Subgroups — C₅×#80088 #14424804

Order 1920.

1424 conjugacy classes of subgroups.

The subgroup lattice has 920 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, complemented
2	C₂×C₅×#915	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#912	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5608	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5239	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5170	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5158	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5040	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4809	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4783	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4771	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×#3013	—	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×#237	—	2	1	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×#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×SD₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
33	C₃×C₅×#121	C₂²	1	1	yes	characteristic
34	C₂×C₅×#216	C₂²	1	1	yes	characteristic
35	C₅×#939	—	2	1	no	—
36	C₅×#938	—	2	1	no	—
37	C₅×#938	C₂²	1	1	yes	characteristic
38	C₂×C₅×#214	C₂²	1	1	yes	characteristic
39	C₂×C₅×#214	C₂²	1	1	yes	characteristic
40	C₂×C₅×#214	C₂²	1	1	yes	characteristic
41	C₅×#924	C₂²	1	1	yes	characteristic
42	C₅×#915	—	2	4	no	—
43	C₅×#912	—	2	4	no	—
44	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
45	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
46	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
47	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
48	C₅×#897	C₂²	1	1	yes	characteristic
49	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₅×#884	—	2	1	no	—
51	C₅×#878	—	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	#80088	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	C₂×C₅×#135	—	3	1	no	—
68	C₅×#537	—	3	1	no	—
69	C₅×#452	—	3	1	no	—
70	C₅×#452	—	3	1	no	—
71	C₅×#451	—	3	1	no	—
72	C₅×#451	—	3	1	no	—
73	C₅×#449	—	3	1	no	—
74	C₅×#449	D₃	1	1	yes	characteristic, complemented
75	C₅×#448	—	3	1	no	—
76	C₅×#448	—	3	1	no	—
77	C₅×#417	—	3	1	no	—
78	C₂×C₅×#103	—	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×D₄	—	2	1	no	—
84	C₂×C₃×C₅×D₄	—	2	1	no	—
85	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
87	C₂²×C₃×C₄×C₅	—	2	1	no	—
88	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₂×C₅×#67	—	2	1	no	—
90	C₂×C₅×#67	—	2	1	no	—
91	C₂×C₅×#67	—	2	1	no	—
92	C₂×C₅×#67	—	2	1	no	—
93	C₂×C₅×#67	D₄	1	1	yes	characteristic
94	C₂×C₅×#67	D₄	1	1	yes	characteristic
95	C₂²×C₅×Dic₃	—	2	1	no	—
96	C₂²×C₅×Dic₃	—	2	1	no	—
97	C₂²×C₅×Dic₃	—	2	1	no	—
98	C₂²×C₅×Dic₃	—	2	1	no	—
99	C₅×D₃×Q₈	—	2	2	no	—
100	C₅×D₃×Q₈	—	2	2	no	—
101	C₅×D₃×Q₈	—	2	2	no	—
102	C₅×D₃×Q₈	D₄	1	4	yes	complemented
103	C₅×#237	—	2	8	no	—
104	C₅×#237	—	2	8	no	—
105	C₅×#237	—	2	2	no	—
106	C₅×#237	—	2	2	no	—
107	C₅×#237	—	2	2	no	—
108	C₅×#237	—	2	2	no	—
109	C₅×#237	—	2	2	no	—
110	C₅×#237	D₄	1	4	yes	complemented
111	C₅×#235	—	2	8	no	—
112	C₅×#235	—	2	2	no	—
113	C₅×#235	—	2	2	no	—
114	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
115	C₂×C₄×C₅×D₃	—	2	1	no	—
116	C₂×C₄×C₅×D₃	—	2	1	no	—
117	C₂×C₄×C₅×D₃	—	2	1	no	—
118	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
119	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
