Subgroups — C₃×#10617359 #14330254

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×#126	C₂	1	1	yes	maximal, characteristic
2	C₃×#65712	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65711	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65711	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65711	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₄⋊C₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄⋊C₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65700	C₂	1	1	yes	maximal, characteristic
9	C₃×#65700	C₂	1	1	yes	maximal, characteristic
10	C₃×#65700	C₂	1	1	yes	maximal, characteristic
11	C₃×#65699	C₂	1	1	yes	maximal, characteristic
12	C₃×C₂²⋊C₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
13	C₃×C₂²⋊C₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
14	C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#65686	C₂	1	1	yes	maximal, characteristic, complemented
16	#10617359	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂³×C₃×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
28	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
33	C₃×C₅×#126	C₄	1	1	yes	characteristic, complemented
34	C₃×#4044	C₄	1	1	yes	characteristic, complemented
35	C₃×#4044	C₄	1	1	yes	characteristic, complemented
36	C₃×#4044	C₄	1	1	yes	characteristic, complemented
37	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₃×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₃×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×#4025	C₄	1	1	yes	characteristic, complemented
44	C₃×#4025	C₄	1	1	yes	characteristic, complemented
45	C₃×#4025	C₄	1	1	yes	characteristic, complemented
46	C₃×#4022	C₄	1	1	yes	characteristic, complemented
47	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
48	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
49	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
50	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
51	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
52	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
53	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
54	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
55	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
56	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
57	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
58	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
59	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
60	C₃×#2373	—	5	1	no	maximal, Hall
61	D₅×#126	C₂×C₃	1	1	yes	characteristic
62	#65712	C₂×C₃	1	1	yes	characteristic, complemented
63	#65711	C₂×C₃	1	1	yes	characteristic, complemented
64	#65711	C₂×C₃	1	1	yes	characteristic, complemented
65	#65711	C₂×C₃	1	1	yes	characteristic, complemented
66	C₄⋊C₄×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
67	C₄⋊C₄×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
68	#65700	C₂×C₃	1	1	yes	characteristic
69	#65700	C₂×C₃	1	1	yes	characteristic
70	#65700	C₂×C₃	1	1	yes	characteristic
71	#65699	C₂×C₃	1	1	yes	characteristic
72	C₂²⋊C₄×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
73	C₂²⋊C₄×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
74	C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
75	#65686	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
77	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
78	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
79	C₂²×C₃×AGL(1,𝔽₅)	—	4	1	no	—
80	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
81	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
82	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
83	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
84	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
85	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
86	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
87	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
94	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
95	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
96	C₃×C₂²⋊AGL(1,𝔽₅)	—	4	1	no	—
97	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
98	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
99	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
