Subgroups — C₃×D₅×#542 #14481299

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66067	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66044	C₂	1	2	yes	maximal, complemented
5	C₃×D₅×#126	C₂	1	2	yes	maximal, complemented
6	C₃×#66016	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×D₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₅×#124	C₂	1	2	yes	maximal, complemented
9	C₃×#66003	C₂	1	2	yes	maximal, complemented
10	C₃×#65996	C₂	1	2	yes	maximal, complemented
11	C₃×D₅×#123	C₂	1	2	yes	maximal, complemented
12	C₃×#65977	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65974	C₂	1	2	yes	maximal, complemented
14	C₃×D₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×D₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
16	C₃×D₅×#121	C₂	1	1	yes	maximal, characteristic
17	C₃×#65937	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#65916	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#65895	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#65868	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	D₅×#542	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
27	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
29	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
30	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
31	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×#126	C₂²	1	2	yes	complemented
33	C₃×C₅×#124	C₂²	1	2	yes	complemented
34	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#123	C₂²	1	2	yes	complemented
36	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₅×#121	C₂²	1	1	yes	characteristic
39	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
42	C₃×#4093	C₂²	1	1	yes	characteristic, complemented
43	C₃×#4093	C₂²	1	2	yes	complemented
44	C₃×#4092	C₂²	1	1	yes	characteristic, complemented
45	C₃×#4092	C₂²	1	2	yes	complemented
46	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
47	C₃×#4090	C₂²	1	2	yes	complemented
48	C₃×#4085	C₂²	1	2	yes	—
49	C₃×#4084	C₂²	1	1	yes	characteristic
50	C₃×#4082	C₂²	1	1	yes	characteristic, complemented
51	C₃×#4082	C₂²	1	2	yes	complemented
52	C₃×#4081	C₂²	1	2	yes	complemented
53	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
54	C₃×#4076	C₂²	1	1	yes	characteristic
55	C₃×#4075	C₂²	1	2	yes	complemented
56	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	complemented
57	C₃×#4072	C₂²	1	1	yes	characteristic, complemented
58	C₃×#4070	C₂²	1	1	yes	characteristic, complemented
59	C₃×#4070	C₂²	1	2	yes	complemented
60	C₃×#4044	C₂²	1	2	yes	complemented
61	C₃×#4044	C₂²	1	2	yes	complemented
62	C₃×#4044	C₂²	1	2	yes	complemented
63	C₃×#4043	C₂²	1	1	yes	characteristic, complemented
64	C₃×#4043	C₂²	1	2	yes	complemented
65	C₃×#4042	C₂²	1	2	yes	complemented
66	C₃×#4042	C₂²	1	2	yes	complemented
67	C₃×#4042	C₂²	1	2	yes	complemented
68	C₃×#4041	C₂²	1	1	yes	characteristic
69	C₃×#4040	C₂²	1	2	yes	complemented
70	C₃×#4040	C₂²	1	2	yes	complemented
71	C₃×#4039	C₂²	1	1	yes	characteristic, complemented
72	C₃×#4038	C₂²	1	1	yes	characteristic, complemented
73	C₃×#4038	C₂²	1	1	yes	characteristic, complemented
74	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
75	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
79	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
80	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
81	C₃×#4034	C₂²	1	1	yes	characteristic, complemented
82	C₃×#4034	C₂²	1	1	yes	characteristic, complemented
83	C₃×#4034	C₂²	1	2	yes	complemented
84	C₃×#4033	C₂²	1	1	yes	characteristic, complemented
85	C₃×#4033	C₂²	1	2	yes	complemented
86	C₃×#4032	C₂²	1	2	yes	complemented
87	C₃×#4031	C₂²	1	2	yes	complemented
88	C₃×#4031	C₂²	1	2	yes	complemented
89	C₃×#4031	C₂²	1	2	yes	complemented
90	C₃×#4031	C₂²	1	2	yes	complemented
91	C₃×#4031	C₂²	1	2	yes	complemented
92	C₃×#4031	C₂²	1	2	yes	complemented
93	C₃×#4030	C₂²	1	2	yes	—
94	C₃×#4029	C₂²	1	2	yes	complemented
95	C₃×#4029	C₂²	1	2	yes	complemented
96	C₃×#4027	C₂²	1	2	yes	complemented
97	C₃×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
98	C₃×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
99	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
102	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
104	C₃×#4025	C₂²	1	2	yes	complemented
105	C₃×#4025	C₂²	1	2	yes	complemented
106	C₃×#4025	C₂²	1	2	yes	complemented
107	C₃×#4024	C₂²	1	2	yes	complemented
108	C₃×#4024	C₂²	1	2	yes	complemented
109	C₃×#4024	C₂²	1	2	yes	complemented
110	C₃×#4023	C₂²	1	1	yes	characteristic, complemented
111	C₃×#4023	C₂²	1	1	yes	characteristic, complemented
112	C₃×#4022	C₂²	1	2	yes	complemented
113	C₃×#4021	C₂²	1	1	yes	characteristic, complemented
114	C₃×#4021	C₂²	1	2	yes	complemented
115	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic, complemented
116	C₃×#4018	C₂²	1	1	yes	characteristic, complemented
117	C₃×#4018	C₂²	1	1	yes	characteristic, complemented
118	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
119	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
120	C₃×C₄²×D₅	C₂²	1	2	yes	—
121	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
122	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
123	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
124	C₂×C₃×#542	—	5	1	no	maximal, Hall
125	C₅×#542	C₂×C₃	1	1	yes	characteristic, complemented
126	#66067	C₂×C₃	1	1	yes	characteristic, complemented
127	D₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
128	#66044	C₂×C₃	1	2	yes	complemented
129	D₅×#126	C₂×C₃	1	2	yes	complemented
130	#66016	C₂×C₃	1	1	yes	characteristic, complemented
131	D₅×#124	C₂×C₃	1	2	yes	complemented
132	D₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
133	#66003	C₂×C₃	1	2	yes	complemented
134	#65996	C₂×C₃	1	2	yes	complemented
135	D₅×#123	C₂×C₃	1	2	yes	complemented
136	#65977	C₂×C₃	1	1	yes	characteristic, complemented
137	#65974	C₂×C₃	1	2	yes	complemented
138	D₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
139	D₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
140	D₅×#121	C₂×C₃	1	1	yes	characteristic
141	#65937	C₂×C₃	1	1	yes	characteristic, complemented
142	#65916	C₂×C₃	1	1	yes	characteristic, complemented
143	C₄×Q₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
144	#65895	C₂×C₃	1	1	yes	characteristic, complemented
145	C₄×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
146	#65868	C₂×C₃	1	1	yes	characteristic, complemented
147	D₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
149	C₂³×C₃×D₅	C₂³	1	2	yes	—
150	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
152	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
154	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
156	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
