Subgroups — C₃×#10617645 #14484118

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 1348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65867	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65866	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65865	C₂	1	2	yes	maximal, complemented
7	C₃×#65864	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65863	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65862	C₂	1	2	yes	maximal, complemented
10	C₃×#65862	C₂	1	2	yes	maximal, complemented
11	C₃×#65861	C₂	1	2	yes	maximal, complemented
12	C₃×#65858	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65856	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#65851	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#65848	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#65847	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#65845	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#65841	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#65829	C₂	1	2	yes	maximal, complemented
21	C₃×#65824	C₂	1	2	yes	maximal, complemented
22	C₃×#65813	C₂	1	2	yes	maximal, complemented
23	C₃×C₄×#709	C₂	1	2	yes	maximal, complemented
24	#10617645	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
26	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×#709	C₂²	1	1	yes	characteristic
28	C₂×C₃×#709	C₂²	1	2	yes	—
29	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
30	C₃×C₅×#117	C₂²	1	1	yes	characteristic
31	C₃×C₅×#117	C₂²	1	1	yes	characteristic
32	C₃×C₅×#117	C₂²	1	2	yes	—
33	C₃×C₅×#117	C₂²	1	2	yes	complemented
34	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
40	C₃×#4099	C₂²	1	2	yes	—
41	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
42	C₃×#4076	C₂²	1	2	yes	—
43	C₃×#4076	C₂²	1	1	yes	characteristic, complemented
44	C₃×#4076	C₂²	1	1	yes	characteristic, complemented
45	C₃×#4075	C₂²	1	2	yes	—
46	C₃×#4075	C₂²	1	2	yes	—
47	C₃×#4075	C₂²	1	2	yes	complemented
48	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
49	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
50	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
51	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
52	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
53	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
54	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
55	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
56	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
57	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
58	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
59	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
60	C₂×C₃×#685	C₂²	1	1	yes	characteristic
61	C₃×#4072	C₂²	1	1	yes	characteristic
62	C₃×#4072	C₂²	1	2	yes	complemented
63	C₃×#4070	C₂²	1	1	yes	characteristic, complemented
64	C₃×#4070	C₂²	1	2	yes	complemented
65	C₃×#4070	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₃×#683	C₂²	1	1	yes	characteristic
67	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
68	C₃×#4044	C₂²	1	2	yes	complemented
69	C₃×#4044	C₂²	1	2	yes	complemented
70	C₃×#4043	C₂²	1	1	yes	characteristic, complemented
71	C₃×#4043	C₂²	1	1	yes	characteristic, complemented
72	C₃×#4042	C₂²	1	2	yes	complemented
73	C₃×#4042	C₂²	1	2	yes	complemented
74	C₃×#4041	C₂²	1	1	yes	characteristic, complemented
75	C₃×#4041	C₂²	1	1	yes	characteristic, complemented
76	C₃×#4040	C₂²	1	2	yes	complemented
77	C₃×#4040	C₂²	1	2	yes	complemented
78	C₃×#4039	C₂²	1	1	yes	characteristic, complemented
79	C₃×#4039	C₂²	1	1	yes	characteristic, complemented
80	C₃×#4038	C₂²	1	1	yes	characteristic, complemented
81	C₃×#4038	C₂²	1	1	yes	characteristic, complemented
82	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
83	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
84	C₃×#4036	C₂²	1	1	yes	characteristic, complemented
85	C₃×#4036	C₂²	1	1	yes	characteristic, complemented
86	C₃×#4035	C₂²	1	2	yes	complemented
87	C₃×#4035	C₂²	1	2	yes	complemented
88	C₃×#4034	C₂²	1	1	yes	characteristic, complemented
89	C₃×#4034	C₂²	1	1	yes	characteristic, complemented
90	C₃×#4033	C₂²	1	1	yes	characteristic, complemented
91	C₃×#4033	C₂²	1	1	yes	characteristic, complemented
92	C₃×#4032	C₂²	1	2	yes	—
93	C₃×#4031	C₂²	1	2	yes	—
94	C₃×#4031	C₂²	1	2	yes	complemented
95	C₃×#4030	C₂²	1	2	yes	—
96	C₃×#4030	C₂²	1	2	yes	—
97	C₃×#4029	C₂²	1	2	yes	—
98	C₃×#4029	C₂²	1	2	yes	complemented
99	C₃×#4028	C₂²	1	2	yes	—
100	C₃×#4027	C₂²	1	2	yes	—
101	C₃×#4027	C₂²	1	2	yes	—
102	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₃×#4025	C₂²	1	2	yes	complemented
104	C₃×#4025	C₂²	1	2	yes	complemented
105	C₃×#4024	C₂²	1	2	yes	—
106	C₃×#4024	C₂²	1	2	yes	—
107	C₃×#4023	C₂²	1	2	yes	—
108	C₃×#4022	C₂²	1	2	yes	complemented
109	C₃×#4022	C₂²	1	2	yes	complemented
110	C₃×#4021	C₂²	1	2	yes	complemented
111	C₃×C₄×D₂₀	C₂²	1	2	yes	complemented
112	C₃×C₄×D₂₀	C₂²	1	2	yes	complemented
113	C₃×C₄×D₂₀	C₂²	1	2	yes	complemented
114	C₃×#4018	C₂²	1	2	yes	complemented
115	C₃×#4018	C₂²	1	2	yes	complemented
116	C₃×#4018	C₂²	1	2	yes	complemented
117	C₃×#4018	C₂²	1	2	yes	complemented
118	C₃×C₄²×D₅	C₂²	1	2	yes	complemented
119	C₃×C₄²×D₅	C₂²	1	2	yes	complemented
120	C₃×#4016	C₂²	1	2	yes	complemented
121	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
122	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
123	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
124	C₃×#3475	—	5	1	no	maximal, Hall
125	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
126	#66125	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×C₄×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
128	#65867	C₂×C₃	1	1	yes	characteristic, complemented
129	#65866	C₂×C₃	1	1	yes	characteristic, complemented
130	#65865	C₂×C₃	1	2	yes	complemented
131	#65864	C₂×C₃	1	1	yes	characteristic, complemented
132	#65863	C₂×C₃	1	1	yes	characteristic, complemented
133	#65862	C₂×C₃	1	2	yes	complemented
134	#65862	C₂×C₃	1	2	yes	complemented
135	#65861	C₂×C₃	1	2	yes	complemented
136	#65858	C₂×C₃	1	1	yes	characteristic, complemented
137	#65856	C₂×C₃	1	1	yes	characteristic, complemented
138	D₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
139	#65851	C₂×C₃	1	1	yes	characteristic, complemented
140	#65848	C₂×C₃	1	1	yes	characteristic, complemented
141	#65847	C₂×C₃	1	1	yes	characteristic, complemented
142	#65845	C₂×C₃	1	1	yes	characteristic, complemented
143	#65841	C₂×C₃	1	1	yes	characteristic, complemented
