Subgroups — C₅×#80228 #14424099

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#918	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#915	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5239	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5186	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×#4809	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4776	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4771	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4733	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4726	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3007	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₅×D₃×#41	—	2	4	no	—
19	C₅×D₃×#41	—	2	4	no	—
20	C₂×C₅×#239	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₅×#237	—	2	1	no	—
24	C₂×C₅×#237	C₂²	1	1	yes	characteristic
25	C₂×C₅×D₃×D₄	—	2	1	no	—
26	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₅×#235	—	2	1	no	—
28	C₂×C₅×#235	C₂²	1	1	yes	characteristic
29	C₂²×C₄×C₅×D₃	—	2	1	no	—
30	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×Q₁₆	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
35	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×#215	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×#918	—	2	4	no	—
41	C₅×#915	—	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×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
46	C₅×#897	C₂²	1	1	yes	characteristic
47	C₅×#896	—	2	1	no	—
48	C₅×D₃×C₄⋊C₄	—	2	1	no	—
49	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
51	C₅×#878	—	2	1	no	—
52	C₃×C₅×#103	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×#835	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
60	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
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	#80228	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
65	C₂²×C₅×#41	—	3	1	no	—
66	C₂×C₅×#137	—	3	1	no	—
67	C₂×C₅×#137	—	3	1	no	—
68	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
69	C₅×#452	—	3	1	no	—
70	C₅×#452	—	3	1	no	—
71	C₅×#452	—	3	1	no	—
72	C₅×#452	D₃	1	1	yes	characteristic, complemented
73	C₅×#451	—	3	1	no	—
74	C₅×#451	—	3	1	no	—
75	C₅×#450	—	3	1	no	—
76	C₅×#450	—	3	1	no	—
77	C₅×#417	—	3	1	no	—
78	C₅×#417	—	3	1	no	—
79	C₅×#407	—	3	1	no	—
80	C₂³×C₅×D₃	—	2	1	no	—
81	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
82	C₃×C₅×#41	—	2	2	no	—
83	C₃×C₅×#41	—	2	2	no	—
84	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	—	2	1	no	—
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₅×#67	—	2	1	no	—
91	C₂×C₅×#67	—	2	1	no	—
92	C₂×C₅×#67	—	2	1	no	—
93	C₂²×C₅×Dic₃	—	2	1	no	—
94	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
95	C₅×#239	—	2	2	no	—
96	C₅×#239	D₄	1	4	yes	—
97	C₅×D₃×Q₈	—	2	2	no	—
98	C₅×D₃×Q₈	—	2	2	no	—
99	C₅×D₃×Q₈	—	2	2	no	—
100	C₅×D₃×Q₈	—	2	2	no	—
101	C₅×#237	—	2	8	no	—
102	C₅×#237	—	2	2	no	—
103	C₅×#237	D₄	1	4	yes	—
104	C₅×D₃×D₄	—	2	8	no	—
105	C₅×D₃×D₄	—	2	2	no	—
106	C₅×D₃×D₄	—	2	2	no	—
107	C₅×#235	—	2	8	no	—
108	C₅×#235	—	2	2	no	—
109	C₅×#235	—	2	2	no	—
110	C₂×C₅×D₁₂	—	2	1	no	—
111	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
112	C₂×C₄×C₅×D₃	—	2	8	no	—
113	C₂×C₄×C₅×D₃	—	2	1	no	—
114	C₂×C₄×C₅×D₃	—	2	1	no	—
115	C₂×C₄×C₅×D₃	—	2	1	no	—
116	C₂×C₄×C₅×D₃	—	2	2	no	—
117	C₂×C₄×C₅×D₃	—	2	2	no	—
118	C₂×C₄×C₅×D₃	—	2	1	no	—
119	C₂×C₄×C₅×D₃	—	2	1	no	—
120	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
121	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
122	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
123	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
124	C₂×C₅×Dic₆	—	2	1	no	—
125	C₂×C₅×Dic₆	—	2	1	no	—
126	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
127	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
