Subgroups — C₃×#10612405 #14453185

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4060	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65964	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65943	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#465	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65465	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65400	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65325	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65158	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65154	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65108	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65100	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65075	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#65062	C₂	1	1	yes	maximal, characteristic, complemented
16	#10612405	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×#713	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×D₄×D₅	—	2	1	no	—
19	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
21	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×#121	C₂²	1	1	yes	characteristic
26	C₃×#4093	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×#688	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×#688	C₂²	1	1	yes	characteristic, complemented
29	C₃×#4086	C₂²	1	1	yes	characteristic, complemented
30	C₃×#4083	—	2	1	no	—
31	C₂×C₃×#686	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×#686	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
34	C₃×#4060	—	2	4	no	—
35	C₂×C₃×D₄₀	—	2	4	no	—
36	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
37	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
38	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×#676	C₂²	1	1	yes	characteristic, complemented
41	C₃×#4041	—	2	1	no	—
42	C₃×#4041	C₂²	1	1	yes	characteristic, complemented
43	C₃×#4041	C₂²	1	1	yes	characteristic, complemented
44	C₃×#4040	—	2	1	no	—
45	C₃×#4039	C₂²	1	1	yes	characteristic, complemented
46	C₃×#4039	C₂²	1	1	yes	characteristic, complemented
47	C₃×#4030	—	2	1	no	—
48	C₃×#4028	—	2	1	no	—
49	C₃×#4028	—	2	1	no	—
50	C₃×D₅×C₂²⋊C₄	—	2	1	no	—
51	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic, complemented
55	C₃×#3952	C₂²	1	1	yes	characteristic, complemented
56	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
57	C₃×#3946	C₂²	1	1	yes	characteristic, complemented
58	C₃×#3941	C₂²	1	1	yes	characteristic, complemented
59	C₃×#3941	C₂²	1	1	yes	characteristic, complemented
60	C₃×#3941	C₂²	1	1	yes	characteristic, complemented
61	C₃×#3941	C₂²	1	1	yes	characteristic, complemented
62	C₃×#3264	—	5	1	no	maximal, Hall
63	C₂×#4060	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂²×D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
65	#65964	C₂×C₃	1	1	yes	characteristic, complemented
66	#65943	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#465	C₂×C₃	1	1	yes	characteristic, complemented
68	#65465	C₂×C₃	1	1	yes	characteristic, complemented
69	#65400	C₂×C₃	1	1	yes	characteristic, complemented
70	#65335	C₂×C₃	1	1	yes	characteristic, complemented
71	#65325	C₂×C₃	1	1	yes	characteristic, complemented
72	#65158	C₂×C₃	1	1	yes	characteristic, complemented
73	#65154	C₂×C₃	1	1	yes	characteristic, complemented
74	#65108	C₂×C₃	1	1	yes	characteristic, complemented
75	#65100	C₂×C₃	1	1	yes	characteristic, complemented
76	#65075	C₂×C₃	1	1	yes	characteristic, complemented
77	#65062	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂³×C₃×D₅	—	2	1	no	—
79	C₂³×C₃×D₅	—	2	1	no	—
80	C₂³×C₃×D₅	—	2	1	no	—
81	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×D₄	—	2	1	no	—
83	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
86	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
87	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
88	C₂×C₃×C₂²⋊D₅	D₄	1	1	yes	characteristic
89	C₃×#713	—	2	2	no	—
90	C₃×#713	—	4	1	no	—
