Subgroups — C₅×D₃×#435 #14414675

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5127	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5111	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4836	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4730	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4728	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×D₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4706	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#435	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×D₄	C₄	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₅×D₄×Dic₃	C₄	1	1	yes	characteristic
24	C₄×C₅×#67	C₂²	1	1	yes	characteristic
25	C₄×C₅×#67	C₂²	1	1	yes	characteristic
26	C₂×C₅×#208	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
28	C₅×D₃×M₁₆	—	2	4	no	—
29	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×D₃×C₈	—	2	4	no	—
32	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
33	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
34	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
35	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
36	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
38	C₅×#893	C₄	1	1	yes	characteristic
39	C₅×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
40	C₅×#67⋊C₄	C₄	1	1	yes	characteristic
41	C₅×#67⋊C₄	C₄	1	1	yes	characteristic
42	C₅×D₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
43	C₅×D₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
44	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
45	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
50	C₅×#830	C₂²	1	1	yes	characteristic, complemented
51	C₅×#830	C₂²	1	1	yes	characteristic, complemented
52	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₅×#815	C₂²	1	1	yes	characteristic, complemented
57	C₅×#815	C₂²	1	1	yes	characteristic, complemented
58	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
61	C₅×#803	C₂²	1	1	yes	characteristic, complemented
62	D₃×#435	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂²×C₅×M₁₆	—	3	1	no	—
64	C₂³×C₅×C₈	—	3	1	no	—
65	C₂×C₄×C₅×D₄	—	3	1	no	—
66	C₅×#435	—	3	1	no	—
67	C₅×#435	—	3	1	no	—
68	C₅×#435	—	3	1	no	—
69	C₅×#435	—	3	1	no	—
70	C₅×#435	—	3	1	no	—
71	C₅×#435	—	3	1	no	—
72	C₅×#435	—	3	1	no	—
73	C₅×#435	D₃	1	1	yes	characteristic, direct product factor
74	C₂×C₅×C₄⋊C₈	—	3	1	no	—
75	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
76	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
77	C₂×C₅×#97	—	3	1	no	—
78	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
84	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
87	C₅×D₃×D₄	—	2	4	no	—
88	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄×C₅×D₃	—	2	2	no	—
90	C₂×C₄×C₅×D₃	—	2	2	no	—
91	C₂×C₄×C₅×D₃	—	2	2	no	—
92	C₂×C₄×C₅×D₃	—	2	2	no	—
93	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
100	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
101	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
102	C₃×C₅×M₁₆	—	2	2	no	—
103	C₂×C₃×C₅×C₈	—	2	2	no	—
104	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
108	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₅×#217	C₂×C₄	1	1	yes	characteristic
113	C₅×#217	C₂×C₄	1	1	yes	characteristic
114	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
119	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
121	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
122	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
123	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
124	C₅×#208	—	2	2	no	—
125	C₂×C₅×C₃⋊C₈	—	2	2	no	—
126	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
127	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
128	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
129	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
130	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
131	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