128	C₃×C₅×Q₁₆	—	2	2	no	—
129	C₃×C₅×SD₁₆	—	2	2	no	—
130	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
131	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
132	C₃×C₅×C₄⋊C₄	—	2	1	no	—
133	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
135	C₅×#217	—	2	1	no	—
136	C₅×#216	—	2	2	no	—
137	C₅×#216	—	2	2	no	—
138	C₅×#215	—	2	2	no	—
139	C₅×#214	—	2	2	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	C₅×Dic₃⋊C₄	—	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×ΓL(1,𝔽₂₅)	—	2	2	no	—
153	C₂×D₃×#41	C₂×C₅	1	1	yes	characteristic
154	C₂×#918	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×#915	C₂×C₅	1	1	yes	characteristic, complemented
156	D₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
157	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
158	#5239	C₂×C₅	1	1	yes	characteristic, complemented
159	#5186	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	#4809	C₂×C₅	1	1	yes	characteristic, complemented
163	#4803	C₂×C₅	1	1	yes	characteristic, complemented
164	#4776	C₂×C₅	1	1	yes	characteristic, complemented
165	#4771	C₂×C₅	1	1	yes	characteristic, complemented
166	#4733	C₂×C₅	1	1	yes	characteristic, complemented
167	#4726	C₂×C₅	1	1	yes	characteristic, complemented
168	C₂×C₅×#41	—	3	1	no	—
169	C₂×C₅×#41	—	3	1	no	—
170	C₂×C₅×#41	—	3	1	no	—
171	C₂×C₅×#41	—	6	1	no	—
172	C₂×C₅×#41	—	6	1	no	—
173	C₂×C₅×#41	—	6	4	no	—
174	C₂×C₅×#41	—	6	4	no	—
175	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
176	C₂²×C₅×Q₈	—	3	1	no	—
177	C₂²×C₅×Q₈	—	3	1	no	—
178	C₂²×C₅×D₄	—	3	1	no	—
179	C₂²×C₅×D₄	—	6	1	no	—
180	C₂³×C₄×C₅	—	3	1	no	—
181	C₂³×C₄×C₅	—	6	1	no	—
182	C₅×#137	—	6	4	no	—
183	C₅×#137	—	6	4	no	—
184	C₂×C₅×Q₁₆	—	3	1	no	—
185	C₂×C₅×Q₁₆	—	3	1	no	—
186	C₂×C₅×Q₁₆	—	3	1	no	—
187	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
188	C₂×C₅×SD₁₆	—	3	1	no	—
189	C₂×C₅×SD₁₆	—	3	1	no	—
190	C₂×C₅×SD₁₆	—	3	1	no	—
191	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
192	C₂×C₅×M₁₆	—	3	1	no	—
193	C₂×C₅×M₁₆	—	3	1	no	—
194	C₅×C₂²⋊Q₈	—	3	1	no	—
195	C₅×C₂²⋊Q₈	—	3	1	no	—
196	C₅×C₂²⋊Q₈	—	3	1	no	—
197	C₅×C₂²⋊Q₈	—	6	1	no	—
198	C₅×C₂²⋊Q₈	—	6	1	no	—
199	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
200	C₂×C₅×C₄⋊C₄	—	3	1	no	—
201	C₂×C₅×C₄⋊C₄	—	6	1	no	—
202	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
203	C₅×#103	—	3	1	no	—
204	C₅×#103	—	3	1	no	—
205	C₅×#103	—	3	1	no	—
206	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
207	C₅×#102	—	3	1	no	—
208	C₅×#102	—	3	1	no	—
209	C₅×#102	—	3	1	no	—
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	#3007	—	3	1	no	Sylow
216	C₂³×C₃×C₅	—	2	1	no	—
217	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₅×D₃	—	2	4	no	—
219	C₂²×C₅×D₃	—	2	1	no	—
220	C₂²×C₅×D₃	—	2	2	no	—
221	C₂²×C₅×D₃	—	2	2	no	—
222	C₂²×C₅×D₃	—	4	1	no	—
223	C₂²×C₅×D₃	—	4	2	no	—
224	C₂²×C₅×D₃	—	4	2	no	—
225	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
227	C₃×C₅×Q₈	—	2	1	no	—
228	C₃×C₅×Q₈	—	2	1	no	—
229	C₃×C₅×Q₈	—	2	1	no	—
230	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
231	C₃×C₅×D₄	—	2	4	no	—
232	C₃×C₅×D₄	—	2	1	no	—
233	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
234	C₂×C₃×C₄×C₅	—	2	4	no	—
235	C₂×C₃×C₄×C₅	—	2	1	no	—
236	C₂×C₃×C₄×C₅	—	2	1	no	—
237	C₂×C₃×C₄×C₅	—	2	1	no	—
238	C₂×C₃×C₄×C₅	—	2	1	no	—
239	C₂×C₃×C₄×C₅	—	2	1	no	—
240	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
241	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
242	C₅×#67	—	2	4	no	—
243	C₅×#67	—	2	4	no	—
244	C₅×#67	—	2	4	no	—
245	C₂×C₅×Dic₃	—	2	1	no	—
246	C₂×C₅×Dic₃	—	2	2	no	—
247	C₂×C₅×Dic₃	—	2	4	no	—
248	C₂×C₅×Dic₃	—	2	1	no	—
249	C₂×C₅×Dic₃	—	2	1	no	—
250	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
251	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
