Subgroups — C₅×#80148 #14424303

Order 1920.

1504 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1004	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#915	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5628	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5218	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5173	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5169	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5047	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4783	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4776	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4772	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4770	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4733	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4727	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3009	—	3	1	no	maximal, Hall
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₅×#67	—	2	1	no	—
19	C₂²×C₅×#67	—	2	1	no	—
20	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₅×#1004	—	2	4	no	—
22	C₅×#1004	—	2	4	no	—
23	C₂×C₅×#237	—	2	1	no	—
24	C₂×C₅×#237	C₂²	1	1	yes	characteristic
25	C₂×C₅×#237	C₂²	1	1	yes	characteristic
26	C₂×C₅×D₃×D₄	—	2	1	no	—
27	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
28	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₅×#235	C₂²	1	1	yes	characteristic
30	C₂×C₅×#235	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₅×#946	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₅×#215	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
39	C₅×#924	C₂²	1	1	yes	characteristic, complemented
40	C₅×#915	—	2	4	no	—
41	C₅×D₃×SD₁₆	—	2	4	no	—
42	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
46	C₅×#897	C₂²	1	1	yes	characteristic, complemented
47	C₅×#894	—	2	1	no	—
48	C₅×#892	C₂²	1	1	yes	characteristic, complemented
49	C₅×#888	—	2	1	no	—
50	C₅×#885	—	2	1	no	—
51	C₅×#883	—	2	1	no	—
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	C₅×#832	C₂²	1	1	yes	characteristic, complemented
56	C₅×#832	C₂²	1	1	yes	characteristic, complemented
57	C₅×#830	C₂²	1	1	yes	characteristic, complemented
58	C₅×#821	C₂²	1	1	yes	characteristic, complemented
59	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₅×#816	C₂²	1	1	yes	characteristic, complemented
62	C₅×#810	C₂²	1	1	yes	characteristic, complemented
63	C₅×#809	C₂²	1	1	yes	characteristic, complemented
64	#80148	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
65	C₂×C₅×H(5,𝔽₂)	—	3	1	no	—
66	C₂×C₅×#137	—	3	1	no	—
67	C₂²×C₅×SD₁₆	—	3	1	no	—
68	C₅×#536	—	3	1	no	—
69	C₅×#452	—	3	1	no	—
70	C₅×#452	—	3	1	no	—
71	C₅×#452	—	3	1	no	—
72	C₅×#452	—	3	1	no	—
73	C₅×#450	—	3	1	no	—
74	C₅×#450	—	3	1	no	—
75	C₅×#450	—	3	1	no	—
76	C₅×#450	D₃	1	1	yes	characteristic, complemented
77	C₅×#418	—	3	1	no	—
78	C₅×#416	—	3	1	no	—
79	C₅×#408	—	3	1	no	—
80	C₂⁴×C₃×C₅	—	2	1	no	—
81	C₂³×C₅×D₃	—	2	1	no	—
82	C₂³×C₅×D₃	—	2	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	2	no	—
86	C₂×C₃×C₅×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₅×#67	—	2	8	no	—
91	C₂×C₅×#67	—	2	8	no	—
92	C₂×C₅×#67	—	2	1	no	—
93	C₂×C₅×#67	—	2	1	no	—
94	C₂×C₅×#67	—	2	1	no	—
95	C₂×C₅×#67	—	2	1	no	—
96	C₂×C₅×#67	—	2	1	no	—
97	C₂×C₅×#67	D₄	1	1	yes	characteristic
98	C₂×C₅×#67	D₄	1	1	yes	characteristic
99	C₂²×C₅×Dic₃	—	2	1	no	—
100	C₂²×C₅×Dic₃	—	2	1	no	—
101	C₅×D₃×Q₈	—	2	2	no	—
102	C₅×D₃×Q₈	—	2	2	no	—
103	C₅×#237	—	2	8	no	—
104	C₅×#237	—	2	2	no	—
105	C₅×#237	—	2	2	no	—
106	C₅×#237	—	2	2	no	—
107	C₅×#237	D₄	1	4	yes	—
108	C₅×D₃×D₄	—	2	8	no	—
109	C₅×D₃×D₄	—	2	2	no	—
110	C₅×D₃×D₄	—	2	2	no	—
111	C₅×D₃×D₄	—	2	2	no	—
112	C₅×D₃×D₄	D₄	1	4	yes	—
113	C₅×#235	—	2	2	no	—
114	C₅×#235	—	2	2	no	—
115	C₅×#235	—	2	2	no	—
116	C₅×#235	—	2	2	no	—
117	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
118	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
119	C₂×C₄×C₅×D₃	—	2	1	no	—
120	C₂×C₄×C₅×D₃	—	2	1	no	—
121	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
122	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
