Subgroups — C₅×#83502 #14453196

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	C₃×C₅×#546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#949	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#213	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5238	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5217	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5058	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5057	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5048	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5046	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5039	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5015	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#5014	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#5011	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3264	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₅×D₃×D₄	—	2	1	no	—
20	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
21	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×#123	—	2	1	no	—
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×#121	—	2	1	no	—
26	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×#120	—	2	1	no	—
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
31	C₅×#949	—	2	4	no	—
32	C₂×C₅×#215	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₅×#215	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₅×#215	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₅×#213	—	2	4	no	—
36	C₂×C₅×#213	C₂²	1	1	yes	characteristic
37	C₂×C₅×#213	C₂²	1	1	yes	characteristic
38	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
42	C₅×#930	C₂²	1	1	yes	characteristic
43	C₅×#930	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₅×#208	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₅×#895	—	2	1	no	—
47	C₅×#882	—	2	1	no	—
48	C₅×#882	—	2	1	no	—
49	C₅×#874	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
51	C₅×#835	C₂²	1	1	yes	characteristic, complemented
52	C₅×#832	C₂²	1	1	yes	characteristic, complemented
53	C₅×#832	C₂²	1	1	yes	characteristic, complemented
54	C₅×#830	C₂²	1	1	yes	characteristic, complemented
55	C₅×#830	C₂²	1	1	yes	characteristic, complemented
56	C₅×#809	C₂²	1	1	yes	characteristic, complemented
57	C₅×#809	C₂²	1	1	yes	characteristic, complemented
58	C₅×#809	C₂²	1	1	yes	characteristic, complemented
59	C₅×#808	C₂²	1	1	yes	characteristic, complemented
60	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
61	C₅×#803	C₂²	1	1	yes	characteristic, complemented
62	#83502	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	D₃	1	1	yes	characteristic, complemented
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	—	3	1	no	—
77	C₅×#435	—	3	1	no	—
78	C₂⁴×C₃×C₅	—	2	1	no	—
79	C₂³×C₅×D₃	—	2	1	no	—
80	C₂³×C₅×D₃	—	2	1	no	—
81	C₃×C₅×#41	—	2	2	no	—
82	C₃×C₅×#41	—	4	1	no	—
83	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×D₄	—	2	2	no	—
85	C₂×C₃×C₅×D₄	—	2	1	no	—
86	C₂×C₃×C₅×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	—	2	1	no	—
88	C₂×C₃×C₅×D₄	—	4	1	no	—
89	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
90	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₄×C₅	—	2	1	no	—
93	C₂²×C₃×C₄×C₅	—	2	1	no	—
94	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
96	C₂×C₅×#67	—	2	1	no	—
97	C₂×C₅×#67	—	2	1	no	—
98	C₅×D₃×D₄	—	4	4	no	—
99	C₂×C₅×D₁₂	—	2	2	no	—
100	C₂×C₅×D₁₂	—	2	2	no	—
101	C₂×C₅×D₁₂	—	2	1	no	—
102	C₂×C₅×D₁₂	—	2	1	no	—
103	C₂×C₅×D₁₂	—	2	1	no	—
104	C₂×C₅×D₁₂	—	2	1	no	—
105	C₂×C₅×D₁₂	—	4	1	no	—
106	C₂×C₅×D₁₂	—	4	1	no	—
107	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
