Subgroups — C₃×C₅×#3201 #14276235

Order 1920.

780 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#537	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#485	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#483	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#470	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#465	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#451	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3201	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
27	C₃×C₅×#124	—	2	1	no	—
28	C₃×C₅×#123	—	2	1	no	—
29	C₃×C₅×#123	—	2	1	no	—
30	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
31	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₃×C₅×#121	—	2	1	no	—
38	C₃×C₅×#121	—	2	1	no	—
39	C₃×C₅×#121	—	2	1	no	—
40	C₃×C₅×#121	C₂²	1	1	yes	characteristic
41	C₃×C₅×#121	C₂²	1	1	yes	characteristic
42	C₃×C₅×#117	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₃×C₅×#107	C₂²	1	1	yes	characteristic
45	C₃×C₅×#107	C₂²	1	1	yes	characteristic
46	C₃×C₅×#106	C₂²	1	1	yes	characteristic
47	C₃×C₅×#106	C₂²	1	1	yes	characteristic
48	C₃×C₅×#103	C₂²	1	1	yes	characteristic
49	C₃×C₅×#103	C₂²	1	1	yes	characteristic
50	C₃×C₅×#103	C₂²	1	1	yes	characteristic
51	C₃×C₅×#103	C₂²	1	1	yes	characteristic
52	C₃×C₅×#103	C₂²	1	1	yes	characteristic
53	C₃×C₅×#103	C₂²	1	1	yes	characteristic
54	C₃×C₅×#102	C₂²	1	1	yes	characteristic
55	C₃×C₅×#102	C₂²	1	1	yes	characteristic
56	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
59	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
60	C₃×#3201	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#537	C₂×C₃	1	1	yes	characteristic
62	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#485	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#484	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#483	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#482	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#470	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#468	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#467	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#465	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#451	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#448	C₂×C₃	1	1	yes	characteristic, complemented
75	C₅×#408	C₂×C₃	1	1	yes	characteristic, complemented
76	C₃×C₅×#41	—	4	1	no	—
77	C₃×C₅×#41	—	4	1	no	—
78	C₃×C₅×#41	—	4	1	no	—
79	C₃×C₅×#41	—	4	1	no	—
80	C₂×C₃×C₅×Q₈	—	2	1	no	—
81	C₂×C₃×C₅×Q₈	—	4	1	no	—
82	C₂×C₃×C₅×Q₈	—	4	1	no	—
83	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
84	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₅×D₄	—	2	1	no	—
88	C₂×C₃×C₅×D₄	—	2	1	no	—
89	C₂×C₃×C₅×D₄	—	2	1	no	—
90	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
91	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
92	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
93	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
94	C₂²×C₃×C₄×C₅	—	2	1	no	—
95	C₂²×C₃×C₄×C₅	—	2	1	no	—
96	C₂²×C₃×C₄×C₅	—	2	1	no	—
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
100	C₃×C₅×Q₁₆	—	4	1	no	—
101	C₃×C₅×Q₁₆	—	4	1	no	—
102	C₃×C₅×SD₁₆	—	4	1	no	—
103	C₃×C₅×SD₁₆	—	4	1	no	—
104	C₃×C₅×M₁₆	—	4	1	no	—
105	C₂×C₃×C₅×C₈	—	4	1	no	—
106	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
