Subgroups — C₅×#75840 #14330634

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#882	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4990	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4957	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4956	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4955	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4955	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4951	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4940	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4939	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4670	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4669	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4665	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4665	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2375	—	3	1	no	maximal, Hall
17	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
19	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
20	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#217	C₂²	1	1	yes	characteristic
28	C₂×C₅×#217	C₂²	1	1	yes	characteristic
29	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
46	C₅×#882	C₄	1	8	yes	complemented
47	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
49	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
50	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
51	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
52	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
53	#75840	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
54	C₂×C₅×#120	—	3	1	no	—
55	C₅×#390	—	3	1	no	—
56	C₅×#390	—	3	1	no	—
57	C₅×#390	—	3	1	no	—
58	C₅×#388	—	3	1	no	—
59	C₅×#388	—	3	1	no	—
60	C₅×#388	—	3	1	no	—
61	C₅×#388	—	3	1	no	—
62	C₅×#388	—	3	1	no	—
63	C₅×#388	D₃	1	1	yes	characteristic, complemented
64	C₅×#386	—	3	1	no	—
65	C₅×#386	—	3	1	no	—
66	C₅×#386	—	3	1	no	—
67	C₅×#379	—	3	1	no	—
68	C₅×#379	—	3	1	no	—
69	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂³×C₅×D₃	—	4	1	no	—
71	C₂³×C₅×D₃	—	4	1	no	—
72	C₂³×C₅×D₃	—	4	1	no	—
73	C₂³×C₅×D₃	—	4	1	no	—
74	C₂³×C₅×D₃	—	4	1	no	—
75	C₂³×C₅×D₃	—	4	1	no	—
76	C₂³×C₅×D₃	C₂×C₄	1	4	yes	complemented
77	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
78	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
79	C₂³×C₅×D₃	C₂³	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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂×C₅×#67	—	4	1	no	—
87	C₂×C₅×#67	—	4	1	no	—
88	C₂×C₅×#67	C₂×C₄	1	4	yes	—
89	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
90	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
91	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
92	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
93	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
94	C₂×C₅×D₁₂	—	4	1	no	—
95	C₂×C₅×D₁₂	—	4	1	no	—
96	C₂×C₅×D₁₂	—	4	1	no	—
97	C₂×C₅×D₁₂	—	4	1	no	—
98	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
99	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
100	C₂×C₄×C₅×D₃	—	4	1	no	—
101	C₂×C₄×C₅×D₃	—	4	1	no	—
102	C₂×C₄×C₅×D₃	—	4	1	no	—
103	C₃×C₅×C₄⋊C₄	—	4	1	no	—
104	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
105	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
106	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	complemented
107	C₃×C₄²×C₅	—	4	1	no	—
108	C₅×#217	—	4	1	no	—
109	C₅×#217	—	4	1	no	—
110	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
111	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
112	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
113	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
114	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
115	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
116	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
117	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
118	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
119	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
120	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
