Subgroups — C₃×C₅×#3316 #14276350

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#548	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#483	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#470	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#465	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3316	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×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₃×C₅×#125	—	2	1	no	—
26	C₃×C₅×#124	—	2	1	no	—
27	C₃×C₅×#124	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
29	C₃×C₅×C₂²⋊Q₈	—	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×#121	—	2	1	no	—
35	C₃×C₅×#121	C₂²	1	1	yes	characteristic
36	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₅×D₄	—	2	1	no	—
39	C₃×C₄×C₅×D₄	—	2	1	no	—
40	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×C₅×#106	C₂²	1	1	yes	characteristic
44	C₃×C₅×#106	C₂²	1	1	yes	characteristic
45	C₃×C₅×#106	C₂²	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₃×C₅×#103	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×#102	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×#97	C₂²	1	1	yes	characteristic
60	C₃×#3316	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#554	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#548	C₂×C₃	1	1	yes	characteristic
63	C₅×#489	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#483	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#481	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#475	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#470	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#465	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#464	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#451	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#441	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#435	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#417	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic, complemented
76	C₃×C₅×#41	—	2	2	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	—	2	2	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×D₄	—	2	1	no	—
86	C₂×C₃×C₅×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
88	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₄×C₅	—	2	1	no	—
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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₃×C₅×Q₁₆	—	2	2	no	—
96	C₃×C₅×Q₁₆	—	4	1	no	—
97	C₃×C₅×SD₁₆	—	4	1	no	—
98	C₃×C₅×M₁₆	—	4	1	no	—
99	C₂×C₃×C₅×C₈	—	4	1	no	—
100	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₃×C₅×C₄⋊C₄	—	2	1	no	—
105	C₃×C₅×C₄⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
113	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₃×C₅×C₄⋊C₄	C₂³	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	D₄	1	1	yes	characteristic
124	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
125	C₃×C₄²×C₅	—	2	1	no	—
126	C₃×C₄²×C₅	—	2	1	no	—
127	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
128	C₃×#554	C₂×C₅	1	1	yes	characteristic, complemented
129	C₃×#548	C₂×C₅	1	1	yes	characteristic
130	C₃×#489	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#483	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#481	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#475	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#470	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#465	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#464	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#451	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#441	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×#435	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#417	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
