Subgroups — C₅×#79878 #14453199

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×#911	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5016	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5015	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4865	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4864	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4781	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4776	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4773	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4773	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4712	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×#237	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₅×D₁₂	—	2	1	no	—
22	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#213	C₂²	1	1	yes	characteristic
27	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
29	C₅×#930	—	2	1	no	—
30	C₅×#930	—	2	1	no	—
31	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
32	C₅×#911	—	2	4	no	—
33	C₅×D₃×D₈	—	2	4	no	—
34	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
40	C₅×#897	C₂²	1	1	yes	characteristic, complemented
41	C₅×#895	C₂²	1	1	yes	characteristic
42	C₅×#895	C₂²	1	1	yes	characteristic, complemented
43	C₅×#895	C₂²	1	1	yes	characteristic, complemented
44	C₅×#886	—	2	1	no	—
45	C₅×#882	—	2	1	no	—
46	C₅×#882	—	2	1	no	—
47	C₅×#882	—	2	1	no	—
48	C₅×#875	C₂²	1	1	yes	characteristic, complemented
49	C₅×#874	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
51	C₃×C₅×#106	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	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
55	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	C₅×#810	C₂²	1	1	yes	characteristic, complemented
58	C₅×#809	C₂²	1	1	yes	characteristic, complemented
59	C₅×#809	C₂²	1	1	yes	characteristic, complemented
60	C₅×#809	C₂²	1	1	yes	characteristic, complemented
61	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
62	#79878	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	—	3	1	no	—
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	D₃	1	1	yes	characteristic, complemented
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×D₄	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	—	2	1	no	—
84	C₂²×C₃×C₄×C₅	—	2	1	no	—
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	C₂²×C₅×Dic₃	—	2	1	no	—
90	C₅×#237	—	2	2	no	—
91	C₅×#237	—	4	1	no	—
92	C₅×D₃×D₄	—	2	2	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	1	no	—
98	C₂×C₅×D₁₂	—	2	1	no	—
99	C₂×C₅×D₁₂	—	2	1	no	—
100	C₂×C₅×D₁₂	—	2	1	no	—
101	C₂×C₅×D₁₂	—	2	1	no	—
102	C₂×C₅×D₁₂	—	2	1	no	—
103	C₂×C₅×D₁₂	—	4	4	no	—
104	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
105	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
106	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
107	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
108	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
109	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
110	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
111	C₃×C₅×D₈	D₄	1	4	yes	complemented
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	C₂³	1	1	yes	characteristic
115	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
117	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
118	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
119	C₅×#214	—	2	2	no	—
120	C₅×#213	—	2	2	no	—
121	C₅×#213	—	2	2	no	—
122	C₅×#213	—	2	2	no	—
