Subgroups — C₅×#75298 #14324035

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4989	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4980	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4940	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4669	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4668	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4667	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4665	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4665	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4665	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4665	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×D₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2325	—	3	1	no	maximal, Hall
17	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
20	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₂×C₅×(C₂×D₃)⋊C₄	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×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
39	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
42	C₅×#895	C₄	1	8	yes	complemented
43	C₅×#893	—	2	4	no	—
44	C₄×C₅×D₁₂	—	2	4	no	—
45	C₃×C₅×#95	C₂²	1	1	yes	characteristic
46	C₃×C₅×#95	C₂²	1	1	yes	characteristic
47	C₃×C₅×#95	C₂²	1	1	yes	characteristic
48	C₃×C₅×#95	C₂²	1	1	yes	characteristic
49	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
50	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
51	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
52	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
53	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
54	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
55	#75298	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
56	C₂×C₅×#121	—	3	1	no	—
57	C₂×C₄×C₅×D₄	—	3	1	no	—
58	C₂×C₄×C₅×D₄	—	3	1	no	—
59	C₅×#388	—	3	1	no	—
60	C₅×#388	—	3	1	no	—
61	C₅×#387	—	3	1	no	—
62	C₅×#387	D₃	1	1	yes	characteristic, complemented
63	C₅×#386	—	3	1	no	—
64	C₅×#386	—	3	1	no	—
65	C₅×#386	—	3	1	no	—
66	C₅×#386	—	3	1	no	—
67	C₅×#385	—	3	1	no	—
68	C₅×#385	—	3	1	no	—
69	C₅×#380	—	3	1	no	—
70	C₂×C₅×#95	—	3	1	no	—
71	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
72	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
73	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
82	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
85	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
86	C₂×C₅×D₁₂	—	2	2	no	—
87	C₂×C₅×D₁₂	—	2	2	no	—
88	C₂×C₅×D₁₂	—	2	2	no	—
89	C₂×C₅×D₁₂	—	2	2	no	—
90	C₂×C₅×D₁₂	—	4	1	no	—
91	C₂×C₅×D₁₂	—	4	1	no	—
92	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
93	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
94	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
95	C₂×C₄×C₅×D₃	—	2	2	no	—
96	C₂×C₄×C₅×D₃	—	2	2	no	—
97	C₂×C₄×C₅×D₃	—	2	2	no	—
98	C₂×C₄×C₅×D₃	—	4	1	no	—
99	C₂×C₄×C₅×D₃	—	4	1	no	—
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	C₂×C₄×C₅×D₃	—	4	1	no	—
104	C₂×C₄×C₅×D₃	—	4	1	no	—
105	C₂×C₄×C₅×D₃	—	4	1	no	—
106	C₂×C₄×C₅×D₃	—	4	1	no	—
107	C₂×C₄×C₅×D₃	—	4	1	no	—
108	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
109	C₂×C₄×C₅×D₃	D₄	1	4	yes	complemented
110	C₃×C₅×C₄⋊C₄	—	2	2	no	—
111	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
112	C₃×C₄²×C₅	—	2	2	no	—
113	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
114	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
115	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
116	C₅×(C₂×D₃)⋊C₄	—	2	2	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	—	2	2	no	—