121	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
122	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
123	C₅×C₄⋊Dic₃	—	4	1	no	—
124	C₅×Dic₃⋊C₄	—	4	1	no	—
125	C₄×C₅×Dic₃	—	4	1	no	—
126	C₄×C₅×Dic₃	—	4	1	no	—
127	C₂×#882	C₂×C₅	1	1	yes	characteristic
128	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
129	#4990	C₂×C₅	1	1	yes	characteristic, complemented
130	#4988	C₂×C₅	1	1	yes	characteristic, complemented
131	#4957	C₂×C₅	1	1	yes	characteristic, complemented
132	#4956	C₂×C₅	1	1	yes	characteristic, complemented
133	#4955	C₂×C₅	1	1	yes	characteristic, complemented
134	#4955	C₂×C₅	1	1	yes	characteristic, complemented
135	#4951	C₂×C₅	1	1	yes	characteristic, complemented
136	#4940	C₂×C₅	1	1	yes	characteristic, complemented
137	#4939	C₂×C₅	1	1	yes	characteristic, complemented
138	#4670	C₂×C₅	1	1	yes	characteristic, complemented
139	#4669	C₂×C₅	1	1	yes	characteristic, complemented
140	#4665	C₂×C₅	1	1	yes	characteristic, complemented
141	#4665	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂⁵×C₅	—	3	1	no	—
143	C₂²×C₅×D₄	—	3	1	no	—
144	C₂²×C₅×D₄	—	3	1	no	—
145	C₂²×C₅×D₄	—	3	1	no	—
146	C₂³×C₄×C₅	—	3	1	no	—
147	C₅×#120	—	3	8	no	—
148	C₂×C₅×C₄⋊C₄	—	3	1	no	—
149	C₂×C₅×C₄⋊C₄	—	3	1	no	—
150	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
151	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
152	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
153	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
154	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
155	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
156	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
157	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
158	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
159	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
160	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
161	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
162	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
163	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
164	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
165	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
166	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
167	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
168	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
169	C₂×C₄²×C₅	—	3	1	no	—
170	C₂×C₄²×C₅	—	3	1	no	—
171	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
172	C₅×#95	—	3	1	no	—
173	C₅×#95	—	3	1	no	—
174	C₅×#95	—	3	1	no	—
175	C₅×#95	—	3	1	no	—
176	C₅×#95	C₂×D₃	1	1	yes	characteristic, complemented
177	C₅×#95	C₂×D₃	1	1	yes	characteristic, complemented
178	#2375	—	3	1	no	Sylow
179	C₂³×C₃×C₅	—	2	1	no	—
180	C₂³×C₃×C₅	—	2	1	no	—
181	C₂³×C₃×C₅	—	2	1	no	—
182	C₂³×C₃×C₅	—	2	1	no	—
183	C₂³×C₃×C₅	—	2	1	no	—
184	C₂³×C₃×C₅	—	2	1	no	—
185	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
186	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
187	C₂²×C₅×D₃	—	2	1	no	—
188	C₂²×C₅×D₃	—	2	1	no	—
189	C₂²×C₅×D₃	—	2	1	no	—
190	C₂²×C₅×D₃	—	2	1	no	—
191	C₂²×C₅×D₃	—	2	1	no	—
192	C₂²×C₅×D₃	—	2	1	no	—
193	C₂²×C₅×D₃	—	2	1	no	—
194	C₂²×C₅×D₃	—	2	1	no	—
195	C₂²×C₅×D₃	—	2	1	no	—
196	C₂²×C₅×D₃	—	2	1	no	—
197	C₂²×C₅×D₃	—	2	1	no	—
198	C₂²×C₅×D₃	—	2	1	no	—
199	C₂²×C₅×D₃	—	2	1	no	—
200	C₂²×C₅×D₃	—	2	1	no	—
201	C₂²×C₅×D₃	—	2	1	no	—
202	C₂²×C₅×D₃	—	2	1	no	—
203	C₂²×C₅×D₃	—	2	1	no	—
204	C₂²×C₅×D₃	—	2	1	no	—
205	C₂²×C₅×D₃	—	4	4	no	—
206	C₂²×C₅×D₃	—	4	4	no	—
207	C₂²×C₅×D₃	—	4	4	no	—
208	C₂²×C₅×D₃	—	4	4	no	—
209	C₂²×C₅×D₃	—	4	4	no	—
210	C₂²×C₅×D₃	—	4	4	no	—
211	C₂²×C₅×D₃	—	4	4	no	—
212	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
213	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
214	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	2	1	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	2	1	no	—
224	C₂×C₃×C₄×C₅	—	2	1	no	—
225	C₂×C₃×C₄×C₅	—	2	1	no	—
226	C₂×C₃×C₄×C₅	—	2	1	no	—
227	C₂×C₃×C₄×C₅	—	2	1	no	—
228	C₂×C₃×C₄×C₅	—	2	1	no	—
229	C₂×C₃×C₄×C₅	—	2	1	no	—
230	C₂×C₃×C₄×C₅	—	2	1	no	—
231	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
