Subgroups — C₃×#10618214 #14480645

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×C₃×D₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#711	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66159	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#66139	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#66050	C₂	1	2	yes	maximal, complemented
7	C₃×#66049	C₂	1	2	yes	maximal, complemented
8	C₃×#66009	C₂	1	2	yes	maximal, complemented
9	C₃×#66002	C₂	1	2	yes	maximal, complemented
10	C₃×#65942	C₂	1	4	yes	maximal, complemented
11	C₃×#65940	C₂	1	4	yes	maximal, complemented
12	C₃×#65923	C₂	1	4	yes	maximal, complemented
13	C₃×#65920	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	#10618214	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
20	C₂³×C₃×Dic₅	C₂²	1	2	yes	complemented
21	C₃×D₅×#41	—	2	8	no	—
22	C₂×C₃×#713	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×#711	—	2	8	no	—
25	C₂×C₃×#711	C₂²	1	2	yes	—
26	C₂×C₃×#711	C₂²	1	2	yes	—
27	C₂×C₃×#711	C₂²	1	2	yes	—
28	C₂×C₃×#711	C₂²	1	2	yes	complemented
29	C₂×C₃×#711	C₂²	1	2	yes	complemented
30	C₂×C₃×#711	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
32	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×#709	C₂²	1	1	yes	characteristic
34	C₂×C₃×#709	C₂²	1	2	yes	complemented
35	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
36	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	complemented
37	C₂²×C₃×Dic₁₀	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	C₃×#4099	C₂²	1	4	yes	complemented
44	C₃×#4090	C₂²	1	2	yes	complemented
45	C₃×#4086	C₂²	1	2	yes	complemented
46	C₃×#4085	C₂²	1	8	yes	complemented
47	C₃×#4084	C₂²	1	4	yes	complemented
48	C₃×#4084	C₂²	1	8	yes	complemented
49	C₃×#4083	C₂²	1	8	yes	complemented
50	C₃×#4082	C₂²	1	2	yes	complemented
51	C₃×#4082	C₂²	1	2	yes	complemented
52	C₃×#4081	C₂²	1	4	yes	complemented
53	C₃×D₄×Dic₅	C₂²	1	8	yes	complemented
54	C₃×#4072	C₂²	1	1	yes	characteristic, complemented
55	C₃×#4070	C₂²	1	4	yes	complemented
56	C₃×#4043	C₂²	1	4	yes	complemented
57	C₃×#4038	C₂²	1	2	yes	complemented
58	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
59	C₃×#4032	C₂²	1	4	yes	complemented
60	C₃×#4030	C₂²	1	8	yes	complemented
61	C₃×#4029	C₂²	1	8	yes	complemented
62	C₃×#4027	C₂²	1	8	yes	complemented
63	C₃×D₅×C₂²⋊C₄	C₂²	1	2	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	complemented
69	C₃×#4015	C₂²	1	2	yes	complemented
70	C₃×#3449	—	5	1	no	maximal, Hall
71	C₂×D₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂²×#711	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#535	C₂×C₃	1	1	yes	characteristic, complemented
74	#66159	C₂×C₃	1	1	yes	characteristic, complemented
75	#66139	C₂×C₃	1	1	yes	characteristic, complemented
76	#66050	C₂×C₃	1	2	yes	complemented
77	#66049	C₂×C₃	1	2	yes	complemented
78	#66009	C₂×C₃	1	2	yes	complemented
79	#66002	C₂×C₃	1	2	yes	complemented
80	#65942	C₂×C₃	1	4	yes	complemented
81	#65940	C₂×C₃	1	4	yes	complemented
82	#65923	C₂×C₃	1	4	yes	complemented
83	#65920	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	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
87	C₂³×C₃×D₅	C₂³	1	2	yes	—
88	C₂³×C₃×D₅	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×C₃×C₂²⋊D₅	—	2	8	no	—
100	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
101	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
102	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
103	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
104	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
105	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
106	C₂²×C₃×Dic₅	—	2	8	no	—
107	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
108	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
109	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
110	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
111	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
112	C₃×#713	—	2	4	no	—
113	C₃×Q₈×D₅	—	2	4	no	—
114	C₃×#711	—	2	8	no	—
115	C₃×#711	—	2	8	no	—
116	C₃×#711	—	2	8	no	—
117	C₃×#711	—	2	8	no	—
