Subgroups — C₃×D₅×#536 #14480459

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66159	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#66150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#66058	C₂	1	2	yes	maximal, complemented
7	C₃×D₅×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
8	C₃×#66009	C₂	1	2	yes	maximal, complemented
9	C₃×D₅×#124	C₂	1	2	yes	maximal, complemented
10	C₃×D₅×#123	C₂	1	4	yes	maximal, complemented
11	C₃×#65982	C₂	1	4	yes	maximal, complemented
12	C₃×#65962	C₂	1	4	yes	maximal, complemented
13	C₃×D₅×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
14	C₃×#65860	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	D₅×#536	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₃×D₅×#41	—	2	8	no	—
20	C₂×C₃×#713	C₂²	1	1	yes	characteristic
21	C₂×C₃×Q₈×D₅	—	2	8	no	—
22	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
23	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
24	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	complemented
26	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	complemented
27	C₂×C₃×#711	C₂²	1	2	yes	—
28	C₂×C₃×#711	C₂²	1	1	yes	characteristic
29	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
30	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
31	C₂×C₃×#709	C₂²	1	1	yes	characteristic
32	C₂×C₃×#709	C₂²	1	2	yes	—
33	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
34	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
35	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
36	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	complemented
38	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
39	C₃×C₅×#124	C₂²	1	2	yes	complemented
40	C₃×C₅×#123	C₂²	1	4	yes	complemented
41	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
42	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
43	C₃×#4093	C₂²	1	2	yes	complemented
44	C₃×#4092	C₂²	1	4	yes	complemented
45	C₃×#4090	C₂²	1	2	yes	complemented
46	C₃×#4090	C₂²	1	2	yes	complemented
47	C₃×#4082	C₂²	1	2	yes	complemented
48	C₃×#4081	C₂²	1	4	yes	complemented
49	C₃×#4075	C₂²	1	4	yes	complemented
50	C₃×#4072	C₂²	1	1	yes	characteristic, complemented
51	C₃×#4070	C₂²	1	4	yes	complemented
52	C₃×#4043	C₂²	1	4	yes	complemented
53	C₃×#4042	C₂²	1	8	yes	complemented
54	C₃×#4040	C₂²	1	8	yes	complemented
55	C₃×#4038	C₂²	1	2	yes	complemented
56	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
57	C₃×D₅×C₄⋊C₄	C₂²	1	8	yes	—
58	C₃×#4034	C₂²	1	8	yes	complemented
59	C₃×#4032	C₂²	1	4	yes	complemented
60	C₃×#4031	C₂²	1	8	yes	complemented
61	C₃×#4029	C₂²	1	8	yes	complemented
62	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
63	C₃×D₅×C₂²⋊C₄	C₂²	1	8	yes	—
64	C₃×#4024	C₂²	1	8	yes	complemented
65	C₃×#4023	C₂²	1	2	yes	complemented
66	C₃×#4021	C₂²	1	2	yes	complemented
67	C₃×#4018	C₂²	1	2	yes	complemented
68	C₃×C₄²×D₅	C₂²	1	2	yes	—
69	C₃×#4015	C₂²	1	2	yes	complemented
70	C₂×C₃×#536	—	5	1	no	maximal, Hall
71	C₂×D₅×#41	C₂×C₃	1	1	yes	characteristic
72	C₂²×Q₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
74	#66159	C₂×C₃	1	1	yes	characteristic, complemented
75	#66150	C₂×C₃	1	1	yes	characteristic, complemented
76	#66058	C₂×C₃	1	2	yes	complemented
77	D₅×C₄⋊Q₈	C₂×C₃	1	2	yes	complemented
78	#66009	C₂×C₃	1	2	yes	complemented
79	D₅×#124	C₂×C₃	1	2	yes	complemented
80	D₅×#123	C₂×C₃	1	4	yes	complemented
81	#65982	C₂×C₃	1	4	yes	complemented
82	#65962	C₂×C₃	1	4	yes	complemented
83	D₅×C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
84	#65860	C₂×C₃	1	1	yes	characteristic, complemented
85	D₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
86	C₂³×C₃×D₅	C₂³	1	2	yes	—
87	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
88	C₃×C₅×#41	—	2	4	no	—
89	C₂×C₃×C₅×Q₈	—	2	4	no	—
90	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
92	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
93	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
94	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
96	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
99	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
100	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
101	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
102	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
