Subgroups — C₂×C₃×#66042 #14483410

Order 1920.

2248 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66042	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃×#4042	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4038	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×D₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#4036	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#4035	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#4029	C₂	1	1	yes	maximal, characteristic
10	C₂×C₃×#4029	C₂	1	1	yes	maximal, characteristic
11	C₂×C₃×#4027	C₂	1	1	yes	maximal, characteristic
12	C₂×C₃×#4025	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#4024	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#4023	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#66042	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
19	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
23	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
24	C₃×C₅×#126	C₂²	1	8	yes	complemented
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
34	C₂×C₃×#685	C₂²	1	1	yes	characteristic
35	C₂×C₃×#685	C₂²	1	1	yes	characteristic
36	C₂×C₃×#685	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
41	C₂×C₃×#683	C₂²	1	1	yes	characteristic
42	C₂×C₃×#683	C₂²	1	1	yes	characteristic
43	C₂×C₃×#683	C₂²	1	1	yes	characteristic
44	C₂×C₃×#683	C₂²	1	1	yes	characteristic
45	C₂×C₃×#683	C₂²	1	1	yes	characteristic
46	C₂×C₃×#683	C₂²	1	1	yes	characteristic
47	C₂×C₃×#683	C₂²	1	1	yes	characteristic
48	C₂×C₃×#683	C₂²	1	1	yes	characteristic
49	C₂×C₃×#683	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
51	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
52	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
53	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
54	C₃×#4042	C₂²	1	8	yes	complemented
55	C₃×#4038	C₂²	1	8	yes	complemented
56	C₃×D₅×C₄⋊C₄	C₂²	1	8	yes	complemented
57	C₃×#4036	C₂²	1	8	yes	complemented
58	C₃×#4035	C₂²	1	8	yes	complemented
59	C₃×#4035	C₂²	1	8	yes	complemented
60	C₃×#4029	C₂²	1	8	yes	—
61	C₃×#4029	C₂²	1	8	yes	—
62	C₃×#4027	C₂²	1	8	yes	—
63	C₃×#4025	C₂²	1	8	yes	complemented
64	C₃×#4024	C₂²	1	8	yes	complemented
65	C₃×#4023	C₂²	1	8	yes	complemented
66	C₃×#4018	C₂²	1	8	yes	complemented
67	C₃×C₄×Dic₁₀	C₂²	1	8	yes	complemented
68	C₂×C₃×#552	—	5	1	no	maximal, Hall
69	C₂×C₅×#126	C₂×C₃	1	1	yes	characteristic, complemented
70	#66042	C₂×C₃	1	16	yes	direct product factor
71	C₂×#4042	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂×#4038	C₂×C₃	1	1	yes	characteristic, complemented
73	C₂×D₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
74	C₂×#4036	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×#4035	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×#4035	C₂×C₃	1	1	yes	characteristic, complemented
77	C₂×#4029	C₂×C₃	1	1	yes	characteristic
78	C₂×#4029	C₂×C₃	1	1	yes	characteristic
79	C₂×#4027	C₂×C₃	1	1	yes	characteristic
80	C₂×#4025	C₂×C₃	1	1	yes	characteristic, complemented
81	C₂×#4024	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂×#4023	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×#4018	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
85	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
86	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
87	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
94	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
95	C₂²×C₃×Dic₅	—	2	4	no	—
96	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
97	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
98	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
99	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
