Subgroups — C₃×#10617742 #14484142

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66163	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66158	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65915	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65914	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65912	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65902	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65890	C₂	1	2	yes	maximal, complemented
9	C₃×#65888	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65881	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65874	C₂	1	2	yes	maximal, complemented
13	C₃×#65873	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65872	C₂	1	2	yes	maximal, complemented
15	C₃×C₄×#711	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#65866	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#65865	C₂	1	2	yes	maximal, complemented
18	C₃×#65863	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#65861	C₂	1	2	yes	maximal, complemented
20	C₃×#65813	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×#65813	C₂	1	2	yes	maximal, complemented
22	C₃×C₄×#709	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×#4018	C₂	1	2	yes	maximal, complemented
24	#10617742	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
26	C₂×C₃×#711	C₂²	1	1	yes	characteristic
27	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×#709	C₂²	1	1	yes	characteristic
29	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
30	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
33	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
35	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
36	C₃×C₅×#117	C₂²	1	2	yes	complemented
37	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
39	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
40	C₃×#4093	C₂²	1	1	yes	characteristic
41	C₃×#4092	C₂²	1	1	yes	characteristic
42	C₃×#4092	C₂²	1	1	yes	characteristic, complemented
43	C₃×#4090	C₂²	1	1	yes	characteristic, complemented
44	C₃×#4085	C₂²	1	2	yes	—
45	C₃×#4085	C₂²	1	2	yes	complemented
46	C₃×#4083	C₂²	1	2	yes	—
47	C₃×#4081	C₂²	1	2	yes	complemented
48	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
49	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
50	C₃×#4076	C₂²	1	1	yes	characteristic
51	C₃×#4076	C₂²	1	2	yes	—
52	C₃×#4075	C₂²	1	2	yes	—
53	C₃×#4075	C₂²	1	2	yes	complemented
54	C₃×#4075	C₂²	1	2	yes	complemented
55	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
56	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
57	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
58	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
60	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
61	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃×#685	C₂²	1	2	yes	—
63	C₂×C₃×#685	C₂²	1	2	yes	—
64	C₃×#4072	C₂²	1	1	yes	characteristic, complemented
65	C₃×#4070	C₂²	1	1	yes	characteristic, complemented
66	C₃×#4070	C₂²	1	2	yes	complemented
67	C₂×C₃×#683	C₂²	1	2	yes	complemented
68	C₂×C₃×#683	C₂²	1	2	yes	complemented
69	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
70	C₃×#4044	C₂²	1	2	yes	complemented
71	C₃×#4044	C₂²	1	2	yes	complemented
72	C₃×#4043	C₂²	1	1	yes	characteristic
73	C₃×#4042	C₂²	1	2	yes	—
74	C₃×#4042	C₂²	1	2	yes	complemented
75	C₃×#4041	C₂²	1	1	yes	characteristic
76	C₃×#4040	C₂²	1	2	yes	—
77	C₃×#4040	C₂²	1	2	yes	complemented
78	C₃×#4039	C₂²	1	1	yes	characteristic
79	C₃×#4038	C₂²	1	1	yes	characteristic, complemented
80	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
81	C₃×#4036	C₂²	1	1	yes	characteristic, complemented
82	C₃×#4035	C₂²	1	2	yes	complemented
83	C₃×#4035	C₂²	1	2	yes	complemented
84	C₃×#4034	C₂²	1	1	yes	characteristic, complemented
85	C₃×#4033	C₂²	1	1	yes	characteristic, complemented
86	C₃×#4032	C₂²	1	2	yes	—
87	C₃×#4031	C₂²	1	2	yes	complemented
88	C₃×#4030	C₂²	1	2	yes	complemented
89	C₃×#4029	C₂²	1	2	yes	—
90	C₃×#4028	C₂²	1	2	yes	—
91	C₃×#4027	C₂²	1	2	yes	—
92	C₃×#4027	C₂²	1	2	yes	complemented
93	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
94	C₃×#4025	C₂²	1	2	yes	complemented
95	C₃×#4024	C₂²	1	2	yes	complemented
96	C₃×#4024	C₂²	1	2	yes	complemented
97	C₃×#4023	C₂²	1	2	yes	complemented
98	C₃×#4022	C₂²	1	2	yes	complemented
99	C₃×#4022	C₂²	1	2	yes	complemented
100	C₃×#4022	C₂²	1	2	yes	complemented
101	C₃×#4021	C₂²	1	1	yes	characteristic
102	C₃×#4021	C₂²	1	2	yes	complemented
103	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
104	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
105	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
106	C₃×C₄×D₂₀	C₂²	1	2	yes	complemented
107	C₃×#4018	C₂²	1	2	yes	—
108	C₃×#4018	C₂²	1	2	yes	—
109	C₃×#4018	C₂²	1	2	yes	—
110	C₃×#4018	C₂²	1	1	yes	characteristic
111	C₃×#4018	C₂²	1	2	yes	complemented
112	C₃×#4018	C₂²	1	2	yes	complemented
113	C₃×#4018	C₂²	1	2	yes	complemented
114	C₃×#4018	C₂²	1	2	yes	complemented
115	C₃×#4018	C₂²	1	1	yes	characteristic, complemented
116	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
117	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic, complemented
118	C₃×#4016	C₂²	1	2	yes	complemented
119	C₃×#4016	C₂²	1	1	yes	characteristic, complemented
120	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
121	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
122	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
123	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
124	C₃×#3475	—	5	1	no	maximal, Hall
125	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
126	#66163	C₂×C₃	1	1	yes	characteristic, complemented
127	#66158	C₂×C₃	1	1	yes	characteristic, complemented
128	#65915	C₂×C₃	1	1	yes	characteristic, complemented
129	#65914	C₂×C₃	1	1	yes	characteristic, complemented
130	#65912	C₂×C₃	1	1	yes	characteristic, complemented
131	#65902	C₂×C₃	1	1	yes	characteristic, complemented
132	#65890	C₂×C₃	1	2	yes	complemented
133	#65888	C₂×C₃	1	1	yes	characteristic, complemented
134	#65881	C₂×C₃	1	2	yes	complemented
135	C₄×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
136	#65874	C₂×C₃	1	2	yes	complemented
137	#65873	C₂×C₃	1	1	yes	characteristic, complemented
138	#65872	C₂×C₃	1	2	yes	complemented
139	C₄×#711	C₂×C₃	1	1	yes	characteristic, complemented
140	#65866	C₂×C₃	1	1	yes	characteristic, complemented
141	#65865	C₂×C₃	1	2	yes	complemented
142	#65863	C₂×C₃	1	1	yes	characteristic, complemented
143	#65861	C₂×C₃	1	2	yes	complemented