100	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
101	C₃×C₄⋊AGL(1,𝔽₅)	—	4	1	no	—
102	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
103	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
104	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
105	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
106	C₃×C₄×AGL(1,𝔽₅)	—	4	1	no	—
107	C₃×C₄×AGL(1,𝔽₅)	—	4	1	no	—
108	C₃×C₄×AGL(1,𝔽₅)	—	4	1	no	—
109	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
110	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
111	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
112	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic, complemented
116	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
117	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
118	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
119	C₃×#685	C₂×C₄	1	1	yes	characteristic
120	C₃×#685	C₂×C₄	1	1	yes	characteristic
121	C₃×#685	C₂×C₄	1	1	yes	characteristic
122	C₃×#685	C₂×C₄	1	1	yes	characteristic
123	C₃×#685	C₂×C₄	1	1	yes	characteristic
124	C₃×#685	C₂×C₄	1	1	yes	characteristic
125	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
126	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
127	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
128	C₃×#683	C₂×C₄	1	1	yes	characteristic, complemented
129	C₃×#683	C₂×C₄	1	1	yes	characteristic, complemented
130	C₃×#683	C₂×C₄	1	1	yes	characteristic, complemented
131	C₃×#683	C₂×C₄	1	1	yes	characteristic, complemented
132	C₃×#683	C₂×C₄	1	1	yes	characteristic, complemented
133	C₃×#683	C₂×C₄	1	1	yes	characteristic, complemented
134	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
135	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
136	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
137	C₂×C₃×#126	—	5	1	no	—
138	C₃×#389	—	5	1	no	—
139	C₃×#388	—	5	1	no	—
140	C₃×#388	—	5	1	no	—
141	C₃×#388	—	5	1	no	—
142	C₃×#387	—	5	1	no	—
143	C₃×#387	—	5	1	no	—
144	C₃×#387	—	5	1	no	—
145	C₃×#385	—	5	1	no	—
146	C₃×C₄×C₄⋊C₄	—	5	1	no	—
147	C₃×C₄×C₄⋊C₄	—	5	1	no	—
148	C₃×C₄×C₄⋊C₄	—	5	1	no	—
149	C₃×C₄×C₂²⋊C₄	—	5	1	no	—
150	C₃×C₄×C₂²⋊C₄	—	5	1	no	—
151	C₃×#376	—	5	1	no	—
152	C₂³×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
160	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
161	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
162	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
166	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
167	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
168	C₅×#126	C₃×C₄	1	1	yes	characteristic, complemented
169	#4044	C₃×C₄	1	1	yes	characteristic, complemented
170	#4044	C₃×C₄	1	1	yes	characteristic, complemented
171	#4044	C₃×C₄	1	1	yes	characteristic, complemented
172	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
175	D₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	D₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
177	D₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
178	#4025	C₃×C₄	1	1	yes	characteristic, complemented
179	#4025	C₃×C₄	1	1	yes	characteristic, complemented
180	#4025	C₃×C₄	1	1	yes	characteristic, complemented
181	#4022	C₃×C₄	1	1	yes	characteristic, complemented
182	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
183	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
184	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
185	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
186	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
187	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
188	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
189	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
190	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
191	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
192	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
193	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
194	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
195	#2373	—	5	1	no	Sylow
196	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₃×D₅	—	2	1	no	—
198	C₂²×C₃×D₅	—	2	1	no	—
199	C₂²×C₃×D₅	—	2	1	no	—
200	C₂²×C₃×D₅	—	2	1	no	—
201	C₂²×C₃×D₅	—	2	1	no	—
202	C₂²×C₃×D₅	—	2	1	no	—
203	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
