Subgroups — C₂×C₅×#5778 #14510027

Order 1920.

2920 conjugacy classes of subgroups.

The subgroup lattice has 808 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×#1007	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#950	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₅×#215	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5778	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#919	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#918	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#914	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×D₃×SD₁₆	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×#577	—	3	1	no	maximal, Hall
14	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₅×#1009	—	2	4	no	—
17	C₅×#1009	C₂²	1	8	yes	complemented
18	C₅×#1007	—	2	4	no	—
19	C₅×#1007	C₂²	1	8	yes	complemented
20	C₂×C₅×#239	—	2	1	no	—
21	C₂×C₅×#239	C₂²	1	2	yes	—
22	C₂×C₅×#239	C₂²	1	2	yes	complemented
23	C₂×C₅×D₃×Q₈	—	2	1	no	—
24	C₂×C₅×D₃×Q₈	C₂²	1	2	yes	complemented
25	C₂×C₅×D₃×D₄	—	2	2	no	—
26	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
27	C₂×C₅×#235	—	2	2	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	C₂²×C₅×D₁₂	—	2	1	no	—
32	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
33	C₃×C₅×#137	C₂²	1	8	yes	complemented
34	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
35	C₂×C₃×C₅×SD₁₆	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	2	yes	complemented
40	C₂×C₅×#215	C₂²	1	2	yes	complemented
41	C₂×C₅×#215	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₅×#215	C₂²	1	8	yes	complemented
43	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₅×#919	C₂²	1	16	yes	complemented
47	C₅×#918	C₂²	1	16	yes	complemented
48	C₅×#914	C₂²	1	16	yes	complemented
49	C₅×D₃×SD₁₆	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×#5778	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
57	C₂×C₅×2₋¹⁺⁴	—	3	1	no	—
58	C₂×C₅×H(5,𝔽₂)	—	3	1	no	—
59	C₅×#577	—	3	16	no	—
60	C₂×C₅×#137	—	3	2	no	—
61	C₂×C₅×#137	D₃	1	1	yes	characteristic, complemented
62	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
63	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
64	C₂×C₅×#135	—	3	1	no	—
65	C₂×C₅×#135	—	3	2	no	—
66	C₂²×C₅×SD₁₆	—	3	1	no	—
67	C₂²×C₅×SD₁₆	—	3	2	no	—
68	C₂×C₅×#131	—	3	1	no	—
69	C₂³×C₅×D₃	—	2	1	no	—
70	C₂³×C₅×D₃	—	2	2	no	—
71	C₃×C₅×#41	—	2	2	no	—
72	C₃×C₅×#41	C₂³	1	4	yes	—
73	C₂×C₃×C₅×Q₈	—	2	1	no	—
74	C₂×C₃×C₅×Q₈	—	2	2	no	—
75	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
76	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	complemented
78	C₂×C₃×C₅×D₄	—	2	1	no	—
79	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	—	2	1	no	—
81	C₂²×C₃×C₄×C₅	—	2	1	no	—
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₅×#67	—	2	1	no	—
84	C₂×C₅×#67	—	2	2	no	—
85	C₂×C₅×#67	D₄	1	2	yes	—
86	C₅×#239	—	2	8	no	—
87	C₅×#239	—	2	4	no	—
88	C₅×#239	—	2	4	no	—
89	C₅×#239	C₂³	1	8	yes	—
90	C₅×#239	C₂³	1	8	yes	complemented
91	C₅×D₃×Q₈	—	2	4	no	—
92	C₅×D₃×Q₈	—	2	8	no	—
93	C₅×D₃×Q₈	C₂³	1	8	yes	complemented
94	C₅×D₃×D₄	—	2	16	no	—
95	C₅×D₃×D₄	—	2	4	no	—
96	C₅×D₃×D₄	C₂³	1	8	yes	—
97	C₅×#235	—	2	2	no	—
98	C₅×#235	—	2	16	no	—
99	C₅×#235	—	2	8	no	—
100	C₅×#235	D₄	1	4	yes	—
101	C₅×#235	C₂³	1	4	yes	—
102	C₅×#235	C₂³	1	4	yes	complemented
103	C₂×C₅×D₁₂	—	2	2	no	—
104	C₂×C₅×D₁₂	—	2	2	no	—
105	C₂×C₅×D₁₂	—	2	1	no	—
106	C₂×C₅×D₁₂	—	2	2	no	—
107	C₂×C₅×D₁₂	—	2	8	no	—
108	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
109	C₂×C₅×D₁₂	C₂³	1	2	yes	—
110	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
111	C₂×C₅×D₁₂	C₂³	1	4	yes	—
112	C₂×C₄×C₅×D₃	—	2	2	no	—
