Subgroups — C₃×#10611879 #14424304

Order 1920.

1504 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4144	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4061	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65507	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65458	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65336	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65072	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65065	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65061	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65059	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65022	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#65016	C₂	1	1	yes	maximal, characteristic, complemented
16	#10611879	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₂²⋊D₅	—	2	1	no	—
19	C₂²×C₃×C₂²⋊D₅	—	2	1	no	—
20	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
21	C₃×#4144	—	2	4	no	—
22	C₃×#4144	—	2	4	no	—
23	C₂×C₃×#711	—	2	1	no	—
24	C₂×C₃×#711	C₂²	1	1	yes	characteristic
25	C₂×C₃×#711	C₂²	1	1	yes	characteristic
26	C₂×C₃×D₄×D₅	—	2	1	no	—
27	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×#709	C₂²	1	1	yes	characteristic
30	C₂×C₃×#709	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×#4092	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×#689	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×#688	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×#687	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃×#687	C₂²	1	1	yes	characteristic, complemented
39	C₃×#4070	C₂²	1	1	yes	characteristic, complemented
40	C₃×#4061	—	2	4	no	—
41	C₃×D₅×SD₁₆	—	2	4	no	—
42	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₃×#677	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃×#676	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic, complemented
46	C₃×#4043	C₂²	1	1	yes	characteristic, complemented
47	C₃×#4040	—	2	1	no	—
48	C₃×#4038	C₂²	1	1	yes	characteristic, complemented
49	C₃×#4034	—	2	1	no	—
50	C₃×#4031	—	2	1	no	—
51	C₃×#4029	—	2	1	no	—
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	C₃×#3964	C₂²	1	1	yes	characteristic, complemented
56	C₃×#3964	C₂²	1	1	yes	characteristic, complemented
57	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic, complemented
58	C₃×#3953	C₂²	1	1	yes	characteristic, complemented
59	C₃×#3952	C₂²	1	1	yes	characteristic, complemented
60	C₃×#3952	C₂²	1	1	yes	characteristic, complemented
61	C₃×#3948	C₂²	1	1	yes	characteristic, complemented
62	C₃×#3942	C₂²	1	1	yes	characteristic, complemented
63	C₃×#3941	C₂²	1	1	yes	characteristic, complemented
64	C₃×#3009	—	5	1	no	maximal, Hall
65	C₂×#4144	C₂×C₃	1	1	yes	characteristic
66	C₂×#4061	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂×D₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
68	#65962	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#450	C₂×C₃	1	1	yes	characteristic, complemented
70	#65507	C₂×C₃	1	1	yes	characteristic, complemented
71	#65462	C₂×C₃	1	1	yes	characteristic, complemented
72	#65458	C₂×C₃	1	1	yes	characteristic, complemented
73	#65336	C₂×C₃	1	1	yes	characteristic, complemented
74	#65072	C₂×C₃	1	1	yes	characteristic, complemented
75	#65065	C₂×C₃	1	1	yes	characteristic, complemented
76	#65061	C₂×C₃	1	1	yes	characteristic, complemented
77	#65059	C₂×C₃	1	1	yes	characteristic, complemented
78	#65022	C₂×C₃	1	1	yes	characteristic, complemented
79	#65016	C₂×C₃	1	1	yes	characteristic, complemented
80	C₂⁴×C₃×C₅	—	2	1	no	—
81	C₂³×C₃×D₅	—	2	1	no	—
82	C₂³×C₃×D₅	—	2	1	no	—
83	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×D₄	—	2	2	no	—
85	C₂×C₃×C₅×D₄	—	2	2	no	—
86	C₂×C₃×C₅×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
91	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
92	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
93	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
94	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
95	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
96	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