252	C₅×D₁₂	—	2	4	no	—
253	C₅×D₁₂	—	2	1	no	—
254	C₅×D₁₂	C₂×D₄	1	2	yes	—
255	C₄×C₅×D₃	—	2	4	no	—
256	C₄×C₅×D₃	—	2	4	no	—
257	C₄×C₅×D₃	—	2	2	no	—
258	C₄×C₅×D₃	—	2	1	no	—
259	C₄×C₅×D₃	—	2	1	no	—
260	C₄×C₅×D₃	—	2	2	no	—
261	C₄×C₅×D₃	—	2	4	no	—
262	C₄×C₅×D₃	—	4	2	no	—
263	C₄×C₅×D₃	—	4	2	no	—
264	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
265	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
266	C₅×Dic₆	—	2	4	no	—
267	C₅×Dic₆	—	2	1	no	—
268	C₅×Dic₆	—	2	1	no	—
269	C₅×Dic₆	—	2	1	no	—
270	C₅×Dic₆	—	4	2	no	—
271	C₅×Dic₆	C₂×D₄	1	2	yes	—
272	C₃×C₅×C₈	—	2	1	no	—
273	C₃×C₅×C₈	—	2	1	no	—
274	C₅×C₃⋊C₈	—	2	1	no	—
275	C₅×C₃⋊C₈	—	2	1	no	—
276	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
277	D₃×#41	—	2	4	no	—
278	D₃×#41	—	2	4	no	—
279	C₂×#239	C₂²×C₅	1	1	yes	characteristic
280	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
281	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
282	C₂×#237	—	2	1	no	—
283	C₂×#237	C₂²×C₅	1	1	yes	characteristic
284	C₂×D₃×D₄	—	2	1	no	—
285	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
286	C₂×#235	—	2	1	no	—
287	C₂×#235	C₂²×C₅	1	1	yes	characteristic
288	C₂²×C₄×D₃	—	2	1	no	—
289	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
290	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
291	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
292	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
293	#946	C₂²×C₅	1	1	yes	characteristic
294	C₂×#216	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	#924	C₂²×C₅	1	1	yes	characteristic, complemented
299	#918	—	2	4	no	—
300	#915	—	2	4	no	—
301	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
302	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
303	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
304	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
305	#897	C₂²×C₅	1	1	yes	characteristic
306	#896	—	2	1	no	—
307	D₃×C₄⋊C₄	—	2	1	no	—
308	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
309	D₃×C₂²⋊C₄	—	2	1	no	—
310	#878	—	2	1	no	—
311	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
312	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
313	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
314	#835	C₂²×C₅	1	1	yes	characteristic, complemented
315	#832	C₂²×C₅	1	1	yes	characteristic, complemented
316	#830	C₂²×C₅	1	1	yes	characteristic, complemented
317	#821	C₂²×C₅	1	1	yes	characteristic, complemented
318	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
319	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
320	#816	C₂²×C₅	1	1	yes	characteristic, complemented
321	#810	C₂²×C₅	1	1	yes	characteristic, complemented
322	#809	C₂²×C₅	1	1	yes	characteristic, complemented
323	C₂⁴×C₅	—	3	1	no	—
324	C₂⁴×C₅	—	6	1	no	—
325	C₅×#41	—	2	2	no	—
326	C₅×#41	—	2	2	no	—
327	C₅×#41	—	3	4	no	—
328	C₅×#41	—	3	4	no	—
329	C₅×#41	—	6	2	no	—
330	C₅×#41	—	6	2	no	—
331	C₅×#41	—	6	8	no	—
332	C₅×#41	—	6	2	no	—
333	C₅×#41	—	6	2	no	—
334	C₅×#41	—	6	8	no	—
335	C₂×C₅×Q₈	—	3	1	no	—
336	C₂×C₅×Q₈	—	3	1	no	—
337	C₂×C₅×Q₈	—	6	1	no	—
338	C₂×C₅×Q₈	—	6	1	no	—
339	C₂×C₅×Q₈	—	6	2	no	—
340	C₂×C₅×Q₈	—	6	2	no	—
341	C₂×C₅×Q₈	—	6	2	no	—
342	C₂×C₅×Q₈	—	6	2	no	—
343	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
344	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
345	C₂×C₅×D₄	—	2	1	no	—
346	C₂×C₅×D₄	—	3	1	no	—
347	C₂×C₅×D₄	—	6	1	no	—
348	C₂×C₅×D₄	—	6	1	no	—
349	C₂×C₅×D₄	—	6	2	no	—
350	C₂×C₅×D₄	—	6	8	no	—
351	C₂×C₅×D₄	—	6	1	no	—
352	C₂×C₅×D₄	—	6	1	no	—
353	C₂×C₅×D₄	—	6	2	no	—
354	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
355	C₂²×C₄×C₅	—	2	1	no	—
356	C₂²×C₄×C₅	—	3	1	no	—
357	C₂²×C₄×C₅	—	3	1	no	—
358	C₂²×C₄×C₅	—	3	1	no	—
359	C₂²×C₄×C₅	—	3	1	no	—
360	C₂²×C₄×C₅	—	3	1	no	—
