Subgroups — C₅×#86313 #14480644

Order 1920.

3112 conjugacy classes of subgroups.

The subgroup lattice has 908 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, complemented
2	C₂²×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5825	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5805	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5716	C₂	1	2	yes	maximal, complemented
7	C₅×#5715	C₂	1	2	yes	maximal, complemented
8	C₅×#5675	C₂	1	2	yes	maximal, complemented
9	C₅×#5668	C₂	1	2	yes	maximal, complemented
10	C₅×#5608	C₂	1	4	yes	maximal, complemented
11	C₅×#5606	C₂	1	4	yes	maximal, complemented
12	C₅×#5589	C₂	1	4	yes	maximal, complemented
13	C₅×#5586	C₂	1	4	yes	maximal, complemented
14	C₅×#5526	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3449	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₅×#67	C₂²	1	2	yes	—
20	C₂³×C₅×Dic₃	C₂²	1	2	yes	complemented
21	C₅×D₃×#41	—	2	8	no	—
22	C₂×C₅×#239	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×#237	—	2	8	no	—
25	C₂×C₅×#237	C₂²	1	2	yes	—
26	C₂×C₅×#237	C₂²	1	2	yes	—
27	C₂×C₅×#237	C₂²	1	2	yes	—
28	C₂×C₅×#237	C₂²	1	2	yes	complemented
29	C₂×C₅×#237	C₂²	1	2	yes	complemented
30	C₂×C₅×#237	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
32	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₅×#235	C₂²	1	1	yes	characteristic
34	C₂×C₅×#235	C₂²	1	2	yes	complemented
35	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	complemented
37	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₅×#127	C₂²	1	2	yes	complemented
39	C₃×C₅×#124	C₂²	1	2	yes	complemented
40	C₃×C₅×#121	C₂²	1	4	yes	complemented
41	C₃×C₅×#120	C₂²	1	4	yes	complemented
42	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
43	C₅×#953	C₂²	1	4	yes	complemented
44	C₅×#944	C₂²	1	2	yes	complemented
45	C₅×#940	C₂²	1	2	yes	complemented
46	C₅×#939	C₂²	1	8	yes	complemented
47	C₅×#938	C₂²	1	8	yes	complemented
48	C₅×#938	C₂²	1	4	yes	complemented
49	C₅×#937	C₂²	1	8	yes	complemented
50	C₅×#936	C₂²	1	2	yes	complemented
51	C₅×#936	C₂²	1	2	yes	complemented
52	C₅×#935	C₂²	1	4	yes	complemented
53	C₅×D₄×Dic₃	C₂²	1	8	yes	complemented
54	C₅×#926	C₂²	1	1	yes	characteristic, complemented
55	C₅×#924	C₂²	1	4	yes	complemented
56	C₅×#897	C₂²	1	4	yes	complemented
57	C₅×#892	C₂²	1	2	yes	complemented
58	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
59	C₅×#886	C₂²	1	4	yes	complemented
60	C₅×#884	C₂²	1	8	yes	complemented
61	C₅×#883	C₂²	1	8	yes	complemented
62	C₅×#67⋊C₄	C₂²	1	8	yes	complemented
63	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
64	C₅×#878	C₂²	1	8	yes	complemented
65	C₅×#877	C₂²	1	2	yes	complemented
66	C₅×#875	C₂²	1	2	yes	complemented
67	C₅×#872	C₂²	1	2	yes	complemented
68	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
69	C₅×#869	C₂²	1	2	yes	complemented
70	#86313	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
71	C₂²×C₅×#41	—	3	1	no	—
72	C₂²×C₅×#41	—	3	1	no	—
73	C₅×#537	—	3	4	no	—
74	C₅×#536	—	3	1	no	—
75	C₅×#536	—	3	2	no	—
76	C₅×#536	—	3	1	no	—
77	C₅×#535	—	3	1	no	—
78	C₅×#535	—	3	2	no	—
79	C₅×#535	D₃	1	1	yes	characteristic, complemented
80	C₅×#534	—	3	4	no	—
81	C₅×#532	—	3	2	no	—
82	C₅×#532	—	3	2	no	—
83	C₅×#525	—	3	4	no	—
84	C₅×#525	—	3	4	no	—
85	C₂×C₅×#117	—	3	1	no	—
86	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
87	C₂³×C₅×D₃	C₂³	1	2	yes	—
88	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
89	C₃×C₅×#41	—	2	4	no	—
90	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₅×D₄	—	2	4	no	—
92	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
93	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
95	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
96	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
97	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
98	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂×C₅×#67	—	2	8	no	—
100	C₂×C₅×#67	C₂³	1	4	yes	—
101	C₂×C₅×#67	C₂³	1	4	yes	—
102	C₂×C₅×#67	C₂³	1	2	yes	—
103	C₂×C₅×#67	C₂³	1	2	yes	—
104	C₂×C₅×#67	C₂³	1	2	yes	—
105	C₂×C₅×#67	C₂³	1	8	yes	—
106	C₂²×C₅×Dic₃	—	2	8	no	—
107	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
108	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
109	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
110	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
