Subgroups — C₅×D₃×#551 #14483229

Order 1920.

2656 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#551	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5705	C₂	1	2	yes	maximal, complemented
3	C₅×D₃×#126	C₂	1	2	yes	maximal, complemented
4	C₅×#5679	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×D₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5659	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5658	C₂	1	2	yes	maximal, complemented
8	C₅×D₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×#123	C₂	1	2	yes	maximal, complemented
10	C₅×#5637	C₂	1	2	yes	maximal, complemented
11	C₅×D₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
12	C₅×D₃×#120	C₂	1	1	yes	maximal, characteristic
13	C₅×#5587	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#5556	C₂	1	2	yes	maximal, complemented
15	C₄×C₅×D₃×D₄	C₂	1	2	yes	maximal, complemented
16	C₅×#5527	C₂	1	2	yes	maximal, complemented
17	C₅×D₃×#117	C₂	1	2	yes	maximal, complemented
18	C₅×#5495	C₂	1	2	yes	maximal, complemented
19	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
20	C₂×C₅×#551	—	3	1	no	maximal, Hall
21	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
22	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₅×D₃×D₄	C₂²	1	2	yes	—
24	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
25	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
26	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
27	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×#126	C₂²	1	2	yes	complemented
29	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₅×#123	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#123	C₂²	1	2	yes	complemented
32	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₃×C₅×#120	C₂²	1	1	yes	characteristic
34	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
35	C₃×C₅×#117	C₂²	1	2	yes	complemented
36	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
37	C₅×#953	C₂²	1	1	yes	characteristic
38	C₂×C₅×#217	C₂²	1	2	yes	complemented
39	C₅×#947	C₂²	1	1	yes	characteristic, complemented
40	C₅×#946	C₂²	1	2	yes	complemented
41	C₅×#937	C₂²	1	2	yes	—
42	C₅×#937	C₂²	1	1	yes	characteristic
43	C₅×#936	C₂²	1	1	yes	characteristic, complemented
44	C₅×#935	C₂²	1	1	yes	characteristic, complemented
45	C₅×#935	C₂²	1	2	yes	complemented
46	C₅×D₄×Dic₃	C₂²	1	2	yes	complemented
47	C₅×#929	C₂²	1	1	yes	characteristic, complemented
48	C₅×#929	C₂²	1	2	yes	complemented
49	C₄×C₅×#67	C₂²	1	2	yes	complemented
50	C₄×C₅×#67	C₂²	1	2	yes	complemented
51	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
52	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
53	C₅×#926	C₂²	1	2	yes	complemented
54	C₅×#924	C₂²	1	2	yes	complemented
55	C₅×#898	C₂²	1	2	yes	complemented
56	C₅×#898	C₂²	1	2	yes	complemented
57	C₅×#898	C₂²	1	2	yes	complemented
58	C₅×#897	C₂²	1	2	yes	complemented
59	C₅×#896	C₂²	1	2	yes	complemented
60	C₅×#896	C₂²	1	2	yes	complemented
61	C₅×#894	C₂²	1	2	yes	complemented
62	C₅×#894	C₂²	1	2	yes	complemented
63	C₅×#894	C₂²	1	2	yes	complemented
64	C₅×#893	C₂²	1	2	yes	complemented
65	C₅×#892	C₂²	1	2	yes	complemented
66	C₅×#892	C₂²	1	2	yes	complemented
67	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
68	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
69	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
70	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
71	C₅×#886	C₂²	1	1	yes	characteristic, complemented
72	C₅×#886	C₂²	1	2	yes	complemented
73	C₅×#885	C₂²	1	2	yes	complemented
74	C₅×#885	C₂²	1	2	yes	complemented
75	C₅×#883	C₂²	1	2	yes	complemented
76	C₅×#883	C₂²	1	2	yes	complemented
77	C₅×#883	C₂²	1	2	yes	complemented
78	C₅×#882	C₂²	1	1	yes	characteristic
79	C₅×#882	C₂²	1	2	yes	—
80	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
81	C₅×#67⋊C₄	C₂²	1	2	yes	complemented
82	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
83	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
84	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
85	C₅×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
86	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
87	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
88	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
89	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
90	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
91	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
92	C₅×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
93	C₅×D₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
94	C₅×#879	C₂²	1	2	yes	complemented
95	C₅×#879	C₂²	1	2	yes	complemented
96	C₅×#879	C₂²	1	2	yes	complemented
97	C₅×#878	C₂²	1	2	yes	complemented
98	C₅×#878	C₂²	1	2	yes	complemented
99	C₅×#877	C₂²	1	2	yes	complemented
100	C₅×#877	C₂²	1	2	yes	complemented
101	C₅×#876	C₂²	1	2	yes	complemented
102	C₅×#875	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
104	C₅×#872	C₂²	1	2	yes	complemented
105	C₅×#872	C₂²	1	2	yes	complemented
106	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
107	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
108	D₃×#551	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
109	C₅×#551	—	3	2	no	—
110	C₅×#551	—	3	1	no	—
111	C₅×#551	—	3	2	no	—
112	C₅×#551	—	3	1	no	—
113	C₅×#551	—	3	2	no	—
114	C₅×#551	—	3	1	no	—
115	C₅×#551	—	3	2	no	—
116	C₅×#551	—	3	2	no	—
117	C₅×#551	—	3	2	no	—
118	C₅×#551	D₃	1	1	yes	characteristic, direct product factor
119	C₂×C₅×#126	—	3	2	no	—
120	C₂×C₅×#124	—	3	1	no	—
121	C₂×C₅×#123	—	3	2	no	—
122	C₂×C₅×#123	—	3	1	no	—
123	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
124	C₂×C₅×#120	—	3	1	no	—
125	C₂×C₄×C₅×D₄	—	3	2	no	—
126	C₂×C₅×#117	—	3	2	no	—
127	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
128	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
129	C₂³×C₅×D₃	—	2	8	no	—
130	C₂³×C₅×D₃	—	4	2	no	—
131	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
132	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
133	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
134	C₂³×C₅×D₃	C₂³	1	2	yes	—
135	C₂³×C₅×D₃	C₂³	1	2	yes	—
136	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic, complemented
137	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
138	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
139	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
140	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
141	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic, complemented
142	C₂×C₅×#67	C₂³	1	2	yes	—
143	C₂×C₅×#67	C₂³	1	2	yes	—
144	C₂×C₅×#67	C₂³	1	1	yes	characteristic
145	C₂×C₅×#67	C₂³	1	1	yes	characteristic
146	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
147	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
148	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic, complemented