91	C₃×D₄×D₅	—	2	2	no	—
92	C₃×D₄×D₅	—	4	1	no	—
93	C₃×D₄×D₅	—	4	4	no	—
94	C₂×C₃×D₂₀	—	2	2	no	—
95	C₂×C₃×D₂₀	—	2	2	no	—
96	C₂×C₃×D₂₀	—	2	1	no	—
97	C₂×C₃×D₂₀	—	2	1	no	—
98	C₂×C₃×D₂₀	—	2	1	no	—
99	C₂×C₃×D₂₀	—	2	1	no	—
100	C₂×C₃×D₂₀	—	2	1	no	—
101	C₂×C₃×D₂₀	—	4	1	no	—
102	C₂×C₃×D₂₀	—	4	1	no	—
103	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
104	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
105	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
106	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₄×D₅	—	2	1	no	—
108	C₂×C₃×C₄×D₅	—	2	1	no	—
109	C₂×C₃×C₄×D₅	—	2	1	no	—
110	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
111	C₃×C₅×SD₁₆	—	2	2	no	—
112	C₂×C₃×C₅×C₈	—	2	2	no	—
113	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
114	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
115	C₃×C₅×C₄⋊C₄	—	2	1	no	—
116	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
119	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
120	C₃×C₂²⋊Dic₅	D₄	1	1	yes	characteristic
121	C₃×#688	—	2	2	no	—
122	C₃×#688	—	4	1	no	—
123	C₃×#686	—	2	2	no	—
124	C₃×#686	—	4	1	no	—
125	C₃×#685	—	2	1	no	—
126	C₃×#685	—	2	1	no	—
127	C₃×#685	—	2	1	no	—
128	C₃×#685	—	2	1	no	—
129	C₃×#685	—	2	1	no	—
130	C₃×#685	—	2	1	no	—
131	C₃×#685	D₄	1	1	yes	characteristic
132	C₃×#683	D₄	1	1	yes	characteristic
133	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
134	C₂×C₃×#168	C₂³	1	1	yes	characteristic
135	C₂×C₃×#168	C₂³	1	1	yes	characteristic
136	C₃×D₄₀	—	2	2	no	—
137	C₃×D₄₀	—	2	2	no	—
138	C₃×D₄₀	—	2	2	no	—
139	C₃×D₄₀	D₄	1	4	yes	complemented
140	C₃×#676	—	2	2	no	—
141	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
142	C₂²×C₃×D₈	—	5	1	no	—
143	C₃×#546	—	5	1	no	—
144	C₃×D₄²	—	5	1	no	—
145	C₃×#496	—	5	1	no	—
146	C₃×#469	—	5	1	no	—
147	C₃×#465	D₅	1	1	yes	characteristic, complemented
148	C₃×#463	—	5	1	no	—
149	C₃×#459	—	5	1	no	—
150	C₃×#450	—	5	1	no	—
151	C₃×#449	—	5	1	no	—
152	C₃×#447	—	5	1	no	—
153	C₃×#447	—	5	1	no	—
154	C₃×#442	—	5	1	no	—
155	C₃×#435	—	5	1	no	—
156	C₂×#713	C₂²×C₃	1	1	yes	characteristic, complemented
157	C₂×D₄×D₅	—	2	1	no	—
158	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
159	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
160	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
162	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₅×#121	C₂²×C₃	1	1	yes	characteristic
165	#4093	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₂×#688	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₂×#688	C₂²×C₃	1	1	yes	characteristic, complemented
168	#4086	C₂²×C₃	1	1	yes	characteristic, complemented
169	#4083	—	2	1	no	—
170	C₂×#686	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₂×#686	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
173	#4060	—	2	4	no	—
174	C₂×D₄₀	—	2	4	no	—
175	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
176	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
177	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic, complemented
178	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₂×#676	C₂²×C₃	1	1	yes	characteristic, complemented
180	#4041	—	2	1	no	—
181	#4041	C₂²×C₃	1	1	yes	characteristic, complemented
182	#4041	C₂²×C₃	1	1	yes	characteristic, complemented
183	#4040	—	2	1	no	—
184	#4039	C₂²×C₃	1	1	yes	characteristic, complemented
185	#4039	C₂²×C₃	1	1	yes	characteristic, complemented
186	#4030	—	2	1	no	—
187	#4028	—	2	1	no	—
188	#4028	—	2	1	no	—
189	D₅×C₂²⋊C₄	—	2	1	no	—
190	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
194	#3952	C₂²×C₃	1	1	yes	characteristic, complemented
195	#3947	C₂²×C₃	1	1	yes	characteristic, complemented
196	#3946	C₂²×C₃	1	1	yes	characteristic, complemented
197	#3941	C₂²×C₃	1	1	yes	characteristic, complemented
198	#3941	C₂²×C₃	1	1	yes	characteristic, complemented
199	#3941	C₂²×C₃	1	1	yes	characteristic, complemented
200	#3941	C₂²×C₃	1	1	yes	characteristic, complemented
