Subgroups — C₅×D₃×#552 #14483394

Order 1920.

2248 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5708	C₂	1	2	yes	maximal, complemented
3	C₅×D₃×#126	C₂	1	2	yes	maximal, complemented
4	C₅×#5694	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5693	C₂	1	2	yes	maximal, complemented
6	C₅×D₃×#125	C₂	1	2	yes	maximal, complemented
7	C₅×D₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×D₃×#123	C₂	1	2	yes	maximal
9	C₅×#5650	C₂	1	2	yes	maximal, complemented
10	C₅×#5642	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5639	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×D₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#5581	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
17	C₅×#5541	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#5531	C₂	1	2	yes	maximal, complemented
19	C₅×#5529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅×D₃×#117	C₂	1	2	yes	maximal, complemented
22	C₅×#5513	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₅×#552	—	3	1	no	maximal, Hall
25	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
27	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
28	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
30	C₃×C₅×#126	C₂²	1	2	yes	complemented
31	C₃×C₅×#125	C₂²	1	2	yes	complemented
32	C₃×C₅×#125	C₂²	1	1	yes	characteristic, 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	C₅×#946	C₂²	1	1	yes	characteristic, complemented
42	C₅×#946	C₂²	1	1	yes	characteristic, complemented
43	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
44	C₅×#935	C₂²	1	2	yes	—
45	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
46	C₅×#929	C₂²	1	2	yes	—
47	C₄×C₅×#67	C₂²	1	1	yes	characteristic
48	C₄×C₅×#67	C₂²	1	1	yes	characteristic
49	C₅×#926	C₂²	1	2	yes	complemented
50	C₅×#926	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
52	C₅×#924	C₂²	1	1	yes	characteristic, complemented
53	C₅×#924	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
55	C₅×#898	C₂²	1	2	yes	complemented
56	C₅×#898	C₂²	1	2	yes	complemented
57	C₅×#898	C₂²	1	2	yes	complemented
58	C₅×#897	C₂²	1	1	yes	characteristic, complemented
59	C₅×#897	C₂²	1	1	yes	characteristic, complemented
60	C₅×#896	C₂²	1	2	yes	complemented
61	C₅×#896	C₂²	1	2	yes	complemented
62	C₅×#894	C₂²	1	2	yes	—
63	C₅×#894	C₂²	1	2	yes	—
64	C₅×#893	C₂²	1	1	yes	characteristic
65	C₅×#892	C₂²	1	2	yes	complemented
66	C₅×#892	C₂²	1	2	yes	complemented
67	C₅×#892	C₂²	1	1	yes	characteristic, complemented
68	C₅×#892	C₂²	1	1	yes	characteristic, complemented
69	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
70	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
71	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
73	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
74	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
75	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
77	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
80	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
81	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
82	C₅×#890	C₂²	1	2	yes	complemented
83	C₅×#890	C₂²	1	2	yes	complemented
84	C₅×#890	C₂²	1	1	yes	characteristic, complemented
85	C₅×#890	C₂²	1	1	yes	characteristic, complemented
86	C₅×#889	C₂²	1	2	yes	complemented
87	C₅×#889	C₂²	1	2	yes	complemented
88	C₅×#889	C₂²	1	2	yes	complemented
89	C₅×#889	C₂²	1	2	yes	complemented
90	C₅×#889	C₂²	1	2	yes	complemented
91	C₅×#889	C₂²	1	2	yes	complemented
92	C₅×#887	C₂²	1	2	yes	complemented
93	C₅×#887	C₂²	1	1	yes	characteristic, complemented
94	C₅×#886	C₂²	1	2	yes	—
95	C₅×#883	C₂²	1	2	yes	—
96	C₅×#883	C₂²	1	2	yes	—
97	C₅×#67⋊C₄	C₂²	1	1	yes	characteristic
98	C₅×#67⋊C₄	C₂²	1	1	yes	characteristic
99	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₅×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
103	C₅×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₅×#879	C₂²	1	2	yes	complemented
105	C₅×#879	C₂²	1	2	yes	complemented
106	C₅×#879	C₂²	1	2	yes	complemented
107	C₅×#878	C₂²	1	2	yes	complemented
108	C₅×#878	C₂²	1	2	yes	complemented
109	C₅×#877	C₂²	1	2	yes	complemented
110	C₅×#877	C₂²	1	2	yes	complemented
111	C₅×#877	C₂²	1	2	yes	complemented
112	C₅×#876	C₂²	1	2	yes	complemented
113	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
114	C₅×#872	C₂²	1	2	yes	complemented
115	C₅×#872	C₂²	1	2	yes	complemented
116	C₅×#872	C₂²	1	2	yes	complemented
117	C₄²×C₅×D₃	C₂²	1	2	yes	—
118	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
119	C₄²×C₅×D₃	C₂²	1	2	yes	—
120	C₅×#870	C₂²	1	2	yes	complemented
121	C₅×#870	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
124	D₃×#552	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
125	C₅×#552	—	3	2	no	—
126	C₅×#552	—	3	2	no	—
127	C₅×#552	—	3	1	no	—
128	C₅×#552	—	3	2	no	—
129	C₅×#552	—	3	1	no	—
130	C₅×#552	—	3	1	no	—
131	C₅×#552	—	3	1	no	—
132	C₅×#552	—	3	1	no	—
133	C₅×#552	—	3	1	no	—
134	C₅×#552	—	3	2	no	—
135	C₅×#552	—	3	1	no	—
136	C₅×#552	D₃	1	1	yes	characteristic, direct product factor
137	C₂×C₅×#126	—	3	2	no	—
138	C₂×C₅×#125	—	3	2	no	—
139	C₂×C₅×#125	—	3	1	no	—
140	C₂×C₅×#123	—	3	2	no	—
141	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
142	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
143	C₂×C₄×C₅×Q₈	—	3	1	no	—
144	C₂×C₄×C₅×D₄	—	3	1	no	—
145	C₂×C₅×#117	—	3	1	no	—
146	C₂×C₅×#117	—	3	2	no	—
147	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
148	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
149	C₂³×C₅×D₃	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	2	yes	—
153	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
155	C₂×C₅×#67	C₂³	1	1	yes	characteristic
156	C₂×C₅×#67	C₂³	1	1	yes	characteristic
157	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
158	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
159	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
160	C₅×D₃×Q₈	—	2	4	no	—
161	C₅×D₃×D₄	—	2	4	no	—
162	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
163	C₂×C₄×C₅×D₃	—	2	8	no	—
164	C₂×C₄×C₅×D₃	—	2	4	no	—
165	C₂×C₄×C₅×D₃	—	2	4	no	—
166	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
167	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
168	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
169	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
170	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
171	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
172	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
173	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
174	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
