Subgroups — C₃×#10617173 #14320561

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4130	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic
4	C₃×#65779	C₂	1	2	yes	maximal
5	C₃×C₄×C₂²⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₄×C₂²⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65711	C₂	1	2	yes	maximal, complemented
8	C₃×#65700	C₂	1	2	yes	maximal, complemented
9	C₃×#65699	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65686	C₂	1	1	yes	maximal, characteristic, complemented
12	#10617173	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×AGL(1,𝔽₅)	C₂²	1	2	yes	—
14	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
18	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
19	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
20	C₃×#4130	—	2	4	no	—
21	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
22	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
23	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
24	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
28	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic, complemented
30	C₃×D₄×Dic₅	C₄	1	1	yes	characteristic, complemented
31	C₃×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic, complemented
32	C₃×C₄×C₂²⋊D₅	C₄	1	1	yes	characteristic, complemented
33	C₃×#4039	C₄	1	1	yes	characteristic, complemented
34	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₃×#4027	C₄	1	1	yes	characteristic, complemented
36	C₃×#4027	C₄	1	1	yes	characteristic, complemented
37	C₃×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic, complemented
40	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
41	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
42	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
43	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
44	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
45	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
46	C₃×#2290	—	5	1	no	maximal, Hall
47	C₂×#4130	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂²×C₄×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
49	C₄×D₄×D₅	C₂×C₃	1	1	yes	characteristic
50	#65779	C₂×C₃	1	2	yes	—
51	C₄×C₂²⋊AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
52	C₄×C₂²⋊AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
53	#65711	C₂×C₃	1	2	yes	complemented
54	#65700	C₂×C₃	1	2	yes	complemented
55	#65699	C₂×C₃	1	2	yes	complemented
56	C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
57	#65686	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
59	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
60	C₂²×C₃×AGL(1,𝔽₅)	—	2	4	no	—
61	C₂²×C₃×AGL(1,𝔽₅)	—	2	4	no	—
62	C₂²×C₃×AGL(1,𝔽₅)	—	2	4	no	—
63	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
64	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
65	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
66	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
67	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic, complemented
70	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
71	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
74	C₃×D₄×D₅	—	2	4	no	—
75	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
76	C₂×C₃×C₄×D₅	—	2	2	no	—
77	C₂×C₃×C₄×D₅	—	2	2	no	—
78	C₂×C₃×C₄×D₅	—	2	2	no	—
79	C₂×C₃×C₄×D₅	—	2	2	no	—
80	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
81	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
82	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic, complemented
83	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic, complemented
84	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
89	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
90	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
91	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
92	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
