Subgroups — C₃×#10618728 #14484115

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	C₃×C₅×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66040	C₂	1	2	yes	maximal, complemented
3	C₃×#66039	C₂	1	2	yes	maximal, complemented
4	C₃×#66029	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#66027	C₂	1	2	yes	maximal, complemented
6	C₃×#66025	C₂	1	2	yes	maximal, complemented
7	C₃×#66022	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65988	C₂	1	2	yes	maximal, complemented
9	C₃×#65983	C₂	1	2	yes	maximal, complemented
10	C₃×#65975	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65969	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65961	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65915	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×#713	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#65899	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#65866	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#65861	C₂	1	2	yes	maximal, complemented
20	C₃×#65856	C₂	1	2	yes	maximal, complemented
21	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#65841	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃×#4038	C₂	1	1	yes	maximal, characteristic, complemented
24	#10618728	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₃×#713	C₂²	1	1	yes	characteristic
26	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×#709	C₂²	1	2	yes	—
28	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
29	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
30	C₃×C₅×#126	C₂²	1	2	yes	complemented
31	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×#125	C₂²	1	2	yes	complemented
33	C₃×C₅×#123	C₂²	1	2	yes	—
34	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₅×#117	C₂²	1	2	yes	complemented
40	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×#4092	C₂²	1	1	yes	characteristic, complemented
42	C₃×#4092	C₂²	1	1	yes	characteristic, complemented
43	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
44	C₃×#4085	C₂²	1	2	yes	—
45	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
46	C₃×#4076	C₂²	1	1	yes	characteristic, complemented
47	C₃×#4076	C₂²	1	1	yes	characteristic, complemented
48	C₃×#4075	C₂²	1	2	yes	complemented
49	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
50	C₃×C₄×C₂²⋊D₅	C₂²	1	1	yes	characteristic
51	C₂×C₃×#685	C₂²	1	2	yes	—
52	C₃×#4072	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
55	C₃×#4044	C₂²	1	2	yes	complemented
56	C₃×#4044	C₂²	1	2	yes	complemented
57	C₃×#4044	C₂²	1	2	yes	complemented
58	C₃×#4043	C₂²	1	2	yes	complemented
59	C₃×#4042	C₂²	1	2	yes	—
60	C₃×#4042	C₂²	1	2	yes	—
61	C₃×#4042	C₂²	1	2	yes	complemented
62	C₃×#4041	C₂²	1	2	yes	—
63	C₃×#4041	C₂²	1	1	yes	characteristic, complemented
64	C₃×#4041	C₂²	1	1	yes	characteristic, complemented
65	C₃×#4040	C₂²	1	2	yes	—
66	C₃×#4040	C₂²	1	2	yes	—
67	C₃×#4040	C₂²	1	2	yes	—
68	C₃×#4040	C₂²	1	2	yes	complemented
69	C₃×#4040	C₂²	1	2	yes	complemented
70	C₃×#4039	C₂²	1	1	yes	characteristic
71	C₃×#4039	C₂²	1	2	yes	—
72	C₃×#4039	C₂²	1	2	yes	complemented
73	C₃×#4039	C₂²	1	2	yes	complemented
74	C₃×#4039	C₂²	1	1	yes	characteristic, complemented
75	C₃×#4039	C₂²	1	2	yes	complemented
76	C₃×#4038	C₂²	1	1	yes	characteristic
77	C₃×#4038	C₂²	1	1	yes	characteristic
78	C₃×#4038	C₂²	1	1	yes	characteristic
79	C₃×#4038	C₂²	1	2	yes	—
80	C₃×#4038	C₂²	1	1	yes	characteristic, complemented
81	C₃×#4038	C₂²	1	2	yes	complemented
82	C₃×#4038	C₂²	1	1	yes	characteristic, complemented
83	C₃×#4038	C₂²	1	2	yes	complemented
84	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
85	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
86	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
87	C₃×#4035	C₂²	1	2	yes	complemented
88	C₃×#4035	C₂²	1	2	yes	complemented
89	C₃×#4034	C₂²	1	1	yes	characteristic, complemented
90	C₃×#4034	C₂²	1	1	yes	characteristic, complemented
91	C₃×#4033	C₂²	1	2	yes	complemented
92	C₃×#4033	C₂²	1	2	yes	complemented
93	C₃×#4033	C₂²	1	2	yes	complemented
94	C₃×#4031	C₂²	1	2	yes	—
95	C₃×#4031	C₂²	1	2	yes	complemented
96	C₃×#4030	C₂²	1	2	yes	—
97	C₃×#4029	C₂²	1	2	yes	complemented
98	C₃×#4028	C₂²	1	2	yes	—
99	C₃×#4028	C₂²	1	2	yes	—
100	C₃×#4027	C₂²	1	1	yes	characteristic
101	C₃×#4027	C₂²	1	2	yes	—
102	C₃×#4027	C₂²	1	1	yes	characteristic
103	C₃×#4027	C₂²	1	2	yes	complemented
104	C₃×#4027	C₂²	1	2	yes	complemented
105	C₃×#4027	C₂²	1	2	yes	complemented
106	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
107	C₃×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
108	C₃×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
109	C₃×#4025	C₂²	1	2	yes	complemented
110	C₃×#4024	C₂²	1	2	yes	complemented
111	C₃×#4023	C₂²	1	2	yes	complemented
112	C₃×#4022	C₂²	1	2	yes	complemented
113	C₃×#4021	C₂²	1	2	yes	complemented
114	C₃×C₄×D₂₀	C₂²	1	2	yes	—
115	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
116	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
117	C₃×#4018	C₂²	1	2	yes	—
118	C₃×#4018	C₂²	1	2	yes	complemented
119	C₃×#4018	C₂²	1	2	yes	complemented
120	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
121	C₃×C₄²×D₅	C₂²	1	2	yes	complemented
122	C₃×C₄²×D₅	C₂²	1	2	yes	complemented
123	C₃×#4016	C₂²	1	1	yes	characteristic, complemented
124	C₃×#3475	—	5	1	no	maximal, Hall
125	C₅×#552	C₂×C₃	1	1	yes	characteristic, complemented
126	#66040	C₂×C₃	1	2	yes	complemented
127	#66039	C₂×C₃	1	2	yes	complemented
128	#66029	C₂×C₃	1	1	yes	characteristic, complemented
129	#66027	C₂×C₃	1	2	yes	complemented
130	#66025	C₂×C₃	1	2	yes	complemented