97	C₂×C₃×C₂²⋊D₅	D₄	1	1	yes	characteristic
98	C₂×C₃×C₂²⋊D₅	D₄	1	1	yes	characteristic
99	C₂²×C₃×Dic₅	—	2	1	no	—
100	C₂²×C₃×Dic₅	—	2	1	no	—
101	C₃×Q₈×D₅	—	2	2	no	—
102	C₃×Q₈×D₅	—	2	2	no	—
103	C₃×#711	—	2	8	no	—
104	C₃×#711	—	2	2	no	—
105	C₃×#711	—	2	2	no	—
106	C₃×#711	—	2	2	no	—
107	C₃×#711	D₄	1	4	yes	—
108	C₃×D₄×D₅	—	2	8	no	—
109	C₃×D₄×D₅	—	2	2	no	—
110	C₃×D₄×D₅	—	2	2	no	—
111	C₃×D₄×D₅	—	2	2	no	—
112	C₃×D₄×D₅	D₄	1	4	yes	—
113	C₃×#709	—	2	2	no	—
114	C₃×#709	—	2	2	no	—
115	C₃×#709	—	2	2	no	—
116	C₃×#709	—	2	2	no	—
117	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
118	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
119	C₂×C₃×C₄×D₅	—	2	1	no	—
120	C₂×C₃×C₄×D₅	—	2	1	no	—
121	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
122	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
123	C₂×C₃×Dic₁₀	—	2	1	no	—
124	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
125	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
126	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
127	C₃×C₅×SD₁₆	—	2	2	no	—
128	C₃×C₅×SD₁₆	—	2	2	no	—
129	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
131	C₃×C₅×C₄⋊C₄	—	2	1	no	—
132	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
134	C₃×C₂²⋊Dic₅	—	2	1	no	—
135	C₃×#689	—	2	2	no	—
136	C₃×#688	—	2	2	no	—
137	C₃×#687	—	2	2	no	—
138	C₃×#687	—	2	2	no	—
139	C₃×#685	—	2	1	no	—
140	C₃×#685	—	2	1	no	—
141	C₃×#685	—	2	1	no	—
142	C₃×C₄⋊Dic₅	—	2	1	no	—
143	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
144	C₃×#683	—	2	1	no	—
145	C₃×#683	—	2	1	no	—
146	C₃×C₄×Dic₅	—	2	1	no	—
147	C₂×C₃×#168	C₂³	1	1	yes	characteristic
148	C₂×C₃×#168	C₂³	1	1	yes	characteristic
149	C₃×Dic₂₀	—	2	2	no	—
150	C₃×#677	—	2	2	no	—
151	C₃×#676	—	2	2	no	—
152	C₃×C₈×D₅	—	2	2	no	—
153	C₂×C₃×H(5,𝔽₂)	—	5	1	no	—
154	C₂×C₃×#137	—	5	1	no	—
155	C₂²×C₃×SD₁₆	—	5	1	no	—
156	C₃×#536	—	5	1	no	—
157	C₃×#452	—	5	1	no	—
158	C₃×#452	—	5	1	no	—
159	C₃×#452	—	5	1	no	—
160	C₃×#452	—	5	1	no	—
161	C₃×#450	—	5	1	no	—
162	C₃×#450	—	5	1	no	—
163	C₃×#450	—	5	1	no	—
164	C₃×#450	D₅	1	1	yes	characteristic, complemented
165	C₃×#418	—	5	1	no	—
166	C₃×#416	—	5	1	no	—
167	C₃×#408	—	5	1	no	—
168	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
169	C₂²×C₂²⋊D₅	—	2	1	no	—
170	C₂²×C₂²⋊D₅	—	2	1	no	—
171	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
172	#4144	—	2	4	no	—
173	#4144	—	2	4	no	—
174	C₂×#711	—	2	1	no	—
175	C₂×#711	C₂²×C₃	1	1	yes	characteristic
176	C₂×#711	C₂²×C₃	1	1	yes	characteristic
177	C₂×D₄×D₅	—	2	1	no	—
178	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
179	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
180	C₂×#709	C₂²×C₃	1	1	yes	characteristic
181	C₂×#709	C₂²×C₃	1	1	yes	characteristic
182	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
185	#4092	C₂²×C₃	1	1	yes	characteristic, complemented
186	C₂×#689	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₂×#688	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₂×#687	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₂×#687	C₂²×C₃	1	1	yes	characteristic, complemented
190	#4070	C₂²×C₃	1	1	yes	characteristic, complemented
191	#4061	—	2	4	no	—
192	D₅×SD₁₆	—	2	4	no	—
193	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
194	C₂×#677	C₂²×C₃	1	1	yes	characteristic, complemented
195	C₂×#676	C₂²×C₃	1	1	yes	characteristic, complemented
196	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
197	#4043	C₂²×C₃	1	1	yes	characteristic, complemented
198	#4040	—	2	1	no	—
199	#4038	C₂²×C₃	1	1	yes	characteristic, complemented
200	#4034	—	2	1	no	—
201	#4031	—	2	1	no	—
202	#4029	—	2	1	no	—
203	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
204	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
205	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
206	#3964	C₂²×C₃	1	1	yes	characteristic, complemented
207	#3964	C₂²×C₃	1	1	yes	characteristic, complemented
208	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
209	#3953	C₂²×C₃	1	1	yes	characteristic, complemented
210	#3952	C₂²×C₃	1	1	yes	characteristic, complemented
