Subgroups — C₃×C₅×#2428 #14275462

Order 1920.

1664 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#392	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2428	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
16	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
17	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
20	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
21	C₃×C₅×#127	—	2	4	no	—
22	C₃×C₅×#121	—	2	4	no	—
23	C₃×C₅×#121	—	2	4	no	—
24	C₃×C₅×#121	—	2	8	no	—
25	C₃×C₄×C₅×D₄	—	2	4	no	—
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
38	C₃×C₅×#95	C₂²	1	1	yes	characteristic
39	C₃×C₅×#95	C₂²	1	1	yes	characteristic
40	C₃×C₅×#95	C₂²	1	2	yes	—
41	C₃×#2428	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
44	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#394	C₂×C₃	1	2	yes	complemented
48	C₅×#392	C₂×C₃	1	2	yes	complemented
49	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#386	C₂×C₃	1	2	yes	complemented
52	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
54	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
55	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	—	2	4	no	—
57	C₂×C₃×C₅×D₄	—	2	4	no	—
58	C₂×C₃×C₅×D₄	—	2	4	no	—
59	C₂×C₃×C₅×D₄	—	2	4	no	—
60	C₂×C₃×C₅×D₄	—	2	4	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	—	2	4	no	—
63	C₂×C₃×C₅×D₄	—	2	4	no	—
64	C₂×C₃×C₅×D₄	—	2	2	no	—
65	C₂×C₃×C₅×D₄	—	2	2	no	—
66	C₂×C₃×C₅×D₄	—	2	2	no	—
67	C₂×C₃×C₅×D₄	—	2	4	no	—
68	C₂×C₃×C₅×D₄	—	2	2	no	—
69	C₂×C₃×C₅×D₄	—	4	2	no	—
70	C₂×C₃×C₅×D₄	—	4	2	no	—
71	C₂×C₃×C₅×D₄	—	4	2	no	—
72	C₂×C₃×C₅×D₄	—	4	2	no	—
73	C₂×C₃×C₅×D₄	D₄	1	4	yes	complemented
74	C₂²×C₃×C₄×C₅	—	2	4	no	—
75	C₂²×C₃×C₄×C₅	—	2	4	no	—
76	C₂²×C₃×C₄×C₅	—	2	2	no	—
77	C₂²×C₃×C₄×C₅	—	2	2	no	—
78	C₂²×C₃×C₄×C₅	—	2	2	no	—
79	C₂²×C₃×C₄×C₅	—	4	2	no	—
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
86	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₃×C₅×C₄⋊C₄	—	2	4	no	—
89	C₃×C₅×C₄⋊C₄	—	2	2	no	—
90	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	complemented
91	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
92	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
93	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
94	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
95	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
96	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
97	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	complemented
98	C₃×C₄²×C₅	—	2	2	no	—
99	C₃×C₄²×C₅	—	2	2	no	—
100	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
102	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
105	C₃×#394	C₂×C₅	1	2	yes	complemented
106	C₃×#392	C₂×C₅	1	2	yes	complemented
107	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
108	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
109	C₃×#386	C₂×C₅	1	2	yes	complemented
110	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
112	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
113	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
114	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
115	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
116	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
117	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
118	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
119	C₅×#127	—	2	4	no	—
120	C₅×#121	—	2	4	no	—
121	C₅×#121	—	2	4	no	—
122	C₅×#121	—	2	8	no	—
123	C₄×C₅×D₄	—	2	4	no	—
124	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
126	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