120	C₂×C₅×Dic₆	—	2	8	no	—
121	C₂×C₅×Dic₆	—	2	1	no	—
122	C₂×C₅×Dic₆	—	2	1	no	—
123	C₂×C₅×Dic₆	—	2	1	no	—
124	C₂×C₅×Dic₆	—	2	2	no	—
125	C₂×C₅×Dic₆	—	2	2	no	—
126	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
127	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
128	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
129	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
130	C₃×C₅×SD₁₆	—	2	2	no	—
131	C₃×C₅×D₈	—	2	2	no	—
132	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
134	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
136	C₅×#217	—	2	1	no	—
137	C₅×#217	—	2	1	no	—
138	C₅×#216	—	2	2	no	—
139	C₅×#214	—	2	2	no	—
140	C₅×#214	—	2	2	no	—
141	C₅×#214	—	2	2	no	—
142	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
143	C₅×C₄⋊Dic₃	—	2	1	no	—
144	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
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×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, complemented
154	C₂×#915	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×#912	C₂×C₅	1	1	yes	characteristic, complemented
156	#5608	C₂×C₅	1	1	yes	characteristic, complemented
157	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
158	#5239	C₂×C₅	1	1	yes	characteristic, complemented
159	#5170	C₂×C₅	1	1	yes	characteristic, complemented
160	#5158	C₂×C₅	1	1	yes	characteristic, complemented
161	#5040	C₂×C₅	1	1	yes	characteristic, complemented
162	#4809	C₂×C₅	1	1	yes	characteristic, complemented
163	D₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
164	#4783	C₂×C₅	1	1	yes	characteristic, complemented
165	#4771	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	—	3	1	no	—
174	C₂×C₅×#41	—	6	1	no	—
175	C₂×C₅×#41	—	6	1	no	—
176	C₂×C₅×#41	—	6	1	no	—
177	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
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	C₅×#135	—	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×SD₁₆	—	3	1	no	—
188	C₂×C₅×SD₁₆	—	3	1	no	—
189	C₂×C₅×SD₁₆	—	3	1	no	—
190	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
191	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
192	C₂×C₅×M₁₆	—	3	1	no	—
193	C₂²×C₅×C₈	—	3	1	no	—
194	C₅×C₂²⋊Q₈	—	3	1	no	—
195	C₅×C₂²⋊Q₈	—	3	1	no	—
196	C₅×C₂²⋊Q₈	—	6	1	no	—
197	C₅×#121	—	3	1	no	—
198	C₅×#121	—	6	1	no	—
199	C₅×#121	—	6	1	no	—
200	C₅×#121	—	6	1	no	—
201	C₅×#121	C₂×D₃	1	1	yes	characteristic
202	C₂×C₅×C₄⋊C₄	—	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	#3013	—	3	1	no	Sylow
216	C₂³×C₃×C₅	—	2	1	no	—
217	C₂³×C₃×C₅	—	2	1	no	—
218	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
221	C₃×C₅×Q₈	—	2	1	no	—
222	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
223	C₃×C₅×D₄	—	2	4	no	—
224	C₃×C₅×D₄	—	2	1	no	—
225	C₃×C₅×D₄	—	2	1	no	—
226	C₃×C₅×D₄	—	2	1	no	—
227	C₃×C₅×D₄	—	8	1	no	—
228	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
229	C₂×C₃×C₄×C₅	—	2	4	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	C₂×D₄	1	1	yes	characteristic
235	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
236	C₅×#67	—	2	4	no	—
237	C₅×#67	—	2	2	no	—
238	C₅×#67	—	2	4	no	—
239	C₅×#67	—	2	2	no	—
240	C₅×#67	—	4	2	no	—
241	C₅×#67	—	8	1	no	—
242	C₂×C₅×Dic₃	—	2	4	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	—	2	4	no	—
247	C₂×C₅×Dic₃	—	2	1	no	—
248	C₂×C₅×Dic₃	—	2	1	no	—