144	#65813	C₂×C₃	1	1	yes	characteristic, complemented
145	#65813	C₂×C₃	1	2	yes	complemented
146	C₄×#709	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂×#4018	C₂×C₃	1	2	yes	complemented
148	C₂³×C₃×D₅	C₂³	1	2	yes	—
149	C₃×C₅×#41	—	2	4	no	—
150	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
152	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
154	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
156	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
157	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
158	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₂²⋊D₅	C₂³	1	1	yes	characteristic
160	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
161	C₂×C₃×C₂²⋊D₅	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
163	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
164	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
165	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
166	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
167	C₃×#711	—	2	4	no	—
168	C₃×D₄×D₅	—	2	4	no	—
169	C₃×#709	—	2	4	no	—
170	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
171	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
172	C₂×C₃×D₂₀	C₂³	1	2	yes	—
173	C₂×C₃×C₄×D₅	—	2	8	no	—
174	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
177	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
178	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
179	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
183	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
184	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
185	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
186	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
194	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
195	C₃×C₄²×C₅	C₂³	1	2	yes	—
196	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
197	C₃×C₄²×C₅	C₂³	1	2	yes	—
198	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
199	C₃×C₄²×C₅	C₂³	1	2	yes	—
200	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
201	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
202	C₃×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
203	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
204	C₃×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
205	C₃×#685	C₂³	1	2	yes	—
206	C₃×#685	C₂³	1	2	yes	—
207	C₃×#685	C₂³	1	2	yes	—
208	C₃×#685	C₂³	1	2	yes	—
209	C₃×#685	C₂³	1	1	yes	characteristic
210	C₃×#685	C₂³	1	1	yes	characteristic
211	C₃×#685	C₂³	1	2	yes	—
212	C₃×#685	C₂³	1	2	yes	—
213	C₃×#685	C₂³	1	2	yes	—
214	C₃×#685	C₂³	1	2	yes	—
215	C₃×#685	C₂³	1	1	yes	characteristic
216	C₃×#685	C₂³	1	1	yes	characteristic
217	C₃×#685	C₂³	1	2	yes	—
218	C₃×#685	C₂³	1	2	yes	—
219	C₃×#685	C₂³	1	2	yes	—
220	C₃×#685	C₂³	1	2	yes	—
221	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
222	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
223	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
224	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
225	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
226	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
227	C₃×#683	C₂³	1	2	yes	—
228	C₃×#683	C₂³	1	2	yes	—
229	C₃×#683	C₂³	1	2	yes	—
230	C₃×#683	C₂³	1	2	yes	—
231	C₃×#683	C₂³	1	1	yes	characteristic
232	C₃×#683	C₂³	1	1	yes	characteristic
233	C₃×#683	C₂³	1	1	yes	characteristic
234	C₃×#683	C₂³	1	1	yes	characteristic
235	C₃×#683	C₂³	1	2	yes	—
236	C₃×#683	C₂³	1	2	yes	—
237	C₃×#683	C₂³	1	2	yes	—
238	C₃×#683	C₂³	1	2	yes	—
239	C₃×#683	C₂³	1	2	yes	—
240	C₃×#683	C₂³	1	2	yes	—
241	C₃×#683	C₂³	1	2	yes	—
242	C₃×#683	C₂³	1	2	yes	—
243	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
244	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
245	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
246	C₃×C₄×Dic₅	C₂³	1	2	yes	—
247	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
248	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
249	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
250	C₃×C₄×Dic₅	C₂³	1	2	yes	—
251	C₃×C₄×Dic₅	C₂³	1	2	yes	—
252	C₃×#556	—	5	1	no	—
253	C₃×#555	—	5	1	no	—
254	C₃×#554	—	5	1	no	—
255	C₃×#553	—	5	2	no	—
256	C₃×#552	—	5	1	no	—
257	C₃×#552	—	5	1	no	—
258	C₃×#552	—	5	2	no	—
259	C₃×#551	—	5	2	no	—
260	C₃×#551	—	5	2	no	—
261	C₃×#547	—	5	1	no	—
262	C₃×#546	—	5	1	no	—
263	C₃×#546	—	5	1	no	—
264	C₃×#533	—	5	1	no	—
265	C₃×#529	—	5	1	no	—
266	C₃×#529	—	5	2	no	—
267	C₃×#529	—	5	2	no	—
268	C₃×#529	—	5	1	no	—
269	C₃×#525	—	5	2	no	—
270	C₃×C₄×#41	—	5	1	no	—
271	C₃×C₄×#41	—	5	1	no	—
272	C₃×C₄×#41	D₅	1	1	yes	characteristic, complemented
273	C₂×C₃×C₄×D₄	—	5	1	no	—
274	C₂×C₃×#117	—	5	2	no	—
275	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
276	C₂×#711	C₂²×C₃	1	1	yes	characteristic
277	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
278	C₂×#709	C₂²×C₃	1	1	yes	characteristic
279	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
280	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
281	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
282	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
283	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
284	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
285	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
286	C₅×#117	C₂²×C₃	1	2	yes	complemented
287	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
288	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	complemented
289	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
290	#4093	C₂²×C₃	1	1	yes	characteristic
291	#4092	C₂²×C₃	1	1	yes	characteristic
292	#4092	C₂²×C₃	1	1	yes	characteristic, complemented
293	#4090	C₂²×C₃	1	1	yes	characteristic, complemented
294	#4085	C₂²×C₃	1	2	yes	—
295	#4085	C₂²×C₃	1	2	yes	complemented
296	#4083	C₂²×C₃	1	2	yes	—
297	#4081	C₂²×C₃	1	2	yes	complemented
298	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
299	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
300	#4076	C₂²×C₃	1	1	yes	characteristic
301	#4076	C₂²×C₃	1	2	yes	—
302	#4075	C₂²×C₃	1	2	yes	—
303	#4075	C₂²×C₃	1	2	yes	complemented
304	#4075	C₂²×C₃	1	2	yes	complemented
305	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
306	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
307	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
308	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic, complemented
309	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic, complemented
310	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