108	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
109	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
110	C₂×C₄×C₅×D₃	—	2	1	no	—
111	C₃×C₅×C₄⋊C₄	—	2	1	no	—
112	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
113	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
115	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
116	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
117	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
118	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
119	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
120	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
121	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
122	C₅×#215	—	2	2	no	—
123	C₅×#215	—	2	2	no	—
124	C₅×#215	—	4	1	no	—
125	C₅×#213	—	2	2	no	—
126	C₅×#213	—	2	2	no	—
127	C₅×#213	—	2	2	no	—
128	C₅×#213	—	2	2	no	—
129	C₅×#213	—	4	1	no	—
130	C₅×#213	D₄	1	4	yes	complemented
131	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
132	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
133	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
134	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
135	C₅×#208	—	2	2	no	—
136	C₂×C₅×C₃⋊C₈	—	2	2	no	—
137	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
138	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
139	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
140	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
141	C₃×#546	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×#949	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂²×#213	C₂×C₅	1	1	yes	characteristic, complemented
144	D₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
145	#5238	C₂×C₅	1	1	yes	characteristic, complemented
146	#5217	C₂×C₅	1	1	yes	characteristic, complemented
147	#5058	C₂×C₅	1	1	yes	characteristic, complemented
148	#5057	C₂×C₅	1	1	yes	characteristic, complemented
149	#5048	C₂×C₅	1	1	yes	characteristic, complemented
150	#5046	C₂×C₅	1	1	yes	characteristic, complemented
151	#5039	C₂×C₅	1	1	yes	characteristic, complemented
152	#5036	C₂×C₅	1	1	yes	characteristic, complemented
153	#5015	C₂×C₅	1	1	yes	characteristic, complemented
154	#5014	C₂×C₅	1	1	yes	characteristic, complemented
155	#5011	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic, complemented
157	C₂²×C₅×D₄	—	3	1	no	—
158	C₂²×C₅×D₄	—	3	1	no	—
159	C₂²×C₅×D₄	—	6	1	no	—
160	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
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	—	3	1	no	—
171	C₂×C₅×D₈	—	6	4	no	—
172	C₂×C₅×M₁₆	—	3	1	no	—
173	C₂²×C₅×C₈	—	3	1	no	—
174	C₅×#127	—	3	1	no	—
175	C₅×#124	C₂×D₃	1	1	yes	characteristic, complemented
176	C₅×#123	—	2	1	no	—
177	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
178	C₅×#121	—	2	1	no	—
179	C₅×#121	—	3	1	no	—
180	C₅×#121	—	3	1	no	—
181	C₅×#121	—	6	1	no	—
182	C₅×#121	C₂×D₃	1	1	yes	characteristic, complemented
183	C₅×#120	—	2	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
188	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
189	C₂×C₅×C₂²⋊C₄	—	2	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	—	3	1	no	—
201	#3264	—	3	1	no	Sylow
202	C₂³×C₃×C₅	—	2	1	no	—
203	C₂³×C₃×C₅	—	2	1	no	—
204	C₂³×C₃×C₅	—	4	2	no	—
205	C₂³×C₃×C₅	—	4	2	no	—
206	C₂³×C₃×C₅	—	8	1	no	—
207	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
208	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₅×D₃	—	2	1	no	—
210	C₂²×C₅×D₃	—	2	1	no	—
211	C₂²×C₅×D₃	—	2	1	no	—
212	C₂²×C₅×D₃	—	4	2	no	—
213	C₂²×C₅×D₃	—	4	2	no	—
214	C₂²×C₅×D₃	—	4	2	no	—
215	C₂²×C₅×D₃	—	4	2	no	—
