Subgroups — C₃×C₅×#3318 #14276352

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#490	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#482	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#478	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#469	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#459	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#447	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#447	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#418	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3318	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×D₄	—	2	1	no	—
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×#127	C₂²	1	1	yes	characteristic
26	C₃×C₅×#126	—	2	1	no	—
27	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×#123	—	2	1	no	—
29	C₃×C₅×#121	—	2	1	no	—
30	C₃×C₅×#121	—	2	1	no	—
31	C₃×C₅×#121	C₂²	1	1	yes	characteristic
32	C₃×C₅×#121	C₂²	1	1	yes	characteristic
33	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#120	—	2	1	no	—
36	C₃×C₅×#120	—	2	1	no	—
37	C₃×C₄×C₅×D₄	—	2	1	no	—
38	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
39	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₅×#102	C₂²	1	1	yes	characteristic
48	C₃×C₅×#102	C₂²	1	1	yes	characteristic
49	C₃×C₅×#102	C₂²	1	1	yes	characteristic
50	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
56	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
57	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
60	C₃×#3318	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#553	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×D₄²	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#490	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#482	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#481	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#478	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#469	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#466	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#459	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#447	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#447	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#442	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#435	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#418	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×C₅×#102	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂⁴×C₃×C₅	—	2	1	no	—
77	C₂⁴×C₃×C₅	—	2	1	no	—
78	C₂×C₃×C₅×D₄	—	2	2	no	—
79	C₂×C₃×C₅×D₄	—	2	2	no	—
80	C₂×C₃×C₅×D₄	—	2	1	no	—
81	C₂×C₃×C₅×D₄	—	2	1	no	—
82	C₂×C₃×C₅×D₄	—	2	1	no	—
83	C₂×C₃×C₅×D₄	—	2	1	no	—
84	C₂×C₃×C₅×D₄	—	2	1	no	—
85	C₂×C₃×C₅×D₄	—	2	1	no	—
86	C₂×C₃×C₅×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	—	2	1	no	—
88	C₂×C₃×C₅×D₄	—	4	1	no	—
89	C₂×C₃×C₅×D₄	—	4	1	no	—
90	C₂×C₃×C₅×D₄	—	4	4	no	—
91	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
92	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
96	C₂²×C₃×C₄×C₅	—	2	1	no	—
97	C₂²×C₃×C₄×C₅	—	2	1	no	—
98	C₂²×C₃×C₄×C₅	—	2	1	no	—
99	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
100	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
101	C₃×C₅×D₈	—	2	2	no	—
102	C₃×C₅×D₈	—	4	1	no	—
103	C₃×C₅×D₈	—	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	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
126	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
127	C₃×C₄²×C₅	—	2	1	no	—
128	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