157	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
158	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
159	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
160	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
161	C₃×Q₈×D₅	—	2	4	no	—
162	C₃×Q₈×D₅	—	4	4	no	—
163	C₃×D₄×D₅	—	2	4	no	—
164	C₃×D₄×D₅	—	4	4	no	—
165	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
166	C₂×C₃×D₂₀	C₂³	1	2	yes	—
167	C₂×C₃×C₄×D₅	—	2	4	no	—
168	C₂×C₃×C₄×D₅	—	4	4	no	—
169	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
172	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
175	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
177	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
180	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
181	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
182	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
183	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
184	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
185	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
186	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
187	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
195	C₃×C₅×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
202	C₃×C₄²×C₅	C₂³	1	2	yes	—
203	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
204	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
205	C₃×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
206	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
207	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
208	C₃×C₂²⋊Dic₅	C₂³	1	1	yes	characteristic
209	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
210	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
211	C₃×#685	C₂³	1	2	yes	—
212	C₃×#685	C₂³	1	2	yes	—
213	C₃×#685	C₂³	1	2	yes	—
214	C₃×#685	C₂³	1	1	yes	characteristic
215	C₃×#685	C₂³	1	2	yes	—
216	C₃×#685	C₂³	1	2	yes	—
217	C₃×#685	C₂³	1	2	yes	—
218	C₃×#685	C₂³	1	2	yes	—
219	C₃×#685	C₂³	1	1	yes	characteristic
220	C₃×#685	C₂³	1	1	yes	characteristic
221	C₃×#685	C₂³	1	1	yes	characteristic
222	C₃×#685	C₂³	1	2	yes	—
223	C₃×#685	C₂³	1	2	yes	—
224	C₃×#685	C₂³	1	2	yes	—
225	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
226	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
227	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
228	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
229	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
230	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
231	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
232	C₃×#683	C₂³	1	2	yes	—
233	C₃×#683	C₂³	1	2	yes	—
234	C₃×#683	C₂³	1	2	yes	—
235	C₃×#683	C₂³	1	2	yes	—
236	C₃×#683	C₂³	1	2	yes	—
237	C₃×#683	C₂³	1	1	yes	characteristic
238	C₃×#683	C₂³	1	2	yes	—
239	C₃×#683	C₂³	1	2	yes	—
240	C₃×#683	C₂³	1	1	yes	characteristic
241	C₃×#683	C₂³	1	1	yes	characteristic
242	C₃×#683	C₂³	1	1	yes	characteristic
243	C₃×#683	C₂³	1	2	yes	—
244	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
245	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
246	C₃×C₄×Dic₅	C₂³	1	2	yes	—
247	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
248	C₃×C₄×Dic₅	C₂³	1	2	yes	—
249	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
250	C₃×C₄×Dic₅	C₂³	1	2	yes	—
251	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
252	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
253	C₃×#542	—	5	1	no	—
254	C₃×#542	—	5	2	no	—
255	C₃×#542	—	5	2	no	—
256	C₃×#542	—	5	1	no	—
257	C₃×#542	—	5	2	no	—
258	C₃×#542	—	5	2	no	—
259	C₃×#542	—	5	1	no	—
260	C₃×#542	—	5	1	no	—
261	C₃×#542	—	5	1	no	—
262	C₃×#542	—	5	1	no	—
263	C₃×#542	—	5	1	no	—
264	C₃×#542	D₅	1	1	yes	characteristic, direct product factor
265	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
266	C₂×C₃×#126	—	5	2	no	—
267	C₂×C₃×#124	—	5	1	no	—
268	C₂×C₃×#124	—	5	2	no	—
269	C₂×C₃×#123	—	5	2	no	—
270	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
271	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
272	C₂×C₃×#121	—	5	1	no	—
273	C₂×C₃×C₄×Q₈	—	5	1	no	—
274	C₂×C₃×C₄×D₄	—	5	1	no	—
275	C₂×C₃×#117	—	5	1	no	—
276	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
277	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
278	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
279	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
280	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
281	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
282	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
283	C₅×#126	C₂²×C₃	1	2	yes	complemented
284	C₅×#124	C₂²×C₃	1	2	yes	complemented
285	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
286	C₅×#123	C₂²×C₃	1	2	yes	complemented
287	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
288	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
289	C₅×#121	C₂²×C₃	1	1	yes	characteristic
290	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
291	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
292	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
293	#4093	C₂²×C₃	1	2	yes	complemented
294	#4093	C₂²×C₃	1	1	yes	characteristic, complemented
295	#4092	C₂²×C₃	1	2	yes	complemented
296	#4092	C₂²×C₃	1	1	yes	characteristic, complemented
297	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
298	#4090	C₂²×C₃	1	2	yes	complemented
299	#4085	C₂²×C₃	1	2	yes	—
300	#4084	C₂²×C₃	1	1	yes	characteristic
301	#4082	C₂²×C₃	1	1	yes	characteristic, complemented
302	#4082	C₂²×C₃	1	2	yes	complemented
303	#4081	C₂²×C₃	1	2	yes	complemented
304	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
305	#4076	C₂²×C₃	1	1	yes	characteristic
306	#4075	C₂²×C₃	1	2	yes	complemented
307	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
308	#4072	C₂²×C₃	1	1	yes	characteristic, complemented
309	#4070	C₂²×C₃	1	1	yes	characteristic, complemented
310	#4070	C₂²×C₃	1	2	yes	complemented
311	#4044	C₂²×C₃	1	2	yes	complemented
312	#4044	C₂²×C₃	1	2	yes	complemented
313	#4044	C₂²×C₃	1	2	yes	complemented
314	#4043	C₂²×C₃	1	1	yes	characteristic, complemented
315	#4043	C₂²×C₃	1	2	yes	complemented
316	#4042	C₂²×C₃	1	2	yes	complemented
317	#4042	C₂²×C₃	1	2	yes	complemented
318	#4042	C₂²×C₃	1	2	yes	complemented
319	#4041	C₂²×C₃	1	1	yes	characteristic
320	#4040	C₂²×C₃	1	2	yes	complemented
321	#4040	C₂²×C₃	1	2	yes	complemented
322	#4039	C₂²×C₃	1	1	yes	characteristic, complemented
323	#4038	C₂²×C₃	1	1	yes	characteristic, complemented
324	#4038	C₂²×C₃	1	1	yes	characteristic, complemented
325	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
326	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
327	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