216	C₂²×C₅×D₃	—	8	1	no	—
217	C₂²×C₅×D₃	—	8	1	no	—
218	C₃×C₅×Q₈	—	2	1	no	—
219	C₃×C₅×Q₈	—	2	1	no	—
220	C₃×C₅×D₄	—	2	2	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	—	4	2	no	—
225	C₃×C₅×D₄	—	4	2	no	—
226	C₃×C₅×D₄	—	8	1	no	—
227	C₃×C₅×D₄	C₂×D₄	1	2	yes	complemented
228	C₂×C₃×C₄×C₅	—	2	1	no	—
229	C₂×C₃×C₄×C₅	—	2	1	no	—
230	C₂×C₃×C₄×C₅	—	2	1	no	—
231	C₂×C₃×C₄×C₅	—	2	1	no	—
232	C₂×C₃×C₄×C₅	—	2	1	no	—
233	C₂×C₃×C₄×C₅	—	2	1	no	—
234	C₂×C₃×C₄×C₅	—	4	2	no	—
235	C₂×C₃×C₄×C₅	—	8	1	no	—
236	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
237	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
238	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
239	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
240	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
241	C₅×#67	—	4	2	no	—
242	C₅×#67	—	4	2	no	—
243	C₂×C₅×Dic₃	—	2	1	no	—
244	C₅×D₁₂	—	2	1	no	—
245	C₅×D₁₂	—	2	1	no	—
246	C₅×D₁₂	—	2	1	no	—
247	C₅×D₁₂	—	2	1	no	—
248	C₅×D₁₂	—	2	1	no	—
249	C₅×D₁₂	—	4	2	no	—
250	C₅×D₁₂	—	4	2	no	—
251	C₅×D₁₂	—	4	2	no	—
252	C₅×D₁₂	—	8	1	no	—
253	C₅×D₁₂	C₂×D₄	1	2	yes	—
254	C₄×C₅×D₃	—	4	2	no	—
255	C₅×C₃⋊C₈	—	2	1	no	—
256	C₅×C₃⋊C₈	—	2	1	no	—
257	C₅×C₃⋊C₈	—	2	1	no	—
258	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	complemented
259	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
261	C₂×D₃×D₄	—	2	1	no	—
262	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
263	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
265	C₃×#123	—	2	1	no	—
266	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₃×#121	—	2	1	no	—
268	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
269	C₃×#120	—	2	1	no	—
270	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
271	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
273	#949	—	2	4	no	—
274	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
275	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
276	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
277	C₂×#213	—	2	4	no	—
278	C₂×#213	C₂²×C₅	1	1	yes	characteristic
279	C₂×#213	C₂²×C₅	1	1	yes	characteristic
280	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
281	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
282	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
283	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
284	#930	C₂²×C₅	1	1	yes	characteristic
285	#930	C₂²×C₅	1	1	yes	characteristic, complemented
286	C₂×#208	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
288	#895	—	2	1	no	—
289	#882	—	2	1	no	—
290	#882	—	2	1	no	—
291	#874	C₂²×C₅	1	1	yes	characteristic, complemented
292	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
293	#835	C₂²×C₅	1	1	yes	characteristic, complemented
294	#832	C₂²×C₅	1	1	yes	characteristic, complemented
295	#832	C₂²×C₅	1	1	yes	characteristic, complemented
296	#830	C₂²×C₅	1	1	yes	characteristic, complemented
297	#830	C₂²×C₅	1	1	yes	characteristic, complemented
298	#809	C₂²×C₅	1	1	yes	characteristic, complemented
299	#809	C₂²×C₅	1	1	yes	characteristic, complemented
300	#809	C₂²×C₅	1	1	yes	characteristic, complemented
301	#808	C₂²×C₅	1	1	yes	characteristic, complemented
302	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
303	#803	C₂²×C₅	1	1	yes	characteristic, complemented
304	C₂⁴×C₅	—	2	1	no	—
305	C₂⁴×C₅	—	6	1	no	—
306	C₂⁴×C₅	—	6	1	no	—
307	C₅×#41	—	2	2	no	—
308	C₅×#41	—	4	1	no	—
309	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
310	C₂×C₅×D₄	—	2	2	no	—
311	C₂×C₅×D₄	—	2	1	no	—
312	C₂×C₅×D₄	—	2	1	no	—
313	C₂×C₅×D₄	—	2	1	no	—
314	C₂×C₅×D₄	—	3	1	no	—
315	C₂×C₅×D₄	—	3	1	no	—
