Subgroups — C₅×#79478 #14414905

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#907	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5547	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×D₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4839	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4834	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4727	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#67⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#67⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4708	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4706	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2929	—	3	1	no	maximal, Hall
17	C₂×C₅×#235	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₅×#939	C₄	1	1	yes	characteristic
23	C₅×#937	C₄	1	1	yes	characteristic
24	C₄×C₅×#67	C₂²	1	1	yes	characteristic
25	C₄×C₅×#67	C₂²	1	1	yes	characteristic
26	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
28	C₅×#907	—	2	4	no	—
29	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
30	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
31	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×D₃×C₈	—	2	4	no	—
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
37	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic, complemented
38	C₅×#896	C₄	1	1	yes	characteristic
39	C₅×#894	C₄	1	1	yes	characteristic
40	C₅×#884	C₄	1	1	yes	characteristic
41	C₅×#883	C₄	1	1	yes	characteristic
42	C₅×#882	C₄	1	1	yes	characteristic
43	C₅×#878	C₄	1	1	yes	characteristic
44	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
45	C₅×#872	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
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
51	C₅×#830	C₂²	1	1	yes	characteristic, complemented
52	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
53	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
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×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
60	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
61	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
62	#79478	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×#131	—	3	1	no	—
64	C₂³×C₅×C₈	—	3	1	no	—
65	C₅×#525	—	3	1	no	—
66	C₅×#435	—	3	1	no	—
67	C₅×#435	—	3	1	no	—
68	C₅×#435	—	3	1	no	—
69	C₅×#435	D₃	1	1	yes	characteristic, complemented
70	C₅×C₈×D₄	—	3	1	no	—
71	C₅×C₈×D₄	—	3	1	no	—
72	C₅×C₈×D₄	—	3	1	no	—
73	C₅×C₈×D₄	—	3	1	no	—
74	C₅×#424	—	3	1	no	—
75	C₅×#408	—	3	1	no	—
76	C₅×#407	—	3	1	no	—
77	C₅×#405	—	3	1	no	—
78	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₅×#67	C₂×C₄	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	C₂×C₅×#67	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
87	C₅×#235	—	2	2	no	—
88	C₅×#235	—	2	2	no	—
89	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
90	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
96	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
97	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
98	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
99	C₃×C₅×M₁₆	—	2	2	no	—
100	C₂×C₃×C₅×C₈	—	2	2	no	—
101	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
109	C₅×#217	C₂×C₄	1	1	yes	characteristic
110	C₅×#217	C₂×C₄	1	1	yes	characteristic
111	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₅×(C₂×D₃)⋊C₄	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×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
118	C₅×Dic₃⋊C₄	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	C₅×Dic₃⋊C₄	C₂×C₄	1	1	yes	characteristic