201	#3264	—	5	1	no	Sylow
202	C₂³×C₃×C₅	—	2	1	no	—
203	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₃×D₅	—	2	1	no	—
205	C₂²×C₃×D₅	—	2	1	no	—
206	C₂²×C₃×D₅	—	2	1	no	—
207	C₂²×C₃×D₅	—	2	1	no	—
208	C₂²×C₃×D₅	—	4	2	no	—
209	C₂²×C₃×D₅	—	4	2	no	—
210	C₂²×C₃×D₅	—	4	2	no	—
211	C₂²×C₃×D₅	—	4	2	no	—
212	C₂²×C₃×D₅	—	4	2	no	—
213	C₂²×C₃×D₅	—	4	2	no	—
214	C₂²×C₃×D₅	—	8	1	no	—
215	C₂²×C₃×D₅	—	8	1	no	—
216	C₂²×C₃×D₅	—	8	1	no	—
217	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
218	C₃×C₅×Q₈	—	2	1	no	—
219	C₃×C₅×Q₈	—	2	1	no	—
220	C₃×C₅×D₄	—	2	1	no	—
221	C₃×C₅×D₄	—	2	1	no	—
222	C₃×C₅×D₄	—	4	2	no	—
223	C₂×C₃×C₄×C₅	—	2	1	no	—
224	C₂×C₃×C₄×C₅	—	2	1	no	—
225	C₂×C₃×C₄×C₅	—	2	1	no	—
226	C₂×C₃×C₄×C₅	—	2	1	no	—
227	C₂×C₃×C₄×C₅	—	2	1	no	—
228	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
229	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
230	C₃×C₂²⋊D₅	—	2	2	no	—
231	C₃×C₂²⋊D₅	—	4	2	no	—
232	C₃×C₂²⋊D₅	—	4	2	no	—
233	C₃×C₂²⋊D₅	—	8	1	no	—
234	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
235	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
236	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
237	C₃×D₂₀	—	2	1	no	—
238	C₃×D₂₀	—	2	1	no	—
239	C₃×D₂₀	—	2	1	no	—
240	C₃×D₂₀	—	2	1	no	—
241	C₃×D₂₀	—	2	1	no	—
242	C₃×D₂₀	—	2	1	no	—
243	C₃×D₂₀	—	4	2	no	—
244	C₃×D₂₀	—	4	2	no	—
245	C₃×D₂₀	—	4	2	no	—
246	C₃×D₂₀	—	4	2	no	—
247	C₃×D₂₀	—	8	1	no	—
248	C₃×D₂₀	C₂×D₄	1	2	yes	—
249	C₃×D₂₀	C₂×D₄	1	2	yes	complemented
250	C₃×C₄×D₅	—	2	1	no	—
251	C₃×C₄×D₅	—	2	1	no	—
252	C₃×C₄×D₅	—	4	2	no	—
253	C₃×C₄×D₅	—	4	2	no	—
254	C₃×C₄×D₅	—	8	1	no	—
255	C₃×C₅×C₈	—	2	1	no	—
256	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
257	C₃×#168	—	2	1	no	—
258	C₃×#168	—	2	1	no	—
259	C₂×C₃×#41	—	5	1	no	—
260	C₂²×C₃×D₄	—	5	1	no	—
261	C₂²×C₃×D₄	—	5	1	no	—
262	C₂²×C₃×D₄	—	5	1	no	—
263	C₂²×C₃×D₄	—	10	1	no	—
264	C₃×AGL(1,ℤ/8)	—	10	4	no	—
265	C₂×C₃×SD₁₆	—	5	1	no	—
266	C₂×C₃×SD₁₆	—	5	1	no	—
267	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic, complemented
268	C₂×C₃×D₈	—	5	1	no	—
269	C₂×C₃×D₈	—	5	1	no	—
270	C₂×C₃×D₈	—	5	1	no	—
271	C₂×C₃×D₈	—	5	1	no	—
272	C₂×C₃×D₈	—	5	1	no	—
273	C₂×C₃×D₈	—	5	1	no	—
274	C₂×C₃×D₈	—	10	4	no	—
275	C₂×C₃×M₁₆	—	5	1	no	—
276	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
277	C₃×#127	—	5	1	no	—
278	C₃×#124	—	5	1	no	—
279	C₃×#123	—	10	1	no	—
280	C₃×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
281	C₃×#121	—	5	1	no	—
282	C₃×#121	—	5	1	no	—
283	C₃×#121	—	10	1	no	—
284	C₃×#121	—	10	1	no	—
285	C₃×#121	C₂×D₅	1	1	yes	characteristic
286	C₃×#120	—	10	1	no	—
287	C₃×#120	—	10	1	no	—
288	C₃×#120	—	10	1	no	—
289	C₃×C₄×D₄	—	5	1	no	—
290	C₃×C₄×D₄	—	5	1	no	—
291	C₃×C₄×D₄	—	5	1	no	—
292	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
293	C₃×#106	C₂×D₅	1	1	yes	characteristic, complemented
294	C₃×C₄⋊C₈	—	5	1	no	—
295	C₃×#103	C₂×D₅	1	1	yes	characteristic, complemented
296	C₃×#102	—	5	1	no	—
297	C₃×#102	—	5	1	no	—
298	C₃×#102	—	5	1	no	—
299	C₃×#102	—	5	1	no	—
300	C₃×#102	C₂×D₅	1	1	yes	characteristic, complemented
301	C₃×C₂²⋊C₈	—	5	1	no	—
302	C₃×C₂²⋊C₈	—	5	1	no	—
303	C₃×#97	—	5	1	no	—
304	C₂³×D₅	—	2	1	no	—
305	C₂³×D₅	—	2	1	no	—
306	C₂³×D₅	—	2	1	no	—
307	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
308	C₂×C₅×D₄	—	2	1	no	—
309	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
310	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
311	C₂×C₂²⋊D₅	—	2	1	no	—
312	C₂×C₂²⋊D₅	—	2	1	no	—
313	C₂×C₂²⋊D₅	—	2	1	no	—
314	C₂×C₂²⋊D₅	C₃×D₄	1	1	yes	characteristic
315	#713	—	2	2	no	—
316	#713	—	4	1	no	—
317	D₄×D₅	—	2	2	no	—
318	D₄×D₅	—	4	1	no	—
319	D₄×D₅	—	4	4	no	—
320	C₂×D₂₀	—	2	2	no	—
321	C₂×D₂₀	—	2	2	no	—
322	C₂×D₂₀	—	2	1	no	—
323	C₂×D₂₀	—	2	1	no	—
324	C₂×D₂₀	—	2	1	no	—
325	C₂×D₂₀	—	2	1	no	—
326	C₂×D₂₀	—	2	1	no	—
327	C₂×D₂₀	—	4	1	no	—
328	C₂×D₂₀	—	4	1	no	—
329	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
330	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
