Subgroups — C₃×C₅×#3267 #14276301

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#470	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#465	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3267	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	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
22	C₃×C₅×#135	—	2	4	no	—
23	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#124	C₂²	1	1	yes	characteristic
36	C₃×C₅×#123	—	2	1	no	—
37	C₃×C₅×#123	—	2	1	no	—
38	C₃×C₅×#123	—	2	1	no	—
39	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₅×#121	—	2	1	no	—
43	C₃×C₅×#121	—	2	1	no	—
44	C₃×C₅×#121	C₂²	1	1	yes	characteristic
45	C₃×C₅×#120	—	2	1	no	—
46	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
47	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
48	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
51	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
56	C₃×C₅×#102	C₂²	1	1	yes	characteristic
57	C₃×C₅×#102	C₂²	1	1	yes	characteristic
58	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
60	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
62	C₃×#3267	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#547	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#546	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#470	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#465	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#463	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#461	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#450	C₂×C₃	1	1	yes	characteristic, complemented
75	C₅×#449	C₂×C₃	1	1	yes	characteristic, complemented
76	C₅×#442	C₂×C₃	1	1	yes	characteristic, complemented
77	C₅×#435	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂⁴×C₃×C₅	—	2	1	no	—
79	C₃×C₅×#41	—	2	2	no	—
80	C₃×C₅×#41	—	2	2	no	—
81	C₃×C₅×#41	—	2	2	no	—
82	C₃×C₅×#41	—	4	1	no	—
83	C₃×C₅×#41	—	4	1	no	—
84	C₃×C₅×#41	—	4	1	no	—
85	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₅×D₄	—	2	2	no	—
89	C₂×C₃×C₅×D₄	—	2	1	no	—
90	C₂×C₃×C₅×D₄	—	2	1	no	—
91	C₂×C₃×C₅×D₄	—	2	1	no	—
92	C₂×C₃×C₅×D₄	—	2	1	no	—
93	C₂×C₃×C₅×D₄	—	2	1	no	—
94	C₂×C₃×C₅×D₄	—	4	1	no	—
95	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
96	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄×C₅	—	2	1	no	—
100	C₂²×C₃×C₄×C₅	—	2	1	no	—
101	C₂²×C₃×C₄×C₅	—	2	1	no	—
102	C₂²×C₃×C₄×C₅	—	2	1	no	—
103	C₂²×C₃×C₄×C₅	—	2	1	no	—
104	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
105	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
106	C₃×C₅×Q₁₆	—	2	2	no	—
107	C₃×C₅×Q₁₆	—	4	1	no	—
108	C₃×C₅×SD₁₆	—	2	2	no	—
109	C₃×C₅×SD₁₆	—	2	2	no	—
110	C₃×C₅×SD₁₆	—	2	2	no	—
111	C₃×C₅×SD₁₆	—	2	2	no	—
112	C₃×C₅×SD₁₆	—	4	1	no	—
113	C₃×C₅×D₈	—	2	2	no	—
114	C₃×C₅×D₈	D₄	1	4	yes	complemented
115	C₃×C₅×M₁₆	—	2	2	no	—
116	C₂×C₃×C₅×C₈	—	2	2	no	—
117	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
118	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
119	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
120	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
121	C₃×C₅×C₄⋊C₄	—	2	1	no	—
122	C₃×C₅×C₄⋊C₄	—	2	1	no	—
123	C₃×C₅×C₄⋊C₄	—	2	1	no	—
124	C₃×C₅×C₄⋊C₄	—	2	1	no	—
125	C₃×C₅×C₄⋊C₄	—	2	1	no	—
126	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
127	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
130	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
131	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
132	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
133	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
134	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
135	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
136	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
137	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
138	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
139	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
140	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