328	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
329	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
330	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
331	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
332	#4034	C₂²×C₃	1	1	yes	characteristic, complemented
333	#4034	C₂²×C₃	1	1	yes	characteristic, complemented
334	#4034	C₂²×C₃	1	2	yes	complemented
335	#4033	C₂²×C₃	1	1	yes	characteristic, complemented
336	#4033	C₂²×C₃	1	2	yes	complemented
337	#4032	C₂²×C₃	1	2	yes	complemented
338	#4031	C₂²×C₃	1	2	yes	complemented
339	#4031	C₂²×C₃	1	2	yes	complemented
340	#4031	C₂²×C₃	1	2	yes	complemented
341	#4031	C₂²×C₃	1	2	yes	complemented
342	#4031	C₂²×C₃	1	2	yes	complemented
343	#4031	C₂²×C₃	1	2	yes	complemented
344	#4030	C₂²×C₃	1	2	yes	—
345	#4029	C₂²×C₃	1	2	yes	complemented
346	#4029	C₂²×C₃	1	2	yes	complemented
347	#4027	C₂²×C₃	1	2	yes	complemented
348	D₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
349	D₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
350	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
351	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
352	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
353	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
354	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
355	#4025	C₂²×C₃	1	2	yes	complemented
356	#4025	C₂²×C₃	1	2	yes	complemented
357	#4025	C₂²×C₃	1	2	yes	complemented
358	#4024	C₂²×C₃	1	2	yes	complemented
359	#4024	C₂²×C₃	1	2	yes	complemented
360	#4024	C₂²×C₃	1	2	yes	complemented
361	#4023	C₂²×C₃	1	1	yes	characteristic, complemented
362	#4023	C₂²×C₃	1	1	yes	characteristic, complemented
363	#4022	C₂²×C₃	1	2	yes	complemented
364	#4021	C₂²×C₃	1	1	yes	characteristic, complemented
365	#4021	C₂²×C₃	1	2	yes	complemented
366	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
367	#4018	C₂²×C₃	1	1	yes	characteristic, complemented
368	#4018	C₂²×C₃	1	1	yes	characteristic, complemented
369	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
370	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
371	C₄²×D₅	C₂²×C₃	1	2	yes	—
372	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
373	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
374	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
375	C₂×#542	—	5	1	no	Sylow
376	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
377	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
378	C₂²×C₃×D₅	—	2	2	no	—
379	C₂²×C₃×D₅	—	2	4	no	—
380	C₂²×C₃×D₅	—	2	4	no	—
381	C₂²×C₃×D₅	—	2	2	no	—
382	C₂²×C₃×D₅	—	2	2	no	—
383	C₂²×C₃×D₅	—	2	4	no	—
384	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
385	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
386	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
387	C₃×C₅×Q₈	—	2	2	no	—
388	C₃×C₅×Q₈	—	4	2	no	—
389	C₃×C₅×D₄	—	2	2	no	—
390	C₃×C₅×D₄	—	4	2	no	—
391	C₂×C₃×C₄×C₅	—	2	2	no	—
392	C₂×C₃×C₄×C₅	—	4	2	no	—
393	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
394	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
395	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
396	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
397	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
398	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
399	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
400	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
401	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
402	C₃×C₂²⋊D₅	—	2	4	no	—
403	C₃×C₂²⋊D₅	—	4	2	no	—
404	C₃×C₂²⋊D₅	—	4	2	no	—
405	C₂×C₃×Dic₅	—	2	2	no	—
406	C₂×C₃×Dic₅	—	4	2	no	—
407	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
408	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
409	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
410	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
411	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
412	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
413	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
414	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
415	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
416	C₃×D₂₀	—	2	2	no	—
417	C₃×D₂₀	—	4	2	no	—
418	C₃×C₄×D₅	—	2	2	no	—
419	C₃×C₄×D₅	—	2	4	no	—
420	C₃×C₄×D₅	—	2	2	no	—
421	C₃×C₄×D₅	—	2	4	no	—
422	C₃×C₄×D₅	—	2	4	no	—
423	C₃×C₄×D₅	—	2	2	no	—
424	C₃×C₄×D₅	—	2	2	no	—
425	C₃×C₄×D₅	—	2	2	no	—
426	C₃×C₄×D₅	—	2	2	no	—
427	C₃×C₄×D₅	—	2	2	no	—
428	C₃×C₄×D₅	—	4	2	no	—
429	C₃×C₄×D₅	—	4	2	no	—
430	C₃×C₄×D₅	#41	1	4	yes	—
431	C₃×Dic₁₀	—	2	2	no	—
432	C₃×Dic₁₀	—	2	4	no	—
433	C₃×Dic₁₀	—	4	2	no	—
434	C₃×Dic₁₀	—	4	2	no	—
435	C₃×Dic₁₀	—	4	2	no	—
436	C₂²×C₃×Q₈	—	5	1	no	—
437	C₂²×C₃×Q₈	—	5	2	no	—
438	C₂²×C₃×D₄	—	5	1	no	—
439	C₂²×C₃×D₄	—	5	2	no	—
440	C₂³×C₃×C₄	—	5	1	no	—
441	C₂³×C₃×C₄	—	5	2	no	—
442	C₃×C₄⋊Q₈	—	5	2	no	—
443	C₃×C₄⋊Q₈	—	5	2	no	—
444	C₃×C₄⋊Q₈	—	5	1	no	—
445	C₃×C₄⋊Q₈	—	5	1	no	—
446	C₃×C₄⋊Q₈	—	5	1	no	—
447	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
448	C₃×#126	—	5	2	no	—
449	C₃×#126	—	5	2	no	—
450	C₃×#126	—	5	2	no	—
451	C₃×#126	—	5	2	no	—
452	C₃×#126	—	5	2	no	—
453	C₃×#126	—	5	2	no	—
454	C₃×#126	—	5	2	no	—
455	C₃×#126	C₂×D₅	1	2	yes	complemented
456	C₃×#124	—	5	1	no	—
457	C₃×#124	—	5	2	no	—
458	C₃×#124	—	5	1	no	—
459	C₃×#124	—	5	2	no	—
460	C₃×#124	—	5	2	no	—
461	C₃×#124	—	5	2	no	—
462	C₃×#124	—	5	2	no	—
463	C₃×#124	—	5	2	no	—
464	C₃×#124	—	5	2	no	—
465	C₃×#124	—	5	2	no	—
466	C₃×#124	—	5	1	no	—
467	C₃×#124	—	5	2	no	—
468	C₃×#124	C₂×D₅	1	1	yes	characteristic, complemented
469	C₃×#124	C₂×D₅	1	2	yes	complemented
470	C₃×#123	—	5	2	no	—
471	C₃×#123	—	5	2	no	—
472	C₃×#123	—	5	2	no	—
473	C₃×#123	—	5	2	no	—
474	C₃×#123	—	5	2	no	—
475	C₃×#123	—	5	2	no	—
476	C₃×#123	—	5	2	no	—
477	C₃×#123	C₂×D₅	1	2	yes	complemented
478	C₃×C₂²⋊Q₈	—	5	2	no	—
479	C₃×C₂²⋊Q₈	—	5	1	no	—
480	C₃×C₂²⋊Q₈	—	5	2	no	—
481	C₃×C₂²⋊Q₈	—	5	1	no	—
482	C₃×C₂²⋊Q₈	—	5	2	no	—
483	C₃×C₂²⋊Q₈	—	5	2	no	—
484	C₃×C₂²⋊Q₈	—	5	2	no	—
485	C₃×C₂²⋊Q₈	—	5	2	no	—
486	C₃×C₂²⋊Q₈	—	5	1	no	—
487	C₃×C₂²⋊Q₈	—	5	2	no	—
488	C₃×C₂²⋊Q₈	—	5	2	no	—
489	C₃×C₂²⋊Q₈	—	5	2	no	—
490	C₃×C₂²⋊Q₈	C₂×D₅	1	2	yes	complemented
491	C₃×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
492	C₃×#121	—	5	1	no	—
493	C₃×#121	—	5	2	no	—
494	C₃×#121	—	5	1	no	—
495	C₃×#121	—	5	1	no	—
496	C₃×#121	—	5	2	no	—
497	C₃×#121	C₂×D₅	1	1	yes	characteristic
498	C₃×C₄×Q₈	—	5	1	no	—
499	C₃×C₄×Q₈	—	5	2	no	—
500	C₃×C₄×Q₈	—	5	1	no	—
501	C₃×C₄×Q₈	—	5	2	no	—
502	C₃×C₄×Q₈	—	5	1	no	—
503	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
504	C₃×C₄×D₄	—	5	1	no	—
505	C₃×C₄×D₄	—	5	2	no	—
506	C₃×C₄×D₄	—	5	1	no	—
507	C₃×C₄×D₄	—	5	2	no	—
508	C₃×C₄×D₄	—	5	1	no	—
509	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
510	C₃×#117	—	5	1	no	—
511	C₃×#117	—	5	1	no	—