123	C₂×C₅×Dic₆	—	2	1	no	—
124	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
125	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
126	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
127	C₃×C₅×SD₁₆	—	2	2	no	—
128	C₃×C₅×SD₁₆	—	2	2	no	—
129	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
131	C₃×C₅×C₄⋊C₄	—	2	1	no	—
132	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
134	C₅×#217	—	2	1	no	—
135	C₅×#216	—	2	2	no	—
136	C₅×#215	—	2	2	no	—
137	C₅×#214	—	2	2	no	—
138	C₅×#214	—	2	2	no	—
139	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
140	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
141	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
142	C₅×C₄⋊Dic₃	—	2	1	no	—
143	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
144	C₅×Dic₃⋊C₄	—	2	1	no	—
145	C₅×Dic₃⋊C₄	—	2	1	no	—
146	C₄×C₅×Dic₃	—	2	1	no	—
147	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
148	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
149	C₅×Dic₁₂	—	2	2	no	—
150	C₅×#204	—	2	2	no	—
151	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
152	C₅×D₃×C₈	—	2	2	no	—
153	C₂×#1004	C₂×C₅	1	1	yes	characteristic
154	C₂×#915	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×D₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
156	#5628	C₂×C₅	1	1	yes	characteristic, complemented
157	C₃×#450	C₂×C₅	1	1	yes	characteristic, complemented
158	#5218	C₂×C₅	1	1	yes	characteristic, complemented
159	#5173	C₂×C₅	1	1	yes	characteristic, complemented
160	#5169	C₂×C₅	1	1	yes	characteristic, complemented
161	#5047	C₂×C₅	1	1	yes	characteristic, complemented
162	#4783	C₂×C₅	1	1	yes	characteristic, complemented
163	#4776	C₂×C₅	1	1	yes	characteristic, complemented
164	#4772	C₂×C₅	1	1	yes	characteristic, complemented
165	#4770	C₂×C₅	1	1	yes	characteristic, complemented
166	#4733	C₂×C₅	1	1	yes	characteristic, complemented
167	#4727	C₂×C₅	1	1	yes	characteristic, complemented
168	C₅×H(5,𝔽₂)	—	6	4	no	—
169	C₅×H(5,𝔽₂)	—	6	4	no	—
170	C₂×C₅×#41	—	3	1	no	—
171	C₂×C₅×#41	—	3	1	no	—
172	C₂×C₅×#41	—	3	1	no	—
173	C₂×C₅×#41	—	3	1	no	—
174	C₂×C₅×#41	—	6	1	no	—
175	C₂²×C₅×Q₈	—	3	1	no	—
176	C₂²×C₅×D₄	—	3	1	no	—
177	C₂²×C₅×D₄	—	3	1	no	—
178	C₂²×C₅×D₄	—	6	1	no	—
179	C₂²×C₅×D₄	—	6	1	no	—
180	C₂²×C₅×D₄	—	6	1	no	—
181	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
182	C₅×#137	—	6	4	no	—
183	C₂×C₅×Q₁₆	—	3	1	no	—
184	C₂×C₅×Q₁₆	—	3	1	no	—
185	C₂×C₅×SD₁₆	—	3	1	no	—
186	C₂×C₅×SD₁₆	—	3	1	no	—
187	C₂×C₅×SD₁₆	—	3	1	no	—
188	C₂×C₅×SD₁₆	—	3	1	no	—
189	C₂×C₅×SD₁₆	—	6	4	no	—
190	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
191	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
192	C₂×C₅×M₁₆	—	3	1	no	—
193	C₂²×C₅×C₈	—	3	1	no	—
194	C₅×C₄⋊Q₈	—	6	1	no	—
195	C₅×#124	—	6	1	no	—
196	C₅×#123	—	6	1	no	—
197	C₅×#123	—	6	1	no	—
198	C₅×C₂²⋊Q₈	—	3	1	no	—
199	C₅×C₂²⋊Q₈	—	3	1	no	—
200	C₅×C₂²⋊Q₈	—	3	1	no	—
201	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
202	C₅×#117	—	3	1	no	—
203	C₅×#103	—	3	1	no	—
204	C₅×#103	—	3	1	no	—
205	C₅×#102	—	3	1	no	—
206	C₅×#102	—	3	1	no	—
207	C₅×#102	—	3	1	no	—
208	C₅×#102	—	3	1	no	—
209	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
210	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
211	C₅×C₂²⋊C₈	—	3	1	no	—
212	C₅×C₂²⋊C₈	—	3	1	no	—
213	C₅×C₂²⋊C₈	—	3	1	no	—
214	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
215	#3009	—	3	1	no	Sylow
216	C₂³×C₃×C₅	—	2	4	no	—
217	C₂³×C₃×C₅	—	2	1	no	—
218	C₂³×C₃×C₅	—	2	1	no	—
219	C₂³×C₃×C₅	—	8	1	no	—
220	C₂³×C₃×C₅	—	8	1	no	—
221	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₅×D₃	—	2	1	no	—
223	C₂²×C₅×D₃	—	2	4	no	—
224	C₂²×C₅×D₃	—	2	4	no	—
225	C₂²×C₅×D₃	—	8	1	no	—
226	C₂²×C₅×D₃	—	8	1	no	—
227	C₂²×C₅×D₃	—	8	1	no	—
228	C₂²×C₅×D₃	—	8	1	no	—
229	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
231	C₃×C₅×Q₈	—	2	1	no	—
232	C₃×C₅×Q₈	—	2	1	no	—
233	C₃×C₅×D₄	—	2	4	no	—
234	C₃×C₅×D₄	—	2	1	no	—
235	C₃×C₅×D₄	—	2	1	no	—
236	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