144	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
149	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
150	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
151	C₅×#125	—	2	1	no	—
152	C₅×#124	—	2	1	no	—
153	C₅×#124	C₂²×C₃	1	1	yes	characteristic
154	C₅×C₂²⋊Q₈	—	2	1	no	—
155	C₅×C₂²⋊Q₈	—	2	1	no	—
156	C₅×C₂²⋊Q₈	—	2	1	no	—
157	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
158	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
159	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
160	C₅×#121	—	2	1	no	—
161	C₅×#121	C₂²×C₃	1	1	yes	characteristic
162	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
163	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
164	C₄×C₅×D₄	—	2	1	no	—
165	C₄×C₅×D₄	—	2	1	no	—
166	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
167	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	C₅×#106	C₂²×C₃	1	1	yes	characteristic
170	C₅×#106	C₂²×C₃	1	1	yes	characteristic
171	C₅×#106	C₂²×C₃	1	1	yes	characteristic
172	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
173	C₅×#103	C₂²×C₃	1	1	yes	characteristic
174	C₅×#103	C₂²×C₃	1	1	yes	characteristic
175	C₅×#103	C₂²×C₃	1	1	yes	characteristic
176	C₅×#103	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×#102	C₂²×C₃	1	1	yes	characteristic
181	C₅×#102	C₂²×C₃	1	1	yes	characteristic
182	C₅×#102	C₂²×C₃	1	1	yes	characteristic
183	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
184	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
185	C₅×#97	C₂²×C₃	1	1	yes	characteristic
186	#3316	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
187	C₂³×C₃×C₅	—	2	1	no	—
188	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
189	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
190	C₃×C₅×Q₈	—	2	1	no	—
191	C₃×C₅×Q₈	—	2	1	no	—
192	C₃×C₅×Q₈	—	2	1	no	—
193	C₃×C₅×Q₈	—	2	1	no	—
194	C₃×C₅×Q₈	—	2	1	no	—
195	C₃×C₅×Q₈	—	4	2	no	—
196	C₃×C₅×Q₈	—	8	1	no	—
197	C₃×C₅×Q₈	#41	1	2	yes	—
198	C₃×C₅×D₄	—	2	2	no	—
199	C₃×C₅×D₄	—	2	1	no	—
200	C₃×C₅×D₄	—	2	1	no	—
201	C₃×C₅×D₄	—	4	2	no	—
202	C₃×C₅×D₄	—	4	2	no	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	—	2	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	—	4	2	no	—
215	C₂×C₃×C₄×C₅	—	4	2	no	—
216	C₂×C₃×C₄×C₅	—	8	1	no	—
217	C₂×C₃×C₄×C₅	—	8	1	no	—
218	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
219	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
223	C₃×C₅×C₈	—	2	1	no	—
224	C₃×C₅×C₈	—	2	1	no	—
225	C₃×C₅×C₈	—	2	1	no	—
226	C₃×C₅×C₈	—	2	1	no	—
227	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
228	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
233	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
234	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
235	C₃×#125	—	2	1	no	—
236	C₃×#124	—	2	1	no	—
237	C₃×#124	C₂²×C₅	1	1	yes	characteristic
238	C₃×C₂²⋊Q₈	—	2	1	no	—
239	C₃×C₂²⋊Q₈	—	2	1	no	—
240	C₃×C₂²⋊Q₈	—	2	1	no	—
241	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
242	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
243	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
244	C₃×#121	—	2	1	no	—
245	C₃×#121	C₂²×C₅	1	1	yes	characteristic