124	C₅×Dic₃⋊C₄	—	4	1	no	—
125	C₅×Dic₃⋊C₄	—	4	1	no	—
126	C₄×C₅×Dic₃	—	2	2	no	—
127	C₂×#895	C₂×C₅	1	1	yes	characteristic
128	C₂×#893	C₂×C₅	1	1	yes	characteristic, complemented
129	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
131	#4989	C₂×C₅	1	1	yes	characteristic, complemented
132	#4980	C₂×C₅	1	1	yes	characteristic, complemented
133	#4940	C₂×C₅	1	1	yes	characteristic, complemented
134	#4669	C₂×C₅	1	1	yes	characteristic, complemented
135	#4668	C₂×C₅	1	1	yes	characteristic, complemented
136	#4667	C₂×C₅	1	1	yes	characteristic, complemented
137	#4665	C₂×C₅	1	1	yes	characteristic, complemented
138	#4665	C₂×C₅	1	1	yes	characteristic, complemented
139	#4665	C₂×C₅	1	1	yes	characteristic, complemented
140	#4665	C₂×C₅	1	1	yes	characteristic, complemented
141	D₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂²×C₅×D₄	—	3	1	no	—
143	C₂²×C₅×D₄	—	3	1	no	—
144	C₂²×C₅×D₄	—	3	1	no	—
145	C₂³×C₄×C₅	—	3	1	no	—
146	C₂³×C₄×C₅	—	3	1	no	—
147	C₂³×C₄×C₅	—	3	1	no	—
148	C₂³×C₄×C₅	—	3	1	no	—
149	C₂³×C₄×C₅	—	3	1	no	—
150	C₅×#121	—	3	8	no	—
151	C₄×C₅×D₄	—	6	4	no	—
152	C₄×C₅×D₄	—	6	4	no	—
153	C₂×C₅×C₄⋊C₄	—	3	1	no	—
154	C₂×C₅×C₄⋊C₄	—	3	1	no	—
155	C₂×C₅×C₄⋊C₄	—	3	1	no	—
156	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
157	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
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	—	3	1	no	—
167	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
168	C₂×C₄²×C₅	—	3	1	no	—
169	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
170	C₅×#95	—	3	1	no	—
171	C₅×#95	—	3	1	no	—
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
177	C₅×#95	C₂×D₃	1	1	yes	characteristic
178	C₅×#95	C₂×D₃	1	1	yes	characteristic
179	C₅×#95	C₂×D₃	1	1	yes	characteristic
180	#2325	—	3	1	no	Sylow
181	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
182	C₂²×C₅×D₃	—	2	1	no	—
183	C₂²×C₅×D₃	—	2	1	no	—
184	C₂²×C₅×D₃	—	2	1	no	—
185	C₂²×C₅×D₃	—	2	1	no	—
186	C₂²×C₅×D₃	—	2	1	no	—
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	C₂²×C₄	1	2	yes	—
199	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
200	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
201	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
202	C₂²×C₅×D₃	#41	1	2	yes	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	—	2	1	no	—
209	C₂×C₃×C₄×C₅	—	2	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	1	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	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	C₂²×C₄	1	2	yes	—
221	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
222	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
223	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
224	C₂×C₅×Dic₃	—	2	1	no	—
225	C₂×C₅×Dic₃	—	2	1	no	—
226	C₂×C₅×Dic₃	—	2	1	no	—
227	C₂×C₅×Dic₃	—	2	1	no	—
228	C₂×C₅×Dic₃	—	2	1	no	—
229	C₂×C₅×Dic₃	—	2	1	no	—
230	C₂×C₅×Dic₃	—	2	1	no	—
231	C₂×C₅×Dic₃	—	2	1	no	—
232	C₂×C₅×Dic₃	—	2	1	no	—
233	C₂×C₅×Dic₃	—	2	1	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	C₂²×C₄	1	2	yes	—
238	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
239	C₅×D₁₂	—	2	8	no	—
240	C₅×D₁₂	—	2	8	no	—
241	C₅×D₁₂	—	4	4	no	—
242	C₄×C₅×D₃	—	4	4	no	—
243	C₄×C₅×D₃	—	4	4	no	—
244	C₄×C₅×D₃	—	4	4	no	—
245	C₄×C₅×D₃	—	4	4	no	—
246	C₄×C₅×D₃	—	4	4	no	—
247	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
248	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
249	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