122	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
123	C₂×C₅×C₃⋊C₈	—	2	2	no	—
124	C₂×C₅×C₃⋊C₈	—	2	2	no	—
125	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
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	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
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	D₄	1	4	yes	complemented
137	C₂×#907	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic, complemented
139	#5547	C₂×C₅	1	1	yes	characteristic
140	C₃×#435	C₂×C₅	1	1	yes	characteristic, complemented
141	#5127	C₂×C₅	1	1	yes	characteristic, complemented
142	#5111	C₂×C₅	1	1	yes	characteristic, complemented
143	D₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
144	#4839	C₂×C₅	1	1	yes	characteristic, complemented
145	#4834	C₂×C₅	1	1	yes	characteristic, complemented
146	#4727	C₂×C₅	1	1	yes	characteristic, complemented
147	#4726	C₂×C₅	1	1	yes	characteristic, complemented
148	#67⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
149	#67⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
150	#4708	C₂×C₅	1	1	yes	characteristic, complemented
151	#4706	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂×C₅×#41	—	3	1	no	—
153	C₂³×C₄×C₅	—	3	1	no	—
154	C₅×#131	—	6	4	no	—
155	C₂×C₅×M₁₆	—	3	1	no	—
156	C₂×C₅×M₁₆	—	3	1	no	—
157	C₂×C₅×M₁₆	—	3	1	no	—
158	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
159	C₂²×C₅×C₈	—	3	1	no	—
160	C₂²×C₅×C₈	—	3	1	no	—
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	—	6	4	no	—
167	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
168	C₅×#123	—	3	1	no	—
169	C₅×#123	—	3	1	no	—
170	C₅×C₂²⋊Q₈	—	3	1	no	—
171	C₅×C₂²⋊Q₈	—	3	1	no	—
172	C₅×#121	—	3	1	no	—
173	C₅×#121	—	3	1	no	—
174	C₅×#120	—	3	1	no	—
175	C₅×#120	—	3	1	no	—
176	C₄×C₅×D₄	—	3	1	no	—
177	C₄×C₅×D₄	—	3	1	no	—
178	C₄×C₅×D₄	—	3	1	no	—
179	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
180	C₅×#117	—	3	1	no	—
181	C₅×C₄⋊C₈	—	3	1	no	—
182	C₅×C₄⋊C₈	—	3	1	no	—
183	C₅×C₄⋊C₈	—	3	1	no	—
184	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
185	C₅×C₂²⋊C₈	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic
192	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
193	C₅×#97	—	3	1	no	—
194	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
195	C₄×C₅×C₈	—	3	1	no	—
196	C₄×C₅×C₈	—	3	1	no	—
197	#2929	—	3	1	no	Sylow
198	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
199	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₅×D₃	—	2	2	no	—
201	C₂²×C₅×D₃	—	2	2	no	—
202	C₂²×C₅×D₃	—	2	2	no	—
203	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
206	C₃×C₅×D₄	—	2	2	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	—	2	1	no	—
209	C₂×C₃×C₄×C₅	—	2	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
213	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
214	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
215	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
216	C₅×#67	—	2	2	no	—
217	C₅×#67	—	2	2	no	—
218	C₅×#67	—	2	2	no	—
219	C₅×#67	—	2	2	no	—
220	C₂×C₅×Dic₃	—	2	2	no	—
221	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
222	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
223	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
224	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
225	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
226	C₅×D₁₂	—	2	2	no	—
227	C₅×D₁₂	—	2	2	no	—
228	C₄×C₅×D₃	—	2	2	no	—
229	C₄×C₅×D₃	—	2	1	no	—
230	C₄×C₅×D₃	—	2	1	no	—
231	C₄×C₅×D₃	—	2	1	no	—
232	C₄×C₅×D₃	—	2	1	no	—
233	C₄×C₅×D₃	—	2	2	no	—
234	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
235	C₄×C₅×D₃	#41	1	2	yes	—