93	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
94	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
95	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
96	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
97	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
98	C₃×C₄×AGL(1,𝔽₅)	D₄	1	4	yes	complemented
99	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
100	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
102	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic, complemented
103	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
104	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
105	C₃×#685	C₂×C₄	1	1	yes	characteristic
106	C₃×#685	C₂×C₄	1	1	yes	characteristic
107	C₃×#685	C₂×C₄	1	1	yes	characteristic, complemented
108	C₃×#685	C₂×C₄	1	1	yes	characteristic, complemented
109	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
110	C₃×#683	C₂×C₄	1	1	yes	characteristic, complemented
111	C₃×#683	C₂×C₄	1	1	yes	characteristic, complemented
112	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
113	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
114	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
115	C₂×C₃×C₄×D₄	—	5	1	no	—
116	C₂×C₃×#117	—	5	1	no	—
117	C₂²×C₃×C₄²	—	5	1	no	—
118	C₃×#388	—	5	2	no	—
119	C₃×#387	—	5	2	no	—
120	C₃×#386	—	5	2	no	—
121	C₃×#385	—	5	2	no	—
122	C₃×C₄×C₄⋊C₄	—	5	1	no	—
123	C₃×C₄×C₂²⋊C₄	—	5	1	no	—
124	C₃×C₄×C₂²⋊C₄	—	5	1	no	—
125	C₃×#376	—	5	1	no	—
126	C₂³×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
127	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
128	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
129	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
131	C₂×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
132	C₂×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
133	#4130	—	2	4	no	—
134	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
135	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
136	C₂×C₄×AGL(1,𝔽₅)	—	2	4	no	—
137	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
141	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
142	C₄×C₅×D₄	C₃×C₄	1	1	yes	characteristic, complemented
143	D₄×Dic₅	C₃×C₄	1	1	yes	characteristic, complemented
144	C₄×C₂²⋊D₅	C₃×C₄	1	1	yes	characteristic, complemented
145	C₄×C₂²⋊D₅	C₃×C₄	1	1	yes	characteristic, complemented
146	#4039	C₃×C₄	1	1	yes	characteristic, complemented
147	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	#4027	C₃×C₄	1	1	yes	characteristic, complemented
149	#4027	C₃×C₄	1	1	yes	characteristic, complemented
150	D₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
151	D₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₄×D₂₀	C₃×C₄	1	1	yes	characteristic, complemented
153	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
154	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
155	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
156	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
157	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
158	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
159	#2290	—	5	1	no	Sylow
160	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₃×D₅	—	2	1	no	—
163	C₂²×C₃×D₅	—	2	1	no	—
164	C₂²×C₃×D₅	—	2	2	no	—
165	C₂²×C₃×D₅	—	2	1	no	—
166	C₂²×C₃×D₅	—	2	2	no	—
167	C₂²×C₃×D₅	—	2	1	no	—
168	C₂²×C₃×D₅	—	2	2	no	—
169	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₃×D₅	#41	1	4	yes	—
172	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
173	C₂×C₃×AGL(1,𝔽₅)	—	2	16	no	—
174	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
175	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
176	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
177	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
178	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