129	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
130	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
131	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
132	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
133	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
136	C₅×#95	C₂²×C₃	1	1	yes	characteristic
137	C₅×#95	C₂²×C₃	1	1	yes	characteristic
138	C₅×#95	C₂²×C₃	1	2	yes	—
139	#2428	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
140	C₂³×C₃×C₅	—	2	2	no	—
141	C₂³×C₃×C₅	—	2	1	no	—
142	C₂³×C₃×C₅	—	2	1	no	—
143	C₂³×C₃×C₅	—	2	2	no	—
144	C₂³×C₃×C₅	—	2	1	no	—
145	C₂³×C₃×C₅	—	2	1	no	—
146	C₂³×C₃×C₅	—	2	2	no	—
147	C₂³×C₃×C₅	—	2	2	no	—
148	C₂³×C₃×C₅	—	2	2	no	—
149	C₂³×C₃×C₅	—	2	1	no	—
150	C₂³×C₃×C₅	—	2	2	no	—
151	C₂³×C₃×C₅	—	2	1	no	—
152	C₂³×C₃×C₅	—	2	2	no	—
153	C₂³×C₃×C₅	—	2	2	no	—
154	C₂³×C₃×C₅	—	2	2	no	—
155	C₂³×C₃×C₅	—	2	2	no	—
156	C₂³×C₃×C₅	—	2	2	no	—
157	C₂³×C₃×C₅	—	2	2	no	—
158	C₂³×C₃×C₅	—	2	2	no	—
159	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
160	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
161	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
162	C₃×C₅×D₄	—	2	8	no	—
163	C₃×C₅×D₄	—	4	8	no	—
164	C₃×C₅×D₄	—	4	8	no	—
165	C₃×C₅×D₄	—	4	8	no	—
166	C₃×C₅×D₄	—	4	8	no	—
167	C₃×C₅×D₄	—	4	4	no	—
168	C₂×C₃×C₄×C₅	—	2	1	no	—
169	C₂×C₃×C₄×C₅	—	2	1	no	—
170	C₂×C₃×C₄×C₅	—	2	1	no	—
171	C₂×C₃×C₄×C₅	—	2	2	no	—
172	C₂×C₃×C₄×C₅	—	2	1	no	—
173	C₂×C₃×C₄×C₅	—	2	2	no	—
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	—	2	1	no	—
176	C₂×C₃×C₄×C₅	—	2	1	no	—
177	C₂×C₃×C₄×C₅	—	2	1	no	—
178	C₂×C₃×C₄×C₅	—	2	1	no	—
179	C₂×C₃×C₄×C₅	—	2	2	no	—
180	C₂×C₃×C₄×C₅	—	2	2	no	—
181	C₂×C₃×C₄×C₅	—	2	1	no	—
182	C₂×C₃×C₄×C₅	—	2	1	no	—
183	C₂×C₃×C₄×C₅	—	2	1	no	—
184	C₂×C₃×C₄×C₅	—	2	2	no	—
185	C₂×C₃×C₄×C₅	—	4	8	no	—
186	C₂×C₃×C₄×C₅	—	4	4	no	—
187	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
188	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
189	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
190	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
191	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
192	C₂×C₃×C₄×C₅	#41	1	2	yes	—
193	C₂×C₃×C₄×C₅	#41	1	2	yes	—
194	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
195	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
196	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
197	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
198	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
199	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
200	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
201	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
202	C₃×#127	—	2	4	no	—
203	C₃×#121	—	2	4	no	—
204	C₃×#121	—	2	4	no	—
205	C₃×#121	—	2	8	no	—
206	C₃×C₄×D₄	—	2	4	no	—
207	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
209	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
210	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
211	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
212	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
213	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
214	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
215	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
216	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
219	C₃×#95	C₂²×C₅	1	1	yes	characteristic
220	C₃×#95	C₂²×C₅	1	1	yes	characteristic
221	C₃×#95	C₂²×C₅	1	2	yes	—
222	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
223	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
224	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