100	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
101	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
102	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
103	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₄×D₅	—	2	4	no	—
105	C₂×C₃×C₄×D₅	—	2	4	no	—
106	C₂×C₃×C₄×D₅	—	2	4	no	—
107	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
108	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
109	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
110	C₂×C₃×Dic₁₀	—	2	4	no	—
111	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
112	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
113	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
114	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
115	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₃×C₄²×C₅	C₂³	1	4	yes	—
119	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
120	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
121	C₃×#685	C₂³	1	4	yes	—
122	C₃×#685	C₂³	1	4	yes	—
123	C₃×#685	C₂³	1	4	yes	—
124	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
125	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
126	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
127	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
128	C₃×#683	C₂³	1	4	yes	—
129	C₃×#683	C₂³	1	4	yes	—
130	C₃×#683	C₂³	1	4	yes	—
131	C₃×#683	C₂³	1	4	yes	—
132	C₃×#683	C₂³	1	4	yes	—
133	C₃×#683	C₂³	1	4	yes	—
134	C₃×#683	C₂³	1	4	yes	—
135	C₃×#683	C₂³	1	4	yes	—
136	C₃×#683	C₂³	1	4	yes	—
137	C₃×C₄×Dic₅	C₂³	1	4	yes	—
138	C₃×C₄×Dic₅	C₂³	1	4	yes	—
139	C₃×C₄×Dic₅	C₂³	1	4	yes	—
140	C₃×C₄×Dic₅	C₂³	1	4	yes	—
141	C₃×#552	—	5	16	no	—
142	C₂×C₃×#126	—	5	1	no	—
143	C₂×C₃×#126	D₅	1	1	yes	characteristic, complemented
144	C₂×C₃×#125	—	5	1	no	—
145	C₂×C₃×#125	—	5	1	no	—
146	C₂×C₃×#125	—	5	1	no	—
147	C₂×C₃×#123	—	5	1	no	—
148	C₂×C₃×#123	—	5	1	no	—
149	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
150	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
151	C₂×C₃×C₄×Q₈	—	5	1	no	—
152	C₂×C₃×C₄×D₄	—	5	1	no	—
153	C₂×C₃×#117	—	5	1	no	—
154	C₂×C₃×#117	—	5	1	no	—
155	C₂×C₃×#117	—	5	1	no	—
156	C₂²×C₃×C₄⋊C₄	—	5	1	no	—
157	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
158	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
159	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
160	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
161	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
162	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
163	C₅×#126	C₂²×C₃	1	8	yes	complemented
164	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
167	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
170	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
171	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
172	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
173	C₂×#685	C₂²×C₃	1	1	yes	characteristic
174	C₂×#685	C₂²×C₃	1	1	yes	characteristic
175	C₂×#685	C₂²×C₃	1	1	yes	characteristic
176	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
177	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
178	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
179	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
180	C₂×#683	C₂²×C₃	1	1	yes	characteristic
181	C₂×#683	C₂²×C₃	1	1	yes	characteristic
182	C₂×#683	C₂²×C₃	1	1	yes	characteristic
183	C₂×#683	C₂²×C₃	1	1	yes	characteristic
184	C₂×#683	C₂²×C₃	1	1	yes	characteristic
185	C₂×#683	C₂²×C₃	1	1	yes	characteristic
186	C₂×#683	C₂²×C₃	1	1	yes	characteristic
187	C₂×#683	C₂²×C₃	1	1	yes	characteristic
188	C₂×#683	C₂²×C₃	1	1	yes	characteristic
189	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