108	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₃×C₅×C₄⋊C₄	—	2	1	no	—
111	C₃×C₅×C₄⋊C₄	—	2	1	no	—
112	C₃×C₅×C₄⋊C₄	—	2	1	no	—
113	C₃×C₅×C₄⋊C₄	—	2	1	no	—
114	C₃×C₅×C₄⋊C₄	—	2	1	no	—
115	C₃×C₅×C₄⋊C₄	—	2	1	no	—
116	C₃×C₅×C₄⋊C₄	—	2	1	no	—
117	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
122	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
123	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
124	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
125	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
126	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
127	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
128	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
129	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
130	C₃×C₄²×C₅	—	2	1	no	—
131	C₃×#537	C₂×C₅	1	1	yes	characteristic
132	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#485	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#484	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#483	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#482	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#470	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#468	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#467	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×#465	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
143	C₃×#451	C₂×C₅	1	1	yes	characteristic, complemented
144	C₃×#448	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
148	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
154	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
155	C₅×C₄⋊Q₈	—	2	1	no	—
156	C₅×#124	—	2	1	no	—
157	C₅×#123	—	2	1	no	—
158	C₅×#123	—	2	1	no	—
159	C₅×C₂²⋊Q₈	—	2	1	no	—
160	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
161	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
162	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
163	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
164	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
165	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
166	C₅×#121	—	2	1	no	—
167	C₅×#121	—	2	1	no	—
168	C₅×#121	—	2	1	no	—
169	C₅×#121	C₂²×C₃	1	1	yes	characteristic
170	C₅×#121	C₂²×C₃	1	1	yes	characteristic
171	C₅×#117	C₂²×C₃	1	1	yes	characteristic
172	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	C₅×#107	C₂²×C₃	1	1	yes	characteristic
174	C₅×#107	C₂²×C₃	1	1	yes	characteristic
175	C₅×#106	C₂²×C₃	1	1	yes	characteristic
176	C₅×#106	C₂²×C₃	1	1	yes	characteristic
177	C₅×#103	C₂²×C₃	1	1	yes	characteristic
178	C₅×#103	C₂²×C₃	1	1	yes	characteristic
179	C₅×#103	C₂²×C₃	1	1	yes	characteristic
180	C₅×#103	C₂²×C₃	1	1	yes	characteristic
181	C₅×#103	C₂²×C₃	1	1	yes	characteristic
182	C₅×#103	C₂²×C₃	1	1	yes	characteristic
183	C₅×#102	C₂²×C₃	1	1	yes	characteristic
184	C₅×#102	C₂²×C₃	1	1	yes	characteristic
185	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
186	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
187	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
188	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
189	#3201	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
190	C₂³×C₃×C₅	—	2	1	no	—
191	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
192	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
