Subgroups — C₅×#80230 #14424531

Order 1920.

1400 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1010	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#915	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5628	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×#5173	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5050	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4809	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4783	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4772	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4739	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4727	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3011	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₅×#1010	—	2	4	no	—
19	C₅×#1010	—	2	4	no	—
20	C₂×C₅×D₃×Q₈	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
23	C₂×C₅×#237	—	2	1	no	—
24	C₂×C₅×#237	—	2	1	no	—
25	C₂×C₅×#237	C₂²	1	1	yes	characteristic
26	C₂×C₅×#237	C₂²	1	1	yes	characteristic
27	C₂×C₅×#235	—	2	1	no	—
28	C₂×C₅×#235	C₂²	1	1	yes	characteristic
29	C₂²×C₅×Dic₆	—	2	1	no	—
30	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₅×#946	C₂²	1	1	yes	characteristic
35	C₂×C₅×#216	C₂²	1	1	yes	characteristic
36	C₂×C₅×#216	C₂²	1	1	yes	characteristic
37	C₂×C₅×#216	C₂²	1	1	yes	characteristic
38	C₂×C₅×#214	C₂²	1	1	yes	characteristic
39	C₅×#924	C₂²	1	1	yes	characteristic
40	C₅×D₃×Q₁₆	—	2	4	no	—
41	C₅×#915	—	2	4	no	—
42	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
43	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
44	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
45	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
46	C₅×#897	C₂²	1	1	yes	characteristic
47	C₅×#894	—	2	1	no	—
48	C₅×#892	C₂²	1	1	yes	characteristic
49	C₅×#888	—	2	1	no	—
50	C₅×#885	—	2	1	no	—
51	C₅×#883	—	2	1	no	—
52	C₃×C₅×#103	C₂²	1	1	yes	characteristic
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic
54	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
55	C₅×#835	C₂²	1	1	yes	characteristic
56	C₅×#832	C₂²	1	1	yes	characteristic
57	C₅×#830	C₂²	1	1	yes	characteristic
58	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
59	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
60	C₅×#816	C₂²	1	1	yes	characteristic
61	C₅×#816	C₂²	1	1	yes	characteristic
62	C₅×#810	C₂²	1	1	yes	characteristic
63	C₅×#810	C₂²	1	1	yes	characteristic
64	#80230	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
65	C₂×C₅×2₋¹⁺⁴	—	3	1	no	—
66	C₂×C₅×#137	—	3	1	no	—
67	C₂²×C₅×Q₁₆	—	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	D₃	1	1	yes	characteristic, complemented
73	C₅×#451	—	3	1	no	—
74	C₅×#451	—	3	1	no	—
75	C₅×#451	—	3	1	no	—
76	C₅×#451	—	3	1	no	—
77	C₅×#419	—	3	1	no	—
78	C₅×#416	—	3	1	no	—
79	C₅×#408	—	3	1	no	—
80	C₃×C₅×#41	—	2	2	no	—
81	C₃×C₅×#41	—	2	2	no	—
82	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×D₄	—	2	1	no	—
85	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₄×C₅	—	2	1	no	—
87	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂×C₅×#67	—	2	1	no	—
89	C₂×C₅×#67	—	2	1	no	—
90	C₂×C₅×#67	D₄	1	1	yes	characteristic
91	C₂×C₅×#67	D₄	1	1	yes	characteristic
92	C₂²×C₅×Dic₃	—	2	1	no	—
93	C₂²×C₅×Dic₃	—	2	1	no	—
94	C₂²×C₅×Dic₃	—	2	1	no	—
95	C₅×D₃×Q₈	—	2	2	no	—
96	C₅×D₃×Q₈	—	2	2	no	—
