Subgroups — C₃×C₅×#3225 #14276259

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 736 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×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#489	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic
14	C₃×C₅×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3225	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×Q₁₆	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×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₃×C₅×#126	—	2	1	no	—
31	C₃×C₅×#124	—	2	1	no	—
32	C₃×C₅×#124	C₂²	1	1	yes	characteristic
33	C₃×C₅×#124	C₂²	1	1	yes	characteristic
34	C₃×C₅×#124	C₂²	1	1	yes	characteristic
35	C₃×C₅×#123	—	2	1	no	—
36	C₃×C₅×#123	—	2	1	no	—
37	C₃×C₅×#123	—	2	1	no	—
38	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
39	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
40	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
41	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₃×C₅×#121	C₂²	1	1	yes	characteristic
43	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
44	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
45	C₃×C₅×#117	C₂²	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₃×C₅×C₄⋊C₈	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×#97	C₂²	1	1	yes	characteristic
59	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
60	C₃×#3225	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#542	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#495	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#489	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#487	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#464	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#463	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#462	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#461	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#451	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#449	C₂×C₃	1	1	yes	characteristic
74	C₅×#448	C₂×C₃	1	1	yes	characteristic, complemented
75	C₅×#433	C₂×C₃	1	1	yes	characteristic, complemented
76	C₃×C₅×#41	—	4	1	no	—
77	C₃×C₅×#41	—	4	1	no	—
78	C₂×C₃×C₅×Q₈	—	2	1	no	—
79	C₂×C₃×C₅×Q₈	—	2	1	no	—
80	C₂×C₃×C₅×Q₈	—	4	1	no	—
81	C₂×C₃×C₅×Q₈	—	4	1	no	—
82	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₅×Q₈	C₂³	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×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	—	2	1	no	—
88	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄×C₅	—	2	1	no	—
91	C₂²×C₃×C₄×C₅	—	2	1	no	—
92	C₂²×C₃×C₄×C₅	—	2	1	no	—
93	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₃×C₅×Q₁₆	—	4	1	no	—
95	C₃×C₅×Q₁₆	—	4	1	no	—
96	C₃×C₅×Q₁₆	—	4	1	no	—
97	C₃×C₅×SD₁₆	—	4	1	no	—
98	C₃×C₅×SD₁₆	—	4	1	no	—
99	C₃×C₅×SD₁₆	—	4	1	no	—
100	C₃×C₅×SD₁₆	—	4	1	no	—
101	C₃×C₅×D₈	—	4	1	no	—
102	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₃×C₅×C₄⋊C₄	—	2	1	no	—
107	C₃×C₅×C₄⋊C₄	—	2	1	no	—
108	C₃×C₅×C₄⋊C₄	—	2	1	no	—
109	C₃×C₅×C₄⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
114	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
115	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
118	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
119	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
120	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
127	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
128	C₃×C₄²×C₅	—	2	1	no	—
129	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
130	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
