Subgroups — C₃×#10611214 #14415673

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#676	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65417	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₈×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65300	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65126	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65125	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65018	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65015	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65015	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65014	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#64996	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#64995	C₂	1	1	yes	maximal, characteristic, complemented
16	#10611214	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×D₄×D₅	C₄	1	1	yes	characteristic
18	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₃×D₄×Dic₅	C₄	1	1	yes	characteristic
24	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
25	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×#681	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₃×#168	C₂²	1	1	yes	characteristic, complemented
28	C₃×D₅×M₁₆	—	2	4	no	—
29	C₂×C₃×#676	—	2	4	no	—
30	C₂×C₃×#676	C₂²	1	1	yes	characteristic
31	C₂×C₃×#676	C₂²	1	1	yes	characteristic
32	C₂×C₃×#676	C₂²	1	1	yes	characteristic
33	C₂×C₃×#676	C₂²	1	1	yes	characteristic
34	C₂×C₃×#676	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×#676	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic, complemented
38	C₃×#4039	C₄	1	1	yes	characteristic
39	C₃×D₅×C₄⋊C₄	C₄	1	1	yes	characteristic
40	C₃×#4027	C₄	1	1	yes	characteristic
41	C₃×#4027	C₄	1	1	yes	characteristic
42	C₃×D₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
43	C₃×D₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
44	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
45	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic, complemented
52	C₃×#3952	C₂²	1	1	yes	characteristic, complemented
53	C₃×#3952	C₂²	1	1	yes	characteristic, complemented
54	C₃×#3952	C₂²	1	1	yes	characteristic, complemented
55	C₃×#3952	C₂²	1	1	yes	characteristic, complemented
56	C₃×#3946	C₂²	1	1	yes	characteristic, complemented
57	C₃×#3946	C₂²	1	1	yes	characteristic, complemented
58	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
60	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
61	C₃×#3935	C₂²	1	1	yes	characteristic, complemented
62	C₃×D₄×M₁₆	—	5	1	no	maximal, Hall
63	C₂×D₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂²×#676	C₂×C₃	1	1	yes	characteristic, complemented
65	C₄×D₄×D₅	C₂×C₃	1	1	yes	characteristic
66	C₅×#435	C₂×C₃	1	1	yes	characteristic, complemented
67	#65417	C₂×C₃	1	1	yes	characteristic, complemented
68	C₈×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
69	#65300	C₂×C₃	1	1	yes	characteristic, complemented
70	#65126	C₂×C₃	1	1	yes	characteristic, complemented
71	#65125	C₂×C₃	1	1	yes	characteristic, complemented
72	#65018	C₂×C₃	1	1	yes	characteristic, complemented
73	#65015	C₂×C₃	1	1	yes	characteristic, complemented
74	#65015	C₂×C₃	1	1	yes	characteristic, complemented
75	#65014	C₂×C₃	1	1	yes	characteristic, complemented
76	#64996	C₂×C₃	1	1	yes	characteristic, complemented
77	#64995	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
80	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
84	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
87	C₃×D₄×D₅	—	2	4	no	—
88	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×D₅	—	2	2	no	—
90	C₂×C₃×C₄×D₅	—	2	2	no	—
91	C₂×C₃×C₄×D₅	—	2	2	no	—
92	C₂×C₃×C₄×D₅	—	2	2	no	—
93	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
102	C₃×C₅×M₁₆	—	2	2	no	—
103	C₂×C₃×C₅×C₈	—	2	2	no	—
104	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
108	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