205	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
206	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
207	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
208	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
209	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
210	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
211	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
212	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
213	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
214	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
215	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
216	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
217	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
218	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
219	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
220	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
221	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
222	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
223	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
224	C₂×C₃×AGL(1,𝔽₅)	—	2	1	no	—
225	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
226	C₂×C₃×AGL(1,𝔽₅)	#41	1	2	yes	—
227	C₂×C₃×AGL(1,𝔽₅)	#41	1	2	yes	—
228	C₂×C₃×AGL(1,𝔽₅)	#41	1	2	yes	—
229	C₂×C₃×AGL(1,𝔽₅)	#41	1	2	yes	—
230	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
231	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
232	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
233	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
234	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
235	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
236	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
237	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
238	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
239	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
240	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
241	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
242	C₃×C₄×D₅	—	2	1	no	—
243	C₃×C₄×D₅	—	2	1	no	—
244	C₃×C₄×D₅	—	2	1	no	—
245	C₃×C₄×D₅	—	2	1	no	—
246	C₃×C₄×D₅	—	2	1	no	—
247	C₃×C₄×D₅	—	2	1	no	—
248	C₃×C₄×D₅	—	2	1	no	—
249	C₃×C₄×D₅	—	2	1	no	—
250	C₃×C₄×D₅	—	2	1	no	—
251	C₃×C₄×D₅	—	2	1	no	—
252	C₃×C₄×D₅	—	2	1	no	—
253	C₃×C₄×D₅	—	2	1	no	—
254	C₂³×C₃×C₄	—	5	1	no	—
255	C₃×#126	—	5	1	no	—
256	C₃×#126	—	5	1	no	—
257	C₃×#126	—	5	1	no	—
258	C₃×#126	—	5	1	no	—
259	C₃×#126	—	5	1	no	—
260	C₃×#126	—	5	1	no	—
261	C₃×#126	—	5	1	no	—
262	C₃×#126	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
263	C₂×C₃×C₄⋊C₄	—	5	1	no	—
264	C₂×C₃×C₄⋊C₄	—	5	1	no	—
265	C₂×C₃×C₄⋊C₄	—	5	1	no	—
266	C₂×C₃×C₄⋊C₄	—	5	1	no	—
267	C₂×C₃×C₄⋊C₄	—	5	1	no	—
268	C₂×C₃×C₄⋊C₄	—	5	1	no	—
269	C₂×C₃×C₄⋊C₄	—	5	1	no	—
270	C₂×C₃×C₄⋊C₄	—	5	1	no	—
271	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
272	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
273	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
274	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
275	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
276	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
277	C₂×C₃×C₄²	—	5	1	no	—
278	C₂×C₃×C₄²	—	5	1	no	—
279	C₂×C₃×C₄²	—	5	1	no	—
280	C₂×C₃×C₄²	—	5	1	no	—
281	C₂×C₃×C₄²	—	5	1	no	—
282	C₂×C₃×C₄²	—	5	1	no	—
283	C₂×C₃×C₄²	—	5	1	no	—
284	C₂×C₃×C₄²	—	5	1	no	—
285	C₃×#95	—	5	1	no	—
286	C₃×#95	—	5	1	no	—
287	C₃×#95	—	5	1	no	—
288	C₃×#95	—	5	1	no	—
289	C₃×#95	—	5	1	no	—
290	C₃×#95	—	5	1	no	—
291	C₃×#95	—	5	1	no	—
292	C₃×#95	—	5	1	no	—
293	C₃×#95	—	5	1	no	—
294	C₃×#95	—	5	1	no	—
295	C₃×#95	—	5	1	no	—
296	C₃×#95	—	5	1	no	—
297	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
298	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
299	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
300	C₂²×AGL(1,𝔽₅)	—	4	1	no	—
301	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
302	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
303	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
304	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
305	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
306	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