113	C₂×C₄×C₅×D₃	—	2	1	no	—
114	C₂×C₄×C₅×D₃	—	2	2	no	—
115	C₂×C₄×C₅×D₃	—	2	2	no	—
116	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
117	C₂×C₅×Dic₆	—	2	2	no	—
118	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
119	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
120	C₃×C₅×Q₁₆	C₂³	1	8	yes	complemented
121	C₃×C₅×SD₁₆	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	8	yes	complemented
126	C₅×#215	C₂³	1	8	yes	complemented
127	C₅×#215	C₂³	1	4	yes	complemented
128	C₅×#214	C₂³	1	4	yes	complemented
129	C₅×#213	C₂³	1	4	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×#1007	C₂×C₅	1	1	yes	characteristic, complemented
139	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×#950	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂²×#215	C₂×C₅	1	1	yes	characteristic, complemented
142	#5778	C₂×C₅	1	16	yes	direct product factor
143	C₂×#919	C₂×C₅	1	2	yes	complemented
144	C₂×#918	C₂×C₅	1	2	yes	complemented
145	C₂×#914	C₂×C₅	1	2	yes	complemented
146	C₂×D₃×SD₁₆	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	C₅×2₋¹⁺⁴	—	3	8	no	—
150	C₅×2₋¹⁺⁴	—	6	4	no	—
151	C₅×H(5,𝔽₂)	—	3	8	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	2	no	—
158	C₂×C₅×#41	—	6	1	no	—
159	C₂×C₅×#41	—	6	1	no	—
160	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
161	C₂²×C₅×Q₈	—	3	2	no	—
162	C₂²×C₅×Q₈	—	6	1	no	—
163	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
164	C₂²×C₅×D₄	—	3	2	no	—
165	C₂²×C₅×D₄	—	3	1	no	—
166	C₂²×C₅×D₄	—	6	1	no	—
167	C₂²×C₅×D₄	—	6	2	no	—
168	C₅×#137	—	3	16	no	—
169	C₅×#137	C₂×D₃	1	8	yes	complemented
170	C₅×AGL(1,ℤ/8)	—	3	16	no	—
171	C₅×AGL(1,ℤ/8)	—	3	8	no	—
172	C₅×#135	—	3	8	no	—
173	C₅×#135	—	3	16	no	—
174	C₂×C₅×Q₁₆	—	3	1	no	—
175	C₂×C₅×Q₁₆	C₂×D₃	1	2	yes	complemented
176	C₂×C₅×SD₁₆	—	3	2	no	—
177	C₂×C₅×SD₁₆	—	3	2	no	—
178	C₂×C₅×SD₁₆	—	3	1	no	—
179	C₂×C₅×SD₁₆	—	3	8	no	—
180	C₂×C₅×SD₁₆	—	3	1	no	—
181	C₂×C₅×SD₁₆	—	3	16	no	—
182	C₂×C₅×SD₁₆	—	3	2	no	—
183	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	complemented
184	C₂×C₅×D₈	—	3	1	no	—
185	C₂×C₅×D₈	—	3	2	no	—
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×#577	—	3	1	no	Sylow
192	C₂³×C₃×C₅	—	2	1	no	—
193	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₅×D₃	—	2	1	no	—
195	C₂²×C₅×D₃	—	2	2	no	—
196	C₂²×C₅×D₃	—	2	4	no	—
197	C₂²×C₅×D₃	—	2	8	no	—
198	C₂²×C₅×D₃	—	8	4	no	—
199	C₂²×C₅×D₃	—	8	2	no	—
200	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
201	C₃×C₅×Q₈	—	2	2	no	—
202	C₃×C₅×Q₈	—	2	4	no	—
203	C₃×C₅×Q₈	—	2	1	no	—
204	C₃×C₅×Q₈	C₂⁴	1	4	yes	—
205	C₃×C₅×Q₈	C₂⁴	1	2	yes	—
206	C₃×C₅×D₄	—	2	4	no	—
207	C₃×C₅×D₄	—	2	1	no	—
208	C₃×C₅×D₄	C₂⁴	1	2	yes	—
209	C₂×C₃×C₄×C₅	—	2	2	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	4	no	—
212	C₂×C₃×C₄×C₅	—	2	4	no	—
213	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
214	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
215	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
216	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
217	C₅×#67	—	2	4	no	—
218	C₅×#67	—	2	8	no	—
219	C₅×#67	C₂×D₄	1	8	yes	—
220	C₂×C₅×Dic₃	—	2	1	no	—
221	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
222	C₅×D₁₂	—	2	8	no	—
223	C₅×D₁₂	—	2	8	no	—
224	C₅×D₁₂	—	2	4	no	—
225	C₅×D₁₂	—	2	2	no	—
226	C₅×D₁₂	—	2	1	no	—
227	C₅×D₁₂	C₂×D₄	1	4	yes	—
228	C₅×D₁₂	C₂⁴	1	4	yes	—
229	C₅×D₁₂	C₂⁴	1	2	yes	—
230	C₄×C₅×D₃	—	2	8	no	—
231	C₄×C₅×D₃	—	2	4	no	—
232	C₄×C₅×D₃	—	2	8	no	—
233	C₄×C₅×D₃	—	2	8	no	—
234	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
235	C₄×C₅×D₃	C₂⁴	1	4	yes	—
236	C₅×Dic₆	—	2	1	no	—
237	C₅×Dic₆	—	2	8	no	—