225	C₂×C₅×D₄	—	2	4	no	—
226	C₂×C₅×D₄	—	2	4	no	—
227	C₂×C₅×D₄	—	2	4	no	—
228	C₂×C₅×D₄	—	2	4	no	—
229	C₂×C₅×D₄	—	2	4	no	—
230	C₂×C₅×D₄	—	2	2	no	—
231	C₂×C₅×D₄	—	2	4	no	—
232	C₂×C₅×D₄	—	2	4	no	—
233	C₂×C₅×D₄	—	2	2	no	—
234	C₂×C₅×D₄	—	2	2	no	—
235	C₂×C₅×D₄	—	2	2	no	—
236	C₂×C₅×D₄	—	2	4	no	—
237	C₂×C₅×D₄	—	2	2	no	—
238	C₂×C₅×D₄	—	4	2	no	—
239	C₂×C₅×D₄	—	4	2	no	—
240	C₂×C₅×D₄	—	4	2	no	—
241	C₂×C₅×D₄	—	4	2	no	—
242	C₂×C₅×D₄	C₃×D₄	1	4	yes	complemented
243	C₂²×C₄×C₅	—	2	4	no	—
244	C₂²×C₄×C₅	—	2	4	no	—
245	C₂²×C₄×C₅	—	2	2	no	—
246	C₂²×C₄×C₅	—	2	2	no	—
247	C₂²×C₄×C₅	—	2	2	no	—
248	C₂²×C₄×C₅	—	4	2	no	—
249	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
250	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
251	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
252	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
253	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
254	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
255	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
256	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
257	C₅×C₄⋊C₄	—	2	4	no	—
258	C₅×C₄⋊C₄	—	2	2	no	—
259	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	complemented
260	C₅×C₂²⋊C₄	—	2	4	no	—
261	C₅×C₂²⋊C₄	—	2	4	no	—
262	C₅×C₂²⋊C₄	—	2	4	no	—
263	C₅×C₂²⋊C₄	—	2	4	no	—
264	C₅×C₂²⋊C₄	—	2	2	no	—
265	C₅×C₂²⋊C₄	—	4	2	no	—
266	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	complemented
267	C₄²×C₅	—	2	2	no	—
268	C₄²×C₅	—	2	2	no	—
269	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic, complemented
270	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
271	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
272	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
273	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
274	#394	C₂×C₃×C₅	1	2	yes	complemented
275	#392	C₂×C₃×C₅	1	2	yes	complemented
276	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
277	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
278	#386	C₂×C₃×C₅	1	2	yes	complemented
279	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
280	C₂²×C₃×C₅	—	2	4	no	—
281	C₂²×C₃×C₅	—	2	2	no	—
282	C₂²×C₃×C₅	—	2	2	no	—
283	C₂²×C₃×C₅	—	2	4	no	—
284	C₂²×C₃×C₅	—	2	2	no	—
285	C₂²×C₃×C₅	—	2	4	no	—
286	C₂²×C₃×C₅	—	4	1	no	—
287	C₂²×C₃×C₅	—	4	2	no	—
288	C₂²×C₃×C₅	—	4	1	no	—
289	C₂²×C₃×C₅	—	4	2	no	—
290	C₂²×C₃×C₅	—	4	2	no	—
291	C₂²×C₃×C₅	—	4	1	no	—
292	C₂²×C₃×C₅	—	4	2	no	—
293	C₂²×C₃×C₅	—	4	1	no	—
294	C₂²×C₃×C₅	—	4	2	no	—
295	C₂²×C₃×C₅	—	4	2	no	—
296	C₂²×C₃×C₅	—	4	2	no	—
297	C₂²×C₃×C₅	—	4	2	no	—
298	C₂²×C₃×C₅	—	4	2	no	—
299	C₂²×C₃×C₅	—	4	2	no	—
300	C₂²×C₃×C₅	—	4	2	no	—
301	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
302	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
303	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
304	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
305	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
306	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
307	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
308	C₃×C₄×C₅	—	2	2	no	—
309	C₃×C₄×C₅	—	2	4	no	—
310	C₃×C₄×C₅	—	2	2	no	—
311	C₃×C₄×C₅	—	2	2	no	—
312	C₃×C₄×C₅	—	4	1	no	—
313	C₃×C₄×C₅	—	4	2	no	—
314	C₃×C₄×C₅	—	4	1	no	—
315	C₃×C₄×C₅	#121	1	4	yes	complemented
316	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
317	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
318	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
319	C₂×C₃×D₄	—	2	4	no	—
320	C₂×C₃×D₄	—	2	4	no	—
321	C₂×C₃×D₄	—	2	4	no	—
322	C₂×C₃×D₄	—	2	4	no	—
323	C₂×C₃×D₄	—	2	4	no	—
324	C₂×C₃×D₄	—	2	2	no	—