246	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
247	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
248	C₃×C₄×D₄	—	2	1	no	—
249	C₃×C₄×D₄	—	2	1	no	—
250	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
253	C₃×#106	C₂²×C₅	1	1	yes	characteristic
254	C₃×#106	C₂²×C₅	1	1	yes	characteristic
255	C₃×#106	C₂²×C₅	1	1	yes	characteristic
256	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
257	C₃×#103	C₂²×C₅	1	1	yes	characteristic
258	C₃×#103	C₂²×C₅	1	1	yes	characteristic
259	C₃×#103	C₂²×C₅	1	1	yes	characteristic
260	C₃×#103	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×#102	C₂²×C₅	1	1	yes	characteristic
265	C₃×#102	C₂²×C₅	1	1	yes	characteristic
266	C₃×#102	C₂²×C₅	1	1	yes	characteristic
267	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
268	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
269	C₃×#97	C₂²×C₅	1	1	yes	characteristic
270	C₅×#41	—	2	2	no	—
271	C₅×#41	—	4	1	no	—
272	C₂×C₅×Q₈	—	2	1	no	—
273	C₂×C₅×Q₈	—	2	1	no	—
274	C₂×C₅×Q₈	—	2	2	no	—
275	C₂×C₅×Q₈	—	4	1	no	—
276	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
277	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
278	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
279	C₂×C₅×D₄	—	2	1	no	—
280	C₂×C₅×D₄	—	2	1	no	—
281	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
282	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
283	C₂²×C₄×C₅	—	2	1	no	—
284	C₂²×C₄×C₅	—	2	1	no	—
285	C₂²×C₄×C₅	—	2	1	no	—
286	C₂²×C₄×C₅	—	2	1	no	—
287	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
288	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
289	C₅×Q₁₆	—	2	2	no	—
290	C₅×Q₁₆	—	4	1	no	—
291	C₅×SD₁₆	—	4	1	no	—
292	C₅×M₁₆	—	4	1	no	—
293	C₂×C₅×C₈	—	4	1	no	—
294	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
295	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
296	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
297	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
298	C₅×C₄⋊C₄	—	2	1	no	—
299	C₅×C₄⋊C₄	—	2	1	no	—
300	C₅×C₄⋊C₄	—	2	1	no	—
301	C₅×C₄⋊C₄	—	2	1	no	—
302	C₅×C₄⋊C₄	—	2	1	no	—
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	C₃×D₄	1	1	yes	characteristic
307	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
308	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
309	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
310	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
311	C₅×C₂²⋊C₄	—	2	1	no	—
312	C₅×C₂²⋊C₄	—	2	1	no	—
313	C₅×C₂²⋊C₄	—	2	1	no	—
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	C₃×D₄	1	1	yes	characteristic
318	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
319	C₄²×C₅	—	2	1	no	—
320	C₄²×C₅	—	2	1	no	—
321	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
322	#554	C₂×C₃×C₅	1	1	yes	characteristic, complemented
323	#548	C₂×C₃×C₅	1	1	yes	characteristic
324	#489	C₂×C₃×C₅	1	1	yes	characteristic, complemented
325	#483	C₂×C₃×C₅	1	1	yes	characteristic, complemented
326	#481	C₂×C₃×C₅	1	1	yes	characteristic, complemented
327	#475	C₂×C₃×C₅	1	1	yes	characteristic, complemented
328	#470	C₂×C₃×C₅	1	1	yes	characteristic, complemented
329	#465	C₂×C₃×C₅	1	1	yes	characteristic, complemented
330	#464	C₂×C₃×C₅	1	1	yes	characteristic, complemented
331	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
332	#451	C₂×C₃×C₅	1	1	yes	characteristic, complemented
333	#441	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	#435	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	#417	C₂×C₃×C₅	1	1	yes	characteristic, complemented