144	#65829	C₂×C₃	1	2	yes	complemented
145	#65824	C₂×C₃	1	2	yes	complemented
146	#65813	C₂×C₃	1	2	yes	complemented
147	C₄×#709	C₂×C₃	1	2	yes	complemented
148	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
149	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
150	C₂²×C₃×C₄×C₅	—	2	4	no	—
151	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
152	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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	—	2	4	no	—
160	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
161	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
162	C₂×C₃×C₂²⋊D₅	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₂²⋊D₅	C₂³	1	1	yes	characteristic
164	C₂×C₃×C₂²⋊D₅	C₂³	1	1	yes	characteristic
165	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
166	C₂×C₃×C₂²⋊D₅	C₂³	1	1	yes	characteristic
167	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
168	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
169	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
170	C₃×#709	—	2	4	no	—
171	C₃×#709	—	2	8	no	—
172	C₂×C₃×D₂₀	C₂³	1	2	yes	—
173	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
174	C₂×C₃×D₂₀	C₂³	1	2	yes	—
175	C₂×C₃×C₄×D₅	—	2	4	no	—
176	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
181	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
182	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
183	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
184	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
185	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
186	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
187	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
188	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₄²×C₅	C₂³	1	2	yes	—
199	C₃×C₄²×C₅	C₂³	1	2	yes	—
200	C₃×C₄²×C₅	C₂³	1	2	yes	—
201	C₃×C₄²×C₅	C₂³	1	2	yes	—
202	C₃×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
203	C₃×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
204	C₃×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
205	C₃×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
206	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
207	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
208	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
209	C₃×#685	C₂³	1	1	yes	characteristic
210	C₃×#685	C₂³	1	2	yes	—
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	2	yes	—
216	C₃×#685	C₂³	1	2	yes	—
217	C₃×#685	C₂³	1	2	yes	—
218	C₃×#685	C₂³	1	2	yes	—
219	C₃×#685	C₂³	1	1	yes	characteristic
220	C₃×#685	C₂³	1	1	yes	characteristic
221	C₃×#685	C₂³	1	2	yes	—
222	C₃×#685	C₂³	1	1	yes	characteristic
223	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
224	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
225	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
226	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
227	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
228	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
229	C₃×#683	C₂³	1	1	yes	characteristic
230	C₃×#683	C₂³	1	2	yes	—
231	C₃×#683	C₂³	1	2	yes	—
232	C₃×#683	C₂³	1	2	yes	—
233	C₃×#683	C₂³	1	2	yes	—
234	C₃×#683	C₂³	1	2	yes	—
235	C₃×#683	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
241	C₃×#683	C₂³	1	2	yes	—
242	C₃×#683	C₂³	1	1	yes	characteristic
243	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
244	C₃×C₄×Dic₅	C₂³	1	2	yes	—
245	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
246	C₃×C₄×Dic₅	C₂³	1	2	yes	—
247	C₃×C₄×Dic₅	C₂³	1	2	yes	—
248	C₃×C₄×Dic₅	C₂³	1	2	yes	—
249	C₃×C₄×Dic₅	C₂³	1	2	yes	—
250	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
251	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
252	C₃×#556	—	5	1	no	—
253	C₃×#555	—	5	1	no	—
254	C₃×#554	—	5	1	no	—
255	C₃×#553	—	5	1	no	—
256	C₃×#553	—	5	1	no	—
257	C₃×#552	—	5	2	no	—
258	C₃×#552	—	5	1	no	—
259	C₃×#552	—	5	1	no	—
260	C₃×#551	—	5	2	no	—
261	C₃×#551	—	5	2	no	—
262	C₃×#547	—	5	1	no	—
263	C₃×#546	—	5	2	no	—
264	C₃×#533	—	5	1	no	—
265	C₃×#529	—	5	2	no	—
266	C₃×#529	—	5	2	no	—
267	C₃×#529	—	5	2	no	—
268	C₃×#525	—	5	1	no	—
269	C₃×#525	—	5	1	no	—
270	C₃×C₄×#41	—	5	1	no	—
271	C₃×C₄×#41	—	5	2	no	—
272	C₂×C₃×C₄×D₄	—	5	1	no	—
273	C₂×C₃×#117	—	5	1	no	—
274	C₂×C₃×#117	D₅	1	1	yes	characteristic, complemented
275	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
276	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
277	C₂×#709	C₂²×C₃	1	2	yes	—
278	C₂×#709	C₂²×C₃	1	1	yes	characteristic
279	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
280	C₅×#117	C₂²×C₃	1	1	yes	characteristic
281	C₅×#117	C₂²×C₃	1	1	yes	characteristic
282	C₅×#117	C₂²×C₃	1	2	yes	—
283	C₅×#117	C₂²×C₃	1	2	yes	complemented
284	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
285	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
286	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
287	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
288	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
289	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	complemented
290	#4099	C₂²×C₃	1	2	yes	—
291	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
292	#4076	C₂²×C₃	1	2	yes	—
293	#4076	C₂²×C₃	1	1	yes	characteristic, complemented
294	#4076	C₂²×C₃	1	1	yes	characteristic, complemented
295	#4075	C₂²×C₃	1	2	yes	—
296	#4075	C₂²×C₃	1	2	yes	—
297	#4075	C₂²×C₃	1	2	yes	complemented
298	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
299	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
300	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
301	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
302	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
303	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
304	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
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	complemented
308	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
309	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
310	C₂×#685	C₂²×C₃	1	1	yes	characteristic
311	#4072	C₂²×C₃	1	1	yes	characteristic
312	#4072	C₂²×C₃	1	2	yes	complemented
313	#4070	C₂²×C₃	1	2	yes	complemented
314	#4070	C₂²×C₃	1	1	yes	characteristic, complemented
315	#4070	C₂²×C₃	1	1	yes	characteristic, complemented
316	C₂×#683	C₂²×C₃	1	1	yes	characteristic
317	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
318	#4044	C₂²×C₃	1	2	yes	complemented