325	C₂×C₃×D₄	—	2	4	no	—
326	C₂×C₃×D₄	—	2	4	no	—
327	C₂×C₃×D₄	—	2	2	no	—
328	C₂×C₃×D₄	—	2	2	no	—
329	C₂×C₃×D₄	—	2	2	no	—
330	C₂×C₃×D₄	—	2	4	no	—
331	C₂×C₃×D₄	—	2	2	no	—
332	C₂×C₃×D₄	—	4	2	no	—
333	C₂×C₃×D₄	—	4	2	no	—
334	C₂×C₃×D₄	—	4	2	no	—
335	C₂×C₃×D₄	—	4	2	no	—
336	C₂×C₃×D₄	C₅×D₄	1	4	yes	complemented
337	C₂²×C₃×C₄	—	2	4	no	—
338	C₂²×C₃×C₄	—	2	4	no	—
339	C₂²×C₃×C₄	—	2	2	no	—
340	C₂²×C₃×C₄	—	2	2	no	—
341	C₂²×C₃×C₄	—	2	2	no	—
342	C₂²×C₃×C₄	—	4	2	no	—
343	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
344	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
345	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
346	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
347	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
348	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
349	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
350	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
351	C₃×C₄⋊C₄	—	2	4	no	—
352	C₃×C₄⋊C₄	—	2	2	no	—
353	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	complemented
354	C₃×C₂²⋊C₄	—	2	4	no	—
355	C₃×C₂²⋊C₄	—	2	4	no	—
356	C₃×C₂²⋊C₄	—	2	4	no	—
357	C₃×C₂²⋊C₄	—	2	4	no	—
358	C₃×C₂²⋊C₄	—	2	2	no	—
359	C₃×C₂²⋊C₄	—	4	2	no	—
360	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	complemented
361	C₃×C₄²	—	2	2	no	—
362	C₃×C₄²	—	2	2	no	—
363	C₂³×C₅	—	2	2	no	—
364	C₂³×C₅	—	2	1	no	—
365	C₂³×C₅	—	2	1	no	—
366	C₂³×C₅	—	2	2	no	—
367	C₂³×C₅	—	2	1	no	—
368	C₂³×C₅	—	2	1	no	—
369	C₂³×C₅	—	2	2	no	—
370	C₂³×C₅	—	2	2	no	—
371	C₂³×C₅	—	2	2	no	—
372	C₂³×C₅	—	2	1	no	—
373	C₂³×C₅	—	2	2	no	—
374	C₂³×C₅	—	2	1	no	—
375	C₂³×C₅	—	2	2	no	—
376	C₂³×C₅	—	2	2	no	—
377	C₂³×C₅	—	2	2	no	—
378	C₂³×C₅	—	2	2	no	—
379	C₂³×C₅	—	2	2	no	—
380	C₂³×C₅	—	2	2	no	—
381	C₂³×C₅	—	2	2	no	—
382	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
383	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
384	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
385	C₅×D₄	—	2	8	no	—
386	C₅×D₄	—	4	8	no	—
387	C₅×D₄	—	4	8	no	—
388	C₅×D₄	—	4	8	no	—
389	C₅×D₄	—	4	8	no	—
390	C₅×D₄	—	4	4	no	—
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	2	1	no	—
394	C₂×C₄×C₅	—	2	2	no	—
395	C₂×C₄×C₅	—	2	1	no	—
396	C₂×C₄×C₅	—	2	2	no	—
397	C₂×C₄×C₅	—	2	1	no	—
398	C₂×C₄×C₅	—	2	1	no	—
399	C₂×C₄×C₅	—	2	1	no	—
400	C₂×C₄×C₅	—	2	1	no	—
401	C₂×C₄×C₅	—	2	1	no	—
402	C₂×C₄×C₅	—	2	2	no	—
403	C₂×C₄×C₅	—	2	2	no	—
404	C₂×C₄×C₅	—	2	1	no	—
405	C₂×C₄×C₅	—	2	1	no	—
406	C₂×C₄×C₅	—	2	1	no	—
407	C₂×C₄×C₅	—	2	2	no	—
408	C₂×C₄×C₅	—	4	8	no	—
409	C₂×C₄×C₅	—	4	4	no	—
410	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
411	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
412	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
413	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
414	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
415	C₂×C₄×C₅	C₃×#41	1	2	yes	—
416	C₂×C₄×C₅	C₃×#41	1	2	yes	—
417	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
418	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
419	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
420	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
421	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
422	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
423	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
424	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
425	#127	—	2	4	no	—
426	#121	—	2	4	no	—
427	#121	—	2	4	no	—
428	#121	—	2	8	no	—
429	C₄×D₄	—	2	4	no	—
430	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
432	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