311	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
312	C₂×#685	C₂²×C₃	1	2	yes	—
313	C₂×#685	C₂²×C₃	1	2	yes	—
314	#4072	C₂²×C₃	1	1	yes	characteristic, complemented
315	#4070	C₂²×C₃	1	1	yes	characteristic, complemented
316	#4070	C₂²×C₃	1	2	yes	complemented
317	C₂×#683	C₂²×C₃	1	2	yes	complemented
318	C₂×#683	C₂²×C₃	1	2	yes	complemented
319	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
320	#4044	C₂²×C₃	1	2	yes	complemented
321	#4044	C₂²×C₃	1	2	yes	complemented
322	#4043	C₂²×C₃	1	1	yes	characteristic
323	#4042	C₂²×C₃	1	2	yes	—
324	#4042	C₂²×C₃	1	2	yes	complemented
325	#4041	C₂²×C₃	1	1	yes	characteristic
326	#4040	C₂²×C₃	1	2	yes	—
327	#4040	C₂²×C₃	1	2	yes	complemented
328	#4039	C₂²×C₃	1	1	yes	characteristic
329	#4038	C₂²×C₃	1	1	yes	characteristic, complemented
330	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
331	#4036	C₂²×C₃	1	1	yes	characteristic, complemented
332	#4035	C₂²×C₃	1	2	yes	complemented
333	#4035	C₂²×C₃	1	2	yes	complemented
334	#4034	C₂²×C₃	1	1	yes	characteristic, complemented
335	#4033	C₂²×C₃	1	1	yes	characteristic, complemented
336	#4032	C₂²×C₃	1	2	yes	—
337	#4031	C₂²×C₃	1	2	yes	complemented
338	#4030	C₂²×C₃	1	2	yes	complemented
339	#4029	C₂²×C₃	1	2	yes	—
340	#4028	C₂²×C₃	1	2	yes	—
341	#4027	C₂²×C₃	1	2	yes	—
342	#4027	C₂²×C₃	1	2	yes	complemented
343	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
344	#4025	C₂²×C₃	1	2	yes	complemented
345	#4024	C₂²×C₃	1	2	yes	complemented
346	#4024	C₂²×C₃	1	2	yes	complemented
347	#4023	C₂²×C₃	1	2	yes	complemented
348	#4022	C₂²×C₃	1	2	yes	complemented
349	#4022	C₂²×C₃	1	2	yes	complemented
350	#4022	C₂²×C₃	1	2	yes	complemented
351	#4021	C₂²×C₃	1	1	yes	characteristic
352	#4021	C₂²×C₃	1	2	yes	complemented
353	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
354	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
355	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
356	C₄×D₂₀	C₂²×C₃	1	2	yes	complemented
357	#4018	C₂²×C₃	1	1	yes	characteristic
358	#4018	C₂²×C₃	1	2	yes	—
359	#4018	C₂²×C₃	1	2	yes	—
360	#4018	C₂²×C₃	1	2	yes	—
361	#4018	C₂²×C₃	1	2	yes	complemented
362	#4018	C₂²×C₃	1	2	yes	complemented
363	#4018	C₂²×C₃	1	2	yes	complemented
364	#4018	C₂²×C₃	1	2	yes	complemented
365	#4018	C₂²×C₃	1	1	yes	characteristic, complemented
366	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
367	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
368	#4016	C₂²×C₃	1	2	yes	complemented
369	#4016	C₂²×C₃	1	1	yes	characteristic, complemented
370	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
371	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
372	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
373	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
374	#3475	—	5	1	no	Sylow
375	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
376	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
377	C₂²×C₃×D₅	—	2	4	no	—
378	C₂²×C₃×D₅	—	2	4	no	—
379	C₂²×C₃×D₅	—	4	2	no	—
380	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
381	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
382	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
383	C₃×C₅×Q₈	—	2	2	no	—
384	C₃×C₅×D₄	—	2	4	no	—
385	C₃×C₅×D₄	#41	1	4	yes	complemented
386	C₂×C₃×C₄×C₅	—	2	4	no	—
387	C₂×C₃×C₄×C₅	—	2	4	no	—
388	C₂×C₃×C₄×C₅	—	2	2	no	—
389	C₂×C₃×C₄×C₅	—	2	2	no	—
390	C₂×C₃×C₄×C₅	—	4	2	no	—
391	C₂×C₃×C₄×C₅	—	4	1	no	—
392	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
393	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
394	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
395	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
396	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
397	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
398	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
399	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
400	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
401	C₃×C₂²⋊D₅	—	2	4	no	—
402	C₃×C₂²⋊D₅	—	2	4	no	—
403	C₃×C₂²⋊D₅	—	2	2	no	—
404	C₃×C₂²⋊D₅	—	2	2	no	—
405	C₃×C₂²⋊D₅	—	4	2	no	—
406	C₂×C₃×Dic₅	—	2	4	no	—
407	C₂×C₃×Dic₅	—	2	4	no	—
408	C₂×C₃×Dic₅	—	4	2	no	—
409	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
410	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
411	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
412	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
413	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
414	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
415	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
416	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
417	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
418	C₃×D₂₀	—	2	2	no	—
419	C₃×D₂₀	—	2	2	no	—
420	C₃×D₂₀	—	4	2	no	—
421	C₃×C₄×D₅	—	2	4	no	—
422	C₃×C₄×D₅	—	2	4	no	—
423	C₃×C₄×D₅	—	2	2	no	—
424	C₃×C₄×D₅	—	2	2	no	—
425	C₃×C₄×D₅	—	2	2	no	—
426	C₃×C₄×D₅	—	2	4	no	—
427	C₃×C₄×D₅	—	4	1	no	—
428	C₃×C₄×D₅	—	4	1	no	—
429	C₃×C₄×D₅	#41	1	4	yes	complemented
430	C₃×Dic₁₀	—	2	2	no	—
431	C₃×Dic₁₀	—	2	2	no	—
432	C₃×Dic₁₀	—	4	2	no	—
433	C₂×C₃×#41	—	5	1	no	—
434	C₂×C₃×#41	—	5	1	no	—
435	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
436	C₂²×C₃×D₄	—	5	1	no	—
437	C₂³×C₃×C₄	—	5	2	no	—
438	C₃×C₄⋊Q₈	—	5	1	no	—
439	C₃×C₄⋊Q₈	—	5	1	no	—
440	C₃×#126	—	5	2	no	—
441	C₃×#126	—	5	2	no	—
442	C₃×#126	—	5	2	no	—
443	C₃×#126	—	5	2	no	—
444	C₃×#126	—	5	2	no	—
445	C₃×#126	—	5	2	no	—
446	C₃×#125	—	5	2	no	—
447	C₃×#125	—	5	2	no	—
448	C₃×#125	—	5	1	no	—
449	C₃×#125	—	5	2	no	—
450	C₃×#125	—	5	1	no	—
451	C₃×#124	—	5	1	no	—
452	C₃×#124	—	5	2	no	—
453	C₃×#124	—	5	1	no	—
454	C₃×#124	—	5	2	no	—
455	C₃×#123	—	5	2	no	—
456	C₃×#123	—	5	2	no	—
457	C₃×#123	—	5	2	no	—
458	C₃×#123	—	5	2	no	—
459	C₃×#123	—	5	2	no	—
460	C₃×#123	—	5	2	no	—
461	C₃×#123	—	5	2	no	—
462	C₃×#123	—	5	2	no	—
463	C₃×C₂²⋊Q₈	—	5	1	no	—
464	C₃×C₂²⋊Q₈	—	5	1	no	—
465	C₃×C₂²⋊Q₈	—	5	1	no	—
466	C₃×C₂²⋊Q₈	—	5	2	no	—
467	C₃×C₂²⋊Q₈	—	5	2	no	—
468	C₃×C₂²⋊Q₈	—	5	2	no	—
469	C₃×C₂²⋊Q₈	—	5	1	no	—
470	C₃×C₂²⋊Q₈	—	5	2	no	—
471	C₃×C₂²⋊Q₈	—	5	2	no	—
472	C₃×#121	—	5	2	no	—
473	C₃×#121	—	5	2	no	—
474	C₃×#121	—	5	2	no	—
475	C₃×#121	—	5	1	no	—
476	C₃×#121	—	5	1	no	—
477	C₃×#121	—	5	2	no	—
478	C₃×#120	—	5	2	no	—
479	C₃×#120	—	5	2	no	—
480	C₃×C₄×Q₈	—	5	1	no	—
481	C₃×C₄×Q₈	—	5	1	no	—
482	C₃×C₄×Q₈	—	5	1	no	—
483	C₃×C₄×Q₈	—	5	1	no	—
484	C₃×C₄×Q₈	—	5	2	no	—
485	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
486	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
487	C₃×C₄×D₄	—	5	1	no	—
488	C₃×C₄×D₄	—	5	1	no	—