512	C₃×#117	—	5	1	no	—
513	C₃×#117	—	5	1	no	—
514	C₃×#117	—	5	1	no	—
515	C₃×#117	—	5	1	no	—
516	C₃×#117	—	5	1	no	—
517	C₃×#117	C₂×D₅	1	1	yes	characteristic, complemented
518	C₂×C₃×C₄⋊C₄	—	5	1	no	—
519	C₂×C₃×C₄⋊C₄	—	5	1	no	—
520	C₂×C₃×C₄⋊C₄	—	5	1	no	—
521	C₂×C₃×C₄⋊C₄	—	5	1	no	—
522	C₂×C₃×C₄⋊C₄	—	5	2	no	—
523	C₂×C₃×C₄⋊C₄	—	5	2	no	—
524	C₂×C₃×C₄⋊C₄	—	5	2	no	—
525	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
526	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
527	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
528	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
529	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
530	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
531	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
532	C₂×C₃×C₄²	—	5	1	no	—
533	C₂×C₃×C₄²	—	5	1	no	—
534	C₂×C₃×C₄²	—	5	2	no	—
535	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
536	C₂³×D₅	C₂³×C₃	1	2	yes	—
537	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
538	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
539	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
540	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
541	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
542	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
543	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
544	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
545	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
546	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
547	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
548	Q₈×D₅	—	2	4	no	—
549	Q₈×D₅	—	4	4	no	—
550	D₄×D₅	—	2	4	no	—
551	D₄×D₅	—	4	4	no	—
552	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
553	C₂×D₂₀	C₂³×C₃	1	2	yes	—
554	C₂×C₄×D₅	—	2	4	no	—
555	C₂×C₄×D₅	—	4	4	no	—
556	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
557	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
558	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
559	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
560	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
561	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
562	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
563	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
564	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
565	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
566	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
567	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
568	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
569	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
570	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
571	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
572	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
573	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
574	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
575	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
576	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
577	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
578	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
579	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
580	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
581	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
582	C₅×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
583	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
584	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
585	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
586	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
587	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
588	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
589	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
590	C₄²×C₅	C₂³×C₃	1	2	yes	—
591	C₂²⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
592	C₂²⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
593	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
594	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
595	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
596	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
597	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
598	#685	C₂³×C₃	1	1	yes	characteristic
599	#685	C₂³×C₃	1	1	yes	characteristic
600	#685	C₂³×C₃	1	1	yes	characteristic
601	#685	C₂³×C₃	1	1	yes	characteristic
602	#685	C₂³×C₃	1	2	yes	—
603	#685	C₂³×C₃	1	2	yes	—
604	#685	C₂³×C₃	1	2	yes	—
605	#685	C₂³×C₃	1	2	yes	—
606	#685	C₂³×C₃	1	2	yes	—
607	#685	C₂³×C₃	1	2	yes	—
608	#685	C₂³×C₃	1	2	yes	—
609	#685	C₂³×C₃	1	2	yes	—
610	#685	C₂³×C₃	1	2	yes	—
611	#685	C₂³×C₃	1	2	yes	—
612	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
613	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
614	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
615	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
616	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
617	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
618	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
619	#683	C₂³×C₃	1	2	yes	—
620	#683	C₂³×C₃	1	2	yes	—
621	#683	C₂³×C₃	1	2	yes	—
622	#683	C₂³×C₃	1	1	yes	characteristic
623	#683	C₂³×C₃	1	1	yes	characteristic
624	#683	C₂³×C₃	1	1	yes	characteristic
625	#683	C₂³×C₃	1	1	yes	characteristic
626	#683	C₂³×C₃	1	2	yes	—
627	#683	C₂³×C₃	1	2	yes	—
628	#683	C₂³×C₃	1	2	yes	—
629	#683	C₂³×C₃	1	2	yes	—
630	#683	C₂³×C₃	1	2	yes	—
631	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
632	C₄×Dic₅	C₂³×C₃	1	2	yes	—
633	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
634	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
635	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
636	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
637	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
638	C₄×Dic₅	C₂³×C₃	1	2	yes	—
639	C₄×Dic₅	C₂³×C₃	1	2	yes	—
640	#542	—	5	1	no	—
641	#542	—	5	2	no	—
642	#542	—	5	2	no	—
643	#542	—	5	1	no	—
644	#542	—	5	2	no	—
645	#542	—	5	2	no	—
646	#542	—	5	1	no	—
647	#542	—	5	1	no	—
648	#542	—	5	1	no	—
649	#542	—	5	1	no	—
650	#542	—	5	1	no	—
651	#542	C₃×D₅	1	1	yes	characteristic, direct product factor
652	C₂×C₄⋊Q₈	—	5	1	no	—
653	C₂×#126	—	5	2	no	—
654	C₂×#124	—	5	1	no	—
655	C₂×#124	—	5	2	no	—
656	C₂×#123	—	5	2	no	—
657	C₂×C₂²⋊Q₈	—	5	2	no	—
658	C₂×C₂²⋊Q₈	—	5	1	no	—
659	C₂×#121	—	5	1	no	—
660	C₂×C₄×Q₈	—	5	1	no	—
661	C₂×C₄×D₄	—	5	1	no	—
662	C₂×#117	—	5	1	no	—
663	C₂²×C₃×C₅	—	2	1	no	—
664	C₂²×C₃×C₅	—	2	2	no	—
665	C₂²×C₃×C₅	—	2	2	no	—
666	C₂²×C₃×C₅	—	2	1	no	—
667	C₂²×C₃×C₅	—	2	1	no	—
668	C₂²×C₃×C₅	—	2	2	no	—
669	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