193	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
194	C₃×C₅×Q₈	—	2	1	no	—
195	C₃×C₅×Q₈	—	2	1	no	—
196	C₃×C₅×Q₈	—	2	1	no	—
197	C₃×C₅×Q₈	—	2	1	no	—
198	C₃×C₅×Q₈	—	2	1	no	—
199	C₃×C₅×Q₈	—	2	1	no	—
200	C₃×C₅×Q₈	—	4	1	no	—
201	C₃×C₅×Q₈	—	4	2	no	—
202	C₃×C₅×D₄	—	2	1	no	—
203	C₃×C₅×D₄	—	2	1	no	—
204	C₃×C₅×D₄	—	4	1	no	—
205	C₃×C₅×D₄	—	4	1	no	—
206	C₃×C₅×D₄	—	4	1	no	—
207	C₃×C₅×D₄	—	4	2	no	—
208	C₃×C₅×D₄	—	8	1	no	—
209	C₃×C₅×D₄	—	8	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	1	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	2	1	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	4	2	no	—
224	C₂×C₃×C₄×C₅	—	4	2	no	—
225	C₂×C₃×C₄×C₅	—	8	1	no	—
226	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
227	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
228	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
229	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
230	C₃×C₅×C₈	—	2	1	no	—
231	C₃×C₅×C₈	—	2	1	no	—
232	C₃×C₅×C₈	—	2	1	no	—
233	C₃×C₅×C₈	—	2	1	no	—
234	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
236	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
242	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
243	C₃×C₄⋊Q₈	—	2	1	no	—
244	C₃×#124	—	2	1	no	—
245	C₃×#123	—	2	1	no	—
246	C₃×#123	—	2	1	no	—
247	C₃×C₂²⋊Q₈	—	2	1	no	—
248	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
249	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
250	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
251	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
252	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
253	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
254	C₃×#121	—	2	1	no	—
255	C₃×#121	—	2	1	no	—
256	C₃×#121	—	2	1	no	—
257	C₃×#121	C₂²×C₅	1	1	yes	characteristic
258	C₃×#121	C₂²×C₅	1	1	yes	characteristic
259	C₃×#117	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
261	C₃×#107	C₂²×C₅	1	1	yes	characteristic
262	C₃×#107	C₂²×C₅	1	1	yes	characteristic
263	C₃×#106	C₂²×C₅	1	1	yes	characteristic
264	C₃×#106	C₂²×C₅	1	1	yes	characteristic
265	C₃×#103	C₂²×C₅	1	1	yes	characteristic
266	C₃×#103	C₂²×C₅	1	1	yes	characteristic
267	C₃×#103	C₂²×C₅	1	1	yes	characteristic
268	C₃×#103	C₂²×C₅	1	1	yes	characteristic
269	C₃×#103	C₂²×C₅	1	1	yes	characteristic
270	C₃×#103	C₂²×C₅	1	1	yes	characteristic
271	C₃×#102	C₂²×C₅	1	1	yes	characteristic
272	C₃×#102	C₂²×C₅	1	1	yes	characteristic
273	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
274	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
275	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
276	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
277	C₅×#41	—	4	1	no	—
278	C₅×#41	—	4	1	no	—
279	C₅×#41	—	4	1	no	—
280	C₅×#41	—	4	1	no	—
281	C₂×C₅×Q₈	—	2	1	no	—
282	C₂×C₅×Q₈	—	4	1	no	—
283	C₂×C₅×Q₈	—	4	1	no	—
284	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
285	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
287	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
288	C₂×C₅×D₄	—	2	1	no	—
289	C₂×C₅×D₄	—	2	1	no	—
290	C₂×C₅×D₄	—	2	1	no	—
291	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
292	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
293	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
294	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