433	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
440	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
441	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
442	#95	C₂²×C₃×C₅	1	1	yes	characteristic
443	#95	C₂²×C₃×C₅	1	1	yes	characteristic
444	#95	C₂²×C₃×C₅	1	2	yes	—
445	C₂×C₃×C₅	—	4	4	no	—
446	C₂×C₃×C₅	—	4	2	no	—
447	C₂×C₃×C₅	—	8	2	no	—
448	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
449	C₂×C₃×C₅	#532	1	1	yes	characteristic
450	C₂×C₃×C₅	#540	1	1	yes	characteristic
451	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
452	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
453	C₂×C₃×C₅	#546	1	1	yes	characteristic
454	C₂×C₃×C₅	#550	1	1	yes	characteristic
455	C₂³×C₃	—	2	2	no	—
456	C₂³×C₃	—	2	1	no	—
457	C₂³×C₃	—	2	1	no	—
458	C₂³×C₃	—	2	2	no	—
459	C₂³×C₃	—	2	1	no	—
460	C₂³×C₃	—	2	1	no	—
461	C₂³×C₃	—	2	2	no	—
462	C₂³×C₃	—	2	2	no	—
463	C₂³×C₃	—	2	2	no	—
464	C₂³×C₃	—	2	1	no	—
465	C₂³×C₃	—	2	2	no	—
466	C₂³×C₃	—	2	1	no	—
467	C₂³×C₃	—	2	2	no	—
468	C₂³×C₃	—	2	2	no	—
469	C₂³×C₃	—	2	2	no	—
470	C₂³×C₃	—	2	2	no	—
471	C₂³×C₃	—	2	2	no	—
472	C₂³×C₃	—	2	2	no	—
473	C₂³×C₃	—	2	2	no	—
474	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
475	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
476	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
477	C₃×D₄	—	2	8	no	—
478	C₃×D₄	—	4	8	no	—
479	C₃×D₄	—	4	8	no	—
480	C₃×D₄	—	4	8	no	—
481	C₃×D₄	—	4	8	no	—
482	C₃×D₄	—	4	4	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	2	no	—
487	C₂×C₃×C₄	—	2	1	no	—
488	C₂×C₃×C₄	—	2	2	no	—
489	C₂×C₃×C₄	—	2	1	no	—
490	C₂×C₃×C₄	—	2	1	no	—
491	C₂×C₃×C₄	—	2	1	no	—
492	C₂×C₃×C₄	—	2	1	no	—
493	C₂×C₃×C₄	—	2	1	no	—
494	C₂×C₃×C₄	—	2	2	no	—
495	C₂×C₃×C₄	—	2	2	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	2	no	—
500	C₂×C₃×C₄	—	4	8	no	—
501	C₂×C₃×C₄	—	4	4	no	—
502	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
503	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
504	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
505	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
506	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
507	C₂×C₃×C₄	C₅×#41	1	2	yes	—
508	C₂×C₃×C₄	C₅×#41	1	2	yes	—
509	C₂²×C₅	—	2	4	no	—
510	C₂²×C₅	—	2	2	no	—
511	C₂²×C₅	—	2	2	no	—
512	C₂²×C₅	—	2	4	no	—
513	C₂²×C₅	—	2	2	no	—
514	C₂²×C₅	—	2	4	no	—
515	C₂²×C₅	—	4	1	no	—
516	C₂²×C₅	—	4	2	no	—
517	C₂²×C₅	—	4	1	no	—
518	C₂²×C₅	—	4	2	no	—
519	C₂²×C₅	—	4	2	no	—
520	C₂²×C₅	—	4	1	no	—
521	C₂²×C₅	—	4	2	no	—
522	C₂²×C₅	—	4	1	no	—
523	C₂²×C₅	—	4	2	no	—
524	C₂²×C₅	—	4	2	no	—
525	C₂²×C₅	—	4	2	no	—
526	C₂²×C₅	—	4	2	no	—
527	C₂²×C₅	—	4	2	no	—
528	C₂²×C₅	—	4	2	no	—
529	C₂²×C₅	—	4	2	no	—
530	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
531	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
532	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
533	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
534	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
535	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
536	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
537	C₄×C₅	—	2	2	no	—
538	C₄×C₅	—	2	4	no	—
539	C₄×C₅	—	2	2	no	—
540	C₄×C₅	—	2	2	no	—
541	C₄×C₅	—	4	1	no	—
542	C₄×C₅	—	4	2	no	—
543	C₄×C₅	—	4	1	no	—
544	C₄×C₅	C₃×#121	1	4	yes	complemented
545	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
546	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
547	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
548	C₂×D₄	—	2	4	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	4	2	no	—
562	C₂×D₄	—	4	2	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	2	no	—