361	C₂²×C₄×C₅	—	6	2	no	—
362	C₂²×C₄×C₅	—	6	2	no	—
363	C₂²×C₄×C₅	—	6	1	no	—
364	C₂²×C₄×C₅	—	6	1	no	—
365	C₂²×C₄×C₅	—	6	8	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	—	2	2	no	—
372	C₅×Q₁₆	—	6	2	no	—
373	C₅×Q₁₆	—	6	2	no	—
374	C₅×Q₁₆	—	6	2	no	—
375	C₅×SD₁₆	—	2	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	C₅×M₁₆	—	6	2	no	—
381	C₂×C₅×C₈	—	3	1	no	—
382	C₂×C₅×C₈	—	3	1	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	—	6	1	no	—
391	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
392	C₅×C₂²⋊C₄	—	2	1	no	—
393	C₅×C₂²⋊C₄	—	6	1	no	—
394	C₅×C₂²⋊C₄	—	6	1	no	—
395	C₅×C₂²⋊C₄	—	6	1	no	—
396	C₂²×#41	—	3	1	no	—
397	C₂×#137	—	3	1	no	—
398	C₂×#137	—	3	1	no	—
399	C₂×C₂²⋊Q₈	—	3	1	no	—
400	#452	—	3	1	no	—
401	#452	—	3	1	no	—
402	#452	—	3	1	no	—
403	#452	C₅×D₃	1	1	yes	characteristic, complemented
404	#451	—	3	1	no	—
405	#451	—	3	1	no	—
406	#450	—	3	1	no	—
407	#450	—	3	1	no	—
408	#417	—	3	1	no	—
409	#417	—	3	1	no	—
410	#407	—	3	1	no	—
411	C₂²×C₃×C₅	—	2	1	no	—
412	C₂²×C₃×C₅	—	2	2	no	—
413	C₂²×C₃×C₅	—	2	1	no	—
414	C₂²×C₃×C₅	—	2	1	no	—
415	C₂²×C₃×C₅	—	4	1	no	—
416	C₂²×C₃×C₅	—	4	1	no	—
417	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₅×D₃	—	2	1	no	—
419	C₂×C₅×D₃	—	2	1	no	—
420	C₂×C₅×D₃	—	2	1	no	—
421	C₂×C₅×D₃	—	2	1	no	—
422	C₂×C₅×D₃	—	2	2	no	—
423	C₂×C₅×D₃	—	4	4	no	—
424	C₂×C₅×D₃	—	4	8	no	—
425	C₂×C₅×D₃	—	4	1	no	—
426	C₂×C₅×D₃	—	4	1	no	—
427	C₂×C₅×D₃	#120	1	2	yes	—
428	C₂×C₅×D₃	#137	1	2	yes	complemented
429	C₃×C₄×C₅	—	2	2	no	—
430	C₃×C₄×C₅	—	2	1	no	—
431	C₃×C₄×C₅	—	4	1	no	—
432	C₃×C₄×C₅	—	4	1	no	—
433	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
434	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
435	C₅×Dic₃	—	2	1	no	—
436	C₅×Dic₃	—	2	2	no	—
437	C₅×Dic₃	—	4	1	no	—
438	C₅×Dic₃	—	4	1	no	—
439	C₅×Dic₃	#120	1	2	yes	—
440	C₂³×D₃	—	2	1	no	—
441	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
442	C₃×#41	—	2	2	no	—
443	C₃×#41	—	2	2	no	—
444	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
445	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
446	C₂×C₃×D₄	—	2	1	no	—
447	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
448	C₂²×C₃×C₄	—	2	1	no	—
449	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
450	C₂×#67	—	2	1	no	—
451	C₂×#67	—	2	1	no	—
452	C₂×#67	—	2	1	no	—
453	C₂²×Dic₃	—	2	1	no	—
454	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
455	#239	—	2	2	no	—
456	#239	C₅×D₄	1	4	yes	—
457	D₃×Q₈	—	2	2	no	—
458	D₃×Q₈	—	2	2	no	—
459	D₃×Q₈	—	2	2	no	—
460	D₃×Q₈	—	2	2	no	—
461	#237	—	2	8	no	—
462	#237	—	2	2	no	—
463	#237	C₅×D₄	1	4	yes	—
464	D₃×D₄	—	2	8	no	—
465	D₃×D₄	—	2	2	no	—
466	D₃×D₄	—	2	2	no	—
467	#235	—	2	8	no	—
468	#235	—	2	2	no	—
469	#235	—	2	2	no	—
470	C₂×D₁₂	—	2	1	no	—
471	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
472	C₂×C₄×D₃	—	2	8	no	—
473	C₂×C₄×D₃	—	2	1	no	—
474	C₂×C₄×D₃	—	2	1	no	—
475	C₂×C₄×D₃	—	2	1	no	—
476	C₂×C₄×D₃	—	2	2	no	—
477	C₂×C₄×D₃	—	2	2	no	—
478	C₂×C₄×D₃	—	2	1	no	—
479	C₂×C₄×D₃	—	2	1	no	—
480	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
481	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
482	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
483	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
484	C₂×Dic₆	—	2	1	no	—
485	C₂×Dic₆	—	2	1	no	—
486	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
487	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
488	C₃×Q₁₆	—	2	2	no	—
489	C₃×SD₁₆	—	2	2	no	—
490	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
491	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
492	C₃×C₄⋊C₄	—	2	1	no	—
493	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
494	C₃×C₂²⋊C₄	—	2	1	no	—
495	#217	—	2	1	no	—
496	#216	—	2	2	no	—
497	#216	—	2	2	no	—
498	#215	—	2	2	no	—
499	#214	—	2	2	no	—