175	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
176	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
177	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
178	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
179	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
180	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
181	C₂×C₅×Dic₆	C₂³	1	2	yes	—
182	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
183	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
198	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
199	C₃×C₄²×C₅	C₂³	1	2	yes	—
200	C₃×C₄²×C₅	C₂³	1	2	yes	—
201	C₅×#217	C₂³	1	1	yes	characteristic
202	C₅×#217	C₂³	1	2	yes	—
203	C₅×#217	C₂³	1	2	yes	—
204	C₅×#217	C₂³	1	2	yes	—
205	C₅×#217	C₂³	1	1	yes	characteristic
206	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
207	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
208	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
209	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
210	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
211	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
212	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
213	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
215	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
217	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
218	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
219	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
220	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
221	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
222	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
223	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
224	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
225	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
226	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
227	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
228	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
229	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
230	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
231	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
232	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
233	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
234	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
235	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
236	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
237	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
238	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
239	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
240	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
241	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
242	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
243	C₄×C₅×Dic₃	C₂³	1	2	yes	—
244	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
245	C₄×C₅×Dic₃	C₂³	1	2	yes	—
246	C₄×C₅×Dic₃	C₂³	1	2	yes	—
247	C₄×C₅×Dic₃	C₂³	1	2	yes	—
248	C₄×C₅×Dic₃	C₂³	1	2	yes	—
249	C₄×C₅×Dic₃	C₂³	1	2	yes	—
250	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
251	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
252	C₃×#552	C₂×C₅	1	1	yes	characteristic, complemented
253	#5708	C₂×C₅	1	2	yes	complemented
254	D₃×#126	C₂×C₅	1	2	yes	complemented
255	#5694	C₂×C₅	1	1	yes	characteristic, complemented
256	#5693	C₂×C₅	1	2	yes	complemented
257	D₃×#125	C₂×C₅	1	2	yes	complemented
258	D₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
259	D₃×#123	C₂×C₅	1	2	yes	—
260	#5650	C₂×C₅	1	2	yes	complemented
261	#5642	C₂×C₅	1	1	yes	characteristic, complemented
262	#5639	C₂×C₅	1	1	yes	characteristic, complemented
263	D₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
264	D₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
265	#5581	C₂×C₅	1	1	yes	characteristic, complemented
266	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
267	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic
268	#5541	C₂×C₅	1	1	yes	characteristic, complemented
269	#5531	C₂×C₅	1	2	yes	complemented
270	#5529	C₂×C₅	1	1	yes	characteristic, complemented
271	D₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
272	D₃×#117	C₂×C₅	1	2	yes	complemented
273	#5513	C₂×C₅	1	1	yes	characteristic, complemented
274	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
275	C₂²×C₅×Q₈	—	3	1	no	—
276	C₂²×C₅×D₄	—	3	1	no	—
277	C₂³×C₄×C₅	—	3	2	no	—
278	C₂³×C₄×C₅	—	3	1	no	—
279	C₂³×C₄×C₅	—	3	1	no	—
280	C₅×#126	—	3	2	no	—
281	C₅×#126	—	3	2	no	—
282	C₅×#126	—	3	2	no	—
283	C₅×#126	—	3	2	no	—
284	C₅×#126	—	3	2	no	—
285	C₅×#126	—	3	2	no	—
286	C₅×#126	—	3	2	no	—
287	C₅×#126	C₂×D₃	1	2	yes	complemented
288	C₅×#125	—	3	2	no	—
289	C₅×#125	—	3	2	no	—
290	C₅×#125	—	3	2	no	—
291	C₅×#125	—	3	2	no	—
292	C₅×#125	—	3	2	no	—
293	C₅×#125	—	3	2	no	—
294	C₅×#125	—	3	2	no	—
295	C₅×#125	—	3	2	no	—
296	C₅×#125	—	3	1	no	—
297	C₅×#125	—	3	1	no	—
298	C₅×#125	—	3	2	no	—
299	C₅×#125	—	3	1	no	—
300	C₅×#125	C₂×D₃	1	2	yes	complemented
301	C₅×#125	C₂×D₃	1	1	yes	characteristic, complemented
302	C₅×#123	—	3	2	no	—
303	C₅×#123	—	3	2	no	—
304	C₅×#123	—	3	2	no	—
305	C₅×#123	—	3	2	no	—
306	C₅×#123	—	3	2	no	—
307	C₅×#123	—	3	2	no	—
308	C₅×#123	—	3	2	no	—
309	C₅×#123	C₂×D₃	1	2	yes	—
310	C₅×C₂²⋊Q₈	—	3	1	no	—
311	C₅×C₂²⋊Q₈	—	3	1	no	—
312	C₅×C₂²⋊Q₈	—	3	1	no	—
313	C₅×C₂²⋊Q₈	—	3	1	no	—
314	C₅×C₂²⋊Q₈	—	3	2	no	—
315	C₅×C₂²⋊Q₈	—	3	2	no	—
316	C₅×C₂²⋊Q₈	—	3	1	no	—
317	C₅×C₂²⋊Q₈	—	3	1	no	—
318	C₅×C₂²⋊Q₈	—	3	2	no	—
319	C₅×C₂²⋊Q₈	—	3	2	no	—
320	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
321	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
322	C₄×C₅×Q₈	—	3	1	no	—
323	C₄×C₅×Q₈	—	3	2	no	—
324	C₄×C₅×Q₈	—	3	1	no	—
325	C₄×C₅×Q₈	—	3	1	no	—
326	C₄×C₅×Q₈	—	3	2	no	—
327	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
328	C₄×C₅×D₄	—	3	1	no	—
329	C₄×C₅×D₄	—	3	1	no	—
330	C₄×C₅×D₄	—	3	1	no	—
331	C₄×C₅×D₄	—	3	1	no	—
332	C₄×C₅×D₄	—	3	1	no	—
333	C₄×C₅×D₄	—	3	1	no	—
334	C₄×C₅×D₄	—	3	1	no	—
335	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
336	C₅×#117	—	3	1	no	—
337	C₅×#117	—	3	2	no	—
338	C₅×#117	—	3	1	no	—
339	C₅×#117	—	3	1	no	—
340	C₅×#117	—	3	2	no	—
341	C₅×#117	—	3	2	no	—
342	C₅×#117	—	3	2	no	—
343	C₅×#117	—	3	2	no	—
344	C₅×#117	—	3	2	no	—
345	C₅×#117	—	3	2	no	—
346	C₅×#117	—	3	2	no	—
347	C₅×#117	—	3	2	no	—
348	C₅×#117	C₂×D₃	1	1	yes	characteristic, complemented
349	C₅×#117	C₂×D₃	1	2	yes	complemented
350	C₂×C₅×C₄⋊C₄	—	3	2	no	—
351	C₂×C₅×C₄⋊C₄	—	3	1	no	—
352	C₂×C₅×C₄⋊C₄	—	3	1	no	—
353	C₂×C₅×C₄⋊C₄	—	3	1	no	—