131	C₃×#542	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#497	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#495	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#489	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#487	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#464	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#463	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#462	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×#461	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×#451	C₂×C₅	1	1	yes	characteristic, complemented
143	C₃×#449	C₂×C₅	1	1	yes	characteristic
144	C₃×#448	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#433	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
147	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₅×Q₁₆	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×SD₁₆	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
156	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
157	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
158	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
159	C₅×#126	—	2	1	no	—
160	C₅×#124	—	2	1	no	—
161	C₅×#124	C₂²×C₃	1	1	yes	characteristic
162	C₅×#124	C₂²×C₃	1	1	yes	characteristic
163	C₅×#124	C₂²×C₃	1	1	yes	characteristic
164	C₅×#123	—	2	1	no	—
165	C₅×#123	—	2	1	no	—
166	C₅×#123	—	2	1	no	—
167	C₅×C₂²⋊Q₈	—	2	1	no	—
168	C₅×C₂²⋊Q₈	—	2	1	no	—
169	C₅×C₂²⋊Q₈	—	2	1	no	—
170	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
171	C₅×#121	C₂²×C₃	1	1	yes	characteristic
172	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
173	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
174	C₅×#117	C₂²×C₃	1	1	yes	characteristic
175	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
176	C₅×C₄⋊C₈	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×#97	C₂²×C₃	1	1	yes	characteristic
188	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
189	#3225	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
190	C₂³×C₃×C₅	—	2	1	no	—
191	C₂³×C₃×C₅	—	2	1	no	—
192	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
193	C₃×C₅×Q₈	—	2	1	no	—
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	—	2	1	no	—
201	C₃×C₅×Q₈	—	4	2	no	—
202	C₃×C₅×Q₈	—	8	1	no	—
203	C₃×C₅×D₄	—	2	1	no	—
204	C₃×C₅×D₄	—	2	1	no	—
205	C₃×C₅×D₄	—	2	1	no	—
206	C₃×C₅×D₄	—	2	1	no	—
207	C₃×C₅×D₄	—	4	2	no	—
208	C₃×C₅×D₄	—	8	1	no	—
209	C₂×C₃×C₄×C₅	—	2	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	—	4	2	no	—
218	C₂×C₃×C₄×C₅	—	4	2	no	—
219	C₂×C₃×C₄×C₅	—	8	1	no	—
220	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
221	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
222	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
223	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
224	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
225	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
226	C₃×C₅×C₈	—	2	1	no	—
227	C₃×C₅×C₈	—	2	1	no	—
228	C₃×C₅×C₈	—	2	1	no	—
229	C₃×C₅×C₈	—	2	1	no	—
230	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
231	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
240	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
241	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
242	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
243	C₃×#126	—	2	1	no	—
244	C₃×#124	—	2	1	no	—
245	C₃×#124	C₂²×C₅	1	1	yes	characteristic
246	C₃×#124	C₂²×C₅	1	1	yes	characteristic
247	C₃×#124	C₂²×C₅	1	1	yes	characteristic
248	C₃×#123	—	2	1	no	—
249	C₃×#123	—	2	1	no	—
250	C₃×#123	—	2	1	no	—