143	C₃×#546	C₂×C₅	1	1	yes	characteristic, complemented
144	C₃×#497	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#470	C₂×C₅	1	1	yes	characteristic, complemented
146	C₃×#465	C₂×C₅	1	1	yes	characteristic, complemented
147	C₃×#463	C₂×C₅	1	1	yes	characteristic, complemented
148	C₃×#461	C₂×C₅	1	1	yes	characteristic, complemented
149	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
150	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
151	C₃×#450	C₂×C₅	1	1	yes	characteristic, complemented
152	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
153	C₃×#442	C₂×C₅	1	1	yes	characteristic, complemented
154	C₃×#435	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
159	C₅×AGL(1,ℤ/8)	—	2	4	no	—
160	C₅×#135	—	2	4	no	—
161	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
162	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
166	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
167	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
169	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
170	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
171	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₅×#124	C₂²×C₃	1	1	yes	characteristic
174	C₅×#123	—	2	1	no	—
175	C₅×#123	—	2	1	no	—
176	C₅×#123	—	2	1	no	—
177	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
178	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
179	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
180	C₅×#121	—	2	1	no	—
181	C₅×#121	—	2	1	no	—
182	C₅×#121	C₂²×C₃	1	1	yes	characteristic
183	C₅×#120	—	2	1	no	—
184	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
185	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
186	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₂×C₅×C₄⋊C₄	—	2	1	no	—
188	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
189	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
190	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
194	C₅×#102	C₂²×C₃	1	1	yes	characteristic
195	C₅×#102	C₂²×C₃	1	1	yes	characteristic
196	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
198	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
199	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
200	#3267	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
201	C₂³×C₃×C₅	—	2	1	no	—
202	C₂³×C₃×C₅	—	2	1	no	—
203	C₂³×C₃×C₅	—	2	1	no	—
204	C₂³×C₃×C₅	—	4	2	no	—
205	C₂³×C₃×C₅	—	4	2	no	—
206	C₂³×C₃×C₅	—	8	1	no	—
207	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
208	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
209	C₃×C₅×Q₈	—	2	1	no	—
210	C₃×C₅×Q₈	—	2	1	no	—
211	C₃×C₅×Q₈	—	2	1	no	—
212	C₃×C₅×Q₈	—	2	1	no	—
213	C₃×C₅×Q₈	—	2	1	no	—
214	C₃×C₅×Q₈	—	2	1	no	—
215	C₃×C₅×D₄	—	2	1	no	—
216	C₃×C₅×D₄	—	2	1	no	—
217	C₃×C₅×D₄	—	2	1	no	—
218	C₃×C₅×D₄	—	2	1	no	—
219	C₃×C₅×D₄	—	4	1	no	—
220	C₃×C₅×D₄	—	4	2	no	—
221	C₃×C₅×D₄	—	4	2	no	—
222	C₃×C₅×D₄	—	4	2	no	—
223	C₃×C₅×D₄	—	4	2	no	—
224	C₃×C₅×D₄	—	8	1	no	—
225	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
226	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
227	C₂×C₃×C₄×C₅	—	2	1	no	—
228	C₂×C₃×C₄×C₅	—	2	1	no	—
229	C₂×C₃×C₄×C₅	—	2	1	no	—
230	C₂×C₃×C₄×C₅	—	2	1	no	—
231	C₂×C₃×C₄×C₅	—	2	1	no	—
232	C₂×C₃×C₄×C₅	—	2	1	no	—
233	C₂×C₃×C₄×C₅	—	2	1	no	—
234	C₂×C₃×C₄×C₅	—	2	1	no	—
235	C₂×C₃×C₄×C₅	—	2	1	no	—
236	C₂×C₃×C₄×C₅	—	4	2	no	—
237	C₂×C₃×C₄×C₅	—	4	2	no	—
238	C₂×C₃×C₄×C₅	—	4	2	no	—
239	C₂×C₃×C₄×C₅	—	4	2	no	—
240	C₂×C₃×C₄×C₅	—	8	1	no	—
241	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
242	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
243	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
245	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
246	C₃×C₅×C₈	—	2	1	no	—
247	C₃×C₅×C₈	—	2	1	no	—
248	C₃×C₅×C₈	—	2	1	no	—
249	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
250	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
253	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
