Subgroups — C₃×#10618424 #14481509

Order 1920.

2080 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66067	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66062	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66041	C₂	1	2	yes	maximal, complemented
5	C₃×#66040	C₂	1	2	yes	maximal, complemented
6	C₃×#66016	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#66014	C₂	1	2	yes	maximal, complemented
8	C₃×#66012	C₂	1	2	yes	maximal, complemented
9	C₃×#66002	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65991	C₂	1	2	yes	maximal, complemented
11	C₃×#65983	C₂	1	2	yes	maximal, complemented
12	C₃×#65972	C₂	1	2	yes	maximal, complemented
13	C₃×#65961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65959	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#65958	C₂	1	2	yes	maximal, complemented
16	C₃×#65953	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#65940	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#65917	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×C₄×#713	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#65896	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×C₄×#711	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#65868	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	#10618424	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₃×#713	C₂²	1	1	yes	characteristic
26	C₂×C₃×#711	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#126	C₂²	1	2	yes	complemented
30	C₃×C₅×#124	C₂²	1	2	yes	—
31	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×#123	C₂²	1	2	yes	—
33	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
35	C₃×C₅×#121	C₂²	1	1	yes	characteristic
36	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₅×#117	C₂²	1	1	yes	characteristic
39	C₃×#4093	C₂²	1	2	yes	—
40	C₃×#4092	C₂²	1	1	yes	characteristic
41	C₃×#4092	C₂²	1	2	yes	—
42	C₃×#4092	C₂²	1	2	yes	complemented
43	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
44	C₃×Q₈×Dic₅	C₂²	1	2	yes	complemented
45	C₃×#4090	C₂²	1	1	yes	characteristic, complemented
46	C₃×#4086	C₂²	1	1	yes	characteristic, complemented
47	C₃×#4085	C₂²	1	2	yes	—
48	C₃×#4084	C₂²	1	1	yes	characteristic
49	C₃×#4084	C₂²	1	2	yes	—
50	C₃×#4083	C₂²	1	2	yes	—
51	C₃×D₄×Dic₅	C₂²	1	2	yes	—
52	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
53	C₃×#4076	C₂²	1	1	yes	characteristic
54	C₃×#4076	C₂²	1	2	yes	—
55	C₃×#4075	C₂²	1	2	yes	complemented
56	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
57	C₃×#4072	C₂²	1	1	yes	characteristic
58	C₃×#4070	C₂²	1	1	yes	characteristic
59	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
60	C₃×#4044	C₂²	1	2	yes	—
61	C₃×#4044	C₂²	1	2	yes	complemented
62	C₃×#4044	C₂²	1	2	yes	complemented
63	C₃×#4043	C₂²	1	1	yes	characteristic
64	C₃×#4043	C₂²	1	2	yes	—
65	C₃×#4042	C₂²	1	2	yes	complemented
66	C₃×#4041	C₂²	1	1	yes	characteristic
67	C₃×#4040	C₂²	1	2	yes	—
68	C₃×#4040	C₂²	1	2	yes	—
69	C₃×#4039	C₂²	1	2	yes	—
70	C₃×#4039	C₂²	1	2	yes	—
71	C₃×#4039	C₂²	1	1	yes	characteristic, complemented
72	C₃×#4038	C₂²	1	1	yes	characteristic
73	C₃×#4038	C₂²	1	1	yes	characteristic
74	C₃×#4038	C₂²	1	1	yes	characteristic
75	C₃×#4038	C₂²	1	1	yes	characteristic
76	C₃×#4038	C₂²	1	2	yes	complemented
77	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	C₃×#4036	C₂²	1	1	yes	characteristic, complemented
80	C₃×#4036	C₂²	1	1	yes	characteristic, complemented
81	C₃×#4036	C₂²	1	2	yes	complemented
82	C₃×#4035	C₂²	1	2	yes	complemented
83	C₃×#4035	C₂²	1	2	yes	complemented
84	C₃×#4033	C₂²	1	1	yes	characteristic, complemented
85	C₃×#4033	C₂²	1	2	yes	complemented
86	C₃×#4032	C₂²	1	2	yes	—
87	C₃×#4032	C₂²	1	2	yes	complemented
88	C₃×#4031	C₂²	1	2	yes	—
89	C₃×#4031	C₂²	1	2	yes	—
90	C₃×#4030	C₂²	1	2	yes	—
91	C₃×#4030	C₂²	1	2	yes	—
92	C₃×#4030	C₂²	1	2	yes	—
93	C₃×#4029	C₂²	1	2	yes	—
94	C₃×#4029	C₂²	1	2	yes	—
95	C₃×#4029	C₂²	1	2	yes	complemented
96	C₃×#4029	C₂²	1	2	yes	complemented
97	C₃×#4028	C₂²	1	2	yes	—
98	C₃×#4027	C₂²	1	2	yes	—
99	C₃×#4027	C₂²	1	2	yes	—
100	C₃×#4027	C₂²	1	2	yes	—
101	C₃×#4027	C₂²	1	2	yes	complemented
102	C₃×#4027	C₂²	1	2	yes	complemented
103	C₃×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₃×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₃×#4025	C₂²	1	2	yes	—
106	C₃×#4025	C₂²	1	2	yes	—
107	C₃×#4025	C₂²	1	2	yes	complemented
108	C₃×#4024	C₂²	1	2	yes	complemented
109	C₃×#4023	C₂²	1	1	yes	characteristic
110	C₃×#4023	C₂²	1	1	yes	characteristic
111	C₃×#4023	C₂²	1	2	yes	complemented
112	C₃×#4022	C₂²	1	2	yes	—
113	C₃×#4021	C₂²	1	1	yes	characteristic, complemented
114	C₃×C₄×D₂₀	C₂²	1	2	yes	—
115	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
116	C₃×#4018	C₂²	1	1	yes	characteristic
117	C₃×#4018	C₂²	1	1	yes	characteristic
118	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
119	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
120	C₃×C₄²×D₅	C₂²	1	2	yes	complemented
121	C₃×#4016	C₂²	1	2	yes	complemented
122	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
123	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
124	C₃×#3455	—	5	1	no	maximal, Hall
125	C₅×#542	C₂×C₃	1	1	yes	characteristic, complemented
126	#66067	C₂×C₃	1	1	yes	characteristic, complemented
127	#66062	C₂×C₃	1	1	yes	characteristic, complemented
128	#66041	C₂×C₃	1	2	yes	complemented
129	#66040	C₂×C₃	1	2	yes	complemented
130	#66016	C₂×C₃	1	1	yes	characteristic, complemented
131	#66014	C₂×C₃	1	2	yes	complemented
132	#66012	C₂×C₃	1	2	yes	complemented
133	#66002	C₂×C₃	1	1	yes	characteristic, complemented
134	#65991	C₂×C₃	1	2	yes	complemented
135	#65983	C₂×C₃	1	2	yes	complemented
136	#65972	C₂×C₃	1	2	yes	complemented
137	#65961	C₂×C₃	1	1	yes	characteristic, complemented
138	#65959	C₂×C₃	1	1	yes	characteristic, complemented
139	#65958	C₂×C₃	1	2	yes	complemented
140	#65953	C₂×C₃	1	1	yes	characteristic, complemented
141	#65940	C₂×C₃	1	1	yes	characteristic, complemented
142	#65917	C₂×C₃	1	1	yes	characteristic, complemented
