Subgroups — C₃×#10618121 #14484790

Order 1920.

2224 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	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66166	C₂	1	2	yes	maximal, complemented
3	C₃×#41×Dic₅	C₂	1	2	yes	maximal, complemented
4	C₃×#66066	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#66055	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#66052	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#66047	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#66015	C₂	1	2	yes	maximal, complemented
9	C₃×#66005	C₂	1	2	yes	maximal, complemented
10	C₃×#65952	C₂	1	2	yes	maximal, complemented
11	C₃×#65935	C₂	1	4	yes	maximal, complemented
12	C₃×#65932	C₂	1	2	yes	maximal, complemented
13	C₃×#65891	C₂	1	2	yes	maximal, complemented
14	C₃×#65872	C₂	1	4	yes	maximal, complemented
15	C₃×C₄×#711	C₂	1	2	yes	maximal, complemented
16	C₃×C₄×#709	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
18	#10618121	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
20	C₂×C₃×#711	C₂²	1	2	yes	—
21	C₂×C₃×#709	C₂²	1	1	yes	characteristic
22	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×#127	C₂²	1	1	yes	characteristic
25	C₃×C₅×#124	C₂²	1	2	yes	—
26	C₃×C₅×#121	C₂²	1	2	yes	—
27	C₃×C₅×#121	C₂²	1	2	yes	—
28	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
29	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
30	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
31	C₃×#4093	C₂²	1	2	yes	—
32	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
33	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
34	C₃×#4090	C₂²	1	2	yes	—
35	C₃×#4086	C₂²	1	2	yes	—
36	C₃×#4085	C₂²	1	4	yes	—
37	C₃×#4085	C₂²	1	4	yes	—
38	C₃×#4085	C₂²	1	4	yes	—
39	C₃×#4084	C₂²	1	2	yes	—
40	C₃×#4082	C₂²	1	2	yes	—
41	C₃×#4082	C₂²	1	2	yes	—
42	C₃×#4081	C₂²	1	4	yes	—
43	C₃×D₄×Dic₅	C₂²	1	2	yes	—
44	C₃×D₄×Dic₅	C₂²	1	4	yes	—
45	C₃×D₄×Dic₅	C₂²	1	4	yes	—
46	C₃×D₄×Dic₅	C₂²	1	2	yes	—
47	C₃×D₄×Dic₅	C₂²	1	2	yes	—
48	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	—
49	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	—
50	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
51	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
52	C₃×#4072	C₂²	1	4	yes	—
53	C₃×#4072	C₂²	1	1	yes	characteristic
54	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
55	C₂×C₃×#683	C₂²	1	2	yes	—
56	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	—
57	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
58	C₃×#4044	C₂²	1	4	yes	—
59	C₃×#4043	C₂²	1	2	yes	—
60	C₃×#4038	C₂²	1	2	yes	—
61	C₃×#4036	C₂²	1	2	yes	—
62	C₃×#4035	C₂²	1	4	yes	—
63	C₃×#4033	C₂²	1	2	yes	—
64	C₃×#4032	C₂²	1	4	yes	—
65	C₃×#4031	C₂²	1	4	yes	—
66	C₃×#4029	C₂²	1	4	yes	—
67	C₃×#4027	C₂²	1	4	yes	—
68	C₃×#4025	C₂²	1	4	yes	—
69	C₃×#4025	C₂²	1	4	yes	—
70	C₃×#4024	C₂²	1	4	yes	—
71	C₃×#4023	C₂²	1	4	yes	—
72	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
73	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
74	C₃×#4018	C₂²	1	2	yes	—
75	C₃×C₄²×D₅	C₂²	1	2	yes	—
76	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
77	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
78	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
79	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
80	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
81	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
82	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
83	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
84	C₃×#3480	—	5	1	no	maximal, Hall
85	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
86	#66166	C₂×C₃	1	2	yes	complemented
87	#41×Dic₅	C₂×C₃	1	2	yes	complemented
88	#66066	C₂×C₃	1	1	yes	characteristic, complemented
89	#66055	C₂×C₃	1	1	yes	characteristic, complemented
90	#66052	C₂×C₃	1	1	yes	characteristic, complemented
91	#66047	C₂×C₃	1	1	yes	characteristic, complemented
92	#66015	C₂×C₃	1	2	yes	complemented
93	#66005	C₂×C₃	1	2	yes	complemented
94	#65952	C₂×C₃	1	2	yes	complemented
95	#65935	C₂×C₃	1	4	yes	complemented
96	#65932	C₂×C₃	1	2	yes	complemented
97	#65891	C₂×C₃	1	2	yes	complemented
98	#65872	C₂×C₃	1	4	yes	complemented