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	D₄	1	4	yes	—
101	C₅×#237	—	2	8	no	—
102	C₅×#237	—	2	8	no	—
103	C₅×#237	—	2	2	no	—
104	C₅×#237	—	2	2	no	—
105	C₅×#237	—	2	2	no	—
106	C₅×#237	D₄	1	4	yes	—
107	C₅×#235	—	2	8	no	—
108	C₅×#235	—	2	2	no	—
109	C₅×#235	—	2	2	no	—
110	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
111	C₂×C₄×C₅×D₃	—	2	1	no	—
112	C₂×C₄×C₅×D₃	—	2	1	no	—
113	C₂×C₄×C₅×D₃	—	2	1	no	—
114	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
115	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
116	C₂×C₅×Dic₆	—	2	8	no	—
117	C₂×C₅×Dic₆	—	2	1	no	—
118	C₂×C₅×Dic₆	—	2	1	no	—
119	C₂×C₅×Dic₆	—	2	1	no	—
120	C₂×C₅×Dic₆	—	2	2	no	—
121	C₂×C₅×Dic₆	—	2	2	no	—
122	C₂×C₅×Dic₆	—	2	1	no	—
123	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
124	C₂×C₅×Dic₆	C₂³	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×Q₁₆	—	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×#216	—	2	2	no	—
137	C₅×#216	—	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×Dic₁₂	—	2	2	no	—
151	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
152	C₅×D₃×C₈	—	2	2	no	—
153	C₂×#1010	C₂×C₅	1	1	yes	characteristic
154	C₂×D₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×#915	C₂×C₅	1	1	yes	characteristic, complemented
156	#5628	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	#5173	C₂×C₅	1	1	yes	characteristic, complemented
161	#5050	C₂×C₅	1	1	yes	characteristic, complemented
162	#4809	C₂×C₅	1	1	yes	characteristic, complemented
163	#4802	C₂×C₅	1	1	yes	characteristic, complemented
164	#4783	C₂×C₅	1	1	yes	characteristic, complemented
165	#4772	C₂×C₅	1	1	yes	characteristic, complemented
166	#4739	C₂×C₅	1	1	yes	characteristic, complemented
167	#4727	C₂×C₅	1	1	yes	characteristic, complemented
168	C₅×2₋¹⁺⁴	—	6	4	no	—
169	C₅×2₋¹⁺⁴	—	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	—	6	1	no	—
174	C₂×C₅×#41	—	6	1	no	—
175	C₂×C₅×#41	—	6	1	no	—
176	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
177	C₂²×C₅×Q₈	—	3	1	no	—
178	C₂²×C₅×Q₈	—	3	1	no	—
179	C₂²×C₅×Q₈	—	3	1	no	—
180	C₂²×C₅×Q₈	—	3	1	no	—
181	C₂²×C₅×Q₈	—	6	1	no	—
182	C₅×#137	—	6	4	no	—
183	C₂×C₅×Q₁₆	—	3	1	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	—	3	1	no	—
188	C₂×C₅×Q₁₆	—	6	4	no	—
189	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
190	C₂×C₅×SD₁₆	—	3	1	no	—
191	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
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
202	C₅×#117	—	3	1	no	—
203	C₅×#103	—	3	1	no	—
204	C₅×#103	—	3	1	no	—
205	C₅×#103	—	3	1	no	—
206	C₅×#103	—	3	1	no	—
207	C₅×#103	—	3	1	no	—
208	C₅×#103	C₂×D₃	1	1	yes	characteristic
209	C₅×#102	—	3	1	no	—
210	C₅×#102	C₂×D₃	1	1	yes	characteristic
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
215	#3011	—	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	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
220	C₃×C₅×Q₈	—	2	1	no	—
221	C₃×C₅×Q₈	—	2	1	no	—
222	C₃×C₅×Q₈	—	2	1	no	—
223	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
224	C₃×C₅×D₄	—	2	4	no	—
225	C₃×C₅×D₄	—	2	1	no	—
226	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
227	C₂×C₃×C₄×C₅	—	2	4	no	—
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	C₂×D₄	1	1	yes	characteristic
234	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