118	C₃×#711	—	2	8	no	—
119	C₃×#711	—	2	4	no	—
120	C₃×D₄×D₅	—	2	8	no	—
121	C₃×D₄×D₅	—	2	4	no	—
122	C₃×#709	—	2	4	no	—
123	C₃×#709	—	2	8	no	—
124	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
125	C₂×C₃×D₂₀	C₂³	1	2	yes	—
126	C₂×C₃×C₄×D₅	—	2	8	no	—
127	C₂×C₃×C₄×D₅	D₄	1	8	yes	complemented
128	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
129	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
130	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
131	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
132	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
134	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
135	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
136	C₂×C₃×Dic₁₀	—	2	4	no	—
137	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
138	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
139	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
140	C₂×C₃×Dic₁₀	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	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
146	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
147	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
148	C₃×#685	C₂³	1	4	yes	—
149	C₃×#685	C₂³	1	8	yes	—
150	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
151	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
152	C₃×#683	C₂³	1	8	yes	—
153	C₃×#683	C₂³	1	4	yes	—
154	C₃×C₄×Dic₅	C₂³	1	4	yes	—
155	C₃×C₄×Dic₅	C₂³	1	2	yes	—
156	C₂²×C₃×#41	—	5	1	no	—
157	C₂²×C₃×#41	—	5	1	no	—
158	C₃×#537	—	5	4	no	—
159	C₃×#536	—	5	1	no	—
160	C₃×#536	—	5	2	no	—
161	C₃×#536	—	5	1	no	—
162	C₃×#535	—	5	1	no	—
163	C₃×#535	—	5	2	no	—
164	C₃×#535	D₅	1	1	yes	characteristic, complemented
165	C₃×#534	—	5	4	no	—
166	C₃×#532	—	5	2	no	—
167	C₃×#532	—	5	2	no	—
168	C₃×#525	—	5	4	no	—
169	C₃×#525	—	5	4	no	—
170	C₂×C₃×#117	—	5	1	no	—
171	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
172	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
174	C₂³×Dic₅	C₂²×C₃	1	2	yes	complemented
175	D₅×#41	—	2	8	no	—
176	C₂×#713	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
178	C₂×#711	—	2	8	no	—
179	C₂×#711	C₂²×C₃	1	2	yes	—
180	C₂×#711	C₂²×C₃	1	2	yes	—
181	C₂×#711	C₂²×C₃	1	2	yes	—
182	C₂×#711	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₂×#711	C₂²×C₃	1	2	yes	complemented
184	C₂×#711	C₂²×C₃	1	2	yes	complemented
185	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
186	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₂×#709	C₂²×C₃	1	1	yes	characteristic
188	C₂×#709	C₂²×C₃	1	2	yes	complemented
189	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
190	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	complemented
191	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₅×#127	C₂²×C₃	1	2	yes	complemented
193	C₅×#124	C₂²×C₃	1	2	yes	complemented
194	C₅×#121	C₂²×C₃	1	4	yes	complemented
195	C₅×#120	C₂²×C₃	1	4	yes	complemented
196	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
197	#4099	C₂²×C₃	1	4	yes	complemented
198	#4090	C₂²×C₃	1	2	yes	complemented
199	#4086	C₂²×C₃	1	2	yes	complemented
200	#4085	C₂²×C₃	1	8	yes	complemented
201	#4084	C₂²×C₃	1	8	yes	complemented
202	#4084	C₂²×C₃	1	4	yes	complemented
203	#4083	C₂²×C₃	1	8	yes	complemented
204	#4082	C₂²×C₃	1	2	yes	complemented
205	#4082	C₂²×C₃	1	2	yes	complemented
206	#4081	C₂²×C₃	1	4	yes	complemented
207	D₄×Dic₅	C₂²×C₃	1	8	yes	complemented
208	#4072	C₂²×C₃	1	1	yes	characteristic, complemented
209	#4070	C₂²×C₃	1	4	yes	complemented
210	#4043	C₂²×C₃	1	4	yes	complemented
211	#4038	C₂²×C₃	1	2	yes	complemented
212	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
213	#4032	C₂²×C₃	1	4	yes	complemented
214	#4030	C₂²×C₃	1	8	yes	complemented
215	#4029	C₂²×C₃	1	8	yes	complemented
216	#4027	C₂²×C₃	1	8	yes	complemented
217	D₅×C₂²⋊C₄	C₂²×C₃	1	2	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	complemented
223	#4015	C₂²×C₃	1	2	yes	complemented
224	#3449	—	5	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×C₃×D₅	—	2	4	no	—
231	C₂²×C₃×D₅	—	4	2	no	—
232	C₂²×C₃×D₅	—	4	4	no	—