237	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
238	C₂×C₃×C₄×C₅	—	2	1	no	—
239	C₂×C₃×C₄×C₅	—	2	1	no	—
240	C₂×C₃×C₄×C₅	—	2	1	no	—
241	C₂×C₃×C₄×C₅	—	2	1	no	—
242	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
243	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
244	C₅×#67	—	2	4	no	—
245	C₅×#67	—	2	4	no	—
246	C₅×#67	—	2	4	no	—
247	C₅×#67	—	2	2	no	—
248	C₅×#67	—	2	4	no	—
249	C₅×#67	—	2	2	no	—
250	C₅×#67	—	2	4	no	—
251	C₂×C₅×Dic₃	—	2	4	no	—
252	C₂×C₅×Dic₃	—	2	1	no	—
253	C₂×C₅×Dic₃	—	2	4	no	—
254	C₂×C₅×Dic₃	—	2	1	no	—
255	C₂×C₅×Dic₃	—	2	1	no	—
256	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
257	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
258	C₅×D₁₂	—	2	2	no	—
259	C₅×D₁₂	—	2	1	no	—
260	C₅×D₁₂	C₂×D₄	1	2	yes	—
261	C₄×C₅×D₃	—	2	4	no	—
262	C₄×C₅×D₃	—	2	1	no	—
263	C₄×C₅×D₃	—	2	1	no	—
264	C₄×C₅×D₃	—	4	2	no	—
265	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
266	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
267	C₅×Dic₆	—	2	1	no	—
268	C₅×Dic₆	—	2	2	no	—
269	C₅×Dic₆	—	2	1	no	—
270	C₅×Dic₆	—	2	1	no	—
271	C₅×Dic₆	—	4	2	no	—
272	C₅×Dic₆	C₂×D₄	1	2	yes	—
273	C₃×C₅×C₈	—	2	1	no	—
274	C₃×C₅×C₈	—	2	1	no	—
275	C₅×C₃⋊C₈	—	2	1	no	—
276	C₅×C₃⋊C₈	—	2	1	no	—
277	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
278	C₂²×#67	—	2	1	no	—
279	C₂²×#67	—	2	1	no	—
280	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
281	#1004	—	2	4	no	—
282	#1004	—	2	4	no	—
283	C₂×#237	—	2	1	no	—
284	C₂×#237	C₂²×C₅	1	1	yes	characteristic
285	C₂×#237	C₂²×C₅	1	1	yes	characteristic
286	C₂×D₃×D₄	—	2	1	no	—
287	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
288	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
289	C₂×#235	C₂²×C₅	1	1	yes	characteristic
290	C₂×#235	C₂²×C₅	1	1	yes	characteristic
291	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
292	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
293	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
294	#946	C₂²×C₅	1	1	yes	characteristic, complemented
295	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
296	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
297	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
298	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
299	#924	C₂²×C₅	1	1	yes	characteristic, complemented
300	#915	—	2	4	no	—
301	D₃×SD₁₆	—	2	4	no	—
302	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
303	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
304	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
305	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
306	#897	C₂²×C₅	1	1	yes	characteristic, complemented
307	#894	—	2	1	no	—
308	#892	C₂²×C₅	1	1	yes	characteristic, complemented
309	#888	—	2	1	no	—
310	#885	—	2	1	no	—
311	#883	—	2	1	no	—
312	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
313	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
314	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
315	#832	C₂²×C₅	1	1	yes	characteristic, complemented
316	#832	C₂²×C₅	1	1	yes	characteristic, complemented
317	#830	C₂²×C₅	1	1	yes	characteristic, complemented
318	#821	C₂²×C₅	1	1	yes	characteristic, complemented
319	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
320	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
321	#816	C₂²×C₅	1	1	yes	characteristic, complemented
322	#810	C₂²×C₅	1	1	yes	characteristic, complemented
323	#809	C₂²×C₅	1	1	yes	characteristic, complemented
324	C₂⁴×C₅	—	2	1	no	—
325	C₂⁴×C₅	—	6	1	no	—
326	C₂⁴×C₅	—	6	1	no	—
327	C₅×#41	—	3	4	no	—
328	C₅×#41	—	6	2	no	—
329	C₅×#41	—	6	2	no	—
330	C₅×#41	—	6	2	no	—
331	C₅×#41	—	6	2	no	—
332	C₅×#41	—	6	2	no	—
333	C₅×#41	—	6	2	no	—
334	C₅×#41	—	6	8	no	—
335	C₅×#41	—	6	2	no	—
336	C₂×C₅×Q₈	—	3	1	no	—
337	C₂×C₅×Q₈	—	3	1	no	—
338	C₂×C₅×Q₈	—	3	1	no	—
339	C₂×C₅×Q₈	—	6	1	no	—
340	C₂×C₅×Q₈	—	6	2	no	—
341	C₂×C₅×Q₈	—	6	2	no	—
342	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
343	C₂×C₅×D₄	—	2	2	no	—
344	C₂×C₅×D₄	—	2	2	no	—
345	C₂×C₅×D₄	—	2	1	no	—
346	C₂×C₅×D₄	—	3	4	no	—
347	C₂×C₅×D₄	—	3	1	no	—
