Subgroups — C₄×C₅×#884 #14321425

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#884	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4951	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4669	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4667	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4665	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4647	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×#121	—	3	1	no	maximal, Hall
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
19	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
20	C₂²×C₅×D₁₂	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×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₂×C₅×#217	C₂²	1	1	yes	characteristic
30	C₂×C₅×#217	C₂²	1	1	yes	characteristic
31	C₄×C₅×#67	—	2	4	no	—
32	C₄×C₅×#67	—	2	4	no	—
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×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
40	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
48	C₅×#884	C₄	1	8	yes	direct product factor
49	C₄×C₅×D₁₂	—	2	4	no	—
50	C₄²×C₅×D₃	—	2	4	no	—
51	C₃×C₅×#95	C₂²	1	1	yes	characteristic
52	C₃×C₅×#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	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
56	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
57	C₄×#884	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
58	C₂×C₅×#121	—	3	1	no	—
59	C₂×C₄×C₅×D₄	—	3	1	no	—
60	C₂×C₄×C₅×D₄	—	3	1	no	—
61	C₂×C₄×C₅×D₄	—	3	1	no	—
62	C₂²×C₄²×C₅	—	3	1	no	—
63	C₅×#390	—	3	1	no	—
64	C₅×#389	—	3	1	no	—
65	C₅×#388	—	3	1	no	—
66	C₅×#388	—	3	1	no	—
67	C₅×#386	—	3	1	no	—
68	C₅×#386	—	3	1	no	—
69	C₅×#380	—	3	1	no	—
70	C₄×C₅×C₄⋊C₄	—	3	1	no	—
71	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
72	C₄×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
73	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
74	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
75	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	—	2	2	no	—
77	C₂²×C₃×C₄×C₅	—	2	2	no	—
78	C₂²×C₃×C₄×C₅	—	2	2	no	—
79	C₂²×C₃×C₄×C₅	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	C₂×C₅×#67	—	2	2	no	—
86	C₂×C₅×#67	—	2	2	no	—
87	C₂×C₅×#67	—	2	2	no	—
88	C₂×C₅×#67	—	2	2	no	—
89	C₂×C₅×#67	C₂×C₄	1	4	yes	complemented
90	C₂×C₅×#67	C₂×C₄	1	4	yes	complemented
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	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
95	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
96	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
97	C₂×C₅×D₁₂	—	2	2	no	—
98	C₂×C₅×D₁₂	—	2	2	no	—
99	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
100	C₂×C₄×C₅×D₃	—	2	2	no	—
101	C₂×C₄×C₅×D₃	—	2	2	no	—
102	C₂×C₄×C₅×D₃	—	2	2	no	—
103	C₂×C₄×C₅×D₃	—	2	2	no	—
104	C₂×C₄×C₅×D₃	—	2	2	no	—
105	C₂×C₄×C₅×D₃	—	2	2	no	—
106	C₂×C₄×C₅×D₃	—	2	2	no	—
107	C₂×C₄×C₅×D₃	—	2	2	no	—
108	C₂×C₄×C₅×D₃	—	2	2	no	—
109	C₂×C₄×C₅×D₃	—	2	2	no	—
110	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
111	C₂×C₄×C₅×D₃	D₄	1	4	yes	complemented
112	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
113	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	complemented
114	C₃×C₄²×C₅	—	2	2	no	—
115	C₃×C₄²×C₅	—	2	2	no	—
116	C₅×#217	—	2	2	no	—
117	C₅×#217	—	2	2	no	—
118	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
119	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
120	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
121	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
122	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
123	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
124	C₅×C₄⋊Dic₃	—	2	2	no	—
125	C₅×Dic₃⋊C₄	—	2	2	no	—
126	C₅×Dic₃⋊C₄	—	2	2	no	—