99	C₄×#711	C₂×C₃	1	2	yes	complemented
100	C₄×#709	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
102	C₃×C₅×#41	—	2	8	no	—
103	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
104	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
105	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
106	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
107	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
108	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
109	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
110	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
111	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
112	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
113	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
114	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
115	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
116	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
117	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
118	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
119	C₃×#711	—	2	8	no	—
120	C₃×#709	—	2	4	no	—
121	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
122	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
123	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
124	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
125	C₂×C₃×Dic₁₀	—	2	4	no	—
126	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
127	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
128	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
129	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
130	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
131	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
135	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
136	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
137	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
138	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
139	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
140	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
141	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
142	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
143	C₃×#685	C₂³	1	2	yes	—
144	C₃×#685	C₂³	1	4	yes	—
145	C₃×#685	C₂³	1	4	yes	—
146	C₃×#685	C₂³	1	2	yes	—
147	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
148	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
149	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
150	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
151	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
152	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
153	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
154	C₃×#683	C₂³	1	2	yes	—
155	C₃×#683	C₂³	1	2	yes	—
156	C₃×#683	C₂³	1	2	yes	—
157	C₃×#683	C₂³	1	4	yes	—
158	C₃×#683	C₂³	1	4	yes	—
159	C₃×#683	C₂³	1	2	yes	—
160	C₃×#683	C₂³	1	2	yes	—
161	C₃×#683	C₂³	1	2	yes	—
162	C₃×C₄×Dic₅	C₂³	1	2	yes	—
163	C₃×C₄×Dic₅	C₂³	1	2	yes	—
164	C₃×C₄×Dic₅	C₂³	1	2	yes	—
165	C₃×C₄×Dic₅	C₂³	1	4	yes	—
166	C₃×C₄×Dic₅	C₂³	1	4	yes	—
167	C₃×C₄×Dic₅	C₂³	1	2	yes	—
168	C₃×C₄×Dic₅	C₂³	1	2	yes	—
169	C₃×C₄×Dic₅	C₂³	1	2	yes	—
170	C₃×C₄×Dic₅	C₂³	1	2	yes	—
171	C₃×#559	—	5	1	no	—
172	C₃×#559	—	5	2	no	—
173	C₃×#557	—	5	1	no	—
174	C₃×#556	—	5	1	no	—
175	C₃×#556	—	5	2	no	—
176	C₃×#553	—	5	4	no	—
177	C₃×#553	—	5	2	no	—
178	C₃×#550	—	5	1	no	—
179	C₃×#548	—	5	2	no	—
180	C₃×#532	—	5	2	no	—
181	C₃×#532	D₅	1	1	yes	characteristic, complemented
182	C₃×#529	—	5	4	no	—
183	C₃×#529	—	5	2	no	—
184	C₃×C₄×#41	—	5	2	no	—
185	C₃×C₄×#41	—	5	2	no	—
186	C₃×C₄×#41	—	5	1	no	—
187	C₂×C₃×C₄×Q₈	—	5	1	no	—
188	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
189	C₂×#711	C₂²×C₃	1	2	yes	—
190	C₂×#709	C₂²×C₃	1	1	yes	characteristic
191	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
192	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
193	C₅×#127	C₂²×C₃	1	1	yes	characteristic
194	C₅×#124	C₂²×C₃	1	2	yes	—
195	C₅×#121	C₂²×C₃	1	2	yes	—
196	C₅×#121	C₂²×C₃	1	2	yes	—
197	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
198	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