500	(C₂×D₃)⋊C₄	—	2	1	no	—
501	(C₂×D₃)⋊C₄	—	2	1	no	—
502	C₄⋊Dic₃	—	2	1	no	—
503	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
504	Dic₃⋊C₄	—	2	1	no	—
505	Dic₃⋊C₄	—	2	1	no	—
506	Dic₃⋊C₄	—	2	1	no	—
507	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
508	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
509	Dic₁₂	—	2	2	no	—
510	#204	—	2	2	no	—
511	ΓL(1,𝔽₂₅)	—	2	2	no	—
512	ΓL(1,𝔽₂₅)	—	2	2	no	—
513	C₂³×C₅	—	2	1	no	—
514	C₂³×C₅	—	3	1	no	—
515	C₂³×C₅	—	3	1	no	—
516	C₂³×C₅	—	6	2	no	—
517	C₂³×C₅	—	6	2	no	—
518	C₂³×C₅	—	6	4	no	—
519	C₂³×C₅	—	6	1	no	—
520	C₂³×C₅	—	12	1	no	—
521	C₂³×C₅	—	12	2	no	—
522	C₂³×C₅	—	12	2	no	—
523	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
524	C₅×Q₈	—	2	1	no	—
525	C₅×Q₈	—	2	1	no	—
526	C₅×Q₈	—	2	1	no	—
527	C₅×Q₈	—	3	2	no	—
528	C₅×Q₈	—	6	4	no	—
529	C₅×Q₈	—	6	1	no	—
530	C₅×Q₈	—	6	1	no	—
531	C₅×Q₈	—	6	1	no	—
532	C₅×Q₈	—	12	2	no	—
533	C₅×Q₈	D₃×D₄	1	2	yes	—
534	C₅×D₄	—	2	4	no	—
535	C₅×D₄	—	2	1	no	—
536	C₅×D₄	—	3	2	no	—
537	C₅×D₄	—	6	4	no	—
538	C₅×D₄	—	6	4	no	—
539	C₅×D₄	—	6	4	no	—
540	C₅×D₄	—	6	4	no	—
541	C₅×D₄	—	6	1	no	—
542	C₅×D₄	D₃×D₄	1	2	yes	—
543	C₂×C₄×C₅	—	2	4	no	—
544	C₂×C₄×C₅	—	2	1	no	—
545	C₂×C₄×C₅	—	2	1	no	—
546	C₂×C₄×C₅	—	2	1	no	—
547	C₂×C₄×C₅	—	2	1	no	—
548	C₂×C₄×C₅	—	2	1	no	—
549	C₂×C₄×C₅	—	3	1	no	—
550	C₂×C₄×C₅	—	3	2	no	—
551	C₂×C₄×C₅	—	3	2	no	—
552	C₂×C₄×C₅	—	3	1	no	—
553	C₂×C₄×C₅	—	6	2	no	—
554	C₂×C₄×C₅	—	6	4	no	—
555	C₂×C₄×C₅	—	6	2	no	—
556	C₂×C₄×C₅	—	6	4	no	—
557	C₂×C₄×C₅	—	6	4	no	—
558	C₂×C₄×C₅	—	6	2	no	—
559	C₂×C₄×C₅	—	6	4	no	—
560	C₂×C₄×C₅	—	6	1	no	—
561	C₂×C₄×C₅	—	6	1	no	—
562	C₂×C₄×C₅	—	6	1	no	—
563	C₂×C₄×C₅	—	6	1	no	—
564	C₂×C₄×C₅	—	6	1	no	—
565	C₂×C₄×C₅	—	12	2	no	—
566	C₂×C₄×C₅	—	12	2	no	—
567	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
568	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
569	C₅×C₈	—	2	1	no	—
570	C₅×C₈	—	2	1	no	—
571	C₅×C₈	—	6	1	no	—
572	C₅×C₈	—	6	1	no	—
573	C₂×#41	—	3	1	no	—
574	C₂×#41	—	3	1	no	—
575	C₂×#41	—	3	1	no	—
576	C₂×#41	—	6	1	no	—
577	C₂×#41	—	6	1	no	—
578	C₂×#41	—	6	4	no	—
579	C₂×#41	—	6	4	no	—
580	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
581	C₂²×Q₈	—	3	1	no	—
582	C₂²×Q₈	—	3	1	no	—
583	C₂²×D₄	—	3	1	no	—
584	C₂²×D₄	—	6	1	no	—
585	C₂³×C₄	—	3	1	no	—
586	C₂³×C₄	—	6	1	no	—
587	#137	—	6	4	no	—
588	#137	—	6	4	no	—
589	C₂×Q₁₆	—	3	1	no	—
590	C₂×Q₁₆	—	3	1	no	—
591	C₂×Q₁₆	—	3	1	no	—
592	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
593	C₂×SD₁₆	—	3	1	no	—
594	C₂×SD₁₆	—	3	1	no	—
595	C₂×SD₁₆	—	3	1	no	—
596	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
597	C₂×M₁₆	—	3	1	no	—
598	C₂×M₁₆	—	3	1	no	—
599	C₂²⋊Q₈	—	3	1	no	—
600	C₂²⋊Q₈	—	3	1	no	—
601	C₂²⋊Q₈	—	3	1	no	—
602	C₂²⋊Q₈	—	6	1	no	—
603	C₂²⋊Q₈	—	6	1	no	—
604	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
605	C₂×C₄⋊C₄	—	3	1	no	—
606	C₂×C₄⋊C₄	—	6	1	no	—
607	C₂×C₂²⋊C₄	—	6	1	no	—
608	#103	—	3	1	no	—
609	#103	—	3	1	no	—
610	#103	—	3	1	no	—
611	#103	C₂×C₅×D₃	1	1	yes	characteristic, complemented
612	#102	—	3	1	no	—
613	#102	—	3	1	no	—
614	#102	—	3	1	no	—
615	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
616	C₂²⋊C₈	—	3	1	no	—
617	C₂²⋊C₈	—	3	1	no	—
618	C₂²⋊C₈	—	3	1	no	—
619	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
620	C₂×C₃×C₅	—	4	1	no	—
621	C₂×C₃×C₅	—	4	2	no	—
622	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
623	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
624	C₂×C₃×C₅	#575	1	1	yes	characteristic
625	C₅×D₃	—	2	2	no	—
626	C₅×D₃	—	2	2	no	—
627	C₅×D₃	—	4	2	no	—
628	C₂³×C₃	—	2	1	no	—
629	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
630	C₂²×D₃	—	2	4	no	—
631	C₂²×D₃	—	2	1	no	—
632	C₂²×D₃	—	2	2	no	—
633	C₂²×D₃	—	2	2	no	—
634	C₂²×D₃	—	4	1	no	—
635	C₂²×D₃	—	4	2	no	—
636	C₂²×D₃	—	4	2	no	—