149	C₅×D₃×Q₈	—	4	2	no	—
150	C₅×D₃×D₄	—	2	8	no	—
151	C₅×D₃×D₄	—	4	2	no	—
152	C₂×C₅×D₁₂	C₂³	1	2	yes	—
153	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
154	C₂×C₄×C₅×D₃	—	2	8	no	—
155	C₂×C₄×C₅×D₃	—	4	4	no	—
156	C₂×C₄×C₅×D₃	—	4	2	no	—
157	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
158	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
159	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
160	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
161	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
162	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
163	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
164	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
165	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
166	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
167	C₂×C₄×C₅×D₃	C₂³	1	2	yes	complemented
168	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic, complemented
169	C₂×C₅×Dic₆	C₂³	1	2	yes	complemented
170	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
171	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
172	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
173	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
174	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	complemented
181	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
182	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic, complemented
183	C₃×C₄²×C₅	C₂³	1	2	yes	complemented
184	C₅×#217	C₂³	1	2	yes	—
185	C₅×#217	C₂³	1	2	yes	—
186	C₅×#217	C₂³	1	2	yes	—
187	C₅×#217	C₂³	1	1	yes	characteristic
188	C₅×#217	C₂³	1	2	yes	—
189	C₅×#217	C₂³	1	2	yes	—
190	C₅×#217	C₂³	1	1	yes	characteristic, complemented
191	C₅×#217	C₂³	1	2	yes	complemented
192	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
193	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
194	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
195	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
196	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
197	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
198	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
199	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
200	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
201	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
202	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
203	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
204	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
205	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	complemented
206	C₅×C₄⋊Dic₃	C₂³	1	2	yes	complemented
207	C₅×C₄⋊Dic₃	C₂³	1	2	yes	complemented
208	C₅×C₄⋊Dic₃	C₂³	1	2	yes	complemented
209	C₅×C₄⋊Dic₃	C₂³	1	2	yes	complemented
210	C₅×Dic₃⋊C₄	C₂³	1	2	yes	complemented
211	C₅×Dic₃⋊C₄	C₂³	1	2	yes	complemented
212	C₅×Dic₃⋊C₄	C₂³	1	2	yes	complemented
213	C₅×Dic₃⋊C₄	C₂³	1	2	yes	complemented
214	C₅×Dic₃⋊C₄	C₂³	1	2	yes	complemented
215	C₅×Dic₃⋊C₄	C₂³	1	2	yes	complemented
216	C₅×Dic₃⋊C₄	C₂³	1	2	yes	complemented
217	C₅×Dic₃⋊C₄	C₂³	1	2	yes	complemented
218	C₄×C₅×Dic₃	C₂³	1	2	yes	complemented
219	C₄×C₅×Dic₃	C₂³	1	2	yes	complemented
220	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic, complemented
221	C₄×C₅×Dic₃	C₂³	1	2	yes	complemented
222	C₄×C₅×Dic₃	C₂³	1	2	yes	complemented
223	C₃×#551	C₂×C₅	1	1	yes	characteristic, complemented
224	#5705	C₂×C₅	1	2	yes	complemented
225	D₃×#126	C₂×C₅	1	2	yes	complemented
226	#5679	C₂×C₅	1	1	yes	characteristic, complemented
227	D₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
228	#5659	C₂×C₅	1	1	yes	characteristic, complemented
229	#5658	C₂×C₅	1	2	yes	complemented
230	D₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
231	D₃×#123	C₂×C₅	1	2	yes	complemented
232	#5637	C₂×C₅	1	2	yes	complemented
233	D₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
234	D₃×#120	C₂×C₅	1	1	yes	characteristic
235	#5587	C₂×C₅	1	1	yes	characteristic, complemented
236	#5556	C₂×C₅	1	2	yes	complemented
237	C₄×D₃×D₄	C₂×C₅	1	2	yes	complemented
238	#5527	C₂×C₅	1	2	yes	complemented
239	D₃×#117	C₂×C₅	1	2	yes	complemented
240	#5495	C₂×C₅	1	2	yes	complemented
241	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
242	C₂⁵×C₅	—	3	1	no	—
243	C₂²×C₅×Q₈	—	3	1	no	—
244	C₂²×C₅×D₄	—	3	2	no	—
245	C₂²×C₅×D₄	—	3	1	no	—
246	C₂³×C₄×C₅	—	3	2	no	—
247	C₂³×C₄×C₅	—	3	2	no	—
248	C₂³×C₄×C₅	—	3	1	no	—
249	C₅×#126	—	3	2	no	—
250	C₅×#126	—	3	2	no	—
251	C₅×#126	—	3	2	no	—
252	C₅×#126	—	3	2	no	—
253	C₅×#126	—	3	2	no	—
254	C₅×#126	—	3	2	no	—
255	C₅×#126	—	3	2	no	—
256	C₅×#126	C₂×D₃	1	2	yes	complemented
257	C₅×#124	—	3	1	no	—
258	C₅×#124	—	3	1	no	—
259	C₅×#124	—	3	2	no	—
260	C₅×#124	—	3	2	no	—
261	C₅×#124	—	3	1	no	—
262	C₅×#124	C₂×D₃	1	1	yes	characteristic, complemented
263	C₅×#123	—	3	2	no	—
264	C₅×#123	—	3	1	no	—
265	C₅×#123	—	3	2	no	—
266	C₅×#123	—	3	1	no	—
267	C₅×#123	—	3	2	no	—
268	C₅×#123	—	3	2	no	—
269	C₅×#123	—	3	2	no	—
270	C₅×#123	—	3	2	no	—
271	C₅×#123	—	3	2	no	—
272	C₅×#123	—	3	2	no	—
273	C₅×#123	—	3	2	no	—
274	C₅×#123	—	3	1	no	—
275	C₅×#123	C₂×D₃	1	1	yes	characteristic, complemented
276	C₅×#123	C₂×D₃	1	2	yes	complemented
277	C₅×C₂²⋊Q₈	—	3	2	no	—
278	C₅×C₂²⋊Q₈	—	3	2	no	—
279	C₅×C₂²⋊Q₈	—	3	2	no	—
280	C₅×C₂²⋊Q₈	—	3	2	no	—
281	C₅×C₂²⋊Q₈	—	3	2	no	—
282	C₅×C₂²⋊Q₈	—	3	2	no	—
283	C₅×C₂²⋊Q₈	—	3	2	no	—
284	C₅×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
285	C₅×#120	—	3	1	no	—
286	C₅×#120	—	3	2	no	—
287	C₅×#120	—	3	1	no	—
288	C₅×#120	—	3	1	no	—
289	C₅×#120	—	3	2	no	—
290	C₅×#120	C₂×D₃	1	1	yes	characteristic
291	C₄×C₅×D₄	—	3	2	no	—
292	C₄×C₅×D₄	—	3	2	no	—
293	C₄×C₅×D₄	—	3	2	no	—
294	C₄×C₅×D₄	—	3	2	no	—
295	C₄×C₅×D₄	—	3	2	no	—
296	C₄×C₅×D₄	—	3	2	no	—
297	C₄×C₅×D₄	—	3	2	no	—
298	C₄×C₅×D₄	C₂×D₃	1	2	yes	complemented
299	C₅×#117	—	3	2	no	—
300	C₅×#117	—	3	2	no	—
301	C₅×#117	—	3	2	no	—
302	C₅×#117	—	3	2	no	—
303	C₅×#117	—	3	2	no	—
304	C₅×#117	—	3	2	no	—
305	C₅×#117	—	3	2	no	—
306	C₅×#117	C₂×D₃	1	2	yes	complemented
307	C₂×C₅×C₄⋊C₄	—	3	2	no	—
308	C₂×C₅×C₄⋊C₄	—	3	2	no	—
309	C₂×C₅×C₄⋊C₄	—	3	2	no	—
310	C₂×C₅×C₄⋊C₄	—	3	2	no	—
311	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
312	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
313	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
314	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
315	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
316	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
317	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
318	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
319	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
320	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
321	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
322	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
323	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