199	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
200	#4093	C₂²×C₃	1	2	yes	—
201	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
202	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
203	#4090	C₂²×C₃	1	2	yes	—
204	#4086	C₂²×C₃	1	2	yes	—
205	#4085	C₂²×C₃	1	4	yes	—
206	#4085	C₂²×C₃	1	4	yes	—
207	#4085	C₂²×C₃	1	4	yes	—
208	#4084	C₂²×C₃	1	2	yes	—
209	#4082	C₂²×C₃	1	2	yes	—
210	#4082	C₂²×C₃	1	2	yes	—
211	#4081	C₂²×C₃	1	4	yes	—
212	D₄×Dic₅	C₂²×C₃	1	2	yes	—
213	D₄×Dic₅	C₂²×C₃	1	2	yes	—
214	D₄×Dic₅	C₂²×C₃	1	4	yes	—
215	D₄×Dic₅	C₂²×C₃	1	4	yes	—
216	D₄×Dic₅	C₂²×C₃	1	2	yes	—
217	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
218	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
219	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
220	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
221	#4072	C₂²×C₃	1	1	yes	characteristic
222	#4072	C₂²×C₃	1	4	yes	—
223	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
224	C₂×#683	C₂²×C₃	1	2	yes	—
225	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
226	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	—
227	#4044	C₂²×C₃	1	4	yes	—
228	#4043	C₂²×C₃	1	2	yes	—
229	#4038	C₂²×C₃	1	2	yes	—
230	#4036	C₂²×C₃	1	2	yes	—
231	#4035	C₂²×C₃	1	4	yes	—
232	#4033	C₂²×C₃	1	2	yes	—
233	#4032	C₂²×C₃	1	4	yes	—
234	#4031	C₂²×C₃	1	4	yes	—
235	#4029	C₂²×C₃	1	4	yes	—
236	#4027	C₂²×C₃	1	4	yes	—
237	#4025	C₂²×C₃	1	4	yes	—
238	#4025	C₂²×C₃	1	4	yes	—
239	#4024	C₂²×C₃	1	4	yes	—
240	#4023	C₂²×C₃	1	4	yes	—
241	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
242	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
243	#4018	C₂²×C₃	1	2	yes	—
244	C₄²×D₅	C₂²×C₃	1	2	yes	—
245	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
246	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
247	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
248	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
249	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
250	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
251	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
252	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
253	#3480	—	5	1	no	Sylow
254	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
255	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
256	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
257	C₃×C₅×Q₈	—	2	4	no	—
258	C₃×C₅×D₄	—	2	8	no	—
259	C₃×C₅×D₄	—	2	4	no	—
260	C₃×C₅×D₄	—	2	4	no	—
261	C₃×C₅×D₄	—	4	2	no	—
262	C₂×C₃×C₄×C₅	—	2	2	no	—
263	C₂×C₃×C₄×C₅	—	2	8	no	—
264	C₂×C₃×C₄×C₅	—	4	1	no	—
265	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
266	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
267	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
268	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
269	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
271	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
272	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
273	C₃×C₂²⋊D₅	—	2	4	no	—
274	C₃×C₂²⋊D₅	—	2	8	no	—
275	C₃×C₂²⋊D₅	—	4	4	no	—
276	C₂×C₃×Dic₅	—	2	4	no	—
277	C₂×C₃×Dic₅	—	2	8	no	—
278	C₂×C₃×Dic₅	—	4	4	no	—
279	C₂×C₃×Dic₅	—	4	2	no	—
280	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
281	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
282	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
283	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
284	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
285	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
286	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
287	C₃×D₂₀	—	2	2	no	—
288	C₃×C₄×D₅	—	2	4	no	—
289	C₃×C₄×D₅	—	2	4	no	—
290	C₃×C₄×D₅	—	4	2	no	—
291	C₃×Dic₁₀	—	2	2	no	—
292	C₃×Dic₁₀	—	2	2	no	—
293	C₃×Dic₁₀	—	2	4	no	—
294	C₃×Dic₁₀	#41	1	4	yes	complemented
295	C₂×C₃×#41	—	5	2	no	—
296	C₂×C₃×#41	—	5	1	no	—
297	C₂×C₃×#41	C₂×D₅	1	2	yes	—
298	C₂²×C₃×Q₈	—	5	1	no	—
299	C₃×C₄⋊Q₈	—	5	2	no	—
300	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
301	C₃×#127	—	5	2	no	—
302	C₃×#127	C₂×D₅	1	1	yes	characteristic
303	C₃×#126	—	5	4	no	—
304	C₃×#126	—	5	4	no	—
305	C₃×#126	—	5	4	no	—