143	C₄×#713	C₂×C₃	1	1	yes	characteristic, complemented
144	#65896	C₂×C₃	1	1	yes	characteristic, complemented
145	C₄×#711	C₂×C₃	1	1	yes	characteristic, complemented
146	#65868	C₂×C₃	1	1	yes	characteristic, complemented
147	D₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
149	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
151	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
152	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
153	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
155	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
156	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
157	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
158	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
159	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
160	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
161	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
162	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
163	C₃×#713	—	2	4	no	—
164	C₃×#711	—	2	4	no	—
165	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
166	C₂×C₃×D₂₀	C₂³	1	2	yes	—
167	C₂×C₃×D₂₀	C₂³	1	2	yes	—
168	C₂×C₃×C₄×D₅	—	2	4	no	—
169	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
173	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
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	1	yes	characteristic
177	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
179	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
180	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
181	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
182	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
187	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
188	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
190	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₂²⋊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×C₄²×C₅	C₂³	1	1	yes	characteristic
197	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
198	C₃×C₄²×C₅	C₂³	1	2	yes	—
199	C₃×C₂²⋊Dic₅	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	1	yes	characteristic
204	C₃×#685	C₂³	1	2	yes	—
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	2	yes	—
210	C₃×#685	C₂³	1	2	yes	—
211	C₃×#685	C₂³	1	1	yes	characteristic
212	C₃×#685	C₂³	1	1	yes	characteristic
213	C₃×#685	C₂³	1	1	yes	characteristic
214	C₃×#685	C₂³	1	1	yes	characteristic
215	C₃×#685	C₂³	1	2	yes	—
216	C₃×#685	C₂³	1	2	yes	—
217	C₃×#685	C₂³	1	2	yes	—
218	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
219	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
220	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
221	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
222	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
223	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
224	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
225	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
226	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
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	2	yes	—
232	C₃×#683	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
237	C₃×#683	C₂³	1	1	yes	characteristic
238	C₃×#683	C₂³	1	2	yes	—
239	C₃×C₄×Dic₅	C₂³	1	2	yes	—
240	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
241	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
242	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
243	C₃×C₄×Dic₅	C₂³	1	2	yes	—
244	C₃×C₄×Dic₅	C₂³	1	2	yes	—
245	C₃×C₄×Dic₅	C₂³	1	2	yes	—
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×#542	—	5	1	no	—
251	C₃×#542	—	5	1	no	—
252	C₃×#542	—	5	1	no	—
253	C₃×#542	D₅	1	1	yes	characteristic, complemented
254	C₃×#541	—	5	1	no	—
255	C₃×#541	—	5	1	no	—
256	C₃×#540	—	5	1	no	—
257	C₃×#540	—	5	1	no	—
258	C₃×#539	—	5	2	no	—
259	C₃×#539	—	5	2	no	—
260	C₃×#538	—	5	2	no	—
261	C₃×#538	—	5	2	no	—
262	C₃×#533	—	5	1	no	—
263	C₃×#532	—	5	1	no	—
264	C₃×#529	—	5	2	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	1	no	—
272	C₂×C₃×#117	—	5	1	no	—
273	C₂×#713	C₂²×C₃	1	1	yes	characteristic
274	C₂×#711	C₂²×C₃	1	1	yes	characteristic
275	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
276	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
277	C₅×#126	C₂²×C₃	1	2	yes	complemented
278	C₅×#124	C₂²×C₃	1	2	yes	—
279	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
280	C₅×#123	C₂²×C₃	1	2	yes	—
281	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
282	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
283	C₅×#121	C₂²×C₃	1	1	yes	characteristic
284	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
285	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
286	C₅×#117	C₂²×C₃	1	1	yes	characteristic
287	#4093	C₂²×C₃	1	2	yes	—
288	#4092	C₂²×C₃	1	2	yes	—
289	#4092	C₂²×C₃	1	1	yes	characteristic
290	#4092	C₂²×C₃	1	2	yes	complemented
291	Q₈×Dic₅	C₂²×C₃	1	2	yes	complemented
292	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
293	#4090	C₂²×C₃	1	1	yes	characteristic, complemented
294	#4086	C₂²×C₃	1	1	yes	characteristic, complemented
295	#4085	C₂²×C₃	1	2	yes	—
296	#4084	C₂²×C₃	1	1	yes	characteristic
297	#4084	C₂²×C₃	1	2	yes	—
298	#4083	C₂²×C₃	1	2	yes	—
299	D₄×Dic₅	C₂²×C₃	1	2	yes	—
300	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
301	#4076	C₂²×C₃	1	1	yes	characteristic
302	#4076	C₂²×C₃	1	2	yes	—
303	#4075	C₂²×C₃	1	2	yes	complemented
304	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
305	#4072	C₂²×C₃	1	1	yes	characteristic
306	#4070	C₂²×C₃	1	1	yes	characteristic
307	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
308	#4044	C₂²×C₃	1	2	yes	—
309	#4044	C₂²×C₃	1	2	yes	complemented
310	#4044	C₂²×C₃	1	2	yes	complemented
311	#4043	C₂²×C₃	1	2	yes	—
312	#4043	C₂²×C₃	1	1	yes	characteristic
313	#4042	C₂²×C₃	1	2	yes	complemented
314	#4041	C₂²×C₃	1	1	yes	characteristic
315	#4040	C₂²×C₃	1	2	yes	—
316	#4040	C₂²×C₃	1	2	yes	—