251	C₃×C₂²⋊Q₈	—	2	1	no	—
252	C₃×C₂²⋊Q₈	—	2	1	no	—
253	C₃×C₂²⋊Q₈	—	2	1	no	—
254	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
255	C₃×#121	C₂²×C₅	1	1	yes	characteristic
256	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
257	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
258	C₃×#117	C₂²×C₅	1	1	yes	characteristic
259	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
260	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
261	C₃×#103	C₂²×C₅	1	1	yes	characteristic
262	C₃×#103	C₂²×C₅	1	1	yes	characteristic
263	C₃×#103	C₂²×C₅	1	1	yes	characteristic
264	C₃×#103	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×#102	C₂²×C₅	1	1	yes	characteristic
268	C₃×#102	C₂²×C₅	1	1	yes	characteristic
269	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
270	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
271	C₃×#97	C₂²×C₅	1	1	yes	characteristic
272	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
273	C₅×#41	—	4	1	no	—
274	C₅×#41	—	4	1	no	—
275	C₂×C₅×Q₈	—	2	1	no	—
276	C₂×C₅×Q₈	—	2	1	no	—
277	C₂×C₅×Q₈	—	4	1	no	—
278	C₂×C₅×Q₈	—	4	1	no	—
279	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
280	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
281	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
282	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
283	C₂×C₅×D₄	—	2	1	no	—
284	C₂×C₅×D₄	—	2	1	no	—
285	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
287	C₂²×C₄×C₅	—	2	1	no	—
288	C₂²×C₄×C₅	—	2	1	no	—
289	C₂²×C₄×C₅	—	2	1	no	—
290	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
291	C₅×Q₁₆	—	4	1	no	—
292	C₅×Q₁₆	—	4	1	no	—
293	C₅×Q₁₆	—	4	1	no	—
294	C₅×SD₁₆	—	4	1	no	—
295	C₅×SD₁₆	—	4	1	no	—
296	C₅×SD₁₆	—	4	1	no	—
297	C₅×SD₁₆	—	4	1	no	—
298	C₅×D₈	—	4	1	no	—
299	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
300	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
301	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
302	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
303	C₅×C₄⋊C₄	—	2	1	no	—
304	C₅×C₄⋊C₄	—	2	1	no	—
305	C₅×C₄⋊C₄	—	2	1	no	—
306	C₅×C₄⋊C₄	—	2	1	no	—
307	C₅×C₄⋊C₄	—	2	1	no	—
308	C₅×C₄⋊C₄	—	2	1	no	—
309	C₅×C₄⋊C₄	—	2	1	no	—
310	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
311	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
312	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
313	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
314	C₅×C₂²⋊C₄	—	2	1	no	—
315	C₅×C₂²⋊C₄	—	2	1	no	—
316	C₅×C₂²⋊C₄	—	2	1	no	—
317	C₅×C₂²⋊C₄	—	2	1	no	—
318	C₅×C₂²⋊C₄	—	2	1	no	—
319	C₅×C₂²⋊C₄	—	2	1	no	—
320	C₅×C₂²⋊C₄	—	2	1	no	—
321	C₅×C₂²⋊C₄	—	2	1	no	—
322	C₅×C₂²⋊C₄	—	2	1	no	—
323	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
324	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
325	C₄²×C₅	—	2	1	no	—
326	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
327	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
328	#542	C₂×C₃×C₅	1	1	yes	characteristic, complemented
329	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
330	#497	C₂×C₃×C₅	1	1	yes	characteristic, complemented
331	#495	C₂×C₃×C₅	1	1	yes	characteristic, complemented
332	#489	C₂×C₃×C₅	1	1	yes	characteristic, complemented
333	#487	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	#464	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	#463	C₂×C₃×C₅	1	1	yes	characteristic, complemented
336	#462	C₂×C₃×C₅	1	1	yes	characteristic, complemented
337	#461	C₂×C₃×C₅	1	1	yes	characteristic, complemented
338	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