319	#4044	C₂²×C₃	1	2	yes	complemented
320	#4043	C₂²×C₃	1	1	yes	characteristic, complemented
321	#4043	C₂²×C₃	1	1	yes	characteristic, complemented
322	#4042	C₂²×C₃	1	2	yes	complemented
323	#4042	C₂²×C₃	1	2	yes	complemented
324	#4041	C₂²×C₃	1	1	yes	characteristic, complemented
325	#4041	C₂²×C₃	1	1	yes	characteristic, complemented
326	#4040	C₂²×C₃	1	2	yes	complemented
327	#4040	C₂²×C₃	1	2	yes	complemented
328	#4039	C₂²×C₃	1	1	yes	characteristic, complemented
329	#4039	C₂²×C₃	1	1	yes	characteristic, complemented
330	#4038	C₂²×C₃	1	1	yes	characteristic, complemented
331	#4038	C₂²×C₃	1	1	yes	characteristic, complemented
332	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
333	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
334	#4036	C₂²×C₃	1	1	yes	characteristic, complemented
335	#4036	C₂²×C₃	1	1	yes	characteristic, complemented
336	#4035	C₂²×C₃	1	2	yes	complemented
337	#4035	C₂²×C₃	1	2	yes	complemented
338	#4034	C₂²×C₃	1	1	yes	characteristic, complemented
339	#4034	C₂²×C₃	1	1	yes	characteristic, complemented
340	#4033	C₂²×C₃	1	1	yes	characteristic, complemented
341	#4033	C₂²×C₃	1	1	yes	characteristic, complemented
342	#4032	C₂²×C₃	1	2	yes	—
343	#4031	C₂²×C₃	1	2	yes	—
344	#4031	C₂²×C₃	1	2	yes	complemented
345	#4030	C₂²×C₃	1	2	yes	—
346	#4030	C₂²×C₃	1	2	yes	—
347	#4029	C₂²×C₃	1	2	yes	—
348	#4029	C₂²×C₃	1	2	yes	complemented
349	#4028	C₂²×C₃	1	2	yes	—
350	#4027	C₂²×C₃	1	2	yes	—
351	#4027	C₂²×C₃	1	2	yes	—
352	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
353	#4025	C₂²×C₃	1	2	yes	complemented
354	#4025	C₂²×C₃	1	2	yes	complemented
355	#4024	C₂²×C₃	1	2	yes	—
356	#4024	C₂²×C₃	1	2	yes	—
357	#4023	C₂²×C₃	1	2	yes	—
358	#4022	C₂²×C₃	1	2	yes	complemented
359	#4022	C₂²×C₃	1	2	yes	complemented
360	#4021	C₂²×C₃	1	2	yes	complemented
361	C₄×D₂₀	C₂²×C₃	1	2	yes	complemented
362	C₄×D₂₀	C₂²×C₃	1	2	yes	complemented
363	C₄×D₂₀	C₂²×C₃	1	2	yes	complemented
364	#4018	C₂²×C₃	1	2	yes	complemented
365	#4018	C₂²×C₃	1	2	yes	complemented
366	#4018	C₂²×C₃	1	2	yes	complemented
367	#4018	C₂²×C₃	1	2	yes	complemented
368	C₄²×D₅	C₂²×C₃	1	2	yes	complemented
369	C₄²×D₅	C₂²×C₃	1	2	yes	complemented
370	#4016	C₂²×C₃	1	2	yes	complemented
371	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
372	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
373	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
374	#3475	—	5	1	no	Sylow
375	C₂³×C₃×C₅	—	2	2	no	—
376	C₂³×C₃×C₅	—	2	2	no	—
377	C₂³×C₃×C₅	—	4	1	no	—
378	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
379	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
380	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
381	C₂²×C₃×D₅	—	2	2	no	—
382	C₂²×C₃×D₅	—	2	2	no	—
383	C₂²×C₃×D₅	—	4	1	no	—
384	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
385	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
386	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
391	C₂×C₃×C₄×C₅	—	2	2	no	—
392	C₂×C₃×C₄×C₅	—	2	2	no	—
393	C₂×C₃×C₄×C₅	—	4	2	no	—
394	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
395	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
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	1	yes	characteristic
399	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
400	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
401	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
402	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
403	C₃×C₂²⋊D₅	—	2	4	no	—
404	C₃×C₂²⋊D₅	—	2	4	no	—
405	C₃×C₂²⋊D₅	—	2	2	no	—
406	C₃×C₂²⋊D₅	—	2	2	no	—
407	C₃×C₂²⋊D₅	—	2	2	no	—
408	C₃×C₂²⋊D₅	—	4	2	no	—
409	C₃×C₂²⋊D₅	#41	1	4	yes	complemented
410	C₂×C₃×Dic₅	—	2	2	no	—
411	C₂×C₃×Dic₅	—	2	2	no	—
412	C₂×C₃×Dic₅	—	4	1	no	—
413	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
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	2	yes	—
418	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
419	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
420	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
421	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
422	C₃×D₂₀	—	2	4	no	—
423	C₃×D₂₀	—	2	2	no	—
424	C₃×D₂₀	—	4	2	no	—
425	C₃×C₄×D₅	—	2	4	no	—
426	C₃×C₄×D₅	—	2	2	no	—
427	C₃×C₄×D₅	—	2	2	no	—
428	C₃×C₄×D₅	—	2	2	no	—
429	C₃×C₄×D₅	—	2	2	no	—
430	C₃×C₄×D₅	—	2	4	no	—
431	C₃×C₄×D₅	—	2	4	no	—
432	C₃×C₄×D₅	—	4	2	no	—
433	C₃×C₄×D₅	—	4	2	no	—
434	C₃×Dic₁₀	—	2	2	no	—
435	C₃×Dic₁₀	—	2	4	no	—
436	C₃×Dic₁₀	—	4	2	no	—
437	C₂×C₃×#41	—	5	1	no	—
438	C₂×C₃×#41	—	5	2	no	—
439	C₂²×C₃×D₄	—	5	1	no	—
440	C₂³×C₃×C₄	—	5	1	no	—
441	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
442	C₃×C₄⋊Q₈	—	5	1	no	—
443	C₃×C₄⋊Q₈	—	5	1	no	—
444	C₃×#126	—	5	2	no	—
445	C₃×#126	—	5	2	no	—
446	C₃×#126	—	5	2	no	—
447	C₃×#126	—	5	2	no	—
448	C₃×#126	—	5	2	no	—
449	C₃×#126	—	5	2	no	—
450	C₃×#125	—	5	2	no	—
451	C₃×#125	—	5	2	no	—
452	C₃×#125	—	5	1	no	—
453	C₃×#125	—	5	1	no	—
454	C₃×#125	—	5	2	no	—
455	C₃×#124	—	5	2	no	—
456	C₃×#124	—	5	2	no	—
457	C₃×#124	—	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×#123	—	5	2	no	—
464	C₃×#123	—	5	2	no	—
465	C₃×#123	—	5	2	no	—
466	C₃×C₂²⋊Q₈	—	5	1	no	—
467	C₃×C₂²⋊Q₈	—	5	1	no	—
468	C₃×C₂²⋊Q₈	—	5	2	no	—
469	C₃×C₂²⋊Q₈	—	5	2	no	—
470	C₃×C₂²⋊Q₈	—	5	2	no	—
471	C₃×C₂²⋊Q₈	—	5	1	no	—
472	C₃×C₂²⋊Q₈	—	5	1	no	—
473	C₃×C₂²⋊Q₈	—	5	2	no	—
474	C₃×C₂²⋊Q₈	—	5	2	no	—
475	C₃×#121	—	5	1	no	—
476	C₃×#121	—	5	1	no	—
477	C₃×#121	—	5	2	no	—
478	C₃×#121	—	5	1	no	—
479	C₃×#121	—	5	1	no	—
480	C₃×#121	—	5	2	no	—
481	C₃×#121	—	5	2	no	—
482	C₃×#120	—	5	2	no	—
483	C₃×#120	—	5	2	no	—
484	C₃×C₄×Q₈	—	5	1	no	—
485	C₃×C₄×Q₈	—	5	1	no	—
486	C₃×C₄×Q₈	—	5	2	no	—
487	C₃×C₄×Q₈	—	5	2	no	—
488	C₃×C₄×Q₈	—	5	2	no	—
489	C₃×C₄×D₄	—	5	1	no	—
490	C₃×C₄×D₄	—	5	1	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	1	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	2	no	—
500	C₃×C₄×D₄	—	5	2	no	—
501	C₃×C₄×D₄	—	5	1	no	—
502	C₃×C₄×D₄	—	5	1	no	—
503	C₃×C₄×D₄	—	5	2	no	—
504	C₃×C₄×D₄	—	5	2	no	—
505	C₃×C₄×D₄	—	5	2	no	—
506	C₃×C₄×D₄	—	5	2	no	—
507	C₃×C₄×D₄	—	5	2	no	—
508	C₃×#117	—	5	1	no	—
509	C₃×#117	—	5	2	no	—
510	C₃×#117	—	5	1	no	—
511	C₃×#117	—	5	1	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	C₂×D₅	1	1	yes	characteristic
518	C₃×#117	C₂×D₅	1	1	yes	characteristic
519	C₃×#117	C₂×D₅	1	2	yes	—
520	C₃×#117	C₂×D₅	1	2	yes	complemented
521	C₃×#117	C₂×D₅	1	1	yes	characteristic, complemented
522	C₃×#117	C₂×D₅	1	1	yes	characteristic, complemented
523	C₂×C₃×C₄⋊C₄	—	5	1	no	—