129	C₃×#553	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×D₄²	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#490	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#482	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#481	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#478	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#469	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#466	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#459	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#447	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#447	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×#442	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#435	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×#418	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
144	C₂²×C₅×D₄	—	2	1	no	—
145	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
146	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
149	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
150	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
151	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
152	C₅×#127	C₂²×C₃	1	1	yes	characteristic
153	C₅×#126	—	2	1	no	—
154	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
155	C₅×#123	—	2	1	no	—
156	C₅×#121	—	2	1	no	—
157	C₅×#121	—	2	1	no	—
158	C₅×#121	C₂²×C₃	1	1	yes	characteristic
159	C₅×#121	C₂²×C₃	1	1	yes	characteristic
160	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
162	C₅×#120	—	2	1	no	—
163	C₅×#120	—	2	1	no	—
164	C₄×C₅×D₄	—	2	1	no	—
165	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
166	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
167	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₅×#102	C₂²×C₃	1	1	yes	characteristic
175	C₅×#102	C₂²×C₃	1	1	yes	characteristic
176	C₅×#102	C₂²×C₃	1	1	yes	characteristic
177	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
178	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
180	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
182	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
186	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
187	#3318	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
188	C₂³×C₃×C₅	—	2	1	no	—
189	C₂³×C₃×C₅	—	2	1	no	—
190	C₂³×C₃×C₅	—	2	1	no	—
191	C₂³×C₃×C₅	—	2	1	no	—
192	C₂³×C₃×C₅	—	4	2	no	—
193	C₂³×C₃×C₅	—	4	2	no	—
194	C₂³×C₃×C₅	—	4	2	no	—
195	C₂³×C₃×C₅	—	4	2	no	—
196	C₂³×C₃×C₅	—	8	1	no	—
197	C₂³×C₃×C₅	—	8	1	no	—
198	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
199	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
200	C₃×C₅×D₄	—	2	2	no	—
201	C₃×C₅×D₄	—	2	1	no	—
202	C₃×C₅×D₄	—	2	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	—	2	1	no	—
208	C₃×C₅×D₄	—	4	2	no	—
209	C₃×C₅×D₄	—	4	2	no	—
210	C₃×C₅×D₄	—	4	2	no	—
211	C₃×C₅×D₄	—	4	2	no	—
212	C₃×C₅×D₄	—	4	2	no	—
213	C₃×C₅×D₄	—	4	2	no	—
214	C₃×C₅×D₄	—	8	1	no	—
215	C₃×C₅×D₄	—	8	1	no	—
216	C₃×C₅×D₄	#41	1	2	yes	—
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	—	2	1	no	—
224	C₂×C₃×C₄×C₅	—	2	1	no	—
225	C₂×C₃×C₄×C₅	—	4	2	no	—
226	C₂×C₃×C₄×C₅	—	8	1	no	—
227	C₂×C₃×C₄×C₅	—	8	1	no	—
228	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
229	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
230	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
231	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
232	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
233	C₃×C₅×C₈	—	2	1	no	—
234	C₃×C₅×C₈	—	2	1	no	—
235	C₃×C₅×C₈	—	2	1	no	—
236	C₃×C₅×C₈	—	2	1	no	—
237	C₂²×C₃×D₄	—	2	1	no	—
238	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
239	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
242	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
243	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
244	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
245	C₃×#127	C₂²×C₅	1	1	yes	characteristic
246	C₃×#126	—	2	1	no	—
247	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
248	C₃×#123	—	2	1	no	—
249	C₃×#121	—	2	1	no	—
