Subgroups — C₅×#86826 #14484150

Order 1920.

2264 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5709	C₂	1	2	yes	maximal, complemented
3	C₅×#5706	C₂	1	2	yes	maximal, complemented
4	C₅×#5693	C₂	1	2	yes	maximal, complemented
5	C₅×#5691	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5691	C₂	1	2	yes	maximal, complemented
7	C₅×#5690	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5658	C₂	1	2	yes	maximal, complemented
9	C₅×#5656	C₂	1	2	yes	maximal, complemented
10	C₅×#5631	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5630	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5624	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5622	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×#239	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#5568	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#5550	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#5532	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#5527	C₂	1	2	yes	maximal, complemented
20	C₅×#5522	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×#893	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅×#3475	—	3	1	no	maximal, Hall
25	C₂×C₅×#239	C₂²	1	1	yes	characteristic
26	C₂×C₅×#237	C₂²	1	1	yes	characteristic
27	C₂×C₅×#235	C₂²	1	1	yes	characteristic
28	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
29	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
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
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	2	yes	—
39	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₅×#947	C₂²	1	1	yes	characteristic
42	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
43	C₅×#944	C₂²	1	1	yes	characteristic, complemented
44	C₅×#937	C₂²	1	2	yes	—
45	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
46	C₅×#930	C₂²	1	1	yes	characteristic
47	C₅×#929	C₂²	1	2	yes	—
48	C₄×C₅×#67	C₂²	1	1	yes	characteristic
49	C₄×C₅×#67	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
51	C₅×#926	C₂²	1	2	yes	—
52	C₅×#924	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, 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×#898	C₂²	1	2	yes	complemented
59	C₅×#897	C₂²	1	2	yes	complemented
60	C₅×#897	C₂²	1	1	yes	characteristic, complemented
61	C₅×#896	C₂²	1	2	yes	complemented
62	C₅×#896	C₂²	1	2	yes	complemented
63	C₅×#896	C₂²	1	2	yes	complemented
64	C₅×#895	C₂²	1	2	yes	—
65	C₅×#895	C₂²	1	1	yes	characteristic
66	C₅×#894	C₂²	1	2	yes	—
67	C₅×#894	C₂²	1	2	yes	—
68	C₅×#894	C₂²	1	2	yes	complemented
69	C₅×#894	C₂²	1	2	yes	complemented
70	C₅×#893	C₂²	1	1	yes	characteristic
71	C₅×#893	C₂²	1	1	yes	characteristic
72	C₅×#893	C₂²	1	2	yes	—
73	C₅×#893	C₂²	1	1	yes	characteristic
74	C₅×#893	C₂²	1	2	yes	—
75	C₅×#893	C₂²	1	1	yes	characteristic
76	C₅×#893	C₂²	1	1	yes	characteristic
77	C₅×#893	C₂²	1	2	yes	complemented
78	C₅×#893	C₂²	1	2	yes	complemented
79	C₅×#892	C₂²	1	2	yes	complemented
80	C₅×#892	C₂²	1	1	yes	characteristic, complemented
81	C₅×#892	C₂²	1	2	yes	complemented
82	C₅×#892	C₂²	1	2	yes	complemented
83	C₅×#892	C₂²	1	1	yes	characteristic, complemented
84	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
85	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
86	C₅×#890	C₂²	1	1	yes	characteristic, complemented
87	C₅×#889	C₂²	1	2	yes	complemented
88	C₅×#889	C₂²	1	2	yes	complemented
89	C₅×#888	C₂²	1	1	yes	characteristic, complemented
90	C₅×#887	C₂²	1	2	yes	complemented
91	C₅×#887	C₂²	1	1	yes	characteristic, complemented
92	C₅×#887	C₂²	1	1	yes	characteristic, complemented
93	C₅×#887	C₂²	1	1	yes	characteristic, complemented
94	C₅×#886	C₂²	1	2	yes	complemented
95	C₅×#885	C₂²	1	2	yes	complemented
96	C₅×#884	C₂²	1	2	yes	—
97	C₅×#884	C₂²	1	2	yes	complemented
98	C₅×#884	C₂²	1	2	yes	complemented
99	C₅×#883	C₂²	1	2	yes	complemented
100	C₅×#882	C₂²	1	2	yes	—
101	C₅×#67⋊C₄	C₂²	1	1	yes	characteristic
102	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
103	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
104	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
105	C₅×#67⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
107	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
108	C₅×#878	C₂²	1	2	yes	—
109	C₅×#877	C₂²	1	2	yes	—
110	C₅×#877	C₂²	1	1	yes	characteristic
111	C₅×#877	C₂²	1	1	yes	characteristic, complemented
112	C₅×#876	C₂²	1	2	yes	complemented
113	C₅×#875	C₂²	1	1	yes	characteristic
114	C₅×#875	C₂²	1	2	yes	complemented
115	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
116	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
117	C₅×#872	C₂²	1	2	yes	complemented
118	C₅×#872	C₂²	1	2	yes	complemented
119	C₅×#872	C₂²	1	2	yes	complemented
120	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
121	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
122	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
123	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
124	#86826	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
125	C₅×#556	—	3	1	no	—
126	C₅×#555	—	3	1	no	—
127	C₅×#554	—	3	1	no	—
128	C₅×#553	—	3	2	no	—
129	C₅×#552	—	3	2	no	—
130	C₅×#552	—	3	1	no	—
131	C₅×#552	D₃	1	1	yes	characteristic, complemented
132	C₅×#551	—	3	2	no	—
133	C₅×#551	—	3	2	no	—
134	C₅×#547	—	3	1	no	—
135	C₅×#546	—	3	1	no	—
136	C₅×#546	—	3	1	no	—
137	C₅×#533	—	3	1	no	—
138	C₅×#529	—	3	2	no	—
139	C₅×#529	—	3	2	no	—
140	C₅×#529	—	3	1	no	—
141	C₅×#529	—	3	1	no	—
142	C₅×#525	—	3	2	no	—
143	C₄×C₅×#41	—	3	1	no	—
144	C₄×C₅×#41	—	3	1	no	—
145	C₄×C₅×#41	—	3	1	no	—
146	C₂×C₄×C₅×D₄	—	3	1	no	—
147	C₂×C₅×#117	—	3	2	no	—
148	C₂³×C₅×D₃	C₂³	1	2	yes	—
149	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
150	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
151	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
152	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
154	C₂×C₅×#67	C₂³	1	1	yes	characteristic
155	C₂×C₅×#67	C₂³	1	2	yes	—
156	C₂×C₅×#67	C₂³	1	1	yes	characteristic
157	C₂×C₅×#67	C₂³	1	2	yes	—
158	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
159	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