238	C₅×Dic₆	C₂×D₄	1	4	yes	—
239	C₅×Dic₆	C₂⁴	1	2	yes	—
240	C₃×C₅×C₈	C₂⁴	1	4	yes	—
241	C₅×C₃⋊C₈	C₂⁴	1	2	yes	—
242	C₅×C₃⋊C₈	C₂⁴	1	2	yes	—
243	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
244	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
245	#1009	—	2	4	no	—
246	#1009	C₂²×C₅	1	8	yes	complemented
247	#1007	—	2	4	no	—
248	#1007	C₂²×C₅	1	8	yes	complemented
249	C₂×#239	—	2	1	no	—
250	C₂×#239	C₂²×C₅	1	2	yes	—
251	C₂×#239	C₂²×C₅	1	2	yes	complemented
252	C₂×D₃×Q₈	—	2	1	no	—
253	C₂×D₃×Q₈	C₂²×C₅	1	2	yes	complemented
254	C₂×D₃×D₄	—	2	2	no	—
255	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
256	C₂×#235	—	2	2	no	—
257	C₂×#235	—	2	1	no	—
258	C₂×#235	C₂²×C₅	1	1	yes	characteristic
259	C₂×#235	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₂²×D₁₂	—	2	1	no	—
261	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
262	C₃×#137	C₂²×C₅	1	8	yes	complemented
263	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	complemented
264	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
265	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
266	#950	C₂²×C₅	1	8	yes	complemented
267	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₂×#215	C₂²×C₅	1	2	yes	complemented
269	C₂×#215	C₂²×C₅	1	2	yes	complemented
270	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₂×#215	C₂²×C₅	1	8	yes	complemented
272	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
275	#919	C₂²×C₅	1	16	yes	complemented
276	#918	C₂²×C₅	1	16	yes	complemented
277	#914	C₂²×C₅	1	16	yes	complemented
278	D₃×SD₁₆	C₂²×C₅	1	16	yes	complemented
279	#908	C₂²×C₅	1	8	yes	complemented
280	#907	C₂²×C₅	1	8	yes	complemented
281	C₂×D₂₄	C₂²×C₅	1	2	yes	complemented
282	C₂×#204	C₂²×C₅	1	2	yes	complemented
283	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	complemented
284	C₂×D₃×C₈	C₂²×C₅	1	2	yes	complemented
285	C₂⁴×C₅	—	6	2	no	—
286	C₂⁴×C₅	—	6	1	no	—
287	C₅×#41	—	2	2	no	—
288	C₅×#41	—	3	4	no	—
289	C₅×#41	—	3	4	no	—
290	C₅×#41	—	3	8	no	—
291	C₅×#41	—	3	8	no	—
292	C₅×#41	—	3	4	no	—
293	C₅×#41	—	6	16	no	—
294	C₅×#41	—	6	8	no	—
295	C₅×#41	—	6	4	no	—
296	C₅×#41	—	6	4	no	—
297	C₅×#41	—	6	8	no	—
298	C₅×#41	—	6	2	no	—
299	C₅×#41	C₂²×D₃	1	4	yes	—
300	C₂×C₅×Q₈	—	2	1	no	—
301	C₂×C₅×Q₈	—	2	2	no	—
302	C₂×C₅×Q₈	—	3	1	no	—
303	C₂×C₅×Q₈	—	3	8	no	—
304	C₂×C₅×Q₈	—	3	1	no	—
305	C₂×C₅×Q₈	—	6	2	no	—
306	C₂×C₅×Q₈	—	6	4	no	—
307	C₂×C₅×Q₈	—	6	8	no	—
308	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
309	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
310	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	complemented
311	C₂×C₅×D₄	—	2	1	no	—
312	C₂×C₅×D₄	—	3	2	no	—
313	C₂×C₅×D₄	—	3	8	no	—
314	C₂×C₅×D₄	—	3	1	no	—
315	C₂×C₅×D₄	—	3	1	no	—
316	C₂×C₅×D₄	—	3	2	no	—
317	C₂×C₅×D₄	—	3	4	no	—
318	C₂×C₅×D₄	—	6	8	no	—
319	C₂×C₅×D₄	—	6	2	no	—
320	C₂×C₅×D₄	—	6	2	no	—
321	C₂×C₅×D₄	—	6	4	no	—
322	C₂×C₅×D₄	—	6	2	no	—
323	C₂×C₅×D₄	—	6	16	no	—
324	C₂×C₅×D₄	—	6	1	no	—
325	C₂×C₅×D₄	—	6	1	no	—
326	C₂×C₅×D₄	—	6	2	no	—
327	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
328	C₂²×C₄×C₅	—	2	1	no	—
329	C₂²×C₄×C₅	—	2	1	no	—
330	C₂²×C₄×C₅	—	3	2	no	—
331	C₂²×C₄×C₅	—	6	2	no	—
332	C₂²×C₄×C₅	—	6	2	no	—
333	C₂²×C₄×C₅	—	6	2	no	—
334	C₂²×C₄×C₅	—	6	1	no	—
335	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
336	C₅×Q₁₆	—	3	4	no	—
337	C₅×Q₁₆	C₂²×D₃	1	8	yes	complemented
338	C₅×SD₁₆	—	3	8	no	—
339	C₅×SD₁₆	—	3	8	no	—
340	C₅×SD₁₆	—	3	4	no	—
341	C₅×SD₁₆	—	3	4	no	—
342	C₅×SD₁₆	—	3	8	no	—
343	C₅×SD₁₆	C₂²×D₃	1	8	yes	complemented
344	C₅×D₈	—	3	4	no	—
345	C₅×D₈	—	3	8	no	—
346	C₅×M₁₆	—	3	8	no	—
347	C₅×M₁₆	C₂²×D₃	1	4	yes	complemented
348	C₂×C₅×C₈	—	3	1	no	—