211	#3952	C₂²×C₃	1	1	yes	characteristic, complemented
212	#3948	C₂²×C₃	1	1	yes	characteristic, complemented
213	#3942	C₂²×C₃	1	1	yes	characteristic, complemented
214	#3941	C₂²×C₃	1	1	yes	characteristic, complemented
215	#3009	—	5	1	no	Sylow
216	C₂³×C₃×C₅	—	2	4	no	—
217	C₂³×C₃×C₅	—	2	1	no	—
218	C₂³×C₃×C₅	—	2	1	no	—
219	C₂³×C₃×C₅	—	8	1	no	—
220	C₂³×C₃×C₅	—	8	1	no	—
221	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₃×D₅	—	2	1	no	—
223	C₂²×C₃×D₅	—	2	4	no	—
224	C₂²×C₃×D₅	—	2	4	no	—
225	C₂²×C₃×D₅	—	8	1	no	—
226	C₂²×C₃×D₅	—	8	1	no	—
227	C₂²×C₃×D₅	—	8	1	no	—
228	C₂²×C₃×D₅	—	8	1	no	—
229	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
231	C₃×C₅×Q₈	—	2	1	no	—
232	C₃×C₅×Q₈	—	2	1	no	—
233	C₃×C₅×D₄	—	2	4	no	—
234	C₃×C₅×D₄	—	2	1	no	—
235	C₃×C₅×D₄	—	2	1	no	—
236	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
237	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
238	C₂×C₃×C₄×C₅	—	2	1	no	—
239	C₂×C₃×C₄×C₅	—	2	1	no	—
240	C₂×C₃×C₄×C₅	—	2	1	no	—
241	C₂×C₃×C₄×C₅	—	2	1	no	—
242	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
243	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
244	C₃×C₂²⋊D₅	—	2	4	no	—
245	C₃×C₂²⋊D₅	—	2	4	no	—
246	C₃×C₂²⋊D₅	—	2	4	no	—
247	C₃×C₂²⋊D₅	—	2	2	no	—
248	C₃×C₂²⋊D₅	—	2	4	no	—
249	C₃×C₂²⋊D₅	—	2	2	no	—
250	C₃×C₂²⋊D₅	—	2	4	no	—
251	C₂×C₃×Dic₅	—	2	4	no	—
252	C₂×C₃×Dic₅	—	2	1	no	—
253	C₂×C₃×Dic₅	—	2	4	no	—
254	C₂×C₃×Dic₅	—	2	1	no	—
255	C₂×C₃×Dic₅	—	2	1	no	—
256	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
257	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
258	C₃×D₂₀	—	2	2	no	—
259	C₃×D₂₀	—	2	1	no	—
260	C₃×D₂₀	C₂×D₄	1	2	yes	—
261	C₃×C₄×D₅	—	2	4	no	—
262	C₃×C₄×D₅	—	2	1	no	—
263	C₃×C₄×D₅	—	2	1	no	—
264	C₃×C₄×D₅	—	4	2	no	—
265	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
266	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
267	C₃×Dic₁₀	—	2	1	no	—
268	C₃×Dic₁₀	—	2	2	no	—
269	C₃×Dic₁₀	—	2	1	no	—
270	C₃×Dic₁₀	—	2	1	no	—
271	C₃×Dic₁₀	—	4	2	no	—
272	C₃×Dic₁₀	C₂×D₄	1	2	yes	—
273	C₃×C₅×C₈	—	2	1	no	—
274	C₃×C₅×C₈	—	2	1	no	—
275	C₃×#168	—	2	1	no	—
276	C₃×#168	—	2	1	no	—
277	C₃×H(5,𝔽₂)	—	10	4	no	—
278	C₃×H(5,𝔽₂)	—	10	4	no	—
279	C₂×C₃×#41	—	5	1	no	—
280	C₂×C₃×#41	—	5	1	no	—
281	C₂×C₃×#41	—	5	1	no	—
282	C₂×C₃×#41	—	5	1	no	—
283	C₂×C₃×#41	—	10	1	no	—
284	C₂²×C₃×Q₈	—	5	1	no	—
285	C₂²×C₃×D₄	—	5	1	no	—
286	C₂²×C₃×D₄	—	5	1	no	—
287	C₂²×C₃×D₄	—	10	1	no	—
288	C₂²×C₃×D₄	—	10	1	no	—
289	C₂²×C₃×D₄	—	10	1	no	—
290	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
291	C₃×#137	—	10	4	no	—
292	C₂×C₃×Q₁₆	—	5	1	no	—
293	C₂×C₃×Q₁₆	—	5	1	no	—
294	C₂×C₃×SD₁₆	—	5	1	no	—
295	C₂×C₃×SD₁₆	—	5	1	no	—
296	C₂×C₃×SD₁₆	—	5	1	no	—
297	C₂×C₃×SD₁₆	—	5	1	no	—
298	C₂×C₃×SD₁₆	—	10	4	no	—
299	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic, complemented
300	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic, complemented
301	C₂×C₃×M₁₆	—	5	1	no	—
302	C₂²×C₃×C₈	—	5	1	no	—
303	C₃×C₄⋊Q₈	—	10	1	no	—
304	C₃×#124	—	10	1	no	—
305	C₃×#123	—	10	1	no	—
306	C₃×#123	—	10	1	no	—
307	C₃×C₂²⋊Q₈	—	5	1	no	—
308	C₃×C₂²⋊Q₈	—	5	1	no	—
309	C₃×C₂²⋊Q₈	—	5	1	no	—
310	C₃×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
311	C₃×#117	—	5	1	no	—
312	C₃×#103	—	5	1	no	—
313	C₃×#103	—	5	1	no	—
314	C₃×#102	—	5	1	no	—
315	C₃×#102	—	5	1	no	—
316	C₃×#102	—	5	1	no	—
317	C₃×#102	—	5	1	no	—
318	C₃×#102	C₂×D₅	1	1	yes	characteristic, complemented
319	C₃×#102	C₂×D₅	1	1	yes	characteristic, complemented
320	C₃×C₂²⋊C₈	—	5	1	no	—
321	C₃×C₂²⋊C₈	—	5	1	no	—
322	C₃×C₂²⋊C₈	—	5	1	no	—
323	C₃×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
324	C₂⁴×C₅	—	2	1	no	—
325	C₂³×D₅	—	2	1	no	—
326	C₂³×D₅	—	2	1	no	—
327	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
328	C₂×C₅×D₄	—	2	2	no	—
329	C₂×C₅×D₄	—	2	2	no	—
330	C₂×C₅×D₄	—	2	1	no	—
331	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
332	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
333	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
334	C₂×C₂²⋊D₅	—	2	8	no	—
335	C₂×C₂²⋊D₅	—	2	8	no	—
336	C₂×C₂²⋊D₅	—	2	1	no	—
337	C₂×C₂²⋊D₅	—	2	1	no	—