103	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
104	C₃×#713	—	2	4	no	—
105	C₃×Q₈×D₅	—	2	8	no	—
106	C₃×Q₈×D₅	—	2	8	no	—
107	C₃×Q₈×D₅	—	2	8	no	—
108	C₃×Q₈×D₅	—	2	8	no	—
109	C₃×Q₈×D₅	—	2	4	no	—
110	C₃×#711	—	2	8	no	—
111	C₃×#711	—	2	4	no	—
112	C₃×D₄×D₅	—	2	8	no	—
113	C₃×D₄×D₅	—	2	4	no	—
114	C₃×#709	—	2	4	no	—
115	C₃×#709	—	2	8	no	—
116	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
117	C₂×C₃×D₂₀	C₂³	1	2	yes	—
118	C₂×C₃×C₄×D₅	—	2	8	no	—
119	C₂×C₃×C₄×D₅	—	2	8	no	—
120	C₂×C₃×C₄×D₅	D₄	1	8	yes	—
121	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
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	4	yes	—
125	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
126	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
127	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
128	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
129	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
131	C₂×C₃×Dic₁₀	—	2	4	no	—
132	C₂×C₃×Dic₁₀	—	2	8	no	—
133	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
134	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
135	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
136	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
137	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
138	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
139	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
140	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
141	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
143	C₃×C₄²×C₅	C₂³	1	2	yes	—
144	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
145	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
146	C₃×#685	C₂³	1	8	yes	—
147	C₃×#685	C₂³	1	4	yes	—
148	C₃×#685	C₂³	1	8	yes	—
149	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
150	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
151	C₃×#683	C₂³	1	8	yes	—
152	C₃×#683	C₂³	1	8	yes	—
153	C₃×#683	C₂³	1	4	yes	—
154	C₃×C₄×Dic₅	C₂³	1	2	yes	—
155	C₃×C₄×Dic₅	C₂³	1	4	yes	—
156	C₂²×C₃×#41	—	5	1	no	—
157	C₂³×C₃×Q₈	—	5	1	no	—
158	C₃×#536	—	5	1	no	—
159	C₃×#536	—	5	1	no	—
160	C₃×#536	—	5	2	no	—
161	C₃×#536	—	5	2	no	—
162	C₃×#536	—	5	4	no	—
163	C₃×#536	—	5	4	no	—
164	C₃×#536	—	5	1	no	—
165	C₃×#536	D₅	1	1	yes	characteristic, direct product factor
166	C₂×C₃×C₄⋊Q₈	—	5	2	no	—
167	C₂×C₃×#124	—	5	2	no	—
168	C₂×C₃×#123	—	5	4	no	—
169	C₂×C₃×C₂²⋊Q₈	—	5	4	no	—
170	C₂×C₃×#117	—	5	1	no	—
171	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
172	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
173	D₅×#41	—	2	8	no	—
174	C₂×#713	C₂²×C₃	1	1	yes	characteristic
175	C₂×Q₈×D₅	—	2	8	no	—
176	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
177	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
178	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
179	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	complemented
180	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	complemented
181	C₂×#711	C₂²×C₃	1	2	yes	—
182	C₂×#711	C₂²×C₃	1	1	yes	characteristic
183	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
184	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
185	C₂×#709	C₂²×C₃	1	1	yes	characteristic
186	C₂×#709	C₂²×C₃	1	2	yes	—
187	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
188	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
189	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
190	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	complemented
192	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
193	C₅×#124	C₂²×C₃	1	2	yes	complemented
194	C₅×#123	C₂²×C₃	1	4	yes	complemented
195	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
196	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
197	#4093	C₂²×C₃	1	2	yes	complemented
198	#4092	C₂²×C₃	1	4	yes	complemented
199	#4090	C₂²×C₃	1	2	yes	complemented
200	#4090	C₂²×C₃	1	2	yes	complemented
201	#4082	C₂²×C₃	1	2	yes	complemented
202	#4081	C₂²×C₃	1	4	yes	complemented
203	#4075	C₂²×C₃	1	4	yes	complemented
204	#4072	C₂²×C₃	1	1	yes	characteristic, complemented
205	#4070	C₂²×C₃	1	4	yes	complemented
206	#4043	C₂²×C₃	1	4	yes	complemented
207	#4042	C₂²×C₃	1	8	yes	complemented
208	#4040	C₂²×C₃	1	8	yes	complemented
209	#4038	C₂²×C₃	1	2	yes	complemented
210	D₅×C₄⋊C₄	C₂²×C₃	1	8	yes	—
211	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