250	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
251	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
252	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
253	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
254	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
258	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
259	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
260	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
261	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
262	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
263	C₂×(C₂×D₃)⋊C₄	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×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
269	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
270	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
272	#895	C₄×C₅	1	8	yes	complemented
273	#893	—	2	4	no	—
274	C₄×D₁₂	—	2	4	no	—
275	C₃×#95	C₂²×C₅	1	1	yes	characteristic
276	C₃×#95	C₂²×C₅	1	1	yes	characteristic
277	C₃×#95	C₂²×C₅	1	1	yes	characteristic
278	C₃×#95	C₂²×C₅	1	1	yes	characteristic
279	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
280	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
281	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
282	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
283	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
284	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
285	C₂⁴×C₅	—	3	1	no	—
286	C₂⁴×C₅	—	3	1	no	—
287	C₂⁴×C₅	—	3	1	no	—
288	C₂×C₅×D₄	—	3	4	no	—
289	C₂×C₅×D₄	—	3	4	no	—
290	C₂×C₅×D₄	—	3	4	no	—
291	C₂×C₅×D₄	—	6	2	no	—
292	C₂×C₅×D₄	—	6	2	no	—
293	C₂×C₅×D₄	—	6	2	no	—
294	C₂×C₅×D₄	—	6	2	no	—
295	C₂×C₅×D₄	—	12	1	no	—
296	C₂×C₅×D₄	—	12	1	no	—
297	C₂²×C₄×C₅	—	3	1	no	—
298	C₂²×C₄×C₅	—	3	1	no	—
299	C₂²×C₄×C₅	—	3	4	no	—
300	C₂²×C₄×C₅	—	3	4	no	—
301	C₂²×C₄×C₅	—	3	1	no	—
302	C₂²×C₄×C₅	—	3	1	no	—
303	C₂²×C₄×C₅	—	3	1	no	—
304	C₂²×C₄×C₅	—	6	2	no	—
305	C₂²×C₄×C₅	—	6	2	no	—
306	C₂²×C₄×C₅	—	6	2	no	—
307	C₂²×C₄×C₅	—	12	1	no	—
308	C₂²×C₄×C₅	—	12	1	no	—
309	C₂²×C₄×C₅	—	12	1	no	—
310	C₂²×C₄×C₅	—	12	1	no	—
311	C₂²×C₄×C₅	—	12	1	no	—
312	C₂²×C₄×C₅	—	12	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	—	12	1	no	—
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	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
323	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
324	C₅×C₄⋊C₄	—	2	2	no	—
325	C₅×C₄⋊C₄	—	6	2	no	—
326	C₅×C₄⋊C₄	—	12	1	no	—
327	C₅×C₄⋊C₄	—	12	1	no	—
328	C₅×C₄⋊C₄	C₄×D₃	1	4	yes	complemented
329	C₅×C₂²⋊C₄	—	3	4	no	—
330	C₅×C₂²⋊C₄	—	3	4	no	—
331	C₅×C₂²⋊C₄	—	6	2	no	—
332	C₅×C₂²⋊C₄	—	6	2	no	—
333	C₅×C₂²⋊C₄	—	6	2	no	—
334	C₅×C₂²⋊C₄	—	6	2	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	C₄²×C₅	—	2	2	no	—
340	C₄²×C₅	—	6	2	no	—
341	C₂×#121	—	3	1	no	—
342	C₂×C₄×D₄	—	3	1	no	—
343	C₂×C₄×D₄	—	3	1	no	—
344	#388	—	3	1	no	—
345	#388	—	3	1	no	—
346	#387	—	3	1	no	—
347	#387	C₅×D₃	1	1	yes	characteristic, complemented
348	#386	—	3	1	no	—
349	#386	—	3	1	no	—
350	#386	—	3	1	no	—
351	#386	—	3	1	no	—
352	#385	—	3	1	no	—
353	#385	—	3	1	no	—
354	#380	—	3	1	no	—
355	C₂×#95	—	3	1	no	—
356	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
357	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
358	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
359	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
360	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
361	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
362	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