250	C₃×#121	—	2	1	no	—
251	C₃×#121	C₂²×C₅	1	1	yes	characteristic
252	C₃×#121	C₂²×C₅	1	1	yes	characteristic
253	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
254	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₃×#120	—	2	1	no	—
256	C₃×#120	—	2	1	no	—
257	C₃×C₄×D₄	—	2	1	no	—
258	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
259	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
260	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
261	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
265	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
266	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₃×#102	C₂²×C₅	1	1	yes	characteristic
268	C₃×#102	C₂²×C₅	1	1	yes	characteristic
269	C₃×#102	C₂²×C₅	1	1	yes	characteristic
270	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
275	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
276	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
277	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
278	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
280	C₂⁴×C₅	—	2	1	no	—
281	C₂⁴×C₅	—	2	1	no	—
282	C₂×C₅×D₄	—	2	2	no	—
283	C₂×C₅×D₄	—	2	2	no	—
284	C₂×C₅×D₄	—	2	1	no	—
285	C₂×C₅×D₄	—	2	1	no	—
286	C₂×C₅×D₄	—	2	1	no	—
287	C₂×C₅×D₄	—	2	1	no	—
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	—	2	1	no	—
292	C₂×C₅×D₄	—	4	1	no	—
293	C₂×C₅×D₄	—	4	1	no	—
294	C₂×C₅×D₄	—	4	4	no	—
295	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
296	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
297	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
298	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
299	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
300	C₂²×C₄×C₅	—	2	1	no	—
301	C₂²×C₄×C₅	—	2	1	no	—
302	C₂²×C₄×C₅	—	2	1	no	—
303	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
304	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
305	C₅×D₈	—	2	2	no	—
306	C₅×D₈	—	4	1	no	—
307	C₅×D₈	—	4	1	no	—
308	C₅×M₁₆	—	4	1	no	—
309	C₂×C₅×C₈	—	4	1	no	—
310	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
311	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
312	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
313	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
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	C₃×D₄	1	1	yes	characteristic
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	C₃×D₄	1	1	yes	characteristic
330	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
331	C₄²×C₅	—	2	1	no	—
332	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
333	#553	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	D₄²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	#490	C₂×C₃×C₅	1	1	yes	characteristic, complemented
336	#482	C₂×C₃×C₅	1	1	yes	characteristic, complemented
337	#481	C₂×C₃×C₅	1	1	yes	characteristic, complemented
338	#478	C₂×C₃×C₅	1	1	yes	characteristic, complemented
339	#469	C₂×C₃×C₅	1	1	yes	characteristic, complemented
340	#466	C₂×C₃×C₅	1	1	yes	characteristic, complemented
341	#459	C₂×C₃×C₅	1	1	yes	characteristic, complemented
342	#447	C₂×C₃×C₅	1	1	yes	characteristic, complemented
343	#447	C₂×C₃×C₅	1	1	yes	characteristic, complemented
344	#442	C₂×C₃×C₅	1	1	yes	characteristic, complemented
345	#435	C₂×C₃×C₅	1	1	yes	characteristic, complemented
346	#418	C₂×C₃×C₅	1	1	yes	characteristic, complemented
347	C₂×#102	C₂×C₃×C₅	1	1	yes	characteristic, complemented
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	2	no	—
352	C₂²×C₃×C₅	—	2	1	no	—
353	C₂²×C₃×C₅	—	2	1	no	—
354	C₂²×C₃×C₅	—	4	1	no	—
355	C₂²×C₃×C₅	—	4	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	—	4	1	no	—
360	C₂²×C₃×C₅	—	4	1	no	—
361	C₂²×C₃×C₅	—	4	1	no	—
362	C₂²×C₃×C₅	—	4	1	no	—
363	C₂²×C₃×C₅	—	4	1	no	—
364	C₂²×C₃×C₅	—	4	1	no	—