317	#4039	C₂²×C₃	1	2	yes	—
318	#4039	C₂²×C₃	1	2	yes	—
319	#4039	C₂²×C₃	1	1	yes	characteristic, complemented
320	#4038	C₂²×C₃	1	1	yes	characteristic
321	#4038	C₂²×C₃	1	1	yes	characteristic
322	#4038	C₂²×C₃	1	1	yes	characteristic
323	#4038	C₂²×C₃	1	1	yes	characteristic
324	#4038	C₂²×C₃	1	2	yes	complemented
325	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
326	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
327	#4036	C₂²×C₃	1	1	yes	characteristic, complemented
328	#4036	C₂²×C₃	1	1	yes	characteristic, complemented
329	#4036	C₂²×C₃	1	2	yes	complemented
330	#4035	C₂²×C₃	1	2	yes	complemented
331	#4035	C₂²×C₃	1	2	yes	complemented
332	#4033	C₂²×C₃	1	2	yes	complemented
333	#4033	C₂²×C₃	1	1	yes	characteristic, complemented
334	#4032	C₂²×C₃	1	2	yes	—
335	#4032	C₂²×C₃	1	2	yes	complemented
336	#4031	C₂²×C₃	1	2	yes	—
337	#4031	C₂²×C₃	1	2	yes	—
338	#4030	C₂²×C₃	1	2	yes	—
339	#4030	C₂²×C₃	1	2	yes	—
340	#4030	C₂²×C₃	1	2	yes	—
341	#4029	C₂²×C₃	1	2	yes	—
342	#4029	C₂²×C₃	1	2	yes	—
343	#4029	C₂²×C₃	1	2	yes	complemented
344	#4029	C₂²×C₃	1	2	yes	complemented
345	#4028	C₂²×C₃	1	2	yes	—
346	#4027	C₂²×C₃	1	2	yes	—
347	#4027	C₂²×C₃	1	2	yes	—
348	#4027	C₂²×C₃	1	2	yes	—
349	#4027	C₂²×C₃	1	2	yes	complemented
350	#4027	C₂²×C₃	1	2	yes	complemented
351	D₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
352	D₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
353	#4025	C₂²×C₃	1	2	yes	—
354	#4025	C₂²×C₃	1	2	yes	—
355	#4025	C₂²×C₃	1	2	yes	complemented
356	#4024	C₂²×C₃	1	2	yes	complemented
357	#4023	C₂²×C₃	1	1	yes	characteristic
358	#4023	C₂²×C₃	1	1	yes	characteristic
359	#4023	C₂²×C₃	1	2	yes	complemented
360	#4022	C₂²×C₃	1	2	yes	—
361	#4021	C₂²×C₃	1	1	yes	characteristic, complemented
362	C₄×D₂₀	C₂²×C₃	1	2	yes	—
363	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
364	#4018	C₂²×C₃	1	1	yes	characteristic
365	#4018	C₂²×C₃	1	1	yes	characteristic
366	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
367	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
368	C₄²×D₅	C₂²×C₃	1	2	yes	complemented
369	#4016	C₂²×C₃	1	2	yes	complemented
370	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
371	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
372	#3455	—	5	1	no	Sylow
373	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
374	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
375	C₂²×C₃×D₅	—	2	2	no	—
376	C₂²×C₃×D₅	—	4	1	no	—
377	C₂²×C₃×D₅	—	4	1	no	—
378	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
379	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
380	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
381	C₃×C₅×Q₈	—	2	2	no	—
382	C₃×C₅×Q₈	—	4	2	no	—
383	C₃×C₅×D₄	—	2	2	no	—
384	C₃×C₅×D₄	—	4	2	no	—
385	C₂×C₃×C₄×C₅	—	2	2	no	—
386	C₂×C₃×C₄×C₅	—	4	2	no	—
387	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
388	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
389	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
390	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
391	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	C₃×C₂²⋊D₅	—	2	4	no	—
397	C₃×C₂²⋊D₅	—	4	2	no	—
398	C₃×C₂²⋊D₅	—	4	2	no	—
399	C₃×C₂²⋊D₅	—	4	2	no	—
400	C₃×C₂²⋊D₅	—	4	2	no	—
401	C₂×C₃×Dic₅	—	2	2	no	—
402	C₂×C₃×Dic₅	—	2	4	no	—
403	C₂×C₃×Dic₅	—	4	2	no	—
404	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
405	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
406	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
407	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
408	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
409	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
410	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
411	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
412	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
413	C₃×D₂₀	—	2	4	no	—
414	C₃×D₂₀	—	2	2	no	—
415	C₃×D₂₀	—	4	2	no	—
416	C₃×C₄×D₅	—	2	2	no	—
417	C₃×C₄×D₅	—	2	2	no	—
418	C₃×C₄×D₅	—	2	2	no	—
419	C₃×C₄×D₅	—	2	4	no	—
420	C₃×C₄×D₅	—	4	2	no	—
421	C₃×C₄×D₅	—	4	1	no	—
422	C₃×C₄×D₅	—	4	2	no	—
423	C₃×C₄×D₅	—	4	1	no	—
424	C₃×C₄×D₅	—	4	1	no	—
425	C₃×C₄×D₅	—	4	1	no	—
426	C₃×C₄×D₅	#41	1	4	yes	—
427	C₃×Dic₁₀	—	2	2	no	—
428	C₃×Dic₁₀	—	4	2	no	—
429	C₂×C₃×#41	—	5	1	no	—
430	C₂×C₃×#41	—	5	1	no	—
431	C₂³×C₃×C₄	—	5	1	no	—
432	C₃×C₄⋊Q₈	—	5	1	no	—
433	C₃×C₄⋊Q₈	—	5	1	no	—
434	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
435	C₃×#127	—	5	1	no	—
436	C₃×#126	—	5	2	no	—
437	C₃×#126	—	5	2	no	—
438	C₃×#126	—	5	2	no	—
439	C₃×#126	—	5	2	no	—
440	C₃×#126	—	5	2	no	—
441	C₃×#126	—	5	2	no	—
442	C₃×#126	—	5	2	no	—
443	C₃×#126	C₂×D₅	1	2	yes	complemented
444	C₃×#125	—	5	2	no	—
445	C₃×#125	—	5	2	no	—
446	C₃×#125	—	5	2	no	—
447	C₃×#125	—	5	1	no	—
448	C₃×#125	—	5	1	no	—
449	C₃×#125	—	5	2	no	—
450	C₃×#124	—	5	2	no	—
451	C₃×#124	—	5	2	no	—
452	C₃×#124	—	5	2	no	—
453	C₃×#124	—	5	1	no	—
454	C₃×#124	C₂×D₅	1	2	yes	—
455	C₃×#124	C₂×D₅	1	1	yes	characteristic, complemented
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×#123	—	5	2	no	—
464	C₃×#123	—	5	2	no	—
465	C₃×#123	C₂×D₅	1	2	yes	—
466	C₃×C₂²⋊Q₈	—	5	1	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	1	no	—
472	C₃×C₂²⋊Q₈	—	5	2	no	—
473	C₃×C₂²⋊Q₈	—	5	2	no	—
474	C₃×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
475	C₃×C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
476	C₃×#121	—	5	1	no	—
477	C₃×#121	—	5	2	no	—
478	C₃×#121	—	5	2	no	—
479	C₃×#121	—	5	1	no	—
480	C₃×#121	—	5	2	no	—
481	C₃×#121	—	5	1	no	—
482	C₃×#121	—	5	2	no	—
483	C₃×#121	—	5	2	no	—
484	C₃×#121	—	5	2	no	—
485	C₃×#121	C₂×D₅	1	1	yes	characteristic
486	C₃×#120	—	5	2	no	—
487	C₃×#120	—	5	2	no	—
488	C₃×C₄×Q₈	—	5	1	no	—
489	C₃×C₄×Q₈	—	5	2	no	—
490	C₃×C₄×Q₈	—	5	1	no	—
491	C₃×C₄×Q₈	—	5	2	no	—
492	C₃×C₄×Q₈	—	5	1	no	—
493	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
494	C₃×C₄×D₄	—	5	2	no	—
495	C₃×C₄×D₄	—	5	1	no	—
496	C₃×C₄×D₄	—	5	2	no	—
497	C₃×C₄×D₄	—	5	2	no	—
498	C₃×C₄×D₄	—	5	1	no	—