637	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
638	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
639	C₃×Q₈	—	2	1	no	—
640	C₃×Q₈	—	2	1	no	—
641	C₃×Q₈	—	2	1	no	—
642	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
643	C₃×D₄	—	2	4	no	—
644	C₃×D₄	—	2	1	no	—
645	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
646	C₂×C₃×C₄	—	2	4	no	—
647	C₂×C₃×C₄	—	2	1	no	—
648	C₂×C₃×C₄	—	2	1	no	—
649	C₂×C₃×C₄	—	2	1	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
653	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
654	#67	—	2	4	no	—
655	#67	—	2	4	no	—
656	#67	—	2	4	no	—
657	C₂×Dic₃	—	2	1	no	—
658	C₂×Dic₃	—	2	2	no	—
659	C₂×Dic₃	—	2	4	no	—
660	C₂×Dic₃	—	2	1	no	—
661	C₂×Dic₃	—	2	1	no	—
662	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
663	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
664	D₁₂	—	2	4	no	—
665	D₁₂	—	2	1	no	—
666	D₁₂	C₂×C₅×D₄	1	2	yes	—
667	C₄×D₃	—	2	4	no	—
668	C₄×D₃	—	2	4	no	—
669	C₄×D₃	—	2	2	no	—
670	C₄×D₃	—	2	1	no	—
671	C₄×D₃	—	2	1	no	—
672	C₄×D₃	—	2	2	no	—
673	C₄×D₃	—	2	4	no	—
674	C₄×D₃	—	4	2	no	—
675	C₄×D₃	—	4	2	no	—
676	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
677	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
678	Dic₆	—	2	4	no	—
679	Dic₆	—	2	1	no	—
680	Dic₆	—	2	1	no	—
681	Dic₆	—	2	1	no	—
682	Dic₆	—	4	2	no	—
683	Dic₆	C₂×C₅×D₄	1	2	yes	—
684	C₃×C₈	—	2	1	no	—
685	C₃×C₈	—	2	1	no	—
686	C₃⋊C₈	—	2	1	no	—
687	C₃⋊C₈	—	2	1	no	—
688	C₂²×C₅	—	2	1	no	—
689	C₂²×C₅	—	2	1	no	—
690	C₂²×C₅	—	2	1	no	—
691	C₂²×C₅	—	2	2	no	—
692	C₂²×C₅	—	3	2	no	—
693	C₂²×C₅	—	3	2	no	—
694	C₂²×C₅	—	4	1	no	—
695	C₂²×C₅	—	4	1	no	—
696	C₂²×C₅	—	6	1	no	—
697	C₂²×C₅	—	6	1	no	—
698	C₂²×C₅	—	6	1	no	—
699	C₂²×C₅	—	6	1	no	—
700	C₂²×C₅	—	6	2	no	—
701	C₂²×C₅	—	12	4	no	—
702	C₂²×C₅	—	12	8	no	—
703	C₂²×C₅	—	12	1	no	—
704	C₂²×C₅	—	12	1	no	—
705	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
706	C₄×C₅	—	2	1	no	—
707	C₄×C₅	—	2	2	no	—
708	C₄×C₅	—	3	2	no	—
709	C₄×C₅	—	4	1	no	—
710	C₄×C₅	—	4	1	no	—
711	C₄×C₅	—	6	1	no	—
712	C₄×C₅	—	6	2	no	—
713	C₄×C₅	—	12	1	no	—
714	C₄×C₅	—	12	1	no	—
715	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
716	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
717	C₂⁴	—	3	1	no	—
718	C₂⁴	—	6	1	no	—
719	#41	—	2	2	no	—
720	#41	—	2	2	no	—
721	#41	—	3	4	no	—
722	#41	—	3	4	no	—
723	#41	—	6	2	no	—
724	#41	—	6	2	no	—
725	#41	—	6	8	no	—
726	#41	—	6	2	no	—
727	#41	—	6	2	no	—
728	#41	—	6	8	no	—
729	C₂×Q₈	—	3	1	no	—
730	C₂×Q₈	—	3	1	no	—
731	C₂×Q₈	—	6	1	no	—
732	C₂×Q₈	—	6	1	no	—
733	C₂×Q₈	—	6	2	no	—
734	C₂×Q₈	—	6	2	no	—
735	C₂×Q₈	—	6	2	no	—
736	C₂×Q₈	—	6	2	no	—
737	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
738	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
739	C₂×D₄	—	2	1	no	—
740	C₂×D₄	—	3	1	no	—
741	C₂×D₄	—	6	1	no	—
742	C₂×D₄	—	6	1	no	—
743	C₂×D₄	—	6	2	no	—
744	C₂×D₄	—	6	8	no	—
745	C₂×D₄	—	6	1	no	—
746	C₂×D₄	—	6	1	no	—
747	C₂×D₄	—	6	2	no	—
748	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	3	1	no	—
751	C₂²×C₄	—	3	1	no	—
752	C₂²×C₄	—	3	1	no	—
753	C₂²×C₄	—	3	1	no	—
754	C₂²×C₄	—	3	1	no	—
755	C₂²×C₄	—	6	2	no	—
756	C₂²×C₄	—	6	2	no	—
757	C₂²×C₄	—	6	1	no	—
758	C₂²×C₄	—	6	1	no	—
759	C₂²×C₄	—	6	8	no	—
760	C₂²×C₄	—	6	1	no	—
761	C₂²×C₄	—	6	1	no	—
762	C₂²×C₄	—	6	1	no	—
763	C₂²×C₄	—	6	1	no	—
764	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
765	Q₁₆	—	2	2	no	—
766	Q₁₆	—	6	2	no	—
767	Q₁₆	—	6	2	no	—
768	Q₁₆	—	6	2	no	—
769	SD₁₆	—	2	2	no	—
770	SD₁₆	—	6	2	no	—
771	SD₁₆	—	6	2	no	—
772	SD₁₆	—	6	2	no	—
773	M₁₆	—	6	2	no	—
774	M₁₆	—	6	2	no	—
775	C₂×C₈	—	3	1	no	—
776	C₂×C₈	—	3	1	no	—
777	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
778	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
779	C₄⋊C₄	—	2	1	no	—
780	C₄⋊C₄	—	3	1	no	—
