Subgroups — C₃×#10611959 #14424100

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4064	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4061	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65528	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65475	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×#65097	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65092	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65065	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65060	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65022	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#65015	C₂	1	1	yes	maximal, characteristic, complemented
16	#10611959	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₃×D₅×#41	—	2	4	no	—
19	C₃×D₅×#41	—	2	4	no	—
20	C₂×C₃×#713	C₂²	1	1	yes	characteristic
21	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×#711	—	2	1	no	—
24	C₂×C₃×#711	C₂²	1	1	yes	characteristic
25	C₂×C₃×D₄×D₅	—	2	1	no	—
26	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×#709	—	2	1	no	—
28	C₂×C₃×#709	C₂²	1	1	yes	characteristic
29	C₂²×C₃×C₄×D₅	—	2	1	no	—
30	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×Q₁₆	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
35	C₂×C₃×#689	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×#689	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×#688	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×#4064	—	2	4	no	—
41	C₃×#4061	—	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×#676	C₂²	1	1	yes	characteristic, complemented
46	C₃×#4043	C₂²	1	1	yes	characteristic
47	C₃×#4042	—	2	1	no	—
48	C₃×D₅×C₄⋊C₄	—	2	1	no	—
49	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₃×D₅×C₂²⋊C₄	—	2	1	no	—
51	C₃×#4024	—	2	1	no	—
52	C₃×C₅×#103	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×#3967	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
60	C₃×#3952	C₂²	1	1	yes	characteristic
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×#3007	—	5	1	no	maximal, Hall
65	C₂×D₅×#41	C₂×C₃	1	1	yes	characteristic
66	C₂×#4064	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂×#4061	C₂×C₃	1	1	yes	characteristic, complemented
68	D₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
70	#65528	C₂×C₃	1	1	yes	characteristic, complemented
71	#65475	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	#65097	C₂×C₃	1	1	yes	characteristic, complemented
75	#65092	C₂×C₃	1	1	yes	characteristic, complemented
76	#65065	C₂×C₃	1	1	yes	characteristic, complemented
77	#65060	C₂×C₃	1	1	yes	characteristic, complemented
78	#65022	C₂×C₃	1	1	yes	characteristic, complemented
79	#65015	C₂×C₃	1	1	yes	characteristic, complemented
80	C₂³×C₃×D₅	—	2	1	no	—
81	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
82	C₃×C₅×#41	—	2	2	no	—
83	C₃×C₅×#41	—	2	2	no	—
84	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	—	2	1	no	—
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
91	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
92	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
93	C₂²×C₃×Dic₅	—	2	1	no	—
94	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
95	C₃×#713	—	2	2	no	—
96	C₃×#713	D₄	1	4	yes	—
97	C₃×Q₈×D₅	—	2	2	no	—
98	C₃×Q₈×D₅	—	2	2	no	—
99	C₃×Q₈×D₅	—	2	2	no	—
100	C₃×Q₈×D₅	—	2	2	no	—
101	C₃×#711	—	2	8	no	—
102	C₃×#711	—	2	2	no	—
103	C₃×#711	D₄	1	4	yes	—
104	C₃×D₄×D₅	—	2	8	no	—
105	C₃×D₄×D₅	—	2	2	no	—
106	C₃×D₄×D₅	—	2	2	no	—
107	C₃×#709	—	2	8	no	—
108	C₃×#709	—	2	2	no	—
109	C₃×#709	—	2	2	no	—
110	C₂×C₃×D₂₀	—	2	1	no	—
111	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
112	C₂×C₃×C₄×D₅	—	2	8	no	—
113	C₂×C₃×C₄×D₅	—	2	1	no	—
114	C₂×C₃×C₄×D₅	—	2	1	no	—
115	C₂×C₃×C₄×D₅	—	2	1	no	—
