1	no	—
481	C₅×D₄	—	3	8	no	—
482	C₅×D₄	—	3	4	no	—
483	C₅×D₄	—	3	4	no	—
484	C₅×D₄	—	3	2	no	—
485	C₅×D₄	—	6	8	no	—
486	C₅×D₄	—	6	8	no	—
487	C₅×D₄	—	6	8	no	—
488	C₅×D₄	—	6	8	no	—
489	C₅×D₄	—	6	4	no	—
490	C₅×D₄	—	6	4	no	—
491	C₅×D₄	—	6	2	no	—
492	C₅×D₄	—	6	1	no	—
493	C₅×D₄	C₂³×D₃	1	4	yes	—
494	C₅×D₄	C₂³×D₃	1	2	yes	—
495	C₂×C₄×C₅	—	2	1	no	—
496	C₂×C₄×C₅	—	2	4	no	—
497	C₂×C₄×C₅	—	3	2	no	—
498	C₂×C₄×C₅	—	3	4	no	—
499	C₂×C₄×C₅	—	3	4	no	—
500	C₂×C₄×C₅	—	6	8	no	—
501	C₂×C₄×C₅	—	6	8	no	—
502	C₂×C₄×C₅	—	6	1	no	—
503	C₂×C₄×C₅	—	6	4	no	—
504	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
505	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
506	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
507	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
508	C₅×C₈	—	3	2	no	—
509	C₅×C₈	—	3	2	no	—
510	C₅×C₈	C₂³×D₃	1	4	yes	—
511	H(5,𝔽₂)	—	3	8	no	—
512	H(5,𝔽₂)	—	3	8	no	—
513	H(5,𝔽₂)	—	6	4	no	—
514	H(5,𝔽₂)	—	6	4	no	—
515	C₂×#41	—	3	1	no	—
516	C₂×#41	—	3	2	no	—
517	C₂×#41	—	3	2	no	—
518	C₂×#41	—	3	1	no	—
519	C₂×#41	—	6	1	no	—
520	C₂×#41	—	6	1	no	—
521	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic, complemented
522	C₂²×D₄	—	3	2	no	—
523	C₂²×D₄	—	3	2	no	—
524	C₂²×D₄	—	3	1	no	—
525	C₂²×D₄	—	6	1	no	—
526	C₂²×D₄	—	6	2	no	—
527	C₂²×D₄	—	6	1	no	—
528	C₂²×D₄	—	6	2	no	—
529	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
530	AGL(1,ℤ/8)	—	3	16	no	—
531	AGL(1,ℤ/8)	—	3	16	no	—
532	AGL(1,ℤ/8)	—	3	8	no	—
533	AGL(1,ℤ/8)	C₂×C₅×D₃	1	8	yes	complemented
534	#135	—	3	8	no	—
535	#135	—	3	16	no	—
536	C₂×Q₁₆	—	3	1	no	—
537	C₂×SD₁₆	—	3	1	no	—
538	C₂×SD₁₆	—	3	1	no	—
539	C₂×SD₁₆	—	3	2	no	—
540	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	complemented
541	C₂×D₈	—	3	2	no	—
542	C₂×D₈	—	3	1	no	—
543	C₂×D₈	—	3	2	no	—
544	C₂×D₈	—	3	8	no	—
545	C₂×D₈	—	3	16	no	—
546	C₂×D₈	—	3	2	no	—
547	C₂×D₈	C₂×C₅×D₃	1	2	yes	complemented
548	#131	—	3	8	no	—
549	C₂×M₁₆	—	3	2	no	—
550	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
551	C₂²×C₈	—	3	1	no	—
552	C₂²×C₈	—	3	2	no	—
553	C₂×C₃×C₅	—	2	2	no	—
554	C₂×C₃×C₅	—	4	2	no	—
555	C₂×C₃×C₅	—	4	4	no	—
556	C₂×C₃×C₅	#576	1	2	yes	complemented
557	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
558	C₅×D₃	—	2	4	no	—
559	C₅×D₃	—	4	4	no	—
560	C₅×D₃	—	4	2	no	—
561	C₂³×C₃	—	2	2	no	—
562	C₂³×C₃	—	2	1	no	—
563	C₂³×C₃	—	2	4	no	—
564	C₂³×C₃	—	8	2	no	—
565	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
566	C₂²×D₃	—	2	2	no	—
567	C₂²×D₃	—	2	1	no	—
568	C₂²×D₃	—	2	4	no	—
569	C₂²×D₃	—	2	8	no	—
570	C₂²×D₃	—	2	8	no	—
571	C₂²×D₃	—	8	4	no	—
572	C₂²×D₃	—	8	4	no	—
573	C₂²×D₃	—	8	2	no	—