306	C₃×#125	—	5	4	no	—
307	C₃×#125	—	5	2	no	—
308	C₃×#124	—	5	2	no	—
309	C₃×#124	—	5	2	no	—
310	C₃×#124	—	5	2	no	—
311	C₃×#124	—	5	4	no	—
312	C₃×#124	C₂×D₅	1	2	yes	—
313	C₃×#123	—	5	4	no	—
314	C₃×#123	—	5	4	no	—
315	C₃×#123	—	5	4	no	—
316	C₃×C₂²⋊Q₈	—	5	2	no	—
317	C₃×C₂²⋊Q₈	—	5	4	no	—
318	C₃×#121	—	5	2	no	—
319	C₃×#121	—	5	4	no	—
320	C₃×#121	—	5	4	no	—
321	C₃×#121	—	5	4	no	—
322	C₃×#121	C₂×D₅	1	2	yes	—
323	C₃×#121	C₂×D₅	1	2	yes	—
324	C₃×C₄×Q₈	—	5	2	no	—
325	C₃×C₄×Q₈	—	5	2	no	—
326	C₃×C₄×Q₈	—	5	2	no	—
327	C₃×C₄×Q₈	—	5	1	no	—
328	C₃×C₄×Q₈	—	5	2	no	—
329	C₃×C₄×Q₈	—	5	1	no	—
330	C₃×C₄×Q₈	—	5	1	no	—
331	C₃×C₄×Q₈	—	5	2	no	—
332	C₃×C₄×Q₈	—	5	1	no	—
333	C₃×C₄×Q₈	—	5	1	no	—
334	C₃×C₄×Q₈	—	5	1	no	—
335	C₃×C₄×D₄	—	5	2	no	—
336	C₃×C₄×D₄	—	5	2	no	—
337	C₃×C₄×D₄	—	5	4	no	—
338	C₃×C₄×D₄	—	5	2	no	—
339	C₃×C₄×D₄	—	5	4	no	—
340	C₃×C₄×D₄	—	5	4	no	—
341	C₃×C₄×D₄	—	5	2	no	—
342	C₃×C₄×D₄	—	5	2	no	—
343	C₃×C₄×D₄	—	5	4	no	—
344	C₃×C₄×D₄	—	5	4	no	—
345	C₃×C₄×D₄	—	5	1	no	—
346	C₃×C₄×D₄	—	5	1	no	—
347	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
348	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
349	C₃×#117	—	5	1	no	—
350	C₃×#117	—	5	4	no	—
351	C₃×#117	—	5	2	no	—
352	C₃×#117	—	5	4	no	—
353	C₃×#117	—	5	2	no	—
354	C₂×C₃×C₄⋊C₄	—	5	2	no	—
355	C₂×C₃×C₄⋊C₄	—	5	1	no	—
356	C₂×C₃×C₄²	—	5	2	no	—
357	C₂×C₃×C₄²	—	5	4	no	—
358	C₂×C₃×C₄²	—	5	2	no	—
359	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
360	C₅×#41	—	2	8	no	—
361	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
362	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
363	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
364	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
365	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
366	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
367	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
368	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
369	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
370	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
371	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
372	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
373	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
374	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
375	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
376	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
377	#711	—	2	8	no	—
378	#709	—	2	4	no	—
379	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
380	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
381	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
382	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
383	C₂×Dic₁₀	—	2	4	no	—
384	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
385	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
386	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
387	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
388	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
389	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
390	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
391	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
392	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
393	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
394	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
395	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
396	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
397	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
398	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
399	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
400	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
401	#685	C₂³×C₃	1	2	yes	—
402	#685	C₂³×C₃	1	2	yes	—
403	#685	C₂³×C₃	1	4	yes	—
404	#685	C₂³×C₃	1	4	yes	—
405	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
406	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
407	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
408	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
409	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