160	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
161	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
162	C₅×#239	—	2	4	no	—
163	C₅×#237	—	2	4	no	—
164	C₅×#235	—	2	4	no	—
165	C₂×C₅×D₁₂	—	2	4	no	—
166	C₂×C₅×D₁₂	C₂³	1	2	yes	—
167	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
168	C₂×C₅×D₁₂	C₂³	1	2	yes	—
169	C₂×C₅×D₁₂	C₂³	1	2	yes	—
170	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
171	C₂×C₄×C₅×D₃	—	2	8	no	—
172	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
173	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
174	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
175	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
176	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
177	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
178	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
179	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
180	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
181	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
182	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
183	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
184	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
185	C₂×C₅×Dic₆	C₂³	1	2	yes	—
186	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₃×C₅×C₄⋊C₄	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	1	yes	characteristic
192	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
195	C₃×C₅×C₄⋊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×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×C₄²×C₅	C₂³	1	1	yes	characteristic
202	C₃×C₄²×C₅	C₂³	1	2	yes	—
203	C₃×C₄²×C₅	C₂³	1	2	yes	—
204	C₅×#217	C₂³	1	2	yes	—
205	C₅×#217	C₂³	1	1	yes	characteristic
206	C₅×#217	C₂³	1	1	yes	characteristic
207	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
213	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
214	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
215	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
216	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
217	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
218	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
219	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
220	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
221	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
223	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
224	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
225	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
226	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
227	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
228	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
229	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
230	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
237	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
238	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
239	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
240	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
241	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
242	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
243	C₄×C₅×Dic₃	C₂³	1	2	yes	—
244	C₄×C₅×Dic₃	C₂³	1	2	yes	—
245	C₄×C₅×Dic₃	C₂³	1	2	yes	—
246	C₄×C₅×Dic₃	C₂³	1	2	yes	—
247	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
248	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
249	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
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	#5709	C₂×C₅	1	2	yes	complemented
254	#5706	C₂×C₅	1	2	yes	complemented
255	#5693	C₂×C₅	1	2	yes	complemented
256	#5691	C₂×C₅	1	1	yes	characteristic, complemented
257	#5691	C₂×C₅	1	2	yes	complemented
258	#5690	C₂×C₅	1	1	yes	characteristic, complemented
259	#5658	C₂×C₅	1	2	yes	complemented
260	#5656	C₂×C₅	1	2	yes	complemented
261	#5631	C₂×C₅	1	1	yes	characteristic, complemented
262	#5630	C₂×C₅	1	1	yes	characteristic, complemented
263	#5624	C₂×C₅	1	1	yes	characteristic, complemented
264	#5622	C₂×C₅	1	1	yes	characteristic, complemented
265	C₄×#239	C₂×C₅	1	1	yes	characteristic, complemented
266	#5568	C₂×C₅	1	1	yes	characteristic, complemented
267	#5550	C₂×C₅	1	1	yes	characteristic, complemented
268	C₄×#237	C₂×C₅	1	1	yes	characteristic, complemented
269	#5532	C₂×C₅	1	1	yes	characteristic, complemented
270	#5527	C₂×C₅	1	2	yes	complemented
271	#5522	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×#893	C₂×C₅	1	1	yes	characteristic, complemented
275	C₂×C₅×#41	—	3	1	no	—
276	C₂×C₅×#41	—	3	1	no	—
277	C₂×C₅×#41	—	3	1	no	—
278	C₂²×C₅×D₄	—	3	1	no	—
279	C₂³×C₄×C₅	—	3	2	no	—
280	C₅×C₄⋊Q₈	—	3	1	no	—
281	C₅×C₄⋊Q₈	—	3	1	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	1	no	—
291	C₅×#125	C₂×D₃	1	2	yes	complemented
292	C₅×#125	C₂×D₃	1	1	yes	characteristic, complemented
293	C₅×#124	—	3	1	no	—
294	C₅×#124	—	3	2	no	—
295	C₅×#124	—	3	1	no	—
296	C₅×#124	—	3	2	no	—
297	C₅×#123	—	3	2	no	—
298	C₅×#123	—	3	2	no	—
299	C₅×#123	—	3	2	no	—
300	C₅×#123	—	3	2	no	—
301	C₅×#123	—	3	2	no	—
302	C₅×#123	—	3	2	no	—
303	C₅×#123	—	3	2	no	—
304	C₅×#123	C₂×D₃	1	2	yes	—
305	C₅×C₂²⋊Q₈	—	3	1	no	—
306	C₅×C₂²⋊Q₈	—	3	2	no	—
307	C₅×C₂²⋊Q₈	—	3	2	no	—
308	C₅×C₂²⋊Q₈	—	3	2	no	—
309	C₅×C₂²⋊Q₈	—	3	1	no	—
310	C₅×C₂²⋊Q₈	—	3	2	no	—
311	C₅×C₂²⋊Q₈	—	3	2	no	—
312	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
313	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
314	C₅×#121	—	3	1	no	—
315	C₅×#121	—	3	2	no	—
316	C₅×#121	—	3	1	no	—
317	C₅×#121	—	3	2	no	—
318	C₅×#121	—	3	2	no	—
319	C₅×#121	—	3	2	no	—
320	C₅×#120	—	3	2	no	—
321	C₅×#120	—	3	2	no	—
322	C₄×C₅×Q₈	—	3	1	no	—
323	C₄×C₅×Q₈	—	3	1	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	—	3	1	no	—
328	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
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	2	no	—
335	C₄×C₅×D₄	—	3	1	no	—
336	C₄×C₅×D₄	—	3	2	no	—
337	C₄×C₅×D₄	—	3	1	no	—
338	C₄×C₅×D₄	—	3	1	no	—
339	C₄×C₅×D₄	—	3	2	no	—
340	C₄×C₅×D₄	—	3	2	no	—
341	C₄×C₅×D₄	—	3	1	no	—
