Subgroups — C₃×#10611211 #14415331

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4053	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65882	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65416	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65400	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65300	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65126	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65125	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65019	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65017	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65016	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65016	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#64995	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×D₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
16	#10611211	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×#709	C₂²	1	1	yes	characteristic
18	C₂×C₃×#709	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₃×#4086	C₄	1	1	yes	characteristic
23	C₃×#4084	C₄	1	1	yes	characteristic
24	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
25	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×#681	C₂²	1	1	yes	characteristic
27	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
28	C₃×#4053	—	2	4	no	—
29	C₃×#4047	—	2	4	no	—
30	C₂×C₃×#676	C₂²	1	1	yes	characteristic
31	C₂×C₃×#676	C₂²	1	1	yes	characteristic
32	C₂×C₃×#676	C₂²	1	1	yes	characteristic
33	C₂×C₃×#676	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
38	C₃×#4041	C₄	1	1	yes	characteristic
39	C₃×#4034	C₄	1	1	yes	characteristic
40	C₃×#4031	C₄	1	1	yes	characteristic
41	C₃×#4031	C₄	1	1	yes	characteristic
42	C₃×#4030	C₄	1	1	yes	characteristic
43	C₃×#4030	C₄	1	1	yes	characteristic
44	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
45	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₃×C₅×#97	C₂²	1	1	yes	characteristic
50	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
51	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
52	C₃×#3952	C₂²	1	1	yes	characteristic
53	C₃×#3952	C₂²	1	1	yes	characteristic
54	C₃×#3952	C₂²	1	1	yes	characteristic
55	C₃×#3952	C₂²	1	1	yes	characteristic
56	C₃×#3947	C₂²	1	1	yes	characteristic
57	C₃×#3947	C₂²	1	1	yes	characteristic
58	C₃×#3946	C₂²	1	1	yes	characteristic
59	C₃×#3946	C₂²	1	1	yes	characteristic
60	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
61	C₃×#3935	C₂²	1	1	yes	characteristic
62	C₃×#2932	—	5	1	no	maximal, Hall
63	C₂×#4053	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂×#4047	C₂×C₃	1	1	yes	characteristic, complemented
65	#65882	C₂×C₃	1	1	yes	characteristic
66	C₅×#435	C₂×C₃	1	1	yes	characteristic, complemented
67	#65416	C₂×C₃	1	1	yes	characteristic, complemented
68	#65400	C₂×C₃	1	1	yes	characteristic, complemented
69	#65300	C₂×C₃	1	1	yes	characteristic, complemented
70	#65126	C₂×C₃	1	1	yes	characteristic, complemented
71	#65125	C₂×C₃	1	1	yes	characteristic, complemented
72	#65019	C₂×C₃	1	1	yes	characteristic, complemented
73	#65017	C₂×C₃	1	1	yes	characteristic, complemented
74	#65016	C₂×C₃	1	1	yes	characteristic, complemented
75	#65016	C₂×C₃	1	1	yes	characteristic, complemented
76	#64995	C₂×C₃	1	1	yes	characteristic, complemented
77	D₅×#97	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
82	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
83	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
84	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