354	C₂×C₅×C₄⋊C₄	—	3	2	no	—
355	C₂×C₅×C₄⋊C₄	—	3	1	no	—
356	C₂×C₅×C₄⋊C₄	—	3	2	no	—
357	C₂×C₅×C₄⋊C₄	—	3	2	no	—
358	C₂×C₅×C₄⋊C₄	—	3	1	no	—
359	C₂×C₅×C₄⋊C₄	—	3	2	no	—
360	C₂×C₅×C₄⋊C₄	—	3	2	no	—
361	C₂×C₅×C₄⋊C₄	—	3	2	no	—
362	C₂×C₅×C₄⋊C₄	—	3	2	no	—
363	C₂×C₅×C₄⋊C₄	—	3	1	no	—
364	C₂×C₅×C₄⋊C₄	—	3	1	no	—
365	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
366	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
367	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
368	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
369	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
370	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
371	C₂×C₄²×C₅	—	3	2	no	—
372	C₂×C₄²×C₅	—	3	2	no	—
373	C₂×C₄²×C₅	—	3	1	no	—
374	C₂×#552	—	3	1	no	Sylow
375	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
376	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
377	C₂²×C₅×D₃	—	2	2	no	—
378	C₂²×C₅×D₃	—	2	2	no	—
379	C₂²×C₅×D₃	—	2	2	no	—
380	C₂²×C₅×D₃	—	2	2	no	—
381	C₂²×C₅×D₃	—	2	2	no	—
382	C₂²×C₅×D₃	#41	1	4	yes	—
383	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
384	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
386	C₃×C₅×Q₈	—	2	2	no	—
387	C₃×C₅×D₄	—	2	2	no	—
388	C₂×C₃×C₄×C₅	—	2	4	no	—
389	C₂×C₃×C₄×C₅	—	2	2	no	—
390	C₂×C₃×C₄×C₅	—	2	2	no	—
391	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
392	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
393	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
394	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	2	yes	—
398	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
399	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
400	C₅×#67	—	2	2	no	—
401	C₅×#67	—	2	2	no	—
402	C₂×C₅×Dic₃	—	2	4	no	—
403	C₂×C₅×Dic₃	—	2	2	no	—
404	C₂×C₅×Dic₃	—	2	2	no	—
405	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
407	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
408	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
409	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
410	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
411	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
412	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
413	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
414	C₅×D₁₂	—	2	2	no	—
415	C₄×C₅×D₃	—	2	4	no	—
416	C₄×C₅×D₃	—	2	4	no	—
417	C₄×C₅×D₃	—	2	4	no	—
418	C₄×C₅×D₃	—	2	4	no	—
419	C₄×C₅×D₃	—	2	2	no	—
420	C₄×C₅×D₃	—	2	2	no	—
421	C₄×C₅×D₃	—	2	2	no	—
422	C₄×C₅×D₃	—	2	4	no	—
423	C₄×C₅×D₃	—	2	2	no	—
424	C₄×C₅×D₃	—	2	4	no	—
425	C₄×C₅×D₃	—	2	2	no	—
426	C₄×C₅×D₃	—	2	2	no	—
427	C₄×C₅×D₃	—	2	2	no	—
428	C₄×C₅×D₃	—	2	2	no	—
429	C₄×C₅×D₃	#41	1	4	yes	—
430	C₅×Dic₆	—	2	2	no	—
431	C₅×Dic₆	—	2	4	no	—
432	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
433	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
434	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
435	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
436	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
437	C₃×#126	C₂²×C₅	1	2	yes	complemented
438	C₃×#125	C₂²×C₅	1	2	yes	complemented
439	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
440	C₃×#123	C₂²×C₅	1	2	yes	—
441	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
442	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
443	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
444	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
445	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
446	C₃×#117	C₂²×C₅	1	2	yes	complemented
447	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
448	#946	C₂²×C₅	1	1	yes	characteristic, complemented
449	#946	C₂²×C₅	1	1	yes	characteristic, complemented
450	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
451	#935	C₂²×C₅	1	2	yes	—
452	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
453	#929	C₂²×C₅	1	2	yes	—
454	C₄×#67	C₂²×C₅	1	1	yes	characteristic
455	C₄×#67	C₂²×C₅	1	1	yes	characteristic
456	#926	C₂²×C₅	1	1	yes	characteristic, complemented
457	#926	C₂²×C₅	1	2	yes	complemented
458	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
459	#924	C₂²×C₅	1	1	yes	characteristic, complemented
460	#924	C₂²×C₅	1	1	yes	characteristic, complemented
461	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
462	#898	C₂²×C₅	1	2	yes	complemented
463	#898	C₂²×C₅	1	2	yes	complemented
464	#898	C₂²×C₅	1	2	yes	complemented
465	#897	C₂²×C₅	1	1	yes	characteristic, complemented
466	#897	C₂²×C₅	1	1	yes	characteristic, complemented
467	#896	C₂²×C₅	1	2	yes	complemented
468	#896	C₂²×C₅	1	2	yes	complemented
469	#894	C₂²×C₅	1	2	yes	—
470	#894	C₂²×C₅	1	2	yes	—
471	#893	C₂²×C₅	1	1	yes	characteristic
472	#892	C₂²×C₅	1	2	yes	complemented
473	#892	C₂²×C₅	1	1	yes	characteristic, complemented
474	#892	C₂²×C₅	1	2	yes	complemented
475	#892	C₂²×C₅	1	1	yes	characteristic, complemented
476	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
477	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
478	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
479	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
480	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
481	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
482	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
483	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
484	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
485	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
486	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
487	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
488	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
489	#890	C₂²×C₅	1	1	yes	characteristic, complemented
490	#890	C₂²×C₅	1	2	yes	complemented
491	#890	C₂²×C₅	1	1	yes	characteristic, complemented
492	#890	C₂²×C₅	1	2	yes	complemented
493	#889	C₂²×C₅	1	2	yes	complemented
494	#889	C₂²×C₅	1	2	yes	complemented
495	#889	C₂²×C₅	1	2	yes	complemented
496	#889	C₂²×C₅	1	2	yes	complemented
497	#889	C₂²×C₅	1	2	yes	complemented
498	#889	C₂²×C₅	1	2	yes	complemented
499	#887	C₂²×C₅	1	2	yes	complemented
500	#887	C₂²×C₅	1	1	yes	characteristic, complemented
501	#886	C₂²×C₅	1	2	yes	—
502	#883	C₂²×C₅	1	2	yes	—
503	#883	C₂²×C₅	1	2	yes	—
504	#67⋊C₄	C₂²×C₅	1	1	yes	characteristic
505	#67⋊C₄	C₂²×C₅	1	1	yes	characteristic
506	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
507	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
508	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
509	D₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
510	D₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