235	C₅×#67	—	2	4	no	—
236	C₅×#67	—	2	2	no	—
237	C₅×#67	—	2	4	no	—
238	C₅×#67	—	2	2	no	—
239	C₂×C₅×Dic₃	—	2	4	no	—
240	C₂×C₅×Dic₃	—	2	4	no	—
241	C₂×C₅×Dic₃	—	2	1	no	—
242	C₂×C₅×Dic₃	—	2	1	no	—
243	C₂×C₅×Dic₃	—	2	4	no	—
244	C₂×C₅×Dic₃	—	2	1	no	—
245	C₂×C₅×Dic₃	—	2	1	no	—
246	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
247	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
248	C₅×D₁₂	—	2	2	no	—
249	C₄×C₅×D₃	—	2	4	no	—
250	C₄×C₅×D₃	—	2	4	no	—
251	C₄×C₅×D₃	—	2	1	no	—
252	C₄×C₅×D₃	—	2	1	no	—
253	C₄×C₅×D₃	—	4	2	no	—
254	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
255	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
256	C₅×Dic₆	—	2	4	no	—
257	C₅×Dic₆	—	2	4	no	—
258	C₅×Dic₆	—	2	1	no	—
259	C₅×Dic₆	—	2	1	no	—
260	C₅×Dic₆	—	2	2	no	—
261	C₅×Dic₆	—	2	4	no	—
262	C₅×Dic₆	—	2	1	no	—
263	C₅×Dic₆	—	2	1	no	—
264	C₅×Dic₆	—	4	2	no	—
265	C₅×Dic₆	C₂×D₄	1	2	yes	—
266	C₅×Dic₆	C₂×D₄	1	2	yes	—
267	C₃×C₅×C₈	—	2	1	no	—
268	C₃×C₅×C₈	—	2	1	no	—
269	C₅×C₃⋊C₈	—	2	1	no	—
270	C₅×C₃⋊C₈	—	2	1	no	—
271	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
272	#1010	—	2	4	no	—
273	#1010	—	2	4	no	—
274	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
275	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
276	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
277	C₂×#237	—	2	1	no	—
278	C₂×#237	—	2	1	no	—
279	C₂×#237	C₂²×C₅	1	1	yes	characteristic
280	C₂×#237	C₂²×C₅	1	1	yes	characteristic
281	C₂×#235	—	2	1	no	—
282	C₂×#235	C₂²×C₅	1	1	yes	characteristic
283	C₂²×Dic₆	—	2	1	no	—
284	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
285	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
286	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
287	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
288	#946	C₂²×C₅	1	1	yes	characteristic
289	C₂×#216	C₂²×C₅	1	1	yes	characteristic
290	C₂×#216	C₂²×C₅	1	1	yes	characteristic
291	C₂×#216	C₂²×C₅	1	1	yes	characteristic
292	C₂×#214	C₂²×C₅	1	1	yes	characteristic
293	#924	C₂²×C₅	1	1	yes	characteristic
294	D₃×Q₁₆	—	2	4	no	—
295	#915	—	2	4	no	—
296	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
297	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
298	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
299	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
300	#897	C₂²×C₅	1	1	yes	characteristic
301	#894	—	2	1	no	—
302	#892	C₂²×C₅	1	1	yes	characteristic
303	#888	—	2	1	no	—
304	#885	—	2	1	no	—
305	#883	—	2	1	no	—
306	C₃×#103	C₂²×C₅	1	1	yes	characteristic
307	C₃×#102	C₂²×C₅	1	1	yes	characteristic
308	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
309	#835	C₂²×C₅	1	1	yes	characteristic
310	#832	C₂²×C₅	1	1	yes	characteristic
311	#830	C₂²×C₅	1	1	yes	characteristic
312	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
313	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
314	#816	C₂²×C₅	1	1	yes	characteristic
315	#816	C₂²×C₅	1	1	yes	characteristic
316	#810	C₂²×C₅	1	1	yes	characteristic
317	#810	C₂²×C₅	1	1	yes	characteristic
318	C₅×#41	—	2	2	no	—
319	C₅×#41	—	2	2	no	—
320	C₅×#41	—	3	4	no	—
321	C₅×#41	—	6	2	no	—
322	C₅×#41	—	6	2	no	—
323	C₅×#41	—	6	8	no	—
324	C₅×#41	—	6	2	no	—
325	C₅×#41	—	6	2	no	—
326	C₅×#41	—	6	8	no	—
327	C₅×#41	—	6	8	no	—
328	C₅×#41	—	6	2	no	—
329	C₂×C₅×Q₈	—	3	1	no	—