85	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
86	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
87	C₃×#709	—	2	2	no	—
88	C₃×#709	—	2	2	no	—
89	C₃×#709	—	2	2	no	—
90	C₃×#709	—	2	2	no	—
91	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
92	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
93	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
99	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
100	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
101	C₃×C₅×M₁₆	—	2	2	no	—
102	C₂×C₃×C₅×C₈	—	2	2	no	—
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
111	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
112	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
113	C₃×#685	C₂×C₄	1	1	yes	characteristic
114	C₃×#685	C₂×C₄	1	1	yes	characteristic
115	C₃×#685	C₂×C₄	1	1	yes	characteristic
116	C₃×#685	C₂×C₄	1	1	yes	characteristic
117	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
118	C₃×#683	C₂×C₄	1	1	yes	characteristic
119	C₃×#683	C₂×C₄	1	1	yes	characteristic
120	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
121	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
122	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
123	C₃×#681	—	2	2	no	—
124	C₂×C₃×#168	—	2	2	no	—
125	C₂×C₃×#168	C₂³	1	1	yes	characteristic
126	C₂×C₃×#168	C₂³	1	1	yes	characteristic
127	C₂×C₃×#168	C₂³	1	1	yes	characteristic
128	C₂×C₃×#168	C₂³	1	1	yes	characteristic
129	C₃×#676	—	2	2	no	—
130	C₃×#676	—	2	2	no	—
131	C₃×#676	—	2	2	no	—
132	C₃×#676	—	2	2	no	—
133	C₃×C₈×D₅	—	2	2	no	—
134	C₃×C₈×D₅	—	2	2	no	—
135	C₃×C₈×D₅	—	2	2	no	—
136	C₃×C₈×D₅	D₄	1	4	yes	complemented
137	C₂×C₃×#131	—	5	1	no	—
138	C₂×C₃×#131	—	5	1	no	—
139	C₃×#532	—	5	1	no	—
140	C₃×#435	—	5	1	no	—
141	C₃×#435	—	5	1	no	—
142	C₃×#435	—	5	1	no	—
143	C₃×#435	—	5	1	no	—
144	C₃×#435	—	5	1	no	—
145	C₃×#435	—	5	1	no	—
146	C₃×#435	—	5	1	no	—
147	C₃×#435	D₅	1	1	yes	characteristic, complemented
148	C₃×#423	—	5	1	no	—
149	C₃×#408	—	5	1	no	—
150	C₃×#408	—	5	1	no	—
151	C₂×C₃×#97	—	5	1	no	—
152	C₂×#709	C₂²×C₃	1	1	yes	characteristic
153	C₂×#709	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
155	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
156	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
157	#4086	C₃×C₄	1	1	yes	characteristic
158	#4084	C₃×C₄	1	1	yes	characteristic
159	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
160	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
161	C₂×#681	C₂²×C₃	1	1	yes	characteristic
162	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
163	#4053	—	2	4	no	—
164	#4047	—	2	4	no	—
165	C₂×#676	C₂²×C₃	1	1	yes	characteristic
166	C₂×#676	C₂²×C₃	1	1	yes	characteristic
167	C₂×#676	C₂²×C₃	1	1	yes	characteristic
168	C₂×#676	C₂²×C₃	1	1	yes	characteristic
169	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
170	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
171	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
172	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
173	#4041	C₃×C₄	1	1	yes	characteristic
174	#4034	C₃×C₄	1	1	yes	characteristic
175	#4031	C₃×C₄	1	1	yes	characteristic
176	#4031	C₃×C₄	1	1	yes	characteristic
177	#4030	C₃×C₄	1	1	yes	characteristic
178	#4030	C₃×C₄	1	1	yes	characteristic
179	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
180	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
181	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
182	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