132	C₅×D₃×C₈	—	2	2	no	—
133	C₅×D₃×C₈	—	2	2	no	—
134	C₅×D₃×C₈	—	2	2	no	—
135	C₅×D₃×C₈	—	2	2	no	—
136	C₅×D₃×C₈	—	2	2	no	—
137	C₅×D₃×C₈	D₄	1	4	yes	complemented
138	C₂×D₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
139	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
140	C₄×D₃×D₄	C₂×C₅	1	1	yes	characteristic
141	C₃×#435	C₂×C₅	1	1	yes	characteristic, complemented
142	#5127	C₂×C₅	1	1	yes	characteristic, complemented
143	#5111	C₂×C₅	1	1	yes	characteristic, complemented
144	#5011	C₂×C₅	1	1	yes	characteristic, complemented
145	#4836	C₂×C₅	1	1	yes	characteristic, complemented
146	D₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
147	#4730	C₂×C₅	1	1	yes	characteristic, complemented
148	#4728	C₂×C₅	1	1	yes	characteristic, complemented
149	D₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
150	D₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
151	#4706	C₂×C₅	1	1	yes	characteristic, complemented
152	D₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂²×C₅×D₄	—	3	1	no	—
154	C₂³×C₄×C₅	—	3	1	no	—
155	C₂³×C₄×C₅	—	3	1	no	—
156	C₂×C₅×M₁₆	—	3	1	no	—
157	C₂×C₅×M₁₆	—	3	1	no	—
158	C₂×C₅×M₁₆	—	3	1	no	—
159	C₂×C₅×M₁₆	—	6	4	no	—
160	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
161	C₂²×C₅×C₈	—	3	1	no	—
162	C₂²×C₅×C₈	—	3	1	no	—
163	C₂²×C₅×C₈	—	3	1	no	—
164	C₂²×C₅×C₈	—	3	1	no	—
165	C₂²×C₅×C₈	—	3	1	no	—
166	C₂²×C₅×C₈	—	3	1	no	—
167	C₂²×C₅×C₈	—	3	1	no	—
168	C₂²×C₅×C₈	—	6	4	no	—
169	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
170	C₄×C₅×D₄	—	3	1	no	—
171	C₄×C₅×D₄	—	3	1	no	—
172	C₄×C₅×D₄	—	3	1	no	—
173	C₄×C₅×D₄	—	3	1	no	—
174	C₄×C₅×D₄	—	3	1	no	—
175	C₄×C₅×D₄	—	3	1	no	—
176	C₄×C₅×D₄	—	3	1	no	—
177	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
178	C₂×C₅×C₄⋊C₄	—	3	1	no	—
179	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
180	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
181	C₂×C₄²×C₅	—	3	1	no	—
182	C₅×C₄⋊C₈	—	3	1	no	—
183	C₅×C₄⋊C₈	—	3	1	no	—
184	C₅×C₄⋊C₈	—	3	1	no	—
185	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
186	C₅×C₂²⋊C₈	—	3	1	no	—
187	C₅×C₂²⋊C₈	—	3	1	no	—
188	C₅×C₂²⋊C₈	—	3	1	no	—
189	C₅×C₂²⋊C₈	—	3	1	no	—
190	C₅×C₂²⋊C₈	—	3	1	no	—
191	C₅×C₂²⋊C₈	—	3	1	no	—
192	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
193	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
194	C₅×#97	—	3	1	no	—
195	C₅×#97	—	3	1	no	—
196	C₅×#97	—	3	1	no	—
197	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
198	C₂×#435	—	3	1	no	Sylow
199	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
200	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₅×D₃	—	2	2	no	—
202	C₂²×C₅×D₃	—	2	2	no	—
203	C₂²×C₅×D₃	—	2	2	no	—
204	C₂²×C₅×D₃	—	2	2	no	—
205	C₂²×C₅×D₃	—	2	2	no	—
206	C₂²×C₅×D₃	M₁₆	1	4	yes	complemented
207	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
210	C₃×C₅×D₄	—	2	2	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	1	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
220	C₅×#67	—	2	2	no	—
221	C₅×#67	—	2	2	no	—
222	C₂×C₅×Dic₃	—	2	2	no	—
223	C₂×C₅×Dic₃	—	2	2	no	—
224	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
225	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
226	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
227	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
228	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
229	C₅×D₁₂	—	2	2	no	—
230	C₄×C₅×D₃	—	2	2	no	—
231	C₄×C₅×D₃	—	2	2	no	—
232	C₄×C₅×D₃	—	2	2	no	—
233	C₄×C₅×D₃	—	2	2	no	—
234	C₄×C₅×D₃	—	2	1	no	—
235	C₄×C₅×D₃	—	2	1	no	—
236	C₄×C₅×D₃	—	2	1	no	—
237	C₄×C₅×D₃	—	2	1	no	—
238	C₄×C₅×D₃	—	2	2	no	—
239	C₄×C₅×D₃	—	2	2	no	—
240	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
241	C₄×C₅×D₃	#41	1	2	yes	—
242	C₃×C₅×C₈	—	2	1	no	—
243	C₃×C₅×C₈	—	2	1	no	—
244	C₃×C₅×C₈	—	2	1	no	—
245	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
246	C₅×C₃⋊C₈	—	2	1	no	—
247	C₅×C₃⋊C₈	—	2	1	no	—
248	C₅×C₃⋊C₈	—	2	1	no	—
249	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	complemented