574	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
575	C₃×Q₈	—	2	1	no	—
576	C₃×Q₈	C₂⁴×C₅	1	2	yes	—
577	C₃×D₄	—	2	4	no	—
578	C₃×D₄	—	2	1	no	—
579	C₃×D₄	—	2	2	no	—
580	C₃×D₄	—	2	4	no	—
581	C₃×D₄	C₂⁴×C₅	1	4	yes	—
582	C₃×D₄	C₂⁴×C₅	1	2	yes	—
583	C₂×C₃×C₄	—	2	1	no	—
584	C₂×C₃×C₄	—	2	4	no	—
585	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
586	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
587	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
588	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
589	#67	—	2	4	no	—
590	#67	—	2	8	no	—
591	#67	—	2	8	no	—
592	#67	—	2	8	no	—
593	#67	C₂×C₅×D₄	1	8	yes	—
594	C₂×Dic₃	—	2	1	no	—
595	C₂×Dic₃	—	2	8	no	—
596	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
597	D₁₂	—	2	8	no	—
598	D₁₂	—	2	4	no	—
599	D₁₂	—	2	2	no	—
600	D₁₂	—	2	1	no	—
601	D₁₂	C₂×C₅×D₄	1	4	yes	—
602	D₁₂	C₂⁴×C₅	1	4	yes	—
603	D₁₂	C₂⁴×C₅	1	2	yes	—
604	C₄×D₃	—	2	4	no	—
605	C₄×D₃	—	2	8	no	—
606	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
607	C₄×D₃	C₂⁴×C₅	1	4	yes	—
608	Dic₆	—	2	1	no	—
609	Dic₆	C₂×C₅×D₄	1	4	yes	—
610	Dic₆	C₂⁴×C₅	1	2	yes	—
611	C₃×C₈	C₂⁴×C₅	1	4	yes	—
612	C₃⋊C₈	C₂⁴×C₅	1	2	yes	—
613	C₃⋊C₈	C₂⁴×C₅	1	2	yes	—
614	C₂²×C₅	—	2	2	no	—
615	C₂²×C₅	—	2	2	no	—
616	C₂²×C₅	—	2	4	no	—
617	C₂²×C₅	—	3	4	no	—
618	C₂²×C₅	—	4	4	no	—
619	C₂²×C₅	—	4	2	no	—
620	C₂²×C₅	—	6	4	no	—
621	C₂²×C₅	—	6	4	no	—
622	C₂²×C₅	—	6	2	no	—
623	C₂²×C₅	—	8	4	no	—
624	C₂²×C₅	—	12	4	no	—
625	C₂²×C₅	—	12	2	no	—
626	C₂²×C₅	—	24	4	no	—
627	C₂²×C₅	—	24	8	no	—
628	C₂²×C₅	—	24	8	no	—
629	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
630	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
631	C₄×C₅	—	2	2	no	—
632	C₄×C₅	—	3	4	no	—
633	C₄×C₅	—	6	2	no	—
634	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
635	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
636	C₄×C₅	C₂⁴×D₃	1	1	yes	characteristic
637	C₂⁴	—	2	1	no	—
638	C₂⁴	—	6	2	no	—
639	C₂⁴	—	6	2	no	—
640	C₂⁴	—	6	1	no	—
641	#41	—	2	2	no	—
642	#41	—	3	4	no	—
643	#41	—	3	4	no	—
644	#41	—	3	8	no	—
645	#41	—	3	8	no	—
646	#41	—	3	4	no	—
647	#41	—	6	8	no	—
648	#41	—	6	4	no	—
649	#41	—	6	4	no	—
650	#41	—	6	8	no	—
651	#41	—	6	2	no	—
652	#41	C₂²×C₅×D₃	1	4	yes	complemented
653	C₂×Q₈	—	3	1	no	—
654	C₂×Q₈	—	3	1	no	—
655	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	2	1	no	—
658	C₂×D₄	—	2	2	no	—
659	C₂×D₄	—	3	2	no	—
660	C₂×D₄	—	3	8	no	—
661	C₂×D₄	—	3	8	no	—
662	C₂×D₄	—	3	1	no	—
663	C₂×D₄	—	3	2	no	—
664	C₂×D₄	—	3	1	no	—
665	C₂×D₄	—	3	4	no	—
666	C₂×D₄	—	6	8	no	—
667	C₂×D₄	—	6	2	no	—
668	C₂×D₄	—	6	4	no	—
669	C₂×D₄	—	6	4	no	—
670	C₂×D₄	—	6	2	no	—