233	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
234	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
235	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
236	C₂²×C₃×D₅	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	C₃×C₂²⋊D₅	—	2	4	no	—
250	C₃×C₂²⋊D₅	—	2	4	no	—
251	C₃×C₂²⋊D₅	—	2	8	no	—
252	C₃×C₂²⋊D₅	—	2	8	no	—
253	C₃×C₂²⋊D₅	—	2	4	no	—
254	C₃×C₂²⋊D₅	—	4	8	no	—
255	C₂×C₃×Dic₅	—	2	4	no	—
256	C₂×C₃×Dic₅	—	2	4	no	—
257	C₂×C₃×Dic₅	—	2	8	no	—
258	C₂×C₃×Dic₅	—	2	8	no	—
259	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
260	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
261	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
262	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
263	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
264	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
265	C₃×D₂₀	—	2	4	no	—
266	C₃×D₂₀	—	2	2	no	—
267	C₃×C₄×D₅	—	2	4	no	—
268	C₃×C₄×D₅	—	2	4	no	—
269	C₃×C₄×D₅	—	2	4	no	—
270	C₃×C₄×D₅	—	4	4	no	—
271	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
272	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
273	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
274	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
275	C₃×Dic₁₀	—	2	4	no	—
276	C₃×Dic₁₀	—	2	4	no	—
277	C₃×Dic₁₀	—	2	2	no	—
278	C₃×Dic₁₀	—	2	4	no	—
279	C₂×C₃×#41	—	5	1	no	—
280	C₂×C₃×#41	—	5	2	no	—
281	C₂×C₃×#41	—	5	2	no	—
282	C₂×C₃×#41	—	5	2	no	—
283	C₂×C₃×#41	—	5	1	no	—
284	C₂×C₃×#41	—	5	2	no	—
285	C₂×C₃×#41	—	5	2	no	—
286	C₂×C₃×#41	—	5	1	no	—
287	C₂×C₃×#41	—	5	2	no	—
288	C₂×C₃×#41	—	10	8	no	—
289	C₂×C₃×#41	—	10	8	no	—
290	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
291	C₂²×C₃×Q₈	—	5	1	no	—
292	C₂²×C₃×Q₈	—	5	1	no	—
293	C₂²×C₃×D₄	—	5	2	no	—
294	C₂²×C₃×D₄	—	5	2	no	—
295	C₂²×C₃×D₄	—	5	1	no	—
296	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic, complemented
297	C₂³×C₃×C₄	—	5	1	no	—
298	C₂³×C₃×C₄	—	5	2	no	—
299	C₂³×C₃×C₄	—	5	2	no	—
300	C₃×C₄⋊Q₈	—	5	2	no	—
301	C₃×C₄⋊Q₈	—	5	2	no	—
302	C₃×#127	—	5	2	no	—
303	C₃×#127	C₂×D₅	1	2	yes	complemented
304	C₃×#124	—	5	2	no	—
305	C₃×#124	—	5	2	no	—
306	C₃×#124	—	5	2	no	—
307	C₃×#124	C₂×D₅	1	2	yes	complemented
308	C₃×#123	—	5	4	no	—
309	C₃×#123	—	5	8	no	—
310	C₃×#123	—	5	4	no	—
311	C₃×C₂²⋊Q₈	—	5	4	no	—
312	C₃×C₂²⋊Q₈	—	5	4	no	—
313	C₃×C₂²⋊Q₈	—	5	8	no	—
314	C₃×#121	—	5	4	no	—
315	C₃×#121	—	5	8	no	—
316	C₃×#121	—	5	8	no	—
317	C₃×#121	—	5	8	no	—
318	C₃×#121	C₂×D₅	1	4	yes	complemented
319	C₃×#120	—	5	4	no	—
320	C₃×#120	—	5	8	no	—
321	C₃×#120	C₂×D₅	1	4	yes	complemented
322	C₃×C₄×D₄	—	5	8	no	—
323	C₃×C₄×D₄	—	5	8	no	—
324	C₃×#117	—	5	1	no	—
325	C₃×#117	—	5	2	no	—
326	C₃×#117	—	5	2	no	—
327	C₃×#117	—	5	2	no	—
328	C₃×#117	C₂×D₅	1	1	yes	characteristic, complemented
329	C₂×C₃×C₄⋊C₄	—	5	2	no	—
330	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
331	C₂×C₃×C₄²	—	5	2	no	—
332	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
333	C₂³×D₅	C₂³×C₃	1	2	yes	—
334	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
335	C₅×#41	—	2	4	no	—
336	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
337	C₂×C₅×D₄	—	2	4	no	—
338	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
339	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
340	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
341	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
342	C₂×C₅×D₄	C₂³×C₃	1	8	yes	—
343	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
344	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
345	C₂×C₂²⋊D₅	—	2	8	no	—
346	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
347	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
348	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
349	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
350	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
351	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
352	C₂²×Dic₅	—	2	8	no	—
353	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
354	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
355	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