565	C₂×D₄	C₃×C₅×D₄	1	4	yes	complemented
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
573	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
574	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
575	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
576	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
577	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
578	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
579	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	4	2	no	—
589	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
590	C₄²	—	2	2	no	—
591	C₄²	—	2	2	no	—
592	C₃×C₅	#2428	1	1	yes	characteristic, direct product factor, Hall
593	C₂²×C₃	—	2	4	no	—
594	C₂²×C₃	—	2	2	no	—
595	C₂²×C₃	—	2	2	no	—
596	C₂²×C₃	—	2	4	no	—
597	C₂²×C₃	—	2	2	no	—
598	C₂²×C₃	—	2	4	no	—
599	C₂²×C₃	—	4	1	no	—
600	C₂²×C₃	—	4	2	no	—
601	C₂²×C₃	—	4	1	no	—
602	C₂²×C₃	—	4	2	no	—
603	C₂²×C₃	—	4	2	no	—
604	C₂²×C₃	—	4	1	no	—
605	C₂²×C₃	—	4	2	no	—
606	C₂²×C₃	—	4	1	no	—
607	C₂²×C₃	—	4	2	no	—
608	C₂²×C₃	—	4	2	no	—
609	C₂²×C₃	—	4	2	no	—
610	C₂²×C₃	—	4	2	no	—
611	C₂²×C₃	—	4	2	no	—
612	C₂²×C₃	—	4	2	no	—
613	C₂²×C₃	—	4	2	no	—
614	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
615	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
616	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
617	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
618	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
619	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
620	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
621	C₃×C₄	—	2	2	no	—
622	C₃×C₄	—	2	4	no	—
623	C₃×C₄	—	2	2	no	—
624	C₃×C₄	—	2	2	no	—
625	C₃×C₄	—	4	1	no	—
626	C₃×C₄	—	4	2	no	—
627	C₃×C₄	—	4	1	no	—
628	C₃×C₄	C₅×#121	1	4	yes	complemented
629	C₂×C₅	—	4	4	no	—
630	C₂×C₅	—	4	2	no	—
631	C₂×C₅	—	8	2	no	—
632	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
633	C₂×C₅	C₃×#532	1	1	yes	characteristic
634	C₂×C₅	C₃×#540	1	1	yes	characteristic
635	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
636	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
637	C₂×C₅	C₃×#546	1	1	yes	characteristic
638	C₂×C₅	C₃×#550	1	1	yes	characteristic
639	C₂³	—	2	2	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
659	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
660	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
661	D₄	—	2	8	no	—
662	D₄	—	4	8	no	—
663	D₄	—	4	8	no	—
664	D₄	—	4	8	no	—
665	D₄	—	4	8	no	—
666	D₄	—	4	4	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	4	8	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
687	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
688	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
689	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
690	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
691	C₂×C₄	C₃×C₅×#41	1	2	yes	—
692	C₂×C₄	C₃×C₅×#41	1	2	yes	—
693	C₂×C₃	—	4	4	no	—
694	C₂×C₃	—	4	2	no	—
695	C₂×C₃	—	8	2	no	—
696	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
697	C₂×C₃	C₅×#532	1	1	yes	characteristic
698	C₂×C₃	C₅×#540	1	1	yes	characteristic
699	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
700	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
701	C₂×C₃	C₅×#546	1	1	yes	characteristic
702	C₂×C₃	C₅×#550	1	1	yes	characteristic
703	C₅	C₃×#2428	1	1	yes	characteristic, direct product factor, Sylow
704	C₂²	—	2	4	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	4	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
726	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