123	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
124	C₅×(C₂×D₃)⋊C₄	—	2	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	D₄	1	1	yes	characteristic
130	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
131	C₅×C₄⋊Dic₃	—	2	1	no	—
132	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
133	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
134	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
135	C₅×D₂₄	—	2	2	no	—
136	C₅×D₂₄	—	4	1	no	—
137	C₅×#204	—	2	2	no	—
138	C₅×#204	—	4	1	no	—
139	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
140	C₅×D₃×C₈	—	2	2	no	—
141	C₂×#911	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×D₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
143	#5554	C₂×C₅	1	1	yes	characteristic, complemented
144	D₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#442	C₂×C₅	1	1	yes	characteristic, complemented
146	#5016	C₂×C₅	1	1	yes	characteristic, complemented
147	#5015	C₂×C₅	1	1	yes	characteristic, complemented
148	#4865	C₂×C₅	1	1	yes	characteristic, complemented
149	#4864	C₂×C₅	1	1	yes	characteristic, complemented
150	#4781	C₂×C₅	1	1	yes	characteristic, complemented
151	#4776	C₂×C₅	1	1	yes	characteristic, complemented
152	#4773	C₂×C₅	1	1	yes	characteristic, complemented
153	#4773	C₂×C₅	1	1	yes	characteristic, complemented
154	#4712	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	—	3	1	no	—
164	C₂×C₅×SD₁₆	—	3	1	no	—
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	—	3	1	no	—
170	C₂×C₅×D₈	—	6	4	no	—
171	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
172	C₂×C₅×M₁₆	—	3	1	no	—
173	C₂²×C₅×C₈	—	3	1	no	—
174	C₅×#127	—	3	1	no	—
175	C₅×#124	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic, complemented
188	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
189	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
190	C₅×#106	C₂×D₃	1	1	yes	characteristic, complemented
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	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	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	C₂²×C₅×D₃	—	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×D₄	—	2	1	no	—
219	C₃×C₅×D₄	—	2	1	no	—
220	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
221	C₃×C₅×D₄	C₂×D₄	1	2	yes	complemented
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	2	1	no	—
224	C₂×C₃×C₄×C₅	—	4	2	no	—
225	C₂×C₃×C₄×C₅	—	8	1	no	—
226	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
227	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
228	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
229	C₅×#67	—	4	2	no	—
230	C₅×#67	—	4	2	no	—
231	C₅×#67	—	4	2	no	—
232	C₅×#67	—	4	2	no	—
233	C₂×C₅×Dic₃	—	2	1	no	—
234	C₂×C₅×Dic₃	—	4	2	no	—
235	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
236	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
237	C₅×D₁₂	—	2	2	no	—
238	C₅×D₁₂	—	2	1	no	—
239	C₅×D₁₂	—	2	1	no	—
240	C₅×D₁₂	—	2	1	no	—
241	C₅×D₁₂	—	2	1	no	—
242	C₅×D₁₂	—	2	1	no	—
243	C₅×D₁₂	—	2	1	no	—
244	C₅×D₁₂	—	4	2	no	—
245	C₅×D₁₂	—	4	2	no	—
246	C₅×D₁₂	—	4	2	no	—
247	C₅×D₁₂	—	8	1	no	—
248	C₅×D₁₂	—	8	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	—	2	1	no	—
253	C₅×Dic₆	—	2	1	no	—
254	C₅×Dic₆	—	2	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×#237	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
261	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₂²×D₁₂	—	2	1	no	—
264	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