190	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
191	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
192	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
193	#4042	C₂²×C₃	1	8	yes	complemented
194	#4038	C₂²×C₃	1	8	yes	complemented
195	D₅×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
196	#4036	C₂²×C₃	1	8	yes	complemented
197	#4035	C₂²×C₃	1	8	yes	complemented
198	#4035	C₂²×C₃	1	8	yes	complemented
199	#4029	C₂²×C₃	1	8	yes	—
200	#4029	C₂²×C₃	1	8	yes	—
201	#4027	C₂²×C₃	1	8	yes	—
202	#4025	C₂²×C₃	1	8	yes	complemented
203	#4024	C₂²×C₃	1	8	yes	complemented
204	#4023	C₂²×C₃	1	8	yes	complemented
205	#4018	C₂²×C₃	1	8	yes	complemented
206	C₄×Dic₁₀	C₂²×C₃	1	8	yes	complemented
207	C₂×#552	—	5	1	no	Sylow
208	C₂³×C₃×C₅	—	2	2	no	—
209	C₂³×C₃×C₅	—	2	2	no	—
210	C₂³×C₃×C₅	—	2	2	no	—
211	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
212	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
213	C₂²×C₃×D₅	—	2	2	no	—
214	C₂²×C₃×D₅	—	2	2	no	—
215	C₂²×C₃×D₅	#41	1	4	yes	—
216	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
217	C₂×C₃×C₄×C₅	—	2	2	no	—
218	C₂×C₃×C₄×C₅	—	2	2	no	—
219	C₂×C₃×C₄×C₅	—	2	2	no	—
220	C₂×C₃×C₄×C₅	—	2	2	no	—
221	C₂×C₃×C₄×C₅	—	2	2	no	—
222	C₂×C₃×C₄×C₅	—	2	2	no	—
223	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
224	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
225	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
226	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
227	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
228	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
229	C₃×C₂²⋊D₅	—	2	8	no	—
230	C₂×C₃×Dic₅	—	2	2	no	—
231	C₂×C₃×Dic₅	—	2	2	no	—
232	C₂×C₃×Dic₅	—	2	2	no	—
233	C₂×C₃×Dic₅	—	2	2	no	—
234	C₂×C₃×Dic₅	—	2	2	no	—
235	C₂×C₃×Dic₅	—	2	2	no	—
236	C₂×C₃×Dic₅	—	2	8	no	—
237	C₂×C₃×Dic₅	#41	1	4	yes	—
238	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
239	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
240	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
241	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
242	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
243	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
244	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
245	C₃×C₄×D₅	—	2	8	no	—
246	C₃×C₄×D₅	—	2	8	no	—
247	C₃×C₄×D₅	—	2	8	no	—
248	C₃×Dic₁₀	—	2	8	no	—
249	C₂²×C₃×Q₈	—	5	1	no	—
250	C₂²×C₃×D₄	—	5	1	no	—
251	C₂³×C₃×C₄	—	5	1	no	—
252	C₂³×C₃×C₄	—	5	1	no	—
253	C₂³×C₃×C₄	—	5	1	no	—
254	C₂³×C₃×C₄	—	5	1	no	—
255	C₃×#126	—	5	8	no	—
256	C₃×#126	C₂×D₅	1	8	yes	complemented
257	C₃×#125	—	5	8	no	—
258	C₃×#125	—	5	8	no	—
259	C₃×#125	—	5	8	no	—
260	C₃×#123	—	5	8	no	—
261	C₃×#123	—	5	8	no	—
262	C₃×C₂²⋊Q₈	—	5	8	no	—
263	C₃×C₂²⋊Q₈	—	5	8	no	—
264	C₃×C₄×Q₈	—	5	8	no	—
265	C₃×C₄×D₄	—	5	8	no	—
266	C₃×#117	—	5	8	no	—
267	C₃×#117	—	5	8	no	—
268	C₃×#117	—	5	8	no	—
269	C₂×C₃×C₄⋊C₄	—	5	1	no	—
270	C₂×C₃×C₄⋊C₄	—	5	1	no	—
271	C₂×C₃×C₄⋊C₄	—	5	1	no	—
272	C₂×C₃×C₄⋊C₄	—	5	1	no	—
273	C₂×C₃×C₄⋊C₄	—	5	1	no	—
274	C₂×C₃×C₄⋊C₄	—	5	1	no	—
275	C₂×C₃×C₄⋊C₄	—	5	1	no	—
276	C₂×C₃×C₄⋊C₄	—	5	1	no	—
277	C₂×C₃×C₄⋊C₄	—	5	1	no	—
278	C₂×C₃×C₄⋊C₄	—	5	1	no	—
279	C₂×C₃×C₄⋊C₄	—	5	1	no	—
280	C₂×C₃×C₄⋊C₄	—	5	1	no	—
281	C₂×C₃×C₄⋊C₄	—	5	1	no	—
282	C₂×C₃×C₄⋊C₄	—	5	8	no	—
283	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
284	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
285	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
286	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
287	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
288	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
289	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