113	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
114	C₃×#685	C₂×C₄	1	1	yes	characteristic
115	C₃×#685	C₂×C₄	1	1	yes	characteristic
116	C₃×#685	C₂×C₄	1	1	yes	characteristic
117	C₃×#685	C₂×C₄	1	1	yes	characteristic
118	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
119	C₃×#683	C₂×C₄	1	1	yes	characteristic
120	C₃×#683	C₂×C₄	1	1	yes	characteristic
121	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
122	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
123	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
124	C₃×#681	—	2	2	no	—
125	C₂×C₃×#168	—	2	2	no	—
126	C₂×C₃×#168	C₂³	1	1	yes	characteristic
127	C₂×C₃×#168	C₂³	1	1	yes	characteristic
128	C₂×C₃×#168	C₂³	1	1	yes	characteristic
129	C₂×C₃×#168	C₂³	1	1	yes	characteristic
130	C₃×#676	—	2	2	no	—
131	C₃×#676	—	2	2	no	—
132	C₃×#676	—	2	2	no	—
133	C₃×#676	—	2	2	no	—
134	C₃×#676	—	2	2	no	—
135	C₃×#676	D₄	1	4	yes	complemented
136	C₃×C₈×D₅	—	2	2	no	—
137	C₃×C₈×D₅	—	2	2	no	—
138	C₂²×C₃×M₁₆	—	5	1	no	—
139	C₂²×C₃×M₁₆	—	5	1	no	—
140	C₂×C₃×C₄×D₄	—	5	1	no	—
141	C₃×#436	—	5	1	no	—
142	C₃×#436	—	5	1	no	—
143	C₃×#435	—	5	1	no	—
144	C₃×#435	—	5	1	no	—
145	C₃×#435	—	5	1	no	—
146	C₃×#435	D₅	1	1	yes	characteristic, complemented
147	C₃×C₈×D₄	—	5	1	no	—
148	C₃×C₈×D₄	—	5	1	no	—
149	C₃×#423	—	5	1	no	—
150	C₃×#407	—	5	1	no	—
151	C₃×#407	—	5	1	no	—
152	C₃×C₄×M₁₆	—	5	1	no	—
153	C₂×D₄×D₅	C₃×C₄	1	1	yes	characteristic
154	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
155	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
157	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
159	D₄×Dic₅	C₃×C₄	1	1	yes	characteristic
160	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
161	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
162	C₂×#681	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₂²×#168	C₂²×C₃	1	1	yes	characteristic, complemented
164	D₅×M₁₆	—	2	4	no	—
165	C₂×#676	—	2	4	no	—
166	C₂×#676	C₂²×C₃	1	1	yes	characteristic
167	C₂×#676	C₂²×C₃	1	1	yes	characteristic
168	C₂×#676	C₂²×C₃	1	1	yes	characteristic
169	C₂×#676	C₂²×C₃	1	1	yes	characteristic
170	C₂×#676	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₂×#676	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
174	#4039	C₃×C₄	1	1	yes	characteristic
175	D₅×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
176	#4027	C₃×C₄	1	1	yes	characteristic
177	#4027	C₃×C₄	1	1	yes	characteristic
178	D₅×C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic
179	D₅×C₂²⋊C₄	C₃×C₄	1	1	yes	characteristic
180	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
181	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
182	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
186	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
188	#3952	C₂²×C₃	1	1	yes	characteristic, complemented
189	#3952	C₂²×C₃	1	1	yes	characteristic, complemented
190	#3952	C₂²×C₃	1	1	yes	characteristic, complemented
191	#3952	C₂²×C₃	1	1	yes	characteristic, complemented
192	#3946	C₂²×C₃	1	1	yes	characteristic, complemented
193	#3946	C₂²×C₃	1	1	yes	characteristic, complemented
194	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
195	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
196	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
197	#3935	C₂²×C₃	1	1	yes	characteristic, complemented
198	D₄×M₁₆	—	5	1	no	Sylow
199	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
200	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₃×D₅	—	2	2	no	—
202	C₂²×C₃×D₅	—	2	2	no	—
203	C₂²×C₃×D₅	—	2	2	no	—
204	C₂²×C₃×D₅	—	2	2	no	—
205	C₂²×C₃×D₅	—	4	1	no	—
206	C₂²×C₃×D₅	—	4	1	no	—
207	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
210	C₃×C₅×D₄	—	2	2	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	1	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
220	C₃×C₂²⋊D₅	—	2	2	no	—
221	C₃×C₂²⋊D₅	M₁₆	1	4	yes	complemented
222	C₂×C₃×Dic₅	—	2	2	no	—