295	C₂²×C₄×C₅	—	2	1	no	—
296	C₂²×C₄×C₅	—	2	1	no	—
297	C₂²×C₄×C₅	—	2	1	no	—
298	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
299	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
300	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
301	C₅×Q₁₆	—	4	1	no	—
302	C₅×Q₁₆	—	4	1	no	—
303	C₅×SD₁₆	—	4	1	no	—
304	C₅×SD₁₆	—	4	1	no	—
305	C₅×M₁₆	—	4	1	no	—
306	C₂×C₅×C₈	—	4	1	no	—
307	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
308	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
309	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
310	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
311	C₅×C₄⋊C₄	—	2	1	no	—
312	C₅×C₄⋊C₄	—	2	1	no	—
313	C₅×C₄⋊C₄	—	2	1	no	—
314	C₅×C₄⋊C₄	—	2	1	no	—
315	C₅×C₄⋊C₄	—	2	1	no	—
316	C₅×C₄⋊C₄	—	2	1	no	—
317	C₅×C₄⋊C₄	—	2	1	no	—
318	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
319	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
320	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
321	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
322	C₅×C₂²⋊C₄	—	2	1	no	—
323	C₅×C₂²⋊C₄	—	2	1	no	—
324	C₅×C₂²⋊C₄	—	2	1	no	—
325	C₅×C₂²⋊C₄	—	2	1	no	—
326	C₅×C₂²⋊C₄	—	2	1	no	—
327	C₅×C₂²⋊C₄	—	2	1	no	—
328	C₅×C₂²⋊C₄	—	2	1	no	—
329	C₅×C₂²⋊C₄	—	2	1	no	—
330	C₅×C₂²⋊C₄	—	2	1	no	—
331	C₄²×C₅	—	2	1	no	—
332	#537	C₂×C₃×C₅	1	1	yes	characteristic
333	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	#485	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	#484	C₂×C₃×C₅	1	1	yes	characteristic, complemented
336	#483	C₂×C₃×C₅	1	1	yes	characteristic, complemented
337	#482	C₂×C₃×C₅	1	1	yes	characteristic, complemented
338	#470	C₂×C₃×C₅	1	1	yes	characteristic, complemented
339	#468	C₂×C₃×C₅	1	1	yes	characteristic, complemented
340	#467	C₂×C₃×C₅	1	1	yes	characteristic, complemented
341	#465	C₂×C₃×C₅	1	1	yes	characteristic, complemented
342	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
343	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
344	#451	C₂×C₃×C₅	1	1	yes	characteristic, complemented
345	#448	C₂×C₃×C₅	1	1	yes	characteristic, complemented
346	#408	C₂×C₃×C₅	1	1	yes	characteristic, complemented
347	C₂²×C₃×C₅	—	2	1	no	—
348	C₂²×C₃×C₅	—	2	1	no	—
349	C₂²×C₃×C₅	—	2	1	no	—
350	C₂²×C₃×C₅	—	2	1	no	—
351	C₂²×C₃×C₅	—	2	1	no	—
352	C₂²×C₃×C₅	—	2	1	no	—
353	C₂²×C₃×C₅	—	2	1	no	—
354	C₂²×C₃×C₅	—	2	1	no	—
355	C₂²×C₃×C₅	—	2	1	no	—
356	C₂²×C₃×C₅	—	4	1	no	—
357	C₂²×C₃×C₅	—	4	1	no	—
358	C₂²×C₃×C₅	—	4	1	no	—
359	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
360	C₃×C₄×C₅	—	2	1	no	—
361	C₃×C₄×C₅	—	2	1	no	—
362	C₃×C₄×C₅	—	2	1	no	—
363	C₃×C₄×C₅	—	4	1	no	—
364	C₃×C₄×C₅	—	4	1	no	—
365	C₃×C₄×C₅	—	4	1	no	—
366	C₃×C₄×C₅	—	4	1	no	—
367	C₃×C₄×C₅	—	4	1	no	—
368	C₃×C₄×C₅	—	4	1	no	—
369	C₃×C₄×C₅	—	4	1	no	—
370	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
371	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
372	C₃×#41	—	4	1	no	—
373	C₃×#41	—	4	1	no	—
374	C₃×#41	—	4	1	no	—
375	C₃×#41	—	4	1	no	—
376	C₂×C₃×Q₈	—	2	1	no	—
377	C₂×C₃×Q₈	—	4	1	no	—
378	C₂×C₃×Q₈	—	4	1	no	—
379	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
380	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
382	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
383	C₂×C₃×D₄	—	2	1	no	—
384	C₂×C₃×D₄	—	2	1	no	—
385	C₂×C₃×D₄	—	2	1	no	—