232	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
233	C₅×#67	—	4	4	no	—
234	C₂×C₅×Dic₃	—	2	1	no	—
235	C₂×C₅×Dic₃	—	2	1	no	—
236	C₂×C₅×Dic₃	—	2	1	no	—
237	C₂×C₅×Dic₃	—	2	1	no	—
238	C₂×C₅×Dic₃	—	2	1	no	—
239	C₂×C₅×Dic₃	—	2	1	no	—
240	C₂×C₅×Dic₃	—	2	1	no	—
241	C₂×C₅×Dic₃	—	2	1	no	—
242	C₂×C₅×Dic₃	—	2	1	no	—
243	C₂×C₅×Dic₃	—	2	1	no	—
244	C₂×C₅×Dic₃	—	2	1	no	—
245	C₂×C₅×Dic₃	—	2	1	no	—
246	C₂×C₅×Dic₃	—	2	1	no	—
247	C₂×C₅×Dic₃	—	2	1	no	—
248	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
249	C₅×D₁₂	—	4	4	no	—
250	C₅×D₁₂	—	4	4	no	—
251	C₄×C₅×D₃	—	4	4	no	—
252	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
253	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
254	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
255	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
256	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
258	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₂×#217	C₂²×C₅	1	1	yes	characteristic
263	C₂×#217	C₂²×C₅	1	1	yes	characteristic
264	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
265	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
266	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
267	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
268	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
269	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
270	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
271	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
272	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
273	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
274	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
275	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
276	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
277	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
278	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
280	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
281	#882	C₄×C₅	1	8	yes	complemented
282	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
283	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
284	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
286	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
288	C₂⁴×C₅	—	3	1	no	—
289	C₂⁴×C₅	—	3	1	no	—
290	C₂⁴×C₅	—	3	1	no	—
291	C₂⁴×C₅	—	3	4	no	—
292	C₂⁴×C₅	—	12	1	no	—
293	C₂⁴×C₅	—	12	1	no	—
294	C₂⁴×C₅	—	12	1	no	—
295	C₂⁴×C₅	—	12	1	no	—
296	C₂⁴×C₅	—	12	1	no	—
297	C₂⁴×C₅	—	12	1	no	—
298	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
299	C₂×C₅×D₄	—	3	4	no	—
300	C₂×C₅×D₄	—	3	4	no	—
301	C₂×C₅×D₄	—	3	4	no	—
302	C₂×C₅×D₄	—	12	1	no	—
303	C₂×C₅×D₄	—	12	1	no	—
304	C₂×C₅×D₄	—	12	1	no	—
305	C₂×C₅×D₄	—	12	1	no	—
306	C₂×C₅×D₄	—	12	1	no	—
307	C₂×C₅×D₄	—	12	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	—	12	1	no	—
314	C₂²×C₄×C₅	—	12	1	no	—
315	C₂²×C₄×C₅	—	12	1	no	—
316	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
317	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
318	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
319	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
320	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
321	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
322	C₅×C₄⋊C₄	—	4	1	no	—
323	C₅×C₄⋊C₄	—	12	1	no	—
324	C₅×C₄⋊C₄	—	12	1	no	—
325	C₅×C₂²⋊C₄	—	3	4	no	—
326	C₅×C₂²⋊C₄	—	3	4	no	—
327	C₅×C₂²⋊C₄	—	4	1	no	—
328	C₅×C₂²⋊C₄	—	4	1	no	—
329	C₅×C₂²⋊C₄	—	12	1	no	—
330	C₅×C₂²⋊C₄	—	12	1	no	—
331	C₅×C₂²⋊C₄	—	12	1	no	—
332	C₅×C₂²⋊C₄	—	12	1	no	—
333	C₅×C₂²⋊C₄	—	12	1	no	—
334	C₅×C₂²⋊C₄	—	12	1	no	—
335	C₅×C₂²⋊C₄	—	12	1	no	—
336	C₅×C₂²⋊C₄	—	12	1	no	—
337	C₅×C₂²⋊C₄	—	12	1	no	—
338	C₅×C₂²⋊C₄	—	12	1	no	—
339	C₅×C₂²⋊C₄	—	12	1	no	—
340	C₅×C₂²⋊C₄	—	12	1	no	—
341	C₅×C₂²⋊C₄	—	12	1	no	—
342	C₅×C₂²⋊C₄	C₄×D₃	1	4	yes	complemented
343	C₄²×C₅	—	4	1	no	—
344	C₄²×C₅	—	12	1	no	—
345	C₄²×C₅	—	12	1	no	—
346	C₂×#120	—	3	1	no	—
347	#390	—	3	1	no	—
348	#390	—	3	1	no	—
349	#390	—	3	1	no	—
350	#388	—	3	1	no	—
351	#388	—	3	1	no	—
352	#388	—	3	1	no	—
353	#388	—	3	1	no	—
354	#388	—	3	1	no	—