249	C₂×C₅×Dic₃	—	4	2	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	2	no	—
253	C₄×C₅×D₃	—	2	4	no	—
254	C₄×C₅×D₃	—	2	4	no	—
255	C₄×C₅×D₃	—	2	1	no	—
256	C₄×C₅×D₃	—	2	1	no	—
257	C₄×C₅×D₃	—	8	1	no	—
258	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
259	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
260	C₅×Dic₆	—	2	4	no	—
261	C₅×Dic₆	—	2	4	no	—
262	C₅×Dic₆	—	2	1	no	—
263	C₅×Dic₆	—	2	1	no	—
264	C₅×Dic₆	—	2	2	no	—
265	C₅×Dic₆	—	2	4	no	—
266	C₅×Dic₆	—	2	1	no	—
267	C₅×Dic₆	—	2	1	no	—
268	C₅×Dic₆	C₂×D₄	1	2	yes	—
269	C₅×Dic₆	C₂×D₄	1	2	yes	—
270	C₃×C₅×C₈	—	2	1	no	—
271	C₃×C₅×C₈	—	2	1	no	—
272	C₅×C₃⋊C₈	—	2	1	no	—
273	C₅×C₃⋊C₈	—	2	1	no	—
274	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
275	#1010	—	2	4	no	—
276	#1010	—	2	4	no	—
277	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
278	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
279	C₂×#237	—	2	1	no	—
280	C₂×#237	—	2	1	no	—
281	C₂×#237	C₂²×C₅	1	1	yes	characteristic
282	C₂×#237	C₂²×C₅	1	1	yes	characteristic
283	C₂×#237	C₂²×C₅	1	1	yes	characteristic
284	C₂×#235	—	2	1	no	—
285	C₂×#235	C₂²×C₅	1	1	yes	characteristic
286	C₂²×Dic₆	—	2	1	no	—
287	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
288	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
289	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
290	C₃×#121	C₂²×C₅	1	1	yes	characteristic
291	C₂×#216	C₂²×C₅	1	1	yes	characteristic
292	#939	—	2	1	no	—
293	#938	—	2	1	no	—
294	#938	C₂²×C₅	1	1	yes	characteristic
295	C₂×#214	C₂²×C₅	1	1	yes	characteristic
296	C₂×#214	C₂²×C₅	1	1	yes	characteristic
297	C₂×#214	C₂²×C₅	1	1	yes	characteristic
298	#924	C₂²×C₅	1	1	yes	characteristic
299	#915	—	2	4	no	—
300	#912	—	2	4	no	—
301	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
302	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
303	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
304	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
305	#897	C₂²×C₅	1	1	yes	characteristic
306	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
307	#884	—	2	1	no	—
308	#878	—	2	1	no	—
309	C₃×#103	C₂²×C₅	1	1	yes	characteristic
310	C₃×#102	C₂²×C₅	1	1	yes	characteristic
311	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
312	#835	C₂²×C₅	1	1	yes	characteristic
313	#832	C₂²×C₅	1	1	yes	characteristic
314	#830	C₂²×C₅	1	1	yes	characteristic
315	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
316	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
317	#816	C₂²×C₅	1	1	yes	characteristic
318	#816	C₂²×C₅	1	1	yes	characteristic
319	#810	C₂²×C₅	1	1	yes	characteristic
320	#810	C₂²×C₅	1	1	yes	characteristic
321	C₅×#41	—	2	2	no	—
322	C₅×#41	—	2	2	no	—
323	C₅×#41	—	3	4	no	—
324	C₅×#41	—	6	2	no	—
325	C₅×#41	—	6	2	no	—
326	C₅×#41	—	6	8	no	—
327	C₅×#41	—	6	2	no	—
328	C₅×#41	—	6	2	no	—
329	C₅×#41	—	6	2	no	—
330	C₅×#41	—	6	2	no	—
331	C₅×#41	—	6	8	no	—
332	C₅×#41	—	6	8	no	—
333	C₅×#41	—	6	2	no	—
334	C₂×C₅×Q₈	—	3	1	no	—
335	C₂×C₅×Q₈	—	3	4	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	1	no	—
341	C₂×C₅×Q₈	—	6	2	no	—
342	C₂×C₅×Q₈	—	6	2	no	—
343	C₂×C₅×Q₈	—	6	8	no	—
344	C₂×C₅×Q₈	—	6	2	no	—
345	C₂×C₅×Q₈	—	6	2	no	—
346	C₂×C₅×Q₈	—	6	2	no	—
347	C₂×C₅×Q₈	—	6	1	no	—
348	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
349	C₂×C₅×D₄	—	2	1	no	—
350	C₂×C₅×D₄	—	2	1	no	—