131	#66022	C₂×C₃	1	1	yes	characteristic, complemented
132	#65988	C₂×C₃	1	2	yes	complemented
133	#65983	C₂×C₃	1	2	yes	complemented
134	#65975	C₂×C₃	1	1	yes	characteristic, complemented
135	#65969	C₂×C₃	1	1	yes	characteristic, complemented
136	#65961	C₂×C₃	1	1	yes	characteristic, complemented
137	#65961	C₂×C₃	1	1	yes	characteristic, complemented
138	#65915	C₂×C₃	1	1	yes	characteristic, complemented
139	C₄×#713	C₂×C₃	1	1	yes	characteristic, complemented
140	#65899	C₂×C₃	1	1	yes	characteristic, complemented
141	C₄×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
142	#65866	C₂×C₃	1	1	yes	characteristic, complemented
143	#65861	C₂×C₃	1	2	yes	complemented
144	#65856	C₂×C₃	1	2	yes	complemented
145	D₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
146	#65841	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂×#4038	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
149	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
150	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
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	2	yes	—
155	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
156	C₂×C₃×C₂²⋊D₅	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
158	C₂×C₃×C₂²⋊D₅	C₂³	1	1	yes	characteristic
159	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
160	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
161	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
162	C₃×#713	—	2	4	no	—
163	C₃×D₄×D₅	—	2	4	no	—
164	C₃×#709	—	2	8	no	—
165	C₂×C₃×D₂₀	C₂³	1	2	yes	—
166	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
167	C₂×C₃×D₂₀	C₂³	1	2	yes	—
168	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
169	C₂×C₃×D₂₀	C₂³	1	2	yes	—
170	C₂×C₃×C₄×D₅	—	2	4	no	—
171	C₂×C₃×C₄×D₅	—	2	4	no	—
172	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
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	2	yes	—
180	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
182	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
183	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
184	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
185	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
186	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
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	2	yes	—
191	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
196	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
197	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
198	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
202	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
204	C₃×C₄²×C₅	C₂³	1	2	yes	—
205	C₃×C₄²×C₅	C₂³	1	2	yes	—
206	C₃×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
207	C₃×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
208	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
209	C₃×#685	C₂³	1	2	yes	—
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	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×#685	C₂³	1	1	yes	characteristic
219	C₃×#685	C₂³	1	1	yes	characteristic
220	C₃×#685	C₂³	1	2	yes	—
221	C₃×#685	C₂³	1	1	yes	characteristic
222	C₃×#685	C₂³	1	2	yes	—
223	C₃×#685	C₂³	1	2	yes	—
224	C₃×#685	C₂³	1	2	yes	—
225	C₃×#685	C₂³	1	2	yes	—
226	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
227	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
228	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
229	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
230	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
231	C₃×C₄⋊Dic₅	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	2	yes	—
236	C₃×#683	C₂³	1	2	yes	—
237	C₃×#683	C₂³	1	2	yes	—
238	C₃×#683	C₂³	1	1	yes	characteristic
239	C₃×#683	C₂³	1	2	yes	—
240	C₃×#683	C₂³	1	2	yes	—
241	C₃×#683	C₂³	1	1	yes	characteristic
242	C₃×C₄×Dic₅	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	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	1	no	—
256	C₃×#553	—	5	1	no	—
257	C₃×#552	—	5	2	no	—
258	C₃×#552	—	5	1	no	—
259	C₃×#552	D₅	1	1	yes	characteristic, complemented
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	—	5	1	no	—
275	C₂×#713	C₂²×C₃	1	1	yes	characteristic
276	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
277	C₂×#709	C₂²×C₃	1	2	yes	—
278	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
279	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
280	C₅×#126	C₂²×C₃	1	2	yes	complemented
281	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
282	C₅×#125	C₂²×C₃	1	2	yes	complemented
283	C₅×#123	C₂²×C₃	1	2	yes	—
284	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
285	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
286	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
287	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
288	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
289	C₅×#117	C₂²×C₃	1	2	yes	complemented
290	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
291	#4092	C₂²×C₃	1	1	yes	characteristic, complemented
292	#4092	C₂²×C₃	1	1	yes	characteristic, complemented
293	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
294	#4085	C₂²×C₃	1	2	yes	—
295	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
296	#4076	C₂²×C₃	1	1	yes	characteristic, complemented
297	#4076	C₂²×C₃	1	1	yes	characteristic, complemented
298	#4075	C₂²×C₃	1	2	yes	complemented
299	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
300	C₄×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
301	C₂×#685	C₂²×C₃	1	2	yes	—
302	#4072	C₂²×C₃	1	1	yes	characteristic, complemented