386	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
387	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
388	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
389	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
390	C₂²×C₃×C₄	—	2	1	no	—
391	C₂²×C₃×C₄	—	2	1	no	—
392	C₂²×C₃×C₄	—	2	1	no	—
393	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
394	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
395	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
396	C₃×Q₁₆	—	4	1	no	—
397	C₃×Q₁₆	—	4	1	no	—
398	C₃×SD₁₆	—	4	1	no	—
399	C₃×SD₁₆	—	4	1	no	—
400	C₃×M₁₆	—	4	1	no	—
401	C₂×C₃×C₈	—	4	1	no	—
402	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
405	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
406	C₃×C₄⋊C₄	—	2	1	no	—
407	C₃×C₄⋊C₄	—	2	1	no	—
408	C₃×C₄⋊C₄	—	2	1	no	—
409	C₃×C₄⋊C₄	—	2	1	no	—
410	C₃×C₄⋊C₄	—	2	1	no	—
411	C₃×C₄⋊C₄	—	2	1	no	—
412	C₃×C₄⋊C₄	—	2	1	no	—
413	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
414	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
415	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
416	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
417	C₃×C₂²⋊C₄	—	2	1	no	—
418	C₃×C₂²⋊C₄	—	2	1	no	—
419	C₃×C₂²⋊C₄	—	2	1	no	—
420	C₃×C₂²⋊C₄	—	2	1	no	—
421	C₃×C₂²⋊C₄	—	2	1	no	—
422	C₃×C₂²⋊C₄	—	2	1	no	—
423	C₃×C₂²⋊C₄	—	2	1	no	—
424	C₃×C₂²⋊C₄	—	2	1	no	—
425	C₃×C₂²⋊C₄	—	2	1	no	—
426	C₃×C₄²	—	2	1	no	—
427	C₂³×C₅	—	2	1	no	—
428	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
429	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
430	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
431	C₅×Q₈	—	2	1	no	—
432	C₅×Q₈	—	2	1	no	—
433	C₅×Q₈	—	2	1	no	—
434	C₅×Q₈	—	2	1	no	—
435	C₅×Q₈	—	2	1	no	—
436	C₅×Q₈	—	2	1	no	—
437	C₅×Q₈	—	4	1	no	—
438	C₅×Q₈	—	4	2	no	—
439	C₅×D₄	—	2	1	no	—
440	C₅×D₄	—	2	1	no	—
441	C₅×D₄	—	4	1	no	—
442	C₅×D₄	—	4	1	no	—
443	C₅×D₄	—	4	1	no	—
444	C₅×D₄	—	4	2	no	—
445	C₅×D₄	—	8	1	no	—
446	C₅×D₄	—	8	1	no	—
447	C₂×C₄×C₅	—	2	1	no	—
448	C₂×C₄×C₅	—	2	1	no	—
449	C₂×C₄×C₅	—	2	1	no	—
450	C₂×C₄×C₅	—	2	1	no	—
451	C₂×C₄×C₅	—	2	1	no	—
452	C₂×C₄×C₅	—	2	1	no	—
453	C₂×C₄×C₅	—	2	1	no	—
454	C₂×C₄×C₅	—	2	1	no	—
455	C₂×C₄×C₅	—	2	1	no	—
456	C₂×C₄×C₅	—	2	1	no	—
457	C₂×C₄×C₅	—	2	1	no	—
458	C₂×C₄×C₅	—	2	1	no	—
459	C₂×C₄×C₅	—	2	1	no	—
460	C₂×C₄×C₅	—	4	2	no	—
461	C₂×C₄×C₅	—	4	2	no	—
462	C₂×C₄×C₅	—	8	1	no	—
463	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
464	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
465	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
466	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
467	C₅×C₈	—	2	1	no	—
468	C₅×C₈	—	2	1	no	—
469	C₅×C₈	—	2	1	no	—
470	C₅×C₈	—	2	1	no	—
471	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
472	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
473	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
474	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
475	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
476	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
477	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
478	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
479	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
480	C₄⋊Q₈	—	2	1	no	—
481	#124	—	2	1	no	—
482	#123	—	2	1	no	—
483	#123	—	2	1	no	—
484	C₂²⋊Q₈	—	2	1	no	—