111	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
112	C₅×#239	—	2	4	no	—
113	C₅×D₃×Q₈	—	2	4	no	—
114	C₅×#237	—	2	8	no	—
115	C₅×#237	—	2	8	no	—
116	C₅×#237	—	2	8	no	—
117	C₅×#237	—	2	8	no	—
118	C₅×#237	—	2	8	no	—
119	C₅×#237	—	2	4	no	—
120	C₅×D₃×D₄	—	2	8	no	—
121	C₅×D₃×D₄	—	2	4	no	—
122	C₅×#235	—	2	4	no	—
123	C₅×#235	—	2	8	no	—
124	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
125	C₂×C₅×D₁₂	C₂³	1	2	yes	—
126	C₂×C₄×C₅×D₃	—	2	8	no	—
127	C₂×C₄×C₅×D₃	D₄	1	8	yes	complemented
128	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
129	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
130	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
131	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
132	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
133	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
134	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
135	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
136	C₂×C₅×Dic₆	—	2	4	no	—
137	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
138	C₂×C₅×Dic₆	C₂³	1	2	yes	—
139	C₂×C₅×Dic₆	C₂³	1	2	yes	—
140	C₂×C₅×Dic₆	C₂³	1	2	yes	—
141	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
142	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
143	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
144	C₃×C₄²×C₅	C₂³	1	2	yes	—
145	C₅×#217	C₂³	1	2	yes	—
146	C₅×#217	C₂³	1	8	yes	—
147	C₅×#217	C₂³	1	8	yes	—
148	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
149	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
150	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
151	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
152	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
153	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
154	C₄×C₅×Dic₃	C₂³	1	2	yes	—
155	C₄×C₅×Dic₃	C₂³	1	4	yes	—
156	C₂×D₃×#41	C₂×C₅	1	1	yes	characteristic, complemented
157	C₂²×#237	C₂×C₅	1	1	yes	characteristic, complemented
158	C₃×#535	C₂×C₅	1	1	yes	characteristic, complemented
159	#5825	C₂×C₅	1	1	yes	characteristic, complemented
160	#5805	C₂×C₅	1	1	yes	characteristic, complemented
161	#5716	C₂×C₅	1	2	yes	complemented
162	#5715	C₂×C₅	1	2	yes	complemented
163	#5675	C₂×C₅	1	2	yes	complemented
164	#5668	C₂×C₅	1	2	yes	complemented
165	#5608	C₂×C₅	1	4	yes	complemented
166	#5606	C₂×C₅	1	4	yes	complemented
167	#5589	C₂×C₅	1	4	yes	complemented
168	#5586	C₂×C₅	1	4	yes	complemented
169	#5526	C₂×C₅	1	1	yes	characteristic, complemented
170	D₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
171	C₂×C₅×#41	—	3	1	no	—
172	C₂×C₅×#41	—	3	2	no	—
173	C₂×C₅×#41	—	3	2	no	—
174	C₂×C₅×#41	—	3	1	no	—
175	C₂×C₅×#41	—	3	2	no	—
176	C₂×C₅×#41	—	3	2	no	—
177	C₂×C₅×#41	—	3	2	no	—
178	C₂×C₅×#41	—	3	1	no	—
179	C₂×C₅×#41	—	3	2	no	—
180	C₂×C₅×#41	—	6	8	no	—
181	C₂×C₅×#41	—	6	8	no	—
182	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
183	C₂²×C₅×Q₈	—	3	1	no	—
184	C₂²×C₅×Q₈	—	3	1	no	—
185	C₂²×C₅×D₄	—	3	2	no	—
186	C₂²×C₅×D₄	—	3	2	no	—
187	C₂²×C₅×D₄	—	3	1	no	—
188	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
189	C₂³×C₄×C₅	—	3	1	no	—
190	C₂³×C₄×C₅	—	3	2	no	—
191	C₂³×C₄×C₅	—	3	2	no	—
192	C₅×C₄⋊Q₈	—	3	2	no	—
193	C₅×C₄⋊Q₈	—	3	2	no	—
194	C₅×#127	—	3	2	no	—
195	C₅×#127	C₂×D₃	1	2	yes	complemented
196	C₅×#124	—	3	2	no	—
197	C₅×#124	—	3	2	no	—
198	C₅×#124	—	3	2	no	—
199	C₅×#124	C₂×D₃	1	2	yes	complemented
200	C₅×#123	—	3	4	no	—
201	C₅×#123	—	3	8	no	—
202	C₅×#123	—	3	4	no	—
203	C₅×C₂²⋊Q₈	—	3	4	no	—
204	C₅×C₂²⋊Q₈	—	3	4	no	—
205	C₅×C₂²⋊Q₈	—	3	8	no	—
206	C₅×#121	—	3	4	no	—
207	C₅×#121	—	3	8	no	—
208	C₅×#121	—	3	8	no	—
209	C₅×#121	—	3	8	no	—
210	C₅×#121	C₂×D₃	1	4	yes	complemented
211	C₅×#120	—	3	4	no	—
212	C₅×#120	—	3	8	no	—
213	C₅×#120	C₂×D₃	1	4	yes	complemented
214	C₄×C₅×D₄	—	3	8	no	—
215	C₄×C₅×D₄	—	3	8	no	—
216	C₅×#117	—	3	1	no	—
217	C₅×#117	—	3	2	no	—
218	C₅×#117	—	3	2	no	—
219	C₅×#117	—	3	2	no	—
220	C₅×#117	C₂×D₃	1	1	yes	characteristic, complemented
221	C₂×C₅×C₄⋊C₄	—	3	2	no	—
222	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
223	C₂×C₄²×C₅	—	3	2	no	—
224	#3449	—	3	1	no	Sylow
225	C₂³×C₃×C₅	—	2	4	no	—
226	C₂³×C₃×C₅	—	4	4	no	—
227	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
228	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
229	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
230	C₂²×C₅×D₃	—	2	4	no	—
231	C₂²×C₅×D₃	—	4	2	no	—