316	C₂×C₅×D₄	—	3	1	no	—
317	C₂×C₅×D₄	—	4	1	no	—
318	C₂×C₅×D₄	—	6	2	no	—
319	C₂×C₅×D₄	—	6	2	no	—
320	C₂×C₅×D₄	—	6	1	no	—
321	C₂×C₅×D₄	—	6	1	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	—	6	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	#67	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	—	2	1	no	—
333	C₂²×C₄×C₅	—	2	1	no	—
334	C₂²×C₄×C₅	—	6	1	no	—
335	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
336	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
337	C₅×SD₁₆	—	6	2	no	—
338	C₅×SD₁₆	—	6	2	no	—
339	C₅×SD₁₆	—	12	1	no	—
340	C₅×D₈	—	3	4	no	—
341	C₅×D₈	—	6	2	no	—
342	C₅×D₈	—	6	2	no	—
343	C₅×D₈	—	6	2	no	—
344	C₅×D₈	—	6	2	no	—
345	C₅×D₈	—	12	1	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	—	3	1	no	—
350	C₂×C₅×C₈	—	3	1	no	—
351	C₂×C₅×C₈	—	6	2	no	—
352	C₅×C₄⋊C₄	—	2	1	no	—
353	C₅×C₄⋊C₄	—	3	1	no	—
354	C₅×C₄⋊C₄	#67	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	—	2	1	no	—
359	C₅×C₂²⋊C₄	—	2	1	no	—
360	C₅×C₂²⋊C₄	—	2	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	#67	1	1	yes	characteristic
365	C₅×C₂²⋊C₄	#67	1	1	yes	characteristic
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	C₅×D₃	1	1	yes	characteristic, complemented
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	—	3	1	no	—
381	#435	—	3	1	no	—
382	C₂²×C₃×C₅	—	2	1	no	—
383	C₂²×C₃×C₅	—	2	1	no	—
384	C₂²×C₃×C₅	—	2	1	no	—
385	C₂²×C₃×C₅	—	2	2	no	—
386	C₂²×C₃×C₅	—	2	1	no	—
387	C₂²×C₃×C₅	—	2	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	—	4	1	no	—
392	C₂²×C₃×C₅	—	4	1	no	—
393	C₂²×C₃×C₅	—	8	4	no	—
394	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	complemented
395	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₅×D₃	—	2	2	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	—	4	1	no	—
404	C₂×C₅×D₃	—	4	1	no	—
405	C₂×C₅×D₃	—	8	4	no	—
406	C₂×C₅×D₃	—	8	4	no	—
407	C₃×C₄×C₅	—	2	1	no	—
408	C₃×C₄×C₅	—	2	1	no	—
409	C₃×C₄×C₅	—	2	1	no	—
410	C₃×C₄×C₅	—	2	1	no	—
411	C₃×C₄×C₅	—	4	1	no	—
412	C₃×C₄×C₅	—	4	1	no	—
413	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
414	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
415	C₅×Dic₃	—	4	1	no	—
416	C₂⁴×C₃	—	2	1	no	—
417	C₂³×D₃	—	2	1	no	—
418	C₂³×D₃	—	2	1	no	—
419	C₃×#41	—	2	2	no	—
420	C₃×#41	—	4	1	no	—
421	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
422	C₂×C₃×D₄	—	2	2	no	—
423	C₂×C₃×D₄	—	2	1	no	—
424	C₂×C₃×D₄	—	2	1	no	—
425	C₂×C₃×D₄	—	2	1	no	—
426	C₂×C₃×D₄	—	4	1	no	—
427	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
428	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
429	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
430	C₂²×C₃×C₄	—	2	1	no	—
431	C₂²×C₃×C₄	—	2	1	no	—
432	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
433	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
434	C₂×#67	—	2	1	no	—
435	C₂×#67	—	2	1	no	—
436	D₃×D₄	—	4	4	no	—
437	C₂×D₁₂	—	2	2	no	—
438	C₂×D₁₂	—	2	2	no	—
439	C₂×D₁₂	—	2	1	no	—
440	C₂×D₁₂	—	2	1	no	—
441	C₂×D₁₂	—	2	1	no	—
442	C₂×D₁₂	—	2	1	no	—
443	C₂×D₁₂	—	4	1	no	—
444	C₂×D₁₂	—	4	1	no	—
445	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
446	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
447	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
448	C₂×C₄×D₃	—	2	1	no	—
449	C₃×C₄⋊C₄	—	2	1	no	—
450	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
451	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
452	C₃×C₂²⋊C₄	—	2	1	no	—
453	C₃×C₂²⋊C₄	—	2	1	no	—
454	C₃×C₂²⋊C₄	—	2	1	no	—
455	C₃×C₂²⋊C₄	—	2	1	no	—
456	C₃×C₂²⋊C₄	—	2	1	no	—
457	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
458	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