410	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
411	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
412	#683	C₂³×C₃	1	2	yes	—
413	#683	C₂³×C₃	1	2	yes	—
414	#683	C₂³×C₃	1	2	yes	—
415	#683	C₂³×C₃	1	2	yes	—
416	#683	C₂³×C₃	1	2	yes	—
417	#683	C₂³×C₃	1	2	yes	—
418	#683	C₂³×C₃	1	4	yes	—
419	#683	C₂³×C₃	1	4	yes	—
420	C₄×Dic₅	C₂³×C₃	1	2	yes	—
421	C₄×Dic₅	C₂³×C₃	1	2	yes	—
422	C₄×Dic₅	C₂³×C₃	1	2	yes	—
423	C₄×Dic₅	C₂³×C₃	1	2	yes	—
424	C₄×Dic₅	C₂³×C₃	1	2	yes	—
425	C₄×Dic₅	C₂³×C₃	1	2	yes	—
426	C₄×Dic₅	C₂³×C₃	1	2	yes	—
427	C₄×Dic₅	C₂³×C₃	1	4	yes	—
428	C₄×Dic₅	C₂³×C₃	1	4	yes	—
429	#559	—	5	1	no	—
430	#559	—	5	2	no	—
431	#557	—	5	1	no	—
432	#556	—	5	1	no	—
433	#556	—	5	2	no	—
434	#553	—	5	4	no	—
435	#553	—	5	2	no	—
436	#550	—	5	1	no	—
437	#548	—	5	2	no	—
438	#532	—	5	2	no	—
439	#532	C₃×D₅	1	1	yes	characteristic, complemented
440	#529	—	5	4	no	—
441	#529	—	5	2	no	—
442	C₄×#41	—	5	2	no	—
443	C₄×#41	—	5	2	no	—
444	C₄×#41	—	5	1	no	—
445	C₂×C₄×Q₈	—	5	1	no	—
446	C₂²×C₃×C₅	—	2	1	no	—
447	C₂²×C₃×C₅	—	2	1	no	—
448	C₂²×C₃×C₅	—	2	4	no	—
449	C₂²×C₃×C₅	—	2	4	no	—
450	C₂²×C₃×C₅	—	2	4	no	—
451	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
452	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
453	C₂×C₃×D₅	—	2	2	no	—
454	C₂×C₃×D₅	—	2	2	no	—
455	C₂×C₃×D₅	—	2	2	no	—
456	C₃×C₄×C₅	—	2	1	no	—
457	C₃×C₄×C₅	—	2	4	no	—
458	C₃×C₄×C₅	—	2	1	no	—
459	C₃×C₄×C₅	—	2	1	no	—
460	C₃×C₄×C₅	C₂×#41	1	2	yes	—
461	C₃×C₄×C₅	C₂×#41	1	2	yes	—
462	C₃×C₄×C₅	C₂×#41	1	2	yes	—
463	C₃×Dic₅	—	2	2	no	—
464	C₃×Dic₅	—	2	2	no	—
465	C₃×Dic₅	—	2	2	no	—
466	C₃×Dic₅	—	2	2	no	—
467	C₃×Dic₅	—	2	2	no	—
468	C₃×Dic₅	—	2	2	no	—
469	C₃×Dic₅	C₂×#41	1	4	yes	—
470	C₃×#41	—	2	8	no	—
471	C₃×#41	—	10	8	no	—
472	C₃×#41	—	10	4	no	—
473	C₂×C₃×Q₈	—	5	1	no	—
474	C₂×C₃×Q₈	—	5	2	no	—
475	C₂×C₃×Q₈	—	5	1	no	—
476	C₂×C₃×Q₈	—	5	1	no	—
477	C₂×C₃×Q₈	—	10	4	no	—
478	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
479	C₂×C₃×D₄	—	5	2	no	—
480	C₂×C₃×D₄	—	5	4	no	—
481	C₂×C₃×D₄	—	5	4	no	—
482	C₂×C₃×D₄	—	5	1	no	—
483	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
484	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
485	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
486	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
487	C₂²×C₃×C₄	—	5	2	no	—
488	C₂²×C₃×C₄	—	5	4	no	—
489	C₂²×C₃×C₄	—	5	2	no	—
490	C₂²×C₃×C₄	—	5	4	no	—
491	C₂²×C₃×C₄	—	5	2	no	—
492	C₂²×C₃×C₄	—	5	2	no	—
493	C₂²×C₃×C₄	—	5	2	no	—
494	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
495	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
496	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
497	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
498	C₃×C₄⋊C₄	—	5	2	no	—
499	C₃×C₄⋊C₄	—	5	2	no	—
500	C₃×C₄⋊C₄	—	5	2	no	—
501	C₃×C₄⋊C₄	—	5	2	no	—
502	C₃×C₄⋊C₄	—	5	4	no	—
503	C₃×C₄⋊C₄	—	5	2	no	—
504	C₃×C₄⋊C₄	—	5	2	no	—
505	C₃×C₄⋊C₄	—	5	4	no	—
506	C₃×C₄⋊C₄	—	5	1	no	—
507	C₃×C₄⋊C₄	—	5	1	no	—
508	C₃×C₄⋊C₄	—	5	2	no	—
509	C₃×C₄⋊C₄	—	5	1	no	—
510	C₃×C₄⋊C₄	—	5	1	no	—
511	C₃×C₄⋊C₄	—	5	4	no	—
512	C₃×C₄⋊C₄	—	5	4	no	—
513	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
514	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
515	C₃×C₂²⋊C₄	—	5	2	no	—
516	C₃×C₂²⋊C₄	—	5	4	no	—
517	C₃×C₂²⋊C₄	—	5	4	no	—
518	C₃×C₂²⋊C₄	—	5	4	no	—
519	C₃×C₂²⋊C₄	—	5	4	no	—
520	C₃×C₂²⋊C₄	—	5	2	no	—
521	C₃×C₂²⋊C₄	—	5	4	no	—
522	C₃×C₂²⋊C₄	—	5	2	no	—
523	C₃×C₂²⋊C₄	—	5	4	no	—
524	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
525	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
526	C₃×C₄²	—	5	4	no	—
527	C₃×C₄²	—	5	2	no	—
528	C₃×C₄²	—	5	4	no	—
529	C₃×C₄²	—	5	2	no	—
530	C₃×C₄²	—	5	2	no	—
531	C₃×C₄²	—	5	2	no	—
532	C₃×C₄²	—	5	2	no	—
533	C₃×C₄²	—	5	2	no	—
534	C₃×C₄²	—	5	2	no	—
535	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
536	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
537	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
538	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
539	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
540	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
541	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
542	C₅×Q₈	—	2	4	no	—