303	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
304	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
305	#4044	C₂²×C₃	1	2	yes	complemented
306	#4044	C₂²×C₃	1	2	yes	complemented
307	#4044	C₂²×C₃	1	2	yes	complemented
308	#4043	C₂²×C₃	1	2	yes	complemented
309	#4042	C₂²×C₃	1	2	yes	—
310	#4042	C₂²×C₃	1	2	yes	—
311	#4042	C₂²×C₃	1	2	yes	complemented
312	#4041	C₂²×C₃	1	2	yes	—
313	#4041	C₂²×C₃	1	1	yes	characteristic, complemented
314	#4041	C₂²×C₃	1	1	yes	characteristic, complemented
315	#4040	C₂²×C₃	1	2	yes	—
316	#4040	C₂²×C₃	1	2	yes	—
317	#4040	C₂²×C₃	1	2	yes	—
318	#4040	C₂²×C₃	1	2	yes	complemented
319	#4040	C₂²×C₃	1	2	yes	complemented
320	#4039	C₂²×C₃	1	1	yes	characteristic
321	#4039	C₂²×C₃	1	2	yes	—
322	#4039	C₂²×C₃	1	1	yes	characteristic, complemented
323	#4039	C₂²×C₃	1	2	yes	complemented
324	#4039	C₂²×C₃	1	2	yes	complemented
325	#4039	C₂²×C₃	1	2	yes	complemented
326	#4038	C₂²×C₃	1	1	yes	characteristic
327	#4038	C₂²×C₃	1	1	yes	characteristic
328	#4038	C₂²×C₃	1	2	yes	—
329	#4038	C₂²×C₃	1	1	yes	characteristic
330	#4038	C₂²×C₃	1	1	yes	characteristic, complemented
331	#4038	C₂²×C₃	1	1	yes	characteristic, complemented
332	#4038	C₂²×C₃	1	2	yes	complemented
333	#4038	C₂²×C₃	1	2	yes	complemented
334	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
335	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
336	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
337	#4035	C₂²×C₃	1	2	yes	complemented
338	#4035	C₂²×C₃	1	2	yes	complemented
339	#4034	C₂²×C₃	1	1	yes	characteristic, complemented
340	#4034	C₂²×C₃	1	1	yes	characteristic, complemented
341	#4033	C₂²×C₃	1	2	yes	complemented
342	#4033	C₂²×C₃	1	2	yes	complemented
343	#4033	C₂²×C₃	1	2	yes	complemented
344	#4031	C₂²×C₃	1	2	yes	—
345	#4031	C₂²×C₃	1	2	yes	complemented
346	#4030	C₂²×C₃	1	2	yes	—
347	#4029	C₂²×C₃	1	2	yes	complemented
348	#4028	C₂²×C₃	1	2	yes	—
349	#4028	C₂²×C₃	1	2	yes	—
350	#4027	C₂²×C₃	1	1	yes	characteristic
351	#4027	C₂²×C₃	1	2	yes	—
352	#4027	C₂²×C₃	1	1	yes	characteristic
353	#4027	C₂²×C₃	1	2	yes	complemented
354	#4027	C₂²×C₃	1	2	yes	complemented
355	#4027	C₂²×C₃	1	2	yes	complemented
356	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
357	D₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
358	D₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
359	#4025	C₂²×C₃	1	2	yes	complemented
360	#4024	C₂²×C₃	1	2	yes	complemented
361	#4023	C₂²×C₃	1	2	yes	complemented
362	#4022	C₂²×C₃	1	2	yes	complemented
363	#4021	C₂²×C₃	1	2	yes	complemented
364	C₄×D₂₀	C₂²×C₃	1	2	yes	—
365	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
366	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
367	#4018	C₂²×C₃	1	2	yes	—
368	#4018	C₂²×C₃	1	2	yes	complemented
369	#4018	C₂²×C₃	1	2	yes	complemented
370	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
371	C₄²×D₅	C₂²×C₃	1	2	yes	complemented
372	C₄²×D₅	C₂²×C₃	1	2	yes	complemented
373	#4016	C₂²×C₃	1	1	yes	characteristic, complemented
374	#3475	—	5	1	no	Sylow
375	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
376	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
377	C₂²×C₃×D₅	—	2	2	no	—
378	C₂²×C₃×D₅	—	2	2	no	—
379	C₂²×C₃×D₅	—	2	2	no	—
380	C₂²×C₃×D₅	—	2	2	no	—
381	C₂²×C₃×D₅	—	4	1	no	—
382	C₂²×C₃×D₅	—	4	1	no	—
383	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
384	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
385	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
386	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
387	C₃×C₅×Q₈	—	2	2	no	—
388	C₃×C₅×D₄	—	2	2	no	—
389	C₂×C₃×C₄×C₅	—	2	4	no	—
390	C₂×C₃×C₄×C₅	—	2	2	no	—
391	C₂×C₃×C₄×C₅	—	2	2	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	2	yes	—
395	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
396	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	2	no	—
403	C₃×C₂²⋊D₅	—	4	2	no	—
404	C₃×C₂²⋊D₅	#41	1	4	yes	complemented
405	C₂×C₃×Dic₅	—	2	2	no	—
406	C₂×C₃×Dic₅	—	2	2	no	—
407	C₂×C₃×Dic₅	—	4	2	no	—
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	2	yes	—
412	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
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	C₃×D₂₀	—	2	4	no	—
417	C₃×D₂₀	—	2	2	no	—
418	C₃×D₂₀	—	2	4	no	—
419	C₃×D₂₀	—	2	2	no	—
420	C₃×D₂₀	—	4	2	no	—
421	C₃×C₄×D₅	—	2	2	no	—
422	C₃×C₄×D₅	—	2	2	no	—
423	C₃×C₄×D₅	—	2	4	no	—
424	C₃×C₄×D₅	—	2	2	no	—
425	C₃×C₄×D₅	—	2	2	no	—
426	C₃×C₄×D₅	—	2	2	no	—
427	C₃×C₄×D₅	—	2	2	no	—
428	C₃×C₄×D₅	—	2	4	no	—
429	C₃×C₄×D₅	—	2	2	no	—
430	C₃×C₄×D₅	—	2	4	no	—
431	C₃×C₄×D₅	—	4	1	no	—
432	C₃×C₄×D₅	—	4	2	no	—
433	C₃×C₄×D₅	—	4	2	no	—
434	C₃×C₄×D₅	#41	1	4	yes	complemented
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	—	5	1	no	—
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	C₂×D₅	1	2	yes	complemented
450	C₃×#125	—	5	2	no	—
451	C₃×#125	—	5	2	no	—
452	C₃×#125	—	5	1	no	—
453	C₃×#125	C₂×D₅	1	2	yes	complemented
454	C₃×#125	C₂×D₅	1	1	yes	characteristic, complemented
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	C₂×D₅	1	2	yes	—
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	2	no	—
472	C₃×C₂²⋊Q₈	—	5	2	no	—
473	C₃×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
474	C₃×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
475	C₃×#121	—	5	2	no	—
476	C₃×#121	—	5	1	no	—
477	C₃×#121	—	5	1	no	—
478	C₃×#121	—	5	2	no	—
479	C₃×#121	—	5	1	no	—
480	C₃×#121	—	5	1	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	2	no	—
486	C₃×C₄×Q₈	—	5	2	no	—
487	C₃×C₄×Q₈	—	5	2	no	—
488	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