223	C₂×C₃×Dic₅	—	2	2	no	—
224	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
225	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
226	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
227	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
228	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
229	C₃×D₂₀	—	2	2	no	—
230	C₃×C₄×D₅	—	2	2	no	—
231	C₃×C₄×D₅	—	2	2	no	—
232	C₃×C₄×D₅	—	2	1	no	—
233	C₃×C₄×D₅	—	2	1	no	—
234	C₃×C₄×D₅	—	2	1	no	—
235	C₃×C₄×D₅	—	2	1	no	—
236	C₃×C₄×D₅	—	2	2	no	—
237	C₃×C₄×D₅	—	2	2	no	—
238	C₃×C₄×D₅	—	2	2	no	—
239	C₃×C₄×D₅	—	4	1	no	—
240	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
241	C₃×C₄×D₅	#41	1	2	yes	—
242	C₃×C₅×C₈	—	2	1	no	—
243	C₃×C₅×C₈	—	2	1	no	—
244	C₃×C₅×C₈	—	2	1	no	—
245	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
246	C₃×#168	—	2	1	no	—
247	C₃×#168	—	2	1	no	—
248	C₃×#168	—	2	1	no	—
249	C₃×#168	C₂×D₄	1	2	yes	complemented
250	C₂²×C₃×D₄	—	5	1	no	—
251	C₂³×C₃×C₄	—	5	1	no	—
252	C₂³×C₃×C₄	—	5	1	no	—
253	C₂×C₃×M₁₆	—	5	1	no	—
254	C₂×C₃×M₁₆	—	5	1	no	—
255	C₂×C₃×M₁₆	—	5	1	no	—
256	C₂×C₃×M₁₆	—	5	1	no	—
257	C₂×C₃×M₁₆	—	5	1	no	—
258	C₂×C₃×M₁₆	—	5	1	no	—
259	C₂×C₃×M₁₆	—	5	1	no	—
260	C₂×C₃×M₁₆	—	10	4	no	—
261	C₂×C₃×M₁₆	—	10	4	no	—
262	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
263	C₂²×C₃×C₈	—	5	1	no	—
264	C₂²×C₃×C₈	—	5	1	no	—
265	C₂²×C₃×C₈	—	5	1	no	—
266	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
267	C₃×C₄×D₄	—	5	1	no	—
268	C₃×C₄×D₄	—	5	1	no	—
269	C₃×C₄×D₄	—	5	1	no	—
270	C₃×C₄×D₄	—	5	1	no	—
271	C₃×C₄×D₄	—	5	1	no	—
272	C₃×C₄×D₄	—	5	1	no	—
273	C₃×C₄×D₄	—	5	1	no	—
274	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
275	C₂×C₃×C₄⋊C₄	—	5	1	no	—
276	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
277	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
278	C₂×C₃×C₄²	—	5	1	no	—
279	C₃×C₄⋊C₈	—	5	1	no	—
280	C₃×C₄⋊C₈	—	5	1	no	—
281	C₃×C₄⋊C₈	—	5	1	no	—
282	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
283	C₃×C₂²⋊C₈	—	5	1	no	—
284	C₃×C₂²⋊C₈	—	5	1	no	—
285	C₃×C₂²⋊C₈	—	5	1	no	—
286	C₃×C₂²⋊C₈	—	5	1	no	—
287	C₃×C₂²⋊C₈	—	5	1	no	—
288	C₃×C₂²⋊C₈	—	5	1	no	—
289	C₃×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
290	C₃×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
291	C₃×#97	—	5	1	no	—
292	C₃×#97	C₂×D₅	1	1	yes	characteristic, complemented
293	C₃×C₄×C₈	—	5	1	no	—
294	C₃×C₄×C₈	—	5	1	no	—
295	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
296	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
297	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
299	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
300	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
301	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
302	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
303	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
304	D₄×D₅	—	2	4	no	—
305	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
306	C₂×C₄×D₅	—	2	2	no	—
307	C₂×C₄×D₅	—	2	2	no	—
308	C₂×C₄×D₅	—	2	2	no	—
309	C₂×C₄×D₅	—	2	2	no	—
310	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
311	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
312	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
313	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
314	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
315	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
316	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
317	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
318	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
319	C₅×M₁₆	—	2	2	no	—
320	C₂×C₅×C₈	—	2	2	no	—
321	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
322	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
323	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
324	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
325	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