365	C₂²×C₃×C₅	—	8	4	no	—
366	C₂²×C₃×C₅	—	8	4	no	—
367	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
368	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
369	C₃×C₄×C₅	—	2	1	no	—
370	C₃×C₄×C₅	—	2	1	no	—
371	C₃×C₄×C₅	—	2	1	no	—
372	C₃×C₄×C₅	—	2	1	no	—
373	C₃×C₄×C₅	—	4	1	no	—
374	C₃×C₄×C₅	—	4	1	no	—
375	C₃×C₄×C₅	—	4	1	no	—
376	C₃×C₄×C₅	—	4	1	no	—
377	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
378	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
379	C₂⁴×C₃	—	2	1	no	—
380	C₂⁴×C₃	—	2	1	no	—
381	C₂×C₃×D₄	—	2	2	no	—
382	C₂×C₃×D₄	—	2	2	no	—
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	—	2	1	no	—
387	C₂×C₃×D₄	—	2	1	no	—
388	C₂×C₃×D₄	—	2	1	no	—
389	C₂×C₃×D₄	—	2	1	no	—
390	C₂×C₃×D₄	—	2	1	no	—
391	C₂×C₃×D₄	—	4	1	no	—
392	C₂×C₃×D₄	—	4	1	no	—
393	C₂×C₃×D₄	—	4	4	no	—
394	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
395	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
396	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
397	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
398	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
399	C₂²×C₃×C₄	—	2	1	no	—
400	C₂²×C₃×C₄	—	2	1	no	—
401	C₂²×C₃×C₄	—	2	1	no	—
402	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
403	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
404	C₃×D₈	—	2	2	no	—
405	C₃×D₈	—	4	1	no	—
406	C₃×D₈	—	4	1	no	—
407	C₃×M₁₆	—	4	1	no	—
408	C₂×C₃×C₈	—	4	1	no	—
409	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
411	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
412	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
413	C₃×C₄⋊C₄	—	2	1	no	—
414	C₃×C₄⋊C₄	—	2	1	no	—
415	C₃×C₄⋊C₄	—	2	1	no	—
416	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
417	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
418	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
419	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
420	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
427	C₃×C₂²⋊C₄	—	2	1	no	—
428	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
429	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
430	C₃×C₄²	—	2	1	no	—
431	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
432	C₂³×C₅	—	2	1	no	—
433	C₂³×C₅	—	2	1	no	—
434	C₂³×C₅	—	2	1	no	—
435	C₂³×C₅	—	2	1	no	—
436	C₂³×C₅	—	4	2	no	—
437	C₂³×C₅	—	4	2	no	—
438	C₂³×C₅	—	4	2	no	—
439	C₂³×C₅	—	4	2	no	—
440	C₂³×C₅	—	8	1	no	—
441	C₂³×C₅	—	8	1	no	—
442	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
443	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
444	C₅×D₄	—	2	2	no	—
445	C₅×D₄	—	2	1	no	—
446	C₅×D₄	—	2	1	no	—
447	C₅×D₄	—	2	1	no	—
448	C₅×D₄	—	2	1	no	—
449	C₅×D₄	—	2	1	no	—
450	C₅×D₄	—	2	1	no	—
451	C₅×D₄	—	2	1	no	—
452	C₅×D₄	—	4	2	no	—
453	C₅×D₄	—	4	2	no	—
454	C₅×D₄	—	4	2	no	—
455	C₅×D₄	—	4	2	no	—
456	C₅×D₄	—	4	2	no	—
457	C₅×D₄	—	4	2	no	—
458	C₅×D₄	—	8	1	no	—
459	C₅×D₄	—	8	1	no	—
460	C₅×D₄	C₃×#41	1	2	yes	—
461	C₂×C₄×C₅	—	2	1	no	—
462	C₂×C₄×C₅	—	2	1	no	—
463	C₂×C₄×C₅	—	2	1	no	—
464	C₂×C₄×C₅	—	2	1	no	—
465	C₂×C₄×C₅	—	2	1	no	—
466	C₂×C₄×C₅	—	2	1	no	—
467	C₂×C₄×C₅	—	2	1	no	—
468	C₂×C₄×C₅	—	2	1	no	—
469	C₂×C₄×C₅	—	4	2	no	—
470	C₂×C₄×C₅	—	8	1	no	—
471	C₂×C₄×C₅	—	8	1	no	—
472	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
473	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
474	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
475	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
476	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
477	C₅×C₈	—	2	1	no	—
478	C₅×C₈	—	2	1	no	—
479	C₅×C₈	—	2	1	no	—
480	C₅×C₈	—	2	1	no	—
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
483	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
484	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
485	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