511	#879	C₂²×C₅	1	2	yes	complemented
512	#879	C₂²×C₅	1	2	yes	complemented
513	#879	C₂²×C₅	1	2	yes	complemented
514	#878	C₂²×C₅	1	2	yes	complemented
515	#878	C₂²×C₅	1	2	yes	complemented
516	#877	C₂²×C₅	1	2	yes	complemented
517	#877	C₂²×C₅	1	2	yes	complemented
518	#877	C₂²×C₅	1	2	yes	complemented
519	#876	C₂²×C₅	1	2	yes	complemented
520	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
521	#872	C₂²×C₅	1	2	yes	complemented
522	#872	C₂²×C₅	1	2	yes	complemented
523	#872	C₂²×C₅	1	2	yes	complemented
524	C₄²×D₃	C₂²×C₅	1	2	yes	—
525	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
526	C₄²×D₃	C₂²×C₅	1	2	yes	—
527	#870	C₂²×C₅	1	2	yes	complemented
528	#870	C₂²×C₅	1	1	yes	characteristic, complemented
529	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
530	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
531	C₂⁴×C₅	—	3	1	no	—
532	C₂⁴×C₅	—	3	1	no	—
533	C₂×C₅×Q₈	—	3	2	no	—
534	C₂×C₅×Q₈	—	3	1	no	—
535	C₂×C₅×Q₈	—	6	4	no	—
536	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
537	C₂×C₅×D₄	—	3	1	no	—
538	C₂×C₅×D₄	—	3	1	no	—
539	C₂×C₅×D₄	—	3	1	no	—
540	C₂×C₅×D₄	—	6	4	no	—
541	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
542	C₂²×C₄×C₅	—	3	1	no	—
543	C₂²×C₄×C₅	—	3	2	no	—
544	C₂²×C₄×C₅	—	3	1	no	—
545	C₂²×C₄×C₅	—	3	1	no	—
546	C₂²×C₄×C₅	—	3	1	no	—
547	C₂²×C₄×C₅	—	3	1	no	—
548	C₂²×C₄×C₅	—	3	2	no	—
549	C₂²×C₄×C₅	—	3	2	no	—
550	C₂²×C₄×C₅	—	3	2	no	—
551	C₂²×C₄×C₅	—	3	1	no	—
552	C₂²×C₄×C₅	—	3	1	no	—
553	C₂²×C₄×C₅	—	3	2	no	—
554	C₂²×C₄×C₅	—	3	2	no	—
555	C₂²×C₄×C₅	—	3	2	no	—
556	C₂²×C₄×C₅	—	3	1	no	—
557	C₂²×C₄×C₅	—	3	1	no	—
558	C₂²×C₄×C₅	—	3	1	no	—
559	C₂²×C₄×C₅	—	3	1	no	—
560	C₂²×C₄×C₅	—	6	4	no	—
561	C₂²×C₄×C₅	—	6	4	no	—
562	C₂²×C₄×C₅	—	6	8	no	—
563	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
564	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
565	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
566	C₅×C₄⋊C₄	—	3	2	no	—
567	C₅×C₄⋊C₄	—	3	1	no	—
568	C₅×C₄⋊C₄	—	3	2	no	—
569	C₅×C₄⋊C₄	—	3	1	no	—
570	C₅×C₄⋊C₄	—	3	2	no	—
571	C₅×C₄⋊C₄	—	3	2	no	—
572	C₅×C₄⋊C₄	—	3	2	no	—
573	C₅×C₄⋊C₄	—	3	2	no	—
574	C₅×C₄⋊C₄	—	3	2	no	—
575	C₅×C₄⋊C₄	—	3	2	no	—
576	C₅×C₄⋊C₄	—	3	2	no	—
577	C₅×C₄⋊C₄	—	3	1	no	—
578	C₅×C₄⋊C₄	—	3	2	no	—
579	C₅×C₄⋊C₄	—	3	2	no	—
580	C₅×C₄⋊C₄	—	3	2	no	—
581	C₅×C₄⋊C₄	—	3	1	no	—
582	C₅×C₄⋊C₄	—	3	1	no	—
583	C₅×C₄⋊C₄	—	3	1	no	—
584	C₅×C₄⋊C₄	—	3	2	no	—
585	C₅×C₄⋊C₄	—	3	2	no	—
586	C₅×C₄⋊C₄	—	3	2	no	—
587	C₅×C₄⋊C₄	—	3	2	no	—
588	C₅×C₄⋊C₄	—	3	2	no	—
589	C₅×C₄⋊C₄	—	3	2	no	—
590	C₅×C₄⋊C₄	—	3	2	no	—
591	C₅×C₄⋊C₄	—	3	2	no	—
592	C₅×C₄⋊C₄	—	3	2	no	—
593	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
594	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
595	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
596	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
597	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
598	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
599	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
600	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
601	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
602	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
603	C₅×C₂²⋊C₄	—	3	1	no	—
604	C₅×C₂²⋊C₄	—	3	2	no	—
605	C₅×C₂²⋊C₄	—	3	2	no	—
606	C₅×C₂²⋊C₄	—	3	1	no	—
607	C₅×C₂²⋊C₄	—	3	2	no	—
608	C₅×C₂²⋊C₄	—	3	1	no	—
609	C₅×C₂²⋊C₄	—	3	1	no	—
610	C₅×C₂²⋊C₄	—	3	2	no	—
611	C₅×C₂²⋊C₄	—	3	2	no	—
612	C₅×C₂²⋊C₄	—	3	2	no	—
613	C₅×C₂²⋊C₄	—	3	2	no	—
614	C₅×C₂²⋊C₄	—	3	1	no	—
615	C₅×C₂²⋊C₄	—	3	1	no	—
616	C₅×C₂²⋊C₄	—	3	2	no	—
617	C₅×C₂²⋊C₄	—	3	2	no	—
618	C₅×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
619	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
620	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
621	C₅×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
622	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
623	C₄²×C₅	—	3	2	no	—
624	C₄²×C₅	—	3	2	no	—
625	C₄²×C₅	—	3	2	no	—
626	C₄²×C₅	—	3	2	no	—
627	C₄²×C₅	—	3	2	no	—
628	C₄²×C₅	—	3	2	no	—
629	C₄²×C₅	—	3	1	no	—
630	C₄²×C₅	—	3	1	no	—
631	C₄²×C₅	—	3	1	no	—
632	C₄²×C₅	C₂²×D₃	1	2	yes	—
633	C₄²×C₅	C₂²×D₃	1	2	yes	—
634	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
635	#552	—	3	2	no	—
636	#552	—	3	2	no	—
637	#552	—	3	1	no	—
638	#552	—	3	2	no	—
639	#552	—	3	1	no	—
640	#552	—	3	1	no	—
641	#552	—	3	1	no	—
642	#552	—	3	1	no	—
643	#552	—	3	1	no	—
644	#552	—	3	2	no	—
645	#552	—	3	1	no	—
646	#552	C₅×D₃	1	1	yes	characteristic, direct product factor
647	C₂×#126	—	3	2	no	—
648	C₂×#125	—	3	2	no	—
649	C₂×#125	—	3	1	no	—
650	C₂×#123	—	3	2	no	—
651	C₂×C₂²⋊Q₈	—	3	1	no	—
652	C₂×C₂²⋊Q₈	—	3	1	no	—
653	C₂×C₄×Q₈	—	3	1	no	—
654	C₂×C₄×D₄	—	3	1	no	—
655	C₂×#117	—	3	1	no	—
656	C₂×#117	—	3	2	no	—
657	C₂²×C₄⋊C₄	—	3	1	no	—
658	C₂²×C₃×C₅	—	2	1	no	—
659	C₂²×C₃×C₅	—	2	1	no	—
660	C₂²×C₃×C₅	—	2	1	no	—
661	C₂²×C₃×C₅	—	2	1	no	—
662	C₂²×C₃×C₅	—	2	1	no	—
663	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
664	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
665	C₂×C₅×D₃	—	2	1	no	—
666	C₂×C₅×D₃	—	2	1	no	—
667	C₂×C₅×D₃	—	2	8	no	—
668	C₂×C₅×D₃	—	2	1	no	—
669	C₂×C₅×D₃	—	2	1	no	—
670	C₂×C₅×D₃	—	2	1	no	—
671	C₂×C₅×D₃	—	4	4	no	—
672	C₂×C₅×D₃	C₂×#41	1	2	yes	—
673	C₂×C₅×D₃	C₂×#41	1	2	yes	—
674	C₂×C₅×D₃	C₂×#41	1	2	yes	—
675	C₂×C₅×D₃	2₋¹⁺⁴	1	2	yes	—
676	C₃×C₄×C₅	—	2	2	no	—
677	C₃×C₄×C₅	—	2	2	no	—
678	C₃×C₄×C₅	—	2	2	no	—
679	C₃×C₄×C₅	—	2	1	no	—
680	C₃×C₄×C₅	—	2	1	no	—
681	C₃×C₄×C₅	—	2	1	no	—
682	C₃×C₄×C₅	—	2	1	no	—
683	C₃×C₄×C₅	—	2	2	no	—
684	C₃×C₄×C₅	C₂×#41	1	2	yes	—
685	C₅×Dic₃	—	2	2	no	—
686	C₅×Dic₃	—	2	2	no	—
687	C₅×Dic₃	—	2	2	no	—
688	C₅×Dic₃	—	2	1	no	—
689	C₅×Dic₃	—	2	1	no	—
690	C₅×Dic₃	—	2	1	no	—
691	C₅×Dic₃	—	2	1	no	—
692	C₅×Dic₃	—	2	2	no	—
693	C₅×Dic₃	C₂×#41	1	2	yes	—
694	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
695	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
696	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
697	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
698	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
699	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
700	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
701	C₂×#67	C₂³×C₅	1	1	yes	characteristic
702	C₂×#67	C₂³×C₅	1	1	yes	characteristic
703	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
704	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
705	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
706	D₃×Q₈	—	2	4	no	—
707	D₃×D₄	—	2	4	no	—
708	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
709	C₂×C₄×D₃	—	2	8	no	—
710	C₂×C₄×D₃	—	2	4	no	—
711	C₂×C₄×D₃	—	2	4	no	—
712	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