489	C₃×C₄×D₄	—	5	2	no	—
490	C₃×C₄×D₄	—	5	2	no	—
491	C₃×C₄×D₄	—	5	1	no	—
492	C₃×C₄×D₄	—	5	1	no	—
493	C₃×C₄×D₄	—	5	1	no	—
494	C₃×C₄×D₄	—	5	1	no	—
495	C₃×C₄×D₄	—	5	2	no	—
496	C₃×C₄×D₄	—	5	1	no	—
497	C₃×C₄×D₄	—	5	2	no	—
498	C₃×C₄×D₄	—	5	2	no	—
499	C₃×C₄×D₄	—	5	1	no	—
500	C₃×C₄×D₄	—	5	1	no	—
501	C₃×C₄×D₄	—	5	1	no	—
502	C₃×C₄×D₄	—	5	2	no	—
503	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
504	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
505	C₃×C₄×D₄	C₂×D₅	1	2	yes	complemented
506	C₃×C₄×D₄	C₂×D₅	1	2	yes	complemented
507	C₃×#117	—	5	1	no	—
508	C₃×#117	—	5	1	no	—
509	C₃×#117	—	5	2	no	—
510	C₃×#117	—	5	1	no	—
511	C₃×#117	—	5	2	no	—
512	C₃×#117	—	5	2	no	—
513	C₃×#117	—	5	2	no	—
514	C₃×#117	—	5	2	no	—
515	C₃×#117	—	5	2	no	—
516	C₃×#117	—	5	2	no	—
517	C₃×#117	—	5	2	no	—
518	C₃×#117	—	5	1	no	—
519	C₃×#117	C₂×D₅	1	2	yes	complemented
520	C₃×#117	C₂×D₅	1	1	yes	characteristic, complemented
521	C₂×C₃×C₄⋊C₄	—	5	2	no	—
522	C₂×C₃×C₄⋊C₄	—	5	2	no	—
523	C₂×C₃×C₄⋊C₄	—	5	1	no	—
524	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
525	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
526	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
527	C₂×C₃×C₄²	—	5	2	no	—
528	C₂×C₃×C₄²	—	5	1	no	—
529	C₂×C₃×C₄²	—	5	1	no	—
530	C₂×C₃×C₄²	C₂×D₅	1	2	yes	complemented
531	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
532	C₂³×D₅	C₂³×C₃	1	2	yes	—
533	C₅×#41	—	2	4	no	—
534	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
535	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
536	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
537	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
538	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
539	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
540	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
541	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
542	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
543	C₂×C₂²⋊D₅	C₂³×C₃	1	1	yes	characteristic
544	C₂×C₂²⋊D₅	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
546	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
547	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
548	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
549	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
550	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
551	#711	—	2	4	no	—
552	D₄×D₅	—	2	4	no	—
553	#709	—	2	4	no	—
554	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
555	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
556	C₂×D₂₀	C₂³×C₃	1	2	yes	—
557	C₂×C₄×D₅	—	2	8	no	—
558	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
559	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
560	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
561	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
562	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
563	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
564	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
565	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
566	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
567	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
568	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
569	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
570	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
571	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
572	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
573	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
574	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
575	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
576	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
577	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
578	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
579	C₄²×C₅	C₂³×C₃	1	2	yes	—
580	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
581	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
582	C₄²×C₅	C₂³×C₃	1	2	yes	—
583	C₄²×C₅	C₂³×C₃	1	2	yes	—
584	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
585	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
586	C₂²⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
587	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
588	C₂²⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
589	#685	C₂³×C₃	1	1	yes	characteristic
590	#685	C₂³×C₃	1	1	yes	characteristic
591	#685	C₂³×C₃	1	2	yes	—
592	#685	C₂³×C₃	1	2	yes	—
593	#685	C₂³×C₃	1	2	yes	—
594	#685	C₂³×C₃	1	2	yes	—
595	#685	C₂³×C₃	1	2	yes	—
596	#685	C₂³×C₃	1	2	yes	—
597	#685	C₂³×C₃	1	1	yes	characteristic
598	#685	C₂³×C₃	1	1	yes	characteristic
599	#685	C₂³×C₃	1	2	yes	—
600	#685	C₂³×C₃	1	2	yes	—
601	#685	C₂³×C₃	1	2	yes	—
602	#685	C₂³×C₃	1	2	yes	—
603	#685	C₂³×C₃	1	2	yes	—
604	#685	C₂³×C₃	1	2	yes	—
605	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
606	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
607	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
608	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
609	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
610	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
611	#683	C₂³×C₃	1	1	yes	characteristic
612	#683	C₂³×C₃	1	1	yes	characteristic
613	#683	C₂³×C₃	1	1	yes	characteristic
614	#683	C₂³×C₃	1	1	yes	characteristic
615	#683	C₂³×C₃	1	2	yes	—
616	#683	C₂³×C₃	1	2	yes	—
617	#683	C₂³×C₃	1	2	yes	—
618	#683	C₂³×C₃	1	2	yes	—
619	#683	C₂³×C₃	1	2	yes	—
620	#683	C₂³×C₃	1	2	yes	—
621	#683	C₂³×C₃	1	2	yes	—
622	#683	C₂³×C₃	1	2	yes	—
623	#683	C₂³×C₃	1	2	yes	—
624	#683	C₂³×C₃	1	2	yes	—
625	#683	C₂³×C₃	1	2	yes	—
626	#683	C₂³×C₃	1	2	yes	—
627	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
628	C₄×Dic₅	C₂³×C₃	1	2	yes	—
629	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
630	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
631	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
632	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
633	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
634	C₄×Dic₅	C₂³×C₃	1	2	yes	—
635	C₄×Dic₅	C₂³×C₃	1	2	yes	—
636	#556	—	5	1	no	—
637	#555	—	5	1	no	—
638	#554	—	5	1	no	—
639	#553	—	5	2	no	—
640	#552	—	5	1	no	—
641	#552	—	5	1	no	—
642	#552	—	5	2	no	—
643	#551	—	5	2	no	—
644	#551	—	5	2	no	—
645	#547	—	5	1	no	—
646	#546	—	5	1	no	—
647	#546	—	5	1	no	—
648	#533	—	5	1	no	—
649	#529	—	5	1	no	—
650	#529	—	5	2	no	—
651	#529	—	5	2	no	—
652	#529	—	5	1	no	—
653	#525	—	5	2	no	—