486	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
487	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
488	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
489	#127	C₂²×C₃×C₅	1	1	yes	characteristic
490	#126	—	2	1	no	—
491	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
492	#123	—	2	1	no	—
493	#121	—	2	1	no	—
494	#121	—	2	1	no	—
495	#121	C₂²×C₃×C₅	1	1	yes	characteristic
496	#121	C₂²×C₃×C₅	1	1	yes	characteristic
497	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
498	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
499	#120	—	2	1	no	—
500	#120	—	2	1	no	—
501	C₄×D₄	—	2	1	no	—
502	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
503	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
504	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
505	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
506	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
507	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
508	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
509	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
510	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
511	#102	C₂²×C₃×C₅	1	1	yes	characteristic
512	#102	C₂²×C₃×C₅	1	1	yes	characteristic
513	#102	C₂²×C₃×C₅	1	1	yes	characteristic
514	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
515	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
516	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
517	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
518	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
519	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
520	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
521	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
522	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
523	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
524	C₂×C₃×C₅	—	2	2	no	—
525	C₂×C₃×C₅	—	4	1	no	—
526	C₂×C₃×C₅	—	4	2	no	—
527	C₂×C₃×C₅	—	8	1	no	—
528	C₂×C₃×C₅	—	8	1	no	—
529	C₂×C₃×C₅	—	8	1	no	—
530	C₂×C₃×C₅	#546	1	1	yes	characteristic
531	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
532	C₂×C₃×C₅	#576	1	1	yes	characteristic
533	C₂³×C₃	—	2	1	no	—
534	C₂³×C₃	—	2	1	no	—
535	C₂³×C₃	—	2	1	no	—
536	C₂³×C₃	—	2	1	no	—
537	C₂³×C₃	—	4	2	no	—
538	C₂³×C₃	—	4	2	no	—
539	C₂³×C₃	—	4	2	no	—
540	C₂³×C₃	—	4	2	no	—
541	C₂³×C₃	—	8	1	no	—
542	C₂³×C₃	—	8	1	no	—
543	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
544	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
545	C₃×D₄	—	2	2	no	—
546	C₃×D₄	—	2	1	no	—
547	C₃×D₄	—	2	1	no	—
548	C₃×D₄	—	2	1	no	—
549	C₃×D₄	—	2	1	no	—
550	C₃×D₄	—	2	1	no	—
551	C₃×D₄	—	2	1	no	—
552	C₃×D₄	—	2	1	no	—
553	C₃×D₄	—	4	2	no	—
554	C₃×D₄	—	4	2	no	—
555	C₃×D₄	—	4	2	no	—
556	C₃×D₄	—	4	2	no	—
557	C₃×D₄	—	4	2	no	—
558	C₃×D₄	—	4	2	no	—
559	C₃×D₄	—	8	1	no	—
560	C₃×D₄	—	8	1	no	—
561	C₃×D₄	C₅×#41	1	2	yes	—
562	C₂×C₃×C₄	—	2	1	no	—
563	C₂×C₃×C₄	—	2	1	no	—
564	C₂×C₃×C₄	—	2	1	no	—
565	C₂×C₃×C₄	—	2	1	no	—
566	C₂×C₃×C₄	—	2	1	no	—
567	C₂×C₃×C₄	—	2	1	no	—
568	C₂×C₃×C₄	—	2	1	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	4	2	no	—
571	C₂×C₃×C₄	—	8	1	no	—
572	C₂×C₃×C₄	—	8	1	no	—
573	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
574	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
575	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
576	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
577	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
578	C₃×C₈	—	2	1	no	—
579	C₃×C₈	—	2	1	no	—
580	C₃×C₈	—	2	1	no	—
581	C₃×C₈	—	2	1	no	—
582	C₂²×C₅	—	2	1	no	—
583	C₂²×C₅	—	2	1	no	—
584	C₂²×C₅	—	2	1	no	—
585	C₂²×C₅	—	2	1	no	—
586	C₂²×C₅	—	2	1	no	—
587	C₂²×C₅	—	2	2	no	—
588	C₂²×C₅	—	4	1	no	—
589	C₂²×C₅	—	4	1	no	—
590	C₂²×C₅	—	4	1	no	—