179	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
180	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
181	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
182	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
183	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
184	C₂×C₃×AGL(1,𝔽₅)	C₂×D₄	1	4	yes	—
185	C₂×C₃×AGL(1,𝔽₅)	#41	1	4	yes	—
186	C₃×C₅×D₄	—	2	2	no	—
187	C₂×C₃×C₄×C₅	—	2	2	no	—
188	C₂×C₃×C₄×C₅	—	2	2	no	—
189	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
194	C₃×C₂²⋊D₅	—	2	2	no	—
195	C₃×C₂²⋊D₅	—	2	2	no	—
196	C₂×C₃×Dic₅	—	2	2	no	—
197	C₂×C₃×Dic₅	—	2	2	no	—
198	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
203	C₃×D₂₀	—	2	2	no	—
204	C₃×C₄×D₅	—	2	1	no	—
205	C₃×C₄×D₅	—	2	1	no	—
206	C₃×C₄×D₅	—	2	2	no	—
207	C₃×C₄×D₅	—	2	1	no	—
208	C₃×C₄×D₅	—	2	1	no	—
209	C₃×C₄×D₅	—	2	2	no	—
210	C₃×C₄×D₅	—	2	2	no	—
211	C₃×C₄×D₅	—	2	2	no	—
212	C₃×C₄×D₅	—	2	2	no	—
213	C₃×C₄×D₅	—	2	2	no	—
214	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
215	C₃×C₄×D₅	#41	1	2	yes	—
216	C₂²×C₃×D₄	—	5	1	no	—
217	C₂³×C₃×C₄	—	5	1	no	—
218	C₂³×C₃×C₄	—	5	1	no	—
219	C₂³×C₃×C₄	—	5	2	no	—
220	C₃×C₄×D₄	—	5	1	no	—
221	C₃×C₄×D₄	—	5	1	no	—
222	C₃×C₄×D₄	—	5	1	no	—
223	C₃×C₄×D₄	—	5	1	no	—
224	C₃×C₄×D₄	—	5	1	no	—
225	C₃×C₄×D₄	—	5	1	no	—
226	C₃×C₄×D₄	—	5	1	no	—
227	C₃×C₄×D₄	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
228	C₃×#117	—	10	4	no	—
229	C₂×C₃×C₄⋊C₄	—	5	1	no	—
230	C₂×C₃×C₄⋊C₄	—	5	2	no	—
231	C₂×C₃×C₄⋊C₄	—	5	2	no	—
232	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
233	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
234	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
235	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
236	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
237	C₂×C₃×C₄²	—	5	1	no	—
238	C₂×C₃×C₄²	—	5	1	no	—
239	C₂×C₃×C₄²	—	5	1	no	—
240	C₂×C₃×C₄²	—	5	1	no	—
241	C₂×C₃×C₄²	—	5	1	no	—
242	C₂×C₃×C₄²	—	5	2	no	—
243	C₂×C₃×C₄²	—	10	4	no	—
244	C₃×#95	—	5	2	no	—
245	C₃×#95	—	5	2	no	—
246	C₃×#95	—	5	2	no	—
247	C₃×#95	—	5	2	no	—
248	C₃×#95	—	5	2	no	—
249	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
250	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
251	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
252	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
253	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
254	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
255	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
256	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
257	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
258	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
259	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
260	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
261	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
262	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
263	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
264	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
265	D₄×D₅	—	2	4	no	—
266	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
267	C₂×C₄×D₅	—	2	2	no	—
268	C₂×C₄×D₅	—	2	2	no	—
269	C₂×C₄×D₅	—	2	2	no	—
270	C₂×C₄×D₅	—	2	2	no	—
271	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
272	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
273	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
274	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
275	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
276	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
277	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
278	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
279	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
280	C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
281	C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