336	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic, complemented
337	C₂²×C₃×C₅	—	2	1	no	—
338	C₂²×C₃×C₅	—	2	1	no	—
339	C₂²×C₃×C₅	—	2	1	no	—
340	C₂²×C₃×C₅	—	2	1	no	—
341	C₂²×C₃×C₅	—	2	1	no	—
342	C₂²×C₃×C₅	—	4	1	no	—
343	C₂²×C₃×C₅	—	4	1	no	—
344	C₂²×C₃×C₅	—	4	1	no	—
345	C₂²×C₃×C₅	#137	1	2	yes	—
346	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
347	C₃×C₄×C₅	—	2	1	no	—
348	C₃×C₄×C₅	—	2	1	no	—
349	C₃×C₄×C₅	—	2	2	no	—
350	C₃×C₄×C₅	—	2	1	no	—
351	C₃×C₄×C₅	—	2	1	no	—
352	C₃×C₄×C₅	—	4	1	no	—
353	C₃×C₄×C₅	—	4	1	no	—
354	C₃×C₄×C₅	—	4	1	no	—
355	C₃×C₄×C₅	—	4	1	no	—
356	C₃×C₄×C₅	—	4	1	no	—
357	C₃×C₄×C₅	—	4	1	no	—
358	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
359	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
360	C₃×#41	—	2	2	no	—
361	C₃×#41	—	4	1	no	—
362	C₂×C₃×Q₈	—	2	1	no	—
363	C₂×C₃×Q₈	—	2	1	no	—
364	C₂×C₃×Q₈	—	2	2	no	—
365	C₂×C₃×Q₈	—	4	1	no	—
366	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
367	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
368	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
369	C₂×C₃×D₄	—	2	1	no	—
370	C₂×C₃×D₄	—	2	1	no	—
371	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
372	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
373	C₂²×C₃×C₄	—	2	1	no	—
374	C₂²×C₃×C₄	—	2	1	no	—
375	C₂²×C₃×C₄	—	2	1	no	—
376	C₂²×C₃×C₄	—	2	1	no	—
377	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
378	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
379	C₃×Q₁₆	—	2	2	no	—
380	C₃×Q₁₆	—	4	1	no	—
381	C₃×SD₁₆	—	4	1	no	—
382	C₃×M₁₆	—	4	1	no	—
383	C₂×C₃×C₈	—	4	1	no	—
384	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
386	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
387	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
388	C₃×C₄⋊C₄	—	2	1	no	—
389	C₃×C₄⋊C₄	—	2	1	no	—
390	C₃×C₄⋊C₄	—	2	1	no	—
391	C₃×C₄⋊C₄	—	2	1	no	—
392	C₃×C₄⋊C₄	—	2	1	no	—
393	C₃×C₄⋊C₄	—	2	1	no	—
394	C₃×C₄⋊C₄	—	2	1	no	—
395	C₃×C₄⋊C₄	—	2	1	no	—
396	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
397	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
398	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
399	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
400	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
401	C₃×C₂²⋊C₄	—	2	1	no	—
402	C₃×C₂²⋊C₄	—	2	1	no	—
403	C₃×C₂²⋊C₄	—	2	1	no	—
404	C₃×C₂²⋊C₄	—	2	1	no	—
405	C₃×C₂²⋊C₄	—	2	1	no	—
406	C₃×C₂²⋊C₄	—	2	1	no	—
407	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
408	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
409	C₃×C₄²	—	2	1	no	—
410	C₃×C₄²	—	2	1	no	—
411	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
412	C₂³×C₅	—	2	1	no	—
413	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
414	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
415	C₅×Q₈	—	2	1	no	—
416	C₅×Q₈	—	2	1	no	—
417	C₅×Q₈	—	2	1	no	—
418	C₅×Q₈	—	2	1	no	—
419	C₅×Q₈	—	2	1	no	—
420	C₅×Q₈	—	4	2	no	—
421	C₅×Q₈	—	8	1	no	—
422	C₅×Q₈	C₃×#41	1	2	yes	—
423	C₅×D₄	—	2	2	no	—
424	C₅×D₄	—	2	1	no	—
425	C₅×D₄	—	2	1	no	—
426	C₅×D₄	—	4	2	no	—
427	C₅×D₄	—	4	2	no	—
428	C₂×C₄×C₅	—	2	1	no	—
429	C₂×C₄×C₅	—	2	1	no	—
430	C₂×C₄×C₅	—	2	1	no	—
431	C₂×C₄×C₅	—	2	1	no	—
432	C₂×C₄×C₅	—	2	1	no	—
433	C₂×C₄×C₅	—	2	1	no	—
434	C₂×C₄×C₅	—	2	1	no	—
435	C₂×C₄×C₅	—	2	1	no	—
436	C₂×C₄×C₅	—	2	1	no	—
437	C₂×C₄×C₅	—	2	1	no	—
438	C₂×C₄×C₅	—	2	1	no	—
439	C₂×C₄×C₅	—	4	2	no	—
440	C₂×C₄×C₅	—	4	2	no	—
441	C₂×C₄×C₅	—	8	1	no	—
442	C₂×C₄×C₅	—	8	1	no	—