459	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
460	#215	—	2	2	no	—
461	#215	—	2	2	no	—
462	#215	—	4	1	no	—
463	#213	—	2	2	no	—
464	#213	—	2	2	no	—
465	#213	—	2	2	no	—
466	#213	—	2	2	no	—
467	#213	—	4	1	no	—
468	#213	C₅×D₄	1	4	yes	complemented
469	(C₂×D₃)⋊C₄	—	2	1	no	—
470	(C₂×D₃)⋊C₄	—	2	1	no	—
471	(C₂×D₃)⋊C₄	—	2	1	no	—
472	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
473	#208	—	2	2	no	—
474	C₂×C₃⋊C₈	—	2	2	no	—
475	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
476	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
477	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
478	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
479	C₂³×C₅	—	2	1	no	—
480	C₂³×C₅	—	2	1	no	—
481	C₂³×C₅	—	4	2	no	—
482	C₂³×C₅	—	4	2	no	—
483	C₂³×C₅	—	6	1	no	—
484	C₂³×C₅	—	6	1	no	—
485	C₂³×C₅	—	6	1	no	—
486	C₂³×C₅	—	8	1	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	—	24	1	no	—
492	C₂³×C₅	—	24	1	no	—
493	C₂³×C₅	C₂×#67	1	1	yes	characteristic
494	C₂³×C₅	C₂×#67	1	1	yes	characteristic
495	C₅×Q₈	—	2	1	no	—
496	C₅×Q₈	—	2	1	no	—
497	C₅×D₄	—	2	2	no	—
498	C₅×D₄	—	2	1	no	—
499	C₅×D₄	—	2	1	no	—
500	C₅×D₄	—	2	1	no	—
501	C₅×D₄	—	3	2	no	—
502	C₅×D₄	—	4	2	no	—
503	C₅×D₄	—	4	2	no	—
504	C₅×D₄	—	6	1	no	—
505	C₅×D₄	—	6	1	no	—
506	C₅×D₄	—	6	1	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	—	24	1	no	—
516	C₅×D₄	D₃×D₄	1	2	yes	complemented
517	C₂×C₄×C₅	—	2	1	no	—
518	C₂×C₄×C₅	—	2	1	no	—
519	C₂×C₄×C₅	—	2	1	no	—
520	C₂×C₄×C₅	—	2	1	no	—
521	C₂×C₄×C₅	—	2	1	no	—
522	C₂×C₄×C₅	—	2	1	no	—
523	C₂×C₄×C₅	—	4	2	no	—
524	C₂×C₄×C₅	—	6	1	no	—
525	C₂×C₄×C₅	—	8	1	no	—
526	C₂×C₄×C₅	—	12	2	no	—
527	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
528	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
529	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
530	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
531	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
532	C₅×C₈	—	3	2	no	—
533	C₅×C₈	—	6	1	no	—
534	C₅×C₈	—	6	1	no	—
535	C₅×C₈	—	6	1	no	—
536	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic, complemented
537	C₂²×D₄	—	3	1	no	—
538	C₂²×D₄	—	3	1	no	—
539	C₂²×D₄	—	6	1	no	—
540	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
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	—	3	1	no	—
551	C₂×D₈	—	6	4	no	—
552	C₂×M₁₆	—	3	1	no	—
553	C₂²×C₈	—	3	1	no	—
554	#127	—	3	1	no	—
555	#124	C₂×C₅×D₃	1	1	yes	characteristic, complemented
556	#123	—	2	1	no	—
557	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
558	#121	—	2	1	no	—
559	#121	—	3	1	no	—
560	#121	—	3	1	no	—
561	#121	—	6	1	no	—
562	#121	C₂×C₅×D₃	1	1	yes	characteristic, complemented
563	#120	—	2	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
568	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
569	C₂×C₂²⋊C₄	—	2	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	—	3	1	no	—
581	C₂×C₃×C₅	—	2	2	no	—
582	C₂×C₃×C₅	—	4	1	no	—
583	C₂×C₃×C₅	—	4	2	no	—
584	C₂×C₃×C₅	—	8	1	no	—
585	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
586	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
587	C₂×C₃×C₅	#576	1	1	yes	characteristic
588	C₅×D₃	—	4	2	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	C₂³×C₃	—	4	2	no	—
594	C₂³×C₃	—	4	2	no	—
595	C₂³×C₃	—	8	1	no	—
596	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
597	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
598	C₂²×D₃	—	2	1	no	—
599	C₂²×D₃	—	2	1	no	—
600	C₂²×D₃	—	2	1	no	—
601	C₂²×D₃	—	4	2	no	—
602	C₂²×D₃	—	4	2	no	—
603	C₂²×D₃	—	4	2	no	—
604	C₂²×D₃	—	4	2	no	—
605	C₂²×D₃	—	8	1	no	—
606	C₂²×D₃	—	8	1	no	—