307	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
308	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	1	yes	characteristic
309	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
310	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
311	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
312	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
313	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
314	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
315	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
316	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
317	C₂²⋊AGL(1,𝔽₅)	—	4	1	no	—
318	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
319	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
320	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
321	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
322	C₄⋊AGL(1,𝔽₅)	—	4	1	no	—
323	C₄×AGL(1,𝔽₅)	—	2	2	no	—
324	C₄×AGL(1,𝔽₅)	—	2	2	no	—
325	C₄×AGL(1,𝔽₅)	—	2	2	no	—
326	C₄×AGL(1,𝔽₅)	—	2	2	no	—
327	C₄×AGL(1,𝔽₅)	—	4	1	no	—
328	C₄×AGL(1,𝔽₅)	—	4	1	no	—
329	C₄×AGL(1,𝔽₅)	—	4	1	no	—
330	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
331	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
332	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
333	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
334	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
335	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
336	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
337	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
338	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
339	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
340	#685	C₂×C₃×C₄	1	1	yes	characteristic
341	#685	C₂×C₃×C₄	1	1	yes	characteristic
342	#685	C₂×C₃×C₄	1	1	yes	characteristic
343	#685	C₂×C₃×C₄	1	1	yes	characteristic
344	#685	C₂×C₃×C₄	1	1	yes	characteristic
345	#685	C₂×C₃×C₄	1	1	yes	characteristic
346	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
347	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
348	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
349	#683	C₂×C₃×C₄	1	1	yes	characteristic, complemented
350	#683	C₂×C₃×C₄	1	1	yes	characteristic, complemented
351	#683	C₂×C₃×C₄	1	1	yes	characteristic, complemented
352	#683	C₂×C₃×C₄	1	1	yes	characteristic, complemented
353	#683	C₂×C₃×C₄	1	1	yes	characteristic, complemented
354	#683	C₂×C₃×C₄	1	1	yes	characteristic, complemented
355	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
356	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
357	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
358	C₂×#126	—	5	1	no	—
359	#389	—	5	1	no	—
360	#388	—	5	1	no	—
361	#388	—	5	1	no	—
362	#388	—	5	1	no	—
363	#387	—	5	1	no	—
364	#387	—	5	1	no	—
365	#387	—	5	1	no	—
366	#385	—	5	1	no	—
367	C₄×C₄⋊C₄	—	5	1	no	—
368	C₄×C₄⋊C₄	—	5	1	no	—
369	C₄×C₄⋊C₄	—	5	1	no	—
370	C₄×C₂²⋊C₄	—	5	1	no	—
371	C₄×C₂²⋊C₄	—	5	1	no	—
372	#376	—	5	1	no	—
373	C₂²×C₃×C₅	—	2	1	no	—
374	C₂²×C₃×C₅	—	2	1	no	—
375	C₂²×C₃×C₅	—	2	1	no	—
376	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
377	C₂×C₃×D₅	—	2	1	no	—
378	C₂×C₃×D₅	—	2	1	no	—
379	C₂×C₃×D₅	—	2	1	no	—
380	C₂×C₃×D₅	—	4	1	no	—
381	C₂×C₃×D₅	—	4	1	no	—
382	C₂×C₃×D₅	—	4	1	no	—
383	C₂×C₃×D₅	—	4	1	no	—
384	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
385	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
386	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
387	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
388	C₂×C₃×D₅	H(5,𝔽₂)	1	1	yes	characteristic
389	C₂×C₃×D₅	2₋¹⁺⁴	1	1	yes	characteristic
390	C₃×AGL(1,𝔽₅)	—	2	2	no	—
391	C₃×AGL(1,𝔽₅)	—	2	2	no	—
392	C₃×AGL(1,𝔽₅)	—	2	2	no	—
393	C₃×AGL(1,𝔽₅)	—	2	2	no	—
394	C₃×AGL(1,𝔽₅)	—	4	1	no	—
395	C₃×AGL(1,𝔽₅)	—	4	1	no	—
396	C₃×AGL(1,𝔽₅)	—	4	1	no	—
397	C₃×AGL(1,𝔽₅)	—	4	1	no	—
398	C₃×C₄×C₅	—	2	1	no	—
399	C₃×C₄×C₅	—	2	1	no	—
400	C₃×C₄×C₅	—	2	1	no	—
401	C₃×C₄×C₅	—	2	1	no	—
402	C₃×C₄×C₅	—	2	1	no	—
403	C₃×C₄×C₅	—	2	1	no	—
404	C₃×Dic₅	—	2	1	no	—
405	C₃×Dic₅	—	2	1	no	—
406	C₃×Dic₅	—	2	1	no	—
407	C₃×Dic₅	—	2	1	no	—
408	C₃×Dic₅	—	2	1	no	—
409	C₃×Dic₅	—	2	1	no	—
410	C₂⁴×C₃	—	5	1	no	—
411	C₂²×C₃×C₄	—	5	1	no	—
412	C₂²×C₃×C₄	—	5	1	no	—
413	C₂²×C₃×C₄	—	5	1	no	—
414	C₂²×C₃×C₄	—	5	1	no	—
415	C₂²×C₃×C₄	—	5	1	no	—