254	C₃×AGL(1,ℤ/8)	—	2	4	no	—
255	C₃×#135	—	2	4	no	—
256	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
258	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
266	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₃×#124	C₂²×C₅	1	1	yes	characteristic
269	C₃×#123	—	2	1	no	—
270	C₃×#123	—	2	1	no	—
271	C₃×#123	—	2	1	no	—
272	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
273	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
274	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
275	C₃×#121	—	2	1	no	—
276	C₃×#121	—	2	1	no	—
277	C₃×#121	C₂²×C₅	1	1	yes	characteristic
278	C₃×#120	—	2	1	no	—
279	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
280	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
281	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
282	C₂×C₃×C₄⋊C₄	—	2	1	no	—
283	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
284	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
286	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
288	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
289	C₃×#102	C₂²×C₅	1	1	yes	characteristic
290	C₃×#102	C₂²×C₅	1	1	yes	characteristic
291	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
292	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
293	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
294	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
295	C₂⁴×C₅	—	2	1	no	—
296	C₅×#41	—	2	2	no	—
297	C₅×#41	—	2	2	no	—
298	C₅×#41	—	2	2	no	—
299	C₅×#41	—	4	1	no	—
300	C₅×#41	—	4	1	no	—
301	C₅×#41	—	4	1	no	—
302	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
303	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
304	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
305	C₂×C₅×D₄	—	2	2	no	—
306	C₂×C₅×D₄	—	2	1	no	—
307	C₂×C₅×D₄	—	2	1	no	—
308	C₂×C₅×D₄	—	2	1	no	—
309	C₂×C₅×D₄	—	2	1	no	—
310	C₂×C₅×D₄	—	2	1	no	—
311	C₂×C₅×D₄	—	4	1	no	—
312	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
313	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
314	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
315	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
316	C₂²×C₄×C₅	—	2	1	no	—
317	C₂²×C₄×C₅	—	2	1	no	—
318	C₂²×C₄×C₅	—	2	1	no	—
319	C₂²×C₄×C₅	—	2	1	no	—
320	C₂²×C₄×C₅	—	2	1	no	—
321	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
322	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
323	C₅×Q₁₆	—	2	2	no	—
324	C₅×Q₁₆	—	4	1	no	—
325	C₅×SD₁₆	—	2	2	no	—
326	C₅×SD₁₆	—	2	2	no	—
327	C₅×SD₁₆	—	2	2	no	—
328	C₅×SD₁₆	—	2	2	no	—
329	C₅×SD₁₆	—	4	1	no	—
330	C₅×D₈	—	2	2	no	—
331	C₅×D₈	C₃×D₄	1	4	yes	complemented
332	C₅×M₁₆	—	2	2	no	—
333	C₂×C₅×C₈	—	2	2	no	—
334	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
335	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
336	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
337	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
338	C₅×C₄⋊C₄	—	2	1	no	—
339	C₅×C₄⋊C₄	—	2	1	no	—
340	C₅×C₄⋊C₄	—	2	1	no	—
341	C₅×C₄⋊C₄	—	2	1	no	—
342	C₅×C₄⋊C₄	—	2	1	no	—
343	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
344	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
345	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
346	C₅×C₂²⋊C₄	—	2	1	no	—
347	C₅×C₂²⋊C₄	—	2	1	no	—
348	C₅×C₂²⋊C₄	—	2	1	no	—
349	C₅×C₂²⋊C₄	—	2	1	no	—
350	C₅×C₂²⋊C₄	—	2	1	no	—
351	C₅×C₂²⋊C₄	—	2	1	no	—
352	C₅×C₂²⋊C₄	—	2	1	no	—
353	C₅×C₂²⋊C₄	—	2	1	no	—
354	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
355	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
356	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
357	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	1	yes	characteristic, complemented
358	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic, complemented
359	#547	C₂×C₃×C₅	1	1	yes	characteristic, complemented
360	#546	C₂×C₃×C₅	1	1	yes	characteristic, complemented
361	#497	C₂×C₃×C₅	1	1	yes	characteristic, complemented
362	#470	C₂×C₃×C₅	1	1	yes	characteristic, complemented