443	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
444	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
445	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
446	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
447	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
448	C₅×C₈	—	2	1	no	—
449	C₅×C₈	—	2	1	no	—
450	C₅×C₈	—	2	1	no	—
451	C₅×C₈	—	2	1	no	—
452	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
453	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
454	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
455	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
456	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
457	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
458	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
459	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
460	#125	—	2	1	no	—
461	#124	—	2	1	no	—
462	#124	C₂²×C₃×C₅	1	1	yes	characteristic
463	C₂²⋊Q₈	—	2	1	no	—
464	C₂²⋊Q₈	—	2	1	no	—
465	C₂²⋊Q₈	—	2	1	no	—
466	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
467	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
468	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
469	#121	—	2	1	no	—
470	#121	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×D₄	—	2	1	no	—
474	C₄×D₄	—	2	1	no	—
475	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
478	#106	C₂²×C₃×C₅	1	1	yes	characteristic
479	#106	C₂²×C₃×C₅	1	1	yes	characteristic
480	#106	C₂²×C₃×C₅	1	1	yes	characteristic
481	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
482	#103	C₂²×C₃×C₅	1	1	yes	characteristic
483	#103	C₂²×C₃×C₅	1	1	yes	characteristic
484	#103	C₂²×C₃×C₅	1	1	yes	characteristic
485	#103	C₂²×C₃×C₅	1	1	yes	characteristic
486	#103	C₂²×C₃×C₅	1	1	yes	characteristic
487	#103	C₂²×C₃×C₅	1	1	yes	characteristic
488	#103	C₂²×C₃×C₅	1	1	yes	characteristic
489	#102	C₂²×C₃×C₅	1	1	yes	characteristic
490	#102	C₂²×C₃×C₅	1	1	yes	characteristic
491	#102	C₂²×C₃×C₅	1	1	yes	characteristic
492	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
493	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
494	#97	C₂²×C₃×C₅	1	1	yes	characteristic
495	C₂×C₃×C₅	—	2	2	no	—
496	C₂×C₃×C₅	—	4	1	no	—
497	C₂×C₃×C₅	—	8	1	no	—
498	C₂×C₃×C₅	#546	1	1	yes	characteristic
499	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
500	C₂×C₃×C₅	#577	1	1	yes	characteristic
501	C₂³×C₃	—	2	1	no	—
502	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
503	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
504	C₃×Q₈	—	2	1	no	—
505	C₃×Q₈	—	2	1	no	—
506	C₃×Q₈	—	2	1	no	—
507	C₃×Q₈	—	2	1	no	—
508	C₃×Q₈	—	2	1	no	—
509	C₃×Q₈	—	4	2	no	—
510	C₃×Q₈	—	8	1	no	—
511	C₃×Q₈	C₅×#41	1	2	yes	—
512	C₃×D₄	—	2	2	no	—
513	C₃×D₄	—	2	1	no	—
514	C₃×D₄	—	2	1	no	—
515	C₃×D₄	—	4	2	no	—
516	C₃×D₄	—	4	2	no	—
517	C₂×C₃×C₄	—	2	1	no	—
518	C₂×C₃×C₄	—	2	1	no	—
519	C₂×C₃×C₄	—	2	1	no	—
520	C₂×C₃×C₄	—	2	1	no	—
521	C₂×C₃×C₄	—	2	1	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	2	1	no	—
524	C₂×C₃×C₄	—	2	1	no	—
525	C₂×C₃×C₄	—	2	1	no	—
526	C₂×C₃×C₄	—	2	1	no	—
527	C₂×C₃×C₄	—	2	1	no	—
528	C₂×C₃×C₄	—	4	2	no	—
529	C₂×C₃×C₄	—	4	2	no	—
530	C₂×C₃×C₄	—	8	1	no	—
531	C₂×C₃×C₄	—	8	1	no	—
532	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
533	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
534	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
535	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
536	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