326	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
327	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
328	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
329	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
330	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
331	#685	C₂×C₃×C₄	1	1	yes	characteristic
332	#685	C₂×C₃×C₄	1	1	yes	characteristic
333	#685	C₂×C₃×C₄	1	1	yes	characteristic
334	#685	C₂×C₃×C₄	1	1	yes	characteristic
335	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
336	#683	C₂×C₃×C₄	1	1	yes	characteristic
337	#683	C₂×C₃×C₄	1	1	yes	characteristic
338	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
339	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
340	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
341	#681	—	2	2	no	—
342	C₂×#168	—	2	2	no	—
343	C₂×#168	C₂³×C₃	1	1	yes	characteristic
344	C₂×#168	C₂³×C₃	1	1	yes	characteristic
345	C₂×#168	C₂³×C₃	1	1	yes	characteristic
346	C₂×#168	C₂³×C₃	1	1	yes	characteristic
347	#676	—	2	2	no	—
348	#676	—	2	2	no	—
349	#676	—	2	2	no	—
350	#676	—	2	2	no	—
351	#676	—	2	2	no	—
352	#676	C₃×D₄	1	4	yes	complemented
353	C₈×D₅	—	2	2	no	—
354	C₈×D₅	—	2	2	no	—
355	C₂²×M₁₆	—	5	1	no	—
356	C₂²×M₁₆	—	5	1	no	—
357	C₂×C₄×D₄	—	5	1	no	—
358	#436	—	5	1	no	—
359	#436	—	5	1	no	—
360	#435	—	5	1	no	—
361	#435	—	5	1	no	—
362	#435	—	5	1	no	—
363	#435	C₃×D₅	1	1	yes	characteristic, complemented
364	C₈×D₄	—	5	1	no	—
365	C₈×D₄	—	5	1	no	—
366	#423	—	5	1	no	—
367	#407	—	5	1	no	—
368	#407	—	5	1	no	—
369	C₄×M₁₆	—	5	1	no	—
370	C₂²×C₃×C₅	—	2	1	no	—
371	C₂²×C₃×C₅	—	2	1	no	—
372	C₂²×C₃×C₅	—	2	1	no	—
373	C₂²×C₃×C₅	—	2	1	no	—
374	C₂²×C₃×C₅	—	2	1	no	—
375	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	complemented
376	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
377	C₂×C₃×D₅	—	2	1	no	—
378	C₂×C₃×D₅	—	2	1	no	—
379	C₂×C₃×D₅	—	2	1	no	—
380	C₂×C₃×D₅	—	2	1	no	—
381	C₂×C₃×D₅	—	2	1	no	—
382	C₂×C₃×D₅	—	2	1	no	—
383	C₂×C₃×D₅	—	2	1	no	—
384	C₂×C₃×D₅	—	4	4	no	—
385	C₂×C₃×D₅	—	4	4	no	—
386	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
387	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	complemented
388	C₃×C₄×C₅	—	2	1	no	—
389	C₃×C₄×C₅	—	2	1	no	—
390	C₃×C₄×C₅	—	2	1	no	—
391	C₃×C₄×C₅	—	2	1	no	—
392	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
393	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
394	C₃×Dic₅	—	2	1	no	—
395	C₃×Dic₅	—	2	1	no	—
396	C₃×Dic₅	—	2	1	no	—
397	C₃×Dic₅	C₄×D₄	1	2	yes	—
398	C₃×Dic₅	C₂×M₁₆	1	2	yes	complemented
399	C₂⁴×C₃	—	5	1	no	—
400	C₂⁴×C₃	—	5	1	no	—
401	C₂×C₃×D₄	—	5	1	no	—
402	C₂×C₃×D₄	—	5	1	no	—
403	C₂×C₃×D₄	—	5	1	no	—
404	C₂×C₃×D₄	—	10	4	no	—
405	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
406	C₂²×C₃×C₄	—	5	1	no	—
407	C₂²×C₃×C₄	—	5	1	no	—
408	C₂²×C₃×C₄	—	5	1	no	—
409	C₂²×C₃×C₄	—	5	1	no	—
410	C₂²×C₃×C₄	—	5	1	no	—
411	C₂²×C₃×C₄	—	5	1	no	—
412	C₂²×C₃×C₄	—	5	1	no	—
413	C₂²×C₃×C₄	—	5	1	no	—
414	C₂²×C₃×C₄	—	5	1	no	—
415	C₂²×C₃×C₄	—	5	1	no	—
416	C₂²×C₃×C₄	—	5	1	no	—
417	C₂²×C₃×C₄	—	10	2	no	—
418	C₂²×C₃×C₄	—	10	2	no	—
419	C₂²×C₃×C₄	—	10	2	no	—
420	C₂²×C₃×C₄	—	10	2	no	—
421	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
422	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
423	C₃×M₁₆	—	2	2	no	—
424	C₃×M₁₆	—	5	4	no	—
425	C₃×M₁₆	—	10	2	no	—
426	C₃×M₁₆	—	10	2	no	—
427	C₃×M₁₆	—	10	2	no	—
428	C₃×M₁₆	—	10	2	no	—
429	C₃×M₁₆	—	10	2	no	—
430	C₃×M₁₆	—	10	2	no	—
431	C₂×C₃×C₈	—	2	2	no	—
432	C₂×C₃×C₈	—	5	1	no	—
433	C₂×C₃×C₈	—	5	1	no	—
434	C₂×C₃×C₈	—	5	1	no	—
435	C₂×C₃×C₈	—	5	1	no	—
436	C₂×C₃×C₈	—	10	2	no	—
437	C₂×C₃×C₈	—	10	2	no	—
438	C₂×C₃×C₈	—	10	2	no	—
439	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
440	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
441	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
442	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
443	C₃×C₄⋊C₄	—	5	1	no	—
444	C₃×C₄⋊C₄	—	5	1	no	—