212	#4034	C₂²×C₃	1	8	yes	complemented
213	#4032	C₂²×C₃	1	4	yes	complemented
214	#4031	C₂²×C₃	1	8	yes	complemented
215	#4029	C₂²×C₃	1	8	yes	complemented
216	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
217	D₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
218	#4024	C₂²×C₃	1	8	yes	complemented
219	#4023	C₂²×C₃	1	2	yes	complemented
220	#4021	C₂²×C₃	1	2	yes	complemented
221	#4018	C₂²×C₃	1	2	yes	complemented
222	C₄²×D₅	C₂²×C₃	1	2	yes	—
223	#4015	C₂²×C₃	1	2	yes	complemented
224	C₂×#536	—	5	1	no	Sylow
225	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
226	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
227	C₂²×C₃×D₅	—	2	4	no	—
228	C₂²×C₃×D₅	—	2	4	no	—
229	C₂²×C₃×D₅	—	2	8	no	—
230	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
231	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
232	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
233	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
234	C₃×C₅×Q₈	—	2	4	no	—
235	C₃×C₅×Q₈	—	2	4	no	—
236	C₃×C₅×Q₈	—	2	2	no	—
237	C₃×C₅×D₄	—	2	4	no	—
238	C₃×C₅×D₄	—	2	2	no	—
239	C₂×C₃×C₄×C₅	—	2	4	no	—
240	C₂×C₃×C₄×C₅	—	2	4	no	—
241	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
242	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
243	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
244	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
245	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
246	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
247	C₃×C₂²⋊D₅	—	2	4	no	—
248	C₃×C₂²⋊D₅	—	2	4	no	—
249	C₃×C₂²⋊D₅	—	2	4	no	—
250	C₂×C₃×Dic₅	—	2	4	no	—
251	C₂×C₃×Dic₅	—	2	4	no	—
252	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
253	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
254	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
255	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
256	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
257	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
258	C₃×D₂₀	—	2	4	no	—
259	C₃×D₂₀	—	2	2	no	—
260	C₃×C₄×D₅	—	2	4	no	—
261	C₃×C₄×D₅	—	2	8	no	—
262	C₃×C₄×D₅	—	2	8	no	—
263	C₃×C₄×D₅	—	2	8	no	—
264	C₃×C₄×D₅	—	2	4	no	—
265	C₃×C₄×D₅	—	2	4	no	—
266	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
267	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
268	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
269	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
270	C₃×Dic₁₀	—	2	4	no	—
271	C₃×Dic₁₀	—	2	4	no	—
272	C₃×Dic₁₀	—	2	2	no	—
273	C₃×Dic₁₀	—	2	8	no	—
274	C₃×Dic₁₀	—	2	8	no	—
275	C₃×Dic₁₀	—	2	4	no	—
276	C₂×C₃×#41	—	5	1	no	—
277	C₂×C₃×#41	—	5	2	no	—
278	C₂×C₃×#41	—	5	1	no	—
279	C₂×C₃×#41	—	5	2	no	—
280	C₂×C₃×#41	—	5	1	no	—
281	C₂×C₃×#41	—	10	8	no	—
282	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
283	C₂²×C₃×Q₈	—	5	2	no	—
284	C₂²×C₃×Q₈	—	5	2	no	—
285	C₂²×C₃×Q₈	—	5	2	no	—
286	C₂²×C₃×Q₈	—	5	2	no	—
287	C₂²×C₃×Q₈	—	5	1	no	—
288	C₂²×C₃×Q₈	—	5	2	no	—
289	C₂²×C₃×Q₈	—	5	1	no	—
290	C₂²×C₃×Q₈	—	10	8	no	—
291	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
292	C₂²×C₃×D₄	—	5	2	no	—
293	C₂²×C₃×D₄	—	5	1	no	—
294	C₂³×C₃×C₄	—	5	1	no	—
295	C₂³×C₃×C₄	—	5	2	no	—
296	C₂³×C₃×C₄	—	5	2	no	—
297	C₃×C₄⋊Q₈	—	5	2	no	—
298	C₃×C₄⋊Q₈	—	5	2	no	—
299	C₃×C₄⋊Q₈	—	5	8	no	—
300	C₃×C₄⋊Q₈	—	5	2	no	—
301	C₃×C₄⋊Q₈	C₂×D₅	1	2	yes	complemented
302	C₃×#124	—	5	2	no	—
303	C₃×#124	—	5	2	no	—
304	C₃×#124	—	5	8	no	—
305	C₃×#124	—	5	2	no	—
306	C₃×#124	C₂×D₅	1	2	yes	complemented
307	C₃×#123	—	5	4	no	—
308	C₃×#123	—	5	4	no	—
309	C₃×#123	—	5	8	no	—
310	C₃×#123	—	5	8	no	—
311	C₃×#123	—	5	4	no	—
312	C₃×#123	C₂×D₅	1	4	yes	complemented
313	C₃×C₂²⋊Q₈	—	5	4	no	—
314	C₃×C₂²⋊Q₈	—	5	4	no	—
315	C₃×C₂²⋊Q₈	—	5	8	no	—
316	C₃×C₂²⋊Q₈	—	5	4	no	—
317	C₃×C₂²⋊Q₈	—	5	8	no	—
318	C₃×C₂²⋊Q₈	C₂×D₅	1	4	yes	complemented
319	C₃×#117	—	5	1	no	—
320	C₃×#117	—	5	2	no	—
321	C₃×#117	—	5	2	no	—
322	C₃×#117	—	5	2	no	—
323	C₃×#117	C₂×D₅	1	1	yes	characteristic, complemented
324	C₂×C₃×C₄⋊C₄	—	5	2	no	—
325	C₂×C₃×C₄⋊C₄	—	5	8	no	—
326	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
327	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
328	C₂×C₃×C₄²	—	5	2	no	—
329	C₂³×D₅	C₂³×C₃	1	2	yes	—
330	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
331	C₅×#41	—	2	4	no	—
332	C₂×C₅×Q₈	—	2	4	no	—