232	C₂²×C₅×D₃	—	4	4	no	—
233	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
234	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
235	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
236	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
237	C₃×C₅×Q₈	—	2	2	no	—
238	C₃×C₅×D₄	—	2	4	no	—
239	C₃×C₅×D₄	—	2	2	no	—
240	C₃×C₅×D₄	—	2	4	no	—
241	C₃×C₅×D₄	—	2	4	no	—
242	C₃×C₅×D₄	—	4	8	no	—
243	C₂×C₃×C₄×C₅	—	2	4	no	—
244	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
245	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
246	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
247	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
248	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
249	C₅×#67	—	2	4	no	—
250	C₅×#67	—	2	4	no	—
251	C₅×#67	—	2	8	no	—
252	C₅×#67	—	2	8	no	—
253	C₅×#67	—	2	4	no	—
254	C₅×#67	—	4	8	no	—
255	C₂×C₅×Dic₃	—	2	4	no	—
256	C₂×C₅×Dic₃	—	2	4	no	—
257	C₂×C₅×Dic₃	—	2	8	no	—
258	C₂×C₅×Dic₃	—	2	8	no	—
259	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
260	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
261	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
262	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
263	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
264	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
265	C₅×D₁₂	—	2	4	no	—
266	C₅×D₁₂	—	2	2	no	—
267	C₄×C₅×D₃	—	2	4	no	—
268	C₄×C₅×D₃	—	2	4	no	—
269	C₄×C₅×D₃	—	2	4	no	—
270	C₄×C₅×D₃	—	4	4	no	—
271	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
272	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
273	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
274	C₄×C₅×D₃	C₂×D₄	1	4	yes	—
275	C₅×Dic₆	—	2	4	no	—
276	C₅×Dic₆	—	2	4	no	—
277	C₅×Dic₆	—	2	2	no	—
278	C₅×Dic₆	—	2	4	no	—
279	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
280	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
281	C₂²×#67	C₂²×C₅	1	2	yes	—
282	C₂³×Dic₃	C₂²×C₅	1	2	yes	complemented
283	D₃×#41	—	2	8	no	—
284	C₂×#239	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
286	C₂×#237	—	2	8	no	—
287	C₂×#237	C₂²×C₅	1	2	yes	—
288	C₂×#237	C₂²×C₅	1	2	yes	—
289	C₂×#237	C₂²×C₅	1	2	yes	—
290	C₂×#237	C₂²×C₅	1	2	yes	complemented
291	C₂×#237	C₂²×C₅	1	2	yes	complemented
292	C₂×#237	C₂²×C₅	1	1	yes	characteristic, complemented
293	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
294	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
295	C₂×#235	C₂²×C₅	1	1	yes	characteristic
296	C₂×#235	C₂²×C₅	1	2	yes	complemented
297	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
298	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	complemented
299	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
300	C₃×#127	C₂²×C₅	1	2	yes	complemented
301	C₃×#124	C₂²×C₅	1	2	yes	complemented
302	C₃×#121	C₂²×C₅	1	4	yes	complemented
303	C₃×#120	C₂²×C₅	1	4	yes	complemented
304	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
305	#953	C₂²×C₅	1	4	yes	complemented
306	#944	C₂²×C₅	1	2	yes	complemented
307	#940	C₂²×C₅	1	2	yes	complemented
308	#939	C₂²×C₅	1	8	yes	complemented
309	#938	C₂²×C₅	1	8	yes	complemented
310	#938	C₂²×C₅	1	4	yes	complemented
311	#937	C₂²×C₅	1	8	yes	complemented
312	#936	C₂²×C₅	1	2	yes	complemented
313	#936	C₂²×C₅	1	2	yes	complemented
314	#935	C₂²×C₅	1	4	yes	complemented
315	D₄×Dic₃	C₂²×C₅	1	8	yes	complemented
316	#926	C₂²×C₅	1	1	yes	characteristic, complemented
317	#924	C₂²×C₅	1	4	yes	complemented
318	#897	C₂²×C₅	1	4	yes	complemented
319	#892	C₂²×C₅	1	2	yes	complemented
320	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
321	#886	C₂²×C₅	1	4	yes	complemented
322	#884	C₂²×C₅	1	8	yes	complemented
323	#883	C₂²×C₅	1	8	yes	complemented
324	#67⋊C₄	C₂²×C₅	1	8	yes	complemented
325	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
326	#878	C₂²×C₅	1	8	yes	complemented
327	#877	C₂²×C₅	1	2	yes	complemented
328	#875	C₂²×C₅	1	2	yes	complemented
329	#872	C₂²×C₅	1	2	yes	complemented
330	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
331	#869	C₂²×C₅	1	2	yes	complemented
332	C₂⁴×C₅	—	3	1	no	—
333	C₂⁴×C₅	—	3	2	no	—
334	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
335	C₅×#41	—	2	4	no	—
336	C₅×#41	—	6	8	no	—
337	C₅×#41	—	6	8	no	—
338	C₅×#41	—	6	8	no	—
339	C₅×#41	—	6	8	no	—
340	C₅×#41	—	6	8	no	—
341	C₅×#41	—	6	8	no	—
342	C₅×#41	—	6	4	no	—