607	C₃×Q₈	—	2	1	no	—
608	C₃×Q₈	—	2	1	no	—
609	C₃×D₄	—	2	2	no	—
610	C₃×D₄	—	2	1	no	—
611	C₃×D₄	—	2	1	no	—
612	C₃×D₄	—	2	1	no	—
613	C₃×D₄	—	4	2	no	—
614	C₃×D₄	—	4	2	no	—
615	C₃×D₄	—	8	1	no	—
616	C₃×D₄	C₂×C₅×D₄	1	2	yes	complemented
617	C₂×C₃×C₄	—	2	1	no	—
618	C₂×C₃×C₄	—	2	1	no	—
619	C₂×C₃×C₄	—	2	1	no	—
620	C₂×C₃×C₄	—	2	1	no	—
621	C₂×C₃×C₄	—	2	1	no	—
622	C₂×C₃×C₄	—	2	1	no	—
623	C₂×C₃×C₄	—	4	2	no	—
624	C₂×C₃×C₄	—	8	1	no	—
625	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
626	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
627	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
628	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
629	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
630	#67	—	4	2	no	—
631	#67	—	4	2	no	—
632	C₂×Dic₃	—	2	1	no	—
633	D₁₂	—	2	1	no	—
634	D₁₂	—	2	1	no	—
635	D₁₂	—	2	1	no	—
636	D₁₂	—	2	1	no	—
637	D₁₂	—	2	1	no	—
638	D₁₂	—	4	2	no	—
639	D₁₂	—	4	2	no	—
640	D₁₂	—	4	2	no	—
641	D₁₂	—	8	1	no	—
642	D₁₂	C₂×C₅×D₄	1	2	yes	—
643	C₄×D₃	—	4	2	no	—
644	C₃⋊C₈	—	2	1	no	—
645	C₃⋊C₈	—	2	1	no	—
646	C₃⋊C₈	—	2	1	no	—
647	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	complemented
648	C₂²×C₅	—	2	1	no	—
649	C₂²×C₅	—	2	1	no	—
650	C₂²×C₅	—	2	1	no	—
651	C₂²×C₅	—	2	2	no	—
652	C₂²×C₅	—	2	1	no	—
653	C₂²×C₅	—	2	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	—	4	1	no	—
659	C₂²×C₅	—	6	2	no	—
660	C₂²×C₅	—	8	4	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	#949	1	2	yes	complemented
672	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
673	C₄×C₅	—	2	1	no	—
674	C₄×C₅	—	2	1	no	—
675	C₄×C₅	—	2	1	no	—
676	C₄×C₅	—	2	1	no	—
677	C₄×C₅	—	4	1	no	—
678	C₄×C₅	—	4	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	—	2	1	no	—
683	C₂⁴	—	6	1	no	—
684	C₂⁴	—	6	1	no	—
685	#41	—	2	2	no	—
686	#41	—	4	1	no	—
687	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	3	1	no	—
693	C₂×D₄	—	3	1	no	—
694	C₂×D₄	—	3	1	no	—
695	C₂×D₄	—	4	1	no	—
696	C₂×D₄	—	6	2	no	—
697	C₂×D₄	—	6	2	no	—
698	C₂×D₄	—	6	1	no	—
699	C₂×D₄	—	6	1	no	—
700	C₂×D₄	—	6	1	no	—
701	C₂×D₄	—	6	1	no	—
702	C₂×D₄	—	6	1	no	—
703	C₂×D₄	—	6	1	no	—
704	C₂×D₄	—	12	1	no	—
705	C₂×D₄	—	12	1	no	—
706	C₂×D₄	—	12	4	no	—
707	C₂×D₄	C₅×#67	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	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	6	1	no	—
713	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
714	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
715	SD₁₆	—	6	2	no	—
716	SD₁₆	—	6	2	no	—
717	SD₁₆	—	12	1	no	—
718	D₈	—	3	4	no	—
719	D₈	—	6	2	no	—
720	D₈	—	6	2	no	—
721	D₈	—	6	2	no	—
722	D₈	—	6	2	no	—
723	D₈	—	12	1	no	—
724	M₁₆	—	6	2	no	—
725	C₂×C₈	—	3	1	no	—
726	C₂×C₈	—	3	1	no	—
727	C₂×C₈	—	3	1	no	—
728	C₂×C₈	—	3	1	no	—
729	C₂×C₈	—	6	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	3	1	no	—
732	C₄⋊C₄	C₅×#67	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	—	2	1	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₂²⋊C₄	—	2	1	no	—
739	C₂²⋊C₄	—	6	1	no	—
740	C₂²⋊C₄	—	6	1	no	—
741	C₂²⋊C₄	—	6	1	no	—
742	C₂²⋊C₄	C₅×#67	1	1	yes	characteristic
743	C₂²⋊C₄	C₅×#67	1	1	yes	characteristic
744	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
745	C₃×C₅	#3264	1	1	yes	characteristic, complemented, Hall
746	C₂²×C₃	—	2	1	no	—
747	C₂²×C₃	—	2	1	no	—
748	C₂²×C₃	—	2	1	no	—
749	C₂²×C₃	—	2	2	no	—
750	C₂²×C₃	—	2	1	no	—
751	C₂²×C₃	—	2	1	no	—
752	C₂²×C₃	—	4	1	no	—
753	C₂²×C₃	—	4	1	no	—
754	C₂²×C₃	—	4	1	no	—
755	C₂²×C₃	—	4	1	no	—
756	C₂²×C₃	—	4	1	no	—
757	C₂²×C₃	—	8	4	no	—
758	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	complemented
759	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