356	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
357	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
358	#713	—	2	4	no	—
359	Q₈×D₅	—	2	4	no	—
360	#711	—	2	8	no	—
361	#711	—	2	8	no	—
362	#711	—	2	8	no	—
363	#711	—	2	8	no	—
364	#711	—	2	8	no	—
365	#711	—	2	4	no	—
366	D₄×D₅	—	2	8	no	—
367	D₄×D₅	—	2	4	no	—
368	#709	—	2	4	no	—
369	#709	—	2	8	no	—
370	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
371	C₂×D₂₀	C₂³×C₃	1	2	yes	—
372	C₂×C₄×D₅	—	2	8	no	—
373	C₂×C₄×D₅	C₃×D₄	1	8	yes	complemented
374	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
375	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
376	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
377	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
378	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
379	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
380	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
381	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
382	C₂×Dic₁₀	—	2	4	no	—
383	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
384	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
385	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
386	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
387	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
388	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
389	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
390	C₄²×C₅	C₂³×C₃	1	2	yes	—
391	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
392	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
393	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
394	#685	C₂³×C₃	1	4	yes	—
395	#685	C₂³×C₃	1	8	yes	—
396	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
397	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
398	#683	C₂³×C₃	1	4	yes	—
399	#683	C₂³×C₃	1	8	yes	—
400	C₄×Dic₅	C₂³×C₃	1	2	yes	—
401	C₄×Dic₅	C₂³×C₃	1	4	yes	—
402	C₂²×#41	—	5	1	no	—
403	C₂²×#41	—	5	1	no	—
404	#537	—	5	4	no	—
405	#536	—	5	1	no	—
406	#536	—	5	2	no	—
407	#536	—	5	1	no	—
408	#535	—	5	1	no	—
409	#535	—	5	2	no	—
410	#535	C₃×D₅	1	1	yes	characteristic, complemented
411	#534	—	5	4	no	—
412	#532	—	5	2	no	—
413	#532	—	5	2	no	—
414	#525	—	5	4	no	—
415	#525	—	5	4	no	—
416	C₂×#117	—	5	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×C₃×D₅	—	2	2	no	—
426	C₂×C₃×D₅	—	2	2	no	—
427	C₂×C₃×D₅	—	2	2	no	—
428	C₂×C₃×D₅	—	2	4	no	—
429	C₂×C₃×D₅	—	4	4	no	—
430	C₂×C₃×D₅	—	4	8	no	—
431	C₂×C₃×D₅	C₂²×D₄	1	2	yes	—
432	C₂×C₃×D₅	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	C₃×Dic₅	—	2	2	no	—
438	C₃×Dic₅	—	2	4	no	—
439	C₃×Dic₅	—	2	4	no	—
440	C₃×Dic₅	C₂²×D₄	1	2	yes	—
441	C₃×Dic₅	C₂²×D₄	1	2	yes	—
442	C₂⁴×C₃	—	5	1	no	—
443	C₂⁴×C₃	—	5	2	no	—
444	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
445	C₃×#41	—	2	4	no	—
446	C₃×#41	—	10	8	no	—
447	C₃×#41	—	10	8	no	—
448	C₃×#41	—	10	8	no	—
449	C₃×#41	—	10	8	no	—
450	C₃×#41	—	10	8	no	—
451	C₃×#41	—	10	8	no	—
452	C₃×#41	—	10	4	no	—
453	C₃×#41	—	10	4	no	—
454	C₃×#41	—	10	4	no	—
455	C₂×C₃×Q₈	—	5	2	no	—
456	C₂×C₃×Q₈	—	5	2	no	—
457	C₂×C₃×Q₈	—	5	1	no	—
458	C₂×C₃×Q₈	—	5	2	no	—
459	C₂×C₃×Q₈	—	10	4	no	—
460	C₂×C₃×Q₈	—	10	4	no	—
461	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
462	C₂×C₃×D₄	—	2	4	no	—
463	C₂×C₃×D₄	—	5	4	no	—
464	C₂×C₃×D₄	—	5	2	no	—
465	C₂×C₃×D₄	—	5	2	no	—
466	C₂×C₃×D₄	—	5	2	no	—
467	C₂×C₃×D₄	—	5	4	no	—
468	C₂×C₃×D₄	—	5	8	no	—
469	C₂×C₃×D₄	—	5	2	no	—
470	C₂×C₃×D₄	—	5	1	no	—
471	C₂×C₃×D₄	—	10	4	no	—
472	C₂×C₃×D₄	—	10	8	no	—
473	C₂×C₃×D₄	—	10	8	no	—
474	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
475	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
476	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
477	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
478	C₂×C₃×D₄	C₂²×D₅	1	8	yes	—
479	C₂²×C₃×C₄	—	5	1	no	—
480	C₂²×C₃×C₄	—	5	8	no	—
481	C₂²×C₃×C₄	—	5	1	no	—
482	C₂²×C₃×C₄	—	5	1	no	—
483	C₂²×C₃×C₄	—	5	1	no	—
484	C₂²×C₃×C₄	—	5	1	no	—
485	C₂²×C₃×C₄	—	5	2	no	—
486	C₂²×C₃×C₄	—	5	4	no	—
487	C₂²×C₃×C₄	—	5	4	no	—
488	C₂²×C₃×C₄	—	5	2	no	—