290	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
291	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
292	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
293	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
294	C₂×C₃×C₄²	—	5	1	no	—
295	C₂×C₃×C₄²	—	5	1	no	—
296	C₂×C₃×C₄²	—	5	1	no	—
297	C₂×C₃×C₄²	—	5	1	no	—
298	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
299	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
300	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
301	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
302	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
303	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
304	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
305	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
306	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
307	C₂×C₂²⋊D₅	—	2	4	no	—
308	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
309	C₂²×Dic₅	—	2	4	no	—
310	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
311	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
312	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
313	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
314	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
315	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
316	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
317	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
318	C₂×C₄×D₅	—	2	4	no	—
319	C₂×C₄×D₅	—	2	4	no	—
320	C₂×C₄×D₅	—	2	4	no	—
321	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
322	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
323	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
324	C₂×Dic₁₀	—	2	4	no	—
325	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
326	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
327	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
328	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
329	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
330	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
331	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
332	C₄²×C₅	C₂³×C₃	1	4	yes	—
333	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
334	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
335	#685	C₂³×C₃	1	4	yes	—
336	#685	C₂³×C₃	1	4	yes	—
337	#685	C₂³×C₃	1	4	yes	—
338	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
339	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
340	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
341	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
342	#683	C₂³×C₃	1	4	yes	—
343	#683	C₂³×C₃	1	4	yes	—
344	#683	C₂³×C₃	1	4	yes	—
345	#683	C₂³×C₃	1	4	yes	—
346	#683	C₂³×C₃	1	4	yes	—
347	#683	C₂³×C₃	1	4	yes	—
348	#683	C₂³×C₃	1	4	yes	—
349	#683	C₂³×C₃	1	4	yes	—
350	#683	C₂³×C₃	1	4	yes	—
351	C₄×Dic₅	C₂³×C₃	1	4	yes	—
352	C₄×Dic₅	C₂³×C₃	1	4	yes	—
353	C₄×Dic₅	C₂³×C₃	1	4	yes	—
354	C₄×Dic₅	C₂³×C₃	1	4	yes	—
355	#552	—	5	16	no	—
356	C₂×#126	—	5	1	no	—
357	C₂×#126	C₃×D₅	1	1	yes	characteristic, complemented
358	C₂×#125	—	5	1	no	—
359	C₂×#125	—	5	1	no	—
360	C₂×#125	—	5	1	no	—
361	C₂×#123	—	5	1	no	—
362	C₂×#123	—	5	1	no	—
363	C₂×C₂²⋊Q₈	—	5	1	no	—
364	C₂×C₂²⋊Q₈	—	5	1	no	—
365	C₂×C₄×Q₈	—	5	1	no	—
366	C₂×C₄×D₄	—	5	1	no	—
367	C₂×#117	—	5	1	no	—
368	C₂×#117	—	5	1	no	—
369	C₂×#117	—	5	1	no	—
370	C₂²×C₄⋊C₄	—	5	1	no	—
371	C₂²×C₃×C₅	—	2	2	no	—
372	C₂²×C₃×C₅	—	2	2	no	—
373	C₂²×C₃×C₅	—	2	2	no	—
374	C₂²×C₃×C₅	—	4	4	no	—
375	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
376	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