127	C₅×Dic₃⋊C₄	—	2	2	no	—
128	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	complemented
129	C₄×C₅×Dic₃	—	2	2	no	—
130	C₄×C₅×Dic₃	—	2	2	no	—
131	C₄×C₅×Dic₃	—	2	2	no	—
132	C₄×C₅×Dic₃	D₄	1	4	yes	complemented
133	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
134	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
135	C₂×#884	C₂×C₅	1	1	yes	characteristic
136	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
137	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
139	#4957	C₂×C₅	1	1	yes	characteristic, complemented
140	#4956	C₂×C₅	1	1	yes	characteristic, complemented
141	#4951	C₂×C₅	1	1	yes	characteristic, complemented
142	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
143	C₄×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
144	#4669	C₂×C₅	1	1	yes	characteristic, complemented
145	#4667	C₂×C₅	1	1	yes	characteristic, complemented
146	#4665	C₂×C₅	1	1	yes	characteristic, complemented
147	#4647	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂²×C₅×D₄	—	3	1	no	—
149	C₂²×C₅×D₄	—	3	1	no	—
150	C₂²×C₅×D₄	—	3	1	no	—
151	C₂³×C₄×C₅	—	3	1	no	—
152	C₂³×C₄×C₅	—	3	1	no	—
153	C₂³×C₄×C₅	—	3	1	no	—
154	C₂³×C₄×C₅	—	3	1	no	—
155	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
156	C₅×#121	—	3	8	no	—
157	C₄×C₅×D₄	—	6	4	no	—
158	C₄×C₅×D₄	—	6	4	no	—
159	C₄×C₅×D₄	—	6	4	no	—
160	C₂×C₅×C₄⋊C₄	—	3	1	no	—
161	C₂×C₅×C₄⋊C₄	—	3	1	no	—
162	C₂×C₅×C₄⋊C₄	—	3	1	no	—
163	C₂×C₅×C₄⋊C₄	—	3	1	no	—
164	C₂×C₅×C₄⋊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×C₅×C₂²⋊C₄	—	3	1	no	—
169	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
170	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
171	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
172	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
173	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
174	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
175	C₂×C₄²×C₅	—	3	1	no	—
176	C₂×C₄²×C₅	—	3	1	no	—
177	C₂×C₄²×C₅	—	3	1	no	—
178	C₂×C₄²×C₅	—	3	1	no	—
179	C₂×C₄²×C₅	—	6	4	no	—
180	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
181	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
182	C₅×#95	—	3	1	no	—
183	C₅×#95	—	3	1	no	—
184	C₅×#95	—	3	1	no	—
185	C₅×#95	—	3	1	no	—
186	C₅×#95	C₂×D₃	1	1	yes	characteristic
187	C₅×#95	C₂×D₃	1	1	yes	characteristic
188	C₄×#121	—	3	1	no	Sylow
189	C₂³×C₃×C₅	—	2	1	no	—
190	C₂³×C₃×C₅	—	2	1	no	—
191	C₂³×C₃×C₅	—	2	1	no	—
192	C₂³×C₃×C₅	—	2	1	no	—
193	C₂³×C₃×C₅	—	2	1	no	—
194	C₂³×C₃×C₅	—	2	1	no	—
195	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
196	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
206	C₂²×C₅×D₃	—	2	1	no	—
207	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
208	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
209	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
210	C₂²×C₅×D₃	#41	1	2	yes	—
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	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	2	1	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	4	4	no	—
224	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
225	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
226	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
227	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
228	C₂×C₃×C₄×C₅	#41	1	2	yes	—
229	C₂×C₃×C₄×C₅	#41	1	2	yes	—
230	C₅×#67	—	2	8	no	—
231	C₅×#67	—	2	8	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	—	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	C₂²×C₄	1	2	yes	—
245	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
246	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
247	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