183	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
184	C₅×#97	C₂²×C₃	1	1	yes	characteristic
185	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
186	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
187	#3952	C₂²×C₃	1	1	yes	characteristic
188	#3952	C₂²×C₃	1	1	yes	characteristic
189	#3952	C₂²×C₃	1	1	yes	characteristic
190	#3952	C₂²×C₃	1	1	yes	characteristic
191	#3947	C₂²×C₃	1	1	yes	characteristic
192	#3947	C₂²×C₃	1	1	yes	characteristic
193	#3946	C₂²×C₃	1	1	yes	characteristic
194	#3946	C₂²×C₃	1	1	yes	characteristic
195	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
196	#3935	C₂²×C₃	1	1	yes	characteristic
197	#2932	—	5	1	no	Sylow
198	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
199	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
203	C₃×C₅×D₄	—	4	1	no	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
209	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
213	C₃×C₂²⋊D₅	—	2	2	no	—
214	C₃×C₂²⋊D₅	—	2	2	no	—
215	C₃×C₂²⋊D₅	—	2	2	no	—
216	C₃×C₂²⋊D₅	—	2	2	no	—
217	C₃×C₂²⋊D₅	—	4	1	no	—
218	C₃×C₂²⋊D₅	—	4	1	no	—
219	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
220	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
221	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
222	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
223	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
224	C₃×D₂₀	—	2	2	no	—
225	C₃×D₂₀	—	2	2	no	—
226	C₃×D₂₀	—	4	1	no	—
227	C₃×C₄×D₅	—	2	1	no	—
228	C₃×C₄×D₅	—	2	1	no	—
229	C₃×C₄×D₅	—	2	1	no	—
230	C₃×C₄×D₅	—	2	1	no	—
231	C₃×C₄×D₅	—	4	1	no	—
232	C₃×C₄×D₅	—	4	1	no	—
233	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
234	C₃×C₄×D₅	#41	1	2	yes	—
235	C₃×Dic₁₀	—	2	2	no	—
236	C₃×Dic₁₀	—	2	2	no	—
237	C₃×C₅×C₈	—	2	1	no	—
238	C₃×C₅×C₈	—	2	1	no	—
239	C₃×C₅×C₈	—	2	1	no	—
240	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
241	C₃×#168	—	2	1	no	—
242	C₃×#168	—	2	1	no	—
243	C₃×#168	—	2	1	no	—
244	C₃×#168	C₂×D₄	1	2	yes	—
245	C₂×C₃×#41	—	5	1	no	—
246	C₂×C₃×#41	—	5	1	no	—
247	C₃×#131	—	10	4	no	—
248	C₃×#131	—	10	4	no	—
249	C₂×C₃×M₁₆	—	5	1	no	—
250	C₂×C₃×M₁₆	—	5	1	no	—
251	C₂×C₃×M₁₆	—	5	1	no	—
252	C₂×C₃×M₁₆	—	5	1	no	—
253	C₂×C₃×M₁₆	—	5	1	no	—
254	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
255	C₂²×C₃×C₈	—	5	1	no	—
256	C₂²×C₃×C₈	—	5	1	no	—
257	C₂²×C₃×C₈	—	5	1	no	—
258	C₂²×C₃×C₈	—	5	1	no	—
259	C₂²×C₃×C₈	—	5	1	no	—
260	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
261	C₃×C₄⋊Q₈	—	5	1	no	—
262	C₃×#127	—	5	1	no	—
263	C₃×#124	—	5	1	no	—
264	C₃×#124	—	5	1	no	—
265	C₃×#121	—	5	1	no	—
266	C₃×#121	—	5	1	no	—
267	C₃×#121	—	5	1	no	—
268	C₃×#121	—	5	1	no	—
269	C₃×C₄×D₄	—	5	1	no	—
270	C₃×C₄×D₄	—	5	1	no	—
271	C₃×C₄×D₄	—	5	1	no	—
272	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
273	C₂×C₃×C₄²	—	5	1	no	—
274	C₃×C₄⋊C₈	—	5	1	no	—
275	C₃×C₄⋊C₈	—	5	1	no	—
276	C₃×C₄⋊C₈	—	5	1	no	—
277	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
278	C₃×C₂²⋊C₈	—	5	1	no	—
279	C₃×C₂²⋊C₈	—	5	1	no	—
280	C₃×C₂²⋊C₈	—	5	1	no	—
281	C₃×C₂²⋊C₈	—	5	1	no	—
282	C₃×C₂²⋊C₈	—	5	1	no	—
283	C₃×C₂²⋊C₈	—	5	1	no	—
284	C₃×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic
285	C₃×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic
286	C₃×#97	—	5	1	no	—
287	C₃×#97	—	5	1	no	—
288	C₃×#97	—	5	1	no	—
289	C₃×#97	C₂×D₅	1	1	yes	characteristic
290	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
291	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
292	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
293	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