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	2	no	—
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	1	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	1	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
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	2	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	2	no	—
518	C₃×#117	—	5	2	no	—
519	C₃×#117	—	5	2	no	—
520	C₃×#117	—	5	2	no	—
521	C₃×#117	C₂×D₅	1	1	yes	characteristic, complemented
522	C₃×#117	C₂×D₅	1	2	yes	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	—	5	1	no	—
527	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
528	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
529	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
530	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
531	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
532	C₂×C₃×C₄²	—	5	2	no	—
533	C₂×C₃×C₄²	—	5	1	no	—
534	C₂×C₃×C₄²	—	5	2	no	—
535	C₂×C₃×C₄²	—	5	2	no	—
536	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
537	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
538	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
539	C₂×C₅×D₄	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	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
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	1	yes	characteristic
547	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
548	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
549	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
550	#713	—	2	4	no	—
551	D₄×D₅	—	2	4	no	—
552	#709	—	2	8	no	—
553	C₂×D₂₀	C₂³×C₃	1	2	yes	—
554	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
555	C₂×D₂₀	C₂³×C₃	1	2	yes	—
556	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
557	C₂×D₂₀	C₂³×C₃	1	2	yes	—
558	C₂×C₄×D₅	—	2	4	no	—
559	C₂×C₄×D₅	—	2	4	no	—
560	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
567	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
568	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
569	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
570	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
571	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
572	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
573	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
574	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
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	2	yes	—
579	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
580	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
581	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
582	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
583	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
584	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
585	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
586	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
587	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
588	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
589	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
590	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
591	C₄²×C₅	C₂³×C₃	1	2	yes	—
592	C₄²×C₅	C₂³×C₃	1	2	yes	—
593	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
594	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
595	C₂²⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
596	C₂²⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
597	#685	C₂³×C₃	1	2	yes	—
598	#685	C₂³×C₃	1	2	yes	—
599	#685	C₂³×C₃	1	1	yes	characteristic
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	1	yes	characteristic
605	#685	C₂³×C₃	1	2	yes	—
606	#685	C₂³×C₃	1	1	yes	characteristic
607	#685	C₂³×C₃	1	2	yes	—
608	#685	C₂³×C₃	1	2	yes	—
609	#685	C₂³×C₃	1	1	yes	characteristic
610	#685	C₂³×C₃	1	2	yes	—
611	#685	C₂³×C₃	1	2	yes	—
612	#685	C₂³×C₃	1	2	yes	—
613	#685	C₂³×C₃	1	2	yes	—
614	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
615	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
616	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
617	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
618	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
619	C₄⋊Dic₅	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	1	yes	characteristic
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	2	yes	—
629	#683	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	2	yes	—
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	2	yes	—
639	C₄×Dic₅	C₂³×C₃	1	2	yes	—
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	C₃×D₅	1	1	yes	characteristic, complemented
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	—	5	1	no	—
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	C₂×#41	1	2	yes	—
669	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
670	C₂×C₃×D₅	—	2	1	no	—
671	C₂×C₃×D₅	—	2	1	no	—
672	C₂×C₃×D₅	—	2	1	no	—
673	C₂×C₃×D₅	—	2	1	no	—
674	C₂×C₃×D₅	—	2	1	no	—
675	C₂×C₃×D₅	—	2	2	no	—
676	C₂×C₃×D₅	—	2	2	no	—
677	C₂×C₃×D₅	—	2	1	no	—
678	C₂×C₃×D₅	—	2	2	no	—
679	C₂×C₃×D₅	—	2	1	no	—
680	C₂×C₃×D₅	—	4	4	no	—
681	C₂×C₃×D₅	—	4	4	no	—
682	C₂×C₃×D₅	C₂×#41	1	2	yes	—
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	1	no	—
689	C₃×C₄×C₅	—	2	2	no	—
690	C₃×C₄×C₅	—	2	2	no	—
691	C₃×C₄×C₅	—	2	1	no	—
692	C₃×C₄×C₅	C₂×#41	1	2	yes	—
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	2	no	—
698	C₃×Dic₅	—	2	2	no	—
699	C₃×Dic₅	C₂×#41	1	2	yes	—
700	C₃×Dic₅	C₂×#41	1	2	yes	—
701	C₂⁴×C₃	—	5	1	no	—
702	C₂⁴×C₃	—	5	1	no	—
703	C₃×#41	—	10	8	no	—
704	C₃×#41	—	10	4	no	—