250	C₂×D₃×D₄	C₄×C₅	1	1	yes	characteristic
251	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
252	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
254	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
256	D₄×Dic₃	C₄×C₅	1	1	yes	characteristic
257	C₄×#67	C₂²×C₅	1	1	yes	characteristic
258	C₄×#67	C₂²×C₅	1	1	yes	characteristic
259	C₂×#208	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
261	D₃×M₁₆	—	2	4	no	—
262	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₂×D₃×C₈	—	2	4	no	—
265	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
266	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
267	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
268	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
269	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
271	#893	C₄×C₅	1	1	yes	characteristic
272	D₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
273	#67⋊C₄	C₄×C₅	1	1	yes	characteristic
274	#67⋊C₄	C₄×C₅	1	1	yes	characteristic
275	D₃×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
276	D₃×C₂²⋊C₄	C₄×C₅	1	1	yes	characteristic
277	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
278	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
279	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
280	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
281	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
282	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
283	#830	C₂²×C₅	1	1	yes	characteristic, complemented
284	#830	C₂²×C₅	1	1	yes	characteristic, complemented
285	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
286	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
287	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
288	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
289	#815	C₂²×C₅	1	1	yes	characteristic, complemented
290	#815	C₂²×C₅	1	1	yes	characteristic, complemented
291	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
292	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
293	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
294	#803	C₂²×C₅	1	1	yes	characteristic, complemented
295	C₂⁴×C₅	—	3	1	no	—
296	C₂⁴×C₅	—	3	1	no	—
297	C₂×C₅×D₄	—	3	1	no	—
298	C₂×C₅×D₄	—	3	1	no	—
299	C₂×C₅×D₄	—	3	1	no	—
300	C₂×C₅×D₄	—	6	4	no	—
301	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
302	C₂²×C₄×C₅	—	3	1	no	—
303	C₂²×C₄×C₅	—	3	1	no	—
304	C₂²×C₄×C₅	—	3	1	no	—
305	C₂²×C₄×C₅	—	3	1	no	—
306	C₂²×C₄×C₅	—	3	1	no	—
307	C₂²×C₄×C₅	—	3	1	no	—
308	C₂²×C₄×C₅	—	3	1	no	—
309	C₂²×C₄×C₅	—	3	1	no	—
310	C₂²×C₄×C₅	—	3	1	no	—
311	C₂²×C₄×C₅	—	3	1	no	—
312	C₂²×C₄×C₅	—	3	1	no	—
313	C₂²×C₄×C₅	—	6	2	no	—
314	C₂²×C₄×C₅	—	6	2	no	—
315	C₂²×C₄×C₅	—	6	2	no	—
316	C₂²×C₄×C₅	—	6	2	no	—
317	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
318	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
319	C₅×M₁₆	—	2	2	no	—
320	C₅×M₁₆	—	6	2	no	—
321	C₅×M₁₆	—	6	2	no	—
322	C₅×M₁₆	—	6	2	no	—
323	C₂×C₅×C₈	—	2	2	no	—
324	C₂×C₅×C₈	—	3	1	no	—
325	C₂×C₅×C₈	—	3	4	no	—
326	C₂×C₅×C₈	—	3	1	no	—
327	C₂×C₅×C₈	—	3	1	no	—
328	C₂×C₅×C₈	—	3	1	no	—
329	C₂×C₅×C₈	—	6	2	no	—
330	C₂×C₅×C₈	—	6	2	no	—
331	C₂×C₅×C₈	—	6	2	no	—
332	C₂×C₅×C₈	—	6	2	no	—
333	C₂×C₅×C₈	—	6	2	no	—
334	C₂×C₅×C₈	—	6	2	no	—
335	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
336	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
337	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
338	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
339	C₅×C₄⋊C₄	—	3	1	no	—
340	C₅×C₄⋊C₄	—	3	1	no	—
341	C₅×C₄⋊C₄	—	3	1	no	—
342	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
343	C₅×C₂²⋊C₄	—	3	1	no	—
344	C₅×C₂²⋊C₄	—	3	1	no	—
345	C₅×C₂²⋊C₄	—	3	1	no	—
346	C₅×C₂²⋊C₄	—	3	1	no	—
347	C₅×C₂²⋊C₄	—	3	1	no	—
348	C₅×C₂²⋊C₄	—	3	1	no	—
349	C₅×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
350	C₅×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
351	C₄²×C₅	—	3	1	no	—
352	C₄²×C₅	—	3	1	no	—