338	C₂×C₂²⋊D₅	—	2	1	no	—
339	C₂×C₂²⋊D₅	—	2	1	no	—
340	C₂×C₂²⋊D₅	—	2	1	no	—
341	C₂×C₂²⋊D₅	C₃×D₄	1	1	yes	characteristic
342	C₂×C₂²⋊D₅	C₃×D₄	1	1	yes	characteristic
343	C₂²×Dic₅	—	2	1	no	—
344	C₂²×Dic₅	—	2	1	no	—
345	Q₈×D₅	—	2	2	no	—
346	Q₈×D₅	—	2	2	no	—
347	#711	—	2	8	no	—
348	#711	—	2	2	no	—
349	#711	—	2	2	no	—
350	#711	—	2	2	no	—
351	#711	C₃×D₄	1	4	yes	—
352	D₄×D₅	—	2	8	no	—
353	D₄×D₅	—	2	2	no	—
354	D₄×D₅	—	2	2	no	—
355	D₄×D₅	—	2	2	no	—
356	D₄×D₅	C₃×D₄	1	4	yes	—
357	#709	—	2	2	no	—
358	#709	—	2	2	no	—
359	#709	—	2	2	no	—
360	#709	—	2	2	no	—
361	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
362	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
363	C₂×C₄×D₅	—	2	1	no	—
364	C₂×C₄×D₅	—	2	1	no	—
365	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
366	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
367	C₂×Dic₁₀	—	2	1	no	—
368	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
369	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
370	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
371	C₅×SD₁₆	—	2	2	no	—
372	C₅×SD₁₆	—	2	2	no	—
373	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
374	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
375	C₅×C₄⋊C₄	—	2	1	no	—
376	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
377	C₅×C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊Dic₅	—	2	1	no	—
379	#689	—	2	2	no	—
380	#688	—	2	2	no	—
381	#687	—	2	2	no	—
382	#687	—	2	2	no	—
383	#685	—	2	1	no	—
384	#685	—	2	1	no	—
385	#685	—	2	1	no	—
386	C₄⋊Dic₅	—	2	1	no	—
387	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
388	#683	—	2	1	no	—
389	#683	—	2	1	no	—
390	C₄×Dic₅	—	2	1	no	—
391	C₂×#168	C₂³×C₃	1	1	yes	characteristic
392	C₂×#168	C₂³×C₃	1	1	yes	characteristic
393	Dic₂₀	—	2	2	no	—
394	#677	—	2	2	no	—
395	#676	—	2	2	no	—
396	C₈×D₅	—	2	2	no	—
397	C₂×H(5,𝔽₂)	—	5	1	no	—
398	C₂×#137	—	5	1	no	—
399	C₂²×SD₁₆	—	5	1	no	—
400	#536	—	5	1	no	—
401	#452	—	5	1	no	—
402	#452	—	5	1	no	—
403	#452	—	5	1	no	—
404	#452	—	5	1	no	—
405	#450	—	5	1	no	—
406	#450	—	5	1	no	—
407	#450	—	5	1	no	—
408	#450	C₃×D₅	1	1	yes	characteristic, complemented
409	#418	—	5	1	no	—
410	#416	—	5	1	no	—
411	#408	—	5	1	no	—
412	C₂²×C₃×C₅	—	2	2	no	—
413	C₂²×C₃×C₅	—	2	2	no	—
414	C₂²×C₃×C₅	—	2	1	no	—
415	C₂²×C₃×C₅	—	2	1	no	—
416	C₂²×C₃×C₅	—	2	1	no	—
417	C₂²×C₃×C₅	—	4	1	no	—
418	C₂²×C₃×C₅	—	4	1	no	—
419	C₂²×C₃×C₅	—	4	1	no	—
420	C₂²×C₃×C₅	—	4	1	no	—
421	C₂²×C₃×C₅	—	8	4	no	—
422	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₃×D₅	—	2	1	no	—
424	C₂×C₃×D₅	—	2	1	no	—
425	C₂×C₃×D₅	—	2	1	no	—
426	C₂×C₃×D₅	—	2	2	no	—
427	C₂×C₃×D₅	—	2	1	no	—
428	C₂×C₃×D₅	—	2	1	no	—
429	C₂×C₃×D₅	—	4	1	no	—
430	C₂×C₃×D₅	—	4	1	no	—
431	C₂×C₃×D₅	—	8	4	no	—
432	C₂×C₃×D₅	—	8	4	no	—
433	C₂×C₃×D₅	#120	1	2	yes	—
434	C₃×C₄×C₅	—	2	1	no	—
435	C₃×C₄×C₅	—	4	1	no	—
436	C₃×C₄×C₅	—	4	1	no	—
437	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
438	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
439	C₃×Dic₅	—	2	1	no	—
440	C₃×Dic₅	—	2	2	no	—
441	C₃×Dic₅	—	4	1	no	—
442	C₃×Dic₅	—	4	1	no	—
443	C₃×Dic₅	#120	1	2	yes	—
444	C₂⁴×C₃	—	2	1	no	—
445	C₂⁴×C₃	—	10	1	no	—
446	C₂⁴×C₃	—	10	1	no	—
447	C₃×#41	—	5	4	no	—
448	C₃×#41	—	10	2	no	—
449	C₃×#41	—	10	2	no	—
450	C₃×#41	—	10	2	no	—
451	C₃×#41	—	10	2	no	—
452	C₃×#41	—	10	2	no	—
453	C₃×#41	—	10	2	no	—
454	C₃×#41	—	10	8	no	—
455	C₃×#41	—	10	2	no	—
456	C₂×C₃×Q₈	—	5	1	no	—
457	C₂×C₃×Q₈	—	5	1	no	—
458	C₂×C₃×Q₈	—	5	1	no	—
459	C₂×C₃×Q₈	—	10	1	no	—
460	C₂×C₃×Q₈	—	10	2	no	—
461	C₂×C₃×Q₈	—	10	2	no	—
462	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
463	C₂×C₃×D₄	—	2	2	no	—
464	C₂×C₃×D₄	—	2	2	no	—
465	C₂×C₃×D₄	—	2	1	no	—
466	C₂×C₃×D₄	—	5	4	no	—
467	C₂×C₃×D₄	—	5	1	no	—
468	C₂×C₃×D₄	—	5	1	no	—
469	C₂×C₃×D₄	—	5	1	no	—
470	C₂×C₃×D₄	—	5	1	no	—
471	C₂×C₃×D₄	—	10	2	no	—
472	C₂×C₃×D₄	—	10	1	no	—
473	C₂×C₃×D₄	—	10	1	no	—
474	C₂×C₃×D₄	—	10	2	no	—
475	C₂×C₃×D₄	—	10	8	no	—
476	C₂×C₃×D₄	—	10	1	no	—
477	C₂×C₃×D₄	—	10	1	no	—
478	C₂×C₃×D₄	—	10	8	no	—
479	C₂×C₃×D₄	—	10	8	no	—
480	C₂×C₃×D₄	—	10	1	no	—
481	C₂×C₃×D₄	—	10	2	no	—