348	C₂×C₅×D₄	—	3	1	no	—
349	C₂×C₅×D₄	—	3	1	no	—
350	C₂×C₅×D₄	—	3	1	no	—
351	C₂×C₅×D₄	—	6	2	no	—
352	C₂×C₅×D₄	—	6	1	no	—
353	C₂×C₅×D₄	—	6	1	no	—
354	C₂×C₅×D₄	—	6	2	no	—
355	C₂×C₅×D₄	—	6	8	no	—
356	C₂×C₅×D₄	—	6	1	no	—
357	C₂×C₅×D₄	—	6	1	no	—
358	C₂×C₅×D₄	—	6	8	no	—
359	C₂×C₅×D₄	—	6	8	no	—
360	C₂×C₅×D₄	—	6	1	no	—
361	C₂×C₅×D₄	—	6	2	no	—
362	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
363	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
364	C₂²×C₄×C₅	—	3	1	no	—
365	C₂²×C₄×C₅	—	3	1	no	—
366	C₂²×C₄×C₅	—	6	1	no	—
367	C₂²×C₄×C₅	—	6	1	no	—
368	C₂²×C₄×C₅	—	6	1	no	—
369	C₂²×C₄×C₅	—	6	1	no	—
370	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
371	C₅×Q₁₆	—	6	2	no	—
372	C₅×Q₁₆	—	6	2	no	—
373	C₅×SD₁₆	—	2	2	no	—
374	C₅×SD₁₆	—	2	2	no	—
375	C₅×SD₁₆	—	6	2	no	—
376	C₅×SD₁₆	—	6	2	no	—
377	C₅×SD₁₆	—	6	2	no	—
378	C₅×SD₁₆	—	6	2	no	—
379	C₅×M₁₆	—	6	2	no	—
380	C₂×C₅×C₈	—	3	1	no	—
381	C₂×C₅×C₈	—	3	1	no	—
382	C₂×C₅×C₈	—	6	2	no	—
383	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
384	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
385	C₅×C₄⋊C₄	—	2	1	no	—
386	C₅×C₄⋊C₄	—	3	1	no	—
387	C₅×C₄⋊C₄	—	6	1	no	—
388	C₅×C₄⋊C₄	—	6	1	no	—
389	C₅×C₄⋊C₄	—	6	1	no	—
390	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
391	C₅×C₂²⋊C₄	—	2	1	no	—
392	C₅×C₂²⋊C₄	—	6	1	no	—
393	C₅×C₂²⋊C₄	—	6	1	no	—
394	C₅×C₂²⋊C₄	—	6	1	no	—
395	C₅×C₂²⋊C₄	—	6	1	no	—
396	C₄²×C₅	—	6	1	no	—
397	C₂×H(5,𝔽₂)	—	3	1	no	—
398	C₂×#137	—	3	1	no	—
399	C₂²×SD₁₆	—	3	1	no	—
400	#536	—	3	1	no	—
401	#452	—	3	1	no	—
402	#452	—	3	1	no	—
403	#452	—	3	1	no	—
404	#452	—	3	1	no	—
405	#450	—	3	1	no	—
406	#450	—	3	1	no	—
407	#450	—	3	1	no	—
408	#450	C₅×D₃	1	1	yes	characteristic, complemented
409	#418	—	3	1	no	—
410	#416	—	3	1	no	—
411	#408	—	3	1	no	—
412	C₂²×C₃×C₅	—	2	2	no	—
413	C₂²×C₃×C₅	—	2	2	no	—
414	C₂²×C₃×C₅	—	2	1	no	—
415	C₂²×C₃×C₅	—	2	1	no	—
416	C₂²×C₃×C₅	—	2	1	no	—
417	C₂²×C₃×C₅	—	4	1	no	—
418	C₂²×C₃×C₅	—	4	1	no	—
419	C₂²×C₃×C₅	—	4	1	no	—
420	C₂²×C₃×C₅	—	4	1	no	—
421	C₂²×C₃×C₅	—	8	4	no	—
422	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₅×D₃	—	2	1	no	—
424	C₂×C₅×D₃	—	2	1	no	—
425	C₂×C₅×D₃	—	2	1	no	—
426	C₂×C₅×D₃	—	2	2	no	—
427	C₂×C₅×D₃	—	2	1	no	—
428	C₂×C₅×D₃	—	2	1	no	—
429	C₂×C₅×D₃	—	4	1	no	—
430	C₂×C₅×D₃	—	4	1	no	—
431	C₂×C₅×D₃	—	8	4	no	—
432	C₂×C₅×D₃	—	8	4	no	—
433	C₂×C₅×D₃	#120	1	2	yes	—
434	C₃×C₄×C₅	—	2	1	no	—
435	C₃×C₄×C₅	—	4	1	no	—
436	C₃×C₄×C₅	—	4	1	no	—
437	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
438	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
439	C₅×Dic₃	—	2	1	no	—
440	C₅×Dic₃	—	2	2	no	—
441	C₅×Dic₃	—	4	1	no	—
442	C₅×Dic₃	—	4	1	no	—
443	C₅×Dic₃	#120	1	2	yes	—
444	C₂⁴×C₃	—	2	1	no	—
445	C₂³×D₃	—	2	1	no	—
446	C₂³×D₃	—	2	1	no	—
447	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
448	C₂×C₃×D₄	—	2	2	no	—
449	C₂×C₃×D₄	—	2	2	no	—
450	C₂×C₃×D₄	—	2	1	no	—
451	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
452	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
453	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
454	C₂×#67	—	2	8	no	—
455	C₂×#67	—	2	8	no	—
456	C₂×#67	—	2	1	no	—
457	C₂×#67	—	2	1	no	—
458	C₂×#67	—	2	1	no	—
459	C₂×#67	—	2	1	no	—
460	C₂×#67	—	2	1	no	—
461	C₂×#67	C₅×D₄	1	1	yes	characteristic
462	C₂×#67	C₅×D₄	1	1	yes	characteristic
463	C₂²×Dic₃	—	2	1	no	—
464	C₂²×Dic₃	—	2	1	no	—
465	D₃×Q₈	—	2	2	no	—
466	D₃×Q₈	—	2	2	no	—
467	#237	—	2	8	no	—
468	#237	—	2	2	no	—
469	#237	—	2	2	no	—
470	#237	—	2	2	no	—
471	#237	C₅×D₄	1	4	yes	—
472	D₃×D₄	—	2	8	no	—
473	D₃×D₄	—	2	2	no	—
474	D₃×D₄	—	2	2	no	—
475	D₃×D₄	—	2	2	no	—
476	D₃×D₄	C₅×D₄	1	4	yes	—
477	#235	—	2	2	no	—
478	#235	—	2	2	no	—
479	#235	—	2	2	no	—
480	#235	—	2	2	no	—
481	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
482	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
483	C₂×C₄×D₃	—	2	1	no	—
484	C₂×C₄×D₃	—	2	1	no	—
485	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
486	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
487	C₂×Dic₆	—	2	1	no	—
488	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