377	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
378	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
379	C₂×C₃×D₅	—	2	8	no	—
380	C₂×C₃×D₅	—	2	2	no	—
381	C₂×C₃×D₅	—	2	2	no	—
382	C₂×C₃×D₅	C₂×#41	1	4	yes	—
383	C₃×C₄×C₅	—	2	2	no	—
384	C₃×C₄×C₅	—	2	2	no	—
385	C₃×C₄×C₅	—	2	2	no	—
386	C₃×C₄×C₅	—	2	2	no	—
387	C₃×C₄×C₅	—	2	2	no	—
388	C₃×C₄×C₅	—	2	2	no	—
389	C₃×Dic₅	—	2	2	no	—
390	C₃×Dic₅	—	2	2	no	—
391	C₃×Dic₅	—	2	2	no	—
392	C₃×Dic₅	—	2	2	no	—
393	C₃×Dic₅	—	2	2	no	—
394	C₃×Dic₅	—	2	2	no	—
395	C₃×Dic₅	C₂×#41	1	4	yes	—
396	C₂⁴×C₃	—	5	1	no	—
397	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
398	C₂×C₃×Q₈	—	5	4	no	—
399	C₂×C₃×Q₈	—	10	4	no	—
400	C₂×C₃×D₄	—	5	4	no	—
401	C₂×C₃×D₄	—	10	4	no	—
402	C₂²×C₃×C₄	—	5	1	no	—
403	C₂²×C₃×C₄	—	5	4	no	—
404	C₂²×C₃×C₄	—	5	1	no	—
405	C₂²×C₃×C₄	—	5	1	no	—
406	C₂²×C₃×C₄	—	5	1	no	—
407	C₂²×C₃×C₄	—	5	1	no	—
408	C₂²×C₃×C₄	—	5	1	no	—
409	C₂²×C₃×C₄	—	5	1	no	—
410	C₂²×C₃×C₄	—	5	4	no	—
411	C₂²×C₃×C₄	—	5	4	no	—
412	C₂²×C₃×C₄	—	5	4	no	—
413	C₂²×C₃×C₄	—	10	4	no	—
414	C₂²×C₃×C₄	—	10	4	no	—
415	C₂²×C₃×C₄	—	10	4	no	—
416	C₂²×C₃×C₄	—	10	4	no	—
417	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
418	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
419	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
420	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
421	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
422	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
423	C₃×C₄⋊C₄	—	5	4	no	—
424	C₃×C₄⋊C₄	—	5	4	no	—
425	C₃×C₄⋊C₄	—	5	4	no	—
426	C₃×C₄⋊C₄	—	5	4	no	—
427	C₃×C₄⋊C₄	—	5	4	no	—
428	C₃×C₄⋊C₄	—	5	4	no	—
429	C₃×C₄⋊C₄	—	5	4	no	—
430	C₃×C₄⋊C₄	—	5	4	no	—
431	C₃×C₄⋊C₄	—	5	4	no	—
432	C₃×C₄⋊C₄	—	5	4	no	—
433	C₃×C₄⋊C₄	—	5	4	no	—
434	C₃×C₄⋊C₄	—	5	4	no	—
435	C₃×C₄⋊C₄	—	5	4	no	—
436	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
437	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
438	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
439	C₃×C₂²⋊C₄	—	5	4	no	—
440	C₃×C₂²⋊C₄	—	5	4	no	—
441	C₃×C₂²⋊C₄	—	5	4	no	—
442	C₃×C₂²⋊C₄	—	5	4	no	—
443	C₃×C₂²⋊C₄	—	5	4	no	—
444	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
445	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
446	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
447	C₃×C₄²	—	5	4	no	—
448	C₃×C₄²	—	5	4	no	—
449	C₃×C₄²	—	5	4	no	—
450	C₃×C₄²	—	5	4	no	—
451	C₃×C₄²	C₂²×D₅	1	4	yes	—
452	C₂³×C₅	—	2	2	no	—
453	C₂³×C₅	—	2	2	no	—
454	C₂³×C₅	—	2	2	no	—
455	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
456	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
457	C₂²×D₅	—	2	2	no	—
458	C₂²×D₅	—	2	2	no	—
459	C₂²×D₅	C₃×#41	1	4	yes	—
460	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
461	C₂×C₄×C₅	—	2	2	no	—
462	C₂×C₄×C₅	—	2	2	no	—
463	C₂×C₄×C₅	—	2	2	no	—
464	C₂×C₄×C₅	—	2	2	no	—
465	C₂×C₄×C₅	—	2	2	no	—
466	C₂×C₄×C₅	—	2	2	no	—
467	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
468	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
469	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
470	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
471	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
472	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
473	C₂²⋊D₅	—	2	8	no	—
474	C₂×Dic₅	—	2	2	no	—
475	C₂×Dic₅	—	2	2	no	—
476	C₂×Dic₅	—	2	2	no	—
477	C₂×Dic₅	—	2	2	no	—
478	C₂×Dic₅	—	2	2	no	—
479	C₂×Dic₅	—	2	2	no	—
480	C₂×Dic₅	—	2	8	no	—
481	C₂×Dic₅	C₃×#41	1	4	yes	—
482	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
483	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
484	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
485	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