482	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
483	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
484	C₂²×C₃×C₄	—	5	1	no	—
485	C₂²×C₃×C₄	—	5	1	no	—
486	C₂²×C₃×C₄	—	10	1	no	—
487	C₂²×C₃×C₄	—	10	1	no	—
488	C₂²×C₃×C₄	—	10	1	no	—
489	C₂²×C₃×C₄	—	10	1	no	—
490	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
491	C₃×Q₁₆	—	10	2	no	—
492	C₃×Q₁₆	—	10	2	no	—
493	C₃×SD₁₆	—	2	2	no	—
494	C₃×SD₁₆	—	2	2	no	—
495	C₃×SD₁₆	—	10	2	no	—
496	C₃×SD₁₆	—	10	2	no	—
497	C₃×SD₁₆	—	10	2	no	—
498	C₃×SD₁₆	—	10	2	no	—
499	C₃×M₁₆	—	10	2	no	—
500	C₂×C₃×C₈	—	5	1	no	—
501	C₂×C₃×C₈	—	5	1	no	—
502	C₂×C₃×C₈	—	10	2	no	—
503	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
504	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
505	C₃×C₄⋊C₄	—	2	1	no	—
506	C₃×C₄⋊C₄	—	5	1	no	—
507	C₃×C₄⋊C₄	—	10	1	no	—
508	C₃×C₄⋊C₄	—	10	1	no	—
509	C₃×C₄⋊C₄	—	10	1	no	—
510	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
511	C₃×C₂²⋊C₄	—	2	1	no	—
512	C₃×C₂²⋊C₄	—	10	1	no	—
513	C₃×C₂²⋊C₄	—	10	1	no	—
514	C₃×C₂²⋊C₄	—	10	1	no	—
515	C₃×C₂²⋊C₄	—	10	1	no	—
516	C₃×C₄²	—	10	1	no	—
517	C₂³×C₅	—	2	4	no	—
518	C₂³×C₅	—	2	1	no	—
519	C₂³×C₅	—	2	1	no	—
520	C₂³×C₅	—	8	1	no	—
521	C₂³×C₅	—	8	1	no	—
522	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
523	C₂²×D₅	—	2	1	no	—
524	C₂²×D₅	—	2	4	no	—
525	C₂²×D₅	—	2	4	no	—
526	C₂²×D₅	—	8	1	no	—
527	C₂²×D₅	—	8	1	no	—
528	C₂²×D₅	—	8	1	no	—
529	C₂²×D₅	—	8	1	no	—
530	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
531	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
532	C₅×Q₈	—	2	1	no	—
533	C₅×Q₈	—	2	1	no	—
534	C₅×D₄	—	2	4	no	—
535	C₅×D₄	—	2	1	no	—
536	C₅×D₄	—	2	1	no	—
537	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
538	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
539	C₂×C₄×C₅	—	2	1	no	—
540	C₂×C₄×C₅	—	2	1	no	—
541	C₂×C₄×C₅	—	2	1	no	—
542	C₂×C₄×C₅	—	2	1	no	—
543	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
544	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
545	C₂²⋊D₅	—	2	4	no	—
546	C₂²⋊D₅	—	2	4	no	—
547	C₂²⋊D₅	—	2	4	no	—
548	C₂²⋊D₅	—	2	2	no	—
549	C₂²⋊D₅	—	2	4	no	—
550	C₂²⋊D₅	—	2	2	no	—
551	C₂²⋊D₅	—	2	4	no	—
552	C₂×Dic₅	—	2	4	no	—
553	C₂×Dic₅	—	2	1	no	—
554	C₂×Dic₅	—	2	4	no	—
555	C₂×Dic₅	—	2	1	no	—
556	C₂×Dic₅	—	2	1	no	—
557	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
558	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
559	D₂₀	—	2	2	no	—
560	D₂₀	—	2	1	no	—
561	D₂₀	C₂×C₃×D₄	1	2	yes	—
562	C₄×D₅	—	2	4	no	—
563	C₄×D₅	—	2	1	no	—
564	C₄×D₅	—	2	1	no	—
565	C₄×D₅	—	4	2	no	—
566	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
567	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
568	Dic₁₀	—	2	1	no	—
569	Dic₁₀	—	2	2	no	—
570	Dic₁₀	—	2	1	no	—
571	Dic₁₀	—	2	1	no	—
572	Dic₁₀	—	4	2	no	—
573	Dic₁₀	C₂×C₃×D₄	1	2	yes	—
574	C₅×C₈	—	2	1	no	—
575	C₅×C₈	—	2	1	no	—
576	#168	—	2	1	no	—
577	#168	—	2	1	no	—
578	H(5,𝔽₂)	—	10	4	no	—
579	H(5,𝔽₂)	—	10	4	no	—
580	C₂×#41	—	5	1	no	—
581	C₂×#41	—	5	1	no	—
582	C₂×#41	—	5	1	no	—
583	C₂×#41	—	5	1	no	—
584	C₂×#41	—	10	1	no	—
585	C₂²×Q₈	—	5	1	no	—
586	C₂²×D₄	—	5	1	no	—
587	C₂²×D₄	—	5	1	no	—
588	C₂²×D₄	—	10	1	no	—
589	C₂²×D₄	—	10	1	no	—
590	C₂²×D₄	—	10	1	no	—
591	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
592	#137	—	10	4	no	—
593	C₂×Q₁₆	—	5	1	no	—
594	C₂×Q₁₆	—	5	1	no	—
595	C₂×SD₁₆	—	5	1	no	—
596	C₂×SD₁₆	—	5	1	no	—
597	C₂×SD₁₆	—	5	1	no	—
598	C₂×SD₁₆	—	5	1	no	—
599	C₂×SD₁₆	—	10	4	no	—
600	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
601	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
602	C₂×M₁₆	—	5	1	no	—
603	C₂²×C₈	—	5	1	no	—
604	C₄⋊Q₈	—	10	1	no	—
605	#124	—	10	1	no	—
606	#123	—	10	1	no	—
607	#123	—	10	1	no	—
608	C₂²⋊Q₈	—	5	1	no	—
609	C₂²⋊Q₈	—	5	1	no	—
610	C₂²⋊Q₈	—	5	1	no	—
611	C₂²⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
612	#117	—	5	1	no	—
613	#103	—	5	1	no	—
614	#103	—	5	1	no	—
615	#102	—	5	1	no	—
616	#102	—	5	1	no	—
617	#102	—	5	1	no	—
618	#102	—	5	1	no	—
619	#102	C₂×C₃×D₅	1	1	yes	characteristic, complemented
620	#102	C₂×C₃×D₅	1	1	yes	characteristic, complemented
621	C₂²⋊C₈	—	5	1	no	—