236	C₅×Dic₆	—	2	2	no	—
237	C₃×C₅×C₈	—	2	1	no	—
238	C₃×C₅×C₈	—	2	1	no	—
239	C₃×C₅×C₈	—	2	1	no	—
240	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
241	C₅×C₃⋊C₈	—	2	1	no	—
242	C₅×C₃⋊C₈	—	2	1	no	—
243	C₅×C₃⋊C₈	—	2	1	no	—
244	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
245	C₂×#235	C₂²×C₅	1	1	yes	characteristic
246	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
248	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
249	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
250	#939	C₄×C₅	1	1	yes	characteristic
251	#937	C₄×C₅	1	1	yes	characteristic
252	C₄×#67	C₂²×C₅	1	1	yes	characteristic
253	C₄×#67	C₂²×C₅	1	1	yes	characteristic
254	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
255	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
256	#907	—	2	4	no	—
257	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
258	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
259	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₂×D₃×C₈	—	2	4	no	—
261	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
262	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
263	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
264	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
265	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
266	#896	C₄×C₅	1	1	yes	characteristic
267	#894	C₄×C₅	1	1	yes	characteristic
268	#884	C₄×C₅	1	1	yes	characteristic
269	#883	C₄×C₅	1	1	yes	characteristic
270	#882	C₄×C₅	1	1	yes	characteristic
271	#878	C₄×C₅	1	1	yes	characteristic
272	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
273	#872	C₂²×C₅	1	1	yes	characteristic
274	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
275	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
276	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
277	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
278	#830	C₂²×C₅	1	1	yes	characteristic
279	#830	C₂²×C₅	1	1	yes	characteristic, complemented
280	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
281	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
282	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
283	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
284	#815	C₂²×C₅	1	1	yes	characteristic, complemented
285	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
286	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
288	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
289	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
290	C₂⁴×C₅	—	3	1	no	—
291	C₅×#41	—	6	2	no	—
292	C₅×#41	—	6	2	no	—
293	C₂×C₅×Q₈	—	3	1	no	—
294	C₂×C₅×D₄	—	3	1	no	—
295	C₂×C₅×D₄	—	3	1	no	—
296	C₂×C₅×D₄	—	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	C₄×D₃	1	1	yes	characteristic
301	C₂²×C₄×C₅	—	3	1	no	—
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	—	6	2	no	—
308	C₂²×C₄×C₅	—	6	2	no	—
309	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
310	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
311	C₅×M₁₆	—	2	2	no	—
312	C₅×M₁₆	—	6	2	no	—
313	C₅×M₁₆	—	6	2	no	—
314	C₅×M₁₆	—	6	2	no	—
315	C₂×C₅×C₈	—	2	2	no	—
316	C₂×C₅×C₈	—	3	1	no	—
317	C₂×C₅×C₈	—	3	4	no	—
318	C₂×C₅×C₈	—	3	1	no	—
319	C₂×C₅×C₈	—	3	1	no	—
320	C₂×C₅×C₈	—	3	1	no	—
321	C₂×C₅×C₈	—	6	2	no	—
322	C₂×C₅×C₈	—	6	2	no	—
323	C₂×C₅×C₈	—	6	2	no	—
324	C₂×C₅×C₈	—	6	2	no	—
325	C₂×C₅×C₈	—	6	2	no	—
326	C₂×C₅×C₈	—	6	2	no	—
327	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
328	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
329	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
330	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