265	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
266	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₂×#213	C₂²×C₅	1	1	yes	characteristic
269	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
271	#930	—	2	1	no	—
272	#930	—	2	1	no	—
273	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
274	#911	—	2	4	no	—
275	D₃×D₈	—	2	4	no	—
276	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
277	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
278	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
280	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
281	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
282	#897	C₂²×C₅	1	1	yes	characteristic, complemented
283	#895	C₂²×C₅	1	1	yes	characteristic
284	#895	C₂²×C₅	1	1	yes	characteristic, complemented
285	#895	C₂²×C₅	1	1	yes	characteristic, complemented
286	#886	—	2	1	no	—
287	#882	—	2	1	no	—
288	#882	—	2	1	no	—
289	#882	—	2	1	no	—
290	#875	C₂²×C₅	1	1	yes	characteristic, complemented
291	#874	C₂²×C₅	1	1	yes	characteristic, complemented
292	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
293	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
294	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
295	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
296	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
297	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
298	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
299	#810	C₂²×C₅	1	1	yes	characteristic, complemented
300	#809	C₂²×C₅	1	1	yes	characteristic, complemented
301	#809	C₂²×C₅	1	1	yes	characteristic, complemented
302	#809	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	—	3	1	no	—
310	C₂×C₅×D₄	—	3	1	no	—
311	C₂×C₅×D₄	—	3	1	no	—
312	C₂×C₅×D₄	—	3	1	no	—
313	C₂×C₅×D₄	—	3	1	no	—
314	C₂×C₅×D₄	—	6	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	1	no	—
320	C₂×C₅×D₄	—	6	2	no	—
321	C₂×C₅×D₄	—	6	2	no	—
322	C₂×C₅×D₄	—	6	2	no	—
323	C₂×C₅×D₄	—	6	1	no	—
324	C₂×C₅×D₄	—	6	1	no	—
325	C₂×C₅×D₄	—	6	1	no	—
326	C₂×C₅×D₄	—	12	4	no	—
327	C₂×C₅×D₄	—	12	1	no	—
328	C₂×C₅×D₄	—	12	1	no	—
329	C₂×C₅×D₄	—	12	1	no	—
330	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
331	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
332	C₂²×C₄×C₅	—	2	1	no	—
333	C₂²×C₄×C₅	—	2	1	no	—
334	C₂²×C₄×C₅	—	3	1	no	—
335	C₂²×C₄×C₅	—	3	1	no	—
336	C₂²×C₄×C₅	—	6	1	no	—
337	C₅×SD₁₆	—	6	2	no	—
338	C₅×SD₁₆	—	6	2	no	—
339	C₅×SD₁₆	—	12	1	no	—
340	C₅×D₈	—	6	2	no	—
341	C₅×D₈	—	6	2	no	—
342	C₅×D₈	—	6	2	no	—
343	C₅×D₈	—	6	2	no	—
344	C₅×D₈	—	12	1	no	—
345	C₅×D₈	D₁₂	1	4	yes	complemented
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	—	6	1	no	—
354	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
355	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	—	3	1	no	—
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	C₅×D₃	1	1	yes	characteristic, complemented
381	#435	—	3	1	no	—
382	C₂²×C₃×C₅	—	2	2	no	—
383	C₂²×C₃×C₅	—	2	2	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	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₅×D₃	—	2	1	no	—
390	C₂×C₅×D₃	—	2	1	no	—
391	C₂×C₅×D₃	—	2	1	no	—
392	C₂×C₅×D₃	—	2	1	no	—
393	C₂×C₅×D₃	—	2	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	—	4	1	no	—
398	C₂×C₅×D₃	—	4	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	—	4	1	no	—
411	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
412	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
413	C₅×Dic₃	—	2	1	no	—