353	C₄²×C₅	—	3	1	no	—
354	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
355	C₂²×M₁₆	—	3	1	no	—
356	C₂³×C₈	—	3	1	no	—
357	C₂×C₄×D₄	—	3	1	no	—
358	#435	—	3	1	no	—
359	#435	—	3	1	no	—
360	#435	—	3	1	no	—
361	#435	—	3	1	no	—
362	#435	—	3	1	no	—
363	#435	—	3	1	no	—
364	#435	—	3	1	no	—
365	#435	C₅×D₃	1	1	yes	characteristic, direct product factor
366	C₂×C₄⋊C₈	—	3	1	no	—
367	C₂×C₂²⋊C₈	—	3	1	no	—
368	C₂×C₂²⋊C₈	—	3	1	no	—
369	C₂×#97	—	3	1	no	—
370	C₂²×C₃×C₅	—	2	1	no	—
371	C₂²×C₃×C₅	—	2	1	no	—
372	C₂²×C₃×C₅	—	2	1	no	—
373	C₂²×C₃×C₅	—	2	1	no	—
374	C₂²×C₃×C₅	—	2	1	no	—
375	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	complemented
376	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
377	C₂×C₅×D₃	—	2	1	no	—
378	C₂×C₅×D₃	—	2	1	no	—
379	C₂×C₅×D₃	—	2	8	no	—
380	C₂×C₅×D₃	—	2	1	no	—
381	C₂×C₅×D₃	—	2	1	no	—
382	C₂×C₅×D₃	—	2	1	no	—
383	C₂×C₅×D₃	—	4	4	no	—
384	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
385	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	—
386	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	complemented
387	C₂×C₅×D₃	#131	1	2	yes	—
388	C₃×C₄×C₅	—	2	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
393	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
394	C₅×Dic₃	—	2	1	no	—
395	C₅×Dic₃	—	2	1	no	—
396	C₅×Dic₃	—	2	1	no	—
397	C₅×Dic₃	—	2	1	no	—
398	C₅×Dic₃	C₄×D₄	1	2	yes	—
399	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
400	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
401	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
403	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
404	C₂×#67	C₂×C₄×C₅	1	1	yes	characteristic
405	C₂×#67	C₂×C₄×C₅	1	1	yes	characteristic
406	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
407	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
408	D₃×D₄	—	2	4	no	—
409	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
410	C₂×C₄×D₃	—	2	2	no	—
411	C₂×C₄×D₃	—	2	2	no	—
412	C₂×C₄×D₃	—	2	2	no	—
413	C₂×C₄×D₃	—	2	2	no	—
414	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
415	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
416	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
417	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
418	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
419	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
420	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
421	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
422	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
423	C₃×M₁₆	—	2	2	no	—
424	C₂×C₃×C₈	—	2	2	no	—
425	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
426	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
427	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
428	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
429	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
430	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
431	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
432	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
433	#217	C₂×C₄×C₅	1	1	yes	characteristic
434	#217	C₂×C₄×C₅	1	1	yes	characteristic
435	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
436	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
437	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
438	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
439	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
440	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
441	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
442	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
443	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
444	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
445	#208	—	2	2	no	—
446	C₂×C₃⋊C₈	—	2	2	no	—
447	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
448	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
449	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