591	C₂²×C₅	—	4	1	no	—
592	C₂²×C₅	—	4	1	no	—
593	C₂²×C₅	—	4	1	no	—
594	C₂²×C₅	—	4	1	no	—
595	C₂²×C₅	—	4	1	no	—
596	C₂²×C₅	—	4	1	no	—
597	C₂²×C₅	—	4	1	no	—
598	C₂²×C₅	—	4	1	no	—
599	C₂²×C₅	—	8	4	no	—
600	C₂²×C₅	—	8	4	no	—
601	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
602	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
603	C₄×C₅	—	2	1	no	—
604	C₄×C₅	—	2	1	no	—
605	C₄×C₅	—	2	1	no	—
606	C₄×C₅	—	2	1	no	—
607	C₄×C₅	—	4	1	no	—
608	C₄×C₅	—	4	1	no	—
609	C₄×C₅	—	4	1	no	—
610	C₄×C₅	—	4	1	no	—
611	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
612	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
613	C₂⁴	—	2	1	no	—
614	C₂⁴	—	2	1	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	4	1	no	—
626	C₂×D₄	—	4	1	no	—
627	C₂×D₄	—	4	4	no	—
628	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
629	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
630	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
631	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
632	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
637	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
638	D₈	—	2	2	no	—
639	D₈	—	4	1	no	—
640	D₈	—	4	1	no	—
641	M₁₆	—	4	1	no	—
642	C₂×C₈	—	4	1	no	—
643	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
644	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
645	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
646	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
651	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
652	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
653	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
654	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
655	C₂²⋊C₄	—	2	1	no	—
656	C₂²⋊C₄	—	2	1	no	—
657	C₂²⋊C₄	—	2	1	no	—
658	C₂²⋊C₄	—	2	1	no	—
659	C₂²⋊C₄	—	2	1	no	—
660	C₂²⋊C₄	—	2	1	no	—
661	C₂²⋊C₄	—	2	1	no	—
662	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
663	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
664	C₄²	—	2	1	no	—
665	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
666	C₃×C₅	#3318	1	1	yes	characteristic, direct product factor, Hall
667	C₂²×C₃	—	2	1	no	—
668	C₂²×C₃	—	2	1	no	—
669	C₂²×C₃	—	2	1	no	—
670	C₂²×C₃	—	2	2	no	—
671	C₂²×C₃	—	2	1	no	—
672	C₂²×C₃	—	2	1	no	—
673	C₂²×C₃	—	4	1	no	—
674	C₂²×C₃	—	4	1	no	—
675	C₂²×C₃	—	4	1	no	—
676	C₂²×C₃	—	4	1	no	—
677	C₂²×C₃	—	4	1	no	—
678	C₂²×C₃	—	4	1	no	—
679	C₂²×C₃	—	4	1	no	—
680	C₂²×C₃	—	4	1	no	—
681	C₂²×C₃	—	4	1	no	—
682	C₂²×C₃	—	4	1	no	—
683	C₂²×C₃	—	4	1	no	—
684	C₂²×C₃	—	8	4	no	—
685	C₂²×C₃	—	8	4	no	—
686	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
687	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
688	C₃×C₄	—	2	1	no	—
689	C₃×C₄	—	2	1	no	—
690	C₃×C₄	—	2	1	no	—
691	C₃×C₄	—	2	1	no	—
692	C₃×C₄	—	4	1	no	—
693	C₃×C₄	—	4	1	no	—
694	C₃×C₄	—	4	1	no	—
695	C₃×C₄	—	4	1	no	—
696	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
697	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
698	C₂×C₅	—	2	2	no	—
699	C₂×C₅	—	4	1	no	—
700	C₂×C₅	—	4	2	no	—
701	C₂×C₅	—	8	1	no	—
702	C₂×C₅	—	8	1	no	—
703	C₂×C₅	—	8	1	no	—
704	C₂×C₅	C₃×#546	1	1	yes	characteristic
705	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
706	C₂×C₅	C₃×#576	1	1	yes	characteristic
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	4	2	no	—
712	C₂³	—	4	2	no	—
713	C₂³	—	4	2	no	—
714	C₂³	—	4	2	no	—
715	C₂³	—	8	1	no	—
716	C₂³	—	8	1	no	—
717	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
718	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
719	D₄	—	2	2	no	—
720	D₄	—	2	1	no	—
721	D₄	—	2	1	no	—
722	D₄	—	2	1	no	—
723	D₄	—	2	1	no	—
724	D₄	—	2	1	no	—
725	D₄	—	2	1	no	—
726	D₄	—	2	1	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	2	no	—
729	D₄	—	4	2	no	—
730	D₄	—	4	2	no	—
731	D₄	—	4	2	no	—