489	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
490	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
491	C₃×SD₁₆	—	2	2	no	—
492	C₃×SD₁₆	—	2	2	no	—
493	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
494	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
495	C₃×C₄⋊C₄	—	2	1	no	—
496	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
497	C₃×C₂²⋊C₄	—	2	1	no	—
498	#217	—	2	1	no	—
499	#216	—	2	2	no	—
500	#215	—	2	2	no	—
501	#214	—	2	2	no	—
502	#214	—	2	2	no	—
503	(C₂×D₃)⋊C₄	—	2	1	no	—
504	(C₂×D₃)⋊C₄	—	2	1	no	—
505	(C₂×D₃)⋊C₄	—	2	1	no	—
506	C₄⋊Dic₃	—	2	1	no	—
507	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
508	Dic₃⋊C₄	—	2	1	no	—
509	Dic₃⋊C₄	—	2	1	no	—
510	C₄×Dic₃	—	2	1	no	—
511	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
512	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
513	Dic₁₂	—	2	2	no	—
514	#204	—	2	2	no	—
515	ΓL(1,𝔽₂₅)	—	2	2	no	—
516	D₃×C₈	—	2	2	no	—
517	C₂³×C₅	—	2	4	no	—
518	C₂³×C₅	—	2	1	no	—
519	C₂³×C₅	—	2	1	no	—
520	C₂³×C₅	—	3	1	no	—
521	C₂³×C₅	—	3	1	no	—
522	C₂³×C₅	—	6	4	no	—
523	C₂³×C₅	—	6	4	no	—
524	C₂³×C₅	—	6	1	no	—
525	C₂³×C₅	—	8	1	no	—
526	C₂³×C₅	—	8	1	no	—
527	C₂³×C₅	—	24	1	no	—
528	C₂³×C₅	—	24	1	no	—
529	C₂³×C₅	—	24	1	no	—
530	C₂³×C₅	—	24	1	no	—
531	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
532	C₅×Q₈	—	2	1	no	—
533	C₅×Q₈	—	2	1	no	—
534	C₅×Q₈	—	3	2	no	—
535	C₅×Q₈	—	6	2	no	—
536	C₅×Q₈	—	6	1	no	—
537	C₅×Q₈	—	6	1	no	—
538	C₅×Q₈	—	6	1	no	—
539	C₅×Q₈	—	12	2	no	—
540	C₅×D₄	—	2	4	no	—
541	C₅×D₄	—	2	1	no	—
542	C₅×D₄	—	2	1	no	—
543	C₅×D₄	—	3	2	no	—
544	C₅×D₄	—	6	2	no	—
545	C₅×D₄	—	6	2	no	—
546	C₅×D₄	—	6	4	no	—
547	C₅×D₄	—	6	2	no	—
548	C₅×D₄	—	6	4	no	—
549	C₅×D₄	—	6	4	no	—
550	C₅×D₄	—	6	4	no	—
551	C₅×D₄	—	6	4	no	—
552	C₅×D₄	—	6	1	no	—
553	C₅×D₄	D₃×D₄	1	2	yes	—
554	C₅×D₄	D₃×D₄	1	2	yes	—
555	C₂×C₄×C₅	—	2	1	no	—
556	C₂×C₄×C₅	—	2	1	no	—
557	C₂×C₄×C₅	—	2	1	no	—
558	C₂×C₄×C₅	—	2	1	no	—
559	C₂×C₄×C₅	—	3	1	no	—
560	C₂×C₄×C₅	—	3	2	no	—
561	C₂×C₄×C₅	—	3	2	no	—
562	C₂×C₄×C₅	—	3	1	no	—
563	C₂×C₄×C₅	—	6	4	no	—
564	C₂×C₄×C₅	—	6	4	no	—
565	C₂×C₄×C₅	—	6	4	no	—
566	C₂×C₄×C₅	—	6	1	no	—
567	C₂×C₄×C₅	—	6	1	no	—
568	C₂×C₄×C₅	—	6	1	no	—
569	C₂×C₄×C₅	—	6	1	no	—
570	C₂×C₄×C₅	—	6	1	no	—
571	C₂×C₄×C₅	—	12	2	no	—
572	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
573	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
574	C₅×C₈	—	2	1	no	—
575	C₅×C₈	—	2	1	no	—
576	C₅×C₈	—	6	1	no	—
577	C₅×C₈	—	6	1	no	—
578	H(5,𝔽₂)	—	6	4	no	—
579	H(5,𝔽₂)	—	6	4	no	—
580	C₂×#41	—	3	1	no	—
581	C₂×#41	—	3	1	no	—
582	C₂×#41	—	3	1	no	—
583	C₂×#41	—	3	1	no	—
584	C₂×#41	—	6	1	no	—
585	C₂²×Q₈	—	3	1	no	—
586	C₂²×D₄	—	3	1	no	—
587	C₂²×D₄	—	3	1	no	—
588	C₂²×D₄	—	6	1	no	—
589	C₂²×D₄	—	6	1	no	—
590	C₂²×D₄	—	6	1	no	—
591	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
592	#137	—	6	4	no	—
593	C₂×Q₁₆	—	3	1	no	—
594	C₂×Q₁₆	—	3	1	no	—
595	C₂×SD₁₆	—	3	1	no	—
596	C₂×SD₁₆	—	3	1	no	—
597	C₂×SD₁₆	—	3	1	no	—
598	C₂×SD₁₆	—	3	1	no	—
599	C₂×SD₁₆	—	6	4	no	—
600	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
601	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
602	C₂×M₁₆	—	3	1	no	—
603	C₂²×C₈	—	3	1	no	—
604	C₄⋊Q₈	—	6	1	no	—
605	#124	—	6	1	no	—
606	#123	—	6	1	no	—
607	#123	—	6	1	no	—
608	C₂²⋊Q₈	—	3	1	no	—
609	C₂²⋊Q₈	—	3	1	no	—
610	C₂²⋊Q₈	—	3	1	no	—
611	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
612	#117	—	3	1	no	—
613	#103	—	3	1	no	—
614	#103	—	3	1	no	—
615	#102	—	3	1	no	—
616	#102	—	3	1	no	—
617	#102	—	3	1	no	—
618	#102	—	3	1	no	—
619	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
620	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
621	C₂²⋊C₈	—	3	1	no	—
622	C₂²⋊C₈	—	3	1	no	—
623	C₂²⋊C₈	—	3	1	no	—
624	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
625	C₂×C₃×C₅	—	4	2	no	—
626	C₂×C₃×C₅	—	4	2	no	—
627	C₂×C₃×C₅	—	4	1	no	—
628	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
629	C₂×C₃×C₅	#577	1	1	yes	characteristic
630	C₂×C₃×C₅	#577	1	1	yes	characteristic
631	C₅×D₃	—	2	2	no	—
632	C₅×D₃	—	4	1	no	—