331	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
332	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
333	C₂×C₄×D₅	—	2	1	no	—
334	C₂×C₄×D₅	—	2	1	no	—
335	C₂×C₄×D₅	—	2	1	no	—
336	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
337	C₅×SD₁₆	—	2	2	no	—
338	C₂×C₅×C₈	—	2	2	no	—
339	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
340	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
341	C₅×C₄⋊C₄	—	2	1	no	—
342	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
343	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
344	C₅×C₂²⋊C₄	—	2	1	no	—
345	C₅×C₂²⋊C₄	—	2	1	no	—
346	C₂²⋊Dic₅	C₃×D₄	1	1	yes	characteristic
347	#688	—	2	2	no	—
348	#688	—	4	1	no	—
349	#686	—	2	2	no	—
350	#686	—	4	1	no	—
351	#685	—	2	1	no	—
352	#685	—	2	1	no	—
353	#685	—	2	1	no	—
354	#685	—	2	1	no	—
355	#685	—	2	1	no	—
356	#685	—	2	1	no	—
357	#685	C₃×D₄	1	1	yes	characteristic
358	#683	C₃×D₄	1	1	yes	characteristic
359	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
360	C₂×#168	C₂³×C₃	1	1	yes	characteristic
361	C₂×#168	C₂³×C₃	1	1	yes	characteristic
362	D₄₀	—	2	2	no	—
363	D₄₀	—	2	2	no	—
364	D₄₀	—	2	2	no	—
365	D₄₀	C₃×D₄	1	4	yes	complemented
366	#676	—	2	2	no	—
367	C₂×AGL(1,ℤ/8)	—	5	1	no	—
368	C₂²×D₈	—	5	1	no	—
369	#546	—	5	1	no	—
370	D₄²	—	5	1	no	—
371	#496	—	5	1	no	—
372	#469	—	5	1	no	—
373	#465	C₃×D₅	1	1	yes	characteristic, complemented
374	#463	—	5	1	no	—
375	#459	—	5	1	no	—
376	#450	—	5	1	no	—
377	#449	—	5	1	no	—
378	#447	—	5	1	no	—
379	#447	—	5	1	no	—
380	#442	—	5	1	no	—
381	#435	—	5	1	no	—
382	C₂²×C₃×C₅	—	2	1	no	—
383	C₂²×C₃×C₅	—	2	1	no	—
384	C₂²×C₃×C₅	—	4	1	no	—
385	C₂²×C₃×C₅	—	4	1	no	—
386	C₂²×C₃×C₅	—	4	1	no	—
387	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	complemented
388	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₃×D₅	—	2	1	no	—
390	C₂×C₃×D₅	—	2	2	no	—
391	C₂×C₃×D₅	—	2	2	no	—
392	C₂×C₃×D₅	—	2	1	no	—
393	C₂×C₃×D₅	—	2	1	no	—
394	C₂×C₃×D₅	—	4	1	no	—
395	C₂×C₃×D₅	—	4	1	no	—
396	C₂×C₃×D₅	—	4	1	no	—
397	C₂×C₃×D₅	—	4	1	no	—
398	C₂×C₃×D₅	—	4	1	no	—
399	C₂×C₃×D₅	—	4	1	no	—
400	C₂×C₃×D₅	—	4	1	no	—
401	C₂×C₃×D₅	—	4	1	no	—
402	C₂×C₃×D₅	—	4	1	no	—
403	C₂×C₃×D₅	—	4	1	no	—
404	C₂×C₃×D₅	—	8	4	no	—
405	C₂×C₃×D₅	—	8	4	no	—
406	C₂×C₃×D₅	—	8	4	no	—
407	C₃×C₄×C₅	—	2	1	no	—
408	C₃×C₄×C₅	—	4	1	no	—
409	C₃×C₄×C₅	—	4	1	no	—
410	C₃×C₄×C₅	—	4	1	no	—
411	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
412	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
413	C₃×Dic₅	—	2	1	no	—
414	C₃×Dic₅	—	2	1	no	—
415	C₃×Dic₅	—	2	1	no	—
416	C₂⁴×C₃	—	10	1	no	—
417	C₂⁴×C₃	—	10	1	no	—
418	C₂⁴×C₃	—	10	1	no	—
419	C₃×#41	—	10	2	no	—
420	C₃×#41	—	20	1	no	—
421	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
422	C₂×C₃×D₄	—	2	1	no	—
423	C₂×C₃×D₄	—	5	1	no	—
424	C₂×C₃×D₄	—	5	1	no	—
425	C₂×C₃×D₄	—	5	1	no	—
426	C₂×C₃×D₄	—	5	1	no	—
427	C₂×C₃×D₄	—	5	1	no	—
428	C₂×C₃×D₄	—	10	2	no	—
429	C₂×C₃×D₄	—	10	2	no	—
430	C₂×C₃×D₄	—	10	1	no	—
431	C₂×C₃×D₄	—	10	1	no	—
432	C₂×C₃×D₄	—	10	1	no	—
433	C₂×C₃×D₄	—	10	1	no	—
434	C₂×C₃×D₄	—	10	1	no	—
435	C₂×C₃×D₄	—	10	1	no	—
436	C₂×C₃×D₄	—	10	2	no	—
437	C₂×C₃×D₄	—	10	1	no	—
438	C₂×C₃×D₄	—	10	1	no	—
439	C₂×C₃×D₄	—	20	1	no	—
440	C₂×C₃×D₄	—	20	1	no	—
441	C₂×C₃×D₄	—	20	1	no	—
442	C₂×C₃×D₄	—	20	4	no	—
443	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
444	C₂²×C₃×C₄	—	5	1	no	—
445	C₂²×C₃×C₄	—	10	1	no	—
446	C₂²×C₃×C₄	—	10	1	no	—
447	C₂²×C₃×C₄	—	10	1	no	—
448	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
449	C₃×SD₁₆	—	2	2	no	—
450	C₃×SD₁₆	—	10	2	no	—
451	C₃×SD₁₆	—	20	1	no	—
452	C₃×D₈	—	5	4	no	—
453	C₃×D₈	—	10	2	no	—
454	C₃×D₈	—	10	2	no	—
455	C₃×D₈	—	10	2	no	—
456	C₃×D₈	—	10	2	no	—
457	C₃×D₈	—	20	1	no	—
458	C₃×M₁₆	—	10	2	no	—
459	C₂×C₃×C₈	—	2	2	no	—
460	C₂×C₃×C₈	—	5	1	no	—
461	C₂×C₃×C₈	—	5	1	no	—
462	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
463	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
464	C₃×C₄⋊C₄	—	2	1	no	—