445	C₃×C₄⋊C₄	—	5	1	no	—
446	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
447	C₃×C₂²⋊C₄	—	5	1	no	—
448	C₃×C₂²⋊C₄	—	5	1	no	—
449	C₃×C₂²⋊C₄	—	5	1	no	—
450	C₃×C₂²⋊C₄	—	5	1	no	—
451	C₃×C₂²⋊C₄	—	5	1	no	—
452	C₃×C₂²⋊C₄	—	5	1	no	—
453	C₃×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
454	C₃×C₂²⋊C₄	C₄×D₅	1	1	yes	characteristic
455	C₃×C₄²	—	5	1	no	—
456	C₃×C₄²	—	5	1	no	—
457	C₃×C₄²	—	5	1	no	—
458	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
459	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
460	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
461	C₂²×D₅	—	2	2	no	—
462	C₂²×D₅	—	2	2	no	—
463	C₂²×D₅	—	2	2	no	—
464	C₂²×D₅	—	2	2	no	—
465	C₂²×D₅	—	4	1	no	—
466	C₂²×D₅	—	4	1	no	—
467	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
468	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
469	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
470	C₅×D₄	—	2	2	no	—
471	C₂×C₄×C₅	—	2	1	no	—
472	C₂×C₄×C₅	—	2	1	no	—
473	C₂×C₄×C₅	—	2	1	no	—
474	C₂×C₄×C₅	—	2	1	no	—
475	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
476	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
477	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
478	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
479	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
480	C₂²⋊D₅	—	2	2	no	—
481	C₂²⋊D₅	C₃×M₁₆	1	4	yes	complemented
482	C₂×Dic₅	—	2	2	no	—
483	C₂×Dic₅	—	2	2	no	—
484	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
485	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
486	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
487	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
488	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
489	D₂₀	—	2	2	no	—
490	C₄×D₅	—	2	2	no	—
491	C₄×D₅	—	2	2	no	—
492	C₄×D₅	—	2	1	no	—
493	C₄×D₅	—	2	1	no	—
494	C₄×D₅	—	2	1	no	—
495	C₄×D₅	—	2	1	no	—
496	C₄×D₅	—	2	2	no	—
497	C₄×D₅	—	2	2	no	—
498	C₄×D₅	—	2	2	no	—
499	C₄×D₅	—	4	1	no	—
500	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
501	C₄×D₅	C₃×#41	1	2	yes	—
502	C₅×C₈	—	2	1	no	—
503	C₅×C₈	—	2	1	no	—
504	C₅×C₈	—	2	1	no	—
505	C₅×C₈	C₂×C₃×D₄	1	2	yes	complemented
506	#168	—	2	1	no	—
507	#168	—	2	1	no	—
508	#168	—	2	1	no	—
509	#168	C₂×C₃×D₄	1	2	yes	complemented
510	C₂²×D₄	—	5	1	no	—
511	C₂³×C₄	—	5	1	no	—
512	C₂³×C₄	—	5	1	no	—
513	C₂×M₁₆	—	5	1	no	—
514	C₂×M₁₆	—	5	1	no	—
515	C₂×M₁₆	—	5	1	no	—
516	C₂×M₁₆	—	5	1	no	—
517	C₂×M₁₆	—	5	1	no	—
518	C₂×M₁₆	—	5	1	no	—
519	C₂×M₁₆	—	5	1	no	—
520	C₂×M₁₆	—	10	4	no	—
521	C₂×M₁₆	—	10	4	no	—
522	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
523	C₂²×C₈	—	5	1	no	—
524	C₂²×C₈	—	5	1	no	—
525	C₂²×C₈	—	5	1	no	—
526	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
527	C₄×D₄	—	5	1	no	—
528	C₄×D₄	—	5	1	no	—
529	C₄×D₄	—	5	1	no	—
530	C₄×D₄	—	5	1	no	—
531	C₄×D₄	—	5	1	no	—
532	C₄×D₄	—	5	1	no	—
533	C₄×D₄	—	5	1	no	—
534	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
535	C₂×C₄⋊C₄	—	5	1	no	—
536	C₂×C₂²⋊C₄	—	5	1	no	—
537	C₂×C₂²⋊C₄	—	5	1	no	—
538	C₂×C₄²	—	5	1	no	—
539	C₄⋊C₈	—	5	1	no	—
540	C₄⋊C₈	—	5	1	no	—
541	C₄⋊C₈	—	5	1	no	—
542	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
543	C₂²⋊C₈	—	5	1	no	—
544	C₂²⋊C₈	—	5	1	no	—
545	C₂²⋊C₈	—	5	1	no	—
546	C₂²⋊C₈	—	5	1	no	—
547	C₂²⋊C₈	—	5	1	no	—
548	C₂²⋊C₈	—	5	1	no	—
549	C₂²⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
550	C₂²⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
551	#97	—	5	1	no	—
552	#97	C₂×C₃×D₅	1	1	yes	characteristic, complemented
553	C₄×C₈	—	5	1	no	—
554	C₄×C₈	—	5	1	no	—
555	C₂×C₃×C₅	—	2	2	no	—
556	C₂×C₃×C₅	—	4	1	no	—
557	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
558	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
559	C₂×C₃×C₅	#568	1	1	yes	characteristic
560	C₃×D₅	—	2	2	no	—
561	C₃×D₅	—	2	2	no	—
562	C₃×D₅	—	4	1	no	—
563	C₂³×C₃	—	5	1	no	—
564	C₂³×C₃	—	5	1	no	—
565	C₂³×C₃	—	5	1	no	—
566	C₂³×C₃	—	10	2	no	—