524	C₂×C₃×C₄⋊C₄	—	5	1	no	—
525	C₂×C₃×C₄⋊C₄	—	5	1	no	—
526	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
527	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
528	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
529	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
530	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
531	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
532	C₂×C₃×C₄²	—	5	1	no	—
533	C₂×C₃×C₄²	—	5	2	no	—
534	C₂×C₃×C₄²	—	5	2	no	—
535	C₂×C₃×C₄²	C₂×D₅	1	2	yes	complemented
536	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
537	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
538	C₂²×C₄×C₅	—	2	4	no	—
539	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
540	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
541	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
542	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
543	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
544	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
545	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
546	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
547	C₂×C₂²⋊D₅	—	2	4	no	—
548	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
549	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
550	C₂×C₂²⋊D₅	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₂²⋊D₅	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₂²⋊D₅	C₂³×C₃	1	1	yes	characteristic
553	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
554	C₂×C₂²⋊D₅	C₂³×C₃	1	1	yes	characteristic
555	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
556	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
557	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
558	#709	—	2	4	no	—
559	#709	—	2	8	no	—
560	C₂×D₂₀	C₂³×C₃	1	2	yes	—
561	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
562	C₂×D₂₀	C₂³×C₃	1	2	yes	—
563	C₂×C₄×D₅	—	2	4	no	—
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×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
568	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
569	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
570	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
571	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
572	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
573	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
574	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
575	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
576	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
577	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
578	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
579	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
580	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
581	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
582	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
583	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
584	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
585	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
586	C₄²×C₅	C₂³×C₃	1	2	yes	—
587	C₄²×C₅	C₂³×C₃	1	2	yes	—
588	C₄²×C₅	C₂³×C₃	1	2	yes	—
589	C₄²×C₅	C₂³×C₃	1	2	yes	—
590	C₂²⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
591	C₂²⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
592	C₂²⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
593	C₂²⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
594	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
595	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
596	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
597	#685	C₂³×C₃	1	1	yes	characteristic
598	#685	C₂³×C₃	1	2	yes	—
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	#685	C₂³×C₃	1	2	yes	—
606	#685	C₂³×C₃	1	2	yes	—
607	#685	C₂³×C₃	1	1	yes	characteristic
608	#685	C₂³×C₃	1	1	yes	characteristic
609	#685	C₂³×C₃	1	2	yes	—
610	#685	C₂³×C₃	1	1	yes	characteristic
611	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
612	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
613	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
614	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
615	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
616	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
617	#683	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
624	#683	C₂³×C₃	1	2	yes	—
625	#683	C₂³×C₃	1	2	yes	—
626	#683	C₂³×C₃	1	2	yes	—
627	#683	C₂³×C₃	1	2	yes	—
628	#683	C₂³×C₃	1	1	yes	characteristic
629	#683	C₂³×C₃	1	2	yes	—
630	#683	C₂³×C₃	1	1	yes	characteristic
631	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
632	C₄×Dic₅	C₂³×C₃	1	2	yes	—
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	C₄×Dic₅	C₂³×C₃	1	2	yes	—
637	C₄×Dic₅	C₂³×C₃	1	2	yes	—
638	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
639	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
640	#556	—	5	1	no	—
641	#555	—	5	1	no	—
642	#554	—	5	1	no	—
643	#553	—	5	1	no	—
644	#553	—	5	1	no	—
645	#552	—	5	2	no	—
646	#552	—	5	1	no	—
647	#552	—	5	1	no	—
648	#551	—	5	2	no	—
649	#551	—	5	2	no	—
650	#547	—	5	1	no	—
651	#546	—	5	2	no	—
652	#533	—	5	1	no	—
653	#529	—	5	2	no	—
654	#529	—	5	2	no	—
655	#529	—	5	2	no	—
656	#525	—	5	1	no	—
657	#525	—	5	1	no	—
658	C₄×#41	—	5	1	no	—
659	C₄×#41	—	5	2	no	—
660	C₂×C₄×D₄	—	5	1	no	—
661	C₂×#117	—	5	1	no	—
662	C₂×#117	C₃×D₅	1	1	yes	characteristic, complemented
663	C₂²×C₃×C₅	—	2	1	no	—
664	C₂²×C₃×C₅	—	2	1	no	—
665	C₂²×C₃×C₅	—	2	1	no	—
666	C₂²×C₃×C₅	—	2	1	no	—
667	C₂²×C₃×C₅	—	2	1	no	—
668	C₂²×C₃×C₅	—	2	1	no	—
669	C₂²×C₃×C₅	—	2	1	no	—
670	C₂²×C₃×C₅	—	4	4	no	—
671	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
672	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
673	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
674	C₂×C₃×D₅	—	2	1	no	—
675	C₂×C₃×D₅	—	2	1	no	—
676	C₂×C₃×D₅	—	2	1	no	—
677	C₂×C₃×D₅	—	2	2	no	—
678	C₂×C₃×D₅	—	2	2	no	—
679	C₂×C₃×D₅	—	2	1	no	—
680	C₂×C₃×D₅	—	2	2	no	—
681	C₂×C₃×D₅	—	2	1	no	—
682	C₂×C₃×D₅	—	4	4	no	—
683	C₂×C₃×D₅	C₂×#41	1	2	yes	—
684	C₃×C₄×C₅	—	2	2	no	—
685	C₃×C₄×C₅	—	2	2	no	—
686	C₃×C₄×C₅	—	2	1	no	—
687	C₃×C₄×C₅	—	2	1	no	—
688	C₃×C₄×C₅	—	2	2	no	—
689	C₃×C₄×C₅	—	2	2	no	—
690	C₃×C₄×C₅	C₂×#41	1	2	yes	—
691	C₃×C₄×C₅	C₂×#41	1	2	yes	—
692	C₃×Dic₅	—	2	2	no	—
693	C₃×Dic₅	—	2	2	no	—
694	C₃×Dic₅	—	2	1	no	—
695	C₃×Dic₅	—	2	1	no	—
696	C₃×Dic₅	—	2	1	no	—
697	C₃×Dic₅	—	2	1	no	—