499	C₃×C₄×D₄	—	5	2	no	—
500	C₃×C₄×D₄	—	5	2	no	—
501	C₃×C₄×D₄	—	5	2	no	—
502	C₃×C₄×D₄	—	5	2	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	1	no	—
507	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
508	C₃×#117	—	5	1	no	—
509	C₃×#117	—	5	1	no	—
510	C₃×#117	—	5	1	no	—
511	C₃×#117	—	5	1	no	—
512	C₃×#117	—	5	1	no	—
513	C₃×#117	—	5	2	no	—
514	C₃×#117	—	5	1	no	—
515	C₃×#117	—	5	1	no	—
516	C₃×#117	—	5	2	no	—
517	C₃×#117	—	5	1	no	—
518	C₃×#117	—	5	1	no	—
519	C₃×#117	C₂×D₅	1	1	yes	characteristic
520	C₂×C₃×C₄⋊C₄	—	5	1	no	—
521	C₂×C₃×C₄⋊C₄	—	5	1	no	—
522	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
523	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
524	C₂×C₃×C₄²	—	5	2	no	—
525	C₂×C₃×C₄²	—	5	1	no	—
526	C₂×C₃×C₄²	—	5	1	no	—
527	C₂×C₃×C₄²	—	5	2	no	—
528	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
529	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
530	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
531	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
532	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
533	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
534	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
535	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
536	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
537	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
538	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
539	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
540	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
541	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
542	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
543	#713	—	2	4	no	—
544	#711	—	2	4	no	—
545	C₂×D₂₀	C₂³×C₃	1	2	yes	—
546	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
547	C₂×D₂₀	C₂³×C₃	1	2	yes	—
548	C₂×C₄×D₅	—	2	4	no	—
549	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
550	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
553	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
554	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
555	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
556	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
557	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
558	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
559	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
560	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
561	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
562	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
563	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
564	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
565	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
566	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
567	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
568	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
569	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
570	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
571	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
572	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
573	C₅×C₂²⋊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	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
577	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
578	C₄²×C₅	C₂³×C₃	1	2	yes	—
579	C₂²⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
580	C₂²⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
581	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
582	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
583	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
584	#685	C₂³×C₃	1	1	yes	characteristic
585	#685	C₂³×C₃	1	1	yes	characteristic
586	#685	C₂³×C₃	1	1	yes	characteristic
587	#685	C₂³×C₃	1	1	yes	characteristic
588	#685	C₂³×C₃	1	2	yes	—
589	#685	C₂³×C₃	1	2	yes	—
590	#685	C₂³×C₃	1	2	yes	—
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	2	yes	—
598	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
599	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
600	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
601	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
602	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
603	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
604	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
605	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
606	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
607	#683	C₂³×C₃	1	2	yes	—
608	#683	C₂³×C₃	1	1	yes	characteristic
609	#683	C₂³×C₃	1	2	yes	—
610	#683	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	2	yes	—
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	C₄×Dic₅	C₂³×C₃	1	2	yes	—
620	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
621	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
622	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
623	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
624	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
625	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
626	C₄×Dic₅	C₂³×C₃	1	2	yes	—
627	C₄×Dic₅	C₂³×C₃	1	2	yes	—
628	C₄×Dic₅	C₂³×C₃	1	2	yes	—
629	C₄×Dic₅	C₂³×C₃	1	2	yes	—
630	#542	—	5	1	no	—
631	#542	—	5	1	no	—
632	#542	—	5	1	no	—
633	#542	C₃×D₅	1	1	yes	characteristic, complemented
634	#541	—	5	1	no	—
635	#541	—	5	1	no	—
636	#540	—	5	1	no	—
637	#540	—	5	1	no	—
638	#539	—	5	2	no	—
639	#539	—	5	2	no	—
640	#538	—	5	2	no	—
641	#538	—	5	2	no	—
642	#533	—	5	1	no	—
643	#532	—	5	1	no	—
644	#529	—	5	2	no	—
645	#529	—	5	2	no	—
646	#529	—	5	2	no	—
647	#529	—	5	2	no	—
648	#525	—	5	1	no	—
649	#525	—	5	1	no	—
650	C₄×#41	—	5	1	no	—
651	C₄×#41	—	5	1	no	—
652	C₂×#117	—	5	1	no	—
653	C₂²×C₃×C₅	—	2	2	no	—
654	C₂²×C₃×C₅	—	2	1	no	—
655	C₂²×C₃×C₅	—	2	2	no	—
656	C₂²×C₃×C₅	—	2	1	no	—
657	C₂²×C₃×C₅	—	2	2	no	—
658	C₂²×C₃×C₅	—	2	1	no	—