485	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
486	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
487	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
488	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
489	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
490	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
491	#121	—	2	1	no	—
492	#121	—	2	1	no	—
493	#121	—	2	1	no	—
494	#121	C₂²×C₃×C₅	1	1	yes	characteristic
495	#121	C₂²×C₃×C₅	1	1	yes	characteristic
496	#117	C₂²×C₃×C₅	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
498	#107	C₂²×C₃×C₅	1	1	yes	characteristic
499	#107	C₂²×C₃×C₅	1	1	yes	characteristic
500	#106	C₂²×C₃×C₅	1	1	yes	characteristic
501	#106	C₂²×C₃×C₅	1	1	yes	characteristic
502	#103	C₂²×C₃×C₅	1	1	yes	characteristic
503	#103	C₂²×C₃×C₅	1	1	yes	characteristic
504	#103	C₂²×C₃×C₅	1	1	yes	characteristic
505	#103	C₂²×C₃×C₅	1	1	yes	characteristic
506	#103	C₂²×C₃×C₅	1	1	yes	characteristic
507	#103	C₂²×C₃×C₅	1	1	yes	characteristic
508	#102	C₂²×C₃×C₅	1	1	yes	characteristic
509	#102	C₂²×C₃×C₅	1	1	yes	characteristic
510	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
511	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
512	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
513	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
514	C₂×C₃×C₅	—	4	1	no	—
515	C₂×C₃×C₅	—	4	1	no	—
516	C₂×C₃×C₅	—	4	1	no	—
517	C₂×C₃×C₅	—	8	1	no	—
518	C₂×C₃×C₅	#534	1	1	yes	characteristic
519	C₂×C₃×C₅	#577	1	1	yes	characteristic
520	C₂×C₃×C₅	#578	1	1	yes	characteristic
521	C₂³×C₃	—	2	1	no	—
522	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
523	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
524	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
525	C₃×Q₈	—	2	1	no	—
526	C₃×Q₈	—	2	1	no	—
527	C₃×Q₈	—	2	1	no	—
528	C₃×Q₈	—	2	1	no	—
529	C₃×Q₈	—	2	1	no	—
530	C₃×Q₈	—	2	1	no	—
531	C₃×Q₈	—	4	1	no	—
532	C₃×Q₈	—	4	2	no	—
533	C₃×D₄	—	2	1	no	—
534	C₃×D₄	—	2	1	no	—
535	C₃×D₄	—	4	1	no	—
536	C₃×D₄	—	4	1	no	—
537	C₃×D₄	—	4	1	no	—
538	C₃×D₄	—	4	2	no	—
539	C₃×D₄	—	8	1	no	—
540	C₃×D₄	—	8	1	no	—
541	C₂×C₃×C₄	—	2	1	no	—
542	C₂×C₃×C₄	—	2	1	no	—
543	C₂×C₃×C₄	—	2	1	no	—
544	C₂×C₃×C₄	—	2	1	no	—
545	C₂×C₃×C₄	—	2	1	no	—
546	C₂×C₃×C₄	—	2	1	no	—
547	C₂×C₃×C₄	—	2	1	no	—
548	C₂×C₃×C₄	—	2	1	no	—
549	C₂×C₃×C₄	—	2	1	no	—
550	C₂×C₃×C₄	—	2	1	no	—
551	C₂×C₃×C₄	—	2	1	no	—
552	C₂×C₃×C₄	—	2	1	no	—
553	C₂×C₃×C₄	—	2	1	no	—
554	C₂×C₃×C₄	—	4	2	no	—
555	C₂×C₃×C₄	—	4	2	no	—
556	C₂×C₃×C₄	—	8	1	no	—
557	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
558	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
559	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
560	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
561	C₃×C₈	—	2	1	no	—
562	C₃×C₈	—	2	1	no	—
563	C₃×C₈	—	2	1	no	—
564	C₃×C₈	—	2	1	no	—
565	C₂²×C₅	—	2	1	no	—
566	C₂²×C₅	—	2	1	no	—
567	C₂²×C₅	—	2	1	no	—
568	C₂²×C₅	—	2	1	no	—
569	C₂²×C₅	—	2	1	no	—
570	C₂²×C₅	—	2	1	no	—
571	C₂²×C₅	—	2	1	no	—
572	C₂²×C₅	—	2	1	no	—
573	C₂²×C₅	—	2	1	no	—
574	C₂²×C₅	—	4	1	no	—
575	C₂²×C₅	—	4	1	no	—
576	C₂²×C₅	—	4	1	no	—
577	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
578	C₄×C₅	—	2	1	no	—
579	C₄×C₅	—	2	1	no	—
580	C₄×C₅	—	2	1	no	—
581	C₄×C₅	—	4	1	no	—
582	C₄×C₅	—	4	1	no	—
583	C₄×C₅	—	4	1	no	—
584	C₄×C₅	—	4	1	no	—