116	C₂×C₃×C₄×D₅	—	2	2	no	—
117	C₂×C₃×C₄×D₅	—	2	2	no	—
118	C₂×C₃×C₄×D₅	—	2	1	no	—
119	C₂×C₃×C₄×D₅	—	2	1	no	—
120	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
121	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
122	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
123	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
124	C₂×C₃×Dic₁₀	—	2	1	no	—
125	C₂×C₃×Dic₁₀	—	2	1	no	—
126	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
127	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
128	C₃×C₅×Q₁₆	—	2	2	no	—
129	C₃×C₅×SD₁₆	—	2	2	no	—
130	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
131	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
132	C₃×C₅×C₄⋊C₄	—	2	1	no	—
133	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
135	C₃×C₂²⋊Dic₅	—	2	1	no	—
136	C₃×#689	—	2	2	no	—
137	C₃×#689	—	2	2	no	—
138	C₃×#688	—	2	2	no	—
139	C₃×#687	—	2	2	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×#683	—	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×#676	—	2	2	no	—
153	C₂²×C₃×#41	—	5	1	no	—
154	C₂×C₃×#137	—	5	1	no	—
155	C₂×C₃×#137	—	5	1	no	—
156	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
157	C₃×#452	—	5	1	no	—
158	C₃×#452	—	5	1	no	—
159	C₃×#452	—	5	1	no	—
160	C₃×#452	D₅	1	1	yes	characteristic, complemented
161	C₃×#451	—	5	1	no	—
162	C₃×#451	—	5	1	no	—
163	C₃×#450	—	5	1	no	—
164	C₃×#450	—	5	1	no	—
165	C₃×#417	—	5	1	no	—
166	C₃×#417	—	5	1	no	—
167	C₃×#407	—	5	1	no	—
168	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
169	D₅×#41	—	2	4	no	—
170	D₅×#41	—	2	4	no	—
171	C₂×#713	C₂²×C₃	1	1	yes	characteristic
172	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
173	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₂×#711	—	2	1	no	—
175	C₂×#711	C₂²×C₃	1	1	yes	characteristic
176	C₂×D₄×D₅	—	2	1	no	—
177	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
178	C₂×#709	—	2	1	no	—
179	C₂×#709	C₂²×C₃	1	1	yes	characteristic
180	C₂²×C₄×D₅	—	2	1	no	—
181	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
182	C₂×C₅×Q₁₆	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
186	C₂×#689	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₂×#689	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₂×#688	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	#4064	—	2	4	no	—
192	#4061	—	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×#676	C₂²×C₃	1	1	yes	characteristic, complemented
197	#4043	C₂²×C₃	1	1	yes	characteristic
198	#4042	—	2	1	no	—
199	D₅×C₄⋊C₄	—	2	1	no	—
200	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
201	D₅×C₂²⋊C₄	—	2	1	no	—
202	#4024	—	2	1	no	—
203	C₅×#103	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	#3967	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
211	#3952	C₂²×C₃	1	1	yes	characteristic
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	#3007	—	5	1	no	Sylow
216	C₂³×C₃×C₅	—	2	1	no	—
217	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₃×D₅	—	2	4	no	—
219	C₂²×C₃×D₅	—	2	1	no	—
220	C₂²×C₃×D₅	—	2	2	no	—
221	C₂²×C₃×D₅	—	2	2	no	—
222	C₂²×C₃×D₅	—	4	1	no	—
223	C₂²×C₃×D₅	—	4	2	no	—
224	C₂²×C₃×D₅	—	4	2	no	—
225	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
227	C₃×C₅×Q₈	—	2	1	no	—
228	C₃×C₅×Q₈	—	2	1	no	—
229	C₃×C₅×Q₈	—	2	1	no	—
230	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
231	C₃×C₅×D₄	—	2	4	no	—
232	C₃×C₅×D₄	—	2	1	no	—
233	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
234	C₂×C₃×C₄×C₅	—	2	4	no	—
235	C₂×C₃×C₄×C₅	—	2	1	no	—
236	C₂×C₃×C₄×C₅	—	2	1	no	—
237	C₂×C₃×C₄×C₅	—	2	1	no	—
238	C₂×C₃×C₄×C₅	—	2	1	no	—
239	C₂×C₃×C₄×C₅	—	2	1	no	—
240	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
241	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
242	C₃×C₂²⋊D₅	—	2	4	no	—