567	C₂³×C₃	—	10	2	no	—
568	C₂³×C₃	—	10	2	no	—
569	C₂³×C₃	—	10	2	no	—
570	C₂³×C₃	—	20	1	no	—
571	C₂³×C₃	—	20	1	no	—
572	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
573	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
574	C₃×D₄	—	2	2	no	—
575	C₃×D₄	—	5	4	no	—
576	C₃×D₄	—	10	2	no	—
577	C₃×D₄	—	10	2	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	2	1	no	—
581	C₂×C₃×C₄	—	2	1	no	—
582	C₂×C₃×C₄	—	5	1	no	—
583	C₂×C₃×C₄	—	5	1	no	—
584	C₂×C₃×C₄	—	5	2	no	—
585	C₂×C₃×C₄	—	5	2	no	—
586	C₂×C₃×C₄	—	5	1	no	—
587	C₂×C₃×C₄	—	5	1	no	—
588	C₂×C₃×C₄	—	5	1	no	—
589	C₂×C₃×C₄	—	10	2	no	—
590	C₂×C₃×C₄	—	10	2	no	—
591	C₂×C₃×C₄	—	10	2	no	—
592	C₂×C₃×C₄	—	10	2	no	—
593	C₂×C₃×C₄	—	10	2	no	—
594	C₂×C₃×C₄	—	10	2	no	—
595	C₂×C₃×C₄	—	10	2	no	—
596	C₂×C₃×C₄	—	10	1	no	—
597	C₂×C₃×C₄	—	10	1	no	—
598	C₂×C₃×C₄	—	10	1	no	—
599	C₂×C₃×C₄	—	10	1	no	—
600	C₂×C₃×C₄	—	20	1	no	—
601	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
602	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
603	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
604	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
605	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
606	C₃×C₈	—	2	1	no	—
607	C₃×C₈	—	2	1	no	—
608	C₃×C₈	—	2	1	no	—
609	C₃×C₈	—	5	2	no	—
610	C₃×C₈	—	10	1	no	—
611	C₃×C₈	—	10	1	no	—
612	C₃×C₈	—	10	1	no	—
613	C₃×C₈	D₄×D₅	1	2	yes	complemented
614	C₂²×C₅	—	2	1	no	—
615	C₂²×C₅	—	2	1	no	—
616	C₂²×C₅	—	2	1	no	—
617	C₂²×C₅	—	2	1	no	—
618	C₂²×C₅	—	2	1	no	—
619	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	complemented
620	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
621	C₂×D₅	—	2	1	no	—
622	C₂×D₅	—	2	1	no	—
623	C₂×D₅	—	2	1	no	—
624	C₂×D₅	—	2	1	no	—
625	C₂×D₅	—	2	1	no	—
626	C₂×D₅	—	2	1	no	—
627	C₂×D₅	—	2	1	no	—
628	C₂×D₅	—	4	4	no	—
629	C₂×D₅	—	4	4	no	—
630	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
631	C₂×D₅	C₂×C₃×M₁₆	1	2	yes	complemented
632	C₄×C₅	—	2	1	no	—
633	C₄×C₅	—	2	1	no	—
634	C₄×C₅	—	2	1	no	—
635	C₄×C₅	—	2	1	no	—
636	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
637	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
638	Dic₅	—	2	1	no	—
639	Dic₅	—	2	1	no	—
640	Dic₅	—	2	1	no	—
641	Dic₅	C₃×C₄×D₄	1	2	yes	—
642	Dic₅	C₂×C₃×M₁₆	1	2	yes	complemented
643	C₂⁴	—	5	1	no	—
644	C₂⁴	—	5	1	no	—
645	C₂×D₄	—	5	1	no	—
646	C₂×D₄	—	5	1	no	—
647	C₂×D₄	—	5	1	no	—
648	C₂×D₄	—	10	4	no	—
649	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic
650	C₂²×C₄	—	5	1	no	—
651	C₂²×C₄	—	5	1	no	—
652	C₂²×C₄	—	5	1	no	—
653	C₂²×C₄	—	5	1	no	—
654	C₂²×C₄	—	5	1	no	—
655	C₂²×C₄	—	5	1	no	—
656	C₂²×C₄	—	5	1	no	—
657	C₂²×C₄	—	5	1	no	—
658	C₂²×C₄	—	5	1	no	—
659	C₂²×C₄	—	5	1	no	—
660	C₂²×C₄	—	5	1	no	—
661	C₂²×C₄	—	10	2	no	—
662	C₂²×C₄	—	10	2	no	—
663	C₂²×C₄	—	10	2	no	—
664	C₂²×C₄	—	10	2	no	—
665	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
666	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
667	M₁₆	—	2	2	no	—
668	M₁₆	—	5	4	no	—
669	M₁₆	—	10	2	no	—
670	M₁₆	—	10	2	no	—
671	M₁₆	—	10	2	no	—
672	M₁₆	—	10	2	no	—
673	M₁₆	—	10	2	no	—
674	M₁₆	—	10	2	no	—
675	C₂×C₈	—	2	2	no	—
676	C₂×C₈	—	5	1	no	—
677	C₂×C₈	—	5	1	no	—
678	C₂×C₈	—	5	1	no	—
679	C₂×C₈	—	5	1	no	—
680	C₂×C₈	—	10	2	no	—
681	C₂×C₈	—	10	2	no	—
682	C₂×C₈	—	10	2	no	—
683	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
684	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
685	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
686	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
687	C₄⋊C₄	—	5	1	no	—
688	C₄⋊C₄	—	5	1	no	—
689	C₄⋊C₄	—	5	1	no	—
690	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
691	C₂²⋊C₄	—	5	1	no	—
692	C₂²⋊C₄	—	5	1	no	—
693	C₂²⋊C₄	—	5	1	no	—
694	C₂²⋊C₄	—	5	1	no	—
695	C₂²⋊C₄	—	5	1	no	—
696	C₂²⋊C₄	—	5	1	no	—
697	C₂²⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
698	C₂²⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
699	C₄²	—	5	1	no	—
700	C₄²	—	5	1	no	—