705	C₂×C₃×Q₈	—	5	2	no	—
706	C₂×C₃×Q₈	—	5	2	no	—
707	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
708	C₂×C₃×D₄	—	5	1	no	—
709	C₂×C₃×D₄	—	5	2	no	—
710	C₂×C₃×D₄	—	5	1	no	—
711	C₂×C₃×D₄	—	5	2	no	—
712	C₂×C₃×D₄	—	5	2	no	—
713	C₂×C₃×D₄	—	5	2	no	—
714	C₂×C₃×D₄	—	5	1	no	—
715	C₂×C₃×D₄	—	5	1	no	—
716	C₂×C₃×D₄	—	5	2	no	—
717	C₂×C₃×D₄	—	10	4	no	—
718	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
719	C₂²×C₃×C₄	—	5	1	no	—
720	C₂²×C₃×C₄	—	5	1	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	2	no	—
725	C₂²×C₃×C₄	—	5	1	no	—
726	C₂²×C₃×C₄	—	5	2	no	—
727	C₂²×C₃×C₄	—	5	2	no	—
728	C₂²×C₃×C₄	—	5	1	no	—
729	C₂²×C₃×C₄	—	5	1	no	—
730	C₂²×C₃×C₄	—	5	1	no	—
731	C₂²×C₃×C₄	—	5	1	no	—
732	C₂²×C₃×C₄	—	5	1	no	—
733	C₂²×C₃×C₄	—	5	1	no	—
734	C₂²×C₃×C₄	—	5	2	no	—
735	C₂²×C₃×C₄	—	5	2	no	—
736	C₂²×C₃×C₄	—	10	4	no	—
737	C₂²×C₃×C₄	—	10	4	no	—
738	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
739	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
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	2	no	—
746	C₃×C₄⋊C₄	—	5	2	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	1	no	—
752	C₃×C₄⋊C₄	—	5	1	no	—
753	C₃×C₄⋊C₄	—	5	1	no	—
754	C₃×C₄⋊C₄	—	5	2	no	—
755	C₃×C₄⋊C₄	—	5	1	no	—
756	C₃×C₄⋊C₄	—	5	2	no	—
757	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
758	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
759	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
760	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
761	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
762	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
763	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
764	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
765	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
766	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
767	C₃×C₂²⋊C₄	—	5	2	no	—
768	C₃×C₂²⋊C₄	—	5	1	no	—
769	C₃×C₂²⋊C₄	—	5	1	no	—
770	C₃×C₂²⋊C₄	—	5	2	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	2	no	—
775	C₃×C₂²⋊C₄	—	5	2	no	—
776	C₃×C₂²⋊C₄	—	5	1	no	—
777	C₃×C₂²⋊C₄	—	5	1	no	—
778	C₃×C₂²⋊C₄	—	5	1	no	—
779	C₃×C₂²⋊C₄	—	5	2	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	C₂²×D₅	1	2	yes	—
788	C₃×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
789	C₃×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
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	1	no	—
794	C₃×C₄²	—	5	2	no	—
795	C₃×C₄²	—	5	1	no	—
796	C₃×C₄²	—	5	2	no	—
797	C₃×C₄²	—	5	2	no	—
798	C₃×C₄²	—	5	2	no	—
799	C₃×C₄²	—	5	2	no	—
800	C₃×C₄²	—	5	1	no	—
801	C₃×C₄²	—	5	2	no	—
802	C₃×C₄²	C₂²×D₅	1	2	yes	—
803	C₃×C₄²	C₂²×D₅	1	2	yes	—
804	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
805	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
806	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
807	C₂²×D₅	—	2	2	no	—
808	C₂²×D₅	—	2	2	no	—
809	C₂²×D₅	—	2	2	no	—
810	C₂²×D₅	—	2	2	no	—
811	C₂²×D₅	—	4	1	no	—
812	C₂²×D₅	—	4	1	no	—
813	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
814	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
815	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
816	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
817	C₅×Q₈	—	2	2	no	—
818	C₅×D₄	—	2	2	no	—
819	C₂×C₄×C₅	—	2	4	no	—
820	C₂×C₄×C₅	—	2	2	no	—
821	C₂×C₄×C₅	—	2	2	no	—
822	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
823	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
824	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
825	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
826	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
827	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
828	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
829	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
830	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
831	C₂²⋊D₅	—	2	4	no	—
832	C₂²⋊D₅	—	2	2	no	—
833	C₂²⋊D₅	—	4	2	no	—
834	C₂²⋊D₅	C₃×#41	1	4	yes	complemented
835	C₂×Dic₅	—	2	2	no	—
836	C₂×Dic₅	—	2	2	no	—
837	C₂×Dic₅	—	4	2	no	—
838	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
839	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
840	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
841	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
842	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
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	D₂₀	—	2	4	no	—
847	D₂₀	—	2	2	no	—
848	D₂₀	—	2	4	no	—
849	D₂₀	—	2	2	no	—
850	D₂₀	—	4	2	no	—
851	C₄×D₅	—	2	2	no	—
852	C₄×D₅	—	2	2	no	—
853	C₄×D₅	—	2	4	no	—
854	C₄×D₅	—	2	2	no	—
855	C₄×D₅	—	2	2	no	—
856	C₄×D₅	—	2	2	no	—
857	C₄×D₅	—	2	2	no	—
858	C₄×D₅	—	2	4	no	—
859	C₄×D₅	—	2	2	no	—
860	C₄×D₅	—	2	4	no	—
861	C₄×D₅	—	4	1	no	—
862	C₄×D₅	—	4	2	no	—
863	C₄×D₅	—	4	2	no	—
864	C₄×D₅	C₃×#41	1	4	yes	complemented
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	—	5	1	no	—
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	C₂×C₃×D₅	1	2	yes	complemented
880	#125	—	5	2	no	—
881	#125	—	5	2	no	—
882	#125	—	5	1	no	—
883	#125	C₂×C₃×D₅	1	2	yes	complemented
884	#125	C₂×C₃×D₅	1	1	yes	characteristic, complemented
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	C₂×C₃×D₅	1	2	yes	—
896	C₂²⋊Q₈	—	5	1	no	—
897	C₂²⋊Q₈	—	5	1	no	—
898	C₂²⋊Q₈	—	5	2	no	—
899	C₂²⋊Q₈	—	5	2	no	—
900	C₂²⋊Q₈	—	5	2	no	—
901	C₂²⋊Q₈	—	5	2	no	—
902	C₂²⋊Q₈	—	5	2	no	—
903	C₂²⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
904	C₂²⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
905	#121	—	5	2	no	—
906	#121	—	5	1	no	—
907	#121	—	5	1	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	2	no	—