671	C₂×D₄	—	6	2	no	—
672	C₂×D₄	—	6	16	no	—
673	C₂×D₄	—	6	8	no	—
674	C₂×D₄	—	6	16	no	—
675	C₂×D₄	—	6	2	no	—
676	C₂×D₄	—	6	1	no	—
677	C₂×D₄	—	6	1	no	—
678	C₂×D₄	—	6	2	no	—
679	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
680	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
681	C₂×D₄	C₂²×C₅×D₃	1	4	yes	complemented
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	3	2	no	—
684	C₂²×C₄	—	6	2	no	—
685	C₂²×C₄	—	6	2	no	—
686	C₂²×C₄	—	6	1	no	—
687	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
688	Q₁₆	—	3	4	no	—
689	SD₁₆	—	3	4	no	—
690	SD₁₆	—	3	4	no	—
691	SD₁₆	—	3	8	no	—
692	SD₁₆	C₂²×C₅×D₃	1	8	yes	complemented
693	D₈	—	3	8	no	—
694	D₈	—	3	4	no	—
695	D₈	—	3	8	no	—
696	D₈	—	3	8	no	—
697	D₈	C₂²×C₅×D₃	1	8	yes	complemented
698	M₁₆	—	3	8	no	—
699	M₁₆	C₂²×C₅×D₃	1	4	yes	complemented
700	C₂×C₈	—	3	1	no	—
701	C₂×C₈	—	3	1	no	—
702	C₂×C₈	—	3	4	no	—
703	C₂×C₈	—	3	8	no	—
704	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
705	C₃×C₅	C₂×#576	1	1	yes	characteristic, complemented, Hall
706	C₂²×C₃	—	2	2	no	—
707	C₂²×C₃	—	2	4	no	—
708	C₂²×C₃	—	2	2	no	—
709	C₂²×C₃	—	4	2	no	—
710	C₂²×C₃	—	4	4	no	—
711	C₂²×C₃	—	8	4	no	—
712	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
713	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
714	C₂×D₃	—	2	4	no	—
715	C₂×D₃	—	2	4	no	—
716	C₂×D₃	—	2	2	no	—
717	C₂×D₃	—	4	4	no	—
718	C₂×D₃	—	4	2	no	—
719	C₂×D₃	—	8	8	no	—
720	C₂×D₃	—	8	8	no	—
721	C₂×D₃	—	8	4	no	—
722	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
723	C₃×C₄	—	2	2	no	—
724	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
725	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
726	C₃×C₄	C₂⁵×C₅	1	1	yes	characteristic
727	Dic₃	—	2	2	no	—
728	Dic₃	C₂²×C₅×D₄	1	4	yes	—
729	C₂×C₅	—	2	2	no	—
730	C₂×C₅	—	4	4	no	—
731	C₂×C₅	—	4	2	no	—
732	C₂×C₅	—	6	4	no	—
733	C₂×C₅	—	12	4	no	—
734	C₂×C₅	—	12	2	no	—
735	C₂×C₅	#5774	1	2	yes	direct product factor
736	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
737	C₂³	—	2	1	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	4	no	—
740	C₂³	—	3	2	no	—
741	C₂³	—	6	8	no	—
742	C₂³	—	6	8	no	—
743	C₂³	—	6	2	no	—
744	C₂³	—	6	1	no	—
745	C₂³	—	6	4	no	—
746	C₂³	—	8	2	no	—
747	C₂³	—	24	2	no	—
748	C₂³	—	24	4	no	—
749	C₂³	—	24	4	no	—
750	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
751	Q₈	—	2	1	no	—
752	Q₈	—	3	4	no	—
753	Q₈	—	3	2	no	—
754	Q₈	—	6	1	no	—
755	Q₈	C₂³×C₅×D₃	1	2	yes	—
756	D₄	—	2	4	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	4	no	—
759	D₄	—	2	1	no	—
760	D₄	—	3	8	no	—
761	D₄	—	3	4	no	—
762	D₄	—	3	4	no	—
763	D₄	—	3	2	no	—