363	C₂×C₅×D₃	—	2	2	no	—
364	C₂×C₅×D₃	—	2	2	no	—
365	C₂×C₅×D₃	—	2	2	no	—
366	C₂×C₅×D₃	—	2	2	no	—
367	C₂×C₅×D₃	—	2	2	no	—
368	C₂×C₅×D₃	—	2	2	no	—
369	C₂×C₅×D₃	—	2	2	no	—
370	C₂×C₅×D₃	—	2	2	no	—
371	C₂×C₅×D₃	—	2	2	no	—
372	C₂×C₅×D₃	—	2	2	no	—
373	C₂×C₅×D₃	—	2	2	no	—
374	C₂×C₅×D₃	—	2	2	no	—
375	C₂×C₅×D₃	—	4	1	no	—
376	C₂×C₅×D₃	—	4	1	no	—
377	C₂×C₅×D₃	—	4	1	no	—
378	C₂×C₅×D₃	—	4	1	no	—
379	C₂×C₅×D₃	—	4	1	no	—
380	C₂×C₅×D₃	—	4	1	no	—
381	C₂×C₅×D₃	—	4	1	no	—
382	C₂×C₅×D₃	—	4	1	no	—
383	C₂×C₅×D₃	C₄×D₄	1	4	yes	—
384	C₃×C₄×C₅	—	2	2	no	—
385	C₃×C₄×C₅	—	2	2	no	—
386	C₃×C₄×C₅	—	2	2	no	—
387	C₃×C₄×C₅	—	2	2	no	—
388	C₃×C₄×C₅	—	4	1	no	—
389	C₃×C₄×C₅	—	4	1	no	—
390	C₃×C₄×C₅	—	4	1	no	—
391	C₅×Dic₃	—	2	2	no	—
392	C₅×Dic₃	—	2	2	no	—
393	C₅×Dic₃	—	4	1	no	—
394	C₅×Dic₃	—	4	1	no	—
395	C₅×Dic₃	—	4	1	no	—
396	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
397	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
398	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
399	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
400	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
401	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
403	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
404	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
405	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
406	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
407	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
408	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
409	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
410	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
411	C₂×D₁₂	—	2	2	no	—
412	C₂×D₁₂	—	2	2	no	—
413	C₂×D₁₂	—	2	2	no	—
414	C₂×D₁₂	—	2	2	no	—
415	C₂×D₁₂	—	4	1	no	—
416	C₂×D₁₂	—	4	1	no	—
417	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
418	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
419	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
420	C₂×C₄×D₃	—	2	2	no	—
421	C₂×C₄×D₃	—	2	2	no	—
422	C₂×C₄×D₃	—	2	2	no	—
423	C₂×C₄×D₃	—	4	1	no	—
424	C₂×C₄×D₃	—	4	1	no	—
425	C₂×C₄×D₃	—	4	1	no	—
426	C₂×C₄×D₃	—	4	1	no	—
427	C₂×C₄×D₃	—	4	1	no	—
428	C₂×C₄×D₃	—	4	1	no	—
429	C₂×C₄×D₃	—	4	1	no	—
430	C₂×C₄×D₃	—	4	1	no	—
431	C₂×C₄×D₃	—	4	1	no	—
432	C₂×C₄×D₃	—	4	1	no	—
433	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
434	C₂×C₄×D₃	C₅×D₄	1	4	yes	complemented
435	C₃×C₄⋊C₄	—	2	2	no	—
436	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
437	C₃×C₄²	—	2	2	no	—
438	(C₂×D₃)⋊C₄	—	2	2	no	—
439	(C₂×D₃)⋊C₄	—	2	2	no	—
440	(C₂×D₃)⋊C₄	—	2	2	no	—
441	(C₂×D₃)⋊C₄	—	2	2	no	—
442	(C₂×D₃)⋊C₄	—	4	1	no	—
443	(C₂×D₃)⋊C₄	—	4	1	no	—
444	(C₂×D₃)⋊C₄	—	4	1	no	—
445	(C₂×D₃)⋊C₄	—	4	1	no	—
446	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
447	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
448	C₄⋊Dic₃	—	2	2	no	—
449	Dic₃⋊C₄	—	4	1	no	—
450	Dic₃⋊C₄	—	4	1	no	—
451	C₄×Dic₃	—	2	2	no	—
452	C₂³×C₅	—	3	2	no	—
453	C₂³×C₅	—	3	2	no	—
454	C₂³×C₅	—	3	2	no	—
455	C₂³×C₅	—	3	2	no	—
456	C₂³×C₅	—	3	2	no	—
457	C₂³×C₅	—	6	1	no	—
458	C₂³×C₅	—	6	1	no	—
459	C₂³×C₅	—	6	1	no	—
460	C₂³×C₅	—	6	1	no	—
461	C₂³×C₅	—	6	1	no	—
462	C₂³×C₅	—	6	1	no	—
463	C₂³×C₅	—	6	1	no	—
464	C₂³×C₅	—	6	1	no	—
465	C₂³×C₅	—	6	1	no	—
466	C₂³×C₅	—	6	1	no	—
467	C₂³×C₅	—	6	1	no	—
468	C₂³×C₅	—	6	1	no	—
469	C₂³×C₅	—	6	1	no	—
470	C₂³×C₅	—	6	1	no	—
471	C₂³×C₅	—	6	1	no	—
472	C₂³×C₅	—	6	1	no	—
473	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
474	C₅×D₄	—	6	8	no	—
475	C₅×D₄	—	6	8	no	—