342	C₄×C₅×D₄	—	3	2	no	—
343	C₄×C₅×D₄	—	3	2	no	—
344	C₄×C₅×D₄	—	3	1	no	—
345	C₄×C₅×D₄	—	3	2	no	—
346	C₄×C₅×D₄	—	3	1	no	—
347	C₄×C₅×D₄	—	3	2	no	—
348	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
349	C₅×#117	—	3	2	no	—
350	C₅×#117	—	3	2	no	—
351	C₅×#117	—	3	2	no	—
352	C₅×#117	—	3	1	no	—
353	C₅×#117	—	3	2	no	—
354	C₅×#117	—	3	1	no	—
355	C₅×#117	—	3	1	no	—
356	C₅×#117	—	3	2	no	—
357	C₅×#117	—	3	1	no	—
358	C₅×#117	—	3	2	no	—
359	C₅×#117	—	3	2	no	—
360	C₅×#117	—	3	2	no	—
361	C₅×#117	C₂×D₃	1	2	yes	—
362	C₅×#117	C₂×D₃	1	1	yes	characteristic, complemented
363	C₂×C₅×C₄⋊C₄	—	3	2	no	—
364	C₂×C₅×C₄⋊C₄	—	3	2	no	—
365	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
366	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
367	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
368	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
369	C₂×C₄²×C₅	—	3	1	no	—
370	C₂×C₄²×C₅	—	3	1	no	—
371	C₂×C₄²×C₅	—	3	2	no	—
372	C₂×C₄²×C₅	—	3	2	no	—
373	C₂×C₄²×C₅	—	3	1	no	—
374	#3475	—	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	4	no	—
378	C₂²×C₅×D₃	—	2	4	no	—
379	C₂²×C₅×D₃	—	4	2	no	—
380	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
381	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
383	C₃×C₅×Q₈	—	2	2	no	—
384	C₃×C₅×D₄	—	2	2	no	—
385	C₂×C₃×C₄×C₅	—	2	4	no	—
386	C₂×C₃×C₄×C₅	—	2	2	no	—
387	C₂×C₃×C₄×C₅	—	2	2	no	—
388	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
389	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
390	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
391	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
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	1	yes	characteristic
397	C₅×#67	—	2	2	no	—
398	C₅×#67	—	2	4	no	—
399	C₅×#67	—	2	2	no	—
400	C₅×#67	—	4	2	no	—
401	C₂×C₅×Dic₃	—	2	2	no	—
402	C₂×C₅×Dic₃	—	4	1	no	—
403	C₂×C₅×Dic₃	—	4	1	no	—
404	C₂×C₅×Dic₃	#41	1	4	yes	complemented
405	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
413	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
414	C₅×D₁₂	—	2	4	no	—
415	C₅×D₁₂	—	2	4	no	—
416	C₅×D₁₂	—	2	2	no	—
417	C₅×D₁₂	—	4	2	no	—
418	C₅×D₁₂	#41	1	4	yes	complemented
419	C₄×C₅×D₃	—	2	4	no	—
420	C₄×C₅×D₃	—	2	4	no	—
421	C₄×C₅×D₃	—	2	2	no	—
422	C₄×C₅×D₃	—	2	4	no	—
423	C₄×C₅×D₃	—	2	4	no	—
424	C₄×C₅×D₃	—	2	4	no	—
425	C₄×C₅×D₃	—	2	4	no	—
426	C₄×C₅×D₃	—	2	2	no	—
427	C₄×C₅×D₃	—	4	2	no	—
428	C₄×C₅×D₃	—	4	2	no	—
429	C₄×C₅×D₃	—	4	1	no	—
430	C₅×Dic₆	—	2	2	no	—
431	C₅×Dic₆	—	2	2	no	—
432	C₅×Dic₆	—	4	2	no	—
433	C₂×#239	C₂²×C₅	1	1	yes	characteristic
434	C₂×#237	C₂²×C₅	1	1	yes	characteristic
435	C₂×#235	C₂²×C₅	1	1	yes	characteristic
436	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
437	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
438	C₃×#126	C₂²×C₅	1	2	yes	complemented
439	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
440	C₃×#125	C₂²×C₅	1	2	yes	complemented
441	C₃×#123	C₂²×C₅	1	2	yes	—
442	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
443	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
444	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
445	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
446	C₃×#117	C₂²×C₅	1	2	yes	—
447	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
448	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
449	#947	C₂²×C₅	1	1	yes	characteristic
450	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
451	#944	C₂²×C₅	1	1	yes	characteristic, complemented
452	#937	C₂²×C₅	1	2	yes	—
453	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
454	#930	C₂²×C₅	1	1	yes	characteristic
455	#929	C₂²×C₅	1	2	yes	—
456	C₄×#67	C₂²×C₅	1	1	yes	characteristic
457	C₄×#67	C₂²×C₅	1	1	yes	characteristic, complemented
458	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
459	#926	C₂²×C₅	1	2	yes	—
460	#924	C₂²×C₅	1	1	yes	characteristic
461	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
462	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
463	#898	C₂²×C₅	1	2	yes	complemented
464	#898	C₂²×C₅	1	2	yes	complemented
465	#898	C₂²×C₅	1	2	yes	complemented
466	#898	C₂²×C₅	1	2	yes	complemented
467	#897	C₂²×C₅	1	2	yes	complemented
468	#897	C₂²×C₅	1	1	yes	characteristic, complemented
469	#896	C₂²×C₅	1	2	yes	complemented
470	#896	C₂²×C₅	1	2	yes	complemented
471	#896	C₂²×C₅	1	2	yes	complemented
472	#895	C₂²×C₅	1	2	yes	—
473	#895	C₂²×C₅	1	1	yes	characteristic
474	#894	C₂²×C₅	1	2	yes	—
475	#894	C₂²×C₅	1	2	yes	—
476	#894	C₂²×C₅	1	2	yes	complemented
477	#894	C₂²×C₅	1	2	yes	complemented
478	#893	C₂²×C₅	1	1	yes	characteristic
479	#893	C₂²×C₅	1	1	yes	characteristic
480	#893	C₂²×C₅	1	2	yes	—
481	#893	C₂²×C₅	1	1	yes	characteristic
482	#893	C₂²×C₅	1	2	yes	—
483	#893	C₂²×C₅	1	1	yes	characteristic
484	#893	C₂²×C₅	1	1	yes	characteristic
485	#893	C₂²×C₅	1	2	yes	complemented
486	#893	C₂²×C₅	1	2	yes	complemented
487	#892	C₂²×C₅	1	2	yes	complemented
488	#892	C₂²×C₅	1	1	yes	characteristic, complemented
489	#892	C₂²×C₅	1	2	yes	complemented
490	#892	C₂²×C₅	1	2	yes	complemented
491	#892	C₂²×C₅	1	1	yes	characteristic, complemented
492	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
493	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
494	#890	C₂²×C₅	1	1	yes	characteristic, complemented
495	#889	C₂²×C₅	1	2	yes	complemented
496	#889	C₂²×C₅	1	2	yes	complemented
497	#888	C₂²×C₅	1	1	yes	characteristic, complemented
498	#887	C₂²×C₅	1	2	yes	complemented
499	#887	C₂²×C₅	1	1	yes	characteristic, complemented
500	#887	C₂²×C₅	1	1	yes	characteristic, complemented
501	#887	C₂²×C₅	1	1	yes	characteristic, complemented
502	#886	C₂²×C₅	1	2	yes	complemented
503	#885	C₂²×C₅	1	2	yes	complemented
504	#884	C₂²×C₅	1	2	yes	—
505	#884	C₂²×C₅	1	2	yes	complemented
506	#884	C₂²×C₅	1	2	yes	complemented
507	#883	C₂²×C₅	1	2	yes	complemented
508	#882	C₂²×C₅	1	2	yes	—
509	#67⋊C₄	C₂²×C₅	1	1	yes	characteristic
510	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
511	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
512	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
513	#67⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