489	C₂²×C₃×C₄	—	5	2	no	—
490	C₂²×C₃×C₄	—	5	2	no	—
491	C₂²×C₃×C₄	—	5	2	no	—
492	C₂²×C₃×C₄	—	5	4	no	—
493	C₂²×C₃×C₄	—	10	8	no	—
494	C₂²×C₃×C₄	—	10	8	no	—
495	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
496	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
497	C₃×C₄⋊C₄	—	5	4	no	—
498	C₃×C₄⋊C₄	—	5	8	no	—
499	C₃×C₄⋊C₄	—	5	2	no	—
500	C₃×C₄⋊C₄	—	5	8	no	—
501	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
502	C₃×C₂²⋊C₄	—	5	2	no	—
503	C₃×C₂²⋊C₄	—	5	8	no	—
504	C₃×C₂²⋊C₄	—	5	8	no	—
505	C₃×C₂²⋊C₄	—	5	4	no	—
506	C₃×C₂²⋊C₄	—	5	8	no	—
507	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
508	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
509	C₃×C₄²	—	5	4	no	—
510	C₃×C₄²	—	5	2	no	—
511	C₃×C₄²	C₂²×D₅	1	2	yes	—
512	C₂³×C₅	—	2	4	no	—
513	C₂³×C₅	—	4	4	no	—
514	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
515	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
516	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
517	C₂²×D₅	—	2	4	no	—
518	C₂²×D₅	—	4	2	no	—
519	C₂²×D₅	—	4	4	no	—
520	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
521	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
522	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
523	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
524	C₅×Q₈	—	2	2	no	—
525	C₅×D₄	—	2	4	no	—
526	C₅×D₄	—	2	2	no	—
527	C₅×D₄	—	2	4	no	—
528	C₅×D₄	—	2	4	no	—
529	C₅×D₄	—	4	8	no	—
530	C₂×C₄×C₅	—	2	4	no	—
531	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
532	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
533	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
534	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
535	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
536	C₂²⋊D₅	—	2	4	no	—
537	C₂²⋊D₅	—	2	4	no	—
538	C₂²⋊D₅	—	2	8	no	—
539	C₂²⋊D₅	—	2	8	no	—
540	C₂²⋊D₅	—	2	4	no	—
541	C₂²⋊D₅	—	4	8	no	—
542	C₂×Dic₅	—	2	4	no	—
543	C₂×Dic₅	—	2	4	no	—
544	C₂×Dic₅	—	2	8	no	—
545	C₂×Dic₅	—	2	8	no	—
546	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
547	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
548	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
549	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
550	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
551	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
552	D₂₀	—	2	4	no	—
553	D₂₀	—	2	2	no	—
554	C₄×D₅	—	2	4	no	—
555	C₄×D₅	—	2	4	no	—
556	C₄×D₅	—	2	4	no	—
557	C₄×D₅	—	4	4	no	—
558	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
559	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
560	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
561	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
562	Dic₁₀	—	2	4	no	—
563	Dic₁₀	—	2	4	no	—
564	Dic₁₀	—	2	2	no	—
565	Dic₁₀	—	2	4	no	—
566	C₂×#41	—	5	1	no	—
567	C₂×#41	—	5	2	no	—
568	C₂×#41	—	5	2	no	—
569	C₂×#41	—	5	1	no	—
570	C₂×#41	—	5	2	no	—
571	C₂×#41	—	5	2	no	—
572	C₂×#41	—	5	2	no	—
573	C₂×#41	—	5	1	no	—
574	C₂×#41	—	5	2	no	—
575	C₂×#41	—	10	8	no	—
576	C₂×#41	—	10	8	no	—
577	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
578	C₂²×Q₈	—	5	1	no	—
579	C₂²×Q₈	—	5	1	no	—
580	C₂²×D₄	—	5	2	no	—
581	C₂²×D₄	—	5	2	no	—
582	C₂²×D₄	—	5	1	no	—
583	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
584	C₂³×C₄	—	5	1	no	—
585	C₂³×C₄	—	5	2	no	—
586	C₂³×C₄	—	5	2	no	—
587	C₄⋊Q₈	—	5	2	no	—
588	C₄⋊Q₈	—	5	2	no	—
589	#127	—	5	2	no	—
590	#127	C₂×C₃×D₅	1	2	yes	complemented
591	#124	—	5	2	no	—
592	#124	—	5	2	no	—
593	#124	—	5	2	no	—
594	#124	C₂×C₃×D₅	1	2	yes	complemented
595	#123	—	5	4	no	—
596	#123	—	5	8	no	—
597	#123	—	5	4	no	—
598	C₂²⋊Q₈	—	5	4	no	—
599	C₂²⋊Q₈	—	5	4	no	—
600	C₂²⋊Q₈	—	5	8	no	—
601	#121	—	5	4	no	—
602	#121	—	5	8	no	—
603	#121	—	5	8	no	—
604	#121	—	5	8	no	—
605	#121	C₂×C₃×D₅	1	4	yes	complemented
606	#120	—	5	4	no	—
607	#120	—	5	8	no	—
608	#120	C₂×C₃×D₅	1	4	yes	complemented
609	C₄×D₄	—	5	8	no	—
610	C₄×D₄	—	5	8	no	—
611	#117	—	5	1	no	—
612	#117	—	5	2	no	—
613	#117	—	5	2	no	—
614	#117	—	5	2	no	—
615	#117	C₂×C₃×D₅	1	1	yes	characteristic, complemented
616	C₂×C₄⋊C₄	—	5	2	no	—
617	C₂×C₂²⋊C₄	—	5	2	no	—