670	C₂×C₃×D₅	—	2	1	no	—
671	C₂×C₃×D₅	—	2	2	no	—
672	C₂×C₃×D₅	—	2	2	no	—
673	C₂×C₃×D₅	—	2	1	no	—
674	C₂×C₃×D₅	—	2	1	no	—
675	C₂×C₃×D₅	—	2	2	no	—
676	C₂×C₃×D₅	—	4	4	no	—
677	C₂×C₃×D₅	—	4	8	no	—
678	C₂×C₃×D₅	C₂×#41	1	2	yes	—
679	C₂×C₃×D₅	H(5,𝔽₂)	1	2	yes	—
680	C₂×C₃×D₅	2₋¹⁺⁴	1	2	yes	—
681	C₃×C₄×C₅	—	2	2	no	—
682	C₃×C₄×C₅	—	2	1	no	—
683	C₃×C₄×C₅	—	2	1	no	—
684	C₃×C₄×C₅	—	2	2	no	—
685	C₃×C₄×C₅	—	2	2	no	—
686	C₃×C₄×C₅	—	2	1	no	—
687	C₃×C₄×C₅	—	2	1	no	—
688	C₃×C₄×C₅	—	2	1	no	—
689	C₃×C₄×C₅	C₂×#41	1	2	yes	—
690	C₃×Dic₅	—	2	2	no	—
691	C₃×Dic₅	—	2	1	no	—
692	C₃×Dic₅	—	2	1	no	—
693	C₃×Dic₅	—	2	2	no	—
694	C₃×Dic₅	—	2	2	no	—
695	C₃×Dic₅	—	2	1	no	—
696	C₃×Dic₅	—	2	1	no	—
697	C₃×Dic₅	—	2	1	no	—
698	C₃×Dic₅	C₂×#41	1	2	yes	—
699	C₂⁴×C₃	—	5	1	no	—
700	C₂⁴×C₃	—	5	2	no	—
701	C₂×C₃×Q₈	—	5	2	no	—
702	C₂×C₃×Q₈	—	5	1	no	—
703	C₂×C₃×Q₈	—	5	2	no	—
704	C₂×C₃×Q₈	—	5	2	no	—
705	C₂×C₃×Q₈	—	5	2	no	—
706	C₂×C₃×Q₈	—	10	4	no	—
707	C₂×C₃×Q₈	—	20	4	no	—
708	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
709	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
710	C₂×C₃×D₄	—	5	2	no	—
711	C₂×C₃×D₄	—	5	2	no	—
712	C₂×C₃×D₄	—	5	2	no	—
713	C₂×C₃×D₄	—	5	1	no	—
714	C₂×C₃×D₄	—	5	2	no	—
715	C₂×C₃×D₄	—	10	4	no	—
716	C₂×C₃×D₄	—	20	4	no	—
717	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
718	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
719	C₂²×C₃×C₄	—	5	1	no	—
720	C₂²×C₃×C₄	—	5	1	no	—
721	C₂²×C₃×C₄	—	5	2	no	—
722	C₂²×C₃×C₄	—	5	1	no	—
723	C₂²×C₃×C₄	—	5	1	no	—
724	C₂²×C₃×C₄	—	5	2	no	—
725	C₂²×C₃×C₄	—	5	1	no	—
726	C₂²×C₃×C₄	—	5	1	no	—
727	C₂²×C₃×C₄	—	5	2	no	—
728	C₂²×C₃×C₄	—	5	1	no	—
729	C₂²×C₃×C₄	—	5	2	no	—
730	C₂²×C₃×C₄	—	5	1	no	—
731	C₂²×C₃×C₄	—	5	1	no	—
732	C₂²×C₃×C₄	—	5	2	no	—
733	C₂²×C₃×C₄	—	5	2	no	—
734	C₂²×C₃×C₄	—	10	4	no	—
735	C₂²×C₃×C₄	—	20	4	no	—
736	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
737	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
738	C₃×C₄⋊C₄	—	5	1	no	—
739	C₃×C₄⋊C₄	—	5	1	no	—
740	C₃×C₄⋊C₄	—	5	1	no	—
741	C₃×C₄⋊C₄	—	5	1	no	—
742	C₃×C₄⋊C₄	—	5	2	no	—
743	C₃×C₄⋊C₄	—	5	2	no	—
744	C₃×C₄⋊C₄	—	5	2	no	—
745	C₃×C₄⋊C₄	—	5	2	no	—
746	C₃×C₄⋊C₄	—	5	2	no	—
747	C₃×C₄⋊C₄	—	5	2	no	—
748	C₃×C₄⋊C₄	—	5	2	no	—
749	C₃×C₄⋊C₄	—	5	2	no	—
750	C₃×C₄⋊C₄	—	5	1	no	—
751	C₃×C₄⋊C₄	—	5	1	no	—
752	C₃×C₄⋊C₄	—	5	1	no	—
753	C₃×C₄⋊C₄	—	5	1	no	—
754	C₃×C₄⋊C₄	—	5	2	no	—
755	C₃×C₄⋊C₄	—	5	2	no	—
756	C₃×C₄⋊C₄	—	5	2	no	—
757	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
758	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
759	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
760	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
761	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
762	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
763	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
764	C₃×C₂²⋊C₄	—	5	1	no	—
765	C₃×C₂²⋊C₄	—	5	1	no	—
766	C₃×C₂²⋊C₄	—	5	2	no	—
767	C₃×C₂²⋊C₄	—	5	2	no	—
768	C₃×C₂²⋊C₄	—	5	2	no	—
769	C₃×C₂²⋊C₄	—	5	2	no	—
770	C₃×C₂²⋊C₄	—	5	2	no	—
771	C₃×C₂²⋊C₄	—	5	1	no	—
772	C₃×C₂²⋊C₄	—	5	1	no	—
773	C₃×C₂²⋊C₄	—	5	1	no	—
774	C₃×C₂²⋊C₄	—	5	1	no	—
775	C₃×C₂²⋊C₄	—	5	2	no	—
776	C₃×C₂²⋊C₄	—	5	2	no	—
777	C₃×C₂²⋊C₄	—	5	2	no	—
778	C₃×C₂²⋊C₄	—	5	2	no	—
779	C₃×C₂²⋊C₄	—	5	2	no	—
780	C₃×C₂²⋊C₄	—	5	2	no	—
781	C₃×C₂²⋊C₄	—	5	2	no	—
782	C₃×C₂²⋊C₄	—	5	2	no	—
783	C₃×C₂²⋊C₄	—	5	2	no	—
784	C₃×C₂²⋊C₄	—	5	2	no	—
785	C₃×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
786	C₃×C₂²⋊C₄	C₂²×D₅	1	1	yes	characteristic
787	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
788	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
789	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
790	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
791	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
792	C₃×C₄²	—	5	1	no	—
793	C₃×C₄²	—	5	1	no	—
794	C₃×C₄²	—	5	1	no	—
795	C₃×C₄²	—	5	1	no	—
796	C₃×C₄²	—	5	1	no	—
797	C₃×C₄²	—	5	1	no	—
798	C₃×C₄²	—	5	2	no	—
799	C₃×C₄²	—	5	2	no	—
800	C₃×C₄²	—	5	2	no	—
801	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
802	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
803	C₃×C₄²	C₂²×D₅	1	2	yes	—
804	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
805	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
806	C₂²×D₅	—	2	2	no	—
807	C₂²×D₅	—	2	4	no	—
808	C₂²×D₅	—	2	4	no	—
809	C₂²×D₅	—	2	2	no	—
810	C₂²×D₅	—	2	2	no	—
811	C₂²×D₅	—	2	4	no	—
812	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
813	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
814	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
815	C₅×Q₈	—	2	2	no	—
816	C₅×Q₈	—	4	2	no	—
817	C₅×D₄	—	2	2	no	—
818	C₅×D₄	—	4	2	no	—
819	C₂×C₄×C₅	—	2	2	no	—
820	C₂×C₄×C₅	—	4	2	no	—
821	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
822	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
823	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
824	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
825	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
826	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
827	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
828	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
829	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
830	C₂²⋊D₅	—	2	4	no	—
831	C₂²⋊D₅	—	4	2	no	—
832	C₂²⋊D₅	—	4	2	no	—
833	C₂×Dic₅	—	2	2	no	—
834	C₂×Dic₅	—	4	2	no	—
835	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
836	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
837	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
838	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
839	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
840	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
841	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
842	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
843	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
844	D₂₀	—	2	2	no	—
845	D₂₀	—	4	2	no	—
846	C₄×D₅	—	2	2	no	—
847	C₄×D₅	—	2	4	no	—
848	C₄×D₅	—	2	2	no	—
849	C₄×D₅	—	2	4	no	—
850	C₄×D₅	—	2	4	no	—
851	C₄×D₅	—	2	2	no	—
852	C₄×D₅	—	2	2	no	—
853	C₄×D₅	—	2	2	no	—
854	C₄×D₅	—	2	2	no	—
855	C₄×D₅	—	2	2	no	—
856	C₄×D₅	—	4	2	no	—
857	C₄×D₅	—	4	2	no	—
858	C₄×D₅	C₃×#41	1	4	yes	—
859	Dic₁₀	—	2	2	no	—
860	Dic₁₀	—	2	4	no	—
861	Dic₁₀	—	4	2	no	—
862	Dic₁₀	—	4	2	no	—
863	Dic₁₀	—	4	2	no	—
864	C₂²×Q₈	—	5	1	no	—
865	C₂²×Q₈	—	5	2	no	—
866	C₂²×D₄	—	5	1	no	—
867	C₂²×D₄	—	5	2	no	—
868	C₂³×C₄	—	5	1	no	—
869	C₂³×C₄	—	5	2	no	—
870	C₄⋊Q₈	—	5	2	no	—
871	C₄⋊Q₈	—	5	2	no	—
872	C₄⋊Q₈	—	5	1	no	—
873	C₄⋊Q₈	—	5	1	no	—
874	C₄⋊Q₈	—	5	1	no	—
875	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
876	#126	—	5	2	no	—
877	#126	—	5	2	no	—
878	#126	—	5	2	no	—
879	#126	—	5	2	no	—
880	#126	—	5	2	no	—