764	D₄	—	6	8	no	—
765	D₄	—	6	8	no	—
766	D₄	—	6	8	no	—
767	D₄	—	6	8	no	—
768	D₄	—	6	4	no	—
769	D₄	—	6	4	no	—
770	D₄	—	6	1	no	—
771	D₄	—	6	2	no	—
772	D₄	C₂³×C₅×D₃	1	4	yes	—
773	D₄	C₂³×C₅×D₃	1	2	yes	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	3	2	no	—
777	C₂×C₄	—	3	4	no	—
778	C₂×C₄	—	3	4	no	—
779	C₂×C₄	—	6	8	no	—
780	C₂×C₄	—	6	8	no	—
781	C₂×C₄	—	6	1	no	—
782	C₂×C₄	—	6	4	no	—
783	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
784	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
785	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
786	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
787	C₈	—	3	2	no	—
788	C₈	—	3	2	no	—
789	C₈	C₂³×C₅×D₃	1	4	yes	—
790	C₂×C₃	—	2	2	no	—
791	C₂×C₃	—	4	2	no	—
792	C₂×C₃	—	4	4	no	—
793	C₂×C₃	C₅×#576	1	2	yes	complemented
794	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
795	D₃	—	2	4	no	—
796	D₃	—	4	4	no	—
797	D₃	—	4	2	no	—
798	C₅	C₂×#5774	1	1	yes	characteristic, direct product factor, Sylow
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	4	no	—
802	C₂²	—	3	4	no	—
803	C₂²	—	4	4	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	6	4	no	—
806	C₂²	—	6	4	no	—
807	C₂²	—	6	2	no	—
808	C₂²	—	8	4	no	—
809	C₂²	—	12	4	no	—
810	C₂²	—	12	2	no	—
811	C₂²	—	24	4	no	—
812	C₂²	—	24	8	no	—
813	C₂²	—	24	8	no	—
814	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
815	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
816	C₄	—	2	2	no	—
817	C₄	—	3	4	no	—
818	C₄	—	6	2	no	—
819	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
820	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
821	C₄	C₂⁴×C₅×D₃	1	1	yes	characteristic
822	C₃	C₂×C₅×#576	1	1	yes	characteristic, complemented, Sylow
823	C₂	—	2	2	no	—
824	C₂	—	4	4	no	—
825	C₂	—	4	2	no	—
826	C₂	—	6	4	no	—
827	C₂	—	12	4	no	—
828	C₂	—	12	2	no	—
829	C₂	C₅×#5774	1	2	yes	direct product factor
830	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁵×C₅
Frattini	C₄	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₅×AGL(1,ℤ/8)	D₃
hypocenter	C₃	C₂×C₅×#576
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×AGL(1,ℤ/8)

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×#1004	C₂	semidirect
3. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
4. C₂×C₅×#950	C₂	semidirect
5. C₂²×C₅×#213	C₂	semidirect
6. C₅×#5774	C₂	direct (N × H)
7. C₂×C₅×#916	C₂	semidirect
8. C₂×C₅×#914	C₂	semidirect
9. C₂×C₅×#911	C₂	semidirect
10. C₂×C₅×D₃×D₈	C₂	semidirect
11. C₂×C₅×#908	C₂	semidirect
12. C₂×C₅×#907	C₂	semidirect
14. C₂×C₃×C₅×#41	C₂²	semidirect
15. C₂²×C₃×C₅×D₄	C₂²	semidirect
18. C₅×#1009	C₂²	semidirect