294	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
295	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
296	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
297	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
298	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
299	#709	—	2	2	no	—
300	#709	—	2	2	no	—
301	#709	—	2	2	no	—
302	#709	—	2	2	no	—
303	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
304	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
305	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
306	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
307	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
308	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
309	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
310	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
311	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
312	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
313	C₅×M₁₆	—	2	2	no	—
314	C₂×C₅×C₈	—	2	2	no	—
315	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
316	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
317	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
318	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
319	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
320	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
321	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
322	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
323	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
324	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
325	#685	C₂×C₃×C₄	1	1	yes	characteristic
326	#685	C₂×C₃×C₄	1	1	yes	characteristic
327	#685	C₂×C₃×C₄	1	1	yes	characteristic
328	#685	C₂×C₃×C₄	1	1	yes	characteristic
329	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
330	#683	C₂×C₃×C₄	1	1	yes	characteristic
331	#683	C₂×C₃×C₄	1	1	yes	characteristic
332	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
333	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
334	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
335	#681	—	2	2	no	—
336	C₂×#168	—	2	2	no	—
337	C₂×#168	C₂³×C₃	1	1	yes	characteristic
338	C₂×#168	C₂³×C₃	1	1	yes	characteristic
339	C₂×#168	C₂³×C₃	1	1	yes	characteristic
340	C₂×#168	C₂³×C₃	1	1	yes	characteristic
341	#676	—	2	2	no	—
342	#676	—	2	2	no	—
343	#676	—	2	2	no	—
344	#676	—	2	2	no	—
345	C₈×D₅	—	2	2	no	—
346	C₈×D₅	—	2	2	no	—
347	C₈×D₅	—	2	2	no	—
348	C₈×D₅	C₃×D₄	1	4	yes	complemented
349	C₂×#131	—	5	1	no	—
350	C₂×#131	—	5	1	no	—
351	#532	—	5	1	no	—
352	#435	—	5	1	no	—
353	#435	—	5	1	no	—
354	#435	—	5	1	no	—
355	#435	—	5	1	no	—
356	#435	—	5	1	no	—
357	#435	—	5	1	no	—
358	#435	—	5	1	no	—
359	#435	C₃×D₅	1	1	yes	characteristic, complemented
360	#423	—	5	1	no	—
361	#408	—	5	1	no	—
362	#408	—	5	1	no	—
363	C₂×#97	—	5	1	no	—
364	C₂²×C₃×C₅	—	2	1	no	—
365	C₂²×C₃×C₅	—	2	1	no	—
366	C₂²×C₃×C₅	—	2	1	no	—
367	C₂²×C₃×C₅	—	2	1	no	—
368	C₂²×C₃×C₅	—	2	1	no	—
369	C₂²×C₃×C₅	—	2	1	no	—
370	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
371	C₂×C₃×D₅	—	2	1	no	—
372	C₂×C₃×D₅	—	2	1	no	—
373	C₂×C₃×D₅	—	2	1	no	—
374	C₂×C₃×D₅	—	2	1	no	—
375	C₂×C₃×D₅	—	2	1	no	—
376	C₂×C₃×D₅	—	2	1	no	—
377	C₂×C₃×D₅	—	2	1	no	—
378	C₂×C₃×D₅	—	2	1	no	—
379	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
380	C₃×C₄×C₅	—	2	1	no	—
381	C₃×C₄×C₅	—	2	1	no	—
382	C₃×C₄×C₅	—	2	1	no	—
383	C₃×C₄×C₅	—	2	1	no	—
384	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