243	C₃×C₂²⋊D₅	—	2	4	no	—
244	C₃×C₂²⋊D₅	—	2	4	no	—
245	C₂×C₃×Dic₅	—	2	1	no	—
246	C₂×C₃×Dic₅	—	2	2	no	—
247	C₂×C₃×Dic₅	—	2	4	no	—
248	C₂×C₃×Dic₅	—	2	1	no	—
249	C₂×C₃×Dic₅	—	2	1	no	—
250	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
251	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
252	C₃×D₂₀	—	2	4	no	—
253	C₃×D₂₀	—	2	1	no	—
254	C₃×D₂₀	C₂×D₄	1	2	yes	—
255	C₃×C₄×D₅	—	2	4	no	—
256	C₃×C₄×D₅	—	2	4	no	—
257	C₃×C₄×D₅	—	2	2	no	—
258	C₃×C₄×D₅	—	2	1	no	—
259	C₃×C₄×D₅	—	2	1	no	—
260	C₃×C₄×D₅	—	2	2	no	—
261	C₃×C₄×D₅	—	2	4	no	—
262	C₃×C₄×D₅	—	4	2	no	—
263	C₃×C₄×D₅	—	4	2	no	—
264	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
265	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
266	C₃×Dic₁₀	—	2	4	no	—
267	C₃×Dic₁₀	—	2	1	no	—
268	C₃×Dic₁₀	—	2	1	no	—
269	C₃×Dic₁₀	—	2	1	no	—
270	C₃×Dic₁₀	—	4	2	no	—
271	C₃×Dic₁₀	C₂×D₄	1	2	yes	—
272	C₃×C₅×C₈	—	2	1	no	—
273	C₃×C₅×C₈	—	2	1	no	—
274	C₃×#168	—	2	1	no	—
275	C₃×#168	—	2	1	no	—
276	C₂×C₃×#41	—	5	1	no	—
277	C₂×C₃×#41	—	5	1	no	—
278	C₂×C₃×#41	—	5	1	no	—
279	C₂×C₃×#41	—	10	1	no	—
280	C₂×C₃×#41	—	10	1	no	—
281	C₂×C₃×#41	—	10	4	no	—
282	C₂×C₃×#41	—	10	4	no	—
283	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
284	C₂²×C₃×Q₈	—	5	1	no	—
285	C₂²×C₃×Q₈	—	5	1	no	—
286	C₂²×C₃×D₄	—	5	1	no	—
287	C₂²×C₃×D₄	—	10	1	no	—
288	C₂³×C₃×C₄	—	5	1	no	—
289	C₂³×C₃×C₄	—	10	1	no	—
290	C₃×#137	—	10	4	no	—
291	C₃×#137	—	10	4	no	—
292	C₂×C₃×Q₁₆	—	5	1	no	—
293	C₂×C₃×Q₁₆	—	5	1	no	—
294	C₂×C₃×Q₁₆	—	5	1	no	—
295	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
296	C₂×C₃×SD₁₆	—	5	1	no	—
297	C₂×C₃×SD₁₆	—	5	1	no	—
298	C₂×C₃×SD₁₆	—	5	1	no	—
299	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic, complemented
300	C₂×C₃×M₁₆	—	5	1	no	—
301	C₂×C₃×M₁₆	—	5	1	no	—
302	C₃×C₂²⋊Q₈	—	5	1	no	—
303	C₃×C₂²⋊Q₈	—	5	1	no	—
304	C₃×C₂²⋊Q₈	—	5	1	no	—
305	C₃×C₂²⋊Q₈	—	10	1	no	—
306	C₃×C₂²⋊Q₈	—	10	1	no	—
307	C₃×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
308	C₂×C₃×C₄⋊C₄	—	5	1	no	—
309	C₂×C₃×C₄⋊C₄	—	10	1	no	—
310	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
311	C₃×#103	—	5	1	no	—
312	C₃×#103	—	5	1	no	—
313	C₃×#103	—	5	1	no	—
314	C₃×#103	C₂×D₅	1	1	yes	characteristic, complemented
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×C₂²⋊C₈	—	5	1	no	—
320	C₃×C₂²⋊C₈	—	5	1	no	—
321	C₃×C₂²⋊C₈	—	5	1	no	—
322	C₃×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
323	C₂³×D₅	—	2	1	no	—
324	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
325	C₅×#41	—	2	2	no	—
326	C₅×#41	—	2	2	no	—
327	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
328	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
329	C₂×C₅×D₄	—	2	1	no	—
330	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
331	C₂²×C₄×C₅	—	2	1	no	—
332	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
333	C₂×C₂²⋊D₅	—	2	1	no	—
334	C₂×C₂²⋊D₅	—	2	1	no	—
335	C₂×C₂²⋊D₅	—	2	1	no	—
336	C₂²×Dic₅	—	2	1	no	—
337	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
338	#713	—	2	2	no	—
339	#713	C₃×D₄	1	4	yes	—
340	Q₈×D₅	—	2	2	no	—
341	Q₈×D₅	—	2	2	no	—
342	Q₈×D₅	—	2	2	no	—
343	Q₈×D₅	—	2	2	no	—
344	#711	—	2	8	no	—
345	#711	—	2	2	no	—
346	#711	C₃×D₄	1	4	yes	—
347	D₄×D₅	—	2	8	no	—
348	D₄×D₅	—	2	2	no	—
349	D₄×D₅	—	2	2	no	—
350	#709	—	2	8	no	—
351	#709	—	2	2	no	—
352	#709	—	2	2	no	—
353	C₂×D₂₀	—	2	1	no	—
354	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
355	C₂×C₄×D₅	—	2	8	no	—
356	C₂×C₄×D₅	—	2	1	no	—
357	C₂×C₄×D₅	—	2	1	no	—
358	C₂×C₄×D₅	—	2	1	no	—
359	C₂×C₄×D₅	—	2	2	no	—
360	C₂×C₄×D₅	—	2	2	no	—
361	C₂×C₄×D₅	—	2	1	no	—
362	C₂×C₄×D₅	—	2	1	no	—
363	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
364	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
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	—	2	1	no	—