19. C₂×C₅×#239	C₂²	semidirect
21. C₅×#1004	C₂²	semidirect
23. C₂×C₅×#237	C₂²	semidirect
26. C₂×C₅×D₃×D₄	C₂²	semidirect
27. C₂×C₅×D₃×D₄	C₂²	semidirect
30. C₂×C₅×#235	C₂²	semidirect
32. C₂²×C₅×D₁₂	C₂²	semidirect
33. C₃×C₅×AGL(1,ℤ/8)	C₂²	semidirect
34. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
35. C₂×C₃×C₅×D₈	C₂²	semidirect
36. C₂×C₃×C₅×M₁₆	C₂²	semidirect
37. C₅×#950	C₂²	semidirect
38. C₂×C₅×#216	C₂²	semidirect
39. C₂×C₅×#215	C₂²	semidirect
40. C₂×C₅×#214	C₂²	semidirect
41. C₂×C₅×#213	C₂²	semidirect
42. C₂×C₅×#213	C₂²	semidirect
43. C₂×C₅×#213	C₂²	semidirect
44. C₂×C₅×#213	C₂²	semidirect
45. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
46. C₅×#916	C₂²	semidirect
47. C₅×#914	C₂²	semidirect
48. C₅×#911	C₂²	semidirect
49. C₅×D₃×D₈	C₂²	semidirect
50. C₅×#908	C₂²	semidirect
51. C₅×#907	C₂²	semidirect
52. C₂×C₅×D₂₄	C₂²	semidirect
53. C₂×C₅×#204	C₂²	semidirect
54. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
55. C₂×C₅×D₃×C₈	C₂²	semidirect
56. C₂×#5774	C₅	direct (N × H)
63. C₂×C₅×AGL(1,ℤ/8)	D₃	semidirect
74. C₃×C₅×#41	C₂³	semidirect
81. C₂×C₃×C₅×D₄	C₂³	semidirect
92. C₅×#239	C₂³	semidirect
95. C₅×#237	C₂³	semidirect
100. C₅×D₃×D₄	C₂³	semidirect
101. C₅×D₃×D₄	C₂³	semidirect
106. C₅×#235	C₂³	semidirect
114. C₂×C₅×D₁₂	C₂³	semidirect
120. C₃×C₅×SD₁₆	C₂³	semidirect
121. C₃×C₅×D₈	C₂³	semidirect
122. C₃×C₅×M₁₆	C₂³	semidirect
124. C₅×#216	C₂³	semidirect
125. C₅×#215	C₂³	semidirect
126. C₅×#214	C₂³	semidirect
127. C₅×#213	C₂³	semidirect
128. C₅×#213	C₂³	semidirect
129. C₅×#213	C₂³	semidirect
132. C₂×C₅×C₃⋊C₈	C₂³	semidirect
133. C₅×D₂₄	C₂³	semidirect
134. C₅×#204	C₂³	semidirect
135. C₅×ΓL(1,𝔽₂₅)	C₂³	semidirect
136. C₅×D₃×C₈	C₂³	semidirect
137. C₂×#1009	C₂×C₅	semidirect
138. C₂×#1004	C₂×C₅	semidirect
139. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
140. C₂×#950	C₂×C₅	semidirect
141. C₂²×#213	C₂×C₅	semidirect
142. #5774	C₂×C₅	direct (N × H)
143. C₂×#916	C₂×C₅	semidirect
144. C₂×#914	C₂×C₅	semidirect
145. C₂×#911	C₂×C₅	semidirect
146. C₂×D₃×D₈	C₂×C₅	semidirect
147. C₂×#908	C₂×C₅	semidirect
148. C₂×#907	C₂×C₅	semidirect
159. C₂×C₅×#41	C₂×D₃	semidirect
167. C₂²×C₅×D₄	C₂×D₃	semidirect
171. C₅×AGL(1,ℤ/8)	C₂×D₃	semidirect
178. C₂×C₅×SD₁₆	C₂×D₃	semidirect
185. C₂×C₅×D₈	C₂×D₃	semidirect
188. C₂×C₅×M₁₆	C₂×D₃	semidirect
245. C₂×C₃×#41	C₂²×C₅	semidirect
246. C₂²×C₃×D₄	C₂²×C₅	semidirect
249. #1009	C₂²×C₅	semidirect
250. C₂×#239	C₂²×C₅	semidirect
252. #1004	C₂²×C₅	semidirect
254. C₂×#237	C₂²×C₅	semidirect
257. C₂×D₃×D₄	C₂²×C₅	semidirect
258. C₂×D₃×D₄	C₂²×C₅	semidirect
261. C₂×#235	C₂²×C₅	semidirect