333	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
334	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
335	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
336	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
337	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
338	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
339	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
340	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
341	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
342	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
343	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
344	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
345	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
346	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
347	#713	—	2	4	no	—
348	Q₈×D₅	—	2	8	no	—
349	Q₈×D₅	—	2	8	no	—
350	Q₈×D₅	—	2	8	no	—
351	Q₈×D₅	—	2	8	no	—
352	Q₈×D₅	—	2	4	no	—
353	#711	—	2	8	no	—
354	#711	—	2	4	no	—
355	D₄×D₅	—	2	8	no	—
356	D₄×D₅	—	2	4	no	—
357	#709	—	2	4	no	—
358	#709	—	2	8	no	—
359	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
360	C₂×D₂₀	C₂³×C₃	1	2	yes	—
361	C₂×C₄×D₅	—	2	8	no	—
362	C₂×C₄×D₅	—	2	8	no	—
363	C₂×C₄×D₅	C₃×D₄	1	8	yes	—
364	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
365	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
366	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
367	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
368	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
369	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
370	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
371	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
372	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
373	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
374	C₂×Dic₁₀	—	2	4	no	—
375	C₂×Dic₁₀	—	2	8	no	—
376	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
377	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
378	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
379	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
380	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
381	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
382	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
383	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
384	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
385	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
386	C₄²×C₅	C₂³×C₃	1	2	yes	—
387	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
388	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
389	#685	C₂³×C₃	1	4	yes	—
390	#685	C₂³×C₃	1	8	yes	—
391	#685	C₂³×C₃	1	8	yes	—
392	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
393	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
394	#683	C₂³×C₃	1	4	yes	—
395	#683	C₂³×C₃	1	8	yes	—
396	#683	C₂³×C₃	1	8	yes	—
397	C₄×Dic₅	C₂³×C₃	1	2	yes	—
398	C₄×Dic₅	C₂³×C₃	1	4	yes	—
399	C₂²×#41	—	5	1	no	—
400	C₂³×Q₈	—	5	1	no	—
401	#536	—	5	1	no	—
402	#536	—	5	1	no	—
403	#536	—	5	2	no	—
404	#536	—	5	2	no	—
405	#536	—	5	4	no	—
406	#536	—	5	4	no	—
407	#536	—	5	1	no	—
408	#536	C₃×D₅	1	1	yes	characteristic, direct product factor
409	C₂×C₄⋊Q₈	—	5	2	no	—
410	C₂×#124	—	5	2	no	—
411	C₂×#123	—	5	4	no	—
412	C₂×C₂²⋊Q₈	—	5	4	no	—
413	C₂×#117	—	5	1	no	—
414	C₂²×C₃×C₅	—	2	2	no	—
415	C₂²×C₃×C₅	—	2	2	no	—
416	C₂²×C₃×C₅	—	2	4	no	—
417	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
418	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
419	C₂×C₃×D₅	—	2	2	no	—
420	C₂×C₃×D₅	—	2	8	no	—
421	C₂×C₃×D₅	—	2	2	no	—
422	C₂×C₃×D₅	—	2	4	no	—
423	C₂×C₃×D₅	—	4	8	no	—
424	C₂×C₃×D₅	C₂²×D₄	1	2	yes	—
425	C₂×C₃×D₅	C₂²×D₄	1	2	yes	—
426	C₂×C₃×D₅	2₋¹⁺⁴	1	4	yes	—
427	C₃×C₄×C₅	—	2	4	no	—
428	C₃×C₄×C₅	—	2	2	no	—
429	C₃×C₄×C₅	—	2	4	no	—
430	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
431	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
432	C₃×Dic₅	—	2	4	no	—
433	C₃×Dic₅	—	2	2	no	—
434	C₃×Dic₅	—	2	4	no	—
435	C₃×Dic₅	C₂²×D₄	1	2	yes	—
436	C₃×Dic₅	C₂²×D₄	1	2	yes	—
437	C₂⁴×C₃	—	5	1	no	—
438	C₂⁴×C₃	—	5	2	no	—
439	C₃×#41	—	2	4	no	—
440	C₃×#41	—	10	8	no	—
441	C₃×#41	—	10	8	no	—
442	C₃×#41	—	10	4	no	—
443	C₃×#41	—	10	4	no	—
444	C₃×#41	—	10	4	no	—
445	C₂×C₃×Q₈	—	2	4	no	—
446	C₂×C₃×Q₈	—	5	4	no	—
447	C₂×C₃×Q₈	—	5	2	no	—