369	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
370	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
371	C₅×Q₁₆	—	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	#689	—	2	2	no	—
381	#688	—	2	2	no	—
382	#687	—	2	2	no	—
383	#685	—	2	1	no	—
384	#685	—	2	1	no	—
385	C₄⋊Dic₅	—	2	1	no	—
386	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
387	#683	—	2	1	no	—
388	#683	—	2	1	no	—
389	#683	—	2	1	no	—
390	C₂×#168	C₂³×C₃	1	1	yes	characteristic
391	C₂×#168	C₂³×C₃	1	1	yes	characteristic
392	Dic₂₀	—	2	2	no	—
393	#677	—	2	2	no	—
394	#676	—	2	2	no	—
395	#676	—	2	2	no	—
396	C₂²×#41	—	5	1	no	—
397	C₂×#137	—	5	1	no	—
398	C₂×#137	—	5	1	no	—
399	C₂×C₂²⋊Q₈	—	5	1	no	—
400	#452	—	5	1	no	—
401	#452	—	5	1	no	—
402	#452	—	5	1	no	—
403	#452	C₃×D₅	1	1	yes	characteristic, complemented
404	#451	—	5	1	no	—
405	#451	—	5	1	no	—
406	#450	—	5	1	no	—
407	#450	—	5	1	no	—
408	#417	—	5	1	no	—
409	#417	—	5	1	no	—
410	#407	—	5	1	no	—
411	C₂²×C₃×C₅	—	2	1	no	—
412	C₂²×C₃×C₅	—	2	2	no	—
413	C₂²×C₃×C₅	—	2	1	no	—
414	C₂²×C₃×C₅	—	2	1	no	—
415	C₂²×C₃×C₅	—	4	1	no	—
416	C₂²×C₃×C₅	—	4	1	no	—
417	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₃×D₅	—	2	1	no	—
419	C₂×C₃×D₅	—	2	1	no	—
420	C₂×C₃×D₅	—	2	1	no	—
421	C₂×C₃×D₅	—	2	1	no	—
422	C₂×C₃×D₅	—	2	2	no	—
423	C₂×C₃×D₅	—	4	4	no	—
424	C₂×C₃×D₅	—	4	8	no	—
425	C₂×C₃×D₅	—	4	1	no	—
426	C₂×C₃×D₅	—	4	1	no	—
427	C₂×C₃×D₅	#120	1	2	yes	—
428	C₂×C₃×D₅	#137	1	2	yes	complemented
429	C₃×C₄×C₅	—	2	2	no	—
430	C₃×C₄×C₅	—	2	1	no	—
431	C₃×C₄×C₅	—	4	1	no	—
432	C₃×C₄×C₅	—	4	1	no	—
433	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
434	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
435	C₃×Dic₅	—	2	1	no	—
436	C₃×Dic₅	—	2	2	no	—
437	C₃×Dic₅	—	4	1	no	—
438	C₃×Dic₅	—	4	1	no	—
439	C₃×Dic₅	#120	1	2	yes	—
440	C₂⁴×C₃	—	5	1	no	—
441	C₂⁴×C₃	—	10	1	no	—
442	C₃×#41	—	2	2	no	—
443	C₃×#41	—	2	2	no	—
444	C₃×#41	—	5	4	no	—
445	C₃×#41	—	5	4	no	—
446	C₃×#41	—	10	2	no	—
447	C₃×#41	—	10	2	no	—
448	C₃×#41	—	10	8	no	—
449	C₃×#41	—	10	2	no	—
450	C₃×#41	—	10	2	no	—
451	C₃×#41	—	10	8	no	—
452	C₂×C₃×Q₈	—	5	1	no	—
453	C₂×C₃×Q₈	—	5	1	no	—
454	C₂×C₃×Q₈	—	10	1	no	—
455	C₂×C₃×Q₈	—	10	1	no	—
456	C₂×C₃×Q₈	—	10	2	no	—
457	C₂×C₃×Q₈	—	10	2	no	—
458	C₂×C₃×Q₈	—	10	2	no	—
459	C₂×C₃×Q₈	—	10	2	no	—
460	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
461	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
462	C₂×C₃×D₄	—	2	1	no	—
463	C₂×C₃×D₄	—	5	1	no	—
464	C₂×C₃×D₄	—	10	1	no	—
465	C₂×C₃×D₄	—	10	1	no	—
466	C₂×C₃×D₄	—	10	2	no	—
467	C₂×C₃×D₄	—	10	8	no	—
468	C₂×C₃×D₄	—	10	1	no	—
469	C₂×C₃×D₄	—	10	1	no	—
470	C₂×C₃×D₄	—	10	2	no	—
471	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
472	C₂²×C₃×C₄	—	2	1	no	—
473	C₂²×C₃×C₄	—	5	1	no	—
474	C₂²×C₃×C₄	—	5	1	no	—
475	C₂²×C₃×C₄	—	5	1	no	—
476	C₂²×C₃×C₄	—	5	1	no	—
477	C₂²×C₃×C₄	—	5	1	no	—
478	C₂²×C₃×C₄	—	10	2	no	—
479	C₂²×C₃×C₄	—	10	2	no	—
480	C₂²×C₃×C₄	—	10	1	no	—
481	C₂²×C₃×C₄	—	10	1	no	—
482	C₂²×C₃×C₄	—	10	8	no	—
483	C₂²×C₃×C₄	—	10	1	no	—
484	C₂²×C₃×C₄	—	10	1	no	—
485	C₂²×C₃×C₄	—	10	1	no	—
486	C₂²×C₃×C₄	—	10	1	no	—
487	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
488	C₃×Q₁₆	—	2	2	no	—
489	C₃×Q₁₆	—	10	2	no	—
490	C₃×Q₁₆	—	10	2	no	—
491	C₃×Q₁₆	—	10	2	no	—
492	C₃×SD₁₆	—	2	2	no	—
493	C₃×SD₁₆	—	10	2	no	—
494	C₃×SD₁₆	—	10	2	no	—
495	C₃×SD₁₆	—	10	2	no	—
496	C₃×M₁₆	—	10	2	no	—
497	C₃×M₁₆	—	10	2	no	—
498	C₂×C₃×C₈	—	5	1	no	—
499	C₂×C₃×C₈	—	5	1	no	—
500	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
501	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
502	C₃×C₄⋊C₄	—	2	1	no	—
503	C₃×C₄⋊C₄	—	5	1	no	—
504	C₃×C₄⋊C₄	—	10	1	no	—
505	C₃×C₄⋊C₄	—	10	1	no	—
506	C₃×C₄⋊C₄	—	10	1	no	—
507	C₃×C₄⋊C₄	—	10	1	no	—