324	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
325	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
326	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
327	C₂×C₄²×C₅	—	3	1	no	—
328	C₂×C₄²×C₅	—	3	2	no	—
329	C₂×#551	—	3	1	no	Sylow
330	C₂³×C₃×C₅	—	2	4	no	—
331	C₂³×C₃×C₅	—	4	1	no	—
332	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
333	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
334	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
335	C₂²×C₅×D₃	—	2	4	no	—
336	C₂²×C₅×D₃	—	2	4	no	—
337	C₂²×C₅×D₃	—	2	4	no	—
338	C₂²×C₅×D₃	—	2	4	no	—
339	C₂²×C₅×D₃	—	2	4	no	—
340	C₂²×C₅×D₃	—	2	4	no	—
341	C₂²×C₅×D₃	—	2	4	no	—
342	C₂²×C₅×D₃	—	2	2	no	—
343	C₂²×C₅×D₃	—	2	2	no	—
344	C₂²×C₅×D₃	—	4	1	no	—
345	C₂²×C₅×D₃	—	4	2	no	—
346	C₂²×C₅×D₃	—	4	16	no	—
347	C₂²×C₅×D₃	#41	1	8	yes	—
348	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
349	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
350	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
351	C₂²×C₅×D₃	C₂⁴	1	1	yes	characteristic
352	C₃×C₅×Q₈	—	4	1	no	—
353	C₃×C₅×D₄	—	2	4	no	—
354	C₃×C₅×D₄	—	4	1	no	—
355	C₂×C₃×C₄×C₅	—	2	4	no	—
356	C₂×C₃×C₄×C₅	—	4	2	no	—
357	C₂×C₃×C₄×C₅	—	4	1	no	—
358	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
359	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
360	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
361	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
362	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
363	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
364	C₅×#67	—	2	4	no	—
365	C₅×#67	—	2	4	no	—
366	C₅×#67	—	4	1	no	—
367	C₅×#67	—	4	1	no	—
368	C₂×C₅×Dic₃	—	2	4	no	—
369	C₂×C₅×Dic₃	—	4	2	no	—
370	C₂×C₅×Dic₃	—	4	1	no	—
371	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
372	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
373	C₂×C₅×Dic₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
375	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
376	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
377	C₅×D₁₂	—	2	4	no	—
378	C₅×D₁₂	—	4	1	no	—
379	C₄×C₅×D₃	—	2	4	no	—
380	C₄×C₅×D₃	—	2	4	no	—
381	C₄×C₅×D₃	—	2	4	no	—
382	C₄×C₅×D₃	—	2	4	no	—
383	C₄×C₅×D₃	—	2	4	no	—
384	C₄×C₅×D₃	—	2	4	no	—
385	C₄×C₅×D₃	—	2	4	no	—
386	C₄×C₅×D₃	—	2	2	no	—
387	C₄×C₅×D₃	—	4	2	no	—
388	C₄×C₅×D₃	—	4	2	no	—
389	C₄×C₅×D₃	—	4	2	no	—
390	C₅×Dic₆	—	4	1	no	—
391	C₅×Dic₆	—	4	2	no	—
392	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
393	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
394	C₂×D₃×D₄	C₂²×C₅	1	2	yes	—
395	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
396	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
397	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
398	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
399	C₃×#126	C₂²×C₅	1	2	yes	complemented
400	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
401	C₃×#123	C₂²×C₅	1	1	yes	characteristic, complemented
402	C₃×#123	C₂²×C₅	1	2	yes	complemented
403	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
404	C₃×#120	C₂²×C₅	1	1	yes	characteristic
405	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
406	C₃×#117	C₂²×C₅	1	2	yes	complemented
407	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
408	#953	C₂²×C₅	1	1	yes	characteristic
409	C₂×#217	C₂²×C₅	1	2	yes	complemented
410	#947	C₂²×C₅	1	1	yes	characteristic, complemented
411	#946	C₂²×C₅	1	2	yes	complemented
412	#937	C₂²×C₅	1	2	yes	—
413	#937	C₂²×C₅	1	1	yes	characteristic
414	#936	C₂²×C₅	1	1	yes	characteristic, complemented
415	#935	C₂²×C₅	1	1	yes	characteristic, complemented
416	#935	C₂²×C₅	1	2	yes	complemented
417	D₄×Dic₃	C₂²×C₅	1	2	yes	complemented
418	#929	C₂²×C₅	1	1	yes	characteristic, complemented
419	#929	C₂²×C₅	1	2	yes	complemented
420	C₄×#67	C₂²×C₅	1	2	yes	complemented
421	C₄×#67	C₂²×C₅	1	2	yes	complemented
422	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
423	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
424	#926	C₂²×C₅	1	2	yes	complemented
425	#924	C₂²×C₅	1	2	yes	complemented
426	#898	C₂²×C₅	1	2	yes	complemented
427	#898	C₂²×C₅	1	2	yes	complemented
428	#898	C₂²×C₅	1	2	yes	complemented
429	#897	C₂²×C₅	1	2	yes	complemented
430	#896	C₂²×C₅	1	2	yes	complemented
431	#896	C₂²×C₅	1	2	yes	complemented
432	#894	C₂²×C₅	1	2	yes	complemented
433	#894	C₂²×C₅	1	2	yes	complemented
434	#894	C₂²×C₅	1	2	yes	complemented
435	#893	C₂²×C₅	1	2	yes	complemented
436	#892	C₂²×C₅	1	2	yes	complemented
437	#892	C₂²×C₅	1	2	yes	complemented
438	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
439	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
440	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
441	D₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
442	#886	C₂²×C₅	1	1	yes	characteristic, complemented
443	#886	C₂²×C₅	1	2	yes	complemented
444	#885	C₂²×C₅	1	2	yes	complemented
445	#885	C₂²×C₅	1	2	yes	complemented
446	#883	C₂²×C₅	1	2	yes	complemented
447	#883	C₂²×C₅	1	2	yes	complemented
448	#883	C₂²×C₅	1	2	yes	complemented
449	#882	C₂²×C₅	1	2	yes	—
450	#882	C₂²×C₅	1	1	yes	characteristic
451	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
452	#67⋊C₄	C₂²×C₅	1	2	yes	complemented
453	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
454	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
455	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
456	D₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
457	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
458	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
459	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
460	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
461	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
462	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
463	D₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
464	D₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
465	#879	C₂²×C₅	1	2	yes	complemented
466	#879	C₂²×C₅	1	2	yes	complemented
467	#879	C₂²×C₅	1	2	yes	complemented
468	#878	C₂²×C₅	1	2	yes	complemented
469	#878	C₂²×C₅	1	2	yes	complemented
470	#877	C₂²×C₅	1	2	yes	complemented
471	#877	C₂²×C₅	1	2	yes	complemented
472	#876	C₂²×C₅	1	2	yes	complemented
473	#875	C₂²×C₅	1	1	yes	characteristic, complemented
474	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
475	#872	C₂²×C₅	1	2	yes	complemented
476	#872	C₂²×C₅	1	2	yes	complemented
477	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
478	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
479	C₂⁴×C₅	—	3	2	no	—
480	C₂⁴×C₅	—	3	1	no	—
481	C₂⁴×C₅	—	3	1	no	—
482	C₂⁴×C₅	—	3	1	no	—
483	C₂⁴×C₅	—	3	2	no	—
484	C₂⁴×C₅	—	6	8	no	—
485	C₂⁴×C₅	—	12	2	no	—
486	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
487	C₂×C₅×Q₈	—	3	2	no	—
488	C₂×C₅×Q₈	—	3	1	no	—
489	C₂×C₅×Q₈	—	12	2	no	—