701	C₄²	—	5	1	no	—
702	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
703	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
704	C₂²×C₃	—	2	1	no	—
705	C₂²×C₃	—	2	1	no	—
706	C₂²×C₃	—	2	1	no	—
707	C₂²×C₃	—	2	1	no	—
708	C₂²×C₃	—	2	1	no	—
709	C₂²×C₃	—	5	2	no	—
710	C₂²×C₃	—	5	2	no	—
711	C₂²×C₃	—	10	1	no	—
712	C₂²×C₃	—	10	1	no	—
713	C₂²×C₃	—	10	1	no	—
714	C₂²×C₃	—	10	1	no	—
715	C₂²×C₃	—	10	1	no	—
716	C₂²×C₃	—	10	1	no	—
717	C₂²×C₃	—	10	1	no	—
718	C₂²×C₃	—	20	4	no	—
719	C₂²×C₃	—	20	4	no	—
720	C₂²×C₃	D₅×M₁₆	1	2	yes	complemented
721	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
722	C₃×C₄	—	2	1	no	—
723	C₃×C₄	—	2	1	no	—
724	C₃×C₄	—	2	1	no	—
725	C₃×C₄	—	2	1	no	—
726	C₃×C₄	—	5	2	no	—
727	C₃×C₄	—	5	2	no	—
728	C₃×C₄	—	10	1	no	—
729	C₃×C₄	—	10	1	no	—
730	C₃×C₄	—	10	1	no	—
731	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
732	C₃×C₄	D₅×#41	1	1	yes	characteristic
733	C₂×C₅	—	2	2	no	—
734	C₂×C₅	—	4	1	no	—
735	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
736	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
737	C₂×C₅	C₃×#568	1	1	yes	characteristic
738	D₅	—	2	2	no	—
739	D₅	—	2	2	no	—
740	D₅	—	4	1	no	—
741	C₂³	—	5	1	no	—
742	C₂³	—	5	1	no	—
743	C₂³	—	5	1	no	—
744	C₂³	—	10	2	no	—
745	C₂³	—	10	2	no	—
746	C₂³	—	10	2	no	—
747	C₂³	—	10	2	no	—
748	C₂³	—	20	1	no	—
749	C₂³	—	20	1	no	—
750	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
751	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
752	D₄	—	2	2	no	—
753	D₄	—	5	4	no	—
754	D₄	—	10	2	no	—
755	D₄	—	10	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	5	1	no	—
761	C₂×C₄	—	5	1	no	—
762	C₂×C₄	—	5	2	no	—
763	C₂×C₄	—	5	2	no	—
764	C₂×C₄	—	5	1	no	—
765	C₂×C₄	—	5	1	no	—
766	C₂×C₄	—	5	1	no	—
767	C₂×C₄	—	10	2	no	—
768	C₂×C₄	—	10	2	no	—
769	C₂×C₄	—	10	2	no	—
770	C₂×C₄	—	10	2	no	—
771	C₂×C₄	—	10	2	no	—
772	C₂×C₄	—	10	2	no	—
773	C₂×C₄	—	10	2	no	—
774	C₂×C₄	—	10	1	no	—
775	C₂×C₄	—	10	1	no	—
776	C₂×C₄	—	10	1	no	—
777	C₂×C₄	—	10	1	no	—
778	C₂×C₄	—	20	1	no	—
779	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
780	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
781	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
782	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
783	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
784	C₈	—	2	1	no	—
785	C₈	—	2	1	no	—
786	C₈	—	2	1	no	—
787	C₈	—	5	2	no	—
788	C₈	—	10	1	no	—
789	C₈	—	10	1	no	—
790	C₈	—	10	1	no	—
791	C₈	C₃×D₄×D₅	1	2	yes	complemented
792	C₂×C₃	—	2	2	no	—
793	C₂×C₃	—	4	1	no	—
794	C₂×C₃	—	10	2	no	—
795	C₂×C₃	—	10	2	no	—
796	C₂×C₃	—	20	1	no	—
797	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
798	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
799	C₂×C₃	#66084	1	1	yes	characteristic
800	C₅	C₃×D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	5	2	no	—
807	C₂²	—	5	2	no	—
808	C₂²	—	10	1	no	—
809	C₂²	—	10	1	no	—
810	C₂²	—	10	1	no	—
811	C₂²	—	10	1	no	—
812	C₂²	—	10	1	no	—
813	C₂²	—	10	1	no	—
814	C₂²	—	10	1	no	—
815	C₂²	—	20	4	no	—
816	C₂²	—	20	4	no	—
817	C₂²	C₃×D₅×M₁₆	1	2	yes	complemented
818	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	1	no	—
823	C₄	—	5	2	no	—
824	C₄	—	5	2	no	—
825	C₄	—	10	1	no	—
826	C₄	—	10	1	no	—
827	C₄	—	10	1	no	—
828	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
829	C₄	C₃×D₅×#41	1	1	yes	characteristic
830	C₃	#10611214	1	1	yes	characteristic, direct product factor, Sylow
831	C₂	—	2	2	no	—
832	C₂	—	4	1	no	—
833	C₂	—	10	2	no	—
834	C₂	—	10	2	no	—
835	C₂	—	20	1	no	—
836	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
837	C₂	C₂×C₃×D₅×M₁₆	1	1	yes	characteristic
838	C₂	C₃×#66084	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#435	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×D₄×D₅	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#435	D₅
hypocenter	C₅	C₃×D₄×M₁₆
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#435