514	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
515	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
516	#878	C₂²×C₅	1	2	yes	—
517	#877	C₂²×C₅	1	2	yes	—
518	#877	C₂²×C₅	1	1	yes	characteristic
519	#877	C₂²×C₅	1	1	yes	characteristic, complemented
520	#876	C₂²×C₅	1	2	yes	complemented
521	#875	C₂²×C₅	1	1	yes	characteristic
522	#875	C₂²×C₅	1	2	yes	complemented
523	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
524	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
525	#872	C₂²×C₅	1	2	yes	complemented
526	#872	C₂²×C₅	1	2	yes	complemented
527	#872	C₂²×C₅	1	2	yes	complemented
528	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
529	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
530	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
531	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
532	C₂⁴×C₅	—	3	2	no	—
533	C₅×#41	—	6	4	no	—
534	C₅×#41	—	6	4	no	—
535	C₅×#41	—	6	4	no	—
536	C₂×C₅×Q₈	—	3	1	no	—
537	C₂×C₅×Q₈	—	3	1	no	—
538	C₂×C₅×Q₈	—	3	2	no	—
539	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
540	C₂×C₅×D₄	—	3	1	no	—
541	C₂×C₅×D₄	—	3	2	no	—
542	C₂×C₅×D₄	—	3	1	no	—
543	C₂×C₅×D₄	—	3	2	no	—
544	C₂×C₅×D₄	—	3	1	no	—
545	C₂×C₅×D₄	—	3	2	no	—
546	C₂×C₅×D₄	—	3	2	no	—
547	C₂×C₅×D₄	—	3	1	no	—
548	C₂×C₅×D₄	—	3	2	no	—
549	C₂×C₅×D₄	—	6	4	no	—
550	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
551	C₂²×C₄×C₅	—	3	1	no	—
552	C₂²×C₄×C₅	—	3	1	no	—
553	C₂²×C₄×C₅	—	3	1	no	—
554	C₂²×C₄×C₅	—	3	1	no	—
555	C₂²×C₄×C₅	—	3	2	no	—
556	C₂²×C₄×C₅	—	3	2	no	—
557	C₂²×C₄×C₅	—	3	2	no	—
558	C₂²×C₄×C₅	—	3	1	no	—
559	C₂²×C₄×C₅	—	3	1	no	—
560	C₂²×C₄×C₅	—	3	2	no	—
561	C₂²×C₄×C₅	—	3	2	no	—
562	C₂²×C₄×C₅	—	3	2	no	—
563	C₂²×C₄×C₅	—	3	2	no	—
564	C₂²×C₄×C₅	—	3	2	no	—
565	C₂²×C₄×C₅	—	3	1	no	—
566	C₂²×C₄×C₅	—	6	8	no	—
567	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
568	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
569	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
570	C₅×C₄⋊C₄	—	3	1	no	—
571	C₅×C₄⋊C₄	—	3	1	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	1	no	—
577	C₅×C₄⋊C₄	—	3	1	no	—
578	C₅×C₄⋊C₄	—	3	1	no	—
579	C₅×C₄⋊C₄	—	3	2	no	—
580	C₅×C₄⋊C₄	—	3	2	no	—
581	C₅×C₄⋊C₄	—	3	2	no	—
582	C₅×C₄⋊C₄	—	3	1	no	—
583	C₅×C₄⋊C₄	—	3	2	no	—
584	C₅×C₄⋊C₄	—	3	2	no	—
585	C₅×C₄⋊C₄	—	3	2	no	—
586	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
587	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
588	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
589	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
590	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
591	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
592	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
593	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
594	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
595	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
596	C₅×C₂²⋊C₄	—	3	1	no	—
597	C₅×C₂²⋊C₄	—	3	2	no	—
598	C₅×C₂²⋊C₄	—	3	1	no	—
599	C₅×C₂²⋊C₄	—	3	2	no	—
600	C₅×C₂²⋊C₄	—	3	2	no	—
601	C₅×C₂²⋊C₄	—	3	2	no	—
602	C₅×C₂²⋊C₄	—	3	2	no	—
603	C₅×C₂²⋊C₄	—	3	2	no	—
604	C₅×C₂²⋊C₄	—	3	2	no	—
605	C₅×C₂²⋊C₄	—	3	2	no	—
606	C₅×C₂²⋊C₄	—	3	2	no	—
607	C₅×C₂²⋊C₄	—	3	2	no	—
608	C₅×C₂²⋊C₄	—	3	2	no	—
609	C₅×C₂²⋊C₄	—	3	1	no	—
610	C₅×C₂²⋊C₄	—	3	2	no	—
611	C₅×C₂²⋊C₄	—	3	1	no	—
612	C₅×C₂²⋊C₄	—	3	2	no	—
613	C₅×C₂²⋊C₄	—	3	2	no	—
614	C₅×C₂²⋊C₄	—	3	2	no	—
615	C₅×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
616	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
617	C₅×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
618	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
619	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
620	C₄²×C₅	—	3	1	no	—
621	C₄²×C₅	—	3	1	no	—
622	C₄²×C₅	—	3	1	no	—
623	C₄²×C₅	—	3	2	no	—
624	C₄²×C₅	—	3	1	no	—
625	C₄²×C₅	—	3	2	no	—
626	C₄²×C₅	—	3	2	no	—
627	C₄²×C₅	—	3	1	no	—
628	C₄²×C₅	—	3	1	no	—
629	C₄²×C₅	—	3	2	no	—
630	C₄²×C₅	—	3	1	no	—
631	C₄²×C₅	—	3	1	no	—
632	C₄²×C₅	—	3	1	no	—
633	C₄²×C₅	C₂²×D₃	1	2	yes	—
634	C₄²×C₅	C₂²×D₃	1	2	yes	—
635	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
636	#556	—	3	1	no	—
637	#555	—	3	1	no	—
638	#554	—	3	1	no	—
639	#553	—	3	2	no	—
640	#552	—	3	2	no	—
641	#552	—	3	1	no	—
642	#552	C₅×D₃	1	1	yes	characteristic, complemented
643	#551	—	3	2	no	—
644	#551	—	3	2	no	—
645	#547	—	3	1	no	—
646	#546	—	3	1	no	—
647	#546	—	3	1	no	—
648	#533	—	3	1	no	—
649	#529	—	3	2	no	—
650	#529	—	3	2	no	—
651	#529	—	3	1	no	—
652	#529	—	3	1	no	—
653	#525	—	3	2	no	—
654	C₄×#41	—	3	1	no	—
655	C₄×#41	—	3	1	no	—
656	C₄×#41	—	3	1	no	—
657	C₂×C₄×D₄	—	3	1	no	—
658	C₂×#117	—	3	2	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	—	2	1	no	—
664	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
665	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
666	C₂×C₅×D₃	—	2	2	no	—
667	C₂×C₅×D₃	—	2	2	no	—
668	C₂×C₅×D₃	—	2	2	no	—
669	C₂×C₅×D₃	—	2	1	no	—
670	C₂×C₅×D₃	—	2	1	no	—
671	C₂×C₅×D₃	—	2	2	no	—
672	C₂×C₅×D₃	—	2	1	no	—
673	C₂×C₅×D₃	—	2	2	no	—
674	C₂×C₅×D₃	—	4	8	no	—
675	C₂×C₅×D₃	C₂×#41	1	4	yes	—
676	C₃×C₄×C₅	—	2	1	no	—
677	C₃×C₄×C₅	—	2	1	no	—
678	C₃×C₄×C₅	—	2	2	no	—
679	C₃×C₄×C₅	—	2	2	no	—
680	C₃×C₄×C₅	—	2	2	no	—
681	C₃×C₄×C₅	—	2	1	no	—
682	C₃×C₄×C₅	—	2	2	no	—
683	C₃×C₄×C₅	—	2	1	no	—
684	C₃×C₄×C₅	C₂×#41	1	2	yes	—
685	C₅×Dic₃	—	2	2	no	—
686	C₅×Dic₃	—	2	1	no	—
687	C₅×Dic₃	—	2	1	no	—
688	C₅×Dic₃	—	2	1	no	—
689	C₅×Dic₃	—	2	2	no	—
690	C₅×Dic₃	—	2	1	no	—
691	C₅×Dic₃	—	2	1	no	—
692	C₅×Dic₃	C₂×#41	1	2	yes	—
693	C₅×Dic₃	C₂×#41	1	2	yes	—
694	C₂³×D₃	C₂³×C₅	1	2	yes	—
695	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
696	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
697	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
698	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
699	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
700	C₂×#67	C₂³×C₅	1	1	yes	characteristic
701	C₂×#67	C₂³×C₅	1	2	yes	—
702	C₂×#67	C₂³×C₅	1	1	yes	characteristic
703	C₂×#67	C₂³×C₅	1	2	yes	—
704	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
705	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