633	C₅×D₃	—	4	2	no	—
634	C₂³×C₃	—	2	4	no	—
635	C₂³×C₃	—	2	1	no	—
636	C₂³×C₃	—	2	1	no	—
637	C₂³×C₃	—	8	1	no	—
638	C₂³×C₃	—	8	1	no	—
639	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
640	C₂²×D₃	—	2	1	no	—
641	C₂²×D₃	—	2	4	no	—
642	C₂²×D₃	—	2	4	no	—
643	C₂²×D₃	—	8	1	no	—
644	C₂²×D₃	—	8	1	no	—
645	C₂²×D₃	—	8	1	no	—
646	C₂²×D₃	—	8	1	no	—
647	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
648	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
649	C₃×Q₈	—	2	1	no	—
650	C₃×Q₈	—	2	1	no	—
651	C₃×D₄	—	2	4	no	—
652	C₃×D₄	—	2	1	no	—
653	C₃×D₄	—	2	1	no	—
654	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
655	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
656	C₂×C₃×C₄	—	2	1	no	—
657	C₂×C₃×C₄	—	2	1	no	—
658	C₂×C₃×C₄	—	2	1	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
661	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
662	#67	—	2	4	no	—
663	#67	—	2	4	no	—
664	#67	—	2	4	no	—
665	#67	—	2	2	no	—
666	#67	—	2	4	no	—
667	#67	—	2	2	no	—
668	#67	—	2	4	no	—
669	C₂×Dic₃	—	2	4	no	—
670	C₂×Dic₃	—	2	1	no	—
671	C₂×Dic₃	—	2	4	no	—
672	C₂×Dic₃	—	2	1	no	—
673	C₂×Dic₃	—	2	1	no	—
674	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
675	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
676	D₁₂	—	2	2	no	—
677	D₁₂	—	2	1	no	—
678	D₁₂	C₂×C₅×D₄	1	2	yes	—
679	C₄×D₃	—	2	4	no	—
680	C₄×D₃	—	2	1	no	—
681	C₄×D₃	—	2	1	no	—
682	C₄×D₃	—	4	2	no	—
683	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
684	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
685	Dic₆	—	2	1	no	—
686	Dic₆	—	2	2	no	—
687	Dic₆	—	2	1	no	—
688	Dic₆	—	2	1	no	—
689	Dic₆	—	4	2	no	—
690	Dic₆	C₂×C₅×D₄	1	2	yes	—
691	C₃×C₈	—	2	1	no	—
692	C₃×C₈	—	2	1	no	—
693	C₃⋊C₈	—	2	1	no	—
694	C₃⋊C₈	—	2	1	no	—
695	C₂²×C₅	—	2	1	no	—
696	C₂²×C₅	—	2	1	no	—
697	C₂²×C₅	—	2	1	no	—
698	C₂²×C₅	—	2	2	no	—
699	C₂²×C₅	—	2	2	no	—
700	C₂²×C₅	—	3	2	no	—
701	C₂²×C₅	—	4	1	no	—
702	C₂²×C₅	—	4	1	no	—
703	C₂²×C₅	—	4	1	no	—
704	C₂²×C₅	—	4	1	no	—
705	C₂²×C₅	—	6	1	no	—
706	C₂²×C₅	—	6	1	no	—
707	C₂²×C₅	—	6	1	no	—
708	C₂²×C₅	—	6	1	no	—
709	C₂²×C₅	—	6	2	no	—
710	C₂²×C₅	—	6	1	no	—
711	C₂²×C₅	—	8	4	no	—
712	C₂²×C₅	—	12	1	no	—
713	C₂²×C₅	—	12	1	no	—
714	C₂²×C₅	—	24	4	no	—
715	C₂²×C₅	—	24	4	no	—
716	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
717	C₄×C₅	—	2	1	no	—
718	C₄×C₅	—	3	2	no	—
719	C₄×C₅	—	4	1	no	—
720	C₄×C₅	—	4	1	no	—
721	C₄×C₅	—	6	1	no	—
722	C₄×C₅	—	6	2	no	—
723	C₄×C₅	—	12	1	no	—
724	C₄×C₅	—	12	1	no	—
725	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
726	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
727	C₂⁴	—	2	1	no	—
728	C₂⁴	—	6	1	no	—
729	C₂⁴	—	6	1	no	—
730	#41	—	3	4	no	—
731	#41	—	6	2	no	—
732	#41	—	6	2	no	—
733	#41	—	6	2	no	—
734	#41	—	6	2	no	—
735	#41	—	6	2	no	—
736	#41	—	6	2	no	—
737	#41	—	6	8	no	—
738	#41	—	6	2	no	—
739	C₂×Q₈	—	3	1	no	—
740	C₂×Q₈	—	3	1	no	—
741	C₂×Q₈	—	3	1	no	—
742	C₂×Q₈	—	6	1	no	—
743	C₂×Q₈	—	6	2	no	—
744	C₂×Q₈	—	6	2	no	—
745	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	1	no	—
749	C₂×D₄	—	3	4	no	—
750	C₂×D₄	—	3	1	no	—
751	C₂×D₄	—	3	1	no	—
752	C₂×D₄	—	3	1	no	—
753	C₂×D₄	—	3	1	no	—
754	C₂×D₄	—	6	2	no	—
755	C₂×D₄	—	6	1	no	—
756	C₂×D₄	—	6	1	no	—
757	C₂×D₄	—	6	2	no	—
758	C₂×D₄	—	6	8	no	—
759	C₂×D₄	—	6	1	no	—
760	C₂×D₄	—	6	1	no	—
761	C₂×D₄	—	6	8	no	—
762	C₂×D₄	—	6	8	no	—
763	C₂×D₄	—	6	1	no	—
764	C₂×D₄	—	6	2	no	—
765	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
766	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
767	C₂²×C₄	—	3	1	no	—
768	C₂²×C₄	—	3	1	no	—
769	C₂²×C₄	—	6	1	no	—
770	C₂²×C₄	—	6	1	no	—
771	C₂²×C₄	—	6	1	no	—
772	C₂²×C₄	—	6	1	no	—
773	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
774	Q₁₆	—	6	2	no	—
775	Q₁₆	—	6	2	no	—
776	SD₁₆	—	2	2	no	—
777	SD₁₆	—	2	2	no	—
778	SD₁₆	—	6	2	no	—
779	SD₁₆	—	6	2	no	—
780	SD₁₆	—	6	2	no	—
781	SD₁₆	—	6	2	no	—
782	M₁₆	—	6	2	no	—
783	C₂×C₈	—	3	1	no	—
784	C₂×C₈	—	3	1	no	—
785	C₂×C₈	—	6	2	no	—
786	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
787	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