476	C₅×D₄	—	12	4	no	—
477	C₂×C₄×C₅	—	2	1	no	—
478	C₂×C₄×C₅	—	2	1	no	—
479	C₂×C₄×C₅	—	2	1	no	—
480	C₂×C₄×C₅	—	2	1	no	—
481	C₂×C₄×C₅	—	2	1	no	—
482	C₂×C₄×C₅	—	2	1	no	—
483	C₂×C₄×C₅	—	2	1	no	—
484	C₂×C₄×C₅	—	2	1	no	—
485	C₂×C₄×C₅	—	2	1	no	—
486	C₂×C₄×C₅	—	2	1	no	—
487	C₂×C₄×C₅	—	2	1	no	—
488	C₂×C₄×C₅	—	2	1	no	—
489	C₂×C₄×C₅	—	2	1	no	—
490	C₂×C₄×C₅	—	2	1	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	2	1	no	—
493	C₂×C₄×C₅	—	2	1	no	—
494	C₂×C₄×C₅	—	3	2	no	—
495	C₂×C₄×C₅	—	3	2	no	—
496	C₂×C₄×C₅	—	6	1	no	—
497	C₂×C₄×C₅	—	6	1	no	—
498	C₂×C₄×C₅	—	6	1	no	—
499	C₂×C₄×C₅	—	6	1	no	—
500	C₂×C₄×C₅	—	6	1	no	—
501	C₂×C₄×C₅	—	6	1	no	—
502	C₂×C₄×C₅	—	6	1	no	—
503	C₂×C₄×C₅	—	6	1	no	—
504	C₂×C₄×C₅	—	6	1	no	—
505	C₂×C₄×C₅	—	6	1	no	—
506	C₂×C₄×C₅	—	6	1	no	—
507	C₂×C₄×C₅	—	6	1	no	—
508	C₂×C₄×C₅	—	6	1	no	—
509	C₂×C₄×C₅	—	12	4	no	—
510	C₂×C₄×C₅	—	12	4	no	—
511	C₂×C₄×C₅	—	12	4	no	—
512	C₂×C₄×C₅	—	12	4	no	—
513	C₂×C₄×C₅	—	12	4	no	—
514	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
515	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
516	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
517	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
518	C₂²×D₄	—	3	1	no	—
519	C₂²×D₄	—	3	1	no	—
520	C₂²×D₄	—	3	1	no	—
521	C₂³×C₄	—	3	1	no	—
522	C₂³×C₄	—	3	1	no	—
523	C₂³×C₄	—	3	1	no	—
524	C₂³×C₄	—	3	1	no	—
525	C₂³×C₄	—	3	1	no	—
526	#121	—	3	8	no	—
527	C₄×D₄	—	6	4	no	—
528	C₄×D₄	—	6	4	no	—
529	C₂×C₄⋊C₄	—	3	1	no	—
530	C₂×C₄⋊C₄	—	3	1	no	—
531	C₂×C₄⋊C₄	—	3	1	no	—
532	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	—	3	1	no	—
535	C₂×C₂²⋊C₄	—	3	1	no	—
536	C₂×C₂²⋊C₄	—	3	1	no	—
537	C₂×C₂²⋊C₄	—	3	1	no	—
538	C₂×C₂²⋊C₄	—	3	1	no	—
539	C₂×C₂²⋊C₄	—	3	1	no	—
540	C₂×C₂²⋊C₄	—	3	1	no	—
541	C₂×C₂²⋊C₄	—	3	1	no	—
542	C₂×C₂²⋊C₄	—	3	1	no	—
543	C₂×C₂²⋊C₄	—	3	1	no	—
544	C₂×C₄²	—	3	1	no	—
545	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
546	#95	—	3	1	no	—
547	#95	—	3	1	no	—
548	#95	—	3	1	no	—
549	#95	—	3	1	no	—
550	#95	—	3	1	no	—
551	#95	—	3	1	no	—
552	#95	C₂×C₅×D₃	1	1	yes	characteristic
553	#95	C₂×C₅×D₃	1	1	yes	characteristic
554	#95	C₂×C₅×D₃	1	1	yes	characteristic
555	#95	C₂×C₅×D₃	1	1	yes	characteristic
556	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
557	C₂×C₃×C₅	#518	1	1	yes	characteristic
558	C₂×C₃×C₅	#520	1	1	yes	characteristic
559	C₂×C₃×C₅	#534	1	1	yes	characteristic
560	C₂×C₃×C₅	#537	1	1	yes	characteristic
561	C₂×C₃×C₅	#538	1	1	yes	characteristic
562	C₂×C₃×C₅	#539	1	1	yes	characteristic
563	C₅×D₃	—	2	4	no	—
564	C₅×D₃	—	4	2	no	—
565	C₅×D₃	—	4	2	no	—
566	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
567	C₂²×D₃	—	2	1	no	—
568	C₂²×D₃	—	2	1	no	—
569	C₂²×D₃	—	2	1	no	—
570	C₂²×D₃	—	2	1	no	—
571	C₂²×D₃	—	2	1	no	—
572	C₂²×D₃	—	2	1	no	—
573	C₂²×D₃	—	2	1	no	—
574	C₂²×D₃	—	2	1	no	—
575	C₂²×D₃	—	2	1	no	—
576	C₂²×D₃	—	2	1	no	—
577	C₂²×D₃	—	2	1	no	—
578	C₂²×D₃	—	2	1	no	—
579	C₂²×D₃	—	2	1	no	—
580	C₂²×D₃	—	2	1	no	—
581	C₂²×D₃	—	2	1	no	—
582	C₂²×D₃	—	2	1	no	—
583	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
584	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
585	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
586	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
587	C₂²×D₃	C₅×#41	1	2	yes	—
588	C₂×C₃×C₄	—	2	1	no	—
589	C₂×C₃×C₄	—	2	1	no	—
590	C₂×C₃×C₄	—	2	1	no	—
591	C₂×C₃×C₄	—	2	1	no	—
592	C₂×C₃×C₄	—	2	1	no	—
593	C₂×C₃×C₄	—	2	1	no	—
594	C₂×C₃×C₄	—	2	1	no	—
595	C₂×C₃×C₄	—	2	1	no	—
596	C₂×C₃×C₄	—	2	1	no	—
597	C₂×C₃×C₄	—	2	1	no	—
598	C₂×C₃×C₄	—	2	1	no	—
