Subgroups — C₅×#86132 #14495594

Order 1920.

1860 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5712	C₂	1	2	yes	maximal, complemented
3	C₅×#5712	C₂	1	2	yes	maximal, complemented
4	C₅×#5699	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×C₃⋊#564	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5684	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5672	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5667	C₂	1	2	yes	maximal, complemented
9	C₅×#5651	C₂	1	2	yes	maximal, complemented
10	C₅×#5646	C₂	1	2	yes	maximal, complemented
11	C₅×#5621	C₂	1	2	yes	maximal, complemented
12	C₅×#5578	C₂	1	2	yes	maximal, complemented
13	C₅×#5557	C₂	1	2	yes	maximal, complemented
14	C₅×#5538	C₂	1	2	yes	maximal, complemented
15	C₅×#5538	C₂	1	2	yes	maximal, complemented
16	C₅×#5528	C₂	1	2	yes	maximal, complemented
17	C₅×#5517	C₂	1	2	yes	maximal, complemented
18	C₅×#5479	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#5470	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#3531	—	3	1	no	maximal, Hall
21	C₃×C₅×#126	C₂²	1	2	yes	—
22	C₃×C₅×#125	C₂²	1	1	yes	characteristic
23	C₃×C₅×#124	C₂²	1	1	yes	characteristic
24	C₃×C₅×#123	C₂²	1	2	yes	—
25	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×#121	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
30	C₃×C₅×#117	C₂²	1	2	yes	—
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
32	C₅×#946	C₂²	1	2	yes	—
33	C₅×#944	C₂²	1	2	yes	—
34	C₅×#939	C₂²	1	2	yes	—
35	C₅×#939	C₂²	1	2	yes	—
36	C₅×#938	C₂²	1	2	yes	—
37	C₅×#936	C₂²	1	2	yes	—
38	C₅×#935	C₂²	1	2	yes	—
39	C₅×#935	C₂²	1	2	yes	—
40	C₅×#930	C₂²	1	1	yes	characteristic
41	C₅×#929	C₂²	1	2	yes	—
42	C₄×C₅×#67	C₂²	1	2	yes	—
43	C₄×C₅×#67	C₂²	1	2	yes	—
44	C₄×C₅×#67	C₂²	1	2	yes	—
45	C₅×#926	C₂²	1	1	yes	characteristic
46	C₅×#926	C₂²	1	1	yes	characteristic
47	C₅×#926	C₂²	1	2	yes	—
48	C₅×#924	C₂²	1	1	yes	characteristic
49	C₅×#924	C₂²	1	2	yes	—
50	C₅×#924	C₂²	1	2	yes	—
51	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
52	C₅×#898	C₂²	1	2	yes	—
53	C₅×#898	C₂²	1	2	yes	—
54	C₅×#898	C₂²	1	2	yes	—
55	C₅×#897	C₂²	1	2	yes	—
56	C₅×#897	C₂²	1	2	yes	—
57	C₅×#896	C₂²	1	2	yes	—
58	C₅×#896	C₂²	1	2	yes	—
59	C₅×#896	C₂²	1	2	yes	—
60	C₅×#894	C₂²	1	2	yes	—
61	C₅×#890	C₂²	1	2	yes	—
62	C₅×#890	C₂²	1	2	yes	—
63	C₅×#890	C₂²	1	2	yes	—
64	C₅×#889	C₂²	1	2	yes	—
65	C₅×#889	C₂²	1	2	yes	—
66	C₅×#889	C₂²	1	2	yes	—
67	C₅×#889	C₂²	1	2	yes	—
68	C₅×#889	C₂²	1	2	yes	—
69	C₅×#888	C₂²	1	2	yes	—
70	C₅×#888	C₂²	1	2	yes	—
71	C₅×#888	C₂²	1	2	yes	—
72	C₅×#886	C₂²	1	2	yes	—
73	C₅×#886	C₂²	1	2	yes	—
74	C₅×#885	C₂²	1	2	yes	—
75	C₅×#885	C₂²	1	2	yes	—
76	C₅×#885	C₂²	1	2	yes	—
77	C₅×#884	C₂²	1	2	yes	—
78	C₅×#883	C₂²	1	2	yes	—
79	C₅×#883	C₂²	1	2	yes	—
80	C₅×#883	C₂²	1	2	yes	—
81	C₅×#879	C₂²	1	2	yes	—
82	C₅×#879	C₂²	1	2	yes	—
83	C₅×#879	C₂²	1	2	yes	—
84	C₅×#879	C₂²	1	2	yes	—
85	C₅×#879	C₂²	1	2	yes	—
86	C₅×#878	C₂²	1	2	yes	—
87	C₅×#878	C₂²	1	2	yes	—
88	C₅×#878	C₂²	1	2	yes	—
89	C₅×#878	C₂²	1	2	yes	—
90	C₅×#878	C₂²	1	2	yes	—
91	C₅×#878	C₂²	1	2	yes	—
92	C₅×#876	C₂²	1	2	yes	—
93	C₅×#875	C₂²	1	1	yes	characteristic
94	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
95	C₅×#872	C₂²	1	2	yes	—
96	C₅×#872	C₂²	1	2	yes	—
97	C₄²×C₅×D₃	C₂²	1	2	yes	—
98	C₅×#870	C₂²	1	1	yes	characteristic
99	C₅×#870	C₂²	1	1	yes	characteristic
100	C₅×#870	C₂²	1	1	yes	characteristic
101	C₅×#869	C₂²	1	1	yes	characteristic
102	C₅×#869	C₂²	1	1	yes	characteristic
103	C₄×C₅×Dic₆	C₂²	1	2	yes	—
104	C₄×C₅×Dic₆	C₂²	1	2	yes	—
105	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
106	C₄×C₅×Dic₆	C₂²	1	2	yes	—
107	C₄×C₅×Dic₆	C₂²	1	2	yes	—
108	#86132	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
109	C₅×#564	—	3	1	no	—
110	C₅×#563	—	3	2	no	—
111	C₅×#563	—	3	2	no	—
112	C₅×#563	—	3	1	no	—
113	C₅×#563	—	3	1	no	—
114	C₅×#563	—	3	2	no	—
115	C₅×#563	—	3	2	no	—
116	C₅×#562	—	3	1	no	—
117	C₅×#562	—	3	2	no	—
118	C₅×#562	—	3	2	no	—
119	C₅×#533	—	3	2	no	—
120	C₅×#533	—	3	2	no	—
121	C₅×#533	—	3	1	no	—
122	C₅×#529	—	3	2	no	—
123	C₅×#529	—	3	2	no	—
124	C₅×#529	—	3	2	no	—
125	C₅×#529	—	3	2	no	—
126	C₅×#529	—	3	1	no	—
127	C₅×#529	D₃	1	1	yes	characteristic, complemented
128	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
129	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
131	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
132	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
133	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
134	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
135	C₂×C₅×#67	C₂³	1	2	yes	—
136	C₂×C₅×#67	C₂³	1	2	yes	—
137	C₂×C₅×#67	C₂³	1	2	yes	—
138	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
139	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
140	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