385	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
386	C₃×Dic₅	—	2	1	no	—
387	C₃×Dic₅	—	2	1	no	—
388	C₃×Dic₅	—	2	1	no	—
389	C₃×Dic₅	—	2	1	no	—
390	C₃×Dic₅	C₄×D₄	1	2	yes	—
391	C₃×#41	—	10	2	no	—
392	C₃×#41	—	10	2	no	—
393	C₃×#41	—	10	2	no	—
394	C₃×#41	—	10	2	no	—
395	C₂×C₃×Q₈	—	5	1	no	—
396	C₂×C₃×Q₈	—	5	1	no	—
397	C₂×C₃×D₄	—	5	1	no	—
398	C₂×C₃×D₄	—	5	1	no	—
399	C₂×C₃×D₄	—	5	1	no	—
400	C₂×C₃×D₄	—	5	1	no	—
401	C₂×C₃×D₄	—	5	1	no	—
402	C₂×C₃×D₄	—	5	1	no	—
403	C₂×C₃×D₄	—	5	1	no	—
404	C₂×C₃×D₄	—	5	1	no	—
405	C₂×C₃×D₄	—	5	1	no	—
406	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
407	C₂²×C₃×C₄	—	5	1	no	—
408	C₂²×C₃×C₄	—	5	1	no	—
409	C₂²×C₃×C₄	—	5	1	no	—
410	C₂²×C₃×C₄	—	5	1	no	—
411	C₂²×C₃×C₄	—	5	1	no	—
412	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
413	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
414	C₃×M₁₆	—	2	2	no	—
415	C₃×M₁₆	—	10	2	no	—
416	C₃×M₁₆	—	10	2	no	—
417	C₃×M₁₆	—	10	2	no	—
418	C₃×M₁₆	—	10	2	no	—
419	C₃×M₁₆	—	10	2	no	—
420	C₂×C₃×C₈	—	2	2	no	—
421	C₂×C₃×C₈	—	5	1	no	—
422	C₂×C₃×C₈	—	5	4	no	—
423	C₂×C₃×C₈	—	5	1	no	—
424	C₂×C₃×C₈	—	5	1	no	—
425	C₂×C₃×C₈	—	5	1	no	—
426	C₂×C₃×C₈	—	10	2	no	—
427	C₂×C₃×C₈	—	10	2	no	—
428	C₂×C₃×C₈	—	10	2	no	—
429	C₂×C₃×C₈	—	10	2	no	—
430	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
431	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
432	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
433	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
434	C₃×C₄⋊C₄	—	5	1	no	—
435	C₃×C₄⋊C₄	—	5	1	no	—
436	C₃×C₄⋊C₄	—	5	1	no	—
437	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
438	C₃×C₂²⋊C₄	—	5	1	no	—
439	C₃×C₂²⋊C₄	—	5	1	no	—
440	C₃×C₂²⋊C₄	—	5	1	no	—
441	C₃×C₂²⋊C₄	—	5	1	no	—
442	C₃×C₂²⋊C₄	—	5	1	no	—
443	C₃×C₂²⋊C₄	—	5	1	no	—
444	C₃×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
445	C₃×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
446	C₃×C₄²	—	5	1	no	—
447	C₃×C₄²	—	5	1	no	—
448	C₃×C₄²	—	5	1	no	—
449	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
450	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
451	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
452	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
453	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
454	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
455	C₅×D₄	—	4	1	no	—
456	C₂×C₄×C₅	—	2	1	no	—
457	C₂×C₄×C₅	—	2	1	no	—
458	C₂×C₄×C₅	—	2	1	no	—
459	C₂×C₄×C₅	—	2	1	no	—
460	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
461	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
462	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
463	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
464	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
465	C₂²⋊D₅	—	2	2	no	—
466	C₂²⋊D₅	—	2	2	no	—
467	C₂²⋊D₅	—	2	2	no	—
468	C₂²⋊D₅	—	2	2	no	—
469	C₂²⋊D₅	—	4	1	no	—
470	C₂²⋊D₅	—	4	1	no	—
471	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
472	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
473	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
474	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
475	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
476	D₂₀	—	2	2	no	—
477	D₂₀	—	2	2	no	—
478	D₂₀	—	4	1	no	—
479	C₄×D₅	—	2	1	no	—
480	C₄×D₅	—	2	1	no	—
481	C₄×D₅	—	2	1	no	—
482	C₄×D₅	—	2	1	no	—
483	C₄×D₅	—	4	1	no	—
484	C₄×D₅	—	4	1	no	—
485	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
486	C₄×D₅	C₃×#41	1	2	yes	—
487	Dic₁₀	—	2	2	no	—
488	Dic₁₀	—	2	2	no	—
489	C₅×C₈	—	2	1	no	—
490	C₅×C₈	—	2	1	no	—