248	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
249	C₂×C₅×Dic₃	#41	1	2	yes	—
250	C₅×D₁₂	—	2	8	no	—
251	C₄×C₅×D₃	—	2	8	no	—
252	C₄×C₅×D₃	—	2	8	no	—
253	C₄×C₅×D₃	—	2	8	no	—
254	C₄×C₅×D₃	—	4	4	no	—
255	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
256	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
257	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
258	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
259	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
260	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
261	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
262	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
267	C₂×#217	C₂²×C₅	1	1	yes	characteristic
268	C₂×#217	C₂²×C₅	1	1	yes	characteristic
269	C₄×#67	—	2	4	no	—
270	C₄×#67	—	2	4	no	—
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
275	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
276	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
277	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
278	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
279	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
280	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
281	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
282	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
283	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
284	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
285	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
286	#884	C₄×C₅	1	8	yes	direct product factor
287	C₄×D₁₂	—	2	4	no	—
288	C₄²×D₃	—	2	4	no	—
289	C₃×#95	C₂²×C₅	1	1	yes	characteristic
290	C₃×#95	C₂²×C₅	1	1	yes	characteristic
291	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
292	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
293	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
294	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
295	C₂⁴×C₅	—	3	1	no	—
296	C₂⁴×C₅	—	3	1	no	—
297	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
298	C₂×C₅×D₄	—	3	4	no	—
299	C₂×C₅×D₄	—	3	4	no	—
300	C₂×C₅×D₄	—	3	4	no	—
301	C₂×C₅×D₄	—	6	2	no	—
302	C₂×C₅×D₄	—	6	2	no	—
303	C₂×C₅×D₄	—	6	2	no	—
304	C₂×C₅×D₄	—	6	2	no	—
305	C₂×C₅×D₄	—	6	2	no	—
306	C₂×C₅×D₄	—	6	2	no	—
307	C₂²×C₄×C₅	—	2	2	no	—
308	C₂²×C₄×C₅	—	2	2	no	—
309	C₂²×C₄×C₅	—	2	2	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	—	3	1	no	—
314	C₂²×C₄×C₅	—	3	4	no	—
315	C₂²×C₄×C₅	—	3	4	no	—
316	C₂²×C₄×C₅	—	3	1	no	—
317	C₂²×C₄×C₅	—	3	1	no	—
318	C₂²×C₄×C₅	—	6	2	no	—
319	C₂²×C₄×C₅	—	6	2	no	—
320	C₂²×C₄×C₅	—	6	2	no	—
321	C₂²×C₄×C₅	—	6	2	no	—
322	C₂²×C₄×C₅	—	6	2	no	—
323	C₂²×C₄×C₅	—	6	2	no	—
324	C₂²×C₄×C₅	—	6	2	no	—
325	C₂²×C₄×C₅	—	6	2	no	—
326	C₂²×C₄×C₅	—	6	2	no	—
327	C₂²×C₄×C₅	—	6	2	no	—
328	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
329	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
330	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
331	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
332	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
333	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
334	C₅×C₄⋊C₄	—	3	4	no	—
335	C₅×C₄⋊C₄	—	6	2	no	—
336	C₅×C₄⋊C₄	—	6	2	no	—
337	C₅×C₄⋊C₄	—	6	2	no	—
338	C₅×C₄⋊C₄	—	6	2	no	—
339	C₅×C₂²⋊C₄	—	2	2	no	—
340	C₅×C₂²⋊C₄	—	3	4	no	—
341	C₅×C₂²⋊C₄	—	6	2	no	—
342	C₅×C₂²⋊C₄	—	6	2	no	—
343	C₅×C₂²⋊C₄	—	6	2	no	—
344	C₅×C₂²⋊C₄	—	6	2	no	—
345	C₅×C₂²⋊C₄	—	6	2	no	—
346	C₅×C₂²⋊C₄	—	6	2	no	—
347	C₅×C₂²⋊C₄	—	6	2	no	—
348	C₅×C₂²⋊C₄	C₄×D₃	1	4	yes	complemented
349	C₄²×C₅	—	2	2	no	—
350	C₄²×C₅	—	2	2	no	—
351	C₄²×C₅	—	3	4	no	—
352	C₄²×C₅	—	6	2	no	—
353	C₄²×C₅	—	6	2	no	—
354	C₄²×C₅	—	6	2	no	—
355	C₂×#121	—	3	1	no	—
