Subgroups — C₅×#85744 #14484117

Order 1920.

2264 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5791	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5533	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5532	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5531	C₂	1	2	yes	maximal, complemented
7	C₅×#5530	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5529	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5528	C₂	1	2	yes	maximal, complemented
10	C₅×#5528	C₂	1	2	yes	maximal, complemented
11	C₅×#5527	C₂	1	2	yes	maximal, complemented
12	C₅×#5524	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5522	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#5517	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#5514	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#5513	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#5511	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅×#5507	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#5495	C₂	1	2	yes	maximal, complemented
21	C₅×#5490	C₂	1	2	yes	maximal, complemented
22	C₅×#5479	C₂	1	2	yes	maximal, complemented
23	C₄×C₅×#235	C₂	1	2	yes	maximal, complemented
24	C₅×#3475	—	3	1	no	maximal, Hall
25	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
26	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
27	C₂×C₅×#235	C₂²	1	2	yes	—
28	C₂×C₅×#235	C₂²	1	1	yes	characteristic
29	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
30	C₃×C₅×#117	C₂²	1	1	yes	characteristic
31	C₃×C₅×#117	C₂²	1	1	yes	characteristic
32	C₃×C₅×#117	C₂²	1	2	yes	—
33	C₃×C₅×#117	C₂²	1	2	yes	complemented
34	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
40	C₅×#953	C₂²	1	2	yes	—
41	C₂×C₅×#217	C₂²	1	1	yes	characteristic
42	C₅×#930	C₂²	1	2	yes	—
43	C₅×#930	C₂²	1	1	yes	characteristic, complemented
44	C₅×#930	C₂²	1	1	yes	characteristic, complemented
45	C₅×#929	C₂²	1	2	yes	—
46	C₅×#929	C₂²	1	2	yes	—
47	C₅×#929	C₂²	1	2	yes	complemented
48	C₄×C₅×#67	C₂²	1	1	yes	characteristic
49	C₄×C₅×#67	C₂²	1	2	yes	—
50	C₄×C₅×#67	C₂²	1	1	yes	characteristic
51	C₄×C₅×#67	C₂²	1	1	yes	characteristic
52	C₄×C₅×#67	C₂²	1	1	yes	characteristic
53	C₄×C₅×#67	C₂²	1	1	yes	characteristic
54	C₄×C₅×#67	C₂²	1	1	yes	characteristic
55	C₄×C₅×#67	C₂²	1	1	yes	characteristic
56	C₄×C₅×#67	C₂²	1	1	yes	characteristic
57	C₄×C₅×#67	C₂²	1	2	yes	complemented
58	C₄×C₅×#67	C₂²	1	2	yes	complemented
59	C₄×C₅×#67	C₂²	1	2	yes	complemented
60	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
61	C₅×#926	C₂²	1	1	yes	characteristic
62	C₅×#926	C₂²	1	2	yes	complemented
63	C₅×#924	C₂²	1	2	yes	complemented
64	C₅×#924	C₂²	1	1	yes	characteristic, complemented
65	C₅×#924	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
67	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
68	C₅×#898	C₂²	1	2	yes	complemented
69	C₅×#898	C₂²	1	2	yes	complemented
70	C₅×#897	C₂²	1	1	yes	characteristic, complemented
71	C₅×#897	C₂²	1	1	yes	characteristic, complemented
72	C₅×#896	C₂²	1	2	yes	complemented
73	C₅×#896	C₂²	1	2	yes	complemented
74	C₅×#895	C₂²	1	1	yes	characteristic, complemented
75	C₅×#895	C₂²	1	1	yes	characteristic, complemented
76	C₅×#894	C₂²	1	2	yes	complemented
77	C₅×#894	C₂²	1	2	yes	complemented
78	C₅×#893	C₂²	1	1	yes	characteristic, complemented
79	C₅×#893	C₂²	1	1	yes	characteristic, complemented
80	C₅×#892	C₂²	1	1	yes	characteristic, complemented
81	C₅×#892	C₂²	1	1	yes	characteristic, complemented
82	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
83	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, 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×#888	C₂²	1	1	yes	characteristic, complemented
89	C₅×#888	C₂²	1	1	yes	characteristic, complemented
90	C₅×#887	C₂²	1	1	yes	characteristic, complemented
91	C₅×#887	C₂²	1	1	yes	characteristic, complemented
92	C₅×#886	C₂²	1	2	yes	—
93	C₅×#885	C₂²	1	2	yes	—
94	C₅×#885	C₂²	1	2	yes	complemented
95	C₅×#884	C₂²	1	2	yes	—
96	C₅×#884	C₂²	1	2	yes	—
97	C₅×#883	C₂²	1	2	yes	—
98	C₅×#883	C₂²	1	2	yes	complemented
99	C₅×#882	C₂²	1	2	yes	—
100	C₅×#67⋊C₄	C₂²	1	2	yes	—
101	C₅×#67⋊C₄	C₂²	1	2	yes	—
102	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₅×#879	C₂²	1	2	yes	complemented
104	C₅×#879	C₂²	1	2	yes	complemented
105	C₅×#878	C₂²	1	2	yes	—
106	C₅×#878	C₂²	1	2	yes	—
107	C₅×#877	C₂²	1	2	yes	—
108	C₅×#876	C₂²	1	2	yes	complemented
109	C₅×#876	C₂²	1	2	yes	complemented
110	C₅×#875	C₂²	1	2	yes	complemented
111	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
112	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
113	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
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	C₅×#872	C₂²	1	2	yes	complemented
118	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
119	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
120	C₅×#870	C₂²	1	2	yes	complemented
121	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
122	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
123	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
124	#85744	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	1	no	—
129	C₅×#553	—	3	1	no	—
130	C₅×#552	—	3	2	no	—
131	C₅×#552	—	3	1	no	—
132	C₅×#552	—	3	1	no	—
133	C₅×#551	—	3	2	no	—
134	C₅×#551	—	3	2	no	—
135	C₅×#547	—	3	1	no	—
136	C₅×#546	—	3	2	no	—
137	C₅×#533	—	3	1	no	—
138	C₅×#529	—	3	2	no	—
139	C₅×#529	—	3	2	no	—
140	C₅×#529	—	3	2	no	—
141	C₅×#525	—	3	1	no	—
142	C₅×#525	—	3	1	no	—
143	C₄×C₅×#41	—	3	1	no	—
144	C₄×C₅×#41	—	3	2	no	—
145	C₂×C₄×C₅×D₄	—	3	1	no	—
146	C₂×C₅×#117	—	3	1	no	—
147	C₂×C₅×#117	D₃	1	1	yes	characteristic, complemented
148	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
149	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
150	C₂²×C₃×C₄×C₅	—	2	4	no	—
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	1	yes	characteristic
154	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
155	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
156	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
157	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
158	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
159	C₂×C₅×#67	—	2	4	no	—