491	C₅×C₈	—	2	1	no	—
492	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
493	#168	—	2	1	no	—
494	#168	—	2	1	no	—
495	#168	—	2	1	no	—
496	#168	C₂×C₃×D₄	1	2	yes	—
497	C₂×#41	—	5	1	no	—
498	C₂×#41	—	5	1	no	—
499	#131	—	10	4	no	—
500	#131	—	10	4	no	—
501	C₂×M₁₆	—	5	1	no	—
502	C₂×M₁₆	—	5	1	no	—
503	C₂×M₁₆	—	5	1	no	—
504	C₂×M₁₆	—	5	1	no	—
505	C₂×M₁₆	—	5	1	no	—
506	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
507	C₂²×C₈	—	5	1	no	—
508	C₂²×C₈	—	5	1	no	—
509	C₂²×C₈	—	5	1	no	—
510	C₂²×C₈	—	5	1	no	—
511	C₂²×C₈	—	5	1	no	—
512	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
513	C₄⋊Q₈	—	5	1	no	—
514	#127	—	5	1	no	—
515	#124	—	5	1	no	—
516	#124	—	5	1	no	—
517	#121	—	5	1	no	—
518	#121	—	5	1	no	—
519	#121	—	5	1	no	—
520	#121	—	5	1	no	—
521	C₄×D₄	—	5	1	no	—
522	C₄×D₄	—	5	1	no	—
523	C₄×D₄	—	5	1	no	—
524	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
525	C₂×C₄²	—	5	1	no	—
526	C₄⋊C₈	—	5	1	no	—
527	C₄⋊C₈	—	5	1	no	—
528	C₄⋊C₈	—	5	1	no	—
529	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
530	C₂²⋊C₈	—	5	1	no	—
531	C₂²⋊C₈	—	5	1	no	—
532	C₂²⋊C₈	—	5	1	no	—
533	C₂²⋊C₈	—	5	1	no	—
534	C₂²⋊C₈	—	5	1	no	—
535	C₂²⋊C₈	—	5	1	no	—
536	C₂²⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
537	C₂²⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
538	#97	—	5	1	no	—
539	#97	—	5	1	no	—
540	#97	—	5	1	no	—
541	#97	C₂×C₃×D₅	1	1	yes	characteristic
542	C₂×C₃×C₅	—	4	1	no	—
543	C₂×C₃×C₅	—	4	1	no	—
544	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
545	C₂×C₃×C₅	#568	1	1	yes	characteristic
546	C₂×C₃×C₅	#568	1	1	yes	characteristic
547	C₃×D₅	—	2	2	no	—
548	C₃×D₅	—	4	1	no	—
549	C₃×D₅	—	4	1	no	—
550	C₂³×C₃	—	5	1	no	—
551	C₂³×C₃	—	5	1	no	—
552	C₂³×C₃	—	5	1	no	—
553	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
554	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
555	C₃×Q₈	—	10	2	no	—
556	C₃×Q₈	—	10	2	no	—
557	C₃×D₄	—	4	1	no	—
558	C₃×D₄	—	10	2	no	—
559	C₃×D₄	—	10	2	no	—
560	C₃×D₄	—	10	2	no	—
561	C₃×D₄	—	10	2	no	—
562	C₃×D₄	—	10	2	no	—
563	C₃×D₄	—	10	2	no	—
564	C₃×D₄	—	20	1	no	—
565	C₃×D₄	—	20	1	no	—
566	C₃×D₄	—	20	1	no	—
567	C₂×C₃×C₄	—	2	1	no	—
568	C₂×C₃×C₄	—	2	1	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	5	1	no	—
572	C₂×C₃×C₄	—	5	2	no	—
573	C₂×C₃×C₄	—	5	2	no	—
574	C₂×C₃×C₄	—	5	1	no	—
575	C₂×C₃×C₄	—	5	1	no	—
576	C₂×C₃×C₄	—	5	1	no	—
577	C₂×C₃×C₄	—	5	1	no	—
578	C₂×C₃×C₄	—	10	1	no	—
579	C₂×C₃×C₄	—	10	1	no	—
580	C₂×C₃×C₄	—	10	1	no	—
581	C₂×C₃×C₄	—	10	1	no	—
582	C₂×C₃×C₄	—	20	1	no	—
583	C₂×C₃×C₄	—	20	1	no	—
584	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
585	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
586	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
587	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
588	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
589	C₃×C₈	—	2	1	no	—
590	C₃×C₈	—	2	1	no	—
591	C₃×C₈	—	2	1	no	—
592	C₃×C₈	—	5	2	no	—
593	C₃×C₈	—	10	1	no	—
594	C₃×C₈	—	10	1	no	—
595	C₃×C₈	—	10	1	no	—
596	C₃×C₈	D₄×D₅	1	2	yes	—
597	C₂²×C₅	—	2	1	no	—
598	C₂²×C₅	—	2	1	no	—
599	C₂²×C₅	—	2	1	no	—
600	C₂²×C₅	—	2	1	no	—
601	C₂²×C₅	—	2	1	no	—
602	C₂²×C₅	—	2	1	no	—
603	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
604	C₂×D₅	—	2	1	no	—
605	C₂×D₅	—	2	1	no	—
606	C₂×D₅	—	2	1	no	—
607	C₂×D₅	—	2	1	no	—
608	C₂×D₅	—	2	1	no	—
609	C₂×D₅	—	2	1	no	—
610	C₂×D₅	—	2	1	no	—
611	C₂×D₅	—	2	1	no	—
612	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
613	C₄×C₅	—	2	1	no	—
614	C₄×C₅	—	2	1	no	—
615	C₄×C₅	—	2	1	no	—
616	C₄×C₅	—	2	1	no	—