356	C₂×C₄×D₄	—	3	1	no	—
357	C₂×C₄×D₄	—	3	1	no	—
358	C₂×C₄×D₄	—	3	1	no	—
359	C₂²×C₄²	—	3	1	no	—
360	#390	—	3	1	no	—
361	#389	—	3	1	no	—
362	#388	—	3	1	no	—
363	#388	—	3	1	no	—
364	#386	—	3	1	no	—
365	#386	—	3	1	no	—
366	#380	—	3	1	no	—
367	C₄×C₄⋊C₄	—	3	1	no	—
368	C₄×C₂²⋊C₄	—	3	1	no	—
369	C₄×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
370	C₂²×C₃×C₅	—	2	2	no	—
371	C₂²×C₃×C₅	—	2	2	no	—
372	C₂²×C₃×C₅	—	2	2	no	—
373	C₂²×C₃×C₅	—	4	1	no	—
374	C₂²×C₃×C₅	—	4	1	no	—
375	C₂²×C₃×C₅	—	4	1	no	—
376	C₂²×C₃×C₅	—	4	1	no	—
377	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
378	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
379	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
380	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
381	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
382	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
383	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
384	C₂×C₅×D₃	—	2	2	no	—
385	C₂×C₅×D₃	—	2	2	no	—
386	C₂×C₅×D₃	—	2	2	no	—
387	C₂×C₅×D₃	—	2	2	no	—
388	C₂×C₅×D₃	—	2	2	no	—
389	C₂×C₅×D₃	—	2	2	no	—
390	C₂×C₅×D₃	—	2	2	no	—
391	C₂×C₅×D₃	—	2	2	no	—
392	C₂×C₅×D₃	—	2	2	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	C₂×C₅×D₃	C₄×D₄	1	4	yes	complemented
398	C₃×C₄×C₅	—	2	2	no	—
399	C₃×C₄×C₅	—	2	2	no	—
400	C₃×C₄×C₅	—	2	2	no	—
401	C₃×C₄×C₅	—	4	1	no	—
402	C₃×C₄×C₅	—	4	1	no	—
403	C₃×C₄×C₅	#121	1	4	yes	complemented
404	C₅×Dic₃	—	2	2	no	—
405	C₅×Dic₃	—	2	2	no	—
406	C₅×Dic₃	—	2	2	no	—
407	C₅×Dic₃	—	4	1	no	—
408	C₅×Dic₃	—	4	1	no	—
409	C₅×Dic₃	C₄×D₄	1	4	yes	complemented
410	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
411	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
412	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
413	C₂²×C₃×C₄	—	2	2	no	—
414	C₂²×C₃×C₄	—	2	2	no	—
415	C₂²×C₃×C₄	—	2	2	no	—
416	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
417	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
418	C₂²×C₃×C₄	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	C₂×#67	—	2	2	no	—
423	C₂×#67	—	2	2	no	—
424	C₂×#67	—	2	2	no	—
425	C₂×#67	—	2	2	no	—
426	C₂×#67	C₂×C₄×C₅	1	4	yes	complemented
427	C₂×#67	C₂×C₄×C₅	1	4	yes	complemented
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	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
434	C₂×D₁₂	—	2	2	no	—
435	C₂×D₁₂	—	2	2	no	—
436	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
437	C₂×C₄×D₃	—	2	2	no	—
438	C₂×C₄×D₃	—	2	2	no	—
439	C₂×C₄×D₃	—	2	2	no	—
440	C₂×C₄×D₃	—	2	2	no	—
441	C₂×C₄×D₃	—	2	2	no	—
442	C₂×C₄×D₃	—	2	2	no	—
443	C₂×C₄×D₃	—	2	2	no	—
444	C₂×C₄×D₃	—	2	2	no	—
445	C₂×C₄×D₃	—	2	2	no	—
446	C₂×C₄×D₃	—	2	2	no	—
447	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
448	C₂×C₄×D₃	C₅×D₄	1	4	yes	complemented
449	C₃×C₂²⋊C₄	—	2	2	no	—
450	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
451	C₃×C₄²	—	2	2	no	—
452	C₃×C₄²	—	2	2	no	—
453	#217	—	2	2	no	—
454	#217	—	2	2	no	—
455	(C₂×D₃)⋊C₄	—	2	2	no	—
456	(C₂×D₃)⋊C₄	—	2	2	no	—
457	(C₂×D₃)⋊C₄	—	2	2	no	—
458	(C₂×D₃)⋊C₄	—	2	2	no	—
459	(C₂×D₃)⋊C₄	—	2	2	no	—
460	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
461	C₄⋊Dic₃	—	2	2	no	—
462	Dic₃⋊C₄	—	2	2	no	—
463	Dic₃⋊C₄	—	2	2	no	—
464	Dic₃⋊C₄	—	2	2	no	—
465	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
466	C₄×Dic₃	—	2	2	no	—
467	C₄×Dic₃	—	2	2	no	—
468	C₄×Dic₃	—	2	2	no	—
469	C₄×Dic₃	C₅×D₄	1	4	yes	complemented
470	C₂³×C₅	—	2	1	no	—
471	C₂³×C₅	—	2	1	no	—
472	C₂³×C₅	—	2	1	no	—
473	C₂³×C₅	—	2	1	no	—
474	C₂³×C₅	—	2	1	no	—
475	C₂³×C₅	—	2	1	no	—
476	C₂³×C₅	—	3	2	no	—
477	C₂³×C₅	—	3	2	no	—
478	C₂³×C₅	—	3	2	no	—
479	C₂³×C₅	—	3	2	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	C₂×C₄×D₃	1	2	yes	—