713	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
714	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
715	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
716	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
717	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
718	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
719	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
720	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
721	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
722	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
723	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
724	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
725	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
726	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
727	C₂×Dic₆	C₂³×C₅	1	2	yes	—
728	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
729	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
730	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
731	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
732	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
733	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
734	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
735	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
736	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
737	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
738	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
739	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
740	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
741	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
742	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
743	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
744	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
745	C₃×C₄²	C₂³×C₅	1	2	yes	—
746	C₃×C₄²	C₂³×C₅	1	2	yes	—
747	#217	C₂³×C₅	1	1	yes	characteristic
748	#217	C₂³×C₅	1	2	yes	—
749	#217	C₂³×C₅	1	2	yes	—
750	#217	C₂³×C₅	1	2	yes	—
751	#217	C₂³×C₅	1	1	yes	characteristic
752	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
753	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
754	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
755	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
756	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
757	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
758	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
759	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
760	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
761	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
762	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
763	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
764	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
765	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
766	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
767	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
768	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
769	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
770	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
771	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
772	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
773	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
774	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
775	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
776	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
777	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
778	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
779	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
780	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
781	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
782	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
783	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
784	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
785	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
786	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
787	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
788	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
789	C₄×Dic₃	C₂³×C₅	1	2	yes	—
790	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
791	C₄×Dic₃	C₂³×C₅	1	2	yes	—
792	C₄×Dic₃	C₂³×C₅	1	2	yes	—
793	C₄×Dic₃	C₂³×C₅	1	2	yes	—
794	C₄×Dic₃	C₂³×C₅	1	2	yes	—
795	C₄×Dic₃	C₂³×C₅	1	2	yes	—
796	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
797	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
798	C₂³×C₅	—	3	1	no	—
799	C₂³×C₅	—	3	4	no	—
800	C₂³×C₅	—	3	1	no	—
801	C₂³×C₅	—	3	1	no	—
802	C₂³×C₅	—	6	2	no	—
803	C₂³×C₅	—	6	2	no	—
804	C₂³×C₅	—	6	2	no	—
805	C₂³×C₅	—	6	2	no	—
806	C₂³×C₅	—	6	2	no	—
807	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
808	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
809	C₅×Q₈	—	2	2	no	—
810	C₅×Q₈	—	6	4	no	—
811	C₅×Q₈	—	6	2	no	—
812	C₅×D₄	—	2	2	no	—
813	C₅×D₄	—	6	2	no	—
814	C₅×D₄	—	6	2	no	—
815	C₅×D₄	—	6	2	no	—
816	C₂×C₄×C₅	—	2	4	no	—
817	C₂×C₄×C₅	—	2	2	no	—
818	C₂×C₄×C₅	—	2	2	no	—
819	C₂×C₄×C₅	—	3	1	no	—
820	C₂×C₄×C₅	—	3	4	no	—
821	C₂×C₄×C₅	—	3	1	no	—
822	C₂×C₄×C₅	—	3	1	no	—
823	C₂×C₄×C₅	—	3	2	no	—
824	C₂×C₄×C₅	—	3	2	no	—
825	C₂×C₄×C₅	—	3	2	no	—
826	C₂×C₄×C₅	—	3	1	no	—
827	C₂×C₄×C₅	—	3	1	no	—
828	C₂×C₄×C₅	—	3	2	no	—
829	C₂×C₄×C₅	—	6	2	no	—
830	C₂×C₄×C₅	—	6	2	no	—
831	C₂×C₄×C₅	—	6	2	no	—
832	C₂×C₄×C₅	—	6	4	no	—
833	C₂×C₄×C₅	—	6	2	no	—
834	C₂×C₄×C₅	—	6	2	no	—
835	C₂×C₄×C₅	—	6	4	no	—
836	C₂×C₄×C₅	—	6	4	no	—
837	C₂×C₄×C₅	—	6	4	no	—
838	C₂×C₄×C₅	—	6	4	no	—
839	C₂×C₄×C₅	—	6	2	no	—
840	C₂×C₄×C₅	—	6	4	no	—
841	C₂×C₄×C₅	—	6	2	no	—
842	C₂×C₄×C₅	—	6	2	no	—
843	C₂×C₄×C₅	—	6	4	no	—
844	C₂×C₄×C₅	—	6	2	no	—
845	C₂×C₄×C₅	—	6	2	no	—
846	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
847	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
848	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
849	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
850	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
851	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
852	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
853	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
854	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
855	C₂²×Q₈	—	3	1	no	—
856	C₂²×D₄	—	3	1	no	—
857	C₂³×C₄	—	3	2	no	—
858	C₂³×C₄	—	3	1	no	—
859	C₂³×C₄	—	3	1	no	—
860	#126	—	3	2	no	—
861	#126	—	3	2	no	—