727	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
728	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
729	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
730	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
731	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
732	C₄	—	2	2	no	—
733	C₄	—	2	4	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	2	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	1	no	—
739	C₄	C₃×C₅×#121	1	4	yes	complemented
740	C₃	C₅×#2428	1	1	yes	characteristic, direct product factor, Sylow
741	C₂	—	4	4	no	—
742	C₂	—	4	2	no	—
743	C₂	—	8	2	no	—
744	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
745	C₂	C₃×C₅×#532	1	1	yes	characteristic
746	C₂	C₃×C₅×#540	1	1	yes	characteristic
747	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
748	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
749	C₂	C₃×C₅×#546	1	1	yes	characteristic
750	C₂	C₃×C₅×#550	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#127	C₂	semidirect
2. C₂×C₃×C₅×#121	C₂	semidirect
3. C₂×C₃×C₅×#121	C₂	semidirect
4. C₂×C₃×C₅×#121	C₂	semidirect
5. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
6. C₃×C₅×#394	C₂	semidirect
7. C₃×C₅×#392	C₂	semidirect
8. C₃×C₅×#390	C₂	semidirect
9. C₃×C₅×#389	C₂	semidirect
10. C₃×C₅×#386	C₂	semidirect
11. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
12. C₅×#2428	C₃	direct (N × H)
41. C₃×#2428	C₅	direct (N × H)
42. C₂×C₅×#127	C₂×C₃	semidirect
43. C₂×C₅×#121	C₂×C₃	semidirect
44. C₂×C₅×#121	C₂×C₃	semidirect
45. C₂×C₅×#121	C₂×C₃	semidirect
46. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
47. C₅×#394	C₂×C₃	semidirect
48. C₅×#392	C₂×C₃	semidirect
49. C₅×#390	C₂×C₃	semidirect
50. C₅×#389	C₂×C₃	semidirect
51. C₅×#386	C₂×C₃	semidirect
52. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
73. C₂×C₃×C₅×D₄	D₄	semidirect
90. C₃×C₅×C₄⋊C₄	D₄	semidirect
97. C₃×C₅×C₂²⋊C₄	D₄	semidirect
100. C₂×C₃×#127	C₂×C₅	semidirect
101. C₂×C₃×#121	C₂×C₅	semidirect
102. C₂×C₃×#121	C₂×C₅	semidirect
103. C₂×C₃×#121	C₂×C₅	semidirect
104. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
105. C₃×#394	C₂×C₅	semidirect
106. C₃×#392	C₂×C₅	semidirect
107. C₃×#390	C₂×C₅	semidirect
108. C₃×#389	C₂×C₅	semidirect
109. C₃×#386	C₂×C₅	semidirect
110. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
139. #2428	C₃×C₅	direct (N × H)
242. C₂×C₅×D₄	C₃×D₄	semidirect
259. C₅×C₄⋊C₄	C₃×D₄	semidirect
266. C₅×C₂²⋊C₄	C₃×D₄	semidirect
269. C₂×#127	C₂×C₃×C₅	semidirect
270. C₂×#121	C₂×C₃×C₅	semidirect
271. C₂×#121	C₂×C₃×C₅	semidirect
272. C₂×#121	C₂×C₃×C₅	semidirect
273. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
274. #394	C₂×C₃×C₅	semidirect
275. #392	C₂×C₃×C₅	semidirect
276. #390	C₂×C₃×C₅	semidirect
277. #389	C₂×C₃×C₅	semidirect
278. #386	C₂×C₃×C₅	semidirect
279. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
315. C₃×C₄×C₅	#121	semidirect
336. C₂×C₃×D₄	C₅×D₄	semidirect
353. C₃×C₄⋊C₄	C₅×D₄	semidirect
360. C₃×C₂²⋊C₄	C₅×D₄	semidirect
544. C₄×C₅	C₃×#121	semidirect
565. C₂×D₄	C₃×C₅×D₄	semidirect
582. C₄⋊C₄	C₃×C₅×D₄	semidirect
589. C₂²⋊C₄	C₃×C₅×D₄	semidirect
592. C₃×C₅	#2428	direct (N × H)
628. C₃×C₄	C₅×#121	semidirect
703. C₅	C₃×#2428	direct (N × H)
739. C₄	C₃×C₅×#121	semidirect
740. C₃	C₅×#2428	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×#127	2
C₂×C₃×C₅×#121	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₅×#389	2
C₃×C₅×#386	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2428	3
C₃×#2428	5

Subgroups — C3×C5×#2428 #14275462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2428 #14275462