654	C₄×#41	—	5	1	no	—
655	C₄×#41	—	5	1	no	—
656	C₄×#41	C₃×D₅	1	1	yes	characteristic, complemented
657	C₂×C₄×D₄	—	5	1	no	—
658	C₂×#117	—	5	2	no	—
659	C₂²×C₃×C₅	—	2	2	no	—
660	C₂²×C₃×C₅	—	2	2	no	—
661	C₂²×C₃×C₅	—	2	1	no	—
662	C₂²×C₃×C₅	—	2	1	no	—
663	C₂²×C₃×C₅	—	2	1	no	—
664	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
665	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
666	C₂×C₃×D₅	—	2	1	no	—
667	C₂×C₃×D₅	—	2	1	no	—
668	C₂×C₃×D₅	—	2	2	no	—
669	C₂×C₃×D₅	—	2	1	no	—
670	C₂×C₃×D₅	—	2	1	no	—
671	C₂×C₃×D₅	—	2	2	no	—
672	C₂×C₃×D₅	—	2	1	no	—
673	C₂×C₃×D₅	—	2	2	no	—
674	C₂×C₃×D₅	—	4	8	no	—
675	C₂×C₃×D₅	C₂×#41	1	2	yes	—
676	C₃×C₄×C₅	—	2	1	no	—
677	C₃×C₄×C₅	—	2	2	no	—
678	C₃×C₄×C₅	—	2	1	no	—
679	C₃×C₄×C₅	—	2	2	no	—
680	C₃×C₄×C₅	—	2	2	no	—
681	C₃×C₄×C₅	—	2	1	no	—
682	C₃×C₄×C₅	—	2	1	no	—
683	C₃×C₄×C₅	C₂×#41	1	2	yes	—
684	C₃×C₄×C₅	C₂×#41	1	2	yes	—
685	C₃×Dic₅	—	2	1	no	—
686	C₃×Dic₅	—	2	2	no	—
687	C₃×Dic₅	—	2	2	no	—
688	C₃×Dic₅	—	2	1	no	—
689	C₃×Dic₅	—	2	1	no	—
690	C₃×Dic₅	—	2	1	no	—
691	C₃×Dic₅	—	2	2	no	—
692	C₃×Dic₅	—	2	1	no	—
693	C₃×Dic₅	C₂×#41	1	2	yes	—
694	C₂⁴×C₃	—	5	2	no	—
695	C₃×#41	—	2	4	no	—
696	C₃×#41	—	10	4	no	—
697	C₃×#41	—	10	4	no	—
698	C₂×C₃×Q₈	—	5	1	no	—
699	C₂×C₃×Q₈	—	5	1	no	—
700	C₂×C₃×Q₈	—	5	2	no	—
701	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
702	C₂×C₃×D₄	—	5	1	no	—
703	C₂×C₃×D₄	—	5	2	no	—
704	C₂×C₃×D₄	—	5	1	no	—
705	C₂×C₃×D₄	—	5	2	no	—
706	C₂×C₃×D₄	—	5	2	no	—
707	C₂×C₃×D₄	—	5	1	no	—
708	C₂×C₃×D₄	—	5	1	no	—
709	C₂×C₃×D₄	—	5	2	no	—
710	C₂×C₃×D₄	—	10	4	no	—
711	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
712	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
713	C₂²×C₃×C₄	—	5	1	no	—
714	C₂²×C₃×C₄	—	5	2	no	—
715	C₂²×C₃×C₄	—	5	2	no	—
716	C₂²×C₃×C₄	—	5	2	no	—
717	C₂²×C₃×C₄	—	5	1	no	—
718	C₂²×C₃×C₄	—	5	1	no	—
719	C₂²×C₃×C₄	—	5	2	no	—
720	C₂²×C₃×C₄	—	5	2	no	—
721	C₂²×C₃×C₄	—	5	1	no	—
722	C₂²×C₃×C₄	—	5	2	no	—
723	C₂²×C₃×C₄	—	5	1	no	—
724	C₂²×C₃×C₄	—	5	1	no	—
725	C₂²×C₃×C₄	—	10	8	no	—
726	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
727	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
728	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
729	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
730	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
731	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
732	C₃×C₄⋊C₄	—	5	1	no	—
733	C₃×C₄⋊C₄	—	5	1	no	—
734	C₃×C₄⋊C₄	—	5	2	no	—
735	C₃×C₄⋊C₄	—	5	2	no	—
736	C₃×C₄⋊C₄	—	5	2	no	—
737	C₃×C₄⋊C₄	—	5	2	no	—
738	C₃×C₄⋊C₄	—	5	2	no	—
739	C₃×C₄⋊C₄	—	5	2	no	—
740	C₃×C₄⋊C₄	—	5	2	no	—
741	C₃×C₄⋊C₄	—	5	1	no	—
742	C₃×C₄⋊C₄	—	5	2	no	—
743	C₃×C₄⋊C₄	—	5	2	no	—
744	C₃×C₄⋊C₄	—	5	1	no	—
745	C₃×C₄⋊C₄	—	5	2	no	—
746	C₃×C₄⋊C₄	—	5	2	no	—
747	C₃×C₄⋊C₄	—	5	2	no	—
748	C₃×C₄⋊C₄	—	5	1	no	—
749	C₃×C₄⋊C₄	—	5	1	no	—
750	C₃×C₄⋊C₄	—	5	1	no	—
751	C₃×C₄⋊C₄	—	5	1	no	—
752	C₃×C₄⋊C₄	—	5	2	no	—
753	C₃×C₄⋊C₄	—	5	2	no	—
754	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
755	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
756	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
757	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
758	C₃×C₂²⋊C₄	—	5	2	no	—
759	C₃×C₂²⋊C₄	—	5	2	no	—
760	C₃×C₂²⋊C₄	—	5	1	no	—
761	C₃×C₂²⋊C₄	—	5	1	no	—
762	C₃×C₂²⋊C₄	—	5	2	no	—
763	C₃×C₂²⋊C₄	—	5	1	no	—
764	C₃×C₂²⋊C₄	—	5	1	no	—
765	C₃×C₂²⋊C₄	—	5	2	no	—
766	C₃×C₂²⋊C₄	—	5	2	no	—
767	C₃×C₂²⋊C₄	—	5	2	no	—
768	C₃×C₂²⋊C₄	—	5	2	no	—
769	C₃×C₂²⋊C₄	—	5	2	no	—
770	C₃×C₂²⋊C₄	—	5	2	no	—
771	C₃×C₂²⋊C₄	—	5	2	no	—
772	C₃×C₂²⋊C₄	—	5	2	no	—
773	C₃×C₂²⋊C₄	—	5	1	no	—
774	C₃×C₂²⋊C₄	—	5	2	no	—
775	C₃×C₂²⋊C₄	—	5	1	no	—
776	C₃×C₂²⋊C₄	—	5	2	no	—
777	C₃×C₂²⋊C₄	—	5	2	no	—
778	C₃×C₂²⋊C₄	—	5	2	no	—
779	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
780	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
781	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
782	C₃×C₄²	—	5	2	no	—
783	C₃×C₄²	—	5	1	no	—
784	C₃×C₄²	—	5	2	no	—
785	C₃×C₄²	—	5	1	no	—
786	C₃×C₄²	—	5	1	no	—
787	C₃×C₄²	—	5	1	no	—
788	C₃×C₄²	—	5	1	no	—
789	C₃×C₄²	—	5	1	no	—
790	C₃×C₄²	—	5	2	no	—
791	C₃×C₄²	C₂²×D₅	1	2	yes	—
792	C₃×C₄²	C₂²×D₅	1	2	yes	—
793	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
794	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
795	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
796	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
797	C₃×C₄²	C₂²×D₅	1	2	yes	—
798	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
799	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
800	C₂²×D₅	—	2	4	no	—
801	C₂²×D₅	—	2	4	no	—
802	C₂²×D₅	—	4	2	no	—
803	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
804	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
805	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
806	C₅×Q₈	—	2	2	no	—
807	C₅×D₄	—	2	4	no	—
808	C₅×D₄	C₃×#41	1	4	yes	complemented
809	C₂×C₄×C₅	—	2	4	no	—
810	C₂×C₄×C₅	—	2	4	no	—
811	C₂×C₄×C₅	—	2	2	no	—
812	C₂×C₄×C₅	—	2	2	no	—
813	C₂×C₄×C₅	—	4	2	no	—
814	C₂×C₄×C₅	—	4	1	no	—
815	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
816	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
817	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
818	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
819	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
820	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
821	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
822	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
823	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
824	C₂²⋊D₅	—	2	4	no	—
825	C₂²⋊D₅	—	2	4	no	—
826	C₂²⋊D₅	—	2	2	no	—
827	C₂²⋊D₅	—	2	2	no	—
828	C₂²⋊D₅	—	4	2	no	—
829	C₂×Dic₅	—	2	4	no	—
830	C₂×Dic₅	—	2	4	no	—
831	C₂×Dic₅	—	4	2	no	—
832	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
833	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
834	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
835	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
836	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
837	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
838	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
839	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
840	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
841	D₂₀	—	2	2	no	—
842	D₂₀	—	2	2	no	—
843	D₂₀	—	4	2	no	—
844	C₄×D₅	—	2	4	no	—
845	C₄×D₅	—	2	4	no	—
846	C₄×D₅	—	2	2	no	—
847	C₄×D₅	—	2	2	no	—
848	C₄×D₅	—	2	2	no	—
849	C₄×D₅	—	2	4	no	—
850	C₄×D₅	—	4	1	no	—
851	C₄×D₅	—	4	1	no	—
852	C₄×D₅	C₃×#41	1	4	yes	complemented