416	C₂²×C₃×C₄	—	5	1	no	—
417	C₂²×C₃×C₄	—	5	1	no	—
418	C₂²×C₃×C₄	—	5	1	no	—
419	C₂²×C₃×C₄	—	5	1	no	—
420	C₂²×C₃×C₄	—	5	1	no	—
421	C₂²×C₃×C₄	—	5	1	no	—
422	C₂²×C₃×C₄	—	5	1	no	—
423	C₂²×C₃×C₄	—	5	1	no	—
424	C₂²×C₃×C₄	—	5	1	no	—
425	C₂²×C₃×C₄	—	10	2	no	—
426	C₂²×C₃×C₄	—	10	2	no	—
427	C₂²×C₃×C₄	—	20	1	no	—
428	C₃×C₄⋊C₄	—	5	1	no	—
429	C₃×C₄⋊C₄	—	5	1	no	—
430	C₃×C₄⋊C₄	—	5	1	no	—
431	C₃×C₄⋊C₄	—	5	1	no	—
432	C₃×C₄⋊C₄	—	5	1	no	—
433	C₃×C₄⋊C₄	—	5	1	no	—
434	C₃×C₄⋊C₄	—	5	1	no	—
435	C₃×C₄⋊C₄	—	5	1	no	—
436	C₃×C₄⋊C₄	—	5	1	no	—
437	C₃×C₄⋊C₄	—	10	2	no	—
438	C₃×C₄⋊C₄	—	10	2	no	—
439	C₃×C₄⋊C₄	—	10	2	no	—
440	C₃×C₄⋊C₄	—	10	2	no	—
441	C₃×C₄⋊C₄	—	20	1	no	—
442	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
443	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
444	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
445	C₃×C₂²⋊C₄	—	5	1	no	—
446	C₃×C₂²⋊C₄	—	5	1	no	—
447	C₃×C₂²⋊C₄	—	5	1	no	—
448	C₃×C₂²⋊C₄	—	5	1	no	—
449	C₃×C₂²⋊C₄	—	5	1	no	—
450	C₃×C₂²⋊C₄	—	5	1	no	—
451	C₃×C₂²⋊C₄	—	5	1	no	—
452	C₃×C₂²⋊C₄	—	5	1	no	—
453	C₃×C₂²⋊C₄	—	5	1	no	—
454	C₃×C₂²⋊C₄	—	10	2	no	—
455	C₃×C₂²⋊C₄	—	10	2	no	—
456	C₃×C₂²⋊C₄	—	20	1	no	—
457	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
458	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
459	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
460	C₃×C₄²	—	5	1	no	—
461	C₃×C₄²	—	5	1	no	—
462	C₃×C₄²	—	5	1	no	—
463	C₃×C₄²	—	10	2	no	—
464	C₃×C₄²	—	10	2	no	—
465	C₃×C₄²	—	10	2	no	—
466	C₃×C₄²	—	10	2	no	—
467	C₃×C₄²	—	20	1	no	—
468	C₃×C₄²	—	20	1	no	—
469	C₃×C₄²	—	20	1	no	—
470	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
471	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
472	C₂²×D₅	—	2	1	no	—
473	C₂²×D₅	—	2	1	no	—
474	C₂²×D₅	—	2	1	no	—
475	C₂²×D₅	—	2	1	no	—
476	C₂²×D₅	—	2	1	no	—
477	C₂²×D₅	—	2	1	no	—
478	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
479	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
480	C₂×AGL(1,𝔽₅)	—	2	1	no	—
481	C₂×AGL(1,𝔽₅)	—	2	1	no	—
482	C₂×AGL(1,𝔽₅)	—	2	1	no	—
483	C₂×AGL(1,𝔽₅)	—	2	1	no	—
484	C₂×AGL(1,𝔽₅)	—	2	1	no	—
485	C₂×AGL(1,𝔽₅)	—	2	1	no	—
486	C₂×AGL(1,𝔽₅)	—	2	1	no	—
487	C₂×AGL(1,𝔽₅)	—	2	1	no	—
488	C₂×AGL(1,𝔽₅)	—	2	1	no	—
489	C₂×AGL(1,𝔽₅)	—	2	1	no	—
490	C₂×AGL(1,𝔽₅)	—	2	1	no	—
491	C₂×AGL(1,𝔽₅)	—	2	1	no	—
492	C₂×AGL(1,𝔽₅)	—	2	1	no	—
493	C₂×AGL(1,𝔽₅)	—	2	1	no	—
494	C₂×AGL(1,𝔽₅)	—	2	1	no	—
495	C₂×AGL(1,𝔽₅)	—	2	1	no	—
496	C₂×AGL(1,𝔽₅)	—	2	1	no	—
497	C₂×AGL(1,𝔽₅)	—	2	1	no	—
498	C₂×AGL(1,𝔽₅)	—	2	1	no	—
499	C₂×AGL(1,𝔽₅)	—	2	1	no	—
500	C₂×AGL(1,𝔽₅)	—	4	4	no	—
501	C₂×AGL(1,𝔽₅)	C₃×#41	1	2	yes	—
502	C₂×AGL(1,𝔽₅)	C₃×#41	1	2	yes	—
503	C₂×AGL(1,𝔽₅)	C₃×#41	1	2	yes	—
504	C₂×AGL(1,𝔽₅)	C₃×#41	1	2	yes	—
505	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
506	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
507	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
508	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
509	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
510	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
511	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
512	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
513	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
514	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
515	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
516	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
517	C₄×D₅	—	2	1	no	—
518	C₄×D₅	—	2	1	no	—
519	C₄×D₅	—	2	1	no	—
520	C₄×D₅	—	2	1	no	—
521	C₄×D₅	—	2	1	no	—
522	C₄×D₅	—	2	1	no	—
523	C₄×D₅	—	2	1	no	—
524	C₄×D₅	—	2	1	no	—
525	C₄×D₅	—	2	1	no	—
526	C₄×D₅	—	2	1	no	—
527	C₄×D₅	—	2	1	no	—
528	C₄×D₅	—	2	1	no	—
529	C₂³×C₄	—	5	1	no	—
530	#126	—	5	1	no	—
531	#126	—	5	1	no	—
532	#126	—	5	1	no	—
533	#126	—	5	1	no	—
534	#126	—	5	1	no	—
535	#126	—	5	1	no	—
536	#126	—	5	1	no	—
537	#126	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
538	C₂×C₄⋊C₄	—	5	1	no	—
539	C₂×C₄⋊C₄	—	5	1	no	—
540	C₂×C₄⋊C₄	—	5	1	no	—
541	C₂×C₄⋊C₄	—	5	1	no	—
542	C₂×C₄⋊C₄	—	5	1	no	—
543	C₂×C₄⋊C₄	—	5	1	no	—
544	C₂×C₄⋊C₄	—	5	1	no	—
545	C₂×C₄⋊C₄	—	5	1	no	—
546	C₂×C₂²⋊C₄	—	5	1	no	—
547	C₂×C₂²⋊C₄	—	5	1	no	—
548	C₂×C₂²⋊C₄	—	5	1	no	—
549	C₂×C₂²⋊C₄	—	5	1	no	—
550	C₂×C₂²⋊C₄	—	5	1	no	—
551	C₂×C₂²⋊C₄	—	5	1	no	—
552	C₂×C₄²	—	5	1	no	—
553	C₂×C₄²	—	5	1	no	—