141	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
142	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
143	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
144	C₂×C₅×Dic₆	C₂³	1	2	yes	—
145	C₂×C₅×Dic₆	C₂³	1	2	yes	—
146	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
147	C₂×C₅×Dic₆	C₂³	1	2	yes	—
148	C₂×C₅×Dic₆	C₂³	1	2	yes	—
149	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
150	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
151	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
152	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
155	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
161	C₃×C₄²×C₅	C₂³	1	2	yes	—
162	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
163	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
164	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
165	C₅×#217	C₂³	1	2	yes	—
166	C₅×#217	C₂³	1	2	yes	—
167	C₅×#217	C₂³	1	2	yes	—
168	C₅×#217	C₂³	1	2	yes	—
169	C₅×#217	C₂³	1	2	yes	—
170	C₅×#217	C₂³	1	2	yes	—
171	C₅×#217	C₂³	1	2	yes	—
172	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
173	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
174	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
175	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
176	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
177	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
178	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
179	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
180	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
181	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
182	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
183	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
184	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
185	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
186	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
187	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
188	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
189	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
190	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
191	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
192	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
193	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
194	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
195	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
196	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
197	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
198	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
199	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
200	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
201	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
202	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
203	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
204	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
205	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
206	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
207	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
208	C₄×C₅×Dic₃	C₂³	1	2	yes	—
209	C₄×C₅×Dic₃	C₂³	1	2	yes	—
210	C₄×C₅×Dic₃	C₂³	1	2	yes	—
211	C₄×C₅×Dic₃	C₂³	1	2	yes	—
212	C₄×C₅×Dic₃	C₂³	1	2	yes	—
213	C₄×C₅×Dic₃	C₂³	1	2	yes	—
214	C₄×C₅×Dic₃	C₂³	1	2	yes	—
215	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
216	#5712	C₂×C₅	1	2	yes	complemented
217	#5712	C₂×C₅	1	2	yes	complemented
218	#5699	C₂×C₅	1	1	yes	characteristic, complemented
219	C₃⋊#564	C₂×C₅	1	1	yes	characteristic, complemented
220	#5684	C₂×C₅	1	1	yes	characteristic, complemented
221	#5672	C₂×C₅	1	1	yes	characteristic, complemented
222	#5667	C₂×C₅	1	2	yes	complemented
223	#5651	C₂×C₅	1	2	yes	complemented
224	#5646	C₂×C₅	1	2	yes	complemented
225	#5621	C₂×C₅	1	2	yes	complemented
226	#5578	C₂×C₅	1	2	yes	complemented
227	#5557	C₂×C₅	1	2	yes	complemented
228	#5538	C₂×C₅	1	2	yes	complemented
229	#5538	C₂×C₅	1	2	yes	complemented
230	#5528	C₂×C₅	1	2	yes	complemented
231	#5517	C₂×C₅	1	2	yes	complemented
232	#5479	C₂×C₅	1	1	yes	characteristic, complemented
233	#5470	C₂×C₅	1	1	yes	characteristic, complemented
234	C₅×C₄⋊Q₈	—	3	2	no	—
235	C₅×C₄⋊Q₈	—	3	2	no	—
236	C₅×C₄⋊Q₈	—	3	2	no	—
237	C₅×C₄⋊Q₈	—	3	2	no	—
238	C₅×C₄⋊Q₈	—	3	1	no	—
239	C₅×C₄⋊Q₈	—	3	1	no	—
240	C₅×#126	—	3	2	no	—
241	C₅×#126	—	3	2	no	—
242	C₅×#126	—	3	2	no	—
243	C₅×#126	—	3	2	no	—
244	C₅×#126	—	3	2	no	—
245	C₅×#126	—	3	2	no	—
246	C₅×#126	—	3	2	no	—
247	C₅×#126	—	3	2	no	—
248	C₅×#126	—	3	2	no	—
249	C₅×#126	C₂×D₃	1	2	yes	—
250	C₅×#125	—	3	2	no	—
251	C₅×#125	—	3	2	no	—
252	C₅×#125	—	3	2	no	—
253	C₅×#125	—	3	2	no	—