349	C₂×C₅×C₈	—	3	1	no	—
350	C₂×C₅×C₈	—	3	4	no	—
351	C₂×C₅×C₈	—	3	8	no	—
352	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
353	C₂×2₋¹⁺⁴	—	3	1	no	—
354	C₂×H(5,𝔽₂)	—	3	1	no	—
355	#577	—	3	16	no	—
356	C₂×#137	—	3	2	no	—
357	C₂×#137	C₅×D₃	1	1	yes	characteristic, complemented
358	C₂×AGL(1,ℤ/8)	—	3	2	no	—
359	C₂×AGL(1,ℤ/8)	—	3	1	no	—
360	C₂×#135	—	3	1	no	—
361	C₂×#135	—	3	2	no	—
362	C₂²×SD₁₆	—	3	1	no	—
363	C₂²×SD₁₆	—	3	2	no	—
364	C₂×#131	—	3	1	no	—
365	C₂²×C₃×C₅	—	2	2	no	—
366	C₂²×C₃×C₅	—	2	2	no	—
367	C₂²×C₃×C₅	—	4	2	no	—
368	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
369	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₅×D₃	—	2	4	no	—
371	C₂×C₅×D₃	—	2	2	no	—
372	C₂×C₅×D₃	—	2	4	no	—
373	C₂×C₅×D₃	—	4	2	no	—
374	C₂×C₅×D₃	—	4	4	no	—
375	C₂×C₅×D₃	—	8	8	no	—
376	C₂×C₅×D₃	—	8	4	no	—
377	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
378	C₃×C₄×C₅	—	2	4	no	—
379	C₃×C₄×C₅	—	2	2	no	—
380	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
381	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
382	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
383	C₅×Dic₃	—	2	2	no	—
384	C₅×Dic₃	C₂²×D₄	1	4	yes	—
385	C₂³×D₃	—	2	1	no	—
386	C₂³×D₃	—	2	2	no	—
387	C₃×#41	—	2	2	no	—
388	C₃×#41	C₂³×C₅	1	4	yes	—
389	C₂×C₃×Q₈	—	2	1	no	—
390	C₂×C₃×Q₈	—	2	2	no	—
391	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
392	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
393	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	complemented
394	C₂×C₃×D₄	—	2	1	no	—
395	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
396	C₂²×C₃×C₄	—	2	1	no	—
397	C₂²×C₃×C₄	—	2	1	no	—
398	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
399	C₂×#67	—	2	1	no	—
400	C₂×#67	—	2	2	no	—
401	C₂×#67	C₅×D₄	1	2	yes	—
402	#239	—	2	8	no	—
403	#239	—	2	4	no	—
404	#239	—	2	4	no	—
405	#239	C₂³×C₅	1	8	yes	—
406	#239	C₂³×C₅	1	8	yes	complemented
407	D₃×Q₈	—	2	4	no	—
408	D₃×Q₈	—	2	8	no	—
409	D₃×Q₈	C₂³×C₅	1	8	yes	complemented
410	D₃×D₄	—	2	16	no	—
411	D₃×D₄	—	2	4	no	—
412	D₃×D₄	C₂³×C₅	1	8	yes	—
413	#235	—	2	2	no	—
414	#235	—	2	16	no	—
415	#235	—	2	8	no	—
416	#235	C₅×D₄	1	4	yes	—
417	#235	C₂³×C₅	1	4	yes	—
418	#235	C₂³×C₅	1	4	yes	complemented
419	C₂×D₁₂	—	2	2	no	—
420	C₂×D₁₂	—	2	2	no	—
421	C₂×D₁₂	—	2	1	no	—
422	C₂×D₁₂	—	2	2	no	—
423	C₂×D₁₂	—	2	8	no	—
424	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
425	C₂×D₁₂	C₂³×C₅	1	2	yes	—
426	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
427	C₂×D₁₂	C₂³×C₅	1	4	yes	—
428	C₂×C₄×D₃	—	2	2	no	—
429	C₂×C₄×D₃	—	2	1	no	—
430	C₂×C₄×D₃	—	2	2	no	—
431	C₂×C₄×D₃	—	2	2	no	—
432	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
433	C₂×Dic₆	—	2	2	no	—
434	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
435	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
436	C₃×Q₁₆	C₂³×C₅	1	8	yes	complemented
437	C₃×SD₁₆	C₂³×C₅	1	8	yes	complemented
438	C₃×M₁₆	C₂³×C₅	1	4	yes	complemented
439	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
440	#216	C₂³×C₅	1	4	yes	complemented
441	#215	C₂³×C₅	1	8	yes	complemented
442	#215	C₂³×C₅	1	8	yes	complemented
443	#215	C₂³×C₅	1	4	yes	complemented
444	#214	C₂³×C₅	1	4	yes	complemented
445	#213	C₂³×C₅	1	4	yes	complemented
446	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
447	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
448	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	complemented
449	D₂₄	C₂³×C₅	1	8	yes	complemented
450	#204	C₂³×C₅	1	8	yes	complemented
451	ΓL(1,𝔽₂₅)	C₂³×C₅	1	8	yes	complemented
452	D₃×C₈	C₂³×C₅	1	8	yes	complemented
453	C₂³×C₅	—	2	1	no	—
454	C₂³×C₅	—	3	2	no	—