781	C₄⋊C₄	—	6	1	no	—
782	C₄⋊C₄	—	6	1	no	—
783	C₄⋊C₄	—	6	1	no	—
784	C₄⋊C₄	—	6	1	no	—
785	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
786	C₂²⋊C₄	—	2	1	no	—
787	C₂²⋊C₄	—	6	1	no	—
788	C₂²⋊C₄	—	6	1	no	—
789	C₂²⋊C₄	—	6	1	no	—
790	C₃×C₅	#3007	1	1	yes	characteristic, complemented, Hall
791	C₂²×C₃	—	2	1	no	—
792	C₂²×C₃	—	2	2	no	—
793	C₂²×C₃	—	2	1	no	—
794	C₂²×C₃	—	2	1	no	—
795	C₂²×C₃	—	4	1	no	—
796	C₂²×C₃	—	4	1	no	—
797	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
798	C₂×D₃	—	2	1	no	—
799	C₂×D₃	—	2	1	no	—
800	C₂×D₃	—	2	1	no	—
801	C₂×D₃	—	2	1	no	—
802	C₂×D₃	—	2	2	no	—
803	C₂×D₃	—	4	4	no	—
804	C₂×D₃	—	4	8	no	—
805	C₂×D₃	—	4	1	no	—
806	C₂×D₃	—	4	1	no	—
807	C₂×D₃	C₅×#120	1	2	yes	—
808	C₂×D₃	C₅×#137	1	2	yes	complemented
809	C₃×C₄	—	2	2	no	—
810	C₃×C₄	—	2	1	no	—
811	C₃×C₄	—	4	1	no	—
812	C₃×C₄	—	4	1	no	—
813	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
814	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
815	Dic₃	—	2	1	no	—
816	Dic₃	—	2	2	no	—
817	Dic₃	—	4	1	no	—
818	Dic₃	—	4	1	no	—
819	Dic₃	C₅×#120	1	2	yes	—
820	C₂×C₅	—	4	1	no	—
821	C₂×C₅	—	4	2	no	—
822	C₂×C₅	—	6	2	no	—
823	C₂×C₅	—	6	2	no	—
824	C₂×C₅	—	12	2	no	—
825	C₂×C₅	D₃×#120	1	1	yes	characteristic
826	C₂×C₅	#5768	1	1	yes	characteristic
827	C₂×C₅	D₃×#137	1	1	yes	characteristic
828	C₂³	—	2	1	no	—
829	C₂³	—	3	1	no	—
830	C₂³	—	3	1	no	—
831	C₂³	—	6	2	no	—
832	C₂³	—	6	2	no	—
833	C₂³	—	6	4	no	—
834	C₂³	—	6	1	no	—
835	C₂³	—	12	1	no	—
836	C₂³	—	12	2	no	—
837	C₂³	—	12	2	no	—
838	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
839	Q₈	—	2	1	no	—
840	Q₈	—	2	1	no	—
841	Q₈	—	2	1	no	—
842	Q₈	—	3	2	no	—
843	Q₈	—	6	4	no	—
844	Q₈	—	6	1	no	—
845	Q₈	—	6	1	no	—
846	Q₈	—	6	1	no	—
847	Q₈	—	12	2	no	—
848	Q₈	C₅×D₃×D₄	1	2	yes	—
849	D₄	—	2	4	no	—
850	D₄	—	2	1	no	—
851	D₄	—	3	2	no	—
852	D₄	—	6	4	no	—
853	D₄	—	6	4	no	—
854	D₄	—	6	4	no	—
855	D₄	—	6	4	no	—
856	D₄	—	6	1	no	—
857	D₄	C₅×D₃×D₄	1	2	yes	—
858	C₂×C₄	—	2	4	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	3	1	no	—
865	C₂×C₄	—	3	2	no	—
866	C₂×C₄	—	3	2	no	—
867	C₂×C₄	—	3	1	no	—
868	C₂×C₄	—	6	2	no	—
869	C₂×C₄	—	6	4	no	—
870	C₂×C₄	—	6	2	no	—
871	C₂×C₄	—	6	4	no	—
872	C₂×C₄	—	6	4	no	—
873	C₂×C₄	—	6	2	no	—
874	C₂×C₄	—	6	4	no	—
875	C₂×C₄	—	6	1	no	—
876	C₂×C₄	—	6	1	no	—
877	C₂×C₄	—	6	1	no	—
878	C₂×C₄	—	6	1	no	—
879	C₂×C₄	—	6	1	no	—
880	C₂×C₄	—	12	2	no	—
881	C₂×C₄	—	12	2	no	—
882	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
883	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
884	C₈	—	2	1	no	—
885	C₈	—	2	1	no	—
886	C₈	—	6	1	no	—
887	C₈	—	6	1	no	—
888	C₂×C₃	—	4	1	no	—
889	C₂×C₃	—	4	2	no	—
890	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
891	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
892	C₂×C₃	C₅×#575	1	1	yes	characteristic
893	D₃	—	2	2	no	—
894	D₃	—	2	2	no	—
895	D₃	—	4	2	no	—
896	C₅	#80228	1	1	yes	characteristic, direct product factor, Sylow
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	3	2	no	—
902	C₂²	—	3	2	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	6	1	no	—
906	C₂²	—	6	1	no	—
907	C₂²	—	6	1	no	—
908	C₂²	—	6	1	no	—
909	C₂²	—	6	2	no	—
910	C₂²	—	12	4	no	—
911	C₂²	—	12	8	no	—
912	C₂²	—	12	1	no	—
913	C₂²	—	12	1	no	—
914	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
915	C₄	—	2	1	no	—
916	C₄	—	2	2	no	—
917	C₄	—	3	2	no	—
918	C₄	—	4	1	no	—
919	C₄	—	4	1	no	—
920	C₄	—	6	1	no	—
921	C₄	—	6	2	no	—
922	C₄	—	12	1	no	—
923	C₄	—	12	1	no	—
924	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
925	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
926	C₃	C₅×#3007	1	1	yes	characteristic, complemented, Sylow
927	C₂	—	4	1	no	—
928	C₂	—	4	2	no	—
929	C₂	—	6	2	no	—
930	C₂	—	6	2	no	—
931	C₂	—	12	2	no	—
932	C₂	C₅×D₃×#120	1	1	yes	characteristic