617	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
618	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
619	Dic₅	—	2	1	no	—
620	Dic₅	—	2	1	no	—
621	Dic₅	—	2	1	no	—
622	Dic₅	—	2	1	no	—
623	Dic₅	C₃×C₄×D₄	1	2	yes	—
624	#41	—	10	2	no	—
625	#41	—	10	2	no	—
626	#41	—	10	2	no	—
627	#41	—	10	2	no	—
628	C₂×Q₈	—	5	1	no	—
629	C₂×Q₈	—	5	1	no	—
630	C₂×D₄	—	5	1	no	—
631	C₂×D₄	—	5	1	no	—
632	C₂×D₄	—	5	1	no	—
633	C₂×D₄	—	5	1	no	—
634	C₂×D₄	—	5	1	no	—
635	C₂×D₄	—	5	1	no	—
636	C₂×D₄	—	5	1	no	—
637	C₂×D₄	—	5	1	no	—
638	C₂×D₄	—	5	1	no	—
639	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic
640	C₂²×C₄	—	5	1	no	—
641	C₂²×C₄	—	5	1	no	—
642	C₂²×C₄	—	5	1	no	—
643	C₂²×C₄	—	5	1	no	—
644	C₂²×C₄	—	5	1	no	—
645	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
646	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
647	M₁₆	—	2	2	no	—
648	M₁₆	—	10	2	no	—
649	M₁₆	—	10	2	no	—
650	M₁₆	—	10	2	no	—
651	M₁₆	—	10	2	no	—
652	M₁₆	—	10	2	no	—
653	C₂×C₈	—	2	2	no	—
654	C₂×C₈	—	5	1	no	—
655	C₂×C₈	—	5	4	no	—
656	C₂×C₈	—	5	1	no	—
657	C₂×C₈	—	5	1	no	—
658	C₂×C₈	—	5	1	no	—
659	C₂×C₈	—	10	2	no	—
660	C₂×C₈	—	10	2	no	—
661	C₂×C₈	—	10	2	no	—
662	C₂×C₈	—	10	2	no	—
663	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
664	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
665	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
666	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
667	C₄⋊C₄	—	5	1	no	—
668	C₄⋊C₄	—	5	1	no	—
669	C₄⋊C₄	—	5	1	no	—
670	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
671	C₂²⋊C₄	—	5	1	no	—
672	C₂²⋊C₄	—	5	1	no	—
673	C₂²⋊C₄	—	5	1	no	—
674	C₂²⋊C₄	—	5	1	no	—
675	C₂²⋊C₄	—	5	1	no	—
676	C₂²⋊C₄	—	5	1	no	—
677	C₂²⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
678	C₂²⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
679	C₄²	—	5	1	no	—
680	C₄²	—	5	1	no	—
681	C₄²	—	5	1	no	—
682	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
683	C₃×C₅	#2932	1	1	yes	characteristic, complemented, Hall
684	C₂²×C₃	—	2	1	no	—
685	C₂²×C₃	—	2	1	no	—
686	C₂²×C₃	—	2	1	no	—
687	C₂²×C₃	—	2	1	no	—
688	C₂²×C₃	—	2	1	no	—
689	C₂²×C₃	—	2	1	no	—
690	C₂²×C₃	—	5	2	no	—
691	C₂²×C₃	—	10	1	no	—
692	C₂²×C₃	—	10	1	no	—
693	C₂²×C₃	—	10	1	no	—
694	C₂²×C₃	—	10	1	no	—
695	C₂²×C₃	—	10	1	no	—
696	C₂²×C₃	—	10	1	no	—
697	C₂²×C₃	—	10	1	no	—
698	C₂²×C₃	—	10	1	no	—
699	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
700	C₃×C₄	—	2	1	no	—
701	C₃×C₄	—	2	1	no	—
702	C₃×C₄	—	2	1	no	—
703	C₃×C₄	—	2	1	no	—
704	C₃×C₄	—	5	2	no	—
705	C₃×C₄	—	10	1	no	—
706	C₃×C₄	—	10	1	no	—
707	C₃×C₄	—	10	1	no	—
708	C₃×C₄	—	10	1	no	—
709	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
710	C₃×C₄	D₅×#41	1	1	yes	characteristic
711	C₂×C₅	—	4	1	no	—
712	C₂×C₅	—	4	1	no	—
713	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
714	C₂×C₅	C₃×#568	1	1	yes	characteristic
715	C₂×C₅	C₃×#568	1	1	yes	characteristic
716	D₅	—	2	2	no	—
717	D₅	—	4	1	no	—
718	D₅	—	4	1	no	—
719	C₂³	—	5	1	no	—
720	C₂³	—	5	1	no	—
721	C₂³	—	5	1	no	—
722	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
723	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
724	Q₈	—	10	2	no	—
725	Q₈	—	10	2	no	—
726	D₄	—	4	1	no	—
727	D₄	—	10	2	no	—
728	D₄	—	10	2	no	—
729	D₄	—	10	2	no	—
730	D₄	—	10	2	no	—
731	D₄	—	10	2	no	—
732	D₄	—	10	2	no	—
733	D₄	—	20	1	no	—
734	D₄	—	20	1	no	—
735	D₄	—	20	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	5	1	no	—
741	C₂×C₄	—	5	2	no	—
742	C₂×C₄	—	5	2	no	—
743	C₂×C₄	—	5	1	no	—
744	C₂×C₄	—	5	1	no	—
745	C₂×C₄	—	5	1	no	—