698	C₃×Dic₅	—	2	2	no	—
699	C₃×Dic₅	—	2	1	no	—
700	C₃×Dic₅	C₂×#41	1	2	yes	—
701	C₂⁴×C₃	—	5	1	no	—
702	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
703	C₃×#41	—	10	8	no	—
704	C₃×#41	—	10	4	no	—
705	C₂×C₃×Q₈	—	5	1	no	—
706	C₂×C₃×Q₈	—	5	2	no	—
707	C₂×C₃×Q₈	—	5	2	no	—
708	C₂×C₃×D₄	—	5	1	no	—
709	C₂×C₃×D₄	—	5	2	no	—
710	C₂×C₃×D₄	—	5	2	no	—
711	C₂×C₃×D₄	—	5	1	no	—
712	C₂×C₃×D₄	—	5	1	no	—
713	C₂×C₃×D₄	—	5	1	no	—
714	C₂×C₃×D₄	—	5	2	no	—
715	C₂×C₃×D₄	—	5	2	no	—
716	C₂×C₃×D₄	—	5	1	no	—
717	C₂×C₃×D₄	—	5	2	no	—
718	C₂×C₃×D₄	—	10	4	no	—
719	C₂²×C₃×C₄	—	2	4	no	—
720	C₂²×C₃×C₄	—	5	1	no	—
721	C₂²×C₃×C₄	—	5	1	no	—
722	C₂²×C₃×C₄	—	5	1	no	—
723	C₂²×C₃×C₄	—	5	2	no	—
724	C₂²×C₃×C₄	—	5	2	no	—
725	C₂²×C₃×C₄	—	5	1	no	—
726	C₂²×C₃×C₄	—	5	1	no	—
727	C₂²×C₃×C₄	—	5	1	no	—
728	C₂²×C₃×C₄	—	5	2	no	—
729	C₂²×C₃×C₄	—	5	1	no	—
730	C₂²×C₃×C₄	—	5	2	no	—
731	C₂²×C₃×C₄	—	5	2	no	—
732	C₂²×C₃×C₄	—	10	4	no	—
733	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
734	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
735	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
736	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
737	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
738	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
739	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
740	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
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	1	no	—
746	C₃×C₄⋊C₄	—	5	1	no	—
747	C₃×C₄⋊C₄	—	5	2	no	—
748	C₃×C₄⋊C₄	—	5	2	no	—
749	C₃×C₄⋊C₄	—	5	2	no	—
750	C₃×C₄⋊C₄	—	5	2	no	—
751	C₃×C₄⋊C₄	—	5	2	no	—
752	C₃×C₄⋊C₄	—	5	2	no	—
753	C₃×C₄⋊C₄	—	5	2	no	—
754	C₃×C₄⋊C₄	—	5	2	no	—
755	C₃×C₄⋊C₄	—	5	1	no	—
756	C₃×C₄⋊C₄	—	5	1	no	—
757	C₃×C₄⋊C₄	—	5	2	no	—
758	C₃×C₄⋊C₄	—	5	2	no	—
759	C₃×C₄⋊C₄	—	5	2	no	—
760	C₃×C₄⋊C₄	—	5	2	no	—
761	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
762	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
763	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
764	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
765	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
766	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
767	C₃×C₂²⋊C₄	—	5	1	no	—
768	C₃×C₂²⋊C₄	—	5	2	no	—
769	C₃×C₂²⋊C₄	—	5	1	no	—
770	C₃×C₂²⋊C₄	—	5	1	no	—
771	C₃×C₂²⋊C₄	—	5	1	no	—
772	C₃×C₂²⋊C₄	—	5	2	no	—
773	C₃×C₂²⋊C₄	—	5	2	no	—
774	C₃×C₂²⋊C₄	—	5	1	no	—
775	C₃×C₂²⋊C₄	—	5	2	no	—
776	C₃×C₂²⋊C₄	—	5	2	no	—
777	C₃×C₂²⋊C₄	—	5	1	no	—
778	C₃×C₂²⋊C₄	—	5	1	no	—
779	C₃×C₂²⋊C₄	—	5	1	no	—
780	C₃×C₂²⋊C₄	—	5	2	no	—
781	C₃×C₂²⋊C₄	—	5	2	no	—
782	C₃×C₂²⋊C₄	—	5	2	no	—
783	C₃×C₂²⋊C₄	—	5	2	no	—
784	C₃×C₂²⋊C₄	—	5	2	no	—
785	C₃×C₂²⋊C₄	—	5	2	no	—
786	C₃×C₂²⋊C₄	—	5	2	no	—
787	C₃×C₂²⋊C₄	—	5	2	no	—
788	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
789	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
790	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
791	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
792	C₃×C₄²	—	5	2	no	—
793	C₃×C₄²	—	5	2	no	—
794	C₃×C₄²	—	5	2	no	—
795	C₃×C₄²	—	5	1	no	—
796	C₃×C₄²	—	5	1	no	—
797	C₃×C₄²	—	5	2	no	—
798	C₃×C₄²	—	5	1	no	—
799	C₃×C₄²	—	5	1	no	—
800	C₃×C₄²	—	5	2	no	—
801	C₃×C₄²	C₂²×D₅	1	2	yes	—
802	C₃×C₄²	C₂²×D₅	1	2	yes	—
803	C₃×C₄²	C₂²×D₅	1	2	yes	—
804	C₃×C₄²	C₂²×D₅	1	2	yes	—
805	C₂³×C₅	—	2	2	no	—
806	C₂³×C₅	—	2	2	no	—
807	C₂³×C₅	—	4	1	no	—
808	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
809	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
810	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
811	C₂²×D₅	—	2	2	no	—
812	C₂²×D₅	—	2	2	no	—
813	C₂²×D₅	—	4	1	no	—
814	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
815	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
816	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
817	C₂×C₄×C₅	—	2	4	no	—
818	C₂×C₄×C₅	—	2	2	no	—
819	C₂×C₄×C₅	—	2	2	no	—
820	C₂×C₄×C₅	—	2	2	no	—
821	C₂×C₄×C₅	—	2	2	no	—
822	C₂×C₄×C₅	—	2	2	no	—
823	C₂×C₄×C₅	—	4	2	no	—
824	C₂×C₄×C₅	C₃×#41	1	4	yes	complemented
825	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
826	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
827	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
828	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
829	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
830	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
831	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
832	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
833	C₂²⋊D₅	—	2	4	no	—
834	C₂²⋊D₅	—	2	4	no	—
835	C₂²⋊D₅	—	2	2	no	—
836	C₂²⋊D₅	—	2	2	no	—
837	C₂²⋊D₅	—	2	2	no	—
838	C₂²⋊D₅	—	4	2	no	—
839	C₂²⋊D₅	C₃×#41	1	4	yes	complemented
840	C₂×Dic₅	—	2	2	no	—
841	C₂×Dic₅	—	2	2	no	—
842	C₂×Dic₅	—	4	1	no	—
843	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
844	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
845	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
846	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
847	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
848	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
849	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
850	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
851	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
852	D₂₀	—	2	4	no	—
853	D₂₀	—	2	2	no	—
854	D₂₀	—	4	2	no	—
855	C₄×D₅	—	2	4	no	—
856	C₄×D₅	—	2	2	no	—
857	C₄×D₅	—	2	2	no	—
858	C₄×D₅	—	2	2	no	—
859	C₄×D₅	—	2	2	no	—
860	C₄×D₅	—	2	4	no	—
861	C₄×D₅	—	2	4	no	—
862	C₄×D₅	—	4	2	no	—
863	C₄×D₅	—	4	2	no	—
864	Dic₁₀	—	2	2	no	—
865	Dic₁₀	—	2	4	no	—
866	Dic₁₀	—	4	2	no	—
867	C₂×#41	—	5	1	no	—
868	C₂×#41	—	5	2	no	—
869	C₂²×D₄	—	5	1	no	—
870	C₂³×C₄	—	5	1	no	—
871	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
872	C₄⋊Q₈	—	5	1	no	—
873	C₄⋊Q₈	—	5	1	no	—
874	#126	—	5	2	no	—
875	#126	—	5	2	no	—
876	#126	—	5	2	no	—
877	#126	—	5	2	no	—
878	#126	—	5	2	no	—
879	#126	—	5	2	no	—
880	#125	—	5	2	no	—
881	#125	—	5	2	no	—
882	#125	—	5	1	no	—
883	#125	—	5	1	no	—
884	#125	—	5	2	no	—
885	#124	—	5	2	no	—
886	#124	—	5	2	no	—
887	#124	—	5	2	no	—
888	#123	—	5	2	no	—
889	#123	—	5	2	no	—
890	#123	—	5	2	no	—
891	#123	—	5	2	no	—
892	#123	—	5	2	no	—
893	#123	—	5	2	no	—
894	#123	—	5	2	no	—
895	#123	—	5	2	no	—
896	C₂²⋊Q₈	—	5	1	no	—
897	C₂²⋊Q₈	—	5	1	no	—
898	C₂²⋊Q₈	—	5	2	no	—
899	C₂²⋊Q₈	—	5	1	no	—
900	C₂²⋊Q₈	—	5	1	no	—
901	C₂²⋊Q₈	—	5	2	no	—
902	C₂²⋊Q₈	—	5	2	no	—
903	C₂²⋊Q₈	—	5	2	no	—
904	C₂²⋊Q₈	—	5	2	no	—
905	#121	—	5	1	no	—
906	#121	—	5	1	no	—