486	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
487	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
488	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
489	C₄×D₅	—	2	8	no	—
490	C₄×D₅	—	2	8	no	—
491	C₄×D₅	—	2	8	no	—
492	Dic₁₀	—	2	8	no	—
493	C₂²×Q₈	—	5	1	no	—
494	C₂²×D₄	—	5	1	no	—
495	C₂³×C₄	—	5	1	no	—
496	C₂³×C₄	—	5	1	no	—
497	C₂³×C₄	—	5	1	no	—
498	C₂³×C₄	—	5	1	no	—
499	#126	—	5	8	no	—
500	#126	C₂×C₃×D₅	1	8	yes	complemented
501	#125	—	5	8	no	—
502	#125	—	5	8	no	—
503	#125	—	5	8	no	—
504	#123	—	5	8	no	—
505	#123	—	5	8	no	—
506	C₂²⋊Q₈	—	5	8	no	—
507	C₂²⋊Q₈	—	5	8	no	—
508	C₄×Q₈	—	5	8	no	—
509	C₄×D₄	—	5	8	no	—
510	#117	—	5	8	no	—
511	#117	—	5	8	no	—
512	#117	—	5	8	no	—
513	C₂×C₄⋊C₄	—	5	1	no	—
514	C₂×C₄⋊C₄	—	5	1	no	—
515	C₂×C₄⋊C₄	—	5	1	no	—
516	C₂×C₄⋊C₄	—	5	1	no	—
517	C₂×C₄⋊C₄	—	5	1	no	—
518	C₂×C₄⋊C₄	—	5	1	no	—
519	C₂×C₄⋊C₄	—	5	1	no	—
520	C₂×C₄⋊C₄	—	5	1	no	—
521	C₂×C₄⋊C₄	—	5	1	no	—
522	C₂×C₄⋊C₄	—	5	1	no	—
523	C₂×C₄⋊C₄	—	5	1	no	—
524	C₂×C₄⋊C₄	—	5	1	no	—
525	C₂×C₄⋊C₄	—	5	1	no	—
526	C₂×C₄⋊C₄	—	5	8	no	—
527	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	—	5	1	no	—
531	C₂×C₂²⋊C₄	—	5	1	no	—
532	C₂×C₂²⋊C₄	—	5	1	no	—
533	C₂×C₂²⋊C₄	—	5	1	no	—
534	C₂×C₂²⋊C₄	—	5	1	no	—
535	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
538	C₂×C₄²	—	5	1	no	—
539	C₂×C₄²	—	5	1	no	—
540	C₂×C₄²	—	5	1	no	—
541	C₂×C₄²	—	5	1	no	—
542	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
543	C₂×C₃×C₅	—	4	2	no	—
544	C₂×C₃×C₅	#552	1	4	yes	complemented
545	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
546	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
547	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
548	C₃×D₅	—	2	4	no	—
549	C₂³×C₃	—	2	2	no	—
550	C₂³×C₃	—	2	2	no	—
551	C₂³×C₃	—	2	2	no	—
552	C₂³×C₃	—	5	4	no	—
553	C₂³×C₃	—	5	2	no	—
554	C₂³×C₃	—	10	2	no	—
555	C₂³×C₃	—	10	2	no	—
556	C₂³×C₃	C₂³×D₅	1	2	yes	—
557	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
558	C₃×Q₈	—	10	8	no	—
559	C₃×D₄	—	10	8	no	—
560	C₂×C₃×C₄	—	2	2	no	—
561	C₂×C₃×C₄	—	2	2	no	—
562	C₂×C₃×C₄	—	2	2	no	—
563	C₂×C₃×C₄	—	2	2	no	—
564	C₂×C₃×C₄	—	2	2	no	—
565	C₂×C₃×C₄	—	2	2	no	—
566	C₂×C₃×C₄	—	5	4	no	—
567	C₂×C₃×C₄	—	5	2	no	—
568	C₂×C₃×C₄	—	5	2	no	—
569	C₂×C₃×C₄	—	5	2	no	—
570	C₂×C₃×C₄	—	5	2	no	—
571	C₂×C₃×C₄	—	5	2	no	—
572	C₂×C₃×C₄	—	5	2	no	—
573	C₂×C₃×C₄	—	5	2	no	—
574	C₂×C₃×C₄	—	10	8	no	—
575	C₂×C₃×C₄	—	10	8	no	—
576	C₂×C₃×C₄	—	10	8	no	—
577	C₂×C₃×C₄	—	10	8	no	—
578	C₂×C₃×C₄	—	10	2	no	—
579	C₂×C₃×C₄	—	10	2	no	—
580	C₂×C₃×C₄	—	10	2	no	—
581	C₂×C₃×C₄	—	10	2	no	—
582	C₂×C₃×C₄	—	10	2	no	—
583	C₂×C₃×C₄	—	10	2	no	—
584	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
585	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
586	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
587	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
588	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
589	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
590	C₂²×C₅	—	2	2	no	—
591	C₂²×C₅	—	2	2	no	—
592	C₂²×C₅	—	2	2	no	—
593	C₂²×C₅	—	4	4	no	—
594	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
595	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
596	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
597	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
598	C₂×D₅	—	2	2	no	—
599	C₂×D₅	—	2	2	no	—
600	C₂×D₅	—	2	8	no	—
601	C₂×D₅	C₂×C₃×#41	1	4	yes	—
602	C₄×C₅	—	2	2	no	—
603	C₄×C₅	—	2	2	no	—
604	C₄×C₅	—	2	2	no	—
605	C₄×C₅	—	2	2	no	—
606	C₄×C₅	—	2	2	no	—
607	C₄×C₅	—	2	2	no	—
608	Dic₅	—	2	2	no	—
609	Dic₅	—	2	2	no	—
610	Dic₅	—	2	2	no	—
611	Dic₅	—	2	2	no	—
612	Dic₅	—	2	2	no	—
613	Dic₅	—	2	2	no	—
614	Dic₅	C₂×C₃×#41	1	4	yes	—
615	C₂⁴	—	5	1	no	—