537	C₃×C₈	—	2	1	no	—
538	C₃×C₈	—	2	1	no	—
539	C₃×C₈	—	2	1	no	—
540	C₃×C₈	—	2	1	no	—
541	C₂²×C₅	—	2	1	no	—
542	C₂²×C₅	—	2	1	no	—
543	C₂²×C₅	—	2	1	no	—
544	C₂²×C₅	—	2	1	no	—
545	C₂²×C₅	—	2	1	no	—
546	C₂²×C₅	—	4	1	no	—
547	C₂²×C₅	—	4	1	no	—
548	C₂²×C₅	—	4	1	no	—
549	C₂²×C₅	C₃×#137	1	2	yes	—
550	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
551	C₄×C₅	—	2	1	no	—
552	C₄×C₅	—	2	1	no	—
553	C₄×C₅	—	2	1	no	—
554	C₄×C₅	—	2	1	no	—
555	C₄×C₅	—	2	2	no	—
556	C₄×C₅	—	4	1	no	—
557	C₄×C₅	—	4	1	no	—
558	C₄×C₅	—	4	1	no	—
559	C₄×C₅	—	4	1	no	—
560	C₄×C₅	—	4	1	no	—
561	C₄×C₅	—	4	1	no	—
562	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
563	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
564	#41	—	2	2	no	—
565	#41	—	4	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	—	4	1	no	—
570	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
571	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
572	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
576	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
582	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
583	Q₁₆	—	2	2	no	—
584	Q₁₆	—	4	1	no	—
585	SD₁₆	—	4	1	no	—
586	M₁₆	—	4	1	no	—
587	C₂×C₈	—	4	1	no	—
588	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
589	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
590	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
591	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
601	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
602	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
603	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
604	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
605	C₂²⋊C₄	—	2	1	no	—
606	C₂²⋊C₄	—	2	1	no	—
607	C₂²⋊C₄	—	2	1	no	—
608	C₂²⋊C₄	—	2	1	no	—
609	C₂²⋊C₄	—	2	1	no	—
610	C₂²⋊C₄	—	2	1	no	—
611	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
612	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
616	C₃×C₅	#3316	1	1	yes	characteristic, direct product factor, Hall
617	C₂²×C₃	—	2	1	no	—
618	C₂²×C₃	—	2	1	no	—
619	C₂²×C₃	—	2	1	no	—
620	C₂²×C₃	—	2	1	no	—
621	C₂²×C₃	—	2	1	no	—
622	C₂²×C₃	—	4	1	no	—
623	C₂²×C₃	—	4	1	no	—
624	C₂²×C₃	—	4	1	no	—
625	C₂²×C₃	C₅×#137	1	2	yes	—
626	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
627	C₃×C₄	—	2	1	no	—
628	C₃×C₄	—	2	1	no	—
629	C₃×C₄	—	2	2	no	—
630	C₃×C₄	—	2	1	no	—
631	C₃×C₄	—	2	1	no	—
632	C₃×C₄	—	4	1	no	—
633	C₃×C₄	—	4	1	no	—
634	C₃×C₄	—	4	1	no	—
635	C₃×C₄	—	4	1	no	—
636	C₃×C₄	—	4	1	no	—
637	C₃×C₄	—	4	1	no	—
638	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
639	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
640	C₂×C₅	—	2	2	no	—
641	C₂×C₅	—	4	1	no	—
642	C₂×C₅	—	8	1	no	—
643	C₂×C₅	C₃×#546	1	1	yes	characteristic
644	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
645	C₂×C₅	C₃×#577	1	1	yes	characteristic
646	C₂³	—	2	1	no	—
647	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
648	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
649	Q₈	—	2	1	no	—
650	Q₈	—	2	1	no	—
651	Q₈	—	2	1	no	—
652	Q₈	—	2	1	no	—
653	Q₈	—	2	1	no	—
654	Q₈	—	4	2	no	—
655	Q₈	—	8	1	no	—
656	Q₈	C₃×C₅×#41	1	2	yes	—
657	D₄	—	2	2	no	—
658	D₄	—	2	1	no	—
659	D₄	—	2	1	no	—
660	D₄	—	4	2	no	—
661	D₄	—	4	2	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	4	2	no	—
674	C₂×C₄	—	4	2	no	—
675	C₂×C₄	—	8	1	no	—
676	C₂×C₄	—	8	1	no	—
677	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