659	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
660	C₂×C₃×D₅	—	2	1	no	—
661	C₂×C₃×D₅	—	2	1	no	—
662	C₂×C₃×D₅	—	2	1	no	—
663	C₂×C₃×D₅	—	2	2	no	—
664	C₂×C₃×D₅	—	2	2	no	—
665	C₂×C₃×D₅	—	2	2	no	—
666	C₂×C₃×D₅	—	2	1	no	—
667	C₂×C₃×D₅	—	2	1	no	—
668	C₂×C₃×D₅	—	4	4	no	—
669	C₂×C₃×D₅	C₂×#41	1	2	yes	—
670	C₃×C₄×C₅	—	2	1	no	—
671	C₃×C₄×C₅	—	2	2	no	—
672	C₃×C₄×C₅	—	2	1	no	—
673	C₃×C₄×C₅	—	2	1	no	—
674	C₃×C₄×C₅	—	2	1	no	—
675	C₃×C₄×C₅	—	2	2	no	—
676	C₃×C₄×C₅	—	2	1	no	—
677	C₃×C₄×C₅	—	2	2	no	—
678	C₃×C₄×C₅	C₂×#41	1	2	yes	—
679	C₃×Dic₅	—	2	2	no	—
680	C₃×Dic₅	—	2	1	no	—
681	C₃×Dic₅	—	2	2	no	—
682	C₃×Dic₅	—	2	2	no	—
683	C₃×Dic₅	—	2	1	no	—
684	C₃×Dic₅	—	2	1	no	—
685	C₃×Dic₅	—	2	1	no	—
686	C₃×Dic₅	—	2	1	no	—
687	C₃×Dic₅	C₂×#41	1	2	yes	—
688	C₂⁴×C₃	—	5	1	no	—
689	C₃×#41	—	10	4	no	—
690	C₃×#41	—	10	4	no	—
691	C₂×C₃×Q₈	—	5	1	no	—
692	C₂×C₃×Q₈	—	5	2	no	—
693	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
694	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
695	C₂×C₃×D₄	—	5	2	no	—
696	C₂×C₃×D₄	—	5	2	no	—
697	C₂×C₃×D₄	—	5	2	no	—
698	C₂×C₃×D₄	—	5	2	no	—
699	C₂×C₃×D₄	—	5	2	no	—
700	C₂×C₃×D₄	—	5	2	no	—
701	C₂×C₃×D₄	—	5	1	no	—
702	C₂×C₃×D₄	—	5	2	no	—
703	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
704	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
705	C₂²×C₃×C₄	—	5	1	no	—
706	C₂²×C₃×C₄	—	5	2	no	—
707	C₂²×C₃×C₄	—	5	1	no	—
708	C₂²×C₃×C₄	—	5	2	no	—
709	C₂²×C₃×C₄	—	5	2	no	—
710	C₂²×C₃×C₄	—	5	1	no	—
711	C₂²×C₃×C₄	—	5	1	no	—
712	C₂²×C₃×C₄	—	5	1	no	—
713	C₂²×C₃×C₄	—	5	1	no	—
714	C₂²×C₃×C₄	—	5	1	no	—
715	C₂²×C₃×C₄	—	5	1	no	—
716	C₂²×C₃×C₄	—	5	1	no	—
717	C₂²×C₃×C₄	—	5	2	no	—
718	C₂²×C₃×C₄	—	5	2	no	—
719	C₂²×C₃×C₄	—	10	4	no	—
720	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
721	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
722	C₃×C₄⋊C₄	—	5	1	no	—
723	C₃×C₄⋊C₄	—	5	1	no	—
724	C₃×C₄⋊C₄	—	5	1	no	—
725	C₃×C₄⋊C₄	—	5	1	no	—
726	C₃×C₄⋊C₄	—	5	2	no	—
727	C₃×C₄⋊C₄	—	5	2	no	—
728	C₃×C₄⋊C₄	—	5	2	no	—
729	C₃×C₄⋊C₄	—	5	2	no	—
730	C₃×C₄⋊C₄	—	5	2	no	—
731	C₃×C₄⋊C₄	—	5	2	no	—
732	C₃×C₄⋊C₄	—	5	2	no	—
733	C₃×C₄⋊C₄	—	5	2	no	—
734	C₃×C₄⋊C₄	—	5	1	no	—
735	C₃×C₄⋊C₄	—	5	1	no	—
736	C₃×C₄⋊C₄	—	5	1	no	—
737	C₃×C₄⋊C₄	—	5	1	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	2	no	—
742	C₃×C₄⋊C₄	—	5	2	no	—
743	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
744	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
745	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
746	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
747	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
748	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
749	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
750	C₃×C₂²⋊C₄	—	5	1	no	—
751	C₃×C₂²⋊C₄	—	5	1	no	—
752	C₃×C₂²⋊C₄	—	5	2	no	—
753	C₃×C₂²⋊C₄	—	5	2	no	—
754	C₃×C₂²⋊C₄	—	5	2	no	—
755	C₃×C₂²⋊C₄	—	5	1	no	—
756	C₃×C₂²⋊C₄	—	5	1	no	—
757	C₃×C₂²⋊C₄	—	5	1	no	—
758	C₃×C₂²⋊C₄	—	5	1	no	—
759	C₃×C₂²⋊C₄	—	5	2	no	—
760	C₃×C₂²⋊C₄	—	5	2	no	—
761	C₃×C₂²⋊C₄	—	5	2	no	—
762	C₃×C₂²⋊C₄	—	5	2	no	—
763	C₃×C₂²⋊C₄	—	5	2	no	—
764	C₃×C₂²⋊C₄	—	5	2	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	C₂²×D₅	1	1	yes	characteristic
770	C₃×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
771	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
772	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
773	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
774	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
775	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
776	C₃×C₄²	—	5	1	no	—
777	C₃×C₄²	—	5	1	no	—
778	C₃×C₄²	—	5	2	no	—
779	C₃×C₄²	—	5	2	no	—
780	C₃×C₄²	—	5	1	no	—
781	C₃×C₄²	—	5	1	no	—
782	C₃×C₄²	—	5	1	no	—
783	C₃×C₄²	—	5	1	no	—
784	C₃×C₄²	—	5	2	no	—
785	C₃×C₄²	—	5	2	no	—
786	C₃×C₄²	—	5	2	no	—
787	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
788	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
789	C₃×C₄²	C₂²×D₅	1	2	yes	—
790	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
791	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
792	C₂²×D₅	—	2	2	no	—
793	C₂²×D₅	—	4	1	no	—
794	C₂²×D₅	—	4	1	no	—
795	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
796	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
797	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
798	C₅×Q₈	—	2	2	no	—
799	C₅×Q₈	—	4	2	no	—
800	C₅×D₄	—	2	2	no	—
801	C₅×D₄	—	4	2	no	—
802	C₂×C₄×C₅	—	2	2	no	—
803	C₂×C₄×C₅	—	4	2	no	—
804	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
805	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
806	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
807	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
808	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
809	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
810	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
811	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
812	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
813	C₂²⋊D₅	—	2	4	no	—
814	C₂²⋊D₅	—	4	2	no	—
815	C₂²⋊D₅	—	4	2	no	—
816	C₂²⋊D₅	—	4	2	no	—
817	C₂²⋊D₅	—	4	2	no	—
818	C₂×Dic₅	—	2	2	no	—
819	C₂×Dic₅	—	2	4	no	—
820	C₂×Dic₅	—	4	2	no	—
821	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
822	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
823	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
824	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
825	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
826	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
827	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
828	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
829	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
830	D₂₀	—	2	4	no	—
831	D₂₀	—	2	2	no	—
832	D₂₀	—	4	2	no	—
833	C₄×D₅	—	2	2	no	—
834	C₄×D₅	—	2	2	no	—
835	C₄×D₅	—	2	2	no	—
836	C₄×D₅	—	2	4	no	—
837	C₄×D₅	—	4	2	no	—
838	C₄×D₅	—	4	1	no	—
839	C₄×D₅	—	4	2	no	—
840	C₄×D₅	—	4	1	no	—
841	C₄×D₅	—	4	1	no	—