881	#126	—	5	2	no	—
882	#126	—	5	2	no	—
883	#126	C₂×C₃×D₅	1	2	yes	complemented
884	#124	—	5	1	no	—
885	#124	—	5	2	no	—
886	#124	—	5	1	no	—
887	#124	—	5	2	no	—
888	#124	—	5	2	no	—
889	#124	—	5	2	no	—
890	#124	—	5	2	no	—
891	#124	—	5	2	no	—
892	#124	—	5	2	no	—
893	#124	—	5	2	no	—
894	#124	—	5	1	no	—
895	#124	—	5	2	no	—
896	#124	C₂×C₃×D₅	1	1	yes	characteristic, complemented
897	#124	C₂×C₃×D₅	1	2	yes	complemented
898	#123	—	5	2	no	—
899	#123	—	5	2	no	—
900	#123	—	5	2	no	—
901	#123	—	5	2	no	—
902	#123	—	5	2	no	—
903	#123	—	5	2	no	—
904	#123	—	5	2	no	—
905	#123	C₂×C₃×D₅	1	2	yes	complemented
906	C₂²⋊Q₈	—	5	2	no	—
907	C₂²⋊Q₈	—	5	1	no	—
908	C₂²⋊Q₈	—	5	2	no	—
909	C₂²⋊Q₈	—	5	1	no	—
910	C₂²⋊Q₈	—	5	2	no	—
911	C₂²⋊Q₈	—	5	2	no	—
912	C₂²⋊Q₈	—	5	2	no	—
913	C₂²⋊Q₈	—	5	2	no	—
914	C₂²⋊Q₈	—	5	1	no	—
915	C₂²⋊Q₈	—	5	2	no	—
916	C₂²⋊Q₈	—	5	2	no	—
917	C₂²⋊Q₈	—	5	2	no	—
918	C₂²⋊Q₈	C₂×C₃×D₅	1	2	yes	complemented
919	C₂²⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
920	#121	—	5	1	no	—
921	#121	—	5	2	no	—
922	#121	—	5	1	no	—
923	#121	—	5	1	no	—
924	#121	—	5	2	no	—
925	#121	C₂×C₃×D₅	1	1	yes	characteristic
926	C₄×Q₈	—	5	1	no	—
927	C₄×Q₈	—	5	2	no	—
928	C₄×Q₈	—	5	1	no	—
929	C₄×Q₈	—	5	2	no	—
930	C₄×Q₈	—	5	1	no	—
931	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
932	C₄×D₄	—	5	1	no	—
933	C₄×D₄	—	5	2	no	—
934	C₄×D₄	—	5	1	no	—
935	C₄×D₄	—	5	2	no	—
936	C₄×D₄	—	5	1	no	—
937	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
938	#117	—	5	1	no	—
939	#117	—	5	1	no	—
940	#117	—	5	1	no	—
941	#117	—	5	1	no	—
942	#117	—	5	1	no	—
943	#117	—	5	1	no	—
944	#117	—	5	1	no	—
945	#117	C₂×C₃×D₅	1	1	yes	characteristic, complemented
946	C₂×C₄⋊C₄	—	5	1	no	—
947	C₂×C₄⋊C₄	—	5	1	no	—
948	C₂×C₄⋊C₄	—	5	1	no	—
949	C₂×C₄⋊C₄	—	5	1	no	—
950	C₂×C₄⋊C₄	—	5	2	no	—
951	C₂×C₄⋊C₄	—	5	2	no	—
952	C₂×C₄⋊C₄	—	5	2	no	—
953	C₂×C₂²⋊C₄	—	5	1	no	—
954	C₂×C₂²⋊C₄	—	5	1	no	—
955	C₂×C₂²⋊C₄	—	5	2	no	—
956	C₂×C₂²⋊C₄	—	5	2	no	—
957	C₂×C₂²⋊C₄	—	5	2	no	—
958	C₂×C₂²⋊C₄	—	5	2	no	—
959	C₂×C₂²⋊C₄	—	5	2	no	—
960	C₂×C₄²	—	5	1	no	—
961	C₂×C₄²	—	5	1	no	—
962	C₂×C₄²	—	5	2	no	—
963	C₂×C₃×C₅	—	4	1	no	—
964	C₂×C₃×C₅	—	4	2	no	—
965	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
966	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
967	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
968	C₃×D₅	—	4	1	no	—
969	C₃×D₅	—	4	2	no	—
970	C₃×D₅	#542	1	4	yes	direct product factor
971	C₂³×C₃	—	5	1	no	—
972	C₂³×C₃	—	5	1	no	—
973	C₂³×C₃	—	5	2	no	—
974	C₂³×C₃	—	10	2	no	—
975	C₂³×C₃	—	10	4	no	—
976	C₂³×C₃	—	10	4	no	—
977	C₂³×C₃	—	10	2	no	—
978	C₂³×C₃	—	10	2	no	—
979	C₂³×C₃	—	10	4	no	—
980	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
981	C₂³×C₃	C₂³×D₅	1	2	yes	—
982	C₃×Q₈	—	2	2	no	—
983	C₃×Q₈	—	4	2	no	—
984	C₃×Q₈	—	10	4	no	—
985	C₃×Q₈	—	10	2	no	—
986	C₃×Q₈	—	20	2	no	—
987	C₃×Q₈	—	20	2	no	—
988	C₃×Q₈	—	20	2	no	—
989	C₃×D₄	—	2	2	no	—
990	C₃×D₄	—	4	2	no	—
991	C₃×D₄	—	10	4	no	—
992	C₃×D₄	—	10	2	no	—
993	C₃×D₄	—	20	2	no	—
994	C₃×D₄	—	20	2	no	—
995	C₃×D₄	—	20	2	no	—
996	C₂×C₃×C₄	—	2	2	no	—
997	C₂×C₃×C₄	—	4	2	no	—
998	C₂×C₃×C₄	—	5	1	no	—
999	C₂×C₃×C₄	—	5	4	no	—
1000	C₂×C₃×C₄	—	5	1	no	—
1001	C₂×C₃×C₄	—	5	1	no	—
1002	C₂×C₃×C₄	—	5	2	no	—
1003	C₂×C₃×C₄	—	5	1	no	—
1004	C₂×C₃×C₄	—	5	1	no	—
1005	C₂×C₃×C₄	—	5	2	no	—
1006	C₂×C₃×C₄	—	5	1	no	—
1007	C₂×C₃×C₄	—	5	2	no	—
1008	C₂×C₃×C₄	—	10	2	no	—
1009	C₂×C₃×C₄	—	10	2	no	—
1010	C₂×C₃×C₄	—	10	2	no	—
1011	C₂×C₃×C₄	—	10	2	no	—
1012	C₂×C₃×C₄	—	10	2	no	—
1013	C₂×C₃×C₄	—	10	4	no	—
1014	C₂×C₃×C₄	—	10	4	no	—
1015	C₂×C₃×C₄	—	10	4	no	—
1016	C₂×C₃×C₄	—	10	2	no	—
1017	C₂×C₃×C₄	—	10	2	no	—
1018	C₂×C₃×C₄	—	10	2	no	—
1019	C₂×C₃×C₄	—	20	2	no	—
1020	C₂×C₃×C₄	—	20	2	no	—
1021	C₂×C₃×C₄	—	20	2	no	—
1022	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1023	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1024	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1025	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1026	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1027	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1028	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1029	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
1030	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
1031	C₂²×C₅	—	2	1	no	—
1032	C₂²×C₅	—	2	2	no	—
1033	C₂²×C₅	—	2	2	no	—
1034	C₂²×C₅	—	2	1	no	—
1035	C₂²×C₅	—	2	1	no	—
1036	C₂²×C₅	—	2	2	no	—
1037	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
1038	C₂×D₅	—	2	1	no	—
1039	C₂×D₅	—	2	2	no	—
1040	C₂×D₅	—	2	2	no	—
1041	C₂×D₅	—	2	1	no	—
1042	C₂×D₅	—	2	1	no	—
1043	C₂×D₅	—	2	2	no	—
1044	C₂×D₅	—	4	4	no	—
1045	C₂×D₅	—	4	8	no	—
1046	C₂×D₅	C₂×C₃×#41	1	2	yes	—
1047	C₂×D₅	C₃×H(5,𝔽₂)	1	2	yes	—
1048	C₂×D₅	C₃×2₋¹⁺⁴	1	2	yes	—
1049	C₄×C₅	—	2	2	no	—
1050	C₄×C₅	—	2	1	no	—
1051	C₄×C₅	—	2	1	no	—
1052	C₄×C₅	—	2	2	no	—
1053	C₄×C₅	—	2	2	no	—
1054	C₄×C₅	—	2	1	no	—
1055	C₄×C₅	—	2	1	no	—
1056	C₄×C₅	—	2	1	no	—
1057	C₄×C₅	C₂×C₃×#41	1	2	yes	—
1058	Dic₅	—	2	2	no	—
1059	Dic₅	—	2	1	no	—
1060	Dic₅	—	2	1	no	—
1061	Dic₅	—	2	2	no	—
1062	Dic₅	—	2	2	no	—
1063	Dic₅	—	2	1	no	—
1064	Dic₅	—	2	1	no	—
1065	Dic₅	—	2	1	no	—
1066	Dic₅	C₂×C₃×#41	1	2	yes	—
1067	C₂⁴	—	5	1	no	—
1068	C₂⁴	—	5	2	no	—
1069	C₂×Q₈	—	5	2	no	—
1070	C₂×Q₈	—	5	1	no	—
1071	C₂×Q₈	—	5	2	no	—
1072	C₂×Q₈	—	5	2	no	—
1073	C₂×Q₈	—	5	2	no	—
1074	C₂×Q₈	—	10	4	no	—
1075	C₂×Q₈	—	20	4	no	—
1076	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
1077	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
1078	C₂×D₄	—	5	2	no	—
1079	C₂×D₄	—	5	2	no	—
1080	C₂×D₄	—	5	2	no	—
1081	C₂×D₄	—	5	1	no	—
1082	C₂×D₄	—	5	2	no	—
1083	C₂×D₄	—	10	4	no	—
1084	C₂×D₄	—	20	4	no	—
1085	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
1086	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
1087	C₂²×C₄	—	5	1	no	—
1088	C₂²×C₄	—	5	1	no	—
1089	C₂²×C₄	—	5	2	no	—
1090	C₂²×C₄	—	5	1	no	—
1091	C₂²×C₄	—	5	1	no	—
1092	C₂²×C₄	—	5	2	no	—
1093	C₂²×C₄	—	5	1	no	—
1094	C₂²×C₄	—	5	1	no	—
1095	C₂²×C₄	—	5	2	no	—
1096	C₂²×C₄	—	5	1	no	—
1097	C₂²×C₄	—	5	2	no	—
1098	C₂²×C₄	—	5	1	no	—
1099	C₂²×C₄	—	5	1	no	—
1100	C₂²×C₄	—	5	2	no	—
1101	C₂²×C₄	—	5	2	no	—
1102	C₂²×C₄	—	10	4	no	—
1103	C₂²×C₄	—	20	4	no	—
1104	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1105	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
1106	C₄⋊C₄	—	5	1	no	—
1107	C₄⋊C₄	—	5	1	no	—
1108	C₄⋊C₄	—	5	1	no	—
1109	C₄⋊C₄	—	5	1	no	—
1110	C₄⋊C₄	—	5	1	no	—
1111	C₄⋊C₄	—	5	1	no	—
1112	C₄⋊C₄	—	5	2	no	—
1113	C₄⋊C₄	—	5	1	no	—
1114	C₄⋊C₄	—	5	2	no	—
1115	C₄⋊C₄	—	5	1	no	—
1116	C₄⋊C₄	—	5	2	no	—
1117	C₄⋊C₄	—	5	2	no	—
1118	C₄⋊C₄	—	5	2	no	—
1119	C₄⋊C₄	—	5	2	no	—
1120	C₄⋊C₄	—	5	2	no	—
1121	C₄⋊C₄	—	5	2	no	—
1122	C₄⋊C₄	—	5	2	no	—
1123	C₄⋊C₄	—	5	2	no	—
1124	C₄⋊C₄	—	5	2	no	—