746	C₂×C₄	—	5	1	no	—
747	C₂×C₄	—	10	1	no	—
748	C₂×C₄	—	10	1	no	—
749	C₂×C₄	—	10	1	no	—
750	C₂×C₄	—	10	1	no	—
751	C₂×C₄	—	20	1	no	—
752	C₂×C₄	—	20	1	no	—
753	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
754	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
755	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
756	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
757	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
758	C₈	—	2	1	no	—
759	C₈	—	2	1	no	—
760	C₈	—	2	1	no	—
761	C₈	—	5	2	no	—
762	C₈	—	10	1	no	—
763	C₈	—	10	1	no	—
764	C₈	—	10	1	no	—
765	C₈	C₃×D₄×D₅	1	2	yes	—
766	C₂×C₃	—	4	1	no	—
767	C₂×C₃	—	4	1	no	—
768	C₂×C₃	—	10	2	no	—
769	C₂×C₃	—	20	1	no	—
770	C₂×C₃	—	20	1	no	—
771	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
772	C₂×C₃	#66079	1	1	yes	characteristic
773	C₂×C₃	#66084	1	1	yes	characteristic
774	C₅	C₃×#2932	1	1	yes	characteristic, complemented, Sylow
775	C₂²	—	2	1	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	1	no	—
781	C₂²	—	5	2	no	—
782	C₂²	—	10	1	no	—
783	C₂²	—	10	1	no	—
784	C₂²	—	10	1	no	—
785	C₂²	—	10	1	no	—
786	C₂²	—	10	1	no	—
787	C₂²	—	10	1	no	—
788	C₂²	—	10	1	no	—
789	C₂²	—	10	1	no	—
790	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
791	C₄	—	2	1	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	1	no	—
794	C₄	—	2	1	no	—
795	C₄	—	5	2	no	—
796	C₄	—	10	1	no	—
797	C₄	—	10	1	no	—
798	C₄	—	10	1	no	—
799	C₄	—	10	1	no	—
800	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
801	C₄	C₃×D₅×#41	1	1	yes	characteristic
802	C₃	#10611211	1	1	yes	characteristic, direct product factor, Sylow
803	C₂	—	4	1	no	—
804	C₂	—	4	1	no	—
805	C₂	—	10	2	no	—
806	C₂	—	20	1	no	—
807	C₂	—	20	1	no	—
808	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
809	C₂	C₃×#66079	1	1	yes	characteristic
810	C₂	C₃×#66084	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#435	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×#65882	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#435	D₅
hypocenter	C₅	C₃×#2932
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#435

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4053	C₂	semidirect
2. C₂×C₃×#4047	C₂	semidirect
4. C₃×C₅×#435	C₂	semidirect
5. C₃×#65416	C₂	semidirect
6. C₃×#65400	C₂	semidirect
7. C₃×#65300	C₂	semidirect
8. C₃×#65126	C₂	semidirect
9. C₃×#65125	C₂	semidirect
10. C₃×#65019	C₂	semidirect
11. C₃×#65017	C₂	semidirect
12. C₃×#65016	C₂	semidirect
13. C₃×#65016	C₂	semidirect
14. C₃×#64995	C₂	semidirect
15. C₃×D₅×#97	C₂	semidirect
16. #10611211	C₃	direct (N × H)
63. C₂×#4053	C₂×C₃	semidirect
64. C₂×#4047	C₂×C₃	semidirect
66. C₅×#435	C₂×C₃	semidirect
67. #65416	C₂×C₃	semidirect
68. #65400	C₂×C₃	semidirect
69. #65300	C₂×C₃	semidirect
70. #65126	C₂×C₃	semidirect
71. #65125	C₂×C₃	semidirect
72. #65019	C₂×C₃	semidirect
73. #65017	C₂×C₃	semidirect
74. #65016	C₂×C₃	semidirect
75. #65016	C₂×C₃	semidirect
76. #64995	C₂×C₃	semidirect
77. D₅×#97	C₂×C₃	semidirect
136. C₃×C₈×D₅	D₄	semidirect
147. C₃×#435	D₅	semidirect
348. C₈×D₅	C₃×D₄	semidirect
359. #435	C₃×D₅	semidirect
683. C₃×C₅	#2932	semidirect
774. C₅	C₃×#2932	semidirect
802. C₃	#10611211	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×#4053	2
C₂×C₃×#4047	2
C₃×#65882	2
C₃×C₅×#435	2
C₃×#65416	2
C₃×#65400	2
C₃×#65300	2
C₃×#65126	2
C₃×#65125	2
C₃×#65019	2
C₃×#65017	2
C₃×#65016	2
C₃×#64995	2
C₃×D₅×#97	2
#10611211	3
C₃×#2932	5

Subgroups — C3×#10611211 #14415331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611211 #14415331