862	#126	—	3	2	no	—
863	#126	—	3	2	no	—
864	#126	—	3	2	no	—
865	#126	—	3	2	no	—
866	#126	—	3	2	no	—
867	#126	C₂×C₅×D₃	1	2	yes	complemented
868	#125	—	3	2	no	—
869	#125	—	3	2	no	—
870	#125	—	3	2	no	—
871	#125	—	3	2	no	—
872	#125	—	3	2	no	—
873	#125	—	3	2	no	—
874	#125	—	3	2	no	—
875	#125	—	3	2	no	—
876	#125	—	3	1	no	—
877	#125	—	3	1	no	—
878	#125	—	3	2	no	—
879	#125	—	3	1	no	—
880	#125	C₂×C₅×D₃	1	2	yes	complemented
881	#125	C₂×C₅×D₃	1	1	yes	characteristic, complemented
882	#123	—	3	2	no	—
883	#123	—	3	2	no	—
884	#123	—	3	2	no	—
885	#123	—	3	2	no	—
886	#123	—	3	2	no	—
887	#123	—	3	2	no	—
888	#123	—	3	2	no	—
889	#123	C₂×C₅×D₃	1	2	yes	—
890	C₂²⋊Q₈	—	3	1	no	—
891	C₂²⋊Q₈	—	3	1	no	—
892	C₂²⋊Q₈	—	3	1	no	—
893	C₂²⋊Q₈	—	3	1	no	—
894	C₂²⋊Q₈	—	3	2	no	—
895	C₂²⋊Q₈	—	3	2	no	—
896	C₂²⋊Q₈	—	3	1	no	—
897	C₂²⋊Q₈	—	3	1	no	—
898	C₂²⋊Q₈	—	3	2	no	—
899	C₂²⋊Q₈	—	3	2	no	—
900	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
901	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
902	C₄×Q₈	—	3	1	no	—
903	C₄×Q₈	—	3	2	no	—
904	C₄×Q₈	—	3	1	no	—
905	C₄×Q₈	—	3	1	no	—
906	C₄×Q₈	—	3	2	no	—
907	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
908	C₄×D₄	—	3	1	no	—
909	C₄×D₄	—	3	1	no	—
910	C₄×D₄	—	3	1	no	—
911	C₄×D₄	—	3	1	no	—
912	C₄×D₄	—	3	1	no	—
913	C₄×D₄	—	3	1	no	—
914	C₄×D₄	—	3	1	no	—
915	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
916	#117	—	3	1	no	—
917	#117	—	3	2	no	—
918	#117	—	3	1	no	—
919	#117	—	3	1	no	—
920	#117	—	3	2	no	—
921	#117	—	3	2	no	—
922	#117	—	3	2	no	—
923	#117	—	3	2	no	—
924	#117	—	3	2	no	—
925	#117	—	3	2	no	—
926	#117	—	3	2	no	—
927	#117	—	3	2	no	—
928	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
929	#117	C₂×C₅×D₃	1	2	yes	complemented
930	C₂×C₄⋊C₄	—	3	2	no	—
931	C₂×C₄⋊C₄	—	3	1	no	—
932	C₂×C₄⋊C₄	—	3	1	no	—
933	C₂×C₄⋊C₄	—	3	1	no	—
934	C₂×C₄⋊C₄	—	3	2	no	—
935	C₂×C₄⋊C₄	—	3	2	no	—
936	C₂×C₄⋊C₄	—	3	1	no	—
937	C₂×C₄⋊C₄	—	3	1	no	—
938	C₂×C₄⋊C₄	—	3	1	no	—
939	C₂×C₄⋊C₄	—	3	2	no	—
940	C₂×C₄⋊C₄	—	3	2	no	—
941	C₂×C₄⋊C₄	—	3	1	no	—
942	C₂×C₄⋊C₄	—	3	2	no	—
943	C₂×C₄⋊C₄	—	3	2	no	—
944	C₂×C₄⋊C₄	—	3	2	no	—
945	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
946	C₂×C₂²⋊C₄	—	3	1	no	—
947	C₂×C₂²⋊C₄	—	3	2	no	—
948	C₂×C₂²⋊C₄	—	3	2	no	—
949	C₂×C₂²⋊C₄	—	3	1	no	—
950	C₂×C₂²⋊C₄	—	3	2	no	—
951	C₂×C₄²	—	3	2	no	—
952	C₂×C₄²	—	3	2	no	—
953	C₂×C₄²	—	3	1	no	—
954	C₂×C₃×C₅	—	2	2	no	—
955	C₂×C₃×C₅	—	4	1	no	—
956	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
957	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
958	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
959	C₅×D₃	—	2	2	no	—
960	C₅×D₃	—	4	1	no	—
961	C₅×D₃	#552	1	4	yes	direct product factor
962	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
963	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
964	C₂²×D₃	—	2	2	no	—
965	C₂²×D₃	—	2	2	no	—
966	C₂²×D₃	—	2	2	no	—
967	C₂²×D₃	—	2	2	no	—
968	C₂²×D₃	—	2	2	no	—
969	C₂²×D₃	C₅×#41	1	4	yes	—
970	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
971	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
972	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
973	C₃×Q₈	—	2	2	no	—
974	C₃×D₄	—	2	2	no	—
975	C₂×C₃×C₄	—	2	4	no	—
976	C₂×C₃×C₄	—	2	2	no	—
977	C₂×C₃×C₄	—	2	2	no	—
978	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
979	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
980	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
981	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
982	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
983	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
984	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
985	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
986	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
987	#67	—	2	2	no	—
988	#67	—	2	2	no	—
989	C₂×Dic₃	—	2	4	no	—
990	C₂×Dic₃	—	2	2	no	—
991	C₂×Dic₃	—	2	2	no	—
992	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
993	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
994	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
995	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
996	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
997	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
998	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
999	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
1000	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1001	D₁₂	—	2	2	no	—
1002	C₄×D₃	—	2	4	no	—
1003	C₄×D₃	—	2	4	no	—
1004	C₄×D₃	—	2	4	no	—
1005	C₄×D₃	—	2	4	no	—
1006	C₄×D₃	—	2	2	no	—
1007	C₄×D₃	—	2	2	no	—
1008	C₄×D₃	—	2	2	no	—
1009	C₄×D₃	—	2	4	no	—
1010	C₄×D₃	—	2	2	no	—
1011	C₄×D₃	—	2	4	no	—
1012	C₄×D₃	—	2	2	no	—
1013	C₄×D₃	—	2	2	no	—
1014	C₄×D₃	—	2	2	no	—
1015	C₄×D₃	—	2	2	no	—
1016	C₄×D₃	C₅×#41	1	4	yes	—
1017	Dic₆	—	2	2	no	—
1018	Dic₆	—	2	4	no	—
1019	C₂²×C₅	—	2	1	no	—
1020	C₂²×C₅	—	2	1	no	—
1021	C₂²×C₅	—	2	1	no	—
1022	C₂²×C₅	—	2	1	no	—
1023	C₂²×C₅	—	2	1	no	—
1024	C₂²×C₅	—	3	2	no	—
1025	C₂²×C₅	—	3	2	no	—
1026	C₂²×C₅	—	3	2	no	—
1027	C₂²×C₅	—	3	2	no	—
1028	C₂²×C₅	—	6	8	no	—
1029	C₂²×C₅	—	6	1	no	—
1030	C₂²×C₅	—	6	1	no	—
1031	C₂²×C₅	—	6	1	no	—
1032	C₂²×C₅	—	6	1	no	—
1033	C₂²×C₅	—	6	1	no	—
1034	C₂²×C₅	—	12	4	no	—
1035	C₂²×C₅	D₃×#41	1	2	yes	—
1036	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
1037	C₄×C₅	—	2	2	no	—
1038	C₄×C₅	—	2	2	no	—
1039	C₄×C₅	—	2	1	no	—
1040	C₄×C₅	—	2	1	no	—
1041	C₄×C₅	—	2	1	no	—
1042	C₄×C₅	—	2	2	no	—
1043	C₄×C₅	—	2	1	no	—
1044	C₄×C₅	—	2	2	no	—
1045	C₄×C₅	—	3	2	no	—
1046	C₄×C₅	—	6	2	no	—
1047	C₄×C₅	—	6	2	no	—
1048	C₄×C₅	—	6	1	no	—
1049	C₄×C₅	—	6	1	no	—
1050	C₄×C₅	—	6	1	no	—
1051	C₄×C₅	—	6	2	no	—
1052	C₄×C₅	—	6	1	no	—
1053	C₄×C₅	—	6	2	no	—
1054	C₄×C₅	D₃×#41	1	2	yes	—
1055	C₂⁴	—	3	1	no	—
1056	C₂⁴	—	3	1	no	—
1057	C₂×Q₈	—	3	2	no	—
1058	C₂×Q₈	—	3	1	no	—
1059	C₂×Q₈	—	6	4	no	—
1060	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
1061	C₂×D₄	—	3	1	no	—
1062	C₂×D₄	—	3	1	no	—
1063	C₂×D₄	—	3	1	no	—
1064	C₂×D₄	—	6	4	no	—
1065	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
1066	C₂²×C₄	—	3	1	no	—
1067	C₂²×C₄	—	3	2	no	—
1068	C₂²×C₄	—	3	1	no	—
1069	C₂²×C₄	—	3	1	no	—
1070	C₂²×C₄	—	3	1	no	—
1071	C₂²×C₄	—	3	1	no	—
1072	C₂²×C₄	—	3	2	no	—
1073	C₂²×C₄	—	3	2	no	—
1074	C₂²×C₄	—	3	2	no	—
1075	C₂²×C₄	—	3	1	no	—
1076	C₂²×C₄	—	3	1	no	—
1077	C₂²×C₄	—	3	2	no	—
1078	C₂²×C₄	—	3	2	no	—
1079	C₂²×C₄	—	3	2	no	—
1080	C₂²×C₄	—	3	1	no	—
1081	C₂²×C₄	—	3	1	no	—
1082	C₂²×C₄	—	3	1	no	—
1083	C₂²×C₄	—	3	1	no	—
1084	C₂²×C₄	—	6	4	no	—
1085	C₂²×C₄	—	6	4	no	—
1086	C₂²×C₄	—	6	8	no	—
1087	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