706	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
707	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
708	#239	—	2	4	no	—
709	#237	—	2	4	no	—
710	#235	—	2	4	no	—
711	C₂×D₁₂	—	2	4	no	—
712	C₂×D₁₂	C₂³×C₅	1	2	yes	—
713	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
714	C₂×D₁₂	C₂³×C₅	1	2	yes	—
715	C₂×D₁₂	C₂³×C₅	1	2	yes	—
716	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
717	C₂×C₄×D₃	—	2	8	no	—
718	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
719	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
720	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
721	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
722	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
723	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
724	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
725	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
726	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
727	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
728	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
729	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
730	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
731	C₂×Dic₆	C₂³×C₅	1	2	yes	—
732	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
733	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
734	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
735	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
736	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
737	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
738	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
739	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
740	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
741	C₃×C₄⋊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×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
745	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
746	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
747	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
748	C₃×C₄²	C₂³×C₅	1	2	yes	—
749	C₃×C₄²	C₂³×C₅	1	2	yes	—
750	#217	C₂³×C₅	1	2	yes	—
751	#217	C₂³×C₅	1	1	yes	characteristic
752	#217	C₂³×C₅	1	1	yes	characteristic
753	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
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	2	yes	—
759	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
760	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
761	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
762	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
763	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
764	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
765	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
766	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
767	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
768	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
769	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
770	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
771	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
772	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
773	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
774	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
775	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
776	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
783	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
784	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
785	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
786	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
787	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
788	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
789	C₄×Dic₃	C₂³×C₅	1	2	yes	—
790	C₄×Dic₃	C₂³×C₅	1	2	yes	—
791	C₄×Dic₃	C₂³×C₅	1	2	yes	—
792	C₄×Dic₃	C₂³×C₅	1	2	yes	—
793	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
794	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
795	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
796	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
797	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
798	C₂³×C₅	—	3	2	no	—
799	C₂³×C₅	—	3	2	no	—
800	C₂³×C₅	—	3	1	no	—
801	C₂³×C₅	—	6	4	no	—
802	C₂³×C₅	—	6	4	no	—
803	C₂³×C₅	—	12	2	no	—
804	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
805	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
806	C₅×Q₈	—	2	2	no	—
807	C₅×Q₈	—	6	2	no	—
808	C₅×Q₈	—	6	2	no	—
809	C₅×Q₈	—	12	2	no	—
810	C₅×D₄	—	2	2	no	—
811	C₅×D₄	—	3	4	no	—
812	C₅×D₄	—	6	4	no	—
813	C₅×D₄	—	6	4	no	—
814	C₅×D₄	—	6	2	no	—
815	C₅×D₄	—	6	4	no	—
816	C₅×D₄	—	6	2	no	—
817	C₅×D₄	—	6	2	no	—
818	C₅×D₄	—	12	2	no	—
819	C₅×D₄	—	12	2	no	—
820	C₂×C₄×C₅	—	2	4	no	—
821	C₂×C₄×C₅	—	2	2	no	—
822	C₂×C₄×C₅	—	2	2	no	—
823	C₂×C₄×C₅	—	3	4	no	—
824	C₂×C₄×C₅	—	3	1	no	—
825	C₂×C₄×C₅	—	3	1	no	—
826	C₂×C₄×C₅	—	3	1	no	—
827	C₂×C₄×C₅	—	3	1	no	—
828	C₂×C₄×C₅	—	3	1	no	—
829	C₂×C₄×C₅	—	3	1	no	—
830	C₂×C₄×C₅	—	3	2	no	—
831	C₂×C₄×C₅	—	3	1	no	—
832	C₂×C₄×C₅	—	3	2	no	—
833	C₂×C₄×C₅	—	6	4	no	—
834	C₂×C₄×C₅	—	6	4	no	—
835	C₂×C₄×C₅	—	6	4	no	—
836	C₂×C₄×C₅	—	6	4	no	—
837	C₂×C₄×C₅	—	6	2	no	—
838	C₂×C₄×C₅	—	6	4	no	—
839	C₂×C₄×C₅	—	6	4	no	—
840	C₂×C₄×C₅	—	6	2	no	—
841	C₂×C₄×C₅	—	6	2	no	—
842	C₂×C₄×C₅	—	12	1	no	—
843	C₂×C₄×C₅	—	12	2	no	—
844	C₂×C₄×C₅	—	12	2	no	—
845	C₂×C₄×C₅	—	12	1	no	—
846	C₂×C₄×C₅	—	12	1	no	—
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	1	yes	characteristic
850	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
851	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
852	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
853	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
854	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
855	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
856	C₂×#41	—	3	1	no	—
857	C₂×#41	—	3	1	no	—
858	C₂×#41	—	3	1	no	—
859	C₂²×D₄	—	3	1	no	—
860	C₂³×C₄	—	3	2	no	—
861	C₄⋊Q₈	—	3	1	no	—
862	C₄⋊Q₈	—	3	1	no	—
863	#126	—	3	2	no	—
864	#126	—	3	2	no	—