343	C₅×#41	—	6	4	no	—
344	C₅×#41	—	6	4	no	—
345	C₂×C₅×Q₈	—	3	2	no	—
346	C₂×C₅×Q₈	—	3	2	no	—
347	C₂×C₅×Q₈	—	3	1	no	—
348	C₂×C₅×Q₈	—	3	2	no	—
349	C₂×C₅×Q₈	—	6	4	no	—
350	C₂×C₅×Q₈	—	6	4	no	—
351	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
352	C₂×C₅×D₄	—	2	4	no	—
353	C₂×C₅×D₄	—	3	4	no	—
354	C₂×C₅×D₄	—	3	2	no	—
355	C₂×C₅×D₄	—	3	2	no	—
356	C₂×C₅×D₄	—	3	2	no	—
357	C₂×C₅×D₄	—	3	4	no	—
358	C₂×C₅×D₄	—	3	8	no	—
359	C₂×C₅×D₄	—	3	2	no	—
360	C₂×C₅×D₄	—	3	1	no	—
361	C₂×C₅×D₄	—	6	4	no	—
362	C₂×C₅×D₄	—	6	8	no	—
363	C₂×C₅×D₄	—	6	8	no	—
364	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
365	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
366	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
367	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
368	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
369	C₂²×C₄×C₅	—	3	1	no	—
370	C₂²×C₄×C₅	—	3	8	no	—
371	C₂²×C₄×C₅	—	3	1	no	—
372	C₂²×C₄×C₅	—	3	1	no	—
373	C₂²×C₄×C₅	—	3	1	no	—
374	C₂²×C₄×C₅	—	3	1	no	—
375	C₂²×C₄×C₅	—	3	2	no	—
376	C₂²×C₄×C₅	—	3	4	no	—
377	C₂²×C₄×C₅	—	3	4	no	—
378	C₂²×C₄×C₅	—	3	2	no	—
379	C₂²×C₄×C₅	—	3	2	no	—
380	C₂²×C₄×C₅	—	3	2	no	—
381	C₂²×C₄×C₅	—	3	2	no	—
382	C₂²×C₄×C₅	—	3	4	no	—
383	C₂²×C₄×C₅	—	6	8	no	—
384	C₂²×C₄×C₅	—	6	8	no	—
385	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
386	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
387	C₅×C₄⋊C₄	—	3	4	no	—
388	C₅×C₄⋊C₄	—	3	2	no	—
389	C₅×C₄⋊C₄	—	3	8	no	—
390	C₅×C₄⋊C₄	—	3	8	no	—
391	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
392	C₅×C₂²⋊C₄	—	3	2	no	—
393	C₅×C₂²⋊C₄	—	3	8	no	—
394	C₅×C₂²⋊C₄	—	3	8	no	—
395	C₅×C₂²⋊C₄	—	3	4	no	—
396	C₅×C₂²⋊C₄	—	3	8	no	—
397	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
398	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
399	C₄²×C₅	—	3	4	no	—
400	C₄²×C₅	—	3	2	no	—
401	C₄²×C₅	C₂²×D₃	1	2	yes	—
402	C₂²×#41	—	3	1	no	—
403	C₂²×#41	—	3	1	no	—
404	#537	—	3	4	no	—
405	#536	—	3	1	no	—
406	#536	—	3	2	no	—
407	#536	—	3	1	no	—
408	#535	—	3	1	no	—
409	#535	—	3	2	no	—
410	#535	C₅×D₃	1	1	yes	characteristic, complemented
411	#534	—	3	4	no	—
412	#532	—	3	2	no	—
413	#532	—	3	2	no	—
414	#525	—	3	4	no	—
415	#525	—	3	4	no	—
416	C₂×#117	—	3	1	no	—
417	C₂²×C₃×C₅	—	2	2	no	—
418	C₂²×C₃×C₅	—	2	4	no	—
419	C₂²×C₃×C₅	—	2	2	no	—
420	C₂²×C₃×C₅	—	2	8	no	—
421	C₂²×C₃×C₅	—	2	4	no	—
422	C₂²×C₃×C₅	—	4	8	no	—
423	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
424	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
425	C₂×C₅×D₃	—	2	2	no	—
426	C₂×C₅×D₃	—	2	2	no	—
427	C₂×C₅×D₃	—	2	2	no	—
428	C₂×C₅×D₃	—	2	4	no	—
429	C₂×C₅×D₃	—	4	4	no	—
430	C₂×C₅×D₃	—	4	8	no	—
431	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
432	C₂×C₅×D₃	C₂²×D₄	1	2	yes	—
433	C₃×C₄×C₅	—	2	2	no	—
434	C₃×C₄×C₅	—	2	4	no	—
435	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
436	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
437	C₅×Dic₃	—	2	2	no	—
438	C₅×Dic₃	—	2	4	no	—
439	C₅×Dic₃	—	2	4	no	—
440	C₅×Dic₃	C₂²×D₄	1	2	yes	—
441	C₅×Dic₃	C₂²×D₄	1	2	yes	—
442	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
443	C₂³×D₃	C₂³×C₅	1	2	yes	—
444	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
445	C₃×#41	—	2	4	no	—
446	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
447	C₂×C₃×D₄	—	2	4	no	—
448	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
449	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
450	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
451	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
452	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
453	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
454	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
455	C₂×#67	—	2	8	no	—
456	C₂×#67	C₂³×C₅	1	4	yes	—
457	C₂×#67	C₂³×C₅	1	4	yes	—
458	C₂×#67	C₂³×C₅	1	2	yes	—
459	C₂×#67	C₂³×C₅	1	2	yes	—
460	C₂×#67	C₂³×C₅	1	2	yes	—
461	C₂×#67	C₂³×C₅	1	8	yes	—
462	C₂²×Dic₃	—	2	8	no	—
463	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
464	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
465	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
466	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
467	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
468	#239	—	2	4	no	—
469	D₃×Q₈	—	2	4	no	—
470	#237	—	2	8	no	—
471	#237	—	2	8	no	—
472	#237	—	2	8	no	—
473	#237	—	2	8	no	—
474	#237	—	2	8	no	—