414	C₅×Dic₃	—	2	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×D₄	C₂³×C₅	1	1	yes	characteristic
420	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
421	C₂²×C₃×C₄	—	2	1	no	—
422	C₂²×C₃×C₄	—	2	1	no	—
423	C₂×#67	—	2	1	no	—
424	C₂×#67	—	2	1	no	—
425	C₂×#67	—	2	1	no	—
426	C₂×#67	—	2	1	no	—
427	C₂²×Dic₃	—	2	1	no	—
428	#237	—	2	2	no	—
429	#237	—	4	1	no	—
430	D₃×D₄	—	2	2	no	—
431	D₃×D₄	—	2	2	no	—
432	D₃×D₄	—	2	2	no	—
433	D₃×D₄	—	4	1	no	—
434	D₃×D₄	—	4	1	no	—
435	D₃×D₄	—	4	1	no	—
436	C₂×D₁₂	—	2	1	no	—
437	C₂×D₁₂	—	2	1	no	—
438	C₂×D₁₂	—	2	1	no	—
439	C₂×D₁₂	—	2	1	no	—
440	C₂×D₁₂	—	2	1	no	—
441	C₂×D₁₂	—	4	4	no	—
442	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
443	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
444	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
445	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
446	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
447	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
448	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
449	C₃×D₈	C₅×D₄	1	4	yes	complemented
450	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
451	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
452	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
453	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
454	C₃×C₂²⋊C₄	—	2	1	no	—
455	C₃×C₂²⋊C₄	—	2	1	no	—
456	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
457	#214	—	2	2	no	—
458	#213	—	2	2	no	—
459	#213	—	2	2	no	—
460	#213	—	2	2	no	—
461	(C₂×D₃)⋊C₄	—	2	1	no	—
462	(C₂×D₃)⋊C₄	—	2	1	no	—
463	(C₂×D₃)⋊C₄	—	2	1	no	—
464	(C₂×D₃)⋊C₄	—	2	1	no	—
465	(C₂×D₃)⋊C₄	—	2	1	no	—
466	(C₂×D₃)⋊C₄	—	2	1	no	—
467	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
468	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
469	C₄⋊Dic₃	—	2	1	no	—
470	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
471	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
472	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
473	D₂₄	—	2	2	no	—
474	D₂₄	—	4	1	no	—
475	#204	—	2	2	no	—
476	#204	—	4	1	no	—
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	—	3	1	no	—
482	C₂³×C₅	—	3	1	no	—
483	C₂³×C₅	—	6	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	—	6	1	no	—
496	C₅×Q₈	—	6	1	no	—
497	C₅×D₄	—	2	1	no	—
498	C₅×D₄	—	2	1	no	—
499	C₅×D₄	—	6	2	no	—
500	C₅×D₄	—	6	1	no	—
501	C₅×D₄	—	6	1	no	—
502	C₅×D₄	—	6	1	no	—
503	C₅×D₄	—	6	1	no	—
504	C₅×D₄	—	6	1	no	—
505	C₅×D₄	—	6	1	no	—
506	C₅×D₄	—	12	2	no	—
507	C₅×D₄	—	12	2	no	—
508	C₅×D₄	—	12	2	no	—
509	C₅×D₄	—	12	2	no	—
510	C₅×D₄	—	12	2	no	—
511	C₅×D₄	—	12	2	no	—
512	C₅×D₄	—	12	2	no	—
513	C₅×D₄	—	24	1	no	—
514	C₅×D₄	—	24	1	no	—
515	C₅×D₄	C₂×D₁₂	1	2	yes	—
516	C₅×D₄	C₂×D₁₂	1	2	yes	complemented
517	C₂×C₄×C₅	—	2	1	no	—
518	C₂×C₄×C₅	—	2	1	no	—
519	C₂×C₄×C₅	—	3	1	no	—
520	C₂×C₄×C₅	—	3	1	no	—
521	C₂×C₄×C₅	—	4	2	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	—	6	1	no	—
527	C₂×C₄×C₅	—	8	1	no	—
528	C₂×C₄×C₅	—	12	2	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	C₂×D₁₂	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	—	3	1	no	—
544	C₂×SD₁₆	—	3	1	no	—
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	—	3	1	no	—
550	C₂×D₈	—	6	4	no	—
551	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
552	C₂×M₁₆	—	3	1	no	—
553	C₂²×C₈	—	3	1	no	—
554	#127	—	3	1	no	—
555	#124	—	3	1	no	—
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	C₂×C₅×D₃	1	1	yes	characteristic, complemented
568	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