865	#126	—	3	2	no	—
866	#126	—	3	2	no	—
867	#126	—	3	2	no	—
868	#126	C₂×C₅×D₃	1	2	yes	complemented
869	#125	—	3	2	no	—
870	#125	—	3	1	no	—
871	#125	—	3	2	no	—
872	#125	C₂×C₅×D₃	1	2	yes	complemented
873	#125	C₂×C₅×D₃	1	1	yes	characteristic, complemented
874	#124	—	3	1	no	—
875	#124	—	3	2	no	—
876	#124	—	3	1	no	—
877	#124	—	3	2	no	—
878	#123	—	3	2	no	—
879	#123	—	3	2	no	—
880	#123	—	3	2	no	—
881	#123	—	3	2	no	—
882	#123	—	3	2	no	—
883	#123	—	3	2	no	—
884	#123	—	3	2	no	—
885	#123	C₂×C₅×D₃	1	2	yes	—
886	C₂²⋊Q₈	—	3	1	no	—
887	C₂²⋊Q₈	—	3	2	no	—
888	C₂²⋊Q₈	—	3	2	no	—
889	C₂²⋊Q₈	—	3	1	no	—
890	C₂²⋊Q₈	—	3	2	no	—
891	C₂²⋊Q₈	—	3	2	no	—
892	C₂²⋊Q₈	—	3	2	no	—
893	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
894	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
895	#121	—	3	1	no	—
896	#121	—	3	2	no	—
897	#121	—	3	1	no	—
898	#121	—	3	2	no	—
899	#121	—	3	2	no	—
900	#121	—	3	2	no	—
901	#120	—	3	2	no	—
902	#120	—	3	2	no	—
903	C₄×Q₈	—	3	1	no	—
904	C₄×Q₈	—	3	1	no	—
905	C₄×Q₈	—	3	1	no	—
906	C₄×Q₈	—	3	1	no	—
907	C₄×Q₈	—	3	2	no	—
908	C₄×Q₈	—	3	1	no	—
909	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
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	—	3	2	no	—
916	C₄×D₄	—	3	1	no	—
917	C₄×D₄	—	3	2	no	—
918	C₄×D₄	—	3	1	no	—
919	C₄×D₄	—	3	2	no	—
920	C₄×D₄	—	3	1	no	—
921	C₄×D₄	—	3	2	no	—
922	C₄×D₄	—	3	2	no	—
923	C₄×D₄	—	3	1	no	—
924	C₄×D₄	—	3	2	no	—
925	C₄×D₄	—	3	1	no	—
926	C₄×D₄	—	3	2	no	—
927	C₄×D₄	—	3	1	no	—
928	C₄×D₄	—	3	2	no	—
929	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
930	#117	—	3	2	no	—
931	#117	—	3	2	no	—
932	#117	—	3	2	no	—
933	#117	—	3	1	no	—
934	#117	—	3	2	no	—
935	#117	—	3	1	no	—
936	#117	—	3	1	no	—
937	#117	—	3	2	no	—
938	#117	—	3	1	no	—
939	#117	—	3	2	no	—
940	#117	—	3	2	no	—
941	#117	—	3	2	no	—
942	#117	C₂×C₅×D₃	1	2	yes	—
943	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
944	C₂×C₄⋊C₄	—	3	2	no	—
945	C₂×C₄⋊C₄	—	3	2	no	—
946	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
947	C₂×C₂²⋊C₄	—	3	2	no	—
948	C₂×C₂²⋊C₄	—	3	2	no	—
949	C₂×C₂²⋊C₄	—	3	2	no	—
950	C₂×C₄²	—	3	1	no	—
951	C₂×C₄²	—	3	1	no	—
952	C₂×C₄²	—	3	2	no	—
953	C₂×C₄²	—	3	2	no	—
954	C₂×C₄²	—	3	1	no	—
955	C₂×C₃×C₅	—	2	2	no	—
956	C₂×C₃×C₅	—	4	1	no	—
957	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
958	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
959	C₂×C₃×C₅	#585	1	1	yes	characteristic
960	C₅×D₃	—	2	4	no	—
961	C₅×D₃	—	4	1	no	—
962	C₅×D₃	—	4	2	no	—
963	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
964	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
965	C₂²×D₃	—	2	4	no	—
966	C₂²×D₃	—	2	4	no	—
967	C₂²×D₃	—	4	2	no	—
968	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
969	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
970	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
971	C₃×Q₈	—	2	2	no	—
972	C₃×D₄	—	2	2	no	—
973	C₂×C₃×C₄	—	2	4	no	—
974	C₂×C₃×C₄	—	2	2	no	—
975	C₂×C₃×C₄	—	2	2	no	—
976	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
977	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
978	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
979	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
980	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
981	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
982	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
983	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
984	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
985	#67	—	2	2	no	—
986	#67	—	2	4	no	—
987	#67	—	2	2	no	—
988	#67	—	4	2	no	—
989	C₂×Dic₃	—	2	2	no	—
990	C₂×Dic₃	—	4	1	no	—
991	C₂×Dic₃	—	4	1	no	—
992	C₂×Dic₃	C₅×#41	1	4	yes	complemented
993	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
994	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
995	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
996	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
997	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
998	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
999	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1000	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1001	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1002	D₁₂	—	2	4	no	—
1003	D₁₂	—	2	4	no	—
1004	D₁₂	—	2	2	no	—
1005	D₁₂	—	4	2	no	—
1006	D₁₂	C₅×#41	1	4	yes	complemented
1007	C₄×D₃	—	2	4	no	—
1008	C₄×D₃	—	2	4	no	—
1009	C₄×D₃	—	2	2	no	—
1010	C₄×D₃	—	2	4	no	—
1011	C₄×D₃	—	2	4	no	—
1012	C₄×D₃	—	2	4	no	—
1013	C₄×D₃	—	2	4	no	—
1014	C₄×D₃	—	2	2	no	—
1015	C₄×D₃	—	4	2	no	—
1016	C₄×D₃	—	4	2	no	—
1017	C₄×D₃	—	4	1	no	—
1018	Dic₆	—	2	2	no	—
1019	Dic₆	—	2	2	no	—
1020	Dic₆	—	4	2	no	—
1021	C₂²×C₅	—	2	1	no	—
1022	C₂²×C₅	—	2	1	no	—
1023	C₂²×C₅	—	2	1	no	—
1024	C₂²×C₅	—	2	1	no	—
1025	C₂²×C₅	—	2	1	no	—
1026	C₂²×C₅	—	3	4	no	—
1027	C₂²×C₅	—	6	2	no	—
1028	C₂²×C₅	—	6	2	no	—
1029	C₂²×C₅	—	6	2	no	—
1030	C₂²×C₅	—	6	1	no	—
1031	C₂²×C₅	—	6	1	no	—
1032	C₂²×C₅	—	6	2	no	—
1033	C₂²×C₅	—	6	1	no	—
1034	C₂²×C₅	—	6	2	no	—
1035	C₂²×C₅	—	12	8	no	—
1036	C₂²×C₅	D₃×#41	1	2	yes	—
1037	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
1038	C₄×C₅	—	2	2	no	—
1039	C₄×C₅	—	2	2	no	—
1040	C₄×C₅	—	2	1	no	—
1041	C₄×C₅	—	2	1	no	—
1042	C₄×C₅	—	2	1	no	—
1043	C₄×C₅	—	2	2	no	—
1044	C₄×C₅	—	2	1	no	—
1045	C₄×C₅	—	2	2	no	—
1046	C₄×C₅	—	3	2	no	—
1047	C₄×C₅	—	3	2	no	—
1048	C₄×C₅	—	6	1	no	—
1049	C₄×C₅	—	6	1	no	—
1050	C₄×C₅	—	6	2	no	—
1051	C₄×C₅	—	6	1	no	—
1052	C₄×C₅	—	6	1	no	—
1053	C₄×C₅	—	6	2	no	—
1054	C₄×C₅	—	6	1	no	—
1055	C₄×C₅	D₃×#41	1	2	yes	—
1056	C₂⁴	—	3	2	no	—
1057	#41	—	6	4	no	—
1058	#41	—	6	4	no	—
1059	#41	—	6	4	no	—
1060	C₂×Q₈	—	3	1	no	—
1061	C₂×Q₈	—	3	1	no	—
1062	C₂×Q₈	—	3	2	no	—
1063	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
1064	C₂×D₄	—	3	1	no	—
1065	C₂×D₄	—	3	2	no	—
1066	C₂×D₄	—	3	1	no	—
1067	C₂×D₄	—	3	2	no	—
1068	C₂×D₄	—	3	1	no	—
1069	C₂×D₄	—	3	2	no	—
1070	C₂×D₄	—	3	2	no	—
1071	C₂×D₄	—	3	1	no	—
1072	C₂×D₄	—	3	2	no	—
1073	C₂×D₄	—	6	4	no	—
1074	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
1075	C₂²×C₄	—	3	1	no	—
1076	C₂²×C₄	—	3	1	no	—
1077	C₂²×C₄	—	3	1	no	—