788	C₄⋊C₄	—	2	1	no	—
789	C₄⋊C₄	—	3	1	no	—
790	C₄⋊C₄	—	6	1	no	—
791	C₄⋊C₄	—	6	1	no	—
792	C₄⋊C₄	—	6	1	no	—
793	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	6	1	no	—
796	C₂²⋊C₄	—	6	1	no	—
797	C₂²⋊C₄	—	6	1	no	—
798	C₂²⋊C₄	—	6	1	no	—
799	C₄²	—	6	1	no	—
800	C₃×C₅	#3009	1	1	yes	characteristic, complemented, Hall
801	C₂²×C₃	—	2	2	no	—
802	C₂²×C₃	—	2	2	no	—
803	C₂²×C₃	—	2	1	no	—
804	C₂²×C₃	—	2	1	no	—
805	C₂²×C₃	—	2	1	no	—
806	C₂²×C₃	—	4	1	no	—
807	C₂²×C₃	—	4	1	no	—
808	C₂²×C₃	—	4	1	no	—
809	C₂²×C₃	—	4	1	no	—
810	C₂²×C₃	—	8	4	no	—
811	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
812	C₂×D₃	—	2	1	no	—
813	C₂×D₃	—	2	1	no	—
814	C₂×D₃	—	2	1	no	—
815	C₂×D₃	—	2	2	no	—
816	C₂×D₃	—	2	1	no	—
817	C₂×D₃	—	2	1	no	—
818	C₂×D₃	—	4	1	no	—
819	C₂×D₃	—	4	1	no	—
820	C₂×D₃	—	8	4	no	—
821	C₂×D₃	—	8	4	no	—
822	C₂×D₃	C₅×#120	1	2	yes	—
823	C₃×C₄	—	2	1	no	—
824	C₃×C₄	—	4	1	no	—
825	C₃×C₄	—	4	1	no	—
826	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
827	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
828	Dic₃	—	2	1	no	—
829	Dic₃	—	2	2	no	—
830	Dic₃	—	4	1	no	—
831	Dic₃	—	4	1	no	—
832	Dic₃	C₅×#120	1	2	yes	—
833	C₂×C₅	—	4	1	no	—
834	C₂×C₅	—	4	2	no	—
835	C₂×C₅	—	4	2	no	—
836	C₂×C₅	—	6	2	no	—
837	C₂×C₅	—	12	1	no	—
838	C₂×C₅	—	12	2	no	—
839	C₂×C₅	D₃×#120	1	1	yes	characteristic
840	C₂×C₅	#5762	1	1	yes	characteristic
841	C₂×C₅	#5775	1	1	yes	characteristic
842	C₂³	—	2	4	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	3	1	no	—
846	C₂³	—	3	1	no	—
847	C₂³	—	6	4	no	—
848	C₂³	—	6	4	no	—
849	C₂³	—	6	1	no	—
850	C₂³	—	8	1	no	—
851	C₂³	—	8	1	no	—
852	C₂³	—	24	1	no	—
853	C₂³	—	24	1	no	—
854	C₂³	—	24	1	no	—
855	C₂³	—	24	1	no	—
856	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
857	Q₈	—	2	1	no	—
858	Q₈	—	2	1	no	—
859	Q₈	—	3	2	no	—
860	Q₈	—	6	2	no	—
861	Q₈	—	6	1	no	—
862	Q₈	—	6	1	no	—
863	Q₈	—	6	1	no	—
864	Q₈	—	12	2	no	—
865	D₄	—	2	4	no	—
866	D₄	—	2	1	no	—
867	D₄	—	2	1	no	—
868	D₄	—	3	2	no	—
869	D₄	—	6	2	no	—
870	D₄	—	6	2	no	—
871	D₄	—	6	4	no	—
872	D₄	—	6	2	no	—
873	D₄	—	6	4	no	—
874	D₄	—	6	4	no	—
875	D₄	—	6	4	no	—
876	D₄	—	6	4	no	—
877	D₄	—	6	1	no	—
878	D₄	C₅×D₃×D₄	1	2	yes	—
879	D₄	C₅×D₃×D₄	1	2	yes	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	3	1	no	—
885	C₂×C₄	—	3	2	no	—
886	C₂×C₄	—	3	2	no	—
887	C₂×C₄	—	3	1	no	—
888	C₂×C₄	—	6	4	no	—
889	C₂×C₄	—	6	4	no	—
890	C₂×C₄	—	6	4	no	—
891	C₂×C₄	—	6	1	no	—
892	C₂×C₄	—	6	1	no	—
893	C₂×C₄	—	6	1	no	—
894	C₂×C₄	—	6	1	no	—
895	C₂×C₄	—	6	1	no	—
896	C₂×C₄	—	12	2	no	—
897	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
898	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
899	C₈	—	2	1	no	—
900	C₈	—	2	1	no	—
901	C₈	—	6	1	no	—
902	C₈	—	6	1	no	—
903	C₂×C₃	—	4	2	no	—
904	C₂×C₃	—	4	2	no	—
905	C₂×C₃	—	4	1	no	—
906	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
907	C₂×C₃	C₅×#577	1	1	yes	characteristic
908	C₂×C₃	C₅×#577	1	1	yes	characteristic
909	D₃	—	2	2	no	—
910	D₃	—	4	1	no	—
911	D₃	—	4	2	no	—
912	C₅	#80148	1	1	yes	characteristic, direct product factor, Sylow
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	3	2	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	6	1	no	—
924	C₂²	—	6	1	no	—
925	C₂²	—	6	1	no	—
926	C₂²	—	6	1	no	—
927	C₂²	—	6	2	no	—
928	C₂²	—	6	1	no	—
929	C₂²	—	8	4	no	—
930	C₂²	—	12	1	no	—
931	C₂²	—	12	1	no	—
932	C₂²	—	24	4	no	—
933	C₂²	—	24	4	no	—
934	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
935	C₄	—	2	1	no	—
936	C₄	—	3	2	no	—
937	C₄	—	4	1	no	—
938	C₄	—	4	1	no	—
939	C₄	—	6	1	no	—
940	C₄	—	6	2	no	—
941	C₄	—	12	1	no	—
942	C₄	—	12	1	no	—
943	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
944	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
945	C₃	C₅×#3009	1	1	yes	characteristic, complemented, Sylow
946	C₂	—	4	1	no	—
947	C₂	—	4	2	no	—
948	C₂	—	4	2	no	—
949	C₂	—	6	2	no	—
950	C₂	—	12	1	no	—
951	C₂	—	12	2	no	—
952	C₂	C₅×D₃×#120	1	1	yes	characteristic
953	C₂	C₅×#5762	1	1	yes	characteristic
954	C₂	C₅×#5775	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×#450	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#1004	C₂