448	C₂×C₃×Q₈	—	5	4	no	—
449	C₂×C₃×Q₈	—	5	2	no	—
450	C₂×C₃×Q₈	—	5	2	no	—
451	C₂×C₃×Q₈	—	5	1	no	—
452	C₂×C₃×Q₈	—	10	8	no	—
453	C₂×C₃×Q₈	—	10	8	no	—
454	C₂×C₃×Q₈	—	10	8	no	—
455	C₂×C₃×Q₈	—	10	8	no	—
456	C₂×C₃×Q₈	—	10	8	no	—
457	C₂×C₃×Q₈	—	10	4	no	—
458	C₂×C₃×Q₈	—	10	4	no	—
459	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
460	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
461	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
462	C₂×C₃×D₄	—	5	2	no	—
463	C₂×C₃×D₄	—	5	2	no	—
464	C₂×C₃×D₄	—	5	2	no	—
465	C₂×C₃×D₄	—	5	2	no	—
466	C₂×C₃×D₄	—	5	1	no	—
467	C₂×C₃×D₄	—	10	4	no	—
468	C₂×C₃×D₄	—	10	8	no	—
469	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
470	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
471	C₂²×C₃×C₄	—	5	1	no	—
472	C₂²×C₃×C₄	—	5	8	no	—
473	C₂²×C₃×C₄	—	5	1	no	—
474	C₂²×C₃×C₄	—	5	1	no	—
475	C₂²×C₃×C₄	—	5	1	no	—
476	C₂²×C₃×C₄	—	5	1	no	—
477	C₂²×C₃×C₄	—	5	2	no	—
478	C₂²×C₃×C₄	—	5	2	no	—
479	C₂²×C₃×C₄	—	5	4	no	—
480	C₂²×C₃×C₄	—	5	4	no	—
481	C₂²×C₃×C₄	—	5	2	no	—
482	C₂²×C₃×C₄	—	5	2	no	—
483	C₂²×C₃×C₄	—	5	2	no	—
484	C₂²×C₃×C₄	—	5	4	no	—
485	C₂²×C₃×C₄	—	10	8	no	—
486	C₂²×C₃×C₄	—	10	8	no	—
487	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
488	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
489	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
490	C₃×C₄⋊C₄	—	5	4	no	—
491	C₃×C₄⋊C₄	—	5	8	no	—
492	C₃×C₄⋊C₄	—	5	8	no	—
493	C₃×C₄⋊C₄	—	5	2	no	—
494	C₃×C₄⋊C₄	—	5	8	no	—
495	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
496	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
497	C₃×C₂²⋊C₄	—	5	2	no	—
498	C₃×C₂²⋊C₄	—	5	8	no	—
499	C₃×C₂²⋊C₄	—	5	4	no	—
500	C₃×C₂²⋊C₄	—	5	8	no	—
501	C₃×C₂²⋊C₄	—	5	8	no	—
502	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
503	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
504	C₃×C₄²	—	5	4	no	—
505	C₃×C₄²	—	5	2	no	—
506	C₃×C₄²	C₂²×D₅	1	2	yes	—
507	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
508	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
509	C₂²×D₅	—	2	4	no	—
510	C₂²×D₅	—	2	4	no	—
511	C₂²×D₅	—	2	8	no	—
512	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
513	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
514	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
515	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
516	C₅×Q₈	—	2	4	no	—
517	C₅×Q₈	—	2	4	no	—
518	C₅×Q₈	—	2	2	no	—
519	C₅×D₄	—	2	4	no	—
520	C₅×D₄	—	2	2	no	—
521	C₂×C₄×C₅	—	2	4	no	—
522	C₂×C₄×C₅	—	2	4	no	—
523	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
524	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
525	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
526	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
527	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
528	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
529	C₂²⋊D₅	—	2	4	no	—
530	C₂²⋊D₅	—	2	4	no	—
531	C₂²⋊D₅	—	2	4	no	—
532	C₂×Dic₅	—	2	4	no	—
533	C₂×Dic₅	—	2	4	no	—
534	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
535	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
536	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
537	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
538	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
539	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
540	D₂₀	—	2	4	no	—
541	D₂₀	—	2	2	no	—
542	C₄×D₅	—	2	4	no	—
543	C₄×D₅	—	2	8	no	—
544	C₄×D₅	—	2	8	no	—
545	C₄×D₅	—	2	8	no	—
546	C₄×D₅	—	2	4	no	—
547	C₄×D₅	—	2	4	no	—
548	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
549	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
550	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
551	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
552	Dic₁₀	—	2	4	no	—
553	Dic₁₀	—	2	4	no	—
554	Dic₁₀	—	2	2	no	—
555	Dic₁₀	—	2	8	no	—
556	Dic₁₀	—	2	8	no	—
557	Dic₁₀	—	2	4	no	—
558	C₂×#41	—	5	1	no	—
559	C₂×#41	—	5	2	no	—
560	C₂×#41	—	5	1	no	—
561	C₂×#41	—	5	2	no	—
562	C₂×#41	—	5	1	no	—
563	C₂×#41	—	10	8	no	—
564	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
565	C₂²×Q₈	—	5	2	no	—
566	C₂²×Q₈	—	5	2	no	—
567	C₂²×Q₈	—	5	1	no	—
568	C₂²×Q₈	—	5	2	no	—
569	C₂²×Q₈	—	5	2	no	—
570	C₂²×Q₈	—	5	2	no	—
571	C₂²×Q₈	—	5	1	no	—
572	C₂²×Q₈	—	10	8	no	—
573	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
574	C₂²×D₄	—	5	2	no	—