363	#465	C₂×C₃×C₅	1	1	yes	characteristic, complemented
364	#463	C₂×C₃×C₅	1	1	yes	characteristic, complemented
365	#461	C₂×C₃×C₅	1	1	yes	characteristic, complemented
366	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
367	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
368	#450	C₂×C₃×C₅	1	1	yes	characteristic, complemented
369	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
370	#442	C₂×C₃×C₅	1	1	yes	characteristic, complemented
371	#435	C₂×C₃×C₅	1	1	yes	characteristic, complemented
372	C₂²×C₃×C₅	—	2	1	no	—
373	C₂²×C₃×C₅	—	2	1	no	—
374	C₂²×C₃×C₅	—	2	2	no	—
375	C₂²×C₃×C₅	—	2	2	no	—
376	C₂²×C₃×C₅	—	2	1	no	—
377	C₂²×C₃×C₅	—	2	1	no	—
378	C₂²×C₃×C₅	—	2	1	no	—
379	C₂²×C₃×C₅	—	2	1	no	—
380	C₂²×C₃×C₅	—	4	1	no	—
381	C₂²×C₃×C₅	—	4	1	no	—
382	C₂²×C₃×C₅	—	4	1	no	—
383	C₂²×C₃×C₅	—	4	1	no	—
384	C₂²×C₃×C₅	—	4	1	no	—
385	C₂²×C₃×C₅	—	4	1	no	—
386	C₂²×C₃×C₅	—	4	1	no	—
387	C₂²×C₃×C₅	—	8	4	no	—
388	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
389	C₃×C₄×C₅	—	2	1	no	—
390	C₃×C₄×C₅	—	2	1	no	—
391	C₃×C₄×C₅	—	2	1	no	—
392	C₃×C₄×C₅	—	2	1	no	—
393	C₃×C₄×C₅	—	4	1	no	—
394	C₃×C₄×C₅	—	4	1	no	—
395	C₃×C₄×C₅	—	4	1	no	—
396	C₃×C₄×C₅	—	4	1	no	—
397	C₃×C₄×C₅	—	4	1	no	—
398	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
399	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
400	C₂⁴×C₃	—	2	1	no	—
401	C₃×#41	—	2	2	no	—
402	C₃×#41	—	2	2	no	—
403	C₃×#41	—	2	2	no	—
404	C₃×#41	—	4	1	no	—
405	C₃×#41	—	4	1	no	—
406	C₃×#41	—	4	1	no	—
407	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
408	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
409	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₃×D₄	—	2	2	no	—
411	C₂×C₃×D₄	—	2	1	no	—
412	C₂×C₃×D₄	—	2	1	no	—
413	C₂×C₃×D₄	—	2	1	no	—
414	C₂×C₃×D₄	—	2	1	no	—
415	C₂×C₃×D₄	—	2	1	no	—
416	C₂×C₃×D₄	—	4	1	no	—
417	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
418	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
419	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
420	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
421	C₂²×C₃×C₄	—	2	1	no	—
422	C₂²×C₃×C₄	—	2	1	no	—
423	C₂²×C₃×C₄	—	2	1	no	—
424	C₂²×C₃×C₄	—	2	1	no	—
425	C₂²×C₃×C₄	—	2	1	no	—
426	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
427	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
428	C₃×Q₁₆	—	2	2	no	—
429	C₃×Q₁₆	—	4	1	no	—
430	C₃×SD₁₆	—	2	2	no	—
431	C₃×SD₁₆	—	2	2	no	—
432	C₃×SD₁₆	—	2	2	no	—
433	C₃×SD₁₆	—	2	2	no	—
434	C₃×SD₁₆	—	4	1	no	—
435	C₃×D₈	—	2	2	no	—
436	C₃×D₈	C₅×D₄	1	4	yes	complemented
437	C₃×M₁₆	—	2	2	no	—
438	C₂×C₃×C₈	—	2	2	no	—
439	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
440	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
441	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
442	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
443	C₃×C₄⋊C₄	—	2	1	no	—
444	C₃×C₄⋊C₄	—	2	1	no	—
445	C₃×C₄⋊C₄	—	2	1	no	—
446	C₃×C₄⋊C₄	—	2	1	no	—
447	C₃×C₄⋊C₄	—	2	1	no	—
448	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
449	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
450	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
451	C₃×C₂²⋊C₄	—	2	1	no	—
452	C₃×C₂²⋊C₄	—	2	1	no	—
453	C₃×C₂²⋊C₄	—	2	1	no	—
454	C₃×C₂²⋊C₄	—	2	1	no	—
455	C₃×C₂²⋊C₄	—	2	1	no	—
456	C₃×C₂²⋊C₄	—	2	1	no	—
457	C₃×C₂²⋊C₄	—	2	1	no	—
458	C₃×C₂²⋊C₄	—	2	1	no	—
459	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
460	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
461	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
462	C₂³×C₅	—	2	1	no	—
463	C₂³×C₅	—	2	1	no	—
464	C₂³×C₅	—	2	1	no	—
465	C₂³×C₅	—	4	2	no	—
466	C₂³×C₅	—	4	2	no	—
467	C₂³×C₅	—	8	1	no	—
468	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
469	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
470	C₅×Q₈	—	2	1	no	—
471	C₅×Q₈	—	2	1	no	—
472	C₅×Q₈	—	2	1	no	—
473	C₅×Q₈	—	2	1	no	—
474	C₅×Q₈	—	2	1	no	—
475	C₅×Q₈	—	2	1	no	—
476	C₅×D₄	—	2	1	no	—
477	C₅×D₄	—	2	1	no	—
478	C₅×D₄	—	2	1	no	—
479	C₅×D₄	—	2	1	no	—