732	D₄	—	4	2	no	—
733	D₄	—	8	1	no	—
734	D₄	—	8	1	no	—
735	D₄	C₃×C₅×#41	1	2	yes	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	8	1	no	—
746	C₂×C₄	—	8	1	no	—
747	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
748	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
749	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
750	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
751	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
752	C₈	—	2	1	no	—
753	C₈	—	2	1	no	—
754	C₈	—	2	1	no	—
755	C₈	—	2	1	no	—
756	C₂×C₃	—	2	2	no	—
757	C₂×C₃	—	4	1	no	—
758	C₂×C₃	—	4	2	no	—
759	C₂×C₃	—	8	1	no	—
760	C₂×C₃	—	8	1	no	—
761	C₂×C₃	—	8	1	no	—
762	C₂×C₃	C₅×#546	1	1	yes	characteristic
763	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
764	C₂×C₃	C₅×#576	1	1	yes	characteristic
765	C₅	C₃×#3318	1	1	yes	characteristic, direct product factor, Sylow
766	C₂²	—	2	1	no	—
767	C₂²	—	2	1	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	1	no	—
771	C₂²	—	2	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	8	4	no	—
784	C₂²	—	8	4	no	—
785	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
786	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	1	no	—
791	C₄	—	4	1	no	—
792	C₄	—	4	1	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	1	no	—
795	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
796	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
797	C₃	C₅×#3318	1	1	yes	characteristic, direct product factor, Sylow
798	C₂	—	2	2	no	—
799	C₂	—	4	1	no	—
800	C₂	—	4	2	no	—
801	C₂	—	8	1	no	—
802	C₂	—	8	1	no	—
803	C₂	—	8	1	no	—
804	C₂	C₃×C₅×#546	1	1	yes	characteristic
805	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
806	C₂	C₃×C₅×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
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×#553	C₂	semidirect
2. C₃×C₅×D₄²	C₂	semidirect
3. C₃×C₅×#490	C₂	semidirect
4. C₃×C₅×#482	C₂	semidirect
5. C₃×C₅×#481	C₂	semidirect
6. C₃×C₅×#478	C₂	semidirect
7. C₃×C₅×#469	C₂	semidirect
8. C₃×C₅×#466	C₂	semidirect
9. C₃×C₅×#459	C₂	semidirect
10. C₃×C₅×#447	C₂	semidirect
11. C₃×C₅×#447	C₂	semidirect
12. C₃×C₅×#442	C₂	semidirect
13. C₃×C₅×#435	C₂	semidirect
14. C₃×C₅×#418	C₂	semidirect
15. C₂×C₃×C₅×#102	C₂	semidirect
16. C₅×#3318	C₃	direct (N × H)
21. C₂×C₃×C₅×D₈	C₂²	semidirect
22. C₂×C₃×C₅×D₈	C₂²	semidirect
23. C₂×C₃×C₅×M₁₆	C₂²	semidirect
24. C₂²×C₃×C₅×C₈	C₂²	semidirect
27. C₃×C₅×#125	C₂²	semidirect
33. C₃×C₅×#121	C₂²	semidirect
34. C₃×C₅×#121	C₂²	semidirect
40. C₃×C₄×C₅×D₄	C₂²	semidirect
41. C₃×C₅×#117	C₂²	semidirect
42. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
43. C₃×C₅×#107	C₂²	semidirect
44. C₃×C₅×#106	C₂²	semidirect
45. C₃×C₅×#106	C₂²	semidirect
46. C₃×C₅×C₄⋊C₈	C₂²	semidirect
50. C₃×C₅×#102	C₂²	semidirect
51. C₃×C₅×#102	C₂²	semidirect
52. C₃×C₅×#102	C₂²	semidirect
53. C₃×C₅×#102	C₂²	semidirect
54. C₃×C₅×#102	C₂²	semidirect
55. C₃×C₅×#102	C₂²	semidirect
56. C₃×C₅×#102	C₂²	semidirect
57. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
58. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
59. C₃×C₅×#97	C₂²	semidirect
60. C₃×#3318	C₅	direct (N × H)
61. C₅×#553	C₂×C₃	semidirect
62. C₅×D₄²	C₂×C₃	semidirect
63. C₅×#490	C₂×C₃	semidirect
64. C₅×#482	C₂×C₃	semidirect
65. C₅×#481	C₂×C₃	semidirect
66. C₅×#478	C₂×C₃	semidirect
67. C₅×#469	C₂×C₃	semidirect
68. C₅×#466	C₂×C₃	semidirect
69. C₅×#459	C₂×C₃	semidirect
70. C₅×#447	C₂×C₃	semidirect
71. C₅×#447	C₂×C₃	semidirect
72. C₅×#442	C₂×C₃	semidirect
73. C₅×#435	C₂×C₃	semidirect
74. C₅×#418	C₂×C₃	semidirect
75. C₂×C₅×#102	C₂×C₃	semidirect
129. C₃×#553	C₂×C₅	semidirect
130. C₃×D₄²	C₂×C₅	semidirect
131. C₃×#490	C₂×C₅	semidirect
132. C₃×#482	C₂×C₅	semidirect
133. C₃×#481	C₂×C₅	semidirect
134. C₃×#478	C₂×C₅	semidirect