450	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
451	ΓL(1,𝔽₂₅)	—	2	2	no	—
452	ΓL(1,𝔽₂₅)	—	2	2	no	—
453	D₃×C₈	—	2	2	no	—
454	D₃×C₈	—	2	2	no	—
455	D₃×C₈	—	2	2	no	—
456	D₃×C₈	—	2	2	no	—
457	D₃×C₈	—	2	2	no	—
458	D₃×C₈	C₅×D₄	1	4	yes	complemented
459	C₂³×C₅	—	3	1	no	—
460	C₂³×C₅	—	3	4	no	—
461	C₂³×C₅	—	3	1	no	—
462	C₂³×C₅	—	3	1	no	—
463	C₂³×C₅	—	6	2	no	—
464	C₂³×C₅	—	6	2	no	—
465	C₂³×C₅	—	6	2	no	—
466	C₂³×C₅	—	6	2	no	—
467	C₂³×C₅	—	6	2	no	—
468	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
469	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
470	C₅×D₄	—	2	2	no	—
471	C₅×D₄	—	6	2	no	—
472	C₅×D₄	—	6	2	no	—
473	C₅×D₄	—	6	2	no	—
474	C₂×C₄×C₅	—	2	1	no	—
475	C₂×C₄×C₅	—	2	1	no	—
476	C₂×C₄×C₅	—	2	1	no	—
477	C₂×C₄×C₅	—	2	1	no	—
478	C₂×C₄×C₅	—	3	1	no	—
479	C₂×C₄×C₅	—	3	2	no	—
480	C₂×C₄×C₅	—	3	2	no	—
481	C₂×C₄×C₅	—	3	1	no	—
482	C₂×C₄×C₅	—	3	1	no	—
483	C₂×C₄×C₅	—	3	1	no	—
484	C₂×C₄×C₅	—	3	1	no	—
485	C₂×C₄×C₅	—	6	2	no	—
486	C₂×C₄×C₅	—	6	2	no	—
487	C₂×C₄×C₅	—	6	2	no	—
488	C₂×C₄×C₅	—	6	2	no	—
489	C₂×C₄×C₅	—	6	2	no	—
490	C₂×C₄×C₅	—	6	2	no	—
491	C₂×C₄×C₅	—	6	2	no	—
492	C₂×C₄×C₅	—	6	2	no	—
493	C₂×C₄×C₅	—	6	1	no	—
494	C₂×C₄×C₅	—	6	1	no	—
495	C₂×C₄×C₅	—	6	1	no	—
496	C₂×C₄×C₅	—	6	1	no	—
497	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
498	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
499	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
500	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
501	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
502	C₅×C₈	—	2	1	no	—
503	C₅×C₈	—	2	1	no	—
504	C₅×C₈	—	2	1	no	—
505	C₅×C₈	—	3	2	no	—
506	C₅×C₈	—	6	1	no	—
507	C₅×C₈	—	6	1	no	—
508	C₅×C₈	—	6	1	no	—
509	C₅×C₈	D₃×D₄	1	2	yes	complemented
510	C₂²×D₄	—	3	1	no	—
511	C₂³×C₄	—	3	1	no	—
512	C₂³×C₄	—	3	1	no	—
513	C₂×M₁₆	—	3	1	no	—
514	C₂×M₁₆	—	3	1	no	—
515	C₂×M₁₆	—	3	1	no	—
516	C₂×M₁₆	—	6	4	no	—
517	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
518	C₂²×C₈	—	3	1	no	—
519	C₂²×C₈	—	3	1	no	—
520	C₂²×C₈	—	3	1	no	—
521	C₂²×C₈	—	3	1	no	—
522	C₂²×C₈	—	3	1	no	—
523	C₂²×C₈	—	3	1	no	—
524	C₂²×C₈	—	3	1	no	—
525	C₂²×C₈	—	6	4	no	—
526	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
527	C₄×D₄	—	3	1	no	—
528	C₄×D₄	—	3	1	no	—
529	C₄×D₄	—	3	1	no	—
530	C₄×D₄	—	3	1	no	—
531	C₄×D₄	—	3	1	no	—
532	C₄×D₄	—	3	1	no	—
533	C₄×D₄	—	3	1	no	—
534	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
535	C₂×C₄⋊C₄	—	3	1	no	—
536	C₂×C₂²⋊C₄	—	3	1	no	—
537	C₂×C₂²⋊C₄	—	3	1	no	—
538	C₂×C₄²	—	3	1	no	—
539	C₄⋊C₈	—	3	1	no	—
540	C₄⋊C₈	—	3	1	no	—
541	C₄⋊C₈	—	3	1	no	—
542	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
543	C₂²⋊C₈	—	3	1	no	—
544	C₂²⋊C₈	—	3	1	no	—
545	C₂²⋊C₈	—	3	1	no	—
546	C₂²⋊C₈	—	3	1	no	—
547	C₂²⋊C₈	—	3	1	no	—
548	C₂²⋊C₈	—	3	1	no	—
549	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
550	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
551	#97	—	3	1	no	—
552	#97	—	3	1	no	—
553	#97	—	3	1	no	—
554	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
555	C₂×C₃×C₅	—	2	2	no	—
556	C₂×C₃×C₅	—	4	1	no	—
557	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
558	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
559	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
560	C₅×D₃	—	2	2	no	—
561	C₅×D₃	—	4	1	no	—
562	C₅×D₃	#435	1	4	yes	direct product factor
563	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
564	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
565	C₂²×D₃	—	2	2	no	—
566	C₂²×D₃	—	2	2	no	—
567	C₂²×D₃	—	2	2	no	—
568	C₂²×D₃	—	2	2	no	—
569	C₂²×D₃	—	2	2	no	—
570	C₂²×D₃	C₅×M₁₆	1	4	yes	complemented
571	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
572	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
573	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
574	C₃×D₄	—	2	2	no	—
575	C₂×C₃×C₄	—	2	1	no	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	2	1	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
580	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