842	C₄×D₅	—	4	1	no	—
843	C₄×D₅	C₃×#41	1	4	yes	—
844	Dic₁₀	—	2	2	no	—
845	Dic₁₀	—	4	2	no	—
846	C₂×#41	—	5	1	no	—
847	C₂×#41	—	5	1	no	—
848	C₂³×C₄	—	5	1	no	—
849	C₄⋊Q₈	—	5	1	no	—
850	C₄⋊Q₈	—	5	1	no	—
851	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
852	#127	—	5	1	no	—
853	#126	—	5	2	no	—
854	#126	—	5	2	no	—
855	#126	—	5	2	no	—
856	#126	—	5	2	no	—
857	#126	—	5	2	no	—
858	#126	—	5	2	no	—
859	#126	—	5	2	no	—
860	#126	C₂×C₃×D₅	1	2	yes	complemented
861	#125	—	5	2	no	—
862	#125	—	5	2	no	—
863	#125	—	5	2	no	—
864	#125	—	5	1	no	—
865	#125	—	5	1	no	—
866	#125	—	5	2	no	—
867	#124	—	5	2	no	—
868	#124	—	5	2	no	—
869	#124	—	5	2	no	—
870	#124	—	5	1	no	—
871	#124	C₂×C₃×D₅	1	2	yes	—
872	#124	C₂×C₃×D₅	1	1	yes	characteristic, complemented
873	#123	—	5	2	no	—
874	#123	—	5	2	no	—
875	#123	—	5	2	no	—
876	#123	—	5	2	no	—
877	#123	—	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	C₂×C₃×D₅	1	2	yes	—
883	C₂²⋊Q₈	—	5	1	no	—
884	C₂²⋊Q₈	—	5	2	no	—
885	C₂²⋊Q₈	—	5	2	no	—
886	C₂²⋊Q₈	—	5	1	no	—
887	C₂²⋊Q₈	—	5	1	no	—
888	C₂²⋊Q₈	—	5	2	no	—
889	C₂²⋊Q₈	—	5	2	no	—
890	C₂²⋊Q₈	—	5	2	no	—
891	C₂²⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
892	C₂²⋊Q₈	C₂×C₃×D₅	1	2	yes	complemented
893	#121	—	5	1	no	—
894	#121	—	5	2	no	—
895	#121	—	5	2	no	—
896	#121	—	5	1	no	—
897	#121	—	5	2	no	—
898	#121	—	5	1	no	—
899	#121	—	5	2	no	—
900	#121	—	5	2	no	—
901	#121	—	5	2	no	—
902	#121	C₂×C₃×D₅	1	1	yes	characteristic
903	#120	—	5	2	no	—
904	#120	—	5	2	no	—
905	C₄×Q₈	—	5	1	no	—
906	C₄×Q₈	—	5	2	no	—
907	C₄×Q₈	—	5	1	no	—
908	C₄×Q₈	—	5	2	no	—
909	C₄×Q₈	—	5	1	no	—
910	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
911	C₄×D₄	—	5	1	no	—
912	C₄×D₄	—	5	2	no	—
913	C₄×D₄	—	5	2	no	—
914	C₄×D₄	—	5	2	no	—
915	C₄×D₄	—	5	1	no	—
916	C₄×D₄	—	5	2	no	—
917	C₄×D₄	—	5	2	no	—
918	C₄×D₄	—	5	2	no	—
919	C₄×D₄	—	5	2	no	—
920	C₄×D₄	—	5	2	no	—
921	C₄×D₄	—	5	2	no	—
922	C₄×D₄	—	5	2	no	—
923	C₄×D₄	—	5	1	no	—
924	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
925	#117	—	5	1	no	—
926	#117	—	5	1	no	—
927	#117	—	5	1	no	—
928	#117	—	5	1	no	—
929	#117	—	5	1	no	—
930	#117	—	5	2	no	—
931	#117	—	5	1	no	—
932	#117	—	5	1	no	—
933	#117	—	5	2	no	—
934	#117	—	5	1	no	—
935	#117	—	5	1	no	—
936	#117	C₂×C₃×D₅	1	1	yes	characteristic
937	C₂×C₄⋊C₄	—	5	1	no	—
938	C₂×C₄⋊C₄	—	5	1	no	—
939	C₂×C₂²⋊C₄	—	5	1	no	—
940	C₂×C₂²⋊C₄	—	5	1	no	—
941	C₂×C₄²	—	5	2	no	—
942	C₂×C₄²	—	5	1	no	—
943	C₂×C₄²	—	5	1	no	—
944	C₂×C₄²	—	5	2	no	—
945	C₂×C₃×C₅	—	4	1	no	—
946	C₂×C₃×C₅	—	4	2	no	—
947	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
948	C₂×C₃×C₅	#585	1	1	yes	characteristic
949	C₂×C₃×C₅	#585	1	1	yes	characteristic
950	C₃×D₅	—	2	2	no	—
951	C₃×D₅	—	4	2	no	—
952	C₃×D₅	—	4	1	no	—
953	C₂³×C₃	—	5	1	no	—
954	C₂³×C₃	—	5	1	no	—
955	C₂³×C₃	—	5	2	no	—
956	C₂³×C₃	—	10	2	no	—
957	C₂³×C₃	—	20	1	no	—
958	C₂³×C₃	—	20	1	no	—
959	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
960	C₂³×C₃	C₂³×D₅	1	2	yes	—
961	C₃×Q₈	—	2	2	no	—
962	C₃×Q₈	—	4	2	no	—
963	C₃×Q₈	—	10	2	no	—
964	C₃×Q₈	—	20	2	no	—
965	C₃×D₄	—	2	2	no	—
966	C₃×D₄	—	4	2	no	—
967	C₃×D₄	—	10	4	no	—
968	C₃×D₄	—	10	4	no	—
969	C₃×D₄	—	10	2	no	—
970	C₃×D₄	—	20	2	no	—
971	C₃×D₄	—	20	2	no	—
972	C₃×D₄	—	20	2	no	—
973	C₃×D₄	—	20	2	no	—
974	C₃×D₄	—	20	2	no	—
975	C₂×C₃×C₄	—	2	2	no	—
976	C₂×C₃×C₄	—	4	2	no	—
977	C₂×C₃×C₄	—	5	1	no	—
978	C₂×C₃×C₄	—	5	4	no	—
979	C₂×C₃×C₄	—	5	1	no	—
980	C₂×C₃×C₄	—	5	1	no	—
981	C₂×C₃×C₄	—	5	2	no	—
982	C₂×C₃×C₄	—	5	2	no	—
983	C₂×C₃×C₄	—	5	2	no	—
984	C₂×C₃×C₄	—	5	1	no	—
985	C₂×C₃×C₄	—	5	1	no	—
986	C₂×C₃×C₄	—	5	1	no	—
987	C₂×C₃×C₄	—	10	2	no	—
988	C₂×C₃×C₄	—	10	4	no	—
989	C₂×C₃×C₄	—	10	2	no	—
990	C₂×C₃×C₄	—	10	2	no	—
991	C₂×C₃×C₄	—	10	4	no	—
992	C₂×C₃×C₄	—	10	2	no	—
993	C₂×C₃×C₄	—	20	1	no	—
994	C₂×C₃×C₄	—	20	2	no	—
995	C₂×C₃×C₄	—	20	1	no	—
996	C₂×C₃×C₄	—	20	1	no	—
997	C₂×C₃×C₄	—	20	2	no	—
998	C₂×C₃×C₄	—	20	1	no	—
999	C₂×C₃×C₄	—	20	2	no	—
1000	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1001	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1002	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1003	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1004	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1005	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1006	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1007	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1008	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1009	C₂²×C₅	—	2	2	no	—
1010	C₂²×C₅	—	2	1	no	—
1011	C₂²×C₅	—	2	2	no	—
1012	C₂²×C₅	—	2	1	no	—
1013	C₂²×C₅	—	2	2	no	—
1014	C₂²×C₅	—	2	1	no	—
1015	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
1016	C₂×D₅	—	2	1	no	—
1017	C₂×D₅	—	2	1	no	—
1018	C₂×D₅	—	2	1	no	—
1019	C₂×D₅	—	2	2	no	—
1020	C₂×D₅	—	2	2	no	—
1021	C₂×D₅	—	2	2	no	—
1022	C₂×D₅	—	2	1	no	—
1023	C₂×D₅	—	2	1	no	—
1024	C₂×D₅	—	4	4	no	—
1025	C₂×D₅	C₂×C₃×#41	1	2	yes	—
1026	C₄×C₅	—	2	1	no	—
1027	C₄×C₅	—	2	2	no	—
1028	C₄×C₅	—	2	1	no	—
1029	C₄×C₅	—	2	1	no	—
1030	C₄×C₅	—	2	1	no	—
1031	C₄×C₅	—	2	2	no	—
1032	C₄×C₅	—	2	1	no	—
1033	C₄×C₅	—	2	2	no	—
1034	C₄×C₅	C₂×C₃×#41	1	2	yes	—
1035	Dic₅	—	2	2	no	—
1036	Dic₅	—	2	1	no	—
1037	Dic₅	—	2	2	no	—
1038	Dic₅	—	2	2	no	—
1039	Dic₅	—	2	1	no	—
1040	Dic₅	—	2	1	no	—
1041	Dic₅	—	2	1	no	—
1042	Dic₅	—	2	1	no	—
1043	Dic₅	C₂×C₃×#41	1	2	yes	—
1044	C₂⁴	—	5	1	no	—
1045	#41	—	10	4	no	—
1046	#41	—	10	4	no	—
1047	C₂×Q₈	—	5	1	no	—
1048	C₂×Q₈	—	5	2	no	—
1049	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
1050	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
1051	C₂×D₄	—	5	2	no	—
1052	C₂×D₄	—	5	2	no	—
1053	C₂×D₄	—	5	2	no	—
1054	C₂×D₄	—	5	2	no	—
1055	C₂×D₄	—	5	2	no	—
1056	C₂×D₄	—	5	2	no	—
1057	C₂×D₄	—	5	1	no	—
1058	C₂×D₄	—	5	2	no	—
1059	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
1060	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
1061	C₂²×C₄	—	5	1	no	—
1062	C₂²×C₄	—	5	2	no	—
1063	C₂²×C₄	—	5	1	no	—
1064	C₂²×C₄	—	5	2	no	—
1065	C₂²×C₄	—	5	2	no	—
1066	C₂²×C₄	—	5	1	no	—