490	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic, complemented
491	C₂×C₅×D₄	—	3	2	no	—
492	C₂×C₅×D₄	—	3	2	no	—
493	C₂×C₅×D₄	—	3	1	no	—
494	C₂×C₅×D₄	—	3	1	no	—
495	C₂×C₅×D₄	—	3	2	no	—
496	C₂×C₅×D₄	—	3	1	no	—
497	C₂×C₅×D₄	—	6	8	no	—
498	C₂×C₅×D₄	—	12	2	no	—
499	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
500	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
501	C₂²×C₄×C₅	—	3	2	no	—
502	C₂²×C₄×C₅	—	3	2	no	—
503	C₂²×C₄×C₅	—	3	1	no	—
504	C₂²×C₄×C₅	—	3	2	no	—
505	C₂²×C₄×C₅	—	3	2	no	—
506	C₂²×C₄×C₅	—	3	2	no	—
507	C₂²×C₄×C₅	—	3	1	no	—
508	C₂²×C₄×C₅	—	3	2	no	—
509	C₂²×C₄×C₅	—	3	2	no	—
510	C₂²×C₄×C₅	—	3	2	no	—
511	C₂²×C₄×C₅	—	3	2	no	—
512	C₂²×C₄×C₅	—	3	2	no	—
513	C₂²×C₄×C₅	—	3	2	no	—
514	C₂²×C₄×C₅	—	3	2	no	—
515	C₂²×C₄×C₅	—	6	8	no	—
516	C₂²×C₄×C₅	—	12	4	no	—
517	C₂²×C₄×C₅	—	12	2	no	—
518	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
519	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
520	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic, complemented
521	C₅×C₄⋊C₄	—	3	2	no	—
522	C₅×C₄⋊C₄	—	3	2	no	—
523	C₅×C₄⋊C₄	—	3	2	no	—
524	C₅×C₄⋊C₄	—	3	2	no	—
525	C₅×C₄⋊C₄	—	3	2	no	—
526	C₅×C₄⋊C₄	—	3	2	no	—
527	C₅×C₄⋊C₄	—	3	2	no	—
528	C₅×C₄⋊C₄	—	3	2	no	—
529	C₅×C₄⋊C₄	—	3	2	no	—
530	C₅×C₄⋊C₄	—	3	2	no	—
531	C₅×C₄⋊C₄	—	3	2	no	—
532	C₅×C₄⋊C₄	—	3	2	no	—
533	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	complemented
534	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	complemented
535	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	complemented
536	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	complemented
537	C₅×C₂²⋊C₄	—	3	2	no	—
538	C₅×C₂²⋊C₄	—	3	2	no	—
539	C₅×C₂²⋊C₄	—	3	2	no	—
540	C₅×C₂²⋊C₄	—	3	2	no	—
541	C₅×C₂²⋊C₄	—	3	2	no	—
542	C₅×C₂²⋊C₄	—	3	2	no	—
543	C₅×C₂²⋊C₄	—	3	1	no	—
544	C₅×C₂²⋊C₄	—	3	1	no	—
545	C₅×C₂²⋊C₄	—	3	2	no	—
546	C₅×C₂²⋊C₄	—	3	2	no	—
547	C₅×C₂²⋊C₄	—	3	2	no	—
548	C₅×C₂²⋊C₄	—	3	2	no	—
549	C₅×C₂²⋊C₄	—	3	2	no	—
550	C₅×C₂²⋊C₄	—	3	2	no	—
551	C₅×C₂²⋊C₄	—	3	2	no	—
552	C₅×C₂²⋊C₄	—	3	2	no	—
553	C₅×C₂²⋊C₄	—	3	2	no	—
554	C₅×C₂²⋊C₄	—	3	2	no	—
555	C₅×C₂²⋊C₄	—	3	2	no	—
556	C₅×C₂²⋊C₄	—	3	2	no	—
557	C₅×C₂²⋊C₄	—	3	2	no	—
558	C₅×C₂²⋊C₄	—	3	2	no	—
559	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
560	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
561	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
562	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
563	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
564	C₅×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
565	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	complemented
566	C₅×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic, complemented
567	C₄²×C₅	—	3	1	no	—
568	C₄²×C₅	—	3	2	no	—
569	C₄²×C₅	—	3	2	no	—
570	C₄²×C₅	—	3	2	no	—
571	C₄²×C₅	—	3	2	no	—
572	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic, complemented
573	C₄²×C₅	C₂²×D₃	1	2	yes	complemented
574	#551	—	3	2	no	—
575	#551	—	3	1	no	—
576	#551	—	3	2	no	—
577	#551	—	3	1	no	—
578	#551	—	3	2	no	—
579	#551	—	3	1	no	—
580	#551	—	3	2	no	—
581	#551	—	3	2	no	—
582	#551	—	3	2	no	—
583	#551	C₅×D₃	1	1	yes	characteristic, direct product factor
584	C₂×#126	—	3	2	no	—
585	C₂×#124	—	3	1	no	—
586	C₂×#123	—	3	2	no	—
587	C₂×#123	—	3	1	no	—
588	C₂×C₂²⋊Q₈	—	3	2	no	—
589	C₂×#120	—	3	1	no	—
590	C₂×C₄×D₄	—	3	2	no	—
591	C₂×#117	—	3	2	no	—
592	C₂²×C₂²⋊C₄	—	3	2	no	—
593	C₂²×C₃×C₅	—	2	2	no	—
594	C₂²×C₃×C₅	—	2	2	no	—
595	C₂²×C₃×C₅	—	2	2	no	—
596	C₂²×C₃×C₅	—	2	2	no	—
597	C₂²×C₃×C₅	—	2	1	no	—
598	C₂²×C₃×C₅	—	2	1	no	—
599	C₂²×C₃×C₅	—	4	4	no	—
600	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
601	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
602	C₂×C₅×D₃	—	2	2	no	—
603	C₂×C₅×D₃	—	2	2	no	—
604	C₂×C₅×D₃	—	2	16	no	—
605	C₂×C₅×D₃	—	2	2	no	—
606	C₂×C₅×D₃	—	2	2	no	—
607	C₂×C₅×D₃	—	2	1	no	—
608	C₂×C₅×D₃	—	2	1	no	—
609	C₂×C₅×D₃	—	4	4	no	—
610	C₂×C₅×D₃	—	4	8	no	—
611	C₂×C₅×D₃	—	4	4	no	—
612	C₂×C₅×D₃	—	4	4	no	—
613	C₂×C₅×D₃	C₂×#41	1	4	yes	—
614	C₂×C₅×D₃	C₂×#41	1	4	yes	—
615	C₂×C₅×D₃	H(5,𝔽₂)	1	2	yes	—
616	C₃×C₄×C₅	—	2	2	no	—
617	C₃×C₄×C₅	—	2	2	no	—
618	C₃×C₄×C₅	—	2	2	no	—
619	C₃×C₄×C₅	—	2	2	no	—
620	C₃×C₄×C₅	—	2	1	no	—
621	C₃×C₄×C₅	—	2	2	no	—
622	C₅×Dic₃	—	2	2	no	—
623	C₅×Dic₃	—	2	2	no	—
624	C₅×Dic₃	—	2	2	no	—
625	C₅×Dic₃	—	2	2	no	—
626	C₅×Dic₃	—	2	1	no	—
627	C₅×Dic₃	—	2	2	no	—
628	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
629	C₂³×D₃	—	2	8	no	—
630	C₂³×D₃	—	4	2	no	—
631	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
632	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
633	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
634	C₂³×D₃	C₂³×C₅	1	2	yes	—
635	C₂³×D₃	C₂³×C₅	1	2	yes	—
636	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic, complemented
637	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
638	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
639	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
640	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
641	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic, complemented
642	C₂×#67	C₂³×C₅	1	2	yes	—
643	C₂×#67	C₂³×C₅	1	2	yes	—
644	C₂×#67	C₂³×C₅	1	1	yes	characteristic
645	C₂×#67	C₂³×C₅	1	1	yes	characteristic
646	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
647	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
648	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic, complemented
649	D₃×Q₈	—	4	2	no	—
650	D₃×D₄	—	2	8	no	—
651	D₃×D₄	—	4	2	no	—
652	C₂×D₁₂	C₂³×C₅	1	2	yes	—
653	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
654	C₂×C₄×D₃	—	2	8	no	—
655	C₂×C₄×D₃	—	4	4	no	—
656	C₂×C₄×D₃	—	4	2	no	—
657	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
658	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
659	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
660	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
661	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
662	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
663	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
664	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
665	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
666	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
667	C₂×C₄×D₃	C₂³×C₅	1	2	yes	complemented
668	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic, complemented
669	C₂×Dic₆	C₂³×C₅	1	2	yes	complemented
670	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	complemented
671	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	complemented
672	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	complemented
673	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	complemented
674	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
675	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