455	C₂³×C₅	—	6	8	no	—
456	C₂³×C₅	—	6	1	no	—
457	C₂³×C₅	—	6	2	no	—
458	C₂³×C₅	—	6	4	no	—
459	C₂³×C₅	—	24	2	no	—
460	C₂³×C₅	—	24	4	no	—
461	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
462	C₅×Q₈	—	2	2	no	—
463	C₅×Q₈	—	2	4	no	—
464	C₅×Q₈	—	2	1	no	—
465	C₅×Q₈	—	3	4	no	—
466	C₅×Q₈	—	3	2	no	—
467	C₅×Q₈	—	6	8	no	—
468	C₅×Q₈	—	6	1	no	—
469	C₅×Q₈	C₂³×D₃	1	4	yes	—
470	C₅×Q₈	C₂³×D₃	1	2	yes	—
471	C₅×D₄	—	2	4	no	—
472	C₅×D₄	—	2	1	no	—
473	C₅×D₄	—	3	8	no	—
474	C₅×D₄	—	3	4	no	—
475	C₅×D₄	—	3	2	no	—
476	C₅×D₄	—	3	4	no	—
477	C₅×D₄	—	6	8	no	—
478	C₅×D₄	—	6	8	no	—
479	C₅×D₄	—	6	8	no	—
480	C₅×D₄	—	6	4	no	—
481	C₅×D₄	—	6	4	no	—
482	C₅×D₄	—	6	2	no	—
483	C₅×D₄	—	6	1	no	—
484	C₅×D₄	C₂³×D₃	1	2	yes	—
485	C₂×C₄×C₅	—	2	4	no	—
486	C₂×C₄×C₅	—	2	1	no	—
487	C₂×C₄×C₅	—	2	2	no	—
488	C₂×C₄×C₅	—	2	4	no	—
489	C₂×C₄×C₅	—	3	2	no	—
490	C₂×C₄×C₅	—	3	4	no	—
491	C₂×C₄×C₅	—	3	4	no	—
492	C₂×C₄×C₅	—	6	8	no	—
493	C₂×C₄×C₅	—	6	8	no	—
494	C₂×C₄×C₅	—	6	8	no	—
495	C₂×C₄×C₅	—	6	1	no	—
496	C₂×C₄×C₅	—	6	4	no	—
497	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
498	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
499	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
500	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
501	C₅×C₈	—	3	2	no	—
502	C₅×C₈	—	3	2	no	—
503	C₅×C₈	C₂³×D₃	1	4	yes	—
504	2₋¹⁺⁴	—	3	8	no	—
505	2₋¹⁺⁴	—	6	4	no	—
506	H(5,𝔽₂)	—	3	8	no	—
507	H(5,𝔽₂)	—	6	4	no	—
508	C₂×#41	—	3	1	no	—
509	C₂×#41	—	3	2	no	—
510	C₂×#41	—	3	2	no	—
511	C₂×#41	—	3	1	no	—
512	C₂×#41	—	6	2	no	—
513	C₂×#41	—	6	1	no	—
514	C₂×#41	—	6	1	no	—
515	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
516	C₂²×Q₈	—	3	2	no	—
517	C₂²×Q₈	—	6	1	no	—
518	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
519	C₂²×D₄	—	3	2	no	—
520	C₂²×D₄	—	3	1	no	—
521	C₂²×D₄	—	6	1	no	—
522	C₂²×D₄	—	6	2	no	—
523	#137	—	3	16	no	—
524	#137	C₂×C₅×D₃	1	8	yes	complemented
525	AGL(1,ℤ/8)	—	3	16	no	—
526	AGL(1,ℤ/8)	—	3	8	no	—
527	#135	—	3	8	no	—
528	#135	—	3	16	no	—
529	C₂×Q₁₆	—	3	1	no	—
530	C₂×Q₁₆	C₂×C₅×D₃	1	2	yes	complemented
531	C₂×SD₁₆	—	3	2	no	—
532	C₂×SD₁₆	—	3	2	no	—
533	C₂×SD₁₆	—	3	1	no	—
534	C₂×SD₁₆	—	3	8	no	—
535	C₂×SD₁₆	—	3	1	no	—
536	C₂×SD₁₆	—	3	16	no	—
537	C₂×SD₁₆	—	3	2	no	—
538	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	complemented
539	C₂×D₈	—	3	1	no	—
540	C₂×D₈	—	3	2	no	—
541	#131	—	3	8	no	—
542	C₂×M₁₆	—	3	2	no	—
543	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
544	C₂²×C₈	—	3	1	no	—
545	C₂²×C₈	—	3	2	no	—
546	C₂×C₃×C₅	—	2	2	no	—
547	C₂×C₃×C₅	—	4	2	no	—
548	C₂×C₃×C₅	#577	1	2	yes	complemented
549	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
550	C₅×D₃	—	2	4	no	—
551	C₅×D₃	—	4	2	no	—
552	C₅×D₃	—	4	4	no	—
553	C₂³×C₃	—	2	1	no	—
554	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
555	C₂²×D₃	—	2	1	no	—
556	C₂²×D₃	—	2	2	no	—
557	C₂²×D₃	—	2	4	no	—
558	C₂²×D₃	—	2	8	no	—
559	C₂²×D₃	—	8	4	no	—
560	C₂²×D₃	—	8	2	no	—
561	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
562	C₃×Q₈	—	2	2	no	—
563	C₃×Q₈	—	2	4	no	—
564	C₃×Q₈	—	2	1	no	—
565	C₃×Q₈	C₂⁴×C₅	1	4	yes	—
566	C₃×Q₈	C₂⁴×C₅	1	2	yes	—
567	C₃×D₄	—	2	4	no	—
568	C₃×D₄	—	2	1	no	—
569	C₃×D₄	C₂⁴×C₅	1	2	yes	—
570	C₂×C₃×C₄	—	2	2	no	—
571	C₂×C₃×C₄	—	2	1	no	—
572	C₂×C₃×C₄	—	2	4	no	—
573	C₂×C₃×C₄	—	2	4	no	—
574	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
575	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
576	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
577	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
578	#67	—	2	4	no	—
579	#67	—	2	8	no	—
580	#67	C₂×C₅×D₄	1	8	yes	—
581	C₂×Dic₃	—	2	1	no	—