282	C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
283	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
284	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
285	C₄×AGL(1,𝔽₅)	—	2	4	no	—
286	C₄×AGL(1,𝔽₅)	—	2	2	no	—
287	C₄×AGL(1,𝔽₅)	—	2	2	no	—
288	C₄×AGL(1,𝔽₅)	—	2	2	no	—
289	C₄×AGL(1,𝔽₅)	C₃×D₄	1	4	yes	complemented
290	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
291	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
292	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
293	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
294	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
295	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
296	#685	C₂×C₃×C₄	1	1	yes	characteristic
297	#685	C₂×C₃×C₄	1	1	yes	characteristic
298	#685	C₂×C₃×C₄	1	1	yes	characteristic, complemented
299	#685	C₂×C₃×C₄	1	1	yes	characteristic, complemented
300	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
301	#683	C₂×C₃×C₄	1	1	yes	characteristic, complemented
302	#683	C₂×C₃×C₄	1	1	yes	characteristic, complemented
303	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
304	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
305	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
306	C₂×C₄×D₄	—	5	1	no	—
307	C₂×#117	—	5	1	no	—
308	C₂²×C₄²	—	5	1	no	—
309	#388	—	5	2	no	—
310	#387	—	5	2	no	—
311	#386	—	5	2	no	—
312	#385	—	5	2	no	—
313	C₄×C₄⋊C₄	—	5	1	no	—
314	C₄×C₂²⋊C₄	—	5	1	no	—
315	C₄×C₂²⋊C₄	—	5	1	no	—
316	#376	—	5	1	no	—
317	C₂²×C₃×C₅	—	2	1	no	—
318	C₂²×C₃×C₅	—	2	1	no	—
319	C₂²×C₃×C₅	—	2	1	no	—
320	C₂²×C₃×C₅	—	2	1	no	—
321	C₂²×C₃×C₅	—	2	1	no	—
322	C₂²×C₃×C₅	#117	1	2	yes	complemented
323	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
324	C₂×C₃×D₅	—	2	1	no	—
325	C₂×C₃×D₅	—	2	1	no	—
326	C₂×C₃×D₅	—	2	4	no	—
327	C₂×C₃×D₅	—	2	4	no	—
328	C₂×C₃×D₅	—	2	1	no	—
329	C₂×C₃×D₅	—	2	1	no	—
330	C₂×C₃×D₅	—	2	1	no	—
331	C₂×C₃×D₅	—	4	2	no	—
332	C₂×C₃×D₅	—	4	2	no	—
333	C₂×C₃×D₅	#117	1	2	yes	complemented
334	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₃×D₅	C₂×#41	1	2	yes	—
336	C₂×C₃×D₅	C₂×#41	1	2	yes	—
337	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
338	C₃×AGL(1,𝔽₅)	—	2	4	no	—
339	C₃×AGL(1,𝔽₅)	—	2	4	no	—
340	C₃×AGL(1,𝔽₅)	—	4	2	no	—
341	C₃×AGL(1,𝔽₅)	—	4	2	no	—
342	C₃×C₄×C₅	—	2	1	no	—
343	C₃×C₄×C₅	—	2	1	no	—
344	C₃×C₄×C₅	—	2	1	no	—
345	C₃×C₄×C₅	—	2	1	no	—
346	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
347	C₃×Dic₅	—	2	1	no	—
348	C₃×Dic₅	—	2	1	no	—
349	C₃×Dic₅	—	2	1	no	—
350	C₃×Dic₅	—	2	1	no	—
351	C₃×Dic₅	C₄×D₄	1	2	yes	—
352	C₂⁴×C₃	—	5	1	no	—
353	C₂⁴×C₃	—	5	1	no	—
354	C₂×C₃×D₄	—	5	1	no	—
355	C₂×C₃×D₄	—	5	1	no	—
356	C₂×C₃×D₄	—	5	1	no	—
357	C₂×C₃×D₄	—	10	4	no	—
358	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
359	C₂²×C₃×C₄	—	5	1	no	—
360	C₂²×C₃×C₄	—	5	2	no	—
361	C₂²×C₃×C₄	—	5	2	no	—
362	C₂²×C₃×C₄	—	5	1	no	—
363	C₂²×C₃×C₄	—	5	1	no	—
364	C₂²×C₃×C₄	—	5	1	no	—
365	C₂²×C₃×C₄	—	5	1	no	—
366	C₂²×C₃×C₄	—	5	1	no	—
367	C₂²×C₃×C₄	—	5	1	no	—
368	C₂²×C₃×C₄	—	5	1	no	—
369	C₂²×C₃×C₄	—	5	1	no	—
370	C₂²×C₃×C₄	—	5	1	no	—
371	C₂²×C₃×C₄	—	5	1	no	—
372	C₂²×C₃×C₄	—	5	2	no	—
373	C₂²×C₃×C₄	—	5	2	no	—
374	C₂²×C₃×C₄	—	10	2	no	—
375	C₂²×C₃×C₄	—	10	2	no	—
376	C₂²×C₃×C₄	—	10	2	no	—
377	C₂²×C₃×C₄	—	10	2	no	—
378	C₂²×C₃×C₄	—	10	4	no	—
379	C₂²×C₃×C₄	—	10	4	no	—
380	C₂²×C₃×C₄	—	10	4	no	—
381	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
382	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
383	C₃×C₄⋊C₄	—	5	1	no	—
384	C₃×C₄⋊C₄	—	5	1	no	—
385	C₃×C₄⋊C₄	—	5	1	no	—
386	C₃×C₄⋊C₄	—	10	4	no	—
387	C₃×C₄⋊C₄	—	10	4	no	—
388	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
389	C₃×C₂²⋊C₄	—	5	1	no	—
390	C₃×C₂²⋊C₄	—	5	1	no	—
391	C₃×C₂²⋊C₄	—	5	1	no	—
392	C₃×C₂²⋊C₄	—	5	1	no	—
393	C₃×C₂²⋊C₄	—	5	1	no	—
394	C₃×C₂²⋊C₄	—	5	1	no	—
395	C₃×C₂²⋊C₄	—	10	4	no	—
396	C₃×C₂²⋊C₄	—	10	4	no	—
397	C₃×C₂²⋊C₄	—	10	4	no	—