331	C₅×C₄⋊C₄	—	3	1	no	—
332	C₅×C₄⋊C₄	—	3	1	no	—
333	C₅×C₄⋊C₄	—	3	1	no	—
334	C₅×C₄⋊C₄	—	3	1	no	—
335	C₅×C₄⋊C₄	—	3	1	no	—
336	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
337	C₅×C₂²⋊C₄	—	3	1	no	—
338	C₅×C₂²⋊C₄	—	3	1	no	—
339	C₅×C₂²⋊C₄	—	3	1	no	—
340	C₅×C₂²⋊C₄	—	3	1	no	—
341	C₅×C₂²⋊C₄	—	3	1	no	—
342	C₅×C₂²⋊C₄	—	3	1	no	—
343	C₅×C₂²⋊C₄	—	3	1	no	—
344	C₅×C₂²⋊C₄	—	3	1	no	—
345	C₅×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
346	C₅×C₂²⋊C₄	C₄×D₃	1	1	yes	characteristic
347	C₄²×C₅	—	3	1	no	—
348	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
349	C₂×#131	—	3	1	no	—
350	C₂³×C₈	—	3	1	no	—
351	#525	—	3	1	no	—
352	#435	—	3	1	no	—
353	#435	—	3	1	no	—
354	#435	—	3	1	no	—
355	#435	C₅×D₃	1	1	yes	characteristic, complemented
356	C₈×D₄	—	3	1	no	—
357	C₈×D₄	—	3	1	no	—
358	C₈×D₄	—	3	1	no	—
359	C₈×D₄	—	3	1	no	—
360	#424	—	3	1	no	—
361	#408	—	3	1	no	—
362	#407	—	3	1	no	—
363	#405	—	3	1	no	—
364	C₂²×C₃×C₅	—	2	1	no	—
365	C₂²×C₃×C₅	—	2	1	no	—
366	C₂²×C₃×C₅	—	2	1	no	—
367	C₂²×C₃×C₅	—	2	1	no	—
368	C₂²×C₃×C₅	—	2	1	no	—
369	C₂²×C₃×C₅	#131	1	2	yes	complemented
370	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
371	C₂×C₅×D₃	—	2	8	no	—
372	C₂×C₅×D₃	—	2	1	no	—
373	C₂×C₅×D₃	—	2	1	no	—
374	C₂×C₅×D₃	—	2	1	no	—
375	C₂×C₅×D₃	—	2	1	no	—
376	C₂×C₅×D₃	—	2	1	no	—
377	C₂×C₅×D₃	—	2	1	no	—
378	C₂×C₅×D₃	—	2	1	no	—
379	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
380	C₂×C₅×D₃	#131	1	2	yes	complemented
381	C₃×C₄×C₅	—	2	1	no	—
382	C₃×C₄×C₅	—	2	1	no	—
383	C₃×C₄×C₅	—	2	1	no	—
384	C₃×C₄×C₅	—	2	1	no	—
385	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
386	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
387	C₅×Dic₃	—	2	1	no	—
388	C₅×Dic₃	—	2	1	no	—
389	C₅×Dic₃	—	2	1	no	—
390	C₅×Dic₃	—	2	1	no	—
391	C₅×Dic₃	C₄×D₄	1	2	yes	—
392	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
393	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
394	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
395	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
396	C₂×#67	C₂×C₄×C₅	1	1	yes	characteristic
397	C₂×#67	C₂×C₄×C₅	1	1	yes	characteristic
398	C₂×#67	C₂×C₄×C₅	1	1	yes	characteristic
399	C₂×#67	C₂×C₄×C₅	1	1	yes	characteristic
400	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
401	#235	—	2	2	no	—
402	#235	—	2	2	no	—
403	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
404	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
405	C₂×C₄×D₃	—	2	2	no	—
406	C₂×C₄×D₃	—	2	2	no	—
407	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
408	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
409	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
411	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
412	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
413	C₃×M₁₆	—	2	2	no	—
414	C₂×C₃×C₈	—	2	2	no	—
415	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
416	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
417	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
418	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
419	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
420	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
421	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
422	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
423	#217	C₂×C₄×C₅	1	1	yes	characteristic
424	#217	C₂×C₄×C₅	1	1	yes	characteristic
425	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
426	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
427	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
428	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