480	C₅×D₄	—	4	1	no	—
481	C₅×D₄	—	4	2	no	—
482	C₅×D₄	—	4	2	no	—
483	C₅×D₄	—	4	2	no	—
484	C₅×D₄	—	4	2	no	—
485	C₅×D₄	—	8	1	no	—
486	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
487	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
488	C₂×C₄×C₅	—	2	1	no	—
489	C₂×C₄×C₅	—	2	1	no	—
490	C₂×C₄×C₅	—	2	1	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	2	1	no	—
493	C₂×C₄×C₅	—	2	1	no	—
494	C₂×C₄×C₅	—	2	1	no	—
495	C₂×C₄×C₅	—	2	1	no	—
496	C₂×C₄×C₅	—	2	1	no	—
497	C₂×C₄×C₅	—	4	2	no	—
498	C₂×C₄×C₅	—	4	2	no	—
499	C₂×C₄×C₅	—	4	2	no	—
500	C₂×C₄×C₅	—	4	2	no	—
501	C₂×C₄×C₅	—	8	1	no	—
502	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
503	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
504	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
505	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
506	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
507	C₅×C₈	—	2	1	no	—
508	C₅×C₈	—	2	1	no	—
509	C₅×C₈	—	2	1	no	—
510	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
511	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
512	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
513	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
514	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
515	AGL(1,ℤ/8)	—	2	4	no	—
516	#135	—	2	4	no	—
517	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
518	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
519	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
520	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
521	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
522	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
523	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
524	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
525	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
526	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
527	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
528	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
529	#124	C₂²×C₃×C₅	1	1	yes	characteristic
530	#123	—	2	1	no	—
531	#123	—	2	1	no	—
532	#123	—	2	1	no	—
533	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
534	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
535	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
536	#121	—	2	1	no	—
537	#121	—	2	1	no	—
538	#121	C₂²×C₃×C₅	1	1	yes	characteristic
539	#120	—	2	1	no	—
540	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
541	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
542	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
543	C₂×C₄⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
546	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
547	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
548	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
549	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
550	#102	C₂²×C₃×C₅	1	1	yes	characteristic
551	#102	C₂²×C₃×C₅	1	1	yes	characteristic
552	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
553	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
554	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
555	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
556	C₂×C₃×C₅	—	4	1	no	—
557	C₂×C₃×C₅	—	4	1	no	—
558	C₂×C₃×C₅	—	4	2	no	—
559	C₂×C₃×C₅	—	4	2	no	—
560	C₂×C₃×C₅	—	8	1	no	—
561	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
562	C₂×C₃×C₅	#575	1	1	yes	characteristic
563	C₂×C₃×C₅	#577	1	1	yes	characteristic
564	C₂³×C₃	—	2	1	no	—
565	C₂³×C₃	—	2	1	no	—
566	C₂³×C₃	—	2	1	no	—
567	C₂³×C₃	—	4	2	no	—
568	C₂³×C₃	—	4	2	no	—
569	C₂³×C₃	—	8	1	no	—
570	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
571	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
572	C₃×Q₈	—	2	1	no	—
573	C₃×Q₈	—	2	1	no	—
574	C₃×Q₈	—	2	1	no	—
575	C₃×Q₈	—	2	1	no	—
576	C₃×Q₈	—	2	1	no	—
577	C₃×Q₈	—	2	1	no	—
578	C₃×D₄	—	2	1	no	—
579	C₃×D₄	—	2	1	no	—
580	C₃×D₄	—	2	1	no	—
581	C₃×D₄	—	2	1	no	—
582	C₃×D₄	—	4	1	no	—