916	C₄×Q₈	—	5	2	no	—
917	C₄×Q₈	—	5	2	no	—
918	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
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	2	no	—
924	C₄×D₄	—	5	2	no	—
925	C₄×D₄	—	5	1	no	—
926	C₄×D₄	—	5	2	no	—
927	C₄×D₄	—	5	2	no	—
928	C₄×D₄	—	5	1	no	—
929	C₄×D₄	—	5	1	no	—
930	C₄×D₄	—	5	2	no	—
931	C₄×D₄	—	5	2	no	—
932	C₄×D₄	—	5	2	no	—
933	C₄×D₄	—	5	2	no	—
934	C₄×D₄	—	5	1	no	—
935	C₄×D₄	—	5	2	no	—
936	C₄×D₄	—	5	1	no	—
937	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
938	#117	—	5	1	no	—
939	#117	—	5	1	no	—
940	#117	—	5	1	no	—
941	#117	—	5	1	no	—
942	#117	—	5	2	no	—
943	#117	—	5	2	no	—
944	#117	—	5	1	no	—
945	#117	—	5	1	no	—
946	#117	—	5	2	no	—
947	#117	—	5	2	no	—
948	#117	—	5	2	no	—
949	#117	—	5	2	no	—
950	#117	—	5	2	no	—
951	#117	C₂×C₃×D₅	1	1	yes	characteristic, complemented
952	#117	C₂×C₃×D₅	1	2	yes	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	—	5	1	no	—
957	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
958	C₂×C₂²⋊C₄	—	5	2	no	—
959	C₂×C₂²⋊C₄	—	5	2	no	—
960	C₂×C₂²⋊C₄	—	5	1	no	—
961	C₂×C₂²⋊C₄	—	5	1	no	—
962	C₂×C₄²	—	5	2	no	—
963	C₂×C₄²	—	5	2	no	—
964	C₂×C₄²	—	5	1	no	—
965	C₂×C₄²	—	5	2	no	—
966	C₂×C₃×C₅	—	2	2	no	—
967	C₂×C₃×C₅	—	4	1	no	—
968	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
969	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
970	C₂×C₃×C₅	#585	1	1	yes	characteristic
971	C₃×D₅	—	2	2	no	—
972	C₃×D₅	—	2	2	no	—
973	C₃×D₅	—	4	2	no	—
974	C₃×D₅	—	4	1	no	—
975	C₂³×C₃	—	5	1	no	—
976	C₂³×C₃	—	5	1	no	—
977	C₂³×C₃	—	5	1	no	—
978	C₂³×C₃	—	5	2	no	—
979	C₂³×C₃	—	10	2	no	—
980	C₂³×C₃	—	10	2	no	—
981	C₂³×C₃	—	10	2	no	—
982	C₂³×C₃	—	10	2	no	—
983	C₂³×C₃	—	20	1	no	—
984	C₂³×C₃	—	20	1	no	—
985	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
986	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
987	C₃×Q₈	—	2	2	no	—
988	C₃×Q₈	—	10	4	no	—
989	C₃×Q₈	—	20	2	no	—
990	C₃×D₄	—	2	2	no	—
991	C₃×D₄	—	5	4	no	—
992	C₃×D₄	—	10	2	no	—
993	C₃×D₄	—	10	4	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	4	no	—
1001	C₂×C₃×C₄	—	2	2	no	—
1002	C₂×C₃×C₄	—	2	2	no	—
1003	C₂×C₃×C₄	—	5	1	no	—
1004	C₂×C₃×C₄	—	5	1	no	—
1005	C₂×C₃×C₄	—	5	4	no	—
1006	C₂×C₃×C₄	—	5	1	no	—
1007	C₂×C₃×C₄	—	5	2	no	—
1008	C₂×C₃×C₄	—	5	1	no	—
1009	C₂×C₃×C₄	—	5	2	no	—
1010	C₂×C₃×C₄	—	5	2	no	—
1011	C₂×C₃×C₄	—	5	1	no	—
1012	C₂×C₃×C₄	—	10	2	no	—
1013	C₂×C₃×C₄	—	10	2	no	—
1014	C₂×C₃×C₄	—	10	2	no	—
1015	C₂×C₃×C₄	—	10	4	no	—
1016	C₂×C₃×C₄	—	10	4	no	—
1017	C₂×C₃×C₄	—	10	2	no	—
1018	C₂×C₃×C₄	—	10	2	no	—
1019	C₂×C₃×C₄	—	10	4	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	—	20	2	no	—
1025	C₂×C₃×C₄	—	20	1	no	—
1026	C₂×C₃×C₄	—	20	2	no	—
1027	C₂×C₃×C₄	—	20	2	no	—
1028	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1029	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
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	C₂×C₃×#41	1	2	yes	—
1043	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
1044	C₂×D₅	—	2	1	no	—
1045	C₂×D₅	—	2	1	no	—
1046	C₂×D₅	—	2	1	no	—
1047	C₂×D₅	—	2	1	no	—
1048	C₂×D₅	—	2	1	no	—
1049	C₂×D₅	—	2	2	no	—
1050	C₂×D₅	—	2	2	no	—
1051	C₂×D₅	—	2	1	no	—
1052	C₂×D₅	—	2	2	no	—
1053	C₂×D₅	—	2	1	no	—
1054	C₂×D₅	—	4	4	no	—
1055	C₂×D₅	—	4	4	no	—
1056	C₂×D₅	C₂×C₃×#41	1	2	yes	—
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	1	no	—
1063	C₄×C₅	—	2	2	no	—
1064	C₄×C₅	—	2	2	no	—
1065	C₄×C₅	—	2	1	no	—
1066	C₄×C₅	C₂×C₃×#41	1	2	yes	—
1067	Dic₅	—	2	2	no	—
1068	Dic₅	—	2	1	no	—
1069	Dic₅	—	2	1	no	—
1070	Dic₅	—	2	1	no	—
1071	Dic₅	—	2	2	no	—
1072	Dic₅	—	2	2	no	—
1073	Dic₅	C₂×C₃×#41	1	2	yes	—
1074	Dic₅	C₂×C₃×#41	1	2	yes	—
1075	C₂⁴	—	5	1	no	—
1076	C₂⁴	—	5	1	no	—
1077	#41	—	10	8	no	—
1078	#41	—	10	4	no	—
1079	C₂×Q₈	—	5	2	no	—
1080	C₂×Q₈	—	5	2	no	—
1081	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
1082	C₂×D₄	—	5	1	no	—
1083	C₂×D₄	—	5	2	no	—
1084	C₂×D₄	—	5	1	no	—
1085	C₂×D₄	—	5	2	no	—
1086	C₂×D₄	—	5	2	no	—
1087	C₂×D₄	—	5	2	no	—
1088	C₂×D₄	—	5	1	no	—
1089	C₂×D₄	—	5	1	no	—
1090	C₂×D₄	—	5	2	no	—
1091	C₂×D₄	—	10	4	no	—
1092	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
1093	C₂²×C₄	—	5	1	no	—
1094	C₂²×C₄	—	5	1	no	—
1095	C₂²×C₄	—	5	1	no	—
1096	C₂²×C₄	—	5	2	no	—
1097	C₂²×C₄	—	5	1	no	—
1098	C₂²×C₄	—	5	2	no	—
1099	C₂²×C₄	—	5	1	no	—
1100	C₂²×C₄	—	5	2	no	—
1101	C₂²×C₄	—	5	2	no	—
1102	C₂²×C₄	—	5	1	no	—
1103	C₂²×C₄	—	5	1	no	—
1104	C₂²×C₄	—	5	1	no	—
1105	C₂²×C₄	—	5	1	no	—
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	—	10	4	no	—
1111	C₂²×C₄	—	10	4	no	—
1112	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
1113	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
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	1	no	—
1119	C₄⋊C₄	—	5	2	no	—
1120	C₄⋊C₄	—	5	2	no	—
1121	C₄⋊C₄	—	5	2	no	—
1122	C₄⋊C₄	—	5	1	no	—
1123	C₄⋊C₄	—	5	1	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	C₂²×C₃×D₅	1	1	yes	characteristic
1132	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1133	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1134	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1135	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1136	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1137	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1138	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1139	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1140	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1141	C₂²⋊C₄	—	5	2	no	—
1142	C₂²⋊C₄	—	5	1	no	—
1143	C₂²⋊C₄	—	5	1	no	—
1144	C₂²⋊C₄	—	5	2	no	—
1145	C₂²⋊C₄	—	5	1	no	—
1146	C₂²⋊C₄	—	5	2	no	—
1147	C₂²⋊C₄	—	5	2	no	—
1148	C₂²⋊C₄	—	5	2	no	—