582	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
583	D₁₂	—	2	8	no	—
584	D₁₂	—	2	8	no	—
585	D₁₂	—	2	4	no	—
586	D₁₂	—	2	2	no	—
587	D₁₂	—	2	1	no	—
588	D₁₂	C₂×C₅×D₄	1	4	yes	—
589	D₁₂	C₂⁴×C₅	1	4	yes	—
590	D₁₂	C₂⁴×C₅	1	2	yes	—
591	C₄×D₃	—	2	8	no	—
592	C₄×D₃	—	2	4	no	—
593	C₄×D₃	—	2	8	no	—
594	C₄×D₃	—	2	8	no	—
595	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
596	C₄×D₃	C₂⁴×C₅	1	4	yes	—
597	Dic₆	—	2	1	no	—
598	Dic₆	—	2	8	no	—
599	Dic₆	C₂×C₅×D₄	1	4	yes	—
600	Dic₆	C₂⁴×C₅	1	2	yes	—
601	C₃×C₈	C₂⁴×C₅	1	4	yes	—
602	C₃⋊C₈	C₂⁴×C₅	1	2	yes	—
603	C₃⋊C₈	C₂⁴×C₅	1	2	yes	—
604	C₂²×C₅	—	2	2	no	—
605	C₂²×C₅	—	2	2	no	—
606	C₂²×C₅	—	3	4	no	—
607	C₂²×C₅	—	4	2	no	—
608	C₂²×C₅	—	6	4	no	—
609	C₂²×C₅	—	6	2	no	—
610	C₂²×C₅	—	6	4	no	—
611	C₂²×C₅	—	12	2	no	—
612	C₂²×C₅	—	12	4	no	—
613	C₂²×C₅	—	24	4	no	—
614	C₂²×C₅	—	24	8	no	—
615	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
616	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
617	C₄×C₅	—	2	2	no	—
618	C₄×C₅	—	2	4	no	—
619	C₄×C₅	—	3	4	no	—
620	C₄×C₅	—	6	2	no	—
621	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
622	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
623	C₄×C₅	C₂⁴×D₃	1	1	yes	characteristic
624	C₂⁴	—	6	2	no	—
625	C₂⁴	—	6	1	no	—
626	#41	—	2	2	no	—
627	#41	—	3	4	no	—
628	#41	—	3	4	no	—
629	#41	—	3	8	no	—
630	#41	—	3	8	no	—
631	#41	—	3	4	no	—
632	#41	—	6	16	no	—
633	#41	—	6	8	no	—
634	#41	—	6	4	no	—
635	#41	—	6	4	no	—
636	#41	—	6	8	no	—
637	#41	—	6	2	no	—
638	#41	C₂²×C₅×D₃	1	4	yes	—
639	C₂×Q₈	—	2	1	no	—
640	C₂×Q₈	—	2	2	no	—
641	C₂×Q₈	—	3	1	no	—
642	C₂×Q₈	—	3	8	no	—
643	C₂×Q₈	—	3	1	no	—
644	C₂×Q₈	—	6	2	no	—
645	C₂×Q₈	—	6	4	no	—
646	C₂×Q₈	—	6	8	no	—
647	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
648	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
649	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	complemented
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	3	2	no	—
652	C₂×D₄	—	3	8	no	—
653	C₂×D₄	—	3	1	no	—
654	C₂×D₄	—	3	1	no	—
655	C₂×D₄	—	3	2	no	—
656	C₂×D₄	—	3	4	no	—
657	C₂×D₄	—	6	8	no	—
658	C₂×D₄	—	6	2	no	—
659	C₂×D₄	—	6	2	no	—
660	C₂×D₄	—	6	4	no	—
661	C₂×D₄	—	6	2	no	—
662	C₂×D₄	—	6	16	no	—
663	C₂×D₄	—	6	1	no	—
664	C₂×D₄	—	6	1	no	—
665	C₂×D₄	—	6	2	no	—
666	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	3	2	no	—
670	C₂²×C₄	—	6	2	no	—
671	C₂²×C₄	—	6	2	no	—
672	C₂²×C₄	—	6	2	no	—
673	C₂²×C₄	—	6	1	no	—
674	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
675	Q₁₆	—	3	4	no	—
676	Q₁₆	C₂²×C₅×D₃	1	8	yes	complemented
677	SD₁₆	—	3	8	no	—
678	SD₁₆	—	3	8	no	—
679	SD₁₆	—	3	4	no	—
680	SD₁₆	—	3	4	no	—
681	SD₁₆	—	3	8	no	—
682	SD₁₆	C₂²×C₅×D₃	1	8	yes	complemented
683	D₈	—	3	4	no	—
684	D₈	—	3	8	no	—
685	M₁₆	—	3	8	no	—
686	M₁₆	C₂²×C₅×D₃	1	4	yes	complemented
687	C₂×C₈	—	3	1	no	—
688	C₂×C₈	—	3	1	no	—
689	C₂×C₈	—	3	4	no	—
690	C₂×C₈	—	3	8	no	—
691	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
692	C₃×C₅	C₂×#577	1	1	yes	characteristic, complemented, Hall
693	C₂²×C₃	—	2	2	no	—
694	C₂²×C₃	—	2	2	no	—
695	C₂²×C₃	—	4	2	no	—
696	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
697	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
698	C₂×D₃	—	2	4	no	—
699	C₂×D₃	—	2	2	no	—
700	C₂×D₃	—	2	4	no	—
701	C₂×D₃	—	4	2	no	—
702	C₂×D₃	—	4	4	no	—
703	C₂×D₃	—	8	8	no	—
704	C₂×D₃	—	8	4	no	—
705	C₂×D₃	C₂²×C₅×D₄	1	4	yes	—
706	C₃×C₄	—	2	4	no	—
707	C₃×C₄	—	2	2	no	—
708	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
709	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
710	C₃×C₄	C₂⁵×C₅	1	1	yes	characteristic
711	Dic₃	—	2	2	no	—
712	Dic₃	C₂²×C₅×D₄	1	4	yes	—
713	C₂×C₅	—	2	2	no	—
714	C₂×C₅	—	4	2	no	—