1078	C₂²×C₄	—	3	1	no	—
1079	C₂²×C₄	—	3	2	no	—
1080	C₂²×C₄	—	3	2	no	—
1081	C₂²×C₄	—	3	2	no	—
1082	C₂²×C₄	—	3	1	no	—
1083	C₂²×C₄	—	3	1	no	—
1084	C₂²×C₄	—	3	2	no	—
1085	C₂²×C₄	—	3	2	no	—
1086	C₂²×C₄	—	3	2	no	—
1087	C₂²×C₄	—	3	2	no	—
1088	C₂²×C₄	—	3	2	no	—
1089	C₂²×C₄	—	3	1	no	—
1090	C₂²×C₄	—	6	8	no	—
1091	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1092	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1093	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
1094	C₄⋊C₄	—	3	1	no	—
1095	C₄⋊C₄	—	3	1	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	1	no	—
1101	C₄⋊C₄	—	3	1	no	—
1102	C₄⋊C₄	—	3	1	no	—
1103	C₄⋊C₄	—	3	2	no	—
1104	C₄⋊C₄	—	3	2	no	—
1105	C₄⋊C₄	—	3	2	no	—
1106	C₄⋊C₄	—	3	1	no	—
1107	C₄⋊C₄	—	3	2	no	—
1108	C₄⋊C₄	—	3	2	no	—
1109	C₄⋊C₄	—	3	2	no	—
1110	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1111	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1112	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1113	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1114	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1115	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1116	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1117	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1118	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1119	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1120	C₂²⋊C₄	—	3	1	no	—
1121	C₂²⋊C₄	—	3	2	no	—
1122	C₂²⋊C₄	—	3	1	no	—
1123	C₂²⋊C₄	—	3	2	no	—
1124	C₂²⋊C₄	—	3	2	no	—
1125	C₂²⋊C₄	—	3	2	no	—
1126	C₂²⋊C₄	—	3	2	no	—
1127	C₂²⋊C₄	—	3	2	no	—
1128	C₂²⋊C₄	—	3	2	no	—
1129	C₂²⋊C₄	—	3	2	no	—
1130	C₂²⋊C₄	—	3	2	no	—
1131	C₂²⋊C₄	—	3	2	no	—
1132	C₂²⋊C₄	—	3	2	no	—
1133	C₂²⋊C₄	—	3	1	no	—
1134	C₂²⋊C₄	—	3	2	no	—
1135	C₂²⋊C₄	—	3	1	no	—
1136	C₂²⋊C₄	—	3	2	no	—
1137	C₂²⋊C₄	—	3	2	no	—
1138	C₂²⋊C₄	—	3	2	no	—
1139	C₂²⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1140	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1141	C₂²⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1142	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1143	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1144	C₄²	—	3	1	no	—
1145	C₄²	—	3	1	no	—
1146	C₄²	—	3	1	no	—
1147	C₄²	—	3	2	no	—
1148	C₄²	—	3	1	no	—
1149	C₄²	—	3	2	no	—
1150	C₄²	—	3	2	no	—
1151	C₄²	—	3	1	no	—
1152	C₄²	—	3	1	no	—
1153	C₄²	—	3	2	no	—
1154	C₄²	—	3	1	no	—
1155	C₄²	—	3	1	no	—
1156	C₄²	—	3	1	no	—
1157	C₄²	C₂²×C₅×D₃	1	2	yes	—
1158	C₄²	C₂²×C₅×D₃	1	2	yes	—
1159	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
1160	C₃×C₅	#3475	1	1	yes	characteristic, complemented, Hall
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	—	2	1	no	—
1166	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
1167	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1168	C₂×D₃	—	2	2	no	—
1169	C₂×D₃	—	2	2	no	—
1170	C₂×D₃	—	2	2	no	—
1171	C₂×D₃	—	2	1	no	—
1172	C₂×D₃	—	2	1	no	—
1173	C₂×D₃	—	2	2	no	—
1174	C₂×D₃	—	2	1	no	—
1175	C₂×D₃	—	2	2	no	—
1176	C₂×D₃	—	4	8	no	—
1177	C₂×D₃	C₂×C₅×#41	1	4	yes	—
1178	C₃×C₄	—	2	1	no	—
1179	C₃×C₄	—	2	1	no	—
1180	C₃×C₄	—	2	2	no	—
1181	C₃×C₄	—	2	2	no	—
1182	C₃×C₄	—	2	2	no	—
1183	C₃×C₄	—	2	1	no	—
1184	C₃×C₄	—	2	2	no	—
1185	C₃×C₄	—	2	1	no	—
1186	C₃×C₄	C₂×C₅×#41	1	2	yes	—
1187	Dic₃	—	2	2	no	—
1188	Dic₃	—	2	1	no	—
1189	Dic₃	—	2	1	no	—
1190	Dic₃	—	2	1	no	—
1191	Dic₃	—	2	2	no	—
1192	Dic₃	—	2	1	no	—
1193	Dic₃	—	2	1	no	—
1194	Dic₃	C₂×C₅×#41	1	2	yes	—
1195	Dic₃	C₂×C₅×#41	1	2	yes	—
1196	C₂×C₅	—	2	2	no	—
1197	C₂×C₅	—	4	1	no	—
1198	C₂×C₅	—	6	4	no	—
1199	C₂×C₅	—	12	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	#5968	1	1	yes	characteristic
1204	C₂³	—	3	2	no	—
1205	C₂³	—	3	2	no	—
1206	C₂³	—	3	1	no	—
1207	C₂³	—	6	4	no	—
1208	C₂³	—	6	4	no	—
1209	C₂³	—	12	2	no	—
1210	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1211	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1212	Q₈	—	2	2	no	—
1213	Q₈	—	6	2	no	—
1214	Q₈	—	6	2	no	—
1215	Q₈	—	12	2	no	—
1216	D₄	—	2	2	no	—
1217	D₄	—	3	4	no	—
1218	D₄	—	6	4	no	—
1219	D₄	—	6	4	no	—
1220	D₄	—	6	2	no	—
1221	D₄	—	6	4	no	—
1222	D₄	—	6	2	no	—
1223	D₄	—	6	2	no	—
1224	D₄	—	12	2	no	—
1225	D₄	—	12	2	no	—
1226	C₂×C₄	—	2	4	no	—
1227	C₂×C₄	—	2	2	no	—
1228	C₂×C₄	—	2	2	no	—
1229	C₂×C₄	—	3	4	no	—
1230	C₂×C₄	—	3	1	no	—
1231	C₂×C₄	—	3	1	no	—
1232	C₂×C₄	—	3	1	no	—
1233	C₂×C₄	—	3	1	no	—
1234	C₂×C₄	—	3	1	no	—
1235	C₂×C₄	—	3	1	no	—
1236	C₂×C₄	—	3	2	no	—
1237	C₂×C₄	—	3	1	no	—
1238	C₂×C₄	—	3	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	4	no	—
1246	C₂×C₄	—	6	2	no	—
1247	C₂×C₄	—	6	2	no	—
1248	C₂×C₄	—	12	1	no	—
1249	C₂×C₄	—	12	2	no	—
1250	C₂×C₄	—	12	2	no	—
1251	C₂×C₄	—	12	1	no	—
1252	C₂×C₄	—	12	1	no	—
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	1	yes	characteristic
1256	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1257	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1258	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1259	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1260	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1261	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1262	C₂×C₃	—	2	2	no	—
1263	C₂×C₃	—	4	1	no	—
1264	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
1265	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
1266	C₂×C₃	C₅×#585	1	1	yes	characteristic
1267	D₃	—	2	4	no	—
1268	D₃	—	4	2	no	—
1269	D₃	—	4	1	no	—
1270	C₅	#86826	1	1	yes	characteristic, direct product factor, Sylow
1271	C₂²	—	2	1	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	1	no	—
1275	C₂²	—	2	1	no	—
1276	C₂²	—	3	4	no	—
1277	C₂²	—	6	2	no	—
1278	C₂²	—	6	2	no	—
1279	C₂²	—	6	2	no	—
1280	C₂²	—	6	1	no	—
1281	C₂²	—	6	1	no	—
1282	C₂²	—	6	2	no	—
1283	C₂²	—	6	1	no	—
1284	C₂²	—	6	2	no	—
1285	C₂²	—	12	8	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	—	3	2	no	—
1298	C₄	—	6	1	no	—
1299	C₄	—	6	1	no	—
1300	C₄	—	6	2	no	—
1301	C₄	—	6	1	no	—
1302	C₄	—	6	1	no	—
1303	C₄	—	6	2	no	—
1304	C₄	—	6	1	no	—
1305	C₄	C₅×D₃×#41	1	2	yes	—
1306	C₃	C₅×#3475	1	1	yes	characteristic, complemented, Sylow
1307	C₂	—	2	2	no	—
1308	C₂	—	4	1	no	—
1309	C₂	—	6	4	no	—