351	C₂×C₅×D₄	—	3	1	no	—
352	C₂×C₅×D₄	—	3	1	no	—
353	C₂×C₅×D₄	—	3	1	no	—
354	C₂×C₅×D₄	—	6	1	no	—
355	C₂×C₅×D₄	—	6	1	no	—
356	C₂×C₅×D₄	—	6	1	no	—
357	C₂×C₅×D₄	—	6	1	no	—
358	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
359	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
360	C₂²×C₄×C₅	—	2	1	no	—
361	C₂²×C₄×C₅	—	3	1	no	—
362	C₂²×C₄×C₅	—	3	1	no	—
363	C₂²×C₄×C₅	—	6	1	no	—
364	C₂²×C₄×C₅	—	6	1	no	—
365	C₂²×C₄×C₅	—	6	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×Q₁₆	—	6	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×D₈	—	2	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	—	3	1	no	—
386	C₅×C₄⋊C₄	—	6	1	no	—
387	C₅×C₄⋊C₄	—	6	1	no	—
388	C₅×C₄⋊C₄	—	6	1	no	—
389	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
390	C₅×C₂²⋊C₄	—	2	1	no	—
391	C₅×C₂²⋊C₄	—	6	1	no	—
392	C₅×C₂²⋊C₄	—	6	1	no	—
393	C₅×C₂²⋊C₄	—	6	1	no	—
394	C₂×2₋¹⁺⁴	—	3	1	no	—
395	C₂×#137	—	3	1	no	—
396	C₂×#135	—	3	1	no	—
397	#537	—	3	1	no	—
398	#452	—	3	1	no	—
399	#452	—	3	1	no	—
400	#451	—	3	1	no	—
401	#451	—	3	1	no	—
402	#449	—	3	1	no	—
403	#449	C₅×D₃	1	1	yes	characteristic, complemented
404	#448	—	3	1	no	—
405	#448	—	3	1	no	—
406	#417	—	3	1	no	—
407	C₂×#103	—	3	1	no	—
408	#408	—	3	1	no	—
409	C₂²×C₃×C₅	—	2	1	no	—
410	C₂²×C₃×C₅	—	2	2	no	—
411	C₂²×C₃×C₅	—	2	1	no	—
412	C₂²×C₃×C₅	—	2	1	no	—
413	C₂²×C₃×C₅	—	4	1	no	—
414	C₂²×C₃×C₅	—	4	1	no	—
415	C₂²×C₃×C₅	—	4	1	no	—
416	C₂²×C₃×C₅	—	4	1	no	—
417	C₂²×C₃×C₅	—	4	1	no	—
418	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
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	1	no	—
423	C₂×C₅×D₃	—	2	1	no	—
424	C₂×C₅×D₃	#120	1	2	yes	—
425	C₃×C₄×C₅	—	2	1	no	—
426	C₃×C₄×C₅	—	2	2	no	—
427	C₃×C₄×C₅	—	4	1	no	—
428	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
429	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
430	C₅×Dic₃	—	2	1	no	—
431	C₅×Dic₃	—	2	2	no	—
432	C₅×Dic₃	—	2	2	no	—
433	C₅×Dic₃	—	4	1	no	—
434	C₅×Dic₃	—	4	1	no	—
435	C₅×Dic₃	#120	1	2	yes	—
436	C₃×#41	—	2	2	no	—
437	C₃×#41	—	2	2	no	—
438	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
439	C₂×C₃×D₄	—	2	1	no	—
440	C₂×C₃×D₄	—	2	1	no	—
441	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
442	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
443	C₂²×C₃×C₄	—	2	1	no	—
444	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
445	C₂×#67	—	2	1	no	—
446	C₂×#67	—	2	1	no	—
447	C₂×#67	—	2	1	no	—
448	C₂×#67	—	2	1	no	—
449	C₂×#67	C₅×D₄	1	1	yes	characteristic
450	C₂×#67	C₅×D₄	1	1	yes	characteristic
451	C₂²×Dic₃	—	2	1	no	—
452	C₂²×Dic₃	—	2	1	no	—
453	C₂²×Dic₃	—	2	1	no	—
454	C₂²×Dic₃	—	2	1	no	—
455	D₃×Q₈	—	2	2	no	—
456	D₃×Q₈	—	2	2	no	—
457	D₃×Q₈	—	2	2	no	—
458	D₃×Q₈	C₅×D₄	1	4	yes	complemented
459	#237	—	2	8	no	—
460	#237	—	2	8	no	—
461	#237	—	2	2	no	—
462	#237	—	2	2	no	—
463	#237	—	2	2	no	—
464	#237	—	2	2	no	—
465	#237	—	2	2	no	—
466	#237	C₅×D₄	1	4	yes	complemented
467	#235	—	2	8	no	—
468	#235	—	2	2	no	—
469	#235	—	2	2	no	—
470	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
471	C₂×C₄×D₃	—	2	1	no	—
472	C₂×C₄×D₃	—	2	1	no	—
473	C₂×C₄×D₃	—	2	1	no	—
474	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
475	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
476	C₂×Dic₆	—	2	8	no	—
477	C₂×Dic₆	—	2	1	no	—
478	C₂×Dic₆	—	2	1	no	—
479	C₂×Dic₆	—	2	1	no	—
480	C₂×Dic₆	—	2	2	no	—
481	C₂×Dic₆	—	2	2	no	—