355	#388	C₅×D₃	1	1	yes	characteristic, complemented
356	#386	—	3	1	no	—
357	#386	—	3	1	no	—
358	#386	—	3	1	no	—
359	#379	—	3	1	no	—
360	#379	—	3	1	no	—
361	C₂²×C₃×C₅	—	2	2	no	—
362	C₂²×C₃×C₅	—	2	2	no	—
363	C₂²×C₃×C₅	—	2	2	no	—
364	C₂²×C₃×C₅	—	4	1	no	—
365	C₂²×C₃×C₅	—	4	1	no	—
366	C₂²×C₃×C₅	—	4	1	no	—
367	C₂²×C₃×C₅	—	4	1	no	—
368	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
369	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
370	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
371	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
372	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
373	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
374	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
375	C₂×C₅×D₃	—	2	2	no	—
376	C₂×C₅×D₃	—	2	2	no	—
377	C₂×C₅×D₃	—	2	2	no	—
378	C₂×C₅×D₃	—	2	2	no	—
379	C₂×C₅×D₃	—	2	2	no	—
380	C₂×C₅×D₃	—	2	2	no	—
381	C₂×C₅×D₃	—	2	2	no	—
382	C₂×C₅×D₃	—	2	2	no	—
383	C₂×C₅×D₃	—	2	2	no	—
384	C₂×C₅×D₃	—	4	16	no	—
385	C₂×C₅×D₃	—	4	1	no	—
386	C₂×C₅×D₃	—	4	1	no	—
387	C₂×C₅×D₃	—	4	1	no	—
388	C₂×C₅×D₃	—	4	1	no	—
389	C₂×C₅×D₃	—	4	1	no	—
390	C₂×C₅×D₃	—	4	1	no	—
391	C₂×C₅×D₃	—	4	1	no	—
392	C₂×C₅×D₃	—	4	1	no	—
393	C₂×C₅×D₃	—	4	1	no	—
394	C₂×C₅×D₃	—	4	1	no	—
395	C₂×C₅×D₃	—	4	1	no	—
396	C₂×C₅×D₃	—	4	1	no	—
397	C₃×C₄×C₅	—	2	2	no	—
398	C₃×C₄×C₅	—	2	2	no	—
399	C₃×C₄×C₅	—	4	1	no	—
400	C₃×C₄×C₅	—	4	1	no	—
401	C₃×C₄×C₅	—	4	1	no	—
402	C₃×C₄×C₅	—	4	1	no	—
403	C₅×Dic₃	—	2	2	no	—
404	C₅×Dic₃	—	4	1	no	—
405	C₅×Dic₃	—	4	1	no	—
406	C₅×Dic₃	—	4	1	no	—
407	C₅×Dic₃	—	4	1	no	—
408	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
409	C₂³×D₃	—	4	1	no	—
410	C₂³×D₃	—	4	1	no	—
411	C₂³×D₃	—	4	1	no	—
412	C₂³×D₃	—	4	1	no	—
413	C₂³×D₃	—	4	1	no	—
414	C₂³×D₃	—	4	1	no	—
415	C₂³×D₃	C₂×C₄×C₅	1	4	yes	complemented
416	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
417	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
418	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
419	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
420	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
421	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
422	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
423	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
424	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
425	C₂×#67	—	4	1	no	—
426	C₂×#67	—	4	1	no	—
427	C₂×#67	C₂×C₄×C₅	1	4	yes	—
428	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
429	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
430	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
431	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
432	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
433	C₂×D₁₂	—	4	1	no	—
434	C₂×D₁₂	—	4	1	no	—
435	C₂×D₁₂	—	4	1	no	—
436	C₂×D₁₂	—	4	1	no	—
437	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
438	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
439	C₂×C₄×D₃	—	4	1	no	—
440	C₂×C₄×D₃	—	4	1	no	—
441	C₂×C₄×D₃	—	4	1	no	—
442	C₃×C₄⋊C₄	—	4	1	no	—
443	C₃×C₂²⋊C₄	—	4	1	no	—
444	C₃×C₂²⋊C₄	—	4	1	no	—
445	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
446	C₃×C₄²	—	4	1	no	—
447	#217	—	4	1	no	—
448	#217	—	4	1	no	—
449	(C₂×D₃)⋊C₄	—	4	1	no	—
450	(C₂×D₃)⋊C₄	—	4	1	no	—
451	(C₂×D₃)⋊C₄	—	4	1	no	—
452	(C₂×D₃)⋊C₄	—	4	1	no	—
453	(C₂×D₃)⋊C₄	—	4	1	no	—
454	(C₂×D₃)⋊C₄	—	4	1	no	—
455	(C₂×D₃)⋊C₄	—	4	1	no	—
456	(C₂×D₃)⋊C₄	—	4	1	no	—
457	(C₂×D₃)⋊C₄	—	4	1	no	—
458	(C₂×D₃)⋊C₄	—	4	1	no	—
459	(C₂×D₃)⋊C₄	—	4	1	no	—
460	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
461	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
462	C₄⋊Dic₃	—	4	1	no	—
463	Dic₃⋊C₄	—	4	1	no	—
464	C₄×Dic₃	—	4	1	no	—
465	C₄×Dic₃	—	4	1	no	—
466	C₂³×C₅	—	2	1	no	—
467	C₂³×C₅	—	2	1	no	—
468	C₂³×C₅	—	2	1	no	—
469	C₂³×C₅	—	2	1	no	—
470	C₂³×C₅	—	2	1	no	—
471	C₂³×C₅	—	2	1	no	—
472	C₂³×C₅	—	3	2	no	—
473	C₂³×C₅	—	3	2	no	—
474	C₂³×C₅	—	3	2	no	—
475	C₂³×C₅	—	6	1	no	—
476	C₂³×C₅	—	6	1	no	—
477	C₂³×C₅	—	6	1	no	—
478	C₂³×C₅	—	6	1	no	—
479	C₂³×C₅	—	6	1	no	—
480	C₂³×C₅	—	6	1	no	—
481	C₂³×C₅	—	6	1	no	—
482	C₂³×C₅	—	6	1	no	—
483	C₂³×C₅	—	6	1	no	—