1149	C₂²⋊C₄	—	5	2	no	—
1150	C₂²⋊C₄	—	5	1	no	—
1151	C₂²⋊C₄	—	5	1	no	—
1152	C₂²⋊C₄	—	5	1	no	—
1153	C₂²⋊C₄	—	5	2	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	C₂²×C₃×D₅	1	2	yes	—
1162	C₂²⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1163	C₂²⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1164	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1165	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1166	C₄²	—	5	2	no	—
1167	C₄²	—	5	1	no	—
1168	C₄²	—	5	2	no	—
1169	C₄²	—	5	1	no	—
1170	C₄²	—	5	2	no	—
1171	C₄²	—	5	2	no	—
1172	C₄²	—	5	2	no	—
1173	C₄²	—	5	2	no	—
1174	C₄²	—	5	1	no	—
1175	C₄²	—	5	2	no	—
1176	C₄²	C₂²×C₃×D₅	1	2	yes	—
1177	C₄²	C₂²×C₃×D₅	1	2	yes	—
1178	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
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	—	5	2	no	—
1186	C₂²×C₃	—	5	2	no	—
1187	C₂²×C₃	—	10	1	no	—
1188	C₂²×C₃	—	10	1	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	—	20	4	no	—
1199	C₂²×C₃	D₅×#41	1	2	yes	—
1200	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
1201	C₃×C₄	—	2	2	no	—
1202	C₃×C₄	—	2	1	no	—
1203	C₃×C₄	—	2	1	no	—
1204	C₃×C₄	—	2	2	no	—
1205	C₃×C₄	—	2	1	no	—
1206	C₃×C₄	—	2	2	no	—
1207	C₃×C₄	—	2	1	no	—
1208	C₃×C₄	—	2	2	no	—
1209	C₃×C₄	—	5	2	no	—
1210	C₃×C₄	—	5	2	no	—
1211	C₃×C₄	—	10	1	no	—
1212	C₃×C₄	—	10	1	no	—
1213	C₃×C₄	—	10	2	no	—
1214	C₃×C₄	—	10	2	no	—
1215	C₃×C₄	—	10	2	no	—
1216	C₃×C₄	—	10	1	no	—
1217	C₃×C₄	D₅×#41	1	2	yes	—
1218	C₂×C₅	—	2	2	no	—
1219	C₂×C₅	—	4	1	no	—
1220	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
1221	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
1222	C₂×C₅	C₃×#585	1	1	yes	characteristic
1223	D₅	—	2	2	no	—
1224	D₅	—	2	2	no	—
1225	D₅	—	4	1	no	—
1226	D₅	—	4	2	no	—
1227	C₂³	—	5	1	no	—
1228	C₂³	—	5	1	no	—
1229	C₂³	—	5	1	no	—
1230	C₂³	—	5	2	no	—
1231	C₂³	—	10	2	no	—
1232	C₂³	—	10	2	no	—
1233	C₂³	—	10	2	no	—
1234	C₂³	—	10	2	no	—
1235	C₂³	—	20	1	no	—
1236	C₂³	—	20	1	no	—
1237	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
1238	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
1239	Q₈	—	2	2	no	—
1240	Q₈	—	10	4	no	—
1241	Q₈	—	20	2	no	—
1242	D₄	—	2	2	no	—
1243	D₄	—	5	4	no	—
1244	D₄	—	10	2	no	—
1245	D₄	—	10	4	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	4	no	—
1253	C₂×C₄	—	2	2	no	—
1254	C₂×C₄	—	2	2	no	—
1255	C₂×C₄	—	5	1	no	—
1256	C₂×C₄	—	5	1	no	—
1257	C₂×C₄	—	5	4	no	—
1258	C₂×C₄	—	5	1	no	—
1259	C₂×C₄	—	5	2	no	—
1260	C₂×C₄	—	5	1	no	—
1261	C₂×C₄	—	5	2	no	—
1262	C₂×C₄	—	5	2	no	—
1263	C₂×C₄	—	5	1	no	—
1264	C₂×C₄	—	10	2	no	—
1265	C₂×C₄	—	10	2	no	—
1266	C₂×C₄	—	10	2	no	—
1267	C₂×C₄	—	10	4	no	—
1268	C₂×C₄	—	10	4	no	—
1269	C₂×C₄	—	10	2	no	—
1270	C₂×C₄	—	10	2	no	—
1271	C₂×C₄	—	10	4	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	—	20	2	no	—
1277	C₂×C₄	—	20	1	no	—
1278	C₂×C₄	—	20	2	no	—
1279	C₂×C₄	—	20	2	no	—
1280	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1281	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
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	—	4	1	no	—
1291	C₂×C₃	—	10	2	no	—
1292	C₂×C₃	—	10	2	no	—
1293	C₂×C₃	—	20	1	no	—
1294	C₂×C₃	—	20	2	no	—
1295	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
1296	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
1297	C₂×C₃	#66287	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	—	5	2	no	—
1305	C₂²	—	5	2	no	—
1306	C₂²	—	10	1	no	—
1307	C₂²	—	10	1	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	—	20	4	no	—
1318	C₂²	C₃×D₅×#41	1	2	yes	—
1319	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
1320	C₄	—	2	2	no	—
1321	C₄	—	2	1	no	—
1322	C₄	—	2	1	no	—
1323	C₄	—	2	2	no	—
1324	C₄	—	2	1	no	—
1325	C₄	—	2	2	no	—
1326	C₄	—	2	1	no	—
1327	C₄	—	2	2	no	—
1328	C₄	—	5	2	no	—
1329	C₄	—	5	2	no	—
1330	C₄	—	10	1	no	—
1331	C₄	—	10	1	no	—
1332	C₄	—	10	2	no	—
1333	C₄	—	10	2	no	—
1334	C₄	—	10	2	no	—
1335	C₄	—	10	1	no	—
1336	C₄	C₃×D₅×#41	1	2	yes	—
1337	C₃	#10618728	1	1	yes	characteristic, direct product factor, Sylow
1338	C₂	—	2	2	no	—
1339	C₂	—	4	1	no	—
1340	C₂	—	10	2	no	—
1341	C₂	—	10	2	no	—
1342	C₂	—	20	1	no	—
1343	C₂	—	20	2	no	—
1344	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
1345	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
1346	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×#552	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#552	D₅
hypocenter	C₅	C₃×#3475
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#552

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#552	C₂	semidirect
2. C₃×#66040	C₂	semidirect
3. C₃×#66039	C₂	semidirect
4. C₃×#66029	C₂	semidirect
5. C₃×#66027	C₂	semidirect
6. C₃×#66025	C₂	semidirect
7. C₃×#66022	C₂	semidirect
8. C₃×#65988	C₂	semidirect
9. C₃×#65983	C₂	semidirect
10. C₃×#65975	C₂	semidirect
11. C₃×#65969	C₂	semidirect
12. C₃×#65961	C₂	semidirect
13. C₃×#65961	C₂	semidirect
14. C₃×#65915	C₂	semidirect
15. C₃×C₄×#713	C₂	semidirect
16. C₃×#65899	C₂	semidirect
17. C₃×C₄×D₄×D₅	C₂	semidirect
18. C₃×#65866	C₂	semidirect
19. C₃×#65861	C₂	semidirect
20. C₃×#65856	C₂	semidirect
21. C₃×D₅×#117	C₂	semidirect
22. C₃×#65841	C₂	semidirect
23. C₂×C₃×#4038	C₂	semidirect
24. #10618728	C₃	direct (N × H)
30. C₃×C₅×#126	C₂²	semidirect
31. C₃×C₅×#125	C₂²	semidirect
32. C₃×C₅×#125	C₂²	semidirect
34. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
35. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₄×C₅×Q₈	C₂²	semidirect
38. C₃×C₅×#117	C₂²	semidirect
39. C₃×C₅×#117	C₂²	semidirect
40. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
41. C₃×#4092	C₂²	semidirect