616	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
617	C₂×Q₈	—	5	4	no	—
618	C₂×Q₈	—	10	4	no	—
619	C₂×D₄	—	5	4	no	—
620	C₂×D₄	—	10	4	no	—
621	C₂²×C₄	—	5	1	no	—
622	C₂²×C₄	—	5	1	no	—
623	C₂²×C₄	—	5	1	no	—
624	C₂²×C₄	—	5	1	no	—
625	C₂²×C₄	—	5	1	no	—
626	C₂²×C₄	—	5	1	no	—
627	C₂²×C₄	—	5	1	no	—
628	C₂²×C₄	—	5	4	no	—
629	C₂²×C₄	—	5	4	no	—
630	C₂²×C₄	—	5	4	no	—
631	C₂²×C₄	—	5	4	no	—
632	C₂²×C₄	—	10	4	no	—
633	C₂²×C₄	—	10	4	no	—
634	C₂²×C₄	—	10	4	no	—
635	C₂²×C₄	—	10	4	no	—
636	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
637	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
638	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
639	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
640	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
641	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
642	C₄⋊C₄	—	5	4	no	—
643	C₄⋊C₄	—	5	4	no	—
644	C₄⋊C₄	—	5	4	no	—
645	C₄⋊C₄	—	5	4	no	—
646	C₄⋊C₄	—	5	4	no	—
647	C₄⋊C₄	—	5	4	no	—
648	C₄⋊C₄	—	5	4	no	—
649	C₄⋊C₄	—	5	4	no	—
650	C₄⋊C₄	—	5	4	no	—
651	C₄⋊C₄	—	5	4	no	—
652	C₄⋊C₄	—	5	4	no	—
653	C₄⋊C₄	—	5	4	no	—
654	C₄⋊C₄	—	5	4	no	—
655	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
656	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
657	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
658	C₂²⋊C₄	—	5	4	no	—
659	C₂²⋊C₄	—	5	4	no	—
660	C₂²⋊C₄	—	5	4	no	—
661	C₂²⋊C₄	—	5	4	no	—
662	C₂²⋊C₄	—	5	4	no	—
663	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
664	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
665	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
666	C₄²	—	5	4	no	—
667	C₄²	—	5	4	no	—
668	C₄²	—	5	4	no	—
669	C₄²	—	5	4	no	—
670	C₄²	C₂²×C₃×D₅	1	4	yes	—
671	C₃×C₅	C₂×#552	1	1	yes	characteristic, complemented, Hall
672	C₂²×C₃	—	2	2	no	—
673	C₂²×C₃	—	2	2	no	—
674	C₂²×C₃	—	2	2	no	—
675	C₂²×C₃	—	4	4	no	—
676	C₂²×C₃	—	5	4	no	—
677	C₂²×C₃	—	10	2	no	—
678	C₂²×C₃	—	10	2	no	—
679	C₂²×C₃	—	10	8	no	—
680	C₂²×C₃	D₅×#41	1	2	yes	—
681	C₂²×C₃	D₅×#41	1	2	yes	—
682	C₂²×C₃	#4150	1	2	yes	—
683	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
684	C₃×C₄	—	2	2	no	—
685	C₃×C₄	—	2	2	no	—
686	C₃×C₄	—	2	2	no	—
687	C₃×C₄	—	2	2	no	—
688	C₃×C₄	—	2	2	no	—
689	C₃×C₄	—	2	2	no	—
690	C₃×C₄	—	5	4	no	—
691	C₃×C₄	—	10	2	no	—
692	C₃×C₄	—	10	2	no	—
693	C₃×C₄	—	10	2	no	—
694	C₃×C₄	—	10	2	no	—
695	C₃×C₄	—	10	2	no	—
696	C₃×C₄	—	10	2	no	—
697	C₂×C₅	—	4	2	no	—
698	C₂×C₅	C₃×#552	1	4	yes	complemented
699	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
700	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
701	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
702	D₅	—	2	4	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	5	4	no	—
707	C₂³	—	5	2	no	—
708	C₂³	—	10	2	no	—
709	C₂³	—	10	2	no	—
710	C₂³	C₂³×C₃×D₅	1	2	yes	—
711	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
712	Q₈	—	10	8	no	—
713	D₄	—	10	8	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	5	4	no	—
721	C₂×C₄	—	5	2	no	—
722	C₂×C₄	—	5	2	no	—
723	C₂×C₄	—	5	2	no	—
724	C₂×C₄	—	5	2	no	—
725	C₂×C₄	—	5	2	no	—
726	C₂×C₄	—	5	2	no	—
727	C₂×C₄	—	5	2	no	—
728	C₂×C₄	—	10	8	no	—
729	C₂×C₄	—	10	8	no	—
730	C₂×C₄	—	10	8	no	—
731	C₂×C₄	—	10	8	no	—
732	C₂×C₄	—	10	2	no	—
733	C₂×C₄	—	10	2	no	—
734	C₂×C₄	—	10	2	no	—
735	C₂×C₄	—	10	2	no	—
736	C₂×C₄	—	10	2	no	—
737	C₂×C₄	—	10	2	no	—
738	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
739	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
740	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
741	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
742	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
743	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