491	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
492	C₅×D₄	—	6	8	no	—
493	C₅×D₄	—	6	8	no	—
494	C₅×D₄	—	6	8	no	—
495	C₂×C₄×C₅	—	2	1	no	—
496	C₂×C₄×C₅	—	2	1	no	—
497	C₂×C₄×C₅	—	2	1	no	—
498	C₂×C₄×C₅	—	2	1	no	—
499	C₂×C₄×C₅	—	2	1	no	—
500	C₂×C₄×C₅	—	2	1	no	—
501	C₂×C₄×C₅	—	2	1	no	—
502	C₂×C₄×C₅	—	2	1	no	—
503	C₂×C₄×C₅	—	2	1	no	—
504	C₂×C₄×C₅	—	2	1	no	—
505	C₂×C₄×C₅	—	2	1	no	—
506	C₂×C₄×C₅	—	2	1	no	—
507	C₂×C₄×C₅	—	3	2	no	—
508	C₂×C₄×C₅	—	3	2	no	—
509	C₂×C₄×C₅	—	3	2	no	—
510	C₂×C₄×C₅	—	3	2	no	—
511	C₂×C₄×C₅	—	3	2	no	—
512	C₂×C₄×C₅	—	3	2	no	—
513	C₂×C₄×C₅	—	4	4	no	—
514	C₂×C₄×C₅	—	6	8	no	—
515	C₂×C₄×C₅	—	6	8	no	—
516	C₂×C₄×C₅	—	6	1	no	—
517	C₂×C₄×C₅	—	6	1	no	—
518	C₂×C₄×C₅	—	6	1	no	—
519	C₂×C₄×C₅	—	6	1	no	—
520	C₂×C₄×C₅	—	6	1	no	—
521	C₂×C₄×C₅	—	6	1	no	—
522	C₂×C₄×C₅	—	6	8	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	—	12	4	no	—
530	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
531	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
532	C₂×C₄×C₅	#235	1	2	yes	—
533	C₂×C₄×C₅	#235	1	2	yes	—
534	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
535	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
536	C₂²×D₄	—	3	1	no	—
537	C₂²×D₄	—	3	1	no	—
538	C₂²×D₄	—	3	1	no	—
539	C₂³×C₄	—	3	1	no	—
540	C₂³×C₄	—	3	1	no	—
541	C₂³×C₄	—	3	1	no	—
542	C₂³×C₄	—	3	1	no	—
543	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
544	#121	—	3	8	no	—
545	C₄×D₄	—	6	4	no	—
546	C₄×D₄	—	6	4	no	—
547	C₄×D₄	—	6	4	no	—
548	C₂×C₄⋊C₄	—	3	1	no	—
549	C₂×C₄⋊C₄	—	3	1	no	—
550	C₂×C₄⋊C₄	—	3	1	no	—
551	C₂×C₄⋊C₄	—	3	1	no	—
552	C₂×C₄⋊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	C₂×C₅×D₃	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
563	C₂×C₄²	—	3	1	no	—
564	C₂×C₄²	—	3	1	no	—
565	C₂×C₄²	—	3	1	no	—
566	C₂×C₄²	—	3	1	no	—
567	C₂×C₄²	—	6	4	no	—
568	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
569	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
570	#95	—	3	1	no	—
571	#95	—	3	1	no	—
572	#95	—	3	1	no	—
573	#95	—	3	1	no	—
574	#95	C₂×C₅×D₃	1	1	yes	characteristic
575	#95	C₂×C₅×D₃	1	1	yes	characteristic
576	C₂×C₃×C₅	—	4	2	no	—
577	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
578	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
579	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
580	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
581	C₂×C₃×C₅	#525	1	1	yes	characteristic
582	C₂×C₃×C₅	#529	1	1	yes	characteristic
583	C₂×C₃×C₅	#532	1	1	yes	characteristic
584	C₅×D₃	—	2	4	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	C₂²×C₄×C₅	1	2	yes	—
605	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
606	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
607	C₂²×D₃	C₅×#41	1	2	yes	—
608	C₂×C₃×C₄	—	2	1	no	—
609	C₂×C₃×C₄	—	2	1	no	—
610	C₂×C₃×C₄	—	2	1	no	—
611	C₂×C₃×C₄	—	2	1	no	—
612	C₂×C₃×C₄	—	2	1	no	—
613	C₂×C₃×C₄	—	2	1	no	—
614	C₂×C₃×C₄	—	2	1	no	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	2	1	no	—
617	C₂×C₃×C₄	—	2	1	no	—
618	C₂×C₃×C₄	—	2	1	no	—
619	C₂×C₃×C₄	—	2	1	no	—
620	C₂×C₃×C₄	—	4	4	no	—
621	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
622	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
623	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
624	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
625	C₂×C₃×C₄	C₅×#41	1	2	yes	—
626	C₂×C₃×C₄	C₅×#41	1	2	yes	—
627	#67	—	2	8	no	—
628	#67	—	2	8	no	—
629	C₂×Dic₃	—	2	1	no	—
630	C₂×Dic₃	—	2	1	no	—
631	C₂×Dic₃	—	2	1	no	—
632	C₂×Dic₃	—	2	1	no	—
633	C₂×Dic₃	—	2	1	no	—
634	C₂×Dic₃	—	2	1	no	—
635	C₂×Dic₃	—	2	1	no	—
636	C₂×Dic₃	—	2	1	no	—
637	C₂×Dic₃	—	2	1	no	—
638	C₂×Dic₃	—	2	1	no	—
639	C₂×Dic₃	—	2	1	no	—
640	C₂×Dic₃	—	2	1	no	—
641	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