622	C₂²⋊C₈	—	5	1	no	—
623	C₂²⋊C₈	—	5	1	no	—
624	C₂²⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
625	C₂×C₃×C₅	—	4	2	no	—
626	C₂×C₃×C₅	—	4	2	no	—
627	C₂×C₃×C₅	—	4	1	no	—
628	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
629	C₂×C₃×C₅	#577	1	1	yes	characteristic
630	C₂×C₃×C₅	#577	1	1	yes	characteristic
631	C₃×D₅	—	2	2	no	—
632	C₃×D₅	—	4	1	no	—
633	C₃×D₅	—	4	2	no	—
634	C₂³×C₃	—	2	4	no	—
635	C₂³×C₃	—	2	1	no	—
636	C₂³×C₃	—	2	1	no	—
637	C₂³×C₃	—	5	1	no	—
638	C₂³×C₃	—	5	1	no	—
639	C₂³×C₃	—	8	1	no	—
640	C₂³×C₃	—	8	1	no	—
641	C₂³×C₃	—	10	4	no	—
642	C₂³×C₃	—	10	4	no	—
643	C₂³×C₃	—	10	1	no	—
644	C₂³×C₃	—	40	1	no	—
645	C₂³×C₃	—	40	1	no	—
646	C₂³×C₃	—	40	1	no	—
647	C₂³×C₃	—	40	1	no	—
648	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
649	C₃×Q₈	—	2	1	no	—
650	C₃×Q₈	—	2	1	no	—
651	C₃×Q₈	—	5	2	no	—
652	C₃×Q₈	—	10	2	no	—
653	C₃×Q₈	—	10	1	no	—
654	C₃×Q₈	—	10	1	no	—
655	C₃×Q₈	—	10	1	no	—
656	C₃×Q₈	—	20	2	no	—
657	C₃×D₄	—	2	4	no	—
658	C₃×D₄	—	2	1	no	—
659	C₃×D₄	—	2	1	no	—
660	C₃×D₄	—	5	2	no	—
661	C₃×D₄	—	10	2	no	—
662	C₃×D₄	—	10	2	no	—
663	C₃×D₄	—	10	4	no	—
664	C₃×D₄	—	10	2	no	—
665	C₃×D₄	—	10	4	no	—
666	C₃×D₄	—	10	4	no	—
667	C₃×D₄	—	10	4	no	—
668	C₃×D₄	—	10	4	no	—
669	C₃×D₄	—	10	1	no	—
670	C₃×D₄	D₄×D₅	1	2	yes	—
671	C₃×D₄	D₄×D₅	1	2	yes	—
672	C₂×C₃×C₄	—	2	1	no	—
673	C₂×C₃×C₄	—	2	1	no	—
674	C₂×C₃×C₄	—	2	1	no	—
675	C₂×C₃×C₄	—	2	1	no	—
676	C₂×C₃×C₄	—	5	1	no	—
677	C₂×C₃×C₄	—	5	2	no	—
678	C₂×C₃×C₄	—	5	2	no	—
679	C₂×C₃×C₄	—	5	1	no	—
680	C₂×C₃×C₄	—	10	4	no	—
681	C₂×C₃×C₄	—	10	4	no	—
682	C₂×C₃×C₄	—	10	4	no	—
683	C₂×C₃×C₄	—	10	1	no	—
684	C₂×C₃×C₄	—	10	1	no	—
685	C₂×C₃×C₄	—	10	1	no	—
686	C₂×C₃×C₄	—	10	1	no	—
687	C₂×C₃×C₄	—	10	1	no	—
688	C₂×C₃×C₄	—	20	2	no	—
689	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
690	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
691	C₃×C₈	—	2	1	no	—
692	C₃×C₈	—	2	1	no	—
693	C₃×C₈	—	10	1	no	—
694	C₃×C₈	—	10	1	no	—
695	C₂²×C₅	—	2	1	no	—
696	C₂²×C₅	—	2	1	no	—
697	C₂²×C₅	—	2	2	no	—
698	C₂²×C₅	—	2	2	no	—
699	C₂²×C₅	—	2	1	no	—
700	C₂²×C₅	—	4	1	no	—
701	C₂²×C₅	—	4	1	no	—
702	C₂²×C₅	—	4	1	no	—
703	C₂²×C₅	—	4	1	no	—
704	C₂²×C₅	—	8	4	no	—
705	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
706	C₂×D₅	—	2	1	no	—
707	C₂×D₅	—	2	1	no	—
708	C₂×D₅	—	2	1	no	—
709	C₂×D₅	—	2	1	no	—
710	C₂×D₅	—	2	1	no	—
711	C₂×D₅	—	2	2	no	—
712	C₂×D₅	—	4	1	no	—
713	C₂×D₅	—	4	1	no	—
714	C₂×D₅	—	8	4	no	—
715	C₂×D₅	—	8	4	no	—
716	C₂×D₅	C₃×#120	1	2	yes	—
717	C₄×C₅	—	2	1	no	—
718	C₄×C₅	—	4	1	no	—
719	C₄×C₅	—	4	1	no	—
720	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
721	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
722	Dic₅	—	2	1	no	—
723	Dic₅	—	2	2	no	—
724	Dic₅	—	4	1	no	—
725	Dic₅	—	4	1	no	—
726	Dic₅	C₃×#120	1	2	yes	—
727	C₂⁴	—	2	1	no	—
728	C₂⁴	—	10	1	no	—
729	C₂⁴	—	10	1	no	—
730	#41	—	5	4	no	—
731	#41	—	10	2	no	—
732	#41	—	10	2	no	—
733	#41	—	10	2	no	—
734	#41	—	10	2	no	—
735	#41	—	10	2	no	—
736	#41	—	10	2	no	—
737	#41	—	10	8	no	—
738	#41	—	10	2	no	—
739	C₂×Q₈	—	5	1	no	—
740	C₂×Q₈	—	5	1	no	—
741	C₂×Q₈	—	5	1	no	—
742	C₂×Q₈	—	10	1	no	—
743	C₂×Q₈	—	10	2	no	—
744	C₂×Q₈	—	10	2	no	—
745	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	1	no	—
749	C₂×D₄	—	5	4	no	—
750	C₂×D₄	—	5	1	no	—
751	C₂×D₄	—	5	1	no	—
752	C₂×D₄	—	5	1	no	—
753	C₂×D₄	—	5	1	no	—
754	C₂×D₄	—	10	2	no	—
755	C₂×D₄	—	10	1	no	—
756	C₂×D₄	—	10	1	no	—
757	C₂×D₄	—	10	2	no	—
758	C₂×D₄	—	10	8	no	—
759	C₂×D₄	—	10	1	no	—
760	C₂×D₄	—	10	1	no	—
761	C₂×D₄	—	10	8	no	—
762	C₂×D₄	—	10	8	no	—
763	C₂×D₄	—	10	1	no	—
764	C₂×D₄	—	10	2	no	—
765	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
766	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
767	C₂²×C₄	—	5	1	no	—
768	C₂²×C₄	—	5	1	no	—
769	C₂²×C₄	—	10	1	no	—
770	C₂²×C₄	—	10	1	no	—
771	C₂²×C₄	—	10	1	no	—
772	C₂²×C₄	—	10	1	no	—
773	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
774	Q₁₆	—	10	2	no	—
775	Q₁₆	—	10	2	no	—
776	SD₁₆	—	2	2	no	—
777	SD₁₆	—	2	2	no	—
778	SD₁₆	—	10	2	no	—
779	SD₁₆	—	10	2	no	—
780	SD₁₆	—	10	2	no	—
781	SD₁₆	—	10	2	no	—
782	M₁₆	—	10	2	no	—
783	C₂×C₈	—	5	1	no	—