581	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
582	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
583	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
584	#67	—	2	2	no	—
585	#67	—	2	2	no	—
586	C₂×Dic₃	—	2	2	no	—
587	C₂×Dic₃	—	2	2	no	—
588	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
589	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
590	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
591	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
592	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
593	D₁₂	—	2	2	no	—
594	C₄×D₃	—	2	2	no	—
595	C₄×D₃	—	2	2	no	—
596	C₄×D₃	—	2	2	no	—
597	C₄×D₃	—	2	2	no	—
598	C₄×D₃	—	2	1	no	—
599	C₄×D₃	—	2	1	no	—
600	C₄×D₃	—	2	1	no	—
601	C₄×D₃	—	2	1	no	—
602	C₄×D₃	—	2	2	no	—
603	C₄×D₃	—	2	2	no	—
604	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
605	C₄×D₃	C₅×#41	1	2	yes	—
606	C₃×C₈	—	2	1	no	—
607	C₃×C₈	—	2	1	no	—
608	C₃×C₈	—	2	1	no	—
609	C₃×C₈	C₂×C₅×D₄	1	2	yes	complemented
610	C₃⋊C₈	—	2	1	no	—
611	C₃⋊C₈	—	2	1	no	—
612	C₃⋊C₈	—	2	1	no	—
613	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	complemented
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	—	3	2	no	—
620	C₂²×C₅	—	3	2	no	—
621	C₂²×C₅	—	3	2	no	—
622	C₂²×C₅	—	3	2	no	—
623	C₂²×C₅	—	6	8	no	—
624	C₂²×C₅	—	6	1	no	—
625	C₂²×C₅	—	6	1	no	—
626	C₂²×C₅	—	6	1	no	—
627	C₂²×C₅	—	6	1	no	—
628	C₂²×C₅	—	6	1	no	—
629	C₂²×C₅	—	12	4	no	—
630	C₂²×C₅	D₃×M₁₆	1	2	yes	complemented
631	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
632	C₄×C₅	—	2	1	no	—
633	C₄×C₅	—	2	1	no	—
634	C₄×C₅	—	2	1	no	—
635	C₄×C₅	—	2	1	no	—
636	C₄×C₅	—	3	2	no	—
637	C₄×C₅	—	6	1	no	—
638	C₄×C₅	—	6	1	no	—
639	C₄×C₅	—	6	1	no	—
640	C₄×C₅	—	6	1	no	—
641	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
642	C₄×C₅	D₃×#41	1	1	yes	characteristic
643	C₂⁴	—	3	1	no	—
644	C₂⁴	—	3	1	no	—
645	C₂×D₄	—	3	1	no	—
646	C₂×D₄	—	3	1	no	—
647	C₂×D₄	—	3	1	no	—
648	C₂×D₄	—	6	4	no	—
649	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
650	C₂²×C₄	—	3	1	no	—
651	C₂²×C₄	—	3	1	no	—
652	C₂²×C₄	—	3	1	no	—
653	C₂²×C₄	—	3	1	no	—
654	C₂²×C₄	—	3	1	no	—
655	C₂²×C₄	—	3	1	no	—
656	C₂²×C₄	—	3	1	no	—
657	C₂²×C₄	—	3	1	no	—
658	C₂²×C₄	—	3	1	no	—
659	C₂²×C₄	—	3	1	no	—
660	C₂²×C₄	—	3	1	no	—
661	C₂²×C₄	—	6	2	no	—
662	C₂²×C₄	—	6	2	no	—
663	C₂²×C₄	—	6	2	no	—
664	C₂²×C₄	—	6	2	no	—
665	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
666	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
667	M₁₆	—	2	2	no	—
668	M₁₆	—	6	2	no	—
669	M₁₆	—	6	2	no	—
670	M₁₆	—	6	2	no	—
671	C₂×C₈	—	2	2	no	—
672	C₂×C₈	—	3	1	no	—
673	C₂×C₈	—	3	4	no	—
674	C₂×C₈	—	3	1	no	—
675	C₂×C₈	—	3	1	no	—
676	C₂×C₈	—	3	1	no	—
677	C₂×C₈	—	6	2	no	—
678	C₂×C₈	—	6	2	no	—
679	C₂×C₈	—	6	2	no	—
680	C₂×C₈	—	6	2	no	—
681	C₂×C₈	—	6	2	no	—
682	C₂×C₈	—	6	2	no	—
683	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
684	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
685	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
686	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
687	C₄⋊C₄	—	3	1	no	—
688	C₄⋊C₄	—	3	1	no	—
689	C₄⋊C₄	—	3	1	no	—
690	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
691	C₂²⋊C₄	—	3	1	no	—
692	C₂²⋊C₄	—	3	1	no	—
693	C₂²⋊C₄	—	3	1	no	—
694	C₂²⋊C₄	—	3	1	no	—
695	C₂²⋊C₄	—	3	1	no	—
696	C₂²⋊C₄	—	3	1	no	—
697	C₂²⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
698	C₂²⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
699	C₄²	—	3	1	no	—
700	C₄²	—	3	1	no	—
701	C₄²	—	3	1	no	—
702	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
703	C₃×C₅	C₂×#435	1	1	yes	characteristic, complemented, Hall
704	C₂²×C₃	—	2	1	no	—
705	C₂²×C₃	—	2	1	no	—
706	C₂²×C₃	—	2	1	no	—
707	C₂²×C₃	—	2	1	no	—
708	C₂²×C₃	—	2	1	no	—
709	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	complemented
710	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
711	C₂×D₃	—	2	1	no	—
712	C₂×D₃	—	2	1	no	—
713	C₂×D₃	—	2	8	no	—
714	C₂×D₃	—	2	1	no	—
715	C₂×D₃	—	2	1	no	—