339	#451	C₂×C₃×C₅	1	1	yes	characteristic, complemented
340	#449	C₂×C₃×C₅	1	1	yes	characteristic
341	#448	C₂×C₃×C₅	1	1	yes	characteristic, complemented
342	#433	C₂×C₃×C₅	1	1	yes	characteristic, complemented
343	C₂²×C₃×C₅	—	2	1	no	—
344	C₂²×C₃×C₅	—	2	1	no	—
345	C₂²×C₃×C₅	—	2	1	no	—
346	C₂²×C₃×C₅	—	4	1	no	—
347	C₂²×C₃×C₅	—	4	1	no	—
348	C₂²×C₃×C₅	—	4	1	no	—
349	C₂²×C₃×C₅	—	4	1	no	—
350	C₂²×C₃×C₅	—	4	1	no	—
351	C₂²×C₃×C₅	—	4	1	no	—
352	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
353	C₃×C₄×C₅	—	2	1	no	—
354	C₃×C₄×C₅	—	2	1	no	—
355	C₃×C₄×C₅	—	2	1	no	—
356	C₃×C₄×C₅	—	2	1	no	—
357	C₃×C₄×C₅	—	2	1	no	—
358	C₃×C₄×C₅	—	4	1	no	—
359	C₃×C₄×C₅	—	4	1	no	—
360	C₃×C₄×C₅	—	4	1	no	—
361	C₃×C₄×C₅	—	4	1	no	—
362	C₃×C₄×C₅	—	4	1	no	—
363	C₃×C₄×C₅	—	4	1	no	—
364	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
365	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
366	C₃×#41	—	4	1	no	—
367	C₃×#41	—	4	1	no	—
368	C₂×C₃×Q₈	—	2	1	no	—
369	C₂×C₃×Q₈	—	2	1	no	—
370	C₂×C₃×Q₈	—	4	1	no	—
371	C₂×C₃×Q₈	—	4	1	no	—
372	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
373	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
375	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₃×D₄	—	2	1	no	—
377	C₂×C₃×D₄	—	2	1	no	—
378	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
380	C₂²×C₃×C₄	—	2	1	no	—
381	C₂²×C₃×C₄	—	2	1	no	—
382	C₂²×C₃×C₄	—	2	1	no	—
383	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
384	C₃×Q₁₆	—	4	1	no	—
385	C₃×Q₁₆	—	4	1	no	—
386	C₃×Q₁₆	—	4	1	no	—
387	C₃×SD₁₆	—	4	1	no	—
388	C₃×SD₁₆	—	4	1	no	—
389	C₃×SD₁₆	—	4	1	no	—
390	C₃×SD₁₆	—	4	1	no	—
391	C₃×D₈	—	4	1	no	—
392	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
393	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
394	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
395	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
396	C₃×C₄⋊C₄	—	2	1	no	—
397	C₃×C₄⋊C₄	—	2	1	no	—
398	C₃×C₄⋊C₄	—	2	1	no	—
399	C₃×C₄⋊C₄	—	2	1	no	—
400	C₃×C₄⋊C₄	—	2	1	no	—
401	C₃×C₄⋊C₄	—	2	1	no	—
402	C₃×C₄⋊C₄	—	2	1	no	—
403	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
404	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
405	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
406	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
407	C₃×C₂²⋊C₄	—	2	1	no	—
408	C₃×C₂²⋊C₄	—	2	1	no	—
409	C₃×C₂²⋊C₄	—	2	1	no	—
410	C₃×C₂²⋊C₄	—	2	1	no	—
411	C₃×C₂²⋊C₄	—	2	1	no	—
412	C₃×C₂²⋊C₄	—	2	1	no	—
413	C₃×C₂²⋊C₄	—	2	1	no	—
414	C₃×C₂²⋊C₄	—	2	1	no	—
415	C₃×C₂²⋊C₄	—	2	1	no	—
416	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
417	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
418	C₃×C₄²	—	2	1	no	—
419	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
420	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
421	C₂³×C₅	—	2	1	no	—
422	C₂³×C₅	—	2	1	no	—
423	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
424	C₅×Q₈	—	2	1	no	—
425	C₅×Q₈	—	2	1	no	—
426	C₅×Q₈	—	2	1	no	—
427	C₅×Q₈	—	2	1	no	—
428	C₅×Q₈	—	2	1	no	—
429	C₅×Q₈	—	2	1	no	—
430	C₅×Q₈	—	2	1	no	—
431	C₅×Q₈	—	2	1	no	—
432	C₅×Q₈	—	4	2	no	—
433	C₅×Q₈	—	8	1	no	—
434	C₅×D₄	—	2	1	no	—
435	C₅×D₄	—	2	1	no	—
436	C₅×D₄	—	2	1	no	—
437	C₅×D₄	—	2	1	no	—
438	C₅×D₄	—	4	2	no	—
439	C₅×D₄	—	8	1	no	—
440	C₂×C₄×C₅	—	2	1	no	—
441	C₂×C₄×C₅	—	2	1	no	—
442	C₂×C₄×C₅	—	2	1	no	—
443	C₂×C₄×C₅	—	2	1	no	—
444	C₂×C₄×C₅	—	2	1	no	—
445	C₂×C₄×C₅	—	2	1	no	—
446	C₂×C₄×C₅	—	2	1	no	—
447	C₂×C₄×C₅	—	2	1	no	—
448	C₂×C₄×C₅	—	4	2	no	—
449	C₂×C₄×C₅	—	4	2	no	—
450	C₂×C₄×C₅	—	8	1	no	—
451	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