569	C₂×C₂²⋊C₄	—	6	1	no	—
570	#106	C₂×C₅×D₃	1	1	yes	characteristic, complemented
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	C₂×C₅×D₃	1	1	yes	characteristic, complemented
577	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
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	—	4	2	no	—
582	C₂×C₃×C₅	—	4	2	no	—
583	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
584	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
585	C₂×C₃×C₅	#576	1	1	yes	characteristic
586	C₅×D₃	—	2	2	no	—
587	C₅×D₃	—	4	1	no	—
588	C₅×D₃	—	8	1	no	—
589	C₅×D₃	—	8	1	no	—
590	C₅×D₃	—	8	1	no	—
591	C₂³×C₃	—	2	1	no	—
592	C₂³×C₃	—	2	1	no	—
593	C₂²×D₃	—	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×D₄	—	2	1	no	—
608	C₃×D₄	—	2	1	no	—
609	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
610	C₃×D₄	C₂×C₅×D₄	1	2	yes	complemented
611	C₂×C₃×C₄	—	2	1	no	—
612	C₂×C₃×C₄	—	2	1	no	—
613	C₂×C₃×C₄	—	4	2	no	—
614	C₂×C₃×C₄	—	8	1	no	—
615	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
616	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
617	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
618	#67	—	4	2	no	—
619	#67	—	4	2	no	—
620	#67	—	4	2	no	—
621	#67	—	4	2	no	—
622	C₂×Dic₃	—	2	1	no	—
623	C₂×Dic₃	—	4	2	no	—
624	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
625	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
626	D₁₂	—	2	2	no	—
627	D₁₂	—	2	1	no	—
628	D₁₂	—	2	1	no	—
629	D₁₂	—	2	1	no	—
630	D₁₂	—	2	1	no	—
631	D₁₂	—	2	1	no	—
632	D₁₂	—	2	1	no	—
633	D₁₂	—	4	2	no	—
634	D₁₂	—	4	2	no	—
635	D₁₂	—	4	2	no	—
636	D₁₂	—	8	1	no	—
637	D₁₂	—	8	1	no	—
638	C₄×D₃	—	2	1	no	—
639	C₄×D₃	—	2	1	no	—
640	C₄×D₃	—	2	1	no	—
641	C₄×D₃	—	2	1	no	—
642	Dic₆	—	2	1	no	—
643	Dic₆	—	2	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	—	2	2	no	—
649	C₂²×C₅	—	2	2	no	—
650	C₂²×C₅	—	3	2	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	—	6	1	no	—
656	C₂²×C₅	—	6	1	no	—
657	C₂²×C₅	—	6	1	no	—
658	C₂²×C₅	—	6	1	no	—
659	C₂²×C₅	—	6	1	no	—
660	C₂²×C₅	—	12	1	no	—
661	C₂²×C₅	—	12	1	no	—
662	C₂²×C₅	—	12	1	no	—
663	C₂²×C₅	—	12	1	no	—
664	C₂²×C₅	—	12	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	—	4	1	no	—
677	C₄×C₅	—	6	1	no	—
678	C₄×C₅	—	6	1	no	—
679	C₄×C₅	—	12	1	no	—
680	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
681	C₄×C₅	#1009	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	—	3	1	no	—
688	C₂×D₄	—	3	1	no	—
689	C₂×D₄	—	3	1	no	—
690	C₂×D₄	—	3	1	no	—
691	C₂×D₄	—	3	1	no	—
692	C₂×D₄	—	6	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	1	no	—
698	C₂×D₄	—	6	2	no	—
699	C₂×D₄	—	6	2	no	—
700	C₂×D₄	—	6	2	no	—
701	C₂×D₄	—	6	1	no	—
702	C₂×D₄	—	6	1	no	—
703	C₂×D₄	—	6	1	no	—
704	C₂×D₄	—	12	4	no	—
705	C₂×D₄	—	12	1	no	—
706	C₂×D₄	—	12	1	no	—
707	C₂×D₄	—	12	1	no	—
708	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
709	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	3	1	no	—
713	C₂²×C₄	—	3	1	no	—
714	C₂²×C₄	—	6	1	no	—
715	SD₁₆	—	6	2	no	—
716	SD₁₆	—	6	2	no	—
717	SD₁₆	—	12	1	no	—
718	D₈	—	6	2	no	—
719	D₈	—	6	2	no	—
720	D₈	—	6	2	no	—
721	D₈	—	6	2	no	—
722	D₈	—	12	1	no	—
723	D₈	C₅×D₁₂	1	4	yes	complemented
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	—	6	1	no	—
732	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
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	—	2	2	no	—
747	C₂²×C₃	—	2	2	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	C₂²×C₅×D₄	1	1	yes	characteristic
753	C₂×D₃	—	2	1	no	—
754	C₂×D₃	—	2	1	no	—
755	C₂×D₃	—	2	1	no	—