583	C₃×D₄	—	4	2	no	—
584	C₃×D₄	—	4	2	no	—
585	C₃×D₄	—	4	2	no	—
586	C₃×D₄	—	4	2	no	—
587	C₃×D₄	—	8	1	no	—
588	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
589	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
590	C₂×C₃×C₄	—	2	1	no	—
591	C₂×C₃×C₄	—	2	1	no	—
592	C₂×C₃×C₄	—	2	1	no	—
593	C₂×C₃×C₄	—	2	1	no	—
594	C₂×C₃×C₄	—	2	1	no	—
595	C₂×C₃×C₄	—	2	1	no	—
596	C₂×C₃×C₄	—	2	1	no	—
597	C₂×C₃×C₄	—	2	1	no	—
598	C₂×C₃×C₄	—	2	1	no	—
599	C₂×C₃×C₄	—	4	2	no	—
600	C₂×C₃×C₄	—	4	2	no	—
601	C₂×C₃×C₄	—	4	2	no	—
602	C₂×C₃×C₄	—	4	2	no	—
603	C₂×C₃×C₄	—	8	1	no	—
604	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
605	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
606	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
607	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
608	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
609	C₃×C₈	—	2	1	no	—
610	C₃×C₈	—	2	1	no	—
611	C₃×C₈	—	2	1	no	—
612	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
613	C₂²×C₅	—	2	1	no	—
614	C₂²×C₅	—	2	1	no	—
615	C₂²×C₅	—	2	1	no	—
616	C₂²×C₅	—	2	1	no	—
617	C₂²×C₅	—	2	1	no	—
618	C₂²×C₅	—	2	1	no	—
619	C₂²×C₅	—	2	2	no	—
620	C₂²×C₅	—	2	2	no	—
621	C₂²×C₅	—	4	1	no	—
622	C₂²×C₅	—	4	1	no	—
623	C₂²×C₅	—	4	1	no	—
624	C₂²×C₅	—	4	1	no	—
625	C₂²×C₅	—	4	1	no	—
626	C₂²×C₅	—	4	1	no	—
627	C₂²×C₅	—	4	1	no	—
628	C₂²×C₅	—	8	4	no	—
629	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
630	C₄×C₅	—	2	1	no	—
631	C₄×C₅	—	2	1	no	—
632	C₄×C₅	—	2	1	no	—
633	C₄×C₅	—	2	1	no	—
634	C₄×C₅	—	4	1	no	—
635	C₄×C₅	—	4	1	no	—
636	C₄×C₅	—	4	1	no	—
637	C₄×C₅	—	4	1	no	—
638	C₄×C₅	—	4	1	no	—
639	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
640	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
641	C₂⁴	—	2	1	no	—
642	#41	—	2	2	no	—
643	#41	—	2	2	no	—
644	#41	—	2	2	no	—
645	#41	—	4	1	no	—
646	#41	—	4	1	no	—
647	#41	—	4	1	no	—
648	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
649	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
650	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
651	C₂×D₄	—	2	2	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	1	no	—
656	C₂×D₄	—	2	1	no	—
657	C₂×D₄	—	4	1	no	—
658	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
659	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
660	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
661	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
668	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
669	Q₁₆	—	2	2	no	—
670	Q₁₆	—	4	1	no	—
671	SD₁₆	—	2	2	no	—
672	SD₁₆	—	2	2	no	—
673	SD₁₆	—	2	2	no	—
674	SD₁₆	—	2	2	no	—
675	SD₁₆	—	4	1	no	—
676	D₈	—	2	2	no	—
677	D₈	C₃×C₅×D₄	1	4	yes	complemented
678	M₁₆	—	2	2	no	—
679	C₂×C₈	—	2	2	no	—
680	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
681	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
682	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
683	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
690	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
691	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	1	no	—
695	C₂²⋊C₄	—	2	1	no	—
696	C₂²⋊C₄	—	2	1	no	—
697	C₂²⋊C₄	—	2	1	no	—
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	2	1	no	—
700	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
701	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
702	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
703	C₃×C₅	#3267	1	1	yes	characteristic, direct product factor, Hall
704	C₂²×C₃	—	2	1	no	—
705	C₂²×C₃	—	2	1	no	—
706	C₂²×C₃	—	2	2	no	—
707	C₂²×C₃	—	2	2	no	—
708	C₂²×C₃	—	2	1	no	—
709	C₂²×C₃	—	2	1	no	—
710	C₂²×C₃	—	2	1	no	—
711	C₂²×C₃	—	2	1	no	—
712	C₂²×C₃	—	4	1	no	—
713	C₂²×C₃	—	4	1	no	—
714	C₂²×C₃	—	4	1	no	—
715	C₂²×C₃	—	4	1	no	—
716	C₂²×C₃	—	4	1	no	—
717	C₂²×C₃	—	4	1	no	—
718	C₂²×C₃	—	4	1	no	—
719	C₂²×C₃	—	8	4	no	—
720	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
721	C₃×C₄	—	2	1	no	—
722	C₃×C₄	—	2	1	no	—
723	C₃×C₄	—	2	1	no	—
724	C₃×C₄	—	2	1	no	—
725	C₃×C₄	—	4	1	no	—