642	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
643	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
644	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
645	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
646	C₂×Dic₃	C₅×#41	1	2	yes	—
647	D₁₂	—	2	8	no	—
648	C₄×D₃	—	2	8	no	—
649	C₄×D₃	—	2	8	no	—
650	C₄×D₃	—	2	8	no	—
651	C₄×D₃	—	4	4	no	—
652	C₂²×C₅	—	2	2	no	—
653	C₂²×C₅	—	2	2	no	—
654	C₂²×C₅	—	2	2	no	—
655	C₂²×C₅	—	3	4	no	—
656	C₂²×C₅	—	4	1	no	—
657	C₂²×C₅	—	4	1	no	—
658	C₂²×C₅	—	4	1	no	—
659	C₂²×C₅	—	4	1	no	—
660	C₂²×C₅	—	6	2	no	—
661	C₂²×C₅	—	6	2	no	—
662	C₂²×C₅	—	6	2	no	—
663	C₂²×C₅	—	6	2	no	—
664	C₂²×C₅	—	6	2	no	—
665	C₂²×C₅	—	6	2	no	—
666	C₂²×C₅	—	6	2	no	—
667	C₂²×C₅	—	6	2	no	—
668	C₂²×C₅	—	6	2	no	—
669	C₂²×C₅	—	12	1	no	—
670	C₂²×C₅	—	12	1	no	—
671	C₂²×C₅	—	12	1	no	—
672	C₂²×C₅	—	12	1	no	—
673	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
674	C₂²×C₅	C₂×#235	1	1	yes	characteristic
675	C₂²×C₅	C₂×#235	1	1	yes	characteristic
676	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
677	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
678	C₂²×C₅	D₃×#41	1	1	yes	characteristic
679	C₂²×C₅	D₃×#41	1	1	yes	characteristic
680	C₄×C₅	—	2	2	no	—
681	C₄×C₅	—	2	2	no	—
682	C₄×C₅	—	2	2	no	—
683	C₄×C₅	—	3	4	no	—
684	C₄×C₅	—	4	1	no	—
685	C₄×C₅	—	4	1	no	—
686	C₄×C₅	—	6	2	no	—
687	C₄×C₅	—	6	2	no	—
688	C₄×C₅	—	6	2	no	—
689	C₄×C₅	—	12	1	no	—
690	C₄×C₅	—	12	1	no	—
691	C₄×C₅	#884	1	4	yes	direct product factor
692	C₂⁴	—	3	1	no	—
693	C₂⁴	—	3	1	no	—
694	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
695	C₂×D₄	—	3	4	no	—
696	C₂×D₄	—	3	4	no	—
697	C₂×D₄	—	3	4	no	—
698	C₂×D₄	—	6	2	no	—
699	C₂×D₄	—	6	2	no	—
700	C₂×D₄	—	6	2	no	—
701	C₂×D₄	—	6	2	no	—
702	C₂×D₄	—	6	2	no	—
703	C₂×D₄	—	6	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	3	1	no	—
708	C₂²×C₄	—	3	1	no	—
709	C₂²×C₄	—	3	1	no	—
710	C₂²×C₄	—	3	1	no	—
711	C₂²×C₄	—	3	4	no	—
712	C₂²×C₄	—	3	4	no	—
713	C₂²×C₄	—	3	1	no	—
714	C₂²×C₄	—	3	1	no	—
715	C₂²×C₄	—	6	2	no	—
716	C₂²×C₄	—	6	2	no	—
717	C₂²×C₄	—	6	2	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	—	6	2	no	—
723	C₂²×C₄	—	6	2	no	—
724	C₂²×C₄	—	6	2	no	—
725	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
726	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
727	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
728	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
729	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
730	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
731	C₄⋊C₄	—	3	4	no	—
732	C₄⋊C₄	—	6	2	no	—
733	C₄⋊C₄	—	6	2	no	—
734	C₄⋊C₄	—	6	2	no	—
735	C₄⋊C₄	—	6	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	3	4	no	—
738	C₂²⋊C₄	—	6	2	no	—
739	C₂²⋊C₄	—	6	2	no	—
740	C₂²⋊C₄	—	6	2	no	—
741	C₂²⋊C₄	—	6	2	no	—
742	C₂²⋊C₄	—	6	2	no	—
743	C₂²⋊C₄	—	6	2	no	—
744	C₂²⋊C₄	—	6	2	no	—
745	C₂²⋊C₄	C₄×C₅×D₃	1	4	yes	complemented
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	3	4	no	—
749	C₄²	—	6	2	no	—
750	C₄²	—	6	2	no	—
751	C₄²	—	6	2	no	—
752	C₃×C₅	C₄×#121	1	1	yes	characteristic, complemented, Hall
753	C₂²×C₃	—	2	2	no	—
754	C₂²×C₃	—	2	2	no	—
755	C₂²×C₃	—	2	2	no	—
756	C₂²×C₃	—	4	1	no	—
757	C₂²×C₃	—	4	1	no	—
758	C₂²×C₃	—	4	1	no	—
759	C₂²×C₃	—	4	1	no	—
760	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
761	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
762	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
763	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
764	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
765	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
766	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
767	C₂×D₃	—	2	2	no	—