554	C₂×C₄²	—	5	1	no	—
555	C₂×C₄²	—	5	1	no	—
556	C₂×C₄²	—	5	1	no	—
557	C₂×C₄²	—	5	1	no	—
558	C₂×C₄²	—	5	1	no	—
559	C₂×C₄²	—	5	1	no	—
560	#95	—	5	1	no	—
561	#95	—	5	1	no	—
562	#95	—	5	1	no	—
563	#95	—	5	1	no	—
564	#95	—	5	1	no	—
565	#95	—	5	1	no	—
566	#95	—	5	1	no	—
567	#95	—	5	1	no	—
568	#95	—	5	1	no	—
569	#95	—	5	1	no	—
570	#95	—	5	1	no	—
571	#95	—	5	1	no	—
572	C₂×C₃×C₅	—	4	1	no	—
573	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
574	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
575	C₂×C₃×C₅	#520	1	1	yes	characteristic
576	C₃×D₅	—	4	1	no	—
577	C₃×D₅	#551	1	1	yes	characteristic
578	C₃×D₅	#552	1	1	yes	characteristic
579	C₃×D₅	#553	1	1	yes	characteristic
580	C₃×D₅	#556	1	1	yes	characteristic
581	C₂³×C₃	—	5	1	no	—
582	C₂³×C₃	—	5	1	no	—
583	C₂³×C₃	—	10	1	no	—
584	C₂³×C₃	—	10	1	no	—
585	C₂³×C₃	—	10	1	no	—
586	C₂³×C₃	—	10	1	no	—
587	C₂³×C₃	—	10	1	no	—
588	C₂³×C₃	—	10	1	no	—
589	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
590	C₂×C₃×C₄	—	5	2	no	—
591	C₂×C₃×C₄	—	5	2	no	—
592	C₂×C₃×C₄	—	5	2	no	—
593	C₂×C₃×C₄	—	5	2	no	—
594	C₂×C₃×C₄	—	5	1	no	—
595	C₂×C₃×C₄	—	5	1	no	—
596	C₂×C₃×C₄	—	5	1	no	—
597	C₂×C₃×C₄	—	5	1	no	—
598	C₂×C₃×C₄	—	5	1	no	—
599	C₂×C₃×C₄	—	5	1	no	—
600	C₂×C₃×C₄	—	10	1	no	—
601	C₂×C₃×C₄	—	10	1	no	—
602	C₂×C₃×C₄	—	10	1	no	—
603	C₂×C₃×C₄	—	10	1	no	—
604	C₂×C₃×C₄	—	10	1	no	—
605	C₂×C₃×C₄	—	10	1	no	—
606	C₂×C₃×C₄	—	10	1	no	—
607	C₂×C₃×C₄	—	10	1	no	—
608	C₂×C₃×C₄	—	10	1	no	—
609	C₂×C₃×C₄	—	10	1	no	—
610	C₂×C₃×C₄	—	10	1	no	—
611	C₂×C₃×C₄	—	10	1	no	—
612	C₂×C₃×C₄	—	10	1	no	—
613	C₂×C₃×C₄	—	10	1	no	—
614	C₂×C₃×C₄	—	10	1	no	—
615	C₂×C₃×C₄	—	10	1	no	—
616	C₂×C₃×C₄	—	10	1	no	—
617	C₂×C₃×C₄	—	10	1	no	—
618	C₂×C₃×C₄	—	10	1	no	—
619	C₂×C₃×C₄	—	10	1	no	—
620	C₂×C₃×C₄	—	10	1	no	—
621	C₂×C₃×C₄	—	10	1	no	—
622	C₂×C₃×C₄	—	10	1	no	—
623	C₂×C₃×C₄	—	10	1	no	—
624	C₂×C₃×C₄	—	10	1	no	—
625	C₂×C₃×C₄	—	10	1	no	—
626	C₂×C₃×C₄	—	10	1	no	—
627	C₂×C₃×C₄	—	10	1	no	—
628	C₂×C₃×C₄	—	10	1	no	—
629	C₂×C₃×C₄	—	10	1	no	—
630	C₂×C₃×C₄	—	10	1	no	—
631	C₂×C₃×C₄	—	10	1	no	—
632	C₂×C₃×C₄	—	20	4	no	—
633	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
634	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
635	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
636	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
637	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
638	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
639	C₂²×C₅	—	2	1	no	—
640	C₂²×C₅	—	2	1	no	—
641	C₂²×C₅	—	2	1	no	—
642	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
643	C₂×D₅	—	2	1	no	—
644	C₂×D₅	—	2	1	no	—
645	C₂×D₅	—	2	1	no	—
646	C₂×D₅	—	4	1	no	—
647	C₂×D₅	—	4	1	no	—
648	C₂×D₅	—	4	1	no	—
649	C₂×D₅	—	4	1	no	—
650	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
651	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
652	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
653	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
654	C₂×D₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
655	C₂×D₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
656	AGL(1,𝔽₅)	—	2	2	no	—
657	AGL(1,𝔽₅)	—	2	2	no	—
658	AGL(1,𝔽₅)	—	2	2	no	—
659	AGL(1,𝔽₅)	—	2	2	no	—
660	AGL(1,𝔽₅)	—	4	1	no	—
661	AGL(1,𝔽₅)	—	4	1	no	—
662	AGL(1,𝔽₅)	—	4	1	no	—
663	AGL(1,𝔽₅)	—	4	1	no	—
664	C₄×C₅	—	2	1	no	—
665	C₄×C₅	—	2	1	no	—
666	C₄×C₅	—	2	1	no	—
667	C₄×C₅	—	2	1	no	—
668	C₄×C₅	—	2	1	no	—
669	C₄×C₅	—	2	1	no	—
670	Dic₅	—	2	1	no	—
671	Dic₅	—	2	1	no	—
672	Dic₅	—	2	1	no	—
673	Dic₅	—	2	1	no	—
674	Dic₅	—	2	1	no	—
675	Dic₅	—	2	1	no	—
676	C₂⁴	—	5	1	no	—
677	C₂²×C₄	—	5	1	no	—
678	C₂²×C₄	—	5	1	no	—
679	C₂²×C₄	—	5	1	no	—
680	C₂²×C₄	—	5	1	no	—
681	C₂²×C₄	—	5	1	no	—
682	C₂²×C₄	—	5	1	no	—
683	C₂²×C₄	—	5	1	no	—
684	C₂²×C₄	—	5	1	no	—
685	C₂²×C₄	—	5	1	no	—
686	C₂²×C₄	—	5	1	no	—
687	C₂²×C₄	—	5	1	no	—
688	C₂²×C₄	—	5	1	no	—
689	C₂²×C₄	—	5	1	no	—
690	C₂²×C₄	—	5	1	no	—
691	C₂²×C₄	—	10	2	no	—
692	C₂²×C₄	—	10	2	no	—
693	C₂²×C₄	—	20	1	no	—
694	C₄⋊C₄	—	5	1	no	—
695	C₄⋊C₄	—	5	1	no	—
696	C₄⋊C₄	—	5	1	no	—
697	C₄⋊C₄	—	5	1	no	—
698	C₄⋊C₄	—	5	1	no	—
699	C₄⋊C₄	—	5	1	no	—
700	C₄⋊C₄	—	5	1	no	—
701	C₄⋊C₄	—	5	1	no	—
702	C₄⋊C₄	—	5	1	no	—
703	C₄⋊C₄	—	10	2	no	—
704	C₄⋊C₄	—	10	2	no	—
705	C₄⋊C₄	—	10	2	no	—
706	C₄⋊C₄	—	10	2	no	—
707	C₄⋊C₄	—	20	1	no	—
708	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