618	C₂×C₄²	—	5	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	C₃×D₅	—	2	2	no	—
625	C₃×D₅	—	2	2	no	—
626	C₃×D₅	—	4	2	no	—
627	C₂³×C₃	—	2	4	no	—
628	C₂³×C₃	—	4	4	no	—
629	C₂³×C₃	—	5	1	no	—
630	C₂³×C₃	—	5	1	no	—
631	C₂³×C₃	—	5	4	no	—
632	C₂³×C₃	—	5	2	no	—
633	C₂³×C₃	—	10	4	no	—
634	C₂³×C₃	—	20	2	no	—
635	C₂³×C₃	—	20	4	no	—
636	C₂³×C₃	C₂³×D₅	1	2	yes	—
637	C₂³×C₃	C₂³×D₅	1	4	yes	—
638	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
639	C₃×Q₈	—	2	2	no	—
640	C₃×Q₈	—	10	4	no	—
641	C₃×Q₈	—	10	4	no	—
642	C₃×Q₈	—	10	4	no	—
643	C₃×Q₈	—	10	2	no	—
644	C₃×D₄	—	2	4	no	—
645	C₃×D₄	—	2	4	no	—
646	C₃×D₄	—	2	4	no	—
647	C₃×D₄	—	2	2	no	—
648	C₃×D₄	—	4	8	no	—
649	C₃×D₄	—	10	4	no	—
650	C₃×D₄	—	10	4	no	—
651	C₃×D₄	—	10	4	no	—
652	C₃×D₄	—	10	8	no	—
653	C₃×D₄	—	10	8	no	—
654	C₃×D₄	—	10	4	no	—
655	C₃×D₄	—	10	2	no	—
656	C₃×D₄	—	20	8	no	—
657	C₂×C₃×C₄	—	2	4	no	—
658	C₂×C₃×C₄	—	5	4	no	—
659	C₂×C₃×C₄	—	5	1	no	—
660	C₂×C₃×C₄	—	5	1	no	—
661	C₂×C₃×C₄	—	5	4	no	—
662	C₂×C₃×C₄	—	5	4	no	—
663	C₂×C₃×C₄	—	5	4	no	—
664	C₂×C₃×C₄	—	5	4	no	—
665	C₂×C₃×C₄	—	5	4	no	—
666	C₂×C₃×C₄	—	5	4	no	—
667	C₂×C₃×C₄	—	5	2	no	—
668	C₂×C₃×C₄	—	10	4	no	—
669	C₂×C₃×C₄	—	10	4	no	—
670	C₂×C₃×C₄	—	10	4	no	—
671	C₂×C₃×C₄	—	10	8	no	—
672	C₂×C₃×C₄	—	10	8	no	—
673	C₂×C₃×C₄	—	10	4	no	—
674	C₂×C₃×C₄	—	10	4	no	—
675	C₂×C₃×C₄	—	20	4	no	—
676	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
677	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
678	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
679	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
680	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
681	C₂²×C₅	—	2	2	no	—
682	C₂²×C₅	—	2	4	no	—
683	C₂²×C₅	—	2	2	no	—
684	C₂²×C₅	—	2	8	no	—
685	C₂²×C₅	—	2	4	no	—
686	C₂²×C₅	—	4	8	no	—
687	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
688	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
689	C₂×D₅	—	2	2	no	—
690	C₂×D₅	—	2	2	no	—
691	C₂×D₅	—	2	2	no	—
692	C₂×D₅	—	2	4	no	—
693	C₂×D₅	—	4	4	no	—
694	C₂×D₅	—	4	8	no	—
695	C₂×D₅	C₂²×C₃×D₄	1	2	yes	—
696	C₂×D₅	C₂²×C₃×D₄	1	2	yes	—
697	C₄×C₅	—	2	2	no	—
698	C₄×C₅	—	2	4	no	—
699	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
700	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
701	Dic₅	—	2	2	no	—
702	Dic₅	—	2	4	no	—
703	Dic₅	—	2	4	no	—
704	Dic₅	C₂²×C₃×D₄	1	2	yes	—
705	Dic₅	C₂²×C₃×D₄	1	2	yes	—
706	C₂⁴	—	5	1	no	—
707	C₂⁴	—	5	2	no	—
708	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
709	#41	—	2	4	no	—
710	#41	—	10	8	no	—
711	#41	—	10	8	no	—
712	#41	—	10	8	no	—
713	#41	—	10	8	no	—
714	#41	—	10	8	no	—
715	#41	—	10	8	no	—
716	#41	—	10	4	no	—
717	#41	—	10	4	no	—
718	#41	—	10	4	no	—
719	C₂×Q₈	—	5	2	no	—
720	C₂×Q₈	—	5	2	no	—
721	C₂×Q₈	—	5	1	no	—
722	C₂×Q₈	—	5	2	no	—
723	C₂×Q₈	—	10	4	no	—
724	C₂×Q₈	—	10	4	no	—
725	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	5	4	no	—
728	C₂×D₄	—	5	2	no	—
729	C₂×D₄	—	5	2	no	—
730	C₂×D₄	—	5	2	no	—
731	C₂×D₄	—	5	4	no	—
732	C₂×D₄	—	5	8	no	—
733	C₂×D₄	—	5	2	no	—
734	C₂×D₄	—	5	1	no	—
735	C₂×D₄	—	10	4	no	—
736	C₂×D₄	—	10	8	no	—
737	C₂×D₄	—	10	8	no	—
738	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
739	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
740	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
741	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
742	C₂×D₄	C₂²×C₃×D₅	1	8	yes	—
743	C₂²×C₄	—	5	1	no	—
744	C₂²×C₄	—	5	8	no	—
745	C₂²×C₄	—	5	1	no	—
746	C₂²×C₄	—	5	1	no	—
747	C₂²×C₄	—	5	1	no	—
748	C₂²×C₄	—	5	1	no	—
749	C₂²×C₄	—	5	2	no	—
750	C₂²×C₄	—	5	4	no	—
751	C₂²×C₄	—	5	4	no	—
752	C₂²×C₄	—	5	2	no	—
753	C₂²×C₄	—	5	2	no	—
754	C₂²×C₄	—	5	2	no	—
755	C₂²×C₄	—	5	2	no	—
756	C₂²×C₄	—	5	4	no	—
757	C₂²×C₄	—	10	8	no	—
758	C₂²×C₄	—	10	8	no	—
759	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
760	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
761	C₄⋊C₄	—	5	4	no	—
762	C₄⋊C₄	—	5	2	no	—
763	C₄⋊C₄	—	5	8	no	—
764	C₄⋊C₄	—	5	8	no	—
765	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
766	C₂²⋊C₄	—	5	2	no	—
767	C₂²⋊C₄	—	5	8	no	—
768	C₂²⋊C₄	—	5	8	no	—
769	C₂²⋊C₄	—	5	4	no	—