726	C₃×C₄	—	4	1	no	—
727	C₃×C₄	—	4	1	no	—
728	C₃×C₄	—	4	1	no	—
729	C₃×C₄	—	4	1	no	—
730	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
731	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
732	C₂×C₅	—	4	1	no	—
733	C₂×C₅	—	4	1	no	—
734	C₂×C₅	—	4	2	no	—
735	C₂×C₅	—	4	2	no	—
736	C₂×C₅	—	8	1	no	—
737	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
738	C₂×C₅	C₃×#575	1	1	yes	characteristic
739	C₂×C₅	C₃×#577	1	1	yes	characteristic
740	C₂³	—	2	1	no	—
741	C₂³	—	2	1	no	—
742	C₂³	—	2	1	no	—
743	C₂³	—	4	2	no	—
744	C₂³	—	4	2	no	—
745	C₂³	—	8	1	no	—
746	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
747	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
748	Q₈	—	2	1	no	—
749	Q₈	—	2	1	no	—
750	Q₈	—	2	1	no	—
751	Q₈	—	2	1	no	—
752	Q₈	—	2	1	no	—
753	Q₈	—	2	1	no	—
754	D₄	—	2	1	no	—
755	D₄	—	2	1	no	—
756	D₄	—	2	1	no	—
757	D₄	—	2	1	no	—
758	D₄	—	4	1	no	—
759	D₄	—	4	2	no	—
760	D₄	—	4	2	no	—
761	D₄	—	4	2	no	—
762	D₄	—	4	2	no	—
763	D₄	—	8	1	no	—
764	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
765	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	2	no	—
777	C₂×C₄	—	4	2	no	—
778	C₂×C₄	—	4	2	no	—
779	C₂×C₄	—	8	1	no	—
780	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
781	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
782	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
783	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
784	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
785	C₈	—	2	1	no	—
786	C₈	—	2	1	no	—
787	C₈	—	2	1	no	—
788	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
789	C₂×C₃	—	4	1	no	—
790	C₂×C₃	—	4	1	no	—
791	C₂×C₃	—	4	2	no	—
792	C₂×C₃	—	4	2	no	—
793	C₂×C₃	—	8	1	no	—
794	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
795	C₂×C₃	C₅×#575	1	1	yes	characteristic
796	C₂×C₃	C₅×#577	1	1	yes	characteristic
797	C₅	C₃×#3267	1	1	yes	characteristic, direct product factor, Sylow
798	C₂²	—	2	1	no	—
799	C₂²	—	2	1	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	8	4	no	—
814	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	2	1	no	—
819	C₄	—	4	1	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	1	no	—
824	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
825	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
826	C₃	C₅×#3267	1	1	yes	characteristic, direct product factor, Sylow
827	C₂	—	4	1	no	—
828	C₂	—	4	1	no	—
829	C₂	—	4	2	no	—
830	C₂	—	4	2	no	—
831	C₂	—	8	1	no	—
832	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
833	C₂	C₃×C₅×#575	1	1	yes	characteristic
834	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
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. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₃×C₅×#135	C₂	semidirect
3. C₃×C₅×#547	C₂	semidirect
4. C₃×C₅×#546	C₂	semidirect
5. C₃×C₅×#497	C₂	semidirect
6. C₃×C₅×#470	C₂	semidirect
7. C₃×C₅×#465	C₂	semidirect
8. C₃×C₅×#463	C₂	semidirect
9. C₃×C₅×#461	C₂	semidirect
10. C₃×C₅×#452	C₂	semidirect
11. C₃×C₅×#452	C₂	semidirect
12. C₃×C₅×#450	C₂	semidirect
13. C₃×C₅×#449	C₂	semidirect
14. C₃×C₅×#442	C₂	semidirect
15. C₃×C₅×#435	C₂	semidirect
16. C₅×#3267	C₃	direct (N × H)
19. C₂×C₃×C₅×#41	C₂²	semidirect
23. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
24. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
29. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
33. C₂²×C₃×C₅×C₈	C₂²	semidirect
34. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
41. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
48. C₃×C₄×C₅×D₄	C₂²	semidirect
51. C₃×C₅×#106	C₂²	semidirect
52. C₃×C₅×C₄⋊C₈	C₂²	semidirect
53. C₃×C₅×#103	C₂²	semidirect
54. C₃×C₅×#103	C₂²	semidirect
55. C₃×C₅×#103	C₂²	semidirect
58. C₃×C₅×#102	C₂²	semidirect
60. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
61. C₃×C₅×#97	C₂²	semidirect
62. C₃×#3267	C₅	direct (N × H)
63. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
64. C₂×C₅×#135	C₂×C₃	semidirect
65. C₅×#547	C₂×C₃	semidirect