907	#121	—	5	2	no	—
908	#121	—	5	1	no	—
909	#121	—	5	1	no	—
910	#121	—	5	2	no	—
911	#121	—	5	2	no	—
912	#120	—	5	2	no	—
913	#120	—	5	2	no	—
914	C₄×Q₈	—	5	1	no	—
915	C₄×Q₈	—	5	1	no	—
916	C₄×Q₈	—	5	2	no	—
917	C₄×Q₈	—	5	2	no	—
918	C₄×Q₈	—	5	2	no	—
919	C₄×D₄	—	5	1	no	—
920	C₄×D₄	—	5	1	no	—
921	C₄×D₄	—	5	1	no	—
922	C₄×D₄	—	5	1	no	—
923	C₄×D₄	—	5	1	no	—
924	C₄×D₄	—	5	1	no	—
925	C₄×D₄	—	5	1	no	—
926	C₄×D₄	—	5	1	no	—
927	C₄×D₄	—	5	2	no	—
928	C₄×D₄	—	5	2	no	—
929	C₄×D₄	—	5	2	no	—
930	C₄×D₄	—	5	2	no	—
931	C₄×D₄	—	5	1	no	—
932	C₄×D₄	—	5	1	no	—
933	C₄×D₄	—	5	2	no	—
934	C₄×D₄	—	5	2	no	—
935	C₄×D₄	—	5	2	no	—
936	C₄×D₄	—	5	2	no	—
937	C₄×D₄	—	5	2	no	—
938	#117	—	5	1	no	—
939	#117	—	5	2	no	—
940	#117	—	5	1	no	—
941	#117	—	5	1	no	—
942	#117	—	5	2	no	—
943	#117	—	5	2	no	—
944	#117	—	5	2	no	—
945	#117	—	5	2	no	—
946	#117	—	5	2	no	—
947	#117	C₂×C₃×D₅	1	1	yes	characteristic
948	#117	C₂×C₃×D₅	1	1	yes	characteristic
949	#117	C₂×C₃×D₅	1	2	yes	—
950	#117	C₂×C₃×D₅	1	2	yes	complemented
951	#117	C₂×C₃×D₅	1	1	yes	characteristic, complemented
952	#117	C₂×C₃×D₅	1	1	yes	characteristic, complemented
953	C₂×C₄⋊C₄	—	5	1	no	—
954	C₂×C₄⋊C₄	—	5	1	no	—
955	C₂×C₄⋊C₄	—	5	1	no	—
956	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
957	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
958	C₂×C₂²⋊C₄	—	5	1	no	—
959	C₂×C₂²⋊C₄	—	5	1	no	—
960	C₂×C₂²⋊C₄	—	5	2	no	—
961	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
962	C₂×C₄²	—	5	1	no	—
963	C₂×C₄²	—	5	2	no	—
964	C₂×C₄²	—	5	2	no	—
965	C₂×C₄²	C₂×C₃×D₅	1	2	yes	complemented
966	C₂×C₃×C₅	—	2	2	no	—
967	C₂×C₃×C₅	—	2	2	no	—
968	C₂×C₃×C₅	—	4	1	no	—
969	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
970	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
971	C₂×C₃×C₅	#585	1	1	yes	characteristic
972	C₃×D₅	—	2	2	no	—
973	C₃×D₅	—	4	2	no	—
974	C₃×D₅	—	4	1	no	—
975	C₂³×C₃	—	2	2	no	—
976	C₂³×C₃	—	2	2	no	—
977	C₂³×C₃	—	4	1	no	—
978	C₂³×C₃	—	5	1	no	—
979	C₂³×C₃	—	5	1	no	—
980	C₂³×C₃	—	5	2	no	—
981	C₂³×C₃	—	10	2	no	—
982	C₂³×C₃	—	10	2	no	—
983	C₂³×C₃	—	20	1	no	—
984	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
985	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
986	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
987	C₃×Q₈	—	10	4	no	—
988	C₃×Q₈	—	10	2	no	—
989	C₃×Q₈	—	20	2	no	—
990	C₃×D₄	—	5	4	no	—
991	C₃×D₄	—	10	4	no	—
992	C₃×D₄	—	10	2	no	—
993	C₃×D₄	—	10	2	no	—
994	C₃×D₄	—	10	4	no	—
995	C₃×D₄	—	10	2	no	—
996	C₃×D₄	—	10	4	no	—
997	C₃×D₄	—	10	2	no	—
998	C₃×D₄	—	20	2	no	—
999	C₃×D₄	—	20	2	no	—
1000	C₂×C₃×C₄	—	2	2	no	—
1001	C₂×C₃×C₄	—	2	4	no	—
1002	C₂×C₃×C₄	—	2	2	no	—
1003	C₂×C₃×C₄	—	2	2	no	—
1004	C₂×C₃×C₄	—	2	2	no	—
1005	C₂×C₃×C₄	—	2	2	no	—
1006	C₂×C₃×C₄	—	4	2	no	—
1007	C₂×C₃×C₄	—	5	1	no	—
1008	C₂×C₃×C₄	—	5	1	no	—
1009	C₂×C₃×C₄	—	5	1	no	—
1010	C₂×C₃×C₄	—	5	1	no	—
1011	C₂×C₃×C₄	—	5	2	no	—
1012	C₂×C₃×C₄	—	5	2	no	—
1013	C₂×C₃×C₄	—	5	2	no	—
1014	C₂×C₃×C₄	—	5	1	no	—
1015	C₂×C₃×C₄	—	5	1	no	—
1016	C₂×C₃×C₄	—	10	4	no	—
1017	C₂×C₃×C₄	—	10	4	no	—
1018	C₂×C₃×C₄	—	10	2	no	—
1019	C₂×C₃×C₄	—	10	2	no	—
1020	C₂×C₃×C₄	—	10	2	no	—
1021	C₂×C₃×C₄	—	10	2	no	—
1022	C₂×C₃×C₄	—	10	2	no	—
1023	C₂×C₃×C₄	—	10	2	no	—
1024	C₂×C₃×C₄	—	10	4	no	—
1025	C₂×C₃×C₄	—	20	2	no	—
1026	C₂×C₃×C₄	—	20	2	no	—
1027	C₂×C₃×C₄	—	20	1	no	—
1028	C₂×C₃×C₄	#709	1	4	yes	complemented
1029	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1030	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1031	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1032	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1033	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1034	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1035	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1036	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1037	C₂²×C₅	—	2	1	no	—
1038	C₂²×C₅	—	2	1	no	—
1039	C₂²×C₅	—	2	1	no	—
1040	C₂²×C₅	—	2	1	no	—
1041	C₂²×C₅	—	2	1	no	—
1042	C₂²×C₅	—	2	1	no	—
1043	C₂²×C₅	—	2	1	no	—
1044	C₂²×C₅	—	4	4	no	—
1045	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
1046	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
1047	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
1048	C₂×D₅	—	2	1	no	—
1049	C₂×D₅	—	2	1	no	—
1050	C₂×D₅	—	2	1	no	—
1051	C₂×D₅	—	2	2	no	—
1052	C₂×D₅	—	2	2	no	—
1053	C₂×D₅	—	2	1	no	—
1054	C₂×D₅	—	2	2	no	—
1055	C₂×D₅	—	2	1	no	—
1056	C₂×D₅	—	4	4	no	—
1057	C₂×D₅	C₂×C₃×#41	1	2	yes	—
1058	C₄×C₅	—	2	2	no	—
1059	C₄×C₅	—	2	2	no	—
1060	C₄×C₅	—	2	1	no	—
1061	C₄×C₅	—	2	1	no	—
1062	C₄×C₅	—	2	2	no	—
1063	C₄×C₅	—	2	2	no	—
1064	C₄×C₅	C₂×C₃×#41	1	2	yes	—
1065	C₄×C₅	C₂×C₃×#41	1	2	yes	—
1066	Dic₅	—	2	2	no	—
1067	Dic₅	—	2	2	no	—
1068	Dic₅	—	2	1	no	—
1069	Dic₅	—	2	1	no	—
1070	Dic₅	—	2	1	no	—
1071	Dic₅	—	2	1	no	—
1072	Dic₅	—	2	2	no	—
1073	Dic₅	—	2	1	no	—
1074	Dic₅	C₂×C₃×#41	1	2	yes	—
1075	C₂⁴	—	5	1	no	—
1076	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
1077	#41	—	10	8	no	—
1078	#41	—	10	4	no	—
1079	C₂×Q₈	—	5	1	no	—
1080	C₂×Q₈	—	5	2	no	—
1081	C₂×Q₈	—	5	2	no	—
1082	C₂×D₄	—	5	1	no	—
1083	C₂×D₄	—	5	2	no	—
1084	C₂×D₄	—	5	2	no	—
1085	C₂×D₄	—	5	1	no	—
1086	C₂×D₄	—	5	1	no	—
1087	C₂×D₄	—	5	1	no	—
1088	C₂×D₄	—	5	2	no	—
1089	C₂×D₄	—	5	2	no	—
1090	C₂×D₄	—	5	1	no	—
1091	C₂×D₄	—	5	2	no	—
1092	C₂×D₄	—	10	4	no	—
1093	C₂²×C₄	—	2	4	no	—
1094	C₂²×C₄	—	5	1	no	—
1095	C₂²×C₄	—	5	1	no	—
1096	C₂²×C₄	—	5	1	no	—
1097	C₂²×C₄	—	5	1	no	—
1098	C₂²×C₄	—	5	2	no	—
1099	C₂²×C₄	—	5	2	no	—
1100	C₂²×C₄	—	5	2	no	—
1101	C₂²×C₄	—	5	1	no	—
1102	C₂²×C₄	—	5	1	no	—
1103	C₂²×C₄	—	5	1	no	—
1104	C₂²×C₄	—	5	2	no	—
1105	C₂²×C₄	—	5	2	no	—
1106	C₂²×C₄	—	10	4	no	—
1107	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1108	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
1109	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1110	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1111	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1112	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1113	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
1114	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1115	C₄⋊C₄	—	5	1	no	—
1116	C₄⋊C₄	—	5	1	no	—
1117	C₄⋊C₄	—	5	1	no	—
1118	C₄⋊C₄	—	5	2	no	—
1119	C₄⋊C₄	—	5	2	no	—
1120	C₄⋊C₄	—	5	1	no	—
1121	C₄⋊C₄	—	5	1	no	—
1122	C₄⋊C₄	—	5	1	no	—
1123	C₄⋊C₄	—	5	2	no	—
1124	C₄⋊C₄	—	5	2	no	—
1125	C₄⋊C₄	—	5	2	no	—
1126	C₄⋊C₄	—	5	2	no	—
1127	C₄⋊C₄	—	5	2	no	—
1128	C₄⋊C₄	—	5	2	no	—
1129	C₄⋊C₄	—	5	2	no	—
1130	C₄⋊C₄	—	5	2	no	—
1131	C₄⋊C₄	—	5	2	no	—
1132	C₄⋊C₄	—	5	2	no	—