1088	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1089	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1090	C₄⋊C₄	—	3	2	no	—
1091	C₄⋊C₄	—	3	1	no	—
1092	C₄⋊C₄	—	3	2	no	—
1093	C₄⋊C₄	—	3	1	no	—
1094	C₄⋊C₄	—	3	2	no	—
1095	C₄⋊C₄	—	3	2	no	—
1096	C₄⋊C₄	—	3	2	no	—
1097	C₄⋊C₄	—	3	2	no	—
1098	C₄⋊C₄	—	3	2	no	—
1099	C₄⋊C₄	—	3	2	no	—
1100	C₄⋊C₄	—	3	2	no	—
1101	C₄⋊C₄	—	3	1	no	—
1102	C₄⋊C₄	—	3	2	no	—
1103	C₄⋊C₄	—	3	2	no	—
1104	C₄⋊C₄	—	3	2	no	—
1105	C₄⋊C₄	—	3	1	no	—
1106	C₄⋊C₄	—	3	1	no	—
1107	C₄⋊C₄	—	3	1	no	—
1108	C₄⋊C₄	—	3	2	no	—
1109	C₄⋊C₄	—	3	2	no	—
1110	C₄⋊C₄	—	3	2	no	—
1111	C₄⋊C₄	—	3	2	no	—
1112	C₄⋊C₄	—	3	2	no	—
1113	C₄⋊C₄	—	3	2	no	—
1114	C₄⋊C₄	—	3	2	no	—
1115	C₄⋊C₄	—	3	2	no	—
1116	C₄⋊C₄	—	3	2	no	—
1117	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1118	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1119	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1120	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1121	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1122	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1123	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1124	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1125	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1126	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1127	C₂²⋊C₄	—	3	1	no	—
1128	C₂²⋊C₄	—	3	2	no	—
1129	C₂²⋊C₄	—	3	2	no	—
1130	C₂²⋊C₄	—	3	1	no	—
1131	C₂²⋊C₄	—	3	2	no	—
1132	C₂²⋊C₄	—	3	1	no	—
1133	C₂²⋊C₄	—	3	1	no	—
1134	C₂²⋊C₄	—	3	2	no	—
1135	C₂²⋊C₄	—	3	2	no	—
1136	C₂²⋊C₄	—	3	2	no	—
1137	C₂²⋊C₄	—	3	2	no	—
1138	C₂²⋊C₄	—	3	1	no	—
1139	C₂²⋊C₄	—	3	1	no	—
1140	C₂²⋊C₄	—	3	2	no	—
1141	C₂²⋊C₄	—	3	2	no	—
1142	C₂²⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1143	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1144	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1145	C₂²⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1146	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1147	C₄²	—	3	2	no	—
1148	C₄²	—	3	2	no	—
1149	C₄²	—	3	2	no	—
1150	C₄²	—	3	2	no	—
1151	C₄²	—	3	2	no	—
1152	C₄²	—	3	2	no	—
1153	C₄²	—	3	1	no	—
1154	C₄²	—	3	1	no	—
1155	C₄²	—	3	1	no	—
1156	C₄²	C₂²×C₅×D₃	1	2	yes	—
1157	C₄²	C₂²×C₅×D₃	1	2	yes	—
1158	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
1159	C₃×C₅	C₂×#552	1	1	yes	characteristic, complemented, Hall
1160	C₂²×C₃	—	2	1	no	—
1161	C₂²×C₃	—	2	1	no	—
1162	C₂²×C₃	—	2	1	no	—
1163	C₂²×C₃	—	2	1	no	—
1164	C₂²×C₃	—	2	1	no	—
1165	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
1166	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1167	C₂×D₃	—	2	1	no	—
1168	C₂×D₃	—	2	1	no	—
1169	C₂×D₃	—	2	8	no	—
1170	C₂×D₃	—	2	1	no	—
1171	C₂×D₃	—	2	1	no	—
1172	C₂×D₃	—	2	1	no	—
1173	C₂×D₃	—	4	4	no	—
1174	C₂×D₃	C₂×C₅×#41	1	2	yes	—
1175	C₂×D₃	C₂×C₅×#41	1	2	yes	—
1176	C₂×D₃	C₂×C₅×#41	1	2	yes	—
1177	C₂×D₃	C₅×2₋¹⁺⁴	1	2	yes	—
1178	C₃×C₄	—	2	2	no	—
1179	C₃×C₄	—	2	2	no	—
1180	C₃×C₄	—	2	2	no	—
1181	C₃×C₄	—	2	1	no	—
1182	C₃×C₄	—	2	1	no	—
1183	C₃×C₄	—	2	1	no	—
1184	C₃×C₄	—	2	1	no	—
1185	C₃×C₄	—	2	2	no	—
1186	C₃×C₄	C₂×C₅×#41	1	2	yes	—
1187	Dic₃	—	2	2	no	—
1188	Dic₃	—	2	2	no	—
1189	Dic₃	—	2	2	no	—
1190	Dic₃	—	2	1	no	—
1191	Dic₃	—	2	1	no	—
1192	Dic₃	—	2	1	no	—
1193	Dic₃	—	2	1	no	—
1194	Dic₃	—	2	2	no	—
1195	Dic₃	C₂×C₅×#41	1	2	yes	—
1196	C₂×C₅	—	2	2	no	—
1197	C₂×C₅	—	3	4	no	—
1198	C₂×C₅	—	4	1	no	—
1199	C₂×C₅	—	6	2	no	—
1200	C₂×C₅	—	12	1	no	—
1201	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
1202	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
1203	C₂×C₅	D₃×2₋¹⁺⁴	1	1	yes	characteristic
1204	C₂³	—	3	1	no	—
1205	C₂³	—	3	4	no	—
1206	C₂³	—	3	1	no	—
1207	C₂³	—	3	1	no	—
1208	C₂³	—	6	2	no	—
1209	C₂³	—	6	2	no	—
1210	C₂³	—	6	2	no	—
1211	C₂³	—	6	2	no	—
1212	C₂³	—	6	2	no	—
1213	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1214	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1215	Q₈	—	2	2	no	—
1216	Q₈	—	6	4	no	—
1217	Q₈	—	6	2	no	—
1218	D₄	—	2	2	no	—
1219	D₄	—	6	2	no	—
1220	D₄	—	6	2	no	—
1221	D₄	—	6	2	no	—
1222	C₂×C₄	—	2	4	no	—
1223	C₂×C₄	—	2	2	no	—
1224	C₂×C₄	—	2	2	no	—
1225	C₂×C₄	—	3	1	no	—
1226	C₂×C₄	—	3	4	no	—
1227	C₂×C₄	—	3	1	no	—
1228	C₂×C₄	—	3	1	no	—
1229	C₂×C₄	—	3	2	no	—
1230	C₂×C₄	—	3	2	no	—
1231	C₂×C₄	—	3	2	no	—
1232	C₂×C₄	—	3	1	no	—
1233	C₂×C₄	—	3	1	no	—
1234	C₂×C₄	—	3	2	no	—
1235	C₂×C₄	—	6	2	no	—
1236	C₂×C₄	—	6	2	no	—
1237	C₂×C₄	—	6	2	no	—
1238	C₂×C₄	—	6	2	no	—
1239	C₂×C₄	—	6	4	no	—
1240	C₂×C₄	—	6	4	no	—
1241	C₂×C₄	—	6	4	no	—
1242	C₂×C₄	—	6	4	no	—
1243	C₂×C₄	—	6	2	no	—
1244	C₂×C₄	—	6	4	no	—
1245	C₂×C₄	—	6	2	no	—
1246	C₂×C₄	—	6	4	no	—
1247	C₂×C₄	—	6	2	no	—
1248	C₂×C₄	—	6	2	no	—
1249	C₂×C₄	—	6	4	no	—
1250	C₂×C₄	—	6	2	no	—
1251	C₂×C₄	—	6	2	no	—
1252	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1253	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1254	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1255	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1256	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1257	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1258	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1259	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1260	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1261	C₂×C₃	—	2	2	no	—
1262	C₂×C₃	—	4	1	no	—
1263	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
1264	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
1265	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1266	D₃	—	2	2	no	—
1267	D₃	—	4	1	no	—
1268	D₃	C₅×#552	1	4	yes	direct product factor
1269	C₅	D₃×#552	1	1	yes	characteristic, direct product factor, Sylow
1270	C₂²	—	2	1	no	—
1271	C₂²	—	2	1	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	1	no	—
1275	C₂²	—	3	2	no	—
1276	C₂²	—	3	2	no	—
1277	C₂²	—	3	2	no	—
1278	C₂²	—	3	2	no	—
1279	C₂²	—	6	8	no	—
1280	C₂²	—	6	1	no	—
1281	C₂²	—	6	1	no	—
1282	C₂²	—	6	1	no	—
1283	C₂²	—	6	1	no	—
1284	C₂²	—	6	1	no	—
1285	C₂²	—	12	4	no	—
1286	C₂²	C₅×D₃×#41	1	2	yes	—
1287	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
1288	C₄	—	2	2	no	—
1289	C₄	—	2	2	no	—
1290	C₄	—	2	1	no	—
1291	C₄	—	2	1	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	2	no	—
1294	C₄	—	2	1	no	—
1295	C₄	—	2	2	no	—
1296	C₄	—	3	2	no	—
1297	C₄	—	6	2	no	—
1298	C₄	—	6	2	no	—
1299	C₄	—	6	1	no	—
1300	C₄	—	6	1	no	—
1301	C₄	—	6	1	no	—
1302	C₄	—	6	2	no	—
1303	C₄	—	6	1	no	—
1304	C₄	—	6	2	no	—
1305	C₄	C₅×D₃×#41	1	2	yes	—
1306	C₃	C₂×C₅×#552	1	1	yes	characteristic, complemented, Sylow
1307	C₂	—	2	2	no	—
1308	C₂	—	3	4	no	—
1309	C₂	—	4	1	no	—
1310	C₂	—	6	2	no	—
1311	C₂	—	12	1	no	—
1312	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