853	Dic₁₀	—	2	2	no	—
854	Dic₁₀	—	2	2	no	—
855	Dic₁₀	—	4	2	no	—
856	C₂×#41	—	5	1	no	—
857	C₂×#41	—	5	1	no	—
858	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
859	C₂²×D₄	—	5	1	no	—
860	C₂³×C₄	—	5	2	no	—
861	C₄⋊Q₈	—	5	1	no	—
862	C₄⋊Q₈	—	5	1	no	—
863	#126	—	5	2	no	—
864	#126	—	5	2	no	—
865	#126	—	5	2	no	—
866	#126	—	5	2	no	—
867	#126	—	5	2	no	—
868	#126	—	5	2	no	—
869	#125	—	5	2	no	—
870	#125	—	5	1	no	—
871	#125	—	5	2	no	—
872	#125	—	5	2	no	—
873	#125	—	5	1	no	—
874	#124	—	5	1	no	—
875	#124	—	5	2	no	—
876	#124	—	5	1	no	—
877	#124	—	5	2	no	—
878	#123	—	5	2	no	—
879	#123	—	5	2	no	—
880	#123	—	5	2	no	—
881	#123	—	5	2	no	—
882	#123	—	5	2	no	—
883	#123	—	5	2	no	—
884	#123	—	5	2	no	—
885	#123	—	5	2	no	—
886	C₂²⋊Q₈	—	5	1	no	—
887	C₂²⋊Q₈	—	5	1	no	—
888	C₂²⋊Q₈	—	5	1	no	—
889	C₂²⋊Q₈	—	5	2	no	—
890	C₂²⋊Q₈	—	5	2	no	—
891	C₂²⋊Q₈	—	5	1	no	—
892	C₂²⋊Q₈	—	5	2	no	—
893	C₂²⋊Q₈	—	5	2	no	—
894	C₂²⋊Q₈	—	5	2	no	—
895	#121	—	5	2	no	—
896	#121	—	5	2	no	—
897	#121	—	5	2	no	—
898	#121	—	5	1	no	—
899	#121	—	5	1	no	—
900	#121	—	5	2	no	—
901	#120	—	5	2	no	—
902	#120	—	5	2	no	—
903	C₄×Q₈	—	5	1	no	—
904	C₄×Q₈	—	5	1	no	—
905	C₄×Q₈	—	5	1	no	—
906	C₄×Q₈	—	5	1	no	—
907	C₄×Q₈	—	5	2	no	—
908	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
909	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
910	C₄×D₄	—	5	1	no	—
911	C₄×D₄	—	5	1	no	—
912	C₄×D₄	—	5	2	no	—
913	C₄×D₄	—	5	2	no	—
914	C₄×D₄	—	5	1	no	—
915	C₄×D₄	—	5	1	no	—
916	C₄×D₄	—	5	1	no	—
917	C₄×D₄	—	5	1	no	—
918	C₄×D₄	—	5	2	no	—
919	C₄×D₄	—	5	1	no	—
920	C₄×D₄	—	5	2	no	—
921	C₄×D₄	—	5	2	no	—
922	C₄×D₄	—	5	1	no	—
923	C₄×D₄	—	5	1	no	—
924	C₄×D₄	—	5	1	no	—
925	C₄×D₄	—	5	2	no	—
926	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
927	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
928	C₄×D₄	C₂×C₃×D₅	1	2	yes	complemented
929	C₄×D₄	C₂×C₃×D₅	1	2	yes	complemented
930	#117	—	5	1	no	—
931	#117	—	5	1	no	—
932	#117	—	5	2	no	—
933	#117	—	5	1	no	—
934	#117	—	5	2	no	—
935	#117	—	5	2	no	—
936	#117	—	5	2	no	—
937	#117	—	5	2	no	—
938	#117	—	5	2	no	—
939	#117	—	5	2	no	—
940	#117	—	5	2	no	—
941	#117	—	5	1	no	—
942	#117	C₂×C₃×D₅	1	2	yes	complemented
943	#117	C₂×C₃×D₅	1	1	yes	characteristic, complemented
944	C₂×C₄⋊C₄	—	5	2	no	—
945	C₂×C₄⋊C₄	—	5	2	no	—
946	C₂×C₄⋊C₄	—	5	1	no	—
947	C₂×C₂²⋊C₄	—	5	2	no	—
948	C₂×C₂²⋊C₄	—	5	2	no	—
949	C₂×C₂²⋊C₄	—	5	2	no	—
950	C₂×C₄²	—	5	2	no	—
951	C₂×C₄²	—	5	1	no	—
952	C₂×C₄²	—	5	1	no	—
953	C₂×C₄²	C₂×C₃×D₅	1	2	yes	complemented
954	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
955	C₂×C₃×C₅	—	2	4	no	—
956	C₂×C₃×C₅	—	4	1	no	—
957	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
958	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
959	C₂×C₃×C₅	#585	1	1	yes	characteristic
960	C₃×D₅	—	2	2	no	—
961	C₃×D₅	—	4	1	no	—
962	C₃×D₅	—	4	2	no	—
963	C₂³×C₃	—	5	1	no	—
964	C₂³×C₃	—	5	2	no	—
965	C₂³×C₃	—	5	1	no	—
966	C₂³×C₃	—	10	4	no	—
967	C₂³×C₃	—	10	4	no	—
968	C₂³×C₃	—	20	2	no	—
969	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
970	C₂³×C₃	C₂³×D₅	1	2	yes	—
971	C₃×Q₈	—	2	2	no	—
972	C₃×Q₈	—	10	2	no	—
973	C₃×Q₈	—	10	2	no	—
974	C₃×Q₈	—	20	2	no	—
975	C₃×D₄	—	2	4	no	—
976	C₃×D₄	—	10	2	no	—
977	C₃×D₄	—	10	2	no	—
978	C₃×D₄	—	10	2	no	—
979	C₃×D₄	—	10	4	no	—
980	C₃×D₄	—	10	4	no	—
981	C₃×D₄	—	10	2	no	—
982	C₃×D₄	—	20	2	no	—
983	C₃×D₄	—	20	2	no	—
984	C₃×D₄	#709	1	4	yes	complemented
985	C₂×C₃×C₄	—	2	4	no	—
986	C₂×C₃×C₄	—	2	2	no	—
987	C₂×C₃×C₄	—	2	4	no	—
988	C₂×C₃×C₄	—	2	2	no	—
989	C₂×C₃×C₄	—	4	1	no	—
990	C₂×C₃×C₄	—	4	2	no	—
991	C₂×C₃×C₄	—	5	1	no	—
992	C₂×C₃×C₄	—	5	4	no	—
993	C₂×C₃×C₄	—	5	1	no	—
994	C₂×C₃×C₄	—	5	1	no	—
995	C₂×C₃×C₄	—	5	1	no	—
996	C₂×C₃×C₄	—	5	2	no	—
997	C₂×C₃×C₄	—	5	1	no	—
998	C₂×C₃×C₄	—	5	2	no	—
999	C₂×C₃×C₄	—	5	1	no	—
1000	C₂×C₃×C₄	—	5	2	no	—
1001	C₂×C₃×C₄	—	10	4	no	—
1002	C₂×C₃×C₄	—	10	4	no	—
1003	C₂×C₃×C₄	—	10	4	no	—
1004	C₂×C₃×C₄	—	10	4	no	—
1005	C₂×C₃×C₄	—	10	2	no	—
1006	C₂×C₃×C₄	—	10	2	no	—
1007	C₂×C₃×C₄	—	10	4	no	—
1008	C₂×C₃×C₄	—	10	2	no	—
1009	C₂×C₃×C₄	—	20	1	no	—
1010	C₂×C₃×C₄	—	20	1	no	—
1011	C₂×C₃×C₄	—	20	2	no	—
1012	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1013	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1014	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1015	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1016	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1017	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1018	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1019	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1020	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1021	C₂²×C₅	—	2	2	no	—
1022	C₂²×C₅	—	2	2	no	—
1023	C₂²×C₅	—	2	1	no	—
1024	C₂²×C₅	—	2	1	no	—
1025	C₂²×C₅	—	2	1	no	—
1026	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
1027	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
1028	C₂×D₅	—	2	1	no	—
1029	C₂×D₅	—	2	1	no	—
1030	C₂×D₅	—	2	2	no	—
1031	C₂×D₅	—	2	1	no	—
1032	C₂×D₅	—	2	1	no	—
1033	C₂×D₅	—	2	2	no	—
1034	C₂×D₅	—	2	1	no	—
1035	C₂×D₅	—	2	2	no	—
1036	C₂×D₅	—	4	8	no	—
1037	C₂×D₅	C₂×C₃×#41	1	2	yes	—
1038	C₄×C₅	—	2	1	no	—
1039	C₄×C₅	—	2	2	no	—
1040	C₄×C₅	—	2	1	no	—
1041	C₄×C₅	—	2	2	no	—
1042	C₄×C₅	—	2	2	no	—
1043	C₄×C₅	—	2	1	no	—
1044	C₄×C₅	—	2	1	no	—
1045	C₄×C₅	C₂×C₃×#41	1	2	yes	—
1046	C₄×C₅	C₂×C₃×#41	1	2	yes	—
1047	Dic₅	—	2	1	no	—
1048	Dic₅	—	2	2	no	—
1049	Dic₅	—	2	2	no	—
1050	Dic₅	—	2	1	no	—
1051	Dic₅	—	2	1	no	—
1052	Dic₅	—	2	1	no	—
1053	Dic₅	—	2	2	no	—
1054	Dic₅	—	2	1	no	—
1055	Dic₅	C₂×C₃×#41	1	2	yes	—
1056	C₂⁴	—	5	2	no	—
1057	#41	—	2	4	no	—
1058	#41	—	10	4	no	—
1059	#41	—	10	4	no	—
1060	C₂×Q₈	—	5	1	no	—
1061	C₂×Q₈	—	5	1	no	—
1062	C₂×Q₈	—	5	2	no	—
1063	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
1064	C₂×D₄	—	5	1	no	—
1065	C₂×D₄	—	5	2	no	—
1066	C₂×D₄	—	5	1	no	—
1067	C₂×D₄	—	5	2	no	—
1068	C₂×D₄	—	5	2	no	—
1069	C₂×D₄	—	5	1	no	—
1070	C₂×D₄	—	5	1	no	—
1071	C₂×D₄	—	5	2	no	—
1072	C₂×D₄	—	10	4	no	—
1073	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
1074	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
1075	C₂²×C₄	—	5	1	no	—
1076	C₂²×C₄	—	5	2	no	—
1077	C₂²×C₄	—	5	2	no	—
1078	C₂²×C₄	—	5	2	no	—
1079	C₂²×C₄	—	5	1	no	—
1080	C₂²×C₄	—	5	1	no	—
1081	C₂²×C₄	—	5	1	no	—
1082	C₂²×C₄	—	5	2	no	—
1083	C₂²×C₄	—	5	2	no	—
1084	C₂²×C₄	—	5	2	no	—
1085	C₂²×C₄	—	5	1	no	—
1086	C₂²×C₄	—	5	1	no	—
1087	C₂²×C₄	—	10	8	no	—
1088	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
1089	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