484	C₂³×C₅	—	6	1	no	—
485	C₂³×C₅	—	6	1	no	—
486	C₂³×C₅	—	6	1	no	—
487	C₂³×C₅	—	6	1	no	—
488	C₂³×C₅	—	6	1	no	—
489	C₂³×C₅	—	6	1	no	—
490	C₂³×C₅	—	6	1	no	—
491	C₂³×C₅	—	6	1	no	—
492	C₂³×C₅	—	6	1	no	—
493	C₂³×C₅	—	12	4	no	—
494	C₂³×C₅	—	12	4	no	—
495	C₂³×C₅	—	12	4	no	—
496	C₂³×C₅	—	12	4	no	—
497	C₂³×C₅	—	12	4	no	—
498	C₂³×C₅	—	12	4	no	—
499	C₂³×C₅	—	12	4	no	—
500	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
501	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
502	C₅×D₄	—	12	4	no	—
503	C₅×D₄	—	12	4	no	—
504	C₅×D₄	—	12	4	no	—
505	C₂×C₄×C₅	—	2	1	no	—
506	C₂×C₄×C₅	—	2	1	no	—
507	C₂×C₄×C₅	—	2	1	no	—
508	C₂×C₄×C₅	—	2	1	no	—
509	C₂×C₄×C₅	—	2	1	no	—
510	C₂×C₄×C₅	—	2	1	no	—
511	C₂×C₄×C₅	—	2	1	no	—
512	C₂×C₄×C₅	—	2	1	no	—
513	C₂×C₄×C₅	—	2	1	no	—
514	C₂×C₄×C₅	—	2	1	no	—
515	C₂×C₄×C₅	—	2	1	no	—
516	C₂×C₄×C₅	—	2	1	no	—
517	C₂×C₄×C₅	—	2	1	no	—
518	C₂×C₄×C₅	—	2	1	no	—
519	C₂×C₄×C₅	—	2	1	no	—
520	C₂×C₄×C₅	—	2	1	no	—
521	C₂×C₄×C₅	—	3	2	no	—
522	C₂×C₄×C₅	—	6	1	no	—
523	C₂×C₄×C₅	—	6	1	no	—
524	C₂×C₄×C₅	—	6	1	no	—
525	C₂×C₄×C₅	—	6	1	no	—
526	C₂×C₄×C₅	—	6	1	no	—
527	C₂×C₄×C₅	—	6	1	no	—
528	C₂×C₄×C₅	—	6	1	no	—
529	C₂×C₄×C₅	—	6	1	no	—
530	C₂×C₄×C₅	—	6	1	no	—
531	C₂×C₄×C₅	—	6	1	no	—
532	C₂×C₄×C₅	—	6	1	no	—
533	C₂×C₄×C₅	—	6	1	no	—
534	C₂×C₄×C₅	—	6	1	no	—
535	C₂×C₄×C₅	—	6	1	no	—
536	C₂×C₄×C₅	—	12	4	no	—
537	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
538	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
539	C₂⁵	—	3	1	no	—
540	C₂²×D₄	—	3	1	no	—
541	C₂²×D₄	—	3	1	no	—
542	C₂²×D₄	—	3	1	no	—
543	C₂³×C₄	—	3	1	no	—
544	#120	—	3	8	no	—
545	C₂×C₄⋊C₄	—	3	1	no	—
546	C₂×C₄⋊C₄	—	3	1	no	—
547	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
548	C₂×C₂²⋊C₄	—	3	1	no	—
549	C₂×C₂²⋊C₄	—	3	1	no	—
550	C₂×C₂²⋊C₄	—	3	1	no	—
551	C₂×C₂²⋊C₄	—	3	1	no	—
552	C₂×C₂²⋊C₄	—	3	1	no	—
553	C₂×C₂²⋊C₄	—	3	1	no	—
554	C₂×C₂²⋊C₄	—	3	1	no	—
555	C₂×C₂²⋊C₄	—	3	1	no	—
556	C₂×C₂²⋊C₄	—	3	1	no	—
557	C₂×C₂²⋊C₄	—	3	1	no	—
558	C₂×C₂²⋊C₄	—	3	1	no	—
559	C₂×C₂²⋊C₄	—	3	1	no	—
560	C₂×C₂²⋊C₄	—	3	1	no	—
561	C₂×C₂²⋊C₄	—	3	1	no	—
562	C₂×C₂²⋊C₄	—	3	1	no	—
563	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
564	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
565	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
566	C₂×C₄²	—	3	1	no	—
567	C₂×C₄²	—	3	1	no	—
568	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
569	#95	—	3	1	no	—
570	#95	—	3	1	no	—
571	#95	—	3	1	no	—
572	#95	—	3	1	no	—
573	#95	C₂×C₅×D₃	1	1	yes	characteristic, complemented
574	#95	C₂×C₅×D₃	1	1	yes	characteristic, complemented
575	C₂×C₃×C₅	—	4	2	no	—
576	C₂×C₃×C₅	#518	1	1	yes	characteristic
577	C₂×C₃×C₅	#518	1	1	yes	characteristic
578	C₂×C₃×C₅	#518	1	1	yes	characteristic
579	C₂×C₃×C₅	#560	1	1	yes	characteristic
580	C₂×C₃×C₅	#560	1	1	yes	characteristic
581	C₂×C₃×C₅	#560	1	1	yes	characteristic
582	C₂×C₃×C₅	H(3,𝔽₄)	1	1	yes	characteristic
583	C₅×D₃	—	4	2	no	—
584	C₅×D₃	—	4	2	no	—
585	C₅×D₃	—	4	2	no	—
586	C₂³×C₃	—	2	1	no	—
587	C₂³×C₃	—	2	1	no	—
588	C₂³×C₃	—	2	1	no	—
589	C₂³×C₃	—	2	1	no	—
590	C₂³×C₃	—	2	1	no	—
591	C₂³×C₃	—	2	1	no	—
592	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
593	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
594	C₂²×D₃	—	2	1	no	—
595	C₂²×D₃	—	2	1	no	—
596	C₂²×D₃	—	2	1	no	—
597	C₂²×D₃	—	2	1	no	—
598	C₂²×D₃	—	2	1	no	—
599	C₂²×D₃	—	2	1	no	—
600	C₂²×D₃	—	2	1	no	—
601	C₂²×D₃	—	2	1	no	—
602	C₂²×D₃	—	2	1	no	—
603	C₂²×D₃	—	2	1	no	—
604	C₂²×D₃	—	2	1	no	—
605	C₂²×D₃	—	2	1	no	—
606	C₂²×D₃	—	2	1	no	—
607	C₂²×D₃	—	2	1	no	—
608	C₂²×D₃	—	2	1	no	—
609	C₂²×D₃	—	2	1	no	—
610	C₂²×D₃	—	2	1	no	—
611	C₂²×D₃	—	2	1	no	—
612	C₂²×D₃	—	4	4	no	—
613	C₂²×D₃	—	4	4	no	—
614	C₂²×D₃	—	4	4	no	—
615	C₂²×D₃	—	4	4	no	—
616	C₂²×D₃	—	4	4	no	—
617	C₂²×D₃	—	4	4	no	—
618	C₂²×D₃	—	4	4	no	—
619	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
620	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
621	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
622	C₂×C₃×C₄	—	2	1	no	—
623	C₂×C₃×C₄	—	2	1	no	—
624	C₂×C₃×C₄	—	2	1	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	—	2	1	no	—