543	C₅×D₄	—	2	8	no	—
544	C₅×D₄	—	2	4	no	—
545	C₅×D₄	—	2	4	no	—
546	C₅×D₄	—	4	2	no	—
547	C₂×C₄×C₅	—	2	2	no	—
548	C₂×C₄×C₅	—	2	8	no	—
549	C₂×C₄×C₅	—	4	1	no	—
550	C₂×C₄×C₅	C₃×#41	1	4	yes	complemented
551	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
552	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
553	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
554	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
555	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
556	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
557	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
558	C₂²⋊D₅	—	2	4	no	—
559	C₂²⋊D₅	—	2	8	no	—
560	C₂²⋊D₅	—	4	4	no	—
561	C₂×Dic₅	—	2	4	no	—
562	C₂×Dic₅	—	2	8	no	—
563	C₂×Dic₅	—	4	4	no	—
564	C₂×Dic₅	—	4	2	no	—
565	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
566	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
567	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
568	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
569	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
570	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
571	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
572	D₂₀	—	2	2	no	—
573	C₄×D₅	—	2	4	no	—
574	C₄×D₅	—	2	4	no	—
575	C₄×D₅	—	4	2	no	—
576	Dic₁₀	—	2	2	no	—
577	Dic₁₀	—	2	2	no	—
578	Dic₁₀	—	2	4	no	—
579	Dic₁₀	C₃×#41	1	4	yes	complemented
580	C₂×#41	—	5	2	no	—
581	C₂×#41	—	5	1	no	—
582	C₂×#41	C₂×C₃×D₅	1	2	yes	—
583	C₂²×Q₈	—	5	1	no	—
584	C₄⋊Q₈	—	5	2	no	—
585	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
586	#127	—	5	2	no	—
587	#127	C₂×C₃×D₅	1	1	yes	characteristic
588	#126	—	5	4	no	—
589	#126	—	5	4	no	—
590	#126	—	5	4	no	—
591	#125	—	5	4	no	—
592	#125	—	5	2	no	—
593	#124	—	5	2	no	—
594	#124	—	5	2	no	—
595	#124	—	5	2	no	—
596	#124	—	5	4	no	—
597	#124	C₂×C₃×D₅	1	2	yes	—
598	#123	—	5	4	no	—
599	#123	—	5	4	no	—
600	#123	—	5	4	no	—
601	C₂²⋊Q₈	—	5	2	no	—
602	C₂²⋊Q₈	—	5	4	no	—
603	#121	—	5	2	no	—
604	#121	—	5	4	no	—
605	#121	—	5	4	no	—
606	#121	—	5	4	no	—
607	#121	C₂×C₃×D₅	1	2	yes	—
608	#121	C₂×C₃×D₅	1	2	yes	—
609	C₄×Q₈	—	5	2	no	—
610	C₄×Q₈	—	5	2	no	—
611	C₄×Q₈	—	5	2	no	—
612	C₄×Q₈	—	5	1	no	—
613	C₄×Q₈	—	5	2	no	—
614	C₄×Q₈	—	5	1	no	—
615	C₄×Q₈	—	5	1	no	—
616	C₄×Q₈	—	5	1	no	—
617	C₄×Q₈	—	5	2	no	—
618	C₄×Q₈	—	5	1	no	—
619	C₄×Q₈	—	5	1	no	—
620	C₄×D₄	—	5	4	no	—
621	C₄×D₄	—	5	2	no	—
622	C₄×D₄	—	5	4	no	—
623	C₄×D₄	—	5	2	no	—
624	C₄×D₄	—	5	2	no	—
625	C₄×D₄	—	5	4	no	—
626	C₄×D₄	—	5	2	no	—
627	C₄×D₄	—	5	2	no	—
628	C₄×D₄	—	5	4	no	—
629	C₄×D₄	—	5	4	no	—
630	C₄×D₄	—	5	1	no	—
631	C₄×D₄	—	5	1	no	—
632	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
633	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
634	#117	—	5	1	no	—
635	#117	—	5	4	no	—
636	#117	—	5	2	no	—
637	#117	—	5	4	no	—
638	#117	—	5	2	no	—
639	C₂×C₄⋊C₄	—	5	2	no	—
640	C₂×C₄⋊C₄	—	5	1	no	—
641	C₂×C₄²	—	5	2	no	—
642	C₂×C₄²	—	5	4	no	—
643	C₂×C₄²	—	5	2	no	—
644	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
645	C₂×C₃×C₅	—	2	2	no	—
646	C₂×C₃×C₅	—	4	4	no	—
647	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
648	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
649	C₂×C₃×C₅	#585	1	1	yes	characteristic
650	C₃×D₅	—	4	2	no	—
651	C₂³×C₃	—	5	2	no	—
652	C₂³×C₃	C₂³×D₅	1	4	yes	—
653	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
654	C₃×Q₈	—	2	4	no	—
655	C₃×Q₈	—	5	4	no	—
656	C₃×Q₈	—	10	4	no	—
657	C₃×Q₈	—	10	2	no	—
658	C₃×Q₈	—	10	2	no	—
659	C₃×D₄	—	2	8	no	—
660	C₃×D₄	—	2	4	no	—
661	C₃×D₄	—	2	4	no	—
662	C₃×D₄	—	4	2	no	—
663	C₃×D₄	—	10	8	no	—
664	C₃×D₄	—	10	4	no	—
665	C₃×D₄	—	10	2	no	—
666	C₃×D₄	—	20	4	no	—
667	C₂×C₃×C₄	—	2	8	no	—
668	C₂×C₃×C₄	—	2	2	no	—
669	C₂×C₃×C₄	—	4	1	no	—
670	C₂×C₃×C₄	—	5	2	no	—
671	C₂×C₃×C₄	—	5	2	no	—
672	C₂×C₃×C₄	—	5	2	no	—
673	C₂×C₃×C₄	—	5	2	no	—
674	C₂×C₃×C₄	—	5	2	no	—
675	C₂×C₃×C₄	—	5	2	no	—
676	C₂×C₃×C₄	—	5	2	no	—
677	C₂×C₃×C₄	—	10	4	no	—
678	C₂×C₃×C₄	—	10	8	no	—
679	C₂×C₃×C₄	—	10	4	no	—
680	C₂×C₃×C₄	—	10	4	no	—
681	C₂×C₃×C₄	—	20	2	no	—
682	C₂×C₃×C₄	—	20	4	no	—
683	C₂×C₃×C₄	—	20	2	no	—
684	C₂×C₃×C₄	#711	1	4	yes	complemented
685	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