709	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
710	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
711	C₂²⋊C₄	—	5	1	no	—
712	C₂²⋊C₄	—	5	1	no	—
713	C₂²⋊C₄	—	5	1	no	—
714	C₂²⋊C₄	—	5	1	no	—
715	C₂²⋊C₄	—	5	1	no	—
716	C₂²⋊C₄	—	5	1	no	—
717	C₂²⋊C₄	—	5	1	no	—
718	C₂²⋊C₄	—	5	1	no	—
719	C₂²⋊C₄	—	5	1	no	—
720	C₂²⋊C₄	—	10	2	no	—
721	C₂²⋊C₄	—	10	2	no	—
722	C₂²⋊C₄	—	20	1	no	—
723	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
724	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
725	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
726	C₄²	—	5	1	no	—
727	C₄²	—	5	1	no	—
728	C₄²	—	5	1	no	—
729	C₄²	—	10	2	no	—
730	C₄²	—	10	2	no	—
731	C₄²	—	10	2	no	—
732	C₄²	—	10	2	no	—
733	C₄²	—	20	1	no	—
734	C₄²	—	20	1	no	—
735	C₄²	—	20	1	no	—
736	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
737	C₃×C₅	#2373	1	1	yes	characteristic, complemented, Hall
738	C₂²×C₃	—	2	1	no	—
739	C₂²×C₃	—	2	1	no	—
740	C₂²×C₃	—	2	1	no	—
741	C₂²×C₃	—	5	1	no	—
742	C₂²×C₃	—	5	1	no	—
743	C₂²×C₃	—	5	1	no	—
744	C₂²×C₃	—	5	1	no	—
745	C₂²×C₃	—	5	1	no	—
746	C₂²×C₃	—	5	1	no	—
747	C₂²×C₃	—	10	1	no	—
748	C₂²×C₃	—	10	1	no	—
749	C₂²×C₃	—	10	1	no	—
750	C₂²×C₃	—	20	1	no	—
751	C₂²×C₃	—	20	1	no	—
752	C₂²×C₃	—	20	1	no	—
753	C₂²×C₃	—	20	1	no	—
754	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
755	C₃×C₄	—	2	1	no	—
756	C₃×C₄	—	2	1	no	—
757	C₃×C₄	—	2	1	no	—
758	C₃×C₄	—	2	1	no	—
759	C₃×C₄	—	2	1	no	—
760	C₃×C₄	—	2	1	no	—
761	C₃×C₄	—	10	2	no	—
762	C₃×C₄	—	10	2	no	—
763	C₃×C₄	—	10	2	no	—
764	C₃×C₄	—	10	2	no	—
765	C₃×C₄	—	10	1	no	—
766	C₃×C₄	—	10	1	no	—
767	C₃×C₄	—	10	1	no	—
768	C₃×C₄	—	10	1	no	—
769	C₃×C₄	—	10	1	no	—
770	C₃×C₄	—	10	1	no	—
771	C₃×C₄	—	20	1	no	—
772	C₃×C₄	—	20	1	no	—
773	C₃×C₄	—	20	1	no	—
774	C₃×C₄	—	20	1	no	—
775	C₂×C₅	—	4	1	no	—
776	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
777	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
778	C₂×C₅	C₃×#520	1	1	yes	characteristic
779	D₅	—	4	1	no	—
780	D₅	C₃×#551	1	1	yes	characteristic
781	D₅	C₃×#552	1	1	yes	characteristic
782	D₅	C₃×#553	1	1	yes	characteristic
783	D₅	C₃×#556	1	1	yes	characteristic
784	C₂³	—	5	1	no	—
785	C₂³	—	5	1	no	—
786	C₂³	—	10	1	no	—
787	C₂³	—	10	1	no	—
788	C₂³	—	10	1	no	—
789	C₂³	—	10	1	no	—
790	C₂³	—	10	1	no	—
791	C₂³	—	10	1	no	—
792	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
793	C₂×C₄	—	5	2	no	—
794	C₂×C₄	—	5	2	no	—
795	C₂×C₄	—	5	2	no	—
796	C₂×C₄	—	5	2	no	—
797	C₂×C₄	—	5	1	no	—
798	C₂×C₄	—	5	1	no	—
799	C₂×C₄	—	5	1	no	—
800	C₂×C₄	—	5	1	no	—
801	C₂×C₄	—	5	1	no	—
802	C₂×C₄	—	5	1	no	—
803	C₂×C₄	—	10	1	no	—
804	C₂×C₄	—	10	1	no	—
805	C₂×C₄	—	10	1	no	—
806	C₂×C₄	—	10	1	no	—
807	C₂×C₄	—	10	1	no	—
808	C₂×C₄	—	10	1	no	—
809	C₂×C₄	—	10	1	no	—
810	C₂×C₄	—	10	1	no	—
811	C₂×C₄	—	10	1	no	—
812	C₂×C₄	—	10	1	no	—
813	C₂×C₄	—	10	1	no	—
814	C₂×C₄	—	10	1	no	—
815	C₂×C₄	—	10	1	no	—
816	C₂×C₄	—	10	1	no	—
817	C₂×C₄	—	10	1	no	—
818	C₂×C₄	—	10	1	no	—
819	C₂×C₄	—	10	1	no	—
820	C₂×C₄	—	10	1	no	—
821	C₂×C₄	—	10	1	no	—
822	C₂×C₄	—	10	1	no	—
823	C₂×C₄	—	10	1	no	—
824	C₂×C₄	—	10	1	no	—
825	C₂×C₄	—	10	1	no	—
826	C₂×C₄	—	10	1	no	—
827	C₂×C₄	—	10	1	no	—
828	C₂×C₄	—	10	1	no	—
829	C₂×C₄	—	10	1	no	—
830	C₂×C₄	—	10	1	no	—
831	C₂×C₄	—	10	1	no	—
832	C₂×C₄	—	10	1	no	—
833	C₂×C₄	—	10	1	no	—
834	C₂×C₄	—	10	1	no	—
835	C₂×C₄	—	20	4	no	—
836	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
837	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
838	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
839	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
840	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
841	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
842	C₂×C₃	—	4	1	no	—
843	C₂×C₃	—	5	1	no	—
844	C₂×C₃	—	5	1	no	—
845	C₂×C₃	—	5	1	no	—
846	C₂×C₃	—	5	1	no	—
847	C₂×C₃	—	20	1	no	—
848	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
849	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
850	C₂×C₃	#66266	1	1	yes	characteristic
851	C₅	C₃×#2373	1	1	yes	characteristic, complemented, Sylow
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	5	1	no	—
856	C₂²	—	5	1	no	—
857	C₂²	—	5	1	no	—
858	C₂²	—	5	1	no	—
859	C₂²	—	5	1	no	—
860	C₂²	—	5	1	no	—
861	C₂²	—	10	1	no	—
862	C₂²	—	10	1	no	—
863	C₂²	—	10	1	no	—