599	C₂×C₃×C₄	—	2	1	no	—
600	C₂×C₃×C₄	—	2	1	no	—
601	C₂×C₃×C₄	—	2	1	no	—
602	C₂×C₃×C₄	—	2	1	no	—
603	C₂×C₃×C₄	—	2	1	no	—
604	C₂×C₃×C₄	—	2	1	no	—
605	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
606	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
607	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
608	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
609	C₂×Dic₃	—	2	1	no	—
610	C₂×Dic₃	—	2	1	no	—
611	C₂×Dic₃	—	2	1	no	—
612	C₂×Dic₃	—	2	1	no	—
613	C₂×Dic₃	—	2	1	no	—
614	C₂×Dic₃	—	2	1	no	—
615	C₂×Dic₃	—	2	1	no	—
616	C₂×Dic₃	—	2	1	no	—
617	C₂×Dic₃	—	2	1	no	—
618	C₂×Dic₃	—	2	1	no	—
619	C₂×Dic₃	—	2	1	no	—
620	C₂×Dic₃	—	2	1	no	—
621	C₂×Dic₃	—	2	1	no	—
622	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
623	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
624	D₁₂	—	2	8	no	—
625	D₁₂	—	2	8	no	—
626	D₁₂	—	4	4	no	—
627	C₄×D₃	—	4	4	no	—
628	C₄×D₃	—	4	4	no	—
629	C₄×D₃	—	4	4	no	—
630	C₄×D₃	—	4	4	no	—
631	C₄×D₃	—	4	4	no	—
632	C₂²×C₅	—	3	4	no	—
633	C₂²×C₅	—	6	2	no	—
634	C₂²×C₅	—	6	2	no	—
635	C₂²×C₅	—	6	2	no	—
636	C₂²×C₅	—	6	2	no	—
637	C₂²×C₅	—	6	2	no	—
638	C₂²×C₅	—	6	2	no	—
639	C₂²×C₅	—	6	2	no	—
640	C₂²×C₅	—	6	2	no	—
641	C₂²×C₅	—	6	2	no	—
642	C₂²×C₅	—	6	2	no	—
643	C₂²×C₅	—	6	2	no	—
644	C₂²×C₅	—	6	2	no	—
645	C₂²×C₅	—	12	1	no	—
646	C₂²×C₅	—	12	1	no	—
647	C₂²×C₅	—	12	1	no	—
648	C₂²×C₅	—	12	1	no	—
649	C₂²×C₅	—	12	1	no	—
650	C₂²×C₅	—	12	1	no	—
651	C₂²×C₅	—	12	1	no	—
652	C₂²×C₅	—	12	1	no	—
653	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
654	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
655	C₂²×C₅	#1007	1	1	yes	characteristic
656	C₂²×C₅	D₃×#41	1	1	yes	characteristic
657	C₂²×C₅	#1009	1	1	yes	characteristic
658	C₂²×C₅	#1009	1	1	yes	characteristic
659	C₂²×C₅	#1009	1	1	yes	characteristic
660	C₄×C₅	—	2	2	no	—
661	C₄×C₅	—	2	2	no	—
662	C₄×C₅	—	2	2	no	—
663	C₄×C₅	—	2	2	no	—
664	C₄×C₅	—	4	1	no	—
665	C₄×C₅	—	4	1	no	—
666	C₄×C₅	—	4	1	no	—
667	C₄×C₅	—	6	2	no	—
668	C₄×C₅	—	6	2	no	—
669	C₄×C₅	—	12	1	no	—
670	C₄×C₅	—	12	1	no	—
671	C₄×C₅	—	12	1	no	—
672	C₂⁴	—	3	1	no	—
673	C₂⁴	—	3	1	no	—
674	C₂⁴	—	3	1	no	—
675	C₂×D₄	—	3	4	no	—
676	C₂×D₄	—	3	4	no	—
677	C₂×D₄	—	3	4	no	—
678	C₂×D₄	—	6	2	no	—
679	C₂×D₄	—	6	2	no	—
680	C₂×D₄	—	6	2	no	—
681	C₂×D₄	—	6	2	no	—
682	C₂×D₄	—	12	1	no	—
683	C₂×D₄	—	12	1	no	—
684	C₂²×C₄	—	3	1	no	—
685	C₂²×C₄	—	3	1	no	—
686	C₂²×C₄	—	3	4	no	—
687	C₂²×C₄	—	3	4	no	—
688	C₂²×C₄	—	3	1	no	—
689	C₂²×C₄	—	3	1	no	—
690	C₂²×C₄	—	3	1	no	—
691	C₂²×C₄	—	6	2	no	—
692	C₂²×C₄	—	6	2	no	—
693	C₂²×C₄	—	6	2	no	—
694	C₂²×C₄	—	12	1	no	—
695	C₂²×C₄	—	12	1	no	—
696	C₂²×C₄	—	12	1	no	—
697	C₂²×C₄	—	12	1	no	—
698	C₂²×C₄	—	12	1	no	—
699	C₂²×C₄	—	12	1	no	—
700	C₂²×C₄	—	12	1	no	—
701	C₂²×C₄	—	12	1	no	—
702	C₂²×C₄	—	12	1	no	—
703	C₂²×C₄	—	12	1	no	—
704	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
705	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
706	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
707	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
708	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
709	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
710	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	6	2	no	—
713	C₄⋊C₄	—	12	1	no	—
714	C₄⋊C₄	—	12	1	no	—
715	C₄⋊C₄	C₄×C₅×D₃	1	4	yes	complemented
716	C₂²⋊C₄	—	3	4	no	—
717	C₂²⋊C₄	—	3	4	no	—
718	C₂²⋊C₄	—	6	2	no	—
719	C₂²⋊C₄	—	6	2	no	—
720	C₂²⋊C₄	—	6	2	no	—
721	C₂²⋊C₄	—	6	2	no	—
722	C₂²⋊C₄	—	12	1	no	—
723	C₂²⋊C₄	—	12	1	no	—
724	C₂²⋊C₄	—	12	1	no	—
725	C₂²⋊C₄	—	12	1	no	—