756	C₂×D₃	—	2	1	no	—
757	C₂×D₃	—	2	1	no	—
758	C₂×D₃	—	4	1	no	—
759	C₂×D₃	—	4	1	no	—
760	C₂×D₃	—	4	1	no	—
761	C₂×D₃	—	4	1	no	—
762	C₂×D₃	—	4	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	—	4	1	no	—
775	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
776	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
777	Dic₃	—	2	1	no	—
778	Dic₃	—	2	1	no	—
779	Dic₃	—	4	1	no	—
780	C₂×C₅	—	4	2	no	—
781	C₂×C₅	—	4	2	no	—
782	C₂×C₅	—	6	2	no	—
783	C₂×C₅	—	12	1	no	—
784	C₂×C₅	—	24	1	no	—
785	C₂×C₅	—	24	1	no	—
786	C₂×C₅	—	24	1	no	—
787	C₂×C₅	D₄×D₁₂	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	—	3	1	no	—
793	C₂³	—	3	1	no	—
794	C₂³	—	6	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	—	6	1	no	—
807	Q₈	—	6	1	no	—
808	D₄	—	2	1	no	—
809	D₄	—	2	1	no	—
810	D₄	—	6	2	no	—
811	D₄	—	6	1	no	—
812	D₄	—	6	1	no	—
813	D₄	—	6	1	no	—
814	D₄	—	6	1	no	—
815	D₄	—	6	1	no	—
816	D₄	—	6	1	no	—
817	D₄	—	12	2	no	—
818	D₄	—	12	2	no	—
819	D₄	—	12	2	no	—
820	D₄	—	12	2	no	—
821	D₄	—	12	2	no	—
822	D₄	—	12	2	no	—
823	D₄	—	12	2	no	—
824	D₄	—	24	1	no	—
825	D₄	—	24	1	no	—
826	D₄	C₂×C₅×D₁₂	1	2	yes	—
827	D₄	C₂×C₅×D₁₂	1	2	yes	complemented
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	3	1	no	—
831	C₂×C₄	—	3	1	no	—
832	C₂×C₄	—	4	2	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	—	6	1	no	—
838	C₂×C₄	—	8	1	no	—
839	C₂×C₄	—	12	2	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	C₂×C₅×D₁₂	1	2	yes	complemented
847	C₂×C₃	—	4	2	no	—
848	C₂×C₃	—	4	2	no	—
849	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
850	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
851	C₂×C₃	C₅×#576	1	1	yes	characteristic
852	D₃	—	2	2	no	—
853	D₃	—	4	1	no	—
854	D₃	—	8	1	no	—
855	D₃	—	8	1	no	—
856	D₃	—	8	1	no	—
857	C₅	#79878	1	1	yes	characteristic, direct product factor, Sylow
858	C₂²	—	2	2	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	3	2	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	6	1	no	—
866	C₂²	—	6	1	no	—
867	C₂²	—	6	1	no	—
868	C₂²	—	6	1	no	—
869	C₂²	—	6	1	no	—
870	C₂²	—	12	1	no	—
871	C₂²	—	12	1	no	—
872	C₂²	—	12	1	no	—
873	C₂²	—	12	1	no	—
874	C₂²	—	12	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	—	4	1	no	—
887	C₄	—	6	1	no	—
888	C₄	—	6	1	no	—
889	C₄	—	12	1	no	—
890	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
891	C₄	C₅×#1009	1	1	yes	characteristic
892	C₃	C₅×#3264	1	1	yes	characteristic, complemented, Sylow
893	C₂	—	4	2	no	—
894	C₂	—	4	2	no	—
895	C₂	—	6	2	no	—
896	C₂	—	12	1	no	—
897	C₂	—	24	1	no	—
898	C₂	—	24	1	no	—
899	C₂	—	24	1	no	—
900	C₂	C₅×D₄×D₁₂	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×#442	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#442	D₃
hypocenter	C₃	C₅×#3264
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#442

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#911	C₂	semidirect
2. C₂×C₅×D₃×D₈	C₂	semidirect
3. C₅×#5554	C₂	semidirect
4. C₅×D₄×D₁₂	C₂	semidirect
5. C₃×C₅×#442	C₂	semidirect
6. C₅×#5016	C₂	semidirect
7. C₅×#5015	C₂	semidirect
8. C₅×#4865	C₂	semidirect
9. C₅×#4864	C₂	semidirect
10. C₅×#4781	C₂	semidirect
11. C₅×#4776	C₂	semidirect
12. C₅×#4773	C₂	semidirect
13. C₅×#4773	C₂	semidirect
14. C₅×#4712	C₂	semidirect
15. C₅×#4706	C₂	semidirect
17. C₂×C₅×#237	C₂²	semidirect
19. C₂×C₅×D₃×D₄	C₂²	semidirect
20. C₂×C₅×D₃×D₄	C₂²	semidirect
23. C₃×C₄×C₅×D₄	C₂²	semidirect
24. C₃×C₄×C₅×D₄	C₂²	semidirect
25. C₂×C₅×#214	C₂²	semidirect
27. C₂×C₅×#213	C₂²	semidirect
28. C₂×C₅×#213	C₂²	semidirect
34. C₂×C₅×D₂₄	C₂²	semidirect