475	#237	—	2	4	no	—
476	D₃×D₄	—	2	8	no	—
477	D₃×D₄	—	2	4	no	—
478	#235	—	2	4	no	—
479	#235	—	2	8	no	—
480	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
481	C₂×D₁₂	C₂³×C₅	1	2	yes	—
482	C₂×C₄×D₃	—	2	8	no	—
483	C₂×C₄×D₃	C₅×D₄	1	8	yes	complemented
484	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
485	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
486	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
487	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
488	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
489	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
490	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
491	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
492	C₂×Dic₆	—	2	4	no	—
493	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
494	C₂×Dic₆	C₂³×C₅	1	2	yes	—
495	C₂×Dic₆	C₂³×C₅	1	2	yes	—
496	C₂×Dic₆	C₂³×C₅	1	2	yes	—
497	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
498	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
499	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
500	C₃×C₄²	C₂³×C₅	1	2	yes	—
501	#217	C₂³×C₅	1	2	yes	—
502	#217	C₂³×C₅	1	8	yes	—
503	#217	C₂³×C₅	1	8	yes	—
504	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
505	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
506	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
507	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
508	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
509	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
510	C₄×Dic₃	C₂³×C₅	1	2	yes	—
511	C₄×Dic₃	C₂³×C₅	1	4	yes	—
512	C₂³×C₅	—	2	4	no	—
513	C₂³×C₅	—	3	1	no	—
514	C₂³×C₅	—	3	1	no	—
515	C₂³×C₅	—	3	4	no	—
516	C₂³×C₅	—	3	2	no	—
517	C₂³×C₅	—	4	4	no	—
518	C₂³×C₅	—	6	4	no	—
519	C₂³×C₅	—	12	2	no	—
520	C₂³×C₅	—	12	4	no	—
521	C₂³×C₅	C₂³×D₃	1	2	yes	—
522	C₂³×C₅	C₂³×D₃	1	4	yes	—
523	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
524	C₅×Q₈	—	2	2	no	—
525	C₅×Q₈	—	6	4	no	—
526	C₅×Q₈	—	6	4	no	—
527	C₅×Q₈	—	6	4	no	—
528	C₅×Q₈	—	6	2	no	—
529	C₅×D₄	—	2	4	no	—
530	C₅×D₄	—	2	4	no	—
531	C₅×D₄	—	2	4	no	—
532	C₅×D₄	—	2	2	no	—
533	C₅×D₄	—	4	8	no	—
534	C₅×D₄	—	6	4	no	—
535	C₅×D₄	—	6	4	no	—
536	C₅×D₄	—	6	4	no	—
537	C₅×D₄	—	6	8	no	—
538	C₅×D₄	—	6	8	no	—
539	C₅×D₄	—	6	4	no	—
540	C₅×D₄	—	6	2	no	—
541	C₅×D₄	—	12	8	no	—
542	C₂×C₄×C₅	—	2	4	no	—
543	C₂×C₄×C₅	—	3	4	no	—
544	C₂×C₄×C₅	—	3	1	no	—
545	C₂×C₄×C₅	—	3	1	no	—
546	C₂×C₄×C₅	—	3	4	no	—
547	C₂×C₄×C₅	—	3	4	no	—
548	C₂×C₄×C₅	—	3	4	no	—
549	C₂×C₄×C₅	—	3	4	no	—
550	C₂×C₄×C₅	—	3	4	no	—
551	C₂×C₄×C₅	—	3	2	no	—
552	C₂×C₄×C₅	—	3	4	no	—
553	C₂×C₄×C₅	—	6	4	no	—
554	C₂×C₄×C₅	—	6	4	no	—
555	C₂×C₄×C₅	—	6	4	no	—
556	C₂×C₄×C₅	—	6	8	no	—
557	C₂×C₄×C₅	—	6	8	no	—
558	C₂×C₄×C₅	—	6	4	no	—
559	C₂×C₄×C₅	—	6	4	no	—
560	C₂×C₄×C₅	—	12	4	no	—
561	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
562	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
563	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
564	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
565	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
566	C₂×#41	—	3	1	no	—
567	C₂×#41	—	3	2	no	—
568	C₂×#41	—	3	2	no	—
569	C₂×#41	—	3	1	no	—
570	C₂×#41	—	3	2	no	—
571	C₂×#41	—	3	2	no	—
572	C₂×#41	—	3	2	no	—
573	C₂×#41	—	3	1	no	—
574	C₂×#41	—	3	2	no	—
575	C₂×#41	—	6	8	no	—
576	C₂×#41	—	6	8	no	—
577	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
578	C₂²×Q₈	—	3	1	no	—
579	C₂²×Q₈	—	3	1	no	—
580	C₂²×D₄	—	3	2	no	—
581	C₂²×D₄	—	3	2	no	—
582	C₂²×D₄	—	3	1	no	—
583	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
584	C₂³×C₄	—	3	1	no	—
585	C₂³×C₄	—	3	2	no	—
586	C₂³×C₄	—	3	2	no	—
587	C₄⋊Q₈	—	3	2	no	—
588	C₄⋊Q₈	—	3	2	no	—
589	#127	—	3	2	no	—
590	#127	C₂×C₅×D₃	1	2	yes	complemented
591	#124	—	3	2	no	—
592	#124	—	3	2	no	—
593	#124	—	3	2	no	—
594	#124	C₂×C₅×D₃	1	2	yes	complemented
595	#123	—	3	4	no	—
596	#123	—	3	8	no	—
597	#123	—	3	4	no	—
598	C₂²⋊Q₈	—	3	4	no	—
599	C₂²⋊Q₈	—	3	4	no	—
600	C₂²⋊Q₈	—	3	8	no	—
601	#121	—	3	4	no	—
602	#121	—	3	8	no	—
603	#121	—	3	8	no	—
604	#121	—	3	8	no	—
605	#121	C₂×C₅×D₃	1	4	yes	complemented
606	#120	—	3	4	no	—
607	#120	—	3	8	no	—
608	#120	C₂×C₅×D₃	1	4	yes	complemented
609	C₄×D₄	—	3	8	no	—
610	C₄×D₄	—	3	8	no	—
611	#117	—	3	1	no	—
612	#117	—	3	2	no	—
613	#117	—	3	2	no	—
614	#117	—	3	2	no	—
615	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