66. C₅×#546	C₂×C₃	semidirect
67. C₅×#497	C₂×C₃	semidirect
68. C₅×#470	C₂×C₃	semidirect
69. C₅×#465	C₂×C₃	semidirect
70. C₅×#463	C₂×C₃	semidirect
71. C₅×#461	C₂×C₃	semidirect
72. C₅×#452	C₂×C₃	semidirect
73. C₅×#452	C₂×C₃	semidirect
74. C₅×#450	C₂×C₃	semidirect
75. C₅×#449	C₂×C₃	semidirect
76. C₅×#442	C₂×C₃	semidirect
77. C₅×#435	C₂×C₃	semidirect
114. C₃×C₅×D₈	D₄	semidirect
140. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
141. C₂×C₃×#135	C₂×C₅	semidirect
142. C₃×#547	C₂×C₅	semidirect
143. C₃×#546	C₂×C₅	semidirect
144. C₃×#497	C₂×C₅	semidirect
145. C₃×#470	C₂×C₅	semidirect
146. C₃×#465	C₂×C₅	semidirect
147. C₃×#463	C₂×C₅	semidirect
148. C₃×#461	C₂×C₅	semidirect
149. C₃×#452	C₂×C₅	semidirect
150. C₃×#452	C₂×C₅	semidirect
151. C₃×#450	C₂×C₅	semidirect
152. C₃×#449	C₂×C₅	semidirect
153. C₃×#442	C₂×C₅	semidirect
154. C₃×#435	C₂×C₅	semidirect
157. C₂×C₅×#41	C₂²×C₃	semidirect
161. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
162. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
167. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
171. C₂²×C₅×C₈	C₂²×C₃	semidirect
172. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
179. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
186. C₄×C₅×D₄	C₂²×C₃	semidirect
189. C₅×#106	C₂²×C₃	semidirect
190. C₅×C₄⋊C₈	C₂²×C₃	semidirect
191. C₅×#103	C₂²×C₃	semidirect
192. C₅×#103	C₂²×C₃	semidirect
193. C₅×#103	C₂²×C₃	semidirect
196. C₅×#102	C₂²×C₃	semidirect
198. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
199. C₅×#97	C₂²×C₃	semidirect
200. #3267	C₃×C₅	direct (N × H)
252. C₂×C₃×#41	C₂²×C₅	semidirect
256. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
257. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
262. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
266. C₂²×C₃×C₈	C₂²×C₅	semidirect
267. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
274. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
281. C₃×C₄×D₄	C₂²×C₅	semidirect
284. C₃×#106	C₂²×C₅	semidirect
285. C₃×C₄⋊C₈	C₂²×C₅	semidirect
286. C₃×#103	C₂²×C₅	semidirect
287. C₃×#103	C₂²×C₅	semidirect
288. C₃×#103	C₂²×C₅	semidirect
291. C₃×#102	C₂²×C₅	semidirect
293. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
294. C₃×#97	C₂²×C₅	semidirect
331. C₅×D₈	C₃×D₄	semidirect
357. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
358. C₂×#135	C₂×C₃×C₅	semidirect
359. #547	C₂×C₃×C₅	semidirect
360. #546	C₂×C₃×C₅	semidirect
361. #497	C₂×C₃×C₅	semidirect
362. #470	C₂×C₃×C₅	semidirect
363. #465	C₂×C₃×C₅	semidirect
364. #463	C₂×C₃×C₅	semidirect
365. #461	C₂×C₃×C₅	semidirect
366. #452	C₂×C₃×C₅	semidirect
367. #452	C₂×C₃×C₅	semidirect
368. #450	C₂×C₃×C₅	semidirect
369. #449	C₂×C₃×C₅	semidirect
370. #442	C₂×C₃×C₅	semidirect
371. #435	C₂×C₃×C₅	semidirect
436. C₃×D₈	C₅×D₄	semidirect
513. C₂×#41	C₂²×C₃×C₅	semidirect
517. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
518. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
523. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
527. C₂²×C₈	C₂²×C₃×C₅	semidirect
528. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
535. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
542. C₄×D₄	C₂²×C₃×C₅	semidirect
545. #106	C₂²×C₃×C₅	semidirect
546. C₄⋊C₈	C₂²×C₃×C₅	semidirect
547. #103	C₂²×C₃×C₅	semidirect
548. #103	C₂²×C₃×C₅	semidirect
549. #103	C₂²×C₃×C₅	semidirect
552. #102	C₂²×C₃×C₅	semidirect
554. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
555. #97	C₂²×C₃×C₅	semidirect
677. D₈	C₃×C₅×D₄	semidirect
703. C₃×C₅	#3267	direct (N × H)
797. C₅	C₃×#3267	direct (N × H)
826. C₃	C₅×#3267	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×AGL(1,ℤ/8)	2
C₂×C₃×C₅×#135	2
C₃×C₅×#547	2
C₃×C₅×#546	2
C₃×C₅×#497	2
C₃×C₅×#470	2
C₃×C₅×#465	2
C₃×C₅×#463	2
C₃×C₅×#461	2
C₃×C₅×#452	2
C₃×C₅×#450	2
C₃×C₅×#449	2
C₃×C₅×#442	2
C₃×C₅×#435	2
C₅×#3267	3
C₃×#3267	5

Subgroups — C3×C5×#3267 #14276301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3267 #14276301