575	C₂²×D₄	—	5	1	no	—
576	C₂³×C₄	—	5	1	no	—
577	C₂³×C₄	—	5	2	no	—
578	C₂³×C₄	—	5	2	no	—
579	C₄⋊Q₈	—	5	2	no	—
580	C₄⋊Q₈	—	5	2	no	—
581	C₄⋊Q₈	—	5	8	no	—
582	C₄⋊Q₈	—	5	2	no	—
583	C₄⋊Q₈	C₂×C₃×D₅	1	2	yes	complemented
584	#124	—	5	2	no	—
585	#124	—	5	2	no	—
586	#124	—	5	8	no	—
587	#124	—	5	2	no	—
588	#124	C₂×C₃×D₅	1	2	yes	complemented
589	#123	—	5	4	no	—
590	#123	—	5	4	no	—
591	#123	—	5	8	no	—
592	#123	—	5	8	no	—
593	#123	—	5	4	no	—
594	#123	C₂×C₃×D₅	1	4	yes	complemented
595	C₂²⋊Q₈	—	5	4	no	—
596	C₂²⋊Q₈	—	5	4	no	—
597	C₂²⋊Q₈	—	5	8	no	—
598	C₂²⋊Q₈	—	5	4	no	—
599	C₂²⋊Q₈	—	5	8	no	—
600	C₂²⋊Q₈	C₂×C₃×D₅	1	4	yes	complemented
601	#117	—	5	1	no	—
602	#117	—	5	2	no	—
603	#117	—	5	2	no	—
604	#117	—	5	2	no	—
605	#117	C₂×C₃×D₅	1	1	yes	characteristic, complemented
606	C₂×C₄⋊C₄	—	5	2	no	—
607	C₂×C₄⋊C₄	—	5	8	no	—
608	C₂×C₂²⋊C₄	—	5	2	no	—
609	C₂×C₂²⋊C₄	—	5	8	no	—
610	C₂×C₄²	—	5	2	no	—
611	C₂×C₃×C₅	—	2	2	no	—
612	C₂×C₃×C₅	—	4	2	no	—
613	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
614	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
615	C₃×D₅	—	2	2	no	—
616	C₃×D₅	—	4	2	no	—
617	C₃×D₅	#536	1	4	yes	direct product factor
618	C₂³×C₃	—	5	1	no	—
619	C₂³×C₃	—	5	4	no	—
620	C₂³×C₃	—	5	1	no	—
621	C₂³×C₃	—	5	2	no	—
622	C₂³×C₃	—	10	4	no	—
623	C₂³×C₃	—	10	4	no	—
624	C₂³×C₃	—	10	8	no	—
625	C₂³×C₃	C₂³×D₅	1	2	yes	—
626	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
627	C₃×Q₈	—	2	4	no	—
628	C₃×Q₈	—	2	4	no	—
629	C₃×Q₈	—	2	2	no	—
630	C₃×Q₈	—	10	8	no	—
631	C₃×Q₈	—	10	8	no	—
632	C₃×Q₈	—	10	4	no	—
633	C₃×Q₈	—	10	4	no	—
634	C₃×Q₈	—	10	4	no	—
635	C₃×Q₈	—	10	2	no	—
636	C₃×D₄	—	2	4	no	—
637	C₃×D₄	—	2	2	no	—
638	C₃×D₄	—	10	4	no	—
639	C₃×D₄	—	10	4	no	—
640	C₃×D₄	—	10	4	no	—
641	C₃×D₄	—	10	4	no	—
642	C₃×D₄	—	10	2	no	—
643	C₂×C₃×C₄	—	2	4	no	—
644	C₂×C₃×C₄	—	2	4	no	—
645	C₂×C₃×C₄	—	5	4	no	—
646	C₂×C₃×C₄	—	5	1	no	—
647	C₂×C₃×C₄	—	5	1	no	—
648	C₂×C₃×C₄	—	5	4	no	—
649	C₂×C₃×C₄	—	5	4	no	—
650	C₂×C₃×C₄	—	5	4	no	—
651	C₂×C₃×C₄	—	5	4	no	—
652	C₂×C₃×C₄	—	5	4	no	—
653	C₂×C₃×C₄	—	5	4	no	—
654	C₂×C₃×C₄	—	5	2	no	—
655	C₂×C₃×C₄	—	10	4	no	—
656	C₂×C₃×C₄	—	10	8	no	—
657	C₂×C₃×C₄	—	10	4	no	—
658	C₂×C₃×C₄	—	10	8	no	—
659	C₂×C₃×C₄	—	10	8	no	—
660	C₂×C₃×C₄	—	10	4	no	—
661	C₂×C₃×C₄	—	10	4	no	—
662	C₂×C₃×C₄	—	10	4	no	—
663	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
664	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
665	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
666	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
667	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
668	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
669	C₂²×C₅	—	2	2	no	—
670	C₂²×C₅	—	2	2	no	—
671	C₂²×C₅	—	2	4	no	—
672	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
673	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
674	C₂×D₅	—	2	2	no	—
675	C₂×D₅	—	2	8	no	—
676	C₂×D₅	—	2	2	no	—
677	C₂×D₅	—	2	4	no	—
678	C₂×D₅	—	4	8	no	—
679	C₂×D₅	C₂²×C₃×D₄	1	2	yes	—
680	C₂×D₅	C₂²×C₃×D₄	1	2	yes	—
681	C₂×D₅	C₃×2₋¹⁺⁴	1	4	yes	—
682	C₄×C₅	—	2	4	no	—
683	C₄×C₅	—	2	2	no	—
684	C₄×C₅	—	2	4	no	—
685	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
686	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
687	Dic₅	—	2	4	no	—
688	Dic₅	—	2	2	no	—
689	Dic₅	—	2	4	no	—
690	Dic₅	C₂²×C₃×D₄	1	2	yes	—
691	Dic₅	C₂²×C₃×D₄	1	2	yes	—
692	C₂⁴	—	5	1	no	—
693	C₂⁴	—	5	2	no	—
694	#41	—	2	4	no	—
695	#41	—	10	8	no	—
696	#41	—	10	8	no	—
697	#41	—	10	4	no	—
698	#41	—	10	4	no	—
699	#41	—	10	4	no	—
700	C₂×Q₈	—	2	4	no	—
701	C₂×Q₈	—	5	4	no	—
702	C₂×Q₈	—	5	2	no	—
703	C₂×Q₈	—	5	4	no	—
704	C₂×Q₈	—	5	2	no	—
705	C₂×Q₈	—	5	2	no	—
706	C₂×Q₈	—	5	1	no	—
707	C₂×Q₈	—	10	8	no	—
708	C₂×Q₈	—	10	8	no	—
709	C₂×Q₈	—	10	8	no	—
710	C₂×Q₈	—	10	8	no	—
711	C₂×Q₈	—	10	8	no	—
712	C₂×Q₈	—	10	4	no	—
713	C₂×Q₈	—	10	4	no	—
714	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
715	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
716	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
717	C₂×D₄	—	5	2	no	—
718	C₂×D₄	—	5	2	no	—
719	C₂×D₄	—	5	2	no	—
720	C₂×D₄	—	5	2	no	—
721	C₂×D₄	—	5	1	no	—
722	C₂×D₄	—	10	4	no	—
723	C₂×D₄	—	10	8	no	—
724	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
725	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
726	C₂²×C₄	—	5	1	no	—
727	C₂²×C₄	—	5	8	no	—
728	C₂²×C₄	—	5	1	no	—