465	C₃×C₄⋊C₄	—	5	1	no	—
466	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
467	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
468	C₃×C₂²⋊C₄	—	2	1	no	—
469	C₃×C₂²⋊C₄	—	2	1	no	—
470	C₃×C₂²⋊C₄	—	5	1	no	—
471	C₃×C₂²⋊C₄	—	5	1	no	—
472	C₃×C₂²⋊C₄	—	10	1	no	—
473	C₃×C₂²⋊C₄	—	10	1	no	—
474	C₃×C₂²⋊C₄	—	10	1	no	—
475	C₃×C₂²⋊C₄	—	10	1	no	—
476	C₃×C₂²⋊C₄	—	10	1	no	—
477	C₃×C₂²⋊C₄	—	10	1	no	—
478	C₃×C₄²	—	5	1	no	—
479	C₂³×C₅	—	2	1	no	—
480	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
481	C₂²×D₅	—	2	1	no	—
482	C₂²×D₅	—	2	1	no	—
483	C₂²×D₅	—	2	1	no	—
484	C₂²×D₅	—	2	1	no	—
485	C₂²×D₅	—	4	2	no	—
486	C₂²×D₅	—	4	2	no	—
487	C₂²×D₅	—	4	2	no	—
488	C₂²×D₅	—	4	2	no	—
489	C₂²×D₅	—	4	2	no	—
490	C₂²×D₅	—	4	2	no	—
491	C₂²×D₅	—	8	1	no	—
492	C₂²×D₅	—	8	1	no	—
493	C₂²×D₅	—	8	1	no	—
494	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
495	C₅×Q₈	—	2	1	no	—
496	C₅×Q₈	—	2	1	no	—
497	C₅×D₄	—	2	1	no	—
498	C₅×D₄	—	2	1	no	—
499	C₅×D₄	—	4	2	no	—
500	C₂×C₄×C₅	—	2	1	no	—
501	C₂×C₄×C₅	—	2	1	no	—
502	C₂×C₄×C₅	—	2	1	no	—
503	C₂×C₄×C₅	—	2	1	no	—
504	C₂×C₄×C₅	—	2	1	no	—
505	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
506	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
507	C₂²⋊D₅	—	2	2	no	—
508	C₂²⋊D₅	—	4	2	no	—
509	C₂²⋊D₅	—	4	2	no	—
510	C₂²⋊D₅	—	8	1	no	—
511	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
512	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
513	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
514	D₂₀	—	2	1	no	—
515	D₂₀	—	2	1	no	—
516	D₂₀	—	2	1	no	—
517	D₂₀	—	2	1	no	—
518	D₂₀	—	2	1	no	—
519	D₂₀	—	2	1	no	—
520	D₂₀	—	4	2	no	—
521	D₂₀	—	4	2	no	—
522	D₂₀	—	4	2	no	—
523	D₂₀	—	4	2	no	—
524	D₂₀	—	8	1	no	—
525	D₂₀	C₂×C₃×D₄	1	2	yes	—
526	D₂₀	C₂×C₃×D₄	1	2	yes	complemented
527	C₄×D₅	—	2	1	no	—
528	C₄×D₅	—	2	1	no	—
529	C₄×D₅	—	4	2	no	—
530	C₄×D₅	—	4	2	no	—
531	C₄×D₅	—	8	1	no	—
532	C₅×C₈	—	2	1	no	—
533	C₅×C₈	C₂×C₃×D₄	1	2	yes	complemented
534	#168	—	2	1	no	—
535	#168	—	2	1	no	—
536	C₂×#41	—	5	1	no	—
537	C₂²×D₄	—	5	1	no	—
538	C₂²×D₄	—	5	1	no	—
539	C₂²×D₄	—	5	1	no	—
540	C₂²×D₄	—	10	1	no	—
541	AGL(1,ℤ/8)	—	10	4	no	—
542	C₂×SD₁₆	—	5	1	no	—
543	C₂×SD₁₆	—	5	1	no	—
544	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
545	C₂×D₈	—	5	1	no	—
546	C₂×D₈	—	5	1	no	—
547	C₂×D₈	—	5	1	no	—
548	C₂×D₈	—	5	1	no	—
549	C₂×D₈	—	5	1	no	—
550	C₂×D₈	—	5	1	no	—
551	C₂×D₈	—	10	4	no	—
552	C₂×M₁₆	—	5	1	no	—
553	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
554	#127	—	5	1	no	—
555	#124	—	5	1	no	—
556	#123	—	10	1	no	—
557	C₂²⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
558	#121	—	5	1	no	—
559	#121	—	5	1	no	—
560	#121	—	10	1	no	—
561	#121	—	10	1	no	—
562	#121	C₂×C₃×D₅	1	1	yes	characteristic
563	#120	—	10	1	no	—
564	#120	—	10	1	no	—
565	#120	—	10	1	no	—
566	C₄×D₄	—	5	1	no	—
567	C₄×D₄	—	5	1	no	—
568	C₄×D₄	—	5	1	no	—
569	C₂×C₂²⋊C₄	—	10	1	no	—
570	#106	C₂×C₃×D₅	1	1	yes	characteristic, complemented
571	C₄⋊C₈	—	5	1	no	—
572	#103	C₂×C₃×D₅	1	1	yes	characteristic, complemented
573	#102	—	5	1	no	—
574	#102	—	5	1	no	—
575	#102	—	5	1	no	—
576	#102	—	5	1	no	—
577	#102	C₂×C₃×D₅	1	1	yes	characteristic, complemented
578	C₂²⋊C₈	—	5	1	no	—
579	C₂²⋊C₈	—	5	1	no	—
580	#97	—	5	1	no	—
581	C₂×C₃×C₅	—	2	2	no	—
582	C₂×C₃×C₅	—	8	1	no	—
583	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
584	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
585	C₂×C₃×C₅	#576	1	1	yes	characteristic
586	C₃×D₅	—	4	1	no	—
587	C₃×D₅	—	4	2	no	—
588	C₃×D₅	—	4	2	no	—
589	C₃×D₅	—	8	1	no	—
590	C₃×D₅	—	8	1	no	—
591	C₂³×C₃	—	2	1	no	—
592	C₂³×C₃	—	5	1	no	—
593	C₂³×C₃	—	10	1	no	—
594	C₂³×C₃	—	10	1	no	—
595	C₂³×C₃	—	10	1	no	—
596	C₂³×C₃	—	10	1	no	—
597	C₂³×C₃	—	20	2	no	—
598	C₂³×C₃	—	20	2	no	—
599	C₂³×C₃	—	20	2	no	—
600	C₂³×C₃	—	20	2	no	—
601	C₂³×C₃	—	20	2	no	—
602	C₂³×C₃	—	20	2	no	—
603	C₂³×C₃	—	40	1	no	—
604	C₂³×C₃	—	40	1	no	—
605	C₂³×C₃	—	40	1	no	—
606	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