784	C₂×C₈	—	5	1	no	—
785	C₂×C₈	—	10	2	no	—
786	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
787	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
788	C₄⋊C₄	—	2	1	no	—
789	C₄⋊C₄	—	5	1	no	—
790	C₄⋊C₄	—	10	1	no	—
791	C₄⋊C₄	—	10	1	no	—
792	C₄⋊C₄	—	10	1	no	—
793	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	10	1	no	—
796	C₂²⋊C₄	—	10	1	no	—
797	C₂²⋊C₄	—	10	1	no	—
798	C₂²⋊C₄	—	10	1	no	—
799	C₄²	—	10	1	no	—
800	C₃×C₅	#3009	1	1	yes	characteristic, complemented, Hall
801	C₂²×C₃	—	2	1	no	—
802	C₂²×C₃	—	2	1	no	—
803	C₂²×C₃	—	2	1	no	—
804	C₂²×C₃	—	2	2	no	—
805	C₂²×C₃	—	2	2	no	—
806	C₂²×C₃	—	4	1	no	—
807	C₂²×C₃	—	4	1	no	—
808	C₂²×C₃	—	4	1	no	—
809	C₂²×C₃	—	4	1	no	—
810	C₂²×C₃	—	5	2	no	—
811	C₂²×C₃	—	8	4	no	—
812	C₂²×C₃	—	10	1	no	—
813	C₂²×C₃	—	10	1	no	—
814	C₂²×C₃	—	10	1	no	—
815	C₂²×C₃	—	10	1	no	—
816	C₂²×C₃	—	10	2	no	—
817	C₂²×C₃	—	10	1	no	—
818	C₂²×C₃	—	20	1	no	—
819	C₂²×C₃	—	20	1	no	—
820	C₂²×C₃	—	40	4	no	—
821	C₂²×C₃	—	40	4	no	—
822	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
823	C₃×C₄	—	2	1	no	—
824	C₃×C₄	—	4	1	no	—
825	C₃×C₄	—	4	1	no	—
826	C₃×C₄	—	5	2	no	—
827	C₃×C₄	—	10	1	no	—
828	C₃×C₄	—	10	2	no	—
829	C₃×C₄	—	20	1	no	—
830	C₃×C₄	—	20	1	no	—
831	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
832	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
833	C₂×C₅	—	4	2	no	—
834	C₂×C₅	—	4	2	no	—
835	C₂×C₅	—	4	1	no	—
836	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
837	C₂×C₅	C₃×#577	1	1	yes	characteristic
838	C₂×C₅	C₃×#577	1	1	yes	characteristic
839	D₅	—	2	2	no	—
840	D₅	—	4	1	no	—
841	D₅	—	4	2	no	—
842	C₂³	—	2	4	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	5	1	no	—
846	C₂³	—	5	1	no	—
847	C₂³	—	8	1	no	—
848	C₂³	—	8	1	no	—
849	C₂³	—	10	4	no	—
850	C₂³	—	10	4	no	—
851	C₂³	—	10	1	no	—
852	C₂³	—	40	1	no	—
853	C₂³	—	40	1	no	—
854	C₂³	—	40	1	no	—
855	C₂³	—	40	1	no	—
856	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
857	Q₈	—	2	1	no	—
858	Q₈	—	2	1	no	—
859	Q₈	—	5	2	no	—
860	Q₈	—	10	2	no	—
861	Q₈	—	10	1	no	—
862	Q₈	—	10	1	no	—
863	Q₈	—	10	1	no	—
864	Q₈	—	20	2	no	—
865	D₄	—	2	4	no	—
866	D₄	—	2	1	no	—
867	D₄	—	2	1	no	—
868	D₄	—	5	2	no	—
869	D₄	—	10	2	no	—
870	D₄	—	10	2	no	—
871	D₄	—	10	4	no	—
872	D₄	—	10	2	no	—
873	D₄	—	10	4	no	—
874	D₄	—	10	4	no	—
875	D₄	—	10	4	no	—
876	D₄	—	10	4	no	—
877	D₄	—	10	1	no	—
878	D₄	C₃×D₄×D₅	1	2	yes	—
879	D₄	C₃×D₄×D₅	1	2	yes	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	5	1	no	—
885	C₂×C₄	—	5	2	no	—
886	C₂×C₄	—	5	2	no	—
887	C₂×C₄	—	5	1	no	—
888	C₂×C₄	—	10	4	no	—
889	C₂×C₄	—	10	4	no	—
890	C₂×C₄	—	10	4	no	—
891	C₂×C₄	—	10	1	no	—
892	C₂×C₄	—	10	1	no	—
893	C₂×C₄	—	10	1	no	—
894	C₂×C₄	—	10	1	no	—
895	C₂×C₄	—	10	1	no	—
896	C₂×C₄	—	20	2	no	—
897	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
898	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
899	C₈	—	2	1	no	—
900	C₈	—	2	1	no	—
901	C₈	—	10	1	no	—
902	C₈	—	10	1	no	—
903	C₂×C₃	—	4	1	no	—
904	C₂×C₃	—	4	2	no	—
905	C₂×C₃	—	4	2	no	—
906	C₂×C₃	—	10	2	no	—
907	C₂×C₃	—	20	1	no	—
908	C₂×C₃	—	20	2	no	—
909	C₂×C₃	D₅×#120	1	1	yes	characteristic
910	C₂×C₃	#66096	1	1	yes	characteristic
911	C₂×C₃	#66109	1	1	yes	characteristic
912	C₅	C₃×#3009	1	1	yes	characteristic, complemented, Sylow
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	5	2	no	—
923	C₂²	—	8	4	no	—
924	C₂²	—	10	1	no	—
925	C₂²	—	10	1	no	—
926	C₂²	—	10	1	no	—
927	C₂²	—	10	2	no	—
928	C₂²	—	10	1	no	—
929	C₂²	—	10	1	no	—
930	C₂²	—	20	1	no	—
931	C₂²	—	20	1	no	—
932	C₂²	—	40	4	no	—
933	C₂²	—	40	4	no	—
934	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
935	C₄	—	2	1	no	—
936	C₄	—	4	1	no	—
937	C₄	—	4	1	no	—
938	C₄	—	5	2	no	—
939	C₄	—	10	1	no	—
940	C₄	—	10	2	no	—
941	C₄	—	20	1	no	—
942	C₄	—	20	1	no	—
943	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
944	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
945	C₃	#10611879	1	1	yes	characteristic, direct product factor, Sylow
946	C₂	—	4	1	no	—
947	C₂	—	4	2	no	—
948	C₂	—	4	2	no	—
949	C₂	—	10	2	no	—
950	C₂	—	20	1	no	—
951	C₂	—	20	2	no	—
952	C₂	C₃×D₅×#120	1	1	yes	characteristic