160	C₂×C₅×#67	C₂³	1	2	yes	—
161	C₂×C₅×#67	C₂³	1	1	yes	characteristic
162	C₂×C₅×#67	C₂³	1	1	yes	characteristic
163	C₂×C₅×#67	C₂³	1	1	yes	characteristic
164	C₂×C₅×#67	C₂³	1	2	yes	—
165	C₂×C₅×#67	C₂³	1	2	yes	—
166	C₂×C₅×#67	C₂³	1	1	yes	characteristic
167	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
168	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
169	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
170	C₅×#235	—	2	4	no	—
171	C₅×#235	—	2	8	no	—
172	C₂×C₅×D₁₂	C₂³	1	2	yes	—
173	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
174	C₂×C₅×D₁₂	C₂³	1	2	yes	—
175	C₂×C₄×C₅×D₃	—	2	4	no	—
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	1	yes	characteristic
181	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
182	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
183	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
184	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
185	C₂×C₅×Dic₆	C₂³	1	2	yes	—
186	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
187	C₂×C₅×Dic₆	C₂³	1	2	yes	—
188	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₄²×C₅	C₂³	1	2	yes	—
199	C₃×C₄²×C₅	C₂³	1	2	yes	—
200	C₃×C₄²×C₅	C₂³	1	2	yes	—
201	C₃×C₄²×C₅	C₂³	1	2	yes	—
202	C₅×#217	C₂³	1	2	yes	—
203	C₅×#217	C₂³	1	2	yes	—
204	C₅×#217	C₂³	1	1	yes	characteristic
205	C₅×#217	C₂³	1	1	yes	characteristic
206	C₅×#217	C₂³	1	2	yes	—
207	C₅×#217	C₂³	1	1	yes	characteristic
208	C₅×#217	C₂³	1	1	yes	characteristic
209	C₅×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
221	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
222	C₅×(C₂×D₃)⋊C₄	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×C₄⋊Dic₃	C₂³	1	2	yes	—
227	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
228	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
241	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
242	C₅×Dic₃⋊C₄	C₂³	1	1	yes	characteristic
243	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
244	C₄×C₅×Dic₃	C₂³	1	2	yes	—
245	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
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	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
253	#5791	C₂×C₅	1	1	yes	characteristic, complemented
254	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
255	#5533	C₂×C₅	1	1	yes	characteristic, complemented
256	#5532	C₂×C₅	1	1	yes	characteristic, complemented
257	#5531	C₂×C₅	1	2	yes	complemented
258	#5530	C₂×C₅	1	1	yes	characteristic, complemented
259	#5529	C₂×C₅	1	1	yes	characteristic, complemented
260	#5528	C₂×C₅	1	2	yes	complemented
261	#5528	C₂×C₅	1	2	yes	complemented
262	#5527	C₂×C₅	1	2	yes	complemented
263	#5524	C₂×C₅	1	1	yes	characteristic, complemented
264	#5522	C₂×C₅	1	1	yes	characteristic, complemented
265	D₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
266	#5517	C₂×C₅	1	1	yes	characteristic, complemented
267	#5514	C₂×C₅	1	1	yes	characteristic, complemented
268	#5513	C₂×C₅	1	1	yes	characteristic, complemented
269	#5511	C₂×C₅	1	1	yes	characteristic, complemented
270	#5507	C₂×C₅	1	1	yes	characteristic, complemented
271	#5495	C₂×C₅	1	2	yes	complemented
272	#5490	C₂×C₅	1	2	yes	complemented
273	#5479	C₂×C₅	1	2	yes	complemented
274	C₄×#235	C₂×C₅	1	2	yes	complemented
275	C₂×C₅×#41	—	3	1	no	—
276	C₂×C₅×#41	—	3	2	no	—
277	C₂²×C₅×D₄	—	3	1	no	—
278	C₂³×C₄×C₅	—	3	1	no	—
279	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
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	—	3	2	no	—
288	C₅×#125	—	3	2	no	—
289	C₅×#125	—	3	2	no	—
290	C₅×#125	—	3	1	no	—
291	C₅×#125	—	3	1	no	—
292	C₅×#125	—	3	2	no	—
293	C₅×#124	—	3	2	no	—
294	C₅×#124	—	3	2	no	—
295	C₅×#124	—	3	2	no	—
296	C₅×#123	—	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×C₂²⋊Q₈	—	3	1	no	—
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	1	no	—
311	C₅×C₂²⋊Q₈	—	3	2	no	—
312	C₅×C₂²⋊Q₈	—	3	2	no	—
313	C₅×#121	—	3	2	no	—
314	C₅×#121	—	3	1	no	—
315	C₅×#121	—	3	1	no	—
316	C₅×#121	—	3	1	no	—
317	C₅×#121	—	3	1	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	2	no	—
325	C₄×C₅×Q₈	—	3	2	no	—
326	C₄×C₅×Q₈	—	3	2	no	—
327	C₄×C₅×D₄	—	3	1	no	—
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	—	3	2	no	—
336	C₄×C₅×D₄	—	3	2	no	—
337	C₄×C₅×D₄	—	3	2	no	—
338	C₄×C₅×D₄	—	3	2	no	—
339	C₄×C₅×D₄	—	3	1	no	—
340	C₄×C₅×D₄	—	3	1	no	—
341	C₄×C₅×D₄	—	3	2	no	—
342	C₄×C₅×D₄	—	3	2	no	—
343	C₄×C₅×D₄	—	3	2	no	—
344	C₄×C₅×D₄	—	3	2	no	—
345	C₄×C₅×D₄	—	3	2	no	—
346	C₅×#117	—	3	1	no	—
347	C₅×#117	—	3	2	no	—
348	C₅×#117	—	3	1	no	—
349	C₅×#117	—	3	1	no	—
350	C₅×#117	—	3	2	no	—
351	C₅×#117	—	3	2	no	—
352	C₅×#117	—	3	2	no	—
353	C₅×#117	—	3	2	no	—
354	C₅×#117	—	3	2	no	—
355	C₅×#117	C₂×D₃	1	1	yes	characteristic
356	C₅×#117	C₂×D₃	1	1	yes	characteristic
357	C₅×#117	C₂×D₃	1	2	yes	—
358	C₅×#117	C₂×D₃	1	2	yes	complemented
359	C₅×#117	C₂×D₃	1	1	yes	characteristic, complemented
360	C₅×#117	C₂×D₃	1	1	yes	characteristic, complemented
361	C₂×C₅×C₄⋊C₄	—	3	1	no	—
362	C₂×C₅×C₄⋊C₄	—	3	1	no	—
363	C₂×C₅×C₄⋊C₄	—	3	1	no	—
364	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
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	1	no	—
368	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
369	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
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	C₂×D₃	1	2	yes	complemented
374	#3475	—	3	1	no	Sylow
375	C₂³×C₃×C₅	—	2	2	no	—
376	C₂³×C₃×C₅	—	2	2	no	—
377	C₂³×C₃×C₅	—	4	1	no	—
378	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
379	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
380	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
381	C₂²×C₅×D₃	—	2	2	no	—
382	C₂²×C₅×D₃	—	2	2	no	—
383	C₂²×C₅×D₃	—	4	1	no	—
384	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
386	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₃×C₄×C₅	—	2	4	no	—
388	C₂×C₃×C₄×C₅	—	2	2	no	—
389	C₂×C₃×C₄×C₅	—	2	2	no	—
390	C₂×C₃×C₄×C₅	—	2	2	no	—
391	C₂×C₃×C₄×C₅	—	2	2	no	—
392	C₂×C₃×C₄×C₅	—	2	2	no	—
393	C₂×C₃×C₄×C₅	—	4	2	no	—
394	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
395	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
396	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