429	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
430	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
431	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
432	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
433	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
434	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
435	Dic₃⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
436	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
437	C₂×C₃⋊C₈	—	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	ΓL(1,𝔽₂₅)	—	2	2	no	—
444	ΓL(1,𝔽₂₅)	—	2	2	no	—
445	ΓL(1,𝔽₂₅)	—	2	2	no	—
446	D₃×C₈	—	2	2	no	—
447	D₃×C₈	—	2	2	no	—
448	D₃×C₈	—	2	2	no	—
449	D₃×C₈	—	2	2	no	—
450	D₃×C₈	C₅×D₄	1	4	yes	complemented
451	C₂³×C₅	—	3	1	no	—
452	C₂³×C₅	—	3	1	no	—
453	C₂³×C₅	—	3	1	no	—
454	C₂³×C₅	—	6	2	no	—
455	C₂³×C₅	—	6	2	no	—
456	C₂³×C₅	—	6	2	no	—
457	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
458	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
459	C₅×Q₈	—	6	2	no	—
460	C₅×D₄	—	2	2	no	—
461	C₅×D₄	—	6	2	no	—
462	C₅×D₄	—	6	2	no	—
463	C₅×D₄	—	6	2	no	—
464	C₅×D₄	—	6	2	no	—
465	C₅×D₄	—	6	2	no	—
466	C₅×D₄	—	6	2	no	—
467	C₂×C₄×C₅	—	2	1	no	—
468	C₂×C₄×C₅	—	2	1	no	—
469	C₂×C₄×C₅	—	2	1	no	—
470	C₂×C₄×C₅	—	2	1	no	—
471	C₂×C₄×C₅	—	3	1	no	—
472	C₂×C₄×C₅	—	3	2	no	—
473	C₂×C₄×C₅	—	3	2	no	—
474	C₂×C₄×C₅	—	3	1	no	—
475	C₂×C₄×C₅	—	3	1	no	—
476	C₂×C₄×C₅	—	3	1	no	—
477	C₂×C₄×C₅	—	3	1	no	—
478	C₂×C₄×C₅	—	6	2	no	—
479	C₂×C₄×C₅	—	6	2	no	—
480	C₂×C₄×C₅	—	6	2	no	—
481	C₂×C₄×C₅	—	6	1	no	—
482	C₂×C₄×C₅	—	6	1	no	—
483	C₂×C₄×C₅	—	6	1	no	—
484	C₂×C₄×C₅	—	6	1	no	—
485	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
486	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
487	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
488	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
489	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
490	C₅×C₈	—	2	1	no	—
491	C₅×C₈	—	2	1	no	—
492	C₅×C₈	—	2	1	no	—
493	C₅×C₈	—	3	2	no	—
494	C₅×C₈	—	6	1	no	—
495	C₅×C₈	—	6	1	no	—
496	C₅×C₈	—	6	1	no	—
497	C₅×C₈	D₃×D₄	1	2	yes	—
498	C₂×#41	—	3	1	no	—
499	C₂³×C₄	—	3	1	no	—
500	#131	—	6	4	no	—
501	C₂×M₁₆	—	3	1	no	—
502	C₂×M₁₆	—	3	1	no	—
503	C₂×M₁₆	—	3	1	no	—
504	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
505	C₂²×C₈	—	3	1	no	—
506	C₂²×C₈	—	3	1	no	—
507	C₂²×C₈	—	3	1	no	—
508	C₂²×C₈	—	3	1	no	—
509	C₂²×C₈	—	3	1	no	—
510	C₂²×C₈	—	3	1	no	—
511	C₂²×C₈	—	3	1	no	—
512	C₂²×C₈	—	6	4	no	—
513	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
514	#123	—	3	1	no	—
515	#123	—	3	1	no	—
516	C₂²⋊Q₈	—	3	1	no	—
517	C₂²⋊Q₈	—	3	1	no	—
518	#121	—	3	1	no	—
519	#121	—	3	1	no	—
520	#120	—	3	1	no	—
521	#120	—	3	1	no	—
522	C₄×D₄	—	3	1	no	—
523	C₄×D₄	—	3	1	no	—
524	C₄×D₄	—	3	1	no	—
525	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
526	#117	—	3	1	no	—
527	C₄⋊C₈	—	3	1	no	—
528	C₄⋊C₈	—	3	1	no	—
529	C₄⋊C₈	—	3	1	no	—
530	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
531	C₂²⋊C₈	—	3	1	no	—
532	C₂²⋊C₈	—	3	1	no	—
533	C₂²⋊C₈	—	3	1	no	—
534	C₂²⋊C₈	—	3	1	no	—
535	C₂²⋊C₈	—	3	1	no	—
536	C₂²⋊C₈	—	3	1	no	—
537	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
538	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
539	#97	—	3	1	no	—
540	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
541	C₄×C₈	—	3	1	no	—
542	C₄×C₈	—	3	1	no	—
543	C₂×C₃×C₅	—	2	2	no	—
544	C₂×C₃×C₅	—	4	1	no	—
545	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
546	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
547	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
548	C₅×D₃	—	2	2	no	—
549	C₅×D₃	—	2	2	no	—