508	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
509	C₃×C₂²⋊C₄	—	2	1	no	—
510	C₃×C₂²⋊C₄	—	10	1	no	—
511	C₃×C₂²⋊C₄	—	10	1	no	—
512	C₃×C₂²⋊C₄	—	10	1	no	—
513	C₂³×C₅	—	2	1	no	—
514	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
515	C₂²×D₅	—	2	4	no	—
516	C₂²×D₅	—	2	1	no	—
517	C₂²×D₅	—	2	2	no	—
518	C₂²×D₅	—	2	2	no	—
519	C₂²×D₅	—	4	1	no	—
520	C₂²×D₅	—	4	2	no	—
521	C₂²×D₅	—	4	2	no	—
522	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
523	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
524	C₅×Q₈	—	2	1	no	—
525	C₅×Q₈	—	2	1	no	—
526	C₅×Q₈	—	2	1	no	—
527	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
528	C₅×D₄	—	2	4	no	—
529	C₅×D₄	—	2	1	no	—
530	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
531	C₂×C₄×C₅	—	2	4	no	—
532	C₂×C₄×C₅	—	2	1	no	—
533	C₂×C₄×C₅	—	2	1	no	—
534	C₂×C₄×C₅	—	2	1	no	—
535	C₂×C₄×C₅	—	2	1	no	—
536	C₂×C₄×C₅	—	2	1	no	—
537	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
538	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
539	C₂²⋊D₅	—	2	4	no	—
540	C₂²⋊D₅	—	2	4	no	—
541	C₂²⋊D₅	—	2	4	no	—
542	C₂×Dic₅	—	2	1	no	—
543	C₂×Dic₅	—	2	2	no	—
544	C₂×Dic₅	—	2	4	no	—
545	C₂×Dic₅	—	2	1	no	—
546	C₂×Dic₅	—	2	1	no	—
547	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
548	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
549	D₂₀	—	2	4	no	—
550	D₂₀	—	2	1	no	—
551	D₂₀	C₂×C₃×D₄	1	2	yes	—
552	C₄×D₅	—	2	4	no	—
553	C₄×D₅	—	2	4	no	—
554	C₄×D₅	—	2	2	no	—
555	C₄×D₅	—	2	1	no	—
556	C₄×D₅	—	2	1	no	—
557	C₄×D₅	—	2	2	no	—
558	C₄×D₅	—	2	4	no	—
559	C₄×D₅	—	4	2	no	—
560	C₄×D₅	—	4	2	no	—
561	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
562	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
563	Dic₁₀	—	2	4	no	—
564	Dic₁₀	—	2	1	no	—
565	Dic₁₀	—	2	1	no	—
566	Dic₁₀	—	2	1	no	—
567	Dic₁₀	—	4	2	no	—
568	Dic₁₀	C₂×C₃×D₄	1	2	yes	—
569	C₅×C₈	—	2	1	no	—
570	C₅×C₈	—	2	1	no	—
571	#168	—	2	1	no	—
572	#168	—	2	1	no	—
573	C₂×#41	—	5	1	no	—
574	C₂×#41	—	5	1	no	—
575	C₂×#41	—	5	1	no	—
576	C₂×#41	—	10	1	no	—
577	C₂×#41	—	10	1	no	—
578	C₂×#41	—	10	4	no	—
579	C₂×#41	—	10	4	no	—
580	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
581	C₂²×Q₈	—	5	1	no	—
582	C₂²×Q₈	—	5	1	no	—
583	C₂²×D₄	—	5	1	no	—
584	C₂²×D₄	—	10	1	no	—
585	C₂³×C₄	—	5	1	no	—
586	C₂³×C₄	—	10	1	no	—
587	#137	—	10	4	no	—
588	#137	—	10	4	no	—
589	C₂×Q₁₆	—	5	1	no	—
590	C₂×Q₁₆	—	5	1	no	—
591	C₂×Q₁₆	—	5	1	no	—
592	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
593	C₂×SD₁₆	—	5	1	no	—
594	C₂×SD₁₆	—	5	1	no	—
595	C₂×SD₁₆	—	5	1	no	—
596	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
597	C₂×M₁₆	—	5	1	no	—
598	C₂×M₁₆	—	5	1	no	—
599	C₂²⋊Q₈	—	5	1	no	—
600	C₂²⋊Q₈	—	5	1	no	—
601	C₂²⋊Q₈	—	5	1	no	—
602	C₂²⋊Q₈	—	10	1	no	—
603	C₂²⋊Q₈	—	10	1	no	—
604	C₂²⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
605	C₂×C₄⋊C₄	—	5	1	no	—
606	C₂×C₄⋊C₄	—	10	1	no	—
607	C₂×C₂²⋊C₄	—	10	1	no	—
608	#103	—	5	1	no	—
609	#103	—	5	1	no	—
610	#103	—	5	1	no	—
611	#103	C₂×C₃×D₅	1	1	yes	characteristic, complemented
612	#102	—	5	1	no	—
613	#102	—	5	1	no	—
614	#102	—	5	1	no	—
615	#102	C₂×C₃×D₅	1	1	yes	characteristic, complemented
616	C₂²⋊C₈	—	5	1	no	—
617	C₂²⋊C₈	—	5	1	no	—
618	C₂²⋊C₈	—	5	1	no	—
619	C₂²⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
620	C₂×C₃×C₅	—	4	1	no	—
621	C₂×C₃×C₅	—	4	2	no	—
622	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
623	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
624	C₂×C₃×C₅	#575	1	1	yes	characteristic
625	C₃×D₅	—	2	2	no	—
626	C₃×D₅	—	2	2	no	—
627	C₃×D₅	—	4	2	no	—
628	C₂³×C₃	—	2	1	no	—
629	C₂³×C₃	—	5	1	no	—
630	C₂³×C₃	—	5	1	no	—
631	C₂³×C₃	—	10	2	no	—
632	C₂³×C₃	—	10	2	no	—
633	C₂³×C₃	—	10	4	no	—
634	C₂³×C₃	—	10	1	no	—
635	C₂³×C₃	—	20	1	no	—
636	C₂³×C₃	—	20	2	no	—