330	C₂×C₅×Q₈	—	3	4	no	—
331	C₂×C₅×Q₈	—	3	1	no	—
332	C₂×C₅×Q₈	—	3	1	no	—
333	C₂×C₅×Q₈	—	3	1	no	—
334	C₂×C₅×Q₈	—	6	1	no	—
335	C₂×C₅×Q₈	—	6	1	no	—
336	C₂×C₅×Q₈	—	6	1	no	—
337	C₂×C₅×Q₈	—	6	2	no	—
338	C₂×C₅×Q₈	—	6	2	no	—
339	C₂×C₅×Q₈	—	6	8	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	—	6	2	no	—
344	C₂×C₅×Q₈	—	6	2	no	—
345	C₂×C₅×Q₈	—	6	1	no	—
346	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
347	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
348	C₂×C₅×D₄	—	2	1	no	—
349	C₂×C₅×D₄	—	3	1	no	—
350	C₂×C₅×D₄	—	3	1	no	—
351	C₂×C₅×D₄	—	3	1	no	—
352	C₂×C₅×D₄	—	6	1	no	—
353	C₂×C₅×D₄	—	6	1	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	—	6	1	no	—
359	C₂²×C₄×C₅	—	6	1	no	—
360	C₂²×C₄×C₅	—	6	1	no	—
361	C₂²×C₄×C₅	—	6	1	no	—
362	C₂²×C₄×C₅	—	6	1	no	—
363	C₂²×C₄×C₅	—	6	1	no	—
364	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
365	C₅×Q₁₆	—	2	2	no	—
366	C₅×Q₁₆	—	6	2	no	—
367	C₅×Q₁₆	—	6	2	no	—
368	C₅×Q₁₆	—	6	2	no	—
369	C₅×Q₁₆	—	6	2	no	—
370	C₅×Q₁₆	—	6	2	no	—
371	C₅×SD₁₆	—	2	2	no	—
372	C₅×SD₁₆	—	6	2	no	—
373	C₅×M₁₆	—	6	2	no	—
374	C₂×C₅×C₈	—	3	1	no	—
375	C₂×C₅×C₈	—	3	1	no	—
376	C₂×C₅×C₈	—	6	2	no	—
377	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
378	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
379	C₅×C₄⋊C₄	—	2	1	no	—
380	C₅×C₄⋊C₄	—	3	1	no	—
381	C₅×C₄⋊C₄	—	6	1	no	—
382	C₅×C₄⋊C₄	—	6	1	no	—
383	C₅×C₄⋊C₄	—	6	1	no	—
384	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
385	C₅×C₂²⋊C₄	—	2	1	no	—
386	C₅×C₂²⋊C₄	—	6	1	no	—
387	C₅×C₂²⋊C₄	—	6	1	no	—
388	C₅×C₂²⋊C₄	—	6	1	no	—
389	C₅×C₂²⋊C₄	—	6	1	no	—
390	C₄²×C₅	—	6	1	no	—
391	C₂×2₋¹⁺⁴	—	3	1	no	—
392	C₂×#137	—	3	1	no	—
393	C₂²×Q₁₆	—	3	1	no	—
394	#536	—	3	1	no	—
395	#452	—	3	1	no	—
396	#452	—	3	1	no	—
397	#452	—	3	1	no	—
398	#452	C₅×D₃	1	1	yes	characteristic, complemented
399	#451	—	3	1	no	—
400	#451	—	3	1	no	—
401	#451	—	3	1	no	—
402	#451	—	3	1	no	—
403	#419	—	3	1	no	—
404	#416	—	3	1	no	—
405	#408	—	3	1	no	—
406	C₂²×C₃×C₅	—	2	1	no	—
407	C₂²×C₃×C₅	—	2	2	no	—
408	C₂²×C₃×C₅	—	2	1	no	—
409	C₂²×C₃×C₅	—	2	1	no	—
410	C₂²×C₃×C₅	—	4	1	no	—
411	C₂²×C₃×C₅	—	4	1	no	—
412	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₅×D₃	—	2	1	no	—
414	C₂×C₅×D₃	—	2	1	no	—
415	C₂×C₅×D₃	—	2	1	no	—
416	C₂×C₅×D₃	—	2	1	no	—
417	C₂×C₅×D₃	—	2	1	no	—
418	C₂×C₅×D₃	#120	1	2	yes	—
419	C₃×C₄×C₅	—	2	1	no	—
420	C₃×C₄×C₅	—	2	2	no	—
421	C₃×C₄×C₅	—	4	1	no	—
422	C₃×C₄×C₅	—	4	1	no	—
423	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
424	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
425	C₅×Dic₃	—	2	1	no	—
426	C₅×Dic₃	—	2	2	no	—
427	C₅×Dic₃	—	2	2	no	—
428	C₅×Dic₃	—	4	1	no	—
429	C₅×Dic₃	—	4	1	no	—
430	C₅×Dic₃	#120	1	2	yes	—
431	C₃×#41	—	2	2	no	—
432	C₃×#41	—	2	2	no	—
433	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
434	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
435	C₂×C₃×D₄	—	2	1	no	—
436	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
437	C₂²×C₃×C₄	—	2	1	no	—
438	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
439	C₂×#67	—	2	1	no	—
440	C₂×#67	—	2	1	no	—
441	C₂×#67	C₅×D₄	1	1	yes	characteristic
442	C₂×#67	C₅×D₄	1	1	yes	characteristic
443	C₂²×Dic₃	—	2	1	no	—
444	C₂²×Dic₃	—	2	1	no	—
445	C₂²×Dic₃	—	2	1	no	—
446	D₃×Q₈	—	2	2	no	—
447	D₃×Q₈	—	2	2	no	—
448	D₃×Q₈	—	2	2	no	—
449	D₃×Q₈	—	2	2	no	—