744	C₂×C₃	—	4	2	no	—
745	C₂×C₃	—	10	4	no	—
746	C₂×C₃	#66042	1	4	yes	direct product factor
747	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
748	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
749	C₂×C₃	C₂×#4150	1	1	yes	characteristic
750	C₅	C₂×C₃×#552	1	1	yes	characteristic, complemented, Sylow
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	4	4	no	—
755	C₂²	—	5	4	no	—
756	C₂²	—	10	2	no	—
757	C₂²	—	10	2	no	—
758	C₂²	—	10	8	no	—
759	C₂²	C₃×D₅×#41	1	2	yes	—
760	C₂²	C₃×D₅×#41	1	2	yes	—
761	C₂²	C₃×#4150	1	2	yes	—
762	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	2	no	—
769	C₄	—	5	4	no	—
770	C₄	—	10	2	no	—
771	C₄	—	10	2	no	—
772	C₄	—	10	2	no	—
773	C₄	—	10	2	no	—
774	C₄	—	10	2	no	—
775	C₄	—	10	2	no	—
776	C₃	C₂×#66042	1	1	yes	characteristic, direct product factor, Sylow
777	C₂	—	4	2	no	—
778	C₂	—	10	4	no	—
779	C₂	C₃×#66042	1	4	yes	direct product factor
780	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
781	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
782	C₂	C₂×C₃×#4150	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#126	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×C₂²⋊D₅	C₂²
hypercenter	C₂×C₃×#126	D₅
hypocenter	C₅	C₂×C₃×#552
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#126

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#126	C₂	semidirect
2. C₃×#66042	C₂	direct (N × H)
3. C₂×C₃×#4042	C₂	semidirect
4. C₂×C₃×#4038	C₂	semidirect
5. C₂×C₃×D₅×C₄⋊C₄	C₂	semidirect
6. C₂×C₃×#4036	C₂	semidirect
7. C₂×C₃×#4035	C₂	semidirect
8. C₂×C₃×#4035	C₂	semidirect
12. C₂×C₃×#4025	C₂	semidirect
13. C₂×C₃×#4024	C₂	semidirect
14. C₂×C₃×#4023	C₂	semidirect
15. C₂×C₃×#4018	C₂	semidirect
16. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
17. C₂×#66042	C₃	direct (N × H)
24. C₃×C₅×#126	C₂²	semidirect
54. C₃×#4042	C₂²	semidirect
55. C₃×#4038	C₂²	semidirect
56. C₃×D₅×C₄⋊C₄	C₂²	semidirect
57. C₃×#4036	C₂²	semidirect
58. C₃×#4035	C₂²	semidirect
59. C₃×#4035	C₂²	semidirect
63. C₃×#4025	C₂²	semidirect
64. C₃×#4024	C₂²	semidirect
65. C₃×#4023	C₂²	semidirect
66. C₃×#4018	C₂²	semidirect
67. C₃×C₄×Dic₁₀	C₂²	semidirect
69. C₂×C₅×#126	C₂×C₃	semidirect
70. #66042	C₂×C₃	direct (N × H)
71. C₂×#4042	C₂×C₃	semidirect
72. C₂×#4038	C₂×C₃	semidirect
73. C₂×D₅×C₄⋊C₄	C₂×C₃	semidirect
74. C₂×#4036	C₂×C₃	semidirect
75. C₂×#4035	C₂×C₃	semidirect
76. C₂×#4035	C₂×C₃	semidirect
80. C₂×#4025	C₂×C₃	semidirect
81. C₂×#4024	C₂×C₃	semidirect
82. C₂×#4023	C₂×C₃	semidirect
83. C₂×#4018	C₂×C₃	semidirect
84. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
143. C₂×C₃×#126	D₅	semidirect
163. C₅×#126	C₂²×C₃	semidirect
193. #4042	C₂²×C₃	semidirect
194. #4038	C₂²×C₃	semidirect
195. D₅×C₄⋊C₄	C₂²×C₃	semidirect
196. #4036	C₂²×C₃	semidirect
197. #4035	C₂²×C₃	semidirect
198. #4035	C₂²×C₃	semidirect
202. #4025	C₂²×C₃	semidirect
203. #4024	C₂²×C₃	semidirect
204. #4023	C₂²×C₃	semidirect
205. #4018	C₂²×C₃	semidirect
206. C₄×Dic₁₀	C₂²×C₃	semidirect
256. C₃×#126	C₂×D₅	semidirect
357. C₂×#126	C₃×D₅	semidirect
500. #126	C₂×C₃×D₅	semidirect
544. C₂×C₃×C₅	#552	semidirect
671. C₃×C₅	C₂×#552	semidirect
698. C₂×C₅	C₃×#552	semidirect
746. C₂×C₃	#66042	direct (N × H)
750. C₅	C₂×C₃×#552	semidirect
776. C₃	C₂×#66042	direct (N × H)
779. C₂	C₃×#66042	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#126	2
C₃×#66042	2
C₂×C₃×#4042	2
C₂×C₃×#4038	2
C₂×C₃×D₅×C₄⋊C₄	2
C₂×C₃×#4036	2
C₂×C₃×#4035	2
C₂×C₃×#4029	2
C₂×C₃×#4027	2
C₂×C₃×#4025	2
C₂×C₃×#4024	2
C₂×C₃×#4023	2
C₂×C₃×#4018	2
C₂×C₃×C₄×Dic₁₀	2
C₂×#66042	3
C₂×C₃×#552	5

Subgroups — C2×C3×#66042 #14483410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66042 #14483410