482	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
483	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
484	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
485	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
486	C₃×SD₁₆	—	2	2	no	—
487	C₃×D₈	—	2	2	no	—
488	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
489	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
490	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
491	C₃×C₂²⋊C₄	—	2	1	no	—
492	#217	—	2	1	no	—
493	#217	—	2	1	no	—
494	#216	—	2	2	no	—
495	#214	—	2	2	no	—
496	#214	—	2	2	no	—
497	#214	—	2	2	no	—
498	(C₂×D₃)⋊C₄	—	2	1	no	—
499	C₄⋊Dic₃	—	2	1	no	—
500	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
501	Dic₃⋊C₄	—	2	1	no	—
502	Dic₃⋊C₄	—	2	1	no	—
503	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
504	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
505	Dic₁₂	—	2	2	no	—
506	Dic₁₂	—	2	2	no	—
507	ΓL(1,𝔽₂₅)	—	2	2	no	—
508	D₃×C₈	—	2	2	no	—
509	C₂³×C₅	—	2	1	no	—
510	C₂³×C₅	—	2	1	no	—
511	C₂³×C₅	—	3	1	no	—
512	C₂³×C₅	—	3	1	no	—
513	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
514	C₅×Q₈	—	2	1	no	—
515	C₅×Q₈	—	3	2	no	—
516	C₅×Q₈	—	3	2	no	—
517	C₅×Q₈	—	6	2	no	—
518	C₅×Q₈	—	6	4	no	—
519	C₅×Q₈	—	6	4	no	—
520	C₅×Q₈	—	6	4	no	—
521	C₅×Q₈	—	6	1	no	—
522	C₅×Q₈	—	6	1	no	—
523	C₅×Q₈	—	6	1	no	—
524	C₅×Q₈	—	6	1	no	—
525	C₅×Q₈	D₃×D₄	1	2	yes	—
526	C₅×D₄	—	2	4	no	—
527	C₅×D₄	—	2	1	no	—
528	C₅×D₄	—	2	1	no	—
529	C₅×D₄	—	2	1	no	—
530	C₅×D₄	—	6	2	no	—
531	C₅×D₄	—	6	2	no	—
532	C₅×D₄	—	6	2	no	—
533	C₅×D₄	—	6	4	no	—
534	C₅×D₄	—	6	4	no	—
535	C₅×D₄	—	8	1	no	—
536	C₅×D₄	—	12	2	no	—
537	C₅×D₄	—	24	1	no	—
538	C₅×D₄	D₃×D₄	1	2	yes	—
539	C₂×C₄×C₅	—	2	4	no	—
540	C₂×C₄×C₅	—	2	1	no	—
541	C₂×C₄×C₅	—	2	1	no	—
542	C₂×C₄×C₅	—	2	1	no	—
543	C₂×C₄×C₅	—	2	1	no	—
544	C₂×C₄×C₅	—	3	1	no	—
545	C₂×C₄×C₅	—	3	2	no	—
546	C₂×C₄×C₅	—	3	2	no	—
547	C₂×C₄×C₅	—	3	1	no	—
548	C₂×C₄×C₅	—	6	4	no	—
549	C₂×C₄×C₅	—	6	4	no	—
550	C₂×C₄×C₅	—	6	4	no	—
551	C₂×C₄×C₅	—	6	4	no	—
552	C₂×C₄×C₅	—	6	4	no	—
553	C₂×C₄×C₅	—	6	1	no	—
554	C₂×C₄×C₅	—	6	1	no	—
555	C₂×C₄×C₅	—	6	1	no	—
556	C₂×C₄×C₅	—	6	1	no	—
557	C₂×C₄×C₅	—	6	1	no	—
558	C₂×C₄×C₅	—	6	1	no	—
559	C₂×C₄×C₅	—	12	2	no	—
560	C₂×C₄×C₅	—	24	1	no	—
561	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
562	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
563	C₅×C₈	—	2	1	no	—
564	C₅×C₈	—	2	1	no	—
565	C₅×C₈	—	6	1	no	—
566	C₅×C₈	—	6	1	no	—
567	2₋¹⁺⁴	—	6	4	no	—
568	2₋¹⁺⁴	—	6	4	no	—
569	C₂×#41	—	3	1	no	—
570	C₂×#41	—	3	1	no	—
571	C₂×#41	—	3	1	no	—
572	C₂×#41	—	3	1	no	—
573	C₂×#41	—	6	1	no	—
574	C₂×#41	—	6	1	no	—
575	C₂×#41	—	6	1	no	—
576	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
577	C₂²×Q₈	—	3	1	no	—
578	C₂²×Q₈	—	3	1	no	—
579	C₂²×Q₈	—	3	1	no	—
580	C₂²×Q₈	—	6	1	no	—
581	#137	—	6	4	no	—
582	#135	—	6	4	no	—
583	C₂×Q₁₆	—	3	1	no	—
584	C₂×Q₁₆	—	3	1	no	—
585	C₂×Q₁₆	—	3	1	no	—
586	C₂×SD₁₆	—	3	1	no	—
587	C₂×SD₁₆	—	3	1	no	—
588	C₂×SD₁₆	—	3	1	no	—
589	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
590	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
591	C₂×M₁₆	—	3	1	no	—
592	C₂²×C₈	—	3	1	no	—
593	C₂²⋊Q₈	—	3	1	no	—
594	C₂²⋊Q₈	—	3	1	no	—
595	C₂²⋊Q₈	—	6	1	no	—
596	#121	—	3	1	no	—
597	#121	—	6	1	no	—
598	#121	—	6	1	no	—
599	#121	—	6	1	no	—
600	#121	C₂×C₅×D₃	1	1	yes	characteristic
601	C₂×C₄⋊C₄	—	3	1	no	—