254	C₅×#125	—	3	2	no	—
255	C₅×#125	—	3	2	no	—
256	C₅×#125	—	3	2	no	—
257	C₅×#125	—	3	2	no	—
258	C₅×#125	—	3	1	no	—
259	C₅×#125	—	3	1	no	—
260	C₅×#125	—	3	1	no	—
261	C₅×#125	C₂×D₃	1	1	yes	characteristic
262	C₅×#124	—	3	2	no	—
263	C₅×#124	—	3	2	no	—
264	C₅×#124	—	3	2	no	—
265	C₅×#124	—	3	2	no	—
266	C₅×#124	—	3	1	no	—
267	C₅×#124	C₂×D₃	1	1	yes	characteristic
268	C₅×#123	—	3	2	no	—
269	C₅×#123	—	3	2	no	—
270	C₅×#123	—	3	2	no	—
271	C₅×#123	—	3	2	no	—
272	C₅×#123	—	3	2	no	—
273	C₅×#123	—	3	2	no	—
274	C₅×#123	—	3	2	no	—
275	C₅×#123	—	3	2	no	—
276	C₅×#123	—	3	2	no	—
277	C₅×#123	C₂×D₃	1	2	yes	—
278	C₅×C₂²⋊Q₈	—	3	2	no	—
279	C₅×C₂²⋊Q₈	—	3	1	no	—
280	C₅×C₂²⋊Q₈	—	3	2	no	—
281	C₅×C₂²⋊Q₈	—	3	2	no	—
282	C₅×C₂²⋊Q₈	—	3	2	no	—
283	C₅×C₂²⋊Q₈	—	3	2	no	—
284	C₅×C₂²⋊Q₈	—	3	2	no	—
285	C₅×C₂²⋊Q₈	—	3	2	no	—
286	C₅×C₂²⋊Q₈	—	3	2	no	—
287	C₅×C₂²⋊Q₈	—	3	2	no	—
288	C₅×C₂²⋊Q₈	—	3	2	no	—
289	C₅×C₂²⋊Q₈	—	3	2	no	—
290	C₅×C₂²⋊Q₈	—	3	2	no	—
291	C₅×C₂²⋊Q₈	—	3	2	no	—
292	C₅×C₂²⋊Q₈	—	3	2	no	—
293	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
294	C₅×#121	—	3	2	no	—
295	C₅×#121	—	3	2	no	—
296	C₅×#121	—	3	2	no	—
297	C₅×#121	—	3	1	no	—
298	C₅×#121	—	3	2	no	—
299	C₅×#121	C₂×D₃	1	1	yes	characteristic
300	C₄×C₅×Q₈	—	3	2	no	—
301	C₄×C₅×Q₈	—	3	2	no	—
302	C₄×C₅×Q₈	—	3	2	no	—
303	C₄×C₅×Q₈	—	3	2	no	—
304	C₄×C₅×Q₈	—	3	1	no	—
305	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
306	C₄×C₅×D₄	—	3	2	no	—
307	C₄×C₅×D₄	—	3	2	no	—
308	C₄×C₅×D₄	—	3	2	no	—
309	C₄×C₅×D₄	—	3	1	no	—
310	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
311	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
312	C₅×#117	—	3	2	no	—
313	C₅×#117	—	3	1	no	—
314	C₅×#117	—	3	1	no	—
315	C₅×#117	—	3	2	no	—
316	C₅×#117	—	3	2	no	—
317	C₅×#117	C₂×D₃	1	2	yes	—
318	C₂×C₄²×C₅	—	3	2	no	—
319	C₂×C₄²×C₅	—	3	2	no	—
320	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
321	#3531	—	3	1	no	Sylow
322	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
323	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
324	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
325	C₃×C₅×Q₈	—	4	1	no	—
326	C₃×C₅×D₄	—	4	2	no	—
327	C₃×C₅×D₄	—	4	1	no	—
328	C₂×C₃×C₄×C₅	—	2	4	no	—
329	C₂×C₃×C₄×C₅	—	2	2	no	—
330	C₂×C₃×C₄×C₅	—	4	1	no	—
331	C₂×C₃×C₄×C₅	—	4	1	no	—
332	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
333	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
334	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
335	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
336	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
337	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
338	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
339	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
340	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
341	C₅×#67	—	4	2	no	—
342	C₅×#67	—	4	2	no	—
343	C₅×#67	—	4	2	no	—
344	C₂×C₅×Dic₃	—	4	2	no	—
345	C₂×C₅×Dic₃	—	4	2	no	—
346	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
347	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
348	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
349	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
350	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
351	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
352	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
353	C₅×D₁₂	—	4	1	no	—
354	C₄×C₅×D₃	—	2	4	no	—
355	C₄×C₅×D₃	—	4	2	no	—
356	C₄×C₅×D₃	—	4	2	no	—
357	C₅×Dic₆	—	4	2	no	—
358	C₅×Dic₆	—	4	2	no	—
359	C₅×Dic₆	—	4	1	no	—
360	C₅×Dic₆	—	4	2	no	—
361	C₅×Dic₆	—	4	2	no	—
362	C₃×#126	C₂²×C₅	1	2	yes	—
363	C₃×#125	C₂²×C₅	1	1	yes	characteristic
364	C₃×#124	C₂²×C₅	1	1	yes	characteristic
365	C₃×#123	C₂²×C₅	1	2	yes	—
366	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
367	C₃×#121	C₂²×C₅	1	1	yes	characteristic
368	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
369	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
370	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
371	C₃×#117	C₂²×C₅	1	2	yes	—
372	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
373	#946	C₂²×C₅	1	2	yes	—
374	#944	C₂²×C₅	1	2	yes	—
375	#939	C₂²×C₅	1	2	yes	—
376	#939	C₂²×C₅	1	2	yes	—
377	#938	C₂²×C₅	1	2	yes	—
378	#936	C₂²×C₅	1	2	yes	—
379	#935	C₂²×C₅	1	2	yes	—
380	#935	C₂²×C₅	1	2	yes	—
381	#930	C₂²×C₅	1	1	yes	characteristic
382	#929	C₂²×C₅	1	2	yes	—
383	C₄×#67	C₂²×C₅	1	2	yes	—
384	C₄×#67	C₂²×C₅	1	2	yes	—
385	C₄×#67	C₂²×C₅	1	2	yes	—
386	#926	C₂²×C₅	1	1	yes	characteristic
387	#926	C₂²×C₅	1	1	yes	characteristic
388	#926	C₂²×C₅	1	2	yes	—
389	#924	C₂²×C₅	1	2	yes	—
390	#924	C₂²×C₅	1	1	yes	characteristic
391	#924	C₂²×C₅	1	2	yes	—
392	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
393	#898	C₂²×C₅	1	2	yes	—
394	#898	C₂²×C₅	1	2	yes	—