42. C₃×#4092	C₂²	semidirect
43. C₃×Q₈×Dic₅	C₂²	semidirect
46. C₃×#4076	C₂²	semidirect
47. C₃×#4076	C₂²	semidirect
48. C₃×#4075	C₂²	semidirect
52. C₃×#4072	C₂²	semidirect
53. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
54. C₂×C₃×C₄×Dic₅	C₂²	semidirect
55. C₃×#4044	C₂²	semidirect
56. C₃×#4044	C₂²	semidirect
57. C₃×#4044	C₂²	semidirect
58. C₃×#4043	C₂²	semidirect
61. C₃×#4042	C₂²	semidirect
63. C₃×#4041	C₂²	semidirect
64. C₃×#4041	C₂²	semidirect
68. C₃×#4040	C₂²	semidirect
69. C₃×#4040	C₂²	semidirect
72. C₃×#4039	C₂²	semidirect
73. C₃×#4039	C₂²	semidirect
74. C₃×#4039	C₂²	semidirect
75. C₃×#4039	C₂²	semidirect
80. C₃×#4038	C₂²	semidirect
81. C₃×#4038	C₂²	semidirect
82. C₃×#4038	C₂²	semidirect
83. C₃×#4038	C₂²	semidirect
85. C₃×D₅×C₄⋊C₄	C₂²	semidirect
86. C₃×D₅×C₄⋊C₄	C₂²	semidirect
87. C₃×#4035	C₂²	semidirect
88. C₃×#4035	C₂²	semidirect
89. C₃×#4034	C₂²	semidirect
90. C₃×#4034	C₂²	semidirect
91. C₃×#4033	C₂²	semidirect
92. C₃×#4033	C₂²	semidirect
93. C₃×#4033	C₂²	semidirect
95. C₃×#4031	C₂²	semidirect
97. C₃×#4029	C₂²	semidirect
103. C₃×#4027	C₂²	semidirect
104. C₃×#4027	C₂²	semidirect
105. C₃×#4027	C₂²	semidirect
109. C₃×#4025	C₂²	semidirect
110. C₃×#4024	C₂²	semidirect
111. C₃×#4023	C₂²	semidirect
112. C₃×#4022	C₂²	semidirect
113. C₃×#4021	C₂²	semidirect
116. C₃×C₄×D₂₀	C₂²	semidirect
118. C₃×#4018	C₂²	semidirect
119. C₃×#4018	C₂²	semidirect
121. C₃×C₄²×D₅	C₂²	semidirect
122. C₃×C₄²×D₅	C₂²	semidirect
123. C₃×#4016	C₂²	semidirect
125. C₅×#552	C₂×C₃	semidirect
126. #66040	C₂×C₃	semidirect
127. #66039	C₂×C₃	semidirect
128. #66029	C₂×C₃	semidirect
129. #66027	C₂×C₃	semidirect
130. #66025	C₂×C₃	semidirect
131. #66022	C₂×C₃	semidirect
132. #65988	C₂×C₃	semidirect
133. #65983	C₂×C₃	semidirect
134. #65975	C₂×C₃	semidirect
135. #65969	C₂×C₃	semidirect
136. #65961	C₂×C₃	semidirect
137. #65961	C₂×C₃	semidirect
138. #65915	C₂×C₃	semidirect
139. C₄×#713	C₂×C₃	semidirect
140. #65899	C₂×C₃	semidirect
141. C₄×D₄×D₅	C₂×C₃	semidirect
142. #65866	C₂×C₃	semidirect
143. #65861	C₂×C₃	semidirect
144. #65856	C₂×C₃	semidirect
145. D₅×#117	C₂×C₃	semidirect
146. #65841	C₂×C₃	semidirect
147. C₂×#4038	C₂×C₃	semidirect
259. C₃×#552	D₅	semidirect
280. C₅×#126	C₂²×C₃	semidirect
281. C₅×#125	C₂²×C₃	semidirect
282. C₅×#125	C₂²×C₃	semidirect
284. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
285. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
286. C₄×C₅×Q₈	C₂²×C₃	semidirect
288. C₅×#117	C₂²×C₃	semidirect
289. C₅×#117	C₂²×C₃	semidirect
290. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
291. #4092	C₂²×C₃	semidirect
292. #4092	C₂²×C₃	semidirect
293. Q₈×Dic₅	C₂²×C₃	semidirect
296. #4076	C₂²×C₃	semidirect
297. #4076	C₂²×C₃	semidirect
298. #4075	C₂²×C₃	semidirect
302. #4072	C₂²×C₃	semidirect
303. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
304. C₂×C₄×Dic₅	C₂²×C₃	semidirect
305. #4044	C₂²×C₃	semidirect
306. #4044	C₂²×C₃	semidirect
307. #4044	C₂²×C₃	semidirect
308. #4043	C₂²×C₃	semidirect
311. #4042	C₂²×C₃	semidirect
313. #4041	C₂²×C₃	semidirect
314. #4041	C₂²×C₃	semidirect
318. #4040	C₂²×C₃	semidirect
319. #4040	C₂²×C₃	semidirect
322. #4039	C₂²×C₃	semidirect
323. #4039	C₂²×C₃	semidirect
324. #4039	C₂²×C₃	semidirect
325. #4039	C₂²×C₃	semidirect
330. #4038	C₂²×C₃	semidirect
331. #4038	C₂²×C₃	semidirect
332. #4038	C₂²×C₃	semidirect
333. #4038	C₂²×C₃	semidirect
335. D₅×C₄⋊C₄	C₂²×C₃	semidirect
336. D₅×C₄⋊C₄	C₂²×C₃	semidirect
337. #4035	C₂²×C₃	semidirect
338. #4035	C₂²×C₃	semidirect
339. #4034	C₂²×C₃	semidirect
340. #4034	C₂²×C₃	semidirect
341. #4033	C₂²×C₃	semidirect
342. #4033	C₂²×C₃	semidirect
343. #4033	C₂²×C₃	semidirect
345. #4031	C₂²×C₃	semidirect
347. #4029	C₂²×C₃	semidirect
353. #4027	C₂²×C₃	semidirect
354. #4027	C₂²×C₃	semidirect
355. #4027	C₂²×C₃	semidirect
359. #4025	C₂²×C₃	semidirect
360. #4024	C₂²×C₃	semidirect
361. #4023	C₂²×C₃	semidirect
362. #4022	C₂²×C₃	semidirect
363. #4021	C₂²×C₃	semidirect
366. C₄×D₂₀	C₂²×C₃	semidirect
368. #4018	C₂²×C₃	semidirect
369. #4018	C₂²×C₃	semidirect
371. C₄²×D₅	C₂²×C₃	semidirect
372. C₄²×D₅	C₂²×C₃	semidirect
373. #4016	C₂²×C₃	semidirect
404. C₃×C₂²⋊D₅	#41	semidirect
434. C₃×C₄×D₅	#41	semidirect
449. C₃×#126	C₂×D₅	semidirect
453. C₃×#125	C₂×D₅	semidirect
454. C₃×#125	C₂×D₅	semidirect
473. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
474. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
488. C₃×C₄×Q₈	C₂×D₅	semidirect
521. C₃×#117	C₂×D₅	semidirect
522. C₃×#117	C₂×D₅	semidirect
527. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
647. #552	C₃×D₅	semidirect
834. C₂²⋊D₅	C₃×#41	semidirect
864. C₄×D₅	C₃×#41	semidirect
879. #126	C₂×C₃×D₅	semidirect
883. #125	C₂×C₃×D₅	semidirect
884. #125	C₂×C₃×D₅	semidirect
903. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
904. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
918. C₄×Q₈	C₂×C₃×D₅	semidirect
951. #117	C₂×C₃×D₅	semidirect
952. #117	C₂×C₃×D₅	semidirect
957. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
1179. C₃×C₅	#3475	semidirect
1298. C₅	C₃×#3475	semidirect
1337. C₃	#10618728	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×#552	2
C₃×#66040	2
C₃×#66039	2
C₃×#66029	2
C₃×#66027	2
C₃×#66025	2
C₃×#66022	2
C₃×#65988	2
C₃×#65983	2
C₃×#65975	2
C₃×#65969	2
C₃×#65961	2
C₃×#65915	2
C₃×C₄×#713	2
C₃×#65899	2
C₃×C₄×D₄×D₅	2
C₃×#65866	2
C₃×#65861	2
C₃×#65856	2
C₃×D₅×#117	2
C₃×#65841	2
C₂×C₃×#4038	2
#10618728	3
C₃×#3475	5

Subgroups — C3×#10618728 #14484115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10618728 #14484115