602	#103	—	3	1	no	—
603	#103	—	3	1	no	—
604	#103	—	3	1	no	—
605	#103	—	3	1	no	—
606	#103	—	3	1	no	—
607	#103	C₂×C₅×D₃	1	1	yes	characteristic
608	#102	—	3	1	no	—
609	#102	C₂×C₅×D₃	1	1	yes	characteristic
610	C₂²⋊C₈	—	3	1	no	—
611	C₂²⋊C₈	—	3	1	no	—
612	C₂²⋊C₈	—	3	1	no	—
613	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
614	C₂×C₃×C₅	—	4	1	no	—
615	C₂×C₃×C₅	—	4	2	no	—
616	C₂×C₃×C₅	—	8	1	no	—
617	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
618	C₂×C₃×C₅	#577	1	1	yes	characteristic
619	C₂×C₃×C₅	#578	1	1	yes	characteristic
620	C₅×D₃	—	2	2	no	—
621	C₅×D₃	—	4	1	no	—
622	C₂³×C₃	—	2	1	no	—
623	C₂³×C₃	—	2	1	no	—
624	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
625	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
626	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
627	C₃×Q₈	—	2	1	no	—
628	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
629	C₃×D₄	—	2	4	no	—
630	C₃×D₄	—	2	1	no	—
631	C₃×D₄	—	2	1	no	—
632	C₃×D₄	—	2	1	no	—
633	C₃×D₄	—	8	1	no	—
634	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
635	C₂×C₃×C₄	—	2	4	no	—
636	C₂×C₃×C₄	—	2	1	no	—
637	C₂×C₃×C₄	—	2	1	no	—
638	C₂×C₃×C₄	—	2	1	no	—
639	C₂×C₃×C₄	—	2	1	no	—
640	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
641	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
642	#67	—	2	4	no	—
643	#67	—	2	2	no	—
644	#67	—	2	4	no	—
645	#67	—	2	2	no	—
646	#67	—	4	2	no	—
647	#67	—	8	1	no	—
648	C₂×Dic₃	—	2	4	no	—
649	C₂×Dic₃	—	2	4	no	—
650	C₂×Dic₃	—	2	1	no	—
651	C₂×Dic₃	—	2	1	no	—
652	C₂×Dic₃	—	2	4	no	—
653	C₂×Dic₃	—	2	1	no	—
654	C₂×Dic₃	—	2	1	no	—
655	C₂×Dic₃	—	4	2	no	—
656	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
657	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
658	D₁₂	—	2	2	no	—
659	C₄×D₃	—	2	4	no	—
660	C₄×D₃	—	2	4	no	—
661	C₄×D₃	—	2	1	no	—
662	C₄×D₃	—	2	1	no	—
663	C₄×D₃	—	8	1	no	—
664	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
665	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
666	Dic₆	—	2	4	no	—
667	Dic₆	—	2	4	no	—
668	Dic₆	—	2	1	no	—
669	Dic₆	—	2	1	no	—
670	Dic₆	—	2	2	no	—
671	Dic₆	—	2	4	no	—
672	Dic₆	—	2	1	no	—
673	Dic₆	—	2	1	no	—
674	Dic₆	C₂×C₅×D₄	1	2	yes	—
675	Dic₆	C₂×C₅×D₄	1	2	yes	—
676	C₃×C₈	—	2	1	no	—
677	C₃×C₈	—	2	1	no	—
678	C₃⋊C₈	—	2	1	no	—
679	C₃⋊C₈	—	2	1	no	—
680	C₂²×C₅	—	2	1	no	—
681	C₂²×C₅	—	2	1	no	—
682	C₂²×C₅	—	2	1	no	—
683	C₂²×C₅	—	2	2	no	—
684	C₂²×C₅	—	3	2	no	—
685	C₂²×C₅	—	4	1	no	—
686	C₂²×C₅	—	4	1	no	—
687	C₂²×C₅	—	4	1	no	—
688	C₂²×C₅	—	4	1	no	—
689	C₂²×C₅	—	4	1	no	—
690	C₂²×C₅	—	6	1	no	—
691	C₂²×C₅	—	6	1	no	—
692	C₂²×C₅	—	6	1	no	—
693	C₂²×C₅	—	6	1	no	—
694	C₂²×C₅	—	6	1	no	—
695	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
696	C₄×C₅	—	2	1	no	—
697	C₄×C₅	—	2	2	no	—
698	C₄×C₅	—	3	2	no	—
699	C₄×C₅	—	4	1	no	—
700	C₄×C₅	—	6	1	no	—
701	C₄×C₅	—	6	2	no	—
702	C₄×C₅	—	6	2	no	—
703	C₄×C₅	—	12	1	no	—
704	C₄×C₅	—	12	1	no	—
705	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
706	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
707	#41	—	2	2	no	—
708	#41	—	2	2	no	—
709	#41	—	3	4	no	—
710	#41	—	6	2	no	—
711	#41	—	6	2	no	—
712	#41	—	6	8	no	—
713	#41	—	6	2	no	—
714	#41	—	6	2	no	—
715	#41	—	6	2	no	—
716	#41	—	6	2	no	—
717	#41	—	6	8	no	—
718	#41	—	6	8	no	—
719	#41	—	6	2	no	—
720	C₂×Q₈	—	3	1	no	—
721	C₂×Q₈	—	3	4	no	—
722	C₂×Q₈	—	3	1	no	—