395	#898	C₂²×C₅	1	2	yes	—
396	#897	C₂²×C₅	1	2	yes	—
397	#897	C₂²×C₅	1	2	yes	—
398	#896	C₂²×C₅	1	2	yes	—
399	#896	C₂²×C₅	1	2	yes	—
400	#896	C₂²×C₅	1	2	yes	—
401	#894	C₂²×C₅	1	2	yes	—
402	#890	C₂²×C₅	1	2	yes	—
403	#890	C₂²×C₅	1	2	yes	—
404	#890	C₂²×C₅	1	2	yes	—
405	#889	C₂²×C₅	1	2	yes	—
406	#889	C₂²×C₅	1	2	yes	—
407	#889	C₂²×C₅	1	2	yes	—
408	#889	C₂²×C₅	1	2	yes	—
409	#889	C₂²×C₅	1	2	yes	—
410	#888	C₂²×C₅	1	2	yes	—
411	#888	C₂²×C₅	1	2	yes	—
412	#888	C₂²×C₅	1	2	yes	—
413	#886	C₂²×C₅	1	2	yes	—
414	#886	C₂²×C₅	1	2	yes	—
415	#885	C₂²×C₅	1	2	yes	—
416	#885	C₂²×C₅	1	2	yes	—
417	#885	C₂²×C₅	1	2	yes	—
418	#884	C₂²×C₅	1	2	yes	—
419	#883	C₂²×C₅	1	2	yes	—
420	#883	C₂²×C₅	1	2	yes	—
421	#883	C₂²×C₅	1	2	yes	—
422	#879	C₂²×C₅	1	2	yes	—
423	#879	C₂²×C₅	1	2	yes	—
424	#879	C₂²×C₅	1	2	yes	—
425	#879	C₂²×C₅	1	2	yes	—
426	#879	C₂²×C₅	1	2	yes	—
427	#878	C₂²×C₅	1	2	yes	—
428	#878	C₂²×C₅	1	2	yes	—
429	#878	C₂²×C₅	1	2	yes	—
430	#878	C₂²×C₅	1	2	yes	—
431	#878	C₂²×C₅	1	2	yes	—
432	#878	C₂²×C₅	1	2	yes	—
433	#876	C₂²×C₅	1	2	yes	—
434	#875	C₂²×C₅	1	1	yes	characteristic
435	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
436	#872	C₂²×C₅	1	2	yes	—
437	#872	C₂²×C₅	1	2	yes	—
438	C₄²×D₃	C₂²×C₅	1	2	yes	—
439	#870	C₂²×C₅	1	1	yes	characteristic
440	#870	C₂²×C₅	1	1	yes	characteristic
441	#870	C₂²×C₅	1	1	yes	characteristic
442	#869	C₂²×C₅	1	1	yes	characteristic
443	#869	C₂²×C₅	1	1	yes	characteristic
444	C₄×Dic₆	C₂²×C₅	1	2	yes	—
445	C₄×Dic₆	C₂²×C₅	1	2	yes	—
446	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
447	C₄×Dic₆	C₂²×C₅	1	2	yes	—
448	C₄×Dic₆	C₂²×C₅	1	2	yes	—
449	C₂×C₅×Q₈	—	3	2	no	—
450	C₂×C₅×Q₈	—	3	1	no	—
451	C₂×C₅×Q₈	—	3	2	no	—
452	C₂×C₅×Q₈	—	3	2	no	—
453	C₂×C₅×Q₈	—	3	2	no	—
454	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
455	C₂×C₅×D₄	—	3	2	no	—
456	C₂×C₅×D₄	—	3	2	no	—
457	C₂×C₅×D₄	—	3	2	no	—
458	C₂×C₅×D₄	—	3	1	no	—
459	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
460	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
461	C₂²×C₄×C₅	—	3	2	no	—
462	C₂²×C₄×C₅	—	3	2	no	—
463	C₂²×C₄×C₅	—	3	2	no	—
464	C₂²×C₄×C₅	—	3	2	no	—
465	C₂²×C₄×C₅	—	3	2	no	—
466	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
467	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
468	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
469	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
470	C₅×C₄⋊C₄	—	3	2	no	—
471	C₅×C₄⋊C₄	—	3	2	no	—
472	C₅×C₄⋊C₄	—	3	2	no	—
473	C₅×C₄⋊C₄	—	3	1	no	—
474	C₅×C₄⋊C₄	—	3	1	no	—
475	C₅×C₄⋊C₄	—	3	2	no	—
476	C₅×C₄⋊C₄	—	3	2	no	—
477	C₅×C₄⋊C₄	—	3	2	no	—
478	C₅×C₄⋊C₄	—	3	1	no	—
479	C₅×C₄⋊C₄	—	3	1	no	—
480	C₅×C₄⋊C₄	—	3	2	no	—
481	C₅×C₄⋊C₄	—	3	2	no	—
482	C₅×C₄⋊C₄	—	3	2	no	—
483	C₅×C₄⋊C₄	—	3	1	no	—
484	C₅×C₄⋊C₄	—	3	2	no	—
485	C₅×C₄⋊C₄	—	3	2	no	—
486	C₅×C₄⋊C₄	—	3	2	no	—
487	C₅×C₄⋊C₄	—	3	2	no	—
488	C₅×C₄⋊C₄	—	3	1	no	—
489	C₅×C₄⋊C₄	—	3	2	no	—
490	C₅×C₄⋊C₄	—	3	2	no	—
491	C₅×C₄⋊C₄	—	3	2	no	—
492	C₅×C₄⋊C₄	—	3	2	no	—
493	C₅×C₄⋊C₄	—	3	2	no	—
494	C₅×C₄⋊C₄	—	3	2	no	—
495	C₅×C₄⋊C₄	—	3	2	no	—
496	C₅×C₄⋊C₄	—	3	2	no	—
497	C₅×C₄⋊C₄	—	3	2	no	—
498	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
499	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
500	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
501	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
502	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
503	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
504	C₅×C₂²⋊C₄	—	3	2	no	—
505	C₅×C₂²⋊C₄	—	3	2	no	—
506	C₅×C₂²⋊C₄	—	3	2	no	—
507	C₅×C₂²⋊C₄	—	3	2	no	—
508	C₅×C₂²⋊C₄	—	3	2	no	—
509	C₅×C₂²⋊C₄	—	3	2	no	—
510	C₅×C₂²⋊C₄	—	3	2	no	—
511	C₅×C₂²⋊C₄	—	3	2	no	—
512	C₅×C₂²⋊C₄	—	3	2	no	—
513	C₅×C₂²⋊C₄	—	3	2	no	—
514	C₅×C₂²⋊C₄	—	3	2	no	—
515	C₅×C₂²⋊C₄	—	3	2	no	—
516	C₅×C₂²⋊C₄	—	3	2	no	—
517	C₅×C₂²⋊C₄	—	3	2	no	—
518	C₅×C₂²⋊C₄	—	3	2	no	—
519	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
520	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
521	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
522	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
523	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
524	C₄²×C₅	—	3	2	no	—
525	C₄²×C₅	—	3	2	no	—
526	C₄²×C₅	—	3	2	no	—
527	C₄²×C₅	—	3	2	no	—
528	C₄²×C₅	—	3	2	no	—
529	C₄²×C₅	—	3	2	no	—
530	C₄²×C₅	—	3	2	no	—
531	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
532	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
533	C₄²×C₅	C₂²×D₃	1	2	yes	—
534	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
535	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
536	#564	—	3	1	no	—
537	#563	—	3	2	no	—
538	#563	—	3	2	no	—
539	#563	—	3	1	no	—
540	#563	—	3	1	no	—
541	#563	—	3	2	no	—
542	#563	—	3	2	no	—
543	#562	—	3	1	no	—
544	#562	—	3	2	no	—
545	#562	—	3	2	no	—
546	#533	—	3	2	no	—