450	D₃×Q₈	—	2	2	no	—
451	D₃×Q₈	C₅×D₄	1	4	yes	—
452	#237	—	2	8	no	—
453	#237	—	2	8	no	—
454	#237	—	2	2	no	—
455	#237	—	2	2	no	—
456	#237	—	2	2	no	—
457	#237	C₅×D₄	1	4	yes	—
458	#235	—	2	8	no	—
459	#235	—	2	2	no	—
460	#235	—	2	2	no	—
461	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
462	C₂×C₄×D₃	—	2	1	no	—
463	C₂×C₄×D₃	—	2	1	no	—
464	C₂×C₄×D₃	—	2	1	no	—
465	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
466	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
467	C₂×Dic₆	—	2	8	no	—
468	C₂×Dic₆	—	2	1	no	—
469	C₂×Dic₆	—	2	1	no	—
470	C₂×Dic₆	—	2	1	no	—
471	C₂×Dic₆	—	2	2	no	—
472	C₂×Dic₆	—	2	2	no	—
473	C₂×Dic₆	—	2	1	no	—
474	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
475	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
476	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
477	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
478	C₃×Q₁₆	—	2	2	no	—
479	C₃×SD₁₆	—	2	2	no	—
480	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
481	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
482	C₃×C₄⋊C₄	—	2	1	no	—
483	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
484	C₃×C₂²⋊C₄	—	2	1	no	—
485	#217	—	2	1	no	—
486	#216	—	2	2	no	—
487	#216	—	2	2	no	—
488	#216	—	2	2	no	—
489	#214	—	2	2	no	—
490	(C₂×D₃)⋊C₄	—	2	1	no	—
491	(C₂×D₃)⋊C₄	—	2	1	no	—
492	(C₂×D₃)⋊C₄	—	2	1	no	—
493	C₄⋊Dic₃	—	2	1	no	—
494	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
495	Dic₃⋊C₄	—	2	1	no	—
496	Dic₃⋊C₄	—	2	1	no	—
497	C₄×Dic₃	—	2	1	no	—
498	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
499	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
500	Dic₁₂	—	2	2	no	—
501	Dic₁₂	—	2	2	no	—
502	ΓL(1,𝔽₂₅)	—	2	2	no	—
503	D₃×C₈	—	2	2	no	—
504	C₂³×C₅	—	2	1	no	—
505	C₂³×C₅	—	3	1	no	—
506	C₂³×C₅	—	3	1	no	—
507	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
508	C₅×Q₈	—	2	1	no	—
509	C₅×Q₈	—	2	1	no	—
510	C₅×Q₈	—	2	1	no	—
511	C₅×Q₈	—	3	2	no	—
512	C₅×Q₈	—	3	2	no	—
513	C₅×Q₈	—	6	2	no	—
514	C₅×Q₈	—	6	4	no	—
515	C₅×Q₈	—	6	4	no	—
516	C₅×Q₈	—	6	4	no	—
517	C₅×Q₈	—	6	1	no	—
518	C₅×Q₈	—	6	1	no	—
519	C₅×Q₈	—	6	1	no	—
520	C₅×Q₈	—	6	1	no	—
521	C₅×Q₈	—	12	2	no	—
522	C₅×Q₈	D₃×D₄	1	2	yes	—
523	C₅×D₄	—	2	4	no	—
524	C₅×D₄	—	2	1	no	—
525	C₅×D₄	—	6	2	no	—
526	C₅×D₄	—	6	2	no	—
527	C₅×D₄	—	6	2	no	—
528	C₅×D₄	—	6	4	no	—
529	C₅×D₄	—	6	4	no	—
530	C₅×D₄	D₃×D₄	1	2	yes	—
531	C₂×C₄×C₅	—	2	4	no	—
532	C₂×C₄×C₅	—	2	1	no	—
533	C₂×C₄×C₅	—	2	1	no	—
534	C₂×C₄×C₅	—	2	1	no	—
535	C₂×C₄×C₅	—	2	1	no	—
536	C₂×C₄×C₅	—	2	1	no	—
537	C₂×C₄×C₅	—	3	1	no	—
538	C₂×C₄×C₅	—	3	2	no	—
539	C₂×C₄×C₅	—	3	2	no	—
540	C₂×C₄×C₅	—	3	1	no	—
541	C₂×C₄×C₅	—	6	4	no	—
542	C₂×C₄×C₅	—	6	4	no	—
543	C₂×C₄×C₅	—	6	4	no	—
544	C₂×C₄×C₅	—	6	4	no	—
545	C₂×C₄×C₅	—	6	4	no	—
546	C₂×C₄×C₅	—	6	1	no	—
547	C₂×C₄×C₅	—	6	1	no	—
548	C₂×C₄×C₅	—	6	1	no	—
549	C₂×C₄×C₅	—	6	1	no	—
550	C₂×C₄×C₅	—	6	1	no	—
551	C₂×C₄×C₅	—	6	1	no	—
552	C₂×C₄×C₅	—	12	2	no	—
553	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
554	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
555	C₅×C₈	—	2	1	no	—
556	C₅×C₈	—	2	1	no	—
557	C₅×C₈	—	6	1	no	—
558	C₅×C₈	—	6	1	no	—
559	2₋¹⁺⁴	—	6	4	no	—
560	2₋¹⁺⁴	—	6	4	no	—
561	C₂×#41	—	3	1	no	—
562	C₂×#41	—	3	1	no	—
563	C₂×#41	—	3	1	no	—
564	C₂×#41	—	6	1	no	—
565	C₂×#41	—	6	1	no	—
566	C₂×#41	—	6	1	no	—