723	C₂×Q₈	—	3	1	no	—
724	C₂×Q₈	—	3	1	no	—
725	C₂×Q₈	—	6	1	no	—
726	C₂×Q₈	—	6	1	no	—
727	C₂×Q₈	—	6	2	no	—
728	C₂×Q₈	—	6	2	no	—
729	C₂×Q₈	—	6	8	no	—
730	C₂×Q₈	—	6	2	no	—
731	C₂×Q₈	—	6	2	no	—
732	C₂×Q₈	—	6	2	no	—
733	C₂×Q₈	—	6	1	no	—
734	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
735	C₂×D₄	—	2	1	no	—
736	C₂×D₄	—	2	1	no	—
737	C₂×D₄	—	3	1	no	—
738	C₂×D₄	—	3	1	no	—
739	C₂×D₄	—	3	1	no	—
740	C₂×D₄	—	6	1	no	—
741	C₂×D₄	—	6	1	no	—
742	C₂×D₄	—	6	1	no	—
743	C₂×D₄	—	6	1	no	—
744	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
745	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	3	1	no	—
748	C₂²×C₄	—	3	1	no	—
749	C₂²×C₄	—	6	1	no	—
750	C₂²×C₄	—	6	1	no	—
751	C₂²×C₄	—	6	1	no	—
752	C₂²×C₄	—	6	1	no	—
753	C₂²×C₄	—	6	1	no	—
754	C₂²×C₄	—	6	1	no	—
755	C₂²×C₄	—	6	1	no	—
756	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
757	Q₁₆	—	6	2	no	—
758	Q₁₆	—	6	2	no	—
759	Q₁₆	—	6	2	no	—
760	SD₁₆	—	2	2	no	—
761	SD₁₆	—	6	2	no	—
762	SD₁₆	—	6	2	no	—
763	SD₁₆	—	6	2	no	—
764	D₈	—	2	2	no	—
765	M₁₆	—	6	2	no	—
766	C₂×C₈	—	3	1	no	—
767	C₂×C₈	—	3	1	no	—
768	C₂×C₈	—	6	2	no	—
769	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
770	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
771	C₄⋊C₄	—	3	1	no	—
772	C₄⋊C₄	—	6	1	no	—
773	C₄⋊C₄	—	6	1	no	—
774	C₄⋊C₄	—	6	1	no	—
775	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
776	C₂²⋊C₄	—	2	1	no	—
777	C₂²⋊C₄	—	6	1	no	—
778	C₂²⋊C₄	—	6	1	no	—
779	C₂²⋊C₄	—	6	1	no	—
780	C₃×C₅	#3013	1	1	yes	characteristic, complemented, Hall
781	C₂²×C₃	—	2	1	no	—
782	C₂²×C₃	—	2	2	no	—
783	C₂²×C₃	—	2	1	no	—
784	C₂²×C₃	—	2	1	no	—
785	C₂²×C₃	—	4	1	no	—
786	C₂²×C₃	—	4	1	no	—
787	C₂²×C₃	—	4	1	no	—
788	C₂²×C₃	—	4	1	no	—
789	C₂²×C₃	—	4	1	no	—
790	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
791	C₂×D₃	—	2	1	no	—
792	C₂×D₃	—	2	1	no	—
793	C₂×D₃	—	2	1	no	—
794	C₂×D₃	—	2	1	no	—
795	C₂×D₃	—	2	1	no	—
796	C₂×D₃	C₅×#120	1	2	yes	—
797	C₃×C₄	—	2	1	no	—
798	C₃×C₄	—	2	2	no	—
799	C₃×C₄	—	4	1	no	—
800	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
801	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
802	Dic₃	—	2	1	no	—
803	Dic₃	—	2	2	no	—
804	Dic₃	—	2	2	no	—
805	Dic₃	—	4	1	no	—
806	Dic₃	—	4	1	no	—
807	Dic₃	C₅×#120	1	2	yes	—
808	C₂×C₅	—	4	1	no	—
809	C₂×C₅	—	4	2	no	—
810	C₂×C₅	—	6	2	no	—
811	C₂×C₅	—	8	1	no	—
812	C₂×C₅	—	12	1	no	—
813	C₂×C₅	D₃×#120	1	1	yes	characteristic
814	C₂×C₅	#5771	1	1	yes	characteristic
815	C₂×C₅	#5775	1	1	yes	characteristic
816	C₂³	—	2	1	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	3	1	no	—
819	C₂³	—	3	1	no	—
820	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
821	Q₈	—	2	1	no	—
822	Q₈	—	3	2	no	—
823	Q₈	—	3	2	no	—
824	Q₈	—	6	2	no	—
825	Q₈	—	6	4	no	—
826	Q₈	—	6	4	no	—
827	Q₈	—	6	4	no	—
828	Q₈	—	6	1	no	—
829	Q₈	—	6	1	no	—
830	Q₈	—	6	1	no	—
831	Q₈	—	6	1	no	—
832	Q₈	C₅×D₃×D₄	1	2	yes	—
833	D₄	—	2	4	no	—
834	D₄	—	2	1	no	—
835	D₄	—	2	1	no	—
836	D₄	—	2	1	no	—
837	D₄	—	6	2	no	—
838	D₄	—	6	2	no	—
839	D₄	—	6	2	no	—
840	D₄	—	6	4	no	—
841	D₄	—	6	4	no	—
842	D₄	—	8	1	no	—
843	D₄	—	12	2	no	—
844	D₄	—	24	1	no	—
845	D₄	C₅×D₃×D₄	1	2	yes	—
846	C₂×C₄	—	2	4	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	3	1	no	—
852	C₂×C₄	—	3	2	no	—
853	C₂×C₄	—	3	2	no	—
854	C₂×C₄	—	3	1	no	—
855	C₂×C₄	—	6	4	no	—
856	C₂×C₄	—	6	4	no	—
857	C₂×C₄	—	6	4	no	—
858	C₂×C₄	—	6	4	no	—