770	C₂²⋊C₄	—	5	8	no	—
771	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
772	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
773	C₄²	—	5	4	no	—
774	C₄²	—	5	2	no	—
775	C₄²	C₂²×C₃×D₅	1	2	yes	—
776	C₃×C₅	#3449	1	1	yes	characteristic, complemented, Hall
777	C₂²×C₃	—	2	2	no	—
778	C₂²×C₃	—	2	2	no	—
779	C₂²×C₃	—	2	4	no	—
780	C₂²×C₃	—	2	4	no	—
781	C₂²×C₃	—	2	8	no	—
782	C₂²×C₃	—	4	8	no	—
783	C₂²×C₃	—	5	2	no	—
784	C₂²×C₃	—	5	2	no	—
785	C₂²×C₃	—	10	2	no	—
786	C₂²×C₃	—	10	2	no	—
787	C₂²×C₃	—	10	2	no	—
788	C₂²×C₃	—	10	4	no	—
789	C₂²×C₃	—	20	4	no	—
790	C₂²×C₃	—	20	8	no	—
791	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
792	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
793	C₃×C₄	—	2	2	no	—
794	C₃×C₄	—	2	4	no	—
795	C₃×C₄	—	5	2	no	—
796	C₃×C₄	—	5	2	no	—
797	C₃×C₄	—	10	2	no	—
798	C₃×C₄	—	10	4	no	—
799	C₃×C₄	—	10	4	no	—
800	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
801	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
802	C₂×C₅	—	2	2	no	—
803	C₂×C₅	—	4	2	no	—
804	C₂×C₅	—	4	4	no	—
805	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
806	C₂×C₅	C₃×#585	1	2	yes	—
807	D₅	—	2	2	no	—
808	D₅	—	2	2	no	—
809	D₅	—	4	2	no	—
810	C₂³	—	2	4	no	—
811	C₂³	—	4	4	no	—
812	C₂³	—	5	1	no	—
813	C₂³	—	5	1	no	—
814	C₂³	—	5	4	no	—
815	C₂³	—	5	2	no	—
816	C₂³	—	10	4	no	—
817	C₂³	—	20	2	no	—
818	C₂³	—	20	4	no	—
819	C₂³	C₂³×C₃×D₅	1	2	yes	—
820	C₂³	C₂³×C₃×D₅	1	4	yes	—
821	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
822	Q₈	—	2	2	no	—
823	Q₈	—	10	4	no	—
824	Q₈	—	10	4	no	—
825	Q₈	—	10	2	no	—
826	Q₈	—	10	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	—	10	4	no	—
833	D₄	—	10	4	no	—
834	D₄	—	10	4	no	—
835	D₄	—	10	8	no	—
836	D₄	—	10	8	no	—
837	D₄	—	10	4	no	—
838	D₄	—	10	2	no	—
839	D₄	—	20	8	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	5	4	no	—
842	C₂×C₄	—	5	1	no	—
843	C₂×C₄	—	5	1	no	—
844	C₂×C₄	—	5	4	no	—
845	C₂×C₄	—	5	4	no	—
846	C₂×C₄	—	5	4	no	—
847	C₂×C₄	—	5	4	no	—
848	C₂×C₄	—	5	4	no	—
849	C₂×C₄	—	5	2	no	—
850	C₂×C₄	—	5	4	no	—
851	C₂×C₄	—	10	4	no	—
852	C₂×C₄	—	10	4	no	—
853	C₂×C₄	—	10	4	no	—
854	C₂×C₄	—	10	8	no	—
855	C₂×C₄	—	10	8	no	—
856	C₂×C₄	—	10	4	no	—
857	C₂×C₄	—	10	4	no	—
858	C₂×C₄	—	20	4	no	—
859	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
860	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
861	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
862	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
863	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
864	C₂×C₃	—	2	2	no	—
865	C₂×C₃	—	4	4	no	—
866	C₂×C₃	—	4	2	no	—
867	C₂×C₃	—	10	2	no	—
868	C₂×C₃	—	10	2	no	—
869	C₂×C₃	—	20	2	no	—
870	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
871	C₂×C₃	#66285	1	2	yes	—
872	C₅	C₃×#3449	1	1	yes	characteristic, complemented, 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	—	4	8	no	—
879	C₂²	—	5	2	no	—
880	C₂²	—	5	2	no	—
881	C₂²	—	10	2	no	—
882	C₂²	—	10	2	no	—
883	C₂²	—	10	2	no	—
884	C₂²	—	10	4	no	—
885	C₂²	—	20	4	no	—
886	C₂²	—	20	8	no	—
887	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
888	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
889	C₄	—	2	2	no	—
890	C₄	—	2	4	no	—
891	C₄	—	5	2	no	—
892	C₄	—	5	2	no	—
893	C₄	—	10	2	no	—
894	C₄	—	10	4	no	—
895	C₄	—	10	4	no	—
896	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
897	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
898	C₃	#10618214	1	1	yes	characteristic, direct product factor, Sylow
899	C₂	—	2	2	no	—
900	C₂	—	4	4	no	—
901	C₂	—	4	2	no	—
902	C₂	—	10	2	no	—
903	C₂	—	10	2	no	—
904	C₂	—	20	2	no	—
905	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
906	C₂	C₃×#66285	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×#535	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#535	D₅
hypocenter	C₅	C₃×#3449
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#535

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×#41	C₂	semidirect
2. C₂²×C₃×#711	C₂	semidirect
3. C₃×C₅×#535	C₂	semidirect
4. C₃×#66159	C₂	semidirect
5. C₃×#66139	C₂	semidirect
6. C₃×#66050	C₂	semidirect