678	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
679	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
680	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
681	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
682	C₈	—	2	1	no	—
683	C₈	—	2	1	no	—
684	C₈	—	2	1	no	—
685	C₈	—	2	1	no	—
686	C₂×C₃	—	2	2	no	—
687	C₂×C₃	—	4	1	no	—
688	C₂×C₃	—	8	1	no	—
689	C₂×C₃	C₅×#546	1	1	yes	characteristic
690	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
691	C₂×C₃	C₅×#577	1	1	yes	characteristic
692	C₅	C₃×#3316	1	1	yes	characteristic, direct product factor, Sylow
693	C₂²	—	2	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	C₃×C₅×#137	1	2	yes	—
702	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
703	C₄	—	2	1	no	—
704	C₄	—	2	1	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
715	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
716	C₃	C₅×#3316	1	1	yes	characteristic, direct product factor, Sylow
717	C₂	—	2	2	no	—
718	C₂	—	4	1	no	—
719	C₂	—	8	1	no	—
720	C₂	C₃×C₅×#546	1	1	yes	characteristic
721	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
722	C₂	C₃×C₅×#577	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×#548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#554	C₂	semidirect
3. C₃×C₅×#489	C₂	semidirect
4. C₃×C₅×#483	C₂	semidirect
5. C₃×C₅×#481	C₂	semidirect
6. C₃×C₅×#475	C₂	semidirect
7. C₃×C₅×#470	C₂	semidirect
8. C₃×C₅×#465	C₂	semidirect
9. C₃×C₅×#464	C₂	semidirect
10. C₃×C₅×#452	C₂	semidirect
11. C₃×C₅×#451	C₂	semidirect
12. C₃×C₅×#441	C₂	semidirect
13. C₃×C₅×#435	C₂	semidirect
14. C₃×C₅×#417	C₂	semidirect
15. C₂×C₃×C₅×#103	C₂	semidirect
16. C₅×#3316	C₃	direct (N × H)
60. C₃×#3316	C₅	direct (N × H)
61. C₅×#554	C₂×C₃	semidirect
63. C₅×#489	C₂×C₃	semidirect
64. C₅×#483	C₂×C₃	semidirect
65. C₅×#481	C₂×C₃	semidirect
66. C₅×#475	C₂×C₃	semidirect
67. C₅×#470	C₂×C₃	semidirect
68. C₅×#465	C₂×C₃	semidirect
69. C₅×#464	C₂×C₃	semidirect
70. C₅×#452	C₂×C₃	semidirect
71. C₅×#451	C₂×C₃	semidirect
72. C₅×#441	C₂×C₃	semidirect
73. C₅×#435	C₂×C₃	semidirect
74. C₅×#417	C₂×C₃	semidirect
75. C₂×C₅×#103	C₂×C₃	semidirect
128. C₃×#554	C₂×C₅	semidirect
130. C₃×#489	C₂×C₅	semidirect
131. C₃×#483	C₂×C₅	semidirect
132. C₃×#481	C₂×C₅	semidirect
133. C₃×#475	C₂×C₅	semidirect
134. C₃×#470	C₂×C₅	semidirect
135. C₃×#465	C₂×C₅	semidirect
136. C₃×#464	C₂×C₅	semidirect
137. C₃×#452	C₂×C₅	semidirect
138. C₃×#451	C₂×C₅	semidirect
139. C₃×#441	C₂×C₅	semidirect
140. C₃×#435	C₂×C₅	semidirect
141. C₃×#417	C₂×C₅	semidirect
142. C₂×C₃×#103	C₂×C₅	semidirect
186. #3316	C₃×C₅	direct (N × H)
322. #554	C₂×C₃×C₅	semidirect
324. #489	C₂×C₃×C₅	semidirect
325. #483	C₂×C₃×C₅	semidirect
326. #481	C₂×C₃×C₅	semidirect
327. #475	C₂×C₃×C₅	semidirect
328. #470	C₂×C₃×C₅	semidirect
329. #465	C₂×C₃×C₅	semidirect
330. #464	C₂×C₃×C₅	semidirect
331. #452	C₂×C₃×C₅	semidirect
332. #451	C₂×C₃×C₅	semidirect
333. #441	C₂×C₃×C₅	semidirect
334. #435	C₂×C₃×C₅	semidirect
335. #417	C₂×C₃×C₅	semidirect
336. C₂×#103	C₂×C₃×C₅	semidirect
616. C₃×C₅	#3316	direct (N × H)
692. C₅	C₃×#3316	direct (N × H)
716. C₃	C₅×#3316	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×#554	2
C₃×C₅×#548	2
C₃×C₅×#489	2
C₃×C₅×#483	2
C₃×C₅×#481	2
C₃×C₅×#475	2
C₃×C₅×#470	2
C₃×C₅×#465	2
C₃×C₅×#464	2
C₃×C₅×#452	2
C₃×C₅×#451	2
C₃×C₅×#441	2
C₃×C₅×#435	2
C₃×C₅×#417	2
C₂×C₃×C₅×#103	2
C₅×#3316	3
C₃×#3316	5

Subgroups — C3×C5×#3316 #14276350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3316 #14276350