686	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
687	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
688	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
689	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
690	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
691	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
692	C₂²×C₅	—	2	1	no	—
693	C₂²×C₅	—	2	1	no	—
694	C₂²×C₅	—	2	4	no	—
695	C₂²×C₅	—	2	4	no	—
696	C₂²×C₅	—	2	4	no	—
697	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
698	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
699	C₂×D₅	—	2	2	no	—
700	C₂×D₅	—	2	2	no	—
701	C₂×D₅	—	2	2	no	—
702	C₄×C₅	—	2	1	no	—
703	C₄×C₅	—	2	4	no	—
704	C₄×C₅	—	2	1	no	—
705	C₄×C₅	—	2	1	no	—
706	C₄×C₅	C₂×C₃×#41	1	2	yes	—
707	C₄×C₅	C₂×C₃×#41	1	2	yes	—
708	C₄×C₅	C₂×C₃×#41	1	2	yes	—
709	Dic₅	—	2	2	no	—
710	Dic₅	—	2	2	no	—
711	Dic₅	—	2	2	no	—
712	Dic₅	—	2	2	no	—
713	Dic₅	—	2	2	no	—
714	Dic₅	—	2	2	no	—
715	Dic₅	C₂×C₃×#41	1	4	yes	—
716	#41	—	2	8	no	—
717	#41	—	10	8	no	—
718	#41	—	10	4	no	—
719	C₂×Q₈	—	5	1	no	—
720	C₂×Q₈	—	5	2	no	—
721	C₂×Q₈	—	5	1	no	—
722	C₂×Q₈	—	5	1	no	—
723	C₂×Q₈	—	10	4	no	—
724	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
725	C₂×D₄	—	5	2	no	—
726	C₂×D₄	—	5	4	no	—
727	C₂×D₄	—	5	4	no	—
728	C₂×D₄	—	5	1	no	—
729	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
730	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
731	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
732	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
733	C₂²×C₄	—	5	2	no	—
734	C₂²×C₄	—	5	4	no	—
735	C₂²×C₄	—	5	2	no	—
736	C₂²×C₄	—	5	4	no	—
737	C₂²×C₄	—	5	2	no	—
738	C₂²×C₄	—	5	2	no	—
739	C₂²×C₄	—	5	2	no	—
740	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
741	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
742	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
743	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
744	C₄⋊C₄	—	5	2	no	—
745	C₄⋊C₄	—	5	1	no	—
746	C₄⋊C₄	—	5	2	no	—
747	C₄⋊C₄	—	5	1	no	—
748	C₄⋊C₄	—	5	2	no	—
749	C₄⋊C₄	—	5	2	no	—
750	C₄⋊C₄	—	5	2	no	—
751	C₄⋊C₄	—	5	1	no	—
752	C₄⋊C₄	—	5	1	no	—
753	C₄⋊C₄	—	5	4	no	—
754	C₄⋊C₄	—	5	2	no	—
755	C₄⋊C₄	—	5	4	no	—
756	C₄⋊C₄	—	5	2	no	—
757	C₄⋊C₄	—	5	4	no	—
758	C₄⋊C₄	—	5	4	no	—
759	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
760	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
761	C₂²⋊C₄	—	5	2	no	—
762	C₂²⋊C₄	—	5	4	no	—
763	C₂²⋊C₄	—	5	4	no	—
764	C₂²⋊C₄	—	5	4	no	—
765	C₂²⋊C₄	—	5	4	no	—
766	C₂²⋊C₄	—	5	2	no	—
767	C₂²⋊C₄	—	5	4	no	—
768	C₂²⋊C₄	—	5	2	no	—
769	C₂²⋊C₄	—	5	4	no	—
770	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
771	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
772	C₄²	—	5	2	no	—
773	C₄²	—	5	2	no	—
774	C₄²	—	5	2	no	—
775	C₄²	—	5	4	no	—
776	C₄²	—	5	2	no	—
777	C₄²	—	5	4	no	—
778	C₄²	—	5	2	no	—
779	C₄²	—	5	2	no	—
780	C₄²	—	5	2	no	—
781	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
782	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
783	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
784	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
785	C₃×C₅	#3480	1	1	yes	characteristic, complemented, Hall
786	C₂²×C₃	—	2	1	no	—
787	C₂²×C₃	—	2	1	no	—
788	C₂²×C₃	—	2	4	no	—
789	C₂²×C₃	—	2	4	no	—
790	C₂²×C₃	—	2	4	no	—
791	C₂²×C₃	—	10	2	no	—
792	C₂²×C₃	—	10	2	no	—
793	C₂²×C₃	—	10	2	no	—
794	C₂²×C₃	C₂×#711	1	2	yes	—
795	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
796	C₃×C₄	—	2	4	no	—
797	C₃×C₄	—	2	1	no	—
798	C₃×C₄	—	2	1	no	—
799	C₃×C₄	—	2	1	no	—
800	C₃×C₄	—	5	4	no	—
801	C₃×C₄	—	10	2	no	—
802	C₃×C₄	—	10	2	no	—
803	C₃×C₄	—	10	2	no	—
804	C₃×C₄	—	10	2	no	—
805	C₃×C₄	—	10	2	no	—
806	C₃×C₄	—	10	2	no	—
807	C₃×C₄	C₂×#711	1	2	yes	—
808	C₃×C₄	C₂×#711	1	2	yes	—
809	C₃×C₄	D₅×#41	1	2	yes	—
810	C₂×C₅	—	2	2	no	—
811	C₂×C₅	—	4	4	no	—
812	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
813	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
814	C₂×C₅	C₃×#585	1	1	yes	characteristic
815	D₅	—	4	2	no	—
816	C₂³	—	5	2	no	—
817	C₂³	C₂³×C₃×D₅	1	4	yes	—
818	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
819	Q₈	—	2	4	no	—
820	Q₈	—	5	4	no	—
821	Q₈	—	10	4	no	—