953	C₂	C₃×#66096	1	1	yes	characteristic
954	C₂	C₃×#66109	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×#450	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4144	C₂
hypercenter	C₃×#450	D₅
hypocenter	C₅	C₃×#3009
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#450

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4061	C₂	semidirect
3. C₂×C₃×D₅×SD₁₆	C₂	semidirect
4. C₃×#65962	C₂	semidirect
5. C₃×C₅×#450	C₂	semidirect
6. C₃×#65507	C₂	semidirect
7. C₃×#65462	C₂	semidirect
8. C₃×#65458	C₂	semidirect
9. C₃×#65336	C₂	semidirect
10. C₃×#65072	C₂	semidirect
11. C₃×#65065	C₂	semidirect
12. C₃×#65061	C₂	semidirect
13. C₃×#65059	C₂	semidirect
14. C₃×#65022	C₂	semidirect
15. C₃×#65016	C₂	semidirect
16. #10611879	C₃	direct (N × H)
20. C₂×C₃×Q₈×D₅	C₂²	semidirect
31. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
32. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
33. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
34. C₃×#4092	C₂²	semidirect
35. C₂×C₃×#689	C₂²	semidirect
36. C₂×C₃×#688	C₂²	semidirect
37. C₂×C₃×#687	C₂²	semidirect
38. C₂×C₃×#687	C₂²	semidirect
39. C₃×#4070	C₂²	semidirect
42. C₂×C₃×Dic₂₀	C₂²	semidirect
43. C₂×C₃×#677	C₂²	semidirect
44. C₂×C₃×#676	C₂²	semidirect
45. C₂×C₃×C₈×D₅	C₂²	semidirect
46. C₃×#4043	C₂²	semidirect
48. C₃×#4038	C₂²	semidirect
52. C₃×C₅×#102	C₂²	semidirect
53. C₃×C₅×#102	C₂²	semidirect
54. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
55. C₃×#3964	C₂²	semidirect
56. C₃×#3964	C₂²	semidirect
57. C₃×C₂²⋊#168	C₂²	semidirect
58. C₃×#3953	C₂²	semidirect
59. C₃×#3952	C₂²	semidirect
60. C₃×#3952	C₂²	semidirect
61. C₃×#3948	C₂²	semidirect
62. C₃×#3942	C₂²	semidirect
63. C₃×#3941	C₂²	semidirect
66. C₂×#4061	C₂×C₃	semidirect
67. C₂×D₅×SD₁₆	C₂×C₃	semidirect
68. #65962	C₂×C₃	semidirect
69. C₅×#450	C₂×C₃	semidirect
70. #65507	C₂×C₃	semidirect
71. #65462	C₂×C₃	semidirect
72. #65458	C₂×C₃	semidirect
73. #65336	C₂×C₃	semidirect
74. #65072	C₂×C₃	semidirect
75. #65065	C₂×C₃	semidirect
76. #65061	C₂×C₃	semidirect
77. #65059	C₂×C₃	semidirect
78. #65022	C₂×C₃	semidirect
79. #65016	C₂×C₃	semidirect
164. C₃×#450	D₅	semidirect
171. C₂×Q₈×D₅	C₂²×C₃	semidirect
182. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
183. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
184. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
185. #4092	C₂²×C₃	semidirect
186. C₂×#689	C₂²×C₃	semidirect
187. C₂×#688	C₂²×C₃	semidirect
188. C₂×#687	C₂²×C₃	semidirect
189. C₂×#687	C₂²×C₃	semidirect
190. #4070	C₂²×C₃	semidirect
193. C₂×Dic₂₀	C₂²×C₃	semidirect
194. C₂×#677	C₂²×C₃	semidirect
195. C₂×#676	C₂²×C₃	semidirect
196. C₂×C₈×D₅	C₂²×C₃	semidirect
197. #4043	C₂²×C₃	semidirect
199. #4038	C₂²×C₃	semidirect
203. C₅×#102	C₂²×C₃	semidirect
204. C₅×#102	C₂²×C₃	semidirect
205. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
206. #3964	C₂²×C₃	semidirect
207. #3964	C₂²×C₃	semidirect
208. C₂²⋊#168	C₂²×C₃	semidirect
209. #3953	C₂²×C₃	semidirect
210. #3952	C₂²×C₃	semidirect
211. #3952	C₂²×C₃	semidirect
212. #3948	C₂²×C₃	semidirect
213. #3942	C₂²×C₃	semidirect
214. #3941	C₂²×C₃	semidirect
299. C₂×C₃×SD₁₆	C₂×D₅	semidirect
300. C₂×C₃×SD₁₆	C₂×D₅	semidirect
310. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
318. C₃×#102	C₂×D₅	semidirect
319. C₃×#102	C₂×D₅	semidirect
323. C₃×C₂²⋊C₈	C₂×D₅	semidirect
408. #450	C₃×D₅	semidirect
600. C₂×SD₁₆	C₂×C₃×D₅	semidirect
601. C₂×SD₁₆	C₂×C₃×D₅	semidirect
611. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
619. #102	C₂×C₃×D₅	semidirect
620. #102	C₂×C₃×D₅	semidirect
624. C₂²⋊C₈	C₂×C₃×D₅	semidirect
800. C₃×C₅	#3009	semidirect
912. C₅	C₃×#3009	semidirect
945. C₃	#10611879	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×#4144	2
C₂×C₃×#4061	2
C₂×C₃×D₅×SD₁₆	2
C₃×#65962	2
C₃×C₅×#450	2
C₃×#65507	2
C₃×#65462	2
C₃×#65458	2
C₃×#65336	2
C₃×#65072	2
C₃×#65065	2
C₃×#65061	2
C₃×#65059	2
C₃×#65022	2
C₃×#65016	2
#10611879	3
C₃×#3009	5

Subgroups — C3×#10611879 #14424304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611879 #14424304