768	C₂×D₃	—	2	2	no	—
769	C₂×D₃	—	2	2	no	—
770	C₂×D₃	—	2	2	no	—
771	C₂×D₃	—	2	2	no	—
772	C₂×D₃	—	2	2	no	—
773	C₂×D₃	—	2	2	no	—
774	C₂×D₃	—	2	2	no	—
775	C₂×D₃	—	2	2	no	—
776	C₂×D₃	—	4	1	no	—
777	C₂×D₃	—	4	1	no	—
778	C₂×D₃	—	4	1	no	—
779	C₂×D₃	—	4	1	no	—
780	C₂×D₃	C₄×C₅×D₄	1	4	yes	complemented
781	C₃×C₄	—	2	2	no	—
782	C₃×C₄	—	2	2	no	—
783	C₃×C₄	—	2	2	no	—
784	C₃×C₄	—	4	1	no	—
785	C₃×C₄	—	4	1	no	—
786	C₃×C₄	C₅×#121	1	4	yes	complemented
787	Dic₃	—	2	2	no	—
788	Dic₃	—	2	2	no	—
789	Dic₃	—	2	2	no	—
790	Dic₃	—	4	1	no	—
791	Dic₃	—	4	1	no	—
792	Dic₃	C₄×C₅×D₄	1	4	yes	complemented
793	C₂×C₅	—	4	2	no	—
794	C₂×C₅	—	6	4	no	—
795	C₂×C₅	—	12	2	no	—
796	C₂×C₅	C₄×#235	1	1	yes	characteristic
797	C₂×C₅	C₂×#884	1	1	yes	characteristic
798	C₂×C₅	#5528	1	1	yes	characteristic
799	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
800	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
801	C₂×C₅	#5547	1	1	yes	characteristic
802	C₂×C₅	#5548	1	1	yes	characteristic
803	C₂³	—	2	1	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	2	1	no	—
806	C₂³	—	2	1	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	3	2	no	—
810	C₂³	—	3	2	no	—
811	C₂³	—	3	2	no	—
812	C₂³	—	3	2	no	—
813	C₂³	—	6	1	no	—
814	C₂³	—	6	1	no	—
815	C₂³	—	6	1	no	—
816	C₂³	—	6	1	no	—
817	C₂³	—	6	1	no	—
818	C₂³	—	6	1	no	—
819	C₂³	—	6	1	no	—
820	C₂³	—	6	1	no	—
821	C₂³	—	6	1	no	—
822	C₂³	—	6	1	no	—
823	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
824	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
825	D₄	—	6	8	no	—
826	D₄	—	6	8	no	—
827	D₄	—	6	8	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	3	2	no	—
841	C₂×C₄	—	3	2	no	—
842	C₂×C₄	—	3	2	no	—
843	C₂×C₄	—	3	2	no	—
844	C₂×C₄	—	3	2	no	—
845	C₂×C₄	—	3	2	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	—	6	8	no	—
848	C₂×C₄	—	6	8	no	—
849	C₂×C₄	—	6	1	no	—
850	C₂×C₄	—	6	1	no	—
851	C₂×C₄	—	6	1	no	—
852	C₂×C₄	—	6	1	no	—
853	C₂×C₄	—	6	1	no	—
854	C₂×C₄	—	6	1	no	—
855	C₂×C₄	—	6	8	no	—
856	C₂×C₄	—	6	1	no	—
857	C₂×C₄	—	6	1	no	—
858	C₂×C₄	—	6	1	no	—
859	C₂×C₄	—	6	1	no	—
860	C₂×C₄	—	6	1	no	—
861	C₂×C₄	—	6	1	no	—
862	C₂×C₄	—	12	4	no	—
863	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
864	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
865	C₂×C₄	C₅×#235	1	2	yes	—
866	C₂×C₄	C₅×#235	1	2	yes	—
867	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
868	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
869	C₂×C₃	—	4	2	no	—
870	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
871	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
872	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
873	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
874	C₂×C₃	C₅×#525	1	1	yes	characteristic
875	C₂×C₃	C₅×#529	1	1	yes	characteristic
876	C₂×C₃	C₅×#532	1	1	yes	characteristic
877	D₃	—	2	4	no	—
878	D₃	—	4	2	no	—
879	C₅	C₄×#884	1	1	yes	characteristic, direct product factor, Sylow
880	C₂²	—	2	2	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	3	4	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	1	no	—
888	C₂²	—	6	2	no	—
889	C₂²	—	6	2	no	—
890	C₂²	—	6	2	no	—
891	C₂²	—	6	2	no	—
892	C₂²	—	6	2	no	—
893	C₂²	—	6	2	no	—
894	C₂²	—	6	2	no	—
895	C₂²	—	6	2	no	—
896	C₂²	—	6	2	no	—
897	C₂²	—	12	1	no	—
898	C₂²	—	12	1	no	—
899	C₂²	—	12	1	no	—
900	C₂²	—	12	1	no	—
901	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
902	C₂²	C₂×C₅×#235	1	1	yes	characteristic
903	C₂²	C₂×C₅×#235	1	1	yes	characteristic
904	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
905	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
906	C₂²	C₅×D₃×#41	1	1	yes	characteristic
907	C₂²	C₅×D₃×#41	1	1	yes	characteristic