715	C₂×C₅	—	6	4	no	—
716	C₂×C₅	—	12	4	no	—
717	C₂×C₅	—	12	2	no	—
718	C₂×C₅	#5778	1	2	yes	direct product factor
719	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
720	C₂³	—	2	1	no	—
721	C₂³	—	3	2	no	—
722	C₂³	—	6	8	no	—
723	C₂³	—	6	1	no	—
724	C₂³	—	6	2	no	—
725	C₂³	—	6	4	no	—
726	C₂³	—	24	2	no	—
727	C₂³	—	24	4	no	—
728	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
729	Q₈	—	2	2	no	—
730	Q₈	—	2	4	no	—
731	Q₈	—	2	1	no	—
732	Q₈	—	3	4	no	—
733	Q₈	—	3	2	no	—
734	Q₈	—	6	8	no	—
735	Q₈	—	6	1	no	—
736	Q₈	C₂³×C₅×D₃	1	4	yes	—
737	Q₈	C₂³×C₅×D₃	1	2	yes	—
738	D₄	—	2	4	no	—
739	D₄	—	2	1	no	—
740	D₄	—	3	8	no	—
741	D₄	—	3	4	no	—
742	D₄	—	3	2	no	—
743	D₄	—	3	4	no	—
744	D₄	—	6	8	no	—
745	D₄	—	6	8	no	—
746	D₄	—	6	8	no	—
747	D₄	—	6	4	no	—
748	D₄	—	6	4	no	—
749	D₄	—	6	2	no	—
750	D₄	—	6	1	no	—
751	D₄	C₂³×C₅×D₃	1	2	yes	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	3	2	no	—
757	C₂×C₄	—	3	4	no	—
758	C₂×C₄	—	3	4	no	—
759	C₂×C₄	—	6	8	no	—
760	C₂×C₄	—	6	8	no	—
761	C₂×C₄	—	6	8	no	—
762	C₂×C₄	—	6	1	no	—
763	C₂×C₄	—	6	4	no	—
764	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
765	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
766	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
767	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
768	C₈	—	3	2	no	—
769	C₈	—	3	2	no	—
770	C₈	C₂³×C₅×D₃	1	4	yes	—
771	C₂×C₃	—	2	2	no	—
772	C₂×C₃	—	4	2	no	—
773	C₂×C₃	C₅×#577	1	2	yes	complemented
774	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
775	D₃	—	2	4	no	—
776	D₃	—	4	4	no	—
777	D₃	—	4	2	no	—
778	C₅	C₂×#5778	1	1	yes	characteristic, direct product factor, Sylow
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	3	4	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	6	4	no	—
784	C₂²	—	6	2	no	—
785	C₂²	—	6	4	no	—
786	C₂²	—	12	4	no	—
787	C₂²	—	12	2	no	—
788	C₂²	—	24	4	no	—
789	C₂²	—	24	8	no	—
790	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
791	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
792	C₄	—	2	2	no	—
793	C₄	—	2	4	no	—
794	C₄	—	3	4	no	—
795	C₄	—	6	2	no	—
796	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
797	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
798	C₄	C₂⁴×C₅×D₃	1	1	yes	characteristic
799	C₃	C₂×C₅×#577	1	1	yes	characteristic, complemented, Sylow
800	C₂	—	2	2	no	—
801	C₂	—	4	2	no	—
802	C₂	—	6	4	no	—
803	C₂	—	12	4	no	—
804	C₂	—	12	2	no	—
805	C₂	C₅×#5778	1	2	yes	direct product factor
806	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×#137	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₅×#137	D₃
hypocenter	C₃	C₂×C₅×#577
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#137

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×#1007	C₂	semidirect
3. C₂×C₃×C₅×#137	C₂	semidirect
4. C₂×C₅×#950	C₂	semidirect
5. C₂²×C₅×#215	C₂	semidirect
6. C₅×#5778	C₂	direct (N × H)
7. C₂×C₅×#919	C₂	semidirect
8. C₂×C₅×#918	C₂	semidirect
9. C₂×C₅×#914	C₂	semidirect
10. C₂×C₅×D₃×SD₁₆	C₂	semidirect
11. C₂×C₅×#908	C₂	semidirect
12. C₂×C₅×#907	C₂	semidirect
15. C₂²×C₃×C₅×Q₈	C₂²	semidirect
17. C₅×#1009	C₂²	semidirect
19. C₅×#1007	C₂²	semidirect
22. C₂×C₅×#239	C₂²	semidirect
24. C₂×C₅×D₃×Q₈	C₂²	semidirect
30. C₂×C₅×#235	C₂²	semidirect
33. C₃×C₅×#137	C₂²	semidirect
34. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
35. C₂×C₃×C₅×SD₁₆	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×#215	C₂²	semidirect
41. C₂×C₅×#215	C₂²	semidirect
42. C₂×C₅×#215	C₂²	semidirect
43. C₂×C₅×#214	C₂²	semidirect
44. C₂×C₅×#213	C₂²	semidirect
45. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
46. C₅×#919	C₂²	semidirect