547	#533	—	3	2	no	—
548	#533	—	3	1	no	—
549	#529	—	3	2	no	—
550	#529	—	3	2	no	—
551	#529	—	3	2	no	—
552	#529	—	3	2	no	—
553	#529	—	3	1	no	—
554	#529	C₅×D₃	1	1	yes	characteristic, complemented
555	C₂²×C₃×C₅	—	2	1	no	—
556	C₂²×C₃×C₅	—	2	2	no	—
557	C₂²×C₃×C₅	—	2	2	no	—
558	C₂²×C₃×C₅	—	2	2	no	—
559	C₂²×C₃×C₅	—	2	1	no	—
560	C₂²×C₃×C₅	—	2	1	no	—
561	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
562	C₂×C₅×D₃	—	2	2	no	—
563	C₂×C₅×D₃	—	2	2	no	—
564	C₂×C₅×D₃	—	2	2	no	—
565	C₃×C₄×C₅	—	2	2	no	—
566	C₃×C₄×C₅	—	2	1	no	—
567	C₃×C₄×C₅	—	2	1	no	—
568	C₃×C₄×C₅	—	2	1	no	—
569	C₃×C₄×C₅	—	2	2	no	—
570	C₃×C₄×C₅	—	2	2	no	—
571	C₃×C₄×C₅	—	2	1	no	—
572	C₃×C₄×C₅	—	2	1	no	—
573	C₃×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
574	C₅×Dic₃	—	2	2	no	—
575	C₅×Dic₃	—	2	2	no	—
576	C₅×Dic₃	—	2	2	no	—
577	C₅×Dic₃	—	2	2	no	—
578	C₅×Dic₃	—	2	2	no	—
579	C₅×Dic₃	—	2	2	no	—
580	C₅×Dic₃	—	2	2	no	—
581	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
582	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
583	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
584	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
585	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
586	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
587	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
588	C₂×#67	C₂³×C₅	1	2	yes	—
589	C₂×#67	C₂³×C₅	1	2	yes	—
590	C₂×#67	C₂³×C₅	1	2	yes	—
591	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
592	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
593	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
594	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
595	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
596	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
597	C₂×Dic₆	C₂³×C₅	1	2	yes	—
598	C₂×Dic₆	C₂³×C₅	1	2	yes	—
599	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
600	C₂×Dic₆	C₂³×C₅	1	2	yes	—
601	C₂×Dic₆	C₂³×C₅	1	2	yes	—
602	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
603	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
604	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
605	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
606	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
607	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
608	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
609	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
610	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
611	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
612	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
613	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
614	C₃×C₄²	C₂³×C₅	1	2	yes	—
615	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
616	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
617	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
618	#217	C₂³×C₅	1	2	yes	—
619	#217	C₂³×C₅	1	2	yes	—
620	#217	C₂³×C₅	1	2	yes	—
621	#217	C₂³×C₅	1	2	yes	—
622	#217	C₂³×C₅	1	2	yes	—
623	#217	C₂³×C₅	1	2	yes	—
624	#217	C₂³×C₅	1	2	yes	—
625	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
626	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
627	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
628	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
629	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
630	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
631	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
632	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
633	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
634	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
635	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
636	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
637	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
638	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
639	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
640	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
641	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
642	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
643	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
644	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
645	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
646	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
647	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
648	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
649	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
650	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
651	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
652	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
653	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