1067	C₂²×C₄	—	5	1	no	—
1068	C₂²×C₄	—	5	1	no	—
1069	C₂²×C₄	—	5	1	no	—
1070	C₂²×C₄	—	5	1	no	—
1071	C₂²×C₄	—	5	1	no	—
1072	C₂²×C₄	—	5	1	no	—
1073	C₂²×C₄	—	5	2	no	—
1074	C₂²×C₄	—	5	2	no	—
1075	C₂²×C₄	—	10	4	no	—
1076	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1077	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
1078	C₄⋊C₄	—	5	1	no	—
1079	C₄⋊C₄	—	5	1	no	—
1080	C₄⋊C₄	—	5	1	no	—
1081	C₄⋊C₄	—	5	1	no	—
1082	C₄⋊C₄	—	5	1	no	—
1083	C₄⋊C₄	—	5	1	no	—
1084	C₄⋊C₄	—	5	1	no	—
1085	C₄⋊C₄	—	5	1	no	—
1086	C₄⋊C₄	—	5	2	no	—
1087	C₄⋊C₄	—	5	2	no	—
1088	C₄⋊C₄	—	5	2	no	—
1089	C₄⋊C₄	—	5	2	no	—
1090	C₄⋊C₄	—	5	2	no	—
1091	C₄⋊C₄	—	5	2	no	—
1092	C₄⋊C₄	—	5	2	no	—
1093	C₄⋊C₄	—	5	2	no	—
1094	C₄⋊C₄	—	5	2	no	—
1095	C₄⋊C₄	—	5	2	no	—
1096	C₄⋊C₄	—	5	2	no	—
1097	C₄⋊C₄	—	5	2	no	—
1098	C₄⋊C₄	—	5	2	no	—
1099	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1100	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1101	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1102	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1103	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1104	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1105	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1106	C₂²⋊C₄	—	5	1	no	—
1107	C₂²⋊C₄	—	5	1	no	—
1108	C₂²⋊C₄	—	5	2	no	—
1109	C₂²⋊C₄	—	5	2	no	—
1110	C₂²⋊C₄	—	5	2	no	—
1111	C₂²⋊C₄	—	5	1	no	—
1112	C₂²⋊C₄	—	5	1	no	—
1113	C₂²⋊C₄	—	5	1	no	—
1114	C₂²⋊C₄	—	5	1	no	—
1115	C₂²⋊C₄	—	5	2	no	—
1116	C₂²⋊C₄	—	5	2	no	—
1117	C₂²⋊C₄	—	5	2	no	—
1118	C₂²⋊C₄	—	5	2	no	—
1119	C₂²⋊C₄	—	5	2	no	—
1120	C₂²⋊C₄	—	5	2	no	—
1121	C₂²⋊C₄	—	5	2	no	—
1122	C₂²⋊C₄	—	5	2	no	—
1123	C₂²⋊C₄	—	5	2	no	—
1124	C₂²⋊C₄	—	5	2	no	—
1125	C₂²⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1126	C₂²⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1127	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1128	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1129	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1130	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1131	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1132	C₄²	—	5	1	no	—
1133	C₄²	—	5	1	no	—
1134	C₄²	—	5	2	no	—
1135	C₄²	—	5	2	no	—
1136	C₄²	—	5	1	no	—
1137	C₄²	—	5	1	no	—
1138	C₄²	—	5	1	no	—
1139	C₄²	—	5	1	no	—
1140	C₄²	—	5	2	no	—
1141	C₄²	—	5	2	no	—
1142	C₄²	—	5	2	no	—
1143	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
1144	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
1145	C₄²	C₂²×C₃×D₅	1	2	yes	—
1146	C₃×C₅	#3455	1	1	yes	characteristic, complemented, Hall
1147	C₂²×C₃	—	2	1	no	—
1148	C₂²×C₃	—	2	2	no	—
1149	C₂²×C₃	—	2	2	no	—
1150	C₂²×C₃	—	2	1	no	—
1151	C₂²×C₃	—	2	2	no	—
1152	C₂²×C₃	—	2	1	no	—
1153	C₂²×C₃	—	5	2	no	—
1154	C₂²×C₃	—	10	1	no	—
1155	C₂²×C₃	—	10	1	no	—
1156	C₂²×C₃	—	10	1	no	—
1157	C₂²×C₃	—	10	2	no	—
1158	C₂²×C₃	—	10	2	no	—
1159	C₂²×C₃	—	10	1	no	—
1160	C₂²×C₃	—	10	2	no	—
1161	C₂²×C₃	—	10	1	no	—
1162	C₂²×C₃	—	20	4	no	—
1163	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
1164	C₃×C₄	—	2	1	no	—
1165	C₃×C₄	—	2	2	no	—
1166	C₃×C₄	—	2	1	no	—
1167	C₃×C₄	—	2	2	no	—
1168	C₃×C₄	—	2	2	no	—
1169	C₃×C₄	—	2	1	no	—
1170	C₃×C₄	—	2	1	no	—
1171	C₃×C₄	—	2	1	no	—
1172	C₃×C₄	—	5	2	no	—
1173	C₃×C₄	—	10	1	no	—
1174	C₃×C₄	—	10	2	no	—
1175	C₃×C₄	—	10	1	no	—
1176	C₃×C₄	—	10	1	no	—
1177	C₃×C₄	—	10	1	no	—
1178	C₃×C₄	—	10	1	no	—
1179	C₃×C₄	—	10	2	no	—
1180	C₃×C₄	—	10	2	no	—
1181	C₃×C₄	D₅×#41	1	2	yes	—
1182	C₂×C₅	—	4	1	no	—
1183	C₂×C₅	—	4	2	no	—
1184	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
1185	C₂×C₅	C₃×#585	1	1	yes	characteristic
1186	C₂×C₅	C₃×#585	1	1	yes	characteristic
1187	D₅	—	2	2	no	—
1188	D₅	—	4	1	no	—
1189	D₅	—	4	2	no	—
1190	C₂³	—	5	1	no	—
1191	C₂³	—	5	1	no	—
1192	C₂³	—	5	2	no	—
1193	C₂³	—	10	2	no	—
1194	C₂³	—	20	1	no	—
1195	C₂³	—	20	1	no	—
1196	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
1197	C₂³	C₂³×C₃×D₅	1	2	yes	—
1198	Q₈	—	2	2	no	—
1199	Q₈	—	4	2	no	—
1200	Q₈	—	10	2	no	—
1201	Q₈	—	20	2	no	—
1202	D₄	—	2	2	no	—
1203	D₄	—	4	2	no	—
1204	D₄	—	10	4	no	—
1205	D₄	—	10	4	no	—
1206	D₄	—	10	2	no	—
1207	D₄	—	20	2	no	—
1208	D₄	—	20	2	no	—
1209	D₄	—	20	2	no	—
1210	D₄	—	20	2	no	—
1211	D₄	—	20	2	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	4	2	no	—
1214	C₂×C₄	—	5	1	no	—
1215	C₂×C₄	—	5	4	no	—
1216	C₂×C₄	—	5	1	no	—
1217	C₂×C₄	—	5	1	no	—
1218	C₂×C₄	—	5	2	no	—
1219	C₂×C₄	—	5	2	no	—
1220	C₂×C₄	—	5	2	no	—
1221	C₂×C₄	—	5	1	no	—
1222	C₂×C₄	—	5	1	no	—
1223	C₂×C₄	—	5	1	no	—
1224	C₂×C₄	—	10	2	no	—
1225	C₂×C₄	—	10	4	no	—
1226	C₂×C₄	—	10	2	no	—
1227	C₂×C₄	—	10	2	no	—
1228	C₂×C₄	—	10	4	no	—
1229	C₂×C₄	—	10	2	no	—
1230	C₂×C₄	—	20	1	no	—
1231	C₂×C₄	—	20	2	no	—
1232	C₂×C₄	—	20	1	no	—
1233	C₂×C₄	—	20	1	no	—
1234	C₂×C₄	—	20	2	no	—
1235	C₂×C₄	—	20	1	no	—
1236	C₂×C₄	—	20	2	no	—
1237	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1238	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1239	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1240	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1241	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1242	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1243	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1244	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1245	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1246	C₂×C₃	—	4	1	no	—
1247	C₂×C₃	—	4	2	no	—
1248	C₂×C₃	—	10	2	no	—
1249	C₂×C₃	—	20	1	no	—
1250	C₂×C₃	—	20	2	no	—
1251	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
1252	C₂×C₃	#66285	1	1	yes	characteristic
1253	C₂×C₃	#66287	1	1	yes	characteristic
1254	C₅	C₃×#3455	1	1	yes	characteristic, complemented, Sylow
1255	C₂²	—	2	1	no	—
1256	C₂²	—	2	2	no	—
1257	C₂²	—	2	2	no	—
1258	C₂²	—	2	1	no	—
1259	C₂²	—	2	2	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	5	2	no	—
1262	C₂²	—	10	1	no	—
1263	C₂²	—	10	1	no	—
1264	C₂²	—	10	1	no	—
1265	C₂²	—	10	2	no	—
1266	C₂²	—	10	2	no	—
1267	C₂²	—	10	1	no	—
1268	C₂²	—	10	2	no	—
1269	C₂²	—	10	1	no	—