607	C₃×Q₈	—	2	1	no	—
608	C₃×Q₈	—	2	1	no	—
609	C₃×D₄	—	2	1	no	—
610	C₃×D₄	—	2	1	no	—
611	C₃×D₄	—	4	2	no	—
612	C₃×D₄	—	5	2	no	—
613	C₃×D₄	—	5	2	no	—
614	C₃×D₄	—	10	2	no	—
615	C₃×D₄	—	10	1	no	—
616	C₃×D₄	—	10	1	no	—
617	C₃×D₄	—	10	1	no	—
618	C₃×D₄	—	10	1	no	—
619	C₃×D₄	—	10	1	no	—
620	C₃×D₄	—	10	1	no	—
621	C₃×D₄	—	20	2	no	—
622	C₃×D₄	—	20	2	no	—
623	C₃×D₄	—	20	2	no	—
624	C₃×D₄	—	20	2	no	—
625	C₃×D₄	—	20	2	no	—
626	C₃×D₄	—	20	2	no	—
627	C₃×D₄	—	40	1	no	—
628	C₃×D₄	—	40	1	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	—	2	1	no	—
631	C₂×C₃×C₄	—	2	1	no	—
632	C₂×C₃×C₄	—	2	1	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	5	1	no	—
635	C₂×C₃×C₄	—	5	1	no	—
636	C₂×C₃×C₄	—	5	1	no	—
637	C₂×C₃×C₄	—	10	1	no	—
638	C₂×C₃×C₄	—	10	1	no	—
639	C₂×C₃×C₄	—	20	2	no	—
640	C₂×C₃×C₄	—	20	2	no	—
641	C₂×C₃×C₄	—	40	1	no	—
642	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
643	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
644	C₃×C₈	—	2	1	no	—
645	C₃×C₈	—	10	1	no	—
646	C₃×C₈	—	10	1	no	—
647	C₃×C₈	D₄×D₅	1	2	yes	complemented
648	C₂²×C₅	—	2	1	no	—
649	C₂²×C₅	—	2	1	no	—
650	C₂²×C₅	—	4	1	no	—
651	C₂²×C₅	—	4	1	no	—
652	C₂²×C₅	—	4	1	no	—
653	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	complemented
654	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
655	C₂×D₅	—	2	1	no	—
656	C₂×D₅	—	2	1	no	—
657	C₂×D₅	—	2	1	no	—
658	C₂×D₅	—	2	2	no	—
659	C₂×D₅	—	2	2	no	—
660	C₂×D₅	—	4	1	no	—
661	C₂×D₅	—	4	1	no	—
662	C₂×D₅	—	4	1	no	—
663	C₂×D₅	—	4	1	no	—
664	C₂×D₅	—	4	1	no	—
665	C₂×D₅	—	4	1	no	—
666	C₂×D₅	—	4	1	no	—
667	C₂×D₅	—	4	1	no	—
668	C₂×D₅	—	4	1	no	—
669	C₂×D₅	—	4	1	no	—
670	C₂×D₅	—	8	4	no	—
671	C₂×D₅	—	8	4	no	—
672	C₂×D₅	—	8	4	no	—
673	C₄×C₅	—	2	1	no	—
674	C₄×C₅	—	4	1	no	—
675	C₄×C₅	—	4	1	no	—
676	C₄×C₅	—	4	1	no	—
677	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
678	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
679	Dic₅	—	2	1	no	—
680	Dic₅	—	2	1	no	—
681	Dic₅	—	2	1	no	—
682	C₂⁴	—	10	1	no	—
683	C₂⁴	—	10	1	no	—
684	C₂⁴	—	10	1	no	—
685	#41	—	10	2	no	—
686	#41	—	20	1	no	—
687	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	5	1	no	—
690	C₂×D₄	—	5	1	no	—
691	C₂×D₄	—	5	1	no	—
692	C₂×D₄	—	5	1	no	—
693	C₂×D₄	—	5	1	no	—
694	C₂×D₄	—	10	2	no	—
695	C₂×D₄	—	10	2	no	—
696	C₂×D₄	—	10	1	no	—
697	C₂×D₄	—	10	1	no	—
698	C₂×D₄	—	10	1	no	—
699	C₂×D₄	—	10	1	no	—
700	C₂×D₄	—	10	1	no	—
701	C₂×D₄	—	10	1	no	—
702	C₂×D₄	—	10	2	no	—
703	C₂×D₄	—	10	1	no	—
704	C₂×D₄	—	10	1	no	—
705	C₂×D₄	—	20	1	no	—
706	C₂×D₄	—	20	1	no	—
707	C₂×D₄	—	20	1	no	—
708	C₂×D₄	—	20	4	no	—
709	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
710	C₂²×C₄	—	5	1	no	—
711	C₂²×C₄	—	10	1	no	—
712	C₂²×C₄	—	10	1	no	—
713	C₂²×C₄	—	10	1	no	—
714	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
715	SD₁₆	—	2	2	no	—
716	SD₁₆	—	10	2	no	—
717	SD₁₆	—	20	1	no	—
718	D₈	—	5	4	no	—
719	D₈	—	10	2	no	—
720	D₈	—	10	2	no	—
721	D₈	—	10	2	no	—
722	D₈	—	10	2	no	—
723	D₈	—	20	1	no	—
724	M₁₆	—	10	2	no	—
725	C₂×C₈	—	2	2	no	—
726	C₂×C₈	—	5	1	no	—
727	C₂×C₈	—	5	1	no	—
728	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
729	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	5	1	no	—
732	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
733	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	5	1	no	—
737	C₂²⋊C₄	—	5	1	no	—
738	C₂²⋊C₄	—	10	1	no	—
739	C₂²⋊C₄	—	10	1	no	—
740	C₂²⋊C₄	—	10	1	no	—
741	C₂²⋊C₄	—	10	1	no	—
742	C₂²⋊C₄	—	10	1	no	—
743	C₂²⋊C₄	—	10	1	no	—
744	C₄²	—	5	1	no	—
745	C₃×C₅	#3264	1	1	yes	characteristic, complemented, Hall
746	C₂²×C₃	—	2	1	no	—
747	C₂²×C₃	—	2	1	no	—
748	C₂²×C₃	—	4	1	no	—
749	C₂²×C₃	—	4	1	no	—
750	C₂²×C₃	—	4	1	no	—
751	C₂²×C₃	—	10	1	no	—
752	C₂²×C₃	—	10	1	no	—
753	C₂²×C₃	—	10	1	no	—
754	C₂²×C₃	—	10	2	no	—
755	C₂²×C₃	—	10	2	no	—
756	C₂²×C₃	—	20	1	no	—
757	C₂²×C₃	—	20	1	no	—
758	C₂²×C₃	—	20	1	no	—
759	C₂²×C₃	—	20	1	no	—
760	C₂²×C₃	—	20	1	no	—
761	C₂²×C₃	—	20	1	no	—
762	C₂²×C₃	—	20	1	no	—