637	C₂³×C₃	—	20	2	no	—
638	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
639	C₃×Q₈	—	2	1	no	—
640	C₃×Q₈	—	2	1	no	—
641	C₃×Q₈	—	2	1	no	—
642	C₃×Q₈	—	5	2	no	—
643	C₃×Q₈	—	10	4	no	—
644	C₃×Q₈	—	10	1	no	—
645	C₃×Q₈	—	10	1	no	—
646	C₃×Q₈	—	10	1	no	—
647	C₃×Q₈	—	20	2	no	—
648	C₃×Q₈	D₄×D₅	1	2	yes	—
649	C₃×D₄	—	2	4	no	—
650	C₃×D₄	—	2	1	no	—
651	C₃×D₄	—	5	2	no	—
652	C₃×D₄	—	10	4	no	—
653	C₃×D₄	—	10	4	no	—
654	C₃×D₄	—	10	4	no	—
655	C₃×D₄	—	10	4	no	—
656	C₃×D₄	—	10	1	no	—
657	C₃×D₄	D₄×D₅	1	2	yes	—
658	C₂×C₃×C₄	—	2	4	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	—	2	1	no	—
661	C₂×C₃×C₄	—	2	1	no	—
662	C₂×C₃×C₄	—	2	1	no	—
663	C₂×C₃×C₄	—	2	1	no	—
664	C₂×C₃×C₄	—	5	1	no	—
665	C₂×C₃×C₄	—	5	2	no	—
666	C₂×C₃×C₄	—	5	2	no	—
667	C₂×C₃×C₄	—	5	1	no	—
668	C₂×C₃×C₄	—	10	2	no	—
669	C₂×C₃×C₄	—	10	4	no	—
670	C₂×C₃×C₄	—	10	2	no	—
671	C₂×C₃×C₄	—	10	4	no	—
672	C₂×C₃×C₄	—	10	4	no	—
673	C₂×C₃×C₄	—	10	2	no	—
674	C₂×C₃×C₄	—	10	4	no	—
675	C₂×C₃×C₄	—	10	1	no	—
676	C₂×C₃×C₄	—	10	1	no	—
677	C₂×C₃×C₄	—	10	1	no	—
678	C₂×C₃×C₄	—	10	1	no	—
679	C₂×C₃×C₄	—	10	1	no	—
680	C₂×C₃×C₄	—	20	2	no	—
681	C₂×C₃×C₄	—	20	2	no	—
682	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
683	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
684	C₃×C₈	—	2	1	no	—
685	C₃×C₈	—	2	1	no	—
686	C₃×C₈	—	10	1	no	—
687	C₃×C₈	—	10	1	no	—
688	C₂²×C₅	—	2	1	no	—
689	C₂²×C₅	—	2	1	no	—
690	C₂²×C₅	—	2	1	no	—
691	C₂²×C₅	—	2	2	no	—
692	C₂²×C₅	—	4	1	no	—
693	C₂²×C₅	—	4	1	no	—
694	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
695	C₂×D₅	—	2	1	no	—
696	C₂×D₅	—	2	1	no	—
697	C₂×D₅	—	2	1	no	—
698	C₂×D₅	—	2	1	no	—
699	C₂×D₅	—	2	2	no	—
700	C₂×D₅	—	4	4	no	—
701	C₂×D₅	—	4	8	no	—
702	C₂×D₅	—	4	1	no	—
703	C₂×D₅	—	4	1	no	—
704	C₂×D₅	C₃×#120	1	2	yes	—
705	C₂×D₅	C₃×#137	1	2	yes	complemented
706	C₄×C₅	—	2	2	no	—
707	C₄×C₅	—	2	1	no	—
708	C₄×C₅	—	4	1	no	—
709	C₄×C₅	—	4	1	no	—
710	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
711	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
712	Dic₅	—	2	1	no	—
713	Dic₅	—	2	2	no	—
714	Dic₅	—	4	1	no	—
715	Dic₅	—	4	1	no	—
716	Dic₅	C₃×#120	1	2	yes	—
717	C₂⁴	—	5	1	no	—
718	C₂⁴	—	10	1	no	—
719	#41	—	2	2	no	—
720	#41	—	2	2	no	—
721	#41	—	5	4	no	—
722	#41	—	5	4	no	—
723	#41	—	10	2	no	—
724	#41	—	10	2	no	—
725	#41	—	10	8	no	—
726	#41	—	10	2	no	—
727	#41	—	10	2	no	—
728	#41	—	10	8	no	—
729	C₂×Q₈	—	5	1	no	—
730	C₂×Q₈	—	5	1	no	—
731	C₂×Q₈	—	10	1	no	—
732	C₂×Q₈	—	10	1	no	—
733	C₂×Q₈	—	10	2	no	—
734	C₂×Q₈	—	10	2	no	—
735	C₂×Q₈	—	10	2	no	—
736	C₂×Q₈	—	10	2	no	—
737	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
738	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
739	C₂×D₄	—	2	1	no	—
740	C₂×D₄	—	5	1	no	—
741	C₂×D₄	—	10	1	no	—
742	C₂×D₄	—	10	1	no	—
743	C₂×D₄	—	10	2	no	—
744	C₂×D₄	—	10	8	no	—
745	C₂×D₄	—	10	1	no	—
746	C₂×D₄	—	10	1	no	—
747	C₂×D₄	—	10	2	no	—
748	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	5	1	no	—
751	C₂²×C₄	—	5	1	no	—
752	C₂²×C₄	—	5	1	no	—
753	C₂²×C₄	—	5	1	no	—
754	C₂²×C₄	—	5	1	no	—
755	C₂²×C₄	—	10	2	no	—
756	C₂²×C₄	—	10	2	no	—
757	C₂²×C₄	—	10	1	no	—
758	C₂²×C₄	—	10	1	no	—
759	C₂²×C₄	—	10	8	no	—
760	C₂²×C₄	—	10	1	no	—
761	C₂²×C₄	—	10	1	no	—
762	C₂²×C₄	—	10	1	no	—
763	C₂²×C₄	—	10	1	no	—
764	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
765	Q₁₆	—	2	2	no	—
766	Q₁₆	—	10	2	no	—
767	Q₁₆	—	10	2	no	—
768	Q₁₆	—	10	2	no	—
769	SD₁₆	—	2	2	no	—
770	SD₁₆	—	10	2	no	—
771	SD₁₆	—	10	2	no	—
772	SD₁₆	—	10	2	no	—
773	M₁₆	—	10	2	no	—
774	M₁₆	—	10	2	no	—
775	C₂×C₈	—	5	1	no	—
776	C₂×C₈	—	5	1	no	—
777	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
778	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
779	C₄⋊C₄	—	2	1	no	—
780	C₄⋊C₄	—	5	1	no	—
781	C₄⋊C₄	—	10	1	no	—
782	C₄⋊C₄	—	10	1	no	—