1313	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
1314	C₂	C₅×D₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₅×#552	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂×C₅×D₃×D₄	C₂²
hypercenter	C₅×#552	D₃
hypocenter	C₃	C₂×C₅×#552
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#552

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#552	C₂	semidirect
2. C₅×#5708	C₂	semidirect
3. C₅×D₃×#126	C₂	semidirect
4. C₅×#5694	C₂	semidirect
5. C₅×#5693	C₂	semidirect
6. C₅×D₃×#125	C₂	semidirect
7. C₅×D₃×#125	C₂	semidirect
9. C₅×#5650	C₂	semidirect
10. C₅×#5642	C₂	semidirect
11. C₅×#5639	C₂	semidirect
12. C₅×D₃×C₂²⋊Q₈	C₂	semidirect
13. C₅×D₃×C₂²⋊Q₈	C₂	semidirect
14. C₅×#5581	C₂	semidirect
15. C₄×C₅×D₃×Q₈	C₂	semidirect
17. C₅×#5541	C₂	semidirect
18. C₅×#5531	C₂	semidirect
19. C₅×#5529	C₂	semidirect
20. C₅×D₃×#117	C₂	semidirect
21. C₅×D₃×#117	C₂	semidirect
22. C₅×#5513	C₂	semidirect
23. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
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. C₅×#946	C₂²	semidirect
42. C₅×#946	C₂²	semidirect
43. C₅×Q₈×Dic₃	C₂²	semidirect
49. C₅×#926	C₂²	semidirect
50. C₅×#926	C₂²	semidirect
51. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
52. C₅×#924	C₂²	semidirect
53. C₅×#924	C₂²	semidirect
54. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
55. C₅×#898	C₂²	semidirect
56. C₅×#898	C₂²	semidirect
57. C₅×#898	C₂²	semidirect
58. C₅×#897	C₂²	semidirect
59. C₅×#897	C₂²	semidirect
60. C₅×#896	C₂²	semidirect
61. C₅×#896	C₂²	semidirect
65. C₅×#892	C₂²	semidirect
66. C₅×#892	C₂²	semidirect
67. C₅×#892	C₂²	semidirect
68. C₅×#892	C₂²	semidirect
79. C₅×D₃×C₄⋊C₄	C₂²	semidirect
80. C₅×D₃×C₄⋊C₄	C₂²	semidirect
81. C₅×D₃×C₄⋊C₄	C₂²	semidirect
82. C₅×#890	C₂²	semidirect
83. C₅×#890	C₂²	semidirect
84. C₅×#890	C₂²	semidirect
85. C₅×#890	C₂²	semidirect
86. C₅×#889	C₂²	semidirect
87. C₅×#889	C₂²	semidirect
88. C₅×#889	C₂²	semidirect
89. C₅×#889	C₂²	semidirect
90. C₅×#889	C₂²	semidirect
91. C₅×#889	C₂²	semidirect
92. C₅×#887	C₂²	semidirect
93. C₅×#887	C₂²	semidirect
104. C₅×#879	C₂²	semidirect
105. C₅×#879	C₂²	semidirect
106. C₅×#879	C₂²	semidirect
107. C₅×#878	C₂²	semidirect
108. C₅×#878	C₂²	semidirect
109. C₅×#877	C₂²	semidirect
110. C₅×#877	C₂²	semidirect
111. C₅×#877	C₂²	semidirect
112. C₅×#876	C₂²	semidirect
114. C₅×#872	C₂²	semidirect
115. C₅×#872	C₂²	semidirect
116. C₅×#872	C₂²	semidirect
120. C₅×#870	C₂²	semidirect
121. C₅×#870	C₂²	semidirect
122. C₄×C₅×Dic₆	C₂²	semidirect
123. C₄×C₅×Dic₆	C₂²	semidirect
124. D₃×#552	C₅	direct (N × H)
136. C₅×#552	D₃	direct (N × H)
252. C₃×#552	C₂×C₅	semidirect
253. #5708	C₂×C₅	semidirect
254. D₃×#126	C₂×C₅	semidirect
255. #5694	C₂×C₅	semidirect
256. #5693	C₂×C₅	semidirect
257. D₃×#125	C₂×C₅	semidirect
258. D₃×#125	C₂×C₅	semidirect
260. #5650	C₂×C₅	semidirect
261. #5642	C₂×C₅	semidirect
262. #5639	C₂×C₅	semidirect
263. D₃×C₂²⋊Q₈	C₂×C₅	semidirect
264. D₃×C₂²⋊Q₈	C₂×C₅	semidirect
265. #5581	C₂×C₅	semidirect
266. C₄×D₃×Q₈	C₂×C₅	semidirect
268. #5541	C₂×C₅	semidirect
269. #5531	C₂×C₅	semidirect
270. #5529	C₂×C₅	semidirect
271. D₃×#117	C₂×C₅	semidirect
272. D₃×#117	C₂×C₅	semidirect
273. #5513	C₂×C₅	semidirect
274. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
287. C₅×#126	C₂×D₃	semidirect
300. C₅×#125	C₂×D₃	semidirect
301. C₅×#125	C₂×D₃	semidirect
320. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
321. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
327. C₄×C₅×Q₈	C₂×D₃	semidirect
348. C₅×#117	C₂×D₃	semidirect
349. C₅×#117	C₂×D₃	semidirect
365. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
437. C₃×#126	C₂²×C₅	semidirect
438. C₃×#125	C₂²×C₅	semidirect
439. C₃×#125	C₂²×C₅	semidirect
441. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
442. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
443. C₃×C₄×Q₈	C₂²×C₅	semidirect
445. C₃×#117	C₂²×C₅	semidirect
446. C₃×#117	C₂²×C₅	semidirect
447. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
448. #946	C₂²×C₅	semidirect
449. #946	C₂²×C₅	semidirect
450. Q₈×Dic₃	C₂²×C₅	semidirect
456. #926	C₂²×C₅	semidirect
457. #926	C₂²×C₅	semidirect
458. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
459. #924	C₂²×C₅	semidirect
460. #924	C₂²×C₅	semidirect
461. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
462. #898	C₂²×C₅	semidirect
463. #898	C₂²×C₅	semidirect
464. #898	C₂²×C₅	semidirect
465. #897	C₂²×C₅	semidirect
466. #897	C₂²×C₅	semidirect
467. #896	C₂²×C₅	semidirect
468. #896	C₂²×C₅	semidirect
472. #892	C₂²×C₅	semidirect
473. #892	C₂²×C₅	semidirect
474. #892	C₂²×C₅	semidirect
475. #892	C₂²×C₅	semidirect
486. D₃×C₄⋊C₄	C₂²×C₅	semidirect
487. D₃×C₄⋊C₄	C₂²×C₅	semidirect
488. D₃×C₄⋊C₄	C₂²×C₅	semidirect
489. #890	C₂²×C₅	semidirect
490. #890	C₂²×C₅	semidirect
491. #890	C₂²×C₅	semidirect
492. #890	C₂²×C₅	semidirect
493. #889	C₂²×C₅	semidirect
494. #889	C₂²×C₅	semidirect
495. #889	C₂²×C₅	semidirect
496. #889	C₂²×C₅	semidirect
497. #889	C₂²×C₅	semidirect
498. #889	C₂²×C₅	semidirect
499. #887	C₂²×C₅	semidirect
500. #887	C₂²×C₅	semidirect
511. #879	C₂²×C₅	semidirect
512. #879	C₂²×C₅	semidirect
513. #879	C₂²×C₅	semidirect
514. #878	C₂²×C₅	semidirect
515. #878	C₂²×C₅	semidirect
516. #877	C₂²×C₅	semidirect
517. #877	C₂²×C₅	semidirect
518. #877	C₂²×C₅	semidirect
519. #876	C₂²×C₅	semidirect
521. #872	C₂²×C₅	semidirect
522. #872	C₂²×C₅	semidirect
523. #872	C₂²×C₅	semidirect
527. #870	C₂²×C₅	semidirect
528. #870	C₂²×C₅	semidirect
529. C₄×Dic₆	C₂²×C₅	semidirect
530. C₄×Dic₆	C₂²×C₅	semidirect
646. #552	C₅×D₃	direct (N × H)
867. #126	C₂×C₅×D₃	semidirect
880. #125	C₂×C₅×D₃	semidirect
881. #125	C₂×C₅×D₃	semidirect
900. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
901. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
907. C₄×Q₈	C₂×C₅×D₃	semidirect
928. #117	C₂×C₅×D₃	semidirect
929. #117	C₂×C₅×D₃	semidirect
945. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
961. C₅×D₃	#552	direct (N × H)
1159. C₃×C₅	C₂×#552	semidirect
1268. D₃	C₅×#552	direct (N × H)
1269. C₅	D₃×#552	direct (N × H)
1306. C₃	C₂×C₅×#552	semidirect

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
C₅×#5708	2
C₅×D₃×#126	2
C₅×#5694	2
C₅×#5693	2
C₅×D₃×#125	2
C₅×D₃×#123	2
C₅×#5650	2
C₅×#5642	2
C₅×#5639	2
C₅×D₃×C₂²⋊Q₈	2
C₅×#5581	2
C₄×C₅×D₃×Q₈	2
C₄×C₅×D₃×D₄	2
C₅×#5541	2
C₅×#5531	2
C₅×#5529	2
C₅×D₃×#117	2
C₅×#5513	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#552	3
D₃×#552	5

Subgroups — C5×D3×#552 #14483394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#552 #14483394