1270	C₂²	—	20	4	no	—
1271	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
1272	C₄	—	2	1	no	—
1273	C₄	—	2	2	no	—
1274	C₄	—	2	1	no	—
1275	C₄	—	2	2	no	—
1276	C₄	—	2	2	no	—
1277	C₄	—	2	1	no	—
1278	C₄	—	2	1	no	—
1279	C₄	—	2	1	no	—
1280	C₄	—	5	2	no	—
1281	C₄	—	10	1	no	—
1282	C₄	—	10	2	no	—
1283	C₄	—	10	1	no	—
1284	C₄	—	10	1	no	—
1285	C₄	—	10	1	no	—
1286	C₄	—	10	1	no	—
1287	C₄	—	10	2	no	—
1288	C₄	—	10	2	no	—
1289	C₄	C₃×D₅×#41	1	2	yes	—
1290	C₃	#10618424	1	1	yes	characteristic, direct product factor, Sylow
1291	C₂	—	4	1	no	—
1292	C₂	—	4	2	no	—
1293	C₂	—	10	2	no	—
1294	C₂	—	20	1	no	—
1295	C₂	—	20	2	no	—
1296	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
1297	C₂	C₃×#66285	1	1	yes	characteristic
1298	C₂	C₃×#66287	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#542	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#542	D₅
hypocenter	C₅	C₃×#3455
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#542

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#542	C₂	semidirect
2. C₃×#66067	C₂	semidirect
3. C₃×#66062	C₂	semidirect
4. C₃×#66041	C₂	semidirect
5. C₃×#66040	C₂	semidirect
6. C₃×#66016	C₂	semidirect
7. C₃×#66014	C₂	semidirect
8. C₃×#66012	C₂	semidirect
9. C₃×#66002	C₂	semidirect
10. C₃×#65991	C₂	semidirect
11. C₃×#65983	C₂	semidirect
12. C₃×#65972	C₂	semidirect
13. C₃×#65961	C₂	semidirect
14. C₃×#65959	C₂	semidirect
15. C₃×#65958	C₂	semidirect
16. C₃×#65953	C₂	semidirect
17. C₃×#65940	C₂	semidirect
18. C₃×#65917	C₂	semidirect
19. C₃×C₄×#713	C₂	semidirect
20. C₃×#65896	C₂	semidirect
21. C₃×C₄×#711	C₂	semidirect
22. C₃×#65868	C₂	semidirect
23. C₃×D₅×#117	C₂	semidirect
24. #10618424	C₃	direct (N × H)
28. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
29. C₃×C₅×#126	C₂²	semidirect
31. C₃×C₅×#124	C₂²	semidirect
34. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₄×C₅×Q₈	C₂²	semidirect
37. C₃×C₄×C₅×D₄	C₂²	semidirect
42. C₃×#4092	C₂²	semidirect
43. C₃×Q₈×Dic₅	C₂²	semidirect
44. C₃×Q₈×Dic₅	C₂²	semidirect
45. C₃×#4090	C₂²	semidirect
46. C₃×#4086	C₂²	semidirect
52. C₃×D₄×Dic₅	C₂²	semidirect
55. C₃×#4075	C₂²	semidirect
59. C₂×C₃×C₄×Dic₅	C₂²	semidirect
61. C₃×#4044	C₂²	semidirect
62. C₃×#4044	C₂²	semidirect
65. C₃×#4042	C₂²	semidirect
71. C₃×#4039	C₂²	semidirect
76. C₃×#4038	C₂²	semidirect
79. C₃×#4036	C₂²	semidirect
80. C₃×#4036	C₂²	semidirect
81. C₃×#4036	C₂²	semidirect
82. C₃×#4035	C₂²	semidirect
83. C₃×#4035	C₂²	semidirect
84. C₃×#4033	C₂²	semidirect
85. C₃×#4033	C₂²	semidirect
87. C₃×#4032	C₂²	semidirect
95. C₃×#4029	C₂²	semidirect
96. C₃×#4029	C₂²	semidirect
101. C₃×#4027	C₂²	semidirect
102. C₃×#4027	C₂²	semidirect
107. C₃×#4025	C₂²	semidirect
108. C₃×#4024	C₂²	semidirect
111. C₃×#4023	C₂²	semidirect
113. C₃×#4021	C₂²	semidirect
115. C₃×C₄×D₂₀	C₂²	semidirect
120. C₃×C₄²×D₅	C₂²	semidirect
121. C₃×#4016	C₂²	semidirect
122. C₃×#4015	C₂²	semidirect
123. C₃×C₄×Dic₁₀	C₂²	semidirect
125. C₅×#542	C₂×C₃	semidirect
126. #66067	C₂×C₃	semidirect
127. #66062	C₂×C₃	semidirect
128. #66041	C₂×C₃	semidirect
129. #66040	C₂×C₃	semidirect
130. #66016	C₂×C₃	semidirect
131. #66014	C₂×C₃	semidirect
132. #66012	C₂×C₃	semidirect
133. #66002	C₂×C₃	semidirect
134. #65991	C₂×C₃	semidirect
135. #65983	C₂×C₃	semidirect
136. #65972	C₂×C₃	semidirect
137. #65961	C₂×C₃	semidirect
138. #65959	C₂×C₃	semidirect
139. #65958	C₂×C₃	semidirect
140. #65953	C₂×C₃	semidirect
141. #65940	C₂×C₃	semidirect
142. #65917	C₂×C₃	semidirect
143. C₄×#713	C₂×C₃	semidirect
144. #65896	C₂×C₃	semidirect
145. C₄×#711	C₂×C₃	semidirect
146. #65868	C₂×C₃	semidirect
147. D₅×#117	C₂×C₃	semidirect
253. C₃×#542	D₅	semidirect
276. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
277. C₅×#126	C₂²×C₃	semidirect
279. C₅×#124	C₂²×C₃	semidirect
282. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
284. C₄×C₅×Q₈	C₂²×C₃	semidirect
285. C₄×C₅×D₄	C₂²×C₃	semidirect
290. #4092	C₂²×C₃	semidirect
291. Q₈×Dic₅	C₂²×C₃	semidirect
292. Q₈×Dic₅	C₂²×C₃	semidirect
293. #4090	C₂²×C₃	semidirect
294. #4086	C₂²×C₃	semidirect
300. D₄×Dic₅	C₂²×C₃	semidirect
303. #4075	C₂²×C₃	semidirect
307. C₂×C₄×Dic₅	C₂²×C₃	semidirect
309. #4044	C₂²×C₃	semidirect
310. #4044	C₂²×C₃	semidirect
313. #4042	C₂²×C₃	semidirect
319. #4039	C₂²×C₃	semidirect
324. #4038	C₂²×C₃	semidirect
327. #4036	C₂²×C₃	semidirect
328. #4036	C₂²×C₃	semidirect
329. #4036	C₂²×C₃	semidirect
330. #4035	C₂²×C₃	semidirect
331. #4035	C₂²×C₃	semidirect
332. #4033	C₂²×C₃	semidirect
333. #4033	C₂²×C₃	semidirect
335. #4032	C₂²×C₃	semidirect
343. #4029	C₂²×C₃	semidirect
344. #4029	C₂²×C₃	semidirect
349. #4027	C₂²×C₃	semidirect
350. #4027	C₂²×C₃	semidirect
355. #4025	C₂²×C₃	semidirect
356. #4024	C₂²×C₃	semidirect
359. #4023	C₂²×C₃	semidirect
361. #4021	C₂²×C₃	semidirect
363. C₄×D₂₀	C₂²×C₃	semidirect
368. C₄²×D₅	C₂²×C₃	semidirect
369. #4016	C₂²×C₃	semidirect
370. #4015	C₂²×C₃	semidirect
371. C₄×Dic₁₀	C₂²×C₃	semidirect
434. C₃×C₄⋊Q₈	C₂×D₅	semidirect
443. C₃×#126	C₂×D₅	semidirect
455. C₃×#124	C₂×D₅	semidirect
475. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
493. C₃×C₄×Q₈	C₂×D₅	semidirect
507. C₃×C₄×D₄	C₂×D₅	semidirect
633. #542	C₃×D₅	semidirect
851. C₄⋊Q₈	C₂×C₃×D₅	semidirect
860. #126	C₂×C₃×D₅	semidirect
872. #124	C₂×C₃×D₅	semidirect
892. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
910. C₄×Q₈	C₂×C₃×D₅	semidirect
924. C₄×D₄	C₂×C₃×D₅	semidirect
1146. C₃×C₅	#3455	semidirect
1254. C₅	C₃×#3455	semidirect
1290. C₃	#10618424	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×C₅×#542	2
C₃×#66067	2
C₃×#66062	2
C₃×#66041	2
C₃×#66040	2
C₃×#66016	2
C₃×#66014	2
C₃×#66012	2
C₃×#66002	2
C₃×#65991	2
C₃×#65983	2
C₃×#65972	2
C₃×#65961	2
C₃×#65959	2
C₃×#65958	2
C₃×#65953	2
C₃×#65940	2
C₃×#65917	2
C₃×C₄×#713	2
C₃×#65896	2
C₃×C₄×#711	2
C₃×#65868	2
C₃×D₅×#117	2
#10618424	3
C₃×#3455	5

Subgroups — C3×#10618424 #14481509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10618424 #14481509