716	C₂×D₃	—	2	1	no	—
717	C₂×D₃	—	4	4	no	—
718	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
719	C₂×D₃	C₂×C₅×M₁₆	1	2	yes	—
720	C₂×D₃	C₂×C₅×M₁₆	1	2	yes	complemented
721	C₂×D₃	C₅×#131	1	2	yes	—
722	C₃×C₄	—	2	1	no	—
723	C₃×C₄	—	2	1	no	—
724	C₃×C₄	—	2	1	no	—
725	C₃×C₄	—	2	1	no	—
726	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
727	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
728	Dic₃	—	2	1	no	—
729	Dic₃	—	2	1	no	—
730	Dic₃	—	2	1	no	—
731	Dic₃	—	2	1	no	—
732	Dic₃	C₄×C₅×D₄	1	2	yes	—
733	C₂×C₅	—	2	2	no	—
734	C₂×C₅	—	3	4	no	—
735	C₂×C₅	—	4	1	no	—
736	C₂×C₅	—	6	2	no	—
737	C₂×C₅	—	12	1	no	—
738	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
739	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
740	C₂×C₅	D₃×#131	1	1	yes	characteristic
741	C₂³	—	3	1	no	—
742	C₂³	—	3	4	no	—
743	C₂³	—	3	1	no	—
744	C₂³	—	3	1	no	—
745	C₂³	—	6	2	no	—
746	C₂³	—	6	2	no	—
747	C₂³	—	6	2	no	—
748	C₂³	—	6	2	no	—
749	C₂³	—	6	2	no	—
750	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
751	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
752	D₄	—	2	2	no	—
753	D₄	—	6	2	no	—
754	D₄	—	6	2	no	—
755	D₄	—	6	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	3	1	no	—
761	C₂×C₄	—	3	2	no	—
762	C₂×C₄	—	3	2	no	—
763	C₂×C₄	—	3	1	no	—
764	C₂×C₄	—	3	1	no	—
765	C₂×C₄	—	3	1	no	—
766	C₂×C₄	—	3	1	no	—
767	C₂×C₄	—	6	2	no	—
768	C₂×C₄	—	6	2	no	—
769	C₂×C₄	—	6	2	no	—
770	C₂×C₄	—	6	2	no	—
771	C₂×C₄	—	6	2	no	—
772	C₂×C₄	—	6	2	no	—
773	C₂×C₄	—	6	2	no	—
774	C₂×C₄	—	6	2	no	—
775	C₂×C₄	—	6	1	no	—
776	C₂×C₄	—	6	1	no	—
777	C₂×C₄	—	6	1	no	—
778	C₂×C₄	—	6	1	no	—
779	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
780	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
781	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
782	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
783	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
784	C₈	—	2	1	no	—
785	C₈	—	2	1	no	—
786	C₈	—	2	1	no	—
787	C₈	—	3	2	no	—
788	C₈	—	6	1	no	—
789	C₈	—	6	1	no	—
790	C₈	—	6	1	no	—
791	C₈	C₅×D₃×D₄	1	2	yes	complemented
792	C₂×C₃	—	2	2	no	—
793	C₂×C₃	—	4	1	no	—
794	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
795	C₂×C₃	C₂²×C₅×M₁₆	1	1	yes	characteristic
796	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
797	D₃	—	2	2	no	—
798	D₃	—	4	1	no	—
799	D₃	C₅×#435	1	4	yes	direct product factor
800	C₅	D₃×#435	1	1	yes	characteristic, direct product factor, Sylow
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	3	2	no	—
807	C₂²	—	3	2	no	—
808	C₂²	—	3	2	no	—
809	C₂²	—	3	2	no	—
810	C₂²	—	6	8	no	—
811	C₂²	—	6	1	no	—
812	C₂²	—	6	1	no	—
813	C₂²	—	6	1	no	—
814	C₂²	—	6	1	no	—
815	C₂²	—	6	1	no	—
816	C₂²	—	12	4	no	—
817	C₂²	C₅×D₃×M₁₆	1	2	yes	complemented
818	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	1	no	—
823	C₄	—	3	2	no	—
824	C₄	—	6	1	no	—
825	C₄	—	6	1	no	—
826	C₄	—	6	1	no	—
827	C₄	—	6	1	no	—
828	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
829	C₄	C₅×D₃×#41	1	1	yes	characteristic
830	C₃	C₂×C₅×#435	1	1	yes	characteristic, complemented, Sylow
831	C₂	—	2	2	no	—
832	C₂	—	3	4	no	—
833	C₂	—	4	1	no	—
834	C₂	—	6	2	no	—
835	C₂	—	12	1	no	—
836	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
837	C₂	C₂×C₅×D₃×M₁₆	1	1	yes	characteristic
838	C₂	C₅×D₃×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#435	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₅×D₃×D₄	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#435	D₃
hypocenter	C₃	C₂×C₅×#435
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#435

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×M₁₆	C₂	semidirect
2. C₂²×C₅×D₃×C₈	C₂	semidirect
4. C₃×C₅×#435	C₂	semidirect
5. C₅×#5127	C₂	semidirect
6. C₅×#5111	C₂	semidirect
7. C₅×#5011	C₂	semidirect
8. C₅×#4836	C₂	semidirect
9. C₅×D₃×C₄⋊C₈	C₂	semidirect
10. C₅×#4730	C₂	semidirect
11. C₅×#4728	C₂	semidirect
12. C₅×D₃×C₂²⋊C₈	C₂	semidirect
13. C₅×D₃×C₂²⋊C₈	C₂	semidirect
14. C₅×#4706	C₂	semidirect