631	C₂×C₃×C₄	—	2	1	no	—
632	C₂×C₃×C₄	—	2	1	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	2	1	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	1	no	—
637	C₂×C₃×C₄	—	2	1	no	—
638	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
639	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
640	#67	—	4	4	no	—
641	C₂×Dic₃	—	2	1	no	—
642	C₂×Dic₃	—	2	1	no	—
643	C₂×Dic₃	—	2	1	no	—
644	C₂×Dic₃	—	2	1	no	—
645	C₂×Dic₃	—	2	1	no	—
646	C₂×Dic₃	—	2	1	no	—
647	C₂×Dic₃	—	2	1	no	—
648	C₂×Dic₃	—	2	1	no	—
649	C₂×Dic₃	—	2	1	no	—
650	C₂×Dic₃	—	2	1	no	—
651	C₂×Dic₃	—	2	1	no	—
652	C₂×Dic₃	—	2	1	no	—
653	C₂×Dic₃	—	2	1	no	—
654	C₂×Dic₃	—	2	1	no	—
655	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
656	D₁₂	—	4	4	no	—
657	D₁₂	—	4	4	no	—
658	C₄×D₃	—	4	4	no	—
659	C₂²×C₅	—	2	2	no	—
660	C₂²×C₅	—	2	2	no	—
661	C₂²×C₅	—	2	2	no	—
662	C₂²×C₅	—	4	1	no	—
663	C₂²×C₅	—	4	1	no	—
664	C₂²×C₅	—	4	1	no	—
665	C₂²×C₅	—	4	1	no	—
666	C₂²×C₅	—	6	2	no	—
667	C₂²×C₅	—	6	2	no	—
668	C₂²×C₅	—	6	2	no	—
669	C₂²×C₅	—	6	2	no	—
670	C₂²×C₅	—	6	2	no	—
671	C₂²×C₅	—	6	2	no	—
672	C₂²×C₅	—	6	2	no	—
673	C₂²×C₅	—	6	2	no	—
674	C₂²×C₅	—	6	2	no	—
675	C₂²×C₅	—	12	16	no	—
676	C₂²×C₅	—	12	1	no	—
677	C₂²×C₅	—	12	1	no	—
678	C₂²×C₅	—	12	1	no	—
679	C₂²×C₅	—	12	1	no	—
680	C₂²×C₅	—	12	1	no	—
681	C₂²×C₅	—	12	1	no	—
682	C₂²×C₅	—	12	1	no	—
683	C₂²×C₅	—	12	1	no	—
684	C₂²×C₅	—	12	1	no	—
685	C₂²×C₅	—	12	1	no	—
686	C₂²×C₅	—	12	1	no	—
687	C₂²×C₅	—	12	1	no	—
688	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
689	C₂²×C₅	#1004	1	1	yes	characteristic
690	C₂²×C₅	#1004	1	1	yes	characteristic
691	C₂²×C₅	#1009	1	1	yes	characteristic
692	C₂²×C₅	#1009	1	1	yes	characteristic
693	C₂²×C₅	#1009	1	1	yes	characteristic
694	C₂²×C₅	#1009	1	1	yes	characteristic
695	C₄×C₅	—	2	2	no	—
696	C₄×C₅	—	2	2	no	—
697	C₄×C₅	—	4	1	no	—
698	C₄×C₅	—	4	1	no	—
699	C₄×C₅	—	4	1	no	—
700	C₄×C₅	—	4	1	no	—
701	C₄×C₅	—	6	2	no	—
702	C₄×C₅	—	12	1	no	—
703	C₄×C₅	—	12	1	no	—
704	C₄×C₅	—	12	1	no	—
705	C₄×C₅	—	12	1	no	—
706	C₂⁴	—	3	1	no	—
707	C₂⁴	—	3	1	no	—
708	C₂⁴	—	3	1	no	—
709	C₂⁴	—	3	4	no	—
710	C₂⁴	—	12	1	no	—
711	C₂⁴	—	12	1	no	—
712	C₂⁴	—	12	1	no	—
713	C₂⁴	—	12	1	no	—
714	C₂⁴	—	12	1	no	—
715	C₂⁴	—	12	1	no	—
716	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
717	C₂×D₄	—	3	4	no	—
718	C₂×D₄	—	3	4	no	—
719	C₂×D₄	—	3	4	no	—
720	C₂×D₄	—	12	1	no	—
721	C₂×D₄	—	12	1	no	—
722	C₂×D₄	—	12	1	no	—
723	C₂×D₄	—	12	1	no	—
724	C₂×D₄	—	12	1	no	—
725	C₂×D₄	—	12	1	no	—
726	C₂²×C₄	—	3	1	no	—
727	C₂²×C₄	—	3	1	no	—
728	C₂²×C₄	—	3	1	no	—
729	C₂²×C₄	—	3	1	no	—
730	C₂²×C₄	—	3	1	no	—
731	C₂²×C₄	—	12	1	no	—
732	C₂²×C₄	—	12	1	no	—
733	C₂²×C₄	—	12	1	no	—
734	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
735	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
736	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
737	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
738	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
739	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
740	C₄⋊C₄	—	4	1	no	—
741	C₄⋊C₄	—	12	1	no	—
742	C₄⋊C₄	—	12	1	no	—
743	C₂²⋊C₄	—	3	4	no	—
744	C₂²⋊C₄	—	3	4	no	—
745	C₂²⋊C₄	—	4	1	no	—
746	C₂²⋊C₄	—	4	1	no	—
747	C₂²⋊C₄	—	12	1	no	—
748	C₂²⋊C₄	—	12	1	no	—
749	C₂²⋊C₄	—	12	1	no	—
750	C₂²⋊C₄	—	12	1	no	—
751	C₂²⋊C₄	—	12	1	no	—
752	C₂²⋊C₄	—	12	1	no	—
753	C₂²⋊C₄	—	12	1	no	—
754	C₂²⋊C₄	—	12	1	no	—
755	C₂²⋊C₄	—	12	1	no	—
756	C₂²⋊C₄	—	12	1	no	—
757	C₂²⋊C₄	—	12	1	no	—
758	C₂²⋊C₄	—	12	1	no	—
759	C₂²⋊C₄	—	12	1	no	—
760	C₂²⋊C₄	C₄×C₅×D₃	1	4	yes	complemented
761	C₄²	—	4	1	no	—
762	C₄²	—	12	1	no	—
763	C₄²	—	12	1	no	—
764	C₃×C₅	#2375	1	1	yes	characteristic, complemented, Hall
765	C₂²×C₃	—	2	2	no	—
766	C₂²×C₃	—	2	2	no	—
767	C₂²×C₃	—	2	2	no	—
768	C₂²×C₃	—	4	1	no	—
769	C₂²×C₃	—	4	1	no	—
770	C₂²×C₃	—	4	1	no	—
771	C₂²×C₃	—	4	1	no	—
772	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
773	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
774	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
775	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
776	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