263. C₂²×D₁₂	C₂²×C₅	semidirect
264. C₃×AGL(1,ℤ/8)	C₂²×C₅	semidirect
265. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
266. C₂×C₃×D₈	C₂²×C₅	semidirect
267. C₂×C₃×M₁₆	C₂²×C₅	semidirect
268. #950	C₂²×C₅	semidirect
269. C₂×#216	C₂²×C₅	semidirect
270. C₂×#215	C₂²×C₅	semidirect
271. C₂×#214	C₂²×C₅	semidirect
272. C₂×#213	C₂²×C₅	semidirect
273. C₂×#213	C₂²×C₅	semidirect
274. C₂×#213	C₂²×C₅	semidirect
275. C₂×#213	C₂²×C₅	semidirect
276. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
277. #916	C₂²×C₅	semidirect
278. #914	C₂²×C₅	semidirect
279. #911	C₂²×C₅	semidirect
280. D₃×D₈	C₂²×C₅	semidirect
281. #908	C₂²×C₅	semidirect
282. #907	C₂²×C₅	semidirect
283. C₂×D₂₄	C₂²×C₅	semidirect
284. C₂×#204	C₂²×C₅	semidirect
285. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
286. C₂×D₃×C₈	C₂²×C₅	semidirect
302. C₅×#41	C₂²×D₃	semidirect
331. C₂×C₅×D₄	C₂²×D₃	semidirect
342. C₅×SD₁₆	C₂²×D₃	semidirect
347. C₅×D₈	C₂²×D₃	semidirect
349. C₅×M₁₆	C₂²×D₃	semidirect
361. C₂×AGL(1,ℤ/8)	C₅×D₃	semidirect
395. C₃×#41	C₂³×C₅	semidirect
402. C₂×C₃×D₄	C₂³×C₅	semidirect
413. #239	C₂³×C₅	semidirect
416. #237	C₂³×C₅	semidirect
421. D₃×D₄	C₂³×C₅	semidirect
422. D₃×D₄	C₂³×C₅	semidirect
427. #235	C₂³×C₅	semidirect
435. C₂×D₁₂	C₂³×C₅	semidirect
441. C₃×SD₁₆	C₂³×C₅	semidirect
442. C₃×D₈	C₂³×C₅	semidirect
443. C₃×M₁₆	C₂³×C₅	semidirect
445. #216	C₂³×C₅	semidirect
446. #215	C₂³×C₅	semidirect
447. #214	C₂³×C₅	semidirect
448. #213	C₂³×C₅	semidirect
449. #213	C₂³×C₅	semidirect
450. #213	C₂³×C₅	semidirect
453. C₂×C₃⋊C₈	C₂³×C₅	semidirect
454. D₂₄	C₂³×C₅	semidirect
455. #204	C₂³×C₅	semidirect
456. ΓL(1,𝔽₂₅)	C₂³×C₅	semidirect
457. D₃×C₈	C₂³×C₅	semidirect
521. C₂×#41	C₂×C₅×D₃	semidirect
529. C₂²×D₄	C₂×C₅×D₃	semidirect
533. AGL(1,ℤ/8)	C₂×C₅×D₃	semidirect
540. C₂×SD₁₆	C₂×C₅×D₃	semidirect
547. C₂×D₈	C₂×C₅×D₃	semidirect
550. C₂×M₁₆	C₂×C₅×D₃	semidirect
556. C₂×C₃×C₅	#576	semidirect
652. #41	C₂²×C₅×D₃	semidirect
681. C₂×D₄	C₂²×C₅×D₃	semidirect
692. SD₁₆	C₂²×C₅×D₃	semidirect
697. D₈	C₂²×C₅×D₃	semidirect
699. M₁₆	C₂²×C₅×D₃	semidirect
705. C₃×C₅	C₂×#576	semidirect
735. C₂×C₅	#5774	direct (N × H)
793. C₂×C₃	C₅×#576	semidirect
798. C₅	C₂×#5774	direct (N × H)
822. C₃	C₂×C₅×#576	semidirect
829. C₂	C₅×#5774	direct (N × H)

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×#1004	2
C₂×C₃×C₅×AGL(1,ℤ/8)	2
C₂×C₅×#950	2
C₂²×C₅×#213	2
C₅×#5774	2
C₂×C₅×#916	2
C₂×C₅×#914	2
C₂×C₅×#911	2
C₂×C₅×D₃×D₈	2
C₂×C₅×#908	2
C₂×C₅×#907	2
C₂×C₅×#576	3
C₂×#5774	5

Subgroups — C2×C5×#5774 #14509960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5774 #14509960