1090	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1091	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1092	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
1093	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1094	C₄⋊C₄	—	5	1	no	—
1095	C₄⋊C₄	—	5	1	no	—
1096	C₄⋊C₄	—	5	2	no	—
1097	C₄⋊C₄	—	5	2	no	—
1098	C₄⋊C₄	—	5	2	no	—
1099	C₄⋊C₄	—	5	2	no	—
1100	C₄⋊C₄	—	5	2	no	—
1101	C₄⋊C₄	—	5	2	no	—
1102	C₄⋊C₄	—	5	1	no	—
1103	C₄⋊C₄	—	5	2	no	—
1104	C₄⋊C₄	—	5	1	no	—
1105	C₄⋊C₄	—	5	1	no	—
1106	C₄⋊C₄	—	5	1	no	—
1107	C₄⋊C₄	—	5	2	no	—
1108	C₄⋊C₄	—	5	2	no	—
1109	C₄⋊C₄	—	5	1	no	—
1110	C₄⋊C₄	—	5	1	no	—
1111	C₄⋊C₄	—	5	2	no	—
1112	C₄⋊C₄	—	5	2	no	—
1113	C₄⋊C₄	—	5	2	no	—
1114	C₄⋊C₄	—	5	2	no	—
1115	C₄⋊C₄	—	5	2	no	—
1116	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1117	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1118	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1119	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1120	C₂²⋊C₄	—	5	2	no	—
1121	C₂²⋊C₄	—	5	2	no	—
1122	C₂²⋊C₄	—	5	1	no	—
1123	C₂²⋊C₄	—	5	1	no	—
1124	C₂²⋊C₄	—	5	2	no	—
1125	C₂²⋊C₄	—	5	1	no	—
1126	C₂²⋊C₄	—	5	1	no	—
1127	C₂²⋊C₄	—	5	2	no	—
1128	C₂²⋊C₄	—	5	2	no	—
1129	C₂²⋊C₄	—	5	2	no	—
1130	C₂²⋊C₄	—	5	2	no	—
1131	C₂²⋊C₄	—	5	2	no	—
1132	C₂²⋊C₄	—	5	2	no	—
1133	C₂²⋊C₄	—	5	2	no	—
1134	C₂²⋊C₄	—	5	2	no	—
1135	C₂²⋊C₄	—	5	1	no	—
1136	C₂²⋊C₄	—	5	2	no	—
1137	C₂²⋊C₄	—	5	1	no	—
1138	C₂²⋊C₄	—	5	2	no	—
1139	C₂²⋊C₄	—	5	2	no	—
1140	C₂²⋊C₄	—	5	2	no	—
1141	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1142	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1143	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1144	C₄²	—	5	1	no	—
1145	C₄²	—	5	2	no	—
1146	C₄²	—	5	1	no	—
1147	C₄²	—	5	2	no	—
1148	C₄²	—	5	2	no	—
1149	C₄²	—	5	1	no	—
1150	C₄²	—	5	1	no	—
1151	C₄²	—	5	1	no	—
1152	C₄²	—	5	1	no	—
1153	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
1154	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
1155	C₄²	C₂²×C₃×D₅	1	2	yes	—
1156	C₄²	C₂²×C₃×D₅	1	2	yes	—
1157	C₄²	C₂²×C₃×D₅	1	2	yes	—
1158	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
1159	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
1160	C₃×C₅	#3475	1	1	yes	characteristic, complemented, Hall
1161	C₂²×C₃	—	2	2	no	—
1162	C₂²×C₃	—	2	2	no	—
1163	C₂²×C₃	—	2	1	no	—
1164	C₂²×C₃	—	2	1	no	—
1165	C₂²×C₃	—	2	1	no	—
1166	C₂²×C₃	—	5	2	no	—
1167	C₂²×C₃	—	10	1	no	—
1168	C₂²×C₃	—	10	1	no	—
1169	C₂²×C₃	—	10	1	no	—
1170	C₂²×C₃	—	10	2	no	—
1171	C₂²×C₃	—	10	2	no	—
1172	C₂²×C₃	—	10	1	no	—
1173	C₂²×C₃	—	10	1	no	—
1174	C₂²×C₃	—	10	2	no	—
1175	C₂²×C₃	—	20	8	no	—
1176	C₂²×C₃	C₂×#709	1	4	yes	—
1177	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
1178	C₃×C₄	—	2	1	no	—
1179	C₃×C₄	—	2	2	no	—
1180	C₃×C₄	—	2	2	no	—
1181	C₃×C₄	—	2	1	no	—
1182	C₃×C₄	—	2	1	no	—
1183	C₃×C₄	—	2	1	no	—
1184	C₃×C₄	—	2	2	no	—
1185	C₃×C₄	—	5	2	no	—
1186	C₃×C₄	—	10	1	no	—
1187	C₃×C₄	—	10	1	no	—
1188	C₃×C₄	—	10	2	no	—
1189	C₃×C₄	—	10	2	no	—
1190	C₃×C₄	—	10	1	no	—
1191	C₃×C₄	—	10	1	no	—
1192	C₃×C₄	—	10	2	no	—
1193	C₃×C₄	—	10	1	no	—
1194	C₃×C₄	C₂×#709	1	2	yes	—
1195	C₃×C₄	D₅×#41	1	2	yes	—
1196	C₂×C₅	—	2	4	no	—
1197	C₂×C₅	—	4	1	no	—
1198	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
1199	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
1200	C₂×C₅	C₃×#585	1	1	yes	characteristic
1201	D₅	—	2	2	no	—
1202	D₅	—	4	2	no	—
1203	D₅	—	4	1	no	—
1204	C₂³	—	5	1	no	—
1205	C₂³	—	5	2	no	—
1206	C₂³	—	5	1	no	—
1207	C₂³	—	10	4	no	—
1208	C₂³	—	10	4	no	—
1209	C₂³	—	20	2	no	—
1210	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
1211	C₂³	C₂³×C₃×D₅	1	2	yes	—
1212	Q₈	—	2	2	no	—
1213	Q₈	—	10	2	no	—
1214	Q₈	—	10	2	no	—
1215	Q₈	—	20	2	no	—
1216	D₄	—	2	4	no	—
1217	D₄	—	10	2	no	—
1218	D₄	—	10	2	no	—
1219	D₄	—	10	2	no	—
1220	D₄	—	10	4	no	—
1221	D₄	—	10	4	no	—
1222	D₄	—	10	2	no	—
1223	D₄	—	20	2	no	—
1224	D₄	—	20	2	no	—
1225	D₄	C₃×#709	1	4	yes	complemented
1226	C₂×C₄	—	2	4	no	—
1227	C₂×C₄	—	2	2	no	—
1228	C₂×C₄	—	2	4	no	—
1229	C₂×C₄	—	2	2	no	—
1230	C₂×C₄	—	4	1	no	—
1231	C₂×C₄	—	4	2	no	—
1232	C₂×C₄	—	5	1	no	—
1233	C₂×C₄	—	5	4	no	—
1234	C₂×C₄	—	5	1	no	—
1235	C₂×C₄	—	5	1	no	—
1236	C₂×C₄	—	5	1	no	—
1237	C₂×C₄	—	5	2	no	—
1238	C₂×C₄	—	5	1	no	—
1239	C₂×C₄	—	5	2	no	—
1240	C₂×C₄	—	5	1	no	—
1241	C₂×C₄	—	5	2	no	—
1242	C₂×C₄	—	10	4	no	—
1243	C₂×C₄	—	10	4	no	—
1244	C₂×C₄	—	10	4	no	—
1245	C₂×C₄	—	10	4	no	—
1246	C₂×C₄	—	10	2	no	—
1247	C₂×C₄	—	10	2	no	—
1248	C₂×C₄	—	10	4	no	—
1249	C₂×C₄	—	10	2	no	—
1250	C₂×C₄	—	20	1	no	—
1251	C₂×C₄	—	20	1	no	—
1252	C₂×C₄	—	20	2	no	—
1253	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1254	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1255	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1256	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1257	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1258	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1259	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1260	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1261	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1262	C₂×C₃	—	2	4	no	—
1263	C₂×C₃	—	4	1	no	—
1264	C₂×C₃	—	10	2	no	—
1265	C₂×C₃	—	20	2	no	—
1266	C₂×C₃	—	20	1	no	—
1267	C₂×C₃	C₂²×#709	1	1	yes	characteristic
1268	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
1269	C₂×C₃	#66283	1	1	yes	characteristic
1270	C₅	C₃×#3475	1	1	yes	characteristic, complemented, Sylow
1271	C₂²	—	2	2	no	—
1272	C₂²	—	2	2	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	1	no	—
1275	C₂²	—	2	1	no	—
1276	C₂²	—	5	2	no	—
1277	C₂²	—	10	1	no	—
1278	C₂²	—	10	1	no	—
1279	C₂²	—	10	1	no	—
1280	C₂²	—	10	2	no	—
1281	C₂²	—	10	2	no	—
1282	C₂²	—	10	1	no	—
1283	C₂²	—	10	1	no	—
1284	C₂²	—	10	2	no	—
1285	C₂²	—	20	8	no	—
1286	C₂²	C₂×C₃×#709	1	4	yes	—
1287	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
1288	C₄	—	2	1	no	—
1289	C₄	—	2	2	no	—
1290	C₄	—	2	2	no	—
1291	C₄	—	2	1	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	1	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	5	2	no	—
1296	C₄	—	10	1	no	—
1297	C₄	—	10	1	no	—
1298	C₄	—	10	2	no	—
1299	C₄	—	10	2	no	—
1300	C₄	—	10	1	no	—
1301	C₄	—	10	1	no	—
1302	C₄	—	10	2	no	—
1303	C₄	—	10	1	no	—
1304	C₄	C₂×C₃×#709	1	2	yes	—
1305	C₄	C₃×D₅×#41	1	2	yes	—
1306	C₃	#10617742	1	1	yes	characteristic, direct product factor, Sylow
1307	C₂	—	2	4	no	—
1308	C₂	—	4	1	no	—
1309	C₂	—	10	2	no	—
1310	C₂	—	20	2	no	—
1311	C₂	—	20	1	no	—
1312	C₂	C₂²×C₃×#709	1	1	yes	characteristic
1313	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
1314	C₂	C₃×#66283	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×C₄×#41	D₅