567	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
568	C₂²×Q₈	—	3	1	no	—
569	C₂²×Q₈	—	3	1	no	—
570	C₂²×Q₈	—	3	1	no	—
571	C₂²×Q₈	—	3	1	no	—
572	C₂²×Q₈	—	6	1	no	—
573	#137	—	6	4	no	—
574	C₂×Q₁₆	—	3	1	no	—
575	C₂×Q₁₆	—	3	1	no	—
576	C₂×Q₁₆	—	3	1	no	—
577	C₂×Q₁₆	—	3	1	no	—
578	C₂×Q₁₆	—	3	1	no	—
579	C₂×Q₁₆	—	6	4	no	—
580	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
581	C₂×SD₁₆	—	3	1	no	—
582	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
583	C₂×M₁₆	—	3	1	no	—
584	C₂²×C₈	—	3	1	no	—
585	C₄⋊Q₈	—	6	1	no	—
586	#124	—	6	1	no	—
587	#123	—	6	1	no	—
588	#123	—	6	1	no	—
589	C₂²⋊Q₈	—	3	1	no	—
590	C₂²⋊Q₈	—	3	1	no	—
591	C₂²⋊Q₈	—	3	1	no	—
592	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
593	#117	—	3	1	no	—
594	#103	—	3	1	no	—
595	#103	—	3	1	no	—
596	#103	—	3	1	no	—
597	#103	—	3	1	no	—
598	#103	—	3	1	no	—
599	#103	C₂×C₅×D₃	1	1	yes	characteristic
600	#102	—	3	1	no	—
601	#102	C₂×C₅×D₃	1	1	yes	characteristic
602	C₂²⋊C₈	—	3	1	no	—
603	C₂²⋊C₈	—	3	1	no	—
604	C₂²⋊C₈	—	3	1	no	—
605	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
606	C₂×C₃×C₅	—	4	1	no	—
607	C₂×C₃×C₅	—	4	2	no	—
608	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
609	C₂×C₃×C₅	#578	1	1	yes	characteristic
610	C₂×C₃×C₅	#578	1	1	yes	characteristic
611	C₅×D₃	—	2	2	no	—
612	C₅×D₃	—	4	1	no	—
613	C₂³×C₃	—	2	1	no	—
614	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
615	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
616	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
617	C₃×Q₈	—	2	1	no	—
618	C₃×Q₈	—	2	1	no	—
619	C₃×Q₈	—	2	1	no	—
620	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
621	C₃×D₄	—	2	4	no	—
622	C₃×D₄	—	2	1	no	—
623	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
624	C₂×C₃×C₄	—	2	4	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
631	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
632	#67	—	2	4	no	—
633	#67	—	2	2	no	—
634	#67	—	2	4	no	—
635	#67	—	2	2	no	—
636	C₂×Dic₃	—	2	4	no	—
637	C₂×Dic₃	—	2	4	no	—
638	C₂×Dic₃	—	2	1	no	—
639	C₂×Dic₃	—	2	1	no	—
640	C₂×Dic₃	—	2	4	no	—
641	C₂×Dic₃	—	2	1	no	—
642	C₂×Dic₃	—	2	1	no	—
643	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
644	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
645	D₁₂	—	2	2	no	—
646	C₄×D₃	—	2	4	no	—
647	C₄×D₃	—	2	4	no	—
648	C₄×D₃	—	2	1	no	—
649	C₄×D₃	—	2	1	no	—
650	C₄×D₃	—	4	2	no	—
651	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
652	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
653	Dic₆	—	2	4	no	—
654	Dic₆	—	2	4	no	—
655	Dic₆	—	2	1	no	—
656	Dic₆	—	2	1	no	—
657	Dic₆	—	2	2	no	—
658	Dic₆	—	2	4	no	—
659	Dic₆	—	2	1	no	—
660	Dic₆	—	2	1	no	—
661	Dic₆	—	4	2	no	—
662	Dic₆	C₂×C₅×D₄	1	2	yes	—
663	Dic₆	C₂×C₅×D₄	1	2	yes	—
664	C₃×C₈	—	2	1	no	—
665	C₃×C₈	—	2	1	no	—
666	C₃⋊C₈	—	2	1	no	—
667	C₃⋊C₈	—	2	1	no	—
668	C₂²×C₅	—	2	1	no	—
669	C₂²×C₅	—	2	1	no	—
670	C₂²×C₅	—	2	1	no	—
671	C₂²×C₅	—	2	2	no	—
672	C₂²×C₅	—	3	2	no	—
673	C₂²×C₅	—	4	1	no	—
674	C₂²×C₅	—	4	1	no	—
675	C₂²×C₅	—	6	1	no	—
676	C₂²×C₅	—	6	1	no	—
677	C₂²×C₅	—	6	1	no	—
678	C₂²×C₅	—	6	1	no	—
679	C₂²×C₅	—	6	1	no	—
680	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
681	C₄×C₅	—	2	1	no	—
682	C₄×C₅	—	2	2	no	—
683	C₄×C₅	—	3	2	no	—
684	C₄×C₅	—	4	1	no	—
685	C₄×C₅	—	4	1	no	—
686	C₄×C₅	—	6	1	no	—
687	C₄×C₅	—	6	2	no	—
688	C₄×C₅	—	6	2	no	—