763	C₂²×C₃	—	20	1	no	—
764	C₂²×C₃	—	20	1	no	—
765	C₂²×C₃	—	20	1	no	—
766	C₂²×C₃	—	40	4	no	—
767	C₂²×C₃	—	40	4	no	—
768	C₂²×C₃	—	40	4	no	—
769	C₂²×C₃	#4060	1	2	yes	complemented
770	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
771	C₃×C₄	—	2	1	no	—
772	C₃×C₄	—	4	1	no	—
773	C₃×C₄	—	4	1	no	—
774	C₃×C₄	—	4	1	no	—
775	C₃×C₄	—	10	1	no	—
776	C₃×C₄	—	10	1	no	—
777	C₃×C₄	—	10	1	no	—
778	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
779	C₃×C₄	#4149	1	1	yes	characteristic
780	C₂×C₅	—	2	2	no	—
781	C₂×C₅	—	8	1	no	—
782	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
783	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
784	C₂×C₅	C₃×#576	1	1	yes	characteristic
785	D₅	—	4	1	no	—
786	D₅	—	4	2	no	—
787	D₅	—	4	2	no	—
788	D₅	—	8	1	no	—
789	D₅	—	8	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	5	1	no	—
792	C₂³	—	10	1	no	—
793	C₂³	—	10	1	no	—
794	C₂³	—	10	1	no	—
795	C₂³	—	10	1	no	—
796	C₂³	—	20	2	no	—
797	C₂³	—	20	2	no	—
798	C₂³	—	20	2	no	—
799	C₂³	—	20	2	no	—
800	C₂³	—	20	2	no	—
801	C₂³	—	20	2	no	—
802	C₂³	—	40	1	no	—
803	C₂³	—	40	1	no	—
804	C₂³	—	40	1	no	—
805	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
806	Q₈	—	2	1	no	—
807	Q₈	—	2	1	no	—
808	D₄	—	2	1	no	—
809	D₄	—	2	1	no	—
810	D₄	—	4	2	no	—
811	D₄	—	5	2	no	—
812	D₄	—	5	2	no	—
813	D₄	—	10	2	no	—
814	D₄	—	10	1	no	—
815	D₄	—	10	1	no	—
816	D₄	—	10	1	no	—
817	D₄	—	10	1	no	—
818	D₄	—	10	1	no	—
819	D₄	—	10	1	no	—
820	D₄	—	20	2	no	—
821	D₄	—	20	2	no	—
822	D₄	—	20	2	no	—
823	D₄	—	20	2	no	—
824	D₄	—	20	2	no	—
825	D₄	—	20	2	no	—
826	D₄	—	40	1	no	—
827	D₄	—	40	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	5	1	no	—
834	C₂×C₄	—	5	1	no	—
835	C₂×C₄	—	5	1	no	—
836	C₂×C₄	—	10	1	no	—
837	C₂×C₄	—	10	1	no	—
838	C₂×C₄	—	20	2	no	—
839	C₂×C₄	—	20	2	no	—
840	C₂×C₄	—	40	1	no	—
841	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
842	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
843	C₈	—	2	1	no	—
844	C₈	—	10	1	no	—
845	C₈	—	10	1	no	—
846	C₈	C₃×D₄×D₅	1	2	yes	complemented
847	C₂×C₃	—	2	2	no	—
848	C₂×C₃	—	8	1	no	—
849	C₂×C₃	—	20	1	no	—
850	C₂×C₃	—	20	2	no	—
851	C₂×C₃	—	20	2	no	—
852	C₂×C₃	—	40	1	no	—
853	C₂×C₃	—	40	1	no	—
854	C₂×C₃	#65943	1	1	yes	characteristic
855	C₂×C₃	C₂×#4060	1	1	yes	characteristic
856	C₂×C₃	#66103	1	1	yes	characteristic
857	C₅	C₃×#3264	1	1	yes	characteristic, complemented, Sylow
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	4	1	no	—
861	C₂²	—	4	1	no	—
862	C₂²	—	4	1	no	—
863	C₂²	—	10	1	no	—
864	C₂²	—	10	1	no	—
865	C₂²	—	10	2	no	—
866	C₂²	—	10	2	no	—
867	C₂²	—	10	1	no	—
868	C₂²	—	20	1	no	—
869	C₂²	—	20	1	no	—
870	C₂²	—	20	1	no	—
871	C₂²	—	20	1	no	—
872	C₂²	—	20	1	no	—
873	C₂²	—	20	1	no	—
874	C₂²	—	20	1	no	—
875	C₂²	—	20	1	no	—
876	C₂²	—	20	1	no	—
877	C₂²	—	20	1	no	—
878	C₂²	—	40	4	no	—
879	C₂²	—	40	4	no	—
880	C₂²	—	40	4	no	—
881	C₂²	C₃×#4060	1	2	yes	complemented
882	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
883	C₄	—	2	1	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	1	no	—
887	C₄	—	10	1	no	—
888	C₄	—	10	1	no	—
889	C₄	—	10	1	no	—
890	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
891	C₄	C₃×#4149	1	1	yes	characteristic
892	C₃	#10612405	1	1	yes	characteristic, direct product factor, Sylow
893	C₂	—	2	2	no	—
894	C₂	—	8	1	no	—
895	C₂	—	20	1	no	—
896	C₂	—	20	2	no	—
897	C₂	—	20	2	no	—
898	C₂	—	40	1	no	—
899	C₂	—	40	1	no	—
900	C₂	C₃×#65943	1	1	yes	characteristic
901	C₂	C₂×C₃×#4060	1	1	yes	characteristic
902	C₂	C₃×#66103	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#465	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#465	D₅
hypocenter	C₅	C₃×#3264
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#465

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4060	C₂	semidirect
2. C₂²×C₃×D₄₀	C₂	semidirect
3. C₃×#65964	C₂	semidirect
4. C₃×#65943	C₂	semidirect
5. C₃×C₅×#465	C₂	semidirect
6. C₃×#65465	C₂	semidirect
7. C₃×#65400	C₂	semidirect