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×M₁₆	C₂	semidirect
2. C₂²×C₃×#676	C₂	semidirect
4. C₃×C₅×#435	C₂	semidirect
5. C₃×#65417	C₂	semidirect
6. C₃×C₈×C₂²⋊D₅	C₂	semidirect
7. C₃×#65300	C₂	semidirect
8. C₃×#65126	C₂	semidirect
9. C₃×#65125	C₂	semidirect
10. C₃×#65018	C₂	semidirect
11. C₃×#65015	C₂	semidirect
12. C₃×#65015	C₂	semidirect
13. C₃×#65014	C₂	semidirect
14. C₃×#64996	C₂	semidirect
15. C₃×#64995	C₂	semidirect
16. #10611214	C₃	direct (N × H)
20. C₂×C₃×C₅×M₁₆	C₂²	semidirect
21. C₂²×C₃×C₅×C₈	C₂²	semidirect
26. C₂×C₃×#681	C₂²	semidirect
27. C₂²×C₃×#168	C₂²	semidirect
34. C₂×C₃×#676	C₂²	semidirect
35. C₂×C₃×#676	C₂²	semidirect
36. C₂×C₃×C₈×D₅	C₂²	semidirect
37. C₂×C₃×C₈×D₅	C₂²	semidirect
46. C₃×C₅×C₄⋊C₈	C₂²	semidirect
47. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
48. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
49. C₃×C₅×#97	C₂²	semidirect
50. C₃×C₂²⋊#168	C₂²	semidirect
51. C₃×C₂²⋊#168	C₂²	semidirect
52. C₃×#3952	C₂²	semidirect
53. C₃×#3952	C₂²	semidirect
54. C₃×#3952	C₂²	semidirect
55. C₃×#3952	C₂²	semidirect
56. C₃×#3946	C₂²	semidirect
57. C₃×#3946	C₂²	semidirect
58. C₃×C₈×Dic₅	C₂²	semidirect
59. C₃×C₈×Dic₅	C₂²	semidirect
60. C₃×C₄⋊#168	C₂²	semidirect
61. C₃×#3935	C₂²	semidirect
63. C₂×D₅×M₁₆	C₂×C₃	semidirect
64. C₂²×#676	C₂×C₃	semidirect
66. C₅×#435	C₂×C₃	semidirect
67. #65417	C₂×C₃	semidirect
68. C₈×C₂²⋊D₅	C₂×C₃	semidirect
69. #65300	C₂×C₃	semidirect
70. #65126	C₂×C₃	semidirect
71. #65125	C₂×C₃	semidirect
72. #65018	C₂×C₃	semidirect
73. #65015	C₂×C₃	semidirect
74. #65015	C₂×C₃	semidirect
75. #65014	C₂×C₃	semidirect
76. #64996	C₂×C₃	semidirect
77. #64995	C₂×C₃	semidirect
135. C₃×#676	D₄	semidirect
146. C₃×#435	D₅	semidirect
156. C₂×C₅×M₁₆	C₂²×C₃	semidirect
157. C₂²×C₅×C₈	C₂²×C₃	semidirect
162. C₂×#681	C₂²×C₃	semidirect
163. C₂²×#168	C₂²×C₃	semidirect
170. C₂×#676	C₂²×C₃	semidirect
171. C₂×#676	C₂²×C₃	semidirect
172. C₂×C₈×D₅	C₂²×C₃	semidirect
173. C₂×C₈×D₅	C₂²×C₃	semidirect
182. C₅×C₄⋊C₈	C₂²×C₃	semidirect
183. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
184. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
185. C₅×#97	C₂²×C₃	semidirect
186. C₂²⋊#168	C₂²×C₃	semidirect
187. C₂²⋊#168	C₂²×C₃	semidirect
188. #3952	C₂²×C₃	semidirect
189. #3952	C₂²×C₃	semidirect
190. #3952	C₂²×C₃	semidirect
191. #3952	C₂²×C₃	semidirect
192. #3946	C₂²×C₃	semidirect
193. #3946	C₂²×C₃	semidirect
194. C₈×Dic₅	C₂²×C₃	semidirect
195. C₈×Dic₅	C₂²×C₃	semidirect
196. C₄⋊#168	C₂²×C₃	semidirect
197. #3935	C₂²×C₃	semidirect
221. C₃×C₂²⋊D₅	M₁₆	semidirect
245. C₃×C₅×C₈	C₂×D₄	semidirect
249. C₃×#168	C₂×D₄	semidirect
262. C₂×C₃×M₁₆	C₂×D₅	semidirect
266. C₂²×C₃×C₈	C₂×D₅	semidirect
282. C₃×C₄⋊C₈	C₂×D₅	semidirect
289. C₃×C₂²⋊C₈	C₂×D₅	semidirect
290. C₃×C₂²⋊C₈	C₂×D₅	semidirect
292. C₃×#97	C₂×D₅	semidirect
352. #676	C₃×D₄	semidirect
363. #435	C₃×D₅	semidirect
375. C₂²×C₃×C₅	C₂×M₁₆	semidirect
387. C₂×C₃×D₅	C₂×M₁₆	semidirect
398. C₃×Dic₅	C₂×M₁₆	semidirect
481. C₂²⋊D₅	C₃×M₁₆	semidirect
505. C₅×C₈	C₂×C₃×D₄	semidirect
509. #168	C₂×C₃×D₄	semidirect
522. C₂×M₁₆	C₂×C₃×D₅	semidirect
526. C₂²×C₈	C₂×C₃×D₅	semidirect
542. C₄⋊C₈	C₂×C₃×D₅	semidirect
549. C₂²⋊C₈	C₂×C₃×D₅	semidirect
550. C₂²⋊C₈	C₂×C₃×D₅	semidirect
552. #97	C₂×C₃×D₅	semidirect
613. C₃×C₈	D₄×D₅	semidirect
619. C₂²×C₅	C₂×C₃×M₁₆	semidirect
631. C₂×D₅	C₂×C₃×M₁₆	semidirect
642. Dic₅	C₂×C₃×M₁₆	semidirect
703. C₃×C₅	D₄×M₁₆	semidirect
720. C₂²×C₃	D₅×M₁₆	semidirect
791. C₈	C₃×D₄×D₅	semidirect
800. C₅	C₃×D₄×M₁₆	semidirect
817. C₂²	C₃×D₅×M₁₆	semidirect
830. C₃	#10611214	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×M₁₆	2
C₂²×C₃×#676	2
C₃×C₄×D₄×D₅	2
C₃×C₅×#435	2
C₃×#65417	2
C₃×C₈×C₂²⋊D₅	2
C₃×#65300	2
C₃×#65126	2
C₃×#65125	2
C₃×#65018	2
C₃×#65015	2
C₃×#65014	2
C₃×#64996	2
C₃×#64995	2
#10611214	3
C₃×D₄×M₁₆	5

Subgroups — C3×#10611214 #14415673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611214 #14415673