654	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
655	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
656	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
657	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
658	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
659	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
660	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
661	C₄×Dic₃	C₂³×C₅	1	2	yes	—
662	C₄×Dic₃	C₂³×C₅	1	2	yes	—
663	C₄×Dic₃	C₂³×C₅	1	2	yes	—
664	C₄×Dic₃	C₂³×C₅	1	2	yes	—
665	C₄×Dic₃	C₂³×C₅	1	2	yes	—
666	C₄×Dic₃	C₂³×C₅	1	2	yes	—
667	C₄×Dic₃	C₂³×C₅	1	2	yes	—
668	C₂³×C₅	—	3	2	no	—
669	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
670	C₂³×C₅	C₂³×D₃	1	2	yes	—
671	C₅×Q₈	—	4	1	no	—
672	C₅×Q₈	—	12	1	no	—
673	C₅×Q₈	—	12	2	no	—
674	C₅×Q₈	—	12	2	no	—
675	C₅×Q₈	—	12	2	no	—
676	C₅×Q₈	—	12	2	no	—
677	C₅×D₄	—	4	1	no	—
678	C₅×D₄	—	4	2	no	—
679	C₅×D₄	—	12	1	no	—
680	C₅×D₄	—	12	2	no	—
681	C₅×D₄	—	12	2	no	—
682	C₅×D₄	—	12	2	no	—
683	C₂×C₄×C₅	—	2	4	no	—
684	C₂×C₄×C₅	—	2	2	no	—
685	C₂×C₄×C₅	—	3	2	no	—
686	C₂×C₄×C₅	—	3	2	no	—
687	C₂×C₄×C₅	—	3	2	no	—
688	C₂×C₄×C₅	—	3	2	no	—
689	C₂×C₄×C₅	—	3	2	no	—
690	C₂×C₄×C₅	—	3	2	no	—
691	C₂×C₄×C₅	—	3	2	no	—
692	C₂×C₄×C₅	—	4	1	no	—
693	C₂×C₄×C₅	—	4	1	no	—
694	C₂×C₄×C₅	—	6	4	no	—
695	C₂×C₄×C₅	—	12	2	no	—
696	C₂×C₄×C₅	—	12	2	no	—
697	C₂×C₄×C₅	—	12	2	no	—
698	C₂×C₄×C₅	—	12	2	no	—
699	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
700	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
701	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
702	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
703	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
704	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
705	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
706	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
707	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
708	C₄⋊Q₈	—	3	2	no	—
709	C₄⋊Q₈	—	3	2	no	—
710	C₄⋊Q₈	—	3	2	no	—
711	C₄⋊Q₈	—	3	2	no	—
712	C₄⋊Q₈	—	3	1	no	—
713	C₄⋊Q₈	—	3	1	no	—
714	#126	—	3	2	no	—
715	#126	—	3	2	no	—
716	#126	—	3	2	no	—
717	#126	—	3	2	no	—
718	#126	—	3	2	no	—
719	#126	—	3	2	no	—
720	#126	—	3	2	no	—
721	#126	—	3	2	no	—
722	#126	—	3	2	no	—
723	#126	C₂×C₅×D₃	1	2	yes	—
724	#125	—	3	2	no	—
725	#125	—	3	2	no	—
726	#125	—	3	2	no	—
727	#125	—	3	2	no	—
728	#125	—	3	2	no	—
729	#125	—	3	2	no	—
730	#125	—	3	2	no	—
731	#125	—	3	2	no	—
732	#125	—	3	1	no	—
733	#125	—	3	1	no	—
734	#125	—	3	1	no	—
735	#125	C₂×C₅×D₃	1	1	yes	characteristic
736	#124	—	3	2	no	—
737	#124	—	3	2	no	—
738	#124	—	3	2	no	—
739	#124	—	3	2	no	—
740	#124	—	3	1	no	—
741	#124	C₂×C₅×D₃	1	1	yes	characteristic
742	#123	—	3	2	no	—
743	#123	—	3	2	no	—
744	#123	—	3	2	no	—
745	#123	—	3	2	no	—
746	#123	—	3	2	no	—
747	#123	—	3	2	no	—
748	#123	—	3	2	no	—
749	#123	—	3	2	no	—
750	#123	—	3	2	no	—
751	#123	C₂×C₅×D₃	1	2	yes	—
752	C₂²⋊Q₈	—	3	2	no	—
753	C₂²⋊Q₈	—	3	1	no	—
754	C₂²⋊Q₈	—	3	2	no	—
755	C₂²⋊Q₈	—	3	2	no	—
756	C₂²⋊Q₈	—	3	2	no	—
757	C₂²⋊Q₈	—	3	2	no	—
758	C₂²⋊Q₈	—	3	2	no	—
759	C₂²⋊Q₈	—	3	2	no	—
760	C₂²⋊Q₈	—	3	2	no	—
761	C₂²⋊Q₈	—	3	2	no	—
762	C₂²⋊Q₈	—	3	2	no	—
763	C₂²⋊Q₈	—	3	2	no	—
764	C₂²⋊Q₈	—	3	2	no	—
765	C₂²⋊Q₈	—	3	2	no	—
766	C₂²⋊Q₈	—	3	2	no	—
767	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
768	#121	—	3	2	no	—
769	#121	—	3	2	no	—
770	#121	—	3	2	no	—
771	#121	—	3	1	no	—
772	#121	—	3	2	no	—
773	#121	C₂×C₅×D₃	1	1	yes	characteristic
774	C₄×Q₈	—	3	2	no	—
775	C₄×Q₈	—	3	2	no	—
776	C₄×Q₈	—	3	2	no	—
777	C₄×Q₈	—	3	2	no	—
778	C₄×Q₈	—	3	1	no	—
779	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
780	C₄×D₄	—	3	2	no	—
781	C₄×D₄	—	3	2	no	—
782	C₄×D₄	—	3	2	no	—
783	C₄×D₄	—	3	1	no	—
784	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
785	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
786	#117	—	3	2	no	—
787	#117	—	3	1	no	—
788	#117	—	3	1	no	—
789	#117	—	3	2	no	—
790	#117	—	3	2	no	—
791	#117	C₂×C₅×D₃	1	2	yes	—
792	C₂×C₄²	—	3	2	no	—
793	C₂×C₄²	—	3	2	no	—
794	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
795	C₂×C₃×C₅	—	4	2	no	—
796	C₂×C₃×C₅	—	4	1	no	—
797	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
798	C₂×C₃×C₅	#585	1	1	yes	characteristic
799	C₂×C₃×C₅	#585	1	1	yes	characteristic
800	C₅×D₃	—	4	2	no	—
801	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
802	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
803	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
804	C₃×Q₈	—	4	1	no	—
805	C₃×D₄	—	4	2	no	—
806	C₃×D₄	—	4	1	no	—
807	C₂×C₃×C₄	—	2	4	no	—
808	C₂×C₃×C₄	—	2	2	no	—
809	C₂×C₃×C₄	—	4	1	no	—
810	C₂×C₃×C₄	—	4	1	no	—
811	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
812	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