616	C₂×C₄⋊C₄	—	3	2	no	—
617	C₂×C₂²⋊C₄	—	3	2	no	—
618	C₂×C₄²	—	3	2	no	—
619	C₂×C₃×C₅	—	2	2	no	—
620	C₂×C₃×C₅	—	4	2	no	—
621	C₂×C₃×C₅	—	4	4	no	—
622	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
623	C₂×C₃×C₅	#585	1	2	yes	—
624	C₅×D₃	—	2	2	no	—
625	C₅×D₃	—	2	2	no	—
626	C₅×D₃	—	4	2	no	—
627	C₂³×C₃	—	2	4	no	—
628	C₂³×C₃	—	4	4	no	—
629	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
630	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
631	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
632	C₂²×D₃	—	2	4	no	—
633	C₂²×D₃	—	4	2	no	—
634	C₂²×D₃	—	4	4	no	—
635	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
636	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
637	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
638	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
639	C₃×Q₈	—	2	2	no	—
640	C₃×D₄	—	2	4	no	—
641	C₃×D₄	—	2	2	no	—
642	C₃×D₄	—	2	4	no	—
643	C₃×D₄	—	2	4	no	—
644	C₃×D₄	—	4	8	no	—
645	C₂×C₃×C₄	—	2	4	no	—
646	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
647	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
648	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
649	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
650	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
651	#67	—	2	4	no	—
652	#67	—	2	4	no	—
653	#67	—	2	8	no	—
654	#67	—	2	8	no	—
655	#67	—	2	4	no	—
656	#67	—	4	8	no	—
657	C₂×Dic₃	—	2	4	no	—
658	C₂×Dic₃	—	2	4	no	—
659	C₂×Dic₃	—	2	8	no	—
660	C₂×Dic₃	—	2	8	no	—
661	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
662	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
663	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
664	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
665	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
666	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
667	D₁₂	—	2	4	no	—
668	D₁₂	—	2	2	no	—
669	C₄×D₃	—	2	4	no	—
670	C₄×D₃	—	2	4	no	—
671	C₄×D₃	—	2	4	no	—
672	C₄×D₃	—	4	4	no	—
673	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
674	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
675	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
676	C₄×D₃	C₂×C₅×D₄	1	4	yes	—
677	Dic₆	—	2	4	no	—
678	Dic₆	—	2	4	no	—
679	Dic₆	—	2	2	no	—
680	Dic₆	—	2	4	no	—
681	C₂²×C₅	—	2	2	no	—
682	C₂²×C₅	—	2	2	no	—
683	C₂²×C₅	—	2	4	no	—
684	C₂²×C₅	—	2	4	no	—
685	C₂²×C₅	—	2	8	no	—
686	C₂²×C₅	—	3	2	no	—
687	C₂²×C₅	—	3	2	no	—
688	C₂²×C₅	—	4	8	no	—
689	C₂²×C₅	—	6	2	no	—
690	C₂²×C₅	—	6	2	no	—
691	C₂²×C₅	—	6	2	no	—
692	C₂²×C₅	—	6	4	no	—
693	C₂²×C₅	—	12	4	no	—
694	C₂²×C₅	—	12	8	no	—
695	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
696	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
697	C₄×C₅	—	2	2	no	—
698	C₄×C₅	—	2	4	no	—
699	C₄×C₅	—	3	2	no	—
700	C₄×C₅	—	3	2	no	—
701	C₄×C₅	—	6	2	no	—
702	C₄×C₅	—	6	4	no	—
703	C₄×C₅	—	6	4	no	—
704	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
705	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
706	C₂⁴	—	3	1	no	—
707	C₂⁴	—	3	2	no	—
708	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
709	#41	—	2	4	no	—
710	#41	—	6	8	no	—
711	#41	—	6	8	no	—
712	#41	—	6	8	no	—
713	#41	—	6	8	no	—
714	#41	—	6	8	no	—
715	#41	—	6	8	no	—
716	#41	—	6	4	no	—
717	#41	—	6	4	no	—
718	#41	—	6	4	no	—
719	C₂×Q₈	—	3	2	no	—
720	C₂×Q₈	—	3	2	no	—
721	C₂×Q₈	—	3	1	no	—
722	C₂×Q₈	—	3	2	no	—
723	C₂×Q₈	—	6	4	no	—
724	C₂×Q₈	—	6	4	no	—
725	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	3	4	no	—
728	C₂×D₄	—	3	2	no	—
729	C₂×D₄	—	3	2	no	—
730	C₂×D₄	—	3	2	no	—
731	C₂×D₄	—	3	4	no	—
732	C₂×D₄	—	3	8	no	—
733	C₂×D₄	—	3	2	no	—
734	C₂×D₄	—	3	1	no	—
735	C₂×D₄	—	6	4	no	—
736	C₂×D₄	—	6	8	no	—
737	C₂×D₄	—	6	8	no	—
738	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
739	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
740	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
741	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
742	C₂×D₄	C₂²×C₅×D₃	1	8	yes	—
743	C₂²×C₄	—	3	1	no	—
744	C₂²×C₄	—	3	8	no	—
745	C₂²×C₄	—	3	1	no	—
746	C₂²×C₄	—	3	1	no	—
747	C₂²×C₄	—	3	1	no	—
748	C₂²×C₄	—	3	1	no	—
749	C₂²×C₄	—	3	2	no	—
750	C₂²×C₄	—	3	4	no	—
751	C₂²×C₄	—	3	4	no	—
752	C₂²×C₄	—	3	2	no	—
753	C₂²×C₄	—	3	2	no	—
754	C₂²×C₄	—	3	2	no	—
755	C₂²×C₄	—	3	2	no	—
756	C₂²×C₄	—	3	4	no	—
757	C₂²×C₄	—	6	8	no	—
758	C₂²×C₄	—	6	8	no	—