1310	C₂	—	12	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×#5968	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
hypercenter	C₅×#552	D₃
hypocenter	C₃	C₅×#3475
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×#5709	C₂	semidirect
3. C₅×#5706	C₂	semidirect
4. C₅×#5693	C₂	semidirect
5. C₅×#5691	C₂	semidirect
6. C₅×#5691	C₂	semidirect
7. C₅×#5690	C₂	semidirect
8. C₅×#5658	C₂	semidirect
9. C₅×#5656	C₂	semidirect
10. C₅×#5631	C₂	semidirect
11. C₅×#5630	C₂	semidirect
12. C₅×#5624	C₂	semidirect
13. C₅×#5622	C₂	semidirect
14. C₄×C₅×#239	C₂	semidirect
15. C₅×#5568	C₂	semidirect
16. C₅×#5550	C₂	semidirect
17. C₄×C₅×#237	C₂	semidirect
18. C₅×#5532	C₂	semidirect
19. C₅×#5527	C₂	semidirect
20. C₅×#5522	C₂	semidirect
21. C₅×D₃×#117	C₂	semidirect
22. C₅×#5513	C₂	semidirect
23. C₂×C₅×#893	C₂	semidirect
30. C₃×C₅×#126	C₂²	semidirect
31. C₃×C₅×#125	C₂²	semidirect
32. C₃×C₅×#125	C₂²	semidirect
35. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
36. C₃×C₄×C₅×Q₈	C₂²	semidirect
39. C₃×C₅×#117	C₂²	semidirect
42. C₅×Q₈×Dic₃	C₂²	semidirect
43. C₅×#944	C₂²	semidirect
49. C₄×C₅×#67	C₂²	semidirect
54. C₂×C₄×C₅×Dic₃	C₂²	semidirect
55. C₅×#898	C₂²	semidirect
56. C₅×#898	C₂²	semidirect
57. C₅×#898	C₂²	semidirect
58. C₅×#898	C₂²	semidirect
59. C₅×#897	C₂²	semidirect
60. C₅×#897	C₂²	semidirect
61. C₅×#896	C₂²	semidirect
62. C₅×#896	C₂²	semidirect
63. C₅×#896	C₂²	semidirect
68. C₅×#894	C₂²	semidirect
69. C₅×#894	C₂²	semidirect
77. C₅×#893	C₂²	semidirect
78. C₅×#893	C₂²	semidirect
79. C₅×#892	C₂²	semidirect
80. C₅×#892	C₂²	semidirect
81. C₅×#892	C₂²	semidirect
82. C₅×#892	C₂²	semidirect
83. C₅×#892	C₂²	semidirect
84. C₅×D₃×C₄⋊C₄	C₂²	semidirect
85. C₅×D₃×C₄⋊C₄	C₂²	semidirect
86. C₅×#890	C₂²	semidirect
87. C₅×#889	C₂²	semidirect
88. C₅×#889	C₂²	semidirect
89. C₅×#888	C₂²	semidirect
90. C₅×#887	C₂²	semidirect
91. C₅×#887	C₂²	semidirect
92. C₅×#887	C₂²	semidirect
93. C₅×#887	C₂²	semidirect
94. C₅×#886	C₂²	semidirect
95. C₅×#885	C₂²	semidirect
97. C₅×#884	C₂²	semidirect
98. C₅×#884	C₂²	semidirect
99. C₅×#883	C₂²	semidirect
102. C₅×#67⋊C₄	C₂²	semidirect
103. C₅×#67⋊C₄	C₂²	semidirect
104. C₅×#67⋊C₄	C₂²	semidirect
105. C₅×#67⋊C₄	C₂²	semidirect
111. C₅×#877	C₂²	semidirect
112. C₅×#876	C₂²	semidirect
114. C₅×#875	C₂²	semidirect
116. C₄×C₅×D₁₂	C₂²	semidirect
117. C₅×#872	C₂²	semidirect
118. C₅×#872	C₂²	semidirect
119. C₅×#872	C₂²	semidirect
120. C₄²×C₅×D₃	C₂²	semidirect
121. C₄²×C₅×D₃	C₂²	semidirect
122. C₄²×C₅×D₃	C₂²	semidirect
123. C₄×C₅×Dic₆	C₂²	semidirect
124. #86826	C₅	direct (N × H)
131. C₅×#552	D₃	semidirect
252. C₃×#552	C₂×C₅	semidirect
253. #5709	C₂×C₅	semidirect
254. #5706	C₂×C₅	semidirect
255. #5693	C₂×C₅	semidirect
256. #5691	C₂×C₅	semidirect
257. #5691	C₂×C₅	semidirect
258. #5690	C₂×C₅	semidirect
259. #5658	C₂×C₅	semidirect
260. #5656	C₂×C₅	semidirect
261. #5631	C₂×C₅	semidirect
262. #5630	C₂×C₅	semidirect
263. #5624	C₂×C₅	semidirect
264. #5622	C₂×C₅	semidirect
265. C₄×#239	C₂×C₅	semidirect
266. #5568	C₂×C₅	semidirect
267. #5550	C₂×C₅	semidirect
268. C₄×#237	C₂×C₅	semidirect
269. #5532	C₂×C₅	semidirect
270. #5527	C₂×C₅	semidirect
271. #5522	C₂×C₅	semidirect
272. D₃×#117	C₂×C₅	semidirect
273. #5513	C₂×C₅	semidirect
274. C₂×#893	C₂×C₅	semidirect
287. C₅×#126	C₂×D₃	semidirect
291. C₅×#125	C₂×D₃	semidirect
292. C₅×#125	C₂×D₃	semidirect
313. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
328. C₄×C₅×Q₈	C₂×D₃	semidirect
362. C₅×#117	C₂×D₃	semidirect
404. C₂×C₅×Dic₃	#41	semidirect
418. C₅×D₁₂	#41	semidirect
438. C₃×#126	C₂²×C₅	semidirect
439. C₃×#125	C₂²×C₅	semidirect
440. C₃×#125	C₂²×C₅	semidirect
443. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
444. C₃×C₄×Q₈	C₂²×C₅	semidirect
447. C₃×#117	C₂²×C₅	semidirect
450. Q₈×Dic₃	C₂²×C₅	semidirect
451. #944	C₂²×C₅	semidirect
457. C₄×#67	C₂²×C₅	semidirect
462. C₂×C₄×Dic₃	C₂²×C₅	semidirect
463. #898	C₂²×C₅	semidirect
464. #898	C₂²×C₅	semidirect
465. #898	C₂²×C₅	semidirect
466. #898	C₂²×C₅	semidirect
467. #897	C₂²×C₅	semidirect
468. #897	C₂²×C₅	semidirect
469. #896	C₂²×C₅	semidirect
470. #896	C₂²×C₅	semidirect
471. #896	C₂²×C₅	semidirect
476. #894	C₂²×C₅	semidirect
477. #894	C₂²×C₅	semidirect
485. #893	C₂²×C₅	semidirect
486. #893	C₂²×C₅	semidirect
487. #892	C₂²×C₅	semidirect
488. #892	C₂²×C₅	semidirect
489. #892	C₂²×C₅	semidirect
490. #892	C₂²×C₅	semidirect
491. #892	C₂²×C₅	semidirect
492. D₃×C₄⋊C₄	C₂²×C₅	semidirect
493. D₃×C₄⋊C₄	C₂²×C₅	semidirect
494. #890	C₂²×C₅	semidirect
495. #889	C₂²×C₅	semidirect
496. #889	C₂²×C₅	semidirect
497. #888	C₂²×C₅	semidirect
498. #887	C₂²×C₅	semidirect
499. #887	C₂²×C₅	semidirect
500. #887	C₂²×C₅	semidirect
501. #887	C₂²×C₅	semidirect
502. #886	C₂²×C₅	semidirect
503. #885	C₂²×C₅	semidirect
505. #884	C₂²×C₅	semidirect
506. #884	C₂²×C₅	semidirect
507. #883	C₂²×C₅	semidirect
510. #67⋊C₄	C₂²×C₅	semidirect
511. #67⋊C₄	C₂²×C₅	semidirect
512. #67⋊C₄	C₂²×C₅	semidirect
513. #67⋊C₄	C₂²×C₅	semidirect
519. #877	C₂²×C₅	semidirect
520. #876	C₂²×C₅	semidirect
522. #875	C₂²×C₅	semidirect
524. C₄×D₁₂	C₂²×C₅	semidirect
525. #872	C₂²×C₅	semidirect
526. #872	C₂²×C₅	semidirect
527. #872	C₂²×C₅	semidirect
528. C₄²×D₃	C₂²×C₅	semidirect
529. C₄²×D₃	C₂²×C₅	semidirect
530. C₄²×D₃	C₂²×C₅	semidirect
531. C₄×Dic₆	C₂²×C₅	semidirect
642. #552	C₅×D₃	semidirect
868. #126	C₂×C₅×D₃	semidirect
872. #125	C₂×C₅×D₃	semidirect
873. #125	C₂×C₅×D₃	semidirect
894. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
909. C₄×Q₈	C₂×C₅×D₃	semidirect
943. #117	C₂×C₅×D₃	semidirect
992. C₂×Dic₃	C₅×#41	semidirect
1006. D₁₂	C₅×#41	semidirect
1160. C₃×C₅	#3475	semidirect
1270. C₅	#86826	direct (N × H)
1306. C₃	C₅×#3475	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×#5709	2
C₅×#5706	2
C₅×#5693	2
C₅×#5691	2
C₅×#5690	2
C₅×#5658	2
C₅×#5656	2
C₅×#5631	2
C₅×#5630	2
C₅×#5624	2
C₅×#5622	2
C₄×C₅×#239	2
C₅×#5568	2
C₅×#5550	2
C₄×C₅×#237	2
C₅×#5532	2
C₅×#5527	2
C₅×#5522	2
C₅×D₃×#117	2
C₅×#5513	2
C₂×C₅×#893	2
C₅×#3475	3
#86826	5

Subgroups — C5×#86826 #14484150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#86826 #14484150