398	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
399	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
400	C₃×C₄²	—	5	4	no	—
401	C₃×C₄²	—	5	1	no	—
402	C₃×C₄²	—	5	1	no	—
403	C₃×C₄²	—	5	1	no	—
404	C₃×C₄²	—	10	2	no	—
405	C₃×C₄²	—	10	2	no	—
406	C₃×C₄²	—	10	4	no	—
407	C₃×C₄²	—	10	2	no	—
408	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
409	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
410	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
411	C₂²×D₅	—	2	1	no	—
412	C₂²×D₅	—	2	1	no	—
413	C₂²×D₅	—	2	2	no	—
414	C₂²×D₅	—	2	1	no	—
415	C₂²×D₅	—	2	2	no	—
416	C₂²×D₅	—	2	1	no	—
417	C₂²×D₅	—	2	2	no	—
418	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
419	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
420	C₂²×D₅	C₃×#41	1	4	yes	—
421	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
422	C₂×AGL(1,𝔽₅)	—	2	16	no	—
423	C₂×AGL(1,𝔽₅)	—	2	2	no	—
424	C₂×AGL(1,𝔽₅)	—	2	2	no	—
425	C₂×AGL(1,𝔽₅)	—	2	2	no	—
426	C₂×AGL(1,𝔽₅)	—	2	2	no	—
427	C₂×AGL(1,𝔽₅)	—	2	2	no	—
428	C₂×AGL(1,𝔽₅)	—	2	2	no	—
429	C₂×AGL(1,𝔽₅)	—	2	2	no	—
430	C₂×AGL(1,𝔽₅)	—	2	2	no	—
431	C₂×AGL(1,𝔽₅)	—	2	2	no	—
432	C₂×AGL(1,𝔽₅)	—	2	2	no	—
433	C₂×AGL(1,𝔽₅)	C₂×C₃×D₄	1	4	yes	—
434	C₂×AGL(1,𝔽₅)	C₃×#41	1	4	yes	—
435	C₅×D₄	—	2	2	no	—
436	C₂×C₄×C₅	—	2	2	no	—
437	C₂×C₄×C₅	—	2	2	no	—
438	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
439	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
440	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
441	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
442	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
443	C₂²⋊D₅	—	2	2	no	—
444	C₂²⋊D₅	—	2	2	no	—
445	C₂×Dic₅	—	2	2	no	—
446	C₂×Dic₅	—	2	2	no	—
447	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
448	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
449	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
450	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
451	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
452	D₂₀	—	2	2	no	—
453	C₄×D₅	—	2	1	no	—
454	C₄×D₅	—	2	1	no	—
455	C₄×D₅	—	2	2	no	—
456	C₄×D₅	—	2	1	no	—
457	C₄×D₅	—	2	1	no	—
458	C₄×D₅	—	2	2	no	—
459	C₄×D₅	—	2	2	no	—
460	C₄×D₅	—	2	2	no	—
461	C₄×D₅	—	2	2	no	—
462	C₄×D₅	—	2	2	no	—
463	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
464	C₄×D₅	C₃×#41	1	2	yes	—
465	C₂²×D₄	—	5	1	no	—
466	C₂³×C₄	—	5	1	no	—
467	C₂³×C₄	—	5	1	no	—
468	C₂³×C₄	—	5	2	no	—
469	C₄×D₄	—	5	1	no	—
470	C₄×D₄	—	5	1	no	—
471	C₄×D₄	—	5	1	no	—
472	C₄×D₄	—	5	1	no	—
473	C₄×D₄	—	5	1	no	—
474	C₄×D₄	—	5	1	no	—
475	C₄×D₄	—	5	1	no	—
476	C₄×D₄	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
477	#117	—	10	4	no	—
478	C₂×C₄⋊C₄	—	5	1	no	—
479	C₂×C₄⋊C₄	—	5	2	no	—
480	C₂×C₄⋊C₄	—	5	2	no	—
481	C₂×C₂²⋊C₄	—	5	1	no	—
482	C₂×C₂²⋊C₄	—	5	1	no	—
483	C₂×C₂²⋊C₄	—	5	2	no	—
484	C₂×C₂²⋊C₄	—	5	2	no	—
485	C₂×C₂²⋊C₄	—	5	2	no	—
486	C₂×C₄²	—	5	1	no	—
487	C₂×C₄²	—	5	1	no	—
488	C₂×C₄²	—	5	1	no	—
489	C₂×C₄²	—	5	1	no	—
490	C₂×C₄²	—	5	1	no	—
491	C₂×C₄²	—	5	2	no	—
492	C₂×C₄²	—	10	4	no	—
493	#95	—	5	2	no	—
494	#95	—	5	2	no	—
495	#95	—	5	2	no	—
496	#95	—	5	2	no	—
497	#95	—	5	2	no	—
498	C₂×C₃×C₅	—	2	2	no	—
499	C₂×C₃×C₅	—	4	1	no	—
500	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
501	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
502	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
503	C₃×D₅	—	2	2	no	—
504	C₃×D₅	—	4	1	no	—
505	C₃×D₅	#525	1	2	yes	—
506	C₃×D₅	#529	1	2	yes	—
507	C₂³×C₃	—	5	1	no	—
508	C₂³×C₃	—	5	4	no	—
509	C₂³×C₃	—	5	1	no	—
510	C₂³×C₃	—	5	1	no	—
511	C₂³×C₃	—	10	1	no	—
512	C₂³×C₃	—	10	1	no	—
513	C₂³×C₃	—	10	2	no	—
514	C₂³×C₃	—	10	1	no	—
515	C₂³×C₃	—	10	2	no	—
516	C₂³×C₃	—	10	1	no	—
517	C₂³×C₃	—	10	2	no	—
518	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
519	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
520	C₃×D₄	—	2	2	no	—
521	C₃×D₄	—	10	2	no	—
522	C₃×D₄	—	10	2	no	—
523	C₃×D₄	—	10	2	no	—