783	C₄⋊C₄	—	10	1	no	—
784	C₄⋊C₄	—	10	1	no	—
785	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
786	C₂²⋊C₄	—	2	1	no	—
787	C₂²⋊C₄	—	10	1	no	—
788	C₂²⋊C₄	—	10	1	no	—
789	C₂²⋊C₄	—	10	1	no	—
790	C₃×C₅	#3007	1	1	yes	characteristic, complemented, Hall
791	C₂²×C₃	—	2	1	no	—
792	C₂²×C₃	—	2	1	no	—
793	C₂²×C₃	—	2	1	no	—
794	C₂²×C₃	—	2	2	no	—
795	C₂²×C₃	—	4	1	no	—
796	C₂²×C₃	—	4	1	no	—
797	C₂²×C₃	—	5	2	no	—
798	C₂²×C₃	—	5	2	no	—
799	C₂²×C₃	—	10	1	no	—
800	C₂²×C₃	—	10	1	no	—
801	C₂²×C₃	—	10	1	no	—
802	C₂²×C₃	—	10	1	no	—
803	C₂²×C₃	—	10	2	no	—
804	C₂²×C₃	—	20	4	no	—
805	C₂²×C₃	—	20	8	no	—
806	C₂²×C₃	—	20	1	no	—
807	C₂²×C₃	—	20	1	no	—
808	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
809	C₃×C₄	—	2	1	no	—
810	C₃×C₄	—	2	2	no	—
811	C₃×C₄	—	4	1	no	—
812	C₃×C₄	—	4	1	no	—
813	C₃×C₄	—	5	2	no	—
814	C₃×C₄	—	10	1	no	—
815	C₃×C₄	—	10	2	no	—
816	C₃×C₄	—	20	1	no	—
817	C₃×C₄	—	20	1	no	—
818	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
819	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
820	C₂×C₅	—	4	1	no	—
821	C₂×C₅	—	4	2	no	—
822	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
823	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
824	C₂×C₅	C₃×#575	1	1	yes	characteristic
825	D₅	—	2	2	no	—
826	D₅	—	2	2	no	—
827	D₅	—	4	2	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	5	1	no	—
830	C₂³	—	5	1	no	—
831	C₂³	—	10	2	no	—
832	C₂³	—	10	2	no	—
833	C₂³	—	10	4	no	—
834	C₂³	—	10	1	no	—
835	C₂³	—	20	1	no	—
836	C₂³	—	20	2	no	—
837	C₂³	—	20	2	no	—
838	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
839	Q₈	—	2	1	no	—
840	Q₈	—	2	1	no	—
841	Q₈	—	2	1	no	—
842	Q₈	—	5	2	no	—
843	Q₈	—	10	4	no	—
844	Q₈	—	10	1	no	—
845	Q₈	—	10	1	no	—
846	Q₈	—	10	1	no	—
847	Q₈	—	20	2	no	—
848	Q₈	C₃×D₄×D₅	1	2	yes	—
849	D₄	—	2	4	no	—
850	D₄	—	2	1	no	—
851	D₄	—	5	2	no	—
852	D₄	—	10	4	no	—
853	D₄	—	10	4	no	—
854	D₄	—	10	4	no	—
855	D₄	—	10	4	no	—
856	D₄	—	10	1	no	—
857	D₄	C₃×D₄×D₅	1	2	yes	—
858	C₂×C₄	—	2	4	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	5	1	no	—
865	C₂×C₄	—	5	2	no	—
866	C₂×C₄	—	5	2	no	—
867	C₂×C₄	—	5	1	no	—
868	C₂×C₄	—	10	2	no	—
869	C₂×C₄	—	10	4	no	—
870	C₂×C₄	—	10	2	no	—
871	C₂×C₄	—	10	4	no	—
872	C₂×C₄	—	10	4	no	—
873	C₂×C₄	—	10	2	no	—
874	C₂×C₄	—	10	4	no	—
875	C₂×C₄	—	10	1	no	—
876	C₂×C₄	—	10	1	no	—
877	C₂×C₄	—	10	1	no	—
878	C₂×C₄	—	10	1	no	—
879	C₂×C₄	—	10	1	no	—
880	C₂×C₄	—	20	2	no	—
881	C₂×C₄	—	20	2	no	—
882	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
883	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
884	C₈	—	2	1	no	—
885	C₈	—	2	1	no	—
886	C₈	—	10	1	no	—
887	C₈	—	10	1	no	—
888	C₂×C₃	—	4	1	no	—
889	C₂×C₃	—	4	2	no	—
890	C₂×C₃	—	10	2	no	—
891	C₂×C₃	—	10	2	no	—
892	C₂×C₃	—	20	2	no	—
893	C₂×C₃	D₅×#120	1	1	yes	characteristic
894	C₂×C₃	#66102	1	1	yes	characteristic
895	C₂×C₃	D₅×#137	1	1	yes	characteristic
896	C₅	C₃×#3007	1	1	yes	characteristic, complemented, Sylow
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	4	1	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	5	2	no	—
904	C₂²	—	5	2	no	—
905	C₂²	—	10	1	no	—
906	C₂²	—	10	1	no	—
907	C₂²	—	10	1	no	—
908	C₂²	—	10	1	no	—
909	C₂²	—	10	2	no	—
910	C₂²	—	20	4	no	—
911	C₂²	—	20	8	no	—
912	C₂²	—	20	1	no	—
913	C₂²	—	20	1	no	—
914	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
915	C₄	—	2	1	no	—
916	C₄	—	2	2	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	1	no	—
919	C₄	—	5	2	no	—
920	C₄	—	10	1	no	—
921	C₄	—	10	2	no	—
922	C₄	—	20	1	no	—
923	C₄	—	20	1	no	—
924	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
925	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
926	C₃	#10611959	1	1	yes	characteristic, direct product factor, Sylow
927	C₂	—	4	1	no	—
928	C₂	—	4	2	no	—
929	C₂	—	10	2	no	—