1133	C₄⋊C₄	—	5	2	no	—
1134	C₄⋊C₄	—	5	2	no	—
1135	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1136	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1137	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1138	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1139	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1140	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1141	C₂²⋊C₄	—	5	1	no	—
1142	C₂²⋊C₄	—	5	2	no	—
1143	C₂²⋊C₄	—	5	1	no	—
1144	C₂²⋊C₄	—	5	1	no	—
1145	C₂²⋊C₄	—	5	1	no	—
1146	C₂²⋊C₄	—	5	2	no	—
1147	C₂²⋊C₄	—	5	2	no	—
1148	C₂²⋊C₄	—	5	1	no	—
1149	C₂²⋊C₄	—	5	2	no	—
1150	C₂²⋊C₄	—	5	2	no	—
1151	C₂²⋊C₄	—	5	1	no	—
1152	C₂²⋊C₄	—	5	1	no	—
1153	C₂²⋊C₄	—	5	1	no	—
1154	C₂²⋊C₄	—	5	2	no	—
1155	C₂²⋊C₄	—	5	2	no	—
1156	C₂²⋊C₄	—	5	2	no	—
1157	C₂²⋊C₄	—	5	2	no	—
1158	C₂²⋊C₄	—	5	2	no	—
1159	C₂²⋊C₄	—	5	2	no	—
1160	C₂²⋊C₄	—	5	2	no	—
1161	C₂²⋊C₄	—	5	2	no	—
1162	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1163	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1164	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1165	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1166	C₄²	—	5	1	no	—
1167	C₄²	—	5	2	no	—
1168	C₄²	—	5	1	no	—
1169	C₄²	—	5	2	no	—
1170	C₄²	—	5	2	no	—
1171	C₄²	—	5	2	no	—
1172	C₄²	—	5	1	no	—
1173	C₄²	—	5	1	no	—
1174	C₄²	—	5	2	no	—
1175	C₄²	C₂²×C₃×D₅	1	2	yes	—
1176	C₄²	C₂²×C₃×D₅	1	2	yes	—
1177	C₄²	C₂²×C₃×D₅	1	2	yes	—
1178	C₄²	C₂²×C₃×D₅	1	2	yes	—
1179	C₃×C₅	#3475	1	1	yes	characteristic, complemented, Hall
1180	C₂²×C₃	—	2	1	no	—
1181	C₂²×C₃	—	2	1	no	—
1182	C₂²×C₃	—	2	1	no	—
1183	C₂²×C₃	—	2	1	no	—
1184	C₂²×C₃	—	2	1	no	—
1185	C₂²×C₃	—	2	1	no	—
1186	C₂²×C₃	—	2	1	no	—
1187	C₂²×C₃	—	4	4	no	—
1188	C₂²×C₃	—	5	2	no	—
1189	C₂²×C₃	—	10	1	no	—
1190	C₂²×C₃	—	10	1	no	—
1191	C₂²×C₃	—	10	1	no	—
1192	C₂²×C₃	—	10	2	no	—
1193	C₂²×C₃	—	10	2	no	—
1194	C₂²×C₃	—	10	1	no	—
1195	C₂²×C₃	—	10	2	no	—
1196	C₂²×C₃	—	10	1	no	—
1197	C₂²×C₃	—	20	4	no	—
1198	C₂²×C₃	C₂×#709	1	2	yes	—
1199	C₂²×C₃	D₅×#41	1	2	yes	—
1200	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
1201	C₃×C₄	—	2	1	no	—
1202	C₃×C₄	—	2	1	no	—
1203	C₃×C₄	—	2	2	no	—
1204	C₃×C₄	—	2	2	no	—
1205	C₃×C₄	—	2	2	no	—
1206	C₃×C₄	—	2	2	no	—
1207	C₃×C₄	—	5	2	no	—
1208	C₃×C₄	—	10	1	no	—
1209	C₃×C₄	—	10	1	no	—
1210	C₃×C₄	—	10	2	no	—
1211	C₃×C₄	—	10	1	no	—
1212	C₃×C₄	—	10	2	no	—
1213	C₃×C₄	—	10	1	no	—
1214	C₃×C₄	—	10	2	no	—
1215	C₃×C₄	—	10	1	no	—
1216	C₃×C₄	C₂×#709	1	2	yes	—
1217	C₃×C₄	C₂×#709	1	2	yes	—
1218	C₂×C₅	—	2	2	no	—
1219	C₂×C₅	—	2	2	no	—
1220	C₂×C₅	—	4	1	no	—
1221	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
1222	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
1223	C₂×C₅	C₃×#585	1	1	yes	characteristic
1224	D₅	—	2	2	no	—
1225	D₅	—	4	1	no	—
1226	D₅	—	4	2	no	—
1227	C₂³	—	2	2	no	—
1228	C₂³	—	2	2	no	—
1229	C₂³	—	4	1	no	—
1230	C₂³	—	5	1	no	—
1231	C₂³	—	5	1	no	—
1232	C₂³	—	5	2	no	—
1233	C₂³	—	10	2	no	—
1234	C₂³	—	10	2	no	—
1235	C₂³	—	20	1	no	—
1236	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
1237	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
1238	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
1239	Q₈	—	10	4	no	—
1240	Q₈	—	10	2	no	—
1241	Q₈	—	20	2	no	—
1242	D₄	—	5	4	no	—
1243	D₄	—	10	4	no	—
1244	D₄	—	10	2	no	—
1245	D₄	—	10	2	no	—
1246	D₄	—	10	4	no	—
1247	D₄	—	10	2	no	—
1248	D₄	—	10	4	no	—
1249	D₄	—	10	2	no	—
1250	D₄	—	20	2	no	—
1251	D₄	—	20	2	no	—
1252	C₂×C₄	—	2	2	no	—
1253	C₂×C₄	—	2	4	no	—
1254	C₂×C₄	—	2	2	no	—
1255	C₂×C₄	—	2	2	no	—
1256	C₂×C₄	—	2	2	no	—
1257	C₂×C₄	—	2	2	no	—
1258	C₂×C₄	—	4	2	no	—
1259	C₂×C₄	—	5	1	no	—
1260	C₂×C₄	—	5	1	no	—
1261	C₂×C₄	—	5	1	no	—
1262	C₂×C₄	—	5	1	no	—
1263	C₂×C₄	—	5	2	no	—
1264	C₂×C₄	—	5	2	no	—
1265	C₂×C₄	—	5	2	no	—
1266	C₂×C₄	—	5	1	no	—
1267	C₂×C₄	—	5	1	no	—
1268	C₂×C₄	—	10	4	no	—
1269	C₂×C₄	—	10	4	no	—
1270	C₂×C₄	—	10	2	no	—
1271	C₂×C₄	—	10	2	no	—
1272	C₂×C₄	—	10	2	no	—
1273	C₂×C₄	—	10	2	no	—
1274	C₂×C₄	—	10	2	no	—
1275	C₂×C₄	—	10	2	no	—
1276	C₂×C₄	—	10	4	no	—
1277	C₂×C₄	—	20	2	no	—
1278	C₂×C₄	—	20	2	no	—
1279	C₂×C₄	—	20	1	no	—
1280	C₂×C₄	C₃×#709	1	4	yes	complemented
1281	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1282	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1283	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1284	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1285	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1286	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1287	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1288	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1289	C₂×C₃	—	2	2	no	—
1290	C₂×C₃	—	2	2	no	—
1291	C₂×C₃	—	4	1	no	—
1292	C₂×C₃	—	10	2	no	—
1293	C₂×C₃	—	20	1	no	—
1294	C₂×C₃	—	20	2	no	—
1295	C₂×C₃	C₂²×#709	1	1	yes	characteristic
1296	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
1297	C₂×C₃	#66283	1	1	yes	characteristic
1298	C₅	C₃×#3475	1	1	yes	characteristic, complemented, Sylow
1299	C₂²	—	2	1	no	—
1300	C₂²	—	2	1	no	—
1301	C₂²	—	2	1	no	—
1302	C₂²	—	2	1	no	—
1303	C₂²	—	2	1	no	—
1304	C₂²	—	2	1	no	—
1305	C₂²	—	2	1	no	—
1306	C₂²	—	4	4	no	—
1307	C₂²	—	5	2	no	—
1308	C₂²	—	10	1	no	—
1309	C₂²	—	10	1	no	—
1310	C₂²	—	10	1	no	—
1311	C₂²	—	10	2	no	—
1312	C₂²	—	10	2	no	—
1313	C₂²	—	10	1	no	—
1314	C₂²	—	10	2	no	—
1315	C₂²	—	10	1	no	—
1316	C₂²	—	20	4	no	—
1317	C₂²	C₂×C₃×#709	1	2	yes	—
1318	C₂²	C₃×D₅×#41	1	2	yes	—
1319	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
1320	C₄	—	2	1	no	—
1321	C₄	—	2	1	no	—
1322	C₄	—	2	2	no	—
1323	C₄	—	2	2	no	—
1324	C₄	—	2	2	no	—
1325	C₄	—	2	2	no	—
1326	C₄	—	5	2	no	—
1327	C₄	—	10	1	no	—
1328	C₄	—	10	1	no	—
1329	C₄	—	10	2	no	—
1330	C₄	—	10	1	no	—
1331	C₄	—	10	2	no	—
1332	C₄	—	10	1	no	—
1333	C₄	—	10	2	no	—
1334	C₄	—	10	1	no	—
1335	C₄	C₂×C₃×#709	1	2	yes	—
1336	C₄	C₂×C₃×#709	1	2	yes	—
1337	C₃	#10617645	1	1	yes	characteristic, direct product factor, Sylow
1338	C₂	—	2	2	no	—
1339	C₂	—	2	2	no	—
1340	C₂	—	4	1	no	—
1341	C₂	—	10	2	no	—
1342	C₂	—	20	1	no	—
1343	C₂	—	20	2	no	—
1344	C₂	C₂²×C₃×#709	1	1	yes	characteristic
1345	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
1346	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	C₂×C₃×C₅×#117	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₂×C₃×#117	D₅
hypocenter	C₅	C₃×#3475
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×#117

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#117	C₂	semidirect
2. C₃×#66125	C₂	semidirect
3. C₂×C₃×C₄×C₂²⋊D₅	C₂	semidirect
4. C₃×#65867	C₂	semidirect