813	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
814	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
815	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
816	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
817	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
818	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
819	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
820	#67	—	4	2	no	—
821	#67	—	4	2	no	—
822	#67	—	4	2	no	—
823	C₂×Dic₃	—	4	2	no	—
824	C₂×Dic₃	—	4	2	no	—
825	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
826	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
827	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
828	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
829	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
830	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
831	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
832	D₁₂	—	4	1	no	—
833	C₄×D₃	—	2	4	no	—
834	C₄×D₃	—	4	2	no	—
835	C₄×D₃	—	4	2	no	—
836	Dic₆	—	4	2	no	—
837	Dic₆	—	4	2	no	—
838	Dic₆	—	4	1	no	—
839	Dic₆	—	4	2	no	—
840	Dic₆	—	4	2	no	—
841	C₂²×C₅	—	2	1	no	—
842	C₂²×C₅	—	2	2	no	—
843	C₂²×C₅	—	2	1	no	—
844	C₂²×C₅	—	2	1	no	—
845	C₂²×C₅	—	2	2	no	—
846	C₂²×C₅	—	2	2	no	—
847	C₂²×C₅	—	6	2	no	—
848	C₂²×C₅	—	6	2	no	—
849	C₂²×C₅	—	6	2	no	—
850	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
851	C₄×C₅	—	2	2	no	—
852	C₄×C₅	—	2	1	no	—
853	C₄×C₅	—	2	1	no	—
854	C₄×C₅	—	2	1	no	—
855	C₄×C₅	—	2	1	no	—
856	C₄×C₅	—	2	1	no	—
857	C₄×C₅	—	2	2	no	—
858	C₄×C₅	—	2	2	no	—
859	C₄×C₅	—	6	2	no	—
860	C₄×C₅	—	6	2	no	—
861	C₄×C₅	—	6	2	no	—
862	C₄×C₅	—	6	2	no	—
863	C₄×C₅	—	6	2	no	—
864	C₄×C₅	—	6	2	no	—
865	C₄×C₅	—	6	2	no	—
866	C₄×C₅	#1010	1	2	yes	—
867	C₂×Q₈	—	3	2	no	—
868	C₂×Q₈	—	3	1	no	—
869	C₂×Q₈	—	3	2	no	—
870	C₂×Q₈	—	3	2	no	—
871	C₂×Q₈	—	3	2	no	—
872	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
873	C₂×D₄	—	3	2	no	—
874	C₂×D₄	—	3	2	no	—
875	C₂×D₄	—	3	2	no	—
876	C₂×D₄	—	3	1	no	—
877	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
878	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
879	C₂²×C₄	—	3	2	no	—
880	C₂²×C₄	—	3	2	no	—
881	C₂²×C₄	—	3	2	no	—
882	C₂²×C₄	—	3	2	no	—
883	C₂²×C₄	—	3	2	no	—
884	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
885	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
886	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
887	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
888	C₄⋊C₄	—	3	2	no	—
889	C₄⋊C₄	—	3	2	no	—
890	C₄⋊C₄	—	3	2	no	—
891	C₄⋊C₄	—	3	1	no	—
892	C₄⋊C₄	—	3	1	no	—
893	C₄⋊C₄	—	3	2	no	—
894	C₄⋊C₄	—	3	2	no	—
895	C₄⋊C₄	—	3	2	no	—
896	C₄⋊C₄	—	3	1	no	—
897	C₄⋊C₄	—	3	1	no	—
898	C₄⋊C₄	—	3	2	no	—
899	C₄⋊C₄	—	3	2	no	—
900	C₄⋊C₄	—	3	2	no	—
901	C₄⋊C₄	—	3	1	no	—
902	C₄⋊C₄	—	3	2	no	—
903	C₄⋊C₄	—	3	2	no	—
904	C₄⋊C₄	—	3	2	no	—
905	C₄⋊C₄	—	3	2	no	—
906	C₄⋊C₄	—	3	1	no	—
907	C₄⋊C₄	—	3	2	no	—
908	C₄⋊C₄	—	3	2	no	—
909	C₄⋊C₄	—	3	2	no	—
910	C₄⋊C₄	—	3	2	no	—
911	C₄⋊C₄	—	3	2	no	—
912	C₄⋊C₄	—	3	2	no	—
913	C₄⋊C₄	—	3	2	no	—
914	C₄⋊C₄	—	3	2	no	—
915	C₄⋊C₄	—	3	2	no	—
916	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
917	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
918	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
919	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
920	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
921	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
922	C₂²⋊C₄	—	3	2	no	—
923	C₂²⋊C₄	—	3	2	no	—
924	C₂²⋊C₄	—	3	2	no	—
925	C₂²⋊C₄	—	3	2	no	—
926	C₂²⋊C₄	—	3	2	no	—
927	C₂²⋊C₄	—	3	2	no	—
928	C₂²⋊C₄	—	3	2	no	—
929	C₂²⋊C₄	—	3	2	no	—
930	C₂²⋊C₄	—	3	2	no	—
931	C₂²⋊C₄	—	3	2	no	—
932	C₂²⋊C₄	—	3	2	no	—
933	C₂²⋊C₄	—	3	2	no	—
934	C₂²⋊C₄	—	3	2	no	—
935	C₂²⋊C₄	—	3	2	no	—
936	C₂²⋊C₄	—	3	2	no	—
937	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
938	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
939	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
940	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
941	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
942	C₄²	—	3	2	no	—
943	C₄²	—	3	2	no	—
944	C₄²	—	3	2	no	—
945	C₄²	—	3	2	no	—
946	C₄²	—	3	2	no	—
947	C₄²	—	3	2	no	—
948	C₄²	—	3	2	no	—
949	C₄²	C₂²×C₅×D₃	1	2	yes	—
950	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
951	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
952	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
953	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
954	C₃×C₅	#3531	1	1	yes	characteristic, complemented, Hall
955	C₂²×C₃	—	2	1	no	—
956	C₂²×C₃	—	2	2	no	—
957	C₂²×C₃	—	2	2	no	—
958	C₂²×C₃	—	2	2	no	—
959	C₂²×C₃	—	2	1	no	—
960	C₂²×C₃	—	2	1	no	—
961	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
962	C₂×D₃	—	2	2	no	—