859	C₂×C₄	—	6	4	no	—
860	C₂×C₄	—	6	1	no	—
861	C₂×C₄	—	6	1	no	—
862	C₂×C₄	—	6	1	no	—
863	C₂×C₄	—	6	1	no	—
864	C₂×C₄	—	6	1	no	—
865	C₂×C₄	—	6	1	no	—
866	C₂×C₄	—	12	2	no	—
867	C₂×C₄	—	24	1	no	—
868	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
869	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
870	C₈	—	2	1	no	—
871	C₈	—	2	1	no	—
872	C₈	—	6	1	no	—
873	C₈	—	6	1	no	—
874	C₂×C₃	—	4	1	no	—
875	C₂×C₃	—	4	2	no	—
876	C₂×C₃	—	8	1	no	—
877	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
878	C₂×C₃	C₅×#577	1	1	yes	characteristic
879	C₂×C₃	C₅×#578	1	1	yes	characteristic
880	D₃	—	2	2	no	—
881	D₃	—	4	1	no	—
882	C₅	#80088	1	1	yes	characteristic, direct product factor, Sylow
883	C₂²	—	2	1	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	3	2	no	—
888	C₂²	—	4	1	no	—
889	C₂²	—	4	1	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	1	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	6	1	no	—
894	C₂²	—	6	1	no	—
895	C₂²	—	6	1	no	—
896	C₂²	—	6	1	no	—
897	C₂²	—	6	1	no	—
898	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
899	C₄	—	2	1	no	—
900	C₄	—	2	2	no	—
901	C₄	—	3	2	no	—
902	C₄	—	4	1	no	—
903	C₄	—	6	1	no	—
904	C₄	—	6	2	no	—
905	C₄	—	6	2	no	—
906	C₄	—	12	1	no	—
907	C₄	—	12	1	no	—
908	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
909	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
910	C₃	C₅×#3013	1	1	yes	characteristic, complemented, Sylow
911	C₂	—	4	1	no	—
912	C₂	—	4	2	no	—
913	C₂	—	6	2	no	—
914	C₂	—	8	1	no	—
915	C₂	—	12	1	no	—
916	C₂	C₅×D₃×#120	1	1	yes	characteristic
917	C₂	C₅×#5771	1	1	yes	characteristic
918	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×#449	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#449	D₃
hypocenter	C₃	C₅×#3013
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#449

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#1010	C₂	semidirect
2. C₂×C₅×#915	C₂	semidirect
3. C₂×C₅×#912	C₂	semidirect
4. C₅×#5608	C₂	semidirect
5. C₃×C₅×#449	C₂	semidirect
6. C₅×#5239	C₂	semidirect
7. C₅×#5170	C₂	semidirect
8. C₅×#5158	C₂	semidirect
9. C₅×#5040	C₂	semidirect
10. C₅×#4809	C₂	semidirect
11. C₅×D₃×#103	C₂	semidirect
12. C₅×#4783	C₂	semidirect
13. C₅×#4771	C₂	semidirect
14. C₅×#4739	C₂	semidirect
15. C₅×#4727	C₂	semidirect
64. #80088	C₅	direct (N × H)
74. C₅×#449	D₃	semidirect
102. C₅×D₃×Q₈	D₄	semidirect
110. C₅×#237	D₄	semidirect
153. C₂×#1010	C₂×C₅	semidirect
154. C₂×#915	C₂×C₅	semidirect
155. C₂×#912	C₂×C₅	semidirect
156. #5608	C₂×C₅	semidirect
157. C₃×#449	C₂×C₅	semidirect
158. #5239	C₂×C₅	semidirect
159. #5170	C₂×C₅	semidirect
160. #5158	C₂×C₅	semidirect
161. #5040	C₂×C₅	semidirect
162. #4809	C₂×C₅	semidirect
163. D₃×#103	C₂×C₅	semidirect
164. #4783	C₂×C₅	semidirect
165. #4771	C₂×C₅	semidirect
166. #4739	C₂×C₅	semidirect
167. #4727	C₂×C₅	semidirect
403. #449	C₅×D₃	semidirect
458. D₃×Q₈	C₅×D₄	semidirect
466. #237	C₅×D₄	semidirect
780. C₃×C₅	#3013	semidirect
882. C₅	#80088	direct (N × H)
910. C₃	C₅×#3013	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×#915	2
C₂×C₅×#912	2
C₅×#5608	2
C₃×C₅×#449	2
C₅×#5239	2
C₅×#5170	2
C₅×#5158	2
C₅×#5040	2
C₅×#4809	2
C₅×D₃×#103	2
C₅×#4783	2
C₅×#4771	2
C₅×#4739	2
C₅×#4727	2
C₅×#3013	3
#80088	5

Subgroups — C5×#80088 #14424804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80088 #14424804