hypercenter	C₅×#450	D₃
hypocenter	C₃	C₅×#3009
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#450

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#915	C₂	semidirect
3. C₂×C₅×D₃×SD₁₆	C₂	semidirect
4. C₅×#5628	C₂	semidirect
5. C₃×C₅×#450	C₂	semidirect
6. C₅×#5218	C₂	semidirect
7. C₅×#5173	C₂	semidirect
8. C₅×#5169	C₂	semidirect
9. C₅×#5047	C₂	semidirect
10. C₅×#4783	C₂	semidirect
11. C₅×#4776	C₂	semidirect
12. C₅×#4772	C₂	semidirect
13. C₅×#4770	C₂	semidirect
14. C₅×#4733	C₂	semidirect
15. C₅×#4727	C₂	semidirect
20. C₂×C₅×D₃×Q₈	C₂²	semidirect
31. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
32. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
33. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
34. C₅×#946	C₂²	semidirect
35. C₂×C₅×#216	C₂²	semidirect
36. C₂×C₅×#215	C₂²	semidirect
37. C₂×C₅×#214	C₂²	semidirect
38. C₂×C₅×#214	C₂²	semidirect
39. C₅×#924	C₂²	semidirect
42. C₂×C₅×Dic₁₂	C₂²	semidirect
43. C₂×C₅×#204	C₂²	semidirect
44. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
45. C₂×C₅×D₃×C₈	C₂²	semidirect
46. C₅×#897	C₂²	semidirect
48. C₅×#892	C₂²	semidirect
52. C₃×C₅×#102	C₂²	semidirect
53. C₃×C₅×#102	C₂²	semidirect
54. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
55. C₅×#832	C₂²	semidirect
56. C₅×#832	C₂²	semidirect
57. C₅×#830	C₂²	semidirect
58. C₅×#821	C₂²	semidirect
59. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
60. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
61. C₅×#816	C₂²	semidirect
62. C₅×#810	C₂²	semidirect
63. C₅×#809	C₂²	semidirect
64. #80148	C₅	direct (N × H)
76. C₅×#450	D₃	semidirect
154. C₂×#915	C₂×C₅	semidirect
155. C₂×D₃×SD₁₆	C₂×C₅	semidirect
156. #5628	C₂×C₅	semidirect
157. C₃×#450	C₂×C₅	semidirect
158. #5218	C₂×C₅	semidirect
159. #5173	C₂×C₅	semidirect
160. #5169	C₂×C₅	semidirect
161. #5047	C₂×C₅	semidirect
162. #4783	C₂×C₅	semidirect
163. #4776	C₂×C₅	semidirect
164. #4772	C₂×C₅	semidirect
165. #4770	C₂×C₅	semidirect
166. #4733	C₂×C₅	semidirect
167. #4727	C₂×C₅	semidirect
190. C₂×C₅×SD₁₆	C₂×D₃	semidirect
191. C₂×C₅×SD₁₆	C₂×D₃	semidirect
201. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
209. C₅×#102	C₂×D₃	semidirect
210. C₅×#102	C₂×D₃	semidirect
214. C₅×C₂²⋊C₈	C₂×D₃	semidirect
280. C₂×D₃×Q₈	C₂²×C₅	semidirect
291. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
292. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
293. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
294. #946	C₂²×C₅	semidirect
295. C₂×#216	C₂²×C₅	semidirect
296. C₂×#215	C₂²×C₅	semidirect
297. C₂×#214	C₂²×C₅	semidirect
298. C₂×#214	C₂²×C₅	semidirect
299. #924	C₂²×C₅	semidirect
302. C₂×Dic₁₂	C₂²×C₅	semidirect
303. C₂×#204	C₂²×C₅	semidirect
304. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
305. C₂×D₃×C₈	C₂²×C₅	semidirect
306. #897	C₂²×C₅	semidirect
308. #892	C₂²×C₅	semidirect
312. C₃×#102	C₂²×C₅	semidirect
313. C₃×#102	C₂²×C₅	semidirect
314. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
315. #832	C₂²×C₅	semidirect
316. #832	C₂²×C₅	semidirect
317. #830	C₂²×C₅	semidirect
318. #821	C₂²×C₅	semidirect
319. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
320. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
321. #816	C₂²×C₅	semidirect
322. #810	C₂²×C₅	semidirect
323. #809	C₂²×C₅	semidirect
408. #450	C₅×D₃	semidirect
600. C₂×SD₁₆	C₂×C₅×D₃	semidirect
601. C₂×SD₁₆	C₂×C₅×D₃	semidirect
611. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
619. #102	C₂×C₅×D₃	semidirect
620. #102	C₂×C₅×D₃	semidirect
624. C₂²⋊C₈	C₂×C₅×D₃	semidirect
800. C₃×C₅	#3009	semidirect
912. C₅	#80148	direct (N × H)
945. C₃	C₅×#3009	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#1004	2
C₂×C₅×#915	2
C₂×C₅×D₃×SD₁₆	2
C₅×#5628	2
C₃×C₅×#450	2
C₅×#5218	2
C₅×#5173	2
C₅×#5169	2
C₅×#5047	2
C₅×#4783	2
C₅×#4776	2
C₅×#4772	2
C₅×#4770	2
C₅×#4733	2
C₅×#4727	2
C₅×#3009	3
#80148	5

Subgroups — C5×#80148 #14424303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80148 #14424303