726	C₄²	—	2	2	no	—
727	C₄²	—	6	2	no	—
728	C₃×C₅	#2325	1	1	yes	characteristic, complemented, Hall
729	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
730	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
731	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
732	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
733	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
734	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
735	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
736	C₂×D₃	—	2	2	no	—
737	C₂×D₃	—	2	2	no	—
738	C₂×D₃	—	2	2	no	—
739	C₂×D₃	—	2	2	no	—
740	C₂×D₃	—	2	2	no	—
741	C₂×D₃	—	2	2	no	—
742	C₂×D₃	—	2	2	no	—
743	C₂×D₃	—	2	2	no	—
744	C₂×D₃	—	2	2	no	—
745	C₂×D₃	—	2	2	no	—
746	C₂×D₃	—	2	2	no	—
747	C₂×D₃	—	2	2	no	—
748	C₂×D₃	—	4	1	no	—
749	C₂×D₃	—	4	1	no	—
750	C₂×D₃	—	4	1	no	—
751	C₂×D₃	—	4	1	no	—
752	C₂×D₃	—	4	1	no	—
753	C₂×D₃	—	4	1	no	—
754	C₂×D₃	—	4	1	no	—
755	C₂×D₃	—	4	1	no	—
756	C₂×D₃	C₄×C₅×D₄	1	4	yes	—
757	C₃×C₄	—	2	2	no	—
758	C₃×C₄	—	2	2	no	—
759	C₃×C₄	—	2	2	no	—
760	C₃×C₄	—	2	2	no	—
761	C₃×C₄	—	4	1	no	—
762	C₃×C₄	—	4	1	no	—
763	C₃×C₄	—	4	1	no	—
764	Dic₃	—	2	2	no	—
765	Dic₃	—	2	2	no	—
766	Dic₃	—	4	1	no	—
767	Dic₃	—	4	1	no	—
768	Dic₃	—	4	1	no	—
769	C₂×C₅	—	6	4	no	—
770	C₂×C₅	—	12	2	no	—
771	C₂×C₅	—	12	2	no	—
772	C₂×C₅	#5521	1	1	yes	characteristic
773	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
774	C₂×C₅	#5574	1	1	yes	characteristic
775	C₂×C₅	#5629	1	1	yes	characteristic
776	C₂×C₅	#5653	1	1	yes	characteristic
777	C₂×C₅	#5692	1	1	yes	characteristic
778	C₂×C₅	#5704	1	1	yes	characteristic
779	C₂³	—	3	2	no	—
780	C₂³	—	3	2	no	—
781	C₂³	—	3	2	no	—
782	C₂³	—	3	2	no	—
783	C₂³	—	3	2	no	—
784	C₂³	—	6	1	no	—
785	C₂³	—	6	1	no	—
786	C₂³	—	6	1	no	—
787	C₂³	—	6	1	no	—
788	C₂³	—	6	1	no	—
789	C₂³	—	6	1	no	—
790	C₂³	—	6	1	no	—
791	C₂³	—	6	1	no	—
792	C₂³	—	6	1	no	—
793	C₂³	—	6	1	no	—
794	C₂³	—	6	1	no	—
795	C₂³	—	6	1	no	—
796	C₂³	—	6	1	no	—
797	C₂³	—	6	1	no	—
798	C₂³	—	6	1	no	—
799	C₂³	—	6	1	no	—
800	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
801	D₄	—	6	8	no	—
802	D₄	—	6	8	no	—
803	D₄	—	12	4	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	3	2	no	—
822	C₂×C₄	—	3	2	no	—
823	C₂×C₄	—	6	1	no	—
824	C₂×C₄	—	6	1	no	—
825	C₂×C₄	—	6	1	no	—
826	C₂×C₄	—	6	1	no	—
827	C₂×C₄	—	6	1	no	—
828	C₂×C₄	—	6	1	no	—
829	C₂×C₄	—	6	1	no	—
830	C₂×C₄	—	6	1	no	—
831	C₂×C₄	—	6	1	no	—
832	C₂×C₄	—	6	1	no	—
833	C₂×C₄	—	6	1	no	—
834	C₂×C₄	—	6	1	no	—
835	C₂×C₄	—	6	1	no	—
836	C₂×C₄	—	12	4	no	—
837	C₂×C₄	—	12	4	no	—
838	C₂×C₄	—	12	4	no	—
839	C₂×C₄	—	12	4	no	—
840	C₂×C₄	—	12	4	no	—
841	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
842	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
843	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
844	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
845	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
846	C₂×C₃	C₅×#518	1	1	yes	characteristic
847	C₂×C₃	C₅×#520	1	1	yes	characteristic
848	C₂×C₃	C₅×#534	1	1	yes	characteristic
849	C₂×C₃	C₅×#537	1	1	yes	characteristic
850	C₂×C₃	C₅×#538	1	1	yes	characteristic
851	C₂×C₃	C₅×#539	1	1	yes	characteristic
852	D₃	—	2	4	no	—
853	D₃	—	4	2	no	—
854	D₃	—	4	2	no	—
855	C₅	#75298	1	1	yes	characteristic, direct product factor, Sylow
856	C₂²	—	3	4	no	—
857	C₂²	—	6	2	no	—
858	C₂²	—	6	2	no	—
859	C₂²	—	6	2	no	—
860	C₂²	—	6	2	no	—
861	C₂²	—	6	2	no	—
862	C₂²	—	6	2	no	—
863	C₂²	—	6	2	no	—
864	C₂²	—	6	2	no	—
865	C₂²	—	6	2	no	—
866	C₂²	—	6	2	no	—
867	C₂²	—	6	2	no	—