524	C₂×C₃×C₄	—	2	2	no	—
525	C₂×C₃×C₄	—	2	2	no	—
526	C₂×C₃×C₄	—	5	1	no	—
527	C₂×C₃×C₄	—	5	2	no	—
528	C₂×C₃×C₄	—	5	2	no	—
529	C₂×C₃×C₄	—	5	4	no	—
530	C₂×C₃×C₄	—	5	4	no	—
531	C₂×C₃×C₄	—	5	1	no	—
532	C₂×C₃×C₄	—	5	1	no	—
533	C₂×C₃×C₄	—	5	1	no	—
534	C₂×C₃×C₄	—	5	1	no	—
535	C₂×C₃×C₄	—	10	2	no	—
536	C₂×C₃×C₄	—	10	2	no	—
537	C₂×C₃×C₄	—	10	1	no	—
538	C₂×C₃×C₄	—	10	1	no	—
539	C₂×C₃×C₄	—	10	2	no	—
540	C₂×C₃×C₄	—	10	1	no	—
541	C₂×C₃×C₄	—	10	1	no	—
542	C₂×C₃×C₄	—	10	2	no	—
543	C₂×C₃×C₄	—	10	2	no	—
544	C₂×C₃×C₄	—	10	2	no	—
545	C₂×C₃×C₄	—	10	2	no	—
546	C₂×C₃×C₄	—	10	2	no	—
547	C₂×C₃×C₄	—	10	2	no	—
548	C₂×C₃×C₄	—	10	2	no	—
549	C₂×C₃×C₄	—	10	16	no	—
550	C₂×C₃×C₄	—	10	2	no	—
551	C₂×C₃×C₄	—	10	2	no	—
552	C₂×C₃×C₄	—	10	2	no	—
553	C₂×C₃×C₄	—	10	2	no	—
554	C₂×C₃×C₄	—	10	2	no	—
555	C₂×C₃×C₄	—	10	2	no	—
556	C₂×C₃×C₄	—	10	2	no	—
557	C₂×C₃×C₄	—	10	2	no	—
558	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
559	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
560	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
561	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
562	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
563	C₂²×C₅	—	2	1	no	—
564	C₂²×C₅	—	2	1	no	—
565	C₂²×C₅	—	2	1	no	—
566	C₂²×C₅	—	2	1	no	—
567	C₂²×C₅	—	2	1	no	—
568	C₂²×C₅	C₃×#117	1	2	yes	complemented
569	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
570	C₂×D₅	—	2	1	no	—
571	C₂×D₅	—	2	1	no	—
572	C₂×D₅	—	2	4	no	—
573	C₂×D₅	—	2	4	no	—
574	C₂×D₅	—	2	1	no	—
575	C₂×D₅	—	2	1	no	—
576	C₂×D₅	—	2	1	no	—
577	C₂×D₅	—	4	2	no	—
578	C₂×D₅	—	4	2	no	—
579	C₂×D₅	C₃×#117	1	2	yes	complemented
580	C₂×D₅	C₂²×C₃×D₄	1	1	yes	characteristic
581	C₂×D₅	C₂×C₃×#41	1	2	yes	—
582	C₂×D₅	C₂×C₃×#41	1	2	yes	—
583	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
584	AGL(1,𝔽₅)	—	2	4	no	—
585	AGL(1,𝔽₅)	—	2	4	no	—
586	AGL(1,𝔽₅)	—	4	2	no	—
587	AGL(1,𝔽₅)	—	4	2	no	—
588	C₄×C₅	—	2	1	no	—
589	C₄×C₅	—	2	1	no	—
590	C₄×C₅	—	2	1	no	—
591	C₄×C₅	—	2	1	no	—
592	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
593	Dic₅	—	2	1	no	—
594	Dic₅	—	2	1	no	—
595	Dic₅	—	2	1	no	—
596	Dic₅	—	2	1	no	—
597	Dic₅	C₃×C₄×D₄	1	2	yes	—
598	C₂⁴	—	5	1	no	—
599	C₂⁴	—	5	1	no	—
600	C₂×D₄	—	5	1	no	—
601	C₂×D₄	—	5	1	no	—
602	C₂×D₄	—	5	1	no	—
603	C₂×D₄	—	10	4	no	—
604	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
605	C₂²×C₄	—	5	1	no	—
606	C₂²×C₄	—	5	2	no	—
607	C₂²×C₄	—	5	2	no	—
608	C₂²×C₄	—	5	1	no	—
609	C₂²×C₄	—	5	1	no	—
610	C₂²×C₄	—	5	1	no	—
611	C₂²×C₄	—	5	1	no	—
612	C₂²×C₄	—	5	1	no	—
613	C₂²×C₄	—	5	1	no	—
614	C₂²×C₄	—	5	1	no	—
615	C₂²×C₄	—	5	1	no	—
616	C₂²×C₄	—	5	1	no	—
617	C₂²×C₄	—	5	1	no	—
618	C₂²×C₄	—	5	2	no	—
619	C₂²×C₄	—	5	2	no	—
620	C₂²×C₄	—	10	2	no	—
621	C₂²×C₄	—	10	2	no	—
622	C₂²×C₄	—	10	2	no	—
623	C₂²×C₄	—	10	2	no	—
624	C₂²×C₄	—	10	4	no	—
625	C₂²×C₄	—	10	4	no	—
626	C₂²×C₄	—	10	4	no	—
627	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
628	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
629	C₄⋊C₄	—	5	1	no	—
630	C₄⋊C₄	—	5	1	no	—
631	C₄⋊C₄	—	5	1	no	—
632	C₄⋊C₄	—	10	4	no	—
633	C₄⋊C₄	—	10	4	no	—
634	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
635	C₂²⋊C₄	—	5	1	no	—
636	C₂²⋊C₄	—	5	1	no	—
637	C₂²⋊C₄	—	5	1	no	—
638	C₂²⋊C₄	—	5	1	no	—
639	C₂²⋊C₄	—	5	1	no	—
640	C₂²⋊C₄	—	5	1	no	—
641	C₂²⋊C₄	—	10	4	no	—
642	C₂²⋊C₄	—	10	4	no	—
643	C₂²⋊C₄	—	10	4	no	—
644	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
645	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
646	C₄²	—	5	4	no	—
647	C₄²	—	5	1	no	—
648	C₄²	—	5	1	no	—
649	C₄²	—	5	1	no	—
650	C₄²	—	10	2	no	—
651	C₄²	—	10	4	no	—
652	C₄²	—	10	2	no	—
653	C₄²	—	10	2	no	—
654	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
655	C₃×C₅	#2290	1	1	yes	characteristic, complemented, Hall
656	C₂²×C₃	—	2	1	no	—
657	C₂²×C₃	—	2	1	no	—
658	C₂²×C₃	—	2	1	no	—
659	C₂²×C₃	—	2	1	no	—
660	C₂²×C₃	—	2	1	no	—
661	C₂²×C₃	—	5	2	no	—
662	C₂²×C₃	—	5	1	no	—