759	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
760	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
761	C₄⋊C₄	—	3	4	no	—
762	C₄⋊C₄	—	3	2	no	—
763	C₄⋊C₄	—	3	8	no	—
764	C₄⋊C₄	—	3	8	no	—
765	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
766	C₂²⋊C₄	—	3	2	no	—
767	C₂²⋊C₄	—	3	8	no	—
768	C₂²⋊C₄	—	3	8	no	—
769	C₂²⋊C₄	—	3	4	no	—
770	C₂²⋊C₄	—	3	8	no	—
771	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
772	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
773	C₄²	—	3	4	no	—
774	C₄²	—	3	2	no	—
775	C₄²	C₂²×C₅×D₃	1	2	yes	—
776	C₃×C₅	#3449	1	1	yes	characteristic, complemented, Hall
777	C₂²×C₃	—	2	2	no	—
778	C₂²×C₃	—	2	4	no	—
779	C₂²×C₃	—	2	2	no	—
780	C₂²×C₃	—	2	8	no	—
781	C₂²×C₃	—	2	4	no	—
782	C₂²×C₃	—	4	8	no	—
783	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
784	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
785	C₂×D₃	—	2	2	no	—
786	C₂×D₃	—	2	2	no	—
787	C₂×D₃	—	2	2	no	—
788	C₂×D₃	—	2	4	no	—
789	C₂×D₃	—	4	4	no	—
790	C₂×D₃	—	4	8	no	—
791	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
792	C₂×D₃	C₂²×C₅×D₄	1	2	yes	—
793	C₃×C₄	—	2	2	no	—
794	C₃×C₄	—	2	4	no	—
795	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
796	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
797	Dic₃	—	2	2	no	—
798	Dic₃	—	2	4	no	—
799	Dic₃	—	2	4	no	—
800	Dic₃	C₂²×C₅×D₄	1	2	yes	—
801	Dic₃	C₂²×C₅×D₄	1	2	yes	—
802	C₂×C₅	—	2	2	no	—
803	C₂×C₅	—	4	4	no	—
804	C₂×C₅	—	4	2	no	—
805	C₂×C₅	—	6	2	no	—
806	C₂×C₅	—	6	2	no	—
807	C₂×C₅	—	12	2	no	—
808	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
809	C₂×C₅	#5966	1	2	yes	—
810	C₂³	—	2	4	no	—
811	C₂³	—	3	1	no	—
812	C₂³	—	3	1	no	—
813	C₂³	—	3	4	no	—
814	C₂³	—	3	2	no	—
815	C₂³	—	4	4	no	—
816	C₂³	—	6	4	no	—
817	C₂³	—	12	2	no	—
818	C₂³	—	12	4	no	—
819	C₂³	C₂³×C₅×D₃	1	2	yes	—
820	C₂³	C₂³×C₅×D₃	1	4	yes	—
821	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
822	Q₈	—	2	2	no	—
823	Q₈	—	6	4	no	—
824	Q₈	—	6	4	no	—
825	Q₈	—	6	2	no	—
826	Q₈	—	6	4	no	—
827	D₄	—	2	4	no	—
828	D₄	—	2	4	no	—
829	D₄	—	2	4	no	—
830	D₄	—	2	2	no	—
831	D₄	—	4	8	no	—
832	D₄	—	6	4	no	—
833	D₄	—	6	4	no	—
834	D₄	—	6	4	no	—
835	D₄	—	6	8	no	—
836	D₄	—	6	8	no	—
837	D₄	—	6	4	no	—
838	D₄	—	6	2	no	—
839	D₄	—	12	8	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	3	4	no	—
842	C₂×C₄	—	3	1	no	—
843	C₂×C₄	—	3	1	no	—
844	C₂×C₄	—	3	4	no	—
845	C₂×C₄	—	3	4	no	—
846	C₂×C₄	—	3	4	no	—
847	C₂×C₄	—	3	4	no	—
848	C₂×C₄	—	3	4	no	—
849	C₂×C₄	—	3	2	no	—
850	C₂×C₄	—	3	4	no	—
851	C₂×C₄	—	6	4	no	—
852	C₂×C₄	—	6	4	no	—
853	C₂×C₄	—	6	4	no	—
854	C₂×C₄	—	6	8	no	—
855	C₂×C₄	—	6	8	no	—
856	C₂×C₄	—	6	4	no	—
857	C₂×C₄	—	6	4	no	—
858	C₂×C₄	—	12	4	no	—
859	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
860	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
861	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
862	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
863	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
864	C₂×C₃	—	2	2	no	—
865	C₂×C₃	—	4	2	no	—
866	C₂×C₃	—	4	4	no	—
867	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
868	C₂×C₃	C₅×#585	1	2	yes	—
869	D₃	—	2	2	no	—
870	D₃	—	2	2	no	—
871	D₃	—	4	2	no	—
872	C₅	#86313	1	1	yes	characteristic, direct product factor, Sylow
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	4	no	—
876	C₂²	—	2	4	no	—
877	C₂²	—	2	8	no	—
878	C₂²	—	3	2	no	—
879	C₂²	—	3	2	no	—
880	C₂²	—	4	8	no	—
881	C₂²	—	6	2	no	—
882	C₂²	—	6	2	no	—
883	C₂²	—	6	2	no	—
884	C₂²	—	6	4	no	—
885	C₂²	—	12	4	no	—
886	C₂²	—	12	8	no	—
887	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
888	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
889	C₄	—	2	2	no	—
890	C₄	—	2	4	no	—
891	C₄	—	3	2	no	—
892	C₄	—	3	2	no	—
893	C₄	—	6	2	no	—
894	C₄	—	6	4	no	—
895	C₄	—	6	4	no	—
896	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
897	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
898	C₃	C₅×#3449	1	1	yes	characteristic, complemented, Sylow
899	C₂	—	2	2	no	—
900	C₂	—	4	4	no	—
901	C₂	—	4	2	no	—
902	C₂	—	6	2	no	—
903	C₂	—	6	2	no	—
904	C₂	—	12	2	no	—
905	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
906	C₂	C₅×#5966	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#535	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#535	D₃
hypocenter	C₃	C₅×#3449
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#535