452	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
453	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
454	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
455	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
456	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
457	C₅×C₈	—	2	1	no	—
458	C₅×C₈	—	2	1	no	—
459	C₅×C₈	—	2	1	no	—
460	C₅×C₈	—	2	1	no	—
461	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
462	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
463	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
464	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
465	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
466	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
467	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
468	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
469	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
470	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
471	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
472	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
473	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
474	#126	—	2	1	no	—
475	#124	—	2	1	no	—
476	#124	C₂²×C₃×C₅	1	1	yes	characteristic
477	#124	C₂²×C₃×C₅	1	1	yes	characteristic
478	#124	C₂²×C₃×C₅	1	1	yes	characteristic
479	#123	—	2	1	no	—
480	#123	—	2	1	no	—
481	#123	—	2	1	no	—
482	C₂²⋊Q₈	—	2	1	no	—
483	C₂²⋊Q₈	—	2	1	no	—
484	C₂²⋊Q₈	—	2	1	no	—
485	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
486	#121	C₂²×C₃×C₅	1	1	yes	characteristic
487	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
488	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
489	#117	C₂²×C₃×C₅	1	1	yes	characteristic
490	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
491	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
492	#103	C₂²×C₃×C₅	1	1	yes	characteristic
493	#103	C₂²×C₃×C₅	1	1	yes	characteristic
494	#103	C₂²×C₃×C₅	1	1	yes	characteristic
495	#103	C₂²×C₃×C₅	1	1	yes	characteristic
496	#103	C₂²×C₃×C₅	1	1	yes	characteristic
497	#103	C₂²×C₃×C₅	1	1	yes	characteristic
498	#102	C₂²×C₃×C₅	1	1	yes	characteristic
499	#102	C₂²×C₃×C₅	1	1	yes	characteristic
500	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
501	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
502	#97	C₂²×C₃×C₅	1	1	yes	characteristic
503	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
504	C₂×C₃×C₅	—	4	1	no	—
505	C₂×C₃×C₅	—	8	1	no	—
506	C₂×C₃×C₅	—	8	1	no	—
507	C₂×C₃×C₅	#535	1	1	yes	characteristic
508	C₂×C₃×C₅	#577	1	1	yes	characteristic
509	C₂×C₃×C₅	#578	1	1	yes	characteristic
510	C₂³×C₃	—	2	1	no	—
511	C₂³×C₃	—	2	1	no	—
512	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
513	C₃×Q₈	—	2	1	no	—
514	C₃×Q₈	—	2	1	no	—
515	C₃×Q₈	—	2	1	no	—
516	C₃×Q₈	—	2	1	no	—
517	C₃×Q₈	—	2	1	no	—
518	C₃×Q₈	—	2	1	no	—
519	C₃×Q₈	—	2	1	no	—
520	C₃×Q₈	—	2	1	no	—
521	C₃×Q₈	—	4	2	no	—
522	C₃×Q₈	—	8	1	no	—
523	C₃×D₄	—	2	1	no	—
524	C₃×D₄	—	2	1	no	—
525	C₃×D₄	—	2	1	no	—
526	C₃×D₄	—	2	1	no	—
527	C₃×D₄	—	4	2	no	—
528	C₃×D₄	—	8	1	no	—
529	C₂×C₃×C₄	—	2	1	no	—
530	C₂×C₃×C₄	—	2	1	no	—
531	C₂×C₃×C₄	—	2	1	no	—
532	C₂×C₃×C₄	—	2	1	no	—
533	C₂×C₃×C₄	—	2	1	no	—
534	C₂×C₃×C₄	—	2	1	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	—	2	1	no	—
537	C₂×C₃×C₄	—	4	2	no	—
538	C₂×C₃×C₄	—	4	2	no	—
539	C₂×C₃×C₄	—	8	1	no	—
540	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
541	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
542	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
543	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