35. C₂×C₅×D₂₄	C₂²	semidirect
36. C₂×C₅×#204	C₂²	semidirect
37. C₂×C₅×#204	C₂²	semidirect
38. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
39. C₂×C₅×D₃×C₈	C₂²	semidirect
40. C₅×#897	C₂²	semidirect
42. C₅×#895	C₂²	semidirect
43. C₅×#895	C₂²	semidirect
48. C₅×#875	C₂²	semidirect
49. C₅×#874	C₂²	semidirect
51. C₃×C₅×#106	C₂²	semidirect
52. C₃×C₅×#102	C₂²	semidirect
53. C₃×C₅×#102	C₂²	semidirect
54. C₃×C₅×#97	C₂²	semidirect
55. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
56. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
57. C₅×#810	C₂²	semidirect
58. C₅×#809	C₂²	semidirect
59. C₅×#809	C₂²	semidirect
60. C₅×#809	C₂²	semidirect
61. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
62. #79878	C₅	direct (N × H)
76. C₅×#442	D₃	semidirect
111. C₃×C₅×D₈	D₄	semidirect
141. C₂×#911	C₂×C₅	semidirect
142. C₂×D₃×D₈	C₂×C₅	semidirect
143. #5554	C₂×C₅	semidirect
144. D₄×D₁₂	C₂×C₅	semidirect
145. C₃×#442	C₂×C₅	semidirect
146. #5016	C₂×C₅	semidirect
147. #5015	C₂×C₅	semidirect
148. #4865	C₂×C₅	semidirect
149. #4864	C₂×C₅	semidirect
150. #4781	C₂×C₅	semidirect
151. #4776	C₂×C₅	semidirect
152. #4773	C₂×C₅	semidirect
153. #4773	C₂×C₅	semidirect
154. #4712	C₂×C₅	semidirect
155. #4706	C₂×C₅	semidirect
187. C₄×C₅×D₄	C₂×D₃	semidirect
188. C₄×C₅×D₄	C₂×D₃	semidirect
190. C₅×#106	C₂×D₃	semidirect
196. C₅×#102	C₂×D₃	semidirect
197. C₅×#102	C₂×D₃	semidirect
200. C₅×#97	C₂×D₃	semidirect
221. C₃×C₅×D₄	C₂×D₄	semidirect
256. C₃×C₅×C₈	C₂×D₄	semidirect
259. C₂×#237	C₂²×C₅	semidirect
261. C₂×D₃×D₄	C₂²×C₅	semidirect
262. C₂×D₃×D₄	C₂²×C₅	semidirect
265. C₃×C₄×D₄	C₂²×C₅	semidirect
266. C₃×C₄×D₄	C₂²×C₅	semidirect
267. C₂×#214	C₂²×C₅	semidirect
269. C₂×#213	C₂²×C₅	semidirect
270. C₂×#213	C₂²×C₅	semidirect
276. C₂×D₂₄	C₂²×C₅	semidirect
277. C₂×D₂₄	C₂²×C₅	semidirect
278. C₂×#204	C₂²×C₅	semidirect
279. C₂×#204	C₂²×C₅	semidirect
280. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
281. C₂×D₃×C₈	C₂²×C₅	semidirect
282. #897	C₂²×C₅	semidirect
284. #895	C₂²×C₅	semidirect
285. #895	C₂²×C₅	semidirect
290. #875	C₂²×C₅	semidirect
291. #874	C₂²×C₅	semidirect
293. C₃×#106	C₂²×C₅	semidirect
294. C₃×#102	C₂²×C₅	semidirect
295. C₃×#102	C₂²×C₅	semidirect
296. C₃×#97	C₂²×C₅	semidirect
297. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
298. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
299. #810	C₂²×C₅	semidirect
300. #809	C₂²×C₅	semidirect
301. #809	C₂²×C₅	semidirect
302. #809	C₂²×C₅	semidirect
303. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
345. C₅×D₈	D₁₂	semidirect
380. #442	C₅×D₃	semidirect
406. C₂×C₅×D₃	AGL(1,ℤ/8)	semidirect
449. C₃×D₈	C₅×D₄	semidirect
516. C₅×D₄	C₂×D₁₂	semidirect
535. C₅×C₈	C₂×D₁₂	semidirect
567. C₄×D₄	C₂×C₅×D₃	semidirect
568. C₄×D₄	C₂×C₅×D₃	semidirect
570. #106	C₂×C₅×D₃	semidirect
576. #102	C₂×C₅×D₃	semidirect
577. #102	C₂×C₅×D₃	semidirect
580. #97	C₂×C₅×D₃	semidirect
610. C₃×D₄	C₂×C₅×D₄	semidirect
645. C₃×C₈	C₂×C₅×D₄	semidirect
723. D₈	C₅×D₁₂	semidirect
745. C₃×C₅	#3264	semidirect
770. C₂×D₃	C₅×AGL(1,ℤ/8)	semidirect
827. D₄	C₂×C₅×D₁₂	semidirect
846. C₈	C₂×C₅×D₁₂	semidirect
857. C₅	#79878	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×#911	2
C₂×C₅×D₃×D₈	2
C₅×#5554	2
C₅×D₄×D₁₂	2
C₃×C₅×#442	2
C₅×#5016	2
C₅×#5015	2
C₅×#4865	2
C₅×#4864	2
C₅×#4781	2
C₅×#4776	2
C₅×#4773	2
C₅×#4712	2
C₅×#4706	2
C₅×#3264	3
#79878	5

Subgroups — C5×#79878 #14453199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79878 #14453199