676	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
677	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic
678	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
679	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
680	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	complemented
681	C₃×C₂²⋊C₄	C₂³×C₅	1	1	yes	characteristic, complemented
682	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic, complemented
683	C₃×C₄²	C₂³×C₅	1	2	yes	complemented
684	#217	C₂³×C₅	1	2	yes	—
685	#217	C₂³×C₅	1	2	yes	—
686	#217	C₂³×C₅	1	2	yes	—
687	#217	C₂³×C₅	1	1	yes	characteristic
688	#217	C₂³×C₅	1	2	yes	—
689	#217	C₂³×C₅	1	2	yes	—
690	#217	C₂³×C₅	1	1	yes	characteristic, complemented
691	#217	C₂³×C₅	1	2	yes	complemented
692	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
693	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
694	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
695	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
696	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
697	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
698	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
699	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
700	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
701	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
702	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
703	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	complemented
704	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	complemented
705	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	complemented
706	C₄⋊Dic₃	C₂³×C₅	1	2	yes	complemented
707	C₄⋊Dic₃	C₂³×C₅	1	2	yes	complemented
708	C₄⋊Dic₃	C₂³×C₅	1	2	yes	complemented
709	C₄⋊Dic₃	C₂³×C₅	1	2	yes	complemented
710	Dic₃⋊C₄	C₂³×C₅	1	2	yes	complemented
711	Dic₃⋊C₄	C₂³×C₅	1	2	yes	complemented
712	Dic₃⋊C₄	C₂³×C₅	1	2	yes	complemented
713	Dic₃⋊C₄	C₂³×C₅	1	2	yes	complemented
714	Dic₃⋊C₄	C₂³×C₅	1	2	yes	complemented
715	Dic₃⋊C₄	C₂³×C₅	1	2	yes	complemented
716	Dic₃⋊C₄	C₂³×C₅	1	2	yes	complemented
717	Dic₃⋊C₄	C₂³×C₅	1	2	yes	complemented
718	C₄×Dic₃	C₂³×C₅	1	2	yes	complemented
719	C₄×Dic₃	C₂³×C₅	1	2	yes	complemented
720	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic, complemented
721	C₄×Dic₃	C₂³×C₅	1	2	yes	complemented
722	C₄×Dic₃	C₂³×C₅	1	2	yes	complemented
723	C₂³×C₅	—	2	4	no	—
724	C₂³×C₅	—	3	1	no	—
725	C₂³×C₅	—	3	8	no	—
726	C₂³×C₅	—	3	2	no	—
727	C₂³×C₅	—	3	1	no	—
728	C₂³×C₅	—	3	1	no	—
729	C₂³×C₅	—	4	1	no	—
730	C₂³×C₅	—	6	4	no	—
731	C₂³×C₅	—	6	4	no	—
732	C₂³×C₅	—	6	2	no	—
733	C₂³×C₅	—	6	4	no	—
734	C₂³×C₅	—	6	2	no	—
735	C₂³×C₅	—	6	4	no	—
736	C₂³×C₅	—	6	4	no	—
737	C₂³×C₅	—	6	4	no	—
738	C₂³×C₅	—	6	4	no	—
739	C₂³×C₅	—	12	2	no	—
740	C₂³×C₅	—	12	1	no	—
741	C₂³×C₅	—	12	16	no	—
742	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
743	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
744	C₂³×C₅	C₂³×D₃	1	2	yes	—
745	C₅×Q₈	—	4	1	no	—
746	C₅×Q₈	—	12	2	no	—
747	C₅×Q₈	—	12	1	no	—
748	C₅×D₄	—	2	4	no	—
749	C₅×D₄	—	4	1	no	—
750	C₅×D₄	—	6	4	no	—
751	C₅×D₄	—	6	4	no	—
752	C₅×D₄	—	6	4	no	—
753	C₅×D₄	—	12	1	no	—
754	C₅×D₄	—	12	1	no	—
755	C₅×D₄	—	12	1	no	—
756	C₂×C₄×C₅	—	2	4	no	—
757	C₂×C₄×C₅	—	3	2	no	—
758	C₂×C₄×C₅	—	3	2	no	—
759	C₂×C₄×C₅	—	3	2	no	—
760	C₂×C₄×C₅	—	3	1	no	—
761	C₂×C₄×C₅	—	3	2	no	—
762	C₂×C₄×C₅	—	3	2	no	—
763	C₂×C₄×C₅	—	4	2	no	—
764	C₂×C₄×C₅	—	4	1	no	—
765	C₂×C₄×C₅	—	6	4	no	—
766	C₂×C₄×C₅	—	6	4	no	—
767	C₂×C₄×C₅	—	6	4	no	—
768	C₂×C₄×C₅	—	6	4	no	—
769	C₂×C₄×C₅	—	6	4	no	—
770	C₂×C₄×C₅	—	6	4	no	—
771	C₂×C₄×C₅	—	6	4	no	—
772	C₂×C₄×C₅	—	6	2	no	—
773	C₂×C₄×C₅	—	6	4	no	—
774	C₂×C₄×C₅	—	12	2	no	—
775	C₂×C₄×C₅	—	12	2	no	—
776	C₂×C₄×C₅	—	12	2	no	—
777	C₂×C₄×C₅	—	12	1	no	—
778	C₂×C₄×C₅	—	12	2	no	—
779	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
780	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
781	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
782	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
783	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
784	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
785	C₂⁵	—	3	1	no	—
786	C₂²×Q₈	—	3	1	no	—
787	C₂²×D₄	—	3	2	no	—
788	C₂²×D₄	—	3	1	no	—
789	C₂³×C₄	—	3	2	no	—
790	C₂³×C₄	—	3	2	no	—
791	C₂³×C₄	—	3	1	no	—
792	#126	—	3	2	no	—
793	#126	—	3	2	no	—
794	#126	—	3	2	no	—
795	#126	—	3	2	no	—
796	#126	—	3	2	no	—
797	#126	—	3	2	no	—
798	#126	—	3	2	no	—
799	#126	C₂×C₅×D₃	1	2	yes	complemented
800	#124	—	3	1	no	—
801	#124	—	3	1	no	—
802	#124	—	3	2	no	—
803	#124	—	3	2	no	—
804	#124	—	3	1	no	—
805	#124	C₂×C₅×D₃	1	1	yes	characteristic, complemented
806	#123	—	3	2	no	—
807	#123	—	3	1	no	—
808	#123	—	3	2	no	—
809	#123	—	3	1	no	—
810	#123	—	3	2	no	—
811	#123	—	3	2	no	—
812	#123	—	3	2	no	—
813	#123	—	3	2	no	—
814	#123	—	3	2	no	—
815	#123	—	3	2	no	—
816	#123	—	3	2	no	—
817	#123	—	3	1	no	—
818	#123	C₂×C₅×D₃	1	1	yes	characteristic, complemented
819	#123	C₂×C₅×D₃	1	2	yes	complemented
820	C₂²⋊Q₈	—	3	2	no	—
821	C₂²⋊Q₈	—	3	2	no	—
822	C₂²⋊Q₈	—	3	2	no	—
823	C₂²⋊Q₈	—	3	2	no	—
824	C₂²⋊Q₈	—	3	2	no	—
825	C₂²⋊Q₈	—	3	2	no	—
826	C₂²⋊Q₈	—	3	2	no	—
827	C₂²⋊Q₈	C₂×C₅×D₃	1	2	yes	complemented
828	#120	—	3	1	no	—
829	#120	—	3	2	no	—
830	#120	—	3	1	no	—
831	#120	—	3	1	no	—
832	#120	—	3	2	no	—
833	#120	C₂×C₅×D₃	1	1	yes	characteristic
834	C₄×D₄	—	3	2	no	—
835	C₄×D₄	—	3	2	no	—
836	C₄×D₄	—	3	2	no	—
837	C₄×D₄	—	3	2	no	—
838	C₄×D₄	—	3	2	no	—
839	C₄×D₄	—	3	2	no	—
840	C₄×D₄	—	3	2	no	—
841	C₄×D₄	C₂×C₅×D₃	1	2	yes	complemented
842	#117	—	3	2	no	—
843	#117	—	3	2	no	—
844	#117	—	3	2	no	—
845	#117	—	3	2	no	—
846	#117	—	3	2	no	—
847	#117	—	3	2	no	—
848	#117	—	3	2	no	—
849	#117	C₂×C₅×D₃	1	2	yes	complemented
850	C₂×C₄⋊C₄	—	3	2	no	—
851	C₂×C₄⋊C₄	—	3	2	no	—
852	C₂×C₄⋊C₄	—	3	2	no	—
853	C₂×C₄⋊C₄	—	3	2	no	—
854	C₂×C₂²⋊C₄	—	3	2	no	—
855	C₂×C₂²⋊C₄	—	3	2	no	—
856	C₂×C₂²⋊C₄	—	3	2	no	—
857	C₂×C₂²⋊C₄	—	3	2	no	—
858	C₂×C₂²⋊C₄	—	3	2	no	—
859	C₂×C₂²⋊C₄	—	3	2	no	—
860	C₂×C₂²⋊C₄	—	3	2	no	—
861	C₂×C₂²⋊C₄	—	3	2	no	—
862	C₂×C₂²⋊C₄	—	3	2	no	—
863	C₂×C₂²⋊C₄	—	3	2	no	—
864	C₂×C₂²⋊C₄	—	3	2	no	—
865	C₂×C₂²⋊C₄	—	3	2	no	—
866	C₂×C₂²⋊C₄	—	3	1	no	—
867	C₂×C₂²⋊C₄	—	3	2	no	—
868	C₂×C₂²⋊C₄	—	3	1	no	—
869	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
870	C₂×C₄²	—	3	1	no	—
871	C₂×C₄²	—	3	2	no	—
872	C₂×C₃×C₅	—	2	4	no	—
873	C₂×C₃×C₅	—	4	1	no	—
874	C₂×C₃×C₅	—	4	1	no	—
875	C₂×C₃×C₅	C₂²×#41	1	2	yes	—
876	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
877	C₅×D₃	—	2	4	no	—
878	C₅×D₃	—	4	1	no	—
879	C₅×D₃	—	4	1	no	—
880	C₅×D₃	#551	1	4	yes	direct product factor
881	C₂³×C₃	—	2	4	no	—
882	C₂³×C₃	—	4	1	no	—
883	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
884	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
885	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
886	C₂²×D₃	—	2	4	no	—
887	C₂²×D₃	—	2	4	no	—
888	C₂²×D₃	—	2	4	no	—
889	C₂²×D₃	—	2	4	no	—
890	C₂²×D₃	—	2	4	no	—