544	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
545	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
546	C₃×C₈	—	2	1	no	—
547	C₃×C₈	—	2	1	no	—
548	C₃×C₈	—	2	1	no	—
549	C₃×C₈	—	2	1	no	—
550	C₂²×C₅	—	2	1	no	—
551	C₂²×C₅	—	2	1	no	—
552	C₂²×C₅	—	2	1	no	—
553	C₂²×C₅	—	4	1	no	—
554	C₂²×C₅	—	4	1	no	—
555	C₂²×C₅	—	4	1	no	—
556	C₂²×C₅	—	4	1	no	—
557	C₂²×C₅	—	4	1	no	—
558	C₂²×C₅	—	4	1	no	—
559	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
560	C₄×C₅	—	2	1	no	—
561	C₄×C₅	—	2	1	no	—
562	C₄×C₅	—	2	1	no	—
563	C₄×C₅	—	2	1	no	—
564	C₄×C₅	—	2	1	no	—
565	C₄×C₅	—	4	1	no	—
566	C₄×C₅	—	4	1	no	—
567	C₄×C₅	—	4	1	no	—
568	C₄×C₅	—	4	1	no	—
569	C₄×C₅	—	4	1	no	—
570	C₄×C₅	—	4	1	no	—
571	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
572	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
573	#41	—	4	1	no	—
574	#41	—	4	1	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	4	1	no	—
578	C₂×Q₈	—	4	1	no	—
579	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
580	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
581	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
582	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
586	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
591	Q₁₆	—	4	1	no	—
592	Q₁₆	—	4	1	no	—
593	Q₁₆	—	4	1	no	—
594	SD₁₆	—	4	1	no	—
595	SD₁₆	—	4	1	no	—
596	SD₁₆	—	4	1	no	—
597	SD₁₆	—	4	1	no	—
598	D₈	—	4	1	no	—
599	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
600	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
601	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
602	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
611	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
612	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
613	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
614	C₂²⋊C₄	—	2	1	no	—
615	C₂²⋊C₄	—	2	1	no	—
616	C₂²⋊C₄	—	2	1	no	—
617	C₂²⋊C₄	—	2	1	no	—
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	1	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
624	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
625	C₄²	—	2	1	no	—
626	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
627	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
628	C₃×C₅	#3225	1	1	yes	characteristic, direct product factor, Hall
629	C₂²×C₃	—	2	1	no	—
630	C₂²×C₃	—	2	1	no	—
631	C₂²×C₃	—	2	1	no	—
632	C₂²×C₃	—	4	1	no	—
633	C₂²×C₃	—	4	1	no	—
634	C₂²×C₃	—	4	1	no	—
635	C₂²×C₃	—	4	1	no	—
636	C₂²×C₃	—	4	1	no	—
637	C₂²×C₃	—	4	1	no	—
638	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
639	C₃×C₄	—	2	1	no	—
640	C₃×C₄	—	2	1	no	—
641	C₃×C₄	—	2	1	no	—
642	C₃×C₄	—	2	1	no	—
643	C₃×C₄	—	2	1	no	—
644	C₃×C₄	—	4	1	no	—
645	C₃×C₄	—	4	1	no	—
646	C₃×C₄	—	4	1	no	—
647	C₃×C₄	—	4	1	no	—
648	C₃×C₄	—	4	1	no	—
649	C₃×C₄	—	4	1	no	—
650	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
651	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
652	C₂×C₅	—	4	1	no	—
653	C₂×C₅	—	8	1	no	—
654	C₂×C₅	—	8	1	no	—
655	C₂×C₅	C₃×#535	1	1	yes	characteristic
656	C₂×C₅	C₃×#577	1	1	yes	characteristic
657	C₂×C₅	C₃×#578	1	1	yes	characteristic
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
661	Q₈	—	2	1	no	—
662	Q₈	—	2	1	no	—
663	Q₈	—	2	1	no	—
664	Q₈	—	2	1	no	—
665	Q₈	—	2	1	no	—
666	Q₈	—	2	1	no	—
667	Q₈	—	2	1	no	—
668	Q₈	—	2	1	no	—
669	Q₈	—	4	2	no	—
670	Q₈	—	8	1	no	—
671	D₄	—	2	1	no	—
672	D₄	—	2	1	no	—
673	D₄	—	2	1	no	—
674	D₄	—	2	1	no	—
675	D₄	—	4	2	no	—
676	D₄	—	8	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	2	no	—
687	C₂×C₄	—	8	1	no	—