397	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
398	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
399	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
400	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
401	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
402	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
403	C₅×#67	—	2	4	no	—
404	C₅×#67	—	2	4	no	—
405	C₅×#67	—	2	2	no	—
406	C₅×#67	—	2	2	no	—
407	C₅×#67	—	2	2	no	—
408	C₅×#67	—	4	2	no	—
409	C₅×#67	#41	1	4	yes	complemented
410	C₂×C₅×Dic₃	—	2	2	no	—
411	C₂×C₅×Dic₃	—	2	2	no	—
412	C₂×C₅×Dic₃	—	4	1	no	—
413	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
414	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
415	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
417	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
418	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
419	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
420	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
421	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
422	C₅×D₁₂	—	2	4	no	—
423	C₅×D₁₂	—	2	2	no	—
424	C₅×D₁₂	—	4	2	no	—
425	C₄×C₅×D₃	—	2	4	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	—	2	2	no	—
430	C₄×C₅×D₃	—	2	4	no	—
431	C₄×C₅×D₃	—	2	4	no	—
432	C₄×C₅×D₃	—	4	2	no	—
433	C₄×C₅×D₃	—	4	2	no	—
434	C₅×Dic₆	—	2	2	no	—
435	C₅×Dic₆	—	2	4	no	—
436	C₅×Dic₆	—	4	2	no	—
437	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
438	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
439	C₂×#235	C₂²×C₅	1	2	yes	—
440	C₂×#235	C₂²×C₅	1	1	yes	characteristic
441	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
442	C₃×#117	C₂²×C₅	1	1	yes	characteristic
443	C₃×#117	C₂²×C₅	1	1	yes	characteristic
444	C₃×#117	C₂²×C₅	1	2	yes	—
445	C₃×#117	C₂²×C₅	1	2	yes	complemented
446	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
447	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
448	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
449	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
450	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
451	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
452	#953	C₂²×C₅	1	2	yes	—
453	C₂×#217	C₂²×C₅	1	1	yes	characteristic
454	#930	C₂²×C₅	1	2	yes	—
455	#930	C₂²×C₅	1	1	yes	characteristic, complemented
456	#930	C₂²×C₅	1	1	yes	characteristic, complemented
457	#929	C₂²×C₅	1	2	yes	—
458	#929	C₂²×C₅	1	2	yes	—
459	#929	C₂²×C₅	1	2	yes	complemented
460	C₄×#67	C₂²×C₅	1	1	yes	characteristic
461	C₄×#67	C₂²×C₅	1	2	yes	—
462	C₄×#67	C₂²×C₅	1	1	yes	characteristic
463	C₄×#67	C₂²×C₅	1	1	yes	characteristic
464	C₄×#67	C₂²×C₅	1	1	yes	characteristic
465	C₄×#67	C₂²×C₅	1	1	yes	characteristic
466	C₄×#67	C₂²×C₅	1	1	yes	characteristic
467	C₄×#67	C₂²×C₅	1	1	yes	characteristic
468	C₄×#67	C₂²×C₅	1	1	yes	characteristic
469	C₄×#67	C₂²×C₅	1	2	yes	complemented
470	C₄×#67	C₂²×C₅	1	2	yes	complemented
471	C₄×#67	C₂²×C₅	1	2	yes	complemented
472	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
473	#926	C₂²×C₅	1	1	yes	characteristic
474	#926	C₂²×C₅	1	2	yes	complemented
475	#924	C₂²×C₅	1	2	yes	complemented
476	#924	C₂²×C₅	1	1	yes	characteristic, complemented
477	#924	C₂²×C₅	1	1	yes	characteristic, complemented
478	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
479	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
480	#898	C₂²×C₅	1	2	yes	complemented
481	#898	C₂²×C₅	1	2	yes	complemented
482	#897	C₂²×C₅	1	1	yes	characteristic, complemented
483	#897	C₂²×C₅	1	1	yes	characteristic, complemented
484	#896	C₂²×C₅	1	2	yes	complemented
485	#896	C₂²×C₅	1	2	yes	complemented
486	#895	C₂²×C₅	1	1	yes	characteristic, complemented
487	#895	C₂²×C₅	1	1	yes	characteristic, complemented
488	#894	C₂²×C₅	1	2	yes	complemented
489	#894	C₂²×C₅	1	2	yes	complemented
490	#893	C₂²×C₅	1	1	yes	characteristic, complemented
491	#893	C₂²×C₅	1	1	yes	characteristic, complemented
492	#892	C₂²×C₅	1	1	yes	characteristic, complemented
493	#892	C₂²×C₅	1	1	yes	characteristic, complemented
494	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
495	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
496	#890	C₂²×C₅	1	1	yes	characteristic, complemented
497	#890	C₂²×C₅	1	1	yes	characteristic, complemented
498	#889	C₂²×C₅	1	2	yes	complemented
499	#889	C₂²×C₅	1	2	yes	complemented
500	#888	C₂²×C₅	1	1	yes	characteristic, complemented
501	#888	C₂²×C₅	1	1	yes	characteristic, complemented
502	#887	C₂²×C₅	1	1	yes	characteristic, complemented
503	#887	C₂²×C₅	1	1	yes	characteristic, complemented
504	#886	C₂²×C₅	1	2	yes	—
505	#885	C₂²×C₅	1	2	yes	—
506	#885	C₂²×C₅	1	2	yes	complemented
507	#884	C₂²×C₅	1	2	yes	—
508	#884	C₂²×C₅	1	2	yes	—
509	#883	C₂²×C₅	1	2	yes	—
510	#883	C₂²×C₅	1	2	yes	complemented
511	#882	C₂²×C₅	1	2	yes	—
512	#67⋊C₄	C₂²×C₅	1	2	yes	—
513	#67⋊C₄	C₂²×C₅	1	2	yes	—
514	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
515	#879	C₂²×C₅	1	2	yes	complemented
516	#879	C₂²×C₅	1	2	yes	complemented
517	#878	C₂²×C₅	1	2	yes	—
518	#878	C₂²×C₅	1	2	yes	—
519	#877	C₂²×C₅	1	2	yes	—
520	#876	C₂²×C₅	1	2	yes	complemented
521	#876	C₂²×C₅	1	2	yes	complemented
522	#875	C₂²×C₅	1	2	yes	complemented
523	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
524	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
525	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
526	#872	C₂²×C₅	1	2	yes	complemented
527	#872	C₂²×C₅	1	2	yes	complemented
528	#872	C₂²×C₅	1	2	yes	complemented
529	#872	C₂²×C₅	1	2	yes	complemented
530	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
531	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
532	#870	C₂²×C₅	1	2	yes	complemented
533	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
534	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
535	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
536	C₂⁴×C₅	—	3	1	no	—
537	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
538	C₅×#41	—	6	8	no	—
539	C₅×#41	—	6	4	no	—
540	C₂×C₅×Q₈	—	3	1	no	—
541	C₂×C₅×Q₈	—	3	2	no	—
542	C₂×C₅×Q₈	—	3	2	no	—
543	C₂×C₅×D₄	—	3	1	no	—
544	C₂×C₅×D₄	—	3	2	no	—
545	C₂×C₅×D₄	—	3	2	no	—
546	C₂×C₅×D₄	—	3	1	no	—
547	C₂×C₅×D₄	—	3	1	no	—
548	C₂×C₅×D₄	—	3	1	no	—
549	C₂×C₅×D₄	—	3	2	no	—
550	C₂×C₅×D₄	—	3	2	no	—
551	C₂×C₅×D₄	—	3	1	no	—
552	C₂×C₅×D₄	—	3	2	no	—
553	C₂×C₅×D₄	—	6	4	no	—
554	C₂²×C₄×C₅	—	2	4	no	—
555	C₂²×C₄×C₅	—	3	1	no	—
556	C₂²×C₄×C₅	—	3	1	no	—
557	C₂²×C₄×C₅	—	3	1	no	—
558	C₂²×C₄×C₅	—	3	2	no	—
559	C₂²×C₄×C₅	—	3	2	no	—
560	C₂²×C₄×C₅	—	3	1	no	—
561	C₂²×C₄×C₅	—	3	1	no	—
562	C₂²×C₄×C₅	—	3	1	no	—
563	C₂²×C₄×C₅	—	3	2	no	—
564	C₂²×C₄×C₅	—	3	1	no	—
565	C₂²×C₄×C₅	—	3	2	no	—
566	C₂²×C₄×C₅	—	3	2	no	—
567	C₂²×C₄×C₅	—	6	4	no	—
568	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
569	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
570	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
571	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
572	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
573	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
574	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
575	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
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	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	—	3	2	no	—
594	C₅×C₄⋊C₄	—	3	2	no	—
595	C₅×C₄⋊C₄	—	3	2	no	—
596	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
597	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
598	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
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×C₂²⋊C₄	—	3	1	no	—
603	C₅×C₂²⋊C₄	—	3	2	no	—
604	C₅×C₂²⋊C₄	—	3	1	no	—
605	C₅×C₂²⋊C₄	—	3	1	no	—
606	C₅×C₂²⋊C₄	—	3	1	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	2	no	—
612	C₅×C₂²⋊C₄	—	3	1	no	—
613	C₅×C₂²⋊C₄	—	3	1	no	—
614	C₅×C₂²⋊C₄	—	3	1	no	—
615	C₅×C₂²⋊C₄	—	3	2	no	—
616	C₅×C₂²⋊C₄	—	3	2	no	—
617	C₅×C₂²⋊C₄	—	3	2	no	—
618	C₅×C₂²⋊C₄	—	3	2	no	—
619	C₅×C₂²⋊C₄	—	3	2	no	—
620	C₅×C₂²⋊C₄	—	3	2	no	—
621	C₅×C₂²⋊C₄	—	3	2	no	—
622	C₅×C₂²⋊C₄	—	3	2	no	—
623	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
624	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
625	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
626	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
627	C₄²×C₅	—	3	2	no	—
628	C₄²×C₅	—	3	2	no	—
629	C₄²×C₅	—	3	2	no	—
630	C₄²×C₅	—	3	1	no	—
631	C₄²×C₅	—	3	1	no	—
632	C₄²×C₅	—	3	2	no	—
633	C₄²×C₅	—	3	1	no	—
634	C₄²×C₅	—	3	1	no	—
635	C₄²×C₅	—	3	2	no	—
636	C₄²×C₅	C₂²×D₃	1	2	yes	—
637	C₄²×C₅	C₂²×D₃	1	2	yes	—
638	C₄²×C₅	C₂²×D₃	1	2	yes	—
639	C₄²×C₅	C₂²×D₃	1	2	yes	—
640	#556	—	3	1	no	—
641	#555	—	3	1	no	—
642	#554	—	3	1	no	—
643	#553	—	3	1	no	—
644	#553	—	3	1	no	—
645	#552	—	3	2	no	—
646	#552	—	3	1	no	—
647	#552	—	3	1	no	—
648	#551	—	3	2	no	—
649	#551	—	3	2	no	—
650	#547	—	3	1	no	—
651	#546	—	3	2	no	—
652	#533	—	3	1	no	—
653	#529	—	3	2	no	—
654	#529	—	3	2	no	—
655	#529	—	3	2	no	—
656	#525	—	3	1	no	—
657	#525	—	3	1	no	—
658	C₄×#41	—	3	1	no	—
659	C₄×#41	—	3	2	no	—
660	C₂×C₄×D₄	—	3	1	no	—
661	C₂×#117	—	3	1	no	—
662	C₂×#117	C₅×D₃	1	1	yes	characteristic, complemented
663	C₂²×C₃×C₅	—	2	1	no	—
664	C₂²×C₃×C₅	—	2	1	no	—
665	C₂²×C₃×C₅	—	2	1	no	—
666	C₂²×C₃×C₅	—	2	1	no	—
667	C₂²×C₃×C₅	—	2	1	no	—
668	C₂²×C₃×C₅	—	2	1	no	—
669	C₂²×C₃×C₅	—	2	1	no	—
670	C₂²×C₃×C₅	—	4	4	no	—
671	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
672	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
673	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
674	C₂×C₅×D₃	—	2	1	no	—
675	C₂×C₅×D₃	—	2	1	no	—
676	C₂×C₅×D₃	—	2	1	no	—
677	C₂×C₅×D₃	—	2	2	no	—
678	C₂×C₅×D₃	—	2	2	no	—
679	C₂×C₅×D₃	—	2	1	no	—
680	C₂×C₅×D₃	—	2	2	no	—
681	C₂×C₅×D₃	—	2	1	no	—
682	C₂×C₅×D₃	—	4	4	no	—
683	C₂×C₅×D₃	C₂×#41	1	2	yes	—
684	C₃×C₄×C₅	—	2	2	no	—
685	C₃×C₄×C₅	—	2	2	no	—
686	C₃×C₄×C₅	—	2	1	no	—
687	C₃×C₄×C₅	—	2	1	no	—
688	C₃×C₄×C₅	—	2	2	no	—
689	C₃×C₄×C₅	—	2	2	no	—
690	C₃×C₄×C₅	C₂×#41	1	2	yes	—
691	C₃×C₄×C₅	C₂×#41	1	2	yes	—
692	C₅×Dic₃	—	2	2	no	—
693	C₅×Dic₃	—	2	2	no	—
694	C₅×Dic₃	—	2	1	no	—
695	C₅×Dic₃	—	2	1	no	—
696	C₅×Dic₃	—	2	1	no	—
697	C₅×Dic₃	—	2	1	no	—
698	C₅×Dic₃	—	2	2	no	—
699	C₅×Dic₃	—	2	1	no	—
700	C₅×Dic₃	C₂×#41	1	2	yes	—
701	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
702	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
703	C₂²×C₃×C₄	—	2	4	no	—
704	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
705	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
706	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
707	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
708	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
709	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
710	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
711	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
712	C₂×#67	—	2	4	no	—
713	C₂×#67	C₂³×C₅	1	2	yes	—
714	C₂×#67	C₂³×C₅	1	1	yes	characteristic
715	C₂×#67	C₂³×C₅	1	1	yes	characteristic
716	C₂×#67	C₂³×C₅	1	1	yes	characteristic
717	C₂×#67	C₂³×C₅	1	2	yes	—
718	C₂×#67	C₂³×C₅	1	2	yes	—
719	C₂×#67	C₂³×C₅	1	1	yes	characteristic
720	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
721	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
722	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
723	#235	—	2	4	no	—
724	#235	—	2	8	no	—
725	C₂×D₁₂	C₂³×C₅	1	2	yes	—
726	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
727	C₂×D₁₂	C₂³×C₅	1	2	yes	—
728	C₂×C₄×D₃	—	2	4	no	—
729	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
730	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
731	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
732	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
733	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
734	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
735	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
736	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
737	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
738	C₂×Dic₆	C₂³×C₅	1	2	yes	—
739	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
740	C₂×Dic₆	C₂³×C₅	1	2	yes	—
741	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
742	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
743	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
744	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
745	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
746	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
747	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
748	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
749	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
750	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
751	C₃×C₄²	C₂³×C₅	1	2	yes	—
752	C₃×C₄²	C₂³×C₅	1	2	yes	—
753	C₃×C₄²	C₂³×C₅	1	2	yes	—
754	C₃×C₄²	C₂³×C₅	1	2	yes	—
755	#217	C₂³×C₅	1	2	yes	—
756	#217	C₂³×C₅	1	2	yes	—
757	#217	C₂³×C₅	1	1	yes	characteristic
758	#217	C₂³×C₅	1	1	yes	characteristic
759	#217	C₂³×C₅	1	2	yes	—
760	#217	C₂³×C₅	1	1	yes	characteristic
761	#217	C₂³×C₅	1	1	yes	characteristic
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	2	yes	—
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	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
770	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
771	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
772	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
773	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
774	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
775	(C₂×D₃)⋊C₄	C₂³×C₅	1	1	yes	characteristic
776	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
777	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
778	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
779	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
780	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
781	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
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	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
786	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
787	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
788	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
789	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
790	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
791	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
792	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
793	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
794	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
795	Dic₃⋊C₄	C₂³×C₅	1	1	yes	characteristic
796	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
797	C₄×Dic₃	C₂³×C₅	1	2	yes	—
798	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
799	C₄×Dic₃	C₂³×C₅	1	2	yes	—
800	C₄×Dic₃	C₂³×C₅	1	2	yes	—
801	C₄×Dic₃	C₂³×C₅	1	2	yes	—
802	C₄×Dic₃	C₂³×C₅	1	2	yes	—
803	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
804	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
805	C₂³×C₅	—	2	2	no	—
806	C₂³×C₅	—	2	2	no	—
807	C₂³×C₅	—	3	1	no	—
808	C₂³×C₅	—	3	1	no	—
809	C₂³×C₅	—	3	2	no	—
810	C₂³×C₅	—	4	1	no	—
811	C₂³×C₅	—	6	2	no	—
812	C₂³×C₅	—	6	2	no	—
813	C₂³×C₅	—	12	1	no	—
814	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
815	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
816	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
817	C₅×Q₈	—	6	4	no	—
818	C₅×Q₈	—	6	2	no	—
819	C₅×Q₈	—	12	2	no	—
820	C₅×D₄	—	3	4	no	—
821	C₅×D₄	—	6	4	no	—
822	C₅×D₄	—	6	2	no	—
823	C₅×D₄	—	6	2	no	—
824	C₅×D₄	—	6	4	no	—
825	C₅×D₄	—	6	2	no	—
826	C₅×D₄	—	6	4	no	—
827	C₅×D₄	—	6	2	no	—
828	C₅×D₄	—	12	2	no	—
829	C₅×D₄	—	12	2	no	—
830	C₂×C₄×C₅	—	2	2	no	—
831	C₂×C₄×C₅	—	2	4	no	—
832	C₂×C₄×C₅	—	2	2	no	—
833	C₂×C₄×C₅	—	2	2	no	—
834	C₂×C₄×C₅	—	2	2	no	—
835	C₂×C₄×C₅	—	2	2	no	—
836	C₂×C₄×C₅	—	3	1	no	—
837	C₂×C₄×C₅	—	3	1	no	—
838	C₂×C₄×C₅	—	3	1	no	—
839	C₂×C₄×C₅	—	3	1	no	—
840	C₂×C₄×C₅	—	3	2	no	—
841	C₂×C₄×C₅	—	3	2	no	—
842	C₂×C₄×C₅	—	3	2	no	—
843	C₂×C₄×C₅	—	3	1	no	—
844	C₂×C₄×C₅	—	3	1	no	—
845	C₂×C₄×C₅	—	4	2	no	—
846	C₂×C₄×C₅	—	6	4	no	—
847	C₂×C₄×C₅	—	6	4	no	—
848	C₂×C₄×C₅	—	6	2	no	—
849	C₂×C₄×C₅	—	6	2	no	—
850	C₂×C₄×C₅	—	6	2	no	—
851	C₂×C₄×C₅	—	6	2	no	—
852	C₂×C₄×C₅	—	6	2	no	—
853	C₂×C₄×C₅	—	6	2	no	—
854	C₂×C₄×C₅	—	6	4	no	—
855	C₂×C₄×C₅	—	12	2	no	—
856	C₂×C₄×C₅	—	12	2	no	—
857	C₂×C₄×C₅	—	12	1	no	—
858	C₂×C₄×C₅	#235	1	4	yes	complemented
859	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
860	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
861	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
862	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
863	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
864	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
865	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
866	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
867	C₂×#41	—	3	1	no	—
868	C₂×#41	—	3	2	no	—
869	C₂²×D₄	—	3	1	no	—
870	C₂³×C₄	—	3	1	no	—
871	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
872	C₄⋊Q₈	—	3	1	no	—
873	C₄⋊Q₈	—	3	1	no	—
874	#126	—	3	2	no	—
875	#126	—	3	2	no	—
876	#126	—	3	2	no	—
877	#126	—	3	2	no	—
878	#126	—	3	2	no	—
879	#126	—	3	2	no	—
880	#125	—	3	2	no	—
881	#125	—	3	2	no	—
882	#125	—	3	1	no	—
883	#125	—	3	1	no	—
884	#125	—	3	2	no	—
885	#124	—	3	2	no	—
886	#124	—	3	2	no	—
887	#124	—	3	2	no	—
888	#123	—	3	2	no	—
889	#123	—	3	2	no	—
890	#123	—	3	2	no	—
891	#123	—	3	2	no	—
892	#123	—	3	2	no	—
893	#123	—	3	2	no	—
894	#123	—	3	2	no	—
895	#123	—	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	1	no	—
900	C₂²⋊Q₈	—	3	1	no	—
901	C₂²⋊Q₈	—	3	2	no	—
902	C₂²⋊Q₈	—	3	2	no	—
903	C₂²⋊Q₈	—	3	2	no	—
904	C₂²⋊Q₈	—	3	2	no	—
905	#121	—	3	1	no	—
906	#121	—	3	1	no	—
907	#121	—	3	2	no	—
908	#121	—	3	1	no	—
909	#121	—	3	1	no	—
910	#121	—	3	2	no	—
911	#121	—	3	2	no	—
912	#120	—	3	2	no	—
913	#120	—	3	2	no	—
914	C₄×Q₈	—	3	1	no	—
915	C₄×Q₈	—	3	1	no	—
916	C₄×Q₈	—	3	2	no	—
917	C₄×Q₈	—	3	2	no	—
918	C₄×Q₈	—	3	2	no	—
919	C₄×D₄	—	3	1	no	—
920	C₄×D₄	—	3	1	no	—
921	C₄×D₄	—	3	1	no	—
922	C₄×D₄	—	3	1	no	—
923	C₄×D₄	—	3	1	no	—
924	C₄×D₄	—	3	1	no	—
925	C₄×D₄	—	3	1	no	—
926	C₄×D₄	—	3	1	no	—
927	C₄×D₄	—	3	2	no	—
928	C₄×D₄	—	3	2	no	—
929	C₄×D₄	—	3	2	no	—
930	C₄×D₄	—	3	2	no	—
931	C₄×D₄	—	3	1	no	—
932	C₄×D₄	—	3	1	no	—
933	C₄×D₄	—	3	2	no	—
934	C₄×D₄	—	3	2	no	—
935	C₄×D₄	—	3	2	no	—
936	C₄×D₄	—	3	2	no	—
937	C₄×D₄	—	3	2	no	—
938	#117	—	3	1	no	—
939	#117	—	3	2	no	—
940	#117	—	3	1	no	—
941	#117	—	3	1	no	—
942	#117	—	3	2	no	—
943	#117	—	3	2	no	—
944	#117	—	3	2	no	—
945	#117	—	3	2	no	—
946	#117	—	3	2	no	—
947	#117	C₂×C₅×D₃	1	1	yes	characteristic
948	#117	C₂×C₅×D₃	1	1	yes	characteristic
949	#117	C₂×C₅×D₃	1	2	yes	—
950	#117	C₂×C₅×D₃	1	2	yes	complemented
951	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
952	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
953	C₂×C₄⋊C₄	—	3	1	no	—
954	C₂×C₄⋊C₄	—	3	1	no	—
955	C₂×C₄⋊C₄	—	3	1	no	—
956	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
957	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
958	C₂×C₂²⋊C₄	—	3	1	no	—
959	C₂×C₂²⋊C₄	—	3	1	no	—
960	C₂×C₂²⋊C₄	—	3	2	no	—
961	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
962	C₂×C₄²	—	3	1	no	—
963	C₂×C₄²	—	3	2	no	—
964	C₂×C₄²	—	3	2	no	—
965	C₂×C₄²	C₂×C₅×D₃	1	2	yes	complemented
966	C₂×C₃×C₅	—	2	2	no	—
967	C₂×C₃×C₅	—	2	2	no	—
968	C₂×C₃×C₅	—	4	1	no	—
969	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
970	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
971	C₂×C₃×C₅	#585	1	1	yes	characteristic
972	C₅×D₃	—	2	2	no	—
973	C₅×D₃	—	4	2	no	—
974	C₅×D₃	—	4	1	no	—
975	C₂³×C₃	—	2	2	no	—
976	C₂³×C₃	—	2	2	no	—
977	C₂³×C₃	—	4	1	no	—
978	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
979	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
980	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
981	C₂²×D₃	—	2	2	no	—
982	C₂²×D₃	—	2	2	no	—
983	C₂²×D₃	—	4	1	no	—
984	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
985	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
986	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
987	C₂×C₃×C₄	—	2	4	no	—
988	C₂×C₃×C₄	—	2	2	no	—
989	C₂×C₃×C₄	—	2	2	no	—
990	C₂×C₃×C₄	—	2	2	no	—
991	C₂×C₃×C₄	—	2	2	no	—
992	C₂×C₃×C₄	—	2	2	no	—
993	C₂×C₃×C₄	—	4	2	no	—
994	C₂×C₃×C₄	C₅×#41	1	4	yes	complemented
995	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
996	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
997	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
998	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
999	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1000	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
1001	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1002	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
1003	#67	—	2	4	no	—
1004	#67	—	2	4	no	—
1005	#67	—	2	2	no	—
1006	#67	—	2	2	no	—
1007	#67	—	2	2	no	—
1008	#67	—	4	2	no	—
1009	#67	C₅×#41	1	4	yes	complemented
1010	C₂×Dic₃	—	2	2	no	—
1011	C₂×Dic₃	—	2	2	no	—
1012	C₂×Dic₃	—	4	1	no	—
1013	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1014	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1015	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1016	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
1017	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
1018	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
1019	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1020	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1021	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
1022	D₁₂	—	2	4	no	—
1023	D₁₂	—	2	2	no	—
1024	D₁₂	—	4	2	no	—
1025	C₄×D₃	—	2	4	no	—
1026	C₄×D₃	—	2	2	no	—
1027	C₄×D₃	—	2	2	no	—
1028	C₄×D₃	—	2	2	no	—
1029	C₄×D₃	—	2	2	no	—
1030	C₄×D₃	—	2	4	no	—
1031	C₄×D₃	—	2	4	no	—
1032	C₄×D₃	—	4	2	no	—
1033	C₄×D₃	—	4	2	no	—
1034	Dic₆	—	2	2	no	—
1035	Dic₆	—	2	4	no	—
1036	Dic₆	—	4	2	no	—
1037	C₂²×C₅	—	2	1	no	—
1038	C₂²×C₅	—	2	1	no	—
1039	C₂²×C₅	—	2	1	no	—
1040	C₂²×C₅	—	2	1	no	—
1041	C₂²×C₅	—	2	1	no	—
1042	C₂²×C₅	—	2	1	no	—
1043	C₂²×C₅	—	2	1	no	—
1044	C₂²×C₅	—	3	2	no	—
1045	C₂²×C₅	—	4	4	no	—
1046	C₂²×C₅	—	6	1	no	—
1047	C₂²×C₅	—	6	1	no	—
1048	C₂²×C₅	—	6	1	no	—
1049	C₂²×C₅	—	6	2	no	—
1050	C₂²×C₅	—	6	2	no	—
1051	C₂²×C₅	—	6	1	no	—
1052	C₂²×C₅	—	6	2	no	—
1053	C₂²×C₅	—	6	1	no	—
1054	C₂²×C₅	—	12	4	no	—
1055	C₂²×C₅	C₂×#235	1	2	yes	—
1056	C₂²×C₅	D₃×#41	1	2	yes	—
1057	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
1058	C₄×C₅	—	2	1	no	—
1059	C₄×C₅	—	2	1	no	—
1060	C₄×C₅	—	2	2	no	—
1061	C₄×C₅	—	2	2	no	—
1062	C₄×C₅	—	2	2	no	—
1063	C₄×C₅	—	2	2	no	—
1064	C₄×C₅	—	3	2	no	—
1065	C₄×C₅	—	6	1	no	—
1066	C₄×C₅	—	6	1	no	—
1067	C₄×C₅	—	6	2	no	—
1068	C₄×C₅	—	6	1	no	—
1069	C₄×C₅	—	6	2	no	—
1070	C₄×C₅	—	6	1	no	—
1071	C₄×C₅	—	6	2	no	—
1072	C₄×C₅	—	6	1	no	—
1073	C₄×C₅	C₂×#235	1	2	yes	—
1074	C₄×C₅	C₂×#235	1	2	yes	—
1075	C₂⁴	—	3	1	no	—
1076	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
1077	#41	—	6	8	no	—
1078	#41	—	6	4	no	—
1079	C₂×Q₈	—	3	1	no	—
1080	C₂×Q₈	—	3	2	no	—
1081	C₂×Q₈	—	3	2	no	—
1082	C₂×D₄	—	3	1	no	—
1083	C₂×D₄	—	3	2	no	—
1084	C₂×D₄	—	3	2	no	—
1085	C₂×D₄	—	3	1	no	—
1086	C₂×D₄	—	3	1	no	—
1087	C₂×D₄	—	3	1	no	—
1088	C₂×D₄	—	3	2	no	—
1089	C₂×D₄	—	3	2	no	—
1090	C₂×D₄	—	3	1	no	—
1091	C₂×D₄	—	3	2	no	—
1092	C₂×D₄	—	6	4	no	—
1093	C₂²×C₄	—	2	4	no	—
1094	C₂²×C₄	—	3	1	no	—
1095	C₂²×C₄	—	3	1	no	—
1096	C₂²×C₄	—	3	1	no	—
1097	C₂²×C₄	—	3	1	no	—
1098	C₂²×C₄	—	3	2	no	—
1099	C₂²×C₄	—	3	2	no	—
1100	C₂²×C₄	—	3	2	no	—
1101	C₂²×C₄	—	3	1	no	—
1102	C₂²×C₄	—	3	1	no	—
1103	C₂²×C₄	—	3	1	no	—
1104	C₂²×C₄	—	3	2	no	—
1105	C₂²×C₄	—	3	2	no	—
1106	C₂²×C₄	—	6	4	no	—
1107	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1108	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
1109	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1110	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1111	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1112	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1113	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
1114	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1115	C₄⋊C₄	—	3	1	no	—
1116	C₄⋊C₄	—	3	1	no	—
1117	C₄⋊C₄	—	3	1	no	—
1118	C₄⋊C₄	—	3	2	no	—
1119	C₄⋊C₄	—	3	2	no	—
1120	C₄⋊C₄	—	3	1	no	—
1121	C₄⋊C₄	—	3	1	no	—
1122	C₄⋊C₄	—	3	1	no	—
1123	C₄⋊C₄	—	3	2	no	—
1124	C₄⋊C₄	—	3	2	no	—
1125	C₄⋊C₄	—	3	2	no	—
1126	C₄⋊C₄	—	3	2	no	—
1127	C₄⋊C₄	—	3	2	no	—
1128	C₄⋊C₄	—	3	2	no	—
1129	C₄⋊C₄	—	3	2	no	—
1130	C₄⋊C₄	—	3	2	no	—
1131	C₄⋊C₄	—	3	2	no	—
1132	C₄⋊C₄	—	3	2	no	—
1133	C₄⋊C₄	—	3	2	no	—
1134	C₄⋊C₄	—	3	2	no	—
1135	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1136	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1137	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1138	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1139	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1140	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1141	C₂²⋊C₄	—	3	1	no	—
1142	C₂²⋊C₄	—	3	2	no	—
1143	C₂²⋊C₄	—	3	1	no	—
1144	C₂²⋊C₄	—	3	1	no	—
1145	C₂²⋊C₄	—	3	1	no	—
1146	C₂²⋊C₄	—	3	2	no	—
1147	C₂²⋊C₄	—	3	2	no	—
1148	C₂²⋊C₄	—	3	1	no	—
1149	C₂²⋊C₄	—	3	2	no	—
1150	C₂²⋊C₄	—	3	2	no	—
1151	C₂²⋊C₄	—	3	1	no	—
1152	C₂²⋊C₄	—	3	1	no	—
1153	C₂²⋊C₄	—	3	1	no	—
1154	C₂²⋊C₄	—	3	2	no	—
1155	C₂²⋊C₄	—	3	2	no	—
1156	C₂²⋊C₄	—	3	2	no	—
1157	C₂²⋊C₄	—	3	2	no	—
1158	C₂²⋊C₄	—	3	2	no	—
1159	C₂²⋊C₄	—	3	2	no	—
1160	C₂²⋊C₄	—	3	2	no	—
1161	C₂²⋊C₄	—	3	2	no	—
1162	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1163	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1164	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1165	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1166	C₄²	—	3	1	no	—
1167	C₄²	—	3	2	no	—
1168	C₄²	—	3	1	no	—
1169	C₄²	—	3	2	no	—
1170	C₄²	—	3	2	no	—
1171	C₄²	—	3	2	no	—
1172	C₄²	—	3	1	no	—
1173	C₄²	—	3	1	no	—
1174	C₄²	—	3	2	no	—
1175	C₄²	C₂²×C₅×D₃	1	2	yes	—
1176	C₄²	C₂²×C₅×D₃	1	2	yes	—
1177	C₄²	C₂²×C₅×D₃	1	2	yes	—
1178	C₄²	C₂²×C₅×D₃	1	2	yes	—
1179	C₃×C₅	#3475	1	1	yes	characteristic, complemented, Hall
1180	C₂²×C₃	—	2	1	no	—
1181	C₂²×C₃	—	2	1	no	—
1182	C₂²×C₃	—	2	1	no	—
1183	C₂²×C₃	—	2	1	no	—
1184	C₂²×C₃	—	2	1	no	—
1185	C₂²×C₃	—	2	1	no	—
1186	C₂²×C₃	—	2	1	no	—
1187	C₂²×C₃	—	4	4	no	—
1188	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
1189	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
1190	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1191	C₂×D₃	—	2	1	no	—
1192	C₂×D₃	—	2	1	no	—
1193	C₂×D₃	—	2	1	no	—
1194	C₂×D₃	—	2	2	no	—
1195	C₂×D₃	—	2	2	no	—
1196	C₂×D₃	—	2	1	no	—
1197	C₂×D₃	—	2	2	no	—
1198	C₂×D₃	—	2	1	no	—
1199	C₂×D₃	—	4	4	no	—
1200	C₂×D₃	C₂×C₅×#41	1	2	yes	—
1201	C₃×C₄	—	2	2	no	—
1202	C₃×C₄	—	2	2	no	—
1203	C₃×C₄	—	2	1	no	—
1204	C₃×C₄	—	2	1	no	—
1205	C₃×C₄	—	2	2	no	—
1206	C₃×C₄	—	2	2	no	—
1207	C₃×C₄	C₂×C₅×#41	1	2	yes	—
1208	C₃×C₄	C₂×C₅×#41	1	2	yes	—
1209	Dic₃	—	2	2	no	—
1210	Dic₃	—	2	2	no	—
1211	Dic₃	—	2	1	no	—
1212	Dic₃	—	2	1	no	—
1213	Dic₃	—	2	1	no	—
1214	Dic₃	—	2	1	no	—
1215	Dic₃	—	2	2	no	—
1216	Dic₃	—	2	1	no	—
1217	Dic₃	C₂×C₅×#41	1	2	yes	—
1218	C₂×C₅	—	2	2	no	—
1219	C₂×C₅	—	2	2	no	—
1220	C₂×C₅	—	4	1	no	—
1221	C₂×C₅	—	6	2	no	—
1222	C₂×C₅	—	12	1	no	—
1223	C₂×C₅	—	12	2	no	—
1224	C₂×C₅	C₂²×#235	1	1	yes	characteristic
1225	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
1226	C₂×C₅	#5964	1	1	yes	characteristic
1227	C₂³	—	2	2	no	—
1228	C₂³	—	2	2	no	—
1229	C₂³	—	3	1	no	—
1230	C₂³	—	3	1	no	—
1231	C₂³	—	3	2	no	—
1232	C₂³	—	4	1	no	—
1233	C₂³	—	6	2	no	—
1234	C₂³	—	6	2	no	—
1235	C₂³	—	12	1	no	—
1236	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1237	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1238	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1239	Q₈	—	6	4	no	—
1240	Q₈	—	6	2	no	—
1241	Q₈	—	12	2	no	—
1242	D₄	—	3	4	no	—
1243	D₄	—	6	4	no	—
1244	D₄	—	6	2	no	—
1245	D₄	—	6	2	no	—
1246	D₄	—	6	4	no	—
1247	D₄	—	6	2	no	—
1248	D₄	—	6	4	no	—
1249	D₄	—	6	2	no	—
1250	D₄	—	12	2	no	—
1251	D₄	—	12	2	no	—
1252	C₂×C₄	—	2	2	no	—
1253	C₂×C₄	—	2	4	no	—
1254	C₂×C₄	—	2	2	no	—
1255	C₂×C₄	—	2	2	no	—
1256	C₂×C₄	—	2	2	no	—
1257	C₂×C₄	—	2	2	no	—
1258	C₂×C₄	—	3	1	no	—
1259	C₂×C₄	—	3	1	no	—
1260	C₂×C₄	—	3	1	no	—
1261	C₂×C₄	—	3	1	no	—
1262	C₂×C₄	—	3	2	no	—
1263	C₂×C₄	—	3	2	no	—
1264	C₂×C₄	—	3	2	no	—
1265	C₂×C₄	—	3	1	no	—
1266	C₂×C₄	—	3	1	no	—
1267	C₂×C₄	—	4	2	no	—
1268	C₂×C₄	—	6	4	no	—
1269	C₂×C₄	—	6	4	no	—
1270	C₂×C₄	—	6	2	no	—
1271	C₂×C₄	—	6	2	no	—
1272	C₂×C₄	—	6	2	no	—
1273	C₂×C₄	—	6	2	no	—
1274	C₂×C₄	—	6	2	no	—
1275	C₂×C₄	—	6	2	no	—
1276	C₂×C₄	—	6	4	no	—
1277	C₂×C₄	—	12	2	no	—
1278	C₂×C₄	—	12	2	no	—
1279	C₂×C₄	—	12	1	no	—
1280	C₂×C₄	C₅×#235	1	4	yes	complemented
1281	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1282	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1283	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1284	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1285	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1286	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1287	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1288	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1289	C₂×C₃	—	2	2	no	—
1290	C₂×C₃	—	2	2	no	—
1291	C₂×C₃	—	4	1	no	—
1292	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
1293	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
1294	C₂×C₃	C₅×#585	1	1	yes	characteristic
1295	D₃	—	2	2	no	—
1296	D₃	—	4	1	no	—
1297	D₃	—	4	2	no	—
1298	C₅	#85744	1	1	yes	characteristic, direct product factor, Sylow
1299	C₂²	—	2	1	no	—
1300	C₂²	—	2	1	no	—
1301	C₂²	—	2	1	no	—
1302	C₂²	—	2	1	no	—
1303	C₂²	—	2	1	no	—
1304	C₂²	—	2	1	no	—
1305	C₂²	—	2	1	no	—
1306	C₂²	—	3	2	no	—
1307	C₂²	—	4	4	no	—
1308	C₂²	—	6	1	no	—
1309	C₂²	—	6	1	no	—
1310	C₂²	—	6	1	no	—
1311	C₂²	—	6	2	no	—
1312	C₂²	—	6	2	no	—
1313	C₂²	—	6	1	no	—
1314	C₂²	—	6	2	no	—
1315	C₂²	—	6	1	no	—
1316	C₂²	—	12	4	no	—
1317	C₂²	C₂×C₅×#235	1	2	yes	—
1318	C₂²	C₅×D₃×#41	1	2	yes	—
1319	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
1320	C₄	—	2	1	no	—
1321	C₄	—	2	1	no	—
1322	C₄	—	2	2	no	—
1323	C₄	—	2	2	no	—
1324	C₄	—	2	2	no	—
1325	C₄	—	2	2	no	—
1326	C₄	—	3	2	no	—
1327	C₄	—	6	1	no	—
1328	C₄	—	6	1	no	—
1329	C₄	—	6	2	no	—
1330	C₄	—	6	1	no	—
1331	C₄	—	6	2	no	—
1332	C₄	—	6	1	no	—
1333	C₄	—	6	2	no	—
1334	C₄	—	6	1	no	—
1335	C₄	C₂×C₅×#235	1	2	yes	—
1336	C₄	C₂×C₅×#235	1	2	yes	—
1337	C₃	C₅×#3475	1	1	yes	characteristic, complemented, Sylow
1338	C₂	—	2	2	no	—
1339	C₂	—	2	2	no	—
1340	C₂	—	4	1	no	—
1341	C₂	—	6	2	no	—
1342	C₂	—	12	1	no	—
1343	C₂	—	12	2	no	—
1344	C₂	C₂²×C₅×#235	1	1	yes	characteristic
1345	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
1346	C₂	C₅×#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₂×C₅×#117	D₃
hypocenter	C₃	C₅×#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×#117

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#117	C₂	semidirect
2. C₅×#5791	C₂	semidirect
3. C₂×C₄×C₅×#67	C₂	semidirect
4. C₅×#5533	C₂	semidirect
5. C₅×#5532	C₂	semidirect
6. C₅×#5531	C₂	semidirect
7. C₅×#5530	C₂	semidirect
8. C₅×#5529	C₂	semidirect
9. C₅×#5528	C₂	semidirect
10. C₅×#5528	C₂	semidirect
11. C₅×#5527	C₂	semidirect
12. C₅×#5524	C₂	semidirect
13. C₅×#5522	C₂	semidirect
14. C₅×D₃×#117	C₂	semidirect
15. C₅×#5517	C₂	semidirect
16. C₅×#5514	C₂	semidirect
17. C₅×#5513	C₂	semidirect
18. C₅×#5511	C₂	semidirect
19. C₅×#5507	C₂	semidirect
20. C₅×#5495	C₂	semidirect
21. C₅×#5490	C₂	semidirect
22. C₅×#5479	C₂	semidirect
23. C₄×C₅×#235	C₂	semidirect
33. C₃×C₅×#117	C₂²	semidirect
34. C₃×C₅×#117	C₂²	semidirect
35. C₃×C₅×#117	C₂²	semidirect
36. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
37. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
39. C₂×C₃×C₄²×C₅	C₂²	semidirect
43. C₅×#930	C₂²	semidirect
44. C₅×#930	C₂²	semidirect
47. C₅×#929	C₂²	semidirect
57. C₄×C₅×#67	C₂²	semidirect
58. C₄×C₅×#67	C₂²	semidirect
59. C₄×C₅×#67	C₂²	semidirect
62. C₅×#926	C₂²	semidirect
63. C₅×#924	C₂²	semidirect
64. C₅×#924	C₂²	semidirect
65. C₅×#924	C₂²	semidirect
68. C₅×#898	C₂²	semidirect
69. C₅×#898	C₂²	semidirect
70. C₅×#897	C₂²	semidirect
71. C₅×#897	C₂²	semidirect
72. C₅×#896	C₂²	semidirect
73. C₅×#896	C₂²	semidirect
74. C₅×#895	C₂²	semidirect
75. C₅×#895	C₂²	semidirect
76. C₅×#894	C₂²	semidirect
77. C₅×#894	C₂²	semidirect
78. C₅×#893	C₂²	semidirect
79. C₅×#893	C₂²	semidirect
80. C₅×#892	C₂²	semidirect
81. C₅×#892	C₂²	semidirect
82. C₅×D₃×C₄⋊C₄	C₂²	semidirect
83. C₅×D₃×C₄⋊C₄	C₂²	semidirect
84. C₅×#890	C₂²	semidirect
85. C₅×#890	C₂²	semidirect
86. C₅×#889	C₂²	semidirect
87. C₅×#889	C₂²	semidirect
88. C₅×#888	C₂²	semidirect
89. C₅×#888	C₂²	semidirect
90. C₅×#887	C₂²	semidirect
91. C₅×#887	C₂²	semidirect
94. C₅×#885	C₂²	semidirect
98. C₅×#883	C₂²	semidirect
103. C₅×#879	C₂²	semidirect
104. C₅×#879	C₂²	semidirect
108. C₅×#876	C₂²	semidirect
109. C₅×#876	C₂²	semidirect
110. C₅×#875	C₂²	semidirect
111. C₄×C₅×D₁₂	C₂²	semidirect
112. C₄×C₅×D₁₂	C₂²	semidirect
113. C₄×C₅×D₁₂	C₂²	semidirect
114. C₅×#872	C₂²	semidirect
115. C₅×#872	C₂²	semidirect
116. C₅×#872	C₂²	semidirect
117. C₅×#872	C₂²	semidirect
118. C₄²×C₅×D₃	C₂²	semidirect
119. C₄²×C₅×D₃	C₂²	semidirect
120. C₅×#870	C₂²	semidirect
121. C₄×C₅×Dic₆	C₂²	semidirect
122. C₄×C₅×Dic₆	C₂²	semidirect
123. C₄×C₅×Dic₆	C₂²	semidirect
124. #85744	C₅	direct (N × H)
147. C₂×C₅×#117	D₃	semidirect
252. C₂×C₃×#117	C₂×C₅	semidirect
253. #5791	C₂×C₅	semidirect
254. C₂×C₄×#67	C₂×C₅	semidirect
255. #5533	C₂×C₅	semidirect
256. #5532	C₂×C₅	semidirect
257. #5531	C₂×C₅	semidirect
258. #5530	C₂×C₅	semidirect
259. #5529	C₂×C₅	semidirect
260. #5528	C₂×C₅	semidirect
261. #5528	C₂×C₅	semidirect
262. #5527	C₂×C₅	semidirect
263. #5524	C₂×C₅	semidirect
264. #5522	C₂×C₅	semidirect
265. D₃×#117	C₂×C₅	semidirect
266. #5517	C₂×C₅	semidirect
267. #5514	C₂×C₅	semidirect
268. #5513	C₂×C₅	semidirect
269. #5511	C₂×C₅	semidirect
270. #5507	C₂×C₅	semidirect
271. #5495	C₂×C₅	semidirect
272. #5490	C₂×C₅	semidirect
273. #5479	C₂×C₅	semidirect
274. C₄×#235	C₂×C₅	semidirect
358. C₅×#117	C₂×D₃	semidirect
359. C₅×#117	C₂×D₃	semidirect
360. C₅×#117	C₂×D₃	semidirect
364. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
365. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
373. C₂×C₄²×C₅	C₂×D₃	semidirect
394. C₂×C₃×C₄×C₅	#41	semidirect
409. C₅×#67	#41	semidirect
445. C₃×#117	C₂²×C₅	semidirect
446. C₃×#117	C₂²×C₅	semidirect
447. C₃×#117	C₂²×C₅	semidirect
448. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
449. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
451. C₂×C₃×C₄²	C₂²×C₅	semidirect
455. #930	C₂²×C₅	semidirect
456. #930	C₂²×C₅	semidirect
459. #929	C₂²×C₅	semidirect
469. C₄×#67	C₂²×C₅	semidirect
470. C₄×#67	C₂²×C₅	semidirect
471. C₄×#67	C₂²×C₅	semidirect
474. #926	C₂²×C₅	semidirect
475. #924	C₂²×C₅	semidirect
476. #924	C₂²×C₅	semidirect
477. #924	C₂²×C₅	semidirect
480. #898	C₂²×C₅	semidirect
481. #898	C₂²×C₅	semidirect
482. #897	C₂²×C₅	semidirect
483. #897	C₂²×C₅	semidirect
484. #896	C₂²×C₅	semidirect
485. #896	C₂²×C₅	semidirect
486. #895	C₂²×C₅	semidirect
487. #895	C₂²×C₅	semidirect
488. #894	C₂²×C₅	semidirect
489. #894	C₂²×C₅	semidirect
490. #893	C₂²×C₅	semidirect
491. #893	C₂²×C₅	semidirect
492. #892	C₂²×C₅	semidirect
493. #892	C₂²×C₅	semidirect
494. D₃×C₄⋊C₄	C₂²×C₅	semidirect
495. D₃×C₄⋊C₄	C₂²×C₅	semidirect
496. #890	C₂²×C₅	semidirect
497. #890	C₂²×C₅	semidirect
498. #889	C₂²×C₅	semidirect
499. #889	C₂²×C₅	semidirect
500. #888	C₂²×C₅	semidirect
501. #888	C₂²×C₅	semidirect
502. #887	C₂²×C₅	semidirect
503. #887	C₂²×C₅	semidirect
506. #885	C₂²×C₅	semidirect
510. #883	C₂²×C₅	semidirect
515. #879	C₂²×C₅	semidirect
516. #879	C₂²×C₅	semidirect
520. #876	C₂²×C₅	semidirect
521. #876	C₂²×C₅	semidirect
522. #875	C₂²×C₅	semidirect
523. C₄×D₁₂	C₂²×C₅	semidirect
524. C₄×D₁₂	C₂²×C₅	semidirect
525. C₄×D₁₂	C₂²×C₅	semidirect
526. #872	C₂²×C₅	semidirect
527. #872	C₂²×C₅	semidirect
528. #872	C₂²×C₅	semidirect
529. #872	C₂²×C₅	semidirect
530. C₄²×D₃	C₂²×C₅	semidirect
531. C₄²×D₃	C₂²×C₅	semidirect
532. #870	C₂²×C₅	semidirect
533. C₄×Dic₆	C₂²×C₅	semidirect
534. C₄×Dic₆	C₂²×C₅	semidirect
535. C₄×Dic₆	C₂²×C₅	semidirect
662. C₂×#117	C₅×D₃	semidirect
858. C₂×C₄×C₅	#235	semidirect
950. #117	C₂×C₅×D₃	semidirect
951. #117	C₂×C₅×D₃	semidirect
952. #117	C₂×C₅×D₃	semidirect
956. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
957. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
965. C₂×C₄²	C₂×C₅×D₃	semidirect
994. C₂×C₃×C₄	C₅×#41	semidirect
1009. #67	C₅×#41	semidirect
1179. C₃×C₅	#3475	semidirect
1280. C₂×C₄	C₅×#235	semidirect
1298. C₅	#85744	direct (N × H)
1337. 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
C₂×C₃×C₅×#117	2
C₅×#5791	2
C₂×C₄×C₅×#67	2
C₅×#5533	2
C₅×#5532	2
C₅×#5531	2
C₅×#5530	2
C₅×#5529	2
C₅×#5528	2
C₅×#5527	2
C₅×#5524	2
C₅×#5522	2
C₅×D₃×#117	2
C₅×#5517	2
C₅×#5514	2
C₅×#5513	2
C₅×#5511	2
C₅×#5507	2
C₅×#5495	2
C₅×#5490	2
C₅×#5479	2
C₄×C₅×#235	2
C₅×#3475	3
#85744	5

Subgroups — C5×#85744 #14484117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#85744 #14484117