930	C₂	—	10	2	no	—
931	C₂	—	20	2	no	—
932	C₂	C₃×D₅×#120	1	1	yes	characteristic
933	C₂	C₃×#66102	1	1	yes	characteristic
934	C₂	C₃×D₅×#137	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×#452	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×D₅×#41	C₂
hypercenter	C₃×#452	D₅
hypocenter	C₅	C₃×#3007
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#452

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4064	C₂	semidirect
3. C₂×C₃×#4061	C₂	semidirect
4. C₃×D₅×C₂²⋊Q₈	C₂	semidirect
5. C₃×C₅×#452	C₂	semidirect
6. C₃×#65528	C₂	semidirect
7. C₃×#65475	C₂	semidirect
8. C₃×#65458	C₂	semidirect
9. C₃×#65336	C₂	semidirect
10. C₃×#65097	C₂	semidirect
11. C₃×#65092	C₂	semidirect
12. C₃×#65065	C₂	semidirect
13. C₃×#65060	C₂	semidirect
14. C₃×#65022	C₂	semidirect
15. C₃×#65015	C₂	semidirect
16. #10611959	C₃	direct (N × H)
22. C₂×C₃×Q₈×D₅	C₂²	semidirect
31. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
32. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
33. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
35. C₂×C₃×#689	C₂²	semidirect
36. C₂×C₃×#689	C₂²	semidirect
37. C₂×C₃×#688	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×#676	C₂²	semidirect
49. C₃×D₅×C₄⋊C₄	C₂²	semidirect
52. C₃×C₅×#103	C₂²	semidirect
53. C₃×C₅×#102	C₂²	semidirect
54. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
55. C₃×#3967	C₂²	semidirect
56. C₃×#3964	C₂²	semidirect
57. C₃×C₂²⋊#168	C₂²	semidirect
58. C₃×#3953	C₂²	semidirect
61. C₃×#3948	C₂²	semidirect
62. C₃×#3942	C₂²	semidirect
63. C₃×#3941	C₂²	semidirect
66. C₂×#4064	C₂×C₃	semidirect
67. C₂×#4061	C₂×C₃	semidirect
68. D₅×C₂²⋊Q₈	C₂×C₃	semidirect
69. C₅×#452	C₂×C₃	semidirect
70. #65528	C₂×C₃	semidirect
71. #65475	C₂×C₃	semidirect
72. #65458	C₂×C₃	semidirect
73. #65336	C₂×C₃	semidirect
74. #65097	C₂×C₃	semidirect
75. #65092	C₂×C₃	semidirect
76. #65065	C₂×C₃	semidirect
77. #65060	C₂×C₃	semidirect
78. #65022	C₂×C₃	semidirect
79. #65015	C₂×C₃	semidirect
160. C₃×#452	D₅	semidirect
173. C₂×Q₈×D₅	C₂²×C₃	semidirect
182. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
183. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
184. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
186. C₂×#689	C₂²×C₃	semidirect
187. C₂×#689	C₂²×C₃	semidirect
188. C₂×#688	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×#676	C₂²×C₃	semidirect
200. D₅×C₄⋊C₄	C₂²×C₃	semidirect
203. C₅×#103	C₂²×C₃	semidirect
204. C₅×#102	C₂²×C₃	semidirect
205. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
206. #3967	C₂²×C₃	semidirect
207. #3964	C₂²×C₃	semidirect
208. C₂²⋊#168	C₂²×C₃	semidirect
209. #3953	C₂²×C₃	semidirect
212. #3948	C₂²×C₃	semidirect
213. #3942	C₂²×C₃	semidirect
214. #3941	C₂²×C₃	semidirect
295. C₂×C₃×Q₁₆	C₂×D₅	semidirect
299. C₂×C₃×SD₁₆	C₂×D₅	semidirect
307. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
314. C₃×#103	C₂×D₅	semidirect
318. C₃×#102	C₂×D₅	semidirect
322. C₃×C₂²⋊C₈	C₂×D₅	semidirect
403. #452	C₃×D₅	semidirect
428. C₂×C₃×D₅	#137	semidirect
592. C₂×Q₁₆	C₂×C₃×D₅	semidirect
596. C₂×SD₁₆	C₂×C₃×D₅	semidirect
604. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
611. #103	C₂×C₃×D₅	semidirect
615. #102	C₂×C₃×D₅	semidirect
619. C₂²⋊C₈	C₂×C₃×D₅	semidirect
705. C₂×D₅	C₃×#137	semidirect
790. C₃×C₅	#3007	semidirect
896. C₅	C₃×#3007	semidirect
926. C₃	#10611959	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
C₂×C₃×#4064	2
C₂×C₃×#4061	2
C₃×D₅×C₂²⋊Q₈	2
C₃×C₅×#452	2
C₃×#65528	2
C₃×#65475	2
C₃×#65458	2
C₃×#65336	2
C₃×#65097	2
C₃×#65092	2
C₃×#65065	2
C₃×#65060	2
C₃×#65022	2
C₃×#65015	2
#10611959	3
C₃×#3007	5

Subgroups — C3×#10611959 #14424100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611959 #14424100