688	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
689	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
690	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
691	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
692	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
693	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
694	C₈	—	2	1	no	—
695	C₈	—	2	1	no	—
696	C₈	—	2	1	no	—
697	C₈	—	2	1	no	—
698	C₂×C₃	—	4	1	no	—
699	C₂×C₃	—	8	1	no	—
700	C₂×C₃	—	8	1	no	—
701	C₂×C₃	C₅×#535	1	1	yes	characteristic
702	C₂×C₃	C₅×#577	1	1	yes	characteristic
703	C₂×C₃	C₅×#578	1	1	yes	characteristic
704	C₅	C₃×#3225	1	1	yes	characteristic, direct product factor, Sylow
705	C₂²	—	2	1	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	2	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	1	no	—
714	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	1	no	—
726	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
727	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
728	C₃	C₅×#3225	1	1	yes	characteristic, direct product factor, Sylow
729	C₂	—	4	1	no	—
730	C₂	—	8	1	no	—
731	C₂	—	8	1	no	—
732	C₂	C₃×C₅×#535	1	1	yes	characteristic
733	C₂	C₃×C₅×#577	1	1	yes	characteristic
734	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×#449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#542	C₂	semidirect
2. C₃×C₅×#536	C₂	semidirect
3. C₃×C₅×#497	C₂	semidirect
4. C₃×C₅×#495	C₂	semidirect
5. C₃×C₅×#489	C₂	semidirect
6. C₃×C₅×#487	C₂	semidirect
7. C₃×C₅×#464	C₂	semidirect
8. C₃×C₅×#463	C₂	semidirect
9. C₃×C₅×#462	C₂	semidirect
10. C₃×C₅×#461	C₂	semidirect
11. C₃×C₅×#452	C₂	semidirect
12. C₃×C₅×#451	C₂	semidirect
14. C₃×C₅×#448	C₂	semidirect
15. C₃×C₅×#433	C₂	semidirect
16. C₅×#3225	C₃	direct (N × H)
60. C₃×#3225	C₅	direct (N × H)
61. C₅×#542	C₂×C₃	semidirect
62. C₅×#536	C₂×C₃	semidirect
63. C₅×#497	C₂×C₃	semidirect
64. C₅×#495	C₂×C₃	semidirect
65. C₅×#489	C₂×C₃	semidirect
66. C₅×#487	C₂×C₃	semidirect
67. C₅×#464	C₂×C₃	semidirect
68. C₅×#463	C₂×C₃	semidirect
69. C₅×#462	C₂×C₃	semidirect
70. C₅×#461	C₂×C₃	semidirect
71. C₅×#452	C₂×C₃	semidirect
72. C₅×#451	C₂×C₃	semidirect
74. C₅×#448	C₂×C₃	semidirect
75. C₅×#433	C₂×C₃	semidirect
131. C₃×#542	C₂×C₅	semidirect
132. C₃×#536	C₂×C₅	semidirect
133. C₃×#497	C₂×C₅	semidirect
134. C₃×#495	C₂×C₅	semidirect
135. C₃×#489	C₂×C₅	semidirect
136. C₃×#487	C₂×C₅	semidirect
137. C₃×#464	C₂×C₅	semidirect
138. C₃×#463	C₂×C₅	semidirect
139. C₃×#462	C₂×C₅	semidirect
140. C₃×#461	C₂×C₅	semidirect
141. C₃×#452	C₂×C₅	semidirect
142. C₃×#451	C₂×C₅	semidirect
144. C₃×#448	C₂×C₅	semidirect
145. C₃×#433	C₂×C₅	semidirect
189. #3225	C₃×C₅	direct (N × H)
328. #542	C₂×C₃×C₅	semidirect
329. #536	C₂×C₃×C₅	semidirect
330. #497	C₂×C₃×C₅	semidirect
331. #495	C₂×C₃×C₅	semidirect
332. #489	C₂×C₃×C₅	semidirect
333. #487	C₂×C₃×C₅	semidirect
334. #464	C₂×C₃×C₅	semidirect
335. #463	C₂×C₃×C₅	semidirect
336. #462	C₂×C₃×C₅	semidirect
337. #461	C₂×C₃×C₅	semidirect
338. #452	C₂×C₃×C₅	semidirect
339. #451	C₂×C₃×C₅	semidirect
341. #448	C₂×C₃×C₅	semidirect
342. #433	C₂×C₃×C₅	semidirect
628. C₃×C₅	#3225	direct (N × H)
704. C₅	C₃×#3225	direct (N × H)
728. C₃	C₅×#3225	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×C₅×#536	2
C₃×C₅×#497	2
C₃×C₅×#495	2
C₃×C₅×#489	2
C₃×C₅×#487	2
C₃×C₅×#464	2
C₃×C₅×#463	2
C₃×C₅×#462	2
C₃×C₅×#461	2
C₃×C₅×#452	2
C₃×C₅×#451	2
C₃×C₅×#449	2
C₃×C₅×#448	2
C₃×C₅×#433	2
C₅×#3225	3
C₃×#3225	5

Subgroups — C3×C5×#3225 #14276259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3225 #14276259