729	C₂²×C₄	—	5	1	no	—
730	C₂²×C₄	—	5	1	no	—
731	C₂²×C₄	—	5	1	no	—
732	C₂²×C₄	—	5	2	no	—
733	C₂²×C₄	—	5	2	no	—
734	C₂²×C₄	—	5	4	no	—
735	C₂²×C₄	—	5	4	no	—
736	C₂²×C₄	—	5	2	no	—
737	C₂²×C₄	—	5	2	no	—
738	C₂²×C₄	—	5	2	no	—
739	C₂²×C₄	—	5	4	no	—
740	C₂²×C₄	—	10	8	no	—
741	C₂²×C₄	—	10	8	no	—
742	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
743	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
744	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
745	C₄⋊C₄	—	5	4	no	—
746	C₄⋊C₄	—	5	2	no	—
747	C₄⋊C₄	—	5	8	no	—
748	C₄⋊C₄	—	5	8	no	—
749	C₄⋊C₄	—	5	8	no	—
750	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
751	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
752	C₂²⋊C₄	—	5	2	no	—
753	C₂²⋊C₄	—	5	8	no	—
754	C₂²⋊C₄	—	5	4	no	—
755	C₂²⋊C₄	—	5	8	no	—
756	C₂²⋊C₄	—	5	8	no	—
757	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
758	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
759	C₄²	—	5	4	no	—
760	C₄²	—	5	2	no	—
761	C₄²	C₂²×C₃×D₅	1	2	yes	—
762	C₃×C₅	C₂×#536	1	1	yes	characteristic, complemented, Hall
763	C₂²×C₃	—	2	2	no	—
764	C₂²×C₃	—	2	2	no	—
765	C₂²×C₃	—	2	4	no	—
766	C₂²×C₃	—	5	2	no	—
767	C₂²×C₃	—	5	4	no	—
768	C₂²×C₃	—	5	2	no	—
769	C₂²×C₃	—	10	8	no	—
770	C₂²×C₃	—	10	2	no	—
771	C₂²×C₃	—	10	2	no	—
772	C₂²×C₃	—	10	4	no	—
773	C₂²×C₃	—	20	8	no	—
774	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
775	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
776	C₃×C₄	—	2	2	no	—
777	C₃×C₄	—	2	4	no	—
778	C₃×C₄	—	2	4	no	—
779	C₃×C₄	—	5	2	no	—
780	C₃×C₄	—	5	2	no	—
781	C₃×C₄	—	10	2	no	—
782	C₃×C₄	—	10	4	no	—
783	C₃×C₄	—	10	4	no	—
784	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
785	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
786	C₂×C₅	—	2	2	no	—
787	C₂×C₅	—	4	2	no	—
788	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
789	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
790	D₅	—	2	2	no	—
791	D₅	—	4	2	no	—
792	D₅	C₃×#536	1	4	yes	direct product factor
793	C₂³	—	5	1	no	—
794	C₂³	—	5	4	no	—
795	C₂³	—	5	1	no	—
796	C₂³	—	5	2	no	—
797	C₂³	—	10	4	no	—
798	C₂³	—	10	4	no	—
799	C₂³	—	10	8	no	—
800	C₂³	C₂³×C₃×D₅	1	2	yes	—
801	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
802	Q₈	—	2	4	no	—
803	Q₈	—	2	4	no	—
804	Q₈	—	2	2	no	—
805	Q₈	—	10	8	no	—
806	Q₈	—	10	8	no	—
807	Q₈	—	10	4	no	—
808	Q₈	—	10	4	no	—
809	Q₈	—	10	4	no	—
810	Q₈	—	10	2	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	2	no	—
813	D₄	—	10	4	no	—
814	D₄	—	10	4	no	—
815	D₄	—	10	4	no	—
816	D₄	—	10	4	no	—
817	D₄	—	10	2	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	5	4	no	—
821	C₂×C₄	—	5	1	no	—
822	C₂×C₄	—	5	1	no	—
823	C₂×C₄	—	5	4	no	—
824	C₂×C₄	—	5	4	no	—
825	C₂×C₄	—	5	4	no	—
826	C₂×C₄	—	5	4	no	—
827	C₂×C₄	—	5	4	no	—
828	C₂×C₄	—	5	4	no	—
829	C₂×C₄	—	5	2	no	—
830	C₂×C₄	—	10	4	no	—
831	C₂×C₄	—	10	4	no	—
832	C₂×C₄	—	10	8	no	—
833	C₂×C₄	—	10	8	no	—
834	C₂×C₄	—	10	8	no	—
835	C₂×C₄	—	10	4	no	—
836	C₂×C₄	—	10	4	no	—
837	C₂×C₄	—	10	4	no	—
838	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
839	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
840	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
841	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
842	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
843	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
844	C₂×C₃	—	2	2	no	—
845	C₂×C₃	—	4	2	no	—
846	C₂×C₃	—	5	4	no	—
847	C₂×C₃	—	10	2	no	—
848	C₂×C₃	—	20	2	no	—
849	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
850	C₂×C₃	D₅×2₋¹⁺⁴	1	2	yes	—
851	C₅	C₂×C₃×#536	1	1	yes	characteristic, complemented, Sylow
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	4	no	—
855	C₂²	—	5	2	no	—
856	C₂²	—	5	4	no	—
857	C₂²	—	5	2	no	—
858	C₂²	—	10	8	no	—
859	C₂²	—	10	2	no	—
860	C₂²	—	10	2	no	—
861	C₂²	—	10	4	no	—
862	C₂²	—	20	8	no	—
863	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
864	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
865	C₄	—	2	2	no	—
866	C₄	—	2	4	no	—
867	C₄	—	2	4	no	—
868	C₄	—	5	2	no	—
869	C₄	—	5	2	no	—
870	C₄	—	10	2	no	—
871	C₄	—	10	4	no	—
872	C₄	—	10	4	no	—
873	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
874	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
875	C₃	D₅×#536	1	1	yes	characteristic, direct product factor, Sylow
876	C₂	—	2	2	no	—
877	C₂	—	4	2	no	—