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×#41	C₂	semidirect
2. C₂²×C₅×#237	C₂	semidirect
3. C₃×C₅×#535	C₂	semidirect
4. C₅×#5825	C₂	semidirect
5. C₅×#5805	C₂	semidirect
6. C₅×#5716	C₂	semidirect
7. C₅×#5715	C₂	semidirect
8. C₅×#5675	C₂	semidirect
9. C₅×#5668	C₂	semidirect
10. C₅×#5608	C₂	semidirect
11. C₅×#5606	C₂	semidirect
12. C₅×#5589	C₂	semidirect
13. C₅×#5586	C₂	semidirect
14. C₅×#5526	C₂	semidirect
15. C₅×D₃×#117	C₂	semidirect
18. C₂²×C₃×C₅×D₄	C₂²	semidirect
20. C₂³×C₅×Dic₃	C₂²	semidirect
22. C₂×C₅×#239	C₂²	semidirect
23. C₂×C₅×D₃×Q₈	C₂²	semidirect
28. C₂×C₅×#237	C₂²	semidirect
29. C₂×C₅×#237	C₂²	semidirect
30. C₂×C₅×#237	C₂²	semidirect
32. C₂×C₅×D₃×D₄	C₂²	semidirect
34. C₂×C₅×#235	C₂²	semidirect
36. C₂²×C₄×C₅×D₃	C₂²	semidirect
37. C₂²×C₅×Dic₆	C₂²	semidirect
38. C₃×C₅×#127	C₂²	semidirect
39. C₃×C₅×#124	C₂²	semidirect
40. C₃×C₅×#121	C₂²	semidirect
41. C₃×C₅×#120	C₂²	semidirect
42. C₃×C₅×#117	C₂²	semidirect
43. C₅×#953	C₂²	semidirect
44. C₅×#944	C₂²	semidirect
45. C₅×#940	C₂²	semidirect
46. C₅×#939	C₂²	semidirect
47. C₅×#938	C₂²	semidirect
48. C₅×#938	C₂²	semidirect
49. C₅×#937	C₂²	semidirect
50. C₅×#936	C₂²	semidirect
51. C₅×#936	C₂²	semidirect
52. C₅×#935	C₂²	semidirect
53. C₅×D₄×Dic₃	C₂²	semidirect
54. C₅×#926	C₂²	semidirect
55. C₅×#924	C₂²	semidirect
56. C₅×#897	C₂²	semidirect
57. C₅×#892	C₂²	semidirect
58. C₅×D₃×C₄⋊C₄	C₂²	semidirect
59. C₅×#886	C₂²	semidirect
60. C₅×#884	C₂²	semidirect
61. C₅×#883	C₂²	semidirect
62. C₅×#67⋊C₄	C₂²	semidirect
64. C₅×#878	C₂²	semidirect
65. C₅×#877	C₂²	semidirect
66. C₅×#875	C₂²	semidirect
67. C₅×#872	C₂²	semidirect
68. C₄²×C₅×D₃	C₂²	semidirect
69. C₅×#869	C₂²	semidirect
70. #86313	C₅	direct (N × H)
79. C₅×#535	D₃	semidirect
127. C₂×C₄×C₅×D₃	D₄	semidirect
156. C₂×D₃×#41	C₂×C₅	semidirect
157. C₂²×#237	C₂×C₅	semidirect
158. C₃×#535	C₂×C₅	semidirect
159. #5825	C₂×C₅	semidirect
160. #5805	C₂×C₅	semidirect
161. #5716	C₂×C₅	semidirect
162. #5715	C₂×C₅	semidirect
163. #5675	C₂×C₅	semidirect
164. #5668	C₂×C₅	semidirect
165. #5608	C₂×C₅	semidirect
166. #5606	C₂×C₅	semidirect
167. #5589	C₂×C₅	semidirect
168. #5586	C₂×C₅	semidirect
169. #5526	C₂×C₅	semidirect
170. D₃×#117	C₂×C₅	semidirect
188. C₂²×C₅×D₄	C₂×D₃	semidirect
195. C₅×#127	C₂×D₃	semidirect
199. C₅×#124	C₂×D₃	semidirect
210. C₅×#121	C₂×D₃	semidirect
213. C₅×#120	C₂×D₃	semidirect
220. C₅×#117	C₂×D₃	semidirect
280. C₂²×C₃×D₄	C₂²×C₅	semidirect
282. C₂³×Dic₃	C₂²×C₅	semidirect
284. C₂×#239	C₂²×C₅	semidirect
285. C₂×D₃×Q₈	C₂²×C₅	semidirect
290. C₂×#237	C₂²×C₅	semidirect
291. C₂×#237	C₂²×C₅	semidirect
292. C₂×#237	C₂²×C₅	semidirect
294. C₂×D₃×D₄	C₂²×C₅	semidirect
296. C₂×#235	C₂²×C₅	semidirect
298. C₂²×C₄×D₃	C₂²×C₅	semidirect
299. C₂²×Dic₆	C₂²×C₅	semidirect
300. C₃×#127	C₂²×C₅	semidirect
301. C₃×#124	C₂²×C₅	semidirect
302. C₃×#121	C₂²×C₅	semidirect
303. C₃×#120	C₂²×C₅	semidirect
304. C₃×#117	C₂²×C₅	semidirect
305. #953	C₂²×C₅	semidirect
306. #944	C₂²×C₅	semidirect
307. #940	C₂²×C₅	semidirect
308. #939	C₂²×C₅	semidirect
309. #938	C₂²×C₅	semidirect
310. #938	C₂²×C₅	semidirect
311. #937	C₂²×C₅	semidirect
312. #936	C₂²×C₅	semidirect
313. #936	C₂²×C₅	semidirect
314. #935	C₂²×C₅	semidirect
315. D₄×Dic₃	C₂²×C₅	semidirect
316. #926	C₂²×C₅	semidirect
317. #924	C₂²×C₅	semidirect
318. #897	C₂²×C₅	semidirect
319. #892	C₂²×C₅	semidirect
320. D₃×C₄⋊C₄	C₂²×C₅	semidirect
321. #886	C₂²×C₅	semidirect
322. #884	C₂²×C₅	semidirect
323. #883	C₂²×C₅	semidirect
324. #67⋊C₄	C₂²×C₅	semidirect
326. #878	C₂²×C₅	semidirect
327. #877	C₂²×C₅	semidirect
328. #875	C₂²×C₅	semidirect
329. #872	C₂²×C₅	semidirect
330. C₄²×D₃	C₂²×C₅	semidirect
331. #869	C₂²×C₅	semidirect
410. #535	C₅×D₃	semidirect
483. C₂×C₄×D₃	C₅×D₄	semidirect
583. C₂²×D₄	C₂×C₅×D₃	semidirect
590. #127	C₂×C₅×D₃	semidirect
594. #124	C₂×C₅×D₃	semidirect
605. #121	C₂×C₅×D₃	semidirect
608. #120	C₂×C₅×D₃	semidirect
615. #117	C₂×C₅×D₃	semidirect
776. C₃×C₅	#3449	semidirect
872. C₅	#86313	direct (N × H)
898. C₃	C₅×#3449	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
C₂²×C₅×#237	2
C₃×C₅×#535	2
C₅×#5825	2
C₅×#5805	2
C₅×#5716	2
C₅×#5715	2
C₅×#5675	2
C₅×#5668	2
C₅×#5608	2
C₅×#5606	2
C₅×#5589	2
C₅×#5586	2
C₅×#5526	2
C₅×D₃×#117	2
C₅×#3449	3
#86313	5

Subgroups — C5×#86313 #14480644

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86313 #14480644