1125	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1126	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1127	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1128	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1129	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1130	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1131	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1132	C₂²⋊C₄	—	5	1	no	—
1133	C₂²⋊C₄	—	5	1	no	—
1134	C₂²⋊C₄	—	5	2	no	—
1135	C₂²⋊C₄	—	5	2	no	—
1136	C₂²⋊C₄	—	5	2	no	—
1137	C₂²⋊C₄	—	5	2	no	—
1138	C₂²⋊C₄	—	5	2	no	—
1139	C₂²⋊C₄	—	5	1	no	—
1140	C₂²⋊C₄	—	5	1	no	—
1141	C₂²⋊C₄	—	5	1	no	—
1142	C₂²⋊C₄	—	5	1	no	—
1143	C₂²⋊C₄	—	5	2	no	—
1144	C₂²⋊C₄	—	5	2	no	—
1145	C₂²⋊C₄	—	5	2	no	—
1146	C₂²⋊C₄	—	5	2	no	—
1147	C₂²⋊C₄	—	5	2	no	—
1148	C₂²⋊C₄	—	5	2	no	—
1149	C₂²⋊C₄	—	5	2	no	—
1150	C₂²⋊C₄	—	5	2	no	—
1151	C₂²⋊C₄	—	5	2	no	—
1152	C₂²⋊C₄	—	5	2	no	—
1153	C₂²⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1154	C₂²⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
1155	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1156	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1157	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1158	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1159	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
1160	C₄²	—	5	1	no	—
1161	C₄²	—	5	1	no	—
1162	C₄²	—	5	1	no	—
1163	C₄²	—	5	1	no	—
1164	C₄²	—	5	1	no	—
1165	C₄²	—	5	1	no	—
1166	C₄²	—	5	2	no	—
1167	C₄²	—	5	2	no	—
1168	C₄²	—	5	2	no	—
1169	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
1170	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
1171	C₄²	C₂²×C₃×D₅	1	2	yes	—
1172	C₃×C₅	C₂×#542	1	1	yes	characteristic, complemented, Hall
1173	C₂²×C₃	—	2	1	no	—
1174	C₂²×C₃	—	2	2	no	—
1175	C₂²×C₃	—	2	2	no	—
1176	C₂²×C₃	—	2	1	no	—
1177	C₂²×C₃	—	2	1	no	—
1178	C₂²×C₃	—	2	2	no	—
1179	C₂²×C₃	—	5	2	no	—
1180	C₂²×C₃	—	5	2	no	—
1181	C₂²×C₃	—	5	2	no	—
1182	C₂²×C₃	—	10	1	no	—
1183	C₂²×C₃	—	10	2	no	—
1184	C₂²×C₃	—	10	2	no	—
1185	C₂²×C₃	—	10	1	no	—
1186	C₂²×C₃	—	10	1	no	—
1187	C₂²×C₃	—	10	2	no	—
1188	C₂²×C₃	—	20	4	no	—
1189	C₂²×C₃	—	20	8	no	—
1190	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
1191	C₃×C₄	—	2	1	no	—
1192	C₃×C₄	—	2	2	no	—
1193	C₃×C₄	—	2	1	no	—
1194	C₃×C₄	—	2	2	no	—
1195	C₃×C₄	—	2	2	no	—
1196	C₃×C₄	—	2	1	no	—
1197	C₃×C₄	—	2	1	no	—
1198	C₃×C₄	—	2	1	no	—
1199	C₃×C₄	—	5	2	no	—
1200	C₃×C₄	—	10	1	no	—
1201	C₃×C₄	—	10	2	no	—
1202	C₃×C₄	—	10	1	no	—
1203	C₃×C₄	—	10	2	no	—
1204	C₃×C₄	—	10	2	no	—
1205	C₃×C₄	—	10	1	no	—
1206	C₃×C₄	—	10	1	no	—
1207	C₃×C₄	—	10	1	no	—
1208	C₃×C₄	D₅×#41	1	2	yes	—
1209	C₂×C₅	—	4	1	no	—
1210	C₂×C₅	—	4	2	no	—
1211	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
1212	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1213	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1214	D₅	—	4	1	no	—
1215	D₅	—	4	2	no	—
1216	D₅	C₃×#542	1	4	yes	direct product factor
1217	C₂³	—	5	1	no	—
1218	C₂³	—	5	1	no	—
1219	C₂³	—	5	2	no	—
1220	C₂³	—	10	2	no	—
1221	C₂³	—	10	4	no	—
1222	C₂³	—	10	4	no	—
1223	C₂³	—	10	2	no	—
1224	C₂³	—	10	2	no	—
1225	C₂³	—	10	4	no	—
1226	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
1227	C₂³	C₂³×C₃×D₅	1	2	yes	—
1228	Q₈	—	2	2	no	—
1229	Q₈	—	4	2	no	—
1230	Q₈	—	10	4	no	—
1231	Q₈	—	10	2	no	—
1232	Q₈	—	20	2	no	—
1233	Q₈	—	20	2	no	—
1234	Q₈	—	20	2	no	—
1235	D₄	—	2	2	no	—
1236	D₄	—	4	2	no	—
1237	D₄	—	10	4	no	—
1238	D₄	—	10	2	no	—
1239	D₄	—	20	2	no	—
1240	D₄	—	20	2	no	—
1241	D₄	—	20	2	no	—
1242	C₂×C₄	—	2	2	no	—
1243	C₂×C₄	—	4	2	no	—
1244	C₂×C₄	—	5	1	no	—
1245	C₂×C₄	—	5	4	no	—
1246	C₂×C₄	—	5	1	no	—
1247	C₂×C₄	—	5	1	no	—
1248	C₂×C₄	—	5	2	no	—
1249	C₂×C₄	—	5	1	no	—
1250	C₂×C₄	—	5	1	no	—
1251	C₂×C₄	—	5	2	no	—
1252	C₂×C₄	—	5	1	no	—
1253	C₂×C₄	—	5	2	no	—
1254	C₂×C₄	—	10	2	no	—
1255	C₂×C₄	—	10	2	no	—
1256	C₂×C₄	—	10	2	no	—
1257	C₂×C₄	—	10	4	no	—
1258	C₂×C₄	—	10	4	no	—
1259	C₂×C₄	—	10	4	no	—
1260	C₂×C₄	—	10	2	no	—
1261	C₂×C₄	—	10	2	no	—
1262	C₂×C₄	—	10	2	no	—
1263	C₂×C₄	—	10	2	no	—
1264	C₂×C₄	—	10	2	no	—
1265	C₂×C₄	—	20	2	no	—
1266	C₂×C₄	—	20	2	no	—
1267	C₂×C₄	—	20	2	no	—
1268	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1269	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1270	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1271	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1272	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1273	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1274	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1275	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
1276	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
1277	C₂×C₃	—	4	1	no	—
1278	C₂×C₃	—	4	2	no	—
1279	C₂×C₃	—	5	4	no	—
1280	C₂×C₃	—	20	1	no	—
1281	C₂×C₃	—	20	2	no	—
1282	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
1283	C₂×C₃	D₅×H(5,𝔽₂)	1	1	yes	characteristic
1284	C₂×C₃	D₅×2₋¹⁺⁴	1	1	yes	characteristic
1285	C₅	C₂×C₃×#542	1	1	yes	characteristic, complemented, Sylow
1286	C₂²	—	2	1	no	—
1287	C₂²	—	2	2	no	—
1288	C₂²	—	2	2	no	—
1289	C₂²	—	2	1	no	—
1290	C₂²	—	2	1	no	—
1291	C₂²	—	2	2	no	—
1292	C₂²	—	5	2	no	—
1293	C₂²	—	5	2	no	—
1294	C₂²	—	5	2	no	—
1295	C₂²	—	10	1	no	—
1296	C₂²	—	10	2	no	—
1297	C₂²	—	10	2	no	—
1298	C₂²	—	10	1	no	—
1299	C₂²	—	10	1	no	—
1300	C₂²	—	10	2	no	—
1301	C₂²	—	20	4	no	—
1302	C₂²	—	20	8	no	—
1303	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
1304	C₄	—	2	1	no	—
1305	C₄	—	2	2	no	—
1306	C₄	—	2	1	no	—
1307	C₄	—	2	2	no	—
1308	C₄	—	2	2	no	—
1309	C₄	—	2	1	no	—
1310	C₄	—	2	1	no	—
1311	C₄	—	2	1	no	—
1312	C₄	—	5	2	no	—
1313	C₄	—	10	1	no	—
1314	C₄	—	10	2	no	—
1315	C₄	—	10	1	no	—
1316	C₄	—	10	2	no	—
1317	C₄	—	10	2	no	—
1318	C₄	—	10	1	no	—
1319	C₄	—	10	1	no	—
1320	C₄	—	10	1	no	—
1321	C₄	C₃×D₅×#41	1	2	yes	—
1322	C₃	D₅×#542	1	1	yes	characteristic, direct product factor, Sylow
1323	C₂	—	4	1	no	—
1324	C₂	—	4	2	no	—
1325	C₂	—	5	4	no	—
1326	C₂	—	20	1	no	—
1327	C₂	—	20	2	no	—
1328	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
1329	C₂	C₃×D₅×H(5,𝔽₂)	1	1	yes	characteristic
1330	C₂	C₃×D₅×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#542	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₃×D₅×#121	C₂
hypercenter	C₃×#542	D₅
hypocenter	C₅	C₂×C₃×#542
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#542

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#542	C₂	semidirect
2. C₃×#66067	C₂	semidirect
3. C₃×D₅×C₄⋊Q₈	C₂	semidirect
4. C₃×#66044	C₂	semidirect
5. C₃×D₅×#126	C₂	semidirect
6. C₃×#66016	C₂	semidirect
7. C₃×D₅×#124	C₂	semidirect
8. C₃×D₅×#124	C₂	semidirect
9. C₃×#66003	C₂	semidirect
10. C₃×#65996	C₂	semidirect
11. C₃×D₅×#123	C₂	semidirect
12. C₃×#65977	C₂	semidirect
13. C₃×#65974	C₂	semidirect
14. C₃×D₅×C₂²⋊Q₈	C₂	semidirect
15. C₃×D₅×C₂²⋊Q₈	C₂	semidirect