585	C₄×C₅	—	4	1	no	—
586	C₄×C₅	—	4	1	no	—
587	C₄×C₅	—	4	1	no	—
588	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
589	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
590	#41	—	4	1	no	—
591	#41	—	4	1	no	—
592	#41	—	4	1	no	—
593	#41	—	4	1	no	—
594	C₂×Q₈	—	2	1	no	—
595	C₂×Q₈	—	4	1	no	—
596	C₂×Q₈	—	4	1	no	—
597	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
598	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
599	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
600	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
605	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
606	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
607	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
612	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
613	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
614	Q₁₆	—	4	1	no	—
615	Q₁₆	—	4	1	no	—
616	SD₁₆	—	4	1	no	—
617	SD₁₆	—	4	1	no	—
618	M₁₆	—	4	1	no	—
619	C₂×C₈	—	4	1	no	—
620	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
621	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
622	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
623	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
632	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
633	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
634	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
635	C₂²⋊C₄	—	2	1	no	—
636	C₂²⋊C₄	—	2	1	no	—
637	C₂²⋊C₄	—	2	1	no	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	2	1	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₄²	—	2	1	no	—
645	C₃×C₅	#3201	1	1	yes	characteristic, direct product factor, Hall
646	C₂²×C₃	—	2	1	no	—
647	C₂²×C₃	—	2	1	no	—
648	C₂²×C₃	—	2	1	no	—
649	C₂²×C₃	—	2	1	no	—
650	C₂²×C₃	—	2	1	no	—
651	C₂²×C₃	—	2	1	no	—
652	C₂²×C₃	—	2	1	no	—
653	C₂²×C₃	—	2	1	no	—
654	C₂²×C₃	—	2	1	no	—
655	C₂²×C₃	—	4	1	no	—
656	C₂²×C₃	—	4	1	no	—
657	C₂²×C₃	—	4	1	no	—
658	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
659	C₃×C₄	—	2	1	no	—
660	C₃×C₄	—	2	1	no	—
661	C₃×C₄	—	2	1	no	—
662	C₃×C₄	—	4	1	no	—
663	C₃×C₄	—	4	1	no	—
664	C₃×C₄	—	4	1	no	—
665	C₃×C₄	—	4	1	no	—
666	C₃×C₄	—	4	1	no	—
667	C₃×C₄	—	4	1	no	—
668	C₃×C₄	—	4	1	no	—
669	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
670	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
671	C₂×C₅	—	4	1	no	—
672	C₂×C₅	—	4	1	no	—
673	C₂×C₅	—	4	1	no	—
674	C₂×C₅	—	8	1	no	—
675	C₂×C₅	C₃×#534	1	1	yes	characteristic
676	C₂×C₅	C₃×#577	1	1	yes	characteristic
677	C₂×C₅	C₃×#578	1	1	yes	characteristic
678	C₂³	—	2	1	no	—
679	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
680	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
681	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
682	Q₈	—	2	1	no	—
683	Q₈	—	2	1	no	—
684	Q₈	—	2	1	no	—
685	Q₈	—	2	1	no	—
686	Q₈	—	2	1	no	—
687	Q₈	—	2	1	no	—
688	Q₈	—	4	1	no	—
689	Q₈	—	4	2	no	—
690	D₄	—	2	1	no	—
691	D₄	—	2	1	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	1	no	—
694	D₄	—	4	1	no	—
695	D₄	—	4	2	no	—
696	D₄	—	8	1	no	—
697	D₄	—	8	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	8	1	no	—
714	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
715	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
716	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