663	C₂²×C₃	—	5	1	no	—
664	C₂²×C₃	—	5	2	no	—
665	C₂²×C₃	—	5	2	no	—
666	C₂²×C₃	—	10	4	no	—
667	C₂²×C₃	—	10	4	no	—
668	C₂²×C₃	—	10	1	no	—
669	C₂²×C₃	—	10	1	no	—
670	C₂²×C₃	—	10	1	no	—
671	C₂²×C₃	—	10	1	no	—
672	C₂²×C₃	—	10	1	no	—
673	C₂²×C₃	—	20	2	no	—
674	C₂²×C₃	—	20	2	no	—
675	C₂²×C₃	#4130	1	2	yes	complemented
676	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
677	C₃×C₄	—	2	1	no	—
678	C₃×C₄	—	2	1	no	—
679	C₃×C₄	—	2	1	no	—
680	C₃×C₄	—	2	1	no	—
681	C₃×C₄	—	5	2	no	—
682	C₃×C₄	—	10	4	no	—
683	C₃×C₄	—	10	4	no	—
684	C₃×C₄	—	10	1	no	—
685	C₃×C₄	—	10	1	no	—
686	C₃×C₄	—	10	1	no	—
687	C₃×C₄	—	10	1	no	—
688	C₃×C₄	—	20	2	no	—
689	C₃×C₄	—	20	2	no	—
690	C₃×C₄	D₄×AGL(1,𝔽₅)	1	2	yes	—
691	C₂×C₅	—	2	2	no	—
692	C₂×C₅	—	4	1	no	—
693	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
694	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
695	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
696	D₅	—	2	2	no	—
697	D₅	—	4	1	no	—
698	D₅	C₃×#525	1	2	yes	—
699	D₅	C₃×#529	1	2	yes	—
700	C₂³	—	5	1	no	—
701	C₂³	—	5	4	no	—
702	C₂³	—	5	1	no	—
703	C₂³	—	5	1	no	—
704	C₂³	—	10	1	no	—
705	C₂³	—	10	1	no	—
706	C₂³	—	10	2	no	—
707	C₂³	—	10	1	no	—
708	C₂³	—	10	2	no	—
709	C₂³	—	10	1	no	—
710	C₂³	—	10	2	no	—
711	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
712	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
713	D₄	—	2	2	no	—
714	D₄	—	10	2	no	—
715	D₄	—	10	2	no	—
716	D₄	—	10	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	5	1	no	—
720	C₂×C₄	—	5	2	no	—
721	C₂×C₄	—	5	2	no	—
722	C₂×C₄	—	5	4	no	—
723	C₂×C₄	—	5	4	no	—
724	C₂×C₄	—	5	1	no	—
725	C₂×C₄	—	5	1	no	—
726	C₂×C₄	—	5	1	no	—
727	C₂×C₄	—	5	1	no	—
728	C₂×C₄	—	10	2	no	—
729	C₂×C₄	—	10	2	no	—
730	C₂×C₄	—	10	1	no	—
731	C₂×C₄	—	10	1	no	—
732	C₂×C₄	—	10	2	no	—
733	C₂×C₄	—	10	1	no	—
734	C₂×C₄	—	10	1	no	—
735	C₂×C₄	—	10	2	no	—
736	C₂×C₄	—	10	2	no	—
737	C₂×C₄	—	10	2	no	—
738	C₂×C₄	—	10	2	no	—
739	C₂×C₄	—	10	2	no	—
740	C₂×C₄	—	10	2	no	—
741	C₂×C₄	—	10	2	no	—
742	C₂×C₄	—	10	16	no	—
743	C₂×C₄	—	10	2	no	—
744	C₂×C₄	—	10	2	no	—
745	C₂×C₄	—	10	2	no	—
746	C₂×C₄	—	10	2	no	—
747	C₂×C₄	—	10	2	no	—
748	C₂×C₄	—	10	2	no	—
749	C₂×C₄	—	10	2	no	—
750	C₂×C₄	—	10	2	no	—
751	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
752	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
753	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
754	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
755	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
756	C₂×C₃	—	2	2	no	—
757	C₂×C₃	—	4	1	no	—
758	C₂×C₃	—	5	2	no	—
759	C₂×C₃	—	5	2	no	—
760	C₂×C₃	—	10	2	no	—
761	C₂×C₃	—	20	1	no	—
762	C₂×C₃	C₂×#4130	1	1	yes	characteristic
763	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
764	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
765	C₅	C₃×#2290	1	1	yes	characteristic, complemented, Sylow
766	C₂²	—	2	1	no	—
767	C₂²	—	2	1	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	2	1	no	—
771	C₂²	—	5	2	no	—
772	C₂²	—	5	1	no	—
773	C₂²	—	5	1	no	—
774	C₂²	—	5	2	no	—
775	C₂²	—	5	2	no	—
776	C₂²	—	10	4	no	—
777	C₂²	—	10	4	no	—
778	C₂²	—	10	1	no	—
779	C₂²	—	10	1	no	—
780	C₂²	—	10	1	no	—
781	C₂²	—	10	1	no	—
782	C₂²	—	10	1	no	—
783	C₂²	—	20	2	no	—
784	C₂²	—	20	2	no	—
785	C₂²	C₃×#4130	1	2	yes	complemented
786	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	1	no	—
791	C₄	—	5	2	no	—
792	C₄	—	10	4	no	—
793	C₄	—	10	4	no	—
794	C₄	—	10	1	no	—
795	C₄	—	10	1	no	—
796	C₄	—	10	1	no	—
797	C₄	—	10	1	no	—
798	C₄	—	20	2	no	—
799	C₄	—	20	2	no	—
800	C₄	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
801	C₃	#10617173	1	1	yes	characteristic, direct product factor, Sylow
802	C₂	—	2	2	no	—
803	C₂	—	4	1	no	—
804	C₂	—	5	2	no	—
805	C₂	—	5	2	no	—
806	C₂	—	10	2	no	—
807	C₂	—	20	1	no	—
808	C₂	C₂×C₃×#4130	1	1	yes	characteristic
809	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