878	C₂	—	5	4	no	—
879	C₂	—	10	2	no	—
880	C₂	—	20	2	no	—
881	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
882	C₂	C₃×D₅×2₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#536	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂×C₃×D₅×#41	C₂
hypercenter	C₃×#536	D₅
hypocenter	C₅	C₂×C₃×#536
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#536

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×Q₈×D₅	C₂	semidirect
3. C₃×C₅×#536	C₂	semidirect
4. C₃×#66159	C₂	semidirect
5. C₃×#66150	C₂	semidirect
6. C₃×#66058	C₂	semidirect
7. C₃×D₅×C₄⋊Q₈	C₂	semidirect
8. C₃×#66009	C₂	semidirect
9. C₃×D₅×#124	C₂	semidirect
10. C₃×D₅×#123	C₂	semidirect
11. C₃×#65982	C₂	semidirect
12. C₃×#65962	C₂	semidirect
13. C₃×D₅×C₂²⋊Q₈	C₂	semidirect
14. C₃×#65860	C₂	semidirect
15. C₃×D₅×#117	C₂	semidirect
16. D₅×#536	C₃	direct (N × H)
18. C₂²×C₃×C₅×Q₈	C₂²	semidirect
25. C₂×C₃×Q₈×D₅	C₂²	semidirect
26. C₂×C₃×Q₈×D₅	C₂²	semidirect
36. C₂²×C₃×Dic₁₀	C₂²	semidirect
37. C₂²×C₃×Dic₁₀	C₂²	semidirect
38. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
39. C₃×C₅×#124	C₂²	semidirect
40. C₃×C₅×#123	C₂²	semidirect
41. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
42. C₃×C₅×#117	C₂²	semidirect
43. C₃×#4093	C₂²	semidirect
44. C₃×#4092	C₂²	semidirect
45. C₃×#4090	C₂²	semidirect
46. C₃×#4090	C₂²	semidirect
47. C₃×#4082	C₂²	semidirect
48. C₃×#4081	C₂²	semidirect
49. C₃×#4075	C₂²	semidirect
50. C₃×#4072	C₂²	semidirect
51. C₃×#4070	C₂²	semidirect
52. C₃×#4043	C₂²	semidirect
53. C₃×#4042	C₂²	semidirect
54. C₃×#4040	C₂²	semidirect
55. C₃×#4038	C₂²	semidirect
58. C₃×#4034	C₂²	semidirect
59. C₃×#4032	C₂²	semidirect
60. C₃×#4031	C₂²	semidirect
61. C₃×#4029	C₂²	semidirect
64. C₃×#4024	C₂²	semidirect
65. C₃×#4023	C₂²	semidirect
66. C₃×#4021	C₂²	semidirect
67. C₃×#4018	C₂²	semidirect
69. C₃×#4015	C₂²	semidirect
72. C₂²×Q₈×D₅	C₂×C₃	semidirect
73. C₅×#536	C₂×C₃	semidirect
74. #66159	C₂×C₃	semidirect
75. #66150	C₂×C₃	semidirect
76. #66058	C₂×C₃	semidirect
77. D₅×C₄⋊Q₈	C₂×C₃	semidirect
78. #66009	C₂×C₃	semidirect
79. D₅×#124	C₂×C₃	semidirect
80. D₅×#123	C₂×C₃	semidirect
81. #65982	C₂×C₃	semidirect
82. #65962	C₂×C₃	semidirect
83. D₅×C₂²⋊Q₈	C₂×C₃	semidirect
84. #65860	C₂×C₃	semidirect
85. D₅×#117	C₂×C₃	semidirect
165. C₃×#536	D₅	direct (N × H)
172. C₂²×C₅×Q₈	C₂²×C₃	semidirect
179. C₂×Q₈×D₅	C₂²×C₃	semidirect
180. C₂×Q₈×D₅	C₂²×C₃	semidirect
190. C₂²×Dic₁₀	C₂²×C₃	semidirect
191. C₂²×Dic₁₀	C₂²×C₃	semidirect
192. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
193. C₅×#124	C₂²×C₃	semidirect
194. C₅×#123	C₂²×C₃	semidirect
195. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
196. C₅×#117	C₂²×C₃	semidirect
197. #4093	C₂²×C₃	semidirect
198. #4092	C₂²×C₃	semidirect
199. #4090	C₂²×C₃	semidirect
200. #4090	C₂²×C₃	semidirect
201. #4082	C₂²×C₃	semidirect
202. #4081	C₂²×C₃	semidirect
203. #4075	C₂²×C₃	semidirect
204. #4072	C₂²×C₃	semidirect
205. #4070	C₂²×C₃	semidirect
206. #4043	C₂²×C₃	semidirect
207. #4042	C₂²×C₃	semidirect
208. #4040	C₂²×C₃	semidirect
209. #4038	C₂²×C₃	semidirect
212. #4034	C₂²×C₃	semidirect
213. #4032	C₂²×C₃	semidirect
214. #4031	C₂²×C₃	semidirect
215. #4029	C₂²×C₃	semidirect
218. #4024	C₂²×C₃	semidirect
219. #4023	C₂²×C₃	semidirect
220. #4021	C₂²×C₃	semidirect
221. #4018	C₂²×C₃	semidirect
223. #4015	C₂²×C₃	semidirect
291. C₂²×C₃×Q₈	C₂×D₅	semidirect
301. C₃×C₄⋊Q₈	C₂×D₅	semidirect
306. C₃×#124	C₂×D₅	semidirect
312. C₃×#123	C₂×D₅	semidirect
318. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
323. C₃×#117	C₂×D₅	semidirect
408. #536	C₃×D₅	direct (N × H)
573. C₂²×Q₈	C₂×C₃×D₅	semidirect
583. C₄⋊Q₈	C₂×C₃×D₅	semidirect
588. #124	C₂×C₃×D₅	semidirect
594. #123	C₂×C₃×D₅	semidirect
600. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
605. #117	C₂×C₃×D₅	semidirect
617. C₃×D₅	#536	direct (N × H)
762. C₃×C₅	C₂×#536	semidirect
792. D₅	C₃×#536	direct (N × H)
851. C₅	C₂×C₃×#536	semidirect
875. C₃	D₅×#536	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₅×#41	2
C₂²×C₃×Q₈×D₅	2
C₃×C₅×#536	2
C₃×#66159	2
C₃×#66150	2
C₃×#66058	2
C₃×D₅×C₄⋊Q₈	2
C₃×#66009	2
C₃×D₅×#124	2
C₃×D₅×#123	2
C₃×#65982	2
C₃×#65962	2
C₃×D₅×C₂²⋊Q₈	2
C₃×#65860	2
C₃×D₅×#117	2
D₅×#536	3
C₂×C₃×#536	5

Subgroups — C3×D5×#536 #14480459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#536 #14480459