822	Q₈	—	10	2	no	—
823	Q₈	—	10	2	no	—
824	D₄	—	2	8	no	—
825	D₄	—	2	4	no	—
826	D₄	—	2	4	no	—
827	D₄	—	4	2	no	—
828	D₄	—	10	8	no	—
829	D₄	—	10	4	no	—
830	D₄	—	10	2	no	—
831	D₄	—	20	4	no	—
832	C₂×C₄	—	2	8	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	4	1	no	—
835	C₂×C₄	—	5	2	no	—
836	C₂×C₄	—	5	2	no	—
837	C₂×C₄	—	5	2	no	—
838	C₂×C₄	—	5	2	no	—
839	C₂×C₄	—	5	2	no	—
840	C₂×C₄	—	5	2	no	—
841	C₂×C₄	—	5	2	no	—
842	C₂×C₄	—	10	4	no	—
843	C₂×C₄	—	10	8	no	—
844	C₂×C₄	—	10	4	no	—
845	C₂×C₄	—	10	4	no	—
846	C₂×C₄	—	20	2	no	—
847	C₂×C₄	—	20	4	no	—
848	C₂×C₄	—	20	2	no	—
849	C₂×C₄	C₃×#711	1	4	yes	complemented
850	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
851	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
852	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
853	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
854	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
855	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
856	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
857	C₂×C₃	—	2	2	no	—
858	C₂×C₃	—	4	4	no	—
859	C₂×C₃	—	20	2	no	—
860	C₂×C₃	C₂²×#711	1	1	yes	characteristic
861	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
862	C₂×C₃	#66283	1	1	yes	characteristic
863	C₅	C₃×#3480	1	1	yes	characteristic, complemented, Sylow
864	C₂²	—	2	1	no	—
865	C₂²	—	2	1	no	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	2	4	no	—
869	C₂²	—	10	2	no	—
870	C₂²	—	10	2	no	—
871	C₂²	—	10	2	no	—
872	C₂²	C₂×C₃×#711	1	2	yes	—
873	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
874	C₄	—	2	4	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	1	no	—
878	C₄	—	5	4	no	—
879	C₄	—	10	2	no	—
880	C₄	—	10	2	no	—
881	C₄	—	10	2	no	—
882	C₄	—	10	2	no	—
883	C₄	—	10	2	no	—
884	C₄	—	10	2	no	—
885	C₄	C₂×C₃×#711	1	2	yes	—
886	C₄	C₂×C₃×#711	1	2	yes	—
887	C₄	C₃×D₅×#41	1	2	yes	—
888	C₃	#10618121	1	1	yes	characteristic, direct product factor, Sylow
889	C₂	—	2	2	no	—
890	C₂	—	4	4	no	—
891	C₂	—	20	2	no	—
892	C₂	C₂²×C₃×#711	1	1	yes	characteristic
893	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
894	C₂	C₃×#66283	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#532	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#532	D₅
hypocenter	C₅	C₃×#3480
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#532

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#532	C₂	semidirect
2. C₃×#66166	C₂	semidirect
3. C₃×#41×Dic₅	C₂	semidirect
4. C₃×#66066	C₂	semidirect
5. C₃×#66055	C₂	semidirect
6. C₃×#66052	C₂	semidirect
7. C₃×#66047	C₂	semidirect
8. C₃×#66015	C₂	semidirect
9. C₃×#66005	C₂	semidirect
10. C₃×#65952	C₂	semidirect
11. C₃×#65935	C₂	semidirect
12. C₃×#65932	C₂	semidirect
13. C₃×#65891	C₂	semidirect
14. C₃×#65872	C₂	semidirect
15. C₃×C₄×#711	C₂	semidirect
16. C₃×C₄×#709	C₂	semidirect
17. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
18. #10618121	C₃	direct (N × H)
85. C₅×#532	C₂×C₃	semidirect
86. #66166	C₂×C₃	semidirect
87. #41×Dic₅	C₂×C₃	semidirect
88. #66066	C₂×C₃	semidirect
89. #66055	C₂×C₃	semidirect
90. #66052	C₂×C₃	semidirect
91. #66047	C₂×C₃	semidirect
92. #66015	C₂×C₃	semidirect
93. #66005	C₂×C₃	semidirect
94. #65952	C₂×C₃	semidirect
95. #65935	C₂×C₃	semidirect
96. #65932	C₂×C₃	semidirect
97. #65891	C₂×C₃	semidirect
98. #65872	C₂×C₃	semidirect
99. C₄×#711	C₂×C₃	semidirect
100. C₄×#709	C₂×C₃	semidirect
101. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
181. C₃×#532	D₅	semidirect
265. C₂×C₃×C₄×C₅	#41	semidirect
294. C₃×Dic₁₀	#41	semidirect
439. #532	C₃×D₅	semidirect
550. C₂×C₄×C₅	C₃×#41	semidirect
579. Dic₁₀	C₃×#41	semidirect
684. C₂×C₃×C₄	#711	semidirect
785. C₃×C₅	#3480	semidirect
849. C₂×C₄	C₃×#711	semidirect
863. C₅	C₃×#3480	semidirect
888. C₃	#10618121	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#532	2
C₃×#66166	2
C₃×#41×Dic₅	2
C₃×#66066	2
C₃×#66055	2
C₃×#66052	2
C₃×#66047	2
C₃×#66015	2
C₃×#66005	2
C₃×#65952	2
C₃×#65935	2
C₃×#65932	2
C₃×#65891	2
C₃×#65872	2
C₃×C₄×#711	2
C₃×C₄×#709	2
C₂×C₃×C₄×Dic₁₀	2
#10618121	3
C₃×#3480	5

Subgroups — C3×#10618121 #14484790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10618121 #14484790