135. C₃×#469	C₂×C₅	semidirect
136. C₃×#466	C₂×C₅	semidirect
137. C₃×#459	C₂×C₅	semidirect
138. C₃×#447	C₂×C₅	semidirect
139. C₃×#447	C₂×C₅	semidirect
140. C₃×#442	C₂×C₅	semidirect
141. C₃×#435	C₂×C₅	semidirect
142. C₃×#418	C₂×C₅	semidirect
143. C₂×C₃×#102	C₂×C₅	semidirect
148. C₂×C₅×D₈	C₂²×C₃	semidirect
149. C₂×C₅×D₈	C₂²×C₃	semidirect
150. C₂×C₅×M₁₆	C₂²×C₃	semidirect
151. C₂²×C₅×C₈	C₂²×C₃	semidirect
154. C₅×#125	C₂²×C₃	semidirect
160. C₅×#121	C₂²×C₃	semidirect
161. C₅×#121	C₂²×C₃	semidirect
167. C₄×C₅×D₄	C₂²×C₃	semidirect
168. C₅×#117	C₂²×C₃	semidirect
169. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
170. C₅×#107	C₂²×C₃	semidirect
171. C₅×#106	C₂²×C₃	semidirect
172. C₅×#106	C₂²×C₃	semidirect
173. C₅×C₄⋊C₈	C₂²×C₃	semidirect
177. C₅×#102	C₂²×C₃	semidirect
178. C₅×#102	C₂²×C₃	semidirect
179. C₅×#102	C₂²×C₃	semidirect
180. C₅×#102	C₂²×C₃	semidirect
181. C₅×#102	C₂²×C₃	semidirect
182. C₅×#102	C₂²×C₃	semidirect
183. C₅×#102	C₂²×C₃	semidirect
184. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
185. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
186. C₅×#97	C₂²×C₃	semidirect
187. #3318	C₃×C₅	direct (N × H)
241. C₂×C₃×D₈	C₂²×C₅	semidirect
242. C₂×C₃×D₈	C₂²×C₅	semidirect
243. C₂×C₃×M₁₆	C₂²×C₅	semidirect
244. C₂²×C₃×C₈	C₂²×C₅	semidirect
247. C₃×#125	C₂²×C₅	semidirect
253. C₃×#121	C₂²×C₅	semidirect
254. C₃×#121	C₂²×C₅	semidirect
260. C₃×C₄×D₄	C₂²×C₅	semidirect
261. C₃×#117	C₂²×C₅	semidirect
262. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
263. C₃×#107	C₂²×C₅	semidirect
264. C₃×#106	C₂²×C₅	semidirect
265. C₃×#106	C₂²×C₅	semidirect
266. C₃×C₄⋊C₈	C₂²×C₅	semidirect
270. C₃×#102	C₂²×C₅	semidirect
271. C₃×#102	C₂²×C₅	semidirect
272. C₃×#102	C₂²×C₅	semidirect
273. C₃×#102	C₂²×C₅	semidirect
274. C₃×#102	C₂²×C₅	semidirect
275. C₃×#102	C₂²×C₅	semidirect
276. C₃×#102	C₂²×C₅	semidirect
277. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
278. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
279. C₃×#97	C₂²×C₅	semidirect
333. #553	C₂×C₃×C₅	semidirect
334. D₄²	C₂×C₃×C₅	semidirect
335. #490	C₂×C₃×C₅	semidirect
336. #482	C₂×C₃×C₅	semidirect
337. #481	C₂×C₃×C₅	semidirect
338. #478	C₂×C₃×C₅	semidirect
339. #469	C₂×C₃×C₅	semidirect
340. #466	C₂×C₃×C₅	semidirect
341. #459	C₂×C₃×C₅	semidirect
342. #447	C₂×C₃×C₅	semidirect
343. #447	C₂×C₃×C₅	semidirect
344. #442	C₂×C₃×C₅	semidirect
345. #435	C₂×C₃×C₅	semidirect
346. #418	C₂×C₃×C₅	semidirect
347. C₂×#102	C₂×C₃×C₅	semidirect
485. C₂×D₈	C₂²×C₃×C₅	semidirect
486. C₂×D₈	C₂²×C₃×C₅	semidirect
487. C₂×M₁₆	C₂²×C₃×C₅	semidirect
488. C₂²×C₈	C₂²×C₃×C₅	semidirect
491. #125	C₂²×C₃×C₅	semidirect
497. #121	C₂²×C₃×C₅	semidirect
498. #121	C₂²×C₃×C₅	semidirect
504. C₄×D₄	C₂²×C₃×C₅	semidirect
505. #117	C₂²×C₃×C₅	semidirect
506. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
507. #107	C₂²×C₃×C₅	semidirect
508. #106	C₂²×C₃×C₅	semidirect
509. #106	C₂²×C₃×C₅	semidirect
510. C₄⋊C₈	C₂²×C₃×C₅	semidirect
514. #102	C₂²×C₃×C₅	semidirect
515. #102	C₂²×C₃×C₅	semidirect
516. #102	C₂²×C₃×C₅	semidirect
517. #102	C₂²×C₃×C₅	semidirect
518. #102	C₂²×C₃×C₅	semidirect
519. #102	C₂²×C₃×C₅	semidirect
520. #102	C₂²×C₃×C₅	semidirect
521. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
522. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
523. #97	C₂²×C₃×C₅	semidirect
666. C₃×C₅	#3318	direct (N × H)
765. C₅	C₃×#3318	direct (N × H)
797. C₃	C₅×#3318	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×#553	2
C₃×C₅×D₄²	2
C₃×C₅×#490	2
C₃×C₅×#482	2
C₃×C₅×#481	2
C₃×C₅×#478	2
C₃×C₅×#469	2
C₃×C₅×#466	2
C₃×C₅×#459	2
C₃×C₅×#447	2
C₃×C₅×#442	2
C₃×C₅×#435	2
C₃×C₅×#418	2
C₂×C₃×C₅×#102	2
C₅×#3318	3
C₃×#3318	5

Subgroups — C3×C5×#3318 #14276352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3318 #14276352