810	C₂	C₃×#41×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₄×C₅×D₄	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×D₄×D₅	C₂²
cosocle	C₂²×D₅	C₂⁴×C₃
hypercenter	C₃×C₄×D₄	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2290
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4130	C₂	semidirect
2. C₂²×C₃×C₄×AGL(1,𝔽₅)	C₂	semidirect
5. C₃×C₄×C₂²⋊AGL(1,𝔽₅)	C₂	semidirect
6. C₃×C₄×C₂²⋊AGL(1,𝔽₅)	C₂	semidirect
7. C₃×#65711	C₂	semidirect
8. C₃×#65700	C₂	semidirect
9. C₃×#65699	C₂	semidirect
10. C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	semidirect
11. C₃×#65686	C₂	semidirect
12. #10617173	C₃	direct (N × H)
29. C₃×C₄×C₅×D₄	C₄	semidirect
30. C₃×D₄×Dic₅	C₄	semidirect
31. C₃×C₄×C₂²⋊D₅	C₄	semidirect
32. C₃×C₄×C₂²⋊D₅	C₄	semidirect
33. C₃×#4039	C₄	semidirect
35. C₃×#4027	C₄	semidirect
36. C₃×#4027	C₄	semidirect
39. C₃×C₄×D₂₀	C₄	semidirect
47. C₂×#4130	C₂×C₃	semidirect
48. C₂²×C₄×AGL(1,𝔽₅)	C₂×C₃	semidirect
51. C₄×C₂²⋊AGL(1,𝔽₅)	C₂×C₃	semidirect
52. C₄×C₂²⋊AGL(1,𝔽₅)	C₂×C₃	semidirect
53. #65711	C₂×C₃	semidirect
54. #65700	C₂×C₃	semidirect
55. #65699	C₂×C₃	semidirect
56. C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	semidirect
57. #65686	C₂×C₃	semidirect
69. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
73. C₂²×C₃×Dic₅	C₂×C₄	semidirect
82. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
83. C₂×C₃×C₄×D₅	C₂×C₄	semidirect
98. C₃×C₄×AGL(1,𝔽₅)	D₄	semidirect
99. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
101. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
102. C₃×C₄²×C₅	C₂×C₄	semidirect
104. C₃×C₂²⋊Dic₅	C₂×C₄	semidirect
107. C₃×#685	C₂×C₄	semidirect
108. C₃×#685	C₂×C₄	semidirect
109. C₃×C₄⋊Dic₅	C₂×C₄	semidirect
110. C₃×#683	C₂×C₄	semidirect
111. C₃×#683	C₂×C₄	semidirect
112. C₃×C₄×Dic₅	C₂×C₄	semidirect
113. C₃×C₄×Dic₅	C₂×C₄	semidirect
114. C₃×C₄×Dic₅	C₂×C₄	semidirect
142. C₄×C₅×D₄	C₃×C₄	semidirect
143. D₄×Dic₅	C₃×C₄	semidirect
144. C₄×C₂²⋊D₅	C₃×C₄	semidirect
145. C₄×C₂²⋊D₅	C₃×C₄	semidirect
146. #4039	C₃×C₄	semidirect
148. #4027	C₃×C₄	semidirect
149. #4027	C₃×C₄	semidirect
152. C₄×D₂₀	C₃×C₄	semidirect
227. C₃×C₄×D₄	AGL(1,𝔽₅)	semidirect
260. C₂²×C₄×C₅	C₂×C₃×C₄	semidirect
264. C₂²×Dic₅	C₂×C₃×C₄	semidirect
273. C₂×C₄×D₅	C₂×C₃×C₄	semidirect
274. C₂×C₄×D₅	C₂×C₃×C₄	semidirect
289. C₄×AGL(1,𝔽₅)	C₃×D₄	semidirect
290. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
292. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
293. C₄²×C₅	C₂×C₃×C₄	semidirect
295. C₂²⋊Dic₅	C₂×C₃×C₄	semidirect
298. #685	C₂×C₃×C₄	semidirect
299. #685	C₂×C₃×C₄	semidirect
300. C₄⋊Dic₅	C₂×C₃×C₄	semidirect
301. #683	C₂×C₃×C₄	semidirect
302. #683	C₂×C₃×C₄	semidirect
303. C₄×Dic₅	C₂×C₃×C₄	semidirect
304. C₄×Dic₅	C₂×C₃×C₄	semidirect
305. C₄×Dic₅	C₂×C₃×C₄	semidirect
322. C₂²×C₃×C₅	#117	semidirect
333. C₂×C₃×D₅	#117	semidirect
382. C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	semidirect
388. C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	semidirect
399. C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	semidirect
408. C₃×C₄²	C₂×AGL(1,𝔽₅)	semidirect
476. C₄×D₄	C₃×AGL(1,𝔽₅)	semidirect
568. C₂²×C₅	C₃×#117	semidirect
579. C₂×D₅	C₃×#117	semidirect
628. C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
634. C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
645. C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
654. C₄²	C₂×C₃×AGL(1,𝔽₅)	semidirect
655. C₃×C₅	#2290	semidirect
675. C₂²×C₃	#4130	semidirect
765. C₅	C₃×#2290	semidirect
785. C₂²	C₃×#4130	semidirect
801. C₃	#10617173	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×#4130	2
C₂²×C₃×C₄×AGL(1,𝔽₅)	2
C₃×C₄×D₄×D₅	2
C₃×#65779	2
C₃×C₄×C₂²⋊AGL(1,𝔽₅)	2
C₃×#65711	2
C₃×#65700	2
C₃×#65699	2
C₃×C₄×C₄⋊AGL(1,𝔽₅)	2
C₃×#65686	2
#10617173	3
C₃×#2290	5

Subgroups — C3×#10617173 #14320561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617173 #14320561