689	C₄×C₅	—	12	1	no	—
690	C₄×C₅	—	12	1	no	—
691	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
692	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
693	#41	—	2	2	no	—
694	#41	—	2	2	no	—
695	#41	—	3	4	no	—
696	#41	—	6	2	no	—
697	#41	—	6	2	no	—
698	#41	—	6	8	no	—
699	#41	—	6	2	no	—
700	#41	—	6	2	no	—
701	#41	—	6	8	no	—
702	#41	—	6	8	no	—
703	#41	—	6	2	no	—
704	C₂×Q₈	—	3	1	no	—
705	C₂×Q₈	—	3	4	no	—
706	C₂×Q₈	—	3	1	no	—
707	C₂×Q₈	—	3	1	no	—
708	C₂×Q₈	—	3	1	no	—
709	C₂×Q₈	—	6	1	no	—
710	C₂×Q₈	—	6	1	no	—
711	C₂×Q₈	—	6	1	no	—
712	C₂×Q₈	—	6	2	no	—
713	C₂×Q₈	—	6	2	no	—
714	C₂×Q₈	—	6	8	no	—
715	C₂×Q₈	—	6	2	no	—
716	C₂×Q₈	—	6	2	no	—
717	C₂×Q₈	—	6	2	no	—
718	C₂×Q₈	—	6	2	no	—
719	C₂×Q₈	—	6	2	no	—
720	C₂×Q₈	—	6	1	no	—
721	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
722	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
723	C₂×D₄	—	2	1	no	—
724	C₂×D₄	—	3	1	no	—
725	C₂×D₄	—	3	1	no	—
726	C₂×D₄	—	3	1	no	—
727	C₂×D₄	—	6	1	no	—
728	C₂×D₄	—	6	1	no	—
729	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	3	1	no	—
732	C₂²×C₄	—	3	1	no	—
733	C₂²×C₄	—	6	1	no	—
734	C₂²×C₄	—	6	1	no	—
735	C₂²×C₄	—	6	1	no	—
736	C₂²×C₄	—	6	1	no	—
737	C₂²×C₄	—	6	1	no	—
738	C₂²×C₄	—	6	1	no	—
739	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
740	Q₁₆	—	2	2	no	—
741	Q₁₆	—	6	2	no	—
742	Q₁₆	—	6	2	no	—
743	Q₁₆	—	6	2	no	—
744	Q₁₆	—	6	2	no	—
745	Q₁₆	—	6	2	no	—
746	SD₁₆	—	2	2	no	—
747	SD₁₆	—	6	2	no	—
748	M₁₆	—	6	2	no	—
749	C₂×C₈	—	3	1	no	—
750	C₂×C₈	—	3	1	no	—
751	C₂×C₈	—	6	2	no	—
752	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
753	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	3	1	no	—
756	C₄⋊C₄	—	6	1	no	—
757	C₄⋊C₄	—	6	1	no	—
758	C₄⋊C₄	—	6	1	no	—
759	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	6	1	no	—
762	C₂²⋊C₄	—	6	1	no	—
763	C₂²⋊C₄	—	6	1	no	—
764	C₂²⋊C₄	—	6	1	no	—
765	C₄²	—	6	1	no	—
766	C₃×C₅	#3011	1	1	yes	characteristic, complemented, Hall
767	C₂²×C₃	—	2	1	no	—
768	C₂²×C₃	—	2	2	no	—
769	C₂²×C₃	—	2	1	no	—
770	C₂²×C₃	—	2	1	no	—
771	C₂²×C₃	—	4	1	no	—
772	C₂²×C₃	—	4	1	no	—
773	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
774	C₂×D₃	—	2	1	no	—
775	C₂×D₃	—	2	1	no	—
776	C₂×D₃	—	2	1	no	—
777	C₂×D₃	—	2	1	no	—
778	C₂×D₃	—	2	1	no	—
779	C₂×D₃	C₅×#120	1	2	yes	—
780	C₃×C₄	—	2	1	no	—
781	C₃×C₄	—	2	2	no	—
782	C₃×C₄	—	4	1	no	—
783	C₃×C₄	—	4	1	no	—
784	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
785	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
786	Dic₃	—	2	1	no	—
787	Dic₃	—	2	2	no	—
788	Dic₃	—	2	2	no	—
789	Dic₃	—	4	1	no	—
790	Dic₃	—	4	1	no	—
791	Dic₃	C₅×#120	1	2	yes	—
792	C₂×C₅	—	4	1	no	—
793	C₂×C₅	—	4	2	no	—
794	C₂×C₅	—	6	2	no	—
795	C₂×C₅	—	12	1	no	—
796	C₂×C₅	D₃×#120	1	1	yes	characteristic
797	C₂×C₅	#5771	1	1	yes	characteristic
798	C₂×C₅	#5779	1	1	yes	characteristic
799	C₂³	—	2	1	no	—
800	C₂³	—	3	1	no	—
801	C₂³	—	3	1	no	—
802	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
803	Q₈	—	2	1	no	—
804	Q₈	—	2	1	no	—
805	Q₈	—	2	1	no	—
806	Q₈	—	3	2	no	—
807	Q₈	—	3	2	no	—
808	Q₈	—	6	2	no	—
809	Q₈	—	6	4	no	—
810	Q₈	—	6	4	no	—
811	Q₈	—	6	4	no	—
812	Q₈	—	6	1	no	—
813	Q₈	—	6	1	no	—
814	Q₈	—	6	1	no	—
815	Q₈	—	6	1	no	—
816	Q₈	—	12	2	no	—
817	Q₈	C₅×D₃×D₄	1	2	yes	—
818	D₄	—	2	4	no	—
819	D₄	—	2	1	no	—
820	D₄	—	6	2	no	—
821	D₄	—	6	2	no	—
822	D₄	—	6	2	no	—