891	C₂²×D₃	—	2	4	no	—
892	C₂²×D₃	—	2	4	no	—
893	C₂²×D₃	—	2	2	no	—
894	C₂²×D₃	—	2	2	no	—
895	C₂²×D₃	—	4	1	no	—
896	C₂²×D₃	—	4	2	no	—
897	C₂²×D₃	—	4	16	no	—
898	C₂²×D₃	C₅×#41	1	8	yes	—
899	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
900	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
901	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
902	C₂²×D₃	C₂⁴×C₅	1	1	yes	characteristic
903	C₃×Q₈	—	4	1	no	—
904	C₃×D₄	—	2	4	no	—
905	C₃×D₄	—	4	1	no	—
906	C₂×C₃×C₄	—	2	4	no	—
907	C₂×C₃×C₄	—	4	2	no	—
908	C₂×C₃×C₄	—	4	1	no	—
909	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
910	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
911	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
912	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
913	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
914	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
915	#67	—	2	4	no	—
916	#67	—	2	4	no	—
917	#67	—	4	1	no	—
918	#67	—	4	1	no	—
919	C₂×Dic₃	—	2	4	no	—
920	C₂×Dic₃	—	4	2	no	—
921	C₂×Dic₃	—	4	1	no	—
922	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
923	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
924	C₂×Dic₃	C₂⁴×C₅	1	1	yes	characteristic
925	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
926	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
927	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
928	D₁₂	—	2	4	no	—
929	D₁₂	—	4	1	no	—
930	C₄×D₃	—	2	4	no	—
931	C₄×D₃	—	2	4	no	—
932	C₄×D₃	—	2	4	no	—
933	C₄×D₃	—	2	4	no	—
934	C₄×D₃	—	2	4	no	—
935	C₄×D₃	—	2	4	no	—
936	C₄×D₃	—	2	4	no	—
937	C₄×D₃	—	2	2	no	—
938	C₄×D₃	—	4	2	no	—
939	C₄×D₃	—	4	2	no	—
940	C₄×D₃	—	4	2	no	—
941	Dic₆	—	4	1	no	—
942	Dic₆	—	4	2	no	—
943	C₂²×C₅	—	2	2	no	—
944	C₂²×C₅	—	2	2	no	—
945	C₂²×C₅	—	2	2	no	—
946	C₂²×C₅	—	2	2	no	—
947	C₂²×C₅	—	2	1	no	—
948	C₂²×C₅	—	2	1	no	—
949	C₂²×C₅	—	3	4	no	—
950	C₂²×C₅	—	3	2	no	—
951	C₂²×C₅	—	3	4	no	—
952	C₂²×C₅	—	4	4	no	—
953	C₂²×C₅	—	6	16	no	—
954	C₂²×C₅	—	6	2	no	—
955	C₂²×C₅	—	6	2	no	—
956	C₂²×C₅	—	6	2	no	—
957	C₂²×C₅	—	6	2	no	—
958	C₂²×C₅	—	6	1	no	—
959	C₂²×C₅	—	6	1	no	—
960	C₂²×C₅	—	12	8	no	—
961	C₂²×C₅	—	12	4	no	—
962	C₂²×C₅	—	12	4	no	—
963	C₂²×C₅	—	12	4	no	—
964	C₂²×C₅	D₃×#41	1	4	yes	—
965	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
966	C₄×C₅	—	2	2	no	—
967	C₄×C₅	—	2	2	no	—
968	C₄×C₅	—	2	2	no	—
969	C₄×C₅	—	2	2	no	—
970	C₄×C₅	—	2	2	no	—
971	C₄×C₅	—	2	1	no	—
972	C₄×C₅	—	6	2	no	—
973	C₄×C₅	—	6	2	no	—
974	C₄×C₅	—	6	2	no	—
975	C₄×C₅	—	6	2	no	—
976	C₄×C₅	—	6	2	no	—
977	C₄×C₅	—	6	1	no	—
978	C₂⁴	—	3	2	no	—
979	C₂⁴	—	3	1	no	—
980	C₂⁴	—	3	1	no	—
981	C₂⁴	—	3	1	no	—
982	C₂⁴	—	3	2	no	—
983	C₂⁴	—	6	8	no	—
984	C₂⁴	—	12	2	no	—
985	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
986	C₂×Q₈	—	3	2	no	—
987	C₂×Q₈	—	3	1	no	—
988	C₂×Q₈	—	12	2	no	—
989	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic, complemented
990	C₂×D₄	—	3	2	no	—
991	C₂×D₄	—	3	2	no	—
992	C₂×D₄	—	3	1	no	—
993	C₂×D₄	—	3	1	no	—
994	C₂×D₄	—	3	2	no	—
995	C₂×D₄	—	3	1	no	—
996	C₂×D₄	—	6	8	no	—
997	C₂×D₄	—	12	2	no	—
998	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
999	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
1000	C₂²×C₄	—	3	2	no	—
1001	C₂²×C₄	—	3	2	no	—
1002	C₂²×C₄	—	3	1	no	—
1003	C₂²×C₄	—	3	2	no	—
1004	C₂²×C₄	—	3	2	no	—
1005	C₂²×C₄	—	3	2	no	—
1006	C₂²×C₄	—	3	1	no	—
1007	C₂²×C₄	—	3	2	no	—
1008	C₂²×C₄	—	3	2	no	—
1009	C₂²×C₄	—	3	2	no	—
1010	C₂²×C₄	—	3	2	no	—
1011	C₂²×C₄	—	3	2	no	—
1012	C₂²×C₄	—	3	2	no	—
1013	C₂²×C₄	—	3	2	no	—
1014	C₂²×C₄	—	6	8	no	—
1015	C₂²×C₄	—	12	4	no	—
1016	C₂²×C₄	—	12	2	no	—
1017	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
1018	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
1019	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic, complemented
1020	C₄⋊C₄	—	3	2	no	—
1021	C₄⋊C₄	—	3	2	no	—
1022	C₄⋊C₄	—	3	2	no	—
1023	C₄⋊C₄	—	3	2	no	—
1024	C₄⋊C₄	—	3	2	no	—
1025	C₄⋊C₄	—	3	2	no	—
1026	C₄⋊C₄	—	3	2	no	—
1027	C₄⋊C₄	—	3	2	no	—
1028	C₄⋊C₄	—	3	2	no	—
1029	C₄⋊C₄	—	3	2	no	—
1030	C₄⋊C₄	—	3	2	no	—
1031	C₄⋊C₄	—	3	2	no	—
1032	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	complemented
1033	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	complemented
1034	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	complemented
1035	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	complemented
1036	C₂²⋊C₄	—	3	2	no	—
1037	C₂²⋊C₄	—	3	2	no	—
1038	C₂²⋊C₄	—	3	2	no	—
1039	C₂²⋊C₄	—	3	2	no	—
1040	C₂²⋊C₄	—	3	2	no	—
1041	C₂²⋊C₄	—	3	2	no	—
1042	C₂²⋊C₄	—	3	1	no	—
1043	C₂²⋊C₄	—	3	1	no	—
1044	C₂²⋊C₄	—	3	2	no	—
1045	C₂²⋊C₄	—	3	2	no	—
1046	C₂²⋊C₄	—	3	2	no	—
1047	C₂²⋊C₄	—	3	2	no	—
1048	C₂²⋊C₄	—	3	2	no	—
1049	C₂²⋊C₄	—	3	2	no	—
1050	C₂²⋊C₄	—	3	2	no	—
1051	C₂²⋊C₄	—	3	2	no	—
1052	C₂²⋊C₄	—	3	2	no	—
1053	C₂²⋊C₄	—	3	2	no	—
1054	C₂²⋊C₄	—	3	2	no	—
1055	C₂²⋊C₄	—	3	2	no	—
1056	C₂²⋊C₄	—	3	2	no	—
1057	C₂²⋊C₄	—	3	2	no	—
1058	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1059	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1060	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1061	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1062	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
1063	C₂²⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
1064	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	complemented
1065	C₂²⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic, complemented
1066	C₄²	—	3	1	no	—
1067	C₄²	—	3	2	no	—
1068	C₄²	—	3	2	no	—
1069	C₄²	—	3	2	no	—
1070	C₄²	—	3	2	no	—
1071	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic, complemented
1072	C₄²	C₂²×C₅×D₃	1	2	yes	complemented
1073	C₃×C₅	C₂×#551	1	1	yes	characteristic, complemented, Hall
1074	C₂²×C₃	—	2	2	no	—
1075	C₂²×C₃	—	2	2	no	—
1076	C₂²×C₃	—	2	2	no	—
1077	C₂²×C₃	—	2	2	no	—
1078	C₂²×C₃	—	2	1	no	—
1079	C₂²×C₃	—	2	1	no	—
1080	C₂²×C₃	—	4	4	no	—
1081	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
1082	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1083	C₂×D₃	—	2	2	no	—
1084	C₂×D₃	—	2	2	no	—
1085	C₂×D₃	—	2	16	no	—
1086	C₂×D₃	—	2	2	no	—
1087	C₂×D₃	—	2	2	no	—
1088	C₂×D₃	—	2	1	no	—
1089	C₂×D₃	—	2	1	no	—
1090	C₂×D₃	—	4	4	no	—
1091	C₂×D₃	—	4	8	no	—
1092	C₂×D₃	—	4	4	no	—
1093	C₂×D₃	—	4	4	no	—
1094	C₂×D₃	C₂×C₅×#41	1	4	yes	—
1095	C₂×D₃	C₂×C₅×#41	1	4	yes	—
1096	C₂×D₃	C₅×H(5,𝔽₂)	1	2	yes	—
1097	C₃×C₄	—	2	2	no	—
1098	C₃×C₄	—	2	2	no	—
1099	C₃×C₄	—	2	2	no	—
1100	C₃×C₄	—	2	2	no	—
1101	C₃×C₄	—	2	1	no	—
1102	C₃×C₄	—	2	2	no	—
1103	Dic₃	—	2	2	no	—
1104	Dic₃	—	2	2	no	—
1105	Dic₃	—	2	2	no	—
1106	Dic₃	—	2	2	no	—
1107	Dic₃	—	2	1	no	—
1108	Dic₃	—	2	2	no	—
1109	C₂×C₅	—	2	4	no	—
1110	C₂×C₅	—	3	4	no	—
1111	C₂×C₅	—	4	1	no	—
1112	C₂×C₅	—	4	1	no	—
1113	C₂×C₅	—	6	4	no	—
1114	C₂×C₅	—	12	1	no	—
1115	C₂×C₅	—	12	1	no	—
1116	C₂×C₅	C₂×D₃×#41	1	2	yes	—
1117	C₂×C₅	D₃×H(5,𝔽₂)	1	1	yes	characteristic
1118	C₂³	—	2	4	no	—
1119	C₂³	—	3	1	no	—