933	C₂	C₅×#5768	1	1	yes	characteristic
934	C₂	C₅×D₃×#137	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×#452	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₃×#41	C₂
hypercenter	C₅×#452	D₃
hypocenter	C₃	C₅×#3007
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#452

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#918	C₂	semidirect
3. C₂×C₅×#915	C₂	semidirect
4. C₅×D₃×C₂²⋊Q₈	C₂	semidirect
5. C₃×C₅×#452	C₂	semidirect
6. C₅×#5239	C₂	semidirect
7. C₅×#5186	C₂	semidirect
8. C₅×#5169	C₂	semidirect
9. C₅×#5047	C₂	semidirect
10. C₅×#4809	C₂	semidirect
11. C₅×#4803	C₂	semidirect
12. C₅×#4776	C₂	semidirect
13. C₅×#4771	C₂	semidirect
14. C₅×#4733	C₂	semidirect
15. C₅×#4726	C₂	semidirect
22. C₂×C₅×D₃×Q₈	C₂²	semidirect
31. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
32. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
33. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
35. C₂×C₅×#216	C₂²	semidirect
36. C₂×C₅×#216	C₂²	semidirect
37. C₂×C₅×#215	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×ΓL(1,𝔽₂₅)	C₂²	semidirect
49. C₅×D₃×C₄⋊C₄	C₂²	semidirect
52. C₃×C₅×#103	C₂²	semidirect
53. C₃×C₅×#102	C₂²	semidirect
54. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
55. C₅×#835	C₂²	semidirect
56. C₅×#832	C₂²	semidirect
57. C₅×#830	C₂²	semidirect
58. C₅×#821	C₂²	semidirect
61. C₅×#816	C₂²	semidirect
62. C₅×#810	C₂²	semidirect
63. C₅×#809	C₂²	semidirect
64. #80228	C₅	direct (N × H)
72. C₅×#452	D₃	semidirect
154. C₂×#918	C₂×C₅	semidirect
155. C₂×#915	C₂×C₅	semidirect
156. D₃×C₂²⋊Q₈	C₂×C₅	semidirect
157. C₃×#452	C₂×C₅	semidirect
158. #5239	C₂×C₅	semidirect
159. #5186	C₂×C₅	semidirect
160. #5169	C₂×C₅	semidirect
161. #5047	C₂×C₅	semidirect
162. #4809	C₂×C₅	semidirect
163. #4803	C₂×C₅	semidirect
164. #4776	C₂×C₅	semidirect
165. #4771	C₂×C₅	semidirect
166. #4733	C₂×C₅	semidirect
167. #4726	C₂×C₅	semidirect
187. C₂×C₅×Q₁₆	C₂×D₃	semidirect
191. C₂×C₅×SD₁₆	C₂×D₃	semidirect
199. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
206. C₅×#103	C₂×D₃	semidirect
210. C₅×#102	C₂×D₃	semidirect
214. C₅×C₂²⋊C₈	C₂×D₃	semidirect
281. C₂×D₃×Q₈	C₂²×C₅	semidirect
290. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
291. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
292. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
294. C₂×#216	C₂²×C₅	semidirect
295. C₂×#216	C₂²×C₅	semidirect
296. C₂×#215	C₂²×C₅	semidirect
297. C₂×#214	C₂²×C₅	semidirect
298. #924	C₂²×C₅	semidirect
301. C₂×Dic₁₂	C₂²×C₅	semidirect
302. C₂×#204	C₂²×C₅	semidirect
303. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
304. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
308. D₃×C₄⋊C₄	C₂²×C₅	semidirect
311. C₃×#103	C₂²×C₅	semidirect
312. C₃×#102	C₂²×C₅	semidirect
313. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
314. #835	C₂²×C₅	semidirect
315. #832	C₂²×C₅	semidirect
316. #830	C₂²×C₅	semidirect
317. #821	C₂²×C₅	semidirect
320. #816	C₂²×C₅	semidirect
321. #810	C₂²×C₅	semidirect
322. #809	C₂²×C₅	semidirect
403. #452	C₅×D₃	semidirect
428. C₂×C₅×D₃	#137	semidirect
592. C₂×Q₁₆	C₂×C₅×D₃	semidirect
596. C₂×SD₁₆	C₂×C₅×D₃	semidirect
604. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
611. #103	C₂×C₅×D₃	semidirect
615. #102	C₂×C₅×D₃	semidirect
619. C₂²⋊C₈	C₂×C₅×D₃	semidirect
790. C₃×C₅	#3007	semidirect
808. C₂×D₃	C₅×#137	semidirect
896. C₅	#80228	direct (N × H)
926. C₃	C₅×#3007	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×#41	2
C₂×C₅×#918	2
C₂×C₅×#915	2
C₅×D₃×C₂²⋊Q₈	2
C₃×C₅×#452	2
C₅×#5239	2
C₅×#5186	2
C₅×#5169	2
C₅×#5047	2
C₅×#4809	2
C₅×#4803	2
C₅×#4776	2
C₅×#4771	2
C₅×#4733	2
C₅×#4726	2
C₅×#3007	3
#80228	5

Subgroups — C5×#80228 #14424099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80228 #14424099