963	C₂×D₃	—	2	2	no	—
964	C₂×D₃	—	2	2	no	—
965	C₃×C₄	—	2	2	no	—
966	C₃×C₄	—	2	1	no	—
967	C₃×C₄	—	2	1	no	—
968	C₃×C₄	—	2	1	no	—
969	C₃×C₄	—	2	2	no	—
970	C₃×C₄	—	2	2	no	—
971	C₃×C₄	—	2	1	no	—
972	C₃×C₄	—	2	1	no	—
973	C₃×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
974	Dic₃	—	2	2	no	—
975	Dic₃	—	2	2	no	—
976	Dic₃	—	2	2	no	—
977	Dic₃	—	2	2	no	—
978	Dic₃	—	2	2	no	—
979	Dic₃	—	2	2	no	—
980	Dic₃	—	2	2	no	—
981	C₂×C₅	—	4	1	no	—
982	C₂×C₅	—	4	2	no	—
983	C₂×C₅	—	12	2	no	—
984	C₂×C₅	C₂×#1010	1	1	yes	characteristic
985	C₂×C₅	#5964	1	1	yes	characteristic
986	C₂×C₅	#5964	1	1	yes	characteristic
987	C₂³	—	3	2	no	—
988	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
989	C₂³	C₂³×C₅×D₃	1	2	yes	—
990	Q₈	—	4	1	no	—
991	Q₈	—	12	1	no	—
992	Q₈	—	12	2	no	—
993	Q₈	—	12	2	no	—
994	Q₈	—	12	2	no	—
995	Q₈	—	12	2	no	—
996	D₄	—	4	1	no	—
997	D₄	—	4	2	no	—
998	D₄	—	12	1	no	—
999	D₄	—	12	2	no	—
1000	D₄	—	12	2	no	—
1001	D₄	—	12	2	no	—
1002	C₂×C₄	—	2	4	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	3	2	no	—
1005	C₂×C₄	—	3	2	no	—
1006	C₂×C₄	—	3	2	no	—
1007	C₂×C₄	—	3	2	no	—
1008	C₂×C₄	—	3	2	no	—
1009	C₂×C₄	—	3	2	no	—
1010	C₂×C₄	—	3	2	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	4	1	no	—
1013	C₂×C₄	—	6	4	no	—
1014	C₂×C₄	—	12	2	no	—
1015	C₂×C₄	—	12	2	no	—
1016	C₂×C₄	—	12	2	no	—
1017	C₂×C₄	—	12	2	no	—
1018	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1019	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1020	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1021	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1022	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1023	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1024	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1025	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1026	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1027	C₂×C₃	—	4	2	no	—
1028	C₂×C₃	—	4	1	no	—
1029	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1030	C₂×C₃	C₅×#585	1	1	yes	characteristic
1031	C₂×C₃	C₅×#585	1	1	yes	characteristic
1032	D₃	—	4	2	no	—
1033	C₅	#86132	1	1	yes	characteristic, direct product factor, Sylow
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	2	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	6	2	no	—
1041	C₂²	—	6	2	no	—
1042	C₂²	—	6	2	no	—
1043	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
1044	C₄	—	2	2	no	—
1045	C₄	—	2	1	no	—
1046	C₄	—	2	1	no	—
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	2	2	no	—
1052	C₄	—	6	2	no	—
1053	C₄	—	6	2	no	—
1054	C₄	—	6	2	no	—
1055	C₄	—	6	2	no	—
1056	C₄	—	6	2	no	—
1057	C₄	—	6	2	no	—
1058	C₄	—	6	2	no	—
1059	C₄	C₅×#1010	1	2	yes	—
1060	C₃	C₅×#3531	1	1	yes	characteristic, complemented, Sylow
1061	C₂	—	4	1	no	—
1062	C₂	—	4	2	no	—
1063	C₂	—	12	2	no	—
1064	C₂	C₂×C₅×#1010	1	1	yes	characteristic
1065	C₂	C₅×#5964	1	1	yes	characteristic
1066	C₂	C₅×#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#529	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₅×#529	D₃
hypocenter	C₃	C₅×#3531
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#529

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#529	C₂	semidirect
2. C₅×#5712	C₂	semidirect
3. C₅×#5712	C₂	semidirect
4. C₅×#5699	C₂	semidirect
5. C₅×C₃⋊#564	C₂	semidirect
6. C₅×#5684	C₂	semidirect
7. C₅×#5672	C₂	semidirect
8. C₅×#5667	C₂	semidirect
9. C₅×#5651	C₂	semidirect
10. C₅×#5646	C₂	semidirect
11. C₅×#5621	C₂	semidirect
12. C₅×#5578	C₂	semidirect
13. C₅×#5557	C₂	semidirect
14. C₅×#5538	C₂	semidirect
15. C₅×#5538	C₂	semidirect
16. C₅×#5528	C₂	semidirect
17. C₅×#5517	C₂	semidirect
18. C₅×#5479	C₂	semidirect
19. C₅×#5470	C₂	semidirect
108. #86132	C₅	direct (N × H)
127. C₅×#529	D₃	semidirect
215. C₃×#529	C₂×C₅	semidirect
216. #5712	C₂×C₅	semidirect
217. #5712	C₂×C₅	semidirect
218. #5699	C₂×C₅	semidirect
219. C₃⋊#564	C₂×C₅	semidirect
220. #5684	C₂×C₅	semidirect
221. #5672	C₂×C₅	semidirect
222. #5667	C₂×C₅	semidirect
223. #5651	C₂×C₅	semidirect
224. #5646	C₂×C₅	semidirect
225. #5621	C₂×C₅	semidirect
226. #5578	C₂×C₅	semidirect
227. #5557	C₂×C₅	semidirect
228. #5538	C₂×C₅	semidirect
229. #5538	C₂×C₅	semidirect
230. #5528	C₂×C₅	semidirect
231. #5517	C₂×C₅	semidirect
232. #5479	C₂×C₅	semidirect
233. #5470	C₂×C₅	semidirect
554. #529	C₅×D₃	semidirect
954. C₃×C₅	#3531	semidirect
1033. C₅	#86132	direct (N × H)
1060. C₃	C₅×#3531	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#529	2
C₅×#5712	2
C₅×#5699	2
C₅×C₃⋊#564	2
C₅×#5684	2
C₅×#5672	2
C₅×#5667	2
C₅×#5651	2
C₅×#5646	2
C₅×#5621	2
C₅×#5578	2
C₅×#5557	2
C₅×#5538	2
C₅×#5528	2
C₅×#5517	2
C₅×#5479	2
C₅×#5470	2
C₅×#3531	3
#86132	5

Subgroups — C5×#86132 #14495594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86132 #14495594