717	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
718	C₈	—	2	1	no	—
719	C₈	—	2	1	no	—
720	C₈	—	2	1	no	—
721	C₈	—	2	1	no	—
722	C₂×C₃	—	4	1	no	—
723	C₂×C₃	—	4	1	no	—
724	C₂×C₃	—	4	1	no	—
725	C₂×C₃	—	8	1	no	—
726	C₂×C₃	C₅×#534	1	1	yes	characteristic
727	C₂×C₃	C₅×#577	1	1	yes	characteristic
728	C₂×C₃	C₅×#578	1	1	yes	characteristic
729	C₅	C₃×#3201	1	1	yes	characteristic, direct product factor, Sylow
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	1	no	—
742	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
743	C₄	—	2	1	no	—
744	C₄	—	2	1	no	—
745	C₄	—	2	1	no	—
746	C₄	—	4	1	no	—
747	C₄	—	4	1	no	—
748	C₄	—	4	1	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
754	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
755	C₃	C₅×#3201	1	1	yes	characteristic, direct product factor, Sylow
756	C₂	—	4	1	no	—
757	C₂	—	4	1	no	—
758	C₂	—	4	1	no	—
759	C₂	—	8	1	no	—
760	C₂	C₃×C₅×#534	1	1	yes	characteristic
761	C₂	C₃×C₅×#577	1	1	yes	characteristic
762	C₂	C₃×C₅×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#537	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#536	C₂	semidirect
3. C₃×C₅×#485	C₂	semidirect
4. C₃×C₅×#484	C₂	semidirect
5. C₃×C₅×#483	C₂	semidirect
6. C₃×C₅×#482	C₂	semidirect
7. C₃×C₅×#470	C₂	semidirect
8. C₃×C₅×#468	C₂	semidirect
9. C₃×C₅×#467	C₂	semidirect
10. C₃×C₅×#465	C₂	semidirect
11. C₃×C₅×#452	C₂	semidirect
12. C₃×C₅×#452	C₂	semidirect
13. C₃×C₅×#451	C₂	semidirect
14. C₃×C₅×#448	C₂	semidirect
15. C₃×C₅×#408	C₂	semidirect
16. C₅×#3201	C₃	direct (N × H)
60. C₃×#3201	C₅	direct (N × H)
62. C₅×#536	C₂×C₃	semidirect
63. C₅×#485	C₂×C₃	semidirect
64. C₅×#484	C₂×C₃	semidirect
65. C₅×#483	C₂×C₃	semidirect
66. C₅×#482	C₂×C₃	semidirect
67. C₅×#470	C₂×C₃	semidirect
68. C₅×#468	C₂×C₃	semidirect
69. C₅×#467	C₂×C₃	semidirect
70. C₅×#465	C₂×C₃	semidirect
71. C₅×#452	C₂×C₃	semidirect
72. C₅×#452	C₂×C₃	semidirect
73. C₅×#451	C₂×C₃	semidirect
74. C₅×#448	C₂×C₃	semidirect
75. C₅×#408	C₂×C₃	semidirect
132. C₃×#536	C₂×C₅	semidirect
133. C₃×#485	C₂×C₅	semidirect
134. C₃×#484	C₂×C₅	semidirect
135. C₃×#483	C₂×C₅	semidirect
136. C₃×#482	C₂×C₅	semidirect
137. C₃×#470	C₂×C₅	semidirect
138. C₃×#468	C₂×C₅	semidirect
139. C₃×#467	C₂×C₅	semidirect
140. C₃×#465	C₂×C₅	semidirect
141. C₃×#452	C₂×C₅	semidirect
142. C₃×#452	C₂×C₅	semidirect
143. C₃×#451	C₂×C₅	semidirect
144. C₃×#448	C₂×C₅	semidirect
145. C₃×#408	C₂×C₅	semidirect
189. #3201	C₃×C₅	direct (N × H)
333. #536	C₂×C₃×C₅	semidirect
334. #485	C₂×C₃×C₅	semidirect
335. #484	C₂×C₃×C₅	semidirect
336. #483	C₂×C₃×C₅	semidirect
337. #482	C₂×C₃×C₅	semidirect
338. #470	C₂×C₃×C₅	semidirect
339. #468	C₂×C₃×C₅	semidirect
340. #467	C₂×C₃×C₅	semidirect
341. #465	C₂×C₃×C₅	semidirect
342. #452	C₂×C₃×C₅	semidirect
343. #452	C₂×C₃×C₅	semidirect
344. #451	C₂×C₃×C₅	semidirect
345. #448	C₂×C₃×C₅	semidirect
346. #408	C₂×C₃×C₅	semidirect
645. C₃×C₅	#3201	direct (N × H)
729. C₅	C₃×#3201	direct (N × H)
755. C₃	C₅×#3201	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×#537	2
C₃×C₅×#536	2
C₃×C₅×#485	2
C₃×C₅×#484	2
C₃×C₅×#483	2
C₃×C₅×#482	2
C₃×C₅×#470	2
C₃×C₅×#468	2
C₃×C₅×#467	2
C₃×C₅×#465	2
C₃×C₅×#452	2
C₃×C₅×#451	2
C₃×C₅×#448	2
C₃×C₅×#408	2
C₅×#3201	3
C₃×#3201	5

Subgroups — C3×C5×#3201 #14276235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3201 #14276235