550	C₅×D₃	—	4	1	no	—
551	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
552	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
553	C₂²×D₃	—	2	2	no	—
554	C₂²×D₃	—	2	2	no	—
555	C₂²×D₃	—	2	2	no	—
556	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
557	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
558	C₂²×D₃	C₂²×C₄×C₅	1	1	yes	characteristic
559	C₃×D₄	—	2	2	no	—
560	C₂×C₃×C₄	—	2	1	no	—
561	C₂×C₃×C₄	—	2	1	no	—
562	C₂×C₃×C₄	—	2	1	no	—
563	C₂×C₃×C₄	—	2	1	no	—
564	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
565	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
566	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
567	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
568	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
569	#67	—	2	2	no	—
570	#67	—	2	2	no	—
571	#67	—	2	2	no	—
572	#67	—	2	2	no	—
573	C₂×Dic₃	—	2	2	no	—
574	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
575	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
576	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
577	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
578	C₂×Dic₃	C₂²×C₄×C₅	1	1	yes	characteristic
579	D₁₂	—	2	2	no	—
580	D₁₂	—	2	2	no	—
581	C₄×D₃	—	2	2	no	—
582	C₄×D₃	—	2	1	no	—
583	C₄×D₃	—	2	1	no	—
584	C₄×D₃	—	2	1	no	—
585	C₄×D₃	—	2	1	no	—
586	C₄×D₃	—	2	2	no	—
587	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
588	C₄×D₃	C₅×#41	1	2	yes	—
589	Dic₆	—	2	2	no	—
590	C₃×C₈	—	2	1	no	—
591	C₃×C₈	—	2	1	no	—
592	C₃×C₈	—	2	1	no	—
593	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
594	C₃⋊C₈	—	2	1	no	—
595	C₃⋊C₈	—	2	1	no	—
596	C₃⋊C₈	—	2	1	no	—
597	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
598	C₂²×C₅	—	2	1	no	—
599	C₂²×C₅	—	2	1	no	—
600	C₂²×C₅	—	2	1	no	—
601	C₂²×C₅	—	2	1	no	—
602	C₂²×C₅	—	2	1	no	—
603	C₂²×C₅	—	3	2	no	—
604	C₂²×C₅	—	3	2	no	—
605	C₂²×C₅	—	6	8	no	—
606	C₂²×C₅	—	6	1	no	—
607	C₂²×C₅	—	6	1	no	—
608	C₂²×C₅	—	6	1	no	—
609	C₂²×C₅	—	6	1	no	—
610	C₂²×C₅	—	6	1	no	—
611	C₂²×C₅	—	6	1	no	—
612	C₂²×C₅	—	6	1	no	—
613	C₂²×C₅	#907	1	2	yes	complemented
614	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
615	C₄×C₅	—	2	1	no	—
616	C₄×C₅	—	2	1	no	—
617	C₄×C₅	—	2	1	no	—
618	C₄×C₅	—	2	1	no	—
619	C₄×C₅	—	3	2	no	—
620	C₄×C₅	—	6	1	no	—
621	C₄×C₅	—	6	1	no	—
622	C₄×C₅	—	6	1	no	—
623	C₄×C₅	—	6	1	no	—
624	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
625	C₄×C₅	D₃×#41	1	1	yes	characteristic
626	C₂⁴	—	3	1	no	—
627	#41	—	6	2	no	—
628	#41	—	6	2	no	—
629	C₂×Q₈	—	3	1	no	—
630	C₂×D₄	—	3	1	no	—
631	C₂×D₄	—	3	1	no	—
632	C₂×D₄	—	3	1	no	—
633	C₂×D₄	—	3	1	no	—
634	C₂×D₄	—	3	1	no	—
635	C₂×D₄	—	3	1	no	—
636	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
637	C₂²×C₄	—	3	1	no	—
638	C₂²×C₄	—	3	1	no	—
639	C₂²×C₄	—	3	1	no	—
640	C₂²×C₄	—	3	1	no	—
641	C₂²×C₄	—	3	1	no	—
642	C₂²×C₄	—	3	1	no	—
643	C₂²×C₄	—	6	2	no	—
644	C₂²×C₄	—	6	2	no	—
645	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
646	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
647	M₁₆	—	2	2	no	—
648	M₁₆	—	6	2	no	—
649	M₁₆	—	6	2	no	—
650	M₁₆	—	6	2	no	—
651	C₂×C₈	—	2	2	no	—
652	C₂×C₈	—	3	1	no	—
653	C₂×C₈	—	3	4	no	—
654	C₂×C₈	—	3	1	no	—
655	C₂×C₈	—	3	1	no	—
656	C₂×C₈	—	3	1	no	—
657	C₂×C₈	—	6	2	no	—
658	C₂×C₈	—	6	2	no	—
659	C₂×C₈	—	6	2	no	—
660	C₂×C₈	—	6	2	no	—
661	C₂×C₈	—	6	2	no	—
662	C₂×C₈	—	6	2	no	—
663	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
664	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
665	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
666	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
667	C₄⋊C₄	—	3	1	no	—
668	C₄⋊C₄	—	3	1	no	—