868	C₂²	—	6	2	no	—
869	C₂²	—	12	1	no	—
870	C₂²	—	12	1	no	—
871	C₂²	—	12	1	no	—
872	C₂²	—	12	1	no	—
873	C₂²	—	12	1	no	—
874	C₂²	—	12	1	no	—
875	C₂²	—	12	1	no	—
876	C₂²	—	12	1	no	—
877	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
878	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
879	C₂²	C₅×#1007	1	1	yes	characteristic
880	C₂²	C₅×D₃×#41	1	1	yes	characteristic
881	C₂²	C₅×#1009	1	1	yes	characteristic
882	C₂²	C₅×#1009	1	1	yes	characteristic
883	C₂²	C₅×#1009	1	1	yes	characteristic
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	1	no	—
891	C₄	—	6	2	no	—
892	C₄	—	6	2	no	—
893	C₄	—	12	1	no	—
894	C₄	—	12	1	no	—
895	C₄	—	12	1	no	—
896	C₃	C₅×#2325	1	1	yes	characteristic, complemented, Sylow
897	C₂	—	6	4	no	—
898	C₂	—	12	2	no	—
899	C₂	—	12	2	no	—
900	C₂	C₅×#5521	1	1	yes	characteristic
901	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
902	C₂	C₅×#5574	1	1	yes	characteristic
903	C₂	C₅×#5629	1	1	yes	characteristic
904	C₂	C₅×#5653	1	1	yes	characteristic
905	C₂	C₅×#5692	1	1	yes	characteristic
906	C₂	C₅×#5704	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×#387	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#895	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#387	D₃
hypocenter	C₃	C₅×#2325
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#387

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#893	C₂	semidirect
3. C₂×C₄×C₅×D₁₂	C₂	semidirect
4. C₃×C₅×#387	C₂	semidirect
5. C₅×#4989	C₂	semidirect
6. C₅×#4980	C₂	semidirect
7. C₅×#4940	C₂	semidirect
8. C₅×#4669	C₂	semidirect
9. C₅×#4668	C₂	semidirect
10. C₅×#4667	C₂	semidirect
11. C₅×#4665	C₂	semidirect
12. C₅×#4665	C₂	semidirect
13. C₅×#4665	C₂	semidirect
14. C₅×#4665	C₂	semidirect
15. C₅×D₃×#95	C₂	semidirect
42. C₅×#895	C₄	semidirect
55. #75298	C₅	direct (N × H)
62. C₅×#387	D₃	semidirect
92. C₂×C₅×D₁₂	C₂×C₄	semidirect
93. C₂×C₅×D₁₂	C₂×C₄	semidirect
94. C₂×C₅×D₁₂	C₂×C₄	semidirect
108. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
109. C₂×C₄×C₅×D₃	D₄	semidirect
111. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
121. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
122. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
128. C₂×#893	C₂×C₅	semidirect
129. C₂×C₄×D₁₂	C₂×C₅	semidirect
130. C₃×#387	C₂×C₅	semidirect
131. #4989	C₂×C₅	semidirect
132. #4980	C₂×C₅	semidirect
133. #4940	C₂×C₅	semidirect
134. #4669	C₂×C₅	semidirect
135. #4668	C₂×C₅	semidirect
136. #4667	C₂×C₅	semidirect
137. #4665	C₂×C₅	semidirect
138. #4665	C₂×C₅	semidirect
139. #4665	C₂×C₅	semidirect
140. #4665	C₂×C₅	semidirect
141. D₃×#95	C₂×C₅	semidirect
272. #895	C₄×C₅	semidirect
328. C₅×C₄⋊C₄	C₄×D₃	semidirect
347. #387	C₅×D₃	semidirect
417. C₂×D₁₂	C₂×C₄×C₅	semidirect
418. C₂×D₁₂	C₂×C₄×C₅	semidirect
419. C₂×D₁₂	C₂×C₄×C₅	semidirect
433. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
434. C₂×C₄×D₃	C₅×D₄	semidirect
436. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
446. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
447. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
715. C₄⋊C₄	C₄×C₅×D₃	semidirect
728. C₃×C₅	#2325	semidirect
855. C₅	#75298	direct (N × H)
896. C₃	C₅×#2325	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#895	2
C₂×C₅×#893	2
C₂×C₄×C₅×D₁₂	2
C₃×C₅×#387	2
C₅×#4989	2
C₅×#4980	2
C₅×#4940	2
C₅×#4669	2
C₅×#4668	2
C₅×#4667	2
C₅×#4665	2
C₅×D₃×#95	2
C₅×#2325	3
#75298	5

Subgroups — C5×#75298 #14324035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#75298 #14324035