47. C₅×#918	C₂²	semidirect
48. C₅×#914	C₂²	semidirect
49. C₅×D₃×SD₁₆	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×#5778	C₅	direct (N × H)
61. C₂×C₅×#137	D₃	semidirect
77. C₂×C₃×C₅×Q₈	C₂³	semidirect
90. C₅×#239	C₂³	semidirect
93. C₅×D₃×Q₈	C₂³	semidirect
102. C₅×#235	C₂³	semidirect
120. C₃×C₅×Q₁₆	C₂³	semidirect
121. C₃×C₅×SD₁₆	C₂³	semidirect
122. C₃×C₅×M₁₆	C₂³	semidirect
124. C₅×#216	C₂³	semidirect
125. C₅×#215	C₂³	semidirect
126. C₅×#215	C₂³	semidirect
127. C₅×#215	C₂³	semidirect
128. C₅×#214	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×#1007	C₂×C₅	semidirect
139. C₂×C₃×#137	C₂×C₅	semidirect
140. C₂×#950	C₂×C₅	semidirect
141. C₂²×#215	C₂×C₅	semidirect
142. #5778	C₂×C₅	direct (N × H)
143. C₂×#919	C₂×C₅	semidirect
144. C₂×#918	C₂×C₅	semidirect
145. C₂×#914	C₂×C₅	semidirect
146. C₂×D₃×SD₁₆	C₂×C₅	semidirect
147. C₂×#908	C₂×C₅	semidirect
148. C₂×#907	C₂×C₅	semidirect
163. C₂²×C₅×Q₈	C₂×D₃	semidirect
169. C₅×#137	C₂×D₃	semidirect
175. C₂×C₅×Q₁₆	C₂×D₃	semidirect
183. C₂×C₅×SD₁₆	C₂×D₃	semidirect
188. C₂×C₅×M₁₆	C₂×D₃	semidirect
244. C₂²×C₃×Q₈	C₂²×C₅	semidirect
246. #1009	C₂²×C₅	semidirect
248. #1007	C₂²×C₅	semidirect
251. C₂×#239	C₂²×C₅	semidirect
253. C₂×D₃×Q₈	C₂²×C₅	semidirect
259. C₂×#235	C₂²×C₅	semidirect
262. C₃×#137	C₂²×C₅	semidirect
263. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
264. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
265. C₂×C₃×M₁₆	C₂²×C₅	semidirect
266. #950	C₂²×C₅	semidirect
267. C₂×#216	C₂²×C₅	semidirect
268. C₂×#215	C₂²×C₅	semidirect
269. C₂×#215	C₂²×C₅	semidirect
270. C₂×#215	C₂²×C₅	semidirect
271. C₂×#215	C₂²×C₅	semidirect
272. C₂×#214	C₂²×C₅	semidirect
273. C₂×#213	C₂²×C₅	semidirect
274. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
275. #919	C₂²×C₅	semidirect
276. #918	C₂²×C₅	semidirect
277. #914	C₂²×C₅	semidirect
278. D₃×SD₁₆	C₂²×C₅	semidirect
279. #908	C₂²×C₅	semidirect
280. #907	C₂²×C₅	semidirect
281. C₂×D₂₄	C₂²×C₅	semidirect
282. C₂×#204	C₂²×C₅	semidirect
283. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
284. C₂×D₃×C₈	C₂²×C₅	semidirect
310. C₂×C₅×Q₈	C₂²×D₃	semidirect
337. C₅×Q₁₆	C₂²×D₃	semidirect
343. C₅×SD₁₆	C₂²×D₃	semidirect
347. C₅×M₁₆	C₂²×D₃	semidirect
357. C₂×#137	C₅×D₃	semidirect
393. C₂×C₃×Q₈	C₂³×C₅	semidirect
406. #239	C₂³×C₅	semidirect
409. D₃×Q₈	C₂³×C₅	semidirect
418. #235	C₂³×C₅	semidirect
436. C₃×Q₁₆	C₂³×C₅	semidirect
437. C₃×SD₁₆	C₂³×C₅	semidirect
438. C₃×M₁₆	C₂³×C₅	semidirect
440. #216	C₂³×C₅	semidirect
441. #215	C₂³×C₅	semidirect
442. #215	C₂³×C₅	semidirect
443. #215	C₂³×C₅	semidirect
444. #214	C₂³×C₅	semidirect
445. #213	C₂³×C₅	semidirect
448. C₂×C₃⋊C₈	C₂³×C₅	semidirect
449. D₂₄	C₂³×C₅	semidirect
450. #204	C₂³×C₅	semidirect
451. ΓL(1,𝔽₂₅)	C₂³×C₅	semidirect
452. D₃×C₈	C₂³×C₅	semidirect
518. C₂²×Q₈	C₂×C₅×D₃	semidirect
524. #137	C₂×C₅×D₃	semidirect
530. C₂×Q₁₆	C₂×C₅×D₃	semidirect
538. C₂×SD₁₆	C₂×C₅×D₃	semidirect
543. C₂×M₁₆	C₂×C₅×D₃	semidirect
548. C₂×C₃×C₅	#577	semidirect
649. C₂×Q₈	C₂²×C₅×D₃	semidirect
676. Q₁₆	C₂²×C₅×D₃	semidirect
682. SD₁₆	C₂²×C₅×D₃	semidirect
686. M₁₆	C₂²×C₅×D₃	semidirect
692. C₃×C₅	C₂×#577	semidirect
718. C₂×C₅	#5778	direct (N × H)
773. C₂×C₃	C₅×#577	semidirect
778. C₅	C₂×#5778	direct (N × H)
799. C₃	C₂×C₅×#577	semidirect
805. C₂	C₅×#5778	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×#1007	2
C₂×C₃×C₅×#137	2
C₂×C₅×#950	2
C₂²×C₅×#215	2
C₅×#5778	2
C₂×C₅×#919	2
C₂×C₅×#918	2
C₂×C₅×#914	2
C₂×C₅×D₃×SD₁₆	2
C₂×C₅×#908	2
C₂×C₅×#907	2
C₂×C₅×#577	3
C₂×#5778	5

Subgroups — C2×C5×#5778 #14510027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5778 #14510027