669	C₄⋊C₄	—	3	1	no	—
670	C₄⋊C₄	—	3	1	no	—
671	C₄⋊C₄	—	3	1	no	—
672	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
673	C₂²⋊C₄	—	3	1	no	—
674	C₂²⋊C₄	—	3	1	no	—
675	C₂²⋊C₄	—	3	1	no	—
676	C₂²⋊C₄	—	3	1	no	—
677	C₂²⋊C₄	—	3	1	no	—
678	C₂²⋊C₄	—	3	1	no	—
679	C₂²⋊C₄	—	3	1	no	—
680	C₂²⋊C₄	—	3	1	no	—
681	C₂²⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
682	C₂²⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
683	C₄²	—	3	1	no	—
684	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
685	C₃×C₅	#2929	1	1	yes	characteristic, complemented, Hall
686	C₂²×C₃	—	2	1	no	—
687	C₂²×C₃	—	2	1	no	—
688	C₂²×C₃	—	2	1	no	—
689	C₂²×C₃	—	2	1	no	—
690	C₂²×C₃	—	2	1	no	—
691	C₂²×C₃	C₅×#131	1	2	yes	complemented
692	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
693	C₂×D₃	—	2	8	no	—
694	C₂×D₃	—	2	1	no	—
695	C₂×D₃	—	2	1	no	—
696	C₂×D₃	—	2	1	no	—
697	C₂×D₃	—	2	1	no	—
698	C₂×D₃	—	2	1	no	—
699	C₂×D₃	—	2	1	no	—
700	C₂×D₃	—	2	1	no	—
701	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
702	C₂×D₃	C₅×#131	1	2	yes	complemented
703	C₃×C₄	—	2	1	no	—
704	C₃×C₄	—	2	1	no	—
705	C₃×C₄	—	2	1	no	—
706	C₃×C₄	—	2	1	no	—
707	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
708	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
709	Dic₃	—	2	1	no	—
710	Dic₃	—	2	1	no	—
711	Dic₃	—	2	1	no	—
712	Dic₃	—	2	1	no	—
713	Dic₃	C₄×C₅×D₄	1	2	yes	—
714	C₂×C₅	—	2	2	no	—
715	C₂×C₅	—	4	1	no	—
716	C₂×C₅	—	6	2	no	—
717	C₂×C₅	—	6	2	no	—
718	C₂×C₅	—	12	1	no	—
719	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
720	C₂×C₅	C₂×#907	1	1	yes	characteristic
721	C₂×C₅	D₃×#131	1	1	yes	characteristic
722	C₂³	—	3	1	no	—
723	C₂³	—	3	1	no	—
724	C₂³	—	3	1	no	—
725	C₂³	—	6	2	no	—
726	C₂³	—	6	2	no	—
727	C₂³	—	6	2	no	—
728	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
729	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
730	Q₈	—	6	2	no	—
731	D₄	—	2	2	no	—
732	D₄	—	6	2	no	—
733	D₄	—	6	2	no	—
734	D₄	—	6	2	no	—
735	D₄	—	6	2	no	—
736	D₄	—	6	2	no	—
737	D₄	—	6	2	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	—	3	1	no	—
743	C₂×C₄	—	3	2	no	—
744	C₂×C₄	—	3	2	no	—
745	C₂×C₄	—	3	1	no	—
746	C₂×C₄	—	3	1	no	—
747	C₂×C₄	—	3	1	no	—
748	C₂×C₄	—	3	1	no	—
749	C₂×C₄	—	6	2	no	—
750	C₂×C₄	—	6	2	no	—
751	C₂×C₄	—	6	2	no	—
752	C₂×C₄	—	6	1	no	—
753	C₂×C₄	—	6	1	no	—
754	C₂×C₄	—	6	1	no	—
755	C₂×C₄	—	6	1	no	—
756	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
757	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
758	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
759	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
760	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
761	C₈	—	2	1	no	—
762	C₈	—	2	1	no	—
763	C₈	—	2	1	no	—
764	C₈	—	3	2	no	—
765	C₈	—	6	1	no	—
766	C₈	—	6	1	no	—
767	C₈	—	6	1	no	—
768	C₈	C₅×D₃×D₄	1	2	yes	—
769	C₂×C₃	—	2	2	no	—
770	C₂×C₃	—	4	1	no	—
771	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
772	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
773	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
774	D₃	—	2	2	no	—
775	D₃	—	2	2	no	—
776	D₃	—	4	1	no	—
777	C₅	#79478	1	1	yes	characteristic, direct product factor, Sylow
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	1	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	3	2	no	—
784	C₂²	—	3	2	no	—
785	C₂²	—	6	8	no	—
786	C₂²	—	6	1	no	—
787	C₂²	—	6	1	no	—
788	C₂²	—	6	1	no	—
789	C₂²	—	6	1	no	—
790	C₂²	—	6	1	no	—
791	C₂²	—	6	1	no	—
792	C₂²	—	6	1	no	—
793	C₂²	C₅×#907	1	2	yes	complemented
794	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	2	1	no	—
799	C₄	—	3	2	no	—
800	C₄	—	6	1	no	—
801	C₄	—	6	1	no	—