777	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
778	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
779	C₂×D₃	—	2	2	no	—
780	C₂×D₃	—	2	2	no	—
781	C₂×D₃	—	2	2	no	—
782	C₂×D₃	—	2	2	no	—
783	C₂×D₃	—	2	2	no	—
784	C₂×D₃	—	2	2	no	—
785	C₂×D₃	—	2	2	no	—
786	C₂×D₃	—	2	2	no	—
787	C₂×D₃	—	2	2	no	—
788	C₂×D₃	—	4	16	no	—
789	C₂×D₃	—	4	1	no	—
790	C₂×D₃	—	4	1	no	—
791	C₂×D₃	—	4	1	no	—
792	C₂×D₃	—	4	1	no	—
793	C₂×D₃	—	4	1	no	—
794	C₂×D₃	—	4	1	no	—
795	C₂×D₃	—	4	1	no	—
796	C₂×D₃	—	4	1	no	—
797	C₂×D₃	—	4	1	no	—
798	C₂×D₃	—	4	1	no	—
799	C₂×D₃	—	4	1	no	—
800	C₂×D₃	—	4	1	no	—
801	C₃×C₄	—	2	2	no	—
802	C₃×C₄	—	2	2	no	—
803	C₃×C₄	—	4	1	no	—
804	C₃×C₄	—	4	1	no	—
805	C₃×C₄	—	4	1	no	—
806	C₃×C₄	—	4	1	no	—
807	Dic₃	—	2	2	no	—
808	Dic₃	—	4	1	no	—
809	Dic₃	—	4	1	no	—
810	Dic₃	—	4	1	no	—
811	Dic₃	—	4	1	no	—
812	C₂×C₅	—	4	2	no	—
813	C₂×C₅	—	12	2	no	—
814	C₂×C₅	—	12	2	no	—
815	C₂×C₅	—	12	2	no	—
816	C₂×C₅	#5521	1	1	yes	characteristic
817	C₂×C₅	#5545	1	1	yes	characteristic
818	C₂×C₅	#5545	1	1	yes	characteristic
819	C₂×C₅	#5620	1	1	yes	characteristic
820	C₂×C₅	#5666	1	1	yes	characteristic
821	C₂×C₅	#5683	1	1	yes	characteristic
822	C₂×C₅	#5711	1	1	yes	characteristic
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	3	2	no	—
830	C₂³	—	3	2	no	—
831	C₂³	—	3	2	no	—
832	C₂³	—	6	1	no	—
833	C₂³	—	6	1	no	—
834	C₂³	—	6	1	no	—
835	C₂³	—	6	1	no	—
836	C₂³	—	6	1	no	—
837	C₂³	—	6	1	no	—
838	C₂³	—	6	1	no	—
839	C₂³	—	6	1	no	—
840	C₂³	—	6	1	no	—
841	C₂³	—	6	1	no	—
842	C₂³	—	6	1	no	—
843	C₂³	—	6	1	no	—
844	C₂³	—	6	1	no	—
845	C₂³	—	6	1	no	—
846	C₂³	—	6	1	no	—
847	C₂³	—	6	1	no	—
848	C₂³	—	6	1	no	—
849	C₂³	—	6	1	no	—
850	C₂³	—	12	4	no	—
851	C₂³	—	12	4	no	—
852	C₂³	—	12	4	no	—
853	C₂³	—	12	4	no	—
854	C₂³	—	12	4	no	—
855	C₂³	—	12	4	no	—
856	C₂³	—	12	4	no	—
857	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
858	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
859	D₄	—	12	4	no	—
860	D₄	—	12	4	no	—
861	D₄	—	12	4	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	3	2	no	—
879	C₂×C₄	—	6	1	no	—
880	C₂×C₄	—	6	1	no	—
881	C₂×C₄	—	6	1	no	—
882	C₂×C₄	—	6	1	no	—
883	C₂×C₄	—	6	1	no	—
884	C₂×C₄	—	6	1	no	—
885	C₂×C₄	—	6	1	no	—
886	C₂×C₄	—	6	1	no	—
887	C₂×C₄	—	6	1	no	—
888	C₂×C₄	—	6	1	no	—
889	C₂×C₄	—	6	1	no	—
890	C₂×C₄	—	6	1	no	—
891	C₂×C₄	—	6	1	no	—
892	C₂×C₄	—	6	1	no	—
893	C₂×C₄	—	12	4	no	—
894	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
895	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
896	C₂×C₃	—	4	2	no	—
897	C₂×C₃	C₅×#518	1	1	yes	characteristic
898	C₂×C₃	C₅×#518	1	1	yes	characteristic
899	C₂×C₃	C₅×#518	1	1	yes	characteristic
900	C₂×C₃	C₅×#560	1	1	yes	characteristic
901	C₂×C₃	C₅×#560	1	1	yes	characteristic
902	C₂×C₃	C₅×#560	1	1	yes	characteristic
903	C₂×C₃	C₅×H(3,𝔽₄)	1	1	yes	characteristic
904	D₃	—	4	2	no	—
905	D₃	—	4	2	no	—
906	D₃	—	4	2	no	—
907	C₅	#75840	1	1	yes	characteristic, direct product factor, Sylow
908	C₂²	—	2	2	no	—
909	C₂²	—	2	2	no	—
910	C₂²	—	2	2	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	4	1	no	—
915	C₂²	—	6	2	no	—
916	C₂²	—	6	2	no	—
917	C₂²	—	6	2	no	—
918	C₂²	—	6	2	no	—
919	C₂²	—	6	2	no	—
920	C₂²	—	6	2	no	—
921	C₂²	—	6	2	no	—
922	C₂²	—	6	2	no	—
923	C₂²	—	6	2	no	—
924	C₂²	—	12	16	no	—
925	C₂²	—	12	1	no	—
926	C₂²	—	12	1	no	—
927	C₂²	—	12	1	no	—
928	C₂²	—	12	1	no	—
929	C₂²	—	12	1	no	—
930	C₂²	—	12	1	no	—
931	C₂²	—	12	1	no	—
932	C₂²	—	12	1	no	—
933	C₂²	—	12	1	no	—
934	C₂²	—	12	1	no	—
935	C₂²	—	12	1	no	—
936	C₂²	—	12	1	no	—
937	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
938	C₂²	C₅×#1004	1	1	yes	characteristic
939	C₂²	C₅×#1004	1	1	yes	characteristic
940	C₂²	C₅×#1009	1	1	yes	characteristic
941	C₂²	C₅×#1009	1	1	yes	characteristic
942	C₂²	C₅×#1009	1	1	yes	characteristic
943	C₂²	C₅×#1009	1	1	yes	characteristic
944	C₄	—	2	2	no	—
945	C₄	—	2	2	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	1	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	1	no	—
950	C₄	—	6	2	no	—
951	C₄	—	12	1	no	—
952	C₄	—	12	1	no	—
953	C₄	—	12	1	no	—
954	C₄	—	12	1	no	—
955	C₃	C₅×#2375	1	1	yes	characteristic, complemented, Sylow
956	C₂	—	4	2	no	—