760	C₂×D₃	—	2	2	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	—	4	1	no	—
768	C₂×D₃	—	4	1	no	—
769	C₂×D₃	—	8	4	no	—
770	C₂×D₃	—	8	4	no	—
771	C₃×C₄	—	2	1	no	—
772	C₃×C₄	—	2	1	no	—
773	C₃×C₄	—	2	1	no	—
774	C₃×C₄	—	2	1	no	—
775	C₃×C₄	—	4	1	no	—
776	C₃×C₄	—	4	1	no	—
777	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
778	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
779	Dic₃	—	4	1	no	—
780	C₂×C₅	—	2	2	no	—
781	C₂×C₅	—	4	1	no	—
782	C₂×C₅	—	4	2	no	—
783	C₂×C₅	—	8	1	no	—
784	C₂×C₅	—	12	2	no	—
785	C₂×C₅	—	24	1	no	—
786	C₂×C₅	—	24	1	no	—
787	C₂×C₅	D₄×#67	1	1	yes	characteristic
788	C₂×C₅	C₂×#949	1	1	yes	characteristic
789	C₂×C₅	#5835	1	1	yes	characteristic
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	4	2	no	—
793	C₂³	—	4	2	no	—
794	C₂³	—	6	1	no	—
795	C₂³	—	6	1	no	—
796	C₂³	—	6	1	no	—
797	C₂³	—	8	1	no	—
798	C₂³	—	12	2	no	—
799	C₂³	—	12	2	no	—
800	C₂³	—	12	2	no	—
801	C₂³	—	12	2	no	—
802	C₂³	—	24	1	no	—
803	C₂³	—	24	1	no	—
804	C₂³	C₂×C₅×#67	1	1	yes	characteristic
805	C₂³	C₂×C₅×#67	1	1	yes	characteristic
806	Q₈	—	2	1	no	—
807	Q₈	—	2	1	no	—
808	D₄	—	2	2	no	—
809	D₄	—	2	1	no	—
810	D₄	—	2	1	no	—
811	D₄	—	2	1	no	—
812	D₄	—	3	2	no	—
813	D₄	—	4	2	no	—
814	D₄	—	4	2	no	—
815	D₄	—	6	1	no	—
816	D₄	—	6	1	no	—
817	D₄	—	6	1	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	—	24	1	no	—
827	D₄	C₅×D₃×D₄	1	2	yes	complemented
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	4	2	no	—
835	C₂×C₄	—	6	1	no	—
836	C₂×C₄	—	8	1	no	—
837	C₂×C₄	—	12	2	no	—
838	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
839	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
840	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
841	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
842	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
843	C₈	—	3	2	no	—
844	C₈	—	6	1	no	—
845	C₈	—	6	1	no	—
846	C₈	—	6	1	no	—
847	C₂×C₃	—	2	2	no	—
848	C₂×C₃	—	4	1	no	—
849	C₂×C₃	—	4	2	no	—
850	C₂×C₃	—	8	1	no	—
851	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
852	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
853	C₂×C₃	C₅×#576	1	1	yes	characteristic
854	D₃	—	4	2	no	—
855	D₃	—	8	1	no	—
856	D₃	—	8	1	no	—
857	C₅	#83502	1	1	yes	characteristic, direct product factor, Sylow
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	6	2	no	—
870	C₂²	—	8	4	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	C₅×#949	1	2	yes	complemented
882	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	4	1	no	—
888	C₄	—	4	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	—	2	2	no	—
894	C₂	—	4	1	no	—
895	C₂	—	4	2	no	—
896	C₂	—	8	1	no	—
897	C₂	—	12	2	no	—
898	C₂	—	24	1	no	—
899	C₂	—	24	1	no	—
900	C₂	C₅×D₄×#67	1	1	yes	characteristic
901	C₂	C₂×C₅×#949	1	1	yes	characteristic
902	C₂	C₅×#5835	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#546	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#546	D₃
hypocenter	C₃	C₅×#3264
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄ ◁ C₅×#546

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#546	C₂	semidirect
2. C₂×C₅×#949	C₂	semidirect
3. C₂²×C₅×#213	C₂	semidirect
4. C₅×D₄×D₁₂	C₂	semidirect
5. C₅×#5238	C₂	semidirect
6. C₅×#5217	C₂	semidirect
7. C₅×#5058	C₂	semidirect
8. C₅×#5057	C₂	semidirect
9. C₅×#5048	C₂	semidirect
10. C₅×#5046	C₂	semidirect
11. C₅×#5039	C₂	semidirect
12. C₅×#5036	C₂	semidirect
13. C₅×#5015	C₂	semidirect
14. C₅×#5014	C₂	semidirect
15. C₅×#5011	C₂	semidirect
17. C₂×C₃×C₅×#41	C₂²	semidirect
18. C₂²×C₃×C₅×D₄	C₂²	semidirect
21. C₂²×C₅×D₁₂	C₂²	semidirect
22. C₃×C₅×#124	C₂²	semidirect
24. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
26. C₃×C₅×#121	C₂²	semidirect
29. C₃×C₄×C₅×D₄	C₂²	semidirect
32. C₂×C₅×#215	C₂²	semidirect
33. C₂×C₅×#215	C₂²	semidirect
34. C₂×C₅×#215	C₂²	semidirect
38. C₂×C₅×#213	C₂²	semidirect
39. C₂×C₅×#213	C₂²	semidirect
40. C₂×C₅×#213	C₂²	semidirect
41. C₂×C₅×#213	C₂²	semidirect
43. C₅×#930	C₂²	semidirect
44. C₂×C₅×#208	C₂²	semidirect
45. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
49. C₅×#874	C₂²	semidirect
50. C₄×C₅×D₁₂	C₂²	semidirect
51. C₅×#835	C₂²	semidirect
52. C₅×#832	C₂²	semidirect
53. C₅×#832	C₂²	semidirect
54. C₅×#830	C₂²	semidirect
55. C₅×#830	C₂²	semidirect
56. C₅×#809	C₂²	semidirect
57. C₅×#809	C₂²	semidirect
58. C₅×#809	C₂²	semidirect
59. C₅×#808	C₂²	semidirect
60. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
61. C₅×#803	C₂²	semidirect
62. #83502	C₅	direct (N × H)
65. C₅×#546	D₃	semidirect
130. C₅×#213	D₄	semidirect
141. C₃×#546	C₂×C₅	semidirect
142. C₂×#949	C₂×C₅	semidirect
143. C₂²×#213	C₂×C₅	semidirect
144. D₄×D₁₂	C₂×C₅	semidirect
145. #5238	C₂×C₅	semidirect
146. #5217	C₂×C₅	semidirect
147. #5058	C₂×C₅	semidirect
148. #5057	C₂×C₅	semidirect
149. #5048	C₂×C₅	semidirect
150. #5046	C₂×C₅	semidirect
151. #5039	C₂×C₅	semidirect
152. #5036	C₂×C₅	semidirect
153. #5015	C₂×C₅	semidirect
154. #5014	C₂×C₅	semidirect
155. #5011	C₂×C₅	semidirect
156. C₂×C₅×#41	C₂×D₃	semidirect
160. C₂²×C₅×D₄	C₂×D₃	semidirect
175. C₅×#124	C₂×D₃	semidirect
177. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
182. C₅×#121	C₂×D₃	semidirect
188. C₄×C₅×D₄	C₂×D₃	semidirect
227. C₃×C₅×D₄	C₂×D₄	semidirect
258. C₅×C₃⋊C₈	C₂×D₄	semidirect
259. C₂×C₃×#41	C₂²×C₅	semidirect
260. C₂²×C₃×D₄	C₂²×C₅	semidirect
263. C₂²×D₁₂	C₂²×C₅	semidirect
264. C₃×#124	C₂²×C₅	semidirect
266. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
268. C₃×#121	C₂²×C₅	semidirect
271. C₃×C₄×D₄	C₂²×C₅	semidirect
274. C₂×#215	C₂²×C₅	semidirect
275. C₂×#215	C₂²×C₅	semidirect
276. C₂×#215	C₂²×C₅	semidirect
280. C₂×#213	C₂²×C₅	semidirect
281. C₂×#213	C₂²×C₅	semidirect
282. C₂×#213	C₂²×C₅	semidirect
283. C₂×#213	C₂²×C₅	semidirect
285. #930	C₂²×C₅	semidirect
286. C₂×#208	C₂²×C₅	semidirect
287. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
291. #874	C₂²×C₅	semidirect
292. C₄×D₁₂	C₂²×C₅	semidirect
293. #835	C₂²×C₅	semidirect
294. #832	C₂²×C₅	semidirect
295. #832	C₂²×C₅	semidirect
296. #830	C₂²×C₅	semidirect
297. #830	C₂²×C₅	semidirect
298. #809	C₂²×C₅	semidirect
299. #809	C₂²×C₅	semidirect
300. #809	C₂²×C₅	semidirect
301. #808	C₂²×C₅	semidirect
302. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
303. #803	C₂²×C₅	semidirect
369. #546	C₅×D₃	semidirect
394. C₂²×C₃×C₅	AGL(1,ℤ/8)	semidirect
468. #213	C₅×D₄	semidirect
516. C₅×D₄	D₃×D₄	semidirect
536. C₂×#41	C₂×C₅×D₃	semidirect
540. C₂²×D₄	C₂×C₅×D₃	semidirect
555. #124	C₂×C₅×D₃	semidirect
557. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
562. #121	C₂×C₅×D₃	semidirect
568. C₄×D₄	C₂×C₅×D₃	semidirect
616. C₃×D₄	C₂×C₅×D₄	semidirect
647. C₃⋊C₈	C₂×C₅×D₄	semidirect
671. C₂²×C₅	#949	semidirect
745. C₃×C₅	#3264	semidirect
758. C₂²×C₃	C₅×AGL(1,ℤ/8)	semidirect
827. D₄	C₅×D₃×D₄	semidirect
857. C₅	#83502	direct (N × H)
881. C₂²	C₅×#949	semidirect
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
C₃×C₅×#546	2
C₂×C₅×#949	2
C₂²×C₅×#213	2
C₅×D₄×D₁₂	2
C₅×#5238	2
C₅×#5217	2
C₅×#5058	2
C₅×#5057	2
C₅×#5048	2
C₅×#5046	2
C₅×#5039	2
C₅×#5036	2
C₅×#5015	2
C₅×#5014	2
C₅×#5011	2
C₅×#3264	3
#83502	5

Subgroups — C5×#83502 #14453196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83502 #14453196