802	C₄	—	6	1	no	—
803	C₄	—	6	1	no	—
804	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
805	C₄	C₅×D₃×#41	1	1	yes	characteristic
806	C₃	C₅×#2929	1	1	yes	characteristic, complemented, Sylow
807	C₂	—	2	2	no	—
808	C₂	—	4	1	no	—
809	C₂	—	6	2	no	—
810	C₂	—	6	2	no	—
811	C₂	—	12	1	no	—
812	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
813	C₂	C₂×C₅×#907	1	1	yes	characteristic
814	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	C₅×#5547	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#435	D₃
hypocenter	C₃	C₅×#2929
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×#907	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×D₄×C₃⋊C₈	C₂	semidirect
8. C₅×#4839	C₂	semidirect
9. C₅×#4834	C₂	semidirect
10. C₅×#4727	C₂	semidirect
11. C₅×#4726	C₂	semidirect
12. C₅×#67⋊C₈	C₂	semidirect
13. C₅×#67⋊C₈	C₂	semidirect
14. C₅×#4708	C₂	semidirect
15. C₅×#4706	C₂	semidirect
19. C₂×C₃×C₅×M₁₆	C₂²	semidirect
27. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
31. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
37. C₂×C₅×D₃×C₈	C₂²	semidirect
46. C₃×C₅×C₄⋊C₈	C₂²	semidirect
48. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
49. C₃×C₅×#97	C₂²	semidirect
51. C₅×#830	C₂²	semidirect
54. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
55. C₅×(C₂×D₃)⋊C₈	C₂²	semidirect
56. C₅×#815	C₂²	semidirect
57. C₅×Dic₃⋊C₈	C₂²	semidirect
58. C₅×Dic₃⋊C₈	C₂²	semidirect
59. C₅×C₈×Dic₃	C₂²	semidirect
60. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
61. C₄×C₅×C₃⋊C₈	C₂²	semidirect
62. #79478	C₅	direct (N × H)
69. C₅×#435	D₃	semidirect
136. C₅×D₃×C₈	D₄	semidirect
137. C₂×#907	C₂×C₅	semidirect
138. C₂²×D₃×C₈	C₂×C₅	semidirect
140. C₃×#435	C₂×C₅	semidirect
141. #5127	C₂×C₅	semidirect
142. #5111	C₂×C₅	semidirect
143. D₄×C₃⋊C₈	C₂×C₅	semidirect
144. #4839	C₂×C₅	semidirect
145. #4834	C₂×C₅	semidirect
146. #4727	C₂×C₅	semidirect
147. #4726	C₂×C₅	semidirect
148. #67⋊C₈	C₂×C₅	semidirect
149. #67⋊C₈	C₂×C₅	semidirect
150. #4708	C₂×C₅	semidirect
151. #4706	C₂×C₅	semidirect
158. C₂×C₅×M₁₆	C₂×D₃	semidirect
184. C₅×C₄⋊C₈	C₂×D₃	semidirect
192. C₅×C₂²⋊C₈	C₂×D₃	semidirect
194. C₅×#97	C₂×D₃	semidirect
247. C₂×C₃×M₁₆	C₂²×C₅	semidirect
255. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
259. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
265. C₂×D₃×C₈	C₂²×C₅	semidirect
274. C₃×C₄⋊C₈	C₂²×C₅	semidirect
276. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
277. C₃×#97	C₂²×C₅	semidirect
279. #830	C₂²×C₅	semidirect
282. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
283. (C₂×D₃)⋊C₈	C₂²×C₅	semidirect
284. #815	C₂²×C₅	semidirect
285. Dic₃⋊C₈	C₂²×C₅	semidirect
286. Dic₃⋊C₈	C₂²×C₅	semidirect
287. C₈×Dic₃	C₂²×C₅	semidirect
288. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
289. C₄×C₃⋊C₈	C₂²×C₅	semidirect
355. #435	C₅×D₃	semidirect
369. C₂²×C₃×C₅	#131	semidirect
380. C₂×C₅×D₃	#131	semidirect
450. D₃×C₈	C₅×D₄	semidirect
504. C₂×M₁₆	C₂×C₅×D₃	semidirect
530. C₄⋊C₈	C₂×C₅×D₃	semidirect
538. C₂²⋊C₈	C₂×C₅×D₃	semidirect
540. #97	C₂×C₅×D₃	semidirect
613. C₂²×C₅	#907	semidirect
685. C₃×C₅	#2929	semidirect
691. C₂²×C₃	C₅×#131	semidirect
702. C₂×D₃	C₅×#131	semidirect
777. C₅	#79478	direct (N × H)
793. C₂²	C₅×#907	semidirect
806. C₃	C₅×#2929	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#907	2
C₂²×C₅×D₃×C₈	2
C₅×#5547	2
C₃×C₅×#435	2
C₅×#5127	2
C₅×#5111	2
C₅×D₄×C₃⋊C₈	2
C₅×#4839	2
C₅×#4834	2
C₅×#4727	2
C₅×#4726	2
C₅×#67⋊C₈	2
C₅×#4708	2
C₅×#4706	2
C₅×#2929	3
#79478	5

Subgroups — C5×#79478 #14414905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79478 #14414905