17. C₃×#65937	C₂	semidirect
18. C₃×#65916	C₂	semidirect
19. C₃×C₄×Q₈×D₅	C₂	semidirect
20. C₃×#65895	C₂	semidirect
21. C₃×C₄×D₄×D₅	C₂	semidirect
22. C₃×#65868	C₂	semidirect
23. C₃×D₅×#117	C₂	semidirect
24. D₅×#542	C₃	direct (N × H)
31. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
32. C₃×C₅×#126	C₂²	semidirect
33. C₃×C₅×#124	C₂²	semidirect
34. C₃×C₅×#124	C₂²	semidirect
35. C₃×C₅×#123	C₂²	semidirect
36. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
37. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
39. C₃×C₄×C₅×Q₈	C₂²	semidirect
40. C₃×C₄×C₅×D₄	C₂²	semidirect
41. C₃×C₅×#117	C₂²	semidirect
42. C₃×#4093	C₂²	semidirect
43. C₃×#4093	C₂²	semidirect
44. C₃×#4092	C₂²	semidirect
45. C₃×#4092	C₂²	semidirect
46. C₃×Q₈×Dic₅	C₂²	semidirect
47. C₃×#4090	C₂²	semidirect
50. C₃×#4082	C₂²	semidirect
51. C₃×#4082	C₂²	semidirect
52. C₃×#4081	C₂²	semidirect
53. C₃×D₄×Dic₅	C₂²	semidirect
55. C₃×#4075	C₂²	semidirect
56. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
57. C₃×#4072	C₂²	semidirect
58. C₃×#4070	C₂²	semidirect
59. C₃×#4070	C₂²	semidirect
60. C₃×#4044	C₂²	semidirect
61. C₃×#4044	C₂²	semidirect
62. C₃×#4044	C₂²	semidirect
63. C₃×#4043	C₂²	semidirect
64. C₃×#4043	C₂²	semidirect
65. C₃×#4042	C₂²	semidirect
66. C₃×#4042	C₂²	semidirect
67. C₃×#4042	C₂²	semidirect
69. C₃×#4040	C₂²	semidirect
70. C₃×#4040	C₂²	semidirect
71. C₃×#4039	C₂²	semidirect
72. C₃×#4038	C₂²	semidirect
73. C₃×#4038	C₂²	semidirect
81. C₃×#4034	C₂²	semidirect
82. C₃×#4034	C₂²	semidirect
83. C₃×#4034	C₂²	semidirect
84. C₃×#4033	C₂²	semidirect
85. C₃×#4033	C₂²	semidirect
86. C₃×#4032	C₂²	semidirect
87. C₃×#4031	C₂²	semidirect
88. C₃×#4031	C₂²	semidirect
89. C₃×#4031	C₂²	semidirect
90. C₃×#4031	C₂²	semidirect
91. C₃×#4031	C₂²	semidirect
92. C₃×#4031	C₂²	semidirect
94. C₃×#4029	C₂²	semidirect
95. C₃×#4029	C₂²	semidirect
96. C₃×#4027	C₂²	semidirect
104. C₃×#4025	C₂²	semidirect
105. C₃×#4025	C₂²	semidirect
106. C₃×#4025	C₂²	semidirect
107. C₃×#4024	C₂²	semidirect
108. C₃×#4024	C₂²	semidirect
109. C₃×#4024	C₂²	semidirect
110. C₃×#4023	C₂²	semidirect
111. C₃×#4023	C₂²	semidirect
112. C₃×#4022	C₂²	semidirect
113. C₃×#4021	C₂²	semidirect
114. C₃×#4021	C₂²	semidirect
115. C₃×C₄×D₂₀	C₂²	semidirect
116. C₃×#4018	C₂²	semidirect
117. C₃×#4018	C₂²	semidirect
121. C₃×#4015	C₂²	semidirect
122. C₃×C₄×Dic₁₀	C₂²	semidirect
123. C₃×C₄×Dic₁₀	C₂²	semidirect
125. C₅×#542	C₂×C₃	semidirect
126. #66067	C₂×C₃	semidirect
127. D₅×C₄⋊Q₈	C₂×C₃	semidirect
128. #66044	C₂×C₃	semidirect
129. D₅×#126	C₂×C₃	semidirect
130. #66016	C₂×C₃	semidirect
131. D₅×#124	C₂×C₃	semidirect
132. D₅×#124	C₂×C₃	semidirect
133. #66003	C₂×C₃	semidirect
134. #65996	C₂×C₃	semidirect
135. D₅×#123	C₂×C₃	semidirect
136. #65977	C₂×C₃	semidirect
137. #65974	C₂×C₃	semidirect
138. D₅×C₂²⋊Q₈	C₂×C₃	semidirect
139. D₅×C₂²⋊Q₈	C₂×C₃	semidirect
141. #65937	C₂×C₃	semidirect
142. #65916	C₂×C₃	semidirect
143. C₄×Q₈×D₅	C₂×C₃	semidirect
144. #65895	C₂×C₃	semidirect
145. C₄×D₄×D₅	C₂×C₃	semidirect
146. #65868	C₂×C₃	semidirect
147. D₅×#117	C₂×C₃	semidirect
264. C₃×#542	D₅	direct (N × H)
282. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
283. C₅×#126	C₂²×C₃	semidirect
284. C₅×#124	C₂²×C₃	semidirect
285. C₅×#124	C₂²×C₃	semidirect
286. C₅×#123	C₂²×C₃	semidirect
287. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
288. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
290. C₄×C₅×Q₈	C₂²×C₃	semidirect
291. C₄×C₅×D₄	C₂²×C₃	semidirect
292. C₅×#117	C₂²×C₃	semidirect
293. #4093	C₂²×C₃	semidirect
294. #4093	C₂²×C₃	semidirect
295. #4092	C₂²×C₃	semidirect
296. #4092	C₂²×C₃	semidirect
297. Q₈×Dic₅	C₂²×C₃	semidirect
298. #4090	C₂²×C₃	semidirect
301. #4082	C₂²×C₃	semidirect
302. #4082	C₂²×C₃	semidirect
303. #4081	C₂²×C₃	semidirect
304. D₄×Dic₅	C₂²×C₃	semidirect
306. #4075	C₂²×C₃	semidirect
307. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
308. #4072	C₂²×C₃	semidirect
309. #4070	C₂²×C₃	semidirect
310. #4070	C₂²×C₃	semidirect
311. #4044	C₂²×C₃	semidirect
312. #4044	C₂²×C₃	semidirect
313. #4044	C₂²×C₃	semidirect
314. #4043	C₂²×C₃	semidirect
315. #4043	C₂²×C₃	semidirect
316. #4042	C₂²×C₃	semidirect
317. #4042	C₂²×C₃	semidirect
318. #4042	C₂²×C₃	semidirect
320. #4040	C₂²×C₃	semidirect
321. #4040	C₂²×C₃	semidirect
322. #4039	C₂²×C₃	semidirect
323. #4038	C₂²×C₃	semidirect
324. #4038	C₂²×C₃	semidirect
332. #4034	C₂²×C₃	semidirect
333. #4034	C₂²×C₃	semidirect
334. #4034	C₂²×C₃	semidirect
335. #4033	C₂²×C₃	semidirect
336. #4033	C₂²×C₃	semidirect
337. #4032	C₂²×C₃	semidirect
338. #4031	C₂²×C₃	semidirect
339. #4031	C₂²×C₃	semidirect
340. #4031	C₂²×C₃	semidirect
341. #4031	C₂²×C₃	semidirect
342. #4031	C₂²×C₃	semidirect
343. #4031	C₂²×C₃	semidirect
345. #4029	C₂²×C₃	semidirect
346. #4029	C₂²×C₃	semidirect
347. #4027	C₂²×C₃	semidirect
355. #4025	C₂²×C₃	semidirect
356. #4025	C₂²×C₃	semidirect
357. #4025	C₂²×C₃	semidirect
358. #4024	C₂²×C₃	semidirect
359. #4024	C₂²×C₃	semidirect
360. #4024	C₂²×C₃	semidirect
361. #4023	C₂²×C₃	semidirect
362. #4023	C₂²×C₃	semidirect
363. #4022	C₂²×C₃	semidirect
364. #4021	C₂²×C₃	semidirect
365. #4021	C₂²×C₃	semidirect
366. C₄×D₂₀	C₂²×C₃	semidirect
367. #4018	C₂²×C₃	semidirect
368. #4018	C₂²×C₃	semidirect
372. #4015	C₂²×C₃	semidirect
373. C₄×Dic₁₀	C₂²×C₃	semidirect
374. C₄×Dic₁₀	C₂²×C₃	semidirect
447. C₃×C₄⋊Q₈	C₂×D₅	semidirect
455. C₃×#126	C₂×D₅	semidirect
468. C₃×#124	C₂×D₅	semidirect
469. C₃×#124	C₂×D₅	semidirect
477. C₃×#123	C₂×D₅	semidirect
490. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
491. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
503. C₃×C₄×Q₈	C₂×D₅	semidirect
509. C₃×C₄×D₄	C₂×D₅	semidirect
517. C₃×#117	C₂×D₅	semidirect
651. #542	C₃×D₅	direct (N × H)
875. C₄⋊Q₈	C₂×C₃×D₅	semidirect
883. #126	C₂×C₃×D₅	semidirect
896. #124	C₂×C₃×D₅	semidirect
897. #124	C₂×C₃×D₅	semidirect
905. #123	C₂×C₃×D₅	semidirect
918. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
919. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
931. C₄×Q₈	C₂×C₃×D₅	semidirect
937. C₄×D₄	C₂×C₃×D₅	semidirect
945. #117	C₂×C₃×D₅	semidirect
970. C₃×D₅	#542	direct (N × H)
1172. C₃×C₅	C₂×#542	semidirect
1216. D₅	C₃×#542	direct (N × H)
1285. C₅	C₂×C₃×#542	semidirect
1322. C₃	D₅×#542	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#542	2
C₃×#66067	2
C₃×D₅×C₄⋊Q₈	2
C₃×#66044	2
C₃×D₅×#126	2
C₃×#66016	2
C₃×D₅×#124	2
C₃×#66003	2
C₃×#65996	2
C₃×D₅×#123	2
C₃×#65977	2
C₃×#65974	2
C₃×D₅×C₂²⋊Q₈	2
C₃×D₅×#121	2
C₃×#65937	2
C₃×#65916	2
C₃×C₄×Q₈×D₅	2
C₃×#65895	2
C₃×C₄×D₄×D₅	2
C₃×#65868	2
C₃×D₅×#117	2
D₅×#542	3
C₂×C₃×#542	5

Subgroups — C3×D5×#542 #14481299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#542 #14481299