864	C₂²	—	20	1	no	—
865	C₂²	—	20	1	no	—
866	C₂²	—	20	1	no	—
867	C₂²	—	20	1	no	—
868	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	10	2	no	—
876	C₄	—	10	2	no	—
877	C₄	—	10	2	no	—
878	C₄	—	10	2	no	—
879	C₄	—	10	1	no	—
880	C₄	—	10	1	no	—
881	C₄	—	10	1	no	—
882	C₄	—	10	1	no	—
883	C₄	—	10	1	no	—
884	C₄	—	10	1	no	—
885	C₄	—	20	1	no	—
886	C₄	—	20	1	no	—
887	C₄	—	20	1	no	—
888	C₄	—	20	1	no	—
889	C₃	#10617359	1	1	yes	characteristic, direct product factor, Sylow
890	C₂	—	4	1	no	—
891	C₂	—	5	1	no	—
892	C₂	—	5	1	no	—
893	C₂	—	5	1	no	—
894	C₂	—	5	1	no	—
895	C₂	—	20	1	no	—
896	C₂	C₃×#41×AGL(1,𝔽₅)	1	1	yes	characteristic
897	C₂	C₃×#41×AGL(1,𝔽₅)	1	1	yes	characteristic
898	C₂	C₃×#66266	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#126	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×D₅	C₂³
cosocle	C₂²×D₅	C₂⁴×C₃
hypercenter	C₃×#126	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2373
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#126

Complements

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

N	H ≅ G/N	type
2. C₃×#65712	C₂	semidirect
3. C₃×#65711	C₂	semidirect
4. C₃×#65711	C₂	semidirect
5. C₃×#65711	C₂	semidirect
6. C₃×C₄⋊C₄×AGL(1,𝔽₅)	C₂	semidirect
7. C₃×C₄⋊C₄×AGL(1,𝔽₅)	C₂	semidirect
14. C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	semidirect
15. C₃×#65686	C₂	semidirect
16. #10617359	C₃	direct (N × H)
33. C₃×C₅×#126	C₄	semidirect
34. C₃×#4044	C₄	semidirect
35. C₃×#4044	C₄	semidirect
36. C₃×#4044	C₄	semidirect
43. C₃×#4025	C₄	semidirect
44. C₃×#4025	C₄	semidirect
45. C₃×#4025	C₄	semidirect
46. C₃×#4022	C₄	semidirect
62. #65712	C₂×C₃	semidirect
63. #65711	C₂×C₃	semidirect
64. #65711	C₂×C₃	semidirect
65. #65711	C₂×C₃	semidirect
66. C₄⋊C₄×AGL(1,𝔽₅)	C₂×C₃	semidirect
67. C₄⋊C₄×AGL(1,𝔽₅)	C₂×C₃	semidirect
74. C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	semidirect
75. #65686	C₂×C₃	semidirect
109. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
110. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
111. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
115. C₃×C₄²×C₅	C₂×C₄	semidirect
125. C₃×C₄⋊Dic₅	C₂×C₄	semidirect
126. C₃×C₄⋊Dic₅	C₂×C₄	semidirect
127. C₃×C₄⋊Dic₅	C₂×C₄	semidirect
128. C₃×#683	C₂×C₄	semidirect
129. C₃×#683	C₂×C₄	semidirect
130. C₃×#683	C₂×C₄	semidirect
131. C₃×#683	C₂×C₄	semidirect
132. C₃×#683	C₂×C₄	semidirect
133. C₃×#683	C₂×C₄	semidirect
134. C₃×C₄×Dic₅	C₂×C₄	semidirect
135. C₃×C₄×Dic₅	C₂×C₄	semidirect
136. C₃×C₄×Dic₅	C₂×C₄	semidirect
168. C₅×#126	C₃×C₄	semidirect
169. #4044	C₃×C₄	semidirect
170. #4044	C₃×C₄	semidirect
171. #4044	C₃×C₄	semidirect
178. #4025	C₃×C₄	semidirect
179. #4025	C₃×C₄	semidirect
180. #4025	C₃×C₄	semidirect
181. #4022	C₃×C₄	semidirect
262. C₃×#126	AGL(1,𝔽₅)	semidirect
330. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
331. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
332. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
336. C₄²×C₅	C₂×C₃×C₄	semidirect
346. C₄⋊Dic₅	C₂×C₃×C₄	semidirect
347. C₄⋊Dic₅	C₂×C₃×C₄	semidirect
348. C₄⋊Dic₅	C₂×C₃×C₄	semidirect
349. #683	C₂×C₃×C₄	semidirect
350. #683	C₂×C₃×C₄	semidirect
351. #683	C₂×C₃×C₄	semidirect
352. #683	C₂×C₃×C₄	semidirect
353. #683	C₂×C₃×C₄	semidirect
354. #683	C₂×C₃×C₄	semidirect
355. C₄×Dic₅	C₂×C₃×C₄	semidirect
356. C₄×Dic₅	C₂×C₃×C₄	semidirect
357. C₄×Dic₅	C₂×C₃×C₄	semidirect
442. C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	semidirect
443. C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	semidirect
444. C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	semidirect
470. C₃×C₄²	C₂×AGL(1,𝔽₅)	semidirect
537. #126	C₃×AGL(1,𝔽₅)	semidirect
708. C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
709. C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
710. C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
736. C₄²	C₂×C₃×AGL(1,𝔽₅)	semidirect
737. C₃×C₅	#2373	semidirect
851. C₅	C₃×#2373	semidirect
889. C₃	#10617359	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₅×#126	2
C₃×#65712	2
C₃×#65711	2
C₃×C₄⋊C₄×AGL(1,𝔽₅)	2
C₃×#65700	2
C₃×#65699	2
C₃×C₂²⋊C₄×AGL(1,𝔽₅)	2
C₃×C₄×C₄⋊AGL(1,𝔽₅)	2
C₃×#65686	2
#10617359	3
C₃×#2373	5

Subgroups — C3×#10617359 #14330254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617359 #14330254