957	C₂	—	12	2	no	—
958	C₂	—	12	2	no	—
959	C₂	—	12	2	no	—
960	C₂	C₅×#5521	1	1	yes	characteristic
961	C₂	C₅×#5545	1	1	yes	characteristic
962	C₂	C₅×#5545	1	1	yes	characteristic
963	C₂	C₅×#5620	1	1	yes	characteristic
964	C₂	C₅×#5666	1	1	yes	characteristic
965	C₂	C₅×#5683	1	1	yes	characteristic
966	C₂	C₅×#5711	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#388	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#882	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#388	D₃
hypocenter	C₃	C₅×#2375
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#388

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#388	C₂	semidirect
3. C₅×#4990	C₂	semidirect
4. C₅×#4988	C₂	semidirect
5. C₅×#4957	C₂	semidirect
6. C₅×#4956	C₂	semidirect
7. C₅×#4955	C₂	semidirect
8. C₅×#4955	C₂	semidirect
9. C₅×#4951	C₂	semidirect
10. C₅×#4940	C₂	semidirect
11. C₅×#4939	C₂	semidirect
12. C₅×#4670	C₂	semidirect
13. C₅×#4669	C₂	semidirect
14. C₅×#4665	C₂	semidirect
15. C₅×#4665	C₂	semidirect
21. C₂²×C₄×C₅×D₃	C₂²	semidirect
22. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
26. C₂×C₃×C₄²×C₅	C₂²	semidirect
39. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
40. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
41. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
42. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
43. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
44. C₂×C₄×C₅×Dic₃	C₂²	semidirect
45. C₂×C₄×C₅×Dic₃	C₂²	semidirect
46. C₅×#882	C₄	semidirect
47. C₃×C₅×#95	C₂²	semidirect
48. C₃×C₅×#95	C₂²	semidirect
49. C₅×C₃⋊#95	C₂²	semidirect
50. C₅×C₃⋊#95	C₂²	semidirect
51. C₅×C₃⋊#95	C₂²	semidirect
52. C₅×C₃⋊#95	C₂²	semidirect
53. #75840	C₅	direct (N × H)
63. C₅×#388	D₃	semidirect
76. C₂³×C₅×D₃	C₂×C₄	semidirect
106. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
121. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
122. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
128. C₃×#388	C₂×C₅	semidirect
129. #4990	C₂×C₅	semidirect
130. #4988	C₂×C₅	semidirect
131. #4957	C₂×C₅	semidirect
132. #4956	C₂×C₅	semidirect
133. #4955	C₂×C₅	semidirect
134. #4955	C₂×C₅	semidirect
135. #4951	C₂×C₅	semidirect
136. #4940	C₂×C₅	semidirect
137. #4939	C₂×C₅	semidirect
138. #4670	C₂×C₅	semidirect
139. #4669	C₂×C₅	semidirect
140. #4665	C₂×C₅	semidirect
141. #4665	C₂×C₅	semidirect
150. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
171. C₂×C₄²×C₅	C₂×D₃	semidirect
176. C₅×#95	C₂×D₃	semidirect
177. C₅×#95	C₂×D₃	semidirect
256. C₂²×C₄×D₃	C₂²×C₅	semidirect
257. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
261. C₂×C₃×C₄²	C₂²×C₅	semidirect
274. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
275. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
276. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
277. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
278. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
279. C₂×C₄×Dic₃	C₂²×C₅	semidirect
280. C₂×C₄×Dic₃	C₂²×C₅	semidirect
281. #882	C₄×C₅	semidirect
282. C₃×#95	C₂²×C₅	semidirect
283. C₃×#95	C₂²×C₅	semidirect
284. C₃⋊#95	C₂²×C₅	semidirect
285. C₃⋊#95	C₂²×C₅	semidirect
286. C₃⋊#95	C₂²×C₅	semidirect
287. C₃⋊#95	C₂²×C₅	semidirect
342. C₅×C₂²⋊C₄	C₄×D₃	semidirect
355. #388	C₅×D₃	semidirect
415. C₂³×D₃	C₂×C₄×C₅	semidirect
445. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
460. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
461. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
547. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
568. C₂×C₄²	C₂×C₅×D₃	semidirect
573. #95	C₂×C₅×D₃	semidirect
574. #95	C₂×C₅×D₃	semidirect
760. C₂²⋊C₄	C₄×C₅×D₃	semidirect
764. C₃×C₅	#2375	semidirect
907. C₅	#75840	direct (N × H)
955. C₃	C₅×#2375	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#882	2
C₃×C₅×#388	2
C₅×#4990	2
C₅×#4988	2
C₅×#4957	2
C₅×#4956	2
C₅×#4955	2
C₅×#4951	2
C₅×#4940	2
C₅×#4939	2
C₅×#4670	2
C₅×#4669	2
C₅×#4665	2
C₅×#2375	3
#75840	5

Subgroups — C5×#75840 #14330634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#75840 #14330634