8. C₃×#65335	C₂	semidirect
9. C₃×#65325	C₂	semidirect
10. C₃×#65158	C₂	semidirect
11. C₃×#65154	C₂	semidirect
12. C₃×#65108	C₂	semidirect
13. C₃×#65100	C₂	semidirect
14. C₃×#65075	C₂	semidirect
15. C₃×#65062	C₂	semidirect
16. #10612405	C₃	direct (N × H)
17. C₂×C₃×#713	C₂²	semidirect
19. C₂×C₃×D₄×D₅	C₂²	semidirect
21. C₂²×C₃×D₂₀	C₂²	semidirect
22. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
23. C₂²×C₃×C₅×C₈	C₂²	semidirect
24. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
26. C₃×#4093	C₂²	semidirect
27. C₂×C₃×#688	C₂²	semidirect
28. C₂×C₃×#688	C₂²	semidirect
29. C₃×#4086	C₂²	semidirect
31. C₂×C₃×#686	C₂²	semidirect
32. C₂×C₃×#686	C₂²	semidirect
38. C₂×C₃×D₄₀	C₂²	semidirect
39. C₂×C₃×D₄₀	C₂²	semidirect
40. C₂×C₃×#676	C₂²	semidirect
42. C₃×#4041	C₂²	semidirect
43. C₃×#4041	C₂²	semidirect
45. C₃×#4039	C₂²	semidirect
46. C₃×#4039	C₂²	semidirect
51. C₃×C₅×#106	C₂²	semidirect
52. C₃×C₅×#103	C₂²	semidirect
53. C₃×C₅×#102	C₂²	semidirect
54. C₃×C₂²⋊#168	C₂²	semidirect
55. C₃×#3952	C₂²	semidirect
56. C₃×#3947	C₂²	semidirect
57. C₃×#3946	C₂²	semidirect
58. C₃×#3941	C₂²	semidirect
59. C₃×#3941	C₂²	semidirect
60. C₃×#3941	C₂²	semidirect
61. C₃×#3941	C₂²	semidirect
63. C₂×#4060	C₂×C₃	semidirect
64. C₂²×D₄₀	C₂×C₃	semidirect
65. #65964	C₂×C₃	semidirect
66. #65943	C₂×C₃	semidirect
67. C₅×#465	C₂×C₃	semidirect
68. #65465	C₂×C₃	semidirect
69. #65400	C₂×C₃	semidirect
70. #65335	C₂×C₃	semidirect
71. #65325	C₂×C₃	semidirect
72. #65158	C₂×C₃	semidirect
73. #65154	C₂×C₃	semidirect
74. #65108	C₂×C₃	semidirect
75. #65100	C₂×C₃	semidirect
76. #65075	C₂×C₃	semidirect
77. #65062	C₂×C₃	semidirect
139. C₃×D₄₀	D₄	semidirect
147. C₃×#465	D₅	semidirect
156. C₂×#713	C₂²×C₃	semidirect
158. C₂×D₄×D₅	C₂²×C₃	semidirect
160. C₂²×D₂₀	C₂²×C₃	semidirect
161. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
162. C₂²×C₅×C₈	C₂²×C₃	semidirect
163. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
165. #4093	C₂²×C₃	semidirect
166. C₂×#688	C₂²×C₃	semidirect
167. C₂×#688	C₂²×C₃	semidirect
168. #4086	C₂²×C₃	semidirect
170. C₂×#686	C₂²×C₃	semidirect
171. C₂×#686	C₂²×C₃	semidirect
177. C₂×D₄₀	C₂²×C₃	semidirect
178. C₂×D₄₀	C₂²×C₃	semidirect
179. C₂×#676	C₂²×C₃	semidirect
181. #4041	C₂²×C₃	semidirect
182. #4041	C₂²×C₃	semidirect
184. #4039	C₂²×C₃	semidirect
185. #4039	C₂²×C₃	semidirect
190. C₅×#106	C₂²×C₃	semidirect
191. C₅×#103	C₂²×C₃	semidirect
192. C₅×#102	C₂²×C₃	semidirect
193. C₂²⋊#168	C₂²×C₃	semidirect
194. #3952	C₂²×C₃	semidirect
195. #3947	C₂²×C₃	semidirect
196. #3946	C₂²×C₃	semidirect
197. #3941	C₂²×C₃	semidirect
198. #3941	C₂²×C₃	semidirect
199. #3941	C₂²×C₃	semidirect
200. #3941	C₂²×C₃	semidirect
249. C₃×D₂₀	C₂×D₄	semidirect
256. C₃×C₅×C₈	C₂×D₄	semidirect
267. C₂×C₃×SD₁₆	C₂×D₅	semidirect
276. C₂²×C₃×C₈	C₂×D₅	semidirect
280. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
293. C₃×#106	C₂×D₅	semidirect
295. C₃×#103	C₂×D₅	semidirect
300. C₃×#102	C₂×D₅	semidirect
365. D₄₀	C₃×D₄	semidirect
373. #465	C₃×D₅	semidirect
387. C₂²×C₃×C₅	AGL(1,ℤ/8)	semidirect
526. D₂₀	C₂×C₃×D₄	semidirect
533. C₅×C₈	C₂×C₃×D₄	semidirect
544. C₂×SD₁₆	C₂×C₃×D₅	semidirect
553. C₂²×C₈	C₂×C₃×D₅	semidirect
557. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
570. #106	C₂×C₃×D₅	semidirect
572. #103	C₂×C₃×D₅	semidirect
577. #102	C₂×C₃×D₅	semidirect
647. C₃×C₈	D₄×D₅	semidirect
653. C₂²×C₅	C₃×AGL(1,ℤ/8)	semidirect
745. C₃×C₅	#3264	semidirect
769. C₂²×C₃	#4060	semidirect
846. C₈	C₃×D₄×D₅	semidirect
857. C₅	C₃×#3264	semidirect
881. C₂²	C₃×#4060	semidirect
892. C₃	#10612405	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×#4060	2
C₂²×C₃×D₄₀	2
C₃×#65964	2
C₃×#65943	2
C₃×C₅×#465	2
C₃×#65465	2
C₃×#65400	2
C₃×#65335	2
C₃×#65325	2
C₃×#65158	2
C₃×#65154	2
C₃×#65108	2
C₃×#65100	2
C₃×#65075	2
C₃×#65062	2
#10612405	3
C₃×#3264	5

Subgroups — C3×#10612405 #14453185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10612405 #14453185