15. C₅×D₃×#97	C₂	semidirect
20. C₂×C₃×C₅×M₁₆	C₂²	semidirect
21. C₂²×C₃×C₅×C₈	C₂²	semidirect
26. C₂×C₅×#208	C₂²	semidirect
27. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
29. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
30. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
36. C₂×C₅×D₃×C₈	C₂²	semidirect
37. C₂×C₅×D₃×C₈	C₂²	semidirect
46. C₃×C₅×C₄⋊C₈	C₂²	semidirect
47. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
48. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
49. C₃×C₅×#97	C₂²	semidirect
50. C₅×#830	C₂²	semidirect
51. C₅×#830	C₂²	semidirect
52. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
53. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
54. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
55. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
56. C₅×#815	C₂²	semidirect
57. C₅×#815	C₂²	semidirect
58. C₅×Dic₃⋊C₈	C₂²	semidirect
59. C₅×Dic₃⋊C₈	C₂²	semidirect
60. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
61. C₅×#803	C₂²	semidirect
62. D₃×#435	C₅	direct (N × H)
73. C₅×#435	D₃	direct (N × H)
137. C₅×D₃×C₈	D₄	semidirect
138. C₂×D₃×M₁₆	C₂×C₅	semidirect
139. C₂²×D₃×C₈	C₂×C₅	semidirect
141. C₃×#435	C₂×C₅	semidirect
142. #5127	C₂×C₅	semidirect
143. #5111	C₂×C₅	semidirect
144. #5011	C₂×C₅	semidirect
145. #4836	C₂×C₅	semidirect
146. D₃×C₄⋊C₈	C₂×C₅	semidirect
147. #4730	C₂×C₅	semidirect
148. #4728	C₂×C₅	semidirect
149. D₃×C₂²⋊C₈	C₂×C₅	semidirect
150. D₃×C₂²⋊C₈	C₂×C₅	semidirect
151. #4706	C₂×C₅	semidirect
152. D₃×#97	C₂×C₅	semidirect
160. C₂×C₅×M₁₆	C₂×D₃	semidirect
169. C₂²×C₅×C₈	C₂×D₃	semidirect
185. C₅×C₄⋊C₈	C₂×D₃	semidirect
192. C₅×C₂²⋊C₈	C₂×D₃	semidirect
193. C₅×C₂²⋊C₈	C₂×D₃	semidirect
197. C₅×#97	C₂×D₃	semidirect
206. C₂²×C₅×D₃	M₁₆	semidirect
245. C₃×C₅×C₈	C₂×D₄	semidirect
249. C₅×C₃⋊C₈	C₂×D₄	semidirect
253. C₂×C₃×M₁₆	C₂²×C₅	semidirect
254. C₂²×C₃×C₈	C₂²×C₅	semidirect
259. C₂×#208	C₂²×C₅	semidirect
260. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
262. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
263. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
269. C₂×D₃×C₈	C₂²×C₅	semidirect
270. C₂×D₃×C₈	C₂²×C₅	semidirect
279. C₃×C₄⋊C₈	C₂²×C₅	semidirect
280. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
281. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
282. C₃×#97	C₂²×C₅	semidirect
283. #830	C₂²×C₅	semidirect
284. #830	C₂²×C₅	semidirect
285. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
286. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
287. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
288. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
289. #815	C₂²×C₅	semidirect
290. #815	C₂²×C₅	semidirect
291. Dic₃⋊C₈	C₂²×C₅	semidirect
292. Dic₃⋊C₈	C₂²×C₅	semidirect
293. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
294. #803	C₂²×C₅	semidirect
365. #435	C₅×D₃	direct (N × H)
375. C₂²×C₃×C₅	C₂×M₁₆	semidirect
386. C₂×C₅×D₃	C₂×M₁₆	semidirect
458. D₃×C₈	C₅×D₄	semidirect
509. C₅×C₈	D₃×D₄	semidirect
517. C₂×M₁₆	C₂×C₅×D₃	semidirect
526. C₂²×C₈	C₂×C₅×D₃	semidirect
542. C₄⋊C₈	C₂×C₅×D₃	semidirect
549. C₂²⋊C₈	C₂×C₅×D₃	semidirect
550. C₂²⋊C₈	C₂×C₅×D₃	semidirect
554. #97	C₂×C₅×D₃	semidirect
562. C₅×D₃	#435	direct (N × H)
570. C₂²×D₃	C₅×M₁₆	semidirect
609. C₃×C₈	C₂×C₅×D₄	semidirect
613. C₃⋊C₈	C₂×C₅×D₄	semidirect
630. C₂²×C₅	D₃×M₁₆	semidirect
703. C₃×C₅	C₂×#435	semidirect
709. C₂²×C₃	C₂×C₅×M₁₆	semidirect
720. C₂×D₃	C₂×C₅×M₁₆	semidirect
791. C₈	C₅×D₃×D₄	semidirect
799. D₃	C₅×#435	direct (N × H)
800. C₅	D₃×#435	direct (N × H)
817. C₂²	C₅×D₃×M₁₆	semidirect
830. C₃	C₂×C₅×#435	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×M₁₆	2
C₂²×C₅×D₃×C₈	2
C₄×C₅×D₃×D₄	2
C₃×C₅×#435	2
C₅×#5127	2
C₅×#5111	2
C₅×#5011	2
C₅×#4836	2
C₅×D₃×C₄⋊C₈	2
C₅×#4730	2
C₅×#4728	2
C₅×D₃×C₂²⋊C₈	2
C₅×#4706	2
C₅×D₃×#97	2
C₂×C₅×#435	3
D₃×#435	5

Subgroups — C5×D3×#435 #14414675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#435 #14414675