823	D₄	—	6	4	no	—
824	D₄	—	6	4	no	—
825	D₄	C₅×D₃×D₄	1	2	yes	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	1	no	—
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	—	3	1	no	—
833	C₂×C₄	—	3	2	no	—
834	C₂×C₄	—	3	2	no	—
835	C₂×C₄	—	3	1	no	—
836	C₂×C₄	—	6	4	no	—
837	C₂×C₄	—	6	4	no	—
838	C₂×C₄	—	6	4	no	—
839	C₂×C₄	—	6	4	no	—
840	C₂×C₄	—	6	4	no	—
841	C₂×C₄	—	6	1	no	—
842	C₂×C₄	—	6	1	no	—
843	C₂×C₄	—	6	1	no	—
844	C₂×C₄	—	6	1	no	—
845	C₂×C₄	—	6	1	no	—
846	C₂×C₄	—	6	1	no	—
847	C₂×C₄	—	12	2	no	—
848	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
849	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
850	C₈	—	2	1	no	—
851	C₈	—	2	1	no	—
852	C₈	—	6	1	no	—
853	C₈	—	6	1	no	—
854	C₂×C₃	—	4	1	no	—
855	C₂×C₃	—	4	2	no	—
856	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
857	C₂×C₃	C₅×#578	1	1	yes	characteristic
858	C₂×C₃	C₅×#578	1	1	yes	characteristic
859	D₃	—	2	2	no	—
860	D₃	—	4	1	no	—
861	C₅	#80230	1	1	yes	characteristic, direct product factor, Sylow
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	3	2	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	6	1	no	—
870	C₂²	—	6	1	no	—
871	C₂²	—	6	1	no	—
872	C₂²	—	6	1	no	—
873	C₂²	—	6	1	no	—
874	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
875	C₄	—	2	1	no	—
876	C₄	—	2	2	no	—
877	C₄	—	3	2	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	1	no	—
880	C₄	—	6	1	no	—
881	C₄	—	6	2	no	—
882	C₄	—	6	2	no	—
883	C₄	—	12	1	no	—
884	C₄	—	12	1	no	—
885	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
886	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
887	C₃	C₅×#3011	1	1	yes	characteristic, complemented, Sylow
888	C₂	—	4	1	no	—
889	C₂	—	4	2	no	—
890	C₂	—	6	2	no	—
891	C₂	—	12	1	no	—
892	C₂	C₅×D₃×#120	1	1	yes	characteristic
893	C₂	C₅×#5771	1	1	yes	characteristic
894	C₂	C₅×#5779	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×#1010	C₂
hypercenter	C₅×#452	D₃
hypocenter	C₃	C₅×#3011
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×D₃×Q₁₆	C₂	semidirect
3. C₂×C₅×#915	C₂	semidirect
4. C₅×#5628	C₂	semidirect
5. C₃×C₅×#452	C₂	semidirect
6. C₅×#5239	C₂	semidirect
7. C₅×#5186	C₂	semidirect
8. C₅×#5173	C₂	semidirect
9. C₅×#5050	C₂	semidirect
10. C₅×#4809	C₂	semidirect
11. C₅×#4802	C₂	semidirect
12. C₅×#4783	C₂	semidirect
13. C₅×#4772	C₂	semidirect
14. C₅×#4739	C₂	semidirect
15. C₅×#4727	C₂	semidirect
64. #80230	C₅	direct (N × H)
72. C₅×#452	D₃	semidirect
154. C₂×D₃×Q₁₆	C₂×C₅	semidirect
155. C₂×#915	C₂×C₅	semidirect
156. #5628	C₂×C₅	semidirect
157. C₃×#452	C₂×C₅	semidirect
158. #5239	C₂×C₅	semidirect
159. #5186	C₂×C₅	semidirect
160. #5173	C₂×C₅	semidirect
161. #5050	C₂×C₅	semidirect
162. #4809	C₂×C₅	semidirect
163. #4802	C₂×C₅	semidirect
164. #4783	C₂×C₅	semidirect
165. #4772	C₂×C₅	semidirect
166. #4739	C₂×C₅	semidirect
167. #4727	C₂×C₅	semidirect
398. #452	C₅×D₃	semidirect
766. C₃×C₅	#3011	semidirect
861. C₅	#80230	direct (N × H)
887. C₃	C₅×#3011	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#1010	2
C₂×C₅×D₃×Q₁₆	2
C₂×C₅×#915	2
C₅×#5628	2
C₃×C₅×#452	2
C₅×#5239	2
C₅×#5186	2
C₅×#5173	2
C₅×#5050	2
C₅×#4809	2
C₅×#4802	2
C₅×#4783	2
C₅×#4772	2
C₅×#4739	2
C₅×#4727	2
C₅×#3011	3
#80230	5

Subgroups — C5×#80230 #14424531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80230 #14424531