5. C₃×#65866	C₂	semidirect
6. C₃×#65865	C₂	semidirect
7. C₃×#65864	C₂	semidirect
8. C₃×#65863	C₂	semidirect
9. C₃×#65862	C₂	semidirect
10. C₃×#65862	C₂	semidirect
11. C₃×#65861	C₂	semidirect
12. C₃×#65858	C₂	semidirect
13. C₃×#65856	C₂	semidirect
14. C₃×D₅×#117	C₂	semidirect
15. C₃×#65851	C₂	semidirect
16. C₃×#65848	C₂	semidirect
17. C₃×#65847	C₂	semidirect
18. C₃×#65845	C₂	semidirect
19. C₃×#65841	C₂	semidirect
20. C₃×#65829	C₂	semidirect
21. C₃×#65824	C₂	semidirect
22. C₃×#65813	C₂	semidirect
23. C₃×C₄×#709	C₂	semidirect
24. #10617645	C₃	direct (N × H)
33. C₃×C₅×#117	C₂²	semidirect
34. C₃×C₅×#117	C₂²	semidirect
35. C₃×C₅×#117	C₂²	semidirect
36. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
37. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
39. C₂×C₃×C₄²×C₅	C₂²	semidirect
43. C₃×#4076	C₂²	semidirect
44. C₃×#4076	C₂²	semidirect
47. C₃×#4075	C₂²	semidirect
57. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
58. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
59. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
62. C₃×#4072	C₂²	semidirect
63. C₃×#4070	C₂²	semidirect
64. C₃×#4070	C₂²	semidirect
65. C₃×#4070	C₂²	semidirect
68. C₃×#4044	C₂²	semidirect
69. C₃×#4044	C₂²	semidirect
70. C₃×#4043	C₂²	semidirect
71. C₃×#4043	C₂²	semidirect
72. C₃×#4042	C₂²	semidirect
73. C₃×#4042	C₂²	semidirect
74. C₃×#4041	C₂²	semidirect
75. C₃×#4041	C₂²	semidirect
76. C₃×#4040	C₂²	semidirect
77. C₃×#4040	C₂²	semidirect
78. C₃×#4039	C₂²	semidirect
79. C₃×#4039	C₂²	semidirect
80. C₃×#4038	C₂²	semidirect
81. C₃×#4038	C₂²	semidirect
82. C₃×D₅×C₄⋊C₄	C₂²	semidirect
83. C₃×D₅×C₄⋊C₄	C₂²	semidirect
84. C₃×#4036	C₂²	semidirect
85. C₃×#4036	C₂²	semidirect
86. C₃×#4035	C₂²	semidirect
87. C₃×#4035	C₂²	semidirect
88. C₃×#4034	C₂²	semidirect
89. C₃×#4034	C₂²	semidirect
90. C₃×#4033	C₂²	semidirect
91. C₃×#4033	C₂²	semidirect
94. C₃×#4031	C₂²	semidirect
98. C₃×#4029	C₂²	semidirect
103. C₃×#4025	C₂²	semidirect
104. C₃×#4025	C₂²	semidirect
108. C₃×#4022	C₂²	semidirect
109. C₃×#4022	C₂²	semidirect
110. C₃×#4021	C₂²	semidirect
111. C₃×C₄×D₂₀	C₂²	semidirect
112. C₃×C₄×D₂₀	C₂²	semidirect
113. C₃×C₄×D₂₀	C₂²	semidirect
114. C₃×#4018	C₂²	semidirect
115. C₃×#4018	C₂²	semidirect
116. C₃×#4018	C₂²	semidirect
117. C₃×#4018	C₂²	semidirect
118. C₃×C₄²×D₅	C₂²	semidirect
119. C₃×C₄²×D₅	C₂²	semidirect
120. C₃×#4016	C₂²	semidirect
121. C₃×C₄×Dic₁₀	C₂²	semidirect
122. C₃×C₄×Dic₁₀	C₂²	semidirect
123. C₃×C₄×Dic₁₀	C₂²	semidirect
125. C₂×C₅×#117	C₂×C₃	semidirect
126. #66125	C₂×C₃	semidirect
127. C₂×C₄×C₂²⋊D₅	C₂×C₃	semidirect
128. #65867	C₂×C₃	semidirect
129. #65866	C₂×C₃	semidirect
130. #65865	C₂×C₃	semidirect
131. #65864	C₂×C₃	semidirect
132. #65863	C₂×C₃	semidirect
133. #65862	C₂×C₃	semidirect
134. #65862	C₂×C₃	semidirect
135. #65861	C₂×C₃	semidirect
136. #65858	C₂×C₃	semidirect
137. #65856	C₂×C₃	semidirect
138. D₅×#117	C₂×C₃	semidirect
139. #65851	C₂×C₃	semidirect
140. #65848	C₂×C₃	semidirect
141. #65847	C₂×C₃	semidirect
142. #65845	C₂×C₃	semidirect
143. #65841	C₂×C₃	semidirect
144. #65829	C₂×C₃	semidirect
145. #65824	C₂×C₃	semidirect
146. #65813	C₂×C₃	semidirect
147. C₄×#709	C₂×C₃	semidirect
274. C₂×C₃×#117	D₅	semidirect
283. C₅×#117	C₂²×C₃	semidirect
284. C₅×#117	C₂²×C₃	semidirect
285. C₅×#117	C₂²×C₃	semidirect
286. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
287. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
289. C₂×C₄²×C₅	C₂²×C₃	semidirect
293. #4076	C₂²×C₃	semidirect
294. #4076	C₂²×C₃	semidirect
297. #4075	C₂²×C₃	semidirect
307. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
308. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
309. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
312. #4072	C₂²×C₃	semidirect
313. #4070	C₂²×C₃	semidirect
314. #4070	C₂²×C₃	semidirect
315. #4070	C₂²×C₃	semidirect
318. #4044	C₂²×C₃	semidirect
319. #4044	C₂²×C₃	semidirect
320. #4043	C₂²×C₃	semidirect
321. #4043	C₂²×C₃	semidirect
322. #4042	C₂²×C₃	semidirect
323. #4042	C₂²×C₃	semidirect
324. #4041	C₂²×C₃	semidirect
325. #4041	C₂²×C₃	semidirect
326. #4040	C₂²×C₃	semidirect
327. #4040	C₂²×C₃	semidirect
328. #4039	C₂²×C₃	semidirect
329. #4039	C₂²×C₃	semidirect
330. #4038	C₂²×C₃	semidirect
331. #4038	C₂²×C₃	semidirect
332. D₅×C₄⋊C₄	C₂²×C₃	semidirect
333. D₅×C₄⋊C₄	C₂²×C₃	semidirect
334. #4036	C₂²×C₃	semidirect
335. #4036	C₂²×C₃	semidirect
336. #4035	C₂²×C₃	semidirect
337. #4035	C₂²×C₃	semidirect
338. #4034	C₂²×C₃	semidirect
339. #4034	C₂²×C₃	semidirect
340. #4033	C₂²×C₃	semidirect
341. #4033	C₂²×C₃	semidirect
344. #4031	C₂²×C₃	semidirect
348. #4029	C₂²×C₃	semidirect
353. #4025	C₂²×C₃	semidirect
354. #4025	C₂²×C₃	semidirect
358. #4022	C₂²×C₃	semidirect
359. #4022	C₂²×C₃	semidirect
360. #4021	C₂²×C₃	semidirect
361. C₄×D₂₀	C₂²×C₃	semidirect
362. C₄×D₂₀	C₂²×C₃	semidirect
363. C₄×D₂₀	C₂²×C₃	semidirect
364. #4018	C₂²×C₃	semidirect
365. #4018	C₂²×C₃	semidirect
366. #4018	C₂²×C₃	semidirect
367. #4018	C₂²×C₃	semidirect
368. C₄²×D₅	C₂²×C₃	semidirect
369. C₄²×D₅	C₂²×C₃	semidirect
370. #4016	C₂²×C₃	semidirect
371. C₄×Dic₁₀	C₂²×C₃	semidirect
372. C₄×Dic₁₀	C₂²×C₃	semidirect
373. C₄×Dic₁₀	C₂²×C₃	semidirect
394. C₂×C₃×C₄×C₅	#41	semidirect
409. C₃×C₂²⋊D₅	#41	semidirect
520. C₃×#117	C₂×D₅	semidirect
521. C₃×#117	C₂×D₅	semidirect
522. C₃×#117	C₂×D₅	semidirect
526. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
527. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
535. C₂×C₃×C₄²	C₂×D₅	semidirect
662. C₂×#117	C₃×D₅	semidirect
824. C₂×C₄×C₅	C₃×#41	semidirect
839. C₂²⋊D₅	C₃×#41	semidirect
950. #117	C₂×C₃×D₅	semidirect
951. #117	C₂×C₃×D₅	semidirect
952. #117	C₂×C₃×D₅	semidirect
956. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
957. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
965. C₂×C₄²	C₂×C₃×D₅	semidirect
1028. C₂×C₃×C₄	#709	semidirect
1179. C₃×C₅	#3475	semidirect
1280. C₂×C₄	C₃×#709	semidirect
1298. C₅	C₃×#3475	semidirect
1337. C₃	#10617645	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×C₅×#117	2
C₃×#66125	2
C₂×C₃×C₄×C₂²⋊D₅	2
C₃×#65867	2
C₃×#65866	2
C₃×#65865	2
C₃×#65864	2
C₃×#65863	2
C₃×#65862	2
C₃×#65861	2
C₃×#65858	2
C₃×#65856	2
C₃×D₅×#117	2
C₃×#65851	2
C₃×#65848	2
C₃×#65847	2
C₃×#65845	2
C₃×#65841	2
C₃×#65829	2
C₃×#65824	2
C₃×#65813	2
C₃×C₄×#709	2
#10617645	3
C₃×#3475	5

Subgroups — C3×#10617645 #14484118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617645 #14484118