hypocenter	C₅	C₃×#3475
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×C₅×#41	C₂	semidirect
2. C₃×#66163	C₂	semidirect
3. C₃×#66158	C₂	semidirect
4. C₃×#65915	C₂	semidirect
5. C₃×#65914	C₂	semidirect
6. C₃×#65912	C₂	semidirect
7. C₃×#65902	C₂	semidirect
8. C₃×#65890	C₂	semidirect
9. C₃×#65888	C₂	semidirect
10. C₃×#65881	C₂	semidirect
11. C₃×C₄×D₄×D₅	C₂	semidirect
12. C₃×#65874	C₂	semidirect
13. C₃×#65873	C₂	semidirect
14. C₃×#65872	C₂	semidirect
15. C₃×C₄×#711	C₂	semidirect
16. C₃×#65866	C₂	semidirect
17. C₃×#65865	C₂	semidirect
18. C₃×#65863	C₂	semidirect
19. C₃×#65861	C₂	semidirect
20. C₃×#65813	C₂	semidirect
21. C₃×#65813	C₂	semidirect
22. C₃×C₄×#709	C₂	semidirect
23. C₂×C₃×#4018	C₂	semidirect
24. #10617742	C₃	direct (N × H)
30. C₃×C₄×C₅×Q₈	C₂²	semidirect
31. C₃×C₄×C₅×Q₈	C₂²	semidirect
34. C₃×C₄×C₅×D₄	C₂²	semidirect
35. C₃×C₄×C₅×D₄	C₂²	semidirect
36. C₃×C₅×#117	C₂²	semidirect
37. C₃×C₅×#117	C₂²	semidirect
38. C₂×C₃×C₄²×C₅	C₂²	semidirect
39. C₂×C₃×C₄²×C₅	C₂²	semidirect
42. C₃×#4092	C₂²	semidirect
43. C₃×#4090	C₂²	semidirect
45. C₃×#4085	C₂²	semidirect
47. C₃×#4081	C₂²	semidirect
53. C₃×#4075	C₂²	semidirect
54. C₃×#4075	C₂²	semidirect
58. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
59. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
60. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
61. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
64. C₃×#4072	C₂²	semidirect
65. C₃×#4070	C₂²	semidirect
66. C₃×#4070	C₂²	semidirect
67. C₂×C₃×#683	C₂²	semidirect
68. C₂×C₃×#683	C₂²	semidirect
69. C₂×C₃×C₄×Dic₅	C₂²	semidirect
70. C₃×#4044	C₂²	semidirect
71. C₃×#4044	C₂²	semidirect
74. C₃×#4042	C₂²	semidirect
77. C₃×#4040	C₂²	semidirect
79. C₃×#4038	C₂²	semidirect
81. C₃×#4036	C₂²	semidirect
82. C₃×#4035	C₂²	semidirect
83. C₃×#4035	C₂²	semidirect
84. C₃×#4034	C₂²	semidirect
85. C₃×#4033	C₂²	semidirect
87. C₃×#4031	C₂²	semidirect
88. C₃×#4030	C₂²	semidirect
92. C₃×#4027	C₂²	semidirect
94. C₃×#4025	C₂²	semidirect
95. C₃×#4024	C₂²	semidirect
96. C₃×#4024	C₂²	semidirect
97. C₃×#4023	C₂²	semidirect
98. C₃×#4022	C₂²	semidirect
99. C₃×#4022	C₂²	semidirect
100. C₃×#4022	C₂²	semidirect
102. C₃×#4021	C₂²	semidirect
106. C₃×C₄×D₂₀	C₂²	semidirect
111. C₃×#4018	C₂²	semidirect
112. C₃×#4018	C₂²	semidirect
113. C₃×#4018	C₂²	semidirect
114. C₃×#4018	C₂²	semidirect
115. C₃×#4018	C₂²	semidirect
117. C₃×C₄²×D₅	C₂²	semidirect
118. C₃×#4016	C₂²	semidirect
119. C₃×#4016	C₂²	semidirect
120. C₃×C₄×Dic₁₀	C₂²	semidirect
121. C₃×C₄×Dic₁₀	C₂²	semidirect
122. C₃×C₄×Dic₁₀	C₂²	semidirect
123. C₃×C₄×Dic₁₀	C₂²	semidirect
125. C₄×C₅×#41	C₂×C₃	semidirect
126. #66163	C₂×C₃	semidirect
127. #66158	C₂×C₃	semidirect
128. #65915	C₂×C₃	semidirect
129. #65914	C₂×C₃	semidirect
130. #65912	C₂×C₃	semidirect
131. #65902	C₂×C₃	semidirect
132. #65890	C₂×C₃	semidirect
133. #65888	C₂×C₃	semidirect
134. #65881	C₂×C₃	semidirect
135. C₄×D₄×D₅	C₂×C₃	semidirect
136. #65874	C₂×C₃	semidirect
137. #65873	C₂×C₃	semidirect
138. #65872	C₂×C₃	semidirect
139. C₄×#711	C₂×C₃	semidirect
140. #65866	C₂×C₃	semidirect
141. #65865	C₂×C₃	semidirect
142. #65863	C₂×C₃	semidirect
143. #65861	C₂×C₃	semidirect
144. #65813	C₂×C₃	semidirect
145. #65813	C₂×C₃	semidirect
146. C₄×#709	C₂×C₃	semidirect
147. C₂×#4018	C₂×C₃	semidirect
272. C₃×C₄×#41	D₅	semidirect
280. C₄×C₅×Q₈	C₂²×C₃	semidirect
281. C₄×C₅×Q₈	C₂²×C₃	semidirect
284. C₄×C₅×D₄	C₂²×C₃	semidirect
285. C₄×C₅×D₄	C₂²×C₃	semidirect
286. C₅×#117	C₂²×C₃	semidirect
287. C₅×#117	C₂²×C₃	semidirect
288. C₂×C₄²×C₅	C₂²×C₃	semidirect
289. C₂×C₄²×C₅	C₂²×C₃	semidirect
292. #4092	C₂²×C₃	semidirect
293. #4090	C₂²×C₃	semidirect
295. #4085	C₂²×C₃	semidirect
297. #4081	C₂²×C₃	semidirect
303. #4075	C₂²×C₃	semidirect
304. #4075	C₂²×C₃	semidirect
308. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
309. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
310. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
311. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
314. #4072	C₂²×C₃	semidirect
315. #4070	C₂²×C₃	semidirect
316. #4070	C₂²×C₃	semidirect
317. C₂×#683	C₂²×C₃	semidirect
318. C₂×#683	C₂²×C₃	semidirect
319. C₂×C₄×Dic₅	C₂²×C₃	semidirect
320. #4044	C₂²×C₃	semidirect
321. #4044	C₂²×C₃	semidirect
324. #4042	C₂²×C₃	semidirect
327. #4040	C₂²×C₃	semidirect
329. #4038	C₂²×C₃	semidirect
331. #4036	C₂²×C₃	semidirect
332. #4035	C₂²×C₃	semidirect
333. #4035	C₂²×C₃	semidirect
334. #4034	C₂²×C₃	semidirect
335. #4033	C₂²×C₃	semidirect
337. #4031	C₂²×C₃	semidirect
338. #4030	C₂²×C₃	semidirect
342. #4027	C₂²×C₃	semidirect
344. #4025	C₂²×C₃	semidirect
345. #4024	C₂²×C₃	semidirect
346. #4024	C₂²×C₃	semidirect
347. #4023	C₂²×C₃	semidirect
348. #4022	C₂²×C₃	semidirect
349. #4022	C₂²×C₃	semidirect
350. #4022	C₂²×C₃	semidirect
352. #4021	C₂²×C₃	semidirect
356. C₄×D₂₀	C₂²×C₃	semidirect
361. #4018	C₂²×C₃	semidirect
362. #4018	C₂²×C₃	semidirect
363. #4018	C₂²×C₃	semidirect
364. #4018	C₂²×C₃	semidirect
365. #4018	C₂²×C₃	semidirect
367. C₄²×D₅	C₂²×C₃	semidirect
368. #4016	C₂²×C₃	semidirect
369. #4016	C₂²×C₃	semidirect
370. C₄×Dic₁₀	C₂²×C₃	semidirect
371. C₄×Dic₁₀	C₂²×C₃	semidirect
372. C₄×Dic₁₀	C₂²×C₃	semidirect
373. C₄×Dic₁₀	C₂²×C₃	semidirect
385. C₃×C₅×D₄	#41	semidirect
429. C₃×C₄×D₅	#41	semidirect
485. C₃×C₄×Q₈	C₂×D₅	semidirect
486. C₃×C₄×Q₈	C₂×D₅	semidirect
505. C₃×C₄×D₄	C₂×D₅	semidirect
506. C₃×C₄×D₄	C₂×D₅	semidirect
519. C₃×#117	C₂×D₅	semidirect
520. C₃×#117	C₂×D₅	semidirect
530. C₂×C₃×C₄²	C₂×D₅	semidirect
531. C₂×C₃×C₄²	C₂×D₅	semidirect
656. C₄×#41	C₃×D₅	semidirect
808. C₅×D₄	C₃×#41	semidirect
852. C₄×D₅	C₃×#41	semidirect
908. C₄×Q₈	C₂×C₃×D₅	semidirect
909. C₄×Q₈	C₂×C₃×D₅	semidirect
928. C₄×D₄	C₂×C₃×D₅	semidirect
929. C₄×D₄	C₂×C₃×D₅	semidirect
942. #117	C₂×C₃×D₅	semidirect
943. #117	C₂×C₃×D₅	semidirect
953. C₂×C₄²	C₂×C₃×D₅	semidirect
954. C₂×C₄²	C₂×C₃×D₅	semidirect
984. C₃×D₄	#709	semidirect
1160. C₃×C₅	#3475	semidirect
1225. D₄	C₃×#709	semidirect
1270. C₅	C₃×#3475	semidirect
1306. C₃	#10617742	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₄×C₅×#41	2
C₃×#66163	2
C₃×#66158	2
C₃×#65915	2
C₃×#65914	2
C₃×#65912	2
C₃×#65902	2
C₃×#65890	2
C₃×#65888	2
C₃×#65881	2
C₃×C₄×D₄×D₅	2
C₃×#65874	2
C₃×#65873	2
C₃×#65872	2
C₃×C₄×#711	2
C₃×#65866	2
C₃×#65865	2
C₃×#65863	2
C₃×#65861	2
C₃×#65813	2
C₃×C₄×#709	2
C₂×C₃×#4018	2
#10617742	3
C₃×#3475	5

Subgroups — C3×#10617742 #14484142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617742 #14484142