7. C₃×#66049	C₂	semidirect
8. C₃×#66009	C₂	semidirect
9. C₃×#66002	C₂	semidirect
10. C₃×#65942	C₂	semidirect
11. C₃×#65940	C₂	semidirect
12. C₃×#65923	C₂	semidirect
13. C₃×#65920	C₂	semidirect
14. C₃×#65860	C₂	semidirect
15. C₃×D₅×#117	C₂	semidirect
16. #10618214	C₃	direct (N × H)
18. C₂²×C₃×C₅×D₄	C₂²	semidirect
20. C₂³×C₃×Dic₅	C₂²	semidirect
22. C₂×C₃×#713	C₂²	semidirect
23. C₂×C₃×Q₈×D₅	C₂²	semidirect
28. C₂×C₃×#711	C₂²	semidirect
29. C₂×C₃×#711	C₂²	semidirect
30. C₂×C₃×#711	C₂²	semidirect
32. C₂×C₃×D₄×D₅	C₂²	semidirect
34. C₂×C₃×#709	C₂²	semidirect
36. C₂²×C₃×C₄×D₅	C₂²	semidirect
37. C₂²×C₃×Dic₁₀	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. C₃×#4099	C₂²	semidirect
44. C₃×#4090	C₂²	semidirect
45. C₃×#4086	C₂²	semidirect
46. C₃×#4085	C₂²	semidirect
47. C₃×#4084	C₂²	semidirect
48. C₃×#4084	C₂²	semidirect
49. C₃×#4083	C₂²	semidirect
50. C₃×#4082	C₂²	semidirect
51. C₃×#4082	C₂²	semidirect
52. C₃×#4081	C₂²	semidirect
53. C₃×D₄×Dic₅	C₂²	semidirect
54. C₃×#4072	C₂²	semidirect
55. C₃×#4070	C₂²	semidirect
56. C₃×#4043	C₂²	semidirect
57. C₃×#4038	C₂²	semidirect
58. C₃×D₅×C₄⋊C₄	C₂²	semidirect
59. C₃×#4032	C₂²	semidirect
60. C₃×#4030	C₂²	semidirect
61. C₃×#4029	C₂²	semidirect
62. C₃×#4027	C₂²	semidirect
64. C₃×#4024	C₂²	semidirect
65. C₃×#4023	C₂²	semidirect
66. C₃×#4021	C₂²	semidirect
67. C₃×#4018	C₂²	semidirect
68. C₃×C₄²×D₅	C₂²	semidirect
69. C₃×#4015	C₂²	semidirect
71. C₂×D₅×#41	C₂×C₃	semidirect
72. C₂²×#711	C₂×C₃	semidirect
73. C₅×#535	C₂×C₃	semidirect
74. #66159	C₂×C₃	semidirect
75. #66139	C₂×C₃	semidirect
76. #66050	C₂×C₃	semidirect
77. #66049	C₂×C₃	semidirect
78. #66009	C₂×C₃	semidirect
79. #66002	C₂×C₃	semidirect
80. #65942	C₂×C₃	semidirect
81. #65940	C₂×C₃	semidirect
82. #65923	C₂×C₃	semidirect
83. #65920	C₂×C₃	semidirect
84. #65860	C₂×C₃	semidirect
85. D₅×#117	C₂×C₃	semidirect
127. C₂×C₃×C₄×D₅	D₄	semidirect
164. C₃×#535	D₅	semidirect
172. C₂²×C₅×D₄	C₂²×C₃	semidirect
174. C₂³×Dic₅	C₂²×C₃	semidirect
176. C₂×#713	C₂²×C₃	semidirect
177. C₂×Q₈×D₅	C₂²×C₃	semidirect
182. C₂×#711	C₂²×C₃	semidirect
183. C₂×#711	C₂²×C₃	semidirect
184. C₂×#711	C₂²×C₃	semidirect
186. C₂×D₄×D₅	C₂²×C₃	semidirect
188. C₂×#709	C₂²×C₃	semidirect
190. C₂²×C₄×D₅	C₂²×C₃	semidirect
191. C₂²×Dic₁₀	C₂²×C₃	semidirect
192. C₅×#127	C₂²×C₃	semidirect
193. C₅×#124	C₂²×C₃	semidirect
194. C₅×#121	C₂²×C₃	semidirect
195. C₅×#120	C₂²×C₃	semidirect
196. C₅×#117	C₂²×C₃	semidirect
197. #4099	C₂²×C₃	semidirect
198. #4090	C₂²×C₃	semidirect
199. #4086	C₂²×C₃	semidirect
200. #4085	C₂²×C₃	semidirect
201. #4084	C₂²×C₃	semidirect
202. #4084	C₂²×C₃	semidirect
203. #4083	C₂²×C₃	semidirect
204. #4082	C₂²×C₃	semidirect
205. #4082	C₂²×C₃	semidirect
206. #4081	C₂²×C₃	semidirect
207. D₄×Dic₅	C₂²×C₃	semidirect
208. #4072	C₂²×C₃	semidirect
209. #4070	C₂²×C₃	semidirect
210. #4043	C₂²×C₃	semidirect
211. #4038	C₂²×C₃	semidirect
212. D₅×C₄⋊C₄	C₂²×C₃	semidirect
213. #4032	C₂²×C₃	semidirect
214. #4030	C₂²×C₃	semidirect
215. #4029	C₂²×C₃	semidirect
216. #4027	C₂²×C₃	semidirect
218. #4024	C₂²×C₃	semidirect
219. #4023	C₂²×C₃	semidirect
220. #4021	C₂²×C₃	semidirect
221. #4018	C₂²×C₃	semidirect
222. C₄²×D₅	C₂²×C₃	semidirect
223. #4015	C₂²×C₃	semidirect
296. C₂²×C₃×D₄	C₂×D₅	semidirect
303. C₃×#127	C₂×D₅	semidirect
307. C₃×#124	C₂×D₅	semidirect
318. C₃×#121	C₂×D₅	semidirect
321. C₃×#120	C₂×D₅	semidirect
328. C₃×#117	C₂×D₅	semidirect
373. C₂×C₄×D₅	C₃×D₄	semidirect
410. #535	C₃×D₅	semidirect
583. C₂²×D₄	C₂×C₃×D₅	semidirect
590. #127	C₂×C₃×D₅	semidirect
594. #124	C₂×C₃×D₅	semidirect
605. #121	C₂×C₃×D₅	semidirect
608. #120	C₂×C₃×D₅	semidirect
615. #117	C₂×C₃×D₅	semidirect
776. C₃×C₅	#3449	semidirect
872. C₅	C₃×#3449	semidirect
898. C₃	#10618214	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×#711	2
C₃×C₅×#535	2
C₃×#66159	2
C₃×#66139	2
C₃×#66050	2
C₃×#66049	2
C₃×#66009	2
C₃×#66002	2
C₃×#65942	2
C₃×#65940	2
C₃×#65923	2
C₃×#65920	2
C₃×#65860	2
C₃×D₅×#117	2
#10618214	3
C₃×#3449	5

Subgroups — C3×#10618214 #14480645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10618214 #14480645