908	C₄	—	2	2	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	2	no	—
911	C₄	—	3	4	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	1	no	—
914	C₄	—	6	2	no	—
915	C₄	—	6	2	no	—
916	C₄	—	6	2	no	—
917	C₄	—	12	1	no	—
918	C₄	—	12	1	no	—
919	C₄	C₅×#884	1	4	yes	direct product factor
920	C₃	C₄×C₅×#121	1	1	yes	characteristic, complemented, Sylow
921	C₂	—	4	2	no	—
922	C₂	—	6	4	no	—
923	C₂	—	12	2	no	—
924	C₂	C₄×C₅×#235	1	1	yes	characteristic
925	C₂	C₂×C₅×#884	1	1	yes	characteristic
926	C₂	C₅×#5528	1	1	yes	characteristic
927	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
928	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
929	C₂	C₅×#5547	1	1	yes	characteristic
930	C₂	C₅×#5548	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×C₂²⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#884	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₄×C₅×#121
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄×C₅×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₅×#67	C₂	semidirect
2. C₂×C₄×C₅×#67	C₂	semidirect
4. C₂×C₄×C₅×D₁₂	C₂	semidirect
5. C₂×C₄²×C₅×D₃	C₂	semidirect
6. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
7. C₅×#4957	C₂	semidirect
8. C₅×#4956	C₂	semidirect
9. C₅×#4951	C₂	semidirect
10. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
11. C₄×C₅×Dic₃⋊C₄	C₂	semidirect
12. C₅×#4669	C₂	semidirect
13. C₅×#4667	C₂	semidirect
14. C₅×#4665	C₂	semidirect
15. C₅×#4647	C₂	semidirect
48. C₅×#884	C₄	direct (N × H)
57. C₄×#884	C₅	direct (N × H)
72. C₄×C₅×C₂²⋊C₄	D₃	semidirect
89. C₂×C₅×#67	C₂×C₄	semidirect
90. C₂×C₅×#67	C₂×C₄	semidirect
99. C₂×C₅×D₁₂	C₂×C₄	semidirect
110. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
111. C₂×C₄×C₅×D₃	D₄	semidirect
113. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
123. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
128. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
132. C₄×C₅×Dic₃	D₄	semidirect
133. C₂×C₄×#67	C₂×C₅	semidirect
134. C₂×C₄×#67	C₂×C₅	semidirect
136. C₂×C₄×D₁₂	C₂×C₅	semidirect
137. C₂×C₄²×D₃	C₂×C₅	semidirect
138. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
139. #4957	C₂×C₅	semidirect
140. #4956	C₂×C₅	semidirect
141. #4951	C₂×C₅	semidirect
142. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
143. C₄×Dic₃⋊C₄	C₂×C₅	semidirect
144. #4669	C₂×C₅	semidirect
145. #4667	C₂×C₅	semidirect
146. #4665	C₂×C₅	semidirect
147. #4647	C₂×C₅	semidirect
286. #884	C₄×C₅	direct (N × H)
348. C₅×C₂²⋊C₄	C₄×D₃	semidirect
369. C₄×C₂²⋊C₄	C₅×D₃	semidirect
397. C₂×C₅×D₃	C₄×D₄	semidirect
403. C₃×C₄×C₅	#121	semidirect
409. C₅×Dic₃	C₄×D₄	semidirect
426. C₂×#67	C₂×C₄×C₅	semidirect
427. C₂×#67	C₂×C₄×C₅	semidirect
436. C₂×D₁₂	C₂×C₄×C₅	semidirect
447. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
448. C₂×C₄×D₃	C₅×D₄	semidirect
450. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
460. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
465. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
469. C₄×Dic₃	C₅×D₄	semidirect
691. C₄×C₅	#884	direct (N × H)
745. C₂²⋊C₄	C₄×C₅×D₃	semidirect
752. C₃×C₅	C₄×#121	semidirect
780. C₂×D₃	C₄×C₅×D₄	semidirect
786. C₃×C₄	C₅×#121	semidirect
792. Dic₃	C₄×C₅×D₄	semidirect
879. C₅	C₄×#884	direct (N × H)
919. C₄	C₅×#884	direct (N × H)
920. C₃	C₄×C₅×#121	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×#67	2
C₂×C₅×#884	2
C₂×C₄×C₅×D₁₂	2
C₂×C₄²×C₅×D₃	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#4957	2
C₅×#4956	2
C₅×#4951	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₄×C₅×Dic₃⋊C₄	2
C₅×#4669	2
C₅×#4667	2
C₅×#4665	2
C₅×#4647	2
C₄×C₅×#121	3
C₄×#884	5

Subgroups — C4×C5×#884 #14321425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#884 #14321425