1120	C₂³	—	3	8	no	—
1121	C₂³	—	3	2	no	—
1122	C₂³	—	3	1	no	—
1123	C₂³	—	3	1	no	—
1124	C₂³	—	4	1	no	—
1125	C₂³	—	6	4	no	—
1126	C₂³	—	6	4	no	—
1127	C₂³	—	6	2	no	—
1128	C₂³	—	6	4	no	—
1129	C₂³	—	6	2	no	—
1130	C₂³	—	6	4	no	—
1131	C₂³	—	6	4	no	—
1132	C₂³	—	6	4	no	—
1133	C₂³	—	6	4	no	—
1134	C₂³	—	12	2	no	—
1135	C₂³	—	12	1	no	—
1136	C₂³	—	12	16	no	—
1137	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1138	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
1139	C₂³	C₂³×C₅×D₃	1	2	yes	—
1140	Q₈	—	4	1	no	—
1141	Q₈	—	12	2	no	—
1142	Q₈	—	12	1	no	—
1143	D₄	—	2	4	no	—
1144	D₄	—	4	1	no	—
1145	D₄	—	6	4	no	—
1146	D₄	—	6	4	no	—
1147	D₄	—	6	4	no	—
1148	D₄	—	12	1	no	—
1149	D₄	—	12	1	no	—
1150	D₄	—	12	1	no	—
1151	C₂×C₄	—	2	4	no	—
1152	C₂×C₄	—	3	2	no	—
1153	C₂×C₄	—	3	2	no	—
1154	C₂×C₄	—	3	2	no	—
1155	C₂×C₄	—	3	1	no	—
1156	C₂×C₄	—	3	2	no	—
1157	C₂×C₄	—	3	2	no	—
1158	C₂×C₄	—	4	2	no	—
1159	C₂×C₄	—	4	1	no	—
1160	C₂×C₄	—	6	4	no	—
1161	C₂×C₄	—	6	4	no	—
1162	C₂×C₄	—	6	4	no	—
1163	C₂×C₄	—	6	4	no	—
1164	C₂×C₄	—	6	4	no	—
1165	C₂×C₄	—	6	4	no	—
1166	C₂×C₄	—	6	4	no	—
1167	C₂×C₄	—	6	2	no	—
1168	C₂×C₄	—	6	4	no	—
1169	C₂×C₄	—	12	2	no	—
1170	C₂×C₄	—	12	2	no	—
1171	C₂×C₄	—	12	2	no	—
1172	C₂×C₄	—	12	1	no	—
1173	C₂×C₄	—	12	2	no	—
1174	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1175	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1176	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1177	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
1178	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1179	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
1180	C₂×C₃	—	2	4	no	—
1181	C₂×C₃	—	4	1	no	—
1182	C₂×C₃	—	4	1	no	—
1183	C₂×C₃	C₂²×C₅×#41	1	2	yes	—
1184	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1185	D₃	—	2	4	no	—
1186	D₃	—	4	1	no	—
1187	D₃	—	4	1	no	—
1188	D₃	C₅×#551	1	4	yes	direct product factor
1189	C₅	D₃×#551	1	1	yes	characteristic, direct product factor, Sylow
1190	C₂²	—	2	2	no	—
1191	C₂²	—	2	2	no	—
1192	C₂²	—	2	2	no	—
1193	C₂²	—	2	2	no	—
1194	C₂²	—	2	1	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	3	4	no	—
1197	C₂²	—	3	2	no	—
1198	C₂²	—	3	4	no	—
1199	C₂²	—	4	4	no	—
1200	C₂²	—	6	16	no	—
1201	C₂²	—	6	2	no	—
1202	C₂²	—	6	2	no	—
1203	C₂²	—	6	2	no	—
1204	C₂²	—	6	2	no	—
1205	C₂²	—	6	1	no	—
1206	C₂²	—	6	1	no	—
1207	C₂²	—	12	8	no	—
1208	C₂²	—	12	4	no	—
1209	C₂²	—	12	4	no	—
1210	C₂²	—	12	4	no	—
1211	C₂²	C₅×D₃×#41	1	4	yes	—
1212	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
1213	C₄	—	2	2	no	—
1214	C₄	—	2	2	no	—
1215	C₄	—	2	2	no	—
1216	C₄	—	2	2	no	—
1217	C₄	—	2	2	no	—
1218	C₄	—	2	1	no	—
1219	C₄	—	6	2	no	—
1220	C₄	—	6	2	no	—
1221	C₄	—	6	2	no	—
1222	C₄	—	6	2	no	—
1223	C₄	—	6	2	no	—
1224	C₄	—	6	1	no	—
1225	C₃	C₂×C₅×#551	1	1	yes	characteristic, complemented, Sylow
1226	C₂	—	2	4	no	—
1227	C₂	—	3	4	no	—
1228	C₂	—	4	1	no	—
1229	C₂	—	4	1	no	—
1230	C₂	—	6	4	no	—
1231	C₂	—	12	1	no	—
1232	C₂	—	12	1	no	—
1233	C₂	C₂×C₅×D₃×#41	1	2	yes	—
1234	C₂	C₅×D₃×H(5,𝔽₂)	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×#551	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₅×D₃×#120	C₂
hypercenter	C₅×#551	D₃
hypocenter	C₃	C₂×C₅×#551
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#551

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#551	C₂	semidirect
2. C₅×#5705	C₂	semidirect
3. C₅×D₃×#126	C₂	semidirect
4. C₅×#5679	C₂	semidirect
5. C₅×D₃×#124	C₂	semidirect
6. C₅×#5659	C₂	semidirect
7. C₅×#5658	C₂	semidirect
8. C₅×D₃×#123	C₂	semidirect
9. C₅×D₃×#123	C₂	semidirect
10. C₅×#5637	C₂	semidirect
11. C₅×D₃×C₂²⋊Q₈	C₂	semidirect
13. C₅×#5587	C₂	semidirect
14. C₅×#5556	C₂	semidirect
15. C₄×C₅×D₃×D₄	C₂	semidirect
16. C₅×#5527	C₂	semidirect
17. C₅×D₃×#117	C₂	semidirect
18. C₅×#5495	C₂	semidirect
19. C₂×C₅×D₃×C₂²⋊C₄	C₂	semidirect
22. C₂×C₅×D₃×Q₈	C₂²	semidirect
27. C₂²×C₄×C₅×D₃	C₂²	semidirect
28. C₃×C₅×#126	C₂²	semidirect
29. C₃×C₅×#124	C₂²	semidirect
30. C₃×C₅×#123	C₂²	semidirect
31. C₃×C₅×#123	C₂²	semidirect
32. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
34. C₃×C₄×C₅×D₄	C₂²	semidirect
35. C₃×C₅×#117	C₂²	semidirect
36. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
38. C₂×C₅×#217	C₂²	semidirect
39. C₅×#947	C₂²	semidirect
40. C₅×#946	C₂²	semidirect
43. C₅×#936	C₂²	semidirect
44. C₅×#935	C₂²	semidirect
45. C₅×#935	C₂²	semidirect
46. C₅×D₄×Dic₃	C₂²	semidirect
47. C₅×#929	C₂²	semidirect
48. C₅×#929	C₂²	semidirect
49. C₄×C₅×#67	C₂²	semidirect
50. C₄×C₅×#67	C₂²	semidirect
51. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
52. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
53. C₅×#926	C₂²	semidirect
54. C₅×#924	C₂²	semidirect
55. C₅×#898	C₂²	semidirect
56. C₅×#898	C₂²	semidirect
57. C₅×#898	C₂²	semidirect
58. C₅×#897	C₂²	semidirect
59. C₅×#896	C₂²	semidirect
60. C₅×#896	C₂²	semidirect
61. C₅×#894	C₂²	semidirect
62. C₅×#894	C₂²	semidirect
63. C₅×#894	C₂²	semidirect
64. C₅×#893	C₂²	semidirect
65. C₅×#892	C₂²	semidirect
66. C₅×#892	C₂²	semidirect
67. C₅×D₃×C₄⋊C₄	C₂²	semidirect
68. C₅×D₃×C₄⋊C₄	C₂²	semidirect
69. C₅×D₃×C₄⋊C₄	C₂²	semidirect
70. C₅×D₃×C₄⋊C₄	C₂²	semidirect
71. C₅×#886	C₂²	semidirect
72. C₅×#886	C₂²	semidirect
73. C₅×#885	C₂²	semidirect
74. C₅×#885	C₂²	semidirect
75. C₅×#883	C₂²	semidirect
76. C₅×#883	C₂²	semidirect
77. C₅×#883	C₂²	semidirect
80. C₅×#67⋊C₄	C₂²	semidirect
81. C₅×#67⋊C₄	C₂²	semidirect
88. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
89. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
90. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
91. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
92. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
93. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
94. C₅×#879	C₂²	semidirect
95. C₅×#879	C₂²	semidirect
96. C₅×#879	C₂²	semidirect
97. C₅×#878	C₂²	semidirect
98. C₅×#878	C₂²	semidirect
99. C₅×#877	C₂²	semidirect
100. C₅×#877	C₂²	semidirect
101. C₅×#876	C₂²	semidirect
102. C₅×#875	C₂²	semidirect
103. C₄×C₅×D₁₂	C₂²	semidirect
104. C₅×#872	C₂²	semidirect
105. C₅×#872	C₂²	semidirect
106. C₄²×C₅×D₃	C₂²	semidirect
107. C₄²×C₅×D₃	C₂²	semidirect
108. D₃×#551	C₅	direct (N × H)
118. C₅×#551	D₃	direct (N × H)
136. C₂×C₃×C₅×Q₈	C₂³	semidirect
141. C₂²×C₃×C₄×C₅	C₂³	semidirect
148. C₂²×C₅×Dic₃	C₂³	semidirect
167. C₂×C₄×C₅×D₃	C₂³	semidirect
168. C₂×C₅×Dic₆	C₂³	semidirect
169. C₂×C₅×Dic₆	C₂³	semidirect
170. C₃×C₅×C₄⋊C₄	C₂³	semidirect
171. C₃×C₅×C₄⋊C₄	C₂³	semidirect
172. C₃×C₅×C₄⋊C₄	C₂³	semidirect
173. C₃×C₅×C₄⋊C₄	C₂³	semidirect
180. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
181. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
182. C₃×C₄²×C₅	C₂³	semidirect
183. C₃×C₄²×C₅	C₂³	semidirect
190. C₅×#217	C₂³	semidirect
191. C₅×#217	C₂³	semidirect
203. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
204. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
205. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
206. C₅×C₄⋊Dic₃	C₂³	semidirect
207. C₅×C₄⋊Dic₃	C₂³	semidirect
208. C₅×C₄⋊Dic₃	C₂³	semidirect
209. C₅×C₄⋊Dic₃	C₂³	semidirect
210. C₅×Dic₃⋊C₄	C₂³	semidirect
211. C₅×Dic₃⋊C₄	C₂³	semidirect
212. C₅×Dic₃⋊C₄	C₂³	semidirect
213. C₅×Dic₃⋊C₄	C₂³	semidirect
214. C₅×Dic₃⋊C₄	C₂³	semidirect
215. C₅×Dic₃⋊C₄	C₂³	semidirect
216. C₅×Dic₃⋊C₄	C₂³	semidirect
217. C₅×Dic₃⋊C₄	C₂³	semidirect
218. C₄×C₅×Dic₃	C₂³	semidirect
219. C₄×C₅×Dic₃	C₂³	semidirect
220. C₄×C₅×Dic₃	C₂³	semidirect
221. C₄×C₅×Dic₃	C₂³	semidirect
222. C₄×C₅×Dic₃	C₂³	semidirect
223. C₃×#551	C₂×C₅	semidirect
224. #5705	C₂×C₅	semidirect
225. D₃×#126	C₂×C₅	semidirect
226. #5679	C₂×C₅	semidirect
227. D₃×#124	C₂×C₅	semidirect
228. #5659	C₂×C₅	semidirect
229. #5658	C₂×C₅	semidirect
230. D₃×#123	C₂×C₅	semidirect
231. D₃×#123	C₂×C₅	semidirect
232. #5637	C₂×C₅	semidirect
233. D₃×C₂²⋊Q₈	C₂×C₅	semidirect
235. #5587	C₂×C₅	semidirect
236. #5556	C₂×C₅	semidirect
237. C₄×D₃×D₄	C₂×C₅	semidirect
238. #5527	C₂×C₅	semidirect
239. D₃×#117	C₂×C₅	semidirect
240. #5495	C₂×C₅	semidirect
241. C₂×D₃×C₂²⋊C₄	C₂×C₅	semidirect
256. C₅×#126	C₂×D₃	semidirect
262. C₅×#124	C₂×D₃	semidirect
275. C₅×#123	C₂×D₃	semidirect
276. C₅×#123	C₂×D₃	semidirect
284. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
298. C₄×C₅×D₄	C₂×D₃	semidirect
306. C₅×#117	C₂×D₃	semidirect
326. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
393. C₂×D₃×Q₈	C₂²×C₅	semidirect
398. C₂²×C₄×D₃	C₂²×C₅	semidirect
399. C₃×#126	C₂²×C₅	semidirect
400. C₃×#124	C₂²×C₅	semidirect
401. C₃×#123	C₂²×C₅	semidirect
402. C₃×#123	C₂²×C₅	semidirect
403. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
405. C₃×C₄×D₄	C₂²×C₅	semidirect
406. C₃×#117	C₂²×C₅	semidirect
407. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
409. C₂×#217	C₂²×C₅	semidirect
410. #947	C₂²×C₅	semidirect
411. #946	C₂²×C₅	semidirect
414. #936	C₂²×C₅	semidirect
415. #935	C₂²×C₅	semidirect
416. #935	C₂²×C₅	semidirect
417. D₄×Dic₃	C₂²×C₅	semidirect
418. #929	C₂²×C₅	semidirect
419. #929	C₂²×C₅	semidirect
420. C₄×#67	C₂²×C₅	semidirect
421. C₄×#67	C₂²×C₅	semidirect
422. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
423. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
424. #926	C₂²×C₅	semidirect
425. #924	C₂²×C₅	semidirect
426. #898	C₂²×C₅	semidirect
427. #898	C₂²×C₅	semidirect
428. #898	C₂²×C₅	semidirect
429. #897	C₂²×C₅	semidirect
430. #896	C₂²×C₅	semidirect
431. #896	C₂²×C₅	semidirect
432. #894	C₂²×C₅	semidirect
433. #894	C₂²×C₅	semidirect
434. #894	C₂²×C₅	semidirect
435. #893	C₂²×C₅	semidirect
436. #892	C₂²×C₅	semidirect
437. #892	C₂²×C₅	semidirect
438. D₃×C₄⋊C₄	C₂²×C₅	semidirect
439. D₃×C₄⋊C₄	C₂²×C₅	semidirect
440. D₃×C₄⋊C₄	C₂²×C₅	semidirect
441. D₃×C₄⋊C₄	C₂²×C₅	semidirect
442. #886	C₂²×C₅	semidirect
443. #886	C₂²×C₅	semidirect
444. #885	C₂²×C₅	semidirect
445. #885	C₂²×C₅	semidirect
446. #883	C₂²×C₅	semidirect
447. #883	C₂²×C₅	semidirect
448. #883	C₂²×C₅	semidirect
451. #67⋊C₄	C₂²×C₅	semidirect
452. #67⋊C₄	C₂²×C₅	semidirect
459. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
460. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
461. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
462. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
463. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
464. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
465. #879	C₂²×C₅	semidirect
466. #879	C₂²×C₅	semidirect
467. #879	C₂²×C₅	semidirect
468. #878	C₂²×C₅	semidirect
469. #878	C₂²×C₅	semidirect
470. #877	C₂²×C₅	semidirect
471. #877	C₂²×C₅	semidirect
472. #876	C₂²×C₅	semidirect
473. #875	C₂²×C₅	semidirect
474. C₄×D₁₂	C₂²×C₅	semidirect
475. #872	C₂²×C₅	semidirect
476. #872	C₂²×C₅	semidirect
477. C₄²×D₃	C₂²×C₅	semidirect
478. C₄²×D₃	C₂²×C₅	semidirect
490. C₂×C₅×Q₈	C₂²×D₃	semidirect
520. C₂²×C₄×C₅	C₂²×D₃	semidirect
533. C₅×C₄⋊C₄	C₂²×D₃	semidirect
534. C₅×C₄⋊C₄	C₂²×D₃	semidirect
535. C₅×C₄⋊C₄	C₂²×D₃	semidirect
536. C₅×C₄⋊C₄	C₂²×D₃	semidirect
565. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
566. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
572. C₄²×C₅	C₂²×D₃	semidirect
573. C₄²×C₅	C₂²×D₃	semidirect
583. #551	C₅×D₃	direct (N × H)
636. C₂×C₃×Q₈	C₂³×C₅	semidirect
641. C₂²×C₃×C₄	C₂³×C₅	semidirect
648. C₂²×Dic₃	C₂³×C₅	semidirect
667. C₂×C₄×D₃	C₂³×C₅	semidirect
668. C₂×Dic₆	C₂³×C₅	semidirect
669. C₂×Dic₆	C₂³×C₅	semidirect
670. C₃×C₄⋊C₄	C₂³×C₅	semidirect
671. C₃×C₄⋊C₄	C₂³×C₅	semidirect
672. C₃×C₄⋊C₄	C₂³×C₅	semidirect
673. C₃×C₄⋊C₄	C₂³×C₅	semidirect
680. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
681. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
682. C₃×C₄²	C₂³×C₅	semidirect
683. C₃×C₄²	C₂³×C₅	semidirect
690. #217	C₂³×C₅	semidirect
691. #217	C₂³×C₅	semidirect
703. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
704. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
705. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
706. C₄⋊Dic₃	C₂³×C₅	semidirect
707. C₄⋊Dic₃	C₂³×C₅	semidirect
708. C₄⋊Dic₃	C₂³×C₅	semidirect
709. C₄⋊Dic₃	C₂³×C₅	semidirect
710. Dic₃⋊C₄	C₂³×C₅	semidirect
711. Dic₃⋊C₄	C₂³×C₅	semidirect
712. Dic₃⋊C₄	C₂³×C₅	semidirect
713. Dic₃⋊C₄	C₂³×C₅	semidirect
714. Dic₃⋊C₄	C₂³×C₅	semidirect
715. Dic₃⋊C₄	C₂³×C₅	semidirect
716. Dic₃⋊C₄	C₂³×C₅	semidirect
717. Dic₃⋊C₄	C₂³×C₅	semidirect
718. C₄×Dic₃	C₂³×C₅	semidirect
719. C₄×Dic₃	C₂³×C₅	semidirect
720. C₄×Dic₃	C₂³×C₅	semidirect
721. C₄×Dic₃	C₂³×C₅	semidirect
722. C₄×Dic₃	C₂³×C₅	semidirect
799. #126	C₂×C₅×D₃	semidirect
805. #124	C₂×C₅×D₃	semidirect
818. #123	C₂×C₅×D₃	semidirect
819. #123	C₂×C₅×D₃	semidirect
827. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
841. C₄×D₄	C₂×C₅×D₃	semidirect
849. #117	C₂×C₅×D₃	semidirect
869. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
880. C₅×D₃	#551	direct (N × H)
989. C₂×Q₈	C₂²×C₅×D₃	semidirect
1019. C₂²×C₄	C₂²×C₅×D₃	semidirect
1032. C₄⋊C₄	C₂²×C₅×D₃	semidirect
1033. C₄⋊C₄	C₂²×C₅×D₃	semidirect
1034. C₄⋊C₄	C₂²×C₅×D₃	semidirect
1035. C₄⋊C₄	C₂²×C₅×D₃	semidirect
1064. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
1065. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
1071. C₄²	C₂²×C₅×D₃	semidirect
1072. C₄²	C₂²×C₅×D₃	semidirect
1073. C₃×C₅	C₂×#551	semidirect
1188. D₃	C₅×#551	direct (N × H)
1189. C₅	D₃×#551	direct (N × H)
1225. C₃	C₂×C₅×#551	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#551	2
C₅×#5705	2
C₅×D₃×#126	2
C₅×#5679	2
C₅×D₃×#124	2
C₅×#5659	2
C₅×#5658	2
C₅×D₃×#123	2
C₅×#5637	2
C₅×D₃×C₂²⋊Q₈	2
C₅×D₃×#120	2
C₅×#5587	2
C₅×#5556	2
C₄×C₅×D₃×D₄	2
C₅×#5527	2
C₅×D₃×#117	2
C₅×#5495	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₂×C₅×#